LMFDB - Embedded newform 720.2.cf.a.11.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.43
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.236691 - 1.39427i) q^{2} +(-1.72177 + 0.188420i) q^{3} +(-1.88795 + 0.660020i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(0.670235 + 2.35601i) q^{6} +(-1.48910 + 2.57919i) q^{7} +(1.36711 + 2.47609i) q^{8} +(2.92900 - 0.648831i) q^{9} +O(q^{10})$	\(q+(-0.236691 - 1.39427i) q^{2} +(-1.72177 + 0.188420i) q^{3} +(-1.88795 + 0.660020i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(0.670235 + 2.35601i) q^{6} +(-1.48910 + 2.57919i) q^{7} +(1.36711 + 2.47609i) q^{8} +(2.92900 - 0.648831i) q^{9} +(-0.132237 + 1.40802i) q^{10} +(-4.02465 + 1.07840i) q^{11} +(3.12627 - 1.49213i) q^{12} +(4.58179 + 1.22769i) q^{13} +(3.94853 + 1.46572i) q^{14} +(1.71187 + 0.263628i) q^{15} +(3.12875 - 2.49218i) q^{16} -4.42618i q^{17} +(-1.59791 - 3.93023i) q^{18} +(-2.73847 - 2.73847i) q^{19} +(1.99445 - 0.148892i) q^{20} +(2.07791 - 4.72135i) q^{21} +(2.45618 + 5.35619i) q^{22} +(2.56943 - 1.48346i) q^{23} +(-2.82039 - 4.00567i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.627254 - 6.67881i) q^{26} +(-4.92081 + 1.66902i) q^{27} +(1.10903 - 5.85222i) q^{28} +(-4.58711 + 1.22911i) q^{29} +(-0.0376167 - 2.44920i) q^{30} +(3.79462 - 2.19083i) q^{31} +(-4.21530 - 3.77243i) q^{32} +(6.72634 - 2.61509i) q^{33} +(-6.17127 + 1.04764i) q^{34} +(2.10590 - 2.10590i) q^{35} +(-5.10157 + 3.15816i) q^{36} +(2.44642 + 2.44642i) q^{37} +(-3.16999 + 4.46633i) q^{38} +(-8.12012 - 1.25050i) q^{39} +(-0.679663 - 2.74555i) q^{40} +(-3.42919 - 5.93954i) q^{41} +(-7.07464 - 1.77966i) q^{42} +(1.03790 + 3.87351i) q^{43} +(6.88660 - 4.69233i) q^{44} +(-2.99712 - 0.131357i) q^{45} +(-2.67650 - 3.23134i) q^{46} +(5.08451 - 8.80663i) q^{47} +(-4.91741 + 4.88048i) q^{48} +(-0.934810 - 1.61914i) q^{49} +(0.492153 - 1.32582i) q^{50} +(0.833979 + 7.62087i) q^{51} +(-9.46051 + 0.706257i) q^{52} +(3.76303 - 3.76303i) q^{53} +(3.49177 + 6.46588i) q^{54} +4.16663 q^{55} +(-8.42205 - 0.161111i) q^{56} +(5.23101 + 4.19904i) q^{57} +(2.79944 + 6.10473i) q^{58} +(-0.804446 + 3.00223i) q^{59} +(-3.40593 + 0.632151i) q^{60} +(-3.55942 - 13.2839i) q^{61} +(-3.95275 - 4.77216i) q^{62} +(-2.68810 + 8.52061i) q^{63} +(-4.26204 + 6.77015i) q^{64} +(-4.10792 - 2.37171i) q^{65} +(-5.23819 - 8.75934i) q^{66} +(3.98445 - 14.8702i) q^{67} +(2.92137 + 8.35642i) q^{68} +(-4.14445 + 3.03831i) q^{69} +(-3.43463 - 2.43774i) q^{70} -9.65235i q^{71} +(5.61081 + 6.36544i) q^{72} +9.33374i q^{73} +(2.83191 - 3.99000i) q^{74} +(-1.58531 - 0.697710i) q^{75} +(6.97756 + 3.36266i) q^{76} +(3.21169 - 11.9862i) q^{77} +(0.178432 + 11.6176i) q^{78} +(-3.33418 - 1.92499i) q^{79} +(-3.66716 + 1.59748i) q^{80} +(8.15804 - 3.80085i) q^{81} +(-7.46964 + 6.18704i) q^{82} +(0.399348 + 1.49039i) q^{83} +(-0.806819 + 10.2852i) q^{84} +(-1.14558 + 4.27536i) q^{85} +(5.15504 - 2.36394i) q^{86} +(7.66636 - 2.98055i) q^{87} +(-8.17235 - 8.49111i) q^{88} +16.6062 q^{89} +(0.526245 + 4.20988i) q^{90} +(-9.98916 + 9.98916i) q^{91} +(-3.87185 + 4.49658i) q^{92} +(-6.12068 + 4.48708i) q^{93} +(-13.4822 - 5.00471i) q^{94} +(1.93639 + 3.35393i) q^{95} +(7.96859 + 5.70102i) q^{96} +(-0.532184 + 0.921769i) q^{97} +(-2.03625 + 1.68661i) q^{98} +(-11.0885 + 5.76996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.236691	−	1.39427i	−0.167366	−	0.985895i
$2$	−0.236691	−	1.39427i	−0.167366	−	0.985895i
$3$	−1.72177	+	0.188420i	−0.994065	+	0.108784i
$3$	−1.72177	+	0.188420i	−0.994065	+	0.108784i
$4$	−1.88795	+	0.660020i	−0.943977	+	0.330010i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	0.670235	+	2.35601i	0.273622	+	0.961837i
$7$	−1.48910	+	2.57919i	−0.562825	+	0.974842i	0.434423	+	0.900709i	$0.356952\pi$
$7$	−1.48910	+	2.57919i	−0.562825	+	0.974842i	−0.997248	+	0.0741329i	$0.976381\pi$
$8$	1.36711	+	2.47609i	0.483345	+	0.875430i
$9$	2.92900	−	0.648831i	0.976332	−	0.216277i
$10$	−0.132237	+	1.40802i	−0.0418169	+	0.445254i
$11$	−4.02465	+	1.07840i	−1.21348	+	0.325151i	−0.808126	−	0.589010i	$-0.799518\pi$
$11$	−4.02465	+	1.07840i	−1.21348	+	0.325151i	−0.405353	+	0.914160i	$0.632851\pi$
$12$	3.12627	−	1.49213i	0.902475	−	0.430741i
$13$	4.58179	+	1.22769i	1.27076	+	0.340499i	0.830322	−	0.557284i	$-0.188157\pi$
$13$	4.58179	+	1.22769i	1.27076	+	0.340499i	0.440438	+	0.897783i	$0.354823\pi$
$14$	3.94853	+	1.46572i	1.05529	+	0.391731i
$15$	1.71187	+	0.263628i	0.442003	+	0.0680685i
$16$	3.12875	−	2.49218i	0.782187	−	0.623044i
$17$		−	4.42618i		−	1.07351i	−0.843739	−	0.536753i	$-0.819651\pi$
$17$		−	4.42618i		−	1.07351i	0.843739	−	0.536753i	$-0.180349\pi$
$18$	−1.59791	−	3.93023i	−0.376631	−	0.926363i
$19$	−2.73847	−	2.73847i	−0.628249	−	0.628249i	0.319379	−	0.947627i	$-0.396526\pi$
$19$	−2.73847	−	2.73847i	−0.628249	−	0.628249i	−0.947627	+	0.319379i	$0.896526\pi$
$20$	1.99445	−	0.148892i	0.445973	−	0.0332933i
$21$	2.07791	−	4.72135i	0.453438	−	1.03028i
$22$	2.45618	+	5.35619i	0.523659	+	1.14194i
$23$	2.56943	−	1.48346i	0.535763	−	0.309323i	−0.207597	−	0.978214i	$-0.566564\pi$
$23$	2.56943	−	1.48346i	0.535763	−	0.309323i	0.743360	+	0.668892i	$0.233231\pi$
$24$	−2.82039	−	4.00567i	−0.575709	−	0.817655i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	0.627254	−	6.67881i	0.123015	−	1.30982i
$27$	−4.92081	+	1.66902i	−0.947010	+	0.321203i
$28$	1.10903	−	5.85222i	0.209587	−	1.10597i
$29$	−4.58711	+	1.22911i	−0.851804	+	0.228240i	−0.658204	−	0.752840i	$-0.728683\pi$
$29$	−4.58711	+	1.22911i	−0.851804	+	0.228240i	−0.193601	+	0.981080i	$0.562017\pi$
$30$	−0.0376167	−	2.44920i	−0.00686784	−	0.447161i
$31$	3.79462	−	2.19083i	0.681534	−	0.393484i	−0.118899	−	0.992906i	$-0.537936\pi$
$31$	3.79462	−	2.19083i	0.681534	−	0.393484i	0.800433	+	0.599422i	$0.204603\pi$
$32$	−4.21530	−	3.77243i	−0.745167	−	0.666877i
$33$	6.72634	−	2.61509i	1.17091	−	0.455228i
$34$	−6.17127	+	1.04764i	−1.05836	+	0.179668i
$35$	2.10590	−	2.10590i	0.355962	−	0.355962i
$36$	−5.10157	+	3.15816i	−0.850262	+	0.526360i
$37$	2.44642	+	2.44642i	0.402189	+	0.402189i	0.879004	−	0.476815i	$-0.158209\pi$
$37$	2.44642	+	2.44642i	0.402189	+	0.402189i	−0.476815	+	0.879004i	$0.658209\pi$
$38$	−3.16999	+	4.46633i	−0.514240	+	0.724534i
$39$	−8.12012	−	1.25050i	−1.30026	−	0.200240i
$40$	−0.679663	−	2.74555i	−0.107464	−	0.434110i
$41$	−3.42919	−	5.93954i	−0.535550	−	0.927600i	−0.999136	−	0.0415485i	$-0.986771\pi$
$41$	−3.42919	−	5.93954i	−0.535550	−	0.927600i	0.463586	−	0.886052i	$-0.346562\pi$
$42$	−7.07464	−	1.77966i	−1.09164	−	0.274608i
$43$	1.03790	+	3.87351i	0.158279	+	0.590705i	0.998802	+	0.0489295i	$0.0155810\pi$
$43$	1.03790	+	3.87351i	0.158279	+	0.590705i	−0.840523	+	0.541775i	$0.817752\pi$
$44$	6.88660	−	4.69233i	1.03819	−	0.707395i
$45$	−2.99712	−	0.131357i	−0.446785	−	0.0195816i
$46$	−2.67650	−	3.23134i	−0.394628	−	0.476436i
$47$	5.08451	−	8.80663i	0.741652	−	1.28458i	−0.210090	−	0.977682i	$-0.567376\pi$
$47$	5.08451	−	8.80663i	0.741652	−	1.28458i	0.951743	−	0.306898i	$-0.0992909\pi$
$48$	−4.91741	+	4.88048i	−0.709767	+	0.704436i
$49$	−0.934810	−	1.61914i	−0.133544	−	0.231305i
$50$	0.492153	−	1.32582i	0.0696009	−	0.187499i
$51$	0.833979	+	7.62087i	0.116780	+	1.06714i
$52$	−9.46051	+	0.706257i	−1.31194	+	0.0979402i
$53$	3.76303	−	3.76303i	0.516892	−	0.516892i	−0.399737	−	0.916630i	$-0.630899\pi$
$53$	3.76303	−	3.76303i	0.516892	−	0.516892i	0.916630	+	0.399737i	$0.130899\pi$
$54$	3.49177	+	6.46588i	0.475169	+	0.879894i
$55$	4.16663			0.561828
$56$	−8.42205	−	0.161111i	−1.12544	−	0.0215293i
$57$	5.23101	+	4.19904i	0.692864	+	0.556177i
$58$	2.79944	+	6.10473i	0.367584	+	0.801590i
$59$	−0.804446	+	3.00223i	−0.104730	+	0.390858i	−0.998314	−	0.0580376i	$-0.981516\pi$
$59$	−0.804446	+	3.00223i	−0.104730	+	0.390858i	0.893584	+	0.448895i	$0.148182\pi$
$60$	−3.40593	+	0.632151i	−0.439704	+	0.0816104i
$61$	−3.55942	−	13.2839i	−0.455737	−	1.70083i	−0.685913	−	0.727683i	$-0.740597\pi$
$61$	−3.55942	−	13.2839i	−0.455737	−	1.70083i	0.230177	−	0.973149i	$-0.426070\pi$
$62$	−3.95275	−	4.77216i	−0.501999	−	0.606065i
$63$	−2.68810	+	8.52061i	−0.338668	+	1.07350i
$64$	−4.26204	+	6.77015i	−0.532756	+	0.846269i
$65$	−4.10792	−	2.37171i	−0.509525	−	0.294174i
$66$	−5.23819	−	8.75934i	−0.644777	−	1.07820i
$67$	3.98445	−	14.8702i	0.486778	−	1.81668i	−0.0851369	−	0.996369i	$-0.527133\pi$
$67$	3.98445	−	14.8702i	0.486778	−	1.81668i	0.571915	−	0.820313i	$-0.306201\pi$
$68$	2.92137	+	8.35642i	0.354268	+	1.01337i
$69$	−4.14445	+	3.03831i	−0.498934	+	0.365769i
$70$	−3.43463	−	2.43774i	−0.410517	−	0.291365i
$71$		−	9.65235i		−	1.14552i	−0.819722	−	0.572761i	$-0.805872\pi$
$71$		−	9.65235i		−	1.14552i	0.819722	−	0.572761i	$-0.194128\pi$
$72$	5.61081	+	6.36544i	0.661240	+	0.750174i
$73$			9.33374i			1.09243i	0.837645	+	0.546216i	$0.183932\pi$
$73$			9.33374i			1.09243i	−0.837645	+	0.546216i	$0.816068\pi$
$74$	2.83191	−	3.99000i	0.329203	−	0.463829i
$75$	−1.58531	−	0.697710i	−0.183056	−	0.0805646i
$76$	6.97756	+	3.36266i	0.800381	+	0.385724i
$77$	3.21169	−	11.9862i	0.366006	−	1.36595i
$78$	0.178432	+	11.6176i	0.0202034	+	1.31543i
$79$	−3.33418	−	1.92499i	−0.375125	−	0.216578i	0.300570	−	0.953760i	$-0.402823\pi$
$79$	−3.33418	−	1.92499i	−0.375125	−	0.216578i	−0.675695	+	0.737181i	$0.736156\pi$
$80$	−3.66716	+	1.59748i	−0.410001	+	0.178604i
$81$	8.15804	−	3.80085i	0.906449	−	0.422316i
$82$	−7.46964	+	6.18704i	−0.824884	+	0.683245i
$83$	0.399348	+	1.49039i	0.0438341	+	0.163591i	0.984373	−	0.176094i	$-0.0563462\pi$
$83$	0.399348	+	1.49039i	0.0438341	+	0.163591i	−0.940539	+	0.339685i	$0.889680\pi$
$84$	−0.806819	+	10.2852i	−0.0880312	+	1.12220i
$85$	−1.14558	+	4.27536i	−0.124256	+	0.463728i
$86$	5.15504	−	2.36394i	0.555882	−	0.254910i
$87$	7.66636	−	2.98055i	0.821920	−	0.319549i
$88$	−8.17235	−	8.49111i	−0.871175	−	0.905156i
$89$	16.6062			1.76025			0.880127	−	0.474738i	$-0.157457\pi$
$89$	16.6062			1.76025			0.880127	+	0.474738i	$0.157457\pi$
$90$	0.526245	+	4.20988i	0.0554711	+	0.443760i
$91$	−9.98916	+	9.98916i	−1.04715	+	1.04715i
$92$	−3.87185	+	4.49658i	−0.403668	+	0.468801i
$93$	−6.12068	+	4.48708i	−0.634685	+	0.465289i
$94$	−13.4822	−	5.00471i	−1.39059	−	0.516197i
$95$	1.93639	+	3.35393i	0.198670	+	0.344106i
$96$	7.96859	+	5.70102i	0.813291	+	0.581857i
$97$	−0.532184	+	0.921769i	−0.0540351	+	0.0935915i	−0.891778	−	0.452474i	$-0.850542\pi$
$97$	−0.532184	+	0.921769i	−0.0540351	+	0.0935915i	0.837743	+	0.546065i	$0.183875\pi$
$98$	−2.03625	+	1.68661i	−0.205692	+	0.170373i
$99$	−11.0885	+	5.76996i	−1.11444	+	0.579902i
$100$	−1.96503	−	0.372383i	−0.196503	−	0.0372383i
$101$	−2.61098	−	9.74430i	−0.259802	−	0.969594i	−0.965356	−	0.260938i	$-0.915968\pi$
$101$	−2.61098	−	9.74430i	−0.259802	−	0.969594i	0.705554	−	0.708656i	$-0.250698\pi$
$102$	10.4281	−	2.96658i	1.03254	−	0.293735i
$103$	5.61640	+	9.72788i	0.553400	+	0.958517i	0.998026	+	0.0628006i	$0.0200032\pi$
$103$	5.61640	+	9.72788i	0.553400	+	0.958517i	−0.444626	+	0.895716i	$0.646663\pi$
$104$	3.22393	+	13.0233i	0.316132	+	1.27704i
$105$	−3.22908	+	4.02267i	−0.315126	+	0.392572i
$106$	−6.13734	−	4.35599i	−0.596111	−	0.423091i
$107$	13.7211	+	13.7211i	1.32646	+	1.32646i	0.908432	+	0.418032i	$0.137280\pi$
$107$	13.7211	+	13.7211i	1.32646	+	1.32646i	0.418032	+	0.908432i	$0.362720\pi$
$108$	8.18868	−	6.39887i	0.787956	−	0.615731i
$109$	−2.96709	+	2.96709i	−0.284196	+	0.284196i	−0.834780	−	0.550584i	$-0.814405\pi$
$109$	−2.96709	+	2.96709i	−0.284196	+	0.284196i	0.550584	+	0.834780i	$0.314405\pi$
$110$	−0.986203	−	5.80939i	−0.0940308	−	0.553903i
$111$	−4.67313	−	3.75122i	−0.443554	−	0.356050i
$112$	1.76879	+	11.7807i	0.167135	+	1.11317i
$113$	14.6636	−	8.46605i	1.37944	−	0.796419i	0.387346	−	0.921934i	$-0.373392\pi$
$113$	14.6636	−	8.46605i	1.37944	−	0.796419i	0.992092	+	0.125516i	$0.0400585\pi$
$114$	4.61645	−	8.28729i	0.432370	−	0.776176i
$115$	−2.86582	+	0.767895i	−0.267239	+	0.0716066i
$116$	7.84901	−	5.34809i	0.728763	−	0.496558i
$117$	14.2166	+	0.623083i	1.31433	+	0.0576040i
$118$	4.37632	+	0.411010i	0.402873	+	0.0378365i
$119$	11.4159	+	6.59100i	1.04650	+	0.604196i
$120$	1.68754	+	4.59915i	0.154051	+	0.419843i
$121$	5.50860	−	3.18039i	0.500782	−	0.289127i
$122$	−17.6788	+	8.10696i	−1.60057	+	0.733969i
$123$	7.02342	+	9.58040i	0.633280	+	0.863836i
$124$	−5.71808	+	6.64071i	−0.513499	+	0.596353i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	12.5162	+	1.73117i	1.11504	+	0.154225i
$127$		−	4.37422i		−	0.388149i	−0.980987	−	0.194075i	$-0.937830\pi$
$127$		−	4.37422i		−	0.388149i	0.980987	−	0.194075i	$-0.0621704\pi$
$128$	10.4482	+	4.33999i	0.923497	+	0.383604i
$129$	−2.51688	−	6.47374i	−0.221599	−	0.569981i
$130$	−2.33448	+	6.28889i	−0.204748	+	0.551573i
$131$	−8.73496	−	2.34052i	−0.763177	−	0.204493i	−0.143822	−	0.989604i	$-0.545939\pi$
$131$	−8.73496	−	2.34052i	−0.763177	−	0.204493i	−0.619355	+	0.785111i	$0.712606\pi$
$132$	−10.9730	+	9.37669i	−0.955079	+	0.816136i
$133$	11.1409	−	2.98519i	0.966037	−	0.258849i
$134$	−21.6761	−	2.03575i	−1.87253	−	0.175862i
$135$	5.18511	−	0.338549i	0.446263	−	0.0291377i
$136$	10.9596	−	6.05105i	0.939779	−	0.518874i
$137$	4.56236	−	7.90224i	0.389789	−	0.675134i	−0.602632	−	0.798019i	$-0.705881\pi$
$137$	4.56236	−	7.90224i	0.389789	−	0.675134i	0.992421	+	0.122885i	$0.0392146\pi$
$138$	5.21717	+	5.05933i	0.444115	+	0.430679i
$139$	5.33483	+	1.42946i	0.452494	+	0.121245i	0.477866	−	0.878433i	$-0.341410\pi$
$139$	5.33483	+	1.42946i	0.452494	+	0.121245i	−0.0253720	+	0.999678i	$0.508077\pi$
$140$	−2.58591	+	5.36578i	−0.218549	+	0.453491i
$141$	−7.09503	+	16.1210i	−0.597509	+	1.35764i
$142$	−13.4579	+	2.28462i	−1.12936	+	0.191721i
$143$	−19.7641			−1.65275
$144$	7.54708	−	9.32960i	0.628924	−	0.777467i
$145$	4.74892			0.394377
$146$	13.0137	−	2.20921i	1.07702	−	0.182836i
$147$	1.91461	+	2.61165i	0.157914	+	0.215405i
$148$	−6.23341	−	3.00404i	−0.512384	−	0.246931i
$149$	−21.3173	−	5.71195i	−1.74638	−	0.467941i	−0.762532	−	0.646951i	$-0.776044\pi$
$149$	−21.3173	−	5.71195i	−1.74638	−	0.467941i	−0.983847	+	0.179010i	$0.942711\pi$
$150$	−0.597565	+	2.37548i	−0.0487910	+	0.193957i
$151$	−3.49253	+	6.04924i	−0.284218	+	0.492281i	−0.972419	−	0.233240i	$-0.925067\pi$
$151$	−3.49253	+	6.04924i	−0.284218	+	0.492281i	0.688201	+	0.725520i	$0.258401\pi$
$152$	3.03692	−	10.5245i	0.246327	−	0.853648i
$153$	−2.87184	−	12.9643i	−0.232175	−	1.04810i
$154$	−17.4721	−	1.64093i	−1.40794	−	0.132230i
$155$	−4.23235	+	1.13405i	−0.339951	+	0.0910895i
$156$	16.1558	−	2.99856i	1.29350	−	0.240077i
$157$	13.5301	+	3.62538i	1.07982	+	0.289337i	0.754522	−	0.656275i	$-0.227869\pi$
$157$	13.5301	+	3.62538i	1.07982	+	0.289337i	0.325298	+	0.945612i	$0.394536\pi$
$158$	−1.89478	+	5.10436i	−0.150740	+	0.406081i
$159$	−5.77005	+	7.18811i	−0.457595	+	0.570054i
$160$	3.09529	+	4.73489i	0.244704	+	0.374326i
$161$			8.83605i			0.696378i
$162$	−7.23032	−	10.4748i	−0.568068	−	0.822982i
$163$	−16.9473	−	16.9473i	−1.32742	−	1.32742i	−0.907616	−	0.419801i	$-0.862100\pi$
$163$	−16.9473	−	16.9473i	−1.32742	−	1.32742i	−0.419801	−	0.907616i	$-0.637900\pi$
$164$	10.3944	+	8.95024i	0.811665	+	0.698897i
$165$	−7.17398	+	0.785074i	−0.558494	+	0.0611179i
$166$	1.98347	−	0.909558i	0.153947	−	0.0705954i
$167$	2.51170	−	1.45013i	0.194362	−	0.112215i	−0.399661	−	0.916663i	$-0.630872\pi$
$167$	2.51170	−	1.45013i	0.194362	−	0.112215i	0.594023	+	0.804448i	$0.297539\pi$
$168$	14.5312	−	1.30948i	1.12111	−	0.101029i
$169$	8.22725	+	4.75000i	0.632865	+	0.365385i
$170$	6.23214	+	0.585303i	0.477983	+	0.0448907i
$171$	−9.79778	−	6.24417i	−0.749255	−	0.477504i
$172$	−4.51611	−	6.62798i	−0.344350	−	0.505378i
$173$	−1.15459	+	0.309370i	−0.0877816	+	0.0235210i	−0.302442	−	0.953168i	$-0.597802\pi$
$173$	−1.15459	+	0.309370i	−0.0877816	+	0.0235210i	0.214661	+	0.976689i	$0.431135\pi$
$174$	−5.97024	−	9.98348i	−0.452603	−	0.756846i
$175$	−2.57919	+	1.48910i	−0.194968	+	0.112565i
$176$	−9.90455	+	13.4042i	−0.746583	+	1.01038i
$177$	0.819393	−	5.32073i	0.0615893	−	0.399931i
$178$	−3.93054	−	23.1535i	−0.294606	−	1.73543i
$179$	7.55957	−	7.55957i	0.565029	−	0.565029i	−0.365703	−	0.930732i	$-0.619171\pi$
$179$	7.55957	−	7.55957i	0.565029	−	0.565029i	0.930732	+	0.365703i	$0.119171\pi$
$180$	5.74513	−	1.73017i	0.428217	−	0.128959i
$181$	3.25387	+	3.25387i	0.241858	+	0.241858i	0.817619	−	0.575760i	$-0.195294\pi$
$181$	3.25387	+	3.25387i	0.241858	+	0.241858i	−0.575760	+	0.817619i	$0.695294\pi$
$182$	16.2919	+	11.5632i	1.20763	+	0.857121i
$183$	8.63145	+	22.2012i	0.638055	+	1.64116i
$184$	7.18586	+	4.33409i	0.529749	+	0.319513i
$185$	−1.72988	−	2.99624i	−0.127183	−	0.220288i
$186$	7.70490	+	7.47180i	0.564950	+	0.547859i
$187$	4.77320	+	17.8138i	0.349051	+	1.30268i
$188$	−3.78677	+	19.9824i	−0.276179	+	1.45737i
$189$	3.02284	−	15.1770i	0.219879	−	1.10397i
$190$	4.21794	−	3.49369i	0.306002	−	0.253459i
$191$	−0.832661	+	1.44221i	−0.0602492	+	0.104355i	−0.894577	−	0.446914i	$-0.852523\pi$
$191$	−0.832661	+	1.44221i	−0.0602492	+	0.104355i	0.834328	+	0.551269i	$0.185856\pi$
$192$	6.06264	−	12.4597i	0.437533	−	0.899202i
$193$	2.12819	+	3.68614i	0.153191	+	0.265334i	0.932399	−	0.361431i	$-0.117712\pi$
$193$	2.12819	+	3.68614i	0.153191	+	0.265334i	−0.779208	+	0.626765i	$0.784378\pi$
$194$	1.41115	+	0.523831i	0.101315	+	0.0376089i
$195$	7.51978	+	3.30953i	0.538502	+	0.237000i
$196$	2.83354	+	2.43987i	0.202396	+	0.174276i
$197$	−1.97413	+	1.97413i	−0.140651	+	0.140651i	−0.773926	−	0.633276i	$-0.781710\pi$
$197$	−1.97413	+	1.97413i	−0.140651	+	0.140651i	0.633276	+	0.773926i	$0.281710\pi$
$198$	10.6694	+	14.0946i	0.758241	+	1.00166i
$199$	13.3688			0.947689			0.473845	−	0.880609i	$-0.342866\pi$
$199$	13.3688			0.947689			0.473845	+	0.880609i	$0.342866\pi$
$200$	−0.0540969	+	2.82791i	−0.00382523	+	0.199963i
$201$	−4.05849	+	26.3538i	−0.286264	+	1.85885i
$202$	−12.9681	+	5.94678i	−0.912436	+	0.418414i
$203$	3.66053	−	13.6613i	0.256919	−	0.958834i
$204$	−6.60444	−	13.8374i	−0.462403	−	0.968813i
$205$	1.77508	+	6.62470i	0.123977	+	0.462689i
$206$	12.2339	−	10.1333i	0.852377	−	0.706017i
$207$	6.56333	−	6.01217i	0.456183	−	0.417875i
$208$	17.3949	−	7.57751i	1.20612	−	0.525406i
$209$	13.9746	+	8.06823i	0.966642	+	0.558091i
$210$	6.37297	+	3.55007i	0.439776	+	0.244978i
$211$	−0.692154	+	2.58316i	−0.0476499	+	0.177832i	−0.985650	−	0.168804i	$-0.946009\pi$
$211$	−0.692154	+	2.58316i	−0.0476499	+	0.177832i	0.938000	+	0.346636i	$0.112676\pi$
$212$	−4.62076	+	9.58811i	−0.317355	+	0.658514i
$213$	1.81869	+	16.6191i	0.124615	+	1.13872i
$214$	15.8831	−	22.3784i	1.08575	−	1.52976i
$215$		−	4.01015i		−	0.273490i
$216$	−10.8599	−	9.90264i	−0.738923	−	0.673790i
$217$			13.0494i			0.885851i
$218$	4.83919	+	3.43463i	0.327752	+	0.232622i
$219$	−1.75866	−	16.0706i	−0.118839	−	1.08595i
$220$	−7.86640	+	2.75006i	−0.530353	+	0.185409i
$221$	5.43396	−	20.2798i	0.365528	−	1.36417i
$222$	−4.12411	+	7.40346i	−0.276792	+	0.496888i
$223$	−8.15431	−	4.70789i	−0.546053	−	0.315264i	0.201475	−	0.979494i	$-0.435426\pi$
$223$	−8.15431	−	4.70789i	−0.546053	−	0.315264i	−0.747529	+	0.664230i	$0.768760\pi$
$224$	16.0068	−	5.25456i	1.06950	−	0.351085i
$225$	2.86100	+	0.902594i	0.190733	+	0.0601729i
$226$	−15.2747	−	18.4412i	−1.01606	−	1.22669i
$227$	−2.95348	−	11.0225i	−0.196029	−	0.731592i	−0.991998	−	0.126254i	$-0.959705\pi$
$227$	−2.95348	−	11.0225i	−0.196029	−	0.731592i	0.795968	−	0.605338i	$-0.206962\pi$
$228$	−12.6474	−	4.47503i	−0.837592	−	0.296366i
$229$	3.53600	−	13.1965i	0.233665	−	0.872051i	−0.745081	−	0.666975i	$-0.767589\pi$
$229$	3.53600	−	13.1965i	0.233665	−	0.872051i	0.978746	−	0.205077i	$-0.0657444\pi$
$230$	1.74896	+	3.81397i	0.115323	+	0.251486i
$231$	−3.27136	+	21.2426i	−0.215240	+	1.39766i
$232$	−9.31445	−	9.67777i	−0.611524	−	0.635376i
$233$	−23.8705			−1.56381			−0.781904	−	0.623399i	$-0.785751\pi$
$233$	−23.8705			−1.56381			−0.781904	+	0.623399i	$0.785751\pi$
$234$	−2.49620	−	19.9692i	−0.163182	−	1.30543i
$235$	−7.19059	+	7.19059i	−0.469062	+	0.469062i
$236$	−0.462777	−	6.19903i	−0.0301242	−	0.403523i
$237$	6.10341	+	2.68617i	0.396459	+	0.174485i
$238$	6.48756	−	17.4769i	0.420526	−	1.13286i
$239$	2.32722	+	4.03086i	0.150535	+	0.260735i	0.931424	−	0.363935i	$-0.118567\pi$
$239$	2.32722	+	4.03086i	0.150535	+	0.260735i	−0.780889	+	0.624670i	$0.785234\pi$
$240$	6.01302	−	3.44146i	0.388139	−	0.222145i
$241$	0.805189	−	1.39463i	0.0518668	−	0.0898359i	−0.838926	−	0.544245i	$-0.816816\pi$
$241$	0.805189	−	1.39463i	0.0518668	−	0.0898359i	0.890793	+	0.454409i	$0.150150\pi$
$242$	−5.73815	−	6.92768i	−0.368862	−	0.445328i
$243$	−13.3301	+	8.08133i	−0.855128	+	0.518417i
$244$	15.4877	+	22.7302i	0.991497	+	1.45515i
$245$	0.483893	+	1.80591i	0.0309148	+	0.115376i
$246$	11.6953	−	12.0601i	0.745662	−	0.768924i
$247$	−9.18512	−	15.9091i	−0.584435	−	1.01227i
$248$	10.6123	+	6.40073i	0.673884	+	0.406447i
$249$	−0.968404	−	2.49086i	−0.0613701	−	0.157852i
$250$	−0.818529	+	1.15326i	−0.0517683	+	0.0729386i
$251$	15.3041	+	15.3041i	0.965986	+	0.965986i	0.999440	−	0.0334542i	$-0.0106508\pi$
$251$	15.3041	+	15.3041i	0.965986	+	0.965986i	−0.0334542	+	0.999440i	$0.510651\pi$
$252$	−0.548767	−	17.8607i	−0.0345691	−	1.12512i
$253$	−8.74129	+	8.74129i	−0.549560	+	0.549560i
$254$	−6.09882	+	1.03534i	−0.382674	+	0.0649629i
$255$	1.16686	−	7.57704i	0.0730719	−	0.474493i
$256$	3.57811	−	15.5948i	0.223632	−	0.974674i
$257$	−22.5791	+	13.0361i	−1.40845	+	0.813167i	−0.995239	−	0.0974693i	$-0.968925\pi$
$257$	−22.5791	+	13.0361i	−1.40845	+	0.813167i	−0.413208	+	0.910636i	$0.635592\pi$
$258$	−8.43039	+	5.04147i	−0.524853	+	0.313868i
$259$	−9.95273	+	2.66683i	−0.618432	+	0.165708i
$260$	9.32094	+	1.76637i	0.578060	+	0.109546i
$261$	−12.6381	+	6.57632i	−0.782281	+	0.407064i
$262$	−1.19583	+	12.7328i	−0.0738785	+	0.786637i
$263$	−14.5935	−	8.42557i	−0.899875	−	0.519543i	−0.0227152	−	0.999742i	$-0.507231\pi$
$263$	−14.5935	−	8.42557i	−0.899875	−	0.519543i	−0.877160	+	0.480199i	$0.840564\pi$
$264$	15.6708	+	13.0799i	0.964472	+	0.805014i
$265$	−4.60875	+	2.66087i	−0.283114	+	0.163456i
$266$	−6.79910	−	14.8268i	−0.416879	−	0.909089i
$267$	−28.5921	+	3.12893i	−1.74981	+	0.191488i
$268$	2.29215	+	30.7041i	0.140016	+	1.87555i
$269$	3.44439	+	3.44439i	0.210008	+	0.210008i	0.804271	−	0.594263i	$-0.202556\pi$
$269$	3.44439	+	3.44439i	0.210008	+	0.210008i	−0.594263	+	0.804271i	$0.702556\pi$
$270$	−1.69930	−	7.14929i	−0.103416	−	0.435092i
$271$		−	26.5803i		−	1.61464i	−0.590116	−	0.807318i	$-0.700918\pi$
$271$		−	26.5803i		−	1.61464i	0.590116	−	0.807318i	$-0.299082\pi$
$272$	−11.0308	−	13.8484i	−0.668842	−	0.839682i
$273$	15.3169	−	19.0812i	0.927021	−	1.15485i
$274$	−12.0977	−	4.49076i	−0.730849	−	0.271297i
$275$	−4.02465	−	1.07840i	−0.242696	−	0.0650301i
$276$	5.81920	−	8.47161i	0.350275	−	0.509931i
$277$	−17.4039	+	4.66336i	−1.04570	+	0.280194i	−0.740473	−	0.672086i	$-0.765399\pi$
$277$	−17.4039	+	4.66336i	−1.04570	+	0.280194i	−0.305226	+	0.952280i	$0.598732\pi$
$278$	0.730346	−	7.77651i	0.0438032	−	0.466404i
$279$	9.69296	−	8.87899i	0.580302	−	0.531571i
$280$	8.09338	+	2.33541i	0.483672	+	0.139567i
$281$	−13.2388	+	22.9302i	−0.789759	+	1.36790i	0.136356	+	0.990660i	$0.456461\pi$
$281$	−13.2388	+	22.9302i	−0.789759	+	1.36790i	−0.926115	+	0.377242i	$0.876872\pi$
$282$	24.1563	+	6.07665i	1.43849	+	0.361859i
$283$	8.13231	+	2.17905i	0.483415	+	0.129531i	0.492293	−	0.870430i	$-0.336159\pi$
$283$	8.13231	+	2.17905i	0.483415	+	0.129531i	−0.00887705	+	0.999961i	$0.502826\pi$
$284$	6.37074	+	18.2232i	0.378034	+	1.08135i
$285$	−3.96597	−	5.40985i	−0.234924	−	0.320452i
$286$	4.67797	+	27.5563i	0.276614	+	1.62944i
$287$	20.4256			1.20568
$288$	−14.7943	−	8.31441i	−0.871761	−	0.489931i
$289$	−2.59105			−0.152415
$290$	−1.12403	−	6.62126i	−0.0660051	−	0.388814i
$291$	0.742619	−	1.68735i	0.0435331	−	0.0989142i
$292$	−6.16046	−	17.6217i	−0.360513	−	1.03123i
$293$	−21.9104	−	5.87088i	−1.28002	−	0.342980i	−0.446158	−	0.894954i	$-0.647208\pi$
$293$	−21.9104	−	5.87088i	−1.28002	−	0.342980i	−0.833861	+	0.551974i	$0.813875\pi$
$294$	3.18816	−	3.28762i	0.185938	−	0.191738i
$295$	1.55407	−	2.69173i	0.0904815	−	0.156719i
$296$	−2.71304	+	9.40207i	−0.157692	+	0.546484i
$297$	18.0047	−	12.0238i	1.04474	−	0.697694i
$298$	−2.91837	+	31.0739i	−0.169056	+	1.80006i
$299$	13.5938	−	3.64245i	0.786150	−	0.210648i
$300$	3.45349	+	0.270909i	0.199387	+	0.0156409i
$301$	−11.5361	−	3.09108i	−0.664927	−	0.178167i
$302$	9.26091	+	3.43772i	0.532905	+	0.197818i
$303$	6.33152	+	16.2855i	0.363736	+	0.935577i
$304$	−15.3927	−	1.74323i	−0.882834	−	0.0999810i
$305$			13.7525i			0.787468i
$306$	−17.3959	+	7.07263i	−0.994457	+	0.404316i
$307$	14.1549	+	14.1549i	0.807860	+	0.807860i	0.984310	−	0.176450i	$-0.0564613\pi$
$307$	14.1549	+	14.1549i	0.807860	+	0.807860i	−0.176450	+	0.984310i	$0.556461\pi$
$308$	1.84760	+	24.7492i	0.105277	+	1.41021i
$309$	−11.5031	−	15.6910i	−0.654387	−	0.892627i
$310$	2.58293	+	5.63260i	0.146701	+	0.319910i
$311$	1.08864	−	0.628525i	0.0617310	−	0.0356404i	−0.468817	−	0.883295i	$-0.655320\pi$
$311$	1.08864	−	0.628525i	0.0617310	−	0.0356404i	0.530548	+	0.847655i	$0.321986\pi$
$312$	−8.00471	−	21.8157i	−0.453177	−	1.23507i
$313$	19.4857	+	11.2500i	1.10139	+	0.635890i	0.936587	−	0.350435i	$-0.113966\pi$
$313$	19.4857	+	11.2500i	1.10139	+	0.635890i	0.164807	+	0.986326i	$0.447300\pi$
$314$	1.85229	−	19.7226i	0.104531	−	1.11301i
$315$	4.80180	−	7.53454i	0.270551	−	0.424523i
$316$	7.56532	+	1.43367i	0.425582	+	0.0806501i
$317$	−25.1969	+	6.75149i	−1.41520	+	0.379202i	−0.883778	−	0.467906i	$-0.845009\pi$
$317$	−25.1969	+	6.75149i	−1.41520	+	0.379202i	−0.531422	+	0.847108i	$0.678342\pi$
$318$	11.3879	+	6.34363i	0.638599	+	0.355733i
$319$	17.1360	−	9.89350i	0.959434	−	0.553929i
$320$	5.86906	−	5.43637i	0.328091	−	0.303902i
$321$	−26.2098	−	21.0392i	−1.46289	−	1.17429i
$322$	12.3198	−	2.09141i	0.686556	−	0.116550i
$323$	−12.1210	+	12.1210i	−0.674429	+	0.674429i
$324$	−12.8934	+	12.5603i	−0.716298	+	0.697794i
$325$	3.35410	+	3.35410i	0.186052	+	0.186052i
$326$	−19.6178	+	27.6404i	−1.08653	+	1.53086i
$327$	4.54959	−	5.66771i	0.251593	−	0.313425i
$328$	10.0188	−	16.6110i	0.553194	−	0.917188i
$329$	15.1426	+	26.2278i	0.834841	+	1.44599i
$330$	2.79262	+	9.81662i	0.153729	+	0.540387i
$331$	−3.74474	−	13.9756i	−0.205829	−	0.768166i	−0.989195	−	0.146605i	$-0.953165\pi$
$331$	−3.74474	−	13.9756i	−0.205829	−	0.768166i	0.783366	−	0.621561i	$-0.213501\pi$
$332$	−1.73764	−	2.55020i	−0.0953652	−	0.139961i
$333$	8.75286	+	5.57824i	0.479654	+	0.305686i
$334$	−2.61637	−	3.15875i	−0.143161	−	0.172839i
$335$	−7.69737	+	13.3322i	−0.420552	+	0.728418i
$336$	−5.26518	−	19.9504i	−0.287239	−	1.08839i
$337$	−3.75130	−	6.49744i	−0.204346	−	0.353938i	0.745578	−	0.666418i	$-0.232174\pi$
$337$	−3.75130	−	6.49744i	−0.204346	−	0.353938i	−0.949924	+	0.312480i	$0.898840\pi$
$338$	4.67545	−	12.5952i	0.254311	−	0.685091i
$339$	−23.6522	+	17.3395i	−1.28461	+	0.941753i
$340$	−0.659022	−	8.82779i	−0.0357405	−	0.478754i
$341$	−12.9094	+	12.9094i	−0.699086	+	0.699086i
$342$	−6.38699	+	15.1386i	−0.345369	+	0.818604i
$343$	−15.2793			−0.825002
$344$	−8.17224	+	7.86544i	−0.440617	+	0.424076i
$345$	4.78961	−	1.86212i	0.257864	−	0.100253i
$346$	0.704625	+	1.53657i	0.0378809	+	0.0826068i
$347$	5.83725	−	21.7849i	0.313360	−	1.16948i	−0.612147	−	0.790744i	$-0.709694\pi$
$347$	5.83725	−	21.7849i	0.313360	−	1.16948i	0.925507	−	0.378731i	$-0.123640\pi$
$348$	−12.5065	+	10.6871i	−0.670420	+	0.572889i
$349$	−0.709833	−	2.64913i	−0.0379965	−	0.141805i	0.944322	−	0.329023i	$-0.106719\pi$
$349$	−0.709833	−	2.64913i	−0.0379965	−	0.141805i	−0.982318	+	0.187218i	$0.940053\pi$
$350$	2.68667	+	3.24362i	0.143608	+	0.173379i
$351$	−24.5951	+	1.60588i	−1.31279	+	0.0857155i
$352$	21.0333	+	10.6369i	1.12108	+	0.566950i
$353$	14.3749	+	8.29934i	0.765097	+	0.441729i	0.831123	−	0.556089i	$-0.187699\pi$
$353$	14.3749	+	8.29934i	0.765097	+	0.441729i	−0.0660255	+	0.997818i	$0.521032\pi$
$354$	−7.61246	+	0.116918i	−0.404598	+	0.00621413i
$355$	−2.49821	+	9.32345i	−0.132591	+	0.494837i
$356$	−31.3518	+	10.9604i	−1.66164	+	0.580902i
$357$	−20.8975	−	9.19721i	−1.10601	−	0.486768i
$358$	−12.3293	−	8.75077i	−0.651626	−	0.462493i
$359$		−	3.42902i		−	0.180977i	−0.995897	−	0.0904885i	$-0.971157\pi$
$359$		−	3.42902i		−	0.180977i	0.995897	−	0.0904885i	$-0.0288428\pi$
$360$	−3.77213	−	7.60073i	−0.198809	−	0.400593i
$361$		−	4.00154i		−	0.210607i
$362$	3.76660	−	5.30693i	0.197968	−	0.278926i
$363$	−8.88531	+	6.51384i	−0.466358	+	0.341888i
$364$	12.2660	−	25.4521i	0.642915	−	1.33405i
$365$	2.41575	−	9.01570i	0.126446	−	0.471903i
$366$	28.9114	−	17.2894i	1.51122	−	0.903730i
$367$	−24.3122	−	14.0366i	−1.26909	−	0.732707i	−0.294271	−	0.955722i	$-0.595077\pi$
$367$	−24.3122	−	14.0366i	−1.26909	−	0.732707i	−0.974815	+	0.223015i	$0.928410\pi$
$368$	4.34204	−	11.0448i	0.226345	−	0.575752i
$369$	−13.8979	−	15.1719i	−0.723494	−	0.789819i
$370$	−3.76811	+	3.12109i	−0.195895	+	0.162258i
$371$	4.10206	+	15.3091i	0.212968	+	0.794808i
$372$	8.59400	−	12.5112i	0.445578	−	0.648675i
$373$	2.26181	−	8.44121i	0.117112	−	0.437069i	−0.882324	−	0.470643i	$-0.844022\pi$
$373$	2.26181	−	8.44121i	0.117112	−	0.437069i	0.999436	+	0.0335735i	$0.0106888\pi$
$374$	23.7074	−	10.8715i	1.22588	−	0.562151i
$375$	1.35071	+	1.08424i	0.0697503	+	0.0559901i
$376$	28.7571	+	0.550113i	1.48303	+	0.0283699i
$377$	−22.5261			−1.16015
$378$	−21.8763	−	0.622378i	−1.12519	−	0.0320117i
$379$	−20.3202	+	20.3202i	−1.04378	+	1.04378i	−0.0447802	+	0.998997i	$0.514259\pi$
$379$	−20.3202	+	20.3202i	−1.04378	+	1.04378i	−0.998997	+	0.0447802i	$0.985741\pi$
$380$	−5.86948	−	5.05401i	−0.301098	−	0.259265i
$381$	0.824189	+	7.53141i	0.0422245	+	0.385846i
$382$	2.20791	+	0.819593i	0.112966	+	0.0419340i
$383$	4.82602	+	8.35891i	0.246598	+	0.427120i	0.962580	−	0.270999i	$-0.0873539\pi$
$383$	4.82602	+	8.35891i	0.246598	+	0.427120i	−0.715982	+	0.698119i	$0.754021\pi$
$384$	−18.8071	−	5.50383i	−0.959747	−	0.280866i
$385$	−6.20451	+	10.7465i	−0.316211	+	0.547693i
$386$	4.63573	−	3.83974i	0.235952	−	0.195438i
$387$	5.55327	+	10.6721i	0.282289	+	0.542492i
$388$	0.396352	−	2.09151i	0.0201217	−	0.106180i
$389$	−3.07884	−	11.4904i	−0.156103	−	0.582585i	−0.999008	−	0.0445229i	$-0.985823\pi$
$389$	−3.07884	−	11.4904i	−0.156103	−	0.582585i	0.842905	−	0.538062i	$-0.180843\pi$
$390$	2.83450	−	11.2679i	0.143530	−	0.570572i
$391$	−6.56606	−	11.3727i	−0.332060	−	0.575144i
$392$	2.73115	−	4.52821i	0.137944	−	0.228709i
$393$	15.4806	+	2.38401i	0.780893	+	0.120258i
$394$	3.21971	+	2.28520i	0.162207	+	0.115127i
$395$	2.72235	+	2.72235i	0.136976	+	0.136976i
$396$	17.1263	−	18.2120i	0.860628	−	0.915190i
$397$	19.2120	−	19.2120i	0.964224	−	0.964224i	−0.0351575	−	0.999382i	$-0.511193\pi$
$397$	19.2120	−	19.2120i	0.964224	−	0.964224i	0.999382	+	0.0351575i	$0.0111933\pi$
$398$	−3.16427	−	18.6397i	−0.158611	−	0.934322i
$399$	−18.6196	+	7.23898i	−0.932145	+	0.362402i
$400$	3.95566	−	0.593915i	0.197783	−	0.0296958i
$401$	−4.58917	+	2.64956i	−0.229172	+	0.132313i	−0.610190	−	0.792255i	$-0.708907\pi$
$401$	−4.58917	+	2.64956i	−0.229172	+	0.132313i	0.381018	+	0.924568i	$0.375574\pi$
$402$	37.7048	−	0.579100i	1.88055	−	0.0288829i
$403$	20.0758	−	5.37929i	1.00005	−	0.267962i
$404$	11.3608	+	16.6735i	0.565223	+	0.829537i
$405$	−8.86379	+	1.55988i	−0.440445	+	0.0775111i
$406$	−19.9139	−	1.87025i	−0.988309	−	0.0928189i
$407$	−12.4842	−	7.20776i	−0.618819	−	0.357276i
$408$	−17.7298	+	12.4835i	−0.877757	+	0.618027i
$409$	−15.7158	+	9.07351i	−0.777095	+	0.448656i	−0.835400	−	0.549643i	$-0.814764\pi$
$409$	−15.7158	+	9.07351i	−0.777095	+	0.448656i	0.0583045	+	0.998299i	$0.481431\pi$
$410$	8.81644	−	4.04294i	0.435413	−	0.199667i
$411$	−6.36641	+	14.4655i	−0.314032	+	0.713531i
$412$	−17.0241	−	14.6589i	−0.838717	−	0.722191i
$413$	−6.54543	−	6.54543i	−0.322080	−	0.322080i
$414$	−9.93605	−	7.72800i	−0.488330	−	0.379810i
$415$		−	1.54296i		−	0.0757410i
$416$	−14.6823	−	22.4595i	−0.719857	−	1.10117i
$417$	−9.45470	−	1.45602i	−0.462998	−	0.0713017i
$418$	7.94160	−	21.3940i	0.388436	−	1.04641i
$419$	6.02111	+	1.61335i	0.294151	+	0.0788174i	0.402876	−	0.915254i	$-0.368010\pi$
$419$	6.02111	+	1.61335i	0.294151	+	0.0788174i	−0.108726	+	0.994072i	$0.534677\pi$
$420$	3.44132	−	9.72588i	0.167919	−	0.474574i
$421$	36.2309	−	9.70803i	1.76578	−	0.473141i	0.777908	−	0.628379i	$-0.216281\pi$
$421$	36.2309	−	9.70803i	1.76578	−	0.473141i	0.987877	+	0.155238i	$0.0496145\pi$
$422$	3.76543	+	0.353638i	0.183298	+	0.0172148i
$423$	9.17850	−	29.0936i	0.446274	−	1.41458i
$424$	14.4621	+	4.17314i	0.702340	+	0.202666i
$425$	2.21309	−	3.83318i	0.107351	−	0.185937i
$426$	22.7410	−	6.46934i	1.10181	−	0.313440i
$427$	39.5621	+	10.6006i	1.91454	+	0.513000i
$428$	−34.9609	−	16.8486i	−1.68990	−	0.814406i
$429$	34.0292	−	3.72393i	1.64294	−	0.179793i
$430$	−5.59122	+	0.949167i	−0.269633	+	0.0457729i
$431$	−24.7314			−1.19127			−0.595635	−	0.803256i	$-0.703099\pi$
$431$	−24.7314			−1.19127			−0.595635	+	0.803256i	$0.703099\pi$
$432$	−11.2365	+	17.4855i	−0.540615	+	0.841270i
$433$	−4.46027			−0.214347			−0.107173	−	0.994240i	$-0.534180\pi$
$433$	−4.46027			−0.214347			−0.107173	+	0.994240i	$0.534180\pi$
$434$	18.1943	−	3.08867i	0.873355	−	0.148261i
$435$	−8.17656	+	0.894790i	−0.392036	+	0.0429019i
$436$	3.64339	−	7.56007i	0.174487	−	0.362062i
$437$	−11.0987	−	2.97389i	−0.530924	−	0.142261i
$438$	−21.9904	+	6.25579i	−1.05074	+	0.298913i
$439$	17.3333	−	30.0222i	0.827274	−	1.43288i	−0.0728945	−	0.997340i	$-0.523224\pi$
$439$	17.3333	−	30.0222i	0.827274	−	1.43288i	0.900169	−	0.435541i	$-0.143443\pi$
$440$	5.69622	+	10.3169i	0.271557	+	0.491841i
$441$	−3.78860	−	4.13592i	−0.180410	−	0.196948i
$442$	−29.5616	−	2.77634i	−1.40610	−	0.132057i
$443$	−28.9974	+	7.76982i	−1.37771	+	0.369155i	−0.870287	−	0.492544i	$-0.836067\pi$
$443$	−28.9974	+	7.76982i	−1.37771	+	0.369155i	−0.507419	+	0.861700i	$0.669400\pi$
$444$	11.2985	+	3.99778i	0.536205	+	0.189726i
$445$	−16.0404	−	4.29800i	−0.760386	−	0.203745i
$446$	−4.63401	+	12.4836i	−0.219426	+	0.591115i
$447$	37.7797	+	5.81808i	1.78692	+	0.275186i
$448$	−11.1149	−	21.0740i	−0.525130	−	0.995654i
$449$			3.79192i			0.178952i	0.995989	+	0.0894759i	$0.0285192\pi$
$449$			3.79192i			0.178952i	−0.995989	+	0.0894759i	$0.971481\pi$
$450$	0.581283	−	4.20263i	0.0274019	−	0.198114i
$451$	20.2065	+	20.2065i	0.951489	+	0.951489i
$452$	−22.0965	+	25.6618i	−1.03933	+	1.20703i
$453$	4.87355	−	11.0735i	0.228979	−	0.520277i
$454$	−14.6693	+	6.72688i	−0.688464	+	0.315708i
$455$	12.2342	−	7.06340i	0.573547	−	0.331137i
$456$	−3.24587	+	18.6930i	−0.152002	+	0.875379i
$457$	−26.8166	−	15.4826i	−1.25443	−	0.724245i	−0.282444	−	0.959284i	$-0.591145\pi$
$457$	−26.8166	−	15.4826i	−1.25443	−	0.724245i	−0.971986	+	0.235039i	$0.924478\pi$
$458$	−19.2364	−	1.80662i	−0.898858	−	0.0844180i
$459$	7.38738	+	21.7804i	0.344813	+	1.01662i
$460$	4.90372	−	3.34125i	0.228637	−	0.155787i
$461$	22.8075	−	6.11126i	1.06225	−	0.284630i	0.314947	−	0.949109i	$-0.398013\pi$
$461$	22.8075	−	6.11126i	1.06225	−	0.284630i	0.747306	+	0.664480i	$0.231347\pi$
$462$	30.3922	−	0.466786i	1.41397	−	0.0217169i
$463$	34.9216	−	20.1620i	1.62294	−	0.937006i	0.636815	−	0.771017i	$-0.280251\pi$
$463$	34.9216	−	20.1620i	1.62294	−	0.937006i	0.986127	−	0.165990i	$-0.0530819\pi$
$464$	−11.2887	+	15.2775i	−0.524066	+	0.709238i
$465$	7.07346	−	2.75004i	0.328024	−	0.127530i
$466$	5.64993	+	33.2818i	0.261728	+	1.54175i
$467$	12.6030	−	12.6030i	0.583196	−	0.583196i	−0.352584	−	0.935780i	$-0.614697\pi$
$467$	12.6030	−	12.6030i	0.583196	−	0.583196i	0.935780	+	0.352584i	$0.114697\pi$
$468$	−27.2516	+	8.20689i	−1.25970	+	0.379364i
$469$	32.4198	+	32.4198i	1.49701	+	1.49701i
$470$	11.7275	+	8.32364i	0.540951	+	0.383941i
$471$	−23.9788	−	3.69274i	−1.10489	−	0.170152i
$472$	−8.53356	+	2.11249i	−0.392789	+	0.0972352i
$473$	−8.35441	−	14.4703i	−0.384136	−	0.665343i
$474$	2.30061	−	9.14556i	0.105671	−	0.420070i
$475$	−1.00235	−	3.74082i	−0.0459910	−	0.171641i
$476$	−25.9030	−	4.90875i	−1.18726	−	0.224992i
$477$	8.58033	−	13.4635i	0.392867	−	0.616450i
$478$	5.06926	−	4.19883i	0.231863	−	0.192050i
$479$	5.32400	−	9.22145i	0.243260	−	0.421339i	−0.718381	−	0.695650i	$-0.755117\pi$
$479$	5.32400	−	9.22145i	0.243260	−	0.421339i	0.961641	+	0.274311i	$0.0884499\pi$
$480$	−6.22154	−	7.56918i	−0.283973	−	0.345484i
$481$	8.20554	+	14.2124i	0.374140	+	0.648030i
$482$	−2.13506	−	0.792552i	−0.0972495	−	0.0360997i
$483$	−1.66488	−	15.2137i	−0.0757549	−	0.692246i
$484$	−8.30087	+	9.64023i	−0.377312	+	0.438192i
$485$	0.752621	−	0.752621i	0.0341748	−	0.0341748i
$486$	14.4226	+	16.6730i	0.654224	+	0.756301i
$487$	13.2254			0.599299			0.299650	−	0.954049i	$-0.403130\pi$
$487$	13.2254			0.599299			0.299650	+	0.954049i	$0.403130\pi$
$488$	28.0261	−	26.9740i	1.26868	−	1.22105i
$489$	32.3726	+	25.9862i	1.46394	+	1.17514i
$490$	2.40339	−	1.10212i	0.108574	−	0.0497887i
$491$	1.16622	−	4.35238i	0.0526306	−	0.196420i	−0.934605	−	0.355688i	$-0.884247\pi$
$491$	1.16622	−	4.35238i	0.0526306	−	0.196420i	0.987235	+	0.159268i	$0.0509133\pi$
$492$	−19.5832	−	13.4518i	−0.882877	−	0.606453i
$493$	5.44027	+	20.3034i	0.245017	+	0.914417i
$494$	−20.0075	+	16.5720i	−0.900178	+	0.745611i
$495$	12.2040	−	2.70344i	0.548531	−	0.121510i
$496$	6.41248	−	16.3114i	0.287929	−	0.732404i
$497$	24.8952	+	14.3733i	1.11670	+	0.644729i
$498$	−3.24371	+	1.93978i	−0.145354	+	0.0869235i
$499$	−2.16470	+	8.07877i	−0.0969052	+	0.361655i	−0.997301	−	0.0734157i	$-0.976610\pi$
$499$	−2.16470	+	8.07877i	−0.0969052	+	0.361655i	0.900396	+	0.435071i	$0.143277\pi$
$500$	1.80169	+	0.868281i	0.0805740	+	0.0388307i
$501$	−4.05135	+	2.97005i	−0.181001	+	0.132692i
$502$	17.7156	−	24.9603i	0.790688	−	1.11403i
$503$			9.76995i			0.435621i	0.975991	+	0.217810i	$0.0698914\pi$
$503$			9.76995i			0.435621i	−0.975991	+	0.217810i	$0.930109\pi$
$504$	−24.7727	+	4.99260i	−1.10346	+	0.222388i
$505$			10.0880i			0.448912i
$506$	14.2567	+	10.1187i	0.633786	+	0.449831i
$507$	−15.0604	−	6.62825i	−0.668857	−	0.294371i
$508$	2.88707	+	8.25833i	0.128093	+	0.366404i
$509$	5.29896	−	19.7760i	0.234872	−	0.876555i	−0.743334	−	0.668920i	$-0.766757\pi$
$509$	5.29896	−	19.7760i	0.234872	−	0.876555i	0.978206	−	0.207635i	$-0.0665767\pi$
$510$	−10.8406	+	0.166498i	−0.480030	+	0.00737267i
$511$	−24.0735	−	13.8988i	−1.06495	−	0.614848i
$512$	−22.5902	−	1.29769i	−0.998354	−	0.0573504i
$513$	18.0461	+	8.90494i	0.796753	+	0.393163i
$514$	23.5200	+	28.3958i	1.03742	+	1.25248i
$515$	−2.90726	−	10.8500i	−0.128109	−	0.478110i
$516$	9.02455	+	10.5609i	0.397284	+	0.464919i
$517$	−10.9663	+	40.9268i	−0.482297	+	1.79996i
$518$	6.07398	+	13.2455i	0.266876	+	0.581975i
$519$	1.92964	−	0.750212i	0.0847019	−	0.0329306i
$520$	0.256604	−	13.4140i	0.0112528	−	0.588241i
$521$	−22.6614			−0.992813			−0.496406	−	0.868090i	$-0.665347\pi$
$521$	−22.6614			−0.992813			−0.496406	+	0.868090i	$0.665347\pi$
$522$	12.1605	+	16.0644i	0.532249	+	0.703118i
$523$	−10.6210	+	10.6210i	−0.464425	+	0.464425i	−0.900103	−	0.435677i	$-0.856509\pi$
$523$	−10.6210	+	10.6210i	−0.464425	+	0.464425i	0.435677	+	0.900103i	$0.356509\pi$
$524$	18.0360	−	1.34644i	0.787906	−	0.0588197i
$525$	4.16020	−	3.04985i	0.181566	−	0.133106i
$526$	−8.29333	+	22.3415i	−0.361606	+	0.974136i
$527$	−9.69699	−	16.7957i	−0.422407	−	0.731631i
$528$	14.5278	−	24.9452i	0.632240	−	1.08560i
$529$	−7.09870	+	12.2953i	−0.308639	+	0.534578i
$530$	4.80080	+	5.79603i	0.208534	+	0.251763i
$531$	−0.408277	+	9.31548i	−0.0177177	+	0.404257i
$532$	−19.0632	+	12.9891i	−0.826494	+	0.563150i
$533$	−8.41995	−	31.4237i	−0.364709	−	1.36111i
$534$	11.1301	+	39.1244i	0.481645	+	1.69308i
$535$	−9.70225	−	16.8048i	−0.419465	−	0.726534i
$536$	42.2671	−	10.4632i	1.82566	−	0.451943i
$537$	−11.5915	+	14.4402i	−0.500210	+	0.623142i
$538$	3.98713	−	5.61764i	0.171898	−	0.242194i
$539$	5.50837	+	5.50837i	0.237262	+	0.237262i
$540$	−9.56581	+	4.06144i	−0.411647	+	0.174777i
$541$	24.3101	−	24.3101i	1.04517	−	1.04517i	0.0462411	−	0.998930i	$-0.485276\pi$
$541$	24.3101	−	24.3101i	1.04517	−	1.04517i	0.998930	−	0.0462411i	$-0.0147242\pi$
$542$	−37.0600	+	6.29131i	−1.59186	+	0.270235i
$543$	−6.21552	−	4.98933i	−0.266733	−	0.214113i
$544$	−16.6974	+	18.6577i	−0.715897	+	0.799942i
$545$	3.63393	−	2.09805i	0.155660	−	0.0898705i
$546$	−30.2296	−	16.8395i	−1.29371	−	0.720663i
$547$	37.6601	−	10.0910i	1.61023	−	0.431460i	0.662119	−	0.749399i	$-0.269657\pi$
$547$	37.6601	−	10.0910i	1.61023	−	0.431460i	0.948111	+	0.317939i	$0.102991\pi$
$548$	−3.39789	+	17.9303i	−0.145151	+	0.765946i
$549$	−19.0445	−	36.5991i	−0.812801	−	1.56201i
$550$	−0.550981	+	5.86668i	−0.0234939	+	0.250156i
$551$	15.9276	+	9.19578i	0.678537	+	0.391753i
$552$	−13.1890	−	6.10835i	−0.561363	−	0.259989i
$553$	9.92983	−	5.73299i	0.422259	−	0.243791i
$554$	10.6213	+	23.1619i	0.451256	+	0.984054i
$555$	3.54301	+	4.83290i	0.150392	+	0.205145i
$556$	−11.0154	+	0.822333i	−0.467157	+	0.0348747i
$557$	27.9018	+	27.9018i	1.18224	+	1.18224i	0.979163	+	0.203074i	$0.0650931\pi$
$557$	27.9018	+	27.9018i	1.18224	+	1.18224i	0.203074	+	0.979163i	$0.434907\pi$
$558$	−14.6739	−	11.4130i	−0.621196	−	0.483150i
$559$			19.0218i			0.804538i
$560$	1.34055	−	11.8371i	0.0566486	−	0.500209i
$561$	−11.5748	−	29.7720i	−0.488690	−	1.25697i
$562$	35.1043	+	13.0310i	1.48079	+	0.549679i
$563$	23.7027	+	6.35112i	0.998950	+	0.267668i	0.721005	−	0.692929i	$-0.243680\pi$
$563$	23.7027	+	6.35112i	0.998950	+	0.267668i	0.277944	+	0.960597i	$0.410347\pi$
$564$	2.75488	−	35.1186i	0.116001	−	1.47876i
$565$	−16.3551	+	4.38235i	−0.688066	+	0.184367i
$566$	1.11332	−	11.8544i	0.0467965	−	0.498276i
$567$	−2.34499	+	26.7009i	−0.0984804	+	1.12133i
$568$	23.9001	−	13.1958i	1.00282	−	0.553682i
$569$	4.73753	−	8.20564i	0.198608	−	0.343999i	−0.749470	−	0.662039i	$-0.769691\pi$
$569$	4.73753	−	8.20564i	0.198608	−	0.343999i	0.948077	+	0.318040i	$0.103025\pi$
$570$	−6.60406	+	6.81008i	−0.276613	+	0.285243i
$571$	−34.9262	−	9.35846i	−1.46162	−	0.391639i	−0.561569	−	0.827430i	$-0.689802\pi$
$571$	−34.9262	−	9.35846i	−1.46162	−	0.391639i	−0.900048	+	0.435790i	$0.856469\pi$
$572$	37.3136	−	13.0447i	1.56016	−	0.545425i
$573$	1.16191	−	2.64005i	0.0485395	−	0.110290i
$574$	−4.83455	−	28.4787i	−0.201790	−	1.18868i
$575$	2.96692			0.123729
$576$	−8.09083	+	22.5951i	−0.337118	+	0.941462i
$577$	5.89048			0.245224			0.122612	−	0.992455i	$-0.460873\pi$
$577$	5.89048			0.245224			0.122612	+	0.992455i	$0.460873\pi$
$578$	0.613279	+	3.61262i	0.0255090	+	0.150265i
$579$	−4.35880	−	5.94569i	−0.181146	−	0.247095i
$580$	−8.96575	+	3.13439i	−0.372283	+	0.130148i
$581$	−4.43866	−	1.18933i	−0.184146	−	0.0493419i
$582$	−2.52839	−	0.636028i	−0.104805	−	0.0263642i
$583$	−11.0868	+	19.2030i	−0.459170	+	0.795305i
$584$	−23.1112	+	12.7602i	−0.956347	+	0.528021i
$585$	−13.5709	−	4.28138i	−0.561088	−	0.177013i
$586$	−2.99957	+	31.9385i	−0.123911	+	1.31937i
$587$	4.34247	−	1.16356i	0.179233	−	0.0480253i	−0.168086	−	0.985772i	$-0.553759\pi$
$587$	4.34247	−	1.16356i	0.179233	−	0.0480253i	0.347319	+	0.937747i	$0.387092\pi$
$588$	−5.33843	−	3.66700i	−0.220153	−	0.151224i
$589$	−16.3910	−	4.39195i	−0.675379	−	0.180967i
$590$	−4.12082	−	1.52968i	−0.169651	−	0.0629759i
$591$	3.02703	−	3.77096i	0.124515	−	0.155116i
$592$	13.7511	+	1.55732i	0.565168	+	0.0640053i
$593$		−	18.2198i		−	0.748196i	−0.927389	−	0.374098i	$-0.877952\pi$
$593$		−	18.2198i		−	0.748196i	0.927389	−	0.374098i	$-0.122048\pi$
$594$	−21.0260	−	22.2574i	−0.862706	−	0.913231i
$595$	−9.32108	−	9.32108i	−0.382127	−	0.382127i
$596$	44.0161	−	3.28594i	1.80297	−	0.134597i
$597$	−23.0180	+	2.51894i	−0.942065	+	0.103093i
$598$	−8.29607	−	18.0912i	−0.339251	−	0.739806i
$599$	15.7258	−	9.07927i	0.642537	−	0.370969i	−0.143054	−	0.989715i	$-0.545692\pi$
$599$	15.7258	−	9.07927i	0.642537	−	0.370969i	0.785591	+	0.618746i	$0.212359\pi$
$600$	−0.439691	−	4.87921i	−0.0179503	−	0.199193i
$601$	18.1261	+	10.4651i	0.739377	+	0.426880i	0.821843	−	0.569714i	$-0.192946\pi$
$601$	18.1261	+	10.4651i	0.739377	+	0.426880i	−0.0824655	+	0.996594i	$0.526279\pi$
$602$	−1.57930	+	16.8160i	−0.0643676	+	0.685367i
$603$	2.02221	−	46.1399i	0.0823509	−	1.87896i
$604$	2.60112	−	13.7258i	0.105838	−	0.558497i
$605$	−6.14405	+	1.64629i	−0.249791	+	0.0669313i
$606$	21.2077	−	12.6825i	0.861504	−	0.515190i
$607$	37.5951	−	21.7055i	1.52594	−	0.881000i	0.526409	−	0.850231i	$-0.323538\pi$
$607$	37.5951	−	21.7055i	1.52594	−	0.881000i	0.999527	−	0.0307684i	$-0.00979543\pi$
$608$	1.21280	+	21.8742i	0.0491855	+	0.887115i
$609$	−3.72854	+	24.2113i	−0.151088	+	0.981092i
$610$	19.1747	−	3.25510i	0.776360	−	0.131795i
$611$	34.1079	−	34.1079i	1.37986	−	1.37986i
$612$	13.9786	+	22.5805i	0.565051	+	0.912761i
$613$	16.6674	+	16.6674i	0.673190	+	0.673190i	0.958450	−	0.285260i	$-0.0920801\pi$
$613$	16.6674	+	16.6674i	0.673190	+	0.673190i	−0.285260	+	0.958450i	$0.592080\pi$
$614$	16.3853	−	23.0860i	0.661257	−	0.931673i
$615$	−4.30451	−	11.0718i	−0.173575	−	0.446456i
$616$	34.0696	−	8.43395i	1.37270	−	0.339814i
$617$	−7.31399	−	12.6682i	−0.294450	−	0.510003i	0.680407	−	0.732835i	$-0.261803\pi$
$617$	−7.31399	−	12.6682i	−0.294450	−	0.510003i	−0.974857	+	0.222832i	$0.928470\pi$
$618$	−19.1547	+	19.7523i	−0.770515	+	0.794552i
$619$	4.26442	+	15.9150i	0.171402	+	0.639679i	0.997137	+	0.0756211i	$0.0240939\pi$
$619$	4.26442	+	15.9150i	0.171402	+	0.639679i	−0.825735	+	0.564058i	$0.809239\pi$
$620$	7.24199	−	4.93448i	0.290845	−	0.198174i
$621$	−10.1677	+	11.5882i	−0.408017	+	0.465020i
$622$	−1.13400	−	1.36908i	−0.0454693	−	0.0548953i
$623$	−24.7282	+	42.8305i	−0.990716	+	1.71597i
$624$	−28.5222	+	16.3243i	−1.14180	+	0.653494i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	11.0735	−	29.8310i	0.442585	−	1.19229i
$627$	−25.5812	−	11.2586i	−1.02162	−	0.449624i
$628$	−27.9370	+	2.08559i	−1.11481	+	0.0832240i
$629$	10.8283	−	10.8283i	0.431752	−	0.431752i
$630$	−11.6417	−	4.91162i	−0.463816	−	0.195684i
$631$	−6.92272			−0.275589			−0.137795	−	0.990461i	$-0.544001\pi$
$631$	−6.92272			−0.275589			−0.137795	+	0.990461i	$0.544001\pi$
$632$	0.208272	−	10.8874i	0.00828461	−	0.433077i
$633$	0.705015	−	4.57802i	0.0280218	−	0.181960i
$634$	15.3773	+	33.5332i	0.610709	+	1.33177i
$635$	−1.13213	+	4.22517i	−0.0449273	+	0.167671i
$636$	6.14930	−	17.3792i	0.243836	−	0.689129i
$637$	−2.29531	−	8.56620i	−0.0909434	−	0.339405i
$638$	−17.8501	−	21.5505i	−0.706693	−	0.853192i
$639$	−6.26274	−	28.2717i	−0.247750	−	1.11841i
$640$	−8.96890	−	6.89630i	−0.354527	−	0.272600i
$641$	−8.67969	−	5.01122i	−0.342827	−	0.197931i	0.318694	−	0.947858i	$-0.396756\pi$
$641$	−8.67969	−	5.01122i	−0.342827	−	0.197931i	−0.661521	+	0.749926i	$0.730089\pi$
$642$	−23.1306	+	41.5233i	−0.912893	+	1.63879i
$643$	2.54449	−	9.49618i	0.100345	−	0.374493i	−0.897430	−	0.441156i	$-0.854569\pi$
$643$	2.54449	−	9.49618i	0.100345	−	0.374493i	0.997776	+	0.0666630i	$0.0212352\pi$
$644$	−5.83197	−	16.6821i	−0.229812	−	0.657365i
$645$	0.755591	+	6.90457i	0.0297514	+	0.271867i
$646$	19.7688	+	14.0309i	0.777792	+	0.552039i
$647$		−	11.4370i		−	0.449637i	−0.974401	−	0.224818i	$-0.927821\pi$
$647$		−	11.4370i		−	0.449637i	0.974401	−	0.224818i	$-0.0721789\pi$
$648$	20.5641	+	15.0039i	0.807836	+	0.589408i
$649$		−	12.9505i		−	0.508350i
$650$	3.88262	−	5.47040i	0.152289	−	0.214567i
$651$	−2.45876	−	22.4681i	−0.0963664	−	0.880593i
$652$	43.1814	+	20.8102i	1.69111	+	0.814991i
$653$	−11.7084	+	43.6963i	−0.458184	+	1.70997i	0.220370	+	0.975416i	$0.429274\pi$
$653$	−11.7084	+	43.6963i	−0.458184	+	1.70997i	−0.678554	+	0.734550i	$0.737393\pi$
$654$	−8.97914	−	5.00185i	−0.351112	−	0.195588i
$655$	7.83155	+	4.52155i	0.306004	+	0.176671i
$656$	−25.5315	−	10.0372i	−0.996836	−	0.391885i
$657$	6.05602	+	27.3385i	0.236268	+	1.06658i
$658$	32.9844	−	27.3208i	1.28587	−	1.06507i
$659$	3.12827	+	11.6749i	0.121860	+	0.454789i	0.999708	−	0.0241506i	$-0.00768812\pi$
$659$	3.12827	+	11.6749i	0.121860	+	0.454789i	−0.877848	+	0.478939i	$0.841021\pi$
$660$	13.0260	−	6.21716i	0.507036	−	0.242003i
$661$	−9.73683	+	36.3383i	−0.378719	+	1.41340i	0.469116	+	0.883137i	$0.344573\pi$
$661$	−9.73683	+	36.3383i	−0.378719	+	1.41340i	−0.847834	+	0.530261i	$0.822094\pi$
$662$	−18.5993	+	8.52905i	−0.722882	+	0.331491i
$663$	−5.53492	+	35.9411i	−0.214959	+	1.39584i
$664$	−3.14438	+	3.02634i	−0.122026	+	0.117445i
$665$	−11.5339			−0.447265
$666$	5.70582	−	13.5241i	0.221096	−	0.524050i
$667$	−9.96290	+	9.96290i	−0.385765	+	0.385765i
$668$	−3.78487	+	4.39556i	−0.146441	+	0.170069i
$669$	14.9269	+	6.56949i	0.577108	+	0.253991i
$670$	20.4106	+	7.57656i	0.788530	+	0.292708i
$671$	28.6508	+	49.6247i	1.10605	+	1.91574i
$672$	−26.5700	+	12.0631i	−1.02496	+	0.465346i
$673$	−6.95994	+	12.0550i	−0.268286	+	0.464685i	−0.968419	−	0.249327i	$-0.919791\pi$
$673$	−6.95994	+	12.0550i	−0.268286	+	0.464685i	0.700133	+	0.714012i	$0.253124\pi$
$674$	−8.17126	+	6.76819i	−0.314745	+	0.260701i
$675$	−5.09606	−	1.01499i	−0.196147	−	0.0390671i
$676$	−18.6678	−	3.53764i	−0.717991	−	0.136063i
$677$	−0.523708	−	1.95450i	−0.0201277	−	0.0751177i	0.955131	−	0.296182i	$-0.0957135\pi$
$677$	−0.523708	−	1.95450i	−0.0201277	−	0.0751177i	−0.975259	+	0.221064i	$0.929047\pi$
$678$	29.7742	+	28.8734i	1.14347	+	1.10888i
$679$	−1.58494	−	2.74520i	−0.0608246	−	0.105351i
$680$	−12.1523	+	3.00831i	−0.466020	+	0.115363i
$681$	7.16208	+	18.4218i	0.274452	+	0.705925i
$682$	21.0547	+	14.9436i	0.806228	+	0.572222i
$683$	−3.78160	−	3.78160i	−0.144699	−	0.144699i	0.631046	−	0.775745i	$-0.282626\pi$
$683$	−3.78160	−	3.78160i	−0.144699	−	0.144699i	−0.775745	+	0.631046i	$0.782626\pi$
$684$	22.6190	+	5.32197i	0.864861	+	0.203491i
$685$	−6.45216	+	6.45216i	−0.246524	+	0.246524i
$686$	3.61646	+	21.3033i	0.138077	+	0.813365i
$687$	−3.60170	+	23.3877i	−0.137413	+	0.892295i
$688$	12.9008	+	9.53259i	0.491839	+	0.363427i
$689$	21.8612	−	12.6216i	0.832847	−	0.480844i
$690$	−3.72994	−	6.23724i	−0.141997	−	0.237448i
$691$	−31.9322	+	8.55622i	−1.21476	+	0.325494i	−0.808628	−	0.588320i	$-0.799789\pi$
$691$	−31.9322	+	8.55622i	−1.21476	+	0.325494i	−0.406132	+	0.913814i	$0.633123\pi$
$692$	1.97562	−	1.34613i	0.0751016	−	0.0511721i
$693$	1.63001	−	37.1913i	0.0619191	−	1.41278i
$694$	−31.7556	−	2.98239i	−1.20543	−	0.113210i
$695$	−4.78308	−	2.76151i	−0.181432	−	0.104750i
$696$	17.8608	+	14.9079i	0.677013	+	0.565082i
$697$	−26.2895	+	15.1782i	−0.995784	+	0.574916i
$698$	−3.52559	+	1.61672i	−0.133445	+	0.0611939i
$699$	41.0995	−	4.49767i	1.55453	−	0.170117i
$700$	3.88656	−	4.51366i	0.146898	−	0.170600i
$701$	13.7191	+	13.7191i	0.518162	+	0.518162i	0.917015	−	0.398853i	$-0.130592\pi$
$701$	13.7191	+	13.7191i	0.518162	+	0.518162i	−0.398853	+	0.917015i	$0.630592\pi$
$702$	8.06047	+	33.9121i	0.304223	+	1.27993i
$703$		−	13.3989i		−	0.505349i
$704$	9.85230	−	31.8437i	0.371323	−	1.20016i
$705$	11.0257	−	13.7354i	0.415252	−	0.517305i
$706$	8.16908	−	22.0068i	0.307447	−	0.828236i
$707$	29.0204	+	7.77599i	1.09142	+	0.292446i
$708$	1.96482	+	10.5861i	0.0738423	+	0.397851i
$709$	14.7648	−	3.95621i	0.554503	−	0.148579i	0.0293233	−	0.999570i	$-0.490665\pi$
$709$	14.7648	−	3.95621i	0.554503	−	0.148579i	0.525180	+	0.850991i	$0.323998\pi$
$710$	13.5907	+	1.27639i	0.510049	+	0.0479022i
$711$	−11.0148	−	3.47497i	−0.413087	−	0.130322i
$712$	22.7024	+	41.1185i	0.850810	+	1.54098i
$713$	6.50000	−	11.2583i	0.243427	−	0.421628i
$714$	−7.87710	+	31.3136i	−0.294793	+	1.17188i
$715$	19.0906	+	5.11531i	0.713948	+	0.191302i
$716$	−9.28266	+	19.2616i	−0.346909	+	0.719840i
$717$	−4.76643	−	6.50173i	−0.178006	−	0.242812i
$718$	−4.78097	+	0.811619i	−0.178424	+	0.0302894i
$719$	−12.3794			−0.461673			−0.230837	−	0.972993i	$-0.574146\pi$
$719$	−12.3794			−0.461673			−0.230837	+	0.972993i	$0.574146\pi$
$720$	−9.70460	+	7.05838i	−0.361669	+	0.263050i
$721$	−33.4534			−1.24587
$722$	−5.57921	+	0.947128i	−0.207637	+	0.0352485i
$723$	−1.12358	+	2.55294i	−0.0417863	+	0.0949450i
$724$	−8.29079	−	3.99554i	−0.308125	−	0.148493i
$725$	−4.58711	−	1.22911i	−0.170361	−	0.0456481i
$726$	11.1851	+	10.8467i	0.415118	+	0.402559i
$727$	−4.34820	+	7.53131i	−0.161266	+	0.279321i	−0.935323	−	0.353795i	$-0.884891\pi$
$727$	−4.34820	+	7.53131i	−0.161266	+	0.279321i	0.774057	+	0.633116i	$0.218224\pi$
$728$	−38.3903	−	11.0778i	−1.42284	−	0.410571i
$729$	21.4288	−	16.4259i	0.793657	−	0.608365i
$730$	−13.1421	−	1.23426i	−0.486410	−	0.0456821i
$731$	17.1448	−	4.59395i	0.634125	−	0.169913i
$732$	−30.9491	−	36.2180i	−1.14391	−	1.33865i
$733$	8.63669	+	2.31419i	0.319003	+	0.0854767i	0.414768	−	0.909927i	$-0.363863\pi$
$733$	8.63669	+	2.31419i	0.319003	+	0.0854767i	−0.0957643	+	0.995404i	$0.530530\pi$
$734$	−13.8163	+	37.2200i	−0.509971	+	1.37382i
$735$	−1.17342	−	3.01820i	−0.0432824	−	0.111328i
$736$	−16.4272	−	3.43975i	−0.605513	−	0.126791i
$737$			64.1442i			2.36278i
$738$	−17.8642	+	22.9684i	−0.657590	+	0.845477i
$739$	2.57597	+	2.57597i	0.0947585	+	0.0947585i	0.752897	−	0.658138i	$-0.228656\pi$
$739$	2.57597	+	2.57597i	0.0947585	+	0.0947585i	−0.658138	+	0.752897i	$0.728656\pi$
$740$	5.24351	+	4.51501i	0.192755	+	0.165975i
$741$	18.8123	+	25.6612i	0.691086	+	0.942686i
$742$	20.3740	−	9.34288i	0.747954	−	0.342988i
$743$	16.2547	−	9.38468i	0.596328	−	0.344290i	−0.171267	−	0.985225i	$-0.554786\pi$
$743$	16.2547	−	9.38468i	0.596328	−	0.344290i	0.767596	+	0.640934i	$0.221453\pi$
$744$	−19.4780	−	9.02103i	−0.714099	−	0.330727i
$745$	19.1125	+	11.0346i	0.700229	+	0.404278i
$746$	−12.3046	−	1.15561i	−0.450505	−	0.0423100i
$747$	2.13670	+	4.10623i	0.0781777	+	0.150239i
$748$	−20.7691	−	30.4813i	−0.759393	−	1.11451i
$749$	−55.8211	+	14.9572i	−2.03966	+	0.546525i
$750$	1.19202	−	2.13988i	0.0435265	−	0.0781373i
$751$	−16.3943	+	9.46525i	−0.598236	+	0.345392i	−0.768347	−	0.640033i	$-0.778921\pi$
$751$	−16.3943	+	9.46525i	−0.598236	+	0.345392i	0.170111	+	0.985425i	$0.445587\pi$
$752$	−6.03954	−	40.2252i	−0.220239	−	1.46686i
$753$	−29.2338	−	23.4666i	−1.06534	−	0.855169i
$754$	5.33173	+	31.4074i	0.194170	+	1.14379i
$755$	4.93919	−	4.93919i	0.179755	−	0.179755i
$756$	4.31016	+	30.6487i	0.156759	+	1.11468i
$757$	−26.0226	−	26.0226i	−0.945808	−	0.945808i	0.0527973	−	0.998605i	$-0.483186\pi$
$757$	−26.0226	−	26.0226i	−0.945808	−	0.945808i	−0.998605	+	0.0527973i	$0.983186\pi$
$758$	33.1413	+	23.5221i	1.20375	+	0.854362i
$759$	13.4035	−	16.6975i	0.486515	−	0.606082i
$760$	−5.65738	+	9.37986i	−0.205215	+	0.340243i
$761$	−9.65297	−	16.7194i	−0.349920	−	0.606079i	0.636315	−	0.771429i	$-0.280458\pi$
$761$	−9.65297	−	16.7194i	−0.349920	−	0.606079i	−0.986235	+	0.165350i	$0.947124\pi$
$762$	10.3057	−	2.93175i	0.373336	−	0.106206i
$763$	−3.23440	−	12.0710i	−0.117093	−	0.436998i
$764$	0.620138	−	3.27240i	0.0224358	−	0.118391i
$765$	−0.581411	+	13.2658i	−0.0210210	+	0.479626i
$766$	10.5123	−	8.70723i	0.379824	−	0.314605i
$767$	−7.37160	+	12.7680i	−0.266173	+	0.461025i
$768$	−3.22233	+	27.5248i	−0.116276	+	0.993217i
$769$	−5.49920	−	9.52489i	−0.198306	−	0.343476i	0.749673	−	0.661808i	$-0.230211\pi$
$769$	−5.49920	−	9.52489i	−0.198306	−	0.343476i	−0.947979	+	0.318332i	$0.896877\pi$
$770$	16.4521	+	6.10713i	0.592891	+	0.220086i
$771$	36.4198	−	26.6995i	1.31163	−	0.961558i
$772$	−6.45085	−	5.55461i	−0.232171	−	0.199915i
$773$	−2.42673	+	2.42673i	−0.0872834	+	0.0872834i	−0.749400	−	0.662117i	$-0.769658\pi$
$773$	−2.42673	+	2.42673i	−0.0872834	+	0.0872834i	0.662117	+	0.749400i	$0.269658\pi$
$774$	13.5653	−	10.2687i	0.487595	−	0.369101i
$775$	4.38165			0.157394
$776$	−3.00993	−	0.0575789i	−0.108050	−	0.00206696i
$777$	16.6338	−	6.46695i	0.596736	−	0.232001i
$778$	−15.2919	+	7.01238i	−0.548241	+	0.251406i
$779$	−6.87451	+	25.6560i	−0.246305	+	0.919222i
$780$	−16.3814	−	1.28503i	−0.586547	−	0.0460116i
$781$	10.4091	+	38.8473i	0.372467	+	1.39007i
$782$	−14.3025	+	11.8467i	−0.511456	+	0.423636i
$783$	20.5209	−	13.7042i	0.733356	−	0.489748i
$784$	−6.95996	−	2.73616i	−0.248570	−	0.0977200i
$785$	−12.1308	−	7.00369i	−0.432965	−	0.249973i
$786$	−0.340172	−	22.1484i	−0.0121335	−	0.790006i
$787$	11.3830	−	42.4820i	0.405761	−	1.51432i	−0.396887	−	0.917867i	$-0.629910\pi$
$787$	11.3830	−	42.4820i	0.405761	−	1.51432i	0.802648	−	0.596453i	$-0.203424\pi$
$788$	2.42410	−	5.03002i	0.0863549	−	0.179187i
$789$	26.7142	+	11.7572i	0.951052	+	0.418568i
$790$	3.15132	−	4.44003i	0.112119	−	0.157969i
$791$			50.4270i			1.79298i
$792$	−29.4461	−	19.5680i	−1.04632	−	0.695317i
$793$		−	65.2340i		−	2.31653i
$794$	−31.3340	−	22.2394i	−1.11200	−	0.789246i
$795$	7.43386	−	5.44978i	0.263652	−	0.193284i
$796$	−25.2397	+	8.82368i	−0.894597	+	0.312747i
$797$	−5.14160	+	19.1887i	−0.182125	+	0.679699i	0.813103	+	0.582120i	$0.197777\pi$
$797$	−5.14160	+	19.1887i	−0.182125	+	0.679699i	−0.995228	+	0.0975793i	$0.968890\pi$
$798$	14.5001	+	24.2473i	0.513300	+	0.858344i
$799$	−38.9797	−	22.5050i	−1.37900	−	0.796168i
$800$	−1.76435	−	5.37467i	−0.0623790	−	0.190023i
$801$	48.6395	−	10.7746i	1.71859	−	0.380703i
$802$	4.78041	+	5.77140i	0.168802	+	0.203795i
$803$	−10.0655	−	37.5651i	−0.355205	−	1.32564i
$804$	−9.73181	−	52.4335i	−0.343214	−	1.84919i
$805$	2.28694	−	8.53497i	0.0806040	−	0.300818i
$806$	−12.2519	−	26.7178i	−0.431556	−	0.941093i
$807$	−6.57943	−	5.28146i	−0.231607	−	0.185916i
$808$	20.5583	−	19.7865i	0.723238	−	0.696087i
$809$	46.8608			1.64754			0.823770	−	0.566924i	$-0.191867\pi$
$809$	46.8608			1.64754			0.823770	+	0.566924i	$0.191867\pi$
$810$	4.27287	+	11.9893i	0.150133	+	0.421260i
$811$	27.0155	−	27.0155i	0.948643	−	0.948643i	−0.0501013	−	0.998744i	$-0.515954\pi$
$811$	27.0155	−	27.0155i	0.948643	−	0.948643i	0.998744	+	0.0501013i	$0.0159544\pi$
$812$	2.10581	+	28.2079i	0.0738994	+	0.989903i
$813$	5.00824	+	45.7652i	0.175647	+	1.60505i
$814$	−7.09464	+	19.1123i	−0.248667	+	0.669887i
$815$	11.9836	+	20.7562i	0.419766	+	0.727056i
$816$	21.6019	+	21.7653i	0.756216	+	0.761939i
$817$	7.76523	−	13.4498i	0.271671	−	0.470548i
$818$	16.3707	+	19.7644i	0.572387	+	0.691045i
$819$	−22.7769	+	35.7395i	−0.795890	+	1.24884i
$820$	−7.72371	−	11.3355i	−0.269724	−	0.395854i
$821$	0.305359	+	1.13962i	0.0106571	+	0.0397728i	0.971050	−	0.238878i	$-0.0767795\pi$
$821$	0.305359	+	1.13962i	0.0106571	+	0.0397728i	−0.960393	+	0.278651i	$0.910113\pi$
$822$	21.6756	+	5.45262i	0.756024	+	0.190182i
$823$	15.1500	+	26.2406i	0.528097	+	0.914691i	0.999463	+	0.0327538i	$0.0104277\pi$
$823$	15.1500	+	26.2406i	0.528097	+	0.914691i	−0.471366	+	0.881938i	$0.656239\pi$
$824$	−16.4089	+	27.2057i	−0.571631	+	0.947757i
$825$	7.13273	+	1.09844i	0.248330	+	0.0382428i
$826$	−7.57683	+	10.6753i	−0.263631	+	0.371442i
$827$	16.4023	+	16.4023i	0.570362	+	0.570362i	0.932230	−	0.361867i	$-0.117861\pi$
$827$	16.4023	+	16.4023i	0.570362	+	0.570362i	−0.361867	+	0.932230i	$0.617861\pi$
$828$	−8.42311	+	15.6826i	−0.292723	+	0.545009i
$829$	29.3862	−	29.3862i	1.02063	−	1.02063i	0.0208438	−	0.999783i	$-0.493365\pi$
$829$	29.3862	−	29.3862i	1.02063	−	1.02063i	0.999783	−	0.0208438i	$-0.00663525\pi$
$830$	−2.15130	+	0.365205i	−0.0746727	+	0.0126765i
$831$	29.0869	−	11.3085i	1.00901	−	0.392287i
$832$	−27.8394	+	25.7870i	−0.965158	+	0.894002i
$833$	−7.16659	+	4.13763i	−0.248308	+	0.143361i
$834$	0.207758	+	13.5270i	0.00719407	+	0.468401i
$835$	−2.80144	+	0.750644i	−0.0969479	+	0.0259771i
$836$	−31.7086	−	6.00894i	−1.09666	−	0.207824i
$837$	−15.0161	+	17.1139i	−0.519032	+	0.591544i
$838$	0.824299	−	8.77690i	0.0284749	−	0.303193i
$839$	−29.8251	−	17.2196i	−1.02968	−	0.594485i	−0.112786	−	0.993619i	$-0.535977\pi$
$839$	−29.8251	−	17.2196i	−1.02968	−	0.594485i	−0.916892	+	0.399134i	$0.869311\pi$
$840$	−14.3750	−	2.49609i	−0.495984	−	0.0861233i
$841$	−5.58390	+	3.22387i	−0.192548	+	0.111168i
$842$	−22.1111	−	48.2177i	−0.761999	−	1.66169i
$843$	18.4736	−	41.9750i	0.636266	−	1.44570i
$844$	−0.398179	−	5.33372i	−0.0137059	−	0.183594i
$845$	−6.71752	−	6.71752i	−0.231090	−	0.231090i
$846$	−42.7367	−	5.91108i	−1.46932	−	0.203227i
$847$			18.9436i			0.650911i
$848$	2.39543	−	21.1517i	0.0822595	−	0.726353i
$849$	−14.4126	−	2.21953i	−0.494638	−	0.0761742i
$850$	−5.86829	−	2.17835i	−0.201281	−	0.0747170i
$851$	9.91506	+	2.65673i	0.339884	+	0.0910716i
$852$	−14.4026	−	30.1758i	−0.493424	−	1.03381i
$853$	3.65558	−	0.979508i	0.125165	−	0.0335377i	−0.195693	−	0.980665i	$-0.562696\pi$
$853$	3.65558	−	0.979508i	0.125165	−	0.0335377i	0.320858	+	0.947127i	$0.396029\pi$
$854$	5.41610	−	57.6691i	0.185335	−	1.97340i
$855$	7.84782	+	8.56726i	0.268390	+	0.292994i
$856$	−15.2164	+	52.7327i	−0.520087	+	1.80237i
$857$	−20.8276	+	36.0745i	−0.711458	+	1.23228i	0.252852	+	0.967505i	$0.418632\pi$
$857$	−20.8276	+	36.0745i	−0.711458	+	1.23228i	−0.964310	+	0.264777i	$0.914702\pi$
$858$	−13.2466	−	46.5643i	−0.452230	−	1.58968i
$859$	−44.1765	−	11.8371i	−1.50728	−	0.403875i	−0.591751	−	0.806121i	$-0.701563\pi$
$859$	−44.1765	−	11.8371i	−1.50728	−	0.403875i	−0.915532	+	0.402246i	$0.868230\pi$
$860$	2.64678	+	7.57099i	0.0902545	+	0.258169i
$861$	−35.1682	+	3.84858i	−1.19853	+	0.131159i
$862$	5.85370	+	34.4821i	0.199378	+	1.17447i
$863$	6.69591			0.227932			0.113966	−	0.993485i	$-0.463645\pi$
$863$	6.69591			0.227932			0.113966	+	0.993485i	$0.463645\pi$
$864$	27.0390	+	11.5280i	0.919884	+	0.392190i
$865$	1.19532			0.0406419
$866$	1.05570	+	6.21880i	0.0358743	+	0.211323i
$867$	4.46120	−	0.488205i	0.151510	−	0.0165803i
$868$	−8.61286	−	24.6367i	−0.292340	−	0.836223i
$869$	15.4948	+	4.15183i	0.525626	+	0.140841i
$870$	3.18289	+	11.1885i	0.107910	+	0.379326i
$871$	36.5118	−	63.2404i	1.23716	−	2.14282i
$872$	−11.4031	−	3.29046i	−0.386158	−	0.111429i
$873$	−0.960691	+	3.04516i	−0.0325145	+	0.103063i
$874$	−1.51943	+	16.1785i	−0.0513955	+	0.547245i
$875$	2.87671	−	0.770812i	0.0972506	−	0.0260582i
$876$	13.9272	+	29.1797i	0.470555	+	0.985892i
$877$	−50.7214	−	13.5908i	−1.71274	−	0.458928i	−0.736647	−	0.676277i	$-0.763592\pi$
$877$	−50.7214	−	13.5908i	−1.71274	−	0.458928i	−0.976094	+	0.217350i	$0.930259\pi$
$878$	−45.9616	−	17.0613i	−1.55113	−	0.575790i
$879$	38.8309	+	5.97996i	1.30973	+	0.201699i
$880$	13.0363	−	10.3840i	0.439454	−	0.350044i
$881$			20.9115i			0.704527i	0.935901	+	0.352263i	$0.114588\pi$
$881$			20.9115i			0.704527i	−0.935901	+	0.352263i	$0.885412\pi$
$882$	−4.86984	+	6.26125i	−0.163976	+	0.210827i
$883$	8.78506	+	8.78506i	0.295641	+	0.295641i	0.839304	−	0.543663i	$-0.182963\pi$
$883$	8.78506	+	8.78506i	0.295641	+	0.295641i	−0.543663	+	0.839304i	$0.682963\pi$
$884$	3.12602	+	41.8739i	0.105139	+	1.40837i
$885$	−2.16858	+	4.92736i	−0.0728960	+	0.165631i
$886$	17.6966	+	38.5910i	0.594529	+	1.29649i
$887$	37.9799	−	21.9277i	1.27524	−	0.736260i	0.299271	−	0.954168i	$-0.403257\pi$
$887$	37.9799	−	21.9277i	1.27524	−	0.736260i	0.975969	+	0.217908i	$0.0699234\pi$
$888$	2.89970	−	16.6994i	0.0973077	−	0.560395i
$889$	11.2819	+	6.51363i	0.378384	+	0.218460i
$890$	−2.19595	+	23.3818i	−0.0736084	+	0.783761i
$891$	−28.7344	+	24.0947i	−0.962639	+	0.807204i
$892$	18.5023	+	3.50628i	0.619502	+	0.117399i
$893$	−38.0405	+	10.1929i	−1.27298	+	0.341093i
$894$	−0.830174	−	54.0521i	−0.0277652	−	1.80777i
$895$	−9.25855	+	5.34543i	−0.309479	+	0.178678i
$896$	−26.7520	+	20.4852i	−0.893721	+	0.684362i
$897$	−22.7191	+	8.83280i	−0.758569	+	0.294919i
$898$	5.28695	−	0.897513i	0.176428	−	0.0299504i
$899$	−14.7136	+	14.7136i	−0.490725	+	0.490725i
$900$	−5.99717	+	0.184262i	−0.199906	+	0.00614206i
$901$	−16.6559	−	16.6559i	−0.554887	−	0.554887i
$902$	23.3906	−	32.9560i	0.778821	−	1.09731i
$903$	20.4449	+	3.14851i	0.680363	+	0.104776i
$904$	41.0094	+	24.7345i	1.36395	+	0.822656i
$905$	−2.30084	−	3.98516i	−0.0764824	−	0.132471i
$906$	−16.5929	−	4.17403i	−0.551262	−	0.138673i
$907$	−9.00496	−	33.6070i	−0.299005	−	1.11590i	−0.937985	−	0.346677i	$-0.887310\pi$
$907$	−9.00496	−	33.6070i	−0.299005	−	1.11590i	0.638980	−	0.769223i	$-0.279357\pi$
$908$	12.8511	+	18.8607i	0.426480	+	0.625915i
$909$	−13.9699	−	26.8469i	−0.463354	−	0.890456i
$910$	−12.7440	−	15.3858i	−0.422459	−	0.510036i
$911$	−14.2630	+	24.7043i	−0.472554	+	0.818488i	−0.999507	−	0.0314066i	$-0.990001\pi$
$911$	−14.2630	+	24.7043i	−0.472554	+	0.818488i	0.526952	+	0.849895i	$0.323335\pi$
$912$	26.8312	+	0.101147i	0.888471	+	0.00334931i
$913$	−3.21447	−	5.56763i	−0.106384	−	0.184262i
$914$	−15.2396	+	41.0541i	−0.504081	+	1.35795i
$915$	−2.59125	−	23.6787i	−0.0856639	−	0.782794i
$916$	2.03417	+	27.2483i	0.0672109	+	0.900308i
$917$	19.0438	−	19.0438i	0.628883	−	0.628883i
$918$	28.6191	−	15.4552i	0.944572	−	0.510097i
$919$	2.94246			0.0970629			0.0485314	−	0.998822i	$-0.484546\pi$
$919$	2.94246			0.0970629			0.0485314	+	0.998822i	$0.484546\pi$
$920$	−5.81926	−	6.04624i	−0.191855	−	0.199339i
$921$	−27.0385	−	21.7044i	−0.890948	−	0.715183i
$922$	−13.9191	−	30.3533i	−0.458400	−	0.999632i
$923$	11.8501	−	44.2250i	0.390049	−	1.45568i
$924$	−7.84437	−	42.2643i	−0.258061	−	1.39039i
$925$	0.895452	+	3.34187i	0.0294423	+	0.109880i
$926$	−36.3768	−	43.9178i	−1.19541	−	1.44323i
$927$	22.7622	+	24.8488i	0.747607	+	0.816143i
$928$	23.9728	+	12.1235i	0.786945	+	0.397972i
$929$	4.41424	+	2.54856i	0.144827	+	0.0836157i	0.570662	−	0.821185i	$-0.306687\pi$
$929$	4.41424	+	2.54856i	0.144827	+	0.0836157i	−0.425836	+	0.904800i	$0.640020\pi$
$930$	−5.50851	−	9.21138i	−0.180631	−	0.302053i
$931$	−1.87401	+	6.99392i	−0.0614183	+	0.229216i
$932$	45.0664	−	15.7550i	1.47620	−	0.516072i
$933$	−1.75596	+	1.28730i	−0.0574875	+	0.0421442i
$934$	−20.5549	−	14.5889i	−0.672577	−	0.477363i
$935$		−	18.4422i		−	0.603126i
$936$	17.8928	+	36.0534i	0.584844	+	1.17844i
$937$			32.3422i			1.05657i	0.849066	+	0.528287i	$0.177166\pi$
$937$			32.3422i			1.05657i	−0.849066	+	0.528287i	$0.822834\pi$
$938$	37.5283	−	52.8753i	1.22534	−	1.72644i
$939$	−35.6696	−	15.6985i	−1.16403	−	0.512302i
$940$	8.82957	−	18.3214i	0.287989	−	0.597579i
$941$	1.73426	−	6.47236i	0.0565354	−	0.210993i	−0.931880	−	0.362767i	$-0.881832\pi$
$941$	1.73426	−	6.47236i	0.0565354	−	0.210993i	0.988415	+	0.151774i	$0.0484987\pi$
$942$	0.526912	+	34.3069i	0.0171677	+	1.11778i
$943$	−17.6221	−	10.1741i	−0.573856	−	0.331316i
$944$	4.96519	+	11.3980i	0.161603	+	0.370975i
$945$	−6.84794	+	13.8775i	−0.222764	+	0.451436i
$946$	−18.1980	+	15.0732i	−0.591667	+	0.490073i
$947$	−2.01859	−	7.53347i	−0.0655953	−	0.244805i	0.925341	−	0.379135i	$-0.123778\pi$
$947$	−2.01859	−	7.53347i	−0.0655953	−	0.244805i	−0.990937	+	0.134330i	$0.957112\pi$
$948$	−13.2959	−	1.04299i	−0.431830	−	0.0338749i
$949$	−11.4589	+	42.7652i	−0.371972	+	1.38822i
$950$	−4.97845	+	2.28296i	−0.161522	+	0.0740691i
$951$	42.1112	−	16.3721i	1.36555	−	0.530902i
$952$	−0.713105	+	37.2775i	−0.0231119	+	1.20817i
$953$	−31.9710			−1.03564			−0.517821	−	0.855489i	$-0.673257\pi$
$953$	−31.9710			−1.03564			−0.517821	+	0.855489i	$0.673257\pi$
$954$	−20.8026	−	8.77658i	−0.673508	−	0.284152i
$955$	1.17756	−	1.17756i	0.0381050	−	0.0381050i
$956$	−7.05414	−	6.07407i	−0.228147	−	0.196450i
$957$	−27.6402	+	20.2631i	−0.893481	+	0.655013i
$958$	−14.1173	−	5.24044i	−0.456109	−	0.169311i
$959$	13.5876	+	23.5344i	0.438766	+	0.759965i
$960$	−9.08087	+	10.4660i	−0.293084	+	0.337790i
$961$	−5.90057	+	10.2201i	−0.190341	+	0.329680i
$962$	17.8737	−	14.8047i	0.576271	−	0.477321i
$963$	49.0916	+	31.2863i	1.58195	+	1.00819i
$964$	−0.599677	+	3.16444i	−0.0193143	+	0.101920i
$965$	−1.10163	−	4.11135i	−0.0354628	−	0.132349i
$966$	−20.8178	+	5.92223i	−0.669803	+	0.190545i
$967$	0.654843	+	1.13422i	0.0210583	+	0.0364741i	0.876363	−	0.481652i	$-0.159963\pi$
$967$	0.654843	+	1.13422i	0.0210583	+	0.0364741i	−0.855304	+	0.518126i	$0.826630\pi$
$968$	15.4058	+	9.29186i	0.495160	+	0.298652i
$969$	18.5857	−	23.1534i	0.597059	−	0.743793i
$970$	−1.22749	−	0.871216i	−0.0394124	−	0.0279730i
$971$	23.9203	+	23.9203i	0.767640	+	0.767640i	0.977691	−	0.210050i	$-0.0673628\pi$
$971$	23.9203	+	23.9203i	0.767640	+	0.767640i	−0.210050	+	0.977691i	$0.567363\pi$
$972$	19.8328	−	24.0553i	0.636138	−	0.771575i
$973$	−11.6309	+	11.6309i	−0.372870	+	0.372870i
$974$	−3.13033	−	18.4397i	−0.100302	−	0.590846i
$975$	−6.40698	−	5.14302i	−0.205187	−	0.164708i
$976$	−44.2424	−	32.6913i	−1.41616	−	1.04642i
$977$	11.1048	−	6.41135i	0.355273	−	0.205117i	−0.311732	−	0.950170i	$-0.600909\pi$
$977$	11.1048	−	6.41135i	0.355273	−	0.205117i	0.667005	+	0.745053i	$0.267576\pi$
$978$	28.5694	−	51.2868i	0.913549	−	1.63997i
$979$	−66.8342	+	17.9082i	−2.13603	+	0.572348i
$980$	−2.10551	−	3.09010i	−0.0672580	−	0.0987098i
$981$	−6.76545	+	10.6157i	−0.216004	+	0.338934i
$982$	−6.34441	−	0.595847i	−0.202458	−	0.0190142i
$983$	−25.4589	−	14.6987i	−0.812013	−	0.468816i	0.0356413	−	0.999365i	$-0.488653\pi$
$983$	−25.4589	−	14.6987i	−0.812013	−	0.468816i	−0.847655	+	0.530549i	$0.821986\pi$
$984$	−14.1202	+	30.4880i	−0.450135	+	0.971923i
$985$	2.41780	−	1.39592i	0.0770375	−	0.0444776i
$986$	27.0206	−	12.3908i	0.860512	−	0.394603i
$987$	−31.0140	−	42.3052i	−0.987187	−	1.34659i
$988$	27.8414	+	23.9733i	0.885753	+	0.762692i
$989$	8.41302	+	8.41302i	0.267518	+	0.267518i
$990$	−6.65790	−	16.3758i	−0.211602	−	0.520457i
$991$		−	37.7238i		−	1.19834i	−0.800624	−	0.599168i	$-0.795498\pi$
$991$		−	37.7238i		−	1.19834i	0.800624	−	0.599168i	$-0.204502\pi$
$992$	−24.2602	−	5.07994i	−0.770263	−	0.161288i
$993$	9.08085	+	23.3571i	0.288172	+	0.741216i
$994$	14.1477	−	38.1126i	0.448737	−	1.20886i
$995$	−12.9133	−	3.46010i	−0.409378	−	0.109693i
$996$	3.47232	+	4.06347i	0.110025	+	0.128756i
$997$	40.1197	−	10.7500i	1.27060	−	0.340457i	0.440341	−	0.897831i	$-0.354858\pi$
$997$	40.1197	−	10.7500i	1.27060	−	0.340457i	0.830262	+	0.557374i	$0.188191\pi$
$998$	11.7763	+	1.10599i	0.372773	+	0.0350097i
$999$	−16.1215	−	7.95524i	−0.510061	−	0.251693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.43	✓	384
9.5	odd	6	inner	720.2.cf.a.491.11	yes	384
16.3	odd	4	inner	720.2.cf.a.371.11	yes	384
144.131	even	12	inner	720.2.cf.a.131.43	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.43	✓	384	1.1	even	1	trivial
720.2.cf.a.131.43	yes	384	144.131	even	12	inner
720.2.cf.a.371.11	yes	384	16.3	odd	4	inner
720.2.cf.a.491.11	yes	384	9.5	odd	6	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.236691 - 1.39427i) q^{2} +(-1.72177 + 0.188420i) q^{3} +(-1.88795 + 0.660020i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(0.670235 + 2.35601i) q^{6} +(-1.48910 + 2.57919i) q^{7} +(1.36711 + 2.47609i) q^{8} +(2.92900 - 0.648831i) q^{9} +O(q^{10})\)	\(q+(-0.236691 - 1.39427i) q^{2} +(-1.72177 + 0.188420i) q^{3} +(-1.88795 + 0.660020i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(0.670235 + 2.35601i) q^{6} +(-1.48910 + 2.57919i) q^{7} +(1.36711 + 2.47609i) q^{8} +(2.92900 - 0.648831i) q^{9} +(-0.132237 + 1.40802i) q^{10} +(-4.02465 + 1.07840i) q^{11} +(3.12627 - 1.49213i) q^{12} +(4.58179 + 1.22769i) q^{13} +(3.94853 + 1.46572i) q^{14} +(1.71187 + 0.263628i) q^{15} +(3.12875 - 2.49218i) q^{16} -4.42618i q^{17} +(-1.59791 - 3.93023i) q^{18} +(-2.73847 - 2.73847i) q^{19} +(1.99445 - 0.148892i) q^{20} +(2.07791 - 4.72135i) q^{21} +(2.45618 + 5.35619i) q^{22} +(2.56943 - 1.48346i) q^{23} +(-2.82039 - 4.00567i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.627254 - 6.67881i) q^{26} +(-4.92081 + 1.66902i) q^{27} +(1.10903 - 5.85222i) q^{28} +(-4.58711 + 1.22911i) q^{29} +(-0.0376167 - 2.44920i) q^{30} +(3.79462 - 2.19083i) q^{31} +(-4.21530 - 3.77243i) q^{32} +(6.72634 - 2.61509i) q^{33} +(-6.17127 + 1.04764i) q^{34} +(2.10590 - 2.10590i) q^{35} +(-5.10157 + 3.15816i) q^{36} +(2.44642 + 2.44642i) q^{37} +(-3.16999 + 4.46633i) q^{38} +(-8.12012 - 1.25050i) q^{39} +(-0.679663 - 2.74555i) q^{40} +(-3.42919 - 5.93954i) q^{41} +(-7.07464 - 1.77966i) q^{42} +(1.03790 + 3.87351i) q^{43} +(6.88660 - 4.69233i) q^{44} +(-2.99712 - 0.131357i) q^{45} +(-2.67650 - 3.23134i) q^{46} +(5.08451 - 8.80663i) q^{47} +(-4.91741 + 4.88048i) q^{48} +(-0.934810 - 1.61914i) q^{49} +(0.492153 - 1.32582i) q^{50} +(0.833979 + 7.62087i) q^{51} +(-9.46051 + 0.706257i) q^{52} +(3.76303 - 3.76303i) q^{53} +(3.49177 + 6.46588i) q^{54} +4.16663 q^{55} +(-8.42205 - 0.161111i) q^{56} +(5.23101 + 4.19904i) q^{57} +(2.79944 + 6.10473i) q^{58} +(-0.804446 + 3.00223i) q^{59} +(-3.40593 + 0.632151i) q^{60} +(-3.55942 - 13.2839i) q^{61} +(-3.95275 - 4.77216i) q^{62} +(-2.68810 + 8.52061i) q^{63} +(-4.26204 + 6.77015i) q^{64} +(-4.10792 - 2.37171i) q^{65} +(-5.23819 - 8.75934i) q^{66} +(3.98445 - 14.8702i) q^{67} +(2.92137 + 8.35642i) q^{68} +(-4.14445 + 3.03831i) q^{69} +(-3.43463 - 2.43774i) q^{70} -9.65235i q^{71} +(5.61081 + 6.36544i) q^{72} +9.33374i q^{73} +(2.83191 - 3.99000i) q^{74} +(-1.58531 - 0.697710i) q^{75} +(6.97756 + 3.36266i) q^{76} +(3.21169 - 11.9862i) q^{77} +(0.178432 + 11.6176i) q^{78} +(-3.33418 - 1.92499i) q^{79} +(-3.66716 + 1.59748i) q^{80} +(8.15804 - 3.80085i) q^{81} +(-7.46964 + 6.18704i) q^{82} +(0.399348 + 1.49039i) q^{83} +(-0.806819 + 10.2852i) q^{84} +(-1.14558 + 4.27536i) q^{85} +(5.15504 - 2.36394i) q^{86} +(7.66636 - 2.98055i) q^{87} +(-8.17235 - 8.49111i) q^{88} +16.6062 q^{89} +(0.526245 + 4.20988i) q^{90} +(-9.98916 + 9.98916i) q^{91} +(-3.87185 + 4.49658i) q^{92} +(-6.12068 + 4.48708i) q^{93} +(-13.4822 - 5.00471i) q^{94} +(1.93639 + 3.35393i) q^{95} +(7.96859 + 5.70102i) q^{96} +(-0.532184 + 0.921769i) q^{97} +(-2.03625 + 1.68661i) q^{98} +(-11.0885 + 5.76996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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