LMFDB - Embedded newform 820.2.k.c.83.1

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			83.1
Character	$\chi$	$=$	820.83
Dual form			820.2.k.c.247.1

$q$-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 $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41421	+	0.00282635i	−0.999998	+	0.00199853i
$2$	−1.41421	+	0.00282635i	−0.999998	+	0.00199853i
$3$	1.90181	−	1.90181i	1.09801	−	1.09801i	0.103369	−	0.994643i	$-0.467038\pi$
$3$	1.90181	−	1.90181i	1.09801	−	1.09801i	0.994643	−	0.103369i	$-0.0329624\pi$
$4$	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	0.620450	−	0.784246i	$-0.286950\pi$
$7$	−0.433364	−	0.433364i	−0.163796	−	0.163796i	−0.784246	+	0.620450i	$0.786950\pi$
$8$	−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	$-0.923035\pi$
$11$		−	1.58829i		−	0.478887i	0.970910	−	0.239444i	$-0.0769651\pi$
$12$	3.78839	−	3.81880i	1.09361	−	1.10239i
$13$	−4.00751	−	4.00751i	−1.11148	−	1.11148i	−0.992950	−	0.118533i	$-0.962181\pi$
$13$	−4.00751	−	4.00751i	−1.11148	−	1.11148i	−0.118533	−	0.992950i	$-0.537819\pi$
$14$	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	−0.990163	−	0.139922i	$-0.955315\pi$
$17$	−3.50563	+	3.50563i	−0.850241	+	0.850241i	0.139922	+	0.990163i	$0.455315\pi$
$18$	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	−0.953665	−	0.300871i	$-0.902723\pi$
$23$	−3.13069	+	3.13069i	−0.652794	+	0.652794i	0.300871	+	0.953665i	$0.402723\pi$
$24$	−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	$-0.780092\pi$
$29$		−	6.86286i		−	1.27440i	0.770698	−	0.637201i	$-0.219908\pi$
$30$	0.805429	−	8.46694i	0.147051	−	1.54585i
$31$		−	6.19687i		−	1.11299i	−0.830851	−	0.556495i	$-0.812146\pi$
$31$		−	6.19687i		−	1.11299i	0.830851	−	0.556495i	$-0.187854\pi$
$32$	−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	−0.0770954	+	0.997024i	$0.524565\pi$
$37$	−6.53361	+	6.53361i	−1.07412	+	1.07412i	−0.997024	+	0.0770954i	$0.975435\pi$
$38$	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	−0.252398	−	0.967623i	$-0.581219\pi$
$43$	4.69005	−	4.69005i	0.715225	−	0.715225i	0.967623	+	0.252398i	$0.0812192\pi$
$44$	−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	−0.961064	−	0.276326i	$-0.910883\pi$
$47$	−8.48312	−	8.48312i	−1.23739	−	1.23739i	−0.276326	−	0.961064i	$-0.589117\pi$
$48$	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	0.991164	−	0.132642i	$-0.0423459\pi$
$53$	6.25014	+	6.25014i	0.858522	+	0.858522i	−0.132642	+	0.991164i	$0.542346\pi$
$54$	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	0.973132	−	0.230247i	$-0.0739534\pi$
$67$	6.08078	+	6.08078i	0.742885	+	0.742885i	−0.230247	+	0.973132i	$0.573953\pi$
$68$	−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	$0.240174\pi$
$71$			11.5429i			1.36989i	−0.728595	+	0.684945i	$0.759826\pi$
$72$	0.0717967	+	11.9747i	0.00846132	+	1.41124i
$73$	−8.09127	−	8.09127i	−0.947011	−	0.947011i	0.0516537	−	0.998665i	$-0.483551\pi$
$73$	−8.09127	−	8.09127i	−0.947011	−	0.947011i	−0.998665	+	0.0516537i	$0.983551\pi$
$74$	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	−0.816366	−	0.577536i	$-0.804014\pi$
$83$	−2.17584	+	2.17584i	−0.238830	+	0.238830i	0.577536	+	0.816366i	$0.304014\pi$
$84$	−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	$-0.954492\pi$
$89$		−	2.68831i		−	0.284960i	0.989798	−	0.142480i	$-0.0455077\pi$
$90$	−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	−0.678934	−	0.734200i	$-0.737558\pi$
$97$	0.544305	−	0.544305i	0.0552658	−	0.0552658i	0.734200	+	0.678934i	$0.237558\pi$
$98$	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	−0.858365	−	0.513039i	$-0.828519\pi$
$103$	−3.50467	+	3.50467i	−0.345326	+	0.345326i	0.513039	+	0.858365i	$0.328519\pi$
$104$	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	0.940953	−	0.338537i	$-0.109932\pi$
$107$	6.23144	+	6.23144i	0.602416	+	0.602416i	−0.338537	+	0.940953i	$0.609932\pi$
$108$	−4.71159	−	4.67407i	−0.453372	−	0.449763i
$109$		−	17.6354i		−	1.68916i	−0.535426	−	0.844582i	$-0.679849\pi$
$109$		−	17.6354i		−	1.68916i	0.535426	−	0.844582i	$-0.320151\pi$
$110$	−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	0.0256206	−	0.999672i	$-0.491844\pi$
$113$	−10.3543	−	10.3543i	−0.974051	−	0.974051i	−0.999672	+	0.0256206i	$0.991844\pi$
$114$	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	0.947238	−	0.320531i	$-0.103861\pi$
$127$	7.06262	+	7.06262i	0.626706	+	0.626706i	−0.320531	+	0.947238i	$0.603861\pi$
$128$	−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	$-0.980258\pi$
$131$		−	1.41883i		−	0.123963i	0.998077	−	0.0619817i	$-0.0197421\pi$
$132$	−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	−0.211271	−	0.977428i	$-0.567760\pi$
$137$	8.96763	−	8.96763i	0.766157	−	0.766157i	0.977428	+	0.211271i	$0.0677602\pi$
$138$	−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	$0.227664\pi$
$149$			16.0098i			1.31158i	−0.754945	+	0.655788i	$0.772336\pi$
$150$	10.6396	+	15.7635i	0.868722	+	1.28708i
$151$			17.3881i			1.41502i	0.706703	+	0.707510i	$0.250182\pi$
$151$			17.3881i			1.41502i	−0.706703	+	0.707510i	$0.749818\pi$
$152$	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	−0.260828	−	0.965385i	$-0.583995\pi$
$157$	8.82808	−	8.82808i	0.704558	−	0.704558i	0.965385	+	0.260828i	$0.0839954\pi$
$158$	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	−0.189756	−	0.981831i	$-0.560770\pi$
$163$	10.1125	−	10.1125i	0.792075	−	0.792075i	0.981831	+	0.189756i	$0.0607696\pi$
$164$	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	0.253794	−	0.967258i	$-0.418321\pi$
$167$	−9.21999	−	9.21999i	−0.713464	−	0.713464i	−0.967258	+	0.253794i	$0.918321\pi$
$168$	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	0.527116	−	0.849793i	$-0.323273\pi$
$173$	−4.24416	−	4.24416i	−0.322677	−	0.322677i	−0.849793	+	0.527116i	$0.823273\pi$
$174$	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	$0.0398588\pi$
$191$			3.45212i			0.249786i	−0.992170	+	0.124893i	$0.960141\pi$
$192$	15.0310	−	15.3958i	1.08477	−	1.11110i
$193$	−0.935101	−	0.935101i	−0.0673100	−	0.0673100i	0.672650	−	0.739960i	$-0.265156\pi$
$193$	−0.935101	−	0.935101i	−0.0673100	−	0.0673100i	−0.739960	+	0.672650i	$0.765156\pi$
$194$	−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	−0.551152	−	0.834405i	$-0.685812\pi$
$197$	3.97564	−	3.97564i	0.283252	−	0.283252i	0.834405	+	0.551152i	$0.185812\pi$
$198$	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	$-0.818687\pi$
$211$		−	15.6677i		−	1.07861i	0.842110	−	0.539305i	$-0.181313\pi$
$212$	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	−0.473219	−	0.880945i	$-0.656908\pi$
$223$	6.08865	−	6.08865i	0.407726	−	0.407726i	0.880945	+	0.473219i	$0.156908\pi$
$224$	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	0.463552	−	0.886070i	$-0.346575\pi$
$227$	−6.36587	−	6.36587i	−0.422518	−	0.422518i	−0.886070	+	0.463552i	$0.846575\pi$
$228$	−7.09263	+	7.14956i	−0.469721	+	0.473491i
$229$			5.75631i			0.380388i	0.981747	+	0.190194i	$0.0609117\pi$
$229$			5.75631i			0.380388i	−0.981747	+	0.190194i	$0.939088\pi$
$230$	−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	−0.960884	−	0.276952i	$-0.910676\pi$
$233$	−18.8947	−	18.8947i	−1.23784	−	1.23784i	−0.276952	−	0.960884i	$-0.589324\pi$
$234$	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	$0.332552\pi$
$251$			27.4019i			1.72959i	−0.502123	+	0.864796i	$0.667448\pi$
$252$	−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	−0.169487	−	0.985532i	$-0.554211\pi$
$257$	13.0822	−	13.0822i	0.816045	−	0.816045i	0.985532	+	0.169487i	$0.0542112\pi$
$258$	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	−0.0992407	−	0.995063i	$-0.531641\pi$
$263$	14.5278	−	14.5278i	0.895823	−	0.895823i	0.995063	+	0.0992407i	$0.0316414\pi$
$264$	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	$-0.832838\pi$
$269$		−	16.4454i		−	1.00269i	0.865246	−	0.501347i	$-0.167162\pi$
$270$	−10.4464	−	0.993728i	−0.635748	−	0.0604763i
$271$		−	28.8912i		−	1.75501i	−0.479565	−	0.877507i	$-0.659205\pi$
$271$		−	28.8912i		−	1.75501i	0.479565	−	0.877507i	$-0.340795\pi$
$272$	−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	−0.834732	−	0.550656i	$-0.814378\pi$
$277$	−4.72797	+	4.72797i	−0.284076	+	0.284076i	0.550656	+	0.834732i	$0.314378\pi$
$278$	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	−0.260878	−	0.965372i	$-0.584012\pi$
$283$	11.8514	−	11.8514i	0.704493	−	0.704493i	0.965372	+	0.260878i	$0.0840121\pi$
$284$	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	0.823728	−	0.566985i	$-0.191890\pi$
$293$	4.39475	+	4.39475i	0.256744	+	0.256744i	−0.566985	+	0.823728i	$0.691890\pi$
$294$	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	0.842499	−	0.538698i	$-0.181084\pi$
$307$	5.32303	+	5.32303i	0.303801	+	0.303801i	−0.538698	+	0.842499i	$0.681084\pi$
$308$	−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	$-0.879463\pi$
$311$		−	13.0392i		−	0.739387i	0.929154	−	0.369694i	$-0.120537\pi$
$312$	43.1131	−	0.258492i	2.44080	−	0.0146343i
$313$	9.22158	+	9.22158i	0.521234	+	0.521234i	0.917944	−	0.396710i	$-0.129848\pi$
$313$	9.22158	+	9.22158i	0.521234	+	0.521234i	−0.396710	+	0.917944i	$0.629848\pi$
$314$	−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	−0.347281	−	0.937761i	$-0.612895\pi$
$317$	10.5132	−	10.5132i	0.590481	−	0.590481i	0.937761	+	0.347281i	$0.112895\pi$
$318$	−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	$0.343914\pi$
$331$			32.0991i			1.76433i	−0.470943	+	0.882164i	$0.656086\pi$
$332$	−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	−0.820050	−	0.572291i	$-0.806055\pi$
$337$	−4.54825	+	4.54825i	−0.247759	+	0.247759i	0.572291	+	0.820050i	$0.306055\pi$
$338$	−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	0.761801	−	0.647812i	$-0.224316\pi$
$347$	2.12338	+	2.12338i	0.113989	+	0.113989i	−0.647812	+	0.761801i	$0.724316\pi$
$348$	−26.2079	−	25.9992i	−1.40489	−	1.39370i
$349$		−	14.0584i		−	0.752527i	−0.926513	−	0.376263i	$-0.877209\pi$
$349$		−	14.0584i		−	0.752527i	0.926513	−	0.376263i	$-0.122791\pi$
$350$	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	0.425332	−	0.905037i	$-0.360157\pi$
$353$	−9.01285	−	9.01285i	−0.479706	−	0.479706i	−0.905037	+	0.425332i	$0.860157\pi$
$354$	−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	0.982131	−	0.188199i	$-0.0602650\pi$
$367$	15.2095	+	15.2095i	0.793932	+	0.793932i	−0.188199	+	0.982131i	$0.560265\pi$
$368$	−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	0.744097	−	0.668072i	$-0.232880\pi$
$373$	1.46829	+	1.46829i	0.0760252	+	0.0760252i	−0.668072	+	0.744097i	$0.732880\pi$
$374$	−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	−0.252523	−	0.967591i	$-0.581260\pi$
$383$	13.9942	−	13.9942i	0.715068	−	0.715068i	0.967591	+	0.252523i	$0.0812603\pi$
$384$	−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	$-0.720925\pi$
$389$		−	30.3206i		−	1.53732i	0.639659	−	0.768659i	$-0.279075\pi$
$390$	−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	−0.0483271	+	0.998832i	$0.515389\pi$
$397$	−20.8645	+	20.8645i	−1.04716	+	1.04716i	−0.998832	+	0.0483271i	$0.984611\pi$
$398$	−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	$-0.930146\pi$
$409$		−	8.80523i		−	0.435391i	0.976017	−	0.217695i	$-0.0698539\pi$
$410$	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	$-0.698270\pi$
$431$		−	33.7234i		−	1.62440i	0.583381	−	0.812199i	$-0.301730\pi$
$432$	−9.46046	−	9.31040i	−0.455167	−	0.447947i
$433$	−16.2481	−	16.2481i	−0.780836	−	0.780836i	0.199136	−	0.979972i	$-0.436186\pi$
$433$	−16.2481	−	16.2481i	−0.780836	−	0.780836i	−0.979972	+	0.199136i	$0.936186\pi$
$434$	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	−0.963812	−	0.266582i	$-0.914106\pi$
$443$	−14.6750	+	14.6750i	−0.697230	+	0.697230i	0.266582	+	0.963812i	$0.414106\pi$
$444$	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	$0.0912253\pi$
$449$			11.9800i			0.565371i	−0.959213	+	0.282686i	$0.908775\pi$
$450$	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	−0.704220	−	0.709982i	$-0.748703\pi$
$457$	0.123192	−	0.123192i	0.00576270	−	0.00576270i	0.709982	+	0.704220i	$0.248703\pi$
$458$	−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	−0.415849	+	0.909434i	$0.636515\pi$
$463$	−28.5167	+	28.5167i	−1.32528	+	1.32528i	−0.909434	+	0.415849i	$0.863485\pi$
$464$	−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	0.887647	−	0.460524i	$-0.152338\pi$
$467$	9.23022	+	9.23022i	0.427124	+	0.427124i	−0.460524	+	0.887647i	$0.652338\pi$
$468$	−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	0.739450	−	0.673212i	$-0.235086\pi$
$487$	1.46175	+	1.46175i	0.0662384	+	0.0662384i	−0.673212	+	0.739450i	$0.735086\pi$
$488$	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	$-0.943333\pi$
$491$		−	7.84785i		−	0.354169i	0.984196	−	0.177084i	$-0.0566665\pi$
$492$	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	−0.972278	−	0.233828i	$-0.924875\pi$
$503$	−16.5617	+	16.5617i	−0.738450	+	0.738450i	0.233828	+	0.972278i	$0.424875\pi$
$504$	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	$0.224663\pi$
$509$			29.2681i			1.29728i	−0.761094	+	0.648642i	$0.775337\pi$
$510$	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	−0.761248	−	0.648461i	$-0.775413\pi$
$523$	−2.57935	+	2.57935i	−0.112787	+	0.112787i	0.648461	+	0.761248i	$0.275413\pi$
$524$	−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	0.754299	−	0.656531i	$-0.227977\pi$
$547$	2.28661	+	2.28661i	0.0977683	+	0.0977683i	−0.656531	+	0.754299i	$0.727977\pi$
$548$	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	−0.536884	−	0.843656i	$-0.680399\pi$
$557$	7.24008	−	7.24008i	0.306772	−	0.306772i	0.843656	+	0.536884i	$0.180399\pi$
$558$	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	−0.999651	−	0.0263999i	$-0.991596\pi$
$563$	−23.0929	+	23.0929i	−0.973252	+	0.973252i	0.0263999	+	0.999651i	$0.491596\pi$
$564$	−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	$-0.923813\pi$
$569$		−	11.3100i		−	0.474140i	0.971493	−	0.237070i	$-0.0761870\pi$
$570$	−1.50792	+	15.8518i	−0.0631600	+	0.663959i
$571$			20.4162i			0.854391i	0.904159	+	0.427195i	$0.140498\pi$
$571$			20.4162i			0.854391i	−0.904159	+	0.427195i	$0.859502\pi$
$572$	−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	−0.682767	−	0.730637i	$-0.739223\pi$
$577$	1.14988	−	1.14988i	0.0478700	−	0.0478700i	0.730637	+	0.682767i	$0.239223\pi$
$578$	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	0.941589	−	0.336765i	$-0.109333\pi$
$587$	14.6537	+	14.6537i	0.604824	+	0.604824i	−0.336765	+	0.941589i	$0.609333\pi$
$588$	−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	0.885467	−	0.464702i	$-0.153839\pi$
$593$	10.2463	+	10.2463i	0.420765	+	0.420765i	−0.464702	+	0.885467i	$0.653839\pi$
$594$	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	0.316770	−	0.948502i	$-0.397402\pi$
$607$	−15.5642	−	15.5642i	−0.631732	−	0.631732i	−0.948502	+	0.316770i	$0.897402\pi$
$608$	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	0.927267	−	0.374401i	$-0.122152\pi$
$613$	13.6883	+	13.6883i	0.552866	+	0.552866i	−0.374401	+	0.927267i	$0.622152\pi$
$614$	−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	−0.962955	−	0.269663i	$-0.913088\pi$
$617$	−17.2210	+	17.2210i	−0.693292	+	0.693292i	0.269663	+	0.962955i	$0.413088\pi$
$618$	−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	$-0.782584\pi$
$631$		−	31.7086i		−	1.26230i	0.775661	−	0.631149i	$-0.217416\pi$
$632$	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	−0.182263	−	0.983250i	$-0.558342\pi$
$643$	20.3110	−	20.3110i	0.800987	−	0.800987i	0.983250	+	0.182263i	$0.0583421\pi$
$644$	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	−0.951684	−	0.307078i	$-0.900649\pi$
$647$	−32.0181	−	32.0181i	−1.25876	−	1.25876i	−0.307078	−	0.951684i	$-0.599351\pi$
$648$	−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	0.638001	−	0.770035i	$-0.279761\pi$
$653$	−3.37399	−	3.37399i	−0.132034	−	0.132034i	−0.770035	+	0.638001i	$0.779761\pi$
$654$	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	0.0312931	−	0.999510i	$-0.490037\pi$
$673$	−25.1177	−	25.1177i	−0.968217	−	0.968217i	−0.999510	+	0.0312931i	$0.990037\pi$
$674$	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	−0.643445	−	0.765492i	$-0.722496\pi$
$677$	3.17557	−	3.17557i	0.122047	−	0.122047i	0.765492	+	0.643445i	$0.222496\pi$
$678$	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	−0.997612	−	0.0690643i	$-0.977999\pi$
$683$	−24.2669	+	24.2669i	−0.928548	+	0.928548i	0.0690643	+	0.997612i	$0.477999\pi$
$684$	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	$-0.793799\pi$
$691$		−	31.7248i		−	1.20687i	0.797413	−	0.603433i	$-0.206201\pi$
$692$	−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	$0.310370\pi$
$709$			44.0802i			1.65547i	−0.561122	+	0.827733i	$0.689630\pi$
$710$	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	0.990813	−	0.135240i	$-0.0431807\pi$
$727$	23.0687	+	23.0687i	0.855572	+	0.855572i	−0.135240	+	0.990813i	$0.543181\pi$
$728$	−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	0.217558	−	0.976047i	$-0.430191\pi$
$733$	−20.5353	−	20.5353i	−0.758489	−	0.758489i	−0.976047	+	0.217558i	$0.930191\pi$
$734$	−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	0.392161	−	0.919897i	$-0.371728\pi$
$743$	35.7641	−	35.7641i	1.31206	−	1.31206i	0.919897	−	0.392161i	$-0.128272\pi$
$744$	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	$0.160020\pi$
$751$			26.4073i			0.963615i	−0.876277	+	0.481807i	$0.839980\pi$
$752$	−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	−0.392340	−	0.919820i	$-0.628334\pi$
$757$	14.5129	−	14.5129i	0.527481	−	0.527481i	0.919820	+	0.392340i	$0.128334\pi$
$758$	−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	$0.128733\pi$
$769$			21.8236i			0.786981i	−0.919329	+	0.393490i	$0.871267\pi$
$770$	−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	0.349922	−	0.936779i	$-0.386208\pi$
$773$	−16.3163	−	16.3163i	−0.586857	−	0.586857i	−0.936779	+	0.349922i	$0.886208\pi$
$774$	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	0.720243	+	0.693721i	$0.244030\pi$
$787$	39.6667	+	39.6667i	1.41396	+	1.41396i	0.693721	+	0.720243i	$0.255970\pi$
$788$	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	−0.967733	−	0.251977i	$-0.918919\pi$
$797$	−20.2066	+	20.2066i	−0.715756	+	0.715756i	0.251977	+	0.967733i	$0.418919\pi$
$798$	−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	$0.0552381\pi$
$809$			9.82224i			0.345332i	−0.984980	+	0.172666i	$0.944762\pi$
$810$	9.20602	−	7.60669i	0.323467	−	0.267272i
$811$			43.9669i			1.54389i	0.635691	+	0.771943i	$0.280715\pi$
$811$			43.9669i			1.54389i	−0.635691	+	0.771943i	$0.719285\pi$
$812$	−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	−0.955700	−	0.294342i	$-0.904899\pi$
$823$	−18.9730	+	18.9730i	−0.661358	+	0.661358i	0.294342	+	0.955700i	$0.404899\pi$
$824$	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	0.669454	−	0.742854i	$-0.266528\pi$
$827$	−2.11082	−	2.11082i	−0.0734004	−	0.0734004i	−0.742854	+	0.669454i	$0.766528\pi$
$828$	26.6151	+	26.4032i	0.924938	+	0.917574i
$829$		−	20.4182i		−	0.709154i	−0.935027	−	0.354577i	$-0.884625\pi$
$829$		−	20.4182i		−	0.709154i	0.935027	−	0.354577i	$-0.115375\pi$
$830$	−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	0.0915087	−	0.995804i	$-0.470831\pi$
$853$	−26.4110	−	26.4110i	−0.904296	−	0.904296i	−0.995804	+	0.0915087i	$0.970831\pi$
$854$	−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	−0.115397	−	0.993319i	$-0.536814\pi$
$857$	25.7008	−	25.7008i	0.877923	−	0.877923i	0.993319	+	0.115397i	$0.0368139\pi$
$858$	−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	0.222349	−	0.974967i	$-0.428628\pi$
$863$	35.1734	−	35.1734i	1.19732	−	1.19732i	0.974967	−	0.222349i	$-0.0713723\pi$
$864$	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	−0.785249	−	0.619180i	$-0.787465\pi$
$877$	−4.91798	+	4.91798i	−0.166068	+	0.166068i	0.619180	+	0.785249i	$0.287465\pi$
$878$	−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	−0.991213	−	0.132275i	$-0.957772\pi$
$883$	−25.5236	+	25.5236i	−0.858938	+	0.858938i	0.132275	+	0.991213i	$0.457772\pi$
$884$	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	0.286078	−	0.958206i	$-0.407648\pi$
$887$	−20.0177	−	20.0177i	−0.672128	−	0.672128i	−0.958206	+	0.286078i	$0.907648\pi$
$888$	−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	−0.849328	−	0.527866i	$-0.822992\pi$
$907$	−41.4762	−	41.4762i	−1.37719	−	1.37719i	−0.527866	−	0.849328i	$-0.677008\pi$
$908$	−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	$-0.635558\pi$
$911$		−	54.9738i		−	1.82136i	0.413110	−	0.910681i	$-0.364442\pi$
$912$	−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	$-0.903837\pi$
$929$		−	18.1372i		−	0.595063i	0.954712	−	0.297532i	$-0.0961634\pi$
$930$	−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	−0.919429	−	0.393255i	$-0.871349\pi$
$937$	−16.1064	+	16.1064i	−0.526174	+	0.526174i	0.393255	+	0.919429i	$0.371349\pi$
$938$	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	0.916332	−	0.400420i	$-0.131136\pi$
$947$	15.8764	+	15.8764i	0.515912	+	0.515912i	−0.400420	+	0.916332i	$0.631136\pi$
$948$	−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	0.847282	−	0.531143i	$-0.178237\pi$
$953$	9.75942	+	9.75942i	0.316139	+	0.316139i	−0.531143	+	0.847282i	$0.678237\pi$
$954$	−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	0.990606	−	0.136750i	$-0.0436656\pi$
$967$	26.5520	+	26.5520i	0.853856	+	0.853856i	−0.136750	+	0.990606i	$0.543666\pi$
$968$	−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	$-0.722701\pi$
$971$		−	47.6809i		−	1.53015i	0.643940	−	0.765076i	$-0.277299\pi$
$972$	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	−0.599774	−	0.800169i	$-0.704743\pi$
$977$	6.26374	−	6.26374i	0.200395	−	0.200395i	0.800169	+	0.599774i	$0.204743\pi$
$978$	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	−0.154968	−	0.987919i	$-0.549527\pi$
$983$	26.1154	−	26.1154i	0.832951	−	0.832951i	0.987919	+	0.154968i	$0.0495275\pi$
$984$	−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	$0.179780\pi$
$991$			33.6990i			1.07048i	−0.844699	+	0.535242i	$0.820220\pi$
$992$	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	−0.428811	−	0.903394i	$-0.641067\pi$
$997$	14.9851	−	14.9851i	0.474584	−	0.474584i	0.903394	+	0.428811i	$0.141067\pi$
$998$	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.83.1	✓	108
4.3	odd	2	inner	820.2.k.c.83.24	yes	108
5.2	odd	4	inner	820.2.k.c.247.24	yes	108
20.7	even	4	inner	820.2.k.c.247.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.k.c.83.1	✓	108	1.1	even	1	trivial
820.2.k.c.83.24	yes	108	4.3	odd	2	inner
820.2.k.c.247.1	yes	108	20.7	even	4	inner
820.2.k.c.247.24	yes	108	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more