LMFDB - Embedded newform 990.2.bg.a.31.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	990.31
Dual form			990.2.bg.a.511.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.978148 + 0.207912i) q^{2} +(-0.556540 + 1.64020i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(0.203361 - 1.72007i) q^{6} +(-0.187148 + 1.78059i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.38053 - 1.82568i) q^{9} +1.00000 q^{10} +(0.353783 - 3.29770i) q^{11} +(0.158706 + 1.72476i) q^{12} +(-0.773058 - 0.858568i) q^{13} +(-0.187148 - 1.78059i) q^{14} +(0.885395 - 1.48865i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-0.205402 - 0.632163i) q^{17} +(2.70809 + 1.29084i) q^{18} +(6.00955 - 4.36619i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(-2.81637 - 1.29793i) q^{21} +(0.339579 + 3.29919i) q^{22} +(0.235796 - 0.408411i) q^{23} +(-0.513836 - 1.65408i) q^{24} +(0.913545 + 0.406737i) q^{25} +(0.934671 + 0.679078i) q^{26} +(4.31934 - 2.88848i) q^{27} +(0.553263 + 1.70277i) q^{28} +(-0.468178 + 4.45442i) q^{29} +(-0.556540 + 1.64020i) q^{30} +(-1.37070 - 1.52231i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.21200 + 2.41558i) q^{33} +(0.332348 + 0.575644i) q^{34} +(0.553263 - 1.70277i) q^{35} +(-2.91729 - 0.699591i) q^{36} +(6.06151 + 4.40394i) q^{37} +(-4.97044 + 5.52023i) q^{38} +(1.83846 - 0.790144i) q^{39} +(0.913545 - 0.406737i) q^{40} +(-1.01150 - 9.62375i) q^{41} +(3.02468 + 0.684009i) q^{42} +(1.58215 + 2.74037i) q^{43} +(-1.01810 - 3.15650i) q^{44} +(1.94893 + 2.28072i) q^{45} +(-0.145730 + 0.448511i) q^{46} +(-6.03753 - 2.68808i) q^{47} +(0.846510 + 1.51110i) q^{48} +(3.71156 + 0.788916i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(1.15119 + 0.0149228i) q^{51} +(-1.05543 - 0.469910i) q^{52} +(2.19708 - 6.76191i) q^{53} +(-3.62440 + 3.72340i) q^{54} +(-1.03168 + 3.15208i) q^{55} +(-0.895199 - 1.55053i) q^{56} +(3.81688 + 12.2868i) q^{57} +(-0.468178 - 4.45442i) q^{58} +(4.12929 - 1.83848i) q^{59} +(0.203361 - 1.72007i) q^{60} +(-3.18831 + 3.54098i) q^{61} +(1.65725 + 1.20406i) q^{62} +(3.69629 - 3.89707i) q^{63} +(0.309017 - 0.951057i) q^{64} +(0.577658 + 1.00053i) q^{65} +(-5.60034 - 1.27916i) q^{66} +(-2.69441 + 4.66686i) q^{67} +(-0.444768 - 0.493965i) q^{68} +(0.538647 + 0.614051i) q^{69} +(-0.187148 + 1.78059i) q^{70} +(0.791178 + 2.43500i) q^{71} +(2.99899 + 0.0777646i) q^{72} +(9.59377 + 6.97028i) q^{73} +(-6.84468 - 3.04745i) q^{74} +(-1.17555 + 1.27203i) q^{75} +(3.71410 - 6.43302i) q^{76} +(5.80564 + 1.24710i) q^{77} +(-1.63401 + 1.15511i) q^{78} +(1.25204 - 0.266129i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(2.33381 + 8.69214i) q^{81} +(2.99028 + 9.20314i) q^{82} +(5.84440 - 6.49087i) q^{83} +(-3.10080 - 0.0401955i) q^{84} +(0.0694797 + 0.661055i) q^{85} +(-2.11734 - 2.35154i) q^{86} +(-7.04559 - 3.24697i) q^{87} +(1.65212 + 2.87585i) q^{88} +10.3715 q^{89} +(-2.38053 - 1.82568i) q^{90} +(1.67343 - 1.21582i) q^{91} +(0.0492949 - 0.469009i) q^{92} +(3.25975 - 1.40099i) q^{93} +(6.46448 + 1.37407i) q^{94} +(-6.78600 + 3.02132i) q^{95} +(-1.14219 - 1.30208i) q^{96} +(14.1368 - 3.00487i) q^{97} -3.79448 q^{98} +(-6.86273 + 7.20437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$3$	−0.556540	+	1.64020i	−0.321318	+	0.946971i
$3$	−0.556540	+	1.64020i	−0.321318	+	0.946971i
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	−0.978148	−	0.207912i	−0.437441	−	0.0929809i
$5$	−0.978148	−	0.207912i	−0.437441	−	0.0929809i
$6$	0.203361	−	1.72007i	0.0830218	−	0.702216i
$7$	−0.187148	+	1.78059i	−0.0707351	+	0.673000i	0.900497	+	0.434863i	$0.143203\pi$
$7$	−0.187148	+	1.78059i	−0.0707351	+	0.673000i	−0.971232	+	0.238137i	$0.923463\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−2.38053	−	1.82568i	−0.793509	−	0.608559i
$10$	1.00000			0.316228
$11$	0.353783	−	3.29770i	0.106670	−	0.994295i
$11$	0.353783	−	3.29770i	0.106670	−	0.994295i
$12$	0.158706	+	1.72476i	0.0458144	+	0.497897i
$13$	−0.773058	−	0.858568i	−0.214408	−	0.238124i	0.626341	−	0.779549i	$-0.284552\pi$
$13$	−0.773058	−	0.858568i	−0.214408	−	0.238124i	−0.840749	+	0.541425i	$0.817885\pi$
$14$	−0.187148	−	1.78059i	−0.0500173	−	0.475883i
$15$	0.885395	−	1.48865i	0.228608	−	0.384367i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	−0.205402	−	0.632163i	−0.0498174	−	0.153322i	0.923053	−	0.384673i	$-0.125686\pi$
$17$	−0.205402	−	0.632163i	−0.0498174	−	0.153322i	−0.972870	+	0.231350i	$0.925686\pi$
$18$	2.70809	+	1.29084i	0.638302	+	0.304254i
$19$	6.00955	−	4.36619i	1.37868	−	1.00167i	0.381683	−	0.924293i	$-0.375345\pi$
$19$	6.00955	−	4.36619i	1.37868	−	1.00167i	0.997002	−	0.0773794i	$-0.0246553\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	−2.81637	−	1.29793i	−0.614583	−	0.283231i
$22$	0.339579	+	3.29919i	0.0723985	+	0.703391i
$23$	0.235796	−	0.408411i	0.0491670	−	0.0851597i	−0.840395	−	0.541975i	$-0.817677\pi$
$23$	0.235796	−	0.408411i	0.0491670	−	0.0851597i	0.889561	+	0.456815i	$0.151010\pi$
$24$	−0.513836	−	1.65408i	−0.104886	−	0.337637i
$25$	0.913545	+	0.406737i	0.182709	+	0.0813473i
$26$	0.934671	+	0.679078i	0.183304	+	0.133178i
$27$	4.31934	−	2.88848i	0.831257	−	0.555889i
$28$	0.553263	+	1.70277i	0.104557	+	0.321793i
$29$	−0.468178	+	4.45442i	−0.0869386	+	0.827165i	0.860977	+	0.508644i	$0.169853\pi$
$29$	−0.468178	+	4.45442i	−0.0869386	+	0.827165i	−0.947916	+	0.318521i	$0.896814\pi$
$30$	−0.556540	+	1.64020i	−0.101610	+	0.299459i
$31$	−1.37070	−	1.52231i	−0.246184	−	0.273416i	0.607370	−	0.794419i	$-0.292225\pi$
$31$	−1.37070	−	1.52231i	−0.246184	−	0.273416i	−0.853555	+	0.521003i	$0.825558\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.21200	+	2.41558i	0.907293	+	0.420498i
$34$	0.332348	+	0.575644i	0.0569972	+	0.0987221i
$35$	0.553263	−	1.70277i	0.0935186	−	0.287821i
$36$	−2.91729	−	0.699591i	−0.486215	−	0.116598i
$37$	6.06151	+	4.40394i	0.996506	+	0.724004i	0.961336	−	0.275378i	$-0.0888029\pi$
$37$	6.06151	+	4.40394i	0.996506	+	0.724004i	0.0351695	+	0.999381i	$0.488803\pi$
$38$	−4.97044	+	5.52023i	−0.806312	+	0.895500i
$39$	1.83846	−	0.790144i	0.294390	−	0.126524i
$40$	0.913545	−	0.406737i	0.144444	−	0.0643107i
$41$	−1.01150	−	9.62375i	−0.157969	−	1.50298i	−0.730398	−	0.683022i	$-0.760665\pi$
$41$	−1.01150	−	9.62375i	−0.157969	−	1.50298i	0.572429	−	0.819955i	$-0.306001\pi$
$42$	3.02468	+	0.684009i	0.466719	+	0.105545i
$43$	1.58215	+	2.74037i	0.241276	+	0.417903i	0.961078	−	0.276277i	$-0.0891007\pi$
$43$	1.58215	+	2.74037i	0.241276	+	0.417903i	−0.719802	+	0.694180i	$0.755767\pi$
$44$	−1.01810	−	3.15650i	−0.153484	−	0.475860i
$45$	1.94893	+	2.28072i	0.290529	+	0.339990i
$46$	−0.145730	+	0.448511i	−0.0214867	+	0.0661294i
$47$	−6.03753	−	2.68808i	−0.880665	−	0.392097i	−0.0839623	−	0.996469i	$-0.526758\pi$
$47$	−6.03753	−	2.68808i	−0.880665	−	0.392097i	−0.796702	+	0.604372i	$0.793424\pi$
$48$	0.846510	+	1.51110i	0.122183	+	0.218108i
$49$	3.71156	+	0.788916i	0.530223	+	0.112702i
$50$	−0.978148	−	0.207912i	−0.138331	−	0.0294032i
$51$	1.15119	+	0.0149228i	0.161199	+	0.00208961i
$52$	−1.05543	−	0.469910i	−0.146362	−	0.0651647i
$53$	2.19708	−	6.76191i	0.301792	−	0.928820i	−0.679063	−	0.734080i	$-0.737614\pi$
$53$	2.19708	−	6.76191i	0.301792	−	0.928820i	0.980855	−	0.194740i	$-0.0623863\pi$
$54$	−3.62440	+	3.72340i	−0.493218	+	0.506691i
$55$	−1.03168	+	3.15208i	−0.139112	+	0.425027i
$56$	−0.895199	−	1.55053i	−0.119626	−	0.207198i
$57$	3.81688	+	12.2868i	0.505559	+	1.62743i
$58$	−0.468178	−	4.45442i	−0.0614748	−	0.584894i
$59$	4.12929	−	1.83848i	0.537588	−	0.239350i	−0.119938	−	0.992781i	$-0.538270\pi$
$59$	4.12929	−	1.83848i	0.537588	−	0.239350i	0.657526	+	0.753432i	$0.271603\pi$
$60$	0.203361	−	1.72007i	0.0262538	−	0.222060i
$61$	−3.18831	+	3.54098i	−0.408222	+	0.453376i	−0.911837	−	0.410552i	$-0.865336\pi$
$61$	−3.18831	+	3.54098i	−0.408222	+	0.453376i	0.503616	+	0.863928i	$0.332003\pi$
$62$	1.65725	+	1.20406i	0.210471	+	0.152916i
$63$	3.69629	−	3.89707i	0.465689	−	0.490985i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.577658	+	1.00053i	0.0716497	+	0.124101i
$66$	−5.60034	−	1.27916i	−0.689354	−	0.157453i
$67$	−2.69441	+	4.66686i	−0.329175	+	0.570148i	−0.982348	−	0.187061i	$-0.940104\pi$
$67$	−2.69441	+	4.66686i	−0.329175	+	0.570148i	0.653174	+	0.757208i	$0.273437\pi$
$68$	−0.444768	−	0.493965i	−0.0539361	−	0.0599021i
$69$	0.538647	+	0.614051i	0.0648455	+	0.0739231i
$70$	−0.187148	+	1.78059i	−0.0223684	+	0.212821i
$71$	0.791178	+	2.43500i	0.0938956	+	0.288981i	0.986964	−	0.160939i	$-0.0514524\pi$
$71$	0.791178	+	2.43500i	0.0938956	+	0.288981i	−0.893069	+	0.449920i	$0.851452\pi$
$72$	2.99899	+	0.0777646i	0.353435	+	0.00916465i
$73$	9.59377	+	6.97028i	1.12287	+	0.815810i	0.984641	−	0.174591i	$-0.0558605\pi$
$73$	9.59377	+	6.97028i	1.12287	+	0.815810i	0.138224	+	0.990401i	$0.455860\pi$
$74$	−6.84468	−	3.04745i	−0.795678	−	0.354259i
$75$	−1.17555	+	1.27203i	−0.135741	+	0.146882i
$76$	3.71410	−	6.43302i	0.426037	−	0.737918i
$77$	5.80564	+	1.24710i	0.661615	+	0.142120i
$78$	−1.63401	+	1.15511i	−0.185015	+	0.130791i
$79$	1.25204	−	0.266129i	0.140866	−	0.0299419i	−0.136939	−	0.990579i	$-0.543727\pi$
$79$	1.25204	−	0.266129i	0.140866	−	0.0299419i	0.277805	+	0.960638i	$0.410393\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	2.33381	+	8.69214i	0.259313	+	0.965793i
$82$	2.99028	+	9.20314i	0.330221	+	1.01632i
$83$	5.84440	−	6.49087i	0.641506	−	0.712465i	−0.331445	−	0.943475i	$-0.607536\pi$
$83$	5.84440	−	6.49087i	0.641506	−	0.712465i	0.972952	+	0.231009i	$0.0742028\pi$
$84$	−3.10080	−	0.0401955i	−0.338325	−	0.00438569i
$85$	0.0694797	+	0.661055i	0.00753613	+	0.0717015i
$86$	−2.11734	−	2.35154i	−0.228318	−	0.253573i
$87$	−7.04559	−	3.24697i	−0.755367	−	0.348112i
$88$	1.65212	+	2.87585i	0.176117	+	0.306566i
$89$	10.3715			1.09937			0.549687	−	0.835371i	$-0.314747\pi$
$89$	10.3715			1.09937			0.549687	+	0.835371i	$0.314747\pi$
$90$	−2.38053	−	1.82568i	−0.250930	−	0.192443i
$91$	1.67343	−	1.21582i	0.175423	−	0.127453i
$92$	0.0492949	−	0.469009i	0.00513935	−	0.0488976i
$93$	3.25975	−	1.40099i	0.338020	−	0.145276i
$94$	6.46448	+	1.37407i	0.666760	+	0.141724i
$95$	−6.78600	+	3.02132i	−0.696229	+	0.309981i
$96$	−1.14219	−	1.30208i	−0.116574	−	0.132893i
$97$	14.1368	−	3.00487i	1.43537	−	0.305098i	0.576421	−	0.817153i	$-0.304449\pi$
$97$	14.1368	−	3.00487i	1.43537	−	0.305098i	0.858953	+	0.512054i	$0.171115\pi$
$98$	−3.79448			−0.383300
$99$	−6.86273	+	7.20437i	−0.689730	+	0.724067i
$100$	1.00000			0.100000
$101$	0.318091	−	0.0676123i	0.0316512	−	0.00672768i	−0.192059	−	0.981383i	$-0.561516\pi$
$101$	0.318091	−	0.0676123i	0.0316512	−	0.00672768i	0.223710	+	0.974656i	$0.428183\pi$
$102$	−1.12914	+	0.224749i	−0.111801	+	0.0222535i
$103$	5.44443	−	2.42402i	0.536456	−	0.238846i	−0.120582	−	0.992703i	$-0.538476\pi$
$103$	5.44443	−	2.42402i	0.536456	−	0.238846i	0.657038	+	0.753858i	$0.271809\pi$
$104$	1.13007	+	0.240204i	0.110812	+	0.0235539i
$105$	2.48497	+	1.85512i	0.242509	+	0.181041i
$106$	−0.743186	+	7.07095i	−0.0721846	+	0.686791i
$107$	−8.37103	+	6.08191i	−0.809258	+	0.587960i	−0.913615	−	0.406580i	$-0.866721\pi$
$107$	−8.37103	+	6.08191i	−0.809258	+	0.587960i	0.104358	+	0.994540i	$0.466721\pi$
$108$	2.77106	−	4.39559i	0.266645	−	0.422966i
$109$	12.5629			1.20330			0.601652	−	0.798758i	$-0.294509\pi$
$109$	12.5629			1.20330			0.601652	+	0.798758i	$0.294509\pi$
$110$	0.353783	−	3.29770i	0.0337319	−	0.314424i
$111$	−10.5968	+	7.49113i	−1.00581	+	0.711026i
$112$	1.19801	+	1.33052i	0.113201	+	0.125723i
$113$	0.511572	+	4.86728i	0.0481247	+	0.457875i	0.991875	+	0.127217i	$0.0406043\pi$
$113$	0.511572	+	4.86728i	0.0481247	+	0.457875i	−0.943750	+	0.330659i	$0.892729\pi$
$114$	−6.28805	−	11.2248i	−0.588930	−	1.05129i
$115$	−0.315557	+	0.350462i	−0.0294259	+	0.0326807i
$116$	1.38407	+	4.25974i	0.128508	+	0.395507i
$117$	0.272818	+	3.45520i	0.0252220	+	0.319433i
$118$	−3.65682	+	2.65683i	−0.336637	+	0.244581i
$119$	1.16406	−	0.247429i	0.106710	−	0.0226818i
$120$	0.158706	+	1.72476i	0.0144878	+	0.157449i
$121$	−10.7497	−	2.33334i	−0.977243	−	0.212122i
$122$	2.38243	−	4.12649i	0.215695	−	0.373595i
$123$	16.3478	+	3.69694i	1.47403	+	0.333342i
$124$	−1.87137	−	0.833190i	−0.168054	−	0.0748226i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	−2.80527	+	4.58041i	−0.249913	+	0.408055i
$127$	−4.77869	−	14.7073i	−0.424040	−	1.30506i	−0.903910	−	0.427723i	$-0.859316\pi$
$127$	−4.77869	−	14.7073i	−0.424040	−	1.30506i	0.479870	−	0.877340i	$-0.340684\pi$
$128$	−0.104528	+	0.994522i	−0.00923910	+	0.0879041i
$129$	−5.37530	+	1.06993i	−0.473269	+	0.0942018i
$130$	−0.773058	−	0.858568i	−0.0678016	−	0.0753014i
$131$	−1.38991	+	2.40739i	−0.121437	+	0.210335i	−0.920335	−	0.391132i	$-0.872084\pi$
$131$	−1.38991	+	2.40739i	−0.121437	+	0.210335i	0.798898	+	0.601467i	$0.205417\pi$
$132$	5.74391	+	0.0868277i	0.499943	+	0.00755738i
$133$	6.64972	+	11.5177i	0.576604	+	0.998707i
$134$	1.66524	−	5.12508i	0.143855	−	0.442739i
$135$	−4.82550	+	1.92732i	−0.415313	+	0.165877i
$136$	0.537750	+	0.390699i	0.0461117	+	0.0335021i
$137$	11.0971	−	12.3245i	0.948086	−	1.05296i	−0.0504421	−	0.998727i	$-0.516063\pi$
$137$	11.0971	−	12.3245i	0.948086	−	1.05296i	0.998528	−	0.0542296i	$-0.0172703\pi$
$138$	−0.654545	−	0.488642i	−0.0557186	−	0.0415959i
$139$	−8.76956	+	3.90446i	−0.743824	+	0.331172i	−0.743417	−	0.668828i	$-0.766796\pi$
$139$	−8.76956	+	3.90446i	−0.743824	+	0.331172i	−0.000407196		1.00000i	$0.500130\pi$
$140$	−0.187148	−	1.78059i	−0.0158169	−	0.150487i
$141$	7.76913	−	8.40675i	0.654279	−	0.707976i
$142$	−1.28015	−	2.21729i	−0.107428	−	0.186071i
$143$	−3.10479	+	2.24557i	−0.259636	+	0.187784i
$144$	−2.94962	+	0.547460i	−0.245802	+	0.0456217i
$145$	1.38407	−	4.25974i	0.114941	−	0.353752i
$146$	−10.8333	−	4.82331i	−0.896572	−	0.399180i
$147$	−3.35961	+	5.64864i	−0.277096	+	0.465892i
$148$	7.32871	+	1.55776i	0.602416	+	0.128047i
$149$	−6.56139	−	1.39467i	−0.537530	−	0.114256i	−0.0688559	−	0.997627i	$-0.521935\pi$
$149$	−6.56139	−	1.39467i	−0.537530	−	0.114256i	−0.468674	+	0.883371i	$0.655268\pi$
$150$	0.885395	−	1.48865i	0.0722922	−	0.121548i
$151$	−8.53865	−	3.80165i	−0.694866	−	0.309374i	0.0287408	−	0.999587i	$-0.490850\pi$
$151$	−8.53865	−	3.80165i	−0.694866	−	0.309374i	−0.723606	+	0.690213i	$0.757517\pi$
$152$	−2.29544	+	7.06464i	−0.186185	+	0.573018i
$153$	−0.665160	+	1.87988i	−0.0537750	+	0.151979i
$154$	−5.93806	−	0.0127853i	−0.478503	−	0.00103027i
$155$	1.02424	+	1.77403i	0.0822687	+	0.142494i
$156$	1.35814	−	1.46960i	0.108738	−	0.117662i
$157$	−0.446642	−	4.24951i	−0.0356459	−	0.339148i	−0.997781	−	0.0665763i	$-0.978792\pi$
$157$	−0.446642	−	4.24951i	−0.0356459	−	0.339148i	0.962135	−	0.272572i	$-0.0878742\pi$
$158$	−1.16935	+	0.520628i	−0.0930284	+	0.0414189i
$159$	9.86814	+	7.36693i	0.782594	+	0.584235i
$160$	0.669131	−	0.743145i	0.0528994	−	0.0587508i
$161$	0.683084	+	0.496290i	0.0538346	+	0.0391131i
$162$	−4.09001	−	8.01697i	−0.321342	−	0.629873i
$163$	5.52797	−	17.0134i	0.432984	−	1.33259i	−0.462154	−	0.886800i	$-0.652923\pi$
$163$	5.52797	−	17.0134i	0.432984	−	1.33259i	0.895138	−	0.445789i	$-0.147077\pi$
$164$	−4.83838	−	8.38032i	−0.377814	−	0.654393i
$165$	−4.59588	−	3.44643i	−0.357789	−	0.268304i
$166$	−4.36716	+	7.56414i	−0.338957	+	0.587091i
$167$	13.6656	+	15.1771i	1.05747	+	1.17444i	0.984187	+	0.177131i	$0.0566816\pi$
$167$	13.6656	+	15.1771i	1.05747	+	1.17444i	0.0732850	+	0.997311i	$0.476652\pi$
$168$	3.04140	−	0.605375i	0.234649	−	0.0467057i
$169$	1.21935	−	11.6013i	0.0937962	−	0.892411i
$170$	−0.205402	−	0.632163i	−0.0157536	−	0.0484847i
$171$	−22.2771	−	0.577652i	−1.70357	−	0.0441741i
$172$	2.55998	+	1.85993i	0.195197	+	0.141819i
$173$	4.21139	+	1.87503i	0.320186	+	0.142556i	0.560535	−	0.828130i	$-0.310595\pi$
$173$	4.21139	+	1.87503i	0.320186	+	0.142556i	−0.240349	+	0.970686i	$0.577262\pi$
$174$	7.56671	+	1.71116i	0.573631	+	0.129722i
$175$	−0.895199	+	1.55053i	−0.0676707	+	0.117209i
$176$	−2.21394	−	2.46951i	−0.166882	−	0.186146i
$177$	0.717362	+	7.79606i	0.0539202	+	0.585988i
$178$	−10.1448	+	2.15635i	−0.760387	+	0.161625i
$179$	10.7134	−	7.78371i	0.800754	−	0.581782i	−0.110381	−	0.993889i	$-0.535207\pi$
$179$	10.7134	−	7.78371i	0.800754	−	0.581782i	0.911135	+	0.412107i	$0.135207\pi$
$180$	2.70809	+	1.29084i	0.201849	+	0.0962136i
$181$	−6.15243	−	18.9352i	−0.457307	−	1.40744i	−0.868406	−	0.495854i	$-0.834855\pi$
$181$	−6.15243	−	18.9352i	−0.457307	−	1.40744i	0.411099	−	0.911591i	$-0.365145\pi$
$182$	−1.38408	+	1.53718i	−0.102595	+	0.113943i
$183$	−4.03350	−	7.20018i	−0.298165	−	0.532252i
$184$	0.0492949	+	0.469009i	0.00363407	+	0.0345758i
$185$	−5.01342	−	5.56796i	−0.368594	−	0.409365i
$186$	−2.89723	+	2.04812i	−0.212435	+	0.150175i
$187$	−2.15735	+	0.453707i	−0.157761	+	0.0331784i
$188$	−6.60890			−0.482004
$189$	4.33485	+	8.23154i	0.315314	+	0.598756i
$190$	6.00955	−	4.36619i	0.435978	−	0.316757i
$191$	1.44955	−	13.7915i	0.104885	−	0.997919i	−0.807856	−	0.589380i	$-0.799372\pi$
$191$	1.44955	−	13.7915i	0.104885	−	0.997919i	0.912741	−	0.408538i	$-0.133961\pi$
$192$	1.38794	+	1.03615i	0.100166	+	0.0747778i
$193$	−4.18429	−	0.889398i	−0.301192	−	0.0640202i	0.0548370	−	0.998495i	$-0.482536\pi$
$193$	−4.18429	−	0.889398i	−0.301192	−	0.0640202i	−0.356029	+	0.934475i	$0.615869\pi$
$194$	−13.2031	+	5.87841i	−0.947929	+	0.422045i
$195$	−1.96257	+	0.390640i	−0.140542	+	0.0279743i
$196$	3.71156	−	0.788916i	0.265111	−	0.0563511i
$197$	−23.5474			−1.67768			−0.838842	−	0.544374i	$-0.816767\pi$
$197$	−23.5474			−1.67768			−0.838842	+	0.544374i	$0.816767\pi$
$198$	5.21488	−	8.47378i	0.370606	−	0.602205i
$199$	13.8024			0.978427			0.489214	−	0.872164i	$-0.337284\pi$
$199$	13.8024			0.978427			0.489214	+	0.872164i	$0.337284\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	−6.15504	−	7.01667i	−0.434143	−	0.494918i
$202$	−0.297082	+	0.132270i	−0.0209027	+	0.00930646i
$203$	−7.84388	−	1.66727i	−0.550532	−	0.117019i
$204$	1.05773	−	0.454599i	0.0740562	−	0.0318283i
$205$	−1.01150	+	9.62375i	−0.0706460	+	0.672152i
$206$	−4.82148	+	3.50301i	−0.335928	+	0.244066i
$207$	−1.30695	+	0.541746i	−0.0908391	+	0.0376540i
$208$	−1.15532			−0.0801068
$209$	−12.2723	−	21.3624i	−0.848894	−	1.47767i
$210$	−2.81637	−	1.29793i	−0.194348	−	0.0895656i
$211$	−5.29415	−	5.87975i	−0.364464	−	0.404778i	0.532822	−	0.846227i	$-0.321131\pi$
$211$	−5.29415	−	5.87975i	−0.364464	−	0.404778i	−0.897286	+	0.441449i	$0.854465\pi$
$212$	−0.743186	−	7.07095i	−0.0510422	−	0.485635i
$213$	−4.43421	−	0.0574804i	−0.303827	−	0.00393849i
$214$	6.92360	−	7.68944i	0.473288	−	0.525639i
$215$	−0.977825	−	3.00944i	−0.0666871	−	0.205242i
$216$	−1.79661	+	4.87567i	−0.122244	+	0.331748i
$217$	2.96714	−	2.15575i	0.201422	−	0.146342i
$218$	−12.2883	+	2.61197i	−0.832271	+	0.176905i
$219$	−16.7720	+	11.8565i	−1.13335	+	0.801187i
$220$	0.339579	+	3.29919i	0.0228944	+	0.222432i
$221$	−0.383967	+	0.665051i	−0.0258284	+	0.0447361i
$222$	8.80777	−	9.53063i	0.591139	−	0.639654i
$223$	−22.9178	−	10.2037i	−1.53469	−	0.683288i	−0.546633	−	0.837372i	$-0.684091\pi$
$223$	−22.9178	−	10.2037i	−1.53469	−	0.683288i	−0.988058	+	0.154084i	$0.950757\pi$
$224$	−1.44846	−	1.05237i	−0.0967794	−	0.0703144i
$225$	−1.43215	−	2.63609i	−0.0954767	−	0.175739i
$226$	−1.51236	−	4.65456i	−0.100601	−	0.309617i
$227$	1.10385	−	10.5024i	0.0732651	−	0.697071i	−0.894816	−	0.446435i	$-0.852693\pi$
$227$	1.10385	−	10.5024i	0.0732651	−	0.697071i	0.968081	−	0.250636i	$-0.0806399\pi$
$228$	8.48440	+	9.67211i	0.561893	+	0.640551i
$229$	13.7450	+	15.2653i	0.908292	+	1.00876i	0.999916	+	0.0129671i	$0.00412767\pi$
$229$	13.7450	+	15.2653i	0.908292	+	1.00876i	−0.0916236	+	0.995794i	$0.529206\pi$
$230$	0.235796	−	0.408411i	0.0155480	−	0.0269298i
$231$	−5.27657	+	8.82837i	−0.347173	+	0.580864i
$232$	−2.23948	−	3.87889i	−0.147029	−	0.254662i
$233$	−0.206257	+	0.634795i	−0.0135124	+	0.0415868i	−0.957585	−	0.288150i	$-0.906960\pi$
$233$	−0.206257	+	0.634795i	−0.0135124	+	0.0415868i	0.944073	+	0.329737i	$0.106960\pi$
$234$	−0.985232	−	3.32297i	−0.0644066	−	0.217229i
$235$	5.34671	+	3.88462i	0.348781	+	0.253404i
$236$	3.02452	−	3.35907i	0.196879	−	0.218657i
$237$	−0.260304	+	2.20171i	−0.0169086	+	0.143016i
$238$	−1.08718	+	0.484045i	−0.0704716	+	0.0313760i
$239$	0.489066	+	4.65315i	0.0316350	+	0.300987i	0.998887	+	0.0471688i	$0.0150199\pi$
$239$	0.489066	+	4.65315i	0.0316350	+	0.300987i	−0.967252	+	0.253818i	$0.918313\pi$
$240$	−0.513836	−	1.65408i	−0.0331680	−	0.106770i
$241$	−8.06748	−	13.9733i	−0.519672	−	0.900099i	−0.999739	−	0.0228665i	$-0.992721\pi$
$241$	−8.06748	−	13.9733i	−0.519672	−	0.900099i	0.480066	−	0.877232i	$-0.340613\pi$
$242$	10.9999	+	0.0473682i	0.707100	+	0.00304495i
$243$	−15.5557	−	1.00960i	−0.997900	−	0.0647658i
$244$	−1.47242	+	4.53165i	−0.0942622	+	0.290109i
$245$	−3.46643	−	1.54335i	−0.221462	−	0.0986012i
$246$	−16.7592	−	0.217249i	−1.06853	−	0.0138513i
$247$	−8.39440	−	1.78428i	−0.534123	−	0.113531i
$248$	2.00371	+	0.425902i	0.127236	+	0.0270448i
$249$	7.39369	+	13.1984i	0.468556	+	0.836416i
$250$	0.913545	+	0.406737i	0.0577777	+	0.0257243i
$251$	−2.31233	+	7.11663i	−0.145953	+	0.449198i	−0.997132	−	0.0756777i	$-0.975888\pi$
$251$	−2.31233	+	7.11663i	−0.145953	+	0.449198i	0.851179	+	0.524875i	$0.175888\pi$
$252$	1.79165	−	5.06357i	0.112863	−	0.318975i
$253$	−1.26340	−	0.922075i	−0.0794292	−	0.0579704i
$254$	7.73209	+	13.3924i	0.485154	+	0.840312i
$255$	−1.12293	−	0.253943i	−0.0703207	−	0.0159025i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	13.8659	−	6.17350i	0.864931	−	0.385092i	0.0741911	−	0.997244i	$-0.476363\pi$
$257$	13.8659	−	6.17350i	0.864931	−	0.385092i	0.790740	+	0.612152i	$0.209696\pi$
$258$	5.03538	−	2.16413i	0.313489	−	0.134733i
$259$	−8.97601	+	9.96887i	−0.557742	+	0.619435i
$260$	0.934671	+	0.679078i	0.0579658	+	0.0421146i
$261$	9.24684	−	9.74912i	0.572365	−	0.603456i
$262$	0.859011	−	2.64376i	0.0530699	−	0.163332i
$263$	−10.8244	−	18.7483i	−0.667458	−	1.15607i	−0.978613	−	0.205712i	$-0.934049\pi$
$263$	−10.8244	−	18.7483i	−0.667458	−	1.15607i	0.311154	−	0.950359i	$-0.399284\pi$
$264$	−5.63644	+	1.10930i	−0.346899	+	0.0682724i
$265$	−3.55495	+	6.15735i	−0.218379	+	0.378243i
$266$	−8.89907	−	9.88341i	−0.545637	−	0.605991i
$267$	−5.77214	+	17.0113i	−0.353249	+	1.04107i
$268$	−0.563286	+	5.35930i	−0.0344081	+	0.327372i
$269$	6.49130	+	19.9782i	0.395782	+	1.21809i	0.928351	+	0.371704i	$0.121227\pi$
$269$	6.49130	+	19.9782i	0.395782	+	1.21809i	−0.532569	+	0.846386i	$0.678773\pi$
$270$	4.31934	−	2.88848i	0.262866	−	0.175787i
$271$	−7.93049	−	5.76184i	−0.481743	−	0.350007i	0.320257	−	0.947331i	$-0.396231\pi$
$271$	−7.93049	−	5.76184i	−0.481743	−	0.350007i	−0.802000	+	0.597324i	$0.796231\pi$
$272$	−0.607230	−	0.270356i	−0.0368187	−	0.0163928i
$273$	1.06286	+	3.42142i	0.0643271	+	0.207074i
$274$	−8.29215	+	14.3624i	−0.500947	+	0.867666i
$275$	1.66449	−	2.86870i	0.100373	−	0.172989i
$276$	0.741836	+	0.341876i	0.0446533	+	0.0205785i
$277$	9.34151	−	1.98560i	0.561277	−	0.119303i	0.0814678	−	0.996676i	$-0.474039\pi$
$277$	9.34151	−	1.98560i	0.561277	−	0.119303i	0.479809	+	0.877373i	$0.340706\pi$
$278$	7.76614	−	5.64243i	0.465782	−	0.338411i
$279$	0.483730	+	6.12636i	0.0289601	+	0.366775i
$280$	0.553263	+	1.70277i	0.0330638	+	0.101760i
$281$	−10.4396	+	11.5943i	−0.622773	+	0.691659i	−0.969160	−	0.246432i	$-0.920742\pi$
$281$	−10.4396	+	11.5943i	−0.622773	+	0.691659i	0.346387	+	0.938092i	$0.387408\pi$
$282$	−5.85149	+	9.83833i	−0.348451	+	0.585864i
$283$	1.55802	+	14.8236i	0.0926150	+	0.881173i	0.937911	+	0.346875i	$0.112757\pi$
$283$	1.55802	+	14.8236i	0.0926150	+	0.881173i	−0.845296	+	0.534298i	$0.820576\pi$
$284$	1.71318	+	1.90268i	0.101659	+	0.112903i
$285$	−1.17890	−	12.8119i	−0.0698320	−	0.758912i
$286$	2.57007	−	2.84202i	0.151971	−	0.168052i
$287$	17.3252			1.02268
$288$	2.77135	−	1.14876i	0.163303	−	0.0676912i
$289$	13.3958	−	9.73265i	0.787991	−	0.572509i
$290$	−0.468178	+	4.45442i	−0.0274924	+	0.261573i
$291$	−2.93910	+	24.8595i	−0.172293	+	1.45729i
$292$	11.5994	+	2.46553i	0.678804	+	0.144284i
$293$	−17.6904	+	7.87628i	−1.03349	+	0.460137i	−0.852158	−	0.523285i	$-0.824706\pi$
$293$	−17.6904	+	7.87628i	−1.03349	+	0.460137i	−0.181328	+	0.983423i	$0.558040\pi$
$294$	2.11178	−	6.22371i	0.123161	−	0.362974i
$295$	−4.42130	+	0.939776i	−0.257418	+	0.0547159i
$296$	−7.49243			−0.435489
$297$	−7.99725	−	15.2658i	−0.464047	−	0.885810i
$298$	6.70798			0.388583
$299$	−0.532933	+	0.113278i	−0.0308203	+	0.00655106i
$300$	−0.556540	+	1.64020i	−0.0321318	+	0.0946971i
$301$	−5.17557	+	2.30431i	−0.298315	+	0.132818i
$302$	9.14247	+	1.94329i	0.526090	+	0.111824i
$303$	−0.0661324	+	0.559362i	−0.00379921	+	0.0321345i
$304$	0.776459	−	7.38751i	0.0445330	−	0.423703i
$305$	3.85485	−	2.80071i	0.220728	−	0.160368i
$306$	0.259776	−	1.97709i	0.0148504	−	0.113023i
$307$	−23.2831			−1.32884			−0.664419	−	0.747361i	$-0.731321\pi$
$307$	−23.2831			−1.32884			−0.664419	+	0.747361i	$0.731321\pi$
$308$	5.81096	−	1.22209i	0.331110	−	0.0696349i
$309$	0.945835	+	10.2790i	0.0538066	+	0.584754i
$310$	−1.37070	−	1.52231i	−0.0778504	−	0.0864616i
$311$	0.923491	+	8.78643i	0.0523664	+	0.498233i	0.988999	+	0.147920i	$0.0472579\pi$
$311$	0.923491	+	8.78643i	0.0523664	+	0.498233i	−0.936633	+	0.350312i	$0.886075\pi$
$312$	−1.02291	+	1.71986i	−0.0579110	+	0.0973679i
$313$	−18.7571	+	20.8319i	−1.06022	+	1.17749i	−0.0766277	+	0.997060i	$0.524415\pi$
$313$	−18.7571	+	20.8319i	−1.06022	+	1.17749i	−0.983588	+	0.180429i	$0.942251\pi$
$314$	1.32041	+	4.06379i	0.0745148	+	0.229333i
$315$	−4.42576	+	3.04341i	−0.249364	+	0.171477i
$316$	1.03555	−	0.752372i	0.0582543	−	0.0423242i
$317$	−5.22661	+	1.11095i	−0.293555	+	0.0623971i	−0.352335	−	0.935874i	$-0.614612\pi$
$317$	−5.22661	+	1.11095i	−0.293555	+	0.0623971i	0.0587798	+	0.998271i	$0.481279\pi$
$318$	−11.1842	−	5.15424i	−0.627177	−	0.289035i
$319$	14.5237	+	3.11981i	0.813172	+	0.174676i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−5.31675	−	17.1150i	−0.296752	−	0.955266i
$322$	−0.771342	−	0.343423i	−0.0429852	−	0.0191382i
$323$	−3.99452	−	2.90219i	−0.222261	−	0.161482i
$324$	5.66746	+	6.99142i	0.314859	+	0.388412i
$325$	−0.357012	−	1.09877i	−0.0198035	−	0.0609489i
$326$	−1.86990	+	17.7909i	−0.103564	+	0.985347i
$327$	−6.99174	+	20.6056i	−0.386644	+	1.13949i
$328$	6.47501	+	7.19123i	0.357523	+	0.397069i
$329$	5.91628	−	10.2473i	0.326175	−	0.564952i
$330$	5.21200	+	2.41558i	0.286911	+	0.132973i
$331$	−8.89204	−	15.4015i	−0.488750	−	0.846541i	0.511166	−	0.859482i	$-0.329214\pi$
$331$	−8.89204	−	15.4015i	−0.488750	−	0.846541i	−0.999916	+	0.0129415i	$0.995880\pi$
$332$	2.69905	−	8.30683i	0.148130	−	0.455897i
$333$	−6.38941	−	21.5501i	−0.350137	−	1.18094i
$334$	−16.5224	−	12.0042i	−0.904067	−	0.656843i
$335$	3.60583	−	4.00468i	0.197007	−	0.218799i
$336$	−2.84907	+	1.22449i	−0.155430	+	0.0668013i
$337$	8.68154	−	3.86527i	0.472913	−	0.210555i	−0.156419	−	0.987691i	$-0.549995\pi$
$337$	8.68154	−	3.86527i	0.472913	−	0.210555i	0.629333	+	0.777136i	$0.283328\pi$
$338$	1.21935	+	11.6013i	0.0663239	+	0.631030i
$339$	−8.26804	−	1.86976i	−0.449058	−	0.101551i
$340$	0.332348	+	0.575644i	0.0180241	+	0.0312187i
$341$	−5.50506	+	3.98158i	−0.298116	+	0.215615i
$342$	21.9104	−	4.06665i	1.18478	−	0.219899i
$343$	−5.97219	+	18.3805i	−0.322468	+	0.992454i
$344$	−2.89074	−	1.28704i	−0.155858	−	0.0693926i
$345$	−0.399208	−	0.712624i	−0.0214926	−	0.0383664i
$346$	−4.50920	−	0.958461i	−0.242416	−	0.0515272i
$347$	−27.4259	−	5.82956i	−1.47230	−	0.312947i	−0.599244	−	0.800566i	$-0.704532\pi$
$347$	−27.4259	−	5.82956i	−1.47230	−	0.312947i	−0.873056	+	0.487619i	$0.837865\pi$
$348$	−7.75713	−	0.100555i	−0.415826	−	0.00539033i
$349$	−6.51166	−	2.89918i	−0.348561	−	0.155189i	0.224986	−	0.974362i	$-0.427766\pi$
$349$	−6.51166	−	2.89918i	−0.348561	−	0.155189i	−0.573547	+	0.819173i	$0.694433\pi$
$350$	0.553263	−	1.70277i	0.0295732	−	0.0910168i
$351$	−5.81905	−	1.47548i	−0.310598	−	0.0787552i
$352$	2.67900	+	1.95524i	0.142791	+	0.104214i
$353$	13.2201	+	22.8980i	0.703637	+	1.21874i	0.967181	+	0.254088i	$0.0817753\pi$
$353$	13.2201	+	22.8980i	0.703637	+	1.21874i	−0.263544	+	0.964647i	$0.584891\pi$
$354$	−2.32258	−	7.47655i	−0.123444	−	0.397374i
$355$	−0.267625	−	2.54628i	−0.0142041	−	0.135143i
$356$	9.47481	−	4.21846i	0.502164	−	0.223578i
$357$	−0.242014	+	2.04701i	−0.0128087	+	0.108339i
$358$	−8.86093	+	9.84106i	−0.468315	+	0.520116i
$359$	30.2118	+	21.9502i	1.59452	+	1.15849i	0.897104	+	0.441819i	$0.145667\pi$
$359$	30.2118	+	21.9502i	1.59452	+	1.15849i	0.697415	+	0.716667i	$0.254333\pi$
$360$	−2.91729	−	0.699591i	−0.153755	−	0.0368717i
$361$	11.1797	−	34.4076i	0.588405	−	1.81092i
$362$	9.95484	+	17.2423i	0.523215	+	0.906235i
$363$	9.80977	−	16.3330i	0.514880	−	0.857262i
$364$	1.03424	−	1.79135i	0.0542088	−	0.0938924i
$365$	−7.93492	−	8.81262i	−0.415333	−	0.461274i
$366$	5.44236	+	6.20422i	0.284477	+	0.324300i
$367$	−0.452827	+	4.30836i	−0.0236374	+	0.224895i	0.976326	+	0.216306i	$0.0694007\pi$
$367$	−0.452827	+	4.30836i	−0.0236374	+	0.224895i	−0.999963	+	0.00858924i	$0.997266\pi$
$368$	−0.145730	−	0.448511i	−0.00759671	−	0.0233803i
$369$	−15.1619	+	24.7562i	−0.789300	+	1.28876i
$370$	6.06151	+	4.40394i	0.315123	+	0.228950i
$371$	11.6290	+	5.17757i	0.603748	+	0.268806i
$372$	2.40809	−	2.60573i	0.124854	−	0.135101i
$373$	10.9133	−	18.9024i	0.565070	−	0.978730i	−0.431973	−	0.901886i	$-0.642183\pi$
$373$	10.9133	−	18.9024i	0.565070	−	0.978730i	0.997043	−	0.0768433i	$-0.0244841\pi$
$374$	2.01588	−	0.892332i	0.104239	−	0.0461414i
$375$	1.41434	−	0.999825i	0.0730360	−	0.0516308i
$376$	6.46448	−	1.37407i	0.333380	−	0.0708622i
$377$	4.18635	−	3.04156i	0.215608	−	0.156648i
$378$	−5.95156	−	7.15039i	−0.306115	−	0.367777i
$379$	−9.92712	−	30.5525i	−0.509922	−	1.56938i	−0.792335	−	0.610086i	$-0.791135\pi$
$379$	−9.92712	−	30.5525i	−0.509922	−	1.56938i	0.282413	−	0.959293i	$-0.408865\pi$
$380$	−4.97044	+	5.52023i	−0.254978	+	0.283182i
$381$	26.7825	+	0.347180i	1.37211	+	0.0177866i
$382$	1.44955	+	13.7915i	0.0741652	+	0.705635i
$383$	7.42434	+	8.24556i	0.379366	+	0.421329i	0.902343	−	0.431018i	$-0.141845\pi$
$383$	7.42434	+	8.24556i	0.379366	+	0.421329i	−0.522977	+	0.852347i	$0.675179\pi$
$384$	−1.57304	−	0.724939i	−0.0802740	−	0.0369944i
$385$	−5.41949	−	2.42691i	−0.276203	−	0.123687i
$386$	4.27777			0.217733
$387$	1.23667	−	9.41203i	0.0628635	−	0.478440i
$388$	11.6924	−	8.49504i	0.593593	−	0.431270i
$389$	3.54900	−	33.7665i	0.179941	−	1.71203i	−0.416303	−	0.909226i	$-0.636674\pi$
$389$	3.54900	−	33.7665i	0.179941	−	1.71203i	0.596245	−	0.802803i	$-0.296659\pi$
$390$	1.83846	−	0.790144i	0.0930941	−	0.0400105i
$391$	−0.306616	−	0.0651732i	−0.0155062	−	0.00329595i
$392$	−3.46643	+	1.54335i	−0.175081	+	0.0779511i
$393$	−3.17507	−	3.61954i	−0.160161	−	0.182582i
$394$	23.0329	−	4.89579i	1.16038	−	0.246646i
$395$	−1.28001			−0.0644044
$396$	−3.33913	+	9.37284i	−0.167798	+	0.471003i
$397$	11.5356			0.578954			0.289477	−	0.957185i	$-0.406519\pi$
$397$	11.5356			0.578954			0.289477	+	0.957185i	$0.406519\pi$
$398$	−13.5008	+	2.86968i	−0.676734	+	0.143844i
$399$	−22.5921	+	4.49685i	−1.13102	+	0.225124i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	27.2848	+	5.79956i	1.36254	+	0.289616i	0.830459	−	0.557080i	$-0.188078\pi$
$401$	27.2848	+	5.79956i	1.36254	+	0.289616i	0.532078	+	0.846696i	$0.321411\pi$
$402$	7.47939	+	5.58364i	0.373038	+	0.278487i
$403$	−0.247381	+	2.35367i	−0.0123229	+	0.117245i
$404$	0.263090	−	0.191146i	0.0130892	−	0.00950988i
$405$	−0.475616	−	8.98742i	−0.0236336	−	0.446589i
$406$	8.01911			0.397982
$407$	16.6673	−	18.4310i	0.826170	−	0.913591i
$408$	−0.940104	+	0.664580i	−0.0465421	+	0.0329016i
$409$	24.2260	+	26.9057i	1.19790	+	1.33040i	0.930269	+	0.366879i	$0.119574\pi$
$409$	24.2260	+	26.9057i	1.19790	+	1.33040i	0.267629	+	0.963522i	$0.413760\pi$
$410$	−1.01150	−	9.62375i	−0.0499543	−	0.475283i
$411$	14.0388	+	25.0605i	0.692482	+	1.23614i
$412$	3.98780	−	4.42890i	0.196465	−	0.218196i
$413$	2.50079	+	7.69664i	0.123056	+	0.378727i
$414$	1.16575	−	0.801637i	0.0572936	−	0.0393983i
$415$	−7.06621	+	5.13391i	−0.346867	+	0.252013i
$416$	1.13007	−	0.240204i	0.0554062	−	0.0117770i
$417$	−1.52349	−	16.5568i	−0.0746058	−	0.810792i
$418$	16.4456	+	18.3440i	0.804382	+	0.897234i
$419$	0.879076	−	1.52260i	0.0429457	−	0.0743841i	−0.843754	−	0.536731i	$-0.819659\pi$
$419$	0.879076	−	1.52260i	0.0429457	−	0.0743841i	0.886699	+	0.462347i	$0.152992\pi$
$420$	3.02468	+	0.684009i	0.147589	+	0.0333762i
$421$	−8.76589	−	3.90283i	−0.427223	−	0.190212i	0.181849	−	0.983326i	$-0.441792\pi$
$421$	−8.76589	−	3.90283i	−0.427223	−	0.190212i	−0.609073	+	0.793114i	$0.708458\pi$
$422$	6.40093	+	4.65054i	0.311592	+	0.226385i
$423$	9.46494	+	17.4216i	0.460201	+	0.847069i
$424$	2.19708	+	6.76191i	0.106700	+	0.328387i
$425$	0.0694797	−	0.661055i	0.00337026	−	0.0320659i
$426$	4.34926	−	0.865700i	0.210722	−	0.0419433i
$427$	−5.70835	−	6.33976i	−0.276246	−	0.306803i
$428$	−5.17358	+	8.96090i	−0.250074	+	0.433141i
$429$	−1.95524	−	6.34224i	−0.0944000	−	0.306206i
$430$	1.58215	+	2.74037i	0.0762983	+	0.132152i
$431$	2.61172	−	8.03804i	0.125802	−	0.387179i	−0.868244	−	0.496137i	$-0.834751\pi$
$431$	2.61172	−	8.03804i	0.125802	−	0.387179i	0.994046	+	0.108958i	$0.0347514\pi$
$432$	0.743639	−	5.14266i	0.0357783	−	0.247427i
$433$	4.91322	+	3.56966i	0.236114	+	0.171547i	0.699550	−	0.714583i	$-0.253384\pi$
$433$	4.91322	+	3.56966i	0.236114	+	0.171547i	−0.463436	+	0.886130i	$0.653384\pi$
$434$	−2.45409	+	2.72555i	−0.117800	+	0.130830i
$435$	6.21654	+	4.64088i	0.298060	+	0.222513i
$436$	11.4767	−	5.10978i	0.549636	−	0.244714i
$437$	−0.366173	−	3.48390i	−0.0175164	−	0.166657i
$438$	13.9404	−	15.0845i	0.666097	−	0.720764i
$439$	8.21763	+	14.2333i	0.392206	+	0.679320i	0.992740	−	0.120279i	$-0.0383788\pi$
$439$	8.21763	+	14.2333i	0.392206	+	0.679320i	−0.600534	+	0.799599i	$0.705045\pi$
$440$	−1.01810	−	3.15650i	−0.0485360	−	0.150480i
$441$	−7.39516	−	8.65414i	−0.352150	−	0.412102i
$442$	0.237305	−	0.730349i	0.0112874	−	0.0347392i
$443$	19.7851	+	8.80891i	0.940020	+	0.418524i	0.818785	−	0.574100i	$-0.194648\pi$
$443$	19.7851	+	8.80891i	0.940020	+	0.418524i	0.121235	+	0.992624i	$0.461315\pi$
$444$	−6.63377	+	11.1536i	−0.314825	+	0.529327i
$445$	−10.1448	−	2.15635i	−0.480911	−	0.102221i
$446$	24.5385	+	5.21581i	1.16193	+	0.246976i
$447$	5.93921	−	9.98582i	0.280915	−	0.472313i
$448$	1.63561	+	0.728220i	0.0772753	+	0.0344052i
$449$	4.56000	−	14.0342i	0.215200	−	0.662317i	−0.783939	−	0.620837i	$-0.786793\pi$
$449$	4.56000	−	14.0342i	0.215200	−	0.662317i	0.999139	−	0.0414798i	$-0.0132072\pi$
$450$	1.94893	+	2.28072i	0.0918733	+	0.107514i
$451$	−32.0941	−	0.0691022i	−1.51125	−	0.00325389i
$452$	2.44705	+	4.23841i	0.115099	+	0.199358i
$453$	10.9876	−	11.8893i	0.516242	−	0.558610i
$454$	1.10385	+	10.5024i	0.0518063	+	0.492904i
$455$	−1.88965	+	0.841325i	−0.0885880	+	0.0394419i
$456$	−10.3099	−	7.69675i	−0.482807	−	0.360433i
$457$	10.0205	−	11.1289i	0.468740	−	0.520588i	−0.461699	−	0.887037i	$-0.652760\pi$
$457$	10.0205	−	11.1289i	0.468740	−	0.520588i	0.930438	+	0.366449i	$0.119427\pi$
$458$	−16.6184	−	12.0740i	−0.776528	−	0.564181i
$459$	−2.71320	−	2.13723i	−0.126641	−	0.0997571i
$460$	−0.145730	+	0.448511i	−0.00679471	+	0.0209120i
$461$	2.77964	+	4.81448i	0.129461	+	0.224233i	0.923468	−	0.383676i	$-0.125342\pi$
$461$	2.77964	+	4.81448i	0.129461	+	0.224233i	−0.794007	+	0.607909i	$0.792009\pi$
$462$	3.32574	−	9.73251i	0.154727	−	0.452797i
$463$	4.78935	−	8.29540i	0.222580	−	0.385520i	−0.733011	−	0.680217i	$-0.761885\pi$
$463$	4.78935	−	8.29540i	0.222580	−	0.385520i	0.955591	+	0.294697i	$0.0952188\pi$
$464$	2.99701	+	3.32851i	0.139133	+	0.154522i
$465$	−3.47980	+	0.692637i	−0.161372	+	0.0321203i
$466$	0.0697689	−	0.663807i	0.00323198	−	0.0307503i
$467$	−2.13351	−	6.56625i	−0.0987269	−	0.303850i	0.889480	−	0.456974i	$-0.151067\pi$
$467$	−2.13351	−	6.56625i	−0.0987269	−	0.303850i	−0.988207	+	0.153124i	$0.951067\pi$
$468$	1.65459	+	3.04551i	0.0764833	+	0.140779i
$469$	−7.80551	−	5.67103i	−0.360425	−	0.261864i
$470$	−6.03753	−	2.68808i	−0.278491	−	0.123992i
$471$	7.21864	+	1.63244i	0.332617	+	0.0752189i
$472$	−2.26004	+	3.91450i	−0.104027	+	0.180179i
$473$	9.59667	−	4.24798i	0.441255	−	0.195322i
$474$	−0.203145	−	2.20772i	−0.00933077	−	0.101404i
$475$	7.26588	−	1.54441i	0.333382	−	0.0708624i
$476$	0.962787	−	0.699506i	0.0441293	−	0.0320618i
$477$	−17.5753	+	12.0858i	−0.804716	+	0.553369i
$478$	−1.44582	−	4.44978i	−0.0661304	−	0.203528i
$479$	15.8598	−	17.6141i	0.724654	−	0.804810i	−0.262441	−	0.964948i	$-0.584527\pi$
$479$	15.8598	−	17.6141i	0.724654	−	0.804810i	0.987095	+	0.160138i	$0.0511940\pi$
$480$	0.846510	+	1.51110i	0.0386377	+	0.0689719i
$481$	−0.904812	−	8.60871i	−0.0412559	−	0.392524i
$482$	10.7964	+	11.9906i	0.491763	+	0.546158i
$483$	−1.19418	+	0.844191i	−0.0543370	+	0.0384120i
$484$	−10.7694	+	2.24067i	−0.489517	+	0.101849i
$485$	−14.4526			−0.656260
$486$	15.4257	−	2.24668i	0.699724	−	0.101912i
$487$	7.68233	−	5.58154i	0.348119	−	0.252924i	−0.399960	−	0.916532i	$-0.630976\pi$
$487$	7.68233	−	5.58154i	0.348119	−	0.252924i	0.748080	+	0.663609i	$0.230976\pi$
$488$	0.498063	−	4.73876i	0.0225463	−	0.214513i
$489$	24.8288	+	18.5356i	1.12280	+	0.838209i
$490$	3.71156	+	0.788916i	0.167671	+	0.0356396i
$491$	6.65155	−	2.96146i	0.300180	−	0.133649i	−0.251120	−	0.967956i	$-0.580799\pi$
$491$	6.65155	−	2.96146i	0.300180	−	0.133649i	0.551300	+	0.834307i	$0.314132\pi$
$492$	16.4382	−	3.27194i	0.741090	−	0.147510i
$493$	2.91209	−	0.618983i	0.131154	−	0.0278776i
$494$	8.58193			0.386119
$495$	8.21063	−	5.62010i	0.369040	−	0.252605i
$496$	−2.04847			−0.0919792
$497$	−4.48380	+	0.953060i	−0.201126	+	0.0427506i
$498$	−9.97623	−	11.3728i	−0.447045	−	0.509626i
$499$	−5.94997	+	2.64910i	−0.266357	+	0.118590i	−0.535570	−	0.844491i	$-0.679903\pi$
$499$	−5.94997	+	2.64910i	−0.266357	+	0.118590i	0.269213	+	0.963081i	$0.413237\pi$
$500$	−0.978148	−	0.207912i	−0.0437441	−	0.00929809i
$501$	−32.4990	+	13.9676i	−1.45195	+	0.624026i
$502$	0.782172	−	7.44187i	0.0349101	−	0.332147i
$503$	−8.37088	+	6.08180i	−0.373239	+	0.271174i	−0.758553	−	0.651611i	$-0.774093\pi$
$503$	−8.37088	+	6.08180i	−0.373239	+	0.271174i	0.385314	+	0.922786i	$0.374093\pi$
$504$	−0.699721	+	5.32542i	−0.0311680	+	0.237213i
$505$	−0.325197			−0.0144711
$506$	1.42750	+	0.639250i	0.0634601	+	0.0284181i
$507$	18.3499	+	8.45659i	0.814949	+	0.375570i
$508$	−10.3476	−	11.4921i	−0.459098	−	0.509881i
$509$	4.18261	+	39.7949i	0.185391	+	1.76388i	0.552322	+	0.833631i	$0.313742\pi$
$509$	4.18261	+	39.7949i	0.185391	+	1.76388i	−0.366931	+	0.930248i	$0.619591\pi$
$510$	1.15119	+	0.0149228i	0.0509756	+	0.000660794i
$511$	−14.2067	+	15.7781i	−0.628465	+	0.697982i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	13.3456	−	36.2175i	0.589222	−	1.59904i
$514$	−12.2794	+	8.92148i	−0.541619	+	0.393509i
$515$	−5.82944	+	1.23909i	−0.256876	+	0.0546006i
$516$	−4.47540	+	3.16376i	−0.197018	+	0.139277i
$517$	−11.0005	+	18.9590i	−0.483800	+	0.833815i
$518$	6.70722	−	11.6172i	0.294698	−	0.510432i
$519$	−5.41924	+	5.86400i	−0.237878	+	0.257401i
$520$	−1.05543	−	0.469910i	−0.0462839	−	0.0206069i
$521$	34.8742	+	25.3376i	1.52787	+	1.11006i	0.957410	+	0.288732i	$0.0932337\pi$
$521$	34.8742	+	25.3376i	1.52787	+	1.11006i	0.570457	+	0.821328i	$0.306766\pi$
$522$	−7.01782	+	11.4586i	−0.307162	+	0.501530i
$523$	13.2096	+	40.6551i	0.577617	+	1.77772i	0.627090	+	0.778947i	$0.284246\pi$
$523$	13.2096	+	40.6551i	0.577617	+	1.77772i	−0.0494735	+	0.998775i	$0.515754\pi$
$524$	−0.290570	+	2.76459i	−0.0126936	+	0.120772i
$525$	−2.04497	−	2.33124i	−0.0892497	−	0.101744i
$526$	14.4858	+	16.0881i	0.631611	+	0.701475i
$527$	−0.680806	+	1.17919i	−0.0296564	+	0.0513664i
$528$	5.28264	−	2.25694i	0.229897	−	0.0982205i
$529$	11.3888	+	19.7260i	0.495165	+	0.857651i
$530$	2.19708	−	6.76191i	0.0954350	−	0.293719i
$531$	−13.1864	−	3.16220i	−0.572239	−	0.137228i
$532$	10.7595	+	7.81722i	0.466482	+	0.338919i
$533$	−7.48069	+	8.30815i	−0.324025	+	0.359866i
$534$	2.10915	−	17.8397i	0.0912719	−	0.771998i
$535$	9.45260	−	4.20857i	0.408671	−	0.181952i
$536$	−0.563286	−	5.35930i	−0.0243302	−	0.231487i
$537$	6.80445	+	21.9040i	0.293634	+	0.945229i
$538$	−10.5031	−	18.1920i	−0.452823	−	0.784312i
$539$	3.91470	−	11.9605i	0.168618	−	0.515176i
$540$	−3.62440	+	3.72340i	−0.155969	+	0.160230i
$541$	0.803973	−	2.47438i	0.0345655	−	0.106382i	−0.932285	−	0.361724i	$-0.882188\pi$
$541$	0.803973	−	2.47438i	0.0345655	−	0.106382i	0.966851	+	0.255342i	$0.0821882\pi$
$542$	8.95515	+	3.98709i	0.384657	+	0.171260i
$543$	34.4817	+	0.446984i	1.47975	+	0.0191819i
$544$	0.650171	+	0.138198i	0.0278758	+	0.00592519i
$545$	−12.2883	−	2.61197i	−0.526374	−	0.111884i
$546$	−1.75099	−	3.12567i	−0.0749353	−	0.133766i
$547$	−41.1553	−	18.3235i	−1.75968	−	0.783458i	−0.989305	−	0.145861i	$-0.953405\pi$
$547$	−41.1553	−	18.3235i	−1.75968	−	0.783458i	−0.770370	−	0.637597i	$-0.779928\pi$
$548$	5.12483	−	15.7726i	0.218922	−	0.673773i
$549$	14.0545	−	2.60857i	0.599834	−	0.111331i
$550$	−1.03168	+	3.15208i	−0.0439911	+	0.134405i
$551$	16.6353	+	28.8132i	0.708688	+	1.22748i
$552$	−0.796705	−	0.180169i	−0.0339100	−	0.00766850i
$553$	0.239551	+	2.27918i	0.0101867	+	0.0969204i
$554$	−8.72455	+	3.88442i	−0.370670	+	0.165033i
$555$	11.9228	−	5.12422i	0.506093	−	0.217511i
$556$	−6.42331	+	7.13380i	−0.272409	+	0.302541i
$557$	26.8272	+	19.4911i	1.13671	+	0.825866i	0.986657	−	0.162813i	$-0.0520567\pi$
$557$	26.8272	+	19.4911i	1.13671	+	0.825866i	0.150050	+	0.988678i	$0.452057\pi$
$558$	−1.74690	−	5.89191i	−0.0739522	−	0.249424i
$559$	1.12970	−	3.47685i	0.0477811	−	0.147055i
$560$	−0.895199	−	1.55053i	−0.0378291	−	0.0655218i
$561$	0.456482	−	3.79100i	0.0192727	−	0.160056i
$562$	7.80085	−	13.5115i	0.329059	−	0.569947i
$563$	−19.7470	−	21.9313i	−0.832238	−	0.924294i	0.165847	−	0.986152i	$-0.446964\pi$
$563$	−19.7470	−	21.9313i	−0.832238	−	0.924294i	−0.998085	+	0.0618575i	$0.980298\pi$
$564$	3.67812	−	10.8399i	0.154877	−	0.456444i
$565$	0.511572	−	4.86728i	0.0215220	−	0.204768i
$566$	−4.60598	−	14.1758i	−0.193604	−	0.595851i
$567$	−15.9139	+	2.52885i	−0.668321	+	0.106202i
$568$	−2.07133	−	1.50491i	−0.0869112	−	0.0631446i
$569$	−20.2839	−	9.03098i	−0.850345	−	0.378598i	−0.0651720	−	0.997874i	$-0.520760\pi$
$569$	−20.2839	−	9.03098i	−0.850345	−	0.378598i	−0.785173	+	0.619276i	$0.787426\pi$
$570$	3.81688	+	12.2868i	0.159872	+	0.514639i
$571$	−3.13532	+	5.43053i	−0.131209	+	0.227261i	−0.924143	−	0.382047i	$-0.875219\pi$
$571$	−3.13532	+	5.43053i	−0.131209	+	0.227261i	0.792934	+	0.609308i	$0.208553\pi$
$572$	−1.92302	+	3.31426i	−0.0804053	+	0.138576i
$573$	21.8141	+	10.0531i	0.911299	+	0.419973i
$574$	−16.9466	+	3.60212i	−0.707339	+	0.150350i
$575$	0.381527	−	0.277195i	0.0159108	−	0.0115598i
$576$	−2.47194	+	1.69985i	−0.102998	+	0.0708271i
$577$	−5.80281	−	17.8592i	−0.241574	−	0.743488i	−0.996181	−	0.0873114i	$-0.972172\pi$
$577$	−5.80281	−	17.8592i	−0.241574	−	0.743488i	0.754607	−	0.656177i	$-0.227828\pi$
$578$	−11.0796	+	12.3051i	−0.460850	+	0.511826i
$579$	3.78751	−	6.36809i	0.157404	−	0.264649i
$580$	−0.468178	−	4.45442i	−0.0194401	−	0.184960i
$581$	10.4638	+	11.6212i	0.434112	+	0.482130i
$582$	−2.29372	−	24.9274i	−0.0950775	−	1.03327i
$583$	−21.5215	−	9.63756i	−0.891329	−	0.399147i
$584$	−11.8585			−0.490710
$585$	0.451519	−	3.43641i	0.0186680	−	0.142078i
$586$	15.6663	−	11.3822i	0.647168	−	0.470195i
$587$	−0.0836286	+	0.795673i	−0.00345172	+	0.0328409i	−0.996112	−	0.0880937i	$-0.971922\pi$
$587$	−0.0836286	+	0.795673i	−0.00345172	+	0.0328409i	0.992660	+	0.120935i	$0.0385892\pi$
$588$	−0.771649	+	6.52677i	−0.0318223	+	0.269159i
$589$	−14.8840	−	3.16369i	−0.613284	−	0.130357i
$590$	4.12929	−	1.83848i	0.170000	−	0.0756890i
$591$	13.1051	−	38.6225i	0.539071	−	1.58872i
$592$	7.32871	−	1.55776i	0.301208	−	0.0640237i
$593$	−32.8682			−1.34973			−0.674867	−	0.737939i	$-0.735799\pi$
$593$	−32.8682			−1.34973			−0.674867	+	0.737939i	$0.735799\pi$
$594$	10.9964	+	13.2695i	0.451189	+	0.544453i
$595$	−1.19007			−0.0487881
$596$	−6.56139	+	1.39467i	−0.268765	+	0.0571278i
$597$	−7.68159	+	22.6387i	−0.314387	+	0.926542i
$598$	0.497735	−	0.221606i	0.0203539	−	0.00906214i
$599$	−29.4730	−	6.26467i	−1.20423	−	0.255968i	−0.438265	−	0.898846i	$-0.644407\pi$
$599$	−29.4730	−	6.26467i	−1.20423	−	0.255968i	−0.765968	+	0.642878i	$0.777740\pi$
$600$	0.203361	−	1.72007i	0.00830218	−	0.0702216i
$601$	3.99620	−	38.0213i	0.163008	−	1.55092i	−0.541180	−	0.840907i	$-0.682022\pi$
$601$	3.99620	−	38.0213i	0.163008	−	1.55092i	0.704188	−	0.710013i	$-0.251311\pi$
$602$	4.58338	−	3.33002i	0.186805	−	0.135722i
$603$	14.9343	−	6.19046i	0.608171	−	0.252095i
$604$	−9.34672			−0.380313
$605$	10.0296	+	4.51733i	0.407763	+	0.183656i
$606$	−0.0516107	−	0.560889i	−0.00209654	−	0.0227845i
$607$	3.33183	+	3.70037i	0.135235	+	0.150193i	0.806958	−	0.590609i	$-0.201112\pi$
$607$	3.33183	+	3.70037i	0.135235	+	0.150193i	−0.671723	+	0.740802i	$0.734446\pi$
$608$	0.776459	+	7.38751i	0.0314896	+	0.299603i
$609$	7.10009	−	11.9376i	0.287710	−	0.483738i
$610$	−3.18831	+	3.54098i	−0.129091	+	0.143370i
$611$	2.35946	+	7.26167i	0.0954536	+	0.293776i
$612$	0.156962	+	1.98790i	0.00634482	+	0.0803561i
$613$	−20.7412	+	15.0694i	−0.837730	+	0.608647i	−0.921736	−	0.387819i	$-0.873229\pi$
$613$	−20.7412	+	15.0694i	−0.837730	+	0.608647i	0.0840055	+	0.996465i	$0.473229\pi$
$614$	22.7743	−	4.84083i	0.919097	−	0.195360i
$615$	−15.2220	−	7.01506i	−0.613808	−	0.282874i
$616$	−5.42989	+	2.40355i	−0.218777	+	0.0968417i
$617$	−0.759033	+	1.31468i	−0.0305575	+	0.0529272i	−0.880900	−	0.473303i	$-0.843062\pi$
$617$	−0.759033	+	1.31468i	−0.0305575	+	0.0529272i	0.850342	+	0.526230i	$0.176395\pi$
$618$	−3.06230	−	9.85776i	−0.123184	−	0.396537i
$619$	−35.0369	−	15.5994i	−1.40825	−	0.626994i	−0.444985	−	0.895538i	$-0.646791\pi$
$619$	−35.0369	−	15.5994i	−1.40825	−	0.626994i	−0.963267	+	0.268544i	$0.913458\pi$
$620$	1.65725	+	1.20406i	0.0665568	+	0.0483563i
$621$	−0.161205	−	2.44516i	−0.00646895	−	0.0981209i
$622$	−2.73011	−	8.40242i	−0.109468	−	0.336906i
$623$	−1.94099	+	18.4673i	−0.0777643	+	0.739878i
$624$	0.642980	−	1.89495i	0.0257398	−	0.0758588i
$625$	0.669131	+	0.743145i	0.0267652	+	0.0297258i
$626$	14.0160	−	24.2765i	0.560194	−	0.970284i
$627$	41.8687	−	8.24007i	1.67207	−	0.329077i
$628$	−2.13646	−	3.70046i	−0.0852541	−	0.147664i
$629$	1.53896	−	4.73644i	0.0613625	−	0.188854i
$630$	3.69629	−	3.89707i	0.147264	−	0.155263i
$631$	17.9574	+	13.0468i	0.714873	+	0.519386i	0.884742	−	0.466081i	$-0.154334\pi$
$631$	17.9574	+	13.0468i	0.714873	+	0.519386i	−0.169869	+	0.985467i	$0.554334\pi$
$632$	−0.856495	+	0.951234i	−0.0340695	+	0.0378381i
$633$	12.5904	−	5.41116i	0.500423	−	0.215074i
$634$	4.88141	−	2.17335i	0.193866	−	0.0863146i
$635$	1.61645	+	15.3795i	0.0641467	+	0.610315i
$636$	12.0114	+	2.71629i	0.476283	+	0.107708i
$637$	−2.19191	−	3.79650i	−0.0868467	−	0.150423i
$638$	−14.8550	−	0.0319844i	−0.588114	−	0.00126628i
$639$	2.56209	−	7.24101i	0.101355	−	0.286450i
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	35.6227	+	15.8602i	1.40701	+	0.626442i	0.962981	−	0.269569i	$-0.0868813\pi$
$641$	35.6227	+	15.8602i	1.40701	+	0.626442i	0.444031	+	0.896011i	$0.353548\pi$
$642$	8.75897	+	15.6356i	0.345689	+	0.617087i
$643$	−15.2709	−	3.24594i	−0.602227	−	0.128007i	−0.103298	−	0.994650i	$-0.532940\pi$
$643$	−15.2709	−	3.24594i	−0.602227	−	0.128007i	−0.498928	+	0.866643i	$0.666273\pi$
$644$	0.825888	+	0.175548i	0.0325445	+	0.00691756i
$645$	5.48028	+	0.0710406i	0.215786	+	0.00279722i
$646$	4.51063	+	2.00826i	0.177468	+	0.0790140i
$647$	−5.37303	+	16.5365i	−0.211236	+	0.650117i	0.788164	+	0.615466i	$0.211032\pi$
$647$	−5.37303	+	16.5365i	−0.211236	+	0.650117i	−0.999399	+	0.0346511i	$0.988968\pi$
$648$	−6.99721	−	5.66031i	−0.274876	−	0.222358i
$649$	−4.60188	−	14.2676i	−0.180640	−	0.560052i
$650$	0.577658	+	1.00053i	0.0226576	+	0.0392442i
$651$	1.88454	+	6.06647i	0.0738609	+	0.237764i
$652$	−1.86990	−	17.7909i	−0.0732309	−	0.696746i
$653$	−41.5491	+	18.4989i	−1.62594	+	0.723916i	−0.998500	−	0.0547466i	$-0.982565\pi$
$653$	−41.5491	+	18.4989i	−1.62594	+	0.723916i	−0.627442	+	0.778663i	$0.715898\pi$
$654$	2.55480	−	21.6090i	0.0999005	−	0.844979i
$655$	1.86006	−	2.06581i	0.0726786	−	0.0807178i
$656$	−7.82866	−	5.68785i	−0.305658	−	0.222073i
$657$	−10.1127	−	34.1080i	−0.394536	−	1.33068i
$658$	−3.65646	+	11.2534i	−0.142544	+	0.438705i
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	0.999309	−	0.0371820i	$-0.0118381\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$	−5.60034	−	1.27916i	−0.217993	−	0.0497911i
$661$	−22.3353	+	38.6858i	−0.868742	+	1.50470i	−0.00545809	+	0.999985i	$0.501737\pi$
$661$	−22.3353	+	38.6858i	−0.868742	+	1.50470i	−0.863283	+	0.504719i	$0.831596\pi$
$662$	11.8999	+	13.2161i	0.462501	+	0.513660i
$663$	−0.877124	−	0.999911i	−0.0340647	−	0.0388333i
$664$	−0.912985	+	8.68647i	−0.0354307	+	0.337101i
$665$	−4.10975	−	12.6485i	−0.159369	−	0.490489i
$666$	10.7303	+	19.7507i	0.415790	+	0.765324i
$667$	1.70884	+	1.24155i	0.0661666	+	0.0480728i
$668$	18.6572	+	8.30672i	0.721869	+	0.321397i
$669$	29.4908	−	31.9111i	1.14018	−	1.23375i
$670$	−2.69441	+	4.66686i	−0.104094	+	0.180296i
$671$	10.5491	+	11.7668i	0.407245	+	0.454254i
$672$	2.53223	−	1.79009i	0.0976827	−	0.0690540i
$673$	−18.4294	+	3.91728i	−0.710399	+	0.151000i	−0.548919	−	0.835876i	$-0.684960\pi$
$673$	−18.4294	+	3.91728i	−0.710399	+	0.151000i	−0.161481	+	0.986876i	$0.551627\pi$
$674$	−7.68819	+	5.58580i	−0.296138	+	0.215157i
$675$	5.12076	−	0.881928i	0.197098	−	0.0339454i
$676$	−3.60476	−	11.0943i	−0.138645	−	0.426704i
$677$	−13.8759	+	15.4107i	−0.533293	+	0.592282i	−0.948236	−	0.317565i	$-0.897135\pi$
$677$	−13.8759	+	15.4107i	−0.533293	+	0.592282i	0.414943	+	0.909847i	$0.363801\pi$
$678$	8.47611	+	0.109875i	0.325523	+	0.00421974i
$679$	2.70477	+	25.7342i	0.103800	+	0.987588i
$680$	−0.444768	−	0.493965i	−0.0170561	−	0.0189427i
$681$	16.6118	+	7.65556i	0.636565	+	0.293362i
$682$	4.55695	−	5.03914i	0.174495	−	0.192959i
$683$	−6.29672			−0.240937			−0.120469	−	0.992717i	$-0.538440\pi$
$683$	−6.29672			−0.240937			−0.120469	+	0.992717i	$0.538440\pi$
$684$	−20.5861	+	8.53322i	−0.787130	+	0.326276i
$685$	−13.4170	+	9.74801i	−0.512637	+	0.372452i
$686$	2.02016	−	19.2205i	0.0771300	−	0.733843i
$687$	−32.6878	+	14.0487i	−1.24712	+	0.535993i
$688$	3.09516	+	0.657897i	0.118002	+	0.0250821i
$689$	−7.50403	+	3.34101i	−0.285881	+	0.127282i
$690$	0.538647	+	0.614051i	0.0205059	+	0.0233765i
$691$	7.11389	−	1.51210i	0.270625	−	0.0575231i	−0.0706002	−	0.997505i	$-0.522491\pi$
$691$	7.11389	−	1.51210i	0.270625	−	0.0575231i	0.341225	+	0.939982i	$0.389158\pi$
$692$	4.60994			0.175244
$693$	−11.5437	−	13.5680i	−0.438509	−	0.515405i
$694$	28.0386			1.06433
$695$	9.38971	−	1.99584i	0.356172	−	0.0757067i
$696$	7.60852	−	1.51444i	0.288400	−	0.0574047i
$697$	−5.87602	+	2.61617i	−0.222570	+	0.0990946i
$698$	6.97214	+	1.48197i	0.263899	+	0.0560935i
$699$	−0.926402	−	0.691593i	−0.0350397	−	0.0261584i
$700$	−0.187148	+	1.78059i	−0.00707351	+	0.0673000i
$701$	2.71057	−	1.96935i	0.102377	−	0.0743812i	−0.535419	−	0.844587i	$-0.679846\pi$
$701$	2.71057	−	1.96935i	0.102377	−	0.0743812i	0.637796	+	0.770205i	$0.279846\pi$
$702$	5.99866	+	0.233386i	0.226405	+	0.00880857i
$703$	55.6554			2.09908
$704$	−3.02698	−	1.35551i	−0.114083	−	0.0510878i
$705$	−9.34722	+	6.60775i	−0.352037	+	0.248862i
$706$	−17.6920	−	19.6490i	−0.665847	−	0.739498i
$707$	0.0608599	+	0.579043i	0.00228887	+	0.0217771i
$708$	3.82629	+	6.83028i	0.143801	+	0.256698i
$709$	−24.2818	+	26.9677i	−0.911923	+	1.01279i	0.0879377	+	0.996126i	$0.471972\pi$
$709$	−24.2818	+	26.9677i	−0.911923	+	1.01279i	−0.999861	+	0.0166675i	$0.994694\pi$
$710$	0.791178	+	2.43500i	0.0296924	+	0.0913838i
$711$	−3.46638	−	1.65229i	−0.129999	−	0.0619658i
$712$	−8.39069	+	6.09620i	−0.314455	+	0.228465i
$713$	−0.944936	+	0.200852i	−0.0353881	+	0.00752198i
$714$	−0.188871	−	2.05259i	−0.00706832	−	0.0768163i
$715$	3.50383	−	1.55097i	0.131036	−	0.0580031i
$716$	6.62122	−	11.4683i	0.247447	−	0.428590i
$717$	−7.90429	−	1.78750i	−0.295191	−	0.0667553i
$718$	−34.1153	−	15.1891i	−1.27317	−	0.566853i
$719$	16.6249	+	12.0787i	0.620003	+	0.450458i	0.852922	−	0.522038i	$-0.174828\pi$
$719$	16.6249	+	12.0787i	0.620003	+	0.450458i	−0.232920	+	0.972496i	$0.574828\pi$
$720$	2.99899	+	0.0777646i	0.111766	+	0.00289812i
$721$	3.29727	+	10.1479i	0.122797	+	0.377929i
$722$	−3.78166	+	35.9801i	−0.140739	+	1.33904i
$723$	27.4089	−	5.45561i	1.01935	−	0.202896i
$724$	−13.3222	−	14.7958i	−0.495115	−	0.549881i
$725$	−2.23948	+	3.87889i	−0.0831721	+	0.144058i
$726$	−6.19958	+	18.0157i	−0.230088	+	0.668625i
$727$	0.357648	+	0.619465i	0.0132644	+	0.0229747i	0.872581	−	0.488469i	$-0.162444\pi$
$727$	0.357648	+	0.619465i	0.0132644	+	0.0229747i	−0.859317	+	0.511443i	$0.829111\pi$
$728$	−0.639194	+	1.96724i	−0.0236901	+	0.0729107i
$729$	10.3133	−	24.9527i	0.381975	−	0.924173i
$730$	9.59377	+	6.97028i	0.355081	+	0.257982i
$731$	1.40739	−	1.56306i	0.0520540	−	0.0578118i
$732$	−6.61336	−	4.93712i	−0.244437	−	0.182481i
$733$	34.5013	−	15.3610i	1.27433	−	0.567370i	0.345692	−	0.938348i	$-0.387644\pi$
$733$	34.5013	−	15.3610i	1.27433	−	0.567370i	0.928642	+	0.370978i	$0.120977\pi$
$734$	−0.452827	−	4.30836i	−0.0167142	−	0.159025i
$735$	4.46062	−	4.82670i	0.164532	−	0.178036i
$736$	0.235796	+	0.408411i	0.00869157	+	0.0150542i
$737$	14.4367	+	10.5364i	0.531782	+	0.388114i
$738$	9.68351	−	27.3676i	0.356455	−	1.00742i
$739$	−4.45088	+	13.6984i	−0.163728	+	0.503904i	−0.998940	−	0.0460242i	$-0.985345\pi$
$739$	−4.45088	+	13.6984i	−0.163728	+	0.503904i	0.835212	+	0.549928i	$0.185345\pi$
$740$	−6.84468	−	3.04745i	−0.251615	−	0.112026i
$741$	7.59840	−	12.7755i	0.279134	−	0.469319i
$742$	−12.4514	−	2.64662i	−0.457104	−	0.0971605i
$743$	−20.5990	−	4.37846i	−0.755705	−	0.160630i	−0.186080	−	0.982535i	$-0.559578\pi$
$743$	−20.5990	−	4.37846i	−0.755705	−	0.160630i	−0.569625	+	0.821904i	$0.692912\pi$
$744$	−1.81371	+	3.04946i	−0.0664938	+	0.111799i
$745$	6.12804	+	2.72838i	0.224514	+	0.0999601i
$746$	−6.74480	+	20.7584i	−0.246945	+	0.760017i
$747$	−25.7630	+	4.78169i	−0.942618	+	0.174953i
$748$	−1.78630	+	1.29196i	−0.0653137	+	0.0472386i
$749$	−9.26276	−	16.0436i	−0.338454	−	0.586219i
$750$	−1.17555	+	1.27203i	−0.0429252	+	0.0464481i
$751$	2.79881	+	26.6289i	0.102130	+	0.971701i	0.918834	+	0.394644i	$0.129132\pi$
$751$	2.79881	+	26.6289i	0.102130	+	0.971701i	−0.816704	+	0.577057i	$0.804201\pi$
$752$	−6.03753	+	2.68808i	−0.220166	+	0.0980243i
$753$	−10.3858	−	7.75338i	−0.378480	−	0.282549i
$754$	−3.46249	+	3.84549i	−0.126097	+	0.140044i
$755$	7.56165	+	5.49386i	0.275197	+	0.199942i
$756$	7.30815	+	5.75674i	0.265795	+	0.209371i
$757$	−4.83847	+	14.8913i	−0.175857	+	0.541233i	−0.999672	−	0.0256267i	$-0.991842\pi$
$757$	−4.83847	+	14.8913i	−0.175857	+	0.541233i	0.823814	+	0.566860i	$0.191842\pi$
$758$	16.0624	+	27.8209i	0.583413	+	1.01050i
$759$	2.21552	−	1.55906i	0.0804183	−	0.0565902i
$760$	3.71410	−	6.43302i	0.134725	−	0.233350i
$761$	22.2529	+	24.7144i	0.806667	+	0.895895i	0.996299	−	0.0859606i	$-0.0273959\pi$
$761$	22.2529	+	24.7144i	0.806667	+	0.895895i	−0.189631	+	0.981855i	$0.560729\pi$
$762$	−26.2694	+	5.22880i	−0.951640	+	0.189419i
$763$	−2.35111	+	22.3693i	−0.0851158	+	0.809823i
$764$	−4.28529	−	13.1888i	−0.155036	−	0.477152i
$765$	1.04147	−	1.70051i	0.0376546	−	0.0614819i
$766$	−8.97645	−	6.52177i	−0.324332	−	0.235641i
$767$	−4.77064	−	2.12403i	−0.172258	−	0.0766941i
$768$	1.68939	+	0.382043i	0.0609607	+	0.0137858i
$769$	24.7389	−	42.8490i	0.892108	−	1.54518i	0.0547637	−	0.998499i	$-0.482559\pi$
$769$	24.7389	−	42.8490i	0.892108	−	1.54518i	0.837344	−	0.546676i	$-0.184107\pi$
$770$	5.80564	+	1.24710i	0.209221	+	0.0449423i
$771$	2.40886	+	26.1787i	0.0867528	+	0.942802i
$772$	−4.18429	+	0.889398i	−0.150596	+	0.0320101i
$773$	1.15828	−	0.841538i	0.0416603	−	0.0302680i	−0.566760	−	0.823883i	$-0.691803\pi$
$773$	1.15828	−	0.841538i	0.0416603	−	0.0302680i	0.608421	+	0.793615i	$0.291803\pi$
$774$	0.747224	+	9.46347i	0.0268584	+	0.340158i
$775$	−0.633013	−	1.94822i	−0.0227385	−	0.0699820i
$776$	−9.67069	+	10.7404i	−0.347158	+	0.385558i
$777$	−11.3555	−	20.2705i	−0.407375	−	0.727202i
$778$	3.54900	+	33.7665i	0.127238	+	1.21059i
$779$	−48.0977	−	53.4180i	−1.72328	−	1.91390i
$780$	−1.63401	+	1.15511i	−0.0585068	+	0.0413597i
$781$	8.30980	−	1.74761i	0.297348	−	0.0625344i
$782$	0.313466			0.0112095
$783$	10.8443	+	20.5925i	0.387544	+	0.735915i
$784$	3.06980	−	2.23034i	0.109636	−	0.0796549i
$785$	−0.446642	+	4.24951i	−0.0159413	+	0.151672i
$786$	3.85823	+	2.88031i	0.137619	+	0.102737i
$787$	−35.7444	−	7.59770i	−1.27415	−	0.270829i	−0.479309	−	0.877646i	$-0.659113\pi$
$787$	−35.7444	−	7.59770i	−1.27415	−	0.270829i	−0.794841	+	0.606818i	$0.792446\pi$
$788$	−21.5116	+	9.57760i	−0.766321	+	0.341188i
$789$	36.7752	−	7.31993i	1.30923	−	0.260596i
$790$	1.25204	−	0.266129i	0.0445456	−	0.00946846i
$791$	−8.76237			−0.311554
$792$	1.31744	−	9.86227i	0.0468131	−	0.350440i
$793$	5.50492			0.195485
$794$	−11.2835	+	2.39838i	−0.400436	+	0.0851154i
$795$	−8.12083	−	9.25764i	−0.288016	−	0.328335i
$796$	12.6091	−	5.61395i	0.446919	−	0.198981i
$797$	37.1783	+	7.90249i	1.31692	+	0.279921i	0.812209	−	0.583366i	$-0.198265\pi$
$797$	37.1783	+	7.90249i	1.31692	+	0.279921i	0.504713	+	0.863287i	$0.331598\pi$
$798$	21.1635	−	9.09575i	0.749179	−	0.321986i
$799$	−0.459184	+	4.36885i	−0.0162448	+	0.154559i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	−24.6896	−	18.9349i	−0.872363	−	0.669033i
$802$	−27.8943			−0.984983
$803$	26.3800	−	29.1714i	0.930930	−	1.02944i
$804$	−8.47685	−	3.90657i	−0.298955	−	0.137774i
$805$	−0.564973	−	0.627466i	−0.0199127	−	0.0221153i
$806$	−0.247381	−	2.35367i	−0.00871362	−	0.0829046i
$807$	−36.3809	−	0.471604i	−1.28067	−	0.0166012i
$808$	−0.217599	+	0.241669i	−0.00765512	+	0.00850187i
$809$	−5.38380	−	16.5696i	−0.189284	−	0.582558i	0.810711	−	0.585446i	$-0.199081\pi$
$809$	−5.38380	−	16.5696i	−0.189284	−	0.582558i	−0.999996	+	0.00288846i	$0.999081\pi$
$810$	2.33381	+	8.69214i	0.0820018	+	0.305411i
$811$	−21.5802	+	15.6789i	−0.757784	+	0.550562i	−0.898230	−	0.439526i	$-0.855146\pi$
$811$	−21.5802	+	15.6789i	−0.757784	+	0.550562i	0.140446	+	0.990088i	$0.455146\pi$
$812$	−7.84388	+	1.66727i	−0.275266	+	0.0585096i
$813$	13.8642	−	9.80092i	0.486240	−	0.343733i
$814$	−12.4711	+	21.4936i	−0.437112	+	0.753350i
$815$	−8.94445	+	15.4922i	−0.313310	+	0.542670i
$816$	0.781387	−	0.845516i	0.0273540	−	0.0295990i
$817$	21.4730	+	9.56040i	0.751246	+	0.334476i
$818$	−29.2906	−	21.2809i	−1.02412	−	0.744068i
$819$	−6.20334	−	0.160854i	−0.216762	−	0.00562070i
$820$	2.99028	+	9.20314i	0.104425	+	0.321388i
$821$	−4.07811	+	38.8006i	−0.142327	+	1.35415i	0.657289	+	0.753639i	$0.271703\pi$
$821$	−4.07811	+	38.8006i	−0.142327	+	1.35415i	−0.799616	+	0.600512i	$0.794964\pi$
$822$	−18.9424	−	21.5941i	−0.660691	−	0.753180i
$823$	14.7508	+	16.3824i	0.514180	+	0.571055i	0.943194	−	0.332243i	$-0.107806\pi$
$823$	14.7508	+	16.3824i	0.514180	+	0.571055i	−0.429014	+	0.903298i	$0.641139\pi$
$824$	−2.97984	+	5.16123i	−0.103808	+	0.179800i
$825$	3.77890	+	4.32665i	0.131564	+	0.150635i
$826$	−4.04636	−	7.00851i	−0.140791	−	0.243857i
$827$	−0.439360	+	1.35221i	−0.0152781	+	0.0470210i	−0.958405	−	0.285412i	$-0.907870\pi$
$827$	−0.439360	+	1.35221i	−0.0152781	+	0.0470210i	0.943127	+	0.332433i	$0.107870\pi$
$828$	−0.973607	+	1.02649i	−0.0338352	+	0.0356731i
$829$	−19.0252	−	13.8226i	−0.660772	−	0.480079i	0.206151	−	0.978520i	$-0.433906\pi$
$829$	−19.0252	−	13.8226i	−0.660772	−	0.480079i	−0.866924	+	0.498441i	$0.833906\pi$
$830$	5.84440	−	6.49087i	0.202862	−	0.225301i
$831$	−1.94214	+	16.4270i	−0.0673721	+	0.569847i
$832$	−1.05543	+	0.469910i	−0.0365906	+	0.0162912i
$833$	−0.263639	−	2.50836i	−0.00913455	−	0.0869094i
$834$	4.93256	+	15.8783i	0.170801	+	0.549820i
$835$	−10.2114	−	17.6867i	−0.353381	−	0.612074i
$836$	−19.9002	−	14.5239i	−0.688262	−	0.502319i
$837$	−10.3177	−	2.61615i	−0.356631	−	0.0904273i
$838$	−0.543299	+	1.67210i	−0.0187679	+	0.0577618i
$839$	17.8724	+	7.95730i	0.617023	+	0.274716i	0.691353	−	0.722517i	$-0.257015\pi$
$839$	17.8724	+	7.95730i	0.617023	+	0.274716i	−0.0743298	+	0.997234i	$0.523682\pi$
$840$	−3.10080	−	0.0401955i	−0.106988	−	0.00138688i
$841$	8.74361	+	1.85851i	0.301504	+	0.0640866i
$842$	9.38578	+	1.99501i	0.323455	+	0.0687525i
$843$	−13.2070	−	23.5757i	−0.454873	−	0.811991i
$844$	−7.22795	−	3.21809i	−0.248796	−	0.110771i
$845$	−3.60476	+	11.0943i	−0.124007	+	0.381656i
$846$	−12.8803	−	15.0731i	−0.442833	−	0.518222i
$847$	6.16650	−	18.7041i	0.211883	−	0.642680i
$848$	−3.55495	−	6.15735i	−0.122077	−	0.211444i
$849$	−25.1808	−	5.69446i	−0.864204	−	0.195433i
$850$	0.0694797	+	0.661055i	0.00238313	+	0.0226740i
$851$	3.22790	−	1.43715i	0.110651	−	0.0492650i
$852$	−4.07423	+	1.75104i	−0.139581	+	0.0599898i
$853$	−0.518549	+	0.575906i	−0.0177548	+	0.0197187i	−0.751957	−	0.659212i	$-0.770890\pi$
$853$	−0.518549	+	0.575906i	−0.0177548	+	0.0197187i	0.734202	+	0.678931i	$0.237556\pi$
$854$	6.90172	+	5.01439i	0.236172	+	0.171589i
$855$	21.6702	+	5.19671i	0.741106	+	0.177724i
$856$	3.19745	−	9.84073i	0.109287	−	0.336349i
$857$	−22.0008	−	38.1065i	−0.751533	−	1.30169i	−0.947079	−	0.320999i	$-0.895981\pi$
$857$	−22.0008	−	38.1065i	−0.751533	−	1.30169i	0.195546	−	0.980694i	$-0.437352\pi$
$858$	3.23114	+	5.79713i	0.110309	+	0.197911i
$859$	5.82967	−	10.0973i	0.198906	−	0.344515i	−0.749268	−	0.662267i	$-0.769595\pi$
$859$	5.82967	−	10.0973i	0.198906	−	0.344515i	0.948174	+	0.317752i	$0.102928\pi$
$860$	−2.11734	−	2.35154i	−0.0722006	−	0.0801869i
$861$	−9.64219	+	28.4169i	−0.328605	+	0.968445i
$862$	−0.883443	+	8.40540i	−0.0300902	+	0.286289i
$863$	−12.1246	−	37.3158i	−0.412727	−	1.27024i	−0.914268	−	0.405110i	$-0.867233\pi$
$863$	−12.1246	−	37.3158i	−0.412727	−	1.27024i	0.501541	−	0.865134i	$-0.332767\pi$
$864$	0.341832	+	5.18490i	0.0116294	+	0.176394i
$865$	−3.72952	−	2.70966i	−0.126807	−	0.0921310i
$866$	−5.54802	−	2.47014i	−0.188530	−	0.0839388i
$867$	8.50819	+	27.3885i	0.288953	+	0.930163i
$868$	1.83379	−	3.17622i	0.0622430	−	0.107808i
$869$	−0.434665	−	4.22301i	−0.0147450	−	0.143256i
$870$	−7.04559	−	3.24697i	−0.238868	−	0.110083i
$871$	6.08975	−	1.29442i	0.206343	−	0.0438596i
$872$	−10.1636	+	7.38427i	−0.344182	+	0.250063i
$873$	−39.1389	−	18.6560i	−1.32465	−	0.631412i
$874$	1.08251	+	3.33164i	0.0366166	+	0.112694i
$875$	1.19801	−	1.33052i	0.0405001	−	0.0449799i
$876$	−10.4995	+	17.6532i	−0.354745	+	0.596447i
$877$	5.59861	+	53.2672i	0.189051	+	1.79870i	0.519072	+	0.854731i	$0.326278\pi$
$877$	5.59861	+	53.2672i	0.189051	+	1.79870i	−0.330020	+	0.943974i	$0.607056\pi$
$878$	−10.9973	−	12.2138i	−0.371142	−	0.412195i
$879$	−3.07327	−	33.3993i	−0.103659	−	1.12653i
$880$	1.65212	+	2.87585i	0.0556931	+	0.0969447i
$881$	−17.6407			−0.594330			−0.297165	−	0.954826i	$-0.596041\pi$
$881$	−17.6407			−0.594330			−0.297165	+	0.954826i	$0.596041\pi$
$882$	9.03285	+	6.92749i	0.304152	+	0.233261i
$883$	−23.5952	+	17.1429i	−0.794043	+	0.576906i	−0.909160	−	0.416446i	$-0.863275\pi$
$883$	−23.5952	+	17.1429i	−0.794043	+	0.576906i	0.115118	+	0.993352i	$0.463275\pi$
$884$	−0.0802710	+	0.763728i	−0.00269981	+	0.0256869i
$885$	0.919207	−	7.77485i	0.0308988	−	0.261349i
$886$	−21.1843	−	4.50285i	−0.711699	−	0.151276i
$887$	−32.1267	+	14.3037i	−1.07871	+	0.480272i	−0.867636	−	0.497199i	$-0.834362\pi$
$887$	−32.1267	+	14.3037i	−1.07871	+	0.480272i	−0.211071	+	0.977471i	$0.567695\pi$
$888$	4.16984	−	12.2891i	0.139931	−	0.412395i
$889$	27.0820	−	5.75646i	0.908301	−	0.193065i
$890$	10.3715			0.347652
$891$	29.4898	−	4.62109i	0.987944	−	0.154812i
$892$	−25.0867			−0.839964
$893$	−48.0195	+	10.2069i	−1.60691	+	0.341560i
$894$	−3.73326	+	11.0024i	−0.124859	+	0.367977i
$895$	−12.0976	+	5.38619i	−0.404377	+	0.180040i
$896$	−1.75127	−	0.372245i	−0.0585059	−	0.0124358i
$897$	0.110799	−	0.937162i	0.00369947	−	0.0312909i
$898$	−1.54247	+	14.6756i	−0.0514730	+	0.489733i
$899$	7.42275	−	5.39295i	0.247563	−	0.179865i
$900$	−2.38053	−	1.82568i	−0.0793509	−	0.0608559i
$901$	−4.72592			−0.157443
$902$	31.4071	−	6.60515i	1.04574	−	0.219927i
$903$	−0.899127	−	9.77143i	−0.0299211	−	0.325173i
$904$	−3.27479	−	3.63702i	−0.108918	−	0.120965i
$905$	2.08113	+	19.8006i	0.0691791	+	0.658195i
$906$	−8.27554	+	13.9140i	−0.274936	+	0.462261i
$907$	19.4062	−	21.5528i	0.644373	−	0.715649i	−0.329139	−	0.944281i	$-0.606759\pi$
$907$	19.4062	−	21.5528i	0.644373	−	0.715649i	0.973513	+	0.228632i	$0.0734253\pi$
$908$	−3.26331	−	10.0434i	−0.108297	−	0.333303i
$909$	−0.880662	−	0.419778i	−0.0292097	−	0.0139232i
$910$	1.67343	−	1.21582i	0.0554737	−	0.0403040i
$911$	36.8429	−	7.83119i	1.22066	−	0.259459i	0.447856	−	0.894106i	$-0.352188\pi$
$911$	36.8429	−	7.83119i	1.22066	−	0.259459i	0.772802	+	0.634647i	$0.218854\pi$
$912$	11.6849	+	5.38500i	0.386925	+	0.178315i
$913$	−19.3373	−	21.5695i	−0.639971	−	0.713845i
$914$	−7.48771	+	12.9691i	−0.247671	+	0.428979i
$915$	2.44836	+	7.88145i	0.0809402	+	0.260553i
$916$	18.7656	+	8.35499i	0.620033	+	0.276057i
$917$	−4.02646	−	2.92540i	−0.132965	−	0.0966051i
$918$	3.09826	+	1.52642i	0.102258	+	0.0503793i
$919$	−2.04823	−	6.30381i	−0.0675649	−	0.207943i	0.911574	−	0.411137i	$-0.134868\pi$
$919$	−2.04823	−	6.30381i	−0.0675649	−	0.207943i	−0.979139	+	0.203193i	$0.934868\pi$
$920$	0.0492949	−	0.469009i	0.00162520	−	0.0154628i
$921$	12.9580	−	38.1890i	0.426980	−	1.25837i
$922$	−3.71989	−	4.13135i	−0.122508	−	0.136059i
$923$	1.47898	−	2.56167i	0.0486813	−	0.0843185i
$924$	−1.22956	+	10.2113i	−0.0404496	+	0.335927i
$925$	3.74622	+	6.48864i	0.123175	+	0.213345i
$926$	−2.95998	+	9.10988i	−0.0972710	+	0.299369i
$927$	−17.3861	−	4.16933i	−0.571034	−	0.136939i
$928$	−3.62355	−	2.63266i	−0.118949	−	0.0864214i
$929$	−5.18796	+	5.76181i	−0.170211	+	0.189039i	−0.822215	−	0.569177i	$-0.807262\pi$
$929$	−5.18796	+	5.76181i	−0.170211	+	0.189039i	0.652004	+	0.758216i	$0.273929\pi$
$930$	3.25975	−	1.40099i	0.106891	−	0.0459403i
$931$	25.7493	−	11.4643i	0.843900	−	0.375729i
$932$	0.0697689	+	0.663807i	0.00228536	+	0.0217437i
$933$	−14.9255	−	3.37529i	−0.488638	−	0.110502i
$934$	3.45208	+	5.97919i	0.112956	+	0.195645i
$935$	2.20454	+	0.00474663i	0.0720962	+	0.000155231i
$936$	−2.25163	−	2.63495i	−0.0735967	−	0.0861262i
$937$	−8.67569	+	26.7010i	−0.283422	+	0.872285i	0.703445	+	0.710750i	$0.251644\pi$
$937$	−8.67569	+	26.7010i	−0.283422	+	0.872285i	−0.986867	+	0.161535i	$0.948356\pi$
$938$	8.81401	+	3.92425i	0.287788	+	0.128131i
$939$	−23.7294	−	42.3593i	−0.774381	−	1.38234i
$940$	6.46448	+	1.37407i	0.210848	+	0.0448172i
$941$	23.7713	+	5.05274i	0.774921	+	0.164715i	0.578365	−	0.815778i	$-0.303691\pi$
$941$	23.7713	+	5.05274i	0.774921	+	0.164715i	0.196556	+	0.980493i	$0.437024\pi$
$942$	−7.40030	−	0.0959297i	−0.241115	−	0.00312556i
$943$	−4.16895	−	1.85614i	−0.135760	−	0.0604442i
$944$	1.39678	−	4.29885i	0.0454613	−	0.139916i
$945$	−2.52869	−	8.95292i	−0.0822583	−	0.291239i
$946$	−8.50376	+	6.15041i	−0.276481	+	0.199967i
$947$	10.4840	+	18.1588i	0.340684	+	0.590082i	0.984560	−	0.175048i	$-0.0560081\pi$
$947$	10.4840	+	18.1588i	0.340684	+	0.590082i	−0.643876	+	0.765130i	$0.722675\pi$
$948$	0.657716	+	2.11724i	0.0213616	+	0.0687647i
$949$	−1.43208	−	13.6253i	−0.0464873	−	0.442297i
$950$	−6.78600	+	3.02132i	−0.220167	+	0.0980247i
$951$	1.08663	−	9.19098i	0.0352365	−	0.298038i
$952$	−0.796312	+	0.884394i	−0.0258086	+	0.0286634i
$953$	−21.2545	−	15.4423i	−0.688502	−	0.500226i	0.187665	−	0.982233i	$-0.439908\pi$
$953$	−21.2545	−	15.4423i	−0.688502	−	0.500226i	−0.876167	+	0.482007i	$0.839908\pi$
$954$	14.6784	−	15.4758i	0.475232	−	0.501046i
$955$	−4.28529	+	13.1888i	−0.138669	+	0.426778i
$956$	2.33939	+	4.05194i	0.0756613	+	0.131049i
$957$	−13.2001	+	22.0855i	−0.426700	+	0.713924i
$958$	−11.8511	+	20.5267i	−0.382891	+	0.663186i
$959$	19.8682	+	22.0658i	0.641576	+	0.712543i
$960$	−1.14219	−	1.30208i	−0.0368639	−	0.0420244i
$961$	2.80175	−	26.6569i	0.0903792	−	0.859901i
$962$	2.67489	+	8.23247i	0.0862420	+	0.265426i
$963$	31.0310	+	0.804643i	0.999961	+	0.0259293i
$964$	−13.0535	−	9.48389i	−0.420424	−	0.305456i
$965$	3.90793	+	1.73992i	0.125801	+	0.0560101i
$966$	0.992566	−	1.07403i	0.0319353	−	0.0345563i
$967$	19.8111	−	34.3139i	0.637084	−	1.10346i	−0.348986	−	0.937128i	$-0.613474\pi$
$967$	19.8111	−	34.3139i	0.637084	−	1.10346i	0.986070	−	0.166333i	$-0.0531927\pi$
$968$	10.0682	−	4.43079i	0.323603	−	0.142411i
$969$	6.98329	−	4.93664i	0.224336	−	0.158588i
$970$	14.1368	−	3.00487i	0.453905	−	0.0964805i
$971$	−19.8042	+	14.3886i	−0.635546	+	0.461751i	−0.858317	−	0.513119i	$-0.828490\pi$
$971$	−19.8042	+	14.3886i	−0.635546	+	0.461751i	0.222771	+	0.974871i	$0.428490\pi$
$972$	−14.6215	+	5.40477i	−0.468985	+	0.173358i
$973$	−5.31104	−	16.3457i	−0.170264	−	0.524019i
$974$	−6.35398	+	7.05681i	−0.203595	+	0.226115i
$975$	2.00090	+	0.0259376i	0.0640800	+	0.000830666i
$976$	0.498063	+	4.73876i	0.0159426	+	0.151684i
$977$	−10.8358	−	12.0344i	−0.346669	−	0.385015i	0.544443	−	0.838798i	$-0.316741\pi$
$977$	−10.8358	−	12.0344i	−0.346669	−	0.385015i	−0.891112	+	0.453783i	$0.850074\pi$
$978$	−28.1400	−	12.9684i	−0.899818	−	0.414682i
$979$	3.66925	−	34.2020i	0.117270	−	1.09310i
$980$	−3.79448			−0.121210
$981$	−29.9062	−	22.9357i	−0.954832	−	0.732281i
$982$	−5.89047	+	4.27968i	−0.187973	+	0.136570i
$983$	−3.83226	+	36.4615i	−0.122230	+	1.16294i	0.745710	+	0.666271i	$0.232111\pi$
$983$	−3.83226	+	36.4615i	−0.122230	+	1.16294i	−0.867940	+	0.496670i	$0.834556\pi$
$984$	−15.3987	+	6.61812i	−0.490892	+	0.210978i
$985$	23.0329	+	4.89579i	0.733888	+	0.155993i
$986$	−2.71976	+	1.21091i	−0.0866147	+	0.0385634i
$987$	13.5150	+	15.4069i	0.430187	+	0.490408i
$988$	−8.39440	+	1.78428i	−0.267061	+	0.0567656i
$989$	1.49227			0.0474513
$990$	−6.86273	+	7.20437i	−0.218112	+	0.228970i
$991$	−52.5985			−1.67084			−0.835422	−	0.549608i	$-0.814777\pi$
$991$	−52.5985			−1.67084			−0.835422	+	0.549608i	$0.814777\pi$
$992$	2.00371	−	0.425902i	0.0636179	−	0.0135224i
$993$	30.2103	−	6.01321i	0.958694	−	0.190823i
$994$	4.18766	−	1.86447i	0.132825	−	0.0591373i
$995$	−13.5008	−	2.86968i	−0.428004	−	0.0909751i
$996$	12.1228	+	9.05008i	0.384124	+	0.286763i
$997$	2.76216	−	26.2802i	0.0874784	−	0.832302i	−0.859528	−	0.511088i	$-0.829243\pi$
$997$	2.76216	−	26.2802i	0.0874784	−	0.832302i	0.947007	−	0.321214i	$-0.104091\pi$
$998$	5.26917	−	3.82828i	0.166793	−	0.121182i
$999$	38.9024	+	1.51355i	1.23082	+	0.0478865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.31.6	✓	88
9.7	even	3	inner	990.2.bg.a.691.1	yes	88
11.5	even	5	inner	990.2.bg.a.841.1	yes	88
99.16	even	15	inner	990.2.bg.a.511.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.31.6	✓	88	1.1	even	1	trivial
990.2.bg.a.511.6	yes	88	99.16	even	15	inner
990.2.bg.a.691.1	yes	88	9.7	even	3	inner
990.2.bg.a.841.1	yes	88	11.5	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 + 0.207912i) q^{2} +(-0.556540 + 1.64020i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(0.203361 - 1.72007i) q^{6} +(-0.187148 + 1.78059i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-2.38053 - 1.82568i) q^{9} +1.00000 q^{10} +(0.353783 - 3.29770i) q^{11} +(0.158706 + 1.72476i) q^{12} +(-0.773058 - 0.858568i) q^{13} +(-0.187148 - 1.78059i) q^{14} +(0.885395 - 1.48865i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-0.205402 - 0.632163i) q^{17} +(2.70809 + 1.29084i) q^{18} +(6.00955 - 4.36619i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(-2.81637 - 1.29793i) q^{21} +(0.339579 + 3.29919i) q^{22} +(0.235796 - 0.408411i) q^{23} +(-0.513836 - 1.65408i) q^{24} +(0.913545 + 0.406737i) q^{25} +(0.934671 + 0.679078i) q^{26} +(4.31934 - 2.88848i) q^{27} +(0.553263 + 1.70277i) q^{28} +(-0.468178 + 4.45442i) q^{29} +(-0.556540 + 1.64020i) q^{30} +(-1.37070 - 1.52231i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.21200 + 2.41558i) q^{33} +(0.332348 + 0.575644i) q^{34} +(0.553263 - 1.70277i) q^{35} +(-2.91729 - 0.699591i) q^{36} +(6.06151 + 4.40394i) q^{37} +(-4.97044 + 5.52023i) q^{38} +(1.83846 - 0.790144i) q^{39} +(0.913545 - 0.406737i) q^{40} +(-1.01150 - 9.62375i) q^{41} +(3.02468 + 0.684009i) q^{42} +(1.58215 + 2.74037i) q^{43} +(-1.01810 - 3.15650i) q^{44} +(1.94893 + 2.28072i) q^{45} +(-0.145730 + 0.448511i) q^{46} +(-6.03753 - 2.68808i) q^{47} +(0.846510 + 1.51110i) q^{48} +(3.71156 + 0.788916i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(1.15119 + 0.0149228i) q^{51} +(-1.05543 - 0.469910i) q^{52} +(2.19708 - 6.76191i) q^{53} +(-3.62440 + 3.72340i) q^{54} +(-1.03168 + 3.15208i) q^{55} +(-0.895199 - 1.55053i) q^{56} +(3.81688 + 12.2868i) q^{57} +(-0.468178 - 4.45442i) q^{58} +(4.12929 - 1.83848i) q^{59} +(0.203361 - 1.72007i) q^{60} +(-3.18831 + 3.54098i) q^{61} +(1.65725 + 1.20406i) q^{62} +(3.69629 - 3.89707i) q^{63} +(0.309017 - 0.951057i) q^{64} +(0.577658 + 1.00053i) q^{65} +(-5.60034 - 1.27916i) q^{66} +(-2.69441 + 4.66686i) q^{67} +(-0.444768 - 0.493965i) q^{68} +(0.538647 + 0.614051i) q^{69} +(-0.187148 + 1.78059i) q^{70} +(0.791178 + 2.43500i) q^{71} +(2.99899 + 0.0777646i) q^{72} +(9.59377 + 6.97028i) q^{73} +(-6.84468 - 3.04745i) q^{74} +(-1.17555 + 1.27203i) q^{75} +(3.71410 - 6.43302i) q^{76} +(5.80564 + 1.24710i) q^{77} +(-1.63401 + 1.15511i) q^{78} +(1.25204 - 0.266129i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(2.33381 + 8.69214i) q^{81} +(2.99028 + 9.20314i) q^{82} +(5.84440 - 6.49087i) q^{83} +(-3.10080 - 0.0401955i) q^{84} +(0.0694797 + 0.661055i) q^{85} +(-2.11734 - 2.35154i) q^{86} +(-7.04559 - 3.24697i) q^{87} +(1.65212 + 2.87585i) q^{88} +10.3715 q^{89} +(-2.38053 - 1.82568i) q^{90} +(1.67343 - 1.21582i) q^{91} +(0.0492949 - 0.469009i) q^{92} +(3.25975 - 1.40099i) q^{93} +(6.46448 + 1.37407i) q^{94} +(-6.78600 + 3.02132i) q^{95} +(-1.14219 - 1.30208i) q^{96} +(14.1368 - 3.00487i) q^{97} -3.79448 q^{98} +(-6.86273 + 7.20437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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