LMFDB - Embedded newform 64.2.i.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,2,Mod(5,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("64.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	64.i (of order $16$, 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:	$0.511042572936$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	64.5
Dual form			64.2.i.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.406933 - 1.35440i) q^{2} +(1.06920 + 0.714416i) q^{3} +(-1.66881 - 1.10230i) q^{4} +(-0.330507 - 0.0657419i) q^{5} +(1.40270 - 1.15741i) q^{6} +(-0.739314 + 1.78486i) q^{7} +(-2.17206 + 1.81168i) q^{8} +(-0.515254 - 1.24393i) q^{9} +O(q^{10})$	\(q+(0.406933 - 1.35440i) q^{2} +(1.06920 + 0.714416i) q^{3} +(-1.66881 - 1.10230i) q^{4} +(-0.330507 - 0.0657419i) q^{5} +(1.40270 - 1.15741i) q^{6} +(-0.739314 + 1.78486i) q^{7} +(-2.17206 + 1.81168i) q^{8} +(-0.515254 - 1.24393i) q^{9} +(-0.223535 + 0.420887i) q^{10} +(0.971610 + 1.45412i) q^{11} +(-0.996787 - 2.37081i) q^{12} +(-3.70516 + 0.737003i) q^{13} +(2.11657 + 1.72765i) q^{14} +(-0.306411 - 0.306411i) q^{15} +(1.56986 + 3.67907i) q^{16} +(4.47305 - 4.47305i) q^{17} +(-1.89446 + 0.191663i) q^{18} +(1.16088 + 5.83613i) q^{19} +(0.479086 + 0.474030i) q^{20} +(-2.06561 + 1.38019i) q^{21} +(2.36484 - 0.724221i) q^{22} +(-1.28371 + 0.531730i) q^{23} +(-3.61665 + 0.385291i) q^{24} +(-4.51448 - 1.86996i) q^{25} +(-0.509557 + 5.31819i) q^{26} +(1.09039 - 5.48174i) q^{27} +(3.20123 - 2.16365i) q^{28} +(3.04996 - 4.56458i) q^{29} +(-0.539692 + 0.290314i) q^{30} -10.2910i q^{31} +(5.62177 - 0.629080i) q^{32} +2.24887i q^{33} +(-4.23807 - 7.87854i) q^{34} +(0.361689 - 0.541305i) q^{35} +(-0.511331 + 2.64386i) q^{36} +(-0.910827 + 4.57904i) q^{37} +(8.37686 + 0.802620i) q^{38} +(-4.48808 - 1.85903i) q^{39} +(0.836983 - 0.455977i) q^{40} +(2.66002 - 1.10181i) q^{41} +(1.02877 + 3.35931i) q^{42} +(-5.83495 + 3.89879i) q^{43} +(-0.0185551 - 3.49765i) q^{44} +(0.0885166 + 0.445003i) q^{45} +(0.197792 + 1.95504i) q^{46} +(-0.0482001 + 0.0482001i) q^{47} +(-0.949897 + 5.05519i) q^{48} +(2.31060 + 2.31060i) q^{49} +(-4.36977 + 5.35348i) q^{50} +(7.97819 - 1.58696i) q^{51} +(6.99562 + 2.85430i) q^{52} +(6.43049 + 9.62391i) q^{53} +(-6.98076 - 3.70752i) q^{54} +(-0.225527 - 0.544471i) q^{55} +(-1.62776 - 5.21622i) q^{56} +(-2.92821 + 7.06933i) q^{57} +(-4.94115 - 5.98835i) q^{58} +(-2.89770 - 0.576389i) q^{59} +(0.173584 + 0.849098i) q^{60} +(-0.675800 - 0.451555i) q^{61} +(-13.9382 - 4.18776i) q^{62} +2.60119 q^{63} +(1.43566 - 7.87013i) q^{64} +1.27304 q^{65} +(3.04588 + 0.915141i) q^{66} +(-2.41244 - 1.61194i) q^{67} +(-12.3953 + 2.53401i) q^{68} +(-1.75242 - 0.348577i) q^{69} +(-0.585962 - 0.710147i) q^{70} +(-2.88474 + 6.96439i) q^{71} +(3.37277 + 1.76842i) q^{72} +(1.92544 + 4.64843i) q^{73} +(5.83121 + 3.09699i) q^{74} +(-3.49095 - 5.22458i) q^{75} +(4.49589 - 11.0190i) q^{76} +(-3.31372 + 0.659140i) q^{77} +(-4.34422 + 5.32217i) q^{78} +(10.5317 + 10.5317i) q^{79} +(-0.276979 - 1.31916i) q^{80} +(2.22588 - 2.22588i) q^{81} +(-0.409851 - 4.05110i) q^{82} +(-0.0104591 - 0.0525816i) q^{83} +(4.96850 - 0.0263579i) q^{84} +(-1.77244 + 1.18431i) q^{85} +(2.90609 + 9.48942i) q^{86} +(6.52202 - 2.70151i) q^{87} +(-4.74478 - 1.39818i) q^{88} +(-7.52277 - 3.11604i) q^{89} +(0.638733 + 0.0611995i) q^{90} +(1.42383 - 7.15808i) q^{91} +(2.72840 + 0.527681i) q^{92} +(7.35206 - 11.0031i) q^{93} +(0.0456681 + 0.0848966i) q^{94} -2.00520i q^{95} +(6.46021 + 3.34367i) q^{96} +12.1748i q^{97} +(4.06974 - 2.18922i) q^{98} +(1.30820 - 1.95786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{1}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	0.406933	−	1.35440i	0.287745	−	0.957707i
$2$	0.406933	−	1.35440i	0.287745	−	0.957707i
$3$	1.06920	+	0.714416i	0.617302	+	0.412468i	0.824525	−	0.565826i	$-0.191443\pi$
$3$	1.06920	+	0.714416i	0.617302	+	0.412468i	−0.207223	+	0.978294i	$0.566443\pi$
$4$	−1.66881	−	1.10230i	−0.834405	−	0.551152i
$5$	−0.330507	−	0.0657419i	−0.147807	−	0.0294007i	0.120632	−	0.992697i	$-0.461508\pi$
$5$	−0.330507	−	0.0657419i	−0.147807	−	0.0294007i	−0.268439	+	0.963297i	$0.586508\pi$
$6$	1.40270	−	1.15741i	0.572649	−	0.472509i
$7$	−0.739314	+	1.78486i	−0.279434	+	0.674614i	−0.999820	−	0.0189592i	$-0.993965\pi$
$7$	−0.739314	+	1.78486i	−0.279434	+	0.674614i	0.720386	+	0.693573i	$0.243965\pi$
$8$	−2.17206	+	1.81168i	−0.767938	+	0.640524i
$9$	−0.515254	−	1.24393i	−0.171751	−	0.414645i
$10$	−0.223535	+	0.420887i	−0.0706881	+	0.133096i
$11$	0.971610	+	1.45412i	0.292951	+	0.438433i	0.948527	−	0.316697i	$-0.102574\pi$
$11$	0.971610	+	1.45412i	0.292951	+	0.438433i	−0.655575	+	0.755130i	$0.727574\pi$
$12$	−0.996787	−	2.37081i	−0.287748	−	0.684392i
$13$	−3.70516	+	0.737003i	−1.02763	+	0.204408i	−0.679990	−	0.733221i	$-0.738016\pi$
$13$	−3.70516	+	0.737003i	−1.02763	+	0.204408i	−0.347638	+	0.937629i	$0.613016\pi$
$14$	2.11657	+	1.72765i	0.565677	+	0.461733i
$15$	−0.306411	−	0.306411i	−0.0791149	−	0.0791149i
$16$	1.56986	+	3.67907i	0.392464	+	0.919767i
$17$	4.47305	−	4.47305i	1.08487	−	1.08487i	0.0888265	−	0.996047i	$-0.471688\pi$
$17$	4.47305	−	4.47305i	1.08487	−	1.08487i	0.996047	−	0.0888265i	$-0.0283117\pi$
$18$	−1.89446	+	0.191663i	−0.446529	+	0.0451755i
$19$	1.16088	+	5.83613i	0.266324	+	1.33890i	0.849944	+	0.526873i	$0.176636\pi$
$19$	1.16088	+	5.83613i	0.266324	+	1.33890i	−0.583621	+	0.812026i	$0.698364\pi$
$20$	0.479086	+	0.474030i	0.107127	+	0.105996i
$21$	−2.06561	+	1.38019i	−0.450752	+	0.301183i
$22$	2.36484	−	0.724221i	0.504185	−	0.154405i
$23$	−1.28371	+	0.531730i	−0.267672	+	0.110873i	−0.512483	−	0.858697i	$-0.671274\pi$
$23$	−1.28371	+	0.531730i	−0.267672	+	0.110873i	0.244811	+	0.969571i	$0.421274\pi$
$24$	−3.61665	+	0.385291i	−0.738245	+	0.0786471i
$25$	−4.51448	−	1.86996i	−0.902897	−	0.373992i
$26$	−0.509557	+	5.31819i	−0.0999323	+	1.04298i
$27$	1.09039	−	5.48174i	0.209845	−	1.05496i
$28$	3.20123	−	2.16365i	0.604976	−	0.408891i
$29$	3.04996	−	4.56458i	0.566362	−	0.847621i	−0.432169	−	0.901793i	$-0.642252\pi$
$29$	3.04996	−	4.56458i	0.566362	−	0.847621i	0.998532	+	0.0541712i	$0.0172517\pi$
$30$	−0.539692	+	0.290314i	−0.0985338	+	0.0530039i
$31$		−	10.2910i		−	1.84832i	−0.382004	−	0.924161i	$-0.624766\pi$
$31$		−	10.2910i		−	1.84832i	0.382004	−	0.924161i	$-0.375234\pi$
$32$	5.62177	−	0.629080i	0.993797	−	0.111207i
$33$			2.24887i			0.391478i
$34$	−4.23807	−	7.87854i	−0.726824	−	1.35116i
$35$	0.361689	−	0.541305i	0.0611366	−	0.0914973i
$36$	−0.511331	+	2.64386i	−0.0852218	+	0.440643i
$37$	−0.910827	+	4.57904i	−0.149739	+	0.752789i	0.830816	+	0.556547i	$0.187874\pi$
$37$	−0.910827	+	4.57904i	−0.149739	+	0.752789i	−0.980555	+	0.196242i	$0.937126\pi$
$38$	8.37686	+	0.802620i	1.35891	+	0.130202i
$39$	−4.48808	−	1.85903i	−0.718669	−	0.297682i
$40$	0.836983	−	0.455977i	0.132339	−	0.0720962i
$41$	2.66002	−	1.10181i	0.415425	−	0.172074i	−0.165174	−	0.986264i	$-0.552819\pi$
$41$	2.66002	−	1.10181i	0.415425	−	0.172074i	0.580599	+	0.814190i	$0.302819\pi$
$42$	1.02877	+	3.35931i	0.158743	+	0.518353i
$43$	−5.83495	+	3.89879i	−0.889821	+	0.594560i	−0.914254	−	0.405142i	$-0.867222\pi$
$43$	−5.83495	+	3.89879i	−0.889821	+	0.594560i	0.0244324	+	0.999701i	$0.492222\pi$
$44$	−0.0185551	−	3.49765i	−0.00279729	−	0.527291i
$45$	0.0885166	+	0.445003i	0.0131953	+	0.0663371i
$46$	0.197792	+	1.95504i	0.0291628	+	0.288255i
$47$	−0.0482001	+	0.0482001i	−0.00703071	+	0.00703071i	−0.710613	−	0.703583i	$-0.751582\pi$
$47$	−0.0482001	+	0.0482001i	−0.00703071	+	0.00703071i	0.703583	+	0.710613i	$0.251582\pi$
$48$	−0.949897	+	5.05519i	−0.137106	+	0.729653i
$49$	2.31060	+	2.31060i	0.330086	+	0.330086i
$50$	−4.36977	+	5.35348i	−0.617979	+	0.757096i
$51$	7.97819	−	1.58696i	1.11717	−	0.222219i
$52$	6.99562	+	2.85430i	0.970118	+	0.395820i
$53$	6.43049	+	9.62391i	0.883296	+	1.32195i	0.946085	+	0.323919i	$0.105001\pi$
$53$	6.43049	+	9.62391i	0.883296	+	1.32195i	−0.0627888	+	0.998027i	$0.519999\pi$
$54$	−6.98076	−	3.70752i	−0.949961	−	0.504530i
$55$	−0.225527	−	0.544471i	−0.0304101	−	0.0734165i
$56$	−1.62776	−	5.21622i	−0.217519	−	0.697046i
$57$	−2.92821	+	7.06933i	−0.387851	+	0.936355i
$58$	−4.94115	−	5.98835i	−0.648805	−	0.786308i
$59$	−2.89770	−	0.576389i	−0.377249	−	0.0750395i	0.00282397	−	0.999996i	$-0.499101\pi$
$59$	−2.89770	−	0.576389i	−0.377249	−	0.0750395i	−0.380073	+	0.924957i	$0.624101\pi$
$60$	0.173584	+	0.849098i	0.0224096	+	0.109618i
$61$	−0.675800	−	0.451555i	−0.0865273	−	0.0578157i	0.511554	−	0.859251i	$-0.329070\pi$
$61$	−0.675800	−	0.451555i	−0.0865273	−	0.0578157i	−0.598081	+	0.801435i	$0.704070\pi$
$62$	−13.9382	−	4.18776i	−1.77015	−	0.531846i
$63$	2.60119			0.327719
$64$	1.43566	−	7.87013i	0.179457	−	0.983766i
$65$	1.27304			0.157901
$66$	3.04588	+	0.915141i	0.374922	+	0.112646i
$67$	−2.41244	−	1.61194i	−0.294727	−	0.196930i	0.399412	−	0.916772i	$-0.369214\pi$
$67$	−2.41244	−	1.61194i	−0.294727	−	0.196930i	−0.694138	+	0.719842i	$0.744214\pi$
$68$	−12.3953	+	2.53401i	−1.50315	+	0.307294i
$69$	−1.75242	−	0.348577i	−0.210966	−	0.0419638i
$70$	−0.585962	−	0.710147i	−0.0700359	−	0.0848788i
$71$	−2.88474	+	6.96439i	−0.342356	+	0.826521i	0.655121	+	0.755524i	$0.272618\pi$
$71$	−2.88474	+	6.96439i	−0.342356	+	0.826521i	−0.997477	+	0.0709962i	$0.977382\pi$
$72$	3.37277	+	1.76842i	0.397485	+	0.208410i
$73$	1.92544	+	4.64843i	0.225356	+	0.544057i	0.995601	−	0.0936903i	$-0.0298663\pi$
$73$	1.92544	+	4.64843i	0.225356	+	0.544057i	−0.770246	+	0.637747i	$0.779866\pi$
$74$	5.83121	+	3.09699i	0.677865	+	0.360018i
$75$	−3.49095	−	5.22458i	−0.403100	−	0.603282i
$76$	4.49589	−	11.0190i	0.515714	−	1.26397i
$77$	−3.31372	+	0.659140i	−0.377634	+	0.0751160i
$78$	−4.34422	+	5.32217i	−0.491886	+	0.602617i
$79$	10.5317	+	10.5317i	1.18490	+	1.18490i	0.978458	+	0.206445i	$0.0661896\pi$
$79$	10.5317	+	10.5317i	1.18490	+	1.18490i	0.206445	+	0.978458i	$0.433810\pi$
$80$	−0.276979	−	1.31916i	−0.0309672	−	0.147487i
$81$	2.22588	−	2.22588i	0.247320	−	0.247320i
$82$	−0.409851	−	4.05110i	−0.0452604	−	0.447369i
$83$	−0.0104591	−	0.0525816i	−0.00114804	−	0.00577158i	0.980207	−	0.197975i	$-0.0634366\pi$
$83$	−0.0104591	−	0.0525816i	−0.00114804	−	0.00577158i	−0.981355	+	0.192204i	$0.938437\pi$
$84$	4.96850	−	0.0263579i	0.542108	−	0.00287589i
$85$	−1.77244	+	1.18431i	−0.192248	+	0.128456i
$86$	2.90609	+	9.48942i	0.313372	+	1.02327i
$87$	6.52202	−	2.70151i	0.699233	−	0.289632i
$88$	−4.74478	−	1.39818i	−0.505795	−	0.149047i
$89$	−7.52277	−	3.11604i	−0.797413	−	0.330299i	−0.0534930	−	0.998568i	$-0.517035\pi$
$89$	−7.52277	−	3.11604i	−0.797413	−	0.330299i	−0.743920	+	0.668269i	$0.767035\pi$
$90$	0.638733	+	0.0611995i	0.0673284	+	0.00645099i
$91$	1.42383	−	7.15808i	0.149258	−	0.750371i
$92$	2.72840	+	0.527681i	0.284455	+	0.0550145i
$93$	7.35206	−	11.0031i	0.762373	−	1.14097i
$94$	0.0456681	+	0.0848966i	0.00471031	+	0.00875642i
$95$		−	2.00520i		−	0.205729i
$96$	6.46021	+	3.34367i	0.659342	+	0.341262i
$97$			12.1748i			1.23616i	0.786115	+	0.618081i	$0.212090\pi$
$97$			12.1748i			1.23616i	−0.786115	+	0.618081i	$0.787910\pi$
$98$	4.06974	−	2.18922i	0.411106	−	0.221145i
$99$	1.30820	−	1.95786i	0.131479	−	0.196772i
$100$	5.47256	+	8.09694i	0.547256	+	0.809694i
$101$	3.22333	−	16.2048i	0.320733	−	1.61244i	−0.398160	−	0.917316i	$-0.630351\pi$
$101$	3.22333	−	16.2048i	0.320733	−	1.61244i	0.718894	−	0.695120i	$-0.244649\pi$
$102$	1.09721	−	11.4515i	0.108640	−	1.13386i
$103$	−5.27535	−	2.18512i	−0.519796	−	0.215306i	0.107331	−	0.994223i	$-0.465769\pi$
$103$	−5.27535	−	2.18512i	−0.519796	−	0.215306i	−0.627127	+	0.778917i	$0.715769\pi$
$104$	6.71262	−	8.31337i	0.658226	−	0.815193i
$105$	0.773434	−	0.320367i	0.0754794	−	0.0312646i
$106$	15.6514	−	4.79318i	1.52020	−	0.465555i
$107$	−5.94629	+	3.97318i	−0.574850	+	0.384102i	−0.808745	−	0.588160i	$-0.799853\pi$
$107$	−5.94629	+	3.97318i	−0.574850	+	0.384102i	0.233895	+	0.972262i	$0.424853\pi$
$108$	−7.86218	+	7.94604i	−0.756539	+	0.764608i
$109$	−0.986910	−	4.96153i	−0.0945288	−	0.475229i	−0.998831	−	0.0483359i	$-0.984608\pi$
$109$	−0.986910	−	4.96153i	−0.0945288	−	0.475229i	0.904302	−	0.426893i	$-0.140392\pi$
$110$	−0.829208	+	0.0838912i	−0.0790618	+	0.00799871i
$111$	−4.24519	+	4.24519i	−0.402936	+	0.402936i
$112$	−7.72725	+	0.0819886i	−0.730156	+	0.00774719i
$113$	−9.81440	−	9.81440i	−0.923261	−	0.923261i	0.0739972	−	0.997258i	$-0.476424\pi$
$113$	−9.81440	−	9.81440i	−0.923261	−	0.923261i	−0.997258	+	0.0739972i	$0.976424\pi$
$114$	8.38312	+	6.84272i	0.785151	+	0.640879i
$115$	0.459232	−	0.0913470i	0.0428236	−	0.00851815i
$116$	−10.1213	+	4.25544i	−0.939744	+	0.395108i
$117$	2.82589	+	4.22924i	0.261253	+	0.390993i
$118$	−1.95984	+	3.69010i	−0.180417	+	0.339702i
$119$	4.67679	+	11.2908i	0.428720	+	1.03502i
$120$	1.22066	+	0.110424i	0.111430	+	0.0100803i
$121$	3.03909	−	7.33701i	0.276281	−	0.667001i
$122$	−0.886592	+	0.731552i	−0.0802683	+	0.0662316i
$123$	3.63124	+	0.722298i	0.327418	+	0.0651274i
$124$	−11.3438	+	17.1738i	−1.01870	+	1.54225i
$125$	2.77009	+	1.85091i	0.247764	+	0.165551i
$126$	1.05851	−	3.52305i	0.0942995	−	0.313858i
$127$	0.460345			0.0408490			0.0204245	−	0.999791i	$-0.493498\pi$
$127$	0.460345			0.0408490			0.0204245	+	0.999791i	$0.493498\pi$
$128$	−10.0751	−	5.14708i	−0.890521	−	0.454941i
$129$	−9.02408			−0.794526
$130$	0.518041	−	1.72420i	0.0454352	−	0.151222i
$131$	−15.2355	−	10.1801i	−1.33114	−	0.889437i	−0.332575	−	0.943077i	$-0.607918\pi$
$131$	−15.2355	−	10.1801i	−1.33114	−	0.889437i	−0.998560	+	0.0536401i	$0.982918\pi$
$132$	2.47894	−	3.75294i	0.215764	−	0.326652i
$133$	−11.2749	−	2.24272i	−0.977660	−	0.194469i
$134$	−3.16492	+	2.61146i	−0.273407	+	0.225596i
$135$	−0.720760	+	1.74007i	−0.0620331	+	0.149761i
$136$	−1.61200	+	17.8194i	−0.138228	+	1.52800i
$137$	3.64275	+	8.79438i	0.311221	+	0.751355i	0.999660	+	0.0260607i	$0.00829631\pi$
$137$	3.64275	+	8.79438i	0.311221	+	0.751355i	−0.688439	+	0.725294i	$0.741704\pi$
$138$	−1.18523	+	2.23163i	−0.100894	+	0.189969i
$139$	3.24499	+	4.85647i	0.275237	+	0.411921i	0.943175	−	0.332296i	$-0.107823\pi$
$139$	3.24499	+	4.85647i	0.275237	+	0.411921i	−0.667939	+	0.744216i	$0.732823\pi$
$140$	−1.20027	+	0.504646i	−0.101442	+	0.0426503i
$141$	−0.0859705	+	0.0171006i	−0.00724002	+	0.00144013i
$142$	8.25868	+	6.74114i	0.693053	+	0.565704i
$143$	−4.67166	−	4.67166i	−0.390664	−	0.390664i
$144$	3.76765	−	3.84845i	0.313970	−	0.320705i
$145$	−1.30812	+	1.30812i	−0.108633	+	0.108633i
$146$	7.07937	−	0.716222i	0.585892	−	0.0592749i
$147$	0.819762	+	4.12122i	0.0676128	+	0.339913i
$148$	6.56748	−	6.63754i	0.539844	−	0.545602i
$149$	15.1308	−	10.1101i	1.23957	−	0.828252i	0.249435	−	0.968392i	$-0.419755\pi$
$149$	15.1308	−	10.1101i	1.23957	−	0.828252i	0.990132	+	0.140140i	$0.0447552\pi$
$150$	−8.49676	+	2.60210i	−0.693758	+	0.212460i
$151$	14.5143	−	6.01204i	1.18116	−	0.489252i	0.296293	−	0.955097i	$-0.404249\pi$
$151$	14.5143	−	6.01204i	1.18116	−	0.489252i	0.884867	+	0.465844i	$0.154249\pi$
$152$	−13.0947	−	10.5733i	−1.06212	−	0.857605i
$153$	−7.86894	−	3.25942i	−0.636166	−	0.263509i
$154$	−0.455723	+	4.75634i	−0.0367232	+	0.383277i
$155$	−0.676551	+	3.40125i	−0.0543419	+	0.273195i
$156$	5.44055	+	8.04959i	0.435593	+	0.644483i
$157$	−3.85444	+	5.76858i	−0.307618	+	0.460383i	−0.952779	−	0.303663i	$-0.901790\pi$
$157$	−3.85444	+	5.76858i	−0.307618	+	0.460383i	0.645161	+	0.764046i	$0.276790\pi$
$158$	18.5498	−	9.97841i	1.47574	−	0.793840i
$159$			14.8839i			1.18037i
$160$	−1.89939	−	0.161670i	−0.150160	−	0.0127812i
$161$		−	2.68436i		−	0.211557i
$162$	−2.10895	−	3.92052i	−0.165695	−	0.308025i
$163$	−9.11685	+	13.6443i	−0.714087	+	1.06871i	0.279987	+	0.960004i	$0.409670\pi$
$163$	−9.11685	+	13.6443i	−0.714087	+	1.06871i	−0.994074	+	0.108703i	$0.965330\pi$
$164$	−5.65359	−	1.09342i	−0.441472	−	0.0853820i
$165$	0.147845	−	0.743268i	0.0115097	−	0.0578633i
$166$	−0.0754728	−	0.00723135i	−0.00585783	−	0.000561261i
$167$	1.98808	+	0.823489i	0.153842	+	0.0637235i	0.458276	−	0.888810i	$-0.348467\pi$
$167$	1.98808	+	0.823489i	0.153842	+	0.0637235i	−0.304434	+	0.952534i	$0.598467\pi$
$168$	1.98615	−	6.74007i	0.153235	−	0.520008i
$169$	1.17464	−	0.486552i	0.0903569	−	0.0374270i
$170$	0.882763	+	2.88253i	0.0677048	+	0.221080i
$171$	6.66161	−	4.45114i	0.509426	−	0.340388i
$172$	14.0351	−	0.0744562i	1.07016	−	0.00567723i
$173$	1.79167	+	9.00732i	0.136218	+	0.684814i	0.987183	+	0.159592i	$0.0510178\pi$
$173$	1.79167	+	9.00732i	0.136218	+	0.684814i	−0.850965	+	0.525222i	$0.823982\pi$
$174$	−1.00490	−	9.93277i	−0.0761814	−	0.753001i
$175$	6.67524	−	6.67524i	0.504601	−	0.504601i
$176$	−3.82451	+	5.85737i	−0.288283	+	0.441516i
$177$	−2.68644	−	2.68644i	−0.201925	−	0.201925i
$178$	−7.28163	+	8.92084i	−0.545782	+	0.668645i
$179$	2.24858	−	0.447270i	0.168067	−	0.0334305i	−0.110340	−	0.993894i	$-0.535194\pi$
$179$	2.24858	−	0.447270i	0.168067	−	0.0334305i	0.278406	+	0.960463i	$0.410194\pi$
$180$	0.342811	−	0.840198i	0.0255516	−	0.0626246i
$181$	−5.64020	−	8.44116i	−0.419233	−	0.627426i	0.560400	−	0.828222i	$-0.310647\pi$
$181$	−5.64020	−	8.44116i	−0.419233	−	0.627426i	−0.979633	+	0.200796i	$0.935647\pi$
$182$	−9.11552	−	4.84130i	−0.675687	−	0.358861i
$183$	−0.399966	−	0.965604i	−0.0295663	−	0.0713795i
$184$	1.82497	−	3.48062i	0.134538	−	0.256594i
$185$	0.602070	−	1.45352i	0.0442650	−	0.106865i
$186$	−11.9109	−	14.4352i	−0.873348	−	1.05844i
$187$	10.8504	+	2.15828i	0.793459	+	0.157829i
$188$	0.133568	−	0.0273057i	0.00974145	−	0.00199148i
$189$	8.97800	+	5.99891i	0.653054	+	0.436356i
$190$	−2.71585	−	0.815983i	−0.197028	−	0.0591976i
$191$	−15.2964			−1.10681			−0.553405	−	0.832912i	$-0.686672\pi$
$191$	−15.2964			−1.10681			−0.553405	+	0.832912i	$0.686672\pi$
$192$	7.15754	−	7.38907i	0.516551	−	0.533260i
$193$	13.0208			0.937258			0.468629	−	0.883395i	$-0.344748\pi$
$193$	13.0208			0.937258			0.468629	+	0.883395i	$0.344748\pi$
$194$	16.4895	+	4.95432i	1.18388	+	0.355700i
$195$	1.36113	+	0.909476i	0.0974724	+	0.0651289i
$196$	−1.30897	−	6.40294i	−0.0934980	−	0.457353i
$197$	4.45565	+	0.886285i	0.317452	+	0.0631452i	0.351245	−	0.936284i	$-0.385759\pi$
$197$	4.45565	+	0.886285i	0.317452	+	0.0631452i	−0.0337925	+	0.999429i	$0.510759\pi$
$198$	−2.11938	−	2.56855i	−0.150618	−	0.182539i
$199$	3.49809	−	8.44513i	0.247973	−	0.598659i	−0.750059	−	0.661371i	$-0.769975\pi$
$199$	3.49809	−	8.44513i	0.247973	−	0.598659i	0.998032	+	0.0627118i	$0.0199749\pi$
$200$	13.1935	−	4.11713i	0.932920	−	0.291125i
$201$	−1.42778	−	3.44697i	−0.100708	−	0.243131i
$202$	−20.6361	−	10.9600i	−1.45195	−	0.771140i
$203$	5.89227	+	8.81841i	0.413556	+	0.618931i
$204$	−15.0634	−	6.14605i	−1.05465	−	0.430309i
$205$	−0.951589	+	0.189283i	−0.0664619	+	0.0132201i
$206$	−5.10625	+	6.25575i	−0.355769	+	0.435859i
$207$	1.32287	+	1.32287i	0.0919461	+	0.0919461i
$208$	−8.52806	−	12.4746i	−0.591315	−	0.864956i
$209$	−7.35849	+	7.35849i	−0.508997	+	0.508997i
$210$	−0.119169	−	1.17791i	−0.00822347	−	0.0812834i
$211$	−1.12050	−	5.63316i	−0.0771387	−	0.387803i	−0.999996	−	0.00266152i	$-0.999153\pi$
$211$	−1.12050	−	5.63316i	−0.0771387	−	0.387803i	0.922858	−	0.385141i	$-0.125847\pi$
$212$	−0.122805	−	23.1488i	−0.00843427	−	1.58987i
$213$	−8.05983	+	5.38541i	−0.552250	+	0.369002i
$214$	2.96154	+	9.67049i	0.202447	+	0.661061i
$215$	2.18481	−	0.904976i	0.149003	−	0.0617189i
$216$	7.56275	+	13.8821i	0.514580	+	0.944555i
$217$	18.3680	+	7.60829i	1.24690	+	0.516484i
$218$	−7.12152	−	0.682340i	−0.482330	−	0.0462139i
$219$	−1.26223	+	6.34566i	−0.0852936	+	0.428800i
$220$	−0.223810	+	1.15722i	−0.0150893	+	0.0780197i
$221$	−13.2767	+	19.8700i	−0.893090	+	1.33660i
$222$	4.02219	+	7.47721i	0.269951	+	0.501837i
$223$		−	13.8411i		−	0.926872i	−0.886130	−	0.463436i	$-0.846616\pi$
$223$		−	13.8411i		−	0.926872i	0.886130	−	0.463436i	$-0.153384\pi$
$224$	−3.03343	+	10.4992i	−0.202680	+	0.701505i
$225$			6.57923i			0.438615i
$226$	−17.2865	+	9.29884i	−1.14988	+	0.618550i
$227$	13.5582	−	20.2913i	0.899890	−	1.34678i	−0.0377913	−	0.999286i	$-0.512032\pi$
$227$	13.5582	−	20.2913i	0.899890	−	1.34678i	0.937682	−	0.347495i	$-0.112968\pi$
$228$	12.6792	−	8.56959i	0.839698	−	0.567535i
$229$	1.91748	−	9.63980i	0.126710	−	0.637016i	−0.864272	−	0.503025i	$-0.832221\pi$
$229$	1.91748	−	9.63980i	0.126710	−	0.637016i	0.990982	−	0.133991i	$-0.0427795\pi$
$230$	0.0631564	−	0.659157i	0.00416441	−	0.0434635i
$231$	−4.01393	−	1.66262i	−0.264097	−	0.109393i
$232$	1.64487	+	15.4401i	0.107991	+	1.01369i
$233$	13.0360	−	5.39971i	0.854020	−	0.353747i	0.0876541	−	0.996151i	$-0.472063\pi$
$233$	13.0360	−	5.39971i	0.854020	−	0.353747i	0.766366	+	0.642404i	$0.222063\pi$
$234$	6.87804	−	2.10637i	0.449631	−	0.137698i
$235$	0.0190993	−	0.0127617i	0.00124590	−	0.000832483i
$236$	4.20036	+	4.15603i	0.273420	+	0.270535i
$237$	3.73645	+	18.7844i	0.242709	+	1.22018i
$238$	17.1954	−	1.73966i	1.11461	−	0.112765i
$239$	−20.8075	+	20.8075i	−1.34592	+	1.34592i	−0.455887	+	0.890038i	$0.650678\pi$
$239$	−20.8075	+	20.8075i	−1.34592	+	1.34592i	−0.890038	+	0.455887i	$0.849322\pi$
$240$	0.646285	−	1.60833i	0.0417175	−	0.103817i
$241$	5.88520	+	5.88520i	0.379099	+	0.379099i	0.870777	−	0.491678i	$-0.163616\pi$
$241$	5.88520	+	5.88520i	0.379099	+	0.379099i	−0.491678	+	0.870777i	$0.663616\pi$
$242$	−8.70055	−	7.10182i	−0.559293	−	0.456522i
$243$	−12.4751	+	2.48145i	−0.800278	+	0.159185i
$244$	0.630031	+	1.49850i	0.0403336	+	0.0959313i
$245$	−0.611767	−	0.915574i	−0.0390843	−	0.0584938i
$246$	2.45595	−	4.62423i	0.156586	−	0.294830i
$247$	−8.60249	−	20.7682i	−0.547363	−	1.32145i
$248$	18.6440	+	22.3527i	1.18389	+	1.41940i
$249$	0.0263822	−	0.0636924i	0.00167191	−	0.00403634i
$250$	3.63412	−	2.99861i	0.229842	−	0.189649i
$251$	8.08063	+	1.60734i	0.510045	+	0.101454i	0.443402	−	0.896323i	$-0.353771\pi$
$251$	8.08063	+	1.60734i	0.510045	+	0.101454i	0.0666425	+	0.997777i	$0.478771\pi$
$252$	−4.34088	−	2.86729i	−0.273450	−	0.180623i
$253$	−2.02046	−	1.35003i	−0.127025	−	0.0848757i
$254$	0.187330	−	0.623492i	0.0117541	−	0.0391214i
$255$	−2.74118			−0.171659
$256$	−11.0711	+	11.5512i	−0.691944	+	0.721951i
$257$	−14.0980			−0.879412			−0.439706	−	0.898142i	$-0.644917\pi$
$257$	−14.0980			−0.879412			−0.439706	+	0.898142i	$0.644917\pi$
$258$	−3.67220	+	12.2222i	−0.228621	+	0.760923i
$259$	−7.49956	−	5.01105i	−0.466000	−	0.311371i
$260$	−2.12445	−	1.40327i	−0.131753	−	0.0870271i
$261$	−7.24954	−	1.44202i	−0.448735	−	0.0892590i
$262$	−19.9878	+	16.4924i	−1.23485	+	1.01891i
$263$	5.62862	−	13.5887i	0.347076	−	0.837915i	−0.649887	−	0.760031i	$-0.725184\pi$
$263$	5.62862	−	13.5887i	0.347076	−	0.837915i	0.996962	−	0.0778837i	$-0.0248163\pi$
$264$	−4.07423	−	4.88468i	−0.250751	−	0.300631i
$265$	−1.49263	−	3.60352i	−0.0916914	−	0.221363i
$266$	−7.62569	+	14.3581i	−0.467561	+	0.880355i
$267$	−5.81720	−	8.70605i	−0.356007	−	0.532802i
$268$	2.24906	+	5.34926i	0.137383	+	0.326758i
$269$	−4.35266	+	0.865799i	−0.265387	+	0.0527887i	−0.325990	−	0.945373i	$-0.605698\pi$
$269$	−4.35266	+	0.865799i	−0.265387	+	0.0527887i	0.0606033	+	0.998162i	$0.480698\pi$
$270$	2.06345	+	1.68429i	0.125578	+	0.102503i
$271$	−8.75941	−	8.75941i	−0.532096	−	0.532096i	0.389099	−	0.921196i	$-0.372786\pi$
$271$	−8.75941	−	8.75941i	−0.532096	−	0.532096i	−0.921196	+	0.389099i	$0.872786\pi$
$272$	23.4787	+	9.43461i	1.42361	+	0.572058i
$273$	6.63620	−	6.63620i	0.401641	−	0.401641i
$274$	13.3935	−	1.35502i	0.809130	−	0.0818600i
$275$	−1.66718	−	8.38146i	−0.100534	−	0.505421i
$276$	2.54021	+	2.51340i	0.152903	+	0.151289i
$277$	−15.3547	+	10.2597i	−0.922572	+	0.616443i	−0.923517	−	0.383557i	$-0.874699\pi$
$277$	−15.3547	+	10.2597i	−0.922572	+	0.616443i	0.000945275		1.00000i	$0.499699\pi$
$278$	7.89811	−	2.41876i	0.473697	−	0.145068i
$279$	−12.8013	+	5.30249i	−0.766397	+	0.317452i
$280$	0.195062	+	1.83101i	0.0116572	+	0.109424i
$281$	14.0773	+	5.83101i	0.839781	+	0.347849i	0.760767	−	0.649025i	$-0.224823\pi$
$281$	14.0773	+	5.83101i	0.839781	+	0.347849i	0.0790137	+	0.996874i	$0.474823\pi$
$282$	−0.0118232	+	0.123397i	−0.000704060	+	0.00734821i
$283$	0.0531107	−	0.267006i	0.00315711	−	0.0158718i	−0.979175	−	0.203020i	$-0.934924\pi$
$283$	0.0531107	−	0.267006i	0.00315711	−	0.0158718i	0.982332	+	0.187148i	$0.0599244\pi$
$284$	12.4910	−	8.44238i	0.741202	−	0.500963i
$285$	1.43255	−	2.14396i	0.0848567	−	0.126997i
$286$	−8.22836	+	4.42625i	−0.486553	+	0.261730i
$287$			5.56235i			0.328335i
$288$	−3.67917	−	6.66897i	−0.216797	−	0.392973i
$289$		−	23.0163i		−	1.35390i
$290$	1.23940	+	2.30403i	0.0727800	+	0.135297i
$291$	−8.69785	+	13.0173i	−0.509877	+	0.763085i
$292$	1.91078	−	9.87976i	0.111820	−	0.578169i
$293$	−3.24074	+	16.2923i	−0.189326	+	0.951807i	0.762924	+	0.646488i	$0.223763\pi$
$293$	−3.24074	+	16.2923i	−0.189326	+	0.951807i	−0.952250	+	0.305319i	$0.901237\pi$
$294$	5.91538	+	0.566776i	0.344992	+	0.0330550i
$295$	0.919819	+	0.381001i	0.0535539	+	0.0221828i
$296$	−6.31737	−	11.5961i	−0.367189	−	0.674007i
$297$	9.03051	−	3.74056i	0.524003	−	0.217049i
$298$	−7.53590	−	24.6074i	−0.436543	−	1.42547i
$299$	4.36447	−	2.91625i	0.252404	−	0.168651i
$300$	0.0666676	+	12.5669i	0.00384906	+	0.725551i
$301$	−2.64494	−	13.2970i	−0.152452	−	0.766427i
$302$	−2.23634	−	22.1047i	−0.128687	−	1.27199i
$303$	15.0233	−	15.0233i	0.863068	−	0.863068i
$304$	−19.6491	+	13.4328i	−1.12695	+	0.770425i
$305$	0.193670	+	0.193670i	0.0110895	+	0.0110895i
$306$	−7.61670	+	9.33134i	−0.435418	+	0.533437i
$307$	6.84456	−	1.36147i	0.390640	−	0.0777031i	0.00413726	−	0.999991i	$-0.498683\pi$
$307$	6.84456	−	1.36147i	0.390640	−	0.0777031i	0.386502	+	0.922288i	$0.373683\pi$
$308$	6.25654	+	2.55274i	0.356500	+	0.145456i
$309$	−4.07931	−	6.10512i	−0.232064	−	0.347308i
$310$	4.33135	+	2.30041i	0.246004	+	0.130654i
$311$	−2.90025	−	7.00183i	−0.164458	−	0.397038i	0.820070	−	0.572263i	$-0.193934\pi$
$311$	−2.90025	−	7.00183i	−0.164458	−	0.397038i	−0.984528	+	0.175226i	$0.943934\pi$
$312$	13.1163	−	4.09305i	0.742566	−	0.231723i
$313$	5.70821	−	13.7808i	0.322647	−	0.778938i	−0.676452	−	0.736487i	$-0.736483\pi$
$313$	5.70821	−	13.7808i	0.322647	−	0.778938i	0.999099	−	0.0424514i	$-0.0135167\pi$
$314$	6.24448	+	7.56789i	0.352396	+	0.427081i
$315$	−0.859710	−	0.171007i	−0.0484392	−	0.00963515i
$316$	−5.96626	−	29.1844i	−0.335628	−	1.64175i
$317$	−12.0391	−	8.04424i	−0.676181	−	0.451809i	0.169478	−	0.985534i	$-0.445792\pi$
$317$	−12.0391	−	8.04424i	−0.676181	−	0.451809i	−0.845658	+	0.533725i	$0.820792\pi$
$318$	20.1588	+	6.05676i	1.13045	+	0.339646i
$319$	9.60080			0.537541
$320$	−0.991892	+	2.50675i	−0.0554485	+	0.140132i
$321$	−9.19627			−0.513286
$322$	−3.63570	−	1.09236i	−0.202610	−	0.0608746i
$323$	31.2979	+	20.9126i	1.74146	+	1.16361i
$324$	−6.16816	+	1.26098i	−0.342675	+	0.0700542i
$325$	18.1051	+	3.60132i	1.00429	+	0.199766i
$326$	14.7700	+	17.9002i	0.818033	+	0.991402i
$327$	2.48939	−	6.00993i	0.137664	−	0.332350i
$328$	−3.78157	+	7.21229i	−0.208802	+	0.398232i
$329$	−0.0503956	−	0.121666i	−0.00277840	−	0.00670764i
$330$	−0.946521	−	0.502703i	−0.0521043	−	0.0276729i
$331$	14.3128	+	21.4207i	0.786705	+	1.17739i	0.980533	+	0.196352i	$0.0629095\pi$
$331$	14.3128	+	21.4207i	0.786705	+	1.17739i	−0.193828	+	0.981035i	$0.562090\pi$
$332$	−0.0405066	+	0.0992779i	−0.00222309	+	0.00544858i
$333$	6.16533	−	1.22636i	0.337858	−	0.0672041i
$334$	1.92435	−	2.35755i	0.105296	−	0.129000i
$335$	0.691356	+	0.691356i	0.0377728	+	0.0377728i
$336$	−8.32053	−	5.43280i	−0.453922	−	0.296384i
$337$	−10.9026	+	10.9026i	−0.593904	+	0.593904i	−0.938684	−	0.344780i	$-0.887954\pi$
$337$	−10.9026	+	10.9026i	−0.593904	+	0.593904i	0.344780	+	0.938684i	$0.387954\pi$
$338$	−0.180986	−	1.78893i	−0.00984436	−	0.0973049i
$339$	−3.48198	−	17.5051i	−0.189115	−	0.950747i
$340$	4.26333	−	0.0226170i	0.231212	−	0.00122658i
$341$	14.9643	−	9.99885i	0.810364	−	0.541468i
$342$	−3.31781	−	10.8338i	−0.179407	−	0.585826i
$343$	−18.3264	+	7.59104i	−0.989532	+	0.409878i
$344$	5.61050	−	19.0394i	0.302498	−	1.02654i
$345$	0.556270	+	0.230415i	0.0299486	+	0.0124051i
$346$	12.9286	+	1.23874i	0.695047	+	0.0665952i
$347$	−3.71315	+	18.6673i	−0.199332	+	1.00211i	0.743472	+	0.668767i	$0.233177\pi$
$347$	−3.71315	+	18.6673i	−0.199332	+	1.00211i	−0.942805	+	0.333345i	$0.891823\pi$
$348$	−13.8619	−	2.68093i	−0.743075	−	0.143713i
$349$	−0.0981410	+	0.146878i	−0.00525337	+	0.00786222i	−0.834087	−	0.551633i	$-0.814005\pi$
$349$	−0.0981410	+	0.146878i	−0.00525337	+	0.00786222i	0.828834	+	0.559495i	$0.189005\pi$
$350$	−6.32458	−	11.7573i	−0.338063	−	0.628456i
$351$			21.1144i			1.12700i
$352$	6.37692	+	7.56348i	0.339891	+	0.403135i
$353$		−	12.0283i		−	0.640199i	−0.947384	−	0.320100i	$-0.896284\pi$
$353$		−	12.0283i		−	0.640199i	0.947384	−	0.320100i	$-0.103716\pi$
$354$	−4.73172	+	2.54532i	−0.251488	+	0.135282i
$355$	1.41128	−	2.11213i	0.0749030	−	0.112100i
$356$	9.11927	+	13.4924i	0.483320	+	0.715098i
$357$	−3.06588	+	15.4132i	−0.162264	+	0.815755i
$358$	0.309238	−	3.22749i	0.0163438	−	0.170578i
$359$	33.9190	+	14.0497i	1.79018	+	0.741516i	0.989879	+	0.141916i	$0.0453263\pi$
$359$	33.9190	+	14.0497i	1.79018	+	0.741516i	0.800300	+	0.599600i	$0.204674\pi$
$360$	−0.998464	−	0.806208i	−0.0526237	−	0.0424909i
$361$	−15.1590	+	6.27907i	−0.797843	+	0.330477i
$362$	−13.7279	+	4.20411i	−0.721523	+	0.220963i
$363$	8.49106	−	5.67355i	0.445665	−	0.297784i
$364$	−10.2665	+	10.3760i	−0.538110	+	0.543850i
$365$	−0.330775	−	1.66292i	−0.0173136	−	0.0870412i
$366$	−1.47058	+	0.148779i	−0.0768682	+	0.00777678i
$367$	−8.38811	+	8.38811i	−0.437856	+	0.437856i	−0.891290	−	0.453434i	$-0.850199\pi$
$367$	−8.38811	+	8.38811i	−0.437856	+	0.437856i	0.453434	+	0.891290i	$0.350199\pi$
$368$	−3.97151	−	3.88812i	−0.207029	−	0.202682i
$369$	−2.74117	−	2.74117i	−0.142700	−	0.142700i
$370$	−1.72365	−	1.40693i	−0.0896085	−	0.0731429i
$371$	−21.9315	+	4.36245i	−1.13863	+	0.226487i
$372$	−24.3980	+	10.2580i	−1.26498	+	0.531850i
$373$	−12.9524	−	19.3846i	−0.670647	−	1.00369i	−0.998265	−	0.0588843i	$-0.981246\pi$
$373$	−12.9524	−	19.3846i	−0.670647	−	1.00369i	0.327617	−	0.944810i	$-0.393754\pi$
$374$	7.33856	−	13.8175i	0.379468	−	0.714487i
$375$	1.63945	+	3.95799i	0.0846609	+	0.204389i
$376$	0.0173704	−	0.192016i	0.000895808	−	0.00990249i
$377$	−7.93648	+	19.1604i	−0.408749	+	0.986808i
$378$	11.7784	−	9.71867i	0.605815	−	0.499874i
$379$	−26.4712	−	5.26545i	−1.35973	−	0.270468i	−0.539254	−	0.842143i	$-0.681294\pi$
$379$	−26.4712	−	5.26545i	−1.35973	−	0.270468i	−0.820480	+	0.571676i	$0.806294\pi$
$380$	−2.21034	+	3.34630i	−0.113388	+	0.171661i
$381$	0.492200	+	0.328877i	0.0252162	+	0.0168489i
$382$	−6.22463	+	20.7175i	−0.318480	+	1.06000i
$383$	3.40990			0.174238			0.0871189	−	0.996198i	$-0.472234\pi$
$383$	3.40990			0.174238			0.0871189	+	0.996198i	$0.472234\pi$
$384$	−7.09513	−	12.7011i	−0.362072	−	0.648148i
$385$	1.13854			0.0580254
$386$	5.29860	−	17.6354i	0.269692	−	0.897619i
$387$	7.85632	+	5.24943i	0.399359	+	0.266843i
$388$	13.4203	−	20.3174i	0.681312	−	1.03146i
$389$	6.70403	+	1.33351i	0.339908	+	0.0676119i	0.362093	−	0.932142i	$-0.382062\pi$
$389$	6.70403	+	1.33351i	0.339908	+	0.0676119i	−0.0221851	+	0.999754i	$0.507062\pi$
$390$	1.78568	−	1.47342i	0.0904217	−	0.0746094i
$391$	−3.36364	+	8.12055i	−0.170107	+	0.410674i
$392$	−9.20482	−	0.832695i	−0.464914	−	0.0420574i
$393$	−9.01703	−	21.7690i	−0.454849	−	1.09810i
$394$	3.01354	−	5.67409i	0.151820	−	0.285856i
$395$	−2.78841	−	4.17316i	−0.140300	−	0.209974i
$396$	−4.34129	+	1.82526i	−0.218158	+	0.0917229i
$397$	25.0619	−	4.98511i	1.25782	−	0.250196i	0.479207	−	0.877702i	$-0.340924\pi$
$397$	25.0619	−	4.98511i	1.25782	−	0.250196i	0.778611	+	0.627506i	$0.215924\pi$
$398$	−10.0146	−	8.17442i	−0.501987	−	0.409747i
$399$	−10.4529	−	10.4529i	−0.523300	−	0.523300i
$400$	−0.207375	−	19.5447i	−0.0103688	−	0.977234i
$401$	2.21860	−	2.21860i	0.110791	−	0.110791i	−0.649538	−	0.760329i	$-0.725038\pi$
$401$	2.21860	−	2.21860i	0.110791	−	0.110791i	0.760329	+	0.649538i	$0.225038\pi$
$402$	−5.24960	+	0.531103i	−0.261826	+	0.0264890i
$403$	7.58451	+	38.1299i	0.377811	+	1.89939i
$404$	−23.2417	+	23.4896i	−1.15632	+	1.16865i
$405$	−0.882002	+	0.589335i	−0.0438270	+	0.0292843i
$406$	14.3414	−	4.39200i	0.711753	−	0.217971i
$407$	−7.54342	+	3.12459i	−0.373914	+	0.154880i
$408$	−14.4540	+	17.9009i	−0.715581	+	0.886225i
$409$	10.6896	+	4.42777i	0.528566	+	0.218939i	0.630975	−	0.775803i	$-0.282655\pi$
$409$	10.6896	+	4.42777i	0.528566	+	0.218939i	−0.102409	+	0.994742i	$0.532655\pi$
$410$	−0.130868	+	1.36586i	−0.00646313	+	0.0674550i
$411$	−2.38802	+	12.0054i	−0.117792	+	0.592182i
$412$	6.39489	+	9.46159i	0.315054	+	0.466139i
$413$	3.17109	−	4.74587i	0.156039	−	0.233529i
$414$	2.33003	−	1.25338i	0.114515	−	0.0616004i
$415$			0.0180662i			0.000886835i
$416$	−20.3659	+	6.47410i	−0.998522	+	0.317419i
$417$			7.51080i			0.367806i
$418$	6.97194	+	12.9608i	0.341009	+	0.633932i
$419$	8.58363	−	12.8463i	0.419338	−	0.627583i	−0.560316	−	0.828279i	$-0.689320\pi$
$419$	8.58363	−	12.8463i	0.419338	−	0.627583i	0.979654	+	0.200696i	$0.0643203\pi$
$420$	−1.64386	−	0.317927i	−0.0802120	−	0.0155133i
$421$	−1.91938	+	9.64937i	−0.0935448	+	0.470281i	0.905409	+	0.424541i	$0.139565\pi$
$421$	−1.91938	+	9.64937i	−0.0935448	+	0.470281i	−0.998953	+	0.0457401i	$0.985435\pi$
$422$	−8.08553	−	0.774706i	−0.393597	−	0.0377121i
$423$	0.0847932	+	0.0351225i	0.00412278	+	0.00170771i
$424$	−31.4028	−	9.25371i	−1.52505	−	0.449400i
$425$	−28.5579	+	11.8291i	−1.38526	+	0.573795i
$426$	4.01419	+	13.1078i	0.194488	+	0.635073i
$427$	1.30559	−	0.872368i	0.0631820	−	0.0422168i
$428$	14.3029	−	0.0758770i	0.691356	−	0.00366765i
$429$	−1.65743	−	8.33244i	−0.0800213	−	0.402294i
$430$	−0.336631	−	3.32737i	−0.0162338	−	0.160460i
$431$	19.6960	−	19.6960i	0.948725	−	0.948725i	−0.0500230	−	0.998748i	$-0.515929\pi$
$431$	19.6960	−	19.6960i	0.948725	−	0.948725i	0.998748	+	0.0500230i	$0.0159295\pi$
$432$	21.8794	−	4.59393i	1.05267	−	0.221026i
$433$	28.0515	+	28.0515i	1.34807	+	1.34807i	0.887757	+	0.460312i	$0.152262\pi$
$433$	28.0515	+	28.0515i	1.34807	+	1.34807i	0.460312	+	0.887757i	$0.347738\pi$
$434$	17.7793	−	21.7816i	0.853432	−	1.04555i
$435$	−2.33317	+	0.464097i	−0.111867	+	0.0222518i
$436$	−3.82215	+	9.36773i	−0.183048	+	0.448633i
$437$	−4.59347	−	6.87462i	−0.219736	−	0.328858i
$438$	8.08093	+	4.29183i	0.386122	+	0.205071i
$439$	6.53568	+	15.7785i	0.311931	+	0.753068i	0.999633	+	0.0270754i	$0.00861943\pi$
$439$	6.53568	+	15.7785i	0.311931	+	0.753068i	−0.687702	+	0.725993i	$0.741381\pi$
$440$	1.47626	+	0.774040i	0.0703781	+	0.0369009i
$441$	1.68369	−	4.06478i	0.0801757	−	0.193561i
$442$	21.5093	+	26.0678i	1.02309	+	1.23992i
$443$	−17.8876	−	3.55806i	−0.849864	−	0.169048i	−0.249103	−	0.968477i	$-0.580136\pi$
$443$	−17.8876	−	3.55806i	−0.849864	−	0.169048i	−0.600761	+	0.799429i	$0.705136\pi$
$444$	11.7639	−	2.40493i	0.558290	−	0.114133i
$445$	2.28148	+	1.52443i	0.108152	+	0.0722651i
$446$	−18.7465	−	5.63243i	−0.887672	−	0.266703i
$447$	23.4007			1.10681
$448$	12.9857	+	8.38094i	0.613516	+	0.395962i
$449$	7.49157			0.353549			0.176775	−	0.984251i	$-0.443434\pi$
$449$	7.49157			0.353549			0.176775	+	0.984251i	$0.443434\pi$
$450$	8.91092	+	2.67731i	0.420065	+	0.126210i
$451$	4.18666	+	2.79744i	0.197142	+	0.131726i
$452$	5.55993	+	27.1968i	0.261517	+	1.27923i
$453$	19.8138	+	3.94121i	0.930934	+	0.185174i
$454$	−21.9653	−	26.6205i	−1.03088	−	1.24936i
$455$	−0.941173	+	2.27219i	−0.0441228	+	0.106522i
$456$	−6.44709	−	20.6599i	−0.301913	−	0.967491i
$457$	−6.33038	−	15.2829i	−0.296123	−	0.714904i	−0.999990	−	0.00457167i	$-0.998545\pi$
$457$	−6.33038	−	15.2829i	−0.296123	−	0.714904i	0.703867	−	0.710332i	$-0.251455\pi$
$458$	−12.2759	−	6.51979i	−0.573614	−	0.304650i
$459$	−19.6427	−	29.3974i	−0.916844	−	1.37215i
$460$	−0.867064	−	0.353772i	−0.0404270	−	0.0164947i
$461$	−16.1652	+	3.21545i	−0.752886	+	0.149758i	−0.556591	−	0.830786i	$-0.687891\pi$
$461$	−16.1652	+	3.21545i	−0.752886	+	0.149758i	−0.196295	+	0.980545i	$0.562891\pi$
$462$	−3.88526	+	4.75989i	−0.180759	+	0.221450i
$463$	25.6472	+	25.6472i	1.19193	+	1.19193i	0.976526	+	0.215401i	$0.0691059\pi$
$463$	25.6472	+	25.6472i	1.19193	+	1.19193i	0.215401	+	0.976526i	$0.430894\pi$
$464$	21.5814	+	4.05526i	1.00189	+	0.188261i
$465$	−3.15328	+	3.15328i	−0.146230	+	0.146230i
$466$	−2.00857	−	19.8534i	−0.0930453	−	0.919690i
$467$	−8.07541	−	40.5978i	−0.373685	−	1.87864i	−0.469004	−	0.883196i	$-0.655387\pi$
$467$	−8.07541	−	40.5978i	−0.373685	−	1.87864i	0.0953188	−	0.995447i	$-0.469613\pi$
$468$	−0.0539667	−	10.1728i	−0.00249461	−	0.470237i
$469$	4.66064	−	3.11414i	0.215208	−	0.143798i
$470$	−0.00951237	−	0.0310612i	−0.000438773	−	0.00143275i
$471$	−8.24233	+	3.41408i	−0.379786	+	0.157313i
$472$	7.33821	−	3.99775i	0.337768	−	0.184011i
$473$	−11.3386	−	4.69660i	−0.521349	−	0.215950i
$474$	26.9621	+	2.58335i	1.23841	+	0.118657i
$475$	5.67256	−	28.5179i	0.260275	−	1.30849i
$476$	4.64117	−	23.9974i	0.212728	−	1.09992i
$477$	8.65817	−	12.9579i	0.396431	−	0.593300i
$478$	19.7144	+	36.6490i	0.901718	+	1.67628i
$479$			7.37082i			0.336781i	0.985720	+	0.168391i	$0.0538570\pi$
$479$			7.37082i			0.336781i	−0.985720	+	0.168391i	$0.946143\pi$
$480$	−1.91533	−	1.52981i	−0.0874223	−	0.0698260i
$481$		−	17.6374i		−	0.804195i
$482$	10.3658	−	5.57604i	0.472149	−	0.253982i
$483$	1.91775	−	2.87011i	0.0872606	−	0.130595i
$484$	−13.1593	+	8.89408i	−0.598149	+	0.404276i
$485$	0.800394	−	4.02385i	0.0363440	−	0.182714i
$486$	−1.71565	+	17.9061i	−0.0778235	+	0.812237i
$487$	−14.2123	−	5.88692i	−0.644020	−	0.266762i	0.0366766	−	0.999327i	$-0.488323\pi$
$487$	−14.2123	−	5.88692i	−0.644020	−	0.266762i	−0.680697	+	0.732565i	$0.738323\pi$
$488$	2.28595	−	0.243528i	0.103480	−	0.0110240i
$489$	−19.4955	+	8.07528i	−0.881615	+	0.365177i
$490$	−1.48900	+	0.456001i	−0.0672663	+	0.0206000i
$491$	13.9347	−	9.31084i	0.628862	−	0.420192i	−0.199882	−	0.979820i	$-0.564056\pi$
$491$	13.9347	−	9.31084i	0.628862	−	0.420192i	0.828744	+	0.559628i	$0.189056\pi$
$492$	−5.26366	−	5.20810i	−0.237304	−	0.234799i
$493$	−6.77499	−	34.0602i	−0.305130	−	1.53399i
$494$	−31.6292	+	3.19993i	−1.42306	+	0.143972i
$495$	−0.561082	+	0.561082i	−0.0252188	+	0.0252188i
$496$	37.8614	−	16.1554i	1.70003	−	0.725400i
$497$	−10.2977	−	10.2977i	−0.461917	−	0.461917i
$498$	−0.0755293	−	0.0616507i	−0.00338455	−	0.00276263i
$499$	−21.0694	+	4.19096i	−0.943194	+	0.187613i	−0.642654	−	0.766156i	$-0.722167\pi$
$499$	−21.0694	+	4.19096i	−0.943194	+	0.187613i	−0.300540	+	0.953769i	$0.597167\pi$
$500$	−2.58248	−	6.14230i	−0.115492	−	0.274692i
$501$	1.53734	+	2.30079i	0.0686832	+	0.102792i
$502$	5.46526	−	10.2903i	0.243926	−	0.459280i
$503$	3.12293	+	7.53942i	0.139245	+	0.336166i	0.978083	−	0.208214i	$-0.0667650\pi$
$503$	3.12293	+	7.53942i	0.139245	+	0.336166i	−0.838839	+	0.544380i	$0.816765\pi$
$504$	−5.64992	+	4.71251i	−0.251667	+	0.209912i
$505$	−2.13067	+	5.14389i	−0.0948135	+	0.228900i
$506$	−2.65068	+	2.18715i	−0.117837	+	0.0972305i
$507$	1.60352	+	0.318961i	0.0712149	+	0.0141655i
$508$	−0.768228	−	0.507439i	−0.0340846	−	0.0225140i
$509$	−5.05284	−	3.37620i	−0.223963	−	0.149647i	0.438527	−	0.898718i	$-0.355500\pi$
$509$	−5.05284	−	3.37620i	−0.223963	−	0.149647i	−0.662490	+	0.749071i	$0.730500\pi$
$510$	−1.11548	+	3.71266i	−0.0493942	+	0.164399i
$511$	−9.72030			−0.430001
$512$	11.1398	+	19.6953i	0.492314	+	0.870418i
$513$	33.2579			1.46837
$514$	−5.73697	+	19.0944i	−0.253047	+	0.842219i
$515$	1.59989	+	1.06901i	0.0704994	+	0.0471062i
$516$	15.0595	+	9.94727i	0.662956	+	0.437904i
$517$	−0.116920	−	0.0232569i	−0.00514215	−	0.00102284i
$518$	−9.83879	+	8.11826i	−0.432292	+	0.356696i
$519$	−4.51932	+	10.9106i	−0.198376	+	0.478923i
$520$	−2.76510	+	2.30633i	−0.121258	+	0.101139i
$521$	9.28701	+	22.4208i	0.406871	+	0.982274i	0.985956	+	0.167006i	$0.0534100\pi$
$521$	9.28701	+	22.4208i	0.406871	+	0.982274i	−0.579085	+	0.815267i	$0.696590\pi$
$522$	−4.90316	+	9.23199i	−0.214605	+	0.404073i
$523$	−11.7557	−	17.5936i	−0.514040	−	0.769315i	0.480123	−	0.877201i	$-0.340592\pi$
$523$	−11.7557	−	17.5936i	−0.514040	−	0.769315i	−0.994163	+	0.107886i	$0.965592\pi$
$524$	14.2037	+	33.7828i	0.620492	+	1.47581i
$525$	11.9061	−	2.36826i	0.519623	−	0.103359i
$526$	−16.1141	−	13.1531i	−0.702607	−	0.573503i
$527$	−46.0322	−	46.0322i	−2.00519	−	2.00519i
$528$	−8.27376	+	3.53041i	−0.360069	+	0.153641i
$529$	−14.8983	+	14.8983i	−0.647751	+	0.647751i
$530$	−5.48802	+	0.555225i	−0.238384	+	0.0241174i
$531$	0.776065	+	3.90154i	0.0336783	+	0.169312i
$532$	16.3436	+	16.1711i	0.708583	+	0.701105i
$533$	−9.04375	+	6.04284i	−0.391728	+	0.261745i
$534$	−14.1587	+	4.33604i	−0.612707	+	0.187639i
$535$	2.22650	−	0.922245i	0.0962598	−	0.0398721i
$536$	8.16027	−	0.869334i	0.352470	−	0.0375495i
$537$	2.72371	+	1.12820i	0.117537	+	0.0486854i
$538$	−0.598605	+	6.24758i	−0.0258077	+	0.269352i
$539$	−1.11488	+	5.60489i	−0.0480213	+	0.241420i
$540$	3.12089	−	2.10935i	0.134302	−	0.0907719i
$541$	−21.5427	+	32.2410i	−0.926195	+	1.38615i	−0.00376128	+	0.999993i	$0.501197\pi$
$541$	−21.5427	+	32.2410i	−0.926195	+	1.38615i	−0.922434	+	0.386156i	$0.873803\pi$
$542$	−15.4283	+	8.29927i	−0.662701	+	0.356484i
$543$		−	13.0547i		−	0.560232i
$544$	22.3325	−	27.9603i	0.957499	−	1.19879i
$545$			1.70470i			0.0730214i
$546$	−6.28760	−	11.6886i	−0.269084	−	0.500225i
$547$	−12.7138	+	19.0275i	−0.543602	+	0.813557i	−0.996972	−	0.0777651i	$-0.975222\pi$
$547$	−12.7138	+	19.0275i	−0.543602	+	0.813557i	0.453370	+	0.891322i	$0.350222\pi$
$548$	3.61501	−	18.6916i	0.154426	−	0.798465i
$549$	−0.213496	+	1.07332i	−0.00911178	+	0.0458080i
$550$	−12.0303	−	1.15267i	−0.512973	−	0.0491500i
$551$	30.1801	+	12.5010i	1.28572	+	0.532561i
$552$	4.43786	−	2.41768i	0.188888	−	0.102903i
$553$	−26.5837	+	11.0113i	−1.13046	+	0.468250i
$554$	7.64738	+	24.9714i	0.324906	+	1.06093i
$555$	1.68215	−	1.12398i	0.0714034	−	0.0477102i
$556$	−0.0619705	−	11.6815i	−0.00262813	−	0.495406i
$557$	1.11280	+	5.59444i	0.0471510	+	0.237044i	0.997173	−	0.0751386i	$-0.0239399\pi$
$557$	1.11280	+	5.59444i	0.0471510	+	0.237044i	−0.950022	+	0.312183i	$0.898940\pi$
$558$	1.97241	+	19.4959i	0.0834988	+	0.825329i
$559$	18.7460	−	18.7460i	0.792873	−	0.792873i
$560$	2.55930	+	0.480906i	0.108150	+	0.0203220i
$561$	10.0593	+	10.0593i	0.424705	+	0.424705i
$562$	13.6260	−	16.6935i	0.574780	−	0.704172i
$563$	31.1060	−	6.18736i	1.31096	−	0.260766i	0.510358	−	0.859962i	$-0.329513\pi$
$563$	31.1060	−	6.18736i	1.31096	−	0.260766i	0.800603	+	0.599196i	$0.204513\pi$
$564$	0.162318	+	0.0662279i	0.00683484	+	0.00278870i
$565$	2.59851	+	3.88895i	0.109320	+	0.163609i
$566$	−0.340021	−	0.180587i	−0.0142921	−	0.00759063i
$567$	2.32726	+	5.61851i	0.0977358	+	0.235955i
$568$	−6.35139	−	20.3533i	−0.266498	−	0.854004i
$569$	−6.06734	+	14.6478i	−0.254356	+	0.614070i	−0.998546	−	0.0538978i	$-0.982835\pi$
$569$	−6.06734	+	14.6478i	−0.254356	+	0.614070i	0.744190	+	0.667967i	$0.232835\pi$
$570$	−2.32083	−	2.81269i	−0.0972088	−	0.117811i
$571$	−7.92899	−	1.57717i	−0.331818	−	0.0660027i	0.0263699	−	0.999652i	$-0.491605\pi$
$571$	−7.92899	−	1.57717i	−0.331818	−	0.0660027i	−0.358188	+	0.933650i	$0.616605\pi$
$572$	2.64653	+	12.9457i	0.110657	+	0.541287i
$573$	−16.3549	−	10.9280i	−0.683236	−	0.456524i
$574$	7.53365	+	2.26350i	0.314449	+	0.0944768i
$575$	6.78960			0.283146
$576$	−10.5296	+	2.26925i	−0.438735	+	0.0945522i
$577$	7.30913			0.304283			0.152142	−	0.988359i	$-0.451383\pi$
$577$	7.30913			0.304283			0.152142	+	0.988359i	$0.451383\pi$
$578$	−31.1734	−	9.36611i	−1.29664	−	0.389579i
$579$	13.9218	+	9.30227i	0.578571	+	0.386589i
$580$	3.62494	−	0.741057i	0.150517	−	0.0307707i
$581$	0.101584	+	0.0202062i	0.00421439	+	0.000838295i
$582$	14.0912	+	17.0775i	0.584097	+	0.707887i
$583$	−7.74636	+	18.7014i	−0.320821	+	0.774532i
$584$	−12.6036	−	6.60837i	−0.521541	−	0.273456i
$585$	−0.655937	−	1.58357i	−0.0271197	−	0.0654726i
$586$	20.7476	+	11.0192i	0.857075	+	0.455197i
$587$	−15.4927	−	23.1865i	−0.639452	−	0.957008i	−0.999708	−	0.0241542i	$-0.992311\pi$
$587$	−15.4927	−	23.1865i	−0.639452	−	0.957008i	0.360256	−	0.932853i	$-0.382689\pi$
$588$	3.17481	−	7.78116i	0.130927	−	0.320890i
$589$	60.0597	−	11.9466i	2.47472	−	0.492251i
$590$	0.890334	−	1.09076i	0.0366545	−	0.0449060i
$591$	4.13080	+	4.13080i	0.169919	+	0.169919i
$592$	−18.2765	+	3.83743i	−0.751158	+	0.157718i
$593$	3.85403	−	3.85403i	0.158266	−	0.158266i	−0.623532	−	0.781798i	$-0.714303\pi$
$593$	3.85403	−	3.85403i	0.158266	−	0.158266i	0.781798	+	0.623532i	$0.214303\pi$
$594$	−1.39141	−	13.7531i	−0.0570901	−	0.564297i
$595$	−0.803434	−	4.03914i	−0.0329376	−	0.165588i
$596$	−36.3949	+	0.193075i	−1.49079	+	0.00790868i
$597$	9.77348	−	6.53043i	0.400002	−	0.267273i
$598$	−2.17372	−	7.09797i	−0.0888901	−	0.290257i
$599$	−17.9005	+	7.41463i	−0.731395	+	0.302954i	−0.717125	−	0.696945i	$-0.754542\pi$
$599$	−17.9005	+	7.41463i	−0.731395	+	0.302954i	−0.0142697	+	0.999898i	$0.504542\pi$
$600$	17.0478	+	5.02360i	0.695973	+	0.205088i
$601$	−4.00096	−	1.65725i	−0.163203	−	0.0676007i	0.299586	−	0.954069i	$-0.403151\pi$
$601$	−4.00096	−	1.65725i	−0.163203	−	0.0676007i	−0.462789	+	0.886468i	$0.653151\pi$
$602$	−19.0858	−	1.82869i	−0.777879	−	0.0745317i
$603$	−0.762128	+	3.83148i	−0.0310363	+	0.156030i
$604$	−30.8488	−	5.96625i	−1.25522	−	0.242763i
$605$	−1.48679	+	2.22514i	−0.0604466	+	0.0904647i
$606$	−14.2341	−	26.4611i	−0.578222	−	1.07491i
$607$			15.7984i			0.641238i	0.947208	+	0.320619i	$0.103891\pi$
$607$			15.7984i			0.641238i	−0.947208	+	0.320619i	$0.896109\pi$
$608$	10.1976	+	32.0790i	0.413566	+	1.30098i
$609$			13.6382i			0.552646i
$610$	0.341119	−	0.183497i	0.0138115	−	0.00742956i
$611$	0.143066	−	0.214113i	0.00578782	−	0.00866209i
$612$	9.53889	+	14.1133i	0.385587	+	0.570497i
$613$	−8.55301	+	42.9989i	−0.345453	+	1.73671i	0.283236	+	0.959050i	$0.408592\pi$
$613$	−8.55301	+	42.9989i	−0.345453	+	1.73671i	−0.628688	+	0.777657i	$0.716408\pi$
$614$	0.941306	−	9.82432i	0.0379880	−	0.396477i
$615$	−1.15266	−	0.477449i	−0.0464799	−	0.0192526i
$616$	6.00344	−	7.43508i	0.241886	−	0.299568i
$617$	8.53227	−	3.53418i	0.343496	−	0.142281i	−0.204265	−	0.978916i	$-0.565480\pi$
$617$	8.53227	−	3.53418i	0.343496	−	0.142281i	0.547761	+	0.836635i	$0.315480\pi$
$618$	−9.92880	+	3.04065i	−0.399395	+	0.122313i
$619$	−1.39325	+	0.930941i	−0.0559995	+	0.0374177i	−0.583255	−	0.812289i	$-0.698221\pi$
$619$	−1.39325	+	0.930941i	−0.0559995	+	0.0374177i	0.527255	+	0.849707i	$0.323221\pi$
$620$	4.87825	−	4.93028i	0.195915	−	0.198005i
$621$	1.51507	+	7.61675i	0.0607975	+	0.305650i
$622$	−10.6635	+	1.07883i	−0.427568	+	0.0432572i
$623$	11.1234	−	11.1234i	0.445649	−	0.445649i
$624$	−0.206163	−	19.4304i	−0.00825311	−	0.777837i
$625$	16.4823	+	16.4823i	0.659293	+	0.659293i
$626$	−16.3419	−	13.3391i	−0.653155	−	0.533137i
$627$	−13.1247	+	2.61067i	−0.524150	+	0.104260i
$628$	12.7911	−	5.37790i	0.510419	−	0.214602i
$629$	16.4081	+	24.5564i	0.654233	+	0.979129i
$630$	−0.581457	+	1.09480i	−0.0231658	+	0.0436181i
$631$	−3.99386	−	9.64202i	−0.158993	−	0.383843i	0.824229	−	0.566257i	$-0.191609\pi$
$631$	−3.99386	−	9.64202i	−0.158993	−	0.383843i	−0.983222	+	0.182414i	$0.941609\pi$
$632$	−41.9553	−	3.79540i	−1.66889	−	0.150973i
$633$	2.82637	−	6.82347i	0.112338	−	0.271209i
$634$	−15.7942	+	13.0322i	−0.627269	+	0.517577i
$635$	−0.152147	−	0.0302640i	−0.00603778	−	0.00120099i
$636$	16.4066	−	24.8384i	0.650563	−	0.984908i
$637$	−10.2641	−	6.85824i	−0.406678	−	0.271733i
$638$	3.90689	−	13.0033i	0.154675	−	0.514807i
$639$	10.1496			0.401513
$640$	2.99151	+	2.36350i	0.118250	+	0.0934256i
$641$	−3.82056			−0.150903			−0.0754515	−	0.997149i	$-0.524040\pi$
$641$	−3.82056			−0.150903			−0.0754515	+	0.997149i	$0.524040\pi$
$642$	−3.74227	+	12.4554i	−0.147696	+	0.491577i
$643$	−14.4622	−	9.66332i	−0.570332	−	0.381084i	0.236707	−	0.971581i	$-0.423932\pi$
$643$	−14.4622	−	9.66332i	−0.570332	−	0.381084i	−0.807040	+	0.590497i	$0.798932\pi$
$644$	−2.95898	+	4.47969i	−0.116600	+	0.176524i
$645$	2.98252	+	0.593260i	0.117437	+	0.0233596i
$646$	41.0603	−	33.8799i	1.61549	−	1.33299i
$647$	15.0550	−	36.3461i	0.591875	−	1.42891i	−0.289815	−	0.957083i	$-0.593594\pi$
$647$	15.0550	−	36.3461i	0.591875	−	1.42891i	0.881690	−	0.471829i	$-0.156406\pi$
$648$	−0.802162	+	8.86730i	−0.0315119	+	0.348340i
$649$	−1.97730	−	4.77362i	−0.0776158	−	0.187381i
$650$	12.2452	−	23.0561i	0.480296	−	0.904333i
$651$	14.2036	+	21.2572i	0.556683	+	0.833135i
$652$	30.2545	−	12.7203i	1.18486	−	0.498164i
$653$	−18.2191	+	3.62400i	−0.712968	+	0.141818i	−0.538232	−	0.842797i	$-0.680907\pi$
$653$	−18.2191	+	3.62400i	−0.712968	+	0.141818i	−0.174737	+	0.984615i	$0.555907\pi$
$654$	−7.12684	−	5.81728i	−0.278682	−	0.227474i
$655$	4.36620	+	4.36620i	0.170601	+	0.170601i
$656$	8.22949	+	8.05669i	0.321308	+	0.314561i
$657$	4.79024	−	4.79024i	0.186885	−	0.186885i
$658$	−0.185292	+	0.0187460i	−0.00722343	+	0.000730796i
$659$	2.52934	+	12.7159i	0.0985293	+	0.495340i	0.998264	+	0.0589024i	$0.0187601\pi$
$659$	2.52934	+	12.7159i	0.0985293	+	0.495340i	−0.899734	+	0.436438i	$0.856240\pi$
$660$	−1.06603	+	1.07740i	−0.0414953	+	0.0419379i
$661$	−10.3862	+	6.93980i	−0.403974	+	0.269927i	−0.740915	−	0.671599i	$-0.765608\pi$
$661$	−10.3862	+	6.93980i	−0.403974	+	0.269927i	0.336941	+	0.941526i	$0.390608\pi$
$662$	34.8366	−	10.6686i	1.35396	−	0.414645i
$663$	−28.3909	+	11.7599i	−1.10261	+	0.456717i
$664$	0.117979	+	0.0952617i	0.00457846	+	0.00369687i
$665$	3.57900	+	1.48247i	0.138788	+	0.0574878i
$666$	0.847894	−	8.84938i	0.0328552	−	0.342907i
$667$	−1.48813	+	7.48135i	−0.0576208	+	0.289679i
$668$	−2.40999	−	3.56571i	−0.0932454	−	0.137962i
$669$	9.88833	−	14.7989i	0.382305	−	0.572160i
$670$	1.21771	−	0.655039i	0.0470443	−	0.0253064i
$671$		−	1.42143i		−	0.0548736i
$672$	−10.7441	+	9.05856i	−0.414463	+	0.349442i
$673$		−	24.6534i		−	0.950320i	−0.879899	−	0.475160i	$-0.842390\pi$
$673$		−	24.6534i		−	0.950320i	0.879899	−	0.475160i	$-0.157610\pi$
$674$	10.3299	+	19.2032i	0.397893	+	0.739679i
$675$	−15.1732	+	22.7082i	−0.584015	+	0.874040i
$676$	−2.49658	−	0.482846i	−0.0960222	−	0.0185710i
$677$	5.08875	−	25.5829i	0.195576	−	0.983229i	−0.750890	−	0.660427i	$-0.770375\pi$
$677$	5.08875	−	25.5829i	0.195576	−	0.983229i	0.946467	−	0.322802i	$-0.104625\pi$
$678$	−25.1259	−	2.40741i	−0.964954	−	0.0924560i
$679$	−21.7303	−	9.00098i	−0.833932	−	0.345426i
$680$	1.70426	−	5.78347i	0.0653554	−	0.221786i
$681$	28.9928	−	12.0092i	1.11101	−	0.460195i
$682$	−7.45297	−	24.3366i	−0.285389	−	0.931896i
$683$	−7.02523	+	4.69411i	−0.268813	+	0.179615i	−0.682670	−	0.730727i	$-0.739181\pi$
$683$	−7.02523	+	4.69411i	−0.268813	+	0.179615i	0.413857	+	0.910342i	$0.364181\pi$
$684$	−16.0235	+	0.0850047i	−0.612673	+	0.00325024i
$685$	−0.625796	−	3.14609i	−0.0239104	−	0.120206i
$686$	2.82370	+	27.9104i	0.107809	+	1.06562i
$687$	8.93699	−	8.93699i	0.340967	−	0.340967i
$688$	−23.5039	−	15.3466i	−0.896080	−	0.585085i
$689$	−30.9189	−	30.9189i	−1.17792	−	1.17792i
$690$	0.538439	−	0.659650i	0.0204980	−	0.0251124i
$691$	44.6617	−	8.88377i	1.69901	−	0.337954i	0.752002	−	0.659160i	$-0.229088\pi$
$691$	44.6617	−	8.88377i	1.69901	−	0.337954i	0.947009	+	0.321206i	$0.104088\pi$
$692$	6.93884	−	17.0065i	0.263775	−	0.646489i
$693$	2.52734	+	3.78243i	0.0960056	+	0.143682i
$694$	23.7720	+	12.6254i	0.902372	+	0.479255i
$695$	−0.753218	−	1.81843i	−0.0285712	−	0.0689770i
$696$	−9.27193	+	17.6836i	−0.351452	+	0.670295i
$697$	6.96991	−	16.8268i	0.264004	−	0.637362i
$698$	0.158996	+	0.192692i	0.00601807	+	0.00729351i
$699$	17.7958	+	3.53980i	0.673098	+	0.133887i
$700$	−18.4979	+	3.78157i	−0.699153	+	0.142930i
$701$	16.3596	+	10.9311i	0.617894	+	0.412863i	0.824742	−	0.565510i	$-0.191321\pi$
$701$	16.3596	+	10.9311i	0.617894	+	0.412863i	−0.206848	+	0.978373i	$0.566321\pi$
$702$	28.5973	+	8.59214i	1.07934	+	0.324289i
$703$	−27.7812			−1.04779
$704$	12.8390	−	5.55908i	0.483887	−	0.209516i
$705$	0.0295381			0.00111247
$706$	−16.2911	−	4.89470i	−0.613123	−	0.184214i
$707$	26.5402	+	17.7336i	0.998148	+	0.666941i
$708$	1.52189	+	7.44443i	0.0571960	+	0.279779i
$709$	2.20271	+	0.438146i	0.0827245	+	0.0164549i	0.236279	−	0.971685i	$-0.424072\pi$
$709$	2.20271	+	0.438146i	0.0827245	+	0.0164549i	−0.153555	+	0.988140i	$0.549072\pi$
$710$	−2.28638	−	2.77094i	−0.0858062	−	0.103991i
$711$	7.67420	−	18.5272i	0.287805	−	0.694823i
$712$	21.9851	−	6.86063i	0.823928	−	0.257113i
$713$	5.47204	+	13.2107i	0.204930	+	0.494744i
$714$	19.6281	+	10.4246i	0.734563	+	0.390131i
$715$	1.23689	+	1.85114i	0.0462572	+	0.0692288i
$716$	−4.24548	−	1.73221i	−0.158661	−	0.0647356i
$717$	−37.1125	+	7.38214i	−1.38599	+	0.275691i
$718$	32.8318	−	40.2227i	1.22527	−	1.50110i
$719$	23.3168	+	23.3168i	0.869569	+	0.869569i	0.992425	−	0.122856i	$-0.0392053\pi$
$719$	23.3168	+	23.3168i	0.869569	+	0.869569i	−0.122856	+	0.992425i	$0.539205\pi$
$720$	−1.49824	+	1.02425i	−0.0558360	+	0.0381715i
$721$	7.80028	−	7.80028i	0.290498	−	0.290498i
$722$	2.33567	+	23.0866i	0.0869248	+	0.859193i
$723$	2.08797	+	10.4969i	0.0776523	+	0.390385i
$724$	0.107712	+	20.3039i	0.00400310	+	0.754589i
$725$	−22.3046	+	14.9034i	−0.828371	+	0.553500i
$726$	−4.22897	−	13.8091i	−0.156952	−	0.512503i
$727$	37.5431	−	15.5509i	1.39240	−	0.576750i	0.444630	−	0.895714i	$-0.353335\pi$
$727$	37.5431	−	15.5509i	1.39240	−	0.576750i	0.947767	+	0.318964i	$0.103335\pi$
$728$	9.87549	+	18.1273i	0.366010	+	0.671842i
$729$	−23.8359	−	9.87315i	−0.882811	−	0.365672i
$730$	−2.38687	−	0.228695i	−0.0883419	−	0.00846438i
$731$	−8.66054	+	43.5395i	−0.320322	+	1.61037i
$732$	−0.396920	+	2.05229i	−0.0146706	+	0.0758549i
$733$	−9.59637	+	14.3620i	−0.354450	+	0.530472i	−0.965255	−	0.261309i	$-0.915846\pi$
$733$	−9.59637	+	14.3620i	−0.354450	+	0.530472i	0.610805	+	0.791781i	$0.290846\pi$
$734$	7.94747	+	14.7743i	0.293347	+	0.545329i
$735$		−	1.41599i		−	0.0522294i
$736$	−6.88222	+	3.79682i	−0.253682	+	0.139953i
$737$		−	5.07415i		−	0.186909i
$738$	−4.82812	+	2.59717i	−0.177726	+	0.0956032i
$739$	17.1676	−	25.6932i	0.631522	−	0.945139i	−0.368359	−	0.929684i	$-0.620080\pi$
$739$	17.1676	−	25.6932i	0.631522	−	0.945139i	0.999881	−	0.0154555i	$-0.00491984\pi$
$740$	−2.60696	+	1.76199i	−0.0958339	+	0.0647722i
$741$	5.63939	−	28.3511i	0.207168	−	1.04150i
$742$	−3.01615	+	31.4793i	−0.110726	+	1.15564i
$743$	−32.9584	−	13.6518i	−1.20913	−	0.500837i	−0.315189	−	0.949029i	$-0.602068\pi$
$743$	−32.9584	−	13.6518i	−1.20913	−	0.500837i	−0.893937	+	0.448192i	$0.852068\pi$
$744$	3.96503	+	37.2190i	0.145365	+	1.36451i
$745$	−5.66551	+	2.34673i	−0.207568	+	0.0859775i
$746$	−31.5252	+	9.65447i	−1.15422	+	0.353475i
$747$	−0.0600190	+	0.0401034i	−0.00219598	+	0.00146731i
$748$	−15.7282	−	15.5622i	−0.575079	−	0.569009i
$749$	−2.69541	−	13.5507i	−0.0984881	−	0.495133i
$750$	6.02785	−	0.609840i	0.220106	−	0.0222682i
$751$	−35.9619	+	35.9619i	−1.31227	+	1.31227i	−0.392528	+	0.919740i	$0.628399\pi$
$751$	−35.9619	+	35.9619i	−1.31227	+	1.31227i	−0.919740	+	0.392528i	$0.871601\pi$
$752$	−0.252999	−	0.101664i	−0.00922592	−	0.00370732i
$753$	7.49149	+	7.49149i	0.273005	+	0.273005i
$754$	22.7212	+	18.5462i	0.827457	+	0.675412i
$755$	−5.19233	+	1.03282i	−0.188968	+	0.0375881i
$756$	−8.36997	−	19.9075i	−0.304413	−	0.724030i
$757$	−0.770529	−	1.15318i	−0.0280054	−	0.0419130i	0.817203	−	0.576350i	$-0.195524\pi$
$757$	−0.770529	−	1.15318i	−0.0280054	−	0.0419130i	−0.845208	+	0.534437i	$0.820524\pi$
$758$	−17.9035	+	33.7099i	−0.650286	+	1.22440i
$759$	−1.19579	−	2.88690i	−0.0434045	−	0.104788i
$760$	3.63277	+	4.35541i	0.131774	+	0.157987i
$761$	7.73362	−	18.6706i	0.280344	−	0.676809i	−0.719500	−	0.694492i	$-0.755629\pi$
$761$	7.73362	−	18.6706i	0.280344	−	0.676809i	0.999844	+	0.0176832i	$0.00562903\pi$
$762$	0.645725	−	0.532805i	0.0233921	−	0.0193015i
$763$	9.58528	+	1.90663i	0.347011	+	0.0690247i
$764$	25.5268	+	16.8613i	0.923528	+	0.610020i
$765$	2.38646	+	1.59458i	0.0862826	+	0.0576522i
$766$	1.38760	−	4.61838i	0.0501361	−	0.166869i
$767$	11.1613			0.403010
$768$	−20.0896	+	4.44118i	−0.724920	+	0.160257i
$769$	−19.0515			−0.687015			−0.343508	−	0.939150i	$-0.611615\pi$
$769$	−19.0515			−0.687015			−0.343508	+	0.939150i	$0.611615\pi$
$770$	0.463311	−	1.54204i	0.0166966	−	0.0555714i
$771$	−15.0736	−	10.0719i	−0.542863	−	0.362729i
$772$	−21.7293	−	14.3529i	−0.782053	−	0.516571i
$773$	−37.2271	−	7.40493i	−1.33896	−	0.266337i	−0.526912	−	0.849920i	$-0.676650\pi$
$773$	−37.2271	−	7.40493i	−1.33896	−	0.266337i	−0.812053	+	0.583583i	$0.801650\pi$
$774$	10.3068	−	8.50445i	0.370471	−	0.305686i
$775$	−19.2438	+	46.4586i	−0.691258	+	1.66884i
$776$	−22.0568	−	26.4443i	−0.791791	−	0.949295i
$777$	−4.43855	−	10.7156i	−0.159232	−	0.384420i
$778$	4.53421	−	8.53730i	0.162559	−	0.306077i
$779$	9.51828	+	14.2451i	0.341028	+	0.510384i
$780$	−1.26894	−	3.01812i	−0.0454355	−	0.108066i
$781$	−12.9299	+	2.57191i	−0.462667	+	0.0920302i
$782$	9.62971	+	7.86025i	0.344358	+	0.281082i
$783$	−21.6962	−	21.6962i	−0.775359	−	0.775359i
$784$	−4.87355	+	12.1282i	−0.174055	+	0.433149i
$785$	1.65316	−	1.65316i	0.0590037	−	0.0590037i
$786$	−33.1533	+	3.35413i	−1.18254	+	0.119638i
$787$	2.05604	+	10.3364i	0.0732900	+	0.368454i	0.999973	−	0.00739098i	$-0.00235264\pi$
$787$	2.05604	+	10.3364i	0.0732900	+	0.368454i	−0.926683	+	0.375845i	$0.877353\pi$
$788$	−6.45869	−	6.39052i	−0.230081	−	0.227653i
$789$	15.7261	−	10.5078i	0.559864	−	0.374089i
$790$	−6.78683	+	2.07844i	−0.241465	+	0.0739475i
$791$	24.7733	−	10.2614i	0.880836	−	0.364854i
$792$	0.705524	+	6.62261i	0.0250697	+	0.235324i
$793$	2.83675	+	1.17502i	0.100736	+	0.0417261i
$794$	3.44666	−	35.9724i	0.122317	−	1.27661i
$795$	0.978497	−	4.91924i	0.0347037	−	0.174467i
$796$	−15.1467	+	10.2374i	−0.536862	+	0.362854i
$797$	5.97698	−	8.94519i	0.211716	−	0.316855i	−0.710379	−	0.703819i	$-0.751476\pi$
$797$	5.97698	−	8.94519i	0.211716	−	0.316855i	0.922095	+	0.386965i	$0.126476\pi$
$798$	−18.4111	+	9.90380i	−0.651745	+	0.350591i
$799$			0.431203i			0.0152549i
$800$	−26.5557	−	7.67251i	−0.938887	−	0.271264i
$801$			10.9634i			0.387372i
$802$	−2.10205	−	3.90770i	−0.0742260	−	0.137986i
$803$	−4.88858	+	7.31627i	−0.172514	+	0.258186i
$804$	−1.41691	+	7.32619i	−0.0499705	+	0.258375i
$805$	−0.176475	+	0.887200i	−0.00621993	+	0.0312697i
$806$	54.7296	+	5.24386i	1.92777	+	0.184707i
$807$	−5.27240	−	2.18390i	−0.185597	−	0.0768769i
$808$	22.3566	+	41.0373i	0.786501	+	1.44369i
$809$	35.5966	−	14.7446i	1.25151	−	0.518393i	0.344217	−	0.938890i	$-0.388144\pi$
$809$	35.5966	−	14.7446i	1.25151	−	0.518393i	0.907294	+	0.420497i	$0.138144\pi$
$810$	0.439280	+	1.43440i	0.0154347	+	0.0503999i
$811$	−13.9743	+	9.33736i	−0.490705	+	0.327879i	−0.776184	−	0.630506i	$-0.782847\pi$
$811$	−13.9743	+	9.33736i	−0.490705	+	0.327879i	0.285479	+	0.958385i	$0.407847\pi$
$812$	−0.112526	−	21.2113i	−0.00394890	−	0.744371i
$813$	−3.10769	−	15.6234i	−0.108991	−	0.547937i
$814$	1.16228	+	11.4883i	0.0407378	+	0.402666i
$815$	3.91019	−	3.91019i	0.136968	−	0.136968i
$816$	18.3632	+	26.8610i	0.642839	+	0.940324i
$817$	−29.5275	−	29.5275i	−1.03304	−	1.03304i
$818$	10.3469	−	12.6762i	0.361772	−	0.443213i
$819$	−9.63782	+	1.91708i	−0.336773	+	0.0669883i
$820$	1.79667	+	0.733062i	0.0627424	+	0.0255997i
$821$	−6.39270	−	9.56735i	−0.223107	−	0.333903i	0.702983	−	0.711207i	$-0.251851\pi$
$821$	−6.39270	−	9.56735i	−0.223107	−	0.333903i	−0.926089	+	0.377304i	$0.876851\pi$
$822$	15.2884	+	8.11973i	0.533243	+	0.283208i
$823$	−7.16774	−	17.3044i	−0.249852	−	0.603195i	0.748339	−	0.663316i	$-0.230851\pi$
$823$	−7.16774	−	17.3044i	−0.249852	−	0.603195i	−0.998191	+	0.0601207i	$0.980851\pi$
$824$	15.4171	−	4.81102i	0.537080	−	0.167600i
$825$	4.20530	−	10.1525i	0.146410	−	0.353465i
$826$	−5.13739	−	6.22618i	−0.178753	−	0.216637i
$827$	13.2520	+	2.63599i	0.460818	+	0.0916624i	0.420040	−	0.907506i	$-0.362016\pi$
$827$	13.2520	+	2.63599i	0.460818	+	0.0916624i	0.0407786	+	0.999168i	$0.487016\pi$
$828$	−0.749418	−	3.66584i	−0.0260441	−	0.127397i
$829$	2.19833	+	1.46888i	0.0763512	+	0.0510162i	0.593160	−	0.805085i	$-0.297880\pi$
$829$	2.19833	+	1.46888i	0.0763512	+	0.0510162i	−0.516809	+	0.856101i	$0.672880\pi$
$830$	0.0244689	+	0.00735174i	0.000849328	+	0.000255183i
$831$	−23.7468			−0.823769
$832$	0.480960	+	30.2182i	0.0166743	+	1.04763i
$833$	20.6709			0.716203
$834$	10.1727	+	3.05640i	0.352250	+	0.105834i
$835$	−0.602936	−	0.402869i	−0.0208655	−	0.0139419i
$836$	20.3912	−	4.16864i	0.705244	−	0.144175i
$837$	−56.4126	−	11.2212i	−1.94991	−	0.387860i
$838$	−13.9061	−	16.8533i	−0.480378	−	0.582187i
$839$	2.75538	−	6.65208i	0.0951264	−	0.229655i	−0.869153	−	0.494544i	$-0.835335\pi$
$839$	2.75538	−	6.65208i	0.0951264	−	0.229655i	0.964279	+	0.264888i	$0.0853351\pi$
$840$	−1.09954	+	2.09707i	−0.0379378	+	0.0723557i
$841$	−0.435350	−	1.05103i	−0.0150121	−	0.0362423i
$842$	12.2881	+	6.52626i	0.423475	+	0.224910i
$843$	10.8857	+	16.2915i	0.374922	+	0.561110i
$844$	−4.33954	+	10.6358i	−0.149373	+	0.366100i
$845$	−0.420213	+	0.0835857i	−0.0144558	+	0.00287543i
$846$	0.0820751	−	0.100552i	0.00282180	−	0.00345703i
$847$	10.8487	+	10.8487i	0.372766	+	0.372766i
$848$	−25.3121	+	38.7664i	−0.869221	+	1.33124i
$849$	0.247539	−	0.247539i	0.00849551	−	0.00849551i
$850$	4.40016	+	43.4926i	0.150924	+	1.49178i
$851$	−1.26557	−	6.36247i	−0.0433833	−	0.218103i
$852$	19.3867	−	0.102847i	0.664177	−	0.00352346i
$853$	−9.12898	+	6.09979i	−0.312570	+	0.208853i	−0.701953	−	0.712223i	$-0.747688\pi$
$853$	−9.12898	+	6.09979i	−0.312570	+	0.208853i	0.389383	+	0.921076i	$0.372688\pi$
$854$	−0.650248	−	2.12329i	−0.0222510	−	0.0726575i
$855$	−2.49434	+	1.03319i	−0.0853045	+	0.0353343i
$856$	5.71755	−	19.4027i	0.195422	−	0.663172i
$857$	32.3059	+	13.3815i	1.10355	+	0.457105i	0.858711	−	0.512460i	$-0.171266\pi$
$857$	32.3059	+	13.3815i	1.10355	+	0.457105i	0.244837	+	0.969564i	$0.421266\pi$
$858$	−11.9599	−	1.14593i	−0.408306	−	0.0391213i
$859$	7.71770	−	38.7995i	0.263325	−	1.32382i	−0.592087	−	0.805874i	$-0.701696\pi$
$859$	7.71770	−	38.7995i	0.263325	−	1.32382i	0.855412	−	0.517949i	$-0.173304\pi$
$860$	−4.64358	−	0.898085i	−0.158345	−	0.0306244i
$861$	−3.97383	+	5.94725i	−0.135428	+	0.202682i
$862$	−18.6614	−	34.6913i	−0.635609	−	1.18159i
$863$		−	15.7292i		−	0.535427i	−0.963499	−	0.267713i	$-0.913732\pi$
$863$		−	15.7292i		−	0.535427i	0.963499	−	0.267713i	$-0.0862681\pi$
$864$	2.68144	−	31.5030i	0.0912244	−	1.07175i
$865$		−	3.09477i		−	0.105225i
$866$	49.4081	−	26.5779i	1.67896	−	0.903155i
$867$	16.4432	−	24.6090i	0.558441	−	0.835766i
$868$	−22.2661	−	32.9439i	−0.755762	−	1.11819i
$869$	−5.08160	+	25.5469i	−0.172381	+	0.866619i
$870$	−0.320872	+	3.34891i	−0.0108786	+	0.113539i
$871$	10.1265	+	4.19453i	0.343123	+	0.142126i
$872$	11.1323	+	8.98877i	0.376988	+	0.304398i
$873$	15.1446	−	6.27311i	0.512568	−	0.212313i
$874$	−11.1802	+	3.42390i	−0.378177	+	0.115815i
$875$	−5.35159	+	3.57581i	−0.180917	+	0.120885i
$876$	9.10126	−	9.19834i	0.307503	−	0.310783i
$877$	10.1260	+	50.9066i	0.341929	+	1.71899i	0.643410	+	0.765522i	$0.277519\pi$
$877$	10.1260	+	50.9066i	0.341929	+	1.71899i	−0.301480	+	0.953472i	$0.597481\pi$
$878$	24.0301	−	2.43113i	0.810975	−	0.0820466i
$879$	−15.1045	+	15.1045i	−0.509462	+	0.509462i
$880$	1.64910	−	1.68447i	0.0555912	−	0.0567836i
$881$	4.72269	+	4.72269i	0.159112	+	0.159112i	0.782173	−	0.623061i	$-0.214111\pi$
$881$	4.72269	+	4.72269i	0.159112	+	0.159112i	−0.623061	+	0.782173i	$0.714111\pi$
$882$	−4.82020	−	3.93449i	−0.162305	−	0.132481i
$883$	11.3177	−	2.25122i	0.380869	−	0.0757596i	−0.000942833	−	1.00000i	$-0.500300\pi$
$883$	11.3177	−	2.25122i	0.380869	−	0.0757596i	0.381812	+	0.924240i	$0.375300\pi$
$884$	44.0591	−	18.5243i	1.48187	−	0.623041i
$885$	0.711275	+	1.06450i	0.0239093	+	0.0357827i
$886$	−12.0981	+	22.7791i	−0.406443	+	0.765277i
$887$	9.14647	+	22.0815i	0.307109	+	0.741426i	0.999796	+	0.0201879i	$0.00642646\pi$
$887$	9.14647	+	22.0815i	0.307109	+	0.741426i	−0.692688	+	0.721238i	$0.743574\pi$
$888$	1.52988	−	16.9117i	0.0513395	−	0.567520i
$889$	−0.340339	+	0.821652i	−0.0114146	+	0.0275573i
$890$	2.99310	−	2.46969i	0.100329	−	0.0827843i
$891$	5.39937	+	1.07400i	0.180886	+	0.0359804i
$892$	−15.2571	+	23.0983i	−0.510847	+	0.773387i
$893$	−0.337257	−	0.225348i	−0.0112859	−	0.00754097i
$894$	9.52252	−	31.6939i	0.318481	−	1.06000i
$895$	−0.772576			−0.0258244
$896$	16.6355	−	14.1774i	0.555752	−	0.473632i
$897$	6.74990			0.225373
$898$	3.04857	−	10.1466i	0.101732	−	0.338597i
$899$	−46.9742	−	31.3871i	−1.56668	−	1.04682i
$900$	7.25230	−	10.9795i	0.241743	−	0.365983i
$901$	71.8121	+	14.2843i	2.39241	+	0.475880i
$902$	5.49255	−	4.53205i	0.182882	−	0.150901i
$903$	6.67162	−	16.1067i	0.222018	−	0.535998i
$904$	39.0980	+	3.53691i	1.30038	+	0.117636i
$905$	1.30919	+	3.16066i	0.0435189	+	0.105064i
$906$	13.4009	−	25.2320i	0.445214	−	0.838278i
$907$	10.4003	+	15.5652i	0.345337	+	0.516833i	0.962961	−	0.269640i	$-0.0869048\pi$
$907$	10.4003	+	15.5652i	0.345337	+	0.516833i	−0.617624	+	0.786473i	$0.711905\pi$
$908$	−44.9933	+	18.9171i	−1.49315	+	0.627785i
$909$	−21.8185	+	4.33997i	−0.723675	+	0.143948i
$910$	2.69447	+	2.19936i	0.0893207	+	0.0729080i
$911$	0.953962	+	0.953962i	0.0316062	+	0.0316062i	0.722733	−	0.691127i	$-0.242886\pi$
$911$	0.953962	+	0.953962i	0.0316062	+	0.0316062i	−0.691127	+	0.722733i	$0.742886\pi$
$912$	−30.6054	+	0.324733i	−1.01345	+	0.0107530i
$913$	0.0662976	−	0.0662976i	0.00219413	−	0.00219413i
$914$	−23.2752	+	2.35476i	−0.769876	+	0.0778886i
$915$	0.0687110	+	0.345433i	0.00227151	+	0.0114197i
$916$	−13.8259	+	13.9734i	−0.456820	+	0.461693i
$917$	29.4339	−	19.6671i	0.971992	−	0.649464i
$918$	−47.8092	+	14.6414i	−1.57794	+	0.483237i
$919$	25.5763	−	10.5941i	0.843685	−	0.349466i	0.0813793	−	0.996683i	$-0.474068\pi$
$919$	25.5763	−	10.5941i	0.843685	−	0.349466i	0.762305	+	0.647218i	$0.224068\pi$
$920$	−0.831987	+	1.03039i	−0.0274298	+	0.0339710i
$921$	8.29085	+	3.43418i	0.273193	+	0.113160i
$922$	−2.22313	+	23.2026i	−0.0732149	+	0.764137i
$923$	5.55567	−	27.9303i	0.182867	−	0.919336i
$924$	4.86577	+	7.19916i	0.160072	+	0.236835i
$925$	12.6745	−	18.9688i	0.416736	−	0.623690i
$926$	45.1733	−	24.2999i	1.48449	−	0.798545i
$927$			7.68808i			0.252510i
$928$	14.2746	−	27.5797i	0.468588	−	0.905347i
$929$			40.9562i			1.34373i	0.740673	+	0.671865i	$0.234507\pi$
$929$			40.9562i			1.34373i	−0.740673	+	0.671865i	$0.765493\pi$
$930$	2.98763	+	5.55398i	0.0979683	+	0.182122i
$931$	−10.8026	+	16.1673i	−0.354042	+	0.529861i
$932$	−27.7068	−	5.35859i	−0.907567	−	0.175526i
$933$	1.90127	−	9.55834i	0.0622448	−	0.312926i
$934$	−58.2719	−	5.58326i	−1.90672	−	0.182690i
$935$	−3.44424	−	1.42665i	−0.112639	−	0.0466565i
$936$	−13.8000	−	4.06655i	−0.451067	−	0.132919i
$937$	−1.45370	+	0.602142i	−0.0474903	+	0.0196711i	−0.406302	−	0.913739i	$-0.633182\pi$
$937$	−1.45370	+	0.602142i	−0.0474903	+	0.0196711i	0.358812	+	0.933410i	$0.383182\pi$
$938$	−2.32123	−	7.57963i	−0.0757908	−	0.247484i
$939$	15.9484	−	10.6564i	0.520458	−	0.347759i
$940$	−0.0459403		0.000243714i	−0.00149841		7.94907e-6i
$941$	11.6410	+	58.5231i	0.379485	+	1.90780i	0.417814	+	0.908532i	$0.362796\pi$
$941$	11.6410	+	58.5231i	0.379485	+	1.90780i	−0.0383299	+	0.999265i	$0.512204\pi$
$942$	1.26996	+	12.5527i	0.0413777	+	0.408990i
$943$	−2.82882	+	2.82882i	−0.0921191	+	0.0921191i
$944$	−2.42840	−	11.5657i	−0.0790378	−	0.376432i
$945$	−2.57291	−	2.57291i	−0.0836969	−	0.0836969i
$946$	−10.9751	+	13.4458i	−0.356832	+	0.437161i
$947$	−31.7435	+	6.31417i	−1.03152	+	0.205183i	−0.681699	−	0.731632i	$-0.738759\pi$
$947$	−31.7435	+	6.31417i	−1.03152	+	0.205183i	−0.349824	+	0.936815i	$0.613759\pi$
$948$	14.4707	−	35.4663i	0.469986	−	1.15189i
$949$	−10.5600	−	15.8041i	−0.342792	−	0.513024i
$950$	−36.3163	−	19.2878i	−1.17826	−	0.625779i
$951$	−7.12521	−	17.2018i	−0.231051	−	0.557806i
$952$	−30.6134	−	16.0513i	−0.992187	−	0.520227i
$953$	−11.5018	+	27.7677i	−0.372579	+	0.899484i	0.620733	+	0.784022i	$0.286835\pi$
$953$	−11.5018	+	27.7677i	−0.372579	+	0.899484i	−0.993312	+	0.115462i	$0.963165\pi$
$954$	−14.0269	−	16.9996i	−0.454137	−	0.550384i
$955$	5.05558	+	1.00562i	0.163595	+	0.0325410i
$956$	57.6599	−	11.7876i	1.86485	−	0.381238i
$957$	10.2652	+	6.85896i	0.331825	+	0.221719i
$958$	9.98305	+	2.99943i	0.322538	+	0.0969073i
$959$	−18.3899			−0.593841
$960$	−2.85139	+	1.97159i	−0.0920282	+	0.0636328i
$961$	−74.9050			−2.41629
$962$	−23.8881	−	7.17724i	−0.770183	−	0.231403i
$963$	8.00623	+	5.34959i	0.257997	+	0.172388i
$964$	−3.33401	−	16.3085i	−0.107381	−	0.525263i
$965$	−4.30347	−	0.856013i	−0.138534	−	0.0275560i
$966$	−3.10689	−	3.76535i	−0.0999626	−	0.121148i
$967$	1.60334	−	3.87079i	0.0515598	−	0.124476i	−0.896001	−	0.444052i	$-0.853540\pi$
$967$	1.60334	−	3.87079i	0.0515598	−	0.124476i	0.947561	+	0.319576i	$0.103540\pi$
$968$	6.69121	+	21.4422i	0.215064	+	0.689180i
$969$	18.5234	+	44.7195i	0.595058	+	1.43660i
$970$	−5.12420	−	2.72149i	−0.164528	−	0.0873819i
$971$	23.3219	+	34.9037i	0.748435	+	1.12011i	0.988773	+	0.149423i	$0.0477415\pi$
$971$	23.3219	+	34.9037i	0.748435	+	1.12011i	−0.240339	+	0.970689i	$0.577258\pi$
$972$	23.5539	+	9.61027i	0.755491	+	0.308250i
$973$	−11.0672	+	2.20140i	−0.354798	+	0.0705737i
$974$	−13.7567	+	16.8536i	−0.440794	+	0.540023i
$975$	16.7851	+	16.7851i	0.537553	+	0.537553i
$976$	0.600394	−	3.19519i	0.0192181	−	0.102276i
$977$	25.9305	−	25.9305i	0.829590	−	0.829590i	−0.157870	−	0.987460i	$-0.550463\pi$
$977$	25.9305	−	25.9305i	0.829590	−	0.829590i	0.987460	+	0.157870i	$0.0504627\pi$
$978$	3.00383	+	29.6908i	0.0960518	+	0.949407i
$979$	−2.77812	−	13.9666i	−0.0887892	−	0.446373i
$980$	0.0116831	+	2.20227i	0.000373202	+	0.0703490i
$981$	−5.66331	+	3.78410i	−0.180816	+	0.120817i
$982$	−6.94014	−	22.6620i	−0.221469	−	0.723174i
$983$	23.7946	−	9.85606i	0.758931	−	0.314359i	0.0305512	−	0.999533i	$-0.490274\pi$
$983$	23.7946	−	9.85606i	0.758931	−	0.314359i	0.728380	+	0.685174i	$0.240274\pi$
$984$	−9.19582	+	5.00976i	−0.293152	+	0.159705i
$985$	−1.41436	−	0.585847i	−0.0450652	−	0.0186666i
$986$	−48.8882	−	4.68416i	−1.55692	−	0.149174i
$987$	0.0330370	−	0.166088i	0.00105158	−	0.00528664i
$988$	−8.53697	+	44.1408i	−0.271597	+	1.40431i
$989$	5.41728	−	8.10753i	0.172259	−	0.257805i
$990$	0.531608	+	0.988254i	0.0168956	+	0.0314088i
$991$		−	44.7350i		−	1.42105i	−0.703670	−	0.710527i	$-0.748456\pi$
$991$		−	44.7350i		−	1.42105i	0.703670	−	0.710527i	$-0.251544\pi$
$992$	−6.47387	−	57.8537i	−0.205546	−	1.83686i
$993$			33.1283i			1.05129i
$994$	−18.1378	+	9.75678i	−0.575295	+	0.309466i
$995$	−1.71134	+	2.56120i	−0.0542532	+	0.0811956i
$996$	−0.114235	+	0.0772093i	−0.00361968	+	0.00244647i
$997$	8.79997	−	44.2404i	0.278698	−	1.40111i	−0.547064	−	0.837091i	$-0.684255\pi$
$997$	8.79997	−	44.2404i	0.278698	−	1.40111i	0.825762	−	0.564018i	$-0.190745\pi$
$998$	−2.89759	+	30.2418i	−0.0917215	+	0.957288i
$999$	24.1079	+	9.98583i	0.762741	+	0.315938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.2.i.a.5.5	✓	56
3.2	odd	2		576.2.bd.a.325.3		56
4.3	odd	2		256.2.i.a.113.2		56
8.3	odd	2		512.2.i.a.481.6		56
8.5	even	2		512.2.i.b.481.2		56
64.13	even	16	inner	64.2.i.a.13.5	yes	56
64.19	odd	16		512.2.i.a.33.6		56
64.45	even	16		512.2.i.b.33.2		56
64.51	odd	16		256.2.i.a.145.2		56
192.77	odd	16		576.2.bd.a.397.3		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.5.5	✓	56	1.1	even	1	trivial
64.2.i.a.13.5	yes	56	64.13	even	16	inner
256.2.i.a.113.2		56	4.3	odd	2
256.2.i.a.145.2		56	64.51	odd	16
512.2.i.a.33.6		56	64.19	odd	16
512.2.i.a.481.6		56	8.3	odd	2
512.2.i.b.33.2		56	64.45	even	16
512.2.i.b.481.2		56	8.5	even	2
576.2.bd.a.325.3		56	3.2	odd	2
576.2.bd.a.397.3		56	192.77	odd	16

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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	64.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.406933 - 1.35440i) q^{2} +(1.06920 + 0.714416i) q^{3} +(-1.66881 - 1.10230i) q^{4} +(-0.330507 - 0.0657419i) q^{5} +(1.40270 - 1.15741i) q^{6} +(-0.739314 + 1.78486i) q^{7} +(-2.17206 + 1.81168i) q^{8} +(-0.515254 - 1.24393i) q^{9} +O(q^{10})\)	\(q+(0.406933 - 1.35440i) q^{2} +(1.06920 + 0.714416i) q^{3} +(-1.66881 - 1.10230i) q^{4} +(-0.330507 - 0.0657419i) q^{5} +(1.40270 - 1.15741i) q^{6} +(-0.739314 + 1.78486i) q^{7} +(-2.17206 + 1.81168i) q^{8} +(-0.515254 - 1.24393i) q^{9} +(-0.223535 + 0.420887i) q^{10} +(0.971610 + 1.45412i) q^{11} +(-0.996787 - 2.37081i) q^{12} +(-3.70516 + 0.737003i) q^{13} +(2.11657 + 1.72765i) q^{14} +(-0.306411 - 0.306411i) q^{15} +(1.56986 + 3.67907i) q^{16} +(4.47305 - 4.47305i) q^{17} +(-1.89446 + 0.191663i) q^{18} +(1.16088 + 5.83613i) q^{19} +(0.479086 + 0.474030i) q^{20} +(-2.06561 + 1.38019i) q^{21} +(2.36484 - 0.724221i) q^{22} +(-1.28371 + 0.531730i) q^{23} +(-3.61665 + 0.385291i) q^{24} +(-4.51448 - 1.86996i) q^{25} +(-0.509557 + 5.31819i) q^{26} +(1.09039 - 5.48174i) q^{27} +(3.20123 - 2.16365i) q^{28} +(3.04996 - 4.56458i) q^{29} +(-0.539692 + 0.290314i) q^{30} -10.2910i q^{31} +(5.62177 - 0.629080i) q^{32} +2.24887i q^{33} +(-4.23807 - 7.87854i) q^{34} +(0.361689 - 0.541305i) q^{35} +(-0.511331 + 2.64386i) q^{36} +(-0.910827 + 4.57904i) q^{37} +(8.37686 + 0.802620i) q^{38} +(-4.48808 - 1.85903i) q^{39} +(0.836983 - 0.455977i) q^{40} +(2.66002 - 1.10181i) q^{41} +(1.02877 + 3.35931i) q^{42} +(-5.83495 + 3.89879i) q^{43} +(-0.0185551 - 3.49765i) q^{44} +(0.0885166 + 0.445003i) q^{45} +(0.197792 + 1.95504i) q^{46} +(-0.0482001 + 0.0482001i) q^{47} +(-0.949897 + 5.05519i) q^{48} +(2.31060 + 2.31060i) q^{49} +(-4.36977 + 5.35348i) q^{50} +(7.97819 - 1.58696i) q^{51} +(6.99562 + 2.85430i) q^{52} +(6.43049 + 9.62391i) q^{53} +(-6.98076 - 3.70752i) q^{54} +(-0.225527 - 0.544471i) q^{55} +(-1.62776 - 5.21622i) q^{56} +(-2.92821 + 7.06933i) q^{57} +(-4.94115 - 5.98835i) q^{58} +(-2.89770 - 0.576389i) q^{59} +(0.173584 + 0.849098i) q^{60} +(-0.675800 - 0.451555i) q^{61} +(-13.9382 - 4.18776i) q^{62} +2.60119 q^{63} +(1.43566 - 7.87013i) q^{64} +1.27304 q^{65} +(3.04588 + 0.915141i) q^{66} +(-2.41244 - 1.61194i) q^{67} +(-12.3953 + 2.53401i) q^{68} +(-1.75242 - 0.348577i) q^{69} +(-0.585962 - 0.710147i) q^{70} +(-2.88474 + 6.96439i) q^{71} +(3.37277 + 1.76842i) q^{72} +(1.92544 + 4.64843i) q^{73} +(5.83121 + 3.09699i) q^{74} +(-3.49095 - 5.22458i) q^{75} +(4.49589 - 11.0190i) q^{76} +(-3.31372 + 0.659140i) q^{77} +(-4.34422 + 5.32217i) q^{78} +(10.5317 + 10.5317i) q^{79} +(-0.276979 - 1.31916i) q^{80} +(2.22588 - 2.22588i) q^{81} +(-0.409851 - 4.05110i) q^{82} +(-0.0104591 - 0.0525816i) q^{83} +(4.96850 - 0.0263579i) q^{84} +(-1.77244 + 1.18431i) q^{85} +(2.90609 + 9.48942i) q^{86} +(6.52202 - 2.70151i) q^{87} +(-4.74478 - 1.39818i) q^{88} +(-7.52277 - 3.11604i) q^{89} +(0.638733 + 0.0611995i) q^{90} +(1.42383 - 7.15808i) q^{91} +(2.72840 + 0.527681i) q^{92} +(7.35206 - 11.0031i) q^{93} +(0.0456681 + 0.0848966i) q^{94} -2.00520i q^{95} +(6.46021 + 3.34367i) q^{96} +12.1748i q^{97} +(4.06974 - 2.18922i) q^{98} +(1.30820 - 1.95786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9	\( 56 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 8 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 8 q^{20} - 8 q^{21} - 8 q^{23} + 32 q^{24} - 8 q^{25} + 32 q^{26} - 8 q^{27} + 32 q^{28} - 8 q^{29} + 72 q^{30} + 32 q^{32} + 32 q^{34} - 8 q^{35} + 72 q^{36} - 8 q^{37} + 32 q^{38} - 8 q^{39} + 32 q^{40} - 8 q^{41} + 32 q^{42} - 8 q^{43} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 8 q^{48} - 8 q^{49} - 32 q^{50} + 24 q^{51} - 56 q^{52} - 8 q^{53} - 72 q^{54} + 56 q^{55} - 64 q^{56} - 8 q^{57} - 80 q^{58} + 56 q^{59} - 104 q^{60} - 8 q^{61} - 40 q^{62} + 64 q^{63} - 104 q^{64} - 16 q^{65} - 88 q^{66} + 72 q^{67} - 56 q^{68} - 8 q^{69} - 104 q^{70} + 56 q^{71} - 80 q^{72} - 8 q^{73} - 64 q^{74} + 56 q^{75} - 72 q^{76} - 8 q^{77} - 32 q^{78} + 24 q^{79} + 32 q^{80} - 8 q^{81} + 72 q^{82} - 8 q^{83} + 104 q^{84} - 8 q^{85} + 96 q^{86} - 8 q^{87} + 72 q^{88} - 8 q^{89} + 136 q^{90} - 8 q^{91} + 144 q^{92} + 16 q^{93} + 88 q^{94} + 128 q^{96} + 128 q^{98} + 16 q^{99}+O(q^{100}) \) 56 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 8 * q^23 + 32 * q^24 - 8 * q^25 + 32 * q^26 - 8 * q^27 + 32 * q^28 - 8 * q^29 + 72 * q^30 + 32 * q^32 + 32 * q^34 - 8 * q^35 + 72 * q^36 - 8 * q^37 + 32 * q^38 - 8 * q^39 + 32 * q^40 - 8 * q^41 + 32 * q^42 - 8 * q^43 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 32 * q^50 + 24 * q^51 - 56 * q^52 - 8 * q^53 - 72 * q^54 + 56 * q^55 - 64 * q^56 - 8 * q^57 - 80 * q^58 + 56 * q^59 - 104 * q^60 - 8 * q^61 - 40 * q^62 + 64 * q^63 - 104 * q^64 - 16 * q^65 - 88 * q^66 + 72 * q^67 - 56 * q^68 - 8 * q^69 - 104 * q^70 + 56 * q^71 - 80 * q^72 - 8 * q^73 - 64 * q^74 + 56 * q^75 - 72 * q^76 - 8 * q^77 - 32 * q^78 + 24 * q^79 + 32 * q^80 - 8 * q^81 + 72 * q^82 - 8 * q^83 + 104 * q^84 - 8 * q^85 + 96 * q^86 - 8 * q^87 + 72 * q^88 - 8 * q^89 + 136 * q^90 - 8 * q^91 + 144 * q^92 + 16 * q^93 + 88 * q^94 + 128 * q^96 + 128 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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