LMFDB - Embedded newform 304.2.k.b.77.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (of order $4$, degree $2$, 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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.17
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.109190 + 1.40999i) q^{2} +(-2.25323 - 2.25323i) q^{3} +(-1.97615 - 0.307915i) q^{4} +(-1.35988 + 1.35988i) q^{5} +(3.42307 - 2.93101i) q^{6} +0.426904i q^{7} +(0.649934 - 2.75274i) q^{8} +7.15410i q^{9} +O(q^{10})$	\(q+(-0.109190 + 1.40999i) q^{2} +(-2.25323 - 2.25323i) q^{3} +(-1.97615 - 0.307915i) q^{4} +(-1.35988 + 1.35988i) q^{5} +(3.42307 - 2.93101i) q^{6} +0.426904i q^{7} +(0.649934 - 2.75274i) q^{8} +7.15410i q^{9} +(-1.76893 - 2.06591i) q^{10} +(2.84768 - 2.84768i) q^{11} +(3.75893 + 5.14654i) q^{12} +(1.43126 + 1.43126i) q^{13} +(-0.601931 - 0.0466138i) q^{14} +6.12825 q^{15} +(3.81038 + 1.21697i) q^{16} +4.88535 q^{17} +(-10.0872 - 0.781158i) q^{18} +(0.707107 + 0.707107i) q^{19} +(3.10606 - 2.26861i) q^{20} +(0.961913 - 0.961913i) q^{21} +(3.70426 + 4.32614i) q^{22} +6.27167i q^{23} +(-7.66701 + 4.73811i) q^{24} +1.30145i q^{25} +(-2.17435 + 1.86179i) q^{26} +(9.36013 - 9.36013i) q^{27} +(0.131450 - 0.843628i) q^{28} +(-1.97136 - 1.97136i) q^{29} +(-0.669145 + 8.64078i) q^{30} +6.04992 q^{31} +(-2.13198 + 5.23972i) q^{32} -12.8329 q^{33} +(-0.533432 + 6.88830i) q^{34} +(-0.580538 - 0.580538i) q^{35} +(2.20285 - 14.1376i) q^{36} +(-0.792637 + 0.792637i) q^{37} +(-1.07422 + 0.919806i) q^{38} -6.44992i q^{39} +(2.85957 + 4.62723i) q^{40} -7.00513i q^{41} +(1.25126 + 1.46132i) q^{42} +(3.77273 - 3.77273i) q^{43} +(-6.50429 + 4.75061i) q^{44} +(-9.72871 - 9.72871i) q^{45} +(-8.84301 - 0.684806i) q^{46} -8.19682 q^{47} +(-5.84353 - 11.3278i) q^{48} +6.81775 q^{49} +(-1.83504 - 0.142106i) q^{50} +(-11.0078 - 11.0078i) q^{51} +(-2.38769 - 3.26910i) q^{52} +(-4.95926 + 4.95926i) q^{53} +(12.1757 + 14.2198i) q^{54} +7.74500i q^{55} +(1.17516 + 0.277460i) q^{56} -3.18655i q^{57} +(2.99486 - 2.56435i) q^{58} +(6.05258 - 6.05258i) q^{59} +(-12.1104 - 1.88698i) q^{60} +(9.43676 + 9.43676i) q^{61} +(-0.660592 + 8.53034i) q^{62} -3.05411 q^{63} +(-7.15517 - 3.57820i) q^{64} -3.89269 q^{65} +(1.40123 - 18.0943i) q^{66} +(0.820089 + 0.820089i) q^{67} +(-9.65420 - 1.50427i) q^{68} +(14.1315 - 14.1315i) q^{69} +(0.881943 - 0.755165i) q^{70} +11.4139i q^{71} +(19.6934 + 4.64969i) q^{72} +15.2072i q^{73} +(-1.03106 - 1.20416i) q^{74} +(2.93247 - 2.93247i) q^{75} +(-1.17962 - 1.61508i) q^{76} +(1.21568 + 1.21568i) q^{77} +(9.09434 + 0.704269i) q^{78} +5.54935 q^{79} +(-6.83660 + 3.52672i) q^{80} -20.7188 q^{81} +(9.87717 + 0.764892i) q^{82} +(-2.33903 - 2.33903i) q^{83} +(-2.19708 + 1.60470i) q^{84} +(-6.64348 + 6.64348i) q^{85} +(4.90758 + 5.73147i) q^{86} +8.88386i q^{87} +(-5.98811 - 9.68972i) q^{88} -5.76670i q^{89} +(14.7797 - 12.6551i) q^{90} +(-0.611011 + 0.611011i) q^{91} +(1.93114 - 12.3938i) q^{92} +(-13.6319 - 13.6319i) q^{93} +(0.895014 - 11.5575i) q^{94} -1.92316 q^{95} +(16.6101 - 7.00245i) q^{96} +5.83616 q^{97} +(-0.744432 + 9.61298i) q^{98} +(20.3725 + 20.3725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.109190	+	1.40999i	−0.0772092	+	0.997015i
$2$	−0.109190	+	1.40999i	−0.0772092	+	0.997015i
$3$	−2.25323	−	2.25323i	−1.30090	−	1.30090i	−0.927783	−	0.373120i	$-0.878288\pi$
$3$	−2.25323	−	2.25323i	−1.30090	−	1.30090i	−0.373120	−	0.927783i	$-0.621712\pi$
$4$	−1.97615	−	0.307915i	−0.988077	−	0.153957i
$5$	−1.35988	+	1.35988i	−0.608157	+	0.608157i	−0.942464	−	0.334307i	$-0.891498\pi$
$5$	−1.35988	+	1.35988i	−0.608157	+	0.608157i	0.334307	+	0.942464i	$0.391498\pi$
$6$	3.42307	−	2.93101i	1.39746	−	1.19658i
$7$			0.426904i			0.161355i	0.996740	+	0.0806773i	$0.0257083\pi$
$7$			0.426904i			0.161355i	−0.996740	+	0.0806773i	$0.974292\pi$
$8$	0.649934	−	2.75274i	0.229787	−	0.973241i
$9$			7.15410i			2.38470i
$10$	−1.76893	−	2.06591i	−0.559386	−	0.653297i
$11$	2.84768	−	2.84768i	0.858607	−	0.858607i	−0.132567	−	0.991174i	$-0.542322\pi$
$11$	2.84768	−	2.84768i	0.858607	−	0.858607i	0.991174	+	0.132567i	$0.0423220\pi$
$12$	3.75893	+	5.14654i	1.08511	+	1.48568i
$13$	1.43126	+	1.43126i	0.396960	+	0.396960i	0.877160	−	0.480199i	$-0.159436\pi$
$13$	1.43126	+	1.43126i	0.396960	+	0.396960i	−0.480199	+	0.877160i	$0.659436\pi$
$14$	−0.601931	−	0.0466138i	−0.160873	−	0.0124581i
$15$	6.12825			1.58231
$16$	3.81038	+	1.21697i	0.952594	+	0.304244i
$17$	4.88535			1.18487			0.592435	−	0.805618i	$-0.298167\pi$
$17$	4.88535			1.18487			0.592435	+	0.805618i	$0.298167\pi$
$18$	−10.0872	−	0.781158i	−2.37758	−	0.184121i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$20$	3.10606	−	2.26861i	0.694536	−	0.507276i
$21$	0.961913	−	0.961913i	0.209907	−	0.209907i
$22$	3.70426	+	4.32614i	0.789751	+	0.922336i
$23$			6.27167i			1.30773i	0.756609	+	0.653867i	$0.226855\pi$
$23$			6.27167i			1.30773i	−0.756609	+	0.653867i	$0.773145\pi$
$24$	−7.66701	+	4.73811i	−1.56502	+	0.967162i
$25$			1.30145i			0.260291i
$26$	−2.17435	+	1.86179i	−0.426424	+	0.365126i
$27$	9.36013	−	9.36013i	1.80136	−	1.80136i
$28$	0.131450	−	0.843628i	0.0248417	−	0.159431i
$29$	−1.97136	−	1.97136i	−0.366073	−	0.366073i	0.499970	−	0.866043i	$-0.333344\pi$
$29$	−1.97136	−	1.97136i	−0.366073	−	0.366073i	−0.866043	+	0.499970i	$0.833344\pi$
$30$	−0.669145	+	8.64078i	−0.122169	+	1.57758i
$31$	6.04992			1.08660			0.543299	−	0.839539i	$-0.317175\pi$
$31$	6.04992			1.08660			0.543299	+	0.839539i	$0.317175\pi$
$32$	−2.13198	+	5.23972i	−0.376885	+	0.926260i
$33$	−12.8329			−2.23393
$34$	−0.533432	+	6.88830i	−0.0914829	+	1.18133i
$35$	−0.580538	−	0.580538i	−0.0981289	−	0.0981289i
$36$	2.20285	−	14.1376i	0.367142	−	2.35627i
$37$	−0.792637	+	0.792637i	−0.130309	+	0.130309i	−0.769253	−	0.638944i	$-0.779371\pi$
$37$	−0.792637	+	0.792637i	−0.130309	+	0.130309i	0.638944	+	0.769253i	$0.279371\pi$
$38$	−1.07422	+	0.919806i	−0.174262	+	0.149212i
$39$		−	6.44992i		−	1.03281i
$40$	2.85957	+	4.62723i	0.452137	+	0.731629i
$41$		−	7.00513i		−	1.09402i	−0.837127	−	0.547008i	$-0.815767\pi$
$41$		−	7.00513i		−	1.09402i	0.837127	−	0.547008i	$-0.184233\pi$
$42$	1.25126	+	1.46132i	0.193073	+	0.225487i
$43$	3.77273	−	3.77273i	0.575337	−	0.575337i	−0.358278	−	0.933615i	$-0.616636\pi$
$43$	3.77273	−	3.77273i	0.575337	−	0.575337i	0.933615	+	0.358278i	$0.116636\pi$
$44$	−6.50429	+	4.75061i	−0.980559	+	0.716181i
$45$	−9.72871	−	9.72871i	−1.45027	−	1.45027i
$46$	−8.84301	−	0.684806i	−1.30383	−	0.100969i
$47$	−8.19682			−1.19563			−0.597815	−	0.801634i	$-0.703964\pi$
$47$	−8.19682			−1.19563			−0.597815	+	0.801634i	$0.703964\pi$
$48$	−5.84353	−	11.3278i	−0.843441	−	1.63502i
$49$	6.81775			0.973965
$50$	−1.83504	−	0.142106i	−0.259514	−	0.0200968i
$51$	−11.0078	−	11.0078i	−1.54140	−	1.54140i
$52$	−2.38769	−	3.26910i	−0.331113	−	0.453343i
$53$	−4.95926	+	4.95926i	−0.681206	+	0.681206i	−0.960272	−	0.279066i	$-0.909975\pi$
$53$	−4.95926	+	4.95926i	−0.681206	+	0.681206i	0.279066	+	0.960272i	$0.409975\pi$
$54$	12.1757	+	14.2198i	1.65690	+	1.93506i
$55$			7.74500i			1.04434i
$56$	1.17516	+	0.277460i	0.157037	+	0.0370771i
$57$		−	3.18655i		−	0.422069i
$58$	2.99486	−	2.56435i	0.393244	−	0.336716i
$59$	6.05258	−	6.05258i	0.787979	−	0.787979i	−0.193183	−	0.981163i	$-0.561881\pi$
$59$	6.05258	−	6.05258i	0.787979	−	0.787979i	0.981163	+	0.193183i	$0.0618812\pi$
$60$	−12.1104	−	1.88698i	−1.56344	−	0.243608i
$61$	9.43676	+	9.43676i	1.20825	+	1.20825i	0.971592	+	0.236662i	$0.0760533\pi$
$61$	9.43676	+	9.43676i	1.20825	+	1.20825i	0.236662	+	0.971592i	$0.423947\pi$
$62$	−0.660592	+	8.53034i	−0.0838953	+	1.08335i
$63$	−3.05411			−0.384782
$64$	−7.15517	−	3.57820i	−0.894396	−	0.447275i
$65$	−3.89269			−0.482828
$66$	1.40123	−	18.0943i	0.172480	−	2.22726i
$67$	0.820089	+	0.820089i	0.100190	+	0.100190i	0.755425	−	0.655235i	$-0.227430\pi$
$67$	0.820089	+	0.820089i	0.100190	+	0.100190i	−0.655235	+	0.755425i	$0.727430\pi$
$68$	−9.65420	−	1.50427i	−1.17074	−	0.182420i
$69$	14.1315	−	14.1315i	1.70124	−	1.70124i
$70$	0.881943	−	0.755165i	0.105412	−	0.0902595i
$71$			11.4139i			1.35458i	0.735718	+	0.677288i	$0.236845\pi$
$71$			11.4139i			1.35458i	−0.735718	+	0.677288i	$0.763155\pi$
$72$	19.6934	+	4.64969i	2.32089	+	0.547972i
$73$			15.2072i			1.77986i	0.456094	+	0.889932i	$0.349248\pi$
$73$			15.2072i			1.77986i	−0.456094	+	0.889932i	$0.650752\pi$
$74$	−1.03106	−	1.20416i	−0.119859	−	0.139981i
$75$	2.93247	−	2.93247i	0.338613	−	0.338613i
$76$	−1.17962	−	1.61508i	−0.135312	−	0.185263i
$77$	1.21568	+	1.21568i	0.138540	+	0.138540i
$78$	9.09434	+	0.704269i	1.02973	+	0.0797427i
$79$	5.54935			0.624351			0.312175	−	0.950024i	$-0.398942\pi$
$79$	5.54935			0.624351			0.312175	+	0.950024i	$0.398942\pi$
$80$	−6.83660	+	3.52672i	−0.764355	+	0.394299i
$81$	−20.7188			−2.30209
$82$	9.87717	+	0.764892i	1.09075	+	0.0844682i
$83$	−2.33903	−	2.33903i	−0.256742	−	0.256742i	0.566986	−	0.823728i	$-0.308110\pi$
$83$	−2.33903	−	2.33903i	−0.256742	−	0.256742i	−0.823728	+	0.566986i	$0.808110\pi$
$84$	−2.19708	+	1.60470i	−0.239721	+	0.175087i
$85$	−6.64348	+	6.64348i	−0.720587	+	0.720587i
$86$	4.90758	+	5.73147i	0.529198	+	0.618040i
$87$			8.88386i			0.952450i
$88$	−5.98811	−	9.68972i	−0.638335	−	1.03293i
$89$		−	5.76670i		−	0.611269i	−0.952149	−	0.305635i	$-0.901131\pi$
$89$		−	5.76670i		−	0.611269i	0.952149	−	0.305635i	$-0.0988686\pi$
$90$	14.7797	−	12.6551i	1.55792	−	1.33397i
$91$	−0.611011	+	0.611011i	−0.0640514	+	0.0640514i
$92$	1.93114	−	12.3938i	0.201335	−	1.29214i
$93$	−13.6319	−	13.6319i	−1.41356	−	1.41356i
$94$	0.895014	−	11.5575i	0.0923136	−	1.19206i
$95$	−1.92316			−0.197312
$96$	16.6101	−	7.00245i	1.69527	−	0.714685i
$97$	5.83616			0.592572			0.296286	−	0.955099i	$-0.404252\pi$
$97$	5.83616			0.592572			0.296286	+	0.955099i	$0.404252\pi$
$98$	−0.744432	+	9.61298i	−0.0751990	+	0.971057i
$99$	20.3725	+	20.3725i	2.04752	+	2.04752i
$100$	0.400737	−	2.57187i	0.0400737	−	0.257187i
$101$	12.2093	−	12.2093i	1.21487	−	1.21487i	0.245470	−	0.969404i	$-0.421058\pi$
$101$	12.2093	−	12.2093i	1.21487	−	1.21487i	0.969404	−	0.245470i	$-0.0789421\pi$
$102$	16.7229	−	14.3190i	1.65581	−	1.41779i
$103$		−	16.1869i		−	1.59495i	−0.603354	−	0.797474i	$-0.706169\pi$
$103$		−	16.1869i		−	1.59495i	0.603354	−	0.797474i	$-0.293831\pi$
$104$	4.87012	−	3.00967i	0.477554	−	0.295122i
$105$			2.61617i			0.255312i
$106$	−6.45101	−	7.53401i	−0.626577	−	0.731768i
$107$	−13.6410	+	13.6410i	−1.31873	+	1.31873i	−0.403943	+	0.914784i	$0.632361\pi$
$107$	−13.6410	+	13.6410i	−1.31873	+	1.31873i	−0.914784	+	0.403943i	$0.867639\pi$
$108$	−21.3792	+	15.6150i	−2.05721	+	1.50255i
$109$	8.49866	+	8.49866i	0.814024	+	0.814024i	0.985234	−	0.171211i	$-0.0547679\pi$
$109$	8.49866	+	8.49866i	0.814024	+	0.814024i	−0.171211	+	0.985234i	$0.554768\pi$
$110$	−10.9204	−	0.845678i	−1.04122	−	0.0806323i
$111$	3.57199			0.339038
$112$	−0.519531	+	1.62666i	−0.0490911	+	0.153705i
$113$	9.16018			0.861718			0.430859	−	0.902419i	$-0.358211\pi$
$113$	9.16018			0.861718			0.430859	+	0.902419i	$0.358211\pi$
$114$	4.49301	+	0.347940i	0.420809	+	0.0325876i
$115$	−8.52873	−	8.52873i	−0.795308	−	0.795308i
$116$	3.28870	+	4.50273i	0.305348	+	0.418068i
$117$	−10.2394	+	10.2394i	−0.946631	+	0.946631i
$118$	7.87321	+	9.19498i	0.724788	+	0.846466i
$119$			2.08557i			0.191184i
$120$	3.98296	−	16.8695i	0.363593	−	1.53997i
$121$		−	5.21852i		−	0.474411i
$122$	−14.3362	+	12.2754i	−1.29794	+	1.11136i
$123$	−15.7842	+	15.7842i	−1.42321	+	1.42321i
$124$	−11.9556	−	1.86286i	−1.07364	−	0.167290i
$125$	−8.56922	−	8.56922i	−0.766454	−	0.766454i
$126$	0.333479	−	4.30627i	0.0297087	−	0.383633i
$127$	5.97418			0.530123			0.265061	−	0.964232i	$-0.414608\pi$
$127$	5.97418			0.530123			0.265061	+	0.964232i	$0.414608\pi$
$128$	5.82651	−	9.69803i	0.514996	−	0.857193i
$129$	−17.0017			−1.49691
$130$	0.425044	−	5.48866i	0.0372788	−	0.481387i
$131$	−2.21854	−	2.21854i	−0.193835	−	0.193835i	0.603516	−	0.797351i	$-0.293766\pi$
$131$	−2.21854	−	2.21854i	−0.193835	−	0.193835i	−0.797351	+	0.603516i	$0.793766\pi$
$132$	25.3599	+	3.95145i	2.20729	+	0.343930i
$133$	−0.301867	+	0.301867i	−0.0261752	+	0.0261752i
$134$	−1.24587	+	1.06677i	−0.107626	+	0.0921552i
$135$			25.4573i			2.19102i
$136$	3.17515	−	13.4481i	0.272267	−	1.15316i
$137$		−	1.77636i		−	0.151764i	−0.997117	−	0.0758822i	$-0.975823\pi$
$137$		−	1.77636i		−	0.151764i	0.997117	−	0.0758822i	$-0.0241773\pi$
$138$	18.3823	+	21.4684i	1.56481	+	1.82751i
$139$	−16.0895	+	16.0895i	−1.36469	+	1.36469i	−0.496869	+	0.867825i	$0.665517\pi$
$139$	−16.0895	+	16.0895i	−1.36469	+	1.36469i	−0.867825	+	0.496869i	$0.834483\pi$
$140$	0.968477	+	1.32599i	0.0818512	+	0.112067i
$141$	18.4693	+	18.4693i	1.55540	+	1.55540i
$142$	−16.0934	−	1.24628i	−1.35053	−	0.104586i
$143$	8.15154			0.681666
$144$	−8.70635	+	27.2598i	−0.725530	+	2.27165i
$145$	5.36163			0.445259
$146$	−21.4420	−	1.66047i	−1.77455	−	0.137422i
$147$	−15.3620	−	15.3620i	−1.26703	−	1.26703i
$148$	1.81044	−	1.32231i	0.148817	−	0.108693i
$149$	−9.94586	+	9.94586i	−0.814797	+	0.814797i	−0.985349	−	0.170552i	$-0.945445\pi$
$149$	−9.94586	+	9.94586i	−0.814797	+	0.814797i	0.170552	+	0.985349i	$0.445445\pi$
$150$	3.81457	+	4.45496i	0.311458	+	0.363746i
$151$			5.29298i			0.430736i	0.976533	+	0.215368i	$0.0690952\pi$
$151$			5.29298i			0.430736i	−0.976533	+	0.215368i	$0.930905\pi$
$152$	2.40606	−	1.48691i	0.195157	−	0.120604i
$153$			34.9502i			2.82556i
$154$	−1.84685	+	1.58136i	−0.148823	+	0.127430i
$155$	−8.22716	+	8.22716i	−0.660822	+	0.660822i
$156$	−1.98603	+	12.7460i	−0.159009	+	1.02050i
$157$	−1.69118	−	1.69118i	−0.134971	−	0.134971i	0.636394	−	0.771365i	$-0.280425\pi$
$157$	−1.69118	−	1.69118i	−0.134971	−	0.134971i	−0.771365	+	0.636394i	$0.780425\pi$
$158$	−0.605935	+	7.82454i	−0.0482056	+	0.622487i
$159$	22.3487			1.77237
$160$	−4.22615	−	10.0246i	−0.334107	−	0.792516i
$161$	−2.67740			−0.211009
$162$	2.26229	−	29.2133i	0.177742	−	2.29522i
$163$	−0.939583	−	0.939583i	−0.0735938	−	0.0735938i	0.669352	−	0.742946i	$-0.266572\pi$
$163$	−0.939583	−	0.939583i	−0.0735938	−	0.0735938i	−0.742946	+	0.669352i	$0.766572\pi$
$164$	−2.15698	+	13.8432i	−0.168432	+	1.08097i
$165$	17.4513	−	17.4513i	1.35858	−	1.35858i
$166$	3.55342	−	3.04262i	0.275799	−	0.236153i
$167$		−	22.9060i		−	1.77252i	−0.463189	−	0.886259i	$-0.653295\pi$
$167$		−	22.9060i		−	1.77252i	0.463189	−	0.886259i	$-0.346705\pi$
$168$	−2.02272	−	3.27308i	−0.156056	−	0.252523i
$169$		−	8.90298i		−	0.684845i
$170$	−8.64186	−	10.0927i	−0.662800	−	0.774072i
$171$	−5.05871	+	5.05871i	−0.386849	+	0.386849i
$172$	−8.61719	+	6.29383i	−0.657055	+	0.479900i
$173$	8.37455	+	8.37455i	0.636706	+	0.636706i	0.949741	−	0.313036i	$-0.101346\pi$
$173$	8.37455	+	8.37455i	0.636706	+	0.636706i	−0.313036	+	0.949741i	$0.601346\pi$
$174$	−12.5262	−	0.970031i	−0.949607	−	0.0735379i
$175$	−0.555595			−0.0419991
$176$	14.3163	−	7.38517i	1.07913	−	0.556678i
$177$	−27.2757			−2.05017
$178$	8.13101	+	0.629668i	0.609445	+	0.0471956i
$179$	−1.26271	−	1.26271i	−0.0943793	−	0.0943793i	0.658341	−	0.752720i	$-0.271259\pi$
$179$	−1.26271	−	1.26271i	−0.0943793	−	0.0943793i	−0.752720	+	0.658341i	$0.771259\pi$
$180$	16.2298	+	22.2211i	1.20970	+	1.65626i
$181$	13.9808	−	13.9808i	1.03918	−	1.03918i	0.0399810	−	0.999200i	$-0.487270\pi$
$181$	13.9808	−	13.9808i	1.03918	−	1.03918i	0.999200	−	0.0399810i	$-0.0127297\pi$
$182$	−0.794804	−	0.928237i	−0.0589148	−	0.0688055i
$183$		−	42.5264i		−	3.14364i
$184$	17.2643	+	4.07618i	1.27274	+	0.300500i
$185$		−	2.15578i		−	0.158496i
$186$	20.7093	−	17.7323i	1.51848	−	1.30020i
$187$	13.9119	−	13.9119i	1.01734	−	1.01734i
$188$	16.1982	+	2.52392i	1.18137	+	0.184076i
$189$	3.99588	+	3.99588i	0.290657	+	0.290657i
$190$	0.209990	−	2.71164i	0.0152343	−	0.196723i
$191$	−2.18693			−0.158241			−0.0791203	−	0.996865i	$-0.525211\pi$
$191$	−2.18693			−0.158241			−0.0791203	+	0.996865i	$0.525211\pi$
$192$	8.05973	+	24.1848i	0.581661	+	1.74538i
$193$	−6.28802			−0.452622			−0.226311	−	0.974055i	$-0.572666\pi$
$193$	−6.28802			−0.452622			−0.226311	+	0.974055i	$0.572666\pi$
$194$	−0.637251	+	8.22893i	−0.0457520	+	0.590803i
$195$	8.77112	+	8.77112i	0.628113	+	0.628113i
$196$	−13.4729	−	2.09929i	−0.962353	−	0.149949i
$197$	−10.1634	+	10.1634i	−0.724113	+	0.724113i	−0.969440	−	0.245327i	$-0.921105\pi$
$197$	−10.1634	+	10.1634i	−0.724113	+	0.724113i	0.245327	+	0.969440i	$0.421105\pi$
$198$	−30.9496	+	26.5006i	−2.19949	+	1.88332i
$199$		−	0.145252i		−	0.0102966i	−0.999987	−	0.00514832i	$-0.998361\pi$
$199$		−	0.145252i		−	0.0102966i	0.999987	−	0.00514832i	$-0.00163877\pi$
$200$	3.58256	+	0.845859i	0.253325	+	0.0598113i
$201$		−	3.69570i		−	0.260675i
$202$	15.8819	+	18.5482i	1.11745	+	1.30505i
$203$	0.841582	−	0.841582i	0.0590675	−	0.0590675i
$204$	18.3637	+	25.1426i	1.28571	+	1.76033i
$205$	9.52613	+	9.52613i	0.665334	+	0.665334i
$206$	22.8235	+	1.76746i	1.59019	+	0.123145i
$207$	−44.8682			−3.11855
$208$	3.71184	+	7.19545i	0.257369	+	0.498915i
$209$	4.02722			0.278569
$210$	−3.68878	−	0.285661i	−0.254550	−	0.0197125i
$211$	−10.4826	−	10.4826i	−0.721654	−	0.721654i	0.247288	−	0.968942i	$-0.420461\pi$
$211$	−10.4826	−	10.4826i	−0.721654	−	0.721654i	−0.968942	+	0.247288i	$0.920461\pi$
$212$	11.3273	−	8.27323i	0.777961	−	0.568208i
$213$	25.7180	−	25.7180i	1.76217	−	1.76217i
$214$	−17.7443	−	20.7232i	−1.21297	−	1.41661i
$215$			10.2609i			0.699790i
$216$	−19.6826	−	31.8495i	−1.33923	−	2.16708i
$217$			2.58273i			0.175327i
$218$	−12.9110	+	11.0551i	−0.874444	+	0.748744i
$219$	34.2652	−	34.2652i	2.31543	−	2.31543i
$220$	2.38480	−	15.3053i	0.160783	−	1.03188i
$221$	6.99221	+	6.99221i	0.470347	+	0.470347i
$222$	−0.390026	+	5.03647i	−0.0261769	+	0.338026i
$223$	−16.5226			−1.10644			−0.553218	−	0.833037i	$-0.686600\pi$
$223$	−16.5226			−1.10644			−0.553218	+	0.833037i	$0.686600\pi$
$224$	−2.23686	−	0.910151i	−0.149456	−	0.0608120i
$225$	−9.31072			−0.620715
$226$	−1.00020	+	12.9158i	−0.0665325	+	0.859145i
$227$	−5.13307	−	5.13307i	−0.340694	−	0.340694i	0.515934	−	0.856628i	$-0.327445\pi$
$227$	−5.13307	−	5.13307i	−0.340694	−	0.340694i	−0.856628	+	0.515934i	$0.827445\pi$
$228$	−0.981186	+	6.29711i	−0.0649806	+	0.417037i
$229$	−1.95657	+	1.95657i	−0.129294	+	0.129294i	−0.768792	−	0.639499i	$-0.779142\pi$
$229$	−1.95657	+	1.95657i	−0.129294	+	0.129294i	0.639499	+	0.768792i	$0.279142\pi$
$230$	12.9567	−	11.0942i	0.854339	−	0.731529i
$231$		−	5.47843i		−	0.360455i
$232$	−6.70790	+	4.14539i	−0.440395	+	0.272158i
$233$		−	4.84340i		−	0.317302i	−0.987335	−	0.158651i	$-0.949286\pi$
$233$		−	4.84340i		−	0.317302i	0.987335	−	0.158651i	$-0.0507144\pi$
$234$	−13.3194	−	15.5555i	−0.870717	−	1.01689i
$235$	11.1467	−	11.1467i	0.727130	−	0.727130i
$236$	−13.8245	+	10.0972i	−0.899900	+	0.657269i
$237$	−12.5040	−	12.5040i	−0.812220	−	0.812220i
$238$	−2.94064	−	0.227724i	−0.190614	−	0.0147612i
$239$	11.8880			0.768971			0.384485	−	0.923131i	$-0.374379\pi$
$239$	11.8880			0.768971			0.384485	+	0.923131i	$0.374379\pi$
$240$	23.3509	+	7.45792i	1.50730	+	0.481407i
$241$	15.0637			0.970341			0.485170	−	0.874420i	$-0.338758\pi$
$241$	15.0637			0.970341			0.485170	+	0.874420i	$0.338758\pi$
$242$	7.35808	+	0.569812i	0.472995	+	0.0366289i
$243$	18.6038	+	18.6038i	1.19344	+	1.19344i
$244$	−15.7428	−	21.5542i	−1.00783	−	1.37987i
$245$	−9.27133	+	9.27133i	−0.592323	+	0.592323i
$246$	−20.5321	−	23.9790i	−1.30908	−	1.52885i
$247$			2.02411i			0.128791i
$248$	3.93205	−	16.6539i	0.249685	−	1.05752i
$249$			10.5408i			0.667993i
$250$	13.0182	−	11.1469i	0.823344	−	0.704989i
$251$	−8.95302	+	8.95302i	−0.565109	+	0.565109i	−0.930754	−	0.365645i	$-0.880848\pi$
$251$	−8.95302	+	8.95302i	−0.565109	+	0.565109i	0.365645	+	0.930754i	$0.380848\pi$
$252$	6.03540	+	0.940406i	0.380194	+	0.0592400i
$253$	17.8597	+	17.8597i	1.12283	+	1.12283i
$254$	−0.652323	+	8.42355i	−0.0409304	+	0.528540i
$255$	29.9386			1.87483
$256$	13.0379	+	9.27427i	0.814872	+	0.579642i
$257$	−8.73446			−0.544841			−0.272420	−	0.962178i	$-0.587824\pi$
$257$	−8.73446			−0.544841			−0.272420	+	0.962178i	$0.587824\pi$
$258$	1.85642	−	23.9722i	0.115576	−	1.49245i
$259$	−0.338380	−	0.338380i	−0.0210259	−	0.0210259i
$260$	7.69255	+	1.19862i	0.477072	+	0.0743350i
$261$	14.1033	−	14.1033i	0.872973	−	0.872973i
$262$	3.37037	−	2.88588i	0.208222	−	0.178290i
$263$			10.3115i			0.635837i	0.948118	+	0.317919i	$0.102984\pi$
$263$			10.3115i			0.635837i	−0.948118	+	0.317919i	$0.897016\pi$
$264$	−8.34057	+	35.3258i	−0.513327	+	2.17415i
$265$		−	13.4880i		−	0.828560i
$266$	−0.392669	−	0.458591i	−0.0240761	−	0.0281180i
$267$	−12.9937	+	12.9937i	−0.795202	+	0.795202i
$268$	−1.36811	−	1.87314i	−0.0835704	−	0.114420i
$269$	0.834972	+	0.834972i	0.0509091	+	0.0509091i	0.732103	−	0.681194i	$-0.238539\pi$
$269$	0.834972	+	0.834972i	0.0509091	+	0.0509091i	−0.681194	+	0.732103i	$0.738539\pi$
$270$	−35.8946	−	2.77969i	−2.18448	−	0.169167i
$271$	2.68110			0.162866			0.0814328	−	0.996679i	$-0.474050\pi$
$271$	2.68110			0.162866			0.0814328	+	0.996679i	$0.474050\pi$
$272$	18.6150	+	5.94534i	1.12870	+	0.360489i
$273$	2.75350			0.166649
$274$	2.50465	+	0.193961i	0.151311	+	0.0117176i
$275$	3.70612	+	3.70612i	0.223487	+	0.223487i
$276$	−32.2774	+	23.5748i	−1.94287	+	1.41904i
$277$	1.50736	−	1.50736i	0.0905685	−	0.0905685i	−0.660371	−	0.750940i	$-0.729601\pi$
$277$	1.50736	−	1.50736i	0.0905685	−	0.0905685i	0.750940	+	0.660371i	$0.229601\pi$
$278$	−20.9293	−	24.4429i	−1.25525	−	1.46599i
$279$			43.2817i			2.59121i
$280$	−1.97538	+	1.22076i	−0.118052	+	0.0729543i
$281$		−	16.8357i		−	1.00433i	−0.864771	−	0.502167i	$-0.832536\pi$
$281$		−	16.8357i		−	1.00433i	0.864771	−	0.502167i	$-0.167464\pi$
$282$	−28.0583	+	24.0249i	−1.67085	+	1.43066i
$283$	6.10908	−	6.10908i	0.363147	−	0.363147i	−0.501823	−	0.864970i	$-0.667337\pi$
$283$	6.10908	−	6.10908i	0.363147	−	0.363147i	0.864970	+	0.501823i	$0.167337\pi$
$284$	3.51450	−	22.5555i	0.208547	−	1.33843i
$285$	4.33332	+	4.33332i	0.256684	+	0.256684i
$286$	−0.890069	+	11.4936i	−0.0526309	+	0.679631i
$287$	2.99052			0.176525
$288$	−37.4855	−	15.2524i	−2.20885	−	0.898756i
$289$	6.86661			0.403918
$290$	−0.585438	+	7.55985i	−0.0343781	+	0.443930i
$291$	−13.1502	−	13.1502i	−0.770879	−	0.770879i
$292$	4.68251	−	30.0517i	0.274023	−	1.75864i
$293$	0.955005	−	0.955005i	0.0557920	−	0.0557920i	−0.678660	−	0.734452i	$-0.737439\pi$
$293$	0.955005	−	0.955005i	0.0557920	−	0.0557920i	0.734452	+	0.678660i	$0.237439\pi$
$294$	23.3376	−	19.9829i	1.36108	−	1.16542i
$295$			16.4616i			0.958430i
$296$	1.66676	+	2.69709i	0.0968786	+	0.156765i
$297$		−	53.3093i		−	3.09332i
$298$	−12.9376	−	15.1096i	−0.749455	−	0.875274i
$299$	−8.97640	+	8.97640i	−0.519119	+	0.519119i
$300$	−6.69797	+	4.89207i	−0.386708	+	0.282444i
$301$	1.61060	+	1.61060i	0.0928332	+	0.0928332i
$302$	−7.46306	−	0.577942i	−0.429451	−	0.0332568i
$303$	−55.0209			−3.16087
$304$	1.83381	+	3.55487i	0.105176	+	0.203886i
$305$	−25.6657			−1.46962
$306$	−49.2795	−	3.81623i	−2.81712	−	0.218159i
$307$	18.7104	+	18.7104i	1.06786	+	1.06786i	0.997523	+	0.0703371i	$0.0224075\pi$
$307$	18.7104	+	18.7104i	1.06786	+	1.06786i	0.0703371	+	0.997523i	$0.477592\pi$
$308$	−2.02805	−	2.77671i	−0.115559	−	0.158218i
$309$	−36.4729	+	36.4729i	−2.07487	+	2.07487i
$310$	−10.7019	−	12.4986i	−0.607828	−	0.709871i
$311$		−	5.79373i		−	0.328532i	−0.986416	−	0.164266i	$-0.947474\pi$
$311$		−	5.79373i		−	0.328532i	0.986416	−	0.164266i	$-0.0525256\pi$
$312$	−17.7550	−	4.19203i	−1.00518	−	0.237327i
$313$		−	7.49683i		−	0.423746i	−0.977297	−	0.211873i	$-0.932044\pi$
$313$		−	7.49683i		−	0.423746i	0.977297	−	0.211873i	$-0.0679563\pi$
$314$	2.56921	−	2.19989i	0.144989	−	0.124147i
$315$	4.15323	−	4.15323i	0.234008	−	0.234008i
$316$	−10.9664	−	1.70873i	−0.616907	−	0.0961235i
$317$	−10.2910	−	10.2910i	−0.578001	−	0.578001i	0.356351	−	0.934352i	$-0.384021\pi$
$317$	−10.2910	−	10.2910i	−0.578001	−	0.578001i	−0.934352	+	0.356351i	$0.884021\pi$
$318$	−2.44026	+	31.5115i	−0.136843	+	1.76708i
$319$	−11.2276			−0.628625
$320$	14.5961	−	4.86425i	0.815947	−	0.271920i
$321$	61.4727			3.43107
$322$	0.292346	−	3.77512i	0.0162918	−	0.210379i
$323$	3.45446	+	3.45446i	0.192211	+	0.192211i
$324$	40.9435	+	6.37962i	2.27464	+	0.354424i
$325$	−1.86272	+	1.86272i	−0.103325	+	0.103325i
$326$	1.42740	−	1.22221i	0.0790563	−	0.0676920i
$327$		−	38.2989i		−	2.11793i
$328$	−19.2833	−	4.55287i	−1.06474	−	0.251390i
$329$		−	3.49926i		−	0.192920i
$330$	22.7006	+	26.5116i	1.24963	+	1.45942i
$331$	−5.15177	+	5.15177i	−0.283167	+	0.283167i	−0.834371	−	0.551204i	$-0.814169\pi$
$331$	−5.15177	+	5.15177i	−0.283167	+	0.283167i	0.551204	+	0.834371i	$0.314169\pi$
$332$	3.90207	+	5.34251i	0.214154	+	0.293209i
$333$	−5.67060	−	5.67060i	−0.310747	−	0.310747i
$334$	32.2973	+	2.50111i	1.76723	+	0.136855i
$335$	−2.23045			−0.121862
$336$	4.83588	−	2.49463i	0.263819	−	0.136093i
$337$	−20.5489			−1.11937			−0.559684	−	0.828706i	$-0.689077\pi$
$337$	−20.5489			−1.11937			−0.559684	+	0.828706i	$0.689077\pi$
$338$	12.5531	+	0.972119i	0.682801	+	0.0528763i
$339$	−20.6400	−	20.6400i	−1.12101	−	1.12101i
$340$	15.1742	−	11.0829i	0.822936	−	0.601056i
$341$	17.2282	−	17.2282i	0.932960	−	0.932960i
$342$	−6.58038	−	7.68510i	−0.355826	−	0.415563i
$343$			5.89885i			0.318508i
$344$	−7.93333	−	12.8374i	−0.427737	−	0.692146i
$345$			38.4344i			2.06924i
$346$	−12.7225	+	10.8936i	−0.683964	+	0.585645i
$347$	−9.86371	+	9.86371i	−0.529512	+	0.529512i	−0.920427	−	0.390915i	$-0.872159\pi$
$347$	−9.86371	+	9.86371i	−0.529512	+	0.529512i	0.390915	+	0.920427i	$0.372159\pi$
$348$	2.73547	−	17.5559i	0.146637	−	0.941094i
$349$	−10.8254	−	10.8254i	−0.579469	−	0.579469i	0.355288	−	0.934757i	$-0.384383\pi$
$349$	−10.8254	−	10.8254i	−0.579469	−	0.579469i	−0.934757	+	0.355288i	$0.884383\pi$
$350$	0.0606656	−	0.783385i	0.00324271	−	0.0418737i
$351$	26.7936			1.43014
$352$	8.84983	+	20.9922i	0.471698	+	1.11889i
$353$	34.1129			1.81565			0.907824	−	0.419351i	$-0.137742\pi$
$353$	34.1129			1.81565			0.907824	+	0.419351i	$0.137742\pi$
$354$	2.97824	−	38.4586i	0.158292	−	2.04405i
$355$	−15.5215	−	15.5215i	−0.823794	−	0.823794i
$356$	−1.77565	+	11.3959i	−0.0941095	+	0.603982i
$357$	4.69928	−	4.69928i	0.248712	−	0.248712i
$358$	1.91828	−	1.64253i	0.101384	−	0.0868106i
$359$		−	26.3874i		−	1.39267i	−0.717715	−	0.696337i	$-0.754812\pi$
$359$		−	26.3874i		−	1.39267i	0.717715	−	0.696337i	$-0.245188\pi$
$360$	−33.1036	+	20.4576i	−1.74472	+	1.07821i
$361$			1.00000i			0.0526316i
$362$	18.1862	+	21.2393i	0.955845	+	1.11631i
$363$	−11.7585	+	11.7585i	−0.617163	+	0.617163i
$364$	1.39559	−	1.01931i	0.0731489	−	0.0534265i
$365$	−20.6799	−	20.6799i	−1.08244	−	1.08244i
$366$	59.9619	+	4.64347i	3.13426	+	0.242718i
$367$	−26.9132			−1.40486			−0.702428	−	0.711755i	$-0.747901\pi$
$367$	−26.9132			−1.40486			−0.702428	+	0.711755i	$0.747901\pi$
$368$	−7.63247	+	23.8974i	−0.397870	+	1.24574i
$369$	50.1153			2.60890
$370$	3.03964	+	0.235390i	0.158023	+	0.0122374i
$371$	−2.11713	−	2.11713i	−0.109916	−	0.109916i
$372$	22.7412	+	31.1361i	1.17908	+	1.61433i
$373$	−7.26937	+	7.26937i	−0.376394	+	0.376394i	−0.869799	−	0.493406i	$-0.835752\pi$
$373$	−7.26937	+	7.26937i	−0.376394	+	0.376394i	0.493406	+	0.869799i	$0.335752\pi$
$374$	18.0966	+	21.1347i	0.935753	+	1.09285i
$375$			38.6169i			1.99417i
$376$	−5.32740	+	22.5637i	−0.274740	+	1.16364i
$377$		−	5.64306i		−	0.290633i
$378$	−6.07047	+	5.19785i	−0.312231	+	0.267348i
$379$	−7.64570	+	7.64570i	−0.392733	+	0.392733i	−0.875660	−	0.482927i	$-0.839574\pi$
$379$	−7.64570	+	7.64570i	−0.392733	+	0.392733i	0.482927	+	0.875660i	$0.339574\pi$
$380$	3.80046	+	0.592170i	0.194960	+	0.0303777i
$381$	−13.4612	−	13.4612i	−0.689639	−	0.689639i
$382$	0.238791	−	3.08355i	0.0122176	−	0.157768i
$383$	19.2292			0.982565			0.491282	−	0.871000i	$-0.336528\pi$
$383$	19.2292			0.982565			0.491282	+	0.871000i	$0.336528\pi$
$384$	−34.9804	+	8.72342i	−1.78508	+	0.445165i
$385$	−3.30637			−0.168508
$386$	0.686591	−	8.86606i	0.0349465	−	0.451270i
$387$	26.9905	+	26.9905i	1.37200	+	1.37200i
$388$	−11.5331	−	1.79704i	−0.585507	−	0.0912308i
$389$	4.69831	−	4.69831i	0.238214	−	0.238214i	−0.577896	−	0.816110i	$-0.696126\pi$
$389$	4.69831	−	4.69831i	0.238214	−	0.238214i	0.816110	+	0.577896i	$0.196126\pi$
$390$	−13.3249	+	11.4095i	−0.674734	+	0.577742i
$391$			30.6393i			1.54950i
$392$	4.43109	−	18.7675i	0.223804	−	0.947902i
$393$			9.99777i			0.504321i
$394$	−13.2206	−	15.4401i	−0.666044	−	0.777860i
$395$	−7.54645	+	7.54645i	−0.379703	+	0.379703i
$396$	−33.9863	−	46.5323i	−1.70788	−	2.33834i
$397$	11.7731	+	11.7731i	0.590873	+	0.590873i	0.937867	−	0.346994i	$-0.112798\pi$
$397$	11.7731	+	11.7731i	0.590873	+	0.590873i	−0.346994	+	0.937867i	$0.612798\pi$
$398$	0.204804	+	0.0158601i	0.0102659	+	0.000794995i
$399$	1.36035			0.0681027
$400$	−1.58384	+	4.95903i	−0.0791918	+	0.247951i
$401$	4.55385			0.227409			0.113704	−	0.993515i	$-0.463728\pi$
$401$	4.55385			0.227409			0.113704	+	0.993515i	$0.463728\pi$
$402$	5.21091	+	0.403535i	0.259897	+	0.0201265i
$403$	8.65901	+	8.65901i	0.431336	+	0.431336i
$404$	−27.8870	+	20.3681i	−1.38743	+	1.01335i
$405$	28.1751	−	28.1751i	1.40003	−	1.40003i
$406$	1.09473	+	1.27852i	0.0543306	+	0.0634517i
$407$			4.51435i			0.223768i
$408$	−37.4560	+	23.1473i	−1.85435	+	1.14596i
$409$		−	12.4451i		−	0.615370i	−0.951488	−	0.307685i	$-0.900446\pi$
$409$		−	12.4451i		−	0.615370i	0.951488	−	0.307685i	$-0.0995542\pi$
$410$	−14.4719	+	12.3916i	−0.714718	+	0.611978i
$411$	−4.00254	+	4.00254i	−0.197431	+	0.197431i
$412$	−4.98420	+	31.9879i	−0.245554	+	1.57593i
$413$	2.58387	+	2.58387i	0.127144	+	0.127144i
$414$	4.89917	−	63.2637i	0.240781	−	3.10924i
$415$	6.36161			0.312279
$416$	−10.5508	+	4.44798i	−0.517297	+	0.218080i
$417$	72.5068			3.55067
$418$	−0.439734	+	5.67835i	−0.0215081	+	0.277737i
$419$	12.2621	+	12.2621i	0.599043	+	0.599043i	0.940058	−	0.341015i	$-0.110771\pi$
$419$	12.2621	+	12.2621i	0.599043	+	0.599043i	−0.341015	+	0.940058i	$0.610771\pi$
$420$	0.805558	−	5.16996i	0.0393072	−	0.252268i
$421$	−13.5240	+	13.5240i	−0.659118	+	0.659118i	−0.955171	−	0.296053i	$-0.904329\pi$
$421$	−13.5240	+	13.5240i	−0.659118	+	0.659118i	0.296053	+	0.955171i	$0.404329\pi$
$422$	15.9250	−	13.6358i	0.775218	−	0.663781i
$423$		−	58.6409i		−	2.85122i
$424$	10.4284	+	16.8747i	0.506446	+	0.819510i
$425$			6.35805i			0.308411i
$426$	33.4541	+	39.0704i	1.62086	+	1.89297i
$427$	−4.02859	+	4.02859i	−0.194957	+	0.194957i
$428$	31.1570	−	22.7565i	1.50603	−	1.09998i
$429$	−18.3673	−	18.3673i	−0.886781	−	0.886781i
$430$	−14.4678	−	1.12039i	−0.697701	−	0.0540302i
$431$	8.31902			0.400713			0.200357	−	0.979723i	$-0.435790\pi$
$431$	8.31902			0.400713			0.200357	+	0.979723i	$0.435790\pi$
$432$	47.0567	−	24.2746i	2.26402	−	1.16791i
$433$	−19.7471			−0.948987			−0.474494	−	0.880259i	$-0.657369\pi$
$433$	−19.7471			−0.948987			−0.474494	+	0.880259i	$0.657369\pi$
$434$	−3.64163	−	0.282009i	−0.174804	−	0.0135369i
$435$	−12.0810	−	12.0810i	−0.579239	−	0.579239i
$436$	−14.1778	−	19.4115i	−0.678994	−	0.929644i
$437$	−4.43474	+	4.43474i	−0.212143	+	0.212143i
$438$	44.5723	+	52.0551i	2.12975	+	2.48729i
$439$		−	4.89254i		−	0.233508i	−0.993161	−	0.116754i	$-0.962751\pi$
$439$		−	4.89254i		−	0.233508i	0.993161	−	0.116754i	$-0.0372489\pi$
$440$	21.3200	+	5.03374i	1.01639	+	0.239974i
$441$			48.7749i			2.32261i
$442$	−10.6224	+	9.09547i	−0.505258	+	0.432628i
$443$	18.2979	−	18.2979i	0.869361	−	0.869361i	−0.123041	−	0.992402i	$-0.539265\pi$
$443$	18.2979	−	18.2979i	0.869361	−	0.869361i	0.992402	+	0.123041i	$0.0392647\pi$
$444$	−7.05880	−	1.09987i	−0.334996	−	0.0521974i
$445$	7.84203	+	7.84203i	0.371748	+	0.371748i
$446$	1.80411	−	23.2967i	0.0854270	−	1.10313i
$447$	44.8206			2.11994
$448$	1.52755	−	3.05457i	0.0721699	−	0.144315i
$449$	−18.3037			−0.863804			−0.431902	−	0.901920i	$-0.642157\pi$
$449$	−18.3037			−0.863804			−0.431902	+	0.901920i	$0.642157\pi$
$450$	1.01664	−	13.1280i	0.0479249	−	0.618862i
$451$	−19.9483	−	19.9483i	−0.939330	−	0.939330i
$452$	−18.1019	−	2.82056i	−0.851444	−	0.132668i
$453$	11.9263	−	11.9263i	0.560346	−	0.560346i
$454$	7.79806	−	6.67710i	0.365981	−	0.313372i
$455$		−	1.66180i		−	0.0779065i
$456$	−8.77175	−	2.07105i	−0.410775	−	0.0969857i
$457$		−	30.9074i		−	1.44579i	−0.690959	−	0.722894i	$-0.742811\pi$
$457$		−	30.9074i		−	1.44579i	0.690959	−	0.722894i	$-0.257189\pi$
$458$	−2.54511	−	2.97238i	−0.118925	−	0.138890i
$459$	45.7275	−	45.7275i	2.13438	−	2.13438i
$460$	14.2280	+	19.4802i	0.663382	+	0.908269i
$461$	−12.4987	−	12.4987i	−0.582122	−	0.582122i	0.353364	−	0.935486i	$-0.385038\pi$
$461$	−12.4987	−	12.4987i	−0.582122	−	0.582122i	−0.935486	+	0.353364i	$0.885038\pi$
$462$	7.72455	+	0.598192i	0.359379	+	0.0278304i
$463$	−1.95150			−0.0906938			−0.0453469	−	0.998971i	$-0.514439\pi$
$463$	−1.95150			−0.0906938			−0.0453469	+	0.998971i	$0.514439\pi$
$464$	−5.11253	−	9.91073i	−0.237343	−	0.460094i
$465$	37.0754			1.71933
$466$	6.82916	+	0.528853i	0.316355	+	0.0244986i
$467$	−2.04065	−	2.04065i	−0.0944299	−	0.0944299i	0.658314	−	0.752744i	$-0.271270\pi$
$467$	−2.04065	−	2.04065i	−0.0944299	−	0.0944299i	−0.752744	+	0.658314i	$0.771270\pi$
$468$	23.3875	−	17.0817i	1.08109	−	0.789604i
$469$	−0.350099	+	0.350099i	−0.0161661	+	0.0161661i
$470$	14.4996	+	16.9339i	0.668819	+	0.781101i
$471$			7.62124i			0.351168i
$472$	−12.7274	−	20.5950i	−0.585827	−	0.947961i
$473$		−	21.4871i		−	0.987976i
$474$	18.9958	−	16.2652i	0.872506	−	0.747085i
$475$	−0.920266	+	0.920266i	−0.0422247	+	0.0422247i
$476$	0.642179	−	4.12142i	0.0294342	−	0.188905i
$477$	−35.4790	−	35.4790i	−1.62447	−	1.62447i
$478$	−1.29805	+	16.7620i	−0.0593716	+	0.766675i
$479$	−16.7032			−0.763187			−0.381594	−	0.924330i	$-0.624625\pi$
$479$	−16.7032			−0.763187			−0.381594	+	0.924330i	$0.624625\pi$
$480$	−13.0653	+	32.1103i	−0.596347	+	1.46563i
$481$	−2.26894			−0.103455
$482$	−1.64481	+	21.2397i	−0.0749192	+	0.967444i
$483$	6.03281	+	6.03281i	0.274502	+	0.274502i
$484$	−1.60686	+	10.3126i	−0.0730391	+	0.468755i
$485$	−7.93647	+	7.93647i	−0.360377	+	0.360377i
$486$	−28.2626	+	24.1999i	−1.28202	+	1.09773i
$487$			17.1358i			0.776499i	0.921554	+	0.388249i	$0.126920\pi$
$487$			17.1358i			0.776499i	−0.921554	+	0.388249i	$0.873080\pi$
$488$	32.1103	−	19.8437i	1.45356	−	0.898282i
$489$			4.23419i			0.191477i
$490$	−12.0602	−	14.0848i	−0.544822	−	0.636288i
$491$	9.14454	−	9.14454i	0.412687	−	0.412687i	−0.469987	−	0.882674i	$-0.655741\pi$
$491$	9.14454	−	9.14454i	0.412687	−	0.412687i	0.882674	+	0.469987i	$0.155741\pi$
$492$	36.0521	−	26.3318i	1.62536	−	1.18713i
$493$	−9.63078	−	9.63078i	−0.433749	−	0.433749i
$494$	−2.85398	−	0.221013i	−0.128407	−	0.00994385i
$495$	−55.4084			−2.49042
$496$	23.0525	+	7.36260i	1.03509	+	0.330590i
$497$	−4.87262			−0.218567
$498$	−14.8624	−	1.15095i	−0.665999	−	0.0515752i
$499$	13.9125	+	13.9125i	0.622810	+	0.622810i	0.946249	−	0.323439i	$-0.104839\pi$
$499$	13.9125	+	13.9125i	0.622810	+	0.622810i	−0.323439	+	0.946249i	$0.604839\pi$
$500$	14.2955	+	19.5727i	0.639315	+	0.875318i
$501$	−51.6125	+	51.6125i	−2.30588	+	2.30588i
$502$	−11.6461	−	13.6013i	−0.519791	−	0.607054i
$503$			35.7157i			1.59248i	0.604978	+	0.796242i	$0.293182\pi$
$503$			35.7157i			1.59248i	−0.604978	+	0.796242i	$0.706818\pi$
$504$	−1.98497	+	8.40718i	−0.0884177	+	0.374486i
$505$			33.2065i			1.47767i
$506$	−27.1321	+	23.2319i	−1.20617	+	1.03279i
$507$	−20.0605	+	20.0605i	−0.890917	+	0.890917i
$508$	−11.8059	−	1.83954i	−0.523802	−	0.0816163i
$509$	−26.3493	−	26.3493i	−1.16791	−	1.16791i	−0.982699	−	0.185212i	$-0.940703\pi$
$509$	−26.3493	−	26.3493i	−1.16791	−	1.16791i	−0.185212	−	0.982699i	$-0.559297\pi$
$510$	−3.26900	+	42.2132i	−0.144754	+	1.86923i
$511$	−6.49200			−0.287189
$512$	−14.5003	+	17.3707i	−0.640827	+	0.767685i
$513$	13.2372			0.584438
$514$	0.953719	−	12.3155i	0.0420667	−	0.543214i
$515$	22.0123	+	22.0123i	0.969978	+	0.969978i
$516$	33.5980	+	5.23507i	1.47907	+	0.230461i
$517$	−23.3419	+	23.3419i	−1.02658	+	1.02658i
$518$	0.514061	−	0.440165i	0.0225865	−	0.0193397i
$519$		−	37.7396i		−	1.65658i
$520$	−2.52999	+	10.7156i	−0.110947	+	0.469908i
$521$			8.18730i			0.358692i	0.983786	+	0.179346i	$0.0573982\pi$
$521$			8.18730i			0.358692i	−0.983786	+	0.179346i	$0.942602\pi$
$522$	18.3456	+	21.4255i	0.802965	+	0.937768i
$523$	−5.00932	+	5.00932i	−0.219042	+	0.219042i	−0.808095	−	0.589053i	$-0.799501\pi$
$523$	−5.00932	+	5.00932i	−0.219042	+	0.219042i	0.589053	+	0.808095i	$0.299501\pi$
$524$	3.70106	+	5.06731i	0.161682	+	0.221366i
$525$	1.25188	+	1.25188i	0.0546367	+	0.0546367i
$526$	−14.5392	−	1.12592i	−0.633939	−	0.0490925i
$527$	29.5559			1.28748
$528$	−48.8984	−	15.6174i	−2.12803	−	0.679659i
$529$	−16.3339			−0.710170
$530$	19.0180	+	1.47276i	0.826087	+	0.0639725i
$531$	43.3008	+	43.3008i	1.87909	+	1.87909i
$532$	0.689485	−	0.503586i	0.0298929	−	0.0218332i
$533$	10.0262	−	10.0262i	0.434281	−	0.434281i
$534$	−16.9022	−	19.7398i	−0.731432	−	0.854226i
$535$		−	37.1003i		−	1.60399i
$536$	2.79050	−	1.72449i	0.120531	−	0.0744866i
$537$			5.69035i			0.245557i
$538$	−1.26847	+	1.08613i	−0.0546878	+	0.0468265i
$539$	19.4148	−	19.4148i	0.836253	−	0.836253i
$540$	7.83869	−	50.3076i	0.337323	−	2.16489i
$541$	18.4542	+	18.4542i	0.793410	+	0.793410i	0.982047	−	0.188637i	$-0.0604069\pi$
$541$	18.4542	+	18.4542i	0.793410	+	0.793410i	−0.188637	+	0.982047i	$0.560407\pi$
$542$	−0.292751	+	3.78034i	−0.0125747	+	0.162379i
$543$	−63.0037			−2.70375
$544$	−10.4155	+	25.5978i	−0.446559	+	1.09750i
$545$	−23.1143			−0.990108
$546$	−0.300655	+	3.88241i	−0.0128669	+	0.166152i
$547$	3.08163	+	3.08163i	0.131761	+	0.131761i	0.769911	−	0.638151i	$-0.220300\pi$
$547$	3.08163	+	3.08163i	0.131761	+	0.131761i	−0.638151	+	0.769911i	$0.720300\pi$
$548$	−0.546966	+	3.51035i	−0.0233652	+	0.149955i
$549$	−67.5115	+	67.5115i	−2.88132	+	2.88132i
$550$	−5.63027	+	4.82092i	−0.240075	+	0.205565i
$551$		−	2.78793i		−	0.118770i
$552$	−29.7159	−	48.0850i	−1.26479	−	2.04663i
$553$			2.36904i			0.100742i
$554$	1.96078	+	2.28996i	0.0833054	+	0.0972909i
$555$	−4.85747	+	4.85747i	−0.206188	+	0.206188i
$556$	36.7496	−	26.8412i	1.55853	−	1.13832i
$557$	3.38264	+	3.38264i	0.143327	+	0.143327i	0.775130	−	0.631802i	$-0.217685\pi$
$557$	3.38264	+	3.38264i	0.143327	+	0.143327i	−0.631802	+	0.775130i	$0.717685\pi$
$558$	−61.0268	−	4.72594i	−2.58347	−	0.200065i
$559$	10.7995			0.456772
$560$	−1.50557	−	2.91857i	−0.0636219	−	0.123332i
$561$	−62.6934			−2.64692
$562$	23.7382	+	1.83829i	1.00134	+	0.0775437i
$563$	−0.0877868	−	0.0877868i	−0.00369977	−	0.00369977i	0.705254	−	0.708954i	$-0.250833\pi$
$563$	−0.0877868	−	0.0877868i	−0.00369977	−	0.00369977i	−0.708954	+	0.705254i	$0.750833\pi$
$564$	−30.8113	−	42.1853i	−1.29739	−	1.77632i
$565$	−12.4568	+	12.4568i	−0.524060	+	0.524060i
$566$	7.94670	+	9.28080i	0.334025	+	0.390101i
$567$		−	8.84493i		−	0.371452i
$568$	31.4194	+	7.41826i	1.31833	+	0.311263i
$569$		−	20.9860i		−	0.879778i	−0.898052	−	0.439889i	$-0.855018\pi$
$569$		−	20.9860i		−	0.879778i	0.898052	−	0.439889i	$-0.144982\pi$
$570$	−6.58311	+	5.63680i	−0.275736	+	0.236099i
$571$	15.6185	−	15.6185i	0.653613	−	0.653613i	−0.300248	−	0.953861i	$-0.597069\pi$
$571$	15.6185	−	15.6185i	0.653613	−	0.653613i	0.953861	+	0.300248i	$0.0970694\pi$
$572$	−16.1087	−	2.50998i	−0.673539	−	0.104948i
$573$	4.92766	+	4.92766i	0.205856	+	0.205856i
$574$	−0.326535	+	4.21660i	−0.0136293	+	0.175998i
$575$	−8.16229			−0.340391
$576$	25.5988	−	51.1888i	1.06662	−	2.13287i
$577$	36.9671			1.53896			0.769479	−	0.638672i	$-0.220516\pi$
$577$	36.9671			1.53896			0.769479	+	0.638672i	$0.220516\pi$
$578$	−0.749767	+	9.68186i	−0.0311862	+	0.402712i
$579$	14.1684	+	14.1684i	0.588817	+	0.588817i
$580$	−10.5954	−	1.65093i	−0.439950	−	0.0685509i
$581$	0.998542	−	0.998542i	0.0414265	−	0.0414265i
$582$	19.9776	−	17.1058i	0.828096	−	0.709059i
$583$			28.2447i			1.16978i
$584$	41.8614	+	9.88366i	1.73224	+	0.408989i
$585$		−	27.8487i		−	1.15140i
$586$	1.24227	+	1.45083i	0.0513178	+	0.0599331i
$587$	−22.4155	+	22.4155i	−0.925186	+	0.925186i	−0.997390	−	0.0722043i	$-0.976997\pi$
$587$	−22.4155	+	22.4155i	−0.925186	+	0.925186i	0.0722043	+	0.997390i	$0.476997\pi$
$588$	25.6275	+	35.0878i	1.05686	+	1.44700i
$589$	4.27794	+	4.27794i	0.176269	+	0.176269i
$590$	−23.2107	−	1.79744i	−0.955569	−	0.0739996i
$591$	45.8010			1.88400
$592$	−3.98486	+	2.05563i	−0.163777	+	0.0844857i
$593$	−5.07323			−0.208333			−0.104166	−	0.994560i	$-0.533217\pi$
$593$	−5.07323			−0.208333			−0.104166	+	0.994560i	$0.533217\pi$
$594$	75.1656	+	5.82085i	3.08408	+	0.238833i
$595$	−2.83613	−	2.83613i	−0.116270	−	0.116270i
$596$	22.7170	−	16.5921i	0.930526	−	0.679638i
$597$	−0.327286	+	0.327286i	−0.0133949	+	0.0133949i
$598$	−11.6765	−	13.6368i	−0.477489	−	0.557650i
$599$			29.9856i			1.22518i	0.790401	+	0.612589i	$0.209872\pi$
$599$			29.9856i			1.22518i	−0.790401	+	0.612589i	$0.790128\pi$
$600$	−6.16643	−	9.97826i	−0.251743	−	0.407361i
$601$			31.6279i			1.29013i	0.764127	+	0.645065i	$0.223170\pi$
$601$			31.6279i			1.29013i	−0.764127	+	0.645065i	$0.776830\pi$
$602$	−2.44679	+	2.09507i	−0.0997236	+	0.0853885i
$603$	−5.86700	+	5.86700i	−0.238923	+	0.238923i
$604$	1.62979	−	10.4597i	0.0663151	−	0.425601i
$605$	7.09657	+	7.09657i	0.288516	+	0.288516i
$606$	6.00774	−	77.5790i	0.244048	−	3.15143i
$607$	−2.82135			−0.114515			−0.0572575	−	0.998359i	$-0.518236\pi$
$607$	−2.82135			−0.114515			−0.0572575	+	0.998359i	$0.518236\pi$
$608$	−5.21258	+	2.19750i	−0.211398	+	0.0891205i
$609$	−3.79256			−0.153682
$610$	2.80245	−	36.1885i	0.113468	−	1.46523i
$611$	−11.7318	−	11.7318i	−0.474618	−	0.474618i
$612$	10.7617	−	69.0671i	0.435016	−	2.79187i
$613$	−18.9131	+	18.9131i	−0.763892	+	0.763892i	−0.977024	−	0.213131i	$-0.931634\pi$
$613$	−18.9131	+	18.9131i	−0.763892	+	0.763892i	0.213131	+	0.977024i	$0.431634\pi$
$614$	−28.4245	+	24.3386i	−1.14712	+	0.982224i
$615$		−	42.9291i		−	1.73107i
$616$	4.13658	−	2.55635i	0.166668	−	0.102998i
$617$		−	20.9264i		−	0.842464i	−0.906953	−	0.421232i	$-0.861598\pi$
$617$		−	20.9264i		−	0.842464i	0.906953	−	0.421232i	$-0.138402\pi$
$618$	−47.4440	−	55.4090i	−1.90848	−	2.22888i
$619$	17.3535	−	17.3535i	0.697495	−	0.697495i	−0.266375	−	0.963869i	$-0.585826\pi$
$619$	17.3535	−	17.3535i	0.697495	−	0.697495i	0.963869	+	0.266375i	$0.0858259\pi$
$620$	18.7914	−	13.7249i	0.754681	−	0.551205i
$621$	58.7037	+	58.7037i	2.35570	+	2.35570i
$622$	8.16911	+	0.632619i	0.327551	+	0.0253657i
$623$	2.46183			0.0986311
$624$	7.84939	−	24.5766i	0.314227	−	0.983853i
$625$	16.7990			0.671958
$626$	10.5705	+	0.818581i	0.422481	+	0.0327171i
$627$	−9.07426	−	9.07426i	−0.362391	−	0.362391i
$628$	2.82130	+	3.86278i	0.112582	+	0.154142i
$629$	−3.87231	+	3.87231i	−0.154399	+	0.154399i
$630$	5.40252	+	6.30951i	0.215242	+	0.251377i
$631$		−	29.1213i		−	1.15930i	−0.814865	−	0.579650i	$-0.803189\pi$
$631$		−	29.1213i		−	1.15930i	0.814865	−	0.579650i	$-0.196811\pi$
$632$	3.60672	−	15.2759i	0.143467	−	0.607644i
$633$			47.2395i			1.87760i
$634$	15.6339	−	13.3866i	0.620903	−	0.531649i
$635$	−8.12417	+	8.12417i	−0.322398	+	0.322398i
$636$	−44.1645	−	6.88149i	−1.75124	−	0.272869i
$637$	9.75799	+	9.75799i	0.386625	+	0.386625i
$638$	1.22594	−	15.8308i	0.0485356	−	0.626748i
$639$	−81.6558			−3.23025
$640$	5.26480	+	21.1115i	0.208109	+	0.834506i
$641$	20.7248			0.818581			0.409291	−	0.912404i	$-0.365776\pi$
$641$	20.7248			0.818581			0.409291	+	0.912404i	$0.365776\pi$
$642$	−6.71222	+	86.6760i	−0.264910	+	3.42083i
$643$	−14.3906	−	14.3906i	−0.567511	−	0.567511i	0.363919	−	0.931431i	$-0.381438\pi$
$643$	−14.3906	−	14.3906i	−0.567511	−	0.567511i	−0.931431	+	0.363919i	$0.881438\pi$
$644$	5.29096	+	0.824412i	0.208493	+	0.0324864i
$645$	23.1202	−	23.1202i	0.910359	−	0.910359i
$646$	−5.24796	+	4.49357i	−0.206478	+	0.176797i
$647$		−	22.0519i		−	0.866950i	−0.901166	−	0.433475i	$-0.857287\pi$
$647$		−	22.0519i		−	0.866950i	0.901166	−	0.433475i	$-0.142713\pi$
$648$	−13.4659	+	57.0335i	−0.528989	+	2.24049i
$649$		−	34.4716i		−	1.35313i
$650$	−2.42303	−	2.82981i	−0.0950390	−	0.110994i
$651$	5.81950	−	5.81950i	0.228084	−	0.228084i
$652$	1.56745	+	2.14607i	0.0613861	+	0.0840467i
$653$	8.10047	+	8.10047i	0.316996	+	0.316996i	0.847612	−	0.530616i	$-0.178039\pi$
$653$	8.10047	+	8.10047i	0.316996	+	0.316996i	−0.530616	+	0.847612i	$0.678039\pi$
$654$	54.0011	+	4.18186i	2.11161	+	0.163524i
$655$	6.03390			0.235764
$656$	8.52506	−	26.6922i	0.332848	−	1.04215i
$657$	−108.793			−4.24444
$658$	4.93392	+	0.382085i	0.192344	+	0.0148952i
$659$	−22.3018	−	22.3018i	−0.868756	−	0.868756i	0.123578	−	0.992335i	$-0.460563\pi$
$659$	−22.3018	−	22.3018i	−0.868756	−	0.868756i	−0.992335	+	0.123578i	$0.960563\pi$
$660$	−39.8599	+	29.1129i	−1.55154	+	1.13322i
$661$	−32.1096	+	32.1096i	−1.24892	+	1.24892i	−0.292720	+	0.956198i	$0.594561\pi$
$661$	−32.1096	+	32.1096i	−1.24892	+	1.24892i	−0.956198	+	0.292720i	$0.905439\pi$
$662$	−6.70143	−	7.82647i	−0.260458	−	0.304185i
$663$		−	31.5101i		−	1.22375i
$664$	−7.95897	+	4.91853i	−0.308868	+	0.190876i
$665$		−	0.821005i		−	0.0318372i
$666$	8.61467	−	7.37633i	0.333812	−	0.285827i
$667$	12.3637	−	12.3637i	0.478726	−	0.478726i
$668$	−7.05309	+	45.2658i	−0.272892	+	1.75139i
$669$	37.2292	+	37.2292i	1.43937	+	1.43937i
$670$	0.243543	−	3.14491i	0.00940889	−	0.121499i
$671$	53.7457			2.07483
$672$	2.98937	+	7.09093i	0.115318	+	0.273539i
$673$	−15.5568			−0.599670			−0.299835	−	0.953991i	$-0.596932\pi$
$673$	−15.5568			−0.599670			−0.299835	+	0.953991i	$0.596932\pi$
$674$	2.24374	−	28.9737i	0.0864255	−	1.11603i
$675$	12.1818	+	12.1818i	0.468877	+	0.468877i
$676$	−2.74136	+	17.5937i	−0.105437	+	0.676680i
$677$	−16.9172	+	16.9172i	−0.650181	+	0.650181i	−0.953037	−	0.302855i	$-0.902060\pi$
$677$	−16.9172	+	16.9172i	−0.650181	+	0.650181i	0.302855	+	0.953037i	$0.402060\pi$
$678$	31.3559	−	26.8486i	1.20422	−	1.03111i
$679$			2.49148i			0.0956142i
$680$	13.9700	+	22.6056i	0.535724	+	0.866886i
$681$			23.1320i			0.886419i
$682$	22.4105	+	26.1728i	0.858142	+	1.00221i
$683$	−23.9375	+	23.9375i	−0.915945	+	0.915945i	−0.996731	−	0.0807866i	$-0.974257\pi$
$683$	−23.9375	+	23.9375i	−0.915945	+	0.915945i	0.0807866	+	0.996731i	$0.474257\pi$
$684$	11.5544	−	8.43914i	0.441795	−	0.322679i
$685$	2.41563	+	2.41563i	0.0922965	+	0.0922965i
$686$	−8.31734	−	0.644097i	−0.317557	−	0.0245918i
$687$	8.81719			0.336397
$688$	18.9669	−	9.78422i	0.723105	−	0.373020i
$689$	−14.1960			−0.540824
$690$	−54.1922	−	4.19666i	−2.06306	−	0.159764i
$691$	−17.3090	−	17.3090i	−0.658466	−	0.658466i	0.296551	−	0.955017i	$-0.404163\pi$
$691$	−17.3090	−	17.3090i	−0.658466	−	0.658466i	−0.955017	+	0.296551i	$0.904163\pi$
$692$	−13.9708	−	19.1281i	−0.531089	−	0.727140i
$693$	−8.69712	+	8.69712i	−0.330376	+	0.330376i
$694$	−12.8307	−	14.9848i	−0.487048	−	0.568814i
$695$		−	43.7596i		−	1.65990i
$696$	24.4550	+	5.77393i	0.926963	+	0.218860i
$697$		−	34.2225i		−	1.29627i
$698$	16.4457	−	14.0817i	0.622479	−	0.532998i
$699$	−10.9133	+	10.9133i	−0.412779	+	0.412779i
$700$	1.09794	+	0.171076i	0.0414983	+	0.00646607i
$701$	−5.04311	−	5.04311i	−0.190476	−	0.190476i	0.605426	−	0.795902i	$-0.293003\pi$
$701$	−5.04311	−	5.04311i	−0.190476	−	0.190476i	−0.795902	+	0.605426i	$0.793003\pi$
$702$	−2.92560	+	37.7788i	−0.110420	+	1.42587i
$703$	−1.12096			−0.0422777
$704$	−30.5652	+	10.1860i	−1.15197	+	0.383901i
$705$	−50.2322			−1.89185
$706$	−3.72480	+	48.0990i	−0.140185	+	1.81023i
$707$	5.21221	+	5.21221i	0.196025	+	0.196025i
$708$	53.9011	+	8.39860i	2.02573	+	0.315639i
$709$	22.8893	−	22.8893i	0.859625	−	0.859625i	−0.131668	−	0.991294i	$-0.542033\pi$
$709$	22.8893	−	22.8893i	0.859625	−	0.859625i	0.991294	+	0.131668i	$0.0420334\pi$
$710$	23.5799	−	20.1904i	0.884940	−	0.757731i
$711$			39.7006i			1.48889i
$712$	−15.8742	−	3.74798i	−0.594913	−	0.140461i
$713$			37.9431i			1.42098i
$714$	6.11283	+	7.13906i	0.228767	+	0.267173i
$715$	−11.0851	+	11.0851i	−0.414560	+	0.414560i
$716$	2.10650	+	2.88411i	0.0787236	+	0.107784i
$717$	−26.7864	−	26.7864i	−1.00036	−	1.00036i
$718$	37.2060	+	2.88125i	1.38852	+	0.107527i
$719$	47.0383			1.75423			0.877117	−	0.480277i	$-0.159464\pi$
$719$	47.0383			1.75423			0.877117	+	0.480277i	$0.159464\pi$
$720$	−25.2305	−	48.9097i	−0.940284	−	1.82276i
$721$	6.91027			0.257352
$722$	−1.40999	−	0.109190i	−0.0524745	−	0.00406364i
$723$	−33.9421	−	33.9421i	−1.26232	−	1.26232i
$724$	−31.9330	+	23.3233i	−1.18678	+	0.866802i
$725$	2.56563	−	2.56563i	0.0952852	−	0.0952852i
$726$	−15.2955	−	17.8634i	−0.567670	−	0.662971i
$727$			1.51972i			0.0563632i	0.999603	+	0.0281816i	$0.00897168\pi$
$727$			1.51972i			0.0563632i	−0.999603	+	0.0281816i	$0.991028\pi$
$728$	1.28484	+	2.07907i	0.0476193	+	0.0770556i
$729$		−	21.6810i		−	0.802999i
$730$	31.4166	−	26.9005i	1.16278	−	0.995631i
$731$	18.4311	−	18.4311i	0.681699	−	0.681699i
$732$	−13.0945	+	84.0388i	−0.483987	+	3.10616i
$733$	9.82014	+	9.82014i	0.362715	+	0.362715i	0.864812	−	0.502097i	$-0.167438\pi$
$733$	9.82014	+	9.82014i	0.362715	+	0.362715i	−0.502097	+	0.864812i	$0.667438\pi$
$734$	2.93866	−	37.9473i	0.108468	−	1.40066i
$735$	41.7809			1.54111
$736$	−32.8618	−	13.3711i	−1.21130	−	0.492865i
$737$	4.67070			0.172047
$738$	−5.47211	+	70.6622i	−0.201431	+	2.60111i
$739$	22.2023	+	22.2023i	0.816723	+	0.816723i	0.985632	−	0.168909i	$-0.0540243\pi$
$739$	22.2023	+	22.2023i	0.816723	+	0.816723i	−0.168909	+	0.985632i	$0.554024\pi$
$740$	−0.663797	+	4.26016i	−0.0244017	+	0.156607i
$741$	4.56078	−	4.56078i	0.167545	−	0.167545i
$742$	3.21630	−	2.75396i	0.118074	−	0.101101i
$743$		−	25.8521i		−	0.948422i	−0.880411	−	0.474211i	$-0.842733\pi$
$743$		−	25.8521i		−	0.948422i	0.880411	−	0.474211i	$-0.157267\pi$
$744$	−46.3848	+	28.6652i	−1.70055	+	1.05092i
$745$		−	27.0504i		−	0.991048i
$746$	−9.45601	−	11.0435i	−0.346209	−	0.404331i
$747$	16.7337	−	16.7337i	0.612253	−	0.612253i
$748$	−31.7757	+	23.2084i	−1.16184	+	0.848582i
$749$	−5.82341	−	5.82341i	−0.212783	−	0.212783i
$750$	−54.4495	−	4.21659i	−1.98821	−	0.153968i
$751$	17.2022			0.627716			0.313858	−	0.949470i	$-0.398378\pi$
$751$	17.2022			0.627716			0.313858	+	0.949470i	$0.398378\pi$
$752$	−31.2330	−	9.97533i	−1.13895	−	0.363763i
$753$	40.3464			1.47031
$754$	7.95668	+	0.616168i	0.289765	+	0.0224395i
$755$	−7.19781	−	7.19781i	−0.261955	−	0.261955i
$756$	−6.66608	−	9.12687i	−0.242443	−	0.331941i
$757$	26.7771	−	26.7771i	0.973231	−	0.973231i	−0.0264204	−	0.999651i	$-0.508411\pi$
$757$	26.7771	−	26.7771i	0.973231	−	0.973231i	0.999651	+	0.0264204i	$0.00841084\pi$
$758$	−9.94554	−	11.6152i	−0.361238	−	0.421884i
$759$		−	80.4840i		−	2.92139i
$760$	−1.24993	+	5.29396i	−0.0453397	+	0.192032i
$761$			3.12787i			0.113385i	0.998392	+	0.0566926i	$0.0180555\pi$
$761$			3.12787i			0.113385i	−0.998392	+	0.0566926i	$0.981945\pi$
$762$	20.4500	−	17.5104i	0.740826	−	0.634333i
$763$	−3.62811	+	3.62811i	−0.131346	+	0.131346i
$764$	4.32171	+	0.673388i	0.156354	+	0.0243623i
$765$	−47.5281	−	47.5281i	−1.71838	−	1.71838i
$766$	−2.09964	+	27.1130i	−0.0758630	+	0.979632i
$767$	17.3257			0.625593
$768$	−8.48043	−	50.2746i	−0.306011	−	1.81413i
$769$	−7.02896			−0.253471			−0.126735	−	0.991937i	$-0.540450\pi$
$769$	−7.02896			−0.253471			−0.126735	+	0.991937i	$0.540450\pi$
$770$	0.361023	−	4.66195i	0.0130104	−	0.168005i
$771$	19.6808	+	19.6808i	0.708785	+	0.708785i
$772$	12.4261	+	1.93617i	0.447225	+	0.0696844i
$773$	33.6318	−	33.6318i	1.20965	−	1.20965i	0.238513	−	0.971139i	$-0.423340\pi$
$773$	33.6318	−	33.6318i	1.20965	−	1.20965i	0.971139	−	0.238513i	$-0.0766598\pi$
$774$	−41.0035	+	35.1093i	−1.47384	+	1.26198i
$775$			7.87368i			0.282831i
$776$	3.79312	−	16.0654i	0.136165	−	0.576715i
$777$			1.52490i			0.0547053i
$778$	6.11157	+	7.13759i	0.219111	+	0.255895i
$779$	4.95337	−	4.95337i	0.177473	−	0.177473i
$780$	−14.6323	−	20.0339i	−0.523922	−	0.717327i
$781$	32.5030	+	32.5030i	1.16305	+	1.16305i
$782$	−43.2012	−	3.34551i	−1.54487	−	0.119635i
$783$	−36.9044			−1.31886
$784$	25.9782	+	8.29703i	0.927793	+	0.296323i
$785$	4.59961			0.164167
$786$	−14.0968	−	1.09166i	−0.502816	−	0.0389382i
$787$	−5.89079	−	5.89079i	−0.209984	−	0.209984i	0.594277	−	0.804261i	$-0.297438\pi$
$787$	−5.89079	−	5.89079i	−0.209984	−	0.209984i	−0.804261	+	0.594277i	$0.797438\pi$
$788$	23.2140	−	16.9550i	0.826963	−	0.603998i
$789$	23.2343	−	23.2343i	0.827162	−	0.827162i
$790$	−9.81644	−	11.4644i	−0.349253	−	0.407886i
$791$			3.91052i			0.139042i
$792$	69.3212	−	42.8395i	2.46322	−	1.52224i
$793$			27.0129i			0.959258i
$794$	−17.8854	+	15.3144i	−0.634730	+	0.543489i
$795$	−30.3915	+	30.3915i	−1.07788	+	1.07788i
$796$	−0.0447252	+	0.287040i	−0.00158524	+	0.0101739i
$797$	−34.0434	−	34.0434i	−1.20588	−	1.20588i	−0.972349	−	0.233531i	$-0.924972\pi$
$797$	−34.0434	−	34.0434i	−1.20588	−	1.20588i	−0.233531	−	0.972349i	$-0.575028\pi$
$798$	−0.148537	+	1.91808i	−0.00525815	+	0.0678994i
$799$	−40.0443			−1.41667
$800$	−6.81925	−	2.77467i	−0.241097	−	0.0980995i
$801$	41.2556			1.45769
$802$	−0.497236	+	6.42090i	−0.0175580	+	0.226730i
$803$	43.3051	+	43.3051i	1.52820	+	1.52820i
$804$	−1.13796	+	7.30328i	−0.0401328	+	0.257567i
$805$	3.64095	−	3.64095i	0.128327	−	0.128327i
$806$	−13.1546	+	11.2637i	−0.463352	+	0.396746i
$807$		−	3.76277i		−	0.132456i
$808$	−25.6739	−	41.5444i	−0.903204	−	1.46153i
$809$			4.18914i			0.147282i	0.997285	+	0.0736412i	$0.0234620\pi$
$809$			4.18914i			0.147282i	−0.997285	+	0.0736412i	$0.976538\pi$
$810$	36.6502	+	42.8031i	1.28776	+	1.50395i
$811$	−2.78079	+	2.78079i	−0.0976468	+	0.0976468i	−0.754243	−	0.656596i	$-0.771996\pi$
$811$	−2.78079	+	2.78079i	−0.0976468	+	0.0976468i	0.656596	+	0.754243i	$0.271996\pi$
$812$	−1.92223	+	1.40396i	−0.0674571	+	0.0492694i
$813$	−6.04115	−	6.04115i	−0.211872	−	0.211872i
$814$	−6.36519	−	0.492923i	−0.223100	−	0.0172769i
$815$	2.55544			0.0895132
$816$	−28.5477	−	55.3401i	−0.999369	−	1.93729i
$817$	5.33545			0.186664
$818$	17.5475	+	1.35888i	0.613533	+	0.0475122i
$819$	−4.37123	−	4.37123i	−0.152743	−	0.152743i
$820$	−15.8919	−	21.7583i	−0.554968	−	0.759834i
$821$	−16.5254	+	16.5254i	−0.576741	+	0.576741i	−0.934004	−	0.357263i	$-0.883710\pi$
$821$	−16.5254	+	16.5254i	−0.576741	+	0.576741i	0.357263	+	0.934004i	$0.383710\pi$
$822$	−5.20651	−	6.08059i	−0.181598	−	0.212085i
$823$			41.5672i			1.44894i	0.689306	+	0.724471i	$0.257916\pi$
$823$			41.5672i			1.44894i	−0.689306	+	0.724471i	$0.742084\pi$
$824$	−44.5585	−	10.5205i	−1.55227	−	0.366497i
$825$		−	16.7015i		−	0.581471i
$826$	−3.92537	+	3.36111i	−0.136581	+	0.116948i
$827$	16.5599	−	16.5599i	0.575845	−	0.575845i	−0.357911	−	0.933756i	$-0.616511\pi$
$827$	16.5599	−	16.5599i	0.575845	−	0.575845i	0.933756	+	0.357911i	$0.116511\pi$
$828$	88.6664	+	13.8156i	3.08137	+	0.480124i
$829$	−12.7276	−	12.7276i	−0.442047	−	0.442047i	0.450653	−	0.892699i	$-0.351191\pi$
$829$	−12.7276	−	12.7276i	−0.442047	−	0.442047i	−0.892699	+	0.450653i	$0.851191\pi$
$830$	−0.694626	+	8.96982i	−0.0241108	+	0.311347i
$831$	−6.79286			−0.235642
$832$	−5.11958	−	15.3623i	−0.177489	−	0.532591i
$833$	33.3071			1.15402
$834$	−7.91703	+	102.234i	−0.274144	+	3.54007i
$835$	31.1494	+	31.1494i	1.07797	+	1.07797i
$836$	−7.95842	−	1.24004i	−0.275248	−	0.0428877i
$837$	56.6281	−	56.6281i	1.95735	−	1.95735i
$838$	−18.6284	+	15.9506i	−0.643507	+	0.551003i
$839$			28.8117i			0.994691i	0.867552	+	0.497346i	$0.165692\pi$
$839$			28.8117i			0.994691i	−0.867552	+	0.497346i	$0.834308\pi$
$840$	7.20165	+	1.70034i	0.248480	+	0.0586673i
$841$		−	21.2275i		−	0.731982i
$842$	−17.5920	−	20.5454i	−0.606261	−	0.708041i
$843$	−37.9347	+	37.9347i	−1.30654	+	1.30654i
$844$	17.4875	+	23.9430i	0.601946	+	0.824154i
$845$	12.1070	+	12.1070i	0.416493	+	0.416493i
$846$	82.6832	+	6.40301i	2.84271	+	0.220140i
$847$	2.22781			0.0765484
$848$	−24.9319	+	12.8613i	−0.856166	+	0.441660i
$849$	−27.5303			−0.944838
$850$	−8.96480	−	0.694237i	−0.307490	−	0.0238121i
$851$	−4.97116	−	4.97116i	−0.170409	−	0.170409i
$852$	−58.7418	+	42.9039i	−2.01246	+	1.46986i
$853$	28.9670	−	28.9670i	0.991810	−	0.991810i	−0.00815631	−	0.999967i	$-0.502596\pi$
$853$	28.9670	−	28.9670i	0.991810	−	0.991810i	0.999967	+	0.00815631i	$0.00259626\pi$
$854$	−5.24040	−	6.12017i	−0.179323	−	0.209428i
$855$		−	13.7585i		−	0.470530i
$856$	28.6844	+	46.4160i	0.980414	+	1.58647i
$857$		−	50.2607i		−	1.71687i	−0.512921	−	0.858436i	$-0.671437\pi$
$857$		−	50.2607i		−	1.71687i	0.512921	−	0.858436i	$-0.328563\pi$
$858$	27.9033	−	23.8922i	0.952602	−	0.815666i
$859$	23.3214	−	23.3214i	0.795714	−	0.795714i	−0.186702	−	0.982417i	$-0.559780\pi$
$859$	23.3214	−	23.3214i	0.795714	−	0.795714i	0.982417	+	0.186702i	$0.0597800\pi$
$860$	3.15949	−	20.2772i	0.107738	−	0.691447i
$861$	−6.73832	−	6.73832i	−0.229641	−	0.229641i
$862$	−0.908357	+	11.7298i	−0.0309387	+	0.399517i
$863$	−43.7842			−1.49043			−0.745215	−	0.666824i	$-0.767653\pi$
$863$	−43.7842			−1.49043			−0.745215	+	0.666824i	$0.767653\pi$
$864$	29.0888	+	69.0001i	0.989623	+	2.34743i
$865$	−22.7768			−0.774434
$866$	2.15620	−	27.8433i	0.0732705	−	0.946154i
$867$	−15.4720	−	15.4720i	−0.525458	−	0.525458i
$868$	0.795262	−	5.10388i	0.0269930	−	0.173237i
$869$	15.8028	−	15.8028i	0.536072	−	0.536072i
$870$	18.3532	−	15.7150i	0.622232	−	0.532787i
$871$			2.34752i			0.0795428i
$872$	28.9182	−	17.8710i	0.979293	−	0.605190i
$873$			41.7524i			1.41311i
$874$	−5.76872	−	6.73718i	−0.195130	−	0.227889i
$875$	3.65823	−	3.65823i	0.123671	−	0.123671i
$876$	−78.2642	+	57.1626i	−2.64430	+	1.93135i
$877$	−25.0695	−	25.0695i	−0.846538	−	0.846538i	0.143162	−	0.989699i	$-0.454273\pi$
$877$	−25.0695	−	25.0695i	−0.846538	−	0.846538i	−0.989699	+	0.143162i	$0.954273\pi$
$878$	6.89844	+	0.534218i	0.232811	+	0.0180290i
$879$	−4.30369			−0.145160
$880$	−9.42547	+	29.5114i	−0.317732	+	0.994828i
$881$	−3.58473			−0.120773			−0.0603863	−	0.998175i	$-0.519233\pi$
$881$	−3.58473			−0.120773			−0.0603863	+	0.998175i	$0.519233\pi$
$882$	−68.7722	−	5.32574i	−2.31568	−	0.179327i
$883$	33.0047	+	33.0047i	1.11070	+	1.11070i	0.993056	+	0.117639i	$0.0375326\pi$
$883$	33.0047	+	33.0047i	1.11070	+	1.11070i	0.117639	+	0.993056i	$0.462467\pi$
$884$	−11.6647	−	15.9707i	−0.392326	−	0.537152i
$885$	37.0917	−	37.0917i	1.24682	−	1.24682i
$886$	23.8020	+	27.7979i	0.799643	+	0.933888i
$887$			43.4950i			1.46042i	0.683224	+	0.730209i	$0.260577\pi$
$887$			43.4950i			1.46042i	−0.683224	+	0.730209i	$0.739423\pi$
$888$	2.32156	−	9.83276i	0.0779064	−	0.329966i
$889$			2.55040i			0.0855377i
$890$	−11.9135	+	10.2009i	−0.399340	+	0.341936i
$891$	−59.0004	+	59.0004i	−1.97659	+	1.97659i
$892$	32.6512	+	5.08755i	1.09324	+	0.170344i
$893$	−5.79603	−	5.79603i	−0.193957	−	0.193957i
$894$	−4.89398	+	63.1967i	−0.163679	+	2.11361i
$895$	3.43426			0.114795
$896$	4.14013	+	2.48736i	0.138312	+	0.0830969i
$897$	40.4518			1.35065
$898$	1.99858	−	25.8081i	0.0666936	−	0.861226i
$899$	−11.9266	−	11.9266i	−0.397774	−	0.397774i
$900$	18.3994	+	2.86691i	0.613314	+	0.0955636i
$901$	−24.2277	+	24.2277i	−0.807141	+	0.807141i
$902$	30.3052	−	25.9488i	1.00905	−	0.864001i
$903$		−	7.25809i		−	0.241534i
$904$	5.95352	−	25.2156i	0.198011	−	0.838659i
$905$			38.0243i			1.26397i
$906$	15.5137	+	18.1182i	0.515410	+	0.601938i
$907$	29.3329	−	29.3329i	0.973983	−	0.973983i	−0.0256871	−	0.999670i	$-0.508177\pi$
$907$	29.3329	−	29.3329i	0.973983	−	0.973983i	0.999670	+	0.0256871i	$0.00817736\pi$
$908$	8.56319	+	11.7243i	0.284179	+	0.389084i
$909$	87.3467	+	87.3467i	2.89711	+	2.89711i
$910$	2.34313	+	0.181453i	0.0776740	+	0.00601510i
$911$	23.1464			0.766876			0.383438	−	0.923567i	$-0.374740\pi$
$911$	23.1464			0.766876			0.383438	+	0.923567i	$0.374740\pi$
$912$	3.87795	−	12.1420i	0.128412	−	0.402060i
$913$	−13.3216			−0.440881
$914$	43.5792	+	3.37479i	1.44147	+	0.111628i
$915$	57.8308	+	57.8308i	1.91183	+	1.91183i
$916$	4.46894	−	3.26402i	0.147658	−	0.107846i
$917$	0.947104	−	0.947104i	0.0312761	−	0.0312761i
$918$	59.4824	+	69.4684i	1.96321	+	2.29280i
$919$		−	35.6541i		−	1.17612i	−0.808818	−	0.588059i	$-0.799892\pi$
$919$		−	35.6541i		−	1.17612i	0.808818	−	0.588059i	$-0.200108\pi$
$920$	−29.0205	+	17.9343i	−0.956777	+	0.591275i
$921$		−	84.3178i		−	2.77837i
$922$	18.9878	−	16.2583i	0.625330	−	0.535439i
$923$	−16.3362	+	16.3362i	−0.537713	+	0.537713i
$924$	−1.68689	+	10.8262i	−0.0554946	+	0.356157i
$925$	−1.03158	−	1.03158i	−0.0339181	−	0.0339181i
$926$	0.213085	−	2.75160i	0.00700240	−	0.0904231i
$927$	115.803			3.80347
$928$	14.5323	−	6.12647i	0.477046	−	0.201111i
$929$	−53.7387			−1.76311			−0.881554	−	0.472083i	$-0.843502\pi$
$929$	−53.7387			−1.76311			−0.881554	+	0.472083i	$0.843502\pi$
$930$	−4.04827	+	52.2760i	−0.132748	+	1.71420i
$931$	4.82088	+	4.82088i	0.157998	+	0.157998i
$932$	−1.49136	+	9.57132i	−0.0488510	+	0.313519i
$933$	−13.0546	+	13.0546i	−0.427388	+	0.427388i
$934$	3.10012	−	2.65448i	0.101439	−	0.0868572i
$935$			37.8370i			1.23740i
$936$	21.5314	+	34.8413i	0.703777	+	1.13882i
$937$		−	5.61713i		−	0.183504i	−0.995782	−	0.0917518i	$-0.970753\pi$
$937$		−	5.61713i		−	0.183504i	0.995782	−	0.0917518i	$-0.0292467\pi$
$938$	−0.455410	−	0.531865i	−0.0148697	−	0.0173660i
$939$	−16.8921	+	16.8921i	−0.551252	+	0.551252i
$940$	−25.4598	+	18.5954i	−0.830408	+	0.606514i
$941$	−31.7763	−	31.7763i	−1.03588	−	1.03588i	−0.999332	−	0.0365464i	$-0.988364\pi$
$941$	−31.7763	−	31.7763i	−1.03588	−	1.03588i	−0.0365464	−	0.999332i	$-0.511636\pi$
$942$	−10.7459	−	0.832166i	−0.350120	−	0.0271134i
$943$	43.9339			1.43068
$944$	30.4285	−	15.6968i	0.990362	−	0.510887i
$945$	−10.8678			−0.353531
$946$	30.2966	+	2.34618i	0.985027	+	0.0762808i
$947$	21.4668	+	21.4668i	0.697577	+	0.697577i	0.963887	−	0.266311i	$-0.0858047\pi$
$947$	21.4668	+	21.4668i	0.697577	+	0.697577i	−0.266311	+	0.963887i	$0.585805\pi$
$948$	20.8596	+	28.5599i	0.677489	+	0.927584i
$949$	−21.7654	+	21.7654i	−0.706535	+	0.706535i
$950$	−1.19708	−	1.39805i	−0.0388385	−	0.0453588i
$951$			46.3761i			1.50385i
$952$	5.74104	+	1.35549i	0.186068	+	0.0439316i
$953$			29.6466i			0.960347i	0.877173	+	0.480174i	$0.159426\pi$
$953$			29.6466i			0.960347i	−0.877173	+	0.480174i	$0.840574\pi$
$954$	53.8990	−	46.1511i	1.74505	−	1.49420i
$955$	2.97396	−	2.97396i	0.0962351	−	0.0962351i
$956$	−23.4925	−	3.66049i	−0.759803	−	0.118389i
$957$	25.2984	+	25.2984i	0.817780	+	0.817780i
$958$	1.82382	−	23.5513i	0.0589251	−	0.760909i
$959$	0.758333			0.0244879
$960$	−43.8486	−	21.9281i	−1.41521	−	0.707727i
$961$	5.60152			0.180694
$962$	0.247746	−	3.19919i	0.00798766	−	0.103146i
$963$	−97.5892	−	97.5892i	−3.14477	−	3.14477i
$964$	−29.7683	−	4.63835i	−0.958772	−	0.149391i
$965$	8.55095	−	8.55095i	0.275265	−	0.275265i
$966$	−9.16493	+	7.84748i	−0.294877	+	0.252489i
$967$		−	26.2908i		−	0.845454i	−0.906257	−	0.422727i	$-0.861073\pi$
$967$		−	26.2908i		−	0.845454i	0.906257	−	0.422727i	$-0.138927\pi$
$968$	−14.3652	−	3.39170i	−0.461716	−	0.109013i
$969$		−	15.5674i		−	0.500097i
$970$	−10.3238	−	12.0569i	−0.331476	−	0.387125i
$971$	−17.3808	+	17.3808i	−0.557777	+	0.557777i	−0.928674	−	0.370897i	$-0.879050\pi$
$971$	−17.3808	+	17.3808i	−0.557777	+	0.557777i	0.370897	+	0.928674i	$0.379050\pi$
$972$	−31.0356	−	42.4924i	−0.995468	−	1.36294i
$973$	−6.86868	−	6.86868i	−0.220200	−	0.220200i
$974$	−24.1614	−	1.87107i	−0.774181	−	0.0599528i
$975$	8.39427			0.268832
$976$	24.4733	+	47.4419i	0.783372	+	1.51858i
$977$	36.2626			1.16014			0.580072	−	0.814565i	$-0.303024\pi$
$977$	36.2626			1.16014			0.580072	+	0.814565i	$0.303024\pi$
$978$	−5.97018	−	0.462333i	−0.190905	−	0.0147838i
$979$	−16.4217	−	16.4217i	−0.524840	−	0.524840i
$980$	21.1764	−	15.4668i	0.676454	−	0.494069i
$981$	−60.8002	+	60.8002i	−1.94120	+	1.94120i
$982$	11.8952	+	13.8922i	0.379592	+	0.443318i
$983$		−	40.6961i		−	1.29801i	−0.760786	−	0.649003i	$-0.775186\pi$
$983$		−	40.6961i		−	1.29801i	0.760786	−	0.649003i	$-0.224814\pi$
$984$	33.1910	+	53.7084i	1.05809	+	1.71216i
$985$		−	27.6421i		−	0.880749i
$986$	14.6309	−	12.5277i	0.465943	−	0.398964i
$987$	−7.88463	+	7.88463i	−0.250971	+	0.250971i
$988$	0.623253	−	3.99995i	0.0198283	−	0.127255i
$989$	23.6614	+	23.6614i	0.752388	+	0.752388i
$990$	6.05006	−	78.1255i	0.192284	−	2.48299i
$991$	−39.7710			−1.26337			−0.631684	−	0.775226i	$-0.717636\pi$
$991$	−39.7710			−1.26337			−0.631684	+	0.775226i	$0.717636\pi$
$992$	−12.8983	+	31.6999i	−0.409522	+	1.00647i
$993$	23.2162			0.736745
$994$	0.532043	−	6.87035i	0.0168754	−	0.217914i
$995$	0.197525	+	0.197525i	0.00626197	+	0.00626197i
$996$	3.24566	−	20.8302i	0.102843	−	0.660029i
$997$	5.98659	−	5.98659i	0.189597	−	0.189597i	−0.605925	−	0.795522i	$-0.707197\pi$
$997$	5.98659	−	5.98659i	0.189597	−	0.189597i	0.795522	+	0.605925i	$0.207197\pi$
$998$	−21.1357	+	18.0974i	−0.669038	+	0.572864i
$999$			14.8384i			0.469465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.17	✓	68
4.3	odd	2		1216.2.k.b.913.33		68
16.5	even	4	inner	304.2.k.b.229.17	yes	68
16.11	odd	4		1216.2.k.b.305.33		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.17	✓	68	1.1	even	1	trivial
304.2.k.b.229.17	yes	68	16.5	even	4	inner
1216.2.k.b.305.33		68	16.11	odd	4
1216.2.k.b.913.33		68	4.3	odd	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.109190 + 1.40999i) q^{2} +(-2.25323 - 2.25323i) q^{3} +(-1.97615 - 0.307915i) q^{4} +(-1.35988 + 1.35988i) q^{5} +(3.42307 - 2.93101i) q^{6} +0.426904i q^{7} +(0.649934 - 2.75274i) q^{8} +7.15410i q^{9} +O(q^{10})\)	\(q+(-0.109190 + 1.40999i) q^{2} +(-2.25323 - 2.25323i) q^{3} +(-1.97615 - 0.307915i) q^{4} +(-1.35988 + 1.35988i) q^{5} +(3.42307 - 2.93101i) q^{6} +0.426904i q^{7} +(0.649934 - 2.75274i) q^{8} +7.15410i q^{9} +(-1.76893 - 2.06591i) q^{10} +(2.84768 - 2.84768i) q^{11} +(3.75893 + 5.14654i) q^{12} +(1.43126 + 1.43126i) q^{13} +(-0.601931 - 0.0466138i) q^{14} +6.12825 q^{15} +(3.81038 + 1.21697i) q^{16} +4.88535 q^{17} +(-10.0872 - 0.781158i) q^{18} +(0.707107 + 0.707107i) q^{19} +(3.10606 - 2.26861i) q^{20} +(0.961913 - 0.961913i) q^{21} +(3.70426 + 4.32614i) q^{22} +6.27167i q^{23} +(-7.66701 + 4.73811i) q^{24} +1.30145i q^{25} +(-2.17435 + 1.86179i) q^{26} +(9.36013 - 9.36013i) q^{27} +(0.131450 - 0.843628i) q^{28} +(-1.97136 - 1.97136i) q^{29} +(-0.669145 + 8.64078i) q^{30} +6.04992 q^{31} +(-2.13198 + 5.23972i) q^{32} -12.8329 q^{33} +(-0.533432 + 6.88830i) q^{34} +(-0.580538 - 0.580538i) q^{35} +(2.20285 - 14.1376i) q^{36} +(-0.792637 + 0.792637i) q^{37} +(-1.07422 + 0.919806i) q^{38} -6.44992i q^{39} +(2.85957 + 4.62723i) q^{40} -7.00513i q^{41} +(1.25126 + 1.46132i) q^{42} +(3.77273 - 3.77273i) q^{43} +(-6.50429 + 4.75061i) q^{44} +(-9.72871 - 9.72871i) q^{45} +(-8.84301 - 0.684806i) q^{46} -8.19682 q^{47} +(-5.84353 - 11.3278i) q^{48} +6.81775 q^{49} +(-1.83504 - 0.142106i) q^{50} +(-11.0078 - 11.0078i) q^{51} +(-2.38769 - 3.26910i) q^{52} +(-4.95926 + 4.95926i) q^{53} +(12.1757 + 14.2198i) q^{54} +7.74500i q^{55} +(1.17516 + 0.277460i) q^{56} -3.18655i q^{57} +(2.99486 - 2.56435i) q^{58} +(6.05258 - 6.05258i) q^{59} +(-12.1104 - 1.88698i) q^{60} +(9.43676 + 9.43676i) q^{61} +(-0.660592 + 8.53034i) q^{62} -3.05411 q^{63} +(-7.15517 - 3.57820i) q^{64} -3.89269 q^{65} +(1.40123 - 18.0943i) q^{66} +(0.820089 + 0.820089i) q^{67} +(-9.65420 - 1.50427i) q^{68} +(14.1315 - 14.1315i) q^{69} +(0.881943 - 0.755165i) q^{70} +11.4139i q^{71} +(19.6934 + 4.64969i) q^{72} +15.2072i q^{73} +(-1.03106 - 1.20416i) q^{74} +(2.93247 - 2.93247i) q^{75} +(-1.17962 - 1.61508i) q^{76} +(1.21568 + 1.21568i) q^{77} +(9.09434 + 0.704269i) q^{78} +5.54935 q^{79} +(-6.83660 + 3.52672i) q^{80} -20.7188 q^{81} +(9.87717 + 0.764892i) q^{82} +(-2.33903 - 2.33903i) q^{83} +(-2.19708 + 1.60470i) q^{84} +(-6.64348 + 6.64348i) q^{85} +(4.90758 + 5.73147i) q^{86} +8.88386i q^{87} +(-5.98811 - 9.68972i) q^{88} -5.76670i q^{89} +(14.7797 - 12.6551i) q^{90} +(-0.611011 + 0.611011i) q^{91} +(1.93114 - 12.3938i) q^{92} +(-13.6319 - 13.6319i) q^{93} +(0.895014 - 11.5575i) q^{94} -1.92316 q^{95} +(16.6101 - 7.00245i) q^{96} +5.83616 q^{97} +(-0.744432 + 9.61298i) q^{98} +(20.3725 + 20.3725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

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