LMFDB - Embedded newform 946.2.w.b.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.b.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} +(-3.30515 - 0.275660i) 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} +(-2.85823 - 1.68241i) 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} +(5.25732 + 0.837694i) 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} +(-3.41929 + 8.50125i) 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} +(4.37322 + 3.03580i) 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} +(-0.141262 - 0.299758i) 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} +(-0.466717 - 3.28362i) 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} +(1.36679 + 0.324080i) 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} + 9 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} - 122 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} + 52 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} - 67 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} + 89 q^{77} + 12 q^{78} - 42 q^{79} + 99 q^{81} - 28 q^{82} - 44 q^{83} + 12 q^{85} - 17 q^{86} - 12 q^{88} - 69 q^{89} - 8 q^{92} + 84 q^{93} - 27 q^{94} - 12 q^{95} - 82 q^{97} - 14 q^{98} + 189 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 + 9 * 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 - 122 * 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 + 52 * 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 - 67 * 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 + 89 * q^77 + 12 * q^78 - 42 * q^79 + 99 * q^81 - 28 * q^82 - 44 * q^83 + 12 * q^85 - 17 * q^86 - 12 * q^88 - 69 * q^89 - 8 * q^92 + 84 * q^93 - 27 * q^94 - 12 * q^95 - 82 * q^97 - 14 * q^98 + 189 * 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	0.875312	−	0.483559i	$-0.160656\pi$
$7$	0.0499568	+	0.0865277i	0.0188819	+	0.0327044i	−0.856430	+	0.516263i	$0.827323\pi$
$8$	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
$11$	−3.30515	−	0.275660i	−0.996540	−	0.0831145i
$11$	−3.30515	−	0.275660i	−0.996540	−	0.0831145i
$12$	−0.904207	−	1.32623i	−0.261022	−	0.382849i
$13$	−4.10412	−	4.42319i	−1.13828	−	1.22677i	−0.970540	−	0.240939i	$-0.922545\pi$
$13$	−4.10412	−	4.42319i	−1.13828	−	1.22677i	−0.167737	−	0.985832i	$-0.553646\pi$
$14$	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	$0.249135\pi$
$17$	2.14585	+	6.95667i	0.520444	+	1.68724i	−0.188582	+	0.982057i	$0.560389\pi$
$18$	−0.349937	−	0.238583i	−0.0824808	−	0.0562345i
$19$	−6.81440	+	1.02711i	−1.56333	+	0.235634i	−0.872950	−	0.487811i	$-0.837796\pi$
$19$	−6.81440	+	1.02711i	−1.56333	+	0.235634i	−0.690382	+	0.723445i	$0.742558\pi$
$20$	2.57180	−	1.00936i	0.575073	−	0.225700i
$21$	−0.0695842	−	0.144493i	−0.0151845	−	0.0315310i
$22$	−2.85823	−	1.68241i	−0.609377	−	0.358691i
$23$	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	$-0.917990\pi$
$29$	−0.262669	−	3.50508i	−0.0487764	−	0.650876i	0.918217	−	0.396077i	$-0.129629\pi$
$30$	−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
$33$	5.25732	+	0.837694i	0.915182	+	0.145824i
$34$	−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	−0.931800	−	0.362972i	$-0.881762\pi$
$41$	−0.429326	+	0.891504i	−0.0670494	+	0.139230i	0.864751	+	0.502201i	$0.167476\pi$
$42$		−	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
$55$	−3.41929	+	8.50125i	−0.461056	+	1.14631i
$56$	−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	0.247646	−	0.968850i	$-0.420343\pi$
$61$	−4.40307	−	3.00196i	−0.563756	−	0.384362i	−0.811402	+	0.584488i	$0.801295\pi$
$62$	−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
$66$	4.37322	+	3.03580i	0.538306	+	0.373682i
$67$	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	−0.936879	−	0.349654i	$-0.886299\pi$
$73$	−5.62380	+	5.21812i	−0.658216	+	0.610735i	0.278663	+	0.960389i	$0.410109\pi$
$74$	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
$77$	−0.141262	−	0.299758i	−0.0160984	−	0.0341606i
$78$	2.15518	+	9.44247i	0.244026	+	1.06915i
$79$	−6.61596	+	3.81973i	−0.744354	+	0.429753i	−0.823650	−	0.567098i	$-0.808066\pi$
$79$	−6.61596	+	3.81973i	−0.744354	+	0.429753i	0.0792961	+	0.996851i	$0.474733\pi$
$80$	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	−0.238799	−	0.971069i	$-0.576754\pi$
$83$	−5.64538	−	0.423063i	−0.619661	−	0.0464372i	−0.380862	+	0.924632i	$0.624373\pi$
$84$	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
$88$	−0.466717	−	3.28362i	−0.0497522	−	0.350035i
$89$	−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
$99$	1.36679	+	0.324080i	0.137368	+	0.0325712i
$100$	−0.196763	−	2.62562i	−0.0196763	−	0.262562i
$101$	−5.42222	−	2.12806i	−0.539531	−	0.211750i	0.0798981	−	0.996803i	$-0.474541\pi$
$101$	−5.42222	−	2.12806i	−0.539531	−	0.211750i	−0.619429	+	0.785053i	$0.712636\pi$
$102$	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	0.934573	−	0.355771i	$-0.115782\pi$
$107$	0.762601	+	1.58356i	0.0737235	+	0.153088i	−0.860850	+	0.508859i	$0.830067\pi$
$108$	2.38430	+	4.95104i	0.229429	+	0.476414i
$109$	14.6541	−	5.75129i	1.40360	−	0.550874i	0.461784	−	0.886992i	$-0.347210\pi$
$109$	14.6541	−	5.75129i	1.40360	−	0.550874i	0.941820	+	0.336119i	$0.109114\pi$
$110$	−6.76923	+	6.17579i	−0.645420	+	0.588839i
$111$	−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
$121$	10.8480	+	1.82219i	0.986184	+	0.165654i
$122$	−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	−0.850885	−	0.525351i	$-0.823934\pi$
$127$	1.01841	−	2.11475i	0.0903693	−	0.187654i	0.941255	+	0.337698i	$0.109648\pi$
$128$	−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	−0.0582701	−	0.998301i	$-0.518558\pi$
$131$	−10.0160	−	4.82346i	−0.875104	−	0.421428i	−0.816834	+	0.576873i	$0.804273\pi$
$132$	2.62295	+	4.63263i	0.228299	+	0.403219i
$133$	−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	−0.851549	−	0.524274i	$-0.824337\pi$
$139$	−3.12554	+	3.36853i	−0.265104	+	0.285715i	0.586445	+	0.809989i	$0.300527\pi$
$140$	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
$143$	12.3454	+	15.7506i	1.03238	+	1.31713i
$144$	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	0.998653	−	0.0518869i	$-0.0165235\pi$
$149$	2.82333	+	7.19374i	0.231296	+	0.589334i	−0.767356	+	0.641221i	$0.778428\pi$
$150$	1.83372	+	3.80777i	0.149723	+	0.310903i
$151$	13.0144	−	6.26742i	1.05910	−	0.510036i	0.178521	−	0.983936i	$-0.442869\pi$
$151$	13.0144	−	6.26742i	1.05910	−	0.510036i	0.880578	+	0.473901i	$0.157154\pi$
$152$	−2.51770	−	6.41500i	−0.204213	−	0.520325i
$153$	−0.459548	−	3.04890i	−0.0371522	−	0.246489i
$154$	0.00278705	−	0.331364i	0.000224587	−	0.0267021i
$155$	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
$165$	6.49283	−	13.1974i	0.505466	−	1.02741i
$166$	−4.90275	−	2.83061i	−0.380528	−	0.219698i
$167$	1.44781	−	4.69368i	0.112035	−	0.363208i	−0.882140	−	0.470987i	$-0.843898\pi$
$167$	1.44781	−	4.69368i	0.112035	−	0.363208i	0.994175	+	0.107779i	$0.0343741\pi$
$168$	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	$0.0343971\pi$
$173$			2.83713i			0.215703i	−0.994167	+	0.107851i	$0.965603\pi$
$174$	−2.44793	+	5.08319i	−0.185577	+	0.385355i
$175$	0.0196593	−	0.262335i	0.00148610	−	0.0198307i
$176$	1.00421	−	3.16094i	0.0756954	−	0.238265i
$177$	−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
$187$	−5.17467	−	23.5843i	−0.378410	−	1.72466i
$188$	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	0.681576	−	0.731748i	$-0.261295\pi$
$193$	−4.38283	−	9.10104i	−0.315483	−	0.655108i	−0.997059	+	0.0766401i	$0.975581\pi$
$194$	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	−0.995839	−	0.0911342i	$-0.970951\pi$
$197$	−7.68009	+	11.2646i	−0.547183	+	0.802571i	0.448655	+	0.893705i	$0.351903\pi$
$198$	1.09083	+	0.885015i	0.0775216	+	0.0628953i
$199$	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
$209$	22.8058	−	1.51628i	1.57751	−	0.104884i
$210$	−0.423397	−	0.130601i	−0.0292172	−	0.00901231i
$211$	14.6965	+	18.4289i	1.01175	+	1.26870i	0.962891	+	0.269890i	$0.0869874\pi$
$211$	14.6965	+	18.4289i	1.01175	+	1.26870i	0.0488601	+	0.998806i	$0.484441\pi$
$212$	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
$220$	−8.77844	+	2.62714i	−0.591842	+	0.177122i
$221$	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	−0.870884	−	0.491489i	$-0.836453\pi$
$227$	−11.0217	+	7.51450i	−0.731539	+	0.498755i	0.139345	+	0.990244i	$0.455500\pi$
$228$	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
$231$	0.190155	+	0.496753i	0.0125113	+	0.0326839i
$232$	3.35875	−	1.03604i	0.220513	−	0.0680191i
$233$	−23.9354	−	16.3189i	−1.56806	−	1.06908i	−0.961776	−	0.273836i	$-0.911707\pi$
$233$	−23.9354	−	16.3189i	−1.56806	−	1.06908i	−0.606283	−	0.795249i	$-0.707340\pi$
$234$	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	0.989268	−	0.146115i	$-0.0466769\pi$
$239$	0.0136394	+	0.0904917i	0.000882262	+	0.00585342i	−0.988385	+	0.151968i	$0.951439\pi$
$240$	−3.66408	−	2.49813i	−0.236516	−	0.161254i
$241$	21.3299	−	6.57940i	1.37398	−	0.423816i	0.482110	−	0.876111i	$-0.339870\pi$
$241$	21.3299	−	6.57940i	1.37398	−	0.423816i	0.891869	+	0.452294i	$0.149394\pi$
$242$	8.98311	+	6.34852i	0.577456	+	0.408098i
$243$	−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
$253$	−3.55463	−	11.8776i	−0.223478	−	0.746738i
$254$	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	−0.182548	−	0.983197i	$-0.558434\pi$
$263$	−14.3885	−	4.43825i	−0.887230	−	0.273674i	−0.704682	+	0.709523i	$0.748911\pi$
$264$	0.353173	+	5.31192i	0.0217363	+	0.326926i
$265$	−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	0.306424	−	0.951895i	$-0.400868\pi$
$271$	−10.9590	−	11.8109i	−0.665709	−	0.717464i	−0.972133	+	0.234432i	$0.924677\pi$
$272$	−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
$275$	6.78140	+	5.50193i	0.408934	+	0.331779i
$276$	3.38008	−	4.95766i	0.203457	−	0.298416i
$277$	−6.30364	+	0.950121i	−0.378749	+	0.0570873i	−0.335658	−	0.941984i	$-0.608959\pi$
$277$	−6.30364	+	0.950121i	−0.378749	+	0.0570873i	−0.0430911	+	0.999071i	$0.513721\pi$
$278$	−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	−0.599206	−	0.800595i	$-0.704517\pi$
$281$	−8.27950	+	3.24946i	−0.493913	+	0.193847i	0.105293	+	0.994441i	$0.466422\pi$
$282$	1.62693	+	10.7940i	0.0968824	+	0.642773i
$283$	1.24853	−	1.83126i	0.0742174	−	0.108857i	−0.787335	−	0.616525i	$-0.788540\pi$
$283$	1.24853	−	1.83126i	0.0742174	−	0.108857i	0.861553	+	0.507668i	$0.169492\pi$
$284$	3.44058	+	11.1541i	0.204161	+	0.661873i
$285$	6.80043	−	29.7946i	0.402823	−	1.76488i
$286$	4.28890	+	19.5473i	0.253608	+	1.15586i
$287$	−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	−0.621336	−	0.783544i	$-0.713410\pi$
$293$	−14.3986	+	3.28638i	−0.841174	+	0.191992i	−0.219837	+	0.975537i	$0.570553\pi$
$294$	−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
$297$	−17.3701	−	5.51839i	−1.00792	−	0.320210i
$298$	−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	0.504405	−	0.863467i	$-0.331712\pi$
$307$	0.154605	+	0.0892610i	0.00882375	+	0.00509439i	−0.495582	+	0.868561i	$0.665045\pi$
$308$	0.146285	−	0.297340i	0.00833534	−	0.0169425i
$309$	−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
$319$	−0.0980470	+	11.6572i	−0.00548958	+	0.652678i
$320$	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
$330$	11.5760	−	9.07330i	0.637236	−	0.499469i
$331$	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	0.468466	−	0.883481i	$-0.344807\pi$
$337$	26.9455	−	15.5570i	1.46782	−	0.847444i	0.999350	+	0.0360372i	$0.0114735\pi$
$338$	−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
$341$	25.1862	−	14.2602i	1.36391	−	0.772232i
$342$	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	$-0.867862\pi$
$347$	0.929324	−	12.4010i	0.0498887	−	0.665719i	0.964955	−	0.262415i	$-0.0845191\pi$
$348$	−4.41102	+	3.51767i	−0.236456	+	0.188567i
$349$	1.00918	+	0.311290i	0.0540200	+	0.0166630i	0.321647	−	0.946860i	$-0.395763\pi$
$349$	1.00918	+	0.311290i	0.0540200	+	0.0166630i	−0.267627	+	0.963522i	$0.586240\pi$
$350$	0.131535	−	0.227826i	0.00703086	−	0.0121778i
$351$	−16.5790	−	28.7156i	−0.884919	−	1.53272i
$352$	2.27625	−	2.41220i	0.121324	−	0.128571i
$353$	−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	0.116179	−	0.993228i	$-0.462935\pi$
$359$	−8.98525	−	3.52645i	−0.474223	−	0.186119i	−0.590402	+	0.807109i	$0.701031\pi$
$360$	−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
$363$	−17.1453	−	4.21794i	−0.899896	−	0.221384i
$364$	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	$0.0112107\pi$
$373$	0.316937	+	4.22923i	0.0164104	+	0.218981i	−0.982969	+	0.183769i	$0.941170\pi$
$374$	5.57064	−	23.4940i	0.288051	−	1.21484i
$375$	−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
$385$	−0.906411	+	0.128832i	−0.0461950	+	0.00656591i
$386$		−	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
$396$	0.598806	+	1.27066i	0.0300911	+	0.0638532i
$397$	−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
$407$	−0.367964	−	0.255433i	−0.0182393	−	0.0126614i
$408$	10.5283	−	5.07018i	0.521230	−	0.251011i
$409$	−9.96160	+	4.79725i	−0.492569	+	0.237209i	−0.663643	−	0.748049i	$-0.730991\pi$
$409$	−9.96160	+	4.79725i	−0.492569	+	0.237209i	0.171074	+	0.985258i	$0.445276\pi$
$410$	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
$418$	21.2052	+	8.52892i	1.03718	+	0.417163i
$419$	−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	$-0.952256\pi$
$431$		−	6.20454i		−	0.298862i	0.988772	−	0.149431i	$-0.0477443\pi$
$432$	−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	−0.999414	−	0.0342390i	$-0.989099\pi$
$439$	−0.718854	+	4.76928i	−0.0343090	+	0.227626i	0.965105	+	0.261865i	$0.0843374\pi$
$440$	−9.04897	−	1.44185i	−0.431393	−	0.0687375i
$441$	−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
$451$	1.66474	−	2.82821i	0.0783894	−	0.133175i
$452$	−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	$0.223853\pi$
$457$	−4.38366	+	19.2061i	−0.205059	+	0.898422i	−0.967801	+	0.251718i	$0.919004\pi$
$458$	−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	0.725774	−	0.687933i	$-0.241482\pi$
$461$	−3.85960	−	5.66099i	−0.179759	−	0.263659i	−0.905534	+	0.424274i	$0.860529\pi$
$462$	−0.0442090	+	0.530064i	−0.00205679	+	0.0246608i
$463$	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
$473$	21.2524	−	4.61885i	0.977188	−	0.212375i
$474$	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	0.927732	−	0.373247i	$-0.121756\pi$
$479$	23.3821	+	13.4997i	1.06836	+	0.616816i	0.140625	+	0.990063i	$0.455089\pi$
$480$	−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
$484$	5.33899	+	9.61744i	0.242681	+	0.437157i
$485$	−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	−0.185373	−	0.982668i	$-0.559349\pi$
$491$	−25.8775	−	17.6430i	−1.16784	−	0.796218i	−0.982464	+	0.186450i	$0.940302\pi$
$492$	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
$495$	1.96863	−	3.34448i	0.0884831	−	0.150323i
$496$	−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	$-0.403208\pi$
$503$	28.5559	−	26.4960i	1.27325	−	1.18140i	0.973830	−	0.227278i	$-0.0729825\pi$
$504$	0.0349634	−	0.0238377i	0.00155739	−	0.00106181i
$505$	−10.0337	+	12.5819i	−0.446495	+	0.559887i
$506$	1.95089	−	12.2436i	0.0867274	−	0.544296i
$507$	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	0.759283	−	0.650761i	$-0.225550\pi$
$523$	−4.20643	−	7.28575i	−0.183934	−	0.318583i	−0.943217	+	0.332178i	$0.892217\pi$
$524$	−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
$528$	−1.98656	+	4.93911i	−0.0864538	+	0.214947i
$529$	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
$539$	−13.2202	+	19.0444i	−0.569436	+	0.820300i
$540$	15.0126	−	2.26278i	0.646039	−	0.0973748i
$541$	4.28167	−	6.28006i	0.184083	−	0.270001i	−0.723093	−	0.690750i	$-0.757280\pi$
$541$	4.28167	−	6.28006i	0.184083	−	0.270001i	0.907177	+	0.420749i	$0.138233\pi$
$542$	−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	0.465510	−	0.885042i	$-0.345871\pi$
$547$	−12.3588	−	18.1270i	−0.528422	−	0.775053i	−0.993933	+	0.109989i	$0.964918\pi$
$548$	10.7105	+	8.54137i	0.457532	+	0.364869i
$549$	1.65451	+	1.53516i	0.0706127	+	0.0655190i
$550$	3.72263	+	7.89941i	0.158734	+	0.336832i
$551$	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	$0.594625\pi$
$557$	−20.2454	+	42.0400i	−0.857825	+	1.78129i	−0.564910	+	0.825152i	$0.691089\pi$
$558$	3.69599			0.156464
$559$	34.2268	+	19.8515i	1.44764	+	0.839630i
$560$			0.276040i			0.0116648i
$561$	5.45385	+	38.3710i	0.230262	+	1.62002i
$562$	−8.86946	−	0.664674i	−0.374135	−	0.0280376i
$563$	29.2750	−	23.3460i	1.23379	−	0.983917i	0.233861	−	0.972270i	$-0.424864\pi$
$563$	29.2750	−	23.3460i	1.23379	−	0.983917i	0.999932	−	0.0116472i	$-0.00370751\pi$
$564$	−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	−0.818310	−	0.574777i	$-0.805089\pi$
$569$	−4.38878	+	4.72998i	−0.183987	+	0.198291i	0.634323	+	0.773068i	$0.281279\pi$
$570$	19.0544	−	23.8934i	0.798101	−	1.00079i
$571$	−31.8994	+	21.7486i	−1.33495	+	0.910151i	−0.999491	−	0.0319050i	$-0.989843\pi$
$571$	−31.8994	+	21.7486i	−1.33495	+	0.910151i	−0.335456	+	0.942056i	$0.608890\pi$
$572$	−4.61709	+	19.4724i	−0.193050	+	0.814182i
$573$	−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
$583$	17.7561	+	19.4623i	0.735384	+	0.806047i
$584$	−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	−0.233674	−	0.972315i	$-0.575075\pi$
$593$	−18.1069	−	2.72918i	−0.743562	−	0.112074i	−0.509888	+	0.860241i	$0.670313\pi$
$594$	−13.2556	−	12.5085i	−0.543884	−	0.513231i
$595$	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	$-0.765615\pi$
$601$	−36.3283			−1.48186			−0.740930	+	0.671582i	$0.765615\pi$
$602$	−0.238153	−	0.610361i	−0.00970638	−	0.0248765i
$603$	−1.95058			−0.0794336
$604$	13.0144	+	6.26742i	0.529550	+	0.255018i
$605$	13.6447	−	27.1554i	0.554736	−	1.10402i
$606$	5.82946	+	7.30991i	0.236805	+	0.296945i
$607$	−15.6396	−	4.82418i	−0.634793	−	0.195808i	−0.0393757	−	0.999224i	$-0.512537\pi$
$607$	−15.6396	−	4.82418i	−0.634793	−	0.195808i	−0.595417	+	0.803417i	$0.703013\pi$
$608$	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	0.966064	−	0.258301i	$-0.0831628\pi$
$613$	23.0061	+	18.3468i	0.929209	+	0.741019i	−0.0368557	+	0.999321i	$0.511734\pi$
$614$	0.100565	+	0.147502i	0.00405847	+	0.00595269i
$615$	−2.98465	−	3.21668i	−0.120353	−	0.129709i
$616$	0.260809	−	0.204423i	0.0105083	−	0.00823644i
$617$	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
$627$	−36.6859	−	0.308560i	−1.46509	−	0.0123227i
$628$	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
$638$	−5.14621	+	10.4602i	−0.203740	+	0.414125i
$639$	−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
$649$	−12.3173	+	38.7708i	−0.483495	+	1.52189i
$650$	−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	0.688504	−	0.725232i	$-0.258268\pi$
$659$	37.9265	−	2.84220i	1.47741	−	0.110716i	0.788904	+	0.614516i	$0.210649\pi$
$660$	14.3663	−	3.15214i	0.559209	−	0.122697i
$661$	−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
$671$	13.7253	+	11.1357i	0.529859	+	0.429889i
$672$	0.156354	+	0.0356868i	0.00603150	+	0.00137665i
$673$	−10.9026	+	27.7794i	−0.420264	+	1.07082i	0.551356	+	0.834270i	$0.314110\pi$
$673$	−10.9026	+	27.7794i	−0.420264	+	1.07082i	−0.971620	+	0.236546i	$0.923985\pi$
$674$	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	−0.888587	−	0.458709i	$-0.848312\pi$
$677$	−6.33957	+	7.94957i	−0.243650	+	0.305527i	0.644937	+	0.764236i	$0.276884\pi$
$678$	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
$682$	28.8793	−	1.92009i	1.10584	−	0.0735241i
$683$	−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
$693$	0.0402387	+	0.134455i	0.00152854	+	0.00510754i
$694$	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	$0.141577\pi$
$701$	33.4741	+	36.0766i	1.26430	+	1.36259i	0.361595	+	0.932335i	$0.382232\pi$
$702$	−2.47789	−	33.0652i	−0.0935221	−	1.24797i
$703$	−0.866390	−	0.340033i	−0.0326765	−	0.0128246i
$704$	3.09744	−	1.18569i	0.116739	−	0.0446874i
$705$	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
$715$	51.6358	−	19.7660i	1.93107	−	0.739206i
$716$	−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
$726$	−13.6173	−	11.2393i	−0.505386	−	0.417130i
$727$	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	0.783775	−	0.621045i	$-0.213292\pi$
$733$	21.3045	+	10.2597i	0.786898	+	0.378950i	0.00312326	+	0.999995i	$0.499006\pi$
$734$	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
$737$	−15.2412	+	1.01334i	−0.561415	+	0.0373267i
$738$	0.362934	−	0.209540i	0.0133598	−	0.00771328i
$739$	1.40429	+	6.15261i	0.0516578	+	0.226328i	0.994167	−	0.107853i	$-0.0343976\pi$
$739$	1.40429	+	6.15261i	0.0516578	+	0.226328i	−0.942509	+	0.334181i	$0.891540\pi$
$740$	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	−0.681160	−	0.732134i	$-0.738524\pi$
$743$	−6.77338	+	4.61801i	−0.248491	+	0.169418i	0.432669	+	0.901553i	$0.357572\pi$
$744$	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
$748$	15.2126	−	18.7503i	0.556229	−	0.685580i
$749$	−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
$759$	4.26498	+	19.4383i	0.154809	+	0.705565i
$760$	−18.9862	+	1.42282i	−0.688700	+	0.0516109i
$761$	−22.4249	+	20.8073i	−0.812902	+	0.754263i	−0.972496	−	0.232920i	$-0.925172\pi$
$761$	−22.4249	+	20.8073i	−0.812902	+	0.754263i	0.159594	+	0.987183i	$0.448981\pi$
$762$	−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	−0.956152	−	0.292870i	$-0.905390\pi$
$769$	−0.0322332	+	0.104497i	−0.00116236	+	0.00376827i	0.954990	+	0.296639i	$0.0958657\pi$
$770$	−0.872546	−	0.277203i	−0.0314444	−	0.00998970i
$771$	−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
$781$	−34.7375	−	17.0901i	−1.24300	−	0.611531i
$782$	−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	$-0.992412\pi$
$787$	−26.6165	−	28.6858i	−0.948776	−	1.02254i	0.0509396	−	0.998702i	$-0.483778\pi$
$788$	−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
$792$	−0.0118142	+	1.40464i	−0.000419800	+	0.0499117i
$793$	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
$803$	20.0259	−	15.6964i	0.706699	−	0.553914i
$804$	−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	0.747635	−	0.664109i	$-0.231189\pi$
$809$	48.6197	−	11.0971i	1.70938	−	0.390154i	0.961742	+	0.273955i	$0.0883320\pi$
$810$	−18.0645	+	10.4296i	−0.634723	+	0.366457i
$811$	16.4478	−	28.4885i	0.577562	−	1.00037i	−0.418196	−	0.908357i	$-0.637338\pi$
$811$	16.4478	−	28.4885i	0.577562	−	1.00037i	0.995758	−	0.0920097i	$-0.0293291\pi$
$812$	0.335585	+	0.103514i	0.0117767	+	0.00363263i
$813$	16.1247	+	20.2197i	0.565518	+	0.709137i
$814$	−0.220696	−	0.389791i	−0.00773539	−	0.0136622i
$815$	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	−0.334151	−	0.942520i	$-0.608449\pi$
$821$	14.6240	−	11.6623i	0.510382	−	0.407016i	0.844533	+	0.535503i	$0.179878\pi$
$822$	−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
$825$	−10.1947	−	9.62011i	−0.354933	−	0.334929i
$826$	1.21181	+	0.182651i	0.0421643	+	0.00635525i
$827$	1.06751	−	1.15050i	0.0371209	−	0.0400068i	−0.714218	−	0.699923i	$-0.753218\pi$
$827$	1.06751	−	1.15050i	0.0371209	−	0.0400068i	0.751339	+	0.659916i	$0.229408\pi$
$828$	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
$836$	15.4046	+	16.8849i	0.532780	+	0.583975i
$837$	−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
$847$	0.384262	+	1.02969i	0.0132034	+	0.0353804i
$848$	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	0.0463876	−	0.998924i	$-0.485229\pi$
$853$	27.2983	−	15.7607i	0.934675	−	0.539635i	0.888287	+	0.459289i	$0.151896\pi$
$854$	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	0.785247	−	0.619183i	$-0.212536\pi$
$857$	43.0172	+	3.22369i	1.46944	+	0.110119i	0.684192	+	0.729302i	$0.260155\pi$
$858$	−4.52029	−	31.8029i	−0.154320	−	1.08573i
$859$		−	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
$869$	22.9197	−	10.8010i	0.777497	−	0.366400i
$870$	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	$0.201641\pi$
$877$	14.0224	+	45.4596i	0.473504	+	1.53506i	−0.332472	+	0.943113i	$0.607883\pi$
$878$	−2.71698	+	3.98508i	−0.0916936	+	0.134490i
$879$	23.4413	−	3.53321i	0.790655	−	0.119172i
$880$	−7.52725	−	5.22526i	−0.253743	−	0.176144i
$881$	−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	−0.908986	−	0.416828i	$-0.863142\pi$
$887$	2.70535	−	11.8529i	0.0908368	−	0.397982i	0.999822	+	0.0188454i	$0.00599902\pi$
$888$	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
$891$	23.2319	+	9.34409i	0.778298	+	0.313039i
$892$	−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
$913$	18.5422	+	2.95449i	0.613658	+	0.0977794i
$914$	−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	0.618593	−	0.785711i	$-0.287703\pi$
$919$	25.3136	+	5.77767i	0.835019	+	0.190588i	0.216426	+	0.976299i	$0.430560\pi$
$920$	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
$924$	−0.269817	+	0.458390i	−0.00887633	+	0.0150799i
$925$	−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
$935$	−66.4776	−	5.54444i	−2.17405	−	0.181323i
$936$	−1.73821	+	1.87335i	−0.0568153	+	0.0612324i
$937$	−1.03288	−	0.155682i	−0.0337428	−	0.00508592i	0.132149	−	0.991230i	$-0.457812\pi$
$937$	−1.03288	−	0.155682i	−0.0337428	−	0.00508592i	−0.165892	+	0.986144i	$0.553050\pi$
$938$	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	$-0.487353\pi$
$941$	17.4783	−	56.6634i	0.569777	−	1.84717i	0.530057	−	0.847962i	$-0.322171\pi$
$942$	−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
$946$	21.1518	+	5.05965i	0.687705	+	0.164503i
$947$	−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	$-0.912336\pi$
$953$	−22.1238	−	38.3196i	−0.716661	−	1.24129i	0.245655	−	0.969357i	$-0.420997\pi$
$954$	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
$957$	1.55525	−	18.6474i	0.0502740	−	0.602783i
$958$	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	$-0.971015\pi$
$967$	−13.8705	−	28.8024i	−0.446045	−	0.926222i	0.549812	−	0.835288i	$-0.314699\pi$
$968$	0.637407	+	10.9815i	0.0204870	+	0.352959i
$969$	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
$979$	29.8146	+	4.75061i	0.952878	+	0.151830i
$980$	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	$-0.954562\pi$
$997$	−5.04414	−	22.0998i	−0.159749	−	0.699908i	0.830080	−	0.557645i	$-0.188295\pi$
$998$	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.b.175.6	yes	264
11.10	odd	2		946.2.w.a.175.6	✓	264
43.29	odd	42		946.2.w.a.373.6	yes	264
473.373	even	42	inner	946.2.w.b.373.6	yes	264

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
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} +(-3.30515 - 0.275660i) 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} +(-2.85823 - 1.68241i) 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} +(5.25732 + 0.837694i) 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} +(-3.41929 + 8.50125i) 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} +(4.37322 + 3.03580i) 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} +(-0.141262 - 0.299758i) 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} +(-0.466717 - 3.28362i) 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} +(1.36679 + 0.324080i) 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	\( 264 q + 44 q^{2} - 44 q^{4} + 44 q^{8} - 20 q^{9} + 5 q^{11} - 7 q^{13} - 32 q^{15} - 44 q^{16} - q^{17} + 20 q^{18} - 21 q^{19} + 9 q^{22} - q^{23} - 7 q^{24} - 14 q^{25} - 7 q^{26} - 11 q^{29} + 4 q^{30} + 5 q^{31} + 44 q^{32} - 122 q^{33} + 15 q^{34} + 134 q^{36} - 72 q^{37} - 28 q^{38} + 86 q^{39} + 14 q^{40} - 28 q^{41} + 45 q^{43} - 9 q^{44} + 98 q^{45} - 6 q^{46} + 6 q^{47} - 140 q^{49} - 140 q^{50} + 7 q^{51} - 12 q^{53} + 42 q^{54} + 52 q^{55} - 2 q^{57} - 3 q^{58} + 44 q^{59} - 4 q^{60} + 71 q^{61} + 2 q^{62} - 24 q^{63} - 44 q^{64} - 68 q^{65} - 67 q^{66} + 25 q^{67} + 27 q^{68} + 74 q^{69} + 47 q^{71} + 20 q^{72} - 57 q^{73} + 2 q^{74} - 28 q^{75} + 28 q^{76} + 89 q^{77} + 12 q^{78} - 42 q^{79} + 99 q^{81} - 28 q^{82} - 44 q^{83} + 12 q^{85} - 17 q^{86} - 12 q^{88} - 69 q^{89} - 8 q^{92} + 84 q^{93} - 27 q^{94} - 12 q^{95} - 82 q^{97} - 14 q^{98} + 189 q^{99}+O(q^{100}) \) 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 + 9 * 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 - 122 * 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 + 52 * 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 - 67 * 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 + 89 * q^77 + 12 * q^78 - 42 * q^79 + 99 * q^81 - 28 * q^82 - 44 * q^83 + 12 * q^85 - 17 * q^86 - 12 * q^88 - 69 * q^89 - 8 * q^92 + 84 * q^93 - 27 * q^94 - 12 * q^95 - 82 * q^97 - 14 * q^98 + 189 * q^99

Introduction

L-functions

Modular forms

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