LMFDB - Embedded newform 930.2.bn.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.16157 - 1.91070i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.15311 + 1.93867i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.16157 - 1.91070i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.15311 + 1.93867i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(2.22854 + 0.183353i) q^{10} +(4.46653 + 0.949390i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-5.51273 + 0.579411i) q^{13} +(-2.83399 + 0.602383i) q^{14} +(2.21796 - 0.283993i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.30955 - 6.16094i) q^{17} +(0.994522 - 0.104528i) q^{18} +(0.779549 - 7.41691i) q^{19} +(-1.45824 + 1.69515i) q^{20} +(-2.64682 + 1.17844i) q^{21} +(-3.39343 + 3.05546i) q^{22} +(8.33848 + 2.70934i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-2.30153 + 4.43880i) q^{25} +(2.77155 - 4.80046i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.17844 - 2.64682i) q^{28} +(-3.63912 - 2.64398i) q^{29} +(-1.07393 + 1.96129i) q^{30} +(-3.37157 + 4.43086i) q^{31} -1.00000i q^{32} +(-2.68401 + 3.69423i) q^{33} +(5.75404 + 2.56186i) q^{34} +(1.20323 - 6.36584i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.25085 - 1.87688i) q^{37} +(5.54220 + 4.99022i) q^{38} +(1.71291 - 5.27180i) q^{39} +(-0.514277 - 2.17612i) q^{40} +(8.35001 - 3.71766i) q^{41} +(0.602383 - 2.83399i) q^{42} +(8.48801 + 0.892126i) q^{43} +(-0.477310 - 4.54130i) q^{44} +(-0.642686 + 2.14172i) q^{45} +(-7.09313 + 5.15346i) q^{46} +(1.91952 + 2.64199i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(0.145749 + 1.38671i) q^{49} +(-2.23826 - 4.47104i) q^{50} +(6.16094 + 1.30955i) q^{51} +(2.25458 + 5.06387i) q^{52} +(6.10466 - 5.49666i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.37417 - 9.63697i) q^{55} +(1.44865 + 2.50914i) q^{56} +(6.45861 + 3.72888i) q^{57} +(4.27804 - 1.39002i) q^{58} +(8.74225 + 3.89230i) q^{59} +(-0.955480 - 2.02165i) q^{60} +3.62921 q^{61} +(-1.60288 - 5.33205i) q^{62} -2.89730i q^{63} +(0.809017 + 0.587785i) q^{64} +(7.51048 + 9.86013i) q^{65} +(-1.41107 - 4.34282i) q^{66} +(-2.49592 - 1.44102i) q^{67} +(-5.45473 + 3.14929i) q^{68} +(-5.86667 + 6.51559i) q^{69} +(4.44283 + 4.71519i) q^{70} +(7.72144 + 8.57552i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-0.383967 + 1.80642i) q^{73} +(-0.392375 + 3.73320i) q^{74} +(-3.11893 - 3.90798i) q^{75} +(-7.29479 + 1.55056i) q^{76} +(7.77639 + 10.7033i) q^{77} +(3.25815 + 4.48446i) q^{78} +(-2.79404 + 0.593891i) q^{79} +(2.06281 + 0.863035i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-1.90036 + 8.94049i) q^{82} +(-5.57015 - 12.5108i) q^{83} +(1.93867 + 2.15311i) q^{84} +(-10.2506 + 9.65849i) q^{85} +(-5.71087 + 6.34257i) q^{86} +(3.89556 - 2.24910i) q^{87} +(3.95455 + 2.28316i) q^{88} +(0.347026 + 1.06804i) q^{89} +(-1.35492 - 1.77881i) q^{90} +(-12.9928 - 9.43984i) q^{91} -8.76760i q^{92} +(-2.67645 - 4.88227i) q^{93} -3.26568 q^{94} +(-15.0770 + 7.12575i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-1.64016 + 0.532919i) q^{97} +(-1.20754 - 0.697175i) q^{98} +(-2.28316 - 3.95455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	$ 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) $ 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.16157	−	1.91070i	−0.519468	−	0.854490i
$5$	−1.16157	−	1.91070i	−0.519468	−	0.854490i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	2.15311	+	1.93867i	0.813801	+	0.732749i	0.966816	−	0.255475i	$-0.0822317\pi$
$7$	2.15311	+	1.93867i	0.813801	+	0.732749i	−0.153015	+	0.988224i	$0.548898\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	2.22854	+	0.183353i	0.704726	+	0.0579814i
$11$	4.46653	+	0.949390i	1.34671	+	0.286252i	0.824160	−	0.566357i	$-0.191648\pi$
$11$	4.46653	+	0.949390i	1.34671	+	0.286252i	0.522550	+	0.852609i	$0.324981\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	−5.51273	+	0.579411i	−1.52896	+	0.160700i	−0.831337	−	0.555769i	$-0.812424\pi$
$13$	−5.51273	+	0.579411i	−1.52896	+	0.160700i	−0.697619	+	0.716469i	$0.745757\pi$
$14$	−2.83399	+	0.602383i	−0.757415	+	0.160994i
$15$	2.21796	−	0.283993i	0.572675	−	0.0733266i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.30955	−	6.16094i	−0.317612	−	1.49425i	−0.790137	−	0.612930i	$-0.789991\pi$
$17$	−1.30955	−	6.16094i	−0.317612	−	1.49425i	0.472525	−	0.881317i	$-0.343343\pi$
$18$	0.994522	−	0.104528i	0.234411	−	0.0246376i
$19$	0.779549	−	7.41691i	0.178841	−	1.70156i	−0.425605	−	0.904909i	$-0.639939\pi$
$19$	0.779549	−	7.41691i	0.178841	−	1.70156i	0.604445	−	0.796647i	$-0.293395\pi$
$20$	−1.45824	+	1.69515i	−0.326072	+	0.379048i
$21$	−2.64682	+	1.17844i	−0.577583	+	0.257156i
$22$	−3.39343	+	3.05546i	−0.723483	+	0.651427i
$23$	8.33848	+	2.70934i	1.73869	+	0.564936i	0.994660	−	0.103207i	$-0.0329104\pi$
$23$	8.33848	+	2.70934i	1.73869	+	0.564936i	0.744033	+	0.668143i	$0.232910\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−2.30153	+	4.43880i	−0.460306	+	0.887760i
$26$	2.77155	−	4.80046i	0.543545	−	0.941448i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	1.17844	−	2.64682i	0.222704	−	0.500201i
$29$	−3.63912	−	2.64398i	−0.675768	−	0.490974i	0.196183	−	0.980567i	$-0.437145\pi$
$29$	−3.63912	−	2.64398i	−0.675768	−	0.490974i	−0.871951	+	0.489593i	$0.837145\pi$
$30$	−1.07393	+	1.96129i	−0.196072	+	0.358082i
$31$	−3.37157	+	4.43086i	−0.605551	+	0.795806i
$31$	−3.37157	+	4.43086i	−0.605551	+	0.795806i
$32$		−	1.00000i		−	0.176777i
$33$	−2.68401	+	3.69423i	−0.467227	+	0.643082i
$34$	5.75404	+	2.56186i	0.986809	+	0.439356i
$35$	1.20323	−	6.36584i	0.203383	−	1.07602i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.25085	−	1.87688i	0.534437	−	0.308557i	−0.208385	−	0.978047i	$-0.566821\pi$
$37$	3.25085	−	1.87688i	0.534437	−	0.308557i	0.742821	+	0.669490i	$0.233487\pi$
$38$	5.54220	+	4.99022i	0.899063	+	0.809520i
$39$	1.71291	−	5.27180i	0.274285	−	0.844163i
$40$	−0.514277	−	2.17612i	−0.0813143	−	0.344076i
$41$	8.35001	−	3.71766i	1.30405	−	0.580602i	0.367140	−	0.930166i	$-0.380337\pi$
$41$	8.35001	−	3.71766i	1.30405	−	0.580602i	0.936912	+	0.349564i	$0.113670\pi$
$42$	0.602383	−	2.83399i	0.0929497	−	0.437294i
$43$	8.48801	+	0.892126i	1.29441	+	0.136048i	0.726571	−	0.687092i	$-0.241113\pi$
$43$	8.48801	+	0.892126i	1.29441	+	0.136048i	0.567839	+	0.823140i	$0.307780\pi$
$44$	−0.477310	−	4.54130i	−0.0719572	−	0.684627i
$45$	−0.642686	+	2.14172i	−0.0958059	+	0.319268i
$46$	−7.09313	+	5.15346i	−1.04583	+	0.759837i
$47$	1.91952	+	2.64199i	0.279991	+	0.385374i	0.925731	−	0.378183i	$-0.123451\pi$
$47$	1.91952	+	2.64199i	0.279991	+	0.385374i	−0.645740	+	0.763557i	$0.723451\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	0.145749	+	1.38671i	0.0208213	+	0.198102i
$50$	−2.23826	−	4.47104i	−0.316538	−	0.632300i
$51$	6.16094	+	1.30955i	0.862704	+	0.183373i
$52$	2.25458	+	5.06387i	0.312654	+	0.702232i
$53$	6.10466	−	5.49666i	0.838540	−	0.755025i	−0.133198	−	0.991090i	$-0.542524\pi$
$53$	6.10466	−	5.49666i	0.838540	−	0.755025i	0.971737	+	0.236065i	$0.0758578\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−3.37417	−	9.63697i	−0.454973	−	1.29945i
$56$	1.44865	+	2.50914i	0.193584	+	0.335297i
$57$	6.45861	+	3.72888i	0.855464	+	0.493902i
$58$	4.27804	−	1.39002i	0.561735	−	0.182519i
$59$	8.74225	+	3.89230i	1.13814	+	0.506734i	0.887254	−	0.461281i	$-0.152610\pi$
$59$	8.74225	+	3.89230i	1.13814	+	0.506734i	0.250890	+	0.968016i	$0.419277\pi$
$60$	−0.955480	−	2.02165i	−0.123352	−	0.260994i
$61$	3.62921			0.464673			0.232337	−	0.972635i	$-0.425363\pi$
$61$	3.62921			0.464673			0.232337	+	0.972635i	$0.425363\pi$
$62$	−1.60288	−	5.33205i	−0.203567	−	0.677171i
$63$		−	2.89730i		−	0.365026i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	7.51048	+	9.86013i	0.931560	+	1.22300i
$66$	−1.41107	−	4.34282i	−0.173691	−	0.534565i
$67$	−2.49592	−	1.44102i	−0.304925	−	0.176049i	0.339728	−	0.940524i	$-0.389665\pi$
$67$	−2.49592	−	1.44102i	−0.304925	−	0.176049i	−0.644653	+	0.764475i	$0.722998\pi$
$68$	−5.45473	+	3.14929i	−0.661483	+	0.381907i
$69$	−5.86667	+	6.51559i	−0.706264	+	0.784385i
$70$	4.44283	+	4.71519i	0.531020	+	0.563572i
$71$	7.72144	+	8.57552i	0.916366	+	1.01773i	0.999775	+	0.0212122i	$0.00675255\pi$
$71$	7.72144	+	8.57552i	0.916366	+	1.01773i	−0.0834090	+	0.996515i	$0.526581\pi$
$72$	−0.406737	−	0.913545i	−0.0479344	−	0.107662i
$73$	−0.383967	+	1.80642i	−0.0449399	+	0.211426i	−0.994888	−	0.100981i	$-0.967802\pi$
$73$	−0.383967	+	1.80642i	−0.0449399	+	0.211426i	0.949948	+	0.312407i	$0.101135\pi$
$74$	−0.392375	+	3.73320i	−0.0456126	+	0.433975i
$75$	−3.11893	−	3.90798i	−0.360143	−	0.451254i
$76$	−7.29479	+	1.55056i	−0.836770	+	0.177861i
$77$	7.77639	+	10.7033i	0.886202	+	1.21975i
$78$	3.25815	+	4.48446i	0.368913	+	0.507765i
$79$	−2.79404	+	0.593891i	−0.314354	+	0.0668180i	−0.362387	−	0.932028i	$-0.618038\pi$
$79$	−2.79404	+	0.593891i	−0.314354	+	0.0668180i	0.0480329	+	0.998846i	$0.484705\pi$
$80$	2.06281	+	0.863035i	0.230629	+	0.0964903i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−1.90036	+	8.94049i	−0.209860	+	0.987312i
$83$	−5.57015	−	12.5108i	−0.611403	−	1.37323i	−0.908298	−	0.418324i	$-0.862618\pi$
$83$	−5.57015	−	12.5108i	−0.611403	−	1.37323i	0.296895	−	0.954910i	$-0.404049\pi$
$84$	1.93867	+	2.15311i	0.211527	+	0.234924i
$85$	−10.2506	+	9.65849i	−1.11183	+	1.04761i
$86$	−5.71087	+	6.34257i	−0.615819	+	0.683937i
$87$	3.89556	−	2.24910i	0.417648	−	0.241129i
$88$	3.95455	+	2.28316i	0.421556	+	0.243385i
$89$	0.347026	+	1.06804i	0.0367847	+	0.113212i	0.967763	−	0.251863i	$-0.0810434\pi$
$89$	0.347026	+	1.06804i	0.0367847	+	0.113212i	−0.930978	+	0.365075i	$0.881043\pi$
$90$	−1.35492	−	1.77881i	−0.142822	−	0.187503i
$91$	−12.9928	−	9.43984i	−1.36202	−	0.989564i
$92$		−	8.76760i		−	0.914085i
$93$	−2.67645	−	4.88227i	−0.277535	−	0.506268i
$94$	−3.26568			−0.336829
$95$	−15.0770	+	7.12575i	−1.54686	+	0.731086i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	−1.64016	+	0.532919i	−0.166533	+	0.0541097i	−0.391097	−	0.920350i	$-0.627904\pi$
$97$	−1.64016	+	0.532919i	−0.166533	+	0.0541097i	0.224564	+	0.974459i	$0.427904\pi$
$98$	−1.20754	−	0.697175i	−0.121980	−	0.0704253i
$99$	−2.28316	−	3.95455i	−0.229466	−	0.397447i
$100$	4.93276	+	0.817219i	0.493276	+	0.0817219i
$101$	0.105144	−	0.323600i	0.0104622	−	0.0321994i	−0.945689	−	0.325072i	$-0.894611\pi$
$101$	0.105144	−	0.323600i	0.0104622	−	0.0321994i	0.956151	+	0.292873i	$0.0946113\pi$
$102$	−4.68076	+	4.21457i	−0.463464	+	0.417305i
$103$	−1.02882	−	2.31078i	−0.101373	−	0.227688i	0.855738	−	0.517410i	$-0.173104\pi$
$103$	−1.02882	−	2.31078i	−0.101373	−	0.227688i	−0.957111	+	0.289722i	$0.906437\pi$
$104$	−5.42196	−	1.15247i	−0.531667	−	0.113009i
$105$	5.32609	+	3.68843i	0.519773	+	0.359954i
$106$	0.858663	+	8.16963i	0.0834007	+	0.793505i
$107$	2.41482	+	11.3608i	0.233449	+	1.09829i	0.926176	+	0.377092i	$0.123076\pi$
$107$	2.41482	+	11.3608i	0.233449	+	1.09829i	−0.692727	+	0.721200i	$0.743591\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	−1.47660	+	1.07281i	−0.141432	+	0.102757i	−0.656252	−	0.754542i	$-0.727859\pi$
$109$	−1.47660	+	1.07281i	−0.141432	+	0.102757i	0.514819	+	0.857299i	$0.327859\pi$
$110$	9.77976	+	2.93471i	0.932464	+	0.279813i
$111$	0.392375	+	3.73320i	0.0372426	+	0.354339i
$112$	−2.88143	−	0.302850i	−0.272269	−	0.0286167i
$113$	2.08059	−	9.78839i	0.195725	−	0.920814i	−0.765154	−	0.643847i	$-0.777337\pi$
$113$	2.08059	−	9.78839i	0.195725	−	0.920814i	0.960879	−	0.276967i	$-0.0893293\pi$
$114$	−6.81301	+	3.03335i	−0.638096	+	0.284099i
$115$	−4.50897	−	19.0794i	−0.420464	−	1.77916i
$116$	−1.39002	+	4.27804i	−0.129060	+	0.397206i
$117$	4.11932	+	3.70905i	0.380831	+	0.342902i
$118$	−8.28750	+	4.78479i	−0.762927	+	0.440476i
$119$	9.12444	−	15.8040i	0.836436	−	1.44875i
$120$	2.19716	+	0.415294i	0.200573	+	0.0379110i
$121$	8.99956	+	4.00686i	0.818142	+	0.364260i
$122$	−2.13320	+	2.93609i	−0.193131	+	0.265822i
$123$			9.14023i			0.824146i
$124$	5.25587	+	1.83734i	0.471991	+	0.164998i
$125$	11.1546	−	0.758434i	0.997696	−	0.0678364i
$126$	2.34397	+	1.70299i	0.208817	+	0.151714i
$127$	1.01530	−	2.28041i	0.0900937	−	0.202354i	−0.862879	−	0.505411i	$-0.831341\pi$
$127$	1.01530	−	2.28041i	0.0900937	−	0.202354i	0.952972	+	0.303058i	$0.0980075\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−4.26738	+	7.39132i	−0.375722	+	0.650770i
$130$	−12.3916	+	0.280463i	−1.08681	+	0.0245982i
$131$	6.75912	−	7.50676i	0.590547	−	0.655869i	−0.371602	−	0.928392i	$-0.621191\pi$
$131$	6.75912	−	7.50676i	0.590547	−	0.655869i	0.962149	+	0.272523i	$0.0878581\pi$
$132$	4.34282	+	1.41107i	0.377994	+	0.122818i
$133$	16.0574	−	14.4582i	1.39235	−	1.25368i
$134$	2.63287	−	1.17223i	0.227446	−	0.101265i
$135$	−1.69515	−	1.45824i	−0.145896	−	0.125505i
$136$	0.658381	−	6.26407i	0.0564557	−	0.537140i
$137$	−1.81722	+	0.190998i	−0.155256	+	0.0163180i	−0.181837	−	0.983329i	$-0.558204\pi$
$137$	−1.81722	+	0.190998i	−0.155256	+	0.0163180i	0.0265816	+	0.999647i	$0.491538\pi$
$138$	−1.82289	−	8.57600i	−0.155174	−	0.730038i
$139$	−8.40379	+	6.10571i	−0.712801	+	0.517880i	−0.884076	−	0.467343i	$-0.845211\pi$
$139$	−8.40379	+	6.10571i	−0.712801	+	0.517880i	0.171275	+	0.985223i	$0.445211\pi$
$140$	−6.42610	+	0.822812i	−0.543104	+	0.0695403i
$141$	−3.19432	+	0.678973i	−0.269010	+	0.0571798i
$142$	−11.4763	+	1.20621i	−0.963069	+	0.101223i
$143$	−25.1729	−	2.64577i	−2.10506	−	0.221251i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	−0.824760	+	10.0244i	−0.0684926	+	0.832482i
$146$	−1.23574	−	1.37242i	−0.102270	−	0.113583i
$147$	−1.32611	−	0.430878i	−0.109375	−	0.0355382i
$148$	−2.78959	−	2.51176i	−0.229303	−	0.206465i
$149$	−5.63341	−	9.75736i	−0.461507	−	0.799354i	0.537529	−	0.843245i	$-0.319358\pi$
$149$	−5.63341	−	9.75736i	−0.461507	−	0.799354i	−0.999036	+	0.0438914i	$0.986024\pi$
$150$	4.99488	−	0.226218i	0.407830	−	0.0184706i
$151$	4.36791	+	13.4430i	0.355455	+	1.09398i	0.955745	+	0.294196i	$0.0950518\pi$
$151$	4.36791	+	13.4430i	0.355455	+	1.09398i	−0.600290	+	0.799782i	$0.704948\pi$
$152$	3.03335	−	6.81301i	0.246037	−	0.552608i
$153$	−3.70221	+	5.09566i	−0.299306	+	0.411959i
$154$	−13.2300			−1.06610
$155$	12.3823	+	1.29531i	0.994573	+	0.104042i
$156$	−5.54309			−0.443803
$157$	9.16708	−	12.6174i	0.731613	−	1.00698i	−0.267445	−	0.963573i	$-0.586179\pi$
$157$	9.16708	−	12.6174i	0.731613	−	1.00698i	0.999058	−	0.0434055i	$-0.0138207\pi$
$158$	1.16183	−	2.60951i	0.0924300	−	0.207601i
$159$	2.53846	+	7.81258i	0.201313	+	0.619578i
$160$	−1.91070	+	1.16157i	−0.151054	+	0.0918298i
$161$	12.7012	+	21.9991i	1.00099	+	1.73377i
$162$	−0.743145	−	0.669131i	−0.0583870	−	0.0525719i
$163$	9.24779	+	3.00479i	0.724343	+	0.235353i	0.647905	−	0.761721i	$-0.275645\pi$
$163$	9.24779	+	3.00479i	0.724343	+	0.235353i	0.0764379	+	0.997074i	$0.475645\pi$
$164$	−6.11600	−	6.79251i	−0.477580	−	0.530406i
$165$	10.1762	+	0.837249i	0.792217	+	0.0651797i
$166$	13.3955	+	2.84729i	1.03969	+	0.220993i
$167$	−17.0025	−	1.78703i	−1.31569	−	0.138285i	−0.579451	−	0.815007i	$-0.696733\pi$
$167$	−17.0025	−	1.78703i	−1.31569	−	0.138285i	−0.736238	+	0.676722i	$0.763400\pi$
$168$	−2.88143	+	0.302850i	−0.222307	+	0.0233654i
$169$	17.3385	−	3.68542i	1.33373	−	0.283494i
$170$	−1.78875	−	13.9700i	−0.137191	−	1.07145i
$171$	−6.03346	+	4.38356i	−0.461390	+	0.335219i
$172$	−1.77448	−	8.34826i	−0.135303	−	0.636549i
$173$	−11.7830	+	1.23844i	−0.895843	+	0.0941569i	−0.541248	−	0.840863i	$-0.682048\pi$
$173$	−11.7830	+	1.23844i	−0.895843	+	0.0941569i	−0.354595	+	0.935020i	$0.615381\pi$
$174$	−0.470190	+	4.47356i	−0.0356450	+	0.339140i
$175$	−13.5608	+	5.09533i	−1.02510	+	0.385171i
$176$	−4.17154	+	1.85729i	−0.314441	+	0.139998i
$177$	−7.11159	+	6.40330i	−0.534540	+	0.481302i
$178$	−1.06804	−	0.347026i	−0.0800526	−	0.0260107i
$179$	−0.00483932	+	0.00537460i	−0.000361707	+	0.000401717i	−0.743326	−	0.668930i	$-0.766753\pi$
$179$	−0.00483932	+	0.00537460i	−0.000361707	+	0.000401717i	0.742964	+	0.669331i	$0.233419\pi$
$180$	2.23550	−	0.0505968i	0.166624	−	0.00377126i
$181$	−3.65376	+	6.32849i	−0.271582	+	0.470393i	−0.969267	−	0.246011i	$-0.920880\pi$
$181$	−3.65376	+	6.32849i	−0.271582	+	0.470393i	0.697685	+	0.716404i	$0.254213\pi$
$182$	15.2740	−	4.96282i	1.13218	−	0.367868i
$183$	−1.47613	+	3.31545i	−0.109119	+	0.245085i
$184$	7.09313	+	5.15346i	0.522913	+	0.379918i
$185$	−7.36223	−	4.03127i	−0.541282	−	0.296385i
$186$	5.52302	+	0.704432i	0.404968	+	0.0516515i
$187$		−	28.7613i		−	2.10323i
$188$	1.91952	−	2.64199i	0.139995	−	0.192687i
$189$	2.64682	+	1.17844i	0.192528	+	0.0857188i
$190$	3.09717	−	16.3859i	0.224692	−	1.18876i
$191$	3.24743	−	5.62472i	0.234976	−	0.406990i	−0.724290	−	0.689496i	$-0.757832\pi$
$191$	3.24743	−	5.62472i	0.234976	−	0.406990i	0.959266	+	0.282506i	$0.0911656\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−12.6807	−	11.4178i	−0.912779	−	0.821870i	0.0716904	−	0.997427i	$-0.477161\pi$
$193$	−12.6807	−	11.4178i	−0.912779	−	0.821870i	−0.984469	+	0.175557i	$0.943827\pi$
$194$	0.532919	−	1.64016i	0.0382613	−	0.117756i
$195$	−12.0625	+	2.85068i	−0.863811	+	0.204142i
$196$	1.27380	−	0.567133i	0.0909859	−	0.0405095i
$197$	5.56692	−	26.1903i	0.396627	−	1.86598i	−0.0954564	−	0.995434i	$-0.530431\pi$
$197$	5.56692	−	26.1903i	0.396627	−	1.86598i	0.492083	−	0.870548i	$-0.336236\pi$
$198$	4.54130	+	0.477310i	0.322736	+	0.0339209i
$199$	−0.613146	−	5.83370i	−0.0434648	−	0.413540i	−0.994522	−	0.104526i	$-0.966668\pi$
$199$	−0.613146	−	5.83370i	−0.0434648	−	0.413540i	0.951057	−	0.309014i	$-0.0999991\pi$
$200$	−3.56055	+	3.51034i	−0.251769	+	0.248218i
$201$	2.33162	−	1.69402i	0.164460	−	0.119487i
$202$	0.199996	+	0.275271i	0.0140717	+	0.0193680i
$203$	−2.70964	−	12.7478i	−0.190179	−	0.894723i
$204$	−0.658381	−	6.26407i	−0.0460959	−	0.438573i
$205$	−16.8024	−	11.6360i	−1.17353	−	0.812696i
$206$	2.47419	+	0.525904i	0.172385	+	0.0366415i
$207$	−3.56610	−	8.00960i	−0.247861	−	0.556706i
$208$	4.11932	−	3.70905i	0.285624	−	0.257177i
$209$	10.5234	−	32.3878i	0.727920	−	2.24031i
$210$	−6.11460	+	2.14089i	−0.421947	+	0.147736i
$211$	3.36638	+	5.83073i	0.231751	+	0.401404i	0.958323	−	0.285685i	$-0.0922212\pi$
$211$	3.36638	+	5.83073i	0.231751	+	0.401404i	−0.726573	+	0.687090i	$0.758888\pi$
$212$	−7.11408	−	4.10732i	−0.488597	−	0.282092i
$213$	−10.9747	+	3.56590i	−0.751976	+	0.244332i
$214$	−10.6105	−	4.72410i	−0.725318	−	0.322933i
$215$	−8.15480	−	17.2543i	−0.556153	−	1.17673i
$216$	1.00000			0.0680414
$217$	−15.8494	+	3.00379i	−1.07592	+	0.203910i
$218$		−	1.82518i		−	0.123616i
$219$	−1.49408	−	1.08551i	−0.100960	−	0.0733519i
$220$	−8.12263	+	6.18702i	−0.547627	+	0.417128i
$221$	10.7889	+	33.2048i	0.725740	+	2.23360i
$222$	−3.25085	−	1.87688i	−0.218183	−	0.125968i
$223$	−8.55782	+	4.94086i	−0.573074	+	0.330864i	−0.758376	−	0.651817i	$-0.774007\pi$
$223$	−8.55782	+	4.94086i	−0.573074	+	0.330864i	0.185302	+	0.982682i	$0.440674\pi$
$224$	1.93867	−	2.15311i	0.129533	−	0.143861i
$225$	4.83870	−	1.25977i	0.322580	−	0.0839846i
$226$	6.69603	+	7.43670i	0.445414	+	0.494682i
$227$	−5.36879	−	12.0585i	−0.356339	−	0.800351i	−0.999403	−	0.0345388i	$-0.989004\pi$
$227$	−5.36879	−	12.0585i	−0.356339	−	0.800351i	0.643064	−	0.765812i	$-0.277663\pi$
$228$	1.55056	−	7.29479i	0.102688	−	0.483110i
$229$	−0.262416	+	2.49672i	−0.0173409	+	0.164988i	−0.999765	−	0.0216744i	$-0.993100\pi$
$229$	−0.262416	+	2.49672i	−0.0173409	+	0.164988i	0.982424	+	0.186662i	$0.0597670\pi$
$230$	18.0859	+	7.56675i	1.19255	+	0.498936i
$231$	−12.9409	+	2.75067i	−0.851448	+	0.180981i
$232$	−2.64398	−	3.63912i	−0.173586	−	0.238920i
$233$	0.881480	+	1.21325i	0.0577477	+	0.0794829i	0.836914	−	0.547334i	$-0.184357\pi$
$233$	0.881480	+	1.21325i	0.0577477	+	0.0794829i	−0.779166	+	0.626817i	$0.784357\pi$
$234$	−5.42196	+	1.15247i	−0.354445	+	0.0753396i
$235$	2.81840	−	6.73647i	0.183852	−	0.439439i
$236$	1.00029	−	9.51716i	0.0651136	−	0.619515i
$237$	0.593891	−	2.79404i	0.0385774	−	0.181492i
$238$	7.42249	+	16.6712i	0.481128	+	1.08063i
$239$	1.95522	+	2.17149i	0.126473	+	0.140462i	0.803055	−	0.595905i	$-0.203206\pi$
$239$	1.95522	+	2.17149i	0.126473	+	0.140462i	−0.676582	+	0.736367i	$0.736540\pi$
$240$	−1.62744	+	1.53344i	−0.105051	+	0.0989831i
$241$	−3.57452	+	3.96991i	−0.230255	+	0.255724i	−0.847190	−	0.531290i	$-0.821708\pi$
$241$	−3.57452	+	3.96991i	−0.230255	+	0.255724i	0.616935	+	0.787014i	$0.288374\pi$
$242$	−8.53143	+	4.92562i	−0.548421	+	0.316631i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−1.12149	−	3.45159i	−0.0717959	−	0.220965i
$245$	2.48029	−	1.88924i	0.158460	−	0.120699i
$246$	−7.39460	−	5.37249i	−0.471462	−	0.342537i
$247$			41.3391i			2.63034i
$248$	−4.57576	+	3.17213i	−0.290561	+	0.201430i
$249$	13.6947			0.867868
$250$	−5.94291	+	9.47005i	−0.375863	+	0.598938i
$251$	−26.6376	−	11.8598i	−1.68135	−	0.748587i	−0.999859	−	0.0167626i	$-0.994664\pi$
$251$	−26.6376	−	11.8598i	−1.68135	−	0.748587i	−0.681494	−	0.731824i	$-0.738669\pi$
$252$	−2.75550	+	0.895315i	−0.173580	+	0.0563995i
$253$	34.6719	+	20.0178i	2.17980	+	1.25851i
$254$	1.24811	+	2.16179i	0.0783134	+	0.135643i
$255$	−4.65419	−	13.2928i	−0.291456	−	0.832428i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−17.2916	+	15.5695i	−1.07862	+	0.971196i	−0.999670	−	0.0256826i	$-0.991824\pi$
$257$	−17.2916	+	15.5695i	−1.07862	+	0.971196i	−0.0789521	+	0.996878i	$0.525157\pi$
$258$	−3.47140	−	7.79690i	−0.216120	−	0.485414i
$259$	10.6381	+	2.26120i	0.661020	+	0.140504i
$260$	7.05668	−	10.1898i	0.437637	−	0.631947i
$261$	0.470190	+	4.47356i	0.0291040	+	0.276906i
$262$	2.10019	+	9.88061i	0.129750	+	0.610426i
$263$	8.41855	+	11.5871i	0.519110	+	0.714494i	0.985422	−	0.170127i	$-0.0544176\pi$
$263$	8.41855	+	11.5871i	0.519110	+	0.714494i	−0.466312	+	0.884620i	$0.654418\pi$
$264$	−3.69423	+	2.68401i	−0.227364	+	0.165190i
$265$	−17.5934	−	5.27943i	−1.08076	−	0.324313i
$266$	2.25859	+	21.4890i	0.138483	+	1.31758i
$267$	−1.11685	−	0.117385i	−0.0683499	−	0.00718387i
$268$	−0.599210	+	2.81906i	−0.0366026	+	0.172202i
$269$	4.15821	−	1.85135i	0.253530	−	0.112879i	−0.276037	−	0.961147i	$-0.589021\pi$
$269$	4.15821	−	1.85135i	0.253530	−	0.112879i	0.529567	+	0.848268i	$0.322354\pi$
$270$	2.17612	−	0.514277i	0.132435	−	0.0312979i
$271$	−9.84757	+	30.3077i	−0.598198	+	1.84106i	−0.0600788	+	0.998194i	$0.519135\pi$
$271$	−9.84757	+	30.3077i	−0.598198	+	1.84106i	−0.538119	+	0.842869i	$0.680865\pi$
$272$	4.68076	+	4.21457i	0.283813	+	0.255546i
$273$	13.9084	−	8.03001i	0.841773	−	0.485998i
$274$	0.913616	−	1.58243i	0.0551936	−	0.0955981i
$275$	−14.4940	+	17.6410i	−0.874022	+	1.06379i
$276$	8.00960	+	3.56610i	0.482121	+	0.214654i
$277$	−9.94511	+	13.6883i	−0.597544	+	0.822448i	−0.995481	−	0.0949645i	$-0.969726\pi$
$277$	−9.94511	+	13.6883i	−0.597544	+	0.822448i	0.397937	+	0.917413i	$0.369726\pi$
$278$		−	10.3877i		−	0.623011i
$279$	5.54879	−	0.459262i	0.332197	−	0.0274953i
$280$	3.11150	−	5.68246i	0.185947	−	0.339592i
$281$	−18.3007	−	13.2962i	−1.09173	−	0.793187i	−0.112038	−	0.993704i	$-0.535738\pi$
$281$	−18.3007	−	13.2962i	−1.09173	−	0.793187i	−0.979690	+	0.200517i	$0.935738\pi$
$282$	1.32827	−	2.98335i	0.0790974	−	0.177656i
$283$	12.3862	−	4.02452i	0.736283	−	0.239233i	0.0832143	−	0.996532i	$-0.473481\pi$
$283$	12.3862	−	4.02452i	0.736283	−	0.239233i	0.653068	+	0.757299i	$0.273481\pi$
$284$	5.76975	−	9.99351i	0.342372	−	0.593005i
$285$	−0.377339	−	16.6718i	−0.0223516	−	0.987552i
$286$	16.9367	−	18.8101i	1.00149	−	1.11227i
$287$	25.1859	+	8.18338i	1.48667	+	0.483050i
$288$	−0.743145	+	0.669131i	−0.0437902	+	0.0394289i
$289$	−20.7120	+	9.22157i	−1.21835	+	0.542445i
$290$	−7.62514	−	6.55945i	−0.447764	−	0.385184i
$291$	0.180266	−	1.71511i	0.0105674	−	0.100542i
$292$	1.83666	−	0.193041i	0.107483	−	0.0112969i
$293$	0.645927	+	3.03885i	0.0377355	+	0.177531i	0.992979	−	0.118288i	$-0.0377406\pi$
$293$	0.645927	+	3.03885i	0.0377355	+	0.177531i	−0.955244	+	0.295820i	$0.904407\pi$
$294$	1.12805	−	0.819578i	0.0657894	−	0.0477988i
$295$	−2.71769	−	21.2250i	−0.158230	−	1.23577i
$296$	3.67173	−	0.780451i	0.213415	−	0.0453628i
$297$	4.54130	−	0.477310i	0.263513	−	0.0276963i
$298$	11.2051	+	1.17770i	0.649094	+	0.0682225i
$299$	−47.5376	−	10.1044i	−2.74917	−	0.584354i
$300$	−2.75290	+	4.17391i	−0.158939	+	0.240981i
$301$	16.5461	+	18.3763i	0.953702	+	1.05919i
$302$	−13.4430	−	4.36791i	−0.773559	−	0.251345i
$303$	0.252858	+	0.227674i	0.0145263	+	0.0130795i
$304$	3.72888	+	6.45861i	0.213866	+	0.370427i
$305$	−4.21557	−	6.93433i	−0.241383	−	0.397058i
$306$	−1.94637	−	5.99030i	−0.111266	−	0.342443i
$307$	−8.67128	+	19.4760i	−0.494896	+	1.11155i	0.477588	+	0.878584i	$0.341511\pi$
$307$	−8.67128	+	19.4760i	−0.494896	+	1.11155i	−0.972484	+	0.232971i	$0.925155\pi$
$308$	7.77639	−	10.7033i	0.443101	−	0.609876i
$309$	2.52946			0.143896
$310$	−8.32608	+	9.25616i	−0.472889	+	0.525714i
$311$	16.5370			0.937730			0.468865	−	0.883270i	$-0.344663\pi$
$311$	16.5370			0.937730			0.468865	+	0.883270i	$0.344663\pi$
$312$	3.25815	−	4.48446i	0.184456	−	0.253882i
$313$	8.30794	−	18.6599i	0.469592	−	1.05472i	−0.511164	−	0.859483i	$-0.670785\pi$
$313$	8.30794	−	18.6599i	0.469592	−	1.05472i	0.980756	−	0.195238i	$-0.0625480\pi$
$314$	4.81942	+	14.8327i	0.271976	+	0.837055i
$315$	−5.53586	+	3.36541i	−0.311911	+	0.189619i
$316$	1.42823	+	2.47377i	0.0803442	+	0.139160i
$317$	21.1537	+	19.0469i	1.18811	+	1.06978i	0.996086	+	0.0883891i	$0.0281719\pi$
$317$	21.1537	+	19.0469i	1.18811	+	1.06978i	0.192024	+	0.981390i	$0.438495\pi$
$318$	−7.81258	−	2.53846i	−0.438108	−	0.142350i
$319$	−13.7441	−	15.2643i	−0.769521	−	0.854640i
$320$	0.183353	−	2.22854i	0.0102498	−	0.124579i
$321$	−11.3608	−	2.41482i	−0.634099	−	0.134782i
$322$	−25.2632	−	2.65527i	−1.40786	−	0.147972i
$323$	−46.7160	+	4.91005i	−2.59935	+	0.273202i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	10.1158	−	25.8034i	0.561125	−	1.43132i
$326$	−7.86664	+	5.71545i	−0.435693	+	0.316550i
$327$	−0.379475	−	1.78529i	−0.0209850	−	0.0987268i
$328$	9.09015	−	0.955414i	0.501920	−	0.0527539i
$329$	−0.989012	+	9.40982i	−0.0545260	+	0.518780i
$330$	−6.65877	+	7.74060i	−0.366553	+	0.426106i
$331$	−2.43879	+	1.08582i	−0.134048	+	0.0596820i	−0.472664	−	0.881242i	$-0.656708\pi$
$331$	−2.43879	+	1.08582i	−0.134048	+	0.0596820i	0.338617	+	0.940924i	$0.390041\pi$
$332$	−10.1772	+	9.16356i	−0.558545	+	0.502916i
$333$	−3.57004	−	1.15998i	−0.195637	−	0.0635663i
$334$	11.4395	−	12.7049i	0.625943	−	0.695181i
$335$	0.145822	+	6.44279i	0.00796711	+	0.352007i
$336$	1.44865	−	2.50914i	0.0790303	−	0.136885i
$337$	12.1501	−	3.94780i	0.661857	−	0.215050i	0.0412221	−	0.999150i	$-0.486875\pi$
$337$	12.1501	−	3.94780i	0.661857	−	0.215050i	0.620635	+	0.784100i	$0.286875\pi$
$338$	−7.20977	+	16.1934i	−0.392160	+	0.880806i
$339$	8.09589	+	5.88201i	0.439708	+	0.319467i
$340$	12.3534	+	6.76423i	0.669955	+	0.366842i
$341$	−19.2658	+	16.5896i	−1.04330	+	0.898380i
$342$		−	7.45776i		−	0.403270i
$343$	9.54637	−	13.1394i	0.515455	−	0.709464i
$344$	7.79690	+	3.47140i	0.420381	+	0.187165i
$345$	19.2638	+	3.64113i	1.03713	+	0.196032i
$346$	5.92394	−	10.2606i	0.318473	−	0.551611i
$347$	−1.16381	+	0.671925i	−0.0624765	+	0.0360708i	−0.530913	−	0.847426i	$-0.678151\pi$
$347$	−1.16381	+	0.671925i	−0.0624765	+	0.0360708i	0.468436	+	0.883497i	$0.344818\pi$
$348$	−3.34282	−	3.00988i	−0.179194	−	0.161347i
$349$	−1.50596	+	4.63485i	−0.0806119	+	0.248098i	−0.983238	−	0.182328i	$-0.941637\pi$
$349$	−1.50596	+	4.63485i	−0.0806119	+	0.248098i	0.902626	+	0.430426i	$0.141637\pi$
$350$	3.84865	−	13.9659i	0.205719	−	0.746509i
$351$	−5.06387	+	2.25458i	−0.270289	+	0.120341i
$352$	0.949390	−	4.46653i	0.0506027	−	0.238067i
$353$	−20.7217	−	2.17794i	−1.10291	−	0.115920i	−0.464465	−	0.885591i	$-0.653753\pi$
$353$	−20.7217	−	2.17794i	−1.10291	−	0.115920i	−0.638440	+	0.769671i	$0.720420\pi$
$354$	−1.00029	−	9.51716i	−0.0531650	−	0.505831i
$355$	7.41628	−	24.7144i	0.393615	−	1.31170i
$356$	0.908525	−	0.660082i	0.0481517	−	0.0349843i
$357$	10.7264	+	14.7636i	0.567702	+	0.781375i
$358$	−0.00150367	−	0.00707420i	−7.94713e−5	−	0.000373883i
$359$	1.78352	+	16.9691i	0.0941307	+	0.895594i	0.935070	+	0.354464i	$0.115337\pi$
$359$	1.78352	+	16.9691i	0.0941307	+	0.895594i	−0.840939	+	0.541130i	$0.817997\pi$
$360$	−1.27306	+	1.83829i	−0.0670960	+	0.0968866i
$361$	−35.8180	−	7.61336i	−1.88516	−	0.400703i
$362$	−2.97223	−	6.67574i	−0.156217	−	0.350869i
$363$	−7.32090	+	6.59177i	−0.384248	+	0.345978i
$364$	−4.96282	+	15.2740i	−0.260122	+	0.800574i
$365$	3.89753	−	1.36463i	0.204006	−	0.0714282i
$366$	−1.81461	−	3.14299i	−0.0948510	−	0.164287i
$367$	15.6596	+	9.04106i	0.817423	+	0.471940i	0.849527	−	0.527545i	$-0.176887\pi$
$367$	15.6596	+	9.04106i	0.817423	+	0.471940i	−0.0321038	+	0.999485i	$0.510221\pi$
$368$	−8.33848	+	2.70934i	−0.434673	+	0.141234i
$369$	−8.35001	−	3.71766i	−0.434684	−	0.193534i
$370$	7.58878	−	3.58664i	0.394522	−	0.186461i
$371$	23.8003			1.23565
$372$	−3.81625	+	4.05416i	−0.197863	+	0.210199i
$373$			13.1061i			0.678609i	0.940677	+	0.339304i	$0.110192\pi$
$373$			13.1061i			0.678609i	−0.940677	+	0.339304i	$0.889808\pi$
$374$	23.2684	+	16.9055i	1.20318	+	0.874161i
$375$	−3.84411	+	10.4987i	−0.198509	+	0.542151i
$376$	1.00915	+	3.10585i	0.0520430	+	0.160172i
$377$	21.5934	+	12.4670i	1.11212	+	0.642082i
$378$	−2.50914	+	1.44865i	−0.129056	+	0.0745105i
$379$	3.55090	−	3.94368i	0.182398	−	0.202573i	−0.645011	−	0.764173i	$-0.723147\pi$
$379$	3.55090	−	3.94368i	0.182398	−	0.202573i	0.827409	+	0.561600i	$0.189814\pi$
$380$	11.4360	+	12.1371i	0.586656	+	0.622619i
$381$	1.67030	+	1.85505i	0.0855719	+	0.0950372i
$382$	2.64170	+	5.93335i	0.135161	+	0.303577i
$383$	−1.92137	+	9.03935i	−0.0981776	+	0.461889i	0.901404	+	0.432978i	$0.142537\pi$
$383$	−1.92137	+	9.03935i	−0.0981776	+	0.461889i	−0.999582	+	0.0289112i	$0.990796\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	11.4179	−	27.2909i	0.581913	−	1.39087i
$386$	16.6907	−	3.54772i	0.849535	−	0.180574i
$387$	−5.01661	−	6.90477i	−0.255009	−	0.350989i
$388$	1.01367	+	1.39520i	0.0514614	+	0.0708305i
$389$	−16.9797	+	3.60914i	−0.860905	+	0.182991i	−0.617149	−	0.786846i	$-0.711713\pi$
$389$	−16.9797	+	3.60914i	−0.860905	+	0.182991i	−0.243755	+	0.969837i	$0.578379\pi$
$390$	4.78389	−	11.4343i	0.242242	−	0.579000i
$391$	5.77242	−	54.9209i	0.291924	−	2.77747i
$392$	−0.289902	+	1.36388i	−0.0146422	+	0.0688863i
$393$	4.10859	+	9.22804i	0.207251	+	0.465493i
$394$	17.9162	+	19.8980i	0.902607	+	1.00245i
$395$	4.38021	+	4.64872i	0.220392	+	0.233902i
$396$	−3.05546	+	3.39343i	−0.153543	+	0.170526i
$397$	13.1052	−	7.56627i	0.657729	−	0.379740i	−0.133682	−	0.991024i	$-0.542680\pi$
$397$	13.1052	−	7.56627i	0.657729	−	0.379740i	0.791411	+	0.611284i	$0.209347\pi$
$398$	5.07996	+	2.93292i	0.254635	+	0.147014i
$399$	6.67705	+	20.5498i	0.334271	+	1.02878i
$400$	−0.747086	−	4.94387i	−0.0373543	−	0.247194i
$401$	17.8680	+	12.9819i	0.892286	+	0.648283i	0.936473	−	0.350740i	$-0.114070\pi$
$401$	17.8680	+	12.9819i	0.892286	+	0.648283i	−0.0441874	+	0.999023i	$0.514070\pi$
$402$			2.88204i			0.143743i
$403$	16.0192	−	26.3797i	0.797975	−	1.31406i
$404$	−0.340253			−0.0169282
$405$	2.02165	−	0.955480i	0.100456	−	0.0474782i
$406$	11.9059	+	5.30085i	0.590880	+	0.263077i
$407$	16.3019	−	5.29682i	0.808056	−	0.262553i
$408$	5.45473	+	3.14929i	0.270049	+	0.155913i
$409$	−5.56744	−	9.64308i	−0.275292	−	0.476820i	0.694917	−	0.719090i	$-0.255441\pi$
$409$	−5.56744	−	9.64308i	−0.275292	−	0.476820i	−0.970209	+	0.242270i	$0.922108\pi$
$410$	19.2900	−	6.75395i	0.952663	−	0.333554i
$411$	0.564646	−	1.73780i	0.0278519	−	0.0857194i
$412$	−1.87976	+	1.69254i	−0.0926089	+	0.0833854i
$413$	11.2772	+	25.3289i	0.554913	+	1.24636i
$414$	8.57600	+	1.82289i	0.421488	+	0.0895899i
$415$	−17.4342	+	25.1749i	−0.855810	+	1.23579i
$416$	0.579411	+	5.51273i	0.0284080	+	0.270284i
$417$	−2.15972	−	10.1607i	−0.105762	−	0.497570i
$418$	20.0167	+	27.5507i	0.979051	+	1.34755i
$419$	−14.5044	+	10.5381i	−0.708588	+	0.514820i	−0.882718	−	0.469903i	$-0.844289\pi$
$419$	−14.5044	+	10.5381i	−0.708588	+	0.514820i	0.174130	+	0.984723i	$0.444289\pi$
$420$	1.86205	−	6.20520i	0.0908589	−	0.302783i
$421$	−0.655055	−	6.23243i	−0.0319254	−	0.303750i	−0.998820	−	0.0485727i	$-0.984533\pi$
$421$	−0.655055	−	6.23243i	−0.0319254	−	0.303750i	0.966894	−	0.255178i	$-0.0821339\pi$
$422$	−6.69587	−	0.703764i	−0.325950	−	0.0342587i
$423$	0.678973	−	3.19432i	0.0330128	−	0.155313i
$424$	7.50444	−	3.34119i	0.364448	−	0.162263i
$425$	30.3612	+	8.36676i	1.47273	+	0.405847i
$426$	3.56590	−	10.9747i	0.172769	−	0.531727i
$427$	7.81411	+	7.03586i	0.378151	+	0.340489i
$428$	10.0586	−	5.80732i	0.486199	−	0.280707i
$429$	12.6558	−	21.9204i	0.611026	−	1.05833i
$430$	18.7523	+	3.54444i	0.904315	+	0.170928i
$431$	−29.2611	−	13.0279i	−1.40946	−	0.627530i	−0.445911	−	0.895077i	$-0.647120\pi$
$431$	−29.2611	−	13.0279i	−1.40946	−	0.627530i	−0.963545	+	0.267547i	$0.913787\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$			16.7972i			0.807223i	0.914930	+	0.403612i	$0.132245\pi$
$433$			16.7972i			0.807223i	−0.914930	+	0.403612i	$0.867755\pi$
$434$	6.88591	−	14.5880i	0.330534	−	0.700245i
$435$	−8.82230	−	4.83075i	−0.422997	−	0.231617i
$436$	1.47660	+	1.07281i	0.0707162	+	0.0513783i
$437$	26.5952	−	59.7337i	1.27222	−	2.85745i
$438$	1.75639	−	0.570686i	0.0839236	−	0.0272684i
$439$	0.849532	−	1.47143i	0.0405460	−	0.0702277i	−0.845040	−	0.534703i	$-0.820424\pi$
$439$	0.849532	−	1.47143i	0.0405460	−	0.0702277i	0.885586	+	0.464475i	$0.153757\pi$
$440$	−0.231041	−	10.2080i	−0.0110144	−	0.486646i
$441$	0.933002	−	1.03620i	0.0444287	−	0.0493430i
$442$	−33.2048	−	10.7889i	−1.57939	−	0.513176i
$443$	10.5772	−	9.52374i	0.502537	−	0.452487i	−0.378453	−	0.925620i	$-0.623544\pi$
$443$	10.5772	−	9.52374i	0.502537	−	0.452487i	0.880991	+	0.473134i	$0.156877\pi$
$444$	3.42923	−	1.52679i	0.162744	−	0.0724583i
$445$	1.63760	−	1.90365i	0.0776296	−	0.0902419i
$446$	1.03292	−	9.82759i	0.0489102	−	0.465350i
$447$	11.2051	−	1.17770i	0.529983	−	0.0557035i
$448$	0.602383	+	2.83399i	0.0284599	+	0.133893i
$449$	−6.79602	+	4.93759i	−0.320724	+	0.233020i	−0.736484	−	0.676455i	$-0.763515\pi$
$449$	−6.79602	+	4.93759i	−0.320724	+	0.233020i	0.415760	+	0.909474i	$0.363515\pi$
$450$	−1.82494	+	4.65506i	−0.0860285	+	0.219442i
$451$	40.8251	−	8.67764i	1.92238	−	0.408614i
$452$	−9.95225	+	1.04602i	−0.468114	+	0.0492008i
$453$	−14.0574	−	1.47749i	−0.660475	−	0.0694187i
$454$	12.9112	+	2.74437i	0.605954	+	0.128800i
$455$	−2.94466	+	35.7903i	−0.138048	+	1.67788i
$456$	4.99022	+	5.54220i	0.233688	+	0.259537i
$457$	−33.1274	−	10.7638i	−1.54964	−	0.503507i	−0.595621	−	0.803266i	$-0.703094\pi$
$457$	−33.1274	−	10.7638i	−1.54964	−	0.503507i	−0.954015	+	0.299758i	$0.903094\pi$
$458$	−1.86564	−	1.67983i	−0.0871758	−	0.0784934i
$459$	−3.14929	−	5.45473i	−0.146996	−	0.254605i
$460$	−16.7522	+	10.1841i	−0.781076	+	0.474838i
$461$	3.90117	+	12.0066i	0.181695	+	0.559201i	0.999876	−	0.0157605i	$-0.00501694\pi$
$461$	3.90117	+	12.0066i	0.181695	+	0.559201i	−0.818180	+	0.574962i	$0.805017\pi$
$462$	5.38112	−	12.0862i	0.250352	−	0.562301i
$463$	−7.40598	+	10.1935i	−0.344185	+	0.473730i	−0.945658	−	0.325163i	$-0.894581\pi$
$463$	−7.40598	+	10.1935i	−0.344185	+	0.473730i	0.601473	+	0.798893i	$0.294581\pi$
$464$	4.49820			0.208824
$465$	−6.21967	+	10.7850i	−0.288430	+	0.500141i
$466$	−1.49966			−0.0694706
$467$	−21.0061	+	28.9124i	−0.972045	+	1.33790i	−0.0310373	+	0.999518i	$0.509881\pi$
$467$	−21.0061	+	28.9124i	−0.972045	+	1.33790i	−0.941007	+	0.338386i	$0.890119\pi$
$468$	2.25458	−	5.06387i	0.104218	−	0.234077i
$469$	−2.58033	−	7.94145i	−0.119149	−	0.366702i
$470$	3.79330	+	6.23973i	0.174972	+	0.287817i
$471$	7.79799	+	13.5065i	0.359312	+	0.622347i
$472$	7.11159	+	6.40330i	0.327337	+	0.294736i
$473$	37.0650	+	12.0431i	1.70425	+	0.553744i
$474$	1.91134	+	2.12276i	0.0877910	+	0.0975017i
$475$	31.1280	+	20.5305i	1.42825	+	0.942004i
$476$	−17.8501	−	3.79415i	−0.818158	−	0.173905i
$477$	−8.16963	−	0.858663i	−0.374062	−	0.0393155i
$478$	−2.90602	+	0.305435i	−0.132918	+	0.0139703i
$479$	33.4010	−	7.09960i	1.52613	−	0.324389i	0.632987	−	0.774162i	$-0.281828\pi$
$479$	33.4010	−	7.09960i	1.52613	−	0.324389i	0.893143	+	0.449773i	$0.148495\pi$
$480$	−0.283993	−	2.21796i	−0.0129624	−	0.101236i
$481$	−16.8336	+	12.2303i	−0.767545	+	0.557654i
$482$	−1.11067	−	5.22530i	−0.0505898	−	0.238006i
$483$	−25.2632	+	2.65527i	−1.14952	+	0.120819i
$484$	1.02974	−	9.79728i	0.0468061	−	0.445331i
$485$	2.92340	+	2.51482i	0.132745	+	0.114192i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	2.47297	−	2.22667i	0.112061	−	0.100900i	−0.611196	−	0.791480i	$-0.709311\pi$
$487$	2.47297	−	2.22667i	0.112061	−	0.100900i	0.723256	+	0.690580i	$0.242644\pi$
$488$	3.45159	+	1.12149i	0.156246	+	0.0507674i
$489$	−6.50643	+	7.22612i	−0.294231	+	0.326776i
$490$	0.0705497	+	3.11706i	0.00318711	+	0.140815i
$491$	6.14213	−	10.6385i	0.277191	−	0.480108i	−0.693495	−	0.720462i	$-0.743930\pi$
$491$	6.14213	−	10.6385i	0.277191	−	0.480108i	0.970685	+	0.240353i	$0.0772633\pi$
$492$	8.69287	−	2.82448i	0.391905	−	0.127338i
$493$	−11.5238	+	25.8828i	−0.519005	+	1.16570i
$494$	−33.4440	−	24.2985i	−1.50472	−	1.09324i
$495$	−4.90390	+	8.95589i	−0.220414	+	0.402537i
$496$	0.123260	−	5.56640i	0.00553454	−	0.249939i
$497$			33.4334i			1.49969i
$498$	−8.04956	+	11.0793i	−0.360709	+	0.496474i
$499$	−26.8215	−	11.9417i	−1.20069	−	0.534583i	−0.293769	−	0.955876i	$-0.594910\pi$
$499$	−26.8215	−	11.9417i	−1.20069	−	0.534583i	−0.906925	+	0.421293i	$0.861576\pi$
$500$	−4.16827	−	10.3743i	−0.186411	−	0.463952i
$501$	8.54806	−	14.8057i	0.381899	−	0.661469i
$502$	25.2520	−	14.5793i	1.12705	−	0.650704i
$503$	7.21776	+	6.49890i	0.321824	+	0.289772i	0.814168	−	0.580629i	$-0.197193\pi$
$503$	7.21776	+	6.49890i	0.321824	+	0.289772i	−0.492344	+	0.870401i	$0.663860\pi$
$504$	0.895315	−	2.75550i	0.0398805	−	0.122740i
$505$	−0.740434	+	0.174984i	−0.0329489	+	0.00778671i
$506$	−36.5744	+	16.2840i	−1.62593	+	0.723910i
$507$	−3.68542	+	17.3385i	−0.163675	+	0.770032i
$508$	−2.48255	−	0.260926i	−0.110145	−	0.0115767i
$509$	−1.69570	−	16.1335i	−0.0751608	−	0.715107i	−0.965605	−	0.260014i	$-0.916273\pi$
$509$	−1.69570	−	16.1335i	−0.0751608	−	0.715107i	0.890444	−	0.455093i	$-0.150394\pi$
$510$	13.4898	+	4.04801i	0.597337	+	0.179249i
$511$	−4.32879	+	3.14505i	−0.191494	+	0.139129i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−1.55056	−	7.29479i	−0.0684587	−	0.322073i
$514$	−2.43219	−	23.1407i	−0.107279	−	1.02069i
$515$	−3.22015	+	4.64989i	−0.141897	+	0.204899i
$516$	8.34826	+	1.77448i	0.367512	+	0.0781170i
$517$	6.06531	+	13.6229i	0.266752	+	0.599135i
$518$	−8.08227	+	7.27731i	−0.355115	+	0.319747i
$519$	3.66120	−	11.2680i	0.160709	−	0.494610i
$520$	4.09594	+	11.6984i	0.179619	+	0.513009i
$521$	0.303586	+	0.525826i	0.0133003	+	0.0230369i	0.872599	−	0.488437i	$-0.162433\pi$
$521$	0.303586	+	0.525826i	0.0133003	+	0.0230369i	−0.859299	+	0.511474i	$0.829100\pi$
$522$	−3.89556	−	2.24910i	−0.170504	−	0.0984405i
$523$	−14.5560	+	4.72952i	−0.636488	+	0.206808i	−0.609447	−	0.792827i	$-0.708608\pi$
$523$	−14.5560	+	4.72952i	−0.636488	+	0.206808i	−0.0270411	+	0.999634i	$0.508608\pi$
$524$	−9.22804	−	4.10859i	−0.403129	−	0.179484i
$525$	0.860870	−	14.4609i	0.0375715	−	0.631125i
$526$	−14.3225			−0.624490
$527$	31.7135	+	14.9696i	1.38146	+	0.652086i
$528$		−	4.56632i		−	0.198723i
$529$	43.5823	+	31.6644i	1.89488	+	1.37671i
$530$	14.6123	−	11.1302i	0.634718	−	0.483465i
$531$	−2.95716	−	9.10122i	−0.128330	−	0.394959i
$532$	−18.7125	−	10.8037i	−0.811292	−	0.468399i
$533$	−43.8773	+	25.3326i	−1.90054	+	1.09728i
$534$	0.751433	−	0.834551i	0.0325177	−	0.0361145i
$535$	18.9021	−	17.8103i	0.817210	−	0.770008i
$536$	−1.92846	−	2.14177i	−0.0832968	−	0.0925105i
$537$	−0.00294162	−	0.00660698i	−0.000126940	−	0.000285112i
$538$	−0.946357	+	4.45226i	−0.0408003	+	0.191950i
$539$	−0.665537	+	6.33216i	−0.0286667	+	0.272746i
$540$	−0.863035	+	2.06281i	−0.0371391	+	0.0887690i
$541$	−31.8827	+	6.77687i	−1.37074	+	0.291360i	−0.833711	−	0.552201i	$-0.813788\pi$
$541$	−31.8827	+	6.77687i	−1.37074	+	0.291360i	−0.537032	+	0.843562i	$0.680455\pi$
$542$	−18.7312	−	25.7813i	−0.804574	−	1.10740i
$543$	−4.29525	−	5.91190i	−0.184327	−	0.253704i
$544$	−6.16094	+	1.30955i	−0.264148	+	0.0561464i
$545$	3.76498	+	1.57519i	0.161274	+	0.0674738i
$546$	−1.67873	+	15.9720i	−0.0718429	+	0.683540i
$547$	5.33193	−	25.0848i	0.227977	−	1.07255i	−0.704048	−	0.710152i	$-0.748626\pi$
$547$	5.33193	−	25.0848i	0.227977	−	1.07255i	0.932025	−	0.362394i	$-0.118041\pi$
$548$	0.743202	+	1.66926i	0.0317480	+	0.0713073i
$549$	−2.42842	−	2.69703i	−0.103642	−	0.115106i
$550$	−5.75250	−	22.0950i	−0.245287	−	0.942135i
$551$	−22.4470	+	24.9299i	−0.956275	+	1.06205i
$552$	−7.59296	+	4.38380i	−0.323178	+	0.186587i
$553$	−7.16725	−	4.13801i	−0.304782	−	0.175966i
$554$	−5.22845	−	16.0915i	−0.222136	−	0.683663i
$555$	6.67724	−	5.08606i	0.283433	−	0.215891i
$556$	8.40379	+	6.10571i	0.356400	+	0.258940i
$557$		−	33.7147i		−	1.42854i	−0.699872	−	0.714268i	$-0.746760\pi$
$557$		−	33.7147i		−	1.42854i	0.699872	−	0.714268i	$-0.253240\pi$
$558$	−2.88995	+	4.75901i	−0.122341	+	0.201465i
$559$	−47.3090			−2.00096
$560$	2.76831	+	5.85732i	0.116983	+	0.247517i
$561$	26.2748	+	11.6983i	1.10932	+	0.493902i
$562$	21.5138	−	6.99025i	0.907503	−	0.294866i
$563$	12.7876	+	7.38290i	0.538932	+	0.311152i	0.744646	−	0.667460i	$-0.232618\pi$
$563$	12.7876	+	7.38290i	0.538932	+	0.311152i	−0.205714	+	0.978612i	$0.565952\pi$
$564$	1.63284	+	2.82816i	0.0687550	+	0.119087i
$565$	−21.1194	+	7.39449i	−0.888499	+	0.311088i
$566$	−4.02452	+	12.3862i	−0.169163	+	0.520631i
$567$	−2.15311	+	1.93867i	−0.0904223	+	0.0814166i
$568$	4.69354	+	10.5419i	0.196937	+	0.442327i
$569$	6.25712	+	1.32999i	0.262312	+	0.0557562i	0.337190	−	0.941437i	$-0.390523\pi$
$569$	6.25712	+	1.32999i	0.262312	+	0.0557562i	−0.0748780	+	0.997193i	$0.523857\pi$
$570$	13.7096	+	9.49416i	0.574230	+	0.397667i
$571$	−4.18840	−	39.8500i	−0.175279	−	1.66767i	−0.629666	−	0.776866i	$-0.716808\pi$
$571$	−4.18840	−	39.8500i	−0.175279	−	1.66767i	0.454387	−	0.890804i	$-0.349858\pi$
$572$	5.26256	+	24.7584i	0.220039	+	1.03520i
$573$	3.81758	+	5.25445i	0.159482	+	0.219508i
$574$	−21.4244	+	15.5657i	−0.894236	+	0.649700i
$575$	−31.2175	+	30.7772i	−1.30186	+	1.28350i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	39.6354	+	4.16585i	1.65004	+	0.173427i	0.883391	−	0.468636i	$-0.155254\pi$
$577$	39.6354	+	4.16585i	1.65004	+	0.173427i	0.766652	+	0.642062i	$0.221921\pi$
$578$	4.71379	−	22.1766i	0.196068	−	0.922427i
$579$	15.5884	−	6.94039i	0.647831	−	0.288433i
$580$	9.78865	−	2.31332i	0.406451	−	0.0960554i
$581$	12.2611	−	37.7358i	0.508676	−	1.56554i
$582$	1.28160	+	1.15396i	0.0531240	+	0.0478330i
$583$	32.4851	−	18.7553i	1.34540	−	0.776765i
$584$	−0.923390	+	1.59936i	−0.0382101	+	0.0661819i
$585$	2.30202	−	12.1791i	0.0951767	−	0.503543i
$586$	−2.83815	−	1.26362i	−0.117243	−	0.0521998i
$587$	−22.8597	+	31.4637i	−0.943522	+	1.29865i	0.0108237	+	0.999941i	$0.496555\pi$
$587$	−22.8597	+	31.4637i	−0.943522	+	1.29865i	−0.954346	+	0.298705i	$0.903445\pi$
$588$			1.39435i			0.0575020i
$589$	30.2350	+	28.4607i	1.24581	+	1.17270i
$590$	18.7688	+	10.2771i	0.772698	+	0.423100i
$591$	21.6618	+	15.7382i	0.891046	+	0.647383i
$592$	−1.52679	+	3.42923i	−0.0627508	+	0.140941i
$593$	9.83908	−	3.19691i	0.404043	−	0.131281i	−0.0999435	−	0.994993i	$-0.531866\pi$
$593$	9.83908	−	3.19691i	0.404043	−	0.131281i	0.503986	+	0.863712i	$0.331866\pi$
$594$	−2.28316	+	3.95455i	−0.0936791	+	0.162257i
$595$	−40.7953	+	0.923335i	−1.67244	+	0.0378530i
$596$	−7.53898	+	8.37288i	−0.308809	+	0.342967i
$597$	5.57874	+	1.81264i	0.228323	+	0.0741865i
$598$	36.1166	−	32.5195i	1.47692	−	1.32982i
$599$	−3.50353	+	1.55987i	−0.143151	+	0.0637347i	−0.477062	−	0.878870i	$-0.658298\pi$
$599$	−3.50353	+	1.55987i	−0.143151	+	0.0637347i	0.333911	+	0.942605i	$0.391631\pi$
$600$	−1.75865	−	4.68051i	−0.0717965	−	0.191081i
$601$	−3.48568	+	33.1640i	−0.142184	+	1.35279i	0.657992	+	0.753025i	$0.271406\pi$
$601$	−3.48568	+	33.1640i	−0.142184	+	1.35279i	−0.800176	+	0.599765i	$0.795261\pi$
$602$	−24.5923	+	2.58476i	−1.00231	+	0.105347i
$603$	0.599210	+	2.81906i	0.0244017	+	0.114801i
$604$	11.4353	−	8.30825i	0.465297	−	0.338058i
$605$	−2.79768	−	21.8497i	−0.113742	−	0.888315i
$606$	−0.332818	+	0.0707427i	−0.0135198	+	0.00287372i
$607$	31.3377	−	3.29372i	1.27196	−	0.133688i	0.555617	−	0.831439i	$-0.312482\pi$
$607$	31.3377	−	3.29372i	1.27196	−	0.133688i	0.716341	+	0.697751i	$0.245816\pi$
$608$	−7.41691	−	0.779549i	−0.300795	−	0.0316149i
$609$	12.7478	+	2.70964i	0.516569	+	0.109800i
$610$	8.08784	+	0.665428i	0.327467	+	0.0269424i
$611$	−12.1126	−	13.4524i	−0.490023	−	0.544225i
$612$	5.99030	+	1.94637i	0.242144	+	0.0786772i
$613$	27.8005	+	25.0317i	1.12285	+	1.01102i	0.999827	+	0.0186173i	$0.00592641\pi$
$613$	27.8005	+	25.0317i	1.12285	+	1.01102i	0.123026	+	0.992403i	$0.460740\pi$
$614$	−10.6596	−	18.4629i	−0.430185	−	0.745103i
$615$	17.4642	−	10.6170i	0.704225	−	0.428118i
$616$	4.08829	+	12.5825i	0.164722	+	0.506962i
$617$	−8.86939	+	19.9210i	−0.357068	+	0.801988i	0.642300	+	0.766453i	$0.277980\pi$
$617$	−8.86939	+	19.9210i	−0.357068	+	0.801988i	−0.999368	+	0.0355351i	$0.988686\pi$
$618$	−1.48678	+	2.04638i	−0.0598070	+	0.0823173i
$619$	19.3476			0.777646			0.388823	−	0.921312i	$-0.372882\pi$
$619$	19.3476			0.777646			0.388823	+	0.921312i	$0.372882\pi$
$620$	−2.59444	−	12.1766i	−0.104195	−	0.489023i
$621$	8.76760			0.351832
$622$	−9.72023	+	13.3788i	−0.389746	+	0.536439i
$623$	−1.32338	+	2.97237i	−0.0530203	+	0.119086i
$624$	1.71291	+	5.27180i	0.0685713	+	0.211041i
$625$	−14.4059	−	20.4321i	−0.576237	−	0.817283i
$626$	10.2129	+	17.6893i	0.408190	+	0.707006i
$627$	25.3074	+	22.7869i	1.01068	+	0.910022i
$628$	−14.8327	−	4.81942i	−0.591887	−	0.192316i
$629$	−15.8205	−	17.5704i	−0.630804	−	0.700579i
$630$	0.531230	−	6.45674i	0.0211647	−	0.257243i
$631$	−25.4360	−	5.40660i	−1.01259	−	0.215233i	−0.328403	−	0.944538i	$-0.606510\pi$
$631$	−25.4360	−	5.40660i	−1.01259	−	0.215233i	−0.684189	+	0.729304i	$0.739844\pi$
$632$	−2.84081	−	0.298581i	−0.113001	−	0.0118769i
$633$	−6.69587	+	0.703764i	−0.266137	+	0.0279721i
$634$	−27.8431	+	5.91823i	−1.10579	+	0.235043i
$635$	−5.53652	+	0.708908i	−0.219710	+	0.0281321i
$636$	6.64578	−	4.82844i	0.263522	−	0.191460i
$637$	−1.60695	−	7.56012i	−0.0636698	−	0.299543i
$638$	20.4277	−	2.14704i	0.808740	−	0.0850020i
$639$	1.20621	−	11.4763i	0.0477168	−	0.453995i
$640$	1.69515	+	1.45824i	0.0670068	+	0.0576419i
$641$	37.5775	−	16.7306i	1.48422	−	0.660817i	0.504908	−	0.863173i	$-0.331526\pi$
$641$	37.5775	−	16.7306i	1.48422	−	0.660817i	0.979312	+	0.202356i	$0.0648597\pi$
$642$	8.63135	−	7.77171i	0.340652	−	0.306725i
$643$	−8.70016	−	2.82685i	−0.343101	−	0.111480i	0.132398	−	0.991197i	$-0.457732\pi$
$643$	−8.70016	−	2.82685i	−0.343101	−	0.111480i	−0.475499	+	0.879716i	$0.657732\pi$
$644$	16.9975	−	18.8776i	0.669795	−	0.743883i
$645$	19.0794	−	0.431832i	0.751252	−	0.0170034i
$646$	23.4867	−	40.6801i	0.924070	−	1.60054i
$647$	20.3458	−	6.61077i	0.799878	−	0.259896i	0.119573	−	0.992825i	$-0.461847\pi$
$647$	20.3458	−	6.61077i	0.799878	−	0.259896i	0.680305	+	0.732929i	$0.261847\pi$
$648$	−0.406737	+	0.913545i	−0.0159781	+	0.0358875i
$649$	35.3522	+	25.6849i	1.38770	+	1.00822i
$650$	14.9295	+	23.3508i	0.585583	+	0.915892i
$651$	3.70242	−	15.7009i	0.145109	−	0.615365i
$652$		−	9.72370i		−	0.380810i
$653$	−4.21891	+	5.80683i	−0.165099	+	0.227239i	−0.883548	−	0.468340i	$-0.844852\pi$
$653$	−4.21891	+	5.80683i	−0.165099	+	0.227239i	0.718449	+	0.695579i	$0.244852\pi$
$654$	1.66738	+	0.742366i	0.0651997	+	0.0290288i
$655$	−22.1943	−	4.19503i	−0.867204	−	0.163914i
$656$	−4.57011	+	7.91567i	−0.178433	+	0.309055i
$657$	1.59936	−	0.923390i	0.0623969	−	0.0360249i
$658$	−7.03138	−	6.33108i	−0.274112	−	0.246811i
$659$	−6.98838	+	21.5080i	−0.272229	+	0.837833i	0.717711	+	0.696341i	$0.245190\pi$
$659$	−6.98838	+	21.5080i	−0.272229	+	0.837833i	−0.989939	+	0.141492i	$0.954810\pi$
$660$	−2.34835	−	9.93687i	−0.0914094	−	0.386792i
$661$	9.82278	−	4.37338i	0.382062	−	0.170105i	−0.206714	−	0.978401i	$-0.566277\pi$
$661$	9.82278	−	4.37338i	0.382062	−	0.170105i	0.588776	+	0.808297i	$0.299610\pi$
$662$	0.555038	−	2.61125i	0.0215722	−	0.101489i
$663$	−34.7224	−	3.64947i	−1.34850	−	0.141734i
$664$	−1.43149	−	13.6197i	−0.0555525	−	0.528547i
$665$	−46.2769	−	13.8868i	−1.79454	−	0.538505i
$666$	3.03686	−	2.20640i	0.117676	−	0.0854965i
$667$	−23.1813	−	31.9063i	−0.897584	−	1.23542i
$668$	3.55448	+	16.7225i	0.137527	+	0.647014i
$669$	−1.03292	−	9.82759i	−0.0399350	−	0.379956i
$670$	−5.29804	−	3.66900i	−0.204681	−	0.141746i
$671$	16.2100	+	3.44554i	0.625780	+	0.133014i
$672$	1.17844	+	2.64682i	0.0454592	+	0.102103i
$673$	−22.5311	+	20.2871i	−0.868512	+	0.782011i	−0.977257	−	0.212058i	$-0.931983\pi$
$673$	−22.5311	+	20.2871i	−0.868512	+	0.782011i	0.108745	+	0.994070i	$0.465317\pi$
$674$	−3.94780	+	12.1501i	−0.152064	+	0.468004i
$675$	−0.817219	+	4.93276i	−0.0314548	+	0.189862i
$676$	−8.86295	−	15.3511i	−0.340883	−	0.590426i
$677$	30.7750	+	17.7679i	1.18278	+	0.682878i	0.956656	−	0.291221i	$-0.0940615\pi$
$677$	30.7750	+	17.7679i	1.18278	+	0.682878i	0.226123	+	0.974099i	$0.427395\pi$
$678$	−9.51729	+	3.09235i	−0.365509	+	0.118761i
$679$	−4.56460	−	2.03229i	−0.175173	−	0.0779921i
$680$	−12.7335	+	6.01817i	−0.488308	+	0.230786i
$681$	13.1997			0.505813
$682$	−2.09714	−	25.3375i	−0.0803035	−	0.970224i
$683$		−	44.0443i		−	1.68531i	−0.538454	−	0.842655i	$-0.680991\pi$
$683$		−	44.0443i		−	1.68531i	0.538454	−	0.842655i	$-0.319009\pi$
$684$	6.03346	+	4.38356i	0.230695	+	0.167610i
$685$	2.47576	+	3.25031i	0.0945940	+	0.124188i
$686$	5.01882	+	15.4463i	0.191620	+	0.589744i
$687$	−2.17413	−	1.25524i	−0.0829483	−	0.0478902i
$688$	−7.39132	+	4.26738i	−0.281792	+	0.162692i
$689$	−30.4685	+	33.8387i	−1.16076	+	1.28915i
$690$	−14.2687	+	13.4446i	−0.543202	+	0.511826i
$691$	26.7336	+	29.6907i	1.01699	+	1.12949i	0.991539	+	0.129811i	$0.0414370\pi$
$691$	26.7336	+	29.6907i	1.01699	+	1.12949i	0.0254556	+	0.999676i	$0.491896\pi$
$692$	4.81897	+	10.8236i	0.183190	+	0.411451i
$693$	2.75067	−	12.9409i	0.104489	−	0.491583i
$694$	0.140471	−	1.33649i	0.00533219	−	0.0507324i
$695$	21.4277	+	8.96492i	0.812800	+	0.340059i
$696$	4.39990	−	0.935229i	0.166778	−	0.0354498i
$697$	−33.8390	−	46.5754i	−1.28175	−	1.76417i
$698$	−2.86450	−	3.94264i	−0.108423	−	0.149231i
$699$	−1.46689	+	0.311798i	−0.0554830	+	0.0117933i
$700$	9.03648	+	11.3226i	0.341547	+	0.427953i
$701$	2.16255	−	20.5753i	0.0816783	−	0.777117i	−0.874637	−	0.484779i	$-0.838900\pi$
$701$	2.16255	−	20.5753i	0.0816783	−	0.777117i	0.956315	−	0.292338i	$-0.0944332\pi$
$702$	1.15247	−	5.42196i	0.0434973	−	0.204639i
$703$	−11.3865	−	25.5744i	−0.429448	−	0.964556i
$704$	3.05546	+	3.39343i	0.115157	+	0.127895i
$705$	5.00772	+	5.31470i	0.188602	+	0.200163i
$706$	13.9419	−	15.4841i	0.524711	−	0.582750i
$707$	0.853742	−	0.492908i	0.0321083	−	0.0185377i
$708$	8.28750	+	4.78479i	0.311463	+	0.179824i
$709$	0.291088	+	0.895878i	0.0109321	+	0.0336454i	0.956374	−	0.292146i	$-0.0943693\pi$
$709$	0.291088	+	0.895878i	0.0109321	+	0.0336454i	−0.945442	+	0.325791i	$0.894369\pi$
$710$	15.6352	+	20.5266i	0.586777	+	0.770351i
$711$	2.31092	+	1.67898i	0.0866664	+	0.0629669i
$712$			1.12300i			0.0420862i
$713$	−40.1184	+	27.8119i	−1.50245	+	1.04157i
$714$	−18.2489			−0.682947
$715$	24.1847	+	51.1710i	0.904455	+	1.91369i
$716$	0.00660698	+	0.00294162i	0.000246915	+	0.000109933i
$717$	−2.77901	+	0.902957i	−0.103784	+	0.0337215i
$718$	−14.7766	−	8.53128i	−0.551458	−	0.318384i
$719$	16.6274	+	28.7995i	0.620096	+	1.07404i	0.989467	+	0.144756i	$0.0462399\pi$
$719$	16.6274	+	28.7995i	0.620096	+	1.07404i	−0.369371	+	0.929282i	$0.620427\pi$
$720$	−0.738927	−	2.11045i	−0.0275382	−	0.0786517i
$721$	2.26466	−	6.96992i	0.0843405	−	0.259573i
$722$	27.2127	−	24.5024i	1.01275	−	0.911884i
$723$	−2.17280	−	4.88020i	−0.0808074	−	0.181496i
$724$	7.14783	+	1.51932i	0.265647	+	0.0564650i
$725$	20.1116	−	10.0681i	0.746927	−	0.373922i
$726$	−1.02974	−	9.79728i	−0.0382171	−	0.363611i
$727$	−0.555532	−	2.61357i	−0.0206035	−	0.0969321i	0.966644	−	0.256122i	$-0.0824450\pi$
$727$	−0.555532	−	2.61357i	−0.0206035	−	0.0969321i	−0.987248	+	0.159190i	$0.949112\pi$
$728$	−9.43984	−	12.9928i	−0.349864	−	0.481546i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−1.18690	+	3.95528i	−0.0439291	+	0.146391i
$731$	−5.61913	−	53.4624i	−0.207831	−	1.97738i
$732$	3.60933	+	0.379356i	0.133405	+	0.0140214i
$733$	−2.37533	+	11.1751i	−0.0877349	+	0.412760i	0.912260	+	0.409611i	$0.134336\pi$
$733$	−2.37533	+	11.1751i	−0.0877349	+	0.412760i	−0.999995	+	0.00314890i	$0.998998\pi$
$734$	−16.5188	+	7.35466i	−0.609722	+	0.271466i
$735$	0.717082	+	3.03428i	0.0264500	+	0.111921i
$736$	2.70934	−	8.33848i	0.0998675	−	0.307360i
$737$	−9.78001	−	8.80596i	−0.360251	−	0.324372i
$738$	7.91567	−	4.57011i	0.291380	−	0.168228i
$739$	−4.99323	+	8.64853i	−0.183679	+	0.318141i	−0.943131	−	0.332422i	$-0.892134\pi$
$739$	−4.99323	+	8.64853i	−0.183679	+	0.318141i	0.759452	+	0.650564i	$0.225467\pi$
$740$	−1.55892	+	8.24763i	−0.0573069	+	0.303189i
$741$	−37.7651	−	16.8141i	−1.38734	−	0.617682i
$742$	−13.9894	+	19.2548i	−0.513569	+	0.706866i
$743$		−	4.45619i		−	0.163482i	−0.996654	−	0.0817408i	$-0.973952\pi$
$743$		−	4.45619i		−	0.163482i	0.996654	−	0.0817408i	$-0.0260480\pi$
$744$	−1.03675	−	5.47039i	−0.0380092	−	0.200554i
$745$	−12.0998	+	22.0976i	−0.443301	+	0.809592i
$746$	−10.6031	−	7.70358i	−0.388206	−	0.282048i
$747$	−5.57015	+	12.5108i	−0.203801	+	0.457745i
$748$	−27.3536	+	8.88773i	−1.00015	+	0.324968i
$749$	−16.8255	+	29.1427i	−0.614792	+	1.06485i
$750$	−6.23412	−	9.28094i	−0.227638	−	0.338892i
$751$	−5.65432	+	6.27976i	−0.206329	+	0.229152i	−0.837424	−	0.546554i	$-0.815939\pi$
$751$	−5.65432	+	6.27976i	−0.206329	+	0.229152i	0.631095	+	0.775706i	$0.282606\pi$
$752$	−3.10585	−	1.00915i	−0.113259	−	0.0367999i
$753$	21.6690	−	19.5109i	0.789663	−	0.711015i
$754$	−22.7783	+	10.1416i	−0.829537	+	0.369334i
$755$	20.6120	−	23.9607i	0.750146	−	0.872020i
$756$	0.302850	−	2.88143i	0.0110146	−	0.104797i
$757$	−40.1217	+	4.21696i	−1.45825	+	0.153268i	−0.800212	−	0.599717i	$-0.795280\pi$
$757$	−40.1217	+	4.21696i	−1.45825	+	0.153268i	−0.658037	+	0.752985i	$0.728613\pi$
$758$	1.10333	+	5.19078i	0.0400749	+	0.188537i
$759$	−32.3895	+	23.5323i	−1.17566	+	0.854170i
$760$	−16.5410	+	2.11795i	−0.600006	+	0.0768261i
$761$	−45.7688	+	9.72845i	−1.65912	+	0.352656i	−0.939720	−	0.341944i	$-0.888915\pi$
$761$	−45.7688	+	9.72845i	−1.65912	+	0.352656i	−0.719396	+	0.694600i	$0.755581\pi$
$762$	−2.48255	+	0.260926i	−0.0899331	+	0.00945235i
$763$	−5.25911	−	0.552755i	−0.190393	−	0.0200111i
$764$	−6.35293	−	1.35036i	−0.229841	−	0.0488542i
$765$	14.0366	+	1.15486i	0.507495	+	0.0417542i
$766$	−6.18364	−	6.86762i	−0.223424	−	0.248137i
$767$	−50.4489	−	16.3918i	−1.82160	−	0.591875i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	0.583429	+	1.01053i	0.0210390	+	0.0364406i	0.876353	−	0.481669i	$-0.159969\pi$
$769$	0.583429	+	1.01053i	0.0210390	+	0.0364406i	−0.855314	+	0.518110i	$0.826636\pi$
$770$	15.3675	+	25.2785i	0.553806	+	0.910974i
$771$	−7.19026	−	22.1294i	−0.258951	−	0.796969i
$772$	−6.94039	+	15.5884i	−0.249790	+	0.561038i
$773$	6.31038	−	8.68550i	0.226969	−	0.312396i	−0.680311	−	0.732924i	$-0.738155\pi$
$773$	6.31038	−	8.68550i	0.226969	−	0.312396i	0.907279	+	0.420528i	$0.138155\pi$
$774$	8.53477			0.306776
$775$	−11.9080	−	25.1635i	−0.427746	−	0.903899i
$776$	−1.72456			−0.0619081
$777$	−6.39262	+	8.79868i	−0.229334	+	0.315651i
$778$	7.06055	−	15.8583i	0.253133	−	0.568546i
$779$	−21.0643	−	64.8294i	−0.754708	−	2.32275i
$780$	6.43867	+	10.5912i	0.230541	+	0.379225i
$781$	26.3465	+	45.6335i	0.942753	+	1.63290i
$782$	41.0390	+	36.9517i	1.46755	+	1.32139i
$783$	−4.27804	−	1.39002i	−0.152885	−	0.0496753i
$784$	−0.933002	−	1.03620i	−0.0333215	−	0.0370073i
$785$	−34.7562	−	2.85957i	−1.24050	−	0.102063i
$786$	−9.88061	−	2.10019i	−0.352430	−	0.0749112i
$787$	21.0652	+	2.21404i	0.750892	+	0.0789219i	0.472240	−	0.881470i	$-0.343446\pi$
$787$	21.0652	+	2.21404i	0.750892	+	0.0789219i	0.278652	+	0.960392i	$0.410112\pi$
$788$	−26.6287	+	2.79879i	−0.948609	+	0.0997029i
$789$	−14.0095	+	2.97781i	−0.498752	+	0.106013i
$790$	−6.33551	+	0.811213i	−0.225407	+	0.0288617i
$791$	23.4562	−	17.0419i	0.834007	−	0.605942i
$792$	−0.949390	−	4.46653i	−0.0337351	−	0.158711i
$793$	−20.0069	+	2.10281i	−0.710465	+	0.0746728i
$794$	−1.58178	+	15.0496i	−0.0561353	+	0.534092i
$795$	11.9789	−	13.9251i	0.424847	−	0.493871i
$796$	−5.35870	+	2.38585i	−0.189934	+	0.0845642i
$797$	18.1045	−	16.3014i	0.641294	−	0.577424i	−0.282993	−	0.959122i	$-0.591327\pi$
$797$	18.1045	−	16.3014i	0.641294	−	0.577424i	0.924287	+	0.381698i	$0.124661\pi$
$798$	−20.5498	−	6.67705i	−0.727457	−	0.236365i
$799$	13.7634	−	15.2859i	0.486916	−	0.540775i
$800$	4.43880	+	2.30153i	0.156935	+	0.0813714i
$801$	0.561499	−	0.972545i	0.0198396	−	0.0343632i
$802$	−21.0051	+	6.82497i	−0.741716	+	0.240998i
$803$	−3.43000	+	7.70391i	−0.121042	+	0.271865i
$804$	−2.33162	−	1.69402i	−0.0822299	−	0.0597435i
$805$	27.2803	−	49.8215i	0.961506	−	1.75598i
$806$	11.9257	+	28.4654i	0.420066	+	1.00265i
$807$			4.55172i			0.160228i
$808$	0.199996	−	0.275271i	0.00703583	−	0.00968399i
$809$	−11.8092	−	5.25779i	−0.415189	−	0.184854i	0.188501	−	0.982073i	$-0.439637\pi$
$809$	−11.8092	−	5.25779i	−0.415189	−	0.184854i	−0.603690	+	0.797219i	$0.706304\pi$
$810$	−0.415294	+	2.19716i	−0.0145920	+	0.0772005i
$811$	21.5647	−	37.3511i	0.757238	−	1.31158i	−0.187015	−	0.982357i	$-0.559881\pi$
$811$	21.5647	−	37.3511i	0.757238	−	1.31158i	0.944254	−	0.329218i	$-0.106785\pi$
$812$	−11.2866	+	6.51632i	−0.396082	+	0.228678i
$813$	−23.6821	−	21.3235i	−0.830568	−	0.747847i
$814$	−5.29682	+	16.3019i	−0.185653	+	0.571382i
$815$	−5.00068	−	21.1600i	−0.175166	−	0.741202i
$816$	−5.75404	+	2.56186i	−0.201432	+	0.0896831i
$817$	13.2336	−	62.2594i	0.462986	−	2.17818i
$818$	11.0739	+	1.16391i	0.387189	+	0.0406952i
$819$	1.67873	+	15.9720i	0.0586595	+	0.558108i
$820$	−5.87429	+	19.5758i	−0.205139	+	0.683616i
$821$	−8.72460	+	6.33880i	−0.304491	+	0.221226i	−0.729529	−	0.683950i	$-0.760261\pi$
$821$	−8.72460	+	6.33880i	−0.304491	+	0.221226i	0.425038	+	0.905175i	$0.360261\pi$
$822$	1.07402	+	1.47826i	0.0374608	+	0.0515603i
$823$	3.15086	+	14.8236i	0.109832	+	0.516720i	0.998326	+	0.0578318i	$0.0184187\pi$
$823$	3.15086	+	14.8236i	0.109832	+	0.516720i	−0.888494	+	0.458888i	$0.848248\pi$
$824$	−0.264401	−	2.51560i	−0.00921083	−	0.0876352i
$825$	−10.2206	−	20.4162i	−0.355836	−	0.710800i
$826$	−27.1201	−	5.76455i	−0.943628	−	0.200574i
$827$	6.62516	+	14.8803i	0.230379	+	0.517440i	0.991334	−	0.131364i	$-0.0419358\pi$
$827$	6.62516	+	14.8803i	0.230379	+	0.517440i	−0.760955	+	0.648805i	$0.775269\pi$
$828$	−6.51559	+	5.86667i	−0.226433	+	0.203881i
$829$	2.49628	−	7.68275i	0.0866993	−	0.266833i	−0.898302	−	0.439378i	$-0.855199\pi$
$829$	2.49628	−	7.68275i	0.0866993	−	0.266833i	0.985002	+	0.172545i	$0.0551990\pi$
$830$	−10.1194	−	28.9020i	−0.351249	−	1.00320i
$831$	−8.45981	−	14.6528i	−0.293468	−	0.508301i
$832$	−4.80046	−	2.77155i	−0.166426	−	0.0960861i
$833$	8.35258	−	2.71392i	0.289400	−	0.0940317i
$834$	9.48960	+	4.22504i	0.328598	+	0.146301i
$835$	16.3350	+	34.5623i	0.565296	+	1.19608i
$836$	−34.0545			−1.17780
$837$	−1.83734	+	5.25587i	−0.0635077	+	0.181669i
$838$		−	17.9285i		−	0.619329i
$839$	11.8390	+	8.60153i	0.408728	+	0.296958i	0.773086	−	0.634301i	$-0.218712\pi$
$839$	11.8390	+	8.60153i	0.408728	+	0.296958i	−0.364359	+	0.931259i	$0.618712\pi$
$840$	3.92562	+	5.15376i	0.135447	+	0.177822i
$841$	−2.70890	−	8.33714i	−0.0934103	−	0.287487i
$842$	5.42718	+	3.13338i	0.187033	+	0.107983i
$843$	19.5903	−	11.3105i	0.674725	−	0.389553i
$844$	4.50509	−	5.00341i	0.155072	−	0.172224i
$845$	−27.1816	−	28.8479i	−0.935075	−	0.992396i
$846$	2.18517	+	2.42687i	0.0751276	+	0.0834376i
$847$	11.6091	+	26.0744i	0.398893	+	0.895928i
$848$	−1.70792	+	8.03512i	−0.0586501	+	0.275927i
$849$	−1.36134	+	12.9523i	−0.0467210	+	0.444521i
$850$	−24.6147	+	19.6448i	−0.844277	+	0.673812i
$851$	32.1923	−	6.84268i	1.10354	−	0.234564i
$852$	6.78275	+	9.33566i	0.232373	+	0.319834i
$853$	5.09309	+	7.01004i	0.174384	+	0.240019i	0.887258	−	0.461273i	$-0.152607\pi$
$853$	5.09309	+	7.01004i	0.174384	+	0.240019i	−0.712874	+	0.701292i	$0.752607\pi$
$854$	−10.2851	+	2.18617i	−0.351950	+	0.0748094i
$855$	15.3839	+	6.43631i	0.526119	+	0.220117i
$856$	−1.21406	+	11.5510i	−0.0414957	+	0.394805i
$857$	1.73396	−	8.15765i	0.0592310	−	0.278660i	−0.938558	−	0.345122i	$-0.887838\pi$
$857$	1.73396	−	8.15765i	0.0592310	−	0.278660i	0.997789	+	0.0664617i	$0.0211710\pi$
$858$	10.2951	+	23.1232i	0.351470	+	0.789414i
$859$	−27.9612	−	31.0540i	−0.954023	−	1.05955i	−0.998167	−	0.0605242i	$-0.980723\pi$
$859$	−27.9612	−	31.0540i	−0.954023	−	1.05955i	0.0441442	−	0.999025i	$-0.485944\pi$
$860$	−13.8898	+	13.0875i	−0.473639	+	0.446282i
$861$	−17.7199	+	19.6799i	−0.603893	+	0.670691i
$862$	27.7390	−	16.0151i	0.944794	−	0.545477i
$863$	−21.0934	−	12.1783i	−0.718029	−	0.414554i	0.0959976	−	0.995382i	$-0.469396\pi$
$863$	−21.0934	−	12.1783i	−0.718029	−	0.414554i	−0.814027	+	0.580827i	$0.802729\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	16.0530	+	21.0752i	0.545818	+	0.716577i
$866$	−13.5892	−	9.87317i	−0.461781	−	0.335504i
$867$		−	22.6721i		−	0.769984i
$868$	7.75449	+	14.1454i	0.263205	+	0.480127i
$869$	−13.0435			−0.442470
$870$	9.09378	−	4.29794i	0.308308	−	0.145714i
$871$	14.5943	+	6.49779i	0.494508	+	0.220169i
$872$	−1.73584	+	0.564010i	−0.0587831	+	0.0190998i
$873$	1.49351	+	0.862281i	0.0505478	+	0.0291838i
$874$	32.6933	+	56.6265i	1.10587	+	1.91542i
$875$	25.4874	+	19.9921i	0.861633	+	0.675856i
$876$	−0.570686	+	1.75639i	−0.0192817	+	0.0593430i
$877$	−25.6774	+	23.1201i	−0.867065	+	0.780709i	−0.977002	−	0.213230i	$-0.931602\pi$
$877$	−25.6774	+	23.1201i	−0.867065	+	0.780709i	0.109937	+	0.993939i	$0.464935\pi$
$878$	0.691072	+	1.55217i	0.0233225	+	0.0523833i
$879$	−3.03885	−	0.645927i	−0.102498	−	0.0217866i
$880$	8.39423	+	5.81318i	0.282969	+	0.195962i
$881$	−1.19868	−	11.4047i	−0.0403846	−	0.384234i	−0.995982	−	0.0895575i	$-0.971455\pi$
$881$	−1.19868	−	11.4047i	−0.0403846	−	0.384234i	0.955597	−	0.294677i	$-0.0952119\pi$
$882$	0.289902	+	1.36388i	0.00976150	+	0.0459242i
$883$	29.8327	+	41.0612i	1.00395	+	1.38182i	0.922870	+	0.385112i	$0.125837\pi$
$883$	29.8327	+	41.0612i	1.00395	+	1.38182i	0.0810806	+	0.996708i	$0.474163\pi$
$884$	28.2457	−	20.5217i	0.950006	−	0.690220i
$885$	20.4954	+	6.15024i	0.688944	+	0.206738i
$886$	1.48775	+	14.1550i	0.0499821	+	0.475548i
$887$	−8.11077	−	0.852476i	−0.272333	−	0.0286234i	−0.0326224	−	0.999468i	$-0.510386\pi$
$887$	−8.11077	−	0.852476i	−0.272333	−	0.0286234i	−0.239711	+	0.970844i	$0.577053\pi$
$888$	−0.780451	+	3.67173i	−0.0261902	+	0.123215i
$889$	6.60703	−	2.94164i	0.221593	−	0.0986595i
$890$	0.577532	+	2.44379i	0.0193589	+	0.0819159i
$891$	−1.41107	+	4.34282i	−0.0472726	+	0.145490i
$892$	7.34355	+	6.61216i	0.245880	+	0.221392i
$893$	21.0918	−	12.1773i	0.705809	−	0.407499i
$894$	−5.63341	+	9.75736i	−0.188409	+	0.326335i
$895$	0.0158904	+	0.00300351i	0.000531158	+	0.000100396i
$896$	−2.64682	−	1.17844i	−0.0884239	−	0.0393689i
$897$	28.5661	−	39.3179i	0.953796	−	1.31279i
$898$		−	8.40034i		−	0.280323i
$899$	23.9846	−	7.21010i	0.799932	−	0.240470i
$900$	−2.69335	−	4.21258i	−0.0897783	−	0.140419i
$901$	−41.8589	−	30.4123i	−1.39452	−	1.01318i
$902$	−16.9760	+	38.1288i	−0.565240	+	1.26955i
$903$	−23.5175	+	7.64131i	−0.782614	+	0.254287i
$904$	5.00353	−	8.66637i	0.166415	−	0.288239i
$905$	16.3359	−	0.369737i	0.543024	−	0.0122905i
$906$	9.45805	−	10.5042i	0.314223	−	0.348980i
$907$	−12.2118	−	3.96786i	−0.405487	−	0.131751i	0.0991706	−	0.995070i	$-0.468381\pi$
$907$	−12.2118	−	3.96786i	−0.405487	−	0.131751i	−0.504657	+	0.863320i	$0.668381\pi$
$908$	−9.80927	+	8.83231i	−0.325532	+	0.293110i
$909$	−0.310837	+	0.138394i	−0.0103098	+	0.00459022i
$910$	−27.2242	−	23.4193i	−0.902472	−	0.776343i
$911$	−3.49771	+	33.2785i	−0.115884	+	1.10257i	0.769802	+	0.638283i	$0.220355\pi$
$911$	−3.49771	+	33.2785i	−0.115884	+	1.10257i	−0.885687	+	0.464284i	$0.846312\pi$
$912$	−7.41691	+	0.779549i	−0.245598	+	0.0258134i
$913$	−13.0016	−	61.1679i	−0.430292	−	2.02436i
$914$	28.1799	−	20.4739i	0.932108	−	0.677216i
$915$	8.04945	−	1.03067i	0.266107	−	0.0340729i
$916$	2.45561	−	0.521956i	0.0811357	−	0.0172459i
$917$	29.1063	−	3.05920i	0.961175	−	0.101024i
$918$	6.26407	+	0.658381i	0.206745	+	0.0217298i
$919$	31.9273	+	6.78635i	1.05318	+	0.223861i	0.701802	−	0.712372i	$-0.252379\pi$
$919$	31.9273	+	6.78635i	1.05318	+	0.223861i	0.351381	+	0.936233i	$0.385712\pi$
$920$	1.60757	−	19.5389i	0.0529999	−	0.644179i
$921$	−14.2653	−	15.8432i	−0.470057	−	0.522052i
$922$	−12.0066	−	3.90117i	−0.395415	−	0.128478i
$923$	−47.5349	−	42.8007i	−1.56463	−	1.40880i
$924$	6.61499	+	11.4575i	0.217617	+	0.376924i
$925$	0.849168	+	18.7496i	0.0279205	+	0.616482i
$926$	−3.89355	−	11.9831i	−0.127950	−	0.393790i
$927$	−1.02882	+	2.31078i	−0.0337910	+	0.0758959i
$928$	−2.64398	+	3.63912i	−0.0867928	+	0.119460i
$929$	0.370801			0.0121656			0.00608280	−	0.999981i	$-0.498064\pi$
$929$	0.370801			0.0121656			0.00608280	+	0.999981i	$0.498064\pi$
$930$	−5.06940	−	11.3711i	−0.166232	−	0.372872i
$931$	10.3987			0.340805
$932$	0.881480	−	1.21325i	0.0288738	−	0.0397414i
$933$	−6.72622	+	15.1073i	−0.220207	+	0.494592i
$934$	−11.0435	−	33.9885i	−0.361356	−	1.11214i
$935$	−54.9541	+	33.4081i	−1.79719	+	1.09256i
$936$	2.77155	+	4.80046i	0.0905909	+	0.156908i
$937$	10.3950	+	9.35966i	0.339588	+	0.305767i	0.821225	−	0.570604i	$-0.193291\pi$
$937$	10.3950	+	9.35966i	0.339588	+	0.305767i	−0.481637	+	0.876371i	$0.659958\pi$
$938$	7.94145	+	2.58033i	0.259298	+	0.0842509i
$939$	13.6676	+	15.1794i	0.446024	+	0.495360i
$940$	−7.27769	−	0.598773i	−0.237372	−	0.0195298i
$941$	−10.0850	−	2.14364i	−0.328763	−	0.0698807i	0.0405733	−	0.999177i	$-0.487082\pi$
$941$	−10.0850	−	2.14364i	−0.328763	−	0.0698807i	−0.369336	+	0.929296i	$0.620415\pi$
$942$	−15.5105	−	1.63022i	−0.505361	−	0.0531155i
$943$	79.6988	−	8.37668i	2.59535	−	0.272782i
$944$	−9.36047	+	1.98963i	−0.304657	+	0.0647569i
$945$	−0.822812	−	6.42610i	−0.0267661	−	0.209041i
$946$	−31.5294	+	22.9074i	−1.02511	+	0.744785i
$947$	−0.745660	−	3.50805i	−0.0242307	−	0.113996i	0.964370	−	0.264557i	$-0.0852256\pi$
$947$	−0.745660	−	3.50805i	−0.0242307	−	0.113996i	−0.988601	+	0.150560i	$0.951892\pi$
$948$	−2.84081	+	0.298581i	−0.0922653	+	0.00969747i
$949$	1.07004	−	10.1808i	0.0347351	−	0.330483i
$950$	−34.9061	+	13.1156i	−1.13250	+	0.425526i
$951$	−26.0042	+	11.5778i	−0.843243	+	0.375436i
$952$	13.5616	−	12.2109i	0.439533	−	0.395757i
$953$	39.3677	+	12.7913i	1.27524	+	0.414352i	0.866903	−	0.498478i	$-0.166107\pi$
$953$	39.3677	+	12.7913i	1.27524	+	0.414352i	0.408341	+	0.912829i	$0.366107\pi$
$954$	5.49666	−	6.10466i	0.177961	−	0.197646i
$955$	−14.5192	+	0.328619i	−0.469831	+	0.0106339i
$956$	1.46101	−	2.53055i	0.0472526	−	0.0818439i
$957$	19.5349	−	6.34727i	0.631474	−	0.205178i
$958$	−13.8889	+	31.1950i	−0.448730	+	1.00787i
$959$	−4.28297	−	3.11176i	−0.138304	−	0.100484i
$960$	1.96129	+	1.07393i	0.0633005	+	0.0346609i
$961$	−8.26507	−	29.8779i	−0.266615	−	0.963803i
$962$		−	20.8074i		−	0.670859i
$963$	6.82691	−	9.39643i	0.219994	−	0.302796i
$964$	4.88020	+	2.17280i	0.157181	+	0.0699813i
$965$	−7.08642	+	37.4915i	−0.228120	+	1.20690i
$966$	12.7012	−	21.9991i	0.408654	−	0.707809i
$967$	−28.2510	+	16.3107i	−0.908490	+	0.524517i	−0.879945	−	0.475075i	$-0.842421\pi$
$967$	−28.2510	+	16.3107i	−0.908490	+	0.524517i	−0.0285451	+	0.999593i	$0.509087\pi$
$968$	7.32090	+	6.59177i	0.235303	+	0.211867i
$969$	14.5156	−	44.6743i	0.466307	−	1.43514i
$970$	−3.75286	+	0.886902i	−0.120497	+	0.0284767i
$971$	11.8774	−	5.28817i	0.381164	−	0.169705i	−0.207205	−	0.978298i	$-0.566437\pi$
$971$	11.8774	−	5.28817i	0.381164	−	0.169705i	0.588369	+	0.808592i	$0.299770\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	−29.9313	−	3.14591i	−0.959554	−	0.100853i
$974$	0.347840	+	3.30947i	0.0111455	+	0.106042i
$975$	19.4581	+	19.7365i	0.623159	+	0.632073i
$976$	−2.93609	+	2.13320i	−0.0939821	+	0.0682820i
$977$	11.0848	+	15.2570i	0.354635	+	0.488113i	0.948644	−	0.316345i	$-0.102456\pi$
$977$	11.0848	+	15.2570i	0.354635	+	0.488113i	−0.594009	+	0.804458i	$0.702456\pi$
$978$	−2.02167	−	9.51122i	−0.0646459	−	0.304135i
$979$	0.536019	+	5.09988i	0.0171312	+	0.162993i
$980$	−2.56322	−	1.77509i	−0.0818792	−	0.0567031i
$981$	1.78529	+	0.379475i	0.0570000	+	0.0121157i
$982$	4.99646	+	11.2222i	0.159443	+	0.358116i
$983$	−22.1404	+	19.9353i	−0.706168	+	0.635836i	−0.941865	−	0.335990i	$-0.890929\pi$
$983$	−22.1404	+	19.9353i	−0.706168	+	0.635836i	0.235698	+	0.971826i	$0.424262\pi$
$984$	−2.82448	+	8.69287i	−0.0900413	+	0.277119i
$985$	−56.5081	+	19.7851i	−1.80050	+	0.630404i
$986$	−14.1661	−	24.5365i	−0.451142	−	0.781400i
$987$	−8.19403	−	4.73083i	−0.260819	−	0.150584i
$988$	39.3158	−	12.7745i	1.25080	−	0.406410i
$989$	68.3600	+	30.4359i	2.17372	+	0.967804i
$990$	−4.36303	−	9.23148i	−0.138666	−	0.293396i
$991$	−42.9450			−1.36419			−0.682096	−	0.731263i	$-0.738931\pi$
$991$	−42.9450			−1.36419			−0.682096	+	0.731263i	$0.738931\pi$
$992$	4.43086	+	3.37157i	0.140680	+	0.107047i
$993$		−	2.66959i		−	0.0847168i
$994$	−27.0482	−	19.6517i	−0.857917	−	0.623313i
$995$	−10.4342	+	7.94776i	−0.330787	+	0.251961i
$996$	−4.23190	−	13.0245i	−0.134093	−	0.412696i
$997$	−34.1013	−	19.6884i	−1.08000	−	0.623538i	−0.149103	−	0.988822i	$-0.547639\pi$
$997$	−34.1013	−	19.6884i	−1.08000	−	0.623538i	−0.930896	+	0.365284i	$0.880972\pi$
$998$	25.4263	−	14.6799i	0.804855	−	0.464683i
$999$	2.51176	−	2.78959i	0.0794684	−	0.0882586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.b.19.3	✓	144
5.4	even	2	inner	930.2.bn.b.19.18	yes	144
31.18	even	15	inner	930.2.bn.b.49.18	yes	144
155.49	even	30	inner	930.2.bn.b.49.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.b.19.3	✓	144	1.1	even	1	trivial
930.2.bn.b.19.18	yes	144	5.4	even	2	inner
930.2.bn.b.49.3	yes	144	155.49	even	30	inner
930.2.bn.b.49.18	yes	144	31.18	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.16157 - 1.91070i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.15311 + 1.93867i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.16157 - 1.91070i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(2.15311 + 1.93867i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(2.22854 + 0.183353i) q^{10} +(4.46653 + 0.949390i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-5.51273 + 0.579411i) q^{13} +(-2.83399 + 0.602383i) q^{14} +(2.21796 - 0.283993i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.30955 - 6.16094i) q^{17} +(0.994522 - 0.104528i) q^{18} +(0.779549 - 7.41691i) q^{19} +(-1.45824 + 1.69515i) q^{20} +(-2.64682 + 1.17844i) q^{21} +(-3.39343 + 3.05546i) q^{22} +(8.33848 + 2.70934i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-2.30153 + 4.43880i) q^{25} +(2.77155 - 4.80046i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.17844 - 2.64682i) q^{28} +(-3.63912 - 2.64398i) q^{29} +(-1.07393 + 1.96129i) q^{30} +(-3.37157 + 4.43086i) q^{31} -1.00000i q^{32} +(-2.68401 + 3.69423i) q^{33} +(5.75404 + 2.56186i) q^{34} +(1.20323 - 6.36584i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.25085 - 1.87688i) q^{37} +(5.54220 + 4.99022i) q^{38} +(1.71291 - 5.27180i) q^{39} +(-0.514277 - 2.17612i) q^{40} +(8.35001 - 3.71766i) q^{41} +(0.602383 - 2.83399i) q^{42} +(8.48801 + 0.892126i) q^{43} +(-0.477310 - 4.54130i) q^{44} +(-0.642686 + 2.14172i) q^{45} +(-7.09313 + 5.15346i) q^{46} +(1.91952 + 2.64199i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(0.145749 + 1.38671i) q^{49} +(-2.23826 - 4.47104i) q^{50} +(6.16094 + 1.30955i) q^{51} +(2.25458 + 5.06387i) q^{52} +(6.10466 - 5.49666i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-3.37417 - 9.63697i) q^{55} +(1.44865 + 2.50914i) q^{56} +(6.45861 + 3.72888i) q^{57} +(4.27804 - 1.39002i) q^{58} +(8.74225 + 3.89230i) q^{59} +(-0.955480 - 2.02165i) q^{60} +3.62921 q^{61} +(-1.60288 - 5.33205i) q^{62} -2.89730i q^{63} +(0.809017 + 0.587785i) q^{64} +(7.51048 + 9.86013i) q^{65} +(-1.41107 - 4.34282i) q^{66} +(-2.49592 - 1.44102i) q^{67} +(-5.45473 + 3.14929i) q^{68} +(-5.86667 + 6.51559i) q^{69} +(4.44283 + 4.71519i) q^{70} +(7.72144 + 8.57552i) q^{71} +(-0.406737 - 0.913545i) q^{72} +(-0.383967 + 1.80642i) q^{73} +(-0.392375 + 3.73320i) q^{74} +(-3.11893 - 3.90798i) q^{75} +(-7.29479 + 1.55056i) q^{76} +(7.77639 + 10.7033i) q^{77} +(3.25815 + 4.48446i) q^{78} +(-2.79404 + 0.593891i) q^{79} +(2.06281 + 0.863035i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-1.90036 + 8.94049i) q^{82} +(-5.57015 - 12.5108i) q^{83} +(1.93867 + 2.15311i) q^{84} +(-10.2506 + 9.65849i) q^{85} +(-5.71087 + 6.34257i) q^{86} +(3.89556 - 2.24910i) q^{87} +(3.95455 + 2.28316i) q^{88} +(0.347026 + 1.06804i) q^{89} +(-1.35492 - 1.77881i) q^{90} +(-12.9928 - 9.43984i) q^{91} -8.76760i q^{92} +(-2.67645 - 4.88227i) q^{93} -3.26568 q^{94} +(-15.0770 + 7.12575i) q^{95} +(0.913545 + 0.406737i) q^{96} +(-1.64016 + 0.532919i) q^{97} +(-1.20754 - 0.697175i) q^{98} +(-2.28316 - 3.95455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9}+O(q^{10}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9	\( 144 q + 36 q^{4} + 2 q^{5} - 72 q^{6} - 18 q^{9} - 18 q^{11} - 8 q^{14} - 36 q^{16} - 24 q^{19} - 2 q^{20} + 28 q^{21} - 18 q^{24} + 10 q^{25} - 12 q^{26} - 4 q^{30} - 4 q^{31} + 10 q^{34} - 2 q^{35} - 72 q^{36} + 16 q^{39} + 4 q^{41} - 2 q^{44} - 2 q^{45} - 2 q^{46} - 78 q^{49} + 32 q^{50} + 10 q^{51} + 36 q^{54} - 50 q^{55} - 12 q^{56} + 28 q^{59} + 88 q^{61} + 36 q^{64} - 124 q^{65} + 6 q^{66} - 46 q^{69} - 10 q^{70} + 140 q^{71} + 34 q^{74} - 32 q^{75} + 24 q^{76} + 16 q^{79} + 12 q^{80} + 18 q^{81} - 8 q^{84} + 74 q^{85} - 98 q^{86} + 148 q^{89} + 44 q^{91} - 108 q^{94} - 80 q^{95} + 18 q^{96} - 2 q^{99}+O(q^{100}) \) 144 * q + 36 * q^4 + 2 * q^5 - 72 * q^6 - 18 * q^9 - 18 * q^11 - 8 * q^14 - 36 * q^16 - 24 * q^19 - 2 * q^20 + 28 * q^21 - 18 * q^24 + 10 * q^25 - 12 * q^26 - 4 * q^30 - 4 * q^31 + 10 * q^34 - 2 * q^35 - 72 * q^36 + 16 * q^39 + 4 * q^41 - 2 * q^44 - 2 * q^45 - 2 * q^46 - 78 * q^49 + 32 * q^50 + 10 * q^51 + 36 * q^54 - 50 * q^55 - 12 * q^56 + 28 * q^59 + 88 * q^61 + 36 * q^64 - 124 * q^65 + 6 * q^66 - 46 * q^69 - 10 * q^70 + 140 * q^71 + 34 * q^74 - 32 * q^75 + 24 * q^76 + 16 * q^79 + 12 * q^80 + 18 * q^81 - 8 * q^84 + 74 * q^85 - 98 * q^86 + 148 * q^89 + 44 * q^91 - 108 * q^94 - 80 * q^95 + 18 * q^96 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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