LMFDB - Embedded newform 304.2.k.b.77.32

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			77.32
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35651 + 0.399868i) q^{2} +(0.0736275 + 0.0736275i) q^{3} +(1.68021 + 1.08484i) q^{4} +(1.57485 - 1.57485i) q^{5} +(0.0704349 + 0.129317i) q^{6} -2.89934i q^{7} +(1.84542 + 2.14346i) q^{8} -2.98916i q^{9} +O(q^{10})$	\(q+(1.35651 + 0.399868i) q^{2} +(0.0736275 + 0.0736275i) q^{3} +(1.68021 + 1.08484i) q^{4} +(1.57485 - 1.57485i) q^{5} +(0.0704349 + 0.129317i) q^{6} -2.89934i q^{7} +(1.84542 + 2.14346i) q^{8} -2.98916i q^{9} +(2.76602 - 1.50656i) q^{10} +(-4.00758 + 4.00758i) q^{11} +(0.0438354 + 0.203584i) q^{12} +(1.25807 + 1.25807i) q^{13} +(1.15935 - 3.93297i) q^{14} +0.231905 q^{15} +(1.64622 + 3.64554i) q^{16} -4.21424 q^{17} +(1.19527 - 4.05481i) q^{18} +(0.707107 + 0.707107i) q^{19} +(4.35455 - 0.937613i) q^{20} +(0.213471 - 0.213471i) q^{21} +(-7.03880 + 3.83380i) q^{22} +6.57200i q^{23} +(-0.0219438 + 0.293691i) q^{24} +0.0397008i q^{25} +(1.20351 + 2.20963i) q^{26} +(0.440967 - 0.440967i) q^{27} +(3.14533 - 4.87150i) q^{28} +(2.01858 + 2.01858i) q^{29} +(0.314580 + 0.0927311i) q^{30} -3.23679 q^{31} +(0.775377 + 5.60346i) q^{32} -0.590136 q^{33} +(-5.71664 - 1.68514i) q^{34} +(-4.56602 - 4.56602i) q^{35} +(3.24277 - 5.02242i) q^{36} +(-2.15603 + 2.15603i) q^{37} +(0.676445 + 1.24194i) q^{38} +0.185257i q^{39} +(6.28189 + 0.469366i) q^{40} -7.32957i q^{41} +(0.374935 - 0.204214i) q^{42} +(5.26837 - 5.26837i) q^{43} +(-11.0812 + 2.38598i) q^{44} +(-4.70747 - 4.70747i) q^{45} +(-2.62793 + 8.91495i) q^{46} -7.26857 q^{47} +(-0.147205 + 0.389619i) q^{48} -1.40616 q^{49} +(-0.0158751 + 0.0538544i) q^{50} +(-0.310284 - 0.310284i) q^{51} +(0.749011 + 3.47863i) q^{52} +(7.26011 - 7.26011i) q^{53} +(0.774502 - 0.421845i) q^{54} +12.6227i q^{55} +(6.21461 - 5.35050i) q^{56} +0.104125i q^{57} +(1.93105 + 3.54538i) q^{58} +(-0.840479 + 0.840479i) q^{59} +(0.389649 + 0.251580i) q^{60} +(-5.11095 - 5.11095i) q^{61} +(-4.39073 - 1.29429i) q^{62} -8.66658 q^{63} +(-1.18884 + 7.91117i) q^{64} +3.96253 q^{65} +(-0.800522 - 0.235976i) q^{66} +(-8.49452 - 8.49452i) q^{67} +(-7.08082 - 4.57180i) q^{68} +(-0.483880 + 0.483880i) q^{69} +(-4.36803 - 8.01963i) q^{70} +7.29443i q^{71} +(6.40714 - 5.51626i) q^{72} -0.267839i q^{73} +(-3.78680 + 2.06254i) q^{74} +(-0.00292307 + 0.00292307i) q^{75} +(0.420988 + 1.95519i) q^{76} +(11.6193 + 11.6193i) q^{77} +(-0.0740782 + 0.251302i) q^{78} -3.46632 q^{79} +(8.33373 + 3.14862i) q^{80} -8.90254 q^{81} +(2.93086 - 9.94260i) q^{82} +(10.6008 + 10.6008i) q^{83} +(0.590260 - 0.127094i) q^{84} +(-6.63680 + 6.63680i) q^{85} +(9.25322 - 5.03992i) q^{86} +0.297246i q^{87} +(-15.9857 - 1.19441i) q^{88} -8.25634i q^{89} +(-4.50334 - 8.26808i) q^{90} +(3.64756 - 3.64756i) q^{91} +(-7.12960 + 11.0423i) q^{92} +(-0.238317 - 0.238317i) q^{93} +(-9.85985 - 2.90647i) q^{94} +2.22717 q^{95} +(-0.355480 + 0.469658i) q^{96} +14.4769 q^{97} +(-1.90747 - 0.562278i) q^{98} +(11.9793 + 11.9793i) 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 $

$2$	1.35651	+	0.399868i	0.959194	+	0.282749i
$2$	1.35651	+	0.399868i	0.959194	+	0.282749i
$3$	0.0736275	+	0.0736275i	0.0425089	+	0.0425089i	0.728042	−	0.685533i	$-0.240431\pi$
$3$	0.0736275	+	0.0736275i	0.0425089	+	0.0425089i	−0.685533	+	0.728042i	$0.740431\pi$
$4$	1.68021	+	1.08484i	0.840106	+	0.542422i
$5$	1.57485	−	1.57485i	0.704294	−	0.704294i	−0.261035	−	0.965329i	$-0.584064\pi$
$5$	1.57485	−	1.57485i	0.704294	−	0.704294i	0.965329	+	0.261035i	$0.0840639\pi$
$6$	0.0704349	+	0.129317i	0.0287549	+	0.0527936i
$7$		−	2.89934i		−	1.09585i	−0.836529	−	0.547923i	$-0.815419\pi$
$7$		−	2.89934i		−	1.09585i	0.836529	−	0.547923i	$-0.184581\pi$
$8$	1.84542	+	2.14346i	0.652455	+	0.757827i
$9$		−	2.98916i		−	0.996386i
$10$	2.76602	−	1.50656i	0.874693	−	0.476416i
$11$	−4.00758	+	4.00758i	−1.20833	+	1.20833i	−0.236762	+	0.971568i	$0.576086\pi$
$11$	−4.00758	+	4.00758i	−1.20833	+	1.20833i	−0.971568	+	0.236762i	$0.923914\pi$
$12$	0.0438354	+	0.203584i	0.0126542	+	0.0587697i
$13$	1.25807	+	1.25807i	0.348925	+	0.348925i	0.859709	−	0.510784i	$-0.170645\pi$
$13$	1.25807	+	1.25807i	0.348925	+	0.348925i	−0.510784	+	0.859709i	$0.670645\pi$
$14$	1.15935	−	3.93297i	0.309850	−	1.05113i
$15$	0.231905			0.0598775
$16$	1.64622	+	3.64554i	0.411556	+	0.911385i
$17$	−4.21424			−1.02210			−0.511052	−	0.859550i	$-0.670744\pi$
$17$	−4.21424			−1.02210			−0.511052	+	0.859550i	$0.670744\pi$
$18$	1.19527	−	4.05481i	0.281727	−	0.955727i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$19$	0.707107	+	0.707107i	0.162221	+	0.162221i
$20$	4.35455	−	0.937613i	0.973706	−	0.209657i
$21$	0.213471	−	0.213471i	0.0465832	−	0.0465832i
$22$	−7.03880	+	3.83380i	−1.50068	+	0.817368i
$23$			6.57200i			1.37036i	0.728375	+	0.685178i	$0.240276\pi$
$23$			6.57200i			1.37036i	−0.728375	+	0.685178i	$0.759724\pi$
$24$	−0.0219438	+	0.293691i	−0.00447927	+	0.0599495i
$25$			0.0397008i			0.00794016i
$26$	1.20351	+	2.20963i	0.236028	+	0.433345i
$27$	0.440967	−	0.440967i	0.0848641	−	0.0848641i
$28$	3.14533	−	4.87150i	0.594412	−	0.920627i
$29$	2.01858	+	2.01858i	0.374841	+	0.374841i	0.869237	−	0.494396i	$-0.164611\pi$
$29$	2.01858	+	2.01858i	0.374841	+	0.374841i	−0.494396	+	0.869237i	$0.664611\pi$
$30$	0.314580	+	0.0927311i	0.0574341	+	0.0169303i
$31$	−3.23679			−0.581345			−0.290673	−	0.956823i	$-0.593879\pi$
$31$	−3.23679			−0.581345			−0.290673	+	0.956823i	$0.593879\pi$
$32$	0.775377	+	5.60346i	0.137069	+	0.990562i
$33$	−0.590136			−0.102729
$34$	−5.71664	−	1.68514i	−0.980396	−	0.288999i
$35$	−4.56602	−	4.56602i	−0.771798	−	0.771798i
$36$	3.24277	−	5.02242i	0.540462	−	0.837070i
$37$	−2.15603	+	2.15603i	−0.354450	+	0.354450i	−0.861762	−	0.507313i	$-0.830639\pi$
$37$	−2.15603	+	2.15603i	−0.354450	+	0.354450i	0.507313	+	0.861762i	$0.330639\pi$
$38$	0.676445	+	1.24194i	0.109734	+	0.201470i
$39$			0.185257i			0.0296648i
$40$	6.28189	+	0.469366i	0.993253	+	0.0742132i
$41$		−	7.32957i		−	1.14469i	−0.820014	−	0.572343i	$-0.806034\pi$
$41$		−	7.32957i		−	1.14469i	0.820014	−	0.572343i	$-0.193966\pi$
$42$	0.374935	−	0.204214i	0.0578537	−	0.0315110i
$43$	5.26837	−	5.26837i	0.803419	−	0.803419i	−0.180209	−	0.983628i	$-0.557678\pi$
$43$	5.26837	−	5.26837i	0.803419	−	0.803419i	0.983628	+	0.180209i	$0.0576775\pi$
$44$	−11.0812	+	2.38598i	−1.67055	+	0.359700i
$45$	−4.70747	−	4.70747i	−0.701749	−	0.701749i
$46$	−2.62793	+	8.91495i	−0.387467	+	1.31444i
$47$	−7.26857			−1.06023			−0.530115	−	0.847926i	$-0.677851\pi$
$47$	−7.26857			−1.06023			−0.530115	+	0.847926i	$0.677851\pi$
$48$	−0.147205	+	0.389619i	−0.0212472	+	0.0562367i
$49$	−1.40616			−0.200880
$50$	−0.0158751	+	0.0538544i	−0.00224507	+	0.00761616i
$51$	−0.310284	−	0.310284i	−0.0434485	−	0.0434485i
$52$	0.749011	+	3.47863i	0.103869	+	0.482399i
$53$	7.26011	−	7.26011i	0.997252	−	0.997252i	−0.00274409	−	0.999996i	$-0.500873\pi$
$53$	7.26011	−	7.26011i	0.997252	−	0.997252i	0.999996	+	0.00274409i	$0.000873471\pi$
$54$	0.774502	−	0.421845i	0.105396	−	0.0574059i
$55$			12.6227i			1.70204i
$56$	6.21461	−	5.35050i	0.830463	−	0.714991i
$57$			0.104125i			0.0137917i
$58$	1.93105	+	3.54538i	0.253559	+	0.465531i
$59$	−0.840479	+	0.840479i	−0.109421	+	0.109421i	−0.759698	−	0.650277i	$-0.774653\pi$
$59$	−0.840479	+	0.840479i	−0.109421	+	0.109421i	0.650277	+	0.759698i	$0.274653\pi$
$60$	0.389649	+	0.251580i	0.0503034	+	0.0324789i
$61$	−5.11095	−	5.11095i	−0.654390	−	0.654390i	0.299657	−	0.954047i	$-0.403128\pi$
$61$	−5.11095	−	5.11095i	−0.654390	−	0.654390i	−0.954047	+	0.299657i	$0.903128\pi$
$62$	−4.39073	−	1.29429i	−0.557623	−	0.164375i
$63$	−8.66658			−1.09189
$64$	−1.18884	+	7.91117i	−0.148605	+	0.988897i
$65$	3.96253			0.491491
$66$	−0.800522	−	0.235976i	−0.0985375	−	0.0290467i
$67$	−8.49452	−	8.49452i	−1.03777	−	1.03777i	−0.999258	−	0.0385125i	$-0.987738\pi$
$67$	−8.49452	−	8.49452i	−1.03777	−	1.03777i	−0.0385125	−	0.999258i	$-0.512262\pi$
$68$	−7.08082	−	4.57180i	−0.858676	−	0.554412i
$69$	−0.483880	+	0.483880i	−0.0582523	+	0.0582523i
$70$	−4.36803	−	8.01963i	−0.522079	−	0.958529i
$71$			7.29443i			0.865689i	0.901468	+	0.432845i	$0.142490\pi$
$71$			7.29443i			0.865689i	−0.901468	+	0.432845i	$0.857510\pi$
$72$	6.40714	−	5.51626i	0.755089	−	0.650097i
$73$		−	0.267839i		−	0.0313482i	−0.999877	−	0.0156741i	$-0.995011\pi$
$73$		−	0.267839i		−	0.0313482i	0.999877	−	0.0156741i	$-0.00498942\pi$
$74$	−3.78680	+	2.06254i	−0.440206	+	0.239766i
$75$	−0.00292307	+	0.00292307i	−0.000337527	+	0.000337527i
$76$	0.420988	+	1.95519i	0.0482906	+	0.224276i
$77$	11.6193	+	11.6193i	1.32414	+	1.32414i
$78$	−0.0740782	+	0.251302i	−0.00838770	+	0.0284543i
$79$	−3.46632			−0.389992			−0.194996	−	0.980804i	$-0.562469\pi$
$79$	−3.46632			−0.389992			−0.194996	+	0.980804i	$0.562469\pi$
$80$	8.33373	+	3.14862i	0.931739	+	0.352026i
$81$	−8.90254			−0.989171
$82$	2.93086	−	9.94260i	0.323659	−	1.09798i
$83$	10.6008	+	10.6008i	1.16359	+	1.16359i	0.983685	+	0.179901i	$0.0575779\pi$
$83$	10.6008	+	10.6008i	1.16359	+	1.16359i	0.179901	+	0.983685i	$0.442422\pi$
$84$	0.590260	−	0.127094i	0.0644026	−	0.0138671i
$85$	−6.63680	+	6.63680i	−0.719862	+	0.719862i
$86$	9.25322	−	5.03992i	0.997800	−	0.543469i
$87$			0.297246i			0.0318681i
$88$	−15.9857	−	1.19441i	−1.70409	−	0.127325i
$89$		−	8.25634i		−	0.875170i	−0.899177	−	0.437585i	$-0.855834\pi$
$89$		−	8.25634i		−	0.875170i	0.899177	−	0.437585i	$-0.144166\pi$
$90$	−4.50334	−	8.26808i	−0.474694	−	0.871532i
$91$	3.64756	−	3.64756i	0.382368	−	0.382368i
$92$	−7.12960	+	11.0423i	−0.743312	+	1.15124i
$93$	−0.238317	−	0.238317i	−0.0247123	−	0.0247123i
$94$	−9.85985	−	2.90647i	−1.01697	−	0.299779i
$95$	2.22717			0.228503
$96$	−0.355480	+	0.469658i	−0.0362810	+	0.0479343i
$97$	14.4769			1.46991			0.734953	−	0.678118i	$-0.237204\pi$
$97$	14.4769			1.46991			0.734953	+	0.678118i	$0.237204\pi$
$98$	−1.90747	−	0.562278i	−0.192683	−	0.0567987i
$99$	11.9793	+	11.9793i	1.20396	+	1.20396i
$100$	−0.0430692	+	0.0667058i	−0.00430692	+	0.00667058i
$101$	3.73800	−	3.73800i	0.371945	−	0.371945i	−0.496240	−	0.868185i	$-0.665286\pi$
$101$	3.73800	−	3.73800i	0.371945	−	0.371945i	0.868185	+	0.496240i	$0.165286\pi$
$102$	−0.296830	−	0.544975i	−0.0293905	−	0.0539606i
$103$		−	13.2152i		−	1.30213i	−0.759021	−	0.651067i	$-0.774322\pi$
$103$		−	13.2152i		−	1.30213i	0.759021	−	0.651067i	$-0.225678\pi$
$104$	−0.374952	+	5.01828i	−0.0367671	+	0.492083i
$105$		−	0.672370i		−	0.0656166i
$106$	12.7515	−	6.94529i	1.23853	−	0.674586i
$107$	8.11169	−	8.11169i	0.784186	−	0.784186i	−0.196348	−	0.980534i	$-0.562908\pi$
$107$	8.11169	−	8.11169i	0.784186	−	0.784186i	0.980534	+	0.196348i	$0.0629082\pi$
$108$	1.21930	−	0.262537i	0.117327	−	0.0252626i
$109$	8.29799	+	8.29799i	0.794804	+	0.794804i	0.982271	−	0.187467i	$-0.0600278\pi$
$109$	8.29799	+	8.29799i	0.794804	+	0.794804i	−0.187467	+	0.982271i	$0.560028\pi$
$110$	−5.04739	+	17.1227i	−0.481250	+	1.63258i
$111$	−0.317487			−0.0301345
$112$	10.5696	−	4.77296i	0.998738	−	0.451002i
$113$	−18.3499			−1.72621			−0.863107	−	0.505021i	$-0.831485\pi$
$113$	−18.3499			−1.72621			−0.863107	+	0.505021i	$0.831485\pi$
$114$	−0.0416362	+	0.141246i	−0.00389959	+	0.0132289i
$115$	10.3499	+	10.3499i	0.965134	+	0.965134i
$116$	1.20180	+	5.58149i	0.111584	+	0.518228i
$117$	3.76056	−	3.76056i	0.347664	−	0.347664i
$118$	−1.47619	+	0.804033i	−0.135895	+	0.0740173i
$119$			12.2185i			1.12007i
$120$	0.427962	+	0.497078i	0.0390674	+	0.0453768i
$121$		−	21.1213i		−	1.92012i
$122$	−4.88933	−	8.97674i	−0.442659	−	0.812716i
$123$	0.539658	−	0.539658i	0.0486594	−	0.0486594i
$124$	−5.43850	−	3.51142i	−0.488391	−	0.315335i
$125$	7.93677	+	7.93677i	0.709886	+	0.709886i
$126$	−11.7563	−	3.46548i	−1.04733	−	0.308730i
$127$	−2.48938			−0.220897			−0.110448	−	0.993882i	$-0.535229\pi$
$127$	−2.48938			−0.220897			−0.110448	+	0.993882i	$0.535229\pi$
$128$	−4.77609	+	10.2562i	−0.422151	+	0.906526i
$129$	0.775794			0.0683049
$130$	5.37519	+	1.58449i	0.471436	+	0.138969i
$131$	−5.59145	−	5.59145i	−0.488527	−	0.488527i	0.419314	−	0.907841i	$-0.362271\pi$
$131$	−5.59145	−	5.59145i	−0.488527	−	0.488527i	−0.907841	+	0.419314i	$0.862271\pi$
$132$	−0.991553	−	0.640206i	−0.0863036	−	0.0557228i
$133$	2.05014	−	2.05014i	0.177770	−	0.177770i
$134$	−8.12617	−	14.9195i	−0.701995	−	1.28885i
$135$		−	1.38891i		−	0.119539i
$136$	−7.77705	−	9.03306i	−0.666877	−	0.774579i
$137$		−	0.0435099i		−	0.00371730i	−0.999998	−	0.00185865i	$-0.999408\pi$
$137$		−	0.0435099i		−	0.00371730i	0.999998	−	0.00185865i	$-0.000591628\pi$
$138$	−0.849874	+	0.462898i	−0.0723461	+	0.0394045i
$139$	1.25835	−	1.25835i	0.106732	−	0.106732i	−0.651724	−	0.758456i	$-0.725954\pi$
$139$	1.25835	−	1.25835i	0.106732	−	0.106732i	0.758456	+	0.651724i	$0.225954\pi$
$140$	−2.71846	−	12.6253i	−0.229752	−	1.06703i
$141$	−0.535167	−	0.535167i	−0.0450692	−	0.0450692i
$142$	−2.91681	+	9.89493i	−0.244773	+	0.830364i
$143$	−10.0836			−0.843233
$144$	10.8971	−	4.92082i	0.908091	−	0.410068i
$145$	6.35792			0.527997
$146$	0.107100	−	0.363325i	0.00886367	−	0.0300690i
$147$	−0.103532	−	0.103532i	−0.00853919	−	0.00853919i
$148$	−5.96155	+	1.28363i	−0.490037	+	0.105514i
$149$	−9.31693	+	9.31693i	−0.763273	+	0.763273i	−0.976912	−	0.213640i	$-0.931468\pi$
$149$	−9.31693	+	9.31693i	−0.763273	+	0.763273i	0.213640	+	0.976912i	$0.431468\pi$
$150$	−0.00513401	+	0.00279632i	−0.000419190	+	0.000228319i
$151$		−	7.44832i		−	0.606135i	−0.952969	−	0.303068i	$-0.901989\pi$
$151$		−	7.44832i		−	0.606135i	0.952969	−	0.303068i	$-0.0980108\pi$
$152$	−0.210745	+	2.82056i	−0.0170937	+	0.228778i
$153$			12.5970i			1.01841i
$154$	11.1155	+	20.4078i	0.895710	+	1.64451i
$155$	−5.09746	+	5.09746i	−0.409438	+	0.409438i
$156$	−0.200975	+	0.311271i	−0.0160909	+	0.0249216i
$157$	12.7885	+	12.7885i	1.02063	+	1.02063i	0.999783	+	0.0208472i	$0.00663636\pi$
$157$	12.7885	+	12.7885i	1.02063	+	1.02063i	0.0208472	+	0.999783i	$0.493364\pi$
$158$	−4.70208	−	1.38607i	−0.374077	−	0.110270i
$159$	1.06909			0.0847841
$160$	10.0457	+	7.60351i	0.794183	+	0.601110i
$161$	19.0544			1.50170
$162$	−12.0763	−	3.55984i	−0.948807	−	0.279687i
$163$	2.74107	+	2.74107i	0.214697	+	0.214697i	0.806259	−	0.591562i	$-0.201489\pi$
$163$	2.74107	+	2.74107i	0.214697	+	0.214697i	−0.591562	+	0.806259i	$0.701489\pi$
$164$	7.95145	−	12.3152i	0.620904	−	0.961658i
$165$	−0.929375	+	0.929375i	−0.0723517	+	0.0723517i
$166$	10.1411	+	18.6189i	0.787102	+	1.44511i
$167$			17.7216i			1.37134i	0.727914	+	0.685669i	$0.240490\pi$
$167$			17.7216i			1.37134i	−0.727914	+	0.685669i	$0.759510\pi$
$168$	0.851511	+	0.0636226i	0.0656955	+	0.00490859i
$169$		−	9.83454i		−	0.756503i
$170$	−11.6567	+	6.34901i	−0.894027	+	0.486947i
$171$	2.11365	−	2.11365i	0.161635	−	0.161635i
$172$	14.5673	−	3.13661i	1.11075	−	0.239165i
$173$	13.8049	+	13.8049i	1.04957	+	1.04957i	0.998706	+	0.0508623i	$0.0161970\pi$
$173$	13.8049	+	13.8049i	1.04957	+	1.04957i	0.0508623	+	0.998706i	$0.483803\pi$
$174$	−0.118859	+	0.403216i	−0.00901069	+	0.0305677i
$175$	0.115106			0.00870120
$176$	−21.2071	−	8.01241i	−1.59855	−	0.603958i
$177$	−0.123765			−0.00930273
$178$	3.30144	−	11.1998i	0.247454	−	0.839458i
$179$	−7.85770	−	7.85770i	−0.587312	−	0.587312i	0.349591	−	0.936903i	$-0.386321\pi$
$179$	−7.85770	−	7.85770i	−0.587312	−	0.587312i	−0.936903	+	0.349591i	$0.886321\pi$
$180$	−2.80267	−	13.0164i	−0.208899	−	0.970187i
$181$	12.9326	−	12.9326i	0.961271	−	0.961271i	−0.0380061	−	0.999278i	$-0.512101\pi$
$181$	12.9326	−	12.9326i	0.961271	−	0.961271i	0.999278	+	0.0380061i	$0.0121006\pi$
$182$	6.40648	−	3.48939i	0.474880	−	0.258651i
$183$		−	0.752614i		−	0.0556348i
$184$	−14.0868	+	12.1281i	−1.03849	+	0.894096i
$185$			6.79085i			0.499273i
$186$	−0.227983	−	0.418574i	−0.0167165	−	0.0306913i
$187$	16.8889	−	16.8889i	1.23504	−	1.23504i
$188$	−12.2127	−	7.88527i	−0.890705	−	0.575092i
$189$	−1.27851	−	1.27851i	−0.0929981	−	0.0929981i
$190$	3.02117	+	0.890574i	0.219179	+	0.0646091i
$191$	−5.15040			−0.372670			−0.186335	−	0.982486i	$-0.559661\pi$
$191$	−5.15040			−0.372670			−0.186335	+	0.982486i	$0.559661\pi$
$192$	−0.670012	+	0.494949i	−0.0483539	+	0.0357199i
$193$	−15.1251			−1.08873			−0.544365	−	0.838848i	$-0.683229\pi$
$193$	−15.1251			−1.08873			−0.544365	+	0.838848i	$0.683229\pi$
$194$	19.6380	+	5.78884i	1.40992	+	0.415615i
$195$	0.291751	+	0.291751i	0.0208928	+	0.0208928i
$196$	−2.36265	−	1.52547i	−0.168761	−	0.108962i
$197$	−13.3159	+	13.3159i	−0.948720	+	0.948720i	−0.998748	−	0.0500278i	$-0.984069\pi$
$197$	−13.3159	+	13.3159i	−0.948720	+	0.948720i	0.0500278	+	0.998748i	$0.484069\pi$
$198$	11.4598	+	21.0401i	0.814414	+	1.49525i
$199$		−	13.9187i		−	0.986668i	−0.869840	−	0.493334i	$-0.835778\pi$
$199$		−	13.9187i		−	0.986668i	0.869840	−	0.493334i	$-0.164222\pi$
$200$	−0.0850971	+	0.0732647i	−0.00601727	+	0.00518060i
$201$		−	1.25086i		−	0.0882289i
$202$	6.56533	−	3.57592i	0.461935	−	0.251601i
$203$	5.85255	−	5.85255i	0.410768	−	0.410768i
$204$	−0.184733	−	0.857954i	−0.0129339	−	0.0600688i
$205$	−11.5430	−	11.5430i	−0.806196	−	0.806196i
$206$	5.28433	−	17.9265i	0.368177	−	1.24900i
$207$	19.6447			1.36540
$208$	−2.51527	+	6.65739i	−0.174403	+	0.461607i
$209$	−5.66757			−0.392034
$210$	0.268859	−	0.912073i	0.0185530	−	0.0629390i
$211$	−3.49295	−	3.49295i	−0.240464	−	0.240464i	0.576578	−	0.817042i	$-0.304388\pi$
$211$	−3.49295	−	3.49295i	−0.240464	−	0.240464i	−0.817042	+	0.576578i	$0.804388\pi$
$212$	20.0746	−	4.32243i	1.37873	−	0.296865i
$213$	−0.537071	+	0.537071i	−0.0367995	+	0.0367995i
$214$	14.2471	−	7.75994i	0.973915	−	0.530459i
$215$		−	16.5938i		−	1.13169i
$216$	1.75896	+	0.131425i	0.119682	+	0.00894234i
$217$			9.38456i			0.637065i
$218$	7.93817	+	14.5744i	0.537641	+	0.987101i
$219$	0.0197203	−	0.0197203i	0.00133258	−	0.00133258i
$220$	−13.6936	+	21.2087i	−0.923224	+	1.42989i
$221$	−5.30180	−	5.30180i	−0.356638	−	0.356638i
$222$	−0.430672	−	0.126953i	−0.0289048	−	0.00852050i
$223$	22.8304			1.52884			0.764418	−	0.644721i	$-0.223027\pi$
$223$	22.8304			1.52884			0.764418	+	0.644721i	$0.223027\pi$
$224$	16.2463	−	2.24808i	1.08550	−	0.150206i
$225$	0.118672			0.00791147
$226$	−24.8917	−	7.33754i	−1.65577	−	0.488086i
$227$	−13.3539	−	13.3539i	−0.886331	−	0.886331i	0.107838	−	0.994169i	$-0.465607\pi$
$227$	−13.3539	−	13.3539i	−0.886331	−	0.886331i	−0.994169	+	0.107838i	$0.965607\pi$
$228$	−0.112960	+	0.174952i	−0.00748093	+	0.0115865i
$229$	−6.94111	+	6.94111i	−0.458681	+	0.458681i	−0.898222	−	0.439541i	$-0.855141\pi$
$229$	−6.94111	+	6.94111i	−0.458681	+	0.458681i	0.439541	+	0.898222i	$0.355141\pi$
$230$	9.90111	+	18.1783i	0.652860	+	1.19864i
$231$			1.71100i			0.112576i
$232$	−0.601615	+	8.05188i	−0.0394979	+	0.528632i
$233$			26.6765i			1.74764i	0.486253	+	0.873818i	$0.338363\pi$
$233$			26.6765i			1.74764i	−0.486253	+	0.873818i	$0.661637\pi$
$234$	6.60495	−	3.59749i	0.431779	−	0.235175i
$235$	−11.4469	+	11.4469i	−0.746713	+	0.746713i
$236$	−2.32397	+	0.500393i	−0.151278	+	0.0325728i
$237$	−0.255217	−	0.255217i	−0.0165781	−	0.0165781i
$238$	−4.88579	+	16.5745i	−0.316699	+	1.07436i
$239$	23.8073			1.53997			0.769984	−	0.638063i	$-0.220264\pi$
$239$	23.8073			1.53997			0.769984	+	0.638063i	$0.220264\pi$
$240$	0.381767	+	0.845417i	0.0246429	+	0.0545714i
$241$	−6.97283			−0.449159			−0.224580	−	0.974456i	$-0.572101\pi$
$241$	−6.97283			−0.449159			−0.224580	+	0.974456i	$0.572101\pi$
$242$	8.44573	−	28.6512i	0.542912	−	1.84177i
$243$	−1.97837	−	1.97837i	−0.126913	−	0.126913i
$244$	−3.04289	−	14.1321i	−0.194801	−	0.904713i
$245$	−2.21449	+	2.21449i	−0.141479	+	0.141479i
$246$	0.947841	−	0.516257i	0.0604321	−	0.0329154i
$247$			1.77918i			0.113206i
$248$	−5.97325	−	6.93794i	−0.379302	−	0.440559i
$249$			1.56102i			0.0989255i
$250$	7.59261	+	13.9399i	0.480199	+	0.881638i
$251$	12.4679	−	12.4679i	0.786965	−	0.786965i	−0.194031	−	0.980995i	$-0.562156\pi$
$251$	12.4679	−	12.4679i	0.786965	−	0.786965i	0.980995	+	0.194031i	$0.0621562\pi$
$252$	−14.5617	−	9.40189i	−0.917300	−	0.592264i
$253$	−26.3378	−	26.3378i	−1.65584	−	1.65584i
$254$	−3.37685	−	0.995422i	−0.211883	−	0.0624583i
$255$	−0.977302			−0.0612010
$256$	−10.5799	+	12.0027i	−0.661244	+	0.750171i
$257$	−27.6219			−1.72301			−0.861505	−	0.507749i	$-0.830478\pi$
$257$	−27.6219			−1.72301			−0.861505	+	0.507749i	$0.830478\pi$
$258$	1.05237	+	0.310215i	0.0655176	+	0.0193131i
$259$	6.25107	+	6.25107i	0.388422	+	0.388422i
$260$	6.65789	+	4.29873i	0.412905	+	0.266596i
$261$	6.03386	−	6.03386i	0.373486	−	0.373486i
$262$	−5.34899	−	9.82067i	−0.330462	−	0.606723i
$263$			9.18253i			0.566219i	0.959088	+	0.283110i	$0.0913660\pi$
$263$			9.18253i			0.566219i	−0.959088	+	0.283110i	$0.908634\pi$
$264$	−1.08905	−	1.26493i	−0.0670263	−	0.0778512i
$265$		−	22.8671i		−	1.40472i
$266$	3.60081	−	1.96124i	0.220780	−	0.120251i
$267$	0.607894	−	0.607894i	0.0372025	−	0.0372025i
$268$	−5.05736	−	23.4878i	−0.308927	−	1.43475i
$269$	12.8438	+	12.8438i	0.783099	+	0.783099i	0.980353	−	0.197253i	$-0.0632021\pi$
$269$	12.8438	+	12.8438i	0.783099	+	0.783099i	−0.197253	+	0.980353i	$0.563202\pi$
$270$	0.555381	−	1.88407i	0.0337994	−	0.114661i
$271$	−1.84803			−0.112260			−0.0561299	−	0.998423i	$-0.517876\pi$
$271$	−1.84803			−0.112260			−0.0561299	+	0.998423i	$0.517876\pi$
$272$	−6.93758	−	15.3632i	−0.420653	−	0.931530i
$273$	0.537122			0.0325081
$274$	0.0173982	−	0.0590214i	0.00105106	−	0.00356562i
$275$	−0.159104	−	0.159104i	−0.00959433	−	0.00959433i
$276$	−1.33796	+	0.288086i	−0.0805355	+	0.0173407i
$277$	−12.4654	+	12.4654i	−0.748974	+	0.748974i	−0.974287	−	0.225312i	$-0.927660\pi$
$277$	−12.4654	+	12.4654i	−0.748974	+	0.748974i	0.225312	+	0.974287i	$0.427660\pi$
$278$	2.21013	−	1.20378i	0.132555	−	0.0721982i
$279$			9.67529i			0.579244i
$280$	1.36085	−	18.2133i	0.0813263	−	1.08845i
$281$			23.8884i			1.42506i	0.701640	+	0.712532i	$0.252452\pi$
$281$			23.8884i			1.42506i	−0.701640	+	0.712532i	$0.747548\pi$
$282$	−0.511961	−	0.939952i	−0.0304868	−	0.0559733i
$283$	1.61023	−	1.61023i	0.0957185	−	0.0957185i	−0.657626	−	0.753345i	$-0.728439\pi$
$283$	1.61023	−	1.61023i	0.0957185	−	0.0957185i	0.753345	+	0.657626i	$0.228439\pi$
$284$	−7.91332	+	12.2562i	−0.469569	+	0.727271i
$285$	0.163981	+	0.163981i	0.00971341	+	0.00971341i
$286$	−13.6784	−	4.03210i	−0.808824	−	0.238423i
$287$	−21.2509			−1.25440
$288$	16.7496	−	2.31773i	0.986982	−	0.136573i
$289$	0.759844			0.0446967
$290$	8.62455	+	2.54233i	0.506451	+	0.149291i
$291$	1.06590	+	1.06590i	0.0624840	+	0.0624840i
$292$	0.290564	−	0.450026i	0.0170040	−	0.0263358i
$293$	−3.20942	+	3.20942i	−0.187496	+	0.187496i	−0.794613	−	0.607117i	$-0.792326\pi$
$293$	−3.20942	+	3.20942i	−0.187496	+	0.187496i	0.607117	+	0.794613i	$0.292326\pi$
$294$	−0.0990428	−	0.181841i	−0.00577629	−	0.0106052i
$295$			2.64725i			0.154129i
$296$	−8.60016	−	0.642581i	−0.499874	−	0.0373492i
$297$			3.53442i			0.205088i
$298$	−16.3640	+	8.91292i	−0.947941	+	0.516312i
$299$	−8.26801	+	8.26801i	−0.478152	+	0.478152i
$300$	−0.00808246	+	0.00174030i	−0.000466641	+	0.000100476i
$301$	−15.2748	−	15.2748i	−0.880424	−	0.880424i
$302$	2.97834	−	10.1037i	0.171384	−	0.581401i
$303$	0.550440			0.0316220
$304$	−1.41373	+	3.74184i	−0.0810829	+	0.214609i
$305$	−16.0980			−0.921766
$306$	−5.03715	+	17.0879i	−0.287955	+	0.976853i
$307$	−9.44204	−	9.44204i	−0.538886	−	0.538886i	0.384316	−	0.923202i	$-0.374437\pi$
$307$	−9.44204	−	9.44204i	−0.538886	−	0.538886i	−0.923202	+	0.384316i	$0.874437\pi$
$308$	6.91776	+	32.1281i	0.394176	+	1.83067i
$309$	0.973003	−	0.973003i	0.0553522	−	0.0553522i
$310$	−8.95304	+	4.87642i	−0.508498	+	0.276962i
$311$		−	24.3583i		−	1.38123i	−0.723220	−	0.690617i	$-0.757339\pi$
$311$		−	24.3583i		−	1.38123i	0.723220	−	0.690617i	$-0.242661\pi$
$312$	−0.397090	+	0.341877i	−0.0224808	+	0.0193550i
$313$		−	2.00706i		−	0.113446i	−0.998390	−	0.0567228i	$-0.981935\pi$
$313$		−	2.00706i		−	0.113446i	0.998390	−	0.0567228i	$-0.0180651\pi$
$314$	12.2339	+	22.4613i	0.690400	+	1.26756i
$315$	−13.6486	+	13.6486i	−0.769009	+	0.769009i
$316$	−5.82415	−	3.76042i	−0.327634	−	0.211540i
$317$	−11.5455	−	11.5455i	−0.648459	−	0.648459i	0.304161	−	0.952621i	$-0.401624\pi$
$317$	−11.5455	−	11.5455i	−0.648459	−	0.648459i	−0.952621	+	0.304161i	$0.901624\pi$
$318$	1.45022	+	0.427493i	0.0813244	+	0.0239726i
$319$	−16.1792			−0.905863
$320$	10.5867	+	14.3311i	0.591812	+	0.801135i
$321$	1.19449			0.0666697
$322$	25.8475	+	7.61926i	1.44042	+	0.424605i
$323$	−2.97992	−	2.97992i	−0.165807	−	0.165807i
$324$	−14.9582	−	9.65787i	−0.831008	−	0.536549i
$325$	−0.0499463	+	0.0499463i	−0.00277052	+	0.00277052i
$326$	2.62221	+	4.81433i	0.145231	+	0.266641i
$327$			1.22192i			0.0675724i
$328$	15.7106	−	13.5261i	0.867475	−	0.746857i
$329$			21.0740i			1.16185i
$330$	−1.63233	+	0.889075i	−0.0898567	+	0.0489419i
$331$	4.06337	−	4.06337i	0.223343	−	0.223343i	−0.586562	−	0.809905i	$-0.699519\pi$
$331$	4.06337	−	4.06337i	0.223343	−	0.223343i	0.809905	+	0.586562i	$0.199519\pi$
$332$	6.31135	+	29.3117i	0.346380	+	1.60869i
$333$	6.44472	+	6.44472i	0.353169	+	0.353169i
$334$	−7.08629	+	24.0394i	−0.387744	+	1.31538i
$335$	−26.7552			−1.46179
$336$	1.12964	+	0.426796i	0.0616268	+	0.0232836i
$337$	−6.88532			−0.375067			−0.187534	−	0.982258i	$-0.560049\pi$
$337$	−6.88532			−0.375067			−0.187534	+	0.982258i	$0.560049\pi$
$338$	3.93251	−	13.3406i	0.213900	−	0.725633i
$339$	−1.35106	−	1.35106i	−0.0733794	−	0.0733794i
$340$	−18.3511	+	3.95133i	−0.995229	+	0.214291i
$341$	12.9717	−	12.9717i	0.702456	−	0.702456i
$342$	3.71236	−	2.02200i	0.200742	−	0.109337i
$343$		−	16.2184i		−	0.875713i
$344$	21.0149	+	1.57018i	1.13305	+	0.0846583i
$345$			1.52408i			0.0820535i
$346$	13.2063	+	24.2466i	0.709975	+	1.30350i
$347$	−10.5446	+	10.5446i	−0.566064	+	0.566064i	−0.931023	−	0.364960i	$-0.881083\pi$
$347$	−10.5446	+	10.5446i	−0.566064	+	0.566064i	0.364960	+	0.931023i	$0.381083\pi$
$348$	−0.322466	+	0.499437i	−0.0172860	+	0.0267726i
$349$	−9.76453	−	9.76453i	−0.522683	−	0.522683i	0.395698	−	0.918381i	$-0.370503\pi$
$349$	−9.76453	−	9.76453i	−0.522683	−	0.522683i	−0.918381	+	0.395698i	$0.870503\pi$
$350$	0.156142	+	0.0460272i	0.00834614	+	0.00246026i
$351$	1.10953			0.0592224
$352$	−25.5637	−	19.3489i	−1.36255	−	1.03130i
$353$	10.3333			0.549984			0.274992	−	0.961447i	$-0.411325\pi$
$353$	10.3333			0.549984			0.274992	+	0.961447i	$0.411325\pi$
$354$	−0.167887	−	0.0494895i	−0.00892312	−	0.00263034i
$355$	11.4876	+	11.4876i	0.609700	+	0.609700i
$356$	8.95685	−	13.8724i	0.474712	−	0.735236i
$357$	−0.899619	+	0.899619i	−0.0476129	+	0.0476129i
$358$	−7.51697	−	13.8010i	−0.397284	−	0.729408i
$359$		−	9.80479i		−	0.517477i	−0.965947	−	0.258739i	$-0.916693\pi$
$359$		−	9.80479i		−	0.517477i	0.965947	−	0.258739i	$-0.0833068\pi$
$360$	1.40301	−	18.7775i	0.0739450	−	0.989664i
$361$			1.00000i			0.0526316i
$362$	22.7144	−	12.3718i	1.19384	−	0.650247i
$363$	1.55511	−	1.55511i	0.0816221	−	0.0816221i
$364$	10.0857	−	2.17164i	0.528635	−	0.113825i
$365$	−0.421806	−	0.421806i	−0.0220783	−	0.0220783i
$366$	0.300946	−	1.02092i	0.0157307	−	0.0533646i
$367$	−7.37122			−0.384775			−0.192387	−	0.981319i	$-0.561623\pi$
$367$	−7.37122			−0.384775			−0.192387	+	0.981319i	$0.561623\pi$
$368$	−23.9585	+	10.8190i	−1.24892	+	0.563978i
$369$	−21.9092			−1.14055
$370$	−2.71544	+	9.21182i	−0.141169	+	0.478900i
$371$	−21.0495	−	21.0495i	−1.09284	−	1.09284i
$372$	−0.141886	−	0.658960i	−0.00735645	−	0.0341655i
$373$	−9.96696	+	9.96696i	−0.516070	+	0.516070i	−0.916380	−	0.400310i	$-0.868902\pi$
$373$	−9.96696	+	9.96696i	−0.516070	+	0.516070i	0.400310	+	0.916380i	$0.368902\pi$
$374$	29.6632	−	16.1565i	1.53385	−	0.835435i
$375$			1.16873i			0.0603529i
$376$	−13.4136	−	15.5799i	−0.691752	−	0.803471i
$377$			5.07902i			0.261583i
$378$	−1.22307	−	2.24554i	−0.0629081	−	0.115498i
$379$	5.65029	−	5.65029i	0.290236	−	0.290236i	−0.546938	−	0.837173i	$-0.684207\pi$
$379$	5.65029	−	5.65029i	0.290236	−	0.290236i	0.837173	+	0.546938i	$0.184207\pi$
$380$	3.74212	+	2.41614i	0.191967	+	0.123945i
$381$	−0.183287	−	0.183287i	−0.00939007	−	0.00939007i
$382$	−6.98654	−	2.05948i	−0.357463	−	0.105372i
$383$	−0.975904			−0.0498664			−0.0249332	−	0.999689i	$-0.507937\pi$
$383$	−0.975904			−0.0498664			−0.0249332	+	0.999689i	$0.507937\pi$
$384$	−1.10679	+	0.403485i	−0.0564805	+	0.0205902i
$385$	36.5973			1.86517
$386$	−20.5173	−	6.04805i	−1.04430	−	0.307838i
$387$	−15.7480	−	15.7480i	−0.800515	−	0.800515i
$388$	24.3242	+	15.7052i	1.23488	+	0.797310i
$389$	6.74533	−	6.74533i	0.342002	−	0.342002i	−0.515118	−	0.857120i	$-0.672252\pi$
$389$	6.74533	−	6.74533i	0.342002	−	0.342002i	0.857120	+	0.515118i	$0.172252\pi$
$390$	0.279100	+	0.512424i	0.0141328	+	0.0259476i
$391$		−	27.6960i		−	1.40065i
$392$	−2.59496	−	3.01405i	−0.131065	−	0.152233i
$393$		−	0.823369i		−	0.0415335i
$394$	−23.3877	+	12.7385i	−1.17826	+	0.641757i
$395$	−5.45893	+	5.45893i	−0.274669	+	0.274669i
$396$	7.13206	+	33.1234i	0.358400	+	1.66451i
$397$	24.1296	+	24.1296i	1.21103	+	1.21103i	0.970688	+	0.240343i	$0.0772600\pi$
$397$	24.1296	+	24.1296i	1.21103	+	1.21103i	0.240343	+	0.970688i	$0.422740\pi$
$398$	5.56562	−	18.8807i	0.278979	−	0.946405i
$399$	0.301894			0.0151136
$400$	−0.144731	+	0.0653564i	−0.00723654	+	0.00326782i
$401$	34.3373			1.71472			0.857361	−	0.514715i	$-0.172102\pi$
$401$	34.3373			1.71472			0.857361	+	0.514715i	$0.172102\pi$
$402$	0.500179	−	1.69680i	0.0249466	−	0.0846286i
$403$	−4.07210	−	4.07210i	−0.202846	−	0.202846i
$404$	10.3358	−	2.22548i	0.514225	−	0.110722i
$405$	−14.0202	+	14.0202i	−0.696667	+	0.696667i
$406$	10.2793	−	5.59877i	0.510151	−	0.277862i
$407$		−	17.2809i		−	0.856584i
$408$	0.0924767	−	1.23769i	0.00457828	−	0.0612746i
$409$		−	34.5320i		−	1.70750i	−0.520687	−	0.853748i	$-0.674324\pi$
$409$		−	34.5320i		−	1.70750i	0.520687	−	0.853748i	$-0.325676\pi$
$410$	−11.0424	−	20.2738i	−0.545347	−	1.00125i
$411$	0.00320353	−	0.00320353i	0.000158018	−	0.000158018i
$412$	14.3365	−	22.2043i	0.706306	−	1.09393i
$413$	2.43683	+	2.43683i	0.119909	+	0.119909i
$414$	26.6482	+	7.85530i	1.30969	+	0.386067i
$415$	33.3892			1.63901
$416$	−6.07405	+	8.02501i	−0.297805	+	0.393458i
$417$	0.185298			0.00907410
$418$	−7.68808	−	2.26628i	−0.376036	−	0.110847i
$419$	21.6398	+	21.6398i	1.05717	+	1.05717i	0.998263	+	0.0589082i	$0.0187619\pi$
$419$	21.6398	+	21.6398i	1.05717	+	1.05717i	0.0589082	+	0.998263i	$0.481238\pi$
$420$	0.729417	−	1.12972i	0.0355919	−	0.0551249i
$421$	7.87493	−	7.87493i	0.383800	−	0.383800i	−0.488669	−	0.872469i	$-0.662517\pi$
$421$	7.87493	−	7.87493i	0.383800	−	0.383800i	0.872469	+	0.488669i	$0.162517\pi$
$422$	−3.34148	−	6.13492i	−0.162661	−	0.298643i
$423$			21.7269i			1.05640i
$424$	28.9597	+	2.16379i	1.40641	+	0.105083i
$425$		−	0.167309i		−	0.00811567i
$426$	−0.943296	+	0.513782i	−0.0457029	+	0.0248928i
$427$	−14.8184	+	14.8184i	−0.717112	+	0.717112i
$428$	22.4293	−	4.82943i	1.08416	−	0.233439i
$429$	−0.742430	−	0.742430i	−0.0358449	−	0.0358449i
$430$	6.63531	−	22.5095i	0.319983	−	1.08551i
$431$	30.7940			1.48329			0.741646	−	0.670791i	$-0.234045\pi$
$431$	30.7940			1.48329			0.741646	+	0.670791i	$0.234045\pi$
$432$	2.33349	+	0.881632i	0.112270	+	0.0424175i
$433$	29.9743			1.44047			0.720236	−	0.693729i	$-0.244033\pi$
$433$	29.9743			1.44047			0.720236	+	0.693729i	$0.244033\pi$
$434$	−3.75258	+	12.7302i	−0.180130	+	0.611069i
$435$	0.468118	+	0.468118i	0.0224445	+	0.0224445i
$436$	4.94035	+	22.9444i	0.236600	+	1.09884i
$437$	−4.64710	+	4.64710i	−0.222301	+	0.222301i
$438$	0.0346362	−	0.0188652i	0.00165498	−	0.000901414i
$439$			20.6482i			0.985484i	0.870175	+	0.492742i	$0.164005\pi$
$439$			20.6482i			0.985484i	−0.870175	+	0.492742i	$0.835995\pi$
$440$	−27.0561	+	23.2941i	−1.28985	+	1.11050i
$441$			4.20324i			0.200154i
$442$	−5.07190	−	9.31194i	−0.241246	−	0.442924i
$443$	1.03257	−	1.03257i	0.0490590	−	0.0490590i	−0.682152	−	0.731211i	$-0.738956\pi$
$443$	1.03257	−	1.03257i	0.0490590	−	0.0490590i	0.731211	+	0.682152i	$0.238956\pi$
$444$	−0.533445	−	0.344424i	−0.0253162	−	0.0163456i
$445$	−13.0025	−	13.0025i	−0.616377	−	0.616377i
$446$	30.9695	+	9.12913i	1.46645	+	0.432277i
$447$	−1.37197			−0.0648917
$448$	22.9372	+	3.44685i	1.08368	+	0.162848i
$449$	1.73551			0.0819038			0.0409519	−	0.999161i	$-0.486961\pi$
$449$	1.73551			0.0819038			0.0409519	+	0.999161i	$0.486961\pi$
$450$	0.160979	+	0.0474531i	0.00758863	+	0.00223696i
$451$	29.3738	+	29.3738i	1.38316	+	1.38316i
$452$	−30.8317	−	19.9068i	−1.45020	−	0.936338i
$453$	0.548401	−	0.548401i	0.0257661	−	0.0257661i
$454$	−12.7749	−	23.4545i	−0.599554	−	1.10077i
$455$		−	11.4887i		−	0.538599i
$456$	−0.223188	+	0.192155i	−0.0104517	+	0.00899846i
$457$		−	7.97316i		−	0.372969i	−0.982458	−	0.186484i	$-0.940291\pi$
$457$		−	7.97316i		−	0.372969i	0.982458	−	0.186484i	$-0.0597093\pi$
$458$	−12.1912	+	6.64012i	−0.569656	+	0.310273i
$459$	−1.85834	+	1.85834i	−0.0867400	+	0.0867400i
$460$	6.16199	+	28.6181i	0.287304	+	1.33432i
$461$	1.14034	+	1.14034i	0.0531108	+	0.0531108i	0.733163	−	0.680053i	$-0.238043\pi$
$461$	1.14034	+	1.14034i	0.0531108	+	0.0531108i	−0.680053	+	0.733163i	$0.738043\pi$
$462$	−0.684175	+	2.32098i	−0.0318307	+	0.107982i
$463$	−2.88674			−0.134158			−0.0670791	−	0.997748i	$-0.521368\pi$
$463$	−2.88674			−0.134158			−0.0670791	+	0.997748i	$0.521368\pi$
$464$	−4.03578	+	10.6819i	−0.187356	+	0.495892i
$465$	−0.750627			−0.0348095
$466$	−10.6671	+	36.1868i	−0.494143	+	1.67632i
$467$	14.5441	+	14.5441i	0.673020	+	0.673020i	0.958411	−	0.285392i	$-0.0921236\pi$
$467$	14.5441	+	14.5441i	0.673020	+	0.673020i	−0.285392	+	0.958411i	$0.592124\pi$
$468$	10.3982	−	2.23891i	0.480655	−	0.103494i
$469$	−24.6285	+	24.6285i	−1.13724	+	1.13724i
$470$	−20.1050	+	10.9505i	−0.927375	+	0.505110i
$471$			1.88316i			0.0867717i
$472$	−3.35257	−	0.250495i	−0.154315	−	0.0115300i
$473$			42.2268i			1.94159i
$474$	−0.244150	−	0.448255i	−0.0112142	−	0.0205891i
$475$	−0.0280727	+	0.0280727i	−0.00128806	+	0.00128806i
$476$	−13.2552	+	20.5297i	−0.607551	+	0.940977i
$477$	−21.7016	−	21.7016i	−0.993648	−	0.993648i
$478$	32.2948	+	9.51978i	1.47713	+	0.435425i
$479$	−12.5319			−0.572597			−0.286298	−	0.958140i	$-0.592425\pi$
$479$	−12.5319			−0.572597			−0.286298	+	0.958140i	$0.592425\pi$
$480$	0.179813	+	1.29947i	0.00820733	+	0.0593123i
$481$	−5.42487			−0.247353
$482$	−9.45868	−	2.78821i	−0.430831	−	0.126999i
$483$	1.40293	+	1.40293i	0.0638356	+	0.0638356i
$484$	22.9134	−	35.4883i	1.04152	−	1.61310i
$485$	22.7989	−	22.7989i	1.03525	−	1.03525i
$486$	−1.89259	−	3.47476i	−0.0858494	−	0.157618i
$487$			1.95168i			0.0884390i	0.999022	+	0.0442195i	$0.0140801\pi$
$487$			1.95168i			0.0884390i	−0.999022	+	0.0442195i	$0.985920\pi$
$488$	1.52326	−	20.3870i	0.0689548	−	0.922875i
$489$			0.403636i			0.0182530i
$490$	−3.88947	+	2.11847i	−0.175709	+	0.0957025i
$491$	16.4704	−	16.4704i	0.743298	−	0.743298i	−0.229913	−	0.973211i	$-0.573844\pi$
$491$	16.4704	−	16.4704i	0.743298	−	0.743298i	0.973211	+	0.229913i	$0.0738441\pi$
$492$	1.49219	−	0.321295i	0.0672729	−	0.0144851i
$493$	−8.50679	−	8.50679i	−0.383127	−	0.383127i
$494$	−0.711435	+	2.41346i	−0.0320090	+	0.108587i
$495$	37.7311			1.69589
$496$	−5.32848	−	11.7999i	−0.239256	−	0.529829i
$497$	21.1490			0.948663
$498$	−0.624200	+	2.11753i	−0.0279711	+	0.0948887i
$499$	16.9579	+	16.9579i	0.759139	+	0.759139i	0.976166	−	0.217027i	$-0.0696359\pi$
$499$	16.9579	+	16.9579i	0.759139	+	0.759139i	−0.217027	+	0.976166i	$0.569636\pi$
$500$	4.72529	+	21.9456i	0.211321	+	0.981438i
$501$	−1.30480	+	1.30480i	−0.0582940	+	0.0582940i
$502$	21.8982	−	11.9272i	0.977365	−	0.532338i
$503$			18.3752i			0.819310i	0.912241	+	0.409655i	$0.134351\pi$
$503$			18.3752i			0.819310i	−0.912241	+	0.409655i	$0.865649\pi$
$504$	−15.9935	−	18.5765i	−0.712407	−	0.827462i
$505$		−	11.7736i		−	0.523918i
$506$	−25.1957	−	46.2590i	−1.12009	−	2.05646i
$507$	0.724093	−	0.724093i	0.0321581	−	0.0321581i
$508$	−4.18268	−	2.70059i	−0.185577	−	0.119819i
$509$	−2.04581	−	2.04581i	−0.0906790	−	0.0906790i	0.660312	−	0.750991i	$-0.270424\pi$
$509$	−2.04581	−	2.04581i	−0.0906790	−	0.0906790i	−0.750991	+	0.660312i	$0.770424\pi$
$510$	−1.32571	−	0.390791i	−0.0587036	−	0.0173045i
$511$	−0.776556			−0.0343528
$512$	−19.1512	+	12.0512i	−0.846371	+	0.532594i
$513$	0.623621			0.0275336
$514$	−37.4693	−	11.0451i	−1.65270	−	0.487179i
$515$	−20.8120	−	20.8120i	−0.917084	−	0.917084i
$516$	1.30350	+	0.841616i	0.0573833	+	0.0370501i
$517$	29.1293	−	29.1293i	1.28111	−	1.28111i
$518$	5.98000	+	10.9792i	0.262746	+	0.482399i
$519$			2.03284i			0.0892319i
$520$	7.31254	+	8.49353i	0.320676	+	0.372466i
$521$		−	39.5353i		−	1.73207i	−0.499982	−	0.866036i	$-0.666660\pi$
$521$		−	39.5353i		−	1.73207i	0.499982	−	0.866036i	$-0.333340\pi$
$522$	10.5977	−	5.77221i	0.463849	−	0.252643i
$523$	−15.8335	+	15.8335i	−0.692352	+	0.692352i	−0.962749	−	0.270397i	$-0.912845\pi$
$523$	−15.8335	+	15.8335i	−0.692352	+	0.692352i	0.270397	+	0.962749i	$0.412845\pi$
$524$	−3.32896	−	15.4607i	−0.145426	−	0.675403i
$525$	0.00847498	+	0.00847498i	0.000369878	+	0.000369878i
$526$	−3.67180	+	12.4562i	−0.160098	+	0.543114i
$527$	13.6406			0.594195
$528$	−0.971495	−	2.15136i	−0.0422789	−	0.0936260i
$529$	−20.1912			−0.877877
$530$	9.14383	−	31.0194i	0.397183	−	1.34740i
$531$	2.51232	+	2.51232i	0.109026	+	0.109026i
$532$	5.66876	−	1.22059i	0.245772	−	0.0529191i
$533$	9.22109	−	9.22109i	0.399410	−	0.399410i
$534$	1.06769	−	0.581534i	0.0462034	−	0.0251654i
$535$		−	25.5494i		−	1.10460i
$536$	2.53169	−	33.8836i	0.109352	−	1.46355i
$537$		−	1.15709i		−	0.0499319i
$538$	12.2868	+	22.5585i	0.529724	+	0.972565i
$539$	5.63530	−	5.63530i	0.242729	−	0.242729i
$540$	1.50675	−	2.33367i	0.0648404	−	0.100425i
$541$	17.7413	+	17.7413i	0.762758	+	0.762758i	0.976820	−	0.214062i	$-0.0686694\pi$
$541$	17.7413	+	17.7413i	0.762758	+	0.762758i	−0.214062	+	0.976820i	$0.568669\pi$
$542$	−2.50686	−	0.738967i	−0.107679	−	0.0317414i
$543$	1.90439			0.0817251
$544$	−3.26763	−	23.6144i	−0.140098	−	1.01246i
$545$	26.1362			1.11955
$546$	0.728609	+	0.214778i	0.0311816	+	0.00919164i
$547$	−5.01473	−	5.01473i	−0.214414	−	0.214414i	0.591725	−	0.806140i	$-0.298447\pi$
$547$	−5.01473	−	5.01473i	−0.214414	−	0.214414i	−0.806140	+	0.591725i	$0.798447\pi$
$548$	0.0472015	−	0.0731059i	0.00201635	−	0.00312293i
$549$	−15.2774	+	15.2774i	−0.652025	+	0.652025i
$550$	−0.152205	−	0.279446i	−0.00649004	−	0.0119156i
$551$			2.85470i			0.121615i
$552$	−1.93014	−	0.144215i	−0.0821522	−	0.00613819i
$553$			10.0500i			0.427371i
$554$	−21.8939	+	11.9249i	−0.930183	+	0.506640i
$555$	−0.499994	+	0.499994i	−0.0212235	+	0.0212235i
$556$	3.47941	−	0.749180i	0.147560	−	0.0317723i
$557$	8.66534	+	8.66534i	0.367162	+	0.367162i	0.866441	−	0.499279i	$-0.166402\pi$
$557$	8.66534	+	8.66534i	0.367162	+	0.367162i	−0.499279	+	0.866441i	$0.666402\pi$
$558$	−3.86883	+	13.1246i	−0.163781	+	0.555607i
$559$	13.2559			0.560666
$560$	9.12891	−	24.1623i	0.385767	−	1.02104i
$561$	2.48698			0.105000
$562$	−9.55220	+	32.4048i	−0.402935	+	1.36691i
$563$	−10.1435	−	10.1435i	−0.427499	−	0.427499i	0.460276	−	0.887776i	$-0.347750\pi$
$563$	−10.1435	−	10.1435i	−0.427499	−	0.427499i	−0.887776	+	0.460276i	$0.847750\pi$
$564$	−0.318621	−	1.47977i	−0.0134163	−	0.0623094i
$565$	−28.8983	+	28.8983i	−1.21576	+	1.21576i
$566$	2.82817	−	1.54041i	0.118877	−	0.0647483i
$567$			25.8115i			1.08398i
$568$	−15.6353	+	13.4613i	−0.656043	+	0.564823i
$569$			18.3199i			0.768011i	0.923331	+	0.384005i	$0.125456\pi$
$569$			18.3199i			0.768011i	−0.923331	+	0.384005i	$0.874544\pi$
$570$	0.156871	+	0.288012i	0.00657059	+	0.0120635i
$571$	−22.3993	+	22.3993i	−0.937383	+	0.937383i	−0.998152	−	0.0607690i	$-0.980645\pi$
$571$	−22.3993	+	22.3993i	−0.937383	+	0.937383i	0.0607690	+	0.998152i	$0.480645\pi$
$572$	−16.9426	−	10.9391i	−0.708405	−	0.457388i
$573$	−0.379211	−	0.379211i	−0.0158418	−	0.0158418i
$574$	−28.8270	−	8.49755i	−1.20321	−	0.354681i
$575$	−0.260914			−0.0108809
$576$	23.6477	+	3.55363i	0.985323	+	0.148068i
$577$	20.6215			0.858483			0.429242	−	0.903190i	$-0.358781\pi$
$577$	20.6215			0.858483			0.429242	+	0.903190i	$0.358781\pi$
$578$	1.03073	+	0.303837i	0.0428728	+	0.0126380i
$579$	−1.11363	−	1.11363i	−0.0462807	−	0.0462807i
$580$	10.6827	+	6.89736i	0.443573	+	0.286397i
$581$	30.7352	−	30.7352i	1.27511	−	1.27511i
$582$	1.01968	+	1.87211i	0.0422670	+	0.0776016i
$583$			58.1908i			2.41002i
$584$	0.574102	−	0.494276i	0.0237565	−	0.0204533i
$585$		−	11.8446i		−	0.489715i
$586$	−5.63694	+	3.07025i	−0.232860	+	0.126831i
$587$	−12.5784	+	12.5784i	−0.519167	+	0.519167i	−0.917319	−	0.398152i	$-0.869652\pi$
$587$	−12.5784	+	12.5784i	−0.519167	+	0.519167i	0.398152	+	0.917319i	$0.369652\pi$
$588$	−0.0616396	−	0.286272i	−0.00254198	−	0.0118057i
$589$	−2.28876	−	2.28876i	−0.0943066	−	0.0943066i
$590$	−1.05855	+	3.59101i	−0.0435799	+	0.147840i
$591$	−1.96084			−0.0806580
$592$	−11.4092	−	4.31059i	−0.468916	−	0.177164i
$593$	−41.3373			−1.69752			−0.848760	−	0.528779i	$-0.822650\pi$
$593$	−41.3373			−1.69752			−0.848760	+	0.528779i	$0.822650\pi$
$594$	−1.41330	+	4.79445i	−0.0579883	+	0.196719i
$595$	19.2423	+	19.2423i	0.788858	+	0.788858i
$596$	−25.7618	+	5.54699i	−1.05525	+	0.227214i
$597$	1.02480	−	1.02480i	0.0419421	−	0.0419421i
$598$	−14.5217	+	7.90949i	−0.593837	+	0.323443i
$599$		−	39.0887i		−	1.59712i	−0.601916	−	0.798560i	$-0.705596\pi$
$599$		−	39.0887i		−	1.59712i	0.601916	−	0.798560i	$-0.294404\pi$
$600$	−0.0116598		0.000871188i	−0.000476009		3.55661e-5i
$601$			35.6361i			1.45363i	0.686835	+	0.726813i	$0.259000\pi$
$601$			35.6361i			1.45363i	−0.686835	+	0.726813i	$0.741000\pi$
$602$	−14.6124	−	26.8282i	−0.595558	−	1.09344i
$603$	−25.3915	+	25.3915i	−1.03402	+	1.03402i
$604$	8.08027	−	12.5147i	0.328781	−	0.509218i
$605$	−33.2629	−	33.2629i	−1.35233	−	1.35233i
$606$	0.746675	+	0.220103i	0.0303316	+	0.00894108i
$607$	−0.931257			−0.0377986			−0.0188993	−	0.999821i	$-0.506016\pi$
$607$	−0.931257			−0.0377986			−0.0188993	+	0.999821i	$0.506016\pi$
$608$	−3.41397	+	4.51052i	−0.138455	+	0.182926i
$609$	0.861818			0.0349226
$610$	−21.8370	−	6.43705i	−0.884153	−	0.260629i
$611$	−9.14435	−	9.14435i	−0.369941	−	0.369941i
$612$	−13.6658	+	21.1657i	−0.552409	+	0.855572i
$613$	13.8162	−	13.8162i	0.558033	−	0.558033i	−0.370714	−	0.928747i	$-0.620887\pi$
$613$	13.8162	−	13.8162i	0.558033	−	0.558033i	0.928747	+	0.370714i	$0.120887\pi$
$614$	−9.03261	−	16.5837i	−0.364526	−	0.669265i
$615$		−	1.69976i		−	0.0685410i
$616$	−3.46300	+	46.3481i	−0.139528	+	1.86742i
$617$		−	10.1607i		−	0.409053i	−0.978861	−	0.204527i	$-0.934435\pi$
$617$		−	10.1607i		−	0.409053i	0.978861	−	0.204527i	$-0.0655655\pi$
$618$	1.70896	−	0.930811i	0.0687443	−	0.0374427i
$619$	−15.5085	+	15.5085i	−0.623337	+	0.623337i	−0.946383	−	0.323046i	$-0.895293\pi$
$619$	−15.5085	+	15.5085i	−0.623337	+	0.623337i	0.323046	+	0.946383i	$0.395293\pi$
$620$	−14.0948	+	3.03486i	−0.566059	+	0.121883i
$621$	2.89803	+	2.89803i	0.116294	+	0.116294i
$622$	9.74011	−	33.0422i	0.390543	−	1.32487i
$623$	−23.9379			−0.959052
$624$	−0.675360	+	0.304974i	−0.0270361	+	0.0122087i
$625$	24.7999			0.991997
$626$	0.802558	−	2.72259i	0.0320767	−	0.108816i
$627$	−0.417289	−	0.417289i	−0.0166649	−	0.0166649i
$628$	7.61382	+	35.3608i	0.303825	+	1.41105i
$629$	9.08605	−	9.08605i	0.362284	−	0.362284i
$630$	−23.9719	+	13.0567i	−0.955065	+	0.520192i
$631$		−	47.6049i		−	1.89512i	−0.319579	−	0.947560i	$-0.603541\pi$
$631$		−	47.6049i		−	1.89512i	0.319579	−	0.947560i	$-0.396459\pi$
$632$	−6.39682	−	7.42992i	−0.254452	−	0.295546i
$633$		−	0.514354i		−	0.0204437i
$634$	−11.0448	−	20.2782i	−0.438647	−	0.805349i
$635$	−3.92040	+	3.92040i	−0.155576	+	0.155576i
$636$	1.79629	+	1.15979i	0.0712277	+	0.0459888i
$637$	−1.76905	−	1.76905i	−0.0700921	−	0.0700921i
$638$	−21.9472	−	6.46955i	−0.868898	−	0.256132i
$639$	21.8042			0.862561
$640$	8.63030	+	23.6735i	0.341142	+	0.935779i
$641$	−10.1447			−0.400693			−0.200347	−	0.979725i	$-0.564207\pi$
$641$	−10.1447			−0.400693			−0.200347	+	0.979725i	$0.564207\pi$
$642$	1.62033	+	0.477637i	0.0639492	+	0.0188508i
$643$	6.24414	+	6.24414i	0.246245	+	0.246245i	0.819428	−	0.573183i	$-0.194291\pi$
$643$	6.24414	+	6.24414i	0.246245	+	0.246245i	−0.573183	+	0.819428i	$0.694291\pi$
$644$	32.0155	+	20.6711i	1.26159	+	0.814556i
$645$	1.22176	−	1.22176i	0.0481067	−	0.0481067i
$646$	−2.85070	−	5.23385i	−0.112159	−	0.205923i
$647$			12.5749i			0.494371i	0.968968	+	0.247186i	$0.0795058\pi$
$647$			12.5749i			0.494371i	−0.968968	+	0.247186i	$0.920494\pi$
$648$	−16.4289	−	19.0822i	−0.645390	−	0.749621i
$649$		−	6.73656i		−	0.264433i
$650$	−0.0877243	+	0.0477805i	−0.00344083	+	0.00187410i
$651$	−0.690962	+	0.690962i	−0.0270809	+	0.0270809i
$652$	1.63194	+	7.57920i	0.0639117	+	0.296824i
$653$	17.1734	+	17.1734i	0.672045	+	0.672045i	0.958187	−	0.286142i	$-0.0923728\pi$
$653$	17.1734	+	17.1734i	0.672045	+	0.672045i	−0.286142	+	0.958187i	$0.592373\pi$
$654$	−0.488607	+	1.65754i	−0.0191060	+	0.0648151i
$655$	−17.6114			−0.688133
$656$	26.7202	−	12.0661i	1.04325	−	0.471103i
$657$	−0.800613			−0.0312349
$658$	−8.42683	+	28.5870i	−0.328512	+	1.11444i
$659$	−22.3974	−	22.3974i	−0.872479	−	0.872479i	0.120263	−	0.992742i	$-0.461626\pi$
$659$	−22.3974	−	22.3974i	−0.872479	−	0.872479i	−0.992742	+	0.120263i	$0.961626\pi$
$660$	−2.56977	+	0.553319i	−0.100028	+	0.0215379i
$661$	−0.493264	+	0.493264i	−0.0191857	+	0.0191857i	−0.716635	−	0.697449i	$-0.754318\pi$
$661$	−0.493264	+	0.493264i	−0.0191857	+	0.0191857i	0.697449	+	0.716635i	$0.254318\pi$
$662$	7.13679	−	3.88717i	0.277379	−	0.151079i
$663$		−	0.780717i		−	0.0303205i
$664$	−3.15944	+	42.2852i	−0.122610	+	1.64098i
$665$		−	6.45733i		−	0.250404i
$666$	6.16526	+	11.3193i	0.238899	+	0.438615i
$667$	−13.2661	+	13.2661i	−0.513666	+	0.513666i
$668$	−19.2252	+	29.7760i	−0.743844	+	1.15207i
$669$	1.68094	+	1.68094i	0.0649891	+	0.0649891i
$670$	−36.2935	−	10.6985i	−1.40214	−	0.413320i
$671$	40.9651			1.58144
$672$	1.36170	+	1.03066i	0.0525286	+	0.0397584i
$673$	−5.93975			−0.228960			−0.114480	−	0.993426i	$-0.536520\pi$
$673$	−5.93975			−0.228960			−0.114480	+	0.993426i	$0.536520\pi$
$674$	−9.33997	−	2.75322i	−0.359762	−	0.106050i
$675$	0.0175067	+	0.0175067i	0.000673835	+	0.000673835i
$676$	10.6689	−	16.5241i	0.410344	−	0.635542i
$677$	6.17121	−	6.17121i	0.237179	−	0.237179i	−0.578502	−	0.815681i	$-0.696363\pi$
$677$	6.17121	−	6.17121i	0.237179	−	0.237179i	0.815681	+	0.578502i	$0.196363\pi$
$678$	−1.29247	−	2.37296i	−0.0496371	−	0.0911331i
$679$		−	41.9734i		−	1.61079i
$680$	−26.4734	−	1.97802i	−1.01521	−	0.0758536i
$681$		−	1.96643i		−	0.0753539i
$682$	22.7831	−	12.4092i	0.872411	−	0.475173i
$683$	−7.84732	+	7.84732i	−0.300269	+	0.300269i	−0.841119	−	0.540850i	$-0.818103\pi$
$683$	−7.84732	+	7.84732i	−0.300269	+	0.300269i	0.540850	+	0.841119i	$0.318103\pi$
$684$	5.84437	−	1.25840i	0.223465	−	0.0481161i
$685$	−0.0685216	−	0.0685216i	−0.00261808	−	0.00261808i
$686$	6.48522	−	22.0004i	0.247607	−	0.839978i
$687$	−1.02211			−0.0389961
$688$	27.8790	+	10.5331i	1.06288	+	0.401572i
$689$	18.2674			0.695932
$690$	−0.609429	+	2.06742i	−0.0232006	+	0.0787052i
$691$	−15.0980	−	15.0980i	−0.574356	−	0.574356i	0.358987	−	0.933343i	$-0.383122\pi$
$691$	−15.0980	−	15.0980i	−0.574356	−	0.574356i	−0.933343	+	0.358987i	$0.883122\pi$
$692$	8.21899	+	38.1714i	0.312439	+	1.45106i
$693$	34.7320	−	34.7320i	1.31936	−	1.31936i
$694$	−18.5202	+	10.0874i	−0.703019	+	0.382911i
$695$		−	3.96342i		−	0.150341i
$696$	−0.637136	+	0.548545i	−0.0241506	+	0.0207925i
$697$			30.8886i			1.16999i
$698$	−9.34111	−	17.1502i	−0.353566	−	0.649143i
$699$	−1.96413	+	1.96413i	−0.0742901	+	0.0742901i
$700$	0.193403	+	0.124872i	0.00730993	+	0.00471973i
$701$	−21.2859	−	21.2859i	−0.803957	−	0.803957i	0.179754	−	0.983712i	$-0.442470\pi$
$701$	−21.2859	−	21.2859i	−0.803957	−	0.803957i	−0.983712	+	0.179754i	$0.942470\pi$
$702$	1.50509	+	0.443666i	0.0568058	+	0.0167451i
$703$	−3.04909			−0.114999
$704$	−26.9403	−	36.4690i	−1.01535	−	1.37448i
$705$	−1.68561			−0.0634839
$706$	14.0171	+	4.13194i	0.527541	+	0.155507i
$707$	−10.8377	−	10.8377i	−0.407595	−	0.407595i
$708$	−0.207951	−	0.134266i	−0.00781528	−	0.00504601i
$709$	10.8171	−	10.8171i	0.406243	−	0.406243i	−0.474183	−	0.880426i	$-0.657257\pi$
$709$	10.8171	−	10.8171i	0.406243	−	0.406243i	0.880426	+	0.474183i	$0.157257\pi$
$710$	10.9895	+	20.1765i	0.412428	+	0.757212i
$711$			10.3614i			0.388582i
$712$	17.6971	−	15.2364i	0.663228	−	0.571009i
$713$		−	21.2722i		−	0.796650i
$714$	−1.58007	+	0.860609i	−0.0591325	+	0.0322075i
$715$	−15.8801	+	15.8801i	−0.593884	+	0.593884i
$716$	−4.67821	−	21.7270i	−0.174833	−	0.811975i
$717$	1.75288	+	1.75288i	0.0654623	+	0.0654623i
$718$	3.92062	−	13.3002i	0.146316	−	0.496361i
$719$	−35.2997			−1.31646			−0.658229	−	0.752818i	$-0.728694\pi$
$719$	−35.2997			−1.31646			−0.658229	+	0.752818i	$0.728694\pi$
$720$	9.41172	−	24.9108i	0.350754	−	0.928372i
$721$	−38.3154			−1.42694
$722$	−0.399868	+	1.35651i	−0.0148815	+	0.0504839i
$723$	−0.513392	−	0.513392i	−0.0190933	−	0.0190933i
$724$	35.7593	−	7.69963i	1.32898	−	0.286155i
$725$	−0.0801393	+	0.0801393i	−0.00297630	+	0.00297630i
$726$	2.73135	−	1.48768i	0.101370	−	0.0552129i
$727$			27.1592i			1.00728i	0.863914	+	0.503639i	$0.168006\pi$
$727$			27.1592i			1.00728i	−0.863914	+	0.503639i	$0.831994\pi$
$728$	14.5497	+	1.08711i	0.539247	+	0.0402911i
$729$			26.4163i			0.978381i
$730$	−0.403515	−	0.740848i	−0.0149348	−	0.0274200i
$731$	−22.2022	+	22.2022i	−0.821178	+	0.821178i
$732$	0.816469	−	1.26455i	0.0301776	−	0.0467391i
$733$	7.13581	+	7.13581i	0.263567	+	0.263567i	0.826501	−	0.562935i	$-0.190328\pi$
$733$	7.13581	+	7.13581i	0.263567	+	0.263567i	−0.562935	+	0.826501i	$0.690328\pi$
$734$	−9.99910	−	2.94751i	−0.369074	−	0.108795i
$735$	−0.326095			−0.0120282
$736$	−36.8259	+	5.09578i	−1.35742	+	0.187833i
$737$	68.0848			2.50794
$738$	−29.7200	−	8.76080i	−1.09401	−	0.322489i
$739$	28.5862	+	28.5862i	1.05156	+	1.05156i	0.998596	+	0.0529638i	$0.0168668\pi$
$739$	28.5862	+	28.5862i	1.05156	+	1.05156i	0.0529638	+	0.998596i	$0.483133\pi$
$740$	−7.36702	+	11.4101i	−0.270817	+	0.419442i
$741$	−0.130996	+	0.130996i	−0.00481227	+	0.00481227i
$742$	−20.1367	−	36.9708i	−0.739243	−	1.35724i
$743$			22.7289i			0.833841i	0.908943	+	0.416921i	$0.136891\pi$
$743$			22.7289i			0.833841i	−0.908943	+	0.416921i	$0.863109\pi$
$744$	0.0710276	−	0.950618i	0.00260400	−	0.0348514i
$745$			29.3455i			1.07514i
$746$	−17.5057	+	9.53477i	−0.640929	+	0.349093i
$747$	31.6874	−	31.6874i	1.15938	−	1.15938i
$748$	46.6988	−	10.0551i	1.70748	−	0.367650i
$749$	−23.5185	−	23.5185i	−0.859348	−	0.859348i
$750$	−0.467337	+	1.58539i	−0.0170647	+	0.0578902i
$751$	−36.5867			−1.33507			−0.667534	−	0.744579i	$-0.732650\pi$
$751$	−36.5867			−1.33507			−0.667534	+	0.744579i	$0.732650\pi$
$752$	−11.9657	−	26.4978i	−0.436344	−	0.966277i
$753$	1.83596			0.0669060
$754$	−2.03094	+	6.88972i	−0.0739623	+	0.250909i
$755$	−11.7300	−	11.7300i	−0.426897	−	0.426897i
$756$	−0.761184	−	3.53516i	−0.0276840	−	0.128572i
$757$	−24.8214	+	24.8214i	−0.902150	+	0.902150i	−0.995622	−	0.0934715i	$-0.970204\pi$
$757$	−24.8214	+	24.8214i	−0.902150	+	0.902150i	0.0934715	+	0.995622i	$0.470204\pi$
$758$	9.92401	−	5.40528i	0.360456	−	0.196328i
$759$		−	3.87837i		−	0.140776i
$760$	4.11007	+	4.77386i	0.149088	+	0.173166i
$761$			16.8000i			0.608998i	0.952513	+	0.304499i	$0.0984891\pi$
$761$			16.8000i			0.608998i	−0.952513	+	0.304499i	$0.901511\pi$
$762$	−0.175339	−	0.321920i	−0.00635186	−	0.0116619i
$763$	24.0587	−	24.0587i	0.870983	−	0.870983i
$764$	−8.65376	−	5.58739i	−0.313082	−	0.202145i
$765$	19.8384	+	19.8384i	0.717260	+	0.717260i
$766$	−1.32382	−	0.390233i	−0.0478315	−	0.0140997i
$767$	−2.11476			−0.0763594
$768$	−1.66270	+	0.104760i	−0.0599977	+	0.00378021i
$769$	7.03649			0.253742			0.126871	−	0.991919i	$-0.459506\pi$
$769$	7.03649			0.253742			0.126871	+	0.991919i	$0.459506\pi$
$770$	49.6445	+	14.6341i	1.78906	+	0.527376i
$771$	−2.03374	−	2.03374i	−0.0732432	−	0.0732432i
$772$	−25.4134	−	16.4084i	−0.914649	−	0.590552i
$773$	8.12055	−	8.12055i	0.292076	−	0.292076i	−0.545824	−	0.837900i	$-0.683783\pi$
$773$	8.12055	−	8.12055i	0.292076	−	0.292076i	0.837900	+	0.545824i	$0.183783\pi$
$774$	−15.0651	−	27.6593i	−0.541504	−	0.994194i
$775$		−	0.128503i		−	0.00461598i
$776$	26.7160	+	31.0306i	0.959047	+	1.11394i
$777$			0.920501i			0.0330228i
$778$	11.8473	−	6.45284i	0.424747	−	0.231346i
$779$	5.18279	−	5.18279i	0.185693	−	0.185693i
$780$	0.173699	+	0.806709i	0.00621943	+	0.0288848i
$781$	−29.2330	−	29.2330i	−1.04604	−	1.04604i
$782$	11.0747	−	37.5698i	0.396032	−	1.34349i
$783$	1.78026			0.0636211
$784$	−2.31486	−	5.12622i	−0.0826734	−	0.183079i
$785$	40.2798			1.43765
$786$	0.329239	−	1.11690i	0.0117436	−	0.0398387i
$787$	19.0607	+	19.0607i	0.679439	+	0.679439i	0.959873	−	0.280434i	$-0.0904785\pi$
$787$	19.0607	+	19.0607i	0.679439	+	0.679439i	−0.280434	+	0.959873i	$0.590478\pi$
$788$	−36.8193	+	7.92786i	−1.31163	+	0.282418i
$789$	−0.676087	+	0.676087i	−0.0240693	+	0.0240693i
$790$	−9.58792	+	5.22222i	−0.341123	+	0.185798i
$791$			53.2026i			1.89167i
$792$	−3.57028	+	47.7839i	−0.126865	+	1.69793i
$793$		−	12.8598i		−	0.456666i
$794$	23.0833	+	42.3806i	0.819196	+	1.50403i
$795$	1.68365	−	1.68365i	0.0597130	−	0.0597130i
$796$	15.0996	−	23.3863i	0.535191	−	0.828905i
$797$	6.44270	+	6.44270i	0.228212	+	0.228212i	0.811945	−	0.583733i	$-0.198409\pi$
$797$	6.44270	+	6.44270i	0.228212	+	0.228212i	−0.583733	+	0.811945i	$0.698409\pi$
$798$	0.409520	+	0.120718i	0.0144969	+	0.00427335i
$799$	30.6315			1.08367
$800$	−0.222462	+	0.0307831i	−0.00786522	+	0.00108835i
$801$	−24.6795			−0.872007
$802$	46.5787	+	13.7304i	1.64475	+	0.484836i
$803$	1.07338	+	1.07338i	0.0378789	+	0.0378789i
$804$	1.35699	−	2.10171i	0.0478573	−	0.0741216i
$805$	30.0079	−	30.0079i	1.05764	−	1.05764i
$806$	−3.89553	−	7.15213i	−0.137214	−	0.251923i
$807$			1.89131i			0.0665774i
$808$	14.9105	+	1.11407i	0.524548	+	0.0391928i
$809$			13.6006i			0.478172i	0.970998	+	0.239086i	$0.0768477\pi$
$809$			13.6006i			0.478172i	−0.970998	+	0.239086i	$0.923152\pi$
$810$	−24.6246	+	13.4122i	−0.865221	+	0.471257i
$811$	21.8828	−	21.8828i	0.768408	−	0.768408i	−0.209418	−	0.977826i	$-0.567157\pi$
$811$	21.8828	−	21.8828i	0.768408	−	0.768408i	0.977826	+	0.209418i	$0.0671569\pi$
$812$	16.1826	−	3.48441i	0.567899	−	0.122279i
$813$	−0.136066	−	0.136066i	−0.00477204	−	0.00477204i
$814$	6.91008	−	23.4417i	0.242198	−	0.821630i
$815$	8.63353			0.302419
$816$	0.620356	−	1.64195i	0.0217168	−	0.0574798i
$817$	7.45060			0.260664
$818$	13.8082	−	46.8428i	0.482793	−	1.63782i
$819$	−10.9031	−	10.9031i	−0.380986	−	0.380986i
$820$	−6.87230	−	31.9170i	−0.239991	−	1.11459i
$821$	−25.5848	+	25.5848i	−0.892915	+	0.892915i	−0.994797	−	0.101881i	$-0.967514\pi$
$821$	−25.5848	+	25.5848i	−0.892915	+	0.892915i	0.101881	+	0.994797i	$0.467514\pi$
$822$	0.00562659	−	0.00306462i	0.000196250	−	0.000106891i
$823$			15.7014i			0.547317i	0.961827	+	0.273659i	$0.0882338\pi$
$823$			15.7014i			0.547317i	−0.961827	+	0.273659i	$0.911766\pi$
$824$	28.3263	−	24.3876i	0.986792	−	0.849583i
$825$		−	0.0234289i		−	0.000815689i
$826$	2.33116	+	4.27998i	0.0811116	+	0.148920i
$827$	−38.1093	+	38.1093i	−1.32519	+	1.32519i	−0.415680	+	0.909511i	$0.636456\pi$
$827$	−38.1093	+	38.1093i	−1.32519	+	1.32519i	−0.909511	+	0.415680i	$0.863544\pi$
$828$	33.0073	+	21.3115i	1.14708	+	0.740626i
$829$	−25.8722	−	25.8722i	−0.898578	−	0.898578i	0.0967323	−	0.995310i	$-0.469161\pi$
$829$	−25.8722	−	25.8722i	−0.898578	−	0.898578i	−0.995310	+	0.0967323i	$0.969161\pi$
$830$	45.2927	+	13.3513i	1.57213	+	0.463429i
$831$	−1.83560			−0.0636761
$832$	−11.4484	+	8.45715i	−0.396903	+	0.293199i
$833$	5.92591			0.205320
$834$	0.251358	+	0.0740948i	0.00870382	+	0.00256569i
$835$	27.9088	+	27.9088i	0.965824	+	0.965824i
$836$	−9.52271	−	6.14843i	−0.329350	−	0.212648i
$837$	−1.42732	+	1.42732i	−0.0493353	+	0.0493353i
$838$	20.7014	+	38.0075i	0.715118	+	1.31295i
$839$		−	2.49013i		−	0.0859687i	−0.999076	−	0.0429844i	$-0.986313\pi$
$839$		−	2.49013i		−	0.0859687i	0.999076	−	0.0429844i	$-0.0136866\pi$
$840$	1.44120	−	1.24081i	0.0497260	−	0.0428118i
$841$		−	20.8507i		−	0.718988i
$842$	13.8313	−	7.53345i	0.476658	−	0.259620i
$843$	−1.75885	+	1.75885i	−0.0605778	+	0.0605778i
$844$	−2.07959	−	9.65820i	−0.0715823	−	0.332449i
$845$	−15.4879	−	15.4879i	−0.532800	−	0.532800i
$846$	−8.68788	+	29.4726i	−0.298696	+	1.01329i
$847$	−61.2378			−2.10416
$848$	38.4187	+	14.5152i	1.31931	+	0.498455i
$849$	0.237115			0.00813777
$850$	0.0669014	−	0.226955i	0.00229470	−	0.00778451i
$851$	−14.1694	−	14.1694i	−0.485722	−	0.485722i
$852$	−1.48503	+	0.319754i	−0.0508763	+	0.0109546i
$853$	−30.4882	+	30.4882i	−1.04389	+	1.04389i	−0.0449036	+	0.998991i	$0.514298\pi$
$853$	−30.4882	+	30.4882i	−1.04389	+	1.04389i	−0.998991	+	0.0449036i	$0.985702\pi$
$854$	−26.0266	+	14.1758i	−0.890612	+	0.485086i
$855$		−	6.65737i		−	0.227677i
$856$	32.3565	+	2.41759i	1.10592	+	0.0826317i
$857$		−	23.1195i		−	0.789746i	−0.918736	−	0.394873i	$-0.870789\pi$
$857$		−	23.1195i		−	0.789746i	0.918736	−	0.394873i	$-0.129211\pi$
$858$	−0.710237	−	1.30398i	−0.0242471	−	0.0445173i
$859$	−6.65127	+	6.65127i	−0.226939	+	0.226939i	−0.811412	−	0.584474i	$-0.801301\pi$
$859$	−6.65127	+	6.65127i	−0.226939	+	0.226939i	0.584474	+	0.811412i	$0.301301\pi$
$860$	18.0017	−	27.8811i	0.613852	−	0.950736i
$861$	−1.56465	−	1.56465i	−0.0533232	−	0.0533232i
$862$	41.7722	+	12.3135i	1.42277	+	0.419400i
$863$	38.5215			1.31129			0.655644	−	0.755070i	$-0.272397\pi$
$863$	38.5215			1.31129			0.655644	+	0.755070i	$0.272397\pi$
$864$	2.81286	+	2.12903i	0.0956953	+	0.0724309i
$865$	43.4813			1.47841
$866$	40.6603	+	11.9858i	1.38169	+	0.407292i
$867$	0.0559454	+	0.0559454i	0.00190001	+	0.00190001i
$868$	−10.1808	+	15.7680i	−0.345558	+	0.535202i
$869$	13.8915	−	13.8915i	0.471238	−	0.471238i
$870$	0.447819	+	0.822190i	0.0151825	+	0.0278748i
$871$		−	21.3733i		−	0.724208i
$872$	−2.47312	+	33.0997i	−0.0837504	+	1.12090i
$873$		−	43.2737i		−	1.46459i
$874$	−8.16205	+	4.44559i	−0.276085	+	0.150374i
$875$	23.0114	−	23.0114i	0.777926	−	0.777926i
$876$	0.0545278	−	0.0117408i	0.00184232	−	0.000396686i
$877$	12.1977	+	12.1977i	0.411887	+	0.411887i	0.882395	−	0.470509i	$-0.155930\pi$
$877$	12.1977	+	12.1977i	0.411887	+	0.411887i	−0.470509	+	0.882395i	$0.655930\pi$
$878$	−8.25654	+	28.0094i	−0.278645	+	0.945271i
$879$	−0.472603			−0.0159405
$880$	−46.0164	+	20.7797i	−1.55121	+	0.700484i
$881$	−26.8757			−0.905467			−0.452733	−	0.891646i	$-0.649551\pi$
$881$	−26.8757			−0.905467			−0.452733	+	0.891646i	$0.649551\pi$
$882$	−1.68074	+	5.70171i	−0.0565934	+	0.191987i
$883$	−20.8890	−	20.8890i	−0.702971	−	0.702971i	0.262076	−	0.965047i	$-0.415593\pi$
$883$	−20.8890	−	20.8890i	−0.702971	−	0.702971i	−0.965047	+	0.262076i	$0.915593\pi$
$884$	−3.15652	−	14.6598i	−0.106165	−	0.493062i
$885$	−0.194911	+	0.194911i	−0.00655185	+	0.00655185i
$886$	1.81358	−	0.987797i	0.0609285	−	0.0331857i
$887$		−	42.1390i		−	1.41489i	−0.706770	−	0.707444i	$-0.749848\pi$
$887$		−	42.1390i		−	1.41489i	0.706770	−	0.707444i	$-0.250152\pi$
$888$	−0.585897	−	0.680520i	−0.0196614	−	0.0228368i
$889$			7.21755i			0.242069i
$890$	−12.4387	−	22.8372i	−0.416945	−	0.765505i
$891$	35.6776	−	35.6776i	1.19524	−	1.19524i
$892$	38.3599	+	24.7674i	1.28438	+	0.829275i
$893$	−5.13965	−	5.13965i	−0.171992	−	0.171992i
$894$	−1.86108	−	0.548604i	−0.0622437	−	0.0183481i
$895$	−24.7494			−0.827280
$896$	29.7361	+	13.8475i	0.993413	+	0.462612i
$897$	−1.21751			−0.0406514
$898$	2.35423	+	0.693975i	0.0785616	+	0.0231582i
$899$	−6.53373	−	6.53373i	−0.217912	−	0.217912i
$900$	0.199394	+	0.128741i	0.00664647	+	0.00429136i
$901$	−30.5958	+	30.5958i	−1.01930	+	1.01930i
$902$	28.1001	+	51.5914i	0.935631	+	1.71780i
$903$		−	2.24929i		−	0.0748517i
$904$	−33.8633	−	39.3323i	−1.12628	−	1.30817i
$905$		−	40.7337i		−	1.35404i
$906$	0.963197	−	0.524621i	0.0320001	−	0.0174294i
$907$	9.90954	−	9.90954i	0.329041	−	0.329041i	−0.523181	−	0.852222i	$-0.675255\pi$
$907$	9.90954	−	9.90954i	0.329041	−	0.329041i	0.852222	+	0.523181i	$0.175255\pi$
$908$	−7.95048	−	36.9243i	−0.263846	−	1.22538i
$909$	−11.1735	−	11.1735i	−0.370601	−	0.370601i
$910$	4.59397	−	15.5845i	0.152288	−	0.516621i
$911$	12.4711			0.413187			0.206594	−	0.978427i	$-0.433762\pi$
$911$	12.4711			0.413187			0.206594	+	0.978427i	$0.433762\pi$
$912$	−0.379592	+	0.171413i	−0.0125695	+	0.00567605i
$913$	−84.9668			−2.81199
$914$	3.18821	−	10.8156i	0.105457	−	0.357749i
$915$	−1.18525	−	1.18525i	−0.0391833	−	0.0391833i
$916$	−19.1926	+	4.13251i	−0.634140	+	0.136542i
$917$	−16.2115	+	16.2115i	−0.535351	+	0.535351i
$918$	−3.26394	+	1.77776i	−0.107726	+	0.0586748i
$919$			46.2832i			1.52674i	0.645961	+	0.763371i	$0.276457\pi$
$919$			46.2832i			1.52674i	−0.645961	+	0.763371i	$0.723543\pi$
$920$	−3.08467	+	41.2845i	−0.101699	+	1.36111i
$921$		−	1.39039i		−	0.0458149i
$922$	1.09089	+	2.00286i	0.0359265	+	0.0659605i
$923$	−9.17688	+	9.17688i	−0.302061	+	0.302061i
$924$	−1.85617	+	2.87485i	−0.0610636	+	0.0945755i
$925$	−0.0855963	−	0.0855963i	−0.00281439	−	0.00281439i
$926$	−3.91588	−	1.15431i	−0.128684	−	0.0379331i
$927$	−39.5023			−1.29743
$928$	−9.74588	+	12.8762i	−0.319924	+	0.422682i
$929$	−49.6022			−1.62740			−0.813698	−	0.581288i	$-0.802549\pi$
$929$	−49.6022			−1.62740			−0.813698	+	0.581288i	$0.802549\pi$
$930$	−1.01823	−	0.300151i	−0.0333890	−	0.00984235i
$931$	−0.994306	−	0.994306i	−0.0325871	−	0.0325871i
$932$	−28.9399	+	44.8222i	−0.947957	+	1.46820i
$933$	1.79344	−	1.79344i	0.0587147	−	0.0587147i
$934$	13.9134	+	25.5448i	0.455261	+	0.835852i
$935$		−	53.1949i		−	1.73966i
$936$	15.0004	+	1.12079i	0.490304	+	0.0366342i
$937$		−	29.9841i		−	0.979539i	−0.871852	−	0.489770i	$-0.837081\pi$
$937$		−	29.9841i		−	0.979539i	0.871852	−	0.489770i	$-0.162919\pi$
$938$	−43.2568	+	23.5605i	−1.41238	+	0.769278i
$939$	0.147775	−	0.147775i	0.00482245	−	0.00482245i
$940$	−31.6513	+	6.81510i	−1.03235	+	0.222284i
$941$	30.3505	+	30.3505i	0.989397	+	0.989397i	0.999944	−	0.0105476i	$-0.00335746\pi$
$941$	30.3505	+	30.3505i	0.989397	+	0.989397i	−0.0105476	+	0.999944i	$0.503357\pi$
$942$	−0.753017	+	2.55452i	−0.0245346	+	0.0832308i
$943$	48.1699			1.56863
$944$	−4.44761	−	1.68038i	−0.144757	−	0.0546918i
$945$	−4.02693			−0.130996
$946$	−16.8851	+	57.2808i	−0.548983	+	1.86236i
$947$	17.6784	+	17.6784i	0.574470	+	0.574470i	0.933374	−	0.358904i	$-0.116850\pi$
$947$	17.6784	+	17.6784i	0.574470	+	0.574470i	−0.358904	+	0.933374i	$0.616850\pi$
$948$	−0.151948	−	0.705688i	−0.00493503	−	0.0229197i
$949$	0.336959	−	0.336959i	0.0109382	−	0.0109382i
$950$	−0.0493062	+	0.0268554i	−0.00159970	+	0.000871305i
$951$		−	1.70013i		−	0.0551305i
$952$	−26.1899	+	22.5483i	−0.848819	+	0.730795i
$953$			3.65186i			0.118296i	0.998249	+	0.0591478i	$0.0188383\pi$
$953$			3.65186i			0.118296i	−0.998249	+	0.0591478i	$0.981162\pi$
$954$	−20.7606	−	38.1161i	−0.672148	−	1.23405i
$955$	−8.11110	+	8.11110i	−0.262469	+	0.262469i
$956$	40.0014	+	25.8273i	1.29374	+	0.835313i
$957$	−1.19124	−	1.19124i	−0.0385072	−	0.0385072i
$958$	−16.9996	−	5.01110i	−0.549231	−	0.161901i
$959$	−0.126150			−0.00407360
$960$	−0.275697	+	1.83464i	−0.00889809	+	0.0592126i
$961$	−20.5232			−0.662038
$962$	−7.35886	−	2.16923i	−0.237259	−	0.0699387i
$963$	−24.2471	−	24.2471i	−0.781352	−	0.781352i
$964$	−11.7158	−	7.56444i	−0.377341	−	0.243634i
$965$	−23.8198	+	23.8198i	−0.766786	+	0.766786i
$966$	1.34210	+	2.46407i	0.0431813	+	0.0792802i
$967$			32.1389i			1.03352i	0.856131	+	0.516759i	$0.172862\pi$
$967$			32.1389i			1.03352i	−0.856131	+	0.516759i	$0.827138\pi$
$968$	45.2727	−	38.9777i	1.45512	−	1.25279i
$969$		−	0.438808i		−	0.0140966i
$970$	40.0434	−	21.8103i	1.28572	−	0.700287i
$971$	27.0698	−	27.0698i	0.868711	−	0.868711i	−0.123619	−	0.992330i	$-0.539450\pi$
$971$	27.0698	−	27.0698i	0.868711	−	0.868711i	0.992330	+	0.123619i	$0.0394500\pi$
$972$	−1.17786	−	5.47031i	−0.0377798	−	0.175460i
$973$	−3.64838	−	3.64838i	−0.116962	−	0.116962i
$974$	−0.780413	+	2.64746i	−0.0250061	+	0.0848302i
$975$	−0.00735484			−0.000235544
$976$	10.2184	−	27.0459i	0.327083	−	0.865719i
$977$	−13.6053			−0.435271			−0.217635	−	0.976030i	$-0.569834\pi$
$977$	−13.6053			−0.435271			−0.217635	+	0.976030i	$0.569834\pi$
$978$	−0.161401	+	0.547534i	−0.00516103	+	0.0175082i
$979$	33.0879	+	33.0879i	1.05749	+	1.05749i
$980$	−6.12320	+	1.31844i	−0.195598	+	0.0421159i
$981$	24.8040	−	24.8040i	0.791931	−	0.791931i
$982$	28.9281	−	15.7562i	0.923134	−	0.502800i
$983$			4.40279i			0.140427i	0.997532	+	0.0702136i	$0.0223681\pi$
$983$			4.40279i			0.140427i	−0.997532	+	0.0702136i	$0.977632\pi$
$984$	2.15263	+	0.160839i	0.0686234	+	0.00512736i
$985$			41.9411i			1.33636i
$986$	−8.13792	−	14.9411i	−0.259164	−	0.475821i
$987$	−1.55163	+	1.55163i	−0.0493889	+	0.0493889i
$988$	−1.93013	+	2.98939i	−0.0614056	+	0.0951052i
$989$	34.6237	+	34.6237i	1.10097	+	1.10097i
$990$	51.1824	+	15.0874i	1.62668	+	0.479510i
$991$	0.414992			0.0131827			0.00659133	−	0.999978i	$-0.497902\pi$
$991$	0.414992			0.0131827			0.00659133	+	0.999978i	$0.497902\pi$
$992$	−2.50974	−	18.1372i	−0.0796842	−	0.575858i
$993$	0.598351			0.0189881
$994$	28.6887	+	8.45681i	0.909952	+	0.268234i
$995$	−21.9198	−	21.9198i	−0.694904	−	0.694904i
$996$	−1.69346	+	2.62284i	−0.0536594	+	0.0831079i
$997$	−7.87298	+	7.87298i	−0.249340	+	0.249340i	−0.820700	−	0.571360i	$-0.806416\pi$
$997$	−7.87298	+	7.87298i	−0.249340	+	0.249340i	0.571360	+	0.820700i	$0.306416\pi$
$998$	16.2225	+	29.7844i	0.513516	+	0.942807i
$999$			1.90148i			0.0601601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.32	✓	68
4.3	odd	2		1216.2.k.b.913.18		68
16.5	even	4	inner	304.2.k.b.229.32	yes	68
16.11	odd	4		1216.2.k.b.305.18		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.32	✓	68	1.1	even	1	trivial
304.2.k.b.229.32	yes	68	16.5	even	4	inner
1216.2.k.b.305.18		68	16.11	odd	4
1216.2.k.b.913.18		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)

\(f(q)\)	\(=\)	\(q+(1.35651 + 0.399868i) q^{2} +(0.0736275 + 0.0736275i) q^{3} +(1.68021 + 1.08484i) q^{4} +(1.57485 - 1.57485i) q^{5} +(0.0704349 + 0.129317i) q^{6} -2.89934i q^{7} +(1.84542 + 2.14346i) q^{8} -2.98916i q^{9} +O(q^{10})\)	\(q+(1.35651 + 0.399868i) q^{2} +(0.0736275 + 0.0736275i) q^{3} +(1.68021 + 1.08484i) q^{4} +(1.57485 - 1.57485i) q^{5} +(0.0704349 + 0.129317i) q^{6} -2.89934i q^{7} +(1.84542 + 2.14346i) q^{8} -2.98916i q^{9} +(2.76602 - 1.50656i) q^{10} +(-4.00758 + 4.00758i) q^{11} +(0.0438354 + 0.203584i) q^{12} +(1.25807 + 1.25807i) q^{13} +(1.15935 - 3.93297i) q^{14} +0.231905 q^{15} +(1.64622 + 3.64554i) q^{16} -4.21424 q^{17} +(1.19527 - 4.05481i) q^{18} +(0.707107 + 0.707107i) q^{19} +(4.35455 - 0.937613i) q^{20} +(0.213471 - 0.213471i) q^{21} +(-7.03880 + 3.83380i) q^{22} +6.57200i q^{23} +(-0.0219438 + 0.293691i) q^{24} +0.0397008i q^{25} +(1.20351 + 2.20963i) q^{26} +(0.440967 - 0.440967i) q^{27} +(3.14533 - 4.87150i) q^{28} +(2.01858 + 2.01858i) q^{29} +(0.314580 + 0.0927311i) q^{30} -3.23679 q^{31} +(0.775377 + 5.60346i) q^{32} -0.590136 q^{33} +(-5.71664 - 1.68514i) q^{34} +(-4.56602 - 4.56602i) q^{35} +(3.24277 - 5.02242i) q^{36} +(-2.15603 + 2.15603i) q^{37} +(0.676445 + 1.24194i) q^{38} +0.185257i q^{39} +(6.28189 + 0.469366i) q^{40} -7.32957i q^{41} +(0.374935 - 0.204214i) q^{42} +(5.26837 - 5.26837i) q^{43} +(-11.0812 + 2.38598i) q^{44} +(-4.70747 - 4.70747i) q^{45} +(-2.62793 + 8.91495i) q^{46} -7.26857 q^{47} +(-0.147205 + 0.389619i) q^{48} -1.40616 q^{49} +(-0.0158751 + 0.0538544i) q^{50} +(-0.310284 - 0.310284i) q^{51} +(0.749011 + 3.47863i) q^{52} +(7.26011 - 7.26011i) q^{53} +(0.774502 - 0.421845i) q^{54} +12.6227i q^{55} +(6.21461 - 5.35050i) q^{56} +0.104125i q^{57} +(1.93105 + 3.54538i) q^{58} +(-0.840479 + 0.840479i) q^{59} +(0.389649 + 0.251580i) q^{60} +(-5.11095 - 5.11095i) q^{61} +(-4.39073 - 1.29429i) q^{62} -8.66658 q^{63} +(-1.18884 + 7.91117i) q^{64} +3.96253 q^{65} +(-0.800522 - 0.235976i) q^{66} +(-8.49452 - 8.49452i) q^{67} +(-7.08082 - 4.57180i) q^{68} +(-0.483880 + 0.483880i) q^{69} +(-4.36803 - 8.01963i) q^{70} +7.29443i q^{71} +(6.40714 - 5.51626i) q^{72} -0.267839i q^{73} +(-3.78680 + 2.06254i) q^{74} +(-0.00292307 + 0.00292307i) q^{75} +(0.420988 + 1.95519i) q^{76} +(11.6193 + 11.6193i) q^{77} +(-0.0740782 + 0.251302i) q^{78} -3.46632 q^{79} +(8.33373 + 3.14862i) q^{80} -8.90254 q^{81} +(2.93086 - 9.94260i) q^{82} +(10.6008 + 10.6008i) q^{83} +(0.590260 - 0.127094i) q^{84} +(-6.63680 + 6.63680i) q^{85} +(9.25322 - 5.03992i) q^{86} +0.297246i q^{87} +(-15.9857 - 1.19441i) q^{88} -8.25634i q^{89} +(-4.50334 - 8.26808i) q^{90} +(3.64756 - 3.64756i) q^{91} +(-7.12960 + 11.0423i) q^{92} +(-0.238317 - 0.238317i) q^{93} +(-9.85985 - 2.90647i) q^{94} +2.22717 q^{95} +(-0.355480 + 0.469658i) q^{96} +14.4769 q^{97} +(-1.90747 - 0.562278i) q^{98} +(11.9793 + 11.9793i) 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

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