LMFDB - Embedded newform 435.2.q.c.41.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(41,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("435.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			41.7
Character	$\chi$	$=$	435.41
Dual form			435.2.q.c.191.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.602660 + 0.602660i) q^{2} +(0.639395 - 1.60971i) q^{3} +1.27360i q^{4} -1.00000 q^{5} +(0.584771 + 1.35545i) q^{6} -0.244261 q^{7} +(-1.97287 - 1.97287i) q^{8} +(-2.18235 - 2.05849i) q^{9} +O(q^{10})$	\(q+(-0.602660 + 0.602660i) q^{2} +(0.639395 - 1.60971i) q^{3} +1.27360i q^{4} -1.00000 q^{5} +(0.584771 + 1.35545i) q^{6} -0.244261 q^{7} +(-1.97287 - 1.97287i) q^{8} +(-2.18235 - 2.05849i) q^{9} +(0.602660 - 0.602660i) q^{10} +(3.28269 - 3.28269i) q^{11} +(2.05013 + 0.814335i) q^{12} -1.85735i q^{13} +(0.147206 - 0.147206i) q^{14} +(-0.639395 + 1.60971i) q^{15} -0.169262 q^{16} +(5.36011 - 5.36011i) q^{17} +(2.55578 - 0.0746466i) q^{18} +(3.59721 + 3.59721i) q^{19} -1.27360i q^{20} +(-0.156179 + 0.393190i) q^{21} +3.95669i q^{22} -1.26886i q^{23} +(-4.43720 + 1.91431i) q^{24} +1.00000 q^{25} +(1.11935 + 1.11935i) q^{26} +(-4.70895 + 2.19676i) q^{27} -0.311091i q^{28} +(-4.25946 - 3.29499i) q^{29} +(-0.584771 - 1.35545i) q^{30} +(2.90055 + 2.90055i) q^{31} +(4.04775 - 4.04775i) q^{32} +(-3.18525 - 7.38312i) q^{33} +6.46065i q^{34} +0.244261 q^{35} +(2.62169 - 2.77944i) q^{36} +(4.65826 - 4.65826i) q^{37} -4.33579 q^{38} +(-2.98981 - 1.18758i) q^{39} +(1.97287 + 1.97287i) q^{40} +(1.54795 + 1.54795i) q^{41} +(-0.142837 - 0.331083i) q^{42} +(-5.71100 - 5.71100i) q^{43} +(4.18084 + 4.18084i) q^{44} +(2.18235 + 2.05849i) q^{45} +(0.764693 + 0.764693i) q^{46} +(-2.82701 - 2.82701i) q^{47} +(-0.108225 + 0.272463i) q^{48} -6.94034 q^{49} +(-0.602660 + 0.602660i) q^{50} +(-5.20101 - 12.0555i) q^{51} +2.36553 q^{52} +13.6207i q^{53} +(1.51400 - 4.16180i) q^{54} +(-3.28269 + 3.28269i) q^{55} +(0.481895 + 0.481895i) q^{56} +(8.09052 - 3.49043i) q^{57} +(4.55277 - 0.581249i) q^{58} -6.93609i q^{59} +(-2.05013 - 0.814335i) q^{60} +(5.93118 + 5.93118i) q^{61} -3.49609 q^{62} +(0.533062 + 0.502808i) q^{63} +4.54031i q^{64} +1.85735i q^{65} +(6.36914 + 2.52989i) q^{66} -1.96159i q^{67} +(6.82664 + 6.82664i) q^{68} +(-2.04250 - 0.811305i) q^{69} +(-0.147206 + 0.147206i) q^{70} -5.69884 q^{71} +(0.244363 + 8.36661i) q^{72} +(6.87061 - 6.87061i) q^{73} +5.61470i q^{74} +(0.639395 - 1.60971i) q^{75} +(-4.58141 + 4.58141i) q^{76} +(-0.801833 + 0.801833i) q^{77} +(2.51755 - 1.08613i) q^{78} +(2.33809 + 2.33809i) q^{79} +0.169262 q^{80} +(0.525277 + 8.98466i) q^{81} -1.86578 q^{82} +1.79812i q^{83} +(-0.500767 - 0.198910i) q^{84} +(-5.36011 + 5.36011i) q^{85} +6.88359 q^{86} +(-8.02747 + 4.74971i) q^{87} -12.9526 q^{88} +(-12.8521 + 12.8521i) q^{89} +(-2.55578 + 0.0746466i) q^{90} +0.453679i q^{91} +1.61602 q^{92} +(6.52364 - 2.81445i) q^{93} +3.40745 q^{94} +(-3.59721 - 3.59721i) q^{95} +(-3.92760 - 9.10382i) q^{96} +(-1.71869 + 1.71869i) q^{97} +(4.18267 - 4.18267i) q^{98} +(-13.9213 + 0.406600i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	$ 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) $ 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.602660	+	0.602660i	−0.426145	+	0.426145i	−0.887313	−	0.461168i	$-0.847431\pi$
$2$	−0.602660	+	0.602660i	−0.426145	+	0.426145i	0.461168	+	0.887313i	$0.347431\pi$
$3$	0.639395	−	1.60971i	0.369155	−	0.929368i
$3$	0.639395	−	1.60971i	0.369155	−	0.929368i
$4$			1.27360i			0.636801i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.584771	+	1.35545i	0.238732	+	0.553359i
$7$	−0.244261			−0.0923220			−0.0461610	−	0.998934i	$-0.514699\pi$
$7$	−0.244261			−0.0923220			−0.0461610	+	0.998934i	$0.514699\pi$
$8$	−1.97287	−	1.97287i	−0.697515	−	0.697515i
$9$	−2.18235	−	2.05849i	−0.727449	−	0.686162i
$10$	0.602660	−	0.602660i	0.190578	−	0.190578i
$11$	3.28269	−	3.28269i	0.989768	−	0.989768i	−0.0101799	−	0.999948i	$-0.503240\pi$
$11$	3.28269	−	3.28269i	0.989768	−	0.989768i	0.999948	+	0.0101799i	$0.00324041\pi$
$12$	2.05013	+	0.814335i	0.591822	+	0.235078i
$13$		−	1.85735i		−	0.515137i	−0.966260	−	0.257569i	$-0.917079\pi$
$13$		−	1.85735i		−	0.515137i	0.966260	−	0.257569i	$-0.0829213\pi$
$14$	0.147206	−	0.147206i	0.0393426	−	0.0393426i
$15$	−0.639395	+	1.60971i	−0.165091	+	0.415626i
$16$	−0.169262			−0.0423155
$17$	5.36011	−	5.36011i	1.30002	−	1.30002i	0.371642	−	0.928376i	$-0.378795\pi$
$17$	5.36011	−	5.36011i	1.30002	−	1.30002i	0.928376	−	0.371642i	$-0.121205\pi$
$18$	2.55578	−	0.0746466i	0.602403	−	0.0175944i
$19$	3.59721	+	3.59721i	0.825257	+	0.825257i	0.986856	−	0.161600i	$-0.0516653\pi$
$19$	3.59721	+	3.59721i	0.825257	+	0.825257i	−0.161600	+	0.986856i	$0.551665\pi$
$20$		−	1.27360i		−	0.284786i
$21$	−0.156179	+	0.393190i	−0.0340811	+	0.0858011i
$22$			3.95669i			0.843570i
$23$		−	1.26886i		−	0.264576i	−0.991211	−	0.132288i	$-0.957768\pi$
$23$		−	1.26886i		−	0.264576i	0.991211	−	0.132288i	$-0.0422324\pi$
$24$	−4.43720	+	1.91431i	−0.905739	+	0.390757i
$25$	1.00000			0.200000
$26$	1.11935	+	1.11935i	0.219523	+	0.219523i
$27$	−4.70895	+	2.19676i	−0.906238	+	0.422768i
$28$		−	0.311091i		−	0.0587907i
$29$	−4.25946	−	3.29499i	−0.790963	−	0.611865i
$29$	−4.25946	−	3.29499i	−0.790963	−	0.611865i
$30$	−0.584771	−	1.35545i	−0.106764	−	0.247470i
$31$	2.90055	+	2.90055i	0.520954	+	0.520954i	0.917859	−	0.396906i	$-0.129916\pi$
$31$	2.90055	+	2.90055i	0.520954	+	0.520954i	−0.396906	+	0.917859i	$0.629916\pi$
$32$	4.04775	−	4.04775i	0.715547	−	0.715547i
$33$	−3.18525	−	7.38312i	−0.554481	−	1.28524i
$34$			6.46065i			1.10799i
$35$	0.244261			0.0412876
$36$	2.62169	−	2.77944i	0.436948	−	0.463240i
$37$	4.65826	−	4.65826i	0.765814	−	0.765814i	−0.211553	−	0.977367i	$-0.567852\pi$
$37$	4.65826	−	4.65826i	0.765814	−	0.765814i	0.977367	+	0.211553i	$0.0678521\pi$
$38$	−4.33579			−0.703359
$39$	−2.98981	−	1.18758i	−0.478752	−	0.190166i
$40$	1.97287	+	1.97287i	0.311938	+	0.311938i
$41$	1.54795	+	1.54795i	0.241749	+	0.241749i	0.817573	−	0.575824i	$-0.195319\pi$
$41$	1.54795	+	1.54795i	0.241749	+	0.241749i	−0.575824	+	0.817573i	$0.695319\pi$
$42$	−0.142837	−	0.331083i	−0.0220402	−	0.0510872i
$43$	−5.71100	−	5.71100i	−0.870920	−	0.870920i	0.121653	−	0.992573i	$-0.461180\pi$
$43$	−5.71100	−	5.71100i	−0.870920	−	0.870920i	−0.992573	+	0.121653i	$0.961180\pi$
$44$	4.18084	+	4.18084i	0.630285	+	0.630285i
$45$	2.18235	+	2.05849i	0.325325	+	0.306861i
$46$	0.764693	+	0.764693i	0.112748	+	0.112748i
$47$	−2.82701	−	2.82701i	−0.412362	−	0.412362i	0.470199	−	0.882561i	$-0.344182\pi$
$47$	−2.82701	−	2.82701i	−0.412362	−	0.412362i	−0.882561	+	0.470199i	$0.844182\pi$
$48$	−0.108225	+	0.272463i	−0.0156210	+	0.0393266i
$49$	−6.94034			−0.991477
$50$	−0.602660	+	0.602660i	−0.0852290	+	0.0852290i
$51$	−5.20101	−	12.0555i	−0.728287	−	1.68810i
$52$	2.36553			0.328040
$53$			13.6207i			1.87095i	0.353397	+	0.935474i	$0.385027\pi$
$53$			13.6207i			1.87095i	−0.353397	+	0.935474i	$0.614973\pi$
$54$	1.51400	−	4.16180i	0.206029	−	0.566349i
$55$	−3.28269	+	3.28269i	−0.442638	+	0.442638i
$56$	0.481895	+	0.481895i	0.0643959	+	0.0643959i
$57$	8.09052	−	3.49043i	1.07161	−	0.462319i
$58$	4.55277	−	0.581249i	0.597808	−	0.0763217i
$59$		−	6.93609i		−	0.903003i	−0.892270	−	0.451501i	$-0.850889\pi$
$59$		−	6.93609i		−	0.903003i	0.892270	−	0.451501i	$-0.149111\pi$
$60$	−2.05013	−	0.814335i	−0.264671	−	0.105130i
$61$	5.93118	+	5.93118i	0.759410	+	0.759410i	0.976215	−	0.216805i	$-0.0695636\pi$
$61$	5.93118	+	5.93118i	0.759410	+	0.759410i	−0.216805	+	0.976215i	$0.569564\pi$
$62$	−3.49609			−0.444004
$63$	0.533062	+	0.502808i	0.0671595	+	0.0633478i
$64$			4.54031i			0.567539i
$65$			1.85735i			0.230376i
$66$	6.36914	+	2.52989i	0.783987	+	0.311408i
$67$		−	1.96159i		−	0.239646i	−0.992795	−	0.119823i	$-0.961767\pi$
$67$		−	1.96159i		−	0.239646i	0.992795	−	0.119823i	$-0.0382328\pi$
$68$	6.82664	+	6.82664i	0.827852	+	0.827852i
$69$	−2.04250	−	0.811305i	−0.245889	−	0.0976697i
$70$	−0.147206	+	0.147206i	−0.0175945	+	0.0175945i
$71$	−5.69884			−0.676328			−0.338164	−	0.941087i	$-0.609806\pi$
$71$	−5.69884			−0.676328			−0.338164	+	0.941087i	$0.609806\pi$
$72$	0.244363	+	8.36661i	0.0287985	+	0.986014i
$73$	6.87061	−	6.87061i	0.804145	−	0.804145i	−0.179596	−	0.983740i	$-0.557479\pi$
$73$	6.87061	−	6.87061i	0.804145	−	0.804145i	0.983740	+	0.179596i	$0.0574790\pi$
$74$			5.61470i			0.652696i
$75$	0.639395	−	1.60971i	0.0738310	−	0.185874i
$76$	−4.58141	+	4.58141i	−0.525524	+	0.525524i
$77$	−0.801833	+	0.801833i	−0.0913774	+	0.0913774i
$78$	2.51755	−	1.08613i	0.285056	−	0.122980i
$79$	2.33809	+	2.33809i	0.263056	+	0.263056i	0.826294	−	0.563238i	$-0.190445\pi$
$79$	2.33809	+	2.33809i	0.263056	+	0.263056i	−0.563238	+	0.826294i	$0.690445\pi$
$80$	0.169262			0.0189240
$81$	0.525277	+	8.98466i	0.0583641	+	0.998295i
$82$	−1.86578			−0.206041
$83$			1.79812i			0.197369i	0.995119	+	0.0986847i	$0.0314635\pi$
$83$			1.79812i			0.197369i	−0.995119	+	0.0986847i	$0.968536\pi$
$84$	−0.500767	−	0.198910i	−0.0546382	−	0.0217029i
$85$	−5.36011	+	5.36011i	−0.581386	+	0.581386i
$86$	6.88359			0.742276
$87$	−8.02747	+	4.74971i	−0.860635	+	0.509222i
$88$	−12.9526			−1.38076
$89$	−12.8521	+	12.8521i	−1.36232	+	1.36232i	−0.491365	+	0.870954i	$0.663502\pi$
$89$	−12.8521	+	12.8521i	−1.36232	+	1.36232i	−0.870954	+	0.491365i	$0.836498\pi$
$90$	−2.55578	+	0.0746466i	−0.269403	+	0.00786844i
$91$			0.453679i			0.0475585i
$92$	1.61602			0.168482
$93$	6.52364	−	2.81445i	0.676470	−	0.291845i
$94$	3.40745			0.351452
$95$	−3.59721	−	3.59721i	−0.369066	−	0.369066i
$96$	−3.92760	−	9.10382i	−0.400859	−	0.929154i
$97$	−1.71869	+	1.71869i	−0.174507	+	0.174507i	−0.788956	−	0.614449i	$-0.789378\pi$
$97$	−1.71869	+	1.71869i	−0.174507	+	0.174507i	0.614449	+	0.788956i	$0.289378\pi$
$98$	4.18267	−	4.18267i	0.422513	−	0.422513i
$99$	−13.9213	+	0.406600i	−1.39915	+	0.0408648i
$100$			1.27360i			0.127360i
$101$	−1.89809	+	1.89809i	−0.188867	+	0.188867i	−0.795206	−	0.606339i	$-0.792637\pi$
$101$	−1.89809	+	1.89809i	−0.188867	+	0.188867i	0.606339	+	0.795206i	$0.292637\pi$
$102$	10.3998	+	4.13091i	1.02973	+	0.409021i
$103$	12.8845			1.26955			0.634774	−	0.772698i	$-0.281093\pi$
$103$	12.8845			1.26955			0.634774	+	0.772698i	$0.281093\pi$
$104$	−3.66432	+	3.66432i	−0.359316	+	0.359316i
$105$	0.156179	−	0.393190i	0.0152415	−	0.0383714i
$106$	−8.20866	−	8.20866i	−0.797295	−	0.797295i
$107$			7.27412i			0.703216i	0.936147	+	0.351608i	$0.114365\pi$
$107$			7.27412i			0.703216i	−0.936147	+	0.351608i	$0.885635\pi$
$108$	−2.79780	−	5.99733i	−0.269219	−	0.577093i
$109$		−	2.37270i		−	0.227264i	−0.993523	−	0.113632i	$-0.963752\pi$
$109$		−	2.37270i		−	0.227264i	0.993523	−	0.113632i	$-0.0362484\pi$
$110$		−	3.95669i		−	0.377256i
$111$	−4.51999	−	10.4769i	−0.429018	−	0.994426i
$112$	0.0413441			0.00390665
$113$	−3.05940	−	3.05940i	−0.287804	−	0.287804i	0.548407	−	0.836211i	$-0.315234\pi$
$113$	−3.05940	−	3.05940i	−0.287804	−	0.287804i	−0.836211	+	0.548407i	$0.815234\pi$
$114$	−2.77229	+	6.97938i	−0.259648	+	0.653679i
$115$			1.26886i			0.118322i
$116$	4.19650	−	5.42486i	0.389636	−	0.503685i
$117$	−3.82334	+	4.05339i	−0.353467	+	0.374736i
$118$	4.18011	+	4.18011i	0.384810	+	0.384810i
$119$	−1.30927	+	1.30927i	−0.120020	+	0.120020i
$120$	4.43720	−	1.91431i	0.405059	−	0.174752i
$121$		−	10.5521i		−	0.959283i
$122$	−7.14897			−0.647238
$123$	3.48151	−	1.50200i	0.313917	−	0.135431i
$124$	−3.69414	+	3.69414i	−0.331743	+	0.331743i
$125$	−1.00000			−0.0894427
$126$	−0.624278	+	0.0182332i	−0.0556151	+	0.00162435i
$127$	5.81555	+	5.81555i	0.516046	+	0.516046i	0.916373	−	0.400326i	$-0.131103\pi$
$127$	5.81555	+	5.81555i	0.516046	+	0.516046i	−0.400326	+	0.916373i	$0.631103\pi$
$128$	5.35923	+	5.35923i	0.473693	+	0.473693i
$129$	−12.8447	+	5.54148i	−1.13091	+	0.487900i
$130$	−1.11935	−	1.11935i	−0.0981738	−	0.0981738i
$131$	1.73746	+	1.73746i	0.151802	+	0.151802i	0.778923	−	0.627120i	$-0.215766\pi$
$131$	1.73746	+	1.73746i	0.151802	+	0.151802i	−0.627120	+	0.778923i	$0.715766\pi$
$132$	9.40315	−	4.05674i	0.818440	−	0.353094i
$133$	−0.878658	−	0.878658i	−0.0761894	−	0.0761894i
$134$	1.18217	+	1.18217i	0.102124	+	0.102124i
$135$	4.70895	−	2.19676i	0.405282	−	0.189067i
$136$	−21.1496			−1.81356
$137$	1.15756	−	1.15756i	0.0988969	−	0.0988969i	−0.655927	−	0.754824i	$-0.727722\pi$
$137$	1.15756	−	1.15756i	0.0988969	−	0.0988969i	0.754824	+	0.655927i	$0.227722\pi$
$138$	1.71988	−	0.741995i	0.146406	−	0.0631628i
$139$	−17.9797			−1.52501			−0.762507	−	0.646980i	$-0.776032\pi$
$139$	−17.9797			−1.52501			−0.762507	+	0.646980i	$0.776032\pi$
$140$			0.311091i			0.0262920i
$141$	−6.35825	+	2.74310i	−0.535461	+	0.231010i
$142$	3.43446	−	3.43446i	0.288214	−	0.288214i
$143$	−6.09712	−	6.09712i	−0.509867	−	0.509867i
$144$	0.369388	+	0.348423i	0.0307823	+	0.0290352i
$145$	4.25946	+	3.29499i	0.353729	+	0.273634i
$146$			8.28129i			0.685365i
$147$	−4.43762	+	11.1719i	−0.366009	+	0.921446i
$148$	5.93277	+	5.93277i	0.487670	+	0.487670i
$149$	−1.77825			−0.145680			−0.0728399	−	0.997344i	$-0.523206\pi$
$149$	−1.77825			−0.145680			−0.0728399	+	0.997344i	$0.523206\pi$
$150$	0.584771	+	1.35545i	0.0477464	+	0.110672i
$151$			9.38866i			0.764039i	0.924154	+	0.382019i	$0.124771\pi$
$151$			9.38866i			0.764039i	−0.924154	+	0.382019i	$0.875229\pi$
$152$		−	14.1937i		−	1.15126i
$153$	−22.7313	+	0.663913i	−1.83772	+	0.0536742i
$154$		−	0.966466i		−	0.0778801i
$155$	−2.90055	−	2.90055i	−0.232978	−	0.232978i
$156$	1.51251	−	3.80782i	0.121098	−	0.304870i
$157$	−13.9689	+	13.9689i	−1.11484	+	1.11484i	−0.122351	+	0.992487i	$0.539043\pi$
$157$	−13.9689	+	13.9689i	−1.11484	+	1.11484i	−0.992487	+	0.122351i	$0.960957\pi$
$158$	−2.81815			−0.224200
$159$	21.9254	+	8.70901i	1.73880	+	0.690670i
$160$	−4.04775	+	4.04775i	−0.320002	+	0.320002i
$161$			0.309934i			0.0244262i
$162$	−5.73126	−	5.09813i	−0.450290	−	0.400547i
$163$	8.01172	−	8.01172i	0.627526	−	0.627526i	−0.319919	−	0.947445i	$-0.603656\pi$
$163$	8.01172	−	8.01172i	0.627526	−	0.627526i	0.947445	+	0.319919i	$0.103656\pi$
$164$	−1.97147	+	1.97147i	−0.153946	+	0.153946i
$165$	3.18525	+	7.38312i	0.247971	+	0.574775i
$166$	−1.08366	−	1.08366i	−0.0841080	−	0.0841080i
$167$	−8.16558			−0.631871			−0.315936	−	0.948781i	$-0.602318\pi$
$167$	−8.16558			−0.631871			−0.315936	+	0.948781i	$0.602318\pi$
$168$	1.08383	−	0.467591i	0.0836196	−	0.0360754i
$169$	9.55024			0.734634
$170$		−	6.46065i		−	0.495510i
$171$	−0.445557	−	15.2552i	−0.0340726	−	1.16659i
$172$	7.27354	−	7.27354i	0.554602	−	0.554602i
$173$	19.9281			1.51511			0.757554	−	0.652773i	$-0.226394\pi$
$173$	19.9281			1.51511			0.757554	+	0.652773i	$0.226394\pi$
$174$	1.97538	−	7.70030i	0.149753	−	0.583758i
$175$	−0.244261			−0.0184644
$176$	−0.555634	+	0.555634i	−0.0418825	+	0.0418825i
$177$	−11.1651	−	4.43491i	−0.839222	−	0.333348i
$178$		−	15.4909i		−	1.16109i
$179$	21.0190			1.57103			0.785517	−	0.618839i	$-0.212397\pi$
$179$	21.0190			1.57103			0.785517	+	0.618839i	$0.212397\pi$
$180$	−2.62169	+	2.77944i	−0.195409	+	0.207167i
$181$	21.2588			1.58015			0.790077	−	0.613007i	$-0.210040\pi$
$181$	21.2588			1.58015			0.790077	+	0.613007i	$0.210040\pi$
$182$	−0.273414	−	0.273414i	−0.0202668	−	0.0202668i
$183$	13.3399	−	5.75512i	0.986111	−	0.425431i
$184$	−2.50330	+	2.50330i	−0.184546	+	0.184546i
$185$	−4.65826	+	4.65826i	−0.342482	+	0.342482i
$186$	−2.23538	+	5.62770i	−0.163906	+	0.412643i
$187$		−	35.1912i		−	2.57343i
$188$	3.60048	−	3.60048i	0.262592	−	0.262592i
$189$	1.15021	−	0.536584i	0.0836657	−	0.0390307i
$190$	4.33579			0.314552
$191$	−10.0502	+	10.0502i	−0.727206	+	0.727206i	−0.970062	−	0.242856i	$-0.921916\pi$
$191$	−10.0502	+	10.0502i	−0.727206	+	0.727206i	0.242856	+	0.970062i	$0.421916\pi$
$192$	7.30859	+	2.90305i	0.527452	+	0.209510i
$193$	12.9332	+	12.9332i	0.930955	+	0.930955i	0.997766	−	0.0668108i	$-0.0212824\pi$
$193$	12.9332	+	12.9332i	0.930955	+	0.930955i	−0.0668108	+	0.997766i	$0.521282\pi$
$194$		−	2.07158i		−	0.148731i
$195$	2.98981	+	1.18758i	0.214104	+	0.0850446i
$196$		−	8.83922i		−	0.631373i
$197$			5.64371i			0.402098i	0.979581	+	0.201049i	$0.0644350\pi$
$197$			5.64371i			0.402098i	−0.979581	+	0.201049i	$0.935565\pi$
$198$	8.14480	−	8.63488i	0.578825	−	0.613654i
$199$	20.8547			1.47835			0.739177	−	0.673511i	$-0.235215\pi$
$199$	20.8547			1.47835			0.739177	+	0.673511i	$0.235215\pi$
$200$	−1.97287	−	1.97287i	−0.139503	−	0.139503i
$201$	−3.15759	−	1.25423i	−0.222720	−	0.0884667i
$202$		−	2.28781i		−	0.160969i
$203$	1.04042	+	0.804838i	0.0730232	+	0.0564886i
$204$	15.3539	−	6.62401i	1.07499	−	0.463773i
$205$	−1.54795	−	1.54795i	−0.108114	−	0.108114i
$206$	−7.76498	+	7.76498i	−0.541012	+	0.541012i
$207$	−2.61194	+	2.76910i	−0.181542	+	0.192466i
$208$			0.314379i			0.0217983i
$209$	23.6171			1.63363
$210$	0.142837	+	0.331083i	0.00985668	+	0.0228469i
$211$	19.7750	−	19.7750i	1.36136	−	1.36136i	0.489185	−	0.872180i	$-0.337294\pi$
$211$	19.7750	−	19.7750i	1.36136	−	1.36136i	0.872180	−	0.489185i	$-0.162706\pi$
$212$	−17.3473			−1.19142
$213$	−3.64381	+	9.17349i	−0.249670	+	0.628557i
$214$	−4.38382	−	4.38382i	−0.299672	−	0.299672i
$215$	5.71100	+	5.71100i	0.389487	+	0.389487i
$216$	13.6241	+	4.95622i	0.927001	+	0.337228i
$217$	−0.708490	−	0.708490i	−0.0480955	−	0.0480955i
$218$	1.42993	+	1.42993i	0.0968473	+	0.0968473i
$219$	−6.66667	−	15.4528i	−0.450492	−	1.04420i
$220$	−4.18084	−	4.18084i	−0.281872	−	0.281872i
$221$	−9.95562	−	9.95562i	−0.669688	−	0.669688i
$222$	9.03805	+	3.59001i	0.606594	+	0.240946i
$223$	−24.3689			−1.63186			−0.815932	−	0.578148i	$-0.803776\pi$
$223$	−24.3689			−1.63186			−0.815932	+	0.578148i	$0.803776\pi$
$224$	−0.988707	+	0.988707i	−0.0660607	+	0.0660607i
$225$	−2.18235	−	2.05849i	−0.145490	−	0.137232i
$226$	3.68755			0.245292
$227$		−	21.0735i		−	1.39869i	−0.714782	−	0.699347i	$-0.753474\pi$
$227$		−	21.0735i		−	1.39869i	0.714782	−	0.699347i	$-0.246526\pi$
$228$	4.44542	+	10.3041i	0.294405	+	0.682405i
$229$	−4.88643	+	4.88643i	−0.322905	+	0.322905i	−0.849880	−	0.526976i	$-0.823326\pi$
$229$	−4.88643	+	4.88643i	−0.322905	+	0.322905i	0.526976	+	0.849880i	$0.323326\pi$
$230$	−0.764693	−	0.764693i	−0.0504224	−	0.0504224i
$231$	0.778032	+	1.80341i	0.0511908	+	0.118656i
$232$	1.90278	+	14.9040i	0.124923	+	0.978493i
$233$			5.77457i			0.378304i	0.981948	+	0.189152i	$0.0605740\pi$
$233$			5.77457i			0.378304i	−0.981948	+	0.189152i	$0.939426\pi$
$234$	−0.138645	−	4.74699i	−0.00906351	−	0.310320i
$235$	2.82701	+	2.82701i	0.184414	+	0.184414i
$236$	8.83382			0.575033
$237$	5.25862	−	2.26869i	0.341584	−	0.147367i
$238$		−	1.57809i		−	0.102292i
$239$			6.32616i			0.409205i	0.978845	+	0.204603i	$0.0655902\pi$
$239$			6.32616i			0.409205i	−0.978845	+	0.204603i	$0.934410\pi$
$240$	0.108225	−	0.272463i	0.00698591	−	0.0175874i
$241$			17.7689i			1.14460i	0.820045	+	0.572299i	$0.193948\pi$
$241$			17.7689i			1.14460i	−0.820045	+	0.572299i	$0.806052\pi$
$242$	6.35934	+	6.35934i	0.408794	+	0.408794i
$243$	14.7986	+	4.89920i	0.949329	+	0.314284i
$244$	−7.55396	+	7.55396i	−0.483593	+	0.483593i
$245$	6.94034			0.443402
$246$	−1.19297	+	3.00336i	−0.0760609	+	0.191487i
$247$	6.68129	−	6.68129i	0.425121	−	0.425121i
$248$		−	11.4448i		−	0.726746i
$249$	2.89446	+	1.14971i	0.183429	+	0.0728599i
$250$	0.602660	−	0.602660i	0.0381156	−	0.0381156i
$251$	22.0012	−	22.0012i	1.38870	−	1.38870i	0.560649	−	0.828053i	$-0.310552\pi$
$251$	22.0012	−	22.0012i	1.38870	−	1.38870i	0.828053	−	0.560649i	$-0.189448\pi$
$252$	−0.640376	+	0.678909i	−0.0403399	+	0.0427672i
$253$	−4.16528	−	4.16528i	−0.261869	−	0.261869i
$254$	−7.00960			−0.439821
$255$	5.20101	+	12.0555i	0.325700	+	0.754943i
$256$	−15.5402			−0.971263
$257$		−	19.0547i		−	1.18860i	−0.804243	−	0.594301i	$-0.797429\pi$
$257$		−	19.0547i		−	1.18860i	0.804243	−	0.594301i	$-0.202571\pi$
$258$	4.40134	−	11.0806i	0.274015	−	0.689848i
$259$	−1.13783	+	1.13783i	−0.0707014	+	0.0707014i
$260$	−2.36553			−0.146704
$261$	2.51294	+	15.9589i	0.155547	+	0.987829i
$262$	−2.09419			−0.129380
$263$	−1.68911	+	1.68911i	−0.104155	+	0.104155i	−0.757264	−	0.653109i	$-0.773464\pi$
$263$	−1.68911	+	1.68911i	−0.104155	+	0.104155i	0.653109	+	0.757264i	$0.273464\pi$
$264$	−8.28186	+	20.8500i	−0.509713	+	1.28323i
$265$		−	13.6207i		−	0.836713i
$266$	1.05907			0.0649355
$267$	12.4706	+	28.9057i	0.763188	+	1.76900i
$268$	2.49828			0.152607
$269$	2.10445	+	2.10445i	0.128310	+	0.128310i	0.768346	−	0.640035i	$-0.221080\pi$
$269$	2.10445	+	2.10445i	0.128310	+	0.128310i	−0.640035	+	0.768346i	$0.721080\pi$
$270$	−1.51400	+	4.16180i	−0.0921388	+	0.253279i
$271$	−1.35402	+	1.35402i	−0.0822508	+	0.0822508i	−0.747035	−	0.664784i	$-0.768523\pi$
$271$	−1.35402	+	1.35402i	−0.0822508	+	0.0822508i	0.664784	+	0.747035i	$0.268523\pi$
$272$	−0.907262	+	0.907262i	−0.0550109	+	0.0550109i
$273$	0.730293	+	0.290080i	0.0441993	+	0.0175565i
$274$			1.39523i			0.0842889i
$275$	3.28269	−	3.28269i	0.197954	−	0.197954i
$276$	1.03328	−	2.60134i	0.0621961	−	0.156582i
$277$	−15.0776			−0.905927			−0.452964	−	0.891529i	$-0.649633\pi$
$277$	−15.0776			−0.905927			−0.452964	+	0.891529i	$0.649633\pi$
$278$	10.8356	−	10.8356i	0.649878	−	0.649878i
$279$	−0.359267	−	12.3007i	−0.0215087	−	0.736426i
$280$	−0.481895	−	0.481895i	−0.0287987	−	0.0287987i
$281$			5.17856i			0.308927i	0.987998	+	0.154464i	$0.0493649\pi$
$281$			5.17856i			0.308927i	−0.987998	+	0.154464i	$0.950635\pi$
$282$	2.17871	−	5.48502i	0.129740	−	0.326628i
$283$			13.1322i			0.780629i	0.920682	+	0.390314i	$0.127634\pi$
$283$			13.1322i			0.780629i	−0.920682	+	0.390314i	$0.872366\pi$
$284$		−	7.25805i		−	0.430686i
$285$	−8.09052	+	3.49043i	−0.479241	+	0.206756i
$286$	7.34898			0.434554
$287$	−0.378104	−	0.378104i	−0.0223188	−	0.0223188i
$288$	−17.1658	+	0.501361i	−1.01151	+	0.0295430i
$289$		−	40.4616i		−	2.38009i
$290$	−4.55277	+	0.581249i	−0.267348	+	0.0341321i
$291$	1.66768	+	3.86553i	0.0977610	+	0.226601i
$292$	8.75042	+	8.75042i	0.512080	+	0.512080i
$293$	−18.7639	+	18.7639i	−1.09620	+	1.09620i	−0.101349	+	0.994851i	$0.532316\pi$
$293$	−18.7639	+	18.7639i	−1.09620	+	1.09620i	−0.994851	+	0.101349i	$0.967684\pi$
$294$	−4.05851	−	9.40726i	−0.236697	−	0.548643i
$295$			6.93609i			0.403835i
$296$	−18.3803			−1.06833
$297$	−8.24673	+	22.6693i	−0.478524	+	1.31541i
$298$	1.07168	−	1.07168i	0.0620807	−	0.0620807i
$299$	−2.35673			−0.136293
$300$	2.05013	+	0.814335i	0.118364	+	0.0470156i
$301$	1.39498	+	1.39498i	0.0804050	+	0.0804050i
$302$	−5.65817	−	5.65817i	−0.325591	−	0.325591i
$303$	1.84175	+	4.26901i	0.105806	+	0.245248i
$304$	−0.608871	−	0.608871i	−0.0349211	−	0.0349211i
$305$	−5.93118	−	5.93118i	−0.339618	−	0.339618i
$306$	13.2992	−	14.0994i	0.760262	−	0.806008i
$307$	−19.1100	−	19.1100i	−1.09066	−	1.09066i	−0.995458	−	0.0952054i	$-0.969649\pi$
$307$	−19.1100	−	19.1100i	−1.09066	−	1.09066i	−0.0952054	−	0.995458i	$-0.530351\pi$
$308$	−1.02122	−	1.02122i	−0.0581892	−	0.0581892i
$309$	8.23830	−	20.7404i	0.468660	−	1.17988i
$310$	3.49609			0.198564
$311$	5.45162	−	5.45162i	0.309133	−	0.309133i	−0.535440	−	0.844573i	$-0.679854\pi$
$311$	5.45162	−	5.45162i	0.309133	−	0.309133i	0.844573	+	0.535440i	$0.179854\pi$
$312$	3.55555	+	8.24144i	0.201293	+	0.466580i
$313$	−12.9814			−0.733752			−0.366876	−	0.930270i	$-0.619573\pi$
$313$	−12.9814			−0.733752			−0.366876	+	0.930270i	$0.619573\pi$
$314$		−	16.8370i		−	0.950165i
$315$	−0.533062	−	0.502808i	−0.0300347	−	0.0283300i
$316$	−2.97780	+	2.97780i	−0.167514	+	0.167514i
$317$	−18.6253	−	18.6253i	−1.04610	−	1.04610i	−0.998885	−	0.0472167i	$-0.984965\pi$
$317$	−18.6253	−	18.6253i	−1.04610	−	1.04610i	−0.0472167	−	0.998885i	$-0.515035\pi$
$318$	−18.4622	+	7.96500i	−1.03531	+	0.446655i
$319$	−24.7989	+	3.16606i	−1.38847	+	0.177266i
$320$		−	4.54031i		−	0.253811i
$321$	11.7092	+	4.65104i	0.653546	+	0.259596i
$322$	−0.186785	−	0.186785i	−0.0104091	−	0.0104091i
$323$	38.5629			2.14570
$324$	−11.4429	+	0.668993i	−0.635715	+	0.0371663i
$325$		−	1.85735i		−	0.103027i
$326$			9.65669i			0.534834i
$327$	−3.81937	−	1.51709i	−0.211211	−	0.0838955i
$328$		−	6.10781i		−	0.337247i
$329$	0.690529	+	0.690529i	0.0380701	+	0.0380701i
$330$	−6.36914	−	2.52989i	−0.350610	−	0.139266i
$331$	−12.5409	+	12.5409i	−0.689309	+	0.689309i	−0.962079	−	0.272770i	$-0.912060\pi$
$331$	−12.5409	+	12.5409i	−0.689309	+	0.689309i	0.272770	+	0.962079i	$0.412060\pi$
$332$	−2.29009			−0.125685
$333$	−19.7549	+	0.576980i	−1.08256	+	0.0316183i
$334$	4.92107	−	4.92107i	0.269269	−	0.269269i
$335$			1.96159i			0.107173i
$336$	0.0264352	−	0.0665520i	0.00144216	−	0.00363071i
$337$	−5.41250	+	5.41250i	−0.294838	+	0.294838i	−0.838988	−	0.544150i	$-0.816852\pi$
$337$	−5.41250	+	5.41250i	−0.294838	+	0.294838i	0.544150	+	0.838988i	$0.316852\pi$
$338$	−5.75555	+	5.75555i	−0.313061	+	0.313061i
$339$	−6.88091	+	2.96858i	−0.373720	+	0.161231i
$340$	−6.82664	−	6.82664i	−0.370227	−	0.370227i
$341$	19.0432			1.03125
$342$	9.46221	+	8.92517i	0.511657	+	0.482618i
$343$	3.40508			0.183857
$344$			22.5341i			1.21496i
$345$	2.04250	+	0.811305i	0.109965	+	0.0436792i
$346$	−12.0099	+	12.0099i	−0.645656	+	0.645656i
$347$	1.95216			0.104797			0.0523986	−	0.998626i	$-0.483313\pi$
$347$	1.95216			0.104797			0.0523986	+	0.998626i	$0.483313\pi$
$348$	−6.04923	−	10.2238i	−0.324273	−	0.548053i
$349$	5.28195			0.282736			0.141368	−	0.989957i	$-0.454850\pi$
$349$	5.28195			0.282736			0.141368	+	0.989957i	$0.454850\pi$
$350$	0.147206	−	0.147206i	0.00786851	−	0.00786851i
$351$	4.08017	+	8.74619i	0.217783	+	0.466837i
$352$		−	26.5750i		−	1.41645i
$353$	−12.3460			−0.657109			−0.328555	−	0.944485i	$-0.606561\pi$
$353$	−12.3460			−0.657109			−0.328555	+	0.944485i	$0.606561\pi$
$354$	9.40152	−	4.05603i	0.499685	−	0.215576i
$355$	5.69884			0.302463
$356$	−16.3684	−	16.3684i	−0.867525	−	0.867525i
$357$	1.27040	+	2.94468i	0.0672369	+	0.155849i
$358$	−12.6673	+	12.6673i	−0.669489	+	0.669489i
$359$	6.34225	−	6.34225i	0.334731	−	0.334731i	−0.519649	−	0.854380i	$-0.673937\pi$
$359$	6.34225	−	6.34225i	0.334731	−	0.334731i	0.854380	+	0.519649i	$0.173937\pi$
$360$	−0.244363	−	8.36661i	−0.0128791	−	0.440959i
$361$			6.87986i			0.362098i
$362$	−12.8118	+	12.8118i	−0.673375	+	0.673375i
$363$	−16.9859	−	6.74697i	−0.891526	−	0.354124i
$364$	−0.577806			−0.0302853
$365$	−6.87061	+	6.87061i	−0.359624	+	0.359624i
$366$	−4.57102	+	11.5078i	−0.238931	+	0.601522i
$367$	−6.21134	−	6.21134i	−0.324229	−	0.324229i	0.526158	−	0.850387i	$-0.323632\pi$
$367$	−6.21134	−	6.21134i	−0.324229	−	0.324229i	−0.850387	+	0.526158i	$0.823632\pi$
$368$			0.214770i			0.0111957i
$369$	−0.191732	−	6.56460i	−0.00998116	−	0.341739i
$370$		−	5.61470i		−	0.291894i
$371$		−	3.32701i		−	0.172730i
$372$	3.58449	+	8.30852i	0.185847	+	0.430777i
$373$	−2.52021			−0.130491			−0.0652457	−	0.997869i	$-0.520783\pi$
$373$	−2.52021			−0.130491			−0.0652457	+	0.997869i	$0.520783\pi$
$374$	21.2083	+	21.2083i	1.09666	+	1.09666i
$375$	−0.639395	+	1.60971i	−0.0330182	+	0.0831252i
$376$			11.1546i			0.575257i
$377$	−6.11996	+	7.91133i	−0.315194	+	0.407454i
$378$	−0.369810	+	1.01657i	−0.0190210	+	0.0522865i
$379$	11.2025	+	11.2025i	0.575435	+	0.575435i	0.933642	−	0.358207i	$-0.116612\pi$
$379$	11.2025	+	11.2025i	0.575435	+	0.575435i	−0.358207	+	0.933642i	$0.616612\pi$
$380$	4.58141	−	4.58141i	0.235021	−	0.235021i
$381$	13.0798	−	5.64292i	0.670098	−	0.289096i
$382$		−	12.1137i		−	0.619791i
$383$	−11.7818			−0.602023			−0.301011	−	0.953621i	$-0.597324\pi$
$383$	−11.7818			−0.602023			−0.301011	+	0.953621i	$0.597324\pi$
$384$	12.0535	−	5.20015i	0.615102	−	0.265369i
$385$	0.801833	−	0.801833i	0.0408652	−	0.0408652i
$386$	−15.5887			−0.793444
$387$	0.707375	+	24.2194i	0.0359579	+	1.23114i
$388$	−2.18893	−	2.18893i	−0.111126	−	0.111126i
$389$	23.1484	+	23.1484i	1.17367	+	1.17367i	0.981328	+	0.192341i	$0.0616079\pi$
$389$	23.1484	+	23.1484i	1.17367	+	1.17367i	0.192341	+	0.981328i	$0.438392\pi$
$390$	−2.51755	+	1.08613i	−0.127481	+	0.0549982i
$391$	−6.80125	−	6.80125i	−0.343954	−	0.343954i
$392$	13.6924	+	13.6924i	0.691570	+	0.691570i
$393$	3.90773	−	1.68589i	0.197119	−	0.0850417i
$394$	−3.40124	−	3.40124i	−0.171352	−	0.171352i
$395$	−2.33809	−	2.33809i	−0.117642	−	0.117642i
$396$	−0.517846	−	17.7302i	−0.0260227	−	0.890978i
$397$	23.1138			1.16005			0.580024	−	0.814599i	$-0.303043\pi$
$397$	23.1138			1.16005			0.580024	+	0.814599i	$0.303043\pi$
$398$	−12.5683	+	12.5683i	−0.629993	+	0.629993i
$399$	−1.97620	+	0.852577i	−0.0989336	+	0.0426822i
$400$	−0.169262			−0.00846309
$401$			24.9277i			1.24483i	0.782688	+	0.622415i	$0.213848\pi$
$401$			24.9277i			1.24483i	−0.782688	+	0.622415i	$0.786152\pi$
$402$	2.65883	−	1.14708i	0.132611	−	0.0572112i
$403$	5.38734	−	5.38734i	0.268363	−	0.268363i
$404$	−2.41741	−	2.41741i	−0.120271	−	0.120271i
$405$	−0.525277	−	8.98466i	−0.0261012	−	0.446451i
$406$	−1.11206	+	0.141976i	−0.0551908	+	0.00704617i
$407$		−	30.5833i		−	1.51596i
$408$	−13.5230	+	34.0448i	−0.669486	+	1.68547i
$409$	−1.85448	−	1.85448i	−0.0916981	−	0.0916981i	0.659770	−	0.751468i	$-0.270654\pi$
$409$	−1.85448	−	1.85448i	−0.0916981	−	0.0916981i	−0.751468	+	0.659770i	$0.770654\pi$
$410$	1.86578			0.0921441
$411$	−1.12320	−	2.60347i	−0.0554033	−	0.128420i
$412$			16.4097i			0.808449i
$413$			1.69422i			0.0833670i
$414$	−0.0947162	−	3.24294i	−0.00465505	−	0.159382i
$415$		−	1.79812i		−	0.0882663i
$416$	−7.51810	−	7.51810i	−0.368605	−	0.368605i
$417$	−11.4961	+	28.9421i	−0.562967	+	1.41730i
$418$	−14.2331	+	14.2331i	−0.696162	+	0.696162i
$419$	−4.07070			−0.198867			−0.0994333	−	0.995044i	$-0.531703\pi$
$419$	−4.07070			−0.198867			−0.0994333	+	0.995044i	$0.531703\pi$
$420$	0.500767	+	0.198910i	0.0244349	+	0.00970582i
$421$	−0.531595	+	0.531595i	−0.0259084	+	0.0259084i	−0.719942	−	0.694034i	$-0.755832\pi$
$421$	−0.531595	+	0.531595i	−0.0259084	+	0.0259084i	0.694034	+	0.719942i	$0.255832\pi$
$422$			23.8352i			1.16028i
$423$	0.350159	+	11.9889i	0.0170253	+	0.582919i
$424$	26.8719	−	26.8719i	1.30501	−	1.30501i
$425$	5.36011	−	5.36011i	0.260004	−	0.260004i
$426$	−3.33252	−	7.72448i	−0.161461	−	0.374252i
$427$	−1.44876	−	1.44876i	−0.0701102	−	0.0701102i
$428$	−9.26432			−0.447808
$429$	−13.7131	+	5.91614i	−0.662073	+	0.285634i
$430$	−6.88359			−0.331956
$431$			39.9362i			1.92366i	0.273651	+	0.961829i	$0.411769\pi$
$431$			39.9362i			1.92366i	−0.273651	+	0.961829i	$0.588231\pi$
$432$	0.797046	−	0.371828i	0.0383479	−	0.0178896i
$433$	3.69560	−	3.69560i	0.177599	−	0.177599i	−0.612709	−	0.790308i	$-0.709920\pi$
$433$	3.69560	−	3.69560i	0.177599	−	0.177599i	0.790308	+	0.612709i	$0.209920\pi$
$434$	0.853958			0.0409913
$435$	8.02747	−	4.74971i	0.384888	−	0.227731i
$436$	3.02188			0.144722
$437$	4.56437	−	4.56437i	0.218343	−	0.218343i
$438$	13.3305	+	5.29502i	0.636956	+	0.253006i
$439$		−	23.5242i		−	1.12275i	−0.827562	−	0.561374i	$-0.810273\pi$
$439$		−	23.5242i		−	1.12275i	0.827562	−	0.561374i	$-0.189727\pi$
$440$	12.9526			0.617493
$441$	15.1462	+	14.2866i	0.721249	+	0.680313i
$442$	11.9997			0.570768
$443$	12.9220	+	12.9220i	0.613941	+	0.613941i	0.943971	−	0.330029i	$-0.107059\pi$
$443$	12.9220	+	12.9220i	0.613941	+	0.613941i	−0.330029	+	0.943971i	$0.607059\pi$
$444$	13.3434	−	5.75666i	0.633251	−	0.273199i
$445$	12.8521	−	12.8521i	0.609247	−	0.609247i
$446$	14.6862	−	14.6862i	0.695411	−	0.695411i
$447$	−1.13700	+	2.86247i	−0.0537784	+	0.135390i
$448$		−	1.10902i		−	0.0523963i
$449$	0.416433	−	0.416433i	0.0196527	−	0.0196527i	−0.697212	−	0.716865i	$-0.745576\pi$
$449$	0.416433	−	0.416433i	0.0196527	−	0.0196527i	0.716865	+	0.697212i	$0.245576\pi$
$450$	2.55578	−	0.0746466i	0.120481	−	0.00351887i
$451$	10.1629			0.478551
$452$	3.89645	−	3.89645i	0.183274	−	0.183274i
$453$	15.1130	+	6.00307i	0.710073	+	0.282049i
$454$	12.7001	+	12.7001i	0.596047	+	0.596047i
$455$		−	0.453679i		−	0.0212688i
$456$	−22.8477	−	9.07536i	−1.06994	−	0.424993i
$457$			35.1536i			1.64442i	0.569187	+	0.822208i	$0.307258\pi$
$457$			35.1536i			1.64442i	−0.569187	+	0.822208i	$0.692742\pi$
$458$		−	5.88972i		−	0.275209i
$459$	−13.4656	+	37.0154i	−0.628521	+	1.72773i
$460$	−1.61602			−0.0753476
$461$	8.26594	+	8.26594i	0.384983	+	0.384983i	0.872894	−	0.487911i	$-0.162241\pi$
$461$	8.26594	+	8.26594i	0.384983	+	0.384983i	−0.487911	+	0.872894i	$0.662241\pi$
$462$	−1.55573	−	0.617954i	−0.0723792	−	0.0287498i
$463$		−	13.7062i		−	0.636979i	−0.947926	−	0.318489i	$-0.896824\pi$
$463$		−	13.7062i		−	0.636979i	0.947926	−	0.318489i	$-0.103176\pi$
$464$	0.720965	+	0.557716i	0.0334699	+	0.0258913i
$465$	−6.52364	+	2.81445i	−0.302527	+	0.130517i
$466$	−3.48010	−	3.48010i	−0.161213	−	0.161213i
$467$	15.4079	−	15.4079i	0.712994	−	0.712994i	−0.254166	−	0.967161i	$-0.581801\pi$
$467$	15.4079	−	15.4079i	0.712994	−	0.712994i	0.967161	+	0.254166i	$0.0818011\pi$
$468$	−5.16240	−	4.86940i	−0.238632	−	0.225088i
$469$			0.479140i			0.0221246i
$470$	−3.40745			−0.157174
$471$	13.5542	+	31.4175i	0.624546	+	1.44764i
$472$	−13.6840	+	13.6840i	−0.629858	+	0.629858i
$473$	−37.4949			−1.72402
$474$	−1.80191	+	4.53641i	−0.0827646	+	0.208364i
$475$	3.59721	+	3.59721i	0.165051	+	0.165051i
$476$	−1.66748	−	1.66748i	−0.0764290	−	0.0764290i
$477$	28.0380	−	29.7251i	1.28377	−	1.36102i
$478$	−3.81253	−	3.81253i	−0.174381	−	0.174381i
$479$	−13.3360	−	13.3360i	−0.609337	−	0.609337i	0.333436	−	0.942773i	$-0.391792\pi$
$479$	−13.3360	−	13.3360i	−0.609337	−	0.609337i	−0.942773	+	0.333436i	$0.891792\pi$
$480$	3.92760	+	9.10382i	0.179269	+	0.415531i
$481$	−8.65204	−	8.65204i	−0.394499	−	0.394499i
$482$	−10.7086	−	10.7086i	−0.487765	−	0.487765i
$483$	0.498904	+	0.198170i	0.0227009	+	0.00901706i
$484$	13.4392			0.610872
$485$	1.71869	−	1.71869i	0.0780419	−	0.0780419i
$486$	−11.8711	+	5.96596i	−0.538483	+	0.270621i
$487$	22.0128			0.997497			0.498748	−	0.866747i	$-0.333793\pi$
$487$	22.0128			0.997497			0.498748	+	0.866747i	$0.333793\pi$
$488$		−	23.4029i		−	1.05940i
$489$	−7.77390	−	18.0192i	−0.351548	−	0.814857i
$490$	−4.18267	+	4.18267i	−0.188954	+	0.188954i
$491$	3.80159	+	3.80159i	0.171563	+	0.171563i	0.787666	−	0.616103i	$-0.211289\pi$
$491$	3.80159	+	3.80159i	0.171563	+	0.171563i	−0.616103	+	0.787666i	$0.711289\pi$
$492$	1.91295	+	4.43405i	0.0862425	+	0.199902i
$493$	−40.4927	+	5.16968i	−1.82370	+	0.232831i
$494$			8.05310i			0.362326i
$495$	13.9213	−	0.406600i	0.625718	−	0.0182753i
$496$	−0.490952	−	0.490952i	−0.0220444	−	0.0220444i
$497$	1.39200			0.0624399
$498$	−2.43726	+	1.05149i	−0.109216	+	0.0471184i
$499$		−	27.8966i		−	1.24882i	−0.781096	−	0.624411i	$-0.785339\pi$
$499$		−	27.8966i		−	1.24882i	0.781096	−	0.624411i	$-0.214661\pi$
$500$		−	1.27360i		−	0.0569572i
$501$	−5.22103	+	13.1442i	−0.233259	+	0.587241i
$502$			26.5185i			1.18358i
$503$	−8.41549	−	8.41549i	−0.375228	−	0.375228i	0.494149	−	0.869377i	$-0.335480\pi$
$503$	−8.41549	−	8.41549i	−0.375228	−	0.375228i	−0.869377	+	0.494149i	$0.835480\pi$
$504$	−0.0596884	−	2.04364i	−0.00265873	−	0.0910308i
$505$	1.89809	−	1.89809i	0.0844639	−	0.0844639i
$506$	5.02050			0.223189
$507$	6.10638	−	15.3731i	0.271194	−	0.682745i
$508$	−7.40669	+	7.40669i	−0.328619	+	0.328619i
$509$			23.8831i			1.05860i	0.848435	+	0.529300i	$0.177545\pi$
$509$			23.8831i			1.05860i	−0.848435	+	0.529300i	$0.822455\pi$
$510$	−10.3998	−	4.13091i	−0.460511	−	0.182920i
$511$	−1.67822	+	1.67822i	−0.0742402	+	0.0742402i
$512$	−1.35299	+	1.35299i	−0.0597944	+	0.0597944i
$513$	−24.8413	−	9.03687i	−1.09677	−	0.398987i
$514$	11.4835	+	11.4835i	0.506517	+	0.506517i
$515$	−12.8845			−0.567759
$516$	−7.05764	−	16.3590i	−0.310695	−	0.720164i
$517$	−18.5604			−0.816286
$518$		−	1.37145i		−	0.0602581i
$519$	12.7420	−	32.0786i	0.559310	−	1.40809i
$520$	3.66432	−	3.66432i	0.160691	−	0.160691i
$521$	−19.0762			−0.835743			−0.417872	−	0.908506i	$-0.637224\pi$
$521$	−19.0762			−0.835743			−0.417872	+	0.908506i	$0.637224\pi$
$522$	−11.1322	−	8.10332i	−0.487244	−	0.354673i
$523$	12.3967			0.542069			0.271035	−	0.962570i	$-0.412634\pi$
$523$	12.3967			0.542069			0.271035	+	0.962570i	$0.412634\pi$
$524$	−2.21283	+	2.21283i	−0.0966679	+	0.0966679i
$525$	−0.156179	+	0.393190i	−0.00681623	+	0.0171602i
$526$		−	2.03592i		−	0.0887703i
$527$	31.0945			1.35450
$528$	0.539141	+	1.24968i	0.0234631	+	0.0543854i
$529$	21.3900			0.929999
$530$	8.20866	+	8.20866i	0.356561	+	0.356561i
$531$	−14.2778	+	15.1370i	−0.619606	+	0.656888i
$532$	1.11906	−	1.11906i	0.0485174	−	0.0485174i
$533$	2.87509	−	2.87509i	0.124534	−	0.124534i
$534$	−24.9359	−	9.90480i	−1.07908	−	0.428623i
$535$		−	7.27412i		−	0.314488i
$536$	−3.86996	+	3.86996i	−0.167157	+	0.167157i
$537$	13.4395	−	33.8346i	0.579956	−	1.46007i
$538$	−2.53654			−0.109358
$539$	−22.7830	+	22.7830i	−0.981332	+	0.981332i
$540$	2.79780	+	5.99733i	0.120398	+	0.258084i
$541$	18.5679	+	18.5679i	0.798298	+	0.798298i	0.982827	−	0.184529i	$-0.0590760\pi$
$541$	18.5679	+	18.5679i	0.798298	+	0.798298i	−0.184529	+	0.982827i	$0.559076\pi$
$542$		−	1.63203i		−	0.0701015i
$543$	13.5928	−	34.2206i	0.583322	−	1.46854i
$544$		−	43.3927i		−	1.86045i
$545$			2.37270i			0.101635i
$546$	−0.614938	+	0.265299i	−0.0263169	+	0.0113537i
$547$	29.3620			1.25543			0.627714	−	0.778444i	$-0.283991\pi$
$547$	29.3620			1.25543			0.627714	+	0.778444i	$0.283991\pi$
$548$	1.47427	+	1.47427i	0.0629776	+	0.0629776i
$549$	−0.734646	−	25.1531i	−0.0313539	−	1.07351i
$550$			3.95669i			0.168714i
$551$	−3.46941	−	27.1750i	−0.147802	−	1.15769i
$552$	2.42899	+	5.63019i	0.103385	+	0.239637i
$553$	−0.571105	−	0.571105i	−0.0242858	−	0.0242858i
$554$	9.08669	−	9.08669i	0.386056	−	0.386056i
$555$	4.51999	+	10.4769i	0.191863	+	0.444721i
$556$		−	22.8989i		−	0.971130i
$557$	−11.4480			−0.485066			−0.242533	−	0.970143i	$-0.577978\pi$
$557$	−11.4480			−0.485066			−0.242533	+	0.970143i	$0.577978\pi$
$558$	7.62968	+	7.19665i	0.322990	+	0.304658i
$559$	−10.6074	+	10.6074i	−0.448643	+	0.448643i
$560$	−0.0413441			−0.00174711
$561$	−56.6477	−	22.5011i	−2.39167	−	0.949996i
$562$	−3.12091	−	3.12091i	−0.131648	−	0.131648i
$563$	3.76134	+	3.76134i	0.158522	+	0.158522i	0.781911	−	0.623390i	$-0.214245\pi$
$563$	3.76134	+	3.76134i	0.158522	+	0.158522i	−0.623390	+	0.781911i	$0.714245\pi$
$564$	−3.49361	−	8.09788i	−0.147108	−	0.340982i
$565$	3.05940	+	3.05940i	0.128710	+	0.128710i
$566$	−7.91426	−	7.91426i	−0.332661	−	0.332661i
$567$	−0.128305	−	2.19460i	−0.00538829	−	0.0921646i
$568$	11.2431	+	11.2431i	0.471749	+	0.471749i
$569$	12.0118	+	12.0118i	0.503562	+	0.503562i	0.912543	−	0.408981i	$-0.134116\pi$
$569$	12.0118	+	12.0118i	0.503562	+	0.503562i	−0.408981	+	0.912543i	$0.634116\pi$
$570$	2.77229	−	6.97938i	0.116118	−	0.292334i
$571$	5.82169			0.243630			0.121815	−	0.992553i	$-0.461129\pi$
$571$	5.82169			0.243630			0.121815	+	0.992553i	$0.461129\pi$
$572$	7.76529	−	7.76529i	0.324683	−	0.324683i
$573$	9.75187	+	22.6040i	0.407390	+	0.944294i
$574$	0.455736			0.0190221
$575$		−	1.26886i		−	0.0529152i
$576$	9.34616	−	9.90853i	0.389423	−	0.412855i
$577$	−17.1795	+	17.1795i	−0.715190	+	0.715190i	−0.967616	−	0.252426i	$-0.918772\pi$
$577$	−17.1795	+	17.1795i	−0.715190	+	0.715190i	0.252426	+	0.967616i	$0.418772\pi$
$578$	24.3846	+	24.3846i	1.01427	+	1.01427i
$579$	29.0882	−	12.5493i	1.20887	−	0.521533i
$580$	−4.19650	+	5.42486i	−0.174250	+	0.225255i
$581$		−	0.439211i		−	0.0182215i
$582$	−3.33464	−	1.32456i	−0.138225	−	0.0549047i
$583$	44.7125	+	44.7125i	1.85180	+	1.85180i
$584$	−27.1097			−1.12181
$585$	3.82334	−	4.05339i	0.158075	−	0.167587i
$586$		−	22.6165i		−	0.934281i
$587$			11.4249i			0.471557i	0.971807	+	0.235778i	$0.0757640\pi$
$587$			11.4249i			0.471557i	−0.971807	+	0.235778i	$0.924236\pi$
$588$	−14.2286	−	5.65176i	−0.586778	−	0.233075i
$589$			20.8678i			0.859841i
$590$	−4.18011	−	4.18011i	−0.172092	−	0.172092i
$591$	9.08475	+	3.60856i	0.373697	+	0.148436i
$592$	−0.788466	+	0.788466i	−0.0324058	+	0.0324058i
$593$	−28.8041			−1.18284			−0.591422	−	0.806362i	$-0.701433\pi$
$593$	−28.8041			−1.18284			−0.591422	+	0.806362i	$0.701433\pi$
$594$	−8.69193	−	18.6319i	−0.356634	−	0.764475i
$595$	1.30927	−	1.30927i	0.0536747	−	0.0536747i
$596$		−	2.26478i		−	0.0927689i
$597$	13.3344	−	33.5701i	0.545742	−	1.37393i
$598$	1.42031	−	1.42031i	0.0580806	−	0.0580806i
$599$	−23.6586	+	23.6586i	−0.966663	+	0.966663i	−0.999462	−	0.0327994i	$-0.989558\pi$
$599$	−23.6586	+	23.6586i	−0.966663	+	0.966663i	0.0327994	+	0.999462i	$0.489558\pi$
$600$	−4.43720	+	1.91431i	−0.181148	+	0.0781513i
$601$	−10.2080	−	10.2080i	−0.416392	−	0.416392i	0.467566	−	0.883958i	$-0.345131\pi$
$601$	−10.2080	−	10.2080i	−0.416392	−	0.416392i	−0.883958	+	0.467566i	$0.845131\pi$
$602$	−1.68139			−0.0685284
$603$	−4.03790	+	4.28087i	−0.164436	+	0.174330i
$604$	−11.9574			−0.486540
$605$			10.5521i			0.429004i
$606$	−3.68271	−	1.46281i	−0.149600	−	0.0594227i
$607$	−28.1984	+	28.1984i	−1.14454	+	1.14454i	−0.156927	+	0.987610i	$0.550159\pi$
$607$	−28.1984	+	28.1984i	−1.14454	+	1.14454i	−0.987610	+	0.156927i	$0.949841\pi$
$608$	29.1212			1.18102
$609$	1.96080	−	1.16017i	0.0794555	−	0.0470124i
$610$	7.14897			0.289454
$611$	−5.25076	+	5.25076i	−0.212423	+	0.212423i
$612$	−0.845560	−	28.9507i	−0.0341797	−	1.17026i
$613$			42.9571i			1.73502i	0.497417	+	0.867511i	$0.334282\pi$
$613$			42.9571i			1.73502i	−0.497417	+	0.867511i	$0.665718\pi$
$614$	23.0336			0.929562
$615$	−3.48151	+	1.50200i	−0.140388	+	0.0605666i
$616$	3.16382			0.127474
$617$	−20.4735	−	20.4735i	−0.824231	−	0.824231i	0.162480	−	0.986712i	$-0.448051\pi$
$617$	−20.4735	−	20.4735i	−0.824231	−	0.824231i	−0.986712	+	0.162480i	$0.948051\pi$
$618$	7.53449	+	17.4643i	0.303082	+	0.702517i
$619$	−22.8170	+	22.8170i	−0.917093	+	0.917093i	−0.996817	−	0.0797239i	$-0.974596\pi$
$619$	−22.8170	+	22.8170i	−0.917093	+	0.917093i	0.0797239	+	0.996817i	$0.474596\pi$
$620$	3.69414	−	3.69414i	0.148360	−	0.148360i
$621$	2.78739	+	5.97501i	0.111854	+	0.239769i
$622$			6.57095i			0.263471i
$623$	3.13926	−	3.13926i	0.125772	−	0.125772i
$624$	0.506060	+	0.201013i	0.0202586	+	0.00804694i
$625$	1.00000			0.0400000
$626$	7.82338	−	7.82338i	0.312685	−	0.312685i
$627$	15.1006	−	38.0167i	0.603061	−	1.51824i
$628$	−17.7908	−	17.7908i	−0.709929	−	0.709929i
$629$		−	49.9376i		−	1.99114i
$630$	0.624278	−	0.0182332i	0.0248718	−	0.000726430i
$631$		−	24.3235i		−	0.968303i	−0.874984	−	0.484151i	$-0.839128\pi$
$631$		−	24.3235i		−	0.968303i	0.874984	−	0.484151i	$-0.160872\pi$
$632$		−	9.22550i		−	0.366971i
$633$	−19.1880	−	44.4760i	−0.762654	−	1.76776i
$634$	22.4495			0.891582
$635$	−5.81555	−	5.81555i	−0.230783	−	0.230783i
$636$	−11.0918	+	27.9242i	−0.439819	+	1.10727i
$637$			12.8907i			0.510747i
$638$	13.0373	−	16.8534i	0.516151	−	0.667232i
$639$	12.4368	+	11.7310i	0.491994	+	0.464070i
$640$	−5.35923	−	5.35923i	−0.211842	−	0.211842i
$641$	17.9235	−	17.9235i	0.707937	−	0.707937i	−0.258164	−	0.966101i	$-0.583118\pi$
$641$	17.9235	−	17.9235i	0.707937	−	0.707937i	0.966101	+	0.258164i	$0.0831176\pi$
$642$	−9.85969	+	4.25370i	−0.389131	+	0.167880i
$643$			5.71309i			0.225302i	0.993635	+	0.112651i	$0.0359342\pi$
$643$			5.71309i			0.225302i	−0.993635	+	0.112651i	$0.964066\pi$
$644$	−0.394732			−0.0155546
$645$	12.8447	−	5.54148i	0.505758	−	0.218196i
$646$	−23.2403	+	23.2403i	−0.914379	+	0.914379i
$647$	−11.0778			−0.435515			−0.217757	−	0.976003i	$-0.569874\pi$
$647$	−11.0778			−0.435515			−0.217757	+	0.976003i	$0.569874\pi$
$648$	16.6893	−	18.7619i	0.655616	−	0.737036i
$649$	−22.7690	−	22.7690i	−0.893763	−	0.893763i
$650$	1.11935	+	1.11935i	0.0439047	+	0.0439047i
$651$	−1.59347	+	0.687460i	−0.0624531	+	0.0269437i
$652$	10.2037	+	10.2037i	0.399609	+	0.399609i
$653$	17.5066	+	17.5066i	0.685087	+	0.685087i	0.961142	−	0.276055i	$-0.0890273\pi$
$653$	17.5066	+	17.5066i	0.685087	+	0.685087i	−0.276055	+	0.961142i	$0.589027\pi$
$654$	3.21607	−	1.38749i	0.125758	−	0.0542551i
$655$	−1.73746	−	1.73746i	−0.0678881	−	0.0678881i
$656$	−0.262009	−	0.262009i	−0.0102297	−	0.0102297i
$657$	−29.1371	+	0.851006i	−1.13675	+	0.0332009i
$658$	−0.832308			−0.0324468
$659$	7.75252	−	7.75252i	0.301995	−	0.301995i	−0.539799	−	0.841794i	$-0.681500\pi$
$659$	7.75252	−	7.75252i	0.301995	−	0.301995i	0.841794	+	0.539799i	$0.181500\pi$
$660$	−9.40315	+	4.05674i	−0.366017	+	0.157908i
$661$	7.38034			0.287062			0.143531	−	0.989646i	$-0.454154\pi$
$661$	7.38034			0.287062			0.143531	+	0.989646i	$0.454154\pi$
$662$		−	15.1158i		−	0.587491i
$663$	−22.3913	+	9.66011i	−0.869605	+	0.375168i
$664$	3.54746	−	3.54746i	0.137668	−	0.137668i
$665$	0.878658	+	0.878658i	0.0340729	+	0.0340729i
$666$	11.5578	−	12.2532i	0.447855	−	0.474803i
$667$	−4.18089	+	5.40467i	−0.161885	+	0.209270i
$668$		−	10.3997i		−	0.402376i
$669$	−15.5814	+	39.2270i	−0.602411	+	1.51660i
$670$	−1.18217	−	1.18217i	−0.0456713	−	0.0456713i
$671$	38.9405			1.50328
$672$	0.959359	+	2.22371i	0.0370081	+	0.0857814i
$673$			27.4702i			1.05890i	0.848341	+	0.529450i	$0.177601\pi$
$673$			27.4702i			1.05890i	−0.848341	+	0.529450i	$0.822399\pi$
$674$		−	6.52380i		−	0.251287i
$675$	−4.70895	+	2.19676i	−0.181248	+	0.0845535i
$676$			12.1632i			0.467815i
$677$	14.3994	+	14.3994i	0.553415	+	0.553415i	0.927425	−	0.374010i	$-0.122017\pi$
$677$	14.3994	+	14.3994i	0.553415	+	0.553415i	−0.374010	+	0.927425i	$0.622017\pi$
$678$	2.35780	−	5.93590i	0.0905509	−	0.227967i
$679$	0.419810	−	0.419810i	0.0161108	−	0.0161108i
$680$	21.1496			0.811050
$681$	−33.9222	−	13.4743i	−1.29990	−	0.516335i
$682$	−11.4766	+	11.4766i	−0.439461	+	0.439461i
$683$		−	5.22624i		−	0.199977i	−0.994989	−	0.0999883i	$-0.968119\pi$
$683$		−	5.22624i		−	0.199977i	0.994989	−	0.0999883i	$-0.0318805\pi$
$684$	19.4290	−	0.567462i	0.742886	−	0.0216974i
$685$	−1.15756	+	1.15756i	−0.0442281	+	0.0442281i
$686$	−2.05211	+	2.05211i	−0.0783498	+	0.0783498i
$687$	4.74139	+	10.9901i	0.180895	+	0.419299i
$688$	0.966655	+	0.966655i	0.0368534	+	0.0368534i
$689$	25.2985			0.963795
$690$	−1.71988	+	0.741995i	−0.0654746	+	0.0282473i
$691$	32.9099			1.25195			0.625976	−	0.779843i	$-0.284701\pi$
$691$	32.9099			1.25195			0.625976	+	0.779843i	$0.284701\pi$
$692$			25.3805i			0.964821i
$693$	3.40044	−	0.0993165i	0.129172	−	0.00377272i
$694$	−1.17649	+	1.17649i	−0.0446588	+	0.0446588i
$695$	17.9797			0.682007
$696$	25.2077	+	6.46660i	0.955496	+	0.245116i
$697$	16.5944			0.628557
$698$	−3.18322	+	3.18322i	−0.120487	+	0.120487i
$699$	9.29539	+	3.69223i	0.351584	+	0.139653i
$700$		−	0.311091i		−	0.0117581i
$701$	−18.7316			−0.707482			−0.353741	−	0.935343i	$-0.615091\pi$
$701$	−18.7316			−0.707482			−0.353741	+	0.935343i	$0.615091\pi$
$702$	−7.72994	−	2.81202i	−0.291748	−	0.106133i
$703$	33.5135			1.26399
$704$	14.9044	+	14.9044i	0.561732	+	0.561732i
$705$	6.35825	−	2.74310i	0.239466	−	0.103311i
$706$	7.44042	−	7.44042i	0.280024	−	0.280024i
$707$	0.463629	−	0.463629i	0.0174366	−	0.0174366i
$708$	5.64830	−	14.2199i	0.212276	−	0.534417i
$709$			7.10248i			0.266739i	0.991066	+	0.133370i	$0.0425798\pi$
$709$			7.10248i			0.266739i	−0.991066	+	0.133370i	$0.957420\pi$
$710$	−3.43446	+	3.43446i	−0.128893	+	0.128893i
$711$	−0.289600	−	9.91546i	−0.0108609	−	0.371859i
$712$	50.7110			1.90047
$713$	3.68040	−	3.68040i	0.137832	−	0.137832i
$714$	−2.54026	−	1.00902i	−0.0950670	−	0.0377617i
$715$	6.09712	+	6.09712i	0.228019	+	0.228019i
$716$			26.7698i			1.00044i
$717$	10.1833	+	4.04492i	0.380302	+	0.151060i
$718$			7.64444i			0.285288i
$719$		−	17.9087i		−	0.667882i	−0.942594	−	0.333941i	$-0.891621\pi$
$719$		−	17.9087i		−	0.667882i	0.942594	−	0.333941i	$-0.108379\pi$
$720$	−0.369388	−	0.348423i	−0.0137663	−	0.0129850i
$721$	−3.14718			−0.117207
$722$	−4.14622	−	4.14622i	−0.154306	−	0.154306i
$723$	28.6029	+	11.3614i	1.06375	+	0.422534i
$724$			27.0752i			1.00624i
$725$	−4.25946	−	3.29499i	−0.158193	−	0.122373i
$726$	14.3028	−	6.17057i	0.530828	−	0.229011i
$727$	−26.3882	−	26.3882i	−0.978683	−	0.978683i	0.0210947	−	0.999777i	$-0.493285\pi$
$727$	−26.3882	−	26.3882i	−0.978683	−	0.978683i	−0.999777	+	0.0210947i	$0.993285\pi$
$728$	0.895050	−	0.895050i	0.0331727	−	0.0331727i
$729$	17.3485	−	20.6889i	0.642535	−	0.766256i
$730$		−	8.28129i		−	0.306504i
$731$	−61.2232			−2.26442
$732$	7.32973	+	16.9897i	0.270915	+	0.627956i
$733$	−3.04397	+	3.04397i	−0.112432	+	0.112432i	−0.761084	−	0.648653i	$-0.775333\pi$
$733$	−3.04397	+	3.04397i	−0.112432	+	0.112432i	0.648653	+	0.761084i	$0.275333\pi$
$734$	7.48666			0.276338
$735$	4.43762	−	11.1719i	0.163684	−	0.412083i
$736$	−5.13603	−	5.13603i	−0.189317	−	0.189317i
$737$	−6.43929	−	6.43929i	−0.237194	−	0.237194i
$738$	4.07177	+	3.84067i	0.149884	+	0.141377i
$739$	−5.25844	−	5.25844i	−0.193435	−	0.193435i	0.603744	−	0.797179i	$-0.293675\pi$
$739$	−5.25844	−	5.25844i	−0.193435	−	0.193435i	−0.797179	+	0.603744i	$0.793675\pi$
$740$	−5.93277	−	5.93277i	−0.218093	−	0.218093i
$741$	−6.48297	−	15.0269i	−0.238158	−	0.552029i
$742$	2.00505	+	2.00505i	0.0736079	+	0.0736079i
$743$	−9.87804	−	9.87804i	−0.362390	−	0.362390i	0.502302	−	0.864692i	$-0.332487\pi$
$743$	−9.87804	−	9.87804i	−0.362390	−	0.362390i	−0.864692	+	0.502302i	$0.832487\pi$
$744$	−18.4228	−	7.31775i	−0.675414	−	0.268282i
$745$	1.77825			0.0651500
$746$	1.51883	−	1.51883i	0.0556083	−	0.0556083i
$747$	3.70140	−	3.92412i	0.135427	−	0.143576i
$748$	44.8195			1.63876
$749$		−	1.77678i		−	0.0649222i
$750$	−0.584771	−	1.35545i	−0.0213528	−	0.0494940i
$751$	3.43450	−	3.43450i	0.125327	−	0.125327i	−0.641661	−	0.766988i	$-0.721755\pi$
$751$	3.43450	−	3.43450i	0.125327	−	0.125327i	0.766988	+	0.641661i	$0.221755\pi$
$752$	0.478505	+	0.478505i	0.0174493	+	0.0174493i
$753$	−21.3481	−	49.4830i	−0.777969	−	1.80326i
$754$	−1.07959	−	8.45611i	−0.0393162	−	0.307953i
$755$		−	9.38866i		−	0.341688i
$756$	0.683394	+	1.46491i	0.0248548	+	0.0532784i
$757$	8.89192	+	8.89192i	0.323182	+	0.323182i	0.849987	−	0.526804i	$-0.176610\pi$
$757$	8.89192	+	8.89192i	0.323182	+	0.323182i	−0.526804	+	0.849987i	$0.676610\pi$
$758$	−13.5026			−0.490438
$759$	−9.36817	+	4.04164i	−0.340043	+	0.146702i
$760$			14.1937i			0.514858i
$761$		−	25.7306i		−	0.932734i	−0.884591	−	0.466367i	$-0.845563\pi$
$761$		−	25.7306i		−	0.932734i	0.884591	−	0.466367i	$-0.154437\pi$
$762$	−4.48191	+	11.2834i	−0.162362	+	0.408756i
$763$			0.579558i			0.0209814i
$764$	−12.7999	−	12.7999i	−0.463085	−	0.463085i
$765$	22.7313	−	0.663913i	0.821853	−	0.0240038i
$766$	7.10044	−	7.10044i	0.256549	−	0.256549i
$767$	−12.8828			−0.465170
$768$	−9.93634	+	25.0153i	−0.358547	+	0.902660i
$769$	0.843523	−	0.843523i	0.0304182	−	0.0304182i	−0.691734	−	0.722152i	$-0.743153\pi$
$769$	0.843523	−	0.843523i	0.0304182	−	0.0304182i	0.722152	+	0.691734i	$0.243153\pi$
$770$			0.966466i			0.0348290i
$771$	−30.6726	−	12.1835i	−1.10465	−	0.438778i
$772$	−16.4718	+	16.4718i	−0.592833	+	0.592833i
$773$	−24.6827	+	24.6827i	−0.887776	+	0.887776i	−0.994309	−	0.106534i	$-0.966025\pi$
$773$	−24.6827	+	24.6827i	−0.887776	+	0.887776i	0.106534	+	0.994309i	$0.466025\pi$
$774$	−15.0224	−	14.1698i	−0.539968	−	0.509322i
$775$	2.90055	+	2.90055i	0.104191	+	0.104191i
$776$	6.78152			0.243442
$777$	1.10406	+	2.55911i	0.0396078	+	0.0918074i
$778$	−27.9012			−1.00031
$779$			11.1366i			0.399010i
$780$	−1.51251	+	3.80782i	−0.0541565	+	0.136342i
$781$	−18.7075	+	18.7075i	−0.669408	+	0.669408i
$782$	8.19768			0.293149
$783$	27.2959	+	6.15892i	0.975477	+	0.220102i
$784$	1.17473			0.0419548
$785$	13.9689	−	13.9689i	0.498571	−	0.498571i
$786$	−1.33902	+	3.37105i	−0.0477612	+	0.120241i
$787$		−	26.4100i		−	0.941416i	−0.882289	−	0.470708i	$-0.843998\pi$
$787$		−	26.4100i		−	0.941416i	0.882289	−	0.470708i	$-0.156002\pi$
$788$	−7.18784			−0.256056
$789$	1.63897	+	3.79899i	0.0583490	+	0.135248i
$790$	2.81815			0.100265
$791$	0.747291	+	0.747291i	0.0265706	+	0.0265706i
$792$	28.2672	+	26.6628i	1.00443	+	0.947422i
$793$	11.0163	−	11.0163i	0.391200	−	0.391200i
$794$	−13.9298	+	13.9298i	−0.494349	+	0.494349i
$795$	−21.9254	−	8.70901i	−0.777614	−	0.308877i
$796$			26.5606i			0.941416i
$797$	10.8587	−	10.8587i	0.384633	−	0.384633i	−0.488135	−	0.872768i	$-0.662323\pi$
$797$	10.8587	−	10.8587i	0.384633	−	0.384633i	0.872768	+	0.488135i	$0.162323\pi$
$798$	0.677161	−	1.70479i	0.0239713	−	0.0603489i
$799$	−30.3062			−1.07216
$800$	4.04775	−	4.04775i	0.143109	−	0.143109i
$801$	54.5036	−	1.59188i	1.92579	−	0.0562464i
$802$	−15.0229	−	15.0229i	−0.530478	−	0.530478i
$803$		−	45.1082i		−	1.59183i
$804$	1.59739	−	4.02152i	0.0563356	−	0.141828i
$805$		−	0.309934i		−	0.0109237i
$806$			6.49347i			0.228723i
$807$	4.73313	−	2.04198i	0.166614	−	0.0718812i
$808$	7.48937			0.263475
$809$	31.1357	+	31.1357i	1.09467	+	1.09467i	0.995022	+	0.0996508i	$0.0317726\pi$
$809$	31.1357	+	31.1357i	1.09467	+	1.09467i	0.0996508	+	0.995022i	$0.468227\pi$
$810$	5.73126	+	5.09813i	0.201376	+	0.179130i
$811$		−	19.8203i		−	0.695987i	−0.937497	−	0.347993i	$-0.886863\pi$
$811$		−	19.8203i		−	0.695987i	0.937497	−	0.347993i	$-0.113137\pi$
$812$	−1.02504	+	1.32508i	−0.0359719	+	0.0465012i
$813$	1.31383	+	3.04533i	0.0460779	+	0.106805i
$814$	18.4313	+	18.4313i	0.646017	+	0.646017i
$815$	−8.01172	+	8.01172i	−0.280638	+	0.280638i
$816$	0.880332	+	2.04053i	0.0308178	+	0.0714329i
$817$		−	41.0874i		−	1.43746i
$818$	2.23524			0.0781534
$819$	0.933892	−	0.990085i	0.0326328	−	0.0345964i
$820$	1.97147	−	1.97147i	0.0688468	−	0.0688468i
$821$	0.0595759			0.00207921			0.00103961	−	0.999999i	$-0.499669\pi$
$821$	0.0595759			0.00207921			0.00103961	+	0.999999i	$0.499669\pi$
$822$	2.24592	+	0.892103i	0.0783354	+	0.0311157i
$823$	−20.0817	−	20.0817i	−0.700003	−	0.700003i	0.264408	−	0.964411i	$-0.414823\pi$
$823$	−20.0817	−	20.0817i	−0.700003	−	0.700003i	−0.964411	+	0.264408i	$0.914823\pi$
$824$	−25.4195	−	25.4195i	−0.885529	−	0.885529i
$825$	−3.18525	−	7.38312i	−0.110896	−	0.257047i
$826$	−1.02104	−	1.02104i	−0.0355264	−	0.0355264i
$827$	30.2171	+	30.2171i	1.05075	+	1.05075i	0.998641	+	0.0521114i	$0.0165951\pi$
$827$	30.2171	+	30.2171i	1.05075	+	1.05075i	0.0521114	+	0.998641i	$0.483405\pi$
$828$	−3.52673	−	3.32656i	−0.122562	−	0.115606i
$829$	−17.2680	−	17.2680i	−0.599743	−	0.599743i	0.340501	−	0.940244i	$-0.389403\pi$
$829$	−17.2680	−	17.2680i	−0.599743	−	0.599743i	−0.940244	+	0.340501i	$0.889403\pi$
$830$	1.08366	+	1.08366i	0.0376142	+	0.0376142i
$831$	−9.64057	+	24.2706i	−0.334428	+	0.841939i
$832$	8.43296			0.292360
$833$	−37.2010	+	37.2010i	−1.28894	+	1.28894i
$834$	−10.5140	−	24.3705i	−0.364070	−	0.843881i
$835$	8.16558			0.282581
$836$			30.0787i			1.04029i
$837$	−20.0304	−	7.28672i	−0.692350	−	0.251866i
$838$	2.45325	−	2.45325i	0.0847461	−	0.0847461i
$839$	−36.2480	−	36.2480i	−1.25142	−	1.25142i	−0.955084	−	0.296335i	$-0.904235\pi$
$839$	−36.2480	−	36.2480i	−1.25142	−	1.25142i	−0.296335	−	0.955084i	$-0.595765\pi$
$840$	−1.08383	+	0.467591i	−0.0373958	+	0.0161334i
$841$	7.28606	+	28.0698i	0.251243	+	0.967924i
$842$		−	0.640743i		−	0.0220814i
$843$	8.33600	+	3.31115i	0.287107	+	0.114042i
$844$	25.1854	+	25.1854i	0.866918	+	0.866918i
$845$	−9.55024			−0.328538
$846$	−7.43625	−	7.01420i	−0.255663	−	0.241153i
$847$			2.57747i			0.0885629i
$848$		−	2.30546i		−	0.0791700i
$849$	21.1391	+	8.39667i	0.725491	+	0.288173i
$850$			6.46065i			0.221599i
$851$	−5.91070	−	5.91070i	−0.202616	−	0.202616i
$852$	−11.6834	−	4.64076i	−0.400266	−	0.158990i
$853$	10.8931	−	10.8931i	0.372973	−	0.372973i	−0.495586	−	0.868559i	$-0.665047\pi$
$853$	10.8931	−	10.8931i	0.372973	−	0.372973i	0.868559	+	0.495586i	$0.165047\pi$
$854$	1.74622			0.0597543
$855$	0.445557	+	15.2552i	0.0152377	+	0.521716i
$856$	14.3509	−	14.3509i	0.490503	−	0.490503i
$857$			38.8605i			1.32745i	0.747977	+	0.663724i	$0.231025\pi$
$857$			38.8605i			1.32745i	−0.747977	+	0.663724i	$0.768975\pi$
$858$	4.69890	−	11.8297i	0.160418	−	0.403861i
$859$	−15.7764	+	15.7764i	−0.538283	+	0.538283i	−0.923025	−	0.384741i	$-0.874291\pi$
$859$	−15.7764	+	15.7764i	−0.538283	+	0.538283i	0.384741	+	0.923025i	$0.374291\pi$
$860$	−7.27354	+	7.27354i	−0.248026	+	0.248026i
$861$	−0.850396	+	0.366881i	−0.0289814	+	0.0125033i
$862$	−24.0679	−	24.0679i	−0.819758	−	0.819758i
$863$	10.7064			0.364449			0.182225	−	0.983257i	$-0.441670\pi$
$863$	10.7064			0.364449			0.182225	+	0.983257i	$0.441670\pi$
$864$	−10.1687	+	27.9526i	−0.345946	+	0.950966i
$865$	−19.9281			−0.677577
$866$			4.45438i			0.151366i
$867$	−65.1315	−	25.8710i	−2.21198	−	0.878624i
$868$	0.902334	−	0.902334i	0.0306272	−	0.0306272i
$869$	15.3505			0.520729
$870$	−1.97538	+	7.70030i	−0.0669715	+	0.261065i
$871$	−3.64337			−0.123451
$872$	−4.68103	+	4.68103i	−0.158520	+	0.158520i
$873$	7.28870	−	0.212881i	0.246685	−	0.00720491i
$874$			5.50153i			0.186092i
$875$	0.244261			0.00825753
$876$	19.6806	−	8.49068i	0.664947	−	0.286874i
$877$	27.1524			0.916872			0.458436	−	0.888727i	$-0.348410\pi$
$877$	27.1524			0.916872			0.458436	+	0.888727i	$0.348410\pi$
$878$	14.1771	+	14.1771i	0.478454	+	0.478454i
$879$	18.2069	+	42.2021i	0.614105	+	1.42344i
$880$	0.555634	−	0.555634i	0.0187304	−	0.0187304i
$881$	−28.0263	+	28.0263i	−0.944231	+	0.944231i	−0.998525	−	0.0542940i	$-0.982709\pi$
$881$	−28.0263	+	28.0263i	−0.944231	+	0.944231i	0.0542940	+	0.998525i	$0.482709\pi$
$882$	−17.7380	+	0.518072i	−0.597269	+	0.0174444i
$883$		−	25.1815i		−	0.847426i	−0.905796	−	0.423713i	$-0.860726\pi$
$883$		−	25.1815i		−	0.847426i	0.905796	−	0.423713i	$-0.139274\pi$
$884$	12.6795	−	12.6795i	0.426458	−	0.426458i
$885$	11.1651	+	4.43491i	0.375311	+	0.149078i
$886$	−15.5751			−0.523256
$887$	22.7054	−	22.7054i	0.762371	−	0.762371i	−0.214379	−	0.976750i	$-0.568773\pi$
$887$	22.7054	−	22.7054i	0.762371	−	0.762371i	0.976750	+	0.214379i	$0.0687729\pi$
$888$	−11.7523	+	29.5870i	−0.394380	+	0.992874i
$889$	−1.42051	−	1.42051i	−0.0476424	−	0.0476424i
$890$			15.4909i			0.519256i
$891$	31.2182	+	27.7695i	1.04585	+	0.930314i
$892$		−	31.0363i		−	1.03917i
$893$		−	20.3387i		−	0.680609i
$894$	−1.03987	−	2.41032i	−0.0347784	−	0.0806132i
$895$	−21.0190			−0.702588
$896$	−1.30905	−	1.30905i	−0.0437323	−	0.0437323i
$897$	−1.50688	+	3.79365i	−0.0503133	+	0.126666i
$898$			0.501935i			0.0167498i
$899$	−2.79750	−	21.9120i	−0.0933017	−	0.730808i
$900$	2.62169	−	2.77944i	0.0873896	−	0.0926480i
$901$	73.0085	+	73.0085i	2.43227	+	2.43227i
$902$	−6.12477	+	6.12477i	−0.203932	+	0.203932i
$903$	3.13745	−	1.35357i	0.104408	−	0.0450439i
$904$			12.0716i			0.401495i
$905$	−21.2588			−0.706667
$906$	−12.7258	+	5.49022i	−0.422788	+	0.182400i
$907$	−7.46460	+	7.46460i	−0.247858	+	0.247858i	−0.820091	−	0.572233i	$-0.806077\pi$
$907$	−7.46460	+	7.46460i	−0.247858	+	0.247858i	0.572233	+	0.820091i	$0.306077\pi$
$908$	26.8392			0.890689
$909$	8.04948	−	0.235101i	0.266984	−	0.00779780i
$910$	0.273414	+	0.273414i	0.00906360	+	0.00906360i
$911$	16.7581	+	16.7581i	0.555221	+	0.555221i	0.927943	−	0.372722i	$-0.121576\pi$
$911$	16.7581	+	16.7581i	0.555221	+	0.555221i	−0.372722	+	0.927943i	$0.621576\pi$
$912$	−1.36942	+	0.590797i	−0.0453459	+	0.0195633i
$913$	5.90267	+	5.90267i	0.195350	+	0.195350i
$914$	−21.1857	−	21.1857i	−0.700760	−	0.700760i
$915$	−13.3399	+	5.75512i	−0.441002	+	0.190259i
$916$	−6.22337	−	6.22337i	−0.205626	−	0.205626i
$917$	−0.424393	−	0.424393i	−0.0140147	−	0.0140147i
$918$	−14.1925	−	30.4229i	−0.468423	−	1.00411i
$919$	−28.4909			−0.939829			−0.469914	−	0.882712i	$-0.655715\pi$
$919$	−28.4909			−0.939829			−0.469914	+	0.882712i	$0.655715\pi$
$920$	2.50330	−	2.50330i	0.0825314	−	0.0825314i
$921$	−42.9804	+	18.5427i	−1.41625	+	0.611003i
$922$	−9.96310			−0.328117
$923$			10.5848i			0.348402i
$924$	−2.29682	+	0.990903i	−0.0755600	+	0.0325983i
$925$	4.65826	−	4.65826i	0.153163	−	0.153163i
$926$	8.26015	+	8.26015i	0.271445	+	0.271445i
$927$	−28.1185	−	26.5226i	−0.923532	−	0.871116i
$928$	−30.5785	+	3.90394i	−1.00379	+	0.128153i
$929$		−	11.7201i		−	0.384524i	−0.981344	−	0.192262i	$-0.938418\pi$
$929$		−	11.7201i		−	0.384524i	0.981344	−	0.192262i	$-0.0615823\pi$
$930$	2.23538	−	5.62770i	0.0733011	−	0.184539i
$931$	−24.9659	−	24.9659i	−0.818223	−	0.818223i
$932$	−7.35449			−0.240904
$933$	−5.28980	−	12.2613i	−0.173180	−	0.401416i
$934$			18.5715i			0.607678i
$935$			35.1912i			1.15087i
$936$	15.5398	−	0.453869i	0.507933	−	0.0148352i
$937$			20.4646i			0.668549i	0.942476	+	0.334274i	$0.108491\pi$
$937$			20.4646i			0.668549i	−0.942476	+	0.334274i	$0.891509\pi$
$938$	−0.288759	−	0.288759i	−0.00942830	−	0.00942830i
$939$	−8.30025	+	20.8963i	−0.270868	+	0.681926i
$940$	−3.60048	+	3.60048i	−0.117435	+	0.117435i
$941$	60.8477			1.98358			0.991789	−	0.127887i	$-0.0408193\pi$
$941$	60.8477			1.98358			0.991789	+	0.127887i	$0.0408193\pi$
$942$	−27.1027	−	10.7655i	−0.883053	−	0.350758i
$943$	1.96414	−	1.96414i	0.0639611	−	0.0639611i
$944$			1.17402i			0.0382110i
$945$	−1.15021	+	0.536584i	−0.0374164	+	0.0174551i
$946$	22.5967	−	22.5967i	0.734682	−	0.734682i
$947$	−32.4378	+	32.4378i	−1.05409	+	1.05409i	−0.0556374	+	0.998451i	$0.517719\pi$
$947$	−32.4378	+	32.4378i	−1.05409	+	1.05409i	−0.998451	+	0.0556374i	$0.982281\pi$
$948$	2.88941	+	6.69739i	0.0938436	+	0.217521i
$949$	−12.7612	−	12.7612i	−0.414245	−	0.414245i
$950$	−4.33579			−0.140672
$951$	−41.8903	+	18.0724i	−1.35839	+	0.586039i
$952$	5.16602			0.167432
$953$		−	30.3784i		−	0.984054i	−0.870580	−	0.492027i	$-0.836256\pi$
$953$		−	30.3784i		−	0.984054i	0.870580	−	0.492027i	$-0.163744\pi$
$954$	1.01674	+	34.8115i	0.0329181	+	1.12707i
$955$	10.0502	−	10.0502i	0.325217	−	0.325217i
$956$	−8.05701			−0.260582
$957$	−10.7599	+	41.9435i	−0.347817	+	1.35584i
$958$	16.0741			0.519332
$959$	−0.282746	+	0.282746i	−0.00913036	+	0.00913036i
$960$	−7.30859	−	2.90305i	−0.235884	−	0.0936956i
$961$		−	14.1737i		−	0.457215i
$962$	10.4285			0.336228
$963$	14.9737	−	15.8746i	0.482520	−	0.511553i
$964$	−22.6305			−0.728880
$965$	−12.9332	−	12.9332i	−0.416336	−	0.416336i
$966$	−0.420099	+	0.181240i	−0.0135165	+	0.00583131i
$967$	−18.4244	+	18.4244i	−0.592490	+	0.592490i	−0.938303	−	0.345813i	$-0.887603\pi$
$967$	−18.4244	+	18.4244i	−0.592490	+	0.592490i	0.345813	+	0.938303i	$0.387603\pi$
$968$	−20.8179	+	20.8179i	−0.669114	+	0.669114i
$969$	24.6569	−	62.0752i	0.792095	−	1.99414i
$970$			2.07158i			0.0665144i
$971$	26.6867	−	26.6867i	0.856419	−	0.856419i	−0.134496	−	0.990914i	$-0.542941\pi$
$971$	26.6867	−	26.6867i	0.856419	−	0.856419i	0.990914	+	0.134496i	$0.0429414\pi$
$972$	−6.23963	+	18.8475i	−0.200136	+	0.604533i
$973$	4.39173			0.140792
$974$	−13.2663	+	13.2663i	−0.425078	+	0.425078i
$975$	−2.98981	−	1.18758i	−0.0957504	−	0.0380331i
$976$	−1.00392	−	1.00392i	−0.0321348	−	0.0321348i
$977$		−	29.5378i		−	0.944997i	−0.881331	−	0.472499i	$-0.843352\pi$
$977$		−	29.5378i		−	0.944997i	0.881331	−	0.472499i	$-0.156648\pi$
$978$	15.5445	+	6.17444i	0.497058	+	0.197437i
$979$			84.3789i			2.69676i
$980$			8.83922i			0.282359i
$981$	−4.88417	+	5.17806i	−0.155940	+	0.165323i
$982$	−4.58214			−0.146222
$983$	17.7320	+	17.7320i	0.565564	+	0.565564i	0.930883	−	0.365318i	$-0.119040\pi$
$983$	17.7320	+	17.7320i	0.565564	+	0.565564i	−0.365318	+	0.930883i	$0.619040\pi$
$984$	−9.83181	−	3.90530i	−0.313427	−	0.124497i
$985$		−	5.64371i		−	0.179824i
$986$	21.2878	−	27.5189i	0.677942	−	0.876381i
$987$	1.55307	−	0.670031i	0.0494349	−	0.0213273i
$988$	8.50930	+	8.50930i	0.270717	+	0.270717i
$989$	−7.24648	+	7.24648i	−0.230425	+	0.230425i
$990$	−8.14480	+	8.63488i	−0.258859	+	0.274434i
$991$		−	35.7897i		−	1.13690i	−0.822719	−	0.568449i	$-0.807544\pi$
$991$		−	35.7897i		−	1.13690i	0.822719	−	0.568449i	$-0.192456\pi$
$992$	23.4814			0.745534
$993$	12.1686	+	28.2058i	0.386160	+	0.895084i
$994$	−0.838906	+	0.838906i	−0.0266085	+	0.0266085i
$995$	−20.8547			−0.661140
$996$	−1.46427	+	3.68638i	−0.0463972	+	0.116808i
$997$	4.95348	+	4.95348i	0.156878	+	0.156878i	0.781182	−	0.624304i	$-0.214617\pi$
$997$	4.95348	+	4.95348i	0.156878	+	0.156878i	−0.624304	+	0.781182i	$0.714617\pi$
$998$	16.8122	+	16.8122i	0.532180	+	0.532180i
$999$	−11.7024	+	32.1686i	−0.370248	+	1.01777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.q.c.41.7	✓	36
3.2	odd	2		435.2.q.d.41.12	yes	36
29.17	odd	4		435.2.q.d.191.12	yes	36
87.17	even	4	inner	435.2.q.c.191.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.q.c.41.7	✓	36	1.1	even	1	trivial
435.2.q.c.191.7	yes	36	87.17	even	4	inner
435.2.q.d.41.12	yes	36	3.2	odd	2
435.2.q.d.191.12	yes	36	29.17	odd	4

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.602660 + 0.602660i) q^{2} +(0.639395 - 1.60971i) q^{3} +1.27360i q^{4} -1.00000 q^{5} +(0.584771 + 1.35545i) q^{6} -0.244261 q^{7} +(-1.97287 - 1.97287i) q^{8} +(-2.18235 - 2.05849i) q^{9} +O(q^{10})\)	\(q+(-0.602660 + 0.602660i) q^{2} +(0.639395 - 1.60971i) q^{3} +1.27360i q^{4} -1.00000 q^{5} +(0.584771 + 1.35545i) q^{6} -0.244261 q^{7} +(-1.97287 - 1.97287i) q^{8} +(-2.18235 - 2.05849i) q^{9} +(0.602660 - 0.602660i) q^{10} +(3.28269 - 3.28269i) q^{11} +(2.05013 + 0.814335i) q^{12} -1.85735i q^{13} +(0.147206 - 0.147206i) q^{14} +(-0.639395 + 1.60971i) q^{15} -0.169262 q^{16} +(5.36011 - 5.36011i) q^{17} +(2.55578 - 0.0746466i) q^{18} +(3.59721 + 3.59721i) q^{19} -1.27360i q^{20} +(-0.156179 + 0.393190i) q^{21} +3.95669i q^{22} -1.26886i q^{23} +(-4.43720 + 1.91431i) q^{24} +1.00000 q^{25} +(1.11935 + 1.11935i) q^{26} +(-4.70895 + 2.19676i) q^{27} -0.311091i q^{28} +(-4.25946 - 3.29499i) q^{29} +(-0.584771 - 1.35545i) q^{30} +(2.90055 + 2.90055i) q^{31} +(4.04775 - 4.04775i) q^{32} +(-3.18525 - 7.38312i) q^{33} +6.46065i q^{34} +0.244261 q^{35} +(2.62169 - 2.77944i) q^{36} +(4.65826 - 4.65826i) q^{37} -4.33579 q^{38} +(-2.98981 - 1.18758i) q^{39} +(1.97287 + 1.97287i) q^{40} +(1.54795 + 1.54795i) q^{41} +(-0.142837 - 0.331083i) q^{42} +(-5.71100 - 5.71100i) q^{43} +(4.18084 + 4.18084i) q^{44} +(2.18235 + 2.05849i) q^{45} +(0.764693 + 0.764693i) q^{46} +(-2.82701 - 2.82701i) q^{47} +(-0.108225 + 0.272463i) q^{48} -6.94034 q^{49} +(-0.602660 + 0.602660i) q^{50} +(-5.20101 - 12.0555i) q^{51} +2.36553 q^{52} +13.6207i q^{53} +(1.51400 - 4.16180i) q^{54} +(-3.28269 + 3.28269i) q^{55} +(0.481895 + 0.481895i) q^{56} +(8.09052 - 3.49043i) q^{57} +(4.55277 - 0.581249i) q^{58} -6.93609i q^{59} +(-2.05013 - 0.814335i) q^{60} +(5.93118 + 5.93118i) q^{61} -3.49609 q^{62} +(0.533062 + 0.502808i) q^{63} +4.54031i q^{64} +1.85735i q^{65} +(6.36914 + 2.52989i) q^{66} -1.96159i q^{67} +(6.82664 + 6.82664i) q^{68} +(-2.04250 - 0.811305i) q^{69} +(-0.147206 + 0.147206i) q^{70} -5.69884 q^{71} +(0.244363 + 8.36661i) q^{72} +(6.87061 - 6.87061i) q^{73} +5.61470i q^{74} +(0.639395 - 1.60971i) q^{75} +(-4.58141 + 4.58141i) q^{76} +(-0.801833 + 0.801833i) q^{77} +(2.51755 - 1.08613i) q^{78} +(2.33809 + 2.33809i) q^{79} +0.169262 q^{80} +(0.525277 + 8.98466i) q^{81} -1.86578 q^{82} +1.79812i q^{83} +(-0.500767 - 0.198910i) q^{84} +(-5.36011 + 5.36011i) q^{85} +6.88359 q^{86} +(-8.02747 + 4.74971i) q^{87} -12.9526 q^{88} +(-12.8521 + 12.8521i) q^{89} +(-2.55578 + 0.0746466i) q^{90} +0.453679i q^{91} +1.61602 q^{92} +(6.52364 - 2.81445i) q^{93} +3.40745 q^{94} +(-3.59721 - 3.59721i) q^{95} +(-3.92760 - 9.10382i) q^{96} +(-1.71869 + 1.71869i) q^{97} +(4.18267 - 4.18267i) q^{98} +(-13.9213 + 0.406600i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8	\( 36 q - 4 q^{2} + 6 q^{3} - 36 q^{5} + 8 q^{6} + 8 q^{7} + 4 q^{8} + 4 q^{10} - 12 q^{11} + 10 q^{12} + 28 q^{14} - 6 q^{15} - 60 q^{16} - 20 q^{17} - 28 q^{18} + 16 q^{19} + 12 q^{21} + 24 q^{24} + 36 q^{25} + 4 q^{26} + 30 q^{27} - 28 q^{29} - 8 q^{30} - 8 q^{31} - 16 q^{32} - 8 q^{33} - 8 q^{35} - 28 q^{36} - 4 q^{37} + 24 q^{38} - 40 q^{39} - 4 q^{40} + 48 q^{41} - 8 q^{42} + 4 q^{43} + 16 q^{44} + 20 q^{46} - 20 q^{47} - 14 q^{48} + 28 q^{49} - 4 q^{50} - 44 q^{52} - 24 q^{54} + 12 q^{55} - 84 q^{56} + 28 q^{57} - 64 q^{58} - 10 q^{60} + 20 q^{61} + 8 q^{62} + 32 q^{63} + 40 q^{66} + 60 q^{68} + 36 q^{69} - 28 q^{70} - 16 q^{71} - 132 q^{72} + 8 q^{73} + 6 q^{75} + 16 q^{76} + 32 q^{77} + 48 q^{78} + 12 q^{79} + 60 q^{80} - 60 q^{81} + 56 q^{82} + 44 q^{84} + 20 q^{85} + 8 q^{86} + 22 q^{87} - 24 q^{88} + 20 q^{89} + 28 q^{90} - 16 q^{92} + 24 q^{93} + 52 q^{94} - 16 q^{95} - 8 q^{96} + 4 q^{97} - 8 q^{98} - 48 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 + 6 * q^3 - 36 * q^5 + 8 * q^6 + 8 * q^7 + 4 * q^8 + 4 * q^10 - 12 * q^11 + 10 * q^12 + 28 * q^14 - 6 * q^15 - 60 * q^16 - 20 * q^17 - 28 * q^18 + 16 * q^19 + 12 * q^21 + 24 * q^24 + 36 * q^25 + 4 * q^26 + 30 * q^27 - 28 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 8 * q^33 - 8 * q^35 - 28 * q^36 - 4 * q^37 + 24 * q^38 - 40 * q^39 - 4 * q^40 + 48 * q^41 - 8 * q^42 + 4 * q^43 + 16 * q^44 + 20 * q^46 - 20 * q^47 - 14 * q^48 + 28 * q^49 - 4 * q^50 - 44 * q^52 - 24 * q^54 + 12 * q^55 - 84 * q^56 + 28 * q^57 - 64 * q^58 - 10 * q^60 + 20 * q^61 + 8 * q^62 + 32 * q^63 + 40 * q^66 + 60 * q^68 + 36 * q^69 - 28 * q^70 - 16 * q^71 - 132 * q^72 + 8 * q^73 + 6 * q^75 + 16 * q^76 + 32 * q^77 + 48 * q^78 + 12 * q^79 + 60 * q^80 - 60 * q^81 + 56 * q^82 + 44 * q^84 + 20 * q^85 + 8 * q^86 + 22 * q^87 - 24 * q^88 + 20 * q^89 + 28 * q^90 - 16 * q^92 + 24 * q^93 + 52 * q^94 - 16 * q^95 - 8 * q^96 + 4 * q^97 - 8 * q^98 - 48 * q^99

Introduction

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