LMFDB - Embedded newform 820.2.s.c.583.74

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] 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, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			583.74
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.74

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.474575 + 1.33221i) q^{2} +0.567590 q^{3} +(-1.54956 + 1.26447i) q^{4} +(1.84871 - 1.25788i) q^{5} +(0.269364 + 0.756148i) q^{6} -4.85551i q^{7} +(-2.41991 - 1.46425i) q^{8} -2.67784 q^{9} +(2.55311 + 1.86591i) q^{10} +(0.359317 - 0.359317i) q^{11} +(-0.879513 + 0.717698i) q^{12} +2.14186i q^{13} +(6.46856 - 2.30431i) q^{14} +(1.04931 - 0.713962i) q^{15} +(0.802254 - 3.91872i) q^{16} -1.84916i q^{17} +(-1.27084 - 3.56744i) q^{18} +(2.98352 - 2.98352i) q^{19} +(-1.27413 + 4.28679i) q^{20} -2.75594i q^{21} +(0.649208 + 0.308162i) q^{22} +(-0.223455 + 0.223455i) q^{23} +(-1.37352 - 0.831093i) q^{24} +(1.83546 - 4.65092i) q^{25} +(-2.85340 + 1.01647i) q^{26} -3.22268 q^{27} +(6.13963 + 7.52390i) q^{28} +(5.02586 - 5.02586i) q^{29} +(1.44912 + 1.05907i) q^{30} +0.514969i q^{31} +(5.60128 - 0.790958i) q^{32} +(0.203945 - 0.203945i) q^{33} +(2.46347 - 0.877565i) q^{34} +(-6.10767 - 8.97644i) q^{35} +(4.14947 - 3.38604i) q^{36} +(2.51172 - 2.51172i) q^{37} +(5.39058 + 2.55877i) q^{38} +1.21569i q^{39} +(-6.31557 + 0.336998i) q^{40} +(6.22861 - 1.48471i) q^{41} +(3.67149 - 1.30790i) q^{42} +(3.08189 + 3.08189i) q^{43} +(-0.102438 + 1.01113i) q^{44} +(-4.95055 + 3.36841i) q^{45} +(-0.403734 - 0.191642i) q^{46} -11.6474 q^{47} +(0.455351 - 2.22423i) q^{48} -16.5760 q^{49} +(7.06706 + 0.237996i) q^{50} -1.04956i q^{51} +(-2.70830 - 3.31893i) q^{52} +11.8589i q^{53} +(-1.52941 - 4.29329i) q^{54} +(0.212294 - 1.11625i) q^{55} +(-7.10968 + 11.7499i) q^{56} +(1.69342 - 1.69342i) q^{57} +(9.08064 + 4.31034i) q^{58} +8.72205 q^{59} +(-0.723183 + 2.43314i) q^{60} -0.783294i q^{61} +(-0.686046 + 0.244391i) q^{62} +13.0023i q^{63} +(3.71195 + 7.08671i) q^{64} +(2.69421 + 3.95967i) q^{65} +(0.368484 + 0.174910i) q^{66} -3.42400 q^{67} +(2.33820 + 2.86538i) q^{68} +(-0.126831 + 0.126831i) q^{69} +(9.05993 - 12.3967i) q^{70} +(-9.98512 + 9.98512i) q^{71} +(6.48014 + 3.92103i) q^{72} +(5.94174 - 5.94174i) q^{73} +(4.53813 + 2.15413i) q^{74} +(1.04179 - 2.63982i) q^{75} +(-0.850578 + 8.39571i) q^{76} +(-1.74467 - 1.74467i) q^{77} +(-1.61956 + 0.576938i) q^{78} +(3.84482 + 3.84482i) q^{79} +(-3.44616 - 8.25372i) q^{80} +6.20436 q^{81} +(4.93389 + 7.59320i) q^{82} +(-1.75745 + 1.75745i) q^{83} +(3.48479 + 4.27049i) q^{84} +(-2.32603 - 3.41856i) q^{85} +(-2.64313 + 5.56831i) q^{86} +(2.85263 - 2.85263i) q^{87} +(-1.39565 + 0.343386i) q^{88} +(-8.65069 + 8.65069i) q^{89} +(-6.83684 - 4.99660i) q^{90} +10.3998 q^{91} +(0.0637051 - 0.628806i) q^{92} +0.292291i q^{93} +(-5.52756 - 15.5168i) q^{94} +(1.76274 - 9.26860i) q^{95} +(3.17923 - 0.448940i) q^{96} -7.38227i q^{97} +(-7.86656 - 22.0827i) q^{98} +(-0.962194 + 0.962194i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

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

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

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 $

$2$	0.474575	+	1.33221i	0.335575	+	0.942013i
$2$	0.474575	+	1.33221i	0.335575	+	0.942013i
$3$	0.567590			0.327698			0.163849	−	0.986485i	$-0.447609\pi$
$3$	0.567590			0.327698			0.163849	+	0.986485i	$0.447609\pi$
$4$	−1.54956	+	1.26447i	−0.774779	+	0.632233i
$5$	1.84871	−	1.25788i	0.826768	−	0.562543i
$5$	1.84871	−	1.25788i	0.826768	−	0.562543i
$6$	0.269364	+	0.756148i	0.109967	+	0.308696i
$7$		−	4.85551i		−	1.83521i	−0.397491	−	0.917606i	$-0.630119\pi$
$7$		−	4.85551i		−	1.83521i	0.397491	−	0.917606i	$-0.369881\pi$
$8$	−2.41991	−	1.46425i	−0.855568	−	0.517690i
$9$	−2.67784			−0.892614
$10$	2.55311	+	1.86591i	0.807366	+	0.590051i
$11$	0.359317	−	0.359317i	0.108338	−	0.108338i	−0.650860	−	0.759198i	$-0.725591\pi$
$11$	0.359317	−	0.359317i	0.108338	−	0.108338i	0.759198	+	0.650860i	$0.225591\pi$
$12$	−0.879513	+	0.717698i	−0.253893	+	0.207181i
$13$			2.14186i			0.594044i	0.954871	+	0.297022i	$0.0959934\pi$
$13$			2.14186i			0.594044i	−0.954871	+	0.297022i	$0.904007\pi$
$14$	6.46856	−	2.30431i	1.72879	−	0.615852i
$15$	1.04931	−	0.713962i	0.270930	−	0.184344i
$16$	0.802254	−	3.91872i	0.200564	−	0.979681i
$17$		−	1.84916i		−	0.448487i	−0.974533	−	0.224244i	$-0.928009\pi$
$17$		−	1.84916i		−	0.448487i	0.974533	−	0.224244i	$-0.0719911\pi$
$18$	−1.27084	−	3.56744i	−0.299539	−	0.840854i
$19$	2.98352	−	2.98352i	0.684468	−	0.684468i	−0.276536	−	0.961004i	$-0.589187\pi$
$19$	2.98352	−	2.98352i	0.684468	−	0.684468i	0.961004	+	0.276536i	$0.0891865\pi$
$20$	−1.27413	+	4.28679i	−0.284904	+	0.958556i
$21$		−	2.75594i		−	0.601395i
$22$	0.649208	+	0.308162i	0.138412	+	0.0657004i
$23$	−0.223455	+	0.223455i	−0.0465935	+	0.0465935i	−0.730020	−	0.683426i	$-0.760489\pi$
$23$	−0.223455	+	0.223455i	−0.0465935	+	0.0465935i	0.683426	+	0.730020i	$0.260489\pi$
$24$	−1.37352	−	0.831093i	−0.280368	−	0.169646i
$25$	1.83546	−	4.65092i	0.367091	−	0.930185i
$26$	−2.85340	+	1.01647i	−0.559597	+	0.199346i
$27$	−3.22268			−0.620206
$28$	6.13963	+	7.52390i	1.16028	+	1.42188i
$29$	5.02586	−	5.02586i	0.933279	−	0.933279i	−0.0646305	−	0.997909i	$-0.520587\pi$
$29$	5.02586	−	5.02586i	0.933279	−	0.933279i	0.997909	+	0.0646305i	$0.0205869\pi$
$30$	1.44912	+	1.05907i	0.264572	+	0.193359i
$31$			0.514969i			0.0924912i	0.998930	+	0.0462456i	$0.0147257\pi$
$31$			0.514969i			0.0924912i	−0.998930	+	0.0462456i	$0.985274\pi$
$32$	5.60128	−	0.790958i	0.990177	−	0.139823i
$33$	0.203945	−	0.203945i	0.0355022	−	0.0355022i
$34$	2.46347	−	0.877565i	0.422481	−	0.150501i
$35$	−6.10767	−	8.97644i	−1.03239	−	1.51729i
$36$	4.14947	−	3.38604i	0.691578	−	0.564340i
$37$	2.51172	−	2.51172i	0.412924	−	0.412924i	−0.469832	−	0.882756i	$-0.655685\pi$
$37$	2.51172	−	2.51172i	0.412924	−	0.412924i	0.882756	+	0.469832i	$0.155685\pi$
$38$	5.39058	+	2.55877i	0.874468	+	0.415087i
$39$			1.21569i			0.194667i
$40$	−6.31557	+	0.336998i	−0.998579	+	0.0532840i
$41$	6.22861	−	1.48471i	0.972746	−	0.231873i
$41$	6.22861	−	1.48471i	0.972746	−	0.231873i
$42$	3.67149	−	1.30790i	0.566523	−	0.201813i
$43$	3.08189	+	3.08189i	0.469984	+	0.469984i	0.901909	−	0.431925i	$-0.142166\pi$
$43$	3.08189	+	3.08189i	0.469984	+	0.469984i	−0.431925	+	0.901909i	$0.642166\pi$
$44$	−0.102438	+	1.01113i	−0.0154432	+	0.152433i
$45$	−4.95055	+	3.36841i	−0.737985	+	0.502134i
$46$	−0.403734	−	0.191642i	−0.0595273	−	0.0282561i
$47$	−11.6474			−1.69895			−0.849474	−	0.527631i	$-0.823080\pi$
$47$	−11.6474			−1.69895			−0.849474	+	0.527631i	$0.823080\pi$
$48$	0.455351	−	2.22423i	0.0657243	−	0.321039i
$49$	−16.5760			−2.36800
$50$	7.06706	+	0.237996i	0.999433	+	0.0336577i
$51$		−	1.04956i		−	0.146968i
$52$	−2.70830	−	3.31893i	−0.375574	−	0.460252i
$53$			11.8589i			1.62895i	0.580198	+	0.814475i	$0.302975\pi$
$53$			11.8589i			1.62895i	−0.580198	+	0.814475i	$0.697025\pi$
$54$	−1.52941	−	4.29329i	−0.208126	−	0.584242i
$55$	0.212294	−	1.11625i	0.0286257	−	0.150515i
$56$	−7.10968	+	11.7499i	−0.950071	+	1.57015i
$57$	1.69342	−	1.69342i	0.224299	−	0.224299i
$58$	9.08064	+	4.31034i	1.19235	+	0.565976i
$59$	8.72205			1.13551			0.567757	−	0.823196i	$-0.307811\pi$
$59$	8.72205			1.13551			0.567757	+	0.823196i	$0.307811\pi$
$60$	−0.723183	+	2.43314i	−0.0933626	+	0.314117i
$61$		−	0.783294i		−	0.100291i	−0.998742	−	0.0501453i	$-0.984032\pi$
$61$		−	0.783294i		−	0.100291i	0.998742	−	0.0501453i	$-0.0159684\pi$
$62$	−0.686046	+	0.244391i	−0.0871279	+	0.0310377i
$63$			13.0023i			1.63814i
$64$	3.71195	+	7.08671i	0.463994	+	0.885838i
$65$	2.69421	+	3.95967i	0.334175	+	0.491136i
$66$	0.368484	+	0.174910i	0.0453572	+	0.0215299i
$67$	−3.42400			−0.418308			−0.209154	−	0.977883i	$-0.567071\pi$
$67$	−3.42400			−0.418308			−0.209154	+	0.977883i	$0.567071\pi$
$68$	2.33820	+	2.86538i	0.283548	+	0.347478i
$69$	−0.126831	+	0.126831i	−0.0152686	+	0.0152686i
$70$	9.05993	−	12.3967i	1.08287	−	1.48169i
$71$	−9.98512	+	9.98512i	−1.18502	+	1.18502i	−0.206588	+	0.978428i	$0.566236\pi$
$71$	−9.98512	+	9.98512i	−1.18502	+	1.18502i	−0.978428	+	0.206588i	$0.933764\pi$
$72$	6.48014	+	3.92103i	0.763692	+	0.462097i
$73$	5.94174	−	5.94174i	0.695428	−	0.695428i	−0.267993	−	0.963421i	$-0.586360\pi$
$73$	5.94174	−	5.94174i	0.695428	−	0.695428i	0.963421	+	0.267993i	$0.0863603\pi$
$74$	4.53813	+	2.15413i	0.527547	+	0.250413i
$75$	1.04179	−	2.63982i	0.120295	−	0.304820i
$76$	−0.850578	+	8.39571i	−0.0975680	+	0.963054i
$77$	−1.74467	−	1.74467i	−0.198823	−	0.198823i
$78$	−1.61956	+	0.576938i	−0.183379	+	0.0653254i
$79$	3.84482	+	3.84482i	0.432577	+	0.432577i	0.889504	−	0.456927i	$-0.151050\pi$
$79$	3.84482	+	3.84482i	0.432577	+	0.432577i	−0.456927	+	0.889504i	$0.651050\pi$
$80$	−3.44616	−	8.25372i	−0.385293	−	0.922794i
$81$	6.20436			0.689374
$82$	4.93389	+	7.59320i	0.544857	+	0.838529i
$83$	−1.75745	+	1.75745i	−0.192906	+	0.192906i	−0.796950	−	0.604045i	$-0.793555\pi$
$83$	−1.75745	+	1.75745i	−0.192906	+	0.192906i	0.604045	+	0.796950i	$0.293555\pi$
$84$	3.48479	+	4.27049i	0.380222	+	0.465948i
$85$	−2.32603	−	3.41856i	−0.252293	−	0.370795i
$86$	−2.64313	+	5.56831i	−0.285016	+	0.600446i
$87$	2.85263	−	2.85263i	0.305834	−	0.305834i
$88$	−1.39565	+	0.343386i	−0.148776	+	0.0366051i
$89$	−8.65069	+	8.65069i	−0.916971	+	0.916971i	−0.996808	−	0.0798366i	$-0.974560\pi$
$89$	−8.65069	+	8.65069i	−0.916971	+	0.916971i	0.0798366	+	0.996808i	$0.474560\pi$
$90$	−6.83684	−	4.99660i	−0.720666	−	0.526688i
$91$	10.3998			1.09020
$92$	0.0637051	−	0.628806i	0.00664171	−	0.0655576i
$93$			0.292291i			0.0303092i
$94$	−5.52756	−	15.5168i	−0.570125	−	1.60043i
$95$	1.76274	−	9.26860i	0.180854	−	0.950938i
$96$	3.17923	−	0.448940i	0.324479	−	0.0458197i
$97$		−	7.38227i		−	0.749556i	−0.927115	−	0.374778i	$-0.877719\pi$
$97$		−	7.38227i		−	0.749556i	0.927115	−	0.374778i	$-0.122281\pi$
$98$	−7.86656	−	22.0827i	−0.794643	−	2.23069i
$99$	−0.962194	+	0.962194i	−0.0967042	+	0.0967042i
$100$	3.03679	+	9.52774i	0.303679	+	0.952774i
$101$	2.26316	−	2.26316i	0.225192	−	0.225192i	−0.585488	−	0.810681i	$-0.699097\pi$
$101$	2.26316	−	2.26316i	0.225192	−	0.225192i	0.810681	+	0.585488i	$0.199097\pi$
$102$	1.39824	−	0.498097i	0.138446	−	0.0493190i
$103$	4.27764	+	4.27764i	0.421488	+	0.421488i	0.885716	−	0.464228i	$-0.153668\pi$
$103$	4.27764	+	4.27764i	0.421488	+	0.421488i	−0.464228	+	0.885716i	$0.653668\pi$
$104$	3.13621	−	5.18310i	0.307531	−	0.508245i
$105$	−3.46665	−	5.09493i	−0.338311	−	0.497215i
$106$	−15.7986	+	5.62796i	−1.53449	+	0.546635i
$107$	1.89759	+	1.89759i	0.183447	+	0.183447i	0.792856	−	0.609409i	$-0.208593\pi$
$107$	1.89759	+	1.89759i	0.183447	+	0.183447i	−0.609409	+	0.792856i	$0.708593\pi$
$108$	4.99373	−	4.07497i	0.480522	−	0.392114i
$109$	4.05812	+	4.05812i	0.388698	+	0.388698i	0.874223	−	0.485525i	$-0.161372\pi$
$109$	4.05812	+	4.05812i	0.388698	+	0.388698i	−0.485525	+	0.874223i	$0.661372\pi$
$110$	1.58783	−	0.246926i	0.151394	−	0.0235435i
$111$	1.42563	−	1.42563i	0.135314	−	0.135314i
$112$	−19.0274	−	3.89536i	−1.79792	−	0.368077i
$113$	−8.38570	−	8.38570i	−0.788861	−	0.788861i	0.192447	−	0.981307i	$-0.438358\pi$
$113$	−8.38570	−	8.38570i	−0.788861	−	0.788861i	−0.981307	+	0.192447i	$0.938358\pi$
$114$	3.05964	+	1.45233i	0.286561	+	0.136023i
$115$	−0.132023	+	0.694183i	−0.0123112	+	0.0647329i
$116$	−1.43283	+	14.1429i	−0.133035	+	1.31313i
$117$		−	5.73555i		−	0.530252i
$118$	4.13927	+	11.6196i	0.381051	+	1.06967i
$119$	−8.97862			−0.823069
$120$	−3.58465	+	0.191277i	−0.327233	+	0.0174611i
$121$			10.7418i			0.976526i
$122$	1.04351	−	0.371732i	0.0944751	−	0.0336550i
$123$	3.53530	−	0.842706i	0.318767	−	0.0759843i
$124$	−0.651161	−	0.797974i	−0.0584759	−	0.0716602i
$125$	−2.45710	−	10.9070i	−0.219770	−	0.975552i
$126$	−17.3218	+	6.17057i	−1.54315	+	0.549718i
$127$	−7.12264	−	7.12264i	−0.632032	−	0.632032i	0.316545	−	0.948577i	$-0.397477\pi$
$127$	−7.12264	−	7.12264i	−0.632032	−	0.632032i	−0.948577	+	0.316545i	$0.897477\pi$
$128$	−7.67937	+	8.30827i	−0.678767	+	0.734354i
$129$	1.74925	+	1.74925i	0.154013	+	0.154013i
$130$	−3.99650	+	5.46840i	−0.350516	+	0.479611i
$131$	2.26133			0.197574			0.0987869	−	0.995109i	$-0.468504\pi$
$131$	2.26133			0.197574			0.0987869	+	0.995109i	$0.468504\pi$
$132$	−0.0581429	+	0.573905i	−0.00506069	+	0.0499520i
$133$	−14.4865	−	14.4865i	−1.25614	−	1.25614i
$134$	−1.62494	−	4.56148i	−0.140374	−	0.394052i
$135$	−5.95781	+	4.05376i	−0.512767	+	0.348892i
$136$	−2.70763	+	4.47481i	−0.232177	+	0.383711i
$137$		−	11.8165i		−	1.00955i	−0.863251	−	0.504776i	$-0.831575\pi$
$137$		−	11.8165i		−	1.00955i	0.863251	−	0.504776i	$-0.168425\pi$
$138$	−0.229155	−	0.108774i	−0.0195070	−	0.00925947i
$139$	18.6439			1.58136			0.790678	−	0.612232i	$-0.209728\pi$
$139$	18.6439			1.58136			0.790678	+	0.612232i	$0.209728\pi$
$140$	20.8146	+	6.18656i	1.75915	+	0.522860i
$141$	−6.61094			−0.556742
$142$	−18.0410	−	8.56357i	−1.51396	−	0.718639i
$143$	0.769605	+	0.769605i	0.0643576	+	0.0643576i
$144$	−2.14831	+	10.4937i	−0.179026	+	0.874477i
$145$	2.96941	−	15.6133i	0.246596	−	1.29661i
$146$	10.7354	+	5.09584i	0.888471	+	0.421734i
$147$	−9.40838			−0.775990
$148$	−0.716070	+	7.06803i	−0.0588606	+	0.580989i
$149$	9.55918	+	9.55918i	0.783119	+	0.783119i	0.980356	−	0.197237i	$-0.0631969\pi$
$149$	9.55918	+	9.55918i	0.783119	+	0.783119i	−0.197237	+	0.980356i	$0.563197\pi$
$150$	4.01119	+	0.135084i	0.327512	+	0.0110296i
$151$	−6.26759	+	6.26759i	−0.510049	+	0.510049i	−0.914541	−	0.404492i	$-0.867448\pi$
$151$	−6.26759	+	6.26759i	−0.510049	+	0.510049i	0.404492	+	0.914541i	$0.367448\pi$
$152$	−11.5885	+	2.85125i	−0.939951	+	0.231267i
$153$			4.95176i			0.400326i
$154$	1.49629	−	3.15224i	0.120574	−	0.254015i
$155$	0.647771	+	0.952028i	0.0520302	+	0.0764687i
$156$	−1.53720	−	1.88379i	−0.123075	−	0.150824i
$157$	2.97369			0.237326			0.118663	−	0.992935i	$-0.462139\pi$
$157$	2.97369			0.237326			0.118663	+	0.992935i	$0.462139\pi$
$158$	−3.29745	+	6.94677i	−0.262331	+	0.552655i
$159$			6.73101i			0.533804i
$160$	9.36022	−	8.50802i	0.739990	−	0.672618i
$161$	1.08499	+	1.08499i	0.0855090	+	0.0855090i
$162$	2.94444	+	8.26550i	0.231337	+	0.649399i
$163$	−6.65600	+	6.65600i	−0.521338	+	0.521338i	−0.917975	−	0.396637i	$-0.870177\pi$
$163$	−6.65600	+	6.65600i	−0.521338	+	0.521338i	0.396637	+	0.917975i	$0.370177\pi$
$164$	−7.77423	+	10.1765i	−0.607065	+	0.794652i
$165$	0.120496	−	0.633573i	0.00938058	−	0.0493236i
$166$	−3.17534	−	1.50725i	−0.246454	−	0.116985i
$167$			17.2412i			1.33417i	0.744983	+	0.667083i	$0.232457\pi$
$167$			17.2412i			1.33417i	−0.744983	+	0.667083i	$0.767543\pi$
$168$	−4.03538	+	6.66913i	−0.311336	+	0.514535i
$169$	8.41246			0.647112
$170$	3.45036	−	4.72112i	0.264630	−	0.362093i
$171$	−7.98941	+	7.98941i	−0.610965	+	0.610965i
$172$	−8.67251	−	0.878621i	−0.661273	−	0.0669942i
$173$	14.1054	−	14.1054i	1.07241	−	1.07241i	0.0752500	−	0.997165i	$-0.476025\pi$
$173$	14.1054	−	14.1054i	1.07241	−	1.07241i	0.997165	−	0.0752500i	$-0.0239755\pi$
$174$	5.15408	+	2.44651i	0.390730	+	0.185469i
$175$	−22.5826	−	8.91208i	−1.70709	−	0.673690i
$176$	−1.11980	−	1.69633i	−0.0844081	−	0.127865i
$177$	4.95055			0.372106
$178$	−15.6299	−	7.41912i	−1.17151	−	0.556086i
$179$	−4.00853	+	4.00853i	−0.299611	+	0.299611i	−0.840862	−	0.541250i	$-0.817951\pi$
$179$	−4.00853	+	4.00853i	−0.299611	+	0.299611i	0.541250	+	0.840862i	$0.317951\pi$
$180$	3.41192	−	11.4794i	0.254309	−	0.855620i
$181$	−16.6818	+	16.6818i	−1.23995	+	1.23995i	−0.279926	+	0.960022i	$0.590310\pi$
$181$	−16.6818	+	16.6818i	−1.23995	+	1.23995i	−0.960022	+	0.279926i	$0.909690\pi$
$182$	4.93549	+	13.8547i	0.365843	+	1.02698i
$183$		−	0.444590i		−	0.0328650i
$184$	0.867934	−	0.213547i	0.0639849	−	0.0157429i
$185$	1.48399	−	7.80289i	0.109105	−	0.573680i
$186$	−0.389393	+	0.138714i	−0.0285517	+	0.0101710i
$187$	−0.664435	−	0.664435i	−0.0485883	−	0.0485883i
$188$	18.0483	−	14.7277i	1.31631	−	1.07413i
$189$			15.6478i			1.13821i
$190$	13.1843	−	2.05031i	0.956487	−	0.148745i
$191$	6.56057	+	6.56057i	0.474706	+	0.474706i	0.903434	−	0.428728i	$-0.141038\pi$
$191$	6.56057	+	6.56057i	0.474706	+	0.474706i	−0.428728	+	0.903434i	$0.641038\pi$
$192$	2.10687	+	4.02234i	0.152050	+	0.290288i
$193$		−	17.4413i		−	1.25545i	−0.778434	−	0.627726i	$-0.783986\pi$
$193$		−	17.4413i		−	1.25545i	0.778434	−	0.627726i	$-0.216014\pi$
$194$	9.83472	−	3.50344i	0.706092	−	0.251533i
$195$	1.52920	+	2.24747i	0.109509	+	0.160944i
$196$	25.6855	−	20.9598i	1.83468	−	1.49713i
$197$	−5.28860	−	5.28860i	−0.376797	−	0.376797i	0.493148	−	0.869945i	$-0.335846\pi$
$197$	−5.28860	−	5.28860i	−0.376797	−	0.376797i	−0.869945	+	0.493148i	$0.835846\pi$
$198$	−1.73848	−	0.825210i	−0.123548	−	0.0586451i
$199$	2.13133	−	2.13133i	0.151086	−	0.151086i	−0.627517	−	0.778603i	$-0.715929\pi$
$199$	2.13133	−	2.13133i	0.151086	−	0.151086i	0.778603	+	0.627517i	$0.215929\pi$
$200$	−11.2518	+	8.56727i	−0.795619	+	0.605797i
$201$	−1.94343			−0.137079
$202$	4.08903	+	1.94096i	0.287703	+	0.136565i
$203$	−24.4031	−	24.4031i	−1.71276	−	1.71276i
$204$	1.32714	+	1.62636i	0.0929182	+	0.113868i
$205$	9.64731	−	10.5797i	0.673797	−	0.738916i
$206$	−3.66865	+	7.72877i	−0.255607	+	0.538489i
$207$	0.598376	−	0.598376i	0.0415900	−	0.0415900i
$208$	8.39334	+	1.71831i	0.581973	+	0.119144i
$209$		−	2.14406i		−	0.148308i
$210$	5.14232	−	7.03623i	0.354854	−	0.485546i
$211$	−10.7816	−	10.7816i	−0.742236	−	0.742236i	0.230772	−	0.973008i	$-0.425875\pi$
$211$	−10.7816	−	10.7816i	−0.742236	−	0.742236i	−0.973008	+	0.230772i	$0.925875\pi$
$212$	−14.9952	−	18.3761i	−1.02988	−	1.26208i
$213$	−5.66745	+	5.66745i	−0.388328	+	0.388328i
$214$	−1.62744	+	3.42854i	−0.111249	+	0.234370i
$215$	9.57418	+	1.82086i	0.652954	+	0.124182i
$216$	7.79861	+	4.71881i	0.530628	+	0.321075i
$217$	2.50044			0.169741
$218$	−3.48038	+	7.33215i	−0.235721	+	0.496596i
$219$	3.37247	−	3.37247i	0.227891	−	0.227891i
$220$	1.08250	+	1.99813i	0.0729822	+	0.134714i
$221$	3.96063			0.266421
$222$	2.57580	+	1.22266i	0.172876	+	0.0820598i
$223$	12.9763	−	12.9763i	0.868955	−	0.868955i	−0.123402	−	0.992357i	$-0.539380\pi$
$223$	12.9763	−	12.9763i	0.868955	−	0.868955i	0.992357	+	0.123402i	$0.0393804\pi$
$224$	−3.84051	−	27.1971i	−0.256605	−	1.81718i
$225$	−4.91506	+	12.4544i	−0.327671	+	0.830296i
$226$	7.19186	−	15.1511i	0.478395	−	1.00784i
$227$	19.6758			1.30593			0.652966	−	0.757387i	$-0.273524\pi$
$227$	19.6758			1.30593			0.652966	+	0.757387i	$0.273524\pi$
$228$	−0.482779	+	4.76532i	−0.0319728	+	0.315591i
$229$	−15.3273	−	15.3273i	−1.01286	−	1.01286i	−0.999916	−	0.0129409i	$-0.995881\pi$
$229$	−15.3273	−	15.3273i	−1.01286	−	1.01286i	−0.0129409	−	0.999916i	$-0.504119\pi$
$230$	−0.987451	+	0.153560i	−0.0651106	+	0.0101254i
$231$	−0.990256	−	0.990256i	−0.0651541	−	0.0651541i
$232$	−19.5212	+	4.80303i	−1.28163	+	0.315334i
$233$			27.2013i			1.78201i	0.453990	+	0.891007i	$0.350000\pi$
$233$			27.2013i			1.78201i	−0.453990	+	0.891007i	$0.650000\pi$
$234$	7.64095	−	2.72195i	0.499504	−	0.177939i
$235$	−21.5327	+	14.6511i	−1.40464	+	0.955731i
$236$	−13.5153	+	11.0287i	−0.879772	+	0.717910i
$237$	2.18228	+	2.18228i	0.141755	+	0.141755i
$238$	−4.26103	−	11.9614i	−0.276202	−	0.775342i
$239$	8.37200	+	8.37200i	0.541539	+	0.541539i	0.923980	−	0.382441i	$-0.124916\pi$
$239$	8.37200	+	8.37200i	0.541539	+	0.541539i	−0.382441	+	0.923980i	$0.624916\pi$
$240$	−1.95601	−	4.68473i	−0.126260	−	0.302398i
$241$			6.20141i			0.399468i	0.979850	+	0.199734i	$0.0640078\pi$
$241$			6.20141i			0.399468i	−0.979850	+	0.199734i	$0.935992\pi$
$242$	−14.3103	+	5.09778i	−0.919900	+	0.327698i
$243$	13.1896			0.846112
$244$	0.990449	+	1.21376i	0.0634070	+	0.0777030i
$245$	−30.6442	+	20.8507i	−1.95779	+	1.33210i
$246$	2.80042	+	4.30982i	0.178549	+	0.274784i
$247$	6.39028	+	6.39028i	0.406604	+	0.406604i
$248$	0.754043	−	1.24618i	0.0478818	−	0.0791325i
$249$	−0.997512	+	0.997512i	−0.0632148	+	0.0632148i
$250$	13.3643	−	8.44956i	0.845234	−	0.534397i
$251$	27.4418			1.73211			0.866055	−	0.499948i	$-0.166648\pi$
$251$	27.4418			1.73211			0.866055	+	0.499948i	$0.166648\pi$
$252$	−16.4410	−	20.1478i	−1.03568	−	1.26919i
$253$			0.160582i			0.0100957i
$254$	6.10861	−	12.8691i	0.383288	−	0.807477i
$255$	−1.32023	−	1.94034i	−0.0826760	−	0.121509i
$256$	−14.7128	−	6.28762i	−0.919549	−	0.392977i
$257$	29.0881			1.81447			0.907233	−	0.420628i	$-0.138190\pi$
$257$	29.0881			1.81447			0.907233	+	0.420628i	$0.138190\pi$
$258$	−1.50021	+	3.16051i	−0.0933992	+	0.196765i
$259$	−12.1957	−	12.1957i	−0.757803	−	0.757803i
$260$	−9.18169	−	2.72900i	−0.569424	−	0.169246i
$261$	−13.4585	+	13.4585i	−0.833058	+	0.833058i
$262$	1.07317	+	3.01257i	0.0663008	+	0.186117i
$263$		−	18.3900i		−	1.13398i	−0.823726	−	0.566989i	$-0.808108\pi$
$263$		−	18.3900i		−	1.13398i	0.823726	−	0.566989i	$-0.191892\pi$
$264$	−0.792154	+	0.194902i	−0.0487537	+	0.0119954i
$265$	14.9172	+	21.9237i	0.916354	+	1.34676i
$266$	12.4241	−	26.1741i	0.761773	−	1.60483i
$267$	−4.91004	+	4.91004i	−0.300490	+	0.300490i
$268$	5.30568	−	4.32953i	0.324096	−	0.264468i
$269$			9.90970i			0.604205i	0.953275	+	0.302102i	$0.0976885\pi$
$269$			9.90970i			0.604205i	−0.953275	+	0.302102i	$0.902312\pi$
$270$	−8.22788	−	6.01323i	−0.500733	−	0.365953i
$271$		−	19.7470i		−	1.19955i	−0.800170	−	0.599773i	$-0.795258\pi$
$271$		−	19.7470i		−	1.19955i	0.800170	−	0.599773i	$-0.204742\pi$
$272$	−7.24635	−	1.48350i	−0.439374	−	0.0899502i
$273$	5.90282			0.357255
$274$	15.7420	−	5.60781i	0.951011	−	0.338780i
$275$	−1.01165	−	2.33067i	−0.0610046	−	0.140545i
$276$	0.0361583	−	0.356904i	0.00217648	−	0.0214831i
$277$	−6.22240	+	6.22240i	−0.373868	+	0.373868i	−0.868884	−	0.495016i	$-0.835162\pi$
$277$	−6.22240	+	6.22240i	−0.373868	+	0.373868i	0.495016	+	0.868884i	$0.335162\pi$
$278$	8.84793	+	24.8376i	0.530664	+	1.48966i
$279$		−	1.37901i		−	0.0825589i
$280$	1.63630	+	30.6653i	0.0977875	+	1.83260i
$281$	2.12494	−	2.12494i	0.126763	−	0.126763i	−0.640879	−	0.767642i	$-0.721430\pi$
$281$	2.12494	−	2.12494i	0.126763	−	0.126763i	0.767642	+	0.640879i	$0.221430\pi$
$282$	−3.13739	−	8.80715i	−0.186829	−	0.524458i
$283$	−18.7750	+	18.7750i	−1.11606	+	1.11606i	−0.123741	+	0.992315i	$0.539489\pi$
$283$	−18.7750	+	18.7750i	−1.11606	+	1.11606i	−0.992315	+	0.123741i	$0.960511\pi$
$284$	2.84668	−	28.0984i	0.168919	−	1.66733i
$285$	1.00051	−	5.26076i	0.0592654	−	0.311621i
$286$	−0.660039	+	1.39051i	−0.0390289	+	0.0822225i
$287$	−7.20903	−	30.2431i	−0.425536	−	1.78520i
$288$	−14.9994	+	2.11806i	−0.883845	+	0.124808i
$289$	13.5806			0.798859
$290$	22.2094	−	3.45382i	1.30418	−	0.202815i
$291$		−	4.19010i		−	0.245628i
$292$	−1.69394	+	16.7202i	−0.0991304	+	0.978476i
$293$	−19.9749			−1.16695			−0.583474	−	0.812132i	$-0.698307\pi$
$293$	−19.9749			−1.16695			−0.583474	+	0.812132i	$0.698307\pi$
$294$	−4.46498	−	12.5339i	−0.260403	−	0.730993i
$295$	16.1245	−	10.9713i	0.938807	−	0.638776i
$296$	−9.75592	+	2.40036i	−0.567051	+	0.139518i
$297$	−1.15797	+	1.15797i	−0.0671920	+	0.0671920i
$298$	−8.19827	+	17.2714i	−0.474913	+	1.00050i
$299$	−0.478608	−	0.478608i	−0.0276786	−	0.0276786i
$300$	1.72365	+	5.40785i	0.0995150	+	0.312222i
$301$	14.9642	−	14.9642i	0.862520	−	0.862520i
$302$	−11.3242	−	5.37529i	−0.651633	−	0.309313i
$303$	1.28454	−	1.28454i	0.0737951	−	0.0737951i
$304$	−9.29806	−	14.0852i	−0.533280	−	0.807839i
$305$	−0.985294	−	1.44808i	−0.0564177	−	0.0829171i
$306$	−6.59677	+	2.34998i	−0.377112	+	0.134339i
$307$	−18.1493	+	18.1493i	−1.03583	+	1.03583i	−0.0365003	+	0.999334i	$0.511621\pi$
$307$	−18.1493	+	18.1493i	−1.03583	+	1.03583i	−0.999334	+	0.0365003i	$0.988379\pi$
$308$	4.90954	+	0.497391i	0.279747	+	0.0283415i
$309$	2.42794	+	2.42794i	0.138121	+	0.138121i
$310$	−0.960884	+	1.31478i	−0.0545745	+	0.0746742i
$311$	3.72725	+	3.72725i	0.211353	+	0.211353i	0.804842	−	0.593489i	$-0.202250\pi$
$311$	3.72725	+	3.72725i	0.211353	+	0.211353i	−0.593489	+	0.804842i	$0.702250\pi$
$312$	1.78008	−	2.94188i	0.100777	−	0.166551i
$313$	−8.40535			−0.475098			−0.237549	−	0.971375i	$-0.576344\pi$
$313$	−8.40535			−0.475098			−0.237549	+	0.971375i	$0.576344\pi$
$314$	1.41124	+	3.96158i	0.0796409	+	0.223565i
$315$	16.3554	+	24.0375i	0.921522	+	1.35436i
$316$	−10.8194	−	1.09613i	−0.608640	−	0.0616620i
$317$	3.05996			0.171865			0.0859323	−	0.996301i	$-0.472613\pi$
$317$	3.05996			0.171865			0.0859323	+	0.996301i	$0.472613\pi$
$318$	−8.96711	+	3.19437i	−0.502850	+	0.179131i
$319$		−	3.61175i		−	0.202219i
$320$	15.7766	+	8.43206i	0.881937	+	0.471367i
$321$	1.07706	+	1.07706i	0.0601153	+	0.0601153i
$322$	−0.930521	+	1.96034i	−0.0518559	+	0.109245i
$323$	−5.51702	−	5.51702i	−0.306975	−	0.306975i
$324$	−9.61401	+	7.84520i	−0.534112	+	0.435845i
$325$	9.96161	+	3.93128i	0.552571	+	0.218068i
$326$	−12.0260	−	5.70841i	−0.666056	−	0.316159i
$327$	2.30335	+	2.30335i	0.127375	+	0.127375i
$328$	−17.2467	−	5.52737i	−0.952289	−	0.305198i
$329$			56.5541i			3.11793i
$330$	0.901236	−	0.140153i	0.0496114	−	0.00771515i
$331$	20.8833	−	20.8833i	1.14785	−	1.14785i	0.160878	−	0.986974i	$-0.448567\pi$
$331$	20.8833	−	20.8833i	1.14785	−	1.14785i	0.986974	−	0.160878i	$-0.0514327\pi$
$332$	0.501035	−	4.94551i	0.0274979	−	0.271420i
$333$	−6.72598	+	6.72598i	−0.368582	+	0.368582i
$334$	−22.9689	+	8.18226i	−1.25680	+	0.447713i
$335$	−6.32998	+	4.30699i	−0.345844	+	0.235316i
$336$	−10.7998	−	2.21096i	−0.589175	−	0.120618i
$337$	−4.57874	−	4.57874i	−0.249420	−	0.249420i	0.571313	−	0.820733i	$-0.306434\pi$
$337$	−4.57874	−	4.57874i	−0.249420	−	0.249420i	−0.820733	+	0.571313i	$0.806434\pi$
$338$	3.99234	+	11.2071i	0.217155	+	0.609588i
$339$	−4.75964	−	4.75964i	−0.258508	−	0.258508i
$340$	7.92697	+	2.35607i	0.429900	+	0.127776i
$341$	0.185037	+	0.185037i	0.0100203	+	0.0100203i
$342$	−14.4351	−	6.85198i	−0.780562	−	0.370513i
$343$			46.4965i			2.51057i
$344$	−2.94525	−	11.9706i	−0.158797	−	0.645409i
$345$	−0.0749348	+	0.394011i	−0.00403435	+	0.0212128i
$346$	25.4854	+	12.0973i	1.37010	+	0.650353i
$347$	23.6158			1.26776			0.633882	−	0.773430i	$-0.281460\pi$
$347$	23.6158			1.26776			0.633882	+	0.773430i	$0.281460\pi$
$348$	−0.813260	+	8.02735i	−0.0435953	+	0.430311i
$349$	−4.13234			−0.221199			−0.110600	−	0.993865i	$-0.535277\pi$
$349$	−4.13234			−0.221199			−0.110600	+	0.993865i	$0.535277\pi$
$350$	1.15559	−	34.3142i	0.0617690	−	1.83417i
$351$		−	6.90252i		−	0.368429i
$352$	1.72843	−	2.29684i	0.0921257	−	0.122422i
$353$	15.3645	+	15.3645i	0.817768	+	0.817768i	0.985784	−	0.168017i	$-0.0537362\pi$
$353$	15.3645	+	15.3645i	0.817768	+	0.817768i	−0.168017	+	0.985784i	$0.553736\pi$
$354$	2.34941	+	6.59516i	0.124870	+	0.350529i
$355$	−5.89947	+	31.0197i	−0.313111	+	1.64636i
$356$	2.46624	−	24.3432i	0.130710	−	1.29019i
$357$	−5.09617			−0.269718
$358$	−7.24254	−	3.43785i	−0.382780	−	0.181696i
$359$	17.9297			0.946292			0.473146	−	0.880984i	$-0.343118\pi$
$359$	17.9297			0.946292			0.473146	+	0.880984i	$0.343118\pi$
$360$	16.9121	−	0.902427i	0.891346	−	0.0475621i
$361$			1.19716i			0.0630083i
$362$	−30.1404	−	14.3069i	−1.58414	−	0.751952i
$363$			6.09693i			0.320006i
$364$	−16.1151	+	13.1502i	−0.844661	+	0.689258i
$365$	3.51053	−	18.4586i	0.183750	−	0.966166i
$366$	0.592286	−	0.210991i	0.0309593	−	0.0110287i
$367$	6.51919	−	6.51919i	0.340299	−	0.340299i	−0.516181	−	0.856480i	$-0.672647\pi$
$367$	6.51919	−	6.51919i	0.340299	−	0.340299i	0.856480	+	0.516181i	$0.172647\pi$
$368$	0.696389	+	1.05492i	0.0363018	+	0.0549917i
$369$	−16.6792	+	3.97582i	−0.868287	+	0.206973i
$370$	11.0993	−	1.72608i	0.577027	−	0.0897344i
$371$	57.5812			2.98947
$372$	−0.369592	−	0.452922i	−0.0191625	−	0.0234829i
$373$	−0.151386	−	0.151386i	−0.00783848	−	0.00783848i	0.703177	−	0.711015i	$-0.251764\pi$
$373$	−0.151386	−	0.151386i	−0.00783848	−	0.00783848i	−0.711015	+	0.703177i	$0.751764\pi$
$374$	0.569841	−	1.20049i	0.0294658	−	0.0620758i
$375$	−1.39462	−	6.19070i	−0.0720181	−	0.319686i
$376$	28.1857	+	17.0547i	1.45357	+	0.879528i
$377$	10.7647	+	10.7647i	0.554408	+	0.554408i
$378$	−20.8461	+	7.42605i	−1.07221	+	0.381955i
$379$	−10.8714			−0.558426			−0.279213	−	0.960229i	$-0.590073\pi$
$379$	−10.8714			−0.558426			−0.279213	+	0.960229i	$0.590073\pi$
$380$	8.98835	+	16.5912i	0.461093	+	0.851108i
$381$	−4.04274	−	4.04274i	−0.207116	−	0.207116i
$382$	−5.62656	+	11.8535i	−0.287880	+	0.606479i
$383$		−	30.1327i		−	1.53971i	−0.638218	−	0.769856i	$-0.720328\pi$
$383$		−	30.1327i		−	1.53971i	0.638218	−	0.769856i	$-0.279672\pi$
$384$	−4.35873	+	4.71569i	−0.222431	+	0.240646i
$385$	−5.41998	−	1.03080i	−0.276228	−	0.0525342i
$386$	23.2354	−	8.27720i	1.18265	−	0.421299i
$387$	−8.25281	−	8.25281i	−0.419514	−	0.419514i
$388$	9.33463	+	11.4393i	0.473894	+	0.580740i
$389$	2.58860			0.131247			0.0656235	−	0.997844i	$-0.479096\pi$
$389$	2.58860			0.131247			0.0656235	+	0.997844i	$0.479096\pi$
$390$	−2.26837	+	3.10381i	−0.114863	+	0.157167i
$391$	0.413203	+	0.413203i	0.0208966	+	0.0208966i
$392$	40.1125	+	24.2714i	2.02599	+	1.22589i
$393$	1.28351			0.0647445
$394$	4.53568	−	9.55536i	0.228504	−	0.481392i
$395$	11.9443	+	2.27162i	0.600983	+	0.114298i
$396$	0.274314	−	2.70764i	0.0137848	−	0.136064i
$397$	10.2982			0.516854			0.258427	−	0.966031i	$-0.416796\pi$
$397$	10.2982			0.516854			0.258427	+	0.966031i	$0.416796\pi$
$398$	3.85085	+	1.82790i	0.193026	+	0.0916243i
$399$	−8.22242	−	8.22242i	−0.411636	−	0.411636i
$400$	−16.7532	−	10.9239i	−0.837659	−	0.546193i
$401$			37.4226i			1.86879i	0.356234	+	0.934397i	$0.384061\pi$
$401$			37.4226i			1.86879i	−0.356234	+	0.934397i	$0.615939\pi$
$402$	−0.922301	−	2.58905i	−0.0460002	−	0.129130i
$403$	−1.10299			−0.0549438
$404$	−0.645207	+	6.36857i	−0.0321002	+	0.316848i
$405$	11.4701	−	7.80437i	0.569952	−	0.387802i
$406$	20.9289	−	44.0912i	1.03869	−	2.18821i
$407$		−	1.80501i		−	0.0894708i
$408$	−1.53682	+	2.53985i	−0.0760841	+	0.125741i
$409$		−	23.2827i		−	1.15125i	−0.817712	−	0.575627i	$-0.804758\pi$
$409$		−	23.2827i		−	1.15125i	0.817712	−	0.575627i	$-0.195242\pi$
$410$	18.6727	+	7.83137i	0.922179	+	0.386764i
$411$		−	6.70692i		−	0.330828i
$412$	−12.0374	−	1.21952i	−0.593039	−	0.0600814i
$413$		−	42.3501i		−	2.08391i
$414$	1.08114	+	0.513187i	0.0531349	+	0.0252218i
$415$	−1.03835	+	5.45969i	−0.0509705	+	0.268006i
$416$	1.69412	+	11.9971i	0.0830610	+	0.588208i
$417$	10.5821			0.518207
$418$	2.85634	−	1.01752i	0.139708	−	0.0497685i
$419$			10.1830i			0.497474i	0.968571	+	0.248737i	$0.0800155\pi$
$419$			10.1830i			0.497474i	−0.968571	+	0.248737i	$0.919984\pi$
$420$	11.8141	+	3.51143i	0.576471	+	0.171340i
$421$	−9.42756	−	9.42756i	−0.459471	−	0.459471i	0.439011	−	0.898482i	$-0.355329\pi$
$421$	−9.42756	−	9.42756i	−0.459471	−	0.459471i	−0.898482	+	0.439011i	$0.855329\pi$
$422$	9.24666	−	19.4800i	0.450121	−	0.948273i
$423$	31.1899			1.51650
$424$	17.3644	−	28.6976i	0.843292	−	1.39368i
$425$	−8.60031	−	3.39405i	−0.417176	−	0.164636i
$426$	−10.2399	−	4.86060i	−0.496123	−	0.235497i
$427$	−3.80330			−0.184054
$428$	−5.33987	−	0.540988i	−0.258113	−	0.0261497i
$429$	0.436820	+	0.436820i	0.0210899	+	0.0210899i
$430$	2.11790	+	13.6189i	0.102134	+	0.656763i
$431$	−16.8167			−0.810033			−0.405017	−	0.914309i	$-0.632734\pi$
$431$	−16.8167			−0.810033			−0.405017	+	0.914309i	$0.632734\pi$
$432$	−2.58541	+	12.6288i	−0.124391	+	0.607604i
$433$	−14.6591	−	14.6591i	−0.704470	−	0.704470i	0.260896	−	0.965367i	$-0.415982\pi$
$433$	−14.6591	−	14.6591i	−0.704470	−	0.704470i	−0.965367	+	0.260896i	$0.915982\pi$
$434$	1.18665	+	3.33111i	0.0569608	+	0.159898i
$435$	1.68541	−	8.86195i	0.0808090	−	0.424898i
$436$	−11.4196	−	1.15694i	−0.546902	−	0.0554072i
$437$			1.33337i			0.0637835i
$438$	6.09333	+	2.89234i	0.291150	+	0.138202i
$439$	0.210791	+	0.210791i	0.0100605	+	0.0100605i	0.712119	−	0.702059i	$-0.247736\pi$
$439$	0.210791	+	0.210791i	0.0100605	+	0.0100605i	−0.702059	+	0.712119i	$0.747736\pi$
$440$	−2.14820	+	2.39038i	−0.102412	+	0.113957i
$441$	44.3880			2.11371
$442$	1.87962	+	5.27639i	0.0894043	+	0.250972i
$443$	5.28456	+	5.28456i	0.251077	+	0.251077i	0.821412	−	0.570335i	$-0.193187\pi$
$443$	5.28456	+	5.28456i	0.251077	+	0.251077i	−0.570335	+	0.821412i	$0.693187\pi$
$444$	−0.406434	+	4.01174i	−0.0192885	+	0.190389i
$445$	−5.11105	+	26.8742i	−0.242287	+	1.27396i
$446$	23.4453	+	11.1289i	1.11017	+	0.526968i
$447$	5.42569	+	5.42569i	0.256626	+	0.256626i
$448$	34.4096	−	18.0234i	1.62570	−	0.851527i
$449$	9.62157			0.454070			0.227035	−	0.973887i	$-0.427097\pi$
$449$	9.62157			0.454070			0.227035	+	0.973887i	$0.427097\pi$
$450$	−18.9245	−	0.637316i	−0.892108	−	0.0300434i
$451$	1.70457	−	2.77153i	0.0802649	−	0.130506i
$452$	23.5976	+	2.39069i	1.10994	+	0.112449i
$453$	−3.55742	+	3.55742i	−0.167142	+	0.167142i
$454$	9.33767	+	26.2123i	0.438238	+	1.23021i
$455$	19.2262	−	13.0818i	0.901339	−	0.613282i
$456$	−6.57751	+	1.61834i	−0.308020	+	0.0757856i
$457$			20.0782i			0.939220i	0.882874	+	0.469610i	$0.155606\pi$
$457$			20.0782i			0.939220i	−0.882874	+	0.469610i	$0.844394\pi$
$458$	13.1452	−	27.6931i	0.614235	−	1.29401i
$459$			5.95926i			0.278154i
$460$	−0.673193	−	1.24261i	−0.0313878	−	0.0579372i
$461$	6.48552			0.302061			0.151030	−	0.988529i	$-0.451741\pi$
$461$	6.48552			0.302061			0.151030	+	0.988529i	$0.451741\pi$
$462$	0.849277	−	1.78918i	0.0395119	−	0.0832401i
$463$	−25.9818			−1.20748			−0.603739	−	0.797182i	$-0.706323\pi$
$463$	−25.9818			−1.20748			−0.603739	+	0.797182i	$0.706323\pi$
$464$	−15.6629	−	23.7270i	−0.727133	−	1.10150i
$465$	0.367668	+	0.540361i	0.0170502	+	0.0250587i
$466$	−36.2377	+	12.9090i	−1.67868	+	0.598000i
$467$	5.61875	+	5.61875i	0.260005	+	0.260005i	0.825056	−	0.565051i	$-0.191144\pi$
$467$	5.61875	+	5.61875i	0.260005	+	0.260005i	−0.565051	+	0.825056i	$0.691144\pi$
$468$	7.25240	+	8.88756i	0.335242	+	0.410828i
$469$			16.6253i			0.767683i
$470$	−29.7371	−	21.7329i	−1.37167	−	1.00247i
$471$	1.68784			0.0777714
$472$	−21.1066	−	12.7713i	−0.971510	−	0.587845i
$473$	2.21475			0.101834
$474$	−1.87160	+	3.94291i	−0.0859654	+	0.181104i
$475$	−8.40002	−	19.3523i	−0.385419	−	0.887943i
$476$	13.9129	−	11.3532i	0.637696	−	0.520371i
$477$		−	31.7564i		−	1.45402i
$478$	−7.18010	+	15.1264i	−0.328410	+	0.691865i
$479$	28.7572	+	28.7572i	1.31395	+	1.31395i	0.918479	+	0.395470i	$0.129418\pi$
$479$	28.7572	+	28.7572i	1.31395	+	1.31395i	0.395470	+	0.918479i	$0.370582\pi$
$480$	5.31276	−	4.82906i	0.242493	−	0.220416i
$481$	5.37974	+	5.37974i	0.245295	+	0.245295i
$482$	−8.26156	+	2.94303i	−0.376304	+	0.134051i
$483$	0.615828	+	0.615828i	0.0280211	+	0.0280211i
$484$	−13.5826	−	16.6450i	−0.617391	−	0.756591i
$485$	−9.28604	−	13.6477i	−0.421658	−	0.619709i
$486$	6.25945	+	17.5713i	0.283934	+	0.797049i
$487$	12.0250	−	12.0250i	0.544904	−	0.544904i	−0.380059	−	0.924962i	$-0.624096\pi$
$487$	12.0250	−	12.0250i	0.544904	−	0.544904i	0.924962	+	0.380059i	$0.124096\pi$
$488$	−1.14694	+	1.89550i	−0.0519194	+	0.0858054i
$489$	−3.77788	+	3.77788i	−0.170842	+	0.170842i
$490$	−42.3205	−	30.9293i	−1.91184	−	1.39724i
$491$			38.8136i			1.75163i	0.482643	+	0.875817i	$0.339677\pi$
$491$			38.8136i			1.75163i	−0.482643	+	0.875817i	$0.660323\pi$
$492$	−4.41257	+	5.77608i	−0.198934	+	0.260406i
$493$	−9.29362	−	9.29362i	−0.418564	−	0.418564i
$494$	−5.48051	+	11.5458i	−0.246580	+	0.519472i
$495$	−0.568489	+	2.98915i	−0.0255517	+	0.134352i
$496$	2.01802	+	0.413136i	0.0906118	+	0.0185504i
$497$	48.4829	+	48.4829i	2.17476	+	2.17476i
$498$	−1.80229	−	0.855499i	−0.0807625	−	0.0383358i
$499$	−20.6132	−	20.6132i	−0.922772	−	0.922772i	0.0744522	−	0.997225i	$-0.476279\pi$
$499$	−20.6132	−	20.6132i	−0.922772	−	0.922772i	−0.997225	+	0.0744522i	$0.976279\pi$
$500$	17.5989	+	13.7941i	0.787049	+	0.616891i
$501$			9.78594i			0.437204i
$502$	13.0232	+	36.5582i	0.581253	+	1.63167i
$503$	−10.8062			−0.481827			−0.240913	−	0.970547i	$-0.577447\pi$
$503$	−10.8062			−0.481827			−0.240913	+	0.970547i	$0.577447\pi$
$504$	19.0386	−	31.4644i	0.848047	−	1.40154i
$505$	1.33713	−	7.03071i	0.0595015	−	0.312862i
$506$	−0.213929	+	0.0762083i	−0.00951030	+	0.00338787i
$507$	4.77482			0.212057
$508$	20.0433	+	2.03060i	0.889276	+	0.0900935i
$509$	−16.6133	−	16.6133i	−0.736369	−	0.736369i	0.235504	−	0.971873i	$-0.424326\pi$
$509$	−16.6133	−	16.6133i	−0.736369	−	0.736369i	−0.971873	+	0.235504i	$0.924326\pi$
$510$	1.95839	−	2.67966i	0.0867189	−	0.118657i
$511$	−28.8502	−	28.8502i	−1.27626	−	1.27626i
$512$	1.39411	−	22.5844i	0.0616115	−	0.998100i
$513$	−9.61496	+	9.61496i	−0.424511	+	0.424511i
$514$	13.8045	+	38.7514i	0.608890	+	1.70925i
$515$	13.2889	+	2.52734i	0.585578	+	0.111368i
$516$	−4.92243	−	0.498696i	−0.216698	−	0.0219539i
$517$	−4.18511	+	4.18511i	−0.184061	+	0.184061i
$518$	10.4594	−	22.0350i	0.459561	−	0.968160i
$519$	8.00609	−	8.00609i	0.351428	−	0.351428i
$520$	−0.721801	−	13.5270i	−0.0316530	−	0.593200i
$521$	25.0805	+	25.0805i	1.09880	+	1.09880i	0.994552	+	0.104244i	$0.0332423\pi$
$521$	25.0805	+	25.0805i	1.09880	+	1.09880i	0.104244	+	0.994552i	$0.466758\pi$
$522$	−24.3165	−	11.5424i	−1.06430	−	0.505198i
$523$	−9.28632	+	9.28632i	−0.406062	+	0.406062i	−0.880363	−	0.474301i	$-0.842701\pi$
$523$	−9.28632	+	9.28632i	−0.406062	+	0.406062i	0.474301	+	0.880363i	$0.342701\pi$
$524$	−3.50407	+	2.85938i	−0.153076	+	0.124913i
$525$	−12.8177	−	5.05841i	−0.559409	−	0.220767i
$526$	24.4993	−	8.72745i	1.06822	−	0.380535i
$527$	0.952260			0.0414811
$528$	−0.635587	−	0.962818i	−0.0276604	−	0.0419013i
$529$			22.9001i			0.995658i
$530$	−22.1277	+	30.2772i	−0.961164	+	1.31516i
$531$	−23.3563			−1.01358
$532$	40.7655	+	4.12999i	1.76741	+	0.179058i
$533$	3.18003	+	13.3408i	0.137743	+	0.577854i
$534$	−8.87138	−	4.21102i	−0.383902	−	0.182228i
$535$	5.89505	+	1.12115i	0.254865	+	0.0484714i
$536$	8.28577	+	5.01358i	0.357891	+	0.216554i
$537$	−2.27520	+	2.27520i	−0.0981821	+	0.0981821i
$538$	−13.2018	+	4.70289i	−0.569169	+	0.202756i
$539$	−5.95605	+	5.95605i	−0.256545	+	0.256545i
$540$	4.10612	−	13.8150i	0.176699	−	0.594502i
$541$		−	6.09162i		−	0.261899i	−0.991389	−	0.130950i	$-0.958197\pi$
$541$		−	6.09162i		−	0.261899i	0.991389	−	0.130950i	$-0.0418026\pi$
$542$	26.3071	−	9.37144i	1.12999	−	0.402538i
$543$	−9.46841	+	9.46841i	−0.406328	+	0.406328i
$544$	−1.46261	−	10.3577i	−0.0627088	−	0.444082i
$545$	12.6069	+	2.39764i	0.540022	+	0.102704i
$546$	2.80133	+	7.86379i	0.119886	+	0.336539i
$547$	−22.3627			−0.956160			−0.478080	−	0.878316i	$-0.658667\pi$
$547$	−22.3627			−0.956160			−0.478080	+	0.878316i	$0.658667\pi$
$548$	14.9415	+	18.3103i	0.638271	+	0.782179i
$549$			2.09754i			0.0895208i
$550$	2.62483	−	2.45380i	0.111923	−	0.104630i
$551$		−	29.9896i		−	1.27760i
$552$	0.492630	−	0.121207i	0.0209677	−	0.00515893i
$553$	18.6686	−	18.6686i	0.793870	−	0.793870i
$554$	−11.2425	−	5.33654i	−0.477650	−	0.226728i
$555$	0.842296	−	4.42884i	0.0357535	−	0.187994i
$556$	−28.8898	+	23.5746i	−1.22520	+	0.999785i
$557$			19.0254i			0.806131i	0.915171	+	0.403066i	$0.132055\pi$
$557$			19.0254i			0.806131i	−0.915171	+	0.403066i	$0.867945\pi$
$558$	1.83712	−	0.654442i	0.0777716	−	0.0277047i
$559$	−6.60096	+	6.60096i	−0.279191	+	0.279191i
$560$	−40.0761	+	16.7329i	−1.69352	+	0.707094i
$561$	−0.377126	−	0.377126i	−0.0159223	−	0.0159223i
$562$	3.83931	+	1.82242i	0.161951	+	0.0768741i
$563$	−30.1937			−1.27251			−0.636257	−	0.771478i	$-0.719518\pi$
$563$	−30.1937			−1.27251			−0.636257	+	0.771478i	$0.719518\pi$
$564$	10.2440	−	8.35931i	0.431352	−	0.351990i
$565$	−26.0510	−	4.95449i	−1.09597	−	0.208437i
$566$	−33.9223	−	16.1020i	−1.42586	−	0.676819i
$567$		−	30.1254i		−	1.26515i
$568$	38.7838	−	9.54242i	1.62733	−	0.400391i
$569$	8.51766			0.357079			0.178539	−	0.983933i	$-0.442863\pi$
$569$	8.51766			0.357079			0.178539	+	0.983933i	$0.442863\pi$
$570$	7.48325	−	1.16373i	0.313439	−	0.0487434i
$571$	−17.0231	+	17.0231i	−0.712395	+	0.712395i	−0.967036	−	0.254641i	$-0.918043\pi$
$571$	−17.0231	+	17.0231i	−0.712395	+	0.712395i	0.254641	+	0.967036i	$0.418043\pi$
$572$	−2.16569	−	0.219408i	−0.0905519	−	0.00917391i
$573$	3.72371	+	3.72371i	0.155560	+	0.155560i
$574$	36.8689	−	23.9566i	1.53888	−	0.999928i
$575$	0.629130	+	1.44941i	0.0262365	+	0.0604447i
$576$	−9.94002	−	18.9771i	−0.414167	−	0.790712i
$577$	−26.2145			−1.09133			−0.545663	−	0.838005i	$-0.683722\pi$
$577$	−26.2145			−1.09133			−0.545663	+	0.838005i	$0.683722\pi$
$578$	6.44502	+	18.0922i	0.268077	+	0.752536i
$579$		−	9.89950i		−	0.411409i
$580$	15.1412	+	27.9484i	0.628705	+	1.16049i
$581$	8.53334	+	8.53334i	0.354022	+	0.354022i
$582$	5.58209	−	1.98852i	0.231385	−	0.0824267i
$583$	4.26112	+	4.26112i	0.176478	+	0.176478i
$584$	−23.0787	+	5.67831i	−0.955003	+	0.234970i
$585$	−7.21466	−	10.6034i	−0.298289	−	0.438395i
$586$	−9.47960	−	26.6107i	−0.391599	−	1.09928i
$587$		−	27.5119i		−	1.13554i	−0.823188	−	0.567769i	$-0.807807\pi$
$587$		−	27.5119i		−	1.13554i	0.823188	−	0.567769i	$-0.192193\pi$
$588$	14.5788	−	11.8966i	0.601220	−	0.490606i
$589$	1.53642	+	1.53642i	0.0633072	+	0.0633072i
$590$	22.2684	+	16.2745i	0.916776	+	0.670012i
$591$	−3.00176	−	3.00176i	−0.123476	−	0.123476i
$592$	−7.82769	−	11.8578i	−0.321716	−	0.487351i
$593$	38.2241			1.56967			0.784837	−	0.619702i	$-0.212747\pi$
$593$	38.2241			1.56967			0.784837	+	0.619702i	$0.212747\pi$
$594$	−2.09219	−	0.993110i	−0.0858437	−	0.0407478i
$595$	−16.5989	+	11.2941i	−0.680487	+	0.463012i
$596$	−26.8998	−	2.72524i	−1.10186	−	0.111630i
$597$	1.20972	−	1.20972i	0.0495106	−	0.0495106i
$598$	0.410470	−	0.864740i	0.0167854	−	0.0353618i
$599$	6.53079			0.266841			0.133420	−	0.991060i	$-0.457404\pi$
$599$	6.53079			0.266841			0.133420	+	0.991060i	$0.457404\pi$
$600$	−6.38638	+	4.86269i	−0.260723	+	0.198519i
$601$	4.46195	−	4.46195i	0.182007	−	0.182007i	−0.610223	−	0.792230i	$-0.708920\pi$
$601$	4.46195	−	4.46195i	0.182007	−	0.182007i	0.792230	+	0.610223i	$0.208920\pi$
$602$	27.0370	+	12.8338i	1.10195	+	0.523065i
$603$	9.16892			0.373387
$604$	1.78684	−	17.6371i	0.0727054	−	0.717645i
$605$	13.5119	+	19.8584i	0.549338	+	0.807360i
$606$	2.32089	+	1.10167i	0.0942798	+	0.0447522i
$607$	−3.20941	+	3.20941i	−0.130266	+	0.130266i	−0.769234	−	0.638968i	$-0.779362\pi$
$607$	−3.20941	+	3.20941i	−0.130266	+	0.130266i	0.638968	+	0.769234i	$0.279362\pi$
$608$	14.3517	−	19.0714i	0.582039	−	0.773448i
$609$	−13.8510	−	13.8510i	−0.561270	−	0.561270i
$610$	1.46155	−	1.99984i	0.0591766	−	0.0809712i
$611$		−	24.9470i		−	1.00925i
$612$	−6.26133	−	7.67303i	−0.253099	−	0.310164i
$613$	16.5644	−	16.5644i	0.669030	−	0.669030i	−0.288461	−	0.957492i	$-0.593144\pi$
$613$	16.5644	−	16.5644i	0.669030	−	0.669030i	0.957492	+	0.288461i	$0.0931436\pi$
$614$	−32.7918	−	15.5654i	−1.32337	−	0.628169i
$615$	5.47571	−	6.00491i	0.220802	−	0.242141i
$616$	1.66732	+	6.77658i	0.0671781	+	0.273036i
$617$	6.12066	+	6.12066i	0.246409	+	0.246409i	0.819495	−	0.573086i	$-0.194254\pi$
$617$	6.12066	+	6.12066i	0.246409	+	0.246409i	−0.573086	+	0.819495i	$0.694254\pi$
$618$	−2.08229	+	4.38677i	−0.0837618	+	0.176462i
$619$	21.2202			0.852914			0.426457	−	0.904508i	$-0.359762\pi$
$619$	21.2202			0.852914			0.426457	+	0.904508i	$0.359762\pi$
$620$	−2.20757	−	0.656138i	−0.0886580	−	0.0263511i
$621$	0.720124	−	0.720124i	0.0288976	−	0.0288976i
$622$	−3.19662	+	6.73434i	−0.128173	+	0.270022i
$623$	42.0036	+	42.0036i	1.68284	+	1.68284i
$624$	4.76397	+	0.975296i	0.190711	+	0.0390431i
$625$	−18.2622	−	17.0731i	−0.730488	−	0.682925i
$626$	−3.98897	−	11.1977i	−0.159431	−	0.447549i
$627$		−	1.21695i		−	0.0486002i
$628$	−4.60791	+	3.76013i	−0.183875	+	0.150046i
$629$	−4.64457	−	4.64457i	−0.185191	−	0.185191i
$630$	−24.2611	+	33.1964i	−0.966584	+	1.32257i
$631$			47.8474i			1.90478i	0.304889	+	0.952388i	$0.401381\pi$
$631$			47.8474i			1.90478i	−0.304889	+	0.952388i	$0.598619\pi$
$632$	−3.67436	−	14.9339i	−0.146158	−	0.594039i
$633$	−6.11953	−	6.11953i	−0.243229	−	0.243229i
$634$	1.45218	+	4.07650i	0.0576735	+	0.161899i
$635$	−22.1271	−	4.20824i	−0.878089	−	0.166999i
$636$	−8.51113	−	10.4301i	−0.337488	−	0.413580i
$637$		−	35.5034i		−	1.40670i
$638$	4.81161	−	1.71405i	0.190493	−	0.0678598i
$639$	26.7386	−	26.7386i	1.05776	−	1.05776i
$640$	−3.74609	+	25.0193i	−0.148077	+	0.988976i
$641$	9.29160	−	9.29160i	0.366996	−	0.366996i	−0.499384	−	0.866381i	$-0.666440\pi$
$641$	9.29160	−	9.29160i	0.366996	−	0.366996i	0.866381	+	0.499384i	$0.166440\pi$
$642$	−0.923718	+	1.94600i	−0.0364562	+	0.0768027i
$643$	−3.05433			−0.120451			−0.0602255	−	0.998185i	$-0.519182\pi$
$643$	−3.05433			−0.120451			−0.0602255	+	0.998185i	$0.519182\pi$
$644$	−3.05318	−	0.309321i	−0.120312	−	0.0121889i
$645$	5.43421	+	1.03350i	0.213972	+	0.0406941i
$646$	4.73158	−	9.96805i	0.186161	−	0.392188i
$647$	−8.76847	+	8.76847i	−0.344724	+	0.344724i	−0.858140	−	0.513416i	$-0.828380\pi$
$647$	−8.76847	+	8.76847i	−0.344724	+	0.344724i	0.513416	+	0.858140i	$0.328380\pi$
$648$	−15.0140	−	9.08473i	−0.589806	−	0.356882i
$649$	3.13398	−	3.13398i	0.123020	−	0.123020i
$650$	−0.509753	+	15.1366i	−0.0199942	+	0.593707i
$651$	1.41922			0.0556238
$652$	1.89757	−	18.7301i	0.0743146	−	0.733529i
$653$		−	1.66374i		−	0.0651071i	−0.999470	−	0.0325536i	$-0.989636\pi$
$653$		−	1.66374i		−	0.0651071i	0.999470	−	0.0325536i	$-0.0103640\pi$
$654$	−1.97543	+	4.16165i	−0.0772453	+	0.162733i
$655$	4.18055	−	2.84450i	0.163348	−	0.111144i
$656$	−0.821235	−	25.5993i	−0.0320639	−	0.999486i
$657$	−15.9110	+	15.9110i	−0.620749	+	0.620749i
$658$	−75.3418	+	26.8392i	−2.93713	+	1.04630i
$659$	−7.30314	−	7.30314i	−0.284490	−	0.284490i	0.550407	−	0.834897i	$-0.314473\pi$
$659$	−7.30314	−	7.30314i	−0.284490	−	0.284490i	−0.834897	+	0.550407i	$0.814473\pi$
$660$	0.614416	+	1.13412i	0.0239161	+	0.0441456i
$661$		−	33.6759i		−	1.30984i	−0.755698	−	0.654920i	$-0.772702\pi$
$661$		−	33.6759i		−	1.30984i	0.755698	−	0.654920i	$-0.227298\pi$
$662$	37.7317	+	17.9103i	1.46648	+	0.696102i
$663$	2.24801			0.0873057
$664$	6.82623	−	1.67953i	0.264909	−	0.0651785i
$665$	−45.0038	−	8.55903i	−1.74517	−	0.331905i
$666$	−12.1524	−	5.76843i	−0.470896	−	0.223522i
$667$			2.24610i			0.0869695i
$668$	−21.8009	−	26.7163i	−0.843504	−	1.03368i
$669$	7.36520	−	7.36520i	0.284755	−	0.284755i
$670$	−8.74186	−	6.38886i	−0.337727	−	0.246823i
$671$	−0.281451	−	0.281451i	−0.0108653	−	0.0108653i
$672$	−2.17983	−	15.4368i	−0.0840889	−	0.595488i
$673$	−35.8613			−1.38235			−0.691175	−	0.722687i	$-0.742907\pi$
$673$	−35.8613			−1.38235			−0.691175	+	0.722687i	$0.742907\pi$
$674$	3.92688	−	8.27279i	0.151258	−	0.318656i
$675$	−5.91509	+	14.9885i	−0.227672	+	0.576906i
$676$	−13.0356	+	10.6373i	−0.501369	+	0.409125i
$677$	−33.0328	−	33.0328i	−1.26955	−	1.26955i	−0.946318	−	0.323237i	$-0.895229\pi$
$677$	−33.0328	−	33.0328i	−1.26955	−	1.26955i	−0.323237	−	0.946318i	$-0.604771\pi$
$678$	4.08202	−	8.59964i	0.156769	−	0.330267i
$679$	−35.8447			−1.37559
$680$	0.623163	+	11.6785i	0.0238972	+	0.447850i
$681$	11.1678			0.427951
$682$	−0.158694	+	0.334322i	−0.00607671	+	0.0128019i
$683$		−	30.4538i		−	1.16528i	−0.812729	−	0.582642i	$-0.802019\pi$
$683$		−	30.4538i		−	1.16528i	0.812729	−	0.582642i	$-0.197981\pi$
$684$	2.27771	−	22.4824i	0.0870906	−	0.859635i
$685$	−14.8638	−	21.8453i	−0.567916	−	0.834665i
$686$	−61.9430	+	22.0661i	−2.36499	+	0.842487i
$687$	−8.69962	−	8.69962i	−0.331911	−	0.331911i
$688$	14.5495	−	9.60461i	0.554696	−	0.366172i
$689$	−25.4001			−0.967668
$690$	−0.560467	+	0.0871591i	−0.0213366	+	0.00331809i
$691$	1.80690	+	1.80690i	0.0687379	+	0.0687379i	0.740640	−	0.671902i	$-0.234522\pi$
$691$	1.80690	+	1.80690i	0.0687379	+	0.0687379i	−0.671902	+	0.740640i	$0.734522\pi$
$692$	−4.02134	+	39.6930i	−0.152868	+	1.50890i
$693$	4.67195	+	4.67195i	0.177473	+	0.177473i
$694$	11.2075	+	31.4612i	0.425430	+	1.19425i
$695$	34.4672	−	23.4519i	1.30741	−	0.889580i
$696$	−11.0801	+	2.72615i	−0.419989	+	0.103334i
$697$	−2.74547	−	11.5177i	−0.103992	−	0.436264i
$698$	−1.96111	−	5.50514i	−0.0742289	−	0.208373i
$699$			15.4392i			0.583962i
$700$	46.2621	−	14.7452i	1.74854	−	0.557315i
$701$	−38.9799			−1.47225			−0.736125	−	0.676845i	$-0.763347\pi$
$701$	−38.9799			−1.47225			−0.736125	+	0.676845i	$0.763347\pi$
$702$	9.19560	−	3.27577i	0.347065	−	0.123636i
$703$		−	14.9875i		−	0.565266i
$704$	3.88014	+	1.21261i	0.146238	+	0.0457019i
$705$	−12.2217	+	8.31580i	−0.460296	+	0.313191i
$706$	−13.1771	+	27.7602i	−0.495926	+	1.04477i
$707$	−10.9888	−	10.9888i	−0.413276	−	0.413276i
$708$	−7.67116	+	6.25980i	−0.288300	+	0.235258i
$709$	−20.6409	+	20.6409i	−0.775185	+	0.775185i	−0.979008	−	0.203823i	$-0.934663\pi$
$709$	−20.6409	+	20.6409i	−0.775185	+	0.775185i	0.203823	+	0.979008i	$0.434663\pi$
$710$	−44.1245	+	6.86187i	−1.65596	+	0.257521i
$711$	−10.2958	−	10.2958i	−0.386124	−	0.386124i
$712$	33.6007	−	8.26715i	1.25924	−	0.309825i
$713$	−0.115072	−	0.115072i	−0.00430949	−	0.00430949i
$714$	−2.41852	−	6.78916i	−0.0905107	−	0.254078i
$715$	2.39085	+	0.454702i	0.0894127	+	0.0170049i
$716$	1.14280	−	11.2801i	0.0427084	−	0.421557i
$717$	4.75186	+	4.75186i	0.177461	+	0.177461i
$718$	8.50898	+	23.8861i	0.317552	+	0.891420i
$719$	−34.6821	+	34.6821i	−1.29342	+	1.29342i	−0.360768	+	0.932656i	$0.617485\pi$
$719$	−34.6821	+	34.6821i	−1.29342	+	1.29342i	−0.932656	+	0.360768i	$0.882515\pi$
$720$	9.22828	+	22.1022i	0.343918	+	0.823699i
$721$	20.7701	−	20.7701i	0.773520	−	0.773520i
$722$	−1.59486	+	0.568141i	−0.0593547	+	0.0211440i
$723$			3.51985i			0.130905i
$724$	4.75584	−	46.9429i	0.176749	−	1.74462i
$725$	−14.1502	−	32.5996i	−0.525524	−	1.21072i
$726$	−8.12237	+	2.89345i	−0.301450	+	0.107386i
$727$			41.6769i			1.54571i	0.634583	+	0.772855i	$0.281172\pi$
$727$			41.6769i			1.54571i	−0.634583	+	0.772855i	$0.718828\pi$
$728$	−25.1666	−	15.2279i	−0.932737	−	0.564384i
$729$	−11.1268			−0.412104
$730$	26.2567	−	4.08322i	0.971804	−	0.151127i
$731$	5.69891	−	5.69891i	0.210782	−	0.210782i
$732$	0.562169	+	0.688917i	0.0207783	+	0.0254631i
$733$	13.7235	−	13.7235i	0.506891	−	0.506891i	−0.406680	−	0.913571i	$-0.633314\pi$
$733$	13.7235	−	13.7235i	0.506891	−	0.506891i	0.913571	+	0.406680i	$0.133314\pi$
$734$	11.7788	+	5.59107i	0.434762	+	0.206370i
$735$	−17.3934	+	11.8346i	−0.641564	+	0.436528i
$736$	−1.07489	+	1.42838i	−0.0396210	+	0.0526507i
$737$	−1.23030	+	1.23030i	−0.0453187	+	0.0453187i
$738$	−13.2122	−	20.3334i	−0.486347	−	0.748483i
$739$	50.1918			1.84633			0.923167	−	0.384399i	$-0.125591\pi$
$739$	50.1918			1.84633			0.923167	+	0.384399i	$0.125591\pi$
$740$	7.56696	+	13.9675i	0.278167	+	0.513455i
$741$	3.62706	+	3.62706i	0.133243	+	0.133243i
$742$	27.3266	+	76.7102i	1.00319	+	2.81612i
$743$	−12.1155	−	12.1155i	−0.444476	−	0.444476i	0.449037	−	0.893513i	$-0.351767\pi$
$743$	−12.1155	−	12.1155i	−0.444476	−	0.444476i	−0.893513	+	0.449037i	$0.851767\pi$
$744$	0.427987	−	0.707319i	0.0156908	−	0.0259316i
$745$	29.6965	+	5.64781i	1.08800	+	0.206920i
$746$	0.129834	−	0.273522i	0.00475356	−	0.0100144i
$747$	4.70618	−	4.70618i	0.172190	−	0.172190i
$748$	1.86973	+	0.189425i	0.0683643	+	0.00692606i
$749$	9.21380	−	9.21380i	0.336665	−	0.336665i
$750$	7.58545	−	4.79588i	0.276981	−	0.175121i
$751$	7.66816	−	7.66816i	0.279815	−	0.279815i	−0.553220	−	0.833035i	$-0.686601\pi$
$751$	7.66816	−	7.66816i	0.279815	−	0.279815i	0.833035	+	0.553220i	$0.186601\pi$
$752$	−9.34417	+	45.6429i	−0.340747	+	1.66443i
$753$	15.5757			0.567609
$754$	−9.23213	+	19.4494i	−0.336214	+	0.708306i
$755$	−3.70305	+	19.4709i	−0.134768	+	0.708617i
$756$	−19.7861	−	24.2471i	−0.719613	−	0.881860i
$757$			26.7517i			0.972308i	0.873873	+	0.486154i	$0.161601\pi$
$757$			26.7517i			0.972308i	−0.873873	+	0.486154i	$0.838399\pi$
$758$	−5.15929	−	14.4829i	−0.187394	−	0.526044i
$759$			0.0911448i			0.00330835i
$760$	−17.8372	+	19.8481i	−0.647024	+	0.719966i
$761$	−21.1004			−0.764888			−0.382444	−	0.923979i	$-0.624917\pi$
$761$	−21.1004			−0.764888			−0.382444	+	0.923979i	$0.624917\pi$
$762$	3.46718	−	7.30435i	0.125603	−	0.264609i
$763$	19.7043	−	19.7043i	0.713342	−	0.713342i
$764$	−18.4616	−	1.87036i	−0.667917	−	0.0676673i
$765$	6.22874	+	9.15436i	0.225201	+	0.330977i
$766$	40.1431	−	14.3002i	1.45043	−	0.516689i
$767$			18.6814i			0.674545i
$768$	−8.35082	−	3.56879i	−0.301334	−	0.128778i
$769$		−	18.5520i		−	0.669004i	−0.942395	−	0.334502i	$-0.891432\pi$
$769$		−	18.5520i		−	0.669004i	0.942395	−	0.334502i	$-0.108568\pi$
$770$	−1.19895	−	7.70973i	−0.0432072	−	0.277839i
$771$	16.5101			0.594597
$772$	22.0539	+	27.0263i	0.793738	+	0.972697i
$773$	9.26097			0.333094			0.166547	−	0.986034i	$-0.446738\pi$
$773$	9.26097			0.333094			0.166547	+	0.986034i	$0.446738\pi$
$774$	7.07789	−	14.9110i	0.254409	−	0.535966i
$775$	2.39508	+	0.945203i	0.0860339	+	0.0339527i
$776$	−10.8095	+	17.8645i	−0.388038	+	0.641297i
$777$	−6.92214	−	6.92214i	−0.248331	−	0.248331i
$778$	1.22848	+	3.44855i	0.0440433	+	0.123637i
$779$	14.1536	−	23.0129i	0.507104	−	0.824523i
$780$	−5.21143	−	1.54895i	−0.186599	−	0.0554614i
$781$			7.17565i			0.256765i
$782$	−0.354377	+	0.746569i	−0.0126725	+	0.0266973i
$783$	−16.1968	+	16.1968i	−0.578825	+	0.578825i
$784$	−13.2982	+	64.9568i	−0.474935	+	2.31989i
$785$	5.49749	−	3.74056i	0.196214	−	0.133506i
$786$	0.609122	+	1.70990i	0.0217267	+	0.0609902i
$787$	−0.0352333	+	0.0352333i	−0.00125593	+	0.00125593i	−0.707734	−	0.706479i	$-0.750283\pi$
$787$	−0.0352333	+	0.0352333i	−0.00125593	+	0.00125593i	0.706479	+	0.707734i	$0.250283\pi$
$788$	14.8822	+	1.50774i	0.530158	+	0.0537109i
$789$		−	10.4380i		−	0.371602i
$790$	2.64220	+	16.9904i	0.0940052	+	0.604490i
$791$	−40.7169	+	40.7169i	−1.44773	+	1.44773i
$792$	3.73732	−	0.919534i	0.132800	−	0.0326742i
$793$	1.67770			0.0595770
$794$	4.88729	+	13.7194i	0.173443	+	0.486883i
$795$	8.46683	+	12.4437i	0.300288	+	0.441332i
$796$	−0.607625	+	5.99761i	−0.0215367	+	0.212580i
$797$	−0.0541144	+	0.0541144i	−0.00191683	+	0.00191683i	−0.708065	−	0.706148i	$-0.750431\pi$
$797$	−0.0541144	+	0.0541144i	−0.00191683	+	0.00191683i	0.706148	+	0.708065i	$0.250431\pi$
$798$	7.05182	−	14.8561i	0.249632	−	0.525901i
$799$			21.5379i			0.761956i
$800$	6.60222	−	27.5029i	0.233424	−	0.972375i
$801$	23.1652	−	23.1652i	0.818501	−	0.818501i
$802$	−49.8546	+	17.7598i	−1.76043	+	0.627121i
$803$		−	4.26994i		−	0.150683i
$804$	3.01145	−	2.45739i	0.106206	−	0.0866656i
$805$	3.37061	+	0.641038i	0.118799	+	0.0225936i
$806$	−0.523451	−	1.46941i	−0.0184378	−	0.0517578i
$807$			5.62464i			0.197997i
$808$	−8.79046	+	2.16282i	−0.309247	+	0.0760876i
$809$	10.6798	−	10.6798i	0.375483	−	0.375483i	−0.493986	−	0.869470i	$-0.664461\pi$
$809$	10.6798	−	10.6798i	0.375483	−	0.375483i	0.869470	+	0.493986i	$0.164461\pi$
$810$	15.8405	+	11.5768i	0.556577	+	0.406766i
$811$	9.42901			0.331097			0.165549	−	0.986202i	$-0.447061\pi$
$811$	9.42901			0.331097			0.165549	+	0.986202i	$0.447061\pi$
$812$	68.6710	+	6.95713i	2.40988	+	0.244147i
$813$		−	11.2082i		−	0.393089i
$814$	2.40464	−	0.856611i	0.0842827	−	0.0300242i
$815$	−3.93254	+	20.6775i	−0.137751	+	0.724301i
$816$	−4.11295	−	0.842017i	−0.143982	−	0.0294765i
$817$	18.3898			0.643377
$818$	31.0174	−	11.0494i	1.08450	−	0.386333i
$819$	−27.8490			−0.973124
$820$	−1.57142	+	28.5925i	−0.0548764	+	0.998493i
$821$	−44.6270			−1.55749			−0.778747	−	0.627338i	$-0.784144\pi$
$821$	−44.6270			−1.55749			−0.778747	+	0.627338i	$0.784144\pi$
$822$	8.93501	−	3.18294i	0.311644	−	0.111018i
$823$	−27.6692			−0.964489			−0.482244	−	0.876037i	$-0.660178\pi$
$823$	−27.6692			−0.964489			−0.482244	+	0.876037i	$0.660178\pi$
$824$	−4.08798	−	16.6150i	−0.142412	−	0.578812i
$825$	−0.574200	−	1.32286i	−0.0199911	−	0.0460562i
$826$	56.4191	−	20.0983i	1.96307	−	0.699309i
$827$		−	32.4356i		−	1.12789i	−0.825811	−	0.563947i	$-0.809282\pi$
$827$		−	32.4356i		−	1.12789i	0.825811	−	0.563947i	$-0.190718\pi$
$828$	−0.170592	+	1.68384i	−0.00592848	+	0.0585176i
$829$	9.41726			0.327075			0.163537	−	0.986537i	$-0.447710\pi$
$829$	9.41726			0.327075			0.163537	+	0.986537i	$0.447710\pi$
$830$	−7.76622	+	1.20774i	−0.269569	+	0.0419212i
$831$	−3.53177	+	3.53177i	−0.122516	+	0.122516i
$832$	−15.1787	+	7.95046i	−0.526227	+	0.275633i
$833$			30.6517i			1.06202i
$834$	5.02200	+	14.0975i	0.173898	+	0.488158i
$835$	21.6875	+	31.8740i	0.750526	+	1.10305i
$836$	2.71109	+	3.32235i	0.0937651	+	0.114906i
$837$		−	1.65958i		−	0.0573636i
$838$	−13.5659	+	4.83262i	−0.468627	+	0.166940i
$839$	21.5233	−	21.5233i	0.743067	−	0.743067i	−0.230100	−	0.973167i	$-0.573905\pi$
$839$	21.5233	−	21.5233i	0.743067	−	0.743067i	0.973167	+	0.230100i	$0.0739052\pi$
$840$	0.928746	+	17.4053i	0.0320448	+	0.600541i
$841$		−	21.5185i		−	0.742018i
$842$	8.08539	−	17.0336i	0.278641	−	0.587015i
$843$	1.20609	−	1.20609i	0.0415401	−	0.0415401i
$844$	30.3397	+	3.07375i	1.04434	+	0.105803i
$845$	15.5522	−	10.5819i	0.535012	−	0.364028i
$846$	14.8019	+	41.5514i	0.508901	+	1.42857i
$847$	52.1569			1.79213
$848$	46.4719	+	9.51388i	1.59585	+	0.326708i
$849$	−10.6565	+	10.6565i	−0.365729	+	0.365729i
$850$	0.440093	−	13.0681i	0.0150951	−	0.448233i
$851$			1.12251i			0.0384792i
$852$	1.61574	−	15.9483i	0.0553545	−	0.546381i
$853$	−19.2376	+	19.2376i	−0.658683	+	0.658683i	−0.955068	−	0.296385i	$-0.904219\pi$
$853$	−19.2376	+	19.2376i	−0.658683	+	0.658683i	0.296385	+	0.955068i	$0.404219\pi$
$854$	−1.80495	−	5.06678i	−0.0617641	−	0.173382i
$855$	−4.72035	+	24.8198i	−0.161432	+	0.848821i
$856$	−1.81346	−	7.37056i	−0.0619828	−	0.251921i
$857$	0.313533	−	0.313533i	0.0107101	−	0.0107101i	−0.701731	−	0.712442i	$-0.747589\pi$
$857$	0.313533	−	0.313533i	0.0107101	−	0.0107101i	0.712442	+	0.701731i	$0.247589\pi$
$858$	−0.374631	+	0.789239i	−0.0127897	+	0.0269442i
$859$			51.4592i			1.75576i	0.478877	+	0.877882i	$0.341044\pi$
$859$			51.4592i			1.75576i	−0.478877	+	0.877882i	$0.658956\pi$
$860$	−17.1382	+	9.28469i	−0.584406	+	0.316605i
$861$	−4.09177	−	17.1657i	−0.139447	−	0.585005i
$862$	−7.98080	−	22.4034i	−0.271827	−	0.763062i
$863$	−11.2077	−	11.2077i	−0.381513	−	0.381513i	0.490134	−	0.871647i	$-0.336948\pi$
$863$	−11.2077	−	11.2077i	−0.381513	−	0.381513i	−0.871647	+	0.490134i	$0.836948\pi$
$864$	−18.0512	+	2.54901i	−0.614113	+	0.0867191i
$865$	8.33384	−	43.8198i	0.283359	−	1.48992i
$866$	12.5721	−	26.4858i	0.427218	−	0.900023i
$867$	7.70821			0.261785
$868$	−3.87457	+	3.16172i	−0.131512	+	0.107316i
$869$	2.76302			0.0937291
$870$	12.6058	−	1.96035i	0.427377	−	0.0664621i
$871$		−	7.33371i		−	0.248493i
$872$	−3.87820	−	15.7624i	−0.131332	−	0.533782i
$873$			19.7686i			0.669064i
$874$	−1.77632	+	0.632782i	−0.0600849	+	0.0214042i
$875$	−52.9591	+	11.9305i	−1.79034	+	0.403324i
$876$	−0.961464	+	9.49021i	−0.0324848	+	0.320645i
$877$	12.4329	−	12.4329i	0.419830	−	0.419830i	−0.465315	−	0.885145i	$-0.654059\pi$
$877$	12.4329	−	12.4329i	0.419830	−	0.419830i	0.885145	+	0.465315i	$0.154059\pi$
$878$	−0.180781	+	0.380854i	−0.00610107	+	0.0128532i
$879$	−11.3376			−0.382406
$880$	−4.20397	−	1.72744i	−0.141716	−	0.0582319i
$881$		−	15.6246i		−	0.526408i	−0.964740	−	0.263204i	$-0.915221\pi$
$881$		−	15.6246i		−	0.526408i	0.964740	−	0.263204i	$-0.0847792\pi$
$882$	21.0654	+	59.1340i	0.709309	+	1.99115i
$883$		−	37.8937i		−	1.27522i	−0.770357	−	0.637612i	$-0.779922\pi$
$883$		−	37.8937i		−	1.27522i	0.770357	−	0.637612i	$-0.220078\pi$
$884$	−6.13723	+	5.00808i	−0.206417	+	0.168440i
$885$	9.15213	−	6.22722i	0.307645	−	0.209326i
$886$	−4.53221	+	9.54805i	−0.152263	+	0.320773i
$887$	−33.1260			−1.11226			−0.556132	−	0.831094i	$-0.687715\pi$
$887$	−33.1260			−1.11226			−0.556132	+	0.831094i	$0.687715\pi$
$888$	−5.53736	+	1.36242i	−0.185822	+	0.0457198i
$889$	−34.5841	+	34.5841i	−1.15991	+	1.15991i
$890$	−38.2276	+	5.94483i	−1.28139	+	0.199271i
$891$	2.22933	−	2.22933i	0.0746855	−	0.0746855i
$892$	−3.69943	+	36.5155i	−0.123866	+	1.22263i
$893$	−34.7503	+	34.7503i	−1.16287	+	1.16287i
$894$	−4.65325	+	9.80305i	−0.155628	+	0.327863i
$895$	−2.36834	+	12.4529i	−0.0791649	+	0.416253i
$896$	40.3409	+	37.2873i	1.34769	+	1.24568i
$897$	−0.271653	−	0.271653i	−0.00907022	−	0.00907022i
$898$	4.56616	+	12.8179i	0.152375	+	0.427740i
$899$	2.58816	+	2.58816i	0.0863200	+	0.0863200i
$900$	−8.13205	−	25.5138i	−0.271068	−	0.850460i
$901$	21.9291			0.730564
$902$	4.50120	+	0.955538i	0.149873	+	0.0318159i
$903$	8.49350	−	8.49350i	0.282646	−	0.282646i
$904$	8.01391	+	32.5714i	0.266539	+	1.08331i
$905$	−9.85603	+	51.8235i	−0.327626	+	1.72267i
$906$	−6.42748	−	3.05096i	−0.213539	−	0.101361i
$907$	−5.96606	+	5.96606i	−0.198100	+	0.198100i	−0.799185	−	0.601085i	$-0.794735\pi$
$907$	−5.96606	+	5.96606i	−0.198100	+	0.198100i	0.601085	+	0.799185i	$0.294735\pi$
$908$	−30.4888	+	24.8794i	−1.01181	+	0.825653i
$909$	−6.06037	+	6.06037i	−0.201010	+	0.201010i
$910$	26.5519	+	19.4051i	0.880187	+	0.643272i
$911$	−2.93195			−0.0971399			−0.0485700	−	0.998820i	$-0.515466\pi$
$911$	−2.93195			−0.0971399			−0.0485700	+	0.998820i	$0.515466\pi$
$912$	−5.27748	−	7.99459i	−0.174755	−	0.264727i
$913$			1.26297i			0.0417981i
$914$	−26.7484	+	9.52863i	−0.884758	+	0.315179i
$915$	−0.559242	−	0.821918i	−0.0184880	−	0.0271718i
$916$	43.1314	+	4.36969i	1.42510	+	0.144379i
$917$		−	10.9799i		−	0.362590i
$918$	−7.93897	+	2.82812i	−0.262025	+	0.0933417i
$919$	0.535197	−	0.535197i	0.0176545	−	0.0176545i	−0.698224	−	0.715879i	$-0.746026\pi$
$919$	0.535197	−	0.535197i	0.0176545	−	0.0176545i	0.715879	+	0.698224i	$0.246026\pi$
$920$	1.33594	−	1.48655i	0.0440446	−	0.0490100i
$921$	−10.3013	+	10.3013i	−0.339441	+	0.339441i
$922$	3.07786	+	8.64006i	0.101364	+	0.284545i
$923$	−21.3867	−	21.3867i	−0.703951	−	0.703951i
$924$	2.78660	+	0.282314i	0.0916725	+	0.00928744i
$925$	−7.07167	−	16.2920i	−0.232515	−	0.535676i
$926$	−12.3303	−	34.6132i	−0.405199	−	1.13746i
$927$	−11.4548	−	11.4548i	−0.376226	−	0.376226i
$928$	24.1760	−	32.1265i	0.793617	−	1.05460i
$929$	−16.9530	−	16.9530i	−0.556209	−	0.556209i	0.372017	−	0.928226i	$-0.378666\pi$
$929$	−16.9530	−	16.9530i	−0.556209	−	0.556209i	−0.928226	+	0.372017i	$0.878666\pi$
$930$	−0.545388	+	0.746253i	−0.0178840	+	0.0244706i
$931$	−49.4550	+	49.4550i	−1.62082	+	1.62082i
$932$	−34.3951	−	42.1499i	−1.12665	−	1.38067i
$933$	2.11555	+	2.11555i	0.0692600	+	0.0692600i
$934$	−4.81883	+	10.1519i	−0.157677	+	0.332179i
$935$	−2.06413	−	0.392565i	−0.0675042	−	0.0128383i
$936$	−8.39827	+	13.8795i	−0.274506	+	0.453667i
$937$		−	26.6009i		−	0.869014i	−0.900668	−	0.434507i	$-0.856923\pi$
$937$		−	26.6009i		−	0.869014i	0.900668	−	0.434507i	$-0.143077\pi$
$938$	−22.1483	+	7.88994i	−0.723168	+	0.257616i
$939$	−4.77079			−0.155689
$940$	14.8403	−	49.9300i	0.484037	−	1.62854i
$941$		−	28.9881i		−	0.944984i	−0.881335	−	0.472492i	$-0.843355\pi$
$941$		−	28.9881i		−	0.944984i	0.881335	−	0.472492i	$-0.156645\pi$
$942$	0.801005	+	2.24855i	0.0260982	+	0.0732617i
$943$	−1.06005	+	1.72358i	−0.0345199	+	0.0561274i
$944$	6.99731	−	34.1793i	0.227743	−	1.11244i
$945$	19.6831	+	28.9282i	0.640291	+	0.941035i
$946$	1.05107	+	2.95051i	0.0341731	+	0.0959293i
$947$	−4.59420	−	4.59420i	−0.149291	−	0.149291i	0.628510	−	0.777801i	$-0.283665\pi$
$947$	−4.59420	−	4.59420i	−0.149291	−	0.149291i	−0.777801	+	0.628510i	$0.783665\pi$
$948$	−6.14099	−	0.622151i	−0.199450	−	0.0202065i
$949$	12.7264	+	12.7264i	0.413115	+	0.413115i
$950$	21.7948	−	20.3747i	0.707117	−	0.661042i
$951$	1.73680			0.0563197
$952$	21.7275	+	13.1469i	0.704192	+	0.426095i
$953$	13.0791	+	13.0791i	0.423672	+	0.423672i	0.886466	−	0.462794i	$-0.153153\pi$
$953$	13.0791	+	13.0791i	0.423672	+	0.423672i	−0.462794	+	0.886466i	$0.653153\pi$
$954$	42.3061	−	15.0708i	1.36971	−	0.487934i
$955$	20.3810	+	3.87615i	0.659514	+	0.125429i
$956$	−23.5590	−	2.38679i	−0.761952	−	0.0771942i
$957$		−	2.04999i		−	0.0662669i
$958$	−24.6631	+	51.9580i	−0.796829	+	1.67869i
$959$	−57.3752			−1.85274
$960$	8.95462	+	4.78595i	0.289009	+	0.154466i
$961$	30.7348			0.991445
$962$	−4.61384	+	9.72002i	−0.148756	+	0.313386i
$963$	−5.08146	−	5.08146i	−0.163748	−	0.163748i
$964$	−7.84146	−	9.60943i	−0.252557	−	0.309499i
$965$	−21.9391	−	32.2439i	−0.706245	−	1.03797i
$966$	−0.528154	+	1.11267i	−0.0169931	+	0.0357995i
$967$	−7.03137			−0.226113			−0.113057	−	0.993589i	$-0.536064\pi$
$967$	−7.03137			−0.226113			−0.113057	+	0.993589i	$0.536064\pi$
$968$	15.7286	−	25.9942i	0.505538	−	0.835484i
$969$	−3.13140	−	3.13140i	−0.100595	−	0.100595i
$970$	13.7746	−	18.8478i	0.442277	−	0.605166i
$971$	28.4240	−	28.4240i	0.912170	−	0.912170i	−0.0842723	−	0.996443i	$-0.526857\pi$
$971$	28.4240	−	28.4240i	0.912170	−	0.912170i	0.996443	+	0.0842723i	$0.0268566\pi$
$972$	−20.4380	+	16.6778i	−0.655550	+	0.534940i
$973$		−	90.5258i		−	2.90212i
$974$	21.7265	+	10.3130i	0.696163	+	0.330450i
$975$	5.65411	+	2.23135i	0.181076	+	0.0714605i
$976$	−3.06951	−	0.628401i	−0.0982527	−	0.0201146i
$977$	−15.7364			−0.503451			−0.251726	−	0.967799i	$-0.580998\pi$
$977$	−15.7364			−0.503451			−0.251726	+	0.967799i	$0.580998\pi$
$978$	−6.82581	−	3.24003i	−0.218265	−	0.103605i
$979$			6.21668i			0.198686i
$980$	21.1200	−	71.0580i	0.674654	−	2.26986i
$981$	−10.8670	−	10.8670i	−0.346957	−	0.346957i
$982$	−51.7078	+	18.4200i	−1.65006	+	0.587805i
$983$	−28.5867	+	28.5867i	−0.911773	+	0.911773i	−0.996412	−	0.0846389i	$-0.973026\pi$
$983$	−28.5867	+	28.5867i	−0.911773	+	0.911773i	0.0846389	+	0.996412i	$0.473026\pi$
$984$	−9.78904	−	3.13728i	−0.312063	−	0.100013i
$985$	−16.4295	−	3.12464i	−0.523489	−	0.0995594i
$986$	7.97052	−	16.7916i	0.253833	−	0.534752i
$987$			32.0995i			1.02174i
$988$	−17.9824	−	1.82181i	−0.572096	−	0.0579597i
$989$	−1.37733			−0.0437964
$990$	−4.25196	+	0.661229i	−0.135136	+	0.0210152i
$991$	2.71197	−	2.71197i	0.0861487	−	0.0861487i	−0.662719	−	0.748868i	$-0.730598\pi$
$991$	2.71197	−	2.71197i	0.0861487	−	0.0861487i	0.748868	+	0.662719i	$0.230598\pi$
$992$	0.407319	+	2.88449i	0.0129324	+	0.0915826i
$993$	11.8532	−	11.8532i	0.376149	−	0.376149i
$994$	−41.5805	+	87.5981i	−1.31885	+	2.77844i
$995$	1.25925	−	6.62118i	0.0399208	−	0.209906i
$996$	0.284382	−	2.80702i	0.00901100	−	0.0889439i
$997$	−16.3556			−0.517986			−0.258993	−	0.965879i	$-0.583391\pi$
$997$	−16.3556			−0.517986			−0.258993	+	0.965879i	$0.583391\pi$
$998$	17.6785	−	37.2435i	0.559604	−	1.17892i
$999$	−8.09448	+	8.09448i	−0.256098	+	0.256098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.583.74	yes	240
4.3	odd	2	inner	820.2.s.c.583.105	yes	240
5.2	odd	4		820.2.j.c.747.16	yes	240
20.7	even	4		820.2.j.c.747.47	yes	240
41.32	even	4		820.2.j.c.483.47	yes	240
164.155	odd	4		820.2.j.c.483.16	✓	240
205.32	odd	4	inner	820.2.s.c.647.105	yes	240
820.647	even	4	inner	820.2.s.c.647.74	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.16	✓	240	164.155	odd	4
820.2.j.c.483.47	yes	240	41.32	even	4
820.2.j.c.747.16	yes	240	5.2	odd	4
820.2.j.c.747.47	yes	240	20.7	even	4
820.2.s.c.583.74	yes	240	1.1	even	1	trivial
820.2.s.c.583.105	yes	240	4.3	odd	2	inner
820.2.s.c.647.74	yes	240	820.647	even	4	inner
820.2.s.c.647.105	yes	240	205.32	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.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.474575 + 1.33221i) q^{2} +0.567590 q^{3} +(-1.54956 + 1.26447i) q^{4} +(1.84871 - 1.25788i) q^{5} +(0.269364 + 0.756148i) q^{6} -4.85551i q^{7} +(-2.41991 - 1.46425i) q^{8} -2.67784 q^{9} +(2.55311 + 1.86591i) q^{10} +(0.359317 - 0.359317i) q^{11} +(-0.879513 + 0.717698i) q^{12} +2.14186i q^{13} +(6.46856 - 2.30431i) q^{14} +(1.04931 - 0.713962i) q^{15} +(0.802254 - 3.91872i) q^{16} -1.84916i q^{17} +(-1.27084 - 3.56744i) q^{18} +(2.98352 - 2.98352i) q^{19} +(-1.27413 + 4.28679i) q^{20} -2.75594i q^{21} +(0.649208 + 0.308162i) q^{22} +(-0.223455 + 0.223455i) q^{23} +(-1.37352 - 0.831093i) q^{24} +(1.83546 - 4.65092i) q^{25} +(-2.85340 + 1.01647i) q^{26} -3.22268 q^{27} +(6.13963 + 7.52390i) q^{28} +(5.02586 - 5.02586i) q^{29} +(1.44912 + 1.05907i) q^{30} +0.514969i q^{31} +(5.60128 - 0.790958i) q^{32} +(0.203945 - 0.203945i) q^{33} +(2.46347 - 0.877565i) q^{34} +(-6.10767 - 8.97644i) q^{35} +(4.14947 - 3.38604i) q^{36} +(2.51172 - 2.51172i) q^{37} +(5.39058 + 2.55877i) q^{38} +1.21569i q^{39} +(-6.31557 + 0.336998i) q^{40} +(6.22861 - 1.48471i) q^{41} +(3.67149 - 1.30790i) q^{42} +(3.08189 + 3.08189i) q^{43} +(-0.102438 + 1.01113i) q^{44} +(-4.95055 + 3.36841i) q^{45} +(-0.403734 - 0.191642i) q^{46} -11.6474 q^{47} +(0.455351 - 2.22423i) q^{48} -16.5760 q^{49} +(7.06706 + 0.237996i) q^{50} -1.04956i q^{51} +(-2.70830 - 3.31893i) q^{52} +11.8589i q^{53} +(-1.52941 - 4.29329i) q^{54} +(0.212294 - 1.11625i) q^{55} +(-7.10968 + 11.7499i) q^{56} +(1.69342 - 1.69342i) q^{57} +(9.08064 + 4.31034i) q^{58} +8.72205 q^{59} +(-0.723183 + 2.43314i) q^{60} -0.783294i q^{61} +(-0.686046 + 0.244391i) q^{62} +13.0023i q^{63} +(3.71195 + 7.08671i) q^{64} +(2.69421 + 3.95967i) q^{65} +(0.368484 + 0.174910i) q^{66} -3.42400 q^{67} +(2.33820 + 2.86538i) q^{68} +(-0.126831 + 0.126831i) q^{69} +(9.05993 - 12.3967i) q^{70} +(-9.98512 + 9.98512i) q^{71} +(6.48014 + 3.92103i) q^{72} +(5.94174 - 5.94174i) q^{73} +(4.53813 + 2.15413i) q^{74} +(1.04179 - 2.63982i) q^{75} +(-0.850578 + 8.39571i) q^{76} +(-1.74467 - 1.74467i) q^{77} +(-1.61956 + 0.576938i) q^{78} +(3.84482 + 3.84482i) q^{79} +(-3.44616 - 8.25372i) q^{80} +6.20436 q^{81} +(4.93389 + 7.59320i) q^{82} +(-1.75745 + 1.75745i) q^{83} +(3.48479 + 4.27049i) q^{84} +(-2.32603 - 3.41856i) q^{85} +(-2.64313 + 5.56831i) q^{86} +(2.85263 - 2.85263i) q^{87} +(-1.39565 + 0.343386i) q^{88} +(-8.65069 + 8.65069i) q^{89} +(-6.83684 - 4.99660i) q^{90} +10.3998 q^{91} +(0.0637051 - 0.628806i) q^{92} +0.292291i q^{93} +(-5.52756 - 15.5168i) q^{94} +(1.76274 - 9.26860i) q^{95} +(3.17923 - 0.448940i) q^{96} -7.38227i q^{97} +(-7.86656 - 22.0827i) q^{98} +(-0.962194 + 0.962194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

L-functions

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