LMFDB - Embedded newform 820.2.k.c.83.14

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			83.14
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866971 - 1.11730i) q^{2} +(-0.278914 + 0.278914i) q^{3} +(-0.496724 + 1.93733i) q^{4} +(-0.644595 + 2.14114i) q^{5} +(0.553441 + 0.0698207i) q^{6} +(1.69878 + 1.69878i) q^{7} +(2.59523 - 1.12462i) q^{8} +2.84441i q^{9} +(2.95115 - 1.13610i) q^{10} +1.33907i q^{11} +(-0.401806 - 0.678893i) q^{12} +(0.601947 + 0.601947i) q^{13} +(0.425256 - 3.37083i) q^{14} +(-0.417409 - 0.776982i) q^{15} +(-3.50653 - 1.92464i) q^{16} +(-2.82679 + 2.82679i) q^{17} +(3.17807 - 2.46602i) q^{18} -5.71431 q^{19} +(-3.82793 - 2.31235i) q^{20} -0.947624 q^{21} +(1.49615 - 1.16094i) q^{22} +(5.69719 - 5.69719i) q^{23} +(-0.410174 + 1.03752i) q^{24} +(-4.16900 - 2.76034i) q^{25} +(0.150686 - 1.19443i) q^{26} +(-1.63009 - 1.63009i) q^{27} +(-4.13492 + 2.44727i) q^{28} -3.34339i q^{29} +(-0.506242 + 1.13999i) q^{30} -2.05260i q^{31} +(0.889654 + 5.58646i) q^{32} +(-0.373486 - 0.373486i) q^{33} +(5.60912 + 0.707632i) q^{34} +(-4.73234 + 2.54230i) q^{35} +(-5.51058 - 1.41289i) q^{36} +(-4.04070 + 4.04070i) q^{37} +(4.95414 + 6.38460i) q^{38} -0.335783 q^{39} +(0.735104 + 6.28169i) q^{40} +1.00000 q^{41} +(0.821562 + 1.05878i) q^{42} +(-7.33467 + 7.33467i) q^{43} +(-2.59423 - 0.665150i) q^{44} +(-6.09030 - 1.83349i) q^{45} +(-11.3048 - 1.42618i) q^{46} +(-2.12311 - 2.12311i) q^{47} +(1.51483 - 0.441211i) q^{48} -1.22833i q^{49} +(0.530264 + 7.05116i) q^{50} -1.57686i q^{51} +(-1.46517 + 0.867171i) q^{52} +(7.01655 + 7.01655i) q^{53} +(-0.408061 + 3.23454i) q^{54} +(-2.86715 - 0.863159i) q^{55} +(6.31919 + 2.49824i) q^{56} +(1.59380 - 1.59380i) q^{57} +(-3.73557 + 2.89862i) q^{58} -0.647781 q^{59} +(1.71261 - 0.422714i) q^{60} +5.98612 q^{61} +(-2.29337 + 1.77954i) q^{62} +(-4.83202 + 4.83202i) q^{63} +(5.47045 - 5.83731i) q^{64} +(-1.67687 + 0.900843i) q^{65} +(-0.0934950 + 0.741098i) q^{66} +(-1.31706 - 1.31706i) q^{67} +(-4.07230 - 6.88057i) q^{68} +3.17805i q^{69} +(6.94332 + 3.08335i) q^{70} +7.49094i q^{71} +(3.19889 + 7.38191i) q^{72} +(10.5380 + 10.5380i) q^{73} +(8.01784 + 1.01151i) q^{74} +(1.93269 - 0.392893i) q^{75} +(2.83843 - 11.0705i) q^{76} +(-2.27478 + 2.27478i) q^{77} +(0.291114 + 0.375170i) q^{78} -17.4243 q^{79} +(6.38123 - 6.26737i) q^{80} -7.62393 q^{81} +(-0.866971 - 1.11730i) q^{82} +(6.41387 - 6.41387i) q^{83} +(0.470708 - 1.83587i) q^{84} +(-4.23043 - 7.87470i) q^{85} +(14.5540 + 1.83609i) q^{86} +(0.932517 + 0.932517i) q^{87} +(1.50595 + 3.47520i) q^{88} -16.0501i q^{89} +(3.23154 + 8.39429i) q^{90} +2.04514i q^{91} +(8.20742 + 13.8673i) q^{92} +(0.572499 + 0.572499i) q^{93} +(-0.531479 + 4.21282i) q^{94} +(3.68341 - 12.2352i) q^{95} +(-1.80628 - 1.31000i) q^{96} +(-1.96505 + 1.96505i) q^{97} +(-1.37241 + 1.06492i) q^{98} -3.80888 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 $

$2$	−0.866971	−	1.11730i	−0.613041	−	0.790051i
$2$	−0.866971	−	1.11730i	−0.613041	−	0.790051i
$3$	−0.278914	+	0.278914i	−0.161031	+	0.161031i	−0.783023	−	0.621992i	$-0.786324\pi$
$3$	−0.278914	+	0.278914i	−0.161031	+	0.161031i	0.621992	+	0.783023i	$0.286324\pi$
$4$	−0.496724	+	1.93733i	−0.248362	+	0.968667i
$5$	−0.644595	+	2.14114i	−0.288272	+	0.957549i
$5$	−0.644595	+	2.14114i	−0.288272	+	0.957549i
$6$	0.553441	+	0.0698207i	0.225941	+	0.0285042i
$7$	1.69878	+	1.69878i	0.642077	+	0.642077i	0.951066	−	0.308989i	$-0.0999906\pi$
$7$	1.69878	+	1.69878i	0.642077	+	0.642077i	−0.308989	+	0.951066i	$0.599991\pi$
$8$	2.59523	−	1.12462i	0.917553	−	0.397614i
$9$			2.84441i			0.948138i
$10$	2.95115	−	1.13610i	0.933235	−	0.359267i
$11$			1.33907i			0.403746i	0.979412	+	0.201873i	$0.0647028\pi$
$11$			1.33907i			0.403746i	−0.979412	+	0.201873i	$0.935297\pi$
$12$	−0.401806	−	0.678893i	−0.115992	−	0.195980i
$13$	0.601947	+	0.601947i	0.166950	+	0.166950i	0.785637	−	0.618687i	$-0.212335\pi$
$13$	0.601947	+	0.601947i	0.166950	+	0.166950i	−0.618687	+	0.785637i	$0.712335\pi$
$14$	0.425256	−	3.37083i	0.113654	−	0.900893i
$15$	−0.417409	−	0.776982i	−0.107774	−	0.200616i
$16$	−3.50653	−	1.92464i	−0.876633	−	0.481160i
$17$	−2.82679	+	2.82679i	−0.685597	+	0.685597i	−0.961256	−	0.275658i	$-0.911104\pi$
$17$	−2.82679	+	2.82679i	−0.685597	+	0.685597i	0.275658	+	0.961256i	$0.411104\pi$
$18$	3.17807	−	2.46602i	0.749078	−	0.581247i
$19$	−5.71431			−1.31095			−0.655476	−	0.755216i	$-0.727532\pi$
$19$	−5.71431			−1.31095			−0.655476	+	0.755216i	$0.727532\pi$
$20$	−3.82793	−	2.31235i	−0.855950	−	0.517058i
$21$	−0.947624			−0.206789
$22$	1.49615	−	1.16094i	0.318980	−	0.247512i
$23$	5.69719	−	5.69719i	1.18795	−	1.18795i	0.210311	−	0.977635i	$-0.432552\pi$
$23$	5.69719	−	5.69719i	1.18795	−	1.18795i	0.977635	−	0.210311i	$-0.0674476\pi$
$24$	−0.410174	+	1.03752i	−0.0837264	+	0.211783i
$25$	−4.16900	−	2.76034i	−0.833799	−	0.552068i
$26$	0.150686	−	1.19443i	0.0295519	−	0.234246i
$27$	−1.63009	−	1.63009i	−0.313711	−	0.313711i
$28$	−4.13492	+	2.44727i	−0.781426	+	0.462491i
$29$		−	3.34339i		−	0.620851i	−0.950598	−	0.310426i	$-0.899528\pi$
$29$		−	3.34339i		−	0.620851i	0.950598	−	0.310426i	$-0.100472\pi$
$30$	−0.506242	+	1.13999i	−0.0924266	+	0.208133i
$31$		−	2.05260i		−	0.368658i	−0.982865	−	0.184329i	$-0.940989\pi$
$31$		−	2.05260i		−	0.368658i	0.982865	−	0.184329i	$-0.0590112\pi$
$32$	0.889654	+	5.58646i	0.157270	+	0.987556i
$33$	−0.373486	−	0.373486i	−0.0650156	−	0.0650156i
$34$	5.60912	+	0.707632i	0.961956	+	0.121358i
$35$	−4.73234	+	2.54230i	−0.799912	+	0.429727i
$36$	−5.51058	−	1.41289i	−0.918430	−	0.235482i
$37$	−4.04070	+	4.04070i	−0.664287	+	0.664287i	−0.956388	−	0.292101i	$-0.905646\pi$
$37$	−4.04070	+	4.04070i	−0.664287	+	0.664287i	0.292101	+	0.956388i	$0.405646\pi$
$38$	4.95414	+	6.38460i	0.803667	+	1.03572i
$39$	−0.335783			−0.0537683
$40$	0.735104	+	6.28169i	0.116230	+	0.993222i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	0.821562	+	1.05878i	0.126770	+	0.163374i
$43$	−7.33467	+	7.33467i	−1.11853	+	1.11853i	−0.126569	+	0.991958i	$0.540397\pi$
$43$	−7.33467	+	7.33467i	−1.11853	+	1.11853i	−0.991958	+	0.126569i	$0.959603\pi$
$44$	−2.59423	−	0.665150i	−0.391095	−	0.100275i
$45$	−6.09030	−	1.83349i	−0.907888	−	0.273321i
$46$	−11.3048	−	1.42618i	−1.66680	−	0.210279i
$47$	−2.12311	−	2.12311i	−0.309687	−	0.309687i	0.535101	−	0.844788i	$-0.320274\pi$
$47$	−2.12311	−	2.12311i	−0.309687	−	0.309687i	−0.844788	+	0.535101i	$0.820274\pi$
$48$	1.51483	−	0.441211i	0.218647	−	0.0636833i
$49$		−	1.22833i		−	0.175475i
$50$	0.530264	+	7.05116i	0.0749906	+	0.997184i
$51$		−	1.57686i		−	0.220805i
$52$	−1.46517	+	0.867171i	−0.203183	+	0.120255i
$53$	7.01655	+	7.01655i	0.963797	+	0.963797i	0.999367	−	0.0355705i	$-0.0113248\pi$
$53$	7.01655	+	7.01655i	0.963797	+	0.963797i	−0.0355705	+	0.999367i	$0.511325\pi$
$54$	−0.408061	+	3.23454i	−0.0555301	+	0.440165i
$55$	−2.86715	−	0.863159i	−0.386606	−	0.116388i
$56$	6.31919	+	2.49824i	0.844438	+	0.333841i
$57$	1.59380	−	1.59380i	0.211104	−	0.211104i
$58$	−3.73557	+	2.89862i	−0.490504	+	0.380607i
$59$	−0.647781			−0.0843340			−0.0421670	−	0.999111i	$-0.513426\pi$
$59$	−0.647781			−0.0843340			−0.0421670	+	0.999111i	$0.513426\pi$
$60$	1.71261	−	0.422714i	0.221097	−	0.0545722i
$61$	5.98612			0.766444			0.383222	−	0.923656i	$-0.374814\pi$
$61$	5.98612			0.766444			0.383222	+	0.923656i	$0.374814\pi$
$62$	−2.29337	+	1.77954i	−0.291259	+	0.226002i
$63$	−4.83202	+	4.83202i	−0.608777	+	0.608777i
$64$	5.47045	−	5.83731i	0.683807	−	0.729663i
$65$	−1.67687	+	0.900843i	−0.207990	+	0.111736i
$66$	−0.0934950	+	0.741098i	−0.0115084	+	0.0912228i
$67$	−1.31706	−	1.31706i	−0.160904	−	0.160904i	0.622063	−	0.782967i	$-0.286295\pi$
$67$	−1.31706	−	1.31706i	−0.160904	−	0.160904i	−0.782967	+	0.622063i	$0.786295\pi$
$68$	−4.07230	−	6.88057i	−0.493839	−	0.834392i
$69$			3.17805i			0.382592i
$70$	6.94332	+	3.08335i	0.829885	+	0.368531i
$71$			7.49094i			0.889011i	0.895776	+	0.444505i	$0.146621\pi$
$71$			7.49094i			0.889011i	−0.895776	+	0.444505i	$0.853379\pi$
$72$	3.19889	+	7.38191i	0.376993	+	0.869967i
$73$	10.5380	+	10.5380i	1.23339	+	1.23339i	0.962655	+	0.270730i	$0.0872650\pi$
$73$	10.5380	+	10.5380i	1.23339	+	1.23339i	0.270730	+	0.962655i	$0.412735\pi$
$74$	8.01784	+	1.01151i	0.932055	+	0.117586i
$75$	1.93269	−	0.392893i	0.223168	−	0.0453674i
$76$	2.83843	−	11.0705i	0.325591	−	1.26988i
$77$	−2.27478	+	2.27478i	−0.259236	+	0.259236i
$78$	0.291114	+	0.375170i	0.0329621	+	0.0424797i
$79$	−17.4243			−1.96039			−0.980194	−	0.198041i	$-0.936542\pi$
$79$	−17.4243			−1.96039			−0.980194	+	0.198041i	$0.936542\pi$
$80$	6.38123	−	6.26737i	0.713443	−	0.700714i
$81$	−7.62393			−0.847104
$82$	−0.866971	−	1.11730i	−0.0957409	−	0.123385i
$83$	6.41387	−	6.41387i	0.704013	−	0.704013i	−0.261256	−	0.965270i	$-0.584137\pi$
$83$	6.41387	−	6.41387i	0.704013	−	0.704013i	0.965270	+	0.261256i	$0.0841367\pi$
$84$	0.470708	−	1.83587i	0.0513584	−	0.200309i
$85$	−4.23043	−	7.87470i	−0.458855	−	0.854131i
$86$	14.5540	+	1.83609i	1.56940	+	0.197991i
$87$	0.932517	+	0.932517i	0.0999763	+	0.0999763i
$88$	1.50595	+	3.47520i	0.160535	+	0.370458i
$89$		−	16.0501i		−	1.70131i	−0.525724	−	0.850655i	$-0.676206\pi$
$89$		−	16.0501i		−	1.70131i	0.525724	−	0.850655i	$-0.323794\pi$
$90$	3.23154	+	8.39429i	0.340635	+	0.884835i
$91$			2.04514i			0.214389i
$92$	8.20742	+	13.8673i	0.855683	+	1.44576i
$93$	0.572499	+	0.572499i	0.0593654	+	0.0593654i
$94$	−0.531479	+	4.21282i	−0.0548179	+	0.434520i
$95$	3.68341	−	12.2352i	0.377910	−	1.25530i
$96$	−1.80628	−	1.31000i	−0.184353	−	0.133702i
$97$	−1.96505	+	1.96505i	−0.199520	+	0.199520i	−0.799794	−	0.600274i	$-0.795058\pi$
$97$	−1.96505	+	1.96505i	−0.199520	+	0.199520i	0.600274	+	0.799794i	$0.295058\pi$
$98$	−1.37241	+	1.06492i	−0.138634	+	0.107573i
$99$	−3.80888			−0.382806
$100$	7.41854	−	6.70561i	0.741854	−	0.670561i
$101$	−7.11355			−0.707824			−0.353912	−	0.935279i	$-0.615149\pi$
$101$	−7.11355			−0.707824			−0.353912	+	0.935279i	$0.615149\pi$
$102$	−1.76183	+	1.36709i	−0.174447	+	0.135362i
$103$	−5.99820	+	5.99820i	−0.591020	+	0.591020i	−0.937907	−	0.346887i	$-0.887239\pi$
$103$	−5.99820	+	5.99820i	−0.591020	+	0.591020i	0.346887	+	0.937907i	$0.387239\pi$
$104$	2.23915	+	0.885229i	0.219567	+	0.0868038i
$105$	0.610834	−	2.02900i	0.0596113	−	0.198010i
$106$	1.75646	−	13.9227i	0.170602	−	1.35230i
$107$	5.12998	+	5.12998i	0.495934	+	0.495934i	0.910170	−	0.414236i	$-0.135951\pi$
$107$	5.12998	+	5.12998i	0.495934	+	0.495934i	−0.414236	+	0.910170i	$0.635951\pi$
$108$	3.96773	−	2.34832i	0.381795	−	0.225968i
$109$			13.2450i			1.26864i	0.773070	+	0.634320i	$0.218720\pi$
$109$			13.2450i			1.26864i	−0.773070	+	0.634320i	$0.781280\pi$
$110$	1.52132	+	3.95180i	0.145052	+	0.376789i
$111$		−	2.25401i		−	0.213942i
$112$	−2.68727	−	9.22634i	−0.253923	−	0.871807i
$113$	11.6481	+	11.6481i	1.09576	+	1.09576i	0.994900	+	0.100864i	$0.0321607\pi$
$113$	11.6481	+	11.6481i	1.09576	+	1.09576i	0.100864	+	0.994900i	$0.467839\pi$
$114$	−3.16253	−	0.398977i	−0.296198	−	0.0373676i
$115$	8.52612	+	15.8709i	0.795065	+	1.47997i
$116$	6.47726	+	1.66074i	0.601398	+	0.154196i
$117$	−1.71219	+	1.71219i	−0.158292	+	0.158292i
$118$	0.561607	+	0.723767i	0.0517002	+	0.0666282i
$119$	−9.60416			−0.880412
$120$	−1.95708	−	1.54702i	−0.178656	−	0.141223i
$121$	9.20688			0.836990
$122$	−5.18979	−	6.68830i	−0.469861	−	0.605530i
$123$	−0.278914	+	0.278914i	−0.0251488	+	0.0251488i
$124$	3.97657	+	1.01958i	0.357107	+	0.0915606i
$125$	8.59760	−	7.14712i	0.768993	−	0.639258i
$126$	9.58804	+	1.20960i	0.854171	+	0.107760i
$127$	−0.0827773	−	0.0827773i	−0.00734530	−	0.00734530i	0.703425	−	0.710770i	$-0.251653\pi$
$127$	−0.0827773	−	0.0827773i	−0.00734530	−	0.00734530i	−0.710770	+	0.703425i	$0.751653\pi$
$128$	−11.2648	−	1.05137i	−0.995673	−	0.0929290i
$129$		−	4.09148i		−	0.360235i
$130$	2.46031	+	1.09256i	0.215783	+	0.0958239i
$131$		−	13.3808i		−	1.16908i	−0.811363	−	0.584542i	$-0.801274\pi$
$131$		−	13.3808i		−	1.16908i	0.811363	−	0.584542i	$-0.198726\pi$
$132$	0.909087	−	0.538048i	0.0791259	−	0.0468311i
$133$	−9.70732	−	9.70732i	−0.841732	−	0.841732i
$134$	−0.329701	+	2.61341i	−0.0284818	+	0.225764i
$135$	4.54100	−	2.43951i	0.390827	−	0.209959i
$136$	−4.15711	+	10.5152i	−0.356469	+	0.901675i
$137$	5.74819	−	5.74819i	0.491101	−	0.491101i	−0.417552	−	0.908653i	$-0.637112\pi$
$137$	5.74819	−	5.74819i	0.491101	−	0.491101i	0.908653	+	0.417552i	$0.137112\pi$
$138$	3.55084	−	2.75528i	0.302267	−	0.234545i
$139$	−8.54773			−0.725009			−0.362505	−	0.931982i	$-0.618078\pi$
$139$	−8.54773			−0.725009			−0.362505	+	0.931982i	$0.618078\pi$
$140$	−2.57462	−	10.4310i	−0.217595	−	0.881577i
$141$	1.18433			0.0997385
$142$	8.36963	−	6.49442i	0.702364	−	0.545000i
$143$	−0.806050	+	0.806050i	−0.0674053	+	0.0674053i
$144$	5.47448	−	9.97402i	0.456206	−	0.831169i
$145$	7.15867	+	2.15513i	0.594495	+	0.178974i
$146$	2.63800	−	20.9103i	0.218322	−	1.73055i
$147$	0.342597	+	0.342597i	0.0282570	+	0.0282570i
$148$	−5.82107	−	9.83530i	−0.478489	−	0.808456i
$149$			10.7043i			0.876931i	0.898748	+	0.438466i	$0.144478\pi$
$149$			10.7043i			0.876931i	−0.898748	+	0.438466i	$0.855522\pi$
$150$	−2.11456	−	1.81877i	−0.172653	−	0.148502i
$151$			9.81279i			0.798554i	0.916830	+	0.399277i	$0.130739\pi$
$151$			9.81279i			0.798554i	−0.916830	+	0.399277i	$0.869261\pi$
$152$	−14.8300	+	6.42643i	−1.20287	+	0.521253i
$153$	−8.04056	−	8.04056i	−0.650041	−	0.650041i
$154$	4.51379	+	0.569448i	0.363731	+	0.0458874i
$155$	4.39491	+	1.32310i	0.353008	+	0.106274i
$156$	0.166791	−	0.650523i	0.0133540	−	0.0520836i
$157$	−5.57771	+	5.57771i	−0.445150	+	0.445150i	−0.893738	−	0.448588i	$-0.851927\pi$
$157$	−5.57771	+	5.57771i	−0.445150	+	0.445150i	0.448588	+	0.893738i	$0.351927\pi$
$158$	15.1064	+	19.4682i	1.20180	+	1.54881i
$159$	−3.91403			−0.310402
$160$	−12.5349	−	1.69612i	−0.990969	−	0.134090i
$161$	19.3565			1.52550
$162$	6.60972	+	8.51823i	0.519309	+	0.669255i
$163$	−11.2263	+	11.2263i	−0.879309	+	0.879309i	−0.993463	−	0.114154i	$-0.963584\pi$
$163$	−11.2263	+	11.2263i	−0.879309	+	0.879309i	0.114154	+	0.993463i	$0.463584\pi$
$164$	−0.496724	+	1.93733i	−0.0387876	+	0.151280i
$165$	1.04043	−	0.558940i	0.0809977	−	0.0435134i
$166$	−12.7269	−	1.60559i	−0.987796	−	0.124618i
$167$	9.18408	+	9.18408i	0.710686	+	0.710686i	0.966679	−	0.255993i	$-0.0824024\pi$
$167$	9.18408	+	9.18408i	0.710686	+	0.710686i	−0.255993	+	0.966679i	$0.582402\pi$
$168$	−2.45930	+	1.06572i	−0.189739	+	0.0822220i
$169$		−	12.2753i		−	0.944255i
$170$	−5.13075	+	11.5538i	−0.393511	+	0.886136i
$171$		−	16.2539i		−	1.24296i
$172$	−10.5664	−	17.8530i	−0.805681	−	1.36128i
$173$	−17.0143	−	17.0143i	−1.29357	−	1.29357i	−0.932563	−	0.361008i	$-0.882433\pi$
$173$	−17.0143	−	17.0143i	−1.29357	−	1.29357i	−0.361008	−	0.932563i	$-0.617567\pi$
$174$	0.233438	−	1.85037i	0.0176969	−	0.140276i
$175$	−2.39299	−	11.7714i	−0.180893	−	0.889833i
$176$	2.57723	−	4.69550i	0.194266	−	0.353936i
$177$	0.180675	−	0.180675i	0.0135804	−	0.0135804i
$178$	−17.9328	+	13.9150i	−1.34412	+	1.04297i
$179$	−6.39788			−0.478200			−0.239100	−	0.970995i	$-0.576852\pi$
$179$	−6.39788			−0.478200			−0.239100	+	0.970995i	$0.576852\pi$
$180$	6.57729	−	10.8882i	0.490242	−	0.811559i
$181$	−9.61218			−0.714468			−0.357234	−	0.934015i	$-0.616280\pi$
$181$	−9.61218			−0.714468			−0.357234	+	0.934015i	$0.616280\pi$
$182$	2.28504	−	1.77308i	0.169379	−	0.131429i
$183$	−1.66961	+	1.66961i	−0.123421	+	0.123421i
$184$	8.37834	−	21.1927i	0.617659	−	1.56235i
$185$	−6.04710	−	11.2563i	−0.444592	−	0.827582i
$186$	0.143314	−	1.13599i	0.0105083	−	0.0832951i
$187$	−3.78528	−	3.78528i	−0.276807	−	0.276807i
$188$	5.16777	−	3.05857i	0.376898	−	0.223069i
$189$		−	5.53831i		−	0.402853i
$190$	−16.8638	+	6.49204i	−1.22343	+	0.470982i
$191$		−	3.47790i		−	0.251652i	−0.992052	−	0.125826i	$-0.959842\pi$
$191$		−	3.47790i		−	0.251652i	0.992052	−	0.125826i	$-0.0401582\pi$
$192$	0.102321	+	3.15389i	0.00738435	+	0.227613i
$193$	1.65269	+	1.65269i	0.118963	+	0.118963i	0.764082	−	0.645119i	$-0.223192\pi$
$193$	1.65269	+	1.65269i	0.118963	+	0.118963i	−0.645119	+	0.764082i	$0.723192\pi$
$194$	3.89919	+	0.491912i	0.279945	+	0.0353172i
$195$	0.216444	−	0.718959i	0.0154999	−	0.0514857i
$196$	2.37968	+	0.610139i	0.169977	+	0.0435814i
$197$	−6.62232	+	6.62232i	−0.471821	+	0.471821i	−0.902503	−	0.430683i	$-0.858273\pi$
$197$	−6.62232	+	6.62232i	−0.471821	+	0.471821i	0.430683	+	0.902503i	$0.358273\pi$
$198$	3.30218	+	4.25566i	0.234676	+	0.302437i
$199$	23.5160			1.66700			0.833502	−	0.552516i	$-0.186332\pi$
$199$	23.5160			1.66700			0.833502	+	0.552516i	$0.186332\pi$
$200$	−13.9238	−	2.47518i	−0.984565	−	0.175022i
$201$	0.734693			0.0518213
$202$	6.16724	+	7.94798i	0.433925	+	0.559218i
$203$	5.67966	−	5.67966i	0.398634	−	0.398634i
$204$	3.05491	+	0.783266i	0.213887	+	0.0548396i
$205$	−0.644595	+	2.14114i	−0.0450205	+	0.149544i
$206$	11.9021	+	1.50153i	0.829256	+	0.104617i
$207$	16.2052	+	16.2052i	1.12634	+	1.12634i
$208$	−0.952213	−	3.26928i	−0.0660241	−	0.226683i
$209$		−	7.65187i		−	0.529291i
$210$	−2.79658	+	1.07660i	−0.192982	+	0.0742923i
$211$			3.44479i			0.237149i	0.992945	+	0.118575i	$0.0378325\pi$
$211$			3.44479i			0.237149i	−0.992945	+	0.118575i	$0.962167\pi$
$212$	−17.0787	+	10.1081i	−1.17297	+	0.694228i
$213$	−2.08933	−	2.08933i	−0.143158	−	0.143158i
$214$	1.28419	−	10.1793i	0.0877855	−	0.695841i
$215$	−10.9767	−	20.4325i	−0.748604	−	1.39348i
$216$	−6.06369	−	2.39723i	−0.412582	−	0.163111i
$217$	3.48691	−	3.48691i	0.236707	−	0.236707i
$218$	14.7987	−	11.4830i	1.00229	−	0.777728i
$219$	−5.87842			−0.397227
$220$	3.09641	−	5.12587i	0.208760	−	0.345586i
$221$	−3.40315			−0.228921
$222$	−2.51841	+	1.95416i	−0.169025	+	0.131155i
$223$	4.72118	−	4.72118i	0.316154	−	0.316154i	−0.531134	−	0.847288i	$-0.678234\pi$
$223$	4.72118	−	4.72118i	0.316154	−	0.316154i	0.847288	+	0.531134i	$0.178234\pi$
$224$	−7.97881	+	11.0015i	−0.533107	+	0.735066i
$225$	7.85155	−	11.8583i	0.523437	−	0.790557i
$226$	2.91589	−	23.1131i	0.193962	−	1.53746i
$227$	6.34763	+	6.34763i	0.421307	+	0.421307i	0.885654	−	0.464347i	$-0.153711\pi$
$227$	6.34763	+	6.34763i	0.421307	+	0.421307i	−0.464347	+	0.885654i	$0.653711\pi$
$228$	2.29605	+	3.87940i	0.152059	+	0.256920i
$229$		−	4.31740i		−	0.285302i	−0.989773	−	0.142651i	$-0.954437\pi$
$229$		−	4.31740i		−	0.285302i	0.989773	−	0.142651i	$-0.0455626\pi$
$230$	10.3407	−	23.2858i	0.681842	−	1.53542i
$231$		−	1.26894i		−	0.0834900i
$232$	−3.76004	−	8.67686i	−0.246859	−	0.569664i
$233$	13.8122	+	13.8122i	0.904866	+	0.904866i	0.995852	−	0.0909864i	$-0.0290020\pi$
$233$	13.8122	+	13.8122i	0.904866	+	0.904866i	−0.0909864	+	0.995852i	$0.529002\pi$
$234$	3.39744	+	0.428613i	0.222098	+	0.0280193i
$235$	5.91442	−	3.17734i	0.385815	−	0.207267i
$236$	0.321769	−	1.25497i	0.0209454	−	0.0816916i
$237$	4.85988	−	4.85988i	0.315683	−	0.315683i
$238$	8.32653	+	10.7307i	0.539729	+	0.695571i
$239$	−26.1364			−1.69062			−0.845311	−	0.534274i	$-0.820585\pi$
$239$	−26.1364			−1.69062			−0.845311	+	0.534274i	$0.820585\pi$
$240$	−0.0317555	+	3.52787i	−0.00204981	+	0.227723i
$241$	17.9549			1.15658			0.578288	−	0.815833i	$-0.303721\pi$
$241$	17.9549			1.15658			0.578288	+	0.815833i	$0.303721\pi$
$242$	−7.98210	−	10.2869i	−0.513109	−	0.661265i
$243$	7.01669	−	7.01669i	0.450121	−	0.450121i
$244$	−2.97345	+	11.5971i	−0.190356	+	0.742429i
$245$	2.63002	+	0.791773i	0.168026	+	0.0505845i
$246$	0.553441	+	0.0698207i	0.0352861	+	0.00445161i
$247$	−3.43971	−	3.43971i	−0.218863	−	0.218863i
$248$	−2.30840	−	5.32697i	−0.146583	−	0.338263i
$249$			3.57783i			0.226736i
$250$	−15.4393	−	3.40977i	−0.976470	−	0.215653i
$251$			7.05309i			0.445187i	0.974911	+	0.222594i	$0.0714523\pi$
$251$			7.05309i			0.445187i	−0.974911	+	0.222594i	$0.928548\pi$
$252$	−6.96106	−	11.7614i	−0.438505	−	0.740900i
$253$	7.62894	+	7.62894i	0.479628	+	0.479628i
$254$	−0.0207217	+	0.164253i	−0.00130020	+	0.0103061i
$255$	3.37629	+	1.01644i	0.211432	+	0.0636518i
$256$	8.59151	+	13.4976i	0.536969	+	0.843602i
$257$	5.88315	−	5.88315i	0.366981	−	0.366981i	−0.499394	−	0.866375i	$-0.666444\pi$
$257$	5.88315	−	5.88315i	0.366981	−	0.366981i	0.866375	+	0.499394i	$0.166444\pi$
$258$	−4.57142	+	3.54720i	−0.284604	+	0.220839i
$259$	−13.7285			−0.853046
$260$	−0.912294	−	3.69612i	−0.0565781	−	0.229224i
$261$	9.50997			0.588652
$262$	−14.9504	+	11.6008i	−0.923637	+	0.716697i
$263$	18.0270	−	18.0270i	1.11159	−	1.11159i	0.118660	−	0.992935i	$-0.462140\pi$
$263$	18.0270	−	18.0270i	1.11159	−	1.11159i	0.992935	−	0.118660i	$-0.0378598\pi$
$264$	−1.38931	−	0.549252i	−0.0855063	−	0.0338041i
$265$	−19.5463	+	10.5006i	−1.20072	+	0.645047i
$266$	−2.43004	+	19.2620i	−0.148995	+	1.18103i
$267$	4.47660	+	4.47660i	0.273964	+	0.273964i
$268$	3.20580	−	1.89737i	0.195825	−	0.115900i
$269$			16.9722i			1.03481i	0.855740	+	0.517405i	$0.173102\pi$
$269$			16.9722i			1.03481i	−0.855740	+	0.517405i	$0.826898\pi$
$270$	−6.66258	−	2.95869i	−0.405472	−	0.180060i
$271$		−	2.31981i		−	0.140918i	−0.997515	−	0.0704592i	$-0.977554\pi$
$271$		−	2.31981i		−	0.140918i	0.997515	−	0.0704592i	$-0.0224465\pi$
$272$	15.3528	−	4.47167i	0.930899	−	0.271135i
$273$	−0.570419	−	0.570419i	−0.0345233	−	0.0345233i
$274$	−11.4060	−	1.43895i	−0.689060	−	0.0869300i
$275$	3.69630	−	5.58259i	0.222895	−	0.336643i
$276$	−6.15695	−	1.57861i	−0.370605	−	0.0950214i
$277$	6.84246	−	6.84246i	0.411124	−	0.411124i	−0.471006	−	0.882130i	$-0.656109\pi$
$277$	6.84246	−	6.84246i	0.411124	−	0.411124i	0.882130	+	0.471006i	$0.156109\pi$
$278$	7.41063	+	9.55039i	0.444460	+	0.572794i
$279$	5.83844			0.349539
$280$	−9.42240	+	11.9200i	−0.563096	+	0.712354i
$281$	18.2191			1.08686			0.543430	−	0.839454i	$-0.317125\pi$
$281$	18.2191			1.08686			0.543430	+	0.839454i	$0.317125\pi$
$282$	−1.02678	−	1.32325i	−0.0611438	−	0.0787985i
$283$	8.74527	−	8.74527i	0.519852	−	0.519852i	−0.397674	−	0.917527i	$-0.630183\pi$
$283$	8.74527	−	8.74527i	0.519852	−	0.519852i	0.917527	+	0.397674i	$0.130183\pi$
$284$	−14.5125	−	3.72093i	−0.861156	−	0.220797i
$285$	2.38520	+	4.43991i	0.141287	+	0.262998i
$286$	1.59942	+	0.201779i	0.0945758	+	0.0119314i
$287$	1.69878	+	1.69878i	0.100276	+	0.100276i
$288$	−15.8902	+	2.53054i	−0.936339	+	0.149114i
$289$			1.01851i			0.0599122i
$290$	−3.79843	−	9.86682i	−0.223051	−	0.579400i
$291$		−	1.09616i		−	0.0642579i
$292$	−25.6502	+	15.1812i	−1.50107	+	0.888414i
$293$	13.0781	+	13.0781i	0.764028	+	0.764028i	0.977048	−	0.213020i	$-0.0683298\pi$
$293$	13.0781	+	13.0781i	0.764028	+	0.764028i	−0.213020	+	0.977048i	$0.568330\pi$
$294$	0.0857626	−	0.679806i	0.00500178	−	0.0396471i
$295$	0.417557	−	1.38699i	0.0243111	−	0.0807539i
$296$	−5.94229	+	15.0308i	−0.345389	+	0.873648i
$297$	2.18281	−	2.18281i	0.126659	−	0.126659i
$298$	11.9599	−	9.28032i	0.692821	−	0.537595i
$299$	6.85880			0.396655
$300$	−0.198847	+	3.93942i	−0.0114804	+	0.227443i
$301$	−24.9199			−1.43636
$302$	10.9638	−	8.50740i	0.630898	−	0.489546i
$303$	1.98407	−	1.98407i	0.113982	−	0.113982i
$304$	20.0374	+	10.9980i	1.14922	+	0.630778i
$305$	−3.85862	+	12.8171i	−0.220944	+	0.733907i
$306$	−2.01280	+	15.9547i	−0.115064	+	0.912067i
$307$	14.0504	+	14.0504i	0.801898	+	0.801898i	0.983392	−	0.181494i	$-0.0580933\pi$
$307$	14.0504	+	14.0504i	0.801898	+	0.801898i	−0.181494	+	0.983392i	$0.558093\pi$
$308$	−3.27708	−	5.53696i	−0.186729	−	0.315497i
$309$		−	3.34596i		−	0.190345i
$310$	−2.33196	−	6.05753i	−0.132447	−	0.344044i
$311$			24.4529i			1.38660i	0.720651	+	0.693298i	$0.243843\pi$
$311$			24.4529i			1.38660i	−0.720651	+	0.693298i	$0.756157\pi$
$312$	−0.871434	+	0.377628i	−0.0493352	+	0.0213790i
$313$	−15.4799	−	15.4799i	−0.874978	−	0.874978i	0.118032	−	0.993010i	$-0.462342\pi$
$313$	−15.4799	−	15.4799i	−0.874978	−	0.874978i	−0.993010	+	0.118032i	$0.962342\pi$
$314$	11.0677	+	1.39627i	0.624586	+	0.0787962i
$315$	−7.23136	−	13.4607i	−0.407441	−	0.758427i
$316$	8.65507	−	33.7567i	0.486886	−	1.89896i
$317$	−5.53854	+	5.53854i	−0.311075	+	0.311075i	−0.845326	−	0.534251i	$-0.820594\pi$
$317$	−5.53854	+	5.53854i	−0.311075	+	0.311075i	0.534251	+	0.845326i	$0.320594\pi$
$318$	3.39335	+	4.37315i	0.190289	+	0.245234i
$319$	4.47704			0.250666
$320$	8.97229	+	15.4757i	0.501566	+	0.865119i
$321$	−2.86165			−0.159722
$322$	−16.7815	−	21.6270i	−0.935196	−	1.20523i
$323$	16.1532	−	16.1532i	0.898785	−	0.898785i
$324$	3.78699	−	14.7701i	0.210388	−	0.820562i
$325$	−0.847935	−	4.17109i	−0.0470350	−	0.231370i
$326$	22.2760	+	2.81028i	1.23375	+	0.155647i
$327$	−3.69422	−	3.69422i	−0.204291	−	0.204291i
$328$	2.59523	−	1.12462i	0.143298	−	0.0620968i
$329$		−	7.21337i		−	0.397686i
$330$	−1.52653	−	0.677894i	−0.0840328	−	0.0373168i
$331$			16.7395i			0.920085i	0.887897	+	0.460043i	$0.152166\pi$
$331$			16.7395i			0.920085i	−0.887897	+	0.460043i	$0.847834\pi$
$332$	9.23988	+	15.6117i	0.507104	+	0.856805i
$333$	−11.4934	−	11.4934i	−0.629835	−	0.629835i
$334$	2.29906	−	18.2237i	0.125799	−	0.997157i
$335$	3.66899	−	1.97105i	0.200458	−	0.107690i
$336$	3.32287	+	1.82384i	0.181278	+	0.0994985i
$337$	−21.0413	+	21.0413i	−1.14619	+	1.14619i	−0.158897	+	0.987295i	$0.550794\pi$
$337$	−21.0413	+	21.0413i	−1.14619	+	1.14619i	−0.987295	+	0.158897i	$0.949206\pi$
$338$	−13.7152	+	10.6423i	−0.746010	+	0.578867i
$339$	−6.49766			−0.352904
$340$	17.3573	−	4.28421i	0.941331	−	0.232344i
$341$	2.74858			0.148844
$342$	−18.1605	+	14.0916i	−0.982005	+	0.761987i
$343$	13.9781	−	13.9781i	0.754745	−	0.754745i
$344$	−10.7864	+	27.2839i	−0.581566	+	1.47105i
$345$	−6.80466	−	2.04855i	−0.366351	−	0.110290i
$346$	−4.25919	+	33.7609i	−0.228976	+	1.81500i
$347$	18.7929	+	18.7929i	1.00886	+	1.00886i	0.999960	+	0.00889698i	$0.00283203\pi$
$347$	18.7929	+	18.7929i	1.00886	+	1.00886i	0.00889698	+	0.999960i	$0.497168\pi$
$348$	−2.26980	+	1.34339i	−0.121674	+	0.0720135i
$349$		−	1.67014i		−	0.0894007i	−0.999000	−	0.0447004i	$-0.985767\pi$
$349$		−	1.67014i		−	0.0894007i	0.999000	−	0.0447004i	$-0.0142333\pi$
$350$	−11.0775	+	12.8791i	−0.592119	+	0.688418i
$351$		−	1.96245i		−	0.104748i
$352$	−7.48067	+	1.19131i	−0.398721	+	0.0634971i
$353$	1.38513	+	1.38513i	0.0737232	+	0.0737232i	0.743007	−	0.669284i	$-0.233399\pi$
$353$	1.38513	+	1.38513i	0.0737232	+	0.0737232i	−0.669284	+	0.743007i	$0.733399\pi$
$354$	−0.358509	−	0.0452286i	−0.0190545	−	0.00240387i
$355$	−16.0392	−	4.82862i	−0.851271	−	0.256276i
$356$	31.0945	+	7.97248i	1.64800	+	0.422541i
$357$	2.67874	−	2.67874i	0.141774	−	0.141774i
$358$	5.54678	+	7.14836i	0.293156	+	0.377803i
$359$	25.0952			1.32447			0.662237	−	0.749294i	$-0.269607\pi$
$359$	25.0952			1.32447			0.662237	+	0.749294i	$0.269607\pi$
$360$	−17.8677	+	2.09094i	−0.941712	+	0.110202i
$361$	13.6533			0.718595
$362$	8.33348	+	10.7397i	0.437998	+	0.564466i
$363$	−2.56793	+	2.56793i	−0.134781	+	0.134781i
$364$	−3.96213	−	1.01587i	−0.207672	−	0.0532462i
$365$	−29.3562	+	15.7707i	−1.53658	+	0.825476i
$366$	3.31296	+	0.417955i	0.173171	+	0.0218469i
$367$	10.2323	+	10.2323i	0.534124	+	0.534124i	0.921797	−	0.387673i	$-0.126721\pi$
$367$	10.2323	+	10.2323i	0.534124	+	0.534124i	−0.387673	+	0.921797i	$0.626721\pi$
$368$	−30.9424	+	9.01231i	−1.61298	+	0.469799i
$369$			2.84441i			0.148074i
$370$	−7.33405	+	16.5153i	−0.381279	+	0.858592i
$371$			23.8391i			1.23766i
$372$	−1.39350	+	0.824748i	−0.0722494	+	0.0427612i
$373$	2.67563	+	2.67563i	0.138539	+	0.138539i	0.772975	−	0.634436i	$-0.218768\pi$
$373$	2.67563	+	2.67563i	0.138539	+	0.138539i	−0.634436	+	0.772975i	$0.718768\pi$
$374$	−0.947571	+	7.51102i	−0.0489977	+	0.388386i
$375$	−0.404560	+	4.39142i	−0.0208914	+	0.226772i
$376$	−7.89765	−	3.12226i	−0.407290	−	0.161018i
$377$	2.01254	−	2.01254i	0.103651	−	0.103651i
$378$	−6.18796	+	4.80155i	−0.318274	+	0.246965i
$379$	−14.8771			−0.764184			−0.382092	−	0.924124i	$-0.624796\pi$
$379$	−14.8771			−0.764184			−0.382092	+	0.924124i	$0.624796\pi$
$380$	21.8739	+	13.2135i	1.12211	+	0.677838i
$381$	0.0461755			0.00236564
$382$	−3.88587	+	3.01524i	−0.198818	+	0.154273i
$383$	−1.00827	+	1.00827i	−0.0515203	+	0.0515203i	−0.732398	−	0.680877i	$-0.761599\pi$
$383$	−1.00827	+	1.00827i	−0.0515203	+	0.0515203i	0.680877	+	0.732398i	$0.261599\pi$
$384$	3.43514	−	2.84865i	0.175299	−	0.145370i
$385$	−3.40432	−	6.33695i	−0.173500	−	0.322961i
$386$	0.413720	−	3.27939i	0.0210578	−	0.166917i
$387$	−20.8628	−	20.8628i	−1.06052	−	1.06052i
$388$	−2.83087	−	4.78304i	−0.143716	−	0.242822i
$389$			18.3980i			0.932817i	0.884569	+	0.466408i	$0.154452\pi$
$389$			18.3980i			0.932817i	−0.884569	+	0.466408i	$0.845548\pi$
$390$	−0.990944	+	0.381483i	−0.0501784	+	0.0193172i
$391$			32.2095i			1.62890i
$392$	−1.38140	−	3.18779i	−0.0697713	−	0.161008i
$393$	3.73209	+	3.73209i	0.188259	+	0.188259i
$394$	13.1405	+	1.65777i	0.662008	+	0.0835172i
$395$	11.2316	−	37.3079i	0.565124	−	1.87717i
$396$	1.89196	−	7.37907i	0.0950746	−	0.370812i
$397$	4.31475	−	4.31475i	0.216551	−	0.216551i	−0.590492	−	0.807043i	$-0.701066\pi$
$397$	4.31475	−	4.31475i	0.216551	−	0.216551i	0.807043	+	0.590492i	$0.201066\pi$
$398$	−20.3877	−	26.2744i	−1.02194	−	1.31702i
$399$	5.41502			0.271090
$400$	9.30604	+	17.7030i	0.465302	+	0.885152i
$401$	−16.1354			−0.805764			−0.402882	−	0.915252i	$-0.631992\pi$
$401$	−16.1354			−0.805764			−0.402882	+	0.915252i	$0.631992\pi$
$402$	−0.636957	−	0.820873i	−0.0317685	−	0.0409414i
$403$	1.23556	−	1.23556i	0.0615474	−	0.0615474i
$404$	3.53347	−	13.7813i	0.175797	−	0.685646i
$405$	4.91435	−	16.3239i	0.244196	−	0.811143i
$406$	−11.2700	−	1.42179i	−0.559320	−	0.0705624i
$407$	−5.41079	−	5.41079i	−0.268203	−	0.268203i
$408$	−1.77337	−	4.09232i	−0.0877951	−	0.202600i
$409$			4.15049i			0.205229i	0.994721	+	0.102614i	$0.0327208\pi$
$409$			4.15049i			0.205229i	−0.994721	+	0.102614i	$0.967279\pi$
$410$	2.95115	−	1.13610i	0.145747	−	0.0561081i
$411$			3.20650i			0.158165i
$412$	−8.64107	−	14.6000i	−0.425715	−	0.719289i
$413$	−1.10044	−	1.10044i	−0.0541489	−	0.0541489i
$414$	4.05665	−	32.1554i	0.199373	−	1.58035i
$415$	9.59867	+	17.8674i	0.471180	+	0.877074i
$416$	−2.82723	+	3.89827i	−0.138616	+	0.191129i
$417$	2.38408	−	2.38408i	0.116749	−	0.116749i
$418$	−8.54945	+	6.63395i	−0.418167	+	0.324477i
$419$	19.1256			0.934349			0.467174	−	0.884165i	$-0.345272\pi$
$419$	19.1256			0.934349			0.467174	+	0.884165i	$0.345272\pi$
$420$	3.62744	+	2.19124i	0.177001	+	0.106922i
$421$	−30.7471			−1.49852			−0.749262	−	0.662274i	$-0.769591\pi$
$421$	−30.7471			−1.49852			−0.749262	+	0.662274i	$0.769591\pi$
$422$	3.84887	−	2.98653i	0.187360	−	0.145382i
$423$	6.03900	−	6.03900i	0.293626	−	0.293626i
$424$	26.1005	+	10.3186i	1.26755	+	0.501116i
$425$	19.5878	−	3.98197i	0.950147	−	0.193154i
$426$	−0.523023	+	4.14579i	−0.0253405	+	0.200864i
$427$	10.1691	+	10.1691i	0.492116	+	0.492116i
$428$	−12.4867	+	7.39030i	−0.603566	+	0.357224i
$429$		−	0.449637i		−	0.0217087i
$430$	−13.3128	+	29.9786i	−0.641998	+	1.44570i
$431$			3.83959i			0.184947i	0.995715	+	0.0924733i	$0.0294773\pi$
$431$			3.83959i			0.184947i	−0.995715	+	0.0924733i	$0.970523\pi$
$432$	2.57862	+	8.85329i	0.124064	+	0.425954i
$433$	−5.27443	−	5.27443i	−0.253473	−	0.253473i	0.568920	−	0.822393i	$-0.307361\pi$
$433$	−5.27443	−	5.27443i	−0.253473	−	0.253473i	−0.822393	+	0.568920i	$0.807361\pi$
$434$	−6.91897	−	0.872880i	−0.332121	−	0.0418996i
$435$	−2.59775	+	1.39556i	−0.124553	+	0.0669119i
$436$	−25.6600	−	6.57911i	−1.22889	−	0.315082i
$437$	−32.5555	+	32.5555i	−1.55734	+	1.55734i
$438$	5.09642	+	6.56796i	0.243516	+	0.313829i
$439$	23.9111			1.14121			0.570607	−	0.821223i	$-0.306708\pi$
$439$	23.9111			1.14121			0.570607	+	0.821223i	$0.306708\pi$
$440$	−8.41164	+	0.984357i	−0.401009	+	0.0469274i
$441$	3.49387			0.166375
$442$	2.95043	+	3.80235i	0.140338	+	0.180859i
$443$	−4.26544	+	4.26544i	−0.202657	+	0.202657i	−0.801137	−	0.598480i	$-0.795771\pi$
$443$	−4.26544	+	4.26544i	−0.202657	+	0.202657i	0.598480	+	0.801137i	$0.295771\pi$
$444$	4.36678	+	1.11962i	0.207238	+	0.0531350i
$445$	34.3656	+	10.3458i	1.62909	+	0.490439i
$446$	−9.36811	−	1.18186i	−0.443593	−	0.0559625i
$447$	−2.98558	−	2.98558i	−0.141213	−	0.141213i
$448$	19.2093	−	0.623201i	0.907556	−	0.0294435i
$449$			14.1752i			0.668969i	0.942401	+	0.334485i	$0.108562\pi$
$449$			14.1752i			0.668969i	−0.942401	+	0.334485i	$0.891438\pi$
$450$	−20.0564	+	1.50829i	−0.945468	+	0.0711015i
$451$			1.33907i			0.0630545i
$452$	−28.3522	+	16.7804i	−1.33358	+	0.789285i
$453$	−2.73692	−	2.73692i	−0.128592	−	0.128592i
$454$	1.58901	−	12.5954i	0.0745758	−	0.591132i
$455$	−4.37895	−	1.31829i	−0.205288	−	0.0618024i
$456$	2.34386	−	5.92870i	0.109761	−	0.277637i
$457$	25.0911	−	25.0911i	1.17371	−	1.17371i	0.192397	−	0.981317i	$-0.438374\pi$
$457$	25.0911	−	25.0911i	1.17371	−	1.17371i	0.981317	−	0.192397i	$-0.0616262\pi$
$458$	−4.82384	+	3.74306i	−0.225403	+	0.174902i
$459$	9.21584			0.430159
$460$	−34.9823	+	8.63450i	−1.63106	+	0.402586i
$461$	30.6852			1.42915			0.714577	−	0.699557i	$-0.246619\pi$
$461$	30.6852			1.42915			0.714577	+	0.699557i	$0.246619\pi$
$462$	−1.41779	+	1.10013i	−0.0659614	+	0.0511828i
$463$	−10.4137	+	10.4137i	−0.483964	+	0.483964i	−0.906395	−	0.422431i	$-0.861177\pi$
$463$	−10.4137	+	10.4137i	−0.483964	+	0.483964i	0.422431	+	0.906395i	$0.361177\pi$
$464$	−6.43482	+	11.7237i	−0.298729	+	0.544258i
$465$	−1.59483	+	0.856773i	−0.0739586	+	0.0397319i
$466$	3.45761	−	27.4071i	0.160171	−	1.26961i
$467$	13.9017	+	13.9017i	0.643296	+	0.643296i	0.951364	−	0.308069i	$-0.0996826\pi$
$467$	13.9017	+	13.9017i	0.643296	+	0.643296i	−0.308069	+	0.951364i	$0.599683\pi$
$468$	−2.46659	−	4.16756i	−0.114018	−	0.192646i
$469$		−	4.47478i		−	0.206626i
$470$	−8.67767	−	3.85354i	−0.400271	−	0.177750i
$471$		−	3.11141i		−	0.143366i
$472$	−1.68114	+	0.728509i	−0.0773809	+	0.0335323i
$473$	−9.82166	−	9.82166i	−0.451600	−	0.451600i
$474$	−9.64333	−	1.21658i	−0.442933	−	0.0558793i
$475$	23.8229	+	15.7734i	1.09307	+	0.723735i
$476$	4.77062	−	18.6065i	0.218661	−	0.852827i
$477$	−19.9580	+	19.9580i	−0.913812	+	0.913812i
$478$	22.6595	+	29.2022i	1.03642	+	1.33568i
$479$	3.51098			0.160421			0.0802104	−	0.996778i	$-0.474441\pi$
$479$	3.51098			0.160421			0.0802104	+	0.996778i	$0.474441\pi$
$480$	3.96923	−	3.02308i	0.181170	−	0.137984i
$481$	−4.86457			−0.221805
$482$	−15.5664	−	20.0610i	−0.709028	−	0.913755i
$483$	−5.39879	+	5.39879i	−0.245654	+	0.245654i
$484$	−4.57328	+	17.8368i	−0.207876	+	0.810764i
$485$	−2.94079	−	5.47411i	−0.133534	−	0.248566i
$486$	−13.9230	−	1.75649i	−0.631561	−	0.0796761i
$487$	−5.10830	−	5.10830i	−0.231479	−	0.231479i	0.581831	−	0.813310i	$-0.302337\pi$
$487$	−5.10830	−	5.10830i	−0.231479	−	0.231479i	−0.813310	+	0.581831i	$0.802337\pi$
$488$	15.5354	−	6.73212i	0.703253	−	0.304749i
$489$		−	6.26233i		−	0.283192i
$490$	−1.39550	−	3.62497i	−0.0630424	−	0.163760i
$491$		−	25.0265i		−	1.12943i	−0.825286	−	0.564715i	$-0.808986\pi$
$491$		−	25.0265i		−	1.12943i	0.825286	−	0.564715i	$-0.191014\pi$
$492$	−0.401806	−	0.678893i	−0.0181148	−	0.0306069i
$493$	9.45105	+	9.45105i	0.425654	+	0.425654i
$494$	−0.861064	+	6.82532i	−0.0387411	+	0.307085i
$495$	2.45518	−	8.15535i	0.110352	−	0.366556i
$496$	−3.95052	+	7.19750i	−0.177384	+	0.323177i
$497$	−12.7254	+	12.7254i	−0.570813	+	0.570813i
$498$	3.99752	−	3.10188i	0.179133	−	0.138998i
$499$	−19.4164			−0.869197			−0.434599	−	0.900624i	$-0.643110\pi$
$499$	−19.4164			−0.869197			−0.434599	+	0.900624i	$0.643110\pi$
$500$	9.57572	+	20.2066i	0.428239	+	0.903665i
$501$	−5.12314			−0.228885
$502$	7.88043	−	6.11482i	0.351721	−	0.272918i
$503$	7.04618	−	7.04618i	0.314174	−	0.314174i	−0.532350	−	0.846524i	$-0.678691\pi$
$503$	7.04618	−	7.04618i	0.314174	−	0.314174i	0.846524	+	0.532350i	$0.178691\pi$
$504$	−7.10602	+	17.9744i	−0.316527	+	0.800644i
$505$	4.58536	−	15.2311i	0.204046	−	0.677776i
$506$	1.90976	−	15.1379i	0.0848991	−	0.672962i
$507$	3.42376	+	3.42376i	0.152054	+	0.152054i
$508$	0.201485	−	0.119250i	0.00893945	−	0.00529086i
$509$			26.3683i			1.16875i	0.811483	+	0.584376i	$0.198661\pi$
$509$			26.3683i			1.16875i	−0.811483	+	0.584376i	$0.801339\pi$
$510$	−1.79148	−	4.65356i	−0.0793280	−	0.206063i
$511$			35.8035i			1.58386i
$512$	7.63233	−	21.3014i	0.337305	−	0.941396i
$513$	9.31483	+	9.31483i	0.411260	+	0.411260i
$514$	−11.6738	−	1.47273i	−0.514908	−	0.0649595i
$515$	−8.97660	−	16.7094i	−0.395556	−	0.736305i
$516$	7.92657	+	2.03234i	0.348948	+	0.0894687i
$517$	2.84300	−	2.84300i	0.125035	−	0.125035i
$518$	11.9022	+	15.3388i	0.522952	+	0.673950i
$519$	9.49104			0.416610
$520$	−3.33875	+	4.22374i	−0.146414	+	0.185223i
$521$	4.91983			0.215541			0.107771	−	0.994176i	$-0.465629\pi$
$521$	4.91983			0.215541			0.107771	+	0.994176i	$0.465629\pi$
$522$	−8.24487	−	10.6255i	−0.360868	−	0.465066i
$523$	3.60109	−	3.60109i	0.157465	−	0.157465i	−0.623977	−	0.781442i	$-0.714484\pi$
$523$	3.60109	−	3.60109i	0.157465	−	0.157465i	0.781442	+	0.623977i	$0.214484\pi$
$524$	25.9231	+	6.64656i	1.13245	+	0.290356i
$525$	3.95064	+	2.61577i	0.172420	+	0.114161i
$526$	−35.7705	−	4.51272i	−1.55967	−	0.196764i
$527$	5.80227	+	5.80227i	0.252751	+	0.252751i
$528$	0.590813	+	2.02847i	0.0257119	+	0.0882777i
$529$		−	41.9158i		−	1.82243i
$530$	28.6784	+	12.7353i	1.24571	+	0.553188i
$531$		−	1.84256i		−	0.0799602i
$532$	23.6282	−	13.9845i	1.02441	−	0.606304i
$533$	0.601947	+	0.601947i	0.0260732	+	0.0260732i
$534$	1.12063	−	8.88280i	0.0484945	−	0.384396i
$535$	−14.2908	+	7.67727i	−0.617845	+	0.331917i
$536$	−4.89927	−	1.93688i	−0.211616	−	0.0836605i
$537$	1.78446	−	1.78446i	0.0770051	−	0.0770051i
$538$	18.9630	−	14.7144i	0.817554	−	0.634381i
$539$	1.64482			0.0708473
$540$	2.47052	+	10.0092i	0.106314	+	0.430728i
$541$	−7.89806			−0.339564			−0.169782	−	0.985482i	$-0.554306\pi$
$541$	−7.89806			−0.339564			−0.169782	+	0.985482i	$0.554306\pi$
$542$	−2.59193	+	2.01121i	−0.111333	+	0.0863887i
$543$	2.68097	−	2.68097i	0.115052	−	0.115052i
$544$	−18.3066	−	13.2769i	−0.784890	−	0.569242i
$545$	−28.3594	−	8.53766i	−1.21479	−	0.365713i
$546$	−0.142793	+	1.13187i	−0.00611100	+	0.0484394i
$547$	14.0572	+	14.0572i	0.601043	+	0.601043i	0.940589	−	0.339546i	$-0.110273\pi$
$547$	14.0572	+	14.0572i	0.601043	+	0.601043i	−0.339546	+	0.940589i	$0.610273\pi$
$548$	8.28090	+	13.9914i	0.353742	+	0.597684i
$549$			17.0270i			0.726694i
$550$	−9.44201	+	0.710062i	−0.402609	+	0.0302771i
$551$			19.1051i			0.813906i
$552$	3.57410	+	8.24777i	0.152124	+	0.351049i
$553$	−29.6000	−	29.6000i	−1.25872	−	1.25872i
$554$	−13.5773	−	1.71288i	−0.576844	−	0.0727732i
$555$	4.82617	+	1.45293i	0.204859	+	0.0616733i
$556$	4.24586	−	16.5598i	0.180065	−	0.702293i
$557$	23.4325	−	23.4325i	0.992868	−	0.992868i	−0.00710642	−	0.999975i	$-0.502262\pi$
$557$	23.4325	−	23.4325i	0.992868	−	0.992868i	0.999975	+	0.00710642i	$0.00226206\pi$
$558$	−5.06176	−	6.52330i	−0.214281	−	0.276153i
$559$	−8.83016			−0.373476
$560$	21.4871	+	0.193412i	0.907997	+	0.00817316i
$561$	2.11153			0.0891490
$562$	−15.7954	−	20.3562i	−0.666289	−	0.858675i
$563$	16.4403	−	16.4403i	0.692876	−	0.692876i	−0.269988	−	0.962864i	$-0.587020\pi$
$563$	16.4403	−	16.4403i	0.692876	−	0.692876i	0.962864	+	0.269988i	$0.0870196\pi$
$564$	−0.588285	+	2.29444i	−0.0247713	+	0.0966134i
$565$	−32.4487	+	17.4320i	−1.36513	+	0.733370i
$566$	−17.3530	−	2.18921i	−0.729401	−	0.0920193i
$567$	−12.9513	−	12.9513i	−0.543905	−	0.543905i
$568$	8.42447	+	19.4407i	0.353483	+	0.815714i
$569$		−	24.5089i		−	1.02747i	−0.857950	−	0.513733i	$-0.828262\pi$
$569$		−	24.5089i		−	1.02747i	0.857950	−	0.513733i	$-0.171738\pi$
$570$	2.89282	−	6.51426i	0.121167	−	0.272852i
$571$			23.9122i			1.00069i	0.865825	+	0.500346i	$0.166794\pi$
$571$			23.9122i			1.00069i	−0.865825	+	0.500346i	$0.833206\pi$
$572$	−1.16120	−	1.96197i	−0.0485524	−	0.0820342i
$573$	0.970036	+	0.970036i	0.0405238	+	0.0405238i
$574$	0.425256	−	3.37083i	0.0177498	−	0.140696i
$575$	−39.4777	+	8.02537i	−1.64633	+	0.334681i
$576$	16.6037	+	15.5602i	0.691821	+	0.648343i
$577$	19.1002	−	19.1002i	0.795153	−	0.795153i	−0.187174	−	0.982327i	$-0.559933\pi$
$577$	19.1002	−	19.1002i	0.795153	−	0.795153i	0.982327	+	0.187174i	$0.0599329\pi$
$578$	1.13798	−	0.883016i	0.0473337	−	0.0367286i
$579$	−0.921918			−0.0383136
$580$	−7.73109	+	12.7982i	−0.321016	+	0.531418i
$581$	21.7914			0.904061
$582$	−1.22474	+	0.950337i	−0.0507671	+	0.0393927i
$583$	−9.39566	+	9.39566i	−0.389129	+	0.389129i
$584$	39.2000	+	15.4974i	1.62211	+	0.641285i
$585$	−2.56237	−	4.76970i	−0.105941	−	0.197203i
$586$	3.27384	−	25.9504i	0.135241	−	1.07200i
$587$	−30.3071	−	30.3071i	−1.25091	−	1.25091i	−0.955313	−	0.295596i	$-0.904482\pi$
$587$	−30.3071	−	30.3071i	−1.25091	−	1.25091i	−0.295596	−	0.955313i	$-0.595518\pi$
$588$	−0.833902	+	0.493549i	−0.0343895	+	0.0203536i
$589$			11.7292i			0.483293i
$590$	−1.91170	+	0.735946i	−0.0787034	+	0.0302984i
$591$		−	3.69411i		−	0.151956i
$592$	21.9457	−	6.39193i	0.901964	−	0.262707i
$593$	20.6682	+	20.6682i	0.848739	+	0.848739i	0.989976	−	0.141237i	$-0.0451078\pi$
$593$	20.6682	+	20.6682i	0.848739	+	0.848739i	−0.141237	+	0.989976i	$0.545108\pi$
$594$	−4.33128	−	0.546424i	−0.177715	−	0.0224200i
$595$	6.19079	−	20.5639i	0.253798	−	0.843038i
$596$	−20.7378	−	5.31709i	−0.849455	−	0.217797i
$597$	−6.55894	+	6.55894i	−0.268440	+	0.268440i
$598$	−5.94638	−	7.66335i	−0.243166	−	0.313378i
$599$	−42.7073			−1.74497			−0.872487	−	0.488637i	$-0.837494\pi$
$599$	−42.7073			−1.74497			−0.872487	+	0.488637i	$0.837494\pi$
$600$	4.57392	−	3.19319i	0.186729	−	0.130362i
$601$	−3.37026			−0.137476			−0.0687378	−	0.997635i	$-0.521897\pi$
$601$	−3.37026			−0.137476			−0.0687378	+	0.997635i	$0.521897\pi$
$602$	21.6048	+	27.8430i	0.880547	+	1.13480i
$603$	3.74626	−	3.74626i	0.152560	−	0.152560i
$604$	−19.0107	−	4.87425i	−0.773533	−	0.198330i
$605$	−5.93471	+	19.7133i	−0.241280	+	0.801458i
$606$	−3.93693	−	0.496673i	−0.159927	−	0.0201760i
$607$	17.5463	+	17.5463i	0.712184	+	0.712184i	0.966992	−	0.254807i	$-0.0820121\pi$
$607$	17.5463	+	17.5463i	0.712184	+	0.712184i	−0.254807	+	0.966992i	$0.582012\pi$
$608$	−5.08376	−	31.9227i	−0.206174	−	1.29464i
$609$			3.16827i			0.128385i
$610$	17.6659	−	6.80084i	0.715272	−	0.275358i
$611$		−	2.55600i		−	0.103405i
$612$	19.5712	−	11.5833i	0.791119	−	0.468228i
$613$	−3.47274	−	3.47274i	−0.140263	−	0.140263i	0.633489	−	0.773752i	$-0.281622\pi$
$613$	−3.47274	−	3.47274i	−0.140263	−	0.140263i	−0.773752	+	0.633489i	$0.781622\pi$
$614$	3.51724	−	27.8798i	0.141944	−	1.12514i
$615$	−0.417409	−	0.776982i	−0.0168315	−	0.0313309i
$616$	−3.34532	+	8.46186i	−0.134787	+	0.340938i
$617$	7.10530	−	7.10530i	0.286049	−	0.286049i	−0.549467	−	0.835516i	$-0.685169\pi$
$617$	7.10530	−	7.10530i	0.286049	−	0.286049i	0.835516	+	0.549467i	$0.185169\pi$
$618$	−3.73845	+	2.90085i	−0.150383	+	0.116689i
$619$	9.30534			0.374013			0.187007	−	0.982359i	$-0.440121\pi$
$619$	9.30534			0.374013			0.187007	+	0.982359i	$0.440121\pi$
$620$	−4.74634	+	7.85720i	−0.190618	+	0.315553i
$621$	−18.5738			−0.745342
$622$	27.3212	−	21.1999i	1.09548	−	0.850040i
$623$	27.2656	−	27.2656i	1.09237	−	1.09237i
$624$	1.17743	+	0.646261i	0.0471350	+	0.0258712i
$625$	9.76104	+	23.0157i	0.390442	+	0.920628i
$626$	−3.87511	+	30.7164i	−0.154880	+	1.22768i
$627$	2.13421	+	2.13421i	0.0852323	+	0.0852323i
$628$	−8.03531	−	13.5765i	−0.320644	−	0.541761i
$629$		−	22.8444i		−	0.910866i
$630$	−8.77034	+	19.7497i	−0.349419	+	0.786846i
$631$		−	34.1175i		−	1.35820i	−0.734047	−	0.679099i	$-0.762371\pi$
$631$		−	34.1175i		−	1.35820i	0.734047	−	0.679099i	$-0.237629\pi$
$632$	−45.2201	+	19.5957i	−1.79876	+	0.779477i
$633$	−0.960801	−	0.960801i	−0.0381884	−	0.0381884i
$634$	10.9900	+	1.38647i	0.436467	+	0.0550636i
$635$	0.230596	−	0.123880i	0.00915092	−	0.00491604i
$636$	1.94419	−	7.58278i	0.0770922	−	0.300677i
$637$	0.739387	−	0.739387i	0.0292956	−	0.0292956i
$638$	−3.88146	−	5.00220i	−0.153668	−	0.198039i
$639$	−21.3073			−0.842905
$640$	9.51234	−	23.4417i	0.376008	−	0.926616i
$641$	−5.37579			−0.212331			−0.106166	−	0.994348i	$-0.533857\pi$
$641$	−5.37579			−0.212331			−0.106166	+	0.994348i	$0.533857\pi$
$642$	2.48096	+	3.19732i	0.0979158	+	0.126188i
$643$	5.72371	−	5.72371i	0.225721	−	0.225721i	−0.585181	−	0.810902i	$-0.698977\pi$
$643$	5.72371	−	5.72371i	0.225721	−	0.225721i	0.810902	+	0.585181i	$0.198977\pi$
$644$	−9.61483	+	37.5000i	−0.378877	+	1.47771i
$645$	8.76046	+	2.63735i	0.344943	+	0.103846i
$646$	−32.0522	−	4.04363i	−1.26108	−	0.159094i
$647$	−7.41644	−	7.41644i	−0.291570	−	0.291570i	0.546130	−	0.837700i	$-0.316100\pi$
$647$	−7.41644	−	7.41644i	−0.291570	−	0.291570i	−0.837700	+	0.546130i	$0.816100\pi$
$648$	−19.7859	+	8.57404i	−0.777262	+	0.336820i
$649$		−	0.867426i		−	0.0340495i
$650$	−3.92523	+	4.56361i	−0.153960	+	0.179000i
$651$			1.94509i			0.0762342i
$652$	−16.1727	−	27.3254i	−0.633371	−	1.07015i
$653$	5.39989	+	5.39989i	0.211314	+	0.211314i	0.804826	−	0.593511i	$-0.202259\pi$
$653$	5.39989	+	5.39989i	0.211314	+	0.211314i	−0.593511	+	0.804826i	$0.702259\pi$
$654$	−0.924776	+	7.33033i	−0.0361616	+	0.286639i
$655$	28.6502	+	8.62519i	1.11946	+	0.337014i
$656$	−3.50653	−	1.92464i	−0.136907	−	0.0751446i
$657$	−29.9746	+	29.9746i	−1.16942	+	1.16942i
$658$	−8.05950	+	6.25378i	−0.314192	+	0.243798i
$659$	−35.7745			−1.39357			−0.696787	−	0.717278i	$-0.745388\pi$
$659$	−35.7745			−1.39357			−0.696787	+	0.717278i	$0.745388\pi$
$660$	0.566045	+	2.29331i	0.0220333	+	0.0892669i
$661$	4.33953			0.168788			0.0843940	−	0.996432i	$-0.473105\pi$
$661$	4.33953			0.168788			0.0843940	+	0.996432i	$0.473105\pi$
$662$	18.7030	−	14.5126i	0.726915	−	0.564050i
$663$	0.949187	−	0.949187i	0.0368634	−	0.0368634i
$664$	9.43230	−	23.8586i	0.366044	−	0.925895i
$665$	27.0421	−	14.5275i	1.04865	−	0.563352i
$666$	−2.87715	+	22.8061i	−0.111487	+	0.883717i
$667$	−19.0479	−	19.0479i	−0.737537	−	0.737537i
$668$	−22.3546	+	13.2307i	−0.864925	+	0.511911i
$669$			2.63361i			0.101821i
$670$	−5.38315	−	2.39052i	−0.207969	−	0.0923540i
$671$			8.01584i			0.309448i
$672$	−0.843058	−	5.29386i	−0.0325217	−	0.204215i
$673$	28.5538	+	28.5538i	1.10067	+	1.10067i	0.994330	+	0.106338i	$0.0339127\pi$
$673$	28.5538	+	28.5538i	1.10067	+	1.10067i	0.106338	+	0.994330i	$0.466087\pi$
$674$	41.7516	+	5.26728i	1.60821	+	0.202888i
$675$	2.29623	+	11.2954i	0.0883820	+	0.434761i
$676$	23.7814	+	6.09745i	0.914669	+	0.234517i
$677$	11.0735	−	11.0735i	0.425590	−	0.425590i	−0.461533	−	0.887123i	$-0.652701\pi$
$677$	11.0735	−	11.0735i	0.425590	−	0.425590i	0.887123	+	0.461533i	$0.152701\pi$
$678$	5.63328	+	7.25984i	0.216345	+	0.278812i
$679$	−6.67635			−0.256215
$680$	−19.8350	−	15.6790i	−0.760638	−	0.601264i
$681$	−3.54089			−0.135687
$682$	−2.38294	−	3.07099i	−0.0912474	−	0.117594i
$683$	−4.27997	+	4.27997i	−0.163768	+	0.163768i	−0.784234	−	0.620465i	$-0.786944\pi$
$683$	−4.27997	+	4.27997i	−0.163768	+	0.163768i	0.620465	+	0.784234i	$0.286944\pi$
$684$	31.4892	+	8.07368i	1.20402	+	0.308705i
$685$	8.60245	+	16.0129i	0.328683	+	0.611823i
$686$	−27.7363	−	3.49914i	−1.05898	−	0.133598i
$687$	1.20418	+	1.20418i	0.0459425	+	0.0459425i
$688$	39.8359	−	11.6026i	1.51873	−	0.442346i
$689$			8.44717i			0.321812i
$690$	3.61059	+	9.37889i	0.137453	+	0.357048i
$691$		−	0.290852i		−	0.0110645i	−0.999985	−	0.00553227i	$-0.998239\pi$
$691$		−	0.290852i		−	0.0110645i	0.999985	−	0.00553227i	$-0.00176099\pi$
$692$	41.4137	−	24.5109i	1.57431	−	0.931766i
$693$	−6.47042	−	6.47042i	−0.245791	−	0.245791i
$694$	4.70445	−	37.2903i	0.178578	−	1.41552i
$695$	5.50982	−	18.3019i	0.209000	−	0.694232i
$696$	3.46883	+	1.37137i	0.131486	+	0.0519816i
$697$	−2.82679	+	2.82679i	−0.107072	+	0.107072i
$698$	−1.86605	+	1.44797i	−0.0706312	+	0.0548063i
$699$	−7.70482			−0.291423
$700$	23.9938	+	1.21111i	0.906879	+	0.0457758i
$701$	33.3518			1.25968			0.629840	−	0.776725i	$-0.283121\pi$
$701$	33.3518			1.25968			0.629840	+	0.776725i	$0.283121\pi$
$702$	−2.19265	+	1.70139i	−0.0827563	+	0.0642148i
$703$	23.0898	−	23.0898i	0.870848	−	0.870848i
$704$	7.81658	+	7.32533i	0.294598	+	0.276084i
$705$	−0.763413	+	2.53582i	−0.0287518	+	0.0955045i
$706$	0.346741	−	2.74848i	0.0130498	−	0.103440i
$707$	−12.0843	−	12.0843i	−0.454478	−	0.454478i
$708$	0.260283	+	0.439774i	0.00978203	+	0.0165277i
$709$		−	12.0477i		−	0.452461i	−0.974074	−	0.226231i	$-0.927360\pi$
$709$		−	12.0477i		−	0.452461i	0.974074	−	0.226231i	$-0.0726403\pi$
$710$	8.51047	+	22.1069i	0.319392	+	0.829656i
$711$		−	49.5619i		−	1.85872i
$712$	−18.0503	−	41.6538i	−0.676464	−	1.56104i
$713$	−11.6940	−	11.6940i	−0.437945	−	0.437945i
$714$	−5.31534	−	0.670570i	−0.198922	−	0.0250954i
$715$	−1.20629	−	2.24545i	−0.0451128	−	0.0839749i
$716$	3.17798	−	12.3948i	0.118767	−	0.463217i
$717$	7.28981	−	7.28981i	0.272243	−	0.272243i
$718$	−21.7568	−	28.0389i	−0.811957	−	1.04640i
$719$	−51.6720			−1.92704			−0.963520	−	0.267636i	$-0.913758\pi$
$719$	−51.6720			−1.92704			−0.963520	+	0.267636i	$0.913758\pi$
$720$	17.8270	+	18.1508i	0.664373	+	0.676442i
$721$	−20.3792			−0.758961
$722$	−11.8370	−	15.2549i	−0.440528	−	0.567727i
$723$	−5.00787	+	5.00787i	−0.186245	+	0.186245i
$724$	4.77460	−	18.6220i	0.177447	−	0.692081i
$725$	−9.22888	+	13.9386i	−0.342752	+	0.517665i
$726$	5.09547	+	0.642832i	0.189111	+	0.0238577i
$727$	−19.3037	−	19.3037i	−0.715934	−	0.715934i	0.251836	−	0.967770i	$-0.418966\pi$
$727$	−19.3037	−	19.3037i	−0.715934	−	0.715934i	−0.967770	+	0.251836i	$0.918966\pi$
$728$	2.30001	+	5.30762i	0.0852441	+	0.196714i
$729$		−	18.9577i		−	0.702137i
$730$	43.0716	+	19.1270i	1.59415	+	0.707923i
$731$		−	41.4672i		−	1.53372i
$732$	−2.40526	−	4.06393i	−0.0889010	−	0.150207i
$733$	−25.8911	−	25.8911i	−0.956308	−	0.956308i	0.0427763	−	0.999085i	$-0.486380\pi$
$733$	−25.8911	−	25.8911i	−0.956308	−	0.956308i	−0.999085	+	0.0427763i	$0.986380\pi$
$734$	2.56147	−	20.3037i	0.0945456	−	0.749425i
$735$	−0.954387	+	0.512714i	−0.0352031	+	0.0189117i
$736$	36.8956	+	26.7586i	1.35999	+	0.986334i
$737$	1.76364	−	1.76364i	0.0649645	−	0.0649645i
$738$	3.17807	−	2.46602i	0.116986	−	0.0907756i
$739$	49.9136			1.83610			0.918050	−	0.396464i	$-0.129763\pi$
$739$	49.9136			1.83610			0.918050	+	0.396464i	$0.129763\pi$
$740$	24.8110	−	6.12397i	0.912071	−	0.225122i
$741$	1.91877			0.0704876
$742$	26.6354	−	20.6678i	0.977817	−	0.758738i
$743$	−26.7229	+	26.7229i	−0.980368	+	0.980368i	−0.999811	−	0.0194432i	$-0.993811\pi$
$743$	−26.7229	+	26.7229i	−0.980368	+	0.980368i	0.0194432	+	0.999811i	$0.493811\pi$
$744$	2.12961	+	0.841923i	0.0780754	+	0.0308664i
$745$	−22.9195	−	6.89994i	−0.839705	−	0.252794i
$746$	0.669791	−	5.30917i	0.0245228	−	0.194383i
$747$	18.2437	+	18.2437i	0.667502	+	0.667502i
$748$	9.21359	−	5.45311i	0.336882	−	0.199385i
$749$			17.4294i			0.636855i
$750$	5.25728	−	3.35522i	0.191969	−	0.122515i
$751$			5.83894i			0.213066i	0.994309	+	0.106533i	$0.0339750\pi$
$751$			5.83894i			0.213066i	−0.994309	+	0.106533i	$0.966025\pi$
$752$	3.35852	+	11.5310i	0.122473	+	0.420491i
$753$	−1.96721	−	1.96721i	−0.0716890	−	0.0716890i
$754$	−3.99343	−	0.503800i	−0.145432	−	0.0183473i
$755$	−21.0106	−	6.32527i	−0.764654	−	0.230200i
$756$	10.7296	+	2.75101i	0.390230	+	0.100053i
$757$	−19.0468	+	19.0468i	−0.692269	+	0.692269i	−0.962731	−	0.270462i	$-0.912824\pi$
$757$	−19.0468	+	19.0468i	−0.692269	+	0.692269i	0.270462	+	0.962731i	$0.412824\pi$
$758$	12.8980	+	16.6222i	0.468476	+	0.603744i
$759$	−4.25564			−0.154470
$760$	−4.20061	−	35.8955i	−0.152372	−	1.30207i
$761$	−34.8494			−1.26329			−0.631644	−	0.775258i	$-0.717620\pi$
$761$	−34.8494			−1.26329			−0.631644	+	0.775258i	$0.717620\pi$
$762$	−0.0400328	−	0.0515920i	−0.00145024	−	0.00186898i
$763$	−22.5003	+	22.5003i	−0.814565	+	0.814565i
$764$	6.73786	+	1.72756i	0.243767	+	0.0625009i
$765$	22.3989	−	12.0331i	0.809834	−	0.435058i
$766$	2.00069	+	0.252401i	0.0722877	+	0.00911963i
$767$	−0.389930	−	0.389930i	−0.0140796	−	0.0140796i
$768$	−6.16097	−	1.36839i	−0.222315	−	0.0493774i
$769$		−	38.2707i		−	1.38008i	−0.723774	−	0.690038i	$-0.757594\pi$
$769$		−	38.2707i		−	1.38008i	0.723774	−	0.690038i	$-0.242406\pi$
$770$	−4.12883	+	9.29761i	−0.148793	+	0.335062i
$771$			3.28179i			0.118191i
$772$	−4.02275	+	2.38089i	−0.144782	+	0.0856900i
$773$	−24.1856	−	24.1856i	−0.869894	−	0.869894i	0.122566	−	0.992460i	$-0.460888\pi$
$773$	−24.1856	−	24.1856i	−0.869894	−	0.869894i	−0.992460	+	0.122566i	$0.960888\pi$
$774$	−5.22261	+	41.3975i	−0.187723	+	1.48800i
$775$	−5.66588	+	8.55728i	−0.203524	+	0.307387i
$776$	−2.88982	+	7.30969i	−0.103738	+	0.262402i
$777$	3.82906	−	3.82906i	0.137367	−	0.137367i
$778$	20.5561	−	15.9505i	0.736973	−	0.571855i
$779$	−5.71431			−0.204736
$780$	1.28535	+	0.776448i	0.0460230	+	0.0278013i
$781$	−10.0309			−0.358934
$782$	35.9877	−	27.9247i	1.28692	−	0.998585i
$783$	−5.45002	+	5.45002i	−0.194768	+	0.194768i
$784$	−2.36409	+	4.30716i	−0.0844317	+	0.153827i
$785$	−8.34732	−	15.5381i	−0.297929	−	0.554577i
$786$	0.934257	−	7.40548i	0.0333238	−	0.264145i
$787$	−6.91387	−	6.91387i	−0.246453	−	0.246453i	0.573060	−	0.819513i	$-0.305756\pi$
$787$	−6.91387	−	6.91387i	−0.246453	−	0.246453i	−0.819513	+	0.573060i	$0.805756\pi$
$788$	−9.54018	−	16.1191i	−0.339855	−	0.574220i
$789$			10.0560i			0.358003i
$790$	−51.4217	+	19.7958i	−1.82950	+	0.704303i
$791$			39.5751i			1.40713i
$792$	−9.88492	+	4.28354i	−0.351245	+	0.152209i
$793$	3.60332	+	3.60332i	0.127958	+	0.127958i
$794$	−8.56164	−	1.08012i	−0.303841	−	0.0383318i
$795$	2.52296	−	8.38049i	0.0894802	−	0.297225i
$796$	−11.6810	+	45.5583i	−0.414021	+	1.61477i
$797$	27.5057	−	27.5057i	0.974302	−	0.974302i	−0.0253757	−	0.999678i	$-0.508078\pi$
$797$	27.5057	−	27.5057i	0.974302	−	0.974302i	0.999678	+	0.0253757i	$0.00807819\pi$
$798$	−4.69466	−	6.05021i	−0.166189	−	0.214175i
$799$	12.0032			0.424641
$800$	11.7116	−	25.7457i	0.414066	−	0.910247i
$801$	45.6532			1.61308
$802$	13.9889	+	18.0281i	0.493966	+	0.636595i
$803$	−14.1112	+	14.1112i	−0.497974	+	0.497974i
$804$	−0.364940	+	1.42335i	−0.0128704	+	0.0501976i
$805$	−12.4771	+	41.4450i	−0.439759	+	1.46074i
$806$	−2.45168	−	0.309298i	−0.0863567	−	0.0108945i
$807$	−4.73377	−	4.73377i	−0.166637	−	0.166637i
$808$	−18.4613	+	8.00005i	−0.649466	+	0.281441i
$809$			17.2778i			0.607454i	0.952759	+	0.303727i	$0.0982310\pi$
$809$			17.2778i			0.607454i	−0.952759	+	0.303727i	$0.901769\pi$
$810$	−22.4993	+	8.66157i	−0.790547	+	0.304336i
$811$		−	25.5883i		−	0.898526i	−0.893399	−	0.449263i	$-0.851687\pi$
$811$		−	25.5883i		−	0.898526i	0.893399	−	0.449263i	$-0.148313\pi$
$812$	8.18218	+	13.8246i	0.287138	+	0.485149i
$813$	0.647027	+	0.647027i	0.0226922	+	0.0226922i
$814$	−1.35449	+	10.7365i	−0.0474747	+	0.376313i
$815$	−16.8007	−	31.2734i	−0.588502	−	1.09546i
$816$	−3.03490	+	5.52932i	−0.106243	+	0.193565i
$817$	41.9126	−	41.9126i	1.46633	−	1.46633i
$818$	4.63735	−	3.59836i	0.162141	−	0.125814i
$819$	−5.81724			−0.203271
$820$	−3.82793	−	2.31235i	−0.133677	−	0.0807509i
$821$	0.601737			0.0210008			0.0105004	−	0.999945i	$-0.496658\pi$
$821$	0.601737			0.0210008			0.0105004	+	0.999945i	$0.496658\pi$
$822$	3.58263	−	2.77994i	0.124958	−	0.0969616i
$823$	−25.3957	+	25.3957i	−0.885238	+	0.885238i	−0.994061	−	0.108823i	$-0.965292\pi$
$823$	−25.3957	+	25.3957i	−0.885238	+	0.885238i	0.108823	+	0.994061i	$0.465292\pi$
$824$	−8.82101	+	22.3124i	−0.307295	+	0.777290i
$825$	0.526113	+	2.58801i	0.0183169	+	0.0901030i
$826$	−0.275473	+	2.18356i	−0.00958492	+	0.0759759i
$827$	3.80865	+	3.80865i	0.132440	+	0.132440i	0.770219	−	0.637779i	$-0.220147\pi$
$827$	3.80865	+	3.80865i	0.132440	+	0.132440i	−0.637779	+	0.770219i	$0.720147\pi$
$828$	−39.4443	+	23.3453i	−1.37078	+	0.811306i
$829$			50.1911i			1.74321i	0.490211	+	0.871604i	$0.336920\pi$
$829$			50.1911i			1.74321i	−0.490211	+	0.871604i	$0.663080\pi$
$830$	11.6415	−	26.2151i	0.404081	−	0.909939i
$831$			3.81692i			0.132407i
$832$	6.80667	−	0.220826i	0.235979	−	0.00765577i
$833$	3.47222	+	3.47222i	0.120305	+	0.120305i
$834$	−4.73067	−	0.596809i	−0.163810	−	0.0206658i
$835$	−25.5845	+	13.7444i	−0.885387	+	0.475646i
$836$	14.8242	+	3.80087i	0.512707	+	0.131456i
$837$	−3.34592	+	3.34592i	−0.115652	+	0.115652i
$838$	−16.5814	−	21.3691i	−0.572794	−	0.738183i
$839$	0.240697			0.00830979			0.00415490	−	0.999991i	$-0.498677\pi$
$839$	0.240697			0.00830979			0.00415490	+	0.999991i	$0.498677\pi$
$840$	−0.696602	−	5.95268i	−0.0240351	−	0.205387i
$841$	17.8218			0.614544
$842$	26.6569	+	34.3538i	0.918656	+	1.18391i
$843$	−5.08156	+	5.08156i	−0.175018	+	0.175018i
$844$	−6.67372	−	1.71111i	−0.229719	−	0.0588989i
$845$	26.2832	+	7.91261i	0.904171	+	0.272202i
$846$	−11.9830	−	1.51175i	−0.411985	−	0.0519749i
$847$	15.6404	+	15.6404i	0.537411	+	0.537411i
$848$	−11.0994	−	38.1081i	−0.381155	−	1.30864i
$849$			4.87836i			0.167425i
$850$	−21.4311	−	18.4332i	−0.735080	−	0.632254i
$851$			46.0412i			1.57827i
$852$	5.08555	−	3.00991i	0.174228	−	0.103118i
$853$	31.8507	+	31.8507i	1.09055	+	1.09055i	0.995470	+	0.0950786i	$0.0303102\pi$
$853$	31.8507	+	31.8507i	1.09055	+	1.09055i	0.0950786	+	0.995470i	$0.469690\pi$
$854$	2.54563	−	20.1782i	0.0871097	−	0.690484i
$855$	34.8018	+	10.4772i	1.19020	+	0.358311i
$856$	19.0828	+	7.54420i	0.652236	+	0.257855i
$857$	10.8177	−	10.8177i	0.369525	−	0.369525i	−0.497779	−	0.867304i	$-0.665851\pi$
$857$	10.8177	−	10.8177i	0.369525	−	0.369525i	0.867304	+	0.497779i	$0.165851\pi$
$858$	−0.502380	+	0.389822i	−0.0171510	+	0.0133083i
$859$	−50.2884			−1.71582			−0.857909	−	0.513801i	$-0.828237\pi$
$859$	−50.2884			−1.71582			−0.857909	+	0.513801i	$0.828237\pi$
$860$	45.0369	−	11.1162i	1.53575	−	0.379060i
$861$	−0.947624			−0.0322950
$862$	4.28998	−	3.32881i	0.146117	−	0.113380i
$863$	−26.1104	+	26.1104i	−0.888808	+	0.888808i	−0.994409	−	0.105601i	$-0.966324\pi$
$863$	−26.1104	+	26.1104i	−0.888808	+	0.888808i	0.105601	+	0.994409i	$0.466324\pi$
$864$	7.65621	−	10.5566i	0.260470	−	0.359144i
$865$	47.3973	−	25.4627i	1.61156	−	0.865757i
$866$	−1.32035	+	10.4659i	−0.0448674	+	0.355646i
$867$	−0.284076	−	0.284076i	−0.00964773	−	0.00964773i
$868$	5.02327	+	8.48733i	0.170501	+	0.288079i
$869$		−	23.3324i		−	0.791498i
$870$	3.81143	+	1.69256i	0.129220	+	0.0573832i
$871$		−	1.58560i		−	0.0537260i
$872$	14.8956	+	34.3738i	0.504429	+	1.16404i
$873$	−5.58941	−	5.58941i	−0.189173	−	0.189173i
$874$	64.5989	+	8.14963i	2.18509	+	0.275665i
$875$	26.7467	+	2.46404i	0.904205	+	0.0832998i
$876$	2.91995	−	11.3885i	0.0986560	−	0.384780i
$877$	27.7273	−	27.7273i	0.936283	−	0.936283i	−0.0618053	−	0.998088i	$-0.519686\pi$
$877$	27.7273	−	27.7273i	0.936283	−	0.936283i	0.998088	+	0.0618053i	$0.0196858\pi$
$878$	−20.7302	−	26.7159i	−0.699611	−	0.901618i
$879$	−7.29531			−0.246065
$880$	8.39247	+	8.54492i	0.282910	+	0.288049i
$881$	−3.72304			−0.125432			−0.0627162	−	0.998031i	$-0.519976\pi$
$881$	−3.72304			−0.125432			−0.0627162	+	0.998031i	$0.519976\pi$
$882$	−3.02908	−	3.90370i	−0.101994	−	0.131444i
$883$	−33.6940	+	33.6940i	−1.13389	+	1.13389i	−0.144369	+	0.989524i	$0.546115\pi$
$883$	−33.6940	+	33.6940i	−1.13389	+	1.13389i	−0.989524	+	0.144369i	$0.953885\pi$
$884$	1.69043	−	6.59305i	0.0568553	−	0.221748i
$885$	0.270390	+	0.503314i	0.00908904	+	0.0169187i
$886$	8.46379	+	1.06777i	0.284346	+	0.0358724i
$887$	−7.51751	−	7.51751i	−0.252413	−	0.252413i	0.569546	−	0.821959i	$-0.307119\pi$
$887$	−7.51751	−	7.51751i	−0.252413	−	0.252413i	−0.821959	+	0.569546i	$0.807119\pi$
$888$	−2.53491	−	5.84969i	−0.0850661	−	0.196303i
$889$		−	0.281240i		−	0.00943249i
$890$	−18.2346	−	47.3663i	−0.611225	−	1.58772i
$891$		−	10.2090i		−	0.342014i
$892$	6.80138	+	11.4916i	0.227727	+	0.384768i
$893$	12.1321	+	12.1321i	0.405985	+	0.405985i
$894$	−0.747383	+	5.92421i	−0.0249962	+	0.198135i
$895$	4.12404	−	13.6988i	0.137852	−	0.457900i
$896$	−17.3502	−	20.9223i	−0.579631	−	0.698966i
$897$	−1.91302	+	1.91302i	−0.0638738	+	0.0638738i
$898$	15.8380	−	12.2895i	0.528520	−	0.410106i
$899$	−6.86263			−0.228882
$900$	19.0735	+	21.1014i	0.635784	+	0.703380i
$901$	−39.6686			−1.32155
$902$	1.49615	−	1.16094i	0.0498163	−	0.0386550i
$903$	6.95051	−	6.95051i	0.231299	−	0.231299i
$904$	43.3293	+	17.1299i	1.44111	+	0.569731i
$905$	6.19596	−	20.5811i	0.205961	−	0.684138i
$906$	−0.685136	+	5.43080i	−0.0227621	+	0.180426i
$907$	30.6517	+	30.6517i	1.01777	+	1.01777i	0.999839	+	0.0179325i	$0.00570840\pi$
$907$	30.6517	+	30.6517i	1.01777	+	1.01777i	0.0179325	+	0.999839i	$0.494292\pi$
$908$	−15.4505	+	9.14446i	−0.512743	+	0.303470i
$909$		−	20.2339i		−	0.671115i
$910$	2.32349	+	6.03552i	0.0770230	+	0.200076i
$911$			1.45573i			0.0482306i	0.999709	+	0.0241153i	$0.00767688\pi$
$911$			1.45573i			0.0482306i	−0.999709	+	0.0241153i	$0.992323\pi$
$912$	−8.65620	+	2.52121i	−0.286636	+	0.0834858i
$913$	8.58863	+	8.58863i	0.284242	+	0.284242i
$914$	−49.7877	−	6.28108i	−1.64683	−	0.207760i
$915$	−2.49866	−	4.65110i	−0.0826030	−	0.153761i
$916$	8.36425	+	2.14456i	0.276363	+	0.0708582i
$917$	22.7310	−	22.7310i	0.750642	−	0.750642i
$918$	−7.98986	−	10.2969i	−0.263705	−	0.339847i
$919$	−12.8338			−0.423349			−0.211675	−	0.977340i	$-0.567892\pi$
$919$	−12.8338			−0.423349			−0.211675	+	0.977340i	$0.567892\pi$
$920$	39.9760	+	31.5999i	1.31797	+	1.04182i
$921$	−7.83770			−0.258261
$922$	−26.6032	−	34.2846i	−0.876129	−	1.12910i
$923$	−4.50914	+	4.50914i	−0.148420	+	0.148420i
$924$	2.45836	+	0.630312i	0.0808740	+	0.0207357i
$925$	27.9994	−	5.69195i	0.920613	−	0.187150i
$926$	20.6635	+	2.60686i	0.679046	+	0.0856667i
$927$	−17.0614	−	17.0614i	−0.560369	−	0.560369i
$928$	18.6777	−	2.97446i	0.613125	−	0.0976413i
$929$			34.9707i			1.14735i	0.819083	+	0.573675i	$0.194483\pi$
$929$			34.9707i			1.14735i	−0.819083	+	0.573675i	$0.805517\pi$
$930$	2.33995	+	1.03911i	0.0767299	+	0.0340738i
$931$			7.01903i			0.230039i
$932$	−33.6196	+	19.8980i	−1.10125	+	0.651780i
$933$	−6.82025	−	6.82025i	−0.223285	−	0.223285i
$934$	3.48003	−	27.5848i	0.113870	−	0.902603i
$935$	10.5448	−	5.66485i	0.344852	−	0.185261i
$936$	−2.51796	+	6.36908i	−0.0823020	+	0.208180i
$937$	40.4607	−	40.4607i	1.32179	−	1.32179i	0.409468	−	0.912324i	$-0.365714\pi$
$937$	40.4607	−	40.4607i	1.32179	−	1.32179i	0.912324	−	0.409468i	$-0.134286\pi$
$938$	−4.99967	+	3.87950i	−0.163245	+	0.126670i
$939$	8.63515			0.281797
$940$	3.21772	+	13.0365i	0.104951	+	0.425203i
$941$	−27.3919			−0.892952			−0.446476	−	0.894796i	$-0.647321\pi$
$941$	−27.3919			−0.892952			−0.446476	+	0.894796i	$0.647321\pi$
$942$	−3.47638	+	2.69750i	−0.113266	+	0.0878892i
$943$	5.69719	−	5.69719i	0.185526	−	0.185526i
$944$	2.27147	+	1.24675i	0.0739299	+	0.0405782i
$945$	11.8583	+	3.56997i	0.385751	+	0.116131i
$946$	−2.45866	+	19.4888i	−0.0799380	+	0.633637i
$947$	−8.68729	−	8.68729i	−0.282299	−	0.282299i	0.551726	−	0.834025i	$-0.313969\pi$
$947$	−8.68729	−	8.68729i	−0.282299	−	0.282299i	−0.834025	+	0.551726i	$0.813969\pi$
$948$	7.00120	+	11.8292i	0.227388	+	0.384196i
$949$			12.6867i			0.411827i
$950$	−3.03009	−	40.2925i	−0.0983091	−	1.30726i
$951$		−	3.08955i		−	0.100186i
$952$	−24.9250	+	10.8010i	−0.807825	+	0.350064i
$953$	−34.0544	−	34.0544i	−1.10313	−	1.10313i	−0.994031	−	0.109099i	$-0.965204\pi$
$953$	−34.0544	−	34.0544i	−1.10313	−	1.10313i	−0.109099	−	0.994031i	$-0.534796\pi$
$954$	39.6020	+	4.99609i	1.28216	+	0.161754i
$955$	7.44669	+	2.24184i	0.240969	+	0.0725442i
$956$	12.9826	−	50.6349i	0.419887	−	1.63765i
$957$	−1.24871	+	1.24871i	−0.0403650	+	0.0403650i
$958$	−3.04392	−	3.92282i	−0.0983445	−	0.126741i
$959$	19.5298			0.630649
$960$	−6.81889	−	1.81390i	−0.220079	−	0.0585434i
$961$	26.7868			0.864091
$962$	4.21744	+	5.43519i	0.135976	+	0.175238i
$963$	−14.5918	+	14.5918i	−0.470214	+	0.470214i
$964$	−8.91863	+	34.7846i	−0.287250	+	1.12034i
$965$	−4.60397	+	2.47334i	−0.148207	+	0.0796195i
$966$	10.7127	+	1.35148i	0.344675	+	0.0434833i
$967$	36.5936	+	36.5936i	1.17677	+	1.17677i	0.980562	+	0.196208i	$0.0628628\pi$
$967$	36.5936	+	36.5936i	1.17677	+	1.17677i	0.196208	+	0.980562i	$0.437137\pi$
$968$	23.8940	−	10.3543i	0.767982	−	0.332799i
$969$			9.01068i			0.289465i
$970$	−3.56665	+	8.03164i	−0.114518	+	0.257880i
$971$			48.2109i			1.54716i	0.633697	+	0.773581i	$0.281537\pi$
$971$			48.2109i			1.54716i	−0.633697	+	0.773581i	$0.718463\pi$
$972$	10.1083	+	17.0790i	0.324224	+	0.547810i
$973$	−14.5207	−	14.5207i	−0.465511	−	0.465511i
$974$	−1.27876	+	10.1363i	−0.0409743	+	0.324787i
$975$	1.39988	+	0.926875i	0.0448319	+	0.0296837i
$976$	−20.9905	−	11.5211i	−0.671890	−	0.368782i
$977$	−6.01851	+	6.01851i	−0.192549	+	0.192549i	−0.796797	−	0.604248i	$-0.793474\pi$
$977$	−6.01851	+	6.01851i	−0.192549	+	0.192549i	0.604248	+	0.796797i	$0.293474\pi$
$978$	−6.99691	+	5.42925i	−0.223736	+	0.173608i
$979$	21.4923			0.686896
$980$	−2.84032	+	4.70194i	−0.0907308	+	0.150198i
$981$	−37.6743			−1.20285
$982$	−27.9621	+	21.6972i	−0.892307	+	0.692386i
$983$	14.8336	−	14.8336i	0.473119	−	0.473119i	−0.429804	−	0.902922i	$-0.641417\pi$
$983$	14.8336	−	14.8336i	0.473119	−	0.473119i	0.902922	+	0.429804i	$0.141417\pi$
$984$	−0.410174	+	1.03752i	−0.0130759	+	0.0330749i
$985$	−9.91062	−	18.4480i	−0.315779	−	0.587804i
$986$	2.36589	−	18.7535i	0.0753452	−	0.597232i
$987$	2.01191	+	2.01191i	0.0640398	+	0.0640398i
$988$	8.37245	−	4.95528i	0.266363	−	0.157648i
$989$			83.5740i			2.65750i
$990$	−11.2406	+	4.32727i	−0.357248	+	0.137530i
$991$		−	35.7158i		−	1.13455i	−0.823529	−	0.567274i	$-0.807998\pi$
$991$		−	35.7158i		−	1.13455i	0.823529	−	0.567274i	$-0.192002\pi$
$992$	11.4668	−	1.82610i	0.364070	−	0.0579789i
$993$	−4.66888	−	4.66888i	−0.148162	−	0.148162i
$994$	25.2507	+	3.18556i	0.800903	+	0.101040i
$995$	−15.1583	+	50.3511i	−0.480550	+	1.59624i
$996$	−6.93146	−	1.77720i	−0.219632	−	0.0563126i
$997$	−23.5661	+	23.5661i	−0.746346	+	0.746346i	−0.973791	−	0.227445i	$-0.926963\pi$
$997$	−23.5661	+	23.5661i	−0.746346	+	0.746346i	0.227445	+	0.973791i	$0.426963\pi$
$998$	16.8334	+	21.6940i	0.532853	+	0.686710i
$999$	13.1734			0.416788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.83.14	✓	108
4.3	odd	2	inner	820.2.k.c.83.41	yes	108
5.2	odd	4	inner	820.2.k.c.247.41	yes	108
20.7	even	4	inner	820.2.k.c.247.14	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.14	✓	108	1.1	even	1	trivial
820.2.k.c.83.41	yes	108	4.3	odd	2	inner
820.2.k.c.247.14	yes	108	20.7	even	4	inner
820.2.k.c.247.41	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+(-0.866971 - 1.11730i) q^{2} +(-0.278914 + 0.278914i) q^{3} +(-0.496724 + 1.93733i) q^{4} +(-0.644595 + 2.14114i) q^{5} +(0.553441 + 0.0698207i) q^{6} +(1.69878 + 1.69878i) q^{7} +(2.59523 - 1.12462i) q^{8} +2.84441i q^{9} +(2.95115 - 1.13610i) q^{10} +1.33907i q^{11} +(-0.401806 - 0.678893i) q^{12} +(0.601947 + 0.601947i) q^{13} +(0.425256 - 3.37083i) q^{14} +(-0.417409 - 0.776982i) q^{15} +(-3.50653 - 1.92464i) q^{16} +(-2.82679 + 2.82679i) q^{17} +(3.17807 - 2.46602i) q^{18} -5.71431 q^{19} +(-3.82793 - 2.31235i) q^{20} -0.947624 q^{21} +(1.49615 - 1.16094i) q^{22} +(5.69719 - 5.69719i) q^{23} +(-0.410174 + 1.03752i) q^{24} +(-4.16900 - 2.76034i) q^{25} +(0.150686 - 1.19443i) q^{26} +(-1.63009 - 1.63009i) q^{27} +(-4.13492 + 2.44727i) q^{28} -3.34339i q^{29} +(-0.506242 + 1.13999i) q^{30} -2.05260i q^{31} +(0.889654 + 5.58646i) q^{32} +(-0.373486 - 0.373486i) q^{33} +(5.60912 + 0.707632i) q^{34} +(-4.73234 + 2.54230i) q^{35} +(-5.51058 - 1.41289i) q^{36} +(-4.04070 + 4.04070i) q^{37} +(4.95414 + 6.38460i) q^{38} -0.335783 q^{39} +(0.735104 + 6.28169i) q^{40} +1.00000 q^{41} +(0.821562 + 1.05878i) q^{42} +(-7.33467 + 7.33467i) q^{43} +(-2.59423 - 0.665150i) q^{44} +(-6.09030 - 1.83349i) q^{45} +(-11.3048 - 1.42618i) q^{46} +(-2.12311 - 2.12311i) q^{47} +(1.51483 - 0.441211i) q^{48} -1.22833i q^{49} +(0.530264 + 7.05116i) q^{50} -1.57686i q^{51} +(-1.46517 + 0.867171i) q^{52} +(7.01655 + 7.01655i) q^{53} +(-0.408061 + 3.23454i) q^{54} +(-2.86715 - 0.863159i) q^{55} +(6.31919 + 2.49824i) q^{56} +(1.59380 - 1.59380i) q^{57} +(-3.73557 + 2.89862i) q^{58} -0.647781 q^{59} +(1.71261 - 0.422714i) q^{60} +5.98612 q^{61} +(-2.29337 + 1.77954i) q^{62} +(-4.83202 + 4.83202i) q^{63} +(5.47045 - 5.83731i) q^{64} +(-1.67687 + 0.900843i) q^{65} +(-0.0934950 + 0.741098i) q^{66} +(-1.31706 - 1.31706i) q^{67} +(-4.07230 - 6.88057i) q^{68} +3.17805i q^{69} +(6.94332 + 3.08335i) q^{70} +7.49094i q^{71} +(3.19889 + 7.38191i) q^{72} +(10.5380 + 10.5380i) q^{73} +(8.01784 + 1.01151i) q^{74} +(1.93269 - 0.392893i) q^{75} +(2.83843 - 11.0705i) q^{76} +(-2.27478 + 2.27478i) q^{77} +(0.291114 + 0.375170i) q^{78} -17.4243 q^{79} +(6.38123 - 6.26737i) q^{80} -7.62393 q^{81} +(-0.866971 - 1.11730i) q^{82} +(6.41387 - 6.41387i) q^{83} +(0.470708 - 1.83587i) q^{84} +(-4.23043 - 7.87470i) q^{85} +(14.5540 + 1.83609i) q^{86} +(0.932517 + 0.932517i) q^{87} +(1.50595 + 3.47520i) q^{88} -16.0501i q^{89} +(3.23154 + 8.39429i) q^{90} +2.04514i q^{91} +(8.20742 + 13.8673i) q^{92} +(0.572499 + 0.572499i) q^{93} +(-0.531479 + 4.21282i) q^{94} +(3.68341 - 12.2352i) q^{95} +(-1.80628 - 1.31000i) q^{96} +(-1.96505 + 1.96505i) q^{97} +(-1.37241 + 1.06492i) q^{98} -3.80888 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

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