LMFDB - Embedded newform 75.9.k.a.13.13

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			13.13
Character	$\chi$	$=$	75.13
Dual form			75.9.k.a.52.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.4052 + 2.12318i) q^{2} +(21.2310 - 41.6683i) q^{3} +(-68.2788 + 22.1851i) q^{4} +(619.380 - 83.6279i) q^{5} +(-196.137 + 603.649i) q^{6} +(-1056.12 + 1056.12i) q^{7} +(3964.00 - 2019.76i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})$	\(q+(-13.4052 + 2.12318i) q^{2} +(21.2310 - 41.6683i) q^{3} +(-68.2788 + 22.1851i) q^{4} +(619.380 - 83.6279i) q^{5} +(-196.137 + 603.649i) q^{6} +(-1056.12 + 1056.12i) q^{7} +(3964.00 - 2019.76i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-8125.36 + 2436.10i) q^{10} +(15691.6 + 11400.6i) q^{11} +(-525.214 + 3316.07i) q^{12} +(-30651.2 - 4854.67i) q^{13} +(11915.2 - 16399.9i) q^{14} +(9665.44 - 27584.0i) q^{15} +(-33981.1 + 24688.7i) q^{16} +(12852.6 + 25224.7i) q^{17} +(20988.8 + 20988.8i) q^{18} +(-119213. - 38734.6i) q^{19} +(-40435.2 + 19451.0i) q^{20} +(21584.2 + 66429.4i) q^{21} +(-234555. - 119512. i) q^{22} +(-13567.5 - 85661.8i) q^{23} -208054. i q^{24} +(376638. - 103595. i) q^{25} +421193. q^{26} +(-101017. + 15999.5i) q^{27} +(48680.6 - 95541.1i) q^{28} +(157511. - 51178.3i) q^{29} +(-71001.6 + 390290. i) q^{30} +(-10896.9 + 33537.3i) q^{31} +(-402232. + 402232. i) q^{32} +(808194. - 411796. i) q^{33} +(-225849. - 310854. i) q^{34} +(-565820. + 742463. i) q^{35} +(127024. + 92288.4i) q^{36} +(-469397. + 2.96366e6i) q^{37} +(1.68031e6 + 266136. i) q^{38} +(-853043. + 1.17411e6i) q^{39} +(2.28631e6 - 1.58250e6i) q^{40} +(1.84547e6 - 1.34081e6i) q^{41} +(-430382. - 844673. i) q^{42} +(3.18242e6 + 3.18242e6i) q^{43} +(-1.32433e6 - 430301. i) q^{44} +(-944169. - 988379. i) q^{45} +(363750. + 1.11951e6i) q^{46} +(4.36808e6 + 2.22565e6i) q^{47} +(307281. + 1.94010e6i) q^{48} +3.53401e6i q^{49} +(-4.82896e6 + 2.18838e6i) q^{50} +1.32394e6 q^{51} +(2.20053e6 - 348530. i) q^{52} +(-3.47200e6 + 6.81418e6i) q^{53} +(1.32018e6 - 428952. i) q^{54} +(1.06725e7 + 5.74907e6i) q^{55} +(-2.05336e6 + 6.31959e6i) q^{56} +(-4.14502e6 + 4.14502e6i) q^{57} +(-2.00280e6 + 1.02048e6i) q^{58} +(1.36187e7 + 1.87445e7i) q^{59} +(-47990.8 + 2.09783e6i) q^{60} +(2.18489e7 + 1.58741e7i) q^{61} +(74870.0 - 472710. i) q^{62} +(3.22625e6 + 510988. i) q^{63} +(1.08583e7 - 1.49452e7i) q^{64} +(-1.93907e7 - 443590. i) q^{65} +(-9.95970e6 + 7.23614e6i) q^{66} +(-2.97526e6 - 5.83928e6i) q^{67} +(-1.43718e6 - 1.43718e6i) q^{68} +(-3.85743e6 - 1.25335e6i) q^{69} +(6.00856e6 - 1.11542e7i) q^{70} +(-1.02618e7 - 3.15826e7i) q^{71} +(-8.66927e6 - 4.41721e6i) q^{72} +(-4.31875e6 - 2.72675e7i) q^{73} -4.07250e7i q^{74} +(3.67979e6 - 1.78933e7i) q^{75} +8.99905e6 q^{76} +(-2.86128e7 + 4.53182e6i) q^{77} +(8.94236e6 - 1.75504e7i) q^{78} +(9.15724e6 - 2.97537e6i) q^{79} +(-1.89825e7 + 1.81334e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-2.18921e7 + 2.18921e7i) q^{82} +(9.32049e6 - 4.74903e6i) q^{83} +(-2.94749e6 - 4.05687e6i) q^{84} +(1.00701e7 + 1.45488e7i) q^{85} +(-4.94178e7 - 3.59041e7i) q^{86} +(1.21160e6 - 7.64976e6i) q^{87} +(8.52282e7 + 1.34988e7i) q^{88} +(-3.02851e7 + 4.16839e7i) q^{89} +(1.47553e7 + 1.12448e7i) q^{90} +(3.74986e7 - 2.72443e7i) q^{91} +(2.82679e6 + 5.54789e6i) q^{92} +(1.16609e6 + 1.16609e6i) q^{93} +(-6.32805e7 - 2.05611e7i) q^{94} +(-7.70774e7 - 1.40219e7i) q^{95} +(8.22050e6 + 2.53001e7i) q^{96} +(-1.24643e8 - 6.35086e7i) q^{97} +(-7.50332e6 - 4.73741e7i) q^{98} -4.24189e7i 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 $

$2$	−13.4052	+	2.12318i	−0.837825	+	0.132698i	−0.560580	−	0.828101i	$-0.689422\pi$
$2$	−13.4052	+	2.12318i	−0.837825	+	0.132698i	−0.277246	+	0.960799i	$0.589422\pi$
$3$	21.2310	−	41.6683i	0.262112	−	0.514423i
$3$	21.2310	−	41.6683i	0.262112	−	0.514423i
$4$	−68.2788	+	22.1851i	−0.266714	+	0.0866607i
$5$	619.380	−	83.6279i	0.991008	−	0.133805i
$5$	619.380	−	83.6279i	0.991008	−	0.133805i
$6$	−196.137	+	603.649i	−0.151341	+	0.465778i
$7$	−1056.12	+	1056.12i	−0.439868	+	0.439868i	−0.891968	−	0.452099i	$-0.850675\pi$
$7$	−1056.12	+	1056.12i	−0.439868	+	0.439868i	0.452099	+	0.891968i	$0.350675\pi$
$8$	3964.00	−	2019.76i	0.967773	−	0.493105i
$9$	−1285.49	−	1769.32i	−0.195928	−	0.269672i
$10$	−8125.36	+	2436.10i	−0.812536	+	0.243610i
$11$	15691.6	+	11400.6i	1.07176	+	0.778679i	0.976228	−	0.216747i	$-0.0695448\pi$
$11$	15691.6	+	11400.6i	1.07176	+	0.778679i	0.0955319	+	0.995426i	$0.469545\pi$
$12$	−525.214	+	3316.07i	−0.0253286	+	0.159919i
$13$	−30651.2	−	4854.67i	−1.07318	−	0.169976i	−0.405257	−	0.914203i	$-0.632818\pi$
$13$	−30651.2	−	4854.67i	−1.07318	−	0.169976i	−0.667927	+	0.744227i	$0.732818\pi$
$14$	11915.2	−	16399.9i	0.310163	−	0.426903i
$15$	9665.44	−	27584.0i	0.190922	−	0.544869i
$16$	−33981.1	+	24688.7i	−0.518510	+	0.376720i
$17$	12852.6	+	25224.7i	0.153885	+	0.302016i	0.955059	−	0.296415i	$-0.0957910\pi$
$17$	12852.6	+	25224.7i	0.153885	+	0.302016i	−0.801174	+	0.598431i	$0.795791\pi$
$18$	20988.8	+	20988.8i	0.199939	+	0.199939i
$19$	−119213.	−	38734.6i	−0.914764	−	0.297225i	−0.186447	−	0.982465i	$-0.559697\pi$
$19$	−119213.	−	38734.6i	−0.914764	−	0.297225i	−0.728317	+	0.685240i	$0.759697\pi$
$20$	−40435.2	+	19451.0i	−0.252720	+	0.121569i
$21$	21584.2	+	66429.4i	0.110984	+	0.341573i
$22$	−234555.	−	119512.i	−1.00128	−	0.510176i
$23$	−13567.5	−	85661.8i	−0.0484829	−	0.306109i	0.951516	−	0.307599i	$-0.0995256\pi$
$23$	−13567.5	−	85661.8i	−0.0484829	−	0.306109i	−0.999999	+	0.00149041i	$0.999526\pi$
$24$		−	208054.i		−	0.627093i
$25$	376638.	−	103595.i	0.964193	−	0.265203i
$26$	421193.			0.921696
$27$	−101017.	+	15999.5i	−0.190081	+	0.0301058i
$28$	48680.6	−	95541.1i	0.0791998	−	0.155438i
$29$	157511.	−	51178.3i	0.222699	−	0.0723592i	−0.195542	−	0.980695i	$-0.562647\pi$
$29$	157511.	−	51178.3i	0.222699	−	0.0723592i	0.418241	+	0.908336i	$0.362647\pi$
$30$	−71001.6	+	390290.i	−0.0876563	+	0.481840i
$31$	−10896.9	+	33537.3i	−0.0117993	+	0.0363146i	−0.956783	−	0.290803i	$-0.906077\pi$
$31$	−10896.9	+	33537.3i	−0.0117993	+	0.0363146i	0.944984	+	0.327118i	$0.106077\pi$
$32$	−402232.	+	402232.i	−0.383598	+	0.383598i
$33$	808194.	−	411796.i	0.681491	−	0.347237i
$34$	−225849.	−	310854.i	−0.169006	−	0.232617i
$35$	−565820.	+	742463.i	−0.377056	+	0.494769i
$36$	127024.	+	92288.4i	0.0756269	+	0.0549461i
$37$	−469397.	+	2.96366e6i	−0.250457	+	1.58132i	0.466702	+	0.884415i	$0.345442\pi$
$37$	−469397.	+	2.96366e6i	−0.250457	+	1.58132i	−0.717159	+	0.696910i	$0.754558\pi$
$38$	1.68031e6	+	266136.i	0.805854	+	0.127635i
$39$	−853043.	+	1.17411e6i	−0.368733	+	0.507518i
$40$	2.28631e6	−	1.58250e6i	0.893091	−	0.618164i
$41$	1.84547e6	−	1.34081e6i	0.653088	−	0.474496i	−0.211234	−	0.977436i	$-0.567748\pi$
$41$	1.84547e6	−	1.34081e6i	0.653088	−	0.474496i	0.864322	+	0.502939i	$0.167748\pi$
$42$	−430382.	−	844673.i	−0.138311	−	0.271451i
$43$	3.18242e6	+	3.18242e6i	0.930858	+	0.930858i	0.997760	−	0.0669020i	$-0.0213115\pi$
$43$	3.18242e6	+	3.18242e6i	0.930858	+	0.930858i	−0.0669020	+	0.997760i	$0.521311\pi$
$44$	−1.32433e6	−	430301.i	−0.353334	−	0.114805i
$45$	−944169.	−	988379.i	−0.230250	−	0.241031i
$46$	363750.	+	1.11951e6i	0.0812403	+	0.250032i
$47$	4.36808e6	+	2.22565e6i	0.895158	+	0.456106i	0.840134	−	0.542379i	$-0.182476\pi$
$47$	4.36808e6	+	2.22565e6i	0.895158	+	0.456106i	0.0550240	+	0.998485i	$0.482476\pi$
$48$	307281.	+	1.94010e6i	0.0578857	+	0.365476i
$49$			3.53401e6i			0.613032i
$50$	−4.82896e6	+	2.18838e6i	−0.772633	+	0.350141i
$51$	1.32394e6			0.195699
$52$	2.20053e6	−	348530.i	0.300963	−	0.0476679i
$53$	−3.47200e6	+	6.81418e6i	−0.440023	+	0.863595i	0.559375	+	0.828915i	$0.311041\pi$
$53$	−3.47200e6	+	6.81418e6i	−0.440023	+	0.863595i	−0.999398	+	0.0346799i	$0.988959\pi$
$54$	1.32018e6	−	428952.i	0.155259	−	0.0504468i
$55$	1.06725e7	+	5.74907e6i	1.16631	+	0.628270i
$56$	−2.05336e6	+	6.31959e6i	−0.208791	+	0.642594i
$57$	−4.14502e6	+	4.14502e6i	−0.392669	+	0.392669i
$58$	−2.00280e6	+	1.02048e6i	−0.176981	+	0.0901762i
$59$	1.36187e7	+	1.87445e7i	1.12390	+	1.54692i	0.799165	+	0.601112i	$0.205275\pi$
$59$	1.36187e7	+	1.87445e7i	1.12390	+	1.54692i	0.324735	+	0.945805i	$0.394725\pi$
$60$	−47990.8	+	2.09783e6i	−0.00370299	+	0.161870i
$61$	2.18489e7	+	1.58741e7i	1.57801	+	1.14649i	0.918930	+	0.394420i	$0.129054\pi$
$61$	2.18489e7	+	1.58741e7i	1.57801	+	1.14649i	0.659081	+	0.752072i	$0.270946\pi$
$62$	74870.0	−	472710.i	0.00506688	−	0.0319910i
$63$	3.22625e6	+	510988.i	0.204803	+	0.0324376i
$64$	1.08583e7	−	1.49452e7i	0.647205	−	0.890802i
$65$	−1.93907e7	−	443590.i	−1.08628	−	0.0248501i
$66$	−9.95970e6	+	7.23614e6i	−0.524892	+	0.381357i
$67$	−2.97526e6	−	5.83928e6i	−0.147647	−	0.289774i	0.805324	−	0.592835i	$-0.201991\pi$
$67$	−2.97526e6	−	5.83928e6i	−0.147647	−	0.289774i	−0.952971	+	0.303061i	$0.901991\pi$
$68$	−1.43718e6	−	1.43718e6i	−0.0672162	−	0.0672162i
$69$	−3.85743e6	−	1.25335e6i	−0.170177	−	0.0552939i
$70$	6.00856e6	−	1.11542e7i	0.250252	−	0.464565i
$71$	−1.02618e7	−	3.15826e7i	−0.403822	−	1.24284i	−0.921875	−	0.387488i	$-0.873343\pi$
$71$	−1.02618e7	−	3.15826e7i	−0.403822	−	1.24284i	0.518053	−	0.855349i	$-0.326657\pi$
$72$	−8.66927e6	−	4.41721e6i	−0.322591	−	0.164368i
$73$	−4.31875e6	−	2.72675e7i	−0.152078	−	0.960184i	−0.939196	−	0.343381i	$-0.888428\pi$
$73$	−4.31875e6	−	2.72675e7i	−0.152078	−	0.960184i	0.787118	−	0.616803i	$-0.211572\pi$
$74$		−	4.07250e7i		−	1.35811i
$75$	3.67979e6	−	1.78933e7i	0.116300	−	0.565515i
$76$	8.99905e6			0.269738
$77$	−2.86128e7	+	4.53182e6i	−0.813949	+	0.128917i
$78$	8.94236e6	−	1.75504e7i	0.241587	−	0.474142i
$79$	9.15724e6	−	2.97537e6i	0.235102	−	0.0763893i	−0.189096	−	0.981959i	$-0.560556\pi$
$79$	9.15724e6	−	2.97537e6i	0.235102	−	0.0763893i	0.424198	+	0.905569i	$0.360556\pi$
$80$	−1.89825e7	+	1.81334e7i	−0.463441	+	0.442711i
$81$	−1.47802e6	+	4.54887e6i	−0.0343352	+	0.105673i
$82$	−2.18921e7	+	2.18921e7i	−0.484209	+	0.484209i
$83$	9.32049e6	−	4.74903e6i	0.196393	−	0.100067i	−0.353028	−	0.935613i	$-0.614848\pi$
$83$	9.32049e6	−	4.74903e6i	0.196393	−	0.100067i	0.549422	+	0.835545i	$0.314848\pi$
$84$	−2.94749e6	−	4.05687e6i	−0.0592018	−	0.0814843i
$85$	1.00701e7	+	1.45488e7i	0.192912	+	0.278710i
$86$	−4.94178e7	−	3.59041e7i	−0.903419	−	0.656373i
$87$	1.21160e6	−	7.64976e6i	0.0211487	−	0.133527i
$88$	8.52282e7	+	1.34988e7i	1.42119	+	0.225095i
$89$	−3.02851e7	+	4.16839e7i	−0.482691	+	0.664368i	−0.979019	−	0.203767i	$-0.934681\pi$
$89$	−3.02851e7	+	4.16839e7i	−0.482691	+	0.664368i	0.496328	+	0.868135i	$0.334681\pi$
$90$	1.47553e7	+	1.12448e7i	0.224894	+	0.171388i
$91$	3.74986e7	−	2.72443e7i	0.546826	−	0.397293i
$92$	2.82679e6	+	5.54789e6i	0.0394587	+	0.0774420i
$93$	1.16609e6	+	1.16609e6i	0.0155883	+	0.0155883i
$94$	−6.32805e7	−	2.05611e7i	−0.810510	−	0.263351i
$95$	−7.70774e7	−	1.40219e7i	−0.946308	−	0.172152i
$96$	8.22050e6	+	2.53001e7i	0.0967862	+	0.297877i
$97$	−1.24643e8	−	6.35086e7i	−1.40793	−	0.717374i	−0.425662	−	0.904882i	$-0.639959\pi$
$97$	−1.24643e8	−	6.35086e7i	−1.40793	−	0.717374i	−0.982263	+	0.187508i	$0.939959\pi$
$98$	−7.50332e6	−	4.73741e7i	−0.0813484	−	0.513614i
$99$		−	4.24189e7i		−	0.441589i
$100$	−2.34181e7	+	1.54291e7i	−0.234181	+	0.154291i
$101$	1.07315e8			1.03127			0.515636	−	0.856808i	$-0.327556\pi$
$101$	1.07315e8			1.03127			0.515636	+	0.856808i	$0.327556\pi$
$102$	−1.77477e7	+	2.81097e6i	−0.163962	+	0.0259690i
$103$	1.50852e7	−	2.96064e7i	0.134030	−	0.263049i	−0.814231	−	0.580542i	$-0.802841\pi$
$103$	1.50852e7	−	2.96064e7i	0.134030	−	0.263049i	0.948261	+	0.317493i	$0.102841\pi$
$104$	−1.31307e8	+	4.26641e7i	−1.12241	+	0.364695i
$105$	1.89242e7	+	3.93400e7i	0.155690	+	0.323651i
$106$	3.20751e7	−	9.87171e7i	0.254065	−	0.781932i
$107$	−6.31249e7	+	6.31249e7i	−0.481577	+	0.481577i	−0.905635	−	0.424058i	$-0.860605\pi$
$107$	−6.31249e7	+	6.31249e7i	−0.481577	+	0.481577i	0.424058	+	0.905635i	$0.360605\pi$
$108$	6.54235e6	−	3.33349e6i	0.0480882	−	0.0245022i
$109$	1.64394e8	+	2.26268e8i	1.16461	+	1.60294i	0.692543	+	0.721377i	$0.256490\pi$
$109$	1.64394e8	+	2.26268e8i	1.16461	+	1.60294i	0.472062	+	0.881565i	$0.343510\pi$
$110$	−1.55273e8	−	5.44078e7i	−1.06054	−	0.371613i
$111$	1.13525e8	+	8.24805e7i	0.747822	+	0.543324i
$112$	9.81390e6	−	6.19625e7i	0.0623691	−	0.393783i
$113$	1.76482e8	+	2.79520e7i	1.08240	+	0.171435i	0.672059	−	0.740498i	$-0.265410\pi$
$113$	1.76482e8	+	2.79520e7i	1.08240	+	0.171435i	0.410339	+	0.911933i	$0.365410\pi$
$114$	4.67642e7	−	6.43654e7i	0.276882	−	0.381095i
$115$	−1.55672e7	−	5.19226e7i	−0.0890057	−	0.296869i
$116$	−9.61924e6	+	6.98878e6i	−0.0531262	+	0.0385984i
$117$	3.08122e7	+	6.04724e7i	0.164429	+	0.322711i
$118$	−2.22360e8	−	2.22360e8i	−1.14691	−	1.14691i
$119$	−4.02144e7	−	1.30664e7i	−0.200536	−	0.0651583i
$120$	−1.73992e7	−	1.28865e8i	−0.0839080	−	0.621454i
$121$	5.00122e7	+	1.53922e8i	0.233311	+	0.718057i
$122$	−3.26592e8	−	1.66407e8i	−1.47424	−	0.751160i
$123$	−1.66881e7	−	1.05364e8i	−0.0729098	−	0.460334i
$124$		−	2.53164e6i		−	0.0107082i
$125$	2.24618e8	−	9.56620e7i	0.920037	−	0.391832i
$126$	−4.43335e7			−0.175894
$127$	−7.73040e7	+	1.22438e7i	−0.297158	+	0.0470652i	−0.303233	−	0.952916i	$-0.598066\pi$
$127$	−7.73040e7	+	1.22438e7i	−0.297158	+	0.0470652i	0.00607537	+	0.999982i	$0.498066\pi$
$128$	−4.77148e7	+	9.36456e7i	−0.177752	+	0.348857i
$129$	2.00172e8	−	6.50397e7i	0.722843	−	0.234866i
$130$	2.60878e8	−	3.52235e7i	0.913408	−	0.123327i
$131$	−1.30581e8	+	4.01888e8i	−0.443401	+	1.36465i	0.440827	+	0.897592i	$0.354685\pi$
$131$	−1.30581e8	+	4.01888e8i	−0.443401	+	1.36465i	−0.884228	+	0.467055i	$0.845315\pi$
$132$	−4.60468e7	+	4.60468e7i	−0.151671	+	0.151671i
$133$	1.66812e8	−	8.49950e7i	0.533115	−	0.271636i
$134$	5.22818e7	+	7.19597e7i	0.162155	+	0.223188i
$135$	−6.12297e7	+	1.83576e7i	−0.184343	+	0.0552688i
$136$	1.01896e8	+	7.40315e7i	0.297852	+	0.216402i
$137$	5.31078e6	−	3.35309e7i	0.0150756	−	0.0951839i	−0.979003	−	0.203845i	$-0.934656\pi$
$137$	5.31078e6	−	3.35309e7i	0.0150756	−	0.0951839i	0.994079	+	0.108661i	$0.0346562\pi$
$138$	5.43707e7	+	8.61148e6i	0.149916	+	0.0237444i
$139$	−7.43063e7	+	1.02274e8i	−0.199052	+	0.273971i	−0.896861	−	0.442312i	$-0.854158\pi$
$139$	−7.43063e7	+	1.02274e8i	−0.199052	+	0.273971i	0.697809	+	0.716284i	$0.254158\pi$
$140$	2.21619e7	−	6.32473e7i	0.0576892	−	0.164638i
$141$	1.85478e8	−	1.34758e8i	0.469262	−	0.340939i
$142$	2.04617e8	+	4.01583e8i	0.503255	+	0.987693i
$143$	−4.25621e8	−	4.25621e8i	−1.01784	−	1.01784i
$144$	8.73644e7	+	2.83864e7i	0.203182	+	0.0660177i
$145$	9.32789e7	−	4.48711e7i	0.211014	−	0.101507i
$146$	1.15788e8	+	3.56358e8i	0.254830	+	0.784286i
$147$	1.47256e8	+	7.50306e7i	0.315358	+	0.160683i
$148$	−3.36992e7	−	2.12769e8i	−0.0702382	−	0.443466i
$149$			3.68959e8i			0.748570i	0.927314	+	0.374285i	$0.122112\pi$
$149$			3.68959e8i			0.748570i	−0.927314	+	0.374285i	$0.877888\pi$
$150$	−1.13378e7	+	2.47676e8i	−0.0223956	+	0.489236i
$151$	−1.79080e8			−0.344460			−0.172230	−	0.985057i	$-0.555097\pi$
$151$	−1.79080e8			−0.344460			−0.172230	+	0.985057i	$0.555097\pi$
$152$	−5.50795e8	+	8.72373e7i	−1.03185	+	0.163429i
$153$	2.81087e7	−	5.51664e7i	0.0512950	−	0.100672i
$154$	3.73938e8	−	1.21500e8i	0.664840	−	0.216020i
$155$	−3.94468e6	+	2.16836e7i	−0.00683416	+	0.0375669i
$156$	3.21969e7	−	9.90919e7i	0.0543645	−	0.167317i
$157$	1.07956e8	−	1.07956e8i	0.177683	−	0.177683i	−0.612662	−	0.790345i	$-0.709901\pi$
$157$	1.07956e8	−	1.07956e8i	0.177683	−	0.177683i	0.790345	+	0.612662i	$0.209901\pi$
$158$	−1.16437e8	+	5.93279e7i	−0.186838	+	0.0951985i
$159$	2.10221e8	+	2.89344e8i	0.328918	+	0.452716i
$160$	−2.15497e8	+	2.82772e8i	−0.328822	+	0.431476i
$161$	1.04798e8	+	7.61405e7i	0.155974	+	0.113321i
$162$	1.01551e7	−	6.41167e7i	0.0147443	−	0.0930917i
$163$	4.46731e6	+	707552.i	0.00632843	+	0.00100232i	0.159598	−	0.987182i	$-0.448980\pi$
$163$	4.46731e6	+	707552.i	0.00632843	+	0.00100232i	−0.153269	+	0.988184i	$0.548980\pi$
$164$	−9.62604e7	+	1.32491e8i	−0.133068	+	0.183152i
$165$	4.66142e8	−	3.22645e8i	0.628901	−	0.435301i
$166$	−1.14860e8	+	8.34507e7i	−0.151264	+	0.109900i
$167$	−9.66195e6	−	1.89626e7i	−0.0124222	−	0.0243800i	0.884712	−	0.466138i	$-0.154355\pi$
$167$	−9.66195e6	−	1.89626e7i	−0.0124222	−	0.0243800i	−0.897134	+	0.441758i	$0.854355\pi$
$168$	2.19731e8	+	2.19731e8i	0.275838	+	0.275838i
$169$	1.40122e8	+	4.55286e7i	0.171775	+	0.0558132i
$170$	−1.65882e8	−	1.73649e8i	−0.198611	−	0.207911i
$171$	8.47126e7	+	2.60719e8i	0.0990749	+	0.304921i
$172$	−2.87894e8	−	1.46689e8i	−0.328942	−	0.167604i
$173$	−6.67008e7	−	4.21132e8i	−0.0744640	−	0.470147i	−0.996538	−	0.0831345i	$-0.973507\pi$
$173$	−6.67008e7	−	4.21132e8i	−0.0744640	−	0.470147i	0.922074	−	0.387013i	$-0.126493\pi$
$174$			1.05119e8i			0.114679i
$175$	−2.88367e8	+	5.07185e8i	−0.307463	+	0.540772i
$176$	−8.14685e8			−0.849062
$177$	1.07019e9	−	1.69502e8i	1.09036	−	0.172696i
$178$	3.17476e8	−	6.23082e8i	0.316251	−	0.620677i
$179$	1.15848e9	−	3.76412e8i	1.12843	−	0.366649i	0.315451	−	0.948942i	$-0.397844\pi$
$179$	1.15848e9	−	3.76412e8i	1.12843	−	0.366649i	0.812980	+	0.582292i	$0.197844\pi$
$180$	8.63940e7	+	4.65388e7i	0.0822988	+	0.0443328i
$181$	−3.73999e8	+	1.15105e9i	−0.348462	+	1.07246i	0.611242	+	0.791444i	$0.290670\pi$
$181$	−3.73999e8	+	1.15105e9i	−0.348462	+	1.07246i	−0.959704	+	0.281013i	$0.909330\pi$
$182$	−4.44832e8	+	4.44832e8i	−0.405425	+	0.405425i
$183$	1.12532e9	−	5.73380e8i	1.00340	−	0.511256i
$184$	−2.26798e8	−	3.12160e8i	−0.197864	−	0.272337i
$185$	−4.28906e7	+	1.87488e9i	−0.0366164	+	1.60062i
$186$	−1.81074e7	−	1.31558e7i	−0.0151288	−	0.0109917i
$187$	−8.58990e7	+	5.42345e8i	−0.0702460	+	0.443516i
$188$	−3.47624e8	−	5.50582e7i	−0.278278	−	0.0440748i
$189$	8.97887e7	−	1.23584e8i	0.0703679	−	0.0968530i
$190$	1.06301e9	+	2.43178e7i	0.815685	+	0.0186599i
$191$	−8.17477e8	+	5.93932e8i	−0.614246	+	0.446276i	−0.850907	−	0.525317i	$-0.823947\pi$
$191$	−8.17477e8	+	5.93932e8i	−0.614246	+	0.446276i	0.236661	+	0.971592i	$0.423947\pi$
$192$	−3.92206e8	−	7.69748e8i	−0.288609	−	0.566426i
$193$	2.79051e7	+	2.79051e7i	0.0201120	+	0.0201120i	0.717091	−	0.696979i	$-0.245473\pi$
$193$	2.79051e7	+	2.79051e7i	0.0201120	+	0.0201120i	−0.696979	+	0.717091i	$0.745473\pi$
$194$	1.80570e9	+	5.86708e8i	1.27479	+	0.414204i
$195$	−4.30169e8	+	7.98560e8i	−0.297509	+	0.552292i
$196$	−7.84024e7	−	2.41298e8i	−0.0531258	−	0.163504i
$197$	−1.26400e9	−	6.44041e8i	−0.839234	−	0.427611i	−0.0191238	−	0.999817i	$-0.506088\pi$
$197$	−1.26400e9	−	6.44041e8i	−0.839234	−	0.427611i	−0.820110	+	0.572206i	$0.806088\pi$
$198$	9.00628e7	+	5.68634e8i	0.0585982	+	0.369975i
$199$		−	1.32861e8i		−	0.0847200i	−0.999102	−	0.0423600i	$-0.986512\pi$
$199$		−	1.32861e8i		−	0.0847200i	0.999102	−	0.0423600i	$-0.0134876\pi$
$200$	1.28375e9	−	1.17137e9i	0.802347	−	0.732105i
$201$	−3.06480e8			−0.187767
$202$	−1.43857e9	+	2.27848e8i	−0.864025	+	0.136848i
$203$	−1.12300e8	+	2.20401e8i	−0.0661296	+	0.129787i
$204$	−9.03973e7	+	2.93719e7i	−0.0521957	+	0.0169594i
$205$	1.03092e9	−	9.84806e8i	0.583726	−	0.557616i
$206$	−1.39361e8	+	4.28908e8i	−0.0773876	+	0.238175i
$207$	−1.34122e8	+	1.34122e8i	−0.0730499	+	0.0730499i
$208$	1.16142e9	−	5.91771e8i	0.620490	−	0.316155i
$209$	−1.42905e9	−	1.96691e9i	−0.748964	−	1.03086i
$210$	−3.37208e8	−	4.87181e8i	−0.173389	−	0.250503i
$211$	5.47534e8	+	3.97807e8i	0.276237	+	0.200698i	0.717274	−	0.696791i	$-0.245389\pi$
$211$	5.47534e8	+	3.97807e8i	0.276237	+	0.200698i	−0.441038	+	0.897489i	$0.645389\pi$
$212$	8.58904e7	−	5.42291e8i	0.0425208	−	0.268466i
$213$	−1.53386e9	−	2.42939e8i	−0.745190	−	0.118026i
$214$	7.12177e8	−	9.80227e8i	0.339573	−	0.467382i
$215$	2.23726e9	+	1.70499e9i	1.04704	+	0.797934i
$216$	−3.68115e8	+	2.67451e8i	−0.169110	+	0.122865i
$217$	−2.39110e7	−	4.69280e7i	−0.0107835	−	0.0211638i
$218$	−2.68414e9	−	2.68414e9i	−1.18844	−	1.18844i
$219$	−1.22788e9	−	3.98963e8i	−0.533802	−	0.173443i
$220$	−8.56249e8	−	1.55769e8i	−0.365518	−	0.0664951i
$221$	−2.71491e8	−	8.35563e8i	−0.113811	−	0.350276i
$222$	−1.69694e9	−	8.64635e8i	−0.698642	−	0.355976i
$223$	−4.84151e8	−	3.05681e9i	−0.195777	−	1.23609i	−0.868311	−	0.496020i	$-0.834794\pi$
$223$	−4.84151e8	−	3.05681e9i	−0.195777	−	1.23609i	0.672534	−	0.740066i	$-0.265206\pi$
$224$		−	8.49614e8i		−	0.337465i
$225$	−6.67455e8	−	5.33223e8i	−0.260431	−	0.208055i
$226$	−2.42513e9			−0.929610
$227$	−3.91636e9	+	6.20290e8i	−1.47496	+	0.233610i	−0.841537	−	0.540200i	$-0.818349\pi$
$227$	−3.91636e9	+	6.20290e8i	−1.47496	+	0.233610i	−0.633418	+	0.773810i	$0.718349\pi$
$228$	1.91059e8	−	3.74975e8i	0.0707015	−	0.138759i
$229$	4.80658e9	−	1.56175e9i	1.74781	−	0.567897i	0.751984	−	0.659182i	$-0.229097\pi$
$229$	4.80658e9	−	1.56175e9i	1.74781	−	0.567897i	0.995825	+	0.0912843i	$0.0290972\pi$
$230$	3.18922e8	+	6.62981e8i	0.113965	+	0.236913i
$231$	−4.18646e8	+	1.28846e9i	−0.147028	+	0.452505i
$232$	5.21004e8	−	5.21004e8i	0.179841	−	0.179841i
$233$	−3.15822e9	+	1.60919e9i	−1.07157	+	0.545990i	−0.898524	−	0.438925i	$-0.855359\pi$
$233$	−3.15822e9	+	1.60919e9i	−1.07157	+	0.545990i	−0.173041	+	0.984915i	$0.555359\pi$
$234$	−5.41438e8	−	7.45225e8i	−0.180586	−	0.248556i
$235$	2.89163e9	+	1.01323e9i	0.948137	+	0.332228i
$236$	−1.34572e9	−	9.77722e8i	−0.433817	−	0.315186i
$237$	7.04393e7	−	4.44736e8i	0.0223266	−	0.140964i
$238$	5.66824e8	+	8.97761e7i	0.176661	+	0.0279803i
$239$	1.71804e9	−	2.36467e9i	0.526551	−	0.724735i	−0.460049	−	0.887894i	$-0.652168\pi$
$239$	1.71804e9	−	2.36467e9i	0.526551	−	0.724735i	0.986600	+	0.163158i	$0.0521681\pi$
$240$	3.52570e8	+	1.17596e9i	0.106268	+	0.354444i
$241$	−2.59205e9	+	1.88323e9i	−0.768377	+	0.558259i	−0.901468	−	0.432845i	$-0.857510\pi$
$241$	−2.59205e9	+	1.88323e9i	−0.768377	+	0.558259i	0.133091	+	0.991104i	$0.457510\pi$
$242$	−9.97227e8	−	1.95717e9i	−0.290759	−	0.570646i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	−1.84399e9	−	5.99147e8i	−0.520234	−	0.169034i
$245$	2.95542e8	+	2.18889e9i	0.0820266	+	0.607519i
$246$	4.47414e8	+	1.37700e9i	0.122171	+	0.376005i
$247$	3.46598e9	+	1.76600e9i	0.931189	+	0.474464i
$248$	2.45418e7	+	1.54951e8i	0.00648784	+	0.0409626i
$249$		−	4.89195e8i		−	0.127258i
$250$	−2.80795e9	+	1.75927e9i	−0.718835	+	0.450374i
$251$	1.37030e9			0.345240			0.172620	−	0.984988i	$-0.444777\pi$
$251$	1.37030e9			0.345240			0.172620	+	0.984988i	$0.444777\pi$
$252$	−2.31621e8	+	3.66852e7i	−0.0574349	+	0.00909679i
$253$	7.63703e8	−	1.49885e9i	0.186398	−	0.365828i
$254$	1.01028e9	−	3.28260e8i	0.242721	−	0.0788648i
$255$	8.20024e8	−	1.10719e8i	0.193939	−	0.0261855i
$256$	−1.02059e9	+	3.14104e9i	−0.237624	+	0.731331i
$257$	2.97637e9	−	2.97637e9i	0.682266	−	0.682266i	−0.278244	−	0.960510i	$-0.589752\pi$
$257$	2.97637e9	−	2.97637e9i	0.682266	−	0.682266i	0.960510	+	0.278244i	$0.0897524\pi$
$258$	−2.54525e9	+	1.29687e9i	−0.574450	+	0.292697i
$259$	−2.63425e9	−	3.62573e9i	−0.585406	−	0.805742i
$260$	1.33382e9	−	3.99898e8i	0.291879	−	0.0875096i
$261$	−2.93028e8	−	2.12898e8i	−0.0631463	−	0.0458785i
$262$	8.97192e8	−	5.66464e9i	0.190406	−	1.20217i
$263$	1.52068e9	+	2.40852e8i	0.317845	+	0.0503416i	0.313318	−	0.949648i	$-0.398559\pi$
$263$	1.52068e9	+	2.40852e8i	0.317845	+	0.0503416i	0.00452616	+	0.999990i	$0.498559\pi$
$264$	2.37195e9	−	3.26471e9i	0.488304	−	0.672093i
$265$	−1.58063e9	+	4.51092e9i	−0.320514	+	0.914706i
$266$	−2.05569e9	+	1.49355e9i	−0.410612	+	0.298327i
$267$	1.09391e9	+	2.14692e9i	0.215247	+	0.422446i
$268$	3.32692e8	+	3.32692e8i	0.0644917	+	0.0644917i
$269$	6.03730e9	+	1.96164e9i	1.15301	+	0.374636i	0.822277	−	0.569087i	$-0.192703\pi$
$269$	6.03730e9	+	1.96164e9i	1.15301	+	0.374636i	0.330735	+	0.943724i	$0.392703\pi$
$270$	7.81820e8	−	3.76088e8i	0.147113	−	0.0707677i
$271$	−1.06804e9	−	3.28709e9i	−0.198021	−	0.609445i	−0.999928	−	0.0119965i	$-0.996181\pi$
$271$	−1.06804e9	−	3.28709e9i	−0.198021	−	0.609445i	0.801907	−	0.597448i	$-0.203819\pi$
$272$	−1.05951e9	−	5.39848e8i	−0.193566	−	0.0986270i
$273$	−3.39089e8	−	2.14093e9i	−0.0610469	−	0.385435i
$274$			4.60765e8i			0.0817480i
$275$	7.09111e9	+	2.66834e9i	1.23989	+	0.466563i
$276$	2.91186e8			0.0501805
$277$	−5.64867e9	+	8.94661e8i	−0.959460	+	0.151964i	−0.616473	−	0.787376i	$-0.711439\pi$
$277$	−5.64867e9	+	8.94661e8i	−0.959460	+	0.151964i	−0.342988	+	0.939340i	$0.611439\pi$
$278$	7.78946e8	−	1.52877e9i	0.130415	−	0.255954i
$279$	7.33461e7	−	2.38316e7i	0.0121049	−	0.00393311i
$280$	−7.43315e8	+	4.08594e9i	−0.120932	+	0.664753i
$281$	3.34167e9	−	1.02846e10i	0.535967	−	1.64954i	−0.205585	−	0.978639i	$-0.565910\pi$
$281$	3.34167e9	−	1.02846e10i	0.535967	−	1.64954i	0.741551	−	0.670896i	$-0.234090\pi$
$282$	−2.20026e9	+	2.20026e9i	−0.347918	+	0.347918i
$283$	−6.76863e9	+	3.44879e9i	−1.05525	+	0.537676i	−0.893457	−	0.449149i	$-0.851727\pi$
$283$	−6.76863e9	+	3.44879e9i	−1.05525	+	0.537676i	−0.161792	+	0.986825i	$0.551727\pi$
$284$	1.40133e9	+	1.92876e9i	0.215410	+	0.296487i
$285$	−2.22070e9	+	2.91398e9i	−0.336597	+	0.441679i
$286$	6.60921e9	+	4.80187e9i	0.987837	+	0.717705i
$287$	−5.32981e8	+	3.36511e9i	−0.0785569	+	0.495988i
$288$	1.22874e9	+	1.94614e8i	0.178604	+	0.0282881i
$289$	3.62915e9	−	4.99510e9i	0.520252	−	0.716065i
$290$	−1.15515e9	+	7.99554e8i	−0.163323	+	0.113046i
$291$	−5.29258e9	+	3.84529e9i	−0.738067	+	0.536237i
$292$	8.99813e8	+	1.76598e9i	0.123772	+	0.242915i
$293$	9.81865e9	+	9.81865e9i	1.33224	+	1.33224i	0.903366	+	0.428870i	$0.141088\pi$
$293$	9.81865e9	+	9.81865e9i	1.33224	+	1.33224i	0.428870	+	0.903366i	$0.358912\pi$
$294$	−2.13330e9	−	6.93151e8i	−0.285537	−	0.0927766i
$295$	1.00027e10	+	1.04711e10i	1.32078	+	1.38262i
$296$	4.12518e9	+	1.26960e10i	0.537373	+	1.65387i
$297$	−1.76752e9	−	9.00597e8i	−0.227164	−	0.115746i
$298$	−7.83364e8	−	4.94597e9i	−0.0993342	−	0.627171i
$299$			2.69150e9i			0.336752i
$300$	1.45713e8	+	1.30337e9i	0.0179892	+	0.160910i
$301$	−6.72205e9			−0.818909
$302$	2.40060e9	−	3.80218e8i	0.288597	−	0.0457093i
$303$	2.27840e9	−	4.47161e9i	0.270308	−	0.530510i
$304$	5.00729e9	−	1.62697e9i	0.586285	−	0.190495i
$305$	1.48603e10	+	8.00495e9i	1.71723	+	0.925037i
$306$	−2.59675e8	+	7.99197e8i	−0.0296172	+	0.0911524i
$307$	−1.22131e10	+	1.22131e10i	−1.37491	+	1.37491i	−0.521903	+	0.853005i	$0.674778\pi$
$307$	−1.22131e10	+	1.22131e10i	−1.37491	+	1.37491i	−0.853005	+	0.521903i	$0.825222\pi$
$308$	1.85311e9	−	9.44206e8i	0.205920	−	0.104921i
$309$	−9.13372e8	−	1.25715e9i	−0.100188	−	0.137896i
$310$	6.84115e6	−	2.99049e8i	0.000740769	−	0.0323813i
$311$	−3.02027e9	−	2.19436e9i	−0.322853	−	0.234566i	0.414539	−	0.910032i	$-0.363943\pi$
$311$	−3.02027e9	−	2.19436e9i	−0.322853	−	0.234566i	−0.737392	+	0.675465i	$0.763943\pi$
$312$	−1.01004e9	+	6.37712e9i	−0.106591	+	0.672986i
$313$	−8.69913e8	−	1.37781e8i	−0.0906355	−	0.0143553i	0.110952	−	0.993826i	$-0.464610\pi$
$313$	−8.69913e8	−	1.37781e8i	−0.0906355	−	0.0143553i	−0.201587	+	0.979471i	$0.564610\pi$
$314$	−1.21796e9	+	1.67638e9i	−0.125289	+	0.172446i
$315$	2.04101e9	+	4.66909e7i	0.207302	+	0.00474231i
$316$	−5.59237e8	+	4.06309e8i	−0.0560851	+	0.0407482i
$317$	−7.10020e9	−	1.39349e10i	−0.703127	−	1.37996i	−0.915317	−	0.402735i	$-0.868060\pi$
$317$	−7.10020e9	−	1.39349e10i	−0.703127	−	1.37996i	0.212190	−	0.977228i	$-0.431940\pi$
$318$	−3.43238e9	−	3.43238e9i	−0.335650	−	0.335650i
$319$	3.05506e9	+	9.92650e8i	0.295024	+	0.0958591i
$320$	5.47558e9	−	1.01648e10i	0.522192	−	0.969390i
$321$	1.29010e9	+	3.97051e9i	0.121507	+	0.373961i
$322$	−1.56650e9	−	7.98173e8i	−0.145716	−	0.0742461i
$323$	−5.55130e8	−	3.50495e9i	−0.0510017	−	0.322012i
$324$		−	3.43382e8i		−	0.0311600i
$325$	−1.20473e10	+	1.34686e9i	−1.07983	+	0.120722i
$326$	−6.13875e7			−0.00543512
$327$	1.29184e10	−	2.04608e9i	1.12985	−	0.178950i
$328$	4.60733e9	−	9.04239e9i	0.398065	−	0.781246i
$329$	−6.96380e9	+	2.26267e9i	−0.594378	+	0.193125i
$330$	−5.56369e9	+	5.31483e9i	−0.469145	+	0.448160i
$331$	−1.33813e9	+	4.11834e9i	−0.111477	+	0.343092i	−0.991196	−	0.132403i	$-0.957731\pi$
$331$	−1.33813e9	+	4.11834e9i	−0.111477	+	0.343092i	0.879719	+	0.475494i	$0.157731\pi$
$332$	−5.31034e8	+	5.31034e8i	−0.0437089	+	0.0437089i
$333$	5.84706e9	−	2.97923e9i	0.475511	−	0.242285i
$334$	1.69781e8	+	2.33684e8i	0.0136428	+	0.0187777i
$335$	−2.33114e9	−	3.36792e9i	−0.185093	−	0.267413i
$336$	−2.37351e9	−	1.72446e9i	−0.186223	−	0.135299i
$337$	9.96059e8	−	6.28887e9i	0.0772263	−	0.487588i	−0.918514	−	0.395388i	$-0.870610\pi$
$337$	9.96059e8	−	6.28887e9i	0.0772263	−	0.487588i	0.995741	−	0.0921998i	$-0.0293898\pi$
$338$	−1.97504e9	−	3.12815e8i	−0.151324	−	0.0239674i
$339$	4.91161e9	−	6.76025e9i	0.371899	−	0.511875i
$340$	−1.01035e9	−	7.69970e8i	−0.0756057	−	0.0576180i
$341$	−5.53337e8	+	4.02023e8i	−0.0409235	+	0.0297326i
$342$	−1.68914e9	−	3.31513e9i	−0.123470	−	0.242324i
$343$	−9.82069e9	−	9.82069e9i	−0.709521	−	0.709521i
$344$	1.90428e10	+	6.18738e9i	1.35987	+	0.441848i
$345$	−2.49403e9	−	4.53714e8i	−0.176046	−	0.0320262i
$346$	1.78828e9	+	5.50375e9i	0.124776	+	0.384020i
$347$	−3.25825e9	−	1.66016e9i	−0.224733	−	0.114507i	0.337999	−	0.941146i	$-0.390250\pi$
$347$	−3.25825e9	−	1.66016e9i	−0.224733	−	0.114507i	−0.562732	+	0.826639i	$0.690250\pi$
$348$	8.69841e7	+	5.49196e8i	0.00593093	+	0.0374464i
$349$			6.06099e9i			0.408547i	0.978914	+	0.204273i	$0.0654832\pi$
$349$			6.06099e9i			0.408547i	−0.978914	+	0.204273i	$0.934517\pi$
$350$	2.78877e9	−	7.41117e9i	0.185841	−	0.493872i
$351$	3.17396e9			0.209109
$352$	−1.08974e10	+	1.72598e9i	−0.709825	+	0.112425i
$353$	2.07890e9	−	4.08007e9i	0.133886	−	0.262766i	−0.814324	−	0.580411i	$-0.802892\pi$
$353$	2.07890e9	−	4.08007e9i	0.133886	−	0.262766i	0.948210	+	0.317645i	$0.102892\pi$
$354$	−1.39863e10	+	4.54441e9i	−0.890612	+	0.289377i
$355$	−8.99713e9	−	1.87034e10i	−0.566488	−	1.17763i
$356$	1.14307e9	−	3.51801e9i	0.0711661	−	0.219027i
$357$	−1.39825e9	+	1.39825e9i	−0.0860818	+	0.0860818i
$358$	−1.47304e10	+	7.50553e9i	−0.896774	+	0.456929i
$359$	1.12201e10	+	1.54432e10i	0.675491	+	0.929734i	0.999869	−	0.0161937i	$-0.00515484\pi$
$359$	1.12201e10	+	1.54432e10i	0.675491	+	0.929734i	−0.324378	+	0.945928i	$0.605155\pi$
$360$	−5.73897e9	−	2.01094e9i	−0.341684	−	0.119726i
$361$	−1.02864e9	−	7.47347e8i	−0.0605665	−	0.0440042i
$362$	2.56965e9	−	1.62241e10i	0.149637	−	0.944772i
$363$	7.47547e9	+	1.18400e9i	0.430538	+	0.0681906i
$364$	−1.95594e9	+	2.69212e9i	−0.111417	+	0.153352i
$365$	−4.95528e9	−	1.65278e10i	−0.279188	−	0.931201i
$366$	−1.38678e10	+	1.00755e10i	−0.772828	+	0.561493i
$367$	2.51101e9	+	4.92813e9i	0.138415	+	0.271655i	0.949800	−	0.312857i	$-0.101286\pi$
$367$	2.51101e9	+	4.92813e9i	0.138415	+	0.271655i	−0.811385	+	0.584512i	$0.801286\pi$
$368$	2.57592e9	+	2.57592e9i	0.140456	+	0.140456i
$369$	−4.74466e9	−	1.54163e9i	−0.255917	−	0.0831525i
$370$	−3.40575e9	−	2.52243e10i	−0.181721	−	1.34590i
$371$	−3.52975e9	−	1.08635e10i	−0.186315	−	0.573420i
$372$	−1.05489e8	−	5.37493e7i	−0.00550852	−	0.00280673i
$373$	−4.11662e9	−	2.59913e10i	−0.212670	−	1.34274i	−0.830758	−	0.556634i	$-0.812092\pi$
$373$	−4.11662e9	−	2.59913e10i	−0.212670	−	1.34274i	0.618088	−	0.786109i	$-0.287908\pi$
$374$		−	7.45262e9i		−	0.380910i
$375$	7.82811e8	−	1.13905e10i	0.0395851	−	0.575992i
$376$	2.18104e10			1.09122
$377$	−5.07634e9	+	8.04014e8i	−0.251296	+	0.0398014i
$378$	−9.41246e8	+	1.84730e9i	−0.0461037	+	0.0904836i
$379$	−1.94588e10	+	6.32254e9i	−0.943102	+	0.306432i	−0.739909	−	0.672707i	$-0.765132\pi$
$379$	−1.94588e10	+	6.32254e9i	−0.943102	+	0.306432i	−0.203192	+	0.979139i	$0.565132\pi$
$380$	5.57383e9	−	7.52572e8i	0.267313	−	0.0360922i
$381$	−1.13107e9	+	3.48107e9i	−0.0536771	+	0.165201i
$382$	9.69743e9	−	9.69743e9i	0.455411	−	0.455411i
$383$	−1.59139e10	+	8.10855e9i	−0.739575	+	0.376832i	−0.782833	−	0.622232i	$-0.786226\pi$
$383$	−1.59139e10	+	8.10855e9i	−0.739575	+	0.376832i	0.0432582	+	0.999064i	$0.486226\pi$
$384$	2.88901e9	+	3.97639e9i	0.132869	+	0.182879i
$385$	−1.73432e10	+	5.19975e9i	−0.789380	+	0.236668i
$386$	−4.33321e8	−	3.14826e8i	−0.0195191	−	0.0141815i
$387$	1.53976e9	−	9.72167e9i	0.0686451	−	0.433408i
$388$	9.91940e9	+	1.57108e9i	0.437682	+	0.0693220i
$389$	−1.75269e9	+	2.41237e9i	−0.0765432	+	0.105353i	−0.845572	−	0.533862i	$-0.820740\pi$
$389$	−1.75269e9	+	2.41237e9i	−0.0765432	+	0.105353i	0.769029	+	0.639214i	$0.220740\pi$
$390$	4.07102e9	−	1.16182e10i	0.175972	−	0.502203i
$391$	1.98642e9	−	1.44322e9i	0.0849891	−	0.0617482i
$392$	7.13784e9	+	1.40088e10i	0.302289	+	0.593276i
$393$	1.39736e10	+	1.39736e10i	0.585785	+	0.585785i
$394$	1.83116e10	+	5.94981e9i	0.759874	+	0.246898i
$395$	5.42299e9	−	2.60868e9i	0.222767	−	0.107160i
$396$	9.41069e8	+	2.89631e9i	0.0382684	+	0.117778i
$397$	4.11641e10	+	2.09742e10i	1.65713	+	0.844351i	0.995525	+	0.0945003i	$0.0301253\pi$
$397$	4.11641e10	+	2.09742e10i	1.65713	+	0.844351i	0.661607	+	0.749851i	$0.269875\pi$
$398$	2.82088e8	+	1.78103e9i	0.0112422	+	0.0709805i
$399$		−	8.75530e9i		−	0.345446i
$400$	−1.02409e10	+	1.28190e10i	−0.400036	+	0.500741i
$401$	−7.81494e9			−0.302237			−0.151119	−	0.988516i	$-0.548288\pi$
$401$	−7.81494e9			−0.302237			−0.151119	+	0.988516i	$0.548288\pi$
$402$	4.10843e9	−	6.50712e8i	0.157316	−	0.0249163i
$403$	4.96817e8	−	9.75057e8i	0.0188354	−	0.0369666i
$404$	−7.32731e9	+	2.38079e9i	−0.275055	+	0.0893707i
$405$	−5.35042e8	+	2.94108e9i	−0.0198869	+	0.109317i
$406$	1.03745e9	−	3.19296e9i	0.0381825	−	0.117514i
$407$	−4.11532e10	+	4.11532e10i	−1.49977	+	1.49977i
$408$	5.24811e9	−	2.67405e9i	0.189392	−	0.0965002i
$409$	−1.31716e10	−	1.81292e10i	−0.470703	−	0.647867i	0.505982	−	0.862544i	$-0.331130\pi$
$409$	−1.31716e10	−	1.81292e10i	−0.470703	−	0.647867i	−0.976685	+	0.214677i	$0.931130\pi$
$410$	−1.17288e10	+	1.53903e10i	−0.415065	+	0.544644i
$411$	−1.28442e9	−	9.33187e8i	−0.0450133	−	0.0327040i
$412$	−3.73178e8	+	2.35616e9i	−0.0129517	+	0.0817740i
$413$	−3.41796e10	−	5.41352e9i	−1.17481	−	0.186071i
$414$	1.51317e9	−	2.08270e9i	0.0515094	−	0.0708967i
$415$	5.37577e9	−	3.72091e9i	0.181238	−	0.125446i
$416$	1.42816e10	−	1.03762e10i	0.476874	−	0.346469i
$417$	2.68397e9	+	5.26759e9i	0.0887634	+	0.174208i
$418$	2.33328e10	+	2.33328e10i	0.764295	+	0.764295i
$419$	−2.92327e10	−	9.49828e9i	−0.948446	−	0.308169i	−0.206362	−	0.978476i	$-0.566163\pi$
$419$	−2.92327e10	−	9.49828e9i	−0.948446	−	0.308169i	−0.742084	+	0.670307i	$0.766163\pi$
$420$	−2.16488e9	−	2.26625e9i	−0.0695725	−	0.0728301i
$421$	2.05824e8	+	6.33463e8i	0.00655192	+	0.0201647i	0.954279	−	0.298917i	$-0.0966255\pi$
$421$	2.05824e8	+	6.33463e8i	0.00655192	+	0.0201647i	−0.947727	+	0.319082i	$0.896625\pi$
$422$	−8.18442e9	−	4.17017e9i	−0.258070	−	0.131493i
$423$	−1.67722e9	−	1.05896e10i	−0.0523878	−	0.330763i
$424$			3.40240e10i			1.05274i
$425$	7.45394e9	+	8.16911e9i	0.228470	+	0.250391i
$426$	2.10775e10			0.640001
$427$	−3.98402e10	+	6.31007e9i	−1.19842	+	0.189811i
$428$	2.90966e9	−	5.71053e9i	0.0867095	−	0.170177i
$429$	−2.67713e10	+	8.69851e9i	−0.790387	+	0.256812i
$430$	−3.36110e10	−	1.81056e10i	−0.983121	−	0.529589i
$431$	1.68515e10	−	5.18635e10i	0.488348	−	1.50298i	−0.338726	−	0.940885i	$-0.609996\pi$
$431$	1.68515e10	−	5.18635e10i	0.488348	−	1.50298i	0.827073	−	0.562094i	$-0.190004\pi$
$432$	3.03765e9	−	3.03765e9i	0.0872173	−	0.0872173i
$433$	5.03046e10	−	2.56315e10i	1.43105	−	0.729158i	0.444992	−	0.895535i	$-0.353207\pi$
$433$	5.03046e10	−	2.56315e10i	1.43105	−	0.729158i	0.986062	+	0.166376i	$0.0532066\pi$
$434$	4.20169e8	+	5.78312e8i	0.0118431	+	0.0163006i
$435$	1.10709e8	−	4.83943e9i	0.00309190	−	0.135157i
$436$	−1.62444e10	−	1.18022e10i	−0.449529	−	0.326602i
$437$	−1.70066e9	+	1.07375e10i	−0.0466327	+	0.294428i
$438$	1.73071e10	+	2.74117e9i	0.470249	+	0.0744801i
$439$	3.00096e9	−	4.13046e9i	0.0807982	−	0.111209i	−0.766705	−	0.642000i	$-0.778105\pi$
$439$	3.00096e9	−	4.13046e9i	0.0807982	−	0.111209i	0.847503	+	0.530791i	$0.178105\pi$
$440$	5.39175e10	+	1.23344e9i	1.43853	+	0.0329084i
$441$	6.25279e9	−	4.54292e9i	0.165318	−	0.120110i
$442$	5.41344e9	+	1.06245e10i	0.141835	+	0.278367i
$443$	−1.99836e10	−	1.99836e10i	−0.518870	−	0.518870i	0.398359	−	0.917229i	$-0.369580\pi$
$443$	−1.99836e10	−	1.99836e10i	−0.518870	−	0.518870i	−0.917229	+	0.398359i	$0.869580\pi$
$444$	−9.58117e9	−	3.11311e9i	−0.246539	−	0.0801055i
$445$	−1.52721e10	+	2.83509e10i	−0.389455	+	0.722980i
$446$	1.29803e10	+	3.99492e10i	0.328053	+	1.00964i
$447$	1.53739e10	+	7.83337e9i	0.385082	+	0.196209i
$448$	4.31624e9	+	2.72517e10i	0.107150	+	0.676520i
$449$			4.62548e10i			1.13808i	0.822311	+	0.569038i	$0.192684\pi$
$449$			4.62548e10i			1.13808i	−0.822311	+	0.569038i	$0.807316\pi$
$450$	1.00795e10	+	5.73084e9i	0.245804	+	0.139755i
$451$	4.42446e10			1.06943
$452$	−1.26701e10	+	2.00675e9i	−0.303547	+	0.0480772i
$453$	−3.80205e9	+	7.46194e9i	−0.0902869	+	0.177198i
$454$	5.11826e10	−	1.66302e10i	1.20476	−	0.391449i
$455$	2.09475e10	−	2.00105e10i	0.488749	−	0.466888i
$456$	−8.05891e9	+	2.48028e10i	−0.186388	+	0.573642i
$457$	4.11115e10	−	4.11115e10i	0.942536	−	0.942536i	−0.0559002	−	0.998436i	$-0.517803\pi$
$457$	4.11115e10	−	4.11115e10i	0.942536	−	0.942536i	0.998436	+	0.0559002i	$0.0178029\pi$
$458$	−6.11173e10	+	3.11408e10i	−1.38900	+	0.707730i
$459$	−1.70191e9	−	2.34248e9i	−0.0383430	−	0.0527746i
$460$	2.21482e9	+	3.19985e9i	0.0494659	+	0.0714658i
$461$	−2.12068e10	−	1.54077e10i	−0.469539	−	0.341140i	0.327722	−	0.944774i	$-0.393719\pi$
$461$	−2.12068e10	−	1.54077e10i	−0.469539	−	0.341140i	−0.797262	+	0.603634i	$0.793719\pi$
$462$	2.87641e9	−	1.81609e10i	0.0631368	−	0.398630i
$463$	1.74887e10	+	2.76994e9i	0.380569	+	0.0602762i	0.343788	−	0.939047i	$-0.388290\pi$
$463$	1.74887e10	+	2.76994e9i	0.380569	+	0.0602762i	0.0367807	+	0.999323i	$0.488290\pi$
$464$	−4.08885e9	+	5.62782e9i	−0.0882124	+	0.121414i
$465$	8.19768e8	+	6.24733e8i	0.0175339	+	0.0133624i
$466$	3.89200e10	−	2.82770e10i	0.825333	−	0.599639i
$467$	−3.84731e10	−	7.55078e10i	−0.808891	−	1.58754i	−0.809196	−	0.587538i	$-0.800097\pi$
$467$	−3.84731e10	−	7.55078e10i	−0.808891	−	1.58754i	0.000305089	−	1.00000i	$-0.499903\pi$
$468$	−3.44541e9	−	3.44541e9i	−0.0718220	−	0.0718220i
$469$	9.30924e9	+	3.02476e9i	0.192408	+	0.0625171i
$470$	−4.09142e10	−	7.44310e9i	−0.838460	−	0.152533i
$471$	−2.20631e9	−	6.79033e9i	−0.0448315	−	0.137977i
$472$	9.18440e10	+	4.67969e10i	1.85047	+	0.942863i
$473$	1.36557e10	+	8.62189e10i	0.272816	+	1.72249i
$474$			6.11134e9i			0.121066i
$475$	−4.89128e10	−	2.23907e9i	−0.960834	−	0.0439838i
$476$	3.03567e9			0.0591326
$477$	1.65197e10	−	2.61646e9i	0.319101	−	0.0505406i
$478$	−1.80100e10	+	3.53466e10i	−0.344987	+	0.677074i
$479$	−8.80545e10	+	2.86106e10i	−1.67267	+	0.543482i	−0.983467	−	0.181089i	$-0.942038\pi$
$479$	−8.80545e10	+	2.86106e10i	−1.67267	+	0.543482i	−0.689200	+	0.724571i	$0.742038\pi$
$480$	7.20741e9	+	1.49829e10i	0.135773	+	0.282248i
$481$	2.87752e10	−	8.85609e10i	0.537573	−	1.65448i
$482$	3.07485e10	−	3.07485e10i	0.569686	−	0.569686i
$483$	5.39762e9	−	2.75022e9i	0.0991776	−	0.0505335i
$484$	−6.82955e9	−	9.40007e9i	−0.124455	−	0.171297i
$485$	−8.25122e10	−	2.89123e10i	−1.49125	−	0.522536i
$486$	−2.45603e9	−	1.78441e9i	−0.0440239	−	0.0319852i
$487$	−3.58718e9	+	2.26486e10i	−0.0637731	+	0.402647i	0.935066	+	0.354474i	$0.115340\pi$
$487$	−3.58718e9	+	2.26486e10i	−0.0637731	+	0.402647i	−0.998839	+	0.0481735i	$0.984660\pi$
$488$	1.18671e11	+	1.87956e10i	2.09250	+	0.331419i
$489$	1.24328e8	−	1.71123e8i	0.00217437	−	0.00299277i
$490$	−8.60920e9	−	2.87151e10i	−0.149341	−	0.498110i
$491$	−2.20603e10	+	1.60278e10i	−0.379565	+	0.275770i	−0.761166	−	0.648557i	$-0.775373\pi$
$491$	−2.20603e10	+	1.60278e10i	−0.379565	+	0.275770i	0.381601	+	0.924327i	$0.375373\pi$
$492$	3.47697e9	+	6.82393e9i	0.0593390	+	0.116459i
$493$	3.31538e9	+	3.31538e9i	0.0561237	+	0.0561237i
$494$	−5.02117e10	−	1.63148e10i	−0.843134	−	0.273951i
$495$	−3.54740e9	−	2.62734e10i	−0.0590867	−	0.437618i
$496$	−4.57703e8	−	1.40866e9i	−0.00756235	−	0.0232745i
$497$	4.41928e10	+	2.25174e10i	0.724313	+	0.369056i
$498$	1.03865e9	+	6.55777e9i	0.0168869	+	0.106620i
$499$			2.44003e10i			0.393544i	0.980449	+	0.196772i	$0.0630458\pi$
$499$			2.44003e10i			0.393544i	−0.980449	+	0.196772i	$0.936954\pi$
$500$	−1.32144e10	+	1.15149e10i	−0.211430	+	0.184238i
$501$	−9.95274e8			−0.0157976
$502$	−1.83692e10	+	2.90939e9i	−0.289251	+	0.0458129i
$503$	−3.44302e10	+	6.75731e10i	−0.537858	+	1.05561i	0.448927	+	0.893569i	$0.351806\pi$
$503$	−3.44302e10	+	6.75731e10i	−0.537858	+	1.05561i	−0.986785	+	0.162037i	$0.948194\pi$
$504$	1.38209e10	−	4.49069e9i	0.214198	−	0.0695971i
$505$	6.64684e10	−	8.97449e9i	1.02200	−	0.137989i
$506$	−7.05527e9	+	2.17139e10i	−0.107625	+	0.331234i
$507$	4.87204e9	−	4.87204e9i	0.0737359	−	0.0737359i
$508$	5.00660e9	−	2.55099e9i	0.0751775	−	0.0383049i
$509$	2.10022e10	+	2.89070e10i	0.312891	+	0.430657i	0.936280	−	0.351254i	$-0.114245\pi$
$509$	2.10022e10	+	2.89070e10i	0.312891	+	0.430657i	−0.623389	+	0.781912i	$0.714245\pi$
$510$	−1.07575e10	+	3.22526e9i	−0.159013	+	0.0476743i
$511$	3.33590e10	+	2.42368e10i	0.489249	+	0.355460i
$512$	1.12212e10	−	7.08478e10i	0.163290	−	1.03097i
$513$	1.26622e10	+	2.00550e9i	0.182827	+	0.0289570i
$514$	−3.35795e10	+	4.62181e10i	−0.481084	+	0.662156i
$515$	6.86755e9	−	1.95991e10i	0.0976277	−	0.278617i
$516$	−1.22246e10	+	8.88167e9i	−0.172439	+	0.125284i
$517$	4.31685e10	+	8.47230e10i	0.604234	+	1.18588i
$518$	4.30107e10	+	4.30107e10i	0.597389	+	0.597389i
$519$	−1.89640e10	−	6.16177e9i	−0.261372	−	0.0849251i
$520$	−7.77608e10	+	3.74062e10i	−1.06352	+	0.511599i
$521$	−1.68533e10	−	5.18692e10i	−0.228736	−	0.703977i	−0.997891	−	0.0649148i	$-0.979322\pi$
$521$	−1.68533e10	−	5.18692e10i	−0.228736	−	0.703977i	0.769155	−	0.639063i	$-0.220678\pi$
$522$	4.38013e9	+	2.23179e9i	0.0589936	+	0.0300587i
$523$	−1.08800e10	−	6.86934e10i	−0.145419	−	0.918139i	−0.947228	−	0.320559i	$-0.896129\pi$
$523$	−1.08800e10	−	6.86934e10i	−0.145419	−	0.918139i	0.801810	−	0.597580i	$-0.203871\pi$
$524$		−	3.03374e10i		−	0.402396i
$525$	1.50112e10	+	2.27838e10i	0.197596	+	0.299909i
$526$	−2.08964e10			−0.272979
$527$	−9.86023e8	+	1.56171e8i	−0.0127833	+	0.00202468i
$528$	−1.72966e10	+	3.39465e10i	−0.222549	+	0.436777i
$529$	6.73243e10	−	2.18750e10i	0.859705	−	0.279335i
$530$	1.16112e10	−	6.38258e10i	0.147154	−	0.808896i
$531$	1.56584e10	−	4.81917e10i	0.196957	−	0.606170i
$532$	−9.50411e9	+	9.50411e9i	−0.118649	+	0.118649i
$533$	−6.30751e10	+	3.21384e10i	−0.781536	+	0.398213i
$534$	−1.92224e10	−	2.64574e10i	−0.236397	−	0.325373i
$535$	−3.38193e10	+	4.43773e10i	−0.412809	+	0.541683i
$536$	−2.35879e10	−	1.71376e10i	−0.285778	−	0.207630i
$537$	8.91123e9	−	5.62633e10i	0.107162	−	0.676594i
$538$	−8.50962e10	−	1.34779e10i	−1.01574	−	0.160877i
$539$	−4.02899e10	+	5.54543e10i	−0.477355	+	0.657023i
$540$	3.77343e9	−	2.61182e9i	0.0443773	−	0.0307163i
$541$	5.89586e8	−	4.28360e8i	0.00688269	−	0.00500057i	−0.584339	−	0.811510i	$-0.698646\pi$
$541$	5.89586e8	−	4.28360e8i	0.00688269	−	0.00500057i	0.591221	+	0.806509i	$0.298646\pi$
$542$	2.12964e10	+	4.17965e10i	0.246779	+	0.484331i
$543$	4.00218e10	+	4.00218e10i	0.460360	+	0.460360i
$544$	−1.53159e10	−	4.97645e9i	−0.174883	−	0.0568229i
$545$	1.20744e11	+	1.26398e11i	1.36861	+	1.43270i
$546$	9.09112e9	+	2.79796e10i	0.102293	+	0.314826i
$547$	6.59619e10	+	3.36093e10i	0.736790	+	0.375413i	0.781764	−	0.623575i	$-0.214320\pi$
$547$	6.59619e10	+	3.36093e10i	0.736790	+	0.375413i	−0.0449735	+	0.998988i	$0.514320\pi$
$548$	3.81274e8	+	2.40727e9i	0.00422781	+	0.0266933i
$549$		−	5.90637e10i		−	0.650176i
$550$	−1.00723e11	−	2.07139e10i	−1.10072	−	0.226366i
$551$	−2.07597e10			−0.225224
$552$	−1.78223e10	+	2.82278e9i	−0.191959	+	0.0304033i
$553$	−6.52882e9	+	1.28135e10i	−0.0698127	+	0.137015i
$554$	7.38220e10	−	2.39862e10i	0.783695	−	0.254638i
$555$	7.72125e10	+	4.15929e10i	0.813797	+	0.438377i
$556$	2.80459e9	−	8.63163e9i	0.0293474	−	0.0903220i
$557$	3.18146e10	−	3.18146e10i	0.330526	−	0.330526i	−0.522260	−	0.852786i	$-0.674911\pi$
$557$	3.18146e10	−	3.18146e10i	0.330526	−	0.330526i	0.852786	+	0.522260i	$0.174911\pi$
$558$	−9.32620e8	+	4.75194e8i	−0.00961985	+	0.00490156i
$559$	−8.20953e10	−	1.12995e11i	−0.840758	−	1.15720i
$560$	8.96733e8	−	3.91991e10i	0.00911824	−	0.398587i
$561$	2.07748e10	+	1.50938e10i	0.209742	+	0.152387i
$562$	−2.29597e10	+	1.44962e11i	−0.230156	+	1.45314i
$563$	8.34988e10	+	1.32249e10i	0.831087	+	0.131631i	0.557459	−	0.830204i	$-0.311776\pi$
$563$	8.34988e10	+	1.32249e10i	0.831087	+	0.131631i	0.273628	+	0.961836i	$0.411776\pi$
$564$	−9.67459e9	+	1.33159e10i	−0.0956129	+	0.131600i
$565$	1.11647e11	+	2.55408e9i	1.09560	+	0.0250635i
$566$	8.34125e10	−	6.06027e10i	0.812765	−	0.590509i
$567$	−3.24320e9	−	6.36514e9i	−0.0313792	−	0.0615851i
$568$	−1.04467e11	−	1.04467e11i	−1.00366	−	1.00366i
$569$	−1.49770e11	−	4.86633e10i	−1.42882	−	0.464250i	−0.510424	−	0.859923i	$-0.670511\pi$
$569$	−1.49770e11	−	4.86633e10i	−1.42882	−	0.464250i	−0.918392	+	0.395673i	$0.870511\pi$
$570$	2.35821e10	−	4.37774e10i	0.223400	−	0.414716i
$571$	−4.47483e10	−	1.37721e11i	−0.420951	−	1.29556i	−0.906818	−	0.421522i	$-0.861496\pi$
$571$	−4.47483e10	−	1.37721e11i	−0.420951	−	1.29556i	0.485867	−	0.874033i	$-0.338504\pi$
$572$	3.85034e10	+	1.96184e10i	0.359679	+	0.183265i
$573$	7.39222e9	+	4.66726e10i	0.0685735	+	0.432956i
$574$		−	4.62416e10i		−	0.425976i
$575$	−1.39842e10	−	3.08579e10i	−0.127928	−	0.282290i
$576$	−4.04010e10			−0.367030
$577$	−1.06506e9	+	1.68689e8i	−0.00960883	+	0.00152189i	−0.161237	−	0.986916i	$-0.551548\pi$
$577$	−1.06506e9	+	1.68689e8i	−0.00960883	+	0.00152189i	0.151628	+	0.988438i	$0.451548\pi$
$578$	−3.80440e10	+	7.46657e10i	−0.340859	+	0.668974i
$579$	1.75521e9	−	5.70303e8i	0.0156176	−	0.00507448i
$580$	−5.37350e9	+	5.13315e9i	−0.0474838	+	0.0453599i
$581$	−4.82803e9	+	1.48592e10i	−0.0423707	+	0.130404i
$582$	6.27840e10	−	6.27840e10i	0.547213	−	0.547213i
$583$	−1.32167e11	+	6.73426e10i	−1.14406	+	0.582929i
$584$	−7.21934e10	−	9.93657e10i	−0.620649	−	0.854250i
$585$	2.41417e10	+	3.48786e10i	0.206131	+	0.297808i
$586$	−1.52468e11	−	1.10774e11i	−1.29297	−	0.939395i
$587$	3.51775e10	−	2.22102e11i	0.296287	−	1.87068i	−0.169134	−	0.985593i	$-0.554097\pi$
$587$	3.51775e10	−	2.22102e11i	0.296287	−	1.87068i	0.465421	−	0.885090i	$-0.345903\pi$
$588$	−1.17190e10	−	1.85611e9i	−0.0980352	−	0.0155273i
$589$	2.59811e9	−	3.57599e9i	0.0215872	−	0.0297122i
$590$	−1.56320e11	−	1.19130e11i	−1.29005	−	0.983131i
$591$	−5.36721e10	+	3.89951e10i	−0.439946	+	0.319639i
$592$	−5.72182e10	−	1.12297e11i	−0.465851	−	0.914285i
$593$	6.44283e10	+	6.44283e10i	0.521024	+	0.521024i	0.917881	−	0.396856i	$-0.129899\pi$
$593$	6.44283e10	+	6.44283e10i	0.521024	+	0.521024i	−0.396856	+	0.917881i	$0.629899\pi$
$594$	2.56061e10	+	8.31993e9i	0.205683	+	0.0668304i
$595$	−2.60007e10	−	4.73004e9i	−0.207452	−	0.0377396i
$596$	−8.18540e9	−	2.51921e10i	−0.0648716	−	0.199654i
$597$	−5.53609e9	−	2.82078e9i	−0.0435819	−	0.0222061i
$598$	−5.71453e9	−	3.60801e10i	−0.0446865	−	0.282139i
$599$			7.20834e10i			0.559922i	0.960011	+	0.279961i	$0.0903216\pi$
$599$			7.20834e10i			0.559922i	−0.960011	+	0.279961i	$0.909678\pi$
$600$	−2.15534e10	−	7.83612e10i	−0.166307	−	0.604639i
$601$	2.24802e11			1.72306			0.861532	−	0.507703i	$-0.169505\pi$
$601$	2.24802e11			1.72306			0.861532	+	0.507703i	$0.169505\pi$
$602$	9.01105e10	−	1.42721e10i	0.686103	−	0.108668i
$603$	−6.50689e9	+	1.27705e10i	−0.0492158	+	0.0965914i
$604$	1.22273e10	−	3.97291e9i	0.0918723	−	0.0298511i
$605$	4.38487e10	+	9.11537e10i	0.327292	+	0.680382i
$606$	−2.10484e10	+	6.47803e10i	−0.156073	+	0.480344i
$607$	−1.18049e11	+	1.18049e11i	−0.869576	+	0.869576i	−0.992425	−	0.122850i	$-0.960797\pi$
$607$	−1.18049e11	+	1.18049e11i	−0.869576	+	0.869576i	0.122850	+	0.992425i	$0.460797\pi$
$608$	6.35316e10	−	3.23710e10i	0.464917	−	0.236887i
$609$	6.79949e9	+	9.35869e9i	0.0494319	+	0.0680371i
$610$	−2.16201e11	−	7.57570e10i	−1.56149	−	0.547146i
$611$	−1.23082e11	−	8.94245e10i	−0.883142	−	0.641640i
$612$	−6.95354e8	+	4.39029e9i	−0.00495679	+	0.0312959i
$613$	−1.09155e11	−	1.72885e10i	−0.773040	−	0.122437i	−0.242561	−	0.970136i	$-0.577988\pi$
$613$	−1.09155e11	−	1.72885e10i	−0.773040	−	0.122437i	−0.530478	+	0.847699i	$0.677988\pi$
$614$	1.37789e11	−	1.89650e11i	0.969485	−	1.33438i
$615$	−1.91477e10	−	6.38650e10i	−0.133849	−	0.446439i
$616$	−1.04268e11	+	7.57550e10i	−0.724149	+	0.526125i
$617$	1.13480e11	+	2.22718e11i	0.783033	+	1.53679i	0.842585	+	0.538564i	$0.181033\pi$
$617$	1.13480e11	+	2.22718e11i	0.783033	+	1.53679i	−0.0595513	+	0.998225i	$0.518967\pi$
$618$	1.49131e10	+	1.49131e10i	0.102238	+	0.102238i
$619$	9.39845e10	+	3.05374e10i	0.640167	+	0.208003i	0.611074	−	0.791574i	$-0.290738\pi$
$619$	9.39845e10	+	3.05374e10i	0.640167	+	0.208003i	0.0290936	+	0.999577i	$0.490738\pi$
$620$	−2.11716e8	−	1.56804e9i	−0.00143280	−	0.0106119i
$621$	2.74109e9	+	8.43620e9i	0.0184313	+	0.0567258i
$622$	4.51464e10	+	2.30032e10i	0.301621	+	0.153683i
$623$	−1.20385e10	−	7.60082e10i	−0.0799136	−	0.504555i
$624$		−	6.09581e10i		−	0.402062i
$625$	1.31124e11	−	7.80355e10i	0.859335	−	0.511414i
$626$	1.19539e10			0.0778416
$627$	−1.12298e11	+	1.77863e10i	−0.726611	+	0.115084i
$628$	−4.97607e9	+	9.76609e9i	−0.0319925	+	0.0627888i
$629$	−8.07904e10	+	2.62504e10i	−0.516127	+	0.167700i
$630$	−2.74593e10	+	3.70752e9i	−0.174312	+	0.0235354i
$631$	8.58083e10	−	2.64091e11i	0.541267	−	1.66585i	−0.188436	−	0.982085i	$-0.560342\pi$
$631$	8.58083e10	−	2.64091e11i	0.541267	−	1.66585i	0.729704	−	0.683764i	$-0.239658\pi$
$632$	3.02898e10	−	3.02898e10i	0.189857	−	0.189857i
$633$	2.82006e10	−	1.43689e10i	0.175648	−	0.0894973i
$634$	1.24766e11	+	1.71726e11i	0.772216	+	1.06286i
$635$	−4.68566e10	+	1.40483e10i	−0.288188	+	0.0864031i
$636$	−2.07728e10	−	1.50923e10i	−0.126960	−	0.0922416i
$637$	1.71565e10	−	1.08322e11i	0.104200	−	0.657896i
$638$	−4.30613e10	−	6.82024e9i	−0.259899	−	0.0411640i
$639$	−4.26883e10	+	5.87554e10i	−0.256038	+	0.352407i
$640$	−2.17222e10	+	6.19925e10i	−0.129474	+	0.369504i
$641$	−1.63678e11	+	1.18919e11i	−0.969523	+	0.704400i	−0.955343	−	0.295500i	$-0.904514\pi$
$641$	−1.63678e11	+	1.18919e11i	−0.969523	+	0.704400i	−0.0141802	+	0.999899i	$0.504514\pi$
$642$	−2.57241e10	−	5.04864e10i	−0.151426	−	0.297190i
$643$	1.13630e11	+	1.13630e11i	0.664737	+	0.664737i	0.956493	−	0.291756i	$-0.0942395\pi$
$643$	1.13630e11	+	1.13630e11i	0.664737	+	0.664737i	−0.291756	+	0.956493i	$0.594239\pi$
$644$	−8.84469e9	−	2.87382e9i	−0.0514209	−	0.0167077i
$645$	1.18543e11	−	5.70243e10i	0.684917	−	0.329474i
$646$	1.48833e10	+	4.58060e10i	0.0854610	+	0.263022i
$647$	1.26044e11	+	6.42227e10i	0.719293	+	0.366498i	0.775010	−	0.631949i	$-0.217745\pi$
$647$	1.26044e11	+	6.42227e10i	0.719293	+	0.366498i	−0.0557174	+	0.998447i	$0.517745\pi$
$648$	3.32876e9	+	2.10170e10i	0.0188792	+	0.119198i
$649$			4.49394e11i			2.53308i
$650$	1.58637e11	−	4.36335e10i	0.888693	−	0.244437i
$651$	−2.46306e9			−0.0137136
$652$	−3.20720e8	+	5.07970e7i	−0.00177474	+	0.000281092i
$653$	9.15770e10	−	1.79730e11i	0.503655	−	0.988479i	−0.489536	−	0.871983i	$-0.662834\pi$
$653$	9.15770e10	−	1.79730e11i	0.503655	−	0.988479i	0.993191	−	0.116496i	$-0.0371663\pi$
$654$	−1.68830e11	+	5.48563e10i	−0.922868	+	0.299858i
$655$	−4.72704e10	+	2.59842e11i	−0.256817	+	1.41170i
$656$	−2.96082e10	+	9.11245e10i	−0.159881	+	0.492062i
$657$	−4.26933e10	+	4.26933e10i	−0.229139	+	0.229139i
$658$	8.85471e10	−	4.51170e10i	0.472357	−	0.240678i
$659$	3.97532e10	+	5.47156e10i	0.210781	+	0.290114i	0.901297	−	0.433203i	$-0.142617\pi$
$659$	3.97532e10	+	5.47156e10i	0.210781	+	0.290114i	−0.690516	+	0.723317i	$0.742617\pi$
$660$	−2.46697e10	+	3.23713e10i	−0.130013	+	0.170602i
$661$	3.38035e10	+	2.45597e10i	0.177075	+	0.128652i	0.672792	−	0.739832i	$-0.265095\pi$
$661$	3.38035e10	+	2.45597e10i	0.177075	+	0.128652i	−0.495717	+	0.868484i	$0.665095\pi$
$662$	9.19394e9	−	5.80482e10i	0.0478707	−	0.302244i
$663$	−4.05805e10	−	6.42732e9i	−0.210021	−	0.0332641i
$664$	2.73545e10	−	3.76503e10i	0.140720	−	0.193685i
$665$	9.62121e10	−	6.65944e10i	0.491975	−	0.340527i
$666$	−7.20556e10	+	5.23515e10i	−0.366244	+	0.266092i
$667$	−6.52105e9	−	1.27983e10i	−0.0329469	−	0.0646618i
$668$	1.08040e9	+	1.08040e9i	0.00542596	+	0.00542596i
$669$	−1.37651e11	−	4.47255e10i	−0.687186	−	0.223280i
$670$	3.84001e10	+	4.01982e10i	0.190561	+	0.199484i
$671$	1.61869e11	+	4.98183e11i	0.798499	+	2.45753i
$672$	−3.54019e10	−	1.80382e10i	−0.173600	−	0.0884536i
$673$	−1.50027e10	−	9.47231e10i	−0.0731321	−	0.461738i	−0.996893	−	0.0787682i	$-0.974901\pi$
$673$	−1.50027e10	−	9.47231e10i	−0.0731321	−	0.461738i	0.923761	−	0.382970i	$-0.125099\pi$
$674$			8.64183e10i			0.418761i
$675$	−3.63892e10	+	1.64908e10i	−0.175290	+	0.0794378i
$676$	−1.05775e10			−0.0506517
$677$	−1.77925e11	+	2.81806e10i	−0.846998	+	0.134151i	−0.564824	−	0.825212i	$-0.691056\pi$
$677$	−1.77925e11	+	2.81806e10i	−0.846998	+	0.134151i	−0.282175	+	0.959363i	$0.591056\pi$
$678$	−5.14879e10	+	1.01051e11i	−0.243661	+	0.478212i
$679$	1.98711e11	−	6.45651e10i	0.934852	−	0.303752i
$680$	6.93032e10	+	3.73323e10i	0.324129	+	0.174602i
$681$	−5.73019e10	+	1.76357e11i	−0.266428	+	0.819983i
$682$	6.56403e9	−	6.56403e9i	0.0303412	−	0.0303412i
$683$	1.41733e11	−	7.22165e10i	0.651310	−	0.331859i	−0.0969262	−	0.995292i	$-0.530901\pi$
$683$	1.41733e11	−	7.22165e10i	0.651310	−	0.331859i	0.748236	+	0.663433i	$0.230901\pi$
$684$	−1.15682e10	−	1.59222e10i	−0.0528494	−	0.0727409i
$685$	4.85266e8	−	2.12125e10i	0.00220403	−	0.0963451i
$686$	1.52499e11	+	1.10797e11i	0.688607	+	0.500303i
$687$	3.69731e10	−	2.33439e11i	0.165981	−	1.04797i
$688$	−1.86712e11	−	2.95722e10i	−0.833331	−	0.131987i
$689$	1.39501e11	−	1.92007e11i	0.619016	−	0.852002i
$690$	3.43963e10	+	7.86863e8i	0.151745	+	0.00347139i
$691$	8.80115e10	−	6.39441e10i	0.386036	−	0.280471i	−0.377793	−	0.925890i	$-0.623317\pi$
$691$	8.80115e10	−	6.39441e10i	0.386036	−	0.280471i	0.763829	+	0.645419i	$0.223317\pi$
$692$	1.38971e10	+	2.72746e10i	0.0606039	+	0.118942i
$693$	4.47996e10	+	4.47996e10i	0.194241	+	0.194241i
$694$	4.72023e10	+	1.53370e10i	0.203482	+	0.0661153i
$695$	−3.74709e10	+	6.95604e10i	−0.160603	+	0.298142i
$696$	−1.06479e10	−	3.27708e10i	−0.0453760	−	0.139653i
$697$	5.75408e10	+	2.93185e10i	0.243806	+	0.124225i
$698$	−1.28685e10	−	8.12488e10i	−0.0542135	−	0.342291i
$699$			1.65762e11i			0.694348i
$700$	8.43739e9	−	4.10274e10i	0.0351411	−	0.170876i
$701$	1.60862e11			0.666164			0.333082	−	0.942898i	$-0.391911\pi$
$701$	1.60862e11			0.666164			0.333082	+	0.942898i	$0.391911\pi$
$702$	−4.25475e10	+	6.73887e9i	−0.175197	+	0.0277484i
$703$	1.70754e11	−	3.35124e11i	0.699118	−	1.37210i
$704$	3.40769e11	−	1.10723e11i	1.38730	−	0.450760i
$705$	1.03612e11	−	9.89773e10i	0.419423	−	0.400663i
$706$	−1.92054e10	+	5.91080e10i	−0.0773043	+	0.237918i
$707$	−1.13337e11	+	1.13337e11i	−0.453623	+	0.453623i
$708$	−6.93110e10	+	3.53157e10i	−0.275848	+	0.140551i
$709$	2.20063e11	+	3.02891e11i	0.870888	+	1.19867i	0.978862	+	0.204520i	$0.0655634\pi$
$709$	2.20063e11	+	3.02891e11i	0.870888	+	1.19867i	−0.107975	+	0.994154i	$0.534437\pi$
$710$	1.60319e11	+	2.31621e11i	0.630887	+	0.911474i
$711$	−1.70359e10	−	1.23773e10i	−0.0666632	−	0.0484337i
$712$	−3.58588e10	+	2.26404e11i	−0.139533	+	0.880975i
$713$	3.02071e9	+	4.78433e8i	0.0116883	+	0.00185124i
$714$	1.57751e10	−	2.17125e10i	0.0606986	−	0.0835445i
$715$	−2.99215e11	−	2.28027e11i	−1.14488	−	0.872494i
$716$	−7.07486e10	+	5.14019e10i	−0.269194	+	0.195581i
$717$	−6.20561e10	−	1.21792e11i	−0.234805	−	0.460831i
$718$	−1.83197e11	−	1.83197e11i	−0.689318	−	0.689318i
$719$	−1.22800e11	−	3.99002e10i	−0.459497	−	0.149300i	0.0701162	−	0.997539i	$-0.477663\pi$
$719$	−1.22800e11	−	3.99002e10i	−0.459497	−	0.149300i	−0.529613	+	0.848239i	$0.677663\pi$
$720$	5.64857e10	+	1.02759e10i	0.210188	+	0.0382374i
$721$	1.53362e10	+	4.71998e10i	0.0567512	+	0.174662i
$722$	1.53758e10	+	7.83437e9i	0.0565834	+	0.0288307i
$723$	2.34392e10	+	1.47989e11i	0.0857805	+	0.541597i
$724$		−	8.68895e10i		−	0.316237i
$725$	5.40226e10	−	3.55930e10i	0.195535	−	0.128829i
$726$	−1.02724e11			−0.369765
$727$	−4.02269e11	+	6.37132e10i	−1.44005	+	0.228082i	−0.827108	−	0.562042i	$-0.810016\pi$
$727$	−4.02269e11	+	6.37132e10i	−1.44005	+	0.228082i	−0.612946	+	0.790125i	$0.710016\pi$
$728$	9.36174e10	−	1.83735e11i	0.333297	−	0.654132i
$729$	9.94839e9	−	3.23243e9i	0.0352243	−	0.0114451i
$730$	1.01518e11	+	2.11038e11i	0.357480	+	0.743136i
$731$	−3.93731e10	+	1.21178e11i	−0.137889	+	0.424379i
$732$	−6.41152e10	+	6.41152e10i	−0.223314	+	0.223314i
$733$	7.79851e10	−	3.97354e10i	0.270144	−	0.137645i	−0.313672	−	0.949532i	$-0.601559\pi$
$733$	7.79851e10	−	3.97354e10i	0.270144	−	0.137645i	0.583816	+	0.811886i	$0.301559\pi$
$734$	−4.41239e10	−	6.07313e10i	−0.152016	−	0.209232i
$735$	9.74820e10	+	3.41578e10i	0.334022	+	0.117042i
$736$	3.99132e10	+	2.89986e10i	0.136021	+	0.0988249i
$737$	1.98848e10	−	1.25548e11i	0.0673986	−	0.425538i
$738$	6.68762e10	+	1.05922e10i	0.225448	+	0.0357075i
$739$	4.86611e10	−	6.69762e10i	0.163156	−	0.224565i	−0.719609	−	0.694379i	$-0.755679\pi$
$739$	4.86611e10	−	6.69762e10i	0.163156	−	0.224565i	0.882765	+	0.469814i	$0.155679\pi$
$740$	−3.86660e10	−	1.28966e11i	−0.128944	−	0.430080i
$741$	1.47173e11	−	1.06927e11i	0.488151	−	0.354662i
$742$	7.03821e10	+	1.38133e11i	0.232192	+	0.455702i
$743$	−2.04096e10	−	2.04096e10i	−0.0669699	−	0.0669699i	0.672829	−	0.739798i	$-0.265079\pi$
$743$	−2.04096e10	−	2.04096e10i	−0.0669699	−	0.0669699i	−0.739798	+	0.672829i	$0.765079\pi$
$744$	6.97758e9	+	2.26715e9i	0.0227726	+	0.00739928i
$745$	3.08553e10	+	2.28526e11i	0.100162	+	0.741839i
$746$	1.10368e11	+	3.39679e11i	0.356360	+	1.09676i
$747$	−2.03839e10	−	1.03861e10i	−0.0654644	−	0.0333558i
$748$	−6.16691e9	−	3.89364e10i	−0.0196998	−	0.124380i
$749$		−	1.33335e11i		−	0.423661i
$750$	1.36902e10	+	1.54353e11i	0.0432678	+	0.487833i
$751$	3.49228e11			1.09787			0.548933	−	0.835866i	$-0.315034\pi$
$751$	3.49228e11			1.09787			0.548933	+	0.835866i	$0.315034\pi$
$752$	−2.03381e11	+	3.22123e10i	−0.635972	+	0.100728i
$753$	2.90929e10	−	5.70981e10i	0.0904914	−	0.177599i
$754$	6.63424e10	−	2.15559e10i	0.205261	−	0.0666932i
$755$	−1.10918e11	+	1.49761e10i	−0.341362	+	0.0460903i
$756$	−3.38895e9	+	1.04301e10i	−0.0103748	+	0.0319302i
$757$	−4.07602e11	+	4.07602e11i	−1.24123	+	1.24123i	−0.281743	+	0.959490i	$0.590912\pi$
$757$	−4.07602e11	+	4.07602e11i	−1.24123	+	1.24123i	−0.959490	+	0.281743i	$0.909088\pi$
$758$	2.47425e11	−	1.26069e11i	0.749491	−	0.381885i
$759$	−4.62403e10	−	6.36443e10i	−0.139333	−	0.191775i
$760$	−3.33856e11	+	1.00095e11i	−1.00070	+	0.300025i
$761$	6.53755e10	+	4.74981e10i	0.194929	+	0.141624i	0.680969	−	0.732312i	$-0.261559\pi$
$761$	6.53755e10	+	4.74981e10i	0.194929	+	0.141624i	−0.486040	+	0.873937i	$0.661559\pi$
$762$	7.77128e9	−	4.90659e10i	0.0230501	−	0.145533i
$763$	−4.12587e11	−	6.53474e10i	−1.21736	−	0.192810i
$764$	4.26399e10	−	5.86888e10i	0.125153	−	0.172259i
$765$	1.27965e10	−	3.65196e10i	0.0373633	−	0.106630i
$766$	1.96114e11	−	1.42485e11i	0.569630	−	0.413860i
$767$	−3.26431e11	−	6.40657e11i	−0.943214	−	1.85116i
$768$	1.09214e11	+	1.09214e11i	0.313930	+	0.313930i
$769$	3.50729e11	+	1.13959e11i	1.00292	+	0.325868i	0.764032	−	0.645179i	$-0.223217\pi$
$769$	3.50729e11	+	1.13959e11i	1.00292	+	0.325868i	0.238888	+	0.971047i	$0.423217\pi$
$770$	2.21449e11	−	1.06526e11i	0.629957	−	0.303036i
$771$	−6.08286e10	−	1.87211e11i	−0.172143	−	0.529803i
$772$	−2.52441e9	−	1.28625e9i	−0.00710706	−	0.00362123i
$773$	3.94589e10	+	2.49133e11i	0.110516	+	0.697773i	0.979275	+	0.202537i	$0.0649185\pi$
$773$	3.94589e10	+	2.49133e11i	0.110516	+	0.697773i	−0.868758	+	0.495236i	$0.835082\pi$
$774$			1.33590e11i			0.372229i
$775$	−6.29901e8	+	1.37603e10i	−0.00174608	+	0.0381435i
$776$	−6.22355e11			−1.71629
$777$	−2.07006e11	+	3.27865e10i	−0.567934	+	0.0899519i
$778$	1.83733e10	−	3.60596e10i	0.0501497	−	0.0984243i
$779$	−2.71940e11	+	8.83586e10i	−0.738454	+	0.239938i
$780$	1.16553e10	−	6.40681e10i	0.0314879	−	0.173086i
$781$	1.99037e11	−	6.12573e11i	0.534970	−	1.64647i
$782$	−2.35641e10	+	2.35641e10i	−0.0630121	+	0.0630121i
$783$	−1.50924e10	+	7.68995e9i	−0.0401523	+	0.0204586i
$784$	−8.72500e10	−	1.20089e11i	−0.230941	−	0.317863i
$785$	5.78374e10	−	7.58936e10i	0.152311	−	0.199860i
$786$	−2.16988e11	−	1.57651e11i	−0.568518	−	0.413053i
$787$	−3.32668e10	+	2.10038e11i	−0.0867185	+	0.547519i	0.905632	+	0.424065i	$0.139397\pi$
$787$	−3.32668e10	+	2.10038e11i	−0.0867185	+	0.547519i	−0.992350	+	0.123454i	$0.960603\pi$
$788$	1.00593e11	+	1.59323e10i	0.260892	+	0.0413213i
$789$	4.23215e10	−	5.82505e10i	0.109208	−	0.150311i
$790$	−6.71576e10	+	4.64839e10i	−0.172420	+	0.119342i
$791$	−2.15908e11	+	1.56866e11i	−0.551521	+	0.400704i
$792$	−8.56759e10	−	1.68148e11i	−0.217750	−	0.427358i
$793$	−5.92631e11	−	5.92631e11i	−1.49862	−	1.49862i
$794$	−5.96346e11	−	1.93764e11i	−1.50043	−	0.487520i
$795$	1.54404e11	+	1.61634e11i	0.386535	+	0.404635i
$796$	2.94754e9	+	9.07160e9i	0.00734189	+	0.0225960i
$797$	−6.52643e9	−	3.32538e9i	−0.0161749	−	0.00824154i	0.445884	−	0.895091i	$-0.352889\pi$
$797$	−6.52643e9	−	3.32538e9i	−0.0161749	−	0.00824154i	−0.462059	+	0.886849i	$0.652889\pi$
$798$	1.85890e10	+	1.17367e11i	0.0458401	+	0.289423i
$799$			1.38789e11i			0.340540i
$800$	−1.09827e11	+	1.93165e11i	−0.268131	+	0.471594i
$801$	1.12683e11			0.273735
$802$	1.04761e11	−	1.65925e10i	0.253222	−	0.0401064i
$803$	2.43099e11	−	4.77109e11i	0.584684	−	1.14751i
$804$	2.09261e10	−	6.79931e9i	0.0500800	−	0.0162720i
$805$	7.12775e10	+	3.83958e10i	0.169734	+	0.0914324i
$806$	−4.58971e9	+	1.41257e10i	−0.0108754	+	0.0334710i
$807$	2.09916e11	−	2.09916e11i	0.494939	−	0.494939i
$808$	4.25395e11	−	2.16749e11i	0.998037	−	0.508525i
$809$	−3.17563e11	−	4.37088e11i	−0.741372	−	1.02041i	−0.998539	−	0.0540440i	$-0.982789\pi$
$809$	−3.17563e11	−	4.37088e11i	−0.741372	−	1.02041i	0.257166	−	0.966367i	$-0.417211\pi$
$810$	9.27909e8	−	4.05618e10i	0.00215558	−	0.0942275i
$811$	−3.50011e11	−	2.54298e11i	−0.809093	−	0.587841i	0.104474	−	0.994528i	$-0.466684\pi$
$811$	−3.50011e11	−	2.54298e11i	−0.809093	−	0.587841i	−0.913568	+	0.406687i	$0.866684\pi$
$812$	2.77808e9	−	1.75401e10i	0.00639030	−	0.0403467i
$813$	−1.59643e11	−	2.52849e10i	−0.365416	−	0.0578762i
$814$	4.64291e11	−	6.39042e11i	1.05753	−	1.45557i
$815$	2.82613e9	+	6.46517e7i	0.00640563	+	0.000146538i
$816$	−4.49890e10	+	3.26865e10i	−0.101472	+	0.0737237i
$817$	−2.56116e11	−	5.02655e11i	−0.574841	−	1.12819i
$818$	2.15060e11	+	2.15060e11i	0.480338	+	0.480338i
$819$	−9.64079e10	−	3.13248e10i	−0.214278	−	0.0696230i
$820$	−4.85418e10	+	9.01124e10i	−0.107364	+	0.199310i
$821$	3.90210e10	+	1.20094e11i	0.0858868	+	0.264332i	0.984772	−	0.173852i	$-0.0556216\pi$
$821$	3.90210e10	+	1.20094e11i	0.0858868	+	0.264332i	−0.898885	+	0.438185i	$0.855622\pi$
$822$	1.91993e10	+	9.78251e9i	0.0420530	+	0.0214271i
$823$	−4.47935e10	−	2.82815e11i	−0.0976373	−	0.616458i	−0.987181	−	0.159607i	$-0.948977\pi$
$823$	−4.47935e10	−	2.82815e11i	−0.0976373	−	0.616458i	0.889543	−	0.456851i	$-0.151023\pi$
$824$		−	1.47828e11i		−	0.320663i
$825$	2.61737e11	−	2.38823e11i	0.565000	−	0.515537i
$826$	4.69678e11			1.00897
$827$	−7.92824e11	+	1.25571e11i	−1.69494	+	0.268452i	−0.927814	−	0.373042i	$-0.878315\pi$
$827$	−7.92824e11	+	1.25571e11i	−1.69494	+	0.268452i	−0.767127	+	0.641495i	$0.778315\pi$
$828$	6.18219e9	−	1.21332e10i	0.0131529	−	0.0258140i
$829$	7.86263e11	−	2.55472e11i	1.66475	−	0.540911i	0.682893	−	0.730519i	$-0.260722\pi$
$829$	7.86263e11	−	2.55472e11i	1.66475	−	0.540911i	0.981860	+	0.189608i	$0.0607217\pi$
$830$	−6.41632e10	+	6.12932e10i	−0.135199	+	0.129152i
$831$	−8.26481e10	+	2.54365e11i	−0.173312	+	0.533400i
$832$	−4.05374e11	+	4.05374e11i	−0.845985	+	0.845985i
$833$	−8.91443e10	+	4.54213e10i	−0.185146	+	0.0943364i
$834$	−4.71632e10	−	6.49146e10i	−0.0974853	−	0.134177i
$835$	−7.57023e9	−	1.09371e10i	−0.0155727	−	0.0224986i
$836$	1.41210e11	+	1.02595e11i	0.289094	+	0.210039i
$837$	5.64192e8	−	3.56217e9i	0.00114954	−	0.00725793i
$838$	4.12037e11	+	6.52602e10i	0.835526	+	0.132334i
$839$	−4.03064e11	+	5.54769e11i	−0.813440	+	1.11960i	0.177343	+	0.984149i	$0.443250\pi$
$839$	−4.03064e11	+	5.54769e11i	−0.813440	+	1.11960i	−0.990783	+	0.135455i	$0.956750\pi$
$840$	1.54473e11	+	1.17721e11i	0.310266	+	0.236449i
$841$	−3.82517e11	+	2.77915e11i	−0.764658	+	0.555557i
$842$	−4.10407e9	−	8.05469e9i	−0.00816519	−	0.0160251i
$843$	−3.57594e11	−	3.57594e11i	−0.708076	−	0.708076i
$844$	−4.62104e10	−	1.50147e10i	−0.0910688	−	0.0295901i
$845$	9.05965e10	+	1.64813e10i	0.177699	+	0.0323270i
$846$	4.49671e10	+	1.38394e11i	0.0877836	+	0.270170i
$847$	−2.15380e11	−	1.09741e11i	−0.418476	−	0.213224i
$848$	−5.02510e10	−	3.17272e11i	−0.0971764	−	0.613548i
$849$			3.55258e11i			0.683775i
$850$	−1.17266e11	−	9.36826e10i	−0.224645	−	0.179466i
$851$	2.60241e11			0.496200
$852$	1.10120e11	−	1.74412e10i	0.208981	−	0.0330993i
$853$	−2.40586e11	+	4.72176e11i	−0.454437	+	0.891882i	0.544163	+	0.838980i	$0.316847\pi$
$853$	−2.40586e11	+	4.72176e11i	−0.454437	+	0.891882i	−0.998600	+	0.0529029i	$0.983153\pi$
$854$	5.20669e11	−	1.69175e11i	0.978881	−	0.318058i
$855$	7.42727e10	+	1.54400e11i	0.138984	+	0.288923i
$856$	−1.22730e11	+	3.77724e11i	−0.228589	+	0.703525i
$857$	6.30468e11	−	6.30468e11i	1.16880	−	1.16880i	0.186307	−	0.982492i	$-0.440348\pi$
$857$	6.30468e11	−	6.30468e11i	1.16880	−	1.16880i	0.982492	−	0.186307i	$-0.0596519\pi$
$858$	3.40406e11	−	1.73445e11i	0.628127	−	0.320047i
$859$	3.02428e11	+	4.16257e11i	0.555456	+	0.764519i	0.990740	−	0.135774i	$-0.0433520\pi$
$859$	3.02428e11	+	4.16257e11i	0.555456	+	0.764519i	−0.435284	+	0.900293i	$0.643352\pi$
$860$	−1.90583e11	−	6.67804e10i	−0.348410	−	0.122083i
$861$	1.28902e11	+	9.36531e10i	0.234557	+	0.170416i
$862$	−1.15782e11	+	7.31020e11i	−0.209707	+	1.32404i
$863$	−1.33918e11	−	2.12105e10i	−0.241433	−	0.0382392i	0.0345453	−	0.999403i	$-0.489002\pi$
$863$	−1.33918e11	−	2.12105e10i	−0.241433	−	0.0382392i	−0.275978	+	0.961164i	$0.589002\pi$
$864$	3.41967e10	−	4.70677e10i	0.0613661	−	0.0844632i
$865$	−7.65315e10	−	2.55263e11i	−0.136702	−	0.455956i
$866$	−6.19923e11	+	4.50401e11i	−1.10222	+	0.800806i
$867$	−1.31086e11	−	2.57272e11i	−0.231996	−	0.455319i
$868$	2.67372e9	+	2.67372e9i	0.00471018	+	0.00471018i
$869$	1.77613e11	+	5.77100e10i	0.311456	+	0.101198i
$870$	8.79089e9	+	6.51086e10i	0.0153446	+	0.113648i
$871$	6.28475e10	+	1.93425e11i	0.109198	+	0.336078i
$872$	1.10866e12	+	5.64892e11i	1.91749	+	0.977011i
$873$	4.78594e10	+	3.02172e11i	0.0823967	+	0.520232i
$874$		−	1.47550e11i		−	0.252867i
$875$	−1.36194e11	+	3.38256e11i	−0.232341	+	0.577049i
$876$	9.26894e10			0.157403
$877$	−1.93086e11	+	3.05818e10i	−0.326402	+	0.0516970i	−0.317485	−	0.948263i	$-0.602838\pi$
$877$	−1.93086e11	+	3.05818e10i	−0.326402	+	0.0516970i	−0.00891675	+	0.999960i	$0.502838\pi$
$878$	−3.14588e10	+	6.17413e10i	−0.0529375	+	0.103896i
$879$	6.17586e11	−	2.00666e11i	1.03453	−	0.336138i
$880$	−5.04600e11	+	6.81305e10i	−0.841427	+	0.113608i
$881$	−1.46971e11	+	4.52329e11i	−0.243965	+	0.750846i	0.751840	+	0.659345i	$0.229166\pi$
$881$	−1.46971e11	+	4.52329e11i	−0.243965	+	0.750846i	−0.995805	+	0.0915007i	$0.970834\pi$
$882$	−7.41745e10	+	7.41745e10i	−0.122569	+	0.122569i
$883$	−9.71654e11	+	4.95082e11i	−1.59834	+	0.814394i	−0.598426	+	0.801178i	$0.704207\pi$
$883$	−9.71654e11	+	4.95082e11i	−1.59834	+	0.814394i	−0.999913	+	0.0132155i	$0.995793\pi$
$884$	3.70741e10	+	5.10282e10i	0.0607103	+	0.0835605i
$885$	6.48680e11	−	1.94484e11i	1.05744	−	0.317037i
$886$	3.10313e11	+	2.25456e11i	0.503576	+	0.365869i
$887$	−4.28084e10	+	2.70281e11i	−0.0691567	+	0.436638i	0.928679	+	0.370884i	$0.120945\pi$
$887$	−4.28084e10	+	2.70281e11i	−0.0691567	+	0.436638i	−0.997836	+	0.0657540i	$0.979055\pi$
$888$	6.16602e11	+	9.76602e10i	0.991638	+	0.157060i
$889$	6.87117e10	−	9.45735e10i	0.110008	−	0.151413i
$890$	1.44531e11	−	4.12474e11i	0.230357	−	0.657411i
$891$	−7.50526e10	+	5.45289e10i	−0.119084	+	0.0865199i
$892$	1.00873e11	+	1.97974e11i	0.159336	+	0.312715i
$893$	−4.34522e11	−	4.34522e11i	−0.683292	−	0.683292i
$894$	−2.22721e11	−	7.23666e10i	−0.348668	−	0.113289i
$895$	6.86058e11	−	3.30023e11i	1.06922	−	0.514342i
$896$	−4.85086e10	−	1.49294e11i	−0.0752639	−	0.231638i
$897$	1.12150e11	+	5.71434e10i	0.173233	+	0.0882666i
$898$	−9.82070e10	−	6.20055e11i	−0.151021	−	0.953509i
$899$			5.84016e9i			0.00894100i
$900$	5.74027e10	+	2.16002e10i	0.0874907	+	0.0329222i
$901$	−2.16510e11			−0.328533
$902$	−5.93108e11	+	9.39390e10i	−0.895999	+	0.141912i
$903$	−1.42716e11	+	2.80096e11i	−0.214646	+	0.421266i
$904$	7.56031e11	−	2.45649e11i	1.13205	−	0.367826i
$905$	−1.35387e11	+	7.44214e11i	−0.201829	+	1.10944i
$906$	3.51242e10	−	1.08101e11i	0.0521307	−	0.160442i
$907$	7.73740e11	−	7.73740e11i	1.14331	−	1.14331i	0.155475	−	0.987840i	$-0.450309\pi$
$907$	7.73740e11	−	7.73740e11i	1.14331	−	1.14331i	0.987840	−	0.155475i	$-0.0496908\pi$
$908$	2.53643e11	−	1.29238e11i	0.373147	−	0.190128i
$909$	−1.37951e11	−	1.89874e11i	−0.202055	−	0.278105i
$910$	−2.38319e11	+	3.12720e11i	−0.347531	+	0.456027i
$911$	−9.27565e11	−	6.73916e11i	−1.34670	−	0.978435i	−0.999169	−	0.0407672i	$-0.987020\pi$
$911$	−9.27565e11	−	6.73916e11i	−1.34670	−	0.978435i	−0.347532	−	0.937668i	$-0.612980\pi$
$912$	3.85171e10	−	2.43187e11i	0.0556768	−	0.351529i
$913$	2.00396e11	+	3.17396e10i	0.288407	+	0.0456791i
$914$	−4.63821e11	+	6.38394e11i	−0.664608	+	0.914754i
$915$	6.49051e11	−	4.49249e11i	0.925965	−	0.640918i
$916$	−2.93540e11	+	2.13269e11i	−0.416951	+	0.302932i
$917$	−2.86534e11	−	5.62354e11i	−0.405227	−	0.795303i
$918$	2.77880e10	+	2.77880e10i	0.0391279	+	0.0391279i
$919$	−9.94994e11	−	3.23293e11i	−1.39495	−	0.453247i	−0.487395	−	0.873182i	$-0.662053\pi$
$919$	−9.94994e11	−	3.23293e11i	−1.39495	−	0.453247i	−0.907554	+	0.419935i	$0.862053\pi$
$920$	−1.66579e11	−	1.74379e11i	−0.232525	−	0.243413i
$921$	2.49602e11	+	7.68197e11i	0.346905	+	1.06766i
$922$	3.16995e11	+	1.61517e11i	0.438661	+	0.223509i
$923$	1.61213e11	+	1.01786e12i	0.222123	+	1.40243i
$924$		−	9.72622e10i		−	0.133431i
$925$	1.30227e11	+	1.16485e12i	0.177883	+	1.59112i
$926$	−2.40321e11			−0.326849
$927$	−7.17750e10	+	1.13680e10i	−0.0971973	+	0.0153945i
$928$	−4.27703e10	+	8.39414e10i	−0.0576700	+	0.113184i
$929$	1.06162e12	−	3.44940e11i	1.42530	−	0.463107i	0.508016	−	0.861348i	$-0.330379\pi$
$929$	1.06162e12	−	3.44940e11i	1.42530	−	0.463107i	0.917281	+	0.398241i	$0.130379\pi$
$930$	−1.23156e10	−	6.63417e9i	−0.0164635	−	0.00886859i
$931$	1.36888e11	−	4.21299e11i	0.182208	−	0.560780i
$932$	1.79939e11	−	1.79939e11i	0.238486	−	0.238486i
$933$	−1.55558e11	+	7.92610e10i	−0.205290	+	0.104600i
$934$	6.76057e11	+	9.30512e11i	0.888374	+	1.22274i
$935$	−7.84892e9	+	3.43101e11i	−0.0102698	+	0.448927i
$936$	2.44279e11	+	1.77479e11i	0.318261	+	0.231230i
$937$	1.51677e11	−	9.57649e11i	0.196771	−	1.24236i	−0.669510	−	0.742803i	$-0.733496\pi$
$937$	1.51677e11	−	9.57649e11i	0.196771	−	1.24236i	0.866281	−	0.499558i	$-0.166504\pi$
$938$	−1.31214e11	−	2.07823e10i	−0.169500	−	0.0268462i
$939$	−2.42102e10	+	3.33225e10i	−0.0311413	+	0.0428623i
$940$	−2.19916e11	−	5.03088e9i	−0.281673	−	0.00644366i
$941$	3.25306e11	−	2.36348e11i	0.414890	−	0.301435i	−0.360688	−	0.932686i	$-0.617458\pi$
$941$	3.25306e11	−	2.36348e11i	0.414890	−	0.301435i	0.775579	+	0.631251i	$0.217458\pi$
$942$	4.39931e10	+	8.63414e10i	0.0558703	+	0.109652i
$943$	−1.39895e11	−	1.39895e11i	−0.176911	−	0.176911i
$944$	−9.25557e11	−	3.00732e11i	−1.16551	−	0.378696i
$945$	4.52783e10	−	8.40540e10i	0.0567757	−	0.105398i
$946$	−3.66116e11	−	1.12679e12i	−0.457145	−	1.40695i
$947$	−7.04063e10	−	3.58738e10i	−0.0875410	−	0.0446044i	0.409672	−	0.912233i	$-0.365643\pi$
$947$	−7.04063e10	−	3.58738e10i	−0.0875410	−	0.0446044i	−0.497213	+	0.867629i	$0.665643\pi$
$948$	5.05702e9	+	3.19288e10i	0.00626126	+	0.0395320i
$949$			8.56749e11i			1.05630i
$950$	6.60440e11	−	7.38353e10i	0.810847	−	0.0906504i
$951$	−7.31389e11			−0.894182
$952$	−1.85801e11	+	2.94280e10i	−0.226204	+	0.0358271i
$953$	−5.41035e11	+	1.06184e12i	−0.655924	+	1.28732i	0.288148	+	0.957586i	$0.406960\pi$
$953$	−5.41035e11	+	1.06184e12i	−0.655924	+	1.28732i	−0.944073	+	0.329738i	$0.893040\pi$
$954$	−2.15894e11	+	7.01483e10i	−0.260644	+	0.0846884i
$955$	−4.56660e11	+	4.36233e11i	−0.549009	+	0.524452i
$956$	−6.48448e10	+	1.99572e11i	−0.0776325	+	0.238928i
$957$	1.06224e11	−	1.06224e11i	0.126641	−	0.126641i
$958$	1.11964e12	−	5.70487e11i	1.32928	−	0.677304i
$959$	2.98040e10	+	4.10216e10i	0.0352371	+	0.0484996i
$960$	−3.07297e11	−	4.43967e11i	−0.361804	−	0.522716i
$961$	6.88997e11	+	5.00586e11i	0.807837	+	0.586928i
$962$	−1.97707e11	+	1.24827e12i	−0.230845	+	1.45750i
$963$	1.92834e11	+	3.05420e10i	0.224222	+	0.0355134i
$964$	1.35202e11	−	1.86090e11i	0.156558	−	0.215484i
$965$	1.96175e10	+	1.49502e10i	0.0226222	+	0.0172400i
$966$	−6.65170e10	+	4.83274e10i	−0.0763878	+	0.0554990i
$967$	5.82449e11	+	1.14312e12i	0.666119	+	1.30733i	0.938545	+	0.345156i	$0.112174\pi$
$967$	5.82449e11	+	1.14312e12i	0.666119	+	1.30733i	−0.272426	+	0.962177i	$0.587826\pi$
$968$	5.09133e11	+	5.09133e11i	0.579869	+	0.579869i
$969$	−1.57831e11	−	5.12825e10i	−0.179019	−	0.0581666i
$970$	1.16748e12	+	2.12388e11i	1.31875	+	0.239907i
$971$	−3.77318e11	−	1.16127e12i	−0.424454	−	1.30633i	−0.903516	−	0.428554i	$-0.859023\pi$
$971$	−3.77318e11	−	1.16127e12i	−0.424454	−	1.30633i	0.479062	−	0.877781i	$-0.340977\pi$
$972$	−1.43081e10	−	7.29035e9i	−0.0160294	−	0.00816739i
$973$	−2.95372e10	−	1.86490e11i	−0.0329547	−	0.208068i
$974$		−	3.11225e11i		−	0.345811i
$975$	−1.99656e11	+	5.30586e11i	−0.220935	+	0.587134i
$976$	−1.13436e12			−1.25012
$977$	1.68538e12	−	2.66938e11i	1.84978	−	0.292977i	0.870000	−	0.493051i	$-0.164118\pi$
$977$	1.68538e12	−	2.66938e11i	1.84978	−	0.292977i	0.979781	+	0.200074i	$0.0641184\pi$
$978$	−1.30332e9	+	2.55791e9i	−0.00142461	+	0.00279595i
$979$	−9.50447e11	+	3.08819e11i	−1.03466	+	0.336181i
$980$	−6.87401e10	−	1.42898e11i	−0.0745257	−	0.154926i
$981$	1.89015e11	−	5.81730e11i	0.204090	−	0.628124i
$982$	2.61694e11	−	2.61694e11i	0.281415	−	0.281415i
$983$	−6.02331e11	+	3.06903e11i	−0.645091	+	0.328690i	−0.745745	−	0.666231i	$-0.767906\pi$
$983$	−6.02331e11	+	3.06903e11i	−0.645091	+	0.328690i	0.100654	+	0.994921i	$0.467906\pi$
$984$	−2.78962e11	−	3.83958e11i	−0.297553	−	0.409547i
$985$	−8.36757e11	−	2.93200e11i	−0.888903	−	0.311472i
$986$	−5.14825e10	−	3.74042e10i	−0.0544693	−	0.0395743i
$987$	−5.35669e10	+	3.38208e11i	−0.0564453	+	0.356382i
$988$	−2.75832e11	−	4.36875e10i	−0.289479	−	0.0458489i
$989$	2.29434e11	−	3.15789e11i	0.239813	−	0.330074i
$990$	1.03337e11	+	3.44669e11i	0.107576	+	0.358807i
$991$	1.33125e12	−	9.67211e11i	1.38028	−	1.00283i	0.383421	−	0.923574i	$-0.374746\pi$
$991$	1.33125e12	−	9.67211e11i	1.38028	−	1.00283i	0.996854	−	0.0792550i	$-0.0252541\pi$
$992$	−9.10668e9	−	1.78729e10i	−0.00940402	−	0.0184564i
$993$	1.43194e11	+	1.43194e11i	0.147275	+	0.147275i
$994$	−6.40222e11	−	2.08021e11i	−0.655821	−	0.213089i
$995$	−1.11109e10	−	8.22915e10i	−0.0113359	−	0.0839581i
$996$	1.08529e10	+	3.34017e10i	0.0110283	+	0.0339415i
$997$	1.10791e12	+	5.64508e11i	1.12130	+	0.571333i	0.913501	−	0.406837i	$-0.133368\pi$
$997$	1.10791e12	+	5.64508e11i	1.12130	+	0.571333i	0.207804	+	0.978170i	$0.433368\pi$
$998$	−5.18061e10	−	3.27091e11i	−0.0522227	−	0.329721i
$999$		−	3.06889e11i		−	0.308120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.k.a.13.13	✓	320
25.2	odd	20	inner	75.9.k.a.52.13	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.9.k.a.13.13	✓	320	1.1	even	1	trivial
75.9.k.a.52.13	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)

\(f(q)\)	\(=\)	\(q+(-13.4052 + 2.12318i) q^{2} +(21.2310 - 41.6683i) q^{3} +(-68.2788 + 22.1851i) q^{4} +(619.380 - 83.6279i) q^{5} +(-196.137 + 603.649i) q^{6} +(-1056.12 + 1056.12i) q^{7} +(3964.00 - 2019.76i) q^{8} +(-1285.49 - 1769.32i) q^{9} +O(q^{10})\)	\(q+(-13.4052 + 2.12318i) q^{2} +(21.2310 - 41.6683i) q^{3} +(-68.2788 + 22.1851i) q^{4} +(619.380 - 83.6279i) q^{5} +(-196.137 + 603.649i) q^{6} +(-1056.12 + 1056.12i) q^{7} +(3964.00 - 2019.76i) q^{8} +(-1285.49 - 1769.32i) q^{9} +(-8125.36 + 2436.10i) q^{10} +(15691.6 + 11400.6i) q^{11} +(-525.214 + 3316.07i) q^{12} +(-30651.2 - 4854.67i) q^{13} +(11915.2 - 16399.9i) q^{14} +(9665.44 - 27584.0i) q^{15} +(-33981.1 + 24688.7i) q^{16} +(12852.6 + 25224.7i) q^{17} +(20988.8 + 20988.8i) q^{18} +(-119213. - 38734.6i) q^{19} +(-40435.2 + 19451.0i) q^{20} +(21584.2 + 66429.4i) q^{21} +(-234555. - 119512. i) q^{22} +(-13567.5 - 85661.8i) q^{23} -208054. i q^{24} +(376638. - 103595. i) q^{25} +421193. q^{26} +(-101017. + 15999.5i) q^{27} +(48680.6 - 95541.1i) q^{28} +(157511. - 51178.3i) q^{29} +(-71001.6 + 390290. i) q^{30} +(-10896.9 + 33537.3i) q^{31} +(-402232. + 402232. i) q^{32} +(808194. - 411796. i) q^{33} +(-225849. - 310854. i) q^{34} +(-565820. + 742463. i) q^{35} +(127024. + 92288.4i) q^{36} +(-469397. + 2.96366e6i) q^{37} +(1.68031e6 + 266136. i) q^{38} +(-853043. + 1.17411e6i) q^{39} +(2.28631e6 - 1.58250e6i) q^{40} +(1.84547e6 - 1.34081e6i) q^{41} +(-430382. - 844673. i) q^{42} +(3.18242e6 + 3.18242e6i) q^{43} +(-1.32433e6 - 430301. i) q^{44} +(-944169. - 988379. i) q^{45} +(363750. + 1.11951e6i) q^{46} +(4.36808e6 + 2.22565e6i) q^{47} +(307281. + 1.94010e6i) q^{48} +3.53401e6i q^{49} +(-4.82896e6 + 2.18838e6i) q^{50} +1.32394e6 q^{51} +(2.20053e6 - 348530. i) q^{52} +(-3.47200e6 + 6.81418e6i) q^{53} +(1.32018e6 - 428952. i) q^{54} +(1.06725e7 + 5.74907e6i) q^{55} +(-2.05336e6 + 6.31959e6i) q^{56} +(-4.14502e6 + 4.14502e6i) q^{57} +(-2.00280e6 + 1.02048e6i) q^{58} +(1.36187e7 + 1.87445e7i) q^{59} +(-47990.8 + 2.09783e6i) q^{60} +(2.18489e7 + 1.58741e7i) q^{61} +(74870.0 - 472710. i) q^{62} +(3.22625e6 + 510988. i) q^{63} +(1.08583e7 - 1.49452e7i) q^{64} +(-1.93907e7 - 443590. i) q^{65} +(-9.95970e6 + 7.23614e6i) q^{66} +(-2.97526e6 - 5.83928e6i) q^{67} +(-1.43718e6 - 1.43718e6i) q^{68} +(-3.85743e6 - 1.25335e6i) q^{69} +(6.00856e6 - 1.11542e7i) q^{70} +(-1.02618e7 - 3.15826e7i) q^{71} +(-8.66927e6 - 4.41721e6i) q^{72} +(-4.31875e6 - 2.72675e7i) q^{73} -4.07250e7i q^{74} +(3.67979e6 - 1.78933e7i) q^{75} +8.99905e6 q^{76} +(-2.86128e7 + 4.53182e6i) q^{77} +(8.94236e6 - 1.75504e7i) q^{78} +(9.15724e6 - 2.97537e6i) q^{79} +(-1.89825e7 + 1.81334e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(-2.18921e7 + 2.18921e7i) q^{82} +(9.32049e6 - 4.74903e6i) q^{83} +(-2.94749e6 - 4.05687e6i) q^{84} +(1.00701e7 + 1.45488e7i) q^{85} +(-4.94178e7 - 3.59041e7i) q^{86} +(1.21160e6 - 7.64976e6i) q^{87} +(8.52282e7 + 1.34988e7i) q^{88} +(-3.02851e7 + 4.16839e7i) q^{89} +(1.47553e7 + 1.12448e7i) q^{90} +(3.74986e7 - 2.72443e7i) q^{91} +(2.82679e6 + 5.54789e6i) q^{92} +(1.16609e6 + 1.16609e6i) q^{93} +(-6.32805e7 - 2.05611e7i) q^{94} +(-7.70774e7 - 1.40219e7i) q^{95} +(8.22050e6 + 2.53001e7i) q^{96} +(-1.24643e8 - 6.35086e7i) q^{97} +(-7.50332e6 - 4.73741e7i) q^{98} -4.24189e7i 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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