LMFDB - Embedded newform 168.2.bc.a.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(37,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("168.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	168.37
Dual form			168.2.bc.a.109.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.189716 - 1.40143i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.92802 + 0.531748i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.865014 + 1.11882i) q^{6} +(0.993295 + 2.45222i) q^{7} +(1.11098 + 2.60110i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.189716 - 1.40143i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.92802 + 0.531748i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.865014 + 1.11882i) q^{6} +(0.993295 + 2.45222i) q^{7} +(1.11098 + 2.60110i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.91917 - 4.68162i) q^{10} +(-0.815768 + 0.470984i) q^{11} +(1.40384 - 1.42451i) q^{12} -6.15117i q^{13} +(3.24817 - 1.85726i) q^{14} -3.57776 q^{15} +(3.43449 - 2.05044i) q^{16} +(1.89187 + 3.27682i) q^{17} +(-1.30853 - 0.536416i) q^{18} +(2.09110 + 1.20730i) q^{19} +(-6.92506 - 1.80141i) q^{20} +(-2.08633 - 1.62703i) q^{21} +(0.814815 + 1.05389i) q^{22} +(-1.49371 + 2.58719i) q^{23} +(-2.26269 - 1.69713i) q^{24} +(3.90019 + 6.75532i) q^{25} +(-8.62043 + 1.16697i) q^{26} +1.00000i q^{27} +(-3.21905 - 4.19973i) q^{28} +2.68125i q^{29} +(0.678758 + 5.01398i) q^{30} +(-5.35686 - 9.27835i) q^{31} +(-3.52512 - 4.42420i) q^{32} +(0.470984 - 0.815768i) q^{33} +(4.23332 - 3.27300i) q^{34} +(-1.30906 + 9.37491i) q^{35} +(-0.503501 + 1.93558i) q^{36} +(-1.47851 - 0.853618i) q^{37} +(1.29523 - 3.15958i) q^{38} +(3.07558 + 5.32707i) q^{39} +(-1.21075 + 10.0467i) q^{40} -4.56000 q^{41} +(-1.88437 + 3.23252i) q^{42} -3.50672i q^{43} +(1.32237 - 1.34185i) q^{44} +(3.09843 - 1.78888i) q^{45} +(3.90915 + 1.60251i) q^{46} +(3.42292 - 5.92866i) q^{47} +(-1.94914 + 3.49297i) q^{48} +(-5.02673 + 4.87155i) q^{49} +(8.72718 - 6.74743i) q^{50} +(-3.27682 - 1.89187i) q^{51} +(3.27087 + 11.8595i) q^{52} +(6.57466 - 3.79588i) q^{53} +(1.40143 - 0.189716i) q^{54} -3.37013 q^{55} +(-5.27492 + 5.30803i) q^{56} -2.41460 q^{57} +(3.75759 - 0.508677i) q^{58} +(0.100623 - 0.0580947i) q^{59} +(6.89798 - 1.90247i) q^{60} +(-7.06184 - 4.07716i) q^{61} +(-11.9867 + 9.26752i) q^{62} +(2.62033 + 0.365889i) q^{63} +(-5.53143 + 5.77955i) q^{64} +(11.0037 - 19.0590i) q^{65} +(-1.23259 - 0.505287i) q^{66} +(-3.44314 + 1.98790i) q^{67} +(-5.39001 - 5.31177i) q^{68} -2.98743i q^{69} +(13.3866 + 0.0559922i) q^{70} -3.92572 q^{71} +(2.80811 + 0.338410i) q^{72} +(-3.11438 - 5.39427i) q^{73} +(-0.915789 + 2.23397i) q^{74} +(-6.75532 - 3.90019i) q^{75} +(-4.67365 - 1.21575i) q^{76} +(-1.96525 - 1.53261i) q^{77} +(6.88203 - 5.32085i) q^{78} +(2.73628 - 4.73937i) q^{79} +(14.3095 - 0.209245i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.865104 + 6.39052i) q^{82} +1.19560i q^{83} +(4.88764 + 2.02755i) q^{84} +13.5373i q^{85} +(-4.91443 + 0.665282i) q^{86} +(-1.34063 - 2.32203i) q^{87} +(-2.13138 - 1.59864i) q^{88} +(0.910509 - 1.57705i) q^{89} +(-3.09481 - 4.00286i) q^{90} +(15.0840 - 6.10992i) q^{91} +(1.50417 - 5.78242i) q^{92} +(9.27835 + 5.35686i) q^{93} +(-8.95799 - 3.67222i) q^{94} +(4.31942 + 7.48146i) q^{95} +(5.26494 + 2.06891i) q^{96} +12.0241 q^{97} +(7.78079 + 6.12040i) q^{98} +0.941967i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 + 16 * q^9	$ 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9} + 6 q^{10} + 22 q^{14} - 10 q^{16} - 2 q^{18} - 40 q^{20} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 16 q^{25} + 6 q^{26} - 26 q^{28} - 8 q^{30} - 24 q^{31} - 8 q^{32} - 24 q^{34} - 4 q^{36} - 26 q^{38} - 6 q^{40} - 4 q^{42} + 20 q^{44} + 16 q^{46} - 24 q^{47} - 16 q^{48} + 8 q^{49} + 52 q^{50} + 44 q^{52} - 64 q^{55} + 40 q^{56} - 16 q^{57} + 34 q^{58} - 22 q^{60} + 100 q^{62} - 20 q^{64} + 12 q^{66} + 16 q^{68} + 38 q^{70} - 80 q^{71} - 8 q^{72} + 8 q^{73} + 10 q^{74} - 32 q^{76} + 12 q^{78} + 8 q^{79} - 56 q^{80} - 16 q^{81} - 16 q^{84} - 22 q^{86} + 24 q^{87} + 50 q^{88} + 12 q^{90} + 64 q^{92} - 48 q^{94} + 24 q^{95} + 10 q^{96} - 48 q^{97} - 64 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 + 16 * q^9 + 6 * q^10 + 22 * q^14 - 10 * q^16 - 2 * q^18 - 40 * q^20 - 12 * q^22 - 8 * q^23 - 6 * q^24 + 16 * q^25 + 6 * q^26 - 26 * q^28 - 8 * q^30 - 24 * q^31 - 8 * q^32 - 24 * q^34 - 4 * q^36 - 26 * q^38 - 6 * q^40 - 4 * q^42 + 20 * q^44 + 16 * q^46 - 24 * q^47 - 16 * q^48 + 8 * q^49 + 52 * q^50 + 44 * q^52 - 64 * q^55 + 40 * q^56 - 16 * q^57 + 34 * q^58 - 22 * q^60 + 100 * q^62 - 20 * q^64 + 12 * q^66 + 16 * q^68 + 38 * q^70 - 80 * q^71 - 8 * q^72 + 8 * q^73 + 10 * q^74 - 32 * q^76 + 12 * q^78 + 8 * q^79 - 56 * q^80 - 16 * q^81 - 16 * q^84 - 22 * q^86 + 24 * q^87 + 50 * q^88 + 12 * q^90 + 64 * q^92 - 48 * q^94 + 24 * q^95 + 10 * q^96 - 48 * q^97 - 64 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.189716	−	1.40143i	−0.134149	−	0.990961i
$2$	−0.189716	−	1.40143i	−0.134149	−	0.990961i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−1.92802	+	0.531748i	−0.964008	+	0.265874i
$5$	3.09843	+	1.78888i	1.38566	+	0.800012i	0.992823	−	0.119596i	$-0.0381600\pi$
$5$	3.09843	+	1.78888i	1.38566	+	0.800012i	0.392838	+	0.919608i	$0.371493\pi$
$6$	0.865014	+	1.11882i	0.353141	+	0.456755i
$7$	0.993295	+	2.45222i	0.375430	+	0.926851i
$7$	0.993295	+	2.45222i	0.375430	+	0.926851i
$8$	1.11098	+	2.60110i	0.392792	+	0.919627i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.91917	−	4.68162i	0.606895	−	1.48046i
$11$	−0.815768	+	0.470984i	−0.245963	+	0.142007i	−0.617914	−	0.786245i	$-0.712022\pi$
$11$	−0.815768	+	0.470984i	−0.245963	+	0.142007i	0.371951	+	0.928252i	$0.378689\pi$
$12$	1.40384	−	1.42451i	0.405253	−	0.411222i
$13$		−	6.15117i		−	1.70603i	−0.521889	−	0.853013i	$-0.674772\pi$
$13$		−	6.15117i		−	1.70603i	0.521889	−	0.853013i	$-0.325228\pi$
$14$	3.24817	−	1.85726i	0.868109	−	0.496373i
$15$	−3.57776			−0.923774
$16$	3.43449	−	2.05044i	0.858622	−	0.512609i
$17$	1.89187	+	3.27682i	0.458847	+	0.794746i	0.998900	−	0.0468845i	$-0.0149293\pi$
$17$	1.89187	+	3.27682i	0.458847	+	0.794746i	−0.540053	+	0.841631i	$0.681596\pi$
$18$	−1.30853	−	0.536416i	−0.308424	−	0.126435i
$19$	2.09110	+	1.20730i	0.479731	+	0.276973i	0.720305	−	0.693658i	$-0.244002\pi$
$19$	2.09110	+	1.20730i	0.479731	+	0.276973i	−0.240573	+	0.970631i	$0.577335\pi$
$20$	−6.92506	−	1.80141i	−1.54849	−	0.402806i
$21$	−2.08633	−	1.62703i	−0.455274	−	0.355048i
$22$	0.814815	+	1.05389i	0.173719	+	0.224690i
$23$	−1.49371	+	2.58719i	−0.311461	+	0.539466i	−0.978679	−	0.205396i	$-0.934152\pi$
$23$	−1.49371	+	2.58719i	−0.311461	+	0.539466i	0.667218	+	0.744863i	$0.267485\pi$
$24$	−2.26269	−	1.69713i	−0.461869	−	0.346424i
$25$	3.90019	+	6.75532i	0.780037	+	1.35106i
$26$	−8.62043	+	1.16697i	−1.69061	+	0.228863i
$27$			1.00000i			0.192450i
$28$	−3.21905	−	4.19973i	−0.608343	−	0.793674i
$29$			2.68125i			0.497897i	0.968517	+	0.248948i	$0.0800849\pi$
$29$			2.68125i			0.497897i	−0.968517	+	0.248948i	$0.919915\pi$
$30$	0.678758	+	5.01398i	0.123924	+	0.915424i
$31$	−5.35686	−	9.27835i	−0.962120	−	1.66644i	−0.717160	−	0.696908i	$-0.754559\pi$
$31$	−5.35686	−	9.27835i	−0.962120	−	1.66644i	−0.244960	−	0.969533i	$-0.578775\pi$
$32$	−3.52512	−	4.42420i	−0.623159	−	0.782095i
$33$	0.470984	−	0.815768i	0.0819877	−	0.142007i
$34$	4.23332	−	3.27300i	0.726009	−	0.561314i
$35$	−1.30906	+	9.37491i	−0.221272	+	1.58465i
$36$	−0.503501	+	1.93558i	−0.0839168	+	0.322597i
$37$	−1.47851	−	0.853618i	−0.243065	−	0.140334i	0.373519	−	0.927622i	$-0.378151\pi$
$37$	−1.47851	−	0.853618i	−0.243065	−	0.140334i	−0.616585	+	0.787288i	$0.711484\pi$
$38$	1.29523	−	3.15958i	0.210114	−	0.512551i
$39$	3.07558	+	5.32707i	0.492488	+	0.853013i
$40$	−1.21075	+	10.0467i	−0.191436	+	1.58853i
$41$	−4.56000			−0.712152			−0.356076	−	0.934457i	$-0.615886\pi$
$41$	−4.56000			−0.712152			−0.356076	+	0.934457i	$0.615886\pi$
$42$	−1.88437	+	3.23252i	−0.290764	+	0.498788i
$43$		−	3.50672i		−	0.534770i	−0.963590	−	0.267385i	$-0.913840\pi$
$43$		−	3.50672i		−	0.534770i	0.963590	−	0.267385i	$-0.0861596\pi$
$44$	1.32237	−	1.34185i	0.199355	−	0.202291i
$45$	3.09843	−	1.78888i	0.461887	−	0.266671i
$46$	3.90915	+	1.60251i	0.576372	+	0.236277i
$47$	3.42292	−	5.92866i	0.499284	−	0.864785i	−0.500716	−	0.865612i	$-0.666930\pi$
$47$	3.42292	−	5.92866i	0.499284	−	0.864785i	1.00000		0.000827022i	$0.000263249\pi$
$48$	−1.94914	+	3.49297i	−0.281334	+	0.504167i
$49$	−5.02673	+	4.87155i	−0.718104	+	0.695936i
$50$	8.72718	−	6.74743i	1.23421	−	0.954231i
$51$	−3.27682	−	1.89187i	−0.458847	−	0.264915i
$52$	3.27087	+	11.8595i	0.453588	+	1.64462i
$53$	6.57466	−	3.79588i	0.903099	−	0.521404i	0.0248947	−	0.999690i	$-0.492075\pi$
$53$	6.57466	−	3.79588i	0.903099	−	0.521404i	0.878204	+	0.478286i	$0.158742\pi$
$54$	1.40143	−	0.189716i	0.190711	−	0.0258171i
$55$	−3.37013			−0.454429
$56$	−5.27492	+	5.30803i	−0.704891	+	0.709315i
$57$	−2.41460			−0.319821
$58$	3.75759	−	0.508677i	0.493396	−	0.0667926i
$59$	0.100623	−	0.0580947i	0.0131000	−	0.00756328i	−0.493436	−	0.869782i	$-0.664259\pi$
$59$	0.100623	−	0.0580947i	0.0131000	−	0.00756328i	0.506536	+	0.862219i	$0.330926\pi$
$60$	6.89798	−	1.90247i	0.890525	−	0.245607i
$61$	−7.06184	−	4.07716i	−0.904176	−	0.522027i	−0.0256236	−	0.999672i	$-0.508157\pi$
$61$	−7.06184	−	4.07716i	−0.904176	−	0.522027i	−0.878553	+	0.477645i	$0.841490\pi$
$62$	−11.9867	+	9.26752i	−1.52231	+	1.17698i
$63$	2.62033	+	0.365889i	0.330130	+	0.0460977i
$64$	−5.53143	+	5.77955i	−0.691429	+	0.722444i
$65$	11.0037	−	19.0590i	1.36484	−	2.36397i
$66$	−1.23259	−	0.505287i	−0.151722	−	0.0621965i
$67$	−3.44314	+	1.98790i	−0.420647	+	0.242861i	−0.695354	−	0.718667i	$-0.744752\pi$
$67$	−3.44314	+	1.98790i	−0.420647	+	0.242861i	0.274707	+	0.961528i	$0.411419\pi$
$68$	−5.39001	−	5.31177i	−0.653634	−	0.644146i
$69$		−	2.98743i		−	0.359644i
$70$	13.3866	+	0.0559922i	1.60001	+	0.00669235i
$71$	−3.92572			−0.465897			−0.232949	−	0.972489i	$-0.574837\pi$
$71$	−3.92572			−0.465897			−0.232949	+	0.972489i	$0.574837\pi$
$72$	2.80811	+	0.338410i	0.330939	+	0.0398820i
$73$	−3.11438	−	5.39427i	−0.364511	−	0.631351i	0.624187	−	0.781275i	$-0.285430\pi$
$73$	−3.11438	−	5.39427i	−0.364511	−	0.631351i	−0.988698	+	0.149924i	$0.952097\pi$
$74$	−0.915789	+	2.23397i	−0.106458	+	0.259694i
$75$	−6.75532	−	3.90019i	−0.780037	−	0.450355i
$76$	−4.67365	−	1.21575i	−0.536105	−	0.139456i
$77$	−1.96525	−	1.53261i	−0.223961	−	0.174657i
$78$	6.88203	−	5.32085i	0.779236	−	0.602467i
$79$	2.73628	−	4.73937i	0.307855	−	0.533221i	−0.670038	−	0.742327i	$-0.733722\pi$
$79$	2.73628	−	4.73937i	0.307855	−	0.533221i	0.977893	+	0.209106i	$0.0670555\pi$
$80$	14.3095	−	0.209245i	1.59985	−	0.0233943i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.865104	+	6.39052i	0.0955348	+	0.705715i
$83$			1.19560i			0.131234i	0.997845	+	0.0656172i	$0.0209016\pi$
$83$			1.19560i			0.131234i	−0.997845	+	0.0656172i	$0.979098\pi$
$84$	4.88764	+	2.02755i	0.533286	+	0.221224i
$85$			13.5373i			1.46833i
$86$	−4.91443	+	0.665282i	−0.529937	+	0.0717392i
$87$	−1.34063	−	2.32203i	−0.143730	−	0.248948i
$88$	−2.13138	−	1.59864i	−0.227206	−	0.170415i
$89$	0.910509	−	1.57705i	0.0965138	−	0.167167i	−0.813726	−	0.581249i	$-0.802564\pi$
$89$	0.910509	−	1.57705i	0.0965138	−	0.167167i	0.910239	+	0.414082i	$0.135897\pi$
$90$	−3.09481	−	4.00286i	−0.326222	−	0.421938i
$91$	15.0840	−	6.10992i	1.58123	−	0.640494i
$92$	1.50417	−	5.78242i	0.156821	−	0.602859i
$93$	9.27835	+	5.35686i	0.962120	+	0.555480i
$94$	−8.95799	−	3.67222i	−0.923947	−	0.378760i
$95$	4.31942	+	7.48146i	0.443163	+	0.767581i
$96$	5.26494	+	2.06891i	0.537351	+	0.211157i
$97$	12.0241			1.22086			0.610431	−	0.792069i	$-0.290996\pi$
$97$	12.0241			1.22086			0.610431	+	0.792069i	$0.290996\pi$
$98$	7.78079	+	6.12040i	0.785978	+	0.618254i
$99$			0.941967i			0.0946713i
$100$	−11.1117	−	10.9504i	−1.11117	−	1.09504i
$101$	1.54240	−	0.890504i	0.153474	−	0.0886085i	−0.421296	−	0.906923i	$-0.638425\pi$
$101$	1.54240	−	0.890504i	0.153474	−	0.0886085i	0.574770	+	0.818315i	$0.305091\pi$
$102$	−2.02967	+	4.95116i	−0.200967	+	0.490238i
$103$	6.21150	−	10.7586i	0.612037	−	1.06008i	−0.378859	−	0.925454i	$-0.623684\pi$
$103$	6.21150	−	10.7586i	0.612037	−	1.06008i	0.990897	−	0.134625i	$-0.0429831\pi$
$104$	15.9998	−	6.83384i	1.56891	−	0.670113i
$105$	−3.55377	−	8.77344i	−0.346813	−	0.856200i
$106$	−6.56698	−	8.49379i	−0.637842	−	0.824990i
$107$	8.41266	+	4.85705i	0.813283	+	0.469549i	0.848095	−	0.529845i	$-0.177750\pi$
$107$	8.41266	+	4.85705i	0.813283	+	0.469549i	−0.0348118	+	0.999394i	$0.511083\pi$
$108$	−0.531748	−	1.92802i	−0.0511674	−	0.185523i
$109$	−12.3647	+	7.13874i	−1.18432	+	0.683767i	−0.957010	−	0.290055i	$-0.906326\pi$
$109$	−12.3647	+	7.13874i	−1.18432	+	0.683767i	−0.227309	+	0.973823i	$0.572993\pi$
$110$	0.639368	+	4.72301i	0.0609614	+	0.450321i
$111$	1.70724			0.162044
$112$	8.43957	+	6.38542i	0.797465	+	0.603366i
$113$	−13.8775			−1.30549			−0.652743	−	0.757580i	$-0.726382\pi$
$113$	−13.8775			−1.30549			−0.652743	+	0.757580i	$0.726382\pi$
$114$	0.458087	+	3.38389i	0.0429038	+	0.316930i
$115$	−9.25634	+	5.34415i	−0.863159	+	0.498345i
$116$	−1.42575	−	5.16950i	−0.132378	−	0.479976i
$117$	−5.32707	−	3.07558i	−0.492488	−	0.284338i
$118$	−0.100505	−	0.129995i	−0.00925228	−	0.0119670i
$119$	−6.15629	+	7.89414i	−0.564346	+	0.723654i
$120$	−3.97483	−	9.30611i	−0.362851	−	0.849528i
$121$	−5.05635	+	8.75785i	−0.459668	+	0.796168i
$122$	−4.37411	+	10.6702i	−0.396013	+	0.966033i
$123$	3.94907	−	2.28000i	0.356076	−	0.205581i
$124$	15.2619	+	15.0403i	1.37055	+	1.35066i
$125$			10.0191i			0.896131i
$126$	0.0156501	−	3.74162i	0.00139422	−	0.333330i
$127$	7.77389			0.689822			0.344911	−	0.938635i	$-0.387909\pi$
$127$	7.77389			0.689822			0.344911	+	0.938635i	$0.387909\pi$
$128$	9.14905	+	6.65545i	0.808669	+	0.588264i
$129$	1.75336	+	3.03691i	0.154375	+	0.267385i
$130$	−28.7974	−	11.8051i	−2.52570	−	1.03538i
$131$	−6.10134	−	3.52261i	−0.533076	−	0.307772i	0.209192	−	0.977875i	$-0.432917\pi$
$131$	−6.10134	−	3.52261i	−0.533076	−	0.307772i	−0.742268	+	0.670103i	$0.766250\pi$
$132$	−0.474281	+	1.82326i	−0.0412809	+	0.158694i
$133$	−0.883475	+	6.32703i	−0.0766070	+	0.548623i
$134$	3.43912	+	4.44819i	0.297095	+	0.384265i
$135$	−1.78888	+	3.09843i	−0.153962	+	0.266671i
$136$	−6.42150	+	8.56145i	−0.550639	+	0.734138i
$137$	9.05379	+	15.6816i	0.773518	+	1.33977i	0.935624	+	0.352999i	$0.114838\pi$
$137$	9.05379	+	15.6816i	0.773518	+	1.33977i	−0.162106	+	0.986773i	$0.551829\pi$
$138$	−4.18667	+	0.566763i	−0.356393	+	0.0482461i
$139$		−	8.32721i		−	0.706305i	−0.935566	−	0.353152i	$-0.885110\pi$
$139$		−	8.32721i		−	0.706305i	0.935566	−	0.353152i	$-0.114890\pi$
$140$	−2.46119	−	18.7711i	−0.208009	−	1.58644i
$141$			6.84583i			0.576523i
$142$	0.744772	+	5.50162i	0.0624998	+	0.461686i
$143$	2.89710	+	5.01792i	0.242268	+	0.419620i
$144$	−0.0584850	−	3.99957i	−0.00487375	−	0.333298i
$145$	−4.79644	+	8.30768i	−0.398323	+	0.689916i
$146$	−6.96884	+	5.38797i	−0.576746	+	0.445911i
$147$	1.91750	−	6.73225i	0.158153	−	0.555267i
$148$	3.30450	+	0.859595i	0.271628	+	0.0706582i
$149$	−17.9316	−	10.3528i	−1.46901	−	0.848134i	−0.469614	−	0.882872i	$-0.655607\pi$
$149$	−17.9316	−	10.3528i	−1.46901	−	0.848134i	−0.999396	+	0.0347378i	$0.988940\pi$
$150$	−4.18425	+	10.2070i	−0.341642	+	0.833401i
$151$	−1.97783	−	3.42570i	−0.160954	−	0.278780i	0.774257	−	0.632871i	$-0.218124\pi$
$151$	−1.97783	−	3.42570i	−0.160954	−	0.278780i	−0.935211	+	0.354091i	$0.884790\pi$
$152$	−0.817123	+	6.78045i	−0.0662775	+	0.549967i
$153$	3.78375			0.305898
$154$	−1.77501	+	3.04493i	−0.143034	+	0.245367i
$155$		−	38.3311i		−	3.07883i
$156$	−8.76243	−	8.63523i	−0.701556	−	0.691372i
$157$	10.2803	−	5.93532i	0.820456	−	0.473690i	−0.0301179	−	0.999546i	$-0.509588\pi$
$157$	10.2803	−	5.93532i	0.820456	−	0.473690i	0.850574	+	0.525856i	$0.176255\pi$
$158$	−7.16101	−	2.93557i	−0.569699	−	0.233541i
$159$	−3.79588	+	6.57466i	−0.301033	+	0.521404i
$160$	−3.00799	−	20.0141i	−0.237802	−	1.58225i
$161$	−7.82805	−	1.09307i	−0.616937	−	0.0861459i
$162$	−1.11882	+	0.865014i	−0.0879025	+	0.0679619i
$163$	14.7683	+	8.52649i	1.15674	+	0.667846i	0.950522	−	0.310659i	$-0.100550\pi$
$163$	14.7683	+	8.52649i	1.15674	+	0.667846i	0.206222	+	0.978505i	$0.433883\pi$
$164$	8.79175	−	2.42477i	0.686520	−	0.189343i
$165$	2.91862	−	1.68507i	0.227214	−	0.131182i
$166$	1.67555	−	0.226825i	0.130048	−	0.0176050i
$167$	10.4339			0.807396			0.403698	−	0.914892i	$-0.367725\pi$
$167$	10.4339			0.807396			0.403698	+	0.914892i	$0.367725\pi$
$168$	1.91420	−	7.23435i	0.147684	−	0.558142i
$169$	−24.8369			−1.91053
$170$	18.9717	−	2.56825i	1.45506	−	0.196976i
$171$	2.09110	−	1.20730i	0.159910	−	0.0923244i
$172$	1.86469	+	6.76102i	0.142181	+	0.515523i
$173$	12.6216	+	7.28708i	0.959602	+	0.554027i	0.896051	−	0.443952i	$-0.146424\pi$
$173$	12.6216	+	7.28708i	0.959602	+	0.554027i	0.0635517	+	0.997979i	$0.479757\pi$
$174$	−2.99983	+	2.31932i	−0.227417	+	0.175827i
$175$	−12.6915	+	16.2741i	−0.959385	+	1.23021i
$176$	−1.83602	+	3.29027i	−0.138395	+	0.248013i
$177$	−0.0580947	+	0.100623i	−0.00436666	+	0.00756328i
$178$	−2.38286	−	0.976824i	−0.178603	−	0.0732161i
$179$	3.27323	−	1.88980i	0.244653	−	0.141251i	−0.372660	−	0.927968i	$-0.621554\pi$
$179$	3.27323	−	1.88980i	0.244653	−	0.141251i	0.617313	+	0.786717i	$0.288221\pi$
$180$	−5.02259	+	5.09657i	−0.374362	+	0.379876i
$181$			1.12363i			0.0835189i	0.999128	+	0.0417595i	$0.0132963\pi$
$181$			1.12363i			0.0835189i	−0.999128	+	0.0417595i	$0.986704\pi$
$182$	−11.4243	−	19.9800i	−0.846826	−	1.48102i
$183$	8.15432			0.602784
$184$	−8.38903	−	1.01098i	−0.618447	−	0.0745302i
$185$	−3.05404	−	5.28975i	−0.224537	−	0.388910i
$186$	5.74701	−	14.0192i	0.421392	−	1.02794i
$187$	−3.08666	−	1.78208i	−0.225719	−	0.130319i
$188$	−3.44688	+	13.2507i	−0.251390	+	0.966406i
$189$	−2.45222	+	0.993295i	−0.178372	+	0.0722516i
$190$	9.66528	−	7.47272i	0.701193	−	0.542128i
$191$	−7.01502	+	12.1504i	−0.507589	+	0.879169i	0.492373	+	0.870384i	$0.336130\pi$
$191$	−7.01502	+	12.1504i	−0.507589	+	0.879169i	−0.999961	+	0.00878494i	$0.997204\pi$
$192$	1.90059	−	7.77096i	0.137163	−	0.560821i
$193$	−0.390098	−	0.675669i	−0.0280798	−	0.0486357i	0.851644	−	0.524121i	$-0.175606\pi$
$193$	−0.390098	−	0.675669i	−0.0280798	−	0.0486357i	−0.879724	+	0.475485i	$0.842273\pi$
$194$	−2.28117	−	16.8509i	−0.163778	−	1.20983i
$195$			22.0074i			1.57598i
$196$	7.10118	−	12.0654i	0.507227	−	0.861812i
$197$			2.37637i			0.169309i	0.996410	+	0.0846545i	$0.0269787\pi$
$197$			2.37637i			0.169309i	−0.996410	+	0.0846545i	$0.973021\pi$
$198$	1.32010	−	0.178706i	0.0938156	−	0.0127001i
$199$	6.79196	+	11.7640i	0.481469	+	0.833929i	0.999774	−	0.0212671i	$-0.00677004\pi$
$199$	6.79196	+	11.7640i	0.481469	+	0.833929i	−0.518305	+	0.855196i	$0.673437\pi$
$200$	−13.2382	+	17.6498i	−0.936083	+	1.24803i
$201$	1.98790	−	3.44314i	0.140216	−	0.242861i
$202$	−1.54060	−	1.99262i	−0.108396	−	0.140200i
$203$	−6.57502	+	2.66328i	−0.461476	+	0.186925i
$204$	7.32377	+	1.90512i	0.512766	+	0.133385i
$205$	−14.1288	−	8.15729i	−0.986801	−	0.569730i
$206$	−16.2559	−	6.66390i	−1.13260	−	0.464296i
$207$	1.49371	+	2.58719i	0.103820	+	0.179822i
$208$	−12.6126	−	21.1261i	−0.874525	−	1.46483i
$209$	−2.27447			−0.157328
$210$	−11.6212	+	6.64483i	−0.801936	+	0.458537i
$211$			14.1932i			0.977103i	0.872535	+	0.488551i	$0.162474\pi$
$211$			14.1932i			0.977103i	−0.872535	+	0.488551i	$0.837526\pi$
$212$	−10.6576	+	10.8146i	−0.731967	+	0.742748i
$213$	3.39977	−	1.96286i	0.232949	−	0.134493i
$214$	5.21081	−	12.7112i	0.356203	−	0.868921i
$215$	6.27311	−	10.8653i	0.427823	−	0.741010i
$216$	−2.60110	+	1.11098i	−0.176982	+	0.0755928i
$217$	17.4316	−	22.3523i	1.18333	−	1.51737i
$218$	12.3502	+	15.9739i	0.836462	+	1.08189i
$219$	5.39427	+	3.11438i	0.364511	+	0.210450i
$220$	6.49767	−	1.79206i	0.438073	−	0.120821i
$221$	20.1563	−	11.6372i	1.35586	−	0.782805i
$222$	−0.323890	−	2.39257i	−0.0217381	−	0.160579i
$223$	−0.198178			−0.0132710			−0.00663548	−	0.999978i	$-0.502112\pi$
$223$	−0.198178			−0.0132710			−0.00663548	+	0.999978i	$0.502112\pi$
$224$	7.34760	−	13.0389i	0.490932	−	0.871198i
$225$	7.80037			0.520025
$226$	2.63278	+	19.4483i	0.175130	+	1.29368i
$227$	−22.3054	+	12.8780i	−1.48046	+	0.854744i	−0.999755	−	0.0221381i	$-0.992953\pi$
$227$	−22.3054	+	12.8780i	−1.48046	+	0.854744i	−0.480705	+	0.876882i	$0.659619\pi$
$228$	4.65538	−	1.28396i	0.308310	−	0.0850320i
$229$	13.9965	+	8.08087i	0.924913	+	0.533999i	0.885199	−	0.465212i	$-0.154022\pi$
$229$	13.9965	+	8.08087i	0.924913	+	0.533999i	0.0397138	+	0.999211i	$0.487355\pi$
$230$	9.24554	+	11.9583i	0.609633	+	0.788504i
$231$	2.46826	+	0.344656i	0.162400	+	0.0226767i
$232$	−6.97421	+	2.97883i	−0.457879	+	0.195570i
$233$	−12.5619	+	21.7579i	−0.822959	+	1.42541i	0.0805094	+	0.996754i	$0.474345\pi$
$233$	−12.5619	+	21.7579i	−0.822959	+	1.42541i	−0.903469	+	0.428654i	$0.858988\pi$
$234$	−3.29959	+	8.04900i	−0.215701	+	0.526180i
$235$	21.2113	−	12.2464i	1.38368	−	0.798865i
$236$	−0.163111	+	0.165513i	−0.0106176	+	0.0107740i
$237$			5.47255i			0.355480i
$238$	12.2310	+	7.12997i	0.792820	+	0.462167i
$239$	16.0389			1.03747			0.518736	−	0.854935i	$-0.326403\pi$
$239$	16.0389			1.03747			0.518736	+	0.854935i	$0.326403\pi$
$240$	−12.2878	+	7.33597i	−0.793173	+	0.473535i
$241$	6.58453	+	11.4047i	0.424147	+	0.734643i	0.996340	−	0.0854750i	$-0.0272408\pi$
$241$	6.58453	+	11.4047i	0.424147	+	0.734643i	−0.572194	+	0.820119i	$0.693907\pi$
$242$	13.2328	+	5.42462i	0.850636	+	0.348708i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	15.7834	+	4.10570i	1.01043	+	0.262841i
$245$	−24.2896	+	6.10194i	−1.55181	+	0.389839i
$246$	−3.94446	−	5.10180i	−0.251490	−	0.325279i
$247$	7.42629	−	12.8627i	0.472523	−	0.818435i
$248$	18.1825	−	24.2418i	1.15459	−	1.53936i
$249$	−0.597802	−	1.03542i	−0.0378841	−	0.0656172i
$250$	14.0410	−	1.90078i	0.888031	−	0.120216i
$251$		−	8.64704i		−	0.545796i	−0.962043	−	0.272898i	$-0.912018\pi$
$251$		−	8.64704i		−	0.545796i	0.962043	−	0.272898i	$-0.0879822\pi$
$252$	−5.24660	+	0.687914i	−0.330505	+	0.0433345i
$253$		−	2.81406i		−	0.176918i
$254$	−1.47483	−	10.8946i	−0.0925392	−	0.683586i
$255$	−6.76867	−	11.7237i	−0.423871	−	0.734166i
$256$	7.59143	−	14.0844i	0.474464	−	0.880275i
$257$	7.23254	−	12.5271i	0.451154	−	0.781421i	−0.547304	−	0.836934i	$-0.684346\pi$
$257$	7.23254	−	12.5271i	0.451154	−	0.781421i	0.998458	+	0.0555126i	$0.0176793\pi$
$258$	3.92338	−	3.03337i	0.244259	−	0.188849i
$259$	0.624659	−	4.47352i	0.0388144	−	0.277971i
$260$	−11.0807	+	42.5972i	−0.687199	+	2.64177i
$261$	2.32203	+	1.34063i	0.143730	+	0.0829828i
$262$	−3.77917	+	9.21890i	−0.233478	+	0.569545i
$263$	−9.94833	−	17.2310i	−0.613440	−	1.06251i	−0.990656	−	0.136384i	$-0.956452\pi$
$263$	−9.94833	−	17.2310i	−0.613440	−	1.06251i	0.377216	−	0.926125i	$-0.376881\pi$
$264$	2.64515	+	0.318771i	0.162798	+	0.0196190i
$265$	27.1615			1.66852
$266$	9.03451	+	0.0377886i	0.553941	+	0.00231697i
$267$			1.82102i			0.111444i
$268$	5.58137	−	5.66358i	0.340937	−	0.345958i
$269$	−14.6930	+	8.48299i	−0.895847	+	0.517217i	−0.875850	−	0.482583i	$-0.839699\pi$
$269$	−14.6930	+	8.48299i	−0.895847	+	0.517217i	−0.0199962	+	0.999800i	$0.506365\pi$
$270$	4.68162	+	1.91917i	0.284914	+	0.116797i
$271$	−0.538186	+	0.932165i	−0.0326925	+	0.0566250i	−0.881909	−	0.471420i	$-0.843742\pi$
$271$	−0.538186	+	0.932165i	−0.0326925	+	0.0566250i	0.849216	+	0.528045i	$0.177075\pi$
$272$	13.2165	+	7.37504i	0.801370	+	0.447178i
$273$	−10.0082	+	12.8333i	−0.605721	+	0.776709i
$274$	20.2591	−	15.6633i	1.22390	−	0.946256i
$275$	−6.36329	−	3.67385i	−0.383721	−	0.221541i
$276$	1.58856	+	5.75981i	0.0956200	+	0.346700i
$277$	−4.23611	+	2.44572i	−0.254523	+	0.146949i	−0.621834	−	0.783149i	$-0.713612\pi$
$277$	−4.23611	+	2.44572i	−0.254523	+	0.146949i	0.367311	+	0.930098i	$0.380279\pi$
$278$	−11.6700	+	1.57980i	−0.699920	+	0.0947504i
$279$	−10.7137			−0.641414
$280$	−25.8394	+	7.01036i	−1.54420	+	0.418949i
$281$	−0.754188			−0.0449911			−0.0224956	−	0.999747i	$-0.507161\pi$
$281$	−0.754188			−0.0449911			−0.0224956	+	0.999747i	$0.507161\pi$
$282$	9.59396	−	1.29876i	0.571312	−	0.0773403i
$283$	−16.8270	+	9.71510i	−1.00026	+	0.577503i	−0.908326	−	0.418262i	$-0.862639\pi$
$283$	−16.8270	+	9.71510i	−1.00026	+	0.577503i	−0.0919376	+	0.995765i	$0.529306\pi$
$284$	7.56885	−	2.08749i	0.449128	−	0.123870i
$285$	−7.48146	−	4.31942i	−0.443163	−	0.255860i
$286$	6.48265	−	5.01206i	0.383327	−	0.296370i
$287$	−4.52942	−	11.1821i	−0.267363	−	0.660058i
$288$	−5.59403	+	0.840746i	−0.329631	+	0.0495414i
$289$	1.34162	−	2.32376i	0.0789189	−	0.136691i
$290$	12.5526	+	5.14578i	0.737114	+	0.302171i
$291$	−10.4132	+	6.01205i	−0.610431	+	0.352433i
$292$	8.87297	+	8.74417i	0.519251	+	0.511714i
$293$		−	21.9433i		−	1.28194i	−0.767564	−	0.640972i	$-0.778532\pi$
$293$		−	21.9433i		−	1.28194i	0.767564	−	0.640972i	$-0.221468\pi$
$294$	−9.79856	−	1.41003i	−0.571464	−	0.0822346i
$295$	0.415698			0.0242029
$296$	0.577746	−	4.79410i	0.0335808	−	0.278652i
$297$	−0.470984	−	0.815768i	−0.0273292	−	0.0473356i
$298$	−11.1068	+	27.0939i	−0.643401	+	1.56951i
$299$	15.9142	+	9.18809i	0.920344	+	0.531361i
$300$	15.0983	+	3.92749i	0.871699	+	0.226754i
$301$	8.59925	−	3.48321i	0.495652	−	0.200769i
$302$	−4.42566	+	3.42170i	−0.254668	+	0.196897i
$303$	−0.890504	+	1.54240i	−0.0511581	+	0.0886085i
$304$	9.65735	−	0.141218i	0.553887	−	0.00809938i
$305$	−14.5871	−	25.2656i	−0.835255	−	1.44670i
$306$	−0.717838	−	5.30266i	−0.0410361	−	0.303133i
$307$		−	2.18555i		−	0.124736i	−0.998053	−	0.0623679i	$-0.980135\pi$
$307$		−	2.18555i		−	0.124736i	0.998053	−	0.0623679i	$-0.0198652\pi$
$308$	4.60400	+	1.90988i	0.262337	+	0.108826i
$309$			12.4230i			0.706720i
$310$	−53.7184	+	7.27203i	−3.05100	+	0.413023i
$311$	−13.6343	−	23.6152i	−0.773129	−	1.33910i	−0.935840	−	0.352424i	$-0.885357\pi$
$311$	−13.6343	−	23.6152i	−0.773129	−	1.33910i	0.162712	−	0.986674i	$-0.447976\pi$
$312$	−10.4393	+	13.9182i	−0.591009	+	0.787962i
$313$	0.683268	−	1.18346i	0.0386206	−	0.0668929i	−0.846069	−	0.533073i	$-0.821037\pi$
$313$	0.683268	−	1.18346i	0.0386206	−	0.0668929i	0.884690	+	0.466181i	$0.154370\pi$
$314$	−10.2683	−	13.2811i	−0.579472	−	0.749494i
$315$	7.46438	+	5.82114i	0.420570	+	0.327984i
$316$	−2.75543	+	10.5926i	−0.155005	+	0.595879i
$317$	−7.09368	−	4.09554i	−0.398421	−	0.230028i	0.287382	−	0.957816i	$-0.407215\pi$
$317$	−7.09368	−	4.09554i	−0.398421	−	0.230028i	−0.685802	+	0.727788i	$0.740549\pi$
$318$	9.93407	+	4.07235i	0.557075	+	0.228366i
$319$	−1.26283	−	2.18728i	−0.0707048	−	0.122464i
$320$	−27.4777	+	8.01248i	−1.53605	+	0.447911i
$321$	−9.71411			−0.542189
$322$	−0.0467535	+	11.1778i	−0.00260547	+	0.622917i
$323$			9.13622i			0.508353i
$324$	1.42451	+	1.40384i	0.0791397	+	0.0779909i
$325$	41.5531	−	23.9907i	2.30495	−	1.33076i
$326$	9.14750	−	22.3144i	0.506633	−	1.23588i
$327$	7.13874	−	12.3647i	0.394773	−	0.683767i
$328$	−5.06608	−	11.8610i	−0.279727	−	0.654914i
$329$	17.9383	+	2.50482i	0.988972	+	0.138095i
$330$	−2.91521	−	3.77056i	−0.160477	−	0.207563i
$331$	−13.3643	−	7.71590i	−0.734570	−	0.424104i	0.0855218	−	0.996336i	$-0.472744\pi$
$331$	−13.3643	−	7.71590i	−0.734570	−	0.424104i	−0.820092	+	0.572232i	$0.806078\pi$
$332$	−0.635759	−	2.30514i	−0.0348918	−	0.126511i
$333$	−1.47851	+	0.853618i	−0.0810218	+	0.0467780i
$334$	−1.97947	−	14.6223i	−0.108312	−	0.800098i
$335$	−14.2245			−0.777165
$336$	−10.5016	−	1.31015i	−0.572909	−	0.0714746i
$337$	−0.543923			−0.0296294			−0.0148147	−	0.999890i	$-0.504716\pi$
$337$	−0.543923			−0.0296294			−0.0148147	+	0.999890i	$0.504716\pi$
$338$	4.71195	+	34.8071i	0.256296	+	1.89326i
$339$	12.0183	−	6.93875i	0.652743	−	0.376861i
$340$	−7.19845	−	26.1002i	−0.390391	−	1.41548i
$341$	8.73990	+	5.04599i	0.473292	+	0.273255i
$342$	−2.08866	−	2.70149i	−0.112942	−	0.146080i
$343$	−16.9391	−	7.48774i	−0.914626	−	0.404300i
$344$	9.12134	−	3.89591i	0.491790	−	0.210053i
$345$	5.34415	−	9.25634i	0.287720	−	0.498345i
$346$	7.81782	−	19.0708i	0.420289	−	1.02525i
$347$	−9.92740	+	5.73159i	−0.532931	+	0.307688i	−0.742209	−	0.670168i	$-0.766222\pi$
$347$	−9.92740	+	5.73159i	−0.532931	+	0.307688i	0.209278	+	0.977856i	$0.432889\pi$
$348$	3.81949	+	3.76404i	0.204746	+	0.201774i
$349$			1.23092i			0.0658899i	0.999457	+	0.0329449i	$0.0104886\pi$
$349$			1.23092i			0.0658899i	−0.999457	+	0.0329449i	$0.989511\pi$
$350$	25.2148	+	14.6988i	1.34779	+	0.785681i
$351$	6.15117			0.328325
$352$	4.95940	+	1.94884i	0.264337	+	0.103874i
$353$	17.1091	+	29.6339i	0.910628	+	1.57725i	0.813179	+	0.582013i	$0.197735\pi$
$353$	17.1091	+	29.6339i	0.910628	+	1.57725i	0.0974483	+	0.995241i	$0.468932\pi$
$354$	0.152038	+	0.0623259i	0.00808071	+	0.00331258i
$355$	−12.1636	−	7.02264i	−0.645575	−	0.372723i
$356$	−0.916884	+	3.52473i	−0.0485948	+	0.186811i
$357$	1.38443	−	9.91467i	0.0732720	−	0.524740i
$358$	−3.26941	−	4.22869i	−0.172794	−	0.223493i
$359$	−16.9536	+	29.3645i	−0.894777	+	1.54980i	−0.0606972	+	0.998156i	$0.519332\pi$
$359$	−16.9536	+	29.3645i	−0.894777	+	1.54980i	−0.834080	+	0.551643i	$0.814001\pi$
$360$	8.09536	+	6.07191i	0.426663	+	0.320018i
$361$	−6.58487	−	11.4053i	−0.346572	−	0.600280i
$362$	1.57469	−	0.213171i	0.0827640	−	0.0112040i
$363$		−	10.1127i		−	0.530779i
$364$	−25.8332	+	19.8009i	−1.35403	+	1.03785i
$365$		−	22.2850i		−	1.16645i
$366$	−1.54700	−	11.4277i	−0.0808632	−	0.597336i
$367$	9.62235	+	16.6664i	0.502282	+	0.869979i	0.999997	+	0.00263748i	$0.000839536\pi$
$367$	9.62235	+	16.6664i	0.502282	+	0.869979i	−0.497714	+	0.867341i	$0.665827\pi$
$368$	0.174720	+	11.9484i	0.00910790	+	0.622855i
$369$	−2.28000	+	3.94907i	−0.118692	+	0.205581i
$370$	−6.83382	+	5.28358i	−0.355273	+	0.274680i
$371$	15.8389	+	12.3521i	0.822315	+	0.641287i
$372$	−20.7373	−	5.39437i	−1.07518	−	0.279685i
$373$	−12.8464	−	7.41686i	−0.665160	−	0.384030i	0.129080	−	0.991634i	$-0.458798\pi$
$373$	−12.8464	−	7.41686i	−0.665160	−	0.384030i	−0.794240	+	0.607604i	$0.792131\pi$
$374$	−1.91188	+	4.66383i	−0.0988609	+	0.241161i
$375$	−5.00953	−	8.67676i	−0.258691	−	0.448066i
$376$	19.2238	+	2.31670i	0.991394	+	0.119475i
$377$	16.4928			0.849425
$378$	1.85726	+	3.24817i	0.0955271	+	0.167068i
$379$			11.7500i			0.603555i	0.953378	+	0.301778i	$0.0975800\pi$
$379$			11.7500i			0.603555i	−0.953378	+	0.301778i	$0.902420\pi$
$380$	−12.3062	−	12.1275i	−0.631293	−	0.622129i
$381$	−6.73239	+	3.88695i	−0.344911	+	0.199134i
$382$	18.3588	+	7.52594i	0.939315	+	0.385061i
$383$	−9.53274	+	16.5112i	−0.487100	+	0.843682i	−0.999890	−	0.0148320i	$-0.995279\pi$
$383$	−9.53274	+	16.5112i	−0.487100	+	0.843682i	0.512790	+	0.858514i	$0.328612\pi$
$384$	−11.2510	−	1.18926i	−0.574152	−	0.0606894i
$385$	−3.34754	−	8.26430i	−0.170606	−	0.421188i
$386$	−0.872895	+	0.674880i	−0.0444292	+	0.0343505i
$387$	−3.03691	−	1.75336i	−0.154375	−	0.0891284i
$388$	−23.1827	+	6.39379i	−1.17692	+	0.324595i
$389$	1.73492	−	1.00165i	0.0879638	−	0.0507859i	−0.455373	−	0.890301i	$-0.650494\pi$
$389$	1.73492	−	1.00165i	0.0879638	−	0.0507859i	0.543337	+	0.839515i	$0.317161\pi$
$390$	30.8418	−	4.17516i	1.56174	−	0.211417i
$391$	−11.3037			−0.571652
$392$	−18.2560	−	7.66281i	−0.922067	−	0.387031i
$393$	7.04522			0.355384
$394$	3.33031	−	0.450835i	0.167779	−	0.0227127i
$395$	16.9563	−	9.78974i	0.853165	−	0.492575i
$396$	−0.500889	−	1.81613i	−0.0251706	−	0.0912639i
$397$	7.34718	+	4.24190i	0.368744	+	0.212895i	0.672910	−	0.739725i	$-0.265044\pi$
$397$	7.34718	+	4.24190i	0.368744	+	0.212895i	−0.304165	+	0.952619i	$0.598378\pi$
$398$	15.1979	−	11.7503i	0.761802	−	0.588988i
$399$	−2.39841	−	5.92111i	−0.120070	−	0.296426i
$400$	27.2465	+	15.2040i	1.36232	+	0.760199i
$401$	7.04632	−	12.2046i	0.351876	−	0.609468i	−0.634702	−	0.772757i	$-0.718877\pi$
$401$	7.04632	−	12.2046i	0.351876	−	0.609468i	0.986578	+	0.163289i	$0.0522104\pi$
$402$	−5.20246	−	2.13268i	−0.259475	−	0.106369i
$403$	−57.0727	+	32.9509i	−2.84299	+	1.64140i
$404$	−2.50024	+	2.53707i	−0.124392	+	0.126224i
$405$		−	3.57776i		−	0.177780i
$406$	4.97978	+	8.70916i	0.247143	+	0.432229i
$407$	1.60816			0.0797135
$408$	1.28046	−	10.6252i	0.0633922	−	0.526025i
$409$	−15.1789	−	26.2906i	−0.750547	−	1.29998i	−0.947558	−	0.319584i	$-0.896457\pi$
$409$	−15.1789	−	26.2906i	−0.750547	−	1.29998i	0.197011	−	0.980401i	$-0.436876\pi$
$410$	−8.75141	+	21.3482i	−0.432201	+	1.05431i
$411$	−15.6816	−	9.05379i	−0.773518	−	0.446591i
$412$	−6.25499	+	24.0458i	−0.308161	+	1.18465i
$413$	0.242409	+	0.189044i	0.0119282	+	0.00930225i
$414$	3.34238	−	2.58417i	0.164269	−	0.127005i
$415$	−2.13879	+	3.70449i	−0.104989	+	0.181846i
$416$	−27.2140	+	21.6836i	−1.33428	+	1.06313i
$417$	4.16360	+	7.21157i	0.203893	+	0.353152i
$418$	0.431503	+	3.18751i	0.0211055	+	0.155906i
$419$			30.8896i			1.50905i	0.656269	+	0.754527i	$0.272134\pi$
$419$			30.8896i			1.50905i	−0.656269	+	0.754527i	$0.727866\pi$
$420$	11.5170	+	15.0256i	0.561971	+	0.733175i
$421$			20.0940i			0.979321i	0.871913	+	0.489661i	$0.162879\pi$
$421$			20.0940i			0.979321i	−0.871913	+	0.489661i	$0.837121\pi$
$422$	19.8908	−	2.69268i	0.968271	−	0.131078i
$423$	−3.42292	−	5.92866i	−0.166428	−	0.288262i
$424$	17.1778	+	12.8842i	0.834228	+	0.625711i
$425$	−14.7573	+	25.5604i	−0.715835	+	1.23986i
$426$	−3.39580	−	4.39216i	−0.164527	−	0.212801i
$427$	2.98358	−	21.3670i	0.144385	−	1.03402i
$428$	−18.8025	−	4.89106i	−0.908852	−	0.236418i
$429$	−5.01792	−	2.89710i	−0.242268	−	0.139873i
$430$	−16.4171	−	6.73000i	−0.791705	−	0.324549i
$431$	−4.00873	−	6.94333i	−0.193094	−	0.334448i	0.753180	−	0.657814i	$-0.228519\pi$
$431$	−4.00873	−	6.94333i	−0.193094	−	0.334448i	−0.946274	+	0.323366i	$0.895186\pi$
$432$	2.05044	+	3.43449i	0.0986516	+	0.165242i
$433$	−26.9812			−1.29663			−0.648316	−	0.761371i	$-0.724527\pi$
$433$	−26.9812			−1.29663			−0.648316	+	0.761371i	$0.724527\pi$
$434$	−34.6323	−	20.1886i	−1.66240	−	0.969082i
$435$		−	9.59289i		−	0.459944i
$436$	20.0432	−	20.3385i	0.959897	−	0.974036i
$437$	−6.24701	+	3.60672i	−0.298835	+	0.172533i
$438$	3.34121	−	8.15054i	0.159649	−	0.389448i
$439$	−18.2576	+	31.6231i	−0.871388	+	1.50929i	−0.0108272	+	0.999941i	$0.503446\pi$
$439$	−18.2576	+	31.6231i	−0.871388	+	1.50929i	−0.860561	+	0.509347i	$0.829887\pi$
$440$	−3.74416	−	8.76605i	−0.178496	−	0.417905i
$441$	1.70552	+	6.78905i	0.0812153	+	0.323288i
$442$	−20.1328	−	26.0399i	−0.957617	−	1.23859i
$443$	−0.190464	−	0.109964i	−0.00904921	−	0.00522457i	0.495469	−	0.868626i	$-0.334996\pi$
$443$	−0.190464	−	0.109964i	−0.00904921	−	0.00522457i	−0.504518	+	0.863401i	$0.668330\pi$
$444$	−3.29158	+	0.907819i	−0.156211	+	0.0430832i
$445$	5.64230	−	3.25758i	0.267471	−	0.154424i
$446$	0.0375975	+	0.277732i	0.00178029	+	0.0131510i
$447$	20.7056			0.979341
$448$	−19.6671	−	7.82347i	−0.929181	−	0.369624i
$449$	20.6799			0.975946			0.487973	−	0.872859i	$-0.337736\pi$
$449$	20.6799			0.975946			0.487973	+	0.872859i	$0.337736\pi$
$450$	−1.47986	−	10.9317i	−0.0697610	−	0.515324i
$451$	3.71990	−	2.14768i	0.175163	−	0.101130i
$452$	26.7560	−	7.37933i	1.25850	−	0.347094i
$453$	3.42570	+	1.97783i	0.160954	+	0.0929266i
$454$	22.2793	+	28.8163i	1.04562	+	1.35242i
$455$	57.6666	+	8.05227i	2.70345	+	0.377496i
$456$	−2.68257	−	6.28060i	−0.125623	−	0.294116i
$457$	4.29209	−	7.43412i	0.200776	−	0.347753i	−0.748003	−	0.663695i	$-0.768987\pi$
$457$	4.29209	−	7.43412i	0.200776	−	0.347753i	0.948779	+	0.315942i	$0.102320\pi$
$458$	8.66942	−	21.1482i	0.405095	−	0.988188i
$459$	−3.27682	+	1.89187i	−0.152949	+	0.0883051i
$460$	15.0046	−	15.2256i	0.699595	−	0.709900i
$461$		−	13.8203i		−	0.643676i	−0.946795	−	0.321838i	$-0.895699\pi$
$461$		−	13.8203i		−	0.643676i	0.946795	−	0.321838i	$-0.104301\pi$
$462$	0.0147419	−	3.52449i	0.000685854	−	0.163974i
$463$	28.8694			1.34168			0.670838	−	0.741604i	$-0.265935\pi$
$463$	28.8694			1.34168			0.670838	+	0.741604i	$0.265935\pi$
$464$	5.49774	+	9.20874i	0.255226	+	0.427505i
$465$	19.1656	+	33.1957i	0.888782	+	1.53941i
$466$	32.8754	+	13.4769i	1.52292	+	0.624303i
$467$	10.7682	+	6.21705i	0.498295	+	0.287691i	0.728009	−	0.685567i	$-0.240446\pi$
$467$	10.7682	+	6.21705i	0.498295	+	0.287691i	−0.229714	+	0.973258i	$0.573779\pi$
$468$	11.9061	+	3.09712i	0.550360	+	0.143164i
$469$	−8.29482	−	6.46876i	−0.383019	−	0.298700i
$470$	−21.1866	−	27.4029i	−0.977264	−	1.26400i
$471$	−5.93532	+	10.2803i	−0.273485	+	0.473690i
$472$	0.262900	+	0.197188i	0.0121010	+	0.00907632i
$473$	1.65161	+	2.86067i	0.0759411	+	0.131534i
$474$	7.66940	−	1.03823i	0.352267	−	0.0476875i
$475$			18.8347i			0.864197i
$476$	7.67173	−	18.4936i	0.351633	−	0.847653i
$477$		−	7.59176i		−	0.347603i
$478$	−3.04284	−	22.4774i	−0.139176	−	1.02809i
$479$	−19.1410	−	33.1532i	−0.874575	−	1.51481i	−0.857215	−	0.514958i	$-0.827807\pi$
$479$	−19.1410	−	33.1532i	−0.874575	−	1.51481i	−0.0173596	−	0.999849i	$-0.505526\pi$
$480$	12.6120	+	15.8287i	0.575658	+	0.722479i
$481$	−5.25075	+	9.09456i	−0.239413	+	0.414676i
$482$	14.7338	−	11.3914i	0.671104	−	0.518865i
$483$	7.32582	−	2.96740i	0.333336	−	0.135021i
$484$	5.09175	−	19.5740i	0.231443	−	0.889726i
$485$	37.2559	+	21.5097i	1.69170	+	0.976704i
$486$	0.536416	−	1.30853i	0.0243323	−	0.0593562i
$487$	0.902290	+	1.56281i	0.0408867	+	0.0708178i	0.885745	−	0.464173i	$-0.153648\pi$
$487$	0.902290	+	1.56281i	0.0408867	+	0.0708178i	−0.844858	+	0.534991i	$0.820315\pi$
$488$	2.75950	−	22.8982i	0.124917	−	1.03655i
$489$	−17.0530			−0.771163
$490$	13.1596	+	32.8825i	0.594489	+	1.48548i
$491$		−	4.10278i		−	0.185156i	−0.995705	−	0.0925780i	$-0.970489\pi$
$491$		−	4.10278i		−	0.185156i	0.995705	−	0.0925780i	$-0.0295108\pi$
$492$	−6.40149	+	6.49578i	−0.288602	+	0.292853i
$493$	−8.78600	+	5.07260i	−0.395701	+	0.228458i
$494$	−19.4351	−	7.96717i	−0.874426	−	0.358460i
$495$	−1.68507	+	2.91862i	−0.0757381	+	0.131182i
$496$	−37.4227	−	20.8825i	−1.68033	−	0.937652i
$497$	−3.89940	−	9.62671i	−0.174912	−	0.431817i
$498$	−1.33766	+	1.03421i	−0.0599420	+	0.0463442i
$499$	38.4522	+	22.2004i	1.72135	+	0.993825i	0.916158	+	0.400817i	$0.131274\pi$
$499$	38.4522	+	22.2004i	1.72135	+	0.993825i	0.805197	+	0.593008i	$0.202060\pi$
$500$	−5.32761	−	19.3169i	−0.238258	−	0.863878i
$501$	−9.03598	+	5.21693i	−0.403698	+	0.233075i
$502$	−12.1182	+	1.64048i	−0.540863	+	0.0732183i
$503$	8.88976			0.396375			0.198187	−	0.980164i	$-0.436495\pi$
$503$	8.88976			0.396375			0.198187	+	0.980164i	$0.436495\pi$
$504$	1.95943	+	7.22223i	0.0872798	+	0.321704i
$505$	6.37202			0.283551
$506$	−3.94371	+	0.533872i	−0.175319	+	0.0237335i
$507$	21.5094	−	12.4184i	0.955264	−	0.551522i
$508$	−14.9882	+	4.13375i	−0.664993	+	0.183405i
$509$	9.56641	+	5.52317i	0.424024	+	0.244810i	0.696797	−	0.717268i	$-0.254608\pi$
$509$	9.56641	+	5.52317i	0.424024	+	0.244810i	−0.272774	+	0.962078i	$0.587941\pi$
$510$	−15.1458	+	11.7100i	−0.670668	+	0.518527i
$511$	10.1344	−	12.9952i	0.448320	−	0.574875i
$512$	−21.1785	−	7.96682i	−0.935967	−	0.352087i
$513$	−1.20730	+	2.09110i	−0.0533035	+	0.0923244i
$514$	−18.9280	−	7.75931i	−0.834880	−	0.342249i
$515$	38.4918	−	22.2233i	1.69615	−	0.979274i
$516$	−4.99538	−	4.92287i	−0.219909	−	0.216717i
$517$			6.44855i			0.283607i
$518$	−6.38783	−	0.0267184i	−0.280665	−	0.00117394i
$519$	−14.5742			−0.639735
$520$	61.7992	+	7.44753i	2.71007	+	0.326596i
$521$	16.9975	+	29.4406i	0.744675	+	1.28982i	0.950346	+	0.311194i	$0.100729\pi$
$521$	16.9975	+	29.4406i	0.744675	+	1.28982i	−0.205671	+	0.978621i	$0.565938\pi$
$522$	1.43827	−	3.50851i	0.0629513	−	0.153563i
$523$	−15.7706	−	9.10516i	−0.689601	−	0.398141i	0.113862	−	0.993497i	$-0.463678\pi$
$523$	−15.7706	−	9.10516i	−0.689601	−	0.398141i	−0.803462	+	0.595356i	$0.797011\pi$
$524$	13.6366	+	3.54727i	0.595718	+	0.154963i
$525$	2.85407	−	20.4395i	0.124562	−	0.892055i
$526$	−22.2607	+	17.2109i	−0.970613	+	0.750430i
$527$	20.2690	−	35.1070i	0.882932	−	1.52928i
$528$	−0.0550910	−	3.76747i	−0.00239753	−	0.163958i
$529$	7.03763	+	12.1895i	0.305984	+	0.529980i
$530$	−5.15297	−	38.0650i	−0.223831	−	1.65344i
$531$		−	0.116189i		−	0.00504219i
$532$	−1.66103	−	12.6684i	−0.0720149	−	0.549245i
$533$			28.0493i			1.21495i
$534$	2.55203	−	0.345476i	0.110437	−	0.0149502i
$535$	17.3774	+	30.0985i	0.751289	+	1.30127i
$536$	−8.99599	−	6.74743i	−0.388568	−	0.291445i
$537$	−1.88980	+	3.27323i	−0.0815510	+	0.141251i
$538$	14.6758	+	18.9818i	0.632720	+	0.818365i
$539$	1.80622	−	6.34156i	0.0777995	−	0.273150i
$540$	1.80141	−	6.92506i	0.0775201	−	0.298007i
$541$	26.0940	+	15.0654i	1.12187	+	0.647712i	0.941877	−	0.335957i	$-0.109060\pi$
$541$	26.0940	+	15.0654i	1.12187	+	0.647712i	0.179992	+	0.983668i	$0.442393\pi$
$542$	1.40847	+	0.577383i	0.0604988	+	0.0248007i
$543$	−0.561816	−	0.973094i	−0.0241098	−	0.0417595i
$544$	7.82822	−	19.9212i	0.335632	−	0.854115i
$545$	−51.0814			−2.18809
$546$	19.8838	+	11.5910i	0.850946	+	0.496051i
$547$		−	36.0927i		−	1.54321i	−0.636101	−	0.771606i	$-0.719454\pi$
$547$		−	36.0927i		−	1.54321i	0.636101	−	0.771606i	$-0.280546\pi$
$548$	−25.7945	−	25.4201i	−1.10189	−	1.08589i
$549$	−7.06184	+	4.07716i	−0.301392	+	0.174009i
$550$	−3.94142	+	9.61470i	−0.168063	+	0.409972i
$551$	−3.23707	+	5.60677i	−0.137904	+	0.238857i
$552$	7.77060	−	3.31898i	0.330739	−	0.141265i
$553$	14.3399	+	2.00235i	0.609794	+	0.0851485i
$554$	4.23116	+	5.47262i	0.179765	+	0.232509i
$555$	5.28975	+	3.05404i	0.224537	+	0.129637i
$556$	4.42797	+	16.0550i	0.187788	+	0.680883i
$557$	−36.7321	+	21.2073i	−1.55639	+	0.898583i	−0.558793	+	0.829307i	$0.688735\pi$
$557$	−36.7321	+	21.2073i	−1.55639	+	0.898583i	−0.997598	+	0.0692757i	$0.977931\pi$
$558$	2.03256	+	15.0145i	0.0860453	+	0.635616i
$559$	−21.5704			−0.912333
$560$	14.7267	+	34.8822i	0.622316	+	1.47404i
$561$	3.56417			0.150479
$562$	0.143082	+	1.05694i	0.00603553	+	0.0445844i
$563$	−10.2656	+	5.92685i	−0.432644	+	0.249787i	−0.700472	−	0.713680i	$-0.747027\pi$
$563$	−10.2656	+	5.92685i	−0.432644	+	0.249787i	0.267828	+	0.963467i	$0.413694\pi$
$564$	−3.64026	−	13.1989i	−0.153282	−	0.555773i
$565$	−42.9985	−	24.8252i	−1.80896	−	1.04440i
$566$	16.8074	+	21.7388i	0.706468	+	0.913751i
$567$	1.62703	−	2.08633i	0.0683290	−	0.0876175i
$568$	−4.36141	−	10.2112i	−0.183001	−	0.428452i
$569$	−2.71207	+	4.69744i	−0.113696	+	0.196927i	−0.917258	−	0.398294i	$-0.869602\pi$
$569$	−2.71207	+	4.69744i	−0.113696	+	0.196927i	0.803562	+	0.595221i	$0.202936\pi$
$570$	−4.63402	+	11.3042i	−0.194098	+	0.473481i
$571$	16.9613	−	9.79262i	0.709809	−	0.409809i	−0.101181	−	0.994868i	$-0.532262\pi$
$571$	16.9613	−	9.79262i	0.709809	−	0.409809i	0.810990	+	0.585059i	$0.198929\pi$
$572$	−8.25392	−	8.13411i	−0.345114	−	0.340104i
$573$		−	14.0300i		−	0.586113i
$574$	−14.8116	+	8.46910i	−0.618226	+	0.353493i
$575$	−23.3031			−0.971804
$576$	2.23952	+	7.68014i	0.0933135	+	0.320006i
$577$	−3.11174	−	5.38970i	−0.129544	−	0.224376i	0.793956	−	0.607975i	$-0.208018\pi$
$577$	−3.11174	−	5.38970i	−0.129544	−	0.224376i	−0.923500	+	0.383599i	$0.874685\pi$
$578$	−3.51111	−	1.43933i	−0.146043	−	0.0598684i
$579$	0.675669	+	0.390098i	0.0280798	+	0.0162119i
$580$	4.83003	−	18.5678i	0.200556	−	0.770988i
$581$	−2.93188	+	1.18759i	−0.121635	+	0.0492694i
$582$	10.4010	+	13.4528i	0.431136	+	0.557635i
$583$	−3.57560	+	6.19312i	−0.148086	+	0.256493i
$584$	10.5710	−	14.0938i	0.437431	−	0.583204i
$585$	−11.0037	−	19.0590i	−0.454947	−	0.787991i
$586$	−30.7521	+	4.16300i	−1.27036	+	0.171972i
$587$		−	0.894279i		−	0.0369108i	−0.999830	−	0.0184554i	$-0.994125\pi$
$587$		−	0.894279i		−	0.0369108i	0.999830	−	0.0184554i	$-0.00587487\pi$
$588$	−0.117113	+	13.9995i	−0.00482968	+	0.577330i
$589$		−	25.8693i		−	1.06593i
$590$	−0.0788645	−	0.582572i	−0.00324680	−	0.0239841i
$591$	−1.18818	−	2.05799i	−0.0488753	−	0.0846545i
$592$	−6.82821	+	0.0998477i	−0.280638	+	0.00410371i
$593$	11.3498	−	19.6584i	0.466080	−	0.807275i	−0.533169	−	0.846009i	$-0.678999\pi$
$593$	11.3498	−	19.6584i	0.466080	−	0.807275i	0.999250	+	0.0387338i	$0.0123324\pi$
$594$	−1.05389	+	0.814815i	−0.0432416	+	0.0334323i
$595$	−33.1965	+	13.4466i	−1.36092	+	0.551256i
$596$	40.0774	+	10.4253i	1.64163	+	0.427036i
$597$	−11.7640	−	6.79196i	−0.481469	−	0.277976i
$598$	9.85728	−	24.0458i	0.403094	−	0.983307i
$599$	19.5178	+	33.8058i	0.797476	+	1.38127i	0.921255	+	0.388959i	$0.127165\pi$
$599$	19.5178	+	33.8058i	0.797476	+	1.38127i	−0.123780	+	0.992310i	$0.539502\pi$
$600$	2.63972	−	21.9043i	0.107766	−	0.894239i
$601$	−0.397117			−0.0161987			−0.00809936	−	0.999967i	$-0.502578\pi$
$601$	−0.397117			−0.0161987			−0.00809936	+	0.999967i	$0.502578\pi$
$602$	−6.51290	−	11.3904i	−0.265446	−	0.464239i
$603$			3.97580i			0.161907i
$604$	5.63490	+	5.55310i	0.229281	+	0.225953i
$605$	−31.3335	+	18.0904i	−1.27389	+	0.735480i
$606$	2.33051	+	0.955362i	0.0946704	+	0.0388089i
$607$	−10.9157	+	18.9066i	−0.443056	+	0.767395i	−0.997915	−	0.0645493i	$-0.979439\pi$
$607$	−10.9157	+	18.9066i	−0.443056	+	0.767395i	0.554859	+	0.831945i	$0.312772\pi$
$608$	−2.03006	−	13.5073i	−0.0823298	−	0.547794i
$609$	4.36249	−	5.59397i	0.176777	−	0.226679i
$610$	−32.6406	+	25.2361i	−1.32158	+	1.02178i
$611$	−36.4682	−	21.0549i	−1.47535	−	0.851791i
$612$	−7.29513	+	2.01200i	−0.294888	+	0.0813303i
$613$	21.6460	−	12.4973i	0.874275	−	0.504763i	0.00550856	−	0.999985i	$-0.498247\pi$
$613$	21.6460	−	12.4973i	0.874275	−	0.504763i	0.868767	+	0.495222i	$0.164913\pi$
$614$	−3.06289	+	0.414633i	−0.123608	+	0.0167332i
$615$	16.3146			0.657867
$616$	1.80312	−	6.81452i	0.0726496	−	0.274565i
$617$	−17.0538			−0.686560			−0.343280	−	0.939233i	$-0.611538\pi$
$617$	−17.0538			−0.686560			−0.343280	+	0.939233i	$0.611538\pi$
$618$	17.4100	−	2.35684i	0.700332	−	0.0948061i
$619$	4.32061	−	2.49451i	0.173660	−	0.100263i	−0.410650	−	0.911793i	$-0.634698\pi$
$619$	4.32061	−	2.49451i	0.173660	−	0.100263i	0.584311	+	0.811530i	$0.301365\pi$
$620$	20.3825	+	73.9030i	0.818580	+	2.96802i
$621$	−2.58719	−	1.49371i	−0.103820	−	0.0599407i
$622$	−30.5085	+	23.5877i	−1.22328	+	0.945780i
$623$	4.77167	+	0.666291i	0.191173	+	0.0266944i
$624$	21.4859	+	11.9895i	0.860123	+	0.479963i
$625$	1.57804	−	2.73324i	0.0631215	−	0.109330i
$626$	−1.78816	−	0.733033i	−0.0714692	−	0.0292979i
$627$	1.96975	−	1.13723i	0.0786642	−	0.0454168i
$628$	−16.6644	+	16.9099i	−0.664984	+	0.674779i
$629$		−	6.45975i		−	0.257567i
$630$	6.74181	−	11.5652i	0.268600	−	0.460767i
$631$	15.7236			0.625947			0.312973	−	0.949762i	$-0.398675\pi$
$631$	15.7236			0.625947			0.312973	+	0.949762i	$0.398675\pi$
$632$	15.3675	+	1.85197i	0.611287	+	0.0736673i
$633$	−7.09662	−	12.2917i	−0.282065	−	0.488551i
$634$	−4.39383	+	10.7183i	−0.174501	+	0.425677i
$635$	24.0869	+	13.9066i	0.955859	+	0.551865i
$636$	3.82246	−	14.6945i	0.151570	−	0.582675i
$637$	29.9657	+	30.9203i	1.18728	+	1.22511i
$638$	−2.82574	+	2.18473i	−0.111872	+	0.0864942i
$639$	−1.96286	+	3.39977i	−0.0776495	+	0.134493i
$640$	16.4419	+	36.9880i	0.649923	+	1.46208i
$641$	−12.3353	−	21.3654i	−0.487216	−	0.843884i	0.512676	−	0.858582i	$-0.328654\pi$
$641$	−12.3353	−	21.3654i	−0.487216	−	0.843884i	−0.999892	+	0.0146989i	$0.995321\pi$
$642$	1.84292	+	13.6136i	0.0727343	+	0.537288i
$643$		−	47.6908i		−	1.88074i	−0.340150	−	0.940371i	$-0.610478\pi$
$643$		−	47.6908i		−	1.88074i	0.340150	−	0.940371i	$-0.389522\pi$
$644$	15.6738	−	2.05509i	0.617636	−	0.0809820i
$645$			12.5462i			0.494007i
$646$	12.8038	−	1.73329i	0.503758	−	0.0681953i
$647$	9.64727	+	16.7096i	0.379273	+	0.656921i	0.990957	−	0.134182i	$-0.0428406\pi$
$647$	9.64727	+	16.7096i	0.379273	+	0.656921i	−0.611683	+	0.791103i	$0.709507\pi$
$648$	1.69713	−	2.26269i	0.0666694	−	0.0888868i
$649$	−0.0547233	+	0.0947835i	−0.00214808	+	0.00372058i
$650$	−41.5046	−	53.6824i	−1.62794	−	2.10560i
$651$	−3.92004	+	28.0735i	−0.153638	+	1.10029i
$652$	−33.0075	−	8.58619i	−1.29267	−	0.336261i
$653$	35.9797	+	20.7729i	1.40799	+	0.812905i	0.995195	−	0.0979172i	$-0.0312180\pi$
$653$	35.9797	+	20.7729i	1.40799	+	0.812905i	0.412799	+	0.910822i	$0.364551\pi$
$654$	−18.6825	−	7.65867i	−0.730545	−	0.299478i
$655$	−12.6030	−	21.8291i	−0.492442	−	0.852934i
$656$	−15.6613	+	9.34998i	−0.611469	+	0.365055i
$657$	−6.22876			−0.243007
$658$	0.107138	−	25.6145i	0.00417667	−	0.998558i
$659$		−	21.7026i		−	0.845414i	−0.906266	−	0.422707i	$-0.861080\pi$
$659$		−	21.7026i		−	0.845414i	0.906266	−	0.422707i	$-0.138920\pi$
$660$	−4.73112	+	4.80081i	−0.184158	+	0.186871i
$661$	−12.7886	+	7.38348i	−0.497417	+	0.287184i	−0.727646	−	0.685952i	$-0.759386\pi$
$661$	−12.7886	+	7.38348i	−0.497417	+	0.287184i	0.230229	+	0.973136i	$0.426052\pi$
$662$	−8.27787	+	20.1930i	−0.321729	+	0.784823i
$663$	−11.6372	+	20.1563i	−0.451953	+	0.782805i
$664$	−3.10988	+	1.32829i	−0.120687	+	0.0515478i
$665$	−14.0557	+	18.0235i	−0.545056	+	0.698919i
$666$	1.47678	+	1.91008i	0.0572242	+	0.0740142i
$667$	−6.93691	−	4.00503i	−0.268598	−	0.155075i
$668$	−20.1166	+	5.54818i	−0.778336	+	0.214665i
$669$	0.171627	−	0.0990889i	0.00663548	−	0.00383100i
$670$	2.69861	+	19.9346i	0.104256	+	0.770140i
$671$	7.68110			0.296526
$672$	0.156235	+	14.9658i	0.00602691	+	0.577319i
$673$	3.09088			0.119145			0.0595724	−	0.998224i	$-0.481026\pi$
$673$	3.09088			0.119145			0.0595724	+	0.998224i	$0.481026\pi$
$674$	0.103191	+	0.762271i	0.00397477	+	0.0293616i
$675$	−6.75532	+	3.90019i	−0.260012	+	0.150118i
$676$	47.8859	−	13.2069i	1.84176	−	0.507959i
$677$	33.6034	+	19.4009i	1.29148	+	0.745638i	0.978917	−	0.204258i	$-0.0654782\pi$
$677$	33.6034	+	19.4009i	1.29148	+	0.745638i	0.312566	+	0.949896i	$0.398812\pi$
$678$	−12.0042	−	15.5264i	−0.461020	−	0.596287i
$679$	11.9435	+	29.4857i	0.458349	+	1.13156i
$680$	−35.2120	+	15.0398i	−1.35032	+	0.576749i
$681$	12.8780	−	22.3054i	0.493487	−	0.854744i
$682$	5.41350	−	13.2057i	0.207294	−	0.505671i
$683$	−22.5229	+	13.0036i	−0.861817	+	0.497570i	−0.864620	−	0.502426i	$-0.832441\pi$
$683$	−22.5229	+	13.0036i	−0.861817	+	0.497570i	0.00280354	+	0.999996i	$0.499108\pi$
$684$	−3.38970	+	3.43963i	−0.129608	+	0.131517i
$685$			64.7846i			2.47529i
$686$	−7.27993	+	25.1595i	−0.277949	+	0.960596i
$687$	−16.1617			−0.616609
$688$	−7.19031	−	12.0438i	−0.274128	−	0.459166i
$689$	−23.3491	−	40.4418i	−0.889530	−	1.54071i
$690$	−13.9860	−	5.73338i	−0.532438	−	0.218266i
$691$	8.60842	+	4.97007i	0.327480	+	0.189070i	0.654722	−	0.755870i	$-0.272786\pi$
$691$	8.60842	+	4.97007i	0.327480	+	0.189070i	−0.327242	+	0.944941i	$0.606119\pi$
$692$	−28.2095	−	7.33810i	−1.07237	−	0.278953i
$693$	−2.30991	+	0.935652i	−0.0877461	+	0.0355425i
$694$	9.91581	+	12.8252i	0.376399	+	0.486837i
$695$	14.8964	−	25.8013i	0.565052	−	0.978698i
$696$	4.55043	−	6.06685i	0.172484	−	0.229963i
$697$	−8.62694	−	14.9423i	−0.326769	−	0.565980i
$698$	1.72506	−	0.233526i	0.0652943	−	0.00883910i
$699$		−	25.1239i		−	0.950272i
$700$	15.8156	−	38.1254i	0.597774	−	1.44101i
$701$		−	32.3250i		−	1.22090i	−0.792056	−	0.610449i	$-0.790989\pi$
$701$		−	32.3250i		−	1.22090i	0.792056	−	0.610449i	$-0.209011\pi$
$702$	−1.16697	−	8.62043i	−0.0440446	−	0.325357i
$703$	−2.06114	−	3.57000i	−0.0777374	−	0.134645i
$704$	1.79029	−	7.31999i	0.0674741	−	0.275882i
$705$	−12.2464	+	21.2113i	−0.461225	+	0.798865i
$706$	38.2840	−	29.5993i	1.44084	−	1.11398i
$707$	3.71576	+	2.89776i	0.139746	+	0.108981i
$708$	0.0585014	−	0.224894i	0.00219862	−	0.00845205i
$709$	−38.2056	−	22.0580i	−1.43484	−	0.828406i	−0.437357	−	0.899288i	$-0.644085\pi$
$709$	−38.2056	−	22.0580i	−1.43484	−	0.828406i	−0.997485	+	0.0708817i	$0.977419\pi$
$710$	−7.53412	+	18.3787i	−0.282750	+	0.689741i
$711$	−2.73628	−	4.73937i	−0.102618	−	0.177740i
$712$	5.11362	+	0.616251i	0.191641	+	0.0230950i
$713$	32.0065			1.19865
$714$	−14.1574	−	0.0592160i	−0.529826	−	0.00221610i
$715$			20.7303i			0.775268i
$716$	−5.30595	+	5.38411i	−0.198293	+	0.201213i
$717$	−13.8901	+	8.01946i	−0.518736	+	0.299492i
$718$	44.3687	+	18.1884i	1.65583	+	0.678785i
$719$	3.22929	−	5.59330i	0.120432	−	0.208595i	−0.799506	−	0.600658i	$-0.794905\pi$
$719$	3.22929	−	5.59330i	0.120432	−	0.208595i	0.919938	+	0.392063i	$0.128239\pi$
$720$	6.97354	−	12.4970i	0.259889	−	0.465737i
$721$	32.5523	+	4.54544i	1.21231	+	0.169281i
$722$	−14.7345	+	11.3920i	−0.548362	+	0.423966i
$723$	−11.4047	−	6.58453i	−0.424147	−	0.244881i
$724$	−0.597489	−	2.16638i	−0.0222055	−	0.0805129i
$725$	−18.1127	+	10.4574i	−0.672690	+	0.388378i
$726$	−14.1722	+	1.91854i	−0.525981	+	0.0712037i
$727$	−25.6040			−0.949600			−0.474800	−	0.880094i	$-0.657480\pi$
$727$	−25.6040			−0.949600			−0.474800	+	0.880094i	$0.657480\pi$
$728$	32.6506	+	32.4469i	1.21011	+	1.20256i
$729$	−1.00000			−0.0370370
$730$	−31.2309	+	4.22783i	−1.15591	+	0.156479i
$731$	11.4909	−	6.63428i	0.425007	−	0.245378i
$732$	−15.7216	+	4.33604i	−0.581089	+	0.160265i
$733$	−8.94596	−	5.16495i	−0.330426	−	0.190772i	0.325604	−	0.945506i	$-0.394432\pi$
$733$	−8.94596	−	5.16495i	−0.330426	−	0.190772i	−0.656030	+	0.754734i	$0.727766\pi$
$734$	21.5313	−	16.6469i	0.794734	−	0.614449i
$735$	17.9844	−	17.4292i	0.663366	−	0.642887i
$736$	16.7118	−	2.51167i	0.616004	−	0.0925813i
$737$	1.87254	−	3.24333i	0.0689757	−	0.119470i
$738$	5.96690	+	2.44606i	0.219645	+	0.0900406i
$739$	40.1335	−	23.1711i	1.47633	−	0.852362i	0.476691	−	0.879071i	$-0.341836\pi$
$739$	40.1335	−	23.1711i	1.47633	−	0.852362i	0.999643	+	0.0267085i	$0.00850260\pi$
$740$	8.70105	+	8.57475i	0.319857	+	0.315214i
$741$			14.8526i			0.545623i
$742$	14.3057	−	24.5405i	0.525177	−	0.900910i
$743$	−38.1002			−1.39776			−0.698880	−	0.715239i	$-0.746318\pi$
$743$	−38.1002			−1.39776			−0.698880	+	0.715239i	$0.746318\pi$
$744$	−3.62563	+	30.0853i	−0.132922	+	1.10298i
$745$	−37.0398	−	64.1548i	−1.35703	−	2.35045i
$746$	−7.95705	+	19.4104i	−0.291328	+	0.710665i
$747$	1.03542	+	0.597802i	0.0378841	+	0.0218724i
$748$	6.89875	+	1.79456i	0.252243	+	0.0656157i
$749$	−3.55429	+	25.4542i	−0.129871	+	0.930075i
$750$	−11.2095	+	8.66662i	−0.409312	+	0.316460i
$751$	3.76000	−	6.51250i	0.137204	−	0.237645i	−0.789233	−	0.614094i	$-0.789522\pi$
$751$	3.76000	−	6.51250i	0.137204	−	0.237645i	0.926437	+	0.376449i	$0.122855\pi$
$752$	−0.400378	−	27.3804i	−0.0146003	−	0.998460i
$753$	4.32352	+	7.48855i	0.157558	+	0.272898i
$754$	−3.12896	−	23.1136i	−0.113950	−	0.841747i
$755$		−	14.1524i		−	0.515059i
$756$	4.19973	−	3.21905i	0.152743	−	0.117076i
$757$		−	41.2006i		−	1.49746i	−0.662873	−	0.748731i	$-0.730663\pi$
$757$		−	41.2006i		−	1.49746i	0.662873	−	0.748731i	$-0.269337\pi$
$758$	16.4668	−	2.22916i	0.598100	−	0.0809666i
$759$	1.40703	+	2.43705i	0.0510720	+	0.0884592i
$760$	−14.6612	+	19.5470i	−0.531818	+	0.709045i
$761$	−14.3106	+	24.7867i	−0.518759	+	0.898517i	0.481003	+	0.876719i	$0.340273\pi$
$761$	−14.3106	+	24.7867i	−0.518759	+	0.898517i	−0.999762	+	0.0217985i	$0.993061\pi$
$762$	6.72453	+	8.69756i	0.243604	+	0.315079i
$763$	−29.7875	−	23.2299i	−1.07838	−	0.840980i
$764$	7.06413	−	27.1563i	0.255571	−	0.982481i
$765$	11.7237	+	6.76867i	0.423871	+	0.244722i
$766$	24.9478	+	10.2270i	0.901400	+	0.369518i
$767$	−0.357350	−	0.618949i	−0.0129032	−	0.0223489i
$768$	0.467830	+	15.9932i	0.0168814	+	0.577103i
$769$	−14.6303			−0.527581			−0.263791	−	0.964580i	$-0.584973\pi$
$769$	−14.6303			−0.527581			−0.263791	+	0.964580i	$0.584973\pi$
$770$	−10.9468	+	6.25921i	−0.394494	+	0.225566i
$771$			14.4651i			0.520947i
$772$	1.11140	+	1.09527i	0.0400001	+	0.0394195i
$773$	36.7815	−	21.2358i	1.32294	−	0.763798i	0.338741	−	0.940880i	$-0.389999\pi$
$773$	36.7815	−	21.2358i	1.32294	−	0.763798i	0.984196	+	0.177082i	$0.0566656\pi$
$774$	−1.88106	+	4.58866i	−0.0676135	+	0.164936i
$775$	41.7855	−	72.3746i	1.50098	−	2.59977i
$776$	13.3586	+	31.2759i	0.479545	+	1.12274i
$777$	1.69579	+	4.18651i	0.0608361	+	0.150190i
$778$	−1.73289	−	2.24134i	−0.0621271	−	0.0803558i
$779$	−9.53541	−	5.50527i	−0.341642	−	0.197247i
$780$	−11.7024	−	42.4306i	−0.419013	−	1.51926i
$781$	3.20247	−	1.84895i	0.114594	−	0.0661606i
$782$	2.14449	+	15.8413i	0.0766868	+	0.566485i
$783$	−2.68125			−0.0958202
$784$	−7.27545	+	27.0383i	−0.259837	+	0.965652i
$785$	42.4703			1.51583
$786$	−1.33659	−	9.87338i	−0.0476746	−	0.352172i
$787$	6.55295	−	3.78335i	0.233588	−	0.134862i	−0.378638	−	0.925545i	$-0.623608\pi$
$787$	6.55295	−	3.78335i	0.233588	−	0.134862i	0.612226	+	0.790683i	$0.290274\pi$
$788$	−1.26363	−	4.58167i	−0.0450149	−	0.163215i
$789$	17.2310	+	9.94833i	0.613440	+	0.354170i
$790$	−16.9365	−	21.9058i	−0.602575	−	0.779375i
$791$	−13.7844	−	34.0306i	−0.490119	−	1.20999i
$792$	−2.45015	+	1.04651i	−0.0870623	+	0.0371861i
$793$	−25.0793	+	43.4386i	−0.890591	+	1.54255i
$794$	4.55085	−	11.1013i	0.161503	−	0.393971i
$795$	−23.5226	+	13.5808i	−0.834259	+	0.481660i
$796$	−19.3505	−	19.0696i	−0.685860	−	0.675904i
$797$		−	11.4622i		−	0.406013i	−0.979177	−	0.203007i	$-0.934929\pi$
$797$		−	11.4622i		−	0.406013i	0.979177	−	0.203007i	$-0.0650713\pi$
$798$	−7.84301	+	4.48453i	−0.277639	+	0.158751i
$799$	25.9029			0.916379
$800$	16.1382	−	41.0685i	0.570573	−	1.45199i
$801$	−0.910509	−	1.57705i	−0.0321713	−	0.0557222i
$802$	−18.4407	−	7.55952i	−0.651163	−	0.266936i
$803$	5.08122	+	2.93365i	0.179312	+	0.103526i
$804$	−2.00182	+	7.69549i	−0.0705987	+	0.271399i
$805$	−22.2993	−	17.3902i	−0.785947	−	0.612925i
$806$	57.0061	+	73.7321i	2.00795	+	2.59710i
$807$	8.48299	−	14.6930i	0.298616	−	0.517217i
$808$	4.02987	+	3.02260i	0.141770	+	0.106335i
$809$	−8.54103	−	14.7935i	−0.300287	−	0.520112i	0.675914	−	0.736980i	$-0.263749\pi$
$809$	−8.54103	−	14.7935i	−0.300287	−	0.520112i	−0.976201	+	0.216869i	$0.930416\pi$
$810$	−5.01398	+	0.678758i	−0.176173	+	0.0238491i
$811$			16.6693i			0.585338i	0.956214	+	0.292669i	$0.0945434\pi$
$811$			16.6693i			0.585338i	−0.956214	+	0.292669i	$0.905457\pi$
$812$	11.2605	−	8.63109i	0.395168	−	0.302892i
$813$		−	1.07637i		−	0.0377500i
$814$	−0.305094	−	2.25372i	−0.0106935	−	0.0789930i
$815$	30.5058	+	52.8375i	1.06857	+	1.85082i
$816$	−15.1334	+	0.221293i	−0.529774	+	0.00774679i
$817$	4.23366	−	7.33291i	0.148117	−	0.256546i
$818$	−33.9647	+	26.2599i	−1.18755	+	0.918155i
$819$	2.25065	−	16.1181i	0.0786439	−	0.563211i
$820$	31.5782	+	8.21440i	1.10276	+	0.286859i
$821$	−37.2593	−	21.5117i	−1.30036	−	0.750762i	−0.319893	−	0.947454i	$-0.603647\pi$
$821$	−37.2593	−	21.5117i	−1.30036	−	0.750762i	−0.980465	+	0.196691i	$0.936980\pi$
$822$	−9.71321	+	23.6944i	−0.338787	+	0.826436i
$823$	−17.3255	−	30.0086i	−0.603928	−	1.04603i	−0.992220	−	0.124497i	$-0.960268\pi$
$823$	−17.3255	−	30.0086i	−0.603928	−	1.04603i	0.388292	−	0.921536i	$-0.373065\pi$
$824$	34.8851	+	4.20407i	1.21528	+	0.146456i
$825$	7.34769			0.255814
$826$	0.218943	−	0.375584i	0.00761801	−	0.0130682i
$827$			36.5937i			1.27249i	0.771489	+	0.636243i	$0.219513\pi$
$827$			36.5937i			1.27249i	−0.771489	+	0.636243i	$0.780487\pi$
$828$	−4.25564	−	4.19386i	−0.147894	−	0.145747i
$829$	6.54607	−	3.77938i	0.227354	−	0.131263i	−0.381997	−	0.924164i	$-0.624763\pi$
$829$	6.54607	−	3.77938i	0.227354	−	0.131263i	0.609351	+	0.792901i	$0.291430\pi$
$830$	5.59735	+	2.29456i	0.194287	+	0.0796455i
$831$	2.44572	−	4.23611i	0.0848410	−	0.146949i
$832$	35.5510	+	34.0248i	1.23251	+	1.17960i
$833$	−25.4731	−	7.25534i	−0.882592	−	0.251383i
$834$	9.31662	−	7.20315i	0.322608	−	0.249425i
$835$	32.3286	+	18.6649i	1.11878	+	0.645926i
$836$	4.38521	−	1.20944i	0.151666	−	0.0418295i
$837$	9.27835	−	5.35686i	0.320707	−	0.185160i
$838$	43.2896	−	5.86025i	1.49541	−	0.202439i
$839$	−33.3899			−1.15275			−0.576374	−	0.817186i	$-0.695533\pi$
$839$	−33.3899			−1.15275			−0.576374	+	0.817186i	$0.695533\pi$
$840$	18.8724	−	18.9909i	0.651160	−	0.655247i
$841$	21.8109			0.752099
$842$	28.1603	−	3.81215i	0.970469	−	0.131375i
$843$	0.653146	−	0.377094i	0.0224956	−	0.0129878i
$844$	−7.54722	−	27.3648i	−0.259786	−	0.941935i
$845$	−76.9553	−	44.4302i	−2.64734	−	1.52844i
$846$	−7.65923	+	5.92174i	−0.263330	+	0.203594i
$847$	−26.4986	−	3.70013i	−0.910503	−	0.127138i
$848$	14.7974	−	26.5178i	0.508144	−	0.910626i
$849$	9.71510	−	16.8270i	0.333421	−	0.577503i
$850$	38.6209	+	15.8321i	1.32469	+	0.543038i
$851$	4.41694	−	2.55012i	0.151411	−	0.0874171i
$852$	−5.51107	+	5.59224i	−0.188806	+	0.191587i
$853$			18.6855i			0.639779i	0.947455	+	0.319889i	$0.103646\pi$
$853$			18.6855i			0.639779i	−0.947455	+	0.319889i	$0.896354\pi$
$854$	−30.5104	−	0.127616i	−1.04404	−	0.00436692i
$855$	8.63884			0.295442
$856$	−3.28735	+	27.2783i	−0.112359	+	0.932352i
$857$	15.4441	+	26.7499i	0.527559	+	0.913759i	0.999484	+	0.0321205i	$0.0102260\pi$
$857$	15.4441	+	26.7499i	0.527559	+	0.913759i	−0.471925	+	0.881639i	$0.656441\pi$
$858$	−3.10810	+	7.58190i	−0.106109	+	0.258842i
$859$	35.3861	+	20.4302i	1.20736	+	0.697069i	0.962182	−	0.272409i	$-0.0878203\pi$
$859$	35.3861	+	20.4302i	1.20736	+	0.697069i	0.245178	+	0.969478i	$0.421154\pi$
$860$	−6.31703	+	24.2843i	−0.215409	+	0.828087i
$861$	9.51365	+	7.41927i	0.324224	+	0.252848i
$862$	−8.97007	+	6.93522i	−0.305522	+	0.236215i
$863$	−1.87676	+	3.25064i	−0.0638857	+	0.110653i	−0.896199	−	0.443652i	$-0.853683\pi$
$863$	−1.87676	+	3.25064i	−0.0638857	+	0.110653i	0.832313	+	0.554305i	$0.187016\pi$
$864$	4.42420	−	3.52512i	0.150514	−	0.119927i
$865$	26.0714	+	45.1571i	0.886455	+	1.53539i
$866$	5.11876	+	37.8123i	0.173943	+	1.28491i
$867$			2.68324i			0.0911277i
$868$	−21.7226	+	52.3648i	−0.737312	+	1.77738i
$869$			5.15496i			0.174870i
$870$	−13.4438	+	1.81992i	−0.455786	+	0.0617012i
$871$	12.2279	+	21.1793i	0.414327	+	0.717635i
$872$	−32.3055	−	24.2307i	−1.09400	−	0.820554i
$873$	6.01205	−	10.4132i	0.203477	−	0.352433i
$874$	6.23972	+	8.07051i	0.211062	+	0.272989i
$875$	−24.5689	+	9.95188i	−0.830580	+	0.336435i
$876$	−12.0563	−	3.13619i	−0.407345	−	0.105962i
$877$	26.0217	+	15.0236i	0.878689	+	0.507311i	0.870226	−	0.492653i	$-0.163973\pi$
$877$	26.0217	+	15.0236i	0.878689	+	0.507311i	0.00846311	+	0.999964i	$0.497306\pi$
$878$	47.7814	+	19.5874i	1.61254	+	0.661042i
$879$	10.9717	+	19.0035i	0.370065	+	0.640972i
$880$	−11.5747	+	6.91024i	−0.390183	+	0.232944i
$881$	42.4160			1.42903			0.714516	−	0.699619i	$-0.246647\pi$
$881$	42.4160			1.42903			0.714516	+	0.699619i	$0.246647\pi$
$882$	9.19082	−	3.67816i	0.309471	−	0.123850i
$883$			20.3124i			0.683568i	0.939779	+	0.341784i	$0.111031\pi$
$883$			20.3124i			0.683568i	−0.939779	+	0.341784i	$0.888969\pi$
$884$	−32.6736	+	33.1548i	−1.09893	+	1.11512i
$885$	−0.360005	+	0.207849i	−0.0121014	+	0.00698676i
$886$	−0.117973	+	0.287784i	−0.00396339	+	0.00966829i
$887$	−8.69219	+	15.0553i	−0.291855	+	0.505508i	−0.974248	−	0.225477i	$-0.927606\pi$
$887$	−8.69219	+	15.0553i	−0.291855	+	0.505508i	0.682393	+	0.730985i	$0.260939\pi$
$888$	1.89671	+	4.44069i	0.0636494	+	0.149020i
$889$	7.72177	+	19.0633i	0.258980	+	0.639362i
$890$	−5.63571	−	7.28928i	−0.188909	−	0.244337i
$891$	0.815768	+	0.470984i	0.0273292	+	0.0157785i
$892$	0.382090	−	0.105381i	0.0127933	−	0.00352840i
$893$	14.3153	−	8.26496i	0.479044	−	0.276576i
$894$	−3.92818	−	29.0174i	−0.131378	−	0.970488i
$895$	13.5225			0.452008
$896$	−7.23289	+	29.0463i	−0.241634	+	0.970367i
$897$	−18.3762			−0.613563
$898$	−3.92331	−	28.9815i	−0.130923	−	0.967125i
$899$	24.8776	−	14.3631i	0.829715	−	0.479036i
$900$	−15.0392	+	4.14783i	−0.501308	+	0.138261i
$901$	24.8769	+	14.3627i	0.828769	+	0.478490i
$902$	−3.71555	−	4.80573i	−0.123714	−	0.160013i
$903$	−5.70556	+	7.31617i	−0.189869	+	0.243467i
$904$	−15.4177	−	36.0967i	−0.512784	−	1.20056i
$905$	−2.01004	+	3.48150i	−0.0668161	+	0.115729i
$906$	2.12188	−	5.17611i	0.0704948	−	0.171965i
$907$	18.8970	−	10.9102i	0.627464	−	0.362266i	−0.152306	−	0.988333i	$-0.548670\pi$
$907$	18.8970	−	10.9102i	0.627464	−	0.362266i	0.779769	+	0.626067i	$0.215336\pi$
$908$	36.1573	−	36.6899i	1.19992	−	1.21760i
$909$		−	1.78101i		−	0.0590723i
$910$	0.344418	−	82.3434i	0.0114173	−	2.72966i
$911$	11.9139			0.394727			0.197363	−	0.980330i	$-0.436762\pi$
$911$	11.9139			0.394727			0.197363	+	0.980330i	$0.436762\pi$
$912$	−8.29290	+	4.95097i	−0.274605	+	0.163943i
$913$	−0.563109	−	0.975334i	−0.0186362	−	0.0322789i
$914$	−11.2327	−	4.60470i	−0.371544	−	0.152310i
$915$	25.2656	+	14.5871i	0.835255	+	0.482234i
$916$	−31.2824	−	8.13745i	−1.03360	−	0.268869i
$917$	2.57777	−	18.4608i	0.0851254	−	0.609629i
$918$	3.27300	+	4.23332i	0.108025	+	0.139720i
$919$	18.8832	−	32.7067i	0.622900	−	1.07890i	−0.366042	−	0.930598i	$-0.619288\pi$
$919$	18.8832	−	32.7067i	0.622900	−	1.07890i	0.988943	−	0.148297i	$-0.0473791\pi$
$920$	−24.1843	−	18.1394i	−0.797333	−	0.598039i
$921$	1.09277	+	1.89274i	0.0360081	+	0.0623679i
$922$	−19.3682	+	2.62193i	−0.637858	+	0.0863488i
$923$			24.1477i			0.794833i
$924$	−4.94212	+	0.647992i	−0.162584	+	0.0213174i
$925$		−	13.3171i		−	0.437863i
$926$	−5.47699	−	40.4585i	−0.179985	−	1.32955i
$927$	−6.21150	−	10.7586i	−0.204012	−	0.353360i
$928$	11.8624	−	9.45175i	0.389402	−	0.310269i
$929$	17.2547	−	29.8860i	0.566108	−	0.980528i	−0.430837	−	0.902430i	$-0.641782\pi$
$929$	17.2547	−	29.8860i	0.566108	−	0.980528i	0.996946	−	0.0780988i	$-0.0248849\pi$
$930$	42.8855	−	33.1570i	1.40627	−	1.08726i
$931$	−16.3928	+	4.11814i	−0.537253	+	0.134967i
$932$	12.6499	−	48.6294i	0.414361	−	1.59291i
$933$	23.6152	+	13.6343i	0.773129	+	0.446366i
$934$	6.66986	−	16.2704i	0.218244	−	0.532385i
$935$	−6.37587	−	11.0433i	−0.208513	−	0.361156i
$936$	2.08162	−	17.2732i	0.0680398	−	0.564591i
$937$	2.63475			0.0860735			0.0430367	−	0.999073i	$-0.486297\pi$
$937$	2.63475			0.0860735			0.0430367	+	0.999073i	$0.486297\pi$
$938$	−7.49186	+	12.8518i	−0.244618	+	0.419627i
$939$			1.36654i			0.0445952i
$940$	−34.3838	+	34.8903i	−1.12148	+	1.13800i
$941$	17.7673	−	10.2579i	0.579197	−	0.334399i	−0.181617	−	0.983369i	$-0.558133\pi$
$941$	17.7673	−	10.2579i	0.579197	−	0.334399i	0.760814	+	0.648970i	$0.224800\pi$
$942$	15.5331	+	6.36761i	0.506097	+	0.207468i
$943$	6.81133	−	11.7976i	0.221808	−	0.384182i
$944$	0.226469	−	0.405846i	0.00737094	−	0.0132092i
$945$	−9.37491	−	1.30906i	−0.304966	−	0.0425839i
$946$	3.69570	−	2.85733i	0.120157	−	0.0928999i
$947$	−27.2353	−	15.7243i	−0.885029	−	0.510972i	−0.0127161	−	0.999919i	$-0.504048\pi$
$947$	−27.2353	−	15.7243i	−0.885029	−	0.510972i	−0.872313	+	0.488947i	$0.837381\pi$
$948$	−2.91002	−	10.5512i	−0.0945129	−	0.342686i
$949$	−33.1810	+	19.1571i	−1.07710	+	0.621865i
$950$	26.3956	−	3.57325i	0.856386	−	0.115932i
$951$	8.19107			0.265614
$952$	−27.3730	−	7.24286i	−0.887163	−	0.234743i
$953$	7.69660			0.249317			0.124659	−	0.992200i	$-0.460216\pi$
$953$	7.69660			0.249317			0.124659	+	0.992200i	$0.460216\pi$
$954$	−10.6393	+	1.44028i	−0.344461	+	0.0466308i
$955$	−43.4711	+	25.0980i	−1.40669	+	0.812154i
$956$	−30.9233	+	8.52866i	−1.00013	+	0.275837i
$957$	2.18728	+	1.26283i	0.0707048	+	0.0408214i
$958$	−42.8305	+	33.1145i	−1.38379	+	1.06988i
$959$	−29.4617	+	37.7784i	−0.951367	+	1.21993i
$960$	19.7901	−	20.6779i	0.638724	−	0.667375i
$961$	−41.8919	+	72.5589i	−1.35135	+	2.34061i
$962$	13.7415	+	5.63317i	0.443045	+	0.181621i
$963$	8.41266	−	4.85705i	0.271094	−	0.156516i
$964$	−18.7595	−	18.4872i	−0.604203	−	0.595433i
$965$		−	2.79135i		−	0.0898568i
$966$	−5.54843	−	9.70367i	−0.178518	−	0.312210i
$967$	−58.4850			−1.88075			−0.940375	−	0.340140i	$-0.889526\pi$
$967$	−58.4850			−1.88075			−0.940375	+	0.340140i	$0.889526\pi$
$968$	−28.3976	−	3.42224i	−0.912732	−	0.109995i
$969$	−4.56811	−	7.91220i	−0.146749	−	0.254177i
$970$	23.0763	−	56.2922i	0.740935	−	1.80743i
$971$	−40.3828	−	23.3150i	−1.29595	−	0.748215i	−0.316245	−	0.948678i	$-0.602422\pi$
$971$	−40.3828	−	23.3150i	−1.29595	−	0.748215i	−0.979701	+	0.200463i	$0.935755\pi$
$972$	−1.93558	−	0.503501i	−0.0620839	−	0.0161498i
$973$	20.4201	−	8.27137i	0.654639	−	0.265168i
$974$	2.01899	−	1.56099i	0.0646927	−	0.0500173i
$975$	−23.9907	+	41.5531i	−0.768317	+	1.33076i
$976$	−32.6138	+	0.476905i	−1.04394	+	0.0152654i
$977$	0.754805	+	1.30736i	0.0241484	+	0.0418262i	0.877847	−	0.478941i	$-0.158979\pi$
$977$	0.754805	+	1.30736i	0.0241484	+	0.0418262i	−0.853699	+	0.520767i	$0.825646\pi$
$978$	3.23522	+	23.8986i	0.103451	+	0.764192i
$979$			1.71534i			0.0548225i
$980$	43.5860	−	24.6806i	1.39230	−	0.788392i
$981$			14.2775i			0.455845i
$982$	−5.74977	+	0.778364i	−0.183482	+	0.0248386i
$983$	−11.0830	−	19.1964i	−0.353494	−	0.612270i	0.633365	−	0.773853i	$-0.281673\pi$
$983$	−11.0830	−	19.1964i	−0.353494	−	0.612270i	−0.986859	+	0.161584i	$0.948340\pi$
$984$	10.3179	+	7.73889i	0.328921	+	0.246707i
$985$	−4.25103	+	7.36301i	−0.135449	+	0.234605i
$986$	8.77574	+	11.3506i	0.279476	+	0.361477i
$987$	−16.7875	+	6.79993i	−0.534351	+	0.216444i
$988$	−7.47829	+	28.7484i	−0.237916	+	0.914609i
$989$	9.07256	+	5.23805i	0.288491	+	0.166560i
$990$	4.40993	+	1.80779i	0.140157	+	0.0574555i
$991$	28.9420	+	50.1291i	0.919374	+	1.59240i	0.800368	+	0.599510i	$0.204638\pi$
$991$	28.9420	+	50.1291i	0.919374	+	1.59240i	0.119007	+	0.992893i	$0.462029\pi$
$992$	−22.1657	+	56.4071i	−0.703761	+	1.79093i
$993$	15.4318			0.489713
$994$	−12.7514	+	7.29108i	−0.404449	+	0.231259i
$995$			48.6000i			1.54072i
$996$	1.70315	+	1.67843i	0.0539665	+	0.0531831i
$997$	44.1522	−	25.4913i	1.39831	−	0.807317i	0.404098	−	0.914716i	$-0.367586\pi$
$997$	44.1522	−	25.4913i	1.39831	−	0.807317i	0.994216	+	0.107399i	$0.0342523\pi$
$998$	23.8173	−	58.0998i	0.753923	−	1.83912i
$999$	0.853618	−	1.47851i	0.0270073	−	0.0467780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.bc.a.37.7	✓	32
3.2	odd	2		504.2.cj.e.37.10		32
4.3	odd	2		672.2.bk.a.625.16		32
7.2	even	3		1176.2.c.e.589.6		16
7.4	even	3	inner	168.2.bc.a.109.15	yes	32
7.5	odd	6		1176.2.c.f.589.6		16
8.3	odd	2		672.2.bk.a.625.1		32
8.5	even	2	inner	168.2.bc.a.37.15	yes	32
12.11	even	2		2016.2.cr.e.1297.1		32
21.11	odd	6		504.2.cj.e.109.2		32
24.5	odd	2		504.2.cj.e.37.2		32
24.11	even	2		2016.2.cr.e.1297.16		32
28.11	odd	6		672.2.bk.a.529.1		32
28.19	even	6		4704.2.c.f.2353.8		16
28.23	odd	6		4704.2.c.e.2353.9		16
56.5	odd	6		1176.2.c.f.589.5		16
56.11	odd	6		672.2.bk.a.529.16		32
56.19	even	6		4704.2.c.f.2353.9		16
56.37	even	6		1176.2.c.e.589.5		16
56.51	odd	6		4704.2.c.e.2353.8		16
56.53	even	6	inner	168.2.bc.a.109.7	yes	32
84.11	even	6		2016.2.cr.e.1873.16		32
168.11	even	6		2016.2.cr.e.1873.1		32
168.53	odd	6		504.2.cj.e.109.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.7	✓	32	1.1	even	1	trivial
168.2.bc.a.37.15	yes	32	8.5	even	2	inner
168.2.bc.a.109.7	yes	32	56.53	even	6	inner
168.2.bc.a.109.15	yes	32	7.4	even	3	inner
504.2.cj.e.37.2		32	24.5	odd	2
504.2.cj.e.37.10		32	3.2	odd	2
504.2.cj.e.109.2		32	21.11	odd	6
504.2.cj.e.109.10		32	168.53	odd	6
672.2.bk.a.529.1		32	28.11	odd	6
672.2.bk.a.529.16		32	56.11	odd	6
672.2.bk.a.625.1		32	8.3	odd	2
672.2.bk.a.625.16		32	4.3	odd	2
1176.2.c.e.589.5		16	56.37	even	6
1176.2.c.e.589.6		16	7.2	even	3
1176.2.c.f.589.5		16	56.5	odd	6
1176.2.c.f.589.6		16	7.5	odd	6
2016.2.cr.e.1297.1		32	12.11	even	2
2016.2.cr.e.1297.16		32	24.11	even	2
2016.2.cr.e.1873.1		32	168.11	even	6
2016.2.cr.e.1873.16		32	84.11	even	6
4704.2.c.e.2353.8		16	56.51	odd	6
4704.2.c.e.2353.9		16	28.23	odd	6
4704.2.c.f.2353.8		16	28.19	even	6
4704.2.c.f.2353.9		16	56.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.189716 - 1.40143i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.92802 + 0.531748i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.865014 + 1.11882i) q^{6} +(0.993295 + 2.45222i) q^{7} +(1.11098 + 2.60110i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.189716 - 1.40143i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-1.92802 + 0.531748i) q^{4} +(3.09843 + 1.78888i) q^{5} +(0.865014 + 1.11882i) q^{6} +(0.993295 + 2.45222i) q^{7} +(1.11098 + 2.60110i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.91917 - 4.68162i) q^{10} +(-0.815768 + 0.470984i) q^{11} +(1.40384 - 1.42451i) q^{12} -6.15117i q^{13} +(3.24817 - 1.85726i) q^{14} -3.57776 q^{15} +(3.43449 - 2.05044i) q^{16} +(1.89187 + 3.27682i) q^{17} +(-1.30853 - 0.536416i) q^{18} +(2.09110 + 1.20730i) q^{19} +(-6.92506 - 1.80141i) q^{20} +(-2.08633 - 1.62703i) q^{21} +(0.814815 + 1.05389i) q^{22} +(-1.49371 + 2.58719i) q^{23} +(-2.26269 - 1.69713i) q^{24} +(3.90019 + 6.75532i) q^{25} +(-8.62043 + 1.16697i) q^{26} +1.00000i q^{27} +(-3.21905 - 4.19973i) q^{28} +2.68125i q^{29} +(0.678758 + 5.01398i) q^{30} +(-5.35686 - 9.27835i) q^{31} +(-3.52512 - 4.42420i) q^{32} +(0.470984 - 0.815768i) q^{33} +(4.23332 - 3.27300i) q^{34} +(-1.30906 + 9.37491i) q^{35} +(-0.503501 + 1.93558i) q^{36} +(-1.47851 - 0.853618i) q^{37} +(1.29523 - 3.15958i) q^{38} +(3.07558 + 5.32707i) q^{39} +(-1.21075 + 10.0467i) q^{40} -4.56000 q^{41} +(-1.88437 + 3.23252i) q^{42} -3.50672i q^{43} +(1.32237 - 1.34185i) q^{44} +(3.09843 - 1.78888i) q^{45} +(3.90915 + 1.60251i) q^{46} +(3.42292 - 5.92866i) q^{47} +(-1.94914 + 3.49297i) q^{48} +(-5.02673 + 4.87155i) q^{49} +(8.72718 - 6.74743i) q^{50} +(-3.27682 - 1.89187i) q^{51} +(3.27087 + 11.8595i) q^{52} +(6.57466 - 3.79588i) q^{53} +(1.40143 - 0.189716i) q^{54} -3.37013 q^{55} +(-5.27492 + 5.30803i) q^{56} -2.41460 q^{57} +(3.75759 - 0.508677i) q^{58} +(0.100623 - 0.0580947i) q^{59} +(6.89798 - 1.90247i) q^{60} +(-7.06184 - 4.07716i) q^{61} +(-11.9867 + 9.26752i) q^{62} +(2.62033 + 0.365889i) q^{63} +(-5.53143 + 5.77955i) q^{64} +(11.0037 - 19.0590i) q^{65} +(-1.23259 - 0.505287i) q^{66} +(-3.44314 + 1.98790i) q^{67} +(-5.39001 - 5.31177i) q^{68} -2.98743i q^{69} +(13.3866 + 0.0559922i) q^{70} -3.92572 q^{71} +(2.80811 + 0.338410i) q^{72} +(-3.11438 - 5.39427i) q^{73} +(-0.915789 + 2.23397i) q^{74} +(-6.75532 - 3.90019i) q^{75} +(-4.67365 - 1.21575i) q^{76} +(-1.96525 - 1.53261i) q^{77} +(6.88203 - 5.32085i) q^{78} +(2.73628 - 4.73937i) q^{79} +(14.3095 - 0.209245i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.865104 + 6.39052i) q^{82} +1.19560i q^{83} +(4.88764 + 2.02755i) q^{84} +13.5373i q^{85} +(-4.91443 + 0.665282i) q^{86} +(-1.34063 - 2.32203i) q^{87} +(-2.13138 - 1.59864i) q^{88} +(0.910509 - 1.57705i) q^{89} +(-3.09481 - 4.00286i) q^{90} +(15.0840 - 6.10992i) q^{91} +(1.50417 - 5.78242i) q^{92} +(9.27835 + 5.35686i) q^{93} +(-8.95799 - 3.67222i) q^{94} +(4.31942 + 7.48146i) q^{95} +(5.26494 + 2.06891i) q^{96} +12.0241 q^{97} +(7.78079 + 6.12040i) q^{98} +0.941967i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 + 16 * q^9	\( 32 q + 2 q^{2} - 2 q^{4} - 16 q^{8} + 16 q^{9} + 6 q^{10} + 22 q^{14} - 10 q^{16} - 2 q^{18} - 40 q^{20} - 12 q^{22} - 8 q^{23} - 6 q^{24} + 16 q^{25} + 6 q^{26} - 26 q^{28} - 8 q^{30} - 24 q^{31} - 8 q^{32} - 24 q^{34} - 4 q^{36} - 26 q^{38} - 6 q^{40} - 4 q^{42} + 20 q^{44} + 16 q^{46} - 24 q^{47} - 16 q^{48} + 8 q^{49} + 52 q^{50} + 44 q^{52} - 64 q^{55} + 40 q^{56} - 16 q^{57} + 34 q^{58} - 22 q^{60} + 100 q^{62} - 20 q^{64} + 12 q^{66} + 16 q^{68} + 38 q^{70} - 80 q^{71} - 8 q^{72} + 8 q^{73} + 10 q^{74} - 32 q^{76} + 12 q^{78} + 8 q^{79} - 56 q^{80} - 16 q^{81} - 16 q^{84} - 22 q^{86} + 24 q^{87} + 50 q^{88} + 12 q^{90} + 64 q^{92} - 48 q^{94} + 24 q^{95} + 10 q^{96} - 48 q^{97} - 64 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 - 2 * q^4 - 16 * q^8 + 16 * q^9 + 6 * q^10 + 22 * q^14 - 10 * q^16 - 2 * q^18 - 40 * q^20 - 12 * q^22 - 8 * q^23 - 6 * q^24 + 16 * q^25 + 6 * q^26 - 26 * q^28 - 8 * q^30 - 24 * q^31 - 8 * q^32 - 24 * q^34 - 4 * q^36 - 26 * q^38 - 6 * q^40 - 4 * q^42 + 20 * q^44 + 16 * q^46 - 24 * q^47 - 16 * q^48 + 8 * q^49 + 52 * q^50 + 44 * q^52 - 64 * q^55 + 40 * q^56 - 16 * q^57 + 34 * q^58 - 22 * q^60 + 100 * q^62 - 20 * q^64 + 12 * q^66 + 16 * q^68 + 38 * q^70 - 80 * q^71 - 8 * q^72 + 8 * q^73 + 10 * q^74 - 32 * q^76 + 12 * q^78 + 8 * q^79 - 56 * q^80 - 16 * q^81 - 16 * q^84 - 22 * q^86 + 24 * q^87 + 50 * q^88 + 12 * q^90 + 64 * q^92 - 48 * q^94 + 24 * q^95 + 10 * q^96 - 48 * q^97 - 64 * q^98

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