LMFDB - Embedded newform 504.2.y.a.173.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(173,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1, 5]))

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

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

chi := DirichletCharacter("504.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.y (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.14
Character	$\chi$	$=$	504.173
Dual form			504.2.y.a.437.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26838 + 0.625475i) q^{2} +(-1.71321 + 0.254787i) q^{3} +(1.21756 - 1.58668i) q^{4} -1.07899i q^{5} +(2.01363 - 1.39473i) q^{6} +(-2.47543 + 0.933935i) q^{7} +(-0.551904 + 2.77406i) q^{8} +(2.87017 - 0.873007i) q^{9} +O(q^{10})$	\(q+(-1.26838 + 0.625475i) q^{2} +(-1.71321 + 0.254787i) q^{3} +(1.21756 - 1.58668i) q^{4} -1.07899i q^{5} +(2.01363 - 1.39473i) q^{6} +(-2.47543 + 0.933935i) q^{7} +(-0.551904 + 2.77406i) q^{8} +(2.87017 - 0.873007i) q^{9} +(0.674878 + 1.36856i) q^{10} -4.35309 q^{11} +(-1.68167 + 3.02853i) q^{12} +(0.286498 + 0.496230i) q^{13} +(2.55563 - 2.73290i) q^{14} +(0.274912 + 1.84853i) q^{15} +(-1.03508 - 3.86376i) q^{16} +(2.73015 + 4.72875i) q^{17} +(-3.09441 + 2.90252i) q^{18} +(3.78291 - 6.55219i) q^{19} +(-1.71200 - 1.31373i) q^{20} +(4.00298 - 2.23073i) q^{21} +(5.52136 - 2.72275i) q^{22} -3.38475i q^{23} +(0.238732 - 4.89316i) q^{24} +3.83579 q^{25} +(-0.673767 - 0.450209i) q^{26} +(-4.69476 + 2.22693i) q^{27} +(-1.53214 + 5.06483i) q^{28} +(-2.26807 + 3.92841i) q^{29} +(-1.50490 - 2.17268i) q^{30} +(5.87332 + 3.39096i) q^{31} +(3.72955 + 4.25328i) q^{32} +(7.45775 - 1.10911i) q^{33} +(-6.42057 - 4.29021i) q^{34} +(1.00770 + 2.67095i) q^{35} +(2.10943 - 5.61697i) q^{36} +(5.79374 + 3.34502i) q^{37} +(-0.699928 + 10.6768i) q^{38} +(-0.617264 - 0.777149i) q^{39} +(2.99317 + 0.595496i) q^{40} +(-0.0203980 - 0.0353304i) q^{41} +(-3.68202 + 5.33317i) q^{42} +(3.79642 + 2.19186i) q^{43} +(-5.30016 + 6.90694i) q^{44} +(-0.941962 - 3.09687i) q^{45} +(2.11707 + 4.29314i) q^{46} +(5.31431 + 9.20466i) q^{47} +(2.75775 + 6.35569i) q^{48} +(5.25553 - 4.62379i) q^{49} +(-4.86523 + 2.39919i) q^{50} +(-5.88214 - 7.40573i) q^{51} +(1.13619 + 0.149611i) q^{52} +(-6.07598 - 10.5239i) q^{53} +(4.56185 - 5.76104i) q^{54} +4.69692i q^{55} +(-1.22459 - 7.38244i) q^{56} +(-4.81150 + 12.1891i) q^{57} +(0.419646 - 6.40133i) q^{58} +(9.29209 + 5.36479i) q^{59} +(3.26774 + 1.81450i) q^{60} +(3.26452 + 5.65431i) q^{61} +(-9.57055 - 0.627408i) q^{62} +(-6.28957 + 4.84162i) q^{63} +(-7.39080 - 3.06203i) q^{64} +(0.535424 - 0.309127i) q^{65} +(-8.76552 + 6.07140i) q^{66} +(3.02506 + 1.74652i) q^{67} +(10.8271 + 1.42570i) q^{68} +(0.862391 + 5.79878i) q^{69} +(-2.94876 - 2.75749i) q^{70} +4.23443i q^{71} +(0.837717 + 8.44383i) q^{72} +(-2.40773 + 1.39011i) q^{73} +(-9.44088 - 0.618907i) q^{74} +(-6.57151 + 0.977311i) q^{75} +(-5.79028 - 13.9800i) q^{76} +(10.7758 - 4.06550i) q^{77} +(1.26901 + 0.599635i) q^{78} +(-5.72281 - 9.91220i) q^{79} +(-4.16894 + 1.11684i) q^{80} +(7.47572 - 5.01135i) q^{81} +(0.0479707 + 0.0320539i) q^{82} +(10.3909 + 5.99917i) q^{83} +(1.33442 - 9.06749i) q^{84} +(5.10225 - 2.94579i) q^{85} +(-6.18625 - 0.405547i) q^{86} +(2.88477 - 7.30806i) q^{87} +(2.40249 - 12.0757i) q^{88} +(6.51255 - 11.2801i) q^{89} +(3.13178 + 3.33882i) q^{90} +(-1.17265 - 0.960812i) q^{91} +(-5.37050 - 4.12114i) q^{92} +(-10.9262 - 4.31298i) q^{93} +(-12.4978 - 8.35101i) q^{94} +(-7.06972 - 4.08170i) q^{95} +(-7.47319 - 6.33652i) q^{96} +(1.14927 + 0.663530i) q^{97} +(-3.77393 + 9.15191i) q^{98} +(-12.4941 + 3.80028i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	$ 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) $ 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.26838	+	0.625475i	−0.896878	+	0.442277i
$2$	−1.26838	+	0.625475i	−0.896878	+	0.442277i
$3$	−1.71321	+	0.254787i	−0.989121	+	0.147101i
$3$	−1.71321	+	0.254787i	−0.989121	+	0.147101i
$4$	1.21756	−	1.58668i	0.608781	−	0.793338i
$5$		−	1.07899i		−	0.482537i	−0.970458	−	0.241268i	$-0.922437\pi$
$5$		−	1.07899i		−	0.482537i	0.970458	−	0.241268i	$-0.0775634\pi$
$6$	2.01363	−	1.39473i	0.822062	−	0.569398i
$7$	−2.47543	+	0.933935i	−0.935625	+	0.352994i
$7$	−2.47543	+	0.933935i	−0.935625	+	0.352994i
$8$	−0.551904	+	2.77406i	−0.195127	+	0.980778i
$9$	2.87017	−	0.873007i	0.956722	−	0.291002i
$10$	0.674878	+	1.36856i	0.213415	+	0.432777i
$11$	−4.35309			−1.31251			−0.656253	−	0.754541i	$-0.727859\pi$
$11$	−4.35309			−1.31251			−0.656253	+	0.754541i	$0.727859\pi$
$12$	−1.68167	+	3.02853i	−0.485458	+	0.874260i
$13$	0.286498	+	0.496230i	0.0794603	+	0.137629i	0.903017	−	0.429604i	$-0.141347\pi$
$13$	0.286498	+	0.496230i	0.0794603	+	0.137629i	−0.823557	+	0.567234i	$0.808014\pi$
$14$	2.55563	−	2.73290i	0.683021	−	0.730399i
$15$	0.274912	+	1.84853i	0.0709819	+	0.477288i
$16$	−1.03508	−	3.86376i	−0.258770	−	0.965939i
$17$	2.73015	+	4.72875i	0.662158	+	1.14689i	0.980048	+	0.198763i	$0.0636925\pi$
$17$	2.73015	+	4.72875i	0.662158	+	1.14689i	−0.317890	+	0.948128i	$0.602974\pi$
$18$	−3.09441	+	2.90252i	−0.729360	+	0.684130i
$19$	3.78291	−	6.55219i	0.867859	−	1.50318i	0.00367934	−	0.999993i	$-0.498829\pi$
$19$	3.78291	−	6.55219i	0.867859	−	1.50318i	0.864180	−	0.503183i	$-0.167838\pi$
$20$	−1.71200	−	1.31373i	−0.382815	−	0.293759i
$21$	4.00298	−	2.23073i	0.873521	−	0.486786i
$22$	5.52136	−	2.72275i	1.17716	−	0.580491i
$23$		−	3.38475i		−	0.705769i	−0.935667	−	0.352884i	$-0.885201\pi$
$23$		−	3.38475i		−	0.705769i	0.935667	−	0.352884i	$-0.114799\pi$
$24$	0.238732	−	4.89316i	0.0487309	−	0.998812i
$25$	3.83579			0.767158
$26$	−0.673767	−	0.450209i	−0.132137	−	0.0882932i
$27$	−4.69476	+	2.22693i	−0.903508	+	0.428572i
$28$	−1.53214	+	5.06483i	−0.289548	+	0.957164i
$29$	−2.26807	+	3.92841i	−0.421170	+	0.729488i	−0.996054	−	0.0887469i	$-0.971714\pi$
$29$	−2.26807	+	3.92841i	−0.421170	+	0.729488i	0.574884	+	0.818235i	$0.305047\pi$
$30$	−1.50490	−	2.17268i	−0.274756	−	0.396675i
$31$	5.87332	+	3.39096i	1.05488	+	0.609035i	0.924011	−	0.382365i	$-0.124890\pi$
$31$	5.87332	+	3.39096i	1.05488	+	0.609035i	0.130868	+	0.991400i	$0.458224\pi$
$32$	3.72955	+	4.25328i	0.659298	+	0.751881i
$33$	7.45775	−	1.10911i	1.29823	−	0.193071i
$34$	−6.42057	−	4.29021i	−1.10112	−	0.735764i
$35$	1.00770	+	2.67095i	0.170333	+	0.451474i
$36$	2.10943	−	5.61697i	0.351572	−	0.936161i
$37$	5.79374	+	3.34502i	0.952485	+	0.549918i	0.893852	−	0.448362i	$-0.147992\pi$
$37$	5.79374	+	3.34502i	0.952485	+	0.549918i	0.0586333	+	0.998280i	$0.481326\pi$
$38$	−0.699928	+	10.6768i	−0.113543	+	1.73200i
$39$	−0.617264	−	0.777149i	−0.0988414	−	0.124443i
$40$	2.99317	+	0.595496i	0.473261	+	0.0941562i
$41$	−0.0203980	−	0.0353304i	−0.00318564	−	0.00551769i	0.864428	−	0.502756i	$-0.167681\pi$
$41$	−0.0203980	−	0.0353304i	−0.00318564	−	0.00551769i	−0.867614	+	0.497239i	$0.834347\pi$
$42$	−3.68202	+	5.33317i	−0.568148	+	0.822927i
$43$	3.79642	+	2.19186i	0.578949	+	0.334256i	0.760715	−	0.649085i	$-0.224848\pi$
$43$	3.79642	+	2.19186i	0.578949	+	0.334256i	−0.181767	+	0.983342i	$0.558182\pi$
$44$	−5.30016	+	6.90694i	−0.799029	+	1.04126i
$45$	−0.941962	−	3.09687i	−0.140419	−	0.461654i
$46$	2.11707	+	4.29314i	0.312146	+	0.632989i
$47$	5.31431	+	9.20466i	0.775172	+	1.34264i	0.934698	+	0.355443i	$0.115670\pi$
$47$	5.31431	+	9.20466i	0.775172	+	1.34264i	−0.159526	+	0.987194i	$0.550997\pi$
$48$	2.75775	+	6.35569i	0.398046	+	0.917365i
$49$	5.25553	−	4.62379i	0.750790	−	0.660541i
$50$	−4.86523	+	2.39919i	−0.688048	+	0.339297i
$51$	−5.88214	−	7.40573i	−0.823664	−	1.03701i
$52$	1.13619	+	0.149611i	0.157561	+	0.0207473i
$53$	−6.07598	−	10.5239i	−0.834600	−	1.44557i	−0.894355	−	0.447357i	$-0.852365\pi$
$53$	−6.07598	−	10.5239i	−0.834600	−	1.44557i	0.0597551	−	0.998213i	$-0.480968\pi$
$54$	4.56185	−	5.76104i	0.620789	−	0.783978i
$55$			4.69692i			0.633332i
$56$	−1.22459	−	7.38244i	−0.163643	−	0.986520i
$57$	−4.81150	+	12.1891i	−0.637299	+	1.61449i
$58$	0.419646	−	6.40133i	0.0551023	−	0.840536i
$59$	9.29209	+	5.36479i	1.20973	+	0.698436i	0.962700	−	0.270572i	$-0.0872129\pi$
$59$	9.29209	+	5.36479i	1.20973	+	0.698436i	0.247028	+	0.969008i	$0.420546\pi$
$60$	3.26774	+	1.81450i	0.421863	+	0.234251i
$61$	3.26452	+	5.65431i	0.417978	+	0.723960i	0.995736	−	0.0922486i	$-0.0294055\pi$
$61$	3.26452	+	5.65431i	0.417978	+	0.723960i	−0.577758	+	0.816208i	$0.696072\pi$
$62$	−9.57055	−	0.627408i	−1.21546	−	0.0796809i
$63$	−6.28957	+	4.84162i	−0.792412	+	0.609987i
$64$	−7.39080	−	3.06203i	−0.923851	−	0.382753i
$65$	0.535424	−	0.309127i	0.0664112	−	0.0383425i
$66$	−8.76552	+	6.07140i	−1.07896	+	0.747338i
$67$	3.02506	+	1.74652i	0.369570	+	0.213371i	0.673271	−	0.739396i	$-0.264889\pi$
$67$	3.02506	+	1.74652i	0.369570	+	0.213371i	−0.303700	+	0.952768i	$0.598222\pi$
$68$	10.8271	+	1.42570i	1.31298	+	0.172891i
$69$	0.862391	+	5.79878i	0.103820	+	0.698091i
$70$	−2.94876	−	2.75749i	−0.352444	−	0.329583i
$71$			4.23443i			0.502534i	0.967918	+	0.251267i	$0.0808472\pi$
$71$			4.23443i			0.502534i	−0.967918	+	0.251267i	$0.919153\pi$
$72$	0.837717	+	8.44383i	0.0987260	+	0.995115i
$73$	−2.40773	+	1.39011i	−0.281804	+	0.162699i	−0.634240	−	0.773136i	$-0.718687\pi$
$73$	−2.40773	+	1.39011i	−0.281804	+	0.162699i	0.352436	+	0.935836i	$0.385353\pi$
$74$	−9.44088	−	0.618907i	−1.09748	−	0.0719465i
$75$	−6.57151	+	0.977311i	−0.758813	+	0.112850i
$76$	−5.79028	−	13.9800i	−0.664190	−	1.60361i
$77$	10.7758	−	4.06550i	1.22801	−	0.463307i
$78$	1.26901	+	0.599635i	0.143687	+	0.0678953i
$79$	−5.72281	−	9.91220i	−0.643866	−	1.11521i	−0.984562	−	0.175036i	$-0.943996\pi$
$79$	−5.72281	−	9.91220i	−0.643866	−	1.11521i	0.340696	−	0.940174i	$-0.389337\pi$
$80$	−4.16894	+	1.11684i	−0.466101	+	0.124866i
$81$	7.47572	−	5.01135i	0.830635	−	0.556817i
$82$	0.0479707	+	0.0320539i	0.00529748	+	0.00353976i
$83$	10.3909	+	5.99917i	1.14055	+	0.658494i	0.946566	−	0.322511i	$-0.104527\pi$
$83$	10.3909	+	5.99917i	1.14055	+	0.658494i	0.193980	+	0.981006i	$0.437860\pi$
$84$	1.33442	−	9.06749i	0.145598	−	0.989344i
$85$	5.10225	−	2.94579i	0.553417	−	0.319516i
$86$	−6.18625	−	0.405547i	−0.667080	−	0.0437312i
$87$	2.88477	−	7.30806i	0.309280	−	0.783507i
$88$	2.40249	−	12.0757i	0.256106	−	1.28728i
$89$	6.51255	−	11.2801i	0.690329	−	1.19568i	−0.281401	−	0.959590i	$-0.590799\pi$
$89$	6.51255	−	11.2801i	0.690329	−	1.19568i	0.971730	−	0.236095i	$-0.0758675\pi$
$90$	3.13178	+	3.33882i	0.330118	+	0.351943i
$91$	−1.17265	−	0.960812i	−0.122927	−	0.100720i
$92$	−5.37050	−	4.12114i	−0.559913	−	0.429659i
$93$	−10.9262	−	4.31298i	−1.13299	−	0.447235i
$94$	−12.4978	−	8.35101i	−1.28905	−	0.861341i
$95$	−7.06972	−	4.08170i	−0.725338	−	0.418774i
$96$	−7.47319	−	6.33652i	−0.762729	−	0.646718i
$97$	1.14927	+	0.663530i	0.116690	+	0.0673713i	0.557209	−	0.830372i	$-0.311872\pi$
$97$	1.14927	+	0.663530i	0.116690	+	0.0673713i	−0.440519	+	0.897743i	$0.645205\pi$
$98$	−3.77393	+	9.15191i	−0.381225	+	0.924482i
$99$	−12.4941	+	3.80028i	−1.25570	+	0.381942i
$100$	4.67032	−	6.08616i	0.467032	−	0.608616i
$101$			2.22106i			0.221004i	0.993876	+	0.110502i	$0.0352459\pi$
$101$			2.22106i			0.221004i	−0.993876	+	0.110502i	$0.964754\pi$
$102$	12.0929	+	5.71414i	1.19737	+	0.565784i
$103$		−	3.64715i		−	0.359364i	−0.983725	−	0.179682i	$-0.942493\pi$
$103$		−	3.64715i		−	0.359364i	0.983725	−	0.179682i	$-0.0575069\pi$
$104$	−1.53469	+	0.520892i	−0.150489	+	0.0510777i
$105$	−2.40693	−	4.31915i	−0.234892	−	0.421506i
$106$	14.2891	+	9.54792i	1.38788	+	0.927376i
$107$	5.43313	−	9.41046i	0.525240	−	0.909743i	−0.474327	−	0.880348i	$-0.657309\pi$
$107$	5.43313	−	9.41046i	0.525240	−	0.909743i	0.999568	−	0.0293946i	$-0.00935794\pi$
$108$	−2.18276	+	10.1605i	−0.210036	+	0.977694i
$109$	−6.73693	+	3.88957i	−0.645281	+	0.372553i	−0.786646	−	0.617404i	$-0.788184\pi$
$109$	−6.73693	+	3.88957i	−0.645281	+	0.372553i	0.141365	+	0.989958i	$0.454851\pi$
$110$	−2.93780	−	5.95746i	−0.280108	−	0.568022i
$111$	−10.7782	−	4.25454i	−1.02302	−	0.403823i
$112$	6.17077	+	8.59777i	0.583083	+	0.812413i
$113$	1.77375	−	1.02408i	0.166860	−	0.0963369i	−0.414244	−	0.910166i	$-0.635954\pi$
$113$	1.77375	−	1.02408i	0.166860	−	0.0963369i	0.581105	+	0.813829i	$0.302621\pi$
$114$	−1.52118	−	18.4699i	−0.142472	−	1.72986i
$115$	−3.65209			−0.340560
$116$	3.47160	+	8.38178i	0.322330	+	0.778229i
$117$	1.25551	+	1.17415i	0.116072	+	0.108550i
$118$	−15.1414	−	0.992613i	−1.39388	−	0.0913774i
$119$	−11.1746	−	9.15593i	−1.02438	−	0.839322i
$120$	−5.27965	−	0.257588i	−0.481964	−	0.0235144i
$121$	7.94937			0.722670
$122$	−7.67726	−	5.12992i	−0.695067	−	0.464441i
$123$	0.0439478	+	0.0553312i	0.00396264	+	0.00498905i
$124$	12.5315	−	5.19034i	1.12536	−	0.466107i
$125$		−	9.53369i		−	0.852719i
$126$	4.94924	−	10.0750i	0.440913	−	0.897550i
$127$	−15.5438			−1.37929			−0.689646	−	0.724147i	$-0.742234\pi$
$127$	−15.5438			−1.37929			−0.689646	+	0.724147i	$0.742234\pi$
$128$	11.2896	−	0.738954i	0.997865	−	0.0653150i
$129$	−7.06252	−	2.78784i	−0.621820	−	0.245456i
$130$	−0.485769	+	0.726985i	−0.0426047	+	0.0637608i
$131$			0.342996i			0.0299677i	0.999888	+	0.0149839i	$0.00476969\pi$
$131$			0.342996i			0.0299677i	−0.999888	+	0.0149839i	$0.995230\pi$
$132$	7.32048	−	13.1834i	0.637166	−	1.14747i
$133$	−3.24501	+	19.7525i	−0.281378	+	1.71276i
$134$	−4.92933	−	0.323148i	−0.425829	−	0.0279157i
$135$	2.40282	+	5.06558i	0.206802	+	0.435976i
$136$	−14.6246	+	4.96377i	−1.25405	+	0.425640i
$137$		−	12.2261i		−	1.04454i	−0.852779	−	0.522272i	$-0.825085\pi$
$137$		−	12.2261i		−	1.04454i	0.852779	−	0.522272i	$-0.174915\pi$
$138$	−4.72083	−	6.81564i	−0.401864	−	0.580186i
$139$	3.91963	+	6.78900i	0.332459	+	0.575836i	0.982993	−	0.183641i	$-0.0587884\pi$
$139$	3.91963	+	6.78900i	0.332459	+	0.575836i	−0.650535	+	0.759477i	$0.725455\pi$
$140$	5.46488	+	1.65316i	0.461867	+	0.139717i
$141$	−11.4498	−	14.4155i	−0.964243	−	1.21400i
$142$	−2.64853	−	5.37085i	−0.222259	−	0.450712i
$143$	−1.24715	−	2.16013i	−0.104292	−	0.180639i
$144$	−6.34394	−	10.1860i	−0.528662	−	0.848833i
$145$	4.23870	+	2.44721i	0.352005	+	0.203230i
$146$	2.18444	−	3.26915i	0.180785	−	0.270557i
$147$	−7.82574	+	9.26055i	−0.645456	+	0.763798i
$148$	12.3617	−	5.12002i	1.01613	−	0.420863i
$149$	−5.84445			−0.478796			−0.239398	−	0.970921i	$-0.576950\pi$
$149$	−5.84445			−0.478796			−0.239398	+	0.970921i	$0.576950\pi$
$150$	7.72387	−	5.34991i	0.630652	−	0.436818i
$151$	−9.63460			−0.784053			−0.392026	−	0.919954i	$-0.628226\pi$
$151$	−9.63460			−0.784053			−0.392026	+	0.919954i	$0.628226\pi$
$152$	16.0884	+	14.1102i	1.30494	+	1.14449i
$153$	11.9642	+	11.1889i	0.967249	+	0.904567i
$154$	−11.1249	+	11.8966i	−0.896468	+	0.958652i
$155$	3.65880	−	6.33722i	0.293882	−	0.509018i
$156$	−1.98464	+	0.0331710i	−0.158898	+	0.00265580i
$157$	−8.40443	+	14.5569i	−0.670747	+	1.16177i	0.306946	+	0.951727i	$0.400693\pi$
$157$	−8.40443	+	14.5569i	−0.670747	+	1.16177i	−0.977693	+	0.210040i	$0.932640\pi$
$158$	13.4585	+	8.99294i	1.07070	+	0.715440i
$159$	13.0908	+	16.4816i	1.03817	+	1.30707i
$160$	4.58923	−	4.02413i	0.362810	−	0.318136i
$161$	3.16114	+	8.37872i	0.249132	+	0.660335i
$162$	−6.34756	+	11.0322i	−0.498711	+	0.866768i
$163$	21.6126	+	12.4780i	1.69283	+	0.977355i	0.952217	+	0.305422i	$0.0987977\pi$
$163$	21.6126	+	12.4780i	1.69283	+	0.977355i	0.740612	+	0.671933i	$0.234536\pi$
$164$	−0.0808938	−	0.0106520i	−0.00631675	−	0.000831778i
$165$	−1.19671	−	8.04680i	−0.0931641	−	0.626442i
$166$	−16.9319	−	1.10999i	−1.31417	−	0.0861517i
$167$	−0.408021	−	0.706713i	−0.0315736	−	0.0546871i	0.849807	−	0.527094i	$-0.176719\pi$
$167$	−0.408021	−	0.706713i	−0.0315736	−	0.0546871i	−0.881380	+	0.472407i	$0.843385\pi$
$168$	3.97893	+	12.3356i	0.306981	+	0.951716i
$169$	6.33584	−	10.9740i	0.487372	−	0.844153i
$170$	−4.62907	+	6.92770i	−0.355033	+	0.531331i
$171$	5.13747	−	22.1084i	0.392872	−	1.69067i
$172$	8.10016	−	3.35496i	0.617631	−	0.255813i
$173$	−4.50520	+	2.60108i	−0.342524	+	0.197756i	−0.661388	−	0.750044i	$-0.730032\pi$
$173$	−4.50520	+	2.60108i	−0.342524	+	0.197756i	0.318864	+	0.947801i	$0.396699\pi$
$174$	0.912035	+	11.0737i	0.0691412	+	0.839498i
$175$	−9.49524	+	3.58238i	−0.717773	+	0.270803i
$176$	4.50580	+	16.8193i	0.339637	+	1.26780i
$177$	−17.2862	−	6.82350i	−1.29931	−	0.512886i
$178$	−1.20498	+	18.3808i	−0.0903167	+	1.37770i
$179$	10.4179	+	18.0443i	0.778669	+	1.34869i	0.932709	+	0.360630i	$0.117438\pi$
$179$	10.4179	+	18.0443i	0.778669	+	1.34869i	−0.154040	+	0.988065i	$0.549229\pi$
$180$	−6.06062	−	2.27604i	−0.451732	−	0.169646i
$181$	−10.1588			−0.755096			−0.377548	−	0.925990i	$-0.623233\pi$
$181$	−10.1588			−0.755096			−0.377548	+	0.925990i	$0.623233\pi$
$182$	2.08833	+	0.485207i	0.154797	+	0.0359659i
$183$	−7.03344	−	8.85525i	−0.519927	−	0.654599i
$184$	9.38949	+	1.86806i	0.692203	+	0.137715i
$185$	3.60923	−	6.25136i	0.265356	−	0.459609i
$186$	16.5562	−	1.36357i	1.21396	−	0.0999820i
$187$	−11.8846	−	20.5847i	−0.869086	−	1.50530i
$188$	21.0753	+	2.77516i	1.53708	+	0.202399i
$189$	9.54176	−	9.89721i	0.694061	−	0.719916i
$190$	11.5201	+	0.755212i	0.835754	+	0.0547888i
$191$	−5.07015	+	2.92725i	−0.366863	+	0.211808i	−0.672087	−	0.740472i	$-0.734602\pi$
$191$	−5.07015	+	2.92725i	−0.366863	+	0.211808i	0.305224	+	0.952281i	$0.401269\pi$
$192$	13.4422	+	3.36281i	0.970104	+	0.242690i
$193$	−4.50471	+	7.80239i	−0.324256	+	0.561629i	−0.981362	−	0.192170i	$-0.938447\pi$
$193$	−4.50471	+	7.80239i	−0.324256	+	0.561629i	0.657105	+	0.753799i	$0.271781\pi$
$194$	−1.87273	−	0.122769i	−0.134454	−	0.00881428i
$195$	−0.838532	+	0.666019i	−0.0600485	+	0.0476946i
$196$	−0.937514	−	13.9686i	−0.0669653	−	0.997755i
$197$	−4.59238			−0.327194			−0.163597	−	0.986527i	$-0.552310\pi$
$197$	−4.59238			−0.327194			−0.163597	+	0.986527i	$0.552310\pi$
$198$	13.4702	−	12.6349i	0.957288	−	0.897925i
$199$	10.7226	−	6.19070i	0.760106	−	0.438847i	−0.0692278	−	0.997601i	$-0.522054\pi$
$199$	10.7226	−	6.19070i	0.760106	−	0.438847i	0.829334	+	0.558753i	$0.188720\pi$
$200$	−2.11699	+	10.6407i	−0.149694	+	0.752412i
$201$	−5.62755	−	2.22141i	−0.396937	−	0.156686i
$202$	−1.38922	−	2.81715i	−0.0977452	−	0.198214i
$203$	1.94557	−	11.8427i	0.136552	−	0.831198i
$204$	−18.9124	+	0.316098i	−1.32413	+	0.0221313i
$205$	−0.0381210	+	0.0220092i	−0.00266249	+	0.00153719i
$206$	2.28120	+	4.62596i	0.158939	+	0.322306i
$207$	−2.95491	−	9.71479i	−0.205380	−	0.675225i
$208$	1.62076	−	1.62060i	0.112380	−	0.112368i
$209$	−16.4673	+	28.5223i	−1.13907	+	1.97293i
$210$	5.75442	+	3.97284i	0.397092	+	0.274152i
$211$	−7.14598	+	4.12573i	−0.491949	+	0.284027i	−0.725383	−	0.688346i	$-0.758337\pi$
$211$	−7.14598	+	4.12573i	−0.491949	+	0.284027i	0.233433	+	0.972373i	$0.425004\pi$
$212$	−24.0959	−	3.17291i	−1.65491	−	0.217916i
$213$	−1.07888	−	7.25445i	−0.0739235	−	0.497067i
$214$	−1.00526	+	15.3343i	−0.0687180	+	1.04823i
$215$	2.36499	−	4.09628i	0.161291	−	0.279364i
$216$	−3.58656	−	14.2526i	−0.244035	−	0.969766i
$217$	−17.7059	−	2.90880i	−1.20196	−	0.197462i
$218$	6.11215	−	9.14722i	0.413967	−	0.619528i
$219$	3.77077	−	2.99500i	0.254805	−	0.202383i
$220$	7.45248	+	5.71879i	0.502446	+	0.385561i
$221$	−1.56436	+	2.70956i	−0.105231	+	0.182265i
$222$	16.3319	−	1.34510i	1.09612	−	0.0902770i
$223$	8.28605	+	4.78395i	0.554875	+	0.320357i	0.751086	−	0.660204i	$-0.229530\pi$
$223$	8.28605	+	4.78395i	0.554875	+	0.320357i	−0.196211	+	0.980562i	$0.562864\pi$
$224$	−13.2046	−	7.04555i	−0.882266	−	0.470751i
$225$	11.0094	−	3.34867i	0.733957	−	0.223245i
$226$	−1.60925	+	2.40835i	−0.107046	+	0.160201i
$227$		−	3.97476i		−	0.263814i	−0.991262	−	0.131907i	$-0.957890\pi$
$227$		−	3.97476i		−	0.263814i	0.991262	−	0.131907i	$-0.0421101\pi$
$228$	13.4819	+	22.4753i	0.892858	+	1.48846i
$229$	19.8359			1.31079			0.655395	−	0.755286i	$-0.272502\pi$
$229$	19.8359			1.31079			0.655395	+	0.755286i	$0.272502\pi$
$230$	4.63223	−	2.28429i	0.305440	−	0.150622i
$231$	−17.4253	+	9.71058i	−1.14650	+	0.638909i
$232$	−9.64589	−	8.45987i	−0.633284	−	0.555417i
$233$	−5.80951	−	3.35412i	−0.380594	−	0.219736i	0.297483	−	0.954727i	$-0.403853\pi$
$233$	−5.80951	−	3.35412i	−0.380594	−	0.219736i	−0.678077	+	0.734991i	$0.737186\pi$
$234$	−2.32686	−	0.703971i	−0.152112	−	0.0460201i
$235$	9.93169	−	5.73406i	0.647872	−	0.374049i
$236$	19.8259	−	8.21157i	1.29056	−	0.534527i
$237$	12.3299	+	15.5236i	0.800911	+	1.00836i
$238$	19.9005	+	4.62372i	1.28996	+	0.299711i
$239$	6.80395	−	3.92826i	0.440111	−	0.254098i	−0.263534	−	0.964650i	$-0.584888\pi$
$239$	6.80395	−	3.92826i	0.440111	−	0.254098i	0.703645	+	0.710552i	$0.251555\pi$
$240$	6.85770	−	2.97557i	0.442663	−	0.192072i
$241$		−	2.61070i		−	0.168170i	−0.996459	−	0.0840849i	$-0.973203\pi$
$241$		−	2.61070i		−	0.168170i	0.996459	−	0.0840849i	$-0.0267967\pi$
$242$	−10.0828	+	4.97213i	−0.648147	+	0.319621i
$243$	−11.5306	+	10.4902i	−0.739690	+	0.672947i
$244$	12.9463	+	1.70475i	0.828802	+	0.109135i
$245$	−4.98900	−	5.67064i	−0.318735	−	0.362284i
$246$	−0.0903507	−	0.0426926i	−0.00576055	−	0.00272198i
$247$	4.33519			0.275841
$248$	−12.6482	+	14.4214i	−0.803164	+	0.915763i
$249$	−19.3302	−	7.63036i	−1.22500	−	0.483555i
$250$	5.96308	+	12.0923i	0.377138	+	0.764785i
$251$		−	9.14128i		−	0.576992i	−0.957481	−	0.288496i	$-0.906845\pi$
$251$		−	9.14128i		−	0.576992i	0.957481	−	0.288496i	$-0.0931552\pi$
$252$	0.0241344	+	15.8745i	0.00152032	+	0.999999i
$253$			14.7341i			0.926325i
$254$	19.7154	−	9.72227i	1.23706	−	0.610030i
$255$	−7.99068	+	6.34674i	−0.500396	+	0.397448i
$256$	−13.8572	+	7.99860i	−0.866076	+	0.499913i
$257$	−6.15896			−0.384185			−0.192093	−	0.981377i	$-0.561527\pi$
$257$	−6.15896			−0.384185			−0.192093	+	0.981377i	$0.561527\pi$
$258$	10.7017	−	0.881391i	0.666257	−	0.0548730i
$259$	−17.4660	−	2.86939i	−1.08529	−	0.178295i
$260$	0.161428	−	1.22593i	0.0100113	−	0.0760288i
$261$	−3.08021	+	13.2552i	−0.190660	+	0.820479i
$262$	−0.214535	−	0.435049i	−0.0132540	−	0.0268774i
$263$			15.4165i			0.950624i	0.879817	+	0.475312i	$0.157665\pi$
$263$			15.4165i			0.950624i	−0.879817	+	0.475312i	$0.842335\pi$
$264$	−1.03922	+	21.3003i	−0.0639595	+	1.31095i
$265$	−11.3551	+	6.55589i	−0.697541	+	0.402725i
$266$	−8.23879	−	27.0833i	−0.505153	−	1.66058i
$267$	−8.28334	+	20.9844i	−0.506932	+	1.28423i
$268$	6.45437	−	2.67330i	0.394263	−	0.163298i
$269$	7.40198	−	4.27354i	0.451307	−	0.260562i	−0.257075	−	0.966391i	$-0.582759\pi$
$269$	7.40198	−	4.27354i	0.451307	−	0.260562i	0.708382	+	0.705829i	$0.249425\pi$
$270$	−6.21607	−	4.92217i	−0.378298	−	0.299553i
$271$	22.4865	+	12.9826i	1.36596	+	0.788637i	0.990409	−	0.138165i	$-0.0441205\pi$
$271$	22.4865	+	12.9826i	1.36596	+	0.788637i	0.375550	+	0.926802i	$0.377454\pi$
$272$	15.4448	−	15.4433i	0.936480	−	0.936385i
$273$	2.25380	+	1.34729i	0.136406	+	0.0815419i
$274$	7.64710	+	15.5073i	0.461978	+	0.936829i
$275$	−16.6975			−1.00690
$276$	10.2508	+	5.69205i	0.617026	+	0.342621i
$277$		−	10.6092i		−	0.637443i	−0.947848	−	0.318722i	$-0.896746\pi$
$277$		−	10.6092i		−	0.637443i	0.947848	−	0.318722i	$-0.103254\pi$
$278$	−9.21792	−	6.15939i	−0.552854	−	0.369415i
$279$	19.8177	+	4.60518i	1.18646	+	0.275705i
$280$	−7.96554	+	1.32132i	−0.476032	+	0.0789637i
$281$	12.9610	+	7.48304i	0.773189	+	0.446401i	0.834011	−	0.551748i	$-0.186039\pi$
$281$	12.9610	+	7.48304i	0.773189	+	0.446401i	−0.0608219	+	0.998149i	$0.519372\pi$
$282$	23.5391	+	11.1227i	1.40173	+	0.662349i
$283$	0.843850	−	1.46159i	0.0501617	−	0.0868825i	−0.839854	−	0.542812i	$-0.817360\pi$
$283$	0.843850	−	1.46159i	0.0501617	−	0.0868825i	0.890016	+	0.455929i	$0.150693\pi$
$284$	6.71866	+	5.15568i	0.398679	+	0.305933i
$285$	13.1519	+	5.19154i	0.779050	+	0.307520i
$286$	2.93297	+	1.95980i	0.173430	+	0.115885i
$287$	0.0834903	+	0.0684076i	0.00492828	+	0.00403798i
$288$	14.4176	+	8.95171i	0.849565	+	0.527484i
$289$	−6.40741	+	11.0980i	−0.376906	+	0.652821i
$290$	−6.90694	−	0.452792i	−0.405590	−	0.0265889i
$291$	−2.13799	−	0.843946i	−0.125331	−	0.0494730i
$292$	−0.725920	+	5.51283i	−0.0424812	+	0.322614i
$293$	26.6359	−	15.3783i	1.55609	−	0.898408i	0.558463	−	0.829530i	$-0.311391\pi$
$293$	26.6359	−	15.3783i	1.55609	−	0.898408i	0.997625	−	0.0688779i	$-0.0219419\pi$
$294$	4.13375	−	16.6407i	0.241085	−	0.970504i
$295$	5.78853	−	10.0260i	0.337021	−	0.583738i
$296$	−12.4769	+	14.2261i	−0.725203	+	0.826873i
$297$	20.4367	−	9.69400i	1.18586	−	0.562503i
$298$	7.41297	−	3.65556i	0.429422	−	0.211761i
$299$	1.67961	−	0.969725i	0.0971345	−	0.0560806i
$300$	−6.45055	+	11.6168i	−0.372423	+	0.670696i
$301$	−11.4448	−	1.88020i	−0.659670	−	0.108373i
$302$	12.2203	−	6.02620i	0.703200	−	0.346769i
$303$	−0.565899	−	3.80515i	−0.0325100	−	0.218600i
$304$	−29.2317	−	7.83419i	−1.67655	−	0.449322i
$305$	6.10091	−	3.52236i	0.349337	−	0.201690i
$306$	−22.1735	−	6.70840i	−1.26757	−	0.383494i
$307$	−15.3621			−0.876762			−0.438381	−	0.898789i	$-0.644448\pi$
$307$	−15.3621			−0.876762			−0.438381	+	0.898789i	$0.644448\pi$
$308$	6.66955	−	22.0477i	0.380033	−	1.25628i
$309$	0.929247	+	6.24833i	0.0528630	+	0.355455i
$310$	−0.676964	+	10.3265i	−0.0384490	+	0.586505i
$311$	3.40909	−	5.90472i	0.193312	−	0.334826i	−0.753034	−	0.657982i	$-0.771410\pi$
$311$	3.40909	−	5.90472i	0.193312	−	0.334826i	0.946346	+	0.323156i	$0.104744\pi$
$312$	2.49653	−	1.28342i	0.141338	−	0.0726591i
$313$	2.25949	−	1.30452i	0.127714	−	0.0737357i	−0.434782	−	0.900536i	$-0.643175\pi$
$313$	2.25949	−	1.30452i	0.127714	−	0.0737357i	0.562496	+	0.826800i	$0.309841\pi$
$314$	1.55502	−	23.7204i	0.0877548	−	1.33862i
$315$	5.22404	+	6.78635i	0.294341	+	0.382368i
$316$	−22.6953	−	2.98848i	−1.27671	−	0.168115i
$317$	−10.7160	−	18.5607i	−0.601871	−	1.04247i	−0.992538	−	0.121939i	$-0.961089\pi$
$317$	−10.7160	−	18.5607i	−0.601871	−	1.04247i	0.390666	−	0.920532i	$-0.372245\pi$
$318$	−26.9129	−	12.7169i	−1.50920	−	0.713128i
$319$	9.87311	−	17.1007i	0.552788	−	0.957457i
$320$	−3.30388	+	7.97457i	−0.184693	+	0.445792i
$321$	−6.91042	+	17.5064i	−0.385702	+	0.977110i
$322$	−9.25019	−	8.65017i	−0.515493	−	0.482055i
$323$	41.3116			2.29864
$324$	1.15076	−	17.9632i	0.0639312	−	0.997954i
$325$	1.09895	+	1.90343i	0.0609586	+	0.105583i
$326$	−35.2176	−	2.30873i	−1.95052	−	0.127869i
$327$	10.5508	−	8.38013i	0.583458	−	0.463422i
$328$	0.109266	−	0.0370863i	0.00603323	−	0.00204775i
$329$	−21.7518	−	17.8223i	−1.19921	−	0.982574i
$330$	6.55095	+	9.45786i	0.360618	+	0.520638i
$331$	3.05388	−	1.76316i	0.167856	−	0.0969119i	−0.413718	−	0.910405i	$-0.635770\pi$
$331$	3.05388	−	1.76316i	0.167856	−	0.0969119i	0.581575	+	0.813493i	$0.302437\pi$
$332$	22.1703	−	9.18257i	1.21675	−	0.503959i
$333$	19.5492	+	4.54278i	1.07129	+	0.248943i
$334$	0.959555	+	0.641172i	0.0525045	+	0.0350834i
$335$	1.88447	−	3.26400i	0.102960	−	0.178331i
$336$	−12.7624	−	13.1575i	−0.696247	−	0.717802i
$337$	14.3841	+	24.9139i	0.783550	+	1.35715i	0.929862	+	0.367909i	$0.119926\pi$
$337$	14.3841	+	24.9139i	0.783550	+	1.35715i	−0.146312	+	0.989238i	$0.546740\pi$
$338$	−1.17228	+	17.8821i	−0.0637636	+	0.972656i
$339$	−2.77788	+	2.20638i	−0.150874	+	0.119834i
$340$	1.53831	−	11.6823i	0.0834263	−	0.633562i
$341$	−25.5671	−	14.7612i	−1.38453	−	0.799361i
$342$	7.31199	+	31.2552i	0.395387	+	1.69009i
$343$	−8.69139	+	16.3542i	−0.469291	+	0.883044i
$344$	−8.17562	+	9.32180i	−0.440800	+	0.502598i
$345$	6.25680	−	0.930507i	0.336855	−	0.0500968i
$346$	4.08739	−	6.11704i	0.219739	−	0.328854i
$347$	−11.5616	+	20.0252i	−0.620658	+	1.07501i	0.368706	+	0.929546i	$0.379801\pi$
$347$	−11.5616	+	20.0252i	−0.620658	+	1.07501i	−0.989363	+	0.145465i	$0.953532\pi$
$348$	−8.08314	−	13.4752i	−0.433302	−	0.722348i
$349$	−5.22401	+	9.04825i	−0.279635	+	0.484342i	−0.971294	−	0.237882i	$-0.923547\pi$
$349$	−5.22401	+	9.04825i	−0.279635	+	0.484342i	0.691659	+	0.722224i	$0.256880\pi$
$350$	9.80286	−	10.4828i	0.523985	−	0.560332i
$351$	−2.45011	−	1.69167i	−0.130777	−	0.0902947i
$352$	−16.2351	−	18.5149i	−0.865333	−	0.986848i
$353$	−8.37085			−0.445535			−0.222768	−	0.974872i	$-0.571509\pi$
$353$	−8.37085			−0.445535			−0.222768	+	0.974872i	$0.571509\pi$
$354$	26.1933	−	2.15729i	1.39216	−	0.114659i
$355$	4.56888			0.242491
$356$	−9.96837	−	24.0675i	−0.528323	−	1.27557i
$357$	21.4773	+	12.8389i	1.13670	+	0.679504i
$358$	−24.5001	−	16.3709i	−1.29487	−	0.865227i
$359$	1.80784	+	1.04376i	0.0954143	+	0.0550875i	0.546948	−	0.837167i	$-0.315790\pi$
$359$	1.80784	+	1.04376i	0.0954143	+	0.0550875i	−0.451534	+	0.892254i	$0.649123\pi$
$360$	9.11077	−	0.903885i	0.480180	−	0.0476389i
$361$	−19.1208	−	33.1182i	−1.00636	−	1.74307i
$362$	12.8852	−	6.35406i	0.677230	−	0.333962i
$363$	−13.6189	+	2.02540i	−0.714808	+	0.106306i
$364$	−2.95228	+	0.690772i	−0.154741	+	0.0362063i
$365$	1.49990	+	2.59791i	0.0785085	+	0.135981i
$366$	14.4598	+	6.83256i	0.755825	+	0.357144i
$367$			14.8270i			0.773962i	0.922088	+	0.386981i	$0.126482\pi$
$367$			14.8270i			0.773962i	−0.922088	+	0.386981i	$0.873518\pi$
$368$	−13.0778	+	3.50349i	−0.681730	+	0.182632i
$369$	−0.0893895	−	0.0835966i	−0.00465343	−	0.00435186i
$370$	−0.667792	+	10.1866i	−0.0347169	+	0.529574i
$371$	24.8693	+	20.3767i	1.29115	+	1.05790i
$372$	−20.1466	+	12.0850i	−1.04455	+	0.626578i
$373$			23.9314i			1.23912i	0.784949	+	0.619560i	$0.212689\pi$
$373$			23.9314i			1.23912i	−0.784949	+	0.619560i	$0.787311\pi$
$374$	27.9493	+	18.6756i	1.44522	+	0.965695i
$375$	2.42906	+	16.3332i	0.125436	+	0.843443i
$376$	−28.4672	+	9.66213i	−1.46809	+	0.498286i
$377$	−2.59919			−0.133865
$378$	−5.91211	+	18.5215i	−0.304086	+	0.952645i
$379$		−	34.2828i		−	1.76099i	−0.474057	−	0.880494i	$-0.657211\pi$
$379$		−	34.2828i		−	1.76099i	0.474057	−	0.880494i	$-0.342789\pi$
$380$	−15.0842	+	6.24762i	−0.773802	+	0.320496i
$381$	26.6298	−	3.96037i	1.36429	−	0.202896i
$382$	4.59994	−	6.88411i	0.235353	−	0.352222i
$383$	−18.9593			−0.968773			−0.484386	−	0.874854i	$-0.660957\pi$
$383$	−18.9593			−0.968773			−0.484386	+	0.874854i	$0.660957\pi$
$384$	−19.1531	+	4.14242i	−0.977401	+	0.211392i
$385$	−4.38662	−	11.6269i	−0.223563	−	0.592562i
$386$	0.833479	−	12.7140i	0.0424229	−	0.647124i
$387$	12.8099	+	2.97671i	0.651162	+	0.151315i
$388$	2.45211	−	1.01563i	0.124487	−	0.0515606i
$389$	14.5825			0.739361			0.369680	−	0.929159i	$-0.379467\pi$
$389$	14.5825			0.739361			0.369680	+	0.929159i	$0.379467\pi$
$390$	0.646997	−	1.36924i	0.0327620	−	0.0693344i
$391$	16.0056	−	9.24086i	0.809440	−	0.467331i
$392$	9.92611	+	17.1310i	0.501344	+	0.865248i
$393$	−0.0873910	−	0.587624i	−0.00440829	−	0.0296417i
$394$	5.82487	−	2.87242i	0.293453	−	0.144710i
$395$	−10.6951	+	6.17483i	−0.538130	+	0.310689i
$396$	−9.18253	+	24.4511i	−0.461439	+	1.22872i
$397$	−1.72126	+	2.98131i	−0.0863876	+	0.149628i	−0.905982	−	0.423317i	$-0.860866\pi$
$397$	−1.72126	+	2.98131i	−0.0863876	+	0.149628i	0.819594	+	0.572945i	$0.194199\pi$
$398$	−9.72819	+	14.5589i	−0.487630	+	0.729770i
$399$	0.526699	−	34.6669i	0.0263679	−	1.73552i
$400$	−3.97035	−	14.8206i	−0.198518	−	0.741028i
$401$			4.79389i			0.239395i	0.992810	+	0.119698i	$0.0381925\pi$
$401$			4.79389i			0.239395i	−0.992810	+	0.119698i	$0.961807\pi$
$402$	8.52730	−	0.702310i	0.425303	−	0.0350280i
$403$			3.88602i			0.193576i
$404$	3.52411	+	2.70429i	0.175331	+	0.134543i
$405$	−5.40718	−	8.06619i	−0.268685	−	0.400812i
$406$	4.93962	+	16.2380i	0.245149	+	0.805878i
$407$	−25.2207	−	14.5612i	−1.25014	−	0.721770i
$408$	23.7903	−	12.2301i	1.17780	−	0.605482i
$409$	2.75014	+	1.58779i	0.135986	+	0.0785113i	0.566449	−	0.824097i	$-0.308317\pi$
$409$	2.75014	+	1.58779i	0.135986	+	0.0785113i	−0.430464	+	0.902608i	$0.641650\pi$
$410$	0.0345856	−	0.0517597i	0.00170806	−	0.00255623i
$411$	3.11505	+	20.9458i	0.153654	+	1.03318i
$412$	−5.78685	−	4.44063i	−0.285097	−	0.218774i
$413$	−28.0123	−	4.60196i	−1.37840	−	0.226448i
$414$	9.82430	+	10.4738i	0.482838	+	0.514759i
$415$	6.47301	−	11.2116i	0.317748	−	0.550355i
$416$	−1.04209	+	3.06927i	−0.0510929	+	0.150484i
$417$	−8.44490	−	10.6323i	−0.413548	−	0.520666i
$418$	3.04685	−	46.4769i	0.149026	−	2.27326i
$419$	−6.20563	+	3.58282i	−0.303165	+	0.175032i	−0.643864	−	0.765140i	$-0.722670\pi$
$419$	−6.20563	+	3.58282i	−0.303165	+	0.175032i	0.340699	+	0.940172i	$0.389336\pi$
$420$	−9.78368	−	1.43982i	−0.477395	−	0.0702562i
$421$	17.8255	+	10.2916i	0.868763	+	0.501581i	0.866937	−	0.498418i	$-0.166085\pi$
$421$	17.8255	+	10.2916i	0.868763	+	0.501581i	0.00182610	+	0.999998i	$0.499419\pi$
$422$	6.48325	−	9.70261i	0.315600	−	0.472316i
$423$	23.2887	+	21.7795i	1.13233	+	1.05895i
$424$	32.5473	−	11.0469i	1.58064	−	0.536487i
$425$	10.4723	+	18.1385i	0.507980	+	0.879847i
$426$	5.90590	+	8.52658i	0.286142	+	0.413114i
$427$	−13.3618	−	10.9480i	−0.646625	−	0.529811i
$428$	−8.31617	−	20.0784i	−0.401977	−	0.970528i
$429$	2.68701	+	3.38300i	0.129730	+	0.163333i
$430$	−0.437579	+	6.67487i	−0.0211019	+	0.321891i
$431$	29.2414	−	16.8825i	1.40851	−	0.813203i	0.413265	−	0.910611i	$-0.364388\pi$
$431$	29.2414	−	16.8825i	1.40851	−	0.813203i	0.995245	+	0.0974074i	$0.0310550\pi$
$432$	13.4638	+	15.8344i	0.647775	+	0.761831i
$433$			33.5963i			1.61454i	0.590186	+	0.807268i	$0.299055\pi$
$433$			33.5963i			1.61454i	−0.590186	+	0.807268i	$0.700945\pi$
$434$	24.2772	−	7.38517i	1.16534	−	0.354499i
$435$	−7.88529	−	3.11262i	−0.378071	−	0.149239i
$436$	−2.03115	+	15.4251i	−0.0972746	+	0.738730i
$437$	−22.1775	−	12.8042i	−1.06090	−	0.612508i
$438$	−2.90946	+	6.15731i	−0.139019	+	0.294208i
$439$	−31.3321	+	18.0896i	−1.49540	+	0.863368i	−0.999986	−	0.00528984i	$-0.998316\pi$
$439$	−31.3321	+	18.0896i	−1.49540	+	0.863368i	−0.495412	+	0.868658i	$0.664983\pi$
$440$	−13.0295	−	2.59225i	−0.621158	−	0.123580i
$441$	11.0476	−	17.8592i	0.526078	−	0.850436i
$442$	0.289444	−	4.41521i	0.0137675	−	0.210010i
$443$	−15.3972	−	26.6687i	−0.731542	−	1.26707i	−0.956224	−	0.292636i	$-0.905468\pi$
$443$	−15.3972	−	26.6687i	−0.731542	−	1.26707i	0.224682	−	0.974432i	$-0.427866\pi$
$444$	−19.8737	+	11.9213i	−0.943162	+	0.565758i
$445$	−12.1710	−	7.02694i	−0.576962	−	0.333109i
$446$	−13.5021	−	0.885144i	−0.639342	−	0.0419128i
$447$	10.0128	−	1.48909i	0.473588	−	0.0704316i
$448$	21.1552	+	0.677307i	0.999488	+	0.0319998i
$449$			4.55118i			0.214783i	0.994217	+	0.107392i	$0.0342499\pi$
$449$			4.55118i			0.214783i	−0.994217	+	0.107392i	$0.965750\pi$
$450$	−11.8695	+	11.1335i	−0.559534	+	0.524836i
$451$	0.0887944	+	0.153796i	0.00418117	+	0.00724199i
$452$	0.534777	−	4.06124i	0.0251538	−	0.191025i
$453$	16.5061	−	2.45477i	0.775523	−	0.115335i
$454$	2.48611	+	5.04150i	0.116679	+	0.236609i
$455$	−1.03670	+	1.26528i	−0.0486013	+	0.0593170i
$456$	−31.1578	−	20.0746i	−1.45910	−	0.940079i
$457$	−11.4190	−	19.7783i	−0.534160	−	0.925192i	−0.999204	−	0.0399044i	$-0.987295\pi$
$457$	−11.4190	−	19.7783i	−0.534160	−	0.925192i	0.465044	−	0.885288i	$-0.346039\pi$
$458$	−25.1594	+	12.4068i	−1.17562	+	0.579733i
$459$	−23.3480	−	16.1205i	−1.08979	−	0.752443i
$460$	−4.44665	+	5.79469i	−0.207326	+	0.270179i
$461$	1.25117	+	0.722363i	0.0582728	+	0.0336438i	0.528853	−	0.848713i	$-0.322622\pi$
$461$	1.25117	+	0.722363i	0.0582728	+	0.0336438i	−0.470581	+	0.882357i	$0.655955\pi$
$462$	16.0281	−	23.2158i	0.745697	−	1.08010i
$463$	−10.8981	−	18.8760i	−0.506477	−	0.877243i	−0.999972	−	0.00749468i	$-0.997614\pi$
$463$	−10.8981	−	18.8760i	−0.506477	−	0.877243i	0.493495	−	0.869748i	$-0.335719\pi$
$464$	17.5261	+	4.69704i	0.813627	+	0.218055i
$465$	−4.65364	+	11.7892i	−0.215807	+	0.546711i
$466$	9.46658	+	0.620592i	0.438531	+	0.0287484i
$467$	−6.45918	−	3.72921i	−0.298895	−	0.172567i	0.343051	−	0.939317i	$-0.388540\pi$
$467$	−6.45918	−	3.72921i	−0.298895	−	0.172567i	−0.641946	+	0.766749i	$0.721873\pi$
$468$	3.39165	−	0.562490i	0.156779	−	0.0260011i
$469$	−9.11948	−	1.49818i	−0.421098	−	0.0691796i
$470$	−9.01062	+	13.4850i	−0.415629	+	0.622016i
$471$	10.6896	−	27.0803i	0.492552	−	1.24780i
$472$	−20.0106	+	22.8160i	−0.921062	+	1.05019i
$473$	−16.5261	−	9.54138i	−0.759873	−	0.438713i
$474$	−25.3485	−	11.9777i	−1.16430	−	0.550155i
$475$	14.5105	−	25.1328i	0.665785	−	1.15317i
$476$	−28.1333	+	6.58262i	−1.28949	+	0.301714i
$477$	−26.6265	−	24.9010i	−1.21915	−	1.14014i
$478$	−6.17295	+	9.23821i	−0.282344	+	0.422546i
$479$	38.2537			1.74785			0.873927	−	0.486057i	$-0.161565\pi$
$479$	38.2537			1.74785			0.873927	+	0.486057i	$0.161565\pi$
$480$	−6.83701	+	8.06346i	−0.312065	+	0.368045i
$481$			3.83337i			0.174787i
$482$	1.63292	+	3.31135i	0.0743777	+	0.150828i
$483$	−7.55048	−	13.5491i	−0.343559	−	0.616504i
$484$	9.67886	−	12.6131i	0.439948	−	0.573321i
$485$	0.715939	−	1.24004i	0.0325091	−	0.0563074i
$486$	8.06383	−	20.5177i	0.365783	−	0.930700i
$487$	−2.86877	−	4.96885i	−0.129996	−	0.225160i	0.793679	−	0.608337i	$-0.208163\pi$
$487$	−2.86877	−	4.96885i	−0.129996	−	0.225160i	−0.923675	+	0.383177i	$0.874830\pi$
$488$	−17.4871	+	5.93532i	−0.791603	+	0.268679i
$489$	−40.2061	−	15.8709i	−1.81818	−	0.717705i
$490$	9.87477	+	4.07202i	0.446097	+	0.183955i
$491$	3.90839	+	6.76953i	0.176383	+	0.305505i	0.940639	−	0.339408i	$-0.110227\pi$
$491$	3.90839	+	6.76953i	0.176383	+	0.305505i	−0.764256	+	0.644913i	$0.776894\pi$
$492$	0.141302	−	0.00236170i	0.00637038	−	0.000106474i
$493$	−24.7687			−1.11552
$494$	−5.49866	+	2.71155i	−0.247396	+	0.121998i
$495$	4.10044	+	13.4809i	0.184301	+	0.605923i
$496$	7.02249	−	26.2030i	0.315319	−	1.17655i
$497$	−3.95468	−	10.4820i	−0.177392	−	0.470183i
$498$	29.2906	−	2.41238i	1.31254	−	0.108101i
$499$			10.8050i			0.483696i	0.970314	+	0.241848i	$0.0777535\pi$
$499$			10.8050i			0.483696i	−0.970314	+	0.241848i	$0.922246\pi$
$500$	−15.1269	−	11.6079i	−0.676494	−	0.519119i
$501$	0.879086	+	1.10679i	0.0392747	+	0.0494476i
$502$	5.71764	+	11.5946i	0.255191	+	0.517492i
$503$	39.4991			1.76118			0.880590	−	0.473879i	$-0.157147\pi$
$503$	39.4991			1.76118			0.880590	+	0.473879i	$0.157147\pi$
$504$	−9.95970	−	20.1197i	−0.443640	−	0.896205i
$505$	2.39650			0.106643
$506$	−9.21581	−	18.6884i	−0.409693	−	0.830801i
$507$	−8.05858	+	20.4150i	−0.357894	+	0.906663i
$508$	−18.9256	+	24.6630i	−0.839687	+	1.09424i
$509$			15.6185i			0.692276i	0.938184	+	0.346138i	$0.112507\pi$
$509$			15.6185i			0.692276i	−0.938184	+	0.346138i	$0.887493\pi$
$510$	6.16547	−	13.0480i	0.273012	−	0.577776i
$511$	4.66191	−	5.68978i	0.206231	−	0.251701i
$512$	12.5733	−	18.8126i	0.555665	−	0.831406i
$513$	−3.16862	+	39.1853i	−0.139898	+	1.73007i
$514$	7.81188	−	3.85227i	0.344567	−	0.169916i
$515$	−3.93522			−0.173407
$516$	−13.0225	+	7.81156i	−0.573282	+	0.343885i
$517$	−23.1337	−	40.0687i	−1.01742	−	1.76222i
$518$	23.9483	−	7.28511i	1.05223	−	0.320089i
$519$	7.05563	−	5.60406i	0.309708	−	0.245991i
$520$	0.562035	+	1.65591i	0.0246469	+	0.0726163i
$521$	1.18845	+	2.05845i	0.0520668	+	0.0901823i	0.890884	−	0.454231i	$-0.150086\pi$
$521$	1.18845	+	2.05845i	0.0520668	+	0.0901823i	−0.838817	+	0.544413i	$0.816752\pi$
$522$	−4.38395	−	18.7392i	−0.191880	−	0.820194i
$523$	14.2730	−	24.7216i	0.624116	−	1.08100i	−0.364595	−	0.931166i	$-0.618793\pi$
$523$	14.2730	−	24.7216i	0.624116	−	1.08100i	0.988711	−	0.149834i	$-0.0478740\pi$
$524$	0.544224	+	0.417619i	0.0237745	+	0.0182438i
$525$	15.3546	−	8.55663i	0.670129	−	0.373442i
$526$	−9.64265	−	19.5540i	−0.420440	−	0.852594i
$527$			37.0313i			1.61311i
$528$	−12.0047	−	27.6669i	−0.522438	−	1.20405i
$529$	11.5435			0.501890
$530$	10.3021	−	15.4177i	0.447493	−	0.669702i
$531$	31.3534	+	7.28578i	1.36062	+	0.316176i
$532$	27.3898	+	29.1987i	1.18750	+	1.26592i
$533$	0.0116880	−	0.0202442i	0.000506264	−	0.000876874i
$534$	−2.61882	−	31.7972i	−0.113328	−	1.37600i
$535$	−10.1537	−	5.86227i	−0.438985	−	0.253448i
$536$	−6.51450	+	7.42779i	−0.281383	+	0.320832i
$537$	−22.4455	−	28.2593i	−0.968593	−	1.21948i
$538$	−6.71552	+	10.0502i	−0.289527	+	0.433295i
$539$	−22.8778	+	20.1278i	−0.985416	+	0.866964i
$540$	10.9630	+	2.35517i	0.471773	+	0.101350i
$541$	14.4163	+	8.32326i	0.619805	+	0.357845i	0.776793	−	0.629756i	$-0.216845\pi$
$541$	14.4163	+	8.32326i	0.619805	+	0.357845i	−0.156988	+	0.987601i	$0.550178\pi$
$542$	−36.6417	−	2.40209i	−1.57390	−	0.103179i
$543$	17.4041	−	2.58833i	0.746882	−	0.111076i
$544$	−9.93050	+	29.2482i	−0.425767	+	1.25401i
$545$	4.19679	+	7.26905i	0.179771	+	0.311372i
$546$	−3.70137	−	0.299181i	−0.158404	−	0.0128038i
$547$	−4.95103	−	2.85848i	−0.211691	−	0.122220i	0.390406	−	0.920643i	$-0.372335\pi$
$547$	−4.95103	−	2.85848i	−0.211691	−	0.122220i	−0.602097	+	0.798423i	$0.705668\pi$
$548$	−19.3988	−	14.8860i	−0.828677	−	0.635899i
$549$	14.3060	+	13.3789i	0.610563	+	0.570996i
$550$	21.1788	−	10.4439i	0.903066	−	0.445329i
$551$	17.1598	+	29.7217i	0.731033	+	1.26619i
$552$	−16.5621	−	0.808047i	−0.704930	−	0.0343927i
$553$	23.4238	+	19.1922i	0.996080	+	0.816137i
$554$	6.63577	+	13.4564i	0.281927	+	0.571709i
$555$	−4.59059	+	11.6295i	−0.194860	+	0.493644i
$556$	15.5443	+	2.04685i	0.659227	+	0.0868058i
$557$	16.2696	+	28.1798i	0.689366	+	1.19402i	0.972043	+	0.234802i	$0.0754441\pi$
$557$	16.2696	+	28.1798i	0.689366	+	1.19402i	−0.282677	+	0.959215i	$0.591223\pi$
$558$	−28.0168	+	6.55439i	−1.18605	+	0.277469i
$559$			2.51186i			0.106240i
$560$	9.27686	−	6.65817i	0.392019	−	0.281359i
$561$	25.6055	+	32.2378i	1.08106	+	1.36108i
$562$	−21.1199	−	1.38454i	−0.890890	−	0.0584033i
$563$	3.67953	+	2.12438i	0.155074	+	0.0895319i	0.575529	−	0.817781i	$-0.304796\pi$
$563$	3.67953	+	2.12438i	0.155074	+	0.0895319i	−0.420455	+	0.907313i	$0.638130\pi$
$564$	−36.8135	+	0.615295i	−1.55013	+	0.0259086i
$565$	−1.10496	−	1.91385i	−0.0464861	−	0.0805163i
$566$	−0.156132	+	2.38166i	−0.00656272	+	0.100108i
$567$	−13.8253	+	19.3871i	−0.580610	+	0.814182i
$568$	−11.7465	−	2.33700i	−0.492874	−	0.0980582i
$569$	−0.293331	+	0.169355i	−0.0122971	+	0.00709971i	−0.506136	−	0.862454i	$-0.668927\pi$
$569$	−0.293331	+	0.169355i	−0.0122971	+	0.00709971i	0.493839	+	0.869553i	$0.335593\pi$
$570$	−19.9287	+	1.64133i	−0.834722	+	0.0687479i
$571$	9.29216	+	5.36483i	0.388865	+	0.224511i	0.681668	−	0.731661i	$-0.261255\pi$
$571$	9.29216	+	5.36483i	0.388865	+	0.224511i	−0.292803	+	0.956173i	$0.594588\pi$
$572$	−4.94591	−	0.651269i	−0.206799	−	0.0272309i
$573$	7.94039	−	6.30680i	0.331715	−	0.263470i
$574$	−0.148684	−	0.0345457i	−0.00620597	−	0.00144191i
$575$		−	12.9832i		−	0.541436i
$576$	−23.8860	−	2.33630i	−0.995251	−	0.0973460i
$577$	9.27162	−	5.35297i	0.385983	−	0.222847i	−0.294435	−	0.955671i	$-0.595132\pi$
$577$	9.27162	−	5.35297i	0.385983	−	0.222847i	0.680418	+	0.732824i	$0.261798\pi$
$578$	1.18552	−	18.0841i	0.0493112	−	0.752198i
$579$	5.72956	−	14.5149i	0.238113	−	0.603218i
$580$	9.04382	−	3.74580i	0.375524	−	0.155536i
$581$	−31.3247	−	5.14614i	−1.29957	−	0.213498i
$582$	3.23965	−	0.266818i	0.134288	−	0.0110600i
$583$	26.4493	+	45.8115i	1.09542	+	1.89732i
$584$	−2.52740	−	7.44640i	−0.104584	−	0.308134i
$585$	1.26689	−	1.35468i	0.0523793	−	0.0560090i
$586$	−24.1657	+	36.1655i	−0.998276	+	1.49398i
$587$	5.06545	+	2.92454i	0.209074	+	0.120709i	0.600881	−	0.799339i	$-0.294817\pi$
$587$	5.06545	+	2.92454i	0.209074	+	0.120709i	−0.391807	+	0.920047i	$0.628150\pi$
$588$	5.16517	+	23.6922i	0.213008	+	0.977050i
$589$	44.4365	−	25.6554i	1.83097	−	1.05711i
$590$	−1.07101	+	16.3374i	−0.0440930	+	0.672599i
$591$	7.86771	−	1.17008i	0.323634	−	0.0481307i
$592$	6.92734	−	25.8480i	0.284712	−	1.06235i
$593$	7.97966	−	13.8212i	0.327685	−	0.567568i	−0.654367	−	0.756177i	$-0.727065\pi$
$593$	7.97966	−	13.8212i	0.327685	−	0.567568i	0.982052	+	0.188610i	$0.0603981\pi$
$594$	−19.8581	+	25.0783i	−0.814788	+	1.02898i
$595$	−9.87911	+	12.0573i	−0.405004	+	0.494300i
$596$	−7.11599	+	9.27325i	−0.291482	+	0.379847i
$597$	−16.7928	+	13.3380i	−0.687282	+	0.545886i
$598$	−1.52384	+	2.28053i	−0.0623146	+	0.0932579i
$599$	−21.9730	−	12.6861i	−0.897790	−	0.518340i	−0.0213078	−	0.999773i	$-0.506783\pi$
$599$	−21.9730	−	12.6861i	−0.897790	−	0.518340i	−0.876483	+	0.481433i	$0.840116\pi$
$600$	0.915724	−	18.7691i	0.0373843	−	0.766247i
$601$	−1.87709	−	1.08374i	−0.0765683	−	0.0442067i	0.461227	−	0.887282i	$-0.347409\pi$
$601$	−1.87709	−	1.08374i	−0.0765683	−	0.0442067i	−0.537795	+	0.843075i	$0.680743\pi$
$602$	15.6924	−	4.77365i	0.639574	−	0.194560i
$603$	10.2072	+	2.37190i	0.415668	+	0.0965914i
$604$	−11.7307	+	15.2870i	−0.477317	+	0.622019i
$605$		−	8.57725i		−	0.348715i
$606$	3.09780	+	4.47241i	0.125839	+	0.181679i
$607$		−	25.3652i		−	1.02954i	−0.857328	−	0.514771i	$-0.827877\pi$
$607$		−	25.3652i		−	1.02954i	0.857328	−	0.514771i	$-0.172123\pi$
$608$	41.9769	−	8.34697i	1.70239	−	0.338514i
$609$	−0.315786	+	20.7848i	−0.0127963	+	0.842243i
$610$	−5.53511	+	8.28365i	−0.224110	+	0.335395i
$611$	−3.04508	+	5.27424i	−0.123191	+	0.213373i
$612$	32.3203	−	5.36017i	1.30647	−	0.216672i
$613$	−34.0398	+	19.6529i	−1.37485	+	0.793772i	−0.991534	−	0.129844i	$-0.958552\pi$
$613$	−34.0398	+	19.6529i	−1.37485	+	0.793772i	−0.383319	+	0.923616i	$0.625219\pi$
$614$	19.4849	−	9.60861i	0.786349	−	0.387772i
$615$	0.0597016	−	0.0474191i	0.00240740	−	0.00191212i
$616$	5.33075	+	32.1364i	0.214782	+	1.29481i
$617$	−1.24420	+	0.718336i	−0.0500894	+	0.0289191i	−0.524836	−	0.851204i	$-0.675873\pi$
$617$	−1.24420	+	0.718336i	−0.0500894	+	0.0289191i	0.474746	+	0.880123i	$0.342540\pi$
$618$	−5.08681	−	7.34402i	−0.204621	−	0.295420i
$619$	26.6042			1.06931			0.534656	−	0.845070i	$-0.320441\pi$
$619$	26.6042			1.06931			0.534656	+	0.845070i	$0.320441\pi$
$620$	−5.60030	−	13.5213i	−0.224914	−	0.543028i
$621$	7.53758	+	15.8906i	0.302473	+	0.637668i
$622$	−0.630763	+	9.62172i	−0.0252913	+	0.385796i
$623$	−5.58652	+	34.0053i	−0.223819	+	1.36240i
$624$	−2.36379	+	3.18937i	−0.0946275	+	0.127677i
$625$	8.89225			0.355690
$626$	−2.04994	+	3.06787i	−0.0819322	+	0.122617i
$627$	20.9449	−	53.0603i	0.836458	−	2.11902i
$628$	12.8642	+	31.0591i	0.513336	+	1.23939i
$629$			36.5296i			1.45653i
$630$	−10.8707	−	5.34016i	−0.433101	−	0.212757i
$631$	32.9585			1.31206			0.656029	−	0.754736i	$-0.272235\pi$
$631$	32.9585			1.31206			0.656029	+	0.754736i	$0.272235\pi$
$632$	30.6555	−	10.4048i	1.21941	−	0.413882i
$633$	11.1914	−	8.88894i	0.444817	−	0.353304i
$634$	25.2012	+	16.8394i	1.00087	+	0.668776i
$635$			16.7716i			0.665559i
$636$	42.0898	−	0.703481i	1.66897	−	0.0278949i
$637$	3.80016	+	1.28324i	0.150568	+	0.0508439i
$638$	−1.82676	+	27.8655i	−0.0723220	+	1.10321i
$639$	3.69668	+	12.1535i	0.146239	+	0.480785i
$640$	−0.797321	−	12.1813i	−0.0315169	−	0.481506i
$641$			24.5826i			0.970956i	0.874249	+	0.485478i	$0.161354\pi$
$641$			24.5826i			0.970956i	−0.874249	+	0.485478i	$0.838646\pi$
$642$	−2.18477	−	26.5270i	−0.0862259	−	1.04694i
$643$	−23.4991	−	40.7016i	−0.926714	−	1.60511i	−0.788782	−	0.614673i	$-0.789288\pi$
$643$	−23.4991	−	40.7016i	−0.926714	−	1.60511i	−0.137932	−	0.990442i	$-0.544045\pi$
$644$	17.1432	+	5.18592i	0.675536	+	0.204354i
$645$	−3.00804	+	7.62035i	−0.118441	+	0.300051i
$646$	−52.3987	+	25.8394i	−2.06160	+	1.01664i
$647$	0.190214	+	0.329461i	0.00747810	+	0.0129525i	0.869740	−	0.493510i	$-0.164286\pi$
$647$	0.190214	+	0.329461i	0.00747810	+	0.0129525i	−0.862262	+	0.506462i	$0.830953\pi$
$648$	9.77591	+	23.5039i	0.384034	+	0.923319i
$649$	−40.4493	−	23.3534i	−1.58777	−	0.916701i
$650$	−2.58443	−	1.72691i	−0.101370	−	0.0677349i
$651$	31.0751	+	0.472128i	1.21793	+	0.0185042i
$652$	46.1133	−	19.0994i	1.80594	−	0.747990i
$653$	−4.05268			−0.158594			−0.0792968	−	0.996851i	$-0.525267\pi$
$653$	−4.05268			−0.158594			−0.0792968	+	0.996851i	$0.525267\pi$
$654$	−8.14079	+	17.2284i	−0.318330	+	0.673684i
$655$	0.370088			0.0144605
$656$	−0.115395	+	0.115383i	−0.00450540	+	0.00450494i
$657$	−5.69702	+	6.09180i	−0.222262	+	0.237664i
$658$	38.7368	+	9.00020i	1.51012	+	0.350864i
$659$	5.89816	−	10.2159i	0.229760	−	0.397956i	−0.727977	−	0.685601i	$-0.759539\pi$
$659$	5.89816	−	10.2159i	0.229760	−	0.397956i	0.957737	+	0.287646i	$0.0928726\pi$
$660$	−14.2247	−	7.89868i	−0.553697	−	0.307456i
$661$	−3.68553	+	6.38353i	−0.143351	+	0.248291i	−0.928756	−	0.370691i	$-0.879121\pi$
$661$	−3.68553	+	6.38353i	−0.143351	+	0.248291i	0.785406	+	0.618981i	$0.212454\pi$
$662$	−2.77066	+	4.14647i	−0.107685	+	0.161157i
$663$	1.98972	−	5.04062i	0.0772744	−	0.195761i
$664$	−22.3768	+	25.5139i	−0.868388	+	0.990131i
$665$	21.3127	+	3.50132i	0.826470	+	0.135775i
$666$	−27.6372	+	6.46559i	−1.07092	+	0.250536i
$667$	13.2967	+	7.67685i	0.514850	+	0.297249i
$668$	−1.61812	−	0.213070i	−0.0626068	−	0.00824394i
$669$	−15.4146	−	6.08473i	−0.595964	−	0.235249i
$670$	−0.348671	+	5.31867i	−0.0134704	+	0.205478i
$671$	−14.2107	−	24.6137i	−0.548599	−	0.950201i
$672$	24.4173	+	8.70615i	0.941917	+	0.335847i
$673$	6.69742	−	11.6003i	0.258167	−	0.447158i	−0.707584	−	0.706629i	$-0.750215\pi$
$673$	6.69742	−	11.6003i	0.258167	−	0.447158i	0.965751	+	0.259471i	$0.0835483\pi$
$674$	−33.8274	−	22.6034i	−1.30298	−	0.870650i
$675$	−18.0081	+	8.54202i	−0.693133	+	0.328783i
$676$	−9.69789	−	23.4144i	−0.372996	−	0.900556i
$677$	−37.2090	+	21.4827i	−1.43006	+	0.825645i	−0.997125	−	0.0757796i	$-0.975855\pi$
$677$	−37.2090	+	21.4827i	−1.43006	+	0.825645i	−0.432935	+	0.901425i	$0.642522\pi$
$678$	2.14337	−	4.53602i	0.0823155	−	0.174205i
$679$	−3.46463	−	0.569182i	−0.132960	−	0.0218432i
$680$	5.35584	+	15.7797i	0.205387	+	0.605126i
$681$	1.01272	+	6.80960i	0.0388075	+	0.260944i
$682$	41.6614	+	2.73116i	1.59530	+	0.104582i
$683$	7.42526	+	12.8609i	0.284120	+	0.492110i	0.972395	−	0.233339i	$-0.0749653\pi$
$683$	7.42526	+	12.8609i	0.284120	+	0.492110i	−0.688276	+	0.725449i	$0.741632\pi$
$684$	−28.8237	−	35.0699i	−1.10210	−	1.34093i
$685$	−13.1918			−0.504031
$686$	0.794826	−	26.1795i	0.0303466	−	0.999539i
$687$	−33.9830	+	5.05392i	−1.29653	+	0.192819i
$688$	4.53923	−	16.9372i	0.173056	−	0.645725i
$689$	3.48152	−	6.03016i	0.132635	−	0.229731i
$690$	−7.35397	+	5.09370i	−0.279961	+	0.193914i
$691$	10.7880	+	18.6853i	0.410393	+	0.710822i	0.994933	−	0.100544i	$-0.0320582\pi$
$691$	10.7880	+	18.6853i	0.410393	+	0.710822i	−0.584540	+	0.811365i	$0.698725\pi$
$692$	−1.35830	+	10.3153i	−0.0516347	+	0.392128i
$693$	27.3791	−	21.0760i	1.04004	−	0.800611i
$694$	2.13916	−	32.6310i	0.0812016	−	1.23866i
$695$	7.32523	−	4.22922i	0.277862	−	0.160424i
$696$	18.6809	+	12.0359i	0.708097	+	0.456218i
$697$	0.111379	−	0.192915i	0.00421879	−	0.00730716i
$698$	0.966565	−	14.7441i	0.0365850	−	0.558072i
$699$	10.8075	+	4.26613i	0.408777	+	0.161360i
$700$	−5.87698	+	19.4276i	−0.222129	+	0.734296i
$701$	15.4969			0.585311			0.292655	−	0.956218i	$-0.405461\pi$
$701$	15.4969			0.585311			0.292655	+	0.956218i	$0.405461\pi$
$702$	4.16576	+	0.613196i	0.157226	+	0.0231436i
$703$	43.8344	−	25.3078i	1.65325	−	0.954502i
$704$	32.1728	+	13.3293i	1.21256	+	0.502366i
$705$	−15.5541	+	12.3541i	−0.585801	+	0.465283i
$706$	10.6174	−	5.23575i	0.399591	−	0.197050i
$707$	−2.07433	−	5.49810i	−0.0780132	−	0.206777i
$708$	−31.8737	+	19.1195i	−1.19789	+	0.718555i
$709$	31.6866	−	18.2942i	1.19001	−	0.687055i	0.231704	−	0.972786i	$-0.425570\pi$
$709$	31.6866	−	18.2942i	1.19001	−	0.687055i	0.958310	+	0.285731i	$0.0922365\pi$
$710$	−5.79507	+	2.85772i	−0.217485	+	0.107248i
$711$	−25.0788	−	23.4536i	−0.940530	−	0.879579i
$712$	27.6973	+	24.2917i	1.03800	+	0.910370i
$713$	11.4776	−	19.8797i	0.429838	−	0.744501i
$714$	−35.2717	−	2.85100i	−1.32001	−	0.106696i
$715$	−2.33075	+	1.34566i	−0.0871651	+	0.0503248i
$716$	41.3149	+	5.44027i	1.54401	+	0.203312i
$717$	−10.6557	+	8.46349i	−0.397945	+	0.316075i
$718$	−2.94587	−	0.193120i	−0.109939	−	0.00720717i
$719$	2.67665	−	4.63610i	0.0998223	−	0.172897i	−0.811789	−	0.583951i	$-0.801506\pi$
$719$	2.67665	−	4.63610i	0.0998223	−	0.172897i	0.911611	+	0.411054i	$0.134839\pi$
$720$	−10.9905	+	6.84502i	−0.409593	+	0.255099i
$721$	3.40620	+	9.02827i	0.126854	+	0.336230i
$722$	44.9670	+	30.0468i	1.67350	+	1.11823i
$723$	0.665172	+	4.47267i	0.0247380	+	0.166340i
$724$	−12.3690	+	16.1187i	−0.459689	+	0.599047i
$725$	−8.69984	+	15.0686i	−0.323104	+	0.559633i
$726$	16.0071	−	11.0873i	0.594079	−	0.411487i
$727$	−31.4979	−	18.1853i	−1.16819	−	0.674455i	−0.214938	−	0.976628i	$-0.568955\pi$
$727$	−31.4979	−	18.1853i	−1.16819	−	0.674455i	−0.953253	+	0.302173i	$0.902288\pi$
$728$	3.31254	−	2.72273i	0.122771	−	0.100911i
$729$	17.0816	−	20.9098i	0.632652	−	0.774436i
$730$	−3.52737	−	2.35698i	−0.130554	−	0.0872356i
$731$			23.9364i			0.885321i
$732$	−22.6141	+	0.377968i	−0.835840	+	0.0139701i
$733$	−7.34939			−0.271456			−0.135728	−	0.990746i	$-0.543337\pi$
$733$	−7.34939			−0.271456			−0.135728	+	0.990746i	$0.543337\pi$
$734$	−9.27390	−	18.8062i	−0.342306	−	0.694150i
$735$	9.99200	+	8.44385i	0.368560	+	0.311456i
$736$	14.3963	−	12.6236i	0.530655	−	0.465312i
$737$	−13.1684	−	7.60276i	−0.485063	−	0.280051i
$738$	0.165667	+	0.0501212i	0.00609829	+	0.00184499i
$739$	−39.1541	+	22.6056i	−1.44031	+	0.831562i	−0.997870	−	0.0652379i	$-0.979219\pi$
$739$	−39.1541	+	22.6056i	−1.44031	+	0.831562i	−0.442437	+	0.896800i	$0.645886\pi$
$740$	−5.52443	−	13.3381i	−0.203082	−	0.490318i
$741$	−7.42708	+	1.10455i	−0.272841	+	0.0405767i
$742$	−44.2888	−	10.2901i	−1.62589	−	0.377763i
$743$	12.8217	−	7.40259i	0.470381	−	0.271575i	−0.246018	−	0.969265i	$-0.579122\pi$
$743$	12.8217	−	7.40259i	0.470381	−	0.271575i	0.716399	+	0.697691i	$0.245789\pi$
$744$	17.9947	−	27.9296i	0.659716	−	1.02395i
$745$			6.30608i			0.231037i
$746$	−14.9685	−	30.3540i	−0.548035	−	1.11134i
$747$	35.0608	+	8.14731i	1.28281	+	0.298095i
$748$	−47.1314	−	6.20618i	−1.72330	−	0.226920i
$749$	−4.66059	+	28.3691i	−0.170294	+	1.03659i
$750$	−13.2970	−	19.1973i	−0.485537	−	0.700988i
$751$	−36.9915			−1.34984			−0.674919	−	0.737892i	$-0.735821\pi$
$751$	−36.9915			−1.34984			−0.674919	+	0.737892i	$0.735821\pi$
$752$	30.0638	−	30.0608i	1.09631	−	1.09620i
$753$	2.32908	+	15.6609i	0.0848764	+	0.570715i
$754$	3.29676	−	1.62573i	0.120061	−	0.0592056i
$755$			10.3956i			0.378334i
$756$	−4.08596	−	27.1902i	−0.148605	−	0.988897i
$757$		−	30.1735i		−	1.09667i	−0.836257	−	0.548337i	$-0.815261\pi$
$757$		−	30.1735i		−	1.09667i	0.836257	−	0.548337i	$-0.184739\pi$
$758$	21.4430	+	43.4835i	0.778845	+	1.57939i
$759$	−3.75406	−	25.2426i	−0.136264	−	0.916248i
$760$	15.2247	−	17.3591i	0.552258	−	0.629681i
$761$	−44.9380			−1.62900			−0.814501	−	0.580162i	$-0.802989\pi$
$761$	−44.9380			−1.62900			−0.814501	+	0.580162i	$0.802989\pi$
$762$	−31.2996	+	21.6795i	−1.13386	+	0.785366i
$763$	13.0442	−	15.9202i	0.472232	−	0.576351i
$764$	−1.52862	+	11.6088i	−0.0553037	+	0.419991i
$765$	12.0726	−	12.9092i	0.436487	−	0.466733i
$766$	24.0475	−	11.8585i	0.868871	−	0.428466i
$767$			6.14801i			0.221992i
$768$	21.7024	−	17.2339i	0.783116	−	0.621875i
$769$	−35.6601	+	20.5884i	−1.28594	+	0.742435i	−0.977927	−	0.208948i	$-0.932996\pi$
$769$	−35.6601	+	20.5884i	−1.28594	+	0.742435i	−0.308009	+	0.951384i	$0.599663\pi$
$770$	12.8362	+	12.0036i	0.462585	+	0.432579i
$771$	10.5516	−	1.56922i	0.380006	−	0.0565142i
$772$	6.89510	+	16.6474i	0.248160	+	0.599154i
$773$	29.6689	−	17.1293i	1.06712	−	0.616100i	0.139724	−	0.990190i	$-0.455378\pi$
$773$	29.6689	−	17.1293i	1.06712	−	0.616100i	0.927392	+	0.374091i	$0.122045\pi$
$774$	−18.1096	+	4.23665i	−0.650937	+	0.152283i
$775$	22.5288	+	13.0070i	0.809259	+	0.467226i
$776$	−2.47496	+	2.82193i	−0.0888457	+	0.101301i
$777$	30.6541	+	0.465731i	1.09971	+	0.0167080i
$778$	−18.4961	+	9.12097i	−0.663117	+	0.327003i
$779$	−0.308656			−0.0110587
$780$	0.0357910	+	2.14140i	0.00128152	+	0.0766744i
$781$		−	18.4328i		−	0.659578i
$782$	−14.5213	+	21.7320i	−0.519280	+	0.777136i
$783$	1.89977	−	23.4938i	0.0678923	−	0.839600i
$784$	−23.3051	−	15.5201i	−0.832324	−	0.554289i
$785$	15.7067	+	9.06826i	0.560596	+	0.323660i
$786$	0.478389	+	0.690668i	0.0170636	+	0.0246353i
$787$	13.7033	−	23.7347i	0.488468	−	0.846052i	−0.511444	−	0.859317i	$-0.670889\pi$
$787$	13.7033	−	23.7347i	0.488468	−	0.846052i	0.999912	+	0.0132648i	$0.00422244\pi$
$788$	−5.59151	+	7.28662i	−0.199189	+	0.259575i
$789$	−3.92794	−	26.4117i	−0.139838	−	0.940283i
$790$	9.70324	−	14.5215i	0.345226	−	0.516653i
$791$	−3.43438	+	4.19160i	−0.122112	+	0.149036i
$792$	−3.64666	−	36.7567i	−0.129578	−	1.30609i
$793$	−1.87056	+	3.23990i	−0.0664254	+	0.115052i
$794$	0.318474	−	4.85803i	0.0113022	−	0.172405i
$795$	17.7834	−	14.1248i	0.630711	−	0.500954i
$796$	3.23282	−	24.5509i	0.114584	−	0.870183i
$797$	−0.545688	+	0.315053i	−0.0193293	+	0.0111598i	−0.509633	−	0.860392i	$-0.670219\pi$
$797$	−0.545688	+	0.315053i	−0.0193293	+	0.0111598i	0.490304	+	0.871551i	$0.336886\pi$
$798$	21.0152	+	44.3002i	0.743932	+	1.56821i
$799$	−29.0177	+	50.2601i	−1.02657	+	1.77808i
$800$	14.3058	+	16.3147i	0.505786	+	0.576812i
$801$	8.84452	−	38.0612i	0.312506	−	1.34483i
$802$	−2.99845	−	6.08046i	−0.105879	−	0.214708i
$803$	10.4811	−	6.05125i	0.369869	−	0.213544i
$804$	−10.3766	+	6.22440i	−0.365953	+	0.219518i
$805$	9.04051	−	3.41082i	0.318636	−	0.120216i
$806$	−2.43061	−	4.92894i	−0.0856145	−	0.173614i
$807$	−11.5923	+	9.20739i	−0.408068	+	0.324115i
$808$	−6.16136	−	1.22581i	−0.216756	−	0.0431240i
$809$	22.8257	−	13.1784i	0.802507	−	0.463328i	−0.0418398	−	0.999124i	$-0.513322\pi$
$809$	22.8257	−	13.1784i	0.802507	−	0.463328i	0.844347	+	0.535797i	$0.179989\pi$
$810$	11.9035	+	6.84892i	0.418248	+	0.240646i
$811$	−24.5049			−0.860484			−0.430242	−	0.902714i	$-0.641572\pi$
$811$	−24.5049			−0.860484			−0.430242	+	0.902714i	$0.641572\pi$
$812$	−16.4218	−	17.5063i	−0.576291	−	0.614350i
$813$	−41.8319	−	16.5126i	−1.46711	−	0.579123i
$814$	41.0970	+	2.69416i	1.44045	+	0.0944302i
$815$	13.4636	−	23.3197i	0.471610	−	0.816852i
$816$	−22.5255	+	30.3927i	−0.788549	+	1.06396i
$817$	28.7230	−	16.5833i	1.00489	−	0.580175i
$818$	−4.48134	−	0.293779i	−0.156686	−	0.0102717i
$819$	−4.20451	−	1.73396i	−0.146917	−	0.0605893i
$820$	−0.0114933	+	0.0872832i	−0.000401363	+	0.00304806i
$821$	12.9083	+	22.3578i	0.450502	+	0.780293i	0.998417	−	0.0562410i	$-0.0179115\pi$
$821$	12.9083	+	22.3578i	0.450502	+	0.780293i	−0.547915	+	0.836534i	$0.684578\pi$
$822$	−17.0521	−	24.6188i	−0.594762	−	0.858680i
$823$	−21.0003	+	36.3737i	−0.732026	+	1.26791i	0.223990	+	0.974592i	$0.428092\pi$
$823$	−21.0003	+	36.3737i	−0.732026	+	1.26791i	−0.956016	+	0.293315i	$0.905242\pi$
$824$	10.1174	+	2.01288i	0.352457	+	0.0701219i
$825$	28.6064	−	4.25432i	0.995945	−	0.148116i
$826$	38.4086	−	11.6840i	1.33641	−	0.406537i
$827$	−20.8614			−0.725420			−0.362710	−	0.931902i	$-0.618149\pi$
$827$	−20.8614			−0.725420			−0.362710	+	0.931902i	$0.618149\pi$
$828$	−19.0120	−	7.13989i	−0.660713	−	0.248128i
$829$	3.26137	+	5.64886i	0.113272	+	0.196193i	0.917088	−	0.398685i	$-0.130533\pi$
$829$	3.26137	+	5.64886i	0.113272	+	0.196193i	−0.803816	+	0.594879i	$0.797200\pi$
$830$	−1.19766	+	18.2692i	−0.0415714	+	0.634134i
$831$	2.70308	+	18.1757i	0.0937689	+	0.630509i
$832$	−0.597984	−	4.54480i	−0.0207314	−	0.157563i
$833$	36.2131	+	12.2285i	1.25471	+	0.423692i
$834$	17.3616	+	8.20370i	0.601181	+	0.284071i
$835$	−0.762533	+	0.440248i	−0.0263885	+	0.0152354i
$836$	25.2056	+	60.8560i	0.871753	+	2.10475i
$837$	−35.1253	−	2.84032i	−1.21411	−	0.0981759i
$838$	5.63012	−	8.42584i	0.194489	−	0.291066i
$839$	5.15003	−	8.92011i	0.177799	−	0.307956i	−0.763328	−	0.646012i	$-0.776436\pi$
$839$	5.15003	−	8.92011i	0.177799	−	0.307956i	0.941126	+	0.338055i	$0.109769\pi$
$840$	13.3100	−	4.29321i	0.459238	−	0.148130i
$841$	4.21172	+	7.29491i	0.145232	+	0.251549i
$842$	−29.0466	−	1.90418i	−1.00101	−	0.0656225i
$843$	−24.1115	−	9.51771i	−0.830444	−	0.327808i
$844$	−2.15448	+	16.3617i	−0.0741602	+	0.563192i
$845$	−11.8408	−	6.83627i	−0.407335	−	0.235175i
$846$	−43.1614	−	13.0581i	−1.48392	−	0.448947i
$847$	−19.6781	+	7.42420i	−0.676148	+	0.255098i
$848$	−34.3727	+	34.3692i	−1.18036	+	1.18024i
$849$	−1.07330	+	2.71901i	−0.0368354	+	0.0933162i
$850$	−24.6280	−	16.4563i	−0.844733	−	0.564448i
$851$	11.3220	−	19.6104i	0.388115	−	0.672235i
$852$	−12.8241	−	7.12093i	−0.439345	−	0.243959i
$853$	−0.252878	+	0.437997i	−0.00865837	+	0.0149967i	−0.870322	−	0.492483i	$-0.836089\pi$
$853$	−0.252878	+	0.437997i	−0.00865837	+	0.0149967i	0.861664	+	0.507480i	$0.169423\pi$
$854$	23.7956	+	5.52871i	0.814267	+	0.189189i
$855$	−23.8546	−	5.54326i	−0.815811	−	0.189575i
$856$	23.1066	+	20.2655i	0.789767	+	0.692660i
$857$	−24.2610			−0.828741			−0.414370	−	0.910108i	$-0.635998\pi$
$857$	−24.2610			−0.828741			−0.414370	+	0.910108i	$0.635998\pi$
$858$	−5.52411	−	2.61026i	−0.188590	−	0.0891129i
$859$	11.4065			0.389185			0.194592	−	0.980884i	$-0.437662\pi$
$859$	11.4065			0.389185			0.194592	+	0.980884i	$0.437662\pi$
$860$	−3.61995	−	8.73995i	−0.123439	−	0.298030i
$861$	−0.160466	−	0.0959243i	−0.00546865	−	0.00326909i
$862$	−26.5296	+	39.7032i	−0.903600	+	1.35230i
$863$	4.51196	+	2.60498i	0.153589	+	0.0886745i	0.574825	−	0.818277i	$-0.305070\pi$
$863$	4.51196	+	2.60498i	0.153589	+	0.0886745i	−0.421236	+	0.906951i	$0.638404\pi$
$864$	−26.9811	−	11.6627i	−0.917916	−	0.396774i
$865$	2.80653	+	4.86104i	0.0954247	+	0.165280i
$866$	−21.0136	−	42.6128i	−0.714072	−	1.44804i
$867$	8.14961	−	20.6456i	0.276775	−	0.701162i
$868$	−26.1734	+	24.5519i	−0.888384	+	0.833347i
$869$	24.9119	+	43.1487i	0.845078	+	1.46372i
$870$	11.9484	−	0.984072i	0.405089	−	0.0333632i
$871$			2.00150i			0.0678183i
$872$	−7.07176	−	20.8353i	−0.239480	−	0.705573i
$873$	3.87786	+	0.901123i	0.131246	+	0.0304984i
$874$	36.1382	+	2.36908i	1.22239	+	0.0801353i
$875$	8.90385	+	23.6000i	0.301005	+	0.797826i
$876$	−0.160947	−	9.62959i	−0.00543791	−	0.325354i
$877$		−	32.7567i		−	1.10611i	−0.833143	−	0.553057i	$-0.813461\pi$
$877$		−	32.7567i		−	1.10611i	0.833143	−	0.553057i	$-0.186539\pi$
$878$	28.4263	−	42.5418i	0.959342	−	1.43572i
$879$	−41.7147	+	33.1327i	−1.40700	+	1.11754i
$880$	18.1477	−	4.86169i	0.611760	−	0.163888i
$881$	−13.2234			−0.445509			−0.222755	−	0.974875i	$-0.571505\pi$
$881$	−13.2234			−0.445509			−0.222755	+	0.974875i	$0.571505\pi$
$882$	−2.84214	+	29.5622i	−0.0956997	+	0.995410i
$883$			48.4001i			1.62879i	0.580309	+	0.814396i	$0.302932\pi$
$883$			48.4001i			1.62879i	−0.580309	+	0.814396i	$0.697068\pi$
$884$	2.39448	+	5.78120i	0.0805351	+	0.194443i
$885$	−7.36246	+	18.6515i	−0.247486	+	0.626964i
$886$	36.2100	+	24.1954i	1.21650	+	0.812861i
$887$	−7.12647			−0.239283			−0.119642	−	0.992817i	$-0.538175\pi$
$887$	−7.12647			−0.239283			−0.119642	+	0.992817i	$0.538175\pi$
$888$	17.7509	−	27.5511i	0.595680	−	0.924556i
$889$	38.4777	−	14.5169i	1.29050	−	0.486882i
$890$	19.8326	+	1.30015i	0.664791	+	0.0435812i
$891$	−32.5424	+	21.8149i	−1.09021	+	0.730825i
$892$	17.6794	−	7.32251i	0.591949	−	0.245176i
$893$	80.4143			2.69096
$894$	−11.7686	+	8.15146i	−0.393600	+	0.272626i
$895$	19.4695	−	11.2407i	0.650795	−	0.375736i
$896$	−27.2564	+	12.3729i	−0.910572	+	0.413351i
$897$	−2.63045	+	2.08928i	−0.0878283	+	0.0697592i
$898$	−2.84665	−	5.77261i	−0.0949938	−	0.192635i
$899$	−26.6422	+	15.3819i	−0.888567	+	0.513014i
$900$	8.09133	−	21.5455i	0.269711	−	0.718184i
$901$	33.1766	−	57.4636i	1.10527	−	1.91439i
$902$	−0.208821	−	0.139533i	−0.00695297	−	0.00464595i
$903$	20.0865	+	0.305176i	0.668435	+	0.0101556i
$904$	1.86190	+	5.48568i	0.0619260	+	0.182451i
$905$			10.9612i			0.364362i
$906$	−19.4005	+	13.4377i	−0.644540	+	0.446438i
$907$			36.3755i			1.20783i	0.797050	+	0.603914i	$0.206393\pi$
$907$			36.3755i			1.20783i	−0.797050	+	0.603914i	$0.793607\pi$
$908$	−6.30666	−	4.83953i	−0.209294	−	0.160605i
$909$	1.93901	+	6.37483i	0.0643128	+	0.211440i
$910$	0.523531	−	2.25328i	0.0173549	−	0.0746954i
$911$	−32.6688	−	18.8614i	−1.08237	−	0.624905i	−0.150833	−	0.988559i	$-0.548195\pi$
$911$	−32.6688	−	18.8614i	−1.08237	−	0.624905i	−0.931534	+	0.363655i	$0.881529\pi$
$912$	52.0760	+	5.97374i	1.72441	+	0.197810i
$913$	−45.2323	−	26.1149i	−1.49697	−	0.864277i
$914$	26.8545	+	17.9441i	0.888268	+	0.593538i
$915$	−9.55468	+	7.58898i	−0.315868	+	0.250884i
$916$	24.1514	−	31.4731i	0.797985	−	1.03990i
$917$	−0.320336	−	0.849064i	−0.0105784	−	0.0280386i
$918$	39.6970	+	5.84337i	1.31020	+	0.192860i
$919$	−1.96033	+	3.39539i	−0.0646653	+	0.112004i	−0.896545	−	0.442952i	$-0.853931\pi$
$919$	−1.96033	+	3.39539i	−0.0646653	+	0.112004i	0.831880	+	0.554955i	$0.187265\pi$
$920$	2.01560	−	10.1311i	0.0664525	−	0.334013i
$921$	26.3185	−	3.91407i	0.867224	−	0.128973i
$922$	−2.03878	−	0.133654i	−0.0671435	−	0.00440167i
$923$	−2.10125	+	1.21316i	−0.0691634	+	0.0399315i
$924$	−5.80886	+	39.4716i	−0.191097	+	1.29852i
$925$	22.2236	+	12.8308i	0.730707	+	0.421874i
$926$	25.6293	+	17.1255i	0.842233	+	0.562777i
$927$	−3.18399	−	10.4679i	−0.104576	−	0.343812i
$928$	−25.1675	+	5.00448i	−0.826165	+	0.164280i
$929$	−2.28750	−	3.96207i	−0.0750504	−	0.129991i	0.826058	−	0.563585i	$-0.190578\pi$
$929$	−2.28750	−	3.96207i	−0.0750504	−	0.129991i	−0.901108	+	0.433594i	$0.857245\pi$
$930$	−1.47127	−	17.8639i	−0.0482450	−	0.585780i
$931$	−10.4148	−	51.9266i	−0.341330	−	1.70183i
$932$	−12.3954	+	5.13396i	−0.406023	+	0.168168i
$933$	−4.33604	+	10.9846i	−0.141956	+	0.359620i
$934$	10.5252	+	0.689992i	0.344395	+	0.0225772i
$935$	−22.2106	+	12.8233i	−0.726363	+	0.419366i
$936$	−3.95007	+	2.83484i	−0.129112	+	0.0926597i
$937$		−	12.9252i		−	0.422246i	−0.977459	−	0.211123i	$-0.932288\pi$
$937$		−	12.9252i		−	0.422246i	0.977459	−	0.211123i	$-0.0677121\pi$
$938$	12.5040	−	3.80374i	0.408270	−	0.124197i
$939$	−3.53860	+	2.81060i	−0.115478	+	0.0917204i
$940$	2.99436	−	22.7400i	0.0976651	−	0.741696i
$941$	−38.6466	−	22.3126i	−1.25984	−	0.727371i	−0.286800	−	0.957991i	$-0.592591\pi$
$941$	−38.6466	−	22.3126i	−1.25984	−	0.727371i	−0.973044	+	0.230619i	$0.925925\pi$
$942$	3.37959	+	41.0342i	0.110113	+	1.33697i
$943$	−0.119585	+	0.0690422i	−0.00389421	+	0.00224832i
$944$	11.1102	−	41.4554i	0.361605	−	1.34926i
$945$	−10.6789	−	10.2954i	−0.347386	−	0.334910i
$946$	26.9293	+	1.76538i	0.875547	+	0.0573975i
$947$	−23.7535	−	41.1422i	−0.771884	−	1.33694i	−0.936529	−	0.350590i	$-0.885981\pi$
$947$	−23.7535	−	41.1422i	−0.771884	−	1.33694i	0.164645	−	0.986353i	$-0.447352\pi$
$948$	39.6433	−	0.662591i	1.28755	−	0.0215200i
$949$	−1.37962	−	0.796525i	−0.0447844	−	0.0258563i
$950$	−2.68478	+	40.9539i	−0.0871057	+	1.32872i
$951$	23.0878	+	29.0680i	0.748673	+	0.942595i
$952$	31.5664	−	25.9459i	1.02307	−	0.840912i
$953$			38.3366i			1.24184i	0.783873	+	0.620921i	$0.213241\pi$
$953$			38.3366i			1.24184i	−0.783873	+	0.620921i	$0.786759\pi$
$954$	49.3474	+	14.9296i	1.59768	+	0.483365i
$955$	3.15846	+	5.47061i	0.102205	+	0.177025i
$956$	2.05136	−	15.5786i	0.0663456	−	0.503847i
$957$	−12.5576	+	31.8126i	−0.405931	+	1.02836i
$958$	−48.5201	+	23.9267i	−1.56761	+	0.773036i
$959$	11.4184	+	30.2648i	0.368718	+	0.977302i
$960$	3.62842	−	14.5039i	0.117107	−	0.468111i
$961$	7.49725	+	12.9856i	0.241847	+	0.418891i
$962$	−2.39767	−	4.86216i	−0.0773041	−	0.156762i
$963$	7.37859	−	31.7527i	0.237772	−	1.02322i
$964$	−4.14233	−	3.17869i	−0.133415	−	0.102379i
$965$	8.41867	+	4.86052i	0.271007	+	0.156466i
$966$	18.0515	+	12.4627i	0.580796	+	0.400981i
$967$	−26.1211	−	45.2432i	−0.840000	−	1.45492i	−0.889894	−	0.456167i	$-0.849222\pi$
$967$	−26.1211	−	45.2432i	−0.840000	−	1.45492i	0.0498945	−	0.998754i	$-0.484112\pi$
$968$	−4.38729	+	22.0520i	−0.141013	+	0.708779i
$969$	−70.7754	+	10.5257i	−2.27363	+	0.338133i
$970$	−0.132466	+	2.02064i	−0.00425321	+	0.0648790i
$971$	−49.7998	−	28.7519i	−1.59815	−	0.922694i	−0.991843	−	0.127465i	$-0.959316\pi$
$971$	−49.7998	−	28.7519i	−1.59815	−	0.922694i	−0.606309	−	0.795229i	$-0.707351\pi$
$972$	2.60529	+	31.0679i	0.0835648	+	0.996502i
$973$	−16.0433	−	13.1450i	−0.514324	−	0.421410i
$974$	6.74657	+	4.50804i	0.216174	+	0.144447i
$975$	−2.36770	−	2.98098i	−0.0758270	−	0.0954677i
$976$	18.4678	−	18.4660i	0.591140	−	0.591081i
$977$	−2.42465	−	1.39987i	−0.0775714	−	0.0447859i	0.460713	−	0.887549i	$-0.347594\pi$
$977$	−2.42465	−	1.39987i	−0.0775714	−	0.0447859i	−0.538284	+	0.842763i	$0.680927\pi$
$978$	60.9234	−	5.01766i	1.94811	−	0.160447i
$979$	−28.3497	+	49.1031i	−0.906060	+	1.56934i
$980$	−15.0719	+	1.01156i	−0.481454	+	0.0323132i
$981$	−15.9405	+	17.0451i	−0.508941	+	0.544208i
$982$	−9.19149	−	6.14172i	−0.293312	−	0.195990i
$983$	−46.2456			−1.47500			−0.737502	−	0.675345i	$-0.763995\pi$
$983$	−46.2456			−1.47500			−0.737502	+	0.675345i	$0.763995\pi$
$984$	−0.177747	+	0.0913763i	−0.00566637	+	0.00291297i
$985$			4.95511i			0.157883i
$986$	31.4160	−	15.4922i	1.00049	−	0.493371i
$987$	41.8062	+	24.9912i	1.33071	+	0.795479i
$988$	5.27837	−	6.87854i	0.167927	−	0.218836i
$989$	7.41891	−	12.8499i	0.235908	−	0.408604i
$990$	−13.6329	−	14.5342i	−0.433282	−	0.461927i
$991$	13.3038	+	23.0429i	0.422610	+	0.731982i	0.996194	−	0.0871649i	$-0.0277807\pi$
$991$	13.3038	+	23.0429i	0.422610	+	0.731982i	−0.573584	+	0.819147i	$0.694447\pi$
$992$	7.48214	+	37.6277i	0.237558	+	1.19468i
$993$	−4.78270	+	3.79875i	−0.151774	+	0.120550i
$994$	11.5723	+	10.8216i	0.367050	+	0.343241i
$995$	−6.67968	−	11.5695i	−0.211760	−	0.366779i
$996$	−35.6427	+	21.3804i	−1.12938	+	0.677462i
$997$	20.5971			0.652317			0.326158	−	0.945315i	$-0.394246\pi$
$997$	20.5971			0.652317			0.326158	+	0.945315i	$0.394246\pi$
$998$	−6.75822	−	13.7048i	−0.213928	−	0.433816i
$999$	−34.6494	−	2.80184i	−1.09626	−	0.0886463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.y.a.173.14	✓	184
7.3	odd	6		504.2.ca.a.101.49	yes	184
8.5	even	2	inner	504.2.y.a.173.17	yes	184
9.5	odd	6		504.2.ca.a.5.44	yes	184
56.45	odd	6		504.2.ca.a.101.44	yes	184
63.59	even	6	inner	504.2.y.a.437.17	yes	184
72.5	odd	6		504.2.ca.a.5.49	yes	184
504.437	even	6	inner	504.2.y.a.437.14	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.y.a.173.14	✓	184	1.1	even	1	trivial
504.2.y.a.173.17	yes	184	8.5	even	2	inner
504.2.y.a.437.14	yes	184	504.437	even	6	inner
504.2.y.a.437.17	yes	184	63.59	even	6	inner
504.2.ca.a.5.44	yes	184	9.5	odd	6
504.2.ca.a.5.49	yes	184	72.5	odd	6
504.2.ca.a.101.44	yes	184	56.45	odd	6
504.2.ca.a.101.49	yes	184	7.3	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26838 + 0.625475i) q^{2} +(-1.71321 + 0.254787i) q^{3} +(1.21756 - 1.58668i) q^{4} -1.07899i q^{5} +(2.01363 - 1.39473i) q^{6} +(-2.47543 + 0.933935i) q^{7} +(-0.551904 + 2.77406i) q^{8} +(2.87017 - 0.873007i) q^{9} +O(q^{10})\)	\(q+(-1.26838 + 0.625475i) q^{2} +(-1.71321 + 0.254787i) q^{3} +(1.21756 - 1.58668i) q^{4} -1.07899i q^{5} +(2.01363 - 1.39473i) q^{6} +(-2.47543 + 0.933935i) q^{7} +(-0.551904 + 2.77406i) q^{8} +(2.87017 - 0.873007i) q^{9} +(0.674878 + 1.36856i) q^{10} -4.35309 q^{11} +(-1.68167 + 3.02853i) q^{12} +(0.286498 + 0.496230i) q^{13} +(2.55563 - 2.73290i) q^{14} +(0.274912 + 1.84853i) q^{15} +(-1.03508 - 3.86376i) q^{16} +(2.73015 + 4.72875i) q^{17} +(-3.09441 + 2.90252i) q^{18} +(3.78291 - 6.55219i) q^{19} +(-1.71200 - 1.31373i) q^{20} +(4.00298 - 2.23073i) q^{21} +(5.52136 - 2.72275i) q^{22} -3.38475i q^{23} +(0.238732 - 4.89316i) q^{24} +3.83579 q^{25} +(-0.673767 - 0.450209i) q^{26} +(-4.69476 + 2.22693i) q^{27} +(-1.53214 + 5.06483i) q^{28} +(-2.26807 + 3.92841i) q^{29} +(-1.50490 - 2.17268i) q^{30} +(5.87332 + 3.39096i) q^{31} +(3.72955 + 4.25328i) q^{32} +(7.45775 - 1.10911i) q^{33} +(-6.42057 - 4.29021i) q^{34} +(1.00770 + 2.67095i) q^{35} +(2.10943 - 5.61697i) q^{36} +(5.79374 + 3.34502i) q^{37} +(-0.699928 + 10.6768i) q^{38} +(-0.617264 - 0.777149i) q^{39} +(2.99317 + 0.595496i) q^{40} +(-0.0203980 - 0.0353304i) q^{41} +(-3.68202 + 5.33317i) q^{42} +(3.79642 + 2.19186i) q^{43} +(-5.30016 + 6.90694i) q^{44} +(-0.941962 - 3.09687i) q^{45} +(2.11707 + 4.29314i) q^{46} +(5.31431 + 9.20466i) q^{47} +(2.75775 + 6.35569i) q^{48} +(5.25553 - 4.62379i) q^{49} +(-4.86523 + 2.39919i) q^{50} +(-5.88214 - 7.40573i) q^{51} +(1.13619 + 0.149611i) q^{52} +(-6.07598 - 10.5239i) q^{53} +(4.56185 - 5.76104i) q^{54} +4.69692i q^{55} +(-1.22459 - 7.38244i) q^{56} +(-4.81150 + 12.1891i) q^{57} +(0.419646 - 6.40133i) q^{58} +(9.29209 + 5.36479i) q^{59} +(3.26774 + 1.81450i) q^{60} +(3.26452 + 5.65431i) q^{61} +(-9.57055 - 0.627408i) q^{62} +(-6.28957 + 4.84162i) q^{63} +(-7.39080 - 3.06203i) q^{64} +(0.535424 - 0.309127i) q^{65} +(-8.76552 + 6.07140i) q^{66} +(3.02506 + 1.74652i) q^{67} +(10.8271 + 1.42570i) q^{68} +(0.862391 + 5.79878i) q^{69} +(-2.94876 - 2.75749i) q^{70} +4.23443i q^{71} +(0.837717 + 8.44383i) q^{72} +(-2.40773 + 1.39011i) q^{73} +(-9.44088 - 0.618907i) q^{74} +(-6.57151 + 0.977311i) q^{75} +(-5.79028 - 13.9800i) q^{76} +(10.7758 - 4.06550i) q^{77} +(1.26901 + 0.599635i) q^{78} +(-5.72281 - 9.91220i) q^{79} +(-4.16894 + 1.11684i) q^{80} +(7.47572 - 5.01135i) q^{81} +(0.0479707 + 0.0320539i) q^{82} +(10.3909 + 5.99917i) q^{83} +(1.33442 - 9.06749i) q^{84} +(5.10225 - 2.94579i) q^{85} +(-6.18625 - 0.405547i) q^{86} +(2.88477 - 7.30806i) q^{87} +(2.40249 - 12.0757i) q^{88} +(6.51255 - 11.2801i) q^{89} +(3.13178 + 3.33882i) q^{90} +(-1.17265 - 0.960812i) q^{91} +(-5.37050 - 4.12114i) q^{92} +(-10.9262 - 4.31298i) q^{93} +(-12.4978 - 8.35101i) q^{94} +(-7.06972 - 4.08170i) q^{95} +(-7.47319 - 6.33652i) q^{96} +(1.14927 + 0.663530i) q^{97} +(-3.77393 + 9.15191i) q^{98} +(-12.4941 + 3.80028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9	\( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) 184 * q - 3 * q^2 + q^4 + 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 3 * q^12 - 3 * q^14 - 2 * q^15 + q^16 - 15 * q^18 - 6 * q^22 - 12 * q^24 - 156 * q^25 + 6 * q^26 - 8 * q^28 - 14 * q^30 - 6 * q^31 - 33 * q^32 - 6 * q^33 - 6 * q^34 + 22 * q^36 - 66 * q^38 + 10 * q^39 - 15 * q^42 + 9 * q^44 + 2 * q^46 - 6 * q^47 - 9 * q^48 - 2 * q^49 + 9 * q^50 + 24 * q^54 + 60 * q^56 + 4 * q^57 + 6 * q^58 + 34 * q^60 - 12 * q^62 - 30 * q^63 - 8 * q^64 - 6 * q^65 - 21 * q^66 - 36 * q^68 + 30 * q^70 + 9 * q^72 - 12 * q^73 - 12 * q^76 + 19 * q^78 + 2 * q^79 + 57 * q^80 + 6 * q^81 + 9 * q^84 + 12 * q^87 - 18 * q^88 + 24 * q^89 + 75 * q^90 - 36 * q^92 - 3 * q^94 + 54 * q^95 - 54 * q^96 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more