LMFDB - Embedded newform 804.2.bd.a.23.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(23,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 28]))

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

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

chi := DirichletCharacter("804.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bd (of order $66$, degree $20$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$2640$
Relative dimension:	$132$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			23.8
Character	$\chi$	$=$	804.23
Dual form			804.2.bd.a.35.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39805 - 0.213188i) q^{2} +(-0.861586 + 1.50255i) q^{3} +(1.90910 + 0.596096i) q^{4} +(-2.23249 + 1.01954i) q^{5} +(1.52487 - 1.91697i) q^{6} +(-3.06753 - 3.21714i) q^{7} +(-2.54194 - 1.24037i) q^{8} +(-1.51534 - 2.58916i) q^{9} +O(q^{10})$	\(q+(-1.39805 - 0.213188i) q^{2} +(-0.861586 + 1.50255i) q^{3} +(1.90910 + 0.596096i) q^{4} +(-2.23249 + 1.01954i) q^{5} +(1.52487 - 1.91697i) q^{6} +(-3.06753 - 3.21714i) q^{7} +(-2.54194 - 1.24037i) q^{8} +(-1.51534 - 2.58916i) q^{9} +(3.33849 - 0.949437i) q^{10} +(1.57520 + 0.150413i) q^{11} +(-2.54052 + 2.35494i) q^{12} +(-1.56534 - 0.301694i) q^{13} +(3.60272 + 5.15169i) q^{14} +(0.391562 - 4.23286i) q^{15} +(3.28934 + 2.27601i) q^{16} +(-1.37562 + 2.66833i) q^{17} +(1.56655 + 3.94283i) q^{18} +(5.04324 - 5.28920i) q^{19} +(-4.86980 + 0.615636i) q^{20} +(7.47687 - 1.83730i) q^{21} +(-2.17014 - 0.546098i) q^{22} +(1.19919 - 0.480083i) q^{23} +(4.05383 - 2.75072i) q^{24} +(0.670243 - 0.773501i) q^{25} +(2.12411 + 0.755496i) q^{26} +(5.19595 - 0.0460952i) q^{27} +(-3.93851 - 7.97039i) q^{28} +(1.44193 + 0.832499i) q^{29} +(-1.44982 + 5.83429i) q^{30} +(1.81495 + 9.41688i) q^{31} +(-4.11345 - 3.88324i) q^{32} +(-1.58317 + 2.23722i) q^{33} +(2.49204 - 3.43720i) q^{34} +(10.1283 + 4.05474i) q^{35} +(-1.34955 - 5.84626i) q^{36} +(1.39286 + 2.41250i) q^{37} +(-8.17831 + 6.31942i) q^{38} +(1.80199 - 2.09207i) q^{39} +(6.93948 + 0.177490i) q^{40} +(-2.52721 + 0.120386i) q^{41} +(-10.8447 + 0.974659i) q^{42} +(-2.95214 - 4.59362i) q^{43} +(2.91755 + 1.22612i) q^{44} +(6.02274 + 4.23532i) q^{45} +(-1.77888 + 0.415529i) q^{46} +(-4.66966 - 3.67226i) q^{47} +(-6.25388 + 2.98143i) q^{48} +(-0.607133 + 12.7453i) q^{49} +(-1.10194 + 0.938508i) q^{50} +(-2.82409 - 4.36593i) q^{51} +(-2.80855 - 1.50906i) q^{52} +(-6.80366 + 10.5867i) q^{53} +(-7.27404 - 1.04327i) q^{54} +(-3.66996 + 1.27019i) q^{55} +(3.80706 + 11.9827i) q^{56} +(3.60212 + 12.1348i) q^{57} +(-1.83842 - 1.47128i) q^{58} +(1.31106 + 1.51305i) q^{59} +(3.27072 - 7.84756i) q^{60} +(-3.51789 + 0.335918i) q^{61} +(-0.529838 - 13.5522i) q^{62} +(-3.68133 + 12.8174i) q^{63} +(4.92296 + 6.30590i) q^{64} +(3.80220 - 0.922403i) q^{65} +(2.69030 - 2.79024i) q^{66} +(8.07546 - 1.33677i) q^{67} +(-4.21677 + 4.27411i) q^{68} +(-0.311854 + 2.21548i) q^{69} +(-13.2954 - 7.82797i) q^{70} +(1.81399 - 0.935176i) q^{71} +(0.640391 + 8.46108i) q^{72} +(13.1491 - 1.25558i) q^{73} +(-1.43297 - 3.66975i) q^{74} +(0.584756 + 1.67351i) q^{75} +(12.7809 - 7.09137i) q^{76} +(-4.34807 - 5.52902i) q^{77} +(-2.96528 + 2.54066i) q^{78} +(10.6353 - 3.68090i) q^{79} +(-9.66392 - 1.72755i) q^{80} +(-4.40750 + 7.84691i) q^{81} +(3.55884 + 0.370465i) q^{82} +(8.02119 - 11.2642i) q^{83} +(15.3693 + 0.949343i) q^{84} +(0.350577 - 7.35952i) q^{85} +(3.14794 + 7.05149i) q^{86} +(-2.49322 + 1.44931i) q^{87} +(-3.81749 - 2.33617i) q^{88} +(10.9904 - 1.58018i) q^{89} +(-7.51720 - 7.20518i) q^{90} +(3.83114 + 5.96137i) q^{91} +(2.57555 - 0.201696i) q^{92} +(-15.7131 - 5.38638i) q^{93} +(5.74555 + 6.12953i) q^{94} +(-5.86642 + 16.9499i) q^{95} +(9.37886 - 2.83494i) q^{96} +(7.46373 + 12.9276i) q^{97} +(3.56595 - 17.6892i) q^{98} +(-1.99751 - 4.30636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	$ 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) $ 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{14}{33}\right)$	$-1$

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 $

$2$	−1.39805	−	0.213188i	−0.988572	−	0.150747i
$2$	−1.39805	−	0.213188i	−0.988572	−	0.150747i
$3$	−0.861586	+	1.50255i	−0.497437	+	0.867500i
$3$	−0.861586	+	1.50255i	−0.497437	+	0.867500i
$4$	1.90910	+	0.596096i	0.954551	+	0.298048i
$5$	−2.23249	+	1.01954i	−0.998400	+	0.455954i	−0.846470	−	0.532437i	$-0.821276\pi$
$5$	−2.23249	+	1.01954i	−0.998400	+	0.455954i	−0.151931	+	0.988391i	$0.548549\pi$
$6$	1.52487	−	1.91697i	0.622525	−	0.782600i
$7$	−3.06753	−	3.21714i	−1.15942	−	1.21596i	−0.972328	−	0.233621i	$-0.924942\pi$
$7$	−3.06753	−	3.21714i	−1.15942	−	1.21596i	−0.187091	−	0.982342i	$-0.559906\pi$
$8$	−2.54194	−	1.24037i	−0.898713	−	0.438537i
$9$	−1.51534	−	2.58916i	−0.505113	−	0.863053i
$10$	3.33849	−	0.949437i	1.05572	−	0.300238i
$11$	1.57520	+	0.150413i	0.474939	+	0.0453512i	0.329782	−	0.944057i	$-0.393025\pi$
$11$	1.57520	+	0.150413i	0.474939	+	0.0453512i	0.145158	+	0.989408i	$0.453631\pi$
$12$	−2.54052	+	2.35494i	−0.733385	+	0.679813i
$13$	−1.56534	−	0.301694i	−0.434147	−	0.0836750i	−0.0325047	−	0.999472i	$-0.510348\pi$
$13$	−1.56534	−	0.301694i	−0.434147	−	0.0836750i	−0.401642	+	0.915797i	$0.631560\pi$
$14$	3.60272	+	5.15169i	0.962867	+	1.37685i
$15$	0.391562	−	4.23286i	0.101101	−	1.09292i
$16$	3.28934	+	2.27601i	0.822335	+	0.569004i
$17$	−1.37562	+	2.66833i	−0.333636	+	0.647164i	−0.994661	−	0.103200i	$-0.967092\pi$
$17$	−1.37562	+	2.66833i	−0.333636	+	0.647164i	0.661024	+	0.750365i	$0.270122\pi$
$18$	1.56655	+	3.94283i	0.369238	+	0.929335i
$19$	5.04324	−	5.28920i	1.15700	−	1.21343i	0.183923	−	0.982941i	$-0.441120\pi$
$19$	5.04324	−	5.28920i	1.15700	−	1.21343i	0.973076	−	0.230485i	$-0.0740314\pi$
$20$	−4.86980	+	0.615636i	−1.08892	+	0.137660i
$21$	7.47687	−	1.83730i	1.63159	−	0.400931i
$22$	−2.17014	−	0.546098i	−0.462676	−	0.116428i
$23$	1.19919	−	0.480083i	0.250048	−	0.100104i	−0.243253	−	0.969963i	$-0.578214\pi$
$23$	1.19919	−	0.480083i	0.250048	−	0.100104i	0.493301	+	0.869859i	$0.335790\pi$
$24$	4.05383	−	2.75072i	0.827484	−	0.561489i
$25$	0.670243	−	0.773501i	0.134049	−	0.154700i
$26$	2.12411	+	0.755496i	0.416572	+	0.148165i
$27$	5.19595	−	0.0460952i	0.999961	−	0.00887103i
$28$	−3.93851	−	7.97039i	−0.744309	−	1.50626i
$29$	1.44193	+	0.832499i	0.267760	+	0.154591i	0.627869	−	0.778319i	$-0.283927\pi$
$29$	1.44193	+	0.832499i	0.267760	+	0.154591i	−0.360109	+	0.932910i	$0.617261\pi$
$30$	−1.44982	+	5.83429i	−0.264700	+	1.06519i
$31$	1.81495	+	9.41688i	0.325975	+	1.69132i	0.662029	+	0.749478i	$0.269695\pi$
$31$	1.81495	+	9.41688i	0.325975	+	1.69132i	−0.336054	+	0.941843i	$0.609092\pi$
$32$	−4.11345	−	3.88324i	−0.727162	−	0.686465i
$33$	−1.58317	+	2.23722i	−0.275595	+	0.389451i
$34$	2.49204	−	3.43720i	0.427382	−	0.589474i
$35$	10.1283	+	4.05474i	1.71199	+	0.685377i
$36$	−1.34955	−	5.84626i	−0.224925	−	0.974376i
$37$	1.39286	+	2.41250i	0.228985	+	0.396613i	0.957507	−	0.288408i	$-0.0931261\pi$
$37$	1.39286	+	2.41250i	0.228985	+	0.396613i	−0.728523	+	0.685022i	$0.759793\pi$
$38$	−8.17831	+	6.31942i	−1.32670	+	1.02515i
$39$	1.80199	−	2.09207i	0.288549	−	0.335000i
$40$	6.93948	+	0.177490i	1.09723	+	0.0280637i
$41$	−2.52721	+	0.120386i	−0.394684	+	0.0188011i	−0.243986	−	0.969779i	$-0.578455\pi$
$41$	−2.52721	+	0.120386i	−0.394684	+	0.0188011i	−0.150698	+	0.988580i	$0.548152\pi$
$42$	−10.8447	+	0.974659i	−1.67338	+	0.150393i
$43$	−2.95214	−	4.59362i	−0.450197	−	0.700521i	0.539771	−	0.841812i	$-0.318511\pi$
$43$	−2.95214	−	4.59362i	−0.450197	−	0.700521i	−0.989968	+	0.141291i	$0.954875\pi$
$44$	2.91755	+	1.22612i	0.439837	+	0.184845i
$45$	6.02274	+	4.23532i	0.897818	+	0.631364i
$46$	−1.77888	+	0.415529i	−0.262281	+	0.0612664i
$47$	−4.66966	−	3.67226i	−0.681140	−	0.535655i	0.216555	−	0.976270i	$-0.430518\pi$
$47$	−4.66966	−	3.67226i	−0.681140	−	0.535655i	−0.897696	+	0.440616i	$0.854760\pi$
$48$	−6.25388	+	2.98143i	−0.902671	+	0.430332i
$49$	−0.607133	+	12.7453i	−0.0867333	+	1.82076i
$50$	−1.10194	+	0.938508i	−0.155837	+	0.132725i
$51$	−2.82409	−	4.36593i	−0.395452	−	0.611353i
$52$	−2.80855	−	1.50906i	−0.389476	−	0.209269i
$53$	−6.80366	+	10.5867i	−0.934554	+	1.45419i	−0.0441490	+	0.999025i	$0.514058\pi$
$53$	−6.80366	+	10.5867i	−0.934554	+	1.45419i	−0.890405	+	0.455169i	$0.849579\pi$
$54$	−7.27404	−	1.04327i	−0.989871	−	0.141971i
$55$	−3.66996	+	1.27019i	−0.494858	+	0.171272i
$56$	3.80706	+	11.9827i	0.508740	+	1.60125i
$57$	3.60212	+	12.1348i	0.477113	+	1.60730i
$58$	−1.83842	−	1.47128i	−0.241396	−	0.193188i
$59$	1.31106	+	1.51305i	0.170686	+	0.196982i	0.834647	−	0.550785i	$-0.185671\pi$
$59$	1.31106	+	1.51305i	0.170686	+	0.196982i	−0.663961	+	0.747767i	$0.731126\pi$
$60$	3.27072	−	7.84756i	0.422249	−	1.01312i
$61$	−3.51789	+	0.335918i	−0.450420	+	0.0430099i	−0.317802	−	0.948157i	$-0.602945\pi$
$61$	−3.51789	+	0.335918i	−0.450420	+	0.0430099i	−0.132619	+	0.991167i	$0.542339\pi$
$62$	−0.529838	−	13.5522i	−0.0672895	−	1.72113i
$63$	−3.68133	+	12.8174i	−0.463804	+	1.61484i
$64$	4.92296	+	6.30590i	0.615370	+	0.788238i
$65$	3.80220	−	0.922403i	0.471605	−	0.114410i
$66$	2.69030	−	2.79024i	0.331154	−	0.343455i
$67$	8.07546	−	1.33677i	0.986574	−	0.163312i
$67$	8.07546	−	1.33677i	0.986574	−	0.163312i
$68$	−4.21677	+	4.27411i	−0.511359	+	0.518312i
$69$	−0.311854	+	2.21548i	−0.0375428	+	0.266713i
$70$	−13.2954	−	7.82797i	−1.58911	−	0.935621i
$71$	1.81399	−	0.935176i	0.215281	−	0.110985i	−0.347214	−	0.937786i	$-0.612872\pi$
$71$	1.81399	−	0.935176i	0.215281	−	0.110985i	0.562494	+	0.826801i	$0.309842\pi$
$72$	0.640391	+	8.46108i	0.0754708	+	0.997148i
$73$	13.1491	−	1.25558i	1.53898	−	0.146955i	0.709185	−	0.705022i	$-0.249063\pi$
$73$	13.1491	−	1.25558i	1.53898	−	0.146955i	0.829796	+	0.558067i	$0.188457\pi$
$74$	−1.43297	−	3.66975i	−0.166580	−	0.426600i
$75$	0.584756	+	1.67351i	0.0675218	+	0.193241i
$76$	12.7809	−	7.09137i	1.46607	−	0.813436i
$77$	−4.34807	−	5.52902i	−0.495508	−	0.630090i
$78$	−2.96528	+	2.54066i	−0.335751	+	0.287674i
$79$	10.6353	−	3.68090i	1.19656	−	0.414134i	0.345108	−	0.938563i	$-0.387842\pi$
$79$	10.6353	−	3.68090i	1.19656	−	0.414134i	0.851454	+	0.524429i	$0.175721\pi$
$80$	−9.66392	−	1.72755i	−1.08046	−	0.193146i
$81$	−4.40750	+	7.84691i	−0.489722	+	0.871879i
$82$	3.55884	+	0.370465i	0.393008	+	0.0409110i
$83$	8.02119	−	11.2642i	0.880440	−	1.23640i	−0.0902135	−	0.995922i	$-0.528755\pi$
$83$	8.02119	−	11.2642i	0.880440	−	1.23640i	0.970653	−	0.240482i	$-0.0773057\pi$
$84$	15.3693	+	0.949343i	1.67693	+	0.103582i
$85$	0.350577	−	7.35952i	0.0380254	−	0.798252i
$86$	3.14794	+	7.05149i	0.339452	+	0.760381i
$87$	−2.49322	+	1.44931i	−0.267302	+	0.155382i
$88$	−3.81749	−	2.33617i	−0.406946	−	0.249036i
$89$	10.9904	−	1.58018i	1.16498	−	0.167499i	0.467428	−	0.884031i	$-0.345181\pi$
$89$	10.9904	−	1.58018i	1.16498	−	0.167499i	0.697554	+	0.716532i	$0.254272\pi$
$90$	−7.51720	−	7.20518i	−0.792382	−	0.759492i
$91$	3.83114	+	5.96137i	0.401613	+	0.624921i
$92$	2.57555	−	0.201696i	0.268520	−	0.0210283i
$93$	−15.7131	−	5.38638i	−1.62937	−	0.558542i
$94$	5.74555	+	6.12953i	0.592609	+	0.632213i
$95$	−5.86642	+	16.9499i	−0.601882	+	1.73902i
$96$	9.37886	−	2.83494i	0.957226	−	0.289340i
$97$	7.46373	+	12.9276i	0.757827	+	1.31259i	0.943957	+	0.330069i	$0.107072\pi$
$97$	7.46373	+	12.9276i	0.757827	+	1.31259i	−0.186130	+	0.982525i	$0.559595\pi$
$98$	3.56595	−	17.6892i	0.360215	−	1.78687i
$99$	−1.99751	−	4.30636i	−0.200758	−	0.432806i
$100$	1.74064	−	1.07716i	0.174064	−	0.107716i
$101$	8.59670	+	2.08554i	0.855404	+	0.207519i	0.639401	−	0.768874i	$-0.279183\pi$
$101$	8.59670	+	2.08554i	0.855404	+	0.207519i	0.216003	+	0.976393i	$0.430698\pi$
$102$	3.01747	+	6.70587i	0.298774	+	0.663980i
$103$	1.17268	+	6.08442i	0.115547	+	0.599516i	0.992829	+	0.119541i	$0.0381423\pi$
$103$	1.17268	+	6.08442i	0.115547	+	0.599516i	−0.877282	+	0.479975i	$0.840646\pi$
$104$	3.60479	+	2.70849i	0.353479	+	0.265589i
$105$	−14.8188	+	11.7248i	−1.44617	+	1.14422i
$106$	11.7688	−	13.3503i	1.14309	−	1.29670i
$107$	−0.454555	+	0.995336i	−0.0439434	+	0.0962227i	−0.930330	−	0.366722i	$-0.880480\pi$
$107$	−0.454555	+	0.995336i	−0.0439434	+	0.0962227i	0.886387	+	0.462945i	$0.153207\pi$
$108$	9.94707	+	3.00928i	0.957157	+	0.289568i
$109$	1.62777	−	1.87855i	0.155912	−	0.179932i	−0.672419	−	0.740170i	$-0.734745\pi$
$109$	1.62777	−	1.87855i	0.155912	−	0.179932i	0.828332	+	0.560238i	$0.189290\pi$
$110$	5.40159	−	0.993396i	0.515021	−	0.0947166i
$111$	−4.82499	+	0.0142678i	−0.457967	+	0.00135424i
$112$	−2.76791	−	17.5640i	−0.261543	−	1.65964i
$113$	0.152859	−	0.108850i	0.0143797	−	0.0102398i	−0.572844	−	0.819664i	$-0.694160\pi$
$113$	0.152859	−	0.108850i	0.0143797	−	0.0102398i	0.587224	+	0.809424i	$0.300221\pi$
$114$	−2.44896	−	17.7331i	−0.229366	−	1.66086i
$115$	−2.18772	+	2.29441i	−0.204005	+	0.213955i
$116$	2.25654	+	2.44885i	0.209515	+	0.227370i
$117$	1.59088	+	4.51008i	0.147077	+	0.416957i
$118$	−1.51037	−	2.39482i	−0.139041	−	0.220461i
$119$	12.8041	−	3.75963i	1.17375	−	0.344645i
$120$	−6.24565	+	10.2740i	−0.570147	+	0.937886i
$121$	−8.34260	−	1.60790i	−0.758418	−	0.146173i
$122$	4.98982	+	0.280341i	0.451757	+	0.0253809i
$123$	1.99652	−	3.90099i	0.180020	−	0.351741i
$124$	−2.14843	+	19.0597i	−0.192934	+	1.71161i
$125$	2.74956	−	9.36414i	0.245928	−	0.837554i
$126$	7.87920	−	17.1346i	0.701935	−	1.52647i
$127$	−2.79086	−	2.92697i	−0.247649	−	0.259727i	0.588163	−	0.808742i	$-0.299851\pi$
$127$	−2.79086	−	2.92697i	−0.247649	−	0.259727i	−0.835812	+	0.549015i	$0.815003\pi$
$128$	−5.53822	−	9.86550i	−0.489514	−	0.871995i
$129$	9.44569	−	0.477952i	0.831647	−	0.0420814i
$130$	−5.51232	+	0.478986i	−0.483462	+	0.0420098i
$131$	−0.990509	+	6.88914i	−0.0865412	+	0.601907i	0.899689	+	0.436531i	$0.143793\pi$
$131$	−0.990509	+	6.88914i	−0.0865412	+	0.601907i	−0.986231	+	0.165376i	$0.947116\pi$
$132$	−4.35603	+	3.32737i	−0.379144	+	0.289610i
$133$	−32.4864			−2.81693
$134$	−11.5749	+	0.147282i	−0.999919	+	0.0127232i
$135$	−11.5529	+	5.40041i	−0.994316	+	0.464793i
$136$	6.80646	−	5.07646i	0.583649	−	0.435303i
$137$	21.7028	+	3.12040i	1.85420	+	0.266594i	0.976954	−	0.213449i	$-0.0684697\pi$
$137$	21.7028	+	3.12040i	1.85420	+	0.266594i	0.877245	+	0.480043i	$0.159379\pi$
$138$	0.908302	−	3.03088i	0.0773198	−	0.258005i
$139$	7.37206	−	3.36671i	0.625290	−	0.285560i	−0.0774620	−	0.996995i	$-0.524682\pi$
$139$	7.37206	−	3.36671i	0.625290	−	0.285560i	0.702752	+	0.711435i	$0.251954\pi$
$140$	16.9189	+	13.7783i	1.42991	+	1.16448i
$141$	9.54109	−	3.85245i	0.803505	−	0.324435i
$142$	−2.73542	+	0.920705i	−0.229551	+	0.0772638i
$143$	−2.42034	−	0.710675i	−0.202399	−	0.0594296i
$144$	0.908500	−	11.9656i	0.0757083	−	0.997130i
$145$	−4.06787	−	0.388434i	−0.337818	−	0.0322577i
$146$	−18.6508	−	1.04785i	−1.54355	−	0.0867206i
$147$	−18.6274	−	11.8934i	−1.53636	−	0.980952i
$148$	1.22103	+	5.43599i	0.100368	+	0.446836i
$149$	−5.09583	−	17.3548i	−0.417467	−	1.42176i	−0.853152	−	0.521662i	$-0.825312\pi$
$149$	−5.09583	−	17.3548i	−0.417467	−	1.42176i	0.435686	−	0.900099i	$-0.356506\pi$
$150$	−0.460747	−	2.46432i	−0.0376198	−	0.201211i
$151$	−9.95148	+	19.3032i	−0.809840	+	1.57087i	0.0111569	+	0.999938i	$0.496449\pi$
$151$	−9.95148	+	19.3032i	−0.809840	+	1.57087i	−0.820997	+	0.570933i	$0.806582\pi$
$152$	−19.3802	+	7.18937i	−1.57194	+	0.583135i
$153$	8.99325	−	0.481725i	0.727061	−	0.0389451i
$154$	4.90011	+	8.65682i	0.394862	+	0.697586i
$155$	−13.6528	−	19.1727i	−1.09662	−	1.53999i
$156$	4.68725	−	2.91982i	0.375280	−	0.233773i
$157$	12.6146	−	5.05014i	1.00676	−	0.403045i	0.191094	−	0.981572i	$-0.438797\pi$
$157$	12.6146	−	5.05014i	1.00676	−	0.403045i	0.815663	+	0.578527i	$0.196372\pi$
$158$	−15.6534	+	2.87879i	−1.24532	+	0.229024i
$159$	−10.0451	−	19.3442i	−0.796632	−	1.53410i
$160$	13.1424	+	4.47544i	1.03900	+	0.353815i
$161$	−5.22305	−	2.38529i	−0.411634	−	0.187987i
$162$	7.83478	−	10.0308i	0.615558	−	0.788091i
$163$	19.7623	+	11.4098i	1.54790	+	0.893682i	0.998302	+	0.0582552i	$0.0185537\pi$
$163$	19.7623	+	11.4098i	1.54790	+	0.893682i	0.549601	+	0.835427i	$0.314780\pi$
$164$	−4.89646	−	1.27663i	−0.382350	−	0.0996881i
$165$	1.25346	−	6.60870i	0.0975821	−	0.514486i
$166$	−13.6154	+	14.0379i	−1.05676	+	1.08955i
$167$	−1.30381	+	5.37438i	−0.100892	+	0.415882i	−0.999750	−	0.0223576i	$-0.992883\pi$
$167$	−1.30381	+	5.37438i	−0.100892	+	0.415882i	0.898858	+	0.438240i	$0.144398\pi$
$168$	−21.2847	−	4.60378i	−1.64215	−	0.355189i
$169$	−9.70952	−	3.88710i	−0.746886	−	0.299008i
$170$	−2.05909	+	10.2143i	−0.157925	+	0.783398i
$171$	−21.3368	−	5.04283i	−1.63167	−	0.385635i
$172$	−2.89770	−	10.5295i	−0.220948	−	0.802863i
$173$	5.86833	+	2.03105i	0.446161	+	0.154418i	0.540905	−	0.841084i	$-0.318082\pi$
$173$	5.86833	+	2.03105i	0.446161	+	0.154418i	−0.0947436	+	0.995502i	$0.530203\pi$
$174$	3.79463	−	1.49469i	0.287670	−	0.113312i
$175$	−4.54445	+	0.216479i	−0.343528	+	0.0163643i
$176$	4.83901	+	4.07993i	0.364754	+	0.307536i
$177$	−3.40303	+	0.666323i	−0.255788	+	0.0500839i
$178$	−15.7021	−	0.133844i	−1.17692	−	0.0100320i
$179$	−2.21623	−	15.4142i	−0.165648	−	1.15211i	−0.887751	−	0.460324i	$-0.847733\pi$
$179$	−2.21623	−	15.4142i	−0.165648	−	1.15211i	0.722102	−	0.691786i	$-0.243176\pi$
$180$	8.97338	+	11.6758i	0.668836	+	0.870262i
$181$	12.6545	+	9.95160i	0.940600	+	0.739696i	0.965611	−	0.259991i	$-0.0837195\pi$
$181$	12.6545	+	9.95160i	0.940600	+	0.739696i	−0.0250107	+	0.999687i	$0.507962\pi$
$182$	−4.08524	−	9.15106i	−0.302818	−	0.678322i
$183$	2.52623	−	5.57525i	0.186745	−	0.412134i
$184$	−3.64376	−	0.267095i	−0.268621	−	0.0196905i
$185$	−5.56920	−	3.96581i	−0.409456	−	0.291572i
$186$	20.8194	+	10.8803i	1.52656	+	0.797781i
$187$	−2.56822	+	3.99623i	−0.187807	+	0.292233i
$188$	−6.72584	−	9.79429i	−0.490533	−	0.714322i
$189$	−16.0870	−	16.5747i	−1.17016	−	1.20563i
$190$	11.8151	−	22.4462i	0.857156	−	1.62842i
$191$	−6.67692	+	5.25079i	−0.483125	+	0.379934i	−0.829808	−	0.558048i	$-0.811550\pi$
$191$	−6.67692	+	5.25079i	−0.483125	+	0.379934i	0.346683	+	0.937982i	$0.387308\pi$
$192$	−13.7165	+	1.96394i	−0.989905	+	0.141735i
$193$	−1.57550	−	1.81823i	−0.113407	−	0.130879i	0.696207	−	0.717841i	$-0.254869\pi$
$193$	−1.57550	−	1.81823i	−0.113407	−	0.130879i	−0.809615	+	0.586962i	$0.800324\pi$
$194$	−7.67869	−	19.6646i	−0.551298	−	1.41183i
$195$	−1.88996	+	6.50774i	−0.135343	+	0.466029i
$196$	−8.75649	+	23.9702i	−0.625464	+	1.71215i
$197$	−5.39287	−	10.4607i	−0.384226	−	0.745294i	0.614833	−	0.788657i	$-0.289223\pi$
$197$	−5.39287	−	10.4607i	−0.384226	−	0.745294i	−0.999059	+	0.0433626i	$0.986193\pi$
$198$	1.87456	+	6.44636i	0.133219	+	0.458123i
$199$	4.89226	−	1.18685i	0.346803	−	0.0841335i	−0.0585742	−	0.998283i	$-0.518655\pi$
$199$	4.89226	−	1.18685i	0.346803	−	0.0841335i	0.405377	+	0.914150i	$0.367140\pi$
$200$	−2.66315	+	1.13485i	−0.188313	+	0.0802459i
$201$	−4.94914	+	13.2856i	−0.349085	+	0.937091i
$202$	−11.5740	−	4.74840i	−0.814346	−	0.334097i
$203$	−1.74491	−	7.19261i	−0.122469	−	0.504822i
$204$	−2.78897	−	10.0184i	−0.195267	−	0.701431i
$205$	5.51924	−	2.84536i	0.385480	−	0.198729i
$206$	−0.342338	−	8.75635i	−0.0238518	−	0.610083i
$207$	−3.06019	−	2.37741i	−0.212698	−	0.165241i
$208$	−4.46227	−	4.55511i	−0.309403	−	0.315840i
$209$	8.73966	−	7.57296i	0.604535	−	0.523833i
$210$	23.2171	−	13.2326i	1.60213	−	0.913138i
$211$	−8.98985	−	11.4315i	−0.618887	−	0.786979i	0.371031	−	0.928620i	$-0.379004\pi$
$211$	−8.98985	−	11.4315i	−0.618887	−	0.786979i	−0.989918	+	0.141642i	$0.954762\pi$
$212$	−19.2996	+	16.1554i	−1.32550	+	1.10956i
$213$	−0.157754	+	3.53135i	−0.0108091	+	0.241964i
$214$	0.847685	−	1.29463i	0.0579465	−	0.0884988i
$215$	11.2740	+	7.24538i	0.768883	+	0.494131i
$216$	−13.2650	−	6.32773i	−0.902568	−	0.430547i
$217$	24.7280	−	34.7256i	1.67864	−	2.35732i
$218$	−2.67619	+	2.27929i	−0.181255	+	0.154373i
$219$	−9.44247	+	20.8390i	−0.638063	+	1.40817i
$220$	−7.76349	+	0.237267i	−0.523414	+	0.0159965i
$221$	2.95833	−	3.76182i	0.198999	−	0.253047i
$222$	6.74863	+	1.00868i	0.452938	+	0.0676983i
$223$	3.00035	−	0.431385i	0.200918	−	0.0288877i	−0.0411209	−	0.999154i	$-0.513093\pi$
$223$	3.00035	−	0.431385i	0.200918	−	0.0288877i	0.242039	+	0.970267i	$0.422184\pi$
$224$	0.125253	+	25.1455i	0.00836882	+	1.68010i
$225$	−3.01836	−	0.563249i	−0.201224	−	0.0375499i
$226$	−0.236910	+	0.119591i	−0.0157590	+	0.00795505i
$227$	1.05756	+	22.2009i	0.0701927	+	1.47353i	0.709571	+	0.704634i	$0.248889\pi$
$227$	1.05756	+	22.2009i	0.0701927	+	1.47353i	−0.639378	+	0.768892i	$0.720808\pi$
$228$	−0.356708	+	25.3139i	−0.0236236	+	1.67645i
$229$	−3.99931	+	11.5552i	−0.264282	+	0.763592i	0.732300	+	0.680982i	$0.238447\pi$
$229$	−3.99931	+	11.5552i	−0.264282	+	0.763592i	−0.996582	+	0.0826100i	$0.973674\pi$
$230$	3.54768	−	2.74131i	0.233927	−	0.180757i
$231$	12.0539	−	1.76948i	0.793088	−	0.116423i
$232$	−2.63270	−	3.90469i	−0.172845	−	0.256356i
$233$	2.53184	−	6.32423i	0.165866	−	0.414314i	−0.822027	−	0.569449i	$-0.807157\pi$
$233$	2.53184	−	6.32423i	0.165866	−	0.414314i	0.987893	+	0.155134i	$0.0495810\pi$
$234$	−1.26265	−	6.64449i	−0.0825417	−	0.434364i
$235$	14.1690	+	3.43737i	0.924285	+	0.224229i
$236$	1.60103	+	3.67008i	0.104218	+	0.238902i
$237$	−3.63245	+	19.1515i	−0.235953	+	1.24402i
$238$	−18.7024	+	2.52648i	−1.21229	+	0.163767i
$239$	2.94275	−	5.09700i	0.190351	−	0.329697i	−0.755016	−	0.655707i	$-0.772371\pi$
$239$	2.94275	−	5.09700i	0.190351	−	0.329697i	0.945367	+	0.326009i	$0.105704\pi$
$240$	10.9220	−	13.0321i	0.705015	−	0.841220i
$241$	1.77183	−	3.87976i	0.114133	−	0.249917i	−0.843941	−	0.536435i	$-0.819771\pi$
$241$	1.77183	−	3.87976i	0.114133	−	0.249917i	0.958075	+	0.286518i	$0.0924978\pi$
$242$	11.3206	+	4.02647i	0.727716	+	0.258832i
$243$	−7.99297	−	13.3833i	−0.512749	−	0.858538i
$244$	−6.91626	−	1.45570i	−0.442768	−	0.0931916i
$245$	−11.6390	−	29.0728i	−0.743587	−	1.85739i
$246$	−3.62289	+	5.02816i	−0.230987	+	0.320584i
$247$	−9.49011	+	6.75788i	−0.603841	+	0.429993i
$248$	7.06690	−	26.1884i	0.448749	−	1.66296i
$249$	10.0141	+	21.7573i	0.634618	+	1.37882i
$250$	−5.84035	+	12.5054i	−0.369376	+	0.790910i
$251$	24.2837	+	12.5191i	1.53277	+	0.790199i	0.998481	−	0.0551003i	$-0.0175478\pi$
$251$	24.2837	+	12.5191i	1.53277	+	0.790199i	0.534292	+	0.845300i	$0.320578\pi$
$252$	−14.6684	+	22.2753i	−0.924024	+	1.40321i
$253$	1.96117	−	0.575852i	0.123298	−	0.0362035i
$254$	3.27778	+	4.68704i	0.205666	+	0.294091i
$255$	10.7560	+	6.86762i	0.673569	+	0.430067i
$256$	5.63952	+	14.9732i	0.352470	+	0.935823i
$257$	−1.20238	+	12.5919i	−0.0750024	+	0.785461i	0.877227	+	0.480076i	$0.159391\pi$
$257$	−1.20238	+	12.5919i	−0.0750024	+	0.785461i	−0.952229	+	0.305385i	$0.901215\pi$
$258$	−13.3075	−	1.34550i	−0.828487	−	0.0837674i
$259$	3.48871	−	11.8815i	0.216778	−	0.738278i
$260$	7.80862	+	0.505512i	0.484270	+	0.0313505i
$261$	−0.0295407	−	4.99491i	−0.00182852	−	0.309177i
$262$	2.85347	−	9.42022i	0.176288	−	0.581983i
$263$	0.239307	+	0.524010i	0.0147563	+	0.0323118i	0.916867	−	0.399194i	$-0.130710\pi$
$263$	0.239307	+	0.524010i	0.0147563	+	0.0323118i	−0.902110	+	0.431505i	$0.857983\pi$
$264$	6.79932	−	3.72318i	0.418469	−	0.229146i
$265$	4.39549	−	30.5713i	0.270013	−	1.87798i
$266$	45.4177	+	6.92571i	2.78474	+	0.424642i
$267$	−7.09488	+	17.8752i	−0.434199	+	1.09394i
$268$	16.2137	+	2.26172i	0.990410	+	0.138157i
$269$		−	16.1436i		−	0.984291i	−0.870513	−	0.492145i	$-0.836213\pi$
$269$		−	16.1436i		−	0.984291i	0.870513	−	0.492145i	$-0.163787\pi$
$270$	17.3029	−	5.08711i	1.05302	−	0.309592i
$271$	−26.9307	−	3.87205i	−1.63592	−	0.235210i	−0.737821	−	0.674997i	$-0.764145\pi$
$271$	−26.9307	−	3.87205i	−1.63592	−	0.235210i	−0.898102	+	0.439786i	$0.855054\pi$
$272$	−10.5980	+	5.64611i	−0.642600	+	0.342346i
$273$	−12.2581	+	0.620263i	−0.741896	+	0.0375400i
$274$	−29.6765	−	8.98926i	−1.79282	−	0.543061i
$275$	1.17211	−	1.11760i	0.0706808	−	0.0673940i
$276$	−1.91600	+	4.04368i	−0.115330	+	0.243401i
$277$	−21.3785	−	6.27728i	−1.28451	−	0.377165i	−0.432946	−	0.901420i	$-0.642526\pi$
$277$	−21.3785	−	6.27728i	−1.28451	−	0.377165i	−0.851561	+	0.524255i	$0.824344\pi$
$278$	−11.0243	+	3.13520i	−0.661192	+	0.188037i
$279$	21.6315	−	18.9690i	1.29505	−	1.13564i
$280$	−20.7161	−	22.8697i	−1.23802	−	1.36673i
$281$	−3.56489	+	18.4964i	−0.212664	+	1.10340i	0.705954	+	0.708257i	$0.250518\pi$
$281$	−3.56489	+	18.4964i	−0.212664	+	1.10340i	−0.918618	+	0.395147i	$0.870694\pi$
$282$	−14.1602	+	3.35189i	−0.843230	+	0.199602i
$283$	−1.75008	−	5.96023i	−0.104032	−	0.354299i	0.890982	−	0.454039i	$-0.150017\pi$
$283$	−1.75008	−	5.96023i	−0.104032	−	0.354299i	−0.995014	+	0.0997396i	$0.968199\pi$
$284$	4.02054	−	0.704036i	0.238575	−	0.0417768i
$285$	−20.4137	−	23.4184i	−1.20920	−	1.38719i
$286$	3.23225	+	1.50955i	0.191127	+	0.0892614i
$287$	8.13960	+	7.76110i	0.480466	+	0.458123i
$288$	−3.82104	+	16.5348i	−0.225157	+	0.974322i
$289$	4.63332	+	6.50659i	0.272549	+	0.382741i
$290$	5.60428	+	1.41027i	0.329095	+	0.0828140i
$291$	−25.8550	+	0.0764547i	−1.51565	+	0.00448186i
$292$	25.8513	+	5.44106i	1.51284	+	0.318414i
$293$	6.40700	+	5.55170i	0.374301	+	0.324334i	0.821615	−	0.570044i	$-0.193074\pi$
$293$	6.40700	+	5.55170i	0.374301	+	0.324334i	−0.447313	+	0.894377i	$0.647619\pi$
$294$	23.5065	+	20.5988i	1.37093	+	1.20134i
$295$	−4.46956	−	2.04118i	−0.260228	−	0.118842i
$296$	−0.548174	−	7.86011i	−0.0318620	−	0.456860i
$297$	8.19157	+	0.708929i	0.475323	+	0.0411362i
$298$	3.42440	+	25.3493i	0.198370	+	1.46845i
$299$	−2.02198	+	0.389704i	−0.116934	+	0.0225372i
$300$	0.118784	+	3.54348i	0.00685802	+	0.204583i
$301$	−5.72252	+	23.5885i	−0.329840	+	1.35962i
$302$	18.0279	−	24.8653i	1.03739	−	1.43084i
$303$	−10.5404	+	11.1201i	−0.605532	+	0.638836i
$304$	28.6272	−	5.91949i	1.64188	−	0.339506i
$305$	7.51119	−	4.33659i	0.430089	−	0.248312i
$306$	−12.6757	−	1.24378i	−0.724624	−	0.0711019i
$307$	−8.00507	−	2.77058i	−0.456873	−	0.158125i	0.0889314	−	0.996038i	$-0.471655\pi$
$307$	−8.00507	−	2.77058i	−0.456873	−	0.158125i	−0.545805	+	0.837912i	$0.683776\pi$
$308$	−5.00508	−	13.1473i	−0.285191	−	0.749138i
$309$	−10.1525	−	3.48024i	−0.577558	−	0.197984i
$310$	14.9999	+	29.7150i	0.851940	+	1.68770i
$311$	27.3733	−	17.5918i	1.55220	−	0.997538i	0.567480	−	0.823387i	$-0.307919\pi$
$311$	27.3733	−	17.5918i	1.55220	−	0.997538i	0.984719	−	0.174150i	$-0.0557178\pi$
$312$	−7.17549	+	3.08280i	−0.406232	+	0.174529i
$313$	−0.626158	−	4.35503i	−0.0353926	−	0.246161i	0.964443	−	0.264291i	$-0.0851378\pi$
$313$	−0.626158	−	4.35503i	−0.0353926	−	0.246161i	−0.999836	+	0.0181300i	$0.994229\pi$
$314$	−18.7125	+	4.37107i	−1.05601	+	0.246674i
$315$	−4.84937	−	32.3680i	−0.273231	−	1.82373i
$316$	22.4980	−	0.687581i	1.26561	−	0.0386794i
$317$	−13.7469	−	0.654848i	−0.772105	−	0.0367799i	−0.342168	−	0.939639i	$-0.611161\pi$
$317$	−13.7469	−	0.654848i	−0.772105	−	0.0367799i	−0.429937	+	0.902859i	$0.641464\pi$
$318$	9.91970	+	29.1857i	0.556269	+	1.63665i
$319$	2.14610	+	1.52823i	0.120159	+	0.0855647i
$320$	−17.4196	−	9.05870i	−0.973787	−	0.506397i
$321$	−1.10391	−	1.54056i	−0.0616141	−	0.0859857i
$322$	6.79359	+	4.44825i	0.378592	+	0.247891i
$323$	7.17574	+	20.7329i	0.399269	+	1.15361i
$324$	−13.0919	+	12.3533i	−0.727326	+	0.686292i
$325$	−1.28252	+	1.00858i	−0.0711413	+	0.0559461i
$326$	−25.1963	−	20.1645i	−1.39549	−	1.11681i
$327$	1.42016	+	4.06435i	0.0785348	+	0.224759i
$328$	6.57335	+	2.82866i	0.362953	+	0.156187i
$329$	2.51018	+	26.2878i	0.138390	+	1.44929i
$330$	−3.16130	+	8.97208i	−0.174024	+	0.493897i
$331$	−12.1369	−	23.5422i	−0.667102	−	1.29400i	−0.942994	−	0.332809i	$-0.892004\pi$
$331$	−12.1369	−	23.5422i	−0.667102	−	1.29400i	0.275892	−	0.961189i	$-0.411027\pi$
$332$	22.0278	−	16.7231i	1.20893	−	0.917798i
$333$	4.13570	−	7.26210i	0.226635	−	0.397960i
$334$	2.96855	−	7.23571i	0.162432	−	0.395921i
$335$	−16.6655	+	11.2176i	−0.910534	+	0.612884i
$336$	28.7757	+	10.9740i	1.56984	+	0.598679i
$337$	−3.33791	−	13.7591i	−0.181828	−	0.749503i	−0.987562	−	0.157227i	$-0.949745\pi$
$337$	−3.33791	−	13.7591i	−0.181828	−	0.749503i	0.805735	−	0.592276i	$-0.201771\pi$
$338$	12.7457	+	7.50433i	0.693276	+	0.408182i
$339$	0.0318524	+	0.323462i	0.00172998	+	0.0175680i
$340$	5.05627	−	13.8411i	0.274214	−	0.750639i
$341$	1.44249	+	15.1064i	0.0781151	+	0.818058i
$342$	28.7549	+	11.5989i	1.55489	+	0.627196i
$343$	19.3496	−	16.7665i	1.04478	−	0.905307i
$344$	1.80639	+	15.3385i	0.0973939	+	0.826995i
$345$	−1.56257	−	5.26399i	−0.0841260	−	0.283404i
$346$	−7.77124	−	4.09057i	−0.417785	−	0.219911i
$347$	0.742642	+	2.14572i	0.0398671	+	0.115189i	0.963178	−	0.268866i	$-0.0866488\pi$
$347$	0.742642	+	2.14572i	0.0398671	+	0.115189i	−0.923311	+	0.384054i	$0.874528\pi$
$348$	−5.62374	+	1.28068i	−0.301464	+	0.0686517i
$349$	25.1112	+	16.1380i	1.34417	+	0.863847i	0.997255	−	0.0740482i	$-0.0235919\pi$
$349$	25.1112	+	16.1380i	1.34417	+	0.863847i	0.346918	+	0.937895i	$0.387228\pi$
$350$	6.39953	+	0.666173i	0.342069	+	0.0356084i
$351$	−8.14733	−	1.49543i	−0.434872	−	0.0798204i
$352$	−5.89540	−	6.73557i	−0.314226	−	0.359007i
$353$	−28.2061	−	1.34362i	−1.50126	−	0.0715137i	−0.719237	−	0.694765i	$-0.755508\pi$
$353$	−28.2061	−	1.34362i	−1.50126	−	0.0715137i	−0.782022	+	0.623251i	$0.785811\pi$
$354$	4.89967	−	0.206070i	0.260415	−	0.0109525i
$355$	−3.09626	+	3.93721i	−0.164332	+	0.208966i
$356$	21.9238	+	3.53461i	1.16196	+	0.187334i
$357$	−5.38281	+	22.4781i	−0.284888	+	1.18967i
$358$	−0.187717	+	22.0223i	−0.00992118	+	1.16392i
$359$	15.3546	−	9.86778i	0.810383	−	0.520802i	−0.0686059	−	0.997644i	$-0.521855\pi$
$359$	15.3546	−	9.86778i	0.810383	−	0.520802i	0.878989	+	0.476842i	$0.158219\pi$
$360$	−10.0561	−	18.2364i	−0.530004	−	0.961142i
$361$	−1.63729	−	34.3710i	−0.0861732	−	1.80900i
$362$	−15.5701	−	16.6106i	−0.818345	−	0.873036i
$363$	9.60383	−	11.1499i	0.504070	−	0.585216i
$364$	3.76049	+	13.6646i	0.197103	+	0.716219i
$365$	−28.0750	+	16.2091i	−1.46951	+	0.848425i
$366$	−4.72038	+	7.25593i	−0.246738	+	0.379274i
$367$	3.61451	−	9.02861i	0.188676	−	0.471290i	−0.803626	−	0.595135i	$-0.797098\pi$
$367$	3.61451	−	9.02861i	0.188676	−	0.471290i	0.992302	+	0.123846i	$0.0395227\pi$
$368$	5.03722	+	1.15022i	0.262583	+	0.0599592i
$369$	4.14128	+	6.36093i	0.215586	+	0.331137i
$370$	6.94057	+	6.73170i	0.360823	+	0.349964i
$371$	54.9293	−	10.5868i	2.85179	−	0.549637i
$372$	−26.7871	−	19.6497i	−1.38885	−	1.01879i
$373$	−1.25645	+	2.17624i	−0.0650567	+	0.112682i	−0.896719	−	0.442600i	$-0.854056\pi$
$373$	−1.25645	+	2.17624i	−0.0650567	+	0.112682i	0.831662	+	0.555282i	$0.187389\pi$
$374$	4.44245	−	5.03942i	0.229714	−	0.260582i
$375$	11.7012	+	12.1994i	0.604245	+	0.629973i
$376$	7.31506	+	15.1268i	0.377245	+	0.780105i
$377$	−2.00595	−	1.73817i	−0.103312	−	0.0895201i
$378$	18.9570	+	26.6018i	0.975044	+	1.36825i
$379$	2.62982	+	6.56897i	0.135085	+	0.337425i	0.980451	−	0.196761i	$-0.0630424\pi$
$379$	2.62982	+	6.56897i	0.135085	+	0.337425i	−0.845367	+	0.534186i	$0.820618\pi$
$380$	−21.3034	+	28.8622i	−1.09284	+	1.48060i
$381$	6.80250	−	1.67158i	0.348503	−	0.0856378i
$382$	10.4541	−	5.91744i	0.534878	−	0.302763i
$383$	10.2112	+	9.73634i	0.521767	+	0.497504i	0.904569	−	0.426327i	$-0.140193\pi$
$383$	10.2112	+	9.73634i	0.521767	+	0.497504i	−0.382803	+	0.923830i	$0.625041\pi$
$384$	19.5951	+	0.178504i	0.999959	+	0.00910926i
$385$	15.3441	+	7.91044i	0.782008	+	0.403153i
$386$	1.81501	+	2.87786i	0.0923818	+	0.146479i
$387$	−7.42013	+	14.6045i	−0.377186	+	0.742386i
$388$	6.54296	+	29.1291i	0.332168	+	1.47881i
$389$	−3.49142	+	18.1152i	−0.177022	+	0.918477i	0.779408	+	0.626516i	$0.215520\pi$
$389$	−3.49142	+	18.1152i	−0.177022	+	0.918477i	−0.956430	+	0.291961i	$0.905692\pi$
$390$	4.02963	−	8.69524i	0.204048	−	0.440301i
$391$	−0.368608	+	3.86024i	−0.0186413	+	0.195221i
$392$	17.3522	−	31.6448i	0.876417	−	1.59830i
$393$	−9.49790	−	7.42388i	−0.479106	−	0.374485i
$394$	5.30942	+	15.7743i	0.267485	+	0.794698i
$395$	−19.9903	+	19.0607i	−1.00582	+	0.959049i
$396$	−1.24645	−	9.41199i	−0.0626366	−	0.472970i
$397$	6.13198	+	13.4272i	0.307755	+	0.673890i	0.998803	−	0.0489195i	$-0.0155778\pi$
$397$	6.13198	+	13.4272i	0.307755	+	0.673890i	−0.691048	+	0.722809i	$0.742850\pi$
$398$	−7.09265	+	0.616307i	−0.355523	+	0.0308927i
$399$	27.9898	−	48.8126i	1.40124	−	2.44369i
$400$	3.96516	−	1.01883i	0.198258	−	0.0509413i
$401$			21.1231i			1.05484i	0.849606	+	0.527418i	$0.176840\pi$
$401$			21.1231i			1.05484i	−0.849606	+	0.527418i	$0.823160\pi$
$402$	9.75147	−	17.5188i	0.486359	−	0.873759i
$403$		−	15.2882i		−	0.761558i
$404$	15.1688	+	9.10596i	0.754676	+	0.453039i
$405$	1.83942	−	22.0118i	0.0914016	−	1.09377i
$406$	0.906097	+	10.4276i	0.0449688	+	0.517515i
$407$	1.83116	+	4.00967i	0.0907670	+	0.198752i
$408$	1.76331	+	14.6009i	0.0872969	+	0.722851i
$409$	7.50900	−	7.15981i	0.371296	−	0.354030i	−0.481341	−	0.876533i	$-0.659850\pi$
$409$	7.50900	−	7.15981i	0.371296	−	0.354030i	0.852637	+	0.522503i	$0.175002\pi$
$410$	−8.32278	+	2.80134i	−0.411033	+	0.138348i
$411$	−23.3874	+	29.9212i	−1.15362	+	1.47590i
$412$	−1.38814	+	12.3148i	−0.0683887	+	0.606707i
$413$	0.845951	−	8.85920i	0.0416265	−	0.435933i
$414$	3.77148	+	3.97613i	0.185358	+	0.195416i
$415$	−6.42290	+	33.3252i	−0.315288	+	1.63587i
$416$	5.26740	+	7.31959i	0.258255	+	0.358872i
$417$	−1.29300	+	13.9776i	−0.0633187	+	0.684487i
$418$	−13.8330	+	8.72420i	−0.676593	+	0.426715i
$419$	−14.8409	−	7.65101i	−0.725025	−	0.373776i	0.0558704	−	0.998438i	$-0.482207\pi$
$419$	−14.8409	−	7.65101i	−0.725025	−	0.373776i	−0.780896	+	0.624662i	$0.785237\pi$
$420$	−35.2797	+	13.5503i	−1.72148	+	0.661187i
$421$	2.24519	+	2.14078i	0.109424	+	0.104335i	0.742816	−	0.669495i	$-0.233490\pi$
$421$	2.24519	+	2.14078i	0.109424	+	0.104335i	−0.633392	+	0.773831i	$0.718338\pi$
$422$	10.1312	+	17.8984i	0.493180	+	0.871280i
$423$	−2.43195	+	17.6552i	−0.118246	+	0.858427i
$424$	30.4259	−	18.4717i	1.47761	−	0.897067i
$425$	1.14196	+	2.85247i	0.0553930	+	0.138365i
$426$	0.973390	−	4.90338i	0.0471609	−	0.237570i
$427$	11.8720	+	10.2871i	0.574524	+	0.497828i
$428$	−1.46111	+	1.62924i	−0.0706252	+	0.0787522i
$429$	3.15316	−	3.02438i	0.152236	−	0.146018i
$430$	−14.2171	−	12.5329i	−0.685608	−	0.604391i
$431$	−8.04136	+	13.9281i	−0.387339	+	0.670891i	−0.992091	−	0.125523i	$-0.959939\pi$
$431$	−8.04136	+	13.9281i	−0.387339	+	0.670891i	0.604752	+	0.796414i	$0.293272\pi$
$432$	17.1962	+	11.6744i	0.827350	+	0.561686i
$433$	12.3184	−	2.37419i	0.591987	−	0.114096i	0.115545	−	0.993302i	$-0.463139\pi$
$433$	12.3184	−	2.37419i	0.591987	−	0.114096i	0.476441	+	0.879206i	$0.341926\pi$
$434$	−41.9740	+	43.2764i	−2.01482	+	2.07734i
$435$	4.08846	−	5.77752i	0.196027	−	0.277011i
$436$	4.22738	−	2.61603i	0.202455	−	0.125285i
$437$	3.50855	−	8.76393i	0.167837	−	0.419236i
$438$	17.6437	−	27.1210i	0.843048	−	1.29589i
$439$	−28.0149	+	16.1744i	−1.33708	+	0.771962i	−0.986373	−	0.164524i	$-0.947391\pi$
$439$	−28.0149	+	16.1744i	−1.33708	+	0.771962i	−0.350704	+	0.936486i	$0.614058\pi$
$440$	10.9043	+	1.32337i	0.519844	+	0.0630892i
$441$	33.9196	−	17.7415i	1.61522	−	0.844832i
$442$	−4.93787	+	4.62854i	−0.234871	+	0.220157i
$443$	−0.0875368	−	1.83762i	−0.00415900	−	0.0873082i	0.995833	−	0.0911905i	$-0.0290672\pi$
$443$	−0.0875368	−	1.83762i	−0.00415900	−	0.0873082i	−0.999992	+	0.00388238i	$0.998764\pi$
$444$	−9.21990	−	2.84891i	−0.437557	−	0.135204i
$445$	−22.9249	+	14.7330i	−1.08675	+	0.698409i
$446$	−4.28661	−	0.0365389i	−0.202977	−	0.00173017i
$447$	30.4670	+	7.29589i	1.44104	+	0.345084i
$448$	5.18560	−	35.1814i	0.244997	−	1.66217i
$449$	24.1831	−	30.7513i	1.14127	−	1.45124i	0.268391	−	0.963310i	$-0.413508\pi$
$449$	24.1831	−	30.7513i	1.14127	−	1.45124i	0.872880	−	0.487934i	$-0.162249\pi$
$450$	4.09975	+	1.43093i	0.193264	+	0.0674547i
$451$	−3.99896	−	0.190494i	−0.188304	−	0.00897001i
$452$	0.356708	−	0.116688i	0.0167781	−	0.00548852i
$453$	−20.4300	−	31.5840i	−0.959886	−	1.48395i
$454$	3.25444	−	31.2635i	0.152738	−	1.46727i
$455$	−14.6309	−	9.40269i	−0.685906	−	0.440805i
$456$	5.89531	−	35.3141i	0.276073	−	1.65373i
$457$	−4.36537	−	12.6129i	−0.204203	−	0.590007i	0.795673	−	0.605726i	$-0.207117\pi$
$457$	−4.36537	−	12.6129i	−0.204203	−	0.590007i	−0.999876	+	0.0157195i	$0.994996\pi$
$458$	8.05468	−	15.3022i	0.376371	−	0.715026i
$459$	−7.02464	+	13.9279i	−0.327882	+	0.650099i
$460$	−5.54426	+	3.07617i	−0.258502	+	0.143427i
$461$	18.3728	−	15.9201i	0.855705	−	0.741472i	−0.111960	−	0.993713i	$-0.535713\pi$
$461$	18.3728	−	15.9201i	0.855705	−	0.741472i	0.967665	+	0.252240i	$0.0811673\pi$
$462$	−17.2292	−	0.0959110i	−0.801575	−	0.00446218i
$463$	−1.69102	−	17.7091i	−0.0785883	−	0.823014i	−0.945730	−	0.324953i	$-0.894652\pi$
$463$	−1.69102	−	17.7091i	−0.0785883	−	0.823014i	0.867142	−	0.498061i	$-0.165954\pi$
$464$	2.84822	+	6.02023i	0.132225	+	0.279482i
$465$	40.5710	−	3.99516i	1.88144	−	0.185271i
$466$	−4.88790	+	8.30185i	−0.226427	+	0.384576i
$467$	−6.72083	−	27.7036i	−0.311003	−	1.28197i	−0.885950	−	0.463781i	$-0.846493\pi$
$467$	−6.72083	−	27.7036i	−0.311003	−	1.28197i	0.574947	−	0.818190i	$-0.305023\pi$
$468$	0.348720	+	9.55853i	0.0161196	+	0.441843i
$469$	−29.0723	−	21.8793i	−1.34243	−	1.01029i
$470$	−19.0762	−	7.82628i	−0.879921	−	0.361000i
$471$	−3.28049	+	23.3053i	−0.151157	+	1.07385i
$472$	−1.45591	−	5.47229i	−0.0670138	−	0.251883i
$473$	−3.95926	−	7.67989i	−0.182047	−	0.353122i
$474$	9.16121	−	26.0004i	0.420789	−	1.19424i
$475$	−0.711007	−	7.44600i	−0.0326232	−	0.341646i
$476$	26.6855	+	0.454966i	1.22313	+	0.0208533i
$477$	37.7205	+	1.57332i	1.72710	+	0.0720374i
$478$	−5.20074	+	6.49851i	−0.237876	+	0.297235i
$479$	16.0649	−	12.6336i	0.734026	−	0.577244i	−0.179630	−	0.983734i	$-0.557490\pi$
$479$	16.0649	−	12.6336i	0.734026	−	0.577244i	0.913655	+	0.406490i	$0.133247\pi$
$480$	−18.0479	+	15.8912i	−0.823769	+	0.725329i
$481$	−1.45246	−	4.19661i	−0.0662264	−	0.191349i
$482$	−3.30422	+	5.04637i	−0.150503	+	0.229856i
$483$	8.08413	−	5.79279i	0.367841	−	0.263581i
$484$	−14.9684	−	8.04264i	−0.680382	−	0.365574i
$485$	−29.8429	−	21.2511i	−1.35510	−	0.964961i
$486$	8.32144	+	20.4145i	0.377468	+	0.926023i
$487$	24.1260	+	1.14926i	1.09325	+	0.0520780i	0.586450	−	0.809985i	$-0.300525\pi$
$487$	24.1260	+	1.14926i	1.09325	+	0.0520780i	0.506801	+	0.862063i	$0.330828\pi$
$488$	9.35896	+	3.50961i	0.423660	+	0.158872i
$489$	−34.1707	+	19.8634i	−1.54525	+	0.898256i
$490$	10.0739	+	43.1265i	0.455094	+	1.94826i
$491$	−0.0870910	−	0.605732i	−0.00393036	−	0.0273363i	0.987762	−	0.155969i	$-0.0498501\pi$
$491$	−0.0870910	−	0.605732i	−0.00393036	−	0.0273363i	−0.991692	+	0.128633i	$0.958941\pi$
$492$	6.13693	−	6.25728i	0.276674	−	0.282100i
$493$	−4.20493	+	2.70234i	−0.189380	+	0.121707i
$494$	14.7084	−	7.42469i	0.661761	−	0.334053i
$495$	8.84996	+	7.57736i	0.397776	+	0.340577i
$496$	−15.4629	+	35.1062i	−0.694307	+	1.57631i
$497$	−8.57306	−	2.96717i	−0.384554	−	0.133096i
$498$	−9.36184	−	32.5528i	−0.419514	−	1.45873i
$499$	−9.42747	+	5.44295i	−0.422031	+	0.243660i	−0.695946	−	0.718094i	$-0.745015\pi$
$499$	−9.42747	+	5.44295i	−0.422031	+	0.243660i	0.273915	+	0.961754i	$0.411681\pi$
$500$	10.8311	−	16.2381i	0.484382	−	0.726190i
$501$	−6.95196	−	6.58954i	−0.310590	−	0.294399i
$502$	−31.2810	−	22.6794i	−1.39614	−	1.01223i
$503$	−8.53736	+	35.1915i	−0.380662	+	1.56911i	0.383159	+	0.923683i	$0.374836\pi$
$503$	−8.53736	+	35.1915i	−0.380662	+	1.56911i	−0.763821	+	0.645428i	$0.776679\pi$
$504$	25.2560	−	28.0149i	1.12499	−	1.24788i
$505$	−21.3184	+	4.10878i	−0.948655	+	0.182838i
$506$	−2.86458	+	0.386973i	−0.127346	+	0.0172031i
$507$	14.2062	−	11.2400i	0.630918	−	0.499186i
$508$	−3.58329	−	7.25151i	−0.158983	−	0.321734i
$509$	17.7831	+	8.12128i	0.788223	+	0.359969i	0.768511	−	0.639836i	$-0.220998\pi$
$509$	17.7831	+	8.12128i	0.788223	+	0.359969i	0.0197118	+	0.999806i	$0.493725\pi$
$510$	−13.5734	−	11.8943i	−0.601040	−	0.526691i
$511$	−44.3746	−	38.4508i	−1.96302	−	1.70096i
$512$	−4.69224	−	22.1356i	−0.207370	−	0.978263i
$513$	25.9606	−	27.7149i	1.14619	−	1.22364i
$514$	4.36543	−	17.3478i	0.192551	−	0.765179i
$515$	−8.82133	−	12.3878i	−0.388714	−	0.545873i
$516$	18.3177	+	4.71807i	0.806391	+	0.207702i
$517$	−6.80328	−	6.48691i	−0.299208	−	0.285294i
$518$	−7.41039	+	15.8672i	−0.325594	+	0.697163i
$519$	−8.10784	+	7.06757i	−0.355895	+	0.310232i
$520$	−10.8091	−	2.37144i	−0.474010	−	0.103994i
$521$	9.42964	+	32.1144i	0.413120	+	1.40696i	0.859051	+	0.511890i	$0.171055\pi$
$521$	9.42964	+	32.1144i	0.413120	+	1.40696i	−0.445931	+	0.895067i	$0.647127\pi$
$522$	−1.02355	+	6.98944i	−0.0447997	+	0.305920i
$523$	−6.98021	+	36.2168i	−0.305223	+	1.58365i	0.428076	+	0.903743i	$0.359192\pi$
$523$	−6.98021	+	36.2168i	−0.305223	+	1.58365i	−0.733299	+	0.679906i	$0.762021\pi$
$524$	−5.99757	+	12.5616i	−0.262005	+	0.548758i
$525$	3.59017	−	7.01480i	0.156688	−	0.306151i
$526$	−0.222852	−	0.783611i	−0.00971680	−	0.0341671i
$527$	−27.6240	−	8.11113i	−1.20332	−	0.353327i
$528$	−10.2995	+	3.75567i	−0.448230	+	0.163445i
$529$	−15.4383	+	14.7204i	−0.671231	+	0.640017i
$530$	−12.6626	+	41.8033i	−0.550027	+	1.81582i
$531$	1.93082	−	5.68734i	0.0837904	−	0.246809i
$532$	−62.0199	−	19.3650i	−2.68890	−	0.839580i
$533$	3.99226	+	0.574001i	0.172924	+	0.0248627i
$534$	13.7298	−	23.4779i	0.594146	−	1.01599i
$535$		−	2.68552i		−	0.116105i
$536$	−22.1855	−	6.61857i	−0.958266	−	0.285879i
$537$	25.0701	+	9.95065i	1.08186	+	0.429402i
$538$	−3.44161	+	22.5696i	−0.148378	+	0.973043i
$539$	−2.87341	+	19.9850i	−0.123767	+	0.860815i
$540$	−25.2748	+	3.42329i	−1.08766	+	0.147315i
$541$	10.2530	+	22.4510i	0.440812	+	0.965243i	0.991449	+	0.130498i	$0.0416577\pi$
$541$	10.2530	+	22.4510i	0.440812	+	0.965243i	−0.550637	+	0.834745i	$0.685615\pi$
$542$	36.8251	+	11.1546i	1.58177	+	0.479132i
$543$	−25.8557	+	10.4399i	−1.10958	+	0.448019i
$544$	16.0203	−	5.63418i	0.686864	−	0.241564i
$545$	−1.71872	+	5.85343i	−0.0736220	+	0.250733i
$546$	17.2698	+	1.74613i	0.739077	+	0.0747273i
$547$	1.94136	−	20.3308i	0.0830066	−	0.869284i	−0.854069	−	0.520159i	$-0.825873\pi$
$547$	1.94136	−	20.3308i	0.0830066	−	0.869284i	0.937076	−	0.349125i	$-0.113521\pi$
$548$	39.5729	+	18.8941i	1.69047	+	0.807117i
$549$	6.20055	+	8.59936i	0.264633	+	0.367012i
$550$	−1.87693	+	1.31259i	−0.0800325	+	0.0559689i
$551$	11.6753	−	3.42817i	0.497383	−	0.146045i
$552$	3.54073	−	5.24482i	0.150704	−	0.223234i
$553$	−44.4660	−	22.9238i	−1.89089	−	0.974821i
$554$	28.5500	+	13.3336i	1.21297	+	0.566490i
$555$	10.7572	−	4.95114i	0.456617	−	0.210164i
$556$	16.0809	−	2.03293i	0.681982	−	0.0862156i
$557$	6.08460	−	4.33282i	0.257813	−	0.183588i	−0.443841	−	0.896105i	$-0.646385\pi$
$557$	6.08460	−	4.33282i	0.257813	−	0.183588i	0.701654	+	0.712518i	$0.252445\pi$
$558$	−34.2860	+	21.9080i	−1.45144	+	0.927441i
$559$	3.23523	+	8.08122i	0.136836	+	0.341799i
$560$	24.0866	+	36.3895i	1.01785	+	1.53774i
$561$	−3.79181	−	7.30198i	−0.160090	−	0.308290i
$562$	8.92712	−	25.0990i	0.376568	−	1.05874i
$563$	3.87302	−	8.48074i	0.163228	−	0.357421i	−0.810290	−	0.586029i	$-0.800690\pi$
$563$	3.87302	−	8.48074i	0.163228	−	0.357421i	0.973518	+	0.228609i	$0.0734176\pi$
$564$	20.5113	−	1.66732i	0.863684	−	0.0702068i
$565$	−0.230278	+	0.398853i	−0.00968786	+	0.0167799i
$566$	1.17606	+	8.70582i	0.0494334	+	0.365933i
$567$	38.7647	−	9.89114i	1.62797	−	0.415389i
$568$	−5.77102	+	0.127148i	−0.242147	+	0.00533502i
$569$	−18.1394	−	4.40057i	−0.760443	−	0.184481i	−0.163256	−	0.986584i	$-0.552200\pi$
$569$	−18.1394	−	4.40057i	−0.760443	−	0.184481i	−0.597187	+	0.802102i	$0.703715\pi$
$570$	23.5469	+	37.0921i	0.986273	+	1.55362i
$571$	4.37590	−	10.9305i	0.183126	−	0.457426i	−0.808191	−	0.588920i	$-0.799553\pi$
$571$	4.37590	−	10.9305i	0.183126	−	0.457426i	0.991317	+	0.131494i	$0.0419774\pi$
$572$	−4.19704	−	2.79950i	−0.175487	−	0.117053i
$573$	−2.13685	−	14.5565i	−0.0892684	−	0.608104i
$574$	−9.72502	−	12.5857i	−0.405915	−	0.525316i
$575$	0.432403	−	1.24935i	0.0180325	−	0.0521014i
$576$	8.86704	−	22.3019i	0.369460	−	0.929247i
$577$	1.53509	+	32.2256i	0.0639068	+	1.34157i	0.772078	+	0.635528i	$0.219217\pi$
$577$	1.53509	+	32.2256i	0.0639068	+	1.34157i	−0.708171	+	0.706041i	$0.750480\pi$
$578$	−5.09050	−	10.0843i	−0.211737	−	0.419453i
$579$	4.08942	−	0.800720i	0.169951	−	0.0332768i
$580$	−7.53443	−	3.16640i	−0.312850	−	0.131478i
$581$	−60.8437	+	8.74801i	−2.52422	+	0.362928i
$582$	36.1629	+	5.40508i	1.49900	+	0.224048i
$583$	−12.3095	+	15.6528i	−0.509806	+	0.648271i
$584$	−34.9816	−	13.1181i	−1.44755	−	0.542830i
$585$	−8.14987	−	8.44674i	−0.336956	−	0.349230i
$586$	−7.77377	−	9.12746i	−0.321132	−	0.377052i
$587$	−23.2764	+	32.6872i	−0.960721	+	1.34914i	−0.0237566	+	0.999718i	$0.507563\pi$
$587$	−23.2764	+	32.6872i	−0.960721	+	1.34914i	−0.936964	+	0.349426i	$0.886377\pi$
$588$	−28.4720	−	33.8095i	−1.17416	−	1.39428i
$589$	58.9610	+	37.8919i	2.42945	+	1.56131i
$590$	5.81352	+	3.80653i	0.239339	+	0.156712i
$591$	20.3642	+	0.909720i	0.837671	+	0.0374209i
$592$	−0.909304	+	11.1057i	−0.0373722	+	0.456442i
$593$	19.5263	+	24.8298i	0.801851	+	1.01964i	0.999227	+	0.0393085i	$0.0125155\pi$
$593$	19.5263	+	24.8298i	0.801851	+	1.01964i	−0.197376	+	0.980328i	$0.563242\pi$
$594$	−11.3011	−	2.73746i	−0.463690	−	0.112319i
$595$	−24.7520	+	21.4477i	−1.01473	+	0.879271i
$596$	0.616663	−	36.1697i	0.0252595	−	1.48157i
$597$	−2.43180	+	8.37345i	−0.0995268	+	0.342703i
$598$	2.90991	−	0.113766i	0.118995	−	0.00465224i
$599$	−5.23936	+	2.70108i	−0.214074	+	0.110363i	−0.561929	−	0.827185i	$-0.689941\pi$
$599$	−5.23936	+	2.70108i	−0.214074	+	0.110363i	0.347855	+	0.937548i	$0.386910\pi$
$600$	0.589360	−	4.97929i	0.0240605	−	0.203279i
$601$	7.14052	+	29.4336i	0.291268	+	1.20062i	0.909862	+	0.414912i	$0.136188\pi$
$601$	7.14052	+	29.4336i	0.291268	+	1.20062i	−0.618593	+	0.785711i	$0.712297\pi$
$602$	13.0292	−	31.7580i	0.531029	−	1.29436i
$603$	−15.6982	−	18.8830i	−0.639279	−	0.768975i
$604$	−30.5049	+	30.9197i	−1.24123	+	1.25810i
$605$	20.2641	−	4.91602i	0.823853	−	0.199865i
$606$	17.1068	−	13.2995i	0.694915	−	0.540253i
$607$	6.84357	+	13.2747i	0.277772	+	0.538802i	0.985911	−	0.167271i	$-0.0534954\pi$
$607$	6.84357	+	13.2747i	0.277772	+	0.538802i	−0.708139	+	0.706073i	$0.750465\pi$
$608$	−41.2843	+	2.17277i	−1.67430	+	0.0881176i
$609$	12.3107	+	3.57523i	0.498854	+	0.144876i
$610$	−11.4255	+	4.46148i	−0.462607	+	0.180640i
$611$	6.20171	+	7.15715i	0.250894	+	0.289547i
$612$	17.4562	+	4.44118i	0.705625	+	0.179524i
$613$	7.54357	−	5.93233i	0.304682	−	0.239605i	−0.454098	−	0.890952i	$-0.650038\pi$
$613$	7.54357	−	5.93233i	0.304682	−	0.239605i	0.758780	+	0.651347i	$0.225796\pi$
$614$	10.6009	+	5.58000i	0.427816	+	0.225191i
$615$	−0.479983	+	10.7445i	−0.0193548	+	0.433259i
$616$	4.19452	+	19.4477i	0.169002	+	0.783569i
$617$	−20.2603	+	31.5256i	−0.815648	+	1.26917i	0.144450	+	0.989512i	$0.453859\pi$
$617$	−20.2603	+	31.5256i	−0.815648	+	1.26917i	−0.960099	+	0.279662i	$0.909778\pi$
$618$	13.4518	+	7.02996i	0.541112	+	0.282787i
$619$	10.6273	+	7.56766i	0.427147	+	0.304170i	0.773338	−	0.633994i	$-0.218586\pi$
$619$	10.6273	+	7.56766i	0.427147	+	0.304170i	−0.346191	+	0.938164i	$0.612525\pi$
$620$	−14.6358	−	44.7409i	−0.587789	−	1.79684i
$621$	6.20880	−	2.54976i	0.249151	−	0.102319i
$622$	−42.0197	+	18.7586i	−1.68484	+	0.752150i
$623$	−38.7971	−	30.5104i	−1.55437	−	1.22237i
$624$	10.6889	−	2.78019i	0.427900	−	0.111297i
$625$	4.13708	+	28.7740i	0.165483	+	1.15096i
$626$	−0.0530365	+	6.22204i	−0.00211976	+	0.248683i
$627$	3.84881	+	19.6566i	0.153707	+	0.785008i
$628$	27.0930	−	2.12170i	1.08113	−	0.0846650i
$629$	−8.35339	+	0.397921i	−0.333072	+	0.0158662i
$630$	−0.120791	+	46.2860i	−0.00481243	+	1.84408i
$631$	−13.8393	−	4.78984i	−0.550935	−	0.190680i	0.0373964	−	0.999301i	$-0.488094\pi$
$631$	−13.8393	−	4.78984i	−0.550935	−	0.190680i	−0.588331	+	0.808620i	$0.700215\pi$
$632$	−31.6000	−	3.83502i	−1.25698	−	0.152549i
$633$	24.9220	−	3.65850i	0.990561	−	0.145412i
$634$	19.0793	+	3.84619i	0.757738	+	0.152752i
$635$	9.21475	+	3.68903i	0.365676	+	0.146395i
$636$	−7.64621	−	42.9179i	−0.303192	−	1.70181i
$637$	4.79555	−	19.7675i	0.190007	−	0.783218i
$638$	−2.67457	−	2.59408i	−0.105887	−	0.102700i
$639$	−5.17013	−	3.27960i	−0.204527	−	0.129739i
$640$	22.4223	+	16.3782i	0.886321	+	0.647405i
$641$	19.7543	+	11.4052i	0.780249	+	0.450477i	0.836519	−	0.547938i	$-0.184587\pi$
$641$	19.7543	+	11.4052i	0.780249	+	0.450477i	−0.0562692	+	0.998416i	$0.517921\pi$
$642$	1.21489	+	2.38912i	0.0479480	+	0.0942912i
$643$	−22.3515	−	10.2076i	−0.881459	−	0.402549i	−0.0773314	−	0.997005i	$-0.524640\pi$
$643$	−22.3515	−	10.2076i	−0.881459	−	0.402549i	−0.804128	+	0.594457i	$0.797367\pi$
$644$	−8.54948	−	7.66720i	−0.336897	−	0.302130i
$645$	−20.6001	+	10.6973i	−0.811129	+	0.421207i
$646$	−5.61205	−	30.5155i	−0.220803	−	1.20062i
$647$	20.2642	−	8.11255i	0.796667	−	0.318937i	0.0626210	−	0.998037i	$-0.480054\pi$
$647$	20.2642	−	8.11255i	0.796667	−	0.318937i	0.734046	+	0.679100i	$0.237630\pi$
$648$	20.9367	−	14.4795i	0.822471	−	0.568808i
$649$	1.83760	+	2.58055i	0.0721321	+	0.101295i
$650$	2.00805	−	1.13664i	0.0787620	−	0.0445825i
$651$	30.8718	+	67.0741i	1.20996	+	2.62884i
$652$	30.9269	+	33.5626i	1.21119	+	1.31441i
$653$	10.2140	−	19.8123i	0.399703	−	0.775315i	−0.599992	−	0.800006i	$-0.704830\pi$
$653$	10.2140	−	19.8123i	0.399703	−	0.775315i	0.999695	+	0.0246904i	$0.00786000\pi$
$654$	−1.11898	−	5.98493i	−0.0437557	−	0.234029i
$655$	−4.81249	−	16.3898i	−0.188039	−	0.640403i
$656$	−8.58686	−	5.35598i	−0.335260	−	0.209116i
$657$	−23.1762	−	32.1424i	−0.904189	−	1.25399i
$658$	2.09487	−	37.2868i	0.0816666	−	1.45359i
$659$	−11.4637	−	1.09466i	−0.446564	−	0.0426417i	−0.130648	−	0.991429i	$-0.541706\pi$
$659$	−11.4637	−	1.09466i	−0.446564	−	0.0426417i	−0.315916	+	0.948787i	$0.602312\pi$
$660$	6.33241	−	11.8695i	0.246489	−	0.462019i
$661$	−33.1532	−	9.73466i	−1.28951	−	0.378634i	−0.436111	−	0.899893i	$-0.643645\pi$
$661$	−33.1532	−	9.73466i	−1.28951	−	0.378634i	−0.853399	+	0.521259i	$0.825463\pi$
$662$	11.9491	+	35.5007i	0.464413	+	1.37977i
$663$	3.10349	+	7.68618i	0.120529	+	0.298507i
$664$	−34.3612	+	18.6837i	−1.33347	+	0.725068i
$665$	72.5256	−	33.1213i	2.81242	−	1.28439i
$666$	−7.33012	+	9.27111i	−0.284036	+	0.359248i
$667$	2.12882	+	0.306078i	0.0824282	+	0.0118514i
$668$	−5.69275	+	9.48305i	−0.220259	+	0.366910i
$669$	−1.93688	+	4.87986i	−0.0748840	+	0.188666i
$670$	25.6907	−	12.1299i	0.992518	−	0.468620i
$671$	−5.59190			−0.215873
$672$	−37.8904	−	21.4768i	−1.46165	−	0.828486i
$673$	−3.69434	+	25.6947i	−0.142407	+	0.990459i	0.785823	+	0.618451i	$0.212240\pi$
$673$	−3.69434	+	25.6947i	−0.142407	+	0.990459i	−0.928230	+	0.372008i	$0.878669\pi$
$674$	1.73331	+	19.9475i	0.0667646	+	0.768348i
$675$	3.44689	−	4.04997i	0.132671	−	0.155883i
$676$	−16.2194	−	13.2087i	−0.623822	−	0.508026i
$677$	−18.3757	−	19.2718i	−0.706234	−	0.740677i	0.268687	−	0.963228i	$-0.413410\pi$
$677$	−18.3757	−	19.2718i	−0.706234	−	0.740677i	−0.974921	+	0.222551i	$0.928562\pi$
$678$	0.0244269	−	0.459007i	0.000938109	−	0.0176281i
$679$	18.6945	−	63.6676i	0.717429	−	2.44334i
$680$	−10.0197	+	18.2726i	−0.384237	+	0.700724i
$681$	−34.2693	−	17.5390i	−1.31320	−	0.672094i
$682$	1.20383	−	21.4271i	0.0460971	−	0.820486i
$683$	−3.51831	−	0.678099i	−0.134624	−	0.0259467i	0.121494	−	0.992592i	$-0.461232\pi$
$683$	−3.51831	−	0.678099i	−0.134624	−	0.0259467i	−0.256118	+	0.966645i	$0.582444\pi$
$684$	−37.7281	−	22.3461i	−1.44257	−	0.854423i
$685$	−51.6328	+	15.1608i	−1.97279	+	0.579263i
$686$	−30.6262	+	19.3154i	−1.16931	+	0.737464i
$687$	−13.9166	−	15.9650i	−0.530953	−	0.609103i
$688$	0.744553	−	21.8291i	0.0283858	−	0.832227i
$689$	13.8440	−	14.5191i	0.527413	−	0.553135i
$690$	1.06234	+	7.69246i	0.0404424	+	0.292847i
$691$	2.01761	−	1.43673i	0.0767536	−	0.0546560i	−0.541036	−	0.840999i	$-0.681968\pi$
$691$	2.01761	−	1.43673i	0.0767536	−	0.0546560i	0.617790	+	0.786343i	$0.288028\pi$
$692$	9.99255	+	7.37557i	0.379860	+	0.280377i
$693$	−7.72672	+	19.6362i	−0.293514	+	0.745917i
$694$	−0.580811	−	3.15816i	−0.0220473	−	0.119882i
$695$	−13.0256	+	15.0323i	−0.494087	+	0.570207i
$696$	8.13531	−	0.591545i	0.308368	−	0.0224225i
$697$	3.15525	−	6.90903i	0.119514	−	0.261698i
$698$	−31.6664	−	27.9152i	−1.19859	−	1.05661i
$699$	7.32110	+	9.25310i	0.276910	+	0.349984i
$700$	−8.80486	−	2.29565i	−0.332793	−	0.0867673i
$701$	3.44292	+	17.8636i	0.130037	+	0.674697i	0.987179	+	0.159617i	$0.0510259\pi$
$701$	3.44292	+	17.8636i	0.130037	+	0.674697i	−0.857142	+	0.515080i	$0.827762\pi$
$702$	11.0716	+	3.82761i	0.417870	+	0.144464i
$703$	19.7847	+	4.79973i	0.746196	+	0.181025i
$704$	6.80614	+	10.6735i	0.256516	+	0.402273i
$705$	−17.3727	+	18.3281i	−0.654292	+	0.690278i
$706$	39.1471	+	7.89165i	1.47332	+	0.297006i
$707$	−19.6612	−	34.0542i	−0.739436	−	1.28074i
$708$	−6.89393	−	0.756453i	−0.259090	−	0.0284293i
$709$	7.28474	−	21.0479i	0.273584	−	0.790470i	−0.721588	−	0.692323i	$-0.756587\pi$
$709$	7.28474	−	21.0479i	0.273584	−	0.790470i	0.995172	−	0.0981469i	$-0.0312915\pi$
$710$	5.16810	−	4.84435i	0.193955	−	0.181805i
$711$	−25.6465	−	21.9586i	−0.961819	−	0.823512i
$712$	−29.8970	−	9.61545i	−1.12044	−	0.360354i
$713$	6.69736	+	10.4213i	0.250818	+	0.390281i
$714$	12.3175	−	30.2781i	0.460972	−	1.13313i
$715$	6.12795	−	0.881066i	0.229172	−	0.0329500i
$716$	4.95733	−	30.7483i	0.185264	−	1.14912i
$717$	5.12308	+	8.81314i	0.191325	+	0.329133i
$718$	−23.5702	+	10.5223i	−0.879631	+	0.392688i
$719$	1.78568	−	37.4860i	0.0665946	−	1.39799i	−0.680243	−	0.732987i	$-0.738126\pi$
$719$	1.78568	−	37.4860i	0.0665946	−	1.39799i	0.746838	−	0.665007i	$-0.231571\pi$
$720$	10.1712	+	27.6393i	0.379058	+	1.03005i
$721$	15.9772	−	22.4368i	0.595022	−	0.835592i
$722$	−5.03845	+	48.4015i	−0.187512	+	1.80132i
$723$	4.30297	+	6.00501i	0.160029	+	0.223329i
$724$	18.2266	+	26.5419i	0.677386	+	0.986422i
$725$	1.61038	−	0.557359i	0.0598081	−	0.0206998i
$726$	−15.8037	+	13.5407i	−0.586529	+	0.502541i
$727$	−15.2496	−	19.3915i	−0.565577	−	0.719189i	0.416190	−	0.909277i	$-0.363365\pi$
$727$	−15.2496	−	19.3915i	−0.565577	−	0.719189i	−0.981767	+	0.190088i	$0.939123\pi$
$728$	−2.34424	−	19.9055i	−0.0868833	−	0.737747i
$729$	26.9958	−	0.479017i	0.999843	−	0.0177414i
$730$	42.7060	−	16.6760i	1.58062	−	0.617205i
$731$	16.3183	−	1.55821i	0.603554	−	0.0576324i
$732$	8.14622	−	9.13784i	0.301093	−	0.337744i
$733$	25.2480	−	13.0163i	0.932557	−	0.480767i	0.0761665	−	0.997095i	$-0.475732\pi$
$733$	25.2480	−	13.0163i	0.932557	−	0.480767i	0.856391	+	0.516329i	$0.172702\pi$
$734$	−6.97807	+	11.8519i	−0.257565	+	0.437462i
$735$	53.7114	+	7.56049i	1.98117	+	0.278873i
$736$	−6.79709	−	2.68194i	−0.250544	−	0.0988575i
$737$	12.9215	−	0.891017i	0.475970	−	0.0328210i
$738$	−4.43365	−	9.77578i	−0.163205	−	0.359851i
$739$	23.4151	−	5.68044i	0.861338	−	0.208958i	0.219325	−	0.975652i	$-0.429614\pi$
$739$	23.4151	−	5.68044i	0.861338	−	0.208958i	0.642013	+	0.766693i	$0.278099\pi$
$740$	−8.26817	−	10.8909i	−0.303944	−	0.400358i
$741$	−1.97753	−	20.0819i	−0.0726464	−	0.737727i
$742$	−79.0510	+	3.09058i	−2.90205	+	0.113459i
$743$	−39.3921	+	3.76149i	−1.44515	+	0.137996i	−0.787961	−	0.615726i	$-0.788863\pi$
$743$	−39.3921	+	3.76149i	−1.44515	+	0.137996i	−0.657194	+	0.753721i	$0.728257\pi$
$744$	33.2607	+	33.1820i	1.21940	+	1.21651i
$745$	29.0704	+	33.5490i	1.06506	+	1.22914i
$746$	2.22054	−	2.77464i	0.0812996	−	0.101587i
$747$	−41.3196	−	3.69908i	−1.51180	−	0.135342i
$748$	−7.28512	+	6.09830i	−0.266371	+	0.222976i
$749$	4.59649	−	1.59086i	0.167952	−	0.0581288i
$750$	−13.7581	−	19.5499i	−0.502374	−	0.713862i
$751$	−11.1315	+	17.3210i	−0.406196	+	0.632053i	−0.982735	−	0.185016i	$-0.940766\pi$
$751$	−11.1315	+	17.3210i	−0.406196	+	0.632053i	0.576540	+	0.817069i	$0.304403\pi$
$752$	−7.00199	−	22.7075i	−0.255336	−	0.828059i
$753$	−39.7331	+	25.7013i	−1.44796	+	0.936607i
$754$	2.43387	+	2.85769i	0.0886363	+	0.104071i
$755$	2.53614	−	53.2402i	0.0922996	−	1.93761i
$756$	−20.8317	−	41.2322i	−0.757642	−	1.49960i
$757$	17.0662	+	13.4210i	0.620283	+	0.487796i	0.878150	−	0.478385i	$-0.158778\pi$
$757$	17.0662	+	13.4210i	0.620283	+	0.487796i	−0.257868	+	0.966180i	$0.583020\pi$
$758$	−2.27620	−	9.74440i	−0.0826753	−	0.353933i
$759$	−0.824469	+	3.44291i	−0.0299263	+	0.124970i
$760$	35.9363	−	35.8092i	1.30355	−	1.29894i
$761$	13.7042	+	21.3242i	0.496777	+	0.773001i	0.995600	−	0.0937032i	$-0.0298705\pi$
$761$	13.7042	+	21.3242i	0.496777	+	0.773001i	−0.498823	+	0.866704i	$0.666234\pi$
$762$	−9.86662	+	0.886751i	−0.357430	+	0.0321236i
$763$	−11.0368	+	0.525747i	−0.399559	+	0.0190333i
$764$	−15.8769	+	6.04421i	−0.574406	+	0.218672i
$765$	−19.5862	+	10.2445i	−0.708141	+	0.370390i
$766$	−12.2001	−	15.7888i	−0.440807	−	0.570473i
$767$	−1.59578	−	2.76398i	−0.0576203	−	0.0998014i
$768$	−27.3569	−	4.42700i	−0.987158	−	0.159745i
$769$	8.01617	+	3.20919i	0.289071	+	0.115726i	0.511666	−	0.859185i	$-0.329029\pi$
$769$	8.01617	+	3.20919i	0.289071	+	0.115726i	−0.222595	+	0.974911i	$0.571453\pi$
$770$	−19.7655	−	14.3304i	−0.712298	−	0.516431i
$771$	−17.8841	−	12.6556i	−0.644079	−	0.455782i
$772$	−1.92396	−	4.41034i	−0.0692448	−	0.158731i
$773$	−3.44943	−	17.8973i	−0.124067	−	0.643722i	−0.989713	−	0.143066i	$-0.954304\pi$
$773$	−3.44943	−	17.8973i	−0.124067	−	0.643722i	0.865646	−	0.500657i	$-0.166908\pi$
$774$	13.4872	−	18.8359i	0.484788	−	0.677043i
$775$	8.50042	+	4.90772i	0.305344	+	0.176291i
$776$	−2.93743	−	42.1189i	−0.105447	−	1.51198i
$777$	14.8467	+	15.4789i	0.532623	+	0.555302i
$778$	8.74312	−	24.5817i	0.313456	−	0.881295i
$779$	−12.1086	+	13.9741i	−0.433835	+	0.500673i
$780$	−7.48736	+	11.2973i	−0.268090	+	0.404510i
$781$	2.99805	−	1.20024i	0.107279	−	0.0429479i
$782$	1.33829	−	5.31824i	0.0478572	−	0.190180i
$783$	7.53057	+	4.25916i	0.269121	+	0.152210i
$784$	−31.0055	+	40.5418i	−1.10734	+	1.44792i
$785$	−23.0132	+	24.1356i	−0.821377	+	0.861435i
$786$	11.6959	+	12.4038i	0.417178	+	0.442430i
$787$	14.0607	−	27.2739i	0.501209	−	0.972210i	−0.493526	−	0.869731i	$-0.664292\pi$
$787$	14.0607	−	27.2739i	0.501209	−	0.972210i	0.994735	−	0.102479i	$-0.0326774\pi$
$788$	−4.05995	−	23.1852i	−0.144630	−	0.825939i
$789$	−0.993537	−	0.0919074i	−0.0353709	−	0.00327199i
$790$	32.0110	−	22.3862i	1.13890	−	0.796465i
$791$	−0.819085	−	0.157866i	−0.0291233	−	0.00561306i
$792$	−0.263916	+	13.4242i	−0.00937783	+	0.477008i
$793$	5.60804	+	0.535503i	0.199147	+	0.0190163i
$794$	−5.71032	−	20.0791i	−0.202652	−	0.712582i
$795$	42.1480	+	32.9443i	1.49484	+	1.16841i
$796$	10.0473	+	0.650438i	0.356117	+	0.0230542i
$797$	20.5397	+	21.5414i	0.727553	+	0.763036i	0.978785	−	0.204891i	$-0.0656841\pi$
$797$	20.5397	+	21.5414i	0.727553	+	0.763036i	−0.251232	+	0.967927i	$0.580836\pi$
$798$	−49.5375	+	62.2755i	−1.75361	+	2.20453i
$799$	16.2225	−	7.40856i	0.573910	−	0.262096i
$800$	−5.76070	+	0.579050i	−0.203671	+	0.0204725i
$801$	−20.7456	−	26.0614i	−0.733008	−	0.920835i
$802$	4.50319	−	29.5312i	0.159013	−	1.04278i
$803$	20.9012			0.737587
$804$	−17.3679	+	22.4133i	−0.612518	+	0.790457i
$805$	14.0923			0.496689
$806$	−3.25925	+	21.3737i	−0.114802	+	0.752855i
$807$	24.2566	+	13.9091i	0.853872	+	0.489623i
$808$	−19.2655	−	15.9644i	−0.677758	−	0.561626i
$809$	−51.3302	+	23.4417i	−1.80468	+	0.824168i	−0.849835	+	0.527049i	$0.823298\pi$
$809$	−51.3302	+	23.4417i	−1.80468	+	0.824168i	−0.954841	+	0.297119i	$0.903974\pi$
$810$	−7.26426	+	30.3815i	−0.255240	+	1.06750i
$811$	24.4455	+	25.6377i	0.858399	+	0.900263i	0.995920	−	0.0902359i	$-0.0287621\pi$
$811$	24.4455	+	25.6377i	0.858399	+	0.900263i	−0.137521	+	0.990499i	$0.543914\pi$
$812$	0.956275	−	14.7716i	0.0335587	−	0.518380i
$813$	29.0211	−	37.1287i	1.01781	−	1.30216i
$814$	−1.70524	−	5.99611i	−0.0597686	−	0.210164i
$815$	−55.7519	−	5.32367i	−1.95291	−	0.186480i
$816$	0.647528	−	20.7887i	0.0226680	−	0.727751i
$817$	−39.1850	−	7.55228i	−1.37091	−	0.264221i
$818$	−12.0244	+	8.40897i	−0.420422	+	0.294013i
$819$	9.62946	−	18.9529i	0.336481	−	0.662269i
$820$	12.2329	−	2.14210i	0.427191	−	0.0748053i
$821$	10.4628	−	20.2949i	0.365153	−	0.708298i	−0.632658	−	0.774431i	$-0.718036\pi$
$821$	10.4628	−	20.2949i	0.365153	−	0.708298i	0.997811	+	0.0661338i	$0.0210664\pi$
$822$	39.0757	−	36.8455i	1.36292	−	1.28513i
$823$	−12.2842	+	12.8833i	−0.428202	+	0.449085i	−0.902121	−	0.431483i	$-0.857990\pi$
$823$	−12.2842	+	12.8833i	−0.428202	+	0.449085i	0.473919	+	0.880568i	$0.342839\pi$
$824$	4.56606	−	16.9208i	0.159066	−	0.589465i
$825$	0.669387	+	2.72407i	0.0233051	+	0.0948398i
$826$	−3.07136	+	12.2053i	−0.106866	+	0.424676i
$827$	44.8727	−	17.9643i	1.56038	−	0.624681i	0.578753	−	0.815503i	$-0.303540\pi$
$827$	44.8727	−	17.9643i	1.56038	−	0.624681i	0.981625	+	0.190822i	$0.0611153\pi$
$828$	−4.42506	−	6.36288i	−0.153781	−	0.221125i
$829$	−14.9441	+	17.2465i	−0.519031	+	0.598994i	−0.953388	−	0.301747i	$-0.902430\pi$
$829$	−14.9441	+	17.2465i	−0.519031	+	0.598994i	0.434357	+	0.900741i	$0.356976\pi$
$830$	16.0841	−	45.2210i	0.558286	−	1.56965i
$831$	27.8513	−	26.7139i	0.966152	−	0.926694i
$832$	−5.80365	−	11.3561i	−0.201205	−	0.393702i
$833$	−33.1734	−	19.1527i	−1.14939	−	0.663601i
$834$	4.78755	−	19.2658i	0.165779	−	0.667120i
$835$	−2.56868	−	13.3276i	−0.0888927	−	0.461219i
$836$	21.1991	−	9.24788i	0.733187	−	0.319845i
$837$	9.86448	+	48.8459i	0.340966	+	1.68836i
$838$	19.1172	+	13.8604i	0.660394	+	0.478800i
$839$	0.336991	+	0.134911i	0.0116342	+	0.00465764i	0.377472	−	0.926021i	$-0.376793\pi$
$839$	0.336991	+	0.134911i	0.0116342	+	0.00465764i	−0.365838	+	0.930679i	$0.619218\pi$
$840$	52.2117	−	11.4228i	1.80147	−	0.394125i
$841$	−13.1139	−	22.7139i	−0.452203	−	0.783239i
$842$	−2.68250	−	3.47157i	−0.0924451	−	0.119638i
$843$	−24.7204	−	21.2927i	−0.851416	−	0.733360i
$844$	−10.3483	−	27.1828i	−0.356202	−	0.935669i
$845$	25.6395	−	1.22136i	0.882025	−	0.0420160i
$846$	7.16388	−	24.1645i	0.246299	−	0.830792i
$847$	20.4184	+	31.7716i	0.701583	+	1.09168i
$848$	−46.4750	+	19.3380i	−1.59596	+	0.664070i
$849$	10.4634	+	2.50566i	0.359104	+	0.0859940i
$850$	−0.988403	−	4.23135i	−0.0339019	−	0.145134i
$851$	2.82851	+	2.22436i	0.0969600	+	0.0762501i
$852$	−2.40619	+	6.64767i	−0.0824348	+	0.227745i
$853$	−1.00802	+	21.1610i	−0.0345141	+	0.724540i	0.913601	+	0.406612i	$0.133290\pi$
$853$	−1.00802	+	21.1610i	−0.0345141	+	0.724540i	−0.948115	+	0.317928i	$0.897013\pi$
$854$	−14.4045	−	16.9129i	−0.492913	−	0.578747i
$855$	52.7756	−	10.4958i	1.80489	−	0.358947i
$856$	2.39004	−	1.96627i	0.0816898	−	0.0672058i
$857$	11.9260	−	18.5571i	0.407383	−	0.633900i	−0.575571	−	0.817752i	$-0.695220\pi$
$857$	11.9260	−	18.5571i	0.407383	−	0.633900i	0.982954	+	0.183852i	$0.0588566\pi$
$858$	−5.05304	+	3.55603i	−0.172508	+	0.121401i
$859$	5.11463	−	1.77019i	0.174509	−	0.0603982i	−0.238416	−	0.971163i	$-0.576628\pi$
$859$	5.11463	−	1.77019i	0.174509	−	0.0603982i	0.412925	+	0.910765i	$0.364507\pi$
$860$	17.2043	+	20.5526i	0.586663	+	0.700837i
$861$	−18.6744	+	5.54335i	−0.636423	+	0.188917i
$862$	14.2115	−	17.7578i	0.484047	−	0.604834i
$863$	15.5978	+	18.0008i	0.530954	+	0.612753i	0.956339	−	0.292259i	$-0.0944069\pi$
$863$	15.5978	+	18.0008i	0.530954	+	0.612753i	−0.425385	+	0.905012i	$0.639861\pi$
$864$	−21.5523	−	19.9875i	−0.733223	−	0.679988i
$865$	−15.1718	+	1.44873i	−0.515855	+	0.0492582i
$866$	−17.7280	+	0.693094i	−0.602421	+	0.0235523i
$867$	−13.7685	+	1.35583i	−0.467603	+	0.0460464i
$868$	67.9079	−	51.5544i	2.30495	−	1.74987i
$869$	17.3063	−	4.19846i	0.587076	−	0.142423i
$870$	−6.94758	+	7.20567i	−0.235545	+	0.244295i
$871$	−13.0441	−	0.343826i	−0.441983	−	0.0116501i
$872$	−6.46780	+	2.75613i	−0.219027	+	0.0933342i
$873$	22.1614	−	38.9144i	0.750051	−	1.31705i
$874$	−6.77350	+	11.5045i	−0.229117	+	0.389144i
$875$	−38.5601	+	19.8791i	−1.30357	+	0.672037i
$876$	−30.4486	+	34.1551i	−1.02876	+	1.15399i
$877$	−3.81392	+	0.364185i	−0.128787	+	0.0122977i	−0.159250	−	0.987238i	$-0.550908\pi$
$877$	−3.81392	+	0.364185i	−0.128787	+	0.0122977i	0.0304635	+	0.999536i	$0.490302\pi$
$878$	42.6145	−	16.6402i	1.43817	−	0.561581i
$879$	−13.8619	+	4.84360i	−0.467551	+	0.163371i
$880$	−14.9627	−	4.17481i	−0.504393	−	0.140733i
$881$	−31.8392	−	40.4869i	−1.07269	−	1.36404i	−0.927152	−	0.374686i	$-0.877751\pi$
$881$	−31.8392	−	40.4869i	−1.07269	−	1.36404i	−0.145540	−	0.989352i	$-0.546492\pi$
$882$	−51.2037	+	17.5723i	−1.72412	+	0.591689i
$883$	21.5930	−	7.47340i	0.726661	−	0.251500i	0.0614029	−	0.998113i	$-0.480443\pi$
$883$	21.5930	−	7.47340i	0.726661	−	0.251500i	0.665259	+	0.746613i	$0.268321\pi$
$884$	7.89016	−	5.41825i	0.265375	−	0.182236i
$885$	6.91789	−	4.95710i	0.232542	−	0.166631i
$886$	−0.269378	+	2.58776i	−0.00904993	+	0.0869374i
$887$	26.8520	−	37.7083i	0.901600	−	1.26612i	−0.0618093	−	0.998088i	$-0.519687\pi$
$887$	26.8520	−	37.7083i	0.901600	−	1.26612i	0.963410	−	0.268033i	$-0.0863735\pi$
$888$	12.2825	+	5.94850i	0.412175	+	0.199619i
$889$	−0.855406	+	17.9572i	−0.0286894	+	0.602264i
$890$	35.1912	−	15.7101i	1.17961	−	0.526605i
$891$	−8.12295	+	11.6975i	−0.272129	+	0.391880i
$892$	5.98512	+	0.964936i	0.200396	+	0.0323085i
$893$	−42.9736	+	6.17867i	−1.43806	+	0.206761i
$894$	−41.0391	−	16.6952i	−1.37255	−	0.558372i
$895$	20.6632	+	32.1525i	0.690693	+	1.07474i
$896$	−14.7500	+	48.0800i	−0.492763	+	1.60624i
$897$	1.15656	−	3.37390i	0.0386163	−	0.112651i
$898$	−40.3651	+	37.8364i	−1.34700	+	1.26262i
$899$	−5.22250	+	15.0894i	−0.174180	+	0.503261i
$900$	−5.42661	−	2.87453i	−0.180887	−	0.0958177i
$901$	−18.8895	−	32.7176i	−0.629301	−	1.08998i
$902$	5.55014	+	1.11885i	0.184800	+	0.0372536i
$903$	−30.5126	−	28.9220i	−1.01540	−	0.962462i
$904$	−0.523572	+	0.0870897i	−0.0174138	+	0.00289656i
$905$	−38.3971	−	9.31504i	−1.27636	−	0.309642i
$906$	21.8289	+	48.5115i	0.725217	+	1.61169i
$907$	4.80297	+	24.9202i	0.159480	+	0.827461i	0.970252	+	0.242098i	$0.0778357\pi$
$907$	4.80297	+	24.9202i	0.159480	+	0.827461i	−0.810772	+	0.585363i	$0.800952\pi$
$908$	−11.2149	+	43.0142i	−0.372179	+	1.42748i
$909$	−7.62713	−	25.4185i	−0.252976	−	0.843080i
$910$	18.4502	+	16.2646i	0.611618	+	0.539166i
$911$	−4.63897	+	10.1579i	−0.153696	+	0.336547i	−0.970780	−	0.239971i	$-0.922862\pi$
$911$	−4.63897	+	10.1579i	−0.153696	+	0.336547i	0.817084	+	0.576519i	$0.195589\pi$
$912$	−15.7705	+	48.1141i	−0.522213	+	1.59322i
$913$	14.3292	−	16.5368i	0.474228	−	0.547288i
$914$	3.41410	+	18.5641i	0.112928	+	0.614047i
$915$	0.0444218	+	15.0223i	0.00146854	+	0.496622i
$916$	−14.5231	+	19.6762i	−0.479857	+	0.650119i
$917$	25.2017	−	17.9461i	0.832235	−	0.592632i
$918$	12.7901	−	17.9744i	0.422135	−	0.593242i
$919$	−31.6105	+	33.1521i	−1.04273	+	1.09359i	−0.0472270	+	0.998884i	$0.515038\pi$
$919$	−31.6105	+	33.1521i	−1.04273	+	1.09359i	−0.995506	+	0.0947023i	$0.969810\pi$
$920$	8.40697	−	3.11868i	0.277170	−	0.102820i
$921$	11.0600	−	9.64096i	0.364440	−	0.317680i
$922$	−29.0801	+	18.3403i	−0.957701	+	0.604005i
$923$	−3.12164	+	0.916597i	−0.102750	+	0.0301702i
$924$	24.0669	+	3.80714i	0.791742	+	0.125246i
$925$	2.79963	+	0.539584i	0.0920512	+	0.0177414i
$926$	−1.41124	+	25.1188i	−0.0463763	+	0.825455i
$927$	13.9765	−	12.2562i	0.459050	−	0.402547i
$928$	−2.69852	−	9.02380i	−0.0885833	−	0.296221i
$929$	−5.00682	+	17.0517i	−0.164268	+	0.559447i	0.835679	+	0.549218i	$0.185074\pi$
$929$	−5.00682	+	17.0517i	−0.164268	+	0.559447i	−0.999948	+	0.0102290i	$0.996744\pi$
$930$	−57.5722	−	3.06380i	−1.88787	−	0.100466i
$931$	64.3505	+	67.4889i	2.10900	+	2.21186i
$932$	8.60339	−	10.5644i	0.281813	−	0.346048i
$933$	2.84811	+	56.2867i	0.0932430	+	1.84274i
$934$	3.48999	+	40.1639i	0.114196	+	1.31420i
$935$	1.65920	−	11.5400i	0.0542615	−	0.377397i
$936$	1.55023	−	13.4377i	0.0506709	−	0.439224i
$937$	31.3742			1.02495			0.512475	−	0.858702i	$-0.328729\pi$
$937$	31.3742			1.02495			0.512475	+	0.858702i	$0.328729\pi$
$938$	35.9802	+	36.7863i	1.17480	+	1.20111i
$939$	7.08315	+	2.81139i	0.231150	+	0.0917463i
$940$	25.0011	+	15.0084i	0.815446	+	0.489519i
$941$	20.0317	+	2.88013i	0.653015	+	0.0938894i	0.460857	−	0.887475i	$-0.347542\pi$
$941$	20.0317	+	2.88013i	0.653015	+	0.0938894i	0.192158	+	0.981364i	$0.438451\pi$
$942$	9.55470	−	31.8827i	0.311309	−	1.03879i
$943$	−2.97281	+	1.35764i	−0.0968080	+	0.0442108i
$944$	0.868815	+	7.96093i	0.0282775	+	0.259106i
$945$	52.8128	+	20.6014i	1.71800	+	0.670163i
$946$	3.89799	+	11.5810i	0.126735	+	0.376530i
$947$	43.0987	+	12.6549i	1.40052	+	0.411230i	0.892863	−	0.450329i	$-0.148693\pi$
$947$	43.0987	+	12.6549i	1.40052	+	0.411230i	0.507658	+	0.861559i	$0.330512\pi$
$948$	−18.3508	+	34.3969i	−0.596007	+	1.11716i
$949$	−20.9615	−	2.00158i	−0.680441	−	0.0649742i
$950$	−0.593372	+	10.5615i	−0.0192515	+	0.342660i
$951$	12.8281	−	20.0913i	0.415980	−	0.651506i
$952$	−37.2107	−	6.32509i	−1.20601	−	0.204997i
$953$	12.5138	+	42.6183i	0.405363	+	1.38054i	0.869130	+	0.494583i	$0.164679\pi$
$953$	12.5138	+	42.6183i	0.405363	+	1.38054i	−0.463767	+	0.885957i	$0.653502\pi$
$954$	−52.3998	−	10.2411i	−1.69651	−	0.331569i
$955$	9.55276	−	18.5298i	0.309120	−	0.599609i
$956$	8.65631	−	7.97652i	0.279965	−	0.257979i
$957$	−4.14531	+	1.90793i	−0.133999	+	0.0616747i
$958$	−25.1530	+	14.2376i	−0.812655	+	0.459996i
$959$	−56.5355	−	79.3930i	−1.82563	−	2.56373i
$960$	28.6197	−	18.3691i	0.923696	−	0.592860i
$961$	−56.6041	+	22.6609i	−1.82594	+	0.730996i
$962$	1.13595	+	6.17672i	0.0366245	+	0.199145i
$963$	3.26589	−	0.331357i	0.105242	−	0.0106778i
$964$	5.69530	−	6.35068i	0.183433	−	0.204541i
$965$	5.37107	+	2.45288i	0.172901	+	0.0789611i
$966$	−12.5370	+	6.37518i	−0.403371	+	0.205118i
$967$	19.5867	+	11.3084i	0.629866	+	0.363654i	0.780700	−	0.624906i	$-0.214863\pi$
$967$	19.5867	+	11.3084i	0.629866	+	0.363654i	−0.150834	+	0.988559i	$0.548196\pi$
$968$	19.2120	+	14.4351i	0.617498	+	0.463962i
$969$	−37.3349	−	7.08127i	−1.19937	−	0.227483i
$970$	37.1915	+	36.0722i	1.19415	+	1.15821i
$971$	1.56478	−	6.45013i	0.0502163	−	0.206994i	−0.941177	−	0.337915i	$-0.890278\pi$
$971$	1.56478	−	6.45013i	0.0502163	−	0.206994i	0.991393	+	0.130921i	$0.0417934\pi$
$972$	−7.28167	−	30.3146i	−0.233560	−	0.972342i
$973$	−33.4452	−	13.3894i	−1.07220	−	0.429246i
$974$	−33.4843	−	6.75009i	−1.07291	−	0.216287i
$975$	−0.410452	−	2.79603i	−0.0131450	−	0.0895448i
$976$	−12.3361	−	6.90183i	−0.394869	−	0.220922i
$977$	16.0029	+	5.53866i	0.511979	+	0.177198i	0.570829	−	0.821069i	$-0.306622\pi$
$977$	16.0029	+	5.53866i	0.511979	+	0.177198i	−0.0588498	+	0.998267i	$0.518743\pi$
$978$	52.0071	−	20.4853i	1.66300	−	0.655049i
$979$	17.5497	−	0.835997i	0.560892	−	0.0267186i
$980$	−4.88985	−	62.4408i	−0.156200	−	1.99460i
$981$	−7.33049	−	1.36792i	−0.234044	−	0.0436744i
$982$	−0.00737674	+	0.865411i	−0.000235401	+	0.0276164i
$983$	−1.37742	−	9.58019i	−0.0439330	−	0.305561i	−0.999926	−	0.0121710i	$-0.996126\pi$
$983$	−1.37742	−	9.58019i	−0.0439330	−	0.305561i	0.955993	−	0.293390i	$-0.0947833\pi$
$984$	−9.91373	+	7.43968i	−0.316038	+	0.237168i
$985$	22.7047	+	17.8552i	0.723432	+	0.568913i
$986$	6.45481	−	2.88158i	0.205563	−	0.0917681i
$987$	−41.6615	−	18.8775i	−1.32610	−	0.600877i
$988$	−22.1459	+	7.24446i	−0.704556	+	0.230477i
$989$	−5.74550	−	4.09135i	−0.182696	−	0.130097i
$990$	−10.7573	−	12.4802i	−0.341890	−	0.396648i
$991$	26.7617	−	41.6420i	0.850114	−	1.32280i	−0.0948047	−	0.995496i	$-0.530223\pi$
$991$	26.7617	−	41.6420i	0.850114	−	1.32280i	0.944918	−	0.327307i	$-0.106141\pi$
$992$	29.1022	−	45.7838i	0.923996	−	1.45364i
$993$	45.8304	+	2.04736i	1.45438	+	0.0649710i
$994$	11.3530	+	5.97593i	0.360096	+	0.189545i
$995$	−9.71187	+	7.63750i	−0.307887	+	0.242125i
$996$	6.14849	+	47.5063i	0.194822	+	1.50530i
$997$	24.7850	+	28.6034i	0.784948	+	0.905878i	0.997456	−	0.0712812i	$-0.0227088\pi$
$997$	24.7850	+	28.6034i	0.784948	+	0.905878i	−0.212509	+	0.977159i	$0.568163\pi$
$998$	14.3405	−	5.59971i	0.453940	−	0.177256i
$999$	7.34843	+	12.4710i	0.232494	+	0.394566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bd.a.23.8	✓	2640
3.2	odd	2	inner	804.2.bd.a.23.125	yes	2640
4.3	odd	2	inner	804.2.bd.a.23.25	yes	2640
12.11	even	2	inner	804.2.bd.a.23.108	yes	2640
67.35	even	33	inner	804.2.bd.a.35.108	yes	2640
201.35	odd	66	inner	804.2.bd.a.35.25	yes	2640
268.35	odd	66	inner	804.2.bd.a.35.125	yes	2640
804.35	even	66	inner	804.2.bd.a.35.8	yes	2640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bd.a.23.8	✓	2640	1.1	even	1	trivial
804.2.bd.a.23.25	yes	2640	4.3	odd	2	inner
804.2.bd.a.23.108	yes	2640	12.11	even	2	inner
804.2.bd.a.23.125	yes	2640	3.2	odd	2	inner
804.2.bd.a.35.8	yes	2640	804.35	even	66	inner
804.2.bd.a.35.25	yes	2640	201.35	odd	66	inner
804.2.bd.a.35.108	yes	2640	67.35	even	33	inner
804.2.bd.a.35.125	yes	2640	268.35	odd	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bd (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39805 - 0.213188i) q^{2} +(-0.861586 + 1.50255i) q^{3} +(1.90910 + 0.596096i) q^{4} +(-2.23249 + 1.01954i) q^{5} +(1.52487 - 1.91697i) q^{6} +(-3.06753 - 3.21714i) q^{7} +(-2.54194 - 1.24037i) q^{8} +(-1.51534 - 2.58916i) q^{9} +O(q^{10})\)	\(q+(-1.39805 - 0.213188i) q^{2} +(-0.861586 + 1.50255i) q^{3} +(1.90910 + 0.596096i) q^{4} +(-2.23249 + 1.01954i) q^{5} +(1.52487 - 1.91697i) q^{6} +(-3.06753 - 3.21714i) q^{7} +(-2.54194 - 1.24037i) q^{8} +(-1.51534 - 2.58916i) q^{9} +(3.33849 - 0.949437i) q^{10} +(1.57520 + 0.150413i) q^{11} +(-2.54052 + 2.35494i) q^{12} +(-1.56534 - 0.301694i) q^{13} +(3.60272 + 5.15169i) q^{14} +(0.391562 - 4.23286i) q^{15} +(3.28934 + 2.27601i) q^{16} +(-1.37562 + 2.66833i) q^{17} +(1.56655 + 3.94283i) q^{18} +(5.04324 - 5.28920i) q^{19} +(-4.86980 + 0.615636i) q^{20} +(7.47687 - 1.83730i) q^{21} +(-2.17014 - 0.546098i) q^{22} +(1.19919 - 0.480083i) q^{23} +(4.05383 - 2.75072i) q^{24} +(0.670243 - 0.773501i) q^{25} +(2.12411 + 0.755496i) q^{26} +(5.19595 - 0.0460952i) q^{27} +(-3.93851 - 7.97039i) q^{28} +(1.44193 + 0.832499i) q^{29} +(-1.44982 + 5.83429i) q^{30} +(1.81495 + 9.41688i) q^{31} +(-4.11345 - 3.88324i) q^{32} +(-1.58317 + 2.23722i) q^{33} +(2.49204 - 3.43720i) q^{34} +(10.1283 + 4.05474i) q^{35} +(-1.34955 - 5.84626i) q^{36} +(1.39286 + 2.41250i) q^{37} +(-8.17831 + 6.31942i) q^{38} +(1.80199 - 2.09207i) q^{39} +(6.93948 + 0.177490i) q^{40} +(-2.52721 + 0.120386i) q^{41} +(-10.8447 + 0.974659i) q^{42} +(-2.95214 - 4.59362i) q^{43} +(2.91755 + 1.22612i) q^{44} +(6.02274 + 4.23532i) q^{45} +(-1.77888 + 0.415529i) q^{46} +(-4.66966 - 3.67226i) q^{47} +(-6.25388 + 2.98143i) q^{48} +(-0.607133 + 12.7453i) q^{49} +(-1.10194 + 0.938508i) q^{50} +(-2.82409 - 4.36593i) q^{51} +(-2.80855 - 1.50906i) q^{52} +(-6.80366 + 10.5867i) q^{53} +(-7.27404 - 1.04327i) q^{54} +(-3.66996 + 1.27019i) q^{55} +(3.80706 + 11.9827i) q^{56} +(3.60212 + 12.1348i) q^{57} +(-1.83842 - 1.47128i) q^{58} +(1.31106 + 1.51305i) q^{59} +(3.27072 - 7.84756i) q^{60} +(-3.51789 + 0.335918i) q^{61} +(-0.529838 - 13.5522i) q^{62} +(-3.68133 + 12.8174i) q^{63} +(4.92296 + 6.30590i) q^{64} +(3.80220 - 0.922403i) q^{65} +(2.69030 - 2.79024i) q^{66} +(8.07546 - 1.33677i) q^{67} +(-4.21677 + 4.27411i) q^{68} +(-0.311854 + 2.21548i) q^{69} +(-13.2954 - 7.82797i) q^{70} +(1.81399 - 0.935176i) q^{71} +(0.640391 + 8.46108i) q^{72} +(13.1491 - 1.25558i) q^{73} +(-1.43297 - 3.66975i) q^{74} +(0.584756 + 1.67351i) q^{75} +(12.7809 - 7.09137i) q^{76} +(-4.34807 - 5.52902i) q^{77} +(-2.96528 + 2.54066i) q^{78} +(10.6353 - 3.68090i) q^{79} +(-9.66392 - 1.72755i) q^{80} +(-4.40750 + 7.84691i) q^{81} +(3.55884 + 0.370465i) q^{82} +(8.02119 - 11.2642i) q^{83} +(15.3693 + 0.949343i) q^{84} +(0.350577 - 7.35952i) q^{85} +(3.14794 + 7.05149i) q^{86} +(-2.49322 + 1.44931i) q^{87} +(-3.81749 - 2.33617i) q^{88} +(10.9904 - 1.58018i) q^{89} +(-7.51720 - 7.20518i) q^{90} +(3.83114 + 5.96137i) q^{91} +(2.57555 - 0.201696i) q^{92} +(-15.7131 - 5.38638i) q^{93} +(5.74555 + 6.12953i) q^{94} +(-5.86642 + 16.9499i) q^{95} +(9.37886 - 2.83494i) q^{96} +(7.46373 + 12.9276i) q^{97} +(3.56595 - 17.6892i) q^{98} +(-1.99751 - 4.30636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9}+O(q^{10}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9	\( 2640 q - 42 q^{4} - 19 q^{6} - 32 q^{9} - 46 q^{10} - 24 q^{12} - 88 q^{13} - 26 q^{16} - 23 q^{18} - 128 q^{22} - 22 q^{24} + 160 q^{25} + 44 q^{28} - 18 q^{30} - 44 q^{33} - 6 q^{34} - 35 q^{36} - 48 q^{37} - 92 q^{40} - 10 q^{42} + 40 q^{45} + 46 q^{46} - 11 q^{48} - 216 q^{49} - 76 q^{52} + 129 q^{54} - 42 q^{57} - 56 q^{58} - 90 q^{60} - 80 q^{61} - 48 q^{64} - 74 q^{66} - 4 q^{69} + 96 q^{70} - 20 q^{72} - 216 q^{73} + 76 q^{76} - 66 q^{78} - 16 q^{81} + 20 q^{82} - 55 q^{84} - 104 q^{85} - 30 q^{88} - 64 q^{90} - 192 q^{93} - 32 q^{94} - 205 q^{96} - 64 q^{97}+O(q^{100}) \) 2640 * q - 42 * q^4 - 19 * q^6 - 32 * q^9 - 46 * q^10 - 24 * q^12 - 88 * q^13 - 26 * q^16 - 23 * q^18 - 128 * q^22 - 22 * q^24 + 160 * q^25 + 44 * q^28 - 18 * q^30 - 44 * q^33 - 6 * q^34 - 35 * q^36 - 48 * q^37 - 92 * q^40 - 10 * q^42 + 40 * q^45 + 46 * q^46 - 11 * q^48 - 216 * q^49 - 76 * q^52 + 129 * q^54 - 42 * q^57 - 56 * q^58 - 90 * q^60 - 80 * q^61 - 48 * q^64 - 74 * q^66 - 4 * q^69 + 96 * q^70 - 20 * q^72 - 216 * q^73 + 76 * q^76 - 66 * q^78 - 16 * q^81 + 20 * q^82 - 55 * q^84 - 104 * q^85 - 30 * q^88 - 64 * q^90 - 192 * q^93 - 32 * q^94 - 205 * q^96 - 64 * q^97

Introduction

L-functions

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