LMFDB - Embedded newform 820.2.k.c.247.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(83,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			247.1
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 0.00282635i) q^{2} +(1.90181 + 1.90181i) q^{3} +(1.99998 + 0.00799412i) q^{4} +(-1.72661 - 1.42085i) q^{5} +(-2.68419 - 2.69494i) q^{6} +(-0.433364 + 0.433364i) q^{7} +(-2.82838 - 0.0169580i) q^{8} +4.23379i q^{9} +(2.43777 + 2.01427i) q^{10} +1.58829i q^{11} +(3.78839 + 3.81880i) q^{12} +(-4.00751 + 4.00751i) q^{13} +(0.614093 - 0.611643i) q^{14} +(-0.581488 - 5.98588i) q^{15} +(3.99987 + 0.0319762i) q^{16} +(-3.50563 - 3.50563i) q^{17} +(0.0119662 - 5.98747i) q^{18} -1.87220 q^{19} +(-3.44183 - 2.85549i) q^{20} -1.64836 q^{21} +(0.00448907 - 2.24618i) q^{22} +(-3.13069 - 3.13069i) q^{23} +(-5.34679 - 5.41129i) q^{24} +(0.962351 + 4.90651i) q^{25} +(5.67879 - 5.65614i) q^{26} +(-2.34643 + 2.34643i) q^{27} +(-0.870186 + 0.863257i) q^{28} +6.86286i q^{29} +(0.805429 + 8.46694i) q^{30} +6.19687i q^{31} +(-5.65657 - 0.0565262i) q^{32} +(-3.02063 + 3.02063i) q^{33} +(4.94780 + 4.96761i) q^{34} +(1.36400 - 0.132503i) q^{35} +(-0.0338454 + 8.46751i) q^{36} +(-6.53361 - 6.53361i) q^{37} +(2.64769 + 0.00529150i) q^{38} -15.2431 q^{39} +(4.85940 + 4.04799i) q^{40} +1.00000 q^{41} +(2.33112 + 0.00465883i) q^{42} +(4.69005 + 4.69005i) q^{43} +(-0.0126970 + 3.17655i) q^{44} +(6.01559 - 7.31009i) q^{45} +(4.41861 + 4.43630i) q^{46} +(-8.48312 + 8.48312i) q^{47} +(7.54620 + 7.66782i) q^{48} +6.62439i q^{49} +(-1.34710 - 6.94156i) q^{50} -13.3341i q^{51} +(-8.04699 + 7.98292i) q^{52} +(6.25014 - 6.25014i) q^{53} +(3.32498 - 3.31172i) q^{54} +(2.25673 - 2.74235i) q^{55} +(1.23307 - 1.21837i) q^{56} +(-3.56057 - 3.56057i) q^{57} +(0.0193969 - 9.70554i) q^{58} +0.968941 q^{59} +(-1.11512 - 11.9763i) q^{60} -1.70966 q^{61} +(0.0175145 - 8.76368i) q^{62} +(-1.83477 - 1.83477i) q^{63} +(7.99942 + 0.0959274i) q^{64} +(12.6135 - 1.22532i) q^{65} +(4.28035 - 4.26327i) q^{66} +(6.08078 - 6.08078i) q^{67} +(-6.98319 - 7.03923i) q^{68} -11.9080i q^{69} +(-1.92935 + 0.183532i) q^{70} -11.5429i q^{71} +(0.0717967 - 11.9747i) q^{72} +(-8.09127 + 8.09127i) q^{73} +(9.22144 + 9.25837i) q^{74} +(-7.50106 + 11.1615i) q^{75} +(-3.74437 - 0.0149666i) q^{76} +(-0.688308 - 0.688308i) q^{77} +(21.5569 + 0.0430823i) q^{78} -5.72448 q^{79} +(-6.86078 - 5.73844i) q^{80} +3.77641 q^{81} +(-1.41421 - 0.00282635i) q^{82} +(-2.17584 - 2.17584i) q^{83} +(-3.29668 - 0.0131771i) q^{84} +(1.07186 + 11.0338i) q^{85} +(-6.61946 - 6.64597i) q^{86} +(-13.0519 + 13.0519i) q^{87} +(0.0269343 - 4.49228i) q^{88} +2.68831i q^{89} +(-8.52797 + 10.3210i) q^{90} -3.47342i q^{91} +(-6.23630 - 6.28636i) q^{92} +(-11.7853 + 11.7853i) q^{93} +(12.0209 - 11.9729i) q^{94} +(3.23256 + 2.66012i) q^{95} +(-10.6502 - 10.8652i) q^{96} +(0.544305 + 0.544305i) q^{97} +(0.0187229 - 9.36828i) q^{98} -6.72448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) $ 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41421	−	0.00282635i	−0.999998	−	0.00199853i
$2$	−1.41421	−	0.00282635i	−0.999998	−	0.00199853i
$3$	1.90181	+	1.90181i	1.09801	+	1.09801i	0.994643	+	0.103369i	$0.0329624\pi$
$3$	1.90181	+	1.90181i	1.09801	+	1.09801i	0.103369	+	0.994643i	$0.467038\pi$
$4$	1.99998	+	0.00799412i	0.999992	+	0.00399706i
$5$	−1.72661	−	1.42085i	−0.772163	−	0.635425i
$5$	−1.72661	−	1.42085i	−0.772163	−	0.635425i
$6$	−2.68419	−	2.69494i	−1.09582	−	1.10020i
$7$	−0.433364	+	0.433364i	−0.163796	+	0.163796i	−0.784246	−	0.620450i	$-0.786950\pi$
$7$	−0.433364	+	0.433364i	−0.163796	+	0.163796i	0.620450	+	0.784246i	$0.286950\pi$
$8$	−2.82838	−	0.0169580i	−0.999982	−	0.00599557i
$9$			4.23379i			1.41126i
$10$	2.43777	+	2.01427i	0.770891	+	0.636967i
$11$			1.58829i			0.478887i	0.970910	+	0.239444i	$0.0769651\pi$
$11$			1.58829i			0.478887i	−0.970910	+	0.239444i	$0.923035\pi$
$12$	3.78839	+	3.81880i	1.09361	+	1.10239i
$13$	−4.00751	+	4.00751i	−1.11148	+	1.11148i	−0.118533	+	0.992950i	$0.537819\pi$
$13$	−4.00751	+	4.00751i	−1.11148	+	1.11148i	−0.992950	+	0.118533i	$0.962181\pi$
$14$	0.614093	−	0.611643i	0.164123	−	0.163469i
$15$	−0.581488	−	5.98588i	−0.150140	−	1.54555i
$16$	3.99987	+	0.0319762i	0.999968	+	0.00799405i
$17$	−3.50563	−	3.50563i	−0.850241	−	0.850241i	0.139922	−	0.990163i	$-0.455315\pi$
$17$	−3.50563	−	3.50563i	−0.850241	−	0.850241i	−0.990163	+	0.139922i	$0.955315\pi$
$18$	0.0119662	−	5.98747i	0.00282045	−	1.41126i
$19$	−1.87220			−0.429512			−0.214756	−	0.976668i	$-0.568896\pi$
$19$	−1.87220			−0.429512			−0.214756	+	0.976668i	$0.568896\pi$
$20$	−3.44183	−	2.85549i	−0.769617	−	0.638506i
$21$	−1.64836			−0.359701
$22$	0.00448907	−	2.24618i	0.000957072	−	0.478886i
$23$	−3.13069	−	3.13069i	−0.652794	−	0.652794i	0.300871	−	0.953665i	$-0.402723\pi$
$23$	−3.13069	−	3.13069i	−0.652794	−	0.652794i	−0.953665	+	0.300871i	$0.902723\pi$
$24$	−5.34679	−	5.41129i	−1.09141	−	1.10458i
$25$	0.962351	+	4.90651i	0.192470	+	0.981303i
$26$	5.67879	−	5.65614i	1.11370	−	1.10926i
$27$	−2.34643	+	2.34643i	−0.451571	+	0.451571i
$28$	−0.870186	+	0.863257i	−0.164450	+	0.163140i
$29$			6.86286i			1.27440i	0.770698	+	0.637201i	$0.219908\pi$
$29$			6.86286i			1.27440i	−0.770698	+	0.637201i	$0.780092\pi$
$30$	0.805429	+	8.46694i	0.147051	+	1.54585i
$31$			6.19687i			1.11299i	0.830851	+	0.556495i	$0.187854\pi$
$31$			6.19687i			1.11299i	−0.830851	+	0.556495i	$0.812146\pi$
$32$	−5.65657	−	0.0565262i	−0.999950	−	0.00999251i
$33$	−3.02063	+	3.02063i	−0.525824	+	0.525824i
$34$	4.94780	+	4.96761i	0.848540	+	0.851938i
$35$	1.36400	−	0.132503i	0.230558	−	0.0223971i
$36$	−0.0338454	+	8.46751i	−0.00564090	+	1.41125i
$37$	−6.53361	−	6.53361i	−1.07412	−	1.07412i	−0.997024	−	0.0770954i	$-0.975435\pi$
$37$	−6.53361	−	6.53361i	−1.07412	−	1.07412i	−0.0770954	−	0.997024i	$-0.524565\pi$
$38$	2.64769	+	0.00529150i	0.429511	+	0.000858394i
$39$	−15.2431			−2.44084
$40$	4.85940	+	4.04799i	0.768339	+	0.640043i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	2.33112	+	0.00465883i	0.359700	+	0.000718874i
$43$	4.69005	+	4.69005i	0.715225	+	0.715225i	0.967623	−	0.252398i	$-0.0812192\pi$
$43$	4.69005	+	4.69005i	0.715225	+	0.715225i	−0.252398	+	0.967623i	$0.581219\pi$
$44$	−0.0126970	+	3.17655i	−0.00191414	+	0.478884i
$45$	6.01559	−	7.31009i	0.896751	−	1.08972i
$46$	4.41861	+	4.43630i	0.651488	+	0.654097i
$47$	−8.48312	+	8.48312i	−1.23739	+	1.23739i	−0.276326	+	0.961064i	$0.589117\pi$
$47$	−8.48312	+	8.48312i	−1.23739	+	1.23739i	−0.961064	+	0.276326i	$0.910883\pi$
$48$	7.54620	+	7.66782i	1.08920	+	1.10675i
$49$			6.62439i			0.946342i
$50$	−1.34710	−	6.94156i	−0.190509	−	0.981686i
$51$		−	13.3341i		−	1.86715i
$52$	−8.04699	+	7.98292i	−1.11592	+	1.10703i
$53$	6.25014	−	6.25014i	0.858522	−	0.858522i	−0.132642	−	0.991164i	$-0.542346\pi$
$53$	6.25014	−	6.25014i	0.858522	−	0.858522i	0.991164	+	0.132642i	$0.0423459\pi$
$54$	3.32498	−	3.31172i	0.452473	−	0.450668i
$55$	2.25673	−	2.74235i	0.304297	−	0.369779i
$56$	1.23307	−	1.21837i	0.164775	−	0.162811i
$57$	−3.56057	−	3.56057i	−0.471610	−	0.471610i
$58$	0.0193969	−	9.70554i	0.00254693	−	1.27440i
$59$	0.968941			0.126145			0.0630727	−	0.998009i	$-0.479910\pi$
$59$	0.968941			0.126145			0.0630727	+	0.998009i	$0.479910\pi$
$60$	−1.11512	−	11.9763i	−0.143961	−	1.54614i
$61$	−1.70966			−0.218899			−0.109450	−	0.993992i	$-0.534909\pi$
$61$	−1.70966			−0.218899			−0.109450	+	0.993992i	$0.534909\pi$
$62$	0.0175145	−	8.76368i	0.00222435	−	1.11299i
$63$	−1.83477	−	1.83477i	−0.231160	−	0.231160i
$64$	7.99942	+	0.0959274i	0.999928	+	0.0119909i
$65$	12.6135	−	1.22532i	1.56451	−	0.151982i
$66$	4.28035	−	4.26327i	0.526874	−	0.524772i
$67$	6.08078	−	6.08078i	0.742885	−	0.742885i	−0.230247	−	0.973132i	$-0.573953\pi$
$67$	6.08078	−	6.08078i	0.742885	−	0.742885i	0.973132	+	0.230247i	$0.0739534\pi$
$68$	−6.98319	−	7.03923i	−0.846836	−	0.853633i
$69$		−	11.9080i		−	1.43355i
$70$	−1.92935	+	0.183532i	−0.230602	+	0.0219363i
$71$		−	11.5429i		−	1.36989i	−0.728595	−	0.684945i	$-0.759826\pi$
$71$		−	11.5429i		−	1.36989i	0.728595	−	0.684945i	$-0.240174\pi$
$72$	0.0717967	−	11.9747i	0.00846132	−	1.41124i
$73$	−8.09127	+	8.09127i	−0.947011	+	0.947011i	−0.998665	−	0.0516537i	$-0.983551\pi$
$73$	−8.09127	+	8.09127i	−0.947011	+	0.947011i	0.0516537	+	0.998665i	$0.483551\pi$
$74$	9.22144	+	9.25837i	1.07197	+	1.07626i
$75$	−7.50106	+	11.1615i	−0.866148	+	1.28882i
$76$	−3.74437	−	0.0149666i	−0.429509	−	0.00171678i
$77$	−0.688308	−	0.688308i	−0.0784400	−	0.0784400i
$78$	21.5569	+	0.0430823i	2.44084	+	0.00487811i
$79$	−5.72448			−0.644054			−0.322027	−	0.946730i	$-0.604364\pi$
$79$	−5.72448			−0.644054			−0.322027	+	0.946730i	$0.604364\pi$
$80$	−6.86078	−	5.73844i	−0.767058	−	0.641577i
$81$	3.77641			0.419601
$82$	−1.41421	−	0.00282635i	−0.156173	−	0.000312118i
$83$	−2.17584	−	2.17584i	−0.238830	−	0.238830i	0.577536	−	0.816366i	$-0.304014\pi$
$83$	−2.17584	−	2.17584i	−0.238830	−	0.238830i	−0.816366	+	0.577536i	$0.804014\pi$
$84$	−3.29668	−	0.0131771i	−0.359698	−	0.00143774i
$85$	1.07186	+	11.0338i	0.116260	+	1.19679i
$86$	−6.61946	−	6.64597i	−0.713795	−	0.716653i
$87$	−13.0519	+	13.0519i	−1.39931	+	1.39931i
$88$	0.0269343	−	4.49228i	0.00287120	−	0.478879i
$89$			2.68831i			0.284960i	0.989798	+	0.142480i	$0.0455077\pi$
$89$			2.68831i			0.284960i	−0.989798	+	0.142480i	$0.954492\pi$
$90$	−8.52797	+	10.3210i	−0.898927	+	1.08793i
$91$		−	3.47342i		−	0.364114i
$92$	−6.23630	−	6.28636i	−0.650179	−	0.655398i
$93$	−11.7853	+	11.7853i	−1.22208	+	1.22208i
$94$	12.0209	−	11.9729i	1.23986	−	1.23491i
$95$	3.23256	+	2.66012i	0.331653	+	0.272923i
$96$	−10.6502	−	10.8652i	−1.08699	−	1.10893i
$97$	0.544305	+	0.544305i	0.0552658	+	0.0552658i	0.734200	−	0.678934i	$-0.237558\pi$
$97$	0.544305	+	0.544305i	0.0552658	+	0.0552658i	−0.678934	+	0.734200i	$0.737558\pi$
$98$	0.0187229	−	9.36828i	0.00189130	−	0.946340i
$99$	−6.72448			−0.675836
$100$	1.88546	+	9.82064i	0.188546	+	0.982064i
$101$	2.43475			0.242267			0.121133	−	0.992636i	$-0.461347\pi$
$101$	2.43475			0.242267			0.121133	+	0.992636i	$0.461347\pi$
$102$	−0.0376869	+	18.8573i	−0.00373156	+	1.86715i
$103$	−3.50467	−	3.50467i	−0.345326	−	0.345326i	0.513039	−	0.858365i	$-0.328519\pi$
$103$	−3.50467	−	3.50467i	−0.345326	−	0.345326i	−0.858365	+	0.513039i	$0.828519\pi$
$104$	11.4027	−	11.2668i	1.11813	−	1.10480i
$105$	2.84606	+	2.34207i	0.277747	+	0.228563i
$106$	−8.85668	+	8.82135i	−0.860237	+	0.856805i
$107$	6.23144	−	6.23144i	0.602416	−	0.602416i	−0.338537	−	0.940953i	$-0.609932\pi$
$107$	6.23144	−	6.23144i	0.602416	−	0.602416i	0.940953	+	0.338537i	$0.109932\pi$
$108$	−4.71159	+	4.67407i	−0.453372	+	0.449763i
$109$			17.6354i			1.68916i	0.535426	+	0.844582i	$0.320151\pi$
$109$			17.6354i			1.68916i	−0.535426	+	0.844582i	$0.679849\pi$
$110$	−3.19924	+	3.87189i	−0.305035	+	0.369170i
$111$		−	24.8514i		−	2.35879i
$112$	−1.74726	+	1.71954i	−0.165100	+	0.162482i
$113$	−10.3543	+	10.3543i	−0.974051	+	0.974051i	−0.999672	−	0.0256206i	$-0.991844\pi$
$113$	−10.3543	+	10.3543i	−0.974051	+	0.974051i	0.0256206	+	0.999672i	$0.491844\pi$
$114$	5.02534	+	5.04547i	0.470666	+	0.472551i
$115$	0.957223	+	9.85372i	0.0892615	+	0.918864i
$116$	−0.0548625	+	13.7256i	−0.00509386	+	1.27439i
$117$	−16.9669	−	16.9669i	−1.56859	−	1.56859i
$118$	−1.37029	−	0.00273857i	−0.126145	−	0.000252106i
$119$	3.03843			0.278533
$120$	1.54316	+	16.9402i	0.140871	+	1.54642i
$121$	8.47734			0.770667
$122$	2.41782	+	0.00483210i	0.218899	+	0.000437478i
$123$	1.90181	+	1.90181i	0.171481	+	0.171481i
$124$	−0.0495385	+	12.3936i	−0.00444869	+	1.11298i
$125$	5.30983	−	9.83899i	0.474926	−	0.880026i
$126$	2.58957	+	2.59994i	0.230697	+	0.231621i
$127$	7.06262	−	7.06262i	0.626706	−	0.626706i	−0.320531	−	0.947238i	$-0.603861\pi$
$127$	7.06262	−	7.06262i	0.626706	−	0.626706i	0.947238	+	0.320531i	$0.103861\pi$
$128$	−11.3126	−	0.158271i	−0.999902	−	0.0139893i
$129$			17.8392i			1.57065i
$130$	−17.8416	+	1.69720i	−1.56481	+	0.148855i
$131$			1.41883i			0.123963i	0.998077	+	0.0619817i	$0.0197421\pi$
$131$			1.41883i			0.123963i	−0.998077	+	0.0619817i	$0.980258\pi$
$132$	−6.06536	+	6.01707i	−0.527922	+	0.523718i
$133$	0.811344	−	0.811344i	0.0703525	−	0.0703525i
$134$	−8.61669	+	8.58232i	−0.744369	+	0.741399i
$135$	7.38531	−	0.717433i	0.635626	−	0.0617468i
$136$	9.85580	+	9.97470i	0.845128	+	0.855323i
$137$	8.96763	+	8.96763i	0.766157	+	0.766157i	0.977428	−	0.211271i	$-0.0677602\pi$
$137$	8.96763	+	8.96763i	0.766157	+	0.766157i	−0.211271	+	0.977428i	$0.567760\pi$
$138$	−0.0336561	+	16.8404i	−0.00286500	+	1.43355i
$139$	−0.876610			−0.0743531			−0.0371765	−	0.999309i	$-0.511836\pi$
$139$	−0.876610			−0.0743531			−0.0371765	+	0.999309i	$0.511836\pi$
$140$	2.72903	−	0.254100i	0.230645	−	0.0214754i
$141$	−32.2666			−2.71734
$142$	−0.0326243	+	16.3241i	−0.00273777	+	1.36989i
$143$	−6.36509	−	6.36509i	−0.532275	−	0.532275i
$144$	−0.135380	+	16.9346i	−0.0112817	+	1.41122i
$145$	9.75112	−	11.8495i	0.809787	−	0.984046i
$146$	11.4656	−	11.4199i	0.948902	−	0.945117i
$147$	−12.5984	+	12.5984i	−1.03909	+	1.03909i
$148$	−13.0149	−	13.1193i	−1.06982	−	1.07840i
$149$		−	16.0098i		−	1.31158i	−0.754945	−	0.655788i	$-0.772336\pi$
$149$		−	16.0098i		−	1.31158i	0.754945	−	0.655788i	$-0.227664\pi$
$150$	10.6396	−	15.7635i	0.868722	−	1.28708i
$151$		−	17.3881i		−	1.41502i	−0.706703	−	0.707510i	$-0.749818\pi$
$151$		−	17.3881i		−	1.41502i	0.706703	−	0.707510i	$-0.250182\pi$
$152$	5.29529	+	0.0317488i	0.429504	+	0.00257517i
$153$	14.8421	−	14.8421i	1.19991	−	1.19991i
$154$	0.971467	+	0.975358i	0.0782830	+	0.0785966i
$155$	8.80484	−	10.6996i	0.707222	−	0.859410i
$156$	−30.4859	−	0.121855i	−2.44083	−	0.00975620i
$157$	8.82808	+	8.82808i	0.704558	+	0.704558i	0.965385	−	0.260828i	$-0.0839954\pi$
$157$	8.82808	+	8.82808i	0.704558	+	0.704558i	−0.260828	+	0.965385i	$0.583995\pi$
$158$	8.09562	+	0.0161794i	0.644053	+	0.00128716i
$159$	23.7732			1.88534
$160$	9.68637	+	8.13476i	0.765775	+	0.643109i
$161$	2.71346			0.213850
$162$	−5.34064	−	0.0106735i	−0.419600	−	0.000838586i
$163$	10.1125	+	10.1125i	0.792075	+	0.792075i	0.981831	−	0.189756i	$-0.0607696\pi$
$163$	10.1125	+	10.1125i	0.792075	+	0.792075i	−0.189756	+	0.981831i	$0.560770\pi$
$164$	1.99998	+	0.00799412i	0.156173	+	0.000624236i
$165$	9.50732	−	0.923572i	0.740144	−	0.0719000i
$166$	3.07095	+	3.08325i	0.238352	+	0.239307i
$167$	−9.21999	+	9.21999i	−0.713464	+	0.713464i	−0.967258	−	0.253794i	$-0.918321\pi$
$167$	−9.21999	+	9.21999i	−0.713464	+	0.713464i	0.253794	+	0.967258i	$0.418321\pi$
$168$	4.66217	+	0.0279529i	0.359694	+	0.00215661i
$169$		−	19.1203i		−	1.47079i
$170$	−1.48466	−	15.6072i	−0.113868	−	1.19702i
$171$		−	7.92650i		−	0.606154i
$172$	9.34253	+	9.41751i	0.712361	+	0.718079i
$173$	−4.24416	+	4.24416i	−0.322677	+	0.322677i	−0.849793	−	0.527116i	$-0.823273\pi$
$173$	−4.24416	+	4.24416i	−0.322677	+	0.322677i	0.527116	+	0.849793i	$0.323273\pi$
$174$	18.4950	−	18.4212i	1.40210	−	1.39651i
$175$	−2.54336	−	1.70926i	−0.192260	−	0.129208i
$176$	−0.0507875	+	6.35296i	−0.00382825	+	0.478872i
$177$	1.84274	+	1.84274i	0.138509	+	0.138509i
$178$	0.00759811	−	3.80183i	0.000569502	−	0.284960i
$179$	7.98914			0.597137			0.298568	−	0.954388i	$-0.403491\pi$
$179$	7.98914			0.597137			0.298568	+	0.954388i	$0.403491\pi$
$180$	12.0895	−	14.5720i	0.901100	−	1.08613i
$181$	−14.1777			−1.05382			−0.526909	−	0.849922i	$-0.676649\pi$
$181$	−14.1777			−1.05382			−0.526909	+	0.849922i	$0.676649\pi$
$182$	−0.00981712	+	4.91215i	−0.000727693	+	0.364113i
$183$	−3.25145	−	3.25145i	−0.240354	−	0.240354i
$184$	8.80168	+	8.90786i	0.648868	+	0.656696i
$185$	1.99768	+	20.5643i	0.146873	+	1.51192i
$186$	16.7002	−	16.6336i	1.22452	−	1.21963i
$187$	5.56796	−	5.56796i	0.407170	−	0.407170i
$188$	−17.0339	+	16.8983i	−1.24233	+	1.23243i
$189$		−	2.03372i		−	0.147931i
$190$	−4.56400	−	3.77111i	−0.331107	−	0.273585i
$191$		−	3.45212i		−	0.249786i	−0.992170	−	0.124893i	$-0.960141\pi$
$191$		−	3.45212i		−	0.249786i	0.992170	−	0.124893i	$-0.0398588\pi$
$192$	15.0310	+	15.3958i	1.08477	+	1.11110i
$193$	−0.935101	+	0.935101i	−0.0673100	+	0.0673100i	−0.739960	−	0.672650i	$-0.765156\pi$
$193$	−0.935101	+	0.935101i	−0.0673100	+	0.0673100i	0.672650	+	0.739960i	$0.265156\pi$
$194$	−0.768224	−	0.771300i	−0.0551552	−	0.0553761i
$195$	26.3188	+	21.6582i	1.88473	+	1.55097i
$196$	−0.0529562	+	13.2487i	−0.00378258	+	0.946334i
$197$	3.97564	+	3.97564i	0.283252	+	0.283252i	0.834405	−	0.551152i	$-0.185812\pi$
$197$	3.97564	+	3.97564i	0.283252	+	0.283252i	−0.551152	+	0.834405i	$0.685812\pi$
$198$	9.50983	+	0.0190058i	0.675834	+	0.00135068i
$199$	23.3783			1.65724			0.828622	−	0.559808i	$-0.189125\pi$
$199$	23.3783			1.65724			0.828622	+	0.559808i	$0.189125\pi$
$200$	−2.63869	−	13.8938i	−0.186583	−	0.982439i
$201$	23.1290			1.63139
$202$	−3.44325	−	0.00688147i	−0.242266	−	0.000484179i
$203$	−2.97412	−	2.97412i	−0.208742	−	0.208742i
$204$	0.106594	−	26.6680i	0.00746311	−	1.86714i
$205$	−1.72661	−	1.42085i	−0.120592	−	0.0992367i
$206$	4.94644	+	4.96625i	0.344635	+	0.346015i
$207$	13.2547	−	13.2547i	0.921263	−	0.921263i
$208$	−16.1577	+	15.9014i	−1.12033	+	1.10256i
$209$		−	2.97360i		−	0.205688i
$210$	−4.01831	−	3.32023i	−0.277290	−	0.229117i
$211$			15.6677i			1.07861i	0.842110	+	0.539305i	$0.181313\pi$
$211$			15.6677i			1.07861i	−0.842110	+	0.539305i	$0.818687\pi$
$212$	12.5501	−	12.4502i	0.861947	−	0.855084i
$213$	21.9524	−	21.9524i	1.50416	−	1.50416i
$214$	−8.83019	+	8.79496i	−0.603619	+	0.601211i
$215$	−1.43400	−	14.7617i	−0.0977983	−	1.00674i
$216$	6.67638	−	6.59680i	0.454270	−	0.448856i
$217$	−2.68550	−	2.68550i	−0.182304	−	0.182304i
$218$	0.0498438	−	24.9402i	0.00337585	−	1.68916i
$219$	−30.7762			−2.07966
$220$	4.53534	−	5.46662i	0.305773	−	0.368560i
$221$	28.0977			1.89006
$222$	−0.0702389	+	35.1451i	−0.00471412	+	2.35879i
$223$	6.08865	+	6.08865i	0.407726	+	0.407726i	0.880945	−	0.473219i	$-0.156908\pi$
$223$	6.08865	+	6.08865i	0.407726	+	0.407726i	−0.473219	+	0.880945i	$0.656908\pi$
$224$	2.47585	−	2.42686i	0.165425	−	0.162151i
$225$	−20.7731	+	4.07439i	−1.38488	+	0.271626i
$226$	14.6724	−	14.6139i	0.975996	−	0.972103i
$227$	−6.36587	+	6.36587i	−0.422518	+	0.422518i	−0.886070	−	0.463552i	$-0.846575\pi$
$227$	−6.36587	+	6.36587i	−0.422518	+	0.422518i	0.463552	+	0.886070i	$0.346575\pi$
$228$	−7.09263	−	7.14956i	−0.469721	−	0.473491i
$229$		−	5.75631i		−	0.380388i	−0.981747	−	0.190194i	$-0.939088\pi$
$229$		−	5.75631i		−	0.380388i	0.981747	−	0.190194i	$-0.0609117\pi$
$230$	−1.32587	−	13.9379i	−0.0874250	−	0.919041i
$231$		−	2.61807i		−	0.172256i
$232$	0.116381	−	19.4108i	0.00764076	−	1.27438i
$233$	−18.8947	+	18.8947i	−1.23784	+	1.23784i	−0.276952	+	0.960884i	$0.589324\pi$
$233$	−18.8947	+	18.8947i	−1.23784	+	1.23784i	−0.960884	+	0.276952i	$0.910676\pi$
$234$	23.9469	+	24.0428i	1.56546	+	1.57173i
$235$	26.7003	−	2.59375i	1.74173	−	0.169198i
$236$	1.93787	+	0.00774582i	0.126144	+	0.000504210i
$237$	−10.8869	−	10.8869i	−0.707179	−	0.707179i
$238$	−4.29698	−	0.00858768i	−0.278532	−	0.000556657i
$239$	−4.29596			−0.277883			−0.138941	−	0.990301i	$-0.544370\pi$
$239$	−4.29596			−0.277883			−0.138941	+	0.990301i	$0.544370\pi$
$240$	−2.13447	−	23.9614i	−0.137780	−	1.54670i
$241$	−6.30046			−0.405848			−0.202924	−	0.979194i	$-0.565044\pi$
$241$	−6.30046			−0.405848			−0.202924	+	0.979194i	$0.565044\pi$
$242$	−11.9887	−	0.0239599i	−0.770665	−	0.00154020i
$243$	14.2213	+	14.2213i	0.912298	+	0.912298i
$244$	−3.41929	−	0.0136672i	−0.218898	−	0.000874954i
$245$	9.41229	−	11.4377i	0.601329	−	0.730730i
$246$	−2.68419	−	2.69494i	−0.171138	−	0.171823i
$247$	7.50286	−	7.50286i	0.477396	−	0.477396i
$248$	0.105087	−	17.5271i	0.00667301	−	1.11297i
$249$		−	8.27610i		−	0.524477i
$250$	−7.53703	+	13.8994i	−0.476684	+	0.879075i
$251$		−	27.4019i		−	1.72959i	−0.502123	−	0.864796i	$-0.667448\pi$
$251$		−	27.4019i		−	1.72959i	0.502123	−	0.864796i	$-0.332552\pi$
$252$	−3.65485	−	3.68418i	−0.230234	−	0.232082i
$253$	4.97244	−	4.97244i	0.312615	−	0.312615i
$254$	−10.0080	+	9.96808i	−0.627958	+	0.625453i
$255$	−18.9458	+	23.0228i	−1.18643	+	1.44174i
$256$	15.9980	+	0.255802i	0.999872	+	0.0159876i
$257$	13.0822	+	13.0822i	0.816045	+	0.816045i	0.985532	−	0.169487i	$-0.0542112\pi$
$257$	13.0822	+	13.0822i	0.816045	+	0.816045i	−0.169487	+	0.985532i	$0.554211\pi$
$258$	0.0504198	−	25.2284i	0.00313900	−	1.57065i
$259$	5.66287			0.351873
$260$	25.2366	−	2.34978i	1.56511	−	0.145727i
$261$	−29.0559			−1.79852
$262$	0.00401011	−	2.00652i	0.000247745	−	0.123963i
$263$	14.5278	+	14.5278i	0.895823	+	0.895823i	0.995063	−	0.0992407i	$-0.0316414\pi$
$263$	14.5278	+	14.5278i	0.895823	+	0.895823i	−0.0992407	+	0.995063i	$0.531641\pi$
$264$	8.59470	−	8.49226i	0.528967	−	0.522662i
$265$	−19.6721	+	1.91101i	−1.20845	+	0.117392i
$266$	−1.14971	+	1.14512i	−0.0704929	+	0.0702117i
$267$	−5.11266	+	5.11266i	−0.312890	+	0.312890i
$268$	12.2101	−	12.1129i	0.745849	−	0.739910i
$269$			16.4454i			1.00269i	0.865246	+	0.501347i	$0.167162\pi$
$269$			16.4454i			1.00269i	−0.865246	+	0.501347i	$0.832838\pi$
$270$	−10.4464	+	0.993728i	−0.635748	+	0.0604763i
$271$			28.8912i			1.75501i	0.479565	+	0.877507i	$0.340795\pi$
$271$			28.8912i			1.75501i	−0.479565	+	0.877507i	$0.659205\pi$
$272$	−13.9100	−	14.1342i	−0.843417	−	0.857011i
$273$	6.60580	−	6.60580i	0.399801	−	0.399801i
$274$	−12.6568	−	12.7075i	−0.764624	−	0.767686i
$275$	−7.79297	+	1.52849i	−0.469934	+	0.0921716i
$276$	0.0951937	−	23.8158i	0.00572999	−	1.43354i
$277$	−4.72797	−	4.72797i	−0.284076	−	0.284076i	0.550656	−	0.834732i	$-0.314378\pi$
$277$	−4.72797	−	4.72797i	−0.284076	−	0.284076i	−0.834732	+	0.550656i	$0.814378\pi$
$278$	1.23971	+	0.00247761i	0.0743529	+	0.000148597i
$279$	−26.2362			−1.57072
$280$	−3.86014	+	0.351638i	−0.230688	+	0.0210144i
$281$	2.72305			0.162443			0.0812217	−	0.996696i	$-0.474118\pi$
$281$	2.72305			0.162443			0.0812217	+	0.996696i	$0.474118\pi$
$282$	45.6318	+	0.0911968i	2.71733	+	0.00543069i
$283$	11.8514	+	11.8514i	0.704493	+	0.704493i	0.965372	−	0.260878i	$-0.0840121\pi$
$283$	11.8514	+	11.8514i	0.704493	+	0.704493i	−0.260878	+	0.965372i	$0.584012\pi$
$284$	0.0922753	−	23.0856i	0.00547553	−	1.36988i
$285$	1.08866	+	11.2068i	0.0644868	+	0.663832i
$286$	8.98358	+	9.01956i	0.531211	+	0.533338i
$287$	−0.433364	+	0.433364i	−0.0255807	+	0.0255807i
$288$	0.239320	−	23.9487i	0.0141020	−	1.41119i
$289$			7.57892i			0.445819i
$290$	−13.8236	+	16.7301i	−0.811752	+	0.982425i
$291$			2.07033i			0.121365i
$292$	−16.2471	+	16.1177i	−0.950789	+	0.943219i
$293$	4.39475	−	4.39475i	0.256744	−	0.256744i	−0.566985	−	0.823728i	$-0.691890\pi$
$293$	4.39475	−	4.39475i	0.256744	−	0.256744i	0.823728	+	0.566985i	$0.191890\pi$
$294$	17.8523	−	17.7811i	1.04117	−	1.03702i
$295$	−1.67298	−	1.37672i	−0.0974047	−	0.0801559i
$296$	18.3687	+	18.5903i	1.06766	+	1.08054i
$297$	−3.72681	−	3.72681i	−0.216252	−	0.216252i
$298$	−0.0452494	+	22.6413i	−0.00262123	+	1.31157i
$299$	25.0925			1.45114
$300$	−15.0912	+	22.2628i	−0.871292	+	1.28535i
$301$	−4.06500			−0.234303
$302$	−0.0491448	+	24.5904i	−0.00282796	+	1.41502i
$303$	4.63045	+	4.63045i	0.266012	+	0.266012i
$304$	−7.48856	−	0.0598659i	−0.429498	−	0.00343354i
$305$	2.95191	+	2.42918i	0.169026	+	0.139094i
$306$	−21.0318	+	20.9479i	−1.20231	+	1.19751i
$307$	5.32303	−	5.32303i	0.303801	−	0.303801i	−0.538698	−	0.842499i	$-0.681084\pi$
$307$	5.32303	−	5.32303i	0.303801	−	0.303801i	0.842499	+	0.538698i	$0.181084\pi$
$308$	−1.37110	−	1.38211i	−0.0781258	−	0.0787529i
$309$		−	13.3305i		−	0.758344i
$310$	−12.4821	+	15.1066i	−0.708938	+	0.857995i
$311$			13.0392i			0.739387i	0.929154	+	0.369694i	$0.120537\pi$
$311$			13.0392i			0.739387i	−0.929154	+	0.369694i	$0.879463\pi$
$312$	43.1131	+	0.258492i	2.44080	+	0.0146343i
$313$	9.22158	−	9.22158i	0.521234	−	0.521234i	−0.396710	−	0.917944i	$-0.629848\pi$
$313$	9.22158	−	9.22158i	0.521234	−	0.521234i	0.917944	+	0.396710i	$0.129848\pi$
$314$	−12.4598	−	12.5097i	−0.703148	−	0.705964i
$315$	0.560990	+	5.77487i	0.0316082	+	0.325377i
$316$	−11.4489	−	0.0457621i	−0.644049	−	0.00257432i
$317$	10.5132	+	10.5132i	0.590481	+	0.590481i	0.937761	−	0.347281i	$-0.112895\pi$
$317$	10.5132	+	10.5132i	0.590481	+	0.590481i	−0.347281	+	0.937761i	$0.612895\pi$
$318$	−33.6203	−	0.0671914i	−1.88533	−	0.00376791i
$319$	−10.9002			−0.610295
$320$	−13.6756	−	11.5316i	−0.764488	−	0.644638i
$321$	23.7021			1.32292
$322$	−3.83740	−	0.00766919i	−0.213850	−	0.000427387i
$323$	6.56325	+	6.56325i	0.365189	+	0.365189i
$324$	7.55276	+	0.0301890i	0.419598	+	0.00167717i
$325$	−23.5195	−	15.8063i	−1.30463	−	0.876774i
$326$	−14.2727	−	14.3298i	−0.790491	−	0.793657i
$327$	−33.5392	+	33.5392i	−1.85472	+	1.85472i
$328$	−2.82838	−	0.0169580i	−0.156171	−	0.000936350i
$329$		−	7.35256i		−	0.405360i
$330$	−13.4480	+	1.27925i	−0.740286	+	0.0704206i
$331$		−	32.0991i		−	1.76433i	−0.470943	−	0.882164i	$-0.656086\pi$
$331$		−	32.0991i		−	1.76433i	0.470943	−	0.882164i	$-0.343914\pi$
$332$	−4.33426	−	4.36905i	−0.237873	−	0.239783i
$333$	27.6619	−	27.6619i	1.51586	−	1.51586i
$334$	13.0651	−	13.0129i	0.714889	−	0.712037i
$335$	−19.1390	+	1.85923i	−1.04568	+	0.101580i
$336$	−6.59321	−	0.0527082i	−0.359689	−	0.00287547i
$337$	−4.54825	−	4.54825i	−0.247759	−	0.247759i	0.572291	−	0.820050i	$-0.306055\pi$
$337$	−4.54825	−	4.54825i	−0.247759	−	0.247759i	−0.820050	+	0.572291i	$0.806055\pi$
$338$	−0.0540406	+	27.0401i	−0.00293942	+	1.47079i
$339$	−39.3839			−2.13904
$340$	2.05550	+	22.0761i	0.111475	+	1.19724i
$341$	−9.84242			−0.532997
$342$	−0.0224031	+	11.2097i	−0.00121142	+	0.606153i
$343$	−5.90432	−	5.90432i	−0.318803	−	0.318803i
$344$	−13.1857	−	13.3448i	−0.710924	−	0.719501i
$345$	−16.9195	+	20.5604i	−0.910914	+	1.10693i
$346$	6.01413	−	5.99013i	0.323321	−	0.322032i
$347$	2.12338	−	2.12338i	0.113989	−	0.113989i	−0.647812	−	0.761801i	$-0.724316\pi$
$347$	2.12338	−	2.12338i	0.113989	−	0.113989i	0.761801	+	0.647812i	$0.224316\pi$
$348$	−26.2079	+	25.9992i	−1.40489	+	1.39370i
$349$			14.0584i			0.752527i	0.926513	+	0.376263i	$0.122791\pi$
$349$			14.0584i			0.752527i	−0.926513	+	0.376263i	$0.877209\pi$
$350$	3.59201	+	2.42444i	0.192001	+	0.129592i
$351$		−	18.8067i		−	1.00383i
$352$	0.0897799	−	8.98428i	0.00478529	−	0.478863i
$353$	−9.01285	+	9.01285i	−0.479706	+	0.479706i	−0.905037	−	0.425332i	$-0.860157\pi$
$353$	−9.01285	+	9.01285i	−0.479706	+	0.479706i	0.425332	+	0.905037i	$0.360157\pi$
$354$	−2.60082	−	2.61124i	−0.138232	−	0.138786i
$355$	−16.4008	+	19.9301i	−0.870463	+	1.05778i
$356$	−0.0214906	+	5.37657i	−0.00113900	+	0.284958i
$357$	5.77853	+	5.77853i	0.305832	+	0.305832i
$358$	−11.2983	−	0.0225801i	−0.597135	−	0.00119340i
$359$	−21.5045			−1.13496			−0.567481	−	0.823386i	$-0.692082\pi$
$359$	−21.5045			−1.13496			−0.567481	+	0.823386i	$0.692082\pi$
$360$	−17.1383	+	20.5737i	−0.903269	+	1.08433i
$361$	−15.4949			−0.815519
$362$	20.0502	+	0.0400711i	1.05382	+	0.00210609i
$363$	16.1223	+	16.1223i	0.846202	+	0.846202i
$364$	0.0277669	−	6.94679i	0.00145538	−	0.364111i
$365$	25.4670	−	2.47394i	1.33300	−	0.129492i
$366$	4.58905	+	4.60743i	0.239873	+	0.240834i
$367$	15.2095	−	15.2095i	0.793932	−	0.793932i	−0.188199	−	0.982131i	$-0.560265\pi$
$367$	15.2095	−	15.2095i	0.793932	−	0.793932i	0.982131	+	0.188199i	$0.0602650\pi$
$368$	−12.4222	−	12.6225i	−0.647554	−	0.657991i
$369$			4.23379i			0.220402i
$370$	−2.76702	−	29.0879i	−0.143851	−	1.51221i
$371$			5.41717i			0.281246i
$372$	−23.6646	+	23.4762i	−1.22695	+	1.21718i
$373$	1.46829	−	1.46829i	0.0760252	−	0.0760252i	−0.668072	−	0.744097i	$-0.732880\pi$
$373$	1.46829	−	1.46829i	0.0760252	−	0.0760252i	0.744097	+	0.668072i	$0.232880\pi$
$374$	−7.89001	+	7.85853i	−0.407983	+	0.406355i
$375$	28.8102	−	8.61360i	1.48775	−	0.444805i
$376$	24.1373	−	23.8496i	1.24479	−	1.22995i
$377$	−27.5030	−	27.5030i	−1.41648	−	1.41648i
$378$	−0.00574801	+	2.87611i	−0.000295646	+	0.147931i
$379$	10.0239			0.514894			0.257447	−	0.966292i	$-0.417119\pi$
$379$	10.0239			0.514894			0.257447	+	0.966292i	$0.417119\pi$
$380$	6.44379	+	5.34604i	0.330560	+	0.274246i
$381$	26.8636			1.37626
$382$	−0.00975690	+	4.88202i	−0.000499206	+	0.249786i
$383$	13.9942	+	13.9942i	0.715068	+	0.715068i	0.967591	−	0.252523i	$-0.0812603\pi$
$383$	13.9942	+	13.9942i	0.715068	+	0.715068i	−0.252523	+	0.967591i	$0.581260\pi$
$384$	−21.2135	−	21.8155i	−1.08254	−	1.11327i
$385$	0.210453	+	2.16642i	0.0107257	+	0.110411i
$386$	1.32507	−	1.31979i	0.0674444	−	0.0671754i
$387$	−19.8567	+	19.8567i	−1.00937	+	1.00937i
$388$	1.08425	+	1.09295i	0.0550445	+	0.0554863i
$389$			30.3206i			1.53732i	0.639659	+	0.768659i	$0.279075\pi$
$389$			30.3206i			1.53732i	−0.639659	+	0.768659i	$0.720925\pi$
$390$	−37.1591	−	30.7036i	−1.88163	−	1.55474i
$391$			21.9501i			1.11006i
$392$	0.112337	−	18.7363i	0.00567385	−	0.946325i
$393$	−2.69834	+	2.69834i	−0.136113	+	0.136113i
$394$	−5.61115	−	5.63362i	−0.282686	−	0.283818i
$395$	9.88393	+	8.13364i	0.497314	+	0.409248i
$396$	−13.4489	−	0.0537563i	−0.675830	−	0.00270135i
$397$	−20.8645	−	20.8645i	−1.04716	−	1.04716i	−0.998832	−	0.0483271i	$-0.984611\pi$
$397$	−20.8645	−	20.8645i	−1.04716	−	1.04716i	−0.0483271	−	0.998832i	$-0.515389\pi$
$398$	−33.0619	−	0.0660754i	−1.65724	−	0.00331206i
$399$	3.08605			0.154496
$400$	3.69239	+	19.6562i	0.184620	+	0.982810i
$401$	−27.4808			−1.37232			−0.686162	−	0.727449i	$-0.740706\pi$
$401$	−27.4808			−1.37232			−0.686162	+	0.727449i	$0.740706\pi$
$402$	−32.7093	−	0.0653707i	−1.63139	−	0.00326040i
$403$	−24.8340	−	24.8340i	−1.23707	−	1.23707i
$404$	4.86947	+	0.0194637i	0.242265	+	0.000968355i
$405$	−6.52038	−	5.36572i	−0.324000	−	0.266625i
$406$	4.19763	+	4.21444i	0.208325	+	0.209159i
$407$	10.3773	−	10.3773i	0.514382	−	0.514382i
$408$	−0.226120	+	37.7139i	−0.0111946	+	1.86712i
$409$			8.80523i			0.435391i	0.976017	+	0.217695i	$0.0698539\pi$
$409$			8.80523i			0.435391i	−0.976017	+	0.217695i	$0.930146\pi$
$410$	2.43777	+	2.01427i	0.120393	+	0.0994775i
$411$			34.1095i			1.68250i
$412$	−6.98127	−	7.03731i	−0.343943	−	0.346703i
$413$	−0.419904	+	0.419904i	−0.0206621	+	0.0206621i
$414$	−18.7824	+	18.7074i	−0.923103	+	0.919420i
$415$	0.665275	+	6.84839i	0.0326571	+	0.336174i
$416$	22.8953	−	22.4422i	1.12253	−	1.10032i
$417$	−1.66715	−	1.66715i	−0.0816406	−	0.0816406i
$418$	−0.00840443	+	4.20529i	−0.000411074	+	0.205688i
$419$	5.76098			0.281442			0.140721	−	0.990049i	$-0.455058\pi$
$419$	5.76098			0.281442			0.140721	+	0.990049i	$0.455058\pi$
$420$	5.67336	+	4.70686i	0.276832	+	0.229671i
$421$	0.285923			0.0139351			0.00696753	−	0.999976i	$-0.497782\pi$
$421$	0.285923			0.0139351			0.00696753	+	0.999976i	$0.497782\pi$
$422$	0.0442825	−	22.1575i	0.00215564	−	1.07861i
$423$	−35.9157	−	35.9157i	−1.74628	−	1.74628i
$424$	−17.7837	+	17.5718i	−0.863654	+	0.853360i
$425$	13.8268	−	20.5741i	0.670698	−	0.997990i
$426$	−31.1074	+	30.9833i	−1.50716	+	1.50115i
$427$	0.740905	−	0.740905i	0.0358549	−	0.0358549i
$428$	12.5126	−	12.4130i	0.604820	−	0.600004i
$429$		−	24.2104i		−	1.16889i
$430$	1.98626	+	20.8803i	0.0957861	+	1.00694i
$431$			33.7234i			1.62440i	0.583381	+	0.812199i	$0.301730\pi$
$431$			33.7234i			1.62440i	−0.583381	+	0.812199i	$0.698270\pi$
$432$	−9.46046	+	9.31040i	−0.455167	+	0.447947i
$433$	−16.2481	+	16.2481i	−0.780836	+	0.780836i	−0.979972	−	0.199136i	$-0.936186\pi$
$433$	−16.2481	+	16.2481i	−0.780836	+	0.780836i	0.199136	+	0.979972i	$0.436186\pi$
$434$	3.79027	+	3.80545i	0.181939	+	0.182668i
$435$	41.0803	−	3.99068i	1.96965	−	0.191338i
$436$	−0.140979	+	35.2705i	−0.00675169	+	1.68915i
$437$	5.86128	+	5.86128i	0.280383	+	0.280383i
$438$	43.5240	+	0.0869843i	2.07966	+	0.00415627i
$439$	33.9364			1.61970			0.809849	−	0.586639i	$-0.199549\pi$
$439$	33.9364			1.61970			0.809849	+	0.586639i	$0.199549\pi$
$440$	−6.42938	+	7.71814i	−0.306509	+	0.367948i
$441$	−28.0463			−1.33554
$442$	−39.7361	−	0.0794141i	−1.89005	−	0.00377734i
$443$	−14.6750	−	14.6750i	−0.697230	−	0.697230i	0.266582	−	0.963812i	$-0.414106\pi$
$443$	−14.6750	−	14.6750i	−0.697230	−	0.697230i	−0.963812	+	0.266582i	$0.914106\pi$
$444$	0.198665	−	49.7024i	0.00942823	−	2.35877i
$445$	3.81969	−	4.64165i	0.181071	−	0.220036i
$446$	−8.59342	−	8.62784i	−0.406910	−	0.408540i
$447$	30.4477	−	30.4477i	1.44013	−	1.44013i
$448$	−3.50824	+	3.42509i	−0.165749	+	0.161820i
$449$		−	11.9800i		−	0.565371i	−0.959213	−	0.282686i	$-0.908775\pi$
$449$		−	11.9800i		−	0.565371i	0.959213	−	0.282686i	$-0.0912253\pi$
$450$	29.3891	−	5.70333i	1.38542	−	0.268858i
$451$			1.58829i			0.0747896i
$452$	−20.7912	+	20.6257i	−0.977937	+	0.970150i
$453$	33.0688	−	33.0688i	1.55371	−	1.55371i
$454$	9.02067	−	8.98469i	0.423361	−	0.421672i
$455$	−4.93522	+	5.99724i	−0.231367	+	0.281155i
$456$	10.0103	+	10.1310i	0.468774	+	0.474429i
$457$	0.123192	+	0.123192i	0.00576270	+	0.00576270i	0.709982	−	0.704220i	$-0.248703\pi$
$457$	0.123192	+	0.123192i	0.00576270	+	0.00576270i	−0.704220	+	0.709982i	$0.748703\pi$
$458$	−0.0162694	+	8.14064i	−0.000760217	+	0.380387i
$459$	16.4515			0.767888
$460$	1.83566	+	19.7149i	0.0855880	+	0.919214i
$461$	−1.83433			−0.0854335			−0.0427167	−	0.999087i	$-0.513601\pi$
$461$	−1.83433			−0.0854335			−0.0427167	+	0.999087i	$0.513601\pi$
$462$	−0.00739958	+	3.70250i	−0.000344260	+	0.172256i
$463$	−28.5167	−	28.5167i	−1.32528	−	1.32528i	−0.909434	−	0.415849i	$-0.863485\pi$
$463$	−28.5167	−	28.5167i	−1.32528	−	1.32528i	−0.415849	−	0.909434i	$-0.636515\pi$
$464$	−0.219448	+	27.4506i	−0.0101876	+	1.27436i
$465$	37.0937	−	3.60341i	1.72018	−	0.167104i
$466$	26.7746	−	26.6678i	1.24031	−	1.23536i
$467$	9.23022	−	9.23022i	0.427124	−	0.427124i	−0.460524	−	0.887647i	$-0.652338\pi$
$467$	9.23022	−	9.23022i	0.427124	−	0.427124i	0.887647	+	0.460524i	$0.152338\pi$
$468$	−33.7980	−	34.0693i	−1.56231	−	1.57485i
$469$			5.27038i			0.243364i
$470$	−37.7672	+	3.59265i	−1.74207	+	0.165717i
$471$			33.5787i			1.54723i
$472$	−2.74053	−	0.0164313i	−0.126143	−	0.000756313i
$473$	−7.44915	+	7.44915i	−0.342512	+	0.342512i
$474$	15.3656	+	15.4271i	0.705765	+	0.708591i
$475$	−1.80171	−	9.18597i	−0.0826683	−	0.421481i
$476$	6.07681	+	0.0242896i	0.278530	+	0.00111331i
$477$	26.4618	+	26.4618i	1.21160	+	1.21160i
$478$	6.07539	+	0.0121419i	0.277882	+	0.000555358i
$479$	−20.4800			−0.935755			−0.467877	−	0.883793i	$-0.654981\pi$
$479$	−20.4800			−0.935755			−0.467877	+	0.883793i	$0.654981\pi$
$480$	2.95087	+	33.8925i	0.134688	+	1.54697i
$481$	52.3670			2.38773
$482$	8.91017	+	0.0178073i	0.405847	+	0.000811101i
$483$	5.16049	+	5.16049i	0.234810	+	0.234810i
$484$	16.9545	+	0.0677688i	0.770661	+	0.00308040i
$485$	−0.166424	−	1.71318i	−0.00755692	−	0.0777914i
$486$	−20.0718	−	20.1521i	−0.910473	−	0.914120i
$487$	1.46175	−	1.46175i	0.0662384	−	0.0662384i	−0.673212	−	0.739450i	$-0.735086\pi$
$487$	1.46175	−	1.46175i	0.0662384	−	0.0662384i	0.739450	+	0.673212i	$0.235086\pi$
$488$	4.83556	+	0.0289924i	0.218896	+	0.00131243i
$489$			38.4643i			1.73942i
$490$	−13.3433	+	16.1488i	−0.602788	+	0.729526i
$491$			7.84785i			0.354169i	0.984196	+	0.177084i	$0.0566665\pi$
$491$			7.84785i			0.354169i	−0.984196	+	0.177084i	$0.943333\pi$
$492$	3.78839	+	3.81880i	0.170794	+	0.172165i
$493$	24.0587	−	24.0587i	1.08355	−	1.08355i
$494$	−10.6318	+	10.5894i	−0.478349	+	0.476440i
$495$	11.6105	+	9.55450i	0.521855	+	0.429443i
$496$	−0.198152	+	24.7867i	−0.00889730	+	1.11295i
$497$	5.00228	+	5.00228i	0.224383	+	0.224383i
$498$	−0.0233912	+	11.7042i	−0.00104818	+	0.524476i
$499$	−23.0671			−1.03262			−0.516312	−	0.856400i	$-0.672696\pi$
$499$	−23.0671			−1.03262			−0.516312	+	0.856400i	$0.672696\pi$
$500$	10.6982	−	19.6354i	0.478440	−	0.878120i
$501$	−35.0694			−1.56679
$502$	−0.0774474	+	38.7520i	−0.00345665	+	1.72959i
$503$	−16.5617	−	16.5617i	−0.738450	−	0.738450i	0.233828	−	0.972278i	$-0.424875\pi$
$503$	−16.5617	−	16.5617i	−0.738450	−	0.738450i	−0.972278	+	0.233828i	$0.924875\pi$
$504$	5.15831	+	5.22054i	0.229769	+	0.232541i
$505$	−4.20386	−	3.45943i	−0.187069	−	0.153942i
$506$	−7.04613	+	7.01803i	−0.313239	+	0.311989i
$507$	36.3632	−	36.3632i	1.61495	−	1.61495i
$508$	14.1816	−	14.0687i	0.629206	−	0.624196i
$509$		−	29.2681i		−	1.29728i	−0.761094	−	0.648642i	$-0.775337\pi$
$509$		−	29.2681i		−	1.29728i	0.761094	−	0.648642i	$-0.224663\pi$
$510$	26.8585	−	32.5055i	1.18931	−	1.43937i
$511$		−	7.01293i		−	0.310234i
$512$	−22.6238	−	0.406973i	−0.999838	−	0.0179858i
$513$	4.39299	−	4.39299i	0.193955	−	0.193955i
$514$	−18.4640	−	18.5380i	−0.814413	−	0.817674i
$515$	1.07157	+	11.0308i	0.0472190	+	0.486076i
$516$	−0.142609	+	35.6781i	−0.00627799	+	1.57064i
$517$	−13.4737	−	13.4737i	−0.592571	−	0.592571i
$518$	−8.00849	−	0.0160053i	−0.351873	−	0.000703231i
$519$	−16.1432			−0.708607
$520$	−35.6965	+	3.25175i	−1.56539	+	0.142599i
$521$	−18.0489			−0.790737			−0.395369	−	0.918523i	$-0.629383\pi$
$521$	−18.0489			−0.790737			−0.395369	+	0.918523i	$0.629383\pi$
$522$	41.0912	+	0.0821222i	1.79851	+	0.00359439i
$523$	−2.57935	−	2.57935i	−0.112787	−	0.112787i	0.648461	−	0.761248i	$-0.275413\pi$
$523$	−2.57935	−	2.57935i	−0.112787	−	0.112787i	−0.761248	+	0.648461i	$0.775413\pi$
$524$	−0.0113423	+	2.83763i	−0.000495489	+	0.123962i
$525$	−1.58630	−	8.08768i	−0.0692317	−	0.352975i
$526$	−20.5043	−	20.5864i	−0.894031	−	0.897611i
$527$	21.7239	−	21.7239i	0.946310	−	0.946310i
$528$	−12.1787	+	11.9855i	−0.530011	+	0.521604i
$529$		−	3.39757i		−	0.147721i
$530$	27.8259	−	2.64697i	1.20868	−	0.114977i
$531$			4.10229i			0.178024i
$532$	1.62916	−	1.61619i	0.0706331	−	0.0700707i
$533$	−4.00751	+	4.00751i	−0.173585	+	0.173585i
$534$	7.24483	−	7.21593i	0.313514	−	0.312264i
$535$	−19.6132	+	1.90529i	−0.847954	+	0.0823730i
$536$	−17.3018	+	17.0956i	−0.747326	+	0.738418i
$537$	15.1939	+	15.1939i	0.655663	+	0.655663i
$538$	0.0464805	−	23.2573i	0.00200392	−	1.00269i
$539$	−10.5215			−0.453191
$540$	14.7762	−	1.37582i	0.635868	−	0.0592057i
$541$	−6.04328			−0.259821			−0.129910	−	0.991526i	$-0.541469\pi$
$541$	−6.04328			−0.259821			−0.129910	+	0.991526i	$0.541469\pi$
$542$	0.0816566	−	40.8582i	0.00350745	−	1.75501i
$543$	−26.9633	−	26.9633i	−1.15711	−	1.15711i
$544$	19.6317	+	20.0280i	0.841702	+	0.858694i
$545$	25.0573	−	30.4494i	1.07334	−	1.30431i
$546$	−9.36067	+	9.32332i	−0.400599	+	0.399001i
$547$	2.28661	−	2.28661i	0.0977683	−	0.0977683i	−0.656531	−	0.754299i	$-0.727977\pi$
$547$	2.28661	−	2.28661i	0.0977683	−	0.0977683i	0.754299	+	0.656531i	$0.227977\pi$
$548$	17.8634	+	18.0068i	0.763088	+	0.769213i
$549$		−	7.23833i		−	0.308925i
$550$	11.0252	−	2.13959i	0.470117	−	0.0912322i
$551$		−	12.8487i		−	0.547371i
$552$	−0.201936	+	33.6802i	−0.00859495	+	1.43353i
$553$	2.48078	−	2.48078i	0.105494	−	0.105494i
$554$	6.67298	+	6.69970i	0.283508	+	0.284643i
$555$	−35.3102	+	42.9087i	−1.49884	+	1.82137i
$556$	−1.75321	−	0.00700772i	−0.0743525	−	0.000297194i
$557$	7.24008	+	7.24008i	0.306772	+	0.306772i	0.843656	−	0.536884i	$-0.180399\pi$
$557$	7.24008	+	7.24008i	0.306772	+	0.306772i	−0.536884	+	0.843656i	$0.680399\pi$
$558$	37.1035	+	0.0741528i	1.57072	+	0.00313914i
$559$	−37.5908			−1.58992
$560$	5.46005	−	0.486380i	0.230729	−	0.0205533i
$561$	21.1784			0.894155
$562$	−3.85096	−	0.00769629i	−0.162443	−	0.000324648i
$563$	−23.0929	−	23.0929i	−0.973252	−	0.973252i	0.0263999	−	0.999651i	$-0.491596\pi$
$563$	−23.0929	−	23.0929i	−0.973252	−	0.973252i	−0.999651	+	0.0263999i	$0.991596\pi$
$564$	−64.5327	−	0.257943i	−2.71732	−	0.0108614i
$565$	32.5898	−	3.16588i	1.37106	−	0.133190i
$566$	−16.7269	−	16.7939i	−0.703084	−	0.705900i
$567$	−1.63656	+	1.63656i	−0.0687291	+	0.0687291i
$568$	−0.195745	+	32.6477i	−0.00821327	+	1.36987i
$569$			11.3100i			0.474140i	0.971493	+	0.237070i	$0.0761870\pi$
$569$			11.3100i			0.474140i	−0.971493	+	0.237070i	$0.923813\pi$
$570$	−1.50792	−	15.8518i	−0.0631600	−	0.663959i
$571$		−	20.4162i		−	0.854391i	−0.904159	−	0.427195i	$-0.859502\pi$
$571$		−	20.4162i		−	0.854391i	0.904159	−	0.427195i	$-0.140498\pi$
$572$	−12.6792	−	12.7810i	−0.530144	−	0.534399i
$573$	6.56528	−	6.56528i	0.274269	−	0.274269i
$574$	0.614093	−	0.611643i	0.0256318	−	0.0255295i
$575$	12.3479	−	18.3736i	0.514945	−	0.766232i
$576$	−0.406136	+	33.8679i	−0.0169223	+	1.41116i
$577$	1.14988	+	1.14988i	0.0478700	+	0.0478700i	0.730637	−	0.682767i	$-0.239223\pi$
$577$	1.14988	+	1.14988i	0.0478700	+	0.0478700i	−0.682767	+	0.730637i	$0.739223\pi$
$578$	0.0214207	−	10.7182i	0.000890984	−	0.445818i
$579$	−3.55678			−0.147815
$580$	19.5968	−	23.6208i	0.813714	−	0.980801i
$581$	1.88587			0.0782389
$582$	0.00585149	−	2.92789i	0.000242552	−	0.121365i
$583$	9.92703	+	9.92703i	0.411136	+	0.411136i
$584$	23.0224	−	22.7479i	0.952672	−	0.941317i
$585$	5.18772	+	53.4028i	0.214486	+	2.20793i
$586$	−6.22752	+	6.20268i	−0.257256	+	0.256230i
$587$	14.6537	−	14.6537i	0.604824	−	0.604824i	−0.336765	−	0.941589i	$-0.609333\pi$
$587$	14.6537	−	14.6537i	0.604824	−	0.604824i	0.941589	+	0.336765i	$0.109333\pi$
$588$	−25.2972	+	25.0958i	−1.04324	+	1.03493i
$589$		−	11.6018i		−	0.478043i
$590$	2.36206	+	1.95170i	0.0972443	+	0.0803504i
$591$			15.1218i			0.622029i
$592$	−25.9247	−	26.3425i	−1.06550	−	1.08267i
$593$	10.2463	−	10.2463i	0.420765	−	0.420765i	−0.464702	−	0.885467i	$-0.653839\pi$
$593$	10.2463	−	10.2463i	0.420765	−	0.420765i	0.885467	+	0.464702i	$0.153839\pi$
$594$	5.25997	+	5.28103i	0.215819	+	0.216683i
$595$	−5.24618	−	4.31717i	−0.215072	−	0.176987i
$596$	0.127984	−	32.0194i	0.00524245	−	1.31157i
$597$	44.4612	+	44.4612i	1.81968	+	1.81968i
$598$	−35.4861	−	0.0709204i	−1.45114	−	0.00290015i
$599$	24.3043			0.993045			0.496523	−	0.868024i	$-0.334610\pi$
$599$	24.3043			0.993045			0.496523	+	0.868024i	$0.334610\pi$
$600$	21.4051	−	31.4417i	0.873860	−	1.28360i
$601$	32.2891			1.31710			0.658550	−	0.752537i	$-0.271170\pi$
$601$	32.2891			1.31710			0.658550	+	0.752537i	$0.271170\pi$
$602$	5.74876	+	0.0114891i	0.234302	+	0.000468261i
$603$	25.7447	+	25.7447i	1.04841	+	1.04841i
$604$	0.139002	−	34.7758i	0.00565592	−	1.41501i
$605$	−14.6370	−	12.0451i	−0.595080	−	0.489701i
$606$	−6.53534	−	6.56151i	−0.265480	−	0.266543i
$607$	−15.5642	+	15.5642i	−0.631732	+	0.631732i	−0.948502	−	0.316770i	$-0.897402\pi$
$607$	−15.5642	+	15.5642i	−0.631732	+	0.631732i	0.316770	+	0.948502i	$0.397402\pi$
$608$	10.5902	+	0.105828i	0.429491	+	0.00429190i
$609$		−	11.3124i		−	0.458403i
$610$	−4.16776	−	3.44371i	−0.168748	−	0.139432i
$611$		−	67.9924i		−	2.75068i
$612$	29.8026	−	29.5653i	1.20470	−	1.19511i
$613$	13.6883	−	13.6883i	0.552866	−	0.552866i	−0.374401	−	0.927267i	$-0.622152\pi$
$613$	13.6883	−	13.6883i	0.552866	−	0.552866i	0.927267	+	0.374401i	$0.122152\pi$
$614$	−7.54293	+	7.51284i	−0.304408	+	0.303194i
$615$	−0.581488	−	5.98588i	−0.0234479	−	0.241374i
$616$	1.93512	+	1.95847i	0.0779683	+	0.0789089i
$617$	−17.2210	−	17.2210i	−0.693292	−	0.693292i	0.269663	−	0.962955i	$-0.413088\pi$
$617$	−17.2210	−	17.2210i	−0.693292	−	0.693292i	−0.962955	+	0.269663i	$0.913088\pi$
$618$	−0.0376766	+	18.8521i	−0.00151557	+	0.758342i
$619$	29.8732			1.20070			0.600352	−	0.799736i	$-0.295027\pi$
$619$	29.8732			1.20070			0.600352	+	0.799736i	$0.295027\pi$
$620$	17.6951	−	21.3286i	0.710651	−	0.856576i
$621$	14.6919			0.589566
$622$	0.0368535	−	18.4402i	0.00147769	−	0.739386i
$623$	−1.16502	−	1.16502i	−0.0466754	−	0.0466754i
$624$	−60.9703	−	0.487416i	−2.44077	−	0.0195122i
$625$	−23.1478	+	9.44358i	−0.925910	+	0.377743i
$626$	−13.0673	+	13.0152i	−0.522275	+	0.520192i
$627$	5.65522	−	5.65522i	0.225848	−	0.225848i
$628$	17.5855	+	17.7266i	0.701736	+	0.707368i
$629$			45.8089i			1.82652i
$630$	−0.777037	−	8.16847i	−0.0309579	−	0.325440i
$631$			31.7086i			1.26230i	0.775661	+	0.631149i	$0.217416\pi$
$631$			31.7086i			1.26230i	−0.775661	+	0.631149i	$0.782584\pi$
$632$	16.1910	+	0.0970758i	0.644042	+	0.00386147i
$633$	−29.7971	+	29.7971i	−1.18433	+	1.18433i
$634$	−14.8382	−	14.8976i	−0.589299	−	0.591659i
$635$	−22.2293	+	2.15943i	−0.882144	+	0.0856944i
$636$	47.5460	+	0.190046i	1.88532	+	0.00753580i
$637$	−26.5473	−	26.5473i	−1.05184	−	1.05184i
$638$	15.4152	+	0.0308079i	0.610294	+	0.00121969i
$639$	48.8702			1.93327
$640$	19.3076	+	16.3468i	0.763198	+	0.646165i
$641$	−19.2164			−0.759001			−0.379500	−	0.925192i	$-0.623904\pi$
$641$	−19.2164			−0.759001			−0.379500	+	0.925192i	$0.623904\pi$
$642$	−33.5197	−	0.0669905i	−1.32292	−	0.00264390i
$643$	20.3110	+	20.3110i	0.800987	+	0.800987i	0.983250	−	0.182263i	$-0.0583421\pi$
$643$	20.3110	+	20.3110i	0.800987	+	0.800987i	−0.182263	+	0.983250i	$0.558342\pi$
$644$	5.42687	+	0.0216917i	0.213849	+	0.000854772i
$645$	25.3469	−	30.8013i	0.998032	−	1.21280i
$646$	−9.26326	−	9.30036i	−0.364458	−	0.365918i
$647$	−32.0181	+	32.0181i	−1.25876	+	1.25876i	−0.307078	+	0.951684i	$0.599351\pi$
$647$	−32.0181	+	32.0181i	−1.25876	+	1.25876i	−0.951684	+	0.307078i	$0.900649\pi$
$648$	−10.6811	−	0.0640404i	−0.419593	−	0.00251575i
$649$			1.53896i			0.0604094i
$650$	33.2169	+	22.4199i	1.30287	+	0.879380i
$651$		−	10.2146i		−	0.400343i
$652$	20.1441	+	20.3058i	0.788903	+	0.795235i
$653$	−3.37399	+	3.37399i	−0.132034	+	0.132034i	−0.770035	−	0.638001i	$-0.779761\pi$
$653$	−3.37399	+	3.37399i	−0.132034	+	0.132034i	0.638001	+	0.770035i	$0.279761\pi$
$654$	47.5263	−	47.3367i	1.85843	−	1.85101i
$655$	2.01595	−	2.44976i	0.0787695	−	0.0957200i
$656$	3.99987	+	0.0319762i	0.156169	+	0.00124846i
$657$	−34.2567	−	34.2567i	−1.33648	−	1.33648i
$658$	−0.0207809	+	10.3981i	−0.000810125	+	0.405359i
$659$	−1.35246			−0.0526844			−0.0263422	−	0.999653i	$-0.508386\pi$
$659$	−1.35246			−0.0526844			−0.0263422	+	0.999653i	$0.508386\pi$
$660$	19.0219	−	1.77113i	0.740425	−	0.0689410i
$661$	−38.1313			−1.48314			−0.741568	−	0.670877i	$-0.765918\pi$
$661$	−38.1313			−1.48314			−0.741568	+	0.670877i	$0.765918\pi$
$662$	−0.0907235	+	45.3949i	−0.00352607	+	1.76432i
$663$	53.4366	+	53.4366i	2.07531	+	2.07531i
$664$	6.11721	+	6.19101i	0.237394	+	0.240258i
$665$	−2.55368	+	0.248072i	−0.0990273	+	0.00961984i
$666$	−39.1980	+	39.0416i	−1.51889	+	1.51283i
$667$	21.4855	−	21.4855i	0.831922	−	0.831922i
$668$	−18.5135	+	18.3661i	−0.716310	+	0.710607i
$669$			23.1589i			0.895376i
$670$	27.0719	−	2.57525i	1.04588	−	0.0994904i
$671$		−	2.71543i		−	0.104828i
$672$	9.32404	+	0.0931752i	0.359683	+	0.00359431i
$673$	−25.1177	+	25.1177i	−0.968217	+	0.968217i	−0.999510	−	0.0312931i	$-0.990037\pi$
$673$	−25.1177	+	25.1177i	−0.968217	+	0.968217i	0.0312931	+	0.999510i	$0.490037\pi$
$674$	6.41934	+	6.44505i	0.247264	+	0.248254i
$675$	−13.7709	−	9.25471i	−0.530042	−	0.356214i
$676$	0.152850	−	38.2402i	0.00587883	−	1.47078i
$677$	3.17557	+	3.17557i	0.122047	+	0.122047i	0.765492	−	0.643445i	$-0.222496\pi$
$677$	3.17557	+	3.17557i	0.122047	+	0.122047i	−0.643445	+	0.765492i	$0.722496\pi$
$678$	55.6972	+	0.111313i	2.13904	+	0.00427494i
$679$	−0.471765			−0.0181047
$680$	−2.84452	−	31.2260i	−0.109082	−	1.19746i
$681$	−24.2134			−0.927859
$682$	13.9193	+	0.0278182i	0.532996	+	0.00106521i
$683$	−24.2669	−	24.2669i	−0.928548	−	0.928548i	0.0690643	−	0.997612i	$-0.477999\pi$
$683$	−24.2669	−	24.2669i	−0.928548	−	0.928548i	−0.997612	+	0.0690643i	$0.977999\pi$
$684$	0.0633653	−	15.8529i	0.00242283	−	0.606149i
$685$	−2.74190	−	28.2253i	−0.104762	−	1.07843i
$686$	8.33327	+	8.36665i	0.318166	+	0.319440i
$687$	10.9474	−	10.9474i	0.417670	−	0.417670i
$688$	18.6096	+	18.9096i	0.709485	+	0.720920i
$689$			50.0950i			1.90847i
$690$	23.9858	−	29.0289i	0.913125	−	1.10511i
$691$			31.7248i			1.20687i	0.797413	+	0.603433i	$0.206201\pi$
$691$			31.7248i			1.20687i	−0.797413	+	0.603433i	$0.793799\pi$
$692$	−8.52217	+	8.45431i	−0.323964	+	0.321385i
$693$	2.91415	−	2.91415i	0.110699	−	0.110699i
$694$	−3.00891	+	2.99691i	−0.114217	+	0.113761i
$695$	1.51356	+	1.24553i	0.0574127	+	0.0472458i
$696$	37.1370	−	36.6943i	1.40767	−	1.39089i
$697$	−3.50563	−	3.50563i	−0.132785	−	0.132785i
$698$	0.0397339	−	19.8815i	0.00150395	−	0.752525i
$699$	−71.8686			−2.71832
$700$	−5.07301	−	3.43882i	−0.191742	−	0.129975i
$701$	−40.2785			−1.52130			−0.760648	−	0.649164i	$-0.775119\pi$
$701$	−40.2785			−1.52130			−0.760648	+	0.649164i	$0.775119\pi$
$702$	−0.0531544	+	26.5966i	−0.00200618	+	1.00383i
$703$	12.2322	+	12.2322i	0.461347	+	0.461347i
$704$	−0.152360	+	12.7054i	−0.00574230	+	0.478853i
$705$	55.7118	+	45.8461i	2.09823	+	1.72667i
$706$	12.7715	−	12.7206i	0.480663	−	0.478746i
$707$	−1.05513	+	1.05513i	−0.0396824	+	0.0396824i
$708$	3.67073	+	3.70019i	0.137954	+	0.139062i
$709$		−	44.0802i		−	1.65547i	−0.561122	−	0.827733i	$-0.689630\pi$
$709$		−	44.0802i		−	1.65547i	0.561122	−	0.827733i	$-0.310370\pi$
$710$	23.2505	−	28.1390i	0.872575	−	1.05604i
$711$		−	24.2362i		−	0.908929i
$712$	0.0455884	−	7.60355i	0.00170850	−	0.284955i
$713$	19.4005	−	19.4005i	0.726553	−	0.726553i
$714$	−8.15573	−	8.18839i	−0.305220	−	0.306443i
$715$	1.94616	+	20.0339i	0.0727821	+	0.749224i
$716$	15.9782	+	0.0638661i	0.597132	+	0.00238679i
$717$	−8.17012	−	8.17012i	−0.305119	−	0.305119i
$718$	30.4118	+	0.0607792i	1.13496	+	0.00226826i
$719$	28.5020			1.06295			0.531473	−	0.847075i	$-0.321639\pi$
$719$	28.5020			1.06295			0.531473	+	0.847075i	$0.321639\pi$
$720$	24.2953	−	29.0471i	0.905434	−	1.08252i
$721$	3.03760			0.113126
$722$	21.9130	+	0.0437940i	0.815518	+	0.00162984i
$723$	−11.9823	−	11.9823i	−0.445626	−	0.445626i
$724$	−28.3551	−	0.113338i	−1.05381	−	0.00421217i
$725$	−33.6727	+	6.60449i	−1.25057	+	0.245284i
$726$	−22.7548	−	22.8459i	−0.844509	−	0.847891i
$727$	23.0687	−	23.0687i	0.855572	−	0.855572i	−0.135240	−	0.990813i	$-0.543181\pi$
$727$	23.0687	−	23.0687i	0.855572	−	0.855572i	0.990813	+	0.135240i	$0.0431807\pi$
$728$	−0.0589024	+	9.82415i	−0.00218307	+	0.364107i
$729$			42.7634i			1.58383i
$730$	−36.0226	+	3.42670i	−1.33326	+	0.126828i
$731$		−	32.8832i		−	1.21623i
$732$	−6.47686	−	6.52885i	−0.239392	−	0.241313i
$733$	−20.5353	+	20.5353i	−0.758489	+	0.758489i	−0.976047	−	0.217558i	$-0.930191\pi$
$733$	−20.5353	+	20.5353i	−0.758489	+	0.758489i	0.217558	+	0.976047i	$0.430191\pi$
$734$	−21.5525	+	21.4665i	−0.795517	+	0.792344i
$735$	39.6528	−	3.85201i	1.46262	−	0.142083i
$736$	17.5320	+	17.8859i	0.646238	+	0.659284i
$737$	9.65804	+	9.65804i	0.355758	+	0.355758i
$738$	0.0119662	−	5.98747i	0.000440481	−	0.220402i
$739$	−35.5923			−1.30929			−0.654643	−	0.755939i	$-0.727181\pi$
$739$	−35.5923			−1.30929			−0.654643	+	0.755939i	$0.727181\pi$
$740$	3.83094	+	41.1442i	0.140828	+	1.51249i
$741$	28.5381			1.04837
$742$	0.0153108	−	7.66102i	0.000562079	−	0.281245i
$743$	35.7641	+	35.7641i	1.31206	+	1.31206i	0.919897	+	0.392161i	$0.128272\pi$
$743$	35.7641	+	35.7641i	1.31206	+	1.31206i	0.392161	+	0.919897i	$0.371728\pi$
$744$	33.5331	−	33.1334i	1.22938	−	1.21473i
$745$	−22.7476	+	27.6427i	−0.833408	+	1.01275i
$746$	−2.08062	+	2.07232i	−0.0761770	+	0.0758732i
$747$	9.21206	−	9.21206i	0.337052	−	0.337052i
$748$	11.1803	−	11.0913i	0.408794	−	0.405539i
$749$			5.40097i			0.197347i
$750$	−40.7681	+	12.1000i	−1.48864	+	0.441830i
$751$		−	26.4073i		−	0.963615i	−0.876277	−	0.481807i	$-0.839980\pi$
$751$		−	26.4073i		−	0.963615i	0.876277	−	0.481807i	$-0.160020\pi$
$752$	−34.2027	+	33.6601i	−1.24724	+	1.22746i
$753$	52.1133	−	52.1133i	1.89911	−	1.89911i
$754$	38.8173	+	38.9728i	1.41364	+	1.41930i
$755$	−24.7059	+	30.0224i	−0.899139	+	1.09263i
$756$	0.0162578	−	4.06741i	0.000591290	−	0.147930i
$757$	14.5129	+	14.5129i	0.527481	+	0.527481i	0.919820	−	0.392340i	$-0.128334\pi$
$757$	14.5129	+	14.5129i	0.527481	+	0.527481i	−0.392340	+	0.919820i	$0.628334\pi$
$758$	−14.1759	−	0.0283311i	−0.514893	−	0.00102903i
$759$	18.9133			0.686510
$760$	−9.09777	−	7.57864i	−0.330011	−	0.274906i
$761$	−50.5111			−1.83103			−0.915514	−	0.402287i	$-0.868216\pi$
$761$	−50.5111			−1.83103			−0.915514	+	0.402287i	$0.868216\pi$
$762$	−37.9908	−	0.0759259i	−1.37626	−	0.00275051i
$763$	−7.64255	−	7.64255i	−0.276679	−	0.276679i
$764$	0.0275966	−	6.90418i	0.000998411	−	0.249784i
$765$	−46.7149	+	4.53804i	−1.68898	+	0.164073i
$766$	−19.7511	−	19.8302i	−0.713637	−	0.716496i
$767$	−3.88304	+	3.88304i	−0.140208	+	0.140208i
$768$	29.9386	+	30.9116i	1.08032	+	1.11543i
$769$		−	21.8236i		−	0.786981i	−0.919329	−	0.393490i	$-0.871267\pi$
$769$		−	21.8236i		−	0.786981i	0.919329	−	0.393490i	$-0.128733\pi$
$770$	−0.291502	−	3.06437i	−0.0105050	−	0.110432i
$771$			49.7598i			1.79206i
$772$	−1.87766	+	1.86271i	−0.0675786	+	0.0670405i
$773$	−16.3163	+	16.3163i	−0.586857	+	0.586857i	−0.936779	−	0.349922i	$-0.886208\pi$
$773$	−16.3163	+	16.3163i	−0.586857	+	0.586857i	0.349922	+	0.936779i	$0.386208\pi$
$774$	28.1376	−	28.0254i	1.01139	−	1.00735i
$775$	−30.4050	+	5.96356i	−1.09218	+	0.214218i
$776$	−1.53027	−	1.54873i	−0.0549335	−	0.0555962i
$777$	10.7697	+	10.7697i	0.386361	+	0.386361i
$778$	0.0856968	−	42.8798i	0.00307238	−	1.53731i
$779$	−1.87220			−0.0670785
$780$	52.4641	+	43.5264i	1.87851	+	1.55849i
$781$	18.3335			0.656023
$782$	0.0620387	−	31.0421i	0.00221850	−	1.11006i
$783$	−16.1032	−	16.1032i	−0.575483	−	0.575483i
$784$	−0.211823	+	26.4967i	−0.00756510	+	0.946311i
$785$	−2.69923	−	27.7861i	−0.0963396	−	0.991727i
$786$	3.82365	−	3.80840i	0.136385	−	0.135841i
$787$	39.6667	−	39.6667i	1.41396	−	1.41396i	0.693721	−	0.720243i	$-0.255970\pi$
$787$	39.6667	−	39.6667i	1.41396	−	1.41396i	0.720243	−	0.693721i	$-0.244030\pi$
$788$	7.91943	+	7.98299i	0.282118	+	0.284382i
$789$			55.2583i			1.96725i
$790$	−13.9550	−	11.5306i	−0.496496	−	0.410241i
$791$		−	8.97437i		−	0.319092i
$792$	19.0194	+	0.114034i	0.675824	+	0.00405202i
$793$	6.85148	−	6.85148i	0.243303	−	0.243303i
$794$	29.4478	+	29.5658i	1.04506	+	1.04925i
$795$	−41.0470	−	33.7782i	−1.45579	−	1.19799i
$796$	46.7563	+	0.186889i	1.65723	+	0.00662410i
$797$	−20.2066	−	20.2066i	−0.715756	−	0.715756i	0.251977	−	0.967733i	$-0.418919\pi$
$797$	−20.2066	−	20.2066i	−0.715756	−	0.715756i	−0.967733	+	0.251977i	$0.918919\pi$
$798$	−4.36433	−	0.00872227i	−0.154495	−	0.000308765i
$799$	59.4774			2.10416
$800$	−5.16626	−	27.8084i	−0.182655	−	0.983177i
$801$	−11.3817			−0.402153
$802$	38.8636	+	0.0776703i	1.37232	+	0.00274264i
$803$	−12.8513	−	12.8513i	−0.453512	−	0.453512i
$804$	46.2577	+	0.184896i	1.63138	+	0.00652078i
$805$	−4.68508	−	3.85542i	−0.165127	−	0.135886i
$806$	35.0503	+	35.1907i	1.23460	+	1.23954i
$807$	−31.2761	+	31.2761i	−1.10097	+	1.10097i
$808$	−6.88640	−	0.0412886i	−0.242263	−	0.00145253i
$809$		−	9.82224i		−	0.345332i	−0.984980	−	0.172666i	$-0.944762\pi$
$809$		−	9.82224i		−	0.345332i	0.984980	−	0.172666i	$-0.0552381\pi$
$810$	9.20602	+	7.60669i	0.323467	+	0.267272i
$811$		−	43.9669i		−	1.54389i	−0.635691	−	0.771943i	$-0.719285\pi$
$811$		−	43.9669i		−	1.54389i	0.635691	−	0.771943i	$-0.280715\pi$
$812$	−5.92442	−	5.97197i	−0.207906	−	0.209575i
$813$	−54.9456	+	54.9456i	−1.92703	+	1.92703i
$814$	−14.7050	+	14.6463i	−0.515409	+	0.513353i
$815$	−3.09196	−	31.8288i	−0.108307	−	1.11492i
$816$	0.426375	−	53.3348i	0.0149261	−	1.86709i
$817$	−8.78071	−	8.78071i	−0.307198	−	0.307198i
$818$	0.0248867	−	12.4525i	0.000870143	−	0.435390i
$819$	14.7057			0.513860
$820$	−3.44183	−	2.85549i	−0.120194	−	0.0997179i
$821$	−7.17510			−0.250413			−0.125206	−	0.992131i	$-0.539959\pi$
$821$	−7.17510			−0.250413			−0.125206	+	0.992131i	$0.539959\pi$
$822$	0.0964056	−	48.2381i	0.00336253	−	1.68250i
$823$	−18.9730	−	18.9730i	−0.661358	−	0.661358i	0.294342	−	0.955700i	$-0.404899\pi$
$823$	−18.9730	−	18.9730i	−0.661358	−	0.661358i	−0.955700	+	0.294342i	$0.904899\pi$
$824$	9.85310	+	9.97196i	0.343249	+	0.347390i
$825$	−17.7277	−	11.9139i	−0.617198	−	0.414787i
$826$	0.595020	−	0.592646i	0.0207034	−	0.0206208i
$827$	−2.11082	+	2.11082i	−0.0734004	+	0.0734004i	−0.742854	−	0.669454i	$-0.766528\pi$
$827$	−2.11082	+	2.11082i	−0.0734004	+	0.0734004i	0.669454	+	0.742854i	$0.266528\pi$
$828$	26.6151	−	26.4032i	0.924938	−	0.917574i
$829$			20.4182i			0.709154i	0.935027	+	0.354577i	$0.115375\pi$
$829$			20.4182i			0.709154i	−0.935027	+	0.354577i	$0.884625\pi$
$830$	−0.921483	−	9.68694i	−0.0319851	−	0.336239i
$831$		−	17.9834i		−	0.623838i
$832$	−32.4422	+	31.6733i	−1.12473	+	1.09808i
$833$	23.2227	−	23.2227i	0.804618	−	0.804618i
$834$	2.35299	+	2.36241i	0.0814773	+	0.0818036i
$835$	29.0196	−	2.81906i	1.00426	−	0.0975574i
$836$	0.0237713	−	5.94714i	0.000822147	−	0.205686i
$837$	−14.5405	−	14.5405i	−0.502594	−	0.502594i
$838$	−8.14724	−	0.0162826i	−0.281442	−	0.000562472i
$839$	−34.8104			−1.20179			−0.600894	−	0.799329i	$-0.705189\pi$
$839$	−34.8104			−1.20179			−0.600894	+	0.799329i	$0.705189\pi$
$840$	−8.01002	−	6.67252i	−0.276372	−	0.230224i
$841$	−18.0989			−0.624100
$842$	−0.404356		0.000808120i	−0.0139350		2.78497e-5i
$843$	5.17873	+	5.17873i	0.178365	+	0.178365i
$844$	−0.125250	+	31.3352i	−0.00431127	+	1.07860i
$845$	−27.1671	+	33.0132i	−0.934577	+	1.13569i
$846$	50.6909	+	50.8939i	1.74279	+	1.74977i
$847$	−3.67377	+	3.67377i	−0.126232	+	0.126232i
$848$	25.1996	−	24.7999i	0.865358	−	0.851632i
$849$			45.0784i			1.54709i
$850$	−19.6121	+	29.0570i	−0.672691	+	0.996647i
$851$			40.9094i			1.40236i
$852$	44.0800	−	43.7290i	1.51016	−	1.49813i
$853$	−26.4110	+	26.4110i	−0.904296	+	0.904296i	−0.995804	−	0.0915087i	$-0.970831\pi$
$853$	−26.4110	+	26.4110i	−0.904296	+	0.904296i	0.0915087	+	0.995804i	$0.470831\pi$
$854$	−1.04989	+	1.04570i	−0.0359265	+	0.0357832i
$855$	−11.2624	+	13.6860i	−0.385166	+	0.468050i
$856$	−17.7305	+	17.5192i	−0.606017	+	0.598794i
$857$	25.7008	+	25.7008i	0.877923	+	0.877923i	0.993319	−	0.115397i	$-0.0368139\pi$
$857$	25.7008	+	25.7008i	0.877923	+	0.877923i	−0.115397	+	0.993319i	$0.536814\pi$
$858$	−0.0684272	+	34.2386i	−0.00233607	+	1.16889i
$859$	−4.87742			−0.166416			−0.0832078	−	0.996532i	$-0.526517\pi$
$859$	−4.87742			−0.166416			−0.0832078	+	0.996532i	$0.526517\pi$
$860$	−2.74998	−	29.5347i	−0.0937735	−	1.00713i
$861$	−1.64836			−0.0561758
$862$	0.0953142	−	47.6920i	0.00324641	−	1.62439i
$863$	35.1734	+	35.1734i	1.19732	+	1.19732i	0.974967	+	0.222349i	$0.0713723\pi$
$863$	35.1734	+	35.1734i	1.19732	+	1.19732i	0.222349	+	0.974967i	$0.428628\pi$
$864$	13.4054	−	13.1401i	0.456061	−	0.447036i
$865$	13.3583	−	1.29767i	0.454196	−	0.0441221i
$866$	23.0242	−	22.9324i	0.782395	−	0.779274i
$867$	−14.4137	+	14.4137i	−0.489515	+	0.489515i
$868$	−5.34949	−	5.39243i	−0.181574	−	0.183031i
$869$		−	9.09213i		−	0.308429i
$870$	−58.1075	+	5.52755i	−1.97003	+	0.187401i
$871$			48.7376i			1.65141i
$872$	0.299061	−	49.8795i	0.0101275	−	1.68913i
$873$	−2.30447	+	2.30447i	−0.0779945	+	0.0779945i
$874$	−8.27251	−	8.30565i	−0.279822	−	0.280943i
$875$	1.96277	+	6.56496i	0.0663538	+	0.221936i
$876$	−61.5518	−	0.246028i	−2.07964	−	0.00831252i
$877$	−4.91798	−	4.91798i	−0.166068	−	0.166068i	0.619180	−	0.785249i	$-0.287465\pi$
$877$	−4.91798	−	4.91798i	−0.166068	−	0.166068i	−0.785249	+	0.619180i	$0.787465\pi$
$878$	−47.9933	−	0.0959163i	−1.61969	−	0.00323702i
$879$	16.7160			0.563816
$880$	9.11431	−	10.8969i	0.307243	−	0.367335i
$881$	−46.2874			−1.55946			−0.779731	−	0.626114i	$-0.784644\pi$
$881$	−46.2874			−1.55946			−0.779731	+	0.626114i	$0.784644\pi$
$882$	39.6633	+	0.0792686i	1.33553	+	0.00266911i
$883$	−25.5236	−	25.5236i	−0.858938	−	0.858938i	0.132275	−	0.991213i	$-0.457772\pi$
$883$	−25.5236	−	25.5236i	−0.858938	−	0.858938i	−0.991213	+	0.132275i	$0.957772\pi$
$884$	56.1950	+	0.224616i	1.89004	+	0.00755467i
$885$	−0.563428	−	5.79997i	−0.0189394	−	0.194964i
$886$	20.7120	+	20.7950i	0.695835	+	0.698622i
$887$	−20.0177	+	20.0177i	−0.672128	+	0.672128i	−0.958206	−	0.286078i	$-0.907648\pi$
$887$	−20.0177	+	20.0177i	−0.672128	+	0.672128i	0.286078	+	0.958206i	$0.407648\pi$
$888$	−0.421431	+	70.2892i	−0.0141423	+	2.35875i
$889$			6.12138i			0.205304i
$890$	−5.41497	+	6.55348i	−0.181510	+	0.219673i
$891$			5.99803i			0.200942i
$892$	12.1285	+	12.2259i	0.406093	+	0.409352i
$893$	15.8821	−	15.8821i	0.531474	−	0.531474i
$894$	−43.1455	+	42.9734i	−1.44300	+	1.43725i
$895$	−13.7941	−	11.3514i	−0.461087	−	0.379435i
$896$	4.97107	−	4.83389i	0.166072	−	0.161489i
$897$	47.7213	+	47.7213i	1.59337	+	1.59337i
$898$	−0.0338597	+	16.9422i	−0.00112991	+	0.565370i
$899$	−42.5283			−1.41840
$900$	−41.5785	+	7.98265i	−1.38595	+	0.266088i
$901$	−43.8214			−1.45990
$902$	0.00448907	−	2.24618i	0.000149470	−	0.0747895i
$903$	−7.73086	−	7.73086i	−0.257267	−	0.257267i
$904$	29.4615	−	29.1103i	0.979874	−	0.968194i
$905$	24.4793	+	20.1444i	0.813719	+	0.669622i
$906$	−46.8598	+	46.6728i	−1.55681	+	1.55060i
$907$	−41.4762	+	41.4762i	−1.37719	+	1.37719i	−0.527866	+	0.849328i	$0.677008\pi$
$907$	−41.4762	+	41.4762i	−1.37719	+	1.37719i	−0.849328	+	0.527866i	$0.822992\pi$
$908$	−12.7825	+	12.6807i	−0.424203	+	0.420825i
$909$			10.3082i			0.341902i
$910$	6.99640	−	8.46741i	0.231928	−	0.280692i
$911$			54.9738i			1.82136i	0.413110	+	0.910681i	$0.364442\pi$
$911$			54.9738i			1.82136i	−0.413110	+	0.910681i	$0.635558\pi$
$912$	−14.1280	−	14.3557i	−0.467824	−	0.475365i
$913$	3.45587	−	3.45587i	0.114373	−	0.114373i
$914$	−0.173872	−	0.174568i	−0.00575117	−	0.00577421i
$915$	0.994147	+	10.2338i	0.0328655	+	0.338320i
$916$	0.0460166	−	11.5125i	0.00152043	−	0.380385i
$917$	−0.614869	−	0.614869i	−0.0203048	−	0.0203048i
$918$	−23.2658	−	0.0464976i	−0.767887	−	0.00153465i
$919$	−30.0697			−0.991908			−0.495954	−	0.868349i	$-0.665182\pi$
$919$	−30.0697			−0.991908			−0.495954	+	0.868349i	$0.665182\pi$
$920$	−2.54029	−	27.8863i	−0.0837508	−	0.919383i
$921$	20.2468			0.667155
$922$	2.59414	+	0.00518448i	0.0854333	+	0.000170742i
$923$	46.2583	+	46.2583i	1.52261	+	1.52261i
$924$	0.0209291	−	5.23609i	0.000688518	−	0.172255i
$925$	25.7696	−	38.3449i	0.847300	−	1.26077i
$926$	40.2480	+	40.4092i	1.32263	+	1.32793i
$927$	14.8380	−	14.8380i	0.487345	−	0.487345i
$928$	0.387931	−	38.8203i	0.0127345	−	1.27434i
$929$			18.1372i			0.595063i	0.954712	+	0.297532i	$0.0961634\pi$
$929$			18.1372i			0.595063i	−0.954712	+	0.297532i	$0.903837\pi$
$930$	−52.4685	+	4.99114i	−1.72051	+	0.163666i
$931$		−	12.4022i		−	0.406465i
$932$	−37.9402	+	37.6381i	−1.24277	+	1.23288i
$933$	−24.7982	+	24.7982i	−0.811856	+	0.811856i
$934$	−13.0796	+	13.0274i	−0.427976	+	0.426269i
$935$	−17.5249	+	1.70243i	−0.573127	+	0.0556754i
$936$	47.7012	+	48.2766i	1.55916	+	1.57797i
$937$	−16.1064	−	16.1064i	−0.526174	−	0.526174i	0.393255	−	0.919429i	$-0.371349\pi$
$937$	−16.1064	−	16.1064i	−0.526174	−	0.526174i	−0.919429	+	0.393255i	$0.871349\pi$
$938$	0.0148960	−	7.45343i	0.000486370	−	0.243363i
$939$	35.0754			1.14464
$940$	53.4209	−	4.97402i	1.74240	−	0.162235i
$941$	53.1895			1.73393			0.866964	−	0.498370i	$-0.166068\pi$
$941$	53.1895			1.73393			0.866964	+	0.498370i	$0.166068\pi$
$942$	0.0949053	−	47.4874i	0.00309218	−	1.54722i
$943$	−3.13069	−	3.13069i	−0.101949	−	0.101949i
$944$	3.87564	+	0.0309830i	0.126141	+	0.00100841i
$945$	−2.88962	+	3.51144i	−0.0939993	+	0.114227i
$946$	10.5557	−	10.5136i	0.343196	−	0.341827i
$947$	15.8764	−	15.8764i	0.515912	−	0.515912i	−0.400420	−	0.916332i	$-0.631136\pi$
$947$	15.8764	−	15.8764i	0.515912	−	0.515912i	0.916332	+	0.400420i	$0.131136\pi$
$948$	−21.6866	−	21.8606i	−0.704347	−	0.710000i
$949$		−	64.8517i		−	2.10517i
$950$	2.52204	+	12.9960i	0.0818258	+	0.421646i
$951$			39.9883i			1.29671i
$952$	−8.59383	−	0.0515258i	−0.278528	−	0.00166996i
$953$	9.75942	−	9.75942i	0.316139	−	0.316139i	−0.531143	−	0.847282i	$-0.678237\pi$
$953$	9.75942	−	9.75942i	0.316139	−	0.316139i	0.847282	+	0.531143i	$0.178237\pi$
$954$	−37.3477	−	37.4973i	−1.20918	−	1.21402i
$955$	−4.90495	+	5.96045i	−0.158721	+	0.192876i
$956$	−8.59185	−	0.0343424i	−0.277880	−	0.00111071i
$957$	−20.7302	−	20.7302i	−0.670111	−	0.670111i
$958$	28.9630	+	0.0578837i	0.935753	+	0.00187014i
$959$	−7.77250			−0.250987
$960$	−4.07736	−	47.9394i	−0.131596	−	1.54724i
$961$	−7.40118			−0.238748
$962$	−74.0580	−	0.148008i	−2.38773	−	0.00477196i
$963$	26.3826	+	26.3826i	0.850168	+	0.850168i
$964$	−12.6008	−	0.0503666i	−0.405845	−	0.00162220i
$965$	2.94319	−	0.285912i	0.0947448	−	0.00920382i
$966$	−7.28343	−	7.31260i	−0.234341	−	0.235279i
$967$	26.5520	−	26.5520i	0.853856	−	0.853856i	−0.136750	−	0.990606i	$-0.543666\pi$
$967$	26.5520	−	26.5520i	0.853856	−	0.853856i	0.990606	+	0.136750i	$0.0436656\pi$
$968$	−23.9771	−	0.143759i	−0.770653	−	0.00462059i
$969$			24.9641i			0.801964i
$970$	0.230516	+	2.42327i	0.00740143	+	0.0778064i
$971$			47.6809i			1.53015i	0.643940	+	0.765076i	$0.277299\pi$
$971$			47.6809i			1.53015i	−0.643940	+	0.765076i	$0.722701\pi$
$972$	28.3287	+	28.5561i	0.908644	+	0.915937i
$973$	0.379891	−	0.379891i	0.0121788	−	0.0121788i
$974$	−2.07136	+	2.06310i	−0.0663706	+	0.0661058i
$975$	−14.6692	−	74.7903i	−0.469790	−	2.39521i
$976$	−6.83842	−	0.0546684i	−0.218892	−	0.00174989i
$977$	6.26374	+	6.26374i	0.200395	+	0.200395i	0.800169	−	0.599774i	$-0.204743\pi$
$977$	6.26374	+	6.26374i	0.200395	+	0.200395i	−0.599774	+	0.800169i	$0.704743\pi$
$978$	0.108714	−	54.3967i	0.00347628	−	1.73941i
$979$	−4.26981			−0.136464
$980$	18.9159	−	22.8000i	0.604245	−	0.728320i
$981$	−74.6645			−2.38385
$982$	0.0221808	−	11.0985i	0.000707818	−	0.354168i
$983$	26.1154	+	26.1154i	0.832951	+	0.832951i	0.987919	−	0.154968i	$-0.0495275\pi$
$983$	26.1154	+	26.1154i	0.832951	+	0.832951i	−0.154968	+	0.987919i	$0.549527\pi$
$984$	−5.34679	−	5.41129i	−0.170450	−	0.172506i
$985$	−1.21557	−	12.5132i	−0.0387313	−	0.398702i
$986$	−34.0920	+	33.9561i	−1.08571	+	1.08138i
$987$	13.9832	−	13.9832i	0.445090	−	0.445090i
$988$	15.0656	−	14.9456i	0.479300	−	0.475484i
$989$		−	29.3662i		−	0.933790i
$990$	−16.3928	−	13.5449i	−0.520996	−	0.430485i
$991$		−	33.6990i		−	1.07048i	−0.844699	−	0.535242i	$-0.820220\pi$
$991$		−	33.6990i		−	1.07048i	0.844699	−	0.535242i	$-0.179780\pi$
$992$	0.350285	−	35.0530i	0.0111216	−	1.11293i
$993$	61.0466	−	61.0466i	1.93725	−	1.93725i
$994$	−7.06014	−	7.08842i	−0.223934	−	0.224831i
$995$	−40.3652	−	33.2172i	−1.27966	−	1.05305i
$996$	0.0661601	−	16.5521i	0.00209636	−	0.524472i
$997$	14.9851	+	14.9851i	0.474584	+	0.474584i	0.903394	−	0.428811i	$-0.141067\pi$
$997$	14.9851	+	14.9851i	0.474584	+	0.474584i	−0.428811	+	0.903394i	$0.641067\pi$
$998$	32.6217	+	0.0651957i	1.03262	+	0.00206373i
$999$	30.6614			0.970082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.k.c.247.1	yes	108
4.3	odd	2	inner	820.2.k.c.247.24	yes	108
5.3	odd	4	inner	820.2.k.c.83.24	yes	108
20.3	even	4	inner	820.2.k.c.83.1	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.1	✓	108	20.3	even	4	inner
820.2.k.c.83.24	yes	108	5.3	odd	4	inner
820.2.k.c.247.1	yes	108	1.1	even	1	trivial
820.2.k.c.247.24	yes	108	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41421 - 0.00282635i) q^{2} +(1.90181 + 1.90181i) q^{3} +(1.99998 + 0.00799412i) q^{4} +(-1.72661 - 1.42085i) q^{5} +(-2.68419 - 2.69494i) q^{6} +(-0.433364 + 0.433364i) q^{7} +(-2.82838 - 0.0169580i) q^{8} +4.23379i q^{9} +(2.43777 + 2.01427i) q^{10} +1.58829i q^{11} +(3.78839 + 3.81880i) q^{12} +(-4.00751 + 4.00751i) q^{13} +(0.614093 - 0.611643i) q^{14} +(-0.581488 - 5.98588i) q^{15} +(3.99987 + 0.0319762i) q^{16} +(-3.50563 - 3.50563i) q^{17} +(0.0119662 - 5.98747i) q^{18} -1.87220 q^{19} +(-3.44183 - 2.85549i) q^{20} -1.64836 q^{21} +(0.00448907 - 2.24618i) q^{22} +(-3.13069 - 3.13069i) q^{23} +(-5.34679 - 5.41129i) q^{24} +(0.962351 + 4.90651i) q^{25} +(5.67879 - 5.65614i) q^{26} +(-2.34643 + 2.34643i) q^{27} +(-0.870186 + 0.863257i) q^{28} +6.86286i q^{29} +(0.805429 + 8.46694i) q^{30} +6.19687i q^{31} +(-5.65657 - 0.0565262i) q^{32} +(-3.02063 + 3.02063i) q^{33} +(4.94780 + 4.96761i) q^{34} +(1.36400 - 0.132503i) q^{35} +(-0.0338454 + 8.46751i) q^{36} +(-6.53361 - 6.53361i) q^{37} +(2.64769 + 0.00529150i) q^{38} -15.2431 q^{39} +(4.85940 + 4.04799i) q^{40} +1.00000 q^{41} +(2.33112 + 0.00465883i) q^{42} +(4.69005 + 4.69005i) q^{43} +(-0.0126970 + 3.17655i) q^{44} +(6.01559 - 7.31009i) q^{45} +(4.41861 + 4.43630i) q^{46} +(-8.48312 + 8.48312i) q^{47} +(7.54620 + 7.66782i) q^{48} +6.62439i q^{49} +(-1.34710 - 6.94156i) q^{50} -13.3341i q^{51} +(-8.04699 + 7.98292i) q^{52} +(6.25014 - 6.25014i) q^{53} +(3.32498 - 3.31172i) q^{54} +(2.25673 - 2.74235i) q^{55} +(1.23307 - 1.21837i) q^{56} +(-3.56057 - 3.56057i) q^{57} +(0.0193969 - 9.70554i) q^{58} +0.968941 q^{59} +(-1.11512 - 11.9763i) q^{60} -1.70966 q^{61} +(0.0175145 - 8.76368i) q^{62} +(-1.83477 - 1.83477i) q^{63} +(7.99942 + 0.0959274i) q^{64} +(12.6135 - 1.22532i) q^{65} +(4.28035 - 4.26327i) q^{66} +(6.08078 - 6.08078i) q^{67} +(-6.98319 - 7.03923i) q^{68} -11.9080i q^{69} +(-1.92935 + 0.183532i) q^{70} -11.5429i q^{71} +(0.0717967 - 11.9747i) q^{72} +(-8.09127 + 8.09127i) q^{73} +(9.22144 + 9.25837i) q^{74} +(-7.50106 + 11.1615i) q^{75} +(-3.74437 - 0.0149666i) q^{76} +(-0.688308 - 0.688308i) q^{77} +(21.5569 + 0.0430823i) q^{78} -5.72448 q^{79} +(-6.86078 - 5.73844i) q^{80} +3.77641 q^{81} +(-1.41421 - 0.00282635i) q^{82} +(-2.17584 - 2.17584i) q^{83} +(-3.29668 - 0.0131771i) q^{84} +(1.07186 + 11.0338i) q^{85} +(-6.61946 - 6.64597i) q^{86} +(-13.0519 + 13.0519i) q^{87} +(0.0269343 - 4.49228i) q^{88} +2.68831i q^{89} +(-8.52797 + 10.3210i) q^{90} -3.47342i q^{91} +(-6.23630 - 6.28636i) q^{92} +(-11.7853 + 11.7853i) q^{93} +(12.0209 - 11.9729i) q^{94} +(3.23256 + 2.66012i) q^{95} +(-10.6502 - 10.8652i) q^{96} +(0.544305 + 0.544305i) q^{97} +(0.0187229 - 9.36828i) q^{98} -6.72448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 12 q^{2} - 4 q^{6} - 24 q^{8} + 4 q^{10} - 16 q^{13} + 52 q^{16} - 8 q^{17} + 18 q^{18} + 38 q^{20} + 72 q^{21} + 10 q^{22} - 12 q^{25} + 24 q^{26} - 58 q^{28} - 70 q^{30} - 38 q^{32} + 8 q^{33}+ \cdots + 122 q^{98}+O(q^{100}) \) 108 * q + 12 * q^2 - 4 * q^6 - 24 * q^8 + 4 * q^10 - 16 * q^13 + 52 * q^16 - 8 * q^17 + 18 * q^18 + 38 * q^20 + 72 * q^21 + 10 * q^22 - 12 * q^25 + 24 * q^26 - 58 * q^28 - 70 * q^30 - 38 * q^32 + 8 * q^33 + 72 * q^36 - 44 * q^37 + 56 * q^38 + 50 * q^40 + 108 * q^41 - 72 * q^42 - 4 * q^45 - 4 * q^46 - 94 * q^48 - 56 * q^50 - 50 * q^52 - 16 * q^53 - 32 * q^56 - 112 * q^57 + 68 * q^58 + 136 * q^60 + 8 * q^61 + 2 * q^62 - 48 * q^65 + 16 * q^66 - 16 * q^68 - 48 * q^70 - 42 * q^72 - 20 * q^73 - 12 * q^76 + 72 * q^77 + 100 * q^78 + 72 * q^80 - 52 * q^81 + 12 * q^82 - 32 * q^85 - 20 * q^86 - 38 * q^88 - 50 * q^90 + 8 * q^92 + 24 * q^93 + 44 * q^96 - 56 * q^97 + 122 * q^98

Introduction

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