LMFDB - Embedded newform 820.2.j.c.483.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			483.16
Character	$\chi$	$=$	820.483
Dual form			820.2.j.c.747.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33221 - 0.474575i) q^{2} +0.567590i q^{3} +(1.54956 + 1.26447i) q^{4} +(-1.84871 + 1.25788i) q^{5} +(0.269364 - 0.756148i) q^{6} +4.85551 q^{7} +(-1.46425 - 2.41991i) q^{8} +2.67784 q^{9} +(3.05983 - 0.798412i) q^{10} +(0.359317 + 0.359317i) q^{11} +(-0.717698 + 0.879513i) q^{12} +2.14186 q^{13} +(-6.46856 - 2.30431i) q^{14} +(-0.713962 - 1.04931i) q^{15} +(0.802254 + 3.91872i) q^{16} +1.84916 q^{17} +(-3.56744 - 1.27084i) q^{18} +(-2.98352 - 2.98352i) q^{19} +(-4.45523 - 0.388467i) q^{20} +2.75594i q^{21} +(-0.308162 - 0.649208i) 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} +3.22268i q^{27} +(7.52390 + 6.13963i) q^{28} +(-5.02586 - 5.02586i) q^{29} +(0.453170 + 1.73673i) q^{30} -0.514969i q^{31} +(0.790958 - 5.60128i) q^{32} +(-0.203945 + 0.203945i) q^{33} +(-2.46347 - 0.877565i) q^{34} +(-8.97644 + 6.10767i) q^{35} +(4.14947 + 3.38604i) q^{36} +(2.51172 - 2.51172i) q^{37} +(2.55877 + 5.39058i) q^{38} +1.21569i q^{39} +(5.75094 + 2.63186i) q^{40} +(6.22861 + 1.48471i) q^{41} +(1.30790 - 3.67149i) 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} +11.6474i q^{47} +(-2.22423 + 0.455351i) q^{48} +16.5760 q^{49} +(-4.65242 + 5.32494i) q^{50} +1.04956i q^{51} +(3.31893 + 2.70830i) q^{52} +11.8589 q^{53} +(1.52941 - 4.29329i) q^{54} +(-1.11625 - 0.212294i) q^{55} +(-7.10968 - 11.7499i) q^{56} +(1.69342 - 1.69342i) q^{57} +(4.31034 + 9.08064i) q^{58} -8.72205 q^{59} +(0.220490 - 2.52874i) q^{60} +0.783294i q^{61} +(-0.244391 + 0.686046i) q^{62} +13.0023 q^{63} +(-3.71195 + 7.08671i) q^{64} +(-3.95967 + 2.69421i) q^{65} +(0.368484 - 0.174910i) q^{66} +3.42400i q^{67} +(2.86538 + 2.33820i) q^{68} +(0.126831 + 0.126831i) q^{69} +(14.8570 - 3.87670i) q^{70} +(-9.98512 - 9.98512i) q^{71} +(-3.92103 - 6.48014i) q^{72} +(-5.94174 + 5.94174i) q^{73} +(-4.53813 + 2.15413i) q^{74} +(2.63982 + 1.04179i) q^{75} +(-0.850578 - 8.39571i) q^{76} +(1.74467 + 1.74467i) q^{77} +(0.576938 - 1.61956i) q^{78} +(-3.84482 + 3.84482i) q^{79} +(-6.41243 - 6.23544i) q^{80} +6.20436 q^{81} +(-7.59320 - 4.93389i) q^{82} +(1.75745 - 1.75745i) q^{83} +(-3.48479 + 4.27049i) q^{84} +(-3.41856 + 2.32603i) q^{85} +(-2.64313 - 5.56831i) q^{86} +(2.85263 - 2.85263i) q^{87} +(0.343386 - 1.39565i) q^{88} +(8.65069 + 8.65069i) q^{89} +(8.19373 - 2.13802i) q^{90} +10.3998 q^{91} +(0.628806 - 0.0637051i) q^{92} +0.292291 q^{93} +(5.52756 - 15.5168i) q^{94} +(9.26860 + 1.76274i) q^{95} +(3.17923 + 0.448940i) q^{96} +7.38227 q^{97} +(-22.0827 - 7.86656i) 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} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.33221	−	0.474575i	−0.942013	−	0.335575i
$2$	−1.33221	−	0.474575i	−0.942013	−	0.335575i
$3$			0.567590i			0.327698i	0.986485	+	0.163849i	$0.0523910\pi$
$3$			0.567590i			0.327698i	−0.986485	+	0.163849i	$0.947609\pi$
$4$	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
$7$	4.85551			1.83521			0.917606	−	0.397491i	$-0.130119\pi$
$7$	4.85551			1.83521			0.917606	+	0.397491i	$0.130119\pi$
$8$	−1.46425	−	2.41991i	−0.517690	−	0.855568i
$9$	2.67784			0.892614
$10$	3.05983	−	0.798412i	0.967602	−	0.252480i
$11$	0.359317	+	0.359317i	0.108338	+	0.108338i	0.759198	−	0.650860i	$-0.225591\pi$
$11$	0.359317	+	0.359317i	0.108338	+	0.108338i	−0.650860	+	0.759198i	$0.725591\pi$
$12$	−0.717698	+	0.879513i	−0.207181	+	0.253893i
$13$	2.14186			0.594044			0.297022	−	0.954871i	$-0.404007\pi$
$13$	2.14186			0.594044			0.297022	+	0.954871i	$0.404007\pi$
$14$	−6.46856	−	2.30431i	−1.72879	−	0.615852i
$15$	−0.713962	−	1.04931i	−0.184344	−	0.270930i
$16$	0.802254	+	3.91872i	0.200564	+	0.979681i
$17$	1.84916			0.448487			0.224244	−	0.974533i	$-0.428009\pi$
$17$	1.84916			0.448487			0.224244	+	0.974533i	$0.428009\pi$
$18$	−3.56744	−	1.27084i	−0.840854	−	0.299539i
$19$	−2.98352	−	2.98352i	−0.684468	−	0.684468i	0.276536	−	0.961004i	$-0.410813\pi$
$19$	−2.98352	−	2.98352i	−0.684468	−	0.684468i	−0.961004	+	0.276536i	$0.910813\pi$
$20$	−4.45523	−	0.388467i	−0.996220	−	0.0868638i
$21$			2.75594i			0.601395i
$22$	−0.308162	−	0.649208i	−0.0657004	−	0.138412i
$23$	0.223455	−	0.223455i	0.0465935	−	0.0465935i	−0.683426	−	0.730020i	$-0.739511\pi$
$23$	0.223455	−	0.223455i	0.0465935	−	0.0465935i	0.730020	+	0.683426i	$0.239511\pi$
$24$	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
$27$			3.22268i			0.620206i
$28$	7.52390	+	6.13963i	1.42188	+	1.16028i
$29$	−5.02586	−	5.02586i	−0.933279	−	0.933279i	0.0646305	−	0.997909i	$-0.479413\pi$
$29$	−5.02586	−	5.02586i	−0.933279	−	0.933279i	−0.997909	+	0.0646305i	$0.979413\pi$
$30$	0.453170	+	1.73673i	0.0827372	+	0.317081i
$31$		−	0.514969i		−	0.0924912i	−0.998930	−	0.0462456i	$-0.985274\pi$
$31$		−	0.514969i		−	0.0924912i	0.998930	−	0.0462456i	$-0.0147257\pi$
$32$	0.790958	−	5.60128i	0.139823	−	0.990177i
$33$	−0.203945	+	0.203945i	−0.0355022	+	0.0355022i
$34$	−2.46347	−	0.877565i	−0.422481	−	0.150501i
$35$	−8.97644	+	6.10767i	−1.51729	+	1.03239i
$36$	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	$0.155685\pi$
$38$	2.55877	+	5.39058i	0.415087	+	0.874468i
$39$			1.21569i			0.194667i
$40$	5.75094	+	2.63186i	0.909303	+	0.416134i
$41$	6.22861	+	1.48471i	0.972746	+	0.231873i
$41$	6.22861	+	1.48471i	0.972746	+	0.231873i
$42$	1.30790	−	3.67149i	0.201813	−	0.566523i
$43$	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
$47$			11.6474i			1.69895i	0.527631	+	0.849474i	$0.323080\pi$
$47$			11.6474i			1.69895i	−0.527631	+	0.849474i	$0.676920\pi$
$48$	−2.22423	+	0.455351i	−0.321039	+	0.0657243i
$49$	16.5760			2.36800
$50$	−4.65242	+	5.32494i	−0.657952	+	0.753060i
$51$			1.04956i			0.146968i
$52$	3.31893	+	2.70830i	0.460252	+	0.375574i
$53$	11.8589			1.62895			0.814475	−	0.580198i	$-0.197025\pi$
$53$	11.8589			1.62895			0.814475	+	0.580198i	$0.197025\pi$
$54$	1.52941	−	4.29329i	0.208126	−	0.584242i
$55$	−1.11625	−	0.212294i	−0.150515	−	0.0286257i
$56$	−7.10968	−	11.7499i	−0.950071	−	1.57015i
$57$	1.69342	−	1.69342i	0.224299	−	0.224299i
$58$	4.31034	+	9.08064i	0.565976	+	1.19235i
$59$	−8.72205			−1.13551			−0.567757	−	0.823196i	$-0.692189\pi$
$59$	−8.72205			−1.13551			−0.567757	+	0.823196i	$0.692189\pi$
$60$	0.220490	−	2.52874i	0.0284651	−	0.326459i
$61$			0.783294i			0.100291i	0.998742	+	0.0501453i	$0.0159684\pi$
$61$			0.783294i			0.100291i	−0.998742	+	0.0501453i	$0.984032\pi$
$62$	−0.244391	+	0.686046i	−0.0310377	+	0.0871279i
$63$	13.0023			1.63814
$64$	−3.71195	+	7.08671i	−0.463994	+	0.885838i
$65$	−3.95967	+	2.69421i	−0.491136	+	0.334175i
$66$	0.368484	−	0.174910i	0.0453572	−	0.0215299i
$67$			3.42400i			0.418308i	0.977883	+	0.209154i	$0.0670710\pi$
$67$			3.42400i			0.418308i	−0.977883	+	0.209154i	$0.932929\pi$
$68$	2.86538	+	2.33820i	0.347478	+	0.283548i
$69$	0.126831	+	0.126831i	0.0152686	+	0.0152686i
$70$	14.8570	−	3.87670i	1.77575	−	0.463354i
$71$	−9.98512	−	9.98512i	−1.18502	−	1.18502i	−0.978428	−	0.206588i	$-0.933764\pi$
$71$	−9.98512	−	9.98512i	−1.18502	−	1.18502i	−0.206588	−	0.978428i	$-0.566236\pi$
$72$	−3.92103	−	6.48014i	−0.462097	−	0.763692i
$73$	−5.94174	+	5.94174i	−0.695428	+	0.695428i	−0.963421	−	0.267993i	$-0.913640\pi$
$73$	−5.94174	+	5.94174i	−0.695428	+	0.695428i	0.267993	+	0.963421i	$0.413640\pi$
$74$	−4.53813	+	2.15413i	−0.527547	+	0.250413i
$75$	2.63982	+	1.04179i	0.304820	+	0.120295i
$76$	−0.850578	−	8.39571i	−0.0975680	−	0.963054i
$77$	1.74467	+	1.74467i	0.198823	+	0.198823i
$78$	0.576938	−	1.61956i	0.0653254	−	0.183379i
$79$	−3.84482	+	3.84482i	−0.432577	+	0.432577i	−0.889504	−	0.456927i	$-0.848950\pi$
$79$	−3.84482	+	3.84482i	−0.432577	+	0.432577i	0.456927	+	0.889504i	$0.348950\pi$
$80$	−6.41243	−	6.23544i	−0.716932	−	0.697143i
$81$	6.20436			0.689374
$82$	−7.59320	−	4.93389i	−0.838529	−	0.544857i
$83$	1.75745	−	1.75745i	0.192906	−	0.192906i	−0.604045	−	0.796950i	$-0.706445\pi$
$83$	1.75745	−	1.75745i	0.192906	−	0.192906i	0.796950	+	0.604045i	$0.206445\pi$
$84$	−3.48479	+	4.27049i	−0.380222	+	0.465948i
$85$	−3.41856	+	2.32603i	−0.370795	+	0.252293i
$86$	−2.64313	−	5.56831i	−0.285016	−	0.600446i
$87$	2.85263	−	2.85263i	0.305834	−	0.305834i
$88$	0.343386	−	1.39565i	0.0366051	−	0.148776i
$89$	8.65069	+	8.65069i	0.916971	+	0.916971i	0.996808	−	0.0798366i	$-0.0254398\pi$
$89$	8.65069	+	8.65069i	0.916971	+	0.916971i	−0.0798366	+	0.996808i	$0.525440\pi$
$90$	8.19373	−	2.13802i	0.863695	−	0.225367i
$91$	10.3998			1.09020
$92$	0.628806	−	0.0637051i	0.0655576	−	0.00664171i
$93$	0.292291			0.0303092
$94$	5.52756	−	15.5168i	0.570125	−	1.60043i
$95$	9.26860	+	1.76274i	0.950938	+	0.180854i
$96$	3.17923	+	0.448940i	0.324479	+	0.0458197i
$97$	7.38227			0.749556			0.374778	−	0.927115i	$-0.377719\pi$
$97$	7.38227			0.749556			0.374778	+	0.927115i	$0.377719\pi$
$98$	−22.0827	−	7.86656i	−2.23069	−	0.794643i
$99$	0.962194	+	0.962194i	0.0967042	+	0.0967042i
$100$	8.72508	−	4.88600i	0.872508	−	0.488600i
$101$	2.26316	+	2.26316i	0.225192	+	0.225192i	0.810681	−	0.585488i	$-0.199097\pi$
$101$	2.26316	+	2.26316i	0.225192	+	0.225192i	−0.585488	+	0.810681i	$0.699097\pi$
$102$	0.498097	−	1.39824i	0.0493190	−	0.138446i
$103$	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	0.609409	−	0.792856i	$-0.291407\pi$
$107$	−1.89759	−	1.89759i	−0.183447	−	0.183447i	−0.792856	+	0.609409i	$0.791407\pi$
$108$	−4.07497	+	4.99373i	−0.392114	+	0.480522i
$109$	−4.05812	+	4.05812i	−0.388698	+	0.388698i	−0.874223	−	0.485525i	$-0.838628\pi$
$109$	−4.05812	+	4.05812i	−0.388698	+	0.388698i	0.485525	+	0.874223i	$0.338628\pi$
$110$	1.38633	+	0.812565i	0.132181	+	0.0774750i
$111$	1.42563	+	1.42563i	0.135314	+	0.135314i
$112$	3.89536	+	19.0274i	0.368077	+	1.79792i
$113$	−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
$117$	5.73555			0.530252
$118$	11.6196	+	4.13927i	1.06967	+	0.381051i
$119$	8.97862			0.823069
$120$	−1.49382	+	3.26417i	−0.136366	+	0.297977i
$121$		−	10.7418i		−	0.976526i
$122$	0.371732	−	1.04351i	0.0336550	−	0.0944751i
$123$	−0.842706	+	3.53530i	−0.0759843	+	0.318767i
$124$	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	0.948577	−	0.316545i	$-0.102523\pi$
$127$	7.12264	+	7.12264i	0.632032	+	0.632032i	−0.316545	+	0.948577i	$0.602523\pi$
$128$	8.30827	−	7.67937i	0.734354	−	0.678767i
$129$	−1.74925	+	1.74925i	−0.154013	+	0.154013i
$130$	6.55371	−	1.71008i	0.574798	−	0.149984i
$131$	2.26133			0.197574			0.0987869	−	0.995109i	$-0.468504\pi$
$131$	2.26133			0.197574			0.0987869	+	0.995109i	$0.468504\pi$
$132$	−0.573905	+	0.0581429i	−0.0499520	+	0.00506069i
$133$	−14.4865	−	14.4865i	−1.25614	−	1.25614i
$134$	1.62494	−	4.56148i	0.140374	−	0.394052i
$135$	−4.05376	−	5.95781i	−0.348892	−	0.512767i
$136$	−2.70763	−	4.47481i	−0.232177	−	0.383711i
$137$	11.8165			1.00955			0.504776	−	0.863251i	$-0.331575\pi$
$137$	11.8165			1.00955			0.504776	+	0.863251i	$0.331575\pi$
$138$	−0.108774	−	0.229155i	−0.00925947	−	0.0195070i
$139$	−18.6439			−1.58136			−0.790678	−	0.612232i	$-0.790272\pi$
$139$	−18.6439			−1.58136			−0.790678	+	0.612232i	$0.790272\pi$
$140$	−21.6324	−	1.88620i	−1.82828	−	0.159413i
$141$	−6.61094			−0.556742
$142$	8.56357	+	18.0410i	0.718639	+	1.51396i
$143$	0.769605	+	0.769605i	0.0643576	+	0.0643576i
$144$	2.14831	+	10.4937i	0.179026	+	0.874477i
$145$	15.6133	+	2.96941i	1.29661	+	0.246596i
$146$	10.7354	−	5.09584i	0.888471	−	0.421734i
$147$			9.40838i			0.775990i
$148$	7.06803	−	0.716070i	0.580989	−	0.0588606i
$149$	−9.55918	+	9.55918i	−0.783119	+	0.783119i	−0.980356	−	0.197237i	$-0.936803\pi$
$149$	−9.55918	+	9.55918i	−0.783119	+	0.783119i	0.197237	+	0.980356i	$0.436803\pi$
$150$	−3.02238	−	2.64067i	−0.246776	−	0.215610i
$151$	−6.26759	−	6.26759i	−0.510049	−	0.510049i	0.404492	−	0.914541i	$-0.367448\pi$
$151$	−6.26759	−	6.26759i	−0.510049	−	0.510049i	−0.914541	+	0.404492i	$0.867448\pi$
$152$	−2.85125	+	11.5885i	−0.231267	+	0.939951i
$153$	4.95176			0.400326
$154$	−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
$157$		−	2.97369i		−	0.237326i	−0.992935	−	0.118663i	$-0.962139\pi$
$157$		−	2.97369i		−	0.237326i	0.992935	−	0.118663i	$-0.0378609\pi$
$158$	6.94677	−	3.29745i	0.552655	−	0.262331i
$159$			6.73101i			0.533804i
$160$	5.58351	+	11.3501i	0.441416	+	0.897303i
$161$	1.08499	−	1.08499i	0.0855090	−	0.0855090i
$162$	−8.26550	−	2.94444i	−0.649399	−	0.231337i
$163$	6.65600	−	6.65600i	0.521338	−	0.521338i	−0.396637	−	0.917975i	$-0.629823\pi$
$163$	6.65600	−	6.65600i	0.521338	−	0.521338i	0.917975	+	0.396637i	$0.129823\pi$
$164$	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
$167$	−17.2412			−1.33417			−0.667083	−	0.744983i	$-0.732457\pi$
$167$	−17.2412			−1.33417			−0.667083	+	0.744983i	$0.732457\pi$
$168$	6.66913	−	4.03538i	0.514535	−	0.311336i
$169$	−8.41246			−0.647112
$170$	5.65811	−	1.47639i	0.433957	−	0.113234i
$171$	−7.98941	−	7.98941i	−0.610965	−	0.610965i
$172$	0.878621	+	8.67251i	0.0669942	+	0.661273i
$173$	−14.1054	+	14.1054i	−1.07241	+	1.07241i	−0.0752500	+	0.997165i	$0.523975\pi$
$173$	−14.1054	+	14.1054i	−1.07241	+	1.07241i	−0.997165	+	0.0752500i	$0.976025\pi$
$174$	−5.15408	+	2.44651i	−0.390730	+	0.185469i
$175$	8.91208	−	22.5826i	0.673690	−	1.70709i
$176$	−1.11980	+	1.69633i	−0.0844081	+	0.127865i
$177$		−	4.95055i		−	0.372106i
$178$	−7.41912	−	15.6299i	−0.556086	−	1.17151i
$179$	4.00853	+	4.00853i	0.299611	+	0.299611i	0.840862	−	0.541250i	$-0.182049\pi$
$179$	4.00853	+	4.00853i	0.299611	+	0.299611i	−0.541250	+	0.840862i	$0.682049\pi$
$180$	−11.9304	−	1.04025i	−0.889240	−	0.0775358i
$181$	−16.6818	−	16.6818i	−1.23995	−	1.23995i	−0.960022	−	0.279926i	$-0.909690\pi$
$181$	−16.6818	−	16.6818i	−1.23995	−	1.23995i	−0.279926	−	0.960022i	$-0.590310\pi$
$182$	−13.8547	−	4.93549i	−1.02698	−	0.365843i
$183$	−0.444590			−0.0328650
$184$	−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
$188$	−14.7277	+	18.0483i	−1.07413	+	1.31631i
$189$			15.6478i			1.13821i
$190$	−11.5112	−	6.74699i	−0.835107	−	0.489478i
$191$	6.56057	−	6.56057i	0.474706	−	0.474706i	−0.428728	−	0.903434i	$-0.641038\pi$
$191$	6.56057	−	6.56057i	0.474706	−	0.474706i	0.903434	+	0.428728i	$0.141038\pi$
$192$	−4.02234	−	2.10687i	−0.290288	−	0.152050i
$193$	−17.4413			−1.25545			−0.627726	−	0.778434i	$-0.716014\pi$
$193$	−17.4413			−1.25545			−0.627726	+	0.778434i	$0.716014\pi$
$194$	−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	0.869945	−	0.493148i	$-0.164154\pi$
$197$	5.28860	+	5.28860i	0.376797	+	0.376797i	−0.493148	+	0.869945i	$0.664154\pi$
$198$	−0.825210	−	1.73848i	−0.0586451	−	0.123548i
$199$	−2.13133	−	2.13133i	−0.151086	−	0.151086i	0.627517	−	0.778603i	$-0.284071\pi$
$199$	−2.13133	−	2.13133i	−0.151086	−	0.151086i	−0.778603	+	0.627517i	$0.784071\pi$
$200$	−13.9424	+	2.36847i	−0.985876	+	0.167476i
$201$	−1.94343			−0.137079
$202$	−1.94096	−	4.08903i	−0.136565	−	0.287703i
$203$	−24.4031	−	24.4031i	−1.71276	−	1.71276i
$204$	−1.32714	+	1.62636i	−0.0929182	+	0.113868i
$205$	−13.3825	+	5.09008i	−0.934674	+	0.355506i
$206$	−3.66865	−	7.72877i	−0.255607	−	0.538489i
$207$	0.598376	−	0.598376i	0.0415900	−	0.0415900i
$208$	1.71831	+	8.39334i	0.119144	+	0.581973i
$209$		−	2.14406i		−	0.148308i
$210$	2.20038	+	8.43270i	0.151840	+	0.581911i
$211$	−10.7816	+	10.7816i	−0.742236	+	0.742236i	−0.973008	−	0.230772i	$-0.925875\pi$
$211$	−10.7816	+	10.7816i	−0.742236	+	0.742236i	0.230772	+	0.973008i	$0.425875\pi$
$212$	18.3761	+	14.9952i	1.26208	+	1.02988i
$213$	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
$217$		−	2.50044i		−	0.169741i
$218$	7.33215	−	3.48038i	0.496596	−	0.235721i
$219$	−3.37247	−	3.37247i	−0.227891	−	0.227891i
$220$	−1.46126	−	1.74042i	−0.0985180	−	0.117339i
$221$	3.96063			0.266421
$222$	−1.22266	−	2.57580i	−0.0820598	−	0.172876i
$223$	−12.9763	+	12.9763i	−0.868955	+	0.868955i	−0.992357	−	0.123402i	$-0.960620\pi$
$223$	−12.9763	+	12.9763i	−0.868955	+	0.868955i	0.123402	+	0.992357i	$0.460620\pi$
$224$	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
$227$		−	19.6758i		−	1.30593i	−0.757387	−	0.652966i	$-0.773524\pi$
$227$		−	19.6758i		−	1.30593i	0.757387	−	0.652966i	$-0.226476\pi$
$228$	4.76532	−	0.482779i	0.315591	−	0.0319728i
$229$	15.3273	−	15.3273i	1.01286	−	1.01286i	0.0129409	−	0.999916i	$-0.495881\pi$
$229$	15.3273	−	15.3273i	1.01286	−	1.01286i	0.999916	−	0.0129409i	$-0.00411933\pi$
$230$	0.505324	−	0.862141i	0.0333201	−	0.0568479i
$231$	−0.990256	+	0.990256i	−0.0651541	+	0.0651541i
$232$	−4.80303	+	19.5212i	−0.315334	+	1.28163i
$233$	27.2013			1.78201			0.891007	−	0.453990i	$-0.150000\pi$
$233$	27.2013			1.78201			0.891007	+	0.453990i	$0.150000\pi$
$234$	−7.64095	−	2.72195i	−0.499504	−	0.177939i
$235$	−14.6511	−	21.5327i	−0.955731	−	1.40464i
$236$	−13.5153	−	11.0287i	−0.879772	−	0.717910i
$237$	−2.18228	−	2.18228i	−0.141755	−	0.141755i
$238$	−11.9614	−	4.26103i	−0.775342	−	0.276202i
$239$	−8.37200	+	8.37200i	−0.541539	+	0.541539i	−0.923980	−	0.382441i	$-0.875084\pi$
$239$	−8.37200	+	8.37200i	−0.541539	+	0.541539i	0.382441	+	0.923980i	$0.375084\pi$
$240$	3.53917	−	3.63963i	0.228452	−	0.234937i
$241$		−	6.20141i		−	0.399468i	−0.979850	−	0.199734i	$-0.935992\pi$
$241$		−	6.20141i		−	0.399468i	0.979850	−	0.199734i	$-0.0640078\pi$
$242$	−5.09778	+	14.3103i	−0.327698	+	0.919900i
$243$			13.1896i			0.846112i
$244$	−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
$248$	−1.24618	+	0.754043i	−0.0791325	+	0.0478818i
$249$	0.997512	+	0.997512i	0.0632148	+	0.0632148i
$250$	1.90282	−	15.6965i	0.120345	−	0.992732i
$251$	27.4418			1.73211			0.866055	−	0.499948i	$-0.166648\pi$
$251$	27.4418			1.73211			0.866055	+	0.499948i	$0.166648\pi$
$252$	20.1478	+	16.4410i	1.26919	+	1.03568i
$253$	0.160582			0.0100957
$254$	−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
$257$		−	29.0881i		−	1.81447i	−0.420628	−	0.907233i	$-0.638190\pi$
$257$		−	29.0881i		−	1.81447i	0.420628	−	0.907233i	$-0.361810\pi$
$258$	3.16051	−	1.50021i	0.196765	−	0.0933992i
$259$	12.1957	−	12.1957i	0.757803	−	0.757803i
$260$	−9.54246	−	0.832039i	−0.591798	−	0.0516009i
$261$	−13.4585	−	13.4585i	−0.833058	−	0.833058i
$262$	−3.01257	−	1.07317i	−0.186117	−	0.0663008i
$263$	−18.3900			−1.13398			−0.566989	−	0.823726i	$-0.691892\pi$
$263$	−18.3900			−1.13398			−0.566989	+	0.823726i	$0.691892\pi$
$264$	0.792154	+	0.194902i	0.0487537	+	0.0119954i
$265$	−21.9237	+	14.9172i	−1.34676	+	0.916354i
$266$	12.4241	+	26.1741i	0.761773	+	1.60483i
$267$	−4.91004	+	4.91004i	−0.300490	+	0.300490i
$268$	−4.32953	+	5.30568i	−0.264468	+	0.324096i
$269$			9.90970i			0.604205i	0.953275	+	0.302102i	$0.0976885\pi$
$269$			9.90970i			0.604205i	−0.953275	+	0.302102i	$0.902312\pi$
$270$	2.57303	+	9.86086i	0.156590	+	0.600113i
$271$			19.7470i			1.19955i	0.800170	+	0.599773i	$0.204742\pi$
$271$			19.7470i			1.19955i	−0.800170	+	0.599773i	$0.795258\pi$
$272$	1.48350	+	7.24635i	0.0899502	+	0.439374i
$273$			5.90282i			0.357255i
$274$	−15.7420	−	5.60781i	−0.951011	−	0.338780i
$275$	2.33067	−	1.01165i	0.140545	−	0.0610046i
$276$	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	$0.335162\pi$
$278$	24.8376	+	8.84793i	1.48966	+	0.530664i
$279$		−	1.37901i		−	0.0825589i
$280$	27.9238	+	12.7790i	1.66876	+	0.763693i
$281$	2.12494	+	2.12494i	0.126763	+	0.126763i	0.767642	−	0.640879i	$-0.221430\pi$
$281$	2.12494	+	2.12494i	0.126763	+	0.126763i	−0.640879	+	0.767642i	$0.721430\pi$
$282$	8.80715	+	3.13739i	0.524458	+	0.186829i
$283$	18.7750	−	18.7750i	1.11606	−	1.11606i	0.123741	−	0.992315i	$-0.460511\pi$
$283$	18.7750	−	18.7750i	1.11606	−	1.11606i	0.992315	−	0.123741i	$-0.0394893\pi$
$284$	−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
$287$	30.2431	+	7.20903i	1.78520	+	0.425536i
$288$	2.11806	−	14.9994i	0.124808	−	0.883845i
$289$	−13.5806			−0.798859
$290$	−19.3910	−	11.3656i	−1.13868	−	0.667408i
$291$			4.19010i			0.245628i
$292$	−16.7202	+	1.69394i	−0.978476	+	0.0991304i
$293$		−	19.9749i		−	1.16695i	−0.812132	−	0.583474i	$-0.801693\pi$
$293$		−	19.9749i		−	1.16695i	0.812132	−	0.583474i	$-0.198307\pi$
$294$	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
$298$	17.2714	−	8.19827i	1.00050	−	0.474913i
$299$	0.478608	−	0.478608i	0.0276786	−	0.0276786i
$300$	2.77325	+	4.95226i	0.160113	+	0.285919i
$301$	14.9642	+	14.9642i	0.862520	+	0.862520i
$302$	5.37529	+	11.3242i	0.309313	+	0.651633i
$303$	−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	$0.988379\pi$
$308$	0.497391	+	4.90954i	0.0283415	+	0.279747i
$309$	−2.42794	+	2.42794i	−0.138121	+	0.138121i
$310$	−0.411157	−	1.57572i	−0.0233522	−	0.0894946i
$311$	3.72725	−	3.72725i	0.211353	−	0.211353i	−0.593489	−	0.804842i	$-0.702250\pi$
$311$	3.72725	−	3.72725i	0.211353	−	0.211353i	0.804842	+	0.593489i	$0.202250\pi$
$312$	2.94188	−	1.78008i	0.166551	−	0.100777i
$313$		−	8.40535i		−	0.475098i	−0.971375	−	0.237549i	$-0.923656\pi$
$313$		−	8.40535i		−	0.475098i	0.971375	−	0.237549i	$-0.0763441\pi$
$314$	−1.41124	+	3.96158i	−0.0796409	+	0.223565i
$315$	−24.0375	+	16.3554i	−1.35436	+	0.921522i
$316$	−10.8194	+	1.09613i	−0.608640	+	0.0616620i
$317$		−	3.05996i		−	0.171865i	−0.996301	−	0.0859323i	$-0.972613\pi$
$317$		−	3.05996i		−	0.171865i	0.996301	−	0.0859323i	$-0.0273869\pi$
$318$	3.19437	−	8.96711i	0.179131	−	0.502850i
$319$		−	3.61175i		−	0.202219i
$320$	−2.05194	−	17.7705i	−0.114707	−	0.993399i
$321$	1.07706	−	1.07706i	0.0601153	−	0.0601153i
$322$	−1.96034	+	0.930521i	−0.109245	+	0.0518559i
$323$	−5.51702	−	5.51702i	−0.306975	−	0.306975i
$324$	9.61401	+	7.84520i	0.534112	+	0.435845i
$325$	3.93128	−	9.96161i	0.218068	−	0.552571i
$326$	−12.0260	+	5.70841i	−0.666056	+	0.316159i
$327$	−2.30335	−	2.30335i	−0.127375	−	0.127375i
$328$	−5.52737	−	17.2467i	−0.305198	−	0.952289i
$329$			56.5541i			3.11793i
$330$	−0.461203	+	0.786867i	−0.0253884	+	0.0433156i
$331$	20.8833	+	20.8833i	1.14785	+	1.14785i	0.986974	+	0.160878i	$0.0514327\pi$
$331$	20.8833	+	20.8833i	1.14785	+	1.14785i	0.160878	+	0.986974i	$0.448567\pi$
$332$	4.94551	−	0.501035i	0.271420	−	0.0274979i
$333$	6.72598	−	6.72598i	0.368582	−	0.368582i
$334$	22.9689	+	8.18226i	1.25680	+	0.447713i
$335$	−4.30699	−	6.32998i	−0.235316	−	0.345844i
$336$	−10.7998	+	2.21096i	−0.589175	+	0.120618i
$337$	4.57874	+	4.57874i	0.249420	+	0.249420i	0.820733	−	0.571313i	$-0.193566\pi$
$337$	4.57874	+	4.57874i	0.249420	+	0.249420i	−0.571313	+	0.820733i	$0.693566\pi$
$338$	11.2071	+	3.99234i	0.609588	+	0.217155i
$339$	4.75964	−	4.75964i	0.258508	−	0.258508i
$340$	−8.23844	−	0.718337i	−0.446792	−	0.0389573i
$341$	0.185037	−	0.185037i	0.0100203	−	0.0100203i
$342$	6.85198	+	14.4351i	0.370513	+	0.780562i
$343$	46.4965			2.51057
$344$	2.94525	−	11.9706i	0.158797	−	0.645409i
$345$	−0.394011	−	0.0749348i	−0.0212128	−	0.00403435i
$346$	25.4854	−	12.0973i	1.37010	−	0.650353i
$347$		−	23.6158i		−	1.26776i	−0.773430	−	0.633882i	$-0.781460\pi$
$347$		−	23.6158i		−	1.26776i	0.773430	−	0.633882i	$-0.218540\pi$
$348$	8.02735	−	0.813260i	0.430311	−	0.0435953i
$349$	4.13234			0.221199			0.110600	−	0.993865i	$-0.464723\pi$
$349$	4.13234			0.221199			0.110600	+	0.993865i	$0.464723\pi$
$350$	−22.5899	+	25.8553i	−1.20748	+	1.38202i
$351$			6.90252i			0.368429i
$352$	2.29684	−	1.72843i	0.122422	−	0.0921257i
$353$	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
$355$	31.0197	+	5.89947i	1.64636	+	0.313111i
$356$	2.46624	+	24.3432i	0.130710	+	1.29019i
$357$			5.09617i			0.269718i
$358$	−3.43785	−	7.24254i	−0.181696	−	0.382780i
$359$	−17.9297			−0.946292			−0.473146	−	0.880984i	$-0.656882\pi$
$359$	−17.9297			−0.946292			−0.473146	+	0.880984i	$0.656882\pi$
$360$	15.4001	+	7.04771i	0.811657	+	0.371447i
$361$		−	1.19716i		−	0.0630083i
$362$	14.3069	+	30.1404i	0.751952	+	1.58414i
$363$	6.09693			0.320006
$364$	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	$0.172647\pi$
$368$	1.05492	+	0.696389i	0.0549917	+	0.0363018i
$369$	16.6792	+	3.97582i	0.868287	+	0.206973i
$370$	5.68004	−	9.69081i	0.295291	−	0.503801i
$371$	57.5812			2.98947
$372$	0.452922	+	0.369592i	0.0234829	+	0.0191625i
$373$	−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
$375$	−6.19070	+	1.39462i	−0.319686	+	0.0720181i
$376$	28.1857	−	17.0547i	1.45357	−	0.879528i
$377$	−10.7647	−	10.7647i	−0.554408	−	0.554408i
$378$	7.42605	−	20.8461i	0.381955	−	1.07221i
$379$	10.8714			0.558426			0.279213	−	0.960229i	$-0.409927\pi$
$379$	10.8714			0.558426			0.279213	+	0.960229i	$0.409927\pi$
$380$	12.1333	+	14.4513i	0.622425	+	0.741336i
$381$	−4.04274	+	4.04274i	−0.207116	+	0.207116i
$382$	−11.8535	+	5.62656i	−0.606479	+	0.287880i
$383$	−30.1327			−1.53971			−0.769856	−	0.638218i	$-0.779672\pi$
$383$	−30.1327			−1.53971			−0.769856	+	0.638218i	$0.779672\pi$
$384$	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
$388$	11.4393	+	9.33463i	0.580740	+	0.473894i
$389$	−2.58860			−0.131247			−0.0656235	−	0.997844i	$-0.520904\pi$
$389$	−2.58860			−0.131247			−0.0656235	+	0.997844i	$0.520904\pi$
$390$	0.970625	+	3.71982i	0.0491495	+	0.188360i
$391$	0.413203	−	0.413203i	0.0208966	−	0.0208966i
$392$	−24.2714	−	40.1125i	−1.22589	−	2.02599i
$393$			1.28351i			0.0647445i
$394$	−4.53568	−	9.55536i	−0.228504	−	0.481392i
$395$	2.27162	−	11.9443i	0.114298	−	0.600983i
$396$	0.274314	+	2.70764i	0.0137848	+	0.136064i
$397$		−	10.2982i		−	0.516854i	−0.966031	−	0.258427i	$-0.916796\pi$
$397$		−	10.2982i		−	0.516854i	0.966031	−	0.258427i	$-0.0832041\pi$
$398$	1.82790	+	3.85085i	0.0916243	+	0.193026i
$399$	8.22242	−	8.22242i	0.411636	−	0.411636i
$400$	19.6982	+	3.46142i	0.984909	+	0.173071i
$401$		−	37.4226i		−	1.86879i	−0.356234	−	0.934397i	$-0.615939\pi$
$401$		−	37.4226i		−	1.86879i	0.356234	−	0.934397i	$-0.384061\pi$
$402$	2.58905	+	0.922301i	0.129130	+	0.0460002i
$403$		−	1.10299i		−	0.0549438i
$404$	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
$407$	1.80501			0.0894708
$408$	2.53985	−	1.53682i	0.125741	−	0.0760841i
$409$		−	23.2827i		−	1.15125i	−0.817712	−	0.575627i	$-0.804758\pi$
$409$		−	23.2827i		−	1.15125i	0.817712	−	0.575627i	$-0.195242\pi$
$410$	20.2439	−	0.430044i	0.999774	−	0.0212383i
$411$			6.70692i			0.330828i
$412$	1.21952	+	12.0374i	0.0600814	+	0.593039i
$413$	−42.3501			−2.08391
$414$	−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
$417$		−	10.5821i		−	0.518207i
$418$	−1.01752	+	2.85634i	−0.0497685	+	0.139708i
$419$			10.1830i			0.497474i	0.968571	+	0.248737i	$0.0800155\pi$
$419$			10.1830i			0.497474i	−0.968571	+	0.248737i	$0.919984\pi$
$420$	1.07059	−	12.2784i	0.0522395	−	0.599122i
$421$	−9.42756	+	9.42756i	−0.459471	+	0.459471i	−0.898482	−	0.439011i	$-0.855329\pi$
$421$	−9.42756	+	9.42756i	−0.459471	+	0.459471i	0.439011	+	0.898482i	$0.355329\pi$
$422$	19.4800	−	9.24666i	0.948273	−	0.450121i
$423$			31.1899i			1.51650i
$424$	−17.3644	−	28.6976i	−0.843292	−	1.39368i
$425$	3.39405	−	8.60031i	0.164636	−	0.417176i
$426$	−10.2399	+	4.86060i	−0.496123	+	0.235497i
$427$			3.80330i			0.184054i
$428$	−0.540988	−	5.33987i	−0.0261497	−	0.258113i
$429$	−0.436820	+	0.436820i	−0.0210899	+	0.0210899i
$430$	11.8907	+	6.96943i	0.573419	+	0.336096i
$431$	−16.8167			−0.810033			−0.405017	−	0.914309i	$-0.632734\pi$
$431$	−16.8167			−0.810033			−0.405017	+	0.914309i	$0.632734\pi$
$432$	−12.6288	+	2.58541i	−0.607604	+	0.124391i
$433$	−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
$437$	−1.33337			−0.0637835
$438$	2.89234	+	6.09333i	0.138202	+	0.291150i
$439$	−0.210791	+	0.210791i	−0.0100605	+	0.0100605i	−0.712119	−	0.702059i	$-0.752264\pi$
$439$	−0.210791	+	0.210791i	−0.0100605	+	0.0100605i	0.702059	+	0.712119i	$0.252264\pi$
$440$	1.12074	+	3.01208i	0.0534291	+	0.143595i
$441$	44.3880			2.11371
$442$	−5.27639	−	1.87962i	−0.250972	−	0.0894043i
$443$	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
$445$	−26.8742	−	5.11105i	−1.27396	−	0.242287i
$446$	23.4453	−	11.1289i	1.11017	−	0.526968i
$447$	−5.42569	−	5.42569i	−0.256626	−	0.256626i
$448$	−18.0234	+	34.4096i	−0.851527	+	1.62570i
$449$	−9.62157			−0.454070			−0.227035	−	0.973887i	$-0.572903\pi$
$449$	−9.62157			−0.454070			−0.227035	+	0.973887i	$0.572903\pi$
$450$	−12.4584	+	14.2593i	−0.587297	+	0.672192i
$451$	1.70457	+	2.77153i	0.0802649	+	0.130506i
$452$	−2.39069	−	23.5976i	−0.112449	−	1.10994i
$453$	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
$457$	−20.0782			−0.939220			−0.469610	−	0.882874i	$-0.655606\pi$
$457$	−20.0782			−0.939220			−0.469610	+	0.882874i	$0.655606\pi$
$458$	−27.6931	+	13.1452i	−1.29401	+	0.614235i
$459$			5.95926i			0.278154i
$460$	−1.08235	+	0.908738i	−0.0504647	+	0.0423701i
$461$	6.48552			0.302061			0.151030	−	0.988529i	$-0.451741\pi$
$461$	6.48552			0.302061			0.151030	+	0.988529i	$0.451741\pi$
$462$	1.78918	−	0.849277i	0.0832401	−	0.0395119i
$463$		−	25.9818i		−	1.20748i	−0.797182	−	0.603739i	$-0.793677\pi$
$463$		−	25.9818i		−	1.20748i	0.797182	−	0.603739i	$-0.206323\pi$
$464$	15.6629	−	23.7270i	0.727133	−	1.10150i
$465$	−0.540361	+	0.367668i	−0.0250587	+	0.0170502i
$466$	−36.2377	−	12.9090i	−1.67868	−	0.598000i
$467$	−5.61875	−	5.61875i	−0.260005	−	0.260005i	0.565051	−	0.825056i	$-0.308856\pi$
$467$	−5.61875	−	5.61875i	−0.260005	−	0.260005i	−0.825056	+	0.565051i	$0.808856\pi$
$468$	8.88756	+	7.25240i	0.410828	+	0.335242i
$469$			16.6253i			0.767683i
$470$	9.29942	+	35.6390i	0.428950	+	1.64391i
$471$	1.68784			0.0777714
$472$	12.7713	+	21.1066i	0.587845	+	0.971510i
$473$			2.21475i			0.101834i
$474$	1.87160	+	3.94291i	0.0859654	+	0.181104i
$475$	−19.3523	+	8.40002i	−0.887943	+	0.385419i
$476$	13.9129	+	11.3532i	0.637696	+	0.520371i
$477$	31.7564			1.45402
$478$	15.1264	−	7.18010i	0.691865	−	0.328410i
$479$	−28.7572	+	28.7572i	−1.31395	+	1.31395i	−0.395470	+	0.918479i	$0.629418\pi$
$479$	−28.7572	+	28.7572i	−1.31395	+	1.31395i	−0.918479	+	0.395470i	$0.870582\pi$
$480$	−6.44219	+	3.16914i	−0.294044	+	0.144651i
$481$	5.37974	−	5.37974i	0.245295	−	0.245295i
$482$	−2.94303	+	8.26156i	−0.134051	+	0.376304i
$483$	0.615828	+	0.615828i	0.0280211	+	0.0280211i
$484$	13.5826	−	16.6450i	0.617391	−	0.756591i
$485$	−13.6477	+	9.28604i	−0.619709	+	0.421658i
$486$	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	$0.124096\pi$
$488$	1.89550	−	1.14694i	0.0858054	−	0.0519194i
$489$	3.77788	+	3.77788i	0.170842	+	0.170842i
$490$	50.7197	−	13.2345i	2.29128	−	0.597873i
$491$		−	38.8136i		−	1.75163i	−0.482643	−	0.875817i	$-0.660323\pi$
$491$		−	38.8136i		−	1.75163i	0.482643	−	0.875817i	$-0.339677\pi$
$492$	−5.77608	+	4.41257i	−0.260406	+	0.198934i
$493$	−9.29362	−	9.29362i	−0.418564	−	0.418564i
$494$	5.48051	+	11.5458i	0.246580	+	0.519472i
$495$	−2.98915	−	0.568489i	−0.134352	−	0.0255517i
$496$	2.01802	−	0.413136i	0.0906118	−	0.0185504i
$497$	−48.4829	−	48.4829i	−2.17476	−	2.17476i
$498$	−0.855499	−	1.80229i	−0.0383358	−	0.0807625i
$499$	20.6132	−	20.6132i	0.922772	−	0.922772i	−0.0744522	−	0.997225i	$-0.523721\pi$
$499$	20.6132	−	20.6132i	0.922772	−	0.922772i	0.997225	+	0.0744522i	$0.0237208\pi$
$500$	−9.98411	+	20.0079i	−0.446503	+	0.894782i
$501$		−	9.78594i		−	0.437204i
$502$	−36.5582	−	13.0232i	−1.63167	−	0.581253i
$503$		−	10.8062i		−	0.481827i	−0.970547	−	0.240913i	$-0.922553\pi$
$503$		−	10.8062i		−	0.481827i	0.970547	−	0.240913i	$-0.0774470\pi$
$504$	−19.0386	−	31.4644i	−0.848047	−	1.40154i
$505$	−7.03071	−	1.33713i	−0.312862	−	0.0595015i
$506$	−0.213929	−	0.0762083i	−0.00951030	−	0.00338787i
$507$		−	4.77482i		−	0.212057i
$508$	2.03060	+	20.0433i	0.0900935	+	0.889276i
$509$	16.6133	−	16.6133i	0.736369	−	0.736369i	−0.235504	−	0.971873i	$-0.575674\pi$
$509$	16.6133	−	16.6133i	0.736369	−	0.736369i	0.971873	+	0.235504i	$0.0756741\pi$
$510$	0.837985	+	3.21148i	0.0371066	+	0.142207i
$511$	−28.8502	+	28.8502i	−1.27626	+	1.27626i
$512$	22.5844	−	1.39411i	0.998100	−	0.0616115i
$513$	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
$518$	−22.0350	+	10.4594i	−0.968160	+	0.459561i
$519$	−8.00609	−	8.00609i	−0.351428	−	0.351428i
$520$	12.3177	+	5.63706i	0.540166	+	0.247202i
$521$	25.0805	−	25.0805i	1.09880	−	1.09880i	0.104244	−	0.994552i	$-0.466758\pi$
$521$	25.0805	−	25.0805i	1.09880	−	1.09880i	0.994552	−	0.104244i	$-0.0332423\pi$
$522$	11.5424	+	24.3165i	0.505198	+	1.06430i
$523$	9.28632	−	9.28632i	0.406062	−	0.406062i	−0.474301	−	0.880363i	$-0.657299\pi$
$523$	9.28632	−	9.28632i	0.406062	−	0.406062i	0.880363	+	0.474301i	$0.157299\pi$
$524$	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
$527$		−	0.952260i		−	0.0414811i
$528$	−0.962818	−	0.635587i	−0.0419013	−	0.0276604i
$529$			22.9001i			0.995658i
$530$	36.2863	−	9.46832i	1.57618	−	0.411277i
$531$	−23.3563			−1.01358
$532$	−4.12999	−	40.7655i	−0.179058	−	1.76741i
$533$	13.3408	+	3.18003i	0.577854	+	0.137743i
$534$	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
$538$	4.70289	−	13.2018i	0.202756	−	0.569169i
$539$	5.95605	+	5.95605i	0.256545	+	0.256545i
$540$	1.25191	−	14.3578i	0.0538734	−	0.617862i
$541$			6.09162i			0.261899i	0.991389	+	0.130950i	$0.0418026\pi$
$541$			6.09162i			0.261899i	−0.991389	+	0.130950i	$0.958197\pi$
$542$	9.37144	−	26.3071i	0.402538	−	1.12999i
$543$	9.46841	−	9.46841i	0.406328	−	0.406328i
$544$	1.46261	−	10.3577i	0.0627088	−	0.444082i
$545$	2.39764	−	12.6069i	0.102704	−	0.540022i
$546$	2.80133	−	7.86379i	0.119886	−	0.336539i
$547$			22.3627i			0.956160i	0.878316	+	0.478080i	$0.158667\pi$
$547$			22.3627i			0.956160i	−0.878316	+	0.478080i	$0.841333\pi$
$548$	18.3103	+	14.9415i	0.782179	+	0.638271i
$549$			2.09754i			0.0895208i
$550$	−3.58504	+	0.241647i	−0.152866	+	0.0103039i
$551$			29.9896i			1.27760i
$552$	0.121207	−	0.492630i	0.00515893	−	0.0209677i
$553$	−18.6686	+	18.6686i	−0.793870	+	0.793870i
$554$	11.2425	−	5.33654i	0.477650	−	0.226728i
$555$	−4.42884	−	0.842296i	−0.187994	−	0.0357535i
$556$	−28.8898	−	23.5746i	−1.22520	−	0.999785i
$557$	−19.0254			−0.806131			−0.403066	−	0.915171i	$-0.632055\pi$
$557$	−19.0254			−0.806131			−0.403066	+	0.915171i	$0.632055\pi$
$558$	−0.654442	+	1.83712i	−0.0277047	+	0.0777716i
$559$	6.60096	+	6.60096i	0.279191	+	0.279191i
$560$	−31.1357	−	30.2763i	−1.31572	−	1.27941i
$561$	−0.377126	+	0.377126i	−0.0159223	+	0.0159223i
$562$	−1.82242	−	3.83931i	−0.0768741	−	0.161951i
$563$		−	30.1937i		−	1.27251i	−0.771478	−	0.636257i	$-0.780482\pi$
$563$		−	30.1937i		−	1.27251i	0.771478	−	0.636257i	$-0.219518\pi$
$564$	−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
$567$	30.1254			1.26515
$568$	−9.54242	+	38.7838i	−0.400391	+	1.62733i
$569$	−8.51766			−0.357079			−0.178539	−	0.983933i	$-0.557137\pi$
$569$	−8.51766			−0.357079			−0.178539	+	0.983933i	$0.557137\pi$
$570$	3.82952	−	6.53361i	0.160401	−	0.273663i
$571$	−17.0231	−	17.0231i	−0.712395	−	0.712395i	0.254641	−	0.967036i	$-0.418043\pi$
$571$	−17.0231	−	17.0231i	−0.712395	−	0.712395i	−0.967036	+	0.254641i	$0.918043\pi$
$572$	0.219408	+	2.16569i	0.00917391	+	0.0905519i
$573$	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
$577$			26.2145i			1.09133i	0.838005	+	0.545663i	$0.183722\pi$
$577$			26.2145i			1.09133i	−0.838005	+	0.545663i	$0.816278\pi$
$578$	18.0922	+	6.44502i	0.752536	+	0.268077i
$579$		−	9.89950i		−	0.411409i
$580$	20.4390	+	24.3438i	0.848683	+	1.01082i
$581$	8.53334	−	8.53334i	0.354022	−	0.354022i
$582$	1.98852	−	5.58209i	0.0824267	−	0.231385i
$583$	4.26112	+	4.26112i	0.176478	+	0.176478i
$584$	23.0787	+	5.67831i	0.955003	+	0.234970i
$585$	−10.6034	+	7.21466i	−0.438395	+	0.298289i
$586$	−9.47960	+	26.6107i	−0.391599	+	1.09928i
$587$	27.5119			1.13554			0.567769	−	0.823188i	$-0.307807\pi$
$587$	27.5119			1.13554			0.567769	+	0.823188i	$0.307807\pi$
$588$	−11.8966	+	14.5788i	−0.490606	+	0.601220i
$589$	−1.53642	+	1.53642i	−0.0633072	+	0.0633072i
$590$	−26.6880	+	6.96379i	−1.09873	+	0.286695i
$591$	−3.00176	+	3.00176i	−0.123476	+	0.123476i
$592$	11.8578	+	7.82769i	0.487351	+	0.321716i
$593$			38.2241i			1.56967i	0.619702	+	0.784837i	$0.287253\pi$
$593$			38.2241i			1.56967i	−0.619702	+	0.784837i	$0.712747\pi$
$594$	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
$598$	−0.864740	+	0.410470i	−0.0353618	+	0.0167854i
$599$	−6.53079			−0.266841			−0.133420	−	0.991060i	$-0.542596\pi$
$599$	−6.53079			−0.266841			−0.133420	+	0.991060i	$0.542596\pi$
$600$	−1.34432	−	7.91356i	−0.0548816	−	0.323070i
$601$	4.46195	+	4.46195i	0.182007	+	0.182007i	0.792230	−	0.610223i	$-0.208920\pi$
$601$	4.46195	+	4.46195i	0.182007	+	0.182007i	−0.610223	+	0.792230i	$0.708920\pi$
$602$	−12.8338	−	27.0370i	−0.523065	−	1.10195i
$603$			9.16892i			0.373387i
$604$	−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	$0.279362\pi$
$608$	−19.0714	+	14.3517i	−0.773448	+	0.582039i
$609$	13.8510	−	13.8510i	0.561270	−	0.561270i
$610$	0.625392	+	2.39675i	0.0253214	+	0.0970414i
$611$			24.9470i			1.00925i
$612$	7.67303	+	6.26133i	0.310164	+	0.253099i
$613$	−16.5644	+	16.5644i	−0.669030	+	0.669030i	−0.957492	−	0.288461i	$-0.906856\pi$
$613$	−16.5644	+	16.5644i	−0.669030	+	0.669030i	0.288461	+	0.957492i	$0.406856\pi$
$614$	32.7918	−	15.5654i	1.32337	−	0.628169i
$615$	−2.88907	−	7.59577i	−0.116499	−	0.306291i
$616$	1.66732	−	6.77658i	0.0671781	−	0.273036i
$617$	−6.12066	−	6.12066i	−0.246409	−	0.246409i	0.573086	−	0.819495i	$-0.305746\pi$
$617$	−6.12066	−	6.12066i	−0.246409	−	0.246409i	−0.819495	+	0.573086i	$0.805746\pi$
$618$	4.38677	−	2.08229i	0.176462	−	0.0837618i
$619$	−21.2202			−0.852914			−0.426457	−	0.904508i	$-0.640238\pi$
$619$	−21.2202			−0.852914			−0.426457	+	0.904508i	$0.640238\pi$
$620$	−0.200048	+	2.29431i	−0.00803413	+	0.0921416i
$621$	0.720124	+	0.720124i	0.0288976	+	0.0288976i
$622$	−6.73434	+	3.19662i	−0.270022	+	0.128173i
$623$	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
$627$	1.21695			0.0486002
$628$	3.76013	−	4.60791i	0.150046	−	0.183875i
$629$	4.64457	−	4.64457i	0.185191	−	0.185191i
$630$	39.7848	−	10.3812i	1.58506	−	0.413597i
$631$		−	47.8474i		−	1.90478i	−0.304889	−	0.952388i	$-0.598619\pi$
$631$		−	47.8474i		−	1.90478i	0.304889	−	0.952388i	$-0.401381\pi$
$632$	14.9339	+	3.67436i	0.594039	+	0.146158i
$633$	−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
$637$	35.5034			1.40670
$638$	−1.71405	+	4.81161i	−0.0678598	+	0.190493i
$639$	−26.7386	−	26.7386i	−1.05776	−	1.05776i
$640$	−5.69981	+	24.6478i	−0.225305	+	0.974288i
$641$	9.29160	+	9.29160i	0.366996	+	0.366996i	0.866381	−	0.499384i	$-0.166440\pi$
$641$	9.29160	+	9.29160i	0.366996	+	0.366996i	−0.499384	+	0.866381i	$0.666440\pi$
$642$	−1.94600	+	0.923718i	−0.0768027	+	0.0364562i
$643$		−	3.05433i		−	0.120451i	−0.998185	−	0.0602255i	$-0.980818\pi$
$643$		−	3.05433i		−	0.120451i	0.998185	−	0.0602255i	$-0.0191820\pi$
$644$	3.05318	−	0.309321i	0.120312	−	0.0121889i
$645$	1.03350	−	5.43421i	0.0406941	−	0.213972i
$646$	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	$0.328380\pi$
$648$	−9.08473	−	15.0140i	−0.356882	−	0.589806i
$649$	−3.13398	−	3.13398i	−0.123020	−	0.123020i
$650$	−9.96481	+	11.4052i	−0.390852	+	0.447351i
$651$	1.41922			0.0556238
$652$	18.7301	−	1.89757i	0.733529	−	0.0743146i
$653$	−1.66374			−0.0651071			−0.0325536	−	0.999470i	$-0.510364\pi$
$653$	−1.66374			−0.0651071			−0.0325536	+	0.999470i	$0.510364\pi$
$654$	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
$658$	26.8392	−	75.3418i	1.04630	−	2.93713i
$659$	7.30314	−	7.30314i	0.284490	−	0.284490i	−0.550407	−	0.834897i	$-0.685527\pi$
$659$	7.30314	−	7.30314i	0.284490	−	0.284490i	0.834897	+	0.550407i	$0.185527\pi$
$660$	0.987846	−	0.829395i	0.0384519	−	0.0322842i
$661$			33.6759i			1.30984i	0.755698	+	0.654920i	$0.227298\pi$
$661$			33.6759i			1.30984i	−0.755698	+	0.654920i	$0.772702\pi$
$662$	−17.9103	−	37.7317i	−0.696102	−	1.46648i
$663$			2.24801i			0.0873057i
$664$	−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
$667$	−2.24610			−0.0869695
$668$	−26.7163	−	21.8009i	−1.03368	−	0.843504i
$669$	−7.36520	−	7.36520i	−0.284755	−	0.284755i
$670$	2.73376	+	10.4768i	0.105614	+	0.404756i
$671$	−0.281451	+	0.281451i	−0.0108653	+	0.0108653i
$672$	15.4368	+	2.17983i	0.595488	+	0.0840889i
$673$		−	35.8613i		−	1.38235i	−0.722687	−	0.691175i	$-0.757093\pi$
$673$		−	35.8613i		−	1.38235i	0.722687	−	0.691175i	$-0.242907\pi$
$674$	−3.92688	−	8.27279i	−0.151258	−	0.318656i
$675$	14.9885	+	5.91509i	0.576906	+	0.227672i
$676$	−13.0356	−	10.6373i	−0.501369	−	0.409125i
$677$	33.0328	+	33.0328i	1.26955	+	1.26955i	0.946318	+	0.323237i	$0.104771\pi$
$677$	33.0328	+	33.0328i	1.26955	+	1.26955i	0.323237	+	0.946318i	$0.395229\pi$
$678$	−8.59964	+	4.08202i	−0.330267	+	0.156769i
$679$	35.8447			1.37559
$680$	10.6344	+	4.86673i	0.407811	+	0.186631i
$681$	11.1678			0.427951
$682$	−0.334322	+	0.158694i	−0.0128019	+	0.00607671i
$683$	−30.4538			−1.16528			−0.582642	−	0.812729i	$-0.697981\pi$
$683$	−30.4538			−1.16528			−0.582642	+	0.812729i	$0.697981\pi$
$684$	−2.27771	−	22.4824i	−0.0870906	−	0.859635i
$685$	−21.8453	+	14.8638i	−0.834665	+	0.567916i
$686$	−61.9430	−	22.0661i	−2.36499	−	0.842487i
$687$	8.69962	+	8.69962i	0.331911	+	0.331911i
$688$	−9.60461	+	14.5495i	−0.366172	+	0.554696i
$689$	25.4001			0.967668
$690$	0.489343	+	0.286817i	0.0186290	+	0.0109189i
$691$	1.80690	−	1.80690i	0.0687379	−	0.0687379i	−0.671902	−	0.740640i	$-0.734522\pi$
$691$	1.80690	−	1.80690i	0.0687379	−	0.0687379i	0.740640	+	0.671902i	$0.234522\pi$
$692$	−39.6930	+	4.02134i	−1.50890	+	0.152868i
$693$	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
$697$	11.5177	+	2.74547i	0.436264	+	0.103992i
$698$	−5.50514	−	1.96111i	−0.208373	−	0.0742289i
$699$			15.4392i			0.583962i
$700$	42.3647	−	23.7241i	1.60124	−	0.896685i
$701$	−38.9799			−1.47225			−0.736125	−	0.676845i	$-0.763347\pi$
$701$	−38.9799			−1.47225			−0.736125	+	0.676845i	$0.763347\pi$
$702$	3.27577	−	9.19560i	0.123636	−	0.347065i
$703$	−14.9875			−0.565266
$704$	−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
$708$	6.25980	−	7.67116i	0.235258	−	0.288300i
$709$	20.6409	+	20.6409i	0.775185	+	0.775185i	0.979008	−	0.203823i	$-0.0653366\pi$
$709$	20.6409	+	20.6409i	0.775185	+	0.775185i	−0.203823	+	0.979008i	$0.565337\pi$
$710$	−38.5250	−	22.5805i	−1.44582	−	0.847431i
$711$	−10.2958	+	10.2958i	−0.386124	+	0.386124i
$712$	8.26715	−	33.6007i	0.309825	−	1.25924i
$713$	−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
$718$	23.8861	+	8.50898i	0.891420	+	0.317552i
$719$	34.6821	+	34.6821i	1.29342	+	1.29342i	0.932656	+	0.360768i	$0.117485\pi$
$719$	34.6821	+	34.6821i	1.29342	+	1.29342i	0.360768	+	0.932656i	$0.382515\pi$
$720$	−17.1715	−	16.6975i	−0.639943	−	0.622280i
$721$	20.7701	+	20.7701i	0.773520	+	0.773520i
$722$	−0.568141	+	1.59486i	−0.0211440	+	0.0593547i
$723$	3.51985			0.130905
$724$	−4.75584	−	46.9429i	−0.176749	−	1.74462i
$725$	−32.5996	+	14.1502i	−1.21072	+	0.525524i
$726$	−8.12237	−	2.89345i	−0.301450	−	0.107386i
$727$	−41.6769			−1.54571			−0.772855	−	0.634583i	$-0.781172\pi$
$727$	−41.6769			−1.54571			−0.772855	+	0.634583i	$0.781172\pi$
$728$	−15.2279	−	25.1666i	−0.564384	−	0.932737i
$729$	11.1268			0.412104
$730$	−13.4367	+	22.9247i	−0.497316	+	0.848480i
$731$	5.69891	+	5.69891i	0.210782	+	0.210782i
$732$	−0.688917	−	0.562169i	−0.0254631	−	0.0207783i
$733$	−13.7235	+	13.7235i	−0.506891	+	0.506891i	−0.913571	−	0.406680i	$-0.866686\pi$
$733$	−13.7235	+	13.7235i	−0.506891	+	0.506891i	0.406680	+	0.913571i	$0.366686\pi$
$734$	−11.7788	+	5.59107i	−0.434762	+	0.206370i
$735$	−11.8346	−	17.3934i	−0.436528	−	0.641564i
$736$	−1.07489	−	1.42838i	−0.0396210	−	0.0526507i
$737$	−1.23030	+	1.23030i	−0.0453187	+	0.0453187i
$738$	−20.3334	−	13.2122i	−0.748483	−	0.486347i
$739$	−50.1918			−1.84633			−0.923167	−	0.384399i	$-0.874409\pi$
$739$	−50.1918			−1.84633			−0.923167	+	0.384399i	$0.874409\pi$
$740$	−12.1660	+	10.2146i	−0.447231	+	0.375495i
$741$	3.62706	−	3.62706i	0.133243	−	0.133243i
$742$	−76.7102	−	27.3266i	−2.81612	−	1.00319i
$743$	−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
$745$	5.64781	−	29.6965i	0.206920	−	1.08800i
$746$	0.129834	+	0.273522i	0.00475356	+	0.0100144i
$747$	4.70618	−	4.70618i	0.172190	−	0.172190i
$748$	0.189425	+	1.86973i	0.00692606	+	0.0683643i
$749$	−9.21380	−	9.21380i	−0.336665	−	0.336665i
$750$	8.90916	+	1.08002i	0.325316	+	0.0394368i
$751$	7.66816	+	7.66816i	0.279815	+	0.279815i	0.833035	−	0.553220i	$-0.186601\pi$
$751$	7.66816	+	7.66816i	0.279815	+	0.279815i	−0.553220	+	0.833035i	$0.686601\pi$
$752$	−45.6429	+	9.34417i	−1.66443	+	0.340747i
$753$			15.5757i			0.567609i
$754$	9.23213	+	19.4494i	0.336214	+	0.708306i
$755$	19.4709	+	3.70305i	0.708617	+	0.134768i
$756$	−19.7861	+	24.2471i	−0.719613	+	0.881860i
$757$	−26.7517			−0.972308			−0.486154	−	0.873873i	$-0.661601\pi$
$757$	−26.7517			−0.972308			−0.486154	+	0.873873i	$0.661601\pi$
$758$	−14.4829	−	5.15929i	−0.526044	−	0.187394i
$759$			0.0911448i			0.00330835i
$760$	−9.30585	−	25.0103i	−0.337559	−	0.907219i
$761$	−21.1004			−0.764888			−0.382444	−	0.923979i	$-0.624917\pi$
$761$	−21.1004			−0.764888			−0.382444	+	0.923979i	$0.624917\pi$
$762$	7.30435	−	3.46718i	0.264609	−	0.125603i
$763$	−19.7043	+	19.7043i	−0.713342	+	0.713342i
$764$	18.4616	−	1.87036i	0.667917	−	0.0676673i
$765$	−9.15436	+	6.22874i	−0.330977	+	0.225201i
$766$	40.1431	+	14.3002i	1.45043	+	0.516689i
$767$	−18.6814			−0.674545
$768$	−3.56879	−	8.35082i	−0.128778	−	0.301334i
$769$		−	18.5520i		−	0.669004i	−0.942395	−	0.334502i	$-0.891432\pi$
$769$		−	18.5520i		−	0.669004i	0.942395	−	0.334502i	$-0.108568\pi$
$770$	6.73135	+	3.94542i	0.242581	+	0.142183i
$771$	16.5101			0.594597
$772$	−27.0263	−	22.0539i	−0.972697	−	0.793738i
$773$			9.26097i			0.333094i	0.986034	+	0.166547i	$0.0532618\pi$
$773$			9.26097i			0.333094i	−0.986034	+	0.166547i	$0.946738\pi$
$774$	−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
$778$	3.44855	+	1.22848i	0.123637	+	0.0440433i
$779$	−14.1536	−	23.0129i	−0.507104	−	0.824523i
$780$	0.472257	−	5.41620i	0.0169095	−	0.193931i
$781$		−	7.17565i		−	0.256765i
$782$	−0.746569	+	0.354377i	−0.0266973	+	0.0126725i
$783$	16.1968	−	16.1968i	0.578825	−	0.578825i
$784$	13.2982	+	64.9568i	0.474935	+	2.31989i
$785$	3.74056	+	5.49749i	0.133506	+	0.196214i
$786$	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	$0.250283\pi$
$788$	1.50774	+	14.8822i	0.0537109	+	0.530158i
$789$		−	10.4380i		−	0.371602i
$790$	−8.69474	+	14.8343i	−0.309345	+	0.527779i
$791$	−40.7169	−	40.7169i	−1.44773	−	1.44773i
$792$	0.919534	−	3.73732i	0.0326742	−	0.132800i
$793$			1.67770i			0.0595770i
$794$	−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	$0.250431\pi$
$798$	−14.8561	+	7.05182i	−0.525901	+	0.249632i
$799$			21.5379i			0.761956i
$800$	−24.5994	−	13.9596i	−0.869720	−	0.493546i
$801$	23.1652	+	23.1652i	0.818501	+	0.818501i
$802$	−17.7598	+	49.8546i	−0.627121	+	1.76043i
$803$	−4.26994			−0.150683
$804$	−3.01145	−	2.45739i	−0.106206	−	0.0866656i
$805$	−0.641038	+	3.37061i	−0.0225936	+	0.118799i
$806$	−0.523451	+	1.46941i	−0.0184378	+	0.0517578i
$807$	−5.62464			−0.197997
$808$	2.16282	−	8.79046i	0.0760876	−	0.309247i
$809$	−10.6798	−	10.6798i	−0.375483	−	0.375483i	0.493986	−	0.869470i	$-0.335539\pi$
$809$	−10.6798	−	10.6798i	−0.375483	−	0.375483i	−0.869470	+	0.493986i	$0.835539\pi$
$810$	18.9843	−	4.95364i	0.667039	−	0.174053i
$811$	9.42901			0.331097			0.165549	−	0.986202i	$-0.447061\pi$
$811$	9.42901			0.331097			0.165549	+	0.986202i	$0.447061\pi$
$812$	−6.95713	−	68.6710i	−0.244147	−	2.40988i
$813$	−11.2082			−0.393089
$814$	−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
$817$		−	18.3898i		−	0.643377i
$818$	−11.0494	+	31.0174i	−0.386333	+	1.08450i
$819$	27.8490			0.973124
$820$	−27.1732	−	9.03434i	−0.948928	−	0.315493i
$821$	−44.6270			−1.55749			−0.778747	−	0.627338i	$-0.784144\pi$
$821$	−44.6270			−1.55749			−0.778747	+	0.627338i	$0.784144\pi$
$822$	3.18294	−	8.93501i	0.111018	−	0.311644i
$823$		−	27.6692i		−	0.964489i	−0.876037	−	0.482244i	$-0.839822\pi$
$823$		−	27.6692i		−	0.964489i	0.876037	−	0.482244i	$-0.160178\pi$
$824$	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
$827$	32.4356			1.12789			0.563947	−	0.825811i	$-0.309282\pi$
$827$	32.4356			1.12789			0.563947	+	0.825811i	$0.309282\pi$
$828$	1.68384	−	0.170592i	0.0585176	−	0.00592848i
$829$	−9.41726			−0.327075			−0.163537	−	0.986537i	$-0.552290\pi$
$829$	−9.41726			−0.327075			−0.163537	+	0.986537i	$0.552290\pi$
$830$	3.97433	−	6.78067i	0.137951	−	0.235361i
$831$	−3.53177	−	3.53177i	−0.122516	−	0.122516i
$832$	−7.95046	+	15.1787i	−0.275633	+	0.526227i
$833$	30.6517			1.06202
$834$	−5.02200	+	14.0975i	−0.173898	+	0.488158i
$835$	31.8740	−	21.6875i	1.10305	−	0.750526i
$836$	2.71109	−	3.32235i	0.0937651	−	0.114906i
$837$	1.65958			0.0573636
$838$	4.83262	−	13.5659i	0.166940	−	0.468627i
$839$	−21.5233	−	21.5233i	−0.743067	−	0.743067i	0.230100	−	0.973167i	$-0.426095\pi$
$839$	−21.5233	−	21.5233i	−0.743067	−	0.743067i	−0.973167	+	0.230100i	$0.926095\pi$
$840$	−7.25325	+	15.8492i	−0.250261	+	0.546851i
$841$			21.5185i			0.742018i
$842$	17.0336	−	8.08539i	0.587015	−	0.278641i
$843$	−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
$847$		−	52.1569i		−	1.79213i
$848$	9.51388	+	46.4719i	0.326708	+	1.59585i
$849$	10.6565	+	10.6565i	0.365729	+	0.365729i
$850$	−8.60307	+	9.84666i	−0.295083	+	0.337738i
$851$		−	1.12251i		−	0.0384792i
$852$	15.9483	−	1.61574i	0.546381	−	0.0553545i
$853$	19.2376	−	19.2376i	0.658683	−	0.658683i	−0.296385	−	0.955068i	$-0.595781\pi$
$853$	19.2376	−	19.2376i	0.658683	−	0.658683i	0.955068	+	0.296385i	$0.0957812\pi$
$854$	1.80495	−	5.06678i	0.0617641	−	0.173382i
$855$	24.8198	+	4.72035i	0.848821	+	0.161432i
$856$	−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	$0.247589\pi$
$858$	0.789239	−	0.374631i	0.0269442	−	0.0127897i
$859$			51.4592i			1.75576i	0.478877	+	0.877882i	$0.341044\pi$
$859$			51.4592i			1.75576i	−0.478877	+	0.877882i	$0.658956\pi$
$860$	−12.5333	−	14.9277i	−0.427383	−	0.509032i
$861$	−4.09177	+	17.1657i	−0.139447	+	0.585005i
$862$	22.4034	+	7.98080i	0.763062	+	0.271827i
$863$	−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
$867$		−	7.70821i		−	0.261785i
$868$	3.16172	−	3.87457i	0.107316	−	0.131512i
$869$	−2.76302			−0.0937291
$870$	6.45097	−	11.0061i	0.218708	−	0.373142i
$871$			7.33371i			0.248493i
$872$	15.7624	+	3.87820i	0.533782	+	0.131332i
$873$	19.7686			0.669064
$874$	1.77632	+	0.632782i	0.0600849	+	0.0214042i
$875$	11.9305	+	52.9591i	0.403324	+	1.79034i
$876$	−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	$0.154059\pi$
$878$	0.380854	−	0.180781i	0.0128532	−	0.00610107i
$879$	11.3376			0.382406
$880$	−0.0635976	−	4.54460i	−0.00214388	−	0.153198i
$881$			15.6246i			0.526408i	0.964740	+	0.263204i	$0.0847792\pi$
$881$			15.6246i			0.526408i	−0.964740	+	0.263204i	$0.915221\pi$
$882$	−59.1340	−	21.0654i	−1.99115	−	0.709309i
$883$	−37.8937			−1.27522			−0.637612	−	0.770357i	$-0.720078\pi$
$883$	−37.8937			−1.27522			−0.637612	+	0.770357i	$0.720078\pi$
$884$	6.13723	+	5.00808i	0.206417	+	0.168440i
$885$	6.22722	+	9.15213i	0.209326	+	0.307645i
$886$	−4.53221	−	9.54805i	−0.152263	−	0.320773i
$887$			33.1260i			1.11226i	0.831094	+	0.556132i	$0.187715\pi$
$887$			33.1260i			1.11226i	−0.831094	+	0.556132i	$0.812285\pi$
$888$	1.36242	−	5.53736i	0.0457198	−	0.185822i
$889$	34.5841	+	34.5841i	1.15991	+	1.15991i
$890$	33.3764	+	19.5628i	1.11878	+	0.655747i
$891$	2.22933	+	2.22933i	0.0746855	+	0.0746855i
$892$	−36.5155	+	3.69943i	−1.22263	+	0.123866i
$893$	34.7503	−	34.7503i	1.16287	−	1.16287i
$894$	4.65325	+	9.80305i	0.155628	+	0.327863i
$895$	−12.4529	−	2.36834i	−0.416253	−	0.0791649i
$896$	40.3409	−	37.2873i	1.34769	−	1.24568i
$897$	0.271653	+	0.271653i	0.00907022	+	0.00907022i
$898$	12.8179	+	4.56616i	0.427740	+	0.152375i
$899$	−2.58816	+	2.58816i	−0.0863200	+	0.0863200i
$900$	23.3644	−	13.0839i	0.778813	−	0.436132i
$901$	21.9291			0.730564
$902$	−0.955538	−	4.50120i	−0.0318159	−	0.149873i
$903$	−8.49350	+	8.49350i	−0.282646	+	0.282646i
$904$	−8.01391	+	32.5714i	−0.266539	+	1.08331i
$905$	51.8235	+	9.85603i	1.72267	+	0.327626i
$906$	−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	$0.294735\pi$
$908$	24.8794	−	30.4888i	0.825653	−	1.01181i
$909$	6.06037	+	6.06037i	0.201010	+	0.201010i
$910$	31.8216	−	8.30333i	1.05488	−	0.275253i
$911$	−2.93195			−0.0971399			−0.0485700	−	0.998820i	$-0.515466\pi$
$911$	−2.93195			−0.0971399			−0.0485700	+	0.998820i	$0.515466\pi$
$912$	7.99459	+	5.27748i	0.264727	+	0.174755i
$913$	1.26297			0.0417981
$914$	26.7484	+	9.52863i	0.884758	+	0.315179i
$915$	0.821918	−	0.559242i	0.0271718	−	0.0184880i
$916$	43.1314	−	4.36969i	1.42510	−	0.144379i
$917$	10.9799			0.362590
$918$	2.82812	−	7.93897i	0.0933417	−	0.262025i
$919$	−0.535197	−	0.535197i	−0.0176545	−	0.0176545i	0.698224	−	0.715879i	$-0.253974\pi$
$919$	−0.535197	−	0.535197i	−0.0176545	−	0.0176545i	−0.715879	+	0.698224i	$0.753974\pi$
$920$	1.87318	−	0.696973i	0.0617568	−	0.0229785i
$921$	−10.3013	−	10.3013i	−0.339441	−	0.339441i
$922$	−8.64006	−	3.07786i	−0.284545	−	0.101364i
$923$	−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
$928$	−32.1265	+	24.1760i	−1.05460	+	0.793617i
$929$	16.9530	−	16.9530i	0.556209	−	0.556209i	−0.372017	−	0.928226i	$-0.621334\pi$
$929$	16.9530	−	16.9530i	0.556209	−	0.556209i	0.928226	+	0.372017i	$0.121334\pi$
$930$	0.894360	−	0.233369i	0.0293272	−	0.00765246i
$931$	−49.4550	−	49.4550i	−1.62082	−	1.62082i
$932$	42.1499	+	34.3951i	1.38067	+	1.12665i
$933$	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
$937$	26.6009			0.869014			0.434507	−	0.900668i	$-0.356923\pi$
$937$	26.6009			0.869014			0.434507	+	0.900668i	$0.356923\pi$
$938$	7.88994	−	22.1483i	0.257616	−	0.723168i
$939$	4.77079			0.155689
$940$	4.52462	−	51.8919i	0.147577	−	1.69253i
$941$			28.9881i			0.944984i	0.881335	+	0.472492i	$0.156645\pi$
$941$			28.9881i			0.944984i	−0.881335	+	0.472492i	$0.843355\pi$
$942$	−2.24855	−	0.801005i	−0.0732617	−	0.0260982i
$943$	1.72358	−	1.06005i	0.0561274	−	0.0345199i
$944$	−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	0.777801	−	0.628510i	$-0.216335\pi$
$947$	4.59420	+	4.59420i	0.149291	+	0.149291i	−0.628510	+	0.777801i	$0.716335\pi$
$948$	−0.622151	−	6.14099i	−0.0202065	−	0.199450i
$949$	−12.7264	+	12.7264i	−0.413115	+	0.413115i
$950$	29.7677	−	2.00647i	0.965792	−	0.0650985i
$951$	1.73680			0.0563197
$952$	−13.1469	−	21.7275i	−0.426095	−	0.704192i
$953$	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
$955$	−3.87615	+	20.3810i	−0.125429	+	0.659514i
$956$	−23.5590	+	2.38679i	−0.761952	+	0.0771942i
$957$	2.04999			0.0662669
$958$	51.9580	−	24.6631i	1.67869	−	0.796829i
$959$	57.3752			1.85274
$960$	10.0863	−	1.16466i	0.325535	−	0.0375892i
$961$	30.7348			0.991445
$962$	−9.72002	+	4.61384i	−0.313386	+	0.148756i
$963$	−5.08146	−	5.08146i	−0.163748	−	0.163748i
$964$	7.84146	−	9.60943i	0.252557	−	0.309499i
$965$	32.2439	−	21.9391i	1.03797	−	0.706245i
$966$	−0.528154	−	1.11267i	−0.0169931	−	0.0357995i
$967$			7.03137i			0.226113i	0.993589	+	0.113057i	$0.0360642\pi$
$967$			7.03137i			0.226113i	−0.993589	+	0.113057i	$0.963936\pi$
$968$	−25.9942	+	15.7286i	−0.835484	+	0.505538i
$969$	3.13140	−	3.13140i	0.100595	−	0.100595i
$970$	22.5885	−	5.89409i	0.725272	−	0.189248i
$971$	28.4240	+	28.4240i	0.912170	+	0.912170i	0.996443	−	0.0842723i	$-0.0268566\pi$
$971$	28.4240	+	28.4240i	0.912170	+	0.912170i	−0.0842723	+	0.996443i	$0.526857\pi$
$972$	−16.6778	+	20.4380i	−0.534940	+	0.655550i
$973$	−90.5258			−2.90212
$974$	−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
$977$			15.7364i			0.503451i	0.967799	+	0.251726i	$0.0809980\pi$
$977$			15.7364i			0.503451i	−0.967799	+	0.251726i	$0.919002\pi$
$978$	−3.24003	−	6.82581i	−0.103605	−	0.218265i
$979$			6.21668i			0.198686i
$980$	−73.8500	−	6.43923i	−2.35905	−	0.205694i
$981$	−10.8670	+	10.8670i	−0.346957	+	0.346957i
$982$	−18.4200	+	51.7078i	−0.587805	+	1.65006i
$983$	28.5867	−	28.5867i	0.911773	−	0.911773i	−0.0846389	−	0.996412i	$-0.526974\pi$
$983$	28.5867	−	28.5867i	0.911773	−	0.911773i	0.996412	+	0.0846389i	$0.0269737\pi$
$984$	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
$987$	−32.0995			−1.02174
$988$	−1.82181	−	17.9824i	−0.0579597	−	0.572096i
$989$	1.37733			0.0437964
$990$	3.71237	+	2.17592i	0.117987	+	0.0691553i
$991$	2.71197	+	2.71197i	0.0861487	+	0.0861487i	0.748868	−	0.662719i	$-0.230598\pi$
$991$	2.71197	+	2.71197i	0.0861487	+	0.0861487i	−0.662719	+	0.748868i	$0.730598\pi$
$992$	−2.88449	−	0.407319i	−0.0915826	−	0.0129324i
$993$	−11.8532	+	11.8532i	−0.376149	+	0.376149i
$994$	41.5805	+	87.5981i	1.31885	+	2.77844i
$995$	6.62118	+	1.25925i	0.209906	+	0.0399208i
$996$	0.284382	+	2.80702i	0.00901100	+	0.0889439i
$997$			16.3556i			0.517986i	0.965879	+	0.258993i	$0.0833907\pi$
$997$			16.3556i			0.517986i	−0.965879	+	0.258993i	$0.916609\pi$
$998$	−37.2435	+	17.6785i	−1.17892	+	0.559604i
$999$	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.j.c.483.16	✓	240
4.3	odd	2	inner	820.2.j.c.483.47	yes	240
5.2	odd	4		820.2.s.c.647.74	yes	240
20.7	even	4		820.2.s.c.647.105	yes	240
41.9	even	4		820.2.s.c.583.105	yes	240
164.91	odd	4		820.2.s.c.583.74	yes	240
205.132	odd	4	inner	820.2.j.c.747.47	yes	240
820.747	even	4	inner	820.2.j.c.747.16	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.16	✓	240	1.1	even	1	trivial
820.2.j.c.483.47	yes	240	4.3	odd	2	inner
820.2.j.c.747.16	yes	240	820.747	even	4	inner
820.2.j.c.747.47	yes	240	205.132	odd	4	inner
820.2.s.c.583.74	yes	240	164.91	odd	4
820.2.s.c.583.105	yes	240	41.9	even	4
820.2.s.c.647.74	yes	240	5.2	odd	4
820.2.s.c.647.105	yes	240	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.33221 - 0.474575i) q^{2} +0.567590i q^{3} +(1.54956 + 1.26447i) q^{4} +(-1.84871 + 1.25788i) q^{5} +(0.269364 - 0.756148i) q^{6} +4.85551 q^{7} +(-1.46425 - 2.41991i) q^{8} +2.67784 q^{9} +(3.05983 - 0.798412i) q^{10} +(0.359317 + 0.359317i) q^{11} +(-0.717698 + 0.879513i) q^{12} +2.14186 q^{13} +(-6.46856 - 2.30431i) q^{14} +(-0.713962 - 1.04931i) q^{15} +(0.802254 + 3.91872i) q^{16} +1.84916 q^{17} +(-3.56744 - 1.27084i) q^{18} +(-2.98352 - 2.98352i) q^{19} +(-4.45523 - 0.388467i) q^{20} +2.75594i q^{21} +(-0.308162 - 0.649208i) 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} +3.22268i q^{27} +(7.52390 + 6.13963i) q^{28} +(-5.02586 - 5.02586i) q^{29} +(0.453170 + 1.73673i) q^{30} -0.514969i q^{31} +(0.790958 - 5.60128i) q^{32} +(-0.203945 + 0.203945i) q^{33} +(-2.46347 - 0.877565i) q^{34} +(-8.97644 + 6.10767i) q^{35} +(4.14947 + 3.38604i) q^{36} +(2.51172 - 2.51172i) q^{37} +(2.55877 + 5.39058i) q^{38} +1.21569i q^{39} +(5.75094 + 2.63186i) q^{40} +(6.22861 + 1.48471i) q^{41} +(1.30790 - 3.67149i) 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} +11.6474i q^{47} +(-2.22423 + 0.455351i) q^{48} +16.5760 q^{49} +(-4.65242 + 5.32494i) q^{50} +1.04956i q^{51} +(3.31893 + 2.70830i) q^{52} +11.8589 q^{53} +(1.52941 - 4.29329i) q^{54} +(-1.11625 - 0.212294i) q^{55} +(-7.10968 - 11.7499i) q^{56} +(1.69342 - 1.69342i) q^{57} +(4.31034 + 9.08064i) q^{58} -8.72205 q^{59} +(0.220490 - 2.52874i) q^{60} +0.783294i q^{61} +(-0.244391 + 0.686046i) q^{62} +13.0023 q^{63} +(-3.71195 + 7.08671i) q^{64} +(-3.95967 + 2.69421i) q^{65} +(0.368484 - 0.174910i) q^{66} +3.42400i q^{67} +(2.86538 + 2.33820i) q^{68} +(0.126831 + 0.126831i) q^{69} +(14.8570 - 3.87670i) q^{70} +(-9.98512 - 9.98512i) q^{71} +(-3.92103 - 6.48014i) q^{72} +(-5.94174 + 5.94174i) q^{73} +(-4.53813 + 2.15413i) q^{74} +(2.63982 + 1.04179i) q^{75} +(-0.850578 - 8.39571i) q^{76} +(1.74467 + 1.74467i) q^{77} +(0.576938 - 1.61956i) q^{78} +(-3.84482 + 3.84482i) q^{79} +(-6.41243 - 6.23544i) q^{80} +6.20436 q^{81} +(-7.59320 - 4.93389i) q^{82} +(1.75745 - 1.75745i) q^{83} +(-3.48479 + 4.27049i) q^{84} +(-3.41856 + 2.32603i) q^{85} +(-2.64313 - 5.56831i) q^{86} +(2.85263 - 2.85263i) q^{87} +(0.343386 - 1.39565i) q^{88} +(8.65069 + 8.65069i) q^{89} +(8.19373 - 2.13802i) q^{90} +10.3998 q^{91} +(0.628806 - 0.0637051i) q^{92} +0.292291 q^{93} +(5.52756 - 15.5168i) q^{94} +(9.26860 + 1.76274i) q^{95} +(3.17923 + 0.448940i) q^{96} +7.38227 q^{97} +(-22.0827 - 7.86656i) q^{98} +(0.962194 + 0.962194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} + 12 q^{8} - 240 q^{9} - 20 q^{10} - 32 q^{13} - 8 q^{14} + 8 q^{16} + 32 q^{17} - 12 q^{18} + 16 q^{20} - 28 q^{22} + 12 q^{24} - 16 q^{25} - 8 q^{28} - 10 q^{30} + 24 q^{33} - 20 q^{34}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 + 12 * q^8 - 240 * q^9 - 20 * q^10 - 32 * q^13 - 8 * q^14 + 8 * q^16 + 32 * q^17 - 12 * q^18 + 16 * q^20 - 28 * q^22 + 12 * q^24 - 16 * q^25 - 8 * q^28 - 10 * q^30 + 24 * q^33 - 20 * q^34 - 8 * q^37 + 16 * q^38 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 + 8 * q^48 + 224 * q^49 - 12 * q^50 - 32 * q^53 + 48 * q^54 + 24 * q^56 - 8 * q^57 + 6 * q^60 - 8 * q^65 - 8 * q^66 + 16 * q^69 + 10 * q^70 - 96 * q^72 - 72 * q^73 + 112 * q^74 + 20 * q^76 - 56 * q^77 + 4 * q^78 + 60 * q^80 + 48 * q^81 - 56 * q^82 - 32 * q^84 - 32 * q^85 - 8 * q^86 - 64 * q^89 + 76 * q^90 + 20 * q^92 - 16 * q^93 + 48 * q^94 + 24 * q^96 - 48 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

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