LMFDB - Embedded newform 462.2.y.c.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (of order $15$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	462.25
Dual form			462.2.y.c.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.348032 - 3.31131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.39315 - 2.24925i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.348032 - 3.31131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.39315 - 2.24925i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-1.66477 + 2.88347i) q^{10} +(-2.61127 + 2.04481i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(4.99010 - 3.62552i) q^{13} +(-2.18756 + 1.48815i) q^{14} +(-1.02889 + 3.16659i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-2.52080 + 1.12233i) q^{17} +(-0.669131 - 0.743145i) q^{18} +(-1.28062 + 1.42227i) q^{19} +(2.69366 - 1.95706i) q^{20} +(-1.83035 + 1.91045i) q^{21} +(3.21722 - 0.805927i) q^{22} +(-1.57878 - 2.73453i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-5.95289 - 1.26533i) q^{25} +(-6.03331 + 1.28242i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(2.60372 - 0.469735i) q^{28} +(-0.159811 + 0.491849i) q^{29} +(2.22790 - 2.47434i) q^{30} +(-0.155861 - 1.48292i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.97935 - 1.45721i) q^{33} +2.75936 q^{34} +(-6.96311 - 5.39595i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.72891 - 0.580048i) q^{37} +(1.74839 - 0.778435i) q^{38} +(-5.63484 + 2.50879i) q^{39} +(-3.25679 + 0.692252i) q^{40} +(-3.61938 - 11.1393i) q^{41} +(2.44916 - 1.00081i) q^{42} -11.0713 q^{43} +(-3.26687 - 0.572309i) q^{44} +(1.66477 - 2.88347i) q^{45} +(0.330055 + 3.14026i) q^{46} +(1.61020 - 1.78831i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-3.11829 - 6.26708i) q^{49} +(4.92358 + 3.57719i) q^{50} +(2.69906 - 0.573704i) q^{51} +(6.03331 + 1.28242i) q^{52} +(-0.0933168 - 0.887850i) q^{53} +(0.500000 + 0.866025i) q^{54} +(5.86219 + 9.35839i) q^{55} +(-2.56967 - 0.629903i) q^{56} +(1.54834 - 1.12494i) q^{57} +(0.346048 - 0.384325i) q^{58} +(1.05518 + 1.17189i) q^{59} +(-3.04169 + 1.35425i) q^{60} +(-1.56464 + 14.8866i) q^{61} +(-0.460770 + 1.41811i) q^{62} +(2.18756 - 1.48815i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-10.2685 - 17.7855i) q^{65} +(-3.31447 + 0.119418i) q^{66} +(-0.0892859 + 0.154648i) q^{67} +(-2.52080 - 1.12233i) q^{68} +(0.975740 + 3.00302i) q^{69} +(4.16639 + 7.76160i) q^{70} +(8.96442 + 6.51303i) q^{71} +(0.104528 - 0.994522i) q^{72} +(2.45747 + 2.72929i) q^{73} +(-2.72891 - 0.580048i) q^{74} +(5.55973 + 2.47535i) q^{75} -1.91386 q^{76} +(0.961412 + 8.72214i) q^{77} +6.16810 q^{78} +(-8.14684 - 3.62721i) q^{79} +(3.25679 + 0.692252i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-1.22430 + 11.6484i) q^{82} +(8.79297 + 6.38847i) q^{83} +(-2.64448 - 0.0818733i) q^{84} +(2.83907 + 8.73776i) q^{85} +(10.1141 + 4.50310i) q^{86} +(0.258580 - 0.447874i) q^{87} +(2.75166 + 1.85159i) q^{88} +(0.291418 + 0.504750i) q^{89} +(-2.69366 + 1.95706i) q^{90} +(-1.20277 - 16.2749i) q^{91} +(0.975740 - 3.00302i) q^{92} +(-0.155861 + 1.48292i) q^{93} +(-2.19837 + 0.978776i) q^{94} +(4.26388 + 4.73552i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(9.88027 - 7.17844i) q^{97} +(0.299645 + 6.99358i) q^{98} +(-3.21722 + 0.805927i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$3$	−0.978148	−	0.207912i	−0.564734	−	0.120038i
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.348032	−	3.31131i	0.155645	−	1.48086i	−0.586133	−	0.810215i	$-0.699350\pi$
$5$	0.348032	−	3.31131i	0.155645	−	1.48086i	0.741777	−	0.670646i	$-0.233983\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	1.39315	−	2.24925i	0.526560	−	0.850138i
$7$	1.39315	−	2.24925i	0.526560	−	0.850138i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	−1.66477	+	2.88347i	−0.526448	+	0.911834i
$11$	−2.61127	+	2.04481i	−0.787329	+	0.616534i
$11$	−2.61127	+	2.04481i	−0.787329	+	0.616534i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	4.99010	−	3.62552i	1.38400	−	1.00554i	0.387510	−	0.921865i	$-0.373335\pi$
$13$	4.99010	−	3.62552i	1.38400	−	1.00554i	0.996493	−	0.0836722i	$-0.0266649\pi$
$14$	−2.18756	+	1.48815i	−0.584649	+	0.397725i
$15$	−1.02889	+	3.16659i	−0.265657	+	0.817609i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	−2.52080	+	1.12233i	−0.611384	+	0.272206i	−0.688981	−	0.724779i	$-0.741942\pi$
$17$	−2.52080	+	1.12233i	−0.611384	+	0.272206i	0.0775971	+	0.996985i	$0.475275\pi$
$18$	−0.669131	−	0.743145i	−0.157716	−	0.175161i
$19$	−1.28062	+	1.42227i	−0.293794	+	0.326291i	−0.871913	−	0.489661i	$-0.837120\pi$
$19$	−1.28062	+	1.42227i	−0.293794	+	0.326291i	0.578119	+	0.815953i	$0.303787\pi$
$20$	2.69366	−	1.95706i	0.602321	−	0.437612i
$21$	−1.83035	+	1.91045i	−0.399415	+	0.416895i
$22$	3.21722	−	0.805927i	0.685913	−	0.171824i
$23$	−1.57878	−	2.73453i	−0.329198	−	0.570188i	0.653155	−	0.757225i	$-0.273445\pi$
$23$	−1.57878	−	2.73453i	−0.329198	−	0.570188i	−0.982353	+	0.187036i	$0.940112\pi$
$24$	0.104528	+	0.994522i	0.0213368	+	0.203006i
$25$	−5.95289	−	1.26533i	−1.19058	−	0.253065i
$26$	−6.03331	+	1.28242i	−1.18323	+	0.251503i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	2.60372	−	0.469735i	0.492057	−	0.0887716i
$29$	−0.159811	+	0.491849i	−0.0296762	+	0.0913340i	−0.964798	−	0.262994i	$-0.915290\pi$
$29$	−0.159811	+	0.491849i	−0.0296762	+	0.0913340i	0.935121	+	0.354328i	$0.115290\pi$
$30$	2.22790	−	2.47434i	0.406757	−	0.451750i
$31$	−0.155861	−	1.48292i	−0.0279934	−	0.266340i	−0.999562	−	0.0295827i	$-0.990582\pi$
$31$	−0.155861	−	1.48292i	−0.0279934	−	0.266340i	0.971569	−	0.236757i	$-0.0760845\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.97935	−	1.45721i	0.518638	−	0.253668i
$34$	2.75936			0.473227
$35$	−6.96311	−	5.39595i	−1.17698	−	0.912082i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	2.72891	−	0.580048i	0.448630	−	0.0953593i	0.0219442	−	0.999759i	$-0.493014\pi$
$37$	2.72891	−	0.580048i	0.448630	−	0.0953593i	0.426686	+	0.904400i	$0.359681\pi$
$38$	1.74839	−	0.778435i	0.283627	−	0.126279i
$39$	−5.63484	+	2.50879i	−0.902296	+	0.401728i
$40$	−3.25679	+	0.692252i	−0.514943	+	0.109455i
$41$	−3.61938	−	11.1393i	−0.565253	−	1.73967i	−0.667199	−	0.744879i	$-0.732507\pi$
$41$	−3.61938	−	11.1393i	−0.565253	−	1.73967i	0.101947	−	0.994790i	$-0.467493\pi$
$42$	2.44916	−	1.00081i	0.377913	−	0.154429i
$43$	−11.0713			−1.68835			−0.844177	−	0.536064i	$-0.819911\pi$
$43$	−11.0713			−1.68835			−0.844177	+	0.536064i	$0.819911\pi$
$44$	−3.26687	−	0.572309i	−0.492500	−	0.0862788i
$45$	1.66477	−	2.88347i	0.248170	−	0.429843i
$46$	0.330055	+	3.14026i	0.0486639	+	0.463006i
$47$	1.61020	−	1.78831i	0.234872	−	0.260852i	−0.614174	−	0.789171i	$-0.710511\pi$
$47$	1.61020	−	1.78831i	0.234872	−	0.260852i	0.849046	+	0.528319i	$0.177177\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−3.11829	−	6.26708i	−0.445469	−	0.895297i
$50$	4.92358	+	3.57719i	0.696299	+	0.505891i
$51$	2.69906	−	0.573704i	0.377944	−	0.0803346i
$52$	6.03331	+	1.28242i	0.836670	+	0.177840i
$53$	−0.0933168	−	0.887850i	−0.0128181	−	0.121956i	0.986242	−	0.165310i	$-0.0528623\pi$
$53$	−0.0933168	−	0.887850i	−0.0128181	−	0.121956i	−0.999060	+	0.0433540i	$0.986196\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	5.86219	+	9.35839i	0.790457	+	1.26188i
$56$	−2.56967	−	0.629903i	−0.343387	−	0.0841744i
$57$	1.54834	−	1.12494i	0.205083	−	0.149001i
$58$	0.346048	−	0.384325i	0.0454383	−	0.0504643i
$59$	1.05518	+	1.17189i	0.137372	+	0.152567i	0.807905	−	0.589312i	$-0.200601\pi$
$59$	1.05518	+	1.17189i	0.137372	+	0.152567i	−0.670533	+	0.741880i	$0.733935\pi$
$60$	−3.04169	+	1.35425i	−0.392681	+	0.174833i
$61$	−1.56464	+	14.8866i	−0.200332	+	1.90603i	0.184145	+	0.982899i	$0.441048\pi$
$61$	−1.56464	+	14.8866i	−0.200332	+	1.90603i	−0.384477	+	0.923134i	$0.625618\pi$
$62$	−0.460770	+	1.41811i	−0.0585179	+	0.180100i
$63$	2.18756	−	1.48815i	0.275606	−	0.187490i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−10.2685	−	17.7855i	−1.27365	−	2.20602i
$66$	−3.31447	+	0.119418i	−0.407984	+	0.0146994i
$67$	−0.0892859	+	0.154648i	−0.0109080	+	0.0188932i	−0.871428	−	0.490524i	$-0.836806\pi$
$67$	−0.0892859	+	0.154648i	−0.0109080	+	0.0188932i	0.860520	+	0.509417i	$0.170139\pi$
$68$	−2.52080	−	1.12233i	−0.305692	−	0.136103i
$69$	0.975740	+	3.00302i	0.117465	+	0.361521i
$70$	4.16639	+	7.76160i	0.497979	+	0.927688i
$71$	8.96442	+	6.51303i	1.06388	+	0.772955i	0.974802	−	0.223070i	$-0.0716079\pi$
$71$	8.96442	+	6.51303i	1.06388	+	0.772955i	0.0890782	+	0.996025i	$0.471608\pi$
$72$	0.104528	−	0.994522i	0.0123188	−	0.117206i
$73$	2.45747	+	2.72929i	0.287625	+	0.319440i	0.869590	−	0.493774i	$-0.164383\pi$
$73$	2.45747	+	2.72929i	0.287625	+	0.319440i	−0.581966	+	0.813213i	$0.697716\pi$
$74$	−2.72891	−	0.580048i	−0.317229	−	0.0674292i
$75$	5.55973	+	2.47535i	0.641982	+	0.285829i
$76$	−1.91386			−0.219534
$77$	0.961412	+	8.72214i	0.109563	+	0.993980i
$78$	6.16810			0.698400
$79$	−8.14684	−	3.62721i	−0.916591	−	0.408093i	−0.106444	−	0.994319i	$-0.533946\pi$
$79$	−8.14684	−	3.62721i	−0.916591	−	0.408093i	−0.810148	+	0.586226i	$0.800613\pi$
$80$	3.25679	+	0.692252i	0.364120	+	0.0773961i
$81$	0.669131	+	0.743145i	0.0743478	+	0.0825716i
$82$	−1.22430	+	11.6484i	−0.135201	+	1.28635i
$83$	8.79297	+	6.38847i	0.965154	+	0.701225i	0.954342	−	0.298716i	$-0.0965584\pi$
$83$	8.79297	+	6.38847i	0.965154	+	0.701225i	0.0108120	+	0.999942i	$0.496558\pi$
$84$	−2.64448	−	0.0818733i	−0.288537	−	0.00893310i
$85$	2.83907	+	8.73776i	0.307940	+	0.947743i
$86$	10.1141	+	4.50310i	1.09063	+	0.485581i
$87$	0.258580	−	0.447874i	0.0277227	−	0.0480171i
$88$	2.75166	+	1.85159i	0.293328	+	0.197380i
$89$	0.291418	+	0.504750i	0.0308902	+	0.0535034i	0.881057	−	0.473010i	$-0.156832\pi$
$89$	0.291418	+	0.504750i	0.0308902	+	0.0535034i	−0.850167	+	0.526513i	$0.823499\pi$
$90$	−2.69366	+	1.95706i	−0.283937	+	0.206292i
$91$	−1.20277	−	16.2749i	−0.126085	−	1.70607i
$92$	0.975740	−	3.00302i	0.101728	−	0.313086i
$93$	−0.155861	+	1.48292i	−0.0161620	+	0.153771i
$94$	−2.19837	+	0.978776i	−0.226744	+	0.100953i
$95$	4.26388	+	4.73552i	0.437465	+	0.485854i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	9.88027	−	7.17844i	1.00319	−	0.728860i	0.0404199	−	0.999183i	$-0.487130\pi$
$97$	9.88027	−	7.17844i	1.00319	−	0.728860i	0.962770	+	0.270323i	$0.0871305\pi$
$98$	0.299645	+	6.99358i	0.0302687	+	0.706459i
$99$	−3.21722	+	0.805927i	−0.323342	+	0.0809987i
$100$	−3.04294	−	5.27053i	−0.304294	−	0.527053i
$101$	−1.05437	−	10.0316i	−0.104914	−	0.998186i	−0.912678	−	0.408680i	$-0.865989\pi$
$101$	−1.05437	−	10.0316i	−0.104914	−	0.998186i	0.807764	−	0.589506i	$-0.200678\pi$
$102$	−2.69906	−	0.573704i	−0.267247	−	0.0568051i
$103$	18.7396	−	3.98322i	1.84646	−	0.392478i	0.854548	−	0.519372i	$-0.173834\pi$
$103$	18.7396	−	3.98322i	1.84646	−	0.392478i	0.991916	+	0.126894i	$0.0405008\pi$
$104$	−4.99010	−	3.62552i	−0.489319	−	0.355511i
$105$	5.68907	+	6.72575i	0.555196	+	0.656366i
$106$	−0.275872	+	0.849047i	−0.0267951	+	0.0824667i
$107$	−1.56961	+	1.74323i	−0.151740	+	0.168524i	−0.814222	−	0.580553i	$-0.802836\pi$
$107$	−1.56961	+	1.74323i	−0.151740	+	0.168524i	0.662482	+	0.749077i	$0.269503\pi$
$108$	−0.104528	−	0.994522i	−0.0100583	−	0.0956979i
$109$	7.83983	−	13.5790i	0.750920	−	1.30063i	−0.196458	−	0.980512i	$-0.562944\pi$
$109$	7.83983	−	13.5790i	0.750920	−	1.30063i	0.947377	−	0.320119i	$-0.103723\pi$
$110$	−1.54898	−	10.9337i	−0.147689	−	1.04249i
$111$	−2.78988			−0.264803
$112$	2.09131	+	1.62063i	0.197610	+	0.153135i
$113$	3.32333	+	10.2282i	0.312633	+	0.962185i	0.976718	+	0.214528i	$0.0688212\pi$
$113$	3.32333	+	10.2282i	0.312633	+	0.962185i	−0.664085	+	0.747657i	$0.731179\pi$
$114$	−1.87203	+	0.397913i	−0.175332	+	0.0372680i
$115$	−9.60432	+	4.27612i	−0.895608	+	0.398750i
$116$	−0.472449	+	0.210348i	−0.0438658	+	0.0195303i
$117$	6.03331	−	1.28242i	0.557780	−	0.118560i
$118$	−0.487300	−	1.49976i	−0.0448596	−	0.138064i
$119$	−0.987434	+	7.23350i	−0.0905179	+	0.663094i
$120$	3.32955			0.303945
$121$	2.63750	−	10.6791i	0.239773	−	0.970829i
$122$	7.48430	−	12.9632i	0.677597	−	1.17363i
$123$	1.22430	+	11.6484i	0.110391	+	1.05030i
$124$	0.997730	−	1.10809i	0.0895988	−	0.0995096i
$125$	−1.11725	+	3.43853i	−0.0999295	+	0.307551i
$126$	−2.60372	+	0.469735i	−0.231958	+	0.0418473i
$127$	0.500255	+	0.363457i	0.0443904	+	0.0322515i	0.609759	−	0.792587i	$-0.291266\pi$
$127$	0.500255	+	0.363457i	0.0443904	+	0.0322515i	−0.565369	+	0.824838i	$0.691266\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	10.8293	+	2.30185i	0.953471	+	0.202666i
$130$	2.14670	+	20.4245i	0.188278	+	1.79134i
$131$	3.63331	+	6.29307i	0.317444	+	0.549829i	0.979954	−	0.199224i	$-0.0638422\pi$
$131$	3.63331	+	6.29307i	0.317444	+	0.549829i	−0.662510	+	0.749053i	$0.730509\pi$
$132$	3.07649	+	1.23902i	0.267774	+	0.107843i
$133$	1.41496	+	4.86187i	0.122693	+	0.421578i
$134$	0.144468	−	0.104962i	0.0124801	−	0.00906732i
$135$	−2.22790	+	2.47434i	−0.191747	+	0.212957i
$136$	1.84637	+	2.05061i	0.158325	+	0.175838i
$137$	10.7340	−	4.77906i	0.917064	−	0.408303i	0.106741	−	0.994287i	$-0.465958\pi$
$137$	10.7340	−	4.77906i	0.917064	−	0.408303i	0.810323	+	0.585984i	$0.199292\pi$
$138$	0.330055	−	3.14026i	0.0280961	−	0.267317i
$139$	−5.26087	+	16.1913i	−0.446221	+	1.37333i	0.434918	+	0.900470i	$0.356777\pi$
$139$	−5.26087	+	16.1913i	−0.446221	+	1.37333i	−0.881139	+	0.472857i	$0.843223\pi$
$140$	−0.649259	−	8.78519i	−0.0548724	−	0.742484i
$141$	−1.94683	+	1.41445i	−0.163953	+	0.119118i
$142$	−5.54031	−	9.59611i	−0.464933	−	0.805287i
$143$	−5.61701	+	19.6710i	−0.469718	+	1.64497i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.57304	+	0.700364i	0.130634	+	0.0581620i
$146$	−1.13490	−	3.49287i	−0.0939253	−	0.289072i
$147$	1.74714	+	6.77846i	0.144102	+	0.559078i
$148$	2.25706	+	1.63985i	0.185529	+	0.134795i
$149$	1.34864	−	12.8315i	0.110485	−	1.05119i	−0.789045	−	0.614335i	$-0.789424\pi$
$149$	1.34864	−	12.8315i	0.110485	−	1.05119i	0.899530	−	0.436859i	$-0.143909\pi$
$150$	−4.07225	−	4.52269i	−0.332498	−	0.369276i
$151$	−1.27469	−	0.270943i	−0.103733	−	0.0220491i	0.155753	−	0.987796i	$-0.450220\pi$
$151$	−1.27469	−	0.270943i	−0.103733	−	0.0220491i	−0.259486	+	0.965747i	$0.583553\pi$
$152$	1.74839	+	0.778435i	0.141813	+	0.0631394i
$153$	−2.75936			−0.223081
$154$	2.66932	−	8.35911i	0.215100	−	0.673596i
$155$	−4.96463			−0.398769
$156$	−5.63484	−	2.50879i	−0.451148	−	0.200864i
$157$	−3.20306	−	0.680832i	−0.255632	−	0.0543363i	0.0783129	−	0.996929i	$-0.475047\pi$
$157$	−3.20306	−	0.680832i	−0.255632	−	0.0543363i	−0.333945	+	0.942593i	$0.608380\pi$
$158$	5.96719	+	6.62724i	0.474724	+	0.527235i
$159$	−0.0933168	+	0.887850i	−0.00740051	+	0.0704111i
$160$	−2.69366	−	1.95706i	−0.212952	−	0.154719i
$161$	−8.35012	−	0.258520i	−0.658081	−	0.0203742i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−1.78350	−	0.794065i	−0.139694	−	0.0621960i	0.335699	−	0.941969i	$-0.391028\pi$
$163$	−1.78350	−	0.794065i	−0.139694	−	0.0621960i	−0.475393	+	0.879773i	$0.657694\pi$
$164$	5.85629	−	10.1434i	0.457299	−	0.792065i
$165$	−3.78837	−	10.3727i	−0.294924	−	0.807514i
$166$	−5.43436	−	9.41258i	−0.421788	−	0.730558i
$167$	−2.62532	+	1.90741i	−0.203153	+	0.147600i	−0.684711	−	0.728815i	$-0.740071\pi$
$167$	−2.62532	+	1.90741i	−0.203153	+	0.147600i	0.481557	+	0.876415i	$0.340071\pi$
$168$	2.38256	+	1.15040i	0.183818	+	0.0887556i
$169$	7.73947	−	23.8196i	0.595343	−	1.83228i
$170$	0.960347	−	9.13709i	0.0736553	−	0.700783i
$171$	−1.74839	+	0.778435i	−0.133703	+	0.0595284i
$172$	−7.40813	−	8.22757i	−0.564865	−	0.627346i
$173$	−15.9182	+	17.6790i	−1.21024	+	1.34411i	−0.287935	+	0.957650i	$0.592969\pi$
$173$	−15.9182	+	17.6790i	−1.21024	+	1.34411i	−0.922306	+	0.386460i	$0.873698\pi$
$174$	−0.418392	+	0.303979i	−0.0317182	+	0.0230446i
$175$	−11.1393	+	11.6268i	−0.842051	+	0.878901i
$176$	−1.76066	−	2.81071i	−0.132714	−	0.211865i
$177$	−0.788469	−	1.36567i	−0.0592649	−	0.102650i
$178$	−0.0609229	−	0.579642i	−0.00456636	−	0.0434460i
$179$	−18.7763	−	3.99103i	−1.40341	−	0.298304i	−0.556856	−	0.830609i	$-0.687992\pi$
$179$	−18.7763	−	3.99103i	−1.40341	−	0.298304i	−0.846552	+	0.532305i	$0.821326\pi$
$180$	3.25679	−	0.692252i	0.242747	−	0.0515974i
$181$	12.3925	+	9.00371i	0.921131	+	0.669241i	0.943805	−	0.330502i	$-0.107218\pi$
$181$	12.3925	+	9.00371i	0.921131	+	0.669241i	−0.0226743	+	0.999743i	$0.507218\pi$
$182$	−5.52080	+	15.3570i	−0.409229	+	1.13834i
$183$	4.62555	−	14.2360i	0.341931	−	1.05235i
$184$	−2.11282	+	2.34652i	−0.155759	+	0.172988i
$185$	−0.970967	−	9.23813i	−0.0713869	−	0.679201i
$186$	0.745542	−	1.29132i	0.0546658	−	0.0946839i
$187$	4.28754	−	8.08528i	0.313536	−	0.591254i
$188$	2.40641			0.175506
$189$	−2.44916	+	1.00081i	−0.178150	+	0.0727985i
$190$	−1.96914	−	6.06039i	−0.142856	−	0.439667i
$191$	25.2374	−	5.36437i	1.82611	−	0.388152i	0.838480	−	0.544932i	$-0.183445\pi$
$191$	25.2374	−	5.36437i	1.82611	−	0.388152i	0.987634	+	0.156780i	$0.0501113\pi$
$192$	0.913545	−	0.406737i	0.0659295	−	0.0293537i
$193$	−7.67470	+	3.41700i	−0.552437	+	0.245961i	−0.663918	−	0.747806i	$-0.731107\pi$
$193$	−7.67470	+	3.41700i	−0.552437	+	0.245961i	0.111480	+	0.993767i	$0.464441\pi$
$194$	−11.9458	+	2.53916i	−0.857659	+	0.182301i
$195$	6.34627	+	19.5318i	0.454466	+	1.39870i
$196$	2.57081	−	6.51083i	0.183629	−	0.465060i
$197$	12.2252			0.871007			0.435504	−	0.900187i	$-0.356570\pi$
$197$	12.2252			0.871007			0.435504	+	0.900187i	$0.356570\pi$
$198$	3.26687	+	0.572309i	0.232167	+	0.0406722i
$199$	12.2912	−	21.2890i	0.871302	−	1.50914i	0.0106517	−	0.999943i	$-0.496609\pi$
$199$	12.2912	−	21.2890i	0.871302	−	1.50914i	0.860650	−	0.509196i	$-0.170057\pi$
$200$	0.636148	+	6.05254i	0.0449824	+	0.427979i
$201$	0.119488	−	0.132705i	0.00842802	−	0.00936027i
$202$	−3.11702	+	9.59322i	−0.219313	+	0.674976i
$203$	0.883652	+	1.04467i	0.0620202	+	0.0733217i
$204$	2.23237	+	1.62191i	0.156297	+	0.113557i
$205$	−38.1454	+	8.10805i	−2.66419	+	0.566291i
$206$	−18.7396	−	3.98322i	−1.30565	−	0.277524i
$207$	−0.330055	−	3.14026i	−0.0229404	−	0.218263i
$208$	3.08405	+	5.34173i	0.213840	+	0.370382i
$209$	0.435771	−	6.33256i	0.0301429	−	0.438033i
$210$	−2.46162	−	8.45823i	−0.169868	−	0.583673i
$211$	−10.1027	+	7.34006i	−0.695500	+	0.505310i	−0.878464	−	0.477809i	$-0.841431\pi$
$211$	−10.1027	+	7.34006i	−0.695500	+	0.505310i	0.182963	+	0.983120i	$0.441431\pi$
$212$	0.597360	−	0.663436i	0.0410269	−	0.0455649i
$213$	−7.41439	−	8.23451i	−0.508026	−	0.564219i
$214$	2.14294	−	0.954099i	0.146488	−	0.0652209i
$215$	−3.85316	+	36.6604i	−0.262784	+	2.50022i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	−3.55259	−	1.71535i	−0.241166	−	0.116445i
$218$	−12.6851	+	9.21627i	−0.859144	+	0.624205i
$219$	−1.83631	−	3.18059i	−0.124087	−	0.214924i
$220$	−3.03207	+	10.6184i	−0.204422	+	0.715895i
$221$	−8.51001	+	14.7398i	−0.572445	+	0.991504i
$222$	2.54868	+	1.13474i	0.171056	+	0.0761591i
$223$	−4.20173	−	12.9316i	−0.281369	−	0.865964i	−0.987464	−	0.157847i	$-0.949545\pi$
$223$	−4.20173	−	12.9316i	−0.281369	−	0.865964i	0.706095	−	0.708117i	$-0.250455\pi$
$224$	−1.25134	−	2.33113i	−0.0836085	−	0.155755i
$225$	−4.92358	−	3.57719i	−0.328239	−	0.238479i
$226$	1.12415	−	10.6956i	0.0747776	−	0.711462i
$227$	4.13612	+	4.59362i	0.274524	+	0.304890i	0.864603	−	0.502456i	$-0.167570\pi$
$227$	4.13612	+	4.59362i	0.274524	+	0.304890i	−0.590079	+	0.807345i	$0.700903\pi$
$228$	1.87203	+	0.397913i	0.123978	+	0.0263524i
$229$	−10.9962	−	4.89584i	−0.726652	−	0.323527i	0.00985919	−	0.999951i	$-0.496862\pi$
$229$	−10.9962	−	4.89584i	−0.726652	−	0.323527i	−0.736512	+	0.676425i	$0.763528\pi$
$230$	10.5132			0.693223
$231$	0.873032	−	8.73143i	0.0574413	−	0.574486i
$232$	0.517160			0.0339532
$233$	19.3307	+	8.60657i	1.26640	+	0.563835i	0.926382	−	0.376585i	$-0.122902\pi$
$233$	19.3307	+	8.60657i	1.26640	+	0.563835i	0.340013	+	0.940421i	$0.389568\pi$
$234$	−6.03331	−	1.28242i	−0.394410	−	0.0838344i
$235$	−5.36125	−	5.95427i	−0.349729	−	0.388414i
$236$	−0.164835	+	1.56830i	−0.0107298	+	0.102088i
$237$	7.21467	+	5.24177i	0.468643	+	0.340489i
$238$	3.84419	−	6.20650i	0.249182	−	0.402308i
$239$	−0.164136	−	0.505157i	−0.0106171	−	0.0326759i	0.945608	−	0.325309i	$-0.105468\pi$
$239$	−0.164136	−	0.505157i	−0.0106171	−	0.0326759i	−0.956225	+	0.292633i	$0.905468\pi$
$240$	−3.04169	−	1.35425i	−0.196340	−	0.0874164i
$241$	−1.86136	+	3.22397i	−0.119901	+	0.207674i	−0.919728	−	0.392556i	$-0.871591\pi$
$241$	−1.86136	+	3.22397i	−0.119901	+	0.207674i	0.799827	+	0.600230i	$0.204924\pi$
$242$	−6.75306	+	8.68309i	−0.434103	+	0.558170i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−12.1098	+	8.79832i	−0.775254	+	0.563255i
$245$	−21.8375	+	8.14446i	−1.39515	+	0.520330i
$246$	3.61938	−	11.1393i	0.230763	−	0.710217i
$247$	−1.23394	+	11.7402i	−0.0785139	+	0.747010i
$248$	−1.36217	+	0.606479i	−0.0864981	+	0.0385114i
$249$	−7.27259	−	8.07703i	−0.460881	−	0.511861i
$250$	2.41923	−	2.68683i	0.153006	−	0.169930i
$251$	11.8300	−	8.59497i	0.746701	−	0.542510i	−0.148102	−	0.988972i	$-0.547316\pi$
$251$	11.8300	−	8.59497i	0.746701	−	0.542510i	0.894802	+	0.446462i	$0.147316\pi$
$252$	2.56967	+	0.629903i	0.161874	+	0.0396802i
$253$	9.71422	+	3.91229i	0.610728	+	0.245964i
$254$	−0.309175	−	0.535506i	−0.0193993	−	0.0336006i
$255$	−0.960347	−	9.13709i	−0.0601393	−	0.572187i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	14.5623	−	3.09531i	0.908372	−	0.193080i	0.270047	−	0.962847i	$-0.412961\pi$
$257$	14.5623	−	3.09531i	0.908372	−	0.193080i	0.638325	+	0.769767i	$0.279628\pi$
$258$	−8.95685	−	6.50754i	−0.557629	−	0.405141i
$259$	2.49710	−	6.94610i	0.155162	−	0.431610i
$260$	6.34627	−	19.5318i	0.393579	−	1.21131i
$261$	−0.346048	+	0.384325i	−0.0214198	+	0.0237891i
$262$	−0.759568	−	7.22681i	−0.0469263	−	0.446474i
$263$	9.45543	−	16.3773i	0.583047	−	1.00987i	−0.412069	−	0.911153i	$-0.635194\pi$
$263$	9.45543	−	16.3773i	0.583047	−	1.00987i	0.995116	−	0.0987142i	$-0.0314729\pi$
$264$	−2.30656	−	2.38323i	−0.141959	−	0.146678i
$265$	−2.97242			−0.182594
$266$	0.684870	−	5.01706i	0.0419921	−	0.307615i
$267$	−0.180106	−	0.554309i	−0.0110223	−	0.0339232i
$268$	−0.174670	+	0.0371272i	−0.0106696	+	0.00226790i
$269$	14.1077	−	6.28114i	0.860159	−	0.382968i	0.0712362	−	0.997459i	$-0.477306\pi$
$269$	14.1077	−	6.28114i	0.860159	−	0.382968i	0.788923	+	0.614492i	$0.210639\pi$
$270$	3.04169	−	1.35425i	0.185111	−	0.0824169i
$271$	−9.51362	+	2.02218i	−0.577911	+	0.122839i	−0.487588	−	0.873074i	$-0.662123\pi$
$271$	−9.51362	+	2.02218i	−0.577911	+	0.122839i	−0.0903230	+	0.995913i	$0.528790\pi$
$272$	−0.852690	−	2.62431i	−0.0517019	−	0.159122i
$273$	−2.20725	+	16.1693i	−0.133589	+	0.978610i
$274$	−11.7498			−0.709830
$275$	18.1320	−	8.86842i	1.09340	−	0.534786i
$276$	−1.57878	+	2.73453i	−0.0950314	+	0.164599i
$277$	−2.69773	−	25.6672i	−0.162091	−	1.54219i	−0.709126	−	0.705082i	$-0.750910\pi$
$277$	−2.69773	−	25.6672i	−0.162091	−	1.54219i	0.547035	−	0.837110i	$-0.315756\pi$
$278$	11.3916	−	12.6517i	0.683225	−	0.758798i
$279$	0.460770	−	1.41811i	0.0275856	−	0.0848997i
$280$	−2.98013	+	8.28975i	−0.178097	+	0.495407i
$281$	−14.8041	−	10.7558i	−0.883136	−	0.641636i	0.0509433	−	0.998702i	$-0.483777\pi$
$281$	−14.8041	−	10.7558i	−0.883136	−	0.641636i	−0.934079	+	0.357066i	$0.883777\pi$
$282$	2.35383	−	0.500321i	0.140168	−	0.0297937i
$283$	26.2817	+	5.58635i	1.56229	+	0.332074i	0.906279	−	0.422680i	$-0.138911\pi$
$283$	26.2817	+	5.58635i	1.56229	+	0.332074i	0.656007	+	0.754754i	$0.272244\pi$
$284$	1.15824	+	11.0199i	0.0687290	+	0.653912i
$285$	−3.18613	−	5.51855i	−0.188730	−	0.326891i
$286$	13.1323	−	15.6857i	0.776530	−	0.927516i
$287$	−30.0975	−	7.37779i	−1.77660	−	0.435497i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−6.28041	+	6.97510i	−0.369436	+	0.410300i
$290$	−1.15218	−	1.27963i	−0.0676585	−	0.0751423i
$291$	−11.1568	+	4.96735i	−0.654026	+	0.291191i
$292$	−0.383894	+	3.65251i	−0.0224657	+	0.213747i
$293$	7.69269	−	23.6757i	0.449412	−	1.38315i	−0.428160	−	0.903703i	$-0.640838\pi$
$293$	7.69269	−	23.6757i	0.449412	−	1.38315i	0.877572	−	0.479445i	$-0.159162\pi$
$294$	1.16095	−	6.90306i	0.0677080	−	0.402594i
$295$	4.24773	−	3.08616i	0.247313	−	0.179683i
$296$	−1.39494	−	2.41610i	−0.0810791	−	0.140433i
$297$	3.31447	−	0.119418i	0.192325	−	0.00692936i
$298$	−6.45107	+	11.1736i	−0.373700	+	0.647268i
$299$	−17.7923	−	7.92166i	−1.02896	−	0.458121i
$300$	1.88064	+	5.78801i	0.108579	+	0.334171i
$301$	−15.4239	+	24.9021i	−0.889020	+	1.43533i
$302$	1.05428	+	0.765982i	0.0606672	+	0.0440773i
$303$	−1.05437	+	10.0316i	−0.0605719	+	0.576303i
$304$	−1.28062	−	1.42227i	−0.0734485	−	0.0815729i
$305$	48.7495	+	10.3620i	2.79139	+	0.593328i
$306$	2.52080	+	1.12233i	0.144105	+	0.0641595i
$307$	29.9103			1.70707			0.853535	−	0.521035i	$-0.174454\pi$
$307$	29.9103			1.70707			0.853535	+	0.521035i	$0.174454\pi$
$308$	−5.83850	+	6.55072i	−0.332680	+	0.373262i
$309$	−19.1582			−1.08987
$310$	4.53542	+	2.01930i	0.257594	+	0.114688i
$311$	19.7754	+	4.20339i	1.12136	+	0.238352i	0.731045	−	0.682329i	$-0.239033\pi$
$311$	19.7754	+	4.20339i	1.12136	+	0.238352i	0.390315	+	0.920682i	$0.372366\pi$
$312$	4.12726	+	4.58379i	0.233660	+	0.259506i
$313$	1.30942	−	12.4583i	0.0740131	−	0.704187i	−0.893103	−	0.449852i	$-0.851477\pi$
$313$	1.30942	−	12.4583i	0.0740131	−	0.704187i	0.967116	−	0.254335i	$-0.0818566\pi$
$314$	2.64922	+	1.92477i	0.149504	+	0.108621i
$315$	−4.16639	−	7.76160i	−0.234749	−	0.437316i
$316$	−2.75576	−	8.48136i	−0.155024	−	0.477114i
$317$	8.41012	+	3.74443i	0.472360	+	0.210308i	0.629089	−	0.777334i	$-0.283428\pi$
$317$	8.41012	+	3.74443i	0.472360	+	0.210308i	−0.156729	+	0.987642i	$0.550095\pi$
$318$	0.446370	−	0.773136i	0.0250312	−	0.0433553i
$319$	−0.588426	−	1.61114i	−0.0329456	−	0.0902063i
$320$	1.66477	+	2.88347i	0.0930636	+	0.161191i
$321$	1.89774	−	1.37879i	0.105922	−	0.0769567i
$322$	7.52306	+	3.63247i	0.419244	+	0.202430i
$323$	1.63192	−	5.02255i	0.0908027	−	0.279462i
$324$	−0.104528	+	0.994522i	−0.00580714	+	0.0552512i
$325$	−34.2929	+	15.2682i	−1.90223	+	0.846927i
$326$	1.30633	+	1.45083i	0.0723511	+	0.0803540i
$327$	−10.4917	+	11.6523i	−0.580195	+	0.644371i
$328$	−9.47567	+	6.88448i	−0.523206	+	0.380132i
$329$	−1.77912	−	6.11314i	−0.0980860	−	0.337028i
$330$	−0.758113	+	11.0168i	−0.0417328	+	0.606455i
$331$	7.58335	+	13.1348i	0.416819	+	0.721951i	0.995617	−	0.0935191i	$-0.0298116\pi$
$331$	7.58335	+	13.1348i	0.416819	+	0.721951i	−0.578799	+	0.815470i	$0.696478\pi$
$332$	1.13609	+	10.8092i	0.0623510	+	0.593230i
$333$	2.72891	+	0.580048i	0.149543	+	0.0317864i
$334$	3.17416	−	0.674689i	0.173682	−	0.0369173i
$335$	0.481012	+	0.349475i	0.0262805	+	0.0190939i
$336$	−1.70866	−	2.02002i	−0.0932151	−	0.110201i
$337$	−8.05189	+	24.7812i	−0.438614	+	1.34992i	0.450723	+	0.892664i	$0.351166\pi$
$337$	−8.05189	+	24.7812i	−0.438614	+	1.34992i	−0.889337	+	0.457252i	$0.848834\pi$
$338$	−16.7587	+	18.6124i	−0.911551	+	1.01238i
$339$	−1.12415	−	10.6956i	−0.0610557	−	0.580906i
$340$	−4.59371	+	7.95654i	−0.249129	+	0.431504i
$341$	3.43928	+	3.55359i	0.186247	+	0.192438i
$342$	1.91386			0.103489
$343$	−18.4405	−	1.71714i	−0.995693	−	0.0927170i
$344$	3.42121	+	10.5294i	0.184459	+	0.567708i
$345$	10.2835	−	2.18583i	0.553645	−	0.117681i
$346$	21.7327	−	9.67604i	1.16836	−	0.520187i
$347$	−31.7414	+	14.1322i	−1.70397	+	0.758656i	−0.705202	+	0.709007i	$0.749144\pi$
$347$	−31.7414	+	14.1322i	−1.70397	+	0.758656i	−0.998767	+	0.0496488i	$0.984190\pi$
$348$	0.505859	−	0.107524i	0.0271169	−	0.00576387i
$349$	−9.24039	−	28.4390i	−0.494627	−	1.52230i	−0.817538	−	0.575875i	$-0.804661\pi$
$349$	−9.24039	−	28.4390i	−0.494627	−	1.52230i	0.322911	−	0.946429i	$-0.395339\pi$
$350$	14.9053	−	6.09083i	0.796720	−	0.325569i
$351$	−6.16810			−0.329229
$352$	0.465221	+	3.28383i	0.0247964	+	0.175029i
$353$	−2.09489	+	3.62846i	−0.111500	+	0.193124i	−0.916375	−	0.400320i	$-0.868899\pi$
$353$	−2.09489	+	3.62846i	−0.111500	+	0.193124i	0.804875	+	0.593444i	$0.202232\pi$
$354$	0.164835	+	1.56830i	0.00876087	+	0.0833541i
$355$	24.6865	−	27.4172i	1.31023	−	1.45515i
$356$	−0.180106	+	0.554309i	−0.00954560	+	0.0293783i
$357$	2.46978	−	6.87013i	0.130715	−	0.363606i
$358$	15.5297	+	11.2830i	0.820772	+	0.596325i
$359$	−1.55230	+	0.329951i	−0.0819270	+	0.0174141i	−0.248693	−	0.968582i	$-0.580001\pi$
$359$	−1.55230	+	0.329951i	−0.0819270	+	0.0174141i	0.166766	+	0.985997i	$0.446668\pi$
$360$	−3.25679	−	0.692252i	−0.171648	−	0.0364849i
$361$	1.60317	+	15.2531i	0.0843773	+	0.802797i
$362$	−7.65902	−	13.2658i	−0.402549	−	0.697235i
$363$	−4.80018	+	9.89739i	−0.251944	+	0.519478i
$364$	11.2898	−	11.7838i	0.591745	−	0.617641i
$365$	9.89280	−	7.18754i	0.517813	−	0.376213i
$366$	−10.0159	+	11.1238i	−0.523542	+	0.581452i
$367$	−9.29869	−	10.3272i	−0.485388	−	0.539077i	0.449847	−	0.893105i	$-0.351478\pi$
$367$	−9.29869	−	10.3272i	−0.485388	−	0.539077i	−0.935235	+	0.354028i	$0.884812\pi$
$368$	2.88457	−	1.28430i	0.150369	−	0.0669485i
$369$	1.22430	−	11.6484i	0.0637344	−	0.606392i
$370$	−2.87046	+	8.83438i	−0.149228	+	0.459278i
$371$	−2.12700	−	1.02701i	−0.110429	−	0.0533198i
$372$	−1.20631	+	0.876437i	−0.0625444	+	0.0454412i
$373$	4.54065	+	7.86464i	0.235106	+	0.407216i	0.959304	−	0.282377i	$-0.0911229\pi$
$373$	4.54065	+	7.86464i	0.235106	+	0.407216i	−0.724197	+	0.689593i	$0.757790\pi$
$374$	−7.20545	+	5.64237i	−0.372585	+	0.291760i
$375$	1.80774	−	3.13110i	0.0933514	−	0.161689i
$376$	−2.19837	−	0.978776i	−0.113372	−	0.0504765i
$377$	0.985732	+	3.03377i	0.0507678	+	0.156247i
$378$	2.64448	+	0.0818733i	0.136018	+	0.00421111i
$379$	−16.7203	−	12.1480i	−0.858863	−	0.624000i	0.0687125	−	0.997637i	$-0.478111\pi$
$379$	−16.7203	−	12.1480i	−0.858863	−	0.624000i	−0.927575	+	0.373636i	$0.878111\pi$
$380$	−0.666084	+	6.33736i	−0.0341694	+	0.325100i
$381$	−0.413756	−	0.459523i	−0.0211974	−	0.0235421i
$382$	−25.2374	−	5.36437i	−1.29126	−	0.274465i
$383$	5.88989	+	2.62235i	0.300960	+	0.133996i	0.551660	−	0.834069i	$-0.313994\pi$
$383$	5.88989	+	2.62235i	0.300960	+	0.133996i	−0.250701	+	0.968065i	$0.580661\pi$
$384$	−1.00000			−0.0510310
$385$	29.2163	−	0.147943i	1.48900	−	0.00753987i
$386$	8.40101			0.427600
$387$	−10.1141	−	4.50310i	−0.514130	−	0.228905i
$388$	11.9458	+	2.53916i	0.606457	+	0.128906i
$389$	19.3870	+	21.5315i	0.982962	+	1.09169i	0.995780	+	0.0917720i	$0.0292531\pi$
$389$	19.3870	+	21.5315i	0.982962	+	1.09169i	−0.0128181	+	0.999918i	$0.504080\pi$
$390$	2.14670	−	20.4245i	0.108702	−	1.03423i
$391$	7.04884	+	5.12128i	0.356475	+	0.258994i
$392$	−4.99674	+	4.90230i	−0.252374	+	0.247604i
$393$	−2.24551	−	6.91096i	−0.113271	−	0.348612i
$394$	−11.1682	−	4.97242i	−0.562648	−	0.250507i
$395$	−14.8462	+	25.7143i	−0.746991	+	1.29383i
$396$	−2.75166	−	1.85159i	−0.138276	−	0.0930458i
$397$	8.35193	+	14.4660i	0.419172	+	0.726026i	0.995856	−	0.0909403i	$-0.0289872\pi$
$397$	8.35193	+	14.4660i	0.419172	+	0.726026i	−0.576685	+	0.816967i	$0.695654\pi$
$398$	−19.8876	+	14.4492i	−0.996877	+	0.724273i
$399$	−0.373200	−	5.04981i	−0.0186834	−	0.252807i
$400$	1.88064	−	5.78801i	0.0940320	−	0.289401i
$401$	−2.74258	+	26.0939i	−0.136958	+	1.30307i	0.682904	+	0.730508i	$0.260717\pi$
$401$	−2.74258	+	26.0939i	−0.136958	+	1.30307i	−0.819862	+	0.572561i	$0.805950\pi$
$402$	−0.163133	+	0.0726317i	−0.00813636	+	0.00362254i
$403$	−6.15410	−	6.83482i	−0.306557	−	0.340466i
$404$	6.74946	−	7.49603i	0.335798	−	0.372941i
$405$	2.69366	−	1.95706i	0.133849	−	0.0972470i
$406$	−0.382349	−	1.31377i	−0.0189757	−	0.0652013i
$407$	−5.93984	+	7.09477i	−0.294427	+	0.351675i
$408$	−1.37968	−	2.38968i	−0.0683044	−	0.118307i
$409$	1.75959	+	16.7414i	0.0870060	+	0.827807i	0.947803	+	0.318858i	$0.103299\pi$
$409$	1.75959	+	16.7414i	0.0870060	+	0.827807i	−0.860797	+	0.508949i	$0.830034\pi$
$410$	38.1454	+	8.10805i	1.88387	+	0.400428i
$411$	−11.4930	+	2.44292i	−0.566909	+	0.120500i
$412$	15.4993	+	11.2609i	0.763597	+	0.554786i
$413$	4.10590	−	0.740743i	0.202038	−	0.0364496i
$414$	−0.975740	+	3.00302i	−0.0479550	+	0.147590i
$415$	24.2144	−	26.8928i	1.18864	−	1.32012i
$416$	−0.644742	−	6.13431i	−0.0316111	−	0.300759i
$417$	8.51226	−	14.7437i	0.416847	−	0.722001i
$418$	−2.97378	+	5.60784i	−0.145452	+	0.274288i
$419$	−7.79672			−0.380894			−0.190447	−	0.981697i	$-0.560994\pi$
$419$	−7.79672			−0.380894			−0.190447	+	0.981697i	$0.560994\pi$
$420$	−1.19147	+	8.72820i	−0.0581380	+	0.425893i
$421$	9.01550	+	27.7469i	0.439389	+	1.35230i	0.888522	+	0.458835i	$0.151733\pi$
$421$	9.01550	+	27.7469i	0.439389	+	1.35230i	−0.449133	+	0.893465i	$0.648267\pi$
$422$	12.2148	−	2.59633i	0.594606	−	0.126387i
$423$	2.19837	−	0.978776i	0.106888	−	0.0475897i
$424$	−0.815559	+	0.363110i	−0.0396071	+	0.0176342i
$425$	16.4262	−	3.49149i	0.796786	−	0.169362i
$426$	3.42410	+	10.5383i	0.165898	+	0.510583i
$427$	31.3040	+	24.2585i	1.51490	+	1.17395i
$428$	−2.34574			−0.113386
$429$	9.58410	−	18.0733i	0.462725	−	0.872588i
$430$	18.4312	−	31.9237i	0.888830	−	1.53950i
$431$	2.66668	+	25.3718i	0.128450	+	1.22212i	0.848879	+	0.528588i	$0.177278\pi$
$431$	2.66668	+	25.3718i	0.128450	+	1.22212i	−0.720429	+	0.693529i	$0.756055\pi$
$432$	0.669131	−	0.743145i	0.0321936	−	0.0357546i
$433$	−0.00422913	+	0.0130159i	−0.000203239	+	0.000625506i	−0.951158	−	0.308704i	$-0.900105\pi$
$433$	−0.00422913	+	0.0130159i	−0.000203239	+	0.000625506i	0.950955	+	0.309330i	$0.100105\pi$
$434$	2.54776	+	3.01202i	0.122296	+	0.144581i
$435$	−1.39305	−	1.01211i	−0.0667918	−	0.0485271i
$436$	15.3370	−	3.25998i	0.734510	−	0.156125i
$437$	5.91106	+	1.25643i	0.282764	+	0.0601034i
$438$	0.383894	+	3.65251i	0.0183432	+	0.174524i
$439$	−19.6988	−	34.1194i	−0.940174	−	1.62843i	−0.765136	−	0.643868i	$-0.777328\pi$
$439$	−19.6988	−	34.1194i	−0.940174	−	1.62843i	−0.175038	−	0.984562i	$-0.556005\pi$
$440$	7.08884	−	8.46717i	0.337947	−	0.403657i
$441$	−0.299645	−	6.99358i	−0.0142688	−	0.333028i
$442$	13.7695	−	10.0041i	0.654947	−	0.475847i
$443$	−12.4242	+	13.7985i	−0.590294	+	0.655587i	−0.962092	−	0.272726i	$-0.912075\pi$
$443$	−12.4242	+	13.7985i	−0.590294	+	0.655587i	0.371798	+	0.928314i	$0.378741\pi$
$444$	−1.86679	−	2.07328i	−0.0885940	−	0.0983936i
$445$	1.77280	−	0.789304i	0.0840390	−	0.0374166i
$446$	−1.42128	+	13.5226i	−0.0672997	+	0.640314i
$447$	−3.98698	+	12.2707i	−0.188578	+	0.580382i
$448$	0.194999	+	2.63856i	0.00921284	+	0.124660i
$449$	−4.64331	+	3.37356i	−0.219131	+	0.159208i	−0.691936	−	0.721959i	$-0.743242\pi$
$449$	−4.64331	+	3.37356i	−0.219131	+	0.159208i	0.472804	+	0.881167i	$0.343242\pi$
$450$	3.04294	+	5.27053i	0.143446	+	0.248455i
$451$	32.2290	+	21.6869i	1.51760	+	1.02119i
$452$	−5.37726	+	9.31369i	−0.252925	+	0.438079i
$453$	1.19050	+	0.530045i	0.0559346	+	0.0249037i
$454$	−1.91014	−	5.87880i	−0.0896471	−	0.275906i
$455$	−54.3097	−	1.68143i	−2.54608	−	0.0788266i
$456$	−1.54834	−	1.12494i	−0.0725077	−	0.0526800i
$457$	0.0272760	−	0.259513i	0.00127592	−	0.0121395i	−0.993865	−	0.110596i	$-0.964724\pi$
$457$	0.0272760	−	0.259513i	0.00127592	−	0.0121395i	0.995141	+	0.0984568i	$0.0313906\pi$
$458$	8.05425	+	8.94515i	0.376350	+	0.417980i
$459$	2.69906	+	0.573704i	0.125981	+	0.0267782i
$460$	−9.60432	−	4.27612i	−0.447804	−	0.199375i
$461$	15.7428			0.733215			0.366607	−	0.930376i	$-0.380519\pi$
$461$	15.7428			0.733215			0.366607	+	0.930376i	$0.380519\pi$
$462$	−4.34895	+	7.62146i	−0.202331	+	0.354582i
$463$	10.4942			0.487708			0.243854	−	0.969812i	$-0.421588\pi$
$463$	10.4942			0.487708			0.243854	+	0.969812i	$0.421588\pi$
$464$	−0.472449	−	0.210348i	−0.0219329	−	0.00976516i
$465$	4.85614	+	1.03221i	0.225198	+	0.0478674i
$466$	−14.1588	−	15.7250i	−0.655896	−	0.728446i
$467$	0.0987883	−	0.939908i	0.00457138	−	0.0434938i	−0.991998	−	0.126250i	$-0.959706\pi$
$467$	0.0987883	−	0.939908i	0.00457138	−	0.0434938i	0.996570	+	0.0827566i	$0.0263724\pi$
$468$	4.99010	+	3.62552i	0.230667	+	0.167590i
$469$	0.223454	+	0.416274i	0.0103181	+	0.0192217i
$470$	2.47593	+	7.62011i	0.114206	+	0.351490i
$471$	2.99152	+	1.33191i	0.137842	+	0.0613711i
$472$	0.788469	−	1.36567i	0.0362922	−	0.0628600i
$473$	28.9101	−	22.6387i	1.32929	−	1.04093i
$474$	−4.45891	−	7.72307i	−0.204805	−	0.354732i
$475$	9.42302	−	6.84622i	0.432358	−	0.314126i
$476$	−6.03626	+	4.10635i	−0.276671	+	0.188214i
$477$	0.275872	−	0.849047i	0.0126313	−	0.0388752i
$478$	−0.0555207	+	0.528244i	−0.00253946	+	0.0241613i
$479$	13.5417	−	6.02916i	0.618737	−	0.275479i	−0.0733356	−	0.997307i	$-0.523364\pi$
$479$	13.5417	−	6.02916i	0.618737	−	0.275479i	0.692073	+	0.721828i	$0.256698\pi$
$480$	2.22790	+	2.47434i	0.101689	+	0.112937i
$481$	11.5145	−	12.7882i	0.525018	−	0.583092i
$482$	3.01175	−	2.18816i	0.137181	−	0.0996681i
$483$	8.11390	+	1.98896i	0.369195	+	0.0905007i
$484$	9.70096	−	5.18568i	0.440953	−	0.235713i
$485$	−20.3314	−	35.2149i	−0.923199	−	1.59903i
$486$	0.104528	+	0.994522i	0.00474151	+	0.0451124i
$487$	−11.1617	−	2.37248i	−0.505783	−	0.107508i	−0.0520489	−	0.998645i	$-0.516575\pi$
$487$	−11.1617	−	2.37248i	−0.505783	−	0.107508i	−0.453734	+	0.891137i	$0.649908\pi$
$488$	14.6415	−	3.11215i	0.662789	−	0.140880i
$489$	1.57943	+	1.14752i	0.0714243	+	0.0518928i
$490$	23.2622	+	1.44178i	1.05088	+	0.0651328i
$491$	−3.30384	+	10.1682i	−0.149100	+	0.458884i	−0.997515	−	0.0704477i	$-0.977557\pi$
$491$	−3.30384	+	10.1682i	−0.149100	+	0.458884i	0.848415	+	0.529332i	$0.177557\pi$
$492$	−7.83724	+	8.70414i	−0.353330	+	0.392413i
$493$	−0.149165	−	1.41921i	−0.00671808	−	0.0639182i
$494$	5.90242	−	10.2233i	0.265563	−	0.459968i
$495$	1.54898	+	10.9337i	0.0696213	+	0.491432i
$496$	1.49108			0.0669517
$497$	27.1382	−	11.0896i	1.21731	−	0.497439i
$498$	3.35862	+	10.3368i	0.150503	+	0.463201i
$499$	−13.3868	+	2.84545i	−0.599275	+	0.127380i	−0.497554	−	0.867433i	$-0.665768\pi$
$499$	−13.3868	+	2.84545i	−0.599275	+	0.127380i	−0.101721	+	0.994813i	$0.532435\pi$
$500$	−3.30291	+	1.47055i	−0.147711	+	0.0657650i
$501$	2.96452	−	1.31989i	0.132445	−	0.0589684i
$502$	−14.3031	+	3.04022i	−0.638379	+	0.135692i
$503$	−11.0470	−	33.9993i	−0.492563	−	1.51595i	−0.820721	−	0.571329i	$-0.806428\pi$
$503$	−11.0470	−	33.9993i	−0.492563	−	1.51595i	0.328158	−	0.944623i	$-0.393572\pi$
$504$	−2.09131	−	1.62063i	−0.0931543	−	0.0721884i
$505$	−33.5848			−1.49450
$506$	−7.28311	−	7.52518i	−0.323774	−	0.334535i
$507$	−12.5227	+	21.6900i	−0.556153	+	0.963286i
$508$	0.0646351	+	0.614962i	0.00286772	+	0.0272845i
$509$	−28.0712	+	31.1762i	−1.24423	+	1.38186i	−0.348477	+	0.937317i	$0.613301\pi$
$509$	−28.0712	+	31.1762i	−1.24423	+	1.38186i	−0.895757	+	0.444544i	$0.853366\pi$
$510$	−2.83907	+	8.73776i	−0.125716	+	0.386914i
$511$	9.56248	−	1.72516i	0.423019	−	0.0763166i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	1.87203	−	0.397913i	0.0826523	−	0.0175683i
$514$	−14.5623	−	3.09531i	−0.642316	−	0.136528i
$515$	−6.66768	−	63.4387i	−0.293813	−	2.79545i
$516$	5.53564	+	9.58801i	0.243693	+	0.422089i
$517$	−0.547922	+	7.96234i	−0.0240976	+	0.350183i
$518$	−5.10645	+	5.32992i	−0.224364	+	0.234183i
$519$	19.2461	−	13.9831i	0.844808	−	0.613789i
$520$	−13.7419	+	15.2619i	−0.602623	+	0.669280i
$521$	8.85310	+	9.83236i	0.387861	+	0.430764i	0.905180	−	0.425029i	$-0.139736\pi$
$521$	8.85310	+	9.83236i	0.387861	+	0.430764i	−0.517318	+	0.855793i	$0.673070\pi$
$522$	0.472449	−	0.210348i	0.0206786	−	0.00920668i
$523$	0.440398	−	4.19011i	0.0192573	−	0.183221i	−0.980665	−	0.195694i	$-0.937304\pi$
$523$	0.440398	−	4.19011i	0.0192573	−	0.183221i	0.999922	+	0.0124737i	$0.00397061\pi$
$524$	−2.24551	+	6.91096i	−0.0980955	+	0.301907i
$525$	13.3132	−	9.05671i	0.581036	−	0.395267i
$526$	−15.2992	+	11.1155i	−0.667077	+	0.484660i
$527$	2.05722	+	3.56321i	0.0896139	+	0.155216i
$528$	1.13780	+	3.11535i	0.0495165	+	0.135578i
$529$	6.51491	−	11.2842i	0.283257	−	0.490615i
$530$	2.71544	+	1.20899i	0.117951	+	0.0525153i
$531$	0.487300	+	1.49976i	0.0211470	+	0.0650839i
$532$	−2.66628	+	4.30475i	−0.115598	+	0.186634i
$533$	−58.4469	−	42.4641i	−2.53161	−	1.83933i
$534$	−0.0609229	+	0.579642i	−0.00263639	+	0.0250836i
$535$	5.22608	+	5.80415i	0.225943	+	0.250935i
$536$	0.174670	+	0.0371272i	0.00754458	+	0.00160365i
$537$	17.5362	+	7.80763i	0.756744	+	0.336924i
$538$	−15.4428			−0.665785
$539$	20.9577	+	9.98876i	0.902712	+	0.430246i
$540$	−3.32955			−0.143281
$541$	6.75271	+	3.00650i	0.290322	+	0.129260i	0.546730	−	0.837309i	$-0.315872\pi$
$541$	6.75271	+	3.00650i	0.290322	+	0.129260i	−0.256408	+	0.966569i	$0.582539\pi$
$542$	9.51362	+	2.02218i	0.408645	+	0.0868602i
$543$	−10.2498	−	11.3835i	−0.439859	−	0.488513i
$544$	−0.288432	+	2.74425i	−0.0123664	+	0.117659i
$545$	−42.2357	−	30.6860i	−1.80918	−	1.31444i
$546$	8.59306	−	13.8736i	0.367749	−	0.593736i
$547$	2.34254	+	7.20958i	0.100160	+	0.308260i	0.988564	−	0.150802i	$-0.0481857\pi$
$547$	2.34254	+	7.20958i	0.100160	+	0.308260i	−0.888404	+	0.459062i	$0.848186\pi$
$548$	10.7340	+	4.77906i	0.458532	+	0.204152i
$549$	−7.48430	+	12.9632i	−0.319422	+	0.553255i
$550$	−20.1715	+	0.726766i	−0.860115	+	0.0309894i
$551$	−0.494885	−	0.857166i	−0.0210828	−	0.0365165i
$552$	2.55452	−	1.85597i	0.108728	−	0.0789952i
$553$	−19.5083	+	13.2711i	−0.829575	+	0.564344i
$554$	−7.97529	+	24.5454i	−0.338837	+	1.04283i
$555$	−0.970967	+	9.23813i	−0.0412152	+	0.392137i
$556$	−15.5527	+	6.92450i	−0.659580	+	0.293664i
$557$	8.86832	+	9.84927i	0.375763	+	0.417327i	0.901130	−	0.433549i	$-0.142739\pi$
$557$	8.86832	+	9.84927i	0.375763	+	0.417327i	−0.525367	+	0.850876i	$0.676072\pi$
$558$	−0.997730	+	1.10809i	−0.0422373	+	0.0469093i
$559$	−55.2468	+	40.1391i	−2.33669	+	1.69770i
$560$	6.09423	−	6.36093i	0.257528	−	0.268799i
$561$	−5.87488	+	7.01717i	−0.248037	+	0.296265i
$562$	9.14941	+	15.8472i	0.385945	+	0.668476i
$563$	−1.96203	−	18.6675i	−0.0826896	−	0.786739i	−0.954764	−	0.297366i	$-0.903892\pi$
$563$	−1.96203	−	18.6675i	−0.0826896	−	0.786739i	0.872074	−	0.489374i	$-0.162775\pi$
$564$	−2.35383	−	0.500321i	−0.0991140	−	0.0210673i
$565$	35.0252	−	7.44484i	1.47352	−	0.313207i
$566$	−21.7374	−	15.7931i	−0.913690	−	0.663835i
$567$	2.60372	−	0.469735i	0.109346	−	0.0197270i
$568$	3.42410	−	10.5383i	0.143672	−	0.442177i
$569$	−21.5759	+	23.9625i	−0.904508	+	1.00456i	0.0954501	+	0.995434i	$0.469571\pi$
$569$	−21.5759	+	23.9625i	−0.904508	+	1.00456i	−0.999958	+	0.00912401i	$0.997096\pi$
$570$	0.666084	+	6.33736i	0.0278992	+	0.265443i
$571$	−2.85958	+	4.95293i	−0.119670	+	0.207274i	−0.919637	−	0.392770i	$-0.871517\pi$
$571$	−2.85958	+	4.95293i	−0.119670	+	0.207274i	0.799967	+	0.600044i	$0.204850\pi$
$572$	−18.3769	+	8.98823i	−0.768378	+	0.375817i
$573$	−25.8012			−1.07786
$574$	24.4946	+	18.9817i	1.02239	+	0.792281i
$575$	5.93823	+	18.2760i	0.247641	+	0.762162i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−0.755159	+	0.336218i	−0.0314377	+	0.0139970i	−0.422395	−	0.906412i	$-0.638811\pi$
$577$	−0.755159	+	0.336218i	−0.0314377	+	0.0139970i	0.390958	+	0.920409i	$0.372144\pi$
$578$	8.57447	−	3.81760i	0.356651	−	0.158791i
$579$	8.21743	−	1.74667i	0.341505	−	0.0725891i
$580$	0.532099	+	1.63763i	0.0220942	+	0.0679990i
$581$	26.6192	−	10.8776i	1.10435	−	0.451277i
$582$	12.2127			0.506232
$583$	2.05916	+	2.12760i	0.0852817	+	0.0881164i
$584$	1.83631	−	3.18059i	0.0759872	−	0.131614i
$585$	−2.14670	−	20.4245i	−0.0887550	−	0.844448i
$586$	−16.6574	+	18.4999i	−0.688110	+	0.764224i
$587$	2.76848	−	8.52050i	0.114267	−	0.351679i	−0.877526	−	0.479529i	$-0.840808\pi$
$587$	2.76848	−	8.52050i	0.114267	−	0.351679i	0.991793	+	0.127850i	$0.0408077\pi$
$588$	−3.86831	+	5.83405i	−0.159526	+	0.240592i
$589$	2.30871	+	1.67737i	0.0951286	+	0.0691150i
$590$	−5.13575	+	1.09164i	−0.211435	+	0.0449420i
$591$	−11.9580	−	2.54176i	−0.491887	−	0.104554i
$592$	0.291621	+	2.77459i	0.0119856	+	0.114035i
$593$	18.4196	+	31.9037i	0.756404	+	1.31013i	0.944673	+	0.328012i	$0.106379\pi$
$593$	18.4196	+	31.9037i	0.756404	+	1.31013i	−0.188270	+	0.982117i	$0.560288\pi$
$594$	−3.07649	−	1.23902i	−0.126230	−	0.0508378i
$595$	23.6087	+	5.78719i	0.967861	+	0.237252i
$596$	10.4380	−	7.58369i	0.427559	−	0.310640i
$597$	−16.4489	+	18.2683i	−0.673208	+	0.747673i
$598$	13.0321	+	14.4736i	0.532921	+	0.591869i
$599$	18.7698	−	8.35687i	0.766915	−	0.341453i	0.0142865	−	0.999898i	$-0.495452\pi$
$599$	18.7698	−	8.35687i	0.766915	−	0.341453i	0.752629	+	0.658445i	$0.228786\pi$
$600$	0.636148	−	6.05254i	0.0259706	−	0.247094i
$601$	−11.2845	+	34.7301i	−0.460304	+	1.41667i	0.404490	+	0.914542i	$0.367449\pi$
$601$	−11.2845	+	34.7301i	−0.460304	+	1.41667i	−0.864794	+	0.502127i	$0.832551\pi$
$602$	24.2191	−	16.4757i	0.987095	−	0.671501i
$603$	−0.144468	+	0.104962i	−0.00588318	+	0.00427438i
$604$	−0.651583	−	1.12857i	−0.0265125	−	0.0459211i
$605$	−34.4439	−	12.4502i	−1.40034	−	0.506175i
$606$	5.04345	−	8.73551i	0.204876	−	0.354856i
$607$	−0.771338	−	0.343422i	−0.0313076	−	0.0139391i	0.391023	−	0.920381i	$-0.372121\pi$
$607$	−0.771338	−	0.343422i	−0.0313076	−	0.0139391i	−0.422331	+	0.906442i	$0.638788\pi$
$608$	0.591414	+	1.82018i	0.0239850	+	0.0738182i
$609$	−0.647142	−	1.20557i	−0.0262235	−	0.0488520i
$610$	−40.3203	−	29.2944i	−1.63252	−	1.18610i
$611$	1.55151	−	14.7617i	0.0627676	−	0.597194i
$612$	−1.84637	−	2.05061i	−0.0746352	−	0.0828908i
$613$	−17.1298	−	3.64105i	−0.691866	−	0.147061i	−0.151458	−	0.988464i	$-0.548397\pi$
$613$	−17.1298	−	3.64105i	−0.691866	−	0.147061i	−0.540408	+	0.841403i	$0.681730\pi$
$614$	−27.3244	−	12.1656i	−1.10272	−	0.490964i
$615$	38.9975			1.57253
$616$	7.99815	−	3.60965i	0.322255	−	0.145437i
$617$	−2.96929			−0.119539			−0.0597697	−	0.998212i	$-0.519037\pi$
$617$	−2.96929			−0.119539			−0.0597697	+	0.998212i	$0.519037\pi$
$618$	17.5019	+	7.79235i	0.704030	+	0.313454i
$619$	−8.82055	−	1.87487i	−0.354528	−	0.0753572i	0.0272051	−	0.999630i	$-0.491339\pi$
$619$	−8.82055	−	1.87487i	−0.354528	−	0.0753572i	−0.381733	+	0.924273i	$0.624673\pi$
$620$	−3.32199	−	3.68944i	−0.133414	−	0.148172i
$621$	−0.330055	+	3.14026i	−0.0132446	+	0.126014i
$622$	−16.3560	−	11.8834i	−0.655818	−	0.476479i
$623$	1.54130	+	0.0477186i	0.0617508	+	0.00191181i
$624$	−1.90605	−	5.86621i	−0.0763030	−	0.234836i
$625$	−16.8014	−	7.48049i	−0.672058	−	0.299219i
$626$	−6.26348	+	10.8487i	−0.250339	+	0.433600i
$627$	−1.74286	+	6.10358i	−0.0696032	+	0.243754i
$628$	−1.63731	−	2.83591i	−0.0653358	−	0.113165i
$629$	−6.22803	+	4.52493i	−0.248328	+	0.180421i
$630$	0.649259	+	8.78519i	0.0258671	+	0.350010i
$631$	3.91297	−	12.0429i	0.155773	−	0.479419i	−0.842466	−	0.538750i	$-0.818897\pi$
$631$	3.91297	−	12.0429i	0.155773	−	0.479419i	0.998238	+	0.0593308i	$0.0188967\pi$
$632$	−0.932167	+	8.86898i	−0.0370796	+	0.352789i
$633$	11.4080	−	5.07919i	0.453429	−	0.201880i
$634$	−6.16003	−	6.84141i	−0.244646	−	0.271707i
$635$	1.37762	−	1.53000i	0.0546692	−	0.0607163i
$636$	−0.722242	+	0.524740i	−0.0286388	+	0.0208073i
$637$	−38.2820	−	19.9679i	−1.51679	−	0.791158i
$638$	−0.117754	+	1.71118i	−0.00466191	+	0.0677463i
$639$	5.54031	+	9.59611i	0.219171	+	0.379616i
$640$	−0.348032	−	3.31131i	−0.0137572	−	0.130891i
$641$	−6.76892	−	1.43878i	−0.267356	−	0.0568283i	0.0722828	−	0.997384i	$-0.476972\pi$
$641$	−6.76892	−	1.43878i	−0.267356	−	0.0568283i	−0.339639	+	0.940556i	$0.610305\pi$
$642$	−2.29448	+	0.487707i	−0.0905560	+	0.0192483i
$643$	−5.52037	−	4.01078i	−0.217702	−	0.158170i	0.473590	−	0.880746i	$-0.342958\pi$
$643$	−5.52037	−	4.01078i	−0.217702	−	0.158170i	−0.691292	+	0.722576i	$0.742958\pi$
$644$	−5.39520	−	6.37833i	−0.212601	−	0.251341i
$645$	11.3911	−	35.0582i	0.448524	−	1.38041i
$646$	−3.53369	+	3.92456i	−0.139031	+	0.154410i
$647$	−4.45027	−	42.3415i	−0.174958	−	1.66462i	−0.631847	−	0.775093i	$-0.717703\pi$
$647$	−4.45027	−	42.3415i	−0.174958	−	1.66462i	0.456889	−	0.889524i	$-0.348964\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−5.15165	−	0.902496i	−0.202220	−	0.0354260i
$650$	37.5383			1.47237
$651$	3.11832	+	2.41649i	0.122216	+	0.0947097i
$652$	−0.603289	−	1.85673i	−0.0236266	−	0.0727152i
$653$	−19.4283	+	4.12962i	−0.760289	+	0.161604i	−0.571712	−	0.820454i	$-0.693721\pi$
$653$	−19.4283	+	4.12962i	−0.760289	+	0.161604i	−0.188577	+	0.982058i	$0.560387\pi$
$654$	14.3241	−	6.37749i	0.560116	−	0.249380i
$655$	22.1028	−	9.84081i	0.863628	−	0.384512i
$656$	11.4566	−	2.43518i	0.447306	−	0.0950778i
$657$	1.13490	+	3.49287i	0.0442768	+	0.136270i
$658$	−0.861131	+	6.30826i	−0.0335704	+	0.245922i
$659$	−31.2817			−1.21856			−0.609280	−	0.792955i	$-0.708542\pi$
$659$	−31.2817			−1.21856			−0.609280	+	0.792955i	$0.708542\pi$
$660$	5.17351	−	9.75600i	0.201379	−	0.379752i
$661$	−20.1978	+	34.9836i	−0.785604	+	1.36071i	0.143034	+	0.989718i	$0.454314\pi$
$661$	−20.1978	+	34.9836i	−0.785604	+	1.36071i	−0.928638	+	0.370988i	$0.879019\pi$
$662$	−1.58535	−	15.0836i	−0.0616165	−	0.586242i
$663$	11.3886	−	12.6483i	0.442297	−	0.491221i
$664$	3.35862	−	10.3368i	0.130340	−	0.401144i
$665$	16.5916	−	2.99328i	0.643394	−	0.116074i
$666$	−2.25706	−	1.63985i	−0.0874592	−	0.0635428i
$667$	1.59728	−	0.339512i	0.0618470	−	0.0131460i
$668$	−3.17416	−	0.674689i	−0.122812	−	0.0261045i
$669$	1.42128	+	13.5226i	0.0549500	+	0.522814i
$670$	−0.297282	−	0.514907i	−0.0114850	−	0.0198926i
$671$	−26.3546	−	42.0724i	−1.01741	−	1.62419i
$672$	0.739324	+	2.54035i	0.0285201	+	0.0979963i
$673$	19.7277	−	14.3330i	0.760447	−	0.552497i	−0.138600	−	0.990348i	$-0.544260\pi$
$673$	19.7277	−	14.3330i	0.760447	−	0.552497i	0.899047	+	0.437851i	$0.144260\pi$
$674$	17.4352	−	19.3637i	0.671578	−	0.745863i
$675$	4.07225	+	4.52269i	0.156741	+	0.174078i
$676$	22.8801	−	10.1869i	0.880006	−	0.391804i
$677$	3.50511	−	33.3489i	0.134712	−	1.28170i	−0.693159	−	0.720785i	$-0.743782\pi$
$677$	3.50511	−	33.3489i	0.134712	−	1.28170i	0.827871	−	0.560918i	$-0.189552\pi$
$678$	−3.32333	+	10.2282i	−0.127632	+	0.392810i
$679$	−2.38146	−	32.2239i	−0.0913922	−	1.23664i
$680$	7.43278	−	5.40023i	0.285034	−	0.207089i
$681$	−3.09067	−	5.35319i	−0.118435	−	0.205135i
$682$	−1.69656	−	4.64525i	−0.0649646	−	0.177876i
$683$	4.19189	−	7.26057i	0.160398	−	0.277818i	−0.774613	−	0.632435i	$-0.782055\pi$
$683$	4.19189	−	7.26057i	0.160398	−	0.277818i	0.935012	+	0.354617i	$0.115389\pi$
$684$	−1.74839	−	0.778435i	−0.0668515	−	0.0297642i
$685$	−12.0892	−	37.2067i	−0.461904	−	1.42159i
$686$	16.1478	+	9.06911i	0.616526	+	0.346260i
$687$	9.73805	+	7.07511i	0.371530	+	0.269932i
$688$	1.15726	−	11.0106i	0.0441203	−	0.419776i
$689$	−3.68458	−	4.09214i	−0.140371	−	0.155898i
$690$	−10.2835	−	2.18583i	−0.391486	−	0.0832130i
$691$	16.2394	+	7.23027i	0.617778	+	0.275052i	0.691670	−	0.722214i	$-0.256875\pi$
$691$	16.2394	+	7.23027i	0.617778	+	0.275052i	−0.0738921	+	0.997266i	$0.523542\pi$
$692$	−23.7894			−0.904339
$693$	−2.66932	+	8.35911i	−0.101399	+	0.317536i
$694$	34.7453			1.31891
$695$	51.7834	+	23.0554i	1.96425	+	0.874543i
$696$	−0.505859	−	0.107524i	−0.0191745	−	0.00407567i
$697$	21.6258	+	24.0179i	0.819135	+	0.909741i
$698$	−3.12567	+	29.7387i	−0.118308	+	1.12563i
$699$	−17.1189	−	12.4376i	−0.647495	−	0.470432i
$700$	−16.0940	−	0.498271i	−0.608296	−	0.0188329i
$701$	13.9129	+	42.8196i	0.525484	+	1.61727i	0.763356	+	0.645978i	$0.223550\pi$
$701$	13.9129	+	42.8196i	0.525484	+	1.61727i	−0.237872	+	0.971297i	$0.576450\pi$
$702$	5.63484	+	2.50879i	0.212673	+	0.0946882i
$703$	−2.66971	+	4.62407i	−0.100690	+	0.174400i
$704$	0.910655	−	3.18915i	0.0343216	−	0.120196i
$705$	4.00613	+	6.93882i	0.150880	+	0.261331i
$706$	3.38961	−	2.46270i	0.127570	−	0.0926848i
$707$	−24.0326	−	11.6040i	−0.903839	−	0.436414i
$708$	0.487300	−	1.49976i	0.0183139	−	0.0563643i
$709$	−5.04240	+	47.9753i	−0.189371	+	1.80175i	0.326621	+	0.945155i	$0.394090\pi$
$709$	−5.04240	+	47.9753i	−0.189371	+	1.80175i	−0.515992	+	0.856593i	$0.672577\pi$
$710$	−33.7039	+	15.0059i	−1.26488	+	0.563162i
$711$	−5.96719	−	6.62724i	−0.223787	−	0.248541i
$712$	0.389993	−	0.433131i	0.0146156	−	0.0162323i
$713$	−3.80900	+	2.76740i	−0.142648	+	0.103640i
$714$	−5.05059	+	5.27162i	−0.189014	+	0.197286i
$715$	63.1819	+	25.4458i	2.36287	+	0.951619i
$716$	−9.59790	−	16.6240i	−0.358690	−	0.621270i
$717$	0.0555207	+	0.528244i	0.00207346	+	0.0197276i
$718$	1.55230	+	0.329951i	0.0579312	+	0.0123136i
$719$	−29.2078	+	6.20831i	−1.08927	+	0.231531i	−0.717335	−	0.696729i	$-0.754638\pi$
$719$	−29.2078	+	6.20831i	−1.08927	+	0.231531i	−0.371933	+	0.928260i	$0.621305\pi$
$720$	2.69366	+	1.95706i	0.100387	+	0.0729353i
$721$	17.1477	−	47.6993i	0.638613	−	1.77641i
$722$	4.73944	−	14.5865i	0.176384	−	0.542853i
$723$	2.49099	−	2.76652i	0.0926409	−	0.102888i
$724$	1.60117	+	15.2341i	0.0595070	+	0.566172i
$725$	1.57369	−	2.72571i	0.0584453	−	0.101230i
$726$	8.41081	−	7.08931i	0.312154	−	0.263109i
$727$	−35.1823			−1.30484			−0.652421	−	0.757857i	$-0.726246\pi$
$727$	−35.1823			−1.30484			−0.652421	+	0.757857i	$0.726246\pi$
$728$	−15.1066	+	6.17312i	−0.559889	+	0.228791i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−11.9610	+	2.54238i	−0.442695	+	0.0940977i
$731$	27.9085	−	12.4257i	1.03223	−	0.459580i
$732$	13.6745	−	6.08828i	0.505424	−	0.225029i
$733$	10.2266	−	2.17373i	0.377729	−	0.0802887i	−0.0151349	−	0.999885i	$-0.504818\pi$
$733$	10.2266	−	2.17373i	0.377729	−	0.0802887i	0.392864	+	0.919597i	$0.371484\pi$
$734$	4.29431	+	13.2165i	0.158506	+	0.487831i
$735$	23.0536	−	3.42621i	0.850345	−	0.126378i
$736$	−3.15756			−0.116389
$737$	−0.0830754	−	0.586400i	−0.00306012	−	0.0216003i
$738$	−5.85629	+	10.1434i	−0.215573	+	0.373383i
$739$	−3.49588	−	33.2611i	−0.128598	−	1.22353i	−0.848402	−	0.529352i	$-0.822435\pi$
$739$	−3.49588	−	33.2611i	−0.128598	−	1.22353i	0.719804	−	0.694177i	$-0.244232\pi$
$740$	6.21557	−	6.90309i	0.228489	−	0.253763i
$741$	3.64790	−	11.2271i	0.134009	−	0.412437i
$742$	1.52539	+	1.80335i	0.0559989	+	0.0662032i
$743$	31.2314	+	22.6909i	1.14577	+	0.832450i	0.987913	−	0.155012i	$-0.0495416\pi$
$743$	31.2314	+	22.6909i	1.14577	+	0.832450i	0.157857	+	0.987462i	$0.449542\pi$
$744$	1.45850	−	0.310014i	0.0534712	−	0.0113657i
$745$	−42.0195	−	8.93152i	−1.53948	−	0.327226i
$746$	−0.949255	−	9.03156i	−0.0347547	−	0.330669i
$747$	5.43436	+	9.41258i	0.198833	+	0.344388i
$748$	8.87746	−	2.22384i	0.324592	−	0.0813118i
$749$	1.73426	+	5.95901i	0.0633686	+	0.217738i
$750$	−2.92499	+	2.12513i	−0.106805	+	0.0775987i
$751$	18.8121	−	20.8929i	0.686463	−	0.762394i	−0.294697	−	0.955591i	$-0.595219\pi$
$751$	18.8121	−	20.8929i	0.686463	−	0.762394i	0.981160	+	0.193197i	$0.0618855\pi$
$752$	1.61020	+	1.78831i	0.0587181	+	0.0652131i
$753$	−13.3584	+	5.94756i	−0.486809	+	0.216741i
$754$	0.333435	−	3.17242i	0.0121430	−	0.115533i
$755$	−1.34081	+	4.12659i	−0.0487971	+	0.150182i
$756$	−2.38256	−	1.15040i	−0.0866527	−	0.0418398i
$757$	−19.0089	+	13.8107i	−0.690889	+	0.501960i	−0.876952	−	0.480578i	$-0.840427\pi$
$757$	−19.0089	+	13.8107i	−0.690889	+	0.501960i	0.186064	+	0.982538i	$0.440427\pi$
$758$	10.3337	+	17.8985i	0.375337	+	0.650102i
$759$	−8.68853	−	5.84650i	−0.315374	−	0.212214i
$760$	3.18613	−	5.51855i	0.115573	−	0.200179i
$761$	−29.9236	−	13.3229i	−1.08473	−	0.482953i	−0.215068	−	0.976599i	$-0.568997\pi$
$761$	−29.9236	−	13.3229i	−1.08473	−	0.482953i	−0.869663	+	0.493646i	$0.835664\pi$
$762$	0.191080	+	0.588085i	0.00692211	+	0.0213041i
$763$	−19.6206	−	36.5513i	−0.710312	−	1.32325i
$764$	20.8736	+	15.1656i	0.755181	+	0.548671i
$765$	−0.960347	+	9.13709i	−0.0347214	+	0.330352i
$766$	−4.31408	−	4.79127i	−0.155874	−	0.173116i
$767$	9.51415	+	2.02230i	0.343536	+	0.0730209i
$768$	0.913545	+	0.406737i	0.0329647	+	0.0146768i
$769$	10.4813			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$769$	10.4813			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$770$	−26.7506	−	11.7482i	−0.964024	−	0.423375i
$771$	−14.8876			−0.536165
$772$	−7.67470	−	3.41700i	−0.276219	−	0.122980i
$773$	−10.1233	−	2.15176i	−0.364108	−	0.0773936i	0.0222247	−	0.999753i	$-0.492925\pi$
$773$	−10.1233	−	2.15176i	−0.364108	−	0.0773936i	−0.386333	+	0.922359i	$0.626258\pi$
$774$	7.40813	+	8.22757i	0.266280	+	0.295734i
$775$	−0.948550	+	9.02485i	−0.0340729	+	0.324182i
$776$	−9.88027	−	7.17844i	−0.354681	−	0.257691i
$777$	−3.88670	+	6.27514i	−0.139435	+	0.225119i
$778$	−8.95330	−	27.5554i	−0.320991	−	0.987909i
$779$	20.4782	+	9.11748i	0.733707	+	0.326668i
$780$	−10.2685	+	17.7855i	−0.367671	+	0.636824i
$781$	−36.7265	+	1.32323i	−1.31418	+	0.0473489i
$782$	−4.35642	−	7.54555i	−0.155785	−	0.269828i
$783$	0.418392	−	0.303979i	0.0149521	−	0.0108633i
$784$	6.55870	−	2.44612i	0.234239	−	0.0873613i
$785$	−3.36921	+	10.3694i	−0.120252	+	0.370099i
$786$	−0.759568	+	7.22681i	−0.0270929	+	0.257772i
$787$	−24.9696	+	11.1172i	−0.890069	+	0.396284i	−0.800245	−	0.599674i	$-0.795297\pi$
$787$	−24.9696	+	11.1172i	−0.890069	+	0.396284i	−0.0898239	+	0.995958i	$0.528630\pi$
$788$	8.18024	+	9.08507i	0.291409	+	0.323642i
$789$	−12.6538	+	14.0535i	−0.450489	+	0.500318i
$790$	24.0216	−	17.4527i	0.854650	−	0.620940i
$791$	27.6356	+	6.77431i	0.982610	+	0.240867i
$792$	1.76066	+	2.81071i	0.0625622	+	0.0998742i
$793$	46.1639	+	79.9582i	1.63933	+	2.83940i
$794$	−1.74603	−	16.6124i	−0.0619643	−	0.589551i
$795$	2.90747	+	0.618001i	0.103117	+	0.0219182i
$796$	24.0453	−	5.11098i	0.852262	−	0.181154i
$797$	−20.9567	−	15.2260i	−0.742325	−	0.539331i	0.151113	−	0.988516i	$-0.451714\pi$
$797$	−20.9567	−	15.2260i	−0.742325	−	0.539331i	−0.893438	+	0.449186i	$0.851714\pi$
$798$	−1.71301	+	4.76503i	−0.0606399	+	0.168680i
$799$	−2.05192	+	6.31517i	−0.0725918	+	0.223415i
$800$	−4.07225	+	4.52269i	−0.143976	+	0.159901i
$801$	0.0609229	+	0.579642i	0.00215260	+	0.0204807i
$802$	13.1188	−	22.7225i	0.463242	−	0.802359i
$803$	−11.9980	−	2.10188i	−0.423400	−	0.0741736i
$804$	0.178572			0.00629774
$805$	−3.76215	+	27.5598i	−0.132598	+	0.971356i
$806$	2.84208	+	8.74701i	0.100108	+	0.308100i
$807$	−15.1053	+	3.21073i	−0.531732	+	0.113023i
$808$	−9.21485	+	4.10271i	−0.324177	+	0.144333i
$809$	8.83367	−	3.93300i	0.310575	−	0.138277i	−0.245530	−	0.969389i	$-0.578962\pi$
$809$	8.83367	−	3.93300i	0.310575	−	0.138277i	0.556105	+	0.831112i	$0.312295\pi$
$810$	−3.25679	+	0.692252i	−0.114432	+	0.0243232i
$811$	8.61970	+	26.5287i	0.302679	+	0.931549i	0.980533	+	0.196353i	$0.0629099\pi$
$811$	8.61970	+	26.5287i	0.302679	+	0.931549i	−0.677855	+	0.735196i	$0.737090\pi$
$812$	−0.185065	+	1.35570i	−0.00649451	+	0.0475759i
$813$	9.72616			0.341111
$814$	8.31202	−	4.06544i	0.291336	−	0.142494i
$815$	−3.25011	+	5.62936i	−0.113846	+	0.197188i
$816$	0.288432	+	2.74425i	0.0100971	+	0.0960678i
$817$	14.1781	−	15.7464i	0.496029	−	0.550896i
$818$	5.20186	−	16.0097i	0.181879	−	0.559765i
$819$	5.52080	−	15.3570i	0.192912	−	0.536619i
$820$	−31.5497	−	22.9222i	−1.10176	−	0.800477i
$821$	−35.1111	+	7.46309i	−1.22539	+	0.260464i	−0.774763	−	0.632251i	$-0.782131\pi$
$821$	−35.1111	+	7.46309i	−1.22539	+	0.260464i	−0.450622	+	0.892715i	$0.648798\pi$
$822$	11.4930	+	2.44292i	0.400865	+	0.0852065i
$823$	3.20670	+	30.5097i	0.111779	+	1.06350i	0.896314	+	0.443419i	$0.146235\pi$
$823$	3.20670	+	30.5097i	0.111779	+	1.06350i	−0.784536	+	0.620083i	$0.787099\pi$
$824$	−9.57911	−	16.5915i	−0.333704	−	0.577993i
$825$	−19.5796	+	4.90477i	−0.681674	+	0.170762i
$826$	−4.05221	−	0.993318i	−0.140995	−	0.0345620i
$827$	−13.8608	+	10.0704i	−0.481986	+	0.350183i	−0.802094	−	0.597198i	$-0.796281\pi$
$827$	−13.8608	+	10.0704i	−0.481986	+	0.350183i	0.320108	+	0.947381i	$0.396281\pi$
$828$	2.11282	−	2.34652i	0.0734256	−	0.0815474i
$829$	−18.2677	−	20.2884i	−0.634464	−	0.704644i	0.337087	−	0.941474i	$-0.390558\pi$
$829$	−18.2677	−	20.2884i	−0.634464	−	0.704644i	−0.971551	+	0.236829i	$0.923892\pi$
$830$	−33.0593	+	14.7189i	−1.14750	+	0.510902i
$831$	−2.69773	+	25.6672i	−0.0935832	+	0.890385i
$832$	−1.90605	+	5.86621i	−0.0660803	+	0.203374i
$833$	14.8943	+	12.2983i	0.516058	+	0.426111i
$834$	−13.7731	+	10.0068i	−0.476924	+	0.346506i
$835$	5.40231	+	9.35708i	0.186955	+	0.323815i
$836$	4.99760	−	3.91347i	0.172846	−	0.135350i
$837$	−0.745542	+	1.29132i	−0.0257697	+	0.0446344i
$838$	7.12265	+	3.17121i	0.246048	+	0.109548i
$839$	11.0207	+	33.9184i	0.380478	+	1.17099i	0.939708	+	0.341979i	$0.111097\pi$
$839$	11.0207	+	33.9184i	0.380478	+	1.17099i	−0.559229	+	0.829013i	$0.688903\pi$
$840$	4.63855	−	7.48900i	0.160045	−	0.258395i
$841$	23.2451	+	16.8886i	0.801556	+	0.582364i
$842$	3.04960	−	29.0150i	0.105096	−	0.999922i
$843$	12.2443	+	13.5987i	0.421716	+	0.468363i
$844$	−12.2148	−	2.59633i	−0.420450	−	0.0893693i
$845$	−76.1805	−	33.9177i	−2.62069	−	1.16681i
$846$	−2.40641			−0.0827342
$847$	−20.3456	−	20.8100i	−0.699084	−	0.715039i
$848$	0.892741			0.0306568
$849$	−24.5459	−	10.9286i	−0.842414	−	0.375067i
$850$	−16.4262	−	3.49149i	−0.563413	−	0.119757i
$851$	−5.89450	−	6.54651i	−0.202061	−	0.224411i
$852$	1.15824	−	11.0199i	0.0396807	−	0.377537i
$853$	17.9135	+	13.0149i	0.613346	+	0.445622i	0.850591	−	0.525828i	$-0.176244\pi$
$853$	17.9135	+	13.0149i	0.613346	+	0.445622i	−0.237245	+	0.971450i	$0.576244\pi$
$854$	−18.7308	−	34.8937i	−0.640954	−	1.19404i
$855$	1.96914	+	6.06039i	0.0673432	+	0.207261i
$856$	2.14294	+	0.954099i	0.0732442	+	0.0326104i
$857$	2.29084	−	3.96785i	0.0782535	−	0.135539i	−0.824243	−	0.566236i	$-0.808399\pi$
$857$	2.29084	−	3.96785i	0.0782535	−	0.135539i	0.902496	+	0.430697i	$0.141732\pi$
$858$	−16.1066	+	12.6126i	−0.549870	+	0.430587i
$859$	4.98465	+	8.63366i	0.170074	+	0.294577i	0.938446	−	0.345427i	$-0.112266\pi$
$859$	4.98465	+	8.63366i	0.170074	+	0.294577i	−0.768372	+	0.640004i	$0.778933\pi$
$860$	−29.8223	+	21.6671i	−1.01693	+	0.738843i
$861$	27.9059	+	13.4742i	0.951029	+	0.459199i
$862$	7.88350	−	24.2629i	0.268513	−	0.826399i
$863$	0.528398	−	5.02737i	0.0179869	−	0.171134i	−0.981841	−	0.189708i	$-0.939246\pi$
$863$	0.528398	−	5.02737i	0.0179869	−	0.171134i	0.999827	+	0.0185741i	$0.00591265\pi$
$864$	−0.913545	+	0.406737i	−0.0310794	+	0.0138375i
$865$	53.0005	+	58.8631i	1.80207	+	2.00140i
$866$	0.00915756	−	0.0101705i	0.000311187	−	0.000345608i
$867$	7.59337	−	5.51691i	0.257884	−	0.187364i
$868$	−1.10240	−	3.78788i	−0.0374177	−	0.128569i
$869$	28.6906	−	7.18712i	0.973261	−	0.243806i
$870$	0.860955	+	1.49122i	0.0291891	+	0.0505570i
$871$	0.115133	+	1.09541i	0.00390112	+	0.0371167i
$872$	−15.3370	−	3.25998i	−0.519377	−	0.110397i
$873$	11.9458	−	2.53916i	0.404304	−	0.0859376i
$874$	−4.88898	−	3.55205i	−0.165372	−	0.120150i
$875$	6.17764	+	7.30335i	0.208842	+	0.246898i
$876$	1.13490	−	3.49287i	0.0383448	−	0.118013i
$877$	−5.86237	+	6.51083i	−0.197958	+	0.219855i	−0.833949	−	0.551842i	$-0.813925\pi$
$877$	−5.86237	+	6.51083i	−0.197958	+	0.219855i	0.635990	+	0.771697i	$0.280592\pi$
$878$	4.11818	+	39.1819i	0.138982	+	1.32232i
$879$	−12.4470	+	21.5589i	−0.419828	+	0.727164i
$880$	−9.91989	+	4.85186i	−0.334399	+	0.163556i
$881$	−0.712468			−0.0240037			−0.0120018	−	0.999928i	$-0.503820\pi$
$881$	−0.712468			−0.0240037			−0.0120018	+	0.999928i	$0.503820\pi$
$882$	−2.57081	+	6.51083i	−0.0865636	+	0.219231i
$883$	−10.7908	−	33.2105i	−0.363138	−	1.11762i	−0.951139	−	0.308763i	$-0.900085\pi$
$883$	−10.7908	−	33.2105i	−0.363138	−	1.11762i	0.588001	−	0.808860i	$-0.299915\pi$
$884$	−16.6481	+	3.53866i	−0.559936	+	0.119018i
$885$	−4.79656	+	2.13556i	−0.161235	+	0.0717862i
$886$	16.9625	−	7.55218i	0.569865	−	0.253720i
$887$	21.2869	−	4.52467i	0.714744	−	0.151924i	0.163834	−	0.986488i	$-0.447614\pi$
$887$	21.2869	−	4.52467i	0.714744	−	0.151924i	0.550910	+	0.834564i	$0.314281\pi$
$888$	0.862119	+	2.65333i	0.0289308	+	0.0890399i
$889$	1.51443	−	0.618852i	0.0507925	−	0.0207556i
$890$	−1.94058			−0.0650483
$891$	−3.26687	−	0.572309i	−0.109444	−	0.0191731i
$892$	6.79855	−	11.7754i	0.227632	−	0.394271i
$893$	0.481408	+	4.58030i	0.0161097	+	0.153274i
$894$	8.63321	−	9.58816i	0.288738	−	0.320676i
$895$	−19.7503	+	60.7852i	−0.660180	+	2.03182i
$896$	0.895057	−	2.48975i	0.0299017	−	0.0831768i
$897$	15.7565	+	11.4478i	0.526095	+	0.382231i
$898$	5.61402	−	1.19330i	0.187342	−	0.0398209i
$899$	0.754279	+	0.160327i	0.0251566	+	0.00534720i
$900$	−0.636148	−	6.05254i	−0.0212049	−	0.201751i
$901$	1.23170	+	2.13336i	0.0410338	+	0.0710726i
$902$	−20.6218	−	32.9206i	−0.686631	−	1.09614i
$903$	20.2643	−	21.1511i	0.674354	−	0.703866i
$904$	8.70060	−	6.32135i	0.289378	−	0.210245i
$905$	34.1271	−	37.9019i	1.13442	−	1.25990i
$906$	−0.871988	−	0.968441i	−0.0289699	−	0.0321743i
$907$	46.5146	−	20.7096i	1.54449	−	0.687652i	0.554949	−	0.831884i	$-0.312738\pi$
$907$	46.5146	−	20.7096i	1.54449	−	0.687652i	0.989544	+	0.144232i	$0.0460712\pi$
$908$	−0.646125	+	6.14747i	−0.0214424	+	0.204011i
$909$	3.11702	−	9.59322i	0.103385	−	0.318187i
$910$	48.9305	+	23.6258i	1.62203	+	0.783188i
$911$	−33.1642	+	24.0952i	−1.09878	+	0.798310i	−0.980860	−	0.194713i	$-0.937622\pi$
$911$	−33.1642	+	24.0952i	−1.09878	+	0.798310i	−0.117919	+	0.993023i	$0.537622\pi$
$912$	0.956928	+	1.65745i	0.0316870	+	0.0548836i
$913$	−36.0241	+	1.29792i	−1.19222	+	0.0429550i
$914$	−0.130471	+	0.225983i	−0.00431561	+	0.00747486i
$915$	−45.5299	−	20.2712i	−1.50517	−	0.670145i
$916$	−3.71960	−	11.4478i	−0.122899	−	0.378245i
$917$	19.2165	+	0.594942i	0.634583	+	0.0196467i
$918$	−2.23237	−	1.62191i	−0.0736792	−	0.0535311i
$919$	2.14163	−	20.3763i	0.0706459	−	0.672151i	−0.900694	−	0.434455i	$-0.856941\pi$
$919$	2.14163	−	20.3763i	0.0706459	−	0.672151i	0.971340	−	0.237696i	$-0.0763923\pi$
$920$	7.03473	+	7.81286i	0.231928	+	0.257582i
$921$	−29.2567	−	6.21870i	−0.964040	−	0.204913i
$922$	−14.3818	−	6.40317i	−0.473638	−	0.210877i
$923$	68.3464			2.24965
$924$	7.07289	−	5.19368i	0.232681	−	0.170859i
$925$	−16.9788			−0.558261
$926$	−9.58695	−	4.26838i	−0.315047	−	0.140268i
$927$	18.7396	+	3.98322i	0.615488	+	0.130826i
$928$	0.346048	+	0.384325i	0.0113596	+	0.0126161i
$929$	0.443960	−	4.22400i	0.0145659	−	0.138585i	−0.984822	−	0.173567i	$-0.944471\pi$
$929$	0.443960	−	4.22400i	0.0145659	−	0.138585i	0.999388	+	0.0349820i	$0.0111374\pi$
$930$	−4.01647	−	2.91814i	−0.131705	−	0.0956895i
$931$	12.9068	+	3.59069i	0.423004	+	0.117680i
$932$	6.53882	+	20.1244i	0.214186	+	0.659197i
$933$	−18.4693	−	8.22307i	−0.604658	−	0.269211i
$934$	−0.472543	+	0.818468i	−0.0154621	+	0.0267811i
$935$	−25.2806	−	17.0113i	−0.826766	−	0.556330i
$936$	−3.08405	−	5.34173i	−0.100805	−	0.174600i
$937$	25.5882	−	18.5909i	0.835929	−	0.607338i	−0.0853017	−	0.996355i	$-0.527185\pi$
$937$	25.5882	−	18.5909i	0.835929	−	0.607338i	0.921230	+	0.389017i	$0.127185\pi$
$938$	−0.0348213	−	0.471172i	−0.00113696	−	0.0153843i
$939$	−3.87105	+	11.9139i	−0.126327	+	0.388794i
$940$	0.837509	−	7.96837i	0.0273165	−	0.259900i
$941$	17.4814	−	7.78321i	0.569876	−	0.253725i	−0.101508	−	0.994835i	$-0.532367\pi$
$941$	17.4814	−	7.78321i	0.569876	−	0.253725i	0.671384	+	0.741109i	$0.265700\pi$
$942$	−2.19115	−	2.43352i	−0.0713915	−	0.0792883i
$943$	−24.7466	+	27.4838i	−0.805859	+	0.894997i
$944$	−1.27577	+	0.926900i	−0.0415227	+	0.0301680i
$945$	2.46162	+	8.45823i	0.0800763	+	0.275146i
$946$	−35.6187	+	8.92264i	−1.15806	+	0.290100i
$947$	−16.4713	−	28.5291i	−0.535245	−	0.927072i	−0.999151	−	0.0411878i	$-0.986886\pi$
$947$	−16.4713	−	28.5291i	−0.535245	−	0.927072i	0.463906	−	0.885884i	$-0.346448\pi$
$948$	0.932167	+	8.86898i	0.0302754	+	0.288051i
$949$	22.1581	+	4.70985i	0.719282	+	0.152888i
$950$	−11.3930	+	2.42165i	−0.369637	+	0.0785687i
$951$	−7.44783	−	5.41117i	−0.241512	−	0.175469i
$952$	7.18460	−	1.29617i	0.232854	−	0.0420091i
$953$	11.4130	−	35.1255i	0.369702	−	1.13783i	−0.577281	−	0.816545i	$-0.695886\pi$
$953$	11.4130	−	35.1255i	0.369702	−	1.13783i	0.946984	−	0.321282i	$-0.104114\pi$
$954$	−0.597360	+	0.663436i	−0.0193402	+	0.0214795i
$955$	−8.97966	−	85.4357i	−0.290575	−	2.76464i
$956$	0.265577	−	0.459993i	0.00858937	−	0.0148772i
$957$	0.240594	+	1.69827i	0.00777730	+	0.0548972i
$958$	−14.8233			−0.478918
$959$	4.20464	−	30.8013i	0.135775	−	0.994627i
$960$	−1.02889	−	3.16659i	−0.0332072	−	0.102201i
$961$	28.1478	−	5.98301i	0.907994	−	0.193000i
$962$	−15.7205	+	6.99922i	−0.506849	+	0.225664i
$963$	−2.14294	+	0.954099i	−0.0690553	+	0.0307454i
$964$	−3.64137	+	0.773998i	−0.117281	+	0.0249288i
$965$	8.64369	+	26.6025i	0.278250	+	0.856366i
$966$	−6.60343	−	5.11722i	−0.212462	−	0.164644i
$967$	2.84229			0.0914020			0.0457010	−	0.998955i	$-0.485448\pi$
$967$	2.84229			0.0914020			0.0457010	+	0.998955i	$0.485448\pi$
$968$	−10.9715	+	0.791619i	−0.352637	+	0.0254436i
$969$	−2.64051	+	4.57350i	−0.0848254	+	0.146922i
$970$	4.25041	+	40.4400i	0.136472	+	1.29845i
$971$	7.39382	−	8.21167i	0.237279	−	0.263525i	−0.612731	−	0.790292i	$-0.709929\pi$
$971$	7.39382	−	8.21167i	0.237279	−	0.263525i	0.850010	+	0.526766i	$0.176596\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	29.0892	+	34.3899i	0.932555	+	1.10249i
$974$	9.23171	+	6.70723i	0.295803	+	0.214913i
$975$	36.7180	−	7.80465i	1.17592	−	0.249949i
$976$	−14.6415	−	3.11215i	−0.468663	−	0.0996174i
$977$	3.87622	+	36.8798i	0.124011	+	1.17989i	0.862655	+	0.505793i	$0.168800\pi$
$977$	3.87622	+	36.8798i	0.124011	+	1.17989i	−0.738643	+	0.674096i	$0.764533\pi$
$978$	−0.976142	−	1.69073i	−0.0312136	−	0.0540635i
$979$	−1.79309	−	0.722147i	−0.0573074	−	0.0230799i
$980$	−20.6646	−	10.7787i	−0.660108	−	0.344313i
$981$	12.6851	−	9.21627i	0.405004	−	0.294253i
$982$	7.15399	−	7.94531i	0.228293	−	0.253545i
$983$	21.1871	+	23.5307i	0.675763	+	0.750511i	0.979323	−	0.202301i	$-0.0648420\pi$
$983$	21.1871	+	23.5307i	0.675763	+	0.750511i	−0.303560	+	0.952812i	$0.598175\pi$
$984$	10.7000	−	4.76393i	0.341102	−	0.151869i
$985$	4.25475	−	40.4813i	0.135568	−	1.28984i
$986$	−0.440977	+	1.35719i	−0.0140436	+	0.0432217i
$987$	0.469248	+	6.34945i	0.0149363	+	0.202105i
$988$	−9.55032	+	6.93872i	−0.303836	+	0.220750i
$989$	17.4791	+	30.2747i	0.555804	+	0.962680i
$990$	3.03207	−	10.6184i	0.0963655	−	0.337476i
$991$	17.5403	−	30.3808i	0.557187	−	0.965077i	−0.440542	−	0.897732i	$-0.645214\pi$
$991$	17.5403	−	30.3808i	0.557187	−	0.965077i	0.997730	−	0.0673450i	$-0.0214528\pi$
$992$	−1.36217	−	0.606479i	−0.0432490	−	0.0192557i
$993$	−4.68677	−	14.4244i	−0.148730	−	0.457744i
$994$	−29.3025	−	0.907207i	−0.929420	−	0.0287749i
$995$	−66.2168	−	48.1093i	−2.09921	−	1.52517i
$996$	1.13609	−	10.8092i	0.0359984	−	0.342502i
$997$	38.5296	+	42.7915i	1.22025	+	1.35522i	0.915260	+	0.402864i	$0.131985\pi$
$997$	38.5296	+	42.7915i	1.22025	+	1.35522i	0.304986	+	0.952357i	$0.401348\pi$
$998$	13.3868	+	2.84545i	0.423752	+	0.0900712i
$999$	−2.54868	−	1.13474i	−0.0806366	−	0.0359017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.c.25.5	✓	40
7.2	even	3	inner	462.2.y.c.289.1	yes	40
11.4	even	5	inner	462.2.y.c.235.1	yes	40
77.37	even	15	inner	462.2.y.c.37.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.c.25.5	✓	40	1.1	even	1	trivial
462.2.y.c.37.5	yes	40	77.37	even	15	inner
462.2.y.c.235.1	yes	40	11.4	even	5	inner
462.2.y.c.289.1	yes	40	7.2	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.348032 - 3.31131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.39315 - 2.24925i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(-0.978148 - 0.207912i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.348032 - 3.31131i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.39315 - 2.24925i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(-1.66477 + 2.88347i) q^{10} +(-2.61127 + 2.04481i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(4.99010 - 3.62552i) q^{13} +(-2.18756 + 1.48815i) q^{14} +(-1.02889 + 3.16659i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(-2.52080 + 1.12233i) q^{17} +(-0.669131 - 0.743145i) q^{18} +(-1.28062 + 1.42227i) q^{19} +(2.69366 - 1.95706i) q^{20} +(-1.83035 + 1.91045i) q^{21} +(3.21722 - 0.805927i) q^{22} +(-1.57878 - 2.73453i) q^{23} +(0.104528 + 0.994522i) q^{24} +(-5.95289 - 1.26533i) q^{25} +(-6.03331 + 1.28242i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(2.60372 - 0.469735i) q^{28} +(-0.159811 + 0.491849i) q^{29} +(2.22790 - 2.47434i) q^{30} +(-0.155861 - 1.48292i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.97935 - 1.45721i) q^{33} +2.75936 q^{34} +(-6.96311 - 5.39595i) q^{35} +(0.309017 + 0.951057i) q^{36} +(2.72891 - 0.580048i) q^{37} +(1.74839 - 0.778435i) q^{38} +(-5.63484 + 2.50879i) q^{39} +(-3.25679 + 0.692252i) q^{40} +(-3.61938 - 11.1393i) q^{41} +(2.44916 - 1.00081i) q^{42} -11.0713 q^{43} +(-3.26687 - 0.572309i) q^{44} +(1.66477 - 2.88347i) q^{45} +(0.330055 + 3.14026i) q^{46} +(1.61020 - 1.78831i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-3.11829 - 6.26708i) q^{49} +(4.92358 + 3.57719i) q^{50} +(2.69906 - 0.573704i) q^{51} +(6.03331 + 1.28242i) q^{52} +(-0.0933168 - 0.887850i) q^{53} +(0.500000 + 0.866025i) q^{54} +(5.86219 + 9.35839i) q^{55} +(-2.56967 - 0.629903i) q^{56} +(1.54834 - 1.12494i) q^{57} +(0.346048 - 0.384325i) q^{58} +(1.05518 + 1.17189i) q^{59} +(-3.04169 + 1.35425i) q^{60} +(-1.56464 + 14.8866i) q^{61} +(-0.460770 + 1.41811i) q^{62} +(2.18756 - 1.48815i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-10.2685 - 17.7855i) q^{65} +(-3.31447 + 0.119418i) q^{66} +(-0.0892859 + 0.154648i) q^{67} +(-2.52080 - 1.12233i) q^{68} +(0.975740 + 3.00302i) q^{69} +(4.16639 + 7.76160i) q^{70} +(8.96442 + 6.51303i) q^{71} +(0.104528 - 0.994522i) q^{72} +(2.45747 + 2.72929i) q^{73} +(-2.72891 - 0.580048i) q^{74} +(5.55973 + 2.47535i) q^{75} -1.91386 q^{76} +(0.961412 + 8.72214i) q^{77} +6.16810 q^{78} +(-8.14684 - 3.62721i) q^{79} +(3.25679 + 0.692252i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-1.22430 + 11.6484i) q^{82} +(8.79297 + 6.38847i) q^{83} +(-2.64448 - 0.0818733i) q^{84} +(2.83907 + 8.73776i) q^{85} +(10.1141 + 4.50310i) q^{86} +(0.258580 - 0.447874i) q^{87} +(2.75166 + 1.85159i) q^{88} +(0.291418 + 0.504750i) q^{89} +(-2.69366 + 1.95706i) q^{90} +(-1.20277 - 16.2749i) q^{91} +(0.975740 - 3.00302i) q^{92} +(-0.155861 + 1.48292i) q^{93} +(-2.19837 + 0.978776i) q^{94} +(4.26388 + 4.73552i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(9.88027 - 7.17844i) q^{97} +(0.299645 + 6.99358i) q^{98} +(-3.21722 + 0.805927i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more