LMFDB - Embedded newform 820.2.k.c.83.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] 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, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.83"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [108] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			83.16
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.607244 - 1.27721i) q^{2} +(1.25708 - 1.25708i) q^{3} +(-1.26251 + 1.55115i) q^{4} +(-0.966894 + 2.01621i) q^{5} +(-2.36890 - 0.842196i) q^{6} +(-2.94147 - 2.94147i) q^{7} +(2.74779 + 0.670560i) q^{8} -0.160500i q^{9} +(3.16226 + 0.0105901i) q^{10} +1.14443i q^{11} +(0.362844 + 3.53700i) q^{12} +(-2.15515 - 2.15515i) q^{13} +(-1.97067 + 5.54305i) q^{14} +(1.31908 + 3.75000i) q^{15} +(-0.812135 - 3.91669i) q^{16} +(1.33568 - 1.33568i) q^{17} +(-0.204991 + 0.0974623i) q^{18} -4.07926 q^{19} +(-1.90674 - 4.04529i) q^{20} -7.39533 q^{21} +(1.46167 - 0.694945i) q^{22} +(-4.41889 + 4.41889i) q^{23} +(4.29714 - 2.61124i) q^{24} +(-3.13023 - 3.89893i) q^{25} +(-1.44387 + 4.06126i) q^{26} +(3.56948 + 3.56948i) q^{27} +(8.27630 - 0.849026i) q^{28} +9.68916i q^{29} +(3.98853 - 3.96190i) q^{30} +7.11862i q^{31} +(-4.50925 + 3.41565i) q^{32} +(1.43863 + 1.43863i) q^{33} +(-2.51703 - 0.894858i) q^{34} +(8.77472 - 3.08654i) q^{35} +(0.248959 + 0.202632i) q^{36} +(-1.04311 + 1.04311i) q^{37} +(2.47710 + 5.21005i) q^{38} -5.41838 q^{39} +(-4.00881 + 4.89177i) q^{40} +1.00000 q^{41} +(4.49077 + 9.44536i) q^{42} +(-1.85155 + 1.85155i) q^{43} +(-1.77518 - 1.44485i) q^{44} +(0.323601 + 0.155186i) q^{45} +(8.32718 + 2.96049i) q^{46} +(1.82513 + 1.82513i) q^{47} +(-5.94451 - 3.90267i) q^{48} +10.3045i q^{49} +(-3.07892 + 6.36555i) q^{50} -3.35812i q^{51} +(6.06385 - 0.622061i) q^{52} +(-5.39627 - 5.39627i) q^{53} +(2.39142 - 6.72650i) q^{54} +(-2.30741 - 1.10654i) q^{55} +(-6.11011 - 10.0550i) q^{56} +(-5.12795 + 5.12795i) q^{57} +(12.3751 - 5.88368i) q^{58} -11.7314 q^{59} +(-7.48217 - 2.68833i) q^{60} -10.8574 q^{61} +(9.09194 - 4.32273i) q^{62} +(-0.472105 + 0.472105i) q^{63} +(7.10070 + 3.68511i) q^{64} +(6.42903 - 2.26144i) q^{65} +(0.963831 - 2.71103i) q^{66} +(-0.398498 - 0.398498i) q^{67} +(0.385532 + 3.75816i) q^{68} +11.1098i q^{69} +(-9.27055 - 9.33285i) q^{70} -12.2885i q^{71} +(0.107625 - 0.441019i) q^{72} +(-2.19340 - 2.19340i) q^{73} +(1.96570 + 0.698848i) q^{74} +(-8.83622 - 0.966313i) q^{75} +(5.15011 - 6.32754i) q^{76} +(3.36630 - 3.36630i) q^{77} +(3.29028 + 6.92039i) q^{78} -6.48862 q^{79} +(8.68212 + 2.14958i) q^{80} +9.45574 q^{81} +(-0.607244 - 1.27721i) q^{82} +(8.52290 - 8.52290i) q^{83} +(9.33668 - 11.4713i) q^{84} +(1.40156 + 3.98449i) q^{85} +(3.48916 + 1.24047i) q^{86} +(12.1800 + 12.1800i) q^{87} +(-0.767406 + 3.14464i) q^{88} +4.57295i q^{89} +(0.00169970 - 0.507541i) q^{90} +12.6786i q^{91} +(-1.27547 - 12.4333i) q^{92} +(8.94867 + 8.94867i) q^{93} +(1.22277 - 3.43937i) q^{94} +(3.94421 - 8.22466i) q^{95} +(-1.37475 + 9.96223i) q^{96} +(13.5309 - 13.5309i) q^{97} +(13.1610 - 6.25734i) q^{98} +0.183680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

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

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

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 $

$2$	−0.607244	−	1.27721i	−0.429386	−	0.903121i
$2$	−0.607244	−	1.27721i	−0.429386	−	0.903121i
$3$	1.25708	−	1.25708i	0.725775	−	0.725775i	−0.244000	−	0.969775i	$-0.578460\pi$
$3$	1.25708	−	1.25708i	0.725775	−	0.725775i	0.969775	+	0.244000i	$0.0784596\pi$
$4$	−1.26251	+	1.55115i	−0.631255	+	0.775575i
$5$	−0.966894	+	2.01621i	−0.432408	+	0.901678i
$5$	−0.966894	+	2.01621i	−0.432408	+	0.901678i
$6$	−2.36890	−	0.842196i	−0.967101	−	0.343825i
$7$	−2.94147	−	2.94147i	−1.11177	−	1.11177i	−0.992911	−	0.118861i	$-0.962076\pi$
$7$	−2.94147	−	2.94147i	−1.11177	−	1.11177i	−0.118861	−	0.992911i	$-0.537924\pi$
$8$	2.74779	+	0.670560i	0.971490	+	0.237079i
$9$		−	0.160500i		−	0.0534998i
$10$	3.16226	+	0.0105901i	0.999994	+	0.00334888i
$11$			1.14443i			0.345057i	0.985004	+	0.172529i	$0.0551937\pi$
$11$			1.14443i			0.345057i	−0.985004	+	0.172529i	$0.944806\pi$
$12$	0.362844	+	3.53700i	0.104744	+	1.02104i
$13$	−2.15515	−	2.15515i	−0.597730	−	0.597730i	0.341978	−	0.939708i	$-0.388903\pi$
$13$	−2.15515	−	2.15515i	−0.597730	−	0.597730i	−0.939708	+	0.341978i	$0.888903\pi$
$14$	−1.97067	+	5.54305i	−0.526685	+	1.48144i
$15$	1.31908	+	3.75000i	0.340585	+	0.968247i
$16$	−0.812135	−	3.91669i	−0.203034	−	0.979172i
$17$	1.33568	−	1.33568i	0.323951	−	0.323951i	−0.526330	−	0.850281i	$-0.676432\pi$
$17$	1.33568	−	1.33568i	0.323951	−	0.323951i	0.850281	+	0.526330i	$0.176432\pi$
$18$	−0.204991	+	0.0974623i	−0.0483168	+	0.0229721i
$19$	−4.07926			−0.935846			−0.467923	−	0.883769i	$-0.654998\pi$
$19$	−4.07926			−0.935846			−0.467923	+	0.883769i	$0.654998\pi$
$20$	−1.90674	−	4.04529i	−0.426359	−	0.904554i
$21$	−7.39533			−1.61379
$22$	1.46167	−	0.694945i	0.311629	−	0.148163i
$23$	−4.41889	+	4.41889i	−0.921403	+	0.921403i	−0.997129	−	0.0757257i	$-0.975873\pi$
$23$	−4.41889	+	4.41889i	−0.921403	+	0.921403i	0.0757257	+	0.997129i	$0.475873\pi$
$24$	4.29714	−	2.61124i	0.877150	−	0.533018i
$25$	−3.13023	−	3.89893i	−0.626046	−	0.779786i
$26$	−1.44387	+	4.06126i	−0.283166	+	0.796479i
$27$	3.56948	+	3.56948i	0.686947	+	0.686947i
$28$	8.27630	−	0.849026i	1.56407	−	0.160451i
$29$			9.68916i			1.79923i	0.436682	+	0.899616i	$0.356153\pi$
$29$			9.68916i			1.79923i	−0.436682	+	0.899616i	$0.643847\pi$
$30$	3.98853	−	3.96190i	0.728202	−	0.723341i
$31$			7.11862i			1.27854i	0.768982	+	0.639271i	$0.220764\pi$
$31$			7.11862i			1.27854i	−0.768982	+	0.639271i	$0.779236\pi$
$32$	−4.50925	+	3.41565i	−0.797131	+	0.603807i
$33$	1.43863	+	1.43863i	0.250434	+	0.250434i
$34$	−2.51703	−	0.894858i	−0.431667	−	0.153467i
$35$	8.77472	−	3.08654i	1.48320	−	0.521721i
$36$	0.248959	+	0.202632i	0.0414932	+	0.0337721i
$37$	−1.04311	+	1.04311i	−0.171487	+	0.171487i	−0.787632	−	0.616145i	$-0.788693\pi$
$37$	−1.04311	+	1.04311i	−0.171487	+	0.171487i	0.616145	+	0.787632i	$0.288693\pi$
$38$	2.47710	+	5.21005i	0.401839	+	0.845182i
$39$	−5.41838			−0.867635
$40$	−4.00881	+	4.89177i	−0.633849	+	0.773457i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	4.49077	+	9.44536i	0.692940	+	1.45745i
$43$	−1.85155	+	1.85155i	−0.282359	+	0.282359i	−0.834049	−	0.551690i	$-0.813983\pi$
$43$	−1.85155	+	1.85155i	−0.282359	+	0.282359i	0.551690	+	0.834049i	$0.313983\pi$
$44$	−1.77518	−	1.44485i	−0.267618	−	0.217819i
$45$	0.323601	+	0.155186i	0.0482396	+	0.0231338i
$46$	8.32718	+	2.96049i	1.22778	+	0.436501i
$47$	1.82513	+	1.82513i	0.266223	+	0.266223i	0.827576	−	0.561353i	$-0.189719\pi$
$47$	1.82513	+	1.82513i	0.266223	+	0.266223i	−0.561353	+	0.827576i	$0.689719\pi$
$48$	−5.94451	−	3.90267i	−0.858016	−	0.563302i
$49$			10.3045i			1.47207i
$50$	−3.07892	+	6.36555i	−0.435425	+	0.900225i
$51$		−	3.35812i		−	0.470231i
$52$	6.06385	−	0.622061i	0.840905	−	0.0862644i
$53$	−5.39627	−	5.39627i	−0.741235	−	0.741235i	0.231581	−	0.972816i	$-0.425610\pi$
$53$	−5.39627	−	5.39627i	−0.741235	−	0.741235i	−0.972816	+	0.231581i	$0.925610\pi$
$54$	2.39142	−	6.72650i	0.325431	−	0.915361i
$55$	−2.30741	−	1.10654i	−0.311131	−	0.149206i
$56$	−6.11011	−	10.0550i	−0.816498	−	1.34365i
$57$	−5.12795	+	5.12795i	−0.679214	+	0.679214i
$58$	12.3751	−	5.88368i	1.62492	−	0.772565i
$59$	−11.7314			−1.52730			−0.763649	−	0.645631i	$-0.776594\pi$
$59$	−11.7314			−1.52730			−0.763649	+	0.645631i	$0.776594\pi$
$60$	−7.48217	−	2.68833i	−0.965944	−	0.347062i
$61$	−10.8574			−1.39015			−0.695075	−	0.718937i	$-0.744629\pi$
$61$	−10.8574			−1.39015			−0.695075	+	0.718937i	$0.744629\pi$
$62$	9.09194	−	4.32273i	1.15468	−	0.548988i
$63$	−0.472105	+	0.472105i	−0.0594796	+	0.0594796i
$64$	7.10070	+	3.68511i	0.887587	+	0.460639i
$65$	6.42903	−	2.26144i	0.797423	−	0.280497i
$66$	0.963831	−	2.71103i	0.118639	−	0.333705i
$67$	−0.398498	−	0.398498i	−0.0486842	−	0.0486842i	0.682346	−	0.731030i	$-0.260960\pi$
$67$	−0.398498	−	0.398498i	−0.0486842	−	0.0486842i	−0.731030	+	0.682346i	$0.760960\pi$
$68$	0.385532	+	3.75816i	0.0467526	+	0.455744i
$69$			11.1098i			1.33746i
$70$	−9.27055	−	9.33285i	−1.10804	−	1.11549i
$71$		−	12.2885i		−	1.45837i	−0.684316	−	0.729185i	$-0.739899\pi$
$71$		−	12.2885i		−	1.45837i	0.684316	−	0.729185i	$-0.260101\pi$
$72$	0.107625	−	0.441019i	0.0126837	−	0.0519746i
$73$	−2.19340	−	2.19340i	−0.256718	−	0.256718i	0.567000	−	0.823718i	$-0.308104\pi$
$73$	−2.19340	−	2.19340i	−0.256718	−	0.256718i	−0.823718	+	0.567000i	$0.808104\pi$
$74$	1.96570	+	0.698848i	0.228508	+	0.0812394i
$75$	−8.83622	−	0.966313i	−1.02032	−	0.111580i
$76$	5.15011	−	6.32754i	0.590758	−	0.725819i
$77$	3.36630	−	3.36630i	0.383625	−	0.383625i
$78$	3.29028	+	6.92039i	0.372550	+	0.783580i
$79$	−6.48862			−0.730027			−0.365013	−	0.931002i	$-0.618936\pi$
$79$	−6.48862			−0.730027			−0.365013	+	0.931002i	$0.618936\pi$
$80$	8.68212	+	2.14958i	0.970691	+	0.240331i
$81$	9.45574			1.05064
$82$	−0.607244	−	1.27721i	−0.0670588	−	0.141044i
$83$	8.52290	−	8.52290i	0.935510	−	0.935510i	−0.0625326	−	0.998043i	$-0.519918\pi$
$83$	8.52290	−	8.52290i	0.935510	−	0.935510i	0.998043	+	0.0625326i	$0.0199177\pi$
$84$	9.33668	−	11.4713i	1.01872	−	1.25162i
$85$	1.40156	+	3.98449i	0.152020	+	0.432178i
$86$	3.48916	+	1.24047i	0.376245	+	0.133763i
$87$	12.1800	+	12.1800i	1.30584	+	1.30584i
$88$	−0.767406	+	3.14464i	−0.0818057	+	0.335220i
$89$			4.57295i			0.484732i	0.970185	+	0.242366i	$0.0779234\pi$
$89$			4.57295i			0.484732i	−0.970185	+	0.242366i	$0.922077\pi$
$90$	0.00169970	−	0.507541i	0.000179165	−	0.0534995i
$91$			12.6786i			1.32908i
$92$	−1.27547	−	12.4333i	−0.132977	−	1.29626i
$93$	8.94867	+	8.94867i	0.927934	+	0.927934i
$94$	1.22277	−	3.43937i	0.126119	−	0.354744i
$95$	3.94421	−	8.22466i	0.404668	−	0.843832i
$96$	−1.37475	+	9.96223i	−0.140310	+	1.01677i
$97$	13.5309	−	13.5309i	1.37386	−	1.37386i	0.519213	−	0.854645i	$-0.326225\pi$
$97$	13.5309	−	13.5309i	1.37386	−	1.37386i	0.854645	−	0.519213i	$-0.173775\pi$
$98$	13.1610	−	6.25734i	1.32946	−	0.632087i
$99$	0.183680			0.0184605
$100$	9.99978	+	0.0669772i	0.999978	+	0.00669772i
$101$	10.9561			1.09017			0.545084	−	0.838381i	$-0.316498\pi$
$101$	10.9561			1.09017			0.545084	+	0.838381i	$0.316498\pi$
$102$	−4.28901	+	2.03920i	−0.424676	+	0.201911i
$103$	−8.31652	+	8.31652i	−0.819451	+	0.819451i	−0.986028	−	0.166577i	$-0.946728\pi$
$103$	−8.31652	+	8.31652i	−0.819451	+	0.819451i	0.166577	+	0.986028i	$0.446728\pi$
$104$	−4.47673	−	7.36704i	−0.438980	−	0.722398i
$105$	7.15050	−	14.9106i	0.697817	−	1.45512i
$106$	−3.61530	+	10.1690i	−0.351149	+	0.987701i
$107$	−13.3603	−	13.3603i	−1.29159	−	1.29159i	−0.933801	−	0.357793i	$-0.883529\pi$
$107$	−13.3603	−	13.3603i	−1.29159	−	1.29159i	−0.357793	−	0.933801i	$-0.616471\pi$
$108$	−10.0433	+	1.03029i	−0.966417	+	0.0991401i
$109$		−	9.75328i		−	0.934195i	−0.884206	−	0.467097i	$-0.845300\pi$
$109$		−	9.75328i		−	0.934195i	0.884206	−	0.467097i	$-0.154700\pi$
$110$	−0.0121196	+	3.61897i	−0.00115556	+	0.345055i
$111$			2.62256i			0.248922i
$112$	−9.13195	+	13.9097i	−0.862888	+	1.31434i
$113$	−1.30067	−	1.30067i	−0.122357	−	0.122357i	0.643277	−	0.765634i	$-0.277574\pi$
$113$	−1.30067	−	1.30067i	−0.122357	−	0.122357i	−0.765634	+	0.643277i	$0.777574\pi$
$114$	9.66337	+	3.43554i	0.905058	+	0.321768i
$115$	−4.63683	−	13.1820i	−0.432387	−	1.22923i
$116$	−15.0293	−	12.2327i	−1.39544	−	1.13577i
$117$	−0.345900	+	0.345900i	−0.0319785	+	0.0319785i
$118$	7.12382	+	14.9834i	0.655801	+	1.37934i
$119$	−7.85775			−0.720319
$120$	1.10995	+	11.1887i	0.101324	+	1.02139i
$121$	9.69029			0.880935
$122$	6.59310	+	13.8672i	0.596911	+	1.25547i
$123$	1.25708	−	1.25708i	0.113347	−	0.113347i
$124$	−11.0420	−	8.98733i	−0.991605	−	0.807086i
$125$	10.8877	−	2.54136i	0.973823	−	0.227307i
$126$	0.889658	+	0.316292i	0.0792570	+	0.0281776i
$127$	8.69518	+	8.69518i	0.771572	+	0.771572i	0.978381	−	0.206809i	$-0.0663079\pi$
$127$	8.69518	+	8.69518i	0.771572	+	0.771572i	−0.206809	+	0.978381i	$0.566308\pi$
$128$	0.394795	−	11.3068i	0.0348953	−	0.999391i
$129$			4.65510i			0.409858i
$130$	−6.79231	−	6.83795i	−0.595725	−	0.599728i
$131$			7.26087i			0.634385i	0.948361	+	0.317192i	$0.102740\pi$
$131$			7.26087i			0.634385i	−0.948361	+	0.317192i	$0.897260\pi$
$132$	−4.04783	+	0.415248i	−0.352318	+	0.0361427i
$133$	11.9990	+	11.9990i	1.04045	+	1.04045i
$134$	−0.266978	+	0.750949i	−0.0230634	+	0.0648721i
$135$	−10.6481	+	3.74552i	−0.916446	+	0.322363i
$136$	4.56583	−	2.77452i	0.391517	−	0.237913i
$137$	−12.1021	+	12.1021i	−1.03395	+	1.03395i	−0.0345460	+	0.999403i	$0.510999\pi$
$137$	−12.1021	+	12.1021i	−1.03395	+	1.03395i	−0.999403	+	0.0345460i	$0.989001\pi$
$138$	14.1895	−	6.74636i	1.20789	−	0.574288i
$139$	−3.92058			−0.332539			−0.166270	−	0.986080i	$-0.553172\pi$
$139$	−3.92058			−0.332539			−0.166270	+	0.986080i	$0.553172\pi$
$140$	−6.29049	+	17.5077i	−0.531643	+	1.47967i
$141$	4.58868			0.386436
$142$	−15.6949	+	7.46208i	−1.31709	+	0.626204i
$143$	2.46640	−	2.46640i	0.206251	−	0.206251i
$144$	−0.628626	+	0.130347i	−0.0523855	+	0.0108623i
$145$	−19.5354	−	9.36839i	−1.62233	−	0.778002i
$146$	−1.46949	+	4.13335i	−0.121616	+	0.342078i
$147$	12.9536	+	12.9536i	1.06839	+	1.06839i
$148$	−0.301085	−	2.93497i	−0.0247490	−	0.241253i
$149$		−	5.71267i		−	0.468000i	−0.972237	−	0.234000i	$-0.924818\pi$
$149$		−	5.71267i		−	0.468000i	0.972237	−	0.234000i	$-0.0751815\pi$
$150$	4.13156	+	11.8725i	0.337340	+	0.969382i
$151$		−	1.78561i		−	0.145311i	−0.997357	−	0.0726553i	$-0.976853\pi$
$151$		−	1.78561i		−	0.145311i	0.997357	−	0.0726553i	$-0.0231473\pi$
$152$	−11.2089	−	2.73539i	−0.909166	−	0.221869i
$153$	−0.214377	−	0.214377i	−0.0173313	−	0.0173313i
$154$	−6.34361	−	2.25529i	−0.511183	−	0.181737i
$155$	−14.3526	−	6.88295i	−1.15283	−	0.552852i
$156$	6.84076	−	8.40472i	0.547699	−	0.672916i
$157$	−14.7660	+	14.7660i	−1.17846	+	1.17846i	−0.198321	+	0.980137i	$0.563549\pi$
$157$	−14.7660	+	14.7660i	−1.17846	+	1.17846i	−0.980137	+	0.198321i	$0.936451\pi$
$158$	3.94017	+	8.28730i	0.313463	+	0.659302i
$159$	−13.5671			−1.07594
$160$	−2.52670	−	12.3942i	−0.199754	−	0.979846i
$161$	25.9961			2.04878
$162$	−5.74194	−	12.0769i	−0.451129	−	0.948853i
$163$	5.08766	−	5.08766i	0.398496	−	0.398496i	−0.479206	−	0.877702i	$-0.659075\pi$
$163$	5.08766	−	5.08766i	0.398496	−	0.398496i	0.877702	+	0.479206i	$0.159075\pi$
$164$	−1.26251	+	1.55115i	−0.0985855	+	0.121124i
$165$	−4.29160	+	1.50959i	−0.334101	+	0.117521i
$166$	−16.0610	−	5.71003i	−1.24657	−	0.443184i
$167$	−1.28357	−	1.28357i	−0.0993259	−	0.0993259i	0.655698	−	0.755024i	$-0.272375\pi$
$167$	−1.28357	−	1.28357i	−0.0993259	−	0.0993259i	−0.755024	+	0.655698i	$0.772375\pi$
$168$	−20.3208	−	4.95901i	−1.56778	−	0.382596i
$169$		−	3.71069i		−	0.285438i
$170$	4.23793	−	4.20964i	0.325034	−	0.322864i
$171$			0.654719i			0.0500676i
$172$	−0.534432	−	5.20964i	−0.0407501	−	0.397231i
$173$	−6.46629	−	6.46629i	−0.491623	−	0.491623i	0.417195	−	0.908817i	$-0.363013\pi$
$173$	−6.46629	−	6.46629i	−0.491623	−	0.491623i	−0.908817	+	0.417195i	$0.863013\pi$
$174$	8.16017	−	22.9527i	0.618621	−	1.74004i
$175$	−2.26110	+	20.6761i	−0.170923	+	1.56296i
$176$	4.48236	−	0.929428i	0.337870	−	0.0700583i
$177$	−14.7473	+	14.7473i	−1.10848	+	1.10848i
$178$	5.84060	−	2.77690i	0.437772	−	0.208137i
$179$	11.2847			0.843454			0.421727	−	0.906723i	$-0.361424\pi$
$179$	11.2847			0.843454			0.421727	+	0.906723i	$0.361424\pi$
$180$	−0.649267	+	0.306030i	−0.0483935	+	0.0228102i
$181$	−10.7861			−0.801722			−0.400861	−	0.916139i	$-0.631289\pi$
$181$	−10.7861			−0.801722			−0.400861	+	0.916139i	$0.631289\pi$
$182$	16.1932	−	7.69900i	1.20032	−	0.570688i
$183$	−13.6486	+	13.6486i	−1.00894	+	1.00894i
$184$	−15.1053	+	9.17906i	−1.11358	+	0.676689i
$185$	−1.09456	−	3.11172i	−0.0804737	−	0.228778i
$186$	5.99527	−	16.8633i	0.439595	−	1.23648i
$187$	1.52859	+	1.52859i	0.111782	+	0.111782i
$188$	−5.13531	+	0.526807i	−0.374531	+	0.0384213i
$189$		−	20.9990i		−	1.52746i
$190$	−12.8997	−	0.0431997i	−0.935841	−	0.00313404i
$191$		−	27.0255i		−	1.95550i	−0.209783	−	0.977748i	$-0.567276\pi$
$191$		−	27.0255i		−	1.95550i	0.209783	−	0.977748i	$-0.432724\pi$
$192$	13.5586	−	4.29366i	0.978510	−	0.309869i
$193$	8.12747	+	8.12747i	0.585028	+	0.585028i	0.936281	−	0.351252i	$-0.114244\pi$
$193$	8.12747	+	8.12747i	0.585028	+	0.585028i	−0.351252	+	0.936281i	$0.614244\pi$
$194$	−25.4984	−	9.06522i	−1.83068	−	0.650845i
$195$	5.23900	−	10.9246i	0.375173	−	0.782328i
$196$	−15.9838	−	13.0095i	−1.14170	−	0.929253i
$197$	1.86439	−	1.86439i	0.132833	−	0.132833i	−0.637564	−	0.770397i	$-0.720058\pi$
$197$	1.86439	−	1.86439i	0.132833	−	0.132833i	0.770397	+	0.637564i	$0.220058\pi$
$198$	−0.111538	−	0.234597i	−0.00792669	−	0.0166721i
$199$	−7.55651			−0.535667			−0.267833	−	0.963465i	$-0.586308\pi$
$199$	−7.55651			−0.535667			−0.267833	+	0.963465i	$0.586308\pi$
$200$	−5.98676	−	12.8124i	−0.423328	−	0.905977i
$201$	−1.00189			−0.0706676
$202$	−6.65300	−	13.9931i	−0.468103	−	0.984554i
$203$	28.5004	−	28.5004i	2.00033	−	2.00033i
$204$	5.20895	+	4.23967i	0.364700	+	0.296836i
$205$	−0.966894	+	2.01621i	−0.0675308	+	0.140818i
$206$	15.6721	+	5.57176i	1.09192	+	0.388203i
$207$	0.709230	+	0.709230i	0.0492949	+	0.0492949i
$208$	−6.69076	+	10.1913i	−0.463921	+	0.706640i
$209$		−	4.66841i		−	0.322921i
$210$	−23.3859	−	0.0783172i	−1.61378	−	0.00540440i
$211$		−	5.56801i		−	0.383318i	−0.981462	−	0.191659i	$-0.938613\pi$
$211$		−	5.56801i		−	0.383318i	0.981462	−	0.191659i	$-0.0613867\pi$
$212$	15.1833	−	1.55758i	1.04279	−	0.106975i
$213$	−15.4476	−	15.4476i	−1.05845	−	1.05845i
$214$	−8.95093	+	25.1769i	−0.611873	+	1.72106i
$215$	−1.94287	−	5.52338i	−0.132503	−	0.376691i
$216$	7.41463	+	12.2017i	0.504502	+	0.830222i
$217$	20.9392	−	20.9392i	1.42145	−	1.42145i
$218$	−12.4570	+	5.92262i	−0.843691	+	0.401130i
$219$	−5.51455			−0.372639
$220$	4.62953	−	2.18212i	0.312123	−	0.147118i
$221$	−5.75719			−0.387270
$222$	3.34955	−	1.59253i	0.224807	−	0.106884i
$223$	−13.7028	+	13.7028i	−0.917606	+	0.917606i	−0.996855	−	0.0792490i	$-0.974748\pi$
$223$	−13.7028	+	13.7028i	−0.917606	+	0.917606i	0.0792490	+	0.996855i	$0.474748\pi$
$224$	23.3109	+	3.21681i	1.55752	+	0.214932i
$225$	−0.625776	+	0.502401i	−0.0417184	+	0.0334934i
$226$	−0.871402	+	2.45105i	−0.0579648	+	0.163042i
$227$	14.3899	+	14.3899i	0.955092	+	0.955092i	0.999034	−	0.0439417i	$-0.0139916\pi$
$227$	14.3899	+	14.3899i	0.955092	+	0.955092i	−0.0439417	+	0.999034i	$0.513992\pi$
$228$	−1.48013	−	14.4283i	−0.0980242	−	0.955539i
$229$			11.0800i			0.732188i	0.930578	+	0.366094i	$0.119305\pi$
$229$			11.0800i			0.732188i	−0.930578	+	0.366094i	$0.880695\pi$
$230$	−14.0205	+	13.9269i	−0.924483	+	0.918312i
$231$		−	8.46340i		−	0.556851i
$232$	−6.49716	+	26.6238i	−0.426559	+	1.74794i
$233$	1.45436	+	1.45436i	0.0952782	+	0.0952782i	0.753139	−	0.657861i	$-0.228539\pi$
$233$	1.45436	+	1.45436i	0.0952782	+	0.0952782i	−0.657861	+	0.753139i	$0.728539\pi$
$234$	0.651831	+	0.231740i	0.0426115	+	0.0151493i
$235$	−5.44457	+	1.91515i	−0.355165	+	0.124930i
$236$	14.8110	−	18.1972i	0.964115	−	1.18454i
$237$	−8.15671	+	8.15671i	−0.529835	+	0.529835i
$238$	4.77157	+	10.0360i	0.309295	+	0.650535i
$239$	9.93038			0.642343			0.321171	−	0.947021i	$-0.395923\pi$
$239$	9.93038			0.642343			0.321171	+	0.947021i	$0.395923\pi$
$240$	13.6163	−	8.21193i	0.878930	−	0.530078i
$241$	0.882903			0.0568728			0.0284364	−	0.999596i	$-0.490947\pi$
$241$	0.882903			0.0568728			0.0284364	+	0.999596i	$0.490947\pi$
$242$	−5.88437	−	12.3765i	−0.378261	−	0.795591i
$243$	1.17818	−	1.17818i	0.0755804	−	0.0755804i
$244$	13.7076	−	16.8415i	0.877540	−	1.07817i
$245$	−20.7761	−	9.96336i	−1.32733	−	0.636536i
$246$	−2.36890	−	0.842196i	−0.151036	−	0.0536965i
$247$	8.79140	+	8.79140i	0.559383	+	0.559383i
$248$	−4.77346	+	19.5605i	−0.303115	+	1.24209i
$249$		−	21.4279i		−	1.35794i
$250$	−9.85732	−	12.3626i	−0.623432	−	0.781878i
$251$			11.1757i			0.705405i	0.935736	+	0.352702i	$0.114737\pi$
$251$			11.1757i			0.705405i	−0.935736	+	0.352702i	$0.885263\pi$
$252$	−0.136268	−	1.32834i	−0.00858410	−	0.0836777i
$253$	−5.05710	−	5.05710i	−0.317937	−	0.317937i
$254$	5.82544	−	16.3856i	0.365521	−	1.02813i
$255$	6.77069	+	3.24695i	0.423997	+	0.203332i
$256$	−14.6809	+	6.36176i	−0.917555	+	0.397610i
$257$	−17.8846	+	17.8846i	−1.11561	+	1.11561i	−0.123234	+	0.992378i	$0.539327\pi$
$257$	−17.8846	+	17.8846i	−1.11561	+	1.11561i	−0.992378	+	0.123234i	$0.960673\pi$
$258$	5.94552	−	2.82678i	0.370152	−	0.175988i
$259$	6.13658			0.381309
$260$	−4.60889	+	12.8275i	−0.285831	+	0.795527i
$261$	1.55511			0.0962586
$262$	9.27362	−	4.40912i	0.572926	−	0.272396i
$263$	−0.351641	+	0.351641i	−0.0216831	+	0.0216831i	−0.717865	−	0.696182i	$-0.754881\pi$
$263$	−0.351641	+	0.351641i	−0.0216831	+	0.0216831i	0.696182	+	0.717865i	$0.254881\pi$
$264$	2.98838	+	4.91776i	0.183922	+	0.302667i
$265$	16.0977	−	5.66241i	0.988872	−	0.347839i
$266$	8.03889	−	22.6116i	0.492896	−	1.38640i
$267$	5.74856	+	5.74856i	0.351806	+	0.351806i
$268$	1.12124	−	0.115022i	0.0684904	−	0.00702611i
$269$		−	1.41478i		−	0.0862604i	−0.999069	−	0.0431302i	$-0.986267\pi$
$269$		−	1.41478i		−	0.0862604i	0.999069	−	0.0431302i	$-0.0137330\pi$
$270$	11.2498	+	11.3254i	0.684642	+	0.689243i
$271$			4.73898i			0.287873i	0.989587	+	0.143936i	$0.0459760\pi$
$271$			4.73898i			0.287873i	−0.989587	+	0.143936i	$0.954024\pi$
$272$	−6.31621	−	4.14670i	−0.382977	−	0.251431i
$273$	15.9380	+	15.9380i	0.964612	+	0.964612i
$274$	22.8057	+	8.10793i	1.37774	+	0.489818i
$275$	4.46203	−	3.58232i	0.269071	−	0.216022i
$276$	−17.2330	−	14.0262i	−1.03730	−	0.844281i
$277$	−4.62144	+	4.62144i	−0.277676	+	0.277676i	−0.832181	−	0.554505i	$-0.812908\pi$
$277$	−4.62144	+	4.62144i	−0.277676	+	0.277676i	0.554505	+	0.832181i	$0.312908\pi$
$278$	2.38075	+	5.00739i	0.142788	+	0.300323i
$279$	1.14253			0.0684018
$280$	26.1808	−	2.59720i	1.56460	−	0.155212i
$281$	17.2137			1.02688			0.513442	−	0.858124i	$-0.328370\pi$
$281$	17.2137			1.02688			0.513442	+	0.858124i	$0.328370\pi$
$282$	−2.78644	−	5.86069i	−0.165930	−	0.348999i
$283$	−10.2472	+	10.2472i	−0.609134	+	0.609134i	−0.942720	−	0.333586i	$-0.891741\pi$
$283$	−10.2472	+	10.2472i	−0.609134	+	0.609134i	0.333586	+	0.942720i	$0.391741\pi$
$284$	19.0612	+	15.5143i	1.13108	+	0.920604i
$285$	−5.38086	−	15.2972i	−0.318735	−	0.906130i
$286$	−4.64781	−	1.65240i	−0.274831	−	0.0977083i
$287$	−2.94147	−	2.94147i	−0.173630	−	0.173630i
$288$	0.548210	+	0.723733i	0.0323036	+	0.0426464i
$289$			13.4319i			0.790112i
$290$	−0.102609	+	30.6396i	−0.00602541	+	1.79922i
$291$		−	34.0189i		−	1.99422i
$292$	6.17147	−	0.633102i	0.361158	−	0.0370495i
$293$	−11.0014	−	11.0014i	−0.642706	−	0.642706i	0.308514	−	0.951220i	$-0.400168\pi$
$293$	−11.0014	−	11.0014i	−0.642706	−	0.642706i	−0.951220	+	0.308514i	$0.900168\pi$
$294$	8.67841	−	24.4104i	0.506135	−	1.42364i
$295$	11.3430	−	23.6530i	0.660416	−	1.37713i
$296$	−3.56573	+	2.16679i	−0.207254	+	0.125942i
$297$	−4.08500	+	4.08500i	−0.237036	+	0.237036i
$298$	−7.29625	+	3.46898i	−0.422660	+	0.200953i
$299$	19.0467			1.10150
$300$	12.6547	−	12.4863i	0.730620	−	0.720898i
$301$	10.8926			0.627837
$302$	−2.28059	+	1.08430i	−0.131233	+	0.0623943i
$303$	13.7726	−	13.7726i	0.791218	−	0.791218i
$304$	3.31291	+	15.9772i	0.190008	+	0.916354i
$305$	10.4980	−	21.8909i	0.601112	−	1.25347i
$306$	−0.143624	+	0.403982i	−0.00821046	+	0.0230941i
$307$	1.21671	+	1.21671i	0.0694414	+	0.0694414i	0.740975	−	0.671533i	$-0.234364\pi$
$307$	1.21671	+	1.21671i	0.0694414	+	0.0694414i	−0.671533	+	0.740975i	$0.734364\pi$
$308$	0.971648	+	9.47161i	0.0553648	+	0.539695i
$309$			20.9091i			1.18947i
$310$	−0.0753868	+	22.5109i	−0.00428168	+	1.27853i
$311$		−	1.77492i		−	0.100647i	−0.998733	−	0.0503233i	$-0.983975\pi$
$311$		−	1.77492i		−	0.100647i	0.998733	−	0.0503233i	$-0.0160252\pi$
$312$	−14.8886	−	3.63335i	−0.842899	−	0.205698i
$313$	−14.0307	−	14.0307i	−0.793064	−	0.793064i	0.188927	−	0.981991i	$-0.439499\pi$
$313$	−14.0307	−	14.0307i	−0.793064	−	0.793064i	−0.981991	+	0.188927i	$0.939499\pi$
$314$	27.8259	+	9.89269i	1.57030	+	0.558277i
$315$	−0.495389	−	1.40834i	−0.0279120	−	0.0793509i
$316$	8.19195	−	10.0648i	0.460833	−	0.566191i
$317$	−5.33855	+	5.33855i	−0.299843	+	0.299843i	−0.840952	−	0.541109i	$-0.818004\pi$
$317$	−5.33855	+	5.33855i	−0.299843	+	0.299843i	0.541109	+	0.840952i	$0.318004\pi$
$318$	8.23853	+	17.3280i	0.461994	+	0.971704i
$319$	−11.0885			−0.620838
$320$	−14.2956	+	10.7534i	−0.799148	+	0.601134i
$321$	−33.5901			−1.87481
$322$	−15.7860	−	33.2024i	−0.879717	−	1.85030i
$323$	−5.44860	+	5.44860i	−0.303168	+	0.303168i
$324$	−11.9380	+	14.6673i	−0.663220	+	0.814848i
$325$	−1.65665	+	15.1489i	−0.0918946	+	0.840308i
$326$	−9.58744	−	3.40854i	−0.530999	−	0.188782i
$327$	−12.2607	−	12.2607i	−0.678016	−	0.678016i
$328$	2.74779	+	0.670560i	0.151721	+	0.0370255i
$329$		−	10.7372i		−	0.591959i
$330$	4.53410	+	4.56457i	0.249594	+	0.251271i
$331$			26.4601i			1.45438i	0.686438	+	0.727188i	$0.259173\pi$
$331$			26.4601i			1.45438i	−0.686438	+	0.727188i	$0.740827\pi$
$332$	2.46005	+	23.9806i	0.135013	+	1.31610i
$333$	0.167419	+	0.167419i	0.00917453	+	0.00917453i
$334$	−0.859946	+	2.41883i	−0.0470542	+	0.132352i
$335$	1.18876	−	0.418151i	0.0649489	−	0.0228460i
$336$	6.00601	+	28.9652i	0.327654	+	1.58018i
$337$	19.0771	−	19.0771i	1.03920	−	1.03920i	0.0399988	−	0.999200i	$-0.487265\pi$
$337$	19.0771	−	19.0771i	1.03920	−	1.03920i	0.999200	−	0.0399988i	$-0.0127354\pi$
$338$	−4.73932	+	2.25330i	−0.257785	+	0.122563i
$339$	−3.27010			−0.177607
$340$	−7.95002	−	2.85643i	−0.431151	−	0.154912i
$341$	−8.14673			−0.441170
$342$	0.836211	−	0.397574i	0.0452171	−	0.0214983i
$343$	9.72010	−	9.72010i	0.524836	−	0.524836i
$344$	−6.32925	+	3.84610i	−0.341250	+	0.207368i
$345$	−22.3997	−	10.7420i	−1.20596	−	0.578330i
$346$	−4.33217	+	12.1854i	−0.232899	+	0.655091i
$347$	21.0246	+	21.0246i	1.12866	+	1.12866i	0.990396	+	0.138263i	$0.0441518\pi$
$347$	21.0246	+	21.0246i	1.12866	+	1.12866i	0.138263	+	0.990396i	$0.455848\pi$
$348$	−34.2705	+	3.51565i	−1.83709	+	0.188459i
$349$			16.5340i			0.885044i	0.896758	+	0.442522i	$0.145916\pi$
$349$			16.5340i			0.885044i	−0.896758	+	0.442522i	$0.854084\pi$
$350$	27.7806	−	9.66752i	1.48494	−	0.516751i
$351$		−	15.3855i		−	0.821217i
$352$	−3.90895	−	5.16050i	−0.208348	−	0.275056i
$353$	−23.2869	−	23.2869i	−1.23944	−	1.23944i	−0.960232	−	0.279204i	$-0.909929\pi$
$353$	−23.2869	−	23.2869i	−1.23944	−	1.23944i	−0.279204	−	0.960232i	$-0.590071\pi$
$354$	27.7906	+	9.88015i	1.47705	+	0.525124i
$355$	24.7761	+	11.8816i	1.31498	+	0.630611i
$356$	−7.09333	−	5.77340i	−0.375946	−	0.305989i
$357$	−9.87782	+	9.87782i	−0.522790	+	0.522790i
$358$	−6.85253	−	14.4128i	−0.362168	−	0.761741i
$359$	−0.831529			−0.0438864			−0.0219432	−	0.999759i	$-0.506985\pi$
$359$	−0.831529			−0.0438864			−0.0219432	+	0.999759i	$0.506985\pi$
$360$	0.785127	+	0.643413i	0.0413798	+	0.0339108i
$361$	−2.35964			−0.124192
$362$	6.54977	+	13.7760i	0.344248	+	0.724052i
$363$	12.1815	−	12.1815i	0.639361	−	0.639361i
$364$	−19.6664	−	16.0069i	−1.03080	−	0.838987i
$365$	6.54314	−	2.30157i	0.342483	−	0.120470i
$366$	25.7202	+	9.14408i	1.34442	+	0.477969i
$367$	−12.7086	−	12.7086i	−0.663384	−	0.663384i	0.292792	−	0.956176i	$-0.405416\pi$
$367$	−12.7086	−	12.7086i	−0.663384	−	0.663384i	−0.956176	+	0.292792i	$0.905416\pi$
$368$	20.8962	+	13.7187i	1.08929	+	0.715136i
$369$		−	0.160500i		−	0.00835527i
$370$	−3.30965	+	3.28755i	−0.172060	+	0.170912i
$371$			31.7460i			1.64817i
$372$	−25.1785	+	2.58294i	−1.30545	+	0.133919i
$373$	4.46736	+	4.46736i	0.231311	+	0.231311i	0.813240	−	0.581929i	$-0.197702\pi$
$373$	4.46736	+	4.46736i	0.231311	+	0.231311i	−0.581929	+	0.813240i	$0.697702\pi$
$374$	1.02410	−	2.88055i	0.0529549	−	0.148950i
$375$	10.4920	−	16.8814i	0.541803	−	0.871750i
$376$	3.79122	+	6.23894i	0.195517	+	0.321749i
$377$	20.8815	−	20.8815i	1.07545	−	1.07545i
$378$	−26.8201	+	12.7515i	−1.37948	+	0.655868i
$379$	−29.9289			−1.53734			−0.768671	−	0.639644i	$-0.779082\pi$
$379$	−29.9289			−1.53734			−0.768671	+	0.639644i	$0.779082\pi$
$380$	7.77807	+	16.5018i	0.399007	+	0.846523i
$381$	21.8611			1.11998
$382$	−34.5171	+	16.4111i	−1.76605	+	0.839663i
$383$	4.25172	−	4.25172i	0.217253	−	0.217253i	−0.590087	−	0.807340i	$-0.700906\pi$
$383$	4.25172	−	4.25172i	0.217253	−	0.217253i	0.807340	+	0.590087i	$0.200906\pi$
$384$	−13.7173	−	14.7099i	−0.700007	−	0.750660i
$385$	3.53232	+	10.0420i	0.180024	+	0.511789i
$386$	5.44510	−	15.3158i	0.277148	−	0.779554i
$387$	0.297173	+	0.297173i	0.0151062	+	0.0151062i
$388$	3.90557	+	38.0715i	0.198275	+	1.93279i
$389$			3.31393i			0.168023i	0.996465	+	0.0840115i	$0.0267732\pi$
$389$			3.31393i			0.168023i	−0.996465	+	0.0840115i	$0.973227\pi$
$390$	−17.1343	−	0.0573811i	−0.867630	−	0.00290561i
$391$			11.8045i			0.596979i
$392$	−6.90978	+	28.3146i	−0.348997	+	1.43010i
$393$	9.12749	+	9.12749i	0.460421	+	0.460421i
$394$	−3.51336	−	1.24907i	−0.177000	−	0.0629274i
$395$	6.27381	−	13.0824i	0.315669	−	0.658249i
$396$	−0.231898	+	0.284915i	−0.0116533	+	0.0143175i
$397$	0.396315	−	0.396315i	0.0198905	−	0.0198905i	−0.697092	−	0.716982i	$-0.745523\pi$
$397$	0.396315	−	0.396315i	0.0198905	−	0.0198905i	0.716982	+	0.697092i	$0.245523\pi$
$398$	4.58864	+	9.65122i	0.230008	+	0.483772i
$399$	30.1675			1.51026
$400$	−12.7287	+	15.4266i	−0.636436	+	0.771330i
$401$	30.5314			1.52467			0.762333	−	0.647185i	$-0.224054\pi$
$401$	30.5314			1.52467			0.762333	+	0.647185i	$0.224054\pi$
$402$	0.608389	+	1.27962i	0.0303437	+	0.0638214i
$403$	15.3417	−	15.3417i	0.764222	−	0.764222i
$404$	−13.8321	+	16.9945i	−0.688175	+	0.845508i
$405$	−9.14270	+	19.0648i	−0.454304	+	0.947337i
$406$	−53.7075	−	19.0942i	−2.66546	−	0.947628i
$407$	−1.19377	−	1.19377i	−0.0591728	−	0.0591728i
$408$	2.25182	−	9.22742i	0.111482	−	0.456825i
$409$		−	36.4533i		−	1.80250i	−0.433297	−	0.901251i	$-0.642650\pi$
$409$		−	36.4533i		−	1.80250i	0.433297	−	0.901251i	$-0.357350\pi$
$410$	3.16226	+	0.0105901i	0.156173	+	0.000523007i
$411$			30.4265i			1.50083i
$412$	−2.40048	−	23.3999i	−0.118263	−	1.15283i
$413$	34.5076	+	34.5076i	1.69801	+	1.69801i
$414$	0.475158	−	1.33651i	0.0233527	−	0.0656858i
$415$	8.94325	+	25.4247i	0.439007	+	1.24805i
$416$	17.0793	+	2.35688i	0.837382	+	0.115555i
$417$	−4.92848	+	4.92848i	−0.241349	+	0.241349i
$418$	−5.96252	+	2.83486i	−0.291636	+	0.138658i
$419$	−30.2292			−1.47679			−0.738396	−	0.674367i	$-0.764416\pi$
$419$	−30.2292			−1.47679			−0.738396	+	0.674367i	$0.764416\pi$
$420$	14.1009	+	29.9162i	0.688055	+	1.45976i
$421$	−11.9077			−0.580344			−0.290172	−	0.956975i	$-0.593712\pi$
$421$	−11.9077			−0.580344			−0.290172	+	0.956975i	$0.593712\pi$
$422$	−7.11150	+	3.38114i	−0.346182	+	0.164591i
$423$	0.292933	−	0.292933i	0.0142429	−	0.0142429i
$424$	−11.2093	−	18.4463i	−0.544372	−	0.895834i
$425$	−9.38874	−	1.02674i	−0.455421	−	0.0498040i
$426$	−10.3493	+	29.1102i	−0.501425	+	1.41039i
$427$	31.9368	+	31.9368i	1.54553	+	1.54553i
$428$	37.5915	−	3.85633i	1.81705	−	0.186403i
$429$		−	6.20093i		−	0.299384i
$430$	−5.87470	+	5.83548i	−0.283303	+	0.281412i
$431$		−	2.28655i		−	0.110139i	−0.998483	−	0.0550696i	$-0.982462\pi$
$431$		−	2.28655i		−	0.110139i	0.998483	−	0.0550696i	$-0.0175381\pi$
$432$	11.0816	−	16.8794i	0.533165	−	0.812112i
$433$	9.07145	+	9.07145i	0.435946	+	0.435946i	0.890645	−	0.454699i	$-0.150253\pi$
$433$	9.07145	+	9.07145i	0.435946	+	0.435946i	−0.454699	+	0.890645i	$0.650253\pi$
$434$	−39.4589	−	14.0285i	−1.89409	−	0.673389i
$435$	−36.3344	+	12.7808i	−1.74210	+	0.612790i
$436$	15.1288	+	12.3136i	0.724538	+	0.589715i
$437$	18.0258	−	18.0258i	0.862292	−	0.862292i
$438$	3.34868	+	7.04322i	0.160006	+	0.336538i
$439$	−2.98987			−0.142699			−0.0713494	−	0.997451i	$-0.522731\pi$
$439$	−2.98987			−0.142699			−0.0713494	+	0.997451i	$0.522731\pi$
$440$	−5.59827	−	4.58779i	−0.266887	−	0.218714i
$441$	1.65387			0.0787556
$442$	3.49602	+	7.35311i	0.166288	+	0.349752i
$443$	−0.190056	+	0.190056i	−0.00902984	+	0.00902984i	−0.711607	−	0.702577i	$-0.752032\pi$
$443$	−0.190056	+	0.190056i	−0.00902984	+	0.00902984i	0.702577	+	0.711607i	$0.252032\pi$
$444$	−4.06798	−	3.31101i	−0.193058	−	0.157133i
$445$	−9.22004	−	4.42156i	−0.437072	−	0.209602i
$446$	25.8222	+	9.18034i	1.22272	+	0.434702i
$447$	−7.18128	−	7.18128i	−0.339663	−	0.339663i
$448$	−10.0468	−	31.7262i	−0.474669	−	1.49892i
$449$			4.45318i			0.210159i	0.994464	+	0.105079i	$0.0335096\pi$
$449$			4.45318i			0.210159i	−0.994464	+	0.105079i	$0.966490\pi$
$450$	1.02167	+	0.494166i	0.0481619	+	0.0232952i
$451$			1.14443i			0.0538889i
$452$	3.65965	−	0.375426i	0.172136	−	0.0176586i
$453$	−2.24465	−	2.24465i	−0.105463	−	0.105463i
$454$	9.64070	−	27.1171i	0.452461	−	1.27267i
$455$	−25.5628	−	12.2589i	−1.19840	−	0.574704i
$456$	−17.5291	+	10.6519i	−0.820877	+	0.498823i
$457$	8.43937	−	8.43937i	0.394777	−	0.394777i	−0.481609	−	0.876386i	$-0.659947\pi$
$457$	8.43937	−	8.43937i	0.394777	−	0.394777i	0.876386	+	0.481609i	$0.159947\pi$
$458$	14.1515	−	6.72827i	0.661255	−	0.314391i
$459$	9.53539			0.445074
$460$	26.3014	+	9.45003i	1.22631	+	0.440610i
$461$	10.5560			0.491640			0.245820	−	0.969315i	$-0.420943\pi$
$461$	10.5560			0.491640			0.245820	+	0.969315i	$0.420943\pi$
$462$	−10.8095	+	5.13935i	−0.502904	+	0.239104i
$463$	19.3155	−	19.3155i	0.897667	−	0.897667i	−0.0975628	−	0.995229i	$-0.531105\pi$
$463$	19.3155	−	19.3155i	0.897667	−	0.897667i	0.995229	+	0.0975628i	$0.0311047\pi$
$464$	37.9494	−	7.86891i	1.76176	−	0.365305i
$465$	−26.6948	+	9.39001i	−1.23794	+	0.435451i
$466$	0.974365	−	2.74066i	0.0451366	−	0.126959i
$467$	1.57153	+	1.57153i	0.0727218	+	0.0727218i	0.742532	−	0.669810i	$-0.233625\pi$
$467$	1.57153	+	1.57153i	0.0727218	+	0.0727218i	−0.669810	+	0.742532i	$0.733625\pi$
$468$	−0.0998406	−	0.973245i	−0.00461513	−	0.0449883i
$469$			2.34434i			0.108251i
$470$	5.75222	+	5.79087i	0.265330	+	0.267113i
$471$			37.1242i			1.71059i
$472$	−32.2354	−	7.86661i	−1.48376	−	0.362090i
$473$	−2.11896	−	2.11896i	−0.0974301	−	0.0974301i
$474$	15.3709	+	5.46469i	0.706009	+	0.251002i
$475$	12.7690	+	15.9047i	0.585883	+	0.729760i
$476$	9.92049	−	12.1886i	0.454705	−	0.558661i
$477$	−0.866099	+	0.866099i	−0.0396560	+	0.0396560i
$478$	−6.03016	−	12.6831i	−0.275813	−	0.580113i
$479$	30.5928			1.39782			0.698910	−	0.715210i	$-0.253669\pi$
$479$	30.5928			1.39782			0.698910	+	0.715210i	$0.253669\pi$
$480$	−18.7567	−	12.4042i	−0.856124	−	0.566172i
$481$	4.49613			0.205006
$482$	−0.536137	−	1.12765i	−0.0244204	−	0.0513630i
$483$	32.6792	−	32.6792i	1.48695	−	1.48695i
$484$	−12.2341	+	15.0311i	−0.556095	+	0.683232i
$485$	14.1983	+	40.3642i	0.644710	+	1.83284i
$486$	−2.22022	−	0.789338i	−0.100711	−	0.0358051i
$487$	1.92248	+	1.92248i	0.0871157	+	0.0871157i	0.749322	−	0.662206i	$-0.230380\pi$
$487$	1.92248	+	1.92248i	0.0871157	+	0.0871157i	−0.662206	+	0.749322i	$0.730380\pi$
$488$	−29.8339	−	7.28055i	−1.35052	−	0.329575i
$489$		−	12.7912i		−	0.578438i
$490$	−0.109126	+	32.5855i	−0.00492979	+	1.47206i
$491$			35.2543i			1.59101i	0.605950	+	0.795503i	$0.292793\pi$
$491$			35.2543i			1.59101i	−0.605950	+	0.795503i	$0.707207\pi$
$492$	0.362844	+	3.53700i	0.0163583	+	0.159460i
$493$	12.9417	+	12.9417i	0.582863	+	0.582863i
$494$	5.88991	−	16.5669i	0.264999	−	0.745382i
$495$	−0.177599	+	0.370338i	−0.00798248	+	0.0166454i
$496$	27.8814	−	5.78128i	1.25191	−	0.259587i
$497$	−36.1461	+	36.1461i	−1.62138	+	1.62138i
$498$	−27.3679	+	13.0120i	−1.22638	+	0.583081i
$499$	9.55038			0.427534			0.213767	−	0.976885i	$-0.431427\pi$
$499$	9.55038			0.427534			0.213767	+	0.976885i	$0.431427\pi$
$500$	−9.80376	+	20.0969i	−0.438438	+	0.898762i
$501$	−3.22711			−0.144177
$502$	14.2737	−	6.78638i	0.637066	−	0.302891i
$503$	−9.01935	+	9.01935i	−0.402153	+	0.402153i	−0.878991	−	0.476838i	$-0.841783\pi$
$503$	−9.01935	+	9.01935i	−0.402153	+	0.402153i	0.476838	+	0.878991i	$0.341783\pi$
$504$	−1.61382	+	0.980670i	−0.0718852	+	0.0436825i
$505$	−10.5933	+	22.0898i	−0.471398	+	0.982981i
$506$	−3.38806	+	9.52984i	−0.150618	+	0.423653i
$507$	−4.66464	−	4.66464i	−0.207164	−	0.207164i
$508$	−24.4653	+	2.50978i	−1.08547	+	0.111353i
$509$			31.1191i			1.37933i	0.724129	+	0.689665i	$0.242242\pi$
$509$			31.1191i			1.37933i	−0.724129	+	0.689665i	$0.757758\pi$
$510$	0.0355628	−	10.6193i	0.00157475	−	0.470229i
$511$			12.9036i			0.570823i
$512$	17.0401	+	14.8874i	0.753075	+	0.657935i
$513$	−14.5608	−	14.5608i	−0.642876	−	0.642876i
$514$	33.7027	+	11.9820i	1.48656	+	0.528504i
$515$	−8.72668	−	24.8091i	−0.384544	−	1.09322i
$516$	−7.22076	−	5.87711i	−0.317876	−	0.258725i
$517$	−2.08873	+	2.08873i	−0.0918622	+	0.0918622i
$518$	−3.72640	−	7.83768i	−0.163729	−	0.344368i
$519$	−16.2573			−0.713615
$520$	19.1821	−	1.90290i	0.841189	−	0.0834478i
$521$	−15.3103			−0.670757			−0.335378	−	0.942084i	$-0.608864\pi$
$521$	−15.3103			−0.670757			−0.335378	+	0.942084i	$0.608864\pi$
$522$	−0.944328	−	1.98619i	−0.0413321	−	0.0869332i
$523$	13.0232	−	13.0232i	0.569464	−	0.569464i	−0.362514	−	0.931978i	$-0.618082\pi$
$523$	13.0232	−	13.0232i	0.569464	−	0.569464i	0.931978	+	0.362514i	$0.118082\pi$
$524$	−11.2627	−	9.16692i	−0.492013	−	0.400459i
$525$	23.1491	+	28.8339i	1.01031	+	1.25841i
$526$	0.662650	+	0.235586i	0.0288929	+	0.0102720i
$527$	9.50822	+	9.50822i	0.414185	+	0.414185i
$528$	4.46632	−	6.80305i	0.194371	−	0.296065i
$529$		−	16.0532i		−	0.697967i
$530$	−17.0073	−	17.1216i	−0.738749	−	0.743713i
$531$			1.88289i			0.0817103i
$532$	−33.7612	+	3.46340i	−1.46373	+	0.150157i
$533$	−2.15515	−	2.15515i	−0.0933497	−	0.0933497i
$534$	3.85132	−	10.8329i	0.166663	−	0.468785i
$535$	39.8554	−	14.0193i	1.72310	−	0.606106i
$536$	−0.827771	−	1.36220i	−0.0357543	−	0.0588382i
$537$	14.1857	−	14.1857i	0.612158	−	0.612158i
$538$	−1.80696	+	0.859114i	−0.0779036	+	0.0370390i
$539$	−11.7927			−0.507949
$540$	7.63351	−	21.2456i	0.328494	−	0.914266i
$541$	12.4150			0.533764			0.266882	−	0.963729i	$-0.414007\pi$
$541$	12.4150			0.533764			0.266882	+	0.963729i	$0.414007\pi$
$542$	6.05265	−	2.87772i	0.259984	−	0.123608i
$543$	−13.5589	+	13.5589i	−0.581870	+	0.581870i
$544$	−1.46071	+	10.5852i	−0.0626275	+	0.453835i
$545$	19.6647	+	9.43039i	0.842343	+	0.403954i
$546$	10.6779	−	30.0344i	0.456970	−	1.28535i
$547$	13.3451	+	13.3451i	0.570594	+	0.570594i	0.932294	−	0.361700i	$-0.117804\pi$
$547$	13.3451	+	13.3451i	0.570594	+	0.570594i	−0.361700	+	0.932294i	$0.617804\pi$
$548$	−3.49314	−	34.0511i	−0.149220	−	1.45459i
$549$			1.74261i			0.0743728i
$550$	−7.28490	−	3.52360i	−0.310629	−	0.150247i
$551$		−	39.5246i		−	1.68380i
$552$	−7.44979	+	30.5274i	−0.317084	+	1.29933i
$553$	19.0861	+	19.0861i	0.811623	+	0.811623i
$554$	8.70888	+	3.09619i	0.370005	+	0.131545i
$555$	−5.28763	−	2.53573i	−0.224448	−	0.107636i
$556$	4.94977	−	6.08141i	0.209917	−	0.257909i
$557$	−5.96080	+	5.96080i	−0.252567	+	0.252567i	−0.822022	−	0.569455i	$-0.807154\pi$
$557$	−5.96080	+	5.96080i	−0.252567	+	0.252567i	0.569455	+	0.822022i	$0.307154\pi$
$558$	−0.693797	−	1.45925i	−0.0293708	−	0.0617751i
$559$	7.98073			0.337549
$560$	−19.2153	−	31.8612i	−0.811994	−	1.34638i
$561$	3.84312			0.162257
$562$	−10.4529	−	21.9855i	−0.440930	−	0.927400i
$563$	8.13479	−	8.13479i	0.342840	−	0.342840i	−0.514594	−	0.857434i	$-0.672057\pi$
$563$	8.13479	−	8.13479i	0.342840	−	0.342840i	0.857434	+	0.514594i	$0.172057\pi$
$564$	−5.79325	+	7.11773i	−0.243940	+	0.299710i
$565$	3.88005	−	1.36482i	0.163235	−	0.0574185i
$566$	19.3104	+	6.86525i	0.811676	+	0.288568i
$567$	−27.8138	−	27.8138i	−1.16807	−	1.16807i
$568$	8.24014	−	33.7661i	0.345749	−	1.41679i
$569$			35.9069i			1.50530i	0.658423	+	0.752648i	$0.271224\pi$
$569$			35.9069i			1.50530i	−0.658423	+	0.752648i	$0.728776\pi$
$570$	−16.2702	+	16.1616i	−0.681485	+	0.676936i
$571$			15.7866i			0.660650i	0.943867	+	0.330325i	$0.107158\pi$
$571$			15.7866i			0.660650i	−0.943867	+	0.330325i	$0.892842\pi$
$572$	0.711903	+	6.93962i	0.0297662	+	0.290160i
$573$	−33.9732	−	33.9732i	−1.41925	−	1.41925i
$574$	−1.97067	+	5.54305i	−0.0822544	+	0.231363i
$575$	31.0611	+	3.39679i	1.29534	+	0.141656i
$576$	0.591459	−	1.13966i	0.0246441	−	0.0474858i
$577$	23.5381	−	23.5381i	0.979903	−	0.979903i	−0.0198993	−	0.999802i	$-0.506335\pi$
$577$	23.5381	−	23.5381i	0.979903	−	0.979903i	0.999802	+	0.0198993i	$0.00633457\pi$
$578$	17.1553	−	8.15643i	0.713566	−	0.339263i
$579$	20.4338			0.849198
$580$	39.1954	−	18.4747i	1.62750	−	0.767119i
$581$	−50.1398			−2.08015
$582$	−43.4492	+	20.6578i	−1.80103	+	0.856292i
$583$	6.17563	−	6.17563i	0.255769	−	0.255769i
$584$	−4.55619	−	7.49780i	−0.188536	−	0.310261i
$585$	−0.362959	−	1.03186i	−0.0150065	−	0.0426620i
$586$	−7.37049	+	20.7315i	−0.304472	+	0.856410i
$587$	−8.62881	−	8.62881i	−0.356149	−	0.356149i	0.506242	−	0.862391i	$-0.331034\pi$
$587$	−8.62881	−	8.62881i	−0.356149	−	0.356149i	−0.862391	+	0.506242i	$0.831034\pi$
$588$	−36.4470	+	3.73892i	−1.50305	+	0.154191i
$589$		−	29.0387i		−	1.19652i
$590$	−37.0978	−	0.124237i	−1.52729	−	0.00511474i
$591$		−	4.68739i		−	0.192813i
$592$	4.93270	+	3.23840i	0.202733	+	0.133098i
$593$	3.10599	+	3.10599i	0.127548	+	0.127548i	0.767999	−	0.640451i	$-0.221253\pi$
$593$	3.10599	+	3.10599i	0.127548	+	0.127548i	−0.640451	+	0.767999i	$0.721253\pi$
$594$	7.69798	+	2.73680i	0.315852	+	0.112292i
$595$	7.59761	−	15.8429i	0.311472	−	0.649496i
$596$	8.86120	+	7.21230i	0.362969	+	0.295427i
$597$	−9.49914	+	9.49914i	−0.388774	+	0.388774i
$598$	−11.5660	−	24.3266i	−0.472969	−	0.994788i
$599$	−15.2163			−0.621720			−0.310860	−	0.950456i	$-0.600617\pi$
$599$	−15.2163			−0.621720			−0.310860	+	0.950456i	$0.600617\pi$
$600$	−23.6321	−	8.58044i	−0.964776	−	0.350295i
$601$	−20.3368			−0.829557			−0.414778	−	0.909922i	$-0.636141\pi$
$601$	−20.3368			−0.829557			−0.414778	+	0.909922i	$0.636141\pi$
$602$	−6.61445	−	13.9121i	−0.269585	−	0.567013i
$603$	−0.0639587	+	0.0639587i	−0.00260460	+	0.00260460i
$604$	2.76974	+	2.25435i	0.112699	+	0.0917281i
$605$	−9.36948	+	19.5377i	−0.380924	+	0.794320i
$606$	−25.9539	−	9.22715i	−1.05430	−	0.374827i
$607$	8.60981	+	8.60981i	0.349461	+	0.349461i	0.859909	−	0.510448i	$-0.170520\pi$
$607$	8.60981	+	8.60981i	0.349461	+	0.349461i	−0.510448	+	0.859909i	$0.670520\pi$
$608$	18.3944	−	13.9333i	0.745992	−	0.565070i
$609$		−	71.6545i		−	2.90359i
$610$	−34.3340	−	0.114981i	−1.39014	−	0.00465545i
$611$		−	7.86686i		−	0.318259i
$612$	0.603183	−	0.0618777i	0.0243822	−	0.00250126i
$613$	26.1789	+	26.1789i	1.05735	+	1.05735i	0.998252	+	0.0591021i	$0.0188238\pi$
$613$	26.1789	+	26.1789i	1.05735	+	1.05735i	0.0591021	+	0.998252i	$0.481176\pi$
$614$	0.815151	−	2.29283i	0.0328968	−	0.0925311i
$615$	1.31908	+	3.75000i	0.0531904	+	0.151215i
$616$	11.5072	−	6.99257i	0.463637	−	0.281739i
$617$	26.4629	−	26.4629i	1.06536	−	1.06536i	0.0676479	−	0.997709i	$-0.478451\pi$
$617$	26.4629	−	26.4629i	1.06536	−	1.06536i	0.997709	−	0.0676479i	$-0.0215495\pi$
$618$	26.7052	−	12.6969i	1.07424	−	0.510744i
$619$	31.3083			1.25839			0.629194	−	0.777249i	$-0.283385\pi$
$619$	31.3083			1.25839			0.629194	+	0.777249i	$0.283385\pi$
$620$	28.7969	−	13.5733i	1.15651	−	0.545118i
$621$	−31.5463			−1.26591
$622$	−2.26694	+	1.07781i	−0.0908961	+	0.0432163i
$623$	13.4512	−	13.4512i	0.538911	−	0.538911i
$624$	4.40046	+	21.2221i	0.176159	+	0.849564i
$625$	−5.40329	+	24.4091i	−0.216132	+	0.976364i
$626$	−9.40006	+	26.4402i	−0.375702	+	1.05676i
$627$	−5.86856	−	5.86856i	−0.234368	−	0.234368i
$628$	−4.26207	−	41.5466i	−0.170075	−	1.65789i
$629$			2.78654i			0.111107i
$630$	−1.49792	+	1.48792i	−0.0596785	+	0.0592801i
$631$			5.66950i			0.225699i	0.993612	+	0.112850i	$0.0359978\pi$
$631$			5.66950i			0.225699i	−0.993612	+	0.112850i	$0.964002\pi$
$632$	−17.8294	−	4.35101i	−0.709214	−	0.173074i
$633$	−6.99944	−	6.99944i	−0.278203	−	0.278203i
$634$	10.0602	+	3.57663i	0.399543	+	0.142046i
$635$	−25.9386	+	9.12402i	−1.02934	+	0.362076i
$636$	17.1286	−	21.0446i	0.679193	−	0.834473i
$637$	22.2077	−	22.2077i	0.879901	−	0.879901i
$638$	6.73343	+	14.1623i	0.266579	+	0.560692i
$639$	−1.97229			−0.0780226
$640$	22.4152	+	11.7285i	0.886040	+	0.463609i
$641$	7.78974			0.307676			0.153838	−	0.988096i	$-0.450837\pi$
$641$	7.78974			0.307676			0.153838	+	0.988096i	$0.450837\pi$
$642$	20.3973	+	42.9014i	0.805019	+	1.69318i
$643$	−23.8043	+	23.8043i	−0.938749	+	0.938749i	−0.998229	−	0.0594809i	$-0.981055\pi$
$643$	−23.8043	+	23.8043i	−0.938749	+	0.938749i	0.0594809	+	0.998229i	$0.481055\pi$
$644$	−32.8203	+	40.3239i	−1.29330	+	1.58898i
$645$	−9.38567	−	4.50099i	−0.369560	−	0.177226i
$646$	10.2676	+	3.65036i	0.403974	+	0.143621i
$647$	6.82292	+	6.82292i	0.268237	+	0.268237i	0.828389	−	0.560153i	$-0.189258\pi$
$647$	6.82292	+	6.82292i	0.268237	+	0.268237i	−0.560153	+	0.828389i	$0.689258\pi$
$648$	25.9824	+	6.34064i	1.02068	+	0.249084i
$649$		−	13.4257i		−	0.527006i
$650$	20.3542	−	7.08316i	0.798358	−	0.277825i
$651$		−	52.6445i		−	2.06330i
$652$	1.46850	+	14.3150i	0.0575110	+	0.560617i
$653$	−21.7093	−	21.7093i	−0.849552	−	0.849552i	0.140525	−	0.990077i	$-0.455121\pi$
$653$	−21.7093	−	21.7093i	−0.849552	−	0.849552i	−0.990077	+	0.140525i	$0.955121\pi$
$654$	−8.21418	+	23.1046i	−0.321200	+	0.903461i
$655$	−14.6395	−	7.02049i	−0.572011	−	0.274313i
$656$	−0.812135	−	3.91669i	−0.0317086	−	0.152921i
$657$	−0.352039	+	0.352039i	−0.0137344	+	0.0137344i
$658$	−13.7136	+	6.52007i	−0.534610	+	0.254179i
$659$	−46.6864			−1.81864			−0.909322	−	0.416093i	$-0.863399\pi$
$659$	−46.6864			−1.81864			−0.909322	+	0.416093i	$0.863399\pi$
$660$	3.07659	−	8.56279i	0.119756	−	0.333306i
$661$	−24.0442			−0.935212			−0.467606	−	0.883937i	$-0.654883\pi$
$661$	−24.0442			−0.935212			−0.467606	+	0.883937i	$0.654883\pi$
$662$	33.7949	−	16.0677i	1.31348	−	0.624489i
$663$	−7.23724	+	7.23724i	−0.281071	+	0.281071i
$664$	29.1343	−	17.7040i	1.13063	−	0.687050i
$665$	−35.7944	+	12.5908i	−1.38805	+	0.488251i
$666$	0.112165	−	0.315494i	0.00434629	−	0.0122251i
$667$	−42.8154	−	42.8154i	−1.65782	−	1.65782i
$668$	3.61154	−	0.370491i	0.139735	−	0.0143347i
$669$			34.4510i			1.33195i
$670$	−1.25593	−	1.26437i	−0.0485209	−	0.0488470i
$671$		−	12.4255i		−	0.479682i
$672$	33.3474	−	25.2598i	1.28640	−	0.974419i
$673$	−23.8673	−	23.8673i	−0.920015	−	0.920015i	0.0770146	−	0.997030i	$-0.475461\pi$
$673$	−23.8673	−	23.8673i	−0.920015	−	0.920015i	−0.997030	+	0.0770146i	$0.975461\pi$
$674$	−35.9499	−	12.7810i	−1.38474	−	0.492305i
$675$	2.74385	−	25.0904i	0.105611	−	0.965732i
$676$	5.75585	+	4.68479i	0.221379	+	0.180184i
$677$	29.3333	−	29.3333i	1.12737	−	1.12737i	0.136765	−	0.990603i	$-0.456329\pi$
$677$	29.3333	−	29.3333i	1.12737	−	1.12737i	0.990603	−	0.136765i	$-0.0436707\pi$
$678$	1.98575	+	4.17659i	0.0762622	+	0.160401i
$679$	−79.6017			−3.05483
$680$	1.17935	+	11.8884i	0.0452261	+	0.455898i
$681$	36.1786			1.38637
$682$	4.94705	+	10.4050i	0.189432	+	0.398430i
$683$	−31.6539	+	31.6539i	−1.21120	+	1.21120i	−0.240569	+	0.970632i	$0.577334\pi$
$683$	−31.6539	+	31.6539i	−1.21120	+	1.21120i	−0.970632	+	0.240569i	$0.922666\pi$
$684$	−1.01557	−	0.826590i	−0.0388312	−	0.0316055i
$685$	−12.6989	−	36.1018i	−0.485201	−	1.37938i
$686$	−18.3170	−	6.51210i	−0.699348	−	0.248633i
$687$	13.9285	+	13.9285i	0.531404	+	0.531404i
$688$	8.75566	+	5.74824i	0.333806	+	0.219150i
$689$			23.2595i			0.886117i
$690$	−0.117654	+	35.1321i	−0.00447900	+	1.33746i
$691$			0.208044i			0.00791435i	0.999992	+	0.00395718i	$0.00125961\pi$
$691$			0.208044i			0.00791435i	−0.999992	+	0.00395718i	$0.998740\pi$
$692$	18.1939	−	1.86643i	0.691630	−	0.0709510i
$693$	−0.540289	−	0.540289i	−0.0205239	−	0.0205239i
$694$	14.0857	−	39.6197i	0.534685	−	1.50394i
$695$	3.79078	−	7.90472i	0.143793	−	0.299843i
$696$	25.3008	+	41.6357i	0.959023	+	1.57820i
$697$	1.33568	−	1.33568i	0.0505926	−	0.0505926i
$698$	21.1173	−	10.0402i	0.799302	−	0.380025i
$699$	3.65649			0.138301
$700$	−29.2170	−	29.6111i	−1.10430	−	1.11919i
$701$	44.9919			1.69932			0.849660	−	0.527331i	$-0.176807\pi$
$701$	44.9919			1.69932			0.849660	+	0.527331i	$0.176807\pi$
$702$	−19.6504	+	9.34274i	−0.741658	+	0.352619i
$703$	4.25514	−	4.25514i	0.160485	−	0.160485i
$704$	−4.21734	+	8.12622i	−0.158947	+	0.306269i
$705$	−4.43676	+	9.25175i	−0.167098	+	0.348441i
$706$	−15.6013	+	43.8830i	−0.587164	+	1.65156i
$707$	−32.2269	−	32.2269i	−1.21202	−	1.21202i
$708$	−4.25667	−	41.4939i	−0.159975	−	1.55944i
$709$		−	9.97817i		−	0.374738i	−0.982290	−	0.187369i	$-0.940004\pi$
$709$		−	9.97817i		−	0.374738i	0.982290	−	0.187369i	$-0.0599960\pi$
$710$	0.130136	−	38.8593i	0.00488391	−	1.45836i
$711$			1.04142i			0.0390563i
$712$	−3.06644	+	12.5655i	−0.114920	+	0.470912i
$713$	−31.4564	−	31.4564i	−1.17805	−	1.17805i
$714$	18.6143	+	6.61777i	0.696621	+	0.247664i
$715$	2.58805	+	7.35755i	0.0967874	+	0.275157i
$716$	−14.2470	+	17.5042i	−0.532435	+	0.654162i
$717$	12.4833	−	12.4833i	0.466196	−	0.466196i
$718$	0.504941	+	1.06203i	0.0188442	+	0.0396348i
$719$	−17.0627			−0.636333			−0.318167	−	0.948035i	$-0.603067\pi$
$719$	−17.0627			−0.636333			−0.318167	+	0.948035i	$0.603067\pi$
$720$	0.345007	−	1.39348i	0.0128577	−	0.0519318i
$721$	48.9256			1.82208
$722$	1.43288	+	3.01375i	0.0533262	+	0.112160i
$723$	1.10988	−	1.10988i	0.0412769	−	0.0412769i
$724$	13.6175	−	16.7308i	0.506091	−	0.621796i
$725$	37.7773	−	30.3293i	1.40302	−	1.12640i
$726$	−22.9554	−	8.16113i	−0.851953	−	0.302888i
$727$	6.56677	+	6.56677i	0.243548	+	0.243548i	0.818316	−	0.574768i	$-0.194908\pi$
$727$	6.56677	+	6.56677i	0.243548	+	0.243548i	−0.574768	+	0.818316i	$0.694908\pi$
$728$	−8.50175	+	34.8381i	−0.315096	+	1.29119i
$729$			25.4051i			0.940929i
$730$	−6.91286	−	6.95932i	−0.255857	−	0.257576i
$731$			4.94618i			0.182941i
$732$	−3.93955	−	38.4027i	−0.145610	−	1.41940i
$733$	−23.7647	−	23.7647i	−0.877768	−	0.877768i	0.115535	−	0.993303i	$-0.463142\pi$
$733$	−23.7647	−	23.7647i	−0.877768	−	0.877768i	−0.993303	+	0.115535i	$0.963142\pi$
$734$	−8.51429	+	23.9487i	−0.314268	+	0.883964i
$735$	−38.6419	+	13.5924i	−1.42533	+	0.501365i
$736$	4.83252	−	35.0193i	0.178129	−	1.29083i
$737$	0.456051	−	0.456051i	0.0167988	−	0.0167988i
$738$	−0.204991	+	0.0974623i	−0.00754582	+	0.00358764i
$739$	−39.2555			−1.44404			−0.722018	−	0.691875i	$-0.756785\pi$
$739$	−39.2555			−1.44404			−0.722018	+	0.691875i	$0.756785\pi$
$740$	6.20864	+	2.23075i	0.228234	+	0.0820042i
$741$	22.1030			0.811973
$742$	40.5461	−	19.2775i	1.48850	−	0.707701i
$743$	13.3988	−	13.3988i	0.491553	−	0.491553i	−0.417242	−	0.908795i	$-0.637003\pi$
$743$	13.3988	−	13.3988i	0.491553	−	0.491553i	0.908795	+	0.417242i	$0.137003\pi$
$744$	18.5884	+	30.5897i	0.681486	+	1.12147i
$745$	11.5180	+	5.52354i	0.421985	+	0.202367i
$746$	2.99297	−	8.41852i	0.109580	−	0.308224i
$747$	−1.36792	−	1.36792i	−0.0500497	−	0.0500497i
$748$	−4.30094	+	0.441213i	−0.157258	+	0.0161323i
$749$			78.5982i			2.87191i
$750$	−27.9322	−	3.14931i	−1.01994	−	0.114997i
$751$			32.4578i			1.18440i	0.805791	+	0.592200i	$0.201741\pi$
$751$			32.4578i			1.18440i	−0.805791	+	0.592200i	$0.798259\pi$
$752$	5.66622	−	8.63073i	0.206626	−	0.314730i
$753$	14.0488	+	14.0488i	0.511965	+	0.511965i
$754$	−39.3502	−	13.9898i	−1.43305	−	0.509480i
$755$	3.60016	+	1.72649i	0.131023	+	0.0628335i
$756$	32.5727	+	26.5115i	1.18466	+	0.964214i
$757$	15.9859	−	15.9859i	0.581017	−	0.581017i	−0.354165	−	0.935183i	$-0.615235\pi$
$757$	15.9859	−	15.9859i	0.581017	−	0.581017i	0.935183	+	0.354165i	$0.115235\pi$
$758$	18.1741	+	38.2253i	0.660113	+	1.38841i
$759$	−12.7143			−0.461501
$760$	16.3530	−	19.9548i	0.593185	−	0.723837i
$761$	−52.1792			−1.89149			−0.945747	−	0.324903i	$-0.894668\pi$
$761$	−52.1792			−1.89149			−0.945747	+	0.324903i	$0.894668\pi$
$762$	−13.2750	−	27.9211i	−0.480902	−	1.01147i
$763$	−28.6890	+	28.6890i	−1.03861	+	1.03861i
$764$	41.9206	+	34.1200i	1.51663	+	1.23442i
$765$	0.639509	−	0.224950i	0.0231215	−	0.00813307i
$766$	−8.01216	−	2.84850i	−0.289491	−	0.102920i
$767$	25.2829	+	25.2829i	0.912912	+	0.912912i
$768$	−10.4578	+	26.4523i	−0.377363	+	0.954514i
$769$		−	9.70677i		−	0.350035i	−0.984565	−	0.175018i	$-0.944002\pi$
$769$		−	9.70677i		−	0.350035i	0.984565	−	0.175018i	$-0.0559982\pi$
$770$	10.6807	−	10.6095i	0.384907	−	0.382338i
$771$			44.9648i			1.61937i
$772$	−22.8680	+	2.34591i	−0.823036	+	0.0844313i
$773$	30.9620	+	30.9620i	1.11363	+	1.11363i	0.992656	+	0.120971i	$0.0386009\pi$
$773$	30.9620	+	30.9620i	1.11363	+	1.11363i	0.120971	+	0.992656i	$0.461399\pi$
$774$	0.199095	−	0.560008i	0.00715632	−	0.0201291i
$775$	27.7550	−	22.2829i	0.996988	−	0.800426i
$776$	46.2535	−	28.1069i	1.66040	−	1.00898i
$777$	7.71418	−	7.71418i	0.276745	−	0.276745i
$778$	4.23257	−	2.01236i	0.151745	−	0.0721467i
$779$	−4.07926			−0.146155
$780$	10.3314	+	21.9189i	0.369924	+	0.784823i
$781$	14.0632			0.503222
$782$	15.0768	−	7.16820i	0.539144	−	0.256334i
$783$	−34.5852	+	34.5852i	−1.23598	+	1.23598i
$784$	40.3595	−	8.36865i	1.44141	−	0.298880i
$785$	−15.4943	−	44.0487i	−0.553015	−	1.57216i
$786$	6.11508	−	17.2003i	0.218118	−	0.613514i
$787$	−12.4690	−	12.4690i	−0.444472	−	0.444472i	0.449040	−	0.893512i	$-0.351766\pi$
$787$	−12.4690	−	12.4690i	−0.444472	−	0.444472i	−0.893512	+	0.449040i	$0.851766\pi$
$788$	0.538139	+	5.24577i	0.0191704	+	0.186873i
$789$			0.884081i			0.0314741i
$790$	−20.5187	−	0.0687151i	−0.730023	−	0.00244477i
$791$			7.65178i			0.272066i
$792$	0.504714	+	0.123168i	0.0179342	+	0.00437659i
$793$	23.3993	+	23.3993i	0.830934	+	0.830934i
$794$	−0.746836	−	0.265516i	−0.0265042	−	0.00942282i
$795$	13.1179	−	27.3542i	0.465245	−	0.970152i
$796$	9.54017	−	11.7213i	0.338143	−	0.415450i
$797$	4.86679	−	4.86679i	0.172390	−	0.172390i	−0.615638	−	0.788029i	$-0.711102\pi$
$797$	4.86679	−	4.86679i	0.172390	−	0.172390i	0.788029	+	0.615638i	$0.211102\pi$
$798$	−18.3190	−	38.5301i	−0.648486	−	1.36395i
$799$	4.87560			0.172486
$800$	27.4324	+	6.88949i	0.969881	+	0.243580i
$801$	0.733957			0.0259331
$802$	−18.5400	−	38.9949i	−0.654671	−	1.37696i
$803$	2.51018	−	2.51018i	0.0885823	−	0.0885823i
$804$	1.26489	−	1.55408i	0.0446093	−	0.0548081i
$805$	−25.1355	+	52.4137i	−0.885909	+	1.84734i
$806$	−28.9106	−	10.2783i	−1.01833	−	0.362039i
$807$	−1.77849	−	1.77849i	−0.0626057	−	0.0626057i
$808$	30.1050	+	7.34669i	1.05909	+	0.258456i
$809$			10.5920i			0.372396i	0.982512	+	0.186198i	$0.0596165\pi$
$809$			10.5920i			0.372396i	−0.982512	+	0.186198i	$0.940383\pi$
$810$	29.9015	+	0.100137i	1.05063	+	0.00351846i
$811$			30.0277i			1.05442i	0.849736	+	0.527208i	$0.176761\pi$
$811$			30.0277i			1.05442i	−0.849736	+	0.527208i	$0.823239\pi$
$812$	8.22635	+	80.1904i	0.288688	+	2.81413i
$813$	5.95728	+	5.95728i	0.208931	+	0.208931i
$814$	−0.799779	+	2.24959i	−0.0280322	+	0.0788482i
$815$	5.33858	+	15.1770i	0.187002	+	0.531629i
$816$	−13.1527	+	2.72725i	−0.460437	+	0.0954728i
$817$	7.55296	−	7.55296i	0.264245	−	0.264245i
$818$	−46.5584	+	22.1361i	−1.62788	+	0.773969i
$819$	2.03491			0.0711055
$820$	−1.90674	−	4.04529i	−0.0665861	−	0.141268i
$821$	−50.6506			−1.76772			−0.883859	−	0.467753i	$-0.845064\pi$
$821$	−50.6506			−1.76772			−0.883859	+	0.467753i	$0.845064\pi$
$822$	38.8609	−	18.4763i	1.35543	−	0.644435i
$823$	1.31967	−	1.31967i	0.0460006	−	0.0460006i	−0.683732	−	0.729733i	$-0.739644\pi$
$823$	1.31967	−	1.31967i	0.0460006	−	0.0460006i	0.729733	+	0.683732i	$0.239644\pi$
$824$	−28.4288	+	17.2753i	−0.990363	+	0.601815i
$825$	1.10587	−	10.1124i	0.0385016	−	0.352068i
$826$	23.1188	−	65.0278i	0.804405	−	2.26261i
$827$	−24.4259	−	24.4259i	−0.849371	−	0.849371i	0.140684	−	0.990055i	$-0.455070\pi$
$827$	−24.4259	−	24.4259i	−0.849371	−	0.849371i	−0.990055	+	0.140684i	$0.955070\pi$
$828$	−1.99553	+	0.204712i	−0.0693496	+	0.00711424i
$829$		−	11.3556i		−	0.394397i	−0.980364	−	0.197198i	$-0.936816\pi$
$829$		−	11.3556i		−	0.394397i	0.980364	−	0.197198i	$-0.0631843\pi$
$830$	27.0419	−	26.8614i	0.938638	−	0.932372i
$831$			11.6190i			0.403060i
$832$	−7.36108	−	23.2450i	−0.255200	−	0.805875i
$833$	13.7636	+	13.7636i	0.476879	+	0.476879i
$834$	9.28747	+	3.30190i	0.321599	+	0.114335i
$835$	3.82904	−	1.34688i	0.132509	−	0.0466107i
$836$	7.24141	+	5.89392i	0.250449	+	0.203845i
$837$	−25.4097	+	25.4097i	−0.878289	+	0.878289i
$838$	18.3565	+	38.6089i	0.634114	+	1.33372i
$839$	42.1009			1.45348			0.726741	−	0.686911i	$-0.241034\pi$
$839$	42.1009			1.45348			0.726741	+	0.686911i	$0.241034\pi$
$840$	29.6465	−	36.1762i	1.02290	−	1.24820i
$841$	−64.8798			−2.23723
$842$	7.23085	+	15.2085i	0.249192	+	0.524121i
$843$	21.6390	−	21.6390i	0.745287	−	0.745287i
$844$	8.63683	+	7.02967i	0.297292	+	0.241971i
$845$	7.48155	+	3.58785i	0.257373	+	0.123426i
$846$	−0.552018	−	0.196254i	−0.0189788	−	0.00674736i
$847$	−28.5037	−	28.5037i	−0.979399	−	0.979399i
$848$	−16.7530	+	25.5180i	−0.575301	+	0.876292i
$849$			25.7632i			0.884189i
$850$	4.38990	+	12.6148i	0.150572	+	0.432685i
$851$		−	9.21883i		−	0.316017i
$852$	43.4642	−	4.45879i	1.48906	−	0.152755i
$853$	−2.58848	−	2.58848i	−0.0886278	−	0.0886278i	0.661403	−	0.750031i	$-0.269961\pi$
$853$	−2.58848	−	2.58848i	−0.0886278	−	0.0886278i	−0.750031	+	0.661403i	$0.769961\pi$
$854$	21.3964	−	60.1833i	0.732171	−	2.05943i
$855$	−1.32005	−	0.633044i	−0.0451449	−	0.0216497i
$856$	−27.7525	−	45.6703i	−0.948562	−	1.56098i
$857$	19.9822	−	19.9822i	0.682580	−	0.682580i	−0.278001	−	0.960581i	$-0.589672\pi$
$857$	19.9822	−	19.9822i	0.682580	−	0.682580i	0.960581	+	0.278001i	$0.0896717\pi$
$858$	−7.91987	+	3.76548i	−0.270380	+	0.128551i
$859$	−5.20980			−0.177756			−0.0888781	−	0.996043i	$-0.528328\pi$
$859$	−5.20980			−0.177756			−0.0888781	+	0.996043i	$0.528328\pi$
$860$	11.0205	+	3.95964i	0.375795	+	0.135023i
$861$	−7.39533			−0.252032
$862$	−2.92039	+	1.38849i	−0.0994690	+	0.0472922i
$863$	−31.9252	+	31.9252i	−1.08675	+	1.08675i	−0.0908841	+	0.995861i	$0.528969\pi$
$863$	−31.9252	+	31.9252i	−1.08675	+	1.08675i	−0.995861	+	0.0908841i	$0.971031\pi$
$864$	−28.2878	−	3.90360i	−0.962369	−	0.132803i
$865$	19.2896	−	6.78520i	0.655867	−	0.230704i
$866$	6.07753	−	17.0947i	0.206523	−	0.580901i
$867$	16.8850	+	16.8850i	0.573444	+	0.573444i
$868$	6.04389	+	58.9158i	0.205143	+	1.99973i
$869$		−	7.42574i		−	0.251901i
$870$	38.3875	+	38.6455i	1.30146	+	1.31020i
$871$			1.71764i			0.0582000i
$872$	6.54016	−	26.8000i	0.221478	−	0.907562i
$873$	−2.17171	−	2.17171i	−0.0735012	−	0.0735012i
$874$	−33.9687	−	12.0766i	−1.14901	−	0.408498i
$875$	−39.5011	−	24.5504i	−1.33538	−	0.829956i
$876$	6.96218	−	8.55390i	0.235230	−	0.289009i
$877$	−36.9090	+	36.9090i	−1.24633	+	1.24633i	−0.289000	+	0.957329i	$0.593323\pi$
$877$	−36.9090	+	36.9090i	−1.24633	+	1.24633i	−0.957329	+	0.289000i	$0.906677\pi$
$878$	1.81558	+	3.81868i	0.0612729	+	0.128874i
$879$	−27.6592			−0.932920
$880$	−2.46004	+	9.93605i	−0.0829279	+	0.334944i
$881$	4.69763			0.158267			0.0791337	−	0.996864i	$-0.474785\pi$
$881$	4.69763			0.158267			0.0791337	+	0.996864i	$0.474785\pi$
$882$	−1.00430	−	2.11233i	−0.0338166	−	0.0711259i
$883$	−22.3142	+	22.3142i	−0.750933	+	0.750933i	−0.974653	−	0.223720i	$-0.928180\pi$
$883$	−22.3142	+	22.3142i	−0.750933	+	0.750933i	0.223720	+	0.974653i	$0.428180\pi$
$884$	7.26851	−	8.93026i	0.244466	−	0.300357i
$885$	−15.4746	−	43.9928i	−0.520174	−	1.47880i
$886$	0.358151	+	0.127331i	0.0120323	+	0.00427775i
$887$	−11.4441	−	11.4441i	−0.384254	−	0.384254i	0.488378	−	0.872632i	$-0.337589\pi$
$887$	−11.4441	−	11.4441i	−0.384254	−	0.384254i	−0.872632	+	0.488378i	$0.837589\pi$
$888$	−1.75858	+	7.20624i	−0.0590141	+	0.241825i
$889$		−	51.1532i		−	1.71562i
$890$	−0.0484280	+	14.4609i	−0.00162331	+	0.484729i
$891$			10.8214i			0.362530i
$892$	−3.95517	−	38.5550i	−0.132429	−	1.29092i
$893$	−7.44519	−	7.44519i	−0.249144	−	0.249144i
$894$	−4.81119	+	13.5328i	−0.160910	+	0.452603i
$895$	−10.9111	+	22.7523i	−0.364717	+	0.760524i
$896$	−34.4200	+	32.0974i	−1.14989	+	1.07230i
$897$	23.9432	−	23.9432i	0.799442	−	0.799442i
$898$	5.68763	−	2.70417i	0.189799	−	0.0902392i
$899$	−68.9734			−2.30039
$900$	0.0107498	−	1.60496i	0.000358327	−	0.0534986i
$901$	−14.4154			−0.480248
$902$	1.46167	−	0.694945i	0.0486682	−	0.0231391i
$903$	13.6928	−	13.6928i	0.455669	−	0.455669i
$904$	−2.70180	−	4.44615i	−0.0898604	−	0.147877i
$905$	10.4290	−	21.7470i	0.346671	−	0.722895i
$906$	−1.50383	+	4.22993i	−0.0499614	+	0.140530i
$907$	24.6619	+	24.6619i	0.818885	+	0.818885i	0.985946	−	0.167062i	$-0.0534279\pi$
$907$	24.6619	+	24.6619i	0.818885	+	0.818885i	−0.167062	+	0.985946i	$0.553428\pi$
$908$	−40.4883	+	4.15351i	−1.34365	+	0.137839i
$909$		−	1.75844i		−	0.0583239i
$910$	−0.134267	+	40.0930i	−0.00445092	+	1.32907i
$911$			31.6709i			1.04931i	0.851316	+	0.524653i	$0.175805\pi$
$911$			31.6709i			1.04931i	−0.851316	+	0.524653i	$0.824195\pi$
$912$	24.2492	+	15.9200i	0.802971	+	0.527164i
$913$	9.75383	+	9.75383i	0.322805	+	0.322805i
$914$	−15.9036	−	5.65406i	−0.526043	−	0.187020i
$915$	−14.3218	−	40.7154i	−0.473464	−	1.34601i
$916$	−17.1868	−	13.9886i	−0.567867	−	0.462198i
$917$	21.3576	−	21.3576i	0.705291	−	0.705291i
$918$	−5.79031	−	12.1787i	−0.191109	−	0.401956i
$919$	26.1820			0.863664			0.431832	−	0.901954i	$-0.357867\pi$
$919$	26.1820			0.863664			0.431832	+	0.901954i	$0.357867\pi$
$920$	−3.90170	−	39.3307i	−0.128635	−	1.29670i
$921$	3.05901			0.100798
$922$	−6.41004	−	13.4821i	−0.211103	−	0.444011i
$923$	−26.4834	+	26.4834i	−0.871712	+	0.871712i
$924$	13.1280	+	10.6851i	0.431880	+	0.351515i
$925$	7.33222	+	0.801839i	0.241082	+	0.0263643i
$926$	−36.3991	−	12.9406i	−1.19615	−	0.425256i
$927$	1.33480	+	1.33480i	0.0438405	+	0.0438405i
$928$	−33.0947	−	43.6909i	−1.08639	−	1.43422i
$929$			39.7587i			1.30444i	0.758030	+	0.652220i	$0.226162\pi$
$929$			39.7587i			1.30444i	−0.758030	+	0.652220i	$0.773838\pi$
$930$	28.2033	+	28.3928i	0.924821	+	0.931036i
$931$		−	42.0347i		−	1.37763i
$932$	−4.09207	+	0.419786i	−0.134040	+	0.0137505i
$933$	−2.23122	−	2.23122i	−0.0730469	−	0.0730469i
$934$	1.05287	−	2.96147i	0.0344509	−	0.0969023i
$935$	−4.55995	+	1.60398i	−0.149126	+	0.0524558i
$936$	−1.18241	+	0.718514i	−0.0386482	+	0.0234854i
$937$	−32.2316	+	32.2316i	−1.05296	+	1.05296i	−0.0544450	+	0.998517i	$0.517339\pi$
$937$	−32.2316	+	32.2316i	−1.05296	+	1.05296i	−0.998517	+	0.0544450i	$0.982661\pi$
$938$	2.99420	−	1.42358i	0.0977642	−	0.0464817i
$939$	−35.2755			−1.15117
$940$	3.90314	−	10.8632i	0.127306	−	0.354320i
$941$	46.7930			1.52541			0.762705	−	0.646747i	$-0.223871\pi$
$941$	46.7930			1.52541			0.762705	+	0.646747i	$0.223871\pi$
$942$	47.4152	−	22.5434i	1.54487	−	0.734504i
$943$	−4.41889	+	4.41889i	−0.143899	+	0.143899i
$944$	9.52749	+	45.9482i	0.310093	+	1.49549i
$945$	42.3385	+	20.3038i	1.37727	+	0.660484i
$946$	−1.41963	+	3.99308i	−0.0461560	+	0.129826i
$947$	−12.6395	−	12.6395i	−0.410729	−	0.410729i	0.471264	−	0.881992i	$-0.343798\pi$
$947$	−12.6395	−	12.6395i	−0.410729	−	0.410729i	−0.881992	+	0.471264i	$0.843798\pi$
$948$	−2.35435	−	22.9502i	−0.0764659	−	0.745389i
$949$			9.45418i			0.306896i
$950$	12.5597	−	25.9667i	0.407491	−	0.842472i
$951$			13.4220i			0.435237i
$952$	−21.5915	−	5.26909i	−0.699783	−	0.170772i
$953$	10.8646	+	10.8646i	0.351937	+	0.351937i	0.860830	−	0.508893i	$-0.169945\pi$
$953$	10.8646	+	10.8646i	0.351937	+	0.351937i	−0.508893	+	0.860830i	$0.669945\pi$
$954$	1.63212	+	0.580254i	0.0528419	+	0.0187864i
$955$	54.4891	+	26.1308i	1.76323	+	0.845572i
$956$	−12.5372	+	15.4035i	−0.405482	+	0.498185i
$957$	−13.9392	+	13.9392i	−0.450589	+	0.450589i
$958$	−18.5773	−	39.0733i	−0.600204	−	1.26240i
$959$	71.1957			2.29903
$960$	−4.45281	+	31.4886i	−0.143714	+	1.01629i
$961$	−19.6747			−0.634668
$962$	−2.73025	−	5.74248i	−0.0880266	−	0.185145i
$963$	−2.14433	+	2.14433i	−0.0691001	+	0.0691001i
$964$	−1.11467	+	1.36952i	−0.0359012	+	0.0441091i
$965$	−24.2451	+	8.52832i	−0.780478	+	0.274536i
$966$	−61.5822	−	21.8938i	−1.98138	−	0.704422i
$967$	8.77191	+	8.77191i	0.282086	+	0.282086i	0.833940	−	0.551855i	$-0.186080\pi$
$967$	8.77191	+	8.77191i	0.282086	+	0.282086i	−0.551855	+	0.833940i	$0.686080\pi$
$968$	26.6269	+	6.49792i	0.855820	+	0.208851i
$969$			13.6987i			0.440064i
$970$	42.9316	−	42.6450i	1.37845	−	1.36925i
$971$		−	1.92970i		−	0.0619272i	−0.999521	−	0.0309636i	$-0.990142\pi$
$971$		−	1.92970i		−	0.0619272i	0.999521	−	0.0309636i	$-0.00985759\pi$
$972$	0.340071	+	3.31500i	0.0109078	+	0.106329i
$973$	11.5323	+	11.5323i	0.369708	+	0.369708i
$974$	1.28799	−	3.62281i	0.0412698	−	0.116082i
$975$	16.9608	+	21.1259i	0.543180	+	0.676570i
$976$	8.81769	+	42.5251i	0.282247	+	1.36120i
$977$	25.4145	−	25.4145i	0.813081	−	0.813081i	−0.172014	−	0.985095i	$-0.555027\pi$
$977$	25.4145	−	25.4145i	0.813081	−	0.813081i	0.985095	+	0.172014i	$0.0550273\pi$
$978$	−16.3370	+	7.76737i	−0.522399	+	0.248373i
$979$	−5.23340			−0.167260
$980$	41.6847	−	19.6480i	1.33157	−	0.627631i
$981$	−1.56540			−0.0499793
$982$	45.0270	−	21.4080i	1.43687	−	0.683156i
$983$	24.2527	−	24.2527i	0.773542	−	0.773542i	−0.205181	−	0.978724i	$-0.565778\pi$
$983$	24.2527	−	24.2527i	0.773542	−	0.773542i	0.978724	+	0.205181i	$0.0657785\pi$
$984$	4.29714	−	2.61124i	0.136988	−	0.0832434i
$985$	1.95635	+	5.56169i	0.0623343	+	0.177210i
$986$	8.67042	−	24.3879i	0.276122	−	0.776669i
$987$	−13.4975	−	13.4975i	−0.429629	−	0.429629i
$988$	−24.7360	+	2.53755i	−0.786957	+	0.0807302i
$989$		−	16.3636i		−	0.520333i
$990$	0.580843	+	0.00194519i	0.0184604	+	6.18221e-5i
$991$		−	45.2519i		−	1.43747i	−0.695282	−	0.718737i	$-0.744721\pi$
$991$		−	45.2519i		−	1.43747i	0.695282	−	0.718737i	$-0.255279\pi$
$992$	−24.3147	−	32.0996i	−0.771992	−	1.01916i
$993$	33.2624	+	33.2624i	1.05555	+	1.05555i
$994$	68.1156	+	24.2165i	2.16049	+	0.768102i
$995$	7.30635	−	15.2355i	0.231627	−	0.482999i
$996$	33.2380	+	27.0530i	1.05319	+	0.857207i
$997$	23.0443	−	23.0443i	0.729819	−	0.729819i	−0.240764	−	0.970584i	$-0.577398\pi$
$997$	23.0443	−	23.0443i	0.729819	−	0.729819i	0.970584	+	0.240764i	$0.0773980\pi$
$998$	−5.79941	−	12.1978i	−0.183577	−	0.386115i
$999$	−7.44675			−0.235605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.16	✓	108
4.3	odd	2	inner	820.2.k.c.83.46	yes	108
5.2	odd	4	inner	820.2.k.c.247.46	yes	108
20.7	even	4	inner	820.2.k.c.247.16	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.16	✓	108	1.1	even	1	trivial
820.2.k.c.83.46	yes	108	4.3	odd	2	inner
820.2.k.c.247.16	yes	108	20.7	even	4	inner
820.2.k.c.247.46	yes	108	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.607244 - 1.27721i) q^{2} +(1.25708 - 1.25708i) q^{3} +(-1.26251 + 1.55115i) q^{4} +(-0.966894 + 2.01621i) q^{5} +(-2.36890 - 0.842196i) q^{6} +(-2.94147 - 2.94147i) q^{7} +(2.74779 + 0.670560i) q^{8} -0.160500i q^{9} +(3.16226 + 0.0105901i) q^{10} +1.14443i q^{11} +(0.362844 + 3.53700i) q^{12} +(-2.15515 - 2.15515i) q^{13} +(-1.97067 + 5.54305i) q^{14} +(1.31908 + 3.75000i) q^{15} +(-0.812135 - 3.91669i) q^{16} +(1.33568 - 1.33568i) q^{17} +(-0.204991 + 0.0974623i) q^{18} -4.07926 q^{19} +(-1.90674 - 4.04529i) q^{20} -7.39533 q^{21} +(1.46167 - 0.694945i) q^{22} +(-4.41889 + 4.41889i) q^{23} +(4.29714 - 2.61124i) q^{24} +(-3.13023 - 3.89893i) q^{25} +(-1.44387 + 4.06126i) q^{26} +(3.56948 + 3.56948i) q^{27} +(8.27630 - 0.849026i) q^{28} +9.68916i q^{29} +(3.98853 - 3.96190i) q^{30} +7.11862i q^{31} +(-4.50925 + 3.41565i) q^{32} +(1.43863 + 1.43863i) q^{33} +(-2.51703 - 0.894858i) q^{34} +(8.77472 - 3.08654i) q^{35} +(0.248959 + 0.202632i) q^{36} +(-1.04311 + 1.04311i) q^{37} +(2.47710 + 5.21005i) q^{38} -5.41838 q^{39} +(-4.00881 + 4.89177i) q^{40} +1.00000 q^{41} +(4.49077 + 9.44536i) q^{42} +(-1.85155 + 1.85155i) q^{43} +(-1.77518 - 1.44485i) q^{44} +(0.323601 + 0.155186i) q^{45} +(8.32718 + 2.96049i) q^{46} +(1.82513 + 1.82513i) q^{47} +(-5.94451 - 3.90267i) q^{48} +10.3045i q^{49} +(-3.07892 + 6.36555i) q^{50} -3.35812i q^{51} +(6.06385 - 0.622061i) q^{52} +(-5.39627 - 5.39627i) q^{53} +(2.39142 - 6.72650i) q^{54} +(-2.30741 - 1.10654i) q^{55} +(-6.11011 - 10.0550i) q^{56} +(-5.12795 + 5.12795i) q^{57} +(12.3751 - 5.88368i) q^{58} -11.7314 q^{59} +(-7.48217 - 2.68833i) q^{60} -10.8574 q^{61} +(9.09194 - 4.32273i) q^{62} +(-0.472105 + 0.472105i) q^{63} +(7.10070 + 3.68511i) q^{64} +(6.42903 - 2.26144i) q^{65} +(0.963831 - 2.71103i) q^{66} +(-0.398498 - 0.398498i) q^{67} +(0.385532 + 3.75816i) q^{68} +11.1098i q^{69} +(-9.27055 - 9.33285i) q^{70} -12.2885i q^{71} +(0.107625 - 0.441019i) q^{72} +(-2.19340 - 2.19340i) q^{73} +(1.96570 + 0.698848i) q^{74} +(-8.83622 - 0.966313i) q^{75} +(5.15011 - 6.32754i) q^{76} +(3.36630 - 3.36630i) q^{77} +(3.29028 + 6.92039i) q^{78} -6.48862 q^{79} +(8.68212 + 2.14958i) q^{80} +9.45574 q^{81} +(-0.607244 - 1.27721i) q^{82} +(8.52290 - 8.52290i) q^{83} +(9.33668 - 11.4713i) q^{84} +(1.40156 + 3.98449i) q^{85} +(3.48916 + 1.24047i) q^{86} +(12.1800 + 12.1800i) q^{87} +(-0.767406 + 3.14464i) q^{88} +4.57295i q^{89} +(0.00169970 - 0.507541i) q^{90} +12.6786i q^{91} +(-1.27547 - 12.4333i) q^{92} +(8.94867 + 8.94867i) q^{93} +(1.22277 - 3.43937i) q^{94} +(3.94421 - 8.22466i) q^{95} +(-1.37475 + 9.96223i) q^{96} +(13.5309 - 13.5309i) q^{97} +(13.1610 - 6.25734i) q^{98} +0.183680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

L-functions

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