LMFDB - Embedded newform 930.2.bn.b.19.18

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			19.18
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.b.49.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.23550 + 0.0505968i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.15311 - 1.93867i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.23550 + 0.0505968i) 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} +(1.35492 - 1.77881i) 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} +(0.955480 - 2.02165i) 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} +(-0.642686 - 2.14172i) 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} +(4.99488 + 0.226218i) 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} +(-4.71519 - 4.44283i) 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} +(-2.11045 - 0.738927i) 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} +(-1.45824 - 1.69515i) 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} +(3.11893 - 3.90798i) 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} +(9.93687 + 2.34835i) 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} +(-2.21796 - 0.283993i) q^{60} +3.62921 q^{61} +(1.60288 + 5.33205i) q^{62} +2.89730i q^{63} +(0.809017 + 0.587785i) q^{64} +(12.3530 - 1.01634i) 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} +(-6.36584 + 1.20323i) 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} +(2.23826 - 4.47104i) 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} +(-1.83829 + 1.27306i) 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} +(2.61576 + 13.8390i) 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} +(-2.22854 + 0.183353i) q^{90} +(-12.9928 - 9.43984i) q^{91} +8.76760i q^{92} +(2.67645 + 4.88227i) q^{93} -3.26568 q^{94} +(2.11795 - 16.5410i) 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
$5$	2.23550	+	0.0505968i	0.999744	+	0.0226276i
$5$	2.23550	+	0.0505968i	0.999744	+	0.0226276i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−2.15311	−	1.93867i	−0.813801	−	0.732749i	0.153015	−	0.988224i	$-0.451102\pi$
$7$	−2.15311	−	1.93867i	−0.813801	−	0.732749i	−0.966816	+	0.255475i	$0.917768\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	1.35492	−	1.77881i	0.428465	−	0.562510i
$11$	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	0.697619	−	0.716469i	$-0.254243\pi$
$13$	5.51273	−	0.579411i	1.52896	−	0.160700i	0.831337	+	0.555769i	$0.187576\pi$
$14$	−2.83399	+	0.602383i	−0.757415	+	0.160994i
$15$	0.955480	−	2.02165i	0.246704	−	0.521987i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.30955	+	6.16094i	0.317612	+	1.49425i	0.790137	+	0.612930i	$0.210009\pi$
$17$	1.30955	+	6.16094i	0.317612	+	1.49425i	−0.472525	+	0.881317i	$0.656657\pi$
$18$	−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	$-0.293395\pi$
$20$	−0.642686	−	2.14172i	−0.143709	−	0.478903i
$21$	−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	−0.744033	−	0.668143i	$-0.767090\pi$
$23$	−8.33848	−	2.70934i	−1.73869	−	0.564936i	−0.994660	+	0.103207i	$0.967090\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	4.99488	+	0.226218i	0.998976	+	0.0452436i
$26$	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
$35$	−4.71519	−	4.44283i	−0.797012	−	0.750976i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.25085	+	1.87688i	−0.534437	+	0.308557i	−0.742821	−	0.669490i	$-0.766513\pi$
$37$	−3.25085	+	1.87688i	−0.534437	+	0.308557i	0.208385	+	0.978047i	$0.433179\pi$
$38$	−5.54220	−	4.99022i	−0.899063	−	0.809520i
$39$	1.71291	−	5.27180i	0.274285	−	0.844163i
$40$	−2.11045	−	0.738927i	−0.333691	−	0.116835i
$41$	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	−0.567839	−	0.823140i	$-0.692220\pi$
$43$	−8.48801	−	0.892126i	−1.29441	−	0.136048i	−0.726571	+	0.687092i	$0.758887\pi$
$44$	−0.477310	−	4.54130i	−0.0719572	−	0.684627i
$45$	−1.45824	−	1.69515i	−0.217381	−	0.252698i
$46$	−7.09313	+	5.15346i	−1.04583	+	0.759837i
$47$	−1.91952	−	2.64199i	−0.279991	−	0.385374i	0.645740	−	0.763557i	$-0.276549\pi$
$47$	−1.91952	−	2.64199i	−0.279991	−	0.385374i	−0.925731	+	0.378183i	$0.876549\pi$
$48$	0.207912	+	0.978148i	0.0300095	+	0.141183i
$49$	0.145749	+	1.38671i	0.0208213	+	0.198102i
$50$	3.11893	−	3.90798i	0.441083	−	0.552671i
$51$	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	−0.971737	−	0.236065i	$-0.924142\pi$
$53$	−6.10466	+	5.49666i	−0.838540	+	0.755025i	0.133198	+	0.991090i	$0.457476\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	9.93687	+	2.34835i	1.33989	+	0.316651i
$56$	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	$0.419277\pi$
$60$	−2.21796	−	0.283993i	−0.286337	−	0.0366633i
$61$	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
$65$	12.3530	−	1.01634i	1.53220	−	0.126062i
$66$	−1.41107	−	4.34282i	−0.173691	−	0.534565i
$67$	2.49592	+	1.44102i	0.304925	+	0.176049i	0.644653	−	0.764475i	$-0.277002\pi$
$67$	2.49592	+	1.44102i	0.304925	+	0.176049i	−0.339728	+	0.940524i	$0.610335\pi$
$68$	5.45473	−	3.14929i	0.661483	−	0.381907i
$69$	−5.86667	+	6.51559i	−0.706264	+	0.784385i
$70$	−6.36584	+	1.20323i	−0.760864	+	0.143814i
$71$	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	−0.949948	−	0.312407i	$-0.898865\pi$
$73$	0.383967	−	1.80642i	0.0449399	−	0.211426i	0.994888	+	0.100981i	$0.0321981\pi$
$74$	−0.392375	+	3.73320i	−0.0456126	+	0.433975i
$75$	2.23826	−	4.47104i	0.258452	−	0.516271i
$76$	−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	$0.484705\pi$
$80$	−1.83829	+	1.27306i	−0.205528	+	0.142332i
$81$	−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	$0.137382\pi$
$83$	5.57015	+	12.5108i	0.611403	+	1.37323i	−0.296895	+	0.954910i	$0.595951\pi$
$84$	1.93867	+	2.15311i	0.211527	+	0.234924i
$85$	2.61576	+	13.8390i	0.283720	+	1.50105i
$86$	−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	$0.881043\pi$
$90$	−2.22854	+	0.183353i	−0.234909	+	0.0193271i
$91$	−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
$95$	2.11795	−	16.5410i	0.217297	−	1.69707i
$96$	0.913545	+	0.406737i	0.0932383	+	0.0415124i
$97$	1.64016	−	0.532919i	0.166533	−	0.0541097i	−0.224564	−	0.974459i	$-0.572096\pi$
$97$	1.64016	−	0.532919i	0.166533	−	0.0541097i	0.391097	+	0.920350i	$0.372096\pi$
$98$	1.20754	+	0.697175i	0.121980	+	0.0704253i
$99$	−2.28316	−	3.95455i	−0.229466	−	0.397447i
$100$	−1.32836	−	4.82032i	−0.132836	−	0.482032i
$101$	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	0.957111	−	0.289722i	$-0.0935629\pi$
$103$	1.02882	+	2.31078i	0.101373	+	0.227688i	−0.855738	+	0.517410i	$0.826896\pi$
$104$	−5.42196	−	1.15247i	−0.531667	−	0.113009i
$105$	−5.97657	+	2.50047i	−0.583253	+	0.244021i
$106$	0.858663	+	8.16963i	0.0834007	+	0.793505i
$107$	−2.41482	−	11.3608i	−0.233449	−	1.09829i	−0.926176	−	0.377092i	$-0.876924\pi$
$107$	−2.41482	−	11.3608i	−0.233449	−	1.09829i	0.692727	−	0.721200i	$-0.256409\pi$
$108$	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	$0.327859\pi$
$110$	7.74060	−	6.65877i	0.738038	−	0.634889i
$111$	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	$0.222663\pi$
$113$	−2.08059	+	9.78839i	−0.195725	+	0.920814i	−0.960879	+	0.276967i	$0.910671\pi$
$114$	−6.81301	+	3.03335i	−0.638096	+	0.284099i
$115$	−18.5035	−	6.47861i	−1.72546	−	0.604133i
$116$	−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
$120$	−1.53344	+	1.62744i	−0.139983	+	0.148564i
$121$	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	−0.952972	−	0.303058i	$-0.901993\pi$
$127$	−1.01530	+	2.28041i	−0.0900937	+	0.202354i	0.862879	+	0.505411i	$0.168659\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−4.26738	+	7.39132i	−0.375722	+	0.650770i
$130$	6.43867	−	10.5912i	0.564709	−	0.928908i
$131$	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
$135$	−2.14172	+	0.642686i	−0.184330	+	0.0553136i
$136$	0.658381	−	6.26407i	0.0564557	−	0.537140i
$137$	1.81722	−	0.190998i	0.155256	−	0.0163180i	−0.0265816	−	0.999647i	$-0.508462\pi$
$137$	1.81722	−	0.190998i	0.155256	−	0.0163180i	0.181837	+	0.983329i	$0.441796\pi$
$138$	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	$0.445211\pi$
$140$	−2.76831	+	5.85732i	−0.233965	+	0.495034i
$141$	−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
$145$	−8.00146	−	6.09473i	−0.664485	−	0.506139i
$146$	−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	$0.986024\pi$
$150$	−2.30153	−	4.43880i	−0.187919	−	0.362427i
$151$	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
$155$	−7.76131	+	9.73458i	−0.623403	+	0.781900i
$156$	−5.54309			−0.443803
$157$	−9.16708	+	12.6174i	−0.731613	+	1.00698i	0.267445	+	0.963573i	$0.413821\pi$
$157$	−9.16708	+	12.6174i	−0.731613	+	1.00698i	−0.999058	+	0.0434055i	$0.986179\pi$
$158$	−1.16183	+	2.60951i	−0.0924300	+	0.207601i
$159$	2.53846	+	7.81258i	0.201313	+	0.619578i
$160$	−0.0505968	+	2.23550i	−0.00400003	+	0.176731i
$161$	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	−0.0764379	−	0.997074i	$-0.524355\pi$
$163$	−9.24779	−	3.00479i	−0.724343	−	0.235353i	−0.647905	+	0.761721i	$0.724355\pi$
$164$	−6.11600	−	6.79251i	−0.477580	−	0.530406i
$165$	6.18702	−	8.12263i	0.481659	−	0.632346i
$166$	13.3955	+	2.84729i	1.03969	+	0.220993i
$167$	17.0025	+	1.78703i	1.31569	+	0.138285i	0.736238	−	0.676722i	$-0.236600\pi$
$167$	17.0025	+	1.78703i	1.31569	+	0.138285i	0.579451	+	0.815007i	$0.303267\pi$
$168$	2.88143	−	0.302850i	0.222307	−	0.0233654i
$169$	17.3385	−	3.68542i	1.33373	−	0.283494i
$170$	12.7335	+	6.01817i	0.976615	+	0.461572i
$171$	−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	0.354595	−	0.935020i	$-0.384619\pi$
$173$	11.7830	−	1.23844i	0.895843	−	0.0941569i	0.541248	+	0.840863i	$0.317952\pi$
$174$	−0.470190	+	4.47356i	−0.0356450	+	0.339140i
$175$	−10.3160	−	10.1705i	−0.779815	−	0.768818i
$176$	−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	$0.233419\pi$
$180$	−1.16157	+	1.91070i	−0.0865780	+	0.142415i
$181$	−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
$190$	−12.1371	−	11.4360i	−0.880516	−	0.829657i
$191$	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	0.984469	−	0.175557i	$-0.0561727\pi$
$193$	12.6807	+	11.4178i	0.912779	+	0.821870i	−0.0716904	+	0.997427i	$0.522839\pi$
$194$	0.532919	−	1.64016i	0.0382613	−	0.117756i
$195$	4.09594	−	11.6984i	0.293316	−	0.837740i
$196$	1.27380	−	0.567133i	0.0909859	−	0.0405095i
$197$	−5.56692	+	26.1903i	−0.396627	+	1.86598i	0.0954564	+	0.995434i	$0.469569\pi$
$197$	−5.56692	+	26.1903i	−0.396627	+	1.86598i	−0.492083	+	0.870548i	$0.663764\pi$
$198$	−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	$-0.0999991\pi$
$200$	−4.68051	−	1.75865i	−0.330962	−	0.124355i
$201$	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
$205$	18.8545	−	7.88834i	1.31686	−	0.550945i
$206$	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
$210$	−1.49001	+	6.30489i	−0.102821	+	0.435079i
$211$	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
$215$	−18.9298	−	2.42381i	−1.29100	−	0.165302i
$216$	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
$220$	−0.837249	−	10.1762i	−0.0564473	−	0.686080i
$221$	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	−0.185302	−	0.982682i	$-0.559326\pi$
$223$	8.55782	−	4.94086i	0.573074	−	0.330864i	0.758376	+	0.651817i	$0.225993\pi$
$224$	1.93867	−	2.15311i	0.129533	−	0.143861i
$225$	−3.17411	−	3.86329i	−0.211608	−	0.257553i
$226$	6.69603	+	7.43670i	0.445414	+	0.494682i
$227$	5.36879	+	12.0585i	0.356339	+	0.800351i	0.999403	+	0.0345388i	$0.0109962\pi$
$227$	5.36879	+	12.0585i	0.356339	+	0.800351i	−0.643064	+	0.765812i	$0.722337\pi$
$228$	−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	$0.0597670\pi$
$230$	−16.1174	+	11.1617i	−1.06275	+	0.735978i
$231$	−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	0.779166	−	0.626817i	$-0.215643\pi$
$233$	−0.881480	−	1.21325i	−0.0577477	−	0.0794829i	−0.836914	+	0.547334i	$0.815643\pi$
$234$	−5.42196	+	1.15247i	−0.354445	+	0.0753396i
$235$	−4.15740	−	6.00328i	−0.271199	−	0.391611i
$236$	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	$0.736540\pi$
$240$	0.415294	+	2.19716i	0.0268071	+	0.141826i
$241$	−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
$245$	0.255659	+	3.10736i	0.0163334	+	0.198522i
$246$	−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
$250$	7.17009	−	8.57845i	0.453476	−	0.542549i
$251$	−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
$255$	13.7065	+	3.23921i	0.858334	+	0.202847i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	17.2916	−	15.5695i	1.07862	−	0.971196i	0.0789521	−	0.996878i	$-0.474843\pi$
$257$	17.2916	−	15.5695i	1.07862	−	0.971196i	0.999670	+	0.0256826i	$0.00817591\pi$
$258$	3.47140	+	7.79690i	0.216120	+	0.485414i
$259$	10.6381	+	2.26120i	0.661020	+	0.140504i
$260$	−4.78389	−	11.4343i	−0.296684	−	0.709127i
$261$	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	0.466312	−	0.884620i	$-0.345582\pi$
$263$	−8.41855	−	11.5871i	−0.519110	−	0.714494i	−0.985422	+	0.170127i	$0.945582\pi$
$264$	−3.69423	+	2.68401i	−0.227364	+	0.165190i
$265$	−13.9251	+	11.9789i	−0.855409	+	0.735857i
$266$	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	$0.322354\pi$
$270$	−0.738927	+	2.11045i	−0.0449696	+	0.128438i
$271$	−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
$275$	22.0950	+	5.75250i	1.33238	+	0.346889i
$276$	8.00960	+	3.56610i	0.482121	+	0.214654i
$277$	9.94511	−	13.6883i	0.597544	−	0.822448i	−0.397937	−	0.917413i	$-0.630274\pi$
$277$	9.94511	−	13.6883i	0.597544	−	0.822448i	0.995481	+	0.0949645i	$0.0302738\pi$
$278$			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	−0.653068	−	0.757299i	$-0.726519\pi$
$283$	−12.3862	+	4.02452i	−0.736283	+	0.239233i	−0.0832143	+	0.996532i	$0.526519\pi$
$284$	5.76975	−	9.99351i	0.342372	−	0.593005i
$285$	−14.2495	−	8.66268i	−0.844069	−	0.513133i
$286$	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
$290$	−9.63388	+	2.89093i	−0.565721	+	0.169761i
$291$	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	0.955244	−	0.295820i	$-0.0955927\pi$
$293$	−0.645927	−	3.03885i	−0.0377355	−	0.177531i	−0.992979	+	0.118288i	$0.962259\pi$
$294$	1.12805	−	0.819578i	0.0657894	−	0.0477988i
$295$	19.3463	+	9.14355i	1.12639	+	0.532358i
$296$	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
$300$	−4.94387	−	0.747086i	−0.285435	−	0.0431330i
$301$	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
$305$	8.11309	+	0.183627i	0.464554	+	0.0105144i
$306$	−1.94637	−	5.99030i	−0.111266	−	0.342443i
$307$	8.67128	−	19.4760i	0.494896	−	1.11155i	−0.477588	−	0.878584i	$-0.658489\pi$
$307$	8.67128	−	19.4760i	0.494896	−	1.11155i	0.972484	−	0.232971i	$-0.0748446\pi$
$308$	−7.77639	+	10.7033i	−0.443101	+	0.609876i
$309$	2.52946			0.143896
$310$	3.31346	+	12.0009i	0.188192	+	0.681604i
$311$	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	$0.329215\pi$
$313$	−8.30794	+	18.6599i	−0.469592	+	1.05472i	−0.980756	+	0.195238i	$0.937452\pi$
$314$	4.81942	+	14.8327i	0.271976	+	0.837055i
$315$	−0.146594	+	6.47690i	−0.00825965	+	0.364932i
$316$	1.42823	+	2.47377i	0.0803442	+	0.139160i
$317$	−21.1537	−	19.0469i	−1.18811	−	1.06978i	−0.996086	−	0.0883891i	$-0.971828\pi$
$317$	−21.1537	−	19.0469i	−1.18811	−	1.06978i	−0.192024	−	0.981390i	$-0.561505\pi$
$318$	7.81258	+	2.53846i	0.438108	+	0.142350i
$319$	−13.7441	−	15.2643i	−0.769521	−	0.854640i
$320$	1.77881	+	1.35492i	0.0994387	+	0.0757426i
$321$	−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
$325$	27.6665	−	1.64701i	1.53466	−	0.0913597i
$326$	−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
$330$	−2.93471	−	9.77976i	−0.161550	−	0.538358i
$331$	−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
$335$	5.50671	+	3.34768i	0.300863	+	0.182903i
$336$	1.44865	−	2.50914i	0.0790303	−	0.136885i
$337$	−12.1501	+	3.94780i	−0.661857	+	0.215050i	−0.620635	−	0.784100i	$-0.713125\pi$
$337$	−12.1501	+	3.94780i	−0.661857	+	0.215050i	−0.0412221	+	0.999150i	$0.513125\pi$
$338$	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
$345$	−13.4446	+	14.2687i	−0.723832	+	0.768203i
$346$	5.92394	−	10.2606i	0.318473	−	0.551611i
$347$	1.16381	−	0.671925i	0.0624765	−	0.0360708i	−0.468436	−	0.883497i	$-0.655182\pi$
$347$	1.16381	−	0.671925i	0.0624765	−	0.0360708i	0.530913	+	0.847426i	$0.321849\pi$
$348$	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	$0.141637\pi$
$350$	−14.2917	+	2.36773i	−0.763923	+	0.126561i
$351$	−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	0.638440	−	0.769671i	$-0.279580\pi$
$353$	20.7217	+	2.17794i	1.10291	+	0.115920i	0.464465	+	0.885591i	$0.346247\pi$
$354$	−1.00029	−	9.51716i	−0.0531650	−	0.505831i
$355$	16.8273	+	19.5612i	0.893103	+	1.03820i
$356$	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	$0.817997\pi$
$360$	0.863035	+	2.06281i	0.0454860	+	0.108719i
$361$	−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
$365$	0.949756	−	4.01882i	0.0497125	−	0.210355i
$366$	−1.81461	−	3.14299i	−0.0948510	−	0.164287i
$367$	−15.6596	−	9.04106i	−0.817423	−	0.471940i	0.0321038	−	0.999485i	$-0.489779\pi$
$367$	−15.6596	−	9.04106i	−0.817423	−	0.471940i	−0.849527	+	0.527545i	$0.823113\pi$
$368$	8.33848	−	2.70934i	0.434673	−	0.141234i
$369$	−8.35001	−	3.71766i	−0.434684	−	0.193534i
$370$	−1.06604	+	8.32569i	−0.0554208	+	0.432832i
$371$	23.8003			1.23565
$372$	3.81625	−	4.05416i	0.197863	−	0.210199i
$373$		−	13.1061i		−	0.678609i	−0.940677	−	0.339304i	$-0.889808\pi$
$373$		−	13.1061i		−	0.678609i	0.940677	−	0.339304i	$-0.110192\pi$
$374$	23.2684	+	16.9055i	1.20318	+	0.874161i
$375$	5.22984	−	9.88174i	0.270068	−	0.510291i
$376$	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	$0.189814\pi$
$380$	−16.3859	+	3.09717i	−0.840581	+	0.158881i
$381$	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	$-0.857463\pi$
$383$	1.92137	−	9.03935i	0.0981776	−	0.461889i	0.999582	−	0.0289112i	$-0.00920399\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−16.8425	−	24.3206i	−0.858375	−	1.23949i
$386$	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	$0.578379\pi$
$390$	−7.05668	−	10.1898i	−0.357329	−	0.515982i
$391$	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
$395$	−6.27611	+	1.18627i	−0.315785	+	0.0596878i
$396$	−3.05546	+	3.39343i	−0.153543	+	0.170526i
$397$	−13.1052	+	7.56627i	−0.657729	+	0.379740i	−0.791411	−	0.611284i	$-0.790653\pi$
$397$	−13.1052	+	7.56627i	−0.657729	+	0.379740i	0.133682	+	0.991024i	$0.457320\pi$
$398$	−5.07996	−	2.93292i	−0.254635	−	0.147014i
$399$	6.67705	+	20.5498i	0.334271	+	1.02878i
$400$	−4.17391	+	2.75290i	−0.208696	+	0.137645i
$401$	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
$405$	−0.283993	+	2.21796i	−0.0141117	+	0.110211i
$406$	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	$0.922108\pi$
$410$	4.70061	−	19.8903i	0.232146	−	0.982310i
$411$	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
$415$	11.8190	+	28.2496i	0.580174	+	1.38672i
$416$	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	$0.444289\pi$
$420$	4.22495	+	4.91137i	0.206157	+	0.239650i
$421$	−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
$425$	5.14732	+	31.0694i	0.249682	+	1.50709i
$426$	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
$430$	−13.0875	+	13.8898i	−0.631138	+	0.669827i
$431$	−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	$-0.867755\pi$
$433$		−	16.7972i		−	0.807223i	0.914930	−	0.403612i	$-0.132245\pi$
$434$	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	$0.153757\pi$
$440$	−8.72485	−	5.30408i	−0.415941	−	0.252862i
$441$	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	−0.880991	−	0.473134i	$-0.843123\pi$
$443$	−10.5772	+	9.52374i	−0.502537	+	0.452487i	0.378453	+	0.925620i	$0.376456\pi$
$444$	3.42923	−	1.52679i	0.162744	−	0.0724583i
$445$	0.721735	+	2.40515i	0.0342135	+	0.114015i
$446$	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	$0.363515\pi$
$450$	−4.99116	+	0.297128i	−0.235286	+	0.0140068i
$451$	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
$455$	−28.5678	−	21.7601i	−1.33928	−	1.02013i
$456$	4.99022	+	5.54220i	0.233688	+	0.259537i
$457$	33.1274	+	10.7638i	1.54964	+	0.503507i	0.954015	−	0.299758i	$-0.0969060\pi$
$457$	33.1274	+	10.7638i	1.54964	+	0.503507i	0.595621	+	0.803266i	$0.296906\pi$
$458$	1.86564	+	1.67983i	0.0871758	+	0.0784934i
$459$	−3.14929	−	5.45473i	−0.146996	−	0.254605i
$460$	−0.443612	+	19.5999i	−0.0206835	+	0.913851i
$461$	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	−0.601473	−	0.798893i	$-0.705419\pi$
$463$	7.40598	−	10.1935i	0.344185	−	0.473730i	0.945658	+	0.325163i	$0.105419\pi$
$464$	4.49820			0.208824
$465$	5.73617	+	11.0497i	0.266009	+	0.512419i
$466$	−1.49966			−0.0694706
$467$	21.0061	−	28.9124i	0.972045	−	1.33790i	0.0310373	−	0.999518i	$-0.490119\pi$
$467$	21.0061	−	28.9124i	0.972045	−	1.33790i	0.941007	−	0.338386i	$-0.109881\pi$
$468$	−2.25458	+	5.06387i	−0.104218	+	0.234077i
$469$	−2.58033	−	7.94145i	−0.119149	−	0.366702i
$470$	−7.30041	−	0.165233i	−0.336743	−	0.00762163i
$471$	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
$475$	5.57159	−	36.8702i	0.255642	−	1.69172i
$476$	−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	$0.148495\pi$
$480$	2.02165	+	0.955480i	0.0922751	+	0.0436115i
$481$	−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
$485$	3.69352	−	1.10835i	0.167714	−	0.0503276i
$486$	0.913545	−	0.406737i	0.0414393	−	0.0184499i
$487$	−2.47297	+	2.22667i	−0.112061	+	0.100900i	−0.723256	−	0.690580i	$-0.757356\pi$
$487$	−2.47297	+	2.22667i	−0.112061	+	0.100900i	0.611196	+	0.791480i	$0.290689\pi$
$488$	−3.45159	−	1.12149i	−0.156246	−	0.0507674i
$489$	−6.50643	+	7.22612i	−0.294231	+	0.326776i
$490$	2.66418	+	1.61963i	0.120355	+	0.0731674i
$491$	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	$0.861576\pi$
$500$	−2.72564	−	10.8430i	−0.121894	−	0.484914i
$501$	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	0.492344	−	0.870401i	$-0.336140\pi$
$503$	−7.21776	−	6.49890i	−0.321824	−	0.289772i	−0.814168	+	0.580629i	$0.802807\pi$
$504$	0.895315	−	2.75550i	0.0398805	−	0.122740i
$505$	0.251422	−	0.718087i	0.0111881	−	0.0319544i
$506$	−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	$-0.150394\pi$
$510$	10.6771	−	9.18482i	0.472788	−	0.406711i
$511$	−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
$515$	2.18301	+	5.21779i	0.0961951	+	0.229923i
$516$	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
$520$	−12.0625	−	2.85068i	−0.528974	−	0.125011i
$521$	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	0.0270411	−	0.999634i	$-0.491392\pi$
$523$	14.5560	−	4.72952i	0.636488	−	0.206808i	0.609447	+	0.792827i	$0.291392\pi$
$524$	−9.22804	−	4.10859i	−0.403129	−	0.179484i
$525$	−13.4871	+	5.28740i	−0.588626	+	0.230761i
$526$	−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
$530$	1.50618	+	18.3066i	0.0654243	+	0.795189i
$531$	−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
$535$	−4.82349	−	25.5193i	−0.208538	−	1.10329i
$536$	−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
$540$	1.27306	+	1.83829i	0.0547837	+	0.0791076i
$541$	−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
$545$	−3.35521	+	2.32355i	−0.143721	+	0.0995301i
$546$	−1.67873	+	15.9720i	−0.0718429	+	0.683540i
$547$	−5.33193	+	25.0848i	−0.227977	+	1.07255i	0.704048	+	0.710152i	$0.251374\pi$
$547$	−5.33193	+	25.0848i	−0.227977	+	1.07255i	−0.932025	+	0.362394i	$0.881959\pi$
$548$	−0.743202	−	1.66926i	−0.0317480	−	0.0713073i
$549$	−2.42842	−	2.69703i	−0.103642	−	0.115106i
$550$	17.6410	−	14.4940i	0.752215	−	0.618027i
$551$	−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
$555$	0.688264	+	8.36540i	0.0292152	+	0.355091i
$556$	8.40379	+	6.10571i	0.356400	+	0.258940i
$557$			33.7147i			1.42854i	0.699872	+	0.714268i	$0.253240\pi$
$557$			33.7147i			1.42854i	−0.699872	+	0.714268i	$0.746760\pi$
$558$	2.88995	−	4.75901i	0.122341	−	0.201465i
$559$	−47.3090			−2.00096
$560$	6.42610	+	0.822812i	0.271552	+	0.0347701i
$561$	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	0.205714	−	0.978612i	$-0.434048\pi$
$563$	−12.7876	−	7.38290i	−0.538932	−	0.311152i	−0.744646	+	0.667460i	$0.767382\pi$
$564$	1.63284	+	2.82816i	0.0687550	+	0.119087i
$565$	−5.14640	+	21.7766i	−0.216511	+	0.916150i
$566$	−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	$0.523857\pi$
$570$	−15.3839	+	6.43631i	−0.644362	+	0.269588i
$571$	−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
$575$	−41.0368	−	15.4191i	−1.71135	−	0.643022i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−39.6354	−	4.16585i	−1.65004	−	0.173427i	−0.766652	−	0.642062i	$-0.778079\pi$
$577$	−39.6354	−	4.16585i	−1.65004	−	0.173427i	−0.883391	+	0.468636i	$0.844746\pi$
$578$	−4.71379	+	22.1766i	−0.196068	+	0.922427i
$579$	15.5884	−	6.94039i	0.647831	−	0.288433i
$580$	−3.32384	+	9.49322i	−0.138015	+	0.394184i
$581$	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
$585$	−9.02106	−	8.50000i	−0.372975	−	0.351432i
$586$	−2.83815	−	1.26362i	−0.117243	−	0.0521998i
$587$	22.8597	−	31.4637i	0.943522	−	1.29865i	−0.0108237	−	0.999941i	$-0.503445\pi$
$587$	22.8597	−	31.4637i	0.943522	−	1.29865i	0.954346	−	0.298705i	$-0.0965546\pi$
$588$		−	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	−0.503986	−	0.863712i	$-0.668134\pi$
$593$	−9.83908	+	3.19691i	−0.404043	+	0.131281i	0.0999435	+	0.994993i	$0.468134\pi$
$594$	−2.28316	+	3.95455i	−0.0936791	+	0.162257i
$595$	21.1973	−	34.8681i	0.869003	−	1.42945i
$596$	−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	$0.391631\pi$
$600$	−3.51034	+	3.56055i	−0.143309	+	0.145359i
$601$	−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
$605$	19.9157	+	9.41267i	0.809690	+	0.382679i
$606$	−0.332818	+	0.0707427i	−0.0135198	+	0.00287372i
$607$	−31.3377	+	3.29372i	−1.27196	+	0.133688i	−0.716341	−	0.697751i	$-0.754184\pi$
$607$	−31.3377	+	3.29372i	−1.27196	+	0.133688i	−0.555617	+	0.831439i	$0.687518\pi$
$608$	7.41691	+	0.779549i	0.300795	+	0.0316149i
$609$	12.7478	+	2.70964i	0.516569	+	0.109800i
$610$	4.91731	−	6.45569i	0.199096	−	0.261383i
$611$	−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	$-0.994074\pi$
$613$	−27.8005	−	25.0317i	−1.12285	−	1.01102i	−0.123026	−	0.992403i	$-0.539260\pi$
$614$	−10.6596	−	18.4629i	−0.430185	−	0.745103i
$615$	0.462466	−	20.4329i	0.0186484	−	0.823935i
$616$	4.08829	+	12.5825i	0.164722	+	0.506962i
$617$	8.86939	−	19.9210i	0.357068	−	0.801988i	−0.642300	−	0.766453i	$-0.722020\pi$
$617$	8.86939	−	19.9210i	0.357068	−	0.801988i	0.999368	−	0.0355351i	$-0.0113136\pi$
$618$	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	$0.372882\pi$
$620$	11.6565	+	4.37329i	0.468137	+	0.175636i
$621$	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
$625$	24.8977	+	2.25986i	0.995906	+	0.0903945i
$626$	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
$630$	5.15376	+	3.92562i	0.205331	+	0.156401i
$631$	−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
$635$	−2.38509	+	5.04648i	−0.0946494	+	0.200263i
$636$	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
$640$	2.14172	−	0.642686i	0.0846588	−	0.0254044i
$641$	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	0.475499	−	0.879716i	$-0.342268\pi$
$643$	8.70016	+	2.82685i	0.343101	+	0.111480i	−0.132398	+	0.991197i	$0.542268\pi$
$644$	16.9975	−	18.8776i	0.669795	−	0.743883i
$645$	−9.91369	+	16.3074i	−0.390351	+	0.642102i
$646$	23.4867	−	40.6801i	0.924070	−	1.60054i
$647$	−20.3458	+	6.61077i	−0.799878	+	0.259896i	−0.680305	−	0.732929i	$-0.738153\pi$
$647$	−20.3458	+	6.61077i	−0.799878	+	0.259896i	−0.119573	+	0.992825i	$0.538153\pi$
$648$	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	−0.718449	−	0.695579i	$-0.755148\pi$
$653$	4.21891	−	5.80683i	0.165099	−	0.227239i	0.883548	+	0.468340i	$0.155148\pi$
$654$	1.66738	+	0.742366i	0.0651997	+	0.0290288i
$655$	15.4898	−	16.4393i	0.605237	−	0.642338i
$656$	−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	$0.954810\pi$
$660$	−9.63697	−	3.37417i	−0.375119	−	0.131339i
$661$	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
$665$	−36.6278	+	31.5087i	−1.42037	+	1.22185i
$666$	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
$670$	5.94509	−	2.48730i	0.229679	−	0.0960929i
$671$	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	−0.108745	−	0.994070i	$-0.534683\pi$
$673$	22.5311	−	20.2871i	0.868512	−	0.782011i	0.977257	+	0.212058i	$0.0680167\pi$
$674$	−3.94780	+	12.1501i	−0.152064	+	0.468004i
$675$	−4.82032	+	1.32836i	−0.185534	+	0.0511285i
$676$	−8.86295	−	15.3511i	−0.340883	−	0.590426i
$677$	−30.7750	−	17.7679i	−1.18278	−	0.682878i	−0.226123	−	0.974099i	$-0.572605\pi$
$677$	−30.7750	−	17.7679i	−1.18278	−	0.682878i	−0.956656	+	0.291221i	$0.905938\pi$
$678$	9.51729	−	3.09235i	0.365509	−	0.118761i
$679$	−4.56460	−	2.03229i	−0.175173	−	0.0779921i
$680$	1.78875	−	13.9700i	0.0685954	−	0.535725i
$681$	13.1997			0.505813
$682$	2.09714	+	25.3375i	0.0803035	+	0.970224i
$683$			44.0443i			1.68531i	0.538454	+	0.842655i	$0.319009\pi$
$683$			44.0443i			1.68531i	−0.538454	+	0.842655i	$0.680991\pi$
$684$	6.03346	+	4.38356i	0.230695	+	0.167610i
$685$	4.07206	−	0.335029i	0.155585	−	0.0128008i
$686$	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
$690$	3.64113	+	19.2638i	0.138616	+	0.733362i
$691$	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
$695$	−19.0956	+	13.2241i	−0.724336	+	0.501618i
$696$	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
$700$	−6.48491	+	12.9539i	−0.245107	+	0.489613i
$701$	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
$705$	−7.17524	+	1.35622i	−0.270235	+	0.0510782i
$706$	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	$0.894369\pi$
$710$	25.7162	−	2.11581i	0.965113	−	0.0794048i
$711$	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
$715$	56.1400	+	7.18828i	2.09952	+	0.268827i
$716$	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	$0.620427\pi$
$720$	2.17612	+	0.514277i	0.0810994	+	0.0191660i
$721$	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
$725$	−17.5789	−	14.0296i	−0.652862	−	0.521045i
$726$	−1.02974	−	9.79728i	−0.0382171	−	0.363611i
$727$	0.555532	+	2.61357i	0.0206035	+	0.0969321i	0.987248	−	0.159190i	$-0.0508883\pi$
$727$	0.555532	+	2.61357i	0.0206035	+	0.0969321i	−0.966644	+	0.256122i	$0.917555\pi$
$728$	9.43984	+	12.9928i	0.349864	+	0.481546i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−2.69304	−	3.13057i	−0.0996740	−	0.115868i
$731$	−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	$-0.865664\pi$
$733$	2.37533	−	11.1751i	0.0877349	−	0.412760i	0.999995	−	0.00314890i	$-0.00100233\pi$
$734$	−16.5188	+	7.35466i	−0.609722	+	0.271466i
$735$	2.94270	+	1.03032i	0.108543	+	0.0380040i
$736$	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	$0.225467\pi$
$740$	6.10902	+	5.75616i	0.224572	+	0.211601i
$741$	−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	$0.0260480\pi$
$743$			4.45619i			0.163482i	−0.996654	+	0.0817408i	$0.973952\pi$
$744$	−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
$750$	−4.92047	−	10.0394i	−0.179670	−	0.366586i
$751$	−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
$755$	9.08426	+	30.2728i	0.330610	+	1.10174i
$756$	0.302850	−	2.88143i	0.0110146	−	0.104797i
$757$	40.1217	−	4.21696i	1.45825	−	0.153268i	0.658037	−	0.752985i	$-0.271387\pi$
$757$	40.1217	−	4.21696i	1.45825	−	0.153268i	0.800212	+	0.599717i	$0.204720\pi$
$758$	−1.10333	−	5.19078i	−0.0400749	−	0.188537i
$759$	−32.3895	+	23.5323i	−1.17566	+	0.854170i
$760$	−7.12575	+	15.0770i	−0.258478	+	0.546899i
$761$	−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
$765$	8.53410	−	11.2040i	0.308551	−	0.405081i
$766$	−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	$0.826636\pi$
$770$	−29.5756	−	0.669395i	−1.06583	−	0.0241233i
$771$	−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	−0.907279	−	0.420528i	$-0.861845\pi$
$773$	−6.31038	+	8.68550i	−0.226969	+	0.312396i	0.680311	+	0.732924i	$0.261845\pi$
$774$	8.53477			0.306776
$775$	−17.8429	+	21.3689i	−0.640936	+	0.767594i
$776$	−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
$780$	−12.3916	−	0.280463i	−0.443689	−	0.0100422i
$781$	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
$785$	−21.1314	+	27.7423i	−0.754211	+	0.990166i
$786$	−9.88061	−	2.10019i	−0.352430	−	0.0749112i
$787$	−21.0652	−	2.21404i	−0.750892	−	0.0789219i	−0.278652	−	0.960392i	$-0.589888\pi$
$787$	−21.0652	−	2.21404i	−0.750892	−	0.0789219i	−0.472240	+	0.881470i	$0.656554\pi$
$788$	26.6287	−	2.79879i	0.948609	−	0.0997029i
$789$	−14.0095	+	2.97781i	−0.498752	+	0.106013i
$790$	−2.72929	+	5.77475i	−0.0971038	+	0.205457i
$791$	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
$795$	5.27943	+	17.5934i	0.187242	+	0.623974i
$796$	−5.35870	+	2.38585i	−0.189934	+	0.0845642i
$797$	−18.1045	+	16.3014i	−0.641294	+	0.577424i	−0.924287	−	0.381698i	$-0.875339\pi$
$797$	−18.1045	+	16.3014i	−0.641294	+	0.577424i	0.282993	+	0.959122i	$0.408673\pi$
$798$	20.5498	+	6.67705i	0.727457	+	0.236365i
$799$	13.7634	−	15.2859i	0.486916	−	0.540775i
$800$	−0.226218	+	4.99488i	−0.00799801	+	0.176596i
$801$	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	$0.706304\pi$
$810$	1.62744	+	1.53344i	0.0571824	+	0.0538796i
$811$	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
$815$	−20.5214	−	7.18510i	−0.718832	−	0.251683i
$816$	−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
$820$	−13.3286	−	15.4941i	−0.465456	−	0.541077i
$821$	−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	$-0.981581\pi$
$823$	−3.15086	−	14.8236i	−0.109832	−	0.516720i	0.888494	−	0.458888i	$-0.151752\pi$
$824$	−0.264401	−	2.51560i	−0.00921083	−	0.0876352i
$825$	14.2420	−	17.8450i	0.495844	−	0.621285i
$826$	−27.1201	−	5.76455i	−0.943628	−	0.200574i
$827$	−6.62516	−	14.8803i	−0.230379	−	0.517440i	0.760955	−	0.648805i	$-0.224731\pi$
$827$	−6.62516	−	14.8803i	−0.230379	−	0.517440i	−0.991334	+	0.131364i	$0.958064\pi$
$828$	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	$0.0551990\pi$
$830$	29.8014	+	7.04288i	1.03442	+	0.244462i
$831$	−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
$835$	37.9185	+	4.85517i	1.31222	+	0.168020i
$836$	−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	$0.618712\pi$
$840$	6.45674	−	0.531230i	0.222779	−	0.0183292i
$841$	−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
$845$	38.9467	−	7.36147i	1.33981	−	0.253242i
$846$	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
$850$	28.1612	+	14.0979i	0.965921	+	0.483553i
$851$	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	0.712874	−	0.701292i	$-0.247393\pi$
$853$	−5.09309	−	7.01004i	−0.174384	−	0.240019i	−0.887258	+	0.461273i	$0.847393\pi$
$854$	−10.2851	+	2.18617i	−0.351950	+	0.0748094i
$855$	−13.7096	+	9.49416i	−0.468857	+	0.324694i
$856$	−1.21406	+	11.5510i	−0.0414957	+	0.394805i
$857$	−1.73396	+	8.15765i	−0.0592310	+	0.278660i	−0.997789	−	0.0664617i	$-0.978829\pi$
$857$	−1.73396	+	8.15765i	−0.0592310	+	0.278660i	0.938558	+	0.345122i	$0.112162\pi$
$858$	−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	$-0.485944\pi$
$860$	3.54444	+	18.7523i	0.120864	+	0.639448i
$861$	−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	0.814027	−	0.580827i	$-0.197271\pi$
$863$	21.0934	+	12.1783i	0.718029	+	0.414554i	−0.0959976	+	0.995382i	$0.530604\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	26.4034	−	2.17235i	0.897744	−	0.0738620i
$866$	−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
$870$	−1.27746	+	9.97683i	−0.0433098	+	0.338246i
$871$	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
$875$	−22.5467	−	23.2581i	−0.762219	−	0.786267i
$876$	−0.570686	+	1.75639i	−0.0192817	+	0.0593430i
$877$	25.6774	−	23.1201i	0.867065	−	0.780709i	−0.109937	−	0.993939i	$-0.535065\pi$
$877$	25.6774	−	23.1201i	0.867065	−	0.780709i	0.977002	+	0.213230i	$0.0683983\pi$
$878$	−0.691072	−	1.55217i	−0.0233225	−	0.0523833i
$879$	−3.03885	−	0.645927i	−0.102498	−	0.0217866i
$880$	−9.41943	+	3.94089i	−0.317529	+	0.132847i
$881$	−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	$-0.874163\pi$
$883$	−29.8327	−	41.0612i	−1.00395	−	1.38182i	−0.0810806	−	0.996708i	$-0.525837\pi$
$884$	28.2457	−	20.5217i	0.950006	−	0.690220i
$885$	16.2219	−	13.9547i	0.545294	−	0.469083i
$886$	1.48775	+	14.1550i	0.0499821	+	0.475548i
$887$	8.11077	+	0.852476i	0.272333	+	0.0286234i	0.239711	−	0.970844i	$-0.422947\pi$
$887$	8.11077	+	0.852476i	0.272333	+	0.0286234i	0.0326224	+	0.999468i	$0.489614\pi$
$888$	0.780451	−	3.67173i	0.0261902	−	0.123215i
$889$	6.60703	−	2.94164i	0.221593	−	0.0986595i
$890$	2.37003	+	0.829814i	0.0794436	+	0.0278154i
$891$	−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
$895$	−0.0110902	+	0.0117701i	−0.000370705	+	0.000393429i
$896$	−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
$905$	−8.48816	+	13.9624i	−0.282156	+	0.464127i
$906$	9.45805	−	10.5042i	0.314223	−	0.348980i
$907$	12.2118	+	3.96786i	0.405487	+	0.131751i	0.504657	−	0.863320i	$-0.331619\pi$
$907$	12.2118	+	3.96786i	0.405487	+	0.131751i	−0.0991706	+	0.995070i	$0.531619\pi$
$908$	9.80927	−	8.83231i	0.325532	−	0.293110i
$909$	−0.310837	+	0.138394i	−0.0103098	+	0.00459022i
$910$	−34.3960	+	10.3215i	−1.14022	+	0.342156i
$911$	−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
$915$	3.46764	−	7.33699i	0.114637	−	0.242553i
$916$	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	$0.385712\pi$
$920$	15.5959	+	11.8794i	0.514182	+	0.391653i
$921$	−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
$925$	−16.6622	+	8.63939i	−0.547850	+	0.284061i
$926$	−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	$0.498064\pi$
$930$	12.3110	+	1.85420i	0.403695	+	0.0608017i
$931$	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
$935$	−1.45523	+	64.2958i	−0.0475911	+	2.10270i
$936$	2.77155	+	4.80046i	0.0905909	+	0.156908i
$937$	−10.3950	−	9.35966i	−0.339588	−	0.305767i	0.481637	−	0.876371i	$-0.340042\pi$
$937$	−10.3950	−	9.35966i	−0.339588	−	0.305767i	−0.821225	+	0.570604i	$0.806709\pi$
$938$	−7.94145	−	2.58033i	−0.259298	−	0.0842509i
$939$	13.6676	+	15.1794i	0.446024	+	0.495360i
$940$	−4.42475	+	5.80904i	−0.144319	+	0.189470i
$941$	−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
$945$	5.85732	+	2.76831i	0.190539	+	0.0900533i
$946$	−31.5294	+	22.9074i	−1.02511	+	0.744785i
$947$	0.745660	+	3.50805i	0.0242307	+	0.113996i	0.988601	−	0.150560i	$-0.0481077\pi$
$947$	0.745660	+	3.50805i	0.0242307	+	0.113996i	−0.964370	+	0.264557i	$0.914774\pi$
$948$	2.84081	−	0.298581i	0.0922653	−	0.00969747i
$949$	1.07004	−	10.1808i	0.0347351	−	0.330483i
$950$	−26.5537	−	26.1793i	−0.861517	−	0.849368i
$951$	−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	−0.408341	−	0.912829i	$-0.633893\pi$
$953$	−39.3677	−	12.7913i	−1.27524	−	0.414352i	−0.866903	+	0.498478i	$0.833893\pi$
$954$	5.49666	−	6.10466i	0.177961	−	0.197646i
$955$	7.54421	−	12.4097i	0.244125	−	0.401569i
$956$	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
$965$	27.7700	+	26.1660i	0.893948	+	0.842313i
$966$	12.7012	−	21.9991i	0.408654	−	0.707809i
$967$	28.2510	−	16.3107i	0.908490	−	0.524517i	0.0285451	−	0.999593i	$-0.490913\pi$
$967$	28.2510	−	16.3107i	0.908490	−	0.524517i	0.879945	+	0.475075i	$0.157579\pi$
$968$	−7.32090	−	6.59177i	−0.235303	−	0.211867i
$969$	14.5156	−	44.6743i	0.466307	−	1.43514i
$970$	1.27432	−	3.63960i	0.0409161	−	0.116860i
$971$	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
$975$	9.74836	−	25.9445i	0.312197	−	0.830889i
$976$	−2.93609	+	2.13320i	−0.0939821	+	0.0682820i
$977$	−11.0848	−	15.2570i	−0.354635	−	0.488113i	0.594009	−	0.804458i	$-0.297544\pi$
$977$	−11.0848	−	15.2570i	−0.354635	−	0.488113i	−0.948644	+	0.316345i	$0.897544\pi$
$978$	2.02167	+	9.51122i	0.0646459	+	0.304135i
$979$	0.536019	+	5.09988i	0.0171312	+	0.162993i
$980$	2.87627	−	1.20337i	0.0918792	−	0.0384404i
$981$	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	−0.235698	−	0.971826i	$-0.575738\pi$
$983$	22.1404	−	19.9353i	0.706168	−	0.635836i	0.941865	+	0.335990i	$0.109071\pi$
$984$	−2.82448	+	8.69287i	−0.0900413	+	0.277119i
$985$	−13.7700	+	58.2666i	−0.438748	+	1.85653i
$986$	−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
$990$	−10.1279	−	1.29680i	−0.321886	−	0.0412150i
$991$	−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
$995$	−1.07552	−	13.0722i	−0.0340963	−	0.414417i
$996$	−4.23190	−	13.0245i	−0.134093	−	0.412696i
$997$	34.1013	+	19.6884i	1.08000	+	0.623538i	0.930896	−	0.365284i	$-0.119028\pi$
$997$	34.1013	+	19.6884i	1.08000	+	0.623538i	0.149103	+	0.988822i	$0.452361\pi$
$998$	−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.19.18	yes	144
5.4	even	2	inner	930.2.bn.b.19.3	✓	144
31.18	even	15	inner	930.2.bn.b.49.3	yes	144
155.49	even	30	inner	930.2.bn.b.49.18	yes	144

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

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.23550 + 0.0505968i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-2.15311 - 1.93867i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(0.406737 - 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(2.23550 + 0.0505968i) 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} +(1.35492 - 1.77881i) 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} +(0.955480 - 2.02165i) 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} +(-0.642686 - 2.14172i) 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} +(4.99488 + 0.226218i) 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} +(-4.71519 - 4.44283i) 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} +(-2.11045 - 0.738927i) 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} +(-1.45824 - 1.69515i) 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} +(3.11893 - 3.90798i) 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} +(9.93687 + 2.34835i) 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} +(-2.21796 - 0.283993i) q^{60} +3.62921 q^{61} +(1.60288 + 5.33205i) q^{62} +2.89730i q^{63} +(0.809017 + 0.587785i) q^{64} +(12.3530 - 1.01634i) 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} +(-6.36584 + 1.20323i) 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} +(2.23826 - 4.47104i) 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} +(-1.83829 + 1.27306i) 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} +(2.61576 + 13.8390i) 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} +(-2.22854 + 0.183353i) q^{90} +(-12.9928 - 9.43984i) q^{91} +8.76760i q^{92} +(2.67645 + 4.88227i) q^{93} -3.26568 q^{94} +(2.11795 - 16.5410i) 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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