LMFDB - Embedded newform 75.9.k.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(13,75)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.4958 + 2.29591i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-38.6136 + 12.5463i) q^{4} +(555.364 - 286.698i) q^{5} +(212.094 - 652.759i) q^{6} +(2517.93 - 2517.93i) q^{7} +(3878.60 - 1976.25i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-14.4958 + 2.29591i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-38.6136 + 12.5463i) q^{4} +(555.364 - 286.698i) q^{5} +(212.094 - 652.759i) q^{6} +(2517.93 - 2517.93i) q^{7} +(3878.60 - 1976.25i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-7392.21 + 5430.98i) q^{10} +(3791.81 + 2754.91i) q^{11} +(297.024 - 1875.33i) q^{12} +(-16636.7 - 2635.00i) q^{13} +(-30718.4 + 42280.3i) q^{14} +(155.251 + 29227.9i) q^{15} +(-43277.4 + 31442.9i) q^{16} +(-6199.29 - 12166.8i) q^{17} +(22696.3 + 22696.3i) q^{18} +(-54035.3 - 17557.1i) q^{19} +(-17847.6 + 18038.2i) q^{20} +(51459.4 + 158376. i) q^{21} +(-61290.3 - 31229.0i) q^{22} +(-14954.7 - 94420.0i) q^{23} +203572. i q^{24} +(226234. - 318444. i) q^{25} +247212. q^{26} +(101017. - 15999.5i) q^{27} +(-65635.5 + 128817. i) q^{28} +(-391224. + 127116. i) q^{29} +(-69355.2 - 423326. i) q^{30} +(-158559. + 487995. i) q^{31} +(-232838. + 232838. i) q^{32} +(-195296. + 99508.4i) q^{33} +(117798. + 162134. i) q^{34} +(676481. - 2.12025e6i) q^{35} +(71835.8 + 52191.8i) q^{36} +(261180. - 1.64903e6i) q^{37} +(823595. + 130445. i) q^{38} +(463011. - 637280. i) q^{39} +(1.58745e6 - 2.20952e6i) q^{40} +(636456. - 462412. i) q^{41} +(-1.10956e6 - 2.17764e6i) q^{42} +(-1.15179e6 - 1.15179e6i) q^{43} +(-180980. - 58803.8i) q^{44} +(-1.22117e6 - 614070. i) q^{45} +(433560. + 1.33436e6i) q^{46} +(-2.52624e6 - 1.28718e6i) q^{47} +(-391345. - 2.47086e6i) q^{48} -6.91510e6i q^{49} +(-2.54832e6 + 5.13550e6i) q^{50} +638587. q^{51} +(675464. - 106983. i) q^{52} +(1.67359e6 - 3.28460e6i) q^{53} +(-1.42758e6 + 463850. i) q^{54} +(2.89566e6 + 442874. i) q^{55} +(4.78999e6 - 1.47421e7i) q^{56} +(1.87880e6 - 1.87880e6i) q^{57} +(5.37926e6 - 2.74087e6i) q^{58} +(-1.39614e7 - 1.92162e7i) q^{59} +(-372698. - 1.12665e6i) q^{60} +(4.27778e6 + 3.10799e6i) q^{61} +(1.17805e6 - 7.43792e6i) q^{62} +(-7.69178e6 - 1.21826e6i) q^{63} +(1.08900e7 - 1.49887e7i) q^{64} +(-9.99489e6 + 3.30633e6i) q^{65} +(2.60251e6 - 1.89084e6i) q^{66} +(1.21152e7 + 2.37774e7i) q^{67} +(392026. + 392026. i) q^{68} +(4.25182e6 + 1.38150e6i) q^{69} +(-4.93823e6 + 3.22878e7i) q^{70} +(-1.49439e7 - 4.59926e7i) q^{71} +(-8.48250e6 - 4.32205e6i) q^{72} +(7.00199e6 + 4.42088e7i) q^{73} +2.45036e7i q^{74} +(8.46581e6 + 1.61876e7i) q^{75} +2.30678e6 q^{76} +(1.64841e7 - 2.61083e6i) q^{77} +(-5.24857e6 + 1.03009e7i) q^{78} +(4.06043e7 - 1.31931e7i) q^{79} +(-1.50201e7 + 2.98698e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-8.16428e6 + 8.16428e6i) q^{82} +(-6.84741e7 + 3.48893e7i) q^{83} +(-3.97407e6 - 5.46984e6i) q^{84} +(-6.93106e6 - 4.97968e6i) q^{85} +(1.93405e7 + 1.40517e7i) q^{86} +(3.00937e6 - 1.90004e7i) q^{87} +(2.01513e7 + 3.19165e6i) q^{88} +(-2.41562e6 + 3.32482e6i) q^{89} +(1.91117e7 + 6.09774e6i) q^{90} +(-4.85248e7 + 3.52553e7i) q^{91} +(1.76208e6 + 3.45828e6i) q^{92} +(-1.69675e7 - 1.69675e7i) q^{93} +(3.95751e7 + 1.28587e7i) q^{94} +(-3.50429e7 + 5.74122e6i) q^{95} +(-4.75855e6 - 1.46453e7i) q^{96} +(4.43728e7 + 2.26091e7i) q^{97} +(1.58764e7 + 1.00240e8i) q^{98} -1.02503e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−14.4958	+	2.29591i	−0.905987	+	0.143494i	−0.592005	−	0.805935i	$-0.701663\pi$
$2$	−14.4958	+	2.29591i	−0.905987	+	0.143494i	−0.313982	+	0.949429i	$0.601663\pi$
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$3$	−21.2310	+	41.6683i	−0.262112	+	0.514423i
$4$	−38.6136	+	12.5463i	−0.150835	+	0.0490091i
$5$	555.364	−	286.698i	0.888583	−	0.458717i
$5$	555.364	−	286.698i	0.888583	−	0.458717i
$6$	212.094	−	652.759i	0.163653	−	0.503672i
$7$	2517.93	−	2517.93i	1.04870	−	1.04870i	0.0499468	−	0.998752i	$-0.484095\pi$
$7$	2517.93	−	2517.93i	1.04870	−	1.04870i	0.998752	−	0.0499468i	$-0.0159052\pi$
$8$	3878.60	−	1976.25i	0.946924	−	0.482482i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	−7392.21	+	5430.98i	−0.739221	+	0.543098i
$11$	3791.81	+	2754.91i	0.258986	+	0.188164i	0.709700	−	0.704504i	$-0.248831\pi$
$11$	3791.81	+	2754.91i	0.258986	+	0.188164i	−0.450714	+	0.892668i	$0.648831\pi$
$12$	297.024	−	1875.33i	0.0143241	−	0.0904386i
$13$	−16636.7	−	2635.00i	−0.582498	−	0.0922587i	−0.141771	−	0.989900i	$-0.545280\pi$
$13$	−16636.7	−	2635.00i	−0.582498	−	0.0922587i	−0.440728	+	0.897641i	$0.645280\pi$
$14$	−30718.4	+	42280.3i	−0.799625	+	1.10059i
$15$	155.251	+	29227.9i	0.00306668	+	0.577342i
$16$	−43277.4	+	31442.9i	−0.660360	+	0.479780i
$17$	−6199.29	−	12166.8i	−0.0742244	−	0.145674i	0.850912	−	0.525308i	$-0.176050\pi$
$17$	−6199.29	−	12166.8i	−0.0742244	−	0.145674i	−0.925137	+	0.379634i	$0.876050\pi$
$18$	22696.3	+	22696.3i	0.216205	+	0.216205i
$19$	−54035.3	−	17557.1i	−0.414633	−	0.134722i	0.0942695	−	0.995547i	$-0.469948\pi$
$19$	−54035.3	−	17557.1i	−0.414633	−	0.134722i	−0.508902	+	0.860824i	$0.669948\pi$
$20$	−17847.6	+	18038.2i	−0.111548	+	0.112739i
$21$	51459.4	+	158376.i	0.264599	+	0.814351i
$22$	−61290.3	−	31229.0i	−0.261638	−	0.133311i
$23$	−14954.7	−	94420.0i	−0.0534399	−	0.337406i	−0.999894	−	0.0145674i	$-0.995363\pi$
$23$	−14954.7	−	94420.0i	−0.0534399	−	0.337406i	0.946454	−	0.322839i	$-0.104637\pi$
$24$			203572.i			0.613584i
$25$	226234.	−	318444.i	0.579158	−	0.815215i
$26$	247212.			0.540975
$27$	101017.	−	15999.5i	0.190081	−	0.0301058i
$28$	−65635.5	+	128817.i	−0.106784	+	0.209576i
$29$	−391224.	+	127116.i	−0.553138	+	0.179725i	−0.572231	−	0.820092i	$-0.693922\pi$
$29$	−391224.	+	127116.i	−0.553138	+	0.179725i	0.0190932	+	0.999818i	$0.493922\pi$
$30$	−69355.2	−	423326.i	−0.0856237	−	0.522624i
$31$	−158559.	+	487995.i	−0.171690	+	0.528407i	−0.999467	−	0.0326501i	$-0.989605\pi$
$31$	−158559.	+	487995.i	−0.171690	+	0.528407i	0.827777	+	0.561057i	$0.189605\pi$
$32$	−232838.	+	232838.i	−0.222051	+	0.222051i
$33$	−195296.	+	99508.4i	−0.164679	+	0.0839081i
$34$	117798.	+	162134.i	0.0881496	+	0.121328i
$35$	676481.	−	2.12025e6i	0.450800	−	1.41291i
$36$	71835.8	+	52191.8i	0.0427692	+	0.0310736i
$37$	261180.	−	1.64903e6i	0.139359	−	0.879876i	−0.814619	−	0.579997i	$-0.803054\pi$
$37$	261180.	−	1.64903e6i	0.139359	−	0.879876i	0.953977	−	0.299879i	$-0.0969462\pi$
$38$	823595.	+	130445.i	0.394984	+	0.0625593i
$39$	463011.	−	637280.i	0.200139	−	0.275468i
$40$	1.58745e6	−	2.20952e6i	0.620098	−	0.863095i
$41$	636456.	−	462412.i	0.225233	−	0.163642i	−0.469446	−	0.882961i	$-0.655546\pi$
$41$	636456.	−	462412.i	0.225233	−	0.163642i	0.694679	+	0.719320i	$0.255546\pi$
$42$	−1.10956e6	−	2.17764e6i	−0.356577	−	0.699823i
$43$	−1.15179e6	−	1.15179e6i	−0.336898	−	0.336898i	0.518300	−	0.855199i	$-0.326565\pi$
$43$	−1.15179e6	−	1.15179e6i	−0.336898	−	0.336898i	−0.855199	+	0.518300i	$0.826565\pi$
$44$	−180980.	−	58803.8i	−0.0482857	−	0.0156890i
$45$	−1.22117e6	−	614070.i	−0.297802	−	0.149750i
$46$	433560.	+	1.33436e6i	0.0968317	+	0.298017i
$47$	−2.52624e6	−	1.28718e6i	−0.517706	−	0.263784i	0.175557	−	0.984469i	$-0.443827\pi$
$47$	−2.52624e6	−	1.28718e6i	−0.517706	−	0.263784i	−0.693263	+	0.720685i	$0.743827\pi$
$48$	−391345.	−	2.47086e6i	−0.0737217	−	0.465460i
$49$		−	6.91510e6i		−	1.19954i
$50$	−2.54832e6	+	5.13550e6i	−0.407731	+	0.821681i
$51$	638587.			0.0943929
$52$	675464.	−	106983.i	0.0923824	−	0.0146319i
$53$	1.67359e6	−	3.28460e6i	0.212102	−	0.416274i	−0.760304	−	0.649567i	$-0.774950\pi$
$53$	1.67359e6	−	3.28460e6i	0.212102	−	0.416274i	0.972406	+	0.233293i	$0.0749502\pi$
$54$	−1.42758e6	+	463850.i	−0.167891	+	0.0545510i
$55$	2.89566e6	+	442874.i	0.316444	+	0.0483982i
$56$	4.78999e6	−	1.47421e7i	0.487060	−	1.49902i
$57$	1.87880e6	−	1.87880e6i	0.177984	−	0.177984i
$58$	5.37926e6	−	2.74087e6i	0.475346	−	0.242201i
$59$	−1.39614e7	−	1.92162e7i	−1.15218	−	1.58584i	−0.736679	−	0.676243i	$-0.763607\pi$
$59$	−1.39614e7	−	1.92162e7i	−1.15218	−	1.58584i	−0.415499	−	0.909594i	$-0.636393\pi$
$60$	−372698.	−	1.12665e6i	−0.0287576	−	0.0869328i
$61$	4.27778e6	+	3.10799e6i	0.308958	+	0.224471i	0.731449	−	0.681896i	$-0.238844\pi$
$61$	4.27778e6	+	3.10799e6i	0.308958	+	0.224471i	−0.422491	+	0.906367i	$0.638844\pi$
$62$	1.17805e6	−	7.43792e6i	0.0797254	−	0.503367i
$63$	−7.69178e6	−	1.21826e6i	−0.488275	−	0.0773351i
$64$	1.08900e7	−	1.49887e7i	0.649092	−	0.893399i
$65$	−9.99489e6	+	3.30633e6i	−0.559918	+	0.185222i
$66$	2.60251e6	−	1.89084e6i	0.137157	−	0.0996502i
$67$	1.21152e7	+	2.37774e7i	0.601218	+	1.17996i	0.968305	+	0.249770i	$0.0803549\pi$
$67$	1.21152e7	+	2.37774e7i	0.601218	+	1.17996i	−0.367088	+	0.930186i	$0.619645\pi$
$68$	392026.	+	392026.i	0.0183349	+	0.0183349i
$69$	4.25182e6	+	1.38150e6i	0.187577	+	0.0609473i
$70$	−4.93823e6	+	3.22878e7i	−0.205674	+	1.34477i
$71$	−1.49439e7	−	4.59926e7i	−0.588072	−	1.80990i	−0.586566	−	0.809902i	$-0.699520\pi$
$71$	−1.49439e7	−	4.59926e7i	−0.588072	−	1.80990i	−0.00150662	−	0.999999i	$-0.500480\pi$
$72$	−8.48250e6	−	4.32205e6i	−0.315641	−	0.160827i
$73$	7.00199e6	+	4.42088e7i	0.246564	+	1.55674i	0.731283	+	0.682075i	$0.238922\pi$
$73$	7.00199e6	+	4.42088e7i	0.246564	+	1.55674i	−0.484718	+	0.874670i	$0.661078\pi$
$74$			2.45036e7i			0.817153i
$75$	8.46581e6	+	1.61876e7i	0.267562	+	0.511609i
$76$	2.30678e6			0.0691435
$77$	1.64841e7	−	2.61083e6i	0.468925	−	0.0742705i
$78$	−5.24857e6	+	1.03009e7i	−0.141796	+	0.278290i
$79$	4.06043e7	−	1.31931e7i	1.04247	−	0.338719i	0.262761	−	0.964861i	$-0.415367\pi$
$79$	4.06043e7	−	1.31931e7i	1.04247	−	0.338719i	0.779709	+	0.626142i	$0.215367\pi$
$80$	−1.50201e7	+	2.98698e7i	−0.366702	+	0.729242i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	−8.16428e6	+	8.16428e6i	−0.180577	+	0.180577i
$83$	−6.84741e7	+	3.48893e7i	−1.44283	+	0.735157i	−0.987859	−	0.155351i	$-0.950349\pi$
$83$	−6.84741e7	+	3.48893e7i	−1.44283	+	0.735157i	−0.454968	+	0.890508i	$0.650349\pi$
$84$	−3.97407e6	−	5.46984e6i	−0.0798212	−	0.109864i
$85$	−6.93106e6	−	4.97968e6i	−0.132777	−	0.0953950i
$86$	1.93405e7	+	1.40517e7i	0.353569	+	0.256883i
$87$	3.00937e6	−	1.90004e7i	0.0525290	−	0.331655i
$88$	2.01513e7	+	3.19165e6i	0.336026	+	0.0532212i
$89$	−2.41562e6	+	3.32482e6i	−0.0385007	+	0.0529917i	−0.827833	−	0.560974i	$-0.810427\pi$
$89$	−2.41562e6	+	3.32482e6i	−0.0385007	+	0.0529917i	0.789333	+	0.613966i	$0.210427\pi$
$90$	1.91117e7	+	6.09774e6i	0.291293	+	0.0929391i
$91$	−4.85248e7	+	3.52553e7i	−0.707617	+	0.514114i
$92$	1.76208e6	+	3.45828e6i	0.0245965	+	0.0482734i
$93$	−1.69675e7	−	1.69675e7i	−0.226823	−	0.226823i
$94$	3.95751e7	+	1.28587e7i	0.506886	+	0.164697i
$95$	−3.50429e7	+	5.74122e6i	−0.430235	+	0.0704871i
$96$	−4.75855e6	−	1.46453e7i	−0.0560260	−	0.172430i
$97$	4.43728e7	+	2.26091e7i	0.501222	+	0.255385i	0.686273	−	0.727344i	$-0.259245\pi$
$97$	4.43728e7	+	2.26091e7i	0.501222	+	0.255385i	−0.185052	+	0.982729i	$0.559245\pi$
$98$	1.58764e7	+	1.00240e8i	0.172127	+	1.08677i
$99$		−	1.02503e7i		−	0.106708i
$100$	−4.74040e6	+	1.51347e7i	−0.0474040	+	0.151347i
$101$	−3.51647e7			−0.337925			−0.168963	−	0.985622i	$-0.554042\pi$
$101$	−3.51647e7			−0.337925			−0.168963	+	0.985622i	$0.554042\pi$
$102$	−9.25682e6	+	1.46614e6i	−0.0855187	+	0.0135448i
$103$	3.42346e7	−	6.71891e7i	0.304170	−	0.596967i	−0.687439	−	0.726242i	$-0.741265\pi$
$103$	3.42346e7	−	6.71891e7i	0.304170	−	0.596967i	0.991609	+	0.129275i	$0.0412651\pi$
$104$	−6.97347e7	+	2.26582e7i	−0.596095	+	0.193683i
$105$	7.39847e7	+	7.32029e7i	0.608674	+	0.602242i
$106$	−1.67188e7	+	5.14553e7i	−0.132429	+	0.407574i
$107$	1.37388e8	−	1.37388e8i	1.04813	−	1.04813i	0.0493485	−	0.998782i	$-0.484285\pi$
$107$	1.37388e8	−	1.37388e8i	1.04813	−	1.04813i	0.998782	−	0.0493485i	$-0.0157145\pi$
$108$	−3.69989e6	+	1.88519e6i	−0.0271953	+	0.0138567i
$109$	−8.88453e7	−	1.22285e8i	−0.629402	−	0.866298i	0.368593	−	0.929591i	$-0.379840\pi$
$109$	−8.88453e7	−	1.22285e8i	−0.629402	−	0.866298i	−0.997995	+	0.0632931i	$0.979840\pi$
$110$	−4.29917e7	+	228360.i	−0.293639	+	0.00155973i
$111$	6.31670e7	+	4.58935e7i	0.416101	+	0.302315i
$112$	−2.97984e7	+	1.88140e8i	−0.189374	+	1.19566i
$113$	−2.05661e8	−	3.25735e7i	−1.26136	−	0.199780i	−0.510290	−	0.860003i	$-0.670462\pi$
$113$	−2.05661e8	−	3.25735e7i	−1.26136	−	0.199780i	−0.751070	+	0.660223i	$0.770462\pi$
$114$	−2.29212e7	+	3.15483e7i	−0.135712	+	0.186791i
$115$	−3.53753e7	−	4.81500e7i	−0.202260	−	0.275299i
$116$	1.35117e7	−	9.81686e6i	0.0746242	−	0.0542176i
$117$	1.67241e7	+	3.28230e7i	0.0892484	+	0.175160i
$118$	2.46499e8	+	2.46499e8i	1.27142	+	1.27142i
$119$	−4.62445e7	−	1.50257e7i	−0.230607	−	0.0749286i
$120$	5.83638e7	+	1.13057e8i	0.281461	+	0.545220i
$121$	−5.94523e7	−	1.82975e8i	−0.277349	−	0.853593i
$122$	−6.91455e7	−	3.52314e7i	−0.312122	−	0.159034i
$123$	5.75529e6	+	3.63375e7i	0.0251447	+	0.158758i
$124$		−	2.08326e7i		−	0.0881164i
$125$	3.43448e7	−	2.41713e8i	0.140676	−	0.990056i
$126$	1.14295e8			0.453468
$127$	1.45084e8	−	2.29791e7i	0.557706	−	0.0883319i	0.128782	−	0.991673i	$-0.458893\pi$
$127$	1.45084e8	−	2.29791e7i	0.557706	−	0.0883319i	0.428923	+	0.903341i	$0.358893\pi$
$128$	−8.51762e7	+	1.67168e8i	−0.317306	+	0.622748i
$129$	7.24467e7	−	2.35394e7i	0.261613	−	0.0850033i
$130$	1.37293e8	−	7.08753e7i	0.480700	−	0.248154i
$131$	3.60540e7	−	1.10963e8i	0.122424	−	0.376784i	−0.870999	−	0.491286i	$-0.836527\pi$
$131$	3.60540e7	−	1.10963e8i	0.122424	−	0.376784i	0.993423	+	0.114502i	$0.0365272\pi$
$132$	6.29263e6	−	6.29263e6i	0.0207270	−	0.0207270i
$133$	−1.80265e8	+	9.18494e7i	−0.576108	+	0.293542i
$134$	−2.30210e8	−	3.16857e8i	−0.714012	−	0.982754i
$135$	5.15140e7	−	3.78468e7i	0.155092	−	0.113945i
$136$	−4.80892e7	−	3.49388e7i	−0.140570	−	0.102130i
$137$	1.33777e7	−	8.44634e7i	0.0379751	−	0.239765i	−0.961398	−	0.275161i	$-0.911269\pi$
$137$	1.33777e7	−	8.44634e7i	0.0379751	−	0.239765i	0.999373	+	0.0353952i	$0.0112690\pi$
$138$	−6.48053e7	−	1.02642e7i	−0.178688	−	0.0283013i
$139$	2.68414e8	−	3.69440e8i	0.719028	−	0.989657i	−0.280527	−	0.959846i	$-0.590509\pi$
$139$	2.68414e8	−	3.69440e8i	0.719028	−	0.989657i	0.999556	−	0.0298114i	$-0.00949067\pi$
$140$	479956.	+	9.03579e7i	0.00124937	+	0.235209i
$141$	1.07269e8	−	7.79358e7i	0.271393	−	0.197179i
$142$	3.22219e8	+	6.32390e8i	0.792496	+	1.55536i
$143$	−5.58241e7	−	5.58241e7i	−0.133499	−	0.133499i
$144$	1.11265e8	+	3.61522e7i	0.258767	+	0.0840784i
$145$	−1.80828e8	+	1.82759e8i	−0.409066	+	0.413435i
$146$	−2.02999e8	−	6.24766e8i	−0.446768	−	1.37501i
$147$	2.88140e8	+	1.46815e8i	0.617070	+	0.314413i
$148$	1.06041e7	+	6.69519e7i	0.0221018	+	0.139545i
$149$			1.85580e7i			0.0376518i	0.999823	+	0.0188259i	$0.00599282\pi$
$149$			1.85580e7i			0.0376518i	−0.999823	+	0.0188259i	$0.994007\pi$
$150$	−1.59884e8	−	2.15216e8i	−0.315820	−	0.425118i
$151$	−6.33602e8			−1.21873			−0.609367	−	0.792888i	$-0.708576\pi$
$151$	−6.33602e8			−1.21873			−0.609367	+	0.792888i	$0.708576\pi$
$152$	−2.44279e8	+	3.86900e7i	−0.457627	+	0.0724810i
$153$	−1.35579e7	+	2.66088e7i	−0.0247415	+	0.0485579i
$154$	−2.32957e8	+	7.56922e7i	−0.414183	+	0.134576i
$155$	5.18491e7	+	3.16474e8i	0.0898286	+	0.548291i
$156$	−9.88301e6	+	3.04168e7i	−0.0166875	+	0.0513588i
$157$	7.95689e8	−	7.95689e8i	1.30962	−	1.30962i	0.387929	−	0.921689i	$-0.373191\pi$
$157$	7.95689e8	−	7.95689e8i	1.30962	−	1.30962i	0.921689	−	0.387929i	$-0.126809\pi$
$158$	−5.58301e8	+	2.84469e8i	−0.895860	+	0.456464i
$159$	1.01332e8	+	1.39471e8i	0.158546	+	0.218220i
$160$	−6.25555e7	+	1.96064e8i	−0.0954522	+	0.299169i
$161$	−2.75397e8	−	2.00088e8i	−0.409880	−	0.297795i
$162$	1.09813e7	−	6.93329e7i	0.0159438	−	0.100665i
$163$	−1.10579e9	−	1.75140e8i	−1.56647	−	0.248104i	−0.687930	−	0.725777i	$-0.741480\pi$
$163$	−1.10579e9	−	1.75140e8i	−1.56647	−	0.248104i	−0.878538	+	0.477673i	$0.841480\pi$
$164$	−1.87743e7	+	2.58406e7i	−0.0259530	+	0.0357213i
$165$	−7.99317e7	+	1.11254e8i	−0.107841	+	0.150100i
$166$	9.12484e8	−	6.62959e8i	1.20169	−	0.873080i
$167$	4.56565e8	+	8.96059e8i	0.586998	+	1.15205i	0.973270	+	0.229664i	$0.0737626\pi$
$167$	4.56565e8	+	8.96059e8i	0.586998	+	1.15205i	−0.386272	+	0.922385i	$0.626237\pi$
$168$	5.12580e8	+	5.12580e8i	0.643464	+	0.643464i
$169$	−5.05968e8	−	1.64399e8i	−0.620264	−	0.201536i
$170$	1.11904e8	+	5.62713e7i	0.133983	+	0.0673738i
$171$	3.83975e7	+	1.18175e8i	0.0449074	+	0.138211i
$172$	5.89255e7	+	3.00240e7i	0.0673270	+	0.0343048i
$173$	−1.68314e8	−	1.06269e9i	−0.187904	−	1.18638i	−0.883670	−	0.468110i	$-0.844935\pi$
$173$	−1.68314e8	−	1.06269e9i	−0.187904	−	1.18638i	0.695766	−	0.718268i	$-0.255065\pi$
$174$			2.82336e8i			0.308013i
$175$	−2.32178e8	−	1.37146e9i	−0.247553	−	1.46228i
$176$	−2.50722e8			−0.261301
$177$	1.09712e9	−	1.73766e8i	1.11779	−	0.177040i
$178$	2.73829e7	−	5.37419e7i	0.0272771	−	0.0535344i
$179$	−4.40299e8	+	1.43062e8i	−0.428880	+	0.139352i	−0.515500	−	0.856890i	$-0.672394\pi$
$179$	−4.40299e8	+	1.43062e8i	−0.428880	+	0.139352i	0.0866193	+	0.996241i	$0.472394\pi$
$180$	5.48583e7	+	8.39025e6i	0.0522579	+	0.00799254i
$181$	2.04156e8	−	6.28327e8i	0.190216	−	0.585425i	−0.809783	−	0.586729i	$-0.800415\pi$
$181$	2.04156e8	−	6.28327e8i	0.190216	−	0.585425i	0.999999	+	0.00130443i	$0.000415212\pi$
$182$	6.22462e8	−	6.22462e8i	0.567319	−	0.567319i
$183$	−2.20326e8	+	1.12262e8i	−0.196455	+	0.100099i
$184$	−2.44600e8	−	3.36664e8i	−0.213396	−	0.293714i
$185$	−3.27723e8	−	9.90691e8i	−0.279782	−	0.845768i
$186$	2.84914e8	+	2.07002e8i	0.238046	+	0.172951i
$187$	1.00119e7	−	6.32127e7i	0.00818748	−	0.0516937i
$188$	1.13697e8	+	1.80078e7i	0.0910158	+	0.0144155i
$189$	2.14067e8	−	2.94638e8i	0.167765	−	0.230909i
$190$	4.94793e8	−	1.63679e8i	0.379673	−	0.125597i
$191$	9.34917e8	−	6.79257e8i	0.702489	−	0.510388i	−0.178253	−	0.983985i	$-0.557044\pi$
$191$	9.34917e8	−	6.79257e8i	0.702489	−	0.510388i	0.880742	+	0.473596i	$0.157044\pi$
$192$	3.93350e8	+	7.71992e8i	0.289450	+	0.568078i
$193$	4.64903e8	+	4.64903e8i	0.335068	+	0.335068i	0.854507	−	0.519439i	$-0.173859\pi$
$193$	4.64903e8	+	4.64903e8i	0.335068	+	0.335068i	−0.519439	+	0.854507i	$0.673859\pi$
$194$	−6.95127e8	−	2.25860e8i	−0.490747	−	0.159453i
$195$	7.44328e7	−	4.86667e8i	0.0514785	−	0.336584i
$196$	8.67591e7	+	2.67017e8i	0.0587883	+	0.180932i
$197$	−9.98583e8	−	5.08803e8i	−0.663009	−	0.337820i	0.0898943	−	0.995951i	$-0.471347\pi$
$197$	−9.98583e8	−	5.08803e8i	−0.663009	−	0.337820i	−0.752903	+	0.658132i	$0.771347\pi$
$198$	2.35338e7	+	1.48587e8i	0.0153120	+	0.0966760i
$199$			2.81007e9i			1.79186i	0.444192	+	0.895932i	$0.353491\pi$
$199$			2.81007e9i			1.79186i	−0.444192	+	0.895932i	$0.646509\pi$
$200$	2.48147e8	−	1.68221e9i	0.155092	−	1.05138i
$201$	−1.24798e9			−0.764582
$202$	5.09740e8	−	8.07348e7i	0.306156	−	0.0484904i
$203$	−6.65004e8	+	1.30514e9i	−0.391597	+	0.768553i
$204$	−2.46582e7	+	8.01192e6i	−0.0142377	+	0.00462611i
$205$	2.20892e8	−	4.39278e8i	0.125073	−	0.248728i
$206$	−3.41997e8	+	1.05256e9i	−0.189913	+	0.584491i
$207$	−1.47835e8	+	1.47835e8i	−0.0805187	+	0.0805187i
$208$	8.02846e8	−	4.09070e8i	0.428923	−	0.218547i
$209$	−1.56523e8	−	2.15436e8i	−0.0820340	−	0.112910i
$210$	−1.24053e9	−	8.91272e8i	−0.637869	−	0.458282i
$211$	1.89321e9	+	1.37550e9i	0.955146	+	0.693954i	0.952018	−	0.306041i	$-0.0990045\pi$
$211$	1.89321e9	+	1.37550e9i	0.955146	+	0.693954i	0.00312740	+	0.999995i	$0.499005\pi$
$212$	−2.34136e7	+	1.47828e8i	−0.0115911	+	0.0731834i
$213$	2.23371e9	+	3.53784e8i	1.08519	+	0.171878i
$214$	−1.67612e9	+	2.30699e9i	−0.799192	+	1.09999i
$215$	−9.69877e8	−	3.09447e8i	−0.453903	−	0.144821i
$216$	3.60185e8	−	2.61689e8i	0.165467	−	0.120218i
$217$	8.29495e8	+	1.62798e9i	0.374089	+	0.734191i
$218$	1.56864e9	+	1.56864e9i	0.694539	+	0.694539i
$219$	−1.99076e9	−	6.46838e8i	−0.865452	−	0.281203i
$220$	−1.17368e8	+	1.92289e7i	−0.0501026	+	0.00820852i
$221$	7.10765e7	+	2.18751e8i	0.0297959	+	0.0917024i
$222$	−1.02102e9	−	5.20237e8i	−0.420362	−	0.214185i
$223$	5.52269e8	+	3.48689e9i	0.223322	+	1.41000i	0.803401	+	0.595439i	$0.203022\pi$
$223$	5.52269e8	+	3.48689e9i	0.223322	+	1.41000i	−0.580079	+	0.814560i	$0.696978\pi$
$224$			1.17254e9i			0.465729i
$225$	−8.54249e8	+	9.07532e6i	−0.333315	+	0.00354105i
$226$	3.05601e9			1.17144
$227$	−1.60876e9	+	2.54803e8i	−0.605883	+	0.0959625i	−0.451836	−	0.892101i	$-0.649231\pi$
$227$	−1.60876e9	+	2.54803e8i	−0.605883	+	0.0959625i	−0.154047	+	0.988063i	$0.549231\pi$
$228$	−4.89753e7	+	9.61194e7i	−0.0181233	+	0.0355690i
$229$	−3.22712e9	+	1.04856e9i	−1.17347	+	0.381285i	−0.829939	−	0.557855i	$-0.811625\pi$
$229$	−3.22712e9	+	1.04856e9i	−1.17347	+	0.381285i	−0.343535	+	0.939140i	$0.611625\pi$
$230$	6.23341e8	+	6.16754e8i	0.222748	+	0.220395i
$231$	−2.41187e8	+	7.42296e8i	−0.0847043	+	0.260693i
$232$	−1.26619e9	+	1.26619e9i	−0.437066	+	0.437066i
$233$	−2.51080e9	+	1.27932e9i	−0.851900	+	0.434065i	−0.824704	−	0.565565i	$-0.808658\pi$
$233$	−2.51080e9	+	1.27932e9i	−0.851900	+	0.434065i	−0.0271968	+	0.999630i	$0.508658\pi$
$234$	−3.17788e8	−	4.37398e8i	−0.105992	−	0.145886i
$235$	−1.77202e9	+	9.41246e6i	−0.581027	+	0.00308625i
$236$	7.80191e8	+	5.66842e8i	0.251509	+	0.182732i
$237$	−3.12336e8	+	1.97201e9i	−0.0989986	+	0.625053i
$238$	7.04848e8	+	1.11637e8i	0.219678	+	0.0347937i
$239$	−1.86224e9	+	2.56315e9i	−0.570746	+	0.785565i	−0.992643	−	0.121079i	$-0.961365\pi$
$239$	−1.86224e9	+	2.56315e9i	−0.570746	+	0.785565i	0.421896	+	0.906644i	$0.361365\pi$
$240$	−9.25729e8	−	1.26003e9i	−0.279022	−	0.379782i
$241$	4.07493e9	−	2.96061e9i	1.20796	−	0.877633i	0.212915	−	0.977071i	$-0.431704\pi$
$241$	4.07493e9	−	2.96061e9i	1.20796	−	0.877633i	0.995044	+	0.0994375i	$0.0317043\pi$
$242$	1.28190e9	+	2.51587e9i	0.373760	+	0.733546i
$243$	−1.58164e8	−	1.58164e8i	−0.0453609	−	0.0453609i
$244$	−2.04175e8	−	6.63404e7i	−0.0576027	−	0.0187162i
$245$	−1.98254e9	−	3.84040e9i	−0.550248	−	1.06589i
$246$	−1.66855e8	−	5.13527e8i	−0.0455616	−	0.140224i
$247$	8.52708e8	+	4.34477e8i	0.229093	+	0.116729i
$248$	3.49411e8	+	2.20609e9i	0.0923697	+	0.583199i
$249$		−	3.59393e9i		−	0.934916i
$250$	5.70948e7	+	3.58267e9i	0.0146163	+	0.917164i
$251$	7.64650e9			1.92650			0.963248	−	0.268615i	$-0.0865661\pi$
$251$	7.64650e9			1.92650			0.963248	+	0.268615i	$0.0865661\pi$
$252$	3.12292e8	−	4.94622e7i	0.0774388	−	0.0122651i
$253$	2.03413e8	−	3.99221e8i	0.0496475	−	0.0974388i
$254$	−2.05035e9	+	6.66200e8i	−0.492599	+	0.160055i
$255$	3.54648e8	−	1.83082e8i	0.0838759	−	0.0432996i
$256$	−6.14754e8	+	1.89202e9i	−0.143134	+	0.440520i
$257$	4.86732e8	−	4.86732e8i	0.111573	−	0.111573i	−0.649116	−	0.760689i	$-0.724861\pi$
$257$	4.86732e8	−	4.86732e8i	0.111573	−	0.111573i	0.760689	+	0.649116i	$0.224861\pi$
$258$	−9.96128e8	+	5.07553e8i	−0.224821	+	0.114552i
$259$	−3.49450e9	−	4.80976e9i	−0.776579	−	1.06887i
$260$	3.44457e8	−	2.53069e8i	0.0753774	−	0.0553790i
$261$	7.27823e8	+	5.28794e8i	0.156842	+	0.113953i
$262$	−2.67871e8	+	1.69127e9i	−0.0568487	+	0.358928i
$263$	2.05808e9	+	3.25968e8i	0.430169	+	0.0681322i	0.367765	−	0.929919i	$-0.380123\pi$
$263$	2.05808e9	+	3.25968e8i	0.430169	+	0.0681322i	0.0624045	+	0.998051i	$0.480123\pi$
$264$	−5.60823e8	+	7.71907e8i	−0.115454	+	0.158909i
$265$	−1.22380e7	−	2.30396e9i	−0.00248158	−	0.467188i
$266$	2.40220e9	−	1.74530e9i	0.479825	−	0.348613i
$267$	−8.72531e7	−	1.71244e8i	−0.0171686	−	0.0336954i
$268$	−7.66132e8	−	7.66132e8i	−0.148513	−	0.148513i
$269$	2.46827e9	+	8.01989e8i	0.471393	+	0.153165i	0.535074	−	0.844805i	$-0.320284\pi$
$269$	2.46827e9	+	8.01989e8i	0.471393	+	0.153165i	−0.0636804	+	0.997970i	$0.520284\pi$
$270$	−6.59844e8	+	6.66891e8i	−0.124161	+	0.125487i
$271$	−1.69374e9	−	5.21279e9i	−0.314028	−	0.966480i	−0.976153	−	0.217086i	$-0.930345\pi$
$271$	−1.69374e9	−	5.21279e9i	−0.314028	−	0.966480i	0.662124	−	0.749394i	$-0.269655\pi$
$272$	6.50848e8	+	3.31624e8i	0.118906	+	0.0605857i
$273$	−4.38796e8	−	2.77045e9i	−0.0789973	−	0.498769i
$274$			1.25508e9i			0.222674i
$275$	1.73512e9	−	5.84224e8i	0.303388	−	0.102152i
$276$	−1.81511e8			−0.0312800
$277$	2.50929e9	−	3.97433e8i	0.426218	−	0.0675064i	0.0603595	−	0.998177i	$-0.480775\pi$
$277$	2.50929e9	−	3.97433e8i	0.426218	−	0.0675064i	0.365859	+	0.930670i	$0.380775\pi$
$278$	−3.04267e9	+	5.97158e9i	−0.509420	+	0.999793i
$279$	1.06725e9	−	3.46769e8i	0.176136	−	0.0572300i
$280$	−1.56633e9	−	9.56050e9i	−0.254831	−	1.55542i
$281$	3.44915e9	−	1.06154e10i	0.553206	−	1.70259i	−0.147429	−	0.989073i	$-0.547100\pi$
$281$	3.44915e9	−	1.06154e10i	0.553206	−	1.70259i	0.700635	−	0.713520i	$-0.252900\pi$
$282$	−1.37602e9	+	1.37602e9i	−0.217585	+	0.217585i
$283$	3.06758e8	−	1.56301e8i	0.0478244	−	0.0243677i	−0.429915	−	0.902869i	$-0.641456\pi$
$283$	3.06758e8	−	1.56301e8i	0.0478244	−	0.0243677i	0.477739	+	0.878502i	$0.341456\pi$
$284$	1.15408e9	+	1.58845e9i	0.177403	+	0.244175i
$285$	5.04770e8	−	1.58207e9i	0.0765093	−	0.239798i
$286$	9.37382e8	+	6.81048e8i	0.140105	+	0.101792i
$287$	4.38229e8	−	2.76687e9i	0.0645912	−	0.407813i
$288$	7.11274e8	+	1.12655e8i	0.103387	+	0.0163749i
$289$	3.99065e9	−	5.49266e9i	0.572074	−	0.787392i
$290$	2.20164e9	−	3.06440e9i	0.311283	−	0.433265i
$291$	−1.88416e9	+	1.36892e9i	−0.262752	+	0.190900i
$292$	−8.25031e8	−	1.61921e9i	−0.113485	−	0.222727i
$293$	2.61113e9	+	2.61113e9i	0.354290	+	0.354290i	0.861703	−	0.507413i	$-0.169398\pi$
$293$	2.61113e9	+	2.61113e9i	0.354290	+	0.354290i	−0.507413	+	0.861703i	$0.669398\pi$
$294$	−4.51389e9	−	1.46665e9i	−0.604173	−	0.196308i
$295$	−1.32629e10	−	6.66927e9i	−1.75125	−	0.880623i
$296$	−2.24587e9	−	6.91208e9i	−0.292562	−	0.900414i
$297$	4.27113e8	+	2.17625e8i	0.0548930	+	0.0279694i
$298$	−4.26074e7	−	2.69013e8i	−0.00540281	−	0.0341120i
$299$			1.61025e9i			0.201469i
$300$	−5.29991e8	−	5.18849e8i	−0.0654310	−	0.0640554i
$301$	−5.80024e9			−0.706610
$302$	9.18457e9	−	1.45469e9i	1.10416	−	0.174881i
$303$	7.46582e8	−	1.46525e9i	0.0885741	−	0.173837i
$304$	2.89055e9	−	9.39198e8i	0.338444	−	0.109967i
$305$	3.26678e9	+	4.99635e8i	0.377503	+	0.0577369i
$306$	1.35441e8	−	4.16843e8i	0.0154477	−	0.0475430i
$307$	−1.59746e8	+	1.59746e8i	−0.0179836	+	0.0179836i	−0.716041	−	0.698058i	$-0.754048\pi$
$307$	−1.59746e8	+	1.59746e8i	−0.0179836	+	0.0179836i	0.698058	+	0.716041i	$0.254048\pi$
$308$	−6.03757e8	+	3.07629e8i	−0.0670902	+	0.0341842i
$309$	2.07282e9	+	2.85299e9i	0.227367	+	0.312944i
$310$	−1.47819e9	−	4.46850e9i	−0.160060	−	0.483854i
$311$	1.67636e9	+	1.21794e9i	0.179194	+	0.130192i	0.673767	−	0.738944i	$-0.264675\pi$
$311$	1.67636e9	+	1.21794e9i	0.179194	+	0.130192i	−0.494572	+	0.869137i	$0.664675\pi$
$312$	5.36413e8	−	3.38678e9i	0.0566084	−	0.357411i
$313$	8.24673e8	+	1.30615e8i	0.0859220	+	0.0136087i	0.199247	−	0.979949i	$-0.436150\pi$
$313$	8.24673e8	+	1.30615e8i	0.0859220	+	0.0136087i	−0.113325	+	0.993558i	$0.536150\pi$
$314$	−9.70731e9	+	1.33610e10i	−0.998574	+	1.37442i
$315$	−4.62101e9	+	1.52864e9i	−0.469347	+	0.155261i
$316$	−1.40235e9	+	1.01887e9i	−0.140640	+	0.102181i
$317$	−3.70123e9	−	7.26408e9i	−0.366530	−	0.719355i	0.631919	−	0.775035i	$-0.282268\pi$
$317$	−3.70123e9	−	7.26408e9i	−0.366530	−	0.719355i	−0.998449	+	0.0556792i	$0.982268\pi$
$318$	−1.78909e9	−	1.78909e9i	−0.174954	−	0.174954i
$319$	−1.83364e9	−	5.95786e8i	−0.177073	−	0.0575344i
$320$	1.75065e9	−	1.14463e10i	0.166955	−	1.09161i
$321$	2.80784e9	+	8.64164e9i	0.264455	+	0.813909i
$322$	4.45149e9	+	2.26815e9i	0.414077	+	0.210983i
$323$	1.21367e8	+	7.66279e8i	0.0111504	+	0.0704007i
$324$		−	1.94192e8i		−	0.0176219i
$325$	−4.60289e9	+	4.70174e9i	−0.412569	+	0.421429i
$326$	1.64314e10			1.45480
$327$	6.98168e9	−	1.10579e9i	0.610617	−	0.0967122i
$328$	1.55472e9	−	3.05131e9i	0.134325	−	0.263627i
$329$	−9.60192e9	+	3.11985e9i	−0.819548	+	0.266287i
$330$	9.03243e8	−	1.79624e9i	0.0761638	−	0.151463i
$331$	−8.52454e8	+	2.62358e9i	−0.0710165	+	0.218566i	−0.980265	−	0.197687i	$-0.936657\pi$
$331$	−8.52454e8	+	2.62358e9i	−0.0710165	+	0.218566i	0.909249	+	0.416253i	$0.136657\pi$
$332$	2.20630e9	−	2.20630e9i	0.181599	−	0.181599i
$333$	−3.25340e9	+	1.65769e9i	−0.264582	+	0.134811i
$334$	−8.67554e9	−	1.19409e10i	−0.697125	−	0.959510i
$335$	1.35453e10	+	9.73173e9i	1.07550	+	0.772700i
$336$	−7.20681e9	−	5.23605e9i	−0.565439	−	0.410816i
$337$	−2.63306e9	+	1.66245e10i	−0.204146	+	1.28893i	0.646389	+	0.763008i	$0.276278\pi$
$337$	−2.63306e9	+	1.66245e10i	−0.204146	+	1.28893i	−0.850535	+	0.525918i	$0.823722\pi$
$338$	7.71186e9	+	1.22144e9i	0.590870	+	0.0935847i
$339$	5.72368e9	−	7.87798e9i	0.433388	−	0.596507i
$340$	3.30110e8	+	1.05324e8i	0.0247026	+	0.00788156i
$341$	−1.94561e9	+	1.41357e9i	−0.143892	+	0.104544i
$342$	−8.27921e8	−	1.62489e9i	−0.0605180	−	0.118773i
$343$	−2.89636e9	−	2.89636e9i	−0.209255	−	0.209255i
$344$	−6.74355e9	−	2.19111e9i	−0.481565	−	0.156470i
$345$	2.75738e9	−	4.51753e8i	0.194635	−	0.0318878i
$346$	4.87969e9	+	1.50181e10i	0.340477	+	1.04788i
$347$	8.09764e8	+	4.12595e8i	0.0558522	+	0.0284581i	0.481694	−	0.876340i	$-0.340022\pi$
$347$	8.09764e8	+	4.12595e8i	0.0558522	+	0.0284581i	−0.425841	+	0.904798i	$0.640022\pi$
$348$	1.22183e8	+	7.71433e8i	0.00833093	+	0.0525994i
$349$			3.27310e9i			0.220627i	0.993897	+	0.110313i	$0.0351854\pi$
$349$			3.27310e9i			0.220627i	−0.993897	+	0.110313i	$0.964815\pi$
$350$	6.51434e9	+	1.93473e10i	0.434109	+	1.28928i
$351$	−1.72275e9			−0.113499
$352$	−1.52432e9	+	2.41429e8i	−0.0992901	+	0.0157260i
$353$	−1.09627e10	+	2.15156e10i	−0.706025	+	1.38565i	0.207242	+	0.978290i	$0.433551\pi$
$353$	−1.09627e10	+	2.15156e10i	−0.706025	+	1.38565i	−0.913267	+	0.407362i	$0.866449\pi$
$354$	−1.55046e10	+	5.03776e9i	−0.987299	+	0.320793i
$355$	−2.14853e10	−	2.12583e10i	−1.35278	−	1.33849i
$356$	5.15616e7	−	1.58690e8i	0.00321016	−	0.00987986i
$357$	1.60791e9	−	1.60791e9i	0.0989897	−	0.0989897i
$358$	6.05403e9	−	3.08468e9i	0.368564	−	0.187793i
$359$	1.53484e10	+	2.11253e10i	0.924031	+	1.27182i	0.962143	+	0.272546i	$0.0878656\pi$
$359$	1.53484e10	+	2.11253e10i	0.924031	+	1.27182i	−0.0381120	+	0.999273i	$0.512134\pi$
$360$	−5.95000e9	+	3.16048e7i	−0.354248	+	0.00188167i
$361$	−1.11284e10	−	8.08528e9i	−0.655247	−	0.476065i
$362$	−1.51682e9	+	9.57682e9i	−0.0883282	+	0.557682i
$363$	8.88649e9	+	1.40748e9i	0.511804	+	0.0810618i
$364$	1.43139e9	−	1.97014e9i	0.0815368	−	0.112226i
$365$	1.65632e10	+	2.25445e10i	0.933198	+	1.27019i
$366$	2.93606e9	−	2.13317e9i	0.163622	−	0.118878i
$367$	1.73561e9	+	3.40633e9i	0.0956727	+	0.187768i	0.933883	−	0.357579i	$-0.116398\pi$
$367$	1.73561e9	+	3.40633e9i	0.0956727	+	0.187768i	−0.838210	+	0.545347i	$0.816398\pi$
$368$	3.61603e9	+	3.61603e9i	0.197170	+	0.197170i
$369$	−1.63631e9	−	5.31670e8i	−0.0882593	−	0.0286772i
$370$	7.02514e9	+	1.36084e10i	0.374842	+	0.726108i
$371$	−4.05641e9	−	1.24843e10i	−0.214115	−	0.658977i
$372$	8.68058e8	+	4.42298e8i	0.0453291	+	0.0230963i
$373$	2.96373e7	+	1.87123e8i	0.00153110	+	0.00966698i	0.988442	−	0.151599i	$-0.0484423\pi$
$373$	2.96373e7	+	1.87123e8i	0.00153110	+	0.00966698i	−0.986911	+	0.161266i	$0.948442\pi$
$374$			9.39304e8i			0.0480087i
$375$	9.34257e9	+	6.56290e9i	0.472434	+	0.331872i
$376$	−1.23421e10			−0.617500
$377$	6.84364e9	−	1.08393e9i	0.338783	−	0.0536580i
$378$	−2.42661e9	+	4.76249e9i	−0.118859	+	0.233274i
$379$	1.41724e10	−	4.60488e9i	0.686887	−	0.223183i	0.0552788	−	0.998471i	$-0.482395\pi$
$379$	1.41724e10	−	4.60488e9i	0.686887	−	0.223183i	0.631608	+	0.775288i	$0.282395\pi$
$380$	1.28110e9	−	6.61349e8i	0.0614397	−	0.0317173i
$381$	−2.12279e9	+	6.53327e9i	−0.100741	+	0.310049i
$382$	−1.19929e10	+	1.19929e10i	−0.563208	+	0.563208i
$383$	−2.80023e10	+	1.42679e10i	−1.30136	+	0.663078i	−0.960826	−	0.277152i	$-0.910609\pi$
$383$	−2.80023e10	+	1.42679e10i	−1.30136	+	0.663078i	−0.340539	+	0.940231i	$0.610609\pi$
$384$	−5.15721e9	−	7.09828e9i	−0.237186	−	0.326459i
$385$	8.40618e9	−	6.17593e9i	0.382610	−	0.281099i
$386$	−7.80651e9	−	5.67176e9i	−0.351647	−	0.255487i
$387$	−5.57274e8	+	3.51849e9i	−0.0248442	+	0.156860i
$388$	−1.99706e9	−	3.16303e8i	−0.0881177	−	0.0139565i
$389$	1.65492e10	−	2.27781e10i	0.722736	−	0.994760i	−0.276693	−	0.960958i	$-0.589238\pi$
$389$	1.65492e10	−	2.27781e10i	0.722736	−	0.994760i	0.999429	−	0.0338019i	$-0.0107615\pi$
$390$	3.83799e7	+	7.22551e9i	0.00165900	+	0.312327i
$391$	−1.05608e9	+	7.67288e8i	−0.0451846	+	0.0328285i
$392$	−1.36659e10	−	2.68209e10i	−0.578755	−	1.13587i
$393$	3.85816e9	+	3.85816e9i	0.161737	+	0.161737i
$394$	1.56434e10	+	5.08285e9i	0.649152	+	0.210922i
$395$	1.87677e10	−	1.89682e10i	0.770945	−	0.779178i
$396$	1.28604e8	+	3.95802e8i	0.00522966	+	0.0160952i
$397$	4.03290e10	+	2.05486e10i	1.62351	+	0.827220i	0.998929	+	0.0462603i	$0.0147304\pi$
$397$	4.03290e10	+	2.05486e10i	1.62351	+	0.827220i	0.624581	+	0.780960i	$0.285270\pi$
$398$	−6.45166e9	−	4.07342e10i	−0.257122	−	1.62340i
$399$		−	9.46136e9i		−	0.373304i
$400$	2.21981e8	+	2.08948e10i	0.00867115	+	0.816204i
$401$	−2.16157e10			−0.835971			−0.417986	−	0.908454i	$-0.637264\pi$
$401$	−2.16157e10			−0.835971			−0.417986	+	0.908454i	$0.637264\pi$
$402$	1.80905e10	−	2.86525e9i	0.692702	−	0.109713i
$403$	3.92378e9	−	7.70084e9i	0.148759	−	0.291956i
$404$	1.35784e9	−	4.41187e8i	0.0509708	−	0.0165614i
$405$	4.83315e8	+	2.95003e9i	0.0179643	+	0.109649i
$406$	6.64327e9	−	2.04459e10i	0.244499	−	0.752491i
$407$	5.53327e9	−	5.53327e9i	0.201653	−	0.201653i
$408$	2.47682e9	−	1.26200e9i	0.0893829	−	0.0455429i
$409$	2.13510e9	+	2.93871e9i	0.0762999	+	0.105018i	0.845461	−	0.534037i	$-0.179326\pi$
$409$	2.13510e9	+	2.93871e9i	0.0762999	+	0.105018i	−0.769161	+	0.639055i	$0.779326\pi$
$410$	−2.19346e9	+	6.87483e9i	−0.0776238	+	0.243291i
$411$	3.23542e9	+	2.35067e9i	0.113387	+	0.0823805i
$412$	−4.78944e8	+	3.02394e9i	−0.0166225	+	0.104950i
$413$	−8.35385e10	−	1.32312e10i	−2.87135	−	0.454777i
$414$	1.80357e9	−	2.48241e9i	0.0613949	−	0.0845029i
$415$	−2.80254e10	+	3.90077e10i	−0.944842	+	1.31510i
$416$	4.48718e9	−	3.26013e9i	0.149831	−	0.108858i
$417$	9.69522e9	+	1.90279e10i	0.320637	+	0.629285i
$418$	2.76355e9	+	2.76355e9i	0.0905237	+	0.0905237i
$419$	4.43820e10	+	1.44206e10i	1.43996	+	0.467872i	0.921885	−	0.387463i	$-0.126649\pi$
$419$	4.43820e10	+	1.44206e10i	1.43996	+	0.467872i	0.518075	+	0.855335i	$0.326649\pi$
$420$	−3.77525e9	−	1.89839e9i	−0.121324	−	0.0610083i
$421$	3.63531e9	+	1.11883e10i	0.115721	+	0.356153i	0.992097	−	0.125475i	$-0.0400456\pi$
$421$	3.63531e9	+	1.11883e10i	0.115721	+	0.356153i	−0.876376	+	0.481628i	$0.840046\pi$
$422$	−3.06016e10	−	1.55923e10i	−0.964928	−	0.491655i
$423$	9.70007e8	+	6.12438e9i	0.0302980	+	0.191294i
$424$		−	1.60471e10i		−	0.496515i
$425$	−5.27693e9	−	7.78413e8i	−0.161743	−	0.0238591i
$426$	−3.31916e10			−1.00784
$427$	1.85968e10	−	2.94545e9i	0.559406	−	0.0886013i
$428$	−3.58135e9	+	7.02879e9i	−0.106726	+	0.209462i
$429$	3.51130e9	−	1.14089e9i	0.103666	−	0.0336833i
$430$	1.47696e10	+	2.25892e9i	0.432011	+	0.0660735i
$431$	−1.95857e10	+	6.02785e10i	−0.567583	+	1.74684i	0.0925646	+	0.995707i	$0.470494\pi$
$431$	−1.95857e10	+	6.02785e10i	−0.567583	+	1.74684i	−0.660148	+	0.751136i	$0.729506\pi$
$432$	−3.86867e9	+	3.86867e9i	−0.111078	+	0.111078i
$433$	−4.15732e10	+	2.11826e10i	−1.18267	+	0.602598i	−0.930930	−	0.365198i	$-0.881001\pi$
$433$	−4.15732e10	+	2.11826e10i	−1.18267	+	0.602598i	−0.251735	+	0.967796i	$0.581001\pi$
$434$	−1.57619e10	−	2.16944e10i	−0.444272	−	0.611488i
$435$	−3.77609e9	−	1.14149e10i	−0.105459	−	0.318799i
$436$	4.96487e9	+	3.60719e9i	0.137392	+	0.0998212i
$437$	−8.49666e8	+	5.36458e9i	−0.0232982	+	0.147099i
$438$	3.03428e10	+	4.80582e9i	0.824440	+	0.130578i
$439$	−1.16554e10	+	1.60423e10i	−0.313811	+	0.431924i	−0.936565	−	0.350494i	$-0.886014\pi$
$439$	−1.16554e10	+	1.60423e10i	−0.313811	+	0.431924i	0.622754	+	0.782418i	$0.286014\pi$
$440$	1.21063e10	−	4.00481e9i	0.323000	−	0.106849i
$441$	−1.22350e10	+	8.88926e9i	−0.323482	+	0.235024i
$442$	−1.53254e9	−	3.00778e9i	−0.0401535	−	0.0788057i
$443$	1.31904e10	+	1.31904e10i	0.342487	+	0.342487i	0.857302	−	0.514814i	$-0.172139\pi$
$443$	1.31904e10	+	1.31904e10i	0.342487	+	0.342487i	−0.514814	+	0.857302i	$0.672139\pi$
$444$	−3.01490e9	−	9.79601e8i	−0.0775785	−	0.0252068i
$445$	−3.88331e8	+	2.53904e9i	−0.00990288	+	0.0647484i
$446$	−1.60112e10	−	4.92773e10i	−0.404654	−	1.24540i
$447$	−7.73278e8	−	3.94005e8i	−0.0193689	−	0.00986897i
$448$	−1.03204e10	−	6.51607e10i	−0.256204	−	1.61761i
$449$		−	2.26202e10i		−	0.556558i	−0.960500	−	0.278279i	$-0.910236\pi$
$449$		−	2.26202e10i		−	0.556558i	0.960500	−	0.278279i	$-0.0897639\pi$
$450$	1.23622e10	−	2.09283e9i	0.301471	−	0.0510369i
$451$	3.68722e9			0.0891237
$452$	8.35001e9	−	1.32251e9i	0.200048	−	0.0316844i
$453$	1.34520e10	−	2.64011e10i	0.319444	−	0.626945i
$454$	2.27353e10	−	7.38715e9i	0.535152	−	0.173882i
$455$	−1.68413e10	+	3.34915e10i	−0.392943	+	0.781428i
$456$	3.57415e9	−	1.10001e10i	0.0826634	−	0.254412i
$457$	5.39619e10	−	5.39619e10i	1.23715	−	1.23715i	0.275990	−	0.961161i	$-0.410994\pi$
$457$	5.39619e10	−	5.39619e10i	1.23715	−	1.23715i	0.961161	−	0.275990i	$-0.0890056\pi$
$458$	4.43723e10	−	2.26088e10i	1.00844	−	0.513826i
$459$	−8.20895e8	−	1.12986e9i	−0.0184942	−	0.0254551i
$460$	1.97008e9	+	1.41542e9i	0.0439999	+	0.0316121i
$461$	−1.28644e10	−	9.34656e9i	−0.284831	−	0.206942i	0.436191	−	0.899854i	$-0.356327\pi$
$461$	−1.28644e10	−	9.34656e9i	−0.284831	−	0.206942i	−0.721022	+	0.692912i	$0.756327\pi$
$462$	1.79195e9	−	1.13139e10i	0.0393330	−	0.248339i
$463$	7.04610e10	+	1.11599e10i	1.53329	+	0.242850i	0.865276	−	0.501297i	$-0.167143\pi$
$463$	7.04610e10	+	1.11599e10i	1.53329	+	0.242850i	0.668017	+	0.744146i	$0.267143\pi$
$464$	1.29343e10	−	1.78025e10i	0.279042	−	0.384068i
$465$	−1.42877e10	−	4.55860e9i	−0.305598	−	0.0975034i
$466$	3.34589e10	−	2.43093e10i	0.709525	−	0.515500i
$467$	−2.66013e10	−	5.22081e10i	−0.559288	−	1.09767i	−0.981553	−	0.191193i	$-0.938765\pi$
$467$	−2.66013e10	−	5.22081e10i	−0.559288	−	1.09767i	0.422264	−	0.906473i	$-0.361235\pi$
$468$	−1.05759e9	−	1.05759e9i	−0.0220462	−	0.0220462i
$469$	9.03750e10	+	2.93646e10i	1.86791	+	0.606922i
$470$	2.56652e10	−	4.20483e9i	0.525960	−	0.0861701i
$471$	1.62617e10	+	5.00483e10i	0.330431	+	1.01696i
$472$	−9.21264e10	−	4.69407e10i	−1.85616	−	0.945762i
$473$	−1.19429e9	−	7.54043e9i	−0.0238597	−	0.150644i
$474$		−	2.93030e10i		−	0.580495i
$475$	−1.78156e10	+	1.32352e10i	−0.349965	+	0.259989i
$476$	1.97418e9			0.0384556
$477$	−7.96288e9	+	1.26120e9i	−0.153814	+	0.0243618i
$478$	2.11098e10	−	4.14304e10i	0.404365	−	0.793611i
$479$	−5.33895e10	+	1.73473e10i	−1.01418	+	0.329526i	−0.768517	−	0.639830i	$-0.779005\pi$
$479$	−5.33895e10	+	1.73473e10i	−1.01418	+	0.329526i	−0.245660	+	0.969356i	$0.579005\pi$
$480$	−6.84151e9	−	6.76921e9i	−0.128880	−	0.127519i
$481$	−8.69038e9	+	2.67462e10i	−0.162352	+	0.499669i
$482$	−5.22721e10	+	5.22721e10i	−0.968460	+	0.968460i
$483$	1.41843e10	−	7.22725e9i	0.260627	−	0.132796i
$484$	4.59134e9	+	6.31943e9i	0.0836677	+	0.115159i
$485$	3.11250e10	−	1.65328e8i	0.562526	−	0.00298798i
$486$	2.65584e9	+	1.92958e9i	0.0476054	+	0.0345874i
$487$	−1.20748e10	+	7.62373e10i	−0.214666	+	1.35535i	0.611197	+	0.791479i	$0.290688\pi$
$487$	−1.20748e10	+	7.62373e10i	−0.214666	+	1.35535i	−0.825863	+	0.563871i	$0.809312\pi$
$488$	2.27340e10	+	3.60071e9i	0.400863	+	0.0634905i
$489$	3.07748e10	−	4.23578e10i	0.538220	−	0.740796i
$490$	3.75557e10	+	5.11178e10i	0.651467	+	0.886724i
$491$	−6.88838e10	+	5.00470e10i	−1.18520	+	0.861097i	−0.992749	−	0.120210i	$-0.961643\pi$
$491$	−6.88838e10	+	5.00470e10i	−1.18520	+	0.861097i	−0.192450	+	0.981307i	$0.561643\pi$
$492$	−6.78135e8	−	1.33092e9i	−0.0115733	−	0.0227138i
$493$	3.97191e9	+	3.97191e9i	0.0672376	+	0.0672376i
$494$	−1.33582e10	−	4.34034e9i	−0.224306	−	0.0728813i
$495$	−2.93875e9	−	5.69266e9i	−0.0489487	−	0.0948188i
$496$	−8.48193e9	−	2.61047e10i	−0.140142	−	0.431313i
$497$	−1.53434e11	−	7.81783e10i	−2.51475	−	1.28133i
$498$	8.25134e9	+	5.20969e10i	0.134155	+	0.847022i
$499$			6.39619e10i			1.03162i	0.856704	+	0.515809i	$0.172509\pi$
$499$			6.39619e10i			1.03162i	−0.856704	+	0.515809i	$0.827491\pi$
$500$	1.70643e9	+	9.76431e9i	0.0273029	+	0.156229i
$501$	−4.70306e10			−0.746499
$502$	−1.10842e11	+	1.75557e10i	−1.74538	+	0.276441i
$503$	3.65438e10	−	7.17213e10i	0.570877	−	1.12041i	−0.407428	−	0.913237i	$-0.633574\pi$
$503$	3.65438e10	−	7.17213e10i	0.570877	−	1.12041i	0.978305	−	0.207171i	$-0.0664258\pi$
$504$	−3.22409e10	+	1.04757e10i	−0.499672	+	0.162353i
$505$	−1.95292e10	+	1.00816e10i	−0.300275	+	0.155012i
$506$	−2.03206e9	+	6.25405e9i	−0.0309981	+	0.0954024i
$507$	1.75925e10	−	1.75925e10i	0.266253	−	0.266253i
$508$	−5.31392e9	+	2.70758e9i	−0.0797922	+	0.0406561i
$509$	−1.64940e10	−	2.27021e10i	−0.245729	−	0.338216i	0.668281	−	0.743909i	$-0.267030\pi$
$509$	−1.64940e10	−	2.27021e10i	−0.245729	−	0.338216i	−0.914010	+	0.405693i	$0.867030\pi$
$510$	−4.72057e9	+	3.46815e9i	−0.0697772	+	0.0512646i
$511$	1.28945e11	+	9.36840e10i	1.89113	+	1.37398i
$512$	1.20810e10	−	7.62763e10i	0.175801	−	1.10997i
$513$	−5.73938e9	−	9.09028e8i	−0.0828696	−	0.0131253i
$514$	−5.93808e9	+	8.17307e9i	−0.0850734	+	0.117093i
$515$	−2.50339e8	−	4.71294e10i	−0.00355876	−	0.669982i
$516$	−2.50210e9	+	1.81788e9i	−0.0352944	+	0.0256429i
$517$	−6.03294e9	−	1.18403e10i	−0.0844437	−	0.165730i
$518$	6.16983e10	+	6.16983e10i	0.856947	+	0.856947i
$519$	4.78540e10	+	1.55487e10i	0.659552	+	0.214302i
$520$	−3.22321e10	+	3.25763e10i	−0.440834	+	0.445542i
$521$	−4.20343e10	−	1.29368e11i	−0.570496	−	1.75581i	−0.651028	−	0.759054i	$-0.725662\pi$
$521$	−4.20343e10	−	1.29368e11i	−0.570496	−	1.75581i	0.0805321	−	0.996752i	$-0.474338\pi$
$522$	−1.17644e10	−	5.99428e9i	−0.158449	−	0.0807337i
$523$	−1.56530e10	−	9.88293e10i	−0.209214	−	1.32093i	−0.838989	−	0.544149i	$-0.816853\pi$
$523$	−1.56530e10	−	9.88293e10i	−0.209214	−	1.32093i	0.629774	−	0.776778i	$-0.283147\pi$
$524$			4.73702e9i			0.0628319i
$525$	6.20756e10	+	1.94430e10i	0.817115	+	0.255933i
$526$	−3.05819e10			−0.399505
$527$	6.92030e9	−	1.09607e9i	0.0897185	−	0.0142100i
$528$	5.32308e9	−	1.04471e10i	0.0684900	−	0.134419i
$529$	6.57867e10	−	2.13754e10i	0.840069	−	0.272955i
$530$	5.46709e9	+	3.33697e10i	0.0692871	+	0.422911i
$531$	−1.60524e10	+	4.94042e10i	−0.201912	+	0.621421i
$532$	5.80830e9	−	5.80830e9i	0.0725107	−	0.0725107i
$533$	−1.18070e10	+	6.01597e9i	−0.146295	+	0.0745413i
$534$	1.65796e9	+	2.28199e9i	0.0203897	+	0.0280640i
$535$	3.69116e10	−	1.15690e11i	0.450555	−	1.41215i
$536$	9.39802e10	+	6.82806e10i	1.13862	+	0.827252i
$537$	3.38687e9	−	2.13839e10i	0.0407288	−	0.257151i
$538$	−3.76208e10	−	5.95855e9i	−0.449055	−	0.0711233i
$539$	1.90505e10	−	2.62207e10i	0.225710	−	0.310663i
$540$	−1.51431e9	+	2.10772e9i	−0.0178090	+	0.0247877i
$541$	5.42778e10	−	3.94351e10i	0.633627	−	0.460357i	−0.224028	−	0.974583i	$-0.571921\pi$
$541$	5.42778e10	−	3.94351e10i	0.633627	−	0.460357i	0.857655	+	0.514226i	$0.171921\pi$
$542$	3.65201e10	+	7.16748e10i	0.423190	+	0.830557i
$543$	2.18468e10	+	2.18468e10i	0.251298	+	0.251298i
$544$	4.27632e9	+	1.38946e9i	0.0488286	+	0.0158654i
$545$	−8.44003e10	−	4.24409e10i	−0.956661	−	0.481060i
$546$	1.27214e10	+	3.91524e10i	0.143141	+	0.440543i
$547$	−9.59444e10	−	4.88861e10i	−1.07169	−	0.546055i	−0.173129	−	0.984899i	$-0.555388\pi$
$547$	−9.59444e10	−	4.88861e10i	−1.07169	−	0.546055i	−0.898563	+	0.438845i	$0.855388\pi$
$548$	5.43145e8	+	3.42928e9i	0.00602273	+	0.0380260i
$549$		−	1.15640e10i		−	0.127298i
$550$	−2.38106e10	+	1.24525e10i	−0.260207	+	0.136083i
$551$	2.33717e10			0.253562
$552$	1.92213e10	−	3.04436e9i	0.207027	−	0.0327898i
$553$	6.90193e10	−	1.35458e11i	0.738023	−	1.44845i
$554$	−3.54617e10	+	1.15222e10i	−0.376462	+	0.122320i
$555$	4.82383e10	+	7.37776e9i	0.508417	+	0.0777593i
$556$	−5.72932e9	+	1.76330e10i	−0.0599521	+	0.184513i
$557$	9.29606e10	−	9.29606e10i	0.965780	−	0.965780i	−0.0336538	−	0.999434i	$-0.510714\pi$
$557$	9.29606e10	−	9.29606e10i	0.965780	−	0.965780i	0.999434	+	0.0336538i	$0.0107144\pi$
$558$	−1.46744e10	+	7.47699e9i	−0.151365	+	0.0771241i
$559$	1.61270e10	+	2.21970e10i	0.165161	+	0.227325i
$560$	3.73904e10	+	1.13029e11i	0.380196	+	1.14931i
$561$	2.42140e9	+	1.75925e9i	0.0244464	+	0.0177613i
$562$	−2.56262e10	+	1.61797e11i	−0.256885	+	1.62191i
$563$	1.69718e10	+	2.68807e9i	0.168925	+	0.0267552i	0.240324	−	0.970693i	$-0.422746\pi$
$563$	1.69718e10	+	2.68807e9i	0.168925	+	0.0267552i	−0.0713987	+	0.997448i	$0.522746\pi$
$564$	−3.16425e9	+	4.35522e9i	−0.0312719	+	0.0430421i
$565$	−1.23556e11	+	4.08725e10i	−1.21246	+	0.401086i
$566$	−4.08784e9	+	2.96999e9i	−0.0398317	+	0.0289394i
$567$	7.73218e9	+	1.51753e10i	0.0748118	+	0.146826i
$568$	−1.48854e11	−	1.48854e11i	−1.43010	−	1.43010i
$569$	−5.13177e9	−	1.66741e9i	−0.0489574	−	0.0159072i	0.284436	−	0.958695i	$-0.408194\pi$
$569$	−5.13177e9	−	1.66741e9i	−0.0489574	−	0.0159072i	−0.333393	+	0.942788i	$0.608194\pi$
$570$	−3.68476e9	+	2.40922e10i	−0.0349068	+	0.228233i
$571$	3.99342e9	+	1.22905e10i	0.0375665	+	0.115618i	0.968081	−	0.250637i	$-0.0806400\pi$
$571$	3.99342e9	+	1.22905e10i	0.0375665	+	0.115618i	−0.930515	+	0.366254i	$0.880640\pi$
$572$	2.85596e9	+	1.45518e9i	0.0266789	+	0.0135936i
$573$	8.45420e9	+	5.33777e10i	0.0784249	+	0.495155i
$574$			4.11141e10i			0.378742i
$575$	−3.34507e10	−	1.65988e10i	−0.306009	−	0.151846i
$576$	−4.05188e10			−0.368101
$577$	1.06873e10	−	1.69270e9i	0.0964196	−	0.0152714i	−0.108038	−	0.994147i	$-0.534457\pi$
$577$	1.06873e10	−	1.69270e9i	0.0964196	−	0.0152714i	0.204458	+	0.978875i	$0.434457\pi$
$578$	−4.52370e10	+	8.87826e10i	−0.405305	+	0.795456i
$579$	−2.92420e10	+	9.50132e9i	−0.260192	+	0.0845414i
$580$	4.68946e9	−	9.32572e9i	0.0414392	−	0.0824082i
$581$	−8.45641e10	+	2.60261e11i	−0.742132	+	2.28405i
$582$	2.41695e10	−	2.41695e10i	0.210657	−	0.210657i
$583$	1.53947e10	−	7.84399e9i	0.133259	−	0.0678989i
$584$	1.14525e11	+	1.57631e11i	0.984579	+	1.35516i
$585$	1.86983e10	+	1.34339e10i	0.159653	+	0.114704i
$586$	−4.38454e10	−	3.18555e10i	−0.371820	−	0.270143i
$587$	−1.56019e10	+	9.85066e10i	−0.131409	+	0.829684i	0.830640	+	0.556809i	$0.187975\pi$
$587$	−1.56019e10	+	9.85066e10i	−0.131409	+	0.829684i	−0.962049	+	0.272875i	$0.912025\pi$
$588$	−1.29681e10	−	2.05395e9i	−0.108484	−	0.0171823i
$589$	1.71356e10	−	2.35851e10i	0.142376	−	0.195964i
$590$	2.07568e11	+	6.62260e10i	1.71298	+	0.546538i
$591$	4.24019e10	−	3.08068e10i	0.347564	−	0.252520i
$592$	4.05470e10	+	7.95779e10i	0.330120	+	0.647896i
$593$	3.15301e9	+	3.15301e9i	0.0254980	+	0.0254980i	0.719741	−	0.694243i	$-0.244261\pi$
$593$	3.15301e9	+	3.15301e9i	0.0254980	+	0.0254980i	−0.694243	+	0.719741i	$0.744261\pi$
$594$	−6.69099e9	−	2.17403e9i	−0.0537458	−	0.0174631i
$595$	−2.99904e10	+	4.91344e9i	−0.239284	+	0.0392029i
$596$	−2.32835e8	−	7.16591e8i	−0.00184528	−	0.00567919i
$597$	−1.17091e11	−	5.96607e10i	−0.921775	−	0.469668i
$598$	−3.69698e9	−	2.33418e10i	−0.0289096	−	0.182528i
$599$			8.96551e10i			0.696415i	0.937418	+	0.348207i	$0.113209\pi$
$599$			8.96551e10i			0.696415i	−0.937418	+	0.348207i	$0.886791\pi$
$600$	6.48263e10	+	4.60549e10i	0.500203	+	0.355362i
$601$	−1.30931e11			−1.00356			−0.501780	−	0.864995i	$-0.667321\pi$
$601$	−1.30931e11			−1.00356			−0.501780	+	0.864995i	$0.667321\pi$
$602$	8.40790e10	−	1.33168e10i	0.640179	−	0.101394i
$603$	2.64960e10	−	5.20013e10i	0.200406	−	0.393319i
$604$	2.44657e10	−	7.94938e9i	0.183827	−	0.0597291i
$605$	−8.54763e10	−	8.45730e10i	−0.638005	−	0.631263i
$606$	−7.45822e9	+	2.29540e10i	−0.0553025	+	0.170204i
$607$	−1.25459e11	+	1.25459e11i	−0.924158	+	0.924158i	−0.997320	−	0.0731625i	$-0.976691\pi$
$607$	−1.25459e11	+	1.25459e11i	−0.924158	+	0.924158i	0.0731625	+	0.997320i	$0.476691\pi$
$608$	1.66694e10	−	8.49349e9i	0.121985	−	0.0621544i
$609$	−4.02643e10	−	5.54191e10i	−0.292719	−	0.402893i
$610$	−4.85017e10	+	2.57628e8i	−0.350298	+	0.00186069i
$611$	3.86367e10	+	2.80712e10i	0.277226	+	0.201417i
$612$	1.89675e8	−	1.19756e9i	0.00135209	−	0.00853676i
$613$	2.02296e10	+	3.20406e9i	0.143267	+	0.0226913i	0.227656	−	0.973742i	$-0.426894\pi$
$613$	2.02296e10	+	3.20406e9i	0.143267	+	0.0226913i	−0.0843890	+	0.996433i	$0.526894\pi$
$614$	1.94889e9	−	2.68241e9i	0.0137124	−	0.0188735i
$615$	1.36142e10	+	1.85305e10i	0.0951680	+	0.129535i
$616$	5.87758e10	−	4.27031e10i	0.408203	−	0.296577i
$617$	4.77468e10	+	9.37085e10i	0.329461	+	0.646604i	0.995013	−	0.0997481i	$-0.0318037\pi$
$617$	4.77468e10	+	9.37085e10i	0.329461	+	0.646604i	−0.665552	+	0.746352i	$0.731804\pi$
$618$	−3.65973e10	−	3.65973e10i	−0.250897	−	0.250897i
$619$	1.13711e11	+	3.69470e10i	0.774535	+	0.251662i	0.669505	−	0.742808i	$-0.266506\pi$
$619$	1.13711e11	+	3.69470e10i	0.774535	+	0.251662i	0.105030	+	0.994469i	$0.466506\pi$
$620$	−5.97267e9	−	1.15697e10i	−0.0404205	−	0.0782987i
$621$	−3.02134e9	−	9.29873e9i	−0.0203158	−	0.0625255i
$622$	−2.70964e10	−	1.38063e10i	−0.181030	−	0.0922393i
$623$	2.28929e9	+	1.44540e10i	0.0151967	+	0.0959479i
$624$			4.21382e10i			0.277931i
$625$	−5.02247e10	−	1.44085e11i	−0.329153	−	0.944277i
$626$	−1.22542e10			−0.0797970
$627$	1.23000e10	−	1.94813e9i	0.0795856	−	0.0126051i
$628$	−2.07415e10	+	4.07074e10i	−0.133352	+	0.261719i
$629$	−2.16825e10	+	7.04508e9i	−0.138518	+	0.0450074i
$630$	6.34756e10	−	3.27683e10i	0.402944	−	0.208013i
$631$	1.47824e10	−	4.54956e10i	0.0932455	−	0.286980i	−0.893547	−	0.448970i	$-0.851791\pi$
$631$	1.47824e10	−	4.54956e10i	0.0932455	−	0.286980i	0.986792	+	0.161990i	$0.0517911\pi$
$632$	1.31415e11	−	1.31415e11i	0.823715	−	0.823715i
$633$	−9.75095e10	+	4.96836e10i	−0.607340	+	0.309455i
$634$	7.03300e10	+	9.68009e10i	0.435295	+	0.599132i
$635$	7.39864e10	−	5.43571e10i	0.455048	−	0.334319i
$636$	−5.66263e9	−	4.11414e9i	−0.0346091	−	0.0251449i
$637$	−1.82213e10	+	1.15045e11i	−0.110668	+	0.698729i
$638$	2.79480e10	+	4.42652e9i	0.168681	+	0.0267165i
$639$	−6.21655e10	+	8.55634e10i	−0.372860	+	0.513198i
$640$	6.22846e8	+	1.17259e11i	0.00371245	+	0.698917i
$641$	−1.11369e10	+	8.09141e9i	−0.0659676	+	0.0479283i	−0.620280	−	0.784380i	$-0.712981\pi$
$641$	−1.11369e10	+	8.09141e9i	−0.0659676	+	0.0479283i	0.554313	+	0.832308i	$0.312981\pi$
$642$	−6.05422e10	−	1.18821e11i	−0.356384	−	0.699443i
$643$	5.96070e10	+	5.96070e10i	0.348701	+	0.348701i	0.859626	−	0.510924i	$-0.170697\pi$
$643$	5.96070e10	+	5.96070e10i	0.348701	+	0.348701i	−0.510924	+	0.859626i	$0.670697\pi$
$644$	1.31445e10	+	4.27090e9i	0.0764187	+	0.0248299i
$645$	3.34856e10	−	3.38432e10i	0.193472	−	0.195539i
$646$	−3.51861e9	−	1.08292e10i	−0.0202042	−	0.0621821i
$647$	−1.96396e11	−	1.00069e11i	−1.12077	−	0.571061i	−0.207427	−	0.978251i	$-0.566509\pi$
$647$	−1.96396e11	−	1.00069e11i	−1.12077	−	0.571061i	−0.913344	+	0.407190i	$0.866509\pi$
$648$	3.25705e9	+	2.05642e10i	0.0184724	+	0.116630i
$649$		−	1.11326e11i		−	0.627507i
$650$	5.59277e10	−	7.87232e10i	0.313310	−	0.441011i
$651$	−8.54460e10			−0.475738
$652$	4.48958e10	−	7.11080e9i	0.248437	−	0.0393485i
$653$	−1.41197e10	+	2.77115e10i	−0.0776556	+	0.152408i	−0.926570	−	0.376123i	$-0.877257\pi$
$653$	−1.41197e10	+	2.77115e10i	−0.0776556	+	0.152408i	0.848914	+	0.528531i	$0.177257\pi$
$654$	−9.86662e10	+	3.20586e10i	−0.539334	+	0.175240i
$655$	−1.17897e10	−	7.19614e10i	−0.0640528	−	0.390962i
$656$	−1.30046e10	+	4.00240e10i	−0.0702233	+	0.216125i
$657$	6.92186e10	−	6.92186e10i	0.371502	−	0.371502i
$658$	1.32025e11	−	6.72698e10i	0.704289	−	0.358853i
$659$	−1.95029e11	−	2.68434e11i	−1.03409	−	1.42330i	−0.901834	−	0.432084i	$-0.857779\pi$
$659$	−1.95029e11	−	2.68434e11i	−1.03409	−	1.42330i	−0.132254	−	0.991216i	$-0.542221\pi$
$660$	1.69062e9	−	5.29879e9i	0.00890983	−	0.0279255i
$661$	4.01769e8	+	2.91902e8i	0.00210461	+	0.00152909i	0.588837	−	0.808252i	$-0.299586\pi$
$661$	4.01769e8	+	2.91902e8i	0.00210461	+	0.00152909i	−0.586732	+	0.809781i	$0.699586\pi$
$662$	6.33349e9	−	3.99881e10i	0.0329770	−	0.208209i
$663$	−1.06240e10	−	1.68268e9i	−0.0549837	−	0.00870856i
$664$	−1.96634e11	+	2.70644e11i	−1.01155	+	1.39228i
$665$	−7.37794e10	+	1.02691e11i	−0.377267	+	0.525106i
$666$	4.33548e10	−	3.14991e10i	0.220364	−	0.160104i
$667$	1.78530e10	+	3.50384e10i	0.0902001	+	0.177028i
$668$	−2.88719e10	−	2.88719e10i	−0.145000	−	0.145000i
$669$	−1.57018e11	−	5.10182e10i	−0.783871	−	0.254695i
$670$	−2.18693e11	−	1.09970e11i	−1.08526	−	0.545728i
$671$	7.65830e9	+	2.35698e10i	0.0377783	+	0.116270i
$672$	−4.88575e10	−	2.48941e10i	−0.239582	−	0.122073i
$673$	−5.43967e9	−	3.43447e10i	−0.0265163	−	0.167417i	0.970877	−	0.239580i	$-0.0770098\pi$
$673$	−5.43967e9	−	3.43447e10i	−0.0265163	−	0.167417i	−0.997393	+	0.0721631i	$0.977010\pi$
$674$		−	2.47030e11i		−	1.19704i
$675$	1.77584e10	−	3.57877e10i	0.0855440	−	0.172393i
$676$	2.15999e10			0.103434
$677$	3.49085e11	−	5.52896e10i	1.66179	−	0.263202i	0.746320	−	0.665587i	$-0.231819\pi$
$677$	3.49085e11	−	5.52896e10i	1.66179	−	0.263202i	0.915471	+	0.402385i	$0.131819\pi$
$678$	−6.48822e10	+	1.27339e11i	−0.307049	+	0.602617i
$679$	1.68655e11	−	5.47994e10i	0.793452	−	0.257808i
$680$	−3.67239e10	−	5.61670e9i	−0.171757	−	0.0262691i
$681$	2.35385e10	−	7.24441e10i	0.109444	−	0.336833i
$682$	2.49577e10	−	2.49577e10i	0.115363	−	0.115363i
$683$	2.89470e11	−	1.47492e11i	1.33021	−	0.677776i	0.363009	−	0.931786i	$-0.381749\pi$
$683$	2.89470e11	−	1.47492e11i	1.33021	−	0.677776i	0.967202	+	0.254009i	$0.0817493\pi$
$684$	−2.96533e9	−	4.08143e9i	−0.0135472	−	0.0186461i
$685$	−1.67860e10	−	5.07433e10i	−0.0762404	−	0.230471i
$686$	4.86348e10	+	3.53352e10i	0.219609	+	0.159555i
$687$	2.48237e10	−	1.56730e11i	0.111439	−	0.703601i
$688$	8.60619e10	+	1.36309e10i	0.384111	+	0.0608373i
$689$	−3.64980e10	+	5.02351e10i	−0.161954	+	0.222911i
$690$	−3.89333e10	+	1.28792e10i	−0.171761	+	0.0568189i
$691$	3.09388e11	−	2.24784e11i	1.35704	−	0.985945i	0.358409	−	0.933565i	$-0.383319\pi$
$691$	3.09388e11	−	2.24784e11i	1.35704	−	0.985945i	0.998627	−	0.0523800i	$-0.0166807\pi$
$692$	1.98321e10	+	3.89227e10i	0.0864858	+	0.169738i
$693$	−2.58095e10	−	2.58095e10i	−0.111904	−	0.111904i
$694$	−1.26855e10	−	4.12175e9i	−0.0546850	−	0.0177682i
$695$	4.31497e10	−	2.82128e11i	0.184943	−	1.20922i
$696$	−2.58774e10	−	7.96424e10i	−0.110277	−	0.339397i
$697$	−9.57166e9	−	4.87700e9i	−0.0405561	−	0.0206644i
$698$	−7.51474e9	−	4.74462e10i	−0.0316586	−	0.199885i
$699$		−	1.31782e11i		−	0.552010i
$700$	2.61720e10	+	5.00439e10i	0.109005	+	0.208430i
$701$	−1.52687e11			−0.632311			−0.316155	−	0.948707i	$-0.602392\pi$
$701$	−1.52687e11			−0.632311			−0.316155	+	0.948707i	$0.602392\pi$
$702$	2.49726e10	−	3.95527e9i	0.102829	−	0.0162865i
$703$	−4.30652e10	+	8.45202e10i	−0.176321	+	0.346050i
$704$	8.25853e10	−	2.68336e10i	0.336211	−	0.109242i
$705$	3.72295e10	−	7.40366e10i	0.150706	−	0.299702i
$706$	1.09516e11	−	3.37055e11i	0.440816	−	1.35669i
$707$	−8.85420e10	+	8.85420e10i	−0.354382	+	0.354382i
$708$	−4.01836e10	+	2.04746e10i	−0.159925	+	0.0814857i
$709$	−1.17655e10	−	1.61938e10i	−0.0465614	−	0.0640863i	0.785101	−	0.619367i	$-0.212611\pi$
$709$	−1.17655e10	−	1.61938e10i	−0.0465614	−	0.0640863i	−0.831663	+	0.555281i	$0.812611\pi$
$710$	3.60253e11	+	2.58827e11i	1.41767	+	1.01854i
$711$	−7.55392e10	−	5.48824e10i	−0.295593	−	0.214761i
$712$	−2.79857e9	+	1.76695e10i	−0.0108897	+	0.0687550i
$713$	4.84477e10	+	7.67337e9i	0.187463	+	0.0296912i
$714$	−1.96164e10	+	2.69996e10i	−0.0754789	+	0.103888i
$715$	−4.70074e10	−	1.49980e10i	−0.179863	−	0.0573866i
$716$	1.52067e10	−	1.10483e10i	0.0578604	−	0.0420381i
$717$	−6.72647e10	−	1.32014e11i	−0.254513	−	0.499511i
$718$	−2.70990e11	−	2.70990e11i	−1.01966	−	1.01966i
$719$	−5.67297e10	−	1.84326e10i	−0.212273	−	0.0689717i	0.200950	−	0.979601i	$-0.435597\pi$
$719$	−5.67297e10	−	1.84326e10i	−0.212273	−	0.0689717i	−0.413223	+	0.910630i	$0.635597\pi$
$720$	7.21573e10	−	1.18218e10i	0.268504	−	0.0439900i
$721$	−8.29771e10	−	2.55377e11i	−0.307056	−	0.945021i
$722$	1.79878e11	+	9.16526e10i	0.661958	+	0.337284i
$723$	3.68485e10	+	2.32652e11i	0.134855	+	0.851439i
$724$			2.68234e10i			0.0976246i
$725$	−4.80286e10	+	1.53341e11i	−0.173839	+	0.555016i
$726$	−1.32048e11			−0.475320
$727$	4.30713e11	−	6.82183e10i	1.54188	−	0.244210i	0.673154	−	0.739502i	$-0.264939\pi$
$727$	4.30713e11	−	6.82183e10i	1.54188	−	0.244210i	0.868726	+	0.495292i	$0.164939\pi$
$728$	−1.18535e11	+	2.32638e11i	−0.422009	+	0.828239i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	−2.91857e11	−	2.88773e11i	−1.02773	−	1.01687i
$731$	−6.87331e9	+	2.11539e10i	−0.0240711	+	0.0740833i
$732$	7.09913e9	−	7.09913e9i	0.0247264	−	0.0247264i
$733$	−2.26751e11	+	1.15535e11i	−0.785476	+	0.400220i	−0.800247	−	0.599671i	$-0.795298\pi$
$733$	−2.26751e11	+	1.15535e11i	−0.785476	+	0.400220i	0.0147704	+	0.999891i	$0.495298\pi$
$734$	−3.29797e10	−	4.53926e10i	−0.113622	−	0.156387i
$735$	2.02114e11	−	1.07357e9i	0.692544	−	0.00367860i
$736$	2.54665e10	+	1.85025e10i	0.0867878	+	0.0630550i
$737$	−1.95661e10	+	1.23536e11i	−0.0663186	+	0.418719i
$738$	2.49403e10	+	3.95015e9i	0.0840768	+	0.0133165i
$739$	−3.29839e10	+	4.53984e10i	−0.110592	+	0.152217i	−0.860725	−	0.509070i	$-0.829989\pi$
$739$	−3.29839e10	+	4.53984e10i	−0.110592	+	0.152217i	0.750133	+	0.661287i	$0.229989\pi$
$740$	2.50841e10	+	3.41425e10i	0.0836512	+	0.113859i
$741$	−3.62078e10	+	2.63065e10i	−0.120096	+	0.0872549i
$742$	8.74638e10	+	1.71657e11i	0.288544	+	0.566300i
$743$	3.22053e11	+	3.22053e11i	1.05675	+	1.05675i	0.998290	+	0.0584614i	$0.0186194\pi$
$743$	3.22053e11	+	3.22053e11i	1.05675	+	1.05675i	0.0584614	+	0.998290i	$0.481381\pi$
$744$	−9.93423e10	−	3.22783e10i	−0.324222	−	0.105346i
$745$	5.32053e9	+	1.03064e10i	0.0172715	+	0.0334567i
$746$	−8.59233e8	−	2.64445e9i	−0.00277431	−	0.00853846i
$747$	1.49753e11	+	7.63029e10i	0.480942	+	0.245052i
$748$	4.06491e8	+	2.56648e9i	0.00129851	+	0.00819846i
$749$		−	6.91868e11i		−	2.19835i
$750$	−1.50496e11	−	7.36848e10i	−0.475641	−	0.232880i
$751$	7.77248e10			0.244343			0.122172	−	0.992509i	$-0.461014\pi$
$751$	7.77248e10			0.244343			0.122172	+	0.992509i	$0.461014\pi$
$752$	1.49802e11	−	2.37263e10i	0.468431	−	0.0741922i
$753$	−1.62343e11	+	3.18616e11i	−0.504957	+	0.991033i
$754$	−9.67154e10	+	3.14248e10i	−0.299234	+	0.0972269i
$755$	−3.51880e11	+	1.81652e11i	−1.08295	+	0.559054i
$756$	−4.56928e9	+	1.40628e10i	−0.0139882	+	0.0430511i
$757$	−2.44584e11	+	2.44584e11i	−0.744809	+	0.744809i	−0.973499	−	0.228690i	$-0.926556\pi$
$757$	−2.44584e11	+	2.44584e11i	−0.744809	+	0.744809i	0.228690	+	0.973499i	$0.426556\pi$
$758$	−1.94867e11	+	9.92898e10i	−0.590285	+	0.300765i
$759$	1.23162e10	+	1.69518e10i	0.0371115	+	0.0510797i
$760$	−1.24571e11	+	9.15213e10i	−0.373391	+	0.274326i
$761$	−2.46721e11	−	1.79253e11i	−0.735643	−	0.534476i	0.155701	−	0.987804i	$-0.450236\pi$
$761$	−2.46721e11	−	1.79253e11i	−0.735643	−	0.534476i	−0.891344	+	0.453328i	$0.850236\pi$
$762$	1.57717e10	−	9.95787e10i	0.0467799	−	0.295356i
$763$	−5.31610e11	−	8.41988e10i	−1.56854	−	0.248432i
$764$	−2.75784e10	+	3.79584e10i	−0.0809460	+	0.111413i
$765$	9.91411e7	+	1.86646e10i	0.000289473	+	0.0544970i
$766$	3.73158e11	−	2.71115e11i	1.08387	−	0.787479i
$767$	1.81637e11	+	3.56482e11i	0.524834	+	1.03005i
$768$	−6.57853e10	−	6.57853e10i	−0.189097	−	0.189097i
$769$	5.94307e11	+	1.93102e11i	1.69944	+	0.552181i	0.988520	−	0.151093i	$-0.0482792\pi$
$769$	5.94307e11	+	1.93102e11i	1.69944	+	0.552181i	0.710919	+	0.703274i	$0.248279\pi$
$770$	−1.07675e11	+	1.08825e11i	−0.306303	+	0.309575i
$771$	9.94746e9	+	3.06151e10i	0.0281510	+	0.0866400i
$772$	−2.37844e10	−	1.21188e10i	−0.0669612	−	0.0341184i
$773$	5.84420e10	+	3.68988e11i	0.163684	+	1.03346i	0.923577	+	0.383413i	$0.125251\pi$
$773$	5.84420e10	+	3.68988e11i	0.163684	+	1.03346i	−0.759893	+	0.650048i	$0.774749\pi$
$774$		−	5.22828e10i		−	0.145678i
$775$	1.19528e11	+	1.60893e11i	0.331330	+	0.445995i
$776$	2.16785e11			0.597838
$777$	2.74606e11	−	4.34934e10i	0.753401	−	0.119327i
$778$	−1.87598e11	+	3.68182e11i	−0.512047	+	1.00495i
$779$	−4.25097e10	+	1.38123e10i	−0.115435	+	0.0375072i
$780$	3.23176e9	+	1.97258e10i	0.00873094	+	0.0532914i
$781$	7.00411e10	−	2.15564e11i	0.188256	−	0.579392i
$782$	1.35471e10	−	1.35471e10i	0.0362260	−	0.0362260i
$783$	−3.74864e10	+	1.91003e10i	−0.0997301	+	0.0508150i
$784$	2.17430e11	+	2.99267e11i	0.575514	+	0.792127i
$785$	2.13775e11	−	6.70019e11i	0.562960	−	1.76445i
$786$	−6.47851e10	−	4.70691e10i	−0.169740	−	0.123324i
$787$	−9.93990e10	+	6.27581e11i	−0.259109	+	1.63595i	0.424019	+	0.905653i	$0.360619\pi$
$787$	−9.93990e10	+	6.27581e11i	−0.259109	+	1.63595i	−0.683128	+	0.730299i	$0.739381\pi$
$788$	4.49425e10	+	7.11820e9i	0.116561	+	0.0184614i
$789$	−5.72777e10	+	7.88360e10i	−0.147801	+	0.203431i
$790$	−2.28504e11	+	3.18048e11i	−0.586658	+	0.816552i
$791$	−5.99858e11	+	4.35822e11i	−1.53229	+	1.11328i
$792$	−2.02572e10	−	3.97569e10i	−0.0514847	−	0.101044i
$793$	−6.29788e10	−	6.29788e10i	−0.159258	−	0.159258i
$794$	−6.31778e11	−	2.05277e11i	−1.58958	−	0.516486i
$795$	9.62620e10	+	4.84056e10i	0.240983	+	0.121179i
$796$	−3.52561e10	−	1.08507e11i	−0.0878176	−	0.270275i
$797$	4.82517e11	+	2.45855e11i	1.19586	+	0.609320i	0.934514	−	0.355926i	$-0.115835\pi$
$797$	4.82517e11	+	2.45855e11i	1.19586	+	0.609320i	0.261343	+	0.965246i	$0.415835\pi$
$798$	2.17224e10	+	1.37150e11i	0.0535669	+	0.338208i
$799$			3.87159e10i			0.0949953i
$800$	2.14700e10	+	1.26821e11i	0.0524169	+	0.309622i
$801$	8.98791e9			0.0218338
$802$	3.13336e11	−	4.96276e10i	0.757379	−	0.119957i
$803$	−9.52411e10	+	1.86921e11i	−0.229067	+	0.449569i
$804$	4.81892e10	−	1.56576e10i	0.115325	−	0.0374715i
$805$	−2.10311e11	−	3.21658e10i	−0.500815	−	0.0765967i
$806$	−3.91978e10	+	1.20638e11i	−0.0928799	+	0.285855i
$807$	−8.58214e10	+	8.58214e10i	−0.202349	+	0.202349i
$808$	−1.36390e11	+	6.94940e10i	−0.319990	+	0.163043i
$809$	−1.63990e11	−	2.25713e11i	−0.382846	−	0.526943i	0.573490	−	0.819213i	$-0.305589\pi$
$809$	−1.63990e11	−	2.25713e11i	−0.382846	−	0.526943i	−0.956336	+	0.292270i	$0.905589\pi$
$810$	−1.37790e10	−	4.16533e10i	−0.0320094	−	0.0967631i
$811$	5.79920e11	+	4.21336e11i	1.34055	+	0.973970i	0.999423	+	0.0339542i	$0.0108101\pi$
$811$	5.79920e11	+	4.21336e11i	1.34055	+	0.973970i	0.341131	+	0.940016i	$0.389190\pi$
$812$	9.30345e9	−	5.87397e10i	0.0214003	−	0.135116i
$813$	2.53168e11	+	4.00978e10i	0.579490	+	0.0917822i
$814$	−6.75053e10	+	9.29130e10i	−0.153759	+	0.211631i
$815$	−6.64327e11	+	2.19761e11i	−1.50574	+	0.498104i
$816$	−2.76364e10	+	2.00790e10i	−0.0623333	+	0.0452878i
$817$	4.20152e10	+	8.24594e10i	0.0943013	+	0.185077i
$818$	−3.76969e10	−	3.76969e10i	−0.0841962	−	0.0841962i
$819$	1.24756e11	+	4.05356e10i	0.277284	+	0.0900952i
$820$	−3.01812e9	+	1.97335e10i	−0.00667546	+	0.0436464i
$821$	−2.58986e10	−	7.97077e10i	−0.0570038	−	0.175440i	0.918501	−	0.395420i	$-0.129401\pi$
$821$	−2.58986e10	−	7.97077e10i	−0.0570038	−	0.175440i	−0.975504	+	0.219980i	$0.929401\pi$
$822$	−5.22969e10	−	2.66466e10i	−0.114548	−	0.0583653i
$823$	6.16512e10	+	3.89250e11i	0.134382	+	0.848457i	0.959132	+	0.282959i	$0.0913160\pi$
$823$	6.16512e10	+	3.89250e11i	0.134382	+	0.848457i	−0.824750	+	0.565498i	$0.808684\pi$
$824$		−	3.28256e11i		−	0.712039i
$825$	−1.24947e10	+	8.47030e10i	−0.0269719	+	0.182845i
$826$	1.24133e12			2.66667
$827$	3.98939e11	−	6.31858e10i	0.852874	−	0.135082i	0.285334	−	0.958428i	$-0.407895\pi$
$827$	3.98939e11	−	6.31858e10i	0.852874	−	0.135082i	0.567539	+	0.823346i	$0.307895\pi$
$828$	3.85367e9	−	7.56325e9i	0.00819885	−	0.0160911i
$829$	−7.71451e11	+	2.50660e11i	−1.63339	+	0.530721i	−0.975048	−	0.221996i	$-0.928743\pi$
$829$	−7.71451e11	+	2.50660e11i	−1.63339	+	0.530721i	−0.658344	+	0.752717i	$0.728743\pi$
$830$	3.16692e11	−	6.29791e11i	0.667306	−	1.32704i
$831$	−3.67145e10	+	1.12996e11i	−0.0769899	+	0.236951i
$832$	−2.20669e11	+	2.20669e11i	−0.460519	+	0.460519i
$833$	−8.41346e10	+	4.28687e10i	−0.174741	+	0.0890349i
$834$	−1.84226e11	−	2.53566e11i	−0.380792	−	0.524115i
$835$	5.10458e11	+	3.66743e11i	1.05006	+	0.754424i
$836$	8.74686e9	+	6.35497e9i	0.0179072	+	0.0130103i
$837$	−8.20946e9	+	5.18325e10i	−0.0167268	+	0.105609i
$838$	−6.76460e11	−	1.07141e11i	−1.37172	−	0.217259i
$839$	−2.02371e11	+	2.78540e11i	−0.408414	+	0.562134i	−0.962831	−	0.270105i	$-0.912941\pi$
$839$	−2.02371e11	+	2.78540e11i	−0.408414	+	0.562134i	0.554416	+	0.832239i	$0.312941\pi$
$840$	4.31624e11	+	1.37713e11i	0.866939	+	0.276603i
$841$	−2.67810e11	+	1.94575e11i	−0.535356	+	0.388959i
$842$	−7.83840e10	−	1.53837e11i	−0.155948	−	0.306065i
$843$	3.69096e11	+	3.69096e11i	0.730851	+	0.730851i
$844$	−9.03613e10	−	2.93602e10i	−0.178079	−	0.0578614i
$845$	−3.28130e11	+	5.37588e10i	−0.643604	+	0.105444i
$846$	−2.81220e10	−	8.65508e10i	−0.0548991	−	0.168962i
$847$	−6.10414e11	−	3.11022e11i	−1.18602	−	0.604306i
$848$	3.08487e10	+	1.94771e11i	0.0596560	+	0.376653i
$849$			1.61005e10i			0.0309890i
$850$	7.82804e10	−	8.31632e8i	0.149961	−	0.00159314i
$851$	−1.59607e11			−0.304323
$852$	−9.06902e10	+	1.43639e10i	−0.172108	+	0.0272593i
$853$	3.84486e11	−	7.54596e11i	0.726247	−	1.42534i	−0.171660	−	0.985156i	$-0.554913\pi$
$853$	3.84486e11	−	7.54596e11i	0.726247	−	1.42534i	0.897907	−	0.440184i	$-0.145087\pi$
$854$	−2.62813e11	+	8.53932e10i	−0.494101	+	0.160543i
$855$	5.52052e10	+	5.46218e10i	0.103304	+	0.102212i
$856$	2.61362e11	−	8.04389e11i	0.486796	−	1.49820i
$857$	7.29602e10	−	7.29602e10i	0.135258	−	0.135258i	−0.636236	−	0.771494i	$-0.719510\pi$
$857$	7.29602e10	−	7.29602e10i	0.135258	−	0.135258i	0.771494	+	0.636236i	$0.219510\pi$
$858$	−4.82797e10	+	2.45997e10i	−0.0890871	+	0.0453922i
$859$	3.36423e11	+	4.63047e11i	0.617893	+	0.850457i	0.997197	−	0.0748149i	$-0.0238366\pi$
$859$	3.36423e11	+	4.63047e11i	0.617893	+	0.850457i	−0.379304	+	0.925272i	$0.623837\pi$
$860$	4.13329e10	−	2.19549e8i	0.0755618	−	0.000401363i
$861$	1.05987e11	+	7.70037e10i	0.192858	+	0.140120i
$862$	1.45516e11	−	9.18752e11i	0.263561	−	1.66406i
$863$	8.75228e11	+	1.38622e11i	1.57789	+	0.249914i	0.883061	−	0.469258i	$-0.155478\pi$
$863$	8.75228e11	+	1.38622e11i	1.57789	+	0.249914i	0.694833	+	0.719171i	$0.255478\pi$
$864$	−1.97952e10	+	2.72458e10i	−0.0355226	+	0.0488927i
$865$	−3.98148e11	−	5.41926e11i	−0.711180	−	0.968001i
$866$	5.54003e11	−	4.02507e11i	0.985010	−	0.715652i
$867$	1.44144e11	+	2.82898e11i	0.255105	+	0.500672i
$868$	−5.24550e10	−	5.24550e10i	−0.0924076	−	0.0924076i
$869$	1.90310e11	+	6.18353e10i	0.333720	+	0.108432i
$870$	8.09451e10	+	1.56799e11i	0.141291	+	0.273695i
$871$	−1.38904e11	−	4.27502e11i	−0.241347	−	0.742790i
$872$	−5.86261e11	−	2.98715e11i	−1.01397	−	0.516643i
$873$	−1.70379e10	−	1.07573e11i	−0.0293332	−	0.185203i
$874$		−	7.97146e10i		−	0.136613i
$875$	−5.22137e11	−	6.95093e11i	−0.890743	−	1.18580i
$876$	8.49861e10			0.144322
$877$	1.12653e11	−	1.78424e10i	0.190434	−	0.0301617i	−0.0604890	−	0.998169i	$-0.519266\pi$
$877$	1.12653e11	−	1.78424e10i	0.190434	−	0.0301617i	0.250923	+	0.968007i	$0.419266\pi$
$878$	1.32123e11	−	2.59305e11i	0.222330	−	0.436348i
$879$	−1.64238e11	+	5.33643e10i	−0.275118	+	0.0893913i
$880$	−1.39242e11	+	7.18814e10i	−0.232188	+	0.119863i
$881$	3.62992e10	−	1.11717e11i	0.0602550	−	0.185446i	−0.916398	−	0.400268i	$-0.868917\pi$
$881$	3.62992e10	−	1.11717e11i	0.0602550	−	0.185446i	0.976653	+	0.214822i	$0.0689171\pi$
$882$	1.56947e11	−	1.56947e11i	0.259346	−	0.259346i
$883$	8.46910e11	−	4.31522e11i	1.39314	−	0.709840i	0.413481	−	0.910513i	$-0.364313\pi$
$883$	8.46910e11	−	4.31522e11i	1.39314	−	0.709840i	0.979658	+	0.200673i	$0.0643128\pi$
$884$	−5.48904e9	−	7.55502e9i	−0.00898851	−	0.0123716i
$885$	5.59481e11	−	4.11045e11i	0.912037	−	0.670064i
$886$	−2.21490e11	−	1.60922e11i	−0.359434	−	0.261144i
$887$	6.51612e9	−	4.11412e10i	0.0105268	−	0.0664633i	−0.981866	−	0.189578i	$-0.939288\pi$
$887$	6.51612e9	−	4.11412e10i	0.0105268	−	0.0664633i	0.992393	+	0.123114i	$0.0392882\pi$
$888$	3.35697e11	+	5.31691e10i	0.539877	+	0.0855082i
$889$	3.07451e11	−	4.23171e11i	0.492232	−	0.677499i
$890$	−2.00236e8	−	3.76969e10i	−0.000319140	−	0.0600822i
$891$	−1.81361e10	+	1.31766e10i	−0.0287762	+	0.0209071i
$892$	−6.50728e10	−	1.27713e11i	−0.102787	−	0.201732i
$893$	1.13907e11	+	1.13907e11i	0.179120	+	0.179120i
$894$	1.21139e10	+	3.93604e9i	0.0189641	+	0.00616183i
$895$	−2.03511e11	+	2.05684e11i	−0.317173	+	0.320560i
$896$	2.06448e11	+	6.35383e11i	0.320317	+	0.985833i
$897$	−6.70962e10	−	3.41872e10i	−0.103640	−	0.0528073i
$898$	5.19338e10	+	3.27897e11i	0.0798628	+	0.504234i
$899$		−	2.11071e11i		−	0.323139i
$900$	3.28718e10	−	1.10681e10i	0.0501018	−	0.0168696i
$901$	−5.03381e10			−0.0763832
$902$	−5.34492e10	+	8.46553e9i	−0.0807449	+	0.0127887i
$903$	1.23145e11	−	2.41686e11i	0.185211	−	0.363496i
$904$	−8.62052e11	+	2.80098e11i	−1.29080	+	0.419407i
$905$	−6.67593e10	−	4.07481e11i	−0.0995216	−	0.607454i
$906$	−1.34383e11	+	4.13589e11i	−0.199449	+	0.613842i
$907$	−8.56938e11	+	8.56938e11i	−1.26625	+	1.26625i	−0.318244	+	0.948009i	$0.603093\pi$
$907$	−8.56938e11	+	8.56938e11i	−1.26625	+	1.26625i	−0.948009	+	0.318244i	$0.896907\pi$
$908$	5.89234e10	−	3.00230e10i	0.0866851	−	0.0441682i
$909$	4.52037e10	+	6.22175e10i	0.0662092	+	0.0911291i
$910$	1.67234e11	−	5.24152e11i	0.243871	−	0.764349i
$911$	−3.50184e10	−	2.54424e10i	−0.0508420	−	0.0369389i	0.562074	−	0.827087i	$-0.310004\pi$
$911$	−3.50184e10	−	2.54424e10i	−0.0508420	−	0.0369389i	−0.612916	+	0.790148i	$0.710004\pi$
$912$	−2.22347e10	+	1.40384e11i	−0.0321405	+	0.202927i
$913$	−3.55758e11	−	5.63465e10i	−0.512002	−	0.0810931i
$914$	−6.58329e11	+	9.06112e11i	−0.943318	+	1.29837i
$915$	−9.01761e10	+	1.25513e11i	−0.128649	+	0.179063i
$916$	1.11455e11	−	8.09771e10i	0.158314	−	0.115022i
$917$	−1.88615e11	−	3.70177e11i	−0.266746	−	0.523519i
$918$	1.44936e10	+	1.44936e10i	0.0204082	+	0.0204082i
$919$	4.98946e11	+	1.62117e11i	0.699506	+	0.227283i	0.637115	−	0.770768i	$-0.280127\pi$
$919$	4.98946e11	+	1.62117e11i	0.699506	+	0.227283i	0.0623909	+	0.998052i	$0.480127\pi$
$920$	−2.32363e11	−	1.16844e11i	−0.324352	−	0.163101i
$921$	−3.26477e9	−	1.00479e10i	−0.00453747	−	0.0139649i
$922$	2.07939e11	+	1.05950e11i	0.287748	+	0.146615i
$923$	1.27427e11	+	8.04544e11i	0.175572	+	1.10852i
$924$		−	3.16888e10i		−	0.0434728i
$925$	−4.66035e11	−	4.56237e11i	−0.636578	−	0.623194i
$926$	−1.04701e12			−1.42399
$927$	−1.62887e11	+	2.57988e10i	−0.220581	+	0.0349366i
$928$	6.14942e10	−	1.20689e11i	0.0829167	−	0.162733i
$929$	−9.07683e11	+	2.94924e11i	−1.21863	+	0.395956i	−0.846582	−	0.532258i	$-0.821344\pi$
$929$	−9.07683e11	+	2.94924e11i	−1.21863	+	0.395956i	−0.372046	+	0.928214i	$0.621344\pi$
$930$	2.17578e11	+	3.32772e10i	0.290859	+	0.0444852i
$931$	−1.21409e11	+	3.73660e11i	−0.161604	+	0.497367i
$932$	8.09005e10	−	8.09005e10i	0.107223	−	0.107223i
$933$	−8.63404e10	+	4.39926e10i	−0.113943	+	0.0580568i
$934$	5.05472e11	+	6.95723e11i	0.664217	+	0.914216i
$935$	−1.25627e10	−	3.79764e10i	−0.0164375	−	0.0496899i
$936$	1.29733e11	+	9.42562e10i	0.169023	+	0.122802i
$937$	−3.66045e10	+	2.31112e11i	−0.0474872	+	0.299822i	−0.999989	−	0.00471089i	$-0.998500\pi$
$937$	−3.66045e10	+	2.31112e11i	−0.0474872	+	0.299822i	0.952502	+	0.304533i	$0.0985005\pi$
$938$	−1.37748e12	−	2.18171e11i	−1.77940	−	0.281829i
$939$	−2.29512e10	+	3.15896e10i	−0.0295218	+	0.0406332i
$940$	6.83059e10	−	2.25957e10i	0.0874877	−	0.0289411i
$941$	1.38758e11	−	1.00814e11i	0.176970	−	0.128576i	−0.495774	−	0.868452i	$-0.665116\pi$
$941$	1.38758e11	−	1.00814e11i	0.176970	−	0.128576i	0.672744	+	0.739875i	$0.265116\pi$
$942$	−3.50632e11	−	6.88154e11i	−0.445295	−	0.873941i
$943$	−5.31790e10	−	5.31790e10i	−0.0672501	−	0.0672501i
$944$	1.20842e12	+	3.92640e11i	1.52170	+	0.494432i
$945$	3.44130e10	−	2.25004e11i	0.0431515	−	0.282139i
$946$	3.46243e10	+	1.06563e11i	0.0432331	+	0.133058i
$947$	7.16201e11	+	3.64923e11i	0.890502	+	0.453733i	0.838492	−	0.544913i	$-0.183437\pi$
$947$	7.16201e11	+	3.64923e11i	0.890502	+	0.453733i	0.0520095	+	0.998647i	$0.483437\pi$
$948$	−1.26811e10	−	8.00653e10i	−0.0157009	−	0.0991314i
$949$		−	7.53940e11i		−	0.929549i
$950$	2.27864e11	−	2.32757e11i	0.279757	−	0.285765i
$951$	3.81262e11			0.466125
$952$	−2.09058e11	+	3.31116e10i	−0.254519	+	0.0403118i
$953$	6.52806e11	−	1.28120e12i	0.791430	−	1.55327i	−0.0410130	−	0.999159i	$-0.513059\pi$
$953$	6.52806e11	−	1.28120e12i	0.791430	−	1.55327i	0.832443	−	0.554110i	$-0.186941\pi$
$954$	1.12533e11	−	3.65641e10i	0.135858	−	0.0441430i
$955$	3.24478e11	−	6.45274e11i	0.390096	−	0.775766i
$956$	3.97496e10	−	1.22337e11i	0.0475884	−	0.146462i
$957$	6.37555e10	−	6.37555e10i	0.0760098	−	0.0760098i
$958$	7.34095e11	−	3.74040e11i	0.871546	−	0.444075i
$959$	−1.78989e11	−	2.46357e11i	−0.211617	−	0.291266i
$960$	4.39781e11	+	3.15964e11i	0.517787	+	0.372009i
$961$	4.77005e11	+	3.46564e11i	0.559280	+	0.406341i
$962$	6.45670e10	−	4.07660e11i	0.0753895	−	0.475990i
$963$	−4.19695e11	−	6.64732e10i	−0.488010	−	0.0772932i
$964$	−1.20203e11	+	1.65445e11i	−0.139190	+	0.191578i
$965$	3.91477e11	+	1.24904e11i	0.451437	+	0.144034i
$966$	−1.89019e11	+	1.37331e11i	−0.217069	+	0.157710i
$967$	7.34969e11	+	1.44246e12i	0.840549	+	1.64967i	0.757231	+	0.653147i	$0.226552\pi$
$967$	7.34969e11	+	1.44246e12i	0.840549	+	1.64967i	0.0833182	+	0.996523i	$0.473448\pi$
$968$	−5.92196e11	−	5.92196e11i	−0.674472	−	0.674472i
$969$	−3.45062e10	−	1.12118e10i	−0.0391384	−	0.0127168i
$970$	−4.50802e11	+	7.38567e10i	−0.509213	+	0.0834264i
$971$	1.07571e10	+	3.31070e10i	0.0121009	+	0.0372428i	0.956925	−	0.290336i	$-0.0937672\pi$
$971$	1.07571e10	+	3.31070e10i	0.0121009	+	0.0372428i	−0.944824	+	0.327579i	$0.893767\pi$
$972$	8.09165e9	+	4.12290e9i	0.00906509	+	0.00461889i
$973$	−2.54376e11	−	1.60607e12i	−0.283809	−	1.79190i
$974$		−	1.13284e12i		−	1.25873i
$975$	−9.81891e10	−	2.91617e11i	−0.108654	−	0.322696i
$976$	−2.82855e11			−0.311720
$977$	−4.69754e11	+	7.44017e10i	−0.515575	+	0.0816591i	−0.408800	−	0.912624i	$-0.634053\pi$
$977$	−4.69754e11	+	7.44017e10i	−0.515575	+	0.0816591i	−0.106775	+	0.994283i	$0.534053\pi$
$978$	−3.48855e11	+	6.84667e11i	−0.381320	+	0.748383i
$979$	−1.83191e10	+	5.95225e9i	−0.0199423	+	0.00647963i
$980$	1.24736e11	+	1.23418e11i	0.135235	+	0.133806i
$981$	−1.02152e11	+	3.14391e11i	−0.110299	+	0.339465i
$982$	8.83622e11	−	8.83622e11i	0.950212	−	0.950212i
$983$	−5.47823e11	+	2.79130e11i	−0.586713	+	0.298945i	−0.722035	−	0.691856i	$-0.756793\pi$
$983$	−5.47823e11	+	2.79130e11i	−0.586713	+	0.298945i	0.135322	+	0.990802i	$0.456793\pi$
$984$	9.41344e10	+	1.29565e11i	0.100408	+	0.138200i
$985$	−7.00450e11	+	3.72060e9i	−0.744102	+	0.00395246i
$986$	−6.66952e10	−	4.84569e10i	−0.0705646	−	0.0512682i
$987$	7.38599e10	−	4.66333e11i	0.0778287	−	0.491391i
$988$	−3.83773e10	−	6.07836e9i	−0.0402760	−	0.00637909i
$989$	−9.15273e10	+	1.25977e11i	−0.0956678	+	0.131675i
$990$	5.56693e10	+	7.57725e10i	0.0579529	+	0.0788808i
$991$	−4.51998e11	+	3.28396e11i	−0.468643	+	0.340489i	−0.796912	−	0.604095i	$-0.793535\pi$
$991$	−4.51998e11	+	3.28396e11i	−0.468643	+	0.340489i	0.328269	+	0.944584i	$0.393535\pi$
$992$	−7.67050e10	−	1.50542e11i	−0.0792095	−	0.155457i
$993$	−9.12217e10	−	9.12217e10i	−0.0938212	−	0.0938212i
$994$	2.40363e12	+	7.80987e11i	2.46220	+	0.800016i
$995$	8.05642e11	+	1.56061e12i	0.821958	+	1.59222i
$996$	4.50907e10	+	1.38775e11i	0.0458194	+	0.141018i
$997$	−1.51604e11	−	7.72462e10i	−0.153437	−	0.0781802i	0.375586	−	0.926788i	$-0.377442\pi$
$997$	−1.51604e11	−	7.72462e10i	−0.153437	−	0.0781802i	−0.529023	+	0.848607i	$0.677442\pi$
$998$	−1.46851e11	−	9.27178e11i	−0.148031	−	0.934633i
$999$		−	1.70758e11i		−	0.171443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.12	✓	320
25.2	odd	20	inner	75.9.k.a.52.12	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.12	✓	320	1.1	even	1	trivial
75.9.k.a.52.12	yes	320	25.2	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.4958 + 2.29591i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-38.6136 + 12.5463i) q^{4} +(555.364 - 286.698i) q^{5} +(212.094 - 652.759i) q^{6} +(2517.93 - 2517.93i) q^{7} +(3878.60 - 1976.25i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-14.4958 + 2.29591i) q^{2} +(-21.2310 + 41.6683i) q^{3} +(-38.6136 + 12.5463i) q^{4} +(555.364 - 286.698i) q^{5} +(212.094 - 652.759i) q^{6} +(2517.93 - 2517.93i) q^{7} +(3878.60 - 1976.25i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-7392.21 + 5430.98i) q^{10} +(3791.81 + 2754.91i) q^{11} +(297.024 - 1875.33i) q^{12} +(-16636.7 - 2635.00i) q^{13} +(-30718.4 + 42280.3i) q^{14} +(155.251 + 29227.9i) q^{15} +(-43277.4 + 31442.9i) q^{16} +(-6199.29 - 12166.8i) q^{17} +(22696.3 + 22696.3i) q^{18} +(-54035.3 - 17557.1i) q^{19} +(-17847.6 + 18038.2i) q^{20} +(51459.4 + 158376. i) q^{21} +(-61290.3 - 31229.0i) q^{22} +(-14954.7 - 94420.0i) q^{23} +203572. i q^{24} +(226234. - 318444. i) q^{25} +247212. q^{26} +(101017. - 15999.5i) q^{27} +(-65635.5 + 128817. i) q^{28} +(-391224. + 127116. i) q^{29} +(-69355.2 - 423326. i) q^{30} +(-158559. + 487995. i) q^{31} +(-232838. + 232838. i) q^{32} +(-195296. + 99508.4i) q^{33} +(117798. + 162134. i) q^{34} +(676481. - 2.12025e6i) q^{35} +(71835.8 + 52191.8i) q^{36} +(261180. - 1.64903e6i) q^{37} +(823595. + 130445. i) q^{38} +(463011. - 637280. i) q^{39} +(1.58745e6 - 2.20952e6i) q^{40} +(636456. - 462412. i) q^{41} +(-1.10956e6 - 2.17764e6i) q^{42} +(-1.15179e6 - 1.15179e6i) q^{43} +(-180980. - 58803.8i) q^{44} +(-1.22117e6 - 614070. i) q^{45} +(433560. + 1.33436e6i) q^{46} +(-2.52624e6 - 1.28718e6i) q^{47} +(-391345. - 2.47086e6i) q^{48} -6.91510e6i q^{49} +(-2.54832e6 + 5.13550e6i) q^{50} +638587. q^{51} +(675464. - 106983. i) q^{52} +(1.67359e6 - 3.28460e6i) q^{53} +(-1.42758e6 + 463850. i) q^{54} +(2.89566e6 + 442874. i) q^{55} +(4.78999e6 - 1.47421e7i) q^{56} +(1.87880e6 - 1.87880e6i) q^{57} +(5.37926e6 - 2.74087e6i) q^{58} +(-1.39614e7 - 1.92162e7i) q^{59} +(-372698. - 1.12665e6i) q^{60} +(4.27778e6 + 3.10799e6i) q^{61} +(1.17805e6 - 7.43792e6i) q^{62} +(-7.69178e6 - 1.21826e6i) q^{63} +(1.08900e7 - 1.49887e7i) q^{64} +(-9.99489e6 + 3.30633e6i) q^{65} +(2.60251e6 - 1.89084e6i) q^{66} +(1.21152e7 + 2.37774e7i) q^{67} +(392026. + 392026. i) q^{68} +(4.25182e6 + 1.38150e6i) q^{69} +(-4.93823e6 + 3.22878e7i) q^{70} +(-1.49439e7 - 4.59926e7i) q^{71} +(-8.48250e6 - 4.32205e6i) q^{72} +(7.00199e6 + 4.42088e7i) q^{73} +2.45036e7i q^{74} +(8.46581e6 + 1.61876e7i) q^{75} +2.30678e6 q^{76} +(1.64841e7 - 2.61083e6i) q^{77} +(-5.24857e6 + 1.03009e7i) q^{78} +(4.06043e7 - 1.31931e7i) q^{79} +(-1.50201e7 + 2.98698e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-8.16428e6 + 8.16428e6i) q^{82} +(-6.84741e7 + 3.48893e7i) q^{83} +(-3.97407e6 - 5.46984e6i) q^{84} +(-6.93106e6 - 4.97968e6i) q^{85} +(1.93405e7 + 1.40517e7i) q^{86} +(3.00937e6 - 1.90004e7i) q^{87} +(2.01513e7 + 3.19165e6i) q^{88} +(-2.41562e6 + 3.32482e6i) q^{89} +(1.91117e7 + 6.09774e6i) q^{90} +(-4.85248e7 + 3.52553e7i) q^{91} +(1.76208e6 + 3.45828e6i) q^{92} +(-1.69675e7 - 1.69675e7i) q^{93} +(3.95751e7 + 1.28587e7i) q^{94} +(-3.50429e7 + 5.74122e6i) q^{95} +(-4.75855e6 - 1.46453e7i) q^{96} +(4.43728e7 + 2.26091e7i) q^{97} +(1.58764e7 + 1.00240e8i) q^{98} -1.02503e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8	\( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) 320 * q + 444 * q^5 - 4540 * q^7 - 17460 * q^8 + 25496 * q^10 - 22680 * q^12 - 133420 * q^13 + 59616 * q^15 + 1310720 * q^16 + 168000 * q^17 - 718900 * q^19 - 641844 * q^20 + 2257100 * q^22 + 1089120 * q^23 - 1459756 * q^25 + 1827840 * q^26 + 3260740 * q^28 + 3913800 * q^29 + 3585384 * q^30 - 641460 * q^32 - 1458000 * q^33 - 4121600 * q^34 + 853140 * q^35 - 22394880 * q^36 - 14553460 * q^37 + 17491260 * q^38 + 3203652 * q^40 + 8749440 * q^41 + 9643860 * q^42 - 23946520 * q^43 + 4277700 * q^44 - 2204496 * q^45 + 26491200 * q^47 - 3661200 * q^48 - 47100924 * q^50 - 169691020 * q^52 - 97028940 * q^53 + 27431764 * q^55 - 4714200 * q^57 + 179119320 * q^58 + 95587200 * q^59 + 38705364 * q^60 + 36738240 * q^61 - 296094660 * q^62 - 9928980 * q^63 - 59695100 * q^64 + 24018972 * q^65 - 88558160 * q^67 + 197811840 * q^68 + 220501420 * q^70 + 38185020 * q^72 + 110964400 * q^73 + 51345576 * q^75 - 97175880 * q^77 - 131709240 * q^78 - 138506200 * q^79 - 339741204 * q^80 + 382637520 * q^81 + 217169400 * q^82 + 862340400 * q^83 + 743029200 * q^84 + 619431268 * q^85 - 335756340 * q^87 - 1380992420 * q^88 - 1141686000 * q^89 - 265834224 * q^90 - 407198400 * q^92 + 402028920 * q^93 + 290042200 * q^94 + 1436174256 * q^95 - 165325860 * q^96 + 1057772920 * q^97 + 1077594720 * q^98

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