LMFDB - Embedded newform 820.2.j.c.483.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(483,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.483"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			483.10
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36551 + 0.367958i) q^{2} +0.984353i q^{3} +(1.72921 - 1.00490i) q^{4} +(0.127778 + 2.23241i) q^{5} +(-0.362201 - 1.34414i) q^{6} -2.37783 q^{7} +(-1.99149 + 2.00847i) q^{8} +2.03105 q^{9} +(-0.995917 - 3.00136i) q^{10} +(2.42433 + 2.42433i) q^{11} +(0.989175 + 1.70216i) q^{12} +0.537595 q^{13} +(3.24694 - 0.874943i) q^{14} +(-2.19748 + 0.125779i) q^{15} +(1.98036 - 3.47537i) q^{16} +5.98392 q^{17} +(-2.77341 + 0.747341i) q^{18} +(0.382078 + 0.382078i) q^{19} +(2.46431 + 3.73192i) q^{20} -2.34063i q^{21} +(-4.20249 - 2.41839i) q^{22} +(-5.12858 + 5.12858i) q^{23} +(-1.97705 - 1.96033i) q^{24} +(-4.96735 + 0.570507i) q^{25} +(-0.734089 + 0.197813i) q^{26} +4.95233i q^{27} +(-4.11178 + 2.38948i) q^{28} +(-1.46623 - 1.46623i) q^{29} +(2.95440 - 0.980334i) q^{30} +1.66059i q^{31} +(-1.42540 + 5.47433i) q^{32} +(-2.38640 + 2.38640i) q^{33} +(-8.17108 + 2.20183i) q^{34} +(-0.303835 - 5.30831i) q^{35} +(3.51212 - 2.04100i) q^{36} +(3.19027 - 3.19027i) q^{37} +(-0.662319 - 0.381141i) q^{38} +0.529183i q^{39} +(-4.73821 - 4.18919i) q^{40} +(5.91705 + 2.44714i) q^{41} +(0.861253 + 3.19614i) q^{42} +(-0.287011 - 0.287011i) q^{43} +(6.62840 + 1.75598i) q^{44} +(0.259523 + 4.53414i) q^{45} +(5.11601 - 8.89022i) q^{46} -3.64014i q^{47} +(3.42099 + 1.94937i) q^{48} -1.34592 q^{49} +(6.57302 - 2.60681i) q^{50} +5.89029i q^{51} +(0.929617 - 0.540229i) q^{52} -10.5416 q^{53} +(-1.82225 - 6.76243i) q^{54} +(-5.10234 + 5.72189i) q^{55} +(4.73543 - 4.77581i) q^{56} +(-0.376100 + 0.376100i) q^{57} +(2.54165 + 1.46263i) q^{58} -1.58121 q^{59} +(-3.67352 + 2.42575i) q^{60} -0.445242i q^{61} +(-0.611030 - 2.26755i) q^{62} -4.82949 q^{63} +(-0.0679329 - 7.99971i) q^{64} +(0.0686928 + 1.20013i) q^{65} +(2.38055 - 4.13674i) q^{66} +6.98956i q^{67} +(10.3475 - 6.01323i) q^{68} +(-5.04834 - 5.04834i) q^{69} +(2.36812 + 7.13672i) q^{70} +(-3.62995 - 3.62995i) q^{71} +(-4.04481 + 4.07931i) q^{72} +(-9.73449 + 9.73449i) q^{73} +(-3.18245 + 5.53023i) q^{74} +(-0.561580 - 4.88962i) q^{75} +(1.04464 + 0.276745i) q^{76} +(-5.76465 - 5.76465i) q^{77} +(-0.194717 - 0.722603i) q^{78} +(-9.18180 + 9.18180i) q^{79} +(8.01151 + 3.97690i) q^{80} +1.21831 q^{81} +(-8.98022 - 1.16435i) q^{82} +(10.8658 - 10.8658i) q^{83} +(-2.35209 - 4.04744i) q^{84} +(0.764613 + 13.3586i) q^{85} +(0.497523 + 0.286307i) q^{86} +(1.44328 - 1.44328i) q^{87} +(-9.69724 + 0.0411734i) q^{88} +(10.0408 + 10.0408i) q^{89} +(-2.02276 - 6.09590i) q^{90} -1.27831 q^{91} +(-3.71471 + 14.0221i) q^{92} -1.63461 q^{93} +(1.33942 + 4.97063i) q^{94} +(-0.804136 + 0.901778i) q^{95} +(-5.38867 - 1.40310i) q^{96} -14.1882 q^{97} +(1.83786 - 0.495241i) q^{98} +(4.92394 + 4.92394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.36551	+	0.367958i	−0.965559	+	0.260186i
$2$	−1.36551	+	0.367958i	−0.965559	+	0.260186i
$3$			0.984353i			0.568317i	0.958777	+	0.284158i	$0.0917141\pi$
$3$			0.984353i			0.568317i	−0.958777	+	0.284158i	$0.908286\pi$
$4$	1.72921	−	1.00490i	0.864607	−	0.502449i
$5$	0.127778	+	2.23241i	0.0571441	+	0.998366i
$5$	0.127778	+	2.23241i	0.0571441	+	0.998366i
$6$	−0.362201	−	1.34414i	−0.147868	−	0.548743i
$7$	−2.37783			−0.898736			−0.449368	−	0.893347i	$-0.648351\pi$
$7$	−2.37783			−0.898736			−0.449368	+	0.893347i	$0.648351\pi$
$8$	−1.99149	+	2.00847i	−0.704098	+	0.710103i
$9$	2.03105			0.677016
$10$	−0.995917	−	3.00136i	−0.314937	−	0.949113i
$11$	2.42433	+	2.42433i	0.730964	+	0.730964i	0.970811	−	0.239847i	$-0.0770973\pi$
$11$	2.42433	+	2.42433i	0.730964	+	0.730964i	−0.239847	+	0.970811i	$0.577097\pi$
$12$	0.989175	+	1.70216i	0.285550	+	0.491370i
$13$	0.537595			0.149102			0.0745510	−	0.997217i	$-0.476248\pi$
$13$	0.537595			0.149102			0.0745510	+	0.997217i	$0.476248\pi$
$14$	3.24694	−	0.874943i	0.867782	−	0.233838i
$15$	−2.19748	+	0.125779i	−0.567388	+	0.0324759i
$16$	1.98036	−	3.47537i	0.495089	−	0.868842i
$17$	5.98392			1.45131			0.725657	−	0.688057i	$-0.241536\pi$
$17$	5.98392			1.45131			0.725657	+	0.688057i	$0.241536\pi$
$18$	−2.77341	+	0.747341i	−0.653699	+	0.176150i
$19$	0.382078	+	0.382078i	0.0876548	+	0.0876548i	0.749575	−	0.661920i	$-0.230258\pi$
$19$	0.382078	+	0.382078i	0.0876548	+	0.0876548i	−0.661920	+	0.749575i	$0.730258\pi$
$20$	2.46431	+	3.73192i	0.551035	+	0.834482i
$21$		−	2.34063i		−	0.510766i
$22$	−4.20249	−	2.41839i	−0.895975	−	0.515602i
$23$	−5.12858	+	5.12858i	−1.06938	+	1.06938i	−0.0719776	+	0.997406i	$0.522931\pi$
$23$	−5.12858	+	5.12858i	−1.06938	+	1.06938i	−0.997406	+	0.0719776i	$0.977069\pi$
$24$	−1.97705	−	1.96033i	−0.403563	−	0.400151i
$25$	−4.96735	+	0.570507i	−0.993469	+	0.114101i
$26$	−0.734089	+	0.197813i	−0.143967	+	0.0387942i
$27$			4.95233i			0.953076i
$28$	−4.11178	+	2.38948i	−0.777053	+	0.451569i
$29$	−1.46623	−	1.46623i	−0.272271	−	0.272271i	0.557743	−	0.830014i	$-0.311668\pi$
$29$	−1.46623	−	1.46623i	−0.272271	−	0.272271i	−0.830014	+	0.557743i	$0.811668\pi$
$30$	2.95440	−	0.980334i	0.539396	−	0.178984i
$31$			1.66059i			0.298252i	0.988818	+	0.149126i	$0.0476459\pi$
$31$			1.66059i			0.298252i	−0.988818	+	0.149126i	$0.952354\pi$
$32$	−1.42540	+	5.47433i	−0.251977	+	0.967733i
$33$	−2.38640	+	2.38640i	−0.415419	+	0.415419i
$34$	−8.17108	+	2.20183i	−1.40133	+	0.377611i
$35$	−0.303835	−	5.30831i	−0.0513574	−	0.897267i
$36$	3.51212	−	2.04100i	0.585353	−	0.340166i
$37$	3.19027	−	3.19027i	0.524478	−	0.524478i	−0.394443	−	0.918921i	$-0.629062\pi$
$37$	3.19027	−	3.19027i	0.524478	−	0.524478i	0.918921	+	0.394443i	$0.129062\pi$
$38$	−0.662319	−	0.381141i	−0.107442	−	0.0618293i
$39$			0.529183i			0.0847372i
$40$	−4.73821	−	4.18919i	−0.749177	−	0.662369i
$41$	5.91705	+	2.44714i	0.924089	+	0.382178i
$41$	5.91705	+	2.44714i	0.924089	+	0.382178i
$42$	0.861253	+	3.19614i	0.132894	+	0.493175i
$43$	−0.287011	−	0.287011i	−0.0437687	−	0.0437687i	0.684884	−	0.728652i	$-0.259853\pi$
$43$	−0.287011	−	0.287011i	−0.0437687	−	0.0437687i	−0.728652	+	0.684884i	$0.759853\pi$
$44$	6.62840	+	1.75598i	0.999268	+	0.264724i
$45$	0.259523	+	4.53414i	0.0386875	+	0.675910i
$46$	5.11601	−	8.89022i	0.754314	−	1.31079i
$47$		−	3.64014i		−	0.530969i	−0.964115	−	0.265484i	$-0.914468\pi$
$47$		−	3.64014i		−	0.530969i	0.964115	−	0.265484i	$-0.0855319\pi$
$48$	3.42099	+	1.94937i	0.493777	+	0.281367i
$49$	−1.34592			−0.192274
$50$	6.57302	−	2.60681i	0.929565	−	0.368658i
$51$			5.89029i			0.824806i
$52$	0.929617	−	0.540229i	0.128915	−	0.0749162i
$53$	−10.5416			−1.44800			−0.724000	−	0.689800i	$-0.757698\pi$
$53$	−10.5416			−1.44800			−0.724000	+	0.689800i	$0.757698\pi$
$54$	−1.82225	−	6.76243i	−0.247977	−	0.920251i
$55$	−5.10234	+	5.72189i	−0.687999	+	0.771540i
$56$	4.73543	−	4.77581i	0.632798	−	0.638195i
$57$	−0.376100	+	0.376100i	−0.0498157	+	0.0498157i
$58$	2.54165	+	1.46263i	0.333735	+	0.192053i
$59$	−1.58121			−0.205856			−0.102928	−	0.994689i	$-0.532821\pi$
$59$	−1.58121			−0.205856			−0.102928	+	0.994689i	$0.532821\pi$
$60$	−3.67352	+	2.42575i	−0.474250	+	0.313163i
$61$		−	0.445242i		−	0.0570074i	−0.999594	−	0.0285037i	$-0.990926\pi$
$61$		−	0.445242i		−	0.0570074i	0.999594	−	0.0285037i	$-0.00907424\pi$
$62$	−0.611030	−	2.26755i	−0.0776008	−	0.287979i
$63$	−4.82949			−0.608459
$64$	−0.0679329	−	7.99971i	−0.00849161	−	0.999964i
$65$	0.0686928	+	1.20013i	0.00852030	+	0.148858i
$66$	2.38055	−	4.13674i	0.293025	−	0.509197i
$67$			6.98956i			0.853911i	0.904273	+	0.426955i	$0.140414\pi$
$67$			6.98956i			0.853911i	−0.904273	+	0.426955i	$0.859586\pi$
$68$	10.3475	−	6.01323i	1.25482	−	0.729212i
$69$	−5.04834	−	5.04834i	−0.607749	−	0.607749i
$70$	2.36812	+	7.13672i	0.283045	+	0.853002i
$71$	−3.62995	−	3.62995i	−0.430796	−	0.430796i	0.458103	−	0.888899i	$-0.348529\pi$
$71$	−3.62995	−	3.62995i	−0.430796	−	0.430796i	−0.888899	+	0.458103i	$0.848529\pi$
$72$	−4.04481	+	4.07931i	−0.476686	+	0.480751i
$73$	−9.73449	+	9.73449i	−1.13934	+	1.13934i	−0.150767	+	0.988569i	$0.548174\pi$
$73$	−9.73449	+	9.73449i	−1.13934	+	1.13934i	−0.988569	+	0.150767i	$0.951826\pi$
$74$	−3.18245	+	5.53023i	−0.369952	+	0.642876i
$75$	−0.561580	−	4.88962i	−0.0648457	−	0.564605i
$76$	1.04464	+	0.276745i	0.119829	+	0.0317448i
$77$	−5.76465	−	5.76465i	−0.656943	−	0.656943i
$78$	−0.194717	−	0.722603i	−0.0220474	−	0.0818187i
$79$	−9.18180	+	9.18180i	−1.03303	+	1.03303i	−0.0335972	+	0.999435i	$0.510696\pi$
$79$	−9.18180	+	9.18180i	−1.03303	+	1.03303i	−0.999435	+	0.0335972i	$0.989304\pi$
$80$	8.01151	+	3.97690i	0.895714	+	0.444631i
$81$	1.21831			0.135367
$82$	−8.98022	−	1.16435i	−0.991699	−	0.128581i
$83$	10.8658	−	10.8658i	1.19268	−	1.19268i	0.216366	−	0.976312i	$-0.430579\pi$
$83$	10.8658	−	10.8658i	1.19268	−	1.19268i	0.976312	−	0.216366i	$-0.0694205\pi$
$84$	−2.35209	−	4.04744i	−0.256634	−	0.441612i
$85$	0.764613	+	13.3586i	0.0829340	+	1.44894i
$86$	0.497523	+	0.286307i	0.0536493	+	0.0308733i
$87$	1.44328	−	1.44328i	0.154736	−	0.154736i
$88$	−9.69724	+	0.0411734i	−1.03373	+	0.00438909i
$89$	10.0408	+	10.0408i	1.06433	+	1.06433i	0.997784	+	0.0665422i	$0.0211967\pi$
$89$	10.0408	+	10.0408i	1.06433	+	1.06433i	0.0665422	+	0.997784i	$0.478803\pi$
$90$	−2.02276	−	6.09590i	−0.213217	−	0.642565i
$91$	−1.27831			−0.134003
$92$	−3.71471	+	14.0221i	−0.387285	+	1.46191i
$93$	−1.63461			−0.169501
$94$	1.33942	+	4.97063i	0.138151	+	0.512681i
$95$	−0.804136	+	0.901778i	−0.0825026	+	0.0925205i
$96$	−5.38867	−	1.40310i	−0.549979	−	0.143203i
$97$	−14.1882			−1.44059			−0.720296	−	0.693666i	$-0.755994\pi$
$97$	−14.1882			−1.44059			−0.720296	+	0.693666i	$0.755994\pi$
$98$	1.83786	−	0.495241i	0.185652	−	0.0500269i
$99$	4.92394	+	4.92394i	0.494874	+	0.494874i
$100$	−8.01630	+	5.97821i	−0.801630	+	0.597821i
$101$	−1.29400	−	1.29400i	−0.128758	−	0.128758i	0.639791	−	0.768549i	$-0.279021\pi$
$101$	−1.29400	−	1.29400i	−0.128758	−	0.128758i	−0.768549	+	0.639791i	$0.779021\pi$
$102$	−2.16738	−	8.04323i	−0.214603	−	0.796398i
$103$	−10.2881	−	10.2881i	−1.01371	−	1.01371i	−0.999905	−	0.0138097i	$-0.995604\pi$
$103$	−10.2881	−	10.2881i	−1.01371	−	1.01371i	−0.0138097	−	0.999905i	$-0.504396\pi$
$104$	−1.07062	+	1.07975i	−0.104982	+	0.105878i
$105$	5.22525	−	0.299081i	0.509932	−	0.0291873i
$106$	14.3946	−	3.87887i	1.39813	−	0.376749i
$107$	−1.98848	−	1.98848i	−0.192234	−	0.192234i	0.604427	−	0.796661i	$-0.293402\pi$
$107$	−1.98848	−	1.98848i	−0.192234	−	0.192234i	−0.796661	+	0.604427i	$0.793402\pi$
$108$	4.97659	+	8.56363i	0.478872	+	0.824036i
$109$	5.17177	−	5.17177i	0.495366	−	0.495366i	−0.414626	−	0.909992i	$-0.636088\pi$
$109$	5.17177	−	5.17177i	0.495366	−	0.495366i	0.909992	+	0.414626i	$0.136088\pi$
$110$	4.86186	−	9.69072i	0.463560	−	0.923974i
$111$	3.14036	+	3.14036i	0.298069	+	0.298069i
$112$	−4.70896	+	8.26384i	−0.444955	+	0.780860i
$113$	13.4782	+	13.4782i	1.26792	+	1.26792i	0.947160	+	0.320761i	$0.103939\pi$
$113$	13.4782	+	13.4782i	1.26792	+	1.26792i	0.320761	+	0.947160i	$0.396061\pi$
$114$	0.375178	−	0.651956i	0.0351386	−	0.0610613i
$115$	−12.1044	−	10.7938i	−1.12875	−	1.00653i
$116$	−4.00882	−	1.06201i	−0.372210	−	0.0986050i
$117$	1.09188			0.100945
$118$	2.15915	−	0.581820i	0.198766	−	0.0535609i
$119$	−14.2288			−1.30435
$120$	4.12364	−	4.66408i	0.376436	−	0.425770i
$121$			0.754776i			0.0686160i
$122$	0.163830	+	0.607981i	0.0148325	+	0.0550440i
$123$	−2.40885	+	5.82447i	−0.217198	+	0.525175i
$124$	1.66873	+	2.87152i	0.149856	+	0.257870i
$125$	−1.90832	−	11.0163i	−0.170686	−	0.985326i
$126$	6.59470	−	1.77705i	0.587503	−	0.158312i
$127$	14.0292	+	14.0292i	1.24489	+	1.24489i	0.957949	+	0.286938i	$0.0926374\pi$
$127$	14.0292	+	14.0292i	1.24489	+	1.24489i	0.286938	+	0.957949i	$0.407363\pi$
$128$	3.03632	+	10.8987i	0.268376	+	0.963314i
$129$	0.282520	−	0.282520i	0.0248745	−	0.0248745i
$130$	−0.535400	−	1.61352i	−0.0469577	−	0.141515i
$131$	−10.8871			−0.951209			−0.475604	−	0.879659i	$-0.657771\pi$
$131$	−10.8871			−0.951209			−0.475604	+	0.879659i	$0.657771\pi$
$132$	−1.72850	+	6.52468i	−0.150447	+	0.567901i
$133$	−0.908518	−	0.908518i	−0.0787785	−	0.0787785i
$134$	−2.57187	−	9.54429i	−0.222175	−	0.824501i
$135$	−11.0556	+	0.632799i	−0.951519	+	0.0544626i
$136$	−11.9169	+	12.0185i	−1.02187	+	1.03058i
$137$	−2.32979			−0.199047			−0.0995236	−	0.995035i	$-0.531732\pi$
$137$	−2.32979			−0.199047			−0.0995236	+	0.995035i	$0.531732\pi$
$138$	8.75111	+	5.03596i	0.744944	+	0.428689i
$139$	−6.92723			−0.587560			−0.293780	−	0.955873i	$-0.594913\pi$
$139$	−6.92723			−0.587560			−0.293780	+	0.955873i	$0.594913\pi$
$140$	−5.85970	−	8.87387i	−0.495235	−	0.749979i
$141$	3.58318			0.301758
$142$	6.29239	+	3.62105i	0.528046	+	0.303872i
$143$	1.30331	+	1.30331i	0.108988	+	0.108988i
$144$	4.02220	−	7.05864i	0.335184	−	0.588220i
$145$	3.08587	−	3.46057i	0.256268	−	0.287385i
$146$	9.71062	−	16.8744i	0.803657	−	1.39654i
$147$		−	1.32486i		−	0.109272i
$148$	2.31076	−	8.72257i	0.189944	−	0.716991i
$149$	4.89996	−	4.89996i	0.401420	−	0.401420i	−0.477313	−	0.878733i	$-0.658389\pi$
$149$	4.89996	−	4.89996i	0.401420	−	0.401420i	0.878733	+	0.477313i	$0.158389\pi$
$150$	2.56602	+	6.47017i	0.209515	+	0.528287i
$151$	10.7169	+	10.7169i	0.872129	+	0.872129i	0.992704	−	0.120575i	$-0.0384739\pi$
$151$	10.7169	+	10.7169i	0.872129	+	0.872129i	−0.120575	+	0.992704i	$0.538474\pi$
$152$	−1.52830	+	0.00648898i	−0.123961	+	0.000526326i
$153$	12.1536			0.982563
$154$	9.99282	+	5.75052i	0.805245	+	0.463390i
$155$	−3.70713	+	0.212187i	−0.297764	+	0.0170433i
$156$	0.531776	+	0.915071i	0.0425761	+	0.0732643i
$157$		−	5.53219i		−	0.441517i	−0.975329	−	0.220758i	$-0.929147\pi$
$157$		−	5.53219i		−	0.441517i	0.975329	−	0.220758i	$-0.0708532\pi$
$158$	9.15928	−	15.9163i	0.728673	−	1.26623i
$159$		−	10.3767i		−	0.822922i
$160$	−12.4031	−	2.48258i	−0.980551	−	0.196265i
$161$	12.1949	−	12.1949i	0.961094	−	0.961094i
$162$	−1.66360	+	0.448286i	−0.130705	+	0.0352207i
$163$	17.2200	−	17.2200i	1.34877	−	1.34877i	0.461780	−	0.886994i	$-0.347211\pi$
$163$	17.2200	−	17.2200i	1.34877	−	1.34877i	0.886994	−	0.461780i	$-0.152789\pi$
$164$	12.6910	−	1.71442i	0.990998	−	0.133874i
$165$	−5.63236	−	5.02250i	−0.438479	−	0.391001i
$166$	−10.8392	+	18.8355i	−0.841283	+	1.46192i
$167$	12.4152			0.960716			0.480358	−	0.877072i	$-0.340507\pi$
$167$	12.4152			0.960716			0.480358	+	0.877072i	$0.340507\pi$
$168$	4.70109	+	4.66133i	0.362697	+	0.359630i
$169$	−12.7110			−0.977769
$170$	−5.95949	−	17.9599i	−0.457072	−	1.37746i
$171$	0.776020	+	0.776020i	0.0593437	+	0.0593437i
$172$	−0.784720	−	0.207886i	−0.0598343	−	0.0158512i
$173$	9.63849	−	9.63849i	0.732801	−	0.732801i	−0.238373	−	0.971174i	$-0.576614\pi$
$173$	9.63849	−	9.63849i	0.732801	−	0.732801i	0.971174	+	0.238373i	$0.0766140\pi$
$174$	−1.43974	+	2.50188i	−0.109147	+	0.189667i
$175$	11.8115	−	1.35657i	0.892866	−	0.102547i
$176$	13.2265	−	3.62440i	0.996984	−	0.273200i
$177$		−	1.55647i		−	0.116991i
$178$	−17.4054	−	10.0162i	−1.30459	−	0.750746i
$179$	−7.05919	−	7.05919i	−0.527629	−	0.527629i	0.392236	−	0.919865i	$-0.371702\pi$
$179$	−7.05919	−	7.05919i	−0.527629	−	0.527629i	−0.919865	+	0.392236i	$0.871702\pi$
$180$	5.00512	+	7.57970i	0.373060	+	0.564958i
$181$	8.11635	+	8.11635i	0.603284	+	0.603284i	0.941182	−	0.337899i	$-0.109716\pi$
$181$	8.11635	+	8.11635i	0.603284	+	0.603284i	−0.337899	+	0.941182i	$0.609716\pi$
$182$	1.74554	−	0.470365i	0.129388	−	0.0348658i
$183$	0.438275			0.0323982
$184$	−0.0871007	−	20.5142i	−0.00642115	−	1.51232i
$185$	7.52966	+	6.71437i	0.553592	+	0.493650i
$186$	2.23207	−	0.601469i	0.163663	−	0.0441018i
$187$	14.5070	+	14.5070i	1.06086	+	1.06086i
$188$	−3.65797	−	6.29458i	−0.266785	−	0.459079i
$189$		−	11.7758i		−	0.856564i
$190$	0.766235	−	1.52727i	0.0555886	−	0.110800i
$191$	7.89114	−	7.89114i	0.570983	−	0.570983i	−0.361420	−	0.932403i	$-0.617708\pi$
$191$	7.89114	−	7.89114i	0.570983	−	0.570983i	0.932403	+	0.361420i	$0.117708\pi$
$192$	7.87454	−	0.0668700i	0.568296	−	0.00482592i
$193$	12.4925			0.899229			0.449614	−	0.893223i	$-0.351561\pi$
$193$	12.4925			0.899229			0.449614	+	0.893223i	$0.351561\pi$
$194$	19.3741	−	5.22066i	1.39098	−	0.374822i
$195$	−1.18136	+	0.0676180i	−0.0845987	+	0.00484223i
$196$	−2.32738	+	1.35251i	−0.166241	+	0.0966078i
$197$	16.9550	+	16.9550i	1.20799	+	1.20799i	0.971676	+	0.236317i	$0.0759404\pi$
$197$	16.9550	+	16.9550i	1.20799	+	1.20799i	0.236317	+	0.971676i	$0.424060\pi$
$198$	−8.53547	−	4.91186i	−0.606589	−	0.349071i
$199$	1.48001	+	1.48001i	0.104915	+	0.104915i	0.757616	−	0.652701i	$-0.226364\pi$
$199$	1.48001	+	1.48001i	0.104915	+	0.104915i	−0.652701	+	0.757616i	$0.726364\pi$
$200$	8.74657	−	11.1129i	0.618476	−	0.785804i
$201$	−6.88020			−0.485292
$202$	2.24310	+	1.29083i	0.157824	+	0.0908222i
$203$	3.48644	+	3.48644i	0.244700	+	0.244700i
$204$	5.91915	+	10.1856i	0.414423	+	0.713132i
$205$	−4.70695	+	13.5220i	−0.328748	+	0.944418i
$206$	17.8340	+	10.2628i	1.24255	+	0.715046i
$207$	−10.4164	+	10.4164i	−0.723990	+	0.723990i
$208$	1.06463	−	1.86834i	0.0738188	−	0.129546i
$209$			1.85257i			0.128145i
$210$	−7.02506	+	2.33107i	−0.484775	+	0.160859i
$211$	8.66840	−	8.66840i	0.596758	−	0.596758i	−0.342691	−	0.939448i	$-0.611338\pi$
$211$	8.66840	−	8.66840i	0.596758	−	0.596758i	0.939448	+	0.342691i	$0.111338\pi$
$212$	−18.2287	+	10.5932i	−1.25195	+	0.727546i
$213$	3.57315	−	3.57315i	0.244828	−	0.244828i
$214$	3.44696	+	1.98361i	0.235630	+	0.135597i
$215$	0.604053	−	0.677401i	0.0411961	−	0.0461983i
$216$	−9.94662	−	9.86251i	−0.676782	−	0.671059i
$217$		−	3.94861i		−	0.268049i
$218$	−5.15909	+	8.96508i	−0.349418	+	0.607192i
$219$	−9.58218	−	9.58218i	−0.647504	−	0.647504i
$220$	−3.07311	+	15.0217i	−0.207189	+	1.01276i
$221$	3.21693			0.216394
$222$	−5.44370	−	3.13266i	−0.365357	−	0.210250i
$223$	18.6741	−	18.6741i	1.25051	−	1.25051i	0.295019	−	0.955491i	$-0.404674\pi$
$223$	18.6741	−	18.6741i	1.25051	−	1.25051i	0.955491	−	0.295019i	$-0.0953260\pi$
$224$	3.38936	−	13.0170i	0.226461	−	0.869737i
$225$	−10.0889	+	1.15873i	−0.672595	+	0.0772485i
$226$	−23.3640	−	13.4451i	−1.55415	−	0.894357i
$227$		−	3.55042i		−	0.235650i	−0.993034	−	0.117825i	$-0.962408\pi$
$227$		−	3.55042i		−	0.235650i	0.993034	−	0.117825i	$-0.0375921\pi$
$228$	−0.272415	+	1.02830i	−0.0180411	+	0.0681008i
$229$	−0.695616	+	0.695616i	−0.0459676	+	0.0459676i	−0.729717	−	0.683749i	$-0.760348\pi$
$229$	−0.695616	+	0.695616i	−0.0459676	+	0.0459676i	0.683749	+	0.729717i	$0.260348\pi$
$230$	20.5004	+	10.2851i	1.35175	+	0.678178i
$231$	5.67446	−	5.67446i	0.373352	−	0.373352i
$232$	5.86485	−	0.0249015i	0.385046	−	0.00163486i
$233$	−17.2606			−1.13078			−0.565391	−	0.824823i	$-0.691275\pi$
$233$	−17.2606			−1.13078			−0.565391	+	0.824823i	$0.691275\pi$
$234$	−1.49097	+	0.401767i	−0.0974678	+	0.0262643i
$235$	8.12630	−	0.465130i	0.530101	−	0.0303417i
$236$	−2.73425	+	1.58896i	−0.177985	+	0.103432i
$237$	−9.03813	−	9.03813i	−0.587090	−	0.587090i
$238$	19.4295	−	5.23559i	1.25942	−	0.339373i
$239$	2.76688	−	2.76688i	0.178975	−	0.178975i	−0.611934	−	0.790909i	$-0.709608\pi$
$239$	2.76688	−	2.76688i	0.178975	−	0.178975i	0.790909	+	0.611934i	$0.209608\pi$
$240$	−3.91468	+	7.88615i	−0.252691	+	0.509049i
$241$			2.06854i			0.133246i	0.997778	+	0.0666232i	$0.0212225\pi$
$241$			2.06854i			0.133246i	−0.997778	+	0.0666232i	$0.978777\pi$
$242$	−0.277726	−	1.03065i	−0.0178529	−	0.0662527i
$243$			16.0562i			1.03001i
$244$	−0.447423	−	0.769918i	−0.0286433	−	0.0492890i
$245$	−0.171978	−	3.00464i	−0.0109873	−	0.191960i
$246$	1.14613	−	8.83970i	0.0730746	−	0.563599i
$247$	0.205403	+	0.205403i	0.0130695	+	0.0130695i
$248$	−3.33526	−	3.30706i	−0.211789	−	0.209998i
$249$	10.6958	+	10.6958i	0.677819	+	0.677819i
$250$	6.65936	+	14.3406i	0.421175	+	0.906979i
$251$	19.4900			1.23020			0.615099	−	0.788450i	$-0.289116\pi$
$251$	19.4900			1.23020			0.615099	+	0.788450i	$0.289116\pi$
$252$	−8.35122	+	4.85315i	−0.526078	+	0.305720i
$253$	−24.8668			−1.56336
$254$	−24.3191	−	13.9948i	−1.52591	−	0.878109i
$255$	−13.1496	+	0.752650i	−0.823458	+	0.0471327i
$256$	−8.15637	−	13.7649i	−0.509773	−	0.860309i
$257$			1.25600i			0.0783474i	0.999232	+	0.0391737i	$0.0124726\pi$
$257$			1.25600i			0.0783474i	−0.999232	+	0.0391737i	$0.987527\pi$
$258$	−0.281827	+	0.489738i	−0.0175458	+	0.0304898i
$259$	−7.58594	+	7.58594i	−0.471367	+	0.471367i
$260$	1.32480	+	2.00626i	0.0821605	+	0.124423i
$261$	−2.97798	−	2.97798i	−0.184332	−	0.184332i
$262$	14.8664	−	4.00599i	0.918448	−	0.247491i
$263$	20.7013			1.27649			0.638247	−	0.769831i	$-0.279660\pi$
$263$	20.7013			1.27649			0.638247	+	0.769831i	$0.279660\pi$
$264$	−0.0405291	−	9.54551i	−0.00249440	−	0.587486i
$265$	−1.34698	−	23.5332i	−0.0827446	−	1.44563i
$266$	1.57488	+	0.906290i	0.0965623	+	0.0555682i
$267$	−9.88372	+	9.88372i	−0.604874	+	0.604874i
$268$	7.02380	+	12.0864i	0.429047	+	0.738297i
$269$			15.4544i			0.942270i	0.882061	+	0.471135i	$0.156155\pi$
$269$			15.4544i			0.942270i	−0.882061	+	0.471135i	$0.843845\pi$
$270$	14.8637	−	4.93211i	0.904577	−	0.300159i
$271$			0.807361i			0.0490437i	0.999699	+	0.0245218i	$0.00780633\pi$
$271$			0.807361i			0.0490437i	−0.999699	+	0.0245218i	$0.992194\pi$
$272$	11.8503	−	20.7963i	0.718530	−	1.26096i
$273$		−	1.25831i		−	0.0761563i
$274$	3.18134	−	0.857265i	0.192192	−	0.0517893i
$275$	−13.4256	−	10.6594i	−0.809594	−	0.642786i
$276$	−13.8027	−	3.65659i	−0.830826	−	0.220101i
$277$	−8.00492	+	8.00492i	−0.480969	+	0.480969i	−0.905441	−	0.424472i	$-0.860460\pi$
$277$	−8.00492	+	8.00492i	−0.480969	+	0.480969i	0.424472	+	0.905441i	$0.360460\pi$
$278$	9.45917	−	2.54893i	0.567323	−	0.152875i
$279$			3.37275i			0.201921i
$280$	11.2667	+	9.96119i	0.673313	+	0.595295i
$281$	−0.765437	−	0.765437i	−0.0456621	−	0.0456621i	0.683907	−	0.729569i	$-0.260279\pi$
$281$	−0.765437	−	0.765437i	−0.0456621	−	0.0456621i	−0.729569	+	0.683907i	$0.760279\pi$
$282$	−4.89286	+	1.31846i	−0.291365	+	0.0785132i
$283$	−2.54743	+	2.54743i	−0.151429	+	0.151429i	−0.778756	−	0.627327i	$-0.784149\pi$
$283$	−2.54743	+	2.54743i	−0.151429	+	0.151429i	0.627327	+	0.778756i	$0.284149\pi$
$284$	−9.92469	−	2.62923i	−0.588922	−	0.156016i
$285$	−0.887668	−	0.791554i	−0.0525809	−	0.0468876i
$286$	−2.25924	−	1.30011i	−0.133592	−	0.0768773i
$287$	−14.0698	−	5.81888i	−0.830512	−	0.343477i
$288$	−2.89505	+	11.1186i	−0.170593	+	0.655171i
$289$	18.8073			1.10631
$290$	−2.94043	+	5.86091i	−0.172668	+	0.344164i
$291$		−	13.9662i		−	0.818713i
$292$	−7.05084	+	26.6152i	−0.412619	+	1.55754i
$293$			13.7106i			0.800981i	0.916301	+	0.400490i	$0.131160\pi$
$293$			13.7106i			0.800981i	−0.916301	+	0.400490i	$0.868840\pi$
$294$	0.487492	+	1.80910i	0.0284311	+	0.105509i
$295$	−0.202044	−	3.52992i	−0.0117635	−	0.205520i
$296$	0.0541816	+	12.7610i	0.00314924	+	0.741717i
$297$	−12.0061	+	12.0061i	−0.696664	+	0.696664i
$298$	−4.88794	+	8.49390i	−0.283151	+	0.492038i
$299$	−2.75710	+	2.75710i	−0.159447	+	0.159447i
$300$	−5.88467	−	7.89087i	−0.339751	−	0.455580i
$301$	0.682463	+	0.682463i	0.0393365	+	0.0393365i
$302$	−18.5774	−	10.6906i	−1.06901	−	0.615176i
$303$	1.27375	−	1.27375i	0.0731751	−	0.0731751i
$304$	2.08451	−	0.571211i	0.119555	−	0.0327612i
$305$	0.993964	−	0.0568921i	0.0569142	−	0.00325763i
$306$	−16.5959	+	4.47203i	−0.948722	+	0.255649i
$307$	14.1654	−	14.1654i	0.808462	−	0.808462i	−0.175939	−	0.984401i	$-0.556296\pi$
$307$	14.1654	−	14.1654i	0.808462	−	0.808462i	0.984401	+	0.175939i	$0.0562961\pi$
$308$	−15.7612	−	4.17542i	−0.898078	−	0.237917i
$309$	10.1271	−	10.1271i	0.576111	−	0.576111i
$310$	4.98404	−	1.65381i	0.283074	−	0.0939303i
$311$	7.48403	−	7.48403i	0.424380	−	0.424380i	−0.462329	−	0.886709i	$-0.652986\pi$
$311$	7.48403	−	7.48403i	0.424380	−	0.424380i	0.886709	+	0.462329i	$0.152986\pi$
$312$	−1.06285	−	1.05386i	−0.0601721	−	0.0596633i
$313$		−	6.82256i		−	0.385634i	−0.981235	−	0.192817i	$-0.938238\pi$
$313$		−	6.82256i		−	0.385634i	0.981235	−	0.192817i	$-0.0617624\pi$
$314$	2.03561	+	7.55423i	0.114876	+	0.426310i
$315$	−0.617103	−	10.7814i	−0.0347698	−	0.607465i
$316$	−6.65051	+	25.1041i	−0.374120	+	1.41221i
$317$			0.246649i			0.0138532i	0.999976	+	0.00692659i	$0.00220482\pi$
$317$			0.246649i			0.0138532i	−0.999976	+	0.00692659i	$0.997795\pi$
$318$	3.81818	+	14.1694i	0.214113	+	0.794579i
$319$		−	7.10924i		−	0.398041i
$320$	17.8500	−	1.17384i	0.997845	−	0.0656197i
$321$	1.95737	−	1.95737i	0.109250	−	0.109250i
$322$	−12.1650	+	21.1394i	−0.677929	+	1.17806i
$323$	2.28633	+	2.28633i	0.127215	+	0.127215i
$324$	2.10671	−	1.22427i	0.117040	−	0.0680153i
$325$	−2.67042	+	0.306702i	−0.148128	+	0.0170127i
$326$	−17.1778	+	29.8503i	−0.951389	+	1.65325i
$327$	5.09085	+	5.09085i	0.281525	+	0.281525i
$328$	−16.6988	+	7.01080i	−0.922035	+	0.387107i
$329$			8.65564i			0.477201i
$330$	9.53909	+	4.78578i	0.525110	+	0.263449i
$331$	−3.89985	−	3.89985i	−0.214355	−	0.214355i	0.591759	−	0.806115i	$-0.298434\pi$
$331$	−3.89985	−	3.89985i	−0.214355	−	0.214355i	−0.806115	+	0.591759i	$0.798434\pi$
$332$	7.87027	−	29.7084i	0.431937	−	1.63046i
$333$	6.47960	−	6.47960i	0.355080	−	0.355080i
$334$	−16.9530	+	4.56827i	−0.927628	+	0.249965i
$335$	−15.6036	+	0.893112i	−0.852515	+	0.0487959i
$336$	−8.13454	−	4.63528i	−0.443775	−	0.252875i
$337$	0.402306	+	0.402306i	0.0219150	+	0.0219150i	0.717979	−	0.696064i	$-0.245067\pi$
$337$	0.402306	+	0.402306i	0.0219150	+	0.0219150i	−0.696064	+	0.717979i	$0.745067\pi$
$338$	17.3569	−	4.67712i	0.944093	−	0.254402i
$339$	−13.2673	+	13.2673i	−0.720580	+	0.720580i
$340$	14.7462	+	22.3315i	0.799725	+	1.21110i
$341$	−4.02583	+	4.02583i	−0.218011	+	0.218011i
$342$	−1.34520	−	0.774117i	−0.0727402	−	0.0418594i
$343$	19.8452			1.07154
$344$	1.14803	−	0.00487441i	0.0618978	−	0.000262811i
$345$	10.6249	−	11.9150i	0.572026	−	0.641485i
$346$	−9.61486	+	16.7080i	−0.516898	+	0.898227i
$347$		−	16.5766i		−	0.889881i	−0.895560	−	0.444940i	$-0.853225\pi$
$347$		−	16.5766i		−	0.889881i	0.895560	−	0.444940i	$-0.146775\pi$
$348$	1.04539	−	3.94610i	0.0560389	−	0.211533i
$349$	−17.0520			−0.912770			−0.456385	−	0.889782i	$-0.650856\pi$
$349$	−17.0520			−0.912770			−0.456385	+	0.889782i	$0.650856\pi$
$350$	−15.6295	+	6.19855i	−0.835434	+	0.331326i
$351$			2.66235i			0.142106i
$352$	−16.7272	+	9.81594i	−0.891564	+	0.523192i
$353$	9.50622	+	9.50622i	0.505965	+	0.505965i	0.913285	−	0.407320i	$-0.133537\pi$
$353$	9.50622	+	9.50622i	0.505965	+	0.505965i	−0.407320	+	0.913285i	$0.633537\pi$
$354$	0.572716	+	2.12537i	0.0304395	+	0.112962i
$355$	7.63972	−	8.56738i	0.405474	−	0.454709i
$356$	27.4528	+	7.27272i	1.45499	+	0.385453i
$357$		−	14.0061i		−	0.741283i
$358$	12.2369	+	7.04188i	0.646738	+	0.372175i
$359$	11.3331			0.598140			0.299070	−	0.954231i	$-0.403324\pi$
$359$	11.3331			0.598140			0.299070	+	0.954231i	$0.403324\pi$
$360$	−9.62354	−	8.50845i	−0.507205	−	0.448435i
$361$		−	18.7080i		−	0.984633i
$362$	−14.0694	−	8.09645i	−0.739472	−	0.425540i
$363$	−0.742966			−0.0389956
$364$	−2.21047	+	1.28457i	−0.115860	+	0.0673299i
$365$	−22.9753	−	20.4876i	−1.20258	−	1.07237i
$366$	−0.598468	+	0.161267i	−0.0312824	+	0.00842956i
$367$	5.67851	−	5.67851i	0.296416	−	0.296416i	−0.543192	−	0.839608i	$-0.682785\pi$
$367$	5.67851	−	5.67851i	0.296416	−	0.296416i	0.839608	+	0.543192i	$0.182785\pi$
$368$	7.66729	+	27.9802i	0.399685	+	1.45857i
$369$	12.0178	+	4.97025i	0.625623	+	0.258741i
$370$	−12.7524	−	6.39791i	−0.662966	−	0.332611i
$371$	25.0661			1.30137
$372$	−2.82659	+	1.64262i	−0.146552	+	0.0851658i
$373$	−12.4490	−	12.4490i	−0.644586	−	0.644586i	0.307093	−	0.951679i	$-0.400644\pi$
$373$	−12.4490	−	12.4490i	−0.644586	−	0.644586i	−0.951679	+	0.307093i	$0.900644\pi$
$374$	−25.1474	−	14.4714i	−1.30034	−	0.748300i
$375$	10.8439	−	1.87847i	0.559977	−	0.0970035i
$376$	7.31112	+	7.24930i	0.377042	+	0.373854i
$377$	−0.788236	−	0.788236i	−0.0405962	−	0.0405962i
$378$	4.33301	+	16.0799i	0.222866	+	0.827062i
$379$	12.2160			0.627496			0.313748	−	0.949506i	$-0.398415\pi$
$379$	12.2160			0.627496			0.313748	+	0.949506i	$0.398415\pi$
$380$	−0.484327	+	2.36744i	−0.0248454	+	0.121447i
$381$	−13.8097	+	13.8097i	−0.707490	+	0.707490i
$382$	−7.87179	+	13.6790i	−0.402756	+	0.699879i
$383$	−31.5722			−1.61327			−0.806633	−	0.591053i	$-0.798712\pi$
$383$	−31.5722			−1.61327			−0.806633	+	0.591053i	$0.798712\pi$
$384$	−10.7281	+	2.98881i	−0.547467	+	0.152522i
$385$	12.1325	−	13.6057i	0.618329	−	0.693410i
$386$	−17.0586	+	4.59672i	−0.868258	+	0.233967i
$387$	−0.582933	−	0.582933i	−0.0296321	−	0.0296321i
$388$	−24.5344	+	14.2577i	−1.24555	+	0.723825i
$389$	−26.4555			−1.34135			−0.670673	−	0.741753i	$-0.733995\pi$
$389$	−26.4555			−1.34135			−0.670673	+	0.741753i	$0.733995\pi$
$390$	1.58827	−	0.527023i	0.0804251	−	0.0266868i
$391$	−30.6890	+	30.6890i	−1.55201	+	1.55201i
$392$	2.68038	−	2.70324i	0.135380	−	0.136534i
$393$		−	10.7167i		−	0.540588i
$394$	−29.3909	−	16.9134i	−1.48069	−	0.852085i
$395$	−21.6708	−	19.3243i	−1.09038	−	0.972313i
$396$	13.4626	+	3.56648i	0.676521	+	0.179222i
$397$		−	37.5243i		−	1.88329i	−0.336607	−	0.941645i	$-0.609279\pi$
$397$		−	37.5243i		−	1.88329i	0.336607	−	0.941645i	$-0.390721\pi$
$398$	−2.56555	−	1.47638i	−0.128599	−	0.0740044i
$399$	0.894302	−	0.894302i	0.0447711	−	0.0447711i
$400$	−7.85440	+	18.3932i	−0.392720	+	0.919658i
$401$			9.48157i			0.473487i	0.971572	+	0.236744i	$0.0760801\pi$
$401$			9.48157i			0.473487i	−0.971572	+	0.236744i	$0.923920\pi$
$402$	9.39495	−	2.53163i	0.468577	−	0.126266i
$403$			0.892727i			0.0444699i
$404$	−3.53794	−	0.937262i	−0.176019	−	0.0466305i
$405$	0.155673	+	2.71976i	0.00773544	+	0.135146i
$406$	−6.04361	−	3.47789i	−0.299940	−	0.172605i
$407$	15.4686			0.766749
$408$	−11.8305	−	11.7305i	−0.585697	−	0.580744i
$409$			32.4759i			1.60583i	0.596093	+	0.802915i	$0.296719\pi$
$409$			32.4759i			1.60583i	−0.596093	+	0.802915i	$0.703281\pi$
$410$	1.45184	−	20.1963i	0.0717011	−	0.997426i
$411$		−	2.29333i		−	0.113122i
$412$	−28.1288	−	7.45180i	−1.38580	−	0.367124i
$413$	3.75985			0.185010
$414$	10.3909	−	18.0565i	0.510683	−	0.887427i
$415$	25.6454	+	22.8686i	1.25888	+	1.12258i
$416$	−0.766287	+	2.94297i	−0.0375703	+	0.144291i
$417$		−	6.81884i		−	0.333920i
$418$	−0.681668	−	2.52969i	−0.0333415	−	0.123731i
$419$			22.4633i			1.09740i	0.836019	+	0.548701i	$0.184877\pi$
$419$			22.4633i			1.09740i	−0.836019	+	0.548701i	$0.815123\pi$
$420$	8.73502	−	5.76802i	0.426225	−	0.281450i
$421$	0.180340	−	0.180340i	0.00878923	−	0.00878923i	−0.702699	−	0.711488i	$-0.748022\pi$
$421$	0.180340	−	0.180340i	0.00878923	−	0.00878923i	0.711488	+	0.702699i	$0.248022\pi$
$422$	−8.64715	+	15.0264i	−0.420936	+	0.731472i
$423$		−	7.39330i		−	0.359475i
$424$	20.9935	−	21.1725i	1.01953	−	1.02823i
$425$	−29.7242	+	3.41387i	−1.44184	+	0.165597i
$426$	−3.56439	+	6.19393i	−0.172695	+	0.300097i
$427$			1.05871i			0.0512346i
$428$	−5.43673	−	1.44029i	−0.262794	−	0.0696189i
$429$	−1.28292	+	1.28292i	−0.0619398	+	0.0619398i
$430$	−0.575583	+	1.14726i	−0.0277571	+	0.0553258i
$431$	18.9292			0.911787			0.455893	−	0.890034i	$-0.349320\pi$
$431$	18.9292			0.911787			0.455893	+	0.890034i	$0.349320\pi$
$432$	17.2112	+	9.80738i	0.828073	+	0.471858i
$433$	1.88134	+	1.88134i	0.0904115	+	0.0904115i	0.750866	−	0.660455i	$-0.229636\pi$
$433$	1.88134	+	1.88134i	0.0904115	+	0.0904115i	−0.660455	+	0.750866i	$0.729636\pi$
$434$	1.45293	+	5.39186i	0.0697427	+	0.258817i
$435$	3.40643	+	3.03759i	0.163326	+	0.145641i
$436$	3.74599	−	14.1402i	0.179400	−	0.677193i
$437$	−3.91904			−0.187473
$438$	16.6104	+	9.55868i	0.793674	+	0.456731i
$439$	−3.81285	+	3.81285i	−0.181978	+	0.181978i	−0.792217	−	0.610239i	$-0.791073\pi$
$439$	−3.81285	+	3.81285i	−0.181978	+	0.181978i	0.610239	+	0.792217i	$0.291073\pi$
$440$	−1.33101	−	21.6430i	−0.0634534	−	1.03179i
$441$	−2.73362			−0.130172
$442$	−4.39273	+	1.18369i	−0.208941	+	0.0563026i
$443$	−1.00722	−	1.00722i	−0.0478543	−	0.0478543i	0.682775	−	0.730629i	$-0.260773\pi$
$443$	−1.00722	−	1.00722i	−0.0478543	−	0.0478543i	−0.730629	+	0.682775i	$0.760773\pi$
$444$	8.58609	+	2.27461i	0.407478	+	0.107948i
$445$	−21.1323	+	23.6983i	−1.00177	+	1.12341i
$446$	−18.6283	+	32.3709i	−0.882076	+	1.53281i
$447$	4.82329	+	4.82329i	0.228134	+	0.228134i
$448$	0.161533	+	19.0220i	0.00763172	+	0.898704i
$449$	24.1621			1.14028			0.570141	−	0.821547i	$-0.306889\pi$
$449$	24.1621			1.14028			0.570141	+	0.821547i	$0.306889\pi$
$450$	13.3501	−	5.29455i	0.629331	−	0.249588i
$451$	8.41223	+	20.2776i	0.396117	+	0.954834i
$452$	36.8509	+	9.76245i	1.73332	+	0.459187i
$453$	−10.5492	+	10.5492i	−0.495645	+	0.495645i
$454$	1.30641	+	4.84812i	0.0613127	+	0.227533i
$455$	−0.163340	−	2.85372i	−0.00765750	−	0.133784i
$456$	−0.00638745	−	1.50439i	−0.000299120	−	0.0704493i
$457$	−8.62879			−0.403638			−0.201819	−	0.979423i	$-0.564685\pi$
$457$	−8.62879			−0.403638			−0.201819	+	0.979423i	$0.564685\pi$
$458$	0.693910	−	1.20582i	0.0324243	−	0.0563445i
$459$			29.6343i			1.38321i
$460$	−31.7778	−	6.50105i	−1.48165	−	0.303113i
$461$	7.56242			0.352217			0.176108	−	0.984371i	$-0.443649\pi$
$461$	7.56242			0.352217			0.176108	+	0.984371i	$0.443649\pi$
$462$	−5.66054	+	9.83647i	−0.263352	+	0.457634i
$463$		−	9.28486i		−	0.431504i	−0.976448	−	0.215752i	$-0.930780\pi$
$463$		−	9.28486i		−	0.431504i	0.976448	−	0.215752i	$-0.0692203\pi$
$464$	−7.99932	+	2.19202i	−0.371359	+	0.101762i
$465$	−0.208867	−	3.64913i	−0.00968599	−	0.169224i
$466$	23.5695	−	6.35120i	1.09184	−	0.294214i
$467$	5.74357	+	5.74357i	0.265781	+	0.265781i	0.827397	−	0.561617i	$-0.189821\pi$
$467$	5.74357	+	5.74357i	0.265781	+	0.265781i	−0.561617	+	0.827397i	$0.689821\pi$
$468$	1.88810	−	1.09723i	0.0872773	−	0.0507195i
$469$		−	16.6200i		−	0.767440i
$470$	−10.9254	+	3.62528i	−0.503949	+	0.167222i
$471$	5.44563			0.250921
$472$	3.14897	−	3.17582i	0.144943	−	0.146179i
$473$		−	1.39162i		−	0.0639867i
$474$	15.6673	+	9.01596i	0.719622	+	0.414117i
$475$	−2.11589	−	1.67994i	−0.0970838	−	0.0770808i
$476$	−24.6046	+	14.2985i	−1.12775	+	0.655369i
$477$	−21.4105			−0.980319
$478$	−2.76009	+	4.79629i	−0.126244	+	0.219377i
$479$	−20.2247	+	20.2247i	−0.924089	+	0.924089i	−0.997315	−	0.0732267i	$-0.976670\pi$
$479$	−20.2247	+	20.2247i	−0.924089	+	0.924089i	0.0732267	+	0.997315i	$0.476670\pi$
$480$	2.44374	−	12.2090i	0.111541	−	0.557263i
$481$	1.71508	−	1.71508i	0.0782007	−	0.0782007i
$482$	−0.761136	−	2.82460i	−0.0346688	−	0.128657i
$483$	12.0041	+	12.0041i	0.546205	+	0.546205i
$484$	0.758473	+	1.30517i	0.0344760	+	0.0593258i
$485$	−1.81294	−	31.6739i	−0.0823213	−	1.43824i
$486$	−5.90802	−	21.9249i	−0.267993	−	0.994533i
$487$	20.8030	−	20.8030i	0.942672	−	0.942672i	−0.0557715	−	0.998444i	$-0.517762\pi$
$487$	20.8030	−	20.8030i	0.942672	−	0.942672i	0.998444	+	0.0557715i	$0.0177618\pi$
$488$	0.894257	+	0.886695i	0.0404811	+	0.0401388i
$489$	16.9506	+	16.9506i	0.766531	+	0.766531i
$490$	1.34042	+	4.03958i	0.0605540	+	0.182489i
$491$			10.3411i			0.466686i	0.972394	+	0.233343i	$0.0749665\pi$
$491$			10.3411i			0.466686i	−0.972394	+	0.233343i	$0.925033\pi$
$492$	1.68759	+	12.4924i	0.0760826	+	0.563201i
$493$	−8.77378	−	8.77378i	−0.395151	−	0.395151i
$494$	−0.356059	−	0.204900i	−0.0160199	−	0.00921887i
$495$	−10.3631	+	11.6214i	−0.465787	+	0.522345i
$496$	5.77118	+	3.28857i	0.259133	+	0.147661i
$497$	8.63141	+	8.63141i	0.387172	+	0.387172i
$498$	−18.5408	−	10.6696i	−0.830833	−	0.478115i
$499$	−21.1016	+	21.1016i	−0.944639	+	0.944639i	−0.998546	−	0.0539071i	$-0.982833\pi$
$499$	−21.1016	+	21.1016i	−0.944639	+	0.944639i	0.0539071	+	0.998546i	$0.482833\pi$
$500$	−14.3701	−	17.1318i	−0.642652	−	0.766158i
$501$			12.2209i			0.545991i
$502$	−26.6137	+	7.17151i	−1.18783	+	0.320080i
$503$			37.1237i			1.65526i	0.561272	+	0.827631i	$0.310312\pi$
$503$			37.1237i			1.65526i	−0.561272	+	0.827631i	$0.689688\pi$
$504$	9.61789	−	9.69991i	0.428415	−	0.432068i
$505$	2.72340	−	3.05409i	0.121190	−	0.135905i
$506$	33.9557	−	9.14994i	1.50952	−	0.406765i
$507$		−	12.5121i		−	0.555682i
$508$	38.3573	+	10.1615i	1.70183	+	0.450845i
$509$	−24.2891	+	24.2891i	−1.07660	+	1.07660i	−0.0797834	+	0.996812i	$0.525423\pi$
$509$	−24.2891	+	24.2891i	−1.07660	+	1.07660i	−0.996812	+	0.0797834i	$0.974577\pi$
$510$	17.6789	−	5.86624i	0.782834	−	0.259762i
$511$	23.1470	−	23.1470i	1.02396	−	1.02396i
$512$	16.2025	+	15.7949i	0.716056	+	0.698043i
$513$	−1.89218	+	1.89218i	−0.0835417	+	0.0835417i
$514$	−0.462157	−	1.71508i	−0.0203849	−	0.0756490i
$515$	21.6527	−	24.2818i	0.954130	−	1.06999i
$516$	0.204633	−	0.772441i	0.00900848	−	0.0340048i
$517$	8.82491	−	8.82491i	0.388119	−	0.388119i
$518$	7.56733	−	13.1499i	0.332490	−	0.577776i
$519$	9.48768	+	9.48768i	0.416463	+	0.416463i
$520$	−2.54724	−	2.25209i	−0.111704	−	0.0987606i
$521$	9.21764	−	9.21764i	0.403832	−	0.403832i	−0.475749	−	0.879581i	$-0.657823\pi$
$521$	9.21764	−	9.21764i	0.403832	−	0.403832i	0.879581	+	0.475749i	$0.157823\pi$
$522$	5.16221	+	2.97067i	0.225944	+	0.130023i
$523$	−3.29111	+	3.29111i	−0.143910	+	0.143910i	−0.775391	−	0.631481i	$-0.782447\pi$
$523$	−3.29111	+	3.29111i	−0.143910	+	0.143910i	0.631481	+	0.775391i	$0.282447\pi$
$524$	−18.8261	+	10.9404i	−0.822421	+	0.477934i
$525$	1.33534	+	11.6267i	0.0582792	+	0.507431i
$526$	−28.2677	+	7.61720i	−1.23253	+	0.332126i
$527$			9.93686i			0.432857i
$528$	3.56769	+	13.0195i	0.155264	+	0.566603i
$529$		−	29.6048i		−	1.28716i
$530$	10.4986	+	31.6391i	0.456028	+	1.37431i
$531$	−3.21152			−0.139368
$532$	−2.48399	−	0.658053i	−0.107695	−	0.0285302i
$533$	3.18098	+	1.31557i	0.137784	+	0.0569836i
$534$	9.85948	−	17.1331i	0.426662	−	0.741421i
$535$	4.18503	−	4.69320i	0.180935	−	0.202905i
$536$	−14.0383	−	13.9196i	−0.606364	−	0.601237i
$537$	6.94874	−	6.94874i	0.299860	−	0.299860i
$538$	−5.68656	−	21.1030i	−0.245165	−	0.909816i
$539$	−3.26295	−	3.26295i	−0.140545	−	0.140545i
$540$	−18.4817	+	12.2041i	−0.795325	+	0.525179i
$541$		−	7.48478i		−	0.321796i	−0.986971	−	0.160898i	$-0.948561\pi$
$541$		−	7.48478i		−	0.321796i	0.986971	−	0.160898i	$-0.0514390\pi$
$542$	−0.297075	−	1.10246i	−0.0127605	−	0.0473546i
$543$	−7.98936	+	7.98936i	−0.342856	+	0.342856i
$544$	−8.52947	+	32.7579i	−0.365698	+	1.40448i
$545$	12.2064	+	10.8847i	0.522864	+	0.466249i
$546$	0.463005	+	1.71823i	0.0198148	+	0.0735334i
$547$			6.24532i			0.267031i	0.991047	+	0.133515i	$0.0426265\pi$
$547$			6.24532i			0.267031i	−0.991047	+	0.133515i	$0.957373\pi$
$548$	−4.02870	+	2.34120i	−0.172098	+	0.100011i
$549$		−	0.904308i		−	0.0385949i
$550$	22.2549	+	9.61541i	0.948954	+	0.410003i
$551$		−	1.12043i		−	0.0477317i
$552$	20.1932	−	0.0857378i	0.859478	−	0.00364925i
$553$	21.8328	−	21.8328i	0.928424	−	0.928424i
$554$	7.98529	−	13.8763i	0.339263	−	0.589545i
$555$	−6.60931	+	7.41185i	−0.280550	+	0.314615i
$556$	−11.9787	+	6.96116i	−0.508008	+	0.295219i
$557$	42.3582			1.79478			0.897388	−	0.441243i	$-0.145462\pi$
$557$	42.3582			1.79478			0.897388	+	0.441243i	$0.145462\pi$
$558$	−1.24103	−	4.60551i	−0.0525370	−	0.194967i
$559$	−0.154296	−	0.154296i	−0.00652601	−	0.00652601i
$560$	−19.0500	−	9.45640i	−0.805010	−	0.399606i
$561$	−14.2800	+	14.2800i	−0.602903	+	0.602903i
$562$	1.32686	+	0.763559i	0.0559701	+	0.0322088i
$563$		−	12.3315i		−	0.519712i	−0.965647	−	0.259856i	$-0.916325\pi$
$563$		−	12.3315i		−	0.519712i	0.965647	−	0.259856i	$-0.0836752\pi$
$564$	6.19609	−	3.60073i	0.260902	−	0.151618i
$565$	−28.3667	+	31.8111i	−1.19340	+	1.33830i
$566$	2.54119	−	4.41588i	0.106814	−	0.185613i
$567$	−2.89693			−0.121660
$568$	14.5197	−	0.0616488i	0.609232	−	0.00258673i
$569$	24.5979			1.03120			0.515600	−	0.856830i	$-0.327569\pi$
$569$	24.5979			1.03120			0.515600	+	0.856830i	$0.327569\pi$
$570$	1.50337	+	0.754246i	0.0629694	+	0.0315919i
$571$	−22.3457	−	22.3457i	−0.935138	−	0.935138i	0.0628830	−	0.998021i	$-0.479970\pi$
$571$	−22.3457	−	22.3457i	−0.935138	−	0.935138i	−0.998021	+	0.0628830i	$0.979970\pi$
$572$	3.56339	+	0.944006i	0.148993	+	0.0394709i
$573$	7.76767	+	7.76767i	0.324499	+	0.324499i
$574$	21.3534	+	2.76863i	0.891276	+	0.115560i
$575$	22.5496	−	28.4013i	0.940382	−	1.18442i
$576$	−0.137975	−	16.2478i	−0.00574896	−	0.676992i
$577$		−	35.6660i		−	1.48479i	−0.669960	−	0.742397i	$-0.733689\pi$
$577$		−	35.6660i		−	1.48479i	0.669960	−	0.742397i	$-0.266311\pi$
$578$	−25.6815	+	6.92030i	−1.06821	+	0.287847i
$579$			12.2970i			0.511047i
$580$	1.85860	−	9.08506i	0.0771743	−	0.377236i
$581$	−25.8371	+	25.8371i	−1.07190	+	1.07190i
$582$	5.13898	+	19.0709i	0.213017	+	0.790515i
$583$	−25.5563	−	25.5563i	−1.05844	−	1.05844i
$584$	−0.165325	−	38.9376i	−0.00684118	−	1.61125i
$585$	0.139518	+	2.43753i	0.00576838	+	0.100780i
$586$	−5.04492	−	18.7219i	−0.208404	−	0.773394i
$587$	−7.69367			−0.317552			−0.158776	−	0.987315i	$-0.550755\pi$
$587$	−7.69367			−0.317552			−0.158776	+	0.987315i	$0.550755\pi$
$588$	−1.33135	−	2.29096i	−0.0549038	−	0.0944776i
$589$	−0.634477	+	0.634477i	−0.0261432	+	0.0261432i
$590$	1.57476	+	4.74578i	0.0648316	+	0.195381i
$591$	−16.6897	+	16.6897i	−0.686522	+	0.686522i
$592$	−4.76950	−	17.4053i	−0.196025	−	0.715352i
$593$		−	39.9129i		−	1.63903i	−0.573059	−	0.819514i	$-0.694243\pi$
$593$		−	39.9129i		−	1.63903i	0.573059	−	0.819514i	$-0.305757\pi$
$594$	11.9766	−	20.8121i	0.491408	−	0.853932i
$595$	−1.81812	−	31.7645i	−0.0745357	−	1.30222i
$596$	3.54911	−	13.3970i	0.145377	−	0.548764i
$597$	−1.45686	+	1.45686i	−0.0596251	+	0.0596251i
$598$	2.75034	−	4.77934i	0.112470	−	0.195442i
$599$	−10.0761			−0.411698			−0.205849	−	0.978584i	$-0.565996\pi$
$599$	−10.0761			−0.411698			−0.205849	+	0.978584i	$0.565996\pi$
$600$	10.9391	+	8.60972i	0.446585	+	0.351490i
$601$	−6.43189	−	6.43189i	−0.262362	−	0.262362i	0.563651	−	0.826013i	$-0.309396\pi$
$601$	−6.43189	−	6.43189i	−0.262362	−	0.262362i	−0.826013	+	0.563651i	$0.809396\pi$
$602$	−1.18303	−	0.680790i	−0.0482165	−	0.0277469i
$603$			14.1961i			0.578111i
$604$	29.3012	+	7.76241i	1.19225	+	0.315848i
$605$	−1.68497	+	0.0964437i	−0.0685038	+	0.00392099i
$606$	−1.27063	+	2.20800i	−0.0516157	+	0.0896940i
$607$	−13.8202	+	13.8202i	−0.560945	+	0.560945i	−0.929576	−	0.368631i	$-0.879827\pi$
$607$	−13.8202	+	13.8202i	−0.560945	+	0.560945i	0.368631	+	0.929576i	$0.379827\pi$
$608$	−2.63623	+	1.54701i	−0.106913	+	0.0627394i
$609$	−3.43189	+	3.43189i	−0.139067	+	0.139067i
$610$	−1.33633	+	0.443424i	−0.0541064	+	0.0179537i
$611$		−	1.95692i		−	0.0791685i
$612$	21.0162	−	12.2132i	0.849531	−	0.493688i
$613$	26.0622	−	26.0622i	1.05264	−	1.05264i	0.0541082	−	0.998535i	$-0.482768\pi$
$613$	26.0622	−	26.0622i	1.05264	−	1.05264i	0.998535	−	0.0541082i	$-0.0172316\pi$
$614$	−14.1307	+	24.5552i	−0.570267	+	0.990968i
$615$	−13.3104	−	4.63330i	−0.536728	−	0.186833i
$616$	23.0584	−	0.0979033i	0.929050	−	0.00394464i
$617$	−7.21441	−	7.21441i	−0.290441	−	0.290441i	0.546813	−	0.837255i	$-0.315841\pi$
$617$	−7.21441	−	7.21441i	−0.290441	−	0.290441i	−0.837255	+	0.546813i	$0.815841\pi$
$618$	−10.1023	+	17.5550i	−0.406373	+	0.706164i
$619$	2.19204			0.0881055			0.0440528	−	0.999029i	$-0.485973\pi$
$619$	2.19204			0.0881055			0.0440528	+	0.999029i	$0.485973\pi$
$620$	−6.19720	+	4.09221i	−0.248886	+	0.164347i
$621$	−25.3984	−	25.3984i	−1.01920	−	1.01920i
$622$	−7.46567	+	12.9733i	−0.299346	+	0.520182i
$623$	−23.8754	−	23.8754i	−0.956548	−	0.956548i
$624$	1.83911	+	1.04797i	0.0736232	+	0.0419525i
$625$	24.3490	−	5.66781i	0.973962	−	0.226712i
$626$	2.51042	+	9.31625i	0.100337	+	0.372352i
$627$	−1.82358			−0.0728269
$628$	−5.55929	−	9.56633i	−0.221840	−	0.381738i
$629$	19.0903	−	19.0903i	0.761182	−	0.761182i
$630$	4.80977	+	14.4950i	0.191626	+	0.577496i
$631$			38.5123i			1.53315i	0.642154	+	0.766576i	$0.278041\pi$
$631$			38.5123i			1.53315i	−0.642154	+	0.766576i	$0.721959\pi$
$632$	−0.155938	−	36.7269i	−0.00620288	−	1.46092i
$633$	8.53277	+	8.53277i	0.339147	+	0.339147i
$634$	−0.0907566	−	0.336801i	−0.00360440	−	0.0133761i
$635$	−29.5263	+	33.1115i	−1.17172	+	1.31399i
$636$	−10.4275	−	17.9434i	−0.413477	−	0.711504i
$637$	−0.723558			−0.0286684
$638$	2.61590	+	9.70770i	0.103565	+	0.384332i
$639$	−7.37261	−	7.37261i	−0.291656	−	0.291656i
$640$	−23.9423	+	8.17094i	−0.946404	+	0.322985i
$641$	3.83627	+	3.83627i	0.151523	+	0.151523i	0.778798	−	0.627275i	$-0.215830\pi$
$641$	3.83627	+	3.83627i	0.151523	+	0.151523i	−0.627275	+	0.778798i	$0.715830\pi$
$642$	−1.95257	+	3.39303i	−0.0770617	+	0.133912i
$643$		−	41.8643i		−	1.65097i	−0.564426	−	0.825484i	$-0.690902\pi$
$643$		−	41.8643i		−	1.65097i	0.564426	−	0.825484i	$-0.309098\pi$
$644$	8.83295	−	33.3423i	0.348067	−	1.31387i
$645$	0.666801	+	0.594602i	0.0262553	+	0.0234124i
$646$	−3.96326	−	2.28072i	−0.155933	−	0.0897337i
$647$	−3.94395	+	3.94395i	−0.155053	+	0.155053i	−0.780370	−	0.625318i	$-0.784969\pi$
$647$	−3.94395	+	3.94395i	−0.155053	+	0.155053i	0.625318	+	0.780370i	$0.284969\pi$
$648$	−2.42625	+	2.44694i	−0.0953119	+	0.0961247i
$649$	−3.83338	−	3.83338i	−0.150473	−	0.150473i
$650$	3.53362	−	1.40141i	0.138600	−	0.0549677i
$651$	3.88683			0.152337
$652$	12.4727	−	47.0814i	0.488469	−	1.84385i
$653$	−44.4052			−1.73771			−0.868854	−	0.495068i	$-0.835143\pi$
$653$	−44.4052			−1.73771			−0.868854	+	0.495068i	$0.835143\pi$
$654$	−8.82481	−	5.07837i	−0.345077	−	0.198580i
$655$	−1.39113	−	24.3045i	−0.0543559	−	0.949654i
$656$	20.2226	−	15.7177i	0.789559	−	0.613675i
$657$	−19.7712	+	19.7712i	−0.771349	+	0.771349i
$658$	−3.18491	−	11.8193i	−0.124161	−	0.460765i
$659$	15.9623	−	15.9623i	0.621802	−	0.621802i	−0.324190	−	0.945992i	$-0.605092\pi$
$659$	15.9623	−	15.9623i	0.621802	−	0.621802i	0.945992	+	0.324190i	$0.105092\pi$
$660$	−14.7867	−	3.02503i	−0.575570	−	0.117749i
$661$		−	36.0355i		−	1.40162i	−0.713348	−	0.700810i	$-0.752822\pi$
$661$		−	36.0355i		−	1.40162i	0.713348	−	0.700810i	$-0.247178\pi$
$662$	6.76025	+	3.89029i	0.262745	+	0.151200i
$663$			3.16659i			0.122980i
$664$	0.184538	+	43.4629i	0.00716148	+	1.68669i
$665$	1.91210	−	2.14428i	0.0741480	−	0.0831515i
$666$	−6.46371	+	11.2322i	−0.250464	+	0.435237i
$667$	15.0393			0.582325
$668$	21.4685	−	12.4760i	0.830642	−	0.482711i
$669$	18.3819	+	18.3819i	0.710686	+	0.710686i
$670$	20.9782	−	6.96102i	0.810458	−	0.268928i
$671$	1.07941	−	1.07941i	0.0416703	−	0.0416703i
$672$	12.8133	+	3.33633i	0.494286	+	0.128702i
$673$			33.8584i			1.30515i	0.757725	+	0.652574i	$0.226311\pi$
$673$			33.8584i			1.30515i	−0.757725	+	0.652574i	$0.773689\pi$
$674$	−0.697384	−	0.401320i	−0.0268622	−	0.0154583i
$675$	−2.82534	−	24.5999i	−0.108747	−	0.946852i
$676$	−21.9800	+	12.7733i	−0.845385	+	0.491279i
$677$	30.0396	+	30.0396i	1.15451	+	1.15451i	0.985637	+	0.168877i	$0.0540140\pi$
$677$	30.0396	+	30.0396i	1.15451	+	1.15451i	0.168877	+	0.985637i	$0.445986\pi$
$678$	13.2348	−	22.9984i	0.508278	−	0.883248i
$679$	33.7371			1.29471
$680$	−28.3531	−	25.0678i	−1.08729	−	0.961306i
$681$	3.49487			0.133924
$682$	4.01596	−	6.97864i	0.153779	−	0.267226i
$683$	−9.38995			−0.359296			−0.179648	−	0.983731i	$-0.557496\pi$
$683$	−9.38995			−0.359296			−0.179648	+	0.983731i	$0.557496\pi$
$684$	2.12172	+	0.562082i	0.0811262	+	0.0214918i
$685$	−0.297696	−	5.20105i	−0.0113744	−	0.198722i
$686$	−27.0987	+	7.30220i	−1.03463	+	0.278799i
$687$	−0.684731	−	0.684731i	−0.0261241	−	0.0261241i
$688$	−1.56585	+	0.429084i	−0.0596976	+	0.0163587i
$689$	−5.66711			−0.215900
$690$	−10.1241	+	20.1796i	−0.385420	+	0.768224i
$691$	−12.8603	+	12.8603i	−0.489230	+	0.489230i	−0.908063	−	0.418833i	$-0.862439\pi$
$691$	−12.8603	+	12.8603i	−0.489230	+	0.489230i	0.418833	+	0.908063i	$0.362439\pi$
$692$	6.98130	−	26.3527i	0.265389	−	1.00178i
$693$	−11.7083	−	11.7083i	−0.444761	−	0.444761i
$694$	6.09951	+	22.6355i	0.231534	+	0.859232i
$695$	−0.885147	−	15.4644i	−0.0335755	−	0.586600i
$696$	0.0245118	+	5.77308i	0.000929119	+	0.218828i
$697$	35.4072	+	14.6435i	1.34114	+	0.554661i
$698$	23.2845	−	6.27441i	0.881333	−	0.237490i
$699$		−	16.9906i		−	0.642643i
$700$	19.0614	−	14.2152i	0.720454	−	0.537283i
$701$	4.43158			0.167378			0.0836892	−	0.996492i	$-0.473330\pi$
$701$	4.43158			0.167378			0.0836892	+	0.996492i	$0.473330\pi$
$702$	−0.979633	−	3.63545i	−0.0369739	−	0.137211i
$703$	2.43787			0.0919460
$704$	19.2293	−	19.5587i	0.724730	−	0.737144i
$705$	0.457852	+	7.99915i	0.0172437	+	0.301265i
$706$	−16.4787	−	9.48290i	−0.620184	−	0.356894i
$707$	3.07691	+	3.07691i	0.115719	+	0.115719i
$708$	−1.56409	−	2.69147i	−0.0587823	−	0.101152i
$709$	26.8484	+	26.8484i	1.00831	+	1.00831i	0.999965	+	0.00834935i	$0.00265771\pi$
$709$	26.8484	+	26.8484i	1.00831	+	1.00831i	0.00834935	+	0.999965i	$0.497342\pi$
$710$	−7.27965	+	14.5099i	−0.273200	+	0.544547i
$711$	−18.6487	+	18.6487i	−0.699380	+	0.699380i
$712$	−40.1630	+	0.170527i	−1.50517	+	0.00639078i
$713$	−8.51650	−	8.51650i	−0.318945	−	0.318945i
$714$	5.15367	+	19.1254i	0.192871	+	0.715752i
$715$	−2.74299	+	3.07606i	−0.102582	+	0.115038i
$716$	−19.3006	−	5.11308i	−0.721298	−	0.191085i
$717$	2.72359	+	2.72359i	0.101714	+	0.101714i
$718$	−15.4755	+	4.17012i	−0.577540	+	0.155628i
$719$	−33.9622	−	33.9622i	−1.26657	−	1.26657i	−0.947846	−	0.318729i	$-0.896744\pi$
$719$	−33.9622	−	33.9622i	−1.26657	−	1.26657i	−0.318729	−	0.947846i	$-0.603256\pi$
$720$	16.2718	+	8.07728i	0.606413	+	0.301023i
$721$	24.4633	+	24.4633i	0.911062	+	0.911062i
$722$	6.88378	+	25.5459i	0.256188	+	0.950721i
$723$	−2.03617			−0.0757261
$724$	22.1910	+	5.87879i	0.824723	+	0.218484i
$725$	8.11974	+	6.44676i	0.301560	+	0.239427i
$726$	1.01452	−	0.273380i	0.0376525	−	0.0101461i
$727$	−12.1156			−0.449344			−0.224672	−	0.974434i	$-0.572131\pi$
$727$	−12.1156			−0.449344			−0.224672	+	0.974434i	$0.572131\pi$
$728$	2.54574	−	2.56745i	0.0943515	−	0.0951562i
$729$	−12.1501			−0.450003
$730$	38.9114	+	19.5220i	1.44018	+	0.722540i
$731$	−1.71745	−	1.71745i	−0.0635222	−	0.0635222i
$732$	0.757871	−	0.440422i	0.0280117	−	0.0162785i
$733$	−22.7663	+	22.7663i	−0.840893	+	0.840893i	−0.988975	−	0.148082i	$-0.952690\pi$
$733$	−22.7663	+	22.7663i	−0.840893	+	0.840893i	0.148082	+	0.988975i	$0.452690\pi$
$734$	−5.66459	+	9.84350i	−0.209084	+	0.363330i
$735$	2.95763	−	0.169288i	0.109094	−	0.00624427i
$736$	−20.7653	−	35.3858i	−0.765418	−	1.30434i
$737$	−16.9450	+	16.9450i	−0.624178	+	0.624178i
$738$	−18.2393	−	2.36485i	−0.671396	−	0.0870514i
$739$	45.6752			1.68019			0.840095	−	0.542440i	$-0.182499\pi$
$739$	45.6752			1.68019			0.840095	+	0.542440i	$0.182499\pi$
$740$	19.7676	+	4.04403i	0.726673	+	0.148661i
$741$	−0.202189	+	0.202189i	−0.00742762	+	0.00742762i
$742$	−34.2280	+	9.22330i	−1.25655	+	0.338598i
$743$	29.1657	+	29.1657i	1.06999	+	1.06999i	0.997359	+	0.0726284i	$0.0231387\pi$
$743$	29.1657	+	29.1657i	1.06999	+	1.06999i	0.0726284	+	0.997359i	$0.476861\pi$
$744$	3.25531	−	3.28307i	0.119346	−	0.120363i
$745$	11.5648	+	10.3126i	0.423703	+	0.377825i
$746$	21.5799	+	12.4185i	0.790098	+	0.454673i
$747$	22.0690	−	22.0690i	0.807463	−	0.807463i
$748$	39.6638	+	10.5076i	1.45025	+	0.384197i
$749$	4.72828	+	4.72828i	0.172767	+	0.172767i
$750$	−14.1162	+	6.55516i	−0.515451	+	0.239361i
$751$	−0.346967	−	0.346967i	−0.0126610	−	0.0126610i	0.700748	−	0.713409i	$-0.252850\pi$
$751$	−0.346967	−	0.346967i	−0.0126610	−	0.0126610i	−0.713409	+	0.700748i	$0.752850\pi$
$752$	−12.6508	−	7.20877i	−0.461328	−	0.262877i
$753$			19.1850i			0.699142i
$754$	1.36638	+	0.786303i	0.0497606	+	0.0286354i
$755$	−22.5552	+	25.2939i	−0.820867	+	0.920541i
$756$	−11.8335	−	20.3629i	−0.430380	−	0.740591i
$757$	−21.9350			−0.797242			−0.398621	−	0.917116i	$-0.630511\pi$
$757$	−21.9350			−0.797242			−0.398621	+	0.917116i	$0.630511\pi$
$758$	−16.6811	+	4.49500i	−0.605884	+	0.163266i
$759$		−	24.4777i		−	0.888484i
$760$	−0.209769	−	3.41097i	−0.00760913	−	0.123729i
$761$	36.0644			1.30733			0.653666	−	0.756783i	$-0.273230\pi$
$761$	36.0644			1.30733			0.653666	+	0.756783i	$0.273230\pi$
$762$	13.7758	−	23.9385i	0.499044	−	0.867202i
$763$	−12.2976	+	12.2976i	−0.445203	+	0.445203i
$764$	5.71567	−	21.5753i	0.206786	−	0.780566i
$765$	1.55297	+	27.1319i	0.0561476	+	0.980958i
$766$	43.1121	−	11.6173i	1.55770	−	0.419749i
$767$	−0.850051			−0.0306936
$768$	13.5496	−	8.02875i	0.488928	−	0.289713i
$769$		−	4.51666i		−	0.162875i	−0.996678	−	0.0814375i	$-0.974049\pi$
$769$		−	4.51666i		−	0.162875i	0.996678	−	0.0814375i	$-0.0259511\pi$
$770$	−11.5607	+	23.0429i	−0.416618	+	0.830409i
$771$	−1.23635			−0.0445261
$772$	21.6022	−	12.5537i	0.777479	−	0.451817i
$773$			19.2603i			0.692743i	0.938097	+	0.346372i	$0.112586\pi$
$773$			19.2603i			0.692743i	−0.938097	+	0.346372i	$0.887414\pi$
$774$	1.01049	+	0.581503i	0.0363214	+	0.0209017i
$775$	−0.947380	−	8.24875i	−0.0340309	−	0.296304i
$776$	28.2556	−	28.4966i	1.01432	−	1.02297i
$777$	−7.46724	−	7.46724i	−0.267886	−	0.267886i
$778$	36.1251	−	9.73451i	1.29515	−	0.348999i
$779$	1.32578	+	3.19578i	0.0475010	+	0.114501i
$780$	−1.97487	+	1.30407i	−0.0707116	+	0.0466932i
$781$		−	17.6004i		−	0.629792i
$782$	30.6138	−	53.1984i	1.09475	−	1.90237i
$783$	7.26123	−	7.26123i	0.259495	−	0.259495i
$784$	−2.66539	+	4.67755i	−0.0951927	+	0.167056i
$785$	12.3501	−	0.706892i	0.440795	−	0.0252300i
$786$	3.94331	+	14.6338i	0.140653	+	0.521969i
$787$	22.9556	−	22.9556i	0.818277	−	0.818277i	−0.167581	−	0.985858i	$-0.553596\pi$
$787$	22.9556	−	22.9556i	0.818277	−	0.818277i	0.985858	+	0.167581i	$0.0535957\pi$
$788$	46.3568	+	12.2807i	1.65139	+	0.437483i
$789$			20.3774i			0.725453i
$790$	36.7022	+	18.4135i	1.30580	+	0.655125i
$791$	−32.0489	−	32.0489i	−1.13953	−	1.13953i
$792$	−19.6956	+	0.0836251i	−0.699852	+	0.00297149i
$793$		−	0.239360i		−	0.00849992i
$794$	13.8074	+	51.2397i	0.490006	+	1.81843i
$795$	23.1650	−	1.32591i	0.821577	−	0.0470251i
$796$	4.04652	+	1.07200i	0.143425	+	0.0379959i
$797$	32.4093	−	32.4093i	1.14800	−	1.14800i	0.161052	−	0.986946i	$-0.448511\pi$
$797$	32.4093	−	32.4093i	1.14800	−	1.14800i	0.986946	−	0.161052i	$-0.0514887\pi$
$798$	−0.892109	+	1.55024i	−0.0315803	+	0.0548779i
$799$		−	21.7823i		−	0.770602i
$800$	3.95731	−	28.0061i	0.139912	−	0.990164i
$801$	20.3934	+	20.3934i	0.720566	+	0.720566i
$802$	−3.48882	−	12.9471i	−0.123195	−	0.457179i
$803$	−47.1993			−1.66563
$804$	−11.8973	+	6.91390i	−0.419586	+	0.243834i
$805$	28.7823	+	25.6659i	1.01444	+	0.904602i
$806$	−0.328486	−	1.21902i	−0.0115704	−	0.0429383i
$807$	−15.2126			−0.535507
$808$	5.17595	−	0.0219765i	0.182089	−	0.000773130i
$809$	29.6375	+	29.6375i	1.04200	+	1.04200i	0.999078	+	0.0429204i	$0.0136662\pi$
$809$	29.6375	+	29.6375i	1.04200	+	1.04200i	0.0429204	+	0.999078i	$0.486334\pi$
$810$	−1.21333	−	3.65657i	−0.0426321	−	0.128479i
$811$	11.2130			0.393743			0.196872	−	0.980429i	$-0.436922\pi$
$811$	11.2130			0.393743			0.196872	+	0.980429i	$0.436922\pi$
$812$	9.53231	+	2.52528i	0.334518	+	0.0886199i
$813$	−0.794728			−0.0278723
$814$	−21.1224	+	5.69179i	−0.740341	+	0.199497i
$815$	40.6425	+	36.2418i	1.42365	+	1.26950i
$816$	20.4709	+	11.6649i	0.716626	+	0.408352i
$817$		−	0.219321i		−	0.00767308i
$818$	−11.9498	−	44.3461i	−0.417814	−	1.55052i
$819$	−2.59631			−0.0907225
$820$	5.44892	+	28.1124i	0.190285	+	0.981729i
$821$	1.27850			0.0446201			0.0223100	−	0.999751i	$-0.492898\pi$
$821$	1.27850			0.0446201			0.0223100	+	0.999751i	$0.492898\pi$
$822$	0.843852	+	3.13156i	0.0294327	+	0.109226i
$823$		−	42.2416i		−	1.47245i	−0.676738	−	0.736224i	$-0.736607\pi$
$823$		−	42.2416i		−	1.47245i	0.676738	−	0.736224i	$-0.263393\pi$
$824$	41.1519	−	0.174726i	1.43360	−	0.00608688i
$825$	10.4926	−	13.2155i	0.365306	−	0.460106i
$826$	−5.13410	+	1.38347i	−0.178638	+	0.0481371i
$827$	5.58556			0.194229			0.0971145	−	0.995273i	$-0.469039\pi$
$827$	5.58556			0.194229			0.0971145	+	0.995273i	$0.469039\pi$
$828$	−7.54476	+	28.4796i	−0.262198	+	0.989735i
$829$	−29.7227			−1.03231			−0.516156	−	0.856495i	$-0.672638\pi$
$829$	−29.7227			−1.03231			−0.516156	+	0.856495i	$0.672638\pi$
$830$	−43.4337	−	21.7908i	−1.50760	−	0.756368i
$831$	−7.87967	−	7.87967i	−0.273343	−	0.273343i
$832$	−0.0365204	−	4.30061i	−0.00126612	−	0.149097i
$833$	−8.05385			−0.279050
$834$	2.50905	+	9.31116i	0.0868812	+	0.322419i
$835$	1.58639	+	27.7158i	0.0548992	+	0.959146i
$836$	1.86164	+	3.20349i	0.0643863	+	0.110795i
$837$	−8.22381			−0.284256
$838$	−8.26554	−	30.6737i	−0.285529	−	1.05961i
$839$	27.2272	+	27.2272i	0.939986	+	0.939986i	0.998298	−	0.0583124i	$-0.0185719\pi$
$839$	27.2272	+	27.2272i	0.939986	+	0.939986i	−0.0583124	+	0.998298i	$0.518572\pi$
$840$	−9.80533	+	11.0904i	−0.338316	+	0.382655i
$841$		−	24.7004i		−	0.851737i
$842$	−0.179898	+	0.312613i	−0.00619968	+	0.0107733i
$843$	0.753460	−	0.753460i	0.0259505	−	0.0259505i
$844$	6.27865	−	23.7004i	0.216120	−	0.815801i
$845$	−1.62419	−	28.3762i	−0.0558737	−	0.976171i
$846$	2.72043	+	10.0956i	0.0935302	+	0.347094i
$847$		−	1.79473i		−	0.0616676i
$848$	−20.8761	+	36.6359i	−0.716889	+	1.25808i
$849$	−2.50757	−	2.50757i	−0.0860597	−	0.0860597i
$850$	39.3324	−	15.5989i	1.34909	−	0.535039i
$851$			32.7232i			1.12174i
$852$	2.58809	−	9.76940i	0.0886664	−	0.334694i
$853$	−4.97627	+	4.97627i	−0.170384	+	0.170384i	−0.787148	−	0.616764i	$-0.788443\pi$
$853$	−4.97627	+	4.97627i	−0.170384	+	0.170384i	0.616764	+	0.787148i	$0.288443\pi$
$854$	−0.389561	−	1.44568i	−0.0133305	−	0.0494700i
$855$	−1.63324	+	1.83156i	−0.0558556	+	0.0626379i
$856$	7.95386	−	0.0337712i	0.271857	−	0.00115427i
$857$	−27.5935	+	27.5935i	−0.942577	+	0.942577i	−0.998439	−	0.0558611i	$-0.982210\pi$
$857$	−27.5935	+	27.5935i	−0.942577	+	0.942577i	0.0558611	+	0.998439i	$0.482210\pi$
$858$	1.27977	−	2.22389i	0.0436906	−	0.0759224i
$859$			29.2969i			0.999599i	0.866141	+	0.499800i	$0.166593\pi$
$859$			29.2969i			0.999599i	−0.866141	+	0.499800i	$0.833407\pi$
$860$	0.363818	−	1.77838i	0.0124061	−	0.0606423i
$861$	5.72783	−	13.8496i	0.195204	−	0.471993i
$862$	−25.8479	+	6.96515i	−0.880384	+	0.237234i
$863$	15.0652	+	15.0652i	0.512825	+	0.512825i	0.915391	−	0.402566i	$-0.131882\pi$
$863$	15.0652	+	15.0652i	0.512825	+	0.512825i	−0.402566	+	0.915391i	$0.631882\pi$
$864$	−27.1107	−	7.05904i	−0.922323	−	0.240154i
$865$	22.7487	+	20.2855i	0.773479	+	0.689728i
$866$	−3.26124	−	1.87673i	−0.110821	−	0.0637738i
$867$			18.5130i			0.628735i
$868$	−3.96796	−	6.82800i	−0.134681	−	0.231757i
$869$	−44.5194			−1.51022
$870$	−5.76920	−	2.89442i	−0.195594	−	0.0981300i
$871$			3.75755i			0.127320i
$872$	0.0878342	+	20.6869i	0.00297444	+	0.700547i
$873$	−28.8169			−0.975305
$874$	5.35147	−	1.44204i	0.181016	−	0.0487779i
$875$	4.53768	+	26.1948i	0.153401	+	0.885547i
$876$	−26.1988	−	6.94051i	−0.885174	−	0.234498i
$877$	−1.18587	+	1.18587i	−0.0400442	+	0.0400442i	−0.726845	−	0.686801i	$-0.759014\pi$
$877$	−1.18587	+	1.18587i	−0.0400442	+	0.0400442i	0.686801	+	0.726845i	$0.259014\pi$
$878$	3.80350	−	6.60945i	0.128362	−	0.223058i
$879$	−13.4961			−0.455211
$880$	9.78123	+	29.0639i	0.329725	+	0.979744i
$881$		−	25.4990i		−	0.859083i	−0.903047	−	0.429541i	$-0.858675\pi$
$881$		−	25.4990i		−	0.859083i	0.903047	−	0.429541i	$-0.141325\pi$
$882$	3.73278	−	1.00586i	0.125689	−	0.0338690i
$883$	−49.4771			−1.66504			−0.832518	−	0.553998i	$-0.813102\pi$
$883$	−49.4771			−1.66504			−0.832518	+	0.553998i	$0.813102\pi$
$884$	5.56275	−	3.23268i	0.187096	−	0.108727i
$885$	3.47469	−	0.198883i	0.116800	−	0.00668537i
$886$	1.74598	+	1.00475i	0.0586572	+	0.0337551i
$887$			37.2624i			1.25115i	0.780164	+	0.625575i	$0.215135\pi$
$887$			37.2624i			1.25115i	−0.780164	+	0.625575i	$0.784865\pi$
$888$	−12.5613	+	0.0533339i	−0.421530	+	0.00178977i
$889$	−33.3590	−	33.3590i	−1.11882	−	1.11882i
$890$	20.1363	−	40.1360i	0.674970	−	1.34536i
$891$	2.95358	+	2.95358i	0.0989486	+	0.0989486i
$892$	13.5259	−	51.0571i	0.452881	−	1.70952i
$893$	1.39082	−	1.39082i	0.0465419	−	0.0465419i
$894$	−8.36100	−	4.81146i	−0.279634	−	0.160919i
$895$	14.8570	−	16.6611i	0.496616	−	0.556918i
$896$	−7.21987	−	25.9152i	−0.241199	−	0.865765i
$897$	−2.71396	−	2.71396i	−0.0906166	−	0.0906166i
$898$	−32.9935	+	8.89066i	−1.10101	+	0.296685i
$899$	2.43481	−	2.43481i	0.0812053	−	0.0812053i
$900$	−16.2815	+	12.1420i	−0.542716	+	0.404734i
$901$	−63.0801			−2.10150
$902$	−18.9483	−	24.5938i	−0.630908	−	0.818884i
$903$	−0.671785	+	0.671785i	−0.0223556	+	0.0223556i
$904$	−53.9123	+	0.228905i	−1.79309	+	0.00761327i
$905$	−17.0820	+	19.1562i	−0.567824	+	0.636772i
$906$	10.5233	−	18.2867i	0.349615	−	0.607534i
$907$	35.2891	−	35.2891i	1.17176	−	1.17176i	0.189966	−	0.981791i	$-0.439162\pi$
$907$	35.2891	−	35.2891i	1.17176	−	1.17176i	0.981791	−	0.189966i	$-0.0608377\pi$
$908$	−3.56781	−	6.13943i	−0.118402	−	0.203744i
$909$	−2.62818	−	2.62818i	−0.0871711	−	0.0871711i
$910$	1.27309	+	3.83667i	0.0422026	+	0.127184i
$911$	−12.6649			−0.419606			−0.209803	−	0.977744i	$-0.567282\pi$
$911$	−12.6649			−0.419606			−0.209803	+	0.977744i	$0.567282\pi$
$912$	0.562274	+	2.05190i	0.0186187	+	0.0679451i
$913$	52.6847			1.74361
$914$	11.7827	−	3.17503i	0.389736	−	0.105021i
$915$	0.0560019	+	0.978412i	0.00185137	+	0.0323453i
$916$	−0.503845	+	1.90189i	−0.0166475	+	0.0628403i
$917$	25.8876			0.854885
$918$	−10.9042	−	40.4659i	−0.359892	−	1.33557i
$919$	−24.6146	−	24.6146i	−0.811961	−	0.811961i	0.172967	−	0.984928i	$-0.444665\pi$
$919$	−24.6146	−	24.6146i	−0.811961	−	0.811961i	−0.984928	+	0.172967i	$0.944665\pi$
$920$	45.7850	−	2.81570i	1.50949	−	0.0928310i
$921$	13.9438	+	13.9438i	0.459463	+	0.459463i
$922$	−10.3265	+	2.78265i	−0.340086	+	0.0916418i
$923$	−1.95144	−	1.95144i	−0.0642325	−	0.0642325i
$924$	4.11009	−	15.5146i	0.135212	−	0.510393i
$925$	−14.0271	+	17.6673i	−0.461209	+	0.580896i
$926$	3.41644	+	12.6785i	0.112271	+	0.416643i
$927$	−20.8956	−	20.8956i	−0.686301	−	0.686301i
$928$	10.1166	−	5.93664i	0.332092	−	0.194880i
$929$	−8.97072	+	8.97072i	−0.294320	+	0.294320i	−0.838784	−	0.544464i	$-0.816733\pi$
$929$	−8.97072	+	8.97072i	−0.294320	+	0.294320i	0.544464	+	0.838784i	$0.316733\pi$
$930$	1.62794	+	4.90605i	0.0533822	+	0.160876i
$931$	−0.514245	−	0.514245i	−0.0168537	−	0.0168537i
$932$	−29.8473	+	17.3452i	−0.977682	+	0.568161i
$933$	7.36692	+	7.36692i	0.241182	+	0.241182i
$934$	−9.95627	−	5.72948i	−0.325779	−	0.187474i
$935$	−30.5320	+	34.2393i	−0.998503	+	1.11975i
$936$	−2.17447	+	2.19302i	−0.0710748	+	0.0716810i
$937$	4.95111			0.161746			0.0808729	−	0.996724i	$-0.474229\pi$
$937$	4.95111			0.161746			0.0808729	+	0.996724i	$0.474229\pi$
$938$	6.11547	+	22.6947i	0.199677	+	0.741009i
$939$	6.71581			0.219162
$940$	13.5847	−	8.97041i	0.443084	−	0.292583i
$941$		−	3.55700i		−	0.115955i	−0.998318	−	0.0579775i	$-0.981535\pi$
$941$		−	3.55700i		−	0.115955i	0.998318	−	0.0579775i	$-0.0184652\pi$
$942$	−7.43603	+	2.00376i	−0.242279	+	0.0652861i
$943$	−42.8965	+	17.7958i	−1.39690	+	0.579510i
$944$	−3.13136	+	5.49529i	−0.101917	+	0.178856i
$945$	26.2885	−	1.50469i	0.855164	−	0.0489475i
$946$	0.512058	+	1.90026i	0.0166484	+	0.0617829i
$947$	7.19716	+	7.19716i	0.233876	+	0.233876i	0.814309	−	0.580432i	$-0.197116\pi$
$947$	7.19716	+	7.19716i	0.233876	+	0.233876i	−0.580432	+	0.814309i	$0.697116\pi$
$948$	−24.7113	−	6.54645i	−0.802584	−	0.212619i
$949$	−5.23322	+	5.23322i	−0.169877	+	0.169877i
$950$	3.50741	+	1.51540i	0.113795	+	0.0491662i
$951$	−0.242790			−0.00787300
$952$	28.3364	−	28.5781i	0.918389	−	0.926221i
$953$	−6.76768	−	6.76768i	−0.219227	−	0.219227i	0.588946	−	0.808173i	$-0.299543\pi$
$953$	−6.76768	−	6.76768i	−0.219227	−	0.219227i	−0.808173	+	0.588946i	$0.799543\pi$
$954$	29.2362	−	7.87817i	0.946556	−	0.255065i
$955$	18.6246	+	16.6080i	0.602678	+	0.537422i
$956$	2.00409	−	7.56496i	0.0648169	−	0.244668i
$957$	6.99800			0.226213
$958$	20.1751	−	35.0587i	0.651827	−	1.13270i
$959$	5.53985			0.178891
$960$	1.15547	+	17.5707i	0.0372928	+	0.567092i
$961$	28.2424			0.911046
$962$	−1.71087	+	2.97302i	−0.0551607	+	0.0958541i
$963$	−4.03870	−	4.03870i	−0.130145	−	0.130145i
$964$	2.07867	+	3.57695i	0.0669495	+	0.115206i
$965$	1.59627	+	27.8884i	0.0513856	+	0.897760i
$966$	−20.8087	−	11.9747i	−0.669508	−	0.385278i
$967$		−	26.0334i		−	0.837179i	−0.908176	−	0.418590i	$-0.862525\pi$
$967$		−	26.0334i		−	0.837179i	0.908176	−	0.418590i	$-0.137475\pi$
$968$	−1.51595	−	1.50313i	−0.0487244	−	0.0483124i
$969$	−2.25055	+	2.25055i	−0.0722982	+	0.0722982i
$970$	14.1303	+	42.5838i	0.453695	+	1.36728i
$971$	−22.7261	−	22.7261i	−0.729316	−	0.729316i	0.241167	−	0.970484i	$-0.422470\pi$
$971$	−22.7261	−	22.7261i	−0.729316	−	0.729316i	−0.970484	+	0.241167i	$0.922470\pi$
$972$	16.1349	+	27.7646i	0.517527	+	0.890551i
$973$	16.4718			0.528061
$974$	−20.7519	+	36.0612i	−0.664935	+	1.15548i
$975$	−0.301903	−	2.62864i	−0.00966863	−	0.0841838i
$976$	−1.54738	−	0.881738i	−0.0495304	−	0.0282237i
$977$		−	5.89849i		−	0.188709i	−0.995539	−	0.0943547i	$-0.969921\pi$
$977$		−	5.89849i		−	0.188709i	0.995539	−	0.0943547i	$-0.0300788\pi$
$978$	−29.3832	−	16.9090i	−0.939571	−	0.540690i
$979$			48.6846i			1.55597i
$980$	−3.31675	−	5.02285i	−0.105950	−	0.160449i
$981$	10.5041	−	10.5041i	0.335371	−	0.335371i
$982$	−3.80508	−	14.1208i	−0.121425	−	0.450613i
$983$	−25.4145	+	25.4145i	−0.810596	+	0.810596i	−0.984723	−	0.174127i	$-0.944290\pi$
$983$	−25.4145	+	25.4145i	−0.810596	+	0.810596i	0.174127	+	0.984723i	$0.444290\pi$
$984$	−6.90110	−	16.4375i	−0.219999	−	0.524008i
$985$	−35.6841	+	40.0170i	−1.13699	+	1.27505i
$986$	15.2090	+	8.75226i	0.484354	+	0.278729i
$987$	−8.52020			−0.271201
$988$	0.561596	+	0.148777i	0.0178667	+	0.00473322i
$989$	2.94392			0.0936112
$990$	9.87467	−	19.6823i	0.313837	−	0.625546i
$991$	28.4839	+	28.4839i	0.904821	+	0.904821i	0.995848	−	0.0910270i	$-0.0290150\pi$
$991$	28.4839	+	28.4839i	0.904821	+	0.904821i	−0.0910270	+	0.995848i	$0.529015\pi$
$992$	−9.09063	−	2.36701i	−0.288628	−	0.0751526i
$993$	3.83883	−	3.83883i	0.121822	−	0.121822i
$994$	−14.9622	−	8.61024i	−0.474573	−	0.273100i
$995$	−3.11489	+	3.49312i	−0.0987486	+	0.110739i
$996$	29.2435	+	7.74713i	0.926616	+	0.245477i
$997$			30.8316i			0.976448i	0.872718	+	0.488224i	$0.162355\pi$
$997$			30.8316i			0.976448i	−0.872718	+	0.488224i	$0.837645\pi$
$998$	21.0499	−	36.5789i	0.666322	−	1.15789i
$999$	15.7993	+	15.7993i	0.499867	+	0.499867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.j.c.483.10	✓	240
4.3	odd	2	inner	820.2.j.c.483.69	yes	240
5.2	odd	4		820.2.s.c.647.52	yes	240
20.7	even	4		820.2.s.c.647.111	yes	240
41.9	even	4		820.2.s.c.583.111	yes	240
164.91	odd	4		820.2.s.c.583.52	yes	240
205.132	odd	4	inner	820.2.j.c.747.69	yes	240
820.747	even	4	inner	820.2.j.c.747.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.10	✓	240	1.1	even	1	trivial
820.2.j.c.483.69	yes	240	4.3	odd	2	inner
820.2.j.c.747.10	yes	240	820.747	even	4	inner
820.2.j.c.747.69	yes	240	205.132	odd	4	inner
820.2.s.c.583.52	yes	240	164.91	odd	4
820.2.s.c.583.111	yes	240	41.9	even	4
820.2.s.c.647.52	yes	240	5.2	odd	4
820.2.s.c.647.111	yes	240	20.7	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36551 + 0.367958i) q^{2} +0.984353i q^{3} +(1.72921 - 1.00490i) q^{4} +(0.127778 + 2.23241i) q^{5} +(-0.362201 - 1.34414i) q^{6} -2.37783 q^{7} +(-1.99149 + 2.00847i) q^{8} +2.03105 q^{9} +(-0.995917 - 3.00136i) q^{10} +(2.42433 + 2.42433i) q^{11} +(0.989175 + 1.70216i) q^{12} +0.537595 q^{13} +(3.24694 - 0.874943i) q^{14} +(-2.19748 + 0.125779i) q^{15} +(1.98036 - 3.47537i) q^{16} +5.98392 q^{17} +(-2.77341 + 0.747341i) q^{18} +(0.382078 + 0.382078i) q^{19} +(2.46431 + 3.73192i) q^{20} -2.34063i q^{21} +(-4.20249 - 2.41839i) q^{22} +(-5.12858 + 5.12858i) q^{23} +(-1.97705 - 1.96033i) q^{24} +(-4.96735 + 0.570507i) q^{25} +(-0.734089 + 0.197813i) q^{26} +4.95233i q^{27} +(-4.11178 + 2.38948i) q^{28} +(-1.46623 - 1.46623i) q^{29} +(2.95440 - 0.980334i) q^{30} +1.66059i q^{31} +(-1.42540 + 5.47433i) q^{32} +(-2.38640 + 2.38640i) q^{33} +(-8.17108 + 2.20183i) q^{34} +(-0.303835 - 5.30831i) q^{35} +(3.51212 - 2.04100i) q^{36} +(3.19027 - 3.19027i) q^{37} +(-0.662319 - 0.381141i) q^{38} +0.529183i q^{39} +(-4.73821 - 4.18919i) q^{40} +(5.91705 + 2.44714i) q^{41} +(0.861253 + 3.19614i) q^{42} +(-0.287011 - 0.287011i) q^{43} +(6.62840 + 1.75598i) q^{44} +(0.259523 + 4.53414i) q^{45} +(5.11601 - 8.89022i) q^{46} -3.64014i q^{47} +(3.42099 + 1.94937i) q^{48} -1.34592 q^{49} +(6.57302 - 2.60681i) q^{50} +5.89029i q^{51} +(0.929617 - 0.540229i) q^{52} -10.5416 q^{53} +(-1.82225 - 6.76243i) q^{54} +(-5.10234 + 5.72189i) q^{55} +(4.73543 - 4.77581i) q^{56} +(-0.376100 + 0.376100i) q^{57} +(2.54165 + 1.46263i) q^{58} -1.58121 q^{59} +(-3.67352 + 2.42575i) q^{60} -0.445242i q^{61} +(-0.611030 - 2.26755i) q^{62} -4.82949 q^{63} +(-0.0679329 - 7.99971i) q^{64} +(0.0686928 + 1.20013i) q^{65} +(2.38055 - 4.13674i) q^{66} +6.98956i q^{67} +(10.3475 - 6.01323i) q^{68} +(-5.04834 - 5.04834i) q^{69} +(2.36812 + 7.13672i) q^{70} +(-3.62995 - 3.62995i) q^{71} +(-4.04481 + 4.07931i) q^{72} +(-9.73449 + 9.73449i) q^{73} +(-3.18245 + 5.53023i) q^{74} +(-0.561580 - 4.88962i) q^{75} +(1.04464 + 0.276745i) q^{76} +(-5.76465 - 5.76465i) q^{77} +(-0.194717 - 0.722603i) q^{78} +(-9.18180 + 9.18180i) q^{79} +(8.01151 + 3.97690i) q^{80} +1.21831 q^{81} +(-8.98022 - 1.16435i) q^{82} +(10.8658 - 10.8658i) q^{83} +(-2.35209 - 4.04744i) q^{84} +(0.764613 + 13.3586i) q^{85} +(0.497523 + 0.286307i) q^{86} +(1.44328 - 1.44328i) q^{87} +(-9.69724 + 0.0411734i) q^{88} +(10.0408 + 10.0408i) q^{89} +(-2.02276 - 6.09590i) q^{90} -1.27831 q^{91} +(-3.71471 + 14.0221i) q^{92} -1.63461 q^{93} +(1.33942 + 4.97063i) q^{94} +(-0.804136 + 0.901778i) q^{95} +(-5.38867 - 1.40310i) q^{96} -14.1882 q^{97} +(1.83786 - 0.495241i) q^{98} +(4.92394 + 4.92394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more