LMFDB - Embedded newform 8.9.d.b.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,9,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	8.d (of order $2$, degree $1$, 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:	$3.25902888049$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 78x^{4} - 514x^{3} + 4237x^{2} - 18333x + 238980 $ x^6 - x^5 + 78x^4 - 514x^3 + 4237x^2 - 18333x + 238980
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.3
Root			$-0.793226 - 7.99733i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.9.d.b.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.413549 - 15.9947i) q^{2} +117.102 q^{3} +(-255.658 + 13.2291i) q^{4} -816.841i q^{5} +(-48.4273 - 1873.00i) q^{6} +1333.52i q^{7} +(317.322 + 4083.69i) q^{8} +7151.84 q^{9} +O(q^{10})$	\(q+(-0.413549 - 15.9947i) q^{2} +117.102 q^{3} +(-255.658 + 13.2291i) q^{4} -816.841i q^{5} +(-48.4273 - 1873.00i) q^{6} +1333.52i q^{7} +(317.322 + 4083.69i) q^{8} +7151.84 q^{9} +(-13065.1 + 337.803i) q^{10} +14838.3 q^{11} +(-29938.0 + 1549.16i) q^{12} +44242.0i q^{13} +(21329.2 - 551.475i) q^{14} -95653.6i q^{15} +(65186.0 - 6764.27i) q^{16} -24172.9 q^{17} +(-2957.63 - 114391. i) q^{18} -99390.6 q^{19} +(10806.1 + 208832. i) q^{20} +156158. i q^{21} +(-6136.34 - 237333. i) q^{22} -68046.4i q^{23} +(37159.0 + 478208. i) q^{24} -276604. q^{25} +(707636. - 18296.2i) q^{26} +69188.3 q^{27} +(-17641.3 - 340925. i) q^{28} +496037. i q^{29} +(-1.52995e6 + 39557.4i) q^{30} -1.07234e6i q^{31} +(-135150. - 1.03983e6i) q^{32} +1.73759e6 q^{33} +(9996.69 + 386638. i) q^{34} +1.08927e6 q^{35} +(-1.82842e6 + 94612.6i) q^{36} -1.73995e6i q^{37} +(41102.9 + 1.58972e6i) q^{38} +5.18082e6i q^{39} +(3.33573e6 - 259202. i) q^{40} -3.60866e6 q^{41} +(2.49769e6 - 64578.7i) q^{42} -2.44063e6 q^{43} +(-3.79352e6 + 196297. i) q^{44} -5.84191e6i q^{45} +(-1.08838e6 + 28140.5i) q^{46} +1.34806e6i q^{47} +(7.63340e6 - 792108. i) q^{48} +3.98653e6 q^{49} +(114389. + 4.42419e6i) q^{50} -2.83070e6 q^{51} +(-585284. - 1.13108e7i) q^{52} +6.31464e6i q^{53} +(-28612.7 - 1.10664e6i) q^{54} -1.21205e7i q^{55} +(-5.44568e6 + 423156. i) q^{56} -1.16388e7 q^{57} +(7.93395e6 - 205136. i) q^{58} +9.59847e6 q^{59} +(1.26541e6 + 2.44546e7i) q^{60} +1.38802e7i q^{61} +(-1.71516e7 + 443463. i) q^{62} +9.53711e6i q^{63} +(-1.65758e7 + 2.59169e6i) q^{64} +3.61387e7 q^{65} +(-718576. - 2.77921e7i) q^{66} +8.44768e6 q^{67} +(6.18001e6 - 319787. i) q^{68} -7.96836e6i q^{69} +(-450467. - 1.74225e7i) q^{70} -2.80319e7i q^{71} +(2.26944e6 + 2.92059e7i) q^{72} -3.31337e7 q^{73} +(-2.78299e7 + 719555. i) q^{74} -3.23909e7 q^{75} +(2.54100e7 - 1.31485e6i) q^{76} +1.97871e7i q^{77} +(8.28655e7 - 2.14252e6i) q^{78} -1.70081e7i q^{79} +(-5.52533e6 - 5.32466e7i) q^{80} -3.88211e7 q^{81} +(1.49236e6 + 5.77193e7i) q^{82} +2.29931e7 q^{83} +(-2.06583e6 - 3.99229e7i) q^{84} +1.97455e7i q^{85} +(1.00932e6 + 3.90371e7i) q^{86} +5.80869e7i q^{87} +(4.70851e6 + 6.05948e7i) q^{88} +7.23911e7 q^{89} +(-9.34394e7 + 2.41592e6i) q^{90} -5.89976e7 q^{91} +(900195. + 1.73966e7i) q^{92} -1.25572e8i q^{93} +(2.15618e7 - 557489. i) q^{94} +8.11863e7i q^{95} +(-1.58263e7 - 1.21766e8i) q^{96} -4.37103e7 q^{97} +(-1.64862e6 - 6.37631e7i) q^{98} +1.06121e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 14 q^{2} - 36 q^{3} - 588 q^{4} - 1284 q^{6} - 6824 q^{8} + 16338 q^{9}+O(q^{10}) $ 6 * q - 14 * q^2 - 36 * q^3 - 588 * q^4 - 1284 * q^6 - 6824 * q^8 + 16338 * q^9	\( 6 q - 14 q^{2} - 36 q^{3} - 588 q^{4} - 1284 q^{6} - 6824 q^{8} + 16338 q^{9} - 4080 q^{10} + 46940 q^{11} - 27336 q^{12} - 51744 q^{14} + 20496 q^{16} - 201076 q^{17} + 267990 q^{18} - 95268 q^{19} - 216480 q^{20} + 49404 q^{22} + 1009296 q^{24} - 447930 q^{25} + 1765104 q^{26} + 419256 q^{27} - 2600640 q^{28} - 4325280 q^{30} + 3232096 q^{32} + 1736856 q^{33} + 2378916 q^{34} + 1989120 q^{35} - 7392228 q^{36} - 8088196 q^{38} + 12694080 q^{40} + 3817100 q^{41} + 19064640 q^{42} - 9881508 q^{43} - 9479368 q^{44} - 19226976 q^{46} + 20590944 q^{48} - 12655482 q^{49} + 11106610 q^{50} - 4303176 q^{51} - 17270880 q^{52} - 7366536 q^{54} + 10545024 q^{56} + 7523736 q^{57} + 7354800 q^{58} + 25243484 q^{59} - 5760960 q^{60} - 5304960 q^{62} - 35364288 q^{64} + 27060480 q^{65} - 12683256 q^{66} + 47850204 q^{67} - 9160216 q^{68} + 56582400 q^{70} - 57502200 q^{72} - 55484916 q^{73} - 114255984 q^{74} - 126075300 q^{75} + 151972920 q^{76} + 175397280 q^{78} - 134958720 q^{80} - 79145442 q^{81} - 48197916 q^{82} + 144646364 q^{83} + 216531840 q^{84} + 41826428 q^{86} - 47377776 q^{88} + 142173452 q^{89} - 205943760 q^{90} - 273971712 q^{91} + 97636800 q^{92} + 220009536 q^{94} - 250689984 q^{96} + 125193612 q^{97} - 257093774 q^{98} + 298320276 q^{99}+O(q^{100}) \) 6 * q - 14 * q^2 - 36 * q^3 - 588 * q^4 - 1284 * q^6 - 6824 * q^8 + 16338 * q^9 - 4080 * q^10 + 46940 * q^11 - 27336 * q^12 - 51744 * q^14 + 20496 * q^16 - 201076 * q^17 + 267990 * q^18 - 95268 * q^19 - 216480 * q^20 + 49404 * q^22 + 1009296 * q^24 - 447930 * q^25 + 1765104 * q^26 + 419256 * q^27 - 2600640 * q^28 - 4325280 * q^30 + 3232096 * q^32 + 1736856 * q^33 + 2378916 * q^34 + 1989120 * q^35 - 7392228 * q^36 - 8088196 * q^38 + 12694080 * q^40 + 3817100 * q^41 + 19064640 * q^42 - 9881508 * q^43 - 9479368 * q^44 - 19226976 * q^46 + 20590944 * q^48 - 12655482 * q^49 + 11106610 * q^50 - 4303176 * q^51 - 17270880 * q^52 - 7366536 * q^54 + 10545024 * q^56 + 7523736 * q^57 + 7354800 * q^58 + 25243484 * q^59 - 5760960 * q^60 - 5304960 * q^62 - 35364288 * q^64 + 27060480 * q^65 - 12683256 * q^66 + 47850204 * q^67 - 9160216 * q^68 + 56582400 * q^70 - 57502200 * q^72 - 55484916 * q^73 - 114255984 * q^74 - 126075300 * q^75 + 151972920 * q^76 + 175397280 * q^78 - 134958720 * q^80 - 79145442 * q^81 - 48197916 * q^82 + 144646364 * q^83 + 216531840 * q^84 + 41826428 * q^86 - 47377776 * q^88 + 142173452 * q^89 - 205943760 * q^90 - 273971712 * q^91 + 97636800 * q^92 + 220009536 * q^94 - 250689984 * q^96 + 125193612 * q^97 - 257093774 * q^98 + 298320276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.413549	−	15.9947i	−0.0258468	−	0.999666i
$2$	−0.413549	−	15.9947i	−0.0258468	−	0.999666i
$3$	117.102			1.44570			0.722851	−	0.691004i	$-0.242831\pi$
$3$	117.102			1.44570			0.722851	+	0.691004i	$0.242831\pi$
$4$	−255.658	+	13.2291i	−0.998664	+	0.0516763i
$5$		−	816.841i		−	1.30695i	−0.756950	−	0.653473i	$-0.773311\pi$
$5$		−	816.841i		−	1.30695i	0.756950	−	0.653473i	$-0.226689\pi$
$6$	−48.4273	−	1873.00i	−0.0373667	−	1.44522i
$7$			1333.52i			0.555402i	0.960668	+	0.277701i	$0.0895724\pi$
$7$			1333.52i			0.555402i	−0.960668	+	0.277701i	$0.910428\pi$
$8$	317.322	+	4083.69i	0.0774713	+	0.996995i
$9$	7151.84			1.09005
$10$	−13065.1	+	337.803i	−1.30651	+	0.0337803i
$11$	14838.3			1.01347			0.506736	−	0.862101i	$-0.330852\pi$
$11$	14838.3			1.01347			0.506736	+	0.862101i	$0.330852\pi$
$12$	−29938.0	+	1549.16i	−1.44377	+	0.0747085i
$13$			44242.0i			1.54904i	0.632551	+	0.774519i	$0.282008\pi$
$13$			44242.0i			1.54904i	−0.632551	+	0.774519i	$0.717992\pi$
$14$	21329.2	−	551.475i	0.555216	−	0.0143553i
$15$		−	95653.6i		−	1.88945i
$16$	65186.0	−	6764.27i	0.994659	−	0.103215i
$17$	−24172.9			−0.289424			−0.144712	−	0.989474i	$-0.546226\pi$
$17$	−24172.9			−0.289424			−0.144712	+	0.989474i	$0.546226\pi$
$18$	−2957.63	−	114391.i	−0.0281744	−	1.08969i
$19$	−99390.6			−0.762660			−0.381330	−	0.924439i	$-0.624534\pi$
$19$	−99390.6			−0.762660			−0.381330	+	0.924439i	$0.624534\pi$
$20$	10806.1	+	208832.i	0.0675381	+	1.30520i
$21$			156158.i			0.802945i
$22$	−6136.34	−	237333.i	−0.0261950	−	1.01313i
$23$		−	68046.4i		−	0.243161i	−0.992582	−	0.121580i	$-0.961204\pi$
$23$		−	68046.4i		−	0.243161i	0.992582	−	0.121580i	$-0.0387962\pi$
$24$	37159.0	+	478208.i	0.112000	+	1.44136i
$25$	−276604.			−0.708107
$26$	707636.	−	18296.2i	1.54852	−	0.0400376i
$27$	69188.3			0.130190
$28$	−17641.3	−	340925.i	−0.0287011	−	0.554659i
$29$			496037.i			0.701330i	0.936501	+	0.350665i	$0.114044\pi$
$29$			496037.i			0.701330i	−0.936501	+	0.350665i	$0.885956\pi$
$30$	−1.52995e6	+	39557.4i	−1.88882	+	0.0488363i
$31$		−	1.07234e6i		−	1.16114i	−0.814211	−	0.580569i	$-0.802830\pi$
$31$		−	1.07234e6i		−	1.16114i	0.814211	−	0.580569i	$-0.197170\pi$
$32$	−135150.	−	1.03983e6i	−0.128889	−	0.991659i
$33$	1.73759e6			1.46518
$34$	9996.69	+	386638.i	0.00748067	+	0.289327i
$35$	1.08927e6			0.725880
$36$	−1.82842e6	+	94612.6i	−1.08860	+	0.0563299i
$37$		−	1.73995e6i		−	0.928390i	−0.885733	−	0.464195i	$-0.846344\pi$
$37$		−	1.73995e6i		−	0.928390i	0.885733	−	0.464195i	$-0.153656\pi$
$38$	41102.9	+	1.58972e6i	0.0197123	+	0.762405i
$39$			5.18082e6i			2.23945i
$40$	3.33573e6	−	259202.i	1.30302	−	0.101251i
$41$	−3.60866e6			−1.27706			−0.638530	−	0.769597i	$-0.720457\pi$
$41$	−3.60866e6			−1.27706			−0.638530	+	0.769597i	$0.720457\pi$
$42$	2.49769e6	−	64578.7i	0.802677	−	0.0207535i
$43$	−2.44063e6			−0.713886			−0.356943	−	0.934126i	$-0.616181\pi$
$43$	−2.44063e6			−0.713886			−0.356943	+	0.934126i	$0.616181\pi$
$44$	−3.79352e6	+	196297.i	−1.01212	+	0.0523725i
$45$		−	5.84191e6i		−	1.42464i
$46$	−1.08838e6	+	28140.5i	−0.243080	+	0.00628493i
$47$			1.34806e6i			0.276260i	0.990414	+	0.138130i	$0.0441092\pi$
$47$			1.34806e6i			0.276260i	−0.990414	+	0.138130i	$0.955891\pi$
$48$	7.63340e6	−	792108.i	1.43798	−	0.149217i
$49$	3.98653e6			0.691529
$50$	114389.	+	4.42419e6i	0.0183023	+	0.707870i
$51$	−2.83070e6			−0.418420
$52$	−585284.	−	1.13108e7i	−0.0800485	−	1.54697i
$53$			6.31464e6i			0.800286i	0.916453	+	0.400143i	$0.131040\pi$
$53$			6.31464e6i			0.800286i	−0.916453	+	0.400143i	$0.868960\pi$
$54$	−28612.7	−	1.10664e6i	−0.00336499	−	0.130146i
$55$		−	1.21205e7i		−	1.32455i
$56$	−5.44568e6	+	423156.i	−0.553732	+	0.0430277i
$57$	−1.16388e7			−1.10258
$58$	7.93395e6	−	205136.i	0.701096	−	0.0181271i
$59$	9.59847e6			0.792125			0.396063	−	0.918224i	$-0.370376\pi$
$59$	9.59847e6			0.792125			0.396063	+	0.918224i	$0.370376\pi$
$60$	1.26541e6	+	2.44546e7i	0.0976400	+	1.88693i
$61$			1.38802e7i			1.00248i	0.865308	+	0.501241i	$0.167123\pi$
$61$			1.38802e7i			1.00248i	−0.865308	+	0.501241i	$0.832877\pi$
$62$	−1.71516e7	+	443463.i	−1.16075	+	0.0300117i
$63$			9.53711e6i			0.605417i
$64$	−1.65758e7	+	2.59169e6i	−0.987996	+	0.154477i
$65$	3.61387e7			2.02451
$66$	−718576.	−	2.77921e7i	−0.0378702	−	1.46469i
$67$	8.44768e6			0.419216			0.209608	−	0.977785i	$-0.432781\pi$
$67$	8.44768e6			0.419216			0.209608	+	0.977785i	$0.432781\pi$
$68$	6.18001e6	−	319787.i	0.289037	−	0.0149563i
$69$		−	7.96836e6i		−	0.351538i
$70$	−450467.	−	1.74225e7i	−0.0187617	−	0.725637i
$71$		−	2.80319e7i		−	1.10311i	−0.834138	−	0.551556i	$-0.814034\pi$
$71$		−	2.80319e7i		−	1.10311i	0.834138	−	0.551556i	$-0.185966\pi$
$72$	2.26944e6	+	2.92059e7i	0.0844478	+	1.08678i
$73$	−3.31337e7			−1.16675			−0.583377	−	0.812202i	$-0.698269\pi$
$73$	−3.31337e7			−1.16675			−0.583377	+	0.812202i	$0.698269\pi$
$74$	−2.78299e7	+	719555.i	−0.928080	+	0.0239959i
$75$	−3.23909e7			−1.02371
$76$	2.54100e7	−	1.31485e6i	0.761641	−	0.0394115i
$77$			1.97871e7i			0.562884i
$78$	8.28655e7	−	2.14252e6i	2.23870	−	0.0578825i
$79$		−	1.70081e7i		−	0.436665i	−0.975874	−	0.218333i	$-0.929938\pi$
$79$		−	1.70081e7i		−	0.436665i	0.975874	−	0.218333i	$-0.0700618\pi$
$80$	−5.52533e6	−	5.32466e7i	−0.134896	−	1.29997i
$81$	−3.88211e7			−0.901837
$82$	1.49236e6	+	5.77193e7i	0.0330079	+	1.27663i
$83$	2.29931e7			0.484491			0.242245	−	0.970215i	$-0.422116\pi$
$83$	2.29931e7			0.484491			0.242245	+	0.970215i	$0.422116\pi$
$84$	−2.06583e6	−	3.99229e7i	−0.0414932	−	0.801872i
$85$			1.97455e7i			0.378261i
$86$	1.00932e6	+	3.90371e7i	0.0184517	+	0.713648i
$87$			5.80869e7i			1.01391i
$88$	4.70851e6	+	6.05948e7i	0.0785150	+	1.01043i
$89$	7.23911e7			1.15379			0.576893	−	0.816820i	$-0.304265\pi$
$89$	7.23911e7			1.15379			0.576893	+	0.816820i	$0.304265\pi$
$90$	−9.34394e7	+	2.41592e6i	−1.42416	+	0.0368224i
$91$	−5.89976e7			−0.860338
$92$	900195.	+	1.73966e7i	0.0125657	+	0.242836i
$93$		−	1.25572e8i		−	1.67866i
$94$	2.15618e7	−	557489.i	0.276168	−	0.00714044i
$95$			8.11863e7i			0.996755i
$96$	−1.58263e7	−	1.21766e8i	−0.186335	−	1.43364i
$97$	−4.37103e7			−0.493739			−0.246869	−	0.969049i	$-0.579402\pi$
$97$	−4.37103e7			−0.493739			−0.246869	+	0.969049i	$0.579402\pi$
$98$	−1.64862e6	−	6.37631e7i	−0.0178738	−	0.691298i
$99$	1.06121e8			1.10474
$100$	7.07161e7	−	3.65923e6i	0.707161	−	0.0365923i
$101$		−	1.38340e8i		−	1.32942i	−0.747100	−	0.664711i	$-0.768554\pi$
$101$		−	1.38340e8i		−	1.32942i	0.747100	−	0.664711i	$-0.231446\pi$
$102$	1.17063e6	+	4.52760e7i	0.0108148	+	0.418280i
$103$			7.63048e7i			0.677958i	0.940794	+	0.338979i	$0.110082\pi$
$103$			7.63048e7i			0.677958i	−0.940794	+	0.338979i	$0.889918\pi$
$104$	−1.80671e8	+	1.40390e7i	−1.54438	+	0.120006i
$105$	1.27556e8			1.04941
$106$	1.01000e8	−	2.61141e6i	0.800018	−	0.0206848i
$107$	4.79331e7			0.365679			0.182840	−	0.983143i	$-0.441471\pi$
$107$	4.79331e7			0.365679			0.182840	+	0.983143i	$0.441471\pi$
$108$	−1.76885e7	+	915301.i	−0.130016	+	0.00672774i
$109$			1.63928e8i			1.16131i	0.814150	+	0.580655i	$0.197203\pi$
$109$			1.63928e8i			1.16131i	−0.814150	+	0.580655i	$0.802797\pi$
$110$	−1.93863e8	+	5.01241e6i	−1.32411	+	0.0342355i
$111$		−	2.03752e8i		−	1.34218i
$112$	9.02028e6	+	8.69268e7i	0.0573255	+	0.552435i
$113$	−1.28461e8			−0.787874			−0.393937	−	0.919137i	$-0.628887\pi$
$113$	−1.28461e8			−0.787874			−0.393937	+	0.919137i	$0.628887\pi$
$114$	4.81322e6	+	1.86159e8i	0.0284981	+	1.10221i
$115$	−5.55831e7			−0.317798
$116$	−6.56215e6	−	1.26816e8i	−0.0362421	−	0.700393i
$117$			3.16412e8i			1.68853i
$118$	−3.96943e6	−	1.53524e8i	−0.0204739	−	0.791861i
$119$		−	3.22351e7i		−	0.160746i
$120$	3.90620e8	−	3.03530e7i	1.88377	−	0.146378i
$121$	5.81486e6			0.0271268
$122$	2.22009e8	−	5.74014e6i	1.00215	−	0.0259109i
$123$	−4.22581e8			−1.84625
$124$	1.41861e7	+	2.74151e8i	0.0600033	+	1.15959i
$125$		−	9.31369e7i		−	0.381489i
$126$	1.52543e8	−	3.94406e6i	0.605215	−	0.0156481i
$127$		−	2.49819e8i		−	0.960309i	−0.877184	−	0.480155i	$-0.840581\pi$
$127$		−	2.49819e8i		−	0.960309i	0.877184	−	0.480155i	$-0.159419\pi$
$128$	4.83081e7	+	2.64053e8i	0.179962	+	0.983674i
$129$	−2.85803e8			−1.03207
$130$	−1.49451e7	−	5.78026e8i	−0.0523270	−	2.02383i
$131$	5.23739e8			1.77840			0.889201	−	0.457517i	$-0.151261\pi$
$131$	5.23739e8			1.77840			0.889201	+	0.457517i	$0.151261\pi$
$132$	−4.44228e8	+	2.29868e7i	−1.46322	+	0.0757150i
$133$		−	1.32539e8i		−	0.423583i
$134$	−3.49353e6	−	1.35118e8i	−0.0108354	−	0.419076i
$135$		−	5.65158e7i		−	0.170151i
$136$	−7.67062e6	−	9.87148e7i	−0.0224220	−	0.288554i
$137$	2.67976e8			0.760701			0.380350	−	0.924842i	$-0.375803\pi$
$137$	2.67976e8			0.760701			0.380350	+	0.924842i	$0.375803\pi$
$138$	−1.27451e8	+	3.29530e6i	−0.351421	+	0.00908613i
$139$	−1.80096e8			−0.482442			−0.241221	−	0.970470i	$-0.577548\pi$
$139$	−1.80096e8			−0.482442			−0.241221	+	0.970470i	$0.577548\pi$
$140$	−2.78481e8	+	1.44101e7i	−0.724910	+	0.0375108i
$141$			1.57860e8i			0.399390i
$142$	−4.48361e8	+	1.15926e7i	−1.10274	+	0.0285119i
$143$			6.56475e8i			1.56991i
$144$	4.66200e8	−	4.83769e7i	1.08423	−	0.112509i
$145$	4.05184e8			0.916600
$146$	1.37024e7	+	5.29963e8i	0.0301568	+	1.16636i
$147$	4.66830e8			0.999745
$148$	2.30181e7	+	4.44833e8i	0.0479758	+	0.927150i
$149$			4.30585e7i			0.0873603i	0.999046	+	0.0436801i	$0.0139082\pi$
$149$			4.30585e7i			0.0873603i	−0.999046	+	0.0436801i	$0.986092\pi$
$150$	1.33952e7	+	5.18081e8i	0.0264596	+	1.02337i
$151$		−	7.72461e8i		−	1.48583i	−0.669386	−	0.742915i	$-0.733443\pi$
$151$		−	7.72461e8i		−	1.48583i	0.669386	−	0.742915i	$-0.266557\pi$
$152$	−3.15389e7	−	4.05881e8i	−0.0590843	−	0.760368i
$153$	−1.72881e8			−0.315487
$154$	3.16488e8	−	8.18293e6i	0.562696	−	0.0145488i
$155$	−8.75928e8			−1.51754
$156$	−6.85378e7	−	1.32452e9i	−0.115726	−	2.23645i
$157$			2.03578e8i			0.335068i	0.985866	+	0.167534i	$0.0535804\pi$
$157$			2.03578e8i			0.335068i	−0.985866	+	0.167534i	$0.946420\pi$
$158$	−2.72039e8	+	7.03369e6i	−0.436519	+	0.0112864i
$159$			7.39456e8i			1.15697i
$160$	−8.49376e8	+	1.10396e8i	−1.29604	+	0.168451i
$161$	9.07412e7			0.135052
$162$	1.60544e7	+	6.20931e8i	0.0233096	+	0.901536i
$163$	1.20346e9			1.70483			0.852413	−	0.522869i	$-0.175138\pi$
$163$	1.20346e9			1.70483			0.852413	+	0.522869i	$0.175138\pi$
$164$	9.22584e8	−	4.77395e7i	1.27535	−	0.0659937i
$165$		−	1.41933e9i		−	1.91491i
$166$	−9.50877e6	−	3.67767e8i	−0.0125225	−	0.484329i
$167$			6.78558e8i			0.872411i	0.899847	+	0.436206i	$0.143678\pi$
$167$			6.78558e8i			0.872411i	−0.899847	+	0.436206i	$0.856322\pi$
$168$	−6.37699e8	+	4.95523e7i	−0.800532	+	0.0622052i
$169$	−1.14163e9			−1.39952
$170$	3.15822e8	−	8.16571e6i	0.378135	−	0.00977683i
$171$	−7.10826e8			−0.831340
$172$	6.23968e8	−	3.22875e7i	0.712932	−	0.0368910i
$173$		−	1.26319e9i		−	1.41022i	−0.709100	−	0.705108i	$-0.750898\pi$
$173$		−	1.26319e9i		−	1.41022i	0.709100	−	0.705108i	$-0.249102\pi$
$174$	9.29080e8	−	2.40218e7i	1.01358	−	0.0262064i
$175$		−	3.68857e8i		−	0.393284i
$176$	9.67246e8	−	1.00370e8i	1.00806	−	0.104605i
$177$	1.12400e9			1.14518
$178$	−2.99372e7	−	1.15787e9i	−0.0298217	−	1.15340i
$179$	−1.46968e9			−1.43156			−0.715780	−	0.698326i	$-0.753929\pi$
$179$	−1.46968e9			−1.43156			−0.715780	+	0.698326i	$0.753929\pi$
$180$	7.72835e7	+	1.49353e9i	0.0736201	+	1.42274i
$181$			2.01947e9i			1.88158i	0.338987	+	0.940791i	$0.389916\pi$
$181$			2.01947e9i			1.88158i	−0.338987	+	0.940791i	$0.610084\pi$
$182$	2.43984e7	+	9.43647e8i	0.0222370	+	0.860050i
$183$			1.62540e9i			1.44929i
$184$	2.77880e8	−	2.15926e7i	0.242430	−	0.0188380i
$185$	−1.42126e9			−1.21336
$186$	−2.00849e9	+	5.19303e7i	−1.67810	+	0.0433879i
$187$	−3.58684e8			−0.293323
$188$	−1.78337e7	−	3.44643e8i	−0.0142761	−	0.275891i
$189$			9.22639e7i			0.0723077i
$190$	1.29855e9	−	3.35745e7i	0.996422	−	0.0257629i
$191$		−	2.15828e9i		−	1.62171i	−0.585245	−	0.810856i	$-0.699002\pi$
$191$		−	2.15828e9i		−	1.62171i	0.585245	−	0.810856i	$-0.300998\pi$
$192$	−1.94106e9	+	3.03492e8i	−1.42835	+	0.223328i
$193$	1.53694e9			1.10771			0.553857	−	0.832612i	$-0.313155\pi$
$193$	1.53694e9			1.10771			0.553857	+	0.832612i	$0.313155\pi$
$194$	1.80764e7	+	6.99132e8i	0.0127616	+	0.493574i
$195$	4.23191e9			2.92683
$196$	−1.01919e9	+	5.27383e7i	−0.690605	+	0.0357357i
$197$			1.28341e9i			0.852119i	0.904695	+	0.426060i	$0.140099\pi$
$197$			1.28341e9i			0.852119i	−0.904695	+	0.426060i	$0.859901\pi$
$198$	−4.38861e7	−	1.69737e9i	−0.0285540	−	1.10437i
$199$		−	2.99425e9i		−	1.90931i	−0.297718	−	0.954654i	$-0.596226\pi$
$199$		−	2.99425e9i		−	1.90931i	0.297718	−	0.954654i	$-0.403774\pi$
$200$	−8.77727e7	−	1.12957e9i	−0.0548579	−	0.705979i
$201$	9.89238e8			0.606062
$202$	−2.21271e9	+	5.72104e7i	−1.32898	+	0.0343613i
$203$	−6.61475e8			−0.389520
$204$	7.23690e8	−	3.74477e7i	0.417861	−	0.0216224i
$205$			2.94771e9i			1.66905i
$206$	1.22047e9	−	3.15558e7i	0.677732	−	0.0175230i
$207$		−	4.86657e8i		−	0.265058i
$208$	2.99265e8	+	2.88396e9i	0.159883	+	1.54076i
$209$	−1.47478e9			−0.772935
$210$	−5.27506e7	−	2.04021e9i	−0.0271238	−	1.04905i
$211$	−9.75301e8			−0.492049			−0.246025	−	0.969264i	$-0.579124\pi$
$211$	−9.75301e8			−0.492049			−0.246025	+	0.969264i	$0.579124\pi$
$212$	−8.35372e7	−	1.61439e9i	−0.0413558	−	0.799216i
$213$		−	3.28259e9i		−	1.59477i
$214$	−1.98227e7	−	7.66673e8i	−0.00945164	−	0.365557i
$215$			1.99361e9i			0.933010i
$216$	2.19550e7	+	2.82543e8i	0.0100860	+	0.129799i
$217$	1.42998e9			0.644898
$218$	2.62198e9	−	6.77923e7i	1.16092	−	0.0300161i
$219$	−3.88002e9			−1.68678
$220$	1.60344e8	+	3.09870e9i	0.0684480	+	1.32278i
$221$		−	1.06946e9i		−	0.448328i
$222$	−3.25894e9	+	8.42612e7i	−1.34173	+	0.0346909i
$223$			1.21034e9i			0.489428i	0.969595	+	0.244714i	$0.0786941\pi$
$223$			1.21034e9i			0.489428i	−0.969595	+	0.244714i	$0.921306\pi$
$224$	1.38663e9	−	1.80225e8i	0.550769	−	0.0715850i
$225$	−1.97823e9			−0.771874
$226$	5.31248e7	+	2.05469e9i	0.0203640	+	0.787611i
$227$	3.51988e9			1.32564			0.662818	−	0.748781i	$-0.269360\pi$
$227$	3.51988e9			1.32564			0.662818	+	0.748781i	$0.269360\pi$
$228$	2.97556e9	−	1.53972e8i	1.10111	−	0.0569772i
$229$			1.82707e9i			0.664375i	0.943213	+	0.332187i	$0.107787\pi$
$229$			1.82707e9i			0.664375i	−0.943213	+	0.332187i	$0.892213\pi$
$230$	2.29863e7	+	8.89032e8i	0.00821406	+	0.317692i
$231$			2.31710e9i			0.813763i
$232$	−2.02566e9	+	1.57404e8i	−0.699222	+	0.0543329i
$233$	−1.20474e8			−0.0408762			−0.0204381	−	0.999791i	$-0.506506\pi$
$233$	−1.20474e8			−0.0408762			−0.0204381	+	0.999791i	$0.506506\pi$
$234$	5.06090e9	−	1.30852e8i	1.68797	−	0.0436431i
$235$	1.10115e9			0.361057
$236$	−2.45392e9	+	1.26979e8i	−0.791067	+	0.0409341i
$237$		−	1.99168e9i		−	0.631288i
$238$	−5.15589e8	+	1.33308e7i	−0.160693	+	0.00415478i
$239$			7.24188e8i			0.221952i	0.993823	+	0.110976i	$0.0353977\pi$
$239$			7.24188e8i			0.221952i	−0.993823	+	0.110976i	$0.964602\pi$
$240$	−6.47026e8	−	6.23527e9i	−0.195019	−	1.87936i
$241$	−3.52203e9			−1.04406			−0.522029	−	0.852928i	$-0.674825\pi$
$241$	−3.52203e9			−1.04406			−0.522029	+	0.852928i	$0.674825\pi$
$242$	−2.40473e6	−	9.30068e7i	−0.000701140	−	0.0271177i
$243$	−4.99997e9			−1.43398
$244$	−1.83623e8	−	3.54859e9i	−0.0518046	−	1.00114i
$245$		−	3.25636e9i		−	0.903791i
$246$	1.74758e8	+	6.75904e9i	0.0477195	+	1.84563i
$247$		−	4.39725e9i		−	1.18139i
$248$	4.37909e9	−	3.40276e8i	1.15765	−	0.0899549i
$249$	2.69254e9			0.700429
$250$	−1.48969e9	+	3.85166e7i	−0.381361	+	0.00986025i
$251$	8.00063e8			0.201572			0.100786	−	0.994908i	$-0.467864\pi$
$251$	8.00063e8			0.201572			0.100786	+	0.994908i	$0.467864\pi$
$252$	−1.26168e8	−	2.43824e9i	−0.0312857	−	0.604608i
$253$		−	1.00969e9i		−	0.246437i
$254$	−3.99577e9	+	1.03312e8i	−0.959988	+	0.0248209i
$255$			2.31223e9i			0.546852i
$256$	4.20346e9	−	8.81871e8i	0.978694	−	0.205327i
$257$	4.21833e9			0.966959			0.483480	−	0.875356i	$-0.339373\pi$
$257$	4.21833e9			0.966959			0.483480	+	0.875356i	$0.339373\pi$
$258$	1.18193e8	+	4.57132e9i	0.0266756	+	1.03172i
$259$	2.32026e9			0.515629
$260$	−9.23915e9	+	4.78084e8i	−2.02180	+	0.104619i
$261$			3.54758e9i			0.764487i
$262$	−2.16592e8	−	8.37703e9i	−0.0459660	−	1.77781i
$263$			3.81008e9i			0.796363i	0.917307	+	0.398181i	$0.130359\pi$
$263$			3.81008e9i			0.796363i	−0.917307	+	0.398181i	$0.869641\pi$
$264$	5.51375e8	+	7.09576e9i	0.113509	+	1.46078i
$265$	5.15806e9			1.04593
$266$	−2.11992e9	+	5.48114e7i	−0.423441	+	0.0109483i
$267$	8.47713e9			1.66803
$268$	−2.15972e9	+	1.11755e8i	−0.418656	+	0.0216635i
$269$		−	2.00340e9i		−	0.382613i	−0.981530	−	0.191306i	$-0.938728\pi$
$269$		−	2.00340e9i		−	0.382613i	0.981530	−	0.191306i	$-0.0612724\pi$
$270$	−9.03951e8	+	2.33720e7i	−0.170094	+	0.00439786i
$271$			6.80675e9i			1.26201i	0.775779	+	0.631005i	$0.217357\pi$
$271$			6.80675e9i			1.26201i	−0.775779	+	0.631005i	$0.782643\pi$
$272$	−1.57574e9	+	1.63512e8i	−0.287878	+	0.0298727i
$273$	−6.90873e9			−1.24379
$274$	−1.10821e8	−	4.28619e9i	−0.0196617	−	0.760447i
$275$	−4.10432e9			−0.717647
$276$	1.05414e8	+	2.03717e9i	0.0181662	+	0.351068i
$277$		−	5.15316e9i		−	0.875296i	−0.899146	−	0.437648i	$-0.855812\pi$
$277$		−	5.15316e9i		−	0.875296i	0.899146	−	0.437648i	$-0.144188\pi$
$278$	7.44785e7	+	2.88057e9i	0.0124696	+	0.482281i
$279$		−	7.66917e9i		−	1.26570i
$280$	3.45651e8	+	4.44825e9i	0.0562348	+	0.723698i
$281$	−3.37008e8			−0.0540523			−0.0270262	−	0.999635i	$-0.508604\pi$
$281$	−3.37008e8			−0.0540523			−0.0270262	+	0.999635i	$0.508604\pi$
$282$	2.52492e9	−	6.52830e7i	0.399256	−	0.0103229i
$283$	−4.40140e9			−0.686191			−0.343096	−	0.939300i	$-0.611475\pi$
$283$	−4.40140e9			−0.686191			−0.343096	+	0.939300i	$0.611475\pi$
$284$	3.70838e8	+	7.16658e9i	0.0570047	+	1.10164i
$285$			9.50707e9i			1.44101i
$286$	1.05001e10	−	2.71484e8i	1.56938	−	0.0405770i
$287$		−	4.81222e9i		−	0.709281i
$288$	−9.66569e8	−	7.43670e9i	−0.140496	−	1.08096i
$289$	−6.39143e9			−0.916234
$290$	−1.67563e8	−	6.48077e9i	−0.0236912	−	0.916294i
$291$	−5.11856e9			−0.713799
$292$	8.47090e9	−	4.38331e8i	1.16519	−	0.0602935i
$293$			8.74620e9i			1.18672i	0.804937	+	0.593361i	$0.202199\pi$
$293$			8.74620e9i			1.18672i	−0.804937	+	0.593361i	$0.797801\pi$
$294$	−1.93057e8	−	7.46678e9i	−0.0258402	−	0.999411i
$295$		−	7.84042e9i		−	1.03526i
$296$	7.10543e9	−	5.52126e8i	0.925600	−	0.0719236i
$297$	1.02663e9			0.131944
$298$	6.88706e8	−	1.78068e7i	0.0873311	−	0.00225798i
$299$	3.01051e9			0.376665
$300$	8.28098e9	−	4.28503e8i	1.02234	−	0.0529016i
$301$		−	3.25463e9i		−	0.396493i
$302$	−1.23553e10	+	3.19450e8i	−1.48533	+	0.0384039i
$303$		−	1.61999e10i		−	1.92195i
$304$	−6.47888e9	+	6.72305e8i	−0.758587	+	0.0787176i
$305$	1.13379e10			1.31019
$306$	7.14947e7	+	2.76517e9i	0.00815433	+	0.315382i
$307$	−5.77148e9			−0.649732			−0.324866	−	0.945760i	$-0.605319\pi$
$307$	−5.77148e9			−0.649732			−0.324866	+	0.945760i	$0.605319\pi$
$308$	−2.61766e8	−	5.05873e9i	−0.0290878	−	0.562132i
$309$			8.93543e9i			0.980126i
$310$	3.62239e8	+	1.40102e10i	0.0392236	+	1.51704i
$311$			1.12479e10i			1.20235i	0.799119	+	0.601173i	$0.205300\pi$
$311$			1.12479e10i			1.20235i	−0.799119	+	0.601173i	$0.794700\pi$
$312$	−2.11569e10	+	1.64399e9i	−2.23271	+	0.173493i
$313$	−1.58220e10			−1.64848			−0.824241	−	0.566239i	$-0.808398\pi$
$313$	−1.58220e10			−1.64848			−0.824241	+	0.566239i	$0.808398\pi$
$314$	3.25617e9	−	8.41896e7i	0.334956	−	0.00866044i
$315$	7.79031e9			0.791247
$316$	2.25003e8	+	4.34827e9i	0.0225652	+	0.436082i
$317$			1.39951e9i			0.138592i	0.997596	+	0.0692962i	$0.0220754\pi$
$317$			1.39951e9i			0.138592i	−0.997596	+	0.0692962i	$0.977925\pi$
$318$	1.18273e10	−	3.05801e8i	1.15659	−	0.0299041i
$319$			7.36033e9i			0.710779i
$320$	2.11700e9	+	1.35398e10i	0.201893	+	1.29126i
$321$	5.61305e9			0.528663
$322$	−3.75259e7	−	1.45137e9i	−0.00349066	−	0.135007i
$323$	2.40256e9			0.220732
$324$	9.92493e9	−	5.13570e8i	0.900632	−	0.0466036i
$325$		−	1.22375e10i		−	1.09688i
$326$	−4.97688e8	−	1.92489e10i	−0.0440643	−	1.70426i
$327$			1.91963e10i			1.67891i
$328$	−1.14511e9	−	1.47367e10i	−0.0989354	−	1.27322i
$329$	−1.79767e9			−0.153435
$330$	−2.27017e10	+	5.86963e8i	−1.91427	+	0.0494943i
$331$	9.50549e9			0.791885			0.395943	−	0.918275i	$-0.370418\pi$
$331$	9.50549e9			0.791885			0.395943	+	0.918275i	$0.370418\pi$
$332$	−5.87837e9	+	3.04179e8i	−0.483843	+	0.0250367i
$333$		−	1.24439e10i		−	1.01199i
$334$	1.08533e10	−	2.80617e8i	0.872120	−	0.0225490i
$335$		−	6.90041e9i		−	0.547893i
$336$	1.05629e9	+	1.01793e10i	0.0828756	+	0.798657i
$337$	2.28904e10			1.77473			0.887367	−	0.461063i	$-0.152532\pi$
$337$	2.28904e10			1.77473			0.887367	+	0.461063i	$0.152532\pi$
$338$	4.72119e8	+	1.82599e10i	0.0361730	+	1.39905i
$339$	−1.50430e10			−1.13903
$340$	−2.61215e8	−	5.04808e9i	−0.0195471	−	0.377756i
$341$		−	1.59116e10i		−	1.17678i
$342$	2.93961e8	+	1.13694e10i	0.0214875	+	0.831062i
$343$			1.30036e10i			0.939478i
$344$	−7.74468e8	−	9.96679e9i	−0.0553057	−	0.711741i
$345$	−6.50888e9			−0.459441
$346$	−2.02044e10	+	5.22392e8i	−1.40975	+	0.0364496i
$347$	2.21529e10			1.52796			0.763982	−	0.645238i	$-0.223242\pi$
$347$	2.21529e10			1.52796			0.763982	+	0.645238i	$0.223242\pi$
$348$	−7.68439e8	−	1.48504e10i	−0.0523953	−	1.01256i
$349$			2.05510e9i			0.138526i	0.997598	+	0.0692629i	$0.0220647\pi$
$349$			2.05510e9i			0.138526i	−0.997598	+	0.0692629i	$0.977935\pi$
$350$	−5.89974e9	+	1.52540e8i	−0.393152	+	0.0101651i
$351$			3.06103e9i			0.201669i
$352$	−2.00539e9	−	1.54293e10i	−0.130625	−	1.00502i
$353$	2.64167e9			0.170130			0.0850649	−	0.996375i	$-0.472890\pi$
$353$	2.64167e9			0.170130			0.0850649	+	0.996375i	$0.472890\pi$
$354$	−4.64828e8	−	1.79780e10i	−0.0295991	−	1.14479i
$355$	−2.28976e10			−1.44171
$356$	−1.85074e10	+	9.57672e8i	−1.15224	+	0.0596234i
$357$		−	3.77479e9i		−	0.232391i
$358$	6.07783e8	+	2.35070e10i	0.0370012	+	1.43108i
$359$		−	3.08043e10i		−	1.85453i	−0.374411	−	0.927263i	$-0.622155\pi$
$359$		−	3.08043e10i		−	1.85453i	0.374411	−	0.927263i	$-0.377845\pi$
$360$	2.38566e10	−	1.85377e9i	1.42036	−	0.110369i
$361$	−7.10507e9			−0.418349
$362$	3.23007e10	−	8.35149e8i	1.88095	−	0.0486329i
$363$	6.80931e8			0.0392172
$364$	1.50832e10	−	7.80487e8i	0.859188	−	0.0444591i
$365$			2.70650e10i			1.52488i
$366$	2.59977e10	−	6.72181e8i	1.44881	−	0.0374595i
$367$			2.79953e10i			1.54320i	0.636111	+	0.771598i	$0.280542\pi$
$367$			2.79953e10i			1.54320i	−0.636111	+	0.771598i	$0.719458\pi$
$368$	−4.60284e8	−	4.43567e9i	−0.0250977	−	0.241862i
$369$	−2.58086e10			−1.39206
$370$	5.87762e8	+	2.27326e10i	0.0313613	+	1.21295i
$371$	−8.42069e9			−0.444480
$372$	1.66121e9	+	3.21036e10i	0.0867469	+	1.67642i
$373$			1.22540e10i			0.633059i	0.948583	+	0.316530i	$0.102518\pi$
$373$			1.22540e10i			0.633059i	−0.948583	+	0.316530i	$0.897482\pi$
$374$	1.48333e8	+	5.73703e9i	0.00758145	+	0.293225i
$375$		−	1.09065e10i		−	0.551519i
$376$	−5.50506e9	+	4.27770e8i	−0.275430	+	0.0214022i
$377$	−2.19457e10			−1.08639
$378$	1.47573e9	−	3.81556e7i	0.0722835	−	0.00186892i
$379$	1.18661e10			0.575108			0.287554	−	0.957764i	$-0.407158\pi$
$379$	1.18661e10			0.575108			0.287554	+	0.957764i	$0.407158\pi$
$380$	−1.07403e9	−	2.07559e10i	−0.0515086	−	0.995424i
$381$		−	2.92543e10i		−	1.38832i
$382$	−3.45209e10	+	8.92553e8i	−1.62117	+	0.0419161i
$383$		−	4.90646e8i		−	0.0228020i	−0.999935	−	0.0114010i	$-0.996371\pi$
$383$		−	4.90646e8i		−	0.0228020i	0.999935	−	0.0114010i	$-0.00362913\pi$
$384$	5.65697e9	+	3.09211e10i	0.260171	+	1.42210i
$385$	1.61629e10			0.735659
$386$	−6.35600e8	−	2.45828e10i	−0.0286309	−	1.10734i
$387$	−1.74550e10			−0.778174
$388$	1.11749e10	−	5.78250e8i	0.493079	−	0.0255146i
$389$			1.59050e10i			0.694600i	0.937754	+	0.347300i	$0.112901\pi$
$389$			1.59050e10i			0.694600i	−0.937754	+	0.347300i	$0.887099\pi$
$390$	−1.75010e9	−	6.76879e10i	−0.0756492	−	2.92586i
$391$			1.64488e9i			0.0703765i
$392$	1.26501e9	+	1.62797e10i	0.0535737	+	0.689451i
$393$	6.13308e10			2.57104
$394$	2.05277e10	−	5.30752e8i	0.851835	−	0.0220245i
$395$	−1.38930e10			−0.570698
$396$	−2.71306e10	+	1.40389e9i	−1.10326	+	0.0570888i
$397$		−	1.30554e10i		−	0.525567i	−0.964855	−	0.262784i	$-0.915359\pi$
$397$		−	1.30554e10i		−	0.525567i	0.964855	−	0.262784i	$-0.0846406\pi$
$398$	−4.78920e10	+	1.23827e9i	−1.90867	+	0.0493495i
$399$		−	1.55206e10i		−	0.612374i
$400$	−1.80307e10	+	1.87102e9i	−0.704325	+	0.0730869i
$401$	−1.78164e10			−0.689036			−0.344518	−	0.938780i	$-0.611958\pi$
$401$	−1.78164e10			−0.689036			−0.344518	+	0.938780i	$0.611958\pi$
$402$	−4.09098e8	−	1.58225e10i	−0.0156647	−	0.605859i
$403$	4.74423e10			1.79865
$404$	1.83012e9	+	3.53678e10i	0.0686997	+	1.32765i
$405$			3.17107e10i			1.17865i
$406$	2.73552e8	+	1.05801e10i	0.0100678	+	0.389390i
$407$		−	2.58179e10i		−	0.940898i
$408$	−8.98243e8	−	1.15597e10i	−0.0324156	−	0.417163i
$409$	−2.61784e9			−0.0935514			−0.0467757	−	0.998905i	$-0.514895\pi$
$409$	−2.61784e9			−0.0935514			−0.0467757	+	0.998905i	$0.514895\pi$
$410$	4.71475e10	−	1.21902e9i	1.66849	−	0.0431395i
$411$	3.13805e10			1.09975
$412$	−1.00945e9	−	1.95079e10i	−0.0350344	−	0.677053i
$413$			1.27997e10i			0.439948i
$414$	−7.78391e9	+	2.01256e8i	−0.264970	+	0.00685091i
$415$		−	1.87817e10i		−	0.633203i
$416$	4.60042e10	−	5.97930e9i	1.53612	−	0.199653i
$417$	−2.10896e10			−0.697467
$418$	6.09895e8	+	2.35887e10i	0.0199779	+	0.772677i
$419$	−3.36609e10			−1.09212			−0.546059	−	0.837747i	$-0.683873\pi$
$419$	−3.36609e10			−1.09212			−0.546059	+	0.837747i	$0.683873\pi$
$420$	−3.26107e10	+	1.68745e9i	−1.04800	+	0.0542294i
$421$		−	2.58536e10i		−	0.822986i	−0.911413	−	0.411493i	$-0.865007\pi$
$421$		−	2.58536e10i		−	0.822986i	0.911413	−	0.411493i	$-0.134993\pi$
$422$	4.03334e8	+	1.55996e10i	0.0127179	+	0.491885i
$423$			9.64112e9i			0.301138i
$424$	−2.57870e10	+	2.00378e9i	−0.797881	+	0.0619992i
$425$	6.68634e9			0.204943
$426$	−5.25039e10	+	1.35751e9i	−1.59424	+	0.0412197i
$427$	−1.85095e10			−0.556780
$428$	−1.22545e10	+	6.34113e8i	−0.365191	+	0.0188970i
$429$			7.68744e10i			2.26962i
$430$	3.18871e10	−	8.24455e8i	0.932699	−	0.0241153i
$431$			1.27699e10i			0.370065i	0.982732	+	0.185032i	$0.0592390\pi$
$431$			1.27699e10i			0.370065i	−0.982732	+	0.185032i	$0.940761\pi$
$432$	4.51011e9	−	4.68008e8i	0.129495	−	0.0134375i
$433$	−1.17785e10			−0.335073			−0.167537	−	0.985866i	$-0.553581\pi$
$433$	−1.17785e10			−0.335073			−0.167537	+	0.985866i	$0.553581\pi$
$434$	−5.91366e8	−	2.28720e10i	−0.0166685	−	0.644682i
$435$	4.74478e10			1.32513
$436$	−2.16863e9	−	4.19096e10i	−0.0600122	−	1.15976i
$437$			6.76317e9i			0.185449i
$438$	1.60458e9	+	6.20596e10i	0.0435978	+	1.68621i
$439$			3.51526e9i			0.0946455i	0.998880	+	0.0473227i	$0.0150689\pi$
$439$			3.51526e9i			0.0946455i	−0.998880	+	0.0473227i	$0.984931\pi$
$440$	4.94963e10	−	3.84610e9i	1.32057	−	0.102615i
$441$	2.85110e10			0.753803
$442$	−1.71057e10	+	4.42274e8i	−0.448178	+	0.0115878i
$443$	−4.01611e10			−1.04277			−0.521387	−	0.853320i	$-0.674585\pi$
$443$	−4.01611e10			−1.04277			−0.521387	+	0.853320i	$0.674585\pi$
$444$	2.69546e9	+	5.20907e10i	0.0693587	+	1.34038i
$445$		−	5.91320e10i		−	1.50794i
$446$	1.93590e10	−	5.00536e8i	0.489265	−	0.0126501i
$447$			5.04223e9i			0.126297i
$448$	−3.45607e9	−	2.21042e10i	−0.0857967	−	0.548735i
$449$	1.01115e10			0.248787			0.124394	−	0.992233i	$-0.460301\pi$
$449$	1.01115e10			0.248787			0.124394	+	0.992233i	$0.460301\pi$
$450$	8.18094e8	+	3.16411e10i	0.0199505	+	0.771616i
$451$	−5.35463e10			−1.29426
$452$	3.28420e10	−	1.69942e9i	0.786821	−	0.0407144i
$453$		−	9.04566e10i		−	2.14807i
$454$	−1.45564e9	−	5.62992e10i	−0.0342634	−	1.32519i
$455$			4.81917e10i			1.12441i
$456$	−3.69326e9	−	4.75294e10i	−0.0854182	−	1.09927i
$457$	−6.56497e9			−0.150511			−0.0752554	−	0.997164i	$-0.523977\pi$
$457$	−6.56497e9			−0.150511			−0.0752554	+	0.997164i	$0.523977\pi$
$458$	2.92233e10	−	7.55582e8i	0.664153	−	0.0171720i
$459$	−1.67248e9			−0.0376800
$460$	1.42103e10	−	7.35316e8i	0.317374	−	0.0164226i
$461$		−	6.65968e10i		−	1.47452i	−0.675611	−	0.737258i	$-0.736120\pi$
$461$		−	6.65968e10i		−	1.47452i	0.675611	−	0.737258i	$-0.263880\pi$
$462$	3.70613e10	−	9.58236e8i	0.813491	−	0.0210332i
$463$			5.14797e10i			1.12024i	0.828410	+	0.560121i	$0.189246\pi$
$463$			5.14797e10i			1.12024i	−0.828410	+	0.560121i	$0.810754\pi$
$464$	3.35533e9	+	3.23347e10i	0.0723874	+	0.697584i
$465$	−1.02573e11			−2.19392
$466$	4.98219e7	+	1.92694e9i	0.00105652	+	0.0408625i
$467$	2.27144e10			0.477567			0.238784	−	0.971073i	$-0.423251\pi$
$467$	2.27144e10			0.477567			0.238784	+	0.971073i	$0.423251\pi$
$468$	−4.18586e9	−	8.08932e10i	−0.0872571	−	1.68628i
$469$			1.12651e10i			0.232833i
$470$	−4.55380e8	−	1.76125e10i	−0.00933216	−	0.360936i
$471$			2.38394e10i			0.484409i
$472$	3.04581e9	+	3.91972e10i	0.0613670	+	0.789744i
$473$	−3.62148e10			−0.723504
$474$	−3.18563e10	+	8.23659e8i	−0.631077	+	0.0163168i
$475$	2.74919e10			0.540045
$476$	4.26442e8	+	8.24116e9i	0.00830678	+	0.160532i
$477$			4.51613e10i			0.872354i
$478$	1.15831e10	−	2.99487e8i	0.221878	−	0.00573675i
$479$		−	4.14283e10i		−	0.786965i	−0.919332	−	0.393483i	$-0.871270\pi$
$479$		−	4.14283e10i		−	0.786965i	0.919332	−	0.393483i	$-0.128730\pi$
$480$	−9.94634e10	+	1.29276e10i	−1.87369	+	0.243529i
$481$	7.69791e10			1.43811
$482$	1.45653e9	+	5.63336e10i	0.0269855	+	1.04371i
$483$	1.06260e10			0.195245
$484$	−1.48662e9	+	7.69256e7i	−0.0270905	+	0.00140181i
$485$			3.57044e10i			0.645290i
$486$	2.06773e9	+	7.99728e10i	0.0370637	+	1.43350i
$487$			1.42793e10i			0.253858i	0.991912	+	0.126929i	$0.0405121\pi$
$487$			1.42793e10i			0.253858i	−0.991912	+	0.126929i	$0.959488\pi$
$488$	−5.66825e10	+	4.40450e9i	−0.999469	+	0.0776636i
$489$	1.40927e11			2.46467
$490$	−5.20843e10	+	1.34666e9i	−0.903489	+	0.0233601i
$491$	−5.84716e9			−0.100605			−0.0503024	−	0.998734i	$-0.516019\pi$
$491$	−5.84716e9			−0.100605			−0.0503024	+	0.998734i	$0.516019\pi$
$492$	1.08036e11	−	5.59038e9i	1.84378	−	0.0954072i
$493$		−	1.19907e10i		−	0.202981i
$494$	−7.03324e10	+	1.81847e9i	−1.18099	+	0.0305351i
$495$		−	8.66838e10i		−	1.44383i
$496$	−7.25356e9	−	6.99012e10i	−0.119846	−	1.15494i
$497$	3.73811e10			0.612670
$498$	−1.11349e9	−	4.30662e10i	−0.0181038	−	0.700195i
$499$	1.12286e11			1.81102			0.905512	−	0.424322i	$-0.139487\pi$
$499$	1.12286e11			1.81102			0.905512	+	0.424322i	$0.139487\pi$
$500$	1.23212e9	+	2.38112e10i	0.0197139	+	0.380979i
$501$			7.94604e10i			1.26125i
$502$	−3.30865e8	−	1.27967e10i	−0.00520998	−	0.201504i
$503$			5.57125e10i			0.870323i	0.900352	+	0.435161i	$0.143309\pi$
$503$			5.57125e10i			0.870323i	−0.900352	+	0.435161i	$0.856691\pi$
$504$	−3.89466e10	+	3.02634e9i	−0.603598	+	0.0469025i
$505$	−1.13002e11			−1.73748
$506$	−1.61496e10	+	4.17556e8i	−0.246355	+	0.00636960i
$507$	−1.33687e11			−2.02328
$508$	3.30489e9	+	6.38683e10i	0.0496252	+	0.959026i
$509$			5.21251e10i			0.776562i	0.921541	+	0.388281i	$0.126931\pi$
$509$			5.21251e10i			0.776562i	−0.921541	+	0.388281i	$0.873069\pi$
$510$	3.69833e10	−	9.56219e8i	0.546670	−	0.0141344i
$511$		−	4.41845e10i		−	0.648016i
$512$	−1.58436e10	−	6.68681e10i	−0.230554	−	0.973060i
$513$	−6.87667e9			−0.0992907
$514$	−1.74448e9	−	6.74707e10i	−0.0249928	−	0.966636i
$515$	6.23289e10			0.886055
$516$	7.30678e10	−	3.78092e9i	1.03069	−	0.0533334i
$517$			2.00029e10i			0.279982i
$518$	−9.59541e8	−	3.71118e10i	−0.0133274	−	0.515457i
$519$		−	1.47922e11i		−	2.03875i
$520$	1.14676e10	+	1.47579e11i	0.156841	+	2.01842i
$521$	−5.67605e10			−0.770362			−0.385181	−	0.922841i	$-0.625861\pi$
$521$	−5.67605e10			−0.770362			−0.385181	+	0.922841i	$0.625861\pi$
$522$	5.67423e10	−	1.46710e9i	0.764232	−	0.0197595i
$523$	−9.53204e10			−1.27403			−0.637014	−	0.770852i	$-0.719831\pi$
$523$	−9.53204e10			−1.27403			−0.637014	+	0.770852i	$0.719831\pi$
$524$	−1.33898e11	+	6.92862e9i	−1.77603	+	0.0919012i
$525$		−	4.31938e10i		−	0.568571i
$526$	6.09409e10	−	1.57565e9i	0.796097	−	0.0205834i
$527$			2.59215e10i			0.336061i
$528$	1.13266e11	−	1.17535e10i	1.45735	−	0.151228i
$529$	7.36807e10			0.940873
$530$	−2.13311e9	−	8.25013e10i	−0.0270339	−	1.04558i
$531$	6.86467e10			0.863458
$532$	1.75338e9	+	3.38847e10i	0.0218892	+	0.423017i
$533$		−	1.59655e11i		−	1.97821i
$534$	−3.50571e9	−	1.35589e11i	−0.0431132	−	1.66747i
$535$		−	3.91537e10i		−	0.477923i
$536$	2.68064e9	+	3.44977e10i	0.0324772	+	0.417956i
$537$	−1.72102e11			−2.06961
$538$	−3.20437e10	+	8.28505e8i	−0.382485	+	0.00988931i
$539$	5.91531e10			0.700846
$540$	7.47655e8	+	1.44487e10i	0.00879278	+	0.169924i
$541$			1.16576e11i			1.36088i	0.732802	+	0.680442i	$0.238212\pi$
$541$			1.16576e11i			1.36088i	−0.732802	+	0.680442i	$0.761788\pi$
$542$	1.08872e11	−	2.81492e9i	1.26159	−	0.0326189i
$543$			2.36484e11i			2.72021i
$544$	3.26697e9	+	2.51358e10i	0.0373035	+	0.287010i
$545$	1.33903e11			1.51777
$546$	2.85710e9	+	1.10503e11i	0.0321480	+	1.24338i
$547$	−6.33069e10			−0.707134			−0.353567	−	0.935409i	$-0.615031\pi$
$547$	−6.33069e10			−0.707134			−0.353567	+	0.935409i	$0.615031\pi$
$548$	−6.85102e10	+	3.54509e9i	−0.759684	+	0.0393102i
$549$			9.92690e10i			1.09276i
$550$	1.69734e9	+	6.56472e10i	0.0185489	+	0.717407i
$551$		−	4.93015e10i		−	0.534876i
$552$	3.25403e10	−	2.52854e9i	0.350482	−	0.0272341i
$553$	2.26807e10			0.242525
$554$	−8.24231e10	+	2.13108e9i	−0.875003	+	0.0226236i
$555$	−1.66433e11			−1.75415
$556$	4.60430e10	−	2.38251e9i	0.481797	−	0.0249308i
$557$		−	4.59938e9i		−	0.0477835i	−0.999715	−	0.0238918i	$-0.992394\pi$
$557$		−	4.59938e9i		−	0.0477835i	0.999715	−	0.0238918i	$-0.00760571\pi$
$558$	−1.22666e11	+	3.17157e9i	−1.26528	+	0.0327143i
$559$		−	1.07979e11i		−	1.10584i
$560$	7.10053e10	−	7.36813e9i	0.722003	−	0.0749213i
$561$	−4.20026e10			−0.424057
$562$	1.39369e8	+	5.39032e9i	0.00139708	+	0.0540343i
$563$	2.80679e10			0.279368			0.139684	−	0.990196i	$-0.455391\pi$
$563$	2.80679e10			0.279368			0.139684	+	0.990196i	$0.455391\pi$
$564$	−2.08836e9	−	4.03583e10i	−0.0206390	−	0.398856i
$565$			1.04932e11i			1.02971i
$566$	1.82019e9	+	7.03989e10i	0.0177358	+	0.685962i
$567$		−	5.17687e10i		−	0.500882i
$568$	1.14474e11	−	8.89516e9i	1.09980	−	0.0854595i
$569$	−7.04379e10			−0.671981			−0.335991	−	0.941865i	$-0.609071\pi$
$569$	−7.04379e10			−0.671981			−0.335991	+	0.941865i	$0.609071\pi$
$570$	1.52062e11	−	3.93164e9i	1.44053	−	0.0372455i
$571$	−1.36062e10			−0.127995			−0.0639976	−	0.997950i	$-0.520385\pi$
$571$	−1.36062e10			−0.127995			−0.0639976	+	0.997950i	$0.520385\pi$
$572$	−8.68459e9	−	1.67833e11i	−0.0811270	−	1.56781i
$573$		−	2.52738e11i		−	2.34451i
$574$	−7.69699e10	+	1.99009e9i	−0.709044	+	0.0183326i
$575$			1.88219e10i			0.172184i
$576$	−1.18548e11	+	1.85354e10i	−1.07697	+	0.168388i
$577$	−6.24509e10			−0.563424			−0.281712	−	0.959499i	$-0.590902\pi$
$577$	−6.24509e10			−0.563424			−0.281712	+	0.959499i	$0.590902\pi$
$578$	2.64317e9	+	1.02229e11i	0.0236817	+	0.915928i
$579$	1.79979e11			1.60142
$580$	−1.03588e11	+	5.36023e9i	−0.915375	+	0.0473665i
$581$			3.06618e10i			0.269087i
$582$	2.11677e9	+	8.18696e10i	0.0184494	+	0.713561i
$583$			9.36982e10i			0.811068i
$584$	−1.05141e10	−	1.35308e11i	−0.0903899	−	1.16325i
$585$	2.58458e11			2.20682
$586$	1.39892e11	−	3.61698e9i	1.18633	−	0.0306729i
$587$	1.12714e11			0.949349			0.474675	−	0.880161i	$-0.342566\pi$
$587$	1.12714e11			0.949349			0.474675	+	0.880161i	$0.342566\pi$
$588$	−1.19349e11	+	6.17575e9i	−0.998409	+	0.0516631i
$589$			1.06580e11i			0.885554i
$590$	−1.25405e11	+	3.24240e9i	−1.03492	+	0.0267583i
$591$			1.50290e11i			1.23191i
$592$	−1.17695e10	−	1.13421e11i	−0.0958234	−	0.923432i
$593$	8.58265e10			0.694069			0.347035	−	0.937852i	$-0.387189\pi$
$593$	8.58265e10			0.694069			0.347035	+	0.937852i	$0.387189\pi$
$594$	−4.24563e8	−	1.64206e10i	−0.00341033	−	0.131900i
$595$	−2.63309e10			−0.210087
$596$	−5.69627e8	−	1.10083e10i	−0.00451446	−	0.0872435i
$597$		−	3.50632e11i		−	2.76029i
$598$	−1.24499e9	−	4.81521e10i	−0.00973559	−	0.376539i
$599$			1.64116e10i			0.127480i	0.997967	+	0.0637402i	$0.0203029\pi$
$599$			1.64116e10i			0.127480i	−0.997967	+	0.0637402i	$0.979697\pi$
$600$	−1.02783e10	−	1.32274e11i	−0.0793082	−	1.02063i
$601$	−9.89850e10			−0.758702			−0.379351	−	0.925253i	$-0.623853\pi$
$601$	−9.89850e10			−0.758702			−0.379351	+	0.925253i	$0.623853\pi$
$602$	−5.20567e10	+	1.34595e9i	−0.396361	+	0.0102481i
$603$	6.04164e10			0.456968
$604$	1.02190e10	+	1.97486e11i	0.0767822	+	1.48384i
$605$		−	4.74982e9i		−	0.0354532i
$606$	−2.59112e11	+	6.69945e9i	−1.92131	+	0.0496762i
$607$		−	1.69608e11i		−	1.24937i	−0.780877	−	0.624684i	$-0.785228\pi$
$607$		−	1.69608e11i		−	1.24937i	0.780877	−	0.624684i	$-0.214772\pi$
$608$	1.34326e10	+	1.03349e11i	0.0982983	+	0.756299i
$609$	−7.74600e10			−0.563129
$610$	−4.68878e9	−	1.81346e11i	−0.0338642	−	1.30975i
$611$	−5.96410e10			−0.427937
$612$	4.41984e10	−	2.28707e9i	0.315066	−	0.0163032i
$613$		−	2.20925e10i		−	0.156460i	−0.996935	−	0.0782299i	$-0.975073\pi$
$613$		−	2.20925e10i		−	0.156460i	0.996935	−	0.0782299i	$-0.0249268\pi$
$614$	2.38679e9	+	9.23129e10i	0.0167935	+	0.649515i
$615$			3.45182e11i			2.41294i
$616$	−8.08044e10	+	6.27889e9i	−0.561193	+	0.0436074i
$617$	1.73682e11			1.19844			0.599218	−	0.800586i	$-0.295478\pi$
$617$	1.73682e11			1.19844			0.599218	+	0.800586i	$0.295478\pi$
$618$	1.42919e11	−	3.69524e9i	0.979798	−	0.0253331i
$619$	−1.11200e11			−0.757427			−0.378714	−	0.925514i	$-0.623634\pi$
$619$	−1.11200e11			−0.757427			−0.378714	+	0.925514i	$0.623634\pi$
$620$	2.23938e11	−	1.15878e10i	1.51552	−	0.0784211i
$621$		−	4.70801e9i		−	0.0316571i
$622$	1.79906e11	−	4.65155e9i	1.20194	−	0.0310768i
$623$			9.65349e10i			0.640814i
$624$	3.50445e10	+	3.37717e11i	0.231143	+	2.22748i
$625$	−1.84127e11			−1.20669
$626$	6.54317e9	+	2.53067e11i	0.0426080	+	1.64793i
$627$	−1.72700e11			−1.11743
$628$	−2.69317e9	−	5.20465e10i	−0.0173151	−	0.334621i
$629$			4.20598e10i			0.268698i
$630$	−3.22167e9	−	1.24603e11i	−0.0204512	−	0.790983i
$631$		−	5.12783e10i		−	0.323457i	−0.986835	−	0.161728i	$-0.948293\pi$
$631$		−	5.12783e10i		−	0.323457i	0.986835	−	0.161728i	$-0.0517069\pi$
$632$	6.94560e10	−	5.39707e9i	0.435353	−	0.0338290i
$633$	−1.14209e11			−0.711356
$634$	2.23847e10	−	5.78766e8i	0.138546	−	0.00358217i
$635$	−2.04063e11			−1.25507
$636$	−9.78236e9	−	1.89048e11i	−0.0597882	−	1.15543i
$637$			1.76372e11i			1.07120i
$638$	1.17726e11	−	3.04385e9i	0.710541	−	0.0183713i
$639$		−	2.00480e11i		−	1.20245i
$640$	2.15689e11	−	3.94601e10i	1.28561	−	0.235200i
$641$	−1.81897e10			−0.107744			−0.0538720	−	0.998548i	$-0.517156\pi$
$641$	−1.81897e10			−0.107744			−0.0538720	+	0.998548i	$0.517156\pi$
$642$	−2.32127e9	−	8.97789e10i	−0.0136642	−	0.528487i
$643$	3.01804e11			1.76555			0.882776	−	0.469794i	$-0.155672\pi$
$643$	3.01804e11			1.76555			0.882776	+	0.469794i	$0.155672\pi$
$644$	−2.31987e10	+	1.20043e9i	−0.134872	+	0.00697899i
$645$			2.33455e11i			1.34885i
$646$	−9.93577e8	−	3.84282e10i	−0.00570521	−	0.220658i
$647$		−	1.73236e11i		−	0.988602i	−0.869291	−	0.494301i	$-0.835424\pi$
$647$		−	1.73236e11i		−	0.988602i	0.869291	−	0.494301i	$-0.164576\pi$
$648$	−1.23188e10	−	1.58533e11i	−0.0698665	−	0.899127i
$649$	1.42424e11			0.802797
$650$	−1.95735e11	+	5.06082e9i	−1.09652	+	0.0283509i
$651$	1.67453e11			0.932330
$652$	−3.07673e11	+	1.59207e10i	−1.70255	+	0.0880991i
$653$		−	5.07276e10i		−	0.278992i	−0.990223	−	0.139496i	$-0.955452\pi$
$653$		−	5.07276e10i		−	0.278992i	0.990223	−	0.139496i	$-0.0445482\pi$
$654$	3.07038e11	−	7.93860e9i	1.67835	−	0.0433943i
$655$		−	4.27812e11i		−	2.32427i
$656$	−2.35234e11	+	2.44100e10i	−1.27024	+	0.131811i
$657$	−2.36967e11			−1.27182
$658$	7.43422e8	+	2.87530e10i	0.00396581	+	0.153384i
$659$	−1.55901e11			−0.826621			−0.413311	−	0.910590i	$-0.635628\pi$
$659$	−1.55901e11			−0.826621			−0.413311	+	0.910590i	$0.635628\pi$
$660$	1.87765e10	+	3.62863e11i	0.0989554	+	1.91235i
$661$			3.02556e10i			0.158489i	0.996855	+	0.0792446i	$0.0252508\pi$
$661$			3.02556e10i			0.158489i	−0.996855	+	0.0792446i	$0.974749\pi$
$662$	−3.93098e9	−	1.52037e11i	−0.0204677	−	0.791621i
$663$		−	1.25236e11i		−	0.648148i
$664$	7.29623e9	+	9.38967e10i	0.0375341	+	0.483035i
$665$	−1.08264e11			−0.553599
$666$	−1.99035e11	+	5.14614e9i	−1.01166	+	0.0261568i
$667$	3.37536e10			0.170536
$668$	−8.97674e9	−	1.73479e11i	−0.0450830	−	0.871245i
$669$			1.41733e11i			0.707567i
$670$	−1.10370e11	+	2.85365e9i	−0.547710	+	0.0141613i
$671$			2.05958e11i			1.01599i
$672$	1.62377e11	−	2.11046e10i	0.796248	−	0.103491i
$673$	2.57800e11			1.25667			0.628337	−	0.777941i	$-0.283736\pi$
$673$	2.57800e11			1.25667			0.628337	+	0.777941i	$0.283736\pi$
$674$	−9.46628e9	−	3.66124e11i	−0.0458712	−	1.77414i
$675$	−1.91378e10			−0.0921884
$676$	2.91866e11	−	1.51028e10i	1.39765	−	0.0723218i
$677$			1.27099e11i			0.605045i	0.953142	+	0.302523i	$0.0978288\pi$
$677$			1.27099e11i			0.605045i	−0.953142	+	0.302523i	$0.902171\pi$
$678$	6.22101e9	+	2.40607e11i	0.0294403	+	1.13865i
$679$		−	5.82886e10i		−	0.274223i
$680$	−8.06343e10	+	6.26568e9i	−0.377124	+	0.0293044i
$681$	4.12184e11			1.91647
$682$	−2.54500e11	+	6.58021e9i	−1.17639	+	0.0304160i
$683$	1.63606e11			0.751825			0.375913	−	0.926655i	$-0.377329\pi$
$683$	1.63606e11			0.751825			0.375913	+	0.926655i	$0.377329\pi$
$684$	1.81728e11	−	9.40361e9i	0.830229	−	0.0429606i
$685$		−	2.18894e11i		−	0.994194i
$686$	2.07988e11	−	5.37761e9i	0.939164	−	0.0242825i
$687$			2.13953e11i			0.960487i
$688$	−1.59095e11	+	1.65091e10i	−0.710073	+	0.0736834i
$689$	−2.79373e11			−1.23967
$690$	2.69174e9	+	1.04107e11i	0.0118751	+	0.459288i
$691$	−2.27235e11			−0.996698			−0.498349	−	0.866977i	$-0.666060\pi$
$691$	−2.27235e11			−0.996698			−0.498349	+	0.866977i	$0.666060\pi$
$692$	1.67110e10	+	3.22946e11i	0.0728748	+	1.40833i
$693$			1.41514e11i			0.613574i
$694$	−9.16131e9	−	3.54328e11i	−0.0394929	−	1.52745i
$695$			1.47110e11i			0.630525i
$696$	−2.37209e11	+	1.84323e10i	−1.01087	+	0.0785492i
$697$	8.72321e10			0.369611
$698$	3.28706e10	−	8.49883e8i	0.138480	−	0.00358045i
$699$	−1.41077e10			−0.0590947
$700$	4.87966e9	+	9.43012e10i	0.0203234	+	0.392758i
$701$		−	2.08347e11i		−	0.862809i	−0.902159	−	0.431404i	$-0.858018\pi$
$701$		−	2.08347e11i		−	0.862809i	0.902159	−	0.431404i	$-0.141982\pi$
$702$	4.89601e10	−	1.26589e9i	0.201602	−	0.00521250i
$703$			1.72935e11i			0.708046i
$704$	−2.45956e11	+	3.84562e10i	−1.00131	+	0.156558i
$705$	1.28947e11			0.521981
$706$	−1.09246e9	−	4.22527e10i	−0.00439731	−	0.170073i
$707$	1.84479e11			0.738364
$708$	−2.87359e11	+	1.48695e10i	−1.14365	+	0.0591785i
$709$		−	1.95088e11i		−	0.772050i	−0.922488	−	0.386025i	$-0.873848\pi$
$709$		−	1.95088e11i		−	0.772050i	0.922488	−	0.386025i	$-0.126152\pi$
$710$	9.46928e9	+	3.66240e11i	0.0372635	+	1.44123i
$711$		−	1.21640e11i		−	0.475988i
$712$	2.29713e10	+	2.95623e11i	0.0893853	+	1.15032i
$713$	−7.29686e10			−0.282343
$714$	−6.03764e10	+	1.56106e9i	−0.232314	+	0.00600657i
$715$	5.36235e11			2.05178
$716$	3.75735e11	−	1.94426e10i	1.42965	−	0.0739778i
$717$			8.48037e10i			0.320877i
$718$	−4.92703e11	+	1.27391e10i	−1.85391	+	0.0479335i
$719$			5.95489e10i			0.222822i	0.993774	+	0.111411i	$0.0355370\pi$
$719$			5.95489e10i			0.222822i	−0.993774	+	0.111411i	$0.964463\pi$
$720$	−3.95163e10	−	3.80811e11i	−0.147044	−	1.41703i
$721$	−1.01754e11			−0.376539
$722$	2.93829e9	+	1.13643e11i	0.0108130	+	0.418210i
$723$	−4.12436e11			−1.50940
$724$	−2.67158e10	−	5.16294e11i	−0.0972332	−	1.87907i
$725$		−	1.37206e11i		−	0.496617i
$726$	−2.81598e8	−	1.08913e10i	−0.00101364	−	0.0392041i
$727$			3.85973e11i			1.38172i	0.722990	+	0.690859i	$0.242767\pi$
$727$			3.85973e11i			1.38172i	−0.722990	+	0.690859i	$0.757233\pi$
$728$	−1.87213e10	−	2.40928e11i	−0.0666515	−	0.857752i
$729$	−3.30800e11			−1.17127
$730$	4.32895e11	−	1.11927e10i	1.52437	−	0.0394133i
$731$	5.89973e10			0.206616
$732$	−2.15026e10	−	4.15546e11i	−0.0748940	−	1.44735i
$733$			1.51989e11i			0.526498i	0.964728	+	0.263249i	$0.0847941\pi$
$733$			1.51989e11i			0.526498i	−0.964728	+	0.263249i	$0.915206\pi$
$734$	4.47775e11	−	1.15774e10i	1.54268	−	0.0398866i
$735$		−	3.81326e11i		−	1.30661i
$736$	−7.07567e10	+	9.19645e9i	−0.241133	+	0.0313407i
$737$	1.25349e11			0.424864
$738$	1.06731e10	+	4.12799e11i	0.0359803	+	1.39160i
$739$	−4.50800e11			−1.51149			−0.755746	−	0.654865i	$-0.772725\pi$
$739$	−4.50800e11			−1.51149			−0.755746	+	0.654865i	$0.772725\pi$
$740$	3.63358e11	−	1.88021e10i	1.21173	−	0.0627017i
$741$		−	5.14925e11i		−	1.70794i
$742$	3.48237e9	+	1.34686e11i	0.0114884	+	0.444331i
$743$		−	4.15542e11i		−	1.36351i	−0.731579	−	0.681757i	$-0.761216\pi$
$743$		−	4.15542e11i		−	1.36351i	0.731579	−	0.681757i	$-0.238784\pi$
$744$	5.12799e11	−	3.98470e10i	1.67361	−	0.130048i
$745$	3.51720e10			0.114175
$746$	1.95999e11	−	5.06764e9i	0.632848	−	0.0163625i
$747$	1.64443e11			0.528121
$748$	9.17005e10	−	4.74508e9i	0.292931	−	0.0151578i
$749$			6.39197e10i			0.203099i
$750$	−1.74446e11	+	4.51037e9i	−0.551334	+	0.0142550i
$751$			4.76424e11i			1.49773i	0.662722	+	0.748865i	$0.269401\pi$
$751$			4.76424e11i			1.49773i	−0.662722	+	0.748865i	$0.730599\pi$
$752$	9.11865e9	+	8.78747e10i	0.0285141	+	0.274785i
$753$	9.36888e10			0.291412
$754$	9.07562e9	+	3.51014e11i	0.0280796	+	1.08602i
$755$	−6.30978e11			−1.94190
$756$	−1.22057e9	−	2.35880e10i	−0.00373660	−	0.0722111i
$757$			1.17954e11i			0.359195i	0.983740	+	0.179598i	$0.0574796\pi$
$757$			1.17954e11i			0.359195i	−0.983740	+	0.179598i	$0.942520\pi$
$758$	−4.90719e9	−	1.89793e11i	−0.0148647	−	0.574916i
$759$		−	1.18237e11i		−	0.356274i
$760$	−3.31540e11	+	2.57622e10i	−0.993760	+	0.0772199i
$761$	−5.67775e11			−1.69293			−0.846463	−	0.532448i	$-0.821272\pi$
$761$	−5.67775e11			−1.69293			−0.846463	+	0.532448i	$0.821272\pi$
$762$	−4.67912e11	+	1.20981e10i	−1.38786	+	0.0358836i
$763$	−2.18601e11			−0.644993
$764$	2.85522e10	+	5.51781e11i	0.0838041	+	1.61955i
$765$			1.41216e11i			0.412324i
$766$	−7.84771e9	+	2.02906e8i	−0.0227944	+	0.000589358i
$767$			4.24656e11i			1.22703i
$768$	4.92232e11	−	1.03269e11i	1.41490	−	0.296841i
$769$	3.38855e11			0.968967			0.484484	−	0.874800i	$-0.339008\pi$
$769$	3.38855e11			0.968967			0.484484	+	0.874800i	$0.339008\pi$
$770$	−6.68415e9	−	2.58520e11i	−0.0190144	−	0.735413i
$771$	4.93974e11			1.39793
$772$	−3.92931e11	+	2.03324e10i	−1.10623	+	0.0572426i
$773$		−	2.46437e10i		−	0.0690222i	−0.999404	−	0.0345111i	$-0.989013\pi$
$773$		−	2.46437e10i		−	0.0690222i	0.999404	−	0.0345111i	$-0.0109874\pi$
$774$	7.21850e9	+	2.79187e11i	0.0201133	+	0.777914i
$775$			2.96612e11i			0.822210i
$776$	−1.38703e10	−	1.78499e11i	−0.0382506	−	0.492255i
$777$	2.71707e11			0.745446
$778$	2.54395e11	−	6.57748e9i	0.694368	−	0.0179532i
$779$	3.58667e11			0.973962
$780$	−1.08192e12	+	5.59845e10i	−2.92292	+	0.151248i
$781$		−	4.15945e11i		−	1.11797i
$782$	2.63093e10	−	6.80239e8i	0.0703530	−	0.00181901i
$783$			3.43200e10i			0.0913061i
$784$	2.59866e11	−	2.69659e10i	0.687836	−	0.0713758i
$785$	1.66291e11			0.437916
$786$	−2.53633e10	−	9.80965e11i	−0.0664531	−	2.57018i
$787$	4.39743e11			1.14630			0.573152	−	0.819449i	$-0.305721\pi$
$787$	4.39743e11			1.14630			0.573152	+	0.819449i	$0.305721\pi$
$788$	−1.69784e10	−	3.28114e11i	−0.0440344	−	0.850981i
$789$			4.46167e11i			1.15130i
$790$	5.74541e9	+	2.22213e11i	0.0147507	+	0.570507i
$791$		−	1.71305e11i		−	0.437586i
$792$	3.36745e10	+	4.33364e11i	0.0855856	+	1.10142i
$793$	−6.14089e11			−1.55288
$794$	−2.08817e11	+	5.39905e9i	−0.525392	+	0.0135842i
$795$	6.04018e11			1.51210
$796$	3.96113e10	+	7.65504e11i	0.0986660	+	1.90676i
$797$		−	3.65324e11i		−	0.905409i	−0.891661	−	0.452704i	$-0.850459\pi$
$797$		−	3.65324e11i		−	0.905409i	0.891661	−	0.452704i	$-0.149541\pi$
$798$	−2.48247e11	+	6.41852e9i	−0.612170	+	0.0158279i
$799$		−	3.25866e10i		−	0.0799562i
$800$	3.73830e10	+	2.87621e11i	0.0912670	+	0.702200i
$801$	5.17730e11			1.25769
$802$	7.36794e9	+	2.84967e11i	0.0178094	+	0.688806i
$803$	−4.91647e11			−1.18247
$804$	−2.52907e11	+	1.30868e10i	−0.605252	+	0.0313190i
$805$		−	7.41211e10i		−	0.176506i
$806$	−1.96197e10	−	7.58823e11i	−0.0464892	−	1.79805i
$807$		−	2.34602e11i		−	0.553144i
$808$	5.64939e11	−	4.38985e10i	1.32543	−	0.102992i
$809$	2.70705e11			0.631979			0.315989	−	0.948763i	$-0.397664\pi$
$809$	2.70705e11			0.631979			0.315989	+	0.948763i	$0.397664\pi$
$810$	5.07202e11	−	1.31139e10i	1.17826	−	0.0304644i
$811$	−4.91862e11			−1.13700			−0.568499	−	0.822684i	$-0.692476\pi$
$811$	−4.91862e11			−1.13700			−0.568499	+	0.822684i	$0.692476\pi$
$812$	1.69111e11	−	8.75075e9i	0.388999	−	0.0201289i
$813$			7.97083e11i			1.82449i
$814$	−4.12948e11	+	1.06769e10i	−0.940584	+	0.0243192i
$815$		−	9.83033e11i		−	2.22811i
$816$	−1.84522e11	+	1.91476e10i	−0.416185	+	0.0431870i
$817$	2.42576e11			0.544453
$818$	1.08261e9	+	4.18715e10i	0.00241800	+	0.0935202i
$819$	−4.21941e11			−0.937814
$820$	−3.89956e10	−	7.53604e11i	−0.0862502	−	1.66682i
$821$			6.14111e11i			1.35168i	0.737048	+	0.675840i	$0.236219\pi$
$821$			6.14111e11i			1.35168i	−0.737048	+	0.675840i	$0.763781\pi$
$822$	−1.29774e10	−	5.01920e11i	−0.0284249	−	1.09938i
$823$		−	3.67833e11i		−	0.801773i	−0.916128	−	0.400887i	$-0.868702\pi$
$823$		−	3.67833e11i		−	0.801773i	0.916128	−	0.400887i	$-0.131298\pi$
$824$	−3.11605e11	+	2.42132e10i	−0.675921	+	0.0525223i
$825$	−4.80624e11			−1.03750
$826$	2.04727e11	−	5.29331e9i	0.439801	−	0.0113712i
$827$	1.16631e11			0.249340			0.124670	−	0.992198i	$-0.460213\pi$
$827$	1.16631e11			0.249340			0.124670	+	0.992198i	$0.460213\pi$
$828$	6.43805e9	+	1.24418e11i	0.0136972	+	0.264704i
$829$		−	2.17080e11i		−	0.459623i	−0.973235	−	0.229811i	$-0.926189\pi$
$829$		−	2.17080e11i		−	0.459623i	0.973235	−	0.229811i	$-0.0738109\pi$
$830$	−3.00407e11	+	7.76715e9i	−0.632991	+	0.0163663i
$831$		−	6.03445e11i		−	1.26542i
$832$	−1.14662e11	−	7.33349e11i	−0.239290	−	1.53044i
$833$	−9.63661e10			−0.200145
$834$	8.72157e9	+	3.37321e11i	0.0180273	+	0.697234i
$835$	5.54274e11			1.14019
$836$	3.77040e11	−	1.95101e10i	0.771902	−	0.0399424i
$837$		−	7.41930e10i		−	0.151169i
$838$	1.39204e10	+	5.38395e11i	0.0282278	+	1.09175i
$839$			7.83812e11i			1.58185i	0.611916	+	0.790923i	$0.290399\pi$
$839$			7.83812e11i			1.58185i	−0.611916	+	0.790923i	$0.709601\pi$
$840$	4.04763e10	+	5.20899e11i	0.0812988	+	1.04625i
$841$	2.54193e11			0.508136
$842$	−4.13519e11	+	1.06917e10i	−0.822711	+	0.0212715i
$843$	−3.94642e10			−0.0781435
$844$	2.49343e11	−	1.29024e10i	0.491392	−	0.0254273i
$845$			9.32529e11i			1.82909i
$846$	1.54206e11	−	3.98707e9i	0.301038	−	0.00778345i
$847$			7.75423e9i			0.0150663i
$848$	4.27139e10	+	4.11626e11i	0.0826011	+	0.796012i
$849$	−5.15412e11			−0.992028
$850$	−2.76513e9	−	1.06946e11i	−0.00529711	−	0.204874i
$851$	−1.18398e11			−0.225748
$852$	4.34258e10	+	8.39220e11i	0.0824118	+	1.59264i
$853$		−	3.27033e10i		−	0.0617726i	−0.999523	−	0.0308863i	$-0.990167\pi$
$853$		−	3.27033e10i		−	0.0617726i	0.999523	−	0.0308863i	$-0.00983297\pi$
$854$	7.65459e9	+	2.96053e11i	0.0143910	+	0.556594i
$855$			5.80632e11i			1.08652i
$856$	1.52102e10	+	1.95744e11i	0.0283297	+	0.364580i
$857$	5.60076e11			1.03830			0.519151	−	0.854682i	$-0.326248\pi$
$857$	5.60076e11			1.03830			0.519151	+	0.854682i	$0.326248\pi$
$858$	1.22958e12	−	3.17913e10i	2.26886	−	0.0586623i
$859$	2.47062e11			0.453768			0.226884	−	0.973922i	$-0.427146\pi$
$859$	2.47062e11			0.453768			0.226884	+	0.973922i	$0.427146\pi$
$860$	−2.63737e10	−	5.09682e11i	−0.0482145	−	0.931764i
$861$		−	5.63520e11i		−	1.02541i
$862$	2.04250e11	−	5.28097e9i	0.369941	−	0.00956499i
$863$		−	6.72583e11i		−	1.21256i	−0.795252	−	0.606279i	$-0.792661\pi$
$863$		−	6.72583e11i		−	1.21256i	0.795252	−	0.606279i	$-0.207339\pi$
$864$	−9.35077e9	−	7.19440e10i	−0.0167800	−	0.129104i
$865$	−1.03183e12			−1.84308
$866$	4.87100e9	+	1.88394e11i	0.00866057	+	0.334961i
$867$	−7.48448e11			−1.32460
$868$	−3.65586e11	+	1.89174e10i	−0.644036	+	0.0333259i
$869$		−	2.52371e11i		−	0.442548i
$870$	−1.96220e10	−	7.58910e11i	−0.0342504	−	1.32469i
$871$			3.73743e11i			0.649381i
$872$	−6.69432e11	+	5.20181e10i	−1.15782	+	0.0899681i
$873$	−3.12609e11			−0.538202
$874$	1.08175e11	−	2.79690e9i	0.185387	−	0.00479327i
$875$	1.24200e11			0.211879
$876$	9.91958e11	−	5.13293e10i	1.68452	−	0.0871664i
$877$		−	5.28180e11i		−	0.892861i	−0.894818	−	0.446430i	$-0.852695\pi$
$877$		−	5.28180e11i		−	0.892861i	0.894818	−	0.446430i	$-0.147305\pi$
$878$	5.62254e10	−	1.45373e9i	0.0946138	−	0.00244628i
$879$			1.02420e12i			1.71565i
$880$	−8.19862e10	−	7.90086e11i	−0.136713	−	1.31748i
$881$	−1.56184e11			−0.259258			−0.129629	−	0.991563i	$-0.541379\pi$
$881$	−1.56184e11			−0.259258			−0.129629	+	0.991563i	$0.541379\pi$
$882$	−1.17907e10	−	4.56024e11i	−0.0194834	−	0.753552i
$883$	−3.88392e11			−0.638892			−0.319446	−	0.947604i	$-0.603497\pi$
$883$	−3.88392e11			−0.638892			−0.319446	+	0.947604i	$0.603497\pi$
$884$	1.41480e10	+	2.73416e11i	0.0231679	+	0.447729i
$885$		−	9.18128e11i		−	1.49668i
$886$	1.66086e10	+	6.42362e11i	0.0269524	+	1.04243i
$887$		−	1.06531e11i		−	0.172099i	−0.996291	−	0.0860497i	$-0.972576\pi$
$887$		−	1.06531e11i		−	0.172099i	0.996291	−	0.0860497i	$-0.0274244\pi$
$888$	8.32059e11	−	6.46550e10i	1.33814	−	0.103980i
$889$	3.33139e11			0.533357
$890$	−9.45796e11	+	2.44540e10i	−1.50743	+	0.0389753i
$891$	−5.76038e11			−0.913987
$892$	−1.60118e10	−	3.09434e11i	−0.0252918	−	0.488774i
$893$		−	1.33985e11i		−	0.210693i
$894$	8.06487e10	−	2.08521e9i	0.126255	−	0.00326437i
$895$			1.20049e12i			1.87097i
$896$	−3.52120e11	+	6.44198e10i	−0.546334	+	0.0999511i
$897$	3.52536e11			0.544546
$898$	−4.18158e9	−	1.61729e11i	−0.00643036	−	0.248704i
$899$	5.31918e11			0.814341
$900$	5.05750e11	−	2.61703e10i	0.770843	−	0.0398876i
$901$		−	1.52643e11i		−	0.231622i
$902$	2.21440e10	+	8.56454e11i	0.0334526	+	1.29383i
$903$		−	3.81123e11i		−	0.573211i
$904$	−4.07635e10	−	5.24594e11i	−0.0610376	−	0.785506i
$905$	1.64959e12			2.45913
$906$	−1.44682e12	+	3.74082e10i	−2.14735	+	0.0555206i
$907$	1.13318e11			0.167444			0.0837222	−	0.996489i	$-0.473319\pi$
$907$	1.13318e11			0.167444			0.0837222	+	0.996489i	$0.473319\pi$
$908$	−8.99885e11	+	4.65649e10i	−1.32386	+	0.0685040i
$909$		−	9.89387e11i		−	1.44914i
$910$	7.70809e11	−	1.99296e10i	1.12404	−	0.0290625i
$911$		−	3.51018e11i		−	0.509630i	−0.966990	−	0.254815i	$-0.917985\pi$
$911$		−	3.51018e11i		−	0.509630i	0.966990	−	0.254815i	$-0.0820146\pi$
$912$	−7.58688e11	+	7.87281e10i	−1.09669	+	0.113802i
$913$	3.41178e11			0.491018
$914$	2.71493e9	+	1.05004e11i	0.00389022	+	0.150461i
$915$	1.32769e12			1.89414
$916$	−2.41705e10	−	4.67105e11i	−0.0343324	−	0.663487i
$917$			6.98416e11i			0.987727i
$918$	6.91654e8	+	2.67508e10i	0.000973908	+	0.0376675i
$919$		−	1.01693e12i		−	1.42570i	−0.701317	−	0.712850i	$-0.747404\pi$
$919$		−	1.01693e12i		−	1.42570i	0.701317	−	0.712850i	$-0.252596\pi$
$920$	−1.76378e10	−	2.26984e11i	−0.0246202	−	0.316843i
$921$	−6.75851e11			−0.939318
$922$	−1.06519e12	+	2.75410e10i	−1.47402	+	0.0381115i
$923$	1.24019e12			1.70876
$924$	−3.06533e10	−	5.92386e11i	−0.0420523	−	0.812675i
$925$			4.81278e11i			0.657399i
$926$	8.23400e11	−	2.12894e10i	1.11987	−	0.0289547i
$927$			5.45720e11i			0.739011i
$928$	5.15795e11	−	6.70393e10i	0.695480	−	0.0903936i
$929$	−7.94179e11			−1.06624			−0.533120	−	0.846039i	$-0.678981\pi$
$929$	−7.94179e11			−1.06624			−0.533120	+	0.846039i	$0.678981\pi$
$930$	4.24188e10	+	1.64062e12i	0.0567057	+	2.19318i
$931$	−3.96224e11			−0.527402
$932$	3.08002e10	−	1.59377e9i	0.0408215	−	0.00211233i
$933$			1.31715e12i			1.73823i
$934$	−9.39353e9	−	3.63310e11i	−0.0123436	−	0.477408i
$935$			2.92988e11i			0.383357i
$936$	−1.29213e12	+	1.00405e11i	−1.68346	+	0.130813i
$937$	1.00215e11			0.130009			0.0650045	−	0.997885i	$-0.479294\pi$
$937$	1.00215e11			0.130009			0.0650045	+	0.997885i	$0.479294\pi$
$938$	1.80182e11	−	4.65868e9i	0.232756	−	0.00601799i
$939$	−1.85279e12			−2.38321
$940$	−2.81518e11	+	1.45673e10i	−0.360575	+	0.0186581i
$941$			6.42320e11i			0.819206i	0.912264	+	0.409603i	$0.134333\pi$
$941$			6.42320e11i			0.819206i	−0.912264	+	0.409603i	$0.865667\pi$
$942$	3.81303e11	−	9.85876e9i	0.484247	−	0.0125204i
$943$			2.45557e11i			0.310531i
$944$	6.25685e11	−	6.49266e10i	0.787894	−	0.0817588i
$945$	7.53649e10			0.0945022
$946$	1.49766e10	+	5.79242e11i	0.0187003	+	0.723262i
$947$	1.17477e12			1.46067			0.730334	−	0.683091i	$-0.239365\pi$
$947$	1.17477e12			1.46067			0.730334	+	0.683091i	$0.239365\pi$
$948$	2.63483e10	+	5.09190e11i	0.0326226	+	0.630444i
$949$		−	1.46590e12i		−	1.80734i
$950$	−1.13692e10	−	4.39723e11i	−0.0139584	−	0.539864i
$951$			1.63885e11i			0.200363i
$952$	1.31638e11	−	1.02289e10i	0.160263	−	0.0124532i
$953$	−2.99042e11			−0.362543			−0.181272	−	0.983433i	$-0.558021\pi$
$953$	−2.99042e11			−0.362543			−0.181272	+	0.983433i	$0.558021\pi$
$954$	7.22339e11	−	1.86764e10i	0.872063	−	0.0225475i
$955$	−1.76297e12			−2.11949
$956$	−9.58038e9	−	1.85144e11i	−0.0114697	−	0.221656i
$957$			8.61908e11i			1.02757i
$958$	−6.62632e11	+	1.71326e10i	−0.786702	+	0.0203405i
$959$			3.57351e11i			0.422494i
$960$	2.47905e11	+	1.58554e12i	0.291877	+	1.86677i
$961$	−2.97012e11			−0.348242
$962$	−3.18346e10	−	1.23125e12i	−0.0371705	−	1.43763i
$963$	3.42810e11			0.398610
$964$	9.00434e11	−	4.65934e10i	1.04266	−	0.0539530i
$965$		−	1.25544e12i		−	1.44772i
$966$	−4.39435e9	−	1.69959e11i	−0.00504645	−	0.195180i
$967$		−	1.38194e12i		−	1.58046i	−0.612808	−	0.790232i	$-0.709960\pi$
$967$		−	1.38194e12i		−	1.58046i	0.612808	−	0.790232i	$-0.290040\pi$
$968$	1.84519e9	+	2.37461e10i	0.00210155	+	0.0270452i
$969$	2.81345e11			0.319112
$970$	5.71080e11	−	1.47655e10i	0.645074	−	0.0166787i
$971$	3.57464e10			0.0402120			0.0201060	−	0.999798i	$-0.493600\pi$
$971$	3.57464e10			0.0402120			0.0201060	+	0.999798i	$0.493600\pi$
$972$	1.27828e12	−	6.61453e10i	1.43206	−	0.0741027i
$973$		−	2.40162e11i		−	0.267949i
$974$	2.28393e11	−	5.90519e9i	0.253773	−	0.00656142i
$975$		−	1.43304e12i		−	1.58577i
$976$	9.38894e10	+	9.04795e11i	0.103471	+	0.997128i
$977$	−8.95645e11			−0.983009			−0.491505	−	0.870875i	$-0.663553\pi$
$977$	−8.95645e11			−0.983009			−0.491505	+	0.870875i	$0.663553\pi$
$978$	−5.82801e10	−	2.25408e12i	−0.0637038	−	2.46385i
$979$	1.07416e12			1.16933
$980$	4.30788e10	+	8.32514e11i	0.0467046	+	0.902583i
$981$			1.17239e12i			1.26589i
$982$	2.41808e9	+	9.35232e10i	0.00260031	+	0.100571i
$983$			7.53183e11i			0.806652i	0.915056	+	0.403326i	$0.132146\pi$
$983$			7.53183e11i			0.806652i	−0.915056	+	0.403326i	$0.867854\pi$
$984$	−1.34095e11	−	1.72569e12i	−0.143031	−	1.84070i
$985$	1.04834e12			1.11367
$986$	−1.91787e11	+	4.95873e9i	−0.202914	+	0.00524642i
$987$	−2.10510e11			−0.221822
$988$	5.81717e10	+	1.12419e12i	0.0610498	+	1.17981i
$989$			1.66076e11i			0.173589i
$990$	−1.38648e12	+	3.58480e10i	−1.44335	+	0.0373185i
$991$			3.87991e11i			0.402279i	0.979563	+	0.201139i	$0.0644644\pi$
$991$			3.87991e11i			0.402279i	−0.979563	+	0.201139i	$0.935536\pi$
$992$	−1.11505e12	+	1.44926e11i	−1.15145	+	0.149658i
$993$	1.11311e12			1.14483
$994$	−1.54589e10	−	5.97898e11i	−0.0158355	−	0.612465i
$995$	−2.44583e12			−2.49536
$996$	−6.88368e11	+	3.56199e10i	−0.699493	+	0.0361956i
$997$			6.83981e11i			0.692251i	0.938188	+	0.346125i	$0.112503\pi$
$997$			6.83981e11i			0.692251i	−0.938188	+	0.346125i	$0.887497\pi$
$998$	−4.64358e10	−	1.79598e12i	−0.0468091	−	1.81042i
$999$		−	1.20384e11i		−	0.120867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.9.d.b.3.3	✓	6
3.2	odd	2		72.9.b.b.19.4		6
4.3	odd	2		32.9.d.b.15.1		6
8.3	odd	2	inner	8.9.d.b.3.4	yes	6
8.5	even	2		32.9.d.b.15.2		6
12.11	even	2		288.9.b.b.271.6		6
16.3	odd	4		256.9.c.n.255.3		12
16.5	even	4		256.9.c.n.255.4		12
16.11	odd	4		256.9.c.n.255.10		12
16.13	even	4		256.9.c.n.255.9		12
24.5	odd	2		288.9.b.b.271.1		6
24.11	even	2		72.9.b.b.19.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.9.d.b.3.3	✓	6	1.1	even	1	trivial
8.9.d.b.3.4	yes	6	8.3	odd	2	inner
32.9.d.b.15.1		6	4.3	odd	2
32.9.d.b.15.2		6	8.5	even	2
72.9.b.b.19.3		6	24.11	even	2
72.9.b.b.19.4		6	3.2	odd	2
256.9.c.n.255.3		12	16.3	odd	4
256.9.c.n.255.4		12	16.5	even	4
256.9.c.n.255.9		12	16.13	even	4
256.9.c.n.255.10		12	16.11	odd	4
288.9.b.b.271.1		6	24.5	odd	2
288.9.b.b.271.6		6	12.11	even	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.413549 - 15.9947i) q^{2} +117.102 q^{3} +(-255.658 + 13.2291i) q^{4} -816.841i q^{5} +(-48.4273 - 1873.00i) q^{6} +1333.52i q^{7} +(317.322 + 4083.69i) q^{8} +7151.84 q^{9} +O(q^{10})\)	\(q+(-0.413549 - 15.9947i) q^{2} +117.102 q^{3} +(-255.658 + 13.2291i) q^{4} -816.841i q^{5} +(-48.4273 - 1873.00i) q^{6} +1333.52i q^{7} +(317.322 + 4083.69i) q^{8} +7151.84 q^{9} +(-13065.1 + 337.803i) q^{10} +14838.3 q^{11} +(-29938.0 + 1549.16i) q^{12} +44242.0i q^{13} +(21329.2 - 551.475i) q^{14} -95653.6i q^{15} +(65186.0 - 6764.27i) q^{16} -24172.9 q^{17} +(-2957.63 - 114391. i) q^{18} -99390.6 q^{19} +(10806.1 + 208832. i) q^{20} +156158. i q^{21} +(-6136.34 - 237333. i) q^{22} -68046.4i q^{23} +(37159.0 + 478208. i) q^{24} -276604. q^{25} +(707636. - 18296.2i) q^{26} +69188.3 q^{27} +(-17641.3 - 340925. i) q^{28} +496037. i q^{29} +(-1.52995e6 + 39557.4i) q^{30} -1.07234e6i q^{31} +(-135150. - 1.03983e6i) q^{32} +1.73759e6 q^{33} +(9996.69 + 386638. i) q^{34} +1.08927e6 q^{35} +(-1.82842e6 + 94612.6i) q^{36} -1.73995e6i q^{37} +(41102.9 + 1.58972e6i) q^{38} +5.18082e6i q^{39} +(3.33573e6 - 259202. i) q^{40} -3.60866e6 q^{41} +(2.49769e6 - 64578.7i) q^{42} -2.44063e6 q^{43} +(-3.79352e6 + 196297. i) q^{44} -5.84191e6i q^{45} +(-1.08838e6 + 28140.5i) q^{46} +1.34806e6i q^{47} +(7.63340e6 - 792108. i) q^{48} +3.98653e6 q^{49} +(114389. + 4.42419e6i) q^{50} -2.83070e6 q^{51} +(-585284. - 1.13108e7i) q^{52} +6.31464e6i q^{53} +(-28612.7 - 1.10664e6i) q^{54} -1.21205e7i q^{55} +(-5.44568e6 + 423156. i) q^{56} -1.16388e7 q^{57} +(7.93395e6 - 205136. i) q^{58} +9.59847e6 q^{59} +(1.26541e6 + 2.44546e7i) q^{60} +1.38802e7i q^{61} +(-1.71516e7 + 443463. i) q^{62} +9.53711e6i q^{63} +(-1.65758e7 + 2.59169e6i) q^{64} +3.61387e7 q^{65} +(-718576. - 2.77921e7i) q^{66} +8.44768e6 q^{67} +(6.18001e6 - 319787. i) q^{68} -7.96836e6i q^{69} +(-450467. - 1.74225e7i) q^{70} -2.80319e7i q^{71} +(2.26944e6 + 2.92059e7i) q^{72} -3.31337e7 q^{73} +(-2.78299e7 + 719555. i) q^{74} -3.23909e7 q^{75} +(2.54100e7 - 1.31485e6i) q^{76} +1.97871e7i q^{77} +(8.28655e7 - 2.14252e6i) q^{78} -1.70081e7i q^{79} +(-5.52533e6 - 5.32466e7i) q^{80} -3.88211e7 q^{81} +(1.49236e6 + 5.77193e7i) q^{82} +2.29931e7 q^{83} +(-2.06583e6 - 3.99229e7i) q^{84} +1.97455e7i q^{85} +(1.00932e6 + 3.90371e7i) q^{86} +5.80869e7i q^{87} +(4.70851e6 + 6.05948e7i) q^{88} +7.23911e7 q^{89} +(-9.34394e7 + 2.41592e6i) q^{90} -5.89976e7 q^{91} +(900195. + 1.73966e7i) q^{92} -1.25572e8i q^{93} +(2.15618e7 - 557489. i) q^{94} +8.11863e7i q^{95} +(-1.58263e7 - 1.21766e8i) q^{96} -4.37103e7 q^{97} +(-1.64862e6 - 6.37631e7i) q^{98} +1.06121e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{2} - 36 q^{3} - 588 q^{4} - 1284 q^{6} - 6824 q^{8} + 16338 q^{9}+O(q^{10}) \) 6 * q - 14 * q^2 - 36 * q^3 - 588 * q^4 - 1284 * q^6 - 6824 * q^8 + 16338 * q^9	\( 6 q - 14 q^{2} - 36 q^{3} - 588 q^{4} - 1284 q^{6} - 6824 q^{8} + 16338 q^{9} - 4080 q^{10} + 46940 q^{11} - 27336 q^{12} - 51744 q^{14} + 20496 q^{16} - 201076 q^{17} + 267990 q^{18} - 95268 q^{19} - 216480 q^{20} + 49404 q^{22} + 1009296 q^{24} - 447930 q^{25} + 1765104 q^{26} + 419256 q^{27} - 2600640 q^{28} - 4325280 q^{30} + 3232096 q^{32} + 1736856 q^{33} + 2378916 q^{34} + 1989120 q^{35} - 7392228 q^{36} - 8088196 q^{38} + 12694080 q^{40} + 3817100 q^{41} + 19064640 q^{42} - 9881508 q^{43} - 9479368 q^{44} - 19226976 q^{46} + 20590944 q^{48} - 12655482 q^{49} + 11106610 q^{50} - 4303176 q^{51} - 17270880 q^{52} - 7366536 q^{54} + 10545024 q^{56} + 7523736 q^{57} + 7354800 q^{58} + 25243484 q^{59} - 5760960 q^{60} - 5304960 q^{62} - 35364288 q^{64} + 27060480 q^{65} - 12683256 q^{66} + 47850204 q^{67} - 9160216 q^{68} + 56582400 q^{70} - 57502200 q^{72} - 55484916 q^{73} - 114255984 q^{74} - 126075300 q^{75} + 151972920 q^{76} + 175397280 q^{78} - 134958720 q^{80} - 79145442 q^{81} - 48197916 q^{82} + 144646364 q^{83} + 216531840 q^{84} + 41826428 q^{86} - 47377776 q^{88} + 142173452 q^{89} - 205943760 q^{90} - 273971712 q^{91} + 97636800 q^{92} + 220009536 q^{94} - 250689984 q^{96} + 125193612 q^{97} - 257093774 q^{98} + 298320276 q^{99}+O(q^{100}) \) 6 * q - 14 * q^2 - 36 * q^3 - 588 * q^4 - 1284 * q^6 - 6824 * q^8 + 16338 * q^9 - 4080 * q^10 + 46940 * q^11 - 27336 * q^12 - 51744 * q^14 + 20496 * q^16 - 201076 * q^17 + 267990 * q^18 - 95268 * q^19 - 216480 * q^20 + 49404 * q^22 + 1009296 * q^24 - 447930 * q^25 + 1765104 * q^26 + 419256 * q^27 - 2600640 * q^28 - 4325280 * q^30 + 3232096 * q^32 + 1736856 * q^33 + 2378916 * q^34 + 1989120 * q^35 - 7392228 * q^36 - 8088196 * q^38 + 12694080 * q^40 + 3817100 * q^41 + 19064640 * q^42 - 9881508 * q^43 - 9479368 * q^44 - 19226976 * q^46 + 20590944 * q^48 - 12655482 * q^49 + 11106610 * q^50 - 4303176 * q^51 - 17270880 * q^52 - 7366536 * q^54 + 10545024 * q^56 + 7523736 * q^57 + 7354800 * q^58 + 25243484 * q^59 - 5760960 * q^60 - 5304960 * q^62 - 35364288 * q^64 + 27060480 * q^65 - 12683256 * q^66 + 47850204 * q^67 - 9160216 * q^68 + 56582400 * q^70 - 57502200 * q^72 - 55484916 * q^73 - 114255984 * q^74 - 126075300 * q^75 + 151972920 * q^76 + 175397280 * q^78 - 134958720 * q^80 - 79145442 * q^81 - 48197916 * q^82 + 144646364 * q^83 + 216531840 * q^84 + 41826428 * q^86 - 47377776 * q^88 + 142173452 * q^89 - 205943760 * q^90 - 273971712 * q^91 + 97636800 * q^92 + 220009536 * q^94 - 250689984 * q^96 + 125193612 * q^97 - 257093774 * q^98 + 298320276 * q^99

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