LMFDB - Embedded newform 460.2.w.a.187.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			187.35
Character	$\chi$	$=$	460.187
Dual form			460.2.w.a.123.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00122474 - 1.41421i) q^{2} +(2.57246 - 0.959477i) q^{3} +(-2.00000 - 0.00346408i) q^{4} +(1.11859 - 1.93617i) q^{5} +(-1.35375 - 3.63918i) q^{6} +(-0.151899 + 0.698270i) q^{7} +(-0.00734842 + 2.82842i) q^{8} +(3.42969 - 2.97185i) q^{9} +O(q^{10})$	\(q+(0.00122474 - 1.41421i) q^{2} +(2.57246 - 0.959477i) q^{3} +(-2.00000 - 0.00346408i) q^{4} +(1.11859 - 1.93617i) q^{5} +(-1.35375 - 3.63918i) q^{6} +(-0.151899 + 0.698270i) q^{7} +(-0.00734842 + 2.82842i) q^{8} +(3.42969 - 2.97185i) q^{9} +(-2.73679 - 1.58430i) q^{10} +(4.76108 + 0.684541i) q^{11} +(-5.14823 + 1.91004i) q^{12} +(-0.683665 + 0.148722i) q^{13} +(0.987316 + 0.215673i) q^{14} +(1.01981 - 6.05398i) q^{15} +(3.99998 + 0.0138563i) q^{16} +(-1.25073 - 2.29054i) q^{17} +(-4.19862 - 4.85396i) q^{18} +(-6.83847 + 2.00795i) q^{19} +(-2.24388 + 3.86846i) q^{20} +(0.279219 + 1.94201i) q^{21} +(0.973917 - 6.73235i) q^{22} +(-0.918730 + 4.70701i) q^{23} +(2.69490 + 7.28304i) q^{24} +(-2.49751 - 4.33156i) q^{25} +(0.209488 + 0.967030i) q^{26} +(2.02389 - 3.70648i) q^{27} +(0.306217 - 1.39601i) q^{28} +(0.0734905 - 0.250286i) q^{29} +(-8.56037 - 1.44965i) q^{30} +(-7.34064 + 3.35236i) q^{31} +(0.0244947 - 5.65680i) q^{32} +(12.9045 - 2.80720i) q^{33} +(-3.24084 + 1.76599i) q^{34} +(1.18206 + 1.07518i) q^{35} +(-6.86967 + 5.93180i) q^{36} +(-0.437802 + 6.12127i) q^{37} +(2.83130 + 9.67351i) q^{38} +(-1.61600 + 1.03854i) q^{39} +(5.46808 + 3.17807i) q^{40} +(-0.612632 + 0.707015i) q^{41} +(2.74676 - 0.392497i) q^{42} +(9.71456 - 3.62334i) q^{43} +(-9.51978 - 1.38557i) q^{44} +(-1.91758 - 9.96475i) q^{45} +(6.65559 + 1.30505i) q^{46} +(5.37396 - 5.37396i) q^{47} +(10.3031 - 3.80224i) q^{48} +(5.90292 + 2.69577i) q^{49} +(-6.12881 + 3.52671i) q^{50} +(-5.41517 - 4.69227i) q^{51} +(1.36784 - 0.295076i) q^{52} +(-2.81945 + 12.9608i) q^{53} +(-5.23928 - 2.86675i) q^{54} +(6.65109 - 8.45255i) q^{55} +(-1.97388 - 0.434766i) q^{56} +(-15.6651 + 11.7267i) q^{57} +(-0.353867 - 0.104238i) q^{58} +(-3.61764 - 2.32492i) q^{59} +(-2.06060 + 12.1044i) q^{60} +(-1.58180 - 3.46365i) q^{61} +(4.73196 + 10.3853i) q^{62} +(1.55418 + 2.84627i) q^{63} +(-7.99989 - 0.0415688i) q^{64} +(-0.476790 + 1.49005i) q^{65} +(-3.95417 - 18.2531i) q^{66} +(-4.39711 - 3.29164i) q^{67} +(2.49352 + 4.58540i) q^{68} +(2.15287 + 12.9901i) q^{69} +(1.52198 - 1.67036i) q^{70} +(-2.96916 + 0.426901i) q^{71} +(8.38042 + 9.72244i) q^{72} +(4.37245 - 8.00755i) q^{73} +(8.65625 + 0.626642i) q^{74} +(-10.5808 - 8.74645i) q^{75} +(13.6839 - 3.99221i) q^{76} +(-1.20120 + 3.22054i) q^{77} +(1.46674 + 2.28665i) q^{78} +(-1.05258 - 0.676450i) q^{79} +(4.50116 - 7.72914i) q^{80} +(-0.287439 + 1.99918i) q^{81} +(0.999120 + 0.867258i) q^{82} +(0.353103 - 4.93702i) q^{83} +(-0.551710 - 3.88499i) q^{84} +(-5.83393 - 0.140550i) q^{85} +(-5.11228 - 13.7429i) q^{86} +(-0.0510921 - 0.714362i) q^{87} +(-1.97115 + 13.4613i) q^{88} +(12.3441 + 5.63737i) q^{89} +(-14.0946 + 2.69966i) q^{90} -0.499974i q^{91} +(1.85376 - 9.41082i) q^{92} +(-15.6670 + 15.6670i) q^{93} +(-7.59334 - 7.60650i) q^{94} +(-3.76170 + 15.4865i) q^{95} +(-5.36456 - 14.5754i) q^{96} +(9.61022 - 0.687336i) q^{97} +(3.81963 - 8.34468i) q^{98} +(18.3634 - 11.8014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{8}{11}\right)$

Coefficient data

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

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

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

$2$	0.00122474	−	1.41421i	0.000866020	−	1.00000i
$2$	0.00122474	−	1.41421i	0.000866020	−	1.00000i
$3$	2.57246	−	0.959477i	1.48521	−	0.553954i	0.529511	−	0.848303i	$-0.322375\pi$
$3$	2.57246	−	0.959477i	1.48521	−	0.553954i	0.955698	+	0.294349i	$0.0951027\pi$
$4$	−2.00000	−	0.00346408i	−0.999999	−	0.00173204i
$5$	1.11859	−	1.93617i	0.500249	−	0.865882i
$5$	1.11859	−	1.93617i	0.500249	−	0.865882i
$6$	−1.35375	−	3.63918i	−0.552668	−	1.48569i
$7$	−0.151899	+	0.698270i	−0.0574125	+	0.263921i	−0.996902	−	0.0786575i	$-0.974937\pi$
$7$	−0.151899	+	0.698270i	−0.0574125	+	0.263921i	0.939489	+	0.342579i	$0.111300\pi$
$8$	−0.00734842	+	2.82842i	−0.00259806	+	0.999997i
$9$	3.42969	−	2.97185i	1.14323	−	0.990615i
$10$	−2.73679	−	1.58430i	−0.865448	−	0.500998i
$11$	4.76108	+	0.684541i	1.43552	+	0.206397i	0.815759	−	0.578393i	$-0.196320\pi$
$11$	4.76108	+	0.684541i	1.43552	+	0.206397i	0.619763	+	0.784789i	$0.287229\pi$
$12$	−5.14823	+	1.91004i	−1.48617	+	0.551381i
$13$	−0.683665	+	0.148722i	−0.189615	+	0.0412481i	−0.306370	−	0.951913i	$-0.599114\pi$
$13$	−0.683665	+	0.148722i	−0.189615	+	0.0412481i	0.116755	+	0.993161i	$0.462751\pi$
$14$	0.987316	+	0.215673i	0.263871	+	0.0576411i
$15$	1.01981	−	6.05398i	0.263315	−	1.56313i
$16$	3.99998	+	0.0138563i	0.999994	+	0.00346407i
$17$	−1.25073	−	2.29054i	−0.303346	−	0.555537i	0.680892	−	0.732384i	$-0.261592\pi$
$17$	−1.25073	−	2.29054i	−0.303346	−	0.555537i	−0.984238	+	0.176846i	$0.943410\pi$
$18$	−4.19862	−	4.85396i	−0.989625	−	1.14409i
$19$	−6.83847	+	2.00795i	−1.56885	+	0.460656i	−0.946667	−	0.322214i	$-0.895573\pi$
$19$	−6.83847	+	2.00795i	−1.56885	+	0.460656i	−0.622185	+	0.782870i	$0.713755\pi$
$20$	−2.24388	+	3.86846i	−0.501748	+	0.865014i
$21$	0.279219	+	1.94201i	0.0609306	+	0.423782i
$22$	0.973917	−	6.73235i	0.207640	−	1.43534i
$23$	−0.918730	+	4.70701i	−0.191568	+	0.981479i
$23$	−0.918730	+	4.70701i	−0.191568	+	0.981479i
$24$	2.69490	+	7.28304i	0.550094	+	1.48664i
$25$	−2.49751	−	4.33156i	−0.499502	−	0.866312i
$26$	0.209488	+	0.967030i	0.0410839	+	0.189650i
$27$	2.02389	−	3.70648i	0.389498	−	0.713313i
$28$	0.306217	−	1.39601i	0.0578696	−	0.263821i
$29$	0.0734905	−	0.250286i	0.0136468	−	0.0464769i	−0.952388	−	0.304888i	$-0.901381\pi$
$29$	0.0734905	−	0.250286i	0.0136468	−	0.0464769i	0.966035	+	0.258411i	$0.0831990\pi$
$30$	−8.56037	−	1.44965i	−1.56290	−	0.264669i
$31$	−7.34064	+	3.35236i	−1.31842	+	0.602101i	−0.945457	−	0.325746i	$-0.894385\pi$
$31$	−7.34064	+	3.35236i	−1.31842	+	0.602101i	−0.372961	+	0.927847i	$0.621657\pi$
$32$	0.0244947	−	5.65680i	0.00433009	−	0.999991i
$33$	12.9045	−	2.80720i	2.24638	−	0.488671i
$34$	−3.24084	+	1.76599i	−0.555800	+	0.302865i
$35$	1.18206	+	1.07518i	0.199804	+	0.181739i
$36$	−6.86967	+	5.93180i	−1.14495	+	0.988634i
$37$	−0.437802	+	6.12127i	−0.0719742	+	1.00633i	0.825253	+	0.564763i	$0.191032\pi$
$37$	−0.437802	+	6.12127i	−0.0719742	+	1.00633i	−0.897228	+	0.441568i	$0.854422\pi$
$38$	2.83130	+	9.67351i	0.459298	+	1.56925i
$39$	−1.61600	+	1.03854i	−0.258768	+	0.166300i
$40$	5.46808	+	3.17807i	0.864579	+	0.502497i
$41$	−0.612632	+	0.707015i	−0.0956771	+	0.110417i	−0.801569	−	0.597902i	$-0.796001\pi$
$41$	−0.612632	+	0.707015i	−0.0956771	+	0.110417i	0.705892	+	0.708320i	$0.250546\pi$
$42$	2.74676	−	0.392497i	0.423835	−	0.0605636i
$43$	9.71456	−	3.62334i	1.48146	−	0.552554i	0.526728	−	0.850034i	$-0.323419\pi$
$43$	9.71456	−	3.62334i	1.48146	−	0.552554i	0.954728	+	0.297480i	$0.0961461\pi$
$44$	−9.51978	−	1.38557i	−1.43516	−	0.208883i
$45$	−1.91758	−	9.96475i	−0.285856	−	1.48546i
$46$	6.65559	+	1.30505i	0.981313	+	0.192418i
$47$	5.37396	−	5.37396i	0.783872	−	0.783872i	−0.196610	−	0.980482i	$-0.562993\pi$
$47$	5.37396	−	5.37396i	0.783872	−	0.783872i	0.980482	+	0.196610i	$0.0629931\pi$
$48$	10.3031	−	3.80224i	1.48712	−	0.548806i
$49$	5.90292	+	2.69577i	0.843274	+	0.385110i
$50$	−6.12881	+	3.52671i	−0.866745	+	0.498752i
$51$	−5.41517	−	4.69227i	−0.758275	−	0.657049i
$52$	1.36784	−	0.295076i	0.189686	−	0.0409197i
$53$	−2.81945	+	12.9608i	−0.387282	+	1.78031i	0.209403	+	0.977829i	$0.432848\pi$
$53$	−2.81945	+	12.9608i	−0.387282	+	1.78031i	−0.596685	+	0.802476i	$0.703516\pi$
$54$	−5.23928	−	2.86675i	−0.712975	−	0.390116i
$55$	6.65109	−	8.45255i	0.896833	−	1.13974i
$56$	−1.97388	−	0.434766i	−0.263771	−	0.0580980i
$57$	−15.6651	+	11.7267i	−2.07489	+	1.55324i
$58$	−0.353867	−	0.104238i	−0.0464650	−	0.0136871i
$59$	−3.61764	−	2.32492i	−0.470977	−	0.302678i	0.283539	−	0.958961i	$-0.408492\pi$
$59$	−3.61764	−	2.32492i	−0.470977	−	0.302678i	−0.754515	+	0.656282i	$0.772128\pi$
$60$	−2.06060	+	12.1044i	−0.266022	+	1.56267i
$61$	−1.58180	−	3.46365i	−0.202528	−	0.443475i	0.780928	−	0.624621i	$-0.214747\pi$
$61$	−1.58180	−	3.46365i	−0.202528	−	0.443475i	−0.983456	+	0.181146i	$0.942019\pi$
$62$	4.73196	+	10.3853i	0.600959	+	1.31894i
$63$	1.55418	+	2.84627i	0.195809	+	0.358597i
$64$	−7.99989	−	0.0415688i	−0.999987	−	0.00519610i
$65$	−0.476790	+	1.49005i	−0.0591385	+	0.184818i
$66$	−3.95417	−	18.2531i	−0.486725	−	2.24681i
$67$	−4.39711	−	3.29164i	−0.537193	−	0.402138i	0.295943	−	0.955206i	$-0.404366\pi$
$67$	−4.39711	−	3.29164i	−0.537193	−	0.402138i	−0.833136	+	0.553068i	$0.813457\pi$
$68$	2.49352	+	4.58540i	0.302384	+	0.556062i
$69$	2.15287	+	12.9901i	0.259175	+	1.56382i
$70$	1.52198	−	1.67036i	0.181912	−	0.199646i
$71$	−2.96916	+	0.426901i	−0.352375	+	0.0506638i	−0.316229	−	0.948683i	$-0.602417\pi$
$71$	−2.96916	+	0.426901i	−0.352375	+	0.0506638i	−0.0361452	+	0.999347i	$0.511508\pi$
$72$	8.38042	+	9.72244i	0.987642	+	1.14580i
$73$	4.37245	−	8.00755i	0.511757	−	0.937213i	−0.486232	−	0.873830i	$-0.661629\pi$
$73$	4.37245	−	8.00755i	0.511757	−	0.937213i	0.997989	−	0.0633832i	$-0.0201890\pi$
$74$	8.65625	+	0.626642i	1.00627	+	0.0728457i
$75$	−10.5808	−	8.74645i	−1.22176	−	1.00995i
$76$	13.6839	−	3.99221i	1.56965	−	0.457938i
$77$	−1.20120	+	3.22054i	−0.136889	+	0.367015i
$78$	1.46674	+	2.28665i	0.166076	+	0.258912i
$79$	−1.05258	−	0.676450i	−0.118424	−	0.0761066i	0.480088	−	0.877220i	$-0.340605\pi$
$79$	−1.05258	−	0.676450i	−0.118424	−	0.0761066i	−0.598512	+	0.801114i	$0.704241\pi$
$80$	4.50116	−	7.72914i	0.503245	−	0.864144i
$81$	−0.287439	+	1.99918i	−0.0319376	+	0.222131i
$82$	0.999120	+	0.867258i	0.110334	+	0.0957727i
$83$	0.353103	−	4.93702i	0.0387580	−	0.541908i	−0.940566	−	0.339611i	$-0.889705\pi$
$83$	0.353103	−	4.93702i	0.0387580	−	0.541908i	0.979324	−	0.202298i	$-0.0648408\pi$
$84$	−0.551710	−	3.88499i	−0.0601966	−	0.423887i
$85$	−5.83393	−	0.140550i	−0.632778	−	0.0152448i
$86$	−5.11228	−	13.7429i	−0.551271	−	1.48193i
$87$	−0.0510921	−	0.714362i	−0.00547765	−	0.0765876i
$88$	−1.97115	+	13.4613i	−0.210126	+	1.43498i
$89$	12.3441	+	5.63737i	1.30847	+	0.597560i	0.942855	−	0.333204i	$-0.108130\pi$
$89$	12.3441	+	5.63737i	1.30847	+	0.597560i	0.365620	+	0.930764i	$0.380857\pi$
$90$	−14.0946	+	2.69966i	−1.48570	+	0.284569i
$91$		−	0.499974i		−	0.0524115i
$92$	1.85376	−	9.41082i	0.193268	−	0.981146i
$93$	−15.6670	+	15.6670i	−1.62459	+	1.62459i
$94$	−7.59334	−	7.60650i	−0.783193	−	0.784551i
$95$	−3.76170	+	15.4865i	−0.385942	+	1.58888i
$96$	−5.36456	−	14.5754i	−0.547518	−	1.48759i
$97$	9.61022	−	0.687336i	0.975770	−	0.0697884i	0.425662	−	0.904882i	$-0.360041\pi$
$97$	9.61022	−	0.687336i	0.975770	−	0.0697884i	0.550108	+	0.835094i	$0.314587\pi$
$98$	3.81963	−	8.34468i	0.385840	−	0.842940i
$99$	18.3634	−	11.8014i	1.84559	−	1.18609i
$100$	4.98001	+	8.67176i	0.498001	+	0.867176i
$101$	−8.20088	−	9.46432i	−0.816018	−	0.941735i	0.183126	−	0.983089i	$-0.441378\pi$
$101$	−8.20088	−	9.46432i	−0.816018	−	0.941735i	−0.999145	+	0.0413541i	$0.986833\pi$
$102$	−6.64250	+	7.65245i	−0.657705	+	0.757706i
$103$	1.96128	−	1.46819i	0.193250	−	0.144665i	−0.498271	−	0.867021i	$-0.666032\pi$
$103$	1.96128	−	1.46819i	0.193250	−	0.144665i	0.691522	+	0.722356i	$0.256941\pi$
$104$	−0.415625	−	1.93478i	−0.0407554	−	0.189721i
$105$	4.07240	+	1.63170i	0.397426	+	0.159238i
$106$	18.3259	+	4.00318i	1.77997	+	0.388823i
$107$	5.49564	+	2.04977i	0.531283	+	0.198158i	0.600766	−	0.799425i	$-0.294862\pi$
$107$	5.49564	+	2.04977i	0.531283	+	0.198158i	−0.0694830	+	0.997583i	$0.522135\pi$
$108$	−4.06062	+	7.40594i	−0.390733	+	0.712637i
$109$	1.05669	−	3.59875i	0.101212	−	0.344698i	−0.893281	−	0.449499i	$-0.851602\pi$
$109$	1.05669	−	3.59875i	0.101212	−	0.344698i	0.994493	+	0.104801i	$0.0334206\pi$
$110$	−11.9456	−	9.41641i	−1.13896	−	0.897819i
$111$	4.74699	+	16.1668i	0.450565	+	1.53448i
$112$	−0.617269	+	2.79096i	−0.0583264	+	0.263721i
$113$	−3.82876	−	2.86617i	−0.360179	−	0.269627i	0.403827	−	0.914835i	$-0.367680\pi$
$113$	−3.82876	−	2.86617i	−0.360179	−	0.269627i	−0.764007	+	0.645208i	$0.776771\pi$
$114$	16.5649	+	22.1681i	1.55145	+	2.07623i
$115$	8.08589	+	7.04403i	0.754013	+	0.656859i
$116$	−0.147848	+	0.500316i	−0.0137273	+	0.0464532i
$117$	−1.90278	+	2.54182i	−0.175912	+	0.234991i
$118$	−3.29236	+	5.11327i	−0.303086	+	0.470714i
$119$	1.78940	−	0.525415i	0.164034	−	0.0481647i
$120$	17.1157	+	2.92895i	1.56244	+	0.267375i
$121$	11.6449	+	3.41925i	1.05863	+	0.310841i
$122$	−4.90028	+	2.23275i	−0.443650	+	0.202144i
$123$	−0.897606	+	2.40657i	−0.0809344	+	0.216993i
$124$	14.6929	−	6.67928i	1.31946	−	0.599817i
$125$	−11.1803	−	0.00963283i	−1.00000	−	0.000861586i
$126$	4.02714	−	2.19446i	0.358766	−	0.195498i
$127$	−0.636631	−	0.850440i	−0.0564919	−	0.0754643i	0.771406	−	0.636344i	$-0.219554\pi$
$127$	−0.636631	−	0.850440i	−0.0564919	−	0.0754643i	−0.827897	+	0.560879i	$0.810463\pi$
$128$	−0.0685849	+	11.3135i	−0.00606210	+	0.999982i
$129$	21.5138	−	18.6418i	1.89418	−	1.64132i
$130$	2.10667	+	0.676107i	0.184767	+	0.0592985i
$131$	−3.74074	−	5.82071i	−0.326830	−	0.508558i	0.638489	−	0.769631i	$-0.279560\pi$
$131$	−3.74074	−	5.82071i	−0.326830	−	0.508558i	−0.965319	+	0.261073i	$0.915924\pi$
$132$	−25.8187	+	5.56969i	−2.24723	+	0.484779i
$133$	−0.363336	−	5.08010i	−0.0315052	−	0.440501i
$134$	−4.66046	+	6.21443i	−0.402603	+	0.536845i
$135$	−4.91248	−	8.06464i	−0.422799	−	0.694093i
$136$	6.48779	−	3.52075i	0.556323	−	0.301902i
$137$	11.1392	+	11.1392i	0.951689	+	0.951689i	0.998886	−	0.0471971i	$-0.0150289\pi$
$137$	11.1392	+	11.1392i	0.951689	+	0.951689i	−0.0471971	+	0.998886i	$0.515029\pi$
$138$	18.3734	−	3.02871i	1.56405	−	0.257821i
$139$	−3.96625			−0.336413			−0.168207	−	0.985752i	$-0.553798\pi$
$139$	−3.96625			−0.336413			−0.168207	+	0.985752i	$0.553798\pi$
$140$	−2.36038	−	2.15445i	−0.199489	−	0.182084i
$141$	8.66809	−	18.9805i	0.729985	−	1.59844i
$142$	0.600093	+	4.19955i	0.0503586	+	0.352418i
$143$	−3.35679	+	0.240083i	−0.280709	+	0.0200767i
$144$	13.7599	−	11.8398i	1.14666	−	0.986649i
$145$	−0.402390	−	0.422257i	−0.0334167	−	0.0350665i
$146$	−11.3190	−	6.19339i	−0.936769	−	0.512568i
$147$	17.7715	+	1.27105i	1.46577	+	0.104834i
$148$	0.896807	−	12.2410i	0.0737171	−	1.00620i
$149$	−7.84795	−	1.12836i	−0.642929	−	0.0924393i	−0.186864	−	0.982386i	$-0.559832\pi$
$149$	−7.84795	−	1.12836i	−0.642929	−	0.0924393i	−0.456065	+	0.889947i	$0.650742\pi$
$150$	−12.3823	+	14.9528i	−1.01101	+	1.22089i
$151$	7.30843	−	11.3721i	0.594752	−	0.925452i	−0.405185	−	0.914235i	$-0.632793\pi$
$151$	7.30843	−	11.3721i	0.594752	−	0.925452i	0.999937	−	0.0112171i	$-0.00357059\pi$
$152$	−5.62908	−	19.3568i	−0.456579	−	1.57004i
$153$	−11.0967	−	4.13887i	−0.897118	−	0.334608i
$154$	4.55306	+	1.70270i	0.366896	+	0.137207i
$155$	−1.72043	+	17.9627i	−0.138188	+	1.44279i
$156$	3.23560	−	2.07148i	0.259055	−	0.165852i
$157$	19.5004	+	10.6480i	1.55630	+	0.849803i	0.999821	+	0.0189402i	$0.00602921\pi$
$157$	19.5004	+	10.6480i	1.55630	+	0.849803i	0.556477	+	0.830863i	$0.312153\pi$
$158$	−0.957933	+	1.48774i	−0.0762091	+	0.118358i
$159$	5.18268	+	36.0464i	0.411014	+	2.85866i
$160$	−10.9251	−	6.37507i	−0.863708	−	0.503993i
$161$	−3.14721	−	1.35651i	−0.248035	−	0.106908i
$162$	2.82691	+	0.408948i	0.222103	+	0.0321300i
$163$	−11.8449	+	15.8229i	−0.927764	+	1.23935i	0.0429416	+	0.999078i	$0.486327\pi$
$163$	−11.8449	+	15.8229i	−0.927764	+	1.23935i	−0.970706	+	0.240271i	$0.922764\pi$
$164$	1.22771	−	1.41191i	0.0958682	−	0.110251i
$165$	8.99962	−	28.1254i	0.700619	−	2.18956i
$166$	−6.98157	−	0.505409i	−0.541875	−	0.0392273i
$167$	−19.1069	+	10.4332i	−1.47854	+	0.807343i	−0.997589	−	0.0694058i	$-0.977890\pi$
$167$	−19.1069	+	10.4332i	−1.47854	+	0.807343i	−0.480949	+	0.876748i	$0.659708\pi$
$168$	−5.49488	+	0.775478i	−0.423939	+	0.0598294i
$169$	−11.3799	+	5.19704i	−0.875380	+	0.399773i
$170$	−0.205912	+	8.25024i	−0.0157928	+	0.632765i
$171$	−17.4865	+	27.2095i	−1.33723	+	2.08077i
$172$	−19.4416	+	7.21302i	−1.48241	+	0.549988i
$173$	−3.49630	−	4.67051i	−0.265819	−	0.355092i	0.647695	−	0.761900i	$-0.275733\pi$
$173$	−3.49630	−	4.67051i	−0.265819	−	0.355092i	−0.913514	+	0.406807i	$0.866642\pi$
$174$	−1.01032	+	0.0713803i	−0.0765923	+	0.00541132i
$175$	3.40397	−	1.08598i	0.257316	−	0.0820921i
$176$	19.0347	+	2.80412i	1.43480	+	0.211368i
$177$	−11.5369	−	2.50971i	−0.867169	−	0.188641i
$178$	7.98756	−	17.4503i	0.598693	−	1.30796i
$179$	−2.32483	+	2.68300i	−0.173766	+	0.200537i	−0.835952	−	0.548803i	$-0.815084\pi$
$179$	−2.32483	+	2.68300i	−0.173766	+	0.200537i	0.662185	+	0.749340i	$0.269629\pi$
$180$	3.80064	+	19.9361i	0.283283	+	1.48595i
$181$	−4.80743	+	10.5268i	−0.357333	+	0.782451i	0.642536	+	0.766256i	$0.277882\pi$
$181$	−4.80743	+	10.5268i	−0.357333	+	0.782451i	−0.999869	+	0.0161949i	$0.994845\pi$
$182$	−0.707069		0.000612336i	−0.0524114		4.53894e-5i
$183$	−7.39240	−	7.39240i	−0.546462	−	0.546462i
$184$	−13.3066	−	2.63314i	−0.980978	−	0.194118i
$185$	11.3621	+	7.69486i	0.835359	+	0.565737i
$186$	22.1373	+	22.1756i	1.62318	+	1.62600i
$187$	−4.38686	−	11.7616i	−0.320799	−	0.860095i
$188$	−10.7665	+	10.7293i	−0.785229	+	0.782513i
$189$	2.28070	+	1.97623i	0.165896	+	0.143750i
$190$	21.8966	+	5.33881i	1.58855	+	0.387318i
$191$	1.95023	+	3.03461i	0.141113	+	0.219577i	0.904615	−	0.426229i	$-0.140158\pi$
$191$	1.95023	+	3.03461i	0.141113	+	0.219577i	−0.763502	+	0.645805i	$0.776522\pi$
$192$	−20.6193	+	7.56878i	−1.48807	+	0.546230i
$193$	3.95011	+	0.282518i	0.284335	+	0.0203361i	0.212778	−	0.977100i	$-0.431749\pi$
$193$	3.95011	+	0.282518i	0.284335	+	0.0203361i	0.0715568	+	0.997437i	$0.477203\pi$
$194$	−0.960270	−	13.5917i	−0.0689434	−	0.975830i
$195$	0.203150	+	4.29056i	0.0145479	+	0.307254i
$196$	−11.7965	−	5.41198i	−0.842606	−	0.386570i
$197$	−2.32506	−	10.6881i	−0.165654	−	0.761497i	−0.982742	−	0.184984i	$-0.940777\pi$
$197$	−2.32506	−	10.6881i	−0.165654	−	0.761497i	0.817088	−	0.576513i	$-0.195587\pi$
$198$	−16.6673	−	25.9842i	−1.18449	−	1.84662i
$199$	−2.50533	−	5.48591i	−0.177598	−	0.388886i	0.799808	−	0.600256i	$-0.204935\pi$
$199$	−2.50533	−	5.48591i	−0.177598	−	0.388886i	−0.977406	+	0.211370i	$0.932207\pi$
$200$	12.2698	−	7.03218i	0.867607	−	0.497250i
$201$	−14.4696	−	4.24867i	−1.02061	−	0.299678i
$202$	−13.3946	+	11.5862i	−0.942442	+	0.815202i
$203$	0.163604	+	0.0893344i	0.0114827	+	0.00627004i
$204$	10.8141	+	9.40328i	0.757136	+	0.658361i
$205$	0.683618	+	1.97702i	0.0477459	+	0.138081i
$206$	−2.07394	−	2.77546i	−0.144498	−	0.193376i
$207$	10.8375	+	18.8739i	0.753261	+	1.31183i
$208$	−2.73671	+	0.585412i	−0.189756	+	0.0405911i
$209$	−33.9330	+	4.87884i	−2.34720	+	0.337476i
$210$	2.31256	−	5.75724i	0.159582	−	0.397288i
$211$	−5.06714	−	17.2571i	−0.348836	−	1.18803i	−0.927926	−	0.372764i	$-0.878410\pi$
$211$	−5.06714	−	17.2571i	−0.348836	−	1.18803i	0.579090	−	0.815264i	$-0.303408\pi$
$212$	5.68380	−	25.9118i	0.390365	−	1.77963i
$213$	−7.22844	+	3.94703i	−0.495285	+	0.270446i
$214$	2.90554	−	7.76949i	0.198618	−	0.531112i
$215$	3.85120	−	22.8621i	0.262650	−	1.55918i
$216$	10.4686	+	5.75165i	0.712299	+	0.391350i
$217$	−1.22581	−	5.63497i	−0.0832136	−	0.382527i
$218$	−5.08811	−	1.49879i	−0.344610	−	0.101511i
$219$	3.56489	−	24.7944i	0.240893	−	1.67545i
$220$	−13.3314	+	16.8820i	−0.898805	+	1.13819i
$221$	1.19573	+	1.37995i	0.0804338	+	0.0928255i
$222$	22.8691	−	6.69346i	1.53487	−	0.449236i
$223$	−4.84080	−	1.05305i	−0.324164	−	0.0705176i	0.0475385	−	0.998869i	$-0.484862\pi$
$223$	−4.84080	−	1.05305i	−0.324164	−	0.0705176i	−0.371703	+	0.928352i	$0.621226\pi$
$224$	3.94625	+	0.876368i	0.263670	+	0.0585548i
$225$	−21.4384	−	7.43371i	−1.42923	−	0.495580i
$226$	−4.05807	+	5.41117i	−0.269939	+	0.359945i
$227$	−1.09881	−	2.94602i	−0.0729305	−	0.195534i	0.895370	−	0.445324i	$-0.146911\pi$
$227$	−1.09881	−	2.94602i	−0.0729305	−	0.195534i	−0.968300	+	0.249789i	$0.919639\pi$
$228$	31.3707	−	23.3992i	2.07758	−	1.54965i
$229$		−	5.30243i		−	0.350395i	−0.984533	−	0.175197i	$-0.943944\pi$
$229$		−	5.30243i		−	0.350395i	0.984533	−	0.175197i	$-0.0560563\pi$
$230$	9.97166	−	11.4265i	0.657512	−	0.753444i
$231$			9.43723i			0.620924i
$232$	0.707372	+	0.209701i	0.0464413	+	0.0137675i
$233$	−0.105509	−	0.282881i	−0.00691213	−	0.0185321i	0.933448	−	0.358713i	$-0.116784\pi$
$233$	−0.105509	−	0.282881i	−0.00691213	−	0.0185321i	−0.940360	+	0.340181i	$0.889512\pi$
$234$	3.59234	+	2.69405i	0.234839	+	0.176116i
$235$	−4.39364	−	16.4162i	−0.286610	−	1.07087i
$236$	7.22722	+	4.66236i	0.470452	+	0.303494i
$237$	−3.35675	−	0.730216i	−0.218044	−	0.0474326i
$238$	−0.740857	−	2.53123i	−0.0480226	−	0.164076i
$239$	−15.2710	−	17.6237i	−0.987799	−	1.13998i	−0.990154	−	0.139984i	$-0.955295\pi$
$239$	−15.2710	−	17.6237i	−0.987799	−	1.13998i	0.00235445	−	0.999997i	$-0.499251\pi$
$240$	4.16312	−	24.2016i	0.268728	−	1.56221i
$241$	3.04637	−	21.1880i	0.196234	−	1.36484i	−0.618857	−	0.785504i	$-0.712404\pi$
$241$	3.04637	−	21.1880i	0.196234	−	1.36484i	0.815091	−	0.579333i	$-0.196687\pi$
$242$	4.84982	−	16.4642i	0.311758	−	1.05836i
$243$	3.87177	+	17.7982i	0.248374	+	1.14176i
$244$	3.15159	+	6.93277i	0.201760	+	0.443825i
$245$	11.8224	−	8.41359i	0.755307	−	0.537525i
$246$	3.40231	+	1.27235i	0.216923	+	0.0811223i
$247$	4.37659	−	2.38980i	0.278476	−	0.152059i
$248$	−9.42793	−	20.7870i	−0.598674	−	1.31998i
$249$	−3.82862	−	13.0391i	−0.242629	−	0.826317i
$250$	−0.0273158	+	15.8114i	−0.00172761	+	0.999999i
$251$	−2.27348	+	0.326877i	−0.143501	+	0.0206323i	−0.213691	−	0.976901i	$-0.568549\pi$
$251$	−2.27348	+	0.326877i	−0.143501	+	0.0206323i	0.0701901	+	0.997534i	$0.477639\pi$
$252$	−3.09850	−	5.69792i	−0.195187	−	0.358935i
$253$	−7.59629	+	21.7816i	−0.477575	+	1.36940i
$254$	−1.20348	+	0.899291i	−0.0755132	+	0.0564265i
$255$	−15.1424	+	5.23596i	−0.948253	+	0.327888i
$256$	15.9996	+	0.110850i	0.999976	+	0.00692811i
$257$	−17.4569	−	9.53216i	−1.08893	−	0.594600i	−0.168576	−	0.985689i	$-0.553917\pi$
$257$	−17.4569	−	9.53216i	−1.08893	−	0.594600i	−0.920353	+	0.391089i	$0.872099\pi$
$258$	−26.3371	−	30.4479i	−1.63968	−	1.89560i
$259$	−4.20780	−	1.23552i	−0.261460	−	0.0767715i
$260$	0.958739	−	2.97845i	0.0594585	−	0.184715i
$261$	−0.491761	−	1.07681i	−0.0304392	−	0.0666526i
$262$	−8.23631	+	5.28308i	−0.508841	+	0.326390i
$263$	4.76762	+	21.9164i	0.293984	+	1.35142i	0.852847	+	0.522162i	$0.174874\pi$
$263$	4.76762	+	21.9164i	0.293984	+	1.35142i	−0.558863	+	0.829260i	$0.688762\pi$
$264$	7.84511	+	36.5199i	0.482833	+	2.24765i
$265$	21.9405	+	19.9568i	1.34780	+	1.22594i
$266$	−7.18479	+	0.507613i	−0.440528	+	0.0311237i
$267$	37.1637	+	2.65800i	2.27438	+	0.162667i
$268$	8.78281	+	6.59850i	0.536496	+	0.403068i
$269$	−11.2767	−	17.5468i	−0.687551	−	1.06985i	−0.993054	−	0.117659i	$-0.962461\pi$
$269$	−11.2767	−	17.5468i	−0.687551	−	1.06985i	0.305504	−	0.952191i	$-0.401175\pi$
$270$	−11.4111	+	6.93741i	−0.694459	+	0.422197i
$271$	−8.39578	−	7.27499i	−0.510008	−	0.441924i	0.361453	−	0.932391i	$-0.382281\pi$
$271$	−8.39578	−	7.27499i	−0.510008	−	0.441924i	−0.871460	+	0.490466i	$0.836826\pi$
$272$	−4.97115	−	9.17943i	−0.301420	−	0.556585i
$273$	−0.479713	−	1.28616i	−0.0290336	−	0.0778420i
$274$	15.7669	−	15.7396i	0.952512	−	0.950864i
$275$	−8.92574	−	22.3326i	−0.538242	−	1.34671i
$276$	−4.26074	−	25.9876i	−0.256466	−	1.56427i
$277$	1.20755	+	1.20755i	0.0725544	+	0.0725544i	0.742453	−	0.669898i	$-0.233662\pi$
$277$	1.20755	+	1.20755i	0.0725544	+	0.0725544i	−0.669898	+	0.742453i	$0.733662\pi$
$278$	−0.00485762	+	5.60913i	−0.000291341	+	0.336413i
$279$	−15.2135	+	33.3128i	−0.910806	+	1.99439i
$280$	−3.04975	+	3.33545i	−0.182257	+	0.199331i
$281$	−13.7597	+	15.8796i	−0.820837	+	0.947297i	−0.999328	−	0.0366449i	$-0.988333\pi$
$281$	−13.7597	+	15.8796i	−0.820837	+	0.947297i	0.178491	+	0.983942i	$0.442878\pi$
$282$	−26.8318	−	12.2818i	−1.59781	−	0.731369i
$283$	25.9413	+	5.64319i	1.54205	+	0.335453i	0.901608	−	0.432554i	$-0.142387\pi$
$283$	25.9413	+	5.64319i	1.54205	+	0.335453i	0.640442	+	0.768006i	$0.278751\pi$
$284$	5.93979	−	0.843515i	0.352462	−	0.0500534i
$285$	5.18215	+	43.4477i	0.306964	+	2.57362i
$286$	0.335417	+	4.74752i	0.0198336	+	0.280727i
$287$	−0.400629	−	0.535178i	−0.0236484	−	0.0315905i
$288$	−16.7271	−	19.4739i	−0.985656	−	1.14751i
$289$	5.50865	−	8.57163i	0.324038	−	0.504213i
$290$	−0.597654	+	0.568548i	−0.0350955	+	0.0333863i
$291$	24.0624	−	10.9889i	1.41056	−	0.644182i
$292$	−8.77263	+	15.9999i	−0.513379	+	0.936325i
$293$	−2.45706	+	1.34165i	−0.143543	+	0.0783803i	−0.549415	−	0.835549i	$-0.685150\pi$
$293$	−2.45706	+	1.34165i	−0.143543	+	0.0783803i	0.405873	+	0.913930i	$0.366968\pi$
$294$	1.81929	−	25.1312i	0.106103	−	1.46568i
$295$	−8.54809	+	4.40374i	−0.497689	+	0.256396i
$296$	−17.3103	−	1.28327i	−1.00614	−	0.0745885i
$297$	12.1732	−	16.2614i	0.706359	−	0.943585i
$298$	−1.60536	+	11.0973i	−0.0929960	+	0.642849i
$299$	−0.0719332	−	3.35465i	−0.00416000	−	0.194005i
$300$	21.1312	+	17.5295i	1.22001	+	1.01207i
$301$	1.05444	+	7.33376i	0.0607767	+	0.422711i
$302$	−16.0737	−	10.3496i	−0.924936	−	0.595553i
$303$	−30.1772	−	16.4780i	−1.73364	−	0.946637i
$304$	−27.3815	+	7.93702i	−1.57044	+	0.455219i
$305$	−8.47560	−	0.811778i	−0.485311	−	0.0464823i
$306$	−5.86684	+	15.6881i	−0.335385	+	0.896828i
$307$	−14.4093	−	5.37438i	−0.822380	−	0.306732i	−0.0971770	−	0.995267i	$-0.530981\pi$
$307$	−14.4093	−	5.37438i	−0.822380	−	0.306732i	−0.725203	+	0.688535i	$0.758254\pi$
$308$	2.41355	−	6.43691i	0.137525	−	0.366777i
$309$	3.63660	−	5.65866i	0.206879	−	0.321910i
$310$	25.4009	+	2.45506i	1.44267	+	0.139438i
$311$	−4.74674	−	0.682478i	−0.269163	−	0.0386998i	0.00641189	−	0.999979i	$-0.497959\pi$
$311$	−4.74674	−	0.682478i	−0.269163	−	0.0386998i	−0.275575	+	0.961280i	$0.588868\pi$
$312$	−2.92556	−	4.57837i	−0.165627	−	0.259199i
$313$	−24.2881	−	1.73712i	−1.37284	−	0.0981877i	−0.634662	−	0.772790i	$-0.718861\pi$
$313$	−24.2881	−	1.73712i	−1.37284	−	0.0981877i	−0.738182	+	0.674602i	$0.764315\pi$
$314$	15.0824	−	27.5646i	0.851150	−	1.55556i
$315$	7.24936	+	0.174650i	0.408455	+	0.00984042i
$316$	2.10281	+	1.35654i	0.118292	+	0.0763116i
$317$	15.3146	−	1.09532i	0.860153	−	0.0615193i	0.365709	−	0.930729i	$-0.380826\pi$
$317$	15.3146	−	1.09532i	0.860153	−	0.0615193i	0.494443	+	0.869210i	$0.335372\pi$
$318$	50.9836	−	7.28527i	2.85902	−	0.408538i
$319$	0.521225	−	1.14132i	0.0291830	−	0.0639019i
$320$	−9.02908	+	15.4427i	−0.504741	+	0.863271i
$321$	16.1040			0.898838
$322$	−1.92225	+	4.44916i	−0.107123	+	0.247942i
$323$	13.1524	+	13.1524i	0.731817	+	0.731817i
$324$	0.581802	−	3.99736i	0.0323223	−	0.222075i
$325$	2.35166	+	2.58990i	0.130447	+	0.143662i
$326$	22.3625	+	16.7706i	1.23854	+	0.928837i
$327$	−0.734633	−	10.2715i	−0.0406253	−	0.568016i
$328$	−1.99523	−	1.73798i	−0.110168	−	0.0959636i
$329$	2.93617	+	4.56877i	0.161876	+	0.251885i
$330$	−39.7643	−	12.7618i	−2.18895	−	0.702515i
$331$	−25.0283	+	21.6872i	−1.37568	+	1.19203i	−0.416536	+	0.909119i	$0.636756\pi$
$331$	−25.0283	+	21.6872i	−1.37568	+	1.19203i	−0.959145	+	0.282916i	$0.908698\pi$
$332$	−0.723306	+	9.87280i	−0.0396966	+	0.541840i
$333$	16.6900	+	22.2952i	0.914604	+	1.22177i
$334$	14.7313	+	27.0340i	0.806062	+	1.47924i
$335$	−11.2917	+	4.83157i	−0.616934	+	0.263977i
$336$	1.08996	+	7.77187i	0.0594623	+	0.423990i
$337$	−1.66390	+	4.46110i	−0.0906386	+	0.243012i	−0.974357	−	0.225007i	$-0.927759\pi$
$337$	−1.66390	+	4.46110i	−0.0906386	+	0.243012i	0.883718	+	0.468019i	$0.155032\pi$
$338$	7.33579	+	16.1000i	0.399014	+	0.875726i
$339$	−12.5993	−	3.69950i	−0.684302	−	0.200929i
$340$	11.6673	+	0.301308i	0.632751	+	0.0163407i
$341$	−37.2442	+	10.9359i	−2.01689	+	0.592212i
$342$	38.4587	+	24.7630i	2.07961	+	1.33903i
$343$	−5.77673	+	7.71681i	−0.311914	+	0.416669i
$344$	10.1769	+	27.5034i	0.548704	+	1.48289i
$345$	27.5592	+	10.3622i	1.48374	+	0.557885i
$346$	−6.60938	+	4.93879i	−0.355323	+	0.265511i
$347$	22.0150	+	16.4802i	1.18182	+	0.884703i	0.995213	−	0.0977307i	$-0.0311584\pi$
$347$	22.0150	+	16.4802i	1.18182	+	0.884703i	0.186612	+	0.982434i	$0.440249\pi$
$348$	0.0997095	+	1.42890i	0.00534499	+	0.0765970i
$349$	1.10816	+	3.77406i	0.0593186	+	0.202021i	0.983821	−	0.179157i	$-0.0573369\pi$
$349$	1.10816	+	3.77406i	0.0593186	+	0.202021i	−0.924502	+	0.381177i	$0.875519\pi$
$350$	−1.53163	−	4.81527i	−0.0818692	−	0.257387i
$351$	−0.832429	+	2.83499i	−0.0444318	+	0.151321i
$352$	3.98893	−	26.9157i	0.212611	−	1.43461i
$353$	16.9976	+	6.33978i	0.904691	+	0.337432i	0.758385	−	0.651807i	$-0.225989\pi$
$353$	16.9976	+	6.33978i	0.904691	+	0.337432i	0.146306	+	0.989239i	$0.453261\pi$
$354$	−3.56339	+	16.3126i	−0.189392	+	0.867005i
$355$	−2.49472	+	6.22633i	−0.132406	+	0.330459i
$356$	−24.6687	−	11.3175i	−1.30744	−	0.599826i
$357$	4.09903	−	3.06849i	0.216944	−	0.162402i
$358$	3.79149	+	3.29110i	0.200386	+	0.173940i
$359$	18.2297	+	21.0382i	0.962125	+	1.11035i	0.993837	+	0.110854i	$0.0353587\pi$
$359$	18.2297	+	21.0382i	0.962125	+	1.11035i	−0.0317116	+	0.999497i	$0.510096\pi$
$360$	28.1986	−	5.35049i	1.48619	−	0.281996i
$361$	26.7489	−	17.1905i	1.40784	−	0.904763i
$362$	14.8812	+	6.81162i	0.782141	+	0.358011i
$363$	33.2367	−	2.37714i	1.74448	−	0.124767i
$364$	−0.00173195	+	0.999946i	−9.07787e−5	+	0.0524114i
$365$	−10.6130	−	17.4230i	−0.555510	−	0.911960i
$366$	−10.4635	+	10.4454i	−0.546935	+	0.545988i
$367$	13.1040	−	13.1040i	0.684023	−	0.684023i	−0.276881	−	0.960904i	$-0.589301\pi$
$367$	13.1040	−	13.1040i	0.684023	−	0.684023i	0.960904	+	0.276881i	$0.0893007\pi$
$368$	−3.74012	+	18.8152i	−0.194967	+	0.980810i
$369$			4.24549i			0.221012i
$370$	10.8961	−	16.0590i	0.566460	−	0.834868i
$371$	−8.62187	−	3.93748i	−0.447625	−	0.204424i
$372$	31.3882	−	31.2796i	1.62740	−	1.62177i
$373$	−2.00479	−	28.0306i	−0.103804	−	1.45137i	−0.736222	−	0.676741i	$-0.763392\pi$
$373$	−2.00479	−	28.0306i	−0.103804	−	1.45137i	0.632418	−	0.774628i	$-0.282063\pi$
$374$	−16.6388	+	6.18955i	−0.860372	+	0.320054i
$375$	−28.7702	+	10.7025i	−1.48569	+	0.552675i
$376$	15.1603	+	15.2393i	0.781833	+	0.785906i
$377$	−0.0130198	+	0.182041i	−0.000670556	+	0.00937560i
$378$	2.79761	−	3.22297i	0.143894	−	0.165772i
$379$	4.98238	−	34.6532i	0.255928	−	1.78002i	−0.305200	−	0.952288i	$-0.598723\pi$
$379$	4.98238	−	34.6532i	0.255928	−	1.78002i	0.561128	−	0.827729i	$-0.310368\pi$
$380$	7.57703	−	30.9600i	0.388693	−	1.58821i
$381$	−2.45368	−	1.57689i	−0.125706	−	0.0807864i
$382$	4.29397	−	2.75432i	0.219699	−	0.140923i
$383$	−3.34428	+	8.96637i	−0.170885	+	0.458160i	−0.993956	−	0.109778i	$-0.964986\pi$
$383$	−3.34428	+	8.96637i	−0.170885	+	0.458160i	0.823071	+	0.567938i	$0.192259\pi$
$384$	10.6786	+	29.1693i	0.544941	+	1.48854i
$385$	4.89186	+	5.92819i	0.249312	+	0.302129i
$386$	0.404378	−	5.58595i	0.0205823	−	0.284318i
$387$	22.5499	−	41.2971i	1.14628	−	2.09925i
$388$	−19.2228	+	1.34138i	−0.975889	+	0.0680983i
$389$	7.27003	−	1.04527i	0.368605	−	0.0529975i	0.0444766	−	0.999010i	$-0.485838\pi$
$389$	7.27003	−	1.04527i	0.368605	−	0.0529975i	0.324129	+	0.946013i	$0.394929\pi$
$390$	6.06802	−	0.282042i	0.307266	−	0.0142818i
$391$	11.9307	−	3.78280i	0.603360	−	0.191305i
$392$	−7.66815	+	16.6761i	−0.387300	+	0.842270i
$393$	−15.2077	−	11.3844i	−0.767129	−	0.574266i
$394$	−15.1181	+	3.27504i	−0.761640	+	0.164994i
$395$	−2.48712	+	1.28130i	−0.125141	+	0.0644691i
$396$	−36.7676	+	23.5392i	−1.84764	+	1.18289i
$397$	13.3628	+	24.4721i	0.670658	+	1.22822i	0.962378	+	0.271715i	$0.0875908\pi$
$397$	13.3628	+	24.4721i	0.670658	+	1.22822i	−0.291719	+	0.956504i	$0.594227\pi$
$398$	−7.76132	+	3.53635i	−0.389040	+	0.177261i
$399$	−5.80891	−	12.7197i	−0.290809	−	0.636783i
$400$	−9.92997	−	17.3608i	−0.496499	−	0.868038i
$401$	−29.3148	−	18.8394i	−1.46391	−	0.940797i	−0.998446	−	0.0557298i	$-0.982251\pi$
$401$	−29.3148	−	18.8394i	−1.46391	−	0.940797i	−0.465463	−	0.885067i	$-0.654112\pi$
$402$	−6.02625	+	20.4580i	−0.300562	+	1.02035i
$403$	4.51997	−	3.38361i	0.225156	−	0.168550i
$404$	16.3690	+	18.9570i	0.814386	+	0.943147i
$405$	3.54923	+	2.79279i	0.176363	+	0.138775i
$406$	0.126538	−	0.231261i	0.00627999	−	0.0114773i
$407$	−6.27467	+	28.8442i	−0.311024	+	1.42975i
$408$	13.3115	−	15.2819i	0.659017	−	0.756565i
$409$	20.1766	+	17.4831i	0.997666	+	0.864483i	0.990778	−	0.135494i	$-0.0432620\pi$
$409$	20.1766	+	17.4831i	0.997666	+	0.864483i	0.00688804	+	0.999976i	$0.497807\pi$
$410$	2.79677	−	0.964360i	0.138122	−	0.0476263i
$411$	39.3430	+	17.9674i	1.94065	+	0.886264i
$412$	−3.92763	+	2.92959i	−0.193501	+	0.144330i
$413$	2.17294	−	2.17294i	0.106923	−	0.106923i
$414$	26.7050	−	15.3035i	1.31248	−	0.752125i
$415$	−9.16393	−	6.20617i	−0.449840	−	0.304649i
$416$	0.824546	+	3.87100i	0.0404267	+	0.189791i
$417$	−10.2030	+	3.80553i	−0.499644	+	0.186358i
$418$	6.85815	+	47.9945i	0.335443	+	2.34749i
$419$	9.04149	−	10.4344i	0.441706	−	0.509755i	−0.490621	−	0.871373i	$-0.663230\pi$
$419$	9.04149	−	10.4344i	0.441706	−	0.509755i	0.932326	+	0.361618i	$0.117775\pi$
$420$	−8.13914	−	3.27750i	−0.397149	−	0.159926i
$421$	−7.45919	+	4.79373i	−0.363538	+	0.233632i	−0.709639	−	0.704565i	$-0.751142\pi$
$421$	−7.45919	+	4.79373i	−0.363538	+	0.233632i	0.346101	+	0.938197i	$0.387506\pi$
$422$	−24.4114	+	7.14488i	−1.18833	+	0.347807i
$423$	2.46045	−	34.4016i	0.119631	−	1.67266i
$424$	−36.6379	−	8.06983i	−1.77929	−	0.391906i
$425$	−6.79790	+	11.1383i	−0.329747	+	0.540285i
$426$	5.57308	+	10.2274i	0.270017	+	0.495519i
$427$	2.65884	−	0.578394i	0.128670	−	0.0279905i
$428$	−10.9842	−	4.11856i	−0.530939	−	0.199078i
$429$	−8.40486	+	3.83837i	−0.405790	+	0.185318i
$430$	−32.3271	−	5.47441i	−1.55895	−	0.264000i
$431$	−6.96841	+	23.7322i	−0.335656	+	1.14314i	0.602843	+	0.797860i	$0.294035\pi$
$431$	−6.96841	+	23.7322i	−0.335656	+	1.14314i	−0.938499	+	0.345281i	$0.887784\pi$
$432$	8.14688	−	14.7978i	0.391967	−	0.711959i
$433$	1.06429	−	1.94910i	0.0511464	−	0.0936677i	−0.850855	−	0.525400i	$-0.823916\pi$
$433$	1.06429	−	1.94910i	0.0511464	−	0.0936677i	0.902002	+	0.431732i	$0.142097\pi$
$434$	−7.97055	+	1.72666i	−0.382599	+	0.0828823i
$435$	−1.44028	−	0.700155i	−0.0690560	−	0.0335698i
$436$	−2.12584	+	7.19383i	−0.101809	+	0.344522i
$437$	−3.16876	−	34.0335i	−0.151582	−	1.62804i
$438$	−35.0601	−	5.07188i	−1.67524	−	0.242344i
$439$	−3.80146	−	26.4397i	−0.181434	−	1.26190i	−0.853376	−	0.521295i	$-0.825449\pi$
$439$	−3.80146	−	26.4397i	−0.181434	−	1.26190i	0.671943	−	0.740603i	$-0.265460\pi$
$440$	23.8585	+	18.8742i	1.13741	+	0.899791i
$441$	28.2566	−	8.29689i	1.34555	−	0.395090i
$442$	1.95301	−	1.68933i	0.0928951	−	0.0803533i
$443$	−14.5097	−	26.5725i	−0.689376	−	1.26250i	−0.954479	−	0.298278i	$-0.903588\pi$
$443$	−14.5097	−	26.5725i	−0.689376	−	1.26250i	0.265103	−	0.964220i	$-0.414594\pi$
$444$	−9.43797	−	32.3499i	−0.447906	−	1.53526i
$445$	24.7229	−	17.5944i	1.17198	−	0.834055i
$446$	−1.49517	+	6.84464i	−0.0707983	+	0.324103i
$447$	−21.2712	+	4.62726i	−1.00609	+	0.218862i
$448$	1.24420	−	5.57977i	0.0587831	−	0.263619i
$449$	−19.6466	−	2.82475i	−0.927178	−	0.133308i	−0.337848	−	0.941201i	$-0.609699\pi$
$449$	−19.6466	−	2.82475i	−0.927178	−	0.133308i	−0.589330	+	0.807893i	$0.700608\pi$
$450$	−10.5391	+	30.3094i	−0.496818	+	1.42880i
$451$	−3.40077	+	2.94679i	−0.160136	+	0.138759i
$452$	7.64757	+	5.74560i	0.359712	+	0.270250i
$453$	7.88932	−	36.2666i	0.370673	−	1.70395i
$454$	−4.16765	+	1.55034i	−0.195597	+	0.0727612i
$455$	−0.968034	−	0.559265i	−0.0453821	−	0.0262188i
$456$	−33.0530	−	44.3936i	−1.54785	−	2.07892i
$457$	−2.42055	+	0.902817i	−0.113228	+	0.0422320i	−0.405440	−	0.914122i	$-0.632882\pi$
$457$	−2.42055	+	0.902817i	−0.113228	+	0.0422320i	0.292211	+	0.956354i	$0.405609\pi$
$458$	−7.49877	−	0.00649409i	−0.350395	−	0.000303449i
$459$	−11.0212			−0.514425
$460$	−16.1474	−	14.1161i	−0.752874	−	0.658164i
$461$	38.5807			1.79688			0.898442	−	0.439092i	$-0.144700\pi$
$461$	38.5807			1.79688			0.898442	+	0.439092i	$0.144700\pi$
$462$	13.3462	+	0.0115581i	0.620924	+	0.000537732i
$463$	−8.39957	+	3.13288i	−0.390361	+	0.145597i	−0.536978	−	0.843596i	$-0.680434\pi$
$463$	−8.39957	+	3.13288i	−0.390361	+	0.145597i	0.146617	+	0.989193i	$0.453162\pi$
$464$	0.297428	−	1.00012i	0.0138078	−	0.0464293i
$465$	12.8090	+	47.8589i	0.594004	+	2.21940i
$466$	−0.400183	+	0.148866i	−0.0185381	+	0.00689607i
$467$	3.56990	−	16.4106i	0.165195	−	0.759391i	−0.817762	−	0.575557i	$-0.804785\pi$
$467$	3.56990	−	16.4106i	0.165195	−	0.759391i	0.982957	−	0.183834i	$-0.0588509\pi$
$468$	3.81436	−	5.07704i	0.176319	−	0.234686i
$469$	2.96637	−	2.57037i	0.136974	−	0.118689i
$470$	−23.2213	+	6.19344i	−1.07112	+	0.285682i
$471$	60.3804	+	8.68138i	2.78218	+	0.400017i
$472$	6.60242	−	10.2151i	0.303901	−	0.470189i
$473$	48.7321	−	10.6010i	2.24071	−	0.487436i
$474$	−1.03679	+	4.74626i	−0.0476214	+	0.218003i
$475$	25.7767	+	24.6064i	1.18272	+	1.12902i
$476$	−3.58061	+	1.04463i	−0.164117	+	0.0478805i
$477$	28.8477	+	52.8306i	1.32085	+	2.41895i
$478$	−24.9423	+	21.5749i	−1.14084	+	0.986812i
$479$	−22.8791	+	6.71790i	−1.04537	+	0.306949i	−0.758946	−	0.651154i	$-0.774285\pi$
$479$	−22.8791	+	6.71790i	−1.04537	+	0.306949i	−0.286426	+	0.958102i	$0.592467\pi$
$480$	−34.2212	−	5.91718i	−1.56198	−	0.270081i
$481$	−0.611060	−	4.25001i	−0.0278619	−	0.193784i
$482$	−29.9606	−	4.33417i	−1.36467	−	0.197416i
$483$	−9.39760	−	0.469898i	−0.427606	−	0.0213811i
$484$	−23.2779	−	6.87884i	−1.05809	−	0.312674i
$485$	9.41909	−	19.3759i	0.427699	−	0.879813i
$486$	25.1752	−	5.45370i	1.14197	−	0.247385i
$487$	13.2426	−	24.2521i	0.600081	−	1.09897i	−0.384348	−	0.923188i	$-0.625574\pi$
$487$	13.2426	−	24.2521i	0.600081	−	1.09897i	0.984430	−	0.175779i	$-0.0562444\pi$
$488$	9.80827	−	4.44853i	0.444000	−	0.201375i
$489$	−15.2888	+	52.0687i	−0.691382	+	2.35463i
$490$	−11.8841	−	16.7297i	−0.536870	−	0.755772i
$491$	15.1752	−	6.93028i	0.684847	−	0.312759i	−0.0424335	−	0.999099i	$-0.513511\pi$
$491$	15.1752	−	6.93028i	0.684847	−	0.312759i	0.727281	+	0.686340i	$0.240784\pi$
$492$	1.80354	−	4.81003i	0.0813101	−	0.216853i
$493$	−0.665205	+	0.144707i	−0.0299593	+	0.00651726i
$494$	−3.37433	−	6.19236i	−0.151818	−	0.278608i
$495$	−2.30848	−	48.7557i	−0.103759	−	2.19140i
$496$	−29.4088	+	13.3076i	−1.32050	+	0.597531i
$497$	0.152921	−	2.13812i	0.00685947	−	0.0959079i
$498$	−18.4447	+	5.39851i	−0.826527	+	0.241913i
$499$	15.8660	−	10.1965i	0.710261	−	0.456457i	−0.134976	−	0.990849i	$-0.543096\pi$
$499$	15.8660	−	10.1965i	0.710261	−	0.456457i	0.845237	+	0.534392i	$0.179459\pi$
$500$	22.3606	+	0.0579952i	0.999997	+	0.00259362i
$501$	−39.1414	+	45.1715i	−1.74871	+	2.01812i
$502$	0.459489	+	3.21558i	0.0205080	+	0.143518i
$503$	16.6338	−	6.20409i	0.741665	−	0.276627i	0.0499046	−	0.998754i	$-0.484108\pi$
$503$	16.6338	−	6.20409i	0.741665	−	0.276627i	0.691760	+	0.722127i	$0.256836\pi$
$504$	−8.06187	+	4.37496i	−0.359104	+	0.194876i
$505$	−27.4980	+	5.29161i	−1.22364	+	0.235474i
$506$	30.7945	+	10.7695i	1.36898	+	0.478760i
$507$	−24.2880	+	24.2880i	−1.07867	+	1.07867i
$508$	1.27031	+	1.70308i	0.0563611	+	0.0755621i
$509$	−23.4432	−	10.7062i	−1.03910	−	0.474542i	−0.178564	−	0.983928i	$-0.557145\pi$
$509$	−23.4432	−	10.7062i	−1.03910	−	0.474542i	−0.860538	+	0.509386i	$0.829872\pi$
$510$	7.38622	+	21.4210i	0.327067	+	0.948536i
$511$	4.92726	+	4.26949i	0.217969	+	0.188871i
$512$	0.176360	−	22.6267i	0.00779410	−	0.999970i
$513$	−6.39787	+	29.4105i	−0.282473	+	1.29851i
$514$	−13.5019	+	24.6760i	−0.595543	+	1.08841i
$515$	−0.648808	−	5.43967i	−0.0285899	−	0.239701i
$516$	−43.0920	+	37.2090i	−1.89702	+	1.63803i
$517$	29.2646	−	21.9072i	1.28705	−	0.963476i
$518$	−1.75244	+	5.94921i	−0.0769979	+	0.261393i
$519$	−13.4753	−	8.66007i	−0.591502	−	0.380135i
$520$	−4.21098	−	1.35951i	−0.184664	−	0.0596184i
$521$	13.2425	+	28.9971i	0.580167	+	1.27039i	0.941205	+	0.337837i	$0.109695\pi$
$521$	13.2425	+	28.9971i	0.580167	+	1.27039i	−0.361038	+	0.932551i	$0.617578\pi$
$522$	−1.52343	+	0.694135i	−0.0666789	+	0.0303815i
$523$	−8.06041	−	14.7615i	−0.352457	−	0.645477i	0.639958	−	0.768410i	$-0.278952\pi$
$523$	−8.06041	−	14.7615i	−0.352457	−	0.645477i	−0.992415	+	0.122933i	$0.960770\pi$
$524$	7.46131	+	11.6544i	0.325949	+	0.509123i
$525$	7.71460	−	6.05966i	0.336693	−	0.264465i
$526$	31.0003	−	6.71558i	1.35168	−	0.292813i
$527$	16.8599	+	12.6211i	0.734427	+	0.549785i
$528$	51.6565	−	11.0499i	2.24806	−	0.480886i
$529$	−21.3119	−	8.64894i	−0.926603	−	0.376041i
$530$	28.2500	−	31.0042i	1.22710	−	1.34673i
$531$	−19.3167	+	2.77732i	−0.838273	+	0.120525i
$532$	0.709073	+	10.1614i	0.0307422	+	0.440554i
$533$	0.313686	−	0.574474i	0.0135873	−	0.0248832i
$534$	3.80449	−	52.5541i	0.164636	−	2.27424i
$535$	10.1161	−	8.34764i	0.437356	−	0.360900i
$536$	9.34244	−	12.4127i	0.403532	−	0.536146i
$537$	−3.40626	+	9.13254i	−0.146991	+	0.394098i
$538$	−24.8288	+	15.9261i	−1.07044	+	0.686624i
$539$	26.2589	+	16.8756i	1.13105	+	0.726883i
$540$	9.79700	+	16.1463i	0.421596	+	0.694825i
$541$	−2.85008	+	19.8227i	−0.122535	+	0.852246i	0.832134	+	0.554575i	$0.187119\pi$
$541$	−2.85008	+	19.8227i	−0.122535	+	0.852246i	−0.954668	+	0.297671i	$0.903790\pi$
$542$	−10.2987	+	11.8645i	−0.442366	+	0.509625i
$543$	−2.26668	+	31.6924i	−0.0972726	+	1.36005i
$544$	−12.9878	+	7.01902i	−0.556845	+	0.300938i
$545$	−5.78580	−	6.07146i	−0.247836	−	0.260073i
$546$	−1.81949	+	0.676841i	−0.0778671	+	0.0289661i
$547$	−1.99177	−	27.8486i	−0.0851621	−	1.19072i	−0.842866	−	0.538123i	$-0.819134\pi$
$547$	−1.99177	−	27.8486i	−0.0851621	−	1.19072i	0.757704	−	0.652598i	$-0.226321\pi$
$548$	−22.2398	−	22.3170i	−0.950039	−	0.953335i
$549$	−15.7185	−	7.17840i	−0.670850	−	0.306367i
$550$	−31.5940	+	12.5955i	−1.34717	+	0.537076i
$551$			1.85914i			0.0792018i
$552$	−36.7572	+	5.99377i	−1.56449	+	0.255112i
$553$	0.632230	−	0.632230i	0.0268852	−	0.0268852i
$554$	1.70921	−	1.70625i	0.0726173	−	0.0724916i
$555$	36.6116	+	8.89301i	1.55407	+	0.377487i
$556$	7.93250	+	0.0137394i	0.336413	+	0.000582681i
$557$	11.0964	−	0.793632i	0.470171	−	0.0336273i	0.165756	−	0.986167i	$-0.446994\pi$
$557$	11.0964	−	0.793632i	0.470171	−	0.0336273i	0.304415	+	0.952540i	$0.401539\pi$
$558$	47.0928	+	21.5559i	1.99360	+	0.912533i
$559$	−6.10263	+	3.92192i	−0.258114	+	0.165880i
$560$	4.71330	+	4.31707i	0.199173	+	0.182430i
$561$	−22.5700	−	26.0472i	−0.952907	−	1.09971i
$562$	22.4403	+	19.4787i	0.946585	+	0.821657i
$563$	22.5557	−	16.8850i	0.950609	−	0.711617i	−0.00691326	−	0.999976i	$-0.502201\pi$
$563$	22.5557	−	16.8850i	0.950609	−	0.711617i	0.957522	+	0.288359i	$0.0931097\pi$
$564$	−17.4019	+	37.9309i	−0.732752	+	1.59718i
$565$	−9.83220	+	4.20705i	−0.413644	+	0.176992i
$566$	8.01244	−	36.6796i	0.336788	−	1.54176i
$567$	−1.35231	−	0.504384i	−0.0567915	−	0.0211821i
$568$	−1.18564	−	8.40117i	−0.0497482	−	0.352505i
$569$	−1.51908	+	5.17352i	−0.0636832	+	0.216885i	−0.985187	−	0.171485i	$-0.945144\pi$
$569$	−1.51908	+	5.17352i	−0.0636832	+	0.216885i	0.921504	+	0.388370i	$0.126962\pi$
$570$	61.4506	−	7.27545i	2.57388	−	0.304735i
$571$	−0.359152	−	1.22316i	−0.0150300	−	0.0511876i	0.951637	−	0.307226i	$-0.0994008\pi$
$571$	−0.359152	−	1.22316i	−0.0150300	−	0.0511876i	−0.966667	+	0.256039i	$0.917583\pi$
$572$	6.71441	−	0.468536i	0.280744	−	0.0195905i
$573$	7.92851	+	5.93521i	0.331218	+	0.247947i
$574$	−0.757346	+	0.565919i	−0.0316110	+	0.0236210i
$575$	22.6832	−	7.77628i	0.945957	−	0.324293i
$576$	−27.5607	+	23.6319i	−1.14836	+	0.984662i
$577$	1.38675	−	1.85248i	0.0577311	−	0.0771198i	−0.770746	−	0.637142i	$-0.780116\pi$
$577$	1.38675	−	1.85248i	0.0577311	−	0.0771198i	0.828478	+	0.560022i	$0.189207\pi$
$578$	−12.1154	−	7.80090i	−0.503933	−	0.324475i
$579$	10.4326	−	3.06328i	0.433563	−	0.127305i
$580$	0.803316	+	0.845907i	0.0333559	+	0.0351244i
$581$	3.39374	+	0.996491i	0.140796	+	0.0413414i
$582$	−15.5112	−	34.0428i	−0.642961	−	1.41112i
$583$	−22.2959	+	59.7775i	−0.923400	+	2.47573i
$584$	22.6166	+	12.4260i	0.935880	+	0.514190i
$585$	2.79296	+	6.52737i	0.115475	+	0.269873i
$586$	1.89438	+	3.47644i	0.0782560	+	0.143611i
$587$	3.91909	+	5.23530i	0.161758	+	0.216084i	0.874096	−	0.485753i	$-0.161455\pi$
$587$	3.91909	+	5.23530i	0.161758	+	0.216084i	−0.712338	+	0.701837i	$0.752364\pi$
$588$	−35.5386	−	2.60365i	−1.46559	−	0.107373i
$589$	43.4674	−	37.6647i	1.79104	−	1.55195i
$590$	6.21736	+	12.0942i	0.255965	+	0.497911i
$591$	−16.2361	−	25.2639i	−0.667865	−	1.03922i
$592$	−1.83602	+	24.4789i	−0.0754598	+	1.00608i
$593$	0.283793	+	3.96795i	0.0116540	+	0.162944i	0.999946	+	0.0103712i	$0.00330133\pi$
$593$	0.283793	+	3.96795i	0.0116540	+	0.162944i	−0.988292	+	0.152573i	$0.951244\pi$
$594$	−22.9822	−	17.2354i	−0.942972	−	0.707175i
$595$	0.984311	−	4.05230i	0.0403528	−	0.166128i
$596$	15.6920	+	2.28391i	0.642768	+	0.0935527i
$597$	−11.7085	−	11.7085i	−0.479196	−	0.479196i
$598$	−4.74428	+	0.0976203i	−0.194008	+	0.00399199i
$599$	12.9910			0.530799			0.265400	−	0.964139i	$-0.414496\pi$
$599$	12.9910			0.530799			0.265400	+	0.964139i	$0.414496\pi$
$600$	24.8164	−	29.8626i	1.01312	−	1.21914i
$601$	−4.11925	+	9.01991i	−0.168028	+	0.367930i	−0.974849	−	0.222866i	$-0.928459\pi$
$601$	−4.11925	+	9.01991i	−0.168028	+	0.367930i	0.806821	+	0.590796i	$0.201186\pi$
$602$	10.3728	−	1.48221i	0.422763	−	0.0604106i
$603$	−24.8630	+	1.77824i	−1.01250	+	0.0724154i
$604$	−14.6562	+	22.7189i	−0.596354	+	0.924420i
$605$	19.6461	−	18.7218i	0.798729	−	0.761149i
$606$	−23.3404	+	42.6568i	−0.948138	+	1.73282i
$607$	−21.3698	−	1.52840i	−0.867373	−	0.0620358i	−0.369444	−	0.929253i	$-0.620452\pi$
$607$	−21.3698	−	1.52840i	−0.867373	−	0.0620358i	−0.497930	+	0.867217i	$0.665906\pi$
$608$	11.1911	+	38.7330i	0.453859	+	1.57083i
$609$	0.506578	+	0.0728349i	0.0205276	+	0.00295142i
$610$	−1.15841	+	11.9853i	−0.0469025	+	0.485271i
$611$	−2.87476	+	4.47322i	−0.116300	+	0.180967i
$612$	22.1791	+	8.31617i	0.896538	+	0.336161i
$613$	29.9689	+	11.1778i	1.21043	+	0.451468i	0.871992	−	0.489520i	$-0.162828\pi$
$613$	29.9689	+	11.1778i	1.21043	+	0.451468i	0.338441	+	0.940988i	$0.390101\pi$
$614$	−7.61816	+	20.3712i	−0.307444	+	0.822114i
$615$	3.65548	+	4.42989i	0.147403	+	0.178630i
$616$	−9.10020	−	3.42116i	−0.366658	−	0.137842i
$617$	2.64971	+	1.44685i	0.106673	+	0.0582481i	0.531700	−	0.846933i	$-0.321553\pi$
$617$	2.64971	+	1.44685i	0.106673	+	0.0582481i	−0.425027	+	0.905181i	$0.639735\pi$
$618$	−7.99810	−	5.14986i	−0.321731	−	0.207158i
$619$	−0.262996	−	1.82917i	−0.0105707	−	0.0735207i	0.983853	−	0.178977i	$-0.0572788\pi$
$619$	−0.262996	−	1.82917i	−0.0105707	−	0.0735207i	−0.994424	+	0.105456i	$0.966370\pi$
$620$	3.50308	−	35.9193i	0.140687	−	1.44255i
$621$	15.5870	+	12.9317i	0.625486	+	0.518933i
$622$	−0.970982	+	6.71206i	−0.0389328	+	0.269129i
$623$	−5.81147	+	7.76321i	−0.232832	+	0.311027i
$624$	−6.47837	+	4.13175i	−0.259342	+	0.165403i
$625$	−12.5249	+	21.6363i	−0.500995	+	0.865450i
$626$	−2.48640	+	34.3464i	−0.0993766	+	1.37276i
$627$	−82.6102	+	45.1086i	−3.29913	+	1.80146i
$628$	−38.9638	−	21.3635i	−1.55482	−	0.852497i
$629$	14.5686	−	6.65325i	0.580887	−	0.265282i
$630$	0.255871	−	10.2519i	0.0101941	−	0.408447i
$631$	13.9840	−	21.7595i	0.556693	−	0.866232i	−0.442846	−	0.896598i	$-0.646031\pi$
$631$	13.9840	−	21.7595i	0.556693	−	0.866232i	0.999539	+	0.0303662i	$0.00966735\pi$
$632$	1.92102	−	2.97216i	0.0764140	−	0.118226i
$633$	−29.5928	−	39.5313i	−1.17621	−	1.57123i
$634$	−1.53026	−	21.6594i	−0.0607744	−	0.860205i
$635$	−2.35873	+	0.281333i	−0.0936032	+	0.0111644i
$636$	−10.2405	−	72.1106i	−0.406062	−	2.85937i
$637$	−4.43654	−	0.965110i	−0.175782	−	0.0382391i
$638$	−1.61344	−	0.738521i	−0.0638766	−	0.0292383i
$639$	−8.91463	+	10.2880i	−0.352657	+	0.406988i
$640$	21.8281	+	12.7880i	0.862833	+	0.505489i
$641$	−17.2800	+	37.8378i	−0.682517	+	1.49450i	0.177436	+	0.984132i	$0.443220\pi$
$641$	−17.2800	+	37.8378i	−0.682517	+	1.49450i	−0.859954	+	0.510372i	$0.829508\pi$
$642$	0.0197232	−	22.7745i	0.000778411	−	0.898837i
$643$	−7.97088	−	7.97088i	−0.314341	−	0.314341i	0.532248	−	0.846589i	$-0.321347\pi$
$643$	−7.97088	−	7.97088i	−0.314341	−	0.314341i	−0.846589	+	0.532248i	$0.821347\pi$
$644$	6.28971	+	2.72392i	0.247849	+	0.107338i
$645$	−12.0286	−	62.5068i	−0.473625	−	2.46120i
$646$	18.6164	−	18.5841i	0.732451	−	0.731183i
$647$	12.1995	+	32.7081i	0.479611	+	1.28589i	0.921346	+	0.388743i	$0.127090\pi$
$647$	12.1995	+	32.7081i	0.479611	+	1.28589i	−0.441735	+	0.897146i	$0.645637\pi$
$648$	−5.65240	−	0.827688i	−0.222047	−	0.0325146i
$649$	−15.6324	−	13.5455i	−0.613625	−	0.531709i
$650$	3.66555	−	3.32258i	0.143775	−	0.130322i
$651$	−8.55997	−	13.3196i	−0.335492	−	0.522035i
$652$	23.7446	−	31.6048i	0.929910	−	1.23774i
$653$	48.0922	+	3.43962i	1.88199	+	0.134603i	0.964656	−	0.263511i	$-0.0848807\pi$
$653$	48.0922	+	3.43962i	1.88199	+	0.134603i	0.917336	+	0.398114i	$0.130335\pi$
$654$	−14.5270	+	1.02635i	−0.568051	+	0.0401334i
$655$	−15.4542	+	0.731728i	−0.603847	+	0.0285910i
$656$	−2.46031	+	2.81956i	−0.0960590	+	0.110085i
$657$	−8.80103	−	40.4577i	−0.343361	−	1.57841i
$658$	6.46481	−	4.14678i	0.252025	−	0.161658i
$659$	9.86064	+	21.5918i	0.384116	+	0.841096i	0.998637	+	0.0521959i	$0.0166220\pi$
$659$	9.86064	+	21.5918i	0.384116	+	0.841096i	−0.614521	+	0.788900i	$0.710651\pi$
$660$	−18.0966	+	56.2195i	−0.704411	+	2.18834i
$661$	−28.3731	−	8.33110i	−1.10359	−	0.324042i	−0.321310	−	0.946974i	$-0.604123\pi$
$661$	−28.3731	−	8.33110i	−1.10359	−	0.324042i	−0.782276	+	0.622932i	$0.785941\pi$
$662$	30.6396	+	35.4219i	1.19084	+	1.37671i
$663$	4.40001	+	2.40258i	0.170882	+	0.0933087i
$664$	13.9614	+	1.03500i	0.541806	+	0.0401658i
$665$	−10.2424	−	4.97907i	−0.397182	−	0.193080i
$666$	31.5506	−	23.5758i	1.22256	−	0.913545i
$667$	1.11058	+	0.575865i	0.0430018	+	0.0222976i
$668$	38.2499	−	20.8001i	1.47993	−	0.804781i
$669$	−13.4631	+	1.93571i	−0.520515	+	0.0748388i
$670$	6.81904	+	15.9748i	0.263442	+	0.617162i
$671$	−5.16006	−	17.5735i	−0.199202	−	0.678419i
$672$	10.9924	−	1.53192i	0.424042	−	0.0590951i
$673$	−37.6805	+	20.5751i	−1.45248	+	0.793113i	−0.995353	−	0.0962901i	$-0.969302\pi$
$673$	−37.6805	+	20.5751i	−1.45248	+	0.793113i	−0.457124	+	0.889403i	$0.651121\pi$
$674$	6.30691	+	2.35858i	0.242933	+	0.0908490i
$675$	−21.1096	+	0.490369i	−0.812507	+	0.0188743i
$676$	22.7778	−	10.3546i	0.876071	−	0.398256i
$677$	10.3597	+	47.6229i	0.398157	+	1.83030i	0.541598	+	0.840638i	$0.317820\pi$
$677$	10.3597	+	47.6229i	0.398157	+	1.83030i	−0.143441	+	0.989659i	$0.545817\pi$
$678$	−5.24731	+	17.8136i	−0.201522	+	0.684128i
$679$	−0.979839	+	6.81493i	−0.0376028	+	0.261533i
$680$	0.440404	−	16.4997i	0.0168887	−	0.632736i
$681$	−5.65328	−	6.52423i	−0.216634	−	0.250009i
$682$	15.4201	+	52.6847i	0.590465	+	2.01740i
$683$	0.273914	+	0.0595864i	0.0104810	+	0.00228001i	0.217803	−	0.975993i	$-0.430111\pi$
$683$	0.273914	+	0.0595864i	0.0104810	+	0.00228001i	−0.207322	+	0.978273i	$0.566475\pi$
$684$	35.0672	−	54.3584i	1.34083	−	2.07845i
$685$	34.0277	−	9.10722i	1.30013	−	0.347969i
$686$	10.9061	+	8.17898i	0.416398	+	0.312275i
$687$	−5.08756	−	13.6403i	−0.194103	−	0.520409i
$688$	38.9082	−	14.3587i	1.48336	−	0.547419i
$689$		−	9.28018i		−	0.353547i
$690$	14.6882	−	38.9619i	0.559169	−	1.48325i
$691$		−	16.0277i		−	0.609721i	−0.952397	−	0.304861i	$-0.901390\pi$
$691$		−	16.0277i		−	0.609721i	0.952397	−	0.304861i	$-0.0986099\pi$
$692$	6.97641	+	9.35312i	0.265203	+	0.355552i
$693$	5.45120	+	14.6152i	0.207074	+	0.555187i
$694$	23.3335	−	31.1137i	0.885726	−	1.18106i
$695$	−4.43661	+	7.67934i	−0.168290	+	0.291294i
$696$	2.02089	−	0.139261i	0.0766016	−	0.00527866i
$697$	2.38568	+	0.518973i	0.0903642	+	0.0196575i
$698$	5.33868	−	1.56256i	0.202072	−	0.0591436i
$699$	−0.542835	−	0.626465i	−0.0205319	−	0.0236951i
$700$	−6.81169	+	2.16016i	−0.257458	+	0.0816463i
$701$	−0.969575	+	6.74355i	−0.0366204	+	0.254700i	−0.999905	−	0.0137819i	$-0.995613\pi$
$701$	−0.969575	+	6.74355i	−0.0366204	+	0.254700i	0.963285	+	0.268482i	$0.0865220\pi$
$702$	4.00826	+	1.18070i	0.151282	+	0.0445628i
$703$	−9.29735	−	42.7392i	−0.350656	−	1.61194i
$704$	−38.0597	−	5.67416i	−1.43443	−	0.213853i
$705$	−27.0534	−	38.0143i	−1.01889	−	1.43170i
$706$	8.98662	−	24.0305i	0.338216	−	0.904399i
$707$	7.85436	−	4.28880i	0.295394	−	0.161297i
$708$	23.0651	+	5.05937i	0.866841	+	0.190143i
$709$	−9.77956	−	33.3061i	−0.367279	−	1.25084i	−0.911292	−	0.411761i	$-0.864914\pi$
$709$	−9.77956	−	33.3061i	−0.367279	−	1.25084i	0.544013	−	0.839077i	$-0.316904\pi$
$710$	8.80230	+	3.53569i	0.330345	+	0.132692i
$711$	−5.62032	+	0.808080i	−0.210778	+	0.0303054i
$712$	−16.0356	+	34.8729i	−0.600958	+	1.30692i
$713$	−9.03552	−	37.6324i	−0.338383	−	1.40934i
$714$	−4.33448	−	5.80066i	−0.162214	−	0.217084i
$715$	−3.29004	+	6.76788i	−0.123040	+	0.253104i
$716$	4.65896	−	5.35794i	0.174113	−	0.200236i
$717$	−56.1935	−	30.6840i	−2.09859	−	1.14591i
$718$	29.7748	−	25.7549i	1.11118	−	0.961163i
$719$	15.0329	+	4.41406i	0.560633	+	0.164617i	0.549757	−	0.835324i	$-0.314720\pi$
$719$	15.0329	+	4.41406i	0.560633	+	0.164617i	0.0108750	+	0.999941i	$0.496538\pi$
$720$	−7.53220	−	39.8853i	−0.280708	−	1.48644i
$721$	0.727278	+	1.59252i	0.0270853	+	0.0593084i
$722$	−24.2783	−	37.8497i	−0.903543	−	1.40862i
$723$	−12.4927	−	57.4281i	−0.464609	−	2.13577i
$724$	9.65131	−	21.0369i	0.358688	−	0.781831i
$725$	−1.26767	+	0.306763i	−0.0470801	+	0.0113929i
$726$	−3.32107	−	47.0067i	−0.123257	−	1.74458i
$727$	5.26837	+	0.376801i	0.195393	+	0.0139748i	0.168693	−	0.985669i	$-0.446045\pi$
$727$	5.26837	+	0.376801i	0.195393	+	0.0139748i	0.0267003	+	0.999643i	$0.491500\pi$
$728$	1.41413	+	0.00367401i	0.0524113	+	0.000136168i
$729$	23.7611	+	36.9730i	0.880040	+	1.36937i
$730$	−24.6528	+	14.9877i	−0.912441	+	0.554720i
$731$	−20.4497	−	17.7197i	−0.756359	−	0.655388i
$732$	14.7592	+	14.8104i	0.545514	+	0.547407i
$733$	−2.68914	−	7.20987i	−0.0993258	−	0.266303i	0.877777	−	0.479069i	$-0.159026\pi$
$733$	−2.68914	−	7.20987i	−0.0993258	−	0.266303i	−0.977103	+	0.212766i	$0.931753\pi$
$734$	−18.5158	−	18.5479i	−0.683431	−	0.684615i
$735$	22.3400	−	32.9869i	0.824024	−	1.21674i
$736$	26.6041	+	5.31237i	0.980641	+	0.195817i
$737$	−18.6818	−	18.6818i	−0.688152	−	0.688152i
$738$	6.00403	+	0.00519962i	0.221012	+	0.000191400i
$739$	−8.49141	+	18.5936i	−0.312361	+	0.683976i	−0.999077	−	0.0429499i	$-0.986324\pi$
$739$	−8.49141	+	18.5936i	−0.312361	+	0.683976i	0.686716	+	0.726926i	$0.259052\pi$
$740$	−22.6975	−	15.4290i	−0.834378	−	0.567183i
$741$	8.96564	−	10.3469i	0.329361	−	0.380103i
$742$	−5.57899	+	12.1883i	−0.204811	+	0.447448i
$743$	−16.2944	−	3.54463i	−0.597783	−	0.130040i	−0.0965145	−	0.995332i	$-0.530769\pi$
$743$	−16.2944	−	3.54463i	−0.597783	−	0.130040i	−0.501268	+	0.865292i	$0.667133\pi$
$744$	−44.1976	−	44.4279i	−1.62036	−	1.62881i
$745$	−10.9633	+	13.9328i	−0.401666	+	0.510458i
$746$	−39.6437	+	2.80087i	−1.45146	+	0.102547i
$747$	−13.4610	−	17.9818i	−0.492513	−	0.657921i
$748$	8.73296	+	23.5384i	0.319309	+	0.860649i
$749$	−2.26607	+	3.52608i	−0.0828005	+	0.128840i
$750$	15.1004	+	40.7003i	0.551388	+	1.48616i
$751$	17.6004	−	8.03783i	0.642248	−	0.293305i	−0.0675441	−	0.997716i	$-0.521516\pi$
$751$	17.6004	−	8.03783i	0.642248	−	0.293305i	0.709792	+	0.704412i	$0.248789\pi$
$752$	21.5702	−	21.4212i	0.786583	−	0.781152i
$753$	−5.53480	+	3.02223i	−0.201699	+	0.110136i
$754$	0.257429	+	0.0186358i	0.00937502	+	0.000678675i
$755$	−13.8433	−	26.8711i	−0.503808	−	0.977941i
$756$	−4.55454	−	3.96036i	−0.165647	−	0.144037i
$757$	6.24906	−	8.34777i	0.227126	−	0.303405i	−0.672473	−	0.740122i	$-0.734768\pi$
$757$	6.24906	−	8.34777i	0.227126	−	0.303405i	0.899599	+	0.436717i	$0.143859\pi$
$758$	−49.0010	−	7.08859i	−1.77980	−	0.257469i
$759$	1.35777	+	63.3206i	0.0492840	+	2.29839i
$760$	−43.7747	−	10.7535i	−1.58787	−	0.390069i
$761$	1.36391	+	9.48619i	0.0494416	+	0.343874i	0.999495	+	0.0317856i	$0.0101194\pi$
$761$	1.36391	+	9.48619i	0.0494416	+	0.343874i	−0.950053	+	0.312088i	$0.898972\pi$
$762$	−2.23306	+	3.46810i	−0.0808952	+	0.125636i
$763$	2.35239	+	1.28450i	0.0851622	+	0.0465021i
$764$	−3.88993	−	6.07597i	−0.140733	−	0.219821i
$765$	−20.4263	+	16.8555i	−0.738513	+	0.609411i
$766$	12.6763	+	4.74051i	0.458012	+	0.171282i
$767$	2.81902	+	1.05144i	0.101789	+	0.0379653i
$768$	41.2647	−	15.0661i	1.48901	−	0.543651i
$769$	2.41714	−	3.76114i	0.0871643	−	0.135630i	−0.794934	−	0.606697i	$-0.792494\pi$
$769$	2.41714	−	3.76114i	0.0871643	−	0.135630i	0.882098	+	0.471066i	$0.156131\pi$
$770$	8.38972	−	6.91088i	0.302344	−	0.249051i
$771$	−54.0529	−	7.77164i	−1.94667	−	0.279889i
$772$	−7.89923	−	0.578718i	−0.284300	−	0.0208285i
$773$	−5.15274	−	0.368531i	−0.185331	−	0.0132551i	−0.0216349	−	0.999766i	$-0.506887\pi$
$773$	−5.15274	−	0.368531i	−0.185331	−	0.0132551i	−0.163696	+	0.986511i	$0.552342\pi$
$774$	−58.3753	−	31.9410i	−2.09826	−	1.14809i
$775$	32.8543	+	23.4239i	1.18016	+	0.841411i
$776$	1.87345	+	27.1868i	0.0672531	+	0.975948i
$777$	−12.0098	+	0.858960i	−0.430850	+	0.0308150i
$778$	−1.46934	−	10.2827i	−0.0526782	−	0.368651i
$779$	2.76981	−	6.06504i	0.0992388	−	0.217303i
$780$	−0.391436	−	8.58182i	−0.0140157	−	0.307278i
$781$	−14.4287			−0.516298
$782$	−5.33508	−	16.8771i	−0.190782	−	0.603525i
$783$	−0.778942	−	0.778942i	−0.0278371	−	0.0278371i
$784$	23.5742	+	10.8648i	0.841935	+	0.388029i
$785$	42.4293	−	25.8453i	1.51436	−	0.922457i
$786$	−16.1186	+	21.4930i	−0.574930	+	0.766631i
$787$	2.68675	+	37.5657i	0.0957723	+	1.33907i	0.787232	+	0.616657i	$0.211513\pi$
$787$	2.68675	+	37.5657i	0.0957723	+	1.33907i	−0.691460	+	0.722415i	$0.743032\pi$
$788$	4.61309	+	21.3843i	0.164334	+	0.761783i
$789$	33.2928	+	51.8045i	1.18525	+	1.84429i
$790$	1.80898	+	3.51889i	0.0643607	+	0.125197i
$791$	2.58295	−	2.23814i	0.0918390	−	0.0795789i
$792$	33.2445	+	52.0261i	1.18129	+	1.84867i
$793$	1.59654	+	2.13273i	0.0566948	+	0.0757354i
$794$	34.6251	−	18.8678i	1.22880	−	0.669594i
$795$	75.5892	+	30.2865i	2.68087	+	1.07415i
$796$	4.99165	+	10.9805i	0.176924	+	0.389193i
$797$	−5.11287	+	13.7081i	−0.181107	+	0.485567i	−0.995502	−	0.0947448i	$-0.969797\pi$
$797$	−5.11287	+	13.7081i	−0.181107	+	0.485567i	0.814395	+	0.580312i	$0.197069\pi$
$798$	−17.9955	+	8.19945i	−0.637035	+	0.290257i
$799$	−19.0306	−	5.58789i	−0.673255	−	0.197685i
$800$	−24.5640	+	14.0218i	−0.868467	+	0.495747i
$801$	59.0900	−	17.3504i	2.08784	−	0.613045i
$802$	−26.6789	+	41.4342i	−0.942065	+	1.46309i
$803$	26.2991	−	35.1315i	0.928076	−	1.23976i
$804$	28.9245	+	8.54745i	1.02009	+	0.301445i
$805$	−6.14687	+	4.57615i	−0.216649	+	0.161288i
$806$	−4.77961	−	6.39635i	−0.168354	−	0.225302i
$807$	−45.8445	−	34.3188i	−1.61380	−	1.20808i
$808$	26.8293	−	23.1260i	0.943852	−	0.813569i
$809$	10.6367	+	36.2252i	0.373966	+	1.27361i	0.904692	+	0.426067i	$0.140101\pi$
$809$	10.6367	+	36.2252i	0.373966	+	1.27361i	−0.530726	+	0.847544i	$0.678081\pi$
$810$	3.95395	−	5.01594i	0.138928	−	0.176242i
$811$	−3.35434	+	11.4238i	−0.117787	+	0.401145i	−0.997188	−	0.0749359i	$-0.976125\pi$
$811$	−3.35434	+	11.4238i	−0.117787	+	0.401145i	0.879402	+	0.476081i	$0.157943\pi$
$812$	−0.326897	−	0.179235i	−0.0114719	−	0.00628992i
$813$	−28.5780	−	10.6590i	−1.00227	−	0.373829i
$814$	40.7842	+	8.90905i	1.42948	+	0.312262i
$815$	17.3863	+	40.6331i	0.609016	+	1.42332i
$816$	−21.5955	−	18.8440i	−0.755994	−	0.659672i
$817$	−59.1572	+	44.2845i	−2.06965	+	1.54932i
$818$	24.7495	−	28.5125i	0.865346	−	0.996917i
$819$	−1.48584	−	1.71476i	−0.0519196	−	0.0599184i
$820$	−1.36039	−	3.95640i	−0.0475067	−	0.138164i
$821$	−11.0783	+	7.11962i	−0.386637	+	0.248477i	−0.719491	−	0.694502i	$-0.755625\pi$
$821$	−11.0783	+	7.11962i	−0.386637	+	0.248477i	0.332854	+	0.942978i	$0.391988\pi$
$822$	25.4579	−	55.6174i	0.887945	−	1.93988i
$823$	54.9324	−	3.92884i	1.91482	−	0.136951i	0.937402	−	0.348249i	$-0.113224\pi$
$823$	54.9324	−	3.92884i	1.91482	−	0.136951i	0.977422	+	0.211298i	$0.0677692\pi$
$824$	4.13825	+	5.55810i	0.144163	+	0.193625i
$825$	−44.3887	−	48.8856i	−1.54542	−	1.70198i
$826$	−3.07033	−	3.07566i	−0.106831	−	0.107016i
$827$	−24.2488	+	24.2488i	−0.843213	+	0.843213i	−0.989275	−	0.146062i	$-0.953340\pi$
$827$	−24.2488	+	24.2488i	−0.843213	+	0.843213i	0.146062	+	0.989275i	$0.453340\pi$
$828$	−21.6097	−	37.7853i	−0.750988	−	1.31313i
$829$		−	45.9815i		−	1.59700i	−0.601993	−	0.798502i	$-0.705626\pi$
$829$		−	45.9815i		−	1.59700i	0.601993	−	0.798502i	$-0.294374\pi$
$830$	−8.78807	+	12.9522i	−0.305038	+	0.449576i
$831$	4.26498	+	1.94775i	0.147950	+	0.0675667i
$832$	5.47543	−	1.16134i	0.189826	−	0.0402623i
$833$	−1.20818	−	16.8925i	−0.0418609	−	0.585292i
$834$	5.36933	+	14.4339i	0.185925	+	0.499805i
$835$	−1.17242	+	48.6647i	−0.0405733	+	1.68411i
$836$	67.8829	−	9.64011i	2.34778	−	0.333410i
$837$	−2.43121	+	33.9928i	−0.0840350	+	1.17496i
$838$	−14.7454	−	12.7994i	−0.509373	−	0.442147i
$839$	−1.52699	+	10.6204i	−0.0527174	+	0.366658i	0.946337	+	0.323181i	$0.104752\pi$
$839$	−1.52699	+	10.6204i	−0.0527174	+	0.366658i	−0.999054	+	0.0434763i	$0.986157\pi$
$840$	−4.64506	+	11.5065i	−0.160270	+	0.397011i
$841$	24.3391	+	15.6418i	0.839280	+	0.539372i
$842$	6.77022	+	10.5547i	0.233317	+	0.363741i
$843$	−20.1602	+	54.0517i	−0.694356	+	1.86164i
$844$	10.0745	+	34.5317i	0.346778	+	1.18863i
$845$	−2.66712	+	27.8469i	−0.0917518	+	0.957961i
$846$	−48.6482	−	3.52174i	−1.67256	−	0.121080i
$847$	−4.15641	+	7.61190i	−0.142816	+	0.261548i
$848$	−11.4573	+	51.8039i	−0.393447	+	1.77895i
$849$	72.1474	−	10.3732i	2.47609	−	0.356008i
$850$	15.7435	+	9.62732i	0.539999	+	0.330214i
$851$	−28.4107	−	7.68454i	−0.973905	−	0.263423i
$852$	14.4705	−	7.86900i	0.495752	−	0.269588i
$853$	−29.2389	−	21.8879i	−1.00112	−	0.749429i	−0.0328815	−	0.999459i	$-0.510468\pi$
$853$	−29.2389	−	21.8879i	−1.00112	−	0.749429i	−0.968238	+	0.250031i	$0.919559\pi$
$854$	−0.814716	−	3.76087i	−0.0278790	−	0.128694i
$855$	33.1221	+	64.2932i	1.13275	+	2.19878i
$856$	−5.83798	+	15.5289i	−0.199538	+	0.530767i
$857$	5.61176	+	10.2772i	0.191694	+	0.351061i	0.955794	−	0.294036i	$-0.0949986\pi$
$857$	5.61176	+	10.2772i	0.191694	+	0.351061i	−0.764100	+	0.645097i	$0.776817\pi$
$858$	5.41798	+	11.8910i	0.184967	+	0.405951i
$859$	−3.26854	−	7.15710i	−0.111521	−	0.244197i	0.845640	−	0.533754i	$-0.179219\pi$
$859$	−3.26854	−	7.15710i	−0.111521	−	0.244197i	−0.957161	+	0.289557i	$0.906492\pi$
$860$	−7.78158	+	45.7107i	−0.265350	+	1.55872i
$861$	−1.54409	−	0.992327i	−0.0526225	−	0.0338184i
$862$	33.5539	+	9.88388i	1.14285	+	0.336646i
$863$	33.9879	−	25.4430i	1.15696	−	0.866090i	0.164227	−	0.986423i	$-0.447487\pi$
$863$	33.9879	−	25.4430i	1.15696	−	0.866090i	0.992734	+	0.120333i	$0.0383963\pi$
$864$	−20.9173	−	11.5395i	−0.711620	−	0.392583i
$865$	−12.9538	+	1.54505i	−0.440444	+	0.0525332i
$866$	−2.75514	−	1.50752i	−0.0936234	−	0.0512275i
$867$	5.94649	−	27.3356i	0.201953	−	0.928365i
$868$	2.43210	+	11.2742i	0.0825509	+	0.382670i
$869$	−4.54835	−	3.94117i	−0.154292	−	0.133695i
$870$	−0.991932	+	2.03600i	−0.0336296	+	0.0690269i
$871$	3.49569	+	1.59643i	0.118447	+	0.0540930i
$872$	10.1710	+	3.01520i	0.344434	+	0.102108i
$873$	30.9174	−	30.9174i	1.04640	−	1.04640i
$874$	−48.1345	+	4.43962i	−1.62817	+	0.150172i
$875$	1.70501	−	7.80543i	0.0576399	−	0.263872i
$876$	−7.21566	+	49.5763i	−0.243794	+	1.67503i
$877$	29.2209	−	10.8988i	0.986718	−	0.368027i	0.196266	−	0.980551i	$-0.437118\pi$
$877$	29.2209	−	10.8988i	0.986718	−	0.368027i	0.790452	+	0.612524i	$0.209846\pi$
$878$	−37.3960	+	5.34369i	−1.26206	+	0.180341i
$879$	−5.03339	+	5.80884i	−0.169772	+	0.195927i
$880$	26.7213	−	33.7178i	0.900776	−	1.13663i
$881$	21.1534	−	13.5945i	0.712676	−	0.458009i	−0.133406	−	0.991061i	$-0.542591\pi$
$881$	21.1534	−	13.5945i	0.712676	−	0.458009i	0.846082	+	0.533052i	$0.178955\pi$
$882$	−11.6990	−	39.9710i	−0.393925	−	1.34589i
$883$	−2.49718	+	34.9152i	−0.0840369	+	1.17499i	0.764059	+	0.645146i	$0.223204\pi$
$883$	−2.49718	+	34.9152i	−0.0840369	+	1.17499i	−0.848096	+	0.529843i	$0.822251\pi$
$884$	−2.38668	−	2.76404i	−0.0802729	−	0.0929647i
$885$	−17.7643	+	19.5301i	−0.597141	+	0.656498i
$886$	−37.5970	+	20.4872i	−1.26309	+	0.688283i
$887$	4.29747	−	0.934857i	0.144295	−	0.0313894i	−0.139838	−	0.990174i	$-0.544658\pi$
$887$	4.29747	−	0.934857i	0.144295	−	0.0313894i	0.284133	+	0.958785i	$0.408294\pi$
$888$	−45.7613	+	13.3077i	−1.53565	+	0.446577i
$889$	0.690540	−	0.315359i	0.0231600	−	0.0105768i
$890$	−24.8520	−	34.9850i	−0.833040	−	1.17270i
$891$	−2.73704	+	9.32150i	−0.0916943	+	0.312282i
$892$	9.67795	+	2.12287i	0.324042	+	0.0710790i
$893$	−25.9590	+	47.5403i	−0.868684	+	1.59088i
$894$	6.51788	+	30.0876i	0.217990	+	1.00628i
$895$	2.59421	+	7.50246i	0.0867150	+	0.250779i
$896$	−7.88946	−	1.76640i	−0.263568	−	0.0590114i
$897$	−3.40376	−	8.56069i	−0.113648	−	0.285833i
$898$	−4.01886	+	27.7809i	−0.134111	+	0.927062i
$899$	0.299580	+	2.08362i	0.00999155	+	0.0694927i
$900$	42.8511	+	14.9417i	1.42837	+	0.498055i
$901$	33.2136	−	9.75240i	1.10651	−	0.324900i
$902$	4.16322	+	4.81303i	0.138620	+	0.160256i
$903$	9.74907	+	17.8541i	0.324429	+	0.594147i
$904$	8.13486	−	10.8083i	0.270562	−	0.359477i
$905$	15.0041	+	21.0832i	0.498754	+	0.700828i
$906$	−51.2791	−	11.2016i	−1.70363	−	0.372148i
$907$	−40.8498	+	8.88633i	−1.35640	+	0.295066i	−0.831227	−	0.555933i	$-0.812361\pi$
$907$	−40.8498	+	8.88633i	−1.35640	+	0.295066i	−0.525168	+	0.850998i	$0.675998\pi$
$908$	2.18741	+	5.89584i	0.0725918	+	0.195660i
$909$	−56.2530	−	8.08796i	−1.86579	−	0.268261i
$910$	−0.792106	+	1.36832i	−0.0262581	+	0.0453594i
$911$	−2.81931	+	2.44294i	−0.0934078	+	0.0809383i	−0.700313	−	0.713836i	$-0.746956\pi$
$911$	−2.81931	+	2.44294i	−0.0934078	+	0.0809383i	0.606905	+	0.794774i	$0.292411\pi$
$912$	−62.8224	+	46.6896i	−2.08026	+	1.54605i
$913$	5.06074	−	23.2639i	0.167486	−	0.769921i
$914$	1.27381	+	3.42427i	0.0421339	+	0.113265i
$915$	−22.5820	+	6.04388i	−0.746538	+	0.199804i
$916$	−0.0183680	+	10.6049i	−0.000606897	+	0.350394i
$917$	4.63264	−	1.72789i	0.152983	−	0.0570598i
$918$	−0.0134981	+	15.5863i	−0.000445502	+	0.514424i
$919$	54.4316			1.79553			0.897767	−	0.440471i	$-0.145189\pi$
$919$	54.4316			1.79553			0.897767	+	0.440471i	$0.145189\pi$
$920$	−19.9829	+	22.8185i	−0.658816	+	0.752304i
$921$	−42.2238			−1.39132
$922$	0.0472513	−	54.5614i	0.00155614	−	1.79688i
$923$	1.96642	−	0.733438i	0.0647256	−	0.0241414i
$924$	0.0326913	−	18.8744i	0.00107546	−	0.620923i
$925$	27.6081	−	13.3916i	0.907748	−	0.440313i
$926$	4.42027	+	11.8826i	0.145259	+	0.390487i
$927$	2.36333	−	10.8641i	0.0776220	−	0.356823i
$928$	−1.41402	−	0.421852i	−0.0464173	−	0.0138480i
$929$	−11.3687	+	9.85105i	−0.372996	+	0.323202i	−0.821106	−	0.570776i	$-0.806643\pi$
$929$	−11.3687	+	9.85105i	−0.372996	+	0.323202i	0.448110	+	0.893978i	$0.352097\pi$
$930$	67.6983	−	18.0561i	2.21992	−	0.592082i
$931$	−45.7799	−	6.58215i	−1.50038	−	0.215721i
$932$	0.210038	+	0.566126i	0.00688002	+	0.0185441i
$933$	−12.8656	+	2.79874i	−0.421201	+	0.0916266i
$934$	−23.2037	−	5.06870i	−0.759247	−	0.165853i
$935$	−27.6796	−	4.66273i	−0.905220	−	0.152488i
$936$	−7.17535	−	5.40054i	−0.234533	−	0.176522i
$937$	−16.2280	−	29.7193i	−0.530145	−	0.970887i	−0.996280	−	0.0861740i	$-0.972536\pi$
$937$	−16.2280	−	29.7193i	−0.530145	−	0.970887i	0.466136	−	0.884713i	$-0.345646\pi$
$938$	−3.63142	−	4.19823i	−0.118570	−	0.137077i
$939$	−64.1468	+	18.8352i	−2.09335	+	0.614664i
$940$	8.73041	+	32.8475i	0.284754	+	1.07137i
$941$	−0.998809	−	6.94687i	−0.0325602	−	0.226461i	0.967043	−	0.254611i	$-0.0819475\pi$
$941$	−0.998809	−	6.94687i	−0.0325602	−	0.226461i	−0.999604	+	0.0281499i	$0.991038\pi$
$942$	12.3513	−	85.3801i	0.402426	−	2.78183i
$943$	−2.76508	−	3.53322i	−0.0900435	−	0.115058i
$944$	−14.4383	−	9.34974i	−0.469925	−	0.304308i
$945$	6.37749	−	2.20522i	0.207460	−	0.0717358i
$946$	−14.9324	−	68.9306i	−0.485495	−	2.24113i
$947$	−14.7762	+	27.0607i	−0.480163	+	0.879353i	0.519527	+	0.854454i	$0.326108\pi$
$947$	−14.7762	+	27.0607i	−0.480163	+	0.879353i	−0.999690	+	0.0248992i	$0.992074\pi$
$948$	6.71095	+	1.47206i	0.217962	+	0.0478102i
$949$	−1.79839	+	6.12476i	−0.0583783	+	0.198818i
$950$	34.8302	−	36.4237i	1.13004	−	1.18174i
$951$	38.3452	−	17.5117i	1.24343	−	0.567854i
$952$	1.47294	+	5.06503i	0.0477384	+	0.164158i
$953$	42.7278	−	9.29486i	1.38409	−	0.301090i	0.541977	−	0.840393i	$-0.317676\pi$
$953$	42.7278	−	9.29486i	1.38409	−	0.301090i	0.842112	+	0.539303i	$0.181312\pi$
$954$	74.7491	−	40.7321i	2.42009	−	1.31875i
$955$	8.05703	−	0.381484i	0.260719	−	0.0123445i
$956$	30.4809	+	35.3002i	0.985823	+	1.14169i
$957$	0.245755	−	3.43611i	0.00794415	−	0.111074i
$958$	9.47252	+	32.3641i	0.306043	+	1.04564i
$959$	−9.47023	+	6.08614i	−0.305810	+	0.196532i
$960$	−8.41006	+	48.3888i	−0.271434	+	1.56174i
$961$	22.3460	−	25.7887i	0.720840	−	0.831894i
$962$	−6.01117	+	0.858963i	−0.193808	+	0.0276941i
$963$	24.9399	−	9.30212i	0.803678	−	0.299757i
$964$	−6.16613	+	42.3653i	−0.198598	+	1.36449i
$965$	4.96556	−	7.33207i	0.159847	−	0.236028i
$966$	−0.676046	+	13.2896i	−0.0217514	+	0.427587i
$967$	−26.6761	+	26.6761i	−0.857844	+	0.857844i	−0.991084	−	0.133239i	$-0.957462\pi$
$967$	−26.6761	+	26.6761i	−0.857844	+	0.857844i	0.133239	+	0.991084i	$0.457462\pi$
$968$	−9.75665	+	32.9115i	−0.313591	+	1.05782i
$969$	46.4533	+	21.2145i	1.49229	+	0.681508i
$970$	−27.3901	−	13.3443i	−0.879442	−	0.428461i
$971$	8.04441	+	6.97052i	0.258158	+	0.223695i	0.774317	−	0.632798i	$-0.218093\pi$
$971$	8.04441	+	6.97052i	0.258158	+	0.223695i	−0.516160	+	0.856492i	$0.672639\pi$
$972$	−7.68187	−	35.6098i	−0.246396	−	1.14218i
$973$	0.602471	−	2.76952i	0.0193143	−	0.0887866i
$974$	−34.2814	−	18.7576i	−1.09845	−	0.601033i
$975$	8.53450	+	4.40605i	0.273323	+	0.141107i
$976$	−6.27915	−	13.8764i	−0.200991	−	0.444174i
$977$	15.8081	−	11.8338i	0.505746	−	0.378597i	−0.315722	−	0.948852i	$-0.602247\pi$
$977$	15.8081	−	11.8338i	0.505746	−	0.378597i	0.821468	+	0.570255i	$0.193156\pi$
$978$	73.6176	+	21.6853i	2.35403	+	0.693421i
$979$	54.9124	+	35.2901i	1.75501	+	1.12788i
$980$	−23.6739	+	16.7862i	−0.756236	+	0.536216i
$981$	−7.07082	−	15.4829i	−0.225754	−	0.494332i
$982$	−9.78231	−	21.4695i	−0.312166	−	0.685118i
$983$	−13.3416	−	24.4334i	−0.425532	−	0.779303i	0.573677	−	0.819082i	$-0.305517\pi$
$983$	−13.3416	−	24.4334i	−0.425532	−	0.779303i	−0.999209	+	0.0397784i	$0.987335\pi$
$984$	−6.80020	−	2.55649i	−0.216782	−	0.0814979i
$985$	−23.2948	−	7.45392i	−0.742235	−	0.237502i
$986$	0.203831	+	0.940919i	0.00649131	+	0.0299650i
$987$	11.9368	+	8.93578i	0.379953	+	0.284429i
$988$	−8.76145	+	4.76443i	−0.278739	+	0.151577i
$989$	8.13005	+	49.0554i	0.258520	+	1.55987i
$990$	−68.9537	+	3.20498i	−2.19149	+	0.101861i
$991$	39.8560	−	5.73043i	1.26607	−	0.182033i	0.523629	−	0.851946i	$-0.324578\pi$
$991$	39.8560	−	5.73043i	1.26607	−	0.182033i	0.742439	+	0.669913i	$0.233669\pi$
$992$	18.7838	+	41.6067i	0.596387	+	1.32101i
$993$	−43.5760	+	79.8034i	−1.38284	+	2.53249i
$994$	−3.02357	−	0.218882i	−0.0959019	−	0.00694252i
$995$	−13.4241	−	1.28574i	−0.425573	−	0.0407606i
$996$	7.61205	+	26.0914i	0.241197	+	0.826736i
$997$	7.25100	−	19.4407i	0.229641	−	0.615693i	−0.770112	−	0.637909i	$-0.779800\pi$
$997$	7.25100	−	19.4407i	0.229641	−	0.615693i	0.999753	+	0.0222164i	$0.00707229\pi$
$998$	−14.4006	−	22.4504i	−0.455842	−	0.710656i
$999$	21.8023	+	14.0115i	0.689795	+	0.443304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.187.35	yes	1360
4.3	odd	2	inner	460.2.w.a.187.63	yes	1360
5.3	odd	4	inner	460.2.w.a.3.1	✓	1360
20.3	even	4	inner	460.2.w.a.3.28	yes	1360
23.8	even	11	inner	460.2.w.a.307.28	yes	1360
92.31	odd	22	inner	460.2.w.a.307.1	yes	1360
115.8	odd	44	inner	460.2.w.a.123.63	yes	1360
460.123	even	44	inner	460.2.w.a.123.35	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.1	✓	1360	5.3	odd	4	inner
460.2.w.a.3.28	yes	1360	20.3	even	4	inner
460.2.w.a.123.35	yes	1360	460.123	even	44	inner
460.2.w.a.123.63	yes	1360	115.8	odd	44	inner
460.2.w.a.187.35	yes	1360	1.1	even	1	trivial
460.2.w.a.187.63	yes	1360	4.3	odd	2	inner
460.2.w.a.307.1	yes	1360	92.31	odd	22	inner
460.2.w.a.307.28	yes	1360	23.8	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00122474 - 1.41421i) q^{2} +(2.57246 - 0.959477i) q^{3} +(-2.00000 - 0.00346408i) q^{4} +(1.11859 - 1.93617i) q^{5} +(-1.35375 - 3.63918i) q^{6} +(-0.151899 + 0.698270i) q^{7} +(-0.00734842 + 2.82842i) q^{8} +(3.42969 - 2.97185i) q^{9} +O(q^{10})\)	\(q+(0.00122474 - 1.41421i) q^{2} +(2.57246 - 0.959477i) q^{3} +(-2.00000 - 0.00346408i) q^{4} +(1.11859 - 1.93617i) q^{5} +(-1.35375 - 3.63918i) q^{6} +(-0.151899 + 0.698270i) q^{7} +(-0.00734842 + 2.82842i) q^{8} +(3.42969 - 2.97185i) q^{9} +(-2.73679 - 1.58430i) q^{10} +(4.76108 + 0.684541i) q^{11} +(-5.14823 + 1.91004i) q^{12} +(-0.683665 + 0.148722i) q^{13} +(0.987316 + 0.215673i) q^{14} +(1.01981 - 6.05398i) q^{15} +(3.99998 + 0.0138563i) q^{16} +(-1.25073 - 2.29054i) q^{17} +(-4.19862 - 4.85396i) q^{18} +(-6.83847 + 2.00795i) q^{19} +(-2.24388 + 3.86846i) q^{20} +(0.279219 + 1.94201i) q^{21} +(0.973917 - 6.73235i) q^{22} +(-0.918730 + 4.70701i) q^{23} +(2.69490 + 7.28304i) q^{24} +(-2.49751 - 4.33156i) q^{25} +(0.209488 + 0.967030i) q^{26} +(2.02389 - 3.70648i) q^{27} +(0.306217 - 1.39601i) q^{28} +(0.0734905 - 0.250286i) q^{29} +(-8.56037 - 1.44965i) q^{30} +(-7.34064 + 3.35236i) q^{31} +(0.0244947 - 5.65680i) q^{32} +(12.9045 - 2.80720i) q^{33} +(-3.24084 + 1.76599i) q^{34} +(1.18206 + 1.07518i) q^{35} +(-6.86967 + 5.93180i) q^{36} +(-0.437802 + 6.12127i) q^{37} +(2.83130 + 9.67351i) q^{38} +(-1.61600 + 1.03854i) q^{39} +(5.46808 + 3.17807i) q^{40} +(-0.612632 + 0.707015i) q^{41} +(2.74676 - 0.392497i) q^{42} +(9.71456 - 3.62334i) q^{43} +(-9.51978 - 1.38557i) q^{44} +(-1.91758 - 9.96475i) q^{45} +(6.65559 + 1.30505i) q^{46} +(5.37396 - 5.37396i) q^{47} +(10.3031 - 3.80224i) q^{48} +(5.90292 + 2.69577i) q^{49} +(-6.12881 + 3.52671i) q^{50} +(-5.41517 - 4.69227i) q^{51} +(1.36784 - 0.295076i) q^{52} +(-2.81945 + 12.9608i) q^{53} +(-5.23928 - 2.86675i) q^{54} +(6.65109 - 8.45255i) q^{55} +(-1.97388 - 0.434766i) q^{56} +(-15.6651 + 11.7267i) q^{57} +(-0.353867 - 0.104238i) q^{58} +(-3.61764 - 2.32492i) q^{59} +(-2.06060 + 12.1044i) q^{60} +(-1.58180 - 3.46365i) q^{61} +(4.73196 + 10.3853i) q^{62} +(1.55418 + 2.84627i) q^{63} +(-7.99989 - 0.0415688i) q^{64} +(-0.476790 + 1.49005i) q^{65} +(-3.95417 - 18.2531i) q^{66} +(-4.39711 - 3.29164i) q^{67} +(2.49352 + 4.58540i) q^{68} +(2.15287 + 12.9901i) q^{69} +(1.52198 - 1.67036i) q^{70} +(-2.96916 + 0.426901i) q^{71} +(8.38042 + 9.72244i) q^{72} +(4.37245 - 8.00755i) q^{73} +(8.65625 + 0.626642i) q^{74} +(-10.5808 - 8.74645i) q^{75} +(13.6839 - 3.99221i) q^{76} +(-1.20120 + 3.22054i) q^{77} +(1.46674 + 2.28665i) q^{78} +(-1.05258 - 0.676450i) q^{79} +(4.50116 - 7.72914i) q^{80} +(-0.287439 + 1.99918i) q^{81} +(0.999120 + 0.867258i) q^{82} +(0.353103 - 4.93702i) q^{83} +(-0.551710 - 3.88499i) q^{84} +(-5.83393 - 0.140550i) q^{85} +(-5.11228 - 13.7429i) q^{86} +(-0.0510921 - 0.714362i) q^{87} +(-1.97115 + 13.4613i) q^{88} +(12.3441 + 5.63737i) q^{89} +(-14.0946 + 2.69966i) q^{90} -0.499974i q^{91} +(1.85376 - 9.41082i) q^{92} +(-15.6670 + 15.6670i) q^{93} +(-7.59334 - 7.60650i) q^{94} +(-3.76170 + 15.4865i) q^{95} +(-5.36456 - 14.5754i) q^{96} +(9.61022 - 0.687336i) q^{97} +(3.81963 - 8.34468i) q^{98} +(18.3634 - 11.8014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more