LMFDB - Embedded newform 696.2.v.c.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [696,2,Mod(307,696)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(696, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("696.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 696 = 2^{3} \cdot 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	696.v (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:	$5.55758798068$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	696.307
Dual form			696.2.v.c.331.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40949 - 0.115545i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97330 + 0.325717i) q^{4} +0.914898 q^{5} +(1.07836 - 0.914954i) q^{6} -4.64436i q^{7} +(-2.74370 - 0.687098i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.40949 - 0.115545i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97330 + 0.325717i) q^{4} +0.914898 q^{5} +(1.07836 - 0.914954i) q^{6} -4.64436i q^{7} +(-2.74370 - 0.687098i) q^{8} -1.00000i q^{9} +(-1.28954 - 0.105712i) q^{10} +(-4.28648 + 4.28648i) q^{11} +(-1.62565 + 1.16502i) q^{12} -3.84591 q^{13} +(-0.536631 + 6.54615i) q^{14} +(-0.646931 + 0.646931i) q^{15} +(3.78782 + 1.28547i) q^{16} +(2.58168 - 2.58168i) q^{17} +(-0.115545 + 1.40949i) q^{18} +(-2.90974 + 2.90974i) q^{19} +(1.80537 + 0.297998i) q^{20} +(3.28406 + 3.28406i) q^{21} +(6.53702 - 5.54646i) q^{22} +6.96381i q^{23} +(2.42594 - 1.45424i) q^{24} -4.16296 q^{25} +(5.42075 + 0.444374i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.51275 - 9.16470i) q^{28} +(2.41585 + 4.81287i) q^{29} +(0.986589 - 0.837090i) q^{30} +(3.26099 + 3.26099i) q^{31} +(-5.19034 - 2.24952i) q^{32} -6.06200i q^{33} +(-3.93713 + 3.34054i) q^{34} -4.24911i q^{35} +(0.325717 - 1.97330i) q^{36} +(1.05641 - 1.05641i) q^{37} +(4.43744 - 3.76503i) q^{38} +(2.71947 - 2.71947i) q^{39} +(-2.51021 - 0.628624i) q^{40} +(4.83041 + 4.83041i) q^{41} +(-4.24937 - 5.00828i) q^{42} +(-2.12803 + 2.12803i) q^{43} +(-9.85470 + 7.06233i) q^{44} -0.914898i q^{45} +(0.804631 - 9.81538i) q^{46} +(-5.07419 + 5.07419i) q^{47} +(-3.58736 + 1.76942i) q^{48} -14.5700 q^{49} +(5.86763 + 0.481008i) q^{50} +3.65104i q^{51} +(-7.58912 - 1.25268i) q^{52} -3.49667i q^{53} +(-0.914954 - 1.07836i) q^{54} +(-3.92170 + 3.92170i) q^{55} +(-3.19113 + 12.7427i) q^{56} -4.11499i q^{57} +(-2.84900 - 7.06280i) q^{58} -12.5194 q^{59} +(-1.48730 + 1.06587i) q^{60} +(1.79447 + 1.79447i) q^{61} +(-4.21953 - 4.97311i) q^{62} -4.64436 q^{63} +(7.05579 + 3.77038i) q^{64} -3.51861 q^{65} +(-0.700432 + 8.54431i) q^{66} +1.37311i q^{67} +(5.93531 - 4.25352i) q^{68} +(-4.92415 - 4.92415i) q^{69} +(-0.490962 + 5.98906i) q^{70} -2.00078 q^{71} +(-0.687098 + 2.74370i) q^{72} +(10.6864 + 10.6864i) q^{73} +(-1.61106 + 1.36693i) q^{74} +(2.94366 - 2.94366i) q^{75} +(-6.68954 + 4.79403i) q^{76} +(19.9080 + 19.9080i) q^{77} +(-4.14727 + 3.51883i) q^{78} +(-10.0272 - 10.0272i) q^{79} +(3.46547 + 1.17608i) q^{80} -1.00000 q^{81} +(-6.25026 - 7.36652i) q^{82} +1.33327 q^{83} +(5.41075 + 7.55010i) q^{84} +(2.36197 - 2.36197i) q^{85} +(3.24531 - 2.75355i) q^{86} +(-5.11147 - 1.69495i) q^{87} +(14.7061 - 8.81560i) q^{88} +(-3.89289 + 3.89289i) q^{89} +(-0.105712 + 1.28954i) q^{90} +17.8618i q^{91} +(-2.26823 + 13.7417i) q^{92} -4.61174 q^{93} +(7.73829 - 6.56570i) q^{94} +(-2.66211 + 2.66211i) q^{95} +(5.26078 - 2.07948i) q^{96} +(-0.137310 - 0.137310i) q^{97} +(20.5363 + 1.68349i) q^{98} +(4.28648 + 4.28648i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 4 q^{2} - 4 q^{8}+O(q^{10}) $ 112 * q - 4 * q^2 - 4 * q^8	$ 112 q - 4 q^{2} - 4 q^{8} - 24 q^{11} - 4 q^{14} - 24 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{19} - 16 q^{20} - 4 q^{24} + 168 q^{25} + 4 q^{26} - 40 q^{30} + 16 q^{32} - 12 q^{40} - 24 q^{41} - 8 q^{43} + 52 q^{44} + 36 q^{46} - 32 q^{48} - 152 q^{49} + 36 q^{50} - 44 q^{52} + 8 q^{54} - 56 q^{56} - 16 q^{58} - 8 q^{59} - 24 q^{60} + 48 q^{66} - 36 q^{68} - 60 q^{70} - 4 q^{72} + 32 q^{73} + 64 q^{74} + 8 q^{76} + 36 q^{78} - 112 q^{81} + 16 q^{82} - 64 q^{83} - 24 q^{84} + 40 q^{88} - 8 q^{89} - 68 q^{94} + 8 q^{97} + 56 q^{98} + 24 q^{99}+O(q^{100}) $ 112 * q - 4 * q^2 - 4 * q^8 - 24 * q^11 - 4 * q^14 - 24 * q^16 + 8 * q^17 + 4 * q^18 - 8 * q^19 - 16 * q^20 - 4 * q^24 + 168 * q^25 + 4 * q^26 - 40 * q^30 + 16 * q^32 - 12 * q^40 - 24 * q^41 - 8 * q^43 + 52 * q^44 + 36 * q^46 - 32 * q^48 - 152 * q^49 + 36 * q^50 - 44 * q^52 + 8 * q^54 - 56 * q^56 - 16 * q^58 - 8 * q^59 - 24 * q^60 + 48 * q^66 - 36 * q^68 - 60 * q^70 - 4 * q^72 + 32 * q^73 + 64 * q^74 + 8 * q^76 + 36 * q^78 - 112 * q^81 + 16 * q^82 - 64 * q^83 - 24 * q^84 + 40 * q^88 - 8 * q^89 - 68 * q^94 + 8 * q^97 + 56 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/696\mathbb{Z}\right)^\times$.

$n$	$175$	$233$	$349$	$553$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.40949	−	0.115545i	−0.996657	−	0.0817024i
$2$	−1.40949	−	0.115545i	−0.996657	−	0.0817024i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.97330	+	0.325717i	0.986649	+	0.162859i
$5$	0.914898			0.409155			0.204577	−	0.978850i	$-0.434418\pi$
$5$	0.914898			0.409155			0.204577	+	0.978850i	$0.434418\pi$
$6$	1.07836	−	0.914954i	0.440238	−	0.373529i
$7$		−	4.64436i		−	1.75540i	−0.479209	−	0.877701i	$-0.659076\pi$
$7$		−	4.64436i		−	1.75540i	0.479209	−	0.877701i	$-0.340924\pi$
$8$	−2.74370	−	0.687098i	−0.970045	−	0.242926i
$9$		−	1.00000i		−	0.333333i
$10$	−1.28954	−	0.105712i	−0.407787	−	0.0334289i
$11$	−4.28648	+	4.28648i	−1.29242	+	1.29242i	−0.359140	+	0.933284i	$0.616930\pi$
$11$	−4.28648	+	4.28648i	−1.29242	+	1.29242i	−0.933284	+	0.359140i	$0.883070\pi$
$12$	−1.62565	+	1.16502i	−0.469285	+	0.336311i
$13$	−3.84591			−1.06666			−0.533331	−	0.845907i	$-0.679060\pi$
$13$	−3.84591			−1.06666			−0.533331	+	0.845907i	$0.679060\pi$
$14$	−0.536631	+	6.54615i	−0.143421	+	1.74953i
$15$	−0.646931	+	0.646931i	−0.167037	+	0.167037i
$16$	3.78782	+	1.28547i	0.946954	+	0.321369i
$17$	2.58168	−	2.58168i	0.626148	−	0.626148i	−0.320948	−	0.947097i	$-0.604002\pi$
$17$	2.58168	−	2.58168i	0.626148	−	0.626148i	0.947097	+	0.320948i	$0.104002\pi$
$18$	−0.115545	+	1.40949i	−0.0272341	+	0.332219i
$19$	−2.90974	+	2.90974i	−0.667540	+	0.667540i	−0.957146	−	0.289606i	$-0.906476\pi$
$19$	−2.90974	+	2.90974i	−0.667540	+	0.667540i	0.289606	+	0.957146i	$0.406476\pi$
$20$	1.80537	+	0.297998i	0.403692	+	0.0666344i
$21$	3.28406	+	3.28406i	0.716640	+	0.716640i
$22$	6.53702	−	5.54646i	1.39370	−	1.18251i
$23$			6.96381i			1.45205i	0.687666	+	0.726027i	$0.258635\pi$
$23$			6.96381i			1.45205i	−0.687666	+	0.726027i	$0.741365\pi$
$24$	2.42594	−	1.45424i	0.495193	−	0.296845i
$25$	−4.16296			−0.832592
$26$	5.42075	+	0.444374i	1.06310	+	0.0871489i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.51275	−	9.16470i	0.285882	−	1.73197i
$29$	2.41585	+	4.81287i	0.448611	+	0.893727i
$29$	2.41585	+	4.81287i	0.448611	+	0.893727i
$30$	0.986589	−	0.837090i	0.180126	−	0.152831i
$31$	3.26099	+	3.26099i	0.585692	+	0.585692i	0.936462	−	0.350770i	$-0.114080\pi$
$31$	3.26099	+	3.26099i	0.585692	+	0.585692i	−0.350770	+	0.936462i	$0.614080\pi$
$32$	−5.19034	−	2.24952i	−0.917532	−	0.397663i
$33$		−	6.06200i		−	1.05526i
$34$	−3.93713	+	3.34054i	−0.675213	+	0.572897i
$35$		−	4.24911i		−	0.718231i
$36$	0.325717	−	1.97330i	0.0542862	−	0.328883i
$37$	1.05641	−	1.05641i	0.173673	−	0.173673i	−0.614918	−	0.788591i	$-0.710811\pi$
$37$	1.05641	−	1.05641i	0.173673	−	0.173673i	0.788591	+	0.614918i	$0.210811\pi$
$38$	4.43744	−	3.76503i	0.719848	−	0.610769i
$39$	2.71947	−	2.71947i	0.435463	−	0.435463i
$40$	−2.51021	−	0.628624i	−0.396899	−	0.0993942i
$41$	4.83041	+	4.83041i	0.754383	+	0.754383i	0.975294	−	0.220911i	$-0.0709030\pi$
$41$	4.83041	+	4.83041i	0.754383	+	0.754383i	−0.220911	+	0.975294i	$0.570903\pi$
$42$	−4.24937	−	5.00828i	−0.655693	−	0.772795i
$43$	−2.12803	+	2.12803i	−0.324522	+	0.324522i	−0.850499	−	0.525977i	$-0.823700\pi$
$43$	−2.12803	+	2.12803i	−0.324522	+	0.324522i	0.525977	+	0.850499i	$0.323700\pi$
$44$	−9.85470	+	7.06233i	−1.48565	+	1.06469i
$45$		−	0.914898i		−	0.136385i
$46$	0.804631	−	9.81538i	0.118636	−	1.44720i
$47$	−5.07419	+	5.07419i	−0.740146	+	0.740146i	−0.972606	−	0.232460i	$-0.925323\pi$
$47$	−5.07419	+	5.07419i	−0.740146	+	0.740146i	0.232460	+	0.972606i	$0.425323\pi$
$48$	−3.58736	+	1.76942i	−0.517791	+	0.255394i
$49$	−14.5700			−2.08144
$50$	5.86763	+	0.481008i	0.829809	+	0.0680248i
$51$			3.65104i			0.511248i
$52$	−7.58912	−	1.25268i	−1.05242	−	0.173715i
$53$		−	3.49667i		−	0.480304i	−0.970735	−	0.240152i	$-0.922803\pi$
$53$		−	3.49667i		−	0.480304i	0.970735	−	0.240152i	$-0.0771973\pi$
$54$	−0.914954	−	1.07836i	−0.124510	−	0.146746i
$55$	−3.92170	+	3.92170i	−0.528801	+	0.528801i
$56$	−3.19113	+	12.7427i	−0.426432	+	1.70282i
$57$		−	4.11499i		−	0.545044i
$58$	−2.84900	−	7.06280i	−0.374092	−	0.927392i
$59$	−12.5194			−1.62989			−0.814945	−	0.579538i	$-0.803233\pi$
$59$	−12.5194			−1.62989			−0.814945	+	0.579538i	$0.803233\pi$
$60$	−1.48730	+	1.06587i	−0.192010	+	0.137603i
$61$	1.79447	+	1.79447i	0.229759	+	0.229759i	0.812592	−	0.582833i	$-0.198056\pi$
$61$	1.79447	+	1.79447i	0.229759	+	0.229759i	−0.582833	+	0.812592i	$0.698056\pi$
$62$	−4.21953	−	4.97311i	−0.535881	−	0.631586i
$63$	−4.64436			−0.585134
$64$	7.05579	+	3.77038i	0.881974	+	0.471298i
$65$	−3.51861			−0.436430
$66$	−0.700432	+	8.54431i	−0.0862173	+	1.05173i
$67$			1.37311i			0.167752i	0.996476	+	0.0838759i	$0.0267299\pi$
$67$			1.37311i			0.167752i	−0.996476	+	0.0838759i	$0.973270\pi$
$68$	5.93531	−	4.25352i	0.719762	−	0.515815i
$69$	−4.92415	−	4.92415i	−0.592799	−	0.592799i
$70$	−0.490962	+	5.98906i	−0.0586812	+	0.715830i
$71$	−2.00078			−0.237449			−0.118724	−	0.992927i	$-0.537880\pi$
$71$	−2.00078			−0.237449			−0.118724	+	0.992927i	$0.537880\pi$
$72$	−0.687098	+	2.74370i	−0.0809752	+	0.323348i
$73$	10.6864	+	10.6864i	1.25074	+	1.25074i	0.955387	+	0.295358i	$0.0954388\pi$
$73$	10.6864	+	10.6864i	1.25074	+	1.25074i	0.295358	+	0.955387i	$0.404561\pi$
$74$	−1.61106	+	1.36693i	−0.187282	+	0.158903i
$75$	2.94366	−	2.94366i	0.339904	−	0.339904i
$76$	−6.68954	+	4.79403i	−0.767342	+	0.549913i
$77$	19.9080	+	19.9080i	2.26872	+	2.26872i
$78$	−4.14727	+	3.51883i	−0.469586	+	0.398429i
$79$	−10.0272	−	10.0272i	−1.12814	−	1.12814i	−0.990479	−	0.137665i	$-0.956040\pi$
$79$	−10.0272	−	10.0272i	−1.12814	−	1.12814i	−0.137665	−	0.990479i	$-0.543960\pi$
$80$	3.46547	+	1.17608i	0.387451	+	0.131490i
$81$	−1.00000			−0.111111
$82$	−6.25026	−	7.36652i	−0.690226	−	0.813496i
$83$	1.33327			0.146345			0.0731725	−	0.997319i	$-0.476688\pi$
$83$	1.33327			0.146345			0.0731725	+	0.997319i	$0.476688\pi$
$84$	5.41075	+	7.55010i	0.590361	+	0.823783i
$85$	2.36197	−	2.36197i	0.256192	−	0.256192i
$86$	3.24531	−	2.75355i	0.349951	−	0.296923i
$87$	−5.11147	−	1.69495i	−0.548007	−	0.181718i
$88$	14.7061	−	8.81560i	1.56767	−	0.939746i
$89$	−3.89289	+	3.89289i	−0.412646	+	0.412646i	−0.882659	−	0.470014i	$-0.844249\pi$
$89$	−3.89289	+	3.89289i	−0.412646	+	0.412646i	0.470014	+	0.882659i	$0.344249\pi$
$90$	−0.105712	+	1.28954i	−0.0111430	+	0.135929i
$91$			17.8618i			1.87242i
$92$	−2.26823	+	13.7417i	−0.236479	+	1.43267i
$93$	−4.61174			−0.478215
$94$	7.73829	−	6.56570i	0.798144	−	0.677200i
$95$	−2.66211	+	2.66211i	−0.273127	+	0.273127i
$96$	5.26078	−	2.07948i	0.536926	−	0.212236i
$97$	−0.137310	−	0.137310i	−0.0139417	−	0.0139417i	0.700102	−	0.714043i	$-0.253138\pi$
$97$	−0.137310	−	0.137310i	−0.0139417	−	0.0139417i	−0.714043	+	0.700102i	$0.753138\pi$
$98$	20.5363	+	1.68349i	2.07448	+	0.170058i
$99$	4.28648	+	4.28648i	0.430808	+	0.430808i
$100$	−8.21477	−	1.35595i	−0.821477	−	0.135595i
$101$	−7.20526	−	7.20526i	−0.716950	−	0.716950i	0.251029	−	0.967980i	$-0.419231\pi$
$101$	−7.20526	−	7.20526i	−0.716950	−	0.716950i	−0.967980	+	0.251029i	$0.919231\pi$
$102$	0.421858	−	5.14609i	0.0417702	−	0.509539i
$103$		−	10.2445i		−	1.00942i	−0.863289	−	0.504710i	$-0.831599\pi$
$103$		−	10.2445i		−	1.00942i	0.863289	−	0.504710i	$-0.168401\pi$
$104$	10.5520	+	2.64251i	1.03471	+	0.259120i
$105$	3.00458	+	3.00458i	0.293217	+	0.293217i
$106$	−0.404021	+	4.92850i	−0.0392420	+	0.478698i
$107$	−9.94126			−0.961058			−0.480529	−	0.876979i	$-0.659555\pi$
$107$	−9.94126			−0.961058			−0.480529	+	0.876979i	$0.659555\pi$
$108$	1.16502	+	1.62565i	0.112104	+	0.156428i
$109$	11.6979			1.12046			0.560230	−	0.828337i	$-0.310713\pi$
$109$	11.6979			1.12046			0.560230	+	0.828337i	$0.310713\pi$
$110$	5.98070	−	5.07444i	0.570238	−	0.483829i
$111$			1.49399i			0.141803i
$112$	5.97020	−	17.5920i	0.564131	−	1.66229i
$113$	−11.1114	−	11.1114i	−1.04527	−	1.04527i	−0.998925	−	0.0463454i	$-0.985243\pi$
$113$	−11.1114	−	11.1114i	−1.04527	−	1.04527i	−0.0463454	−	0.998925i	$-0.514757\pi$
$114$	−0.475465	+	5.80002i	−0.0445314	+	0.543222i
$115$			6.37117i			0.594115i
$116$	3.19955	+	10.2841i	0.297071	+	0.954855i
$117$			3.84591i			0.355554i
$118$	17.6459	+	1.44655i	1.62444	+	0.133166i
$119$	−11.9902	−	11.9902i	−1.09914	−	1.09914i
$120$	2.21949	−	1.33048i	0.202611	−	0.121456i
$121$		−	25.7479i		−	2.34072i
$122$	−2.32194	−	2.73662i	−0.210219	−	0.247762i
$123$	−6.83123			−0.615951
$124$	5.37275	+	7.49708i	0.482488	+	0.673257i
$125$	−8.38317			−0.749814
$126$	6.54615	+	0.536631i	0.583178	+	0.0478069i
$127$	−4.46327	−	4.46327i	−0.396051	−	0.396051i	0.480787	−	0.876838i	$-0.340351\pi$
$127$	−4.46327	−	4.46327i	−0.396051	−	0.396051i	−0.876838	+	0.480787i	$0.840351\pi$
$128$	−9.50939	−	6.12956i	−0.840519	−	0.541782i
$129$		−	3.00949i		−	0.264971i
$130$	4.95943	+	0.406557i	0.434971	+	0.0356574i
$131$	−1.16009	−	1.16009i	−0.101358	−	0.101358i	0.654609	−	0.755967i	$-0.272833\pi$
$131$	−1.16009	−	1.16009i	−0.101358	−	0.101358i	−0.755967	+	0.654609i	$0.772833\pi$
$132$	1.97450	−	11.9621i	0.171858	−	1.04117i
$133$	13.5139	+	13.5139i	1.17180	+	1.17180i
$134$	0.158655	−	1.93538i	0.0137057	−	0.167191i
$135$	0.646931	+	0.646931i	0.0556789	+	0.0556789i
$136$	−8.85721	+	5.30948i	−0.759499	+	0.455284i
$137$	−12.8626	+	12.8626i	−1.09893	+	1.09893i	−0.104394	+	0.994536i	$0.533290\pi$
$137$	−12.8626	+	12.8626i	−1.09893	+	1.09893i	−0.994536	+	0.104394i	$0.966710\pi$
$138$	6.37156	+	7.50948i	0.542384	+	0.639250i
$139$	−2.56351			−0.217434			−0.108717	−	0.994073i	$-0.534674\pi$
$139$	−2.56351			−0.217434			−0.108717	+	0.994073i	$0.534674\pi$
$140$	1.38401	−	8.38477i	0.116970	−	0.708642i
$141$		−	7.17598i		−	0.604327i
$142$	2.82007	+	0.231179i	0.236655	+	0.0194001i
$143$	16.4854	−	16.4854i	1.37858	−	1.37858i
$144$	1.28547	−	3.78782i	0.107123	−	0.315651i
$145$	2.21025	+	4.40328i	0.183552	+	0.365673i
$146$	−13.8275	−	16.2970i	−1.14437	−	1.34875i
$147$	10.3026	−	10.3026i	0.849742	−	0.849742i
$148$	2.42871	−	1.74052i	0.199638	−	0.143070i
$149$	−3.54840			−0.290696			−0.145348	−	0.989381i	$-0.546430\pi$
$149$	−3.54840			−0.290696			−0.145348	+	0.989381i	$0.546430\pi$
$150$	−4.48917	+	3.80892i	−0.366539	+	0.310997i
$151$	1.69205			0.137697			0.0688487	−	0.997627i	$-0.478067\pi$
$151$	1.69205			0.137697			0.0688487	+	0.997627i	$0.478067\pi$
$152$	9.98273	−	5.98418i	0.809706	−	0.485381i
$153$	−2.58168	−	2.58168i	−0.208716	−	0.208716i
$154$	−25.7597	−	30.3602i	−2.07578	−	2.44650i
$155$	2.98348	+	2.98348i	0.239639	+	0.239639i
$156$	6.25210	−	4.48054i	0.500568	−	0.358730i
$157$	13.4234	−	13.4234i	1.07130	−	1.07130i	0.0740459	−	0.997255i	$-0.476409\pi$
$157$	13.4234	−	13.4234i	1.07130	−	1.07130i	0.997255	−	0.0740459i	$-0.0235911\pi$
$158$	12.9746	+	15.2917i	1.03220	+	1.21654i
$159$	2.47252	+	2.47252i	0.196083	+	0.196083i
$160$	−4.74863	−	2.05808i	−0.375412	−	0.162706i
$161$	32.3424			2.54894
$162$	1.40949	+	0.115545i	0.110740	+	0.00907805i
$163$	0.310867	+	0.310867i	0.0243490	+	0.0243490i	0.719176	−	0.694827i	$-0.244519\pi$
$163$	0.310867	+	0.310867i	0.0243490	+	0.0243490i	−0.694827	+	0.719176i	$0.744519\pi$
$164$	7.95849	+	11.1052i	0.621454	+	0.867170i
$165$		−	5.54611i		−	0.431764i
$166$	−1.87922	−	0.154052i	−0.145856	−	0.0119567i
$167$	22.0042			1.70273			0.851366	−	0.524571i	$-0.175774\pi$
$167$	22.0042			1.70273			0.851366	+	0.524571i	$0.175774\pi$
$168$	−6.75400	−	11.2669i	−0.521083	−	0.869263i
$169$	1.79099			0.137768
$170$	−3.60207	+	3.05625i	−0.276267	+	0.234404i
$171$	2.90974	+	2.90974i	0.222513	+	0.222513i
$172$	−4.89238	+	3.50611i	−0.373041	+	0.267338i
$173$	−3.34034			−0.253961			−0.126981	−	0.991905i	$-0.540529\pi$
$173$	−3.34034			−0.253961			−0.126981	+	0.991905i	$0.540529\pi$
$174$	7.00870	+	2.97961i	0.531328	+	0.225884i
$175$			19.3343i			1.46153i
$176$	−21.7466	+	10.7262i	−1.63921	+	0.808522i
$177$	8.85257	−	8.85257i	0.665400	−	0.665400i
$178$	5.93678	−	5.03717i	0.444980	−	0.377552i
$179$		−	11.4685i		−	0.857197i	−0.903495	−	0.428599i	$-0.859007\pi$
$179$		−	11.4685i		−	0.857197i	0.903495	−	0.428599i	$-0.140993\pi$
$180$	0.297998	−	1.80537i	0.0222115	−	0.134564i
$181$		−	2.68944i		−	0.199904i	−0.994992	−	0.0999522i	$-0.968131\pi$
$181$		−	2.68944i		−	0.199904i	0.994992	−	0.0999522i	$-0.0318690\pi$
$182$	2.06383	−	25.1759i	0.152981	−	1.86616i
$183$	−2.53777			−0.187597
$184$	4.78482	−	19.1066i	0.352741	−	1.40856i
$185$	0.966508	−	0.966508i	0.0710591	−	0.0710591i
$186$	6.50018	+	0.532862i	0.476617	+	0.0390714i
$187$			22.1326i			1.61850i
$188$	−11.6656	+	8.36014i	−0.850804	+	0.609726i
$189$	3.28406	−	3.28406i	0.238880	−	0.238880i
$190$	4.05980	−	3.44462i	0.294529	−	0.249899i
$191$	−1.13948	−	1.13948i	−0.0824496	−	0.0824496i	0.664679	−	0.747129i	$-0.268568\pi$
$191$	−1.13948	−	1.13948i	−0.0824496	−	0.0824496i	−0.747129	+	0.664679i	$0.768568\pi$
$192$	−7.65526	+	2.32314i	−0.552471	+	0.167658i
$193$	−7.52134	+	7.52134i	−0.541398	+	0.541398i	−0.923939	−	0.382541i	$-0.875049\pi$
$193$	−7.52134	+	7.52134i	−0.541398	+	0.541398i	0.382541	+	0.923939i	$0.375049\pi$
$194$	0.177671	+	0.209402i	0.0127561	+	0.0150342i
$195$	2.48803	−	2.48803i	0.178172	−	0.178172i
$196$	−28.7511	−	4.74571i	−2.05365	−	0.338980i
$197$		−	12.2428i		−	0.872261i	−0.899883	−	0.436131i	$-0.856349\pi$
$197$		−	12.2428i		−	0.872261i	0.899883	−	0.436131i	$-0.143651\pi$
$198$	−5.54646	−	6.53702i	−0.394170	−	0.464566i
$199$			15.8857i			1.12611i	0.826420	+	0.563054i	$0.190374\pi$
$199$			15.8857i			1.12611i	−0.826420	+	0.563054i	$0.809626\pi$
$200$	11.4219	+	2.86036i	0.807652	+	0.202258i
$201$	−0.970934	−	0.970934i	−0.0684844	−	0.0684844i
$202$	9.32318	+	10.9882i	0.655977	+	0.773130i
$203$	22.3527	−	11.2201i	1.56885	−	0.787493i
$204$	−1.18921	+	7.20459i	−0.0832611	+	0.504422i
$205$	4.41933	+	4.41933i	0.308659	+	0.308659i
$206$	−1.18370	+	14.4395i	−0.0824721	+	1.00605i
$207$	6.96381			0.484018
$208$	−14.5676	−	4.94381i	−1.01008	−	0.342792i
$209$		−	24.9451i		−	1.72549i
$210$	−3.88774	−	4.58207i	−0.268280	−	0.316193i
$211$	16.1153	+	16.1153i	1.10942	+	1.10942i	0.993226	+	0.116197i	$0.0370704\pi$
$211$	16.1153	+	16.1153i	1.10942	+	1.10942i	0.116197	+	0.993226i	$0.462930\pi$
$212$	1.13892	−	6.89997i	0.0782216	−	0.473892i
$213$	1.41476	−	1.41476i	0.0969380	−	0.0969380i
$214$	14.0121	+	1.14866i	0.957845	+	0.0785208i
$215$	−1.94693	+	1.94693i	−0.132780	+	0.132780i
$216$	−1.45424	−	2.42594i	−0.0989484	−	0.165064i
$217$	15.1452	−	15.1452i	1.02812	−	1.02812i
$218$	−16.4881	−	1.35164i	−1.11671	−	0.0915443i
$219$	−15.1128			−1.02123
$220$	−9.01604	+	6.46131i	−0.607861	+	0.435622i
$221$	−9.92888	+	9.92888i	−0.667889	+	0.667889i
$222$	0.172623	−	2.10576i	0.0115857	−	0.141329i
$223$			0.818647i			0.0548206i	0.999624	+	0.0274103i	$0.00872607\pi$
$223$			0.818647i			0.0548206i	−0.999624	+	0.0274103i	$0.991274\pi$
$224$	−10.4476	+	24.1058i	−0.698058	+	1.61064i
$225$			4.16296i			0.277531i
$226$	14.3775	+	16.9452i	0.956375	+	1.12718i
$227$	10.0517			0.667156			0.333578	−	0.942723i	$-0.391744\pi$
$227$	10.0517			0.667156			0.333578	+	0.942723i	$0.391744\pi$
$228$	1.34032	−	8.12011i	0.0887651	−	0.537767i
$229$	−11.4035	+	11.4035i	−0.753563	+	0.753563i	−0.975142	−	0.221579i	$-0.928879\pi$
$229$	−11.4035	+	11.4035i	−0.753563	+	0.753563i	0.221579	+	0.975142i	$0.428879\pi$
$230$	0.736155	−	8.98007i	0.0485406	−	0.592129i
$231$	−28.1541			−1.85240
$232$	−3.32145	−	14.8650i	−0.218064	−	0.975934i
$233$	22.8184			1.49488			0.747440	−	0.664329i	$-0.231283\pi$
$233$	22.8184			1.49488			0.747440	+	0.664329i	$0.231283\pi$
$234$	0.444374	−	5.42075i	0.0290496	−	0.354365i
$235$	−4.64236	+	4.64236i	−0.302834	+	0.302834i
$236$	−24.7046	−	4.07779i	−1.60813	−	0.265442i
$237$	14.1806			0.921126
$238$	15.5146	+	18.2854i	1.00566	+	1.18527i
$239$			1.01574i			0.0657028i	0.999460	+	0.0328514i	$0.0104588\pi$
$239$			1.01574i			0.0657028i	−0.999460	+	0.0328514i	$0.989541\pi$
$240$	−3.28207	+	1.61884i	−0.211857	+	0.104496i
$241$			16.2254i			1.04517i	0.852586	+	0.522586i	$0.175033\pi$
$241$			16.2254i			1.04517i	−0.852586	+	0.522586i	$0.824967\pi$
$242$	−2.97503	+	36.2913i	−0.191242	+	2.33289i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	2.95654	+	4.12552i	0.189273	+	0.264109i
$245$	−13.3301			−0.851629
$246$	9.62852	+	0.789312i	0.613892	+	0.0503247i
$247$	11.1906	−	11.1906i	0.712040	−	0.712040i
$248$	−6.70657	−	11.1878i	−0.425868	−	0.710427i
$249$	−0.942762	+	0.942762i	−0.0597451	+	0.0597451i
$250$	11.8160	+	0.968631i	0.747307	+	0.0612616i
$251$	−13.6194	+	13.6194i	−0.859646	+	0.859646i	−0.991296	−	0.131650i	$-0.957972\pi$
$251$	−13.6194	+	13.6194i	−0.859646	+	0.859646i	0.131650	+	0.991296i	$0.457972\pi$
$252$	−9.16470	−	1.51275i	−0.577322	−	0.0952941i
$253$	−29.8502	−	29.8502i	−1.87667	−	1.87667i
$254$	5.77521	+	6.80662i	0.362369	+	0.427085i
$255$			3.34033i			0.209180i
$256$	12.6951	+	9.73828i	0.793444	+	0.608643i
$257$	−10.4155			−0.649702			−0.324851	−	0.945765i	$-0.605314\pi$
$257$	−10.4155			−0.649702			−0.324851	+	0.945765i	$0.605314\pi$
$258$	−0.347731	+	4.24184i	−0.0216488	+	0.264085i
$259$	−4.90635	−	4.90635i	−0.304866	−	0.304866i
$260$	−6.94327	−	1.14607i	−0.430603	−	0.0710764i
$261$	4.81287	−	2.41585i	0.297909	−	0.149537i
$262$	1.50109	+	1.76918i	0.0927378	+	0.109300i
$263$	10.1131	+	10.1131i	0.623598	+	0.623598i	0.946450	−	0.322852i	$-0.104641\pi$
$263$	10.1131	+	10.1131i	0.623598	+	0.623598i	−0.322852	+	0.946450i	$0.604641\pi$
$264$	−4.16519	+	16.6323i	−0.256350	+	1.02365i
$265$		−	3.19909i		−	0.196519i
$266$	−17.4861	−	20.6091i	−1.07214	−	1.26362i
$267$		−	5.50538i		−	0.336924i
$268$	−0.447245	+	2.70955i	−0.0273198	+	0.165512i
$269$	11.2546	−	11.2546i	0.686206	−	0.686206i	−0.275185	−	0.961391i	$-0.588739\pi$
$269$	11.2546	−	11.2546i	0.686206	−	0.686206i	0.961391	+	0.275185i	$0.0887393\pi$
$270$	−0.837090	−	0.986589i	−0.0509437	−	0.0600419i
$271$	−10.3949	+	10.3949i	−0.631448	+	0.631448i	−0.948431	−	0.316983i	$-0.897330\pi$
$271$	−10.3949	+	10.3949i	−0.631448	+	0.631448i	0.316983	+	0.948431i	$0.397330\pi$
$272$	13.0976	−	6.46024i	0.794158	−	0.391709i
$273$	−12.6302	−	12.6302i	−0.764413	−	0.764413i
$274$	19.6159	−	16.6435i	1.18504	−	1.00547i
$275$	17.8445	−	17.8445i	1.07606	−	1.07606i
$276$	−8.11295	−	11.3207i	−0.488342	−	0.681427i
$277$		−	1.64002i		−	0.0985391i	−0.998786	−	0.0492695i	$-0.984311\pi$
$277$		−	1.64002i		−	0.0985391i	0.998786	−	0.0492695i	$-0.0156893\pi$
$278$	3.61323	+	0.296200i	0.216707	+	0.0177649i
$279$	3.26099	−	3.26099i	0.195231	−	0.195231i
$280$	−2.91956	+	11.6583i	−0.174477	+	0.696716i
$281$	−6.42751			−0.383433			−0.191717	−	0.981450i	$-0.561405\pi$
$281$	−6.42751			−0.383433			−0.191717	+	0.981450i	$0.561405\pi$
$282$	−0.829147	+	10.1144i	−0.0493750	+	0.602307i
$283$		−	0.954877i		−	0.0567615i	−0.999597	−	0.0283808i	$-0.990965\pi$
$283$		−	0.954877i		−	0.0567615i	0.999597	−	0.0283808i	$-0.00903509\pi$
$284$	−3.94813	−	0.651688i	−0.234279	−	0.0386705i
$285$		−	3.76480i		−	0.223007i
$286$	−25.1408	+	21.3311i	−1.48660	+	1.26134i
$287$	22.4341	−	22.4341i	1.32425	−	1.32425i
$288$	−2.24952	+	5.19034i	−0.132554	+	0.305844i
$289$			3.66991i			0.215877i
$290$	−2.60654	−	6.46174i	−0.153062	−	0.379447i
$291$	0.194186			0.0113834
$292$	17.6067	+	24.5681i	1.03035	+	1.43774i
$293$	−3.09811	−	3.09811i	−0.180994	−	0.180994i	0.610795	−	0.791789i	$-0.290850\pi$
$293$	−3.09811	−	3.09811i	−0.180994	−	0.180994i	−0.791789	+	0.610795i	$0.790850\pi$
$294$	−15.7117	+	13.3309i	−0.916328	+	0.777476i
$295$	−11.4540			−0.666877
$296$	−3.62433	+	2.17262i	−0.210660	+	0.126281i
$297$	−6.06200			−0.351753
$298$	5.00141	+	0.409998i	0.289724	+	0.0237506i
$299$		−	26.7821i		−	1.54885i
$300$	6.76752	−	4.84992i	0.390723	−	0.280010i
$301$	9.88334	+	9.88334i	0.569666	+	0.569666i
$302$	−2.38492	−	0.195508i	−0.137237	−	0.0112502i
$303$	10.1898			0.585387
$304$	−14.7620	+	7.28116i	−0.846656	+	0.417603i
$305$	1.64176	+	1.64176i	0.0940068	+	0.0940068i
$306$	3.34054	+	3.93713i	0.190966	+	0.225071i
$307$	14.8242	−	14.8242i	0.846062	−	0.846062i	−0.143577	−	0.989639i	$-0.545860\pi$
$307$	14.8242	−	14.8242i	0.846062	−	0.846062i	0.989639	+	0.143577i	$0.0458604\pi$
$308$	32.8000	+	45.7687i	1.86895	+	2.60791i
$309$	7.24396	+	7.24396i	0.412094	+	0.412094i
$310$	−3.86044	−	4.54989i	−0.219258	−	0.258416i
$311$	−2.61912	−	2.61912i	−0.148517	−	0.148517i	0.628938	−	0.777455i	$-0.283490\pi$
$311$	−2.61912	−	2.61912i	−0.148517	−	0.148517i	−0.777455	+	0.628938i	$0.783490\pi$
$312$	−9.32994	+	5.59286i	−0.528204	+	0.316634i
$313$	−29.7357			−1.68076			−0.840380	−	0.541997i	$-0.817668\pi$
$313$	−29.7357			−1.68076			−0.840380	+	0.541997i	$0.817668\pi$
$314$	−20.4710	+	17.3690i	−1.15525	+	0.980191i
$315$	−4.24911			−0.239410
$316$	−16.5206	−	23.0526i	−0.929355	−	1.29681i
$317$	−17.8824	+	17.8824i	−1.00437	+	1.00437i	−0.00438378	+	0.999990i	$0.501395\pi$
$317$	−17.8824	+	17.8824i	−1.00437	+	1.00437i	−0.999990	+	0.00438378i	$0.998605\pi$
$318$	−3.19929	−	3.77066i	−0.179407	−	0.211448i
$319$	−30.9858	−	10.2748i	−1.73487	−	0.575278i
$320$	6.45533	+	3.44951i	0.360864	+	0.192834i
$321$	7.02953	−	7.02953i	0.392350	−	0.392350i
$322$	−45.5861	−	3.73699i	−2.54042	−	0.208254i
$323$			15.0240i			0.835958i
$324$	−1.97330	−	0.325717i	−0.109628	−	0.0180954i
$325$	16.0104			0.888095
$326$	−0.402243	−	0.474081i	−0.0222782	−	0.0262569i
$327$	−8.27170	+	8.27170i	−0.457426	+	0.457426i
$328$	−9.93424	−	16.5722i	−0.548526	−	0.915045i
$329$	23.5663	+	23.5663i	1.29925	+	1.29925i
$330$	−0.640824	+	7.81717i	−0.0352762	+	0.430321i
$331$	−3.42756	−	3.42756i	−0.188396	−	0.188396i	0.606606	−	0.795002i	$-0.292530\pi$
$331$	−3.42756	−	3.42756i	−0.188396	−	0.188396i	−0.795002	+	0.606606i	$0.792530\pi$
$332$	2.63093	+	0.434268i	0.144391	+	0.0238335i
$333$	−1.05641	−	1.05641i	−0.0578910	−	0.0578910i
$334$	−31.0145	−	2.54246i	−1.69704	−	0.139117i
$335$			1.25625i			0.0686365i
$336$	8.21783	+	16.6610i	0.448320	+	0.908931i
$337$	18.1190	+	18.1190i	0.987004	+	0.987004i	0.999917	−	0.0129130i	$-0.00411045\pi$
$337$	18.1190	+	18.1190i	0.987004	+	0.987004i	−0.0129130	+	0.999917i	$0.504110\pi$
$338$	−2.52437	−	0.206939i	−0.137308	−	0.0112560i
$339$	15.7139			0.853460
$340$	5.43021	−	3.89154i	0.294494	−	0.211048i
$341$	−27.9564			−1.51392
$342$	−3.76503	−	4.43744i	−0.203590	−	0.239949i
$343$			35.1580i			1.89835i
$344$	7.30085	−	4.37652i	0.393636	−	0.235966i
$345$	−4.50510	−	4.50510i	−0.242546	−	0.242546i
$346$	4.70816	+	0.385958i	0.253112	+	0.0207492i
$347$			12.6835i			0.680884i	0.940266	+	0.340442i	$0.110577\pi$
$347$			12.6835i			0.680884i	−0.940266	+	0.340442i	$0.889423\pi$
$348$	−9.53439	−	5.00954i	−0.511097	−	0.268539i
$349$			17.1711i			0.919148i	0.888140	+	0.459574i	$0.151998\pi$
$349$			17.1711i			0.919148i	−0.888140	+	0.459574i	$0.848002\pi$
$350$	2.23397	−	27.2514i	0.119411	−	1.45665i
$351$	−2.71947	−	2.71947i	−0.145154	−	0.145154i
$352$	31.8909	−	12.6058i	1.69979	−	0.671891i
$353$			3.67104i			0.195390i	0.995216	+	0.0976949i	$0.0311469\pi$
$353$			3.67104i			0.195390i	−0.995216	+	0.0976949i	$0.968853\pi$
$354$	−13.5004	+	11.4547i	−0.717540	+	0.608811i
$355$	−1.83051			−0.0971533
$356$	−8.94982	+	6.41386i	−0.474340	+	0.339934i
$357$	16.9567			0.897445
$358$	−1.32513	+	16.1647i	−0.0700351	+	0.854332i
$359$	−9.41380	−	9.41380i	−0.496841	−	0.496841i	0.413612	−	0.910453i	$-0.364267\pi$
$359$	−9.41380	−	9.41380i	−0.496841	−	0.496841i	−0.910453	+	0.413612i	$0.864267\pi$
$360$	−0.628624	+	2.51021i	−0.0331314	+	0.132300i
$361$			2.06684i			0.108781i
$362$	−0.310750	+	3.79072i	−0.0163327	+	0.199236i
$363$	18.2065	+	18.2065i	0.955594	+	0.955594i
$364$	−5.81788	+	35.2466i	−0.304940	+	1.84742i
$365$	9.77693	+	9.77693i	0.511748	+	0.511748i
$366$	3.57695	+	0.293225i	0.186970	+	0.0153271i
$367$	−14.8428	−	14.8428i	−0.774786	−	0.774786i	0.204153	−	0.978939i	$-0.434556\pi$
$367$	−14.8428	−	14.8428i	−0.774786	−	0.774786i	−0.978939	+	0.204153i	$0.934556\pi$
$368$	−8.95179	+	26.3776i	−0.466645	+	1.37503i
$369$	4.83041	−	4.83041i	0.251461	−	0.251461i
$370$	−1.47395	+	1.25060i	−0.0766272	+	0.0650158i
$371$	−16.2398			−0.843127
$372$	−9.10035	−	1.50212i	−0.471831	−	0.0778815i
$373$		−	33.8108i		−	1.75066i	−0.483528	−	0.875329i	$-0.660645\pi$
$373$		−	33.8108i		−	1.75066i	0.483528	−	0.875329i	$-0.339355\pi$
$374$	2.55731	−	31.1956i	0.132235	−	1.61309i
$375$	5.92780	−	5.92780i	0.306110	−	0.306110i
$376$	17.4085	−	10.4356i	0.897776	−	0.538175i
$377$	−9.29112	−	18.5098i	−0.478517	−	0.953305i
$378$	−5.00828	+	4.24937i	−0.257598	+	0.218564i
$379$	20.9270	−	20.9270i	1.07495	−	1.07495i	0.0779954	−	0.996954i	$-0.475148\pi$
$379$	20.9270	−	20.9270i	1.07495	−	1.07495i	0.996954	−	0.0779954i	$-0.0248520\pi$
$380$	−6.12024	+	4.38605i	−0.313962	+	0.225000i
$381$	6.31202			0.323374
$382$	1.47442	+	1.73774i	0.0754376	+	0.0889103i
$383$	−7.95543			−0.406503			−0.203252	−	0.979127i	$-0.565151\pi$
$383$	−7.95543			−0.406503			−0.203252	+	0.979127i	$0.565151\pi$
$384$	11.0584	−	2.38990i	0.564322	−	0.121959i
$385$	18.2138	+	18.2138i	0.928259	+	0.928259i
$386$	11.4703	−	9.73217i	0.583822	−	0.495354i
$387$	2.12803	+	2.12803i	0.108174	+	0.108174i
$388$	−0.226230	−	0.315678i	−0.0114851	−	0.0160261i
$389$	5.56978	−	5.56978i	0.282399	−	0.282399i	−0.551666	−	0.834065i	$-0.686008\pi$
$389$	5.56978	−	5.56978i	0.282399	−	0.282399i	0.834065	+	0.551666i	$0.186008\pi$
$390$	−3.79433	+	3.21937i	−0.192133	+	0.163019i
$391$	17.9783	+	17.9783i	0.909201	+	0.909201i
$392$	39.9759	+	10.0110i	2.01909	+	0.505634i
$393$	1.64062			0.0827583
$394$	−1.41459	+	17.2560i	−0.0712659	+	0.869345i
$395$	−9.17383	−	9.17383i	−0.461586	−	0.461586i
$396$	7.06233	+	9.85470i	0.354896	+	0.495217i
$397$			24.7512i			1.24223i	0.783721	+	0.621113i	$0.213319\pi$
$397$			24.7512i			1.24223i	−0.783721	+	0.621113i	$0.786681\pi$
$398$	1.83551	−	22.3907i	0.0920057	−	1.12234i
$399$	−19.1115			−0.956771
$400$	−15.7685	−	5.35138i	−0.788427	−	0.267569i
$401$	29.8285			1.48957			0.744783	−	0.667307i	$-0.232553\pi$
$401$	29.8285			1.48957			0.744783	+	0.667307i	$0.232553\pi$
$402$	1.25633	+	1.48070i	0.0626601	+	0.0738508i
$403$	−12.5415	−	12.5415i	−0.624735	−	0.624735i
$404$	−11.8713	−	16.5650i	−0.590617	−	0.824140i
$405$	−0.914898			−0.0454616
$406$	−32.8022	+	13.2318i	−1.62794	+	0.656682i
$407$			9.05658i			0.448918i
$408$	2.50862	−	10.0174i	0.124195	−	0.495933i
$409$	9.26631	−	9.26631i	0.458189	−	0.458189i	−0.439871	−	0.898061i	$-0.644976\pi$
$409$	9.26631	−	9.26631i	0.458189	−	0.458189i	0.898061	+	0.439871i	$0.144976\pi$
$410$	−5.71835	−	6.73961i	−0.282409	−	0.332846i
$411$		−	18.1905i		−	0.897272i
$412$	3.33681	−	20.2155i	0.164393	−	0.995945i
$413$			58.1447i			2.86111i
$414$	−9.81538	−	0.804631i	−0.482400	−	0.0395454i
$415$	1.21980			0.0598778
$416$	19.9616	+	8.65144i	0.978696	+	0.424172i
$417$	1.81267	−	1.81267i	0.0887670	−	0.0887670i
$418$	−2.88227	+	35.1598i	−0.140977	+	1.71972i
$419$		−	26.4510i		−	1.29222i	−0.763245	−	0.646109i	$-0.776395\pi$
$419$		−	26.4510i		−	1.29222i	0.763245	−	0.646109i	$-0.223605\pi$
$420$	4.95028	+	6.90757i	0.241549	+	0.337055i
$421$	−11.8969	+	11.8969i	−0.579821	+	0.579821i	−0.934854	−	0.355032i	$-0.884470\pi$
$421$	−11.8969	+	11.8969i	−0.579821	+	0.579821i	0.355032	+	0.934854i	$0.384470\pi$
$422$	−20.8522	−	24.5763i	−1.01507	−	1.19636i
$423$	5.07419	+	5.07419i	0.246715	+	0.246715i
$424$	−2.40255	+	9.59381i	−0.116678	+	0.465916i
$425$	−10.7474	+	10.7474i	−0.521326	+	0.521326i
$426$	−2.15756	+	1.83062i	−0.104534	+	0.0886939i
$427$	8.33417	−	8.33417i	0.403319	−	0.403319i
$428$	−19.6171	−	3.23804i	−0.948227	−	0.156516i
$429$			23.3139i			1.12561i
$430$	2.96913	−	2.51922i	0.143184	−	0.121487i
$431$		−	23.9003i		−	1.15124i	−0.817718	−	0.575619i	$-0.804761\pi$
$431$		−	23.9003i		−	1.15124i	0.817718	−	0.575619i	$-0.195239\pi$
$432$	1.76942	+	3.58736i	0.0851314	+	0.172597i
$433$	−12.6088	−	12.6088i	−0.605940	−	0.605940i	0.335942	−	0.941883i	$-0.390945\pi$
$433$	−12.6088	−	12.6088i	−0.605940	−	0.605940i	−0.941883	+	0.335942i	$0.890945\pi$
$434$	−23.0969	+	19.5970i	−1.10869	+	0.940687i
$435$	−4.67648	−	1.55071i	−0.224220	−	0.0743506i
$436$	23.0835	+	3.81022i	1.10550	+	0.182477i
$437$	−20.2629	−	20.2629i	−0.969304	−	0.969304i
$438$	21.3013	+	1.74620i	1.01781	+	0.0834368i
$439$	−9.79778			−0.467623			−0.233811	−	0.972282i	$-0.575120\pi$
$439$	−9.79778			−0.467623			−0.233811	+	0.972282i	$0.575120\pi$
$440$	13.4545	−	8.06537i	0.641420	−	0.384502i
$441$			14.5700i			0.693812i
$442$	15.1418	−	12.8474i	0.720224	−	0.611088i
$443$	−11.8030	−	11.8030i	−0.560778	−	0.560778i	0.368750	−	0.929529i	$-0.379786\pi$
$443$	−11.8030	−	11.8030i	−0.560778	−	0.560778i	−0.929529	+	0.368750i	$0.879786\pi$
$444$	−0.486618	+	2.94809i	−0.0230939	+	0.139910i
$445$	−3.56160	+	3.56160i	−0.168836	+	0.168836i
$446$	0.0945903	−	1.15387i	0.00447898	−	0.0546374i
$447$	2.50909	−	2.50909i	0.118676	−	0.118676i
$448$	17.5110	−	32.7696i	0.827317	−	1.54822i
$449$	−13.4942	+	13.4942i	−0.636829	+	0.636829i	−0.949772	−	0.312943i	$-0.898685\pi$
$449$	−13.4942	+	13.4942i	−0.636829	+	0.636829i	0.312943	+	0.949772i	$0.398685\pi$
$450$	0.481008	−	5.86763i	0.0226749	−	0.276603i
$451$	−41.4109			−1.94997
$452$	−18.3069	−	25.5452i	−0.861085	−	1.20155i
$453$	−1.19646	+	1.19646i	−0.0562147	+	0.0562147i
$454$	−14.1677	−	1.16142i	−0.664925	−	0.0545082i
$455$			16.3417i			0.766110i
$456$	−2.82740	+	11.2903i	−0.132405	+	0.528717i
$457$		−	17.5134i		−	0.819243i	−0.912255	−	0.409622i	$-0.865661\pi$
$457$		−	17.5134i		−	0.819243i	0.912255	−	0.409622i	$-0.134339\pi$
$458$	17.3907	−	14.7554i	0.812612	−	0.689476i
$459$	3.65104			0.170416
$460$	−2.07520	+	12.5722i	−0.0967567	+	0.586183i
$461$	23.8713	−	23.8713i	1.11180	−	1.11180i	0.118892	−	0.992907i	$-0.462066\pi$
$461$	23.8713	−	23.8713i	1.11180	−	1.11180i	0.992907	−	0.118892i	$-0.0379343\pi$
$462$	39.6828	+	3.25306i	1.84621	+	0.151346i
$463$	42.4619			1.97337			0.986686	−	0.162636i	$-0.0519995\pi$
$463$	42.4619			1.97337			0.986686	+	0.162636i	$0.0519995\pi$
$464$	2.96397	+	21.3358i	0.137599	+	0.990488i
$465$	−4.21927			−0.195664
$466$	−32.1621	−	2.63654i	−1.48988	−	0.122135i
$467$	−29.6201	+	29.6201i	−1.37065	+	1.37065i	−0.511179	+	0.859474i	$0.670791\pi$
$467$	−29.6201	+	29.6201i	−1.37065	+	1.37065i	−0.859474	+	0.511179i	$0.829209\pi$
$468$	−1.25268	+	7.58912i	−0.0579050	+	0.350807i
$469$	6.37720			0.294472
$470$	7.07974	−	6.00694i	0.326564	−	0.277080i
$471$			18.9835i			0.874713i
$472$	34.3496	+	8.60207i	1.58107	+	0.395942i
$473$		−	18.2436i		−	0.838839i
$474$	−19.9873	−	1.63849i	−0.918046	−	0.0752582i
$475$	12.1131	−	12.1131i	0.555789	−	0.555789i
$476$	−19.7549	−	27.5657i	−0.905463	−	1.26347i
$477$	−3.49667			−0.160101
$478$	0.117364	−	1.43167i	0.00536808	−	0.0654832i
$479$	−8.56458	+	8.56458i	−0.391326	+	0.391326i	−0.875160	−	0.483834i	$-0.839244\pi$
$479$	−8.56458	+	8.56458i	−0.391326	+	0.391326i	0.483834	+	0.875160i	$0.339244\pi$
$480$	4.81307	−	1.90251i	0.219686	−	0.0868372i
$481$	−4.06286	+	4.06286i	−0.185250	+	0.185250i
$482$	1.87476	−	22.8695i	0.0853932	−	1.04168i
$483$	−22.8695	+	22.8695i	−1.04060	+	1.04060i
$484$	8.38653	−	50.8083i	0.381206	−	2.30947i
$485$	−0.125625	−	0.125625i	−0.00570433	−	0.00570433i
$486$	−1.07836	+	0.914954i	−0.0489154	+	0.0415032i
$487$			13.1379i			0.595333i	0.954670	+	0.297666i	$0.0962083\pi$
$487$			13.1379i			0.595333i	−0.954670	+	0.297666i	$0.903792\pi$
$488$	−3.69052	−	6.15647i	−0.167062	−	0.278690i
$489$	−0.439632			−0.0198808
$490$	18.7886	+	1.54022i	0.848782	+	0.0695802i
$491$	4.27353	+	4.27353i	0.192862	+	0.192862i	0.796931	−	0.604070i	$-0.206455\pi$
$491$	4.27353	+	4.27353i	0.192862	+	0.192862i	−0.604070	+	0.796931i	$0.706455\pi$
$492$	−13.4801	−	2.22505i	−0.607728	−	0.100313i
$493$	18.6622	+	6.18833i	0.840503	+	0.278708i
$494$	−17.0660	+	14.4800i	−0.767834	+	0.651484i
$495$	3.92170	+	3.92170i	0.176267	+	0.176267i
$496$	8.16012	+	16.5440i	0.366400	+	0.742846i
$497$			9.29233i			0.416818i
$498$	1.43774	−	1.21988i	0.0644267	−	0.0546641i
$499$			40.7962i			1.82629i	0.407635	+	0.913145i	$0.366354\pi$
$499$			40.7962i			1.82629i	−0.407635	+	0.913145i	$0.633646\pi$
$500$	−16.5425	−	2.73054i	−0.739803	−	0.122114i
$501$	−15.5593	+	15.5593i	−0.695138	+	0.695138i
$502$	20.7699	−	17.6226i	0.927007	−	0.786537i
$503$	5.28904	−	5.28904i	0.235827	−	0.235827i	−0.579293	−	0.815120i	$-0.696671\pi$
$503$	5.28904	−	5.28904i	0.235827	−	0.235827i	0.815120	+	0.579293i	$0.196671\pi$
$504$	12.7427	+	3.19113i	0.567606	+	0.142144i
$505$	−6.59208	−	6.59208i	−0.293344	−	0.293344i
$506$	38.6244	+	45.5225i	1.71707	+	2.02372i
$507$	−1.26642	+	1.26642i	−0.0562437	+	0.0562437i
$508$	−7.35360	−	10.2611i	−0.326263	−	0.455264i
$509$		−	0.817861i		−	0.0362511i	−0.999836	−	0.0181255i	$-0.994230\pi$
$509$		−	0.817861i		−	0.0362511i	0.999836	−	0.0181255i	$-0.00576985\pi$
$510$	0.385957	−	4.70815i	0.0170905	−	0.208480i
$511$	49.6313	−	49.6313i	2.19556	−	2.19556i
$512$	−16.7684	−	15.1928i	−0.741064	−	0.671434i
$513$	−4.11499			−0.181681
$514$	14.6805	+	1.20346i	0.647529	+	0.0530822i
$515$		−	9.37267i		−	0.413009i
$516$	0.980243	−	5.93863i	0.0431528	−	0.261434i
$517$		−	43.5008i		−	1.91317i
$518$	6.34853	+	7.48233i	0.278938	+	0.328755i
$519$	2.36198	−	2.36198i	0.103679	−	0.103679i
$520$	9.65402	+	2.41763i	0.423357	+	0.106020i
$521$			3.74408i			0.164031i	0.996631	+	0.0820155i	$0.0261357\pi$
$521$			3.74408i			0.164031i	−0.996631	+	0.0820155i	$0.973864\pi$
$522$	−7.06280	+	2.84900i	−0.309131	+	0.124697i
$523$	−24.9377			−1.09045			−0.545226	−	0.838289i	$-0.683556\pi$
$523$	−24.9377			−1.09045			−0.545226	+	0.838289i	$0.683556\pi$
$524$	−1.91135	−	2.66707i	−0.0834977	−	0.116512i
$525$	−13.6714	−	13.6714i	−0.596669	−	0.596669i
$526$	−13.0857	−	15.4227i	−0.570564	−	0.672463i
$527$	16.8377			0.733460
$528$	7.79255	−	22.9618i	0.339127	−	0.999282i
$529$	−25.4946			−1.10846
$530$	−0.369638	+	4.50907i	−0.0160561	+	0.195862i
$531$			12.5194i			0.543297i
$532$	22.2652	+	31.0686i	0.965319	+	1.34699i
$533$	−18.5773	−	18.5773i	−0.804672	−	0.804672i
$534$	−0.636117	+	7.75975i	−0.0275275	+	0.335797i
$535$	−9.09524			−0.393221
$536$	0.943459	−	3.76740i	0.0407512	−	0.162727i
$537$	8.10947	+	8.10947i	0.349949	+	0.349949i
$538$	−17.1636	+	14.5628i	−0.739976	+	0.627847i
$539$	62.4543	−	62.4543i	2.69010	−	2.69010i
$540$	1.06587	+	1.48730i	0.0458678	+	0.0640034i
$541$	−3.58655	−	3.58655i	−0.154198	−	0.154198i	0.625792	−	0.779990i	$-0.284776\pi$
$541$	−3.58655	−	3.58655i	−0.154198	−	0.154198i	−0.779990	+	0.625792i	$0.784776\pi$
$542$	15.8526	−	13.4504i	0.680928	−	0.577746i
$543$	1.90172	+	1.90172i	0.0816106	+	0.0816106i
$544$	−19.2073	+	7.59225i	−0.823507	+	0.325515i
$545$	10.7024			0.458442
$546$	16.3427	+	19.2614i	0.699403	+	0.824311i
$547$	27.2489			1.16508			0.582540	−	0.812802i	$-0.302059\pi$
$547$	27.2489			1.16508			0.582540	+	0.812802i	$0.302059\pi$
$548$	−29.5714	+	21.1923i	−1.26323	+	0.905288i
$549$	1.79447	−	1.79447i	0.0765862	−	0.0765862i
$550$	−27.2134	+	23.0897i	−1.16038	+	0.984548i
$551$	−21.0337	−	6.97470i	−0.896064	−	0.297132i
$552$	10.1270	+	16.8938i	0.431035	+	0.719047i
$553$	−46.5697	+	46.5697i	−1.98035	+	1.98035i
$554$	−0.189495	+	2.31158i	−0.00805088	+	0.0982096i
$555$			1.36685i			0.0580195i
$556$	−5.05857	−	0.834978i	−0.214531	−	0.0354110i
$557$	−16.7849			−0.711201			−0.355600	−	0.934638i	$-0.615724\pi$
$557$	−16.7849			−0.711201			−0.355600	+	0.934638i	$0.615724\pi$
$558$	−4.97311	+	4.21953i	−0.210529	+	0.178627i
$559$	8.18421	−	8.18421i	0.346155	−	0.346155i
$560$	5.46213	−	16.0949i	0.230817	−	0.680132i
$561$	−15.6501	−	15.6501i	−0.660749	−	0.660749i
$562$	9.05949	+	0.742665i	0.382151	+	0.0313274i
$563$	−22.7209	−	22.7209i	−0.957573	−	0.957573i	0.0415630	−	0.999136i	$-0.486766\pi$
$563$	−22.7209	−	22.7209i	−0.957573	−	0.957573i	−0.999136	+	0.0415630i	$0.986766\pi$
$564$	2.33734	−	14.1604i	0.0984198	−	0.596259i
$565$	−10.1658	−	10.1658i	−0.427678	−	0.427678i
$566$	−0.110331	+	1.34589i	−0.00463756	+	0.0565718i
$567$			4.64436i			0.195045i
$568$	5.48954	+	1.37473i	0.230336	+	0.0576824i
$569$	6.60361	+	6.60361i	0.276838	+	0.276838i	0.831845	−	0.555008i	$-0.187285\pi$
$569$	6.60361	+	6.60361i	0.276838	+	0.276838i	−0.555008	+	0.831845i	$0.687285\pi$
$570$	−0.435002	+	5.30643i	−0.0182202	+	0.222262i
$571$	11.2896			0.472456			0.236228	−	0.971698i	$-0.424089\pi$
$571$	11.2896			0.472456			0.236228	+	0.971698i	$0.424089\pi$
$572$	37.9002	−	27.1611i	1.58469	−	1.13566i
$573$	1.61146			0.0673198
$574$	−34.2127	+	29.0285i	−1.42801	+	1.21162i
$575$		−	28.9901i		−	1.20897i
$576$	3.77038	−	7.05579i	0.157099	−	0.293991i
$577$	−16.4894	−	16.4894i	−0.686463	−	0.686463i	0.274985	−	0.961448i	$-0.411327\pi$
$577$	−16.4894	−	16.4894i	−0.686463	−	0.686463i	−0.961448	+	0.274985i	$0.911327\pi$
$578$	0.424038	−	5.17268i	0.0176377	−	0.215155i
$579$		−	10.6368i		−	0.442050i
$580$	2.92727	+	9.40891i	0.121548	+	0.390684i
$581$		−	6.19217i		−	0.256894i
$582$	−0.273702	−	0.0224371i	−0.0113453	−	0.000930050i
$583$	14.9884	+	14.9884i	0.620756	+	0.620756i
$584$	−21.9776	−	36.6628i	−0.909440	−	1.51712i
$585$			3.51861i			0.145477i
$586$	4.00878	+	4.72472i	0.165601	+	0.195176i
$587$	−1.31711			−0.0543629			−0.0271814	−	0.999631i	$-0.508653\pi$
$587$	−1.31711			−0.0543629			−0.0271814	+	0.999631i	$0.508653\pi$
$588$	23.6858	−	16.9743i	0.976786	−	0.700010i
$589$	−18.9773			−0.781945
$590$	16.1442	+	1.32345i	0.664648	+	0.0544855i
$591$	8.65694	+	8.65694i	0.356099	+	0.356099i
$592$	5.35948	−	2.64350i	0.220273	−	0.108647i
$593$			42.7470i			1.75541i	0.479202	+	0.877705i	$0.340926\pi$
$593$			42.7470i			1.75541i	−0.479202	+	0.877705i	$0.659074\pi$
$594$	8.54431	+	0.700432i	0.350577	+	0.0287391i
$595$	−10.9698	−	10.9698i	−0.449719	−	0.449719i
$596$	−7.00204	−	1.15577i	−0.286815	−	0.0473423i
$597$	−11.2329	−	11.2329i	−0.459731	−	0.459731i
$598$	−3.09453	+	37.7490i	−0.126545	+	1.54367i
$599$	−1.15513	−	1.15513i	−0.0471972	−	0.0471972i	0.683114	−	0.730311i	$-0.260625\pi$
$599$	−1.15513	−	1.15513i	−0.0471972	−	0.0471972i	−0.730311	+	0.683114i	$0.760625\pi$
$600$	−10.0991	+	6.05394i	−0.412294	+	0.247151i
$601$	7.27484	−	7.27484i	0.296747	−	0.296747i	−0.542991	−	0.839738i	$-0.682708\pi$
$601$	7.27484	−	7.27484i	0.296747	−	0.296747i	0.839738	+	0.542991i	$0.182708\pi$
$602$	−12.7885	−	15.0724i	−0.521219	−	0.614305i
$603$	1.37311			0.0559173
$604$	3.33893	+	0.551131i	0.135859	+	0.0224252i
$605$		−	23.5567i		−	0.957716i
$606$	−14.3623	−	1.17737i	−0.583430	−	0.0478276i
$607$	8.44741	−	8.44741i	0.342870	−	0.342870i	−0.514575	−	0.857445i	$-0.672050\pi$
$607$	8.44741	−	8.44741i	0.342870	−	0.342870i	0.857445	+	0.514575i	$0.172050\pi$
$608$	21.6481	−	8.55703i	0.877945	−	0.347033i
$609$	−7.87195	+	23.7395i	−0.318987	+	0.961973i
$610$	−2.12434	−	2.50373i	−0.0860120	−	0.101373i
$611$	19.5148	−	19.5148i	0.789486	−	0.789486i
$612$	−4.25352	−	5.93531i	−0.171938	−	0.239921i
$613$	−44.2839			−1.78861			−0.894304	−	0.447459i	$-0.852329\pi$
$613$	−44.2839			−1.78861			−0.894304	+	0.447459i	$0.852329\pi$
$614$	−22.6074	+	19.1817i	−0.912359	+	0.774108i
$615$	−6.24988			−0.252019
$616$	−40.9428	−	68.3002i	−1.64963	−	2.75189i
$617$	26.5748	+	26.5748i	1.06986	+	1.06986i	0.997369	+	0.0724933i	$0.0230956\pi$
$617$	26.5748	+	26.5748i	1.06986	+	1.06986i	0.0724933	+	0.997369i	$0.476904\pi$
$618$	−9.37325	−	11.0473i	−0.377048	−	0.444386i
$619$	33.5144	+	33.5144i	1.34706	+	1.34706i	0.888838	+	0.458221i	$0.151513\pi$
$619$	33.5144	+	33.5144i	1.34706	+	1.34706i	0.458221	+	0.888838i	$0.348487\pi$
$620$	4.91552	+	6.85906i	0.197412	+	0.275466i
$621$	−4.92415	+	4.92415i	−0.197600	+	0.197600i
$622$	3.38899	+	3.99424i	0.135886	+	0.160154i
$623$	18.0800	+	18.0800i	0.724359	+	0.724359i
$624$	13.7966	−	6.80503i	0.552308	−	0.272419i
$625$	13.1451			0.525802
$626$	41.9120	+	3.43580i	1.67514	+	0.137322i
$627$	17.6388	+	17.6388i	0.704428	+	0.704428i
$628$	30.8605	−	22.1161i	1.23147	−	0.882528i
$629$		−	5.45462i		−	0.217490i
$630$	5.98906	+	0.490962i	0.238610	+	0.0195604i
$631$	24.6422			0.980991			0.490495	−	0.871444i	$-0.336816\pi$
$631$	24.6422			0.980991			0.490495	+	0.871444i	$0.336816\pi$
$632$	20.6219	+	34.4012i	0.820295	+	1.36841i
$633$	−22.7905			−0.905840
$634$	27.2712	−	23.1387i	1.08308	−	0.918957i
$635$	−4.08344	−	4.08344i	−0.162046	−	0.162046i
$636$	4.07367	+	5.68435i	0.161532	+	0.225399i
$637$	56.0350			2.22019
$638$	42.4868	+	18.0624i	1.68207	+	0.715098i
$639$			2.00078i			0.0791496i
$640$	−8.70012	−	5.60792i	−0.343903	−	0.221673i
$641$	−18.2577	+	18.2577i	−0.721137	+	0.721137i	−0.968837	−	0.247700i	$-0.920325\pi$
$641$	−18.2577	+	18.2577i	−0.721137	+	0.721137i	0.247700	+	0.968837i	$0.420325\pi$
$642$	−10.7202	+	9.09580i	−0.423094	+	0.358983i
$643$			13.6381i			0.537835i	0.963163	+	0.268918i	$0.0866659\pi$
$643$			13.6381i			0.537835i	−0.963163	+	0.268918i	$0.913334\pi$
$644$	63.8212	+	10.5345i	2.51491	+	0.415116i
$645$		−	2.75338i		−	0.108414i
$646$	1.73594	−	21.1761i	0.0682998	−	0.833163i
$647$	30.9257			1.21582			0.607908	−	0.794008i	$-0.292009\pi$
$647$	30.9257			1.21582			0.607908	+	0.794008i	$0.292009\pi$
$648$	2.74370	+	0.687098i	0.107783	+	0.0269917i
$649$	53.6643	−	53.6643i	2.10651	−	2.10651i
$650$	−22.5664	−	1.84991i	−0.885126	−	0.0725595i
$651$			21.4186i			0.839460i
$652$	0.512178	+	0.714687i	0.0200584	+	0.0279893i
$653$	−6.34246	+	6.34246i	−0.248200	+	0.248200i	−0.820231	−	0.572032i	$-0.806155\pi$
$653$	−6.34246	+	6.34246i	−0.248200	+	0.248200i	0.572032	+	0.820231i	$0.306155\pi$
$654$	12.6146	−	10.7031i	0.493269	−	0.418524i
$655$	−1.06137	−	1.06137i	−0.0414710	−	0.0414710i
$656$	12.0873	+	24.5061i	0.471931	+	0.956801i
$657$	10.6864	−	10.6864i	0.416915	−	0.416915i
$658$	−30.4934	−	35.9394i	−1.18876	−	1.40106i
$659$	−0.742066	+	0.742066i	−0.0289068	+	0.0289068i	−0.721412	−	0.692506i	$-0.756507\pi$
$659$	−0.742066	+	0.742066i	−0.0289068	+	0.0289068i	0.692506	+	0.721412i	$0.256507\pi$
$660$	1.80646	−	10.9441i	0.0703165	−	0.426000i
$661$		−	0.743392i		−	0.0289146i	−0.999895	−	0.0144573i	$-0.995398\pi$
$661$		−	0.743392i		−	0.0289146i	0.999895	−	0.0144573i	$-0.00460206\pi$
$662$	4.43506	+	5.22714i	0.172374	+	0.203158i
$663$		−	14.0416i		−	0.545329i
$664$	−3.65809	−	0.916085i	−0.141961	−	0.0355510i
$665$	12.3638	+	12.3638i	0.479448	+	0.479448i
$666$	1.36693	+	1.61106i	0.0529676	+	0.0624273i
$667$	−33.5159	+	16.8235i	−1.29774	+	0.651408i
$668$	43.4208	+	7.16713i	1.68000	+	0.277305i
$669$	−0.578871	−	0.578871i	−0.0223804	−	0.0223804i
$670$	0.145153	−	1.77067i	0.00560777	−	0.0684070i
$671$	−15.3840			−0.593891
$672$	−9.65783	−	24.4329i	−0.372559	−	0.942521i
$673$		−	20.3011i		−	0.782550i	−0.920274	−	0.391275i	$-0.872034\pi$
$673$		−	20.3011i		−	0.782550i	0.920274	−	0.391275i	$-0.127966\pi$
$674$	−23.4449	−	27.6320i	−0.903063	−	1.06434i
$675$	−2.94366	−	2.94366i	−0.113301	−	0.113301i
$676$	3.53416	+	0.583356i	0.135929	+	0.0224368i
$677$	−7.85493	+	7.85493i	−0.301889	+	0.301889i	−0.841753	−	0.539863i	$-0.818476\pi$
$677$	−7.85493	+	7.85493i	−0.301889	+	0.301889i	0.539863	+	0.841753i	$0.318476\pi$
$678$	−22.1485	−	1.81565i	−0.850607	−	0.0697298i
$679$	−0.637717	+	0.637717i	−0.0244733	+	0.0244733i
$680$	−8.10344	+	4.85763i	−0.310753	+	0.186282i
$681$	−7.10764	+	7.10764i	−0.272365	+	0.272365i
$682$	39.4041	+	3.23021i	1.50886	+	0.123691i
$683$	39.1884			1.49950			0.749752	−	0.661719i	$-0.230173\pi$
$683$	39.1884			1.49950			0.749752	+	0.661719i	$0.230173\pi$
$684$	4.79403	+	6.68954i	0.183304	+	0.255781i
$685$	−11.7680	+	11.7680i	−0.449632	+	0.449632i
$686$	4.06232	−	49.5547i	0.155100	−	1.89201i
$687$		−	16.1270i		−	0.615282i
$688$	−10.7961	+	5.32507i	−0.411599	+	0.203016i
$689$			13.4478i			0.512322i
$690$	5.82933	+	6.87041i	0.221919	+	0.261552i
$691$	−0.170687			−0.00649324			−0.00324662	−	0.999995i	$-0.501033\pi$
$691$	−0.170687			−0.00649324			−0.00324662	+	0.999995i	$0.501033\pi$
$692$	−6.59148	−	1.08801i	−0.250571	−	0.0413598i
$693$	19.9080	−	19.9080i	0.756241	−	0.756241i
$694$	1.46551	−	17.8771i	0.0556298	−	0.678607i
$695$	−2.34535			−0.0889641
$696$	12.8598	+	8.16252i	0.487448	+	0.309399i
$697$	24.9411			0.944711
$698$	1.98403	−	24.2024i	0.0750966	−	0.916075i
$699$	−16.1350	+	16.1350i	−0.610282	+	0.610282i
$700$	−6.29751	+	38.1523i	−0.238023	+	1.44202i
$701$	7.84477			0.296293			0.148146	−	0.988965i	$-0.452669\pi$
$701$	7.84477			0.296293			0.148146	+	0.988965i	$0.452669\pi$
$702$	3.51883	+	4.14727i	0.132810	+	0.156529i
$703$			6.14776i			0.231867i
$704$	−46.4062	+	14.0829i	−1.74900	+	0.530768i
$705$		−	6.56529i		−	0.247263i
$706$	0.424169	−	5.17428i	0.0159638	−	0.194737i
$707$	−33.4638	+	33.4638i	−1.25854	+	1.25854i
$708$	20.3522	−	14.5853i	0.764882	−	0.548150i
$709$	29.0576			1.09128			0.545640	−	0.838019i	$-0.316286\pi$
$709$	29.0576			1.09128			0.545640	+	0.838019i	$0.316286\pi$
$710$	2.58007	+	0.211505i	0.0968285	+	0.00793766i
$711$	−10.0272	+	10.0272i	−0.376048	+	0.376048i
$712$	13.3557	−	8.00614i	0.500527	−	0.300043i
$713$	−22.7089	+	22.7089i	−0.850456	+	0.850456i
$714$	−23.9003	−	1.95926i	−0.894445	−	0.0733235i
$715$	15.0825	−	15.0825i	0.564052	−	0.564052i
$716$	3.73549	−	22.6308i	0.139602	−	0.845753i
$717$	−0.718238	−	0.718238i	−0.0268231	−	0.0268231i
$718$	12.1809	+	14.3563i	0.454587	+	0.535773i
$719$			9.00931i			0.335990i	0.985788	+	0.167995i	$0.0537293\pi$
$719$			9.00931i			0.335990i	−0.985788	+	0.167995i	$0.946271\pi$
$720$	1.17608	−	3.46547i	0.0438298	−	0.129150i
$721$	−47.5791			−1.77194
$722$	0.238812	−	2.91318i	0.00888767	−	0.108417i
$723$	−11.4731	−	11.4731i	−0.426690	−	0.426690i
$724$	0.875996	−	5.30707i	0.0325561	−	0.197236i
$725$	−10.0571	−	20.0358i	−0.373510	−	0.744110i
$726$	−23.5581	−	27.7655i	−0.874325	−	1.03047i
$727$	−24.3547	−	24.3547i	−0.903266	−	0.903266i	0.0924517	−	0.995717i	$-0.470530\pi$
$727$	−24.3547	−	24.3547i	−0.903266	−	0.903266i	−0.995717	+	0.0924517i	$0.970530\pi$
$728$	12.2728	−	49.0073i	0.454859	−	1.81633i
$729$			1.00000i			0.0370370i
$730$	−12.6508	−	14.9101i	−0.468226	−	0.551848i
$731$			10.9878i			0.406398i
$732$	−5.00777	−	0.826594i	−0.185093	−	0.0305518i
$733$	−26.6646	+	26.6646i	−0.984880	+	0.984880i	−0.999887	−	0.0150072i	$-0.995223\pi$
$733$	−26.6646	+	26.6646i	−0.984880	+	0.984880i	0.0150072	+	0.999887i	$0.495223\pi$
$734$	19.2057	+	22.6357i	0.708894	+	0.835498i
$735$	9.42581	−	9.42581i	0.347676	−	0.347676i
$736$	15.6652	−	36.1445i	0.577428	−	1.33231i
$737$	−5.88581	−	5.88581i	−0.216806	−	0.216806i
$738$	−7.36652	+	6.25026i	−0.271165	+	0.230075i
$739$	−13.3691	+	13.3691i	−0.491791	+	0.491791i	−0.908870	−	0.417079i	$-0.863054\pi$
$739$	−13.3691	+	13.3691i	−0.491791	+	0.491791i	0.417079	+	0.908870i	$0.363054\pi$
$740$	2.22202	−	1.59240i	0.0816830	−	0.0585378i
$741$			15.8259i			0.581378i
$742$	22.8897	+	1.87642i	0.840308	+	0.0688855i
$743$	22.9146	−	22.9146i	0.840656	−	0.840656i	−0.148288	−	0.988944i	$-0.547376\pi$
$743$	22.9146	−	22.9146i	0.840656	−	0.840656i	0.988944	+	0.148288i	$0.0473764\pi$
$744$	12.6532	+	3.16872i	0.463890	+	0.116171i
$745$	−3.24642			−0.118940
$746$	−3.90666	+	47.6559i	−0.143033	+	1.74480i
$747$		−	1.33327i		−	0.0487817i
$748$	−7.20897	+	43.6743i	−0.263586	+	1.59689i
$749$			46.1708i			1.68704i
$750$	−9.04007	+	7.67022i	−0.330097	+	0.280077i
$751$	−28.5915	+	28.5915i	−1.04332	+	1.04332i	−0.0443004	+	0.999018i	$0.514106\pi$
$751$	−28.5915	+	28.5915i	−1.04332	+	1.04332i	−0.999018	+	0.0443004i	$0.985894\pi$
$752$	−25.7428	+	12.6974i	−0.938744	+	0.463025i
$753$		−	19.2607i		−	0.701898i
$754$	10.9570	+	27.1629i	0.399030	+	0.989214i
$755$	1.54806			0.0563395
$756$	7.55010	−	5.41075i	0.274594	−	0.196787i
$757$	−17.0107	−	17.0107i	−0.618266	−	0.618266i	0.326820	−	0.945086i	$-0.394023\pi$
$757$	−17.0107	−	17.0107i	−0.618266	−	0.618266i	−0.945086	+	0.326820i	$0.894023\pi$
$758$	−31.9143	+	27.0783i	−1.15918	+	0.983529i
$759$	42.2146			1.53229
$760$	9.13318	−	5.47491i	0.331295	−	0.198596i
$761$	−31.5770			−1.14466			−0.572332	−	0.820022i	$-0.693961\pi$
$761$	−31.5770			−1.14466			−0.572332	+	0.820022i	$0.693961\pi$
$762$	−8.89670	−	0.729320i	−0.322293	−	0.0264205i
$763$		−	54.3294i		−	1.96686i
$764$	−1.87738	−	2.61967i	−0.0679212	−	0.0947765i
$765$	−2.36197	−	2.36197i	−0.0853972	−	0.0853972i
$766$	11.2131	+	0.919207i	0.405144	+	0.0332123i
$767$	48.1485			1.73854
$768$	−15.8628	+	2.09079i	−0.572400	+	0.0754450i
$769$	32.4673	+	32.4673i	1.17080	+	1.17080i	0.982019	+	0.188781i	$0.0604536\pi$
$769$	32.4673	+	32.4673i	1.17080	+	1.17080i	0.188781	+	0.982019i	$0.439546\pi$
$770$	−23.5675	−	27.7765i	−0.849314	−	1.00100i
$771$	7.36488	−	7.36488i	0.265240	−	0.265240i
$772$	−17.2917	+	12.3920i	−0.622341	+	0.445999i
$773$	−12.2206	−	12.2206i	−0.439545	−	0.439545i	0.452314	−	0.891859i	$-0.350599\pi$
$773$	−12.2206	−	12.2206i	−0.439545	−	0.439545i	−0.891859	+	0.452314i	$0.850599\pi$
$774$	−2.75355	−	3.24531i	−0.0989742	−	0.116650i
$775$	−13.5754	−	13.5754i	−0.487643	−	0.487643i
$776$	0.282393	+	0.471084i	0.0101373	+	0.0169109i
$777$	6.93863			0.248922
$778$	−8.49409	+	7.20697i	−0.304528	+	0.258382i
$779$	−28.1105			−1.00716
$780$	5.72003	−	4.09924i	0.204810	−	0.146776i
$781$	8.57630	−	8.57630i	0.306884	−	0.306884i
$782$	−23.2628	−	27.4174i	−0.831877	−	0.980445i
$783$	−1.69495	+	5.11147i	−0.0605725	+	0.182669i
$784$	−55.1887	−	18.7294i	−1.97102	−	0.668908i
$785$	12.2810	−	12.2810i	0.438328	−	0.438328i
$786$	−2.31243	−	0.189565i	−0.0824816	−	0.00676156i
$787$		−	30.0075i		−	1.06965i	−0.844962	−	0.534826i	$-0.820377\pi$
$787$		−	30.0075i		−	1.06965i	0.844962	−	0.534826i	$-0.179623\pi$
$788$	3.98768	−	24.1586i	0.142055	−	0.860616i
$789$	−14.3020			−0.509166
$790$	11.8704	+	13.9904i	0.422330	+	0.497755i
$791$	−51.6052	+	51.6052i	−1.83487	+	1.83487i
$792$	−8.81560	−	14.7061i	−0.313249	−	0.522557i
$793$	−6.90137	−	6.90137i	−0.245075	−	0.245075i
$794$	2.85987	−	34.8864i	0.101493	−	1.23807i
$795$	2.26210	+	2.26210i	0.0802284	+	0.0802284i
$796$	−5.17424	+	31.3472i	−0.183396	+	1.11107i
$797$	4.41620	+	4.41620i	0.156430	+	0.156430i	0.780983	−	0.624553i	$-0.214719\pi$
$797$	4.41620	+	4.41620i	0.156430	+	0.156430i	−0.624553	+	0.780983i	$0.714719\pi$
$798$	26.9374	+	2.20823i	0.953573	+	0.0781705i
$799$			26.1998i			0.926883i
$800$	21.6072	+	9.36466i	0.763930	+	0.331091i
$801$	3.89289	+	3.89289i	0.137549	+	0.137549i
$802$	−42.0429	−	3.44653i	−1.48459	−	0.121701i
$803$	−91.6139			−3.23298
$804$	−1.59969	−	2.23219i	−0.0564168	−	0.0787234i
$805$	29.5900			1.04291
$806$	16.2279	+	19.1261i	0.571604	+	0.673689i
$807$			15.9164i			0.560285i
$808$	14.8184	+	24.7198i	0.521308	+	0.869640i
$809$	30.0733	+	30.0733i	1.05732	+	1.05732i	0.998254	+	0.0590685i	$0.0188130\pi$
$809$	30.0733	+	30.0733i	1.05732	+	1.05732i	0.0590685	+	0.998254i	$0.481187\pi$
$810$	1.28954	+	0.105712i	0.0453097	+	0.00371433i
$811$		−	29.8721i		−	1.04895i	−0.851426	−	0.524475i	$-0.824262\pi$
$811$		−	29.8721i		−	1.04895i	0.851426	−	0.524475i	$-0.175738\pi$
$812$	47.7631	−	14.8599i	1.67615	−	0.521479i
$813$		−	14.7007i		−	0.515575i
$814$	1.04644	−	12.7651i	0.0366777	−	0.447417i
$815$	0.284411	+	0.284411i	0.00996249	+	0.00996249i
$816$	−4.69332	+	13.8295i	−0.164299	+	0.484128i
$817$		−	12.3840i		−	0.433263i
$818$	−14.1314	+	11.9901i	−0.494093	+	0.419222i
$819$	17.8618			0.624140
$820$	7.28121	+	10.1601i	0.254271	+	0.354807i
$821$	−3.45595			−0.120613			−0.0603067	−	0.998180i	$-0.519208\pi$
$821$	−3.45595			−0.120613			−0.0603067	+	0.998180i	$0.519208\pi$
$822$	−2.10182	+	25.6393i	−0.0733093	+	0.894272i
$823$	27.6536	+	27.6536i	0.963944	+	0.963944i	0.999372	−	0.0354286i	$-0.0112796\pi$
$823$	27.6536	+	27.6536i	0.963944	+	0.963944i	−0.0354286	+	0.999372i	$0.511280\pi$
$824$	−7.03898	+	28.1079i	−0.245214	+	0.979184i
$825$			25.2359i			0.878601i
$826$	6.71831	−	81.9541i	0.233760	−	2.85155i
$827$	6.98855	+	6.98855i	0.243016	+	0.243016i	0.818097	−	0.575081i	$-0.195029\pi$
$827$	6.98855	+	6.98855i	0.243016	+	0.243016i	−0.575081	+	0.818097i	$0.695029\pi$
$828$	13.7417	+	2.26823i	0.477556	+	0.0788265i
$829$	7.57407	+	7.57407i	0.263058	+	0.263058i	0.826295	−	0.563237i	$-0.190444\pi$
$829$	7.57407	+	7.57407i	0.263058	+	0.263058i	−0.563237	+	0.826295i	$0.690444\pi$
$830$	−1.71929	−	0.140942i	−0.0596776	−	0.00489216i
$831$	1.15967	+	1.15967i	0.0402284	+	0.0402284i
$832$	−27.1359	−	14.5005i	−0.940769	−	0.502716i
$833$	−37.6151	+	37.6151i	−1.30329	+	1.30329i
$834$	−2.76438	+	2.34549i	−0.0957227	+	0.0812178i
$835$	20.1316			0.696681
$836$	8.12505	−	49.2241i	0.281011	−	1.70245i
$837$			4.61174i			0.159405i
$838$	−3.05628	+	37.2824i	−0.105577	+	1.28790i
$839$	19.1516	−	19.1516i	0.661186	−	0.661186i	−0.294473	−	0.955660i	$-0.595144\pi$
$839$	19.1516	−	19.1516i	0.661186	−	0.661186i	0.955660	+	0.294473i	$0.0951443\pi$
$840$	−6.17922	−	10.3081i	−0.213203	−	0.355663i
$841$	−17.3274	+	23.2543i	−0.597496	+	0.801872i
$842$	18.1432	−	15.3939i	0.625256	−	0.530510i
$843$	4.54494	−	4.54494i	0.156536	−	0.156536i
$844$	26.5513	+	37.0493i	0.913933	+	1.27529i
$845$	1.63857			0.0563686
$846$	−6.56570	−	7.73829i	−0.225733	−	0.266048i
$847$	−119.582			−4.10890
$848$	4.49488	−	13.2447i	0.154355	−	0.454826i
$849$	0.675200	+	0.675200i	0.0231728	+	0.0231728i
$850$	16.3901	−	13.9065i	0.562177	−	0.476990i
$851$	7.35664	+	7.35664i	0.252182	+	0.252182i
$852$	3.25256	−	2.33094i	0.111431	−	0.0798567i
$853$	−19.1086	+	19.1086i	−0.654265	+	0.654265i	−0.954017	−	0.299752i	$-0.903096\pi$
$853$	−19.1086	+	19.1086i	−0.654265	+	0.654265i	0.299752	+	0.954017i	$0.403096\pi$
$854$	−12.7099	+	10.7839i	−0.434922	+	0.369018i
$855$	2.66211	+	2.66211i	0.0910424	+	0.0910424i
$856$	27.2758	+	6.83062i	0.932269	+	0.233466i
$857$	−7.63255			−0.260723			−0.130361	−	0.991467i	$-0.541614\pi$
$857$	−7.63255			−0.260723			−0.130361	+	0.991467i	$0.541614\pi$
$858$	2.69380	−	32.8606i	0.0919647	−	1.12184i
$859$	13.6987	+	13.6987i	0.467394	+	0.467394i	0.901069	−	0.433675i	$-0.142783\pi$
$859$	13.6987	+	13.6987i	0.467394	+	0.467394i	−0.433675	+	0.901069i	$0.642783\pi$
$860$	−4.47603	+	3.20773i	−0.152631	+	0.109383i
$861$			31.7267i			1.08124i
$862$	−2.76156	+	33.6872i	−0.0940590	+	1.14739i
$863$	−2.62409			−0.0893250			−0.0446625	−	0.999002i	$-0.514221\pi$
$863$	−2.62409			−0.0893250			−0.0446625	+	0.999002i	$0.514221\pi$
$864$	−2.07948	−	5.26078i	−0.0707452	−	0.178975i
$865$	−3.05607			−0.103909
$866$	16.3150	+	19.2288i	0.554408	+	0.653421i
$867$	−2.59502	−	2.59502i	−0.0881313	−	0.0881313i
$868$	34.8191	−	24.9530i	1.18184	−	0.846960i
$869$	85.9626			2.91608
$870$	6.41225	+	2.72604i	0.217396	+	0.0924214i
$871$		−	5.28084i		−	0.178935i
$872$	−32.0957	−	8.03763i	−1.08690	−	0.272189i
$873$	−0.137310	+	0.137310i	−0.00464724	+	0.00464724i
$874$	26.2189	+	30.9015i	0.886869	+	1.04526i
$875$			38.9345i			1.31622i
$876$	−29.8221	−	4.92250i	−1.00759	−	0.166316i
$877$			18.0814i			0.610566i	0.952262	+	0.305283i	$0.0987510\pi$
$877$			18.0814i			0.610566i	−0.952262	+	0.305283i	$0.901249\pi$
$878$	13.8098	+	1.13208i	0.466059	+	0.0382059i
$879$	4.38140			0.147781
$880$	−19.8959	+	9.81342i	−0.670691	+	0.330810i
$881$	−17.3747	+	17.3747i	−0.585370	+	0.585370i	−0.936374	−	0.351004i	$-0.885840\pi$
$881$	−17.3747	+	17.3747i	−0.585370	+	0.585370i	0.351004	+	0.936374i	$0.385840\pi$
$882$	1.68349	−	20.5363i	0.0566861	−	0.691492i
$883$		−	23.6139i		−	0.794670i	−0.917674	−	0.397335i	$-0.869935\pi$
$883$		−	23.6139i		−	0.794670i	0.917674	−	0.397335i	$-0.130065\pi$
$884$	−22.8267	+	16.3586i	−0.767743	+	0.550201i
$885$	8.09920	−	8.09920i	0.272252	−	0.272252i
$886$	15.2724	+	18.0000i	0.513087	+	0.604720i
$887$	−15.9688	−	15.9688i	−0.536179	−	0.536179i	0.386225	−	0.922404i	$-0.373779\pi$
$887$	−15.9688	−	15.9688i	−0.536179	−	0.536179i	−0.922404	+	0.386225i	$0.873779\pi$
$888$	1.02652	−	4.09906i	0.0344477	−	0.137556i
$889$	−20.7290	+	20.7290i	−0.695229	+	0.695229i
$890$	5.43155	−	4.60850i	0.182066	−	0.154477i
$891$	4.28648	−	4.28648i	0.143603	−	0.143603i
$892$	−0.266647	+	1.61543i	−0.00892801	+	0.0540888i
$893$		−	29.5291i		−	0.988154i
$894$	−3.82644	+	3.24662i	−0.127975	+	0.108583i
$895$		−	10.4925i		−	0.350726i
$896$	−28.4679	+	44.1650i	−0.951044	+	1.47545i
$897$	18.9378	+	18.9378i	0.632316	+	0.632316i
$898$	20.5790	−	17.4606i	0.686730	−	0.582669i
$899$	−7.81667	+	23.5728i	−0.260700	+	0.786197i
$900$	−1.35595	+	8.21477i	−0.0451983	+	0.273826i
$901$	−9.02726	−	9.02726i	−0.300742	−	0.300742i
$902$	58.3681	+	4.78481i	1.94345	+	0.159317i
$903$	−13.9772			−0.465131
$904$	22.8517	+	38.1209i	0.760036	+	1.26788i
$905$		−	2.46056i		−	0.0817918i
$906$	1.82464	−	1.54815i	0.0606196	−	0.0514339i
$907$	−18.2748	−	18.2748i	−0.606805	−	0.606805i	0.335305	−	0.942110i	$-0.391161\pi$
$907$	−18.2748	−	18.2748i	−0.606805	−	0.606805i	−0.942110	+	0.335305i	$0.891161\pi$
$908$	19.8350	+	3.27402i	0.658249	+	0.108652i
$909$	−7.20526	+	7.20526i	−0.238983	+	0.238983i
$910$	1.88819	−	23.0334i	0.0625930	−	0.763549i
$911$	−16.9036	+	16.9036i	−0.560043	+	0.560043i	−0.929319	−	0.369277i	$-0.879605\pi$
$911$	−16.9036	+	16.9036i	−0.560043	+	0.560043i	0.369277	+	0.929319i	$0.379605\pi$
$912$	5.28972	−	15.5868i	0.175160	−	0.516132i
$913$	−5.71503	+	5.71503i	−0.189140	+	0.189140i
$914$	−2.02358	+	24.6849i	−0.0669342	+	0.816504i
$915$	−2.32180			−0.0767563
$916$	−26.2168	+	18.7882i	−0.866227	+	0.620779i
$917$	−5.38789	+	5.38789i	−0.177924	+	0.177924i
$918$	−5.14609	−	0.421858i	−0.169846	−	0.0139234i
$919$		−	40.5884i		−	1.33889i	−0.742862	−	0.669445i	$-0.766532\pi$
$919$		−	40.5884i		−	1.33889i	0.742862	−	0.669445i	$-0.233468\pi$
$920$	4.37762	−	17.4806i	0.144326	−	0.576318i
$921$			20.9646i			0.690807i
$922$	−36.4045	+	30.8881i	−1.19892	+	1.01725i
$923$	7.69480			0.253278
$924$	−55.5565	−	9.17027i	−1.82767	−	0.301680i
$925$	−4.39780	+	4.39780i	−0.144599	+	0.144599i
$926$	−59.8495	−	4.90625i	−1.96677	−	0.161229i
$927$	−10.2445			−0.336474
$928$	−1.71243	−	30.4149i	−0.0562134	−	0.998419i
$929$	14.7949			0.485404			0.242702	−	0.970101i	$-0.421966\pi$
$929$	14.7949			0.485404			0.242702	+	0.970101i	$0.421966\pi$
$930$	5.94700	+	0.487515i	0.195010	+	0.0159862i
$931$	42.3950	−	42.3950i	1.38944	−	1.38944i
$932$	45.0274	+	7.43233i	1.47492	+	0.243454i
$933$	3.70400			0.121263
$934$	45.1715	−	38.3266i	1.47806	−	1.25409i
$935$			20.2491i			0.662216i
$936$	2.64251	−	10.5520i	0.0863732	−	0.344903i
$937$		−	11.9679i		−	0.390975i	−0.980706	−	0.195487i	$-0.937371\pi$
$937$		−	11.9679i		−	0.390975i	0.980706	−	0.195487i	$-0.0626288\pi$
$938$	−8.98858	−	0.736852i	−0.293487	−	0.0240591i
$939$	21.0263	−	21.0263i	0.686168	−	0.686168i
$940$	−10.6729	+	7.64867i	−0.348111	+	0.249472i
$941$	−39.6942			−1.29399			−0.646997	−	0.762493i	$-0.723975\pi$
$941$	−39.6942			−1.29399			−0.646997	+	0.762493i	$0.723975\pi$
$942$	2.19344	−	26.7570i	0.0714662	−	0.871789i
$943$	−33.6380	+	33.6380i	−1.09541	+	1.09541i
$944$	−47.4213	−	16.0934i	−1.54343	−	0.523796i
$945$	3.00458	−	3.00458i	0.0977389	−	0.0977389i
$946$	−2.10795	+	25.7140i	−0.0685352	+	0.836035i
$947$	40.5916	−	40.5916i	1.31905	−	1.31905i	0.404519	−	0.914530i	$-0.367439\pi$
$947$	40.5916	−	40.5916i	1.31905	−	1.31905i	0.914530	−	0.404519i	$-0.132561\pi$
$948$	27.9825	+	4.61885i	0.908828	+	0.150013i
$949$	−41.0987	−	41.0987i	−1.33412	−	1.33412i
$950$	−18.4729	+	15.6737i	−0.599340	+	0.508521i
$951$		−	25.2895i		−	0.820068i
$952$	24.6591	+	41.1360i	0.799207	+	1.33323i
$953$	−17.2729			−0.559524			−0.279762	−	0.960069i	$-0.590255\pi$
$953$	−17.2729			−0.559524			−0.279762	+	0.960069i	$0.590255\pi$
$954$	4.92850	+	0.404021i	0.159566	+	0.0130807i
$955$	−1.04250	−	1.04250i	−0.0337347	−	0.0337347i
$956$	−0.330844	+	2.00436i	−0.0107003	+	0.0648257i
$957$	29.1756	−	14.6449i	0.943114	−	0.473401i
$958$	13.0612	−	11.0821i	0.421990	−	0.358045i
$959$	59.7387	+	59.7387i	1.92906	+	1.92906i
$960$	−7.00378	+	2.12543i	−0.226046	+	0.0685981i
$961$		−	9.73184i		−	0.313930i
$962$	6.19598	−	5.25710i	0.199766	−	0.169496i
$963$			9.94126i			0.320353i
$964$	−5.28491	+	32.0177i	−0.170215	+	1.03122i
$965$	−6.88126	+	6.88126i	−0.221516	+	0.221516i
$966$	34.8767	−	29.5918i	1.12214	−	0.952101i
$967$	24.5902	−	24.5902i	0.790769	−	0.790769i	−0.190850	−	0.981619i	$-0.561125\pi$
$967$	24.5902	−	24.5902i	0.790769	−	0.790769i	0.981619	+	0.190850i	$0.0611245\pi$
$968$	−17.6913	+	70.6445i	−0.568620	+	2.27060i
$969$	−10.6236	−	10.6236i	−0.341278	−	0.341278i
$970$	0.162551	+	0.191582i	0.00521920	+	0.00615131i
$971$	−15.3572	+	15.3572i	−0.492837	+	0.492837i	−0.909199	−	0.416362i	$-0.863305\pi$
$971$	−15.3572	+	15.3572i	−0.492837	+	0.492837i	0.416362	+	0.909199i	$0.363305\pi$
$972$	1.62565	−	1.16502i	0.0521427	−	0.0373679i
$973$			11.9058i			0.381684i
$974$	1.51801	−	18.5176i	0.0486401	−	0.593342i
$975$	−11.3210	+	11.3210i	−0.362563	+	0.362563i
$976$	4.49038	+	9.10388i	0.143734	+	0.291408i
$977$	20.5110			0.656205			0.328103	−	0.944642i	$-0.393591\pi$
$977$	20.5110			0.656205			0.328103	+	0.944642i	$0.393591\pi$
$978$	0.619655	+	0.0507971i	0.0198144	+	0.00162431i
$979$		−	33.3736i		−	1.06663i
$980$	−26.3043	−	4.34184i	−0.840260	−	0.138695i
$981$		−	11.6979i		−	0.373487i
$982$	−5.52969	−	6.51726i	−0.176460	−	0.207974i
$983$	−22.1203	+	22.1203i	−0.705527	+	0.705527i	−0.965591	−	0.260064i	$-0.916256\pi$
$983$	−22.1203	+	22.1203i	−0.705527	+	0.705527i	0.260064	+	0.965591i	$0.416256\pi$
$984$	18.7429	+	4.69372i	0.597500	+	0.149630i
$985$		−	11.2009i		−	0.356890i
$986$	−25.5891	−	10.8787i	−0.814922	−	0.346448i
$987$	−33.3278			−1.06084
$988$	25.7273	−	18.4374i	0.818495	−	0.586572i
$989$	−14.8192	−	14.8192i	−0.471223	−	0.471223i
$990$	−5.07444	−	5.98070i	−0.161276	−	0.190079i
$991$	29.3668			0.932867			0.466433	−	0.884556i	$-0.345539\pi$
$991$	29.3668			0.932867			0.466433	+	0.884556i	$0.345539\pi$
$992$	−9.59001	−	24.2613i	−0.304483	−	0.770299i
$993$	4.84731			0.153825
$994$	1.07368	−	13.0974i	0.0340550	−	0.415424i
$995$			14.5338i			0.460752i
$996$	−2.16742	+	1.55328i	−0.0686775	+	0.0492175i
$997$	−30.3534	−	30.3534i	−0.961302	−	0.961302i	0.0379765	−	0.999279i	$-0.487909\pi$
$997$	−30.3534	−	30.3534i	−0.961302	−	0.961302i	−0.999279	+	0.0379765i	$0.987909\pi$
$998$	4.71379	−	57.5017i	0.149212	−	1.82018i
$999$	1.49399			0.0472678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	696.2.v.c.307.1	✓	112
8.3	odd	2	inner	696.2.v.c.307.30	yes	112
29.12	odd	4	inner	696.2.v.c.331.30	yes	112
232.99	even	4	inner	696.2.v.c.331.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
696.2.v.c.307.1	✓	112	1.1	even	1	trivial
696.2.v.c.307.30	yes	112	8.3	odd	2	inner
696.2.v.c.331.1	yes	112	232.99	even	4	inner
696.2.v.c.331.30	yes	112	29.12	odd	4	inner

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:	\( N \)	\(=\)	\( 696 = 2^{3} \cdot 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	696.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40949 - 0.115545i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97330 + 0.325717i) q^{4} +0.914898 q^{5} +(1.07836 - 0.914954i) q^{6} -4.64436i q^{7} +(-2.74370 - 0.687098i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.40949 - 0.115545i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97330 + 0.325717i) q^{4} +0.914898 q^{5} +(1.07836 - 0.914954i) q^{6} -4.64436i q^{7} +(-2.74370 - 0.687098i) q^{8} -1.00000i q^{9} +(-1.28954 - 0.105712i) q^{10} +(-4.28648 + 4.28648i) q^{11} +(-1.62565 + 1.16502i) q^{12} -3.84591 q^{13} +(-0.536631 + 6.54615i) q^{14} +(-0.646931 + 0.646931i) q^{15} +(3.78782 + 1.28547i) q^{16} +(2.58168 - 2.58168i) q^{17} +(-0.115545 + 1.40949i) q^{18} +(-2.90974 + 2.90974i) q^{19} +(1.80537 + 0.297998i) q^{20} +(3.28406 + 3.28406i) q^{21} +(6.53702 - 5.54646i) q^{22} +6.96381i q^{23} +(2.42594 - 1.45424i) q^{24} -4.16296 q^{25} +(5.42075 + 0.444374i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.51275 - 9.16470i) q^{28} +(2.41585 + 4.81287i) q^{29} +(0.986589 - 0.837090i) q^{30} +(3.26099 + 3.26099i) q^{31} +(-5.19034 - 2.24952i) q^{32} -6.06200i q^{33} +(-3.93713 + 3.34054i) q^{34} -4.24911i q^{35} +(0.325717 - 1.97330i) q^{36} +(1.05641 - 1.05641i) q^{37} +(4.43744 - 3.76503i) q^{38} +(2.71947 - 2.71947i) q^{39} +(-2.51021 - 0.628624i) q^{40} +(4.83041 + 4.83041i) q^{41} +(-4.24937 - 5.00828i) q^{42} +(-2.12803 + 2.12803i) q^{43} +(-9.85470 + 7.06233i) q^{44} -0.914898i q^{45} +(0.804631 - 9.81538i) q^{46} +(-5.07419 + 5.07419i) q^{47} +(-3.58736 + 1.76942i) q^{48} -14.5700 q^{49} +(5.86763 + 0.481008i) q^{50} +3.65104i q^{51} +(-7.58912 - 1.25268i) q^{52} -3.49667i q^{53} +(-0.914954 - 1.07836i) q^{54} +(-3.92170 + 3.92170i) q^{55} +(-3.19113 + 12.7427i) q^{56} -4.11499i q^{57} +(-2.84900 - 7.06280i) q^{58} -12.5194 q^{59} +(-1.48730 + 1.06587i) q^{60} +(1.79447 + 1.79447i) q^{61} +(-4.21953 - 4.97311i) q^{62} -4.64436 q^{63} +(7.05579 + 3.77038i) q^{64} -3.51861 q^{65} +(-0.700432 + 8.54431i) q^{66} +1.37311i q^{67} +(5.93531 - 4.25352i) q^{68} +(-4.92415 - 4.92415i) q^{69} +(-0.490962 + 5.98906i) q^{70} -2.00078 q^{71} +(-0.687098 + 2.74370i) q^{72} +(10.6864 + 10.6864i) q^{73} +(-1.61106 + 1.36693i) q^{74} +(2.94366 - 2.94366i) q^{75} +(-6.68954 + 4.79403i) q^{76} +(19.9080 + 19.9080i) q^{77} +(-4.14727 + 3.51883i) q^{78} +(-10.0272 - 10.0272i) q^{79} +(3.46547 + 1.17608i) q^{80} -1.00000 q^{81} +(-6.25026 - 7.36652i) q^{82} +1.33327 q^{83} +(5.41075 + 7.55010i) q^{84} +(2.36197 - 2.36197i) q^{85} +(3.24531 - 2.75355i) q^{86} +(-5.11147 - 1.69495i) q^{87} +(14.7061 - 8.81560i) q^{88} +(-3.89289 + 3.89289i) q^{89} +(-0.105712 + 1.28954i) q^{90} +17.8618i q^{91} +(-2.26823 + 13.7417i) q^{92} -4.61174 q^{93} +(7.73829 - 6.56570i) q^{94} +(-2.66211 + 2.66211i) q^{95} +(5.26078 - 2.07948i) q^{96} +(-0.137310 - 0.137310i) q^{97} +(20.5363 + 1.68349i) q^{98} +(4.28648 + 4.28648i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) 112 * q - 4 * q^2 - 4 * q^8	\( 112 q - 4 q^{2} - 4 q^{8} - 24 q^{11} - 4 q^{14} - 24 q^{16} + 8 q^{17} + 4 q^{18} - 8 q^{19} - 16 q^{20} - 4 q^{24} + 168 q^{25} + 4 q^{26} - 40 q^{30} + 16 q^{32} - 12 q^{40} - 24 q^{41} - 8 q^{43} + 52 q^{44} + 36 q^{46} - 32 q^{48} - 152 q^{49} + 36 q^{50} - 44 q^{52} + 8 q^{54} - 56 q^{56} - 16 q^{58} - 8 q^{59} - 24 q^{60} + 48 q^{66} - 36 q^{68} - 60 q^{70} - 4 q^{72} + 32 q^{73} + 64 q^{74} + 8 q^{76} + 36 q^{78} - 112 q^{81} + 16 q^{82} - 64 q^{83} - 24 q^{84} + 40 q^{88} - 8 q^{89} - 68 q^{94} + 8 q^{97} + 56 q^{98} + 24 q^{99}+O(q^{100}) \) 112 * q - 4 * q^2 - 4 * q^8 - 24 * q^11 - 4 * q^14 - 24 * q^16 + 8 * q^17 + 4 * q^18 - 8 * q^19 - 16 * q^20 - 4 * q^24 + 168 * q^25 + 4 * q^26 - 40 * q^30 + 16 * q^32 - 12 * q^40 - 24 * q^41 - 8 * q^43 + 52 * q^44 + 36 * q^46 - 32 * q^48 - 152 * q^49 + 36 * q^50 - 44 * q^52 + 8 * q^54 - 56 * q^56 - 16 * q^58 - 8 * q^59 - 24 * q^60 + 48 * q^66 - 36 * q^68 - 60 * q^70 - 4 * q^72 + 32 * q^73 + 64 * q^74 + 8 * q^76 + 36 * q^78 - 112 * q^81 + 16 * q^82 - 64 * q^83 - 24 * q^84 + 40 * q^88 - 8 * q^89 - 68 * q^94 + 8 * q^97 + 56 * q^98 + 24 * q^99

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