LMFDB - Embedded newform 370.2.v.b.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(99,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.v (of order $18$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.4
Character	$\chi$	$=$	370.169
Dual form			370.2.v.b.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.400420 - 1.10014i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0612182 - 2.23523i) q^{5} -1.17075i q^{6} +(-3.81475 - 0.672643i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.24815 - 1.04732i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.400420 - 1.10014i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0612182 - 2.23523i) q^{5} -1.17075i q^{6} +(-3.81475 - 0.672643i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.24815 - 1.04732i) q^{9} +(0.706967 - 2.12137i) q^{10} +(-1.57993 - 2.73651i) q^{11} +(0.400420 - 1.10014i) q^{12} +(-1.40293 - 1.17720i) q^{13} +(-3.35463 - 1.93680i) q^{14} +(-2.43456 + 0.962379i) q^{15} +(0.173648 + 0.984808i) q^{16} +(4.46534 - 3.74687i) q^{17} +(1.53108 - 0.557269i) q^{18} +(2.67996 + 7.36313i) q^{19} +(1.38988 - 1.75164i) q^{20} +(0.787496 + 4.46611i) q^{21} +(-0.548703 - 3.11185i) q^{22} +(0.0262094 - 0.0453960i) q^{23} +(0.752543 - 0.896846i) q^{24} +(-4.99250 + 0.273673i) q^{25} +(-0.915697 - 1.58603i) q^{26} +(-4.69369 - 2.70990i) q^{27} +(-2.48990 - 2.96735i) q^{28} +(3.42104 - 1.97514i) q^{29} +(-2.61689 + 0.0716712i) q^{30} -1.88120i q^{31} +(-0.173648 + 0.984808i) q^{32} +(-2.37793 + 2.83390i) q^{33} +(5.47755 - 1.99367i) q^{34} +(-1.26998 + 8.56801i) q^{35} +1.62935 q^{36} +(5.80760 - 1.80882i) q^{37} +7.83567i q^{38} +(-0.733326 + 2.01480i) q^{39} +(1.90516 - 1.17063i) q^{40} +(2.75128 + 2.30860i) q^{41} +(-0.787496 + 4.46611i) q^{42} +2.80385 q^{43} +(0.548703 - 3.11185i) q^{44} +(-2.41742 - 2.72579i) q^{45} +(0.0401551 - 0.0336941i) q^{46} +(9.42768 + 5.44307i) q^{47} +(1.01390 - 0.585375i) q^{48} +(7.52199 + 2.73778i) q^{49} +(-4.78502 - 1.45037i) q^{50} +(-5.91010 - 3.41220i) q^{51} +(-0.318018 - 1.80357i) q^{52} +(-12.8005 + 2.25707i) q^{53} +(-3.48378 - 4.15181i) q^{54} +(-6.02002 + 3.69902i) q^{55} +(-1.32485 - 3.63999i) q^{56} +(7.02739 - 5.89668i) q^{57} +(3.89026 - 0.685958i) q^{58} +(12.1068 - 2.13476i) q^{59} +(-2.48359 - 0.827681i) q^{60} +(0.0728097 - 0.0867712i) q^{61} +(0.643409 - 1.76775i) q^{62} +(-5.46586 + 3.15571i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.54542 + 3.20793i) q^{65} +(-3.20377 + 1.84970i) q^{66} +(4.55499 + 0.803167i) q^{67} +5.82909 q^{68} +(-0.0604369 - 0.0106567i) q^{69} +(-4.12382 + 7.61694i) q^{70} +(-12.4415 + 4.52834i) q^{71} +(1.53108 + 0.557269i) q^{72} +4.68205i q^{73} +(6.07601 + 0.286577i) q^{74} +(2.30018 + 5.38289i) q^{75} +(-2.67996 + 7.36313i) q^{76} +(4.18633 + 11.5018i) q^{77} +(-1.37820 + 1.64248i) q^{78} +(-5.72931 - 1.01023i) q^{79} +(2.19064 - 0.448432i) q^{80} +(-0.253039 + 1.43505i) q^{81} +(1.79577 + 3.11037i) q^{82} +(0.100220 + 0.119438i) q^{83} +(-2.26750 + 3.92743i) q^{84} +(-8.64847 - 9.75169i) q^{85} +(2.63476 + 0.958973i) q^{86} +(-3.54279 - 2.97275i) q^{87} +(1.57993 - 2.73651i) q^{88} +(2.80059 - 0.493820i) q^{89} +(-1.33936 - 3.38821i) q^{90} +(4.55998 + 5.43438i) q^{91} +(0.0492576 - 0.0179283i) q^{92} +(-2.06959 + 0.753270i) q^{93} +(6.99748 + 8.33927i) q^{94} +(16.2942 - 6.44108i) q^{95} +(1.15296 - 0.203298i) q^{96} +(-8.58698 + 14.8731i) q^{97} +(6.13199 + 5.14535i) q^{98} +(-4.83800 - 1.76089i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	$ 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.400420	−	1.10014i	−0.231182	−	0.635169i	0.768808	−	0.639479i	$-0.220850\pi$
$3$	−0.400420	−	1.10014i	−0.231182	−	0.635169i	−0.999991	+	0.00431076i	$0.998628\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.0612182	−	2.23523i	−0.0273776	−	0.999625i
$5$	−0.0612182	−	2.23523i	−0.0273776	−	0.999625i
$6$		−	1.17075i		−	0.477956i
$7$	−3.81475	−	0.672643i	−1.44184	−	0.254235i	−0.602620	−	0.798029i	$-0.705876\pi$
$7$	−3.81475	−	0.672643i	−1.44184	−	0.254235i	−0.839219	+	0.543794i	$0.816987\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	1.24815	−	1.04732i	0.416051	−	0.349108i
$10$	0.706967	−	2.12137i	0.223563	−	0.670835i
$11$	−1.57993	−	2.73651i	−0.476366	−	0.825090i	0.523267	−	0.852169i	$-0.324713\pi$
$11$	−1.57993	−	2.73651i	−0.476366	−	0.825090i	−0.999633	+	0.0270785i	$0.991380\pi$
$12$	0.400420	−	1.10014i	0.115591	−	0.317584i
$13$	−1.40293	−	1.17720i	−0.389102	−	0.326496i	0.427161	−	0.904176i	$-0.359514\pi$
$13$	−1.40293	−	1.17720i	−0.389102	−	0.326496i	−0.816263	+	0.577680i	$0.803958\pi$
$14$	−3.35463	−	1.93680i	−0.896563	−	0.517631i
$15$	−2.43456	+	0.962379i	−0.628601	+	0.248485i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	4.46534	−	3.74687i	1.08300	−	0.908748i	0.0868373	−	0.996223i	$-0.472324\pi$
$17$	4.46534	−	3.74687i	1.08300	−	0.908748i	0.996167	+	0.0874741i	$0.0278795\pi$
$18$	1.53108	−	0.557269i	0.360880	−	0.131350i
$19$	2.67996	+	7.36313i	0.614825	+	1.68922i	0.719309	+	0.694690i	$0.244459\pi$
$19$	2.67996	+	7.36313i	0.614825	+	1.68922i	−0.104484	+	0.994527i	$0.533319\pi$
$20$	1.38988	−	1.75164i	0.310787	−	0.391678i
$21$	0.787496	+	4.46611i	0.171846	+	0.974585i
$22$	−0.548703	−	3.11185i	−0.116984	−	0.663448i
$23$	0.0262094	−	0.0453960i	0.00546504	−	0.00946572i	−0.863280	−	0.504725i	$-0.831594\pi$
$23$	0.0262094	−	0.0453960i	0.00546504	−	0.00946572i	0.868745	+	0.495260i	$0.164927\pi$
$24$	0.752543	−	0.896846i	0.153612	−	0.183068i
$25$	−4.99250	+	0.273673i	−0.998501	+	0.0547347i
$26$	−0.915697	−	1.58603i	−0.179583	−	0.311047i
$27$	−4.69369	−	2.70990i	−0.903301	−	0.521521i
$28$	−2.48990	−	2.96735i	−0.470547	−	0.560776i
$29$	3.42104	−	1.97514i	0.635270	−	0.366774i	−0.147520	−	0.989059i	$-0.547129\pi$
$29$	3.42104	−	1.97514i	0.635270	−	0.366774i	0.782790	+	0.622286i	$0.213796\pi$
$30$	−2.61689	+	0.0716712i	−0.477777	+	0.0130853i
$31$		−	1.88120i		−	0.337874i	−0.985627	−	0.168937i	$-0.945967\pi$
$31$		−	1.88120i		−	0.337874i	0.985627	−	0.168937i	$-0.0540334\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−2.37793	+	2.83390i	−0.413944	+	0.493319i
$34$	5.47755	−	1.99367i	0.939392	−	0.341911i
$35$	−1.26998	+	8.56801i	−0.214666	+	1.44826i
$36$	1.62935			0.271558
$37$	5.80760	−	1.80882i	0.954763	−	0.297369i
$37$	5.80760	−	1.80882i	0.954763	−	0.297369i
$38$			7.83567i			1.27111i
$39$	−0.733326	+	2.01480i	−0.117426	+	0.322626i
$40$	1.90516	−	1.17063i	0.301232	−	0.185093i
$41$	2.75128	+	2.30860i	0.429678	+	0.360543i	0.831830	−	0.555030i	$-0.187293\pi$
$41$	2.75128	+	2.30860i	0.429678	+	0.360543i	−0.402152	+	0.915573i	$0.631738\pi$
$42$	−0.787496	+	4.46611i	−0.121513	+	0.689136i
$43$	2.80385			0.427583			0.213792	−	0.976879i	$-0.431419\pi$
$43$	2.80385			0.427583			0.213792	+	0.976879i	$0.431419\pi$
$44$	0.548703	−	3.11185i	0.0827201	−	0.469129i
$45$	−2.41742	−	2.72579i	−0.360367	−	0.406337i
$46$	0.0401551	−	0.0336941i	0.00592055	−	0.00496793i
$47$	9.42768	+	5.44307i	1.37517	+	0.793954i	0.991573	−	0.129548i	$-0.0413526\pi$
$47$	9.42768	+	5.44307i	1.37517	+	0.793954i	0.383595	+	0.923502i	$0.374686\pi$
$48$	1.01390	−	0.585375i	0.146344	−	0.0844915i
$49$	7.52199	+	2.73778i	1.07457	+	0.391112i
$50$	−4.78502	−	1.45037i	−0.676704	−	0.205113i
$51$	−5.91010	−	3.41220i	−0.827580	−	0.477804i
$52$	−0.318018	−	1.80357i	−0.0441012	−	0.250110i
$53$	−12.8005	+	2.25707i	−1.75828	+	0.310033i	−0.957395	−	0.288783i	$-0.906750\pi$
$53$	−12.8005	+	2.25707i	−1.75828	+	0.310033i	−0.800887	+	0.598815i	$0.795638\pi$
$54$	−3.48378	−	4.15181i	−0.474083	−	0.564990i
$55$	−6.02002	+	3.69902i	−0.811739	+	0.498776i
$56$	−1.32485	−	3.63999i	−0.177040	−	0.486414i
$57$	7.02739	−	5.89668i	0.930801	−	0.781035i
$58$	3.89026	−	0.685958i	0.510816	−	0.0900706i
$59$	12.1068	−	2.13476i	1.57618	−	0.277922i	0.683956	−	0.729524i	$-0.260258\pi$
$59$	12.1068	−	2.13476i	1.57618	−	0.277922i	0.892220	+	0.451601i	$0.149147\pi$
$60$	−2.48359	−	0.827681i	−0.320630	−	0.106853i
$61$	0.0728097	−	0.0867712i	0.00932233	−	0.0111099i	−0.761363	−	0.648326i	$-0.775470\pi$
$61$	0.0728097	−	0.0867712i	0.00932233	−	0.0111099i	0.770685	+	0.637216i	$0.219914\pi$
$62$	0.643409	−	1.76775i	0.0817130	−	0.224505i
$63$	−5.46586	+	3.15571i	−0.688633	+	0.397583i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−2.54542	+	3.20793i	−0.315721	+	0.397895i
$66$	−3.20377	+	1.84970i	−0.394357	+	0.227682i
$67$	4.55499	+	0.803167i	0.556480	+	0.0981225i	0.444813	−	0.895623i	$-0.353270\pi$
$67$	4.55499	+	0.803167i	0.556480	+	0.0981225i	0.111667	+	0.993746i	$0.464381\pi$
$68$	5.82909			0.706881
$69$	−0.0604369	−	0.0106567i	−0.00727575	−	0.00128291i
$70$	−4.12382	+	7.61694i	−0.492891	+	0.910398i
$71$	−12.4415	+	4.52834i	−1.47654	+	0.537416i	−0.949867	−	0.312654i	$-0.898782\pi$
$71$	−12.4415	+	4.52834i	−1.47654	+	0.537416i	−0.526670	+	0.850070i	$0.676560\pi$
$72$	1.53108	+	0.557269i	0.180440	+	0.0656748i
$73$			4.68205i			0.547992i	0.961731	+	0.273996i	$0.0883456\pi$
$73$			4.68205i			0.547992i	−0.961731	+	0.273996i	$0.911654\pi$
$74$	6.07601	+	0.286577i	0.706322	+	0.0333140i
$75$	2.30018	+	5.38289i	0.265602	+	0.621563i
$76$	−2.67996	+	7.36313i	−0.307412	+	0.844608i
$77$	4.18633	+	11.5018i	0.477076	+	1.31076i
$78$	−1.37820	+	1.64248i	−0.156051	+	0.185974i
$79$	−5.72931	−	1.01023i	−0.644598	−	0.113660i	−0.158214	−	0.987405i	$-0.550573\pi$
$79$	−5.72931	−	1.01023i	−0.644598	−	0.113660i	−0.486384	+	0.873745i	$0.661685\pi$
$80$	2.19064	−	0.448432i	0.244921	−	0.0501362i
$81$	−0.253039	+	1.43505i	−0.0281154	+	0.159450i
$82$	1.79577	+	3.11037i	0.198310	+	0.343483i
$83$	0.100220	+	0.119438i	0.0110006	+	0.0131100i	0.771517	−	0.636209i	$-0.219498\pi$
$83$	0.100220	+	0.119438i	0.0110006	+	0.0131100i	−0.760516	+	0.649319i	$0.775054\pi$
$84$	−2.26750	+	3.92743i	−0.247405	+	0.428518i
$85$	−8.64847	−	9.75169i	−0.938058	−	1.05772i
$86$	2.63476	+	0.958973i	0.284113	+	0.103409i
$87$	−3.54279	−	2.97275i	−0.379826	−	0.318712i
$88$	1.57993	−	2.73651i	0.168421	−	0.291713i
$89$	2.80059	−	0.493820i	0.296862	−	0.0523449i	−0.0232333	−	0.999730i	$-0.507396\pi$
$89$	2.80059	−	0.493820i	0.296862	−	0.0523449i	0.320096	+	0.947385i	$0.396285\pi$
$90$	−1.33936	−	3.38821i	−0.141180	−	0.357149i
$91$	4.55998	+	5.43438i	0.478016	+	0.569678i
$92$	0.0492576	−	0.0179283i	0.00513545	−	0.00186915i
$93$	−2.06959	+	0.753270i	−0.214607	+	0.0781105i
$94$	6.99748	+	8.33927i	0.721735	+	0.860130i
$95$	16.2942	−	6.44108i	1.67175	−	0.660841i
$96$	1.15296	−	0.203298i	0.117674	−	0.0207491i
$97$	−8.58698	+	14.8731i	−0.871876	+	1.51013i	−0.0118226	+	0.999930i	$0.503763\pi$
$97$	−8.58698	+	14.8731i	−0.871876	+	1.51013i	−0.860054	+	0.510204i	$0.829570\pi$
$98$	6.13199	+	5.14535i	0.619424	+	0.519759i
$99$	−4.83800	−	1.76089i	−0.486238	−	0.176976i
$100$	−4.00039	−	2.99947i	−0.400039	−	0.299947i
$101$	4.22216	−	7.31300i	0.420121	−	0.727670i	−0.575830	−	0.817569i	$-0.695321\pi$
$101$	4.22216	−	7.31300i	0.420121	−	0.727670i	0.995951	+	0.0898990i	$0.0286544\pi$
$102$	−4.38664	−	5.22779i	−0.434342	−	0.517629i
$103$	−1.21290	−	2.10081i	−0.119511	−	0.206999i	0.800063	−	0.599916i	$-0.204799\pi$
$103$	−1.21290	−	2.10081i	−0.119511	−	0.206999i	−0.919574	+	0.392917i	$0.871466\pi$
$104$	0.318018	−	1.80357i	0.0311842	−	0.176855i
$105$	9.93458	−	2.03364i	0.969515	−	0.198463i
$106$	−12.8005	−	2.25707i	−1.24329	−	0.219226i
$107$	1.73125	−	2.06323i	0.167367	−	0.199460i	−0.675842	−	0.737047i	$-0.736220\pi$
$107$	1.73125	−	2.06323i	0.167367	−	0.199460i	0.843208	+	0.537587i	$0.180664\pi$
$108$	−1.85368	−	5.09295i	−0.178371	−	0.490069i
$109$	6.74310	−	18.5265i	0.645872	−	1.77452i	0.0134304	−	0.999910i	$-0.495725\pi$
$109$	6.74310	−	18.5265i	0.645872	−	1.77452i	0.632441	−	0.774608i	$-0.282053\pi$
$110$	−6.92211	+	1.41698i	−0.659997	+	0.135104i
$111$	−4.31544	−	5.66490i	−0.409604	−	0.537689i
$112$		−	3.87360i		−	0.366020i
$113$	10.9126	+	3.97185i	1.02657	+	0.373640i	0.799773	−	0.600303i	$-0.204953\pi$
$113$	10.9126	+	3.97185i	1.02657	+	0.373640i	0.226795	+	0.973943i	$0.427175\pi$
$114$	8.62037	−	3.13756i	0.807372	−	0.293859i
$115$	−0.103075	−	0.0558050i	−0.00961179	−	0.00520384i
$116$	3.89026	+	0.685958i	0.361201	+	0.0636896i
$117$	−2.98397			−0.275869
$118$	12.1068	+	2.13476i	1.11452	+	0.196521i
$119$	−19.5544	+	11.2898i	−1.79255	+	1.03493i
$120$	−2.05073	−	1.62720i	−0.187205	−	0.148543i
$121$	0.507660	−	0.879293i	0.0461509	−	0.0799357i
$122$	0.0980962	−	0.0566359i	0.00888122	−	0.00512757i
$123$	1.43812	−	3.95122i	0.129671	−	0.356269i
$124$	1.20921	−	1.44108i	0.108591	−	0.129413i
$125$	0.917355	+	11.1426i	0.0820508	+	0.996628i
$126$	−6.21554	+	1.09597i	−0.553725	+	0.0976366i
$127$	−11.3628	+	2.00358i	−1.00829	+	0.177789i	−0.653314	−	0.757087i	$-0.726622\pi$
$127$	−11.3628	+	2.00358i	−1.00829	+	0.177789i	−0.354975	+	0.934876i	$0.615511\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−1.12272	−	3.08464i	−0.0988497	−	0.271587i
$130$	−3.48909	+	2.14389i	−0.306014	+	0.188031i
$131$	1.27569	+	1.52031i	0.111457	+	0.132830i	0.818889	−	0.573952i	$-0.194591\pi$
$131$	1.27569	+	1.52031i	0.111457	+	0.132830i	−0.707431	+	0.706782i	$0.750146\pi$
$132$	−3.64319	+	0.642394i	−0.317099	+	0.0559132i
$133$	−5.27061	−	29.8911i	−0.457020	−	2.59189i
$134$	4.00559	+	2.31263i	0.346030	+	0.199781i
$135$	−5.76991	+	10.6574i	−0.496595	+	0.917240i
$136$	5.47755	+	1.99367i	0.469696	+	0.170955i
$137$	−11.0451	+	6.37688i	−0.943644	+	0.544813i	−0.891101	−	0.453805i	$-0.850066\pi$
$137$	−11.0451	+	6.37688i	−0.943644	+	0.544813i	−0.0525435	+	0.998619i	$0.516733\pi$
$138$	−0.0531473	−	0.0306846i	−0.00452420	−	0.00261205i
$139$	11.7633	−	9.87061i	0.997753	−	0.837214i	0.0110816	−	0.999939i	$-0.496473\pi$
$139$	11.7633	−	9.87061i	0.997753	−	0.837214i	0.986672	+	0.162724i	$0.0520281\pi$
$140$	−6.48027	+	5.74715i	−0.547683	+	0.485723i
$141$	2.21314	−	12.5513i	0.186380	−	1.05701i
$142$	−13.2400			−1.11108
$143$	−1.00489	+	5.69902i	−0.0840332	+	0.476576i
$144$	1.24815	+	1.04732i	0.104013	+	0.0872770i
$145$	−4.62431	−	7.52589i	−0.384028	−	0.624991i
$146$	−1.60135	+	4.39969i	−0.132529	+	0.364121i
$147$		−	9.37154i		−	0.772952i
$148$	5.61156	+	2.34741i	0.461268	+	0.192956i
$149$	8.31712			0.681365			0.340683	−	0.940178i	$-0.389342\pi$
$149$	8.31712			0.681365			0.340683	+	0.940178i	$0.389342\pi$
$150$	0.320403	+	5.84497i	0.0261608	+	0.477240i
$151$	−4.39822	+	1.60082i	−0.357922	+	0.130273i	−0.514721	−	0.857358i	$-0.672105\pi$
$151$	−4.39822	+	1.60082i	−0.357922	+	0.130273i	0.156799	+	0.987630i	$0.449882\pi$
$152$	−5.03667	+	6.00247i	−0.408528	+	0.486865i
$153$	1.64924	−	9.35331i	0.133333	−	0.756171i
$154$			12.2400i			0.986327i
$155$	−4.20492	+	0.115164i	−0.337747	+	0.00925018i
$156$	−1.85685	+	1.07205i	−0.148667	+	0.0858328i
$157$	7.98121	+	9.51164i	0.636970	+	0.759111i	0.983888	−	0.178784i	$-0.0572163\pi$
$157$	7.98121	+	9.51164i	0.636970	+	0.759111i	−0.346918	+	0.937895i	$0.612772\pi$
$158$	−5.03827	−	2.90885i	−0.400823	−	0.231416i
$159$	7.60867	+	13.1786i	0.603407	+	1.04513i
$160$	2.21190	+	0.327855i	0.174866	+	0.0259192i
$161$	−0.130517	+	0.155545i	−0.0102862	+	0.0122586i
$162$	−0.728596	+	1.26196i	−0.0572439	+	0.0991493i
$163$	−3.14656	−	17.8450i	−0.246457	−	1.39773i	−0.817083	−	0.576519i	$-0.804411\pi$
$163$	−3.14656	−	17.8450i	−0.246457	−	1.39773i	0.570626	−	0.821210i	$-0.306701\pi$
$164$	0.623665	+	3.53698i	0.0487000	+	0.276192i
$165$	6.48000	+	5.14173i	0.504467	+	0.400283i
$166$	0.0533260	+	0.146512i	0.00413890	+	0.0113715i
$167$	13.2553	−	4.82455i	1.02573	−	0.373335i	0.226276	−	0.974063i	$-0.427345\pi$
$167$	13.2553	−	4.82455i	1.02573	−	0.373335i	0.799453	+	0.600728i	$0.205123\pi$
$168$	−3.47402	+	2.91505i	−0.268026	+	0.224901i
$169$	−1.67501	−	9.49945i	−0.128847	−	0.730727i
$170$	−4.79163	−	12.1215i	−0.367501	−	0.929679i
$171$	11.0566	+	6.38351i	0.845517	+	0.488160i
$172$	2.14787	+	1.80228i	0.163774	+	0.137423i
$173$	0.942189	−	2.58864i	0.0716333	−	0.196811i	−0.898709	−	0.438545i	$-0.855494\pi$
$173$	0.942189	−	2.58864i	0.0716333	−	0.196811i	0.970343	+	0.241734i	$0.0777162\pi$
$174$	−2.31239	−	4.00517i	−0.175302	−	0.303632i
$175$	19.2292	+	2.31418i	1.45359	+	0.174935i
$176$	2.42059	−	2.03112i	0.182459	−	0.153101i
$177$	−7.19636	−	12.4645i	−0.540912	−	0.936886i
$178$	2.80059	+	0.493820i	0.209913	+	0.0370134i
$179$			6.88706i			0.514763i	0.966310	+	0.257382i	$0.0828598\pi$
$179$			6.88706i			0.514763i	−0.966310	+	0.257382i	$0.917140\pi$
$180$	−0.0997457	−	3.64196i	−0.00743460	−	0.271456i
$181$	4.29631	+	3.60503i	0.319342	+	0.267960i	0.788340	−	0.615239i	$-0.210941\pi$
$181$	4.29631	+	3.60503i	0.319342	+	0.267960i	−0.468998	+	0.883199i	$0.655385\pi$
$182$	2.42632	+	6.66625i	0.179851	+	0.494135i
$183$	−0.124615	−	0.0453563i	−0.00921183	−	0.00335283i
$184$	0.0524188			0.00386436
$185$	−4.39866	−	12.8706i	−0.323396	−	0.946264i
$186$	−2.20241			−0.161489
$187$	−17.3083	−	6.29969i	−1.26571	−	0.460679i
$188$	3.72328	+	10.2296i	0.271548	+	0.746072i
$189$	16.0824	+	13.4948i	1.16982	+	0.981600i
$190$	17.5145	−	0.479686i	1.27064	−	0.0348001i
$191$			13.3454i			0.965637i	0.875721	+	0.482818i	$0.160387\pi$
$191$			13.3454i			0.965637i	−0.875721	+	0.482818i	$0.839613\pi$
$192$	1.15296	+	0.203298i	0.0832079	+	0.0146718i
$193$	3.14471	+	5.44680i	0.226361	+	0.392069i	0.956727	−	0.290987i	$-0.0939837\pi$
$193$	3.14471	+	5.44680i	0.226361	+	0.392069i	−0.730366	+	0.683056i	$0.760650\pi$
$194$	−13.1560	+	11.0392i	−0.944547	+	0.792569i
$195$	4.54843	+	1.51581i	0.325720	+	0.108549i
$196$	4.00237	+	6.93231i	0.285884	+	0.495165i
$197$	5.08518	−	13.9714i	0.362304	−	0.995422i	−0.615909	−	0.787817i	$-0.711211\pi$
$197$	5.08518	−	13.9714i	0.362304	−	0.995422i	0.978213	−	0.207604i	$-0.0665667\pi$
$198$	−3.94398	−	3.30939i	−0.280286	−	0.235188i
$199$	−10.4111	−	6.01084i	−0.738022	−	0.426097i	0.0833276	−	0.996522i	$-0.473445\pi$
$199$	−10.4111	−	6.01084i	−0.738022	−	0.426097i	−0.821350	+	0.570425i	$0.806779\pi$
$200$	−2.73326	−	4.18680i	−0.193271	−	0.296051i
$201$	−0.940307	−	5.33275i	−0.0663242	−	0.376143i
$202$	6.46872	−	5.42790i	0.455138	−	0.381906i
$203$	−14.3789	+	5.23351i	−1.00920	+	0.367320i
$204$	−2.33408	−	6.41284i	−0.163418	−	0.448988i
$205$	4.99182	−	6.29107i	0.348644	−	0.439388i
$206$	−0.421236	−	2.38895i	−0.0293489	−	0.166446i
$207$	−0.0148310	−	0.0841108i	−0.00103083	−	0.00584611i
$208$	0.915697	−	1.58603i	0.0634921	−	0.109972i
$209$	15.9152	−	18.9669i	1.10087	−	1.31197i
$210$	10.0310	+	1.48683i	0.692204	+	0.102601i
$211$	−11.9726	−	20.7372i	−0.824231	−	1.42761i	−0.902506	−	0.430678i	$-0.858275\pi$
$211$	−11.9726	−	20.7372i	−0.824231	−	1.42761i	0.0782753	−	0.996932i	$-0.475059\pi$
$212$	−11.2566	−	6.49898i	−0.773104	−	0.446352i
$213$	9.96366	+	11.8742i	0.682699	+	0.813609i
$214$	2.33251	−	1.34668i	0.159447	−	0.0920568i
$215$	−0.171647	−	6.26725i	−0.0117062	−	0.427423i
$216$		−	5.41980i		−	0.368771i
$217$	−1.26538	+	7.17631i	−0.0858993	+	0.487159i
$218$	12.6729	−	15.1030i	0.858316	−	1.02290i
$219$	5.15093	−	1.87478i	0.348068	−	0.126686i
$220$	−6.98929	−	1.03598i	−0.471218	−	0.0698454i
$221$	−10.6754			−0.718102
$222$	−2.11768	−	6.79924i	−0.142129	−	0.456335i
$223$		−	10.3038i		−	0.689995i	−0.938604	−	0.344998i	$-0.887880\pi$
$223$		−	10.3038i		−	0.689995i	0.938604	−	0.344998i	$-0.112120\pi$
$224$	1.32485	−	3.63999i	0.0885201	−	0.243207i
$225$	−5.94478	+	5.57035i	−0.396319	+	0.371357i
$226$	8.89600	+	7.46463i	0.591753	+	0.496540i
$227$	−2.36191	+	13.3951i	−0.156766	+	0.889063i	0.800388	+	0.599482i	$0.204627\pi$
$227$	−2.36191	+	13.3951i	−0.156766	+	0.889063i	−0.957154	+	0.289580i	$0.906484\pi$
$228$	9.17361			0.607537
$229$	−2.76999	+	15.7094i	−0.183046	+	1.03811i	0.745394	+	0.666624i	$0.232261\pi$
$229$	−2.76999	+	15.7094i	−0.183046	+	1.03811i	−0.928440	+	0.371482i	$0.878850\pi$
$230$	−0.0777724	−	0.0876932i	−0.00512816	−	0.00578232i
$231$	10.9774	−	9.21112i	0.722259	−	0.606048i
$232$	3.42104	+	1.97514i	0.224602	+	0.129674i
$233$	−6.41359	+	3.70289i	−0.420168	+	0.242584i	−0.695149	−	0.718865i	$-0.744662\pi$
$233$	−6.41359	+	3.70289i	−0.420168	+	0.242584i	0.274981	+	0.961450i	$0.411328\pi$
$234$	−2.80402	−	1.02058i	−0.183304	−	0.0667174i
$235$	11.5894	−	21.4062i	0.756007	−	1.39639i
$236$	10.6466	+	6.14680i	0.693033	+	0.400123i
$237$	1.18273	+	6.70759i	0.0768265	+	0.435705i
$238$	−22.2365	+	3.92089i	−1.44138	+	0.254154i
$239$	−7.85591	−	9.36231i	−0.508157	−	0.605598i	0.449581	−	0.893239i	$-0.351573\pi$
$239$	−7.85591	−	9.36231i	−0.508157	−	0.605598i	−0.957738	+	0.287642i	$0.907129\pi$
$240$	−1.37052	−	2.23046i	−0.0884664	−	0.143976i
$241$	3.03748	+	8.34541i	0.195661	+	0.537575i	0.998261	−	0.0589423i	$-0.0187728\pi$
$241$	3.03748	+	8.34541i	0.195661	+	0.537575i	−0.802600	+	0.596518i	$0.796551\pi$
$242$	0.777780	−	0.652635i	0.0499976	−	0.0419530i
$243$	−14.3323	+	2.52717i	−0.919418	+	0.162118i
$244$	0.111551	−	0.0196694i	0.00714132	−	0.00125921i
$245$	5.65909	−	16.9810i	0.361546	−	1.08488i
$246$	2.70279	−	3.22106i	0.172324	−	0.205367i
$247$	4.90806	−	13.4848i	0.312292	−	0.858016i
$248$	1.62917	−	0.940601i	0.103452	−	0.0597282i
$249$	0.0912686	−	0.158082i	0.00578391	−	0.0100180i
$250$	−2.94898	+	10.7844i	−0.186510	+	0.682066i
$251$	−20.9005	+	12.0669i	−1.31923	+	0.761657i	−0.983604	−	0.180340i	$-0.942280\pi$
$251$	−20.9005	+	12.0669i	−1.31923	+	0.761657i	−0.335623	+	0.941996i	$0.608947\pi$
$252$	−6.21554	−	1.09597i	−0.391542	−	0.0690395i
$253$	−0.165636			−0.0104134
$254$	−11.3628	−	2.00358i	−0.712968	−	0.125716i
$255$	−7.26525	+	13.4193i	−0.454967	+	0.840351i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	19.5648	+	7.12102i	1.22042	+	0.444197i	0.870307	−	0.492510i	$-0.163921\pi$
$257$	19.5648	+	7.12102i	1.22042	+	0.444197i	0.350114	+	0.936707i	$0.386143\pi$
$258$		−	3.28261i		−	0.204366i
$259$	−23.3712	+	2.99376i	−1.45222	+	0.186023i
$260$	−4.01193	+	0.821255i	−0.248809	+	0.0509321i
$261$	2.20137	−	6.04820i	0.136261	−	0.374374i
$262$	0.678780	+	1.86493i	0.0419351	+	0.115216i
$263$	−10.7738	+	12.8397i	−0.664341	+	0.791731i	−0.988002	−	0.154442i	$-0.950642\pi$
$263$	−10.7738	+	12.8397i	−0.664341	+	0.791731i	0.323660	+	0.946173i	$0.395086\pi$
$264$	−3.64319	−	0.642394i	−0.224223	−	0.0395366i
$265$	5.82870	+	28.4739i	0.358054	+	1.74914i
$266$	5.27061	−	29.8911i	0.323162	−	1.83274i
$267$	−1.66469	−	2.88332i	−0.101877	−	0.176456i
$268$	2.97306	+	3.54315i	0.181608	+	0.216432i
$269$	−14.9199	+	25.8420i	−0.909681	+	1.57561i	−0.0951726	+	0.995461i	$0.530340\pi$
$269$	−14.9199	+	25.8420i	−0.909681	+	1.57561i	−0.814508	+	0.580152i	$0.802993\pi$
$270$	−9.06698	+	8.04122i	−0.551799	+	0.489373i
$271$	−8.68882	−	3.16247i	−0.527809	−	0.192107i	0.0643510	−	0.997927i	$-0.479502\pi$
$271$	−8.68882	−	3.16247i	−0.527809	−	0.192107i	−0.592160	+	0.805821i	$0.701724\pi$
$272$	4.46534	+	3.74687i	0.270751	+	0.227187i
$273$	4.15269	−	7.19267i	0.251332	−	0.435320i
$274$	−12.5600	+	2.21467i	−0.758777	+	0.133793i
$275$	8.63671	+	13.2297i	0.520813	+	0.797779i
$276$	−0.0394474	−	0.0470116i	−0.00237445	−	0.00282976i
$277$	1.09983	−	0.400305i	0.0660823	−	0.0240520i	−0.308768	−	0.951138i	$-0.599917\pi$
$277$	1.09983	−	0.400305i	0.0660823	−	0.0240520i	0.374850	+	0.927086i	$0.377694\pi$
$278$	14.4299	−	5.25204i	0.865446	−	0.314997i
$279$	−1.97023	−	2.34802i	−0.117954	−	0.140573i
$280$	−8.05511	+	3.18417i	−0.481385	+	0.190291i
$281$	28.0576	−	4.94731i	1.67378	−	0.295132i	0.745356	−	0.666666i	$-0.232279\pi$
$281$	28.0576	−	4.94731i	1.67378	−	0.295132i	0.928419	+	0.371535i	$0.121168\pi$
$282$	6.37247	−	11.0374i	0.379475	−	0.657270i
$283$	−0.162463	−	0.136323i	−0.00965744	−	0.00810356i	0.637946	−	0.770081i	$-0.279784\pi$
$283$	−0.162463	−	0.136323i	−0.00965744	−	0.00810356i	−0.647604	+	0.761977i	$0.724229\pi$
$284$	−12.4415	−	4.52834i	−0.738269	−	0.268708i
$285$	−13.6106	−	15.3469i	−0.806225	−	0.909069i
$286$	−2.89347	+	5.01163i	−0.171094	+	0.296344i
$287$	−8.94258	−	10.6573i	−0.527864	−	0.629083i
$288$	0.814673	+	1.41106i	0.0480051	+	0.0831472i
$289$	2.94825	−	16.7203i	0.173426	−	0.983549i
$290$	−1.77143	−	8.65363i	−0.104022	−	0.508159i
$291$	19.8009	+	3.49144i	1.16075	+	0.204672i
$292$	−3.00956	+	3.58666i	−0.176121	+	0.209893i
$293$	−0.946580	−	2.60071i	−0.0552998	−	0.151935i	0.908967	−	0.416868i	$-0.136872\pi$
$293$	−0.946580	−	2.60071i	−0.0552998	−	0.151935i	−0.964267	+	0.264933i	$0.914650\pi$
$294$	3.20526	−	8.80637i	0.186934	−	0.513598i
$295$	−5.51284	−	26.9309i	−0.320970	−	1.56798i
$296$	4.47028	+	4.12511i	0.259830	+	0.239767i
$297$			17.1258i			0.993739i
$298$	7.81554	+	2.84462i	0.452742	+	0.164785i
$299$	−0.0902100	+	0.0328337i	−0.00521698	+	0.00189882i
$300$	−1.69802	+	5.60206i	−0.0980351	+	0.323435i
$301$	−10.6960	−	1.88599i	−0.616506	−	0.108707i
$302$	−4.68049			−0.269332
$303$	−9.73599	−	1.71672i	−0.559318	−	0.0986228i
$304$	−6.78589	+	3.91784i	−0.389198	+	0.224703i
$305$	−0.198411	−	0.157434i	−0.0113610	−	0.00901467i
$306$	4.74880	−	8.22517i	0.271471	−	0.470201i
$307$	26.0567	−	15.0438i	1.48713	−	0.858596i	0.487240	−	0.873268i	$-0.338004\pi$
$307$	26.0567	−	15.0438i	1.48713	−	0.858596i	0.999892	+	0.0146715i	$0.00467026\pi$
$308$	−4.18633	+	11.5018i	−0.238538	+	0.655378i
$309$	−1.82552	+	2.17557i	−0.103850	+	0.123764i
$310$	−3.99072	−	1.32995i	−0.226658	−	0.0755360i
$311$	1.54935	−	0.273192i	0.0878555	−	0.0154913i	−0.129548	−	0.991573i	$-0.541352\pi$
$311$	1.54935	−	0.273192i	0.0878555	−	0.0154913i	0.217403	+	0.976082i	$0.430241\pi$
$312$	−2.11153	+	0.372319i	−0.119542	+	0.0210784i
$313$	−16.3282	+	13.7010i	−0.922925	+	0.774426i	−0.974534	−	0.224242i	$-0.928010\pi$
$313$	−16.3282	+	13.7010i	−0.922925	+	0.774426i	0.0516088	+	0.998667i	$0.483565\pi$
$314$	4.24671	+	11.6678i	0.239656	+	0.658449i
$315$	7.38836	+	12.0243i	0.416287	+	0.677490i
$316$	−3.73954	−	4.45661i	−0.210366	−	0.250704i
$317$	12.0836	−	2.13067i	0.678683	−	0.119670i	0.176328	−	0.984332i	$-0.443578\pi$
$317$	12.0836	−	2.13067i	0.678683	−	0.119670i	0.502355	+	0.864661i	$0.332467\pi$
$318$	2.64246	+	14.9862i	0.148182	+	0.840382i
$319$	−10.8100	−	6.24114i	−0.605242	−	0.349437i
$320$	1.96637	+	1.06460i	0.109924	+	0.0595129i
$321$	−2.96307	−	1.07847i	−0.165383	−	0.0601944i
$322$	−0.175846	+	0.101525i	−0.00979950	+	0.00565774i
$323$	39.5556	+	22.8374i	2.20093	+	1.27071i
$324$	−1.11627	+	0.936665i	−0.0620152	+	0.0520369i
$325$	7.32630	+	5.49322i	0.406390	+	0.304709i
$326$	3.14656	−	17.8450i	0.174272	−	0.988344i
$327$	−23.0819			−1.27643
$328$	−0.623665	+	3.53698i	−0.0344361	+	0.195297i
$329$	−32.3030	−	27.1054i	−1.78092	−	1.49437i
$330$	4.33063	+	7.04793i	0.238393	+	0.387976i
$331$	−5.77290	+	15.8609i	−0.317307	+	0.871794i	0.673822	+	0.738893i	$0.264651\pi$
$331$	−5.77290	+	15.8609i	−0.317307	+	0.871794i	−0.991129	+	0.132901i	$0.957571\pi$
$332$			0.155915i			0.00855694i
$333$	5.35434	−	8.34012i	0.293416	−	0.457036i
$334$	14.1060			0.771848
$335$	1.51641	−	10.2306i	0.0828506	−	0.558958i
$336$	−4.26151	+	1.55106i	−0.232485	+	0.0846175i
$337$	−16.6418	+	19.8330i	−0.906538	+	1.08037i	0.0898925	+	0.995951i	$0.471348\pi$
$337$	−16.6418	+	19.8330i	−0.906538	+	1.08037i	−0.996430	+	0.0844184i	$0.973097\pi$
$338$	1.67501	−	9.49945i	0.0911085	−	0.516702i
$339$		−	13.5958i		−	0.738423i
$340$	−0.356846	−	13.0294i	−0.0193527	−	0.706616i
$341$	−5.14793	+	2.97216i	−0.278776	+	0.160952i
$342$	8.20649	+	9.78011i	0.443756	+	0.528848i
$343$	−3.37053	−	1.94598i	−0.181992	−	0.105073i
$344$	1.40193	+	2.42821i	0.0755867	+	0.130920i
$345$	−0.0201202	+	0.135743i	−0.00108324	+	0.00730815i
$346$	1.77074	−	2.11028i	0.0951953	−	0.113449i
$347$	−8.20851	+	14.2176i	−0.440656	+	0.763238i	−0.997738	−	0.0672191i	$-0.978587\pi$
$347$	−8.20851	+	14.2176i	−0.440656	+	0.763238i	0.557083	+	0.830457i	$0.311921\pi$
$348$	−0.803084	−	4.55452i	−0.0430498	−	0.244148i
$349$	3.63461	+	20.6129i	0.194556	+	1.10338i	0.913049	+	0.407849i	$0.133721\pi$
$349$	3.63461	+	20.6129i	0.194556	+	1.10338i	−0.718493	+	0.695534i	$0.755168\pi$
$350$	17.2781	+	8.75140i	0.923551	+	0.467782i
$351$	3.39482	+	9.32719i	0.181202	+	0.497849i
$352$	2.96929	−	1.08073i	0.158264	−	0.0576033i
$353$	−9.83024	+	8.24855i	−0.523211	+	0.439026i	−0.865749	−	0.500478i	$-0.833158\pi$
$353$	−9.83024	+	8.24855i	−0.523211	+	0.439026i	0.342538	+	0.939504i	$0.388713\pi$
$354$	−2.49927	−	14.1741i	−0.132835	−	0.753343i
$355$	10.8835	+	27.5324i	0.577638	+	1.46127i
$356$	2.46280	+	1.42190i	0.130528	+	0.0753605i
$357$	20.2504	+	16.9921i	1.07176	+	0.899316i
$358$	−2.35551	+	6.47172i	−0.124493	+	0.342041i
$359$	9.12465	+	15.8044i	0.481581	+	0.834122i	0.999777	−	0.0211396i	$-0.00672945\pi$
$359$	9.12465	+	15.8044i	0.481581	+	0.834122i	−0.518196	+	0.855262i	$0.673396\pi$
$360$	1.15189	−	3.45644i	0.0607102	−	0.182170i
$361$	−32.4786	+	27.2528i	−1.70940	+	1.43436i
$362$	2.80422	+	4.85704i	0.147386	+	0.255281i
$363$	−1.17063	−	0.206413i	−0.0614420	−	0.0108339i
$364$			7.09408i			0.371831i
$365$	10.4655	−	0.286627i	0.547787	−	0.0150027i
$366$	−0.101587	−	0.0852419i	−0.00531005	−	0.00445566i
$367$	0.440339	+	1.20982i	0.0229855	+	0.0631521i	0.950655	−	0.310251i	$-0.100413\pi$
$367$	0.440339	+	1.20982i	0.0229855	+	0.0631521i	−0.927669	+	0.373403i	$0.878191\pi$
$368$	0.0492576	+	0.0179283i	0.00256773	+	0.000934576i
$369$	5.85187			0.304636
$370$	0.268604	−	13.5988i	0.0139641	−	0.706969i
$371$	50.3488			2.61398
$372$	−2.06959	−	0.753270i	−0.107303	−	0.0390552i
$373$	2.26014	+	6.20968i	0.117025	+	0.321525i	0.984352	−	0.176215i	$-0.0563855\pi$
$373$	2.26014	+	6.20968i	0.117025	+	0.321525i	−0.867326	+	0.497740i	$0.834163\pi$
$374$	−14.1098	−	11.8395i	−0.729602	−	0.612209i
$375$	11.8912	−	5.47096i	0.614058	−	0.282519i
$376$			10.8861i			0.561410i
$377$	−7.12459	−	1.25626i	−0.366935	−	0.0647006i
$378$	10.4971	+	18.1814i	0.539911	+	0.935153i
$379$	6.96442	−	5.84385i	0.357738	−	0.300178i	−0.446150	−	0.894958i	$-0.647205\pi$
$379$	6.96442	−	5.84385i	0.357738	−	0.300178i	0.803889	+	0.594780i	$0.202761\pi$
$380$	16.6223	+	5.53957i	0.852708	+	0.284174i
$381$	6.75413	+	11.6985i	0.346025	+	0.599332i
$382$	−4.56438	+	12.5405i	−0.233534	+	0.641630i
$383$	12.0599	+	10.1195i	0.616233	+	0.517081i	0.896617	−	0.442807i	$-0.146017\pi$
$383$	12.0599	+	10.1195i	0.616233	+	0.517081i	−0.280384	+	0.959888i	$0.590462\pi$
$384$	1.01390	+	0.585375i	0.0517403	+	0.0298723i
$385$	25.4530	−	10.0615i	1.29720	−	0.512783i
$386$	1.09215	+	6.19387i	0.0555888	+	0.315260i
$387$	3.49963	−	2.93654i	0.177896	−	0.149273i
$388$	−16.1383	+	5.87384i	−0.819296	+	0.298199i
$389$	5.47718	+	15.0484i	0.277704	+	0.762985i	0.997622	+	0.0689259i	$0.0219572\pi$
$389$	5.47718	+	15.0484i	0.277704	+	0.762985i	−0.719918	+	0.694059i	$0.755821\pi$
$390$	3.75569	+	2.98005i	0.190177	+	0.150901i
$391$	−0.0530588	−	0.300912i	−0.00268330	−	0.0152178i
$392$	1.39001	+	7.88313i	0.0702060	+	0.398158i
$393$	1.16175	−	2.01220i	0.0586023	−	0.101502i
$394$	9.55701	−	11.3896i	0.481475	−	0.573800i
$395$	−1.90736	+	12.8682i	−0.0959699	+	0.647468i
$396$	−2.57425	−	4.45873i	−0.129361	−	0.224060i
$397$	7.99684	+	4.61698i	0.401350	+	0.231719i	0.687066	−	0.726595i	$-0.258898\pi$
$397$	7.99684	+	4.61698i	0.401350	+	0.231719i	−0.285716	+	0.958314i	$0.592232\pi$
$398$	−7.72739	−	9.20914i	−0.387339	−	0.461613i
$399$	−30.7741	+	17.7674i	−1.54063	+	0.889484i
$400$	−1.13646	−	4.86913i	−0.0568228	−	0.243457i
$401$			11.8921i			0.593863i	0.954899	+	0.296931i	$0.0959632\pi$
$401$			11.8921i			0.593863i	−0.954899	+	0.296931i	$0.904037\pi$
$402$	0.940307	−	5.33275i	0.0468983	−	0.265973i
$403$	−2.21454	+	2.63919i	−0.110314	+	0.131467i
$404$	7.93506	−	2.88813i	0.394784	−	0.143690i
$405$	3.22316	+	0.477748i	0.160160	+	0.0237395i
$406$	−15.3018			−0.759413
$407$	−14.1254	−	13.0348i	−0.700172	−	0.646109i
$408$		−	6.82440i		−	0.337858i
$409$	−1.37922	+	3.78938i	−0.0681982	+	0.187373i	−0.969110	−	0.246630i	$-0.920677\pi$
$409$	−1.37922	+	3.78938i	−0.0681982	+	0.187373i	0.900912	+	0.434003i	$0.142899\pi$
$410$	6.84245	−	4.20437i	0.337925	−	0.207639i
$411$	11.4382	+	9.59775i	0.564202	+	0.473422i
$412$	0.421236	−	2.38895i	0.0207528	−	0.117695i
$413$	−47.6204			−2.34325
$414$	0.0148310	−	0.0841108i	0.000728904	−	0.00413382i
$415$	0.260835	−	0.231327i	0.0128039	−	0.0113554i
$416$	1.40293	−	1.17720i	0.0687842	−	0.0577168i
$417$	−15.5694	−	8.98898i	−0.762435	−	0.440192i
$418$	21.4424	−	12.3798i	1.04878	−	0.605516i
$419$	32.4698	+	11.8180i	1.58625	+	0.577349i	0.976552	−	0.215281i	$-0.0690668\pi$
$419$	32.4698	+	11.8180i	1.58625	+	0.577349i	0.609702	+	0.792631i	$0.291289\pi$
$420$	8.91753	+	4.82796i	0.435131	+	0.235580i
$421$	−30.7230	−	17.7379i	−1.49735	−	0.864493i	−0.497351	−	0.867550i	$-0.665694\pi$
$421$	−30.7230	−	17.7379i	−1.49735	−	0.864493i	−0.999995	+	0.00305655i	$0.999027\pi$
$422$	−4.15805	−	23.5815i	−0.202411	−	1.14793i
$423$	17.4678	−	3.08005i	0.849315	−	0.149757i
$424$	−8.35492	−	9.95701i	−0.405751	−	0.483555i
$425$	−21.2678	+	19.9283i	−1.03164	+	0.966664i
$426$	5.30155	+	14.5659i	0.256861	+	0.705720i
$427$	−0.336117	+	0.282035i	−0.0162658	+	0.0136486i
$428$	2.65243	−	0.467695i	0.128210	−	0.0226069i
$429$	6.67212	−	1.17648i	0.322133	−	0.0568008i
$430$	1.98223	−	5.94799i	0.0955916	−	0.286838i
$431$	−19.7147	+	23.4951i	−0.949626	+	1.13172i	0.0415462	+	0.999137i	$0.486772\pi$
$431$	−19.7147	+	23.4951i	−0.949626	+	1.13172i	−0.991172	+	0.132583i	$0.957673\pi$
$432$	1.85368	−	5.09295i	0.0891853	−	0.245035i
$433$	−3.91141	+	2.25826i	−0.187971	+	0.108525i	−0.591032	−	0.806648i	$-0.701279\pi$
$433$	−3.91141	+	2.25826i	−0.187971	+	0.108525i	0.403062	+	0.915173i	$0.367946\pi$
$434$	−3.64351	+	6.31074i	−0.174894	+	0.302925i
$435$	−6.42790	+	8.10093i	−0.308194	+	0.388410i
$436$	17.0741	−	9.85775i	0.817702	−	0.472101i
$437$	0.404497	+	0.0713237i	0.0193497	+	0.00341187i
$438$	5.48150			0.261916
$439$	−32.1437	−	5.66780i	−1.53413	−	0.270509i	−0.658164	−	0.752875i	$-0.728667\pi$
$439$	−32.1437	−	5.66780i	−1.53413	−	0.270509i	−0.875970	+	0.482365i	$0.839778\pi$
$440$	−6.21346	−	3.36398i	−0.296215	−	0.160371i
$441$	12.2559	−	4.46080i	0.583616	−	0.212419i
$442$	−10.0316	−	3.65119i	−0.477152	−	0.173669i
$443$			8.51396i			0.404510i	0.979333	+	0.202255i	$0.0648270\pi$
$443$			8.51396i			0.404510i	−0.979333	+	0.202255i	$0.935173\pi$
$444$	0.335510	−	7.11348i	0.0159226	−	0.337591i
$445$	−1.27525	−	6.22974i	−0.0604526	−	0.295318i
$446$	3.52412	−	9.68243i	0.166872	−	0.458476i
$447$	−3.33034	−	9.15004i	−0.157520	−	0.432782i
$448$	2.48990	−	2.96735i	0.117637	−	0.140194i
$449$	−16.7028	−	2.94515i	−0.788253	−	0.138990i	−0.234991	−	0.971998i	$-0.575506\pi$
$449$	−16.7028	−	2.94515i	−0.788253	−	0.138990i	−0.553262	+	0.833007i	$0.686617\pi$
$450$	−7.49144	+	3.20119i	−0.353150	+	0.150905i
$451$	1.97069	−	11.1763i	0.0927962	−	0.526273i
$452$	5.80645	+	10.0571i	0.273113	+	0.473045i
$453$	3.52227	+	4.19768i	0.165491	+	0.197224i
$454$	−6.80086	+	11.7794i	−0.319180	+	0.552836i
$455$	11.8679	−	10.5253i	0.556377	−	0.493434i
$456$	8.62037	+	3.13756i	0.403686	+	0.146930i
$457$	−1.93215	−	1.62126i	−0.0903821	−	0.0758395i	0.596477	−	0.802630i	$-0.296567\pi$
$457$	−1.93215	−	1.62126i	−0.0903821	−	0.0758395i	−0.686859	+	0.726791i	$0.741011\pi$
$458$	−7.97586	+	13.8146i	−0.372688	+	0.645514i
$459$	−31.1125	+	5.48598i	−1.45221	+	0.256064i
$460$	−0.0430893	−	0.109004i	−0.00200905	−	0.00508236i
$461$	−10.1000	−	12.0367i	−0.470402	−	0.560604i	0.477719	−	0.878513i	$-0.341464\pi$
$461$	−10.1000	−	12.0367i	−0.470402	−	0.560604i	−0.948121	+	0.317909i	$0.897019\pi$
$462$	13.4658	−	4.90114i	0.626484	−	0.228022i
$463$	6.15029	−	2.23852i	0.285828	−	0.104033i	−0.195127	−	0.980778i	$-0.562512\pi$
$463$	6.15029	−	2.23852i	0.285828	−	0.104033i	0.480956	+	0.876745i	$0.340290\pi$
$464$	2.53919	+	3.02608i	0.117879	+	0.140482i
$465$	1.81043	+	4.57990i	0.0839566	+	0.212388i
$466$	−7.29327	+	1.28600i	−0.337854	+	0.0595728i
$467$	13.1213	−	22.7268i	0.607183	−	1.05167i	−0.384520	−	0.923117i	$-0.625633\pi$
$467$	13.1213	−	22.7268i	0.607183	−	1.05167i	0.991702	−	0.128555i	$-0.0410337\pi$
$468$	−2.28586	−	1.91806i	−0.105664	−	0.0886624i
$469$	−16.8359	−	6.12776i	−0.777408	−	0.282954i
$470$	18.2118	−	16.1515i	0.840048	−	0.745012i
$471$	7.26834	−	12.5891i	0.334907	−	0.580077i
$472$	7.90217	+	9.41744i	0.363727	+	0.433473i
$473$	−4.42988	−	7.67278i	−0.203686	−	0.352795i
$474$	−1.18273	+	6.70759i	−0.0543245	+	0.308090i
$475$	−15.3948	−	36.0270i	−0.706362	−	1.65303i
$476$	−22.2365	−	3.92089i	−1.01921	−	0.179714i
$477$	−13.6131	+	16.2234i	−0.623299	+	0.742819i
$478$	−4.18004	−	11.4846i	−0.191191	−	0.525292i
$479$	5.16143	−	14.1809i	0.235832	−	0.647943i	−0.764164	−	0.645022i	$-0.776848\pi$
$479$	5.16143	−	14.1809i	0.235832	−	0.647943i	0.999996	−	0.00292050i	$-0.000929625\pi$
$480$	−0.525001	−	2.56469i	−0.0239629	−	0.117062i
$481$	−10.2770	−	4.29903i	−0.468590	−	0.196019i
$482$			8.88100i			0.404519i
$483$	0.223383	+	0.0813049i	0.0101643	+	0.00369950i
$484$	0.954089	−	0.347260i	0.0433677	−	0.0157845i
$485$	33.7705	+	18.2834i	1.53344	+	0.830205i
$486$	−14.3323	−	2.52717i	−0.650127	−	0.114635i
$487$	10.2551			0.464703			0.232351	−	0.972632i	$-0.425358\pi$
$487$	10.2551			0.464703			0.232351	+	0.972632i	$0.425358\pi$
$488$	0.111551	+	0.0196694i	0.00504967	+	0.000890394i
$489$	−18.3721	+	10.6072i	−0.830817	+	0.479673i
$490$	11.1256	−	14.0214i	0.502605	−	0.633422i
$491$	12.4486	−	21.5615i	0.561796	−	0.973059i	−0.435544	−	0.900167i	$-0.643444\pi$
$491$	12.4486	−	21.5615i	0.561796	−	0.973059i	0.997340	−	0.0728915i	$-0.0232227\pi$
$492$	3.64146	−	2.10240i	0.164170	−	0.0947834i
$493$	7.87552	−	21.6378i	0.354696	−	0.974518i
$494$	9.22413	−	10.9929i	0.415013	−	0.494594i
$495$	−3.63982	+	10.9219i	−0.163598	+	0.490901i
$496$	1.85262	−	0.326667i	0.0831852	−	0.0146678i
$497$	50.5072	−	8.90578i	2.26556	−	0.399479i
$498$	0.139832	−	0.117333i	0.00626600	−	0.00525780i
$499$	8.15738	+	22.4122i	0.365174	+	1.00331i	0.977172	+	0.212449i	$0.0681439\pi$
$499$	8.15738	+	22.4122i	0.365174	+	1.00331i	−0.611998	+	0.790860i	$0.709634\pi$
$500$	−6.45962	+	9.12542i	−0.288883	+	0.408101i
$501$	−10.6154	−	12.6509i	−0.474261	−	0.565202i
$502$	−23.7672	+	4.19079i	−1.06078	+	0.187044i
$503$	0.295948	+	1.67841i	0.0131957	+	0.0748364i	0.990694	−	0.136105i	$-0.0434583\pi$
$503$	0.295948	+	1.67841i	0.0131957	+	0.0748364i	−0.977499	+	0.210941i	$0.932347\pi$
$504$	−5.46586	−	3.15571i	−0.243469	−	0.140567i
$505$	−16.6047	−	8.98981i	−0.738899	−	0.400041i
$506$	−0.155647	−	0.0566508i	−0.00691934	−	0.00251843i
$507$	−9.78006	+	5.64652i	−0.434348	+	0.250771i
$508$	−9.99232	−	5.76907i	−0.443337	−	0.255961i
$509$	−23.9226	+	20.0734i	−1.06035	+	0.889739i	−0.994144	−	0.108067i	$-0.965534\pi$
$509$	−23.9226	+	20.0734i	−1.06035	+	0.889739i	−0.0662058	+	0.997806i	$0.521089\pi$
$510$	−11.4168	+	10.1252i	−0.505543	+	0.448351i
$511$	3.14935	−	17.8608i	0.139319	−	0.790116i
$512$	−1.00000			−0.0441942
$513$	7.37446	−	41.8226i	0.325590	−	1.84651i
$514$	15.9494	+	13.3831i	0.703498	+	0.590305i
$515$	−4.62153	+	2.83972i	−0.203649	+	0.125133i
$516$	1.12272	−	3.08464i	0.0494249	−	0.135794i
$517$		−	34.3986i		−	1.51285i
$518$	−22.9857	−	5.18020i	−1.00993	−	0.227605i
$519$	−3.22515			−0.141568
$520$	−4.05086	−	0.600432i	−0.177642	−	0.0263307i
$521$	36.4875	−	13.2804i	1.59855	−	0.581824i	0.619419	−	0.785061i	$-0.287368\pi$
$521$	36.4875	−	13.2804i	1.59855	−	0.581824i	0.979130	+	0.203237i	$0.0651462\pi$
$522$	4.13721	−	4.93054i	0.181081	−	0.215804i
$523$	−1.53590	+	8.71055i	−0.0671604	+	0.380886i	0.932638	+	0.360813i	$0.117501\pi$
$523$	−1.53590	+	8.71055i	−0.0671604	+	0.380886i	−0.999799	+	0.0200724i	$0.993610\pi$
$524$			1.98462i			0.0866985i
$525$	−5.15383	−	22.0816i	−0.224932	−	0.963719i
$526$	−14.5155	+	8.38053i	−0.632906	+	0.365409i
$527$	−7.04861	−	8.40020i	−0.307042	−	0.365919i
$528$	−3.20377	−	1.84970i	−0.139426	−	0.0804978i
$529$	11.4986	+	19.9162i	0.499940	+	0.865922i
$530$	−4.26145	+	28.7502i	−0.185106	+	1.24883i
$531$	12.8754	−	15.3443i	0.558744	−	0.665885i
$532$	15.1761	−	26.2858i	0.657968	−	1.13963i
$533$	−1.14218	−	6.47760i	−0.0494731	−	0.280576i
$534$	−0.578140	−	3.27879i	−0.0250186	−	0.141887i
$535$	−4.71777	−	3.74344i	−0.203967	−	0.161843i
$536$	1.58193	+	4.34632i	0.0683290	+	0.187732i
$537$	7.57677	−	2.75772i	0.326962	−	0.119004i
$538$	−22.8586	+	19.1806i	−0.985503	+	0.826935i
$539$	−4.39222	−	24.9095i	−0.189186	−	1.07293i
$540$	−11.2704	+	4.45519i	−0.485002	+	0.191721i
$541$	24.4959	+	14.1427i	1.05316	+	0.608044i	0.923533	−	0.383519i	$-0.125288\pi$
$541$	24.4959	+	14.1427i	1.05316	+	0.608044i	0.129630	+	0.991562i	$0.458621\pi$
$542$	−7.08319	−	5.94351i	−0.304249	−	0.255295i
$543$	2.24573	−	6.17008i	0.0963734	−	0.264784i
$544$	2.91454	+	5.04814i	0.124960	+	0.216437i
$545$	−41.8238	−	13.9382i	−1.79154	−	0.597048i
$546$	6.36229	−	5.33860i	0.272281	−	0.228471i
$547$	21.8895	+	37.9137i	0.935927	+	1.62107i	0.772973	+	0.634439i	$0.218769\pi$
$547$	21.8895	+	37.9137i	0.935927	+	1.62107i	0.162953	+	0.986634i	$0.447898\pi$
$548$	−12.5600	−	2.21467i	−0.536536	−	0.0946058i
$549$		−	0.184559i		−	0.00787678i
$550$	3.59103	+	15.3858i	0.153122	+	0.656051i
$551$	23.7114	+	19.8962i	1.01014	+	0.847608i
$552$	−0.0209895	−	0.0576682i	−0.000893373	−	0.00245452i
$553$	21.1764	+	7.70756i	0.900510	+	0.327759i
$554$	1.17041			0.0497261
$555$	−12.3982	+	9.99280i	−0.526273	+	0.424171i
$556$	15.3559			0.651237
$557$	7.02487	+	2.55684i	0.297653	+	0.108337i	0.486530	−	0.873664i	$-0.338262\pi$
$557$	7.02487	+	2.55684i	0.297653	+	0.108337i	−0.188877	+	0.982001i	$0.560485\pi$
$558$	−1.04834	−	2.88028i	−0.0443796	−	0.121932i
$559$	−3.93360	−	3.30068i	−0.166374	−	0.139604i
$560$	−8.65838	+	0.237135i	−0.365883	+	0.0100208i
$561$			21.5641i			0.910437i
$562$	28.0576	+	4.94731i	1.18354	+	0.208690i
$563$	−7.21335	−	12.4939i	−0.304006	−	0.526555i	0.673033	−	0.739612i	$-0.264991\pi$
$563$	−7.21335	−	12.4939i	−0.304006	−	0.526555i	−0.977040	+	0.213058i	$0.931658\pi$
$564$	9.76319	−	8.19229i	0.411105	−	0.344958i
$565$	8.20995	−	24.6352i	0.345395	−	1.03641i
$566$	−0.106040	−	0.183667i	−0.00445721	−	0.00772012i
$567$	1.93056	−	5.30416i	0.0810757	−	0.222754i
$568$	−10.1424	−	8.51050i	−0.425567	−	0.357093i
$569$	−21.6406	−	12.4942i	−0.907223	−	0.523785i	−0.0276861	−	0.999617i	$-0.508814\pi$
$569$	−21.6406	−	12.4942i	−0.907223	−	0.523785i	−0.879536	+	0.475831i	$0.842147\pi$
$570$	−7.54089	−	19.0764i	−0.315853	−	0.799024i
$571$	2.47000	+	14.0081i	0.103366	+	0.586220i	0.991860	+	0.127332i	$0.0406412\pi$
$571$	2.47000	+	14.0081i	0.103366	+	0.586220i	−0.888494	+	0.458889i	$0.848248\pi$
$572$	−4.43305	+	3.71977i	−0.185355	+	0.155531i
$573$	14.6818	−	5.34375i	0.613342	−	0.223238i
$574$	−4.75825	−	13.0732i	−0.198605	−	0.545664i
$575$	−0.118427	+	0.233813i	−0.00493874	+	0.00975066i
$576$	0.282933	+	1.60459i	0.0117889	+	0.0668580i
$577$	1.38672	+	7.86446i	0.0577297	+	0.327402i	0.999972	−	0.00753148i	$-0.00239737\pi$
$577$	1.38672	+	7.86446i	0.0577297	+	0.327402i	−0.942242	+	0.334933i	$0.891286\pi$
$578$	8.48913	−	14.7036i	0.353101	−	0.611590i
$579$	4.73306	−	5.64064i	0.196699	−	0.234417i
$580$	1.29512	−	8.73761i	0.0537769	−	0.362810i
$581$	−0.301976	−	0.523037i	−0.0125281	−	0.0216992i
$582$	17.4127	+	10.0532i	0.721778	+	0.416719i
$583$	26.4003	+	31.4627i	1.09339	+	1.30305i
$584$	−4.05477	+	2.34102i	−0.167788	+	0.0968723i
$585$	0.182674	+	6.66987i	0.00755262	+	0.275765i
$586$		−	2.76761i		−	0.114329i
$587$	6.01674	−	34.1226i	0.248337	−	1.40839i	−0.564275	−	0.825587i	$-0.690844\pi$
$587$	6.01674	−	34.1226i	0.248337	−	1.40839i	0.812612	−	0.582804i	$-0.198045\pi$
$588$	6.02391	−	7.17902i	0.248422	−	0.296058i
$589$	13.8515	−	5.04154i	0.570742	−	0.207733i
$590$	4.03052	−	27.1922i	0.165934	−	1.11949i
$591$	−17.4068			−0.716019
$592$	2.78982	+	5.40527i	0.114661	+	0.222155i
$593$		−	31.3108i		−	1.28578i	−0.765958	−	0.642890i	$-0.777735\pi$
$593$		−	31.3108i		−	1.28578i	0.765958	−	0.642890i	$-0.222265\pi$
$594$	−5.85737	+	16.0930i	−0.240331	+	0.660303i
$595$	26.4323	+	43.0175i	1.08362	+	1.76355i
$596$	6.37129	+	5.34614i	0.260978	+	0.218987i
$597$	−2.44399	+	13.8606i	−0.100026	+	0.567275i
$598$	−0.0959994			−0.00392571
$599$	3.48256	−	19.7506i	0.142294	−	0.806987i	−0.827207	−	0.561898i	$-0.810071\pi$
$599$	3.48256	−	19.7506i	0.142294	−	0.806987i	0.969500	−	0.245090i	$-0.0788174\pi$
$600$	−3.51163	+	4.68346i	−0.143362	+	0.191201i
$601$	−16.3450	+	13.7151i	−0.666726	+	0.559449i	−0.912094	−	0.409980i	$-0.865536\pi$
$601$	−16.3450	+	13.7151i	−0.666726	+	0.559449i	0.245368	+	0.969430i	$0.421091\pi$
$602$	−9.40588	−	5.43049i	−0.383355	−	0.221330i
$603$	6.52649	−	3.76807i	0.265779	−	0.153448i
$604$	−4.39822	−	1.60082i	−0.178961	−	0.0651365i
$605$	−1.99650	−	1.08091i	−0.0811693	−	0.0439452i
$606$	−8.56168	−	4.94309i	−0.347795	−	0.200799i
$607$	−0.528719	−	2.99851i	−0.0214600	−	0.121706i	0.972196	−	0.234169i	$-0.0752370\pi$
$607$	−0.528719	−	2.99851i	−0.0214600	−	0.121706i	−0.993656	+	0.112463i	$0.964126\pi$
$608$	−7.71663	+	1.36065i	−0.312951	+	0.0551817i
$609$	11.5152	+	13.7233i	0.466621	+	0.556097i
$610$	−0.132600	−	0.215800i	−0.00536880	−	0.00873751i
$611$	−6.81879	−	18.7345i	−0.275859	−	0.757916i
$612$	7.27559	−	6.10494i	0.294098	−	0.246778i
$613$	7.12661	−	1.25661i	0.287841	−	0.0507541i	−0.0278634	−	0.999612i	$-0.508870\pi$
$613$	7.12661	−	1.25661i	0.287841	−	0.0507541i	0.315704	+	0.948858i	$0.397759\pi$
$614$	29.6306	−	5.22467i	1.19579	−	0.210850i
$615$	−8.91991	−	2.97265i	−0.359686	−	0.119869i
$616$	−7.86772	+	9.37638i	−0.316999	+	0.377785i
$617$	4.63330	−	12.7299i	0.186530	−	0.512486i	−0.810816	−	0.585301i	$-0.800976\pi$
$617$	4.63330	−	12.7299i	0.186530	−	0.512486i	0.997345	+	0.0728155i	$0.0231984\pi$
$618$	−2.45952	+	1.42000i	−0.0989363	+	0.0571209i
$619$	16.7671	−	29.0415i	0.673926	−	1.16727i	−0.302855	−	0.953037i	$-0.597940\pi$
$619$	16.7671	−	29.0415i	0.673926	−	1.16727i	0.976781	−	0.214238i	$-0.0687268\pi$
$620$	−3.29518	−	2.61465i	−0.132338	−	0.105007i
$621$	−0.246037	+	0.142050i	−0.00987314	+	0.00570026i
$622$	1.54935	+	0.273192i	0.0621232	+	0.0109540i
$623$	−11.0157			−0.441336
$624$	−2.11153	−	0.372319i	−0.0845288	−	0.0149047i
$625$	24.8502	−	2.73263i	0.994008	−	0.109305i
$626$	−20.0295	+	7.29015i	−0.800540	+	0.291373i
$627$	−27.2391	−	9.91423i	−1.08783	−	0.395936i
$628$			12.4166i			0.495475i
$629$	19.1555	−	29.8373i	0.763779	−	1.18969i
$630$	2.83024	+	13.8261i	0.112760	+	0.550844i
$631$	2.13360	−	5.86201i	0.0849372	−	0.233363i	−0.889952	−	0.456055i	$-0.849262\pi$
$631$	2.13360	−	5.86201i	0.0849372	−	0.233363i	0.974889	+	0.222692i	$0.0714843\pi$
$632$	−1.98977	−	5.46685i	−0.0791488	−	0.217459i
$633$	−18.0199	+	21.4752i	−0.716225	+	0.853564i
$634$	12.0836	+	2.13067i	0.479901	+	0.0846195i
$635$	5.17407	+	25.2759i	0.205327	+	1.00304i
$636$	−2.64246	+	14.9862i	−0.104781	+	0.594240i
$637$	−7.32991	−	12.6958i	−0.290422	−	0.503025i
$638$	−8.02346	−	9.56198i	−0.317652	−	0.378563i
$639$	−10.7863	+	18.6824i	−0.426698	+	0.739063i
$640$	1.48367	+	1.67294i	0.0586474	+	0.0661286i
$641$	−11.8514	−	4.31355i	−0.468101	−	0.170375i	0.0971910	−	0.995266i	$-0.469014\pi$
$641$	−11.8514	−	4.31355i	−0.468101	−	0.170375i	−0.565292	+	0.824891i	$0.691236\pi$
$642$	−2.41552	−	2.02686i	−0.0953330	−	0.0799939i
$643$	15.4047	−	26.6817i	0.607501	−	1.05222i	−0.384149	−	0.923271i	$-0.625505\pi$
$643$	15.4047	−	26.6817i	0.607501	−	1.05222i	0.991651	−	0.128952i	$-0.0411614\pi$
$644$	−0.199964	+	0.0352591i	−0.00787970	+	0.00138940i
$645$	−6.82615	+	2.69837i	−0.268779	+	0.106248i
$646$	29.3592	+	34.9890i	1.15512	+	1.37662i
$647$	−15.3762	+	5.59648i	−0.604501	+	0.220020i	−0.626096	−	0.779746i	$-0.715348\pi$
$647$	−15.3762	+	5.59648i	−0.604501	+	0.220020i	0.0215943	+	0.999767i	$0.493126\pi$
$648$	−1.36931	+	0.498389i	−0.0537917	+	0.0195786i
$649$	−24.9697	−	29.7578i	−0.980147	−	1.16809i
$650$	5.00568	+	7.66768i	0.196339	+	0.300751i
$651$	8.40165	−	1.48144i	0.329287	−	0.0580621i
$652$	9.06015	−	15.6926i	0.354823	−	0.614571i
$653$	−8.20666	−	6.88621i	−0.321152	−	0.269478i	0.467931	−	0.883765i	$-0.344999\pi$
$653$	−8.20666	−	6.88621i	−0.321152	−	0.269478i	−0.789083	+	0.614287i	$0.789444\pi$
$654$	−21.6899	−	7.89448i	−0.848142	−	0.308699i
$655$	3.32014	−	2.94453i	0.129729	−	0.115052i
$656$	−1.79577	+	3.11037i	−0.0701131	+	0.121439i
$657$	4.90362	+	5.84391i	0.191308	+	0.227992i
$658$	−21.0843	−	36.5190i	−0.821950	−	1.42366i
$659$	−2.85317	+	16.1811i	−0.111144	+	0.630328i	0.877444	+	0.479680i	$0.159247\pi$
$659$	−2.85317	+	16.1811i	−0.111144	+	0.630328i	−0.988587	+	0.150648i	$0.951864\pi$
$660$	1.65893	+	8.10405i	0.0645736	+	0.315450i
$661$	−37.0623	−	6.53508i	−1.44156	−	0.254185i	−0.602451	−	0.798156i	$-0.705809\pi$
$661$	−37.0623	−	6.53508i	−1.44156	−	0.254185i	−0.839104	+	0.543971i	$0.816920\pi$
$662$	−10.8495	+	12.9299i	−0.421678	+	0.502536i
$663$	4.27462	+	11.7444i	0.166013	+	0.456116i
$664$	−0.0533260	+	0.146512i	−0.00206945	+	0.00568577i
$665$	−66.4908	+	13.6109i	−2.57840	+	0.527808i
$666$	7.88392	−	6.00585i	0.305496	−	0.232722i
$667$		−	0.207068i		−	0.00801772i
$668$	13.2553	+	4.82455i	0.512864	+	0.186667i
$669$	−11.3357	+	4.12586i	−0.438263	+	0.159515i
$670$	4.92404	−	9.09498i	0.190232	−	0.351370i
$671$	−0.352485	−	0.0621526i	−0.0136075	−	0.00239937i
$672$	−4.53501			−0.174942
$673$	−27.5521	−	4.85817i	−1.06205	−	0.187269i	−0.384787	−	0.923006i	$-0.625725\pi$
$673$	−27.5521	−	4.85817i	−1.06205	−	0.187269i	−0.677268	+	0.735737i	$0.736836\pi$
$674$	−22.4215	+	12.9450i	−0.863643	+	0.498624i
$675$	24.1749	+	12.2447i	0.930492	+	0.471297i
$676$	4.82300	−	8.35368i	0.185500	−	0.321295i
$677$	−26.6112	+	15.3640i	−1.02275	+	0.590487i	−0.914900	−	0.403680i	$-0.867731\pi$
$677$	−26.6112	+	15.3640i	−1.02275	+	0.590487i	−0.107853	+	0.994167i	$0.534398\pi$
$678$	4.65004	−	12.7759i	0.178584	−	0.490654i
$679$	42.7614	−	50.9611i	1.64103	−	1.95571i
$680$	4.12097	−	12.3656i	0.158032	−	0.474200i
$681$	15.6823	−	2.76521i	0.600946	−	0.105963i
$682$	−5.85401	+	1.03222i	−0.224162	+	0.0395258i
$683$	1.68483	−	1.41374i	0.0644681	−	0.0540952i	−0.609984	−	0.792414i	$-0.708824\pi$
$683$	1.68483	−	1.41374i	0.0644681	−	0.0540952i	0.674452	+	0.738318i	$0.264380\pi$
$684$	4.36658	+	11.9971i	0.166960	+	0.458720i
$685$	14.9299	+	24.2979i	0.570444	+	0.928375i
$686$	−2.50170	−	2.98141i	−0.0955153	−	0.113831i
$687$	18.3918	−	3.24296i	0.701689	−	0.123727i
$688$	0.486883	+	2.76125i	0.0185623	+	0.105272i
$689$	20.6152	+	11.9022i	0.785376	+	0.453437i
$690$	−0.0653336	+	0.120675i	−0.00248721	+	0.00459402i
$691$	24.8083	+	9.02948i	0.943752	+	0.343498i	0.767646	−	0.640874i	$-0.221428\pi$
$691$	24.8083	+	9.02948i	0.943752	+	0.343498i	0.176105	+	0.984371i	$0.443650\pi$
$692$	2.38571	−	1.37739i	0.0906909	−	0.0523604i
$693$	17.2713	+	9.97160i	0.656083	+	0.378790i
$694$	−12.5762	+	10.5527i	−0.477385	+	0.400573i
$695$	−22.7832	−	25.6895i	−0.864217	−	0.974458i
$696$	0.803084	−	4.55452i	0.0304408	−	0.172639i
$697$	20.9354			0.792985
$698$	−3.63461	+	20.6129i	−0.137572	+	0.780210i
$699$	6.64184	+	5.57317i	0.251218	+	0.210797i
$700$	13.2429	+	14.1331i	0.500535	+	0.534180i
$701$	15.8620	−	43.5806i	0.599101	−	1.64602i	−0.153968	−	0.988076i	$-0.549205\pi$
$701$	15.8620	−	43.5806i	0.599101	−	1.64602i	0.753069	−	0.657941i	$-0.228572\pi$
$702$			9.92579i			0.374625i
$703$	28.8827	+	37.9145i	1.08933	+	1.42997i
$704$	3.15985			0.119091
$705$	−28.1906	−	4.17850i	−1.06172	−	0.157371i
$706$	−12.0586	+	4.38896i	−0.453831	+	0.165181i
$707$	−21.0255	+	25.0572i	−0.790745	+	0.942374i
$708$	2.49927	−	14.1741i	0.0939283	−	0.532694i
$709$			2.53774i			0.0953067i	0.998864	+	0.0476534i	$0.0151743\pi$
$709$			2.53774i			0.0953067i	−0.998864	+	0.0476534i	$0.984826\pi$
$710$	0.810528	+	29.5944i	0.0304186	+	1.11066i
$711$	−8.20909	+	4.73952i	−0.307865	+	0.177746i
$712$	1.82796	+	2.17848i	0.0685056	+	0.0816418i
$713$	−0.0853990	−	0.0493051i	−0.00319822	−	0.00184649i
$714$	13.2175	+	22.8933i	0.494652	+	0.856762i
$715$	12.8001	+	1.89728i	0.478698	+	0.0709542i
$716$	−4.42692	+	5.27580i	−0.165442	+	0.197166i
$717$	−7.15423	+	12.3915i	−0.267180	+	0.462769i
$718$	3.16896	+	17.9721i	0.118265	+	0.670711i
$719$	−0.394614	−	2.23797i	−0.0147166	−	0.0834621i	0.976565	−	0.215223i	$-0.0690479\pi$
$719$	−0.394614	−	2.23797i	−0.0147166	−	0.0834621i	−0.991281	+	0.131761i	$0.957937\pi$
$720$	2.26460	−	2.85402i	0.0843966	−	0.106363i
$721$	3.21382	+	8.82989i	0.119689	+	0.328842i
$722$	−39.8409	+	14.5009i	−1.48272	+	0.539668i
$723$	7.96489	−	6.68334i	0.296217	−	0.248556i
$724$	0.973894	+	5.52323i	0.0361945	+	0.205269i
$725$	−16.5390	+	10.7971i	−0.614243	+	0.400995i
$726$	−1.02943	−	0.594343i	−0.0382058	−	0.0220581i
$727$	−26.7832	−	22.4737i	−0.993332	−	0.833505i	−0.00728565	−	0.999973i	$-0.502319\pi$
$727$	−26.7832	−	22.4737i	−0.993332	−	0.833505i	−0.986047	+	0.166469i	$0.946764\pi$
$728$	−2.42632	+	6.66625i	−0.0899253	+	0.247068i
$729$	10.7050	+	18.5416i	0.396481	+	0.686725i
$730$	9.93234	+	3.31005i	0.367612	+	0.122511i
$731$	12.5201	−	10.5056i	0.463074	−	0.388565i
$732$	−0.0663064	−	0.114846i	−0.00245076	−	0.00424483i
$733$	21.8656	+	3.85550i	0.807625	+	0.142406i	0.562191	−	0.827007i	$-0.309958\pi$
$733$	21.8656	+	3.85550i	0.807625	+	0.142406i	0.245434	+	0.969413i	$0.421070\pi$
$734$			1.28746i			0.0475212i
$735$	−20.9476	+	0.573709i	−0.772662	+	0.0211616i
$736$	0.0401551	+	0.0336941i	0.00148014	+	0.00124198i
$737$	−4.99867	−	13.7337i	−0.184128	−	0.505888i
$738$	5.49896	+	2.00146i	0.202419	+	0.0736746i
$739$	35.9405			1.32209			0.661046	−	0.750345i	$-0.270113\pi$
$739$	35.9405			1.32209			0.661046	+	0.750345i	$0.270113\pi$
$740$	4.90348	−	12.6868i	0.180255	−	0.466378i
$741$	−16.8005			−0.617181
$742$	47.3124	+	17.2203i	1.73689	+	0.632177i
$743$	−9.56742	−	26.2863i	−0.350995	−	0.964350i	−0.982051	−	0.188613i	$-0.939601\pi$
$743$	−9.56742	−	26.2863i	−0.350995	−	0.964350i	0.631057	−	0.775737i	$-0.282621\pi$
$744$	−1.68715	−	1.41568i	−0.0618538	−	0.0519015i
$745$	−0.509159	−	18.5907i	−0.0186542	−	0.681110i
$746$			6.60820i			0.241943i
$747$	0.250180	+	0.0441135i	0.00915360	+	0.00161403i
$748$	−9.20953	−	15.9514i	−0.336734	−	0.583240i
$749$	−7.99210	+	6.70617i	−0.292025	+	0.245038i
$750$	13.0452	−	1.07399i	0.476345	−	0.0392167i
$751$	−6.09994	−	10.5654i	−0.222590	−	0.385537i	0.733004	−	0.680225i	$-0.238118\pi$
$751$	−6.09994	−	10.5654i	−0.222590	−	0.385537i	−0.955594	+	0.294688i	$0.904784\pi$
$752$	−3.72328	+	10.2296i	−0.135774	+	0.373036i
$753$	21.6443	+	18.1617i	0.788763	+	0.661850i
$754$	−6.26526	−	3.61725i	−0.228167	−	0.131733i
$755$	3.84745	+	9.73303i	0.140023	+	0.354221i
$756$	3.64559	+	20.6752i	0.132589	+	0.751949i
$757$	−26.3574	+	22.1165i	−0.957977	+	0.803838i	−0.980623	−	0.195906i	$-0.937235\pi$
$757$	−26.3574	+	22.1165i	−0.957977	+	0.803838i	0.0226462	+	0.999744i	$0.492791\pi$
$758$	8.54313	−	3.10945i	0.310301	−	0.112940i
$759$	0.0663238	+	0.182223i	0.00240740	+	0.00661428i
$760$	13.7252	+	10.8907i	0.497867	+	0.395046i
$761$	−0.0643946	−	0.365200i	−0.00233430	−	0.0132385i	0.983618	−	0.180263i	$-0.0576950\pi$
$761$	−0.0643946	−	0.365200i	−0.00233430	−	0.0132385i	−0.985953	+	0.167025i	$0.946584\pi$
$762$	2.34568	+	13.3030i	0.0849752	+	0.481918i
$763$	−38.1849	+	66.1383i	−1.38239	+	2.39437i
$764$	−8.57823	+	10.2231i	−0.310350	+	0.369860i
$765$	−21.0078	−	3.11384i	−0.759537	−	0.112581i
$766$	7.87155	+	13.6339i	0.284411	+	0.492614i
$767$	−19.4981	−	11.2572i	−0.704034	−	0.406474i
$768$	0.752543	+	0.896846i	0.0271551	+	0.0323621i
$769$	−17.0519	+	9.84491i	−0.614906	+	0.355016i	−0.774883	−	0.632104i	$-0.782191\pi$
$769$	−17.0519	+	9.84491i	−0.614906	+	0.355016i	0.159977	+	0.987121i	$0.448858\pi$
$770$	27.3592	−	0.749311i	0.985957	−	0.0270033i
$771$		−	24.3755i		−	0.877863i
$772$	−1.09215	+	6.19387i	−0.0393072	+	0.222922i
$773$	11.2401	−	13.3954i	0.404277	−	0.481798i	−0.525042	−	0.851076i	$-0.675950\pi$
$773$	11.2401	−	13.3954i	0.404277	−	0.481798i	0.929319	+	0.369278i	$0.120395\pi$
$774$	4.29293	−	1.56250i	0.154306	−	0.0561629i
$775$	0.514835	+	9.39191i	0.0184934	+	0.337367i
$776$	−17.1740			−0.616510
$777$	12.6519	+	24.5129i	0.453883	+	0.879396i
$778$			16.0142i			0.574137i
$779$	−9.62518	+	26.4450i	−0.344858	+	0.947490i
$780$	2.50995	+	4.08485i	0.0898708	+	0.146261i
$781$	32.0486	+	26.8919i	1.14679	+	0.962270i
$782$	0.0530588	−	0.300912i	0.00189738	−	0.0107606i
$783$	−21.4097			−0.765120
$784$	−1.39001	+	7.88313i	−0.0496432	+	0.281540i
$785$	20.7721	−	18.4221i	0.741388	−	0.657514i
$786$	1.77990	−	1.49351i	0.0634868	−	0.0532718i
$787$	−34.3821	−	19.8505i	−1.22559	−	0.707594i	−0.259485	−	0.965747i	$-0.583553\pi$
$787$	−34.3821	−	19.8505i	−1.22559	−	0.707594i	−0.966104	+	0.258153i	$0.916886\pi$
$788$	12.8761	−	7.43403i	0.458693	−	0.264826i
$789$	18.4396	+	6.71146i	0.656467	+	0.238934i
$790$	−6.19351	+	11.4398i	−0.220355	+	0.407009i
$791$	−38.9570	−	22.4918i	−1.38515	−	0.799718i
$792$	−0.894027	−	5.07028i	−0.0317679	−	0.180165i
$793$	−0.204294	+	0.0360225i	−0.00725468	+	0.00127920i
$794$	5.93547	+	7.07362i	0.210642	+	0.251033i
$795$	28.9914	−	17.8139i	1.02822	−	0.631794i
$796$	−4.11166	−	11.2967i	−0.145734	−	0.400400i
$797$	−22.9229	+	19.2346i	−0.811969	+	0.681323i	−0.951077	−	0.308954i	$-0.900021\pi$
$797$	−22.9229	+	19.2346i	−0.811969	+	0.681323i	0.139108	+	0.990277i	$0.455577\pi$
$798$	−34.9950	+	6.17056i	−1.23881	+	0.218436i
$799$	62.4922	−	11.0191i	2.21082	−	0.389827i
$800$	0.597424	−	4.96418i	0.0211221	−	0.175510i
$801$	2.97838	−	3.54949i	0.105236	−	0.125415i
$802$	−4.06733	+	11.1749i	−0.143623	+	0.394600i
$803$	12.8125	−	7.39729i	0.452143	−	0.261045i
$804$	2.70751	−	4.68954i	0.0954864	−	0.165387i
$805$	0.355668	+	0.282214i	0.0125357	+	0.00994675i
$806$	−2.98365	+	1.72261i	−0.105095	+	0.0606763i
$807$	34.4041	+	6.06637i	1.21108	+	0.213546i
$808$	8.44432			0.297070
$809$	−29.5770	−	5.21522i	−1.03987	−	0.183357i	−0.372461	−	0.928048i	$-0.621486\pi$
$809$	−29.5770	−	5.21522i	−1.03987	−	0.183357i	−0.667410	+	0.744690i	$0.732597\pi$
$810$	2.86538	+	1.55132i	0.100679	+	0.0545080i
$811$	−14.5024	+	5.27845i	−0.509249	+	0.185352i	−0.583849	−	0.811862i	$-0.698454\pi$
$811$	−14.5024	+	5.27845i	−0.509249	+	0.185352i	0.0746002	+	0.997214i	$0.476232\pi$
$812$	−14.3789	−	5.23351i	−0.504602	−	0.183660i
$813$			10.8253i			0.379659i
$814$	−8.81543	−	17.0799i	−0.308981	−	0.598649i
$815$	−39.6951	+	8.12572i	−1.39046	+	0.284632i
$816$	2.33408	−	6.41284i	0.0817092	−	0.224494i
$817$	7.51420	+	20.6451i	0.262889	+	0.722281i
$818$	−2.59209	+	3.08913i	−0.0906304	+	0.108009i
$819$	11.3831	+	2.00715i	0.397758	+	0.0701355i
$820$	7.86778	−	1.61056i	0.274755	−	0.0562433i
$821$	8.12974	−	46.1061i	0.283730	−	1.60911i	−0.426057	−	0.904696i	$-0.640098\pi$
$821$	8.12974	−	46.1061i	0.283730	−	1.60911i	0.709787	−	0.704416i	$-0.248791\pi$
$822$	7.46572	+	12.9310i	0.260397	+	0.451021i
$823$	26.0922	+	31.0955i	0.909518	+	1.08392i	0.996149	+	0.0876813i	$0.0279457\pi$
$823$	26.0922	+	31.0955i	0.909518	+	1.08392i	−0.0866301	+	0.996241i	$0.527610\pi$
$824$	1.21290	−	2.10081i	0.0422534	−	0.0731850i
$825$	11.0962	−	14.7990i	0.386322	−	0.515237i
$826$	−44.7486	−	16.2871i	−1.55700	−	0.566702i
$827$	21.4368	+	17.9876i	0.745430	+	0.625490i	0.934290	−	0.356514i	$-0.116035\pi$
$827$	21.4368	+	17.9876i	0.745430	+	0.625490i	−0.188860	+	0.982004i	$0.560479\pi$
$828$	0.0427042	−	0.0739658i	0.00148407	−	0.00257049i
$829$	−34.7797	+	6.13260i	−1.20795	+	0.212994i	−0.741132	−	0.671360i	$-0.765711\pi$
$829$	−34.7797	+	6.13260i	−1.20795	+	0.212994i	−0.466818	+	0.884354i	$0.654600\pi$
$830$	0.324224	−	0.128165i	0.0112540	−	0.00444868i
$831$	−0.880786	−	1.04968i	−0.0305541	−	0.0364130i
$832$	1.72095	−	0.626373i	0.0596631	−	0.0217156i
$833$	43.8464	−	15.9588i	1.51919	−	0.552939i
$834$	−11.5560	−	13.7719i	−0.400152	−	0.476882i
$835$	−11.5954	−	29.3334i	−0.401277	−	1.01512i
$836$	24.3834	−	4.29946i	0.843319	−	0.148700i
$837$	−5.09787	+	8.82977i	−0.176208	+	0.305202i
$838$	26.4696	+	22.2107i	0.914378	+	0.767255i
$839$	27.5788	+	10.0379i	0.952126	+	0.346546i	0.770943	−	0.636904i	$-0.219785\pi$
$839$	27.5788	+	10.0379i	0.952126	+	0.346546i	0.181183	+	0.983449i	$0.442007\pi$
$840$	6.72847	+	7.58677i	0.232154	+	0.261769i
$841$	−6.69768	+	11.6007i	−0.230954	+	0.400025i
$842$	−22.8034	−	27.1761i	−0.785858	−	0.936549i
$843$	−16.6776	−	28.8864i	−0.574406	−	0.994900i
$844$	4.15805	−	23.5815i	0.143126	−	0.811709i
$845$	−21.1309	+	4.32557i	−0.726926	+	0.148804i
$846$	17.4678	+	3.08005i	0.600556	+	0.105894i
$847$	−2.52804	+	3.01281i	−0.0868646	+	0.103521i
$848$	−4.44556	−	12.2141i	−0.152661	−	0.419433i
$849$	−0.0849214	+	0.233319i	−0.00291449	+	0.00800750i
$850$	−26.8011	+	11.4524i	−0.919270	+	0.392816i
$851$	0.0701002	−	0.311050i	0.00240301	−	0.0106626i
$852$			15.5007i			0.531046i
$853$	27.9471	+	10.1719i	0.956889	+	0.348279i	0.772814	−	0.634633i	$-0.218849\pi$
$853$	27.9471	+	10.1719i	0.956889	+	0.348279i	0.184075	+	0.982912i	$0.441071\pi$
$854$	−0.412308	+	0.150068i	−0.0141089	+	0.00513522i
$855$	13.5918	−	25.1048i	0.464828	−	0.858565i
$856$	2.65243	+	0.467695i	0.0906583	+	0.0159855i
$857$	32.5701			1.11257			0.556286	−	0.830991i	$-0.312226\pi$
$857$	32.5701			1.11257			0.556286	+	0.830991i	$0.312226\pi$
$858$	6.67212	+	1.17648i	0.227783	+	0.0401642i
$859$	−4.23678	+	2.44611i	−0.144557	+	0.0834601i	−0.570534	−	0.821274i	$-0.693264\pi$
$859$	−4.23678	+	2.44611i	−0.144557	+	0.0834601i	0.425977	+	0.904734i	$0.359930\pi$
$860$	3.89702	−	4.91132i	0.132887	−	0.167475i
$861$	−8.14384	+	14.1055i	−0.277541	+	0.480716i
$862$	−26.5616	+	15.3353i	−0.904692	+	0.522324i
$863$	0.409525	−	1.12516i	0.0139404	−	0.0383009i	−0.932527	−	0.361100i	$-0.882401\pi$
$863$	0.409525	−	1.12516i	0.0139404	−	0.0383009i	0.946468	+	0.322799i	$0.104624\pi$
$864$	3.48378	−	4.15181i	0.118521	−	0.141247i
$865$	−5.84389	−	1.94754i	−0.198698	−	0.0662182i
$866$	−4.44790	+	0.784284i	−0.151146	+	0.0266511i
$867$	−19.5753	+	3.45166i	−0.664812	+	0.117224i
$868$	−5.58218	+	4.68400i	−0.189471	+	0.158985i
$869$	6.28738	+	17.2744i	0.213285	+	0.585995i
$870$	−8.81093	+	5.41391i	−0.298718	+	0.183549i
$871$	−5.44484	−	6.48890i	−0.184491	−	0.219868i
$872$	19.4160	−	3.42356i	0.657508	−	0.115936i
$873$	4.85908	+	27.5572i	0.164455	+	0.932671i
$874$	0.355708	+	0.205368i	0.0120320	+	0.00694669i
$875$	3.99554	−	43.1234i	0.135074	−	1.45784i
$876$	5.15093	+	1.87478i	0.174034	+	0.0633431i
$877$	18.1225	−	10.4630i	0.611952	−	0.353311i	−0.161777	−	0.986827i	$-0.551722\pi$
$877$	18.1225	−	10.4630i	0.611952	−	0.353311i	0.773729	+	0.633517i	$0.218389\pi$
$878$	−28.2667	−	16.3198i	−0.953954	−	0.550766i
$879$	−2.48212	+	2.08275i	−0.0837199	+	0.0702494i
$880$	−4.68819	−	5.28623i	−0.158039	−	0.178199i
$881$	0.975014	−	5.52958i	0.0328490	−	0.186296i	−0.963968	−	0.266018i	$-0.914292\pi$
$881$	0.975014	−	5.52958i	0.0328490	−	0.186296i	0.996817	+	0.0797216i	$0.0254031\pi$
$882$	13.0425			0.439164
$883$	8.64141	−	49.0079i	0.290807	−	1.64925i	−0.392967	−	0.919553i	$-0.628551\pi$
$883$	8.64141	−	49.0079i	0.290807	−	1.64925i	0.683774	−	0.729694i	$-0.260338\pi$
$884$	−8.17780	−	6.86199i	−0.275049	−	0.230794i
$885$	−27.4204	+	16.8486i	−0.921726	+	0.566359i
$886$	−2.91195	+	8.00051i	−0.0978287	+	0.268782i
$887$			3.17806i			0.106709i	0.998576	+	0.0533545i	$0.0169913\pi$
$887$			3.17806i			0.106709i	−0.998576	+	0.0533545i	$0.983009\pi$
$888$	2.74823	−	6.56973i	0.0922246	−	0.220466i
$889$	44.6941			1.49899
$890$	0.932355	−	6.29020i	0.0312526	−	0.210848i
$891$	4.32683	−	1.57484i	0.144954	−	0.0527590i
$892$	6.62317	−	7.89319i	0.221760	−	0.264284i
$893$	−14.8122	+	84.0044i	−0.495673	+	2.81110i
$894$		−	9.73726i		−	0.325663i
$895$	15.3942	−	0.421614i	0.514570	−	0.0140930i
$896$	3.35463	−	1.93680i	0.112070	−	0.0647039i
$897$	0.0722437	+	0.0860967i	0.00241215	+	0.00287469i
$898$	−14.6882	−	8.48023i	−0.490151	−	0.282989i
$899$	−3.71563	−	6.43566i	−0.123923	−	0.214641i
$900$	−8.13452	+	0.445909i	−0.271151	+	0.0148636i
$901$	−48.7016	+	58.0403i	−1.62249	+	1.93360i
$902$	5.67438	−	9.82831i	0.188936	−	0.327247i
$903$	2.20802	+	12.5223i	0.0734783	+	0.416716i
$904$	2.01656	+	11.4365i	0.0670698	+	0.380372i
$905$	7.79506	−	9.82393i	0.259117	−	0.326558i
$906$	1.87416	+	5.14921i	0.0622648	+	0.171071i
$907$	−40.4496	+	14.7225i	−1.34311	+	0.488852i	−0.910790	−	0.412869i	$-0.864527\pi$
$907$	−40.4496	+	14.7225i	−1.34311	+	0.488852i	−0.432318	+	0.901721i	$0.642304\pi$
$908$	−10.4195	+	8.74302i	−0.345784	+	0.290147i
$909$	−2.38918	−	13.5497i	−0.0792440	−	0.449415i
$910$	14.7521	−	5.83147i	0.489026	−	0.193311i
$911$	−24.3443	−	14.0552i	−0.806563	−	0.465669i	0.0391980	−	0.999231i	$-0.487520\pi$
$911$	−24.3443	−	14.0552i	−0.806563	−	0.465669i	−0.845761	+	0.533562i	$0.820853\pi$
$912$	7.02739	+	5.89668i	0.232700	+	0.195259i
$913$	0.168502	−	0.462957i	0.00557662	−	0.0153216i
$914$	−1.26112	−	2.18432i	−0.0417141	−	0.0722510i
$915$	−0.0937529	+	0.281320i	−0.00309938	+	0.00930017i
$916$	−12.2197	+	10.2536i	−0.403751	+	0.338788i
$917$	−3.84381	−	6.65767i	−0.126934	−	0.219856i
$918$	−31.1125	−	5.48598i	−1.02687	−	0.181064i
$919$		−	6.80380i		−	0.224437i	−0.993684	−	0.112218i	$-0.964204\pi$
$919$		−	6.80380i		−	0.224437i	0.993684	−	0.112218i	$-0.0357956\pi$
$920$	−0.00320898	−	0.117168i	−0.000105797	−	0.00386292i
$921$	−26.9840	−	22.6423i	−0.889153	−	0.746088i
$922$	−5.37408	−	14.7652i	−0.176986	−	0.486265i
$923$	22.7853	+	8.29318i	0.749988	+	0.272973i
$924$	14.3300			0.471421
$925$	−28.4994	+	10.6199i	−0.937055	+	0.349181i
$926$	6.54500			0.215082
$927$	−3.71411	−	1.35182i	−0.121987	−	0.0443997i
$928$	1.35107	+	3.71204i	0.0443511	+	0.121854i
$929$	30.7158	+	25.7736i	1.00775	+	0.845604i	0.988039	−	0.154202i	$-0.0492805\pi$
$929$	30.7158	+	25.7736i	1.00775	+	0.845604i	0.0197124	+	0.999806i	$0.493725\pi$
$930$	0.134828	+	4.92290i	0.00442118	+	0.161428i
$931$			62.7225i			2.05565i
$932$	−7.29327	−	1.28600i	−0.238899	−	0.0421243i
$933$	−0.920941	−	1.59512i	−0.0301502	−	0.0522218i
$934$	20.1030	−	16.8685i	0.657792	−	0.551953i
$935$	−13.0217	+	39.0736i	−0.425854	+	1.27784i
$936$	−1.49199	−	2.58420i	−0.0487671	−	0.0844671i
$937$	−0.00624233	+	0.0171507i	−0.000203928	+	0.000560288i	−0.939795	−	0.341740i	$-0.888984\pi$
$937$	−0.00624233	+	0.0171507i	−0.000203928	+	0.000560288i	0.939591	+	0.342300i	$0.111206\pi$
$938$	−13.7247	−	11.5164i	−0.448128	−	0.376024i
$939$	21.6112	+	12.4772i	0.705255	+	0.407179i
$940$	22.6376	−	8.94863i	0.738358	−	0.291872i
$941$	6.67589	+	37.8608i	0.217628	+	1.23423i	0.876288	+	0.481787i	$0.160012\pi$
$941$	6.67589	+	37.8608i	0.217628	+	1.23423i	−0.658661	+	0.752440i	$0.728877\pi$
$942$	11.1357	−	9.34400i	0.362822	−	0.304444i
$943$	0.176911	−	0.0643902i	0.00576100	−	0.00209683i
$944$	4.20466	+	11.5522i	0.136850	+	0.375992i
$945$	29.1794	−	36.7741i	0.949205	−	1.19626i
$946$	−1.53848	−	8.72516i	−0.0500203	−	0.283679i
$947$	−8.50967	−	48.2607i	−0.276527	−	1.56826i	−0.734069	−	0.679075i	$-0.762381\pi$
$947$	−8.50967	−	48.2607i	−0.276527	−	1.56826i	0.457542	−	0.889188i	$-0.348730\pi$
$948$	−3.40553	+	5.89855i	−0.110607	+	0.191576i
$949$	5.51169	−	6.56858i	0.178917	−	0.213225i
$950$	−2.14442	−	39.1196i	−0.0695741	−	1.26921i
$951$	−7.18255	−	12.4405i	−0.232910	−	0.403412i
$952$	−19.5544	−	11.2898i	−0.633763	−	0.365903i
$953$	0.362485	+	0.431993i	0.0117420	+	0.0139936i	0.771884	−	0.635764i	$-0.219315\pi$
$953$	0.362485	+	0.431993i	0.0117420	+	0.0139936i	−0.760141	+	0.649758i	$0.774870\pi$
$954$	−18.3408	+	10.5891i	−0.593806	+	0.342834i
$955$	29.8300	−	0.816979i	0.965275	−	0.0264368i
$956$		−	12.2216i		−	0.395276i
$957$	−2.53763	+	14.3916i	−0.0820299	+	0.465215i
$958$	9.70032	−	11.5604i	0.313403	−	0.373499i
$959$	46.4235	−	16.8968i	1.49909	−	0.545625i
$960$	0.383836	−	2.58958i	0.0123883	−	0.0835784i
$961$	27.4611			0.885841
$962$	−8.18685	−	7.55471i	−0.263955	−	0.243574i
$963$		−	4.38840i		−	0.141414i
$964$	−3.03748	+	8.34541i	−0.0978307	+	0.268788i
$965$	11.9823	−	7.36260i	0.385725	−	0.237010i
$966$	0.182104	+	0.152803i	0.00585909	+	0.00491636i
$967$	3.86499	−	21.9194i	0.124290	−	0.704882i	−0.857438	−	0.514588i	$-0.827945\pi$
$967$	3.86499	−	21.9194i	0.124290	−	0.704882i	0.981727	−	0.190294i	$-0.0609440\pi$
$968$	1.01532			0.0326336
$969$	9.28562	−	52.6614i	0.298297	−	1.69173i
$970$	25.4806	+	28.7309i	0.818132	+	0.922495i
$971$	2.52205	−	2.11625i	0.0809363	−	0.0679136i	−0.601422	−	0.798932i	$-0.705399\pi$
$971$	2.52205	−	2.11625i	0.0809363	−	0.0679136i	0.682358	+	0.731018i	$0.260954\pi$
$972$	−12.6036	−	7.27670i	−0.404261	−	0.233400i
$973$	−51.5135	+	29.7414i	−1.65145	+	0.953464i
$974$	9.63664	+	3.50745i	0.308778	+	0.112386i
$975$	3.10974	−	10.2596i	0.0995913	−	0.328569i
$976$	0.0980962	+	0.0566359i	0.00313998	+	0.00181287i
$977$	9.66508	+	54.8134i	0.309213	+	1.75364i	0.602977	+	0.797758i	$0.293981\pi$
$977$	9.66508	+	54.8134i	0.309213	+	1.75364i	−0.293764	+	0.955878i	$0.594908\pi$
$978$	−20.8920	+	3.68383i	−0.668054	+	0.117796i
$979$	−5.77608	−	6.88367i	−0.184604	−	0.220003i
$980$	15.2503	−	9.37060i	0.487152	−	0.299333i
$981$	−10.9868	−	30.1861i	−0.350783	−	0.963768i
$982$	19.0723	−	16.0036i	0.608622	−	0.510694i
$983$	12.6944	−	2.23836i	0.404887	−	0.0713925i	0.0325039	−	0.999472i	$-0.489652\pi$
$983$	12.6944	−	2.23836i	0.404887	−	0.0713925i	0.372383	+	0.928079i	$0.378541\pi$
$984$	4.14092	−	0.730155i	0.132008	−	0.0232765i
$985$	−31.5406	−	10.5112i	−1.00497	−	0.334916i
$986$	14.8011	−	17.6393i	0.471364	−	0.561750i
$987$	−16.8851	+	46.3914i	−0.537459	+	1.47666i
$988$	12.4276	−	7.17510i	0.395376	−	0.228270i
$989$	0.0734872	−	0.127284i	0.00233676	−	0.00404738i
$990$	−7.15580	+	9.01829i	−0.227426	+	0.286620i
$991$	−36.2811	+	20.9469i	−1.15251	+	0.665399i	−0.949497	−	0.313777i	$-0.898405\pi$
$991$	−36.2811	+	20.9469i	−1.15251	+	0.665399i	−0.203009	+	0.979177i	$0.565072\pi$
$992$	1.85262	+	0.326667i	0.0588208	+	0.0103717i
$993$	19.7609			0.627092
$994$	50.5072	+	8.90578i	1.60199	+	0.282474i
$995$	−12.7983	+	23.6391i	−0.405732	+	0.749411i
$996$	0.171529	−	0.0624314i	0.00543510	−	0.00197821i
$997$	−29.9417	−	10.8979i	−0.948262	−	0.345139i	−0.178839	−	0.983878i	$-0.557234\pi$
$997$	−29.9417	−	10.8979i	−0.948262	−	0.345139i	−0.769423	+	0.638739i	$0.779456\pi$
$998$			23.8506i			0.754977i
$999$	−32.1608	−	7.24796i	−1.01752	−	0.229315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.v.b.169.4	yes	60
5.4	even	2		370.2.v.a.169.7	✓	60
37.30	even	18		370.2.v.a.289.7	yes	60
185.104	even	18	inner	370.2.v.b.289.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.v.a.169.7	✓	60	5.4	even	2
370.2.v.a.289.7	yes	60	37.30	even	18
370.2.v.b.169.4	yes	60	1.1	even	1	trivial
370.2.v.b.289.4	yes	60	185.104	even	18	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.400420 - 1.10014i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0612182 - 2.23523i) q^{5} -1.17075i q^{6} +(-3.81475 - 0.672643i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.24815 - 1.04732i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.400420 - 1.10014i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.0612182 - 2.23523i) q^{5} -1.17075i q^{6} +(-3.81475 - 0.672643i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.24815 - 1.04732i) q^{9} +(0.706967 - 2.12137i) q^{10} +(-1.57993 - 2.73651i) q^{11} +(0.400420 - 1.10014i) q^{12} +(-1.40293 - 1.17720i) q^{13} +(-3.35463 - 1.93680i) q^{14} +(-2.43456 + 0.962379i) q^{15} +(0.173648 + 0.984808i) q^{16} +(4.46534 - 3.74687i) q^{17} +(1.53108 - 0.557269i) q^{18} +(2.67996 + 7.36313i) q^{19} +(1.38988 - 1.75164i) q^{20} +(0.787496 + 4.46611i) q^{21} +(-0.548703 - 3.11185i) q^{22} +(0.0262094 - 0.0453960i) q^{23} +(0.752543 - 0.896846i) q^{24} +(-4.99250 + 0.273673i) q^{25} +(-0.915697 - 1.58603i) q^{26} +(-4.69369 - 2.70990i) q^{27} +(-2.48990 - 2.96735i) q^{28} +(3.42104 - 1.97514i) q^{29} +(-2.61689 + 0.0716712i) q^{30} -1.88120i q^{31} +(-0.173648 + 0.984808i) q^{32} +(-2.37793 + 2.83390i) q^{33} +(5.47755 - 1.99367i) q^{34} +(-1.26998 + 8.56801i) q^{35} +1.62935 q^{36} +(5.80760 - 1.80882i) q^{37} +7.83567i q^{38} +(-0.733326 + 2.01480i) q^{39} +(1.90516 - 1.17063i) q^{40} +(2.75128 + 2.30860i) q^{41} +(-0.787496 + 4.46611i) q^{42} +2.80385 q^{43} +(0.548703 - 3.11185i) q^{44} +(-2.41742 - 2.72579i) q^{45} +(0.0401551 - 0.0336941i) q^{46} +(9.42768 + 5.44307i) q^{47} +(1.01390 - 0.585375i) q^{48} +(7.52199 + 2.73778i) q^{49} +(-4.78502 - 1.45037i) q^{50} +(-5.91010 - 3.41220i) q^{51} +(-0.318018 - 1.80357i) q^{52} +(-12.8005 + 2.25707i) q^{53} +(-3.48378 - 4.15181i) q^{54} +(-6.02002 + 3.69902i) q^{55} +(-1.32485 - 3.63999i) q^{56} +(7.02739 - 5.89668i) q^{57} +(3.89026 - 0.685958i) q^{58} +(12.1068 - 2.13476i) q^{59} +(-2.48359 - 0.827681i) q^{60} +(0.0728097 - 0.0867712i) q^{61} +(0.643409 - 1.76775i) q^{62} +(-5.46586 + 3.15571i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-2.54542 + 3.20793i) q^{65} +(-3.20377 + 1.84970i) q^{66} +(4.55499 + 0.803167i) q^{67} +5.82909 q^{68} +(-0.0604369 - 0.0106567i) q^{69} +(-4.12382 + 7.61694i) q^{70} +(-12.4415 + 4.52834i) q^{71} +(1.53108 + 0.557269i) q^{72} +4.68205i q^{73} +(6.07601 + 0.286577i) q^{74} +(2.30018 + 5.38289i) q^{75} +(-2.67996 + 7.36313i) q^{76} +(4.18633 + 11.5018i) q^{77} +(-1.37820 + 1.64248i) q^{78} +(-5.72931 - 1.01023i) q^{79} +(2.19064 - 0.448432i) q^{80} +(-0.253039 + 1.43505i) q^{81} +(1.79577 + 3.11037i) q^{82} +(0.100220 + 0.119438i) q^{83} +(-2.26750 + 3.92743i) q^{84} +(-8.64847 - 9.75169i) q^{85} +(2.63476 + 0.958973i) q^{86} +(-3.54279 - 2.97275i) q^{87} +(1.57993 - 2.73651i) q^{88} +(2.80059 - 0.493820i) q^{89} +(-1.33936 - 3.38821i) q^{90} +(4.55998 + 5.43438i) q^{91} +(0.0492576 - 0.0179283i) q^{92} +(-2.06959 + 0.753270i) q^{93} +(6.99748 + 8.33927i) q^{94} +(16.2942 - 6.44108i) q^{95} +(1.15296 - 0.203298i) q^{96} +(-8.58698 + 14.8731i) q^{97} +(6.13199 + 5.14535i) q^{98} +(-4.83800 - 1.76089i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9	\( 60 q + 6 q^{5} + 30 q^{8} - 6 q^{9} - 9 q^{10} + 6 q^{11} + 3 q^{13} + 9 q^{14} - 6 q^{15} - 3 q^{17} - 12 q^{18} + 3 q^{19} + 3 q^{20} + 12 q^{21} + 3 q^{22} + 18 q^{23} - 18 q^{25} - 27 q^{26} + 18 q^{30} + 66 q^{33} + 21 q^{34} + 9 q^{35} - 72 q^{36} - 6 q^{37} + 12 q^{39} + 12 q^{40} - 57 q^{41} - 12 q^{42} - 60 q^{43} - 3 q^{44} + 9 q^{45} - 21 q^{46} + 18 q^{47} - 6 q^{49} + 6 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{55} - 30 q^{57} - 15 q^{58} - 12 q^{59} - 9 q^{60} + 42 q^{61} + 12 q^{62} + 9 q^{63} - 30 q^{64} - 15 q^{65} + 18 q^{67} + 24 q^{68} + 36 q^{69} - 12 q^{70} + 18 q^{71} - 12 q^{72} + 3 q^{74} - 78 q^{75} - 3 q^{76} - 21 q^{77} - 6 q^{78} - 24 q^{79} - 36 q^{81} - 27 q^{82} - 30 q^{83} + 12 q^{84} - 30 q^{85} - 18 q^{86} + 30 q^{87} - 6 q^{88} + 3 q^{89} + 57 q^{91} - 15 q^{92} - 60 q^{93} + 3 q^{94} + 6 q^{95} - 84 q^{97} + 6 q^{98} - 45 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 30 * q^8 - 6 * q^9 - 9 * q^10 + 6 * q^11 + 3 * q^13 + 9 * q^14 - 6 * q^15 - 3 * q^17 - 12 * q^18 + 3 * q^19 + 3 * q^20 + 12 * q^21 + 3 * q^22 + 18 * q^23 - 18 * q^25 - 27 * q^26 + 18 * q^30 + 66 * q^33 + 21 * q^34 + 9 * q^35 - 72 * q^36 - 6 * q^37 + 12 * q^39 + 12 * q^40 - 57 * q^41 - 12 * q^42 - 60 * q^43 - 3 * q^44 + 9 * q^45 - 21 * q^46 + 18 * q^47 - 6 * q^49 + 6 * q^50 + 3 * q^52 + 6 * q^53 + 3 * q^55 - 30 * q^57 - 15 * q^58 - 12 * q^59 - 9 * q^60 + 42 * q^61 + 12 * q^62 + 9 * q^63 - 30 * q^64 - 15 * q^65 + 18 * q^67 + 24 * q^68 + 36 * q^69 - 12 * q^70 + 18 * q^71 - 12 * q^72 + 3 * q^74 - 78 * q^75 - 3 * q^76 - 21 * q^77 - 6 * q^78 - 24 * q^79 - 36 * q^81 - 27 * q^82 - 30 * q^83 + 12 * q^84 - 30 * q^85 - 18 * q^86 + 30 * q^87 - 6 * q^88 + 3 * q^89 + 57 * q^91 - 15 * q^92 - 60 * q^93 + 3 * q^94 + 6 * q^95 - 84 * q^97 + 6 * q^98 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more