LMFDB - Embedded newform 315.2.be.c.311.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.4
Character	$\chi$	$=$	315.311
Dual form			315.2.be.c.236.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67628 - 0.967799i) q^{2} +(-1.71487 - 0.243339i) q^{3} +(0.873269 + 1.51255i) q^{4} -1.00000 q^{5} +(2.63910 + 2.06755i) q^{6} +(2.28906 - 1.32673i) q^{7} +0.490599i q^{8} +(2.88157 + 0.834589i) q^{9} +O(q^{10})$	\(q+(-1.67628 - 0.967799i) q^{2} +(-1.71487 - 0.243339i) q^{3} +(0.873269 + 1.51255i) q^{4} -1.00000 q^{5} +(2.63910 + 2.06755i) q^{6} +(2.28906 - 1.32673i) q^{7} +0.490599i q^{8} +(2.88157 + 0.834589i) q^{9} +(1.67628 + 0.967799i) q^{10} +4.75489i q^{11} +(-1.12948 - 2.80632i) q^{12} +(-1.44470 - 0.834098i) q^{13} +(-5.12110 + 0.00860774i) q^{14} +(1.71487 + 0.243339i) q^{15} +(2.22134 - 3.84747i) q^{16} +(0.551181 - 0.954674i) q^{17} +(-4.02260 - 4.18778i) q^{18} +(3.85705 - 2.22687i) q^{19} +(-0.873269 - 1.51255i) q^{20} +(-4.24829 + 1.71815i) q^{21} +(4.60178 - 7.97051i) q^{22} -8.57962i q^{23} +(0.119382 - 0.841315i) q^{24} +1.00000 q^{25} +(1.61448 + 2.79636i) q^{26} +(-4.73844 - 2.13241i) q^{27} +(4.00570 + 2.30372i) q^{28} +(2.66862 - 1.54073i) q^{29} +(-2.63910 - 2.06755i) q^{30} +(-3.43483 + 1.98310i) q^{31} +(-6.59742 + 3.80902i) q^{32} +(1.15705 - 8.15402i) q^{33} +(-1.84786 + 1.06686i) q^{34} +(-2.28906 + 1.32673i) q^{35} +(1.25403 + 5.08733i) q^{36} +(0.755979 + 1.30939i) q^{37} -8.62064 q^{38} +(2.27451 + 1.78192i) q^{39} -0.490599i q^{40} +(3.80002 - 6.58183i) q^{41} +(8.78413 + 1.23140i) q^{42} +(0.0488091 + 0.0845398i) q^{43} +(-7.19199 + 4.15230i) q^{44} +(-2.88157 - 0.834589i) q^{45} +(-8.30335 + 14.3818i) q^{46} +(2.75934 - 4.77933i) q^{47} +(-4.74555 + 6.05739i) q^{48} +(3.47960 - 6.07391i) q^{49} +(-1.67628 - 0.967799i) q^{50} +(-1.17751 + 1.50302i) q^{51} -2.91357i q^{52} +(11.1220 + 6.42128i) q^{53} +(5.87919 + 8.16037i) q^{54} -4.75489i q^{55} +(0.650891 + 1.12301i) q^{56} +(-7.15623 + 2.88022i) q^{57} -5.96445 q^{58} +(-6.68767 - 11.5834i) q^{59} +(1.12948 + 2.80632i) q^{60} +(9.30116 + 5.37003i) q^{61} +7.67696 q^{62} +(7.70337 - 1.91263i) q^{63} +5.86011 q^{64} +(1.44470 + 0.834098i) q^{65} +(-9.83099 + 12.5486i) q^{66} +(2.53008 + 4.38223i) q^{67} +1.92532 q^{68} +(-2.08775 + 14.7130i) q^{69} +(5.12110 - 0.00860774i) q^{70} +4.66184i q^{71} +(-0.409449 + 1.41370i) q^{72} +(3.66562 + 2.11635i) q^{73} -2.92654i q^{74} +(-1.71487 - 0.243339i) q^{75} +(6.73648 + 3.88931i) q^{76} +(6.30843 + 10.8842i) q^{77} +(-2.08816 - 5.18826i) q^{78} +(3.10659 - 5.38077i) q^{79} +(-2.22134 + 3.84747i) q^{80} +(7.60692 + 4.80986i) q^{81} +(-12.7398 + 7.35531i) q^{82} +(-2.60200 - 4.50680i) q^{83} +(-6.30868 - 4.92533i) q^{84} +(-0.551181 + 0.954674i) q^{85} -0.188950i q^{86} +(-4.95125 + 1.99277i) q^{87} -2.33275 q^{88} +(-7.15835 - 12.3986i) q^{89} +(4.02260 + 4.18778i) q^{90} +(-4.41363 + 0.00741859i) q^{91} +(12.9771 - 7.49232i) q^{92} +(6.37285 - 2.56493i) q^{93} +(-9.25085 + 5.34098i) q^{94} +(-3.85705 + 2.22687i) q^{95} +(12.2406 - 4.92658i) q^{96} +(-1.33124 + 0.768589i) q^{97} +(-11.7111 + 6.81400i) q^{98} +(-3.96838 + 13.7016i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.67628	−	0.967799i	−1.18531	−	0.684337i	−0.228070	−	0.973645i	$-0.573242\pi$
$2$	−1.67628	−	0.967799i	−1.18531	−	0.684337i	−0.957236	+	0.289307i	$0.906575\pi$
$3$	−1.71487	−	0.243339i	−0.990082	−	0.140492i
$3$	−1.71487	−	0.243339i	−0.990082	−	0.140492i
$4$	0.873269	+	1.51255i	0.436635	+	0.756273i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	2.63910	+	2.06755i	1.07741	+	0.844075i
$7$	2.28906	−	1.32673i	0.865184	−	0.501455i
$7$	2.28906	−	1.32673i	0.865184	−	0.501455i
$8$			0.490599i			0.173453i
$9$	2.88157	+	0.834589i	0.960524	+	0.278196i
$10$	1.67628	+	0.967799i	0.530085	+	0.306045i
$11$			4.75489i			1.43365i	0.697252	+	0.716826i	$0.254406\pi$
$11$			4.75489i			1.43365i	−0.697252	+	0.716826i	$0.745594\pi$
$12$	−1.12948	−	2.80632i	−0.326054	−	0.810116i
$13$	−1.44470	−	0.834098i	−0.400688	−	0.231337i	0.286093	−	0.958202i	$-0.407643\pi$
$13$	−1.44470	−	0.834098i	−0.400688	−	0.231337i	−0.686781	+	0.726865i	$0.740977\pi$
$14$	−5.12110	+	0.00860774i	−1.36867	+	0.00230051i
$15$	1.71487	+	0.243339i	0.442778	+	0.0628297i
$16$	2.22134	−	3.84747i	0.555335	−	0.961868i
$17$	0.551181	−	0.954674i	0.133681	−	0.231542i	−0.791412	−	0.611283i	$-0.790654\pi$
$17$	0.551181	−	0.954674i	0.133681	−	0.231542i	0.925093	+	0.379741i	$0.123987\pi$
$18$	−4.02260	−	4.18778i	−0.948136	−	0.987070i
$19$	3.85705	−	2.22687i	0.884867	−	0.510878i	0.0126072	−	0.999921i	$-0.495987\pi$
$19$	3.85705	−	2.22687i	0.884867	−	0.510878i	0.872260	+	0.489042i	$0.162654\pi$
$20$	−0.873269	−	1.51255i	−0.195269	−	0.338216i
$21$	−4.24829	+	1.71815i	−0.927053	+	0.374930i
$22$	4.60178	−	7.97051i	0.981102	−	1.69932i
$23$		−	8.57962i		−	1.78897i	−0.447093	−	0.894487i	$-0.647541\pi$
$23$		−	8.57962i		−	1.78897i	0.447093	−	0.894487i	$-0.352459\pi$
$24$	0.119382	−	0.841315i	0.0243687	−	0.171733i
$25$	1.00000			0.200000
$26$	1.61448	+	2.79636i	0.316625	+	0.548411i
$27$	−4.73844	−	2.13241i	−0.911913	−	0.410383i
$28$	4.00570	+	2.30372i	0.757006	+	0.435363i
$29$	2.66862	−	1.54073i	0.495549	−	0.286106i	−0.231324	−	0.972877i	$-0.574306\pi$
$29$	2.66862	−	1.54073i	0.495549	−	0.286106i	0.726874	+	0.686771i	$0.240973\pi$
$30$	−2.63910	−	2.06755i	−0.481831	−	0.377482i
$31$	−3.43483	+	1.98310i	−0.616913	+	0.356175i	−0.775666	−	0.631143i	$-0.782586\pi$
$31$	−3.43483	+	1.98310i	−0.616913	+	0.356175i	0.158753	+	0.987318i	$0.449253\pi$
$32$	−6.59742	+	3.80902i	−1.16627	+	0.673346i
$33$	1.15705	−	8.15402i	0.201416	−	1.41943i
$34$	−1.84786	+	1.06686i	−0.316906	+	0.182966i
$35$	−2.28906	+	1.32673i	−0.386922	+	0.224257i
$36$	1.25403	+	5.08733i	0.209006	+	0.847889i
$37$	0.755979	+	1.30939i	0.124282	+	0.215263i	0.921452	−	0.388492i	$-0.127004\pi$
$37$	0.755979	+	1.30939i	0.124282	+	0.215263i	−0.797170	+	0.603755i	$0.793671\pi$
$38$	−8.62064			−1.39845
$39$	2.27451	+	1.78192i	0.364213	+	0.285336i
$40$		−	0.490599i		−	0.0775706i
$41$	3.80002	−	6.58183i	0.593464	−	1.02791i	−0.400298	−	0.916385i	$-0.631093\pi$
$41$	3.80002	−	6.58183i	0.593464	−	1.02791i	0.993762	−	0.111524i	$-0.0355733\pi$
$42$	8.78413	+	1.23140i	1.35542	+	0.190009i
$43$	0.0488091	+	0.0845398i	0.00744332	+	0.0128922i	0.869723	−	0.493540i	$-0.164297\pi$
$43$	0.0488091	+	0.0845398i	0.00744332	+	0.0128922i	−0.862280	+	0.506432i	$0.830964\pi$
$44$	−7.19199	+	4.15230i	−1.08423	+	0.625982i
$45$	−2.88157	−	0.834589i	−0.429559	−	0.124413i
$46$	−8.30335	+	14.3818i	−1.22426	+	2.12048i
$47$	2.75934	−	4.77933i	0.402492	−	0.697136i	−0.591534	−	0.806280i	$-0.701478\pi$
$47$	2.75934	−	4.77933i	0.402492	−	0.697136i	0.994026	+	0.109144i	$0.0348109\pi$
$48$	−4.74555	+	6.05739i	−0.684962	+	0.874309i
$49$	3.47960	−	6.07391i	0.497086	−	0.867701i
$50$	−1.67628	−	0.967799i	−0.237061	−	0.136867i
$51$	−1.17751	+	1.50302i	−0.164885	+	0.210465i
$52$		−	2.91357i		−	0.404039i
$53$	11.1220	+	6.42128i	1.52772	+	0.882030i	0.999457	+	0.0329498i	$0.0104902\pi$
$53$	11.1220	+	6.42128i	1.52772	+	0.882030i	0.528264	+	0.849080i	$0.322843\pi$
$54$	5.87919	+	8.16037i	0.800057	+	1.11049i
$55$		−	4.75489i		−	0.641149i
$56$	0.650891	+	1.12301i	0.0869789	+	0.150069i
$57$	−7.15623	+	2.88022i	−0.947865	+	0.381495i
$58$	−5.96445			−0.783171
$59$	−6.68767	−	11.5834i	−0.870661	−	1.50803i	−0.861314	−	0.508072i	$-0.830358\pi$
$59$	−6.68767	−	11.5834i	−0.870661	−	1.50803i	−0.00934638	−	0.999956i	$-0.502975\pi$
$60$	1.12948	+	2.80632i	0.145816	+	0.362295i
$61$	9.30116	+	5.37003i	1.19089	+	0.687562i	0.958509	−	0.285063i	$-0.0920144\pi$
$61$	9.30116	+	5.37003i	1.19089	+	0.687562i	0.232383	+	0.972624i	$0.425348\pi$
$62$	7.67696			0.974975
$63$	7.70337	−	1.91263i	0.970533	−	0.240969i
$64$	5.86011			0.732513
$65$	1.44470	+	0.834098i	0.179193	+	0.103457i
$66$	−9.83099	+	12.5486i	−1.21011	+	1.54463i
$67$	2.53008	+	4.38223i	0.309099	+	0.535375i	0.978165	−	0.207828i	$-0.0666393\pi$
$67$	2.53008	+	4.38223i	0.309099	+	0.535375i	−0.669067	+	0.743202i	$0.733306\pi$
$68$	1.92532			0.233479
$69$	−2.08775	+	14.7130i	−0.251336	+	1.77123i
$70$	5.12110	−	0.00860774i	0.612089	−	0.00102882i
$71$			4.66184i			0.553259i	0.960977	+	0.276629i	$0.0892175\pi$
$71$			4.66184i			0.553259i	−0.960977	+	0.276629i	$0.910783\pi$
$72$	−0.409449	+	1.41370i	−0.0482540	+	0.166606i
$73$	3.66562	+	2.11635i	0.429029	+	0.247700i	0.698933	−	0.715187i	$-0.253659\pi$
$73$	3.66562	+	2.11635i	0.429029	+	0.247700i	−0.269904	+	0.962887i	$0.586992\pi$
$74$		−	2.92654i		−	0.340203i
$75$	−1.71487	−	0.243339i	−0.198016	−	0.0280983i
$76$	6.73648	+	3.88931i	0.772727	+	0.446134i
$77$	6.30843	+	10.8842i	0.718912	+	1.24037i
$78$	−2.08816	−	5.18826i	−0.236438	−	0.587455i
$79$	3.10659	−	5.38077i	0.349519	−	0.605384i	−0.636645	−	0.771157i	$-0.719678\pi$
$79$	3.10659	−	5.38077i	0.349519	−	0.605384i	0.986164	+	0.165773i	$0.0530117\pi$
$80$	−2.22134	+	3.84747i	−0.248353	+	0.430161i
$81$	7.60692	+	4.80986i	0.845214	+	0.534429i
$82$	−12.7398	+	7.35531i	−1.40687	+	0.812259i
$83$	−2.60200	−	4.50680i	−0.285607	−	0.494685i	0.687149	−	0.726516i	$-0.258862\pi$
$83$	−2.60200	−	4.50680i	−0.285607	−	0.494685i	−0.972756	+	0.231831i	$0.925528\pi$
$84$	−6.30868	−	4.92533i	−0.688333	−	0.537398i
$85$	−0.551181	+	0.954674i	−0.0597840	+	0.103549i
$86$		−	0.188950i		−	0.0203750i
$87$	−4.95125	+	1.99277i	−0.530830	+	0.213647i
$88$	−2.33275			−0.248672
$89$	−7.15835	−	12.3986i	−0.758783	−	1.31425i	−0.943471	−	0.331454i	$-0.892461\pi$
$89$	−7.15835	−	12.3986i	−0.758783	−	1.31425i	0.184688	−	0.982797i	$-0.440873\pi$
$90$	4.02260	+	4.18778i	0.424019	+	0.441431i
$91$	−4.41363	+	0.00741859i	−0.462674	+	0.000777679i
$92$	12.9771	−	7.49232i	1.35295	−	0.781128i
$93$	6.37285	−	2.56493i	0.660834	−	0.265971i
$94$	−9.25085	+	5.34098i	−0.954152	+	0.550880i
$95$	−3.85705	+	2.22687i	−0.395725	+	0.228472i
$96$	12.2406	−	4.92658i	1.24930	−	0.502817i
$97$	−1.33124	+	0.768589i	−0.135166	+	0.0780384i	−0.566058	−	0.824365i	$-0.691532\pi$
$97$	−1.33124	+	0.768589i	−0.135166	+	0.0780384i	0.430892	+	0.902404i	$0.358199\pi$
$98$	−11.7111	+	6.81400i	−1.18300	+	0.688318i
$99$	−3.96838	+	13.7016i	−0.398837	+	1.37706i
$100$	0.873269	+	1.51255i	0.0873269	+	0.151255i
$101$	13.4376			1.33709			0.668546	−	0.743671i	$-0.266917\pi$
$101$	13.4376			1.33709			0.668546	+	0.743671i	$0.266917\pi$
$102$	3.42846	−	1.37988i	0.339468	−	0.136628i
$103$			1.33852i			0.131888i	0.997823	+	0.0659442i	$0.0210059\pi$
$103$			1.33852i			0.131888i	−0.997823	+	0.0659442i	$0.978994\pi$
$104$	0.409208	−	0.708769i	0.0401262	−	0.0695006i
$105$	4.24829	−	1.71815i	0.414591	−	0.167674i
$106$	−12.4290	−	21.5277i	−1.20721	−	2.09095i
$107$	−6.41639	+	3.70450i	−0.620295	+	0.358128i	−0.776984	−	0.629520i	$-0.783251\pi$
$107$	−6.41639	+	3.70450i	−0.620295	+	0.358128i	0.156689	+	0.987648i	$0.449918\pi$
$108$	−0.912564	−	9.02928i	−0.0878115	−	0.868843i
$109$	6.82606	−	11.8231i	0.653818	−	1.13245i	−0.328371	−	0.944549i	$-0.606500\pi$
$109$	6.82606	−	11.8231i	0.653818	−	1.13245i	0.982189	−	0.187897i	$-0.0601671\pi$
$110$	−4.60178	+	7.97051i	−0.438762	+	0.759958i
$111$	−0.977781	−	2.42940i	−0.0928068	−	0.230589i
$112$	−0.0197569	−	11.7542i	−0.00186685	−	1.11067i
$113$	9.29802	+	5.36821i	0.874684	+	0.504999i	0.868902	−	0.494984i	$-0.164826\pi$
$113$	9.29802	+	5.36821i	0.874684	+	0.504999i	0.00578218	+	0.999983i	$0.498159\pi$
$114$	14.7833	+	2.09773i	1.38458	+	0.196471i
$115$			8.57962i			0.800054i
$116$	4.66084	+	2.69094i	0.432748	+	0.249847i
$117$	−3.46688	−	3.60925i	−0.320513	−	0.333675i
$118$			25.8893i			2.38330i
$119$	−0.00490228	−	2.91657i	−0.000449391	−	0.267362i
$120$	−0.119382	+	0.841315i	−0.0108980	+	0.0768012i
$121$	−11.6090			−1.05536
$122$	−10.3942	−	18.0033i	−0.941048	−	1.62994i
$123$	−8.11817	+	10.3623i	−0.731990	+	0.934338i
$124$	−5.99906	−	3.46356i	−0.538731	−	0.311037i
$125$	−1.00000			−0.0894427
$126$	−14.7640	−	4.24921i	−1.31528	−	0.378550i
$127$	0.0601044			0.00533340			0.00266670	−	0.999996i	$-0.499151\pi$
$127$	0.0601044			0.00533340			0.00266670	+	0.999996i	$0.499151\pi$
$128$	3.37168	+	1.94664i	0.298017	+	0.172060i
$129$	−0.0631296	−	0.156852i	−0.00555825	−	0.0138101i
$130$	−1.61448	−	2.79636i	−0.141599	−	0.245257i
$131$	10.7285			0.937351			0.468675	−	0.883370i	$-0.344731\pi$
$131$	10.7285			0.937351			0.468675	+	0.883370i	$0.344731\pi$
$132$	13.3438	−	5.37057i	1.16143	−	0.467448i
$133$	5.87458	−	10.2147i	0.509390	−	0.885725i
$134$		−	9.79444i		−	0.846111i
$135$	4.73844	+	2.13241i	0.407820	+	0.183529i
$136$	0.468362	+	0.270409i	0.0401617	+	0.0231874i
$137$		−	7.11878i		−	0.608199i	−0.952640	−	0.304099i	$-0.901645\pi$
$137$		−	7.11878i		−	0.608199i	0.952640	−	0.304099i	$-0.0983555\pi$
$138$	17.7388	−	22.6425i	1.51003	−	1.92745i
$139$	−15.1361	−	8.73885i	−1.28383	−	0.741220i	−0.306284	−	0.951940i	$-0.599086\pi$
$139$	−15.1361	−	8.73885i	−1.28383	−	0.741220i	−0.977546	+	0.210720i	$0.932419\pi$
$140$	−4.00570	−	2.30372i	−0.338543	−	0.194700i
$141$	−5.89492	+	7.52448i	−0.496442	+	0.633675i
$142$	4.51173	−	7.81454i	0.378616	−	0.655782i
$143$	3.96604	−	6.86939i	0.331657	−	0.574447i
$144$	9.61201	−	9.23287i	0.801001	−	0.769406i
$145$	−2.66862	+	1.54073i	−0.221616	+	0.127950i
$146$	−4.09640	−	7.09517i	−0.339021	−	0.587201i
$147$	−7.44509	+	9.56926i	−0.614060	+	0.789259i
$148$	−1.32035	+	2.28691i	−0.108532	+	0.187983i
$149$			19.4465i			1.59312i	0.604561	+	0.796559i	$0.293349\pi$
$149$			19.4465i			1.59312i	−0.604561	+	0.796559i	$0.706651\pi$
$150$	2.63910	+	2.06755i	0.215481	+	0.168815i
$151$	−20.3727			−1.65791			−0.828954	−	0.559317i	$-0.811064\pi$
$151$	−20.3727			−1.65791			−0.828954	+	0.559317i	$0.811064\pi$
$152$	1.09250	+	1.89227i	0.0886135	+	0.153483i
$153$	2.38503	−	2.29095i	0.192818	−	0.185212i
$154$	−0.0409288	−	24.3503i	−0.00329814	−	1.96220i
$155$	3.43483	−	1.98310i	0.275892	−	0.159286i
$156$	−0.708984	+	4.99640i	−0.0567641	+	0.400032i
$157$	−6.29240	+	3.63292i	−0.502189	+	0.289939i	−0.729617	−	0.683856i	$-0.760302\pi$
$157$	−6.29240	+	3.63292i	−0.502189	+	0.289939i	0.227428	+	0.973795i	$0.426968\pi$
$158$	−10.4150	+	6.01311i	−0.828574	+	0.478377i
$159$	−17.5102	−	13.7181i	−1.38865	−	1.08791i
$160$	6.59742	−	3.80902i	0.521572	−	0.301130i
$161$	−11.3828	−	19.6393i	−0.897090	−	1.54779i
$162$	−8.09633	−	15.4246i	−0.636108	−	1.21187i
$163$	−1.19919	−	2.07706i	−0.0939279	−	0.162688i	0.815233	−	0.579133i	$-0.196609\pi$
$163$	−1.19919	−	2.07706i	−0.0939279	−	0.162688i	−0.909161	+	0.416446i	$0.863276\pi$
$164$	13.2738			1.03651
$165$	−1.15705	+	8.15402i	−0.0900760	+	0.634790i
$166$			10.0729i			0.781805i
$167$	3.20798	−	5.55638i	0.248241	−	0.429966i	−0.714797	−	0.699332i	$-0.753481\pi$
$167$	3.20798	−	5.55638i	0.248241	−	0.429966i	0.963038	+	0.269366i	$0.0868142\pi$
$168$	−0.842922	−	2.08421i	−0.0650328	−	0.160800i
$169$	−5.10856	−	8.84829i	−0.392966	−	0.680637i
$170$	1.84786	−	1.06686i	0.141725	−	0.0818248i
$171$	12.9729	−	3.19783i	0.992061	−	0.244544i
$172$	−0.0852470	+	0.147652i	−0.00650002	+	0.0112584i
$173$	−10.7027	+	18.5376i	−0.813710	+	1.40939i	0.0965409	+	0.995329i	$0.469222\pi$
$173$	−10.7027	+	18.5376i	−0.813710	+	1.40939i	−0.910251	+	0.414058i	$0.864111\pi$
$174$	10.2283	+	1.45138i	0.775403	+	0.110029i
$175$	2.28906	−	1.32673i	0.173037	−	0.100291i
$176$	18.2943	+	10.5622i	1.37899	+	0.796158i
$177$	8.64982	+	21.4914i	0.650160	+	1.61539i
$178$			27.7114i			2.07705i
$179$	1.38469	+	0.799451i	0.103497	+	0.0597537i	0.550855	−	0.834601i	$-0.314302\pi$
$179$	1.38469	+	0.799451i	0.103497	+	0.0597537i	−0.447358	+	0.894355i	$0.647635\pi$
$180$	−1.25403	−	5.08733i	−0.0934702	−	0.379188i
$181$		−	13.7483i		−	1.02190i	−0.859610	−	0.510950i	$-0.829294\pi$
$181$		−	13.7483i		−	1.02190i	0.859610	−	0.510950i	$-0.170706\pi$
$182$	7.40564	+	4.25907i	0.548943	+	0.315703i
$183$	−14.6436	−	11.4722i	−1.08248	−	0.848053i
$184$	4.20916			0.310303
$185$	−0.755979	−	1.30939i	−0.0555807	−	0.0962685i
$186$	−13.1650	−	1.86810i	−0.965305	−	0.136976i
$187$	4.53937	+	2.62080i	0.331951	+	0.191652i
$188$	9.63860			0.702967
$189$	−13.6757	+	1.40539i	−0.994761	+	0.102227i
$190$	8.62064			0.625407
$191$	5.08874	+	2.93798i	0.368208	+	0.212585i	0.672675	−	0.739938i	$-0.265145\pi$
$191$	5.08874	+	2.93798i	0.368208	+	0.212585i	−0.304467	+	0.952523i	$0.598478\pi$
$192$	−10.0493	−	1.42599i	−0.725248	−	0.102912i
$193$	13.5411	+	23.4539i	0.974711	+	1.68825i	0.680886	+	0.732390i	$0.261595\pi$
$193$	13.5411	+	23.4539i	0.974711	+	1.68825i	0.293825	+	0.955859i	$0.405072\pi$
$194$	2.97536			0.213618
$195$	−2.27451	−	1.78192i	−0.162881	−	0.127606i
$196$	12.2257	−	0.0410989i	0.873264	−	0.00293564i
$197$		−	6.58789i		−	0.469367i	−0.972072	−	0.234684i	$-0.924595\pi$
$197$		−	6.58789i		−	0.469367i	0.972072	−	0.234684i	$-0.0754055\pi$
$198$	19.9124	−	19.1270i	1.41512	−	1.35930i
$199$	17.7662	+	10.2573i	1.25941	+	0.727121i	0.972960	−	0.230973i	$-0.0741910\pi$
$199$	17.7662	+	10.2573i	1.25941	+	0.727121i	0.286451	+	0.958095i	$0.407524\pi$
$200$			0.490599i			0.0346906i
$201$	−3.27240	−	8.13063i	−0.230817	−	0.573491i
$202$	−22.5251	−	13.0049i	−1.58486	−	0.915022i
$203$	4.06450	−	7.06733i	0.285272	−	0.496030i
$204$	−3.30167	−	0.468504i	−0.231163	−	0.0328018i
$205$	−3.80002	+	6.58183i	−0.265405	+	0.459695i
$206$	1.29542	−	2.24373i	0.0902562	−	0.156328i
$207$	7.16046	−	24.7228i	0.497686	−	1.71835i
$208$	−6.41834	+	3.70563i	−0.445032	+	0.256939i
$209$	10.5885	+	18.3398i	0.732422	+	1.26859i
$210$	−8.78413	−	1.23140i	−0.606163	−	0.0849747i
$211$	−2.21647	+	3.83905i	−0.152588	+	0.264291i	−0.932178	−	0.361999i	$-0.882094\pi$
$211$	−2.21647	+	3.83905i	−0.152588	+	0.264291i	0.779590	+	0.626290i	$0.215428\pi$
$212$			22.4300i			1.54050i
$213$	1.13441	−	7.99446i	0.0777282	−	0.547772i
$214$	14.3409			0.980321
$215$	−0.0488091	−	0.0845398i	−0.00332875	−	0.00576557i
$216$	1.04616	−	2.32468i	0.0711822	−	0.158174i
$217$	−5.23150	+	9.09650i	−0.355137	+	0.617511i
$218$	−22.8847	+	13.2125i	−1.54995	+	0.894864i
$219$	−5.77109	−	4.52126i	−0.389974	−	0.305518i
$220$	7.19199	−	4.15230i	0.484884	−	0.279948i
$221$	−1.59258	+	0.919478i	−0.107129	+	0.0618508i
$222$	−0.712140	+	5.01864i	−0.0477957	+	0.336829i
$223$	−2.25751	+	1.30337i	−0.151174	+	0.0872803i	−0.573679	−	0.819080i	$-0.694484\pi$
$223$	−2.25751	+	1.30337i	−0.151174	+	0.0872803i	0.422505	+	0.906361i	$0.361151\pi$
$224$	−10.0484	+	17.4720i	−0.671385	+	1.16740i
$225$	2.88157	+	0.834589i	0.192105	+	0.0556393i
$226$	−10.3907	−	17.9972i	−0.691179	−	1.19716i
$227$	−13.1846			−0.875092			−0.437546	−	0.899196i	$-0.644152\pi$
$227$	−13.1846			−0.875092			−0.437546	+	0.899196i	$0.644152\pi$
$228$	−10.6058	−	8.30891i	−0.702385	−	0.550271i
$229$			21.7171i			1.43510i	0.696504	+	0.717552i	$0.254738\pi$
$229$			21.7171i			1.43510i	−0.696504	+	0.717552i	$0.745262\pi$
$230$	8.30335	−	14.3818i	0.547507	−	0.948309i
$231$	−8.16960	−	20.2001i	−0.537520	−	1.32907i
$232$	0.755879	+	1.30922i	0.0496259	+	0.0859546i
$233$	11.4014	−	6.58259i	0.746929	−	0.431240i	−0.0776542	−	0.996980i	$-0.524743\pi$
$233$	11.4014	−	6.58259i	0.746929	−	0.431240i	0.824583	+	0.565741i	$0.191410\pi$
$234$	2.31843	+	9.40534i	0.151560	+	0.614846i
$235$	−2.75934	+	4.77933i	−0.180000	+	0.311769i
$236$	11.6803	−	20.2308i	0.760321	−	1.31692i
$237$	−6.63676	+	8.47139i	−0.431104	+	0.550276i
$238$	−2.81444	+	4.89373i	−0.182433	+	0.317213i
$239$	−1.24326	−	0.717795i	−0.0804196	−	0.0464303i	0.459251	−	0.888307i	$-0.348118\pi$
$239$	−1.24326	−	0.717795i	−0.0804196	−	0.0464303i	−0.539671	+	0.841876i	$0.681451\pi$
$240$	4.74555	−	6.05739i	0.306324	−	0.391003i
$241$		−	3.57588i		−	0.230343i	−0.993346	−	0.115171i	$-0.963258\pi$
$241$		−	3.57588i		−	0.230343i	0.993346	−	0.115171i	$-0.0367417\pi$
$242$	19.4598	+	11.2351i	1.25093	+	0.722222i
$243$	−11.8745	−	10.0993i	−0.761748	−	0.647873i
$244$			18.7579i			1.20085i
$245$	−3.47960	+	6.07391i	−0.222304	+	0.388048i
$246$	23.6369	−	9.51334i	1.50704	−	0.606549i
$247$	−7.42971			−0.472741
$248$	−0.972907	−	1.68512i	−0.0617796	−	0.107005i
$249$	3.36542	+	8.36175i	0.213275	+	0.529904i
$250$	1.67628	+	0.967799i	0.106017	+	0.0612090i
$251$	3.33971			0.210801			0.105400	−	0.994430i	$-0.466388\pi$
$251$	3.33971			0.210801			0.105400	+	0.994430i	$0.466388\pi$
$252$	9.62005	+	9.98146i	0.606006	+	0.628773i
$253$	40.7951			2.56477
$254$	−0.100752	−	0.0581690i	−0.00632172	−	0.00364985i
$255$	1.17751	−	1.50302i	0.0737388	−	0.0941227i
$256$	−9.62802	−	16.6762i	−0.601751	−	1.04226i
$257$	−5.56494			−0.347132			−0.173566	−	0.984822i	$-0.555529\pi$
$257$	−5.56494			−0.347132			−0.173566	+	0.984822i	$0.555529\pi$
$258$	−0.0459787	+	0.324024i	−0.00286251	+	0.0201729i
$259$	3.46769	+	1.99431i	0.215472	+	0.123920i
$260$			2.91357i			0.180692i
$261$	8.97568	−	2.21252i	0.555581	−	0.136951i
$262$	−17.9839	−	10.3830i	−1.11105	−	0.641464i
$263$		−	17.3934i		−	1.07252i	−0.844052	−	0.536261i	$-0.819836\pi$
$263$		−	17.3934i		−	1.07252i	0.844052	−	0.536261i	$-0.180164\pi$
$264$	4.00036	+	0.567647i	0.246205	+	0.0349363i
$265$	−11.1220	−	6.42128i	−0.683218	−	0.394456i
$266$	−19.7332	+	11.4372i	−1.20992	+	0.701261i
$267$	9.25859	+	23.0040i	0.566616	+	1.40782i
$268$	−4.41889	+	7.65374i	−0.269926	+	0.467526i
$269$	−6.65501	+	11.5268i	−0.405763	+	0.702803i	−0.994410	−	0.105588i	$-0.966328\pi$
$269$	−6.65501	+	11.5268i	−0.405763	+	0.702803i	0.588647	+	0.808390i	$0.299661\pi$
$270$	−5.87919	−	8.16037i	−0.357796	−	0.496624i
$271$	−10.8074	+	6.23963i	−0.656500	+	0.379031i	−0.790942	−	0.611891i	$-0.790409\pi$
$271$	−10.8074	+	6.23963i	−0.656500	+	0.379031i	0.134442	+	0.990921i	$0.457076\pi$
$272$	−2.44872	−	4.24131i	−0.148476	−	0.257167i
$273$	7.57061	+	1.06128i	0.458194	+	0.0642318i
$274$	−6.88955	+	11.9330i	−0.416213	+	0.720902i
$275$			4.75489i			0.286731i
$276$	−24.0772	+	9.69055i	−1.44928	+	0.583302i
$277$	21.2911			1.27926			0.639628	−	0.768684i	$-0.279088\pi$
$277$	21.2911			1.27926			0.639628	+	0.768684i	$0.279088\pi$
$278$	16.9149	+	29.2975i	1.01449	+	1.75715i
$279$	−11.5528	+	2.84777i	−0.691646	+	0.170492i
$280$	−0.650891	−	1.12301i	−0.0388982	−	0.0671128i
$281$	−18.7733	+	10.8388i	−1.11992	+	0.646586i	−0.941381	−	0.337346i	$-0.890471\pi$
$281$	−18.7733	+	10.8388i	−1.11992	+	0.646586i	−0.178540	+	0.983933i	$0.557137\pi$
$282$	17.1637	−	6.90801i	1.02208	−	0.411366i
$283$	−0.992992	+	0.573304i	−0.0590272	+	0.0340794i	−0.529223	−	0.848483i	$-0.677517\pi$
$283$	−0.992992	+	0.573304i	−0.0590272	+	0.0340794i	0.470196	+	0.882562i	$0.344183\pi$
$284$	−7.05125	+	4.07104i	−0.418415	+	0.241572i
$285$	7.15623	−	2.88022i	0.423898	−	0.170610i
$286$	−13.2964	+	7.67667i	−0.786231	+	0.453931i
$287$	−0.0337979	−	20.1078i	−0.00199503	−	1.18693i
$288$	−22.1899	+	5.46984i	−1.30755	+	0.322313i
$289$	7.89240	+	13.6700i	0.464259	+	0.804120i
$290$	5.96445			0.350245
$291$	2.46993	−	0.994091i	0.144790	−	0.0582747i
$292$			7.39257i			0.432618i
$293$	−9.65939	+	16.7306i	−0.564307	+	0.977409i	0.432806	+	0.901487i	$0.357523\pi$
$293$	−9.65939	+	16.7306i	−0.564307	+	0.977409i	−0.997114	+	0.0759223i	$0.975810\pi$
$294$	21.7411	−	8.83538i	1.26797	−	0.515290i
$295$	6.68767	+	11.5834i	0.389371	+	0.674411i
$296$	−0.642388	+	0.370883i	−0.0373380	+	0.0215571i
$297$	10.1394	−	22.5308i	0.588346	−	1.30737i
$298$	18.8203	−	32.5977i	1.09023	−	1.88833i
$299$	−7.15625	+	12.3950i	−0.413857	+	0.716821i
$300$	−1.12948	−	2.80632i	−0.0652108	−	0.162023i
$301$	0.223888	+	0.128761i	0.0129047	+	0.00742164i
$302$	34.1503	+	19.7167i	1.96513	+	1.13457i
$303$	−23.0438	−	3.26989i	−1.32383	−	0.187850i
$304$		−	19.7865i		−	1.13483i
$305$	−9.30116	−	5.37003i	−0.532583	−	0.307487i
$306$	−6.21515	+	1.53204i	−0.355296	+	0.0875810i
$307$			27.3731i			1.56227i	0.624364	+	0.781133i	$0.285358\pi$
$307$			27.3731i			1.56227i	−0.624364	+	0.781133i	$0.714642\pi$
$308$	−10.9539	+	19.0467i	−0.624159	+	1.08528i
$309$	0.325714	−	2.29539i	0.0185292	−	0.130580i
$310$	−7.67696			−0.436022
$311$	11.1921	+	19.3853i	0.634645	+	1.09924i	0.986590	+	0.163216i	$0.0521869\pi$
$311$	11.1921	+	19.3853i	0.634645	+	1.09924i	−0.351946	+	0.936020i	$0.614480\pi$
$312$	−0.874211	+	1.11587i	−0.0494924	+	0.0631739i
$313$	−5.08013	−	2.93301i	−0.287146	−	0.165784i	0.349508	−	0.936933i	$-0.386349\pi$
$313$	−5.08013	−	2.93301i	−0.287146	−	0.165784i	−0.636654	+	0.771150i	$0.719682\pi$
$314$	14.0637			0.793663
$315$	−7.70337	+	1.91263i	−0.434036	+	0.107764i
$316$	10.8516			0.610448
$317$	−13.9161	−	8.03448i	−0.781608	−	0.451262i	0.0553919	−	0.998465i	$-0.482359\pi$
$317$	−13.9161	−	8.03448i	−0.781608	−	0.451262i	−0.837000	+	0.547203i	$0.815693\pi$
$318$	16.0756	+	39.9417i	0.901477	+	2.23982i
$319$	7.32598	+	12.6890i	0.410176	+	0.710446i
$320$	−5.86011			−0.327590
$321$	11.9047	−	4.79139i	0.664457	−	0.267430i
$322$	0.0738511	+	43.9371i	0.00411556	+	2.44852i
$323$		−	4.90963i		−	0.273179i
$324$	−0.632242	+	15.7061i	−0.0351246	+	0.872563i
$325$	−1.44470	−	0.834098i	−0.0801376	−	0.0462674i
$326$			4.64230i			0.257113i
$327$	−14.5828	+	18.6140i	−0.806432	+	1.02936i
$328$	3.22904	+	1.86429i	0.178294	+	0.102938i
$329$	−0.0245420	−	14.6011i	−0.00135304	−	0.804982i
$330$	9.83099	−	12.5486i	0.541178	−	0.690778i
$331$	9.90167	−	17.1502i	0.544245	−	0.942660i	−0.454409	−	0.890793i	$-0.650150\pi$
$331$	9.90167	−	17.1502i	0.544245	−	0.942660i	0.998654	−	0.0518669i	$-0.0165172\pi$
$332$	4.54449	−	7.87129i	0.249412	−	0.431993i
$333$	1.08560	+	4.40404i	0.0594906	+	0.241340i
$334$	−10.7549	+	6.20936i	−0.588483	+	0.339761i
$335$	−2.53008	−	4.38223i	−0.138233	−	0.239427i
$336$	−2.82637	+	20.1618i	−0.154191	+	1.09992i
$337$	8.72200	−	15.1070i	0.475118	−	0.822928i	−0.524476	−	0.851425i	$-0.675739\pi$
$337$	8.72200	−	15.1070i	0.475118	−	0.822928i	0.999594	+	0.0284971i	$0.00907214\pi$
$338$			19.7762i			1.07569i
$339$	−14.6386	−	11.4684i	−0.795061	−	0.622876i
$340$	−1.92532			−0.104415
$341$	−9.42941	−	16.3322i	−0.510631	−	0.884439i
$342$	−24.8410	−	7.19469i	−1.34325	−	0.389044i
$343$	−0.0933881	−	18.5200i	−0.00504248	−	0.999987i
$344$	−0.0414752	+	0.0239457i	−0.00223619	+	0.00129107i
$345$	2.08775	−	14.7130i	0.112401	−	0.792119i
$346$	35.8813	−	20.7161i	1.92899	−	1.11370i
$347$	10.4321	−	6.02296i	0.560023	−	0.323329i	−0.193132	−	0.981173i	$-0.561865\pi$
$347$	10.4321	−	6.02296i	0.560023	−	0.323329i	0.753155	+	0.657844i	$0.228531\pi$
$348$	−7.33793	−	5.74877i	−0.393355	−	0.308167i
$349$	3.69358	−	2.13249i	0.197713	−	0.114150i	−0.397875	−	0.917440i	$-0.630252\pi$
$349$	3.69358	−	2.13249i	0.197713	−	0.114150i	0.595588	+	0.803290i	$0.296919\pi$
$350$	−5.12110	+	0.00860774i	−0.273734	+	0.000460103i
$351$	5.06699	+	7.03302i	0.270456	+	0.375395i
$352$	−18.1115	−	31.3700i	−0.965345	−	1.67203i
$353$	−10.8898			−0.579604			−0.289802	−	0.957087i	$-0.593589\pi$
$353$	−10.8898			−0.579604			−0.289802	+	0.957087i	$0.593589\pi$
$354$	6.29986	−	44.3968i	0.334834	−	2.35966i
$355$		−	4.66184i		−	0.247425i
$356$	12.5023	−	21.6547i	0.662622	−	1.14770i
$357$	−0.701308	+	5.00274i	−0.0371171	+	0.264773i
$358$	−1.54741	−	2.68020i	−0.0817834	−	0.141653i
$359$	−12.7834	+	7.38048i	−0.674680	+	0.389527i	−0.797848	−	0.602859i	$-0.794028\pi$
$359$	−12.7834	+	7.38048i	−0.674680	+	0.389527i	0.123168	+	0.992386i	$0.460695\pi$
$360$	0.409449	−	1.41370i	0.0215799	−	0.0745084i
$361$	0.417877	−	0.723785i	0.0219935	−	0.0380939i
$362$	−13.3056	+	23.0459i	−0.699325	+	1.21127i
$363$	19.9079	+	2.82491i	1.04489	+	0.148269i
$364$	−3.86551	−	6.66934i	−0.202608	−	0.349568i
$365$	−3.66562	−	2.11635i	−0.191868	−	0.110775i
$366$	13.4439	+	33.4027i	0.702721	+	1.74599i
$367$		−	0.599619i		−	0.0312999i	−0.999878	−	0.0156499i	$-0.995018\pi$
$367$		−	0.599619i		−	0.0312999i	0.999878	−	0.0156499i	$-0.00498173\pi$
$368$	−33.0099	−	19.0583i	−1.72076	−	0.993480i
$369$	16.4432	−	15.7946i	0.855997	−	0.822232i
$370$			2.92654i			0.152144i
$371$	33.9782	−	0.0571117i	1.76406	−	0.00296509i
$372$	9.44480	+	7.39936i	0.489690	+	0.383639i
$373$	−17.3848			−0.900153			−0.450077	−	0.892990i	$-0.648603\pi$
$373$	−17.3848			−0.900153			−0.450077	+	0.892990i	$0.648603\pi$
$374$	−5.07282	−	8.78639i	−0.262309	−	0.454333i
$375$	1.71487	+	0.243339i	0.0885556	+	0.0125659i
$376$	2.34473	+	1.35373i	0.120920	+	0.0698135i
$377$	−5.14047			−0.264748
$378$	24.2844	+	10.8795i	1.24905	+	0.559582i
$379$	−33.4612			−1.71879			−0.859394	−	0.511314i	$-0.829159\pi$
$379$	−33.4612			−1.71879			−0.859394	+	0.511314i	$0.829159\pi$
$380$	−6.73648	−	3.88931i	−0.345574	−	0.199517i
$381$	−0.103071	−	0.0146257i	−0.00528051	−	0.000749298i
$382$	−5.68676	−	9.84975i	−0.290960	−	0.503957i
$383$	14.3467			0.733082			0.366541	−	0.930402i	$-0.380542\pi$
$383$	14.3467			0.733082			0.366541	+	0.930402i	$0.380542\pi$
$384$	−5.30830	−	4.15870i	−0.270888	−	0.212223i
$385$	−6.30843	−	10.8842i	−0.321507	−	0.554712i
$386$		−	52.4203i		−	2.66812i
$387$	0.0700910	+	0.284343i	0.00356292	+	0.0144540i
$388$	−2.32505	−	1.34237i	−0.118037	−	0.0681485i
$389$		−	34.5962i		−	1.75410i	−0.480403	−	0.877048i	$-0.659510\pi$
$389$		−	34.5962i		−	1.75410i	0.480403	−	0.877048i	$-0.340490\pi$
$390$	2.08816	+	5.18826i	0.105738	+	0.262718i
$391$	−8.19074	−	4.72893i	−0.414223	−	0.239152i
$392$	2.97986	+	1.70709i	0.150505	+	0.0862211i
$393$	−18.3980	−	2.61065i	−0.928054	−	0.131690i
$394$	−6.37575	+	11.0431i	−0.321206	+	0.556344i
$395$	−3.10659	+	5.38077i	−0.156310	+	0.270736i
$396$	−24.1897	+	5.96279i	−1.21558	+	0.299642i
$397$	−18.3484	+	10.5935i	−0.920880	+	0.531670i	−0.883916	−	0.467646i	$-0.845102\pi$
$397$	−18.3484	+	10.5935i	−0.920880	+	0.531670i	−0.0369641	+	0.999317i	$0.511769\pi$
$398$	−19.8540	−	34.3882i	−0.995192	−	1.72372i
$399$	−12.5598	+	16.0874i	−0.628775	+	0.805375i
$400$	2.22134	−	3.84747i	0.111067	−	0.192374i
$401$			10.9720i			0.547915i	0.961742	+	0.273957i	$0.0883327\pi$
$401$			10.9720i			0.547915i	−0.961742	+	0.273957i	$0.911667\pi$
$402$	−2.38337	+	16.7962i	−0.118871	+	0.837719i
$403$	6.61639			0.329586
$404$	11.7346	+	20.3250i	0.583821	+	1.01121i
$405$	−7.60692	−	4.80986i	−0.377991	−	0.239004i
$406$	−13.6530	+	7.91319i	−0.677587	+	0.392725i
$407$	−6.22602	+	3.59459i	−0.308612	+	0.178177i
$408$	−0.737381	−	0.577688i	−0.0365058	−	0.0285998i
$409$	6.06029	−	3.49891i	0.299662	−	0.173010i	−0.342629	−	0.939471i	$-0.611317\pi$
$409$	6.06029	−	3.49891i	0.299662	−	0.173010i	0.642291	+	0.766461i	$0.277984\pi$
$410$	12.7398	−	7.35531i	0.629173	−	0.363253i
$411$	−1.73227	+	12.2078i	−0.0854468	+	0.602166i
$412$	−2.02458	+	1.16889i	−0.0997437	+	0.0575871i
$413$	−30.6765	−	17.6424i	−1.50949	−	0.868125i
$414$	−35.9296	+	34.5124i	−1.76584	+	1.69619i
$415$	2.60200	+	4.50680i	0.127727	+	0.221230i
$416$	12.7084			0.623080
$417$	23.8300	+	18.6692i	1.16696	+	0.914236i
$418$		−	40.9902i		−	2.00489i
$419$	8.25420	−	14.2967i	0.403244	−	0.698439i	−0.590871	−	0.806766i	$-0.701216\pi$
$419$	8.25420	−	14.2967i	0.403244	−	0.698439i	0.994115	+	0.108327i	$0.0345492\pi$
$420$	6.30868	+	4.92533i	0.307832	+	0.240332i
$421$	0.566727	+	0.981600i	0.0276206	+	0.0478403i	0.879505	−	0.475889i	$-0.157874\pi$
$421$	0.566727	+	0.981600i	0.0276206	+	0.0478403i	−0.851885	+	0.523729i	$0.824540\pi$
$422$	7.43085	−	4.29020i	0.361728	−	0.208844i
$423$	11.9400	−	11.4691i	0.580544	−	0.557645i
$424$	−3.15027	+	5.45644i	−0.152991	+	0.264988i
$425$	0.551181	−	0.954674i	0.0267362	−	0.0463085i
$426$	−9.63861	+	12.3031i	−0.466992	+	0.596085i
$427$	28.4155	−	0.0477618i	1.37512	−	0.00231135i
$428$	−11.2065	−	6.47006i	−0.541685	−	0.312742i
$429$	−8.47285	+	10.8150i	−0.409073	+	0.522155i
$430$			0.188950i			0.00911196i
$431$	22.5589	+	13.0244i	1.08662	+	0.627363i	0.932676	−	0.360716i	$-0.117468\pi$
$431$	22.5589	+	13.0244i	1.08662	+	0.627363i	0.153949	+	0.988079i	$0.450801\pi$
$432$	−18.7301	+	13.4942i	−0.901152	+	0.649241i
$433$		−	18.1879i		−	0.874057i	−0.899448	−	0.437028i	$-0.856031\pi$
$433$		−	18.1879i		−	0.874057i	0.899448	−	0.437028i	$-0.143969\pi$
$434$	17.5730	−	10.1852i	0.843532	−	0.488906i
$435$	4.95125	−	1.99277i	0.237394	−	0.0955460i
$436$	23.8439			1.14192
$437$	−19.1057	−	33.0920i	−0.913949	−	1.58301i
$438$	5.29827	+	13.1641i	0.253161	+	0.629006i
$439$	−23.2893	−	13.4461i	−1.11154	−	0.641747i	−0.172312	−	0.985043i	$-0.555124\pi$
$439$	−23.2893	−	13.4461i	−1.11154	−	0.641747i	−0.939228	+	0.343295i	$0.888457\pi$
$440$	2.33275			0.111209
$441$	15.0959	−	14.5984i	0.718854	−	0.695161i
$442$	3.55948			0.169307
$443$	3.57698	+	2.06517i	0.169947	+	0.0981192i	0.582561	−	0.812787i	$-0.302051\pi$
$443$	3.57698	+	2.06517i	0.169947	+	0.0981192i	−0.412614	+	0.910906i	$0.635384\pi$
$444$	2.82072	−	3.60046i	0.133865	−	0.170870i
$445$	7.15835	+	12.3986i	0.339338	+	0.587751i
$446$	5.04561			0.238917
$447$	4.73208	−	33.3482i	0.223820	−	1.57732i
$448$	13.4141	−	7.77475i	0.633759	−	0.367322i
$449$			6.94270i			0.327646i	0.986490	+	0.163823i	$0.0523826\pi$
$449$			6.94270i			0.327646i	−0.986490	+	0.163823i	$0.947617\pi$
$450$	−4.02260	−	4.18778i	−0.189627	−	0.197414i
$451$	31.2959	+	18.0687i	1.47367	+	0.850821i
$452$			18.7516i			0.882000i
$453$	34.9366	+	4.95747i	1.64146	+	0.232922i
$454$	22.1010	+	12.7600i	1.03725	+	0.598858i
$455$	4.41363	−	0.00741859i	0.206914	−	0.000347789i
$456$	−1.41304	−	3.51084i	−0.0661715	−	0.164410i
$457$	12.0030	−	20.7898i	0.561476	−	0.972505i	−0.435892	−	0.899999i	$-0.643567\pi$
$457$	12.0030	−	20.7898i	0.561476	−	0.972505i	0.997368	−	0.0725057i	$-0.0230995\pi$
$458$	21.0178	−	36.4038i	0.982096	−	1.70104i
$459$	−4.64750	+	3.34832i	−0.216927	+	0.156286i
$460$	−12.9771	+	7.49232i	−0.605059	+	0.349331i
$461$	12.6467	+	21.9048i	0.589017	+	1.02021i	0.994361	+	0.106044i	$0.0338183\pi$
$461$	12.6467	+	21.9048i	0.589017	+	1.02021i	−0.405344	+	0.914164i	$0.632848\pi$
$462$	−5.85517	+	41.7676i	−0.272407	+	1.94320i
$463$	−6.12809	+	10.6142i	−0.284796	+	0.493282i	−0.972560	−	0.232653i	$-0.925259\pi$
$463$	−6.12809	+	10.6142i	−0.284796	+	0.493282i	0.687763	+	0.725935i	$0.258593\pi$
$464$		−	13.6899i		−	0.635538i
$465$	−6.37285	+	2.56493i	−0.295534	+	0.118946i
$466$	−25.4825			−1.18045
$467$	−6.36303	−	11.0211i	−0.294446	−	0.509995i	0.680410	−	0.732832i	$-0.261802\pi$
$467$	−6.36303	−	11.0211i	−0.294446	−	0.509995i	−0.974856	+	0.222837i	$0.928468\pi$
$468$	2.43163	−	8.39566i	0.112402	−	0.388090i
$469$	11.6055	+	6.67447i	0.535894	+	0.308198i
$470$	9.25085	−	5.34098i	0.426710	−	0.246361i
$471$	11.6747	−	4.69881i	0.537942	−	0.216510i
$472$	5.68280	−	3.28097i	0.261572	−	0.151019i
$473$	−0.401977	+	0.232082i	−0.0184829	+	0.0106711i
$474$	19.3236	−	7.77734i	0.887564	−	0.357225i
$475$	3.85705	−	2.22687i	0.176973	−	0.102176i
$476$	4.40717	−	2.55437i	0.202002	−	0.117079i
$477$	26.6897	+	27.7857i	1.22204	+	1.27222i
$478$	1.38936	+	2.40645i	0.0635479	+	0.110068i
$479$	2.16361			0.0988581			0.0494290	−	0.998778i	$-0.484260\pi$
$479$	2.16361			0.0988581			0.0494290	+	0.998778i	$0.484260\pi$
$480$	−12.2406	+	4.92658i	−0.558705	+	0.224867i
$481$		−	2.52224i		−	0.115004i
$482$	−3.46073	+	5.99416i	−0.157632	+	0.273027i
$483$	14.7411	+	36.4487i	0.670741	+	1.65847i
$484$	−10.1377	−	17.5591i	−0.460807	−	0.798141i
$485$	1.33124	−	0.768589i	0.0604483	−	0.0348998i
$486$	10.1308	+	28.4214i	0.459541	+	1.28922i
$487$	−15.3690	+	26.6200i	−0.696438	+	1.20627i	0.273256	+	0.961941i	$0.411900\pi$
$487$	−15.3690	+	26.6200i	−0.696438	+	1.20627i	−0.969694	+	0.244324i	$0.921434\pi$
$488$	−2.63453	+	4.56315i	−0.119260	+	0.206564i
$489$	1.55103	+	3.85370i	0.0701400	+	0.174270i
$490$	11.7111	−	6.81400i	0.529053	−	0.307825i
$491$	−26.0110	−	15.0174i	−1.17386	−	0.677728i	−0.219273	−	0.975663i	$-0.570369\pi$
$491$	−26.0110	−	15.0174i	−1.17386	−	0.677728i	−0.954586	+	0.297935i	$0.903702\pi$
$492$	−22.7628	−	3.23002i	−1.02623	−	0.145621i
$493$		−	3.39688i		−	0.152988i
$494$	12.4542	+	7.19046i	0.560343	+	0.323514i
$495$	3.96838	−	13.7016i	0.178365	−	0.615839i
$496$			17.6205i			0.791186i
$497$	6.18498	+	10.6712i	0.277434	+	0.478671i
$498$	2.45111	−	17.2737i	0.109837	−	0.774051i
$499$	10.1454			0.454172			0.227086	−	0.973875i	$-0.427080\pi$
$499$	10.1454			0.454172			0.227086	+	0.973875i	$0.427080\pi$
$500$	−0.873269	−	1.51255i	−0.0390538	−	0.0676431i
$501$	−6.85336	+	8.74786i	−0.306185	+	0.390826i
$502$	−5.59828	−	3.23217i	−0.249864	−	0.144259i
$503$	−10.0869			−0.449754			−0.224877	−	0.974387i	$-0.572198\pi$
$503$	−10.0869			−0.449754			−0.224877	+	0.974387i	$0.572198\pi$
$504$	0.938335	+	3.77927i	0.0417968	+	0.168342i
$505$	−13.4376			−0.597966
$506$	−68.3840	−	39.4815i	−3.04004	−	1.75517i
$507$	6.60740	+	16.4168i	0.293445	+	0.729095i
$508$	0.0524873	+	0.0909107i	0.00232875	+	0.00403351i
$509$	37.9808			1.68347			0.841735	−	0.539891i	$-0.181534\pi$
$509$	37.9808			1.68347			0.841735	+	0.539891i	$0.181534\pi$
$510$	−3.42846	+	1.37988i	−0.151815	+	0.0611021i
$511$	11.1987	−	0.0188231i	0.495399	−	0.000832685i
$512$			29.4854i			1.30308i
$513$	−23.0250	+	2.32707i	−1.01658	+	0.102743i
$514$	9.32839	+	5.38575i	0.411458	+	0.237555i
$515$		−	1.33852i		−	0.0589823i
$516$	0.182117	−	0.232461i	0.00801726	−	0.0102335i
$517$	22.7252	+	13.1204i	0.999451	+	0.577033i
$518$	−3.88272	−	6.69903i	−0.170597	−	0.294339i
$519$	22.8646	−	29.1852i	1.00365	−	1.28109i
$520$	−0.409208	+	0.708769i	−0.0179450	+	0.0310816i
$521$	−13.1955	+	22.8553i	−0.578107	+	1.00131i	0.417589	+	0.908636i	$0.362875\pi$
$521$	−13.1955	+	22.8553i	−0.578107	+	1.00131i	−0.995696	+	0.0926749i	$0.970458\pi$
$522$	−17.1870	−	4.97786i	−0.752254	−	0.217875i
$523$	−7.48915	+	4.32386i	−0.327478	+	0.189069i	−0.654721	−	0.755871i	$-0.727214\pi$
$523$	−7.48915	+	4.32386i	−0.327478	+	0.189069i	0.327243	+	0.944940i	$0.393880\pi$
$524$	9.36884	+	16.2273i	0.409280	+	0.708894i
$525$	−4.24829	+	1.71815i	−0.185411	+	0.0749861i
$526$	−16.8333	+	29.1561i	−0.733966	+	1.27127i
$527$			4.37218i			0.190455i
$528$	−28.8022	−	22.5646i	−1.25345	−	0.981997i
$529$	−50.6099			−2.20043
$530$	12.4290	+	21.5277i	0.539882	+	0.935102i
$531$	−9.60365	−	38.9598i	−0.416763	−	1.69071i
$532$	20.5803	−	0.0345921i	0.892268	−	0.00149976i
$533$	−10.9798	+	6.33918i	−0.475587	+	0.274581i
$534$	6.74324	−	47.5214i	0.291809	−	2.05645i
$535$	6.41639	−	3.70450i	0.277405	−	0.160160i
$536$	−2.14992	+	1.24126i	−0.0928624	+	0.0536141i
$537$	−2.18003	−	1.70790i	−0.0940751	−	0.0737015i
$538$	22.3113	−	12.8814i	0.961908	−	0.555358i
$539$	28.8808	+	16.5451i	1.24398	+	0.712649i
$540$	0.912564	+	9.02928i	0.0392705	+	0.388558i
$541$	−20.9386	−	36.2666i	−0.900219	−	1.55922i	−0.827210	−	0.561893i	$-0.810073\pi$
$541$	−20.9386	−	36.2666i	−0.900219	−	1.55922i	−0.0730090	−	0.997331i	$-0.523260\pi$
$542$	24.1548			1.03754
$543$	−3.34548	+	23.5765i	−0.143568	+	1.01177i
$544$			8.39784i			0.360055i
$545$	−6.82606	+	11.8231i	−0.292396	+	0.506445i
$546$	−11.6633	−	9.10583i	−0.499144	−	0.389694i
$547$	−2.52795	−	4.37854i	−0.108087	−	0.187213i	0.806908	−	0.590677i	$-0.201139\pi$
$547$	−2.52795	−	4.37854i	−0.108087	−	0.187213i	−0.914995	+	0.403464i	$0.867806\pi$
$548$	10.7675	−	6.21661i	0.459964	−	0.265561i
$549$	22.3202	+	23.2368i	0.952603	+	0.991721i
$550$	4.60178	−	7.97051i	0.196220	−	0.339864i
$551$	6.86198	−	11.8853i	0.292330	−	0.506331i
$552$	−7.21817	−	1.02425i	−0.307226	−	0.0435950i
$553$	−0.0276305	−	16.4385i	−0.00117497	−	0.699037i
$554$	−35.6897	−	20.6055i	−1.51631	−	0.875443i
$555$	0.977781	+	2.42940i	0.0415045	+	0.103122i
$556$		−	30.5255i		−	1.29457i
$557$	−28.2505	−	16.3104i	−1.19701	−	0.691094i	−0.237123	−	0.971480i	$-0.576204\pi$
$557$	−28.2505	−	16.3104i	−1.19701	−	0.691094i	−0.959887	+	0.280386i	$0.909538\pi$
$558$	22.1217	+	6.40711i	0.936487	+	0.271234i
$559$		−	0.162846i		−	0.00688767i
$560$	0.0197569	+	11.7542i	0.000834882	+	0.496706i
$561$	−7.14669	−	5.59895i	−0.301733	−	0.236388i
$562$	41.9590			1.76993
$563$	−3.61718	−	6.26513i	−0.152446	−	0.264044i	0.779680	−	0.626178i	$-0.215382\pi$
$563$	−3.61718	−	6.26513i	−0.152446	−	0.264044i	−0.932126	+	0.362134i	$0.882048\pi$
$564$	−16.5290	−	2.34544i	−0.695995	−	0.0987610i
$565$	−9.29802	−	5.36821i	−0.391171	−	0.225842i
$566$	2.21937			0.0932872
$567$	23.7941	+	0.917763i	0.999257	+	0.0385424i
$568$	−2.28710			−0.0959645
$569$	16.3484	+	9.43876i	0.685361	+	0.395693i	0.801872	−	0.597496i	$-0.203838\pi$
$569$	16.3484	+	9.43876i	0.685361	+	0.395693i	−0.116511	+	0.993189i	$0.537171\pi$
$570$	−14.7833	−	2.09773i	−0.619204	−	0.0878644i
$571$	−15.3158	−	26.5278i	−0.640947	−	1.11015i	−0.985222	−	0.171283i	$-0.945209\pi$
$571$	−15.3158	−	26.5278i	−0.640947	−	1.11015i	0.344275	−	0.938869i	$-0.388125\pi$
$572$	13.8537			0.579252
$573$	−8.01161	−	6.27655i	−0.334690	−	0.262207i
$574$	−19.4036	+	33.7389i	−0.809893	+	1.40824i
$575$		−	8.57962i		−	0.357795i
$576$	16.8863	+	4.89078i	0.703597	+	0.203782i
$577$	7.17505	+	4.14252i	0.298701	+	0.172455i	0.641859	−	0.766822i	$-0.278163\pi$
$577$	7.17505	+	4.14252i	0.298701	+	0.172455i	−0.343158	+	0.939278i	$0.611497\pi$
$578$		−	30.5530i		−	1.27084i
$579$	−17.5140	−	43.5155i	−0.727859	−	1.80844i
$580$	−4.66084	−	2.69094i	−0.193531	−	0.111735i
$581$	−11.9354	−	6.86419i	−0.495165	−	0.284775i
$582$	−5.10236	−	0.724019i	−0.211500	−	0.0300116i
$583$	−30.5324	+	52.8838i	−1.26452	+	2.19022i
$584$	−1.03828	+	1.79835i	−0.0429643	+	0.0744164i
$585$	3.46688	+	3.60925i	0.143338	+	0.149224i
$586$	32.3836	−	18.6967i	1.33775	−	0.772353i
$587$	−1.29227	−	2.23827i	−0.0533376	−	0.0923834i	0.838124	−	0.545480i	$-0.183653\pi$
$587$	−1.29227	−	2.23827i	−0.0533376	−	0.0923834i	−0.891461	+	0.453097i	$0.850319\pi$
$588$	−20.9755	−	2.90450i	−0.865016	−	0.119780i
$589$	−8.83219	+	15.2978i	−0.363924	+	0.630335i
$590$		−	25.8893i		−	1.06585i
$591$	−1.60309	+	11.2974i	−0.0659422	+	0.464712i
$592$	6.71714			0.276073
$593$	7.57018	+	13.1119i	0.310870	+	0.538443i	0.978551	−	0.206005i	$-0.0660463\pi$
$593$	7.57018	+	13.1119i	0.310870	+	0.538443i	−0.667681	+	0.744448i	$0.732713\pi$
$594$	−38.8016	+	27.9549i	−1.59205	+	1.14700i
$595$	0.00490228	+	2.91657i	0.000200974	+	0.119568i
$596$	−29.4137	+	16.9820i	−1.20483	+	0.695611i
$597$	−27.9707	−	21.9132i	−1.14477	−	0.896846i
$598$	23.9917	−	13.8516i	0.981094	−	0.566435i
$599$	0.256504	−	0.148092i	0.0104805	−	0.00605089i	−0.494751	−	0.869035i	$-0.664741\pi$
$599$	0.256504	−	0.148092i	0.0104805	−	0.00605089i	0.505231	+	0.862984i	$0.331407\pi$
$600$	0.119382	−	0.841315i	0.00487374	−	0.0343466i
$601$	4.14552	−	2.39342i	0.169099	−	0.0976296i	−0.413062	−	0.910703i	$-0.635541\pi$
$601$	4.14552	−	2.39342i	0.169099	−	0.0976296i	0.582161	+	0.813073i	$0.302207\pi$
$602$	−0.250684	−	0.432517i	−0.0102171	−	0.0176281i
$603$	3.63326	+	14.7393i	0.147958	+	0.600231i
$604$	−17.7909	−	30.8147i	−0.723900	−	1.25383i
$605$	11.6090			0.471971
$606$	35.4632	+	27.7830i	1.44059	+	1.12861i
$607$			5.89875i			0.239423i	0.992809	+	0.119711i	$0.0381969\pi$
$607$			5.89875i			0.239423i	−0.992809	+	0.119711i	$0.961803\pi$
$608$	−16.9644	+	29.3832i	−0.687996	+	1.19164i
$609$	−8.68986	+	11.1305i	−0.352131	+	0.451032i
$610$	10.3942	+	18.0033i	0.420850	+	0.728933i
$611$	−7.97285	+	4.60313i	−0.322547	+	0.186223i
$612$	5.54794	+	1.60685i	0.224262	+	0.0649530i
$613$	13.5388	−	23.4499i	0.546828	−	0.947134i	−0.451661	−	0.892189i	$-0.649168\pi$
$613$	13.5388	−	23.4499i	0.546828	−	0.947134i	0.998489	−	0.0549446i	$-0.0174982\pi$
$614$	26.4917	−	45.8849i	1.06912	−	1.85176i
$615$	8.11817	−	10.3623i	0.327356	−	0.417849i
$616$	−5.33980	+	3.09491i	−0.215147	+	0.124698i
$617$	−10.3098	−	5.95234i	−0.415055	−	0.239632i	0.277904	−	0.960609i	$-0.410360\pi$
$617$	−10.3098	−	5.95234i	−0.415055	−	0.239632i	−0.692959	+	0.720977i	$0.743694\pi$
$618$	−2.76747	+	3.53249i	−0.111324	+	0.142098i
$619$			39.6262i			1.59271i	0.604829	+	0.796355i	$0.293241\pi$
$619$			39.6262i			1.59271i	−0.604829	+	0.796355i	$0.706759\pi$
$620$	5.99906	+	3.46356i	0.240928	+	0.139100i
$621$	−18.2953	+	40.6540i	−0.734164	+	1.63139i
$622$		−	43.3267i		−	1.73724i
$623$	−32.8355	−	18.8840i	−1.31552	−	0.756573i
$624$	11.9084	−	4.79285i	0.476716	−	0.191868i
$625$	1.00000			0.0400000
$626$	5.67713	+	9.83308i	0.226904	+	0.393009i
$627$	−13.6951	−	34.0271i	−0.546931	−	1.35891i
$628$	−10.9899	−	6.34504i	−0.438546	−	0.253195i
$629$	1.66672			0.0664567
$630$	14.7640	+	4.24921i	0.588212	+	0.169293i
$631$	14.7767			0.588253			0.294126	−	0.955767i	$-0.404971\pi$
$631$	14.7767			0.588253			0.294126	+	0.955767i	$0.404971\pi$
$632$	2.63980	+	1.52409i	0.105006	+	0.0606251i
$633$	4.73516	−	6.04412i	0.188206	−	0.240232i
$634$	15.5515	+	26.9360i	0.617630	+	1.06977i
$635$	−0.0601044			−0.00238517
$636$	5.45809	−	38.4646i	0.216427	−	1.52522i
$637$	−10.0932	+	5.87265i	−0.399908	+	0.232683i
$638$		−	28.3603i		−	1.12279i
$639$	−3.89072	+	13.4334i	−0.153915	+	0.531419i
$640$	−3.37168	−	1.94664i	−0.133277	−	0.0769477i
$641$		−	31.6377i		−	1.24961i	−0.780780	−	0.624807i	$-0.785178\pi$
$641$		−	31.6377i		−	1.24961i	0.780780	−	0.624807i	$-0.214822\pi$
$642$	−24.5927	−	3.48968i	−0.970598	−	0.137727i
$643$	34.3241	+	19.8170i	1.35361	+	0.781507i	0.988753	−	0.149556i	$-0.0477844\pi$
$643$	34.3241	+	19.8170i	1.35361	+	0.781507i	0.364857	+	0.931063i	$0.381118\pi$
$644$	19.7651	−	34.3674i	0.778853	−	1.35427i
$645$	0.0631296	+	0.156852i	0.00248572	+	0.00617605i
$646$	−4.75153	+	8.22990i	−0.186947	+	0.323801i
$647$	−11.9974	+	20.7801i	−0.471665	+	0.816949i	−0.999475	−	0.0324145i	$-0.989680\pi$
$647$	−11.9974	+	20.7801i	−0.471665	+	0.816949i	0.527809	+	0.849363i	$0.323014\pi$
$648$	−2.35971	+	3.73195i	−0.0926983	+	0.146605i
$649$	55.0777	−	31.7991i	2.16199	−	1.24823i
$650$	1.61448	+	2.79636i	0.0633251	+	0.109682i
$651$	11.1849	−	14.3263i	0.438370	−	0.561492i
$652$	2.09443	−	3.62766i	0.0820243	−	0.142070i
$653$			26.5244i			1.03798i	0.854781	+	0.518989i	$0.173692\pi$
$653$			26.5244i			1.03798i	−0.854781	+	0.518989i	$0.826308\pi$
$654$	42.4595	−	17.0890i	1.66030	−	0.668233i
$655$	−10.7285			−0.419196
$656$	−16.8823	−	29.2410i	−0.659142	−	1.14167i
$657$	8.79648	+	9.15770i	0.343183	+	0.357276i
$658$	−14.0898	+	24.4992i	−0.549276	+	0.955077i
$659$	−36.8475	+	21.2739i	−1.43537	+	0.828714i	−0.997524	−	0.0703335i	$-0.977594\pi$
$659$	−36.8475	+	21.2739i	−1.43537	+	0.828714i	−0.437851	+	0.899047i	$0.644260\pi$
$660$	−13.3438	+	5.37057i	−0.519405	+	0.209049i
$661$	−22.7332	+	13.1250i	−0.884220	+	0.510505i	−0.872047	−	0.489421i	$-0.837208\pi$
$661$	−22.7332	+	13.1250i	−0.884220	+	0.510505i	−0.0121725	+	0.999926i	$0.503875\pi$
$662$	−33.1959	+	19.1657i	−1.29019	+	0.744894i
$663$	2.95482	−	1.18925i	0.114756	−	0.0461867i
$664$	2.21103	−	1.27654i	0.0858047	−	0.0495394i
$665$	−5.87458	+	10.2147i	−0.227806	+	0.396108i
$666$	2.44246	−	8.43304i	0.0946434	−	0.326774i
$667$	−13.2188	−	22.8957i	−0.511836	−	0.886525i
$668$	11.2057			0.433562
$669$	4.18850	−	1.68578i	0.161937	−	0.0651760i
$670$			9.79444i			0.378392i
$671$	−25.5339	+	44.2260i	−0.985725	+	1.70733i
$672$	21.4833	−	27.5172i	0.828736	−	1.06150i
$673$	−6.40668	−	11.0967i	−0.246959	−	0.427746i	0.715721	−	0.698386i	$-0.246098\pi$
$673$	−6.40668	−	11.0967i	−0.246959	−	0.427746i	−0.962681	+	0.270640i	$0.912765\pi$
$674$	−29.2410	+	16.8823i	−1.12632	+	0.650281i
$675$	−4.73844	−	2.13241i	−0.182383	−	0.0820765i
$676$	8.92230	−	15.4539i	0.343165	−	0.594380i
$677$	9.67024	−	16.7493i	0.371657	−	0.643729i	−0.618163	−	0.786050i	$-0.712123\pi$
$677$	9.67024	−	16.7493i	0.371657	−	0.643729i	0.989821	+	0.142320i	$0.0454563\pi$
$678$	13.4393	+	33.3914i	0.516134	+	1.28239i
$679$	−2.02757	+	3.52553i	−0.0778111	+	0.135297i
$680$	−0.468362	−	0.270409i	−0.0179609	−	0.0103697i
$681$	22.6099	+	3.20832i	0.866413	+	0.122943i
$682$			36.5031i			1.39778i
$683$	32.5792	+	18.8096i	1.24661	+	0.719731i	0.970432	−	0.241376i	$-0.0775986\pi$
$683$	32.5792	+	18.8096i	1.24661	+	0.719731i	0.276178	+	0.961106i	$0.410932\pi$
$684$	16.1657	+	16.8295i	0.618111	+	0.643493i
$685$			7.11878i			0.271995i
$686$	−17.7671	+	31.1351i	−0.678352	+	1.18874i
$687$	5.28460	−	37.2420i	0.201620	−	1.42087i
$688$	0.433686			0.0165341
$689$	−10.7120	−	18.5536i	−0.408093	−	0.706837i
$690$	−17.7388	+	22.6425i	−0.675306	+	0.861984i
$691$	17.6095	+	10.1669i	0.669898	+	0.386766i	0.796038	−	0.605247i	$-0.206926\pi$
$691$	17.6095	+	10.1669i	0.669898	+	0.386766i	−0.126140	+	0.992012i	$0.540259\pi$
$692$	−37.3853			−1.42118
$693$	9.09434	+	36.6286i	0.345465	+	1.39141i
$694$	−23.3160			−0.885065
$695$	15.1361	+	8.73885i	0.574146	+	0.331484i
$696$	−0.977652	−	2.42908i	−0.0370578	−	0.0920741i
$697$	−4.18900	−	7.25556i	−0.158670	−	0.274824i
$698$	−8.25529			−0.312467
$699$	−21.1537	+	8.51390i	−0.800106	+	0.322025i
$700$	4.00570	+	2.30372i	0.151401	+	0.0870726i
$701$			47.0337i			1.77644i	0.459419	+	0.888220i	$0.348058\pi$
$701$			47.0337i			1.77644i	−0.459419	+	0.888220i	$0.651942\pi$
$702$	−1.68713	−	16.6931i	−0.0636764	−	0.630041i
$703$	5.83169	+	3.36693i	0.219946	+	0.126986i
$704$			27.8641i			1.05017i
$705$	5.89492	−	7.52448i	0.222015	−	0.283388i
$706$	18.2543	+	10.5391i	0.687009	+	0.396645i
$707$	30.7595	−	17.8280i	1.15683	−	0.670491i
$708$	−24.9531	+	31.8510i	−0.937796	+	1.19704i
$709$	7.24566	−	12.5498i	0.272116	−	0.471319i	−0.697287	−	0.716792i	$-0.745610\pi$
$709$	7.24566	−	12.5498i	0.272116	−	0.471319i	0.969404	+	0.245472i	$0.0789431\pi$
$710$	−4.51173	+	7.81454i	−0.169322	+	0.293274i
$711$	13.4426	−	12.9124i	0.504137	−	0.484251i
$712$	6.08276	−	3.51188i	0.227961	−	0.131613i
$713$	17.0142	+	29.4695i	0.637188	+	1.10364i
$714$	6.01723	−	7.70725i	0.225189	−	0.288437i
$715$	−3.96604	+	6.86939i	−0.148322	+	0.256901i
$716$			2.79254i			0.104362i
$717$	1.95736	+	1.53346i	0.0730989	+	0.0572681i
$718$	28.5713			1.06627
$719$	7.17917	+	12.4347i	0.267738	+	0.463735i	0.968277	−	0.249878i	$-0.0803906\pi$
$719$	7.17917	+	12.4347i	0.267738	+	0.463735i	−0.700540	+	0.713614i	$0.747057\pi$
$720$	−9.61201	+	9.23287i	−0.358219	+	0.344089i
$721$	1.77585	+	3.06396i	0.0661361	+	0.114108i
$722$	−1.40096	+	0.808842i	−0.0521382	+	0.0301020i
$723$	−0.870149	+	6.13218i	−0.0323612	+	0.228058i
$724$	20.7949	−	12.0059i	0.772836	−	0.446197i
$725$	2.66862	−	1.54073i	0.0991099	−	0.0572211i
$726$	−30.6372	−	24.0022i	−1.13705	−	0.890803i
$727$	41.4780	−	23.9473i	1.53833	−	0.888157i	0.539396	−	0.842052i	$-0.318653\pi$
$727$	41.4780	−	23.9473i	1.53833	−	0.888157i	0.998937	−	0.0461048i	$-0.0146808\pi$
$728$	−0.00363955	−	2.16532i	−0.000134891	−	0.0802522i
$729$	17.9056	+	20.2086i	0.663172	+	0.748467i
$730$	4.09640	+	7.09517i	0.151615	+	0.262604i
$731$	0.107611			0.00398012
$732$	4.56453	−	32.1674i	0.168710	−	1.18894i
$733$		−	13.6124i		−	0.502787i	−0.967885	−	0.251393i	$-0.919111\pi$
$733$		−	13.6124i		−	0.502787i	0.967885	−	0.251393i	$-0.0808888\pi$
$734$	−0.580311	+	1.00513i	−0.0214197	+	0.0371000i
$735$	7.44509	−	9.56926i	0.274616	−	0.352967i
$736$	32.6800	+	56.6034i	1.20460	+	2.08643i
$737$	−20.8370	+	12.0303i	−0.767542	+	0.443140i
$738$	−42.8493	+	10.5624i	−1.57730	+	0.388807i
$739$	−1.60805	+	2.78523i	−0.0591532	+	0.102456i	−0.894086	−	0.447896i	$-0.852173\pi$
$739$	−1.60805	+	2.78523i	−0.0591532	+	0.102456i	0.834932	+	0.550353i	$0.185507\pi$
$740$	1.32035	−	2.28691i	0.0485369	−	0.0840683i
$741$	12.7410	+	1.80793i	0.468052	+	0.0664161i
$742$	−57.0121	−	32.7883i	−2.09298	−	1.20370i
$743$	−5.01891	−	2.89767i	−0.184126	−	0.106305i	0.405104	−	0.914271i	$-0.367235\pi$
$743$	−5.01891	−	2.89767i	−0.184126	−	0.106305i	−0.589230	+	0.807966i	$0.700569\pi$
$744$	1.25836	+	3.12652i	0.0461335	+	0.114624i
$745$		−	19.4465i		−	0.712464i
$746$	29.1418	+	16.8250i	1.06696	+	0.616008i
$747$	−3.73653	−	15.1583i	−0.136713	−	0.554612i
$748$			9.15467i			0.334728i
$749$	−9.77264	+	16.9926i	−0.357085	+	0.620897i
$750$	−2.63910	−	2.06755i	−0.0963662	−	0.0754964i
$751$	18.9712			0.692267			0.346134	−	0.938185i	$-0.387494\pi$
$751$	18.9712			0.692267			0.346134	+	0.938185i	$0.387494\pi$
$752$	−12.2589	−	21.2330i	−0.447036	−	0.774288i
$753$	−5.72718	−	0.812681i	−0.208710	−	0.0296157i
$754$	8.61684	+	4.97494i	0.313807	+	0.181177i
$755$	20.3727			0.741439
$756$	−14.0683	−	19.4579i	−0.511659	−	0.707675i
$757$	49.3445			1.79346			0.896729	−	0.442580i	$-0.145937\pi$
$757$	49.3445			1.79346			0.896729	+	0.442580i	$0.145937\pi$
$758$	56.0903	+	32.3837i	2.03729	+	1.17623i
$759$	−69.9585	−	9.92703i	−2.53933	−	0.360328i
$760$	−1.09250	−	1.89227i	−0.0396291	−	0.0686397i
$761$	−3.62240			−0.131312			−0.0656560	−	0.997842i	$-0.520914\pi$
$761$	−3.62240			−0.131312			−0.0656560	+	0.997842i	$0.520914\pi$
$762$	0.158621	+	0.124269i	0.00574625	+	0.00450180i
$763$	−0.0607119	−	36.1201i	−0.00219792	−	1.30763i
$764$			10.2626i			0.371288i
$765$	−2.38503	+	2.29095i	−0.0862309	+	0.0828295i
$766$	−24.0490	−	13.8847i	−0.868927	−	0.501675i
$767$			22.3127i			0.805665i
$768$	12.4529	+	30.9404i	0.449354	+	1.11647i
$769$	−34.3159	−	19.8123i	−1.23746	−	0.714450i	−0.268889	−	0.963171i	$-0.586656\pi$
$769$	−34.3159	−	19.8123i	−1.23746	−	0.714450i	−0.968575	+	0.248721i	$0.919990\pi$
$770$	0.0409288	+	24.3503i	0.00147497	+	0.877523i
$771$	9.54317	+	1.35417i	0.343689	+	0.0487691i
$772$	−23.6501	+	40.9631i	−0.851185	+	1.47430i
$773$	−10.1781	+	17.6290i	−0.366082	+	0.634073i	−0.988949	−	0.148255i	$-0.952634\pi$
$773$	−10.1781	+	17.6290i	−0.366082	+	0.634073i	0.622867	+	0.782328i	$0.285968\pi$
$774$	0.157695	−	0.544472i	0.00566824	−	0.0195706i
$775$	−3.43483	+	1.98310i	−0.123383	+	0.0712350i
$776$	−0.377069	−	0.653103i	−0.0135360	−	0.0234450i
$777$	−5.46135	−	4.26380i	−0.195925	−	0.152963i
$778$	−33.4821	+	57.9928i	−1.20039	+	2.07914i
$779$		−	33.8486i		−	1.21275i
$780$	0.708984	−	4.99640i	0.0253857	−	0.178900i
$781$	−22.1665			−0.793181
$782$	9.15330	+	15.8540i	0.327321	+	0.566937i
$783$	−15.9305	+	1.61005i	−0.569311	+	0.0575386i
$784$	−15.6398	−	26.8799i	−0.558565	−	0.959996i
$785$	6.29240	−	3.63292i	0.224586	−	0.129665i
$786$	28.3135	+	22.1817i	1.00991	+	0.791195i
$787$	−23.7326	+	13.7020i	−0.845976	+	0.488425i	−0.859291	−	0.511487i	$-0.829095\pi$
$787$	−23.7326	+	13.7020i	−0.845976	+	0.488425i	0.0133149	+	0.999911i	$0.495762\pi$
$788$	9.96449	−	5.75300i	0.354970	−	0.204942i
$789$	−4.23248	+	29.8274i	−0.150680	+	1.06188i
$790$	10.4150	−	6.01311i	0.370550	−	0.213937i
$791$	28.4059	−	0.0477456i	1.01000	−	0.00169764i
$792$	−6.72198	−	1.94688i	−0.238855	−	0.0691795i
$793$	−8.95826	−	15.5162i	−0.318117	−	0.550995i
$794$	41.0093			1.45537
$795$	17.5102	+	13.7181i	0.621024	+	0.486530i
$796$			35.8296i			1.26995i
$797$	−5.82842	+	10.0951i	−0.206453	+	0.357588i	−0.950595	−	0.310434i	$-0.899525\pi$
$797$	−5.82842	+	10.0951i	−0.206453	+	0.357588i	0.744141	+	0.668022i	$0.232859\pi$
$798$	36.6230	−	14.8115i	1.29644	−	0.524322i
$799$	−3.04180	−	5.26855i	−0.107611	−	0.186388i
$800$	−6.59742	+	3.80902i	−0.233254	+	0.134669i
$801$	−10.2795	−	41.7018i	−0.363210	−	1.47346i
$802$	10.6187	−	18.3921i	0.374958	−	0.649447i
$803$	−10.0630	+	17.4296i	−0.355116	+	0.615078i
$804$	9.44028	−	12.0499i	0.332933	−	0.424967i
$805$	11.3828	+	19.6393i	0.401191	+	0.692194i
$806$	−11.0909	−	6.40334i	−0.390661	−	0.225548i
$807$	14.2174	−	18.1476i	0.500477	−	0.638826i
$808$			6.59248i			0.231923i
$809$	16.5950	+	9.58115i	0.583450	+	0.336855i	0.762503	−	0.646984i	$-0.223970\pi$
$809$	16.5950	+	9.58115i	0.583450	+	0.336855i	−0.179053	+	0.983839i	$0.557303\pi$
$810$	8.09633	+	15.4246i	0.284476	+	0.541966i
$811$			15.3856i			0.540261i	0.962824	+	0.270131i	$0.0870669\pi$
$811$			15.3856i			0.540261i	−0.962824	+	0.270131i	$0.912933\pi$
$812$	14.2391	−	0.0239336i	0.499694	−	0.000839903i
$813$	20.0516	−	8.07032i	0.703240	−	0.283039i
$814$	13.9154			0.487734
$815$	1.19919	+	2.07706i	0.0420058	+	0.0727562i
$816$	3.16717	+	7.86917i	0.110873	+	0.275476i
$817$	0.376518	+	0.217383i	0.0131727	+	0.00760526i
$818$	−13.5450			−0.473589
$819$	−12.7244	−	3.66219i	−0.444626	−	0.127967i
$820$	−13.2738			−0.463540
$821$	−30.0527	−	17.3509i	−1.04885	−	0.605551i	−0.126519	−	0.991964i	$-0.540381\pi$
$821$	−30.0527	−	17.3509i	−1.04885	−	0.605551i	−0.922326	+	0.386413i	$0.873714\pi$
$822$	14.7185	−	18.7872i	0.513365	−	0.655277i
$823$	0.522365	+	0.904763i	0.0182085	+	0.0315380i	0.874986	−	0.484148i	$-0.160870\pi$
$823$	0.522365	+	0.904763i	0.0182085	+	0.0315380i	−0.856778	+	0.515686i	$0.827537\pi$
$824$	−0.656678			−0.0228765
$825$	1.15705	−	8.15402i	0.0402832	−	0.283887i
$826$	34.3480	+	59.2622i	1.19512	+	2.06199i
$827$		−	40.5483i		−	1.41000i	−0.709206	−	0.705001i	$-0.750947\pi$
$827$		−	40.5483i		−	1.41000i	0.709206	−	0.705001i	$-0.249053\pi$
$828$	43.6474	−	10.7591i	1.51685	−	0.373906i
$829$	−23.7000	−	13.6832i	−0.823133	−	0.475236i	0.0283624	−	0.999598i	$-0.490971\pi$
$829$	−23.7000	−	13.6832i	−0.823133	−	0.475236i	−0.851496	+	0.524361i	$0.824304\pi$
$830$		−	10.0729i		−	0.349634i
$831$	−36.5115	−	5.18094i	−1.26657	−	0.179725i
$832$	−8.46610	−	4.88790i	−0.293509	−	0.169458i
$833$	−3.88071	−	6.66971i	−0.134459	−	0.231092i
$834$	−21.8777	−	54.3575i	−0.757563	−	1.88225i
$835$	−3.20798	+	5.55638i	−0.111017	+	0.192287i
$836$	−18.4932	+	32.0312i	−0.639602	+	1.10782i
$837$	20.5045	−	2.07233i	0.708739	−	0.0716302i
$838$	−27.6727	+	15.9768i	−0.955936	+	0.551910i
$839$	18.1031	+	31.3556i	0.624990	+	1.08251i	0.988543	+	0.150941i	$0.0482302\pi$
$839$	18.1031	+	31.3556i	0.624990	+	1.08251i	−0.363553	+	0.931574i	$0.618436\pi$
$840$	0.842922	+	2.08421i	0.0290836	+	0.0719120i
$841$	−9.75233	+	16.8915i	−0.336287	+	0.582467i
$842$		−	2.19391i		−	0.0756072i
$843$	34.8313	−	14.0188i	1.19965	−	0.482834i
$844$	−7.74232			−0.266502
$845$	5.10856	+	8.84829i	0.175740	+	0.304390i
$846$	−31.1145	+	7.66977i	−1.06974	+	0.263692i
$847$	−26.5736	+	15.4019i	−0.913080	+	0.529216i
$848$	49.4114	−	28.5277i	1.69679	−	0.979644i
$849$	1.84236	−	0.741510i	0.0632297	−	0.0254486i
$850$	−1.84786	+	1.06686i	−0.0633812	+	0.0365932i
$851$	11.2341	−	6.48601i	0.385100	−	0.222338i
$852$	13.0826	−	5.26548i	0.448204	−	0.180392i
$853$	−4.39453	+	2.53718i	−0.150466	+	0.0868714i	−0.573343	−	0.819316i	$-0.694354\pi$
$853$	−4.39453	+	2.53718i	−0.150466	+	0.0868714i	0.422877	+	0.906187i	$0.361020\pi$
$854$	−47.6784	−	27.4204i	−1.63152	−	0.938307i
$855$	−12.9729	+	3.19783i	−0.443663	+	0.109364i
$856$	−1.81743	−	3.14788i	−0.0621184	−	0.107592i
$857$	22.8307			0.779882			0.389941	−	0.920840i	$-0.372495\pi$
$857$	22.8307			0.779882			0.389941	+	0.920840i	$0.372495\pi$
$858$	24.6696	−	9.92898i	0.842207	−	0.338970i
$859$		−	28.9305i		−	0.987097i	−0.869718	−	0.493548i	$-0.835700\pi$
$859$		−	28.9305i		−	0.987097i	0.869718	−	0.493548i	$-0.164300\pi$
$860$	0.0852470	−	0.147652i	0.00290690	−	0.00503489i
$861$	−4.83504	+	34.4905i	−0.164778	+	1.17543i
$862$	−25.2100	−	43.6650i	−0.858655	−	1.48723i
$863$	32.0320	−	18.4937i	1.09038	−	0.629532i	0.156703	−	0.987646i	$-0.449913\pi$
$863$	32.0320	−	18.4937i	1.09038	−	0.629532i	0.933678	+	0.358114i	$0.116580\pi$
$864$	39.3839	−	3.98042i	1.33987	−	0.135416i
$865$	10.7027	−	18.5376i	0.363902	−	0.630297i
$866$	−17.6023	+	30.4880i	−0.598150	+	1.03603i
$867$	−10.2080	−	25.3629i	−0.346682	−	0.861369i
$868$	−18.3274	+	0.0308054i	−0.622072	+	0.00104560i
$869$	25.5850	+	14.7715i	0.867911	+	0.501089i
$870$	−10.2283	−	1.45138i	−0.346771	−	0.0492064i
$871$		−	8.44135i		−	0.286024i
$872$	5.80040	+	3.34886i	0.196426	+	0.113407i
$873$	−4.47751	+	1.10371i	−0.151541	+	0.0373550i
$874$			73.9618i			2.50180i
$875$	−2.28906	+	1.32673i	−0.0773844	+	0.0448515i
$876$	1.79890	−	12.6773i	0.0607791	−	0.428327i
$877$	30.4143			1.02702			0.513508	−	0.858085i	$-0.328346\pi$
$877$	30.4143			1.02702			0.513508	+	0.858085i	$0.328346\pi$
$878$	26.0262	+	45.0788i	0.878343	+	1.52133i
$879$	20.6358	−	26.3403i	0.696028	−	0.888435i
$880$	−18.2943	−	10.5622i	−0.616701	−	0.356052i
$881$	28.4402			0.958174			0.479087	−	0.877767i	$-0.340968\pi$
$881$	28.4402			0.958174			0.479087	+	0.877767i	$0.340968\pi$
$882$	−39.4333	+	9.86108i	−1.32779	+	0.332040i
$883$	7.79800			0.262423			0.131212	−	0.991354i	$-0.458113\pi$
$883$	7.79800			0.262423			0.131212	+	0.991354i	$0.458113\pi$
$884$	−2.78151	−	1.60590i	−0.0935522	−	0.0540124i
$885$	−8.64982	−	21.4914i	−0.290760	−	0.722425i
$886$	−3.99734	−	6.92359i	−0.134293	−	0.232603i
$887$	7.22171			0.242481			0.121241	−	0.992623i	$-0.461313\pi$
$887$	7.22171			0.242481			0.121241	+	0.992623i	$0.461313\pi$
$888$	1.19186	−	0.479699i	0.0399963	−	0.0160976i
$889$	0.137583	−	0.0797420i	0.00461437	−	0.00267446i
$890$		−	27.7114i		−	0.928887i
$891$	−22.8703	+	36.1701i	−0.766185	+	1.21174i
$892$	−3.94283	−	2.27639i	−0.132016	−	0.0762192i
$893$		−	24.5788i		−	0.822498i
$894$	−40.2067	+	51.3212i	−1.34471	+	1.71644i
$895$	−1.38469	−	0.799451i	−0.0462850	−	0.0267227i
$896$	10.3006	−	0.0173137i	0.344120	−	0.000578409i
$897$	15.2882	−	19.5144i	0.510459	−	0.651568i
$898$	6.71913	−	11.6379i	0.224220	−	0.388361i
$899$	−6.11082	+	10.5843i	−0.203807	+	0.353005i
$900$	1.25403	+	5.08733i	0.0418011	+	0.169578i
$901$	12.2604	−	7.07857i	0.408455	−	0.235821i
$902$	−34.9737	−	60.5762i	−1.16450	−	2.01697i
$903$	−0.352607	−	0.275289i	−0.0117340	−	0.00916103i
$904$	−2.63364	+	4.56160i	−0.0875937	+	0.151717i
$905$			13.7483i			0.457008i
$906$	−53.7656	−	42.1217i	−1.78624	−	1.39940i
$907$	−44.0527			−1.46274			−0.731372	−	0.681978i	$-0.761120\pi$
$907$	−44.0527			−1.46274			−0.731372	+	0.681978i	$0.761120\pi$
$908$	−11.5137	−	19.9423i	−0.382095	−	0.661809i
$909$	38.7214	+	11.2149i	1.28431	+	0.371974i
$910$	−7.40564	−	4.25907i	−0.245495	−	0.141187i
$911$	10.5862	−	6.11197i	0.350738	−	0.202498i	−0.314272	−	0.949333i	$-0.601761\pi$
$911$	10.5862	−	6.11197i	0.350738	−	0.202498i	0.665010	+	0.746834i	$0.268427\pi$
$912$	−4.81482	+	33.9314i	−0.159435	+	1.12358i
$913$	21.4293	−	12.3722i	0.709207	−	0.409461i
$914$	−40.2406	+	23.2329i	−1.33104	+	0.768477i
$915$	14.6436	+	11.4722i	0.484102	+	0.379261i
$916$	−32.8481	+	18.9649i	−1.08533	+	0.626616i
$917$	24.5581	−	14.2337i	0.810981	−	0.470039i
$918$	11.0310	−	1.11487i	0.364077	−	0.0367962i
$919$	0.0935824	+	0.162090i	0.00308700	+	0.00534684i	0.867565	−	0.497324i	$-0.165684\pi$
$919$	0.0935824	+	0.162090i	0.00308700	+	0.00534684i	−0.864478	+	0.502671i	$0.832351\pi$
$920$	−4.20916			−0.138772
$921$	6.66093	−	46.9414i	0.219485	−	1.54677i
$922$		−	48.9580i		−	1.61235i
$923$	3.88844	−	6.73497i	0.127989	−	0.221684i
$924$	23.4194	−	29.9971i	0.770442	−	0.986831i
$925$	0.755979	+	1.30939i	0.0248564	+	0.0430526i
$926$	20.5447	−	11.8615i	0.675142	−	0.389794i
$927$	−1.11712	+	3.85705i	−0.0366909	+	0.126682i
$928$	−11.7373	+	20.3296i	−0.385296	+	0.667353i
$929$	9.60791	−	16.6414i	0.315225	−	0.545986i	−0.664260	−	0.747502i	$-0.731253\pi$
$929$	9.60791	−	16.6414i	0.315225	−	0.545986i	0.979485	+	0.201515i	$0.0645865\pi$
$930$	13.1650	+	1.86810i	0.431697	+	0.0612574i
$931$	−0.104804	−	31.1760i	−0.00343480	−	1.02175i
$932$	19.9129	+	11.4967i	0.652270	+	0.376588i
$933$	−14.4758	−	35.9667i	−0.473917	−	1.17750i
$934$			24.6325i			0.806001i
$935$	−4.53937	−	2.62080i	−0.148453	−	0.0857095i
$936$	1.77069	−	1.70085i	0.0578770	−	0.0555940i
$937$		−	12.8045i		−	0.418303i	−0.977883	−	0.209152i	$-0.932930\pi$
$937$		−	12.8045i		−	0.418303i	0.977883	−	0.209152i	$-0.0670702\pi$
$938$	−12.9945	−	22.4201i	−0.424287	−	0.732042i
$939$	7.99805	+	6.26593i	0.261007	+	0.204481i
$940$	−9.63860			−0.314377
$941$	−3.77052	−	6.53073i	−0.122915	−	0.212896i	0.798001	−	0.602656i	$-0.205891\pi$
$941$	−3.77052	−	6.53073i	−0.122915	−	0.212896i	−0.920916	+	0.389761i	$0.872558\pi$
$942$	−24.1175	−	3.42225i	−0.785792	−	0.111503i
$943$	−56.4696	−	32.6028i	−1.83890	−	1.06169i
$944$	−59.4224			−1.93403
$945$	13.6757	−	1.40539i	0.444871	−	0.0457173i
$946$	0.898434			0.0292106
$947$	−10.7102	−	6.18354i	−0.348035	−	0.200938i	0.315785	−	0.948831i	$-0.397732\pi$
$947$	−10.7102	−	6.18354i	−0.348035	−	0.200938i	−0.663819	+	0.747893i	$0.731066\pi$
$948$	−18.6090	−	2.64060i	−0.604394	−	0.0857628i
$949$	−3.53049	−	6.11498i	−0.114604	−	0.198501i
$950$	−8.62064			−0.279690
$951$	21.9093	+	17.1644i	0.710457	+	0.556595i
$952$	1.43087	−	0.00240506i	0.0463747	−	7.79483e-5i
$953$		−	28.8225i		−	0.933652i	−0.884349	−	0.466826i	$-0.845398\pi$
$953$		−	28.8225i		−	0.933652i	0.884349	−	0.466826i	$-0.154602\pi$
$954$	−17.8483	−	72.4067i	−0.577861	−	2.34425i
$955$	−5.08874	−	2.93798i	−0.164668	−	0.0950709i
$956$		−	2.50731i		−	0.0810923i
$957$	−9.47540	−	23.5426i	−0.306296	−	0.761026i
$958$	−3.62682	−	2.09394i	−0.117177	−	0.0676522i
$959$	−9.44467	−	16.2953i	−0.304984	−	0.526204i
$960$	10.0493	+	1.42599i	0.324341	+	0.0460236i
$961$	−7.63465	+	13.2236i	−0.246279	+	0.426568i
$962$	−2.44102	+	4.22798i	−0.0787017	+	0.136315i
$963$	−21.5810	+	5.31975i	−0.695439	+	0.171426i
$964$	5.40869	−	3.12271i	0.174202	−	0.100576i
$965$	−13.5411	−	23.4539i	−0.435904	−	0.755008i
$966$	10.5650	−	75.3645i	0.339922	−	2.42481i
$967$	5.73819	−	9.93883i	0.184528	−	0.319611i	−0.758890	−	0.651219i	$-0.774258\pi$
$967$	5.73819	−	9.93883i	0.184528	−	0.319611i	0.943417	+	0.331608i	$0.107591\pi$
$968$		−	5.69535i		−	0.183055i
$969$	−1.19470	+	8.41939i	−0.0383794	+	0.270470i
$970$	−2.97536			−0.0955330
$971$	−1.83549	−	3.17917i	−0.0589038	−	0.102024i	0.835070	−	0.550144i	$-0.185427\pi$
$971$	−1.83549	−	3.17917i	−0.0589038	−	0.102024i	−0.893974	+	0.448120i	$0.852094\pi$
$972$	4.90612	−	26.7801i	0.157364	−	0.858974i
$973$	−46.2416	+	0.0777246i	−1.48244	+	0.00249174i
$974$	51.5256	−	29.7483i	1.65099	−	0.953197i
$975$	2.27451	+	1.78192i	0.0728426	+	0.0570672i
$976$	41.3221	−	23.8573i	1.32269	−	0.763654i
$977$	−13.1394	+	7.58605i	−0.420367	+	0.242699i	−0.695234	−	0.718783i	$-0.744699\pi$
$977$	−13.1394	+	7.58605i	−0.420367	+	0.242699i	0.274867	+	0.961482i	$0.411366\pi$
$978$	1.12965	−	7.96095i	0.0361223	−	0.254563i
$979$	58.9541	−	34.0371i	1.88418	−	1.08783i
$980$	−12.2257	+	0.0410989i	−0.390536	+	0.00131286i
$981$	29.5372	−	28.3721i	0.943050	−	0.905852i
$982$	29.0677	+	50.3468i	0.927589	+	1.60663i
$983$	55.9491			1.78450			0.892249	−	0.451543i	$-0.149126\pi$
$983$	55.9491			1.78450			0.892249	+	0.451543i	$0.149126\pi$
$984$	−5.08374	−	3.98277i	−0.162064	−	0.126966i
$985$			6.58789i			0.209908i
$986$	−3.28749	+	5.69410i	−0.104695	+	0.181337i
$987$	−3.51091	+	25.0449i	−0.111754	+	0.797189i
$988$	−6.48813	−	11.2378i	−0.206415	−	0.357521i
$989$	0.725320	−	0.418764i	0.0230638	−	0.0133159i
$990$	−19.9124	+	19.1270i	−0.632859	+	0.607896i
$991$	−19.8776	+	34.4290i	−0.631432	+	1.09367i	0.355827	+	0.934552i	$0.384199\pi$
$991$	−19.8776	+	34.4290i	−0.631432	+	1.09367i	−0.987259	+	0.159121i	$0.949134\pi$
$992$	15.1073	−	26.1667i	0.479658	−	0.830792i
$993$	−21.1534	+	27.0009i	−0.671283	+	0.856849i
$994$	−0.0401279	−	23.8738i	−0.00127278	−	0.757230i
$995$	−17.7662	−	10.2573i	−0.563226	−	0.325179i
$996$	−9.70862	+	12.3924i	−0.307629	+	0.392669i
$997$			23.5775i			0.746708i	0.927689	+	0.373354i	$0.121792\pi$
$997$			23.5775i			0.746708i	−0.927689	+	0.373354i	$0.878208\pi$
$998$	−17.0066	−	9.81874i	−0.538333	−	0.310807i
$999$	−0.789995	−	7.81654i	−0.0249943	−	0.247304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.311.4	yes	32
3.2	odd	2		945.2.be.c.206.13		32
7.5	odd	6		315.2.t.c.131.13	yes	32
9.2	odd	6		315.2.t.c.101.4	✓	32
9.7	even	3		945.2.t.c.521.13		32
21.5	even	6		945.2.t.c.341.4		32
63.47	even	6	inner	315.2.be.c.236.4	yes	32
63.61	odd	6		945.2.be.c.656.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.4	✓	32	9.2	odd	6
315.2.t.c.131.13	yes	32	7.5	odd	6
315.2.be.c.236.4	yes	32	63.47	even	6	inner
315.2.be.c.311.4	yes	32	1.1	even	1	trivial
945.2.t.c.341.4		32	21.5	even	6
945.2.t.c.521.13		32	9.7	even	3
945.2.be.c.206.13		32	3.2	odd	2
945.2.be.c.656.13		32	63.61	odd	6

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67628 - 0.967799i) q^{2} +(-1.71487 - 0.243339i) q^{3} +(0.873269 + 1.51255i) q^{4} -1.00000 q^{5} +(2.63910 + 2.06755i) q^{6} +(2.28906 - 1.32673i) q^{7} +0.490599i q^{8} +(2.88157 + 0.834589i) q^{9} +O(q^{10})\)	\(q+(-1.67628 - 0.967799i) q^{2} +(-1.71487 - 0.243339i) q^{3} +(0.873269 + 1.51255i) q^{4} -1.00000 q^{5} +(2.63910 + 2.06755i) q^{6} +(2.28906 - 1.32673i) q^{7} +0.490599i q^{8} +(2.88157 + 0.834589i) q^{9} +(1.67628 + 0.967799i) q^{10} +4.75489i q^{11} +(-1.12948 - 2.80632i) q^{12} +(-1.44470 - 0.834098i) q^{13} +(-5.12110 + 0.00860774i) q^{14} +(1.71487 + 0.243339i) q^{15} +(2.22134 - 3.84747i) q^{16} +(0.551181 - 0.954674i) q^{17} +(-4.02260 - 4.18778i) q^{18} +(3.85705 - 2.22687i) q^{19} +(-0.873269 - 1.51255i) q^{20} +(-4.24829 + 1.71815i) q^{21} +(4.60178 - 7.97051i) q^{22} -8.57962i q^{23} +(0.119382 - 0.841315i) q^{24} +1.00000 q^{25} +(1.61448 + 2.79636i) q^{26} +(-4.73844 - 2.13241i) q^{27} +(4.00570 + 2.30372i) q^{28} +(2.66862 - 1.54073i) q^{29} +(-2.63910 - 2.06755i) q^{30} +(-3.43483 + 1.98310i) q^{31} +(-6.59742 + 3.80902i) q^{32} +(1.15705 - 8.15402i) q^{33} +(-1.84786 + 1.06686i) q^{34} +(-2.28906 + 1.32673i) q^{35} +(1.25403 + 5.08733i) q^{36} +(0.755979 + 1.30939i) q^{37} -8.62064 q^{38} +(2.27451 + 1.78192i) q^{39} -0.490599i q^{40} +(3.80002 - 6.58183i) q^{41} +(8.78413 + 1.23140i) q^{42} +(0.0488091 + 0.0845398i) q^{43} +(-7.19199 + 4.15230i) q^{44} +(-2.88157 - 0.834589i) q^{45} +(-8.30335 + 14.3818i) q^{46} +(2.75934 - 4.77933i) q^{47} +(-4.74555 + 6.05739i) q^{48} +(3.47960 - 6.07391i) q^{49} +(-1.67628 - 0.967799i) q^{50} +(-1.17751 + 1.50302i) q^{51} -2.91357i q^{52} +(11.1220 + 6.42128i) q^{53} +(5.87919 + 8.16037i) q^{54} -4.75489i q^{55} +(0.650891 + 1.12301i) q^{56} +(-7.15623 + 2.88022i) q^{57} -5.96445 q^{58} +(-6.68767 - 11.5834i) q^{59} +(1.12948 + 2.80632i) q^{60} +(9.30116 + 5.37003i) q^{61} +7.67696 q^{62} +(7.70337 - 1.91263i) q^{63} +5.86011 q^{64} +(1.44470 + 0.834098i) q^{65} +(-9.83099 + 12.5486i) q^{66} +(2.53008 + 4.38223i) q^{67} +1.92532 q^{68} +(-2.08775 + 14.7130i) q^{69} +(5.12110 - 0.00860774i) q^{70} +4.66184i q^{71} +(-0.409449 + 1.41370i) q^{72} +(3.66562 + 2.11635i) q^{73} -2.92654i q^{74} +(-1.71487 - 0.243339i) q^{75} +(6.73648 + 3.88931i) q^{76} +(6.30843 + 10.8842i) q^{77} +(-2.08816 - 5.18826i) q^{78} +(3.10659 - 5.38077i) q^{79} +(-2.22134 + 3.84747i) q^{80} +(7.60692 + 4.80986i) q^{81} +(-12.7398 + 7.35531i) q^{82} +(-2.60200 - 4.50680i) q^{83} +(-6.30868 - 4.92533i) q^{84} +(-0.551181 + 0.954674i) q^{85} -0.188950i q^{86} +(-4.95125 + 1.99277i) q^{87} -2.33275 q^{88} +(-7.15835 - 12.3986i) q^{89} +(4.02260 + 4.18778i) q^{90} +(-4.41363 + 0.00741859i) q^{91} +(12.9771 - 7.49232i) q^{92} +(6.37285 - 2.56493i) q^{93} +(-9.25085 + 5.34098i) q^{94} +(-3.85705 + 2.22687i) q^{95} +(12.2406 - 4.92658i) q^{96} +(-1.33124 + 0.768589i) q^{97} +(-11.7111 + 6.81400i) q^{98} +(-3.96838 + 13.7016i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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