LMFDB - Embedded newform 930.2.bf.a.893.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (of order $12$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			893.44
Character	$\chi$	$=$	930.893
Dual form			930.2.bf.a.377.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.747225 + 1.56258i) q^{3} +1.00000i q^{4} +(-2.18104 + 0.493020i) q^{5} +(-1.63328 + 0.576543i) q^{6} +(-3.79793 - 1.01765i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.88331 - 2.33520i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.747225 + 1.56258i) q^{3} +1.00000i q^{4} +(-2.18104 + 0.493020i) q^{5} +(-1.63328 + 0.576543i) q^{6} +(-3.79793 - 1.01765i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.88331 - 2.33520i) q^{9} +(-1.89085 - 1.19361i) q^{10} +(-0.225535 - 0.130213i) q^{11} +(-1.56258 - 0.747225i) q^{12} +(3.81277 - 1.02163i) q^{13} +(-1.96595 - 3.40513i) q^{14} +(0.859344 - 3.77644i) q^{15} -1.00000 q^{16} +(-1.09590 + 4.08994i) q^{17} +(0.319533 - 2.98293i) q^{18} +(3.85397 - 2.22509i) q^{19} +(-0.493020 - 2.18104i) q^{20} +(4.42807 - 5.17415i) q^{21} +(-0.0674030 - 0.251552i) q^{22} +(2.45373 - 2.45373i) q^{23} +(-0.576543 - 1.63328i) q^{24} +(4.51386 - 2.15059i) q^{25} +(3.41843 + 1.97363i) q^{26} +(5.05619 - 1.19790i) q^{27} +(1.01765 - 3.79793i) q^{28} -5.25460 q^{29} +(3.27800 - 2.06270i) q^{30} +(-1.71838 - 5.29596i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.371993 - 0.255118i) q^{33} +(-3.66694 + 2.11711i) q^{34} +(8.78515 + 0.347083i) q^{35} +(2.33520 - 1.88331i) q^{36} +(0.196556 + 0.0526671i) q^{37} +(4.29854 + 1.15179i) q^{38} +(-1.25262 + 6.72114i) q^{39} +(1.19361 - 1.89085i) q^{40} +(-9.80119 - 5.65872i) q^{41} +(6.78979 - 0.527559i) q^{42} +(-0.797629 + 2.97679i) q^{43} +(0.130213 - 0.225535i) q^{44} +(5.25887 + 4.16465i) q^{45} +3.47009 q^{46} +(-4.49966 - 4.49966i) q^{47} +(0.747225 - 1.56258i) q^{48} +(7.32645 + 4.22993i) q^{49} +(4.71248 + 1.67108i) q^{50} +(-5.57198 - 4.76853i) q^{51} +(1.02163 + 3.81277i) q^{52} +(1.20308 + 4.48997i) q^{53} +(4.42231 + 2.72822i) q^{54} +(0.556098 + 0.172806i) q^{55} +(3.40513 - 1.96595i) q^{56} +(0.597098 + 7.68477i) q^{57} +(-3.71556 - 3.71556i) q^{58} +(-4.15001 - 7.18804i) q^{59} +(3.77644 + 0.859344i) q^{60} +2.18907 q^{61} +(2.52973 - 4.95989i) q^{62} +(4.77626 + 10.7855i) q^{63} -1.00000i q^{64} +(-7.81211 + 4.10798i) q^{65} +(0.443434 + 0.0826430i) q^{66} +(-3.84020 - 14.3318i) q^{67} +(-4.08994 - 1.09590i) q^{68} +(2.00066 + 5.66763i) q^{69} +(5.96661 + 6.45746i) q^{70} +(1.34039 + 0.773872i) q^{71} +(2.98293 + 0.319533i) q^{72} +(-13.1503 + 3.52362i) q^{73} +(0.101745 + 0.176228i) q^{74} +(-0.0123994 + 8.66025i) q^{75} +(2.22509 + 3.85397i) q^{76} +(0.724054 + 0.724054i) q^{77} +(-5.63830 + 3.86683i) q^{78} +(5.52132 - 3.18774i) q^{79} +(2.18104 - 0.493020i) q^{80} +(-1.90629 + 8.79580i) q^{81} +(-2.92917 - 10.9318i) q^{82} +(1.30341 + 4.86439i) q^{83} +(5.17415 + 4.42807i) q^{84} +(0.373770 - 9.46062i) q^{85} +(-2.66892 + 1.54090i) q^{86} +(3.92637 - 8.21072i) q^{87} +(0.251552 - 0.0674030i) q^{88} -16.1989 q^{89} +(0.773734 + 6.66343i) q^{90} -15.5203 q^{91} +(2.45373 + 2.45373i) q^{92} +(9.55937 + 1.27216i) q^{93} -6.36348i q^{94} +(-7.30864 + 6.75309i) q^{95} +(1.63328 - 0.576543i) q^{96} +(1.09975 - 1.09975i) q^{97} +(2.18957 + 8.17160i) q^{98} +(0.120680 + 0.771899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.747225	+	1.56258i	−0.431411	+	0.902156i
$3$	−0.747225	+	1.56258i	−0.431411	+	0.902156i
$4$			1.00000i			0.500000i
$5$	−2.18104	+	0.493020i	−0.975390	+	0.220485i
$5$	−2.18104	+	0.493020i	−0.975390	+	0.220485i
$6$	−1.63328	+	0.576543i	−0.666783	+	0.235373i
$7$	−3.79793	−	1.01765i	−1.43548	−	0.384636i	−0.544532	−	0.838740i	$-0.683293\pi$
$7$	−3.79793	−	1.01765i	−1.43548	−	0.384636i	−0.890949	+	0.454104i	$0.849960\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.88331	−	2.33520i	−0.627770	−	0.778399i
$10$	−1.89085	−	1.19361i	−0.597938	−	0.377453i
$11$	−0.225535	−	0.130213i	−0.0680013	−	0.0392606i	0.465614	−	0.884988i	$-0.345834\pi$
$11$	−0.225535	−	0.130213i	−0.0680013	−	0.0392606i	−0.533615	+	0.845727i	$0.679167\pi$
$12$	−1.56258	−	0.747225i	−0.451078	−	0.215705i
$13$	3.81277	−	1.02163i	1.05747	−	0.283349i	0.312135	−	0.950038i	$-0.398956\pi$
$13$	3.81277	−	1.02163i	1.05747	−	0.283349i	0.745336	+	0.666689i	$0.232289\pi$
$14$	−1.96595	−	3.40513i	−0.525423	−	0.910059i
$15$	0.859344	−	3.77644i	0.221882	−	0.975074i
$16$	−1.00000			−0.250000
$17$	−1.09590	+	4.08994i	−0.265794	+	0.991957i	0.695969	+	0.718072i	$0.254975\pi$
$17$	−1.09590	+	4.08994i	−0.265794	+	0.991957i	−0.961763	+	0.273885i	$0.911691\pi$
$18$	0.319533	−	2.98293i	0.0753146	−	0.703084i
$19$	3.85397	−	2.22509i	0.884160	−	0.510470i	0.0121324	−	0.999926i	$-0.496138\pi$
$19$	3.85397	−	2.22509i	0.884160	−	0.510470i	0.872028	+	0.489456i	$0.162805\pi$
$20$	−0.493020	−	2.18104i	−0.110243	−	0.487695i
$21$	4.42807	−	5.17415i	0.966283	−	1.12909i
$22$	−0.0674030	−	0.251552i	−0.0143704	−	0.0536310i
$23$	2.45373	−	2.45373i	0.511637	−	0.511637i	−0.403391	−	0.915028i	$-0.632168\pi$
$23$	2.45373	−	2.45373i	0.511637	−	0.511637i	0.915028	+	0.403391i	$0.132168\pi$
$24$	−0.576543	−	1.63328i	−0.117686	−	0.333392i
$25$	4.51386	−	2.15059i	0.902772	−	0.430118i
$26$	3.41843	+	1.97363i	0.670410	+	0.387061i
$27$	5.05619	−	1.19790i	0.973064	−	0.230537i
$28$	1.01765	−	3.79793i	0.192318	−	0.717741i
$29$	−5.25460			−0.975754			−0.487877	−	0.872912i	$-0.662229\pi$
$29$	−5.25460			−0.975754			−0.487877	+	0.872912i	$0.662229\pi$
$30$	3.27800	−	2.06270i	0.598478	−	0.376596i
$31$	−1.71838	−	5.29596i	−0.308631	−	0.951182i
$31$	−1.71838	−	5.29596i	−0.308631	−	0.951182i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.371993	−	0.255118i	0.0647557	−	0.0444104i
$34$	−3.66694	+	2.11711i	−0.628875	+	0.363081i
$35$	8.78515	+	0.347083i	1.48496	+	0.0586678i
$36$	2.33520	−	1.88331i	0.389199	−	0.313885i
$37$	0.196556	+	0.0526671i	0.0323137	+	0.00865842i	0.274940	−	0.961461i	$-0.411342\pi$
$37$	0.196556	+	0.0526671i	0.0323137	+	0.00865842i	−0.242626	+	0.970120i	$0.578009\pi$
$38$	4.29854	+	1.15179i	0.697315	+	0.186845i
$39$	−1.25262	+	6.72114i	−0.200580	+	1.07624i
$40$	1.19361	−	1.89085i	0.188726	−	0.298969i
$41$	−9.80119	−	5.65872i	−1.53069	−	0.883744i	−0.999330	−	0.0365970i	$-0.988348\pi$
$41$	−9.80119	−	5.65872i	−1.53069	−	0.883744i	−0.531359	−	0.847147i	$-0.678318\pi$
$42$	6.78979	−	0.527559i	1.04769	−	0.0814041i
$43$	−0.797629	+	2.97679i	−0.121637	+	0.453957i	−0.999698	−	0.0245935i	$-0.992171\pi$
$43$	−0.797629	+	2.97679i	−0.121637	+	0.453957i	0.878060	+	0.478550i	$0.158838\pi$
$44$	0.130213	−	0.225535i	0.0196303	−	0.0340007i
$45$	5.25887	+	4.16465i	0.783946	+	0.620829i
$46$	3.47009			0.511637
$47$	−4.49966	−	4.49966i	−0.656342	−	0.656342i	0.298170	−	0.954513i	$-0.403624\pi$
$47$	−4.49966	−	4.49966i	−0.656342	−	0.656342i	−0.954513	+	0.298170i	$0.903624\pi$
$48$	0.747225	−	1.56258i	0.107853	−	0.225539i
$49$	7.32645	+	4.22993i	1.04664	+	0.604276i
$50$	4.71248	+	1.67108i	0.666445	+	0.236327i
$51$	−5.57198	−	4.76853i	−0.780233	−	0.667728i
$52$	1.02163	+	3.81277i	0.141674	+	0.528736i
$53$	1.20308	+	4.48997i	0.165256	+	0.616744i	0.998007	+	0.0630969i	$0.0200977\pi$
$53$	1.20308	+	4.48997i	0.165256	+	0.616744i	−0.832751	+	0.553647i	$0.813236\pi$
$54$	4.42231	+	2.72822i	0.601800	+	0.371263i
$55$	0.556098	+	0.172806i	0.0749842	+	0.0233011i
$56$	3.40513	−	1.96595i	0.455029	−	0.262711i
$57$	0.597098	+	7.68477i	0.0790875	+	1.01787i
$58$	−3.71556	−	3.71556i	−0.487877	−	0.487877i
$59$	−4.15001	−	7.18804i	−0.540286	−	0.935803i	−0.998887	−	0.0471605i	$-0.984983\pi$
$59$	−4.15001	−	7.18804i	−0.540286	−	0.935803i	0.458601	−	0.888642i	$-0.348351\pi$
$60$	3.77644	+	0.859344i	0.487537	+	0.110941i
$61$	2.18907			0.280281			0.140141	−	0.990132i	$-0.455245\pi$
$61$	2.18907			0.280281			0.140141	+	0.990132i	$0.455245\pi$
$62$	2.52973	−	4.95989i	0.321276	−	0.629906i
$63$	4.77626	+	10.7855i	0.601752	+	1.35884i
$64$		−	1.00000i		−	0.125000i
$65$	−7.81211	+	4.10798i	−0.968973	+	0.509532i
$66$	0.443434	+	0.0826430i	0.0545830	+	0.0101726i
$67$	−3.84020	−	14.3318i	−0.469155	−	1.75091i	−0.642732	−	0.766091i	$-0.722199\pi$
$67$	−3.84020	−	14.3318i	−0.469155	−	1.75091i	0.173577	−	0.984820i	$-0.444468\pi$
$68$	−4.08994	−	1.09590i	−0.495978	−	0.132897i
$69$	2.00066	+	5.66763i	0.240851	+	0.682302i
$70$	5.96661	+	6.45746i	0.713147	+	0.771814i
$71$	1.34039	+	0.773872i	0.159075	+	0.0918418i	0.577424	−	0.816444i	$-0.304058\pi$
$71$	1.34039	+	0.773872i	0.159075	+	0.0918418i	−0.418350	+	0.908286i	$0.637391\pi$
$72$	2.98293	+	0.319533i	0.351542	+	0.0376573i
$73$	−13.1503	+	3.52362i	−1.53913	+	0.412409i	−0.925985	−	0.377560i	$-0.876763\pi$
$73$	−13.1503	+	3.52362i	−1.53913	+	0.412409i	−0.613146	+	0.789969i	$0.710096\pi$
$74$	0.101745	+	0.176228i	0.0118276	+	0.0204860i
$75$	−0.0123994	+	8.66025i	−0.00143176	+	0.999999i
$76$	2.22509	+	3.85397i	0.255235	+	0.442080i
$77$	0.724054	+	0.724054i	0.0825136	+	0.0825136i
$78$	−5.63830	+	3.86683i	−0.638412	+	0.437832i
$79$	5.52132	−	3.18774i	0.621197	−	0.358648i	−0.156138	−	0.987735i	$-0.549904\pi$
$79$	5.52132	−	3.18774i	0.621197	−	0.358648i	0.777335	+	0.629087i	$0.216571\pi$
$80$	2.18104	−	0.493020i	0.243848	−	0.0551213i
$81$	−1.90629	+	8.79580i	−0.211810	+	0.977311i
$82$	−2.92917	−	10.9318i	−0.323473	−	1.20722i
$83$	1.30341	+	4.86439i	0.143068	+	0.533936i	0.999834	+	0.0182307i	$0.00580333\pi$
$83$	1.30341	+	4.86439i	0.143068	+	0.533936i	−0.856766	+	0.515705i	$0.827530\pi$
$84$	5.17415	+	4.42807i	0.564546	+	0.483142i
$85$	0.373770	−	9.46062i	0.0405410	−	1.02615i
$86$	−2.66892	+	1.54090i	−0.287797	+	0.166160i
$87$	3.92637	−	8.21072i	0.420951	−	0.880282i
$88$	0.251552	−	0.0674030i	0.0268155	−	0.00718519i
$89$	−16.1989			−1.71708			−0.858541	−	0.512745i	$-0.828629\pi$
$89$	−16.1989			−1.71708			−0.858541	+	0.512745i	$0.828629\pi$
$90$	0.773734	+	6.66343i	0.0815587	+	0.702387i
$91$	−15.5203			−1.62697
$92$	2.45373	+	2.45373i	0.255819	+	0.255819i
$93$	9.55937	+	1.27216i	0.991261	+	0.131917i
$94$		−	6.36348i		−	0.656342i
$95$	−7.30864	+	6.75309i	−0.749850	+	0.692852i
$96$	1.63328	−	0.576543i	0.166696	−	0.0588431i
$97$	1.09975	−	1.09975i	0.111663	−	0.111663i	−0.649068	−	0.760731i	$-0.724841\pi$
$97$	1.09975	−	1.09975i	0.111663	−	0.111663i	0.760731	+	0.649068i	$0.224841\pi$
$98$	2.18957	+	8.17160i	0.221180	+	0.825456i
$99$	0.120680	+	0.771899i	0.0121288	+	0.0775788i
$100$	2.15059	+	4.51386i	0.215059	+	0.451386i
$101$		−	13.7066i		−	1.36386i	−0.731417	−	0.681930i	$-0.761141\pi$
$101$		−	13.7066i		−	1.36386i	0.731417	−	0.681930i	$-0.238859\pi$
$102$	−0.568122	−	7.31185i	−0.0562525	−	0.723981i
$103$	13.8135	−	3.70130i	1.36108	−	0.364700i	0.496867	−	0.867827i	$-0.334484\pi$
$103$	13.8135	−	3.70130i	1.36108	−	0.364700i	0.864213	+	0.503126i	$0.167817\pi$
$104$	−1.97363	+	3.41843i	−0.193531	+	0.335205i
$105$	−7.10683	+	13.4681i	−0.693555	+	1.31436i
$106$	−2.32418	+	4.02559i	−0.225744	+	0.391000i
$107$	0.255089	−	0.952005i	0.0246604	−	0.0920338i	−0.952499	−	0.304542i	$-0.901497\pi$
$107$	0.255089	−	0.952005i	0.0246604	−	0.0920338i	0.977159	+	0.212508i	$0.0681632\pi$
$108$	1.19790	+	5.05619i	0.115268	+	0.486532i
$109$		−	16.5426i		−	1.58449i	−0.610202	−	0.792246i	$-0.708912\pi$
$109$		−	16.5426i		−	1.58449i	0.610202	−	0.792246i	$-0.291088\pi$
$110$	0.271029	+	0.515413i	0.0258416	+	0.0491427i
$111$	−0.229168	+	0.267781i	−0.0217517	+	0.0254166i
$112$	3.79793	+	1.01765i	0.358870	+	0.0961590i
$113$	4.49168	+	16.7632i	0.422542	+	1.57695i	0.769234	+	0.638968i	$0.220638\pi$
$113$	4.49168	+	16.7632i	0.422542	+	1.57695i	−0.346692	+	0.937979i	$0.612695\pi$
$114$	−5.01174	+	5.85616i	−0.469392	+	0.548480i
$115$	−4.14194	+	6.56141i	−0.386238	+	0.611855i
$116$		−	5.25460i		−	0.487877i
$117$	−9.56632	−	6.97952i	−0.884407	−	0.645257i
$118$	2.14821	−	8.01721i	0.197758	−	0.738044i
$119$	8.32427	−	14.4181i	0.763085	−	1.32170i
$120$	2.06270	+	3.27800i	0.188298	+	0.299239i
$121$	−5.46609	−	9.46754i	−0.496917	−	0.860686i
$122$	1.54790	+	1.54790i	0.140141	+	0.140141i
$123$	16.1659	−	11.0868i	1.45763	−	0.999664i
$124$	5.29596	−	1.71838i	0.475591	−	0.154315i
$125$	−8.78462	+	6.91595i	−0.785721	+	0.618581i
$126$	−4.24915	+	11.0038i	−0.378544	+	0.980296i
$127$	3.78694	+	1.01471i	0.336037	+	0.0900408i	0.422892	−	0.906180i	$-0.361015\pi$
$127$	3.78694	+	1.01471i	0.336037	+	0.0900408i	−0.0868550	+	0.996221i	$0.527682\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−4.05547	−	3.47069i	−0.357064	−	0.305578i
$130$	−8.42878	−	2.61922i	−0.739253	−	0.229720i
$131$	4.80305	−	2.77304i	0.419644	−	0.242282i	−0.275281	−	0.961364i	$-0.588771\pi$
$131$	4.80305	−	2.77304i	0.419644	−	0.242282i	0.694925	+	0.719082i	$0.255438\pi$
$132$	0.255118	+	0.371993i	0.0222052	+	0.0323778i
$133$	−16.9014	+	4.52873i	−1.46554	+	0.392690i
$134$	7.41870	−	12.8496i	0.640878	−	1.11003i
$135$	−10.4372	+	5.10548i	−0.898287	+	0.439409i
$136$	−2.11711	−	3.66694i	−0.181541	−	0.314438i
$137$	2.04448	−	0.547817i	0.174672	−	0.0468032i	−0.170423	−	0.985371i	$-0.554513\pi$
$137$	2.04448	−	0.547817i	0.174672	−	0.0468032i	0.345095	+	0.938568i	$0.387847\pi$
$138$	−2.59294	+	5.42230i	−0.220726	+	0.461577i
$139$			8.98460i			0.762064i	0.924562	+	0.381032i	$0.124431\pi$
$139$			8.98460i			0.762064i	−0.924562	+	0.381032i	$0.875569\pi$
$140$	−0.347083	+	8.78515i	−0.0293339	+	0.742481i
$141$	10.3933	−	3.66882i	0.875276	−	0.308970i
$142$	0.400586	+	1.49501i	0.0336164	+	0.125458i
$143$	−0.992941	−	0.266058i	−0.0830339	−	0.0222489i
$144$	1.88331	+	2.33520i	0.156942	+	0.194600i
$145$	11.4605	−	2.59062i	0.951741	−	0.215139i
$146$	−11.7903	−	6.80712i	−0.975770	−	0.563361i
$147$	−12.0841	+	8.28746i	−0.996681	+	0.683538i
$148$	−0.0526671	+	0.196556i	−0.00432921	+	0.0161568i
$149$	−0.868246	−	1.50385i	−0.0711295	−	0.123200i	0.828267	−	0.560333i	$-0.189327\pi$
$149$	−0.868246	−	1.50385i	−0.0711295	−	0.123200i	−0.899397	+	0.437134i	$0.855994\pi$
$150$	−6.13249	+	6.11495i	−0.500715	+	0.499284i
$151$	2.13775			0.173967			0.0869837	−	0.996210i	$-0.472277\pi$
$151$	2.13775			0.173967			0.0869837	+	0.996210i	$0.472277\pi$
$152$	−1.15179	+	4.29854i	−0.0934225	+	0.348658i
$153$	11.6147	−	5.14349i	0.938996	−	0.415827i
$154$			1.02397i			0.0825136i
$155$	6.35888	+	10.7035i	0.510757	+	0.859725i
$156$	−6.72114	−	1.25262i	−0.538122	−	0.100290i
$157$	−10.5251	+	10.5251i	−0.839995	+	0.839995i	−0.988858	−	0.148863i	$-0.952439\pi$
$157$	−10.5251	+	10.5251i	−0.839995	+	0.839995i	0.148863	+	0.988858i	$0.452439\pi$
$158$	6.15823	+	1.65009i	0.489923	+	0.131274i
$159$	−7.91490	−	1.47510i	−0.627693	−	0.116983i
$160$	1.89085	+	1.19361i	0.149484	+	0.0943631i
$161$	−11.8161	+	6.82203i	−0.931240	+	0.537652i
$162$	−7.56752	+	4.87162i	−0.594560	+	0.382750i
$163$	−6.55056	−	6.55056i	−0.513079	−	0.513079i	0.402389	−	0.915469i	$-0.368180\pi$
$163$	−6.55056	−	6.55056i	−0.513079	−	0.513079i	−0.915469	+	0.402389i	$0.868180\pi$
$164$	5.65872	−	9.80119i	0.441872	−	0.765345i
$165$	−0.685553	+	0.739823i	−0.0533702	+	0.0575951i
$166$	−2.51799	+	4.36129i	−0.195434	+	0.338502i
$167$	2.31775	−	8.64995i	0.179353	−	0.669353i	−0.816417	−	0.577463i	$-0.804043\pi$
$167$	2.31775	−	8.64995i	0.179353	−	0.669353i	0.995769	−	0.0918896i	$-0.0292907\pi$
$168$	0.527559	+	6.78979i	0.0407021	+	0.523844i
$169$	2.23514	−	1.29046i	0.171934	−	0.0992660i
$170$	6.95397	−	6.42538i	0.533345	−	0.492804i
$171$	−12.4542	−	4.80924i	−0.952399	−	0.367772i
$172$	−2.97679	−	0.797629i	−0.226978	−	0.0608187i
$173$	−0.217580	−	0.812020i	−0.0165423	−	0.0617367i	0.957161	−	0.289555i	$-0.0935074\pi$
$173$	−0.217580	−	0.812020i	−0.0165423	−	0.0617367i	−0.973704	+	0.227818i	$0.926841\pi$
$174$	8.58222	−	3.02950i	0.650616	−	0.229666i
$175$	−19.3319	+	3.57425i	−1.46135	+	0.270188i
$176$	0.225535	+	0.130213i	0.0170003	+	0.00981515i
$177$	14.3329	−	1.11365i	1.07732	−	0.0837069i
$178$	−11.4544	−	11.4544i	−0.858541	−	0.858541i
$179$	9.42040	+	16.3166i	0.704114	+	1.21956i	0.967010	+	0.254737i	$0.0819889\pi$
$179$	9.42040	+	16.3166i	0.704114	+	1.21956i	−0.262896	+	0.964824i	$0.584678\pi$
$180$	−4.16465	+	5.25887i	−0.310414	+	0.391973i
$181$	1.43029	−	2.47733i	0.106313	−	0.184139i	−0.807961	−	0.589236i	$-0.799429\pi$
$181$	1.43029	−	2.47733i	0.106313	−	0.184139i	0.914274	+	0.405097i	$0.132762\pi$
$182$	−10.9745	−	10.9745i	−0.813483	−	0.813483i
$183$	−1.63572	+	3.42059i	−0.120916	+	0.252857i
$184$			3.47009i			0.255819i
$185$	−0.454663	−	0.0179628i	−0.0334275	−	0.00132065i
$186$	5.85994	+	7.65905i	0.429672	+	0.561589i
$187$	0.779725	−	0.779725i	0.0570192	−	0.0570192i
$188$	4.49966	−	4.49966i	0.328171	−	0.328171i
$189$	−20.4221	−	0.595886i	−1.48549	−	0.0433443i
$190$	−9.94314	−	0.392833i	−0.721351	−	0.0284991i
$191$	−2.96477	−	1.71171i	−0.214523	−	0.123855i	0.388889	−	0.921285i	$-0.372859\pi$
$191$	−2.96477	−	1.71171i	−0.214523	−	0.123855i	−0.603412	+	0.797430i	$0.706192\pi$
$192$	1.56258	+	0.747225i	0.112769	+	0.0539263i
$193$	−3.51371	+	13.1133i	−0.252922	+	0.943919i	0.716312	+	0.697780i	$0.245829\pi$
$193$	−3.51371	+	13.1133i	−0.252922	+	0.943919i	−0.969235	+	0.246139i	$0.920838\pi$
$194$	1.55528			0.111663
$195$	−0.581643	−	15.2766i	−0.0416523	−	1.09398i
$196$	−4.22993	+	7.32645i	−0.302138	+	0.523318i
$197$	−0.118824	+	0.0318387i	−0.00846584	+	0.00226841i	−0.263049	−	0.964782i	$-0.584728\pi$
$197$	−0.118824	+	0.0318387i	−0.00846584	+	0.00226841i	0.254584	+	0.967051i	$0.418062\pi$
$198$	−0.460482	+	0.631149i	−0.0327250	+	0.0448538i
$199$	−9.88901	−	5.70942i	−0.701013	−	0.404730i	0.106712	−	0.994290i	$-0.465968\pi$
$199$	−9.88901	−	5.70942i	−0.701013	−	0.404730i	−0.807725	+	0.589560i	$0.799301\pi$
$200$	−1.67108	+	4.71248i	−0.118164	+	0.333223i
$201$	25.2641	+	4.70848i	1.78199	+	0.332111i
$202$	9.69205	−	9.69205i	0.681930	−	0.681930i
$203$	19.9566	+	5.34735i	1.40068	+	0.375310i
$204$	4.76853	−	5.57198i	0.333864	−	0.390117i
$205$	24.1666	+	7.50971i	1.68787	+	0.524501i
$206$	12.3848	+	7.15037i	0.862890	+	0.498190i
$207$	−10.3511	−	1.10881i	−0.719448	−	0.0770675i
$208$	−3.81277	+	1.02163i	−0.264368	+	0.0708371i
$209$	−1.15894			−0.0801654
$210$	−14.5487	+	4.49813i	−1.00396	+	0.310400i
$211$	−4.52765	−	7.84211i	−0.311696	−	0.539873i	0.667034	−	0.745028i	$-0.267564\pi$
$211$	−4.52765	−	7.84211i	−0.311696	−	0.539873i	−0.978730	+	0.205154i	$0.934230\pi$
$212$	−4.48997	+	1.20308i	−0.308372	+	0.0826281i
$213$	−2.21081	+	1.51620i	−0.151482	+	0.103889i
$214$	0.853544	−	0.492794i	0.0583471	−	0.0336867i
$215$	0.272042	−	6.88575i	0.0185531	−	0.469604i
$216$	−2.72822	+	4.42231i	−0.185632	+	0.300900i
$217$	1.13686	+	21.8624i	0.0771750	+	1.48411i
$218$	11.6974	−	11.6974i	0.792246	−	0.792246i
$219$	4.32032	−	23.1814i	0.291940	−	1.56645i
$220$	−0.172806	+	0.556098i	−0.0116506	+	0.0374921i
$221$			16.7136i			1.12428i
$222$	−0.351396	+	0.0273031i	−0.0235842	+	0.00183246i
$223$	−5.00992	+	18.6973i	−0.335489	+	1.25206i	0.567850	+	0.823132i	$0.307776\pi$
$223$	−5.00992	+	18.6973i	−0.335489	+	1.25206i	−0.903338	+	0.428929i	$0.858891\pi$
$224$	1.96595	+	3.40513i	0.131356	+	0.227515i
$225$	−13.5231	−	6.49053i	−0.901537	−	0.432702i
$226$	−8.67726	+	15.0294i	−0.577203	+	0.999744i
$227$	−20.2537	+	5.42697i	−1.34429	+	0.360201i	−0.858023	−	0.513612i	$-0.828307\pi$
$227$	−20.2537	+	5.42697i	−1.34429	+	0.360201i	−0.486264	+	0.873812i	$0.661641\pi$
$228$	−7.68477	+	0.597098i	−0.508936	+	0.0395438i
$229$	−2.59523	+	1.49835i	−0.171497	+	0.0990141i	−0.583292	−	0.812263i	$-0.698236\pi$
$229$	−2.59523	+	1.49835i	−0.171497	+	0.0990141i	0.411794	+	0.911277i	$0.364902\pi$
$230$	−7.56841	+	1.71083i	−0.499046	+	0.112809i
$231$	−1.67242	+	0.590361i	−0.110037	+	0.0388429i
$232$	3.71556	−	3.71556i	0.243938	−	0.243938i
$233$	−15.6830	+	15.6830i	−1.02743	+	1.02743i	−0.0278173	+	0.999613i	$0.508856\pi$
$233$	−15.6830	+	15.6830i	−1.02743	+	1.02743i	−0.999613	+	0.0278173i	$0.991144\pi$
$234$	−1.82915	−	11.6997i	−0.119575	−	0.764832i
$235$	12.0323	+	7.59551i	0.784904	+	0.495476i
$236$	7.18804	−	4.15001i	0.467901	−	0.270143i
$237$	0.855422	+	11.0095i	0.0555656	+	0.715141i
$238$	16.0813	−	4.30896i	1.04239	−	0.279308i
$239$	14.4663	−	25.0564i	0.935749	−	1.62077i	0.162457	−	0.986716i	$-0.448058\pi$
$239$	14.4663	−	25.0564i	0.935749	−	1.62077i	0.773292	−	0.634050i	$-0.218609\pi$
$240$	−0.859344	+	3.77644i	−0.0554704	+	0.243768i
$241$	7.28823	+	12.6236i	0.469476	+	0.813157i	0.999391	−	0.0348943i	$-0.0111094\pi$
$241$	7.28823	+	12.6236i	0.469476	+	0.813157i	−0.529915	+	0.848051i	$0.677776\pi$
$242$	2.82946	−	10.5597i	0.181884	−	0.678802i
$243$	−12.3197	−	9.55117i	−0.790310	−	0.612708i
$244$			2.18907i			0.140141i
$245$	−18.0647	−	5.61355i	−1.15411	−	0.358637i
$246$	19.2706	+	3.59146i	1.22865	+	0.228983i
$247$	12.4211	−	12.4211i	0.790333	−	0.790333i
$248$	4.95989	+	2.52973i	0.314953	+	0.160638i
$249$	−8.57493	−	1.59811i	−0.543414	−	0.101276i
$250$	−11.1020	−	1.32135i	−0.702151	−	0.0835697i
$251$	−21.9482	+	12.6718i	−1.38536	+	0.799837i	−0.992788	−	0.119886i	$-0.961747\pi$
$251$	−21.9482	+	12.6718i	−1.38536	+	0.799837i	−0.392570	+	0.919722i	$0.628414\pi$
$252$	−10.7855	+	4.77626i	−0.679420	+	0.300876i
$253$	−0.872907	+	0.233895i	−0.0548792	+	0.0147048i
$254$	1.96027	+	3.39528i	0.122998	+	0.213039i
$255$	14.5037	+	7.65326i	0.908256	+	0.479266i
$256$	1.00000			0.0625000
$257$	4.52881	−	1.21349i	0.282500	−	0.0756955i	−0.114787	−	0.993390i	$-0.536619\pi$
$257$	4.52881	−	1.21349i	0.282500	−	0.0756955i	0.397287	+	0.917695i	$0.369952\pi$
$258$	−0.413498	−	5.32180i	−0.0257432	−	0.331321i
$259$	−0.692910	−	0.400052i	−0.0430553	−	0.0248580i
$260$	−4.10798	−	7.81211i	−0.254766	−	0.484487i
$261$	9.89603	+	12.2705i	0.612549	+	0.759526i
$262$	5.35710	+	1.43543i	0.330963	+	0.0886812i
$263$	5.43999	−	5.43999i	0.335444	−	0.335444i	−0.519205	−	0.854650i	$-0.673772\pi$
$263$	5.43999	−	5.43999i	0.335444	−	0.335444i	0.854650	+	0.519205i	$0.173772\pi$
$264$	−0.0826430	+	0.443434i	−0.00508632	+	0.0272915i
$265$	−4.83761	−	9.19965i	−0.297172	−	0.565130i
$266$	−15.1534	−	8.74883i	−0.929116	−	0.536425i
$267$	12.1042	−	25.3121i	0.740767	−	1.54908i
$268$	14.3318	−	3.84020i	0.875456	−	0.234578i
$269$	4.48837	−	7.77409i	0.273661	−	0.473995i	−0.696135	−	0.717911i	$-0.745099\pi$
$269$	4.48837	−	7.77409i	0.273661	−	0.473995i	0.969796	+	0.243916i	$0.0784320\pi$
$270$	−10.9903	−	3.77006i	−0.668848	−	0.229439i
$271$	−24.4726			−1.48660			−0.743301	−	0.668957i	$-0.766741\pi$
$271$	−24.4726			−1.48660			−0.743301	+	0.668957i	$0.766741\pi$
$272$	1.09590	−	4.08994i	0.0664485	−	0.247989i
$273$	11.5971	−	24.2517i	0.701890	−	1.46778i
$274$	1.83303	+	1.05830i	0.110738	+	0.0639344i
$275$	−1.29807	−	0.102728i	−0.0782764	−	0.00619475i
$276$	−5.66763	+	2.00066i	−0.341151	+	0.120425i
$277$	−22.6397	+	22.6397i	−1.36029	+	1.36029i	−0.486744	+	0.873545i	$0.661815\pi$
$277$	−22.6397	+	22.6397i	−1.36029	+	1.36029i	−0.873545	+	0.486744i	$0.838185\pi$
$278$	−6.35307	+	6.35307i	−0.381032	+	0.381032i
$279$	−9.13085	+	13.9867i	−0.546650	+	0.837361i
$280$	−6.45746	+	5.96661i	−0.385907	+	0.356573i
$281$		−	0.0358575i		−	0.00213908i	−0.999999	−	0.00106954i	$-0.999660\pi$
$281$		−	0.0358575i		−	0.00213908i	0.999999	−	0.00106954i	$-0.000340445\pi$
$282$	9.94344	+	4.75495i	0.592123	+	0.283153i
$283$	−19.5773	−	19.5773i	−1.16375	−	1.16375i	−0.983648	−	0.180103i	$-0.942357\pi$
$283$	−19.5773	−	19.5773i	−1.16375	−	1.16375i	−0.180103	−	0.983648i	$-0.557643\pi$
$284$	−0.773872	+	1.34039i	−0.0459209	+	0.0795373i
$285$	−5.09104	−	16.4664i	−0.301567	−	0.975385i
$286$	−0.513984	−	0.890247i	−0.0303925	−	0.0526414i
$287$	31.4656	+	31.4656i	1.85736	+	1.85736i
$288$	−0.319533	+	2.98293i	−0.0188286	+	0.175771i
$289$	−0.804211	−	0.464311i	−0.0473065	−	0.0273124i
$290$	9.93563	+	6.27194i	0.583440	+	0.368301i
$291$	0.896688	+	2.54021i	0.0525648	+	0.148910i
$292$	−3.52362	−	13.1503i	−0.206204	−	0.769566i
$293$	25.8796	+	6.93442i	1.51190	+	0.405113i	0.917067	−	0.398734i	$-0.130550\pi$
$293$	25.8796	+	6.93442i	1.51190	+	0.405113i	0.594836	+	0.803847i	$0.297217\pi$
$294$	−14.4049	−	2.68464i	−0.840109	−	0.156571i
$295$	12.5952	+	13.6313i	0.733320	+	0.793648i
$296$	−0.176228	+	0.101745i	−0.0102430	+	0.00591381i
$297$	−1.29633	−	0.388210i	−0.0752206	−	0.0225263i
$298$	0.449437	−	1.67732i	0.0260352	−	0.0971647i
$299$	6.84869	−	11.8623i	0.396070	−	0.686013i
$300$	−8.66025	−	0.0123994i	−0.499999	−	0.000715879i
$301$	6.05868	−	10.4939i	0.349216	−	0.604860i
$302$	1.51162	+	1.51162i	0.0869837	+	0.0869837i
$303$	21.4177	+	10.2419i	1.23041	+	0.588384i
$304$	−3.85397	+	2.22509i	−0.221040	+	0.127618i
$305$	−4.77444	+	1.07925i	−0.273383	+	0.0617979i
$306$	11.8499	+	4.57586i	0.677411	+	0.261584i
$307$	10.1195	+	2.71151i	0.577550	+	0.154754i	0.535757	−	0.844372i	$-0.320026\pi$
$307$	10.1195	+	2.71151i	0.577550	+	0.154754i	0.0417928	+	0.999126i	$0.486693\pi$
$308$	−0.724054	+	0.724054i	−0.0412568	+	0.0412568i
$309$	−4.53818	+	24.3503i	−0.258168	+	1.38524i
$310$	−3.07211	+	12.0649i	−0.174484	+	0.685241i
$311$			19.8765i			1.12709i	0.826084	+	0.563547i	$0.190564\pi$
$311$			19.8765i			1.12709i	−0.826084	+	0.563547i	$0.809436\pi$
$312$	−3.86683	−	5.63830i	−0.218916	−	0.319206i
$313$	1.02635	−	3.83038i	0.0580126	−	0.216506i	−0.930834	−	0.365442i	$-0.880918\pi$
$313$	1.02635	−	3.83038i	0.0580126	−	0.216506i	0.988847	+	0.148936i	$0.0475847\pi$
$314$	−14.8847			−0.839995
$315$	−15.7346	−	21.1687i	−0.886547	−	1.19272i
$316$	3.18774	+	5.52132i	0.179324	+	0.310599i
$317$	2.43934	−	9.10376i	0.137007	−	0.511318i	−0.862974	−	0.505248i	$-0.831401\pi$
$317$	2.43934	−	9.10376i	0.137007	−	0.511318i	0.999982	−	0.00607024i	$-0.00193223\pi$
$318$	−4.55363	−	6.63974i	−0.255355	−	0.372338i
$319$	1.18509	+	0.684215i	0.0663526	+	0.0383087i
$320$	0.493020	+	2.18104i	0.0275607	+	0.121924i
$321$	1.29697	+	1.10996i	0.0723901	+	0.0619519i
$322$	−13.1792	−	3.53134i	−0.734446	−	0.196794i
$323$	4.87693	+	18.2010i	0.271360	+	1.01273i
$324$	−8.79580	−	1.90629i	−0.488655	−	0.105905i
$325$	15.0132	−	12.8112i	0.832783	−	0.710637i
$326$		−	9.26389i		−	0.513079i
$327$	25.8491	+	12.3610i	1.42946	+	0.683567i
$328$	10.9318	−	2.92917i	0.603608	−	0.161736i
$329$	12.5103	+	21.6684i	0.689714	+	1.19462i
$330$	−1.00789	+	0.0383745i	−0.0554827	+	0.00211245i
$331$	−0.625145	+	1.08278i	−0.0343611	+	0.0595152i	−0.882695	−	0.469947i	$-0.844273\pi$
$331$	−0.625145	+	1.08278i	−0.0343611	+	0.0595152i	0.848333	+	0.529462i	$0.177606\pi$
$332$	−4.86439	+	1.30341i	−0.266968	+	0.0715338i
$333$	−0.247188	−	0.558186i	−0.0135458	−	0.0305884i
$334$	7.75533	−	4.47754i	0.424353	−	0.245000i
$335$	15.4415	+	29.3650i	0.843660	+	1.60438i
$336$	−4.42807	+	5.17415i	−0.241571	+	0.282273i
$337$	21.6918	−	21.6918i	1.18163	−	1.18163i	0.202304	−	0.979323i	$-0.435157\pi$
$337$	21.6918	−	21.6918i	1.18163	−	1.18163i	0.979323	−	0.202304i	$-0.0648429\pi$
$338$	2.49297	+	0.667990i	0.135600	+	0.0363339i
$339$	−29.5501	−	5.50726i	−1.60494	−	0.299113i
$340$	9.46062	+	0.373770i	0.513074	+	0.0202705i
$341$	−0.302045	+	1.41818i	−0.0163566	+	0.0767987i
$342$	−5.40582	−	12.2071i	−0.292313	−	0.660085i
$343$	−4.05882	−	4.05882i	−0.219155	−	0.219155i
$344$	−1.54090	−	2.66892i	−0.0830799	−	0.143899i
$345$	−7.15777	−	11.3750i	−0.385361	−	0.612407i
$346$	0.420332	−	0.728037i	0.0225972	−	0.0391395i
$347$	4.62501	−	17.2608i	0.248283	−	0.926606i	−0.723421	−	0.690407i	$-0.757431\pi$
$347$	4.62501	−	17.2608i	0.248283	−	0.926606i	0.971705	−	0.236199i	$-0.0759019\pi$
$348$	8.21072	+	3.92637i	0.440141	+	0.210475i
$349$		−	5.52625i		−	0.295814i	−0.989001	−	0.147907i	$-0.952746\pi$
$349$		−	5.52625i		−	0.295814i	0.989001	−	0.147907i	$-0.0472536\pi$
$350$	−16.1971	−	11.1423i	−0.865770	−	0.595582i
$351$	18.0543	−	9.73287i	0.963665	−	0.519502i
$352$	0.0674030	+	0.251552i	0.00359259	+	0.0134077i
$353$	18.3117	+	4.90659i	0.974631	+	0.261152i	0.710782	−	0.703412i	$-0.248341\pi$
$353$	18.3117	+	4.90659i	0.974631	+	0.261152i	0.263849	+	0.964564i	$0.415008\pi$
$354$	10.9223	+	9.34740i	0.580516	+	0.496809i
$355$	−3.30497	−	1.02701i	−0.175410	−	0.0545079i
$356$		−	16.1989i		−	0.858541i
$357$	16.3093	+	23.7809i	0.863178	+	1.25862i
$358$	−4.87636	+	18.1988i	−0.257724	+	0.961838i
$359$	15.8626	−	27.4748i	0.837196	−	1.45007i	−0.0550345	−	0.998484i	$-0.517527\pi$
$359$	15.8626	−	27.4748i	0.837196	−	1.45007i	0.892230	−	0.451581i	$-0.149140\pi$
$360$	−6.66343	+	0.773734i	−0.351194	+	0.0407793i
$361$	0.402031	−	0.696339i	0.0211596	−	0.0366494i
$362$	2.76311	−	0.740372i	0.145226	−	0.0389131i
$363$	18.8782	−	1.46681i	0.990848	−	0.0769877i
$364$		−	15.5203i		−	0.813483i
$365$	26.9442	−	14.1685i	1.41032	−	0.741615i
$366$	−3.57535	+	1.26209i	−0.186887	+	0.0659705i
$367$	−3.12148	−	11.6495i	−0.162940	−	0.608099i	−0.998294	−	0.0583873i	$-0.981404\pi$
$367$	−3.12148	−	11.6495i	−0.162940	−	0.608099i	0.835354	−	0.549712i	$-0.185262\pi$
$368$	−2.45373	+	2.45373i	−0.127909	+	0.127909i
$369$	5.24445	+	33.5448i	0.273015	+	1.74627i
$370$	−0.308794	−	0.334197i	−0.0160534	−	0.0173741i
$371$		−	18.2769i		−	0.948888i
$372$	−1.27216	+	9.55937i	−0.0659584	+	0.495630i
$373$	−5.72451	−	5.72451i	−0.296404	−	0.296404i	0.543200	−	0.839603i	$-0.317213\pi$
$373$	−5.72451	−	5.72451i	−0.296404	−	0.296404i	−0.839603	+	0.543200i	$0.817213\pi$
$374$	1.10270			0.0570192
$375$	−4.24263	−	18.8944i	−0.219089	−	0.975705i
$376$	6.36348			0.328171
$377$	−20.0345	+	5.36824i	−1.03183	+	0.276478i
$378$	−14.0192	−	14.8619i	−0.721072	−	0.764416i
$379$	−15.2650	+	8.81324i	−0.784109	+	0.452706i	−0.837885	−	0.545847i	$-0.816208\pi$
$379$	−15.2650	+	8.81324i	−0.784109	+	0.452706i	0.0537753	+	0.998553i	$0.482875\pi$
$380$	−6.75309	−	7.30864i	−0.346426	−	0.374925i
$381$	−4.41526	+	5.15918i	−0.226201	+	0.264313i
$382$	−0.886046	−	3.30677i	−0.0453340	−	0.169189i
$383$	−9.86701	−	36.8242i	−0.504180	−	1.88163i	−0.470911	−	0.882180i	$-0.656075\pi$
$383$	−9.86701	−	36.8242i	−0.504180	−	1.88163i	−0.0332689	−	0.999446i	$-0.510592\pi$
$384$	0.576543	+	1.63328i	0.0294216	+	0.0833479i
$385$	−1.93616	−	1.22222i	−0.0986760	−	0.0622899i
$386$	−11.7571	+	6.78796i	−0.598420	+	0.345498i
$387$	8.45358	−	3.74360i	0.429720	−	0.190298i
$388$	1.09975	+	1.09975i	0.0558314	+	0.0558314i
$389$	−6.86018	−	11.8822i	−0.347825	−	0.602450i	0.638038	−	0.770005i	$-0.279746\pi$
$389$	−6.86018	−	11.8822i	−0.347825	−	0.602450i	−0.985863	+	0.167555i	$0.946413\pi$
$390$	10.3909	−	11.2135i	0.526165	−	0.567817i
$391$	7.34657	+	12.7246i	0.371532	+	0.643512i
$392$	−8.17160	+	2.18957i	−0.412728	+	0.110590i
$393$	0.744140	+	9.57723i	0.0375369	+	0.483107i
$394$	−0.106534	−	0.0615077i	−0.00536713	−	0.00309871i
$395$	−10.4706	+	9.67470i	−0.526833	+	0.486787i
$396$	−0.771899	+	0.120680i	−0.0387894	+	0.00606439i
$397$	−28.5932	−	7.66153i	−1.43505	−	0.384521i	−0.544255	−	0.838920i	$-0.683187\pi$
$397$	−28.5932	−	7.66153i	−1.43505	−	0.384521i	−0.890798	+	0.454399i	$0.849854\pi$
$398$	−2.95541	−	11.0298i	−0.148141	−	0.552872i
$399$	5.55268	−	29.7938i	0.277982	−	1.49156i
$400$	−4.51386	+	2.15059i	−0.225693	+	0.107530i
$401$			23.4886i			1.17296i	0.809963	+	0.586481i	$0.199487\pi$
$401$			23.4886i			1.17296i	−0.809963	+	0.586481i	$0.800513\pi$
$402$	14.5350	+	21.1938i	0.724941	+	1.05705i
$403$	−11.9623	−	18.4367i	−0.595884	−	0.918397i
$404$	13.7066			0.681930
$405$	−0.178813	−	20.1238i	−0.00888530	−	0.999961i
$406$	10.3303	+	17.8926i	0.512683	+	0.887993i
$407$	−0.0374724	−	0.0374724i	−0.00185744	−	0.00185744i
$408$	7.31185	−	0.568122i	0.361990	−	0.0281262i
$409$	−32.0543	+	18.5066i	−1.58499	+	0.915092i	−0.590870	+	0.806767i	$0.701215\pi$
$409$	−32.0543	+	18.5066i	−1.58499	+	0.915092i	−0.994116	+	0.108325i	$0.965451\pi$
$410$	11.7782	+	22.3986i	0.581686	+	1.10619i
$411$	−0.671680	+	3.60401i	−0.0331315	+	0.177773i
$412$	3.70130	+	13.8135i	0.182350	+	0.680540i
$413$	8.44654	+	31.5229i	0.415627	+	1.55114i
$414$	−6.53526	−	8.10335i	−0.321190	−	0.398258i
$415$	−5.24103	−	9.96681i	−0.257272	−	0.489252i
$416$	−3.41843	−	1.97363i	−0.167602	−	0.0967653i
$417$	−14.0392	−	6.71352i	−0.687501	−	0.328762i
$418$	−0.819493	−	0.819493i	−0.0400827	−	0.0400827i
$419$	−24.7793			−1.21055			−0.605273	−	0.796018i	$-0.706936\pi$
$419$	−24.7793			−1.21055			−0.605273	+	0.796018i	$0.706936\pi$
$420$	−13.4681	−	7.10683i	−0.657178	−	0.346778i
$421$	11.8864	−	20.5878i	0.579305	−	1.00339i	−0.416254	−	0.909248i	$-0.636657\pi$
$421$	11.8864	−	20.5878i	0.579305	−	1.00339i	0.995559	−	0.0941378i	$-0.0300094\pi$
$422$	2.34368	−	8.74674i	0.114089	−	0.425785i
$423$	−2.03334	+	18.9818i	−0.0988643	+	0.922928i
$424$	−4.02559	−	2.32418i	−0.195500	−	0.112872i
$425$	3.84907	+	20.8183i	0.186707	+	1.00983i
$426$	−2.63539	−	0.491159i	−0.127685	−	0.0237967i
$427$	−8.31391	−	2.22771i	−0.402338	−	0.107806i
$428$	0.952005	+	0.255089i	0.0460169	+	0.0123302i
$429$	1.15769	−	1.35274i	0.0558936	−	0.0653111i
$430$	5.06132	−	4.67660i	0.244079	−	0.225526i
$431$	−6.73190	+	3.88667i	−0.324264	+	0.187214i	−0.653292	−	0.757106i	$-0.726612\pi$
$431$	−6.73190	+	3.88667i	−0.324264	+	0.187214i	0.329027	+	0.944320i	$0.393279\pi$
$432$	−5.05619	+	1.19790i	−0.243266	+	0.0576342i
$433$	19.9432	+	19.9432i	0.958408	+	0.958408i	0.999169	−	0.0407605i	$-0.0129781\pi$
$433$	19.9432	+	19.9432i	0.958408	+	0.958408i	−0.0407605	+	0.999169i	$0.512978\pi$
$434$	−14.6551	+	16.2629i	−0.703470	+	0.780645i
$435$	−4.51550	+	19.8437i	−0.216502	+	0.951432i
$436$	16.5426			0.792246
$437$	3.99682	−	14.9163i	0.191194	−	0.713545i
$438$	19.4467	−	13.3368i	0.929197	−	0.637257i
$439$	19.1289	+	11.0441i	0.912974	+	0.527106i	0.881387	−	0.472395i	$-0.156610\pi$
$439$	19.1289	+	11.0441i	0.912974	+	0.527106i	0.0315873	+	0.999501i	$0.489944\pi$
$440$	−0.515413	+	0.271029i	−0.0245713	+	0.0129208i
$441$	−3.92026	−	25.0750i	−0.186679	−	1.19405i
$442$	−11.8183	+	11.8183i	−0.562139	+	0.562139i
$443$	−6.52073	−	24.3357i	−0.309809	−	1.15622i	−0.928726	−	0.370767i	$-0.879095\pi$
$443$	−6.52073	−	24.3357i	−0.309809	−	1.15622i	0.618916	−	0.785457i	$-0.287572\pi$
$444$	−0.267781	−	0.229168i	−0.0127083	−	0.0108758i
$445$	35.3305	−	7.98639i	1.67483	−	0.378591i
$446$	−16.7635	+	9.67841i	−0.793775	+	0.458286i
$447$	2.99865	−	0.232992i	0.141831	−	0.0110201i
$448$	−1.01765	+	3.79793i	−0.0480795	+	0.179435i
$449$	11.5523			0.545185			0.272593	−	0.962130i	$-0.412119\pi$
$449$	11.5523			0.545185			0.272593	+	0.962130i	$0.412119\pi$
$450$	−4.97275	−	14.1517i	−0.234418	−	0.667119i
$451$	1.47367	+	2.55248i	0.0693926	+	0.120192i
$452$	−16.7632	+	4.49168i	−0.788473	+	0.211271i
$453$	−1.59738	+	3.34040i	−0.0750514	+	0.156946i
$454$	−18.1590	−	10.4841i	−0.852244	−	0.492043i
$455$	33.8503	−	7.65181i	1.58693	−	0.358722i
$456$	−5.85616	−	5.01174i	−0.274240	−	0.234696i
$457$	16.3279	−	16.3279i	0.763789	−	0.763789i	−0.213216	−	0.977005i	$-0.568394\pi$
$457$	16.3279	−	16.3279i	0.763789	−	0.763789i	0.977005	+	0.213216i	$0.0683940\pi$
$458$	−2.89460	−	0.775605i	−0.135256	−	0.0362417i
$459$	−0.641702	+	21.9923i	−0.0299521	+	1.02651i
$460$	−6.56141	−	4.14194i	−0.305927	−	0.193119i
$461$			5.11822i			0.238379i	0.992872	+	0.119190i	$0.0380296\pi$
$461$			5.11822i			0.238379i	−0.992872	+	0.119190i	$0.961970\pi$
$462$	−1.60003	−	0.765134i	−0.0744401	−	0.0355972i
$463$	13.0478	+	13.0478i	0.606381	+	0.606381i	0.941998	−	0.335618i	$-0.108945\pi$
$463$	13.0478	+	13.0478i	0.606381	+	0.606381i	−0.335618	+	0.941998i	$0.608945\pi$
$464$	5.25460			0.243938
$465$	−21.4766	+	1.93833i	−0.995952	+	0.0898881i
$466$	−22.1792			−1.02743
$467$	3.08661	+	3.08661i	0.142831	+	0.142831i	0.774907	−	0.632076i	$-0.217797\pi$
$467$	3.08661	+	3.08661i	0.142831	+	0.142831i	−0.632076	+	0.774907i	$0.717797\pi$
$468$	6.97952	−	9.56632i	0.322628	−	0.442203i
$469$			58.3392i			2.69385i
$470$	3.13732	+	13.8790i	0.144714	+	0.640190i
$471$	−8.58169	−	24.3109i	−0.395423	−	1.12019i
$472$	8.01721	+	2.14821i	0.369022	+	0.0988792i
$473$	0.567509	−	0.567509i	0.0260941	−	0.0260941i
$474$	−7.17999	+	8.38974i	−0.329788	+	0.385353i
$475$	12.6110	−	18.3320i	0.578633	−	0.841132i
$476$	14.4181	+	8.32427i	0.660851	+	0.381542i
$477$	8.21918	−	11.2654i	0.376330	−	0.515809i
$478$	27.9468	−	7.48832i	1.27826	−	0.342508i
$479$	9.26360	+	16.0450i	0.423264	+	0.733116i	0.996257	−	0.0864453i	$-0.0275508\pi$
$479$	9.26360	+	16.0450i	0.423264	+	0.733116i	−0.572992	+	0.819561i	$0.694217\pi$
$480$	−3.27800	+	2.06270i	−0.149619	+	0.0941490i
$481$	0.803230			0.0366241
$482$	−3.77267	+	14.0798i	−0.171840	+	0.641316i
$483$	−1.83068	−	23.5612i	−0.0832988	−	1.07207i
$484$	9.46754	−	5.46609i	0.430343	−	0.248459i
$485$	−1.85640	+	2.94080i	−0.0842949	+	0.133535i
$486$	−1.95765	−	15.4650i	−0.0888009	−	0.701509i
$487$	−4.69626	−	17.5267i	−0.212808	−	0.794210i	−0.986927	−	0.161170i	$-0.948473\pi$
$487$	−4.69626	−	17.5267i	−0.212808	−	0.794210i	0.774119	−	0.633041i	$-0.218193\pi$
$488$	−1.54790	+	1.54790i	−0.0700703	+	0.0700703i
$489$	15.1305	−	5.34103i	0.684225	−	0.241530i
$490$	−8.80431	−	16.7431i	−0.397738	−	0.756375i
$491$	−6.57336	−	3.79513i	−0.296651	−	0.171272i	0.344286	−	0.938865i	$-0.388121\pi$
$491$	−6.57336	−	3.79513i	−0.296651	−	0.171272i	−0.640938	+	0.767593i	$0.721454\pi$
$492$	11.0868	+	16.1659i	0.499832	+	0.728815i
$493$	5.75849	−	21.4910i	0.259350	−	0.967906i
$494$	17.5660			0.790333
$495$	−0.643769	−	1.62404i	−0.0289353	−	0.0729954i
$496$	1.71838	+	5.29596i	0.0771577	+	0.237795i
$497$	−4.30316	−	4.30316i	−0.193023	−	0.193023i
$498$	−4.93336	−	7.19343i	−0.221069	−	0.322345i
$499$	22.7085	−	13.1108i	1.01657	−	0.586919i	0.103464	−	0.994633i	$-0.467007\pi$
$499$	22.7085	−	13.1108i	1.01657	−	0.586919i	0.913110	+	0.407714i	$0.133674\pi$
$500$	−6.91595	−	8.78462i	−0.309291	−	0.392860i
$501$	11.7844	+	10.0851i	0.526486	+	0.450570i
$502$	−24.4800	−	6.55940i	−1.09260	−	0.292760i
$503$	−33.4545	−	8.96410i	−1.49166	−	0.399690i	−0.581364	−	0.813644i	$-0.697481\pi$
$503$	−33.4545	−	8.96410i	−1.49166	−	0.399690i	−0.910298	+	0.413954i	$0.864147\pi$
$504$	−11.0038	−	4.24915i	−0.490148	−	0.189272i
$505$	6.75765	+	29.8947i	0.300711	+	1.33030i
$506$	−0.782627	−	0.451850i	−0.0347920	−	0.0200872i
$507$	0.346292	+	4.45684i	0.0153794	+	0.197935i
$508$	−1.01471	+	3.78694i	−0.0450204	+	0.168018i
$509$	−8.15621	+	14.1270i	−0.361518	+	0.626167i	−0.988211	−	0.153099i	$-0.951075\pi$
$509$	−8.15621	+	14.1270i	−0.361518	+	0.626167i	0.626693	+	0.779266i	$0.284408\pi$
$510$	4.84398	+	15.6673i	0.214495	+	0.693761i
$511$	53.5299			2.36802
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	16.8209	−	15.8671i	0.742662	−	0.700551i
$514$	4.06042	+	2.34429i	0.179098	+	0.103402i
$515$	−28.3029	+	14.8830i	−1.24717	+	0.655823i
$516$	3.47069	−	4.05547i	0.152789	−	0.178532i
$517$	0.428917	+	1.60074i	0.0188638	+	0.0704005i
$518$	−0.207082	−	0.772840i	−0.00909866	−	0.0339567i
$519$	1.43143	+	0.266775i	0.0628327	+	0.0117101i
$520$	2.61922	−	8.42878i	0.114860	−	0.369626i
$521$	6.84869	−	3.95409i	0.300046	−	0.173232i	−0.342417	−	0.939548i	$-0.611246\pi$
$521$	6.84869	−	3.95409i	0.300046	−	0.173232i	0.642464	+	0.766316i	$0.277912\pi$
$522$	−1.67901	+	15.6741i	−0.0734885	+	0.686037i
$523$	11.5676	+	11.5676i	0.505817	+	0.505817i	0.913240	−	0.407423i	$-0.133572\pi$
$523$	11.5676	+	11.5676i	0.505817	+	0.505817i	−0.407423	+	0.913240i	$0.633572\pi$
$524$	2.77304	+	4.80305i	0.121141	+	0.209822i
$525$	8.86020	−	32.8784i	0.386691	−	1.43493i
$526$	7.69331			0.335444
$527$	23.5433	−	1.22427i	1.02556	−	0.0533300i
$528$	−0.371993	+	0.255118i	−0.0161889	+	0.0111026i
$529$			10.9585i			0.476455i
$530$	3.08442	−	9.92584i	0.133979	−	0.431151i
$531$	−8.96972	+	23.2284i	−0.389253	+	1.00803i
$532$	−4.52873	−	16.9014i	−0.196345	−	0.732770i
$533$	−43.1508	−	11.5622i	−1.86907	−	0.500815i
$534$	26.4574	−	9.33937i	1.14492	−	0.404154i
$535$	−0.0870014	+	2.20212i	−0.00376140	+	0.0952061i
$536$	12.8496	+	7.41870i	0.555017	+	0.320439i
$537$	−32.5352	+	2.52795i	−1.40400	+	0.109089i
$538$	8.67087	−	2.32335i	0.373828	−	0.100167i
$539$	−1.10158	−	1.90799i	−0.0474484	−	0.0821831i
$540$	−5.10548	−	10.4372i	−0.219705	−	0.449143i
$541$	12.3963	+	21.4710i	0.532958	+	0.923110i	0.999259	+	0.0384839i	$0.0122528\pi$
$541$	12.3963	+	21.4710i	0.532958	+	0.923110i	−0.466302	+	0.884626i	$0.654414\pi$
$542$	−17.3047	−	17.3047i	−0.743301	−	0.743301i
$543$	2.80228	+	4.08607i	0.120258	+	0.175350i
$544$	3.66694	−	2.11711i	0.157219	−	0.0907704i
$545$	8.15583	+	36.0800i	0.349357	+	1.54550i
$546$	25.3489	−	8.94810i	1.08483	−	0.382943i
$547$	4.86690	+	18.1635i	0.208094	+	0.776616i	0.988484	+	0.151324i	$0.0483536\pi$
$547$	4.86690	+	18.1635i	0.208094	+	0.776616i	−0.780391	+	0.625292i	$0.784980\pi$
$548$	0.547817	+	2.04448i	0.0234016	+	0.0873360i
$549$	−4.12269	−	5.11190i	−0.175952	−	0.218170i
$550$	−0.845233	−	0.990512i	−0.0360408	−	0.0422356i
$551$	−20.2510	+	11.6919i	−0.862723	+	0.498093i
$552$	−5.42230	−	2.59294i	−0.230788	−	0.110363i
$553$	−24.2136	+	6.48801i	−1.02967	+	0.275898i
$554$	−32.0174			−1.36029
$555$	0.367804	−	0.697025i	0.0156124	−	0.0295870i
$556$	−8.98460			−0.381032
$557$	−18.5856	−	18.5856i	−0.787496	−	0.787496i	0.193587	−	0.981083i	$-0.437988\pi$
$557$	−18.5856	−	18.5856i	−0.787496	−	0.787496i	−0.981083	+	0.193587i	$0.937988\pi$
$558$	−16.3466	+	3.43360i	−0.692006	+	0.145356i
$559$			12.1647i			0.514512i
$560$	−8.78515	−	0.347083i	−0.371240	−	0.0146669i
$561$	0.635753	+	1.80101i	0.0268415	+	0.0760388i
$562$	0.0253551	−	0.0253551i	0.00106954	−	0.00106954i
$563$	−6.51191	−	24.3028i	−0.274444	−	1.02424i	−0.956213	−	0.292672i	$-0.905456\pi$
$563$	−6.51191	−	24.3028i	−0.274444	−	1.02424i	0.681769	−	0.731568i	$-0.261211\pi$
$564$	3.66882	+	10.3933i	0.154485	+	0.437638i
$565$	−18.0611	−	34.3466i	−0.759836	−	1.44497i
$566$		−	27.6865i		−	1.16375i
$567$	16.1910	−	31.4659i	0.679958	−	1.32144i
$568$	−1.49501	+	0.400586i	−0.0627291	+	0.0168082i
$569$	18.5120	−	32.0637i	0.776063	−	1.34418i	−0.158132	−	0.987418i	$-0.550547\pi$
$569$	18.5120	−	32.0637i	0.776063	−	1.34418i	0.934195	−	0.356763i	$-0.116120\pi$
$570$	8.04359	−	15.2434i	0.336909	−	0.638476i
$571$	21.6539	−	37.5056i	0.906186	−	1.56956i	0.0868683	−	0.996220i	$-0.472314\pi$
$571$	21.6539	−	37.5056i	0.906186	−	1.56956i	0.819317	−	0.573340i	$-0.194353\pi$
$572$	0.266058	−	0.992941i	0.0111244	−	0.0415169i
$573$	4.89003	−	3.35365i	0.204284	−	0.140101i
$574$			44.4991i			1.85736i
$575$	5.79882	−	16.3527i	0.241827	−	0.681957i
$576$	−2.33520	+	1.88331i	−0.0972999	+	0.0784712i
$577$	22.6716	+	6.07484i	0.943832	+	0.252899i	0.697743	−	0.716348i	$-0.254188\pi$
$577$	22.6716	+	6.07484i	0.943832	+	0.252899i	0.246089	+	0.969247i	$0.420854\pi$
$578$	−0.240345	−	0.896980i	−0.00999704	−	0.0373095i
$579$	−17.8651	−	15.2891i	−0.742448	−	0.635392i
$580$	2.59062	+	11.4605i	0.107570	+	0.475870i
$581$		−	19.8010i		−	0.821484i
$582$	−1.16215	+	2.43025i	−0.0481725	+	0.100737i
$583$	0.313313	−	1.16930i	0.0129761	−	0.0484275i
$584$	6.80712	−	11.7903i	0.281681	−	0.487885i
$585$	24.3056	+	10.5062i	1.00491	+	0.434379i
$586$	13.3963	+	23.2030i	0.553395	+	0.958508i
$587$	−13.7989	−	13.7989i	−0.569541	−	0.569541i	0.362459	−	0.932000i	$-0.381937\pi$
$587$	−13.7989	−	13.7989i	−0.569541	−	0.569541i	−0.932000	+	0.362459i	$0.881937\pi$
$588$	−8.28746	−	12.0841i	−0.341769	−	0.498340i
$589$	−18.4066	−	16.5869i	−0.758429	−	0.683450i
$590$	−0.732673	+	18.5450i	−0.0301637	+	0.763484i
$591$	0.0390375	−	0.209462i	0.00160579	−	0.00861612i
$592$	−0.196556	−	0.0526671i	−0.00807841	−	0.00216460i
$593$	−11.9050	+	11.9050i	−0.488880	+	0.488880i	−0.907953	−	0.419072i	$-0.862355\pi$
$593$	−11.9050	+	11.9050i	−0.488880	+	0.488880i	0.419072	+	0.907953i	$0.362355\pi$
$594$	−0.642137	−	1.19115i	−0.0263472	−	0.0488734i
$595$	−11.0472	+	35.5504i	−0.452890	+	1.45742i
$596$	1.50385	−	0.868246i	0.0615999	−	0.0355647i
$597$	16.3107	−	11.1861i	0.667554	−	0.457818i
$598$	13.2307	−	3.54514i	0.541042	−	0.144972i
$599$	14.1782	−	24.5573i	0.579304	−	1.00338i	−0.416256	−	0.909248i	$-0.636658\pi$
$599$	14.1782	−	24.5573i	0.579304	−	1.00338i	0.995559	−	0.0941358i	$-0.0300088\pi$
$600$	−6.11495	−	6.13249i	−0.249642	−	0.250358i
$601$	−11.6264	−	20.1374i	−0.474249	−	0.821423i	0.525316	−	0.850907i	$-0.323947\pi$
$601$	−11.6264	−	20.1374i	−0.474249	−	0.821423i	−0.999565	+	0.0294837i	$0.990614\pi$
$602$	11.7045	−	3.13620i	0.477038	−	0.127822i
$603$	−26.2354	+	35.9589i	−1.06839	+	1.46436i
$604$			2.13775i			0.0869837i
$605$	16.5894	+	17.9542i	0.674457	+	0.729942i
$606$	7.90246	+	22.3867i	0.321015	+	0.909399i
$607$	2.03110	+	7.58016i	0.0824397	+	0.307669i	0.994817	−	0.101681i	$-0.0324221\pi$
$607$	2.03110	+	7.58016i	0.0824397	+	0.307669i	−0.912377	+	0.409350i	$0.865755\pi$
$608$	−4.29854	−	1.15179i	−0.174329	−	0.0467113i
$609$	−23.2677	+	27.1881i	−0.942855	+	1.10172i
$610$	−4.13918	−	2.61289i	−0.167591	−	0.105793i
$611$	−21.7531	−	12.5592i	−0.880037	−	0.508090i
$612$	5.14349	+	11.6147i	0.207913	+	0.469498i
$613$	0.570360	−	2.12861i	0.0230366	−	0.0859739i	−0.953451	−	0.301550i	$-0.902496\pi$
$613$	0.570360	−	2.12861i	0.0230366	−	0.0859739i	0.976487	+	0.215576i	$0.0691628\pi$
$614$	5.23823	+	9.07288i	0.211398	+	0.366152i
$615$	−29.7924	+	32.1509i	−1.20135	+	1.29645i
$616$	−1.02397			−0.0412568
$617$	12.5021	−	46.6586i	0.503317	−	1.87840i	0.0260192	−	0.999661i	$-0.491717\pi$
$617$	12.5021	−	46.6586i	0.503317	−	1.87840i	0.477297	−	0.878742i	$-0.341616\pi$
$618$	−20.4273	+	14.0093i	−0.821705	+	0.563537i
$619$		−	19.7493i		−	0.793791i	−0.917864	−	0.396895i	$-0.870088\pi$
$619$		−	19.7493i		−	0.793791i	0.917864	−	0.396895i	$-0.129912\pi$
$620$	−10.7035	+	6.35888i	−0.429863	+	0.255379i
$621$	9.46717	−	15.3458i	0.379905	−	0.615807i
$622$	−14.0548	+	14.0548i	−0.563547	+	0.563547i
$623$	61.5223	+	16.4849i	2.46484	+	0.660452i
$624$	1.25262	−	6.72114i	0.0501449	−	0.269061i
$625$	15.7499	−	19.4150i	0.629996	−	0.776598i
$626$	3.43423	−	1.98275i	0.137259	−	0.0792467i
$627$	0.865988	−	1.81093i	0.0345842	−	0.0723217i
$628$	−10.5251	−	10.5251i	−0.419997	−	0.419997i
$629$	−0.430811	+	0.746186i	−0.0171776	+	0.0297524i
$630$	3.84247	−	26.0946i	0.153088	−	1.03963i
$631$	−3.73706	+	6.47277i	−0.148770	+	0.257677i	−0.930773	−	0.365597i	$-0.880865\pi$
$631$	−3.73706	+	6.47277i	−0.148770	+	0.257677i	0.782003	+	0.623274i	$0.214198\pi$
$632$	−1.65009	+	6.15823i	−0.0656372	+	0.244961i
$633$	15.6371	−	1.21498i	0.621519	−	0.0482913i
$634$	8.16221	−	4.71245i	0.324163	−	0.187155i
$635$	−8.75974	−	0.346079i	−0.347620	−	0.0137337i
$636$	1.47510	−	7.91490i	0.0584916	−	0.313846i
$637$	32.2555	+	8.64283i	1.27801	+	0.342441i
$638$	0.354176	+	1.32180i	0.0140219	+	0.0523306i
$639$	−0.717218	−	4.58751i	−0.0283727	−	0.181479i
$640$	−1.19361	+	1.89085i	−0.0471816	+	0.0747422i
$641$	−1.54921	−	0.894440i	−0.0611903	−	0.0353282i	0.469093	−	0.883149i	$-0.344581\pi$
$641$	−1.54921	−	0.894440i	−0.0611903	−	0.0353282i	−0.530283	+	0.847821i	$0.677914\pi$
$642$	0.132240	+	1.70196i	0.00521911	+	0.0671710i
$643$	14.7320	+	14.7320i	0.580974	+	0.580974i	0.935171	−	0.354197i	$-0.115246\pi$
$643$	14.7320	+	14.7320i	0.580974	+	0.580974i	−0.354197	+	0.935171i	$0.615246\pi$
$644$	−6.82203	−	11.8161i	−0.268826	−	0.465620i
$645$	10.5563	+	5.57029i	0.415652	+	0.219330i
$646$	−9.42151	+	16.3185i	−0.370684	+	0.642044i
$647$	−12.7257	−	12.7257i	−0.500298	−	0.500298i	0.411233	−	0.911530i	$-0.365098\pi$
$647$	−12.7257	−	12.7257i	−0.500298	−	0.500298i	−0.911530	+	0.411233i	$0.865098\pi$
$648$	−4.87162	−	7.56752i	−0.191375	−	0.297280i
$649$			2.16154i			0.0848478i
$650$	19.6748	+	1.55705i	0.771710	+	0.0610727i
$651$	−35.0112	−	14.5597i	−1.37220	−	0.570639i
$652$	6.55056	−	6.55056i	0.256540	−	0.256540i
$653$	−14.0607	+	14.0607i	−0.550237	+	0.550237i	−0.926509	−	0.376272i	$-0.877206\pi$
$653$	−14.0607	+	14.0607i	−0.550237	+	0.550237i	0.376272	+	0.926509i	$0.377206\pi$
$654$	9.53751	+	27.0186i	0.372946	+	1.05651i
$655$	−9.10847	+	8.41611i	−0.355897	+	0.328845i
$656$	9.80119	+	5.65872i	0.382672	+	0.220936i
$657$	32.9945	+	24.0726i	1.28724	+	0.939160i
$658$	−6.47580	+	24.1680i	−0.252453	+	0.942167i
$659$	11.6213			0.452703			0.226352	−	0.974046i	$-0.427320\pi$
$659$	11.6213			0.452703			0.226352	+	0.974046i	$0.427320\pi$
$660$	−0.739823	−	0.685553i	−0.0287976	−	0.0266851i
$661$	−2.90630	+	5.03386i	−0.113042	+	0.195794i	−0.916995	−	0.398898i	$-0.869393\pi$
$661$	−2.90630	+	5.03386i	−0.113042	+	0.195794i	0.803953	+	0.594692i	$0.202726\pi$
$662$	−1.20769	+	0.323599i	−0.0469381	+	0.0125770i
$663$	−26.1163	−	12.4888i	−1.01427	−	0.485025i
$664$	−4.36129	−	2.51799i	−0.169251	−	0.0977170i
$665$	34.6299	−	18.2101i	1.34289	−	0.706157i
$666$	0.219909	−	0.569486i	0.00852129	−	0.0220671i
$667$	−12.8933	+	12.8933i	−0.499232	+	0.499232i
$668$	8.64995	+	2.31775i	0.334676	+	0.0896763i
$669$	−25.4724	−	21.7995i	−0.984821	−	0.842815i
$670$	−9.84538	+	31.6830i	−0.380360	+	1.22402i
$671$	−0.493711	−	0.285044i	−0.0190595	−	0.0110040i
$672$	−6.78979	+	0.527559i	−0.261922	+	0.0203510i
$673$	23.7356	−	6.35992i	0.914939	−	0.245157i	0.229518	−	0.973304i	$-0.426285\pi$
$673$	23.7356	−	6.35992i	0.914939	−	0.245157i	0.685421	+	0.728147i	$0.259618\pi$
$674$	30.6768			1.18163
$675$	20.2467	−	16.2810i	0.779297	−	0.626655i
$676$	1.29046	+	2.23514i	0.0496330	+	0.0859669i
$677$	4.51088	−	1.20869i	0.173367	−	0.0464536i	−0.171091	−	0.985255i	$-0.554729\pi$
$677$	4.51088	−	1.20869i	0.173367	−	0.0464536i	0.344458	+	0.938802i	$0.388063\pi$
$678$	−17.0008	−	24.7893i	−0.652914	−	0.952027i
$679$	−5.29594	+	3.05761i	−0.203240	+	0.117340i
$680$	6.42538	+	6.95397i	0.246402	+	0.266672i
$681$	6.65402	−	35.7032i	0.254982	−	1.36815i
$682$	−1.21638	+	0.789226i	−0.0465777	+	0.0302210i
$683$	−18.5960	+	18.5960i	−0.711554	+	0.711554i	−0.966860	−	0.255306i	$-0.917824\pi$
$683$	−18.5960	+	18.5960i	−0.711554	+	0.711554i	0.255306	+	0.966860i	$0.417824\pi$
$684$	4.80924	−	12.4542i	0.183886	−	0.476199i
$685$	−4.18901	+	2.20278i	−0.160054	+	0.0841640i
$686$		−	5.74003i		−	0.219155i
$687$	−0.402080	−	5.17486i	−0.0153403	−	0.197433i
$688$	0.797629	−	2.97679i	0.0304093	−	0.113489i
$689$	9.17415	+	15.8901i	0.349507	+	0.605364i
$690$	2.98200	−	13.1046i	0.113523	−	0.498884i
$691$	−19.5164	+	33.8034i	−0.742439	+	1.28594i	0.208943	+	0.977928i	$0.432998\pi$
$691$	−19.5164	+	33.8034i	−0.742439	+	1.28594i	−0.951382	+	0.308014i	$0.900336\pi$
$692$	0.812020	−	0.217580i	0.0308684	−	0.00827115i
$693$	0.327191	−	3.05443i	0.0124290	−	0.116028i
$694$	15.4756	−	8.93483i	0.587445	−	0.339161i
$695$	−4.42959	−	19.5958i	−0.168024	−	0.743310i
$696$	3.02950	+	8.58222i	0.114833	+	0.325308i
$697$	33.8849	−	33.8849i	1.28348	−	1.28348i
$698$	3.90765	−	3.90765i	0.147907	−	0.147907i
$699$	−12.7872	−	36.2248i	−0.483658	−	1.37015i
$700$	−3.57425	−	19.3319i	−0.135094	−	0.730676i
$701$	30.4055	−	17.5547i	1.14840	−	0.663030i	0.199904	−	0.979815i	$-0.435937\pi$
$701$	30.4055	−	17.5547i	1.14840	−	0.663030i	0.948497	+	0.316785i	$0.102604\pi$
$702$	19.6485	+	5.88411i	0.741583	+	0.222081i
$703$	0.874710	−	0.234378i	0.0329903	−	0.00883973i
$704$	−0.130213	+	0.225535i	−0.00490757	+	0.00850017i
$705$	−20.8595	+	13.1259i	−0.785612	+	0.494352i
$706$	9.47881	+	16.4178i	0.356740	+	0.617891i
$707$	−13.9486	+	52.0568i	−0.524590	+	1.95780i
$708$	1.11365	+	14.3329i	0.0418534	+	0.538662i
$709$			26.4736i			0.994236i	0.867683	+	0.497118i	$0.165608\pi$
$709$			26.4736i			0.994236i	−0.867683	+	0.497118i	$0.834392\pi$
$710$	−1.61076	−	3.06317i	−0.0604508	−	0.114959i
$711$	−17.8423	−	6.88988i	−0.669140	−	0.258391i
$712$	11.4544	−	11.4544i	0.429271	−	0.429271i
$713$	−17.2113	−	8.77838i	−0.644567	−	0.328753i
$714$	−5.28323	+	28.3480i	−0.197720	+	1.06090i
$715$	2.29681	+	0.0907424i	0.0858960	+	0.00339357i
$716$	−16.3166	+	9.42040i	−0.609781	+	0.352057i
$717$	28.3430	+	41.3276i	1.05849	+	1.54341i
$718$	30.6442	−	8.21108i	1.14363	−	0.306435i
$719$	17.1054	+	29.6274i	0.637923	+	1.10492i	0.985888	+	0.167408i	$0.0535397\pi$
$719$	17.1054	+	29.6274i	0.637923	+	1.10492i	−0.347964	+	0.937508i	$0.613127\pi$
$720$	−5.25887	−	4.16465i	−0.195987	−	0.155207i
$721$	−56.2291			−2.09408
$722$	0.776665	−	0.208107i	0.0289045	−	0.00774493i
$723$	−25.1713	+	1.95578i	−0.936131	+	0.0727363i
$724$	2.47733	+	1.43029i	0.0920694	+	0.0531563i
$725$	−23.7185	+	11.3005i	−0.880884	+	0.419690i
$726$	14.3861	+	12.3117i	0.533918	+	0.456930i
$727$	19.4715	+	5.21737i	0.722157	+	0.193501i	0.601134	−	0.799148i	$-0.294716\pi$
$727$	19.4715	+	5.21737i	0.722157	+	0.193501i	0.121023	+	0.992650i	$0.461382\pi$
$728$	10.9745	−	10.9745i	0.406742	−	0.406742i
$729$	24.1301	−	12.1136i	0.893706	−	0.448654i
$730$	29.0711	+	9.03375i	1.07597	+	0.334354i
$731$	−11.3008	−	6.52452i	−0.417975	−	0.241318i
$732$	−3.42059	−	1.63572i	−0.126429	−	0.0604581i
$733$	−33.8859	+	9.07969i	−1.25160	+	0.335366i	−0.822956	−	0.568105i	$-0.807677\pi$
$733$	−33.8859	+	9.07969i	−1.25160	+	0.335366i	−0.428648	+	0.903472i	$0.641010\pi$
$734$	6.03023	−	10.4447i	0.222580	−	0.385519i
$735$	22.2700	−	24.0330i	0.821443	−	0.886470i
$736$	−3.47009			−0.127909
$737$	−1.00009	+	3.73237i	−0.0368386	+	0.137484i
$738$	−20.0114	+	27.4282i	−0.736630	+	1.00964i
$739$	−2.62763	−	1.51706i	−0.0966590	−	0.0558061i	0.450891	−	0.892579i	$-0.351106\pi$
$739$	−2.62763	−	1.51706i	−0.0966590	−	0.0558061i	−0.547550	+	0.836773i	$0.684440\pi$
$740$	0.0179628	−	0.454663i	0.000660325	−	0.0167137i
$741$	10.1276	+	28.6902i	0.372045	+	1.05396i
$742$	12.9237	−	12.9237i	0.474444	−	0.474444i
$743$	−6.64399	+	6.64399i	−0.243744	+	0.243744i	−0.818397	−	0.574653i	$-0.805137\pi$
$743$	−6.64399	+	6.64399i	−0.243744	+	0.243744i	0.574653	+	0.818397i	$0.305137\pi$
$744$	−7.65905	+	5.85994i	−0.280794	+	0.214836i
$745$	2.63510	+	2.85188i	0.0965428	+	0.104485i
$746$		−	8.09567i		−	0.296404i
$747$	8.90458	−	12.2049i	0.325802	−	0.446553i
$748$	0.779725	+	0.779725i	0.0285096	+	0.0285096i
$749$	−1.93762	+	3.35605i	−0.0707990	+	0.122628i
$750$	10.3604	−	16.3604i	0.378308	−	0.597397i
$751$	−16.7324	−	28.9814i	−0.610576	−	1.05755i	−0.991144	−	0.132795i	$-0.957605\pi$
$751$	−16.7324	−	28.9814i	−0.610576	−	1.05755i	0.380568	−	0.924753i	$-0.375729\pi$
$752$	4.49966	+	4.49966i	0.164086	+	0.164086i
$753$	−3.40045	−	43.7645i	−0.123919	−	1.59487i
$754$	−17.9625	−	10.3706i	−0.654155	−	0.377677i
$755$	−4.66251	+	1.05395i	−0.169686	+	0.0383573i
$756$	0.595886	−	20.4221i	0.0216721	−	0.742744i
$757$	6.22167	+	23.2196i	0.226131	+	0.843931i	0.981948	+	0.189149i	$0.0605728\pi$
$757$	6.22167	+	23.2196i	0.226131	+	0.843931i	−0.755818	+	0.654782i	$0.772761\pi$
$758$	−17.0259	−	4.56207i	−0.618408	−	0.165702i
$759$	0.286779	−	1.53876i	0.0104094	−	0.0558534i
$760$	0.392833	−	9.94314i	0.0142495	−	0.360676i
$761$	2.83289	−	1.63557i	0.102692	−	0.0592893i	−0.447774	−	0.894147i	$-0.647783\pi$
$761$	2.83289	−	1.63557i	0.102692	−	0.0592893i	0.550466	+	0.834857i	$0.314450\pi$
$762$	−6.77015	+	0.526033i	−0.245257	+	0.0190562i
$763$	−16.8346	+	62.8275i	−0.609453	+	2.27451i
$764$	1.71171	−	2.96477i	0.0619275	−	0.107262i
$765$	−22.7963	+	16.9445i	−0.824204	+	0.612628i
$766$	19.0616	−	33.0156i	0.688723	−	1.19290i
$767$	−23.1665	−	23.1665i	−0.836495	−	0.836495i
$768$	−0.747225	+	1.56258i	−0.0269632	+	0.0563847i
$769$	−16.4357	+	9.48913i	−0.592685	+	0.342187i	−0.766159	−	0.642652i	$-0.777834\pi$
$769$	−16.4357	+	9.48913i	−0.592685	+	0.342187i	0.173473	+	0.984839i	$0.444501\pi$
$770$	−0.504836	−	2.23331i	−0.0181930	−	0.0804830i
$771$	−1.48786	+	7.98338i	−0.0535841	+	0.287515i
$772$	−13.1133	−	3.51371i	−0.471959	−	0.126461i
$773$	11.5049	−	11.5049i	0.413801	−	0.413801i	−0.469260	−	0.883060i	$-0.655479\pi$
$773$	11.5049	−	11.5049i	0.413801	−	0.413801i	0.883060	+	0.469260i	$0.155479\pi$
$774$	8.62471	+	3.33046i	0.310009	+	0.119711i
$775$	−19.1460	−	20.2097i	−0.687744	−	0.725953i
$776$			1.55528i			0.0558314i
$777$	1.14287	−	0.783798i	0.0410003	−	0.0281186i
$778$	3.55109	−	13.2528i	0.127313	−	0.475138i
$779$	−50.3646			−1.80450
$780$	15.2766	−	0.581643i	0.546991	−	0.0208262i
$781$	−0.201536	−	0.349070i	−0.00721152	−	0.0124907i
$782$	−3.80286	+	14.1925i	−0.135990	+	0.507522i
$783$	−26.5682	+	6.29450i	−0.949471	+	0.224947i
$784$	−7.32645	−	4.22993i	−0.261659	−	0.151069i
$785$	17.7666	−	28.1447i	0.634116	−	1.00453i
$786$	−6.24594	+	7.29831i	−0.222785	+	0.260322i
$787$	−15.7808	−	4.22846i	−0.562526	−	0.150728i	−0.0336594	−	0.999433i	$-0.510716\pi$
$787$	−15.7808	−	4.22846i	−0.562526	−	0.150728i	−0.528867	+	0.848705i	$0.677383\pi$
$788$	−0.0318387	−	0.118824i	−0.00113421	−	0.00423292i
$789$	4.43552	+	12.5653i	0.157909	+	0.447337i
$790$	−14.2449	−	0.562786i	−0.506810	−	0.0200230i
$791$		−	68.2363i		−	2.42620i
$792$	−0.631149	−	0.460482i	−0.0224269	−	0.0163625i
$793$	8.34639	−	2.23641i	0.296389	−	0.0794172i
$794$	−14.8009	−	25.6360i	−0.525266	−	0.909787i
$795$	17.9900	−	0.684950i	0.638038	−	0.0242927i
$796$	5.70942	−	9.88901i	0.202365	−	0.350507i
$797$	−18.0930	+	4.84801i	−0.640887	+	0.171725i	−0.564605	−	0.825361i	$-0.690972\pi$
$797$	−18.0930	+	4.84801i	−0.640887	+	0.171725i	−0.0762819	+	0.997086i	$0.524305\pi$
$798$	24.9938	−	17.1411i	0.884769	−	0.606787i
$799$	23.3345	−	13.4722i	0.825515	−	0.476611i
$800$	−4.71248	−	1.67108i	−0.166611	−	0.0590818i
$801$	30.5076	+	37.8277i	1.07793	+	1.33658i
$802$	−16.6089	+	16.6089i	−0.586481	+	0.586481i
$803$	3.42468	+	0.917641i	0.120854	+	0.0323828i
$804$	−4.70848	+	25.2641i	−0.166055	+	0.890997i
$805$	22.4080	−	20.7047i	0.789778	−	0.729745i
$806$	4.57810	−	21.4953i	0.161257	−	0.757141i
$807$	8.79381	+	12.8224i	0.309557	+	0.451371i
$808$	9.69205	+	9.69205i	0.340965	+	0.340965i
$809$	7.07834	+	12.2601i	0.248861	+	0.431040i	0.963210	−	0.268749i	$-0.0866103\pi$
$809$	7.07834	+	12.2601i	0.248861	+	0.431040i	−0.714349	+	0.699790i	$0.753277\pi$
$810$	14.1032	−	14.3561i	0.495538	−	0.504423i
$811$	−16.6227	+	28.7914i	−0.583703	+	1.01100i	0.411333	+	0.911485i	$0.365063\pi$
$811$	−16.6227	+	28.7914i	−0.583703	+	1.01100i	−0.995036	+	0.0995175i	$0.968270\pi$
$812$	−5.34735	+	19.9566i	−0.187655	+	0.700338i
$813$	18.2865	−	38.2403i	0.641336	−	1.34115i
$814$		−	0.0529940i		−	0.00185744i
$815$	17.5166	+	11.0575i	0.613579	+	0.387326i
$816$	5.57198	+	4.76853i	0.195058	+	0.166932i
$817$	3.54959	+	13.2473i	0.124184	+	0.463463i
$818$	−35.7520	−	9.57971i	−1.25004	−	0.334947i
$819$	29.2295	+	36.2429i	1.02136	+	1.26643i
$820$	−7.50971	+	24.1666i	−0.262250	+	0.843936i
$821$			15.7116i			0.548339i	0.961681	+	0.274169i	$0.0884029\pi$
$821$			15.7116i			0.548339i	−0.961681	+	0.274169i	$0.911597\pi$
$822$	−3.02337	+	2.07347i	−0.105452	+	0.0723206i
$823$	−11.6952	+	43.6471i	−0.407669	+	1.52144i	0.391409	+	0.920217i	$0.371988\pi$
$823$	−11.6952	+	43.6471i	−0.407669	+	1.52144i	−0.799079	+	0.601226i	$0.794679\pi$
$824$	−7.15037	+	12.3848i	−0.249095	+	0.431445i
$825$	1.13047	−	1.95157i	0.0393579	−	0.0679451i
$826$	−16.3175	+	28.2627i	−0.567757	+	0.983384i
$827$	−36.4686	+	9.77174i	−1.26814	+	0.339797i	−0.829317	−	0.558778i	$-0.811270\pi$
$827$	−36.4686	+	9.77174i	−1.26814	+	0.339797i	−0.438821	+	0.898575i	$0.644604\pi$
$828$	1.10881	−	10.3511i	0.0385337	−	0.359724i
$829$		−	47.2497i		−	1.64105i	−0.571611	−	0.820525i	$-0.693681\pi$
$829$		−	47.2497i		−	1.64105i	0.571611	−	0.820525i	$-0.306319\pi$
$830$	3.34164	−	10.7536i	0.115990	−	0.373262i
$831$	−18.4594	−	52.2933i	−0.640349	−	1.81403i
$832$	−1.02163	−	3.81277i	−0.0354186	−	0.132184i
$833$	−25.3292	+	25.3292i	−0.877605	+	0.877605i
$834$	−5.18001	−	14.6744i	−0.179369	−	0.508132i
$835$	−0.790497	+	20.0086i	−0.0273563	+	0.692425i
$836$		−	1.15894i		−	0.0400827i
$837$	−15.0325	−	24.7189i	−0.519600	−	0.854410i
$838$	−17.5216	−	17.5216i	−0.605273	−	0.605273i
$839$	28.9385			0.999066			0.499533	−	0.866295i	$-0.333505\pi$
$839$	28.9385			0.999066			0.499533	+	0.866295i	$0.333505\pi$
$840$	−4.49813	−	14.5487i	−0.155200	−	0.501978i
$841$	−1.38923			−0.0479043
$842$	22.9627	−	6.15283i	0.791346	−	0.212040i
$843$	0.0560302	+	0.0267936i	0.00192978	+	0.000922822i
$844$	7.84211	−	4.52765i	0.269937	−	0.155848i
$845$	−4.23870	+	3.91651i	−0.145816	+	0.134732i
$846$	−14.8600	+	11.9844i	−0.510896	+	0.412032i
$847$	11.1251	+	41.5196i	0.382265	+	1.42663i
$848$	−1.20308	−	4.48997i	−0.0413140	−	0.154186i
$849$	45.2198	−	15.9625i	1.55194	−	0.547830i
$850$	−11.9990	+	17.4424i	−0.411563	+	0.598271i
$851$	0.611526	−	0.353065i	0.0209628	−	0.0121029i
$852$	−1.51620	−	2.21081i	−0.0519443	−	0.0757410i
$853$	−3.29501	−	3.29501i	−0.112819	−	0.112819i	0.648444	−	0.761263i	$-0.275420\pi$
$853$	−3.29501	−	3.29501i	−0.112819	−	0.112819i	−0.761263	+	0.648444i	$0.775420\pi$
$854$	−4.30360	−	7.45405i	−0.147266	−	0.255072i
$855$	29.5342	+	4.34895i	1.01005	+	0.148731i
$856$	0.492794	+	0.853544i	0.0168434	+	0.0291735i
$857$	−38.2009	+	10.2359i	−1.30492	+	0.349651i	−0.843307	−	0.537432i	$-0.819394\pi$
$857$	−38.2009	+	10.2359i	−1.30492	+	0.349651i	−0.461609	+	0.887083i	$0.652728\pi$
$858$	1.77514	−	0.137927i	0.0606024	−	0.00470873i
$859$	13.5146	+	7.80266i	0.461113	+	0.266223i	0.712512	−	0.701660i	$-0.247557\pi$
$859$	13.5146	+	7.80266i	0.461113	+	0.266223i	−0.251399	+	0.967883i	$0.580891\pi$
$860$	6.88575	+	0.272042i	0.234802	+	0.00927655i
$861$	−72.6794	+	25.6556i	−2.47691	+	0.874341i
$862$	−7.50846	−	2.01189i	−0.255739	−	0.0685251i
$863$	11.2748	+	42.0783i	0.383800	+	1.43236i	0.840049	+	0.542510i	$0.182526\pi$
$863$	11.2748	+	42.0783i	0.383800	+	1.43236i	−0.456249	+	0.889852i	$0.650807\pi$
$864$	−4.42231	−	2.72822i	−0.150450	−	0.0928159i
$865$	0.874893	+	1.66378i	0.0297472	+	0.0565701i
$866$			28.2039i			0.958408i
$867$	1.32645	−	0.909698i	0.0450486	−	0.0308950i
$868$	−21.8624	+	1.13686i	−0.742057	+	0.0385875i
$869$	−1.66033			−0.0563230
$870$	−17.2245	+	10.8387i	−0.583967	+	0.367465i
$871$	−29.2836	−	50.7207i	−0.992237	−	1.71860i
$872$	11.6974	+	11.6974i	0.396123	+	0.396123i
$873$	−4.63931	−	0.496964i	−0.157017	−	0.0168197i
$874$	13.3736	−	7.72126i	0.452369	−	0.261176i
$875$	40.4014	−	17.3266i	1.36582	−	0.585746i
$876$	23.1814	+	4.32032i	0.783227	+	0.145970i
$877$	5.42960	+	20.2635i	0.183344	+	0.684251i	0.994979	+	0.100085i	$0.0319115\pi$
$877$	5.42960	+	20.2635i	0.183344	+	0.684251i	−0.811634	+	0.584166i	$0.801422\pi$
$878$	5.71684	+	21.3356i	0.192934	+	0.720040i
$879$	−30.1735	+	35.2574i	−1.01773	+	1.18920i
$880$	−0.556098	−	0.172806i	−0.0187461	−	0.00582528i
$881$	26.6525	+	15.3878i	0.897944	+	0.518428i	0.876533	−	0.481343i	$-0.159851\pi$
$881$	26.6525	+	15.3878i	0.897944	+	0.518428i	0.0214113	+	0.999771i	$0.493184\pi$
$882$	14.9586	−	20.5027i	0.503684	−	0.690363i
$883$	−7.40694	−	7.40694i	−0.249263	−	0.249263i	0.571405	−	0.820668i	$-0.306399\pi$
$883$	−7.40694	−	7.40694i	−0.249263	−	0.249263i	−0.820668	+	0.571405i	$0.806399\pi$
$884$	−16.7136			−0.562139
$885$	−30.7115	+	9.49530i	−1.03236	+	0.319181i
$886$	12.5971	−	21.8188i	0.423207	−	0.733017i
$887$	−12.7797	+	47.6943i	−0.429099	+	1.60142i	0.325707	+	0.945471i	$0.394398\pi$
$887$	−12.7797	+	47.6943i	−0.429099	+	1.60142i	−0.754806	+	0.655948i	$0.772269\pi$
$888$	−0.0273031	−	0.351396i	−0.000916231	−	0.0117921i
$889$	−13.3499	−	7.70757i	−0.447742	−	0.258504i
$890$	30.6297	+	19.3352i	1.02671	+	0.648117i
$891$	1.57526	−	1.73554i	0.0527732	−	0.0581427i
$892$	−18.6973	−	5.00992i	−0.626031	−	0.167744i
$893$	−27.3536	−	7.32939i	−0.915355	−	0.245269i
$894$	2.28512	+	1.95562i	0.0764258	+	0.0654057i
$895$	−28.5907	−	30.9427i	−0.955681	−	1.03430i
$896$	−3.40513	+	1.96595i	−0.113757	+	0.0656778i
$897$	13.4182	+	19.5654i	0.448022	+	0.653270i
$898$	8.16869	+	8.16869i	0.272593	+	0.272593i
$899$	9.02941	+	27.8281i	0.301148	+	0.928119i
$900$	6.49053	−	13.5231i	0.216351	−	0.450769i
$901$	−19.6822			−0.655708
$902$	−0.762830	+	2.84692i	−0.0253995	+	0.0947921i
$903$	11.8704	+	17.3085i	0.395023	+	0.575991i
$904$	−15.0294	−	8.67726i	−0.499872	−	0.288601i
$905$	−1.89814	+	6.10832i	−0.0630964	+	0.203048i
$906$	−3.49154	+	1.23250i	−0.115999	+	0.0409472i
$907$	−6.40291	+	6.40291i	−0.212605	+	0.212605i	−0.805373	−	0.592768i	$-0.798035\pi$
$907$	−6.40291	+	6.40291i	−0.212605	+	0.212605i	0.592768	+	0.805373i	$0.298035\pi$
$908$	−5.42697	−	20.2537i	−0.180100	−	0.672143i
$909$	−32.0077	+	25.8138i	−1.06163	+	0.856191i
$910$	29.3464	+	18.5251i	0.972825	+	0.614103i
$911$	44.4529	−	25.6649i	1.47279	−	0.850317i	0.473260	−	0.880923i	$-0.343077\pi$
$911$	44.4529	−	25.6649i	1.47279	−	0.850317i	0.999532	+	0.0306061i	$0.00974375\pi$
$912$	−0.597098	−	7.68477i	−0.0197719	−	0.254468i
$913$	0.339441	−	1.26681i	0.0112338	−	0.0419253i
$914$	23.0912			0.763789
$915$	1.88116	−	8.26688i	0.0621892	−	0.273295i
$916$	−1.49835	−	2.59523i	−0.0495070	−	0.0857487i
$917$	−21.0636	+	5.64398i	−0.695582	+	0.186381i
$918$	−16.0047	+	15.0971i	−0.528232	+	0.498280i
$919$	15.5763	+	8.99301i	0.513816	+	0.296652i	0.734401	−	0.678716i	$-0.237463\pi$
$919$	15.5763	+	8.99301i	0.513816	+	0.296652i	−0.220585	+	0.975368i	$0.570797\pi$
$920$	−1.71083	−	7.56841i	−0.0564043	−	0.249523i
$921$	−11.7985	+	13.7864i	−0.388773	+	0.454277i
$922$	−3.61913	+	3.61913i	−0.119190	+	0.119190i
$923$	5.90119	+	1.58122i	0.194240	+	0.0520465i
$924$	−0.590361	−	1.67242i	−0.0194214	−	0.0550187i
$925$	1.00049	−	0.184980i	0.0328960	−	0.00608212i
$926$			18.4523i			0.606381i
$927$	−34.6583	−	25.2864i	−1.13833	−	0.830515i
$928$	3.71556	+	3.71556i	0.121969	+	0.121969i
$929$	−59.3125			−1.94598			−0.972991	−	0.230844i	$-0.925851\pi$
$929$	−59.3125			−1.94598			−0.972991	+	0.230844i	$0.925851\pi$
$930$	−16.5568	−	13.8156i	−0.542920	−	0.453032i
$931$	37.6479			1.23386
$932$	−15.6830	−	15.6830i	−0.513715	−	0.513715i
$933$	−31.0587	−	14.8522i	−1.01681	−	0.486240i
$934$			4.36513i			0.142831i
$935$	−1.31619	+	2.08503i	−0.0430440	+	0.0681878i
$936$	11.6997	−	1.82915i	0.382416	−	0.0597875i
$937$	6.05658	+	1.62286i	0.197860	+	0.0530164i	0.356388	−	0.934338i	$-0.384008\pi$
$937$	6.05658	+	1.62286i	0.197860	+	0.0530164i	−0.158528	+	0.987354i	$0.550675\pi$
$938$	−41.2521	+	41.2521i	−1.34693	+	1.34693i
$939$	5.21836	+	4.46591i	0.170295	+	0.145739i
$940$	−7.59551	+	12.0323i	−0.247738	+	0.392452i
$941$	−24.7350	−	14.2807i	−0.806336	−	0.465539i	0.0393456	−	0.999226i	$-0.487473\pi$
$941$	−24.7350	−	14.2807i	−0.806336	−	0.465539i	−0.845682	+	0.533687i	$0.820806\pi$
$942$	11.1223	−	23.2586i	0.362383	−	0.757806i
$943$	−37.9344	+	10.1645i	−1.23531	+	0.331001i
$944$	4.15001	+	7.18804i	0.135071	+	0.233951i
$945$	44.8351	−	8.76884i	1.45849	−	0.285251i
$946$	0.802580			0.0260941
$947$	−11.0586	+	41.2713i	−0.359356	+	1.34114i	0.515556	+	0.856856i	$0.327585\pi$
$947$	−11.0586	+	41.2713i	−0.359356	+	1.34114i	−0.874913	+	0.484280i	$0.839081\pi$
$948$	−11.0095	+	0.855422i	−0.357571	+	0.0277828i
$949$	−46.5394	+	26.8695i	−1.51073	+	0.872221i
$950$	21.8800	−	4.04538i	0.709882	−	0.131250i
$951$	12.4026	+	10.6142i	0.402182	+	0.344190i
$952$	4.30896	+	16.0813i	0.139654	+	0.521197i
$953$	5.51805	−	5.51805i	0.178747	−	0.178747i	−0.612062	−	0.790810i	$-0.709660\pi$
$953$	5.51805	−	5.51805i	0.178747	−	0.178747i	0.790810	+	0.612062i	$0.209660\pi$
$954$	13.7777	−	2.15403i	0.446069	−	0.0697392i
$955$	7.31018	+	2.27161i	0.236552	+	0.0735077i
$956$	25.0564	+	14.4663i	0.810383	+	0.467875i
$957$	−1.95467	+	1.34054i	−0.0631856	+	0.0433336i
$958$	−4.79519	+	17.8959i	−0.154926	+	0.578190i
$959$	−8.32228			−0.268741
$960$	−3.77644	−	0.859344i	−0.121884	−	0.0277352i
$961$	−25.0943	+	18.2010i	−0.809494	+	0.587128i
$962$	0.567969	+	0.567969i	0.0183121	+	0.0183121i
$963$	−2.70353	+	1.19724i	−0.0871201	+	0.0385804i
$964$	−12.6236	+	7.28823i	−0.406578	+	0.234738i
$965$	1.19840	−	30.3330i	0.0385777	−	0.976455i
$966$	15.3658	−	17.9548i	0.494387	−	0.577685i
$967$	−17.5987	−	4.71555i	−0.565935	−	0.151642i	−0.0355034	−	0.999370i	$-0.511303\pi$
$967$	−17.5987	−	4.71555i	−0.565935	−	0.151642i	−0.530432	+	0.847728i	$0.677970\pi$
$968$	10.5597	+	2.82946i	0.339401	+	0.0909422i
$969$	−32.0846	−	5.97962i	−1.03071	−	0.192093i
$970$	−3.39213	+	0.766786i	−0.108915	+	0.0246200i
$971$	15.4636	+	8.92793i	0.496251	+	0.286511i	0.727164	−	0.686464i	$-0.240838\pi$
$971$	15.4636	+	8.92793i	0.496251	+	0.286511i	−0.230913	+	0.972974i	$0.574171\pi$
$972$	9.55117	−	12.3197i	0.306354	−	0.395155i
$973$	9.14319	−	34.1229i	0.293117	−	1.09393i
$974$	9.07248	−	15.7140i	0.290701	−	0.503509i
$975$	8.80027	+	33.0322i	0.281834	+	1.05788i
$976$	−2.18907			−0.0700703
$977$	33.0354	+	33.0354i	1.05690	+	1.05690i	0.998281	+	0.0586159i	$0.0186687\pi$
$977$	33.0354	+	33.0354i	1.05690	+	1.05690i	0.0586159	+	0.998281i	$0.481331\pi$
$978$	14.4756	+	6.92221i	0.462877	+	0.221348i
$979$	3.65342	+	2.10930i	0.116764	+	0.0674137i
$980$	5.61355	−	18.0647i	0.179318	−	0.577056i
$981$	−38.6302	+	31.1548i	−1.23337	+	0.994696i
$982$	−1.96450	−	7.33163i	−0.0626898	−	0.233962i
$983$	−13.0795	−	48.8132i	−0.417170	−	1.55690i	−0.780449	−	0.625220i	$-0.785009\pi$
$983$	−13.0795	−	48.8132i	−0.417170	−	1.55690i	0.363278	−	0.931681i	$-0.381657\pi$
$984$	−3.59146	+	19.2706i	−0.114492	+	0.614323i
$985$	0.243462	−	0.128024i	0.00775734	−	0.00407918i
$986$	19.2683	−	11.1246i	0.613628	−	0.354278i
$987$	−43.2067	+	3.35711i	−1.37528	+	0.106858i
$988$	12.4211	+	12.4211i	0.395167	+	0.395167i
$989$	5.34707	+	9.26140i	0.170027	+	0.294495i
$990$	0.693159	−	1.60359i	0.0220300	−	0.0509653i
$991$	25.2465			0.801981			0.400991	−	0.916082i	$-0.368666\pi$
$991$	25.2465			0.801981			0.400991	+	0.916082i	$0.368666\pi$
$992$	−2.52973	+	4.95989i	−0.0803189	+	0.157477i
$993$	−1.22481	−	1.78592i	−0.0388682	−	0.0566745i
$994$		−	6.08558i		−	0.193023i
$995$	24.3832	+	7.57699i	0.772998	+	0.240207i
$996$	1.59811	−	8.57493i	0.0506381	−	0.271707i
$997$	−3.66137	−	13.6644i	−0.115957	−	0.432757i	0.883400	−	0.468620i	$-0.155249\pi$
$997$	−3.66137	−	13.6644i	−0.115957	−	0.432757i	−0.999357	+	0.0358632i	$0.988582\pi$
$998$	25.3281	+	6.78664i	0.801747	+	0.214827i
$999$	1.05692	+	0.0308392i	0.0334393	+	0.000975709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.893.44	yes	256
3.2	odd	2	inner	930.2.bf.a.893.17	yes	256
5.2	odd	4	inner	930.2.bf.a.707.28	yes	256
15.2	even	4	inner	930.2.bf.a.707.64	yes	256
31.5	even	3	inner	930.2.bf.a.563.64	yes	256
93.5	odd	6	inner	930.2.bf.a.563.28	yes	256
155.67	odd	12	inner	930.2.bf.a.377.17	✓	256
465.377	even	12	inner	930.2.bf.a.377.44	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.17	✓	256	155.67	odd	12	inner
930.2.bf.a.377.44	yes	256	465.377	even	12	inner
930.2.bf.a.563.28	yes	256	93.5	odd	6	inner
930.2.bf.a.563.64	yes	256	31.5	even	3	inner
930.2.bf.a.707.28	yes	256	5.2	odd	4	inner
930.2.bf.a.707.64	yes	256	15.2	even	4	inner
930.2.bf.a.893.17	yes	256	3.2	odd	2	inner
930.2.bf.a.893.44	yes	256	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.747225 + 1.56258i) q^{3} +1.00000i q^{4} +(-2.18104 + 0.493020i) q^{5} +(-1.63328 + 0.576543i) q^{6} +(-3.79793 - 1.01765i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.88331 - 2.33520i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.747225 + 1.56258i) q^{3} +1.00000i q^{4} +(-2.18104 + 0.493020i) q^{5} +(-1.63328 + 0.576543i) q^{6} +(-3.79793 - 1.01765i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.88331 - 2.33520i) q^{9} +(-1.89085 - 1.19361i) q^{10} +(-0.225535 - 0.130213i) q^{11} +(-1.56258 - 0.747225i) q^{12} +(3.81277 - 1.02163i) q^{13} +(-1.96595 - 3.40513i) q^{14} +(0.859344 - 3.77644i) q^{15} -1.00000 q^{16} +(-1.09590 + 4.08994i) q^{17} +(0.319533 - 2.98293i) q^{18} +(3.85397 - 2.22509i) q^{19} +(-0.493020 - 2.18104i) q^{20} +(4.42807 - 5.17415i) q^{21} +(-0.0674030 - 0.251552i) q^{22} +(2.45373 - 2.45373i) q^{23} +(-0.576543 - 1.63328i) q^{24} +(4.51386 - 2.15059i) q^{25} +(3.41843 + 1.97363i) q^{26} +(5.05619 - 1.19790i) q^{27} +(1.01765 - 3.79793i) q^{28} -5.25460 q^{29} +(3.27800 - 2.06270i) q^{30} +(-1.71838 - 5.29596i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.371993 - 0.255118i) q^{33} +(-3.66694 + 2.11711i) q^{34} +(8.78515 + 0.347083i) q^{35} +(2.33520 - 1.88331i) q^{36} +(0.196556 + 0.0526671i) q^{37} +(4.29854 + 1.15179i) q^{38} +(-1.25262 + 6.72114i) q^{39} +(1.19361 - 1.89085i) q^{40} +(-9.80119 - 5.65872i) q^{41} +(6.78979 - 0.527559i) q^{42} +(-0.797629 + 2.97679i) q^{43} +(0.130213 - 0.225535i) q^{44} +(5.25887 + 4.16465i) q^{45} +3.47009 q^{46} +(-4.49966 - 4.49966i) q^{47} +(0.747225 - 1.56258i) q^{48} +(7.32645 + 4.22993i) q^{49} +(4.71248 + 1.67108i) q^{50} +(-5.57198 - 4.76853i) q^{51} +(1.02163 + 3.81277i) q^{52} +(1.20308 + 4.48997i) q^{53} +(4.42231 + 2.72822i) q^{54} +(0.556098 + 0.172806i) q^{55} +(3.40513 - 1.96595i) q^{56} +(0.597098 + 7.68477i) q^{57} +(-3.71556 - 3.71556i) q^{58} +(-4.15001 - 7.18804i) q^{59} +(3.77644 + 0.859344i) q^{60} +2.18907 q^{61} +(2.52973 - 4.95989i) q^{62} +(4.77626 + 10.7855i) q^{63} -1.00000i q^{64} +(-7.81211 + 4.10798i) q^{65} +(0.443434 + 0.0826430i) q^{66} +(-3.84020 - 14.3318i) q^{67} +(-4.08994 - 1.09590i) q^{68} +(2.00066 + 5.66763i) q^{69} +(5.96661 + 6.45746i) q^{70} +(1.34039 + 0.773872i) q^{71} +(2.98293 + 0.319533i) q^{72} +(-13.1503 + 3.52362i) q^{73} +(0.101745 + 0.176228i) q^{74} +(-0.0123994 + 8.66025i) q^{75} +(2.22509 + 3.85397i) q^{76} +(0.724054 + 0.724054i) q^{77} +(-5.63830 + 3.86683i) q^{78} +(5.52132 - 3.18774i) q^{79} +(2.18104 - 0.493020i) q^{80} +(-1.90629 + 8.79580i) q^{81} +(-2.92917 - 10.9318i) q^{82} +(1.30341 + 4.86439i) q^{83} +(5.17415 + 4.42807i) q^{84} +(0.373770 - 9.46062i) q^{85} +(-2.66892 + 1.54090i) q^{86} +(3.92637 - 8.21072i) q^{87} +(0.251552 - 0.0674030i) q^{88} -16.1989 q^{89} +(0.773734 + 6.66343i) q^{90} -15.5203 q^{91} +(2.45373 + 2.45373i) q^{92} +(9.55937 + 1.27216i) q^{93} -6.36348i q^{94} +(-7.30864 + 6.75309i) q^{95} +(1.63328 - 0.576543i) q^{96} +(1.09975 - 1.09975i) q^{97} +(2.18957 + 8.17160i) q^{98} +(0.120680 + 0.771899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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