LMFDB - Embedded newform 630.2.bk.c.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(101,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bk (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:	$5.03057532734$
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			101.2
Character	$\chi$	$=$	630.101
Dual form			630.2.bk.c.131.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.61337 - 0.630115i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.630115 + 1.61337i) q^{6} +(2.57812 + 0.594391i) q^{7} +1.00000i q^{8} +(2.20591 + 2.03321i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.61337 - 0.630115i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.630115 + 1.61337i) q^{6} +(2.57812 + 0.594391i) q^{7} +1.00000i q^{8} +(2.20591 + 2.03321i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.676813 - 0.390758i) q^{11} +(1.61337 + 0.630115i) q^{12} +(2.26905 - 1.31003i) q^{13} +(0.594391 - 2.57812i) q^{14} +(-1.35238 + 1.08216i) q^{15} +1.00000 q^{16} +(-3.02795 + 5.24457i) q^{17} +(2.03321 - 2.20591i) q^{18} +(6.09668 - 3.51992i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.78492 - 2.58348i) q^{21} +(-0.390758 - 0.676813i) q^{22} +(3.99168 + 2.30460i) q^{23} +(0.630115 - 1.61337i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.31003 - 2.26905i) q^{26} +(-2.27779 - 4.67030i) q^{27} +(-2.57812 - 0.594391i) q^{28} +(3.96237 + 2.28767i) q^{29} +(1.08216 + 1.35238i) q^{30} -7.48063i q^{31} -1.00000i q^{32} +(-1.33817 + 0.203967i) q^{33} +(5.24457 + 3.02795i) q^{34} +(1.80382 - 1.93552i) q^{35} +(-2.20591 - 2.03321i) q^{36} +(-5.42975 - 9.40460i) q^{37} +(-3.51992 - 6.09668i) q^{38} +(-4.48628 + 0.683808i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-5.46910 - 9.47275i) q^{41} +(-2.58348 + 3.78492i) q^{42} +(-4.45098 + 7.70932i) q^{43} +(-0.676813 + 0.390758i) q^{44} +(2.86377 - 0.893768i) q^{45} +(2.30460 - 3.99168i) q^{46} +1.00253 q^{47} +(-1.61337 - 0.630115i) q^{48} +(6.29340 + 3.06482i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(8.18988 - 6.55346i) q^{51} +(-2.26905 + 1.31003i) q^{52} +(-8.30234 - 4.79336i) q^{53} +(-4.67030 + 2.27779i) q^{54} -0.781517i q^{55} +(-0.594391 + 2.57812i) q^{56} +(-12.0541 + 1.83732i) q^{57} +(2.28767 - 3.96237i) q^{58} +2.64005 q^{59} +(1.35238 - 1.08216i) q^{60} -2.13177i q^{61} -7.48063 q^{62} +(4.47858 + 6.55304i) q^{63} -1.00000 q^{64} -2.62007i q^{65} +(0.203967 + 1.33817i) q^{66} +12.0588 q^{67} +(3.02795 - 5.24457i) q^{68} +(-4.98788 - 6.23338i) q^{69} +(-1.93552 - 1.80382i) q^{70} +10.1200i q^{71} +(-2.03321 + 2.20591i) q^{72} +(7.67003 + 4.42830i) q^{73} +(-9.40460 + 5.42975i) q^{74} +(0.260988 + 1.71227i) q^{75} +(-6.09668 + 3.51992i) q^{76} +(1.97717 - 0.605130i) q^{77} +(0.683808 + 4.48628i) q^{78} +15.9369 q^{79} +(0.500000 - 0.866025i) q^{80} +(0.732082 + 8.97018i) q^{81} +(-9.47275 + 5.46910i) q^{82} +(2.03248 - 3.52036i) q^{83} +(3.78492 + 2.58348i) q^{84} +(3.02795 + 5.24457i) q^{85} +(7.70932 + 4.45098i) q^{86} +(-4.95126 - 6.18761i) q^{87} +(0.390758 + 0.676813i) q^{88} +(3.78927 + 6.56320i) q^{89} +(-0.893768 - 2.86377i) q^{90} +(6.62855 - 2.02872i) q^{91} +(-3.99168 - 2.30460i) q^{92} +(-4.71366 + 12.0690i) q^{93} -1.00253i q^{94} -7.03984i q^{95} +(-0.630115 + 1.61337i) q^{96} +(-5.00436 - 2.88927i) q^{97} +(3.06482 - 6.29340i) q^{98} +(2.28748 + 0.514128i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	$ 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) $ 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.61337	−	0.630115i	−0.931478	−	0.363797i
$3$	−1.61337	−	0.630115i	−0.931478	−	0.363797i
$4$	−1.00000			−0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.630115	+	1.61337i	−0.257243	+	0.658655i
$7$	2.57812	+	0.594391i	0.974437	+	0.224659i
$7$	2.57812	+	0.594391i	0.974437	+	0.224659i
$8$			1.00000i			0.353553i
$9$	2.20591	+	2.03321i	0.735304	+	0.677738i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	0.676813	−	0.390758i	0.204067	−	0.117818i	−0.394484	−	0.918903i	$-0.629077\pi$
$11$	0.676813	−	0.390758i	0.204067	−	0.117818i	0.598551	+	0.801085i	$0.295743\pi$
$12$	1.61337	+	0.630115i	0.465739	+	0.181898i
$13$	2.26905	−	1.31003i	0.629320	−	0.363338i	−0.151168	−	0.988508i	$-0.548304\pi$
$13$	2.26905	−	1.31003i	0.629320	−	0.363338i	0.780489	+	0.625170i	$0.214970\pi$
$14$	0.594391	−	2.57812i	0.158858	−	0.689031i
$15$	−1.35238	+	1.08216i	−0.349183	+	0.279412i
$16$	1.00000			0.250000
$17$	−3.02795	+	5.24457i	−0.734386	+	1.27199i	0.220606	+	0.975363i	$0.429197\pi$
$17$	−3.02795	+	5.24457i	−0.734386	+	1.27199i	−0.954992	+	0.296631i	$0.904137\pi$
$18$	2.03321	−	2.20591i	0.479233	−	0.519938i
$19$	6.09668	−	3.51992i	1.39867	−	0.807525i	0.404421	−	0.914573i	$-0.367473\pi$
$19$	6.09668	−	3.51992i	1.39867	−	0.807525i	0.994254	+	0.107048i	$0.0341397\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	−3.78492	−	2.58348i	−0.825937	−	0.563762i
$22$	−0.390758	−	0.676813i	−0.0833100	−	0.144297i
$23$	3.99168	+	2.30460i	0.832322	+	0.480542i	0.854647	−	0.519209i	$-0.173773\pi$
$23$	3.99168	+	2.30460i	0.832322	+	0.480542i	−0.0223248	+	0.999751i	$0.507107\pi$
$24$	0.630115	−	1.61337i	0.128622	−	0.329327i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.31003	−	2.26905i	−0.256919	−	0.444997i
$27$	−2.27779	−	4.67030i	−0.438360	−	0.898799i
$28$	−2.57812	−	0.594391i	−0.487219	−	0.112329i
$29$	3.96237	+	2.28767i	0.735793	+	0.424810i	0.820538	−	0.571592i	$-0.193674\pi$
$29$	3.96237	+	2.28767i	0.735793	+	0.424810i	−0.0847445	+	0.996403i	$0.527007\pi$
$30$	1.08216	+	1.35238i	0.197574	+	0.246910i
$31$		−	7.48063i		−	1.34356i	−0.740750	−	0.671780i	$-0.765530\pi$
$31$		−	7.48063i		−	1.34356i	0.740750	−	0.671780i	$-0.234470\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.33817	+	0.203967i	−0.232946	+	0.0355061i
$34$	5.24457	+	3.02795i	0.899436	+	0.519289i
$35$	1.80382	−	1.93552i	0.304901	−	0.327163i
$36$	−2.20591	−	2.03321i	−0.367652	−	0.338869i
$37$	−5.42975	−	9.40460i	−0.892645	−	1.54611i	−0.836692	−	0.547673i	$-0.815514\pi$
$37$	−5.42975	−	9.40460i	−0.892645	−	1.54611i	−0.0559531	−	0.998433i	$-0.517820\pi$
$38$	−3.51992	−	6.09668i	−0.571007	−	0.989013i
$39$	−4.48628	+	0.683808i	−0.718380	+	0.109497i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−5.46910	−	9.47275i	−0.854129	−	1.47940i	−0.877450	−	0.479667i	$-0.840757\pi$
$41$	−5.46910	−	9.47275i	−0.854129	−	1.47940i	0.0233211	−	0.999728i	$-0.492576\pi$
$42$	−2.58348	+	3.78492i	−0.398640	+	0.584026i
$43$	−4.45098	+	7.70932i	−0.678768	+	1.17566i	0.296585	+	0.955007i	$0.404152\pi$
$43$	−4.45098	+	7.70932i	−0.678768	+	1.17566i	−0.975352	+	0.220654i	$0.929181\pi$
$44$	−0.676813	+	0.390758i	−0.102033	+	0.0589090i
$45$	2.86377	−	0.893768i	0.426906	−	0.133235i
$46$	2.30460	−	3.99168i	0.339794	−	0.588541i
$47$	1.00253			0.146234			0.0731172	−	0.997323i	$-0.476705\pi$
$47$	1.00253			0.146234			0.0731172	+	0.997323i	$0.476705\pi$
$48$	−1.61337	−	0.630115i	−0.232870	−	0.0909492i
$49$	6.29340	+	3.06482i	0.899057	+	0.437832i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	8.18988	−	6.55346i	1.14681	−	0.917667i
$52$	−2.26905	+	1.31003i	−0.314660	+	0.181669i
$53$	−8.30234	−	4.79336i	−1.14041	−	0.658418i	−0.193881	−	0.981025i	$-0.562107\pi$
$53$	−8.30234	−	4.79336i	−1.14041	−	0.658418i	−0.946533	+	0.322607i	$0.895441\pi$
$54$	−4.67030	+	2.27779i	−0.635547	+	0.309967i
$55$		−	0.781517i		−	0.105380i
$56$	−0.594391	+	2.57812i	−0.0794289	+	0.344516i
$57$	−12.0541	+	1.83732i	−1.59661	+	0.243359i
$58$	2.28767	−	3.96237i	0.300386	−	0.520284i
$59$	2.64005			0.343705			0.171853	−	0.985123i	$-0.445025\pi$
$59$	2.64005			0.343705			0.171853	+	0.985123i	$0.445025\pi$
$60$	1.35238	−	1.08216i	0.174591	−	0.139706i
$61$		−	2.13177i		−	0.272945i	−0.990644	−	0.136473i	$-0.956423\pi$
$61$		−	2.13177i		−	0.272945i	0.990644	−	0.136473i	$-0.0435765\pi$
$62$	−7.48063			−0.950041
$63$	4.47858	+	6.55304i	0.564248	+	0.825606i
$64$	−1.00000			−0.125000
$65$		−	2.62007i		−	0.324980i
$66$	0.203967	+	1.33817i	0.0251066	+	0.164717i
$67$	12.0588			1.47321			0.736607	−	0.676321i	$-0.236427\pi$
$67$	12.0588			1.47321			0.736607	+	0.676321i	$0.236427\pi$
$68$	3.02795	−	5.24457i	0.367193	−	0.635997i
$69$	−4.98788	−	6.23338i	−0.600471	−	0.750410i
$70$	−1.93552	−	1.80382i	−0.231339	−	0.215597i
$71$			10.1200i			1.20103i	0.799614	+	0.600514i	$0.205037\pi$
$71$			10.1200i			1.20103i	−0.799614	+	0.600514i	$0.794963\pi$
$72$	−2.03321	+	2.20591i	−0.239617	+	0.259969i
$73$	7.67003	+	4.42830i	0.897710	+	0.518293i	0.876456	−	0.481481i	$-0.159901\pi$
$73$	7.67003	+	4.42830i	0.897710	+	0.518293i	0.0212532	+	0.999774i	$0.493234\pi$
$74$	−9.40460	+	5.42975i	−1.09326	+	0.631195i
$75$	0.260988	+	1.71227i	0.0301363	+	0.197716i
$76$	−6.09668	+	3.51992i	−0.699337	+	0.403763i
$77$	1.97717	−	0.605130i	0.225319	−	0.0689609i
$78$	0.683808	+	4.48628i	0.0774260	+	0.507971i
$79$	15.9369			1.79305			0.896523	−	0.442998i	$-0.146085\pi$
$79$	15.9369			1.79305			0.896523	+	0.442998i	$0.146085\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	0.732082	+	8.97018i	0.0813425	+	0.996686i
$82$	−9.47275	+	5.46910i	−1.04609	+	0.603961i
$83$	2.03248	−	3.52036i	0.223094	−	0.386410i	−0.732652	−	0.680603i	$-0.761718\pi$
$83$	2.03248	−	3.52036i	0.223094	−	0.386410i	0.955746	+	0.294194i	$0.0950511\pi$
$84$	3.78492	+	2.58348i	0.412969	+	0.281881i
$85$	3.02795	+	5.24457i	0.328428	+	0.568853i
$86$	7.70932	+	4.45098i	0.831317	+	0.479961i
$87$	−4.95126	−	6.18761i	−0.530831	−	0.663381i
$88$	0.390758	+	0.676813i	0.0416550	+	0.0721485i
$89$	3.78927	+	6.56320i	0.401662	+	0.695698i	0.993927	−	0.110045i	$-0.0350995\pi$
$89$	3.78927	+	6.56320i	0.401662	+	0.695698i	−0.592265	+	0.805743i	$0.701766\pi$
$90$	−0.893768	−	2.86377i	−0.0942114	−	0.301868i
$91$	6.62855	−	2.02872i	0.694860	−	0.212668i
$92$	−3.99168	−	2.30460i	−0.416161	−	0.240271i
$93$	−4.71366	+	12.0690i	−0.488783	+	1.25150i
$94$		−	1.00253i		−	0.103403i
$95$		−	7.03984i		−	0.722273i
$96$	−0.630115	+	1.61337i	−0.0643108	+	0.164664i
$97$	−5.00436	−	2.88927i	−0.508115	−	0.293361i	0.223943	−	0.974602i	$-0.428107\pi$
$97$	−5.00436	−	2.88927i	−0.508115	−	0.293361i	−0.732059	+	0.681242i	$0.761440\pi$
$98$	3.06482	−	6.29340i	0.309594	−	0.635729i
$99$	2.28748	+	0.514128i	0.229901	+	0.0516718i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	0.499392	+	0.864973i	0.0496914	+	0.0860680i	0.889801	−	0.456348i	$-0.150843\pi$
$101$	0.499392	+	0.864973i	0.0496914	+	0.0860680i	−0.840110	+	0.542416i	$0.817510\pi$
$102$	−6.55346	−	8.18988i	−0.648889	−	0.810919i
$103$	−5.08667	−	2.93679i	−0.501204	−	0.289370i	0.228007	−	0.973660i	$-0.426779\pi$
$103$	−5.08667	−	2.93679i	−0.501204	−	0.289370i	−0.729211	+	0.684289i	$0.760113\pi$
$104$	1.31003	+	2.26905i	0.128459	+	0.222498i
$105$	−4.12982	+	1.98610i	−0.403029	+	0.193823i
$106$	−4.79336	+	8.30234i	−0.465572	+	0.806394i
$107$	−4.22082	+	2.43689i	−0.408042	+	0.235583i	−0.689948	−	0.723859i	$-0.742367\pi$
$107$	−4.22082	+	2.43689i	−0.408042	+	0.235583i	0.281906	+	0.959442i	$0.409033\pi$
$108$	2.27779	+	4.67030i	0.219180	+	0.449400i
$109$	0.338969	−	0.587111i	0.0324673	−	0.0562350i	−0.849335	−	0.527854i	$-0.822997\pi$
$109$	0.338969	−	0.587111i	0.0324673	−	0.0562350i	0.881802	+	0.471619i	$0.156330\pi$
$110$	−0.781517			−0.0745147
$111$	2.83420	+	18.5944i	0.269011	+	1.76491i
$112$	2.57812	+	0.594391i	0.243609	+	0.0561647i
$113$	−2.66192	+	1.53686i	−0.250413	+	0.144576i	−0.619953	−	0.784639i	$-0.712848\pi$
$113$	−2.66192	+	1.53686i	−0.250413	+	0.144576i	0.369541	+	0.929215i	$0.379515\pi$
$114$	1.83732	+	12.0541i	0.172081	+	1.12897i
$115$	3.99168	−	2.30460i	0.372226	−	0.214905i
$116$	−3.96237	−	2.28767i	−0.367897	−	0.212405i
$117$	7.66889	+	1.72364i	0.708990	+	0.159350i
$118$		−	2.64005i		−	0.243036i
$119$	−10.9237	+	11.7213i	−1.00138	+	1.07449i
$120$	−1.08216	−	1.35238i	−0.0987872	−	0.123455i
$121$	−5.19462	+	8.99734i	−0.472238	+	0.817940i
$122$	−2.13177			−0.193001
$123$	2.85474	+	18.7292i	0.257403	+	1.68875i
$124$			7.48063i			0.671780i
$125$	−1.00000			−0.0894427
$126$	6.55304	−	4.47858i	0.583791	−	0.398983i
$127$	−0.401239			−0.0356042			−0.0178021	−	0.999842i	$-0.505667\pi$
$127$	−0.401239			−0.0356042			−0.0178021	+	0.999842i	$0.505667\pi$
$128$			1.00000i			0.0883883i
$129$	12.0388	−	9.63334i	1.05996	−	0.848168i
$130$	−2.62007			−0.229795
$131$	11.0798	−	19.1907i	0.968042	−	1.67670i	0.266833	−	0.963743i	$-0.414023\pi$
$131$	11.0798	−	19.1907i	0.968042	−	1.67670i	0.701209	−	0.712956i	$-0.252644\pi$
$132$	1.33817	−	0.203967i	0.116473	−	0.0177530i
$133$	17.8102	−	5.45096i	1.54434	−	0.472658i
$134$		−	12.0588i		−	1.04172i
$135$	−5.18349	−	0.362528i	−0.446124	−	0.0312015i
$136$	−5.24457	−	3.02795i	−0.449718	−	0.259645i
$137$	−16.6279	+	9.60012i	−1.42062	+	0.820194i	−0.996352	−	0.0853444i	$-0.972801\pi$
$137$	−16.6279	+	9.60012i	−1.42062	+	0.820194i	−0.424265	+	0.905538i	$0.639468\pi$
$138$	−6.23338	+	4.98788i	−0.530620	+	0.424597i
$139$	0.151908	−	0.0877042i	0.0128847	−	0.00743897i	−0.493544	−	0.869721i	$-0.664299\pi$
$139$	0.151908	−	0.0877042i	0.0128847	−	0.00743897i	0.506429	+	0.862282i	$0.330965\pi$
$140$	−1.80382	+	1.93552i	−0.152450	+	0.163581i
$141$	−1.61745	−	0.631711i	−0.136214	−	0.0531996i
$142$	10.1200			0.849256
$143$	1.02381	−	1.77330i	0.0856156	−	0.148291i
$144$	2.20591	+	2.03321i	0.183826	+	0.169434i
$145$	3.96237	−	2.28767i	0.329057	−	0.189981i
$146$	4.42830	−	7.67003i	0.366488	−	0.634777i
$147$	−8.22237	−	8.91025i	−0.678170	−	0.734905i
$148$	5.42975	+	9.40460i	0.446323	+	0.773053i
$149$	−1.06540	−	0.615111i	−0.0872812	−	0.0503918i	0.455724	−	0.890121i	$-0.349380\pi$
$149$	−1.06540	−	0.615111i	−0.0872812	−	0.0503918i	−0.543005	+	0.839729i	$0.682714\pi$
$150$	1.71227	−	0.260988i	0.139807	−	0.0213096i
$151$	−0.936323	−	1.62176i	−0.0761969	−	0.131977i	0.825409	−	0.564535i	$-0.190944\pi$
$151$	−0.936323	−	1.62176i	−0.0761969	−	0.131977i	−0.901606	+	0.432558i	$0.857611\pi$
$152$	3.51992	+	6.09668i	0.285503	+	0.494506i
$153$	−17.3427	+	5.41257i	−1.40208	+	0.437580i
$154$	−0.605130	−	1.97717i	−0.0487627	−	0.159325i
$155$	−6.47842	−	3.74031i	−0.520359	−	0.300429i
$156$	4.48628	−	0.683808i	0.359190	−	0.0547484i
$157$			6.92615i			0.552767i	0.961047	+	0.276383i	$0.0891360\pi$
$157$			6.92615i			0.552767i	−0.961047	+	0.276383i	$0.910864\pi$
$158$		−	15.9369i		−	1.26787i
$159$	10.3744	+	12.9649i	0.822740	+	1.02818i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	8.92119	+	8.31414i	0.703088	+	0.655246i
$162$	8.97018	−	0.732082i	0.704764	−	0.0575178i
$163$	9.12797	+	15.8101i	0.714958	+	1.23834i	0.962976	+	0.269588i	$0.0868876\pi$
$163$	9.12797	+	15.8101i	0.714958	+	1.23834i	−0.248018	+	0.968756i	$0.579779\pi$
$164$	5.46910	+	9.47275i	0.427065	+	0.739698i
$165$	−0.492445	+	1.26087i	−0.0383368	+	0.0981589i
$166$	−3.52036	−	2.03248i	−0.273233	−	0.157751i
$167$	−10.7511	−	18.6214i	−0.831942	−	1.44097i	−0.896496	−	0.443051i	$-0.853896\pi$
$167$	−10.7511	−	18.6214i	−0.831942	−	1.44097i	0.0645545	−	0.997914i	$-0.479437\pi$
$168$	2.58348	−	3.78492i	0.199320	−	0.292013i
$169$	−3.06762	+	5.31327i	−0.235971	+	0.408713i
$170$	5.24457	−	3.02795i	0.402240	−	0.232233i
$171$	20.6055	+	4.63123i	1.57574	+	0.354159i
$172$	4.45098	−	7.70932i	0.339384	−	0.587830i
$173$	−6.62032			−0.503334			−0.251667	−	0.967814i	$-0.580979\pi$
$173$	−6.62032			−0.503334			−0.251667	+	0.967814i	$0.580979\pi$
$174$	−6.18761	+	4.95126i	−0.469081	+	0.375354i
$175$	−0.774302	−	2.52991i	−0.0585317	−	0.191243i
$176$	0.676813	−	0.390758i	0.0510167	−	0.0294545i
$177$	−4.25937	−	1.66354i	−0.320154	−	0.125039i
$178$	6.56320	−	3.78927i	0.491933	−	0.284018i
$179$	8.99427	+	5.19284i	0.672263	+	0.388131i	0.796934	−	0.604067i	$-0.206454\pi$
$179$	8.99427	+	5.19284i	0.672263	+	0.388131i	−0.124671	+	0.992198i	$0.539787\pi$
$180$	−2.86377	+	0.893768i	−0.213453	+	0.0666175i
$181$		−	0.766824i		−	0.0569975i	−0.999594	−	0.0284988i	$-0.990927\pi$
$181$		−	0.766824i		−	0.0569975i	0.999594	−	0.0284988i	$-0.00907267\pi$
$182$	−2.02872	−	6.62855i	−0.150379	−	0.491341i
$183$	−1.34326	+	3.43933i	−0.0992966	+	0.254242i
$184$	−2.30460	+	3.99168i	−0.169897	+	0.294270i
$185$	−10.8595			−0.798406
$186$	12.0690	+	4.71366i	0.884942	+	0.345622i
$187$			4.73279i			0.346096i
$188$	−1.00253			−0.0731172
$189$	−3.09642	−	13.3945i	−0.225231	−	0.974305i
$190$	−7.03984			−0.510724
$191$		−	13.5359i		−	0.979421i	−0.871885	−	0.489711i	$-0.837102\pi$
$191$		−	13.5359i		−	0.979421i	0.871885	−	0.489711i	$-0.162898\pi$
$192$	1.61337	+	0.630115i	0.116435	+	0.0454746i
$193$	−9.39501			−0.676268			−0.338134	−	0.941098i	$-0.609796\pi$
$193$	−9.39501			−0.676268			−0.338134	+	0.941098i	$0.609796\pi$
$194$	−2.88927	+	5.00436i	−0.207437	+	0.359292i
$195$	−1.65094	+	4.22714i	−0.118227	+	0.302711i
$196$	−6.29340	−	3.06482i	−0.449528	−	0.218916i
$197$			12.0072i			0.855480i	0.903902	+	0.427740i	$0.140690\pi$
$197$			12.0072i			0.855480i	−0.903902	+	0.427740i	$0.859310\pi$
$198$	0.514128	−	2.28748i	0.0365375	−	0.162564i
$199$	3.77973	+	2.18223i	0.267938	+	0.154694i	0.627950	−	0.778253i	$-0.283894\pi$
$199$	3.77973	+	2.18223i	0.267938	+	0.154694i	−0.360012	+	0.932948i	$0.617227\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	−19.4553	−	7.59842i	−1.37227	−	0.535951i
$202$	0.864973	−	0.499392i	0.0608593	−	0.0351371i
$203$	8.85568	+	8.25309i	0.621547	+	0.579254i
$204$	−8.18988	+	6.55346i	−0.573406	+	0.458834i
$205$	−10.9382			−0.763956
$206$	−2.93679	+	5.08667i	−0.204616	+	0.354405i
$207$	4.11955	+	13.1997i	0.286328	+	0.917440i
$208$	2.26905	−	1.31003i	0.157330	−	0.0908346i
$209$	2.75088	−	4.76466i	0.190282	−	0.329578i
$210$	1.98610	+	4.12982i	0.137054	+	0.284985i
$211$	−5.82791	−	10.0942i	−0.401210	−	0.694916i	0.592662	−	0.805451i	$-0.298077\pi$
$211$	−5.82791	−	10.0942i	−0.401210	−	0.694916i	−0.993872	+	0.110535i	$0.964744\pi$
$212$	8.30234	+	4.79336i	0.570207	+	0.329209i
$213$	6.37679	−	16.3274i	0.436931	−	1.11873i
$214$	2.43689	+	4.22082i	0.166583	+	0.288529i
$215$	4.45098	+	7.70932i	0.303554	+	0.525771i
$216$	4.67030	−	2.27779i	0.317774	−	0.154984i
$217$	4.44642	−	19.2860i	0.301843	−	1.30922i
$218$	−0.587111	−	0.338969i	−0.0397642	−	0.0229579i
$219$	−9.58425	−	11.9775i	−0.647644	−	0.809363i
$220$			0.781517i			0.0526898i
$221$			15.8669i			1.06732i
$222$	18.5944	−	2.83420i	1.24798	−	0.190219i
$223$	−8.63803	−	4.98717i	−0.578446	−	0.333966i	0.182070	−	0.983286i	$-0.441720\pi$
$223$	−8.63803	−	4.98717i	−0.578446	−	0.333966i	−0.760515	+	0.649320i	$0.775054\pi$
$224$	0.594391	−	2.57812i	0.0397144	−	0.172258i
$225$	0.657860	−	2.92698i	0.0438573	−	0.195132i
$226$	1.53686	+	2.66192i	0.102231	+	0.177068i
$227$	8.57982	+	14.8607i	0.569463	+	0.986339i	0.996619	+	0.0821609i	$0.0261821\pi$
$227$	8.57982	+	14.8607i	0.569463	+	0.986339i	−0.427156	+	0.904178i	$0.640485\pi$
$228$	12.0541	−	1.83732i	0.798305	−	0.121679i
$229$	−11.1667	−	6.44708i	−0.737914	−	0.426035i	0.0833964	−	0.996516i	$-0.473423\pi$
$229$	−11.1667	−	6.44708i	−0.737914	−	0.426035i	−0.821310	+	0.570482i	$0.806757\pi$
$230$	−2.30460	−	3.99168i	−0.151961	−	0.263203i
$231$	−3.57120	−	0.269547i	−0.234968	−	0.0177349i
$232$	−2.28767	+	3.96237i	−0.150193	+	0.260142i
$233$	12.8761	−	7.43401i	0.843540	−	0.487018i	−0.0149261	−	0.999889i	$-0.504751\pi$
$233$	12.8761	−	7.43401i	0.843540	−	0.487018i	0.858466	+	0.512871i	$0.171418\pi$
$234$	1.72364	−	7.66889i	0.112678	−	0.501331i
$235$	0.501266	−	0.868218i	0.0326990	−	0.0566363i
$236$	−2.64005			−0.171853
$237$	−25.7121	−	10.0421i	−1.67018	−	0.652304i
$238$	11.7213	+	10.9237i	0.759781	+	0.708081i
$239$	−1.84122	+	1.06303i	−0.119099	+	0.0687617i	−0.558366	−	0.829595i	$-0.688571\pi$
$239$	−1.84122	+	1.06303i	−0.119099	+	0.0687617i	0.439267	+	0.898356i	$0.355238\pi$
$240$	−1.35238	+	1.08216i	−0.0872957	+	0.0698531i
$241$	−15.9733	+	9.22217i	−1.02893	+	0.594052i	−0.916678	−	0.399627i	$-0.869139\pi$
$241$	−15.9733	+	9.22217i	−1.02893	+	0.594052i	−0.112251	+	0.993680i	$0.535806\pi$
$242$	8.99734	+	5.19462i	0.578371	+	0.333923i
$243$	4.47112	−	14.9335i	0.286823	−	0.957984i
$244$			2.13177i			0.136473i
$245$	5.80091	−	3.91783i	0.370607	−	0.250301i
$246$	18.7292	−	2.85474i	1.19413	−	0.182012i
$247$	9.22244	−	15.9737i	0.586810	−	1.01638i
$248$	7.48063			0.475020
$249$	−5.49737	+	4.39894i	−0.348382	+	0.278771i
$250$			1.00000i			0.0632456i
$251$	14.4909			0.914655			0.457328	−	0.889298i	$-0.348807\pi$
$251$	14.4909			0.914655			0.457328	+	0.889298i	$0.348807\pi$
$252$	−4.47858	−	6.55304i	−0.282124	−	0.412803i
$253$	3.60216			0.226466
$254$			0.401239i			0.0251760i
$255$	−1.58052	−	10.3694i	−0.0989760	−	0.649355i
$256$	1.00000			0.0625000
$257$	−3.40934	+	5.90514i	−0.212669	+	0.368353i	−0.952549	−	0.304386i	$-0.901549\pi$
$257$	−3.40934	+	5.90514i	−0.212669	+	0.368353i	0.739880	+	0.672739i	$0.234882\pi$
$258$	−9.63334	−	12.0388i	−0.599745	−	0.749504i
$259$	−8.40853	−	27.4736i	−0.522481	−	1.70713i
$260$			2.62007i			0.162490i
$261$	4.08930	+	13.1027i	0.253121	+	0.811040i
$262$	−19.1907	−	11.0798i	−1.18560	−	0.684509i
$263$	−16.0760	+	9.28146i	−0.991286	+	0.572319i	−0.905658	−	0.424008i	$-0.860623\pi$
$263$	−16.0760	+	9.28146i	−0.991286	+	0.572319i	−0.0856274	+	0.996327i	$0.527289\pi$
$264$	−0.203967	−	1.33817i	−0.0125533	−	0.0823587i
$265$	−8.30234	+	4.79336i	−0.510008	+	0.294454i
$266$	−5.45096	−	17.8102i	−0.334220	−	1.09201i
$267$	−1.97791	−	12.9765i	−0.121046	−	0.794151i
$268$	−12.0588			−0.736607
$269$	0.646992	−	1.12062i	0.0394478	−	0.0683256i	−0.845627	−	0.533774i	$-0.820773\pi$
$269$	0.646992	−	1.12062i	0.0394478	−	0.0683256i	0.885075	+	0.465448i	$0.154107\pi$
$270$	−0.362528	+	5.18349i	−0.0220628	+	0.315457i
$271$	−23.9309	+	13.8165i	−1.45370	+	0.839295i	−0.998689	−	0.0511902i	$-0.983699\pi$
$271$	−23.9309	+	13.8165i	−1.45370	+	0.839295i	−0.455012	+	0.890485i	$0.650365\pi$
$272$	−3.02795	+	5.24457i	−0.183597	+	0.317999i
$273$	−11.9726	−	0.903667i	−0.724615	−	0.0546924i
$274$	9.60012	+	16.6279i	0.579964	+	1.00453i
$275$	−0.676813	−	0.390758i	−0.0408134	−	0.0235636i
$276$	4.98788	+	6.23338i	0.300235	+	0.375205i
$277$	12.2264	+	21.1767i	0.734611	+	1.27238i	0.954894	+	0.296948i	$0.0959688\pi$
$277$	12.2264	+	21.1767i	0.734611	+	1.27238i	−0.220282	+	0.975436i	$0.570698\pi$
$278$	−0.0877042	−	0.151908i	−0.00526015	−	0.00911084i
$279$	15.2097	−	16.5016i	0.910582	−	0.987925i
$280$	1.93552	+	1.80382i	0.115670	+	0.107799i
$281$	2.32984	+	1.34513i	0.138986	+	0.0802438i	0.567881	−	0.823111i	$-0.307763\pi$
$281$	2.32984	+	1.34513i	0.138986	+	0.0802438i	−0.428894	+	0.903355i	$0.641097\pi$
$282$	−0.631711	+	1.61745i	−0.0376178	+	0.0963179i
$283$			7.15360i			0.425237i	0.977135	+	0.212619i	$0.0681992\pi$
$283$			7.15360i			0.425237i	−0.977135	+	0.212619i	$0.931801\pi$
$284$		−	10.1200i		−	0.600514i
$285$	−4.43591	+	11.3579i	−0.262761	+	0.672781i
$286$	−1.77330	−	1.02381i	−0.104857	−	0.0605394i
$287$	−8.46946	−	27.6727i	−0.499936	−	1.63347i
$288$	2.03321	−	2.20591i	0.119808	−	0.129985i
$289$	−9.83699	−	17.0382i	−0.578646	−	1.00224i
$290$	−2.28767	−	3.96237i	−0.134337	−	0.232678i
$291$	6.25330	+	7.81477i	0.366575	+	0.458110i
$292$	−7.67003	−	4.42830i	−0.448855	−	0.259146i
$293$	2.65334	+	4.59573i	0.155010	+	0.268485i	0.933063	−	0.359714i	$-0.117126\pi$
$293$	2.65334	+	4.59573i	0.155010	+	0.268485i	−0.778053	+	0.628199i	$0.783792\pi$
$294$	−8.91025	+	8.22237i	−0.519656	+	0.479539i
$295$	1.32003	−	2.28635i	0.0768549	−	0.133117i
$296$	9.40460	−	5.42975i	0.546631	−	0.315598i
$297$	−3.36659	−	2.27086i	−0.195350	−	0.131768i
$298$	−0.615111	+	1.06540i	−0.0356324	+	0.0617171i
$299$	12.0764			0.698397
$300$	−0.260988	−	1.71227i	−0.0150682	−	0.0988582i
$301$	−16.0575	+	17.2299i	−0.925539	+	0.993116i
$302$	−1.62176	+	0.936323i	−0.0933218	+	0.0538794i
$303$	−0.260671	−	1.71019i	−0.0149752	−	0.0982480i
$304$	6.09668	−	3.51992i	0.349669	−	0.201881i
$305$	−1.84617	−	1.06588i	−0.105711	−	0.0610324i
$306$	5.41257	+	17.3427i	0.309416	+	0.991417i
$307$			28.5768i			1.63097i	0.578782	+	0.815483i	$0.303528\pi$
$307$			28.5768i			1.63097i	−0.578782	+	0.815483i	$0.696472\pi$
$308$	−1.97717	+	0.605130i	−0.112660	+	0.0344805i
$309$	6.35615	+	7.94330i	0.361589	+	0.451879i
$310$	−3.74031	+	6.47842i	−0.212436	+	0.367949i
$311$	−28.3469			−1.60740			−0.803702	−	0.595032i	$-0.797139\pi$
$311$	−28.3469			−1.60740			−0.803702	+	0.595032i	$0.797139\pi$
$312$	−0.683808	−	4.48628i	−0.0387130	−	0.253986i
$313$		−	13.9219i		−	0.786915i	−0.919343	−	0.393457i	$-0.871279\pi$
$313$		−	13.9219i		−	0.786915i	0.919343	−	0.393457i	$-0.128721\pi$
$314$	6.92615			0.390865
$315$	7.91439	−	0.602040i	0.445925	−	0.0339211i
$316$	−15.9369			−0.896523
$317$			6.48605i			0.364293i	0.983271	+	0.182146i	$0.0583045\pi$
$317$			6.48605i			0.364293i	−0.983271	+	0.182146i	$0.941696\pi$
$318$	12.9649	−	10.3744i	0.727034	−	0.581765i
$319$	3.57571			0.200201
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	8.34526	−	1.27200i	0.465787	−	0.0709962i
$322$	8.31414	−	8.92119i	0.463329	−	0.497158i
$323$			42.6326i			2.37214i
$324$	−0.732082	−	8.97018i	−0.0406712	−	0.498343i
$325$	−2.26905	−	1.31003i	−0.125864	−	0.0726677i
$326$	15.8101	−	9.12797i	0.875641	−	0.505552i
$327$	−0.916828	+	0.733637i	−0.0507007	+	0.0405702i
$328$	9.47275	−	5.46910i	0.523045	−	0.301980i
$329$	2.58465	+	0.595896i	0.142496	+	0.0328528i
$330$	1.26087	+	0.492445i	0.0694088	+	0.0271082i
$331$	−20.2311			−1.11200			−0.556001	−	0.831182i	$-0.687665\pi$
$331$	−20.2311			−1.11200			−0.556001	+	0.831182i	$0.687665\pi$
$332$	−2.03248	+	3.52036i	−0.111547	+	0.193205i
$333$	7.14403	−	31.7855i	0.391490	−	1.74184i
$334$	−18.6214	+	10.7511i	−1.01892	+	0.588272i
$335$	6.02939	−	10.4432i	0.329421	−	0.570574i
$336$	−3.78492	−	2.58348i	−0.206484	−	0.140941i
$337$	−6.26528	−	10.8518i	−0.341292	−	0.591134i	0.643381	−	0.765546i	$-0.277531\pi$
$337$	−6.26528	−	10.8518i	−0.341292	−	0.591134i	−0.984673	+	0.174412i	$0.944198\pi$
$338$	5.31327	+	3.06762i	0.289004	+	0.166856i
$339$	5.26306	−	0.802206i	0.285850	−	0.0435699i
$340$	−3.02795	−	5.24457i	−0.164214	−	0.284427i
$341$	−2.92312	−	5.06299i	−0.158296	−	0.274176i
$342$	4.63123	−	20.6055i	0.250428	−	1.11422i
$343$	14.4034	+	11.6422i	0.777712	+	0.628621i
$344$	−7.70932	−	4.45098i	−0.415659	−	0.239981i
$345$	−7.89220	+	1.20295i	−0.424902	+	0.0647644i
$346$			6.62032i			0.355911i
$347$		−	0.288364i		−	0.0154802i	−0.999970	−	0.00774011i	$-0.997536\pi$
$347$		−	0.288364i		−	0.0154802i	0.999970	−	0.00774011i	$-0.00246378\pi$
$348$	4.95126	+	6.18761i	0.265415	+	0.331691i
$349$	6.77506	+	3.91159i	0.362661	+	0.209382i	0.670247	−	0.742138i	$-0.266188\pi$
$349$	6.77506	+	3.91159i	0.362661	+	0.209382i	−0.307586	+	0.951520i	$0.599521\pi$
$350$	−2.52991	+	0.774302i	−0.135230	+	0.0413882i
$351$	−11.2867	−	7.61315i	−0.602437	−	0.406360i
$352$	−0.390758	−	0.676813i	−0.0208275	−	0.0360743i
$353$	2.12459	+	3.67991i	0.113081	+	0.195862i	0.917011	−	0.398862i	$-0.130595\pi$
$353$	2.12459	+	3.67991i	0.113081	+	0.195862i	−0.803930	+	0.594724i	$0.797261\pi$
$354$	−1.66354	+	4.25937i	−0.0884159	+	0.226383i
$355$	8.76422	+	5.06002i	0.465156	+	0.268558i
$356$	−3.78927	−	6.56320i	−0.200831	−	0.347849i
$357$	25.0098	−	12.0276i	1.32366	−	0.636568i
$358$	5.19284	−	8.99427i	0.274450	−	0.475362i
$359$	−9.71995	+	5.61182i	−0.513000	+	0.296180i	−0.734066	−	0.679078i	$-0.762380\pi$
$359$	−9.71995	+	5.61182i	−0.513000	+	0.296180i	0.221066	+	0.975259i	$0.429046\pi$
$360$	0.893768	+	2.86377i	0.0471057	+	0.150934i
$361$	15.2797	−	26.4652i	0.804194	−	1.39291i
$362$	−0.766824			−0.0403034
$363$	14.0502	−	11.2428i	0.737443	−	0.590095i
$364$	−6.62855	+	2.02872i	−0.347430	+	0.106334i
$365$	7.67003	−	4.42830i	0.401468	−	0.231788i
$366$	3.43933	+	1.34326i	0.179777	+	0.0702133i
$367$	−5.74548	+	3.31715i	−0.299912	+	0.173154i	−0.642403	−	0.766367i	$-0.722063\pi$
$367$	−5.74548	+	3.31715i	−0.299912	+	0.173154i	0.342492	+	0.939521i	$0.388729\pi$
$368$	3.99168	+	2.30460i	0.208081	+	0.120135i
$369$	7.19580	−	32.0159i	0.374598	−	1.66668i
$370$			10.8595i			0.564558i
$371$	−18.5553	−	17.2927i	−0.963342	−	0.897791i
$372$	4.71366	−	12.0690i	0.244392	−	0.625749i
$373$	15.2013	−	26.3293i	0.787091	−	1.36328i	−0.140651	−	0.990059i	$-0.544919\pi$
$373$	15.2013	−	26.3293i	0.787091	−	1.36328i	0.927742	−	0.373223i	$-0.121747\pi$
$374$	4.73279			0.244727
$375$	1.61337	+	0.630115i	0.0833139	+	0.0325390i
$376$			1.00253i			0.0517017i
$377$	11.9877			0.617400
$378$	−13.3945	+	3.09642i	−0.688938	+	0.159263i
$379$	−7.50620			−0.385568			−0.192784	−	0.981241i	$-0.561752\pi$
$379$	−7.50620			−0.385568			−0.192784	+	0.981241i	$0.561752\pi$
$380$			7.03984i			0.361136i
$381$	0.647346	+	0.252827i	0.0331645	+	0.0129527i
$382$	−13.5359			−0.692555
$383$	−2.08909	+	3.61841i	−0.106748	+	0.184892i	−0.914451	−	0.404697i	$-0.867377\pi$
$383$	−2.08909	+	3.61841i	−0.106748	+	0.184892i	0.807703	+	0.589589i	$0.200710\pi$
$384$	0.630115	−	1.61337i	0.0321554	−	0.0823318i
$385$	0.464527	−	2.01484i	0.0236745	−	0.102686i
$386$			9.39501i			0.478193i
$387$	−25.4932	+	7.95628i	−1.29589	+	0.404440i
$388$	5.00436	+	2.88927i	0.254058	+	0.146680i
$389$	−12.3398	+	7.12437i	−0.625651	+	0.361220i	−0.779066	−	0.626942i	$-0.784306\pi$
$389$	−12.3398	+	7.12437i	−0.625651	+	0.361220i	0.153415	+	0.988162i	$0.450973\pi$
$390$	4.22714	+	1.65094i	0.214049	+	0.0835988i
$391$	−24.1732	+	13.9564i	−1.22249	+	0.705806i
$392$	−3.06482	+	6.29340i	−0.154797	+	0.317865i
$393$	−29.9681	+	23.9801i	−1.51169	+	1.20964i
$394$	12.0072			0.604916
$395$	7.96847	−	13.8018i	0.400937	−	0.694443i
$396$	−2.28748	−	0.514128i	−0.114950	−	0.0258359i
$397$	15.1562	−	8.75045i	0.760669	−	0.439172i	−0.0688669	−	0.997626i	$-0.521938\pi$
$397$	15.1562	−	8.75045i	0.760669	−	0.439172i	0.829536	+	0.558453i	$0.188605\pi$
$398$	2.18223	−	3.77973i	0.109385	−	0.189461i
$399$	−32.1691	−	2.42806i	−1.61047	−	0.121555i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	10.4560	+	6.03677i	0.522147	+	0.301462i	0.737813	−	0.675006i	$-0.235859\pi$
$401$	10.4560	+	6.03677i	0.522147	+	0.301462i	−0.215666	+	0.976467i	$0.569192\pi$
$402$	−7.59842	+	19.4553i	−0.378975	+	0.970340i
$403$	−9.79988	−	16.9739i	−0.488167	−	0.845530i
$404$	−0.499392	−	0.864973i	−0.0248457	−	0.0430340i
$405$	8.13444	+	3.85109i	0.404204	+	0.191362i
$406$	8.25309	−	8.85568i	0.409594	−	0.439500i
$407$	−7.34985	−	4.24344i	−0.364319	−	0.210339i
$408$	6.55346	+	8.18988i	0.324444	+	0.405459i
$409$		−	35.1360i		−	1.73737i	−0.495369	−	0.868683i	$-0.664967\pi$
$409$		−	35.1360i		−	1.73737i	0.495369	−	0.868683i	$-0.335033\pi$
$410$			10.9382i			0.540199i
$411$	32.8761	−	5.01104i	1.62166	−	0.247176i
$412$	5.08667	+	2.93679i	0.250602	+	0.144685i
$413$	6.80637	+	1.56922i	0.334919	+	0.0772164i
$414$	13.1997	−	4.11955i	0.648728	−	0.202465i
$415$	−2.03248	−	3.52036i	−0.0997706	−	0.172808i
$416$	−1.31003	−	2.26905i	−0.0642297	−	0.111249i
$417$	−0.300347	+	0.0457795i	−0.0147081	+	0.00224183i
$418$	−4.76466	−	2.75088i	−0.233047	−	0.134550i
$419$	1.20192	+	2.08178i	0.0587176	+	0.101702i	0.893890	−	0.448286i	$-0.147966\pi$
$419$	1.20192	+	2.08178i	0.0587176	+	0.101702i	−0.835172	+	0.549988i	$0.814632\pi$
$420$	4.12982	−	1.98610i	0.201515	−	0.0969115i
$421$	0.667716	−	1.15652i	0.0325425	−	0.0563652i	−0.849295	−	0.527918i	$-0.822973\pi$
$421$	0.667716	−	1.15652i	0.0325425	−	0.0563652i	0.881838	+	0.471553i	$0.156306\pi$
$422$	−10.0942	+	5.82791i	−0.491380	+	0.283698i
$423$	2.21150	+	2.03836i	0.107527	+	0.0991086i
$424$	4.79336	−	8.30234i	0.232786	−	0.403197i
$425$	6.05590			0.293754
$426$	−16.3274	−	6.37679i	−0.791063	−	0.308957i
$427$	1.26710	−	5.49595i	0.0613195	−	0.265968i
$428$	4.22082	−	2.43689i	0.204021	−	0.117792i
$429$	−2.76917	+	2.21586i	−0.133697	+	0.106983i
$430$	7.70932	−	4.45098i	0.371776	−	0.214645i
$431$	27.5465	+	15.9040i	1.32687	+	0.766067i	0.984814	−	0.173613i	$-0.0555442\pi$
$431$	27.5465	+	15.9040i	1.32687	+	0.766067i	0.342054	+	0.939680i	$0.388878\pi$
$432$	−2.27779	−	4.67030i	−0.109590	−	0.224700i
$433$			33.1620i			1.59367i	0.604200	+	0.796833i	$0.293493\pi$
$433$			33.1620i			1.59367i	−0.604200	+	0.796833i	$0.706507\pi$
$434$	−19.2860	−	4.44642i	−0.925756	−	0.213435i
$435$	−7.83425	+	1.19411i	−0.375624	+	0.0572533i
$436$	−0.338969	+	0.587111i	−0.0162337	+	0.0281175i
$437$	32.4480			1.55220
$438$	−11.9775	+	9.58425i	−0.572306	+	0.457953i
$439$			28.5876i			1.36441i	0.731159	+	0.682207i	$0.238980\pi$
$439$			28.5876i			1.36441i	−0.731159	+	0.682207i	$0.761020\pi$
$440$	0.781517			0.0372573
$441$	7.65123	+	19.5565i	0.364344	+	0.931264i
$442$	15.8669			0.754711
$443$		−	34.9678i		−	1.66137i	−0.556744	−	0.830684i	$-0.687950\pi$
$443$		−	34.9678i		−	1.66137i	0.556744	−	0.830684i	$-0.312050\pi$
$444$	−2.83420	−	18.5944i	−0.134505	−	0.882453i
$445$	7.57854			0.359257
$446$	−4.98717	+	8.63803i	−0.236149	+	0.409023i
$447$	1.33130	+	1.66373i	0.0629681	+	0.0786915i
$448$	−2.57812	−	0.594391i	−0.121805	−	0.0280823i
$449$			12.6187i			0.595515i	0.954642	+	0.297758i	$0.0962387\pi$
$449$			12.6187i			0.595515i	−0.954642	+	0.297758i	$0.903761\pi$
$450$	−2.92698	−	0.657860i	−0.137979	−	0.0310118i
$451$	−7.40311	−	4.27419i	−0.348599	−	0.201264i
$452$	2.66192	−	1.53686i	0.125206	−	0.0722879i
$453$	0.488739	+	3.20649i	0.0229630	+	0.150654i
$454$	14.8607	−	8.57982i	0.697447	−	0.402671i
$455$	1.55735	−	6.75485i	0.0730095	−	0.316672i
$456$	−1.83732	−	12.0541i	−0.0860403	−	0.564487i
$457$	30.3662			1.42047			0.710236	−	0.703964i	$-0.248588\pi$
$457$	30.3662			1.42047			0.710236	+	0.703964i	$0.248588\pi$
$458$	−6.44708	+	11.1667i	−0.301252	+	0.521784i
$459$	31.3907	+	2.19544i	1.46519	+	0.102474i
$460$	−3.99168	+	2.30460i	−0.186113	+	0.107452i
$461$	−0.772644	+	1.33826i	−0.0359856	+	0.0623289i	−0.883457	−	0.468512i	$-0.844790\pi$
$461$	−0.772644	+	1.33826i	−0.0359856	+	0.0623289i	0.847472	+	0.530841i	$0.178124\pi$
$462$	−0.269547	+	3.57120i	−0.0125404	+	0.166147i
$463$	−7.01500	−	12.1503i	−0.326015	−	0.564674i	0.655703	−	0.755019i	$-0.272373\pi$
$463$	−7.01500	−	12.1503i	−0.326015	−	0.564674i	−0.981717	+	0.190346i	$0.939039\pi$
$464$	3.96237	+	2.28767i	0.183948	+	0.106203i
$465$	8.09524	+	10.1166i	0.375408	+	0.469148i
$466$	−7.43401	−	12.8761i	−0.344374	−	0.596473i
$467$	−5.25258	−	9.09774i	−0.243061	−	0.420993i	0.718524	−	0.695502i	$-0.244818\pi$
$467$	−5.25258	−	9.09774i	−0.243061	−	0.420993i	−0.961585	+	0.274509i	$0.911485\pi$
$468$	−7.66889	−	1.72364i	−0.354495	−	0.0796752i
$469$	31.0890	+	7.16763i	1.43556	+	0.330971i
$470$	−0.868218	−	0.501266i	−0.0400479	−	0.0231217i
$471$	4.36427	−	11.1744i	0.201095	−	0.514890i
$472$			2.64005i			0.121518i
$473$			6.95703i			0.319884i
$474$	−10.0421	+	25.7121i	−0.461249	+	1.18100i
$475$	−6.09668	−	3.51992i	−0.279735	−	0.161505i
$476$	10.9237	−	11.7213i	0.500689	−	0.537246i
$477$	−8.56829	−	27.4541i	−0.392315	−	1.25704i
$478$	1.06303	+	1.84122i	0.0486219	+	0.0842155i
$479$	4.88677	+	8.46413i	0.223282	+	0.386736i	0.955803	−	0.294009i	$-0.0949896\pi$
$479$	4.88677	+	8.46413i	0.223282	+	0.386736i	−0.732521	+	0.680745i	$0.761656\pi$
$480$	1.08216	+	1.35238i	0.0493936	+	0.0617274i
$481$	−24.6407	−	14.2263i	−1.12352	−	0.648664i
$482$	9.22217	+	15.9733i	0.420058	+	0.727563i
$483$	−9.15430	−	19.0351i	−0.416535	−	0.866129i
$484$	5.19462	−	8.99734i	0.236119	−	0.408970i
$485$	−5.00436	+	2.88927i	−0.227236	+	0.131195i
$486$	−14.9335	−	4.47112i	−0.677397	−	0.202814i
$487$	0.414656	−	0.718204i	0.0187898	−	0.0325449i	−0.856478	−	0.516184i	$-0.827352\pi$
$487$	0.414656	−	0.718204i	0.0187898	−	0.0325449i	0.875267	+	0.483639i	$0.160685\pi$
$488$	2.13177			0.0965006
$489$	−4.76459	−	31.2592i	−0.215462	−	1.41359i
$490$	−3.91783	−	5.80091i	−0.176990	−	0.262059i
$491$	21.3419	−	12.3218i	0.963147	−	0.556073i	0.0660068	−	0.997819i	$-0.478974\pi$
$491$	21.3419	−	12.3218i	0.963147	−	0.556073i	0.897140	+	0.441746i	$0.145641\pi$
$492$	−2.85474	−	18.7292i	−0.128702	−	0.844377i
$493$	−23.9957	+	13.8539i	−1.08071	+	0.623950i
$494$	−15.9737	−	9.22244i	−0.718692	−	0.414937i
$495$	1.58899	−	1.72396i	0.0714198	−	0.0774861i
$496$		−	7.48063i		−	0.335890i
$497$	−6.01527	+	26.0907i	−0.269822	+	1.17033i
$498$	4.39894	+	5.49737i	0.197121	+	0.246343i
$499$	−14.5236	+	25.1555i	−0.650164	+	1.12612i	0.332919	+	0.942955i	$0.391966\pi$
$499$	−14.5236	+	25.1555i	−0.650164	+	1.12612i	−0.983083	+	0.183162i	$0.941367\pi$
$500$	1.00000			0.0447214
$501$	5.61180	+	36.8175i	0.250717	+	1.64489i
$502$		−	14.4909i		−	0.646759i
$503$	1.72372			0.0768570			0.0384285	−	0.999261i	$-0.487765\pi$
$503$	1.72372			0.0768570			0.0384285	+	0.999261i	$0.487765\pi$
$504$	−6.55304	+	4.47858i	−0.291896	+	0.199492i
$505$	0.998784			0.0444453
$506$		−	3.60216i		−	0.160136i
$507$	8.29717	−	6.63931i	0.368490	−	0.294862i
$508$	0.401239			0.0178021
$509$	−6.33911	+	10.9797i	−0.280976	+	0.486665i	−0.971625	−	0.236525i	$-0.923992\pi$
$509$	−6.33911	+	10.9797i	−0.280976	+	0.486665i	0.690649	+	0.723190i	$0.257325\pi$
$510$	−10.3694	+	1.58052i	−0.459164	+	0.0699866i
$511$	17.1421	+	15.9757i	0.758323	+	0.706722i
$512$		−	1.00000i		−	0.0441942i
$513$	−30.3260	−	20.4557i	−1.33893	−	0.903141i
$514$	5.90514	+	3.40934i	0.260465	+	0.150379i
$515$	−5.08667	+	2.93679i	−0.224145	+	0.129410i
$516$	−12.0388	+	9.63334i	−0.529979	+	0.424084i
$517$	0.678527	−	0.391748i	0.0298416	−	0.0172291i
$518$	−27.4736	+	8.40853i	−1.20712	+	0.369450i
$519$	10.6810	+	4.17156i	0.468844	+	0.183111i
$520$	2.62007			0.114898
$521$	−20.9088	+	36.2152i	−0.916032	+	1.58661i	−0.110650	+	0.993859i	$0.535293\pi$
$521$	−20.9088	+	36.2152i	−0.916032	+	1.58661i	−0.805383	+	0.592755i	$0.798040\pi$
$522$	13.1027	−	4.08930i	0.573492	−	0.178984i
$523$	−23.2073	+	13.3987i	−1.01478	+	0.585885i	−0.912589	−	0.408879i	$-0.865920\pi$
$523$	−23.2073	+	13.3987i	−1.01478	+	0.585885i	−0.102195	+	0.994764i	$0.532586\pi$
$524$	−11.0798	+	19.1907i	−0.484021	+	0.838349i
$525$	−0.344902	+	4.56958i	−0.0150528	+	0.199433i
$526$	9.28146	+	16.0760i	0.404691	+	0.700945i
$527$	39.2327	+	22.6510i	1.70900	+	0.986693i
$528$	−1.33817	+	0.203967i	−0.0582364	+	0.00887651i
$529$	−0.877671	−	1.52017i	−0.0381596	−	0.0660944i
$530$	4.79336	+	8.30234i	0.208210	+	0.360630i
$531$	5.82372	+	5.36779i	0.252728	+	0.232942i
$532$	−17.8102	+	5.45096i	−0.772169	+	0.236329i
$533$	−24.8193	−	14.3294i	−1.07504	−	0.620676i
$534$	−12.9765	+	1.97791i	−0.561550	+	0.0855925i
$535$			4.87379i			0.210712i
$536$			12.0588i			0.520860i
$537$	−11.2390	−	14.0454i	−0.484997	−	0.606103i
$538$	−1.12062	−	0.646992i	−0.0483135	−	0.0278938i
$539$	5.45706	−	0.384885i	0.235052	−	0.0165782i
$540$	5.18349	+	0.362528i	0.223062	+	0.0156007i
$541$	5.58077	+	9.66618i	0.239936	+	0.415581i	0.960696	−	0.277604i	$-0.0895402\pi$
$541$	5.58077	+	9.66618i	0.239936	+	0.415581i	−0.720760	+	0.693185i	$0.756207\pi$
$542$	13.8165	+	23.9309i	0.593471	+	1.02792i
$543$	−0.483187	+	1.23717i	−0.0207355	+	0.0530920i
$544$	5.24457	+	3.02795i	0.224859	+	0.129822i
$545$	−0.338969	−	0.587111i	−0.0145198	−	0.0251491i
$546$	−0.903667	+	11.9726i	−0.0386734	+	0.512380i
$547$	1.68877	−	2.92504i	0.0722067	−	0.125066i	−0.827661	−	0.561228i	$-0.810329\pi$
$547$	1.68877	−	2.92504i	0.0722067	−	0.125066i	0.899868	+	0.436162i	$0.143663\pi$
$548$	16.6279	−	9.60012i	0.710308	−	0.410097i
$549$	4.33434	−	4.70249i	0.184985	−	0.200697i
$550$	−0.390758	+	0.676813i	−0.0166620	+	0.0288594i
$551$	32.2097			1.37218
$552$	6.23338	−	4.98788i	0.265310	−	0.212298i
$553$	41.0873	+	9.47277i	1.74721	+	0.402823i
$554$	21.1767	−	12.2264i	0.899711	−	0.519449i
$555$	17.5204	+	6.84273i	0.743698	+	0.290458i
$556$	−0.151908	+	0.0877042i	−0.00644234	+	0.00371949i
$557$	−19.1518	−	11.0573i	−0.811489	−	0.468513i	0.0359839	−	0.999352i	$-0.488544\pi$
$557$	−19.1518	−	11.0573i	−0.811489	−	0.468513i	−0.847473	+	0.530839i	$0.821877\pi$
$558$	−16.5016	−	15.2097i	−0.698568	−	0.643879i
$559$			23.3237i			0.986489i
$560$	1.80382	−	1.93552i	0.0762252	−	0.0817907i
$561$	2.98220	−	7.63573i	0.125909	−	0.322381i
$562$	1.34513	−	2.32984i	0.0567410	−	0.0982782i
$563$	−13.1400			−0.553784			−0.276892	−	0.960901i	$-0.589304\pi$
$563$	−13.1400			−0.553784			−0.276892	+	0.960901i	$0.589304\pi$
$564$	1.61745	+	0.631711i	0.0681071	+	0.0265998i
$565$			3.07372i			0.129313i
$566$	7.15360			0.300688
$567$	−3.44440	+	23.5613i	−0.144651	+	0.989483i
$568$	−10.1200			−0.424628
$569$			16.5457i			0.693634i	0.937933	+	0.346817i	$0.112737\pi$
$569$			16.5457i			0.693634i	−0.937933	+	0.346817i	$0.887263\pi$
$570$	11.3579	+	4.43591i	0.475728	+	0.185800i
$571$	−41.9796			−1.75679			−0.878397	−	0.477932i	$-0.841387\pi$
$571$	−41.9796			−1.75679			−0.878397	+	0.477932i	$0.841387\pi$
$572$	−1.02381	+	1.77330i	−0.0428078	+	0.0741453i
$573$	−8.52915	+	21.8383i	−0.356311	+	0.912310i
$574$	−27.6727	+	8.46946i	−1.15503	+	0.353508i
$575$		−	4.60919i		−	0.192217i
$576$	−2.20591	−	2.03321i	−0.0919129	−	0.0847172i
$577$	0.965716	+	0.557556i	0.0402033	+	0.0232114i	0.519967	−	0.854186i	$-0.325944\pi$
$577$	0.965716	+	0.557556i	0.0402033	+	0.0232114i	−0.479764	+	0.877398i	$0.659278\pi$
$578$	−17.0382	+	9.83699i	−0.708694	+	0.409165i
$579$	15.1576	+	5.91994i	0.629929	+	0.246024i
$580$	−3.96237	+	2.28767i	−0.164528	+	0.0949905i
$581$	7.33245	−	7.86782i	0.304201	−	0.326412i
$582$	7.81477	−	6.25330i	0.323933	−	0.259207i
$583$	−7.49218			−0.310294
$584$	−4.42830	+	7.67003i	−0.183244	+	0.317388i
$585$	5.32716	−	5.77964i	0.220251	−	0.238959i
$586$	4.59573	−	2.65334i	0.189848	−	0.109609i
$587$	−7.06492	+	12.2368i	−0.291600	+	0.505067i	−0.974188	−	0.225737i	$-0.927521\pi$
$587$	−7.06492	+	12.2368i	−0.291600	+	0.505067i	0.682588	+	0.730803i	$0.260854\pi$
$588$	8.22237	+	8.91025i	0.339085	+	0.367453i
$589$	−26.3312	−	45.6070i	−1.08496	−	1.87920i
$590$	−2.28635	−	1.32003i	−0.0941276	−	0.0543446i
$591$	7.56593	−	19.3721i	0.311221	−	0.796861i
$592$	−5.42975	−	9.40460i	−0.223161	−	0.386527i
$593$	−1.63329	−	2.82894i	−0.0670711	−	0.116171i	0.830540	−	0.556959i	$-0.188032\pi$
$593$	−1.63329	−	2.82894i	−0.0670711	−	0.116171i	−0.897611	+	0.440789i	$0.854699\pi$
$594$	−2.27086	+	3.36659i	−0.0931744	+	0.138133i
$595$	4.68910	+	15.3209i	0.192234	+	0.628096i
$596$	1.06540	+	0.615111i	0.0436406	+	0.0251959i
$597$	−4.72304	−	5.90241i	−0.193301	−	0.241569i
$598$		−	12.0764i		−	0.493841i
$599$		−	10.7220i		−	0.438088i	−0.975715	−	0.219044i	$-0.929706\pi$
$599$		−	10.7220i		−	0.438088i	0.975715	−	0.219044i	$-0.0702938\pi$
$600$	−1.71227	+	0.260988i	−0.0699033	+	0.0106548i
$601$	−34.1874	−	19.7381i	−1.39453	−	0.805134i	−0.400720	−	0.916201i	$-0.631240\pi$
$601$	−34.1874	−	19.7381i	−1.39453	−	0.805134i	−0.993813	+	0.111067i	$0.964573\pi$
$602$	17.2299	+	16.0575i	0.702239	+	0.654455i
$603$	26.6006	+	24.5181i	1.08326	+	0.998454i
$604$	0.936323	+	1.62176i	0.0380985	+	0.0659885i
$605$	5.19462	+	8.99734i	0.211191	+	0.365794i
$606$	−1.71019	+	0.260671i	−0.0694718	+	0.0105890i
$607$	20.3492	+	11.7486i	0.825947	+	0.476861i	0.852463	−	0.522788i	$-0.175108\pi$
$607$	20.3492	+	11.7486i	0.825947	+	0.476861i	−0.0265161	+	0.999648i	$0.508441\pi$
$608$	−3.51992	−	6.09668i	−0.142752	−	0.247253i
$609$	−9.08708	−	18.8954i	−0.368227	−	0.765679i
$610$	−1.06588	+	1.84617i	−0.0431564	+	0.0747491i
$611$	2.27479	−	1.31335i	0.0920283	−	0.0531325i
$612$	17.3427	−	5.41257i	0.701038	−	0.218790i
$613$	4.76729	−	8.25719i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$613$	4.76729	−	8.25719i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$614$	28.5768			1.15327
$615$	17.6473	+	6.89232i	0.711609	+	0.277925i
$616$	0.605130	+	1.97717i	0.0243814	+	0.0796624i
$617$	−22.4936	+	12.9867i	−0.905559	+	0.522825i	−0.879000	−	0.476823i	$-0.841788\pi$
$617$	−22.4936	+	12.9867i	−0.905559	+	0.522825i	−0.0265594	+	0.999647i	$0.508455\pi$
$618$	7.94330	−	6.35615i	0.319527	−	0.255682i
$619$	−11.1464	+	6.43535i	−0.448010	+	0.258658i	−0.706989	−	0.707224i	$-0.749947\pi$
$619$	−11.1464	+	6.43535i	−0.448010	+	0.258658i	0.258980	+	0.965883i	$0.416614\pi$
$620$	6.47842	+	3.74031i	0.260179	+	0.150215i
$621$	1.67096	−	23.8917i	0.0670535	−	0.958741i
$622$			28.3469i			1.13661i
$623$	5.86807	+	19.1730i	0.235099	+	0.768151i
$624$	−4.48628	+	0.683808i	−0.179595	+	0.0273742i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.9219			−0.556433
$627$	−7.44046	+	5.95378i	−0.297143	+	0.237771i
$628$		−	6.92615i		−	0.276383i
$629$	65.7641			2.62219
$630$	−0.602040	−	7.91439i	−0.0239858	−	0.315317i
$631$	25.3213			1.00802			0.504012	−	0.863697i	$-0.331857\pi$
$631$	25.3213			1.00802			0.504012	+	0.863697i	$0.331857\pi$
$632$			15.9369i			0.633937i
$633$	3.04203	+	19.9580i	0.120910	+	0.793258i
$634$	6.48605			0.257594
$635$	−0.200619	+	0.347483i	−0.00796134	+	0.0137894i
$636$	−10.3744	−	12.9649i	−0.411370	−	0.514091i
$637$	18.2950	−	1.29034i	0.724876	−	0.0511253i
$638$		−	3.57571i		−	0.141564i
$639$	−20.5762	+	22.3239i	−0.813983	+	0.883121i
$640$	0.866025	+	0.500000i	0.0342327	+	0.0197642i
$641$	−18.0859	+	10.4419i	−0.714349	+	0.412430i	−0.812669	−	0.582725i	$-0.801986\pi$
$641$	−18.0859	+	10.4419i	−0.714349	+	0.412430i	0.0983201	+	0.995155i	$0.468653\pi$
$642$	−1.27200	−	8.34526i	−0.0502019	−	0.329361i
$643$	1.18971	−	0.686880i	0.0469177	−	0.0270879i	−0.476358	−	0.879252i	$-0.658043\pi$
$643$	1.18971	−	0.686880i	0.0469177	−	0.0270879i	0.523275	+	0.852164i	$0.324710\pi$
$644$	−8.92119	−	8.31414i	−0.351544	−	0.327623i
$645$	−2.32331	−	15.2426i	−0.0914801	−	0.600177i
$646$	42.6326			1.67736
$647$	−18.1195	+	31.3838i	−0.712349	+	1.23383i	0.251624	+	0.967825i	$0.419036\pi$
$647$	−18.1195	+	31.3838i	−0.712349	+	1.23383i	−0.963973	+	0.266000i	$0.914298\pi$
$648$	−8.97018	+	0.732082i	−0.352382	+	0.0287589i
$649$	1.78682	−	1.03162i	0.0701389	−	0.0404947i
$650$	−1.31003	+	2.26905i	−0.0513838	+	0.0889993i
$651$	−19.3261	+	28.3136i	−0.757449	+	1.10970i
$652$	−9.12797	−	15.8101i	−0.357479	−	0.619172i
$653$	27.5805	+	15.9236i	1.07931	+	0.623138i	0.930709	−	0.365760i	$-0.119191\pi$
$653$	27.5805	+	15.9236i	1.07931	+	0.623138i	0.148598	+	0.988898i	$0.452524\pi$
$654$	0.733637	+	0.916828i	0.0286875	+	0.0358508i
$655$	−11.0798	−	19.1907i	−0.432922	−	0.749842i
$656$	−5.46910	−	9.47275i	−0.213532	−	0.369849i
$657$	7.91574	+	25.3632i	0.308822	+	0.989514i
$658$	0.595896	−	2.58465i	0.0232305	−	0.100760i
$659$	20.7307	+	11.9689i	0.807552	+	0.466240i	0.846105	−	0.533016i	$-0.178942\pi$
$659$	20.7307	+	11.9689i	0.807552	+	0.466240i	−0.0385530	+	0.999257i	$0.512275\pi$
$660$	0.492445	−	1.26087i	0.0191684	−	0.0490794i
$661$			38.6122i			1.50184i	0.660394	+	0.750920i	$0.270389\pi$
$661$			38.6122i			1.50184i	−0.660394	+	0.750920i	$0.729611\pi$
$662$			20.2311i			0.786304i
$663$	9.99796	−	25.5991i	0.388289	−	0.994188i
$664$	3.52036	+	2.03248i	0.136616	+	0.0788755i
$665$	4.18442	−	18.1496i	0.162265	−	0.703810i
$666$	−31.7855	−	7.14403i	−1.23167	−	0.276825i
$667$	10.5443	+	18.2633i	0.408278	+	0.707158i
$668$	10.7511	+	18.6214i	0.415971	+	0.720483i
$669$	10.7938	+	13.4891i	0.417314	+	0.521519i
$670$	−10.4432	−	6.02939i	−0.403456	−	0.232936i
$671$	−0.833006	−	1.44281i	−0.0321579	−	0.0556990i
$672$	−2.58348	+	3.78492i	−0.0996600	+	0.146006i
$673$	−7.83794	+	13.5757i	−0.302131	+	0.523305i	−0.976618	−	0.214981i	$-0.931031\pi$
$673$	−7.83794	+	13.5757i	−0.302131	+	0.523305i	0.674488	+	0.738286i	$0.264365\pi$
$674$	−10.8518	+	6.26528i	−0.417995	+	0.241330i
$675$	−2.90570	+	4.30777i	−0.111841	+	0.165806i
$676$	3.06762	−	5.31327i	0.117985	−	0.204357i
$677$	−1.50086			−0.0576829			−0.0288414	−	0.999584i	$-0.509182\pi$
$677$	−1.50086			−0.0576829			−0.0288414	+	0.999584i	$0.509182\pi$
$678$	−0.802206	−	5.26306i	−0.0308085	−	0.202127i
$679$	−11.1845	−	10.4234i	−0.429221	−	0.400014i
$680$	−5.24457	+	3.02795i	−0.201120	+	0.116117i
$681$	−4.47847	−	29.3820i	−0.171615	−	1.12592i
$682$	−5.06299	+	2.92312i	−0.193872	+	0.111932i
$683$	−42.4921	−	24.5328i	−1.62591	−	0.938722i	−0.985295	−	0.170862i	$-0.945345\pi$
$683$	−42.4921	−	24.5328i	−1.62591	−	0.938722i	−0.640619	−	0.767859i	$-0.721322\pi$
$684$	−20.6055	−	4.63123i	−0.787871	−	0.177079i
$685$			19.2002i			0.733603i
$686$	11.6422	−	14.4034i	0.444502	−	0.549925i
$687$	13.9535	+	17.4378i	0.532361	+	0.665293i
$688$	−4.45098	+	7.70932i	−0.169692	+	0.293915i
$689$	−25.1179			−0.956914
$690$	1.20295	+	7.89220i	0.0457954	+	0.300451i
$691$			16.9964i			0.646575i	0.946301	+	0.323287i	$0.104788\pi$
$691$			16.9964i			0.646575i	−0.946301	+	0.323287i	$0.895212\pi$
$692$	6.62032			0.251667
$693$	5.59182	+	2.68514i	0.212415	+	0.102000i
$694$	−0.288364			−0.0109462
$695$		−	0.175408i		−	0.00665362i
$696$	6.18761	−	4.95126i	0.234541	−	0.187677i
$697$	66.2406			2.50904
$698$	3.91159	−	6.77506i	0.148056	−	0.256440i
$699$	−25.4581	+	3.88038i	−0.962915	+	0.146769i
$700$	0.774302	+	2.52991i	0.0292659	+	0.0956217i
$701$		−	27.6593i		−	1.04468i	−0.852738	−	0.522338i	$-0.825060\pi$
$701$		−	27.6593i		−	1.04468i	0.852738	−	0.522338i	$-0.174940\pi$
$702$	−7.61315	+	11.2867i	−0.287340	+	0.425987i
$703$	−66.2069	−	38.2246i	−2.49704	−	1.44167i
$704$	−0.676813	+	0.390758i	−0.0255084	+	0.0147273i
$705$	−1.35580	+	1.08490i	−0.0510625	+	0.0408597i
$706$	3.67991	−	2.12459i	0.138495	−	0.0799602i
$707$	0.773360	+	2.52684i	0.0290852	+	0.0950315i
$708$	4.25937	+	1.66354i	0.160077	+	0.0625195i
$709$	−29.0834			−1.09225			−0.546125	−	0.837703i	$-0.683898\pi$
$709$	−29.0834			−1.09225			−0.546125	+	0.837703i	$0.683898\pi$
$710$	5.06002	−	8.76422i	0.189899	−	0.328915i
$711$	35.1554	+	32.4032i	1.31843	+	1.21521i
$712$	−6.56320	+	3.78927i	−0.245966	+	0.142009i
$713$	17.2398	−	29.8603i	0.645637	−	1.11828i
$714$	−12.0276	−	25.0098i	−0.450122	−	0.935968i
$715$	−1.02381	−	1.77330i	−0.0382885	−	0.0663176i
$716$	−8.99427	−	5.19284i	−0.336131	−	0.194066i
$717$	3.64040	−	0.554877i	0.135953	−	0.0207223i
$718$	5.61182	+	9.71995i	0.209431	+	0.362745i
$719$	−19.0668	−	33.0246i	−0.711070	−	1.23161i	−0.964456	−	0.264245i	$-0.914877\pi$
$719$	−19.0668	−	33.0246i	−0.711070	−	1.23161i	0.253385	−	0.967365i	$-0.418456\pi$
$720$	2.86377	−	0.893768i	0.106726	−	0.0333088i
$721$	−11.3684	−	10.5949i	−0.423383	−	0.394573i
$722$	−26.4652	−	15.2797i	−0.984933	−	0.568651i
$723$	31.5818	−	4.81376i	1.17454	−	0.179026i
$724$			0.766824i			0.0284988i
$725$		−	4.57535i		−	0.169924i
$726$	−11.2428	−	14.0502i	−0.417260	−	0.521451i
$727$	9.20054	+	5.31193i	0.341229	+	0.197009i	0.660815	−	0.750548i	$-0.270211\pi$
$727$	9.20054	+	5.31193i	0.341229	+	0.197009i	−0.319586	+	0.947557i	$0.603544\pi$
$728$	2.02872	+	6.62855i	0.0751895	+	0.245670i
$729$	−16.6234	+	21.2759i	−0.615681	+	0.787996i
$730$	−4.42830	−	7.67003i	−0.163899	−	0.283881i
$731$	−26.9547	−	46.6869i	−0.996955	−	1.72678i
$732$	1.34326	−	3.43933i	0.0496483	−	0.127121i
$733$	3.12334	+	1.80326i	0.115363	+	0.0666051i	0.556571	−	0.830800i	$-0.312117\pi$
$733$	3.12334	+	1.80326i	0.115363	+	0.0666051i	−0.441208	+	0.897405i	$0.645450\pi$
$734$	3.31715	+	5.74548i	0.122438	+	0.212070i
$735$	−11.8277	+	2.66566i	−0.436271	+	0.0983244i
$736$	2.30460	−	3.99168i	0.0849485	−	0.147135i
$737$	8.16154	−	4.71207i	0.300634	−	0.173571i
$738$	−32.0159	−	7.19580i	−1.17852	−	0.264881i
$739$	−5.13310	+	8.89079i	−0.188824	+	0.327053i	−0.944858	−	0.327479i	$-0.893801\pi$
$739$	−5.13310	+	8.89079i	−0.188824	+	0.327053i	0.756034	+	0.654532i	$0.227134\pi$
$740$	10.8595			0.399203
$741$	−24.9445	+	19.9603i	−0.916358	+	0.733260i
$742$	−17.2927	+	18.5553i	−0.634834	+	0.681186i
$743$	35.2305	−	20.3403i	1.29248	−	0.746214i	0.313388	−	0.949625i	$-0.398536\pi$
$743$	35.2305	−	20.3403i	1.29248	−	0.746214i	0.979093	+	0.203411i	$0.0652027\pi$
$744$	−12.0690	−	4.71366i	−0.442471	−	0.172811i
$745$	−1.06540	+	0.615111i	−0.0390333	+	0.0225359i
$746$	−26.3293	−	15.2013i	−0.963986	−	0.556557i
$747$	11.6411	−	3.63313i	0.425926	−	0.132929i
$748$		−	4.73279i		−	0.173048i
$749$	−12.3303	+	3.77378i	−0.450538	+	0.137891i
$750$	0.630115	−	1.61337i	0.0230085	−	0.0589119i
$751$	11.1412	−	19.2971i	0.406547	−	0.704161i	−0.587953	−	0.808895i	$-0.700066\pi$
$751$	11.1412	−	19.2971i	0.406547	−	0.704161i	0.994500	+	0.104734i	$0.0333993\pi$
$752$	1.00253			0.0365586
$753$	−23.3791	−	9.13091i	−0.851981	−	0.332749i
$754$		−	11.9877i		−	0.436567i
$755$	−1.87265			−0.0681526
$756$	3.09642	+	13.3945i	0.112616	+	0.487153i
$757$	40.9255			1.48746			0.743732	−	0.668478i	$-0.233054\pi$
$757$	40.9255			1.48746			0.743732	+	0.668478i	$0.233054\pi$
$758$			7.50620i			0.272638i
$759$	−5.81161	−	2.26978i	−0.210948	−	0.0823876i
$760$	7.03984			0.255362
$761$	−14.6756	+	25.4189i	−0.531990	+	0.921434i	0.467312	+	0.884092i	$0.345222\pi$
$761$	−14.6756	+	25.4189i	−0.531990	+	0.921434i	−0.999303	+	0.0373420i	$0.988111\pi$
$762$	0.252827	−	0.647346i	0.00915894	−	0.0234509i
$763$	1.22288	−	1.31216i	0.0442711	−	0.0475035i
$764$			13.5359i			0.489711i
$765$	−3.98393	+	17.7255i	−0.144039	+	0.640867i
$766$	3.61841	+	2.08909i	0.130738	+	0.0754819i
$767$	5.99040	−	3.45856i	0.216301	−	0.124881i
$768$	−1.61337	−	0.630115i	−0.0582174	−	0.0227373i
$769$	31.8034	−	18.3617i	1.14686	−	0.662141i	0.198741	−	0.980052i	$-0.436315\pi$
$769$	31.8034	−	18.3617i	1.14686	−	0.662141i	0.948120	+	0.317912i	$0.102982\pi$
$770$	−2.01484	−	0.464527i	−0.0726099	−	0.0167404i
$771$	9.22143	−	7.37889i	0.332102	−	0.265744i
$772$	9.39501			0.338134
$773$	−16.9345	+	29.3314i	−0.609091	+	1.05498i	0.382299	+	0.924039i	$0.375132\pi$
$773$	−16.9345	+	29.3314i	−0.609091	+	1.05498i	−0.991391	+	0.130938i	$0.958201\pi$
$774$	7.95628	+	25.4932i	0.285983	+	0.916332i
$775$	−6.47842	+	3.74031i	−0.232712	+	0.134356i
$776$	2.88927	−	5.00436i	0.103719	−	0.179646i
$777$	−3.74546	+	49.6233i	−0.134368	+	1.78023i
$778$	7.12437	+	12.3398i	0.255421	+	0.442402i
$779$	−66.6867	−	38.5016i	−2.38930	−	1.37946i
$780$	1.65094	−	4.22714i	0.0591133	−	0.151356i
$781$	3.95449	+	6.84938i	0.141503	+	0.245090i
$782$	13.9564	+	24.1732i	0.499080	+	0.864433i
$783$	1.65869	−	23.7163i	0.0592769	−	0.847550i
$784$	6.29340	+	3.06482i	0.224764	+	0.109458i
$785$	5.99822	+	3.46308i	0.214086	+	0.123602i
$786$	23.9801	+	29.9681i	0.855343	+	1.06892i
$787$		−	3.26792i		−	0.116489i	−0.998302	−	0.0582443i	$-0.981450\pi$
$787$		−	3.26792i		−	0.116489i	0.998302	−	0.0582443i	$-0.0185502\pi$
$788$		−	12.0072i		−	0.427740i
$789$	31.7848	−	4.84470i	1.13157	−	0.172476i
$790$	−13.8018	−	7.96847i	−0.491046	−	0.283505i
$791$	−7.77625	+	2.37999i	−0.276492	+	0.0846227i
$792$	−0.514128	+	2.28748i	−0.0182688	+	0.0812822i
$793$	−2.79269	−	4.83708i	−0.0991714	−	0.171770i
$794$	−8.75045	−	15.1562i	−0.310542	−	0.537874i
$795$	16.4151	−	2.50202i	0.582183	−	0.0887375i
$796$	−3.77973	−	2.18223i	−0.133969	−	0.0773471i
$797$	−13.7568	−	23.8275i	−0.487292	−	0.844014i	0.512601	−	0.858627i	$-0.328682\pi$
$797$	−13.7568	−	23.8275i	−0.487292	−	0.844014i	−0.999893	+	0.0146125i	$0.995349\pi$
$798$	−2.42806	+	32.1691i	−0.0859522	+	1.13877i
$799$	−3.03562	+	5.25785i	−0.107393	+	0.186009i
$800$	−0.866025	+	0.500000i	−0.0306186	+	0.0176777i
$801$	−4.98561	+	22.1822i	−0.176158	+	0.783771i
$802$	6.03677	−	10.4560i	0.213166	−	0.369214i
$803$	6.92157			0.244257
$804$	19.4553	+	7.59842i	0.686134	+	0.267976i
$805$	11.6609	−	3.56891i	0.410991	−	0.125787i
$806$	−16.9739	+	9.79988i	−0.597880	+	0.345186i
$807$	−1.74996	+	1.40030i	−0.0616014	+	0.0492928i
$808$	−0.864973	+	0.499392i	−0.0304296	+	0.0175686i
$809$	−6.97997	−	4.02989i	−0.245403	−	0.141683i	0.372255	−	0.928131i	$-0.378585\pi$
$809$	−6.97997	−	4.02989i	−0.245403	−	0.141683i	−0.617657	+	0.786447i	$0.711918\pi$
$810$	3.85109	−	8.13444i	0.135313	−	0.285815i
$811$			22.0290i			0.773544i	0.922175	+	0.386772i	$0.126410\pi$
$811$			22.0290i			0.773544i	−0.922175	+	0.386772i	$0.873590\pi$
$812$	−8.85568	−	8.25309i	−0.310774	−	0.289627i
$813$	47.3154	−	7.21191i	1.65942	−	0.252933i
$814$	−4.24344	+	7.34985i	−0.148732	+	0.257612i
$815$	18.2559			0.639478
$816$	8.18988	−	6.55346i	0.286703	−	0.229417i
$817$			62.6684i			2.19249i
$818$	−35.1360			−1.22850
$819$	18.7468	+	9.00207i	0.655067	+	0.314558i
$820$	10.9382			0.381978
$821$		−	29.5069i		−	1.02980i	−0.857251	−	0.514899i	$-0.827829\pi$
$821$		−	29.5069i		−	1.02980i	0.857251	−	0.514899i	$-0.172171\pi$
$822$	−5.01104	−	32.8761i	−0.174780	−	1.14669i
$823$	25.2464			0.880035			0.440017	−	0.897989i	$-0.354972\pi$
$823$	25.2464			0.880035			0.440017	+	0.897989i	$0.354972\pi$
$824$	2.93679	−	5.08667i	0.102308	−	0.177202i
$825$	0.845726	+	1.05691i	0.0294444	+	0.0367968i
$826$	1.56922	−	6.80637i	0.0546003	−	0.236824i
$827$		−	30.4760i		−	1.05975i	−0.848075	−	0.529877i	$-0.822238\pi$
$827$		−	30.4760i		−	1.05975i	0.848075	−	0.529877i	$-0.177762\pi$
$828$	−4.11955	−	13.1997i	−0.143164	−	0.458720i
$829$	−29.4517	−	17.0040i	−1.02290	−	0.590572i	−0.107958	−	0.994156i	$-0.534431\pi$
$829$	−29.4517	−	17.0040i	−1.02290	−	0.590572i	−0.914943	+	0.403584i	$0.867764\pi$
$830$	−3.52036	+	2.03248i	−0.122193	+	0.0705484i
$831$	−6.38188	−	41.8698i	−0.221385	−	1.45245i
$832$	−2.26905	+	1.31003i	−0.0786650	+	0.0454173i
$833$	−35.1298	+	23.7260i	−1.21717	+	0.822058i
$834$	0.0457795	+	0.300347i	0.00158522	+	0.0104002i
$835$	−21.5021			−0.744111
$836$	−2.75088	+	4.76466i	−0.0951411	+	0.164789i
$837$	−34.9368	+	17.0393i	−1.20759	+	0.588964i
$838$	2.08178	−	1.20192i	0.0719140	−	0.0415196i
$839$	11.5670	−	20.0346i	0.399336	−	0.691670i	−0.594308	−	0.804237i	$-0.702574\pi$
$839$	11.5670	−	20.0346i	0.399336	−	0.691670i	0.993644	+	0.112567i	$0.0359073\pi$
$840$	−1.98610	−	4.12982i	−0.0685268	−	0.142492i
$841$	−4.03309	−	6.98552i	−0.139072	−	0.240880i
$842$	−1.15652	−	0.667716i	−0.0398562	−	0.0230110i
$843$	−2.91130	−	3.63826i	−0.100270	−	0.125308i
$844$	5.82791	+	10.0942i	0.200605	+	0.347458i
$845$	3.06762	+	5.31327i	0.105529	+	0.182782i
$846$	2.03836	−	2.21150i	0.0700804	−	0.0760328i
$847$	−18.7403	+	20.1086i	−0.643924	+	0.690939i
$848$	−8.30234	−	4.79336i	−0.285103	−	0.164605i
$849$	4.50759	−	11.5414i	0.154700	−	0.396099i
$850$		−	6.05590i		−	0.207716i
$851$		−	50.0535i		−	1.71581i
$852$	−6.37679	+	16.3274i	−0.218465	+	0.559366i
$853$	−19.2922	−	11.1383i	−0.660551	−	0.381369i	0.131936	−	0.991258i	$-0.457881\pi$
$853$	−19.2922	−	11.1383i	−0.660551	−	0.381369i	−0.792487	+	0.609889i	$0.791214\pi$
$854$	−5.49595	−	1.26710i	−0.188068	−	0.0433594i
$855$	14.3135	−	15.5293i	0.489512	−	0.531090i
$856$	−2.43689	−	4.22082i	−0.0832913	−	0.144265i
$857$	1.08582	+	1.88069i	0.0370908	+	0.0642432i	0.883975	−	0.467534i	$-0.154858\pi$
$857$	1.08582	+	1.88069i	0.0370908	+	0.0642432i	−0.846884	+	0.531778i	$0.821524\pi$
$858$	2.21586	+	2.76917i	0.0756482	+	0.0945379i
$859$	3.14298	+	1.81460i	0.107237	+	0.0619135i	0.552659	−	0.833407i	$-0.313613\pi$
$859$	3.14298	+	1.81460i	0.107237	+	0.0619135i	−0.445422	+	0.895321i	$0.646946\pi$
$860$	−4.45098	−	7.70932i	−0.151777	−	0.262886i
$861$	−3.77260	+	49.9829i	−0.128570	+	1.70341i
$862$	15.9040	−	27.5465i	0.541691	−	0.938237i
$863$	−16.4116	+	9.47522i	−0.558656	+	0.322540i	−0.752606	−	0.658471i	$-0.771203\pi$
$863$	−16.4116	+	9.47522i	−0.558656	+	0.322540i	0.193950	+	0.981011i	$0.437870\pi$
$864$	−4.67030	+	2.27779i	−0.158887	+	0.0774919i
$865$	−3.31016	+	5.73336i	−0.112549	+	0.194940i
$866$	33.1620			1.12689
$867$	5.13468	+	33.6872i	0.174383	+	1.14408i
$868$	−4.44642	+	19.2860i	−0.150921	+	0.654608i
$869$	10.7863	−	6.22749i	0.365901	−	0.211253i
$870$	1.19411	+	7.83425i	0.0404842	+	0.265606i
$871$	27.3619	−	15.7974i	0.927124	−	0.535275i
$872$	0.587111	+	0.338969i	0.0198821	+	0.0114789i
$873$	−5.16467	−	16.5484i	−0.174797	−	0.560078i
$874$		−	32.4480i		−	1.09757i
$875$	−2.57812	−	0.594391i	−0.0871563	−	0.0200941i
$876$	9.58425	+	11.9775i	0.323822	+	0.404681i
$877$	−2.79895	+	4.84792i	−0.0945138	+	0.163703i	−0.909406	−	0.415910i	$-0.863463\pi$
$877$	−2.79895	+	4.84792i	−0.0945138	+	0.163703i	0.814892	+	0.579613i	$0.196796\pi$
$878$	28.5876			0.964786
$879$	−1.38498	−	9.08651i	−0.0467144	−	0.306480i
$880$		−	0.781517i		−	0.0263449i
$881$	39.1755			1.31985			0.659927	−	0.751330i	$-0.270587\pi$
$881$	39.1755			1.31985			0.659927	+	0.751330i	$0.270587\pi$
$882$	19.5565	−	7.65123i	0.658503	−	0.257630i
$883$	−30.6078			−1.03003			−0.515017	−	0.857180i	$-0.672214\pi$
$883$	−30.6078			−1.03003			−0.515017	+	0.857180i	$0.672214\pi$
$884$		−	15.8669i		−	0.533661i
$885$	−3.57035	+	2.85696i	−0.120016	+	0.0960356i
$886$	−34.9678			−1.17476
$887$	18.8619	−	32.6698i	0.633322	−	1.09695i	−0.353546	−	0.935417i	$-0.615024\pi$
$887$	18.8619	−	32.6698i	0.633322	−	1.09695i	0.986868	−	0.161529i	$-0.0516424\pi$
$888$	−18.5944	+	2.83420i	−0.623989	+	0.0951096i
$889$	−1.03444	−	0.238493i	−0.0346941	−	0.00799879i
$890$		−	7.57854i		−	0.254033i
$891$	4.00065	+	5.78507i	0.134027	+	0.193807i
$892$	8.63803	+	4.98717i	0.289223	+	0.166983i
$893$	6.11212	−	3.52883i	0.204534	−	0.118088i
$894$	1.66373	−	1.33130i	0.0556433	−	0.0445252i
$895$	8.99427	−	5.19284i	0.300645	−	0.173578i
$896$	−0.594391	+	2.57812i	−0.0198572	+	0.0861289i
$897$	−19.4837	−	7.60952i	−0.650541	−	0.254075i
$898$	12.6187			0.421093
$899$	17.1132	−	29.6410i	0.570759	−	0.988583i
$900$	−0.657860	+	2.92698i	−0.0219287	+	0.0975660i
$901$	50.2782	−	29.0281i	1.67501	−	0.967066i
$902$	−4.27419	+	7.40311i	−0.142315	+	0.246497i
$903$	36.7635	−	17.6801i	1.22341	−	0.588358i
$904$	−1.53686	−	2.66192i	−0.0511153	−	0.0885342i
$905$	−0.664089	−	0.383412i	−0.0220751	−	0.0127450i
$906$	3.20649	−	0.488739i	0.106528	−	0.0162373i
$907$	−0.332710	−	0.576270i	−0.0110474	−	0.0191347i	0.860449	−	0.509537i	$-0.170183\pi$
$907$	−0.332710	−	0.576270i	−0.0110474	−	0.0191347i	−0.871496	+	0.490402i	$0.836850\pi$
$908$	−8.57982	−	14.8607i	−0.284731	−	0.493169i
$909$	−0.657060	+	2.92342i	−0.0217933	+	0.0969638i
$910$	−6.75485	−	1.55735i	−0.223921	−	0.0516255i
$911$	16.9363	+	9.77817i	0.561124	+	0.323965i	0.753597	−	0.657337i	$-0.228317\pi$
$911$	16.9363	+	9.77817i	0.561124	+	0.323965i	−0.192472	+	0.981302i	$0.561651\pi$
$912$	−12.0541	+	1.83732i	−0.399153	+	0.0608396i
$913$		−	3.17684i		−	0.105138i
$914$		−	30.3662i		−	1.00443i
$915$	2.30691	+	2.88296i	0.0762643	+	0.0953077i
$916$	11.1667	+	6.44708i	0.368957	+	0.213017i
$917$	39.9717	−	42.8902i	1.31998	−	1.41636i
$918$	2.19544	−	31.3907i	0.0724602	−	1.03605i
$919$	−0.579801	−	1.00424i	−0.0191259	−	0.0331270i	0.856304	−	0.516472i	$-0.172755\pi$
$919$	−0.579801	−	1.00424i	−0.0191259	−	0.0331270i	−0.875430	+	0.483345i	$0.839422\pi$
$920$	2.30460	+	3.99168i	0.0759803	+	0.131602i
$921$	18.0067	−	46.1049i	0.593340	−	1.51921i
$922$	1.33826	+	0.772644i	0.0440732	+	0.0254457i
$923$	13.2576	+	22.9629i	0.436380	+	0.755832i
$924$	3.57120	+	0.269547i	0.117484	+	0.00886743i
$925$	−5.42975	+	9.40460i	−0.178529	+	0.309221i
$926$	−12.1503	+	7.01500i	−0.399285	+	0.230527i
$927$	−5.24961	−	16.8206i	−0.172420	−	0.552460i
$928$	2.28767	−	3.96237i	0.0750966	−	0.130071i
$929$	−26.5737			−0.871854			−0.435927	−	0.899982i	$-0.643579\pi$
$929$	−26.5737			−0.871854			−0.435927	+	0.899982i	$0.643579\pi$
$930$	10.1166	−	8.09524i	0.331738	−	0.265453i
$931$	49.1568	−	3.46701i	1.61105	−	0.113627i
$932$	−12.8761	+	7.43401i	−0.421770	+	0.243509i
$933$	45.7339	+	17.8618i	1.49726	+	0.584769i
$934$	−9.09774	+	5.25258i	−0.297687	+	0.171870i
$935$	4.09872	+	2.36639i	0.134042	+	0.0773894i
$936$	−1.72364	+	7.66889i	−0.0563389	+	0.250666i
$937$		−	23.9521i		−	0.782482i	−0.920288	−	0.391241i	$-0.872046\pi$
$937$		−	23.9521i		−	0.782482i	0.920288	−	0.391241i	$-0.127954\pi$
$938$	7.16763	−	31.0890i	0.234032	−	1.01509i
$939$	−8.77242	+	22.4612i	−0.286277	+	0.732994i
$940$	−0.501266	+	0.868218i	−0.0163495	+	0.0283182i
$941$	43.3460			1.41304			0.706519	−	0.707694i	$-0.250264\pi$
$941$	43.3460			1.41304			0.706519	+	0.707694i	$0.250264\pi$
$942$	−11.1744	−	4.36427i	−0.364082	−	0.142196i
$943$		−	50.4162i		−	1.64178i
$944$	2.64005			0.0859263
$945$	−13.1482	−	4.01566i	−0.427710	−	0.130630i
$946$	6.95703			0.226192
$947$		−	29.0648i		−	0.944480i	−0.881470	−	0.472240i	$-0.843446\pi$
$947$		−	29.0648i		−	0.944480i	0.881470	−	0.472240i	$-0.156554\pi$
$948$	25.7121	+	10.0421i	0.835091	+	0.326152i
$949$	23.2049			0.753263
$950$	−3.51992	+	6.09668i	−0.114201	+	0.197803i
$951$	4.08696	−	10.4644i	0.132529	−	0.339331i
$952$	−11.7213	−	10.9237i	−0.379890	−	0.354041i
$953$		−	11.6767i		−	0.378247i	−0.981953	−	0.189123i	$-0.939435\pi$
$953$		−	11.6767i		−	0.378247i	0.981953	−	0.189123i	$-0.0605646\pi$
$954$	−27.4541	+	8.56829i	−0.888861	+	0.277409i
$955$	−11.7224	−	6.76794i	−0.379328	−	0.219005i
$956$	1.84122	−	1.06303i	0.0595494	−	0.0343809i
$957$	−5.76894	−	2.25311i	−0.186483	−	0.0728327i
$958$	8.46413	−	4.88677i	0.273464	−	0.157884i
$959$	−48.5749	+	14.8668i	−1.56857	+	0.480073i
$960$	1.35238	−	1.08216i	0.0436479	−	0.0349266i
$961$	−24.9598			−0.805156
$962$	−14.2263	+	24.6407i	−0.458675	+	0.794448i
$963$	−14.2655	−	3.20627i	−0.459699	−	0.103321i
$964$	15.9733	−	9.22217i	0.514464	−	0.297026i
$965$	−4.69750	+	8.13632i	−0.151218	+	0.261917i
$966$	−19.0351	+	9.15430i	−0.612446	+	0.294535i
$967$	7.59505	+	13.1550i	0.244240	+	0.423037i	0.961918	−	0.273339i	$-0.0881280\pi$
$967$	7.59505	+	13.1550i	0.244240	+	0.423037i	−0.717677	+	0.696376i	$0.754795\pi$
$968$	−8.99734	−	5.19462i	−0.289185	−	0.166961i
$969$	26.8634	−	68.7821i	0.862978	−	2.20960i
$970$	2.88927	+	5.00436i	0.0927688	+	0.160680i
$971$	−21.6059	−	37.4226i	−0.693368	−	1.20095i	−0.970728	−	0.240182i	$-0.922793\pi$
$971$	−21.6059	−	37.4226i	−0.693368	−	1.20095i	0.277360	−	0.960766i	$-0.410540\pi$
$972$	−4.47112	+	14.9335i	−0.143411	+	0.478992i
$973$	0.443768	−	0.135819i	0.0142265	−	0.00435416i
$974$	−0.718204	−	0.414656i	−0.0230128	−	0.0132864i
$975$	2.83533	+	3.54333i	0.0908034	+	0.113477i
$976$		−	2.13177i		−	0.0682363i
$977$		−	4.06628i		−	0.130092i	−0.997882	−	0.0650459i	$-0.979281\pi$
$977$		−	4.06628i		−	0.130092i	0.997882	−	0.0650459i	$-0.0207194\pi$
$978$	−31.2592	+	4.76459i	−0.999559	+	0.152355i
$979$	5.12925	+	2.96138i	0.163932	+	0.0946460i
$980$	−5.80091	+	3.91783i	−0.185303	+	0.125151i
$981$	1.94146	−	0.605918i	0.0619859	−	0.0193455i
$982$	−12.3218	−	21.3419i	−0.393203	−	0.681048i
$983$	18.1546	+	31.4447i	0.579041	+	1.00293i	0.995590	+	0.0938154i	$0.0299063\pi$
$983$	18.1546	+	31.4447i	0.579041	+	1.00293i	−0.416548	+	0.909114i	$0.636760\pi$
$984$	−18.7292	+	2.85474i	−0.597065	+	0.0910058i
$985$	10.3986	+	6.00362i	0.331326	+	0.191291i
$986$	13.8539	+	23.9957i	0.441199	+	0.764179i
$987$	−3.79450	−	2.59003i	−0.120780	−	0.0824414i
$988$	−9.22244	+	15.9737i	−0.293405	+	0.508192i
$989$	−35.5337	+	20.5154i	−1.12991	+	0.652352i
$990$	−1.72396	−	1.58899i	−0.0547909	−	0.0505014i
$991$	22.0204	−	38.1404i	0.699501	−	1.21157i	−0.269139	−	0.963101i	$-0.586739\pi$
$991$	22.0204	−	38.1404i	0.699501	−	1.21157i	0.968640	−	0.248469i	$-0.0799275\pi$
$992$	−7.48063			−0.237510
$993$	32.6402	+	12.7479i	1.03581	+	0.404543i
$994$	26.0907	+	6.01527i	0.827547	+	0.190793i
$995$	3.77973	−	2.18223i	0.119826	−	0.0691814i
$996$	5.49737	−	4.39894i	0.174191	−	0.139386i
$997$	−4.08179	+	2.35662i	−0.129272	+	0.0746350i	−0.563241	−	0.826292i	$-0.690446\pi$
$997$	−4.08179	+	2.35662i	−0.129272	+	0.0746350i	0.433970	+	0.900928i	$0.357113\pi$
$998$	25.1555	+	14.5236i	0.796285	+	0.459735i
$999$	−31.5545	+	46.7802i	−0.998340	+	1.48006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bk.c.101.2	yes	32
3.2	odd	2		1890.2.bk.c.521.7		32
7.5	odd	6		630.2.t.c.551.2	yes	32
9.4	even	3		1890.2.t.c.1151.14		32
9.5	odd	6		630.2.t.c.311.2	✓	32
21.5	even	6		1890.2.t.c.1601.14		32
63.5	even	6	inner	630.2.bk.c.131.10	yes	32
63.40	odd	6		1890.2.bk.c.341.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.c.311.2	✓	32	9.5	odd	6
630.2.t.c.551.2	yes	32	7.5	odd	6
630.2.bk.c.101.2	yes	32	1.1	even	1	trivial
630.2.bk.c.131.10	yes	32	63.5	even	6	inner
1890.2.t.c.1151.14		32	9.4	even	3
1890.2.t.c.1601.14		32	21.5	even	6
1890.2.bk.c.341.7		32	63.40	odd	6
1890.2.bk.c.521.7		32	3.2	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.61337 - 0.630115i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.630115 + 1.61337i) q^{6} +(2.57812 + 0.594391i) q^{7} +1.00000i q^{8} +(2.20591 + 2.03321i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.61337 - 0.630115i) q^{3} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.630115 + 1.61337i) q^{6} +(2.57812 + 0.594391i) q^{7} +1.00000i q^{8} +(2.20591 + 2.03321i) q^{9} +(-0.866025 - 0.500000i) q^{10} +(0.676813 - 0.390758i) q^{11} +(1.61337 + 0.630115i) q^{12} +(2.26905 - 1.31003i) q^{13} +(0.594391 - 2.57812i) q^{14} +(-1.35238 + 1.08216i) q^{15} +1.00000 q^{16} +(-3.02795 + 5.24457i) q^{17} +(2.03321 - 2.20591i) q^{18} +(6.09668 - 3.51992i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-3.78492 - 2.58348i) q^{21} +(-0.390758 - 0.676813i) q^{22} +(3.99168 + 2.30460i) q^{23} +(0.630115 - 1.61337i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.31003 - 2.26905i) q^{26} +(-2.27779 - 4.67030i) q^{27} +(-2.57812 - 0.594391i) q^{28} +(3.96237 + 2.28767i) q^{29} +(1.08216 + 1.35238i) q^{30} -7.48063i q^{31} -1.00000i q^{32} +(-1.33817 + 0.203967i) q^{33} +(5.24457 + 3.02795i) q^{34} +(1.80382 - 1.93552i) q^{35} +(-2.20591 - 2.03321i) q^{36} +(-5.42975 - 9.40460i) q^{37} +(-3.51992 - 6.09668i) q^{38} +(-4.48628 + 0.683808i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-5.46910 - 9.47275i) q^{41} +(-2.58348 + 3.78492i) q^{42} +(-4.45098 + 7.70932i) q^{43} +(-0.676813 + 0.390758i) q^{44} +(2.86377 - 0.893768i) q^{45} +(2.30460 - 3.99168i) q^{46} +1.00253 q^{47} +(-1.61337 - 0.630115i) q^{48} +(6.29340 + 3.06482i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(8.18988 - 6.55346i) q^{51} +(-2.26905 + 1.31003i) q^{52} +(-8.30234 - 4.79336i) q^{53} +(-4.67030 + 2.27779i) q^{54} -0.781517i q^{55} +(-0.594391 + 2.57812i) q^{56} +(-12.0541 + 1.83732i) q^{57} +(2.28767 - 3.96237i) q^{58} +2.64005 q^{59} +(1.35238 - 1.08216i) q^{60} -2.13177i q^{61} -7.48063 q^{62} +(4.47858 + 6.55304i) q^{63} -1.00000 q^{64} -2.62007i q^{65} +(0.203967 + 1.33817i) q^{66} +12.0588 q^{67} +(3.02795 - 5.24457i) q^{68} +(-4.98788 - 6.23338i) q^{69} +(-1.93552 - 1.80382i) q^{70} +10.1200i q^{71} +(-2.03321 + 2.20591i) q^{72} +(7.67003 + 4.42830i) q^{73} +(-9.40460 + 5.42975i) q^{74} +(0.260988 + 1.71227i) q^{75} +(-6.09668 + 3.51992i) q^{76} +(1.97717 - 0.605130i) q^{77} +(0.683808 + 4.48628i) q^{78} +15.9369 q^{79} +(0.500000 - 0.866025i) q^{80} +(0.732082 + 8.97018i) q^{81} +(-9.47275 + 5.46910i) q^{82} +(2.03248 - 3.52036i) q^{83} +(3.78492 + 2.58348i) q^{84} +(3.02795 + 5.24457i) q^{85} +(7.70932 + 4.45098i) q^{86} +(-4.95126 - 6.18761i) q^{87} +(0.390758 + 0.676813i) q^{88} +(3.78927 + 6.56320i) q^{89} +(-0.893768 - 2.86377i) q^{90} +(6.62855 - 2.02872i) q^{91} +(-3.99168 - 2.30460i) q^{92} +(-4.71366 + 12.0690i) q^{93} -1.00253i q^{94} -7.03984i q^{95} +(-0.630115 + 1.61337i) q^{96} +(-5.00436 - 2.88927i) q^{97} +(3.06482 - 6.29340i) q^{98} +(2.28748 + 0.514128i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7	\( 32 q - 2 q^{3} - 32 q^{4} + 16 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{11} + 2 q^{12} + 6 q^{14} + 2 q^{15} + 32 q^{16} - 6 q^{17} + 8 q^{18} - 16 q^{20} + 18 q^{23} + 2 q^{24} - 16 q^{25} - 12 q^{26} - 8 q^{27} + 2 q^{28} + 6 q^{29} - 4 q^{30} + 20 q^{33} + 2 q^{35} + 2 q^{37} + 30 q^{39} + 6 q^{41} + 10 q^{42} - 28 q^{43} + 6 q^{44} + 6 q^{45} + 48 q^{47} - 2 q^{48} + 8 q^{49} + 34 q^{51} + 36 q^{53} - 46 q^{54} - 6 q^{56} + 18 q^{57} - 60 q^{59} - 2 q^{60} + 32 q^{63} - 32 q^{64} - 34 q^{66} - 8 q^{67} + 6 q^{68} - 28 q^{69} + 6 q^{70} - 8 q^{72} - 30 q^{73} - 18 q^{74} + 4 q^{75} - 6 q^{77} - 22 q^{78} - 8 q^{79} + 16 q^{80} + 20 q^{81} - 24 q^{82} - 6 q^{83} + 6 q^{85} + 30 q^{86} - 22 q^{87} + 12 q^{89} + 4 q^{90} - 66 q^{91} - 18 q^{92} - 32 q^{93} - 2 q^{96} - 96 q^{97} + 24 q^{98} - 24 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 - 32 * q^4 + 16 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^11 + 2 * q^12 + 6 * q^14 + 2 * q^15 + 32 * q^16 - 6 * q^17 + 8 * q^18 - 16 * q^20 + 18 * q^23 + 2 * q^24 - 16 * q^25 - 12 * q^26 - 8 * q^27 + 2 * q^28 + 6 * q^29 - 4 * q^30 + 20 * q^33 + 2 * q^35 + 2 * q^37 + 30 * q^39 + 6 * q^41 + 10 * q^42 - 28 * q^43 + 6 * q^44 + 6 * q^45 + 48 * q^47 - 2 * q^48 + 8 * q^49 + 34 * q^51 + 36 * q^53 - 46 * q^54 - 6 * q^56 + 18 * q^57 - 60 * q^59 - 2 * q^60 + 32 * q^63 - 32 * q^64 - 34 * q^66 - 8 * q^67 + 6 * q^68 - 28 * q^69 + 6 * q^70 - 8 * q^72 - 30 * q^73 - 18 * q^74 + 4 * q^75 - 6 * q^77 - 22 * q^78 - 8 * q^79 + 16 * q^80 + 20 * q^81 - 24 * q^82 - 6 * q^83 + 6 * q^85 + 30 * q^86 - 22 * q^87 + 12 * q^89 + 4 * q^90 - 66 * q^91 - 18 * q^92 - 32 * q^93 - 2 * q^96 - 96 * q^97 + 24 * q^98 - 24 * q^99

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