LMFDB - Embedded newform 820.2.j.c.747.69

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			747.69
Character	$\chi$	$=$	820.747
Dual form			820.2.j.c.483.69

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.367958 + 1.36551i) q^{2} +0.984353i q^{3} +(-1.72921 + 1.00490i) q^{4} +(0.127778 - 2.23241i) q^{5} +(-1.34414 + 0.362201i) q^{6} +2.37783 q^{7} +(-2.00847 - 1.99149i) q^{8} +2.03105 q^{9} +(3.09539 - 0.646954i) q^{10} +(-2.42433 + 2.42433i) q^{11} +(-0.989175 - 1.70216i) q^{12} +0.537595 q^{13} +(0.874943 + 3.24694i) q^{14} +(2.19748 + 0.125779i) q^{15} +(1.98036 - 3.47537i) q^{16} +5.98392 q^{17} +(0.747341 + 2.77341i) q^{18} +(-0.382078 + 0.382078i) q^{19} +(2.02239 + 3.98872i) q^{20} +2.34063i q^{21} +(-4.20249 - 2.41839i) q^{22} +(5.12858 + 5.12858i) q^{23} +(1.96033 - 1.97705i) q^{24} +(-4.96735 - 0.570507i) q^{25} +(0.197813 + 0.734089i) q^{26} +4.95233i q^{27} +(-4.11178 + 2.38948i) q^{28} +(-1.46623 + 1.46623i) q^{29} +(0.636831 + 3.04696i) q^{30} +1.66059i q^{31} +(5.47433 + 1.42540i) q^{32} +(-2.38640 - 2.38640i) q^{33} +(2.20183 + 8.17108i) 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} +(-4.70247 + 4.22928i) q^{40} +(5.91705 - 2.44714i) q^{41} +(-3.19614 + 0.861253i) q^{42} +(0.287011 - 0.287011i) q^{43} +(1.75598 - 6.62840i) 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} +(-1.04875 - 6.99286i) q^{50} +5.89029i q^{51} +(-0.929617 + 0.540229i) q^{52} -10.5416 q^{53} +(-6.76243 + 1.82225i) q^{54} +(5.10234 + 5.72189i) q^{55} +(-4.77581 - 4.73543i) q^{56} +(-0.376100 - 0.376100i) q^{57} +(-2.54165 - 1.46263i) q^{58} +1.58121 q^{59} +(-3.92631 + 1.99075i) q^{60} +0.445242i q^{61} +(-2.26755 + 0.611030i) 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} +(7.36032 - 1.53835i) q^{70} +(3.62995 - 3.62995i) q^{71} +(-4.07931 - 4.04481i) q^{72} +(-9.73449 - 9.73449i) q^{73} +(-3.18245 + 5.53023i) q^{74} +(0.561580 - 4.88962i) q^{75} +(0.276745 - 1.04464i) q^{76} +(-5.76465 + 5.76465i) q^{77} +(-0.722603 + 0.194717i) q^{78} +(9.18180 + 9.18180i) q^{79} +(-7.50542 - 4.86505i) q^{80} +1.21831 q^{81} +(5.51881 + 7.17933i) 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} +(6.28689 - 1.31399i) q^{90} +1.27831 q^{91} +(-14.0221 - 3.71471i) q^{92} -1.63461 q^{93} +(4.97063 - 1.33942i) q^{94} +(0.804136 + 0.901778i) q^{95} +(-1.40310 + 5.38867i) q^{96} -14.1882 q^{97} +(-0.495241 - 1.83786i) 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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.367958	+	1.36551i	0.260186	+	0.965559i
$2$	0.367958	+	1.36551i	0.260186	+	0.965559i
$3$			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
$6$	−1.34414	+	0.362201i	−0.548743	+	0.147868i
$7$	2.37783			0.898736			0.449368	−	0.893347i	$-0.351649\pi$
$7$	2.37783			0.898736			0.449368	+	0.893347i	$0.351649\pi$
$8$	−2.00847	−	1.99149i	−0.710103	−	0.704098i
$9$	2.03105			0.677016
$10$	3.09539	−	0.646954i	0.978849	−	0.204585i
$11$	−2.42433	+	2.42433i	−0.730964	+	0.730964i	−0.970811	−	0.239847i	$-0.922903\pi$
$11$	−2.42433	+	2.42433i	−0.730964	+	0.730964i	0.239847	+	0.970811i	$0.422903\pi$
$12$	−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	$0.476248\pi$
$14$	0.874943	+	3.24694i	0.233838	+	0.867782i
$15$	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	$0.241536\pi$
$18$	0.747341	+	2.77341i	0.176150	+	0.653699i
$19$	−0.382078	+	0.382078i	−0.0876548	+	0.0876548i	−0.749575	−	0.661920i	$-0.769742\pi$
$19$	−0.382078	+	0.382078i	−0.0876548	+	0.0876548i	0.661920	+	0.749575i	$0.269742\pi$
$20$	2.02239	+	3.98872i	0.452221	+	0.891906i
$21$			2.34063i			0.510766i
$22$	−4.20249	−	2.41839i	−0.895975	−	0.515602i
$23$	5.12858	+	5.12858i	1.06938	+	1.06938i	0.997406	+	0.0719776i	$0.0229310\pi$
$23$	5.12858	+	5.12858i	1.06938	+	1.06938i	0.0719776	+	0.997406i	$0.477069\pi$
$24$	1.96033	−	1.97705i	0.400151	−	0.403563i
$25$	−4.96735	−	0.570507i	−0.993469	−	0.114101i
$26$	0.197813	+	0.734089i	0.0387942	+	0.143967i
$27$			4.95233i			0.953076i
$28$	−4.11178	+	2.38948i	−0.777053	+	0.451569i
$29$	−1.46623	+	1.46623i	−0.272271	+	0.272271i	−0.830014	−	0.557743i	$-0.811668\pi$
$29$	−1.46623	+	1.46623i	−0.272271	+	0.272271i	0.557743	+	0.830014i	$0.311668\pi$
$30$	0.636831	+	3.04696i	0.116269	+	0.556296i
$31$			1.66059i			0.298252i	0.988818	+	0.149126i	$0.0476459\pi$
$31$			1.66059i			0.298252i	−0.988818	+	0.149126i	$0.952354\pi$
$32$	5.47433	+	1.42540i	0.967733	+	0.251977i
$33$	−2.38640	−	2.38640i	−0.415419	−	0.415419i
$34$	2.20183	+	8.17108i	0.377611	+	1.40133i
$35$	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	0.918921	−	0.394443i	$-0.129062\pi$
$37$	3.19027	+	3.19027i	0.524478	+	0.524478i	−0.394443	+	0.918921i	$0.629062\pi$
$38$	−0.662319	−	0.381141i	−0.107442	−	0.0618293i
$39$			0.529183i			0.0847372i
$40$	−4.70247	+	4.22928i	−0.743526	+	0.668707i
$41$	5.91705	−	2.44714i	0.924089	−	0.382178i
$41$	5.91705	−	2.44714i	0.924089	−	0.382178i
$42$	−3.19614	+	0.861253i	−0.493175	+	0.132894i
$43$	0.287011	−	0.287011i	0.0437687	−	0.0437687i	−0.684884	−	0.728652i	$-0.740147\pi$
$43$	0.287011	−	0.287011i	0.0437687	−	0.0437687i	0.728652	+	0.684884i	$0.240147\pi$
$44$	1.75598	−	6.62840i	0.264724	−	0.999268i
$45$	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
$50$	−1.04875	−	6.99286i	−0.148315	−	0.988940i
$51$			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	$0.757698\pi$
$54$	−6.76243	+	1.82225i	−0.920251	+	0.247977i
$55$	5.10234	+	5.72189i	0.687999	+	0.771540i
$56$	−4.77581	−	4.73543i	−0.638195	−	0.632798i
$57$	−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	$-0.467179\pi$
$59$	1.58121			0.205856			0.102928	+	0.994689i	$0.467179\pi$
$60$	−3.92631	+	1.99075i	−0.506885	+	0.257005i
$61$			0.445242i			0.0570074i	0.999594	+	0.0285037i	$0.00907424\pi$
$61$			0.445242i			0.0570074i	−0.999594	+	0.0285037i	$0.990926\pi$
$62$	−2.26755	+	0.611030i	−0.287979	+	0.0776008i
$63$	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
$70$	7.36032	−	1.53835i	0.879727	−	0.183868i
$71$	3.62995	−	3.62995i	0.430796	−	0.430796i	−0.458103	−	0.888899i	$-0.651471\pi$
$71$	3.62995	−	3.62995i	0.430796	−	0.430796i	0.888899	+	0.458103i	$0.151471\pi$
$72$	−4.07931	−	4.04481i	−0.480751	−	0.476686i
$73$	−9.73449	−	9.73449i	−1.13934	−	1.13934i	−0.988569	−	0.150767i	$-0.951826\pi$
$73$	−9.73449	−	9.73449i	−1.13934	−	1.13934i	−0.150767	−	0.988569i	$-0.548174\pi$
$74$	−3.18245	+	5.53023i	−0.369952	+	0.642876i
$75$	0.561580	−	4.88962i	0.0648457	−	0.564605i
$76$	0.276745	−	1.04464i	0.0317448	−	0.119829i
$77$	−5.76465	+	5.76465i	−0.656943	+	0.656943i
$78$	−0.722603	+	0.194717i	−0.0818187	+	0.0220474i
$79$	9.18180	+	9.18180i	1.03303	+	1.03303i	0.999435	+	0.0335972i	$0.0106963\pi$
$79$	9.18180	+	9.18180i	1.03303	+	1.03303i	0.0335972	+	0.999435i	$0.489304\pi$
$80$	−7.50542	−	4.86505i	−0.839131	−	0.543929i
$81$	1.21831			0.135367
$82$	5.51881	+	7.17933i	0.609450	+	0.792824i
$83$	−10.8658	−	10.8658i	−1.19268	−	1.19268i	−0.976312	−	0.216366i	$-0.930579\pi$
$83$	−10.8658	−	10.8658i	−1.19268	−	1.19268i	−0.216366	−	0.976312i	$-0.569421\pi$
$84$	−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	0.0665422	−	0.997784i	$-0.478803\pi$
$89$	10.0408	−	10.0408i	1.06433	−	1.06433i	0.997784	−	0.0665422i	$-0.0211967\pi$
$90$	6.28689	−	1.31399i	0.662697	−	0.138507i
$91$	1.27831			0.134003
$92$	−14.0221	−	3.71471i	−1.46191	−	0.387285i
$93$	−1.63461			−0.169501
$94$	4.97063	−	1.33942i	0.512681	−	0.138151i
$95$	0.804136	+	0.901778i	0.0825026	+	0.0925205i
$96$	−1.40310	+	5.38867i	−0.143203	+	0.549979i
$97$	−14.1882			−1.44059			−0.720296	−	0.693666i	$-0.755994\pi$
$97$	−14.1882			−1.44059			−0.720296	+	0.693666i	$0.755994\pi$
$98$	−0.495241	−	1.83786i	−0.0500269	−	0.185652i
$99$	−4.92394	+	4.92394i	−0.494874	+	0.494874i
$100$	9.16290	−	4.00515i	0.916290	−	0.400515i
$101$	−1.29400	+	1.29400i	−0.128758	+	0.128758i	−0.768549	−	0.639791i	$-0.779021\pi$
$101$	−1.29400	+	1.29400i	−0.128758	+	0.128758i	0.639791	+	0.768549i	$0.279021\pi$
$102$	−8.04323	+	2.16738i	−0.796398	+	0.214603i
$103$	10.2881	−	10.2881i	1.01371	−	1.01371i	0.0138097	−	0.999905i	$-0.495604\pi$
$103$	10.2881	−	10.2881i	1.01371	−	1.01371i	0.999905	−	0.0138097i	$-0.00439591\pi$
$104$	−1.07975	−	1.07062i	−0.105878	−	0.104982i
$105$	5.22525	+	0.299081i	0.509932	+	0.0291873i
$106$	−3.87887	−	14.3946i	−0.376749	−	1.39813i
$107$	1.98848	−	1.98848i	0.192234	−	0.192234i	−0.604427	−	0.796661i	$-0.706598\pi$
$107$	1.98848	−	1.98848i	0.192234	−	0.192234i	0.796661	+	0.604427i	$0.206598\pi$
$108$	−4.97659	−	8.56363i	−0.478872	−	0.824036i
$109$	5.17177	+	5.17177i	0.495366	+	0.495366i	0.909992	−	0.414626i	$-0.136088\pi$
$109$	5.17177	+	5.17177i	0.495366	+	0.495366i	−0.414626	+	0.909992i	$0.636088\pi$
$110$	−5.93583	+	9.07269i	−0.565959	+	0.865047i
$111$	−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	0.320761	−	0.947160i	$-0.396061\pi$
$113$	13.4782	−	13.4782i	1.26792	−	1.26792i	0.947160	−	0.320761i	$-0.103939\pi$
$114$	0.375178	−	0.651956i	0.0351386	−	0.0610613i
$115$	12.1044	−	10.7938i	1.12875	−	1.00653i
$116$	1.06201	−	4.00882i	0.0986050	−	0.372210i
$117$	1.09188			0.100945
$118$	0.581820	+	2.15915i	0.0535609	+	0.198766i
$119$	14.2288			1.30435
$120$	−4.16310	−	4.62889i	−0.380037	−	0.422558i
$121$		−	0.754776i		−	0.0686160i
$122$	−0.607981	+	0.163830i	−0.0550440	+	0.0148325i
$123$	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
$126$	1.77705	+	6.59470i	0.158312	+	0.587503i
$127$	−14.0292	+	14.0292i	−1.24489	+	1.24489i	−0.286938	+	0.957949i	$0.592637\pi$
$127$	−14.0292	+	14.0292i	−1.24489	+	1.24489i	−0.957949	+	0.286938i	$0.907363\pi$
$128$	−10.8987	+	3.03632i	−0.963314	+	0.268376i
$129$	0.282520	+	0.282520i	0.0248745	+	0.0248745i
$130$	1.66407	−	0.347799i	0.145948	−	0.0305040i
$131$	10.8871			0.951209			0.475604	−	0.879659i	$-0.342229\pi$
$131$	10.8871			0.951209			0.475604	+	0.879659i	$0.342229\pi$
$132$	6.52468	+	1.72850i	0.567901	+	0.150447i
$133$	−0.908518	+	0.908518i	−0.0787785	+	0.0787785i
$134$	−9.54429	+	2.57187i	−0.824501	+	0.222175i
$135$	11.0556	+	0.632799i	0.951519	+	0.0544626i
$136$	−12.0185	−	11.9169i	−1.03058	−	1.02187i
$137$	−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	$-0.405087\pi$
$139$	6.92723			0.587560			0.293780	+	0.955873i	$0.405087\pi$
$140$	4.80891	+	9.48451i	0.406427	+	0.801588i
$141$	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
$148$	−8.72257	−	2.31076i	−0.716991	−	0.189944i
$149$	4.89996	+	4.89996i	0.401420	+	0.401420i	0.878733	−	0.477313i	$-0.158389\pi$
$149$	4.89996	+	4.89996i	0.401420	+	0.401420i	−0.477313	+	0.878733i	$0.658389\pi$
$150$	6.88345	−	1.03234i	0.562031	−	0.0842899i
$151$	−10.7169	+	10.7169i	−0.872129	+	0.872129i	−0.992704	−	0.120575i	$-0.961526\pi$
$151$	−10.7169	+	10.7169i	−0.872129	+	0.872129i	0.120575	+	0.992704i	$0.461526\pi$
$152$	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	$0.0708532\pi$
$157$			5.53219i			0.441517i	−0.975329	+	0.220758i	$0.929147\pi$
$158$	−9.15928	+	15.9163i	−0.728673	+	1.26623i
$159$		−	10.3767i		−	0.822922i
$160$	3.88158	−	12.0388i	0.306866	−	0.951753i
$161$	12.1949	+	12.1949i	0.961094	+	0.961094i
$162$	0.448286	+	1.66360i	0.0352207	+	0.130705i
$163$	−17.2200	−	17.2200i	−1.34877	−	1.34877i	−0.886994	−	0.461780i	$-0.847211\pi$
$163$	−17.2200	−	17.2200i	−1.34877	−	1.34877i	−0.461780	−	0.886994i	$-0.652789\pi$
$164$	−7.77272	+	10.1777i	−0.606948	+	0.794742i
$165$	−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	$-0.659493\pi$
$167$	−12.4152			−0.960716			−0.480358	+	0.877072i	$0.659493\pi$
$168$	4.66133	−	4.70109i	0.359630	−	0.362697i
$169$	−12.7110			−0.977769
$170$	18.5226	−	3.87132i	1.42062	−	0.296917i
$171$	−0.776020	+	0.776020i	−0.0593437	+	0.0593437i
$172$	−0.207886	+	0.784720i	−0.0158512	+	0.0598343i
$173$	9.63849	+	9.63849i	0.732801	+	0.732801i	0.971174	−	0.238373i	$-0.0766140\pi$
$173$	9.63849	+	9.63849i	0.732801	+	0.732801i	−0.238373	+	0.971174i	$0.576614\pi$
$174$	1.43974	−	2.50188i	0.109147	−	0.189667i
$175$	−11.8115	−	1.35657i	−0.892866	−	0.102547i
$176$	3.62440	+	13.2265i	0.273200	+	0.996984i
$177$			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	$-0.628298\pi$
$179$	7.05919	−	7.05919i	0.527629	−	0.527629i	0.919865	+	0.392236i	$0.128298\pi$
$180$	4.10758	+	8.10129i	0.306161	+	0.603835i
$181$	8.11635	−	8.11635i	0.603284	−	0.603284i	−0.337899	−	0.941182i	$-0.609716\pi$
$181$	8.11635	−	8.11635i	0.603284	−	0.603284i	0.941182	+	0.337899i	$0.109716\pi$
$182$	0.470365	+	1.74554i	0.0348658	+	0.129388i
$183$	−0.438275			−0.0323982
$184$	−0.0871007	−	20.5142i	−0.00642115	−	1.51232i
$185$	7.52966	−	6.71437i	0.553592	−	0.493650i
$186$	−0.601469	−	2.23207i	−0.0441018	−	0.163663i
$187$	−14.5070	+	14.5070i	−1.06086	+	1.06086i
$188$	3.65797	+	6.29458i	0.266785	+	0.459079i
$189$			11.7758i			0.856564i
$190$	−0.935495	+	1.42987i	−0.0678679	+	0.103734i
$191$	−7.89114	−	7.89114i	−0.570983	−	0.570983i	0.361420	−	0.932403i	$-0.382292\pi$
$191$	−7.89114	−	7.89114i	−0.570983	−	0.570983i	−0.932403	+	0.361420i	$0.882292\pi$
$192$	−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	$0.351561\pi$
$194$	−5.22066	−	19.3741i	−0.374822	−	1.39098i
$195$	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	0.236317	−	0.971676i	$-0.424060\pi$
$197$	16.9550	−	16.9550i	1.20799	−	1.20799i	0.971676	−	0.236317i	$-0.0759404\pi$
$198$	−8.53547	−	4.91186i	−0.606589	−	0.349071i
$199$	−1.48001	+	1.48001i	−0.104915	+	0.104915i	−0.757616	−	0.652701i	$-0.773636\pi$
$199$	−1.48001	+	1.48001i	−0.104915	+	0.104915i	0.652701	+	0.757616i	$0.273636\pi$
$200$	8.84062	+	11.0383i	0.625127	+	0.780523i
$201$	−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
$210$	1.51428	+	7.24516i	0.104495	+	0.499963i
$211$	−8.66840	−	8.66840i	−0.596758	−	0.596758i	0.342691	−	0.939448i	$-0.388662\pi$
$211$	−8.66840	−	8.66840i	−0.596758	−	0.596758i	−0.939448	+	0.342691i	$0.888662\pi$
$212$	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
$216$	9.86251	−	9.94662i	0.671059	−	0.676782i
$217$			3.94861i			0.268049i
$218$	−5.15909	+	8.96508i	−0.349418	+	0.607192i
$219$	9.58218	−	9.58218i	0.647504	−	0.647504i
$220$	−14.5730	−	4.76704i	−0.982508	−	0.321394i
$221$	3.21693			0.216394
$222$	−5.44370	−	3.13266i	−0.365357	−	0.210250i
$223$	−18.6741	−	18.6741i	−1.25051	−	1.25051i	−0.955491	−	0.295019i	$-0.904674\pi$
$223$	−18.6741	−	18.6741i	−1.25051	−	1.25051i	−0.295019	−	0.955491i	$-0.595326\pi$
$224$	13.0170	+	3.38936i	0.869737	+	0.226461i
$225$	−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	$-0.0375921\pi$
$228$	1.02830	+	0.272415i	0.0681008	+	0.0180411i
$229$	−0.695616	−	0.695616i	−0.0459676	−	0.0459676i	0.683749	−	0.729717i	$-0.260348\pi$
$229$	−0.695616	−	0.695616i	−0.0459676	−	0.0459676i	−0.729717	+	0.683749i	$0.760348\pi$
$230$	19.1929	+	12.5570i	1.26554	+	0.827986i
$231$	−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	$0.691275\pi$
$234$	0.401767	+	1.49097i	0.0262643	+	0.0974678i
$235$	−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
$238$	5.23559	+	19.4295i	0.339373	+	1.25942i
$239$	−2.76688	−	2.76688i	−0.178975	−	0.178975i	0.611934	−	0.790909i	$-0.290392\pi$
$239$	−2.76688	−	2.76688i	−0.178975	−	0.178975i	−0.790909	+	0.611934i	$0.790392\pi$
$240$	4.78893	−	7.38798i	0.309124	−	0.476892i
$241$		−	2.06854i		−	0.133246i	−0.997778	−	0.0666232i	$-0.978777\pi$
$241$		−	2.06854i		−	0.133246i	0.997778	−	0.0666232i	$-0.0212225\pi$
$242$	1.03065	−	0.277726i	0.0662527	−	0.0178529i
$243$			16.0562i			1.03001i
$244$	−0.447423	−	0.769918i	−0.0286433	−	0.0492890i
$245$	−0.171978	+	3.00464i	−0.0109873	+	0.191960i
$246$	−7.06699	+	5.43246i	−0.450575	+	0.346361i
$247$	−0.205403	+	0.205403i	−0.0130695	+	0.0130695i
$248$	3.30706	−	3.33526i	0.209998	−	0.211789i
$249$	10.6958	−	10.6958i	0.677819	−	0.677819i
$250$	−15.7450	+	1.44770i	−0.995800	+	0.0915606i
$251$	−19.4900			−1.23020			−0.615099	−	0.788450i	$-0.710884\pi$
$251$	−19.4900			−1.23020			−0.615099	+	0.788450i	$0.710884\pi$
$252$	−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	$-0.987527\pi$
$257$		−	1.25600i		−	0.0783474i	0.999232	−	0.0391737i	$-0.0124726\pi$
$258$	−0.281827	+	0.489738i	−0.0175458	+	0.0304898i
$259$	7.58594	+	7.58594i	0.471367	+	0.471367i
$260$	1.08723	+	2.14432i	0.0674271	+	0.132985i
$261$	−2.97798	+	2.97798i	−0.184332	+	0.184332i
$262$	4.00599	+	14.8664i	0.247491	+	0.918448i
$263$	−20.7013			−1.27649			−0.638247	−	0.769831i	$-0.720340\pi$
$263$	−20.7013			−1.27649			−0.638247	+	0.769831i	$0.720340\pi$
$264$	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	$-0.843845\pi$
$269$		−	15.4544i		−	0.942270i	0.882061	−	0.471135i	$-0.156155\pi$
$270$	3.20393	+	15.3294i	0.194985	+	0.932917i
$271$			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
$274$	−0.857265	−	3.18134i	−0.0517893	−	0.192192i
$275$	13.4256	−	10.6594i	0.809594	−	0.642786i
$276$	3.65659	−	13.8027i	0.220101	−	0.830826i
$277$	−8.00492	−	8.00492i	−0.480969	−	0.480969i	0.424472	−	0.905441i	$-0.360460\pi$
$277$	−8.00492	−	8.00492i	−0.480969	−	0.480969i	−0.905441	+	0.424472i	$0.860460\pi$
$278$	2.54893	+	9.45917i	0.152875	+	0.567323i
$279$			3.37275i			0.201921i
$280$	−11.1817	+	10.0565i	−0.668233	+	0.600991i
$281$	−0.765437	+	0.765437i	−0.0456621	+	0.0456621i	−0.729569	−	0.683907i	$-0.760279\pi$
$281$	−0.765437	+	0.765437i	−0.0456621	+	0.0456621i	0.683907	+	0.729569i	$0.260279\pi$
$282$	1.31846	+	4.89286i	0.0785132	+	0.291365i
$283$	2.54743	+	2.54743i	0.151429	+	0.151429i	0.778756	−	0.627327i	$-0.215851\pi$
$283$	2.54743	+	2.54743i	0.151429	+	0.151429i	−0.627327	+	0.778756i	$0.715851\pi$
$284$	−2.62923	+	9.92469i	−0.156016	+	0.588922i
$285$	−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
$288$	11.1186	+	2.89505i	0.655171	+	0.170593i
$289$	18.8073			1.10631
$290$	−3.58996	+	5.48712i	−0.210810	+	0.322215i
$291$		−	13.9662i		−	0.818713i
$292$	26.6152	+	7.05084i	1.55754	+	0.412619i
$293$		−	13.7106i		−	0.800981i	−0.916301	−	0.400490i	$-0.868840\pi$
$293$		−	13.7106i		−	0.800981i	0.916301	−	0.400490i	$-0.131160\pi$
$294$	1.80910	−	0.487492i	0.105509	−	0.0284311i
$295$	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
$300$	3.94248	+	9.01953i	0.227619	+	0.520743i
$301$	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
$304$	0.571211	+	2.08451i	0.0327612	+	0.119555i
$305$	0.993964	+	0.0568921i	0.0569142	+	0.00325763i
$306$	4.47203	+	16.5959i	0.255649	+	0.948722i
$307$	−14.1654	−	14.1654i	−0.808462	−	0.808462i	0.175939	−	0.984401i	$-0.443704\pi$
$307$	−14.1654	−	14.1654i	−0.808462	−	0.808462i	−0.984401	+	0.175939i	$0.943704\pi$
$308$	4.17542	−	15.7612i	0.237917	−	0.898078i
$309$	10.1271	+	10.1271i	0.576111	+	0.576111i
$310$	1.07433	+	5.14019i	0.0610177	+	0.291943i
$311$	−7.48403	−	7.48403i	−0.424380	−	0.424380i	0.462329	−	0.886709i	$-0.347014\pi$
$311$	−7.48403	−	7.48403i	−0.424380	−	0.424380i	−0.886709	+	0.462329i	$0.847014\pi$
$312$	1.05386	−	1.06285i	0.0596633	−	0.0601721i
$313$			6.82256i			0.385634i	0.981235	+	0.192817i	$0.0617624\pi$
$313$			6.82256i			0.385634i	−0.981235	+	0.192817i	$0.938238\pi$
$314$	−7.55423	+	2.03561i	−0.426310	+	0.114876i
$315$	0.617103	−	10.7814i	0.0347698	−	0.607465i
$316$	−25.1041	−	6.65051i	−1.41221	−	0.374120i
$317$		−	0.246649i		−	0.0138532i	−0.999976	−	0.00692659i	$-0.997795\pi$
$317$		−	0.246649i		−	0.0138532i	0.999976	−	0.00692659i	$-0.00220482\pi$
$318$	14.1694	−	3.81818i	0.794579	−	0.214113i
$319$		−	7.10924i		−	0.398041i
$320$	17.8673	+	0.870533i	0.998815	+	0.0486643i
$321$	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
$328$	−16.7577	−	6.86875i	−0.925289	−	0.379263i
$329$		−	8.65564i		−	0.477201i
$330$	−8.93073	−	5.84295i	−0.491621	−	0.321644i
$331$	3.89985	−	3.89985i	0.214355	−	0.214355i	−0.591759	−	0.806115i	$-0.701566\pi$
$331$	3.89985	−	3.89985i	0.214355	−	0.214355i	0.806115	+	0.591759i	$0.201566\pi$
$332$	29.7084	+	7.87027i	1.63046	+	0.431937i
$333$	6.47960	+	6.47960i	0.355080	+	0.355080i
$334$	−4.56827	−	16.9530i	−0.249965	−	0.927628i
$335$	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	−0.696064	−	0.717979i	$-0.745067\pi$
$337$	0.402306	−	0.402306i	0.0219150	−	0.0219150i	0.717979	+	0.696064i	$0.245067\pi$
$338$	−4.67712	−	17.3569i	−0.254402	−	0.944093i
$339$	13.2673	+	13.2673i	0.720580	+	0.720580i
$340$	12.1018	+	23.8682i	0.656315	+	1.29444i
$341$	−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	$-0.146775\pi$
$348$	3.94610	+	1.04539i	0.211533	+	0.0560389i
$349$	−17.0520			−0.912770			−0.456385	−	0.889782i	$-0.650856\pi$
$349$	−17.0520			−0.912770			−0.456385	+	0.889782i	$0.650856\pi$
$350$	−2.49374	−	16.6279i	−0.133296	−	0.888796i
$351$			2.66235i			0.142106i
$352$	−16.7272	+	9.81594i	−0.891564	+	0.523192i
$353$	9.50622	−	9.50622i	0.505965	−	0.505965i	−0.407320	−	0.913285i	$-0.633537\pi$
$353$	9.50622	−	9.50622i	0.505965	−	0.505965i	0.913285	+	0.407320i	$0.133537\pi$
$354$	−2.12537	+	0.572716i	−0.112962	+	0.0304395i
$355$	−7.63972	−	8.56738i	−0.405474	−	0.454709i
$356$	−7.27272	+	27.4528i	−0.385453	+	1.45499i
$357$			14.0061i			0.741283i
$358$	12.2369	+	7.04188i	0.646738	+	0.372175i
$359$	−11.3331			−0.598140			−0.299070	−	0.954231i	$-0.596676\pi$
$359$	−11.3331			−0.598140			−0.299070	+	0.954231i	$0.596676\pi$
$360$	−9.55095	+	8.58987i	−0.503379	+	0.452726i
$361$			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
$366$	−0.161267	−	0.598468i	−0.00842956	−	0.0312824i
$367$	−5.67851	−	5.67851i	−0.296416	−	0.296416i	0.543192	−	0.839608i	$-0.317215\pi$
$367$	−5.67851	−	5.67851i	−0.296416	−	0.296416i	−0.839608	+	0.543192i	$0.817215\pi$
$368$	27.9802	−	7.66729i	1.45857	−	0.399685i
$369$	12.0178	−	4.97025i	0.625623	−	0.258741i
$370$	11.9391	+	7.81119i	0.620685	+	0.406084i
$371$	−25.0661			−1.30137
$372$	2.82659	−	1.64262i	0.146552	−	0.0851658i
$373$	−12.4490	+	12.4490i	−0.644586	+	0.644586i	−0.951679	−	0.307093i	$-0.900644\pi$
$373$	−12.4490	+	12.4490i	−0.644586	+	0.644586i	0.307093	+	0.951679i	$0.400644\pi$
$374$	−25.1474	−	14.4714i	−1.30034	−	0.748300i
$375$	−10.8439	−	1.87847i	−0.559977	−	0.0970035i
$376$	−7.24930	+	7.31112i	−0.373854	+	0.377042i
$377$	−0.788236	+	0.788236i	−0.0405962	+	0.0405962i
$378$	−16.0799	+	4.33301i	−0.827062	+	0.222866i
$379$	−12.2160			−0.627496			−0.313748	−	0.949506i	$-0.601585\pi$
$379$	−12.2160			−0.627496			−0.313748	+	0.949506i	$0.601585\pi$
$380$	−2.29672	−	0.751292i	−0.117819	−	0.0385405i
$381$	−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	$-0.201288\pi$
$383$	31.5722			1.61327			0.806633	+	0.591053i	$0.201288\pi$
$384$	−2.98881	−	10.7281i	−0.152522	−	0.547467i
$385$	12.1325	+	13.6057i	0.618329	+	0.693410i
$386$	4.59672	+	17.0586i	0.233967	+	0.868258i
$387$	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	$0.733995\pi$
$390$	0.342357	+	1.63803i	0.0173359	+	0.0829449i
$391$	30.6890	+	30.6890i	1.55201	+	1.55201i
$392$	2.70324	+	2.68038i	0.136534	+	0.135380i
$393$			10.7167i			0.540588i
$394$	29.3909	+	16.9134i	1.48069	+	0.852085i
$395$	21.6708	−	19.3243i	1.09038	−	0.972313i
$396$	3.56648	−	13.4626i	0.179222	−	0.676521i
$397$			37.5243i			1.88329i	0.336607	+	0.941645i	$0.390721\pi$
$397$			37.5243i			1.88329i	−0.336607	+	0.941645i	$0.609279\pi$
$398$	−2.56555	−	1.47638i	−0.128599	−	0.0740044i
$399$	−0.894302	−	0.894302i	−0.0447711	−	0.0447711i
$400$	−11.8198	+	16.1335i	−0.590992	+	0.806677i
$401$		−	9.48157i		−	0.473487i	−0.971572	−	0.236744i	$-0.923920\pi$
$401$		−	9.48157i		−	0.473487i	0.971572	−	0.236744i	$-0.0760801\pi$
$402$	−2.53163	−	9.39495i	−0.126266	−	0.468577i
$403$			0.892727i			0.0444699i
$404$	0.937262	−	3.53794i	0.0466305	−	0.176019i
$405$	0.155673	−	2.71976i	0.00773544	−	0.135146i
$406$	−6.04361	−	3.47789i	−0.299940	−	0.172605i
$407$	−15.4686			−0.766749
$408$	11.7305	−	11.8305i	0.580744	−	0.585697i
$409$		−	32.4759i		−	1.60583i	−0.596093	−	0.802915i	$-0.703281\pi$
$409$		−	32.4759i		−	1.60583i	0.596093	−	0.802915i	$-0.296719\pi$
$410$	16.7324	−	11.4029i	0.826355	−	0.563149i
$411$		−	2.29333i		−	0.113122i
$412$	−7.45180	+	28.1288i	−0.367124	+	1.38580i
$413$	3.75985			0.185010
$414$	−10.3909	+	18.0565i	−0.510683	+	0.887427i
$415$	−25.6454	+	22.8686i	−1.25888	+	1.12258i
$416$	2.94297	+	0.766287i	0.144291	+	0.0375703i
$417$			6.81884i			0.333920i
$418$	2.52969	−	0.681668i	0.123731	−	0.0333415i
$419$			22.4633i			1.09740i	0.836019	+	0.548701i	$0.184877\pi$
$419$			22.4633i			1.09740i	−0.836019	+	0.548701i	$0.815123\pi$
$420$	−9.33611	+	4.73367i	−0.455556	+	0.230979i
$421$	0.180340	+	0.180340i	0.00878923	+	0.00878923i	0.711488	−	0.702699i	$-0.248022\pi$
$421$	0.180340	+	0.180340i	0.00878923	+	0.00878923i	−0.702699	+	0.711488i	$0.748022\pi$
$422$	8.64715	−	15.0264i	0.420936	−	0.731472i
$423$		−	7.39330i		−	0.359475i
$424$	21.1725	+	20.9935i	1.02823	+	1.01953i
$425$	−29.7242	−	3.41387i	−1.44184	−	0.165597i
$426$	−3.56439	+	6.19393i	−0.172695	+	0.300097i
$427$			1.05871i			0.0512346i
$428$	−1.44029	+	5.43673i	−0.0696189	+	0.262794i
$429$	−1.28292	−	1.28292i	−0.0619398	−	0.0619398i
$430$	0.702728	−	1.07409i	0.0338886	−	0.0517974i
$431$	−18.9292			−0.911787			−0.455893	−	0.890034i	$-0.650680\pi$
$431$	−18.9292			−0.911787			−0.455893	+	0.890034i	$0.650680\pi$
$432$	17.2112	+	9.80738i	0.828073	+	0.471858i
$433$	1.88134	−	1.88134i	0.0904115	−	0.0904115i	−0.660455	−	0.750866i	$-0.729636\pi$
$433$	1.88134	−	1.88134i	0.0904115	−	0.0904115i	0.750866	+	0.660455i	$0.229636\pi$
$434$	−5.39186	+	1.45293i	−0.258817	+	0.0697427i
$435$	−3.40643	+	3.03759i	−0.163326	+	0.145641i
$436$	−14.1402	−	3.74599i	−0.677193	−	0.179400i
$437$	−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	$-0.208927\pi$
$439$	3.81285	+	3.81285i	0.181978	+	0.181978i	−0.610239	+	0.792217i	$0.708927\pi$
$440$	1.14718	−	21.6535i	0.0546896	−	1.03229i
$441$	−2.73362			−0.130172
$442$	1.18369	+	4.39273i	0.0563026	+	0.208941i
$443$	1.00722	−	1.00722i	0.0478543	−	0.0478543i	−0.682775	−	0.730629i	$-0.739227\pi$
$443$	1.00722	−	1.00722i	0.0478543	−	0.0478543i	0.730629	+	0.682775i	$0.239227\pi$
$444$	2.27461	−	8.58609i	0.107948	−	0.407478i
$445$	−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	$0.306889\pi$
$450$	−2.13005	−	14.2028i	−0.100412	−	0.669529i
$451$	−8.41223	+	20.2776i	−0.396117	+	0.954834i
$452$	−9.76245	+	36.8509i	−0.459187	+	1.73332i
$453$	−10.5492	−	10.5492i	−0.495645	−	0.495645i
$454$	4.84812	−	1.30641i	0.227533	−	0.0613127i
$455$	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
$460$	−10.0845	+	30.8285i	−0.470192	+	1.43739i
$461$	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	$-0.0692203\pi$
$464$	2.19202	+	7.99932i	0.101762	+	0.371359i
$465$	−0.208867	+	3.64913i	−0.00968599	+	0.169224i
$466$	−6.35120	−	23.5695i	−0.294214	−	1.09184i
$467$	−5.74357	+	5.74357i	−0.265781	+	0.265781i	−0.827397	−	0.561617i	$-0.810179\pi$
$467$	−5.74357	+	5.74357i	−0.265781	+	0.265781i	0.561617	+	0.827397i	$0.310179\pi$
$468$	−1.88810	+	1.09723i	−0.0872773	+	0.0507195i
$469$			16.6200i			0.767440i
$470$	−2.35500	−	11.2677i	−0.108628	−	0.519738i
$471$	−5.44563			−0.250921
$472$	−3.17582	−	3.14897i	−0.146179	−	0.144943i
$473$			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	$-0.0233297\pi$
$479$	20.2247	+	20.2247i	0.924089	+	0.924089i	−0.0732267	+	0.997315i	$0.523330\pi$
$480$	11.8505	+	3.82084i	0.540897	+	0.174397i
$481$	1.71508	+	1.71508i	0.0782007	+	0.0782007i
$482$	2.82460	−	0.761136i	0.128657	−	0.0346688i
$483$	−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
$486$	−21.9249	+	5.90802i	−0.994533	+	0.267993i
$487$	−20.8030	−	20.8030i	−0.942672	−	0.942672i	0.0557715	−	0.998444i	$-0.482238\pi$
$487$	−20.8030	−	20.8030i	−0.942672	−	0.942672i	−0.998444	+	0.0557715i	$0.982238\pi$
$488$	0.886695	−	0.894257i	0.0401388	−	0.0404811i
$489$	16.9506	−	16.9506i	0.766531	−	0.766531i
$490$	−4.16614	+	0.870746i	−0.188207	+	0.0393363i
$491$			10.3411i			0.466686i	0.972394	+	0.233343i	$0.0749665\pi$
$491$			10.3411i			0.466686i	−0.972394	+	0.233343i	$0.925033\pi$
$492$	−10.0184	−	7.65111i	−0.451665	−	0.344938i
$493$	−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	$-0.0171675\pi$
$499$	21.1016	+	21.1016i	0.944639	+	0.944639i	−0.0539071	+	0.998546i	$0.517167\pi$
$500$	−7.77034	−	20.9672i	−0.347500	−	0.937680i
$501$		−	12.2209i		−	0.545991i
$502$	−7.17151	−	26.6137i	−0.320080	−	1.18783i
$503$			37.1237i			1.65526i	0.561272	+	0.827631i	$0.310312\pi$
$503$			37.1237i			1.65526i	−0.561272	+	0.827631i	$0.689688\pi$
$504$	−9.69991	−	9.61789i	−0.432068	−	0.428415i
$505$	2.72340	+	3.05409i	0.121190	+	0.135905i
$506$	−9.14994	−	33.9557i	−0.406765	−	1.50952i
$507$		−	12.5121i		−	0.555682i
$508$	10.1615	−	38.3573i	0.450845	−	1.70183i
$509$	−24.2891	−	24.2891i	−1.07660	−	1.07660i	−0.996812	−	0.0797834i	$-0.974577\pi$
$509$	−24.2891	−	24.2891i	−1.07660	−	1.07660i	−0.0797834	−	0.996812i	$-0.525423\pi$
$510$	3.81075	+	18.2328i	0.168743	+	0.807360i
$511$	−23.1470	−	23.1470i	−1.02396	−	1.02396i
$512$	15.7949	−	16.2025i	0.698043	−	0.716056i
$513$	−1.89218	−	1.89218i	−0.0835417	−	0.0835417i
$514$	1.71508	−	0.462157i	0.0756490	−	0.0203849i
$515$	−21.6527	−	24.2818i	−0.954130	−	1.06999i
$516$	−0.772441	−	0.204633i	−0.0340048	−	0.00900848i
$517$	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
$520$	−2.52802	+	2.27364i	−0.110861	+	0.0997056i
$521$	9.21764	+	9.21764i	0.403832	+	0.403832i	0.879581	−	0.475749i	$-0.157823\pi$
$521$	9.21764	+	9.21764i	0.403832	+	0.403832i	−0.475749	+	0.879581i	$0.657823\pi$
$522$	−5.16221	−	2.97067i	−0.225944	−	0.130023i
$523$	3.29111	+	3.29111i	0.143910	+	0.143910i	0.775391	−	0.631481i	$-0.217553\pi$
$523$	3.29111	+	3.29111i	0.143910	+	0.143910i	−0.631481	+	0.775391i	$0.717553\pi$
$524$	−18.8261	+	10.9404i	−0.822421	+	0.477934i
$525$	1.33534	−	11.6267i	0.0582792	−	0.507431i
$526$	−7.61720	−	28.2677i	−0.332126	−	1.23253i
$527$			9.93686i			0.432857i
$528$	−13.0195	+	3.56769i	−0.566603	+	0.155264i
$529$			29.6048i			1.28716i
$530$	−32.6304	+	6.81993i	−1.41737	+	0.296239i
$531$	3.21152			0.139368
$532$	0.658053	−	2.48399i	0.0285302	−	0.107695i
$533$	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
$536$	13.9196	−	14.0383i	0.601237	−	0.606364i
$537$	6.94874	+	6.94874i	0.299860	+	0.299860i
$538$	21.1030	−	5.68656i	0.909816	−	0.245165i
$539$	3.26295	−	3.26295i	0.140545	−	0.140545i
$540$	−19.7535	+	10.0156i	−0.850054	+	0.431001i
$541$			7.48478i			0.321796i	0.986971	+	0.160898i	$0.0514390\pi$
$541$			7.48478i			0.321796i	−0.986971	+	0.160898i	$0.948561\pi$
$542$	−1.10246	+	0.297075i	−0.0473546	+	0.0127605i
$543$	7.98936	+	7.98936i	0.342856	+	0.342856i
$544$	32.7579	+	8.52947i	1.40448	+	0.365698i
$545$	12.2064	−	10.8847i	0.522864	−	0.466249i
$546$	−1.71823	+	0.463005i	−0.0735334	+	0.0198148i
$547$			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
$550$	19.4955	+	14.4105i	0.831292	+	0.614466i
$551$		−	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	$0.145462\pi$
$558$	−4.60551	+	1.24103i	−0.194967	+	0.0525370i
$559$	0.154296	−	0.154296i	0.00652601	−	0.00652601i
$560$	−17.8466	−	11.5683i	−0.754157	−	0.488849i
$561$	−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	$0.327569\pi$
$570$	−1.40750	−	0.920857i	−0.0589535	−	0.0385705i
$571$	22.3457	−	22.3457i	0.935138	−	0.935138i	−0.0628830	−	0.998021i	$-0.520030\pi$
$571$	22.3457	−	22.3457i	0.935138	−	0.935138i	0.998021	+	0.0628830i	$0.0200295\pi$
$572$	0.944006	−	3.56339i	0.0394709	−	0.148993i
$573$	7.76767	−	7.76767i	0.324499	−	0.324499i
$574$	13.1228	+	17.0712i	0.547735	+	0.712540i
$575$	−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	$0.266311\pi$
$577$			35.6660i			1.48479i	−0.669960	+	0.742397i	$0.733689\pi$
$578$	6.92030	+	25.6815i	0.287847	+	1.06821i
$579$			12.2970i			0.511047i
$580$	−8.81365	−	2.88308i	−0.365967	−	0.119713i
$581$	−25.8371	−	25.8371i	−1.07190	−	1.07190i
$582$	19.0709	−	5.13898i	0.790515	−	0.213017i
$583$	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
$586$	18.7219	−	5.04492i	0.773394	−	0.208404i
$587$	7.69367			0.317552			0.158776	−	0.987315i	$-0.449245\pi$
$587$	7.69367			0.317552			0.158776	+	0.987315i	$0.449245\pi$
$588$	1.33135	+	2.29096i	0.0549038	+	0.0944776i
$589$	−0.634477	−	0.634477i	−0.0261432	−	0.0261432i
$590$	4.89447	−	1.02297i	0.201502	−	0.0421150i
$591$	16.6897	+	16.6897i	0.686522	+	0.686522i
$592$	17.4053	−	4.76950i	0.715352	−	0.196025i
$593$			39.9129i			1.63903i	0.573059	+	0.819514i	$0.305757\pi$
$593$			39.9129i			1.63903i	−0.573059	+	0.819514i	$0.694243\pi$
$594$	11.9766	−	20.8121i	0.491408	−	0.853932i
$595$	1.81812	−	31.7645i	0.0745357	−	1.30222i
$596$	−13.3970	−	3.54911i	−0.548764	−	0.145377i
$597$	−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	$-0.434004\pi$
$599$	10.0761			0.411698			0.205849	+	0.978584i	$0.434004\pi$
$600$	−10.8656	+	8.70230i	−0.443584	+	0.355270i
$601$	−6.43189	+	6.43189i	−0.262362	+	0.262362i	−0.826013	−	0.563651i	$-0.809396\pi$
$601$	−6.43189	+	6.43189i	−0.262362	+	0.262362i	0.563651	+	0.826013i	$0.309396\pi$
$602$	1.18303	+	0.680790i	0.0482165	+	0.0277469i
$603$			14.1961i			0.578111i
$604$	7.76241	−	29.3012i	0.315848	−	1.19225i
$605$	−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	$-0.120173\pi$
$607$	13.8202	+	13.8202i	0.560945	+	0.560945i	−0.368631	+	0.929576i	$0.620173\pi$
$608$	−2.63623	+	1.54701i	−0.106913	+	0.0627394i
$609$	−3.43189	−	3.43189i	−0.139067	−	0.139067i
$610$	0.288051	+	1.37820i	0.0116628	+	0.0558016i
$611$		−	1.95692i		−	0.0791685i
$612$	−21.0162	+	12.2132i	−0.849531	+	0.493688i
$613$	26.0622	+	26.0622i	1.05264	+	1.05264i	0.998535	+	0.0541082i	$0.0172316\pi$
$613$	26.0622	+	26.0622i	1.05264	+	1.05264i	0.0541082	+	0.998535i	$0.482768\pi$
$614$	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	−0.837255	−	0.546813i	$-0.815841\pi$
$617$	−7.21441	+	7.21441i	−0.290441	+	0.290441i	0.546813	+	0.837255i	$0.315841\pi$
$618$	−10.1023	+	17.5550i	−0.406373	+	0.706164i
$619$	−2.19204			−0.0881055			−0.0440528	−	0.999029i	$-0.514027\pi$
$619$	−2.19204			−0.0881055			−0.0440528	+	0.999029i	$0.514027\pi$
$620$	−6.62365	+	3.35838i	−0.266012	+	0.134876i
$621$	−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
$626$	−9.31625	+	2.51042i	−0.372352	+	0.100337i
$627$	1.82358			0.0728269
$628$	−5.55929	−	9.56633i	−0.221840	−	0.381738i
$629$	19.0903	+	19.0903i	0.761182	+	0.761182i
$630$	14.9492	−	3.12446i	0.595589	−	0.124481i
$631$			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
$634$	0.336801	−	0.0907566i	0.0133761	−	0.00360440i
$635$	29.5263	+	33.1115i	1.17172	+	1.31399i
$636$	10.4275	+	17.9434i	0.413477	+	0.711504i
$637$	−0.723558			−0.0286684
$638$	9.70770	−	2.61590i	0.384332	−	0.103565i
$639$	7.37261	−	7.37261i	0.291656	−	0.291656i
$640$	5.38572	+	24.7183i	0.212889	+	0.977076i
$641$	3.83627	−	3.83627i	0.151523	−	0.151523i	−0.627275	−	0.778798i	$-0.715830\pi$
$641$	3.83627	−	3.83627i	0.151523	−	0.151523i	0.778798	+	0.627275i	$0.215830\pi$
$642$	−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	$-0.309098\pi$
$644$	−33.3423	−	8.83295i	−1.31387	−	0.348067i
$645$	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	$-0.215031\pi$
$647$	3.94395	+	3.94395i	0.155053	+	0.155053i	−0.625318	+	0.780370i	$0.715031\pi$
$648$	−2.44694	−	2.42625i	−0.0961247	−	0.0953119i
$649$	−3.83338	+	3.83338i	−0.150473	+	0.150473i
$650$	−0.563801	−	3.75933i	−0.0221141	−	0.147453i
$651$	−3.88683			−0.152337
$652$	47.0814	+	12.4727i	1.84385	+	0.488469i
$653$	−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
$656$	3.21318	−	25.4101i	0.125454	−	0.992099i
$657$	−19.7712	−	19.7712i	−0.771349	−	0.771349i
$658$	11.8193	−	3.18491i	0.460765	−	0.124161i
$659$	−15.9623	−	15.9623i	−0.621802	−	0.621802i	0.324190	−	0.945992i	$-0.394908\pi$
$659$	−15.9623	−	15.9623i	−0.621802	−	0.621802i	−0.945992	+	0.324190i	$0.894908\pi$
$660$	4.69245	−	14.3449i	0.182653	−	0.558376i
$661$			36.0355i			1.40162i	0.713348	+	0.700810i	$0.247178\pi$
$661$			36.0355i			1.40162i	−0.713348	+	0.700810i	$0.752822\pi$
$662$	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
$670$	4.52192	+	21.6354i	0.174697	+	0.835850i
$671$	−1.07941	−	1.07941i	−0.0416703	−	0.0416703i
$672$	−3.33633	+	12.8133i	−0.128702	+	0.494286i
$673$		−	33.8584i		−	1.30515i	−0.757725	−	0.652574i	$-0.773689\pi$
$673$		−	33.8584i		−	1.30515i	0.757725	−	0.652574i	$-0.226311\pi$
$674$	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	0.168877	−	0.985637i	$-0.445986\pi$
$677$	30.0396	−	30.0396i	1.15451	−	1.15451i	0.985637	−	0.168877i	$-0.0540140\pi$
$678$	−13.2348	+	22.9984i	−0.508278	+	0.883248i
$679$	−33.7371			−1.29471
$680$	−28.1392	+	25.3077i	−1.07909	+	0.970504i
$681$	3.49487			0.133924
$682$	4.01596	−	6.97864i	0.153779	−	0.267226i
$683$	9.38995			0.359296			0.179648	−	0.983731i	$-0.442504\pi$
$683$	9.38995			0.359296			0.179648	+	0.983731i	$0.442504\pi$
$684$	0.562082	−	2.12172i	0.0214918	−	0.0811262i
$685$	−0.297696	+	5.20105i	−0.0113744	+	0.198722i
$686$	−7.30220	−	27.0987i	−0.278799	−	1.03463i
$687$	0.684731	−	0.684731i	0.0261241	−	0.0261241i
$688$	−0.429084	−	1.56585i	−0.0163587	−	0.0596976i
$689$	−5.66711			−0.215900
$690$	−12.3605	+	18.8926i	−0.470558	+	0.719230i
$691$	12.8603	+	12.8603i	0.489230	+	0.489230i	0.908063	−	0.418833i	$-0.137561\pi$
$691$	12.8603	+	12.8603i	0.489230	+	0.489230i	−0.418833	+	0.908063i	$0.637561\pi$
$692$	−26.3527	−	6.98130i	−1.00178	−	0.265389i
$693$	−11.7083	+	11.7083i	−0.444761	+	0.444761i
$694$	22.6355	−	6.09951i	0.859232	−	0.231534i
$695$	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
$698$	−6.27441	−	23.2845i	−0.237490	−	0.881333i
$699$		−	16.9906i		−	0.642643i
$700$	21.7878	−	9.52358i	0.823503	−	0.359957i
$701$	4.43158			0.167378			0.0836892	−	0.996492i	$-0.473330\pi$
$701$	4.43158			0.167378			0.0836892	+	0.996492i	$0.473330\pi$
$702$	−3.63545	+	0.979633i	−0.137211	+	0.0369739i
$703$	−2.43787			−0.0919460
$704$	−19.5587	−	19.2293i	−0.737144	−	0.724730i
$705$	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	0.00834935	−	0.999965i	$-0.497342\pi$
$709$	26.8484	−	26.8484i	1.00831	−	1.00831i	0.999965	−	0.00834935i	$-0.00265771\pi$
$710$	8.88771	−	13.5845i	0.333550	−	0.509818i
$711$	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
$714$	−19.1254	+	5.15367i	−0.715752	+	0.192871i
$715$	2.74299	+	3.07606i	0.102582	+	0.115038i
$716$	−5.11308	+	19.3006i	−0.191085	+	0.721298i
$717$	2.72359	−	2.72359i	0.101714	−	0.101714i
$718$	−4.17012	−	15.4755i	−0.155628	−	0.577540i
$719$	33.9622	−	33.9622i	1.26657	−	1.26657i	0.318729	−	0.947846i	$-0.396744\pi$
$719$	33.9622	−	33.9622i	1.26657	−	1.26657i	0.947846	−	0.318729i	$-0.103256\pi$
$720$	−15.2439	−	9.88116i	−0.568105	−	0.368249i
$721$	24.4633	−	24.4633i	0.911062	−	0.911062i
$722$	−25.5459	+	6.88378i	−0.950721	+	0.256188i
$723$	2.03617			0.0757261
$724$	−5.87879	+	22.1910i	−0.218484	+	0.824723i
$725$	8.11974	−	6.44676i	0.301560	−	0.239427i
$726$	0.273380	+	1.01452i	0.0101461	+	0.0376525i
$727$	12.1156			0.449344			0.224672	−	0.974434i	$-0.427869\pi$
$727$	12.1156			0.449344			0.224672	+	0.974434i	$0.427869\pi$
$728$	−2.56745	−	2.54574i	−0.0951562	−	0.0943515i
$729$	−12.1501			−0.450003
$730$	−36.4298	−	23.8343i	−1.34833	−	0.882147i
$731$	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	0.148082	−	0.988975i	$-0.452690\pi$
$733$	−22.7663	−	22.7663i	−0.840893	−	0.840893i	−0.988975	+	0.148082i	$0.952690\pi$
$734$	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
$738$	11.2090	+	14.5816i	0.412608	+	0.536755i
$739$	−45.6752			−1.68019			−0.840095	−	0.542440i	$-0.817501\pi$
$739$	−45.6752			−1.68019			−0.840095	+	0.542440i	$0.817501\pi$
$740$	−6.27313	+	19.1771i	−0.230605	+	0.704965i
$741$	−0.202189	−	0.202189i	−0.00742762	−	0.00742762i
$742$	−9.22330	−	34.2280i	−0.338598	−	1.25655i
$743$	−29.1657	+	29.1657i	−1.06999	+	1.06999i	−0.0726284	+	0.997359i	$0.523139\pi$
$743$	−29.1657	+	29.1657i	−1.06999	+	1.06999i	−0.997359	+	0.0726284i	$0.976861\pi$
$744$	3.28307	+	3.25531i	0.120363	+	0.119346i
$745$	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
$748$	10.5076	−	39.6638i	0.384197	−	1.45025i
$749$	4.72828	−	4.72828i	0.172767	−	0.172767i
$750$	−1.42505	−	15.4986i	−0.0520354	−	0.565929i
$751$	0.346967	−	0.346967i	0.0126610	−	0.0126610i	−0.700748	−	0.713409i	$-0.747150\pi$
$751$	0.346967	−	0.346967i	0.0126610	−	0.0126610i	0.713409	+	0.700748i	$0.247150\pi$
$752$	−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	$0.630511\pi$
$758$	−4.49500	−	16.6811i	−0.163266	−	0.605884i
$759$		−	24.4777i		−	0.888484i
$760$	0.180797	−	3.41263i	0.00655819	−	0.123789i
$761$	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
$764$	21.5753	+	5.71567i	0.780566	+	0.206786i
$765$	1.55297	−	27.1319i	0.0561476	−	0.980958i
$766$	11.6173	+	43.1121i	0.419749	+	1.55770i
$767$	0.850051			0.0306936
$768$	13.5496	−	8.02875i	0.488928	−	0.289713i
$769$			4.51666i			0.162875i	0.996678	+	0.0814375i	$0.0259511\pi$
$769$			4.51666i			0.162875i	−0.996678	+	0.0814375i	$0.974049\pi$
$770$	−14.1144	+	21.5733i	−0.508648	+	0.777449i
$771$	1.23635			0.0445261
$772$	−21.6022	+	12.5537i	−0.777479	+	0.451817i
$773$		−	19.2603i		−	0.692743i	−0.938097	−	0.346372i	$-0.887414\pi$
$773$		−	19.2603i		−	0.692743i	0.938097	−	0.346372i	$-0.112586\pi$
$774$	1.01049	+	0.581503i	0.0363214	+	0.0209017i
$775$	0.947380	−	8.24875i	0.0340309	−	0.296304i
$776$	28.4966	+	28.2556i	1.02297	+	1.01432i
$777$	−7.46724	+	7.46724i	−0.267886	+	0.267886i
$778$	−9.73451	−	36.1251i	−0.348999	−	1.29515i
$779$	−1.32578	+	3.19578i	−0.0475010	+	0.114501i
$780$	−2.11077	+	1.07022i	−0.0755776	+	0.0383199i
$781$			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
$786$	−14.6338	+	3.94331i	−0.521969	+	0.140653i
$787$	−22.9556	−	22.9556i	−0.818277	−	0.818277i	0.167581	−	0.985858i	$-0.446404\pi$
$787$	−22.9556	−	22.9556i	−0.818277	−	0.818277i	−0.985858	+	0.167581i	$0.946404\pi$
$788$	−12.2807	+	46.3568i	−0.437483	+	1.65139i
$789$		−	20.3774i		−	0.725453i
$790$	34.3615	+	22.4811i	1.22253	+	0.799840i
$791$	32.0489	−	32.0489i	1.13953	−	1.13953i
$792$	19.6956	−	0.0836251i	0.699852	−	0.00297149i
$793$			0.239360i			0.00849992i
$794$	−51.2397	+	13.8074i	−1.81843	+	0.490006i
$795$	−23.1650	−	1.32591i	−0.821577	−	0.0470251i
$796$	1.07200	−	4.04652i	0.0379959	−	0.143425i
$797$	32.4093	+	32.4093i	1.14800	+	1.14800i	0.986946	+	0.161052i	$0.0514887\pi$
$797$	32.4093	+	32.4093i	1.14800	+	1.14800i	0.161052	+	0.986946i	$0.448511\pi$
$798$	0.892109	−	1.55024i	0.0315803	−	0.0548779i
$799$		−	21.7823i		−	0.770602i
$800$	−26.3797	−	10.2036i	−0.932662	−	0.360751i
$801$	20.3934	−	20.3934i	0.720566	−	0.720566i
$802$	12.9471	−	3.48882i	0.457179	−	0.123195i
$803$	47.1993			1.66563
$804$	11.8973	−	6.91390i	0.419586	−	0.243834i
$805$	28.7823	−	25.6659i	1.01444	−	0.904602i
$806$	−1.21902	+	0.328486i	−0.0429383	+	0.0115704i
$807$	15.2126			0.535507
$808$	5.17595	−	0.0219765i	0.182089	−	0.000773130i
$809$	29.6375	−	29.6375i	1.04200	−	1.04200i	0.0429204	−	0.999078i	$-0.486334\pi$
$809$	29.6375	−	29.6375i	1.04200	−	1.04200i	0.999078	−	0.0429204i	$-0.0136662\pi$
$810$	3.77114	−	0.788188i	0.132504	−	0.0276941i
$811$	−11.2130			−0.393743			−0.196872	−	0.980429i	$-0.563078\pi$
$811$	−11.2130			−0.393743			−0.196872	+	0.980429i	$0.563078\pi$
$812$	2.52528	−	9.53231i	0.0886199	−	0.334518i
$813$	−0.794728			−0.0278723
$814$	−5.69179	−	21.1224i	−0.199497	−	0.740341i
$815$	−40.6425	+	36.2418i	−1.42365	+	1.26950i
$816$	20.4709	+	11.6649i	0.716626	+	0.408352i
$817$			0.219321i			0.00767308i
$818$	44.3461	−	11.9498i	1.55052	−	0.417814i
$819$	2.59631			0.0907225
$820$	21.7276	+	18.6524i	0.758760	+	0.651371i
$821$	1.27850			0.0446201			0.0223100	−	0.999751i	$-0.492898\pi$
$821$	1.27850			0.0446201			0.0223100	+	0.999751i	$0.492898\pi$
$822$	3.13156	−	0.843852i	0.109226	−	0.0294327i
$823$		−	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
$826$	1.38347	+	5.13410i	0.0481371	+	0.178638i
$827$	−5.58556			−0.194229			−0.0971145	−	0.995273i	$-0.530961\pi$
$827$	−5.58556			−0.194229			−0.0971145	+	0.995273i	$0.530961\pi$
$828$	−28.4796	−	7.54476i	−0.989735	−	0.262198i
$829$	−29.7227			−1.03231			−0.516156	−	0.856495i	$-0.672638\pi$
$829$	−29.7227			−1.03231			−0.516156	+	0.856495i	$0.672638\pi$
$830$	−40.6636	−	26.6043i	−1.41146	−	0.923448i
$831$	7.87967	−	7.87967i	0.273343	−	0.273343i
$832$	0.0365204	+	4.30061i	0.00126612	+	0.149097i
$833$	−8.05385			−0.279050
$834$	−9.31116	+	2.50905i	−0.322419	+	0.0868812i
$835$	−1.58639	+	27.7158i	−0.0548992	+	0.959146i
$836$	1.86164	+	3.20349i	0.0643863	+	0.110795i
$837$	−8.22381			−0.284256
$838$	−30.6737	+	8.26554i	−1.05961	+	0.285529i
$839$	−27.2272	+	27.2272i	−0.939986	+	0.939986i	−0.998298	−	0.0583124i	$-0.981428\pi$
$839$	−27.2272	+	27.2272i	−0.939986	+	0.939986i	0.0583124	+	0.998298i	$0.481428\pi$
$840$	−9.89915	−	11.0067i	−0.341553	−	0.379768i
$841$			24.7004i			0.851737i
$842$	−0.179898	+	0.312613i	−0.00619968	+	0.0107733i
$843$	−0.753460	−	0.753460i	−0.0259505	−	0.0259505i
$844$	23.7004	+	6.27865i	0.815801	+	0.216120i
$845$	−1.62419	+	28.3762i	−0.0558737	+	0.976171i
$846$	10.0956	−	2.72043i	0.347094	−	0.0935302i
$847$		−	1.79473i		−	0.0616676i
$848$	−20.8761	+	36.6359i	−0.716889	+	1.25808i
$849$	−2.50757	+	2.50757i	−0.0860597	+	0.0860597i
$850$	−6.27561	−	41.8447i	−0.215252	−	1.43526i
$851$			32.7232i			1.12174i
$852$	−9.76940	−	2.58809i	−0.334694	−	0.0886664i
$853$	−4.97627	−	4.97627i	−0.170384	−	0.170384i	0.616764	−	0.787148i	$-0.288443\pi$
$853$	−4.97627	−	4.97627i	−0.170384	−	0.170384i	−0.787148	+	0.616764i	$0.788443\pi$
$854$	−1.44568	+	0.389561i	−0.0494700	+	0.0133305i
$855$	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	0.0558611	−	0.998439i	$-0.482210\pi$
$857$	−27.5935	−	27.5935i	−0.942577	−	0.942577i	−0.998439	+	0.0558611i	$0.982210\pi$
$858$	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	$0.833407\pi$
$860$	1.72526	+	0.564358i	0.0588307	+	0.0192444i
$861$	5.72783	+	13.8496i	0.195204	+	0.471993i
$862$	−6.96515	−	25.8479i	−0.237234	−	0.880384i
$863$	−15.0652	+	15.0652i	−0.512825	+	0.512825i	−0.915391	−	0.402566i	$-0.868118\pi$
$863$	−15.0652	+	15.0652i	−0.512825	+	0.512825i	0.402566	+	0.915391i	$0.368118\pi$
$864$	−7.05904	+	27.1107i	−0.240154	+	0.922323i
$865$	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
$870$	−5.40127	−	3.53379i	−0.183120	−	0.119807i
$871$			3.75755i			0.127320i
$872$	−0.0878342	−	20.6869i	−0.00297444	−	0.700547i
$873$	−28.8169			−0.975305
$874$	−1.44204	−	5.35147i	−0.0487779	−	0.181016i
$875$	−4.53768	+	26.1948i	−0.153401	+	0.885547i
$876$	−6.94051	+	26.1988i	−0.234498	+	0.885174i
$877$	−1.18587	−	1.18587i	−0.0400442	−	0.0400442i	0.686801	−	0.726845i	$-0.259014\pi$
$877$	−1.18587	−	1.18587i	−0.0400442	−	0.0400442i	−0.726845	+	0.686801i	$0.759014\pi$
$878$	−3.80350	+	6.60945i	−0.128362	+	0.223058i
$879$	13.4961			0.455211
$880$	29.9901	−	6.40112i	1.01097	−	0.215782i
$881$			25.4990i			0.859083i	0.903047	+	0.429541i	$0.141325\pi$
$881$			25.4990i			0.859083i	−0.903047	+	0.429541i	$0.858675\pi$
$882$	−1.00586	−	3.73278i	−0.0338690	−	0.125689i
$883$	49.4771			1.66504			0.832518	−	0.553998i	$-0.186898\pi$
$883$	49.4771			1.66504			0.832518	+	0.553998i	$0.186898\pi$
$884$	−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
$890$	24.5844	−	37.5763i	0.824069	−	1.25956i
$891$	−2.95358	+	2.95358i	−0.0989486	+	0.0989486i
$892$	51.0571	+	13.5259i	1.70952	+	0.452881i
$893$	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
$896$	−25.9152	+	7.21987i	−0.865765	+	0.241199i
$897$	−2.71396	+	2.71396i	−0.0906166	+	0.0906166i
$898$	8.89066	+	32.9935i	0.296685	+	1.10101i
$899$	−2.43481	−	2.43481i	−0.0812053	−	0.0812053i
$900$	18.6103	−	8.13466i	0.620343	−	0.271155i
$901$	−63.0801			−2.10150
$902$	−30.7845	−	4.02565i	−1.02501	−	0.134040i
$903$	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	−0.981791	−	0.189966i	$-0.939162\pi$
$907$	−35.2891	−	35.2891i	−1.17176	−	1.17176i	−0.189966	−	0.981791i	$-0.560838\pi$
$908$	3.56781	+	6.13943i	0.118402	+	0.203744i
$909$	−2.62818	+	2.62818i	−0.0871711	+	0.0871711i
$910$	3.95687	−	0.827008i	0.131169	−	0.0274150i
$911$	12.6649			0.419606			0.209803	−	0.977744i	$-0.432718\pi$
$911$	12.6649			0.419606			0.209803	+	0.977744i	$0.432718\pi$
$912$	−2.05190	+	0.562274i	−0.0679451	+	0.0186187i
$913$	52.6847			1.74361
$914$	−3.17503	−	11.7827i	−0.105021	−	0.389736i
$915$	−0.0560019	+	0.978412i	−0.00185137	+	0.0323453i
$916$	1.90189	+	0.503845i	0.0628403	+	0.0166475i
$917$	25.8876			0.854885
$918$	−40.4659	+	10.9042i	−1.33557	+	0.359892i
$919$	24.6146	−	24.6146i	0.811961	−	0.811961i	−0.172967	−	0.984928i	$-0.555335\pi$
$919$	24.6146	−	24.6146i	0.811961	−	0.811961i	0.984928	+	0.172967i	$0.0553353\pi$
$920$	−45.8072	−	2.42681i	−1.51022	−	0.0800096i
$921$	13.9438	−	13.9438i	0.459463	−	0.459463i
$922$	2.78265	+	10.3265i	0.0916418	+	0.340086i
$923$	1.95144	−	1.95144i	0.0642325	−	0.0642325i
$924$	15.5146	+	4.11009i	0.510393	+	0.135212i
$925$	−14.0271	−	17.6673i	−0.461209	−	0.580896i
$926$	12.6785	−	3.41644i	0.416643	−	0.112271i
$927$	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	0.544464	−	0.838784i	$-0.316733\pi$
$929$	−8.97072	−	8.97072i	−0.294320	−	0.294320i	−0.838784	+	0.544464i	$0.816733\pi$
$930$	−5.05976	+	1.05752i	−0.165916	+	0.0346774i
$931$	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
$936$	−2.19302	−	2.17447i	−0.0716810	−	0.0710748i
$937$	4.95111			0.161746			0.0808729	−	0.996724i	$-0.474229\pi$
$937$	4.95111			0.161746			0.0808729	+	0.996724i	$0.474229\pi$
$938$	−22.6947	+	6.11547i	−0.741009	+	0.199677i
$939$	−6.71581			−0.219162
$940$	14.5195	−	7.36180i	0.473574	−	0.240115i
$941$			3.55700i			0.115955i	0.998318	+	0.0579775i	$0.0184652\pi$
$941$			3.55700i			0.115955i	−0.998318	+	0.0579775i	$0.981535\pi$
$942$	−2.00376	−	7.43603i	−0.0652861	−	0.242279i
$943$	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
$946$	−1.90026	+	0.512058i	−0.0617829	+	0.0166484i
$947$	−7.19716	+	7.19716i	−0.233876	+	0.233876i	−0.814309	−	0.580432i	$-0.802884\pi$
$947$	−7.19716	+	7.19716i	−0.233876	+	0.233876i	0.580432	+	0.814309i	$0.302884\pi$
$948$	6.54645	−	24.7113i	0.212619	−	0.802584i
$949$	−5.23322	−	5.23322i	−0.169877	−	0.169877i
$950$	3.07252	+	2.27112i	0.0996858	+	0.0736848i
$951$	0.242790			0.00787300
$952$	−28.5781	−	28.3364i	−0.926221	−	0.918389i
$953$	−6.76768	+	6.76768i	−0.219227	+	0.219227i	−0.808173	−	0.588946i	$-0.799543\pi$
$953$	−6.76768	+	6.76768i	−0.219227	+	0.219227i	0.588946	+	0.808173i	$0.299543\pi$
$954$	−7.87817	−	29.2362i	−0.255065	−	0.946556i
$955$	−18.6246	+	16.6080i	−0.602678	+	0.537422i
$956$	7.56496	+	2.00409i	0.244668	+	0.0648169i
$957$	6.99800			0.226213
$958$	−20.1751	+	35.0587i	−0.651827	+	1.13270i
$959$	−5.53985			−0.178891
$960$	−0.856912	+	17.5878i	−0.0276567	+	0.567643i
$961$	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	$-0.137475\pi$
$968$	−1.50313	+	1.51595i	−0.0483124	+	0.0487244i
$969$	−2.25055	−	2.25055i	−0.0722982	−	0.0722982i
$970$	−43.9180	+	9.17911i	−1.41012	+	0.294723i
$971$	22.7261	−	22.7261i	0.729316	−	0.729316i	−0.241167	−	0.970484i	$-0.577530\pi$
$971$	22.7261	−	22.7261i	0.729316	−	0.729316i	0.970484	+	0.241167i	$0.0775303\pi$
$972$	−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	$0.0300788\pi$
$977$			5.89849i			0.188709i	−0.995539	+	0.0943547i	$0.969921\pi$
$978$	29.3832	+	16.9090i	0.939571	+	0.540690i
$979$			48.6846i			1.55597i
$980$	−2.72197	−	5.36849i	−0.0869503	−	0.171490i
$981$	10.5041	+	10.5041i	0.335371	+	0.335371i
$982$	−14.1208	+	3.80508i	−0.450613	+	0.121425i
$983$	25.4145	+	25.4145i	0.810596	+	0.810596i	0.984723	−	0.174127i	$-0.0557105\pi$
$983$	25.4145	+	25.4145i	0.810596	+	0.810596i	−0.174127	+	0.984723i	$0.555710\pi$
$984$	6.76127	−	16.4955i	0.215542	−	0.525857i
$985$	−35.6841	−	40.0170i	−1.13699	−	1.27505i
$986$	−15.2090	−	8.75226i	−0.484354	−	0.278729i
$987$	8.52020			0.271201
$988$	0.148777	−	0.561596i	0.00473322	−	0.0178667i
$989$	2.94392			0.0936112
$990$	−12.0560	+	18.4271i	−0.383163	+	0.585651i
$991$	−28.4839	+	28.4839i	−0.904821	+	0.904821i	−0.995848	−	0.0910270i	$-0.970985\pi$
$991$	−28.4839	+	28.4839i	−0.904821	+	0.904821i	0.0910270	+	0.995848i	$0.470985\pi$
$992$	−2.36701	+	9.09063i	−0.0751526	+	0.288628i
$993$	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
$996$	−7.74713	+	29.2435i	−0.245477	+	0.926616i
$997$		−	30.8316i		−	0.976448i	−0.872718	−	0.488224i	$-0.837645\pi$
$997$		−	30.8316i		−	0.976448i	0.872718	−	0.488224i	$-0.162355\pi$
$998$	−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.747.69	yes	240
4.3	odd	2	inner	820.2.j.c.747.10	yes	240
5.3	odd	4		820.2.s.c.583.111	yes	240
20.3	even	4		820.2.s.c.583.52	yes	240
41.32	even	4		820.2.s.c.647.52	yes	240
164.155	odd	4		820.2.s.c.647.111	yes	240
205.73	odd	4	inner	820.2.j.c.483.10	✓	240
820.483	even	4	inner	820.2.j.c.483.69	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.10	✓	240	205.73	odd	4	inner
820.2.j.c.483.69	yes	240	820.483	even	4	inner
820.2.j.c.747.10	yes	240	4.3	odd	2	inner
820.2.j.c.747.69	yes	240	1.1	even	1	trivial
820.2.s.c.583.52	yes	240	20.3	even	4
820.2.s.c.583.111	yes	240	5.3	odd	4
820.2.s.c.647.52	yes	240	41.32	even	4
820.2.s.c.647.111	yes	240	164.155	odd	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+(0.367958 + 1.36551i) q^{2} +0.984353i q^{3} +(-1.72921 + 1.00490i) q^{4} +(0.127778 - 2.23241i) q^{5} +(-1.34414 + 0.362201i) q^{6} +2.37783 q^{7} +(-2.00847 - 1.99149i) q^{8} +2.03105 q^{9} +(3.09539 - 0.646954i) q^{10} +(-2.42433 + 2.42433i) q^{11} +(-0.989175 - 1.70216i) q^{12} +0.537595 q^{13} +(0.874943 + 3.24694i) q^{14} +(2.19748 + 0.125779i) q^{15} +(1.98036 - 3.47537i) q^{16} +5.98392 q^{17} +(0.747341 + 2.77341i) q^{18} +(-0.382078 + 0.382078i) q^{19} +(2.02239 + 3.98872i) q^{20} +2.34063i q^{21} +(-4.20249 - 2.41839i) q^{22} +(5.12858 + 5.12858i) q^{23} +(1.96033 - 1.97705i) q^{24} +(-4.96735 - 0.570507i) q^{25} +(0.197813 + 0.734089i) q^{26} +4.95233i q^{27} +(-4.11178 + 2.38948i) q^{28} +(-1.46623 + 1.46623i) q^{29} +(0.636831 + 3.04696i) q^{30} +1.66059i q^{31} +(5.47433 + 1.42540i) q^{32} +(-2.38640 - 2.38640i) q^{33} +(2.20183 + 8.17108i) 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} +(-4.70247 + 4.22928i) q^{40} +(5.91705 - 2.44714i) q^{41} +(-3.19614 + 0.861253i) q^{42} +(0.287011 - 0.287011i) q^{43} +(1.75598 - 6.62840i) 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} +(-1.04875 - 6.99286i) q^{50} +5.89029i q^{51} +(-0.929617 + 0.540229i) q^{52} -10.5416 q^{53} +(-6.76243 + 1.82225i) q^{54} +(5.10234 + 5.72189i) q^{55} +(-4.77581 - 4.73543i) q^{56} +(-0.376100 - 0.376100i) q^{57} +(-2.54165 - 1.46263i) q^{58} +1.58121 q^{59} +(-3.92631 + 1.99075i) q^{60} +0.445242i q^{61} +(-2.26755 + 0.611030i) 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} +(7.36032 - 1.53835i) q^{70} +(3.62995 - 3.62995i) q^{71} +(-4.07931 - 4.04481i) q^{72} +(-9.73449 - 9.73449i) q^{73} +(-3.18245 + 5.53023i) q^{74} +(0.561580 - 4.88962i) q^{75} +(0.276745 - 1.04464i) q^{76} +(-5.76465 + 5.76465i) q^{77} +(-0.722603 + 0.194717i) q^{78} +(9.18180 + 9.18180i) q^{79} +(-7.50542 - 4.86505i) q^{80} +1.21831 q^{81} +(5.51881 + 7.17933i) 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} +(6.28689 - 1.31399i) q^{90} +1.27831 q^{91} +(-14.0221 - 3.71471i) q^{92} -1.63461 q^{93} +(4.97063 - 1.33942i) q^{94} +(0.804136 + 0.901778i) q^{95} +(-1.40310 + 5.38867i) q^{96} -14.1882 q^{97} +(-0.495241 - 1.83786i) 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

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