LMFDB - Embedded newform 946.2.w.a.175.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(175,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 1]))

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

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

chi := DirichletCharacter("946.175");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.w (of order $42$, degree $12$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$22$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			175.6
Character	$\chi$	$=$	946.175
Dual form			946.2.w.a.373.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 - 0.433884i) q^{2} +(-1.60065 - 0.119952i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.814345 - 2.64004i) q^{5} +(1.39009 + 0.802569i) q^{6} +(-0.0499568 - 0.0865277i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.418799 - 0.0631238i) q^{9} +O(q^{10})$	\(q+(-0.900969 - 0.433884i) q^{2} +(-1.60065 - 0.119952i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.814345 - 2.64004i) q^{5} +(1.39009 + 0.802569i) q^{6} +(-0.0499568 - 0.0865277i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.418799 - 0.0631238i) q^{9} +(-1.87917 + 2.02527i) q^{10} +(1.00421 + 3.16094i) q^{11} +(-0.904207 - 1.32623i) q^{12} +(4.10412 + 4.42319i) q^{13} +(0.00746655 + 0.0996342i) q^{14} +(-1.62016 + 4.12810i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-2.14585 - 6.95667i) q^{17} +(0.349937 + 0.238583i) q^{18} +(6.81440 - 1.02711i) q^{19} +(2.57180 - 1.00936i) q^{20} +(0.0695842 + 0.144493i) q^{21} +(0.466717 - 3.28362i) q^{22} +(1.36571 + 3.47976i) q^{23} +(0.239234 + 1.58721i) q^{24} +(-2.17547 - 1.48321i) q^{25} +(-1.77853 - 5.76586i) q^{26} +(5.35746 + 1.22281i) q^{27} +(0.0365025 - 0.0930069i) q^{28} +(0.262669 + 3.50508i) q^{29} +(3.25083 - 3.01633i) q^{30} +(-7.21030 + 4.91590i) q^{31} +(0.623490 - 0.781831i) q^{32} +(-1.22823 - 5.18002i) q^{33} +(-1.08504 + 7.19879i) q^{34} +(-0.269119 + 0.0614246i) q^{35} +(-0.211765 - 0.366787i) q^{36} +(0.116963 + 0.0675284i) q^{37} +(-6.58521 - 2.03127i) q^{38} +(-6.03868 - 7.57227i) q^{39} +(-2.75506 - 0.206463i) q^{40} +(0.429326 - 0.891504i) q^{41} -0.160375i q^{42} +(6.26993 - 1.92040i) q^{43} +(-1.84521 + 2.75594i) q^{44} +(-0.507697 + 1.05424i) q^{45} +(0.279354 - 3.72771i) q^{46} +(-4.24011 - 5.31693i) q^{47} +(0.473123 - 1.53383i) q^{48} +(3.49501 - 6.05353i) q^{49} +(1.31649 + 2.28023i) q^{50} +(2.60028 + 11.3926i) q^{51} +(-0.899311 + 5.96654i) q^{52} +(-5.82288 - 5.40284i) q^{53} +(-4.29635 - 3.42623i) q^{54} +(9.16280 - 0.0770669i) q^{55} +(-0.0732418 + 0.0679585i) q^{56} +(-11.0307 + 0.826635i) q^{57} +(1.28414 - 3.27193i) q^{58} +(2.72935 - 11.9581i) q^{59} +(-4.23763 + 1.30714i) q^{60} +(4.40307 + 3.00196i) q^{61} +(8.62918 - 1.30064i) q^{62} +(0.0154599 + 0.0393912i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(15.0196 - 7.23304i) q^{65} +(-1.14093 + 5.19995i) q^{66} +(4.55409 - 0.686418i) q^{67} +(4.10103 - 6.01510i) q^{68} +(-1.76861 - 5.73370i) q^{69} +(0.269119 + 0.0614246i) q^{70} +(10.8658 + 4.26450i) q^{71} +(0.0316504 + 0.422345i) q^{72} +(5.62380 - 5.21812i) q^{73} +(-0.0760802 - 0.111589i) q^{74} +(3.30426 + 2.63506i) q^{75} +(5.05174 + 4.68733i) q^{76} +(0.223342 - 0.244803i) q^{77} +(2.15518 + 9.44247i) q^{78} +(6.61596 - 3.81973i) q^{79} +(2.39264 + 1.38139i) q^{80} +(-7.21461 - 2.22541i) q^{81} +(-0.773619 + 0.616940i) q^{82} +(5.64538 + 0.423063i) q^{83} +(-0.0695842 + 0.144493i) q^{84} -20.1134 q^{85} +(-6.48225 - 0.990198i) q^{86} -5.64191i q^{87} +(2.85823 - 1.68241i) q^{88} +(-9.07738 - 0.680256i) q^{89} +(0.914838 - 0.729559i) q^{90} +(0.177700 - 0.576088i) q^{91} +(-1.86908 + 3.23735i) q^{92} +(12.1308 - 7.00374i) q^{93} +(1.51328 + 6.63010i) q^{94} +(2.83767 - 18.8267i) q^{95} +(-1.09177 + 1.17665i) q^{96} +(9.75450 - 12.2318i) q^{97} +(-5.77542 + 3.93762i) q^{98} +(-0.221033 - 1.38719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q - 44 q^{2} - 44 q^{4} - 44 q^{8} - 20 q^{9}+O(q^{10}) $ 264 * q - 44 * q^2 - 44 * q^4 - 44 * q^8 - 20 * q^9	$ 264 q - 44 q^{2} - 44 q^{4} - 44 q^{8} - 20 q^{9} + 5 q^{11} + 7 q^{13} - 32 q^{15} - 44 q^{16} + q^{17} - 20 q^{18} + 21 q^{19} + 12 q^{22} - q^{23} + 7 q^{24} - 14 q^{25} - 7 q^{26} + 11 q^{29} - 4 q^{30} + 5 q^{31} - 44 q^{32} + 41 q^{33} + 15 q^{34} + 134 q^{36} - 72 q^{37} - 28 q^{38} - 86 q^{39} - 14 q^{40} + 28 q^{41} - 45 q^{43} - 9 q^{44} + 98 q^{45} + 6 q^{46} + 6 q^{47} - 140 q^{49} + 140 q^{50} - 7 q^{51} - 12 q^{53} - 42 q^{54} - 42 q^{55} + 2 q^{57} - 3 q^{58} + 44 q^{59} - 4 q^{60} - 71 q^{61} - 2 q^{62} + 24 q^{63} - 44 q^{64} + 68 q^{65} + 97 q^{66} + 25 q^{67} - 27 q^{68} + 74 q^{69} + 47 q^{71} - 20 q^{72} + 57 q^{73} - 2 q^{74} - 28 q^{75} - 28 q^{76} + 11 q^{77} + 12 q^{78} + 42 q^{79} + 99 q^{81} - 28 q^{82} + 44 q^{83} - 12 q^{85} - 17 q^{86} - 9 q^{88} - 69 q^{89} - 8 q^{92} + 84 q^{93} + 27 q^{94} + 12 q^{95} - 82 q^{97} + 14 q^{98} - 88 q^{99}+O(q^{100}) $ 264 * q - 44 * q^2 - 44 * q^4 - 44 * q^8 - 20 * q^9 + 5 * q^11 + 7 * q^13 - 32 * q^15 - 44 * q^16 + q^17 - 20 * q^18 + 21 * q^19 + 12 * q^22 - q^23 + 7 * q^24 - 14 * q^25 - 7 * q^26 + 11 * q^29 - 4 * q^30 + 5 * q^31 - 44 * q^32 + 41 * q^33 + 15 * q^34 + 134 * q^36 - 72 * q^37 - 28 * q^38 - 86 * q^39 - 14 * q^40 + 28 * q^41 - 45 * q^43 - 9 * q^44 + 98 * q^45 + 6 * q^46 + 6 * q^47 - 140 * q^49 + 140 * q^50 - 7 * q^51 - 12 * q^53 - 42 * q^54 - 42 * q^55 + 2 * q^57 - 3 * q^58 + 44 * q^59 - 4 * q^60 - 71 * q^61 - 2 * q^62 + 24 * q^63 - 44 * q^64 + 68 * q^65 + 97 * q^66 + 25 * q^67 - 27 * q^68 + 74 * q^69 + 47 * q^71 - 20 * q^72 + 57 * q^73 - 2 * q^74 - 28 * q^75 - 28 * q^76 + 11 * q^77 + 12 * q^78 + 42 * q^79 + 99 * q^81 - 28 * q^82 + 44 * q^83 - 12 * q^85 - 17 * q^86 - 9 * q^88 - 69 * q^89 - 8 * q^92 + 84 * q^93 + 27 * q^94 + 12 * q^95 - 82 * q^97 + 14 * q^98 - 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	−0.900969	−	0.433884i	−0.637081	−	0.306802i
$2$	−0.900969	−	0.433884i	−0.637081	−	0.306802i
$3$	−1.60065	−	0.119952i	−0.924136	−	0.0692544i	−0.395845	−	0.918318i	$-0.629548\pi$
$3$	−1.60065	−	0.119952i	−0.924136	−	0.0692544i	−0.528291	+	0.849063i	$0.677167\pi$
$4$	0.623490	+	0.781831i	0.311745	+	0.390916i
$5$	0.814345	−	2.64004i	0.364186	−	1.18066i	−0.569324	−	0.822113i	$-0.692795\pi$
$5$	0.814345	−	2.64004i	0.364186	−	1.18066i	0.933511	−	0.358550i	$-0.116729\pi$
$6$	1.39009	+	0.802569i	0.567502	+	0.327648i
$7$	−0.0499568	−	0.0865277i	−0.0188819	−	0.0327044i	0.856430	−	0.516263i	$-0.172677\pi$
$7$	−0.0499568	−	0.0865277i	−0.0188819	−	0.0327044i	−0.875312	+	0.483559i	$0.839344\pi$
$8$	−0.222521	−	0.974928i	−0.0786730	−	0.344689i
$9$	−0.418799	−	0.0631238i	−0.139600	−	0.0210413i
$10$	−1.87917	+	2.02527i	−0.594246	+	0.640445i
$11$	1.00421	+	3.16094i	0.302782	+	0.953060i
$11$	1.00421	+	3.16094i	0.302782	+	0.953060i
$12$	−0.904207	−	1.32623i	−0.261022	−	0.382849i
$13$	4.10412	+	4.42319i	1.13828	+	1.22677i	0.970540	+	0.240939i	$0.0774554\pi$
$13$	4.10412	+	4.42319i	1.13828	+	1.22677i	0.167737	+	0.985832i	$0.446354\pi$
$14$	0.00746655	+	0.0996342i	0.00199552	+	0.0266284i
$15$	−1.62016	+	4.12810i	−0.418324	+	1.06587i
$16$	−0.222521	+	0.974928i	−0.0556302	+	0.243732i
$17$	−2.14585	−	6.95667i	−0.520444	−	1.68724i	−0.709027	−	0.705182i	$-0.750865\pi$
$17$	−2.14585	−	6.95667i	−0.520444	−	1.68724i	0.188582	−	0.982057i	$-0.439611\pi$
$18$	0.349937	+	0.238583i	0.0824808	+	0.0562345i
$19$	6.81440	−	1.02711i	1.56333	−	0.235634i	0.690382	−	0.723445i	$-0.257442\pi$
$19$	6.81440	−	1.02711i	1.56333	−	0.235634i	0.872950	+	0.487811i	$0.162204\pi$
$20$	2.57180	−	1.00936i	0.575073	−	0.225700i
$21$	0.0695842	+	0.144493i	0.0151845	+	0.0315310i
$22$	0.466717	−	3.28362i	0.0995043	−	0.700071i
$23$	1.36571	+	3.47976i	0.284769	+	0.725580i	0.999653	+	0.0263371i	$0.00838433\pi$
$23$	1.36571	+	3.47976i	0.284769	+	0.725580i	−0.714884	+	0.699243i	$0.753520\pi$
$24$	0.239234	+	1.58721i	0.0488333	+	0.323988i
$25$	−2.17547	−	1.48321i	−0.435095	−	0.296643i
$26$	−1.77853	−	5.76586i	−0.348799	−	1.13078i
$27$	5.35746	+	1.22281i	1.03104	+	0.235329i
$28$	0.0365025	−	0.0930069i	0.00689833	−	0.0175767i
$29$	0.262669	+	3.50508i	0.0487764	+	0.650876i	0.966994	+	0.254800i	$0.0820095\pi$
$29$	0.262669	+	3.50508i	0.0487764	+	0.650876i	−0.918217	+	0.396077i	$0.870371\pi$
$30$	3.25083	−	3.01633i	0.593518	−	0.550704i
$31$	−7.21030	+	4.91590i	−1.29501	+	0.882921i	−0.997421	−	0.0717737i	$-0.977134\pi$
$31$	−7.21030	+	4.91590i	−1.29501	+	0.882921i	−0.297587	+	0.954695i	$0.596182\pi$
$32$	0.623490	−	0.781831i	0.110218	−	0.138210i
$33$	−1.22823	−	5.18002i	−0.213808	−	0.901726i
$34$	−1.08504	+	7.19879i	−0.186083	+	1.23458i
$35$	−0.269119	+	0.0614246i	−0.0454894	+	0.0103827i
$36$	−0.211765	−	0.366787i	−0.0352941	−	0.0611312i
$37$	0.116963	+	0.0675284i	0.0192285	+	0.0111016i	0.509583	−	0.860421i	$-0.329800\pi$
$37$	0.116963	+	0.0675284i	0.0192285	+	0.0111016i	−0.490355	+	0.871523i	$0.663133\pi$
$38$	−6.58521	−	2.03127i	−1.06826	−	0.329515i
$39$	−6.03868	−	7.57227i	−0.966963	−	1.21253i
$40$	−2.75506	−	0.206463i	−0.435613	−	0.0326447i
$41$	0.429326	−	0.891504i	0.0670494	−	0.139230i	−0.864751	−	0.502201i	$-0.832524\pi$
$41$	0.429326	−	0.891504i	0.0670494	−	0.139230i	0.931800	+	0.362972i	$0.118238\pi$
$42$		−	0.160375i		−	0.0247464i
$43$	6.26993	−	1.92040i	0.956156	−	0.292859i
$43$	6.26993	−	1.92040i	0.956156	−	0.292859i
$44$	−1.84521	+	2.75594i	−0.278176	+	0.415474i
$45$	−0.507697	+	1.05424i	−0.0756830	+	0.157157i
$46$	0.279354	−	3.72771i	0.0411884	−	0.549621i
$47$	−4.24011	−	5.31693i	−0.618483	−	0.775553i	0.369647	−	0.929172i	$-0.379479\pi$
$47$	−4.24011	−	5.31693i	−0.618483	−	0.775553i	−0.988130	+	0.153619i	$0.950907\pi$
$48$	0.473123	−	1.53383i	0.0682894	−	0.221389i
$49$	3.49501	−	6.05353i	0.499287	−	0.864790i
$50$	1.31649	+	2.28023i	0.186180	+	0.322473i
$51$	2.60028	+	11.3926i	0.364113	+	1.59528i
$52$	−0.899311	+	5.96654i	−0.124712	+	0.827410i
$53$	−5.82288	−	5.40284i	−0.799834	−	0.742137i	0.170121	−	0.985423i	$-0.445584\pi$
$53$	−5.82288	−	5.40284i	−0.799834	−	0.742137i	−0.969955	+	0.243286i	$0.921775\pi$
$54$	−4.29635	−	3.42623i	−0.584659	−	0.466250i
$55$	9.16280	−	0.0770669i	1.23551	−	0.0103917i
$56$	−0.0732418	+	0.0679585i	−0.00978735	+	0.00908134i
$57$	−11.0307	+	0.826635i	−1.46105	+	0.109491i
$58$	1.28414	−	3.27193i	0.168616	−	0.429626i
$59$	2.72935	−	11.9581i	0.355331	−	1.55681i	−0.409337	−	0.912383i	$-0.634240\pi$
$59$	2.72935	−	11.9581i	0.355331	−	1.55681i	0.764668	−	0.644424i	$-0.222903\pi$
$60$	−4.23763	+	1.30714i	−0.547076	+	0.168751i
$61$	4.40307	+	3.00196i	0.563756	+	0.384362i	0.811402	−	0.584488i	$-0.198705\pi$
$61$	4.40307	+	3.00196i	0.563756	+	0.384362i	−0.247646	+	0.968850i	$0.579657\pi$
$62$	8.62918	−	1.30064i	1.09591	−	0.165181i
$63$	0.0154599	+	0.0393912i	0.00194777	+	0.00496282i
$64$	−0.900969	+	0.433884i	−0.112621	+	0.0542355i
$65$	15.0196	−	7.23304i	1.86295	−	0.897148i
$66$	−1.14093	+	5.19995i	−0.140439	+	0.640069i
$67$	4.55409	−	0.686418i	0.556370	−	0.0838593i	0.135162	−	0.990823i	$-0.456844\pi$
$67$	4.55409	−	0.686418i	0.556370	−	0.0838593i	0.421208	+	0.906964i	$0.361606\pi$
$68$	4.10103	−	6.01510i	0.497322	−	0.729438i
$69$	−1.76861	−	5.73370i	−0.212916	−	0.690256i
$70$	0.269119	+	0.0614246i	0.0321659	+	0.00734165i
$71$	10.8658	+	4.26450i	1.28953	+	0.506103i	0.908278	−	0.418368i	$-0.137398\pi$
$71$	10.8658	+	4.26450i	1.28953	+	0.506103i	0.381253	+	0.924471i	$0.375493\pi$
$72$	0.0316504	+	0.422345i	0.00373004	+	0.0497739i
$73$	5.62380	−	5.21812i	0.658216	−	0.610735i	−0.278663	−	0.960389i	$-0.589891\pi$
$73$	5.62380	−	5.21812i	0.658216	−	0.610735i	0.936879	+	0.349654i	$0.113701\pi$
$74$	−0.0760802	−	0.111589i	−0.00884415	−	0.0129720i
$75$	3.30426	+	2.63506i	0.381543	+	0.304270i
$76$	5.05174	+	4.68733i	0.579474	+	0.537673i
$77$	0.223342	−	0.244803i	0.0254522	−	0.0278979i
$78$	2.15518	+	9.44247i	0.244026	+	1.06915i
$79$	6.61596	−	3.81973i	0.744354	−	0.429753i	−0.0792961	−	0.996851i	$-0.525267\pi$
$79$	6.61596	−	3.81973i	0.744354	−	0.429753i	0.823650	+	0.567098i	$0.191934\pi$
$80$	2.39264	+	1.38139i	0.267506	+	0.154444i
$81$	−7.21461	−	2.22541i	−0.801623	−	0.247268i
$82$	−0.773619	+	0.616940i	−0.0854319	+	0.0681296i
$83$	5.64538	+	0.423063i	0.619661	+	0.0464372i	0.380862	−	0.924632i	$-0.375627\pi$
$83$	5.64538	+	0.423063i	0.619661	+	0.0464372i	0.238799	+	0.971069i	$0.423246\pi$
$84$	−0.0695842	+	0.144493i	−0.00759226	+	0.0157655i
$85$	−20.1134			−2.18160
$86$	−6.48225	−	0.990198i	−0.698999	−	0.106776i
$87$		−	5.64191i		−	0.604876i
$88$	2.85823	−	1.68241i	0.304689	−	0.179346i
$89$	−9.07738	−	0.680256i	−0.962200	−	0.0721070i	−0.415642	−	0.909528i	$-0.636443\pi$
$89$	−9.07738	−	0.680256i	−0.962200	−	0.0721070i	−0.546558	+	0.837421i	$0.684062\pi$
$90$	0.914838	−	0.729559i	0.0964324	−	0.0769023i
$91$	0.177700	−	0.576088i	0.0186280	−	0.0603904i
$92$	−1.86908	+	3.23735i	−0.194865	+	0.337517i
$93$	12.1308	−	7.00374i	1.25791	−	0.726254i
$94$	1.51328	+	6.63010i	0.156083	+	0.683843i
$95$	2.83767	−	18.8267i	0.291139	−	1.93158i
$96$	−1.09177	+	1.17665i	−0.111428	+	0.120091i
$97$	9.75450	−	12.2318i	0.990420	−	1.24195i	0.0201811	−	0.999796i	$-0.493576\pi$
$97$	9.75450	−	12.2318i	0.990420	−	1.24195i	0.970239	−	0.242151i	$-0.0778529\pi$
$98$	−5.77542	+	3.93762i	−0.583406	+	0.397759i
$99$	−0.221033	−	1.38719i	−0.0222146	−	0.139418i
$100$	−0.196763	−	2.62562i	−0.0196763	−	0.262562i
$101$	5.42222	+	2.12806i	0.539531	+	0.211750i	0.619429	−	0.785053i	$-0.287364\pi$
$101$	5.42222	+	2.12806i	0.539531	+	0.211750i	−0.0798981	+	0.996803i	$0.525459\pi$
$102$	2.60028	−	11.3926i	0.257466	−	1.12803i
$103$	4.02545	−	1.24169i	0.396640	−	0.122347i	−0.0900175	−	0.995940i	$-0.528692\pi$
$103$	4.02545	−	1.24169i	0.396640	−	0.122347i	0.486657	+	0.873593i	$0.338216\pi$
$104$	3.39904	−	4.98547i	0.333303	−	0.488865i
$105$	0.438133	−	0.0660380i	0.0427574	−	0.00644465i
$106$	2.90203	+	7.39424i	0.281870	+	0.718192i
$107$	−0.762601	−	1.58356i	−0.0737235	−	0.153088i	0.860850	−	0.508859i	$-0.169933\pi$
$107$	−0.762601	−	1.58356i	−0.0737235	−	0.153088i	−0.934573	+	0.355771i	$0.884218\pi$
$108$	2.38430	+	4.95104i	0.229429	+	0.476414i
$109$	−14.6541	+	5.75129i	−1.40360	+	0.550874i	−0.941820	−	0.336119i	$-0.890886\pi$
$109$	−14.6541	+	5.75129i	−1.40360	+	0.550874i	−0.461784	+	0.886992i	$0.652790\pi$
$110$	−8.28883	−	3.90615i	−0.790309	−	0.372437i
$111$	−0.179116	−	0.122119i	−0.0170010	−	0.0115911i
$112$	0.0954747	−	0.0294500i	0.00902151	−	0.00278277i
$113$	−13.0605	−	2.98098i	−1.22863	−	0.280427i	−0.441527	−	0.897248i	$-0.645563\pi$
$113$	−13.0605	−	2.98098i	−1.22863	−	0.280427i	−0.787103	+	0.616821i	$0.788420\pi$
$114$	10.2970	+	4.04126i	0.964399	+	0.378499i
$115$	10.2989	−	0.771794i	0.960375	−	0.0719702i
$116$	−2.57661	+	2.39074i	−0.239232	+	0.221975i
$117$	−1.43959	−	2.11149i	−0.133090	−	0.195208i
$118$	−7.64747	+	9.58963i	−0.704007	+	0.882797i
$119$	−0.494745	+	0.533208i	−0.0453532	+	0.0488791i
$120$	4.38512	+	0.660951i	0.400305	+	0.0603363i
$121$	−8.98311	+	6.34852i	−0.816647	+	0.577138i
$122$	−2.66453	−	4.61510i	−0.241235	−	0.417831i
$123$	−0.794139	+	1.37549i	−0.0716051	+	0.124024i
$124$	−8.33895	−	2.57223i	−0.748860	−	0.230993i
$125$	5.11283	−	4.07735i	0.457306	−	0.364689i
$126$	0.00316231	−	0.0421980i	0.000281721	−	0.00375930i
$127$	−1.01841	+	2.11475i	−0.0903693	+	0.187654i	−0.941255	−	0.337698i	$-0.890352\pi$
$127$	−1.01841	+	2.11475i	−0.0903693	+	0.187654i	0.850885	+	0.525351i	$0.176066\pi$
$128$	1.00000			0.0883883
$129$	−10.2663	+	2.32180i	−0.903900	+	0.204423i
$130$	−16.6705			−1.46210
$131$	10.0160	+	4.82346i	0.875104	+	0.421428i	0.816834	−	0.576873i	$-0.195727\pi$
$131$	10.0160	+	4.82346i	0.875104	+	0.421428i	0.0582701	+	0.998301i	$0.481442\pi$
$132$	3.28411	−	4.18996i	0.285845	−	0.364689i
$133$	−0.429299	−	0.538324i	−0.0372249	−	0.0466786i
$134$	−4.40092	−	1.35750i	−0.380181	−	0.117270i
$135$	7.59108	−	13.1481i	0.653337	−	1.13161i
$136$	−6.30475	+	3.64005i	−0.540628	+	0.312132i
$137$	13.3558	−	3.04838i	1.14107	−	0.260441i	0.390094	−	0.920775i	$-0.372443\pi$
$137$	13.3558	−	3.04838i	1.14107	−	0.260441i	0.750972	+	0.660335i	$0.229586\pi$
$138$	−0.894295	+	5.93326i	−0.0761274	+	0.505072i
$139$	3.12554	−	3.36853i	0.265104	−	0.285715i	−0.586445	−	0.809989i	$-0.699473\pi$
$139$	3.12554	−	3.36853i	0.265104	−	0.285715i	0.851549	+	0.524274i	$0.175663\pi$
$140$	−0.215817	−	0.172108i	−0.0182398	−	0.0145458i
$141$	6.14915	+	9.01915i	0.517852	+	0.759550i
$142$	−7.93943	−	8.55667i	−0.666262	−	0.718060i
$143$	−9.86003	+	17.4147i	−0.824537	+	1.45629i
$144$	0.154733	−	0.394253i	0.0128944	−	0.0328544i
$145$	9.46746	+	2.16089i	0.786229	+	0.179452i
$146$	−7.33092	+	2.26129i	−0.606712	+	0.187146i
$147$	−6.32042	+	9.27036i	−0.521300	+	0.764606i
$148$	0.0201292	+	0.133548i	0.00165461	+	0.0109776i
$149$	−2.82333	−	7.19374i	−0.231296	−	0.589334i	0.767356	−	0.641221i	$-0.221572\pi$
$149$	−2.82333	−	7.19374i	−0.231296	−	0.589334i	−0.998653	+	0.0518869i	$0.983476\pi$
$150$	−1.83372	−	3.80777i	−0.149723	−	0.310903i
$151$	−13.0144	+	6.26742i	−1.05910	+	0.510036i	−0.880578	−	0.473901i	$-0.842846\pi$
$151$	−13.0144	+	6.26742i	−1.05910	+	0.510036i	−0.178521	+	0.983936i	$0.557131\pi$
$152$	−2.51770	−	6.41500i	−0.204213	−	0.520325i
$153$	0.459548	+	3.04890i	0.0371522	+	0.246489i
$154$	−0.307440	+	0.123655i	−0.0247742	+	0.00996443i
$155$	7.10651	+	23.0387i	0.570808	+	1.85052i
$156$	2.15518	−	9.44247i	0.172553	−	0.756002i
$157$	8.22159	+	3.22674i	0.656154	+	0.257522i	0.669976	−	0.742383i	$-0.266304\pi$
$157$	8.22159	+	3.22674i	0.656154	+	0.257522i	−0.0138216	+	0.999904i	$0.504400\pi$
$158$	−7.61810	+	0.570897i	−0.606063	+	0.0454182i
$159$	8.67231	+	9.34653i	0.687759	+	0.741228i
$160$	−1.55633	−	2.28272i	−0.123039	−	0.180465i
$161$	0.232869	−	0.292009i	0.0183527	−	0.0230135i
$162$	5.53457	+	5.13533i	0.434837	+	0.403469i
$163$	−0.340124	+	2.25658i	−0.0266406	+	0.176749i	−0.998194	−	0.0600714i	$-0.980867\pi$
$163$	−0.340124	+	2.25658i	−0.0266406	+	0.176749i	0.971553	+	0.236820i	$0.0761052\pi$
$164$	0.964687	−	0.220183i	0.0753294	−	0.0171934i
$165$	−14.6757	−	0.975740i	−1.14250	−	0.0759613i
$166$	−4.90275	−	2.83061i	−0.380528	−	0.219698i
$167$	−1.44781	+	4.69368i	−0.112035	+	0.363208i	−0.994175	−	0.107779i	$-0.965626\pi$
$167$	−1.44781	+	4.69368i	−0.112035	+	0.363208i	0.882140	+	0.470987i	$0.156102\pi$
$168$	0.125386	−	0.0999923i	0.00967377	−	0.00771457i
$169$	−1.74931	+	23.3429i	−0.134562	+	1.79561i
$170$	18.1215	+	8.72686i	1.38986	+	0.669319i
$171$	−2.91870			−0.223199
$172$	5.41067	+	3.70468i	0.412560	+	0.282479i
$173$		−	2.83713i		−	0.215703i	−0.994167	−	0.107851i	$-0.965603\pi$
$173$		−	2.83713i		−	0.215703i	0.994167	−	0.107851i	$-0.0343971\pi$
$174$	−2.44793	+	5.08319i	−0.185577	+	0.385355i
$175$	−0.0196593	+	0.262335i	−0.00148610	+	0.0198307i
$176$	−3.30515	+	0.275660i	−0.249135	+	0.0207786i
$177$	−5.80313	+	18.8133i	−0.436190	+	1.41409i
$178$	7.88329	+	4.55142i	0.590877	+	0.341143i
$179$	−18.8802	+	10.9005i	−1.41117	+	0.814742i	−0.995499	−	0.0947716i	$-0.969788\pi$
$179$	−18.8802	+	10.9005i	−1.41117	+	0.814742i	−0.415675	+	0.909513i	$0.636455\pi$
$180$	−1.14078	+	0.260377i	−0.0850290	+	0.0194073i
$181$	−18.0073	−	2.71417i	−1.33847	−	0.201742i	−0.559516	−	0.828819i	$-0.689013\pi$
$181$	−18.0073	−	2.71417i	−1.33847	−	0.201742i	−0.778957	+	0.627077i	$0.784251\pi$
$182$	−0.410057	+	0.441936i	−0.0303954	+	0.0327585i
$183$	−6.68769	−	5.33325i	−0.494368	−	0.394245i
$184$	3.08862	−	2.10578i	0.227696	−	0.155240i
$185$	0.273526	−	0.253795i	0.0201100	−	0.0186594i
$186$	−13.9683	+	1.04678i	−1.02421	+	0.0767537i
$187$	19.8347	−	13.7689i	1.45046	−	1.00688i
$188$	1.51328	−	6.63010i	0.110367	−	0.483550i
$189$	−0.161835	−	0.524656i	−0.0117718	−	0.0381631i
$190$	−10.7253	+	15.7311i	−0.778093	+	1.14125i
$191$	2.43199	+	16.1352i	0.175973	+	1.16750i	0.886122	+	0.463451i	$0.153389\pi$
$191$	2.43199	+	16.1352i	0.175973	+	1.16750i	−0.710150	+	0.704051i	$0.751373\pi$
$192$	1.49418	−	0.586423i	0.107833	−	0.0423214i
$193$	4.38283	+	9.10104i	0.315483	+	0.655108i	0.997059	−	0.0766401i	$-0.0244192\pi$
$193$	4.38283	+	9.10104i	0.315483	+	0.655108i	−0.681576	+	0.731748i	$0.738705\pi$
$194$	−14.0957	+	6.78811i	−1.01201	+	0.487358i
$195$	−24.9087	+	9.77594i	−1.78375	+	0.700070i
$196$	6.91194	−	1.04181i	0.493710	−	0.0744149i
$197$	7.68009	−	11.2646i	0.547183	−	0.802571i	−0.448655	−	0.893705i	$-0.648097\pi$
$197$	7.68009	−	11.2646i	0.547183	−	0.802571i	0.995839	+	0.0911342i	$0.0290492\pi$
$198$	−0.402735	+	1.34572i	−0.0286212	+	0.0956360i
$199$	17.6548	+	4.02960i	1.25152	+	0.285651i	0.796395	−	0.604777i	$-0.206738\pi$
$199$	17.6548	+	4.02960i	1.25152	+	0.285651i	0.455124	+	0.890428i	$0.349595\pi$
$200$	−0.961937	+	2.45098i	−0.0680192	+	0.173310i
$201$	−7.37184	+	0.552443i	−0.519969	+	0.0389663i
$202$	−3.96192	−	4.26993i	−0.278759	−	0.300431i
$203$	0.290164	−	0.197831i	0.0203655	−	0.0138850i
$204$	−7.28583	+	9.13615i	−0.510110	+	0.639658i
$205$	−2.00399	−	1.85943i	−0.139965	−	0.129868i
$206$	−4.16556	−	0.627856i	−0.290228	−	0.0437448i
$207$	−0.352301	−	1.54353i	−0.0244866	−	0.107283i
$208$	−5.22554	+	3.01697i	−0.362326	+	0.209189i
$209$	10.0897	+	20.5085i	0.697922	+	1.41860i
$210$	−0.423397	−	0.130601i	−0.0292172	−	0.00901231i
$211$	−14.6965	−	18.4289i	−1.01175	−	1.26870i	−0.962891	−	0.269890i	$-0.913013\pi$
$211$	−14.6965	−	18.4289i	−1.01175	−	1.26870i	−0.0488601	−	0.998806i	$-0.515559\pi$
$212$	0.593606	−	7.92113i	0.0407690	−	0.544025i
$213$	−16.8808	−	8.12935i	−1.15665	−	0.557014i
$214$			1.75762i			0.120148i
$215$	0.0359445	−	18.1168i	0.00245139	−	1.23555i
$216$		−	5.49524i		−	0.373904i
$217$	0.785565	+	0.378308i	0.0533276	+	0.0256812i
$218$	15.6982	+	1.17642i	1.06322	+	0.0796772i
$219$	−9.62766	+	7.67780i	−0.650577	+	0.518818i
$220$	5.77316	+	7.11571i	0.389227	+	0.479741i
$221$	21.9638	−	38.0424i	1.47745	−	2.55901i
$222$	0.108392	+	0.187741i	0.00727483	+	0.0126004i
$223$	−2.65983	+	0.607088i	−0.178115	+	0.0406536i	−0.310648	−	0.950525i	$-0.600546\pi$
$223$	−2.65983	+	0.607088i	−0.178115	+	0.0406536i	0.132533	+	0.991179i	$0.457689\pi$
$224$	−0.0987976	−	0.0148913i	−0.00660120	−	0.000994970i
$225$	0.817460	+	0.758492i	0.0544974	+	0.0505662i
$226$	10.4737	+	8.35252i	0.696702	+	0.555601i
$227$	11.0217	−	7.51450i	0.731539	−	0.498755i	−0.139345	−	0.990244i	$-0.544500\pi$
$227$	11.0217	−	7.51450i	0.731539	−	0.498755i	0.870884	+	0.491489i	$0.163547\pi$
$228$	−7.52381	−	8.10874i	−0.498276	−	0.537014i
$229$	1.20786	+	16.1177i	0.0798174	+	1.06509i	0.883005	+	0.469363i	$0.155516\pi$
$229$	1.20786	+	16.1177i	0.0798174	+	1.06509i	−0.803188	+	0.595726i	$0.796865\pi$
$230$	−9.61383	−	3.77315i	−0.633917	−	0.248794i
$231$	−0.386857	+	0.365053i	−0.0254533	+	0.0240188i
$232$	3.35875	−	1.03604i	0.220513	−	0.0680191i
$233$	23.9354	+	16.3189i	1.56806	+	1.06908i	0.961776	+	0.273836i	$0.0882926\pi$
$233$	23.9354	+	16.3189i	1.56806	+	1.06908i	0.606283	+	0.795249i	$0.292660\pi$
$234$	0.380885	+	2.52701i	0.0248992	+	0.165196i
$235$	−17.4898	+	6.86425i	−1.14091	+	0.447774i
$236$	11.0509	−	5.32184i	0.719353	−	0.346422i
$237$	−11.0480	+	5.32045i	−0.717647	+	0.345600i
$238$	0.677100	−	0.265742i	0.0438899	−	0.0172255i
$239$	−0.0136394	−	0.0904917i	−0.000882262	−	0.00585342i	0.988385	−	0.151968i	$-0.0485612\pi$
$239$	−0.0136394	−	0.0904917i	−0.000882262	−	0.00585342i	−0.989268	+	0.146115i	$0.953323\pi$
$240$	−3.66408	−	2.49813i	−0.236516	−	0.161254i
$241$	−21.3299	+	6.57940i	−1.37398	+	0.423816i	−0.891869	−	0.452294i	$-0.850606\pi$
$241$	−21.3299	+	6.57940i	−1.37398	+	0.423816i	−0.482110	+	0.876111i	$0.660130\pi$
$242$	10.8480	−	1.82219i	0.697337	−	0.117135i
$243$	−4.06500	−	1.59540i	−0.260770	−	0.102345i
$244$	0.398241	+	5.31416i	0.0254948	+	0.340204i
$245$	−13.1354	−	14.1566i	−0.839193	−	0.904434i
$246$	1.31230	−	0.894708i	0.0836690	−	0.0570445i
$247$	32.5102	+	25.9260i	2.06857	+	1.64963i
$248$	6.39709	+	5.93563i	0.406215	+	0.376913i
$249$	−8.98554	−	1.35435i	−0.569435	−	0.0858286i
$250$	−6.37560	+	1.45519i	−0.403228	+	0.0920342i
$251$	−6.78167	−	11.7462i	−0.428055	−	0.741413i	0.568645	−	0.822583i	$-0.307468\pi$
$251$	−6.78167	−	11.7462i	−0.428055	−	0.741413i	−0.996700	+	0.0811697i	$0.974134\pi$
$252$	−0.0211582	+	0.0366471i	−0.00133284	+	0.00230855i
$253$	−9.62786	+	7.81134i	−0.605299	+	0.491095i
$254$	1.83511	−	1.46345i	0.115145	−	0.0918252i
$255$	32.1944	+	2.41264i	2.01609	+	0.151085i
$256$	−0.900969	−	0.433884i	−0.0563106	−	0.0271177i
$257$		−	24.1463i		−	1.50620i	−0.657904	−	0.753102i	$-0.728557\pi$
$257$		−	24.1463i		−	1.50620i	0.657904	−	0.753102i	$-0.271443\pi$
$258$	10.2570	+	2.36252i	0.638575	+	0.147084i
$259$		−	0.0134940i		−	0.000838477i
$260$	15.0196	+	7.23304i	0.931474	+	0.448574i
$261$	0.111248	−	1.48450i	0.00688609	−	0.0918885i
$262$	−6.93130	−	8.69158i	−0.428217	−	0.536968i
$263$	14.3885	+	4.43825i	0.887230	+	0.273674i	0.704682	−	0.709523i	$-0.251089\pi$
$263$	14.3885	+	4.43825i	0.887230	+	0.273674i	0.182548	+	0.983197i	$0.441566\pi$
$264$	−4.77684	+	2.35010i	−0.293994	+	0.144639i
$265$	−19.0056	+	10.9729i	−1.16750	+	0.674058i
$266$	0.153215	+	0.671279i	0.00939422	+	0.0411588i
$267$	14.4481	+	2.17770i	0.884210	+	0.133273i
$268$	3.37609	+	3.13255i	0.206227	+	0.191351i
$269$	2.62241	−	3.28839i	0.159891	−	0.200497i	−0.695432	−	0.718592i	$-0.744787\pi$
$269$	2.62241	−	3.28839i	0.159891	−	0.200497i	0.855323	+	0.518095i	$0.173359\pi$
$270$	−12.5441	+	8.55242i	−0.763409	+	0.520484i
$271$	10.9590	+	11.8109i	0.665709	+	0.717464i	0.972133	−	0.234432i	$-0.0753229\pi$
$271$	10.9590	+	11.8109i	0.665709	+	0.717464i	−0.306424	+	0.951895i	$0.599132\pi$
$272$	7.25974	−	0.544043i	0.440187	−	0.0329874i
$273$	−0.353538	+	0.900800i	−0.0213971	+	0.0545189i
$274$	−13.3558	−	3.04838i	−0.806855	−	0.184159i
$275$	2.50371	−	8.36601i	0.150979	−	0.504489i
$276$	3.38008	−	4.95766i	0.203457	−	0.298416i
$277$	6.30364	−	0.950121i	0.378749	−	0.0570873i	0.0430911	−	0.999071i	$-0.486279\pi$
$277$	6.30364	−	0.950121i	0.378749	−	0.0570873i	0.335658	+	0.941984i	$0.391041\pi$
$278$	−4.27756	+	1.67882i	−0.256551	+	0.100689i
$279$	3.32998	−	1.60363i	0.199360	−	0.0960069i
$280$	0.119769	+	0.248703i	0.00715758	+	0.0148629i
$281$	8.27950	−	3.24946i	0.493913	−	0.193847i	−0.105293	−	0.994441i	$-0.533578\pi$
$281$	8.27950	−	3.24946i	0.493913	−	0.193847i	0.599206	+	0.800595i	$0.295483\pi$
$282$	−1.62693	−	10.7940i	−0.0968824	−	0.642773i
$283$	−1.24853	+	1.83126i	−0.0742174	+	0.108857i	−0.861553	−	0.507668i	$-0.830508\pi$
$283$	−1.24853	+	1.83126i	−0.0742174	+	0.108857i	0.787335	+	0.616525i	$0.211460\pi$
$284$	3.44058	+	11.1541i	0.204161	+	0.661873i
$285$	−6.80043	+	29.7946i	−0.402823	+	1.76488i
$286$	16.4395	−	11.4120i	0.972090	−	0.674805i
$287$	−0.0985876	+	0.00738812i	−0.00581944	+	0.000436107i
$288$	−0.310469	+	0.288073i	−0.0182946	+	0.0169749i
$289$	−29.7445	+	20.2794i	−1.74967	+	1.19291i
$290$	−7.59231	−	6.05467i	−0.445836	−	0.355542i
$291$	−17.0808	+	18.4087i	−1.00129	+	1.07914i
$292$	7.58607	+	1.14342i	0.443941	+	0.0669134i
$293$	14.3986	−	3.28638i	0.841174	−	0.191992i	0.219837	−	0.975537i	$-0.429447\pi$
$293$	14.3986	−	3.28638i	0.841174	−	0.191992i	0.621336	+	0.783544i	$0.286590\pi$
$294$	9.71676	−	5.60997i	0.566693	−	0.327180i
$295$	−29.3472	−	16.9436i	−1.70866	−	0.986494i
$296$	0.0398087	−	0.129057i	0.00231383	−	0.00750127i
$297$	1.51482	+	18.1626i	0.0878985	+	1.05390i
$298$	−0.577510	+	7.70633i	−0.0334542	+	0.446416i
$299$	−9.78661	+	20.3221i	−0.565975	+	1.17526i
$300$			4.22630i			0.244006i
$301$	−0.479394	−	0.446586i	−0.0276318	−	0.0257408i
$302$	14.4449			0.831212
$303$	−8.42381	−	4.05669i	−0.483935	−	0.233051i
$304$	−0.514993	+	6.87211i	−0.0295369	+	0.394142i
$305$	11.5109	−	9.17966i	0.659114	−	0.525626i
$306$	0.908830	−	2.94635i	0.0519543	−	0.168432i
$307$	−0.154605	−	0.0892610i	−0.00882375	−	0.00509439i	0.495582	−	0.868561i	$-0.334955\pi$
$307$	−0.154605	−	0.0892610i	−0.00882375	−	0.00509439i	−0.504405	+	0.863467i	$0.668288\pi$
$308$	0.330646	+	0.0219836i	0.0188403	+	0.00125263i
$309$	−6.59229	+	1.50465i	−0.375022	+	0.0855963i
$310$	3.59339	−	23.8406i	0.204091	−	1.35405i
$311$	17.4695	+	16.2093i	0.990604	+	0.919146i	0.996727	−	0.0808355i	$-0.0257589\pi$
$311$	17.4695	+	16.2093i	0.990604	+	0.919146i	−0.00612395	+	0.999981i	$0.501949\pi$
$312$	−6.03868	+	7.57227i	−0.341873	+	0.428695i
$313$	−7.99039	−	11.7197i	−0.451643	−	0.662439i	0.531122	−	0.847295i	$-0.321771\pi$
$313$	−7.99039	−	11.7197i	−0.451643	−	0.662439i	−0.982766	+	0.184856i	$0.940818\pi$
$314$	−6.00737	−	6.47440i	−0.339015	−	0.365372i
$315$	0.116584	−	0.00873677i	0.00656877	−	0.000492261i
$316$	7.11137	+	2.79101i	0.400046	+	0.157006i
$317$	−3.55651	+	15.5821i	−0.199753	+	0.875177i	0.771330	+	0.636436i	$0.219592\pi$
$317$	−3.55651	+	15.5821i	−0.199753	+	0.875177i	−0.971083	+	0.238741i	$0.923265\pi$
$318$	−3.75817	−	12.1837i	−0.210748	−	0.683228i
$319$	−10.8156	+	4.35013i	−0.605556	+	0.243560i
$320$	0.411772	+	2.73193i	0.0230187	+	0.152719i
$321$	1.03071	+	2.62620i	0.0575285	+	0.146580i
$322$	−0.336506	+	0.162053i	−0.0187528	+	0.00903085i
$323$	−21.7679	−	45.2015i	−1.21120	−	2.51508i
$324$	−2.75834	−	7.02813i	−0.153241	−	0.390452i
$325$	−2.36787	−	15.7098i	−0.131346	−	0.871423i
$326$	1.28553	−	1.88553i	0.0711991	−	0.104430i
$327$	24.1459	−	7.44802i	1.33527	−	0.411877i
$328$	−0.964687	−	0.220183i	−0.0532659	−	0.0121576i
$329$	−0.248239	+	0.632503i	−0.0136859	+	0.0348710i
$330$	12.7990	+	7.24665i	0.704560	+	0.398915i
$331$	9.84719	+	10.6128i	0.541251	+	0.583330i	0.943155	−	0.332352i	$-0.107842\pi$
$331$	9.84719	+	10.6128i	0.541251	+	0.583330i	−0.401905	+	0.915681i	$0.631652\pi$
$332$	3.18908	+	4.67751i	0.175023	+	0.256712i
$333$	−0.0447212	−	0.0356640i	−0.00245071	−	0.00195437i
$334$	3.34094	−	3.60068i	0.182808	−	0.197020i
$335$	1.89643	−	12.5820i	0.103613	−	0.687426i
$336$	−0.156354	+	0.0356868i	−0.00852982	+	0.00194688i
$337$	−26.9455	+	15.5570i	−1.46782	+	0.847444i	−0.999350	−	0.0360372i	$-0.988527\pi$
$337$	−26.9455	+	15.5570i	−1.46782	+	0.847444i	−0.468466	+	0.883481i	$0.655193\pi$
$338$	11.7042	−	20.2722i	0.636623	−	1.10266i
$339$	20.5478	+	6.33814i	1.11600	+	0.344241i
$340$	−12.5405	−	15.7253i	−0.680103	−	0.852822i
$341$	−22.7795	−	17.8547i	−1.23358	−	0.966887i
$342$	2.62966	+	1.26638i	0.142196	+	0.0684778i
$343$	−1.39779			−0.0754737
$344$	−3.26745	−	5.68540i	−0.176169	−	0.306536i
$345$	−16.5775			−0.892501
$346$	−1.23098	+	2.55616i	−0.0661781	+	0.137420i
$347$	−0.929324	+	12.4010i	−0.0498887	+	0.665719i	0.915066	+	0.403304i	$0.132138\pi$
$347$	−0.929324	+	12.4010i	−0.0498887	+	0.665719i	−0.964955	+	0.262415i	$0.915481\pi$
$348$	4.41102	−	3.51767i	0.236456	−	0.188567i
$349$	−1.00918	−	0.311290i	−0.0540200	−	0.0166630i	0.267627	−	0.963522i	$-0.413760\pi$
$349$	−1.00918	−	0.311290i	−0.0540200	−	0.0166630i	−0.321647	+	0.946860i	$0.604237\pi$
$350$	0.131535	−	0.227826i	0.00703086	−	0.0121778i
$351$	16.5790	+	28.7156i	0.884919	+	1.53272i
$352$	3.09744	+	1.18569i	0.165094	+	0.0631975i
$353$	−11.2661	−	1.69809i	−0.599633	−	0.0903801i	−0.157790	−	0.987473i	$-0.550437\pi$
$353$	−11.2661	−	1.69809i	−0.599633	−	0.0903801i	−0.441843	+	0.897093i	$0.645675\pi$
$354$	13.3912	−	14.4323i	0.711736	−	0.767068i
$355$	20.1070	−	25.2133i	1.06717	−	1.33818i
$356$	−5.12781	−	7.52111i	−0.271773	−	0.398618i
$357$	0.855873	−	0.794134i	0.0452976	−	0.0420300i
$358$	21.7400	−	1.62919i	1.14900	−	0.0861054i
$359$	8.98525	+	3.52645i	0.474223	+	0.186119i	0.590402	−	0.807109i	$-0.298969\pi$
$359$	8.98525	+	3.52645i	0.474223	+	0.186119i	−0.116179	+	0.993228i	$0.537065\pi$
$360$	1.14078	+	0.260377i	0.0601246	+	0.0137230i
$361$	27.2253	−	8.39789i	1.43291	−	0.441994i
$362$	15.0464	+	10.2585i	0.790821	+	0.539173i
$363$	15.1403	−	9.08422i	0.794662	−	0.476798i
$364$	0.561198	−	0.220254i	0.0294147	−	0.0115444i
$365$	−9.19635	−	19.0964i	−0.481359	−	0.999552i
$366$	3.71139	+	7.70677i	0.193997	+	0.402840i
$367$	−9.21534	−	23.4803i	−0.481037	−	1.22566i	−0.941207	−	0.337831i	$-0.890307\pi$
$367$	−9.21534	−	23.4803i	−0.481037	−	1.22566i	0.460170	−	0.887831i	$-0.347788\pi$
$368$	−3.69641	+	0.557145i	−0.192689	+	0.0290432i
$369$	−0.236076	+	0.346261i	−0.0122897	+	0.0180256i
$370$	−0.356556	+	0.109983i	−0.0185365	+	0.00571774i
$371$	−0.176603	+	0.773749i	−0.00916878	+	0.0401710i
$372$	13.0392	+	5.11751i	0.676051	+	0.265330i
$373$	−0.316937	−	4.22923i	−0.0164104	−	0.218981i	−0.999380	−	0.0352123i	$-0.988789\pi$
$373$	−0.316937	−	4.22923i	−0.0164104	−	0.218981i	0.982969	−	0.183769i	$-0.0588298\pi$
$374$	−23.8446	+	3.79936i	−1.23297	+	0.196460i
$375$	−8.67294	+	5.91311i	−0.447869	+	0.305352i
$376$	−4.24011	+	5.31693i	−0.218667	+	0.274200i
$377$	−14.4256	+	15.5471i	−0.742955	+	0.800715i
$378$	−0.0818315	+	0.542917i	−0.00420896	+	0.0279246i
$379$	7.00728	+	30.7009i	0.359940	+	1.57700i	0.753339	+	0.657632i	$0.228442\pi$
$379$	7.00728	+	30.7009i	0.359940	+	1.57700i	−0.393399	+	0.919368i	$0.628701\pi$
$380$	16.4886	−	9.51970i	0.845847	−	0.488350i
$381$	1.88379	−	3.26281i	0.0965093	−	0.167159i
$382$	4.80965	−	15.5925i	0.246083	−	0.797782i
$383$	−0.234813	+	0.187257i	−0.0119984	+	0.00956840i	−0.629471	−	0.777024i	$-0.716728\pi$
$383$	−0.234813	+	0.187257i	−0.0119984	+	0.00956840i	0.617472	+	0.786593i	$0.288157\pi$
$384$	−1.60065	−	0.119952i	−0.0816829	−	0.00612128i
$385$	−0.464413	−	0.788986i	−0.0236687	−	0.0402105i
$386$		−	10.1014i		−	0.514148i
$387$	−2.74707	+	0.408481i	−0.139641	+	0.0207643i
$388$	15.6450			0.794255
$389$	5.75626	−	11.9530i	0.291854	−	0.606041i	−0.702556	−	0.711628i	$-0.747958\pi$
$389$	5.75626	−	11.9530i	0.291854	−	0.606041i	0.994410	+	0.105587i	$0.0336723\pi$
$390$	26.6836	+	1.99966i	1.35118	+	0.101257i
$391$	21.2769	−	16.9678i	1.07602	−	0.858098i
$392$	−6.67947	−	2.06034i	−0.337364	−	0.104063i
$393$	−15.4536	−	8.92212i	−0.779529	−	0.450061i
$394$	−11.8071	+	6.81681i	−0.594831	+	0.343426i
$395$	−4.69657	−	20.5770i	−0.236310	−	1.03534i
$396$	0.946737	−	1.03771i	0.0475753	−	0.0521468i
$397$	−2.50080	−	2.32041i	−0.125512	−	0.116458i	0.614920	−	0.788590i	$-0.289188\pi$
$397$	−2.50080	−	2.32041i	−0.125512	−	0.116458i	−0.740432	+	0.672132i	$0.765379\pi$
$398$	−14.1581	−	11.2907i	−0.709681	−	0.565952i
$399$	0.622585	+	0.913164i	0.0311682	+	0.0457154i
$400$	1.93011	−	1.79088i	0.0965057	−	0.0895442i
$401$	−0.923372	−	12.3215i	−0.0461110	−	0.615308i	−0.971615	−	0.236569i	$-0.923977\pi$
$401$	−0.923372	−	12.3215i	−0.0461110	−	0.615308i	0.925504	−	0.378739i	$-0.123642\pi$
$402$	6.88149	+	2.70079i	0.343218	+	0.134703i
$403$	−51.3358	−	11.7171i	−2.55722	−	0.583669i
$404$	1.71691	+	5.56608i	0.0854195	+	0.276923i
$405$	−11.7504	+	17.2346i	−0.583880	+	0.856395i
$406$	−0.347264	+	0.0523417i	−0.0172344	+	0.00259767i
$407$	−0.0959980	+	0.437525i	−0.00475844	+	0.0216873i
$408$	10.5283	−	5.07018i	0.521230	−	0.251011i
$409$	9.96160	−	4.79725i	0.492569	−	0.237209i	−0.171074	−	0.985258i	$-0.554724\pi$
$409$	9.96160	−	4.79725i	0.492569	−	0.237209i	0.663643	+	0.748049i	$0.269009\pi$
$410$	0.998756	+	2.54479i	0.0493250	+	0.125678i
$411$	−21.7437	+	3.27733i	−1.07254	+	0.161659i
$412$	3.48062	+	2.37305i	0.171478	+	0.116912i
$413$	−1.17105	+	0.361222i	−0.0576238	+	0.0177746i
$414$	−0.352301	+	1.54353i	−0.0173146	+	0.0758603i
$415$	5.71420	−	14.5595i	0.280499	−	0.714699i
$416$	6.01706	−	0.450916i	0.295011	−	0.0221080i
$417$	−5.40695	+	5.01692i	−0.264780	+	0.245680i
$418$	−0.192232	−	22.8553i	−0.00940240	−	1.11789i
$419$	−24.4012	−	19.4593i	−1.19208	−	0.950650i	−0.192547	−	0.981288i	$-0.561675\pi$
$419$	−24.4012	−	19.4593i	−1.19208	−	0.950650i	−0.999531	+	0.0306375i	$0.990246\pi$
$420$	0.324802	+	0.301372i	0.0158487	+	0.0147055i
$421$	−0.351706	+	2.33341i	−0.0171411	+	0.113724i	−0.995765	−	0.0919338i	$-0.970695\pi$
$421$	−0.351706	+	2.33341i	−0.0171411	+	0.113724i	0.978624	+	0.205657i	$0.0659333\pi$
$422$	5.24513	+	22.9804i	0.255329	+	1.11867i
$423$	1.44013	+	2.49438i	0.0700215	+	0.121281i
$424$	−3.97167	+	6.87913i	−0.192881	+	0.334080i
$425$	−5.64998	+	18.3168i	−0.274064	+	0.888495i
$426$	11.6819	+	14.6486i	0.565988	+	0.709726i
$427$	0.0397897	−	0.530956i	0.00192556	−	0.0256948i
$428$	0.762601	−	1.58356i	0.0368617	−	0.0765442i
$429$	17.8714	−	26.6921i	0.862839	−	1.28871i
$430$	−7.89295	+	16.3070i	−0.380632	+	0.786395i
$431$			6.20454i			0.298862i	0.988772	+	0.149431i	$0.0477443\pi$
$431$			6.20454i			0.298862i	−0.988772	+	0.149431i	$0.952256\pi$
$432$	−2.38430	+	4.95104i	−0.114714	+	0.238207i
$433$	4.98234	+	0.373375i	0.239436	+	0.0179432i	0.193908	−	0.981020i	$-0.437884\pi$
$433$	4.98234	+	0.373375i	0.239436	+	0.0179432i	0.0455283	+	0.998963i	$0.485503\pi$
$434$	−0.543628	−	0.681687i	−0.0260950	−	0.0327220i
$435$	−14.8949	−	4.59446i	−0.714155	−	0.220288i
$436$	−13.6332	−	7.87113i	−0.652911	−	0.376959i
$437$	12.8806	+	22.3098i	0.616161	+	1.06722i
$438$	12.0055	−	2.74018i	0.573645	−	0.130931i
$439$	0.718854	−	4.76928i	0.0343090	−	0.227626i	−0.965105	−	0.261865i	$-0.915663\pi$
$439$	0.718854	−	4.76928i	0.0343090	−	0.227626i	0.999414	+	0.0342390i	$0.0109007\pi$
$440$	−2.11405	−	8.91592i	−0.100783	−	0.425050i
$441$	−1.84583	+	2.31460i	−0.0878966	+	0.110219i
$442$	−36.2947	+	24.7453i	−1.72636	+	1.17701i
$443$	−20.3989	+	18.9274i	−0.969180	+	0.899267i	−0.994947	−	0.100401i	$-0.967988\pi$
$443$	−20.3989	+	18.9274i	−0.969180	+	0.899267i	0.0257675	+	0.999668i	$0.491797\pi$
$444$	−0.0162004	−	0.216179i	−0.000768835	−	0.0102594i
$445$	−9.18803	+	23.4107i	−0.435554	+	1.10977i
$446$	2.65983	+	0.607088i	0.125946	+	0.0287465i
$447$	3.65627	+	11.8533i	0.172935	+	0.560643i
$448$	0.0825525	+	0.0562833i	0.00390024	+	0.00265914i
$449$	2.86508	+	19.0085i	0.135211	+	0.897068i	0.948857	+	0.315707i	$0.102242\pi$
$449$	2.86508	+	19.0085i	0.135211	+	0.897068i	−0.813645	+	0.581361i	$0.802520\pi$
$450$	−0.407409	−	1.03806i	−0.0192054	−	0.0489347i
$451$	3.24913	+	0.461814i	0.152995	+	0.0217460i
$452$	−5.81248	−	12.0697i	−0.273396	−	0.567713i
$453$	21.5834	−	8.47084i	1.01407	−	0.397995i
$454$	−13.1907	+	1.98817i	−0.619068	+	0.0933096i
$455$	−1.37619	−	0.938269i	−0.0645167	−	0.0439867i
$456$	3.26047	+	10.5702i	0.152685	+	0.494994i
$457$	4.38366	−	19.2061i	0.205059	−	0.898422i	−0.762742	−	0.646703i	$-0.776147\pi$
$457$	4.38366	−	19.2061i	0.205059	−	0.898422i	0.967801	−	0.251718i	$-0.0809957\pi$
$458$	5.90497	−	15.0456i	0.275921	−	0.703036i
$459$	−2.98964	−	39.8940i	−0.139545	−	1.86209i
$460$	7.02466	+	7.57078i	0.327526	+	0.352989i
$461$	3.85960	+	5.66099i	0.179759	+	0.263659i	0.905534	−	0.424274i	$-0.139471\pi$
$461$	3.85960	+	5.66099i	0.179759	+	0.263659i	−0.725774	+	0.687933i	$0.758518\pi$
$462$	0.506937	−	0.161051i	0.0235848	−	0.00749276i
$463$	14.5244	−	15.6535i	0.675004	−	0.727482i	−0.298939	−	0.954272i	$-0.596633\pi$
$463$	14.5244	−	15.6535i	0.675004	−	0.727482i	0.973944	+	0.226790i	$0.0728233\pi$
$464$	−3.47565	−	0.523869i	−0.161353	−	0.0243200i
$465$	−8.61149	−	37.7294i	−0.399348	−	1.74966i
$466$	−14.4845	−	25.0880i	−0.670984	−	1.16218i
$467$	−3.77736	−	2.18086i	−0.174795	−	0.100918i	0.410050	−	0.912063i	$-0.365511\pi$
$467$	−3.77736	−	2.18086i	−0.174795	−	0.100918i	−0.584845	+	0.811145i	$0.698845\pi$
$468$	0.753261	−	2.44201i	0.0348195	−	0.112882i
$469$	−0.286902	−	0.359763i	−0.0132479	−	0.0166123i
$470$	18.7361	+	1.40407i	0.864231	+	0.0647651i
$471$	−12.7728	−	6.15107i	−0.588541	−	0.283427i
$472$	−12.2656			−0.564570
$473$	12.3666	+	17.8904i	0.568618	+	0.822602i
$474$	12.2624			0.563230
$475$	−16.3480	−	7.87277i	−0.750096	−	0.361227i
$476$	−0.725347	−	0.0543572i	−0.0332462	−	0.00249146i
$477$	2.09757	+	2.63027i	0.0960411	+	0.120432i
$478$	−0.0269742	+	0.0874482i	−0.00123377	+	0.00399979i
$479$	−23.3821	−	13.4997i	−1.06836	−	0.616816i	−0.140625	−	0.990063i	$-0.544911\pi$
$479$	−23.3821	−	13.4997i	−1.06836	−	0.616816i	−0.927732	+	0.373247i	$0.878244\pi$
$480$	2.21733	+	3.84052i	0.101207	+	0.175295i
$481$	0.181338	+	0.794492i	0.00826828	+	0.0362257i
$482$	22.0723	+	3.32686i	1.00536	+	0.151534i
$483$	−0.407770	+	0.439471i	−0.0185542	+	0.0199966i
$484$	−10.5644	−	3.06504i	−0.480198	−	0.139320i
$485$	−24.3488	−	35.7132i	−1.10562	−	1.62165i
$486$	2.97022	+	3.20114i	0.134732	+	0.145207i
$487$	−1.53625	−	20.4999i	−0.0696142	−	0.928937i	−0.917238	−	0.398340i	$-0.869587\pi$
$487$	−1.53625	−	20.4999i	−0.0696142	−	0.928937i	0.847624	−	0.530598i	$-0.178033\pi$
$488$	1.94692	−	4.96068i	0.0881331	−	0.224559i
$489$	0.815102	−	3.57119i	0.0368602	−	0.161495i
$490$	5.69229	+	18.4539i	0.257151	+	0.833664i
$491$	25.8775	+	17.6430i	1.16784	+	0.796218i	0.982464	−	0.186450i	$-0.0596984\pi$
$491$	25.8775	+	17.6430i	1.16784	+	0.796218i	0.185373	+	0.982668i	$0.440651\pi$
$492$	−1.57054	+	0.236720i	−0.0708053	+	0.0106722i
$493$	23.8200	−	9.34866i	1.07280	−	0.421042i
$494$	−18.0418	−	37.4642i	−0.811739	−	1.68559i
$495$	−3.84224	−	0.546115i	−0.172696	−	0.0245461i
$496$	−3.18820	−	8.12341i	−0.143155	−	0.364752i
$497$	−0.173822	−	1.15323i	−0.00779697	−	0.0517295i
$498$	7.50806	+	5.11891i	0.336444	+	0.229384i
$499$	−2.19064	−	7.10187i	−0.0980663	−	0.317923i	0.893225	−	0.449610i	$-0.148437\pi$
$499$	−2.19064	−	7.10187i	−0.0980663	−	0.317923i	−0.991291	+	0.131687i	$0.957961\pi$
$500$	6.37560	+	1.45519i	0.285125	+	0.0650780i
$501$	2.88045	−	7.33927i	0.128689	−	0.327894i
$502$	1.01359	+	13.5254i	0.0452387	+	0.603669i
$503$	−28.5559	+	26.4960i	−1.27325	+	1.18140i	−0.299416	+	0.954123i	$0.596792\pi$
$503$	−28.5559	+	26.4960i	−1.27325	+	1.18140i	−0.973830	+	0.227278i	$0.927018\pi$
$504$	0.0349634	−	0.0238377i	0.00155739	−	0.00106181i
$505$	10.0337	−	12.5819i	0.446495	−	0.559887i
$506$	12.0636	−	2.86040i	0.536293	−	0.127160i
$507$	5.60006	−	37.1540i	0.248707	−	1.65007i
$508$	−2.28835	+	0.522300i	−0.101529	+	0.0231733i
$509$	19.3897	+	33.5839i	0.859431	+	1.48858i	0.872472	+	0.488664i	$0.162516\pi$
$509$	19.3897	+	33.5839i	0.859431	+	1.48858i	−0.0130407	+	0.999915i	$0.504151\pi$
$510$	−27.9594	−	16.1424i	−1.23806	−	0.714796i
$511$	−0.732459	−	0.225934i	−0.0324021	−	0.00999472i
$512$	0.623490	+	0.781831i	0.0275546	+	0.0345524i
$513$	37.7639	+	2.83001i	1.66732	+	0.124948i
$514$	−10.4767	+	21.7551i	−0.462107	+	0.959574i
$515$		−	11.6385i		−	0.512855i
$516$	−8.21621	−	6.57892i	−0.361698	−	0.289621i
$517$	12.5485	−	18.7421i	0.551884	−	0.824275i
$518$	−0.00585483	+	0.0121577i	−0.000257247	+	0.000534178i
$519$	−0.340320	+	4.54125i	−0.0149384	+	0.199339i
$520$	−10.3939	−	13.0335i	−0.455801	−	0.571556i
$521$	−5.80194	+	18.8094i	−0.254188	+	0.824056i	0.735085	+	0.677975i	$0.237142\pi$
$521$	−5.80194	+	18.8094i	−0.254188	+	0.824056i	−0.989273	+	0.146081i	$0.953334\pi$
$522$	−0.744333	+	1.28922i	−0.0325786	+	0.0564278i
$523$	4.20643	+	7.28575i	0.183934	+	0.318583i	0.943217	−	0.332178i	$-0.107783\pi$
$523$	4.20643	+	7.28575i	0.183934	+	0.318583i	−0.759283	+	0.650761i	$0.774450\pi$
$524$	2.47375	+	10.8382i	0.108066	+	0.473470i
$525$	0.0629354	−	0.417549i	0.00274672	−	0.0182233i
$526$	−11.0379	−	10.2416i	−0.481274	−	0.446557i
$527$	49.6704	+	39.6109i	2.16368	+	1.72548i
$528$	5.32345	−	0.0447748i	0.231674	−	0.00194857i
$529$	6.61661	−	6.13931i	0.287679	−	0.266927i
$530$	21.8844	−	1.64001i	0.950596	−	0.0712373i
$531$	−1.89789	+	4.83574i	−0.0823614	+	0.209853i
$532$	0.153215	−	0.671279i	0.00664271	−	0.0291036i
$533$	5.70529	−	1.75985i	0.247124	−	0.0762276i
$534$	−12.0724	−	8.23084i	−0.522425	−	0.356183i
$535$	−4.80168	+	0.723737i	−0.207595	+	0.0312899i
$536$	−1.68259	−	4.28716i	−0.0726767	−	0.185177i
$537$	31.5282	−	15.1832i	1.36054	−	0.655202i
$538$	−3.78949	+	1.82492i	−0.163376	+	0.0786779i
$539$	22.6446	+	4.96848i	0.975372	+	0.214008i
$540$	15.0126	−	2.26278i	0.646039	−	0.0973748i
$541$	−4.28167	+	6.28006i	−0.184083	+	0.270001i	−0.907177	−	0.420749i	$-0.861767\pi$
$541$	−4.28167	+	6.28006i	−0.184083	+	0.270001i	0.723093	+	0.690750i	$0.242720\pi$
$542$	−4.74910	−	15.3962i	−0.203991	−	0.661323i
$543$	28.4978	+	6.50445i	1.22296	+	0.279133i
$544$	−6.77685	−	2.65972i	−0.290555	−	0.114035i
$545$	3.25020	+	43.3709i	0.139223	+	1.85780i
$546$	0.709369	−	0.658198i	0.0303582	−	0.0281683i
$547$	12.3588	+	18.1270i	0.528422	+	0.775053i	0.993933	−	0.109989i	$-0.0350816\pi$
$547$	12.3588	+	18.1270i	0.528422	+	0.775053i	−0.465510	+	0.885042i	$0.654129\pi$
$548$	10.7105	+	8.54137i	0.457532	+	0.364869i
$549$	−1.65451	−	1.53516i	−0.0706127	−	0.0655190i
$550$	−5.88564	+	6.45119i	−0.250965	+	0.275080i
$551$	5.39002	+	23.6152i	0.229623	+	1.00604i
$552$	−5.19639	+	3.00014i	−0.221173	+	0.127694i
$553$	−0.661025	−	0.381643i	−0.0281096	−	0.0162291i
$554$	−6.09163	−	1.87902i	−0.258808	−	0.0798318i
$555$	−0.468263	+	0.373427i	−0.0198766	+	0.0158511i
$556$	4.58236	+	0.343400i	0.194335	+	0.0145634i
$557$	20.2454	−	42.0400i	0.857825	−	1.78129i	0.292914	−	0.956139i	$-0.405375\pi$
$557$	20.2454	−	42.0400i	0.857825	−	1.78129i	0.564910	−	0.825152i	$-0.308911\pi$
$558$	−3.69599			−0.156464
$559$	34.2268	+	19.8515i	1.44764	+	0.839630i
$560$		−	0.276040i		−	0.0116648i
$561$	−33.4001	+	19.6599i	−1.41015	+	0.830043i
$562$	−8.86946	−	0.664674i	−0.374135	−	0.0280376i
$563$	−29.2750	+	23.3460i	−1.23379	+	0.983917i	−0.233861	+	0.972270i	$0.575136\pi$
$563$	−29.2750	+	23.3460i	−1.23379	+	0.983917i	−0.999932	+	0.0116472i	$0.996292\pi$
$564$	−3.21752	+	10.4310i	−0.135482	+	0.439222i
$565$	−18.5057	+	32.0528i	−0.778540	+	1.34847i
$566$	1.91944	−	1.10819i	0.0806800	−	0.0465806i
$567$	0.167859	+	0.735438i	0.00704941	+	0.0308855i
$568$	1.73972	−	11.5423i	0.0729970	−	0.484304i
$569$	4.38878	−	4.72998i	0.183987	−	0.198291i	−0.634323	−	0.773068i	$-0.718721\pi$
$569$	4.38878	−	4.72998i	0.183987	−	0.198291i	0.818310	+	0.574777i	$0.194911\pi$
$570$	19.0544	−	23.8934i	0.798101	−	1.00079i
$571$	31.8994	−	21.7486i	1.33495	−	0.910151i	0.335456	−	0.942056i	$-0.391110\pi$
$571$	31.8994	−	21.7486i	1.33495	−	0.910151i	0.999491	+	0.0319050i	$0.0101574\pi$
$572$	−19.7630	+	3.14901i	−0.826332	+	0.131667i
$573$	−1.95731	−	26.1185i	−0.0817680	−	1.09112i
$574$	0.0920299	+	0.0361191i	0.00384126	+	0.00150758i
$575$	2.19017	−	9.59576i	0.0913364	−	0.400171i
$576$	0.404713	−	0.124838i	0.0168631	−	0.00520156i
$577$	−12.0050	+	17.6080i	−0.499773	+	0.733032i	−0.990384	−	0.138346i	$-0.955821\pi$
$577$	−12.0050	+	17.6080i	−0.499773	+	0.733032i	0.490611	+	0.871379i	$0.336774\pi$
$578$	35.5978	−	5.36550i	1.48067	−	0.223175i
$579$	−5.92369	−	15.0933i	−0.246180	−	0.627257i
$580$	4.21341	+	8.74924i	0.174953	+	0.363293i
$581$	−0.245419	−	0.509617i	−0.0101817	−	0.0211425i
$582$	23.3765	−	9.17459i	0.968986	−	0.380299i
$583$	11.2307	−	23.8314i	0.465126	−	0.986995i
$584$	−6.33870	−	4.32166i	−0.262297	−	0.178831i
$585$	−6.74676	+	2.08110i	−0.278944	+	0.0860429i
$586$	−14.3986	−	3.28638i	−0.594800	−	0.135759i
$587$	21.5427	+	8.45488i	0.889162	+	0.348970i	0.765562	−	0.643362i	$-0.222461\pi$
$587$	21.5427	+	8.45488i	0.889162	+	0.348970i	0.123600	+	0.992332i	$0.460556\pi$
$588$	−11.1886	+	0.838468i	−0.461409	+	0.0345778i
$589$	−44.0847	+	40.9047i	−1.81648	+	1.68545i
$590$	19.0893	+	27.9989i	0.785896	+	1.15270i
$591$	−13.6443	+	17.1095i	−0.561254	+	0.703790i
$592$	−0.0918620	+	0.0990037i	−0.00377550	+	0.00406903i
$593$	18.1069	+	2.72918i	0.743562	+	0.112074i	0.509888	−	0.860241i	$-0.329687\pi$
$593$	18.1069	+	2.72918i	0.743562	+	0.112074i	0.233674	+	0.972315i	$0.424925\pi$
$594$	6.51565	−	17.0212i	0.267340	−	0.698388i
$595$	1.00480	+	1.74036i	0.0411927	+	0.0713479i
$596$	3.86397	−	6.69259i	0.158274	−	0.274139i
$597$	−27.7759	−	8.56773i	−1.13679	−	0.350654i
$598$	17.6349	−	14.0633i	0.721143	−	0.575093i
$599$	0.610676	−	8.14890i	0.0249515	−	0.332955i	−0.970734	−	0.240159i	$-0.922800\pi$
$599$	0.610676	−	8.14890i	0.0249515	−	0.332955i	0.995685	−	0.0927963i	$-0.0295805\pi$
$600$	1.83372	−	3.80777i	0.0748615	−	0.155451i
$601$	36.3283			1.48186			0.740930	−	0.671582i	$-0.234385\pi$
$601$	36.3283			1.48186			0.740930	+	0.671582i	$0.234385\pi$
$602$	0.238153	+	0.610361i	0.00970638	+	0.0248765i
$603$	−1.95058			−0.0794336
$604$	−13.0144	−	6.26742i	−0.529550	−	0.255018i
$605$	9.44501	+	28.8857i	0.383994	+	1.17437i
$606$	5.82946	+	7.30991i	0.236805	+	0.296945i
$607$	15.6396	+	4.82418i	0.634793	+	0.195808i	0.595417	−	0.803417i	$-0.296987\pi$
$607$	15.6396	+	4.82418i	0.634793	+	0.195808i	0.0393757	+	0.999224i	$0.487463\pi$
$608$	3.44569	−	5.96811i	0.139741	−	0.242039i
$609$	−0.488182	+	0.281852i	−0.0197821	+	0.0114212i
$610$	−14.3539	+	3.27618i	−0.581172	+	0.132649i
$611$	6.11586	−	40.5761i	0.247421	−	1.64153i
$612$	−2.09720	+	2.26025i	−0.0847744	+	0.0913651i
$613$	−23.0061	−	18.3468i	−0.929209	−	0.741019i	0.0368557	−	0.999321i	$-0.488266\pi$
$613$	−23.0061	−	18.3468i	−0.929209	−	0.741019i	−0.966064	+	0.258301i	$0.916837\pi$
$614$	0.100565	+	0.147502i	0.00405847	+	0.00595269i
$615$	2.98465	+	3.21668i	0.120353	+	0.129709i
$616$	−0.288363	−	0.163268i	−0.0116185	−	0.00657827i
$617$	13.6654	−	34.8188i	0.550148	−	1.40175i	−0.337541	−	0.941311i	$-0.609595\pi$
$617$	13.6654	−	34.8188i	0.550148	−	1.40175i	0.887689	−	0.460443i	$-0.152310\pi$
$618$	6.59229	+	1.50465i	0.265181	+	0.0605257i
$619$	−37.4946	+	11.5655i	−1.50703	+	0.464858i	−0.934783	−	0.355220i	$-0.884406\pi$
$619$	−37.4946	+	11.5655i	−1.50703	+	0.464858i	−0.572251	+	0.820078i	$0.693930\pi$
$620$	−13.5816	+	19.9205i	−0.545449	+	0.800027i
$621$	3.06164	+	20.3127i	0.122860	+	0.815120i
$622$	−8.70650	−	22.1838i	−0.349099	−	0.889490i
$623$	0.394616	+	0.819428i	0.0158100	+	0.0328297i
$624$	8.72615	−	4.20229i	0.349326	−	0.168226i
$625$	−11.4104	−	29.0733i	−0.456418	−	1.16293i
$626$	2.11408	+	14.0260i	0.0844958	+	0.560593i
$627$	−13.6901	−	34.0372i	−0.546730	−	1.35932i
$628$	2.60331	+	8.43973i	0.103884	+	0.336782i
$629$	0.218789	−	0.958576i	0.00872367	−	0.0382209i
$630$	−0.108829	−	0.0427124i	−0.00433587	−	0.00170170i
$631$	−34.1579	+	2.55978i	−1.35980	+	0.101903i	−0.734569	−	0.678534i	$-0.762616\pi$
$631$	−34.1579	+	2.55978i	−1.35980	+	0.101903i	−0.625234	+	0.780437i	$0.714997\pi$
$632$	−5.19615	−	5.60012i	−0.206692	−	0.222761i
$633$	21.3134	+	31.2611i	0.847133	+	1.24252i
$634$	9.96512	−	12.4959i	0.395765	−	0.496274i
$635$	4.75369	+	4.41078i	0.188645	+	0.175037i
$636$	−1.90031	+	12.6077i	−0.0753523	+	0.499930i
$637$	41.1198	−	9.38533i	1.62923	−	0.371860i
$638$	11.6319	+	0.773371i	0.460513	+	0.0306181i
$639$	−4.28139	−	2.47186i	−0.169369	−	0.0977853i
$640$	0.814345	−	2.64004i	0.0321898	−	0.104357i
$641$	18.6148	−	14.8448i	0.735240	−	0.586334i	−0.182646	−	0.983179i	$-0.558466\pi$
$641$	18.6148	−	14.8448i	0.735240	−	0.586334i	0.917886	+	0.396844i	$0.129895\pi$
$642$	0.210830	−	2.81333i	0.00832080	−	0.111033i
$643$	39.7126	+	19.1246i	1.56611	+	0.754200i	0.997651	−	0.0685090i	$-0.0218242\pi$
$643$	39.7126	+	19.1246i	1.56611	+	0.754200i	0.568462	+	0.822709i	$0.307538\pi$
$644$	0.373494			0.0147177
$645$	−2.23068	+	28.9943i	−0.0878329	+	1.14165i
$646$			50.1699i			1.97391i
$647$	−7.69730	+	15.9836i	−0.302612	+	0.628380i	−0.995717	−	0.0924566i	$-0.970528\pi$
$647$	−7.69730	+	15.9836i	−0.302612	+	0.628380i	0.693105	+	0.720837i	$0.256242\pi$
$648$	−0.564215	+	7.52892i	−0.0221644	+	0.295764i
$649$	40.5396	−	3.38113i	1.59132	−	0.132721i
$650$	−4.68285	+	15.1814i	−0.183676	+	0.595464i
$651$	−1.21204	−	0.699769i	−0.0475034	−	0.0274261i
$652$	−1.97633	+	1.14103i	−0.0773990	+	0.0446863i
$653$	−31.0323	+	7.08291i	−1.21439	+	0.277176i	−0.781288	−	0.624171i	$-0.785437\pi$
$653$	−31.0323	+	7.08291i	−1.21439	+	0.277176i	−0.433098	+	0.901347i	$0.642580\pi$
$654$	−24.9863	−	3.76607i	−0.977041	−	0.147265i
$655$	20.8906	−	22.5148i	0.816265	−	0.879725i
$656$	0.773619	+	0.616940i	0.0302047	+	0.0240875i
$657$	−2.68463	+	1.83035i	−0.104737	+	0.0714087i
$658$	0.498089	−	0.462159i	0.0194175	−	0.0180168i
$659$	−37.9265	+	2.84220i	−1.47741	+	0.110716i	−0.788904	−	0.614516i	$-0.789351\pi$
$659$	−37.9265	+	2.84220i	−1.47741	+	0.110716i	−0.688504	+	0.725232i	$0.741732\pi$
$660$	−8.38727	−	12.0823i	−0.326474	−	0.470302i
$661$	−3.05058	+	13.3655i	−0.118654	+	0.519857i	0.880312	+	0.474395i	$0.157333\pi$
$661$	−3.05058	+	13.3655i	−0.118654	+	0.519857i	−0.998966	+	0.0454618i	$0.985524\pi$
$662$	−4.26731	−	13.8343i	−0.165854	−	0.537685i
$663$	−39.7197	+	58.2580i	−1.54258	+	2.26255i
$664$	−0.843760	−	5.59798i	−0.0327442	−	0.217244i
$665$	−1.77080	+	0.694986i	−0.0686685	+	0.0269504i
$666$	0.0248184	+	0.0515359i	0.000961693	+	0.00199698i
$667$	−11.8381	+	5.70093i	−0.458373	+	0.220741i
$668$	−4.57236	+	1.79452i	−0.176910	+	0.0694320i
$669$	4.33027	−	0.652684i	0.167418	−	0.0252342i
$670$	−7.16773	+	10.5131i	−0.276914	+	0.406158i
$671$	−5.06741	+	16.9325i	−0.195625	+	0.653671i
$672$	0.156354	+	0.0356868i	0.00603150	+	0.00137665i
$673$	10.9026	−	27.7794i	0.420264	−	1.07082i	−0.551356	−	0.834270i	$-0.685890\pi$
$673$	10.9026	−	27.7794i	0.420264	−	1.07082i	0.971620	−	0.236546i	$-0.0760152\pi$
$674$	31.0270	−	2.32515i	1.19512	−	0.0895616i
$675$	−9.84134	−	10.6064i	−0.378793	−	0.408242i
$676$	−19.3409	+	13.1864i	−0.743880	+	0.507169i
$677$	6.33957	−	7.94957i	0.243650	−	0.305527i	−0.644937	−	0.764236i	$-0.723116\pi$
$677$	6.33957	−	7.94957i	0.243650	−	0.305527i	0.888587	+	0.458709i	$0.151688\pi$
$678$	−15.7629	−	14.6258i	−0.605369	−	0.561701i
$679$	−1.54569	−	0.232975i	−0.0593181	−	0.00894077i
$680$	4.47564	+	19.6091i	0.171633	+	0.751973i
$681$	−18.5433	+	10.7060i	−0.710582	+	0.410255i
$682$	12.7768	+	25.9702i	0.489248	+	0.994451i
$683$	−23.0731	−	7.11712i	−0.882869	−	0.272329i	−0.180016	−	0.983664i	$-0.557615\pi$
$683$	−23.0731	−	7.11712i	−0.882869	−	0.272329i	−0.702853	+	0.711335i	$0.748091\pi$
$684$	−1.81978	−	2.28193i	−0.0695811	−	0.0872519i
$685$	2.82840	−	37.7424i	0.108068	−	1.44206i
$686$	1.25937	+	0.606480i	0.0480829	+	0.0231555i
$687$		−	25.9437i		−	0.989814i
$688$	0.477063	+	6.54006i	0.0181879	+	0.249338i
$689$		−	47.9296i		−	1.82597i
$690$	14.9358	+	7.19270i	0.568596	+	0.273821i
$691$	−2.88953	−	0.216540i	−0.109923	−	0.00823757i	0.0196551	−	0.999807i	$-0.493743\pi$
$691$	−2.88953	−	0.216540i	−0.109923	−	0.00823757i	−0.129578	+	0.991569i	$0.541362\pi$
$692$	2.21816	−	1.76892i	0.0843216	−	0.0672442i
$693$	−0.108988	+	0.0884250i	−0.00414012	+	0.00335899i
$694$	6.21787	−	10.7697i	0.236027	−	0.408811i
$695$	−6.34779	−	10.9947i	−0.240785	−	0.417052i
$696$	−5.50046	+	1.25544i	−0.208494	+	0.0475875i
$697$	−7.12317	−	1.07364i	−0.269809	−	0.0406672i
$698$	0.774173	+	0.718328i	0.0293029	+	0.0271891i
$699$	−36.3547	−	28.9919i	−1.37506	−	1.09657i
$700$	−0.217359	+	0.148193i	−0.00821541	+	0.00560117i
$701$	−33.4741	−	36.0766i	−1.26430	−	1.36259i	−0.902706	−	0.430257i	$-0.858423\pi$
$701$	−33.4741	−	36.0766i	−1.26430	−	1.36259i	−0.361595	−	0.932335i	$-0.617768\pi$
$702$	−2.47789	−	33.0652i	−0.0935221	−	1.24797i
$703$	0.866390	+	0.340033i	0.0326765	+	0.0128246i
$704$	−2.27625	−	2.41220i	−0.0857893	−	0.0909132i
$705$	28.8185	−	8.88932i	1.08537	−	0.334791i
$706$	9.41361	+	6.41809i	0.354286	+	0.241548i
$707$	−0.0867401	−	0.575483i	−0.00326220	−	0.0216433i
$708$	−18.3270	+	7.19283i	−0.688772	+	0.270323i
$709$	33.8122	−	16.2831i	1.26984	−	0.611524i	0.327083	−	0.944996i	$-0.393934\pi$
$709$	33.8122	−	16.2831i	1.26984	−	0.611524i	0.942760	+	0.333471i	$0.108220\pi$
$710$	−29.0554	+	13.9923i	−1.09043	+	0.525123i
$711$	−3.01188	+	1.18207i	−0.112954	+	0.0443313i
$712$	1.35671	+	9.00116i	0.0508447	+	0.337333i
$713$	−26.9533	−	18.3764i	−1.00941	−	0.688203i
$714$	−1.11568	+	0.344141i	−0.0417531	+	0.0128791i
$715$	37.9461	+	40.2125i	1.41910	+	1.50386i
$716$	−20.2940	−	7.96480i	−0.758422	−	0.297659i
$717$	0.0109773	+	0.146482i	0.000409954	+	0.00547046i
$718$	−6.56536	−	7.07577i	−0.245017	−	0.264066i
$719$	−32.7993	+	22.3622i	−1.22321	+	0.833968i	−0.990356	−	0.138545i	$-0.955757\pi$
$719$	−32.7993	+	22.3622i	−1.22321	+	0.833968i	−0.232850	+	0.972513i	$0.574805\pi$
$720$	−0.914838	−	0.729559i	−0.0340940	−	0.0271891i
$721$	−0.308539	−	0.286282i	−0.0114906	−	0.0106617i
$722$	−28.1728	−	4.24637i	−1.04848	−	0.158034i
$723$	34.9309	−	7.97275i	1.29909	−	0.296510i
$724$	−9.10536	−	15.7709i	−0.338398	−	0.586122i
$725$	4.62734	−	8.01479i	0.171855	−	0.297662i
$726$	−17.5825	+	1.61545i	−0.652547	+	0.0599549i
$727$	3.50757	−	2.79720i	0.130089	−	0.103742i	−0.556284	−	0.830992i	$-0.687773\pi$
$727$	3.50757	−	2.79720i	0.130089	−	0.103742i	0.686373	+	0.727250i	$0.259202\pi$
$728$	−0.601186	−	0.0450527i	−0.0222814	−	0.00166976i
$729$	26.7223	+	12.8688i	0.989715	+	0.476622i
$730$			21.1954i			0.784478i
$731$	−26.8139	−	39.4969i	−0.991748	−	1.46085i
$732$		−	8.55387i		−	0.316160i
$733$	−21.3045	−	10.2597i	−0.786898	−	0.378950i	−0.00312326	−	0.999995i	$-0.500994\pi$
$733$	−21.3045	−	10.2597i	−0.786898	−	0.378950i	−0.783775	+	0.621045i	$0.786708\pi$
$734$	−1.88499	+	25.1534i	−0.0695761	+	0.928429i
$735$	19.3271	+	24.2355i	0.712892	+	0.893938i
$736$	3.57209	+	1.10184i	0.131669	+	0.0406145i
$737$	6.74300	+	13.7059i	0.248382	+	0.504863i
$738$	0.362934	−	0.209540i	0.0133598	−	0.00771328i
$739$	−1.40429	−	6.15261i	−0.0516578	−	0.226328i	0.942509	−	0.334181i	$-0.108460\pi$
$739$	−1.40429	−	6.15261i	−0.0516578	−	0.226328i	−0.994167	+	0.107853i	$0.965602\pi$
$740$	0.368965	+	0.0556126i	0.0135634	+	0.00204436i
$741$	−48.9276	−	45.3982i	−1.79740	−	1.66774i
$742$	0.494831	−	0.620498i	0.0181658	−	0.0227792i
$743$	6.77338	−	4.61801i	0.248491	−	0.169418i	−0.432669	−	0.901553i	$-0.642428\pi$
$743$	6.77338	−	4.61801i	0.248491	−	0.169418i	0.681160	+	0.732134i	$0.261476\pi$
$744$	−9.52751	−	10.2682i	−0.349295	−	0.376451i
$745$	−21.2909	+	1.59554i	−0.780040	+	0.0584559i
$746$	−1.54944	+	3.94792i	−0.0567291	+	0.144544i
$747$	−2.33758	−	0.533537i	−0.0855275	−	0.0195211i
$748$	23.1317	+	6.92266i	0.845778	+	0.253118i
$749$	−0.0989246	+	0.145096i	−0.00361462	+	0.00530168i
$750$	10.3797	−	1.56448i	0.379011	−	0.0571268i
$751$	−31.5056	+	12.3650i	−1.14966	+	0.451207i	−0.862191	−	0.506584i	$-0.830908\pi$
$751$	−31.5056	+	12.3650i	−1.14966	+	0.451207i	−0.287466	+	0.957791i	$0.592813\pi$
$752$	6.12713	−	2.95067i	0.223434	−	0.107600i
$753$	9.44610	+	19.6150i	0.344235	+	0.714811i
$754$	19.7426	−	7.74841i	0.718984	−	0.282180i
$755$	5.94802	+	39.4625i	0.216470	+	1.43619i
$756$	0.309290	−	0.453646i	0.0112488	−	0.0164989i
$757$	−3.25841	−	10.5635i	−0.118429	−	0.383937i	0.876877	−	0.480715i	$-0.159623\pi$
$757$	−3.25841	−	10.5635i	−0.118429	−	0.383937i	−0.995306	+	0.0967775i	$0.969146\pi$
$758$	7.00728	−	30.7009i	0.254516	−	1.11511i
$759$	16.3478	−	11.3483i	0.593389	−	0.411919i
$760$	−18.9862	+	1.42282i	−0.688700	+	0.0516109i
$761$	22.4249	−	20.8073i	0.812902	−	0.754263i	−0.159594	−	0.987183i	$-0.551019\pi$
$761$	22.4249	−	20.8073i	0.812902	−	0.754263i	0.972496	+	0.232920i	$0.0748280\pi$
$762$	−3.11292	+	2.12235i	−0.112769	+	0.0768846i
$763$	1.22972	+	0.980665i	0.0445187	+	0.0355025i
$764$	−11.0987	+	11.9615i	−0.401536	+	0.432753i
$765$	8.42346	+	1.26963i	0.304551	+	0.0459036i
$766$	0.292807	−	0.0668314i	0.0105796	−	0.00241472i
$767$	64.0943	−	37.0049i	2.31431	−	1.33617i
$768$	1.39009	+	0.802569i	0.0501606	+	0.0289602i
$769$	0.0322332	−	0.104497i	0.00116236	−	0.00376827i	−0.954990	−	0.296639i	$-0.904134\pi$
$769$	0.0322332	−	0.104497i	0.00116236	−	0.00376827i	0.956152	+	0.292870i	$0.0946105\pi$
$770$	0.0760930	+	0.912353i	0.00274220	+	0.0328789i
$771$	−2.89640	+	38.6498i	−0.104311	+	1.39194i
$772$	−4.38283	+	9.10104i	−0.157742	+	0.327554i
$773$			18.4128i			0.662261i	0.943585	+	0.331130i	$0.107430\pi$
$773$			18.4128i			0.662261i	−0.943585	+	0.331130i	$0.892570\pi$
$774$	2.65225	+	0.823878i	0.0953333	+	0.0296137i
$775$	22.9771			0.825363
$776$	−14.0957	−	6.78811i	−0.506005	−	0.243679i
$777$	−0.00161864	+	0.0215992i	−5.80683e−5	+	0.000774867i
$778$	−10.3724	+	8.27173i	−0.371869	+	0.296556i
$779$	2.00993	−	6.51604i	0.0720132	−	0.233461i
$780$	−23.1735	−	13.3792i	−0.829743	−	0.479052i
$781$	−2.56829	+	38.6286i	−0.0919007	+	1.38224i
$782$	−26.5319	+	6.05573i	−0.948779	+	0.216553i
$783$	−2.87879	+	19.0995i	−0.102880	+	0.682561i
$784$	5.12405	+	4.75442i	0.183002	+	0.169801i
$785$	15.2139	−	19.0777i	0.543009	−	0.680911i
$786$	10.0520	+	14.7436i	0.358544	+	0.525887i
$787$	26.6165	+	28.6858i	0.948776	+	1.02254i	0.999716	+	0.0238359i	$0.00758793\pi$
$787$	26.6165	+	28.6858i	0.948776	+	1.02254i	−0.0509396	+	0.998702i	$0.516222\pi$
$788$	13.5955	−	1.01884i	0.484319	−	0.0362947i
$789$	−22.4985	−	8.83001i	−0.800968	−	0.314357i
$790$	−4.69657	+	20.5770i	−0.167096	+	0.732097i
$791$	0.394525	+	1.27902i	0.0140277	+	0.0454766i
$792$	−1.30323	+	0.524170i	−0.0463081	+	0.0186256i
$793$	4.79248	+	31.7960i	0.170186	+	1.12911i
$794$	1.24636	+	3.17567i	0.0442317	+	0.112700i
$795$	31.7375	−	15.2840i	1.12561	−	0.542066i
$796$	7.85715	+	16.3155i	0.278489	+	0.578289i
$797$	0.151918	+	0.387080i	0.00538120	+	0.0137111i	0.933539	−	0.358476i	$-0.116703\pi$
$797$	0.151918	+	0.387080i	0.00538120	+	0.0137111i	−0.928158	+	0.372187i	$0.878608\pi$
$798$	−0.164722	−	1.09286i	−0.00583111	−	0.0386869i
$799$	−27.8895	+	40.9063i	−0.986658	+	1.44716i
$800$	−2.51601	+	0.776086i	−0.0889543	+	0.0274388i
$801$	3.75866	+	0.857889i	0.132806	+	0.0303120i
$802$	−4.51419	+	11.5020i	−0.159401	+	0.406148i
$803$	22.1417	+	12.5364i	0.781363	+	0.442400i
$804$	−5.02818	−	5.41909i	−0.177330	−	0.191117i
$805$	−0.581280	−	0.852582i	−0.0204874	−	0.0300496i
$806$	41.1681	+	32.8305i	1.45009	+	1.15640i
$807$	−4.59200	+	4.94900i	−0.161646	+	0.174213i
$808$	0.868151	−	5.75981i	0.0305415	−	0.202629i
$809$	−48.6197	+	11.0971i	−1.70938	+	0.390154i	−0.961742	−	0.273955i	$-0.911668\pi$
$809$	−48.6197	+	11.0971i	−1.70938	+	0.390154i	−0.747635	+	0.664109i	$0.768811\pi$
$810$	18.0645	−	10.4296i	0.634723	−	0.366457i
$811$	−16.4478	+	28.4885i	−0.577562	+	1.00037i	0.418196	+	0.908357i	$0.362662\pi$
$811$	−16.4478	+	28.4885i	−0.577562	+	1.00037i	−0.995758	+	0.0920097i	$0.970671\pi$
$812$	0.335585	+	0.103514i	0.0117767	+	0.00363263i
$813$	−16.1247	−	20.2197i	−0.565518	−	0.709137i
$814$	0.276326	−	0.352545i	0.00968523	−	0.0123567i
$815$	5.68048	+	2.73558i	0.198979	+	0.0958231i
$816$	−11.6856			−0.409077
$817$	40.7534	−	19.5263i	1.42578	−	0.683138i
$818$	−11.0565			−0.386583
$819$	−0.110785	+	0.230048i	−0.00387115	+	0.00803853i
$820$	0.204294	−	2.72612i	0.00713427	−	0.0952002i
$821$	−14.6240	+	11.6623i	−0.510382	+	0.407016i	−0.844533	−	0.535503i	$-0.820122\pi$
$821$	−14.6240	+	11.6623i	−0.510382	+	0.407016i	0.334151	+	0.942520i	$0.391551\pi$
$822$	21.0123	+	6.48145i	0.732890	+	0.226067i
$823$	−19.0494	+	32.9946i	−0.664021	+	1.15012i	0.315528	+	0.948916i	$0.397818\pi$
$823$	−19.0494	+	32.9946i	−0.664021	+	1.15012i	−0.979550	+	0.201203i	$0.935515\pi$
$824$	−2.10630	−	3.64822i	−0.0733766	−	0.127092i
$825$	−5.01109	+	13.0907i	−0.174464	+	0.455761i
$826$	1.21181	+	0.182651i	0.0421643	+	0.00635525i
$827$	−1.06751	+	1.15050i	−0.0371209	+	0.0400068i	−0.751339	−	0.659916i	$-0.770592\pi$
$827$	−1.06751	+	1.15050i	−0.0371209	+	0.0400068i	0.714218	+	0.699923i	$0.246782\pi$
$828$	0.987124	−	1.23781i	0.0343049	−	0.0430170i
$829$	−5.75949	−	8.44762i	−0.200035	−	0.293398i	0.713094	−	0.701069i	$-0.247293\pi$
$829$	−5.75949	−	8.44762i	−0.200035	−	0.293398i	−0.913129	+	0.407671i	$0.866341\pi$
$830$	−11.4655	+	10.6384i	−0.397972	+	0.369264i
$831$	−10.2039	+	0.764676i	−0.353969	+	0.0265263i
$832$	−5.61683	−	2.20444i	−0.194729	−	0.0764253i
$833$	−49.6122	−	11.3236i	−1.71896	−	0.392341i
$834$	7.04825	−	2.17410i	0.244061	−	0.0752829i
$835$	11.2125	+	7.64455i	0.388024	+	0.264550i
$836$	−9.74335	+	20.6753i	−0.336981	+	0.715071i
$837$	−44.6401	+	17.5199i	−1.54299	+	0.605578i
$838$	13.5417	+	28.1195i	0.467789	+	0.971373i
$839$	−7.05233	−	14.6443i	−0.243473	−	0.505578i	0.743042	−	0.669244i	$-0.233382\pi$
$839$	−7.05233	−	14.6443i	−0.243473	−	0.505578i	−0.986516	+	0.163667i	$0.947668\pi$
$840$	−0.161876	−	0.412454i	−0.00558526	−	0.0142310i
$841$	16.4595	−	2.48087i	0.567570	−	0.0855474i
$842$	1.32931	−	1.94973i	0.0458109	−	0.0671923i
$843$	−13.6424	+	4.20811i	−0.469868	+	0.144935i
$844$	5.24513	−	22.9804i	0.180545	−	0.791019i
$845$	60.2017	+	23.6274i	2.07100	+	0.812808i
$846$	−0.215242	−	2.87220i	−0.00740017	−	0.0987484i
$847$	0.998090	+	0.460136i	0.0342948	+	0.0158105i
$848$	6.56309	−	4.47464i	0.225378	−	0.153660i
$849$	2.21812	−	2.78144i	0.0761258	−	0.0954587i
$850$	13.0378	−	14.0514i	0.447193	−	0.481960i
$851$	−0.0752462	+	0.499226i	−0.00257941	+	0.0171132i
$852$	−4.16921	−	18.2665i	−0.142835	−	0.625800i
$853$	−27.2983	+	15.7607i	−0.934675	+	0.539635i	−0.888287	−	0.459289i	$-0.848104\pi$
$853$	−27.2983	+	15.7607i	−0.934675	+	0.539635i	−0.0463876	+	0.998924i	$0.514771\pi$
$854$	−0.266223	+	0.461111i	−0.00910995	+	0.0157789i
$855$	−2.37683	+	7.70550i	−0.0812859	+	0.263522i
$856$	−1.37416	+	1.09586i	−0.0469678	+	0.0374556i
$857$	−43.0172	−	3.22369i	−1.46944	−	0.110119i	−0.684192	−	0.729302i	$-0.739845\pi$
$857$	−43.0172	−	3.22369i	−1.46944	−	0.110119i	−0.785247	+	0.619183i	$0.787464\pi$
$858$	−27.6828	+	16.2947i	−0.945076	+	0.556290i
$859$		−	29.7048i		−	1.01351i	−0.862089	−	0.506757i	$-0.830844\pi$
$859$		−	29.7048i		−	1.01351i	0.862089	−	0.506757i	$-0.169156\pi$
$860$	14.1867	−	11.2675i	0.483761	−	0.384219i
$861$	0.158690			0.00540816
$862$	2.69205	−	5.59010i	0.0916916	−	0.190400i
$863$	−30.8672	−	2.31317i	−1.05073	−	0.0787414i	−0.461847	−	0.886960i	$-0.652813\pi$
$863$	−30.8672	−	2.31317i	−1.05073	−	0.0787414i	−0.588883	+	0.808218i	$0.700432\pi$
$864$	4.29635	−	3.42623i	0.146165	−	0.116563i
$865$	−7.49014	−	2.31040i	−0.254672	−	0.0785560i
$866$	−4.32693	−	2.49815i	−0.147035	−	0.0848907i
$867$	50.0431	−	28.8924i	1.69955	−	0.981237i
$868$	0.194018	+	0.850050i	0.00658542	+	0.0288526i
$869$	18.7178	+	17.0769i	0.634957	+	0.579293i
$870$	11.4264	+	10.6021i	0.387390	+	0.359445i
$871$	21.7267	+	17.3264i	0.736180	+	0.587084i
$872$	8.86793	+	13.0069i	0.300306	+	0.440468i
$873$	−4.85729	+	4.50691i	−0.164394	+	0.152536i
$874$	−1.92513	−	25.6891i	−0.0651185	−	0.868946i
$875$	−0.608224	−	0.238710i	−0.0205617	−	0.00806989i
$876$	−12.0055	−	2.74018i	−0.405628	−	0.0925819i
$877$	−14.0224	−	45.4596i	−0.473504	−	1.53506i	−0.805976	−	0.591949i	$-0.798359\pi$
$877$	−14.0224	−	45.4596i	−0.473504	−	1.53506i	0.332472	−	0.943113i	$-0.392117\pi$
$878$	−2.71698	+	3.98508i	−0.0916936	+	0.134490i
$879$	−23.4413	+	3.53321i	−0.790655	+	0.119172i
$880$	−1.96378	+	8.95022i	−0.0661990	+	0.301712i
$881$	−32.2754	+	15.5430i	−1.08739	+	0.523658i	−0.889671	−	0.456602i	$-0.849066\pi$
$881$	−32.2754	+	15.5430i	−1.08739	+	0.523658i	−0.197715	+	0.980259i	$0.563352\pi$
$882$	2.66730	−	1.28450i	0.0898127	−	0.0432515i
$883$	−6.89839	−	17.5768i	−0.232149	−	0.591507i	0.766567	−	0.642165i	$-0.221963\pi$
$883$	−6.89839	−	17.5768i	−0.232149	−	0.591507i	−0.998716	+	0.0506578i	$0.983868\pi$
$884$	43.4370	−	6.54707i	1.46094	−	0.220202i
$885$	44.9421	+	30.6410i	1.51071	+	1.02999i
$886$	26.5910	−	8.20225i	0.893343	−	0.275560i
$887$	−2.70535	+	11.8529i	−0.0908368	+	0.397982i	−0.999822	−	0.0188454i	$-0.994001\pi$
$887$	−2.70535	+	11.8529i	−0.0908368	+	0.397982i	0.908986	+	0.416828i	$0.136858\pi$
$888$	−0.0792004	+	0.201799i	−0.00265779	+	0.00677195i
$889$	0.233861	−	0.0175255i	0.00784345	−	0.000587785i
$890$	18.4357	−	17.1058i	0.617964	−	0.573387i
$891$	−0.210605	−	25.0397i	−0.00705555	−	0.838863i
$892$	−2.13302	−	1.70102i	−0.0714186	−	0.0569545i
$893$	−34.3549	−	31.8767i	−1.14964	−	1.06671i
$894$	1.84878	−	12.2659i	0.0618325	−	0.410232i
$895$	13.4028	+	58.7214i	0.448005	+	1.96284i
$896$	−0.0499568	−	0.0865277i	−0.00166894	−	0.00289069i
$897$	18.1026	−	31.3547i	0.604429	−	1.04690i
$898$	5.66615	−	18.3692i	0.189082	−	0.612988i
$899$	−19.1245	−	23.9814i	−0.637838	−	0.799824i
$900$	−0.0833350	+	1.11203i	−0.00277783	+	0.0370676i
$901$	−25.0908	+	52.1015i	−0.835894	+	1.73575i
$902$	−2.72699	−	1.82582i	−0.0907988	−	0.0607933i
$903$	0.713773	+	0.772332i	0.0237529	+	0.0257016i
$904$			13.3964i			0.445558i
$905$	−21.8297	+	45.3298i	−0.725643	+	1.50681i
$906$	−23.1213	−	1.73270i	−0.768153	−	0.0575651i
$907$	−17.0234	−	21.3467i	−0.565254	−	0.708806i	0.414265	−	0.910156i	$-0.364039\pi$
$907$	−17.0234	−	21.3467i	−0.565254	−	0.708806i	−0.979519	+	0.201350i	$0.935467\pi$
$908$	12.7470	+	3.93193i	0.423024	+	0.130486i
$909$	−2.13649	−	1.23350i	−0.0708628	−	0.0409127i
$910$	0.832803	+	1.44246i	0.0276071	+	0.0478170i
$911$	36.0202	−	8.22137i	1.19340	−	0.272386i	0.420727	−	0.907188i	$-0.361775\pi$
$911$	36.0202	−	8.22137i	1.19340	−	0.272386i	0.772675	+	0.634801i	$0.218918\pi$
$912$	1.64865	−	10.9381i	0.0545922	−	0.362196i
$913$	4.33189	+	18.2696i	0.143365	+	0.604635i
$914$	−12.2827	+	15.4021i	−0.406277	+	0.509455i
$915$	−19.5261	+	13.3127i	−0.645513	+	0.440103i
$916$	−11.8483	+	10.9936i	−0.391477	+	0.363238i
$917$	−0.0830053	−	1.10763i	−0.00274108	−	0.0365771i
$918$	−14.6158	+	37.2404i	−0.482393	+	1.22912i
$919$	−25.3136	−	5.77767i	−0.835019	−	0.190588i	−0.216426	−	0.976299i	$-0.569440\pi$
$919$	−25.3136	−	5.77767i	−0.835019	−	0.190588i	−0.618593	+	0.785711i	$0.712297\pi$
$920$	−3.04416	−	9.86892i	−0.100363	−	0.325369i
$921$	0.236761	+	0.161421i	0.00780153	+	0.00531900i
$922$	−1.02117	−	6.77500i	−0.0336303	−	0.223123i
$923$	25.7317	+	65.5634i	0.846970	+	2.15804i
$924$	−0.526612	−	0.0748498i	−0.0173242	−	0.00246238i
$925$	−0.154290	−	0.320387i	−0.00507303	−	0.0105343i
$926$	−19.8778	+	7.80147i	−0.653226	+	0.256372i
$927$	−1.76424	+	0.265916i	−0.0579451	+	0.00873382i
$928$	2.90415	+	1.98002i	0.0953334	+	0.0649972i
$929$	3.26257	+	10.5770i	0.107041	+	0.347020i	0.993209	−	0.116346i	$-0.0371180\pi$
$929$	3.26257	+	10.5770i	0.107041	+	0.347020i	−0.886167	+	0.463365i	$0.846642\pi$
$930$	−8.61149	+	37.7294i	−0.282382	+	1.23720i
$931$	17.5988	−	44.8410i	0.576777	−	1.46960i
$932$	2.16486	+	28.8881i	0.0709125	+	0.946261i
$933$	−26.0182	−	28.0409i	−0.851797	−	0.918019i
$934$	2.45704	+	3.60382i	0.0803968	+	0.117921i
$935$	−20.1981	−	63.5771i	−0.660548	−	2.07920i
$936$	−1.73821	+	1.87335i	−0.0568153	+	0.0612324i
$937$	1.03288	+	0.155682i	0.0337428	+	0.00508592i	0.165892	−	0.986144i	$-0.446950\pi$
$937$	1.03288	+	0.155682i	0.0337428	+	0.00508592i	−0.132149	+	0.991230i	$0.542188\pi$
$938$	0.102394	+	0.448618i	0.00334328	+	0.0146479i
$939$	11.3840	+	19.7177i	0.371503	+	0.643462i
$940$	−16.2714	−	9.39431i	−0.530715	−	0.306408i
$941$	−17.4783	+	56.6634i	−0.569777	+	1.84717i	−0.0397206	+	0.999211i	$0.512647\pi$
$941$	−17.4783	+	56.6634i	−0.569777	+	1.84717i	−0.530057	+	0.847962i	$0.677829\pi$
$942$	8.83908	+	11.0839i	0.287993	+	0.361131i
$943$	3.68856	+	0.276419i	0.120116	+	0.00900144i
$944$	11.0509	+	5.32184i	0.359677	+	0.173211i
$945$	−1.51691			−0.0493449
$946$	−3.37960	−	21.4844i	−0.109880	−	0.698517i
$947$	−27.6558			−0.898694			−0.449347	−	0.893357i	$-0.648343\pi$
$947$	−27.6558			−0.898694			−0.449347	+	0.893357i	$0.648343\pi$
$948$	−11.0480	−	5.32045i	−0.358823	−	0.172800i
$949$	46.1614	+	3.45932i	1.49846	+	0.112294i
$950$	11.3131	+	14.1862i	0.367047	+	0.460262i
$951$	7.56183	−	24.5149i	0.245209	−	0.794949i
$952$	0.629930	+	0.363690i	0.0204162	+	0.0117873i
$953$	22.1238	+	38.3196i	0.716661	+	1.24129i	0.962316	+	0.271935i	$0.0876637\pi$
$953$	22.1238	+	38.3196i	0.716661	+	1.24129i	−0.245655	+	0.969357i	$0.579003\pi$
$954$	−0.748613	−	3.27989i	−0.0242373	−	0.106190i
$955$	44.5781	+	6.71907i	1.44251	+	0.217424i
$956$	0.0622452	−	0.0670844i	0.00201316	−	0.00216967i
$957$	17.8338	−	5.66568i	0.576483	−	0.183145i
$958$	15.2093	+	22.3079i	0.491389	+	0.720736i
$959$	−0.930984	−	1.00336i	−0.0300630	−	0.0324002i
$960$	−0.331402	−	4.42225i	−0.0106960	−	0.142728i
$961$	16.4968	−	42.0331i	0.532154	−	1.35591i
$962$	0.181338	−	0.794492i	0.00584656	−	0.0256155i
$963$	0.219417	+	0.711331i	0.00707060	+	0.0229223i
$964$	−18.4430	−	12.5742i	−0.594007	−	0.404987i
$965$	27.5963	−	4.15947i	0.888356	−	0.133898i
$966$	0.558067	−	0.219025i	0.0179555	−	0.00704702i
$967$	13.8705	+	28.8024i	0.446045	+	0.926222i	0.995857	+	0.0909333i	$0.0289850\pi$
$967$	13.8705	+	28.8024i	0.446045	+	0.926222i	−0.549812	+	0.835288i	$0.685301\pi$
$968$	8.18828	+	7.34521i	0.263181	+	0.236084i
$969$	29.4208	+	74.9629i	0.945132	+	2.40816i
$970$	6.44217	+	42.7410i	0.206846	+	1.37233i
$971$	−16.3647	−	11.1573i	−0.525169	−	0.358054i	0.271531	−	0.962430i	$-0.412470\pi$
$971$	−16.3647	−	11.1573i	−0.525169	−	0.358054i	−0.796699	+	0.604376i	$0.793423\pi$
$972$	−1.28716	−	4.17286i	−0.0412856	−	0.133845i
$973$	−0.447613	−	0.102165i	−0.0143498	−	0.00327525i
$974$	−7.51044	+	19.1363i	−0.240650	+	0.613166i
$975$	1.90571	+	25.4299i	0.0610316	+	0.814409i
$976$	−3.90647	+	3.62468i	−0.125043	+	0.116023i
$977$	−32.0477	+	21.8497i	−1.02530	+	0.699034i	−0.954425	−	0.298451i	$-0.903530\pi$
$977$	−32.0477	+	21.8497i	−1.02530	+	0.699034i	−0.0708703	+	0.997486i	$0.522578\pi$
$978$	−2.28386	+	2.86388i	−0.0730299	+	0.0915766i
$979$	−6.96538	−	29.3762i	−0.222614	−	0.938867i
$980$	2.87829	−	19.0962i	0.0919437	−	0.610006i
$981$	6.50015	−	1.48362i	0.207534	−	0.0473682i
$982$	−15.6598	−	27.1236i	−0.499726	−	0.865550i
$983$	−27.8884	−	16.1014i	−0.889501	−	0.513554i	−0.0157220	−	0.999876i	$-0.505005\pi$
$983$	−27.8884	−	16.1014i	−0.889501	−	0.513554i	−0.873779	+	0.486323i	$0.838338\pi$
$984$	1.51771	+	0.468153i	0.0483830	+	0.0149242i
$985$	−23.4848	−	29.4490i	−0.748289	−	0.938325i
$986$	−25.5173	−	1.91226i	−0.812637	−	0.0608987i
$987$	0.473215	−	0.982640i	0.0150626	−	0.0312778i
$988$			41.5821i			1.32290i
$989$	15.2454	+	19.1952i	0.484776	+	0.610371i
$990$	3.22479	+	2.15912i	0.102490	+	0.0686212i
$991$	−6.04636	+	12.5554i	−0.192069	+	0.398835i	−0.974657	−	0.223705i	$-0.928185\pi$
$991$	−6.04636	+	12.5554i	−0.192069	+	0.398835i	0.782588	+	0.622540i	$0.213899\pi$
$992$	−0.652143	+	8.70225i	−0.0207056	+	0.276297i
$993$	−14.4889	−	18.1685i	−0.459791	−	0.576560i
$994$	−0.343761	+	1.11444i	−0.0109034	+	0.0353480i
$995$	25.0155	−	43.3281i	0.793044	−	1.37359i
$996$	−4.54352	−	7.86960i	−0.143967	−	0.249358i
$997$	5.04414	+	22.0998i	0.159749	+	0.699908i	0.989829	+	0.142263i	$0.0454378\pi$
$997$	5.04414	+	22.0998i	0.159749	+	0.699908i	−0.830080	+	0.557645i	$0.811705\pi$
$998$	−1.10769	+	7.34904i	−0.0350633	+	0.232630i
$999$	0.544049	+	0.504804i	0.0172129	+	0.0159713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.w.a.175.6	✓	264
11.10	odd	2		946.2.w.b.175.6	yes	264
43.29	odd	42		946.2.w.b.373.6	yes	264
473.373	even	42	inner	946.2.w.a.373.6	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.w.a.175.6	✓	264	1.1	even	1	trivial
946.2.w.a.373.6	yes	264	473.373	even	42	inner
946.2.w.b.175.6	yes	264	11.10	odd	2
946.2.w.b.373.6	yes	264	43.29	odd	42

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.w (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 - 0.433884i) q^{2} +(-1.60065 - 0.119952i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.814345 - 2.64004i) q^{5} +(1.39009 + 0.802569i) q^{6} +(-0.0499568 - 0.0865277i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.418799 - 0.0631238i) q^{9} +O(q^{10})\)	\(q+(-0.900969 - 0.433884i) q^{2} +(-1.60065 - 0.119952i) q^{3} +(0.623490 + 0.781831i) q^{4} +(0.814345 - 2.64004i) q^{5} +(1.39009 + 0.802569i) q^{6} +(-0.0499568 - 0.0865277i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(-0.418799 - 0.0631238i) q^{9} +(-1.87917 + 2.02527i) q^{10} +(1.00421 + 3.16094i) q^{11} +(-0.904207 - 1.32623i) q^{12} +(4.10412 + 4.42319i) q^{13} +(0.00746655 + 0.0996342i) q^{14} +(-1.62016 + 4.12810i) q^{15} +(-0.222521 + 0.974928i) q^{16} +(-2.14585 - 6.95667i) q^{17} +(0.349937 + 0.238583i) q^{18} +(6.81440 - 1.02711i) q^{19} +(2.57180 - 1.00936i) q^{20} +(0.0695842 + 0.144493i) q^{21} +(0.466717 - 3.28362i) q^{22} +(1.36571 + 3.47976i) q^{23} +(0.239234 + 1.58721i) q^{24} +(-2.17547 - 1.48321i) q^{25} +(-1.77853 - 5.76586i) q^{26} +(5.35746 + 1.22281i) q^{27} +(0.0365025 - 0.0930069i) q^{28} +(0.262669 + 3.50508i) q^{29} +(3.25083 - 3.01633i) q^{30} +(-7.21030 + 4.91590i) q^{31} +(0.623490 - 0.781831i) q^{32} +(-1.22823 - 5.18002i) q^{33} +(-1.08504 + 7.19879i) q^{34} +(-0.269119 + 0.0614246i) q^{35} +(-0.211765 - 0.366787i) q^{36} +(0.116963 + 0.0675284i) q^{37} +(-6.58521 - 2.03127i) q^{38} +(-6.03868 - 7.57227i) q^{39} +(-2.75506 - 0.206463i) q^{40} +(0.429326 - 0.891504i) q^{41} -0.160375i q^{42} +(6.26993 - 1.92040i) q^{43} +(-1.84521 + 2.75594i) q^{44} +(-0.507697 + 1.05424i) q^{45} +(0.279354 - 3.72771i) q^{46} +(-4.24011 - 5.31693i) q^{47} +(0.473123 - 1.53383i) q^{48} +(3.49501 - 6.05353i) q^{49} +(1.31649 + 2.28023i) q^{50} +(2.60028 + 11.3926i) q^{51} +(-0.899311 + 5.96654i) q^{52} +(-5.82288 - 5.40284i) q^{53} +(-4.29635 - 3.42623i) q^{54} +(9.16280 - 0.0770669i) q^{55} +(-0.0732418 + 0.0679585i) q^{56} +(-11.0307 + 0.826635i) q^{57} +(1.28414 - 3.27193i) q^{58} +(2.72935 - 11.9581i) q^{59} +(-4.23763 + 1.30714i) q^{60} +(4.40307 + 3.00196i) q^{61} +(8.62918 - 1.30064i) q^{62} +(0.0154599 + 0.0393912i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(15.0196 - 7.23304i) q^{65} +(-1.14093 + 5.19995i) q^{66} +(4.55409 - 0.686418i) q^{67} +(4.10103 - 6.01510i) q^{68} +(-1.76861 - 5.73370i) q^{69} +(0.269119 + 0.0614246i) q^{70} +(10.8658 + 4.26450i) q^{71} +(0.0316504 + 0.422345i) q^{72} +(5.62380 - 5.21812i) q^{73} +(-0.0760802 - 0.111589i) q^{74} +(3.30426 + 2.63506i) q^{75} +(5.05174 + 4.68733i) q^{76} +(0.223342 - 0.244803i) q^{77} +(2.15518 + 9.44247i) q^{78} +(6.61596 - 3.81973i) q^{79} +(2.39264 + 1.38139i) q^{80} +(-7.21461 - 2.22541i) q^{81} +(-0.773619 + 0.616940i) q^{82} +(5.64538 + 0.423063i) q^{83} +(-0.0695842 + 0.144493i) q^{84} -20.1134 q^{85} +(-6.48225 - 0.990198i) q^{86} -5.64191i q^{87} +(2.85823 - 1.68241i) q^{88} +(-9.07738 - 0.680256i) q^{89} +(0.914838 - 0.729559i) q^{90} +(0.177700 - 0.576088i) q^{91} +(-1.86908 + 3.23735i) q^{92} +(12.1308 - 7.00374i) q^{93} +(1.51328 + 6.63010i) q^{94} +(2.83767 - 18.8267i) q^{95} +(-1.09177 + 1.17665i) q^{96} +(9.75450 - 12.2318i) q^{97} +(-5.77542 + 3.93762i) q^{98} +(-0.221033 - 1.38719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q - 44 q^{2} - 44 q^{4} - 44 q^{8} - 20 q^{9}+O(q^{10}) \) 264 * q - 44 * q^2 - 44 * q^4 - 44 * q^8 - 20 * q^9	\( 264 q - 44 q^{2} - 44 q^{4} - 44 q^{8} - 20 q^{9} + 5 q^{11} + 7 q^{13} - 32 q^{15} - 44 q^{16} + q^{17} - 20 q^{18} + 21 q^{19} + 12 q^{22} - q^{23} + 7 q^{24} - 14 q^{25} - 7 q^{26} + 11 q^{29} - 4 q^{30} + 5 q^{31} - 44 q^{32} + 41 q^{33} + 15 q^{34} + 134 q^{36} - 72 q^{37} - 28 q^{38} - 86 q^{39} - 14 q^{40} + 28 q^{41} - 45 q^{43} - 9 q^{44} + 98 q^{45} + 6 q^{46} + 6 q^{47} - 140 q^{49} + 140 q^{50} - 7 q^{51} - 12 q^{53} - 42 q^{54} - 42 q^{55} + 2 q^{57} - 3 q^{58} + 44 q^{59} - 4 q^{60} - 71 q^{61} - 2 q^{62} + 24 q^{63} - 44 q^{64} + 68 q^{65} + 97 q^{66} + 25 q^{67} - 27 q^{68} + 74 q^{69} + 47 q^{71} - 20 q^{72} + 57 q^{73} - 2 q^{74} - 28 q^{75} - 28 q^{76} + 11 q^{77} + 12 q^{78} + 42 q^{79} + 99 q^{81} - 28 q^{82} + 44 q^{83} - 12 q^{85} - 17 q^{86} - 9 q^{88} - 69 q^{89} - 8 q^{92} + 84 q^{93} + 27 q^{94} + 12 q^{95} - 82 q^{97} + 14 q^{98} - 88 q^{99}+O(q^{100}) \) 264 * q - 44 * q^2 - 44 * q^4 - 44 * q^8 - 20 * q^9 + 5 * q^11 + 7 * q^13 - 32 * q^15 - 44 * q^16 + q^17 - 20 * q^18 + 21 * q^19 + 12 * q^22 - q^23 + 7 * q^24 - 14 * q^25 - 7 * q^26 + 11 * q^29 - 4 * q^30 + 5 * q^31 - 44 * q^32 + 41 * q^33 + 15 * q^34 + 134 * q^36 - 72 * q^37 - 28 * q^38 - 86 * q^39 - 14 * q^40 + 28 * q^41 - 45 * q^43 - 9 * q^44 + 98 * q^45 + 6 * q^46 + 6 * q^47 - 140 * q^49 + 140 * q^50 - 7 * q^51 - 12 * q^53 - 42 * q^54 - 42 * q^55 + 2 * q^57 - 3 * q^58 + 44 * q^59 - 4 * q^60 - 71 * q^61 - 2 * q^62 + 24 * q^63 - 44 * q^64 + 68 * q^65 + 97 * q^66 + 25 * q^67 - 27 * q^68 + 74 * q^69 + 47 * q^71 - 20 * q^72 + 57 * q^73 - 2 * q^74 - 28 * q^75 - 28 * q^76 + 11 * q^77 + 12 * q^78 + 42 * q^79 + 99 * q^81 - 28 * q^82 + 44 * q^83 - 12 * q^85 - 17 * q^86 - 9 * q^88 - 69 * q^89 - 8 * q^92 + 84 * q^93 + 27 * q^94 + 12 * q^95 - 82 * q^97 + 14 * q^98 - 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more