LMFDB - Embedded newform 820.2.k.c.247.24

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			247.24
Character	$\chi$	$=$	820.247
Dual form			820.2.k.c.83.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00282635 - 1.41421i) 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} +(0.0169580 + 2.82838i) q^{8} +4.23379i q^{9} +(-2.00451 + 2.44580i) q^{10} -1.58829i q^{11} +(3.81880 + 3.78839i) 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} +(5.98747 - 0.0119662i) q^{18} +1.87220 q^{19} +(3.46455 + 2.82788i) q^{20} -1.64836 q^{21} +(-2.24618 + 0.00448907i) 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} +(-0.863257 + 0.870186i) q^{28} +6.86286i q^{29} +(8.46366 - 0.839265i) q^{30} -6.19687i q^{31} +(-0.0565262 - 5.65657i) 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} +(-0.00529150 - 2.64769i) q^{38} +15.2431 q^{39} +(3.98943 - 4.90759i) q^{40} +1.00000 q^{41} +(0.00465883 + 2.33112i) 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} +(-7.66782 - 7.54620i) q^{48} +6.62439i q^{49} +(6.93612 - 1.37484i) q^{50} +13.3341i q^{51} +(7.98292 - 8.04699i) 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} +(9.70554 - 0.0193969i) q^{58} -0.968941 q^{59} +(-1.21082 - 11.9670i) q^{60} -1.70966 q^{61} +(-8.76368 + 0.0175145i) 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} +(7.03923 + 6.98319i) q^{68} -11.9080i q^{69} +(0.191243 + 1.92860i) q^{70} +11.5429i q^{71} +(-11.9747 + 0.0717967i) 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} +(-0.0430823 - 21.5569i) q^{78} +5.72448 q^{79} +(-6.95165 - 5.62802i) q^{80} +3.77641 q^{81} +(-0.00282635 - 1.41421i) 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} +(4.49228 - 0.0269343i) q^{88} +2.68831i q^{89} +(-10.3550 - 8.48665i) q^{90} +3.47342i q^{91} +(-6.28636 - 6.23630i) 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} +(9.36828 - 0.0187229i) 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 $

$2$	−0.00282635	−	1.41421i	−0.00199853	−	0.999998i
$2$	−0.00282635	−	1.41421i	−0.00199853	−	0.999998i
$3$	−1.90181	−	1.90181i	−1.09801	−	1.09801i	−0.994643	−	0.103369i	$-0.967038\pi$
$3$	−1.90181	−	1.90181i	−1.09801	−	1.09801i	−0.103369	−	0.994643i	$-0.532962\pi$
$4$	−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	$-0.713050\pi$
$7$	0.433364	−	0.433364i	0.163796	−	0.163796i	0.784246	+	0.620450i	$0.213050\pi$
$8$	0.0169580	+	2.82838i	0.00599557	+	0.999982i
$9$			4.23379i			1.41126i
$10$	−2.00451	+	2.44580i	−0.633880	+	0.773431i
$11$		−	1.58829i		−	0.478887i	−0.970910	−	0.239444i	$-0.923035\pi$
$11$		−	1.58829i		−	0.478887i	0.970910	−	0.239444i	$-0.0769651\pi$
$12$	3.81880	+	3.78839i	1.10239	+	1.09361i
$13$	−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	$0.955315\pi$
$18$	5.98747	−	0.0119662i	1.41126	−	0.00282045i
$19$	1.87220			0.429512			0.214756	−	0.976668i	$-0.431104\pi$
$19$	1.87220			0.429512			0.214756	+	0.976668i	$0.431104\pi$
$20$	3.46455	+	2.82788i	0.774696	+	0.632333i
$21$	−1.64836			−0.359701
$22$	−2.24618	+	0.00448907i	−0.478886	+	0.000957072i
$23$	3.13069	+	3.13069i	0.652794	+	0.652794i	0.953665	−	0.300871i	$-0.0972774\pi$
$23$	3.13069	+	3.13069i	0.652794	+	0.652794i	−0.300871	+	0.953665i	$0.597277\pi$
$24$	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
$28$	−0.863257	+	0.870186i	−0.163140	+	0.164450i
$29$			6.86286i			1.27440i	0.770698	+	0.637201i	$0.219908\pi$
$29$			6.86286i			1.27440i	−0.770698	+	0.637201i	$0.780092\pi$
$30$	8.46366	−	0.839265i	1.54525	−	0.153228i
$31$		−	6.19687i		−	1.11299i	−0.830851	−	0.556495i	$-0.812146\pi$
$31$		−	6.19687i		−	1.11299i	0.830851	−	0.556495i	$-0.187854\pi$
$32$	−0.0565262	−	5.65657i	−0.00999251	−	0.999950i
$33$	−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	$-0.524565\pi$
$38$	−0.00529150	−	2.64769i	−0.000858394	−	0.429511i
$39$	15.2431			2.44084
$40$	3.98943	−	4.90759i	0.630784	−	0.775958i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	0.00465883	+	2.33112i	0.000718874	+	0.359700i
$43$	−4.69005	−	4.69005i	−0.715225	−	0.715225i	0.252398	−	0.967623i	$-0.418781\pi$
$43$	−4.69005	−	4.69005i	−0.715225	−	0.715225i	−0.967623	+	0.252398i	$0.918781\pi$
$44$	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	$-0.410883\pi$
$47$	8.48312	−	8.48312i	1.23739	−	1.23739i	0.961064	−	0.276326i	$-0.0891170\pi$
$48$	−7.66782	−	7.54620i	−1.10675	−	1.08920i
$49$			6.62439i			0.946342i
$50$	6.93612	−	1.37484i	0.980916	−	0.194431i
$51$			13.3341i			1.86715i
$52$	7.98292	−	8.04699i	1.10703	−	1.11592i
$53$	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
$58$	9.70554	−	0.0193969i	1.27440	−	0.00254693i
$59$	−0.968941			−0.126145			−0.0630727	−	0.998009i	$-0.520090\pi$
$59$	−0.968941			−0.126145			−0.0630727	+	0.998009i	$0.520090\pi$
$60$	−1.21082	−	11.9670i	−0.156316	−	1.54494i
$61$	−1.70966			−0.218899			−0.109450	−	0.993992i	$-0.534909\pi$
$61$	−1.70966			−0.218899			−0.109450	+	0.993992i	$0.534909\pi$
$62$	−8.76368	+	0.0175145i	−1.11299	+	0.00222435i
$63$	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	$-0.926047\pi$
$67$	−6.08078	+	6.08078i	−0.742885	+	0.742885i	0.230247	+	0.973132i	$0.426047\pi$
$68$	7.03923	+	6.98319i	0.853633	+	0.846836i
$69$		−	11.9080i		−	1.43355i
$70$	0.191243	+	1.92860i	0.0228579	+	0.230512i
$71$			11.5429i			1.36989i	0.728595	+	0.684945i	$0.240174\pi$
$71$			11.5429i			1.36989i	−0.728595	+	0.684945i	$0.759826\pi$
$72$	−11.9747	+	0.0717967i	−1.41124	+	0.00846132i
$73$	−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
$78$	−0.0430823	−	21.5569i	−0.00487811	−	2.44084i
$79$	5.72448			0.644054			0.322027	−	0.946730i	$-0.395636\pi$
$79$	5.72448			0.644054			0.322027	+	0.946730i	$0.395636\pi$
$80$	−6.95165	−	5.62802i	−0.777218	−	0.629232i
$81$	3.77641			0.419601
$82$	−0.00282635	−	1.41421i	−0.000312118	−	0.156173i
$83$	2.17584	+	2.17584i	0.238830	+	0.238830i	0.816366	−	0.577536i	$-0.195986\pi$
$83$	2.17584	+	2.17584i	0.238830	+	0.238830i	−0.577536	+	0.816366i	$0.695986\pi$
$84$	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
$88$	4.49228	−	0.0269343i	0.478879	−	0.00287120i
$89$			2.68831i			0.284960i	0.989798	+	0.142480i	$0.0455077\pi$
$89$			2.68831i			0.284960i	−0.989798	+	0.142480i	$0.954492\pi$
$90$	−10.3550	−	8.48665i	−1.09151	−	0.894572i
$91$			3.47342i			0.364114i
$92$	−6.28636	−	6.23630i	−0.655398	−	0.650179i
$93$	−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	$0.737558\pi$
$98$	9.36828	−	0.0187229i	0.946340	−	0.00189130i
$99$	6.72448			0.675836
$100$	−1.96391	−	9.80526i	−0.196391	−	0.980526i
$101$	2.43475			0.242267			0.121133	−	0.992636i	$-0.461347\pi$
$101$	2.43475			0.242267			0.121133	+	0.992636i	$0.461347\pi$
$102$	18.8573	−	0.0376869i	1.86715	−	0.00373156i
$103$	3.50467	+	3.50467i	0.345326	+	0.345326i	0.858365	−	0.513039i	$-0.171481\pi$
$103$	3.50467	+	3.50467i	0.345326	+	0.345326i	−0.513039	+	0.858365i	$0.671481\pi$
$104$	−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	$-0.890068\pi$
$107$	−6.23144	+	6.23144i	−0.602416	+	0.602416i	0.338537	+	0.940953i	$0.390068\pi$
$108$	−4.67407	+	4.71159i	−0.449763	+	0.453372i
$109$			17.6354i			1.68916i	0.535426	+	0.844582i	$0.320151\pi$
$109$			17.6354i			1.68916i	−0.535426	+	0.844582i	$0.679849\pi$
$110$	3.88464	+	3.18374i	0.370386	+	0.303557i
$111$			24.8514i			2.35879i
$112$	1.71954	−	1.74726i	0.162482	−	0.165100i
$113$	−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
$118$	0.00273857	+	1.37029i	0.000252106	+	0.126145i
$119$	−3.03843			−0.278533
$120$	−16.9205	+	1.74618i	−1.54462	+	0.159403i
$121$	8.47734			0.770667
$122$	0.00483210	+	2.41782i	0.000437478	+	0.218899i
$123$	−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	$-0.896139\pi$
$127$	−7.06262	+	7.06262i	−0.626706	+	0.626706i	0.320531	+	0.947238i	$0.396139\pi$
$128$	0.158271	+	11.3126i	0.0139893	+	0.999902i
$129$			17.8392i			1.57065i
$130$	−1.76850	−	17.8347i	−0.155108	−	1.56420i
$131$		−	1.41883i		−	0.123963i	−0.998077	−	0.0619817i	$-0.980258\pi$
$131$		−	1.41883i		−	0.123963i	0.998077	−	0.0619817i	$-0.0197421\pi$
$132$	6.01707	−	6.06536i	0.523718	−	0.527922i
$133$	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	$0.567760\pi$
$138$	−16.8404	+	0.0336561i	−1.43355	+	0.00286500i
$139$	0.876610			0.0743531			0.0371765	−	0.999309i	$-0.488164\pi$
$139$	0.876610			0.0743531			0.0371765	+	0.999309i	$0.488164\pi$
$140$	2.72691	−	0.275908i	0.230466	−	0.0233185i
$141$	−32.2666			−2.71734
$142$	16.3241	−	0.0326243i	1.36989	−	0.00273777i
$143$	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
$148$	13.1193	+	13.0149i	1.07840	+	1.06982i
$149$		−	16.0098i		−	1.31158i	−0.754945	−	0.655788i	$-0.772336\pi$
$149$		−	16.0098i		−	1.31158i	0.754945	−	0.655788i	$-0.227664\pi$
$150$	−15.8059	−	10.5765i	−1.29055	−	0.863570i
$151$			17.3881i			1.41502i	0.706703	+	0.707510i	$0.250182\pi$
$151$			17.3881i			1.41502i	−0.706703	+	0.707510i	$0.749818\pi$
$152$	0.0317488	+	5.29529i	0.00257517	+	0.429504i
$153$	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	$0.583995\pi$
$158$	−0.0161794	−	8.09562i	−0.00128716	−	0.644053i
$159$	−23.7732			−1.88534
$160$	−7.93956	+	9.84700i	−0.627677	+	0.778474i
$161$	2.71346			0.213850
$162$	−0.0106735	−	5.34064i	−0.000838586	−	0.419600i
$163$	−10.1125	−	10.1125i	−0.792075	−	0.792075i	0.189756	−	0.981831i	$-0.439230\pi$
$163$	−10.1125	−	10.1125i	−0.792075	−	0.792075i	−0.981831	+	0.189756i	$0.939230\pi$
$164$	−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	$-0.581679\pi$
$167$	9.21999	−	9.21999i	0.713464	−	0.713464i	0.967258	+	0.253794i	$0.0816786\pi$
$168$	−0.0279529	−	4.66217i	−0.00215661	−	0.359694i
$169$		−	19.1203i		−	1.47079i
$170$	15.6012	−	1.54703i	1.19655	−	0.118652i
$171$			7.92650i			0.606154i
$172$	9.41751	+	9.34253i	0.718079	+	0.712361i
$173$	−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
$178$	3.80183	−	0.00759811i	0.284960	−	0.000569502i
$179$	−7.98914			−0.597137			−0.298568	−	0.954388i	$-0.596509\pi$
$179$	−7.98914			−0.597137			−0.298568	+	0.954388i	$0.596509\pi$
$180$	−11.9726	+	14.6682i	−0.892388	+	1.09330i
$181$	−14.1777			−1.05382			−0.526909	−	0.849922i	$-0.676649\pi$
$181$	−14.1777			−1.05382			−0.526909	+	0.849922i	$0.676649\pi$
$182$	4.91215	−	0.00981712i	0.364113	−	0.000727693i
$183$	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
$188$	−16.8983	+	17.0339i	−1.23243	+	1.24233i
$189$		−	2.03372i		−	0.147931i
$190$	−3.75284	+	4.57903i	−0.272259	+	0.332198i
$191$			3.45212i			0.249786i	0.992170	+	0.124893i	$0.0398588\pi$
$191$			3.45212i			0.249786i	−0.992170	+	0.124893i	$0.960141\pi$
$192$	15.3958	+	15.0310i	1.11110	+	1.08477i
$193$	−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	$0.685812\pi$
$198$	−0.0190058	−	9.50983i	−0.00135068	−	0.675834i
$199$	−23.3783			−1.65724			−0.828622	−	0.559808i	$-0.810875\pi$
$199$	−23.3783			−1.65724			−0.828622	+	0.559808i	$0.810875\pi$
$200$	−13.8611	+	2.80510i	−0.980131	+	0.198350i
$201$	23.1290			1.63139
$202$	−0.00688147	−	3.44325i	−0.000484179	−	0.242266i
$203$	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
$208$	−15.9014	+	16.1577i	−1.10256	+	1.12033i
$209$		−	2.97360i		−	0.205688i
$210$	3.30414	−	4.03155i	0.228007	−	0.278204i
$211$		−	15.6677i		−	1.07861i	−0.842110	−	0.539305i	$-0.818687\pi$
$211$		−	15.6677i		−	1.07861i	0.842110	−	0.539305i	$-0.181313\pi$
$212$	−12.4502	+	12.5501i	−0.855084	+	0.861947i
$213$	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
$218$	24.9402	−	0.0498438i	1.68916	−	0.00337585i
$219$	30.7762			2.07966
$220$	4.49150	−	5.50270i	0.302817	−	0.370992i
$221$	28.0977			1.89006
$222$	35.1451	−	0.0702389i	2.35879	−	0.00471412i
$223$	−6.08865	−	6.08865i	−0.407726	−	0.407726i	0.473219	−	0.880945i	$-0.343092\pi$
$223$	−6.08865	−	6.08865i	−0.407726	−	0.407726i	−0.880945	+	0.473219i	$0.843092\pi$
$224$	−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	$-0.653425\pi$
$227$	6.36587	−	6.36587i	0.422518	−	0.422518i	0.886070	+	0.463552i	$0.153425\pi$
$228$	7.14956	+	7.09263i	0.473491	+	0.469721i
$229$		−	5.75631i		−	0.380388i	−0.981747	−	0.190194i	$-0.939088\pi$
$229$		−	5.75631i		−	0.380388i	0.981747	−	0.190194i	$-0.0609117\pi$
$230$	−13.9325	+	1.38157i	−0.918684	+	0.0910977i
$231$			2.61807i			0.172256i
$232$	−19.4108	+	0.116381i	−1.27438	+	0.00764076i
$233$	−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
$238$	0.00858768	+	4.29698i	0.000556657	+	0.278532i
$239$	4.29596			0.277883			0.138941	−	0.990301i	$-0.455630\pi$
$239$	4.29596			0.277883			0.138941	+	0.990301i	$0.455630\pi$
$240$	2.51729	+	23.9242i	0.162490	+	1.54430i
$241$	−6.30046			−0.405848			−0.202924	−	0.979194i	$-0.565044\pi$
$241$	−6.30046			−0.405848			−0.202924	+	0.979194i	$0.565044\pi$
$242$	−0.0239599	−	11.9887i	−0.00154020	−	0.770665i
$243$	−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
$248$	17.5271	−	0.105087i	1.11297	−	0.00667301i
$249$		−	8.27610i		−	0.524477i
$250$	−13.9294	−	7.48142i	−0.880973	−	0.473166i
$251$			27.4019i			1.72959i	0.502123	+	0.864796i	$0.332552\pi$
$251$			27.4019i			1.72959i	−0.502123	+	0.864796i	$0.667448\pi$
$252$	−3.68418	−	3.65485i	−0.232082	−	0.230234i
$253$	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	$0.554211\pi$
$258$	25.2284	−	0.0504198i	1.57065	−	0.00313900i
$259$	−5.66287			−0.351873
$260$	−25.2170	+	2.55144i	−1.56389	+	0.158234i
$261$	−29.0559			−1.79852
$262$	−2.00652	+	0.00401011i	−0.123963	+	0.000247745i
$263$	−14.5278	−	14.5278i	−0.895823	−	0.895823i	0.0992407	−	0.995063i	$-0.468359\pi$
$263$	−14.5278	−	14.5278i	−0.895823	−	0.895823i	−0.995063	+	0.0992407i	$0.968359\pi$
$264$	−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
$268$	12.1129	−	12.2101i	0.739910	−	0.745849i
$269$			16.4454i			1.00269i	0.865246	+	0.501347i	$0.167162\pi$
$269$			16.4454i			1.00269i	−0.865246	+	0.501347i	$0.832838\pi$
$270$	1.03547	+	10.4424i	0.0630170	+	0.635501i
$271$		−	28.8912i		−	1.75501i	−0.479565	−	0.877507i	$-0.659205\pi$
$271$		−	28.8912i		−	1.75501i	0.479565	−	0.877507i	$-0.340795\pi$
$272$	−14.1342	−	13.9100i	−0.857011	−	0.843417i
$273$	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	$0.814378\pi$
$278$	−0.00247761	−	1.23971i	−0.000148597	−	0.0743529i
$279$	26.2362			1.57072
$280$	−0.397900	−	3.85565i	−0.0237790	−	0.230419i
$281$	2.72305			0.162443			0.0812217	−	0.996696i	$-0.474118\pi$
$281$	2.72305			0.162443			0.0812217	+	0.996696i	$0.474118\pi$
$282$	0.0911968	+	45.6318i	0.00543069	+	2.71733i
$283$	−11.8514	−	11.8514i	−0.704493	−	0.704493i	0.260878	−	0.965372i	$-0.415988\pi$
$283$	−11.8514	−	11.8514i	−0.704493	−	0.704493i	−0.965372	+	0.260878i	$0.915988\pi$
$284$	−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
$288$	23.9487	−	0.239320i	1.41119	−	0.0141020i
$289$			7.57892i			0.445819i
$290$	−16.7852	−	13.7567i	−0.985662	−	0.807819i
$291$		−	2.07033i		−	0.121365i
$292$	16.1177	−	16.2471i	0.943219	−	0.950789i
$293$	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
$298$	−22.6413	+	0.0452494i	−1.31157	+	0.00262123i
$299$	−25.0925			−1.45114
$300$	−14.9128	+	22.3828i	−0.860989	+	1.29227i
$301$	−4.06500			−0.234303
$302$	24.5904	−	0.0491448i	1.41502	−	0.00282796i
$303$	−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	$-0.818916\pi$
$307$	−5.32303	+	5.32303i	−0.303801	+	0.303801i	0.538698	+	0.842499i	$0.318916\pi$
$308$	1.38211	+	1.37110i	0.0787529	+	0.0781258i
$309$		−	13.3305i		−	0.758344i
$310$	15.1563	+	12.4217i	0.860821	+	0.705503i
$311$		−	13.0392i		−	0.739387i	−0.929154	−	0.369694i	$-0.879463\pi$
$311$		−	13.0392i		−	0.739387i	0.929154	−	0.369694i	$-0.120537\pi$
$312$	0.258492	+	43.1131i	0.0146343	+	2.44080i
$313$	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	$0.612895\pi$
$318$	0.0671914	+	33.6203i	0.00376791	+	1.88533i
$319$	10.9002			0.610295
$320$	13.9482	+	11.2004i	0.779726	+	0.626120i
$321$	23.7021			1.32292
$322$	−0.00766919	−	3.83740i	−0.000427387	−	0.213850i
$323$	−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
$328$	0.0169580	+	2.82838i	0.000936350	+	0.156171i
$329$		−	7.35256i		−	0.405360i
$330$	−1.33300	−	13.4427i	−0.0733791	−	0.739999i
$331$			32.0991i			1.76433i	0.470943	+	0.882164i	$0.343914\pi$
$331$			32.0991i			1.76433i	−0.470943	+	0.882164i	$0.656086\pi$
$332$	−4.36905	−	4.33426i	−0.239783	−	0.237873i
$333$	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	$0.806055\pi$
$338$	−27.0401	+	0.0540406i	−1.47079	+	0.00293942i
$339$	39.3839			2.13904
$340$	−2.23192	−	22.0589i	−0.121043	−	1.19631i
$341$	−9.84242			−0.532997
$342$	11.2097	−	0.0224031i	0.606153	−	0.00121142i
$343$	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	$-0.775684\pi$
$347$	−2.12338	+	2.12338i	−0.113989	+	0.113989i	0.647812	+	0.761801i	$0.275684\pi$
$348$	−25.9992	+	26.2079i	−1.39370	+	1.40489i
$349$			14.0584i			0.752527i	0.926513	+	0.376263i	$0.122791\pi$
$349$			14.0584i			0.752527i	−0.926513	+	0.376263i	$0.877209\pi$
$350$	2.41006	−	3.60167i	0.128823	−	0.192517i
$351$			18.8067i			1.00383i
$352$	−8.98428	+	0.0897799i	−0.478863	+	0.00478529i
$353$	−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
$358$	0.0225801	+	11.2983i	0.00119340	+	0.597135i
$359$	21.5045			1.13496			0.567481	−	0.823386i	$-0.307918\pi$
$359$	21.5045			1.13496			0.567481	+	0.823386i	$0.307918\pi$
$360$	20.7777	+	16.8904i	1.09508	+	0.890202i
$361$	−15.4949			−0.815519
$362$	0.0400711	+	20.0502i	0.00210609	+	1.05382i
$363$	−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	$-0.939735\pi$
$367$	−15.2095	+	15.2095i	−0.793932	+	0.793932i	0.188199	+	0.982131i	$0.439735\pi$
$368$	12.6225	+	12.4222i	0.657991	+	0.647554i
$369$			4.23379i			0.220402i
$370$	29.0766	−	2.88327i	1.51162	−	0.149894i
$371$		−	5.41717i		−	0.281246i
$372$	23.4762	−	23.6646i	1.21718	−	1.22695i
$373$	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
$378$	−2.87611	+	0.00574801i	−0.147931	+	0.000295646i
$379$	−10.0239			−0.514894			−0.257447	−	0.966292i	$-0.582881\pi$
$379$	−10.0239			−0.514894			−0.257447	+	0.966292i	$0.582881\pi$
$380$	6.48632	+	5.29436i	0.332741	+	0.271595i
$381$	26.8636			1.37626
$382$	4.88202	−	0.00975690i	0.249786	−	0.000499206i
$383$	−13.9942	−	13.9942i	−0.715068	−	0.715068i	0.252523	−	0.967591i	$-0.418740\pi$
$383$	−13.9942	−	13.9942i	−0.715068	−	0.715068i	−0.967591	+	0.252523i	$0.918740\pi$
$384$	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
$388$	−1.09295	−	1.08425i	−0.0554863	−	0.0550445i
$389$			30.3206i			1.53732i	0.639659	+	0.768659i	$0.279075\pi$
$389$			30.3206i			1.53732i	−0.639659	+	0.768659i	$0.720925\pi$
$390$	−30.5548	+	37.2816i	−1.54720	+	1.88783i
$391$		−	21.9501i		−	1.11006i
$392$	−18.7363	+	0.112337i	−0.946325	+	0.00567385i
$393$	−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	$-0.515389\pi$
$398$	0.0660754	+	33.0619i	0.00331206	+	1.65724i
$399$	−3.08605			−0.154496
$400$	4.00617	+	19.5947i	0.200309	+	0.979733i
$401$	−27.4808			−1.37232			−0.686162	−	0.727449i	$-0.740706\pi$
$401$	−27.4808			−1.37232			−0.686162	+	0.727449i	$0.740706\pi$
$402$	−0.0653707	−	32.7093i	−0.00326040	−	1.63139i
$403$	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
$408$	−37.7139	+	0.226120i	−1.86712	+	0.0111946i
$409$			8.80523i			0.435391i	0.976017	+	0.217695i	$0.0698539\pi$
$409$			8.80523i			0.435391i	−0.976017	+	0.217695i	$0.930146\pi$
$410$	−2.00451	+	2.44580i	−0.0989955	+	0.120790i
$411$		−	34.1095i		−	1.68250i
$412$	−7.03731	−	6.98127i	−0.346703	−	0.343943i
$413$	−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
$418$	−4.20529	+	0.00840443i	−0.205688	+	0.000411074i
$419$	−5.76098			−0.281442			−0.140721	−	0.990049i	$-0.544942\pi$
$419$	−5.76098			−0.281442			−0.140721	+	0.990049i	$0.544942\pi$
$420$	−5.71081	−	4.66135i	−0.278659	−	0.227451i
$421$	0.285923			0.0139351			0.00696753	−	0.999976i	$-0.497782\pi$
$421$	0.285923			0.0139351			0.00696753	+	0.999976i	$0.497782\pi$
$422$	−22.1575	+	0.0442825i	−1.07861	+	0.00215564i
$423$	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
$428$	12.4130	−	12.5126i	0.600004	−	0.604820i
$429$		−	24.2104i		−	1.16889i
$430$	20.8722	−	2.06971i	1.00655	−	0.0998101i
$431$		−	33.7234i		−	1.62440i	−0.583381	−	0.812199i	$-0.698270\pi$
$431$		−	33.7234i		−	1.62440i	0.583381	−	0.812199i	$-0.301730\pi$
$432$	9.31040	−	9.46046i	0.447947	−	0.455167i
$433$	−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
$438$	−0.0869843	−	43.5240i	−0.00415627	−	2.07966i
$439$	−33.9364			−1.61970			−0.809849	−	0.586639i	$-0.800451\pi$
$439$	−33.9364			−1.61970			−0.809849	+	0.586639i	$0.800451\pi$
$440$	−7.79468	−	6.33637i	−0.371597	−	0.302074i
$441$	−28.0463			−1.33554
$442$	−0.0794141	−	39.7361i	−0.00377734	−	1.89005i
$443$	14.6750	+	14.6750i	0.697230	+	0.697230i	0.963812	−	0.266582i	$-0.0858945\pi$
$443$	14.6750	+	14.6750i	0.697230	+	0.697230i	−0.266582	+	0.963812i	$0.585894\pi$
$444$	−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
$448$	−3.42509	+	3.50824i	−0.161820	+	0.165749i
$449$		−	11.9800i		−	0.565371i	−0.959213	−	0.282686i	$-0.908775\pi$
$449$		−	11.9800i		−	0.565371i	0.959213	−	0.282686i	$-0.0912253\pi$
$450$	5.82076	+	29.3661i	0.274393	+	1.38433i
$451$		−	1.58829i		−	0.0747896i
$452$	20.6257	−	20.7912i	0.970150	−	0.977937i
$453$	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	$0.748703\pi$
$458$	−8.14064	+	0.0162694i	−0.380387	+	0.000760217i
$459$	−16.4515			−0.767888
$460$	1.99320	+	19.6996i	0.0929336	+	0.918500i
$461$	−1.83433			−0.0854335			−0.0427167	−	0.999087i	$-0.513601\pi$
$461$	−1.83433			−0.0854335			−0.0427167	+	0.999087i	$0.513601\pi$
$462$	3.70250	−	0.00739958i	0.172256	−	0.000344260i
$463$	28.5167	+	28.5167i	1.32528	+	1.32528i	0.909434	+	0.415849i	$0.136515\pi$
$463$	28.5167	+	28.5167i	1.32528	+	1.32528i	0.415849	+	0.909434i	$0.363485\pi$
$464$	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	$-0.847662\pi$
$467$	−9.23022	+	9.23022i	−0.427124	+	0.427124i	0.460524	+	0.887647i	$0.347662\pi$
$468$	34.0693	+	33.7980i	1.57485	+	1.56231i
$469$			5.27038i			0.243364i
$470$	3.74358	+	37.7525i	0.172678	+	1.74139i
$471$		−	33.5787i		−	1.54723i
$472$	−0.0164313	−	2.74053i	−0.000756313	−	0.126143i
$473$	−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
$478$	−0.0121419	−	6.07539i	−0.000555358	−	0.277882i
$479$	20.4800			0.935755			0.467877	−	0.883793i	$-0.345019\pi$
$479$	20.4800			0.935755			0.467877	+	0.883793i	$0.345019\pi$
$480$	33.8267	−	3.62759i	1.54397	−	0.165576i
$481$	52.3670			2.38773
$482$	0.0178073	+	8.91017i	0.000811101	+	0.405847i
$483$	−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	$-0.764914\pi$
$487$	−1.46175	+	1.46175i	−0.0662384	+	0.0662384i	0.673212	+	0.739450i	$0.264914\pi$
$488$	−0.0289924	−	4.83556i	−0.00131243	−	0.218896i
$489$			38.4643i			1.73942i
$490$	−16.2020	−	13.2786i	−0.731930	−	0.599867i
$491$		−	7.84785i		−	0.354169i	−0.984196	−	0.177084i	$-0.943333\pi$
$491$		−	7.84785i		−	0.354169i	0.984196	−	0.177084i	$-0.0566665\pi$
$492$	3.81880	+	3.78839i	0.172165	+	0.170794i
$493$	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
$498$	−11.7042	+	0.0233912i	−0.524476	+	0.00104818i
$499$	23.0671			1.03262			0.516312	−	0.856400i	$-0.327304\pi$
$499$	23.0671			1.03262			0.516312	+	0.856400i	$0.327304\pi$
$500$	−10.5409	+	19.7203i	−0.471405	+	0.881917i
$501$	−35.0694			−1.56679
$502$	38.7520	−	0.0774474i	1.72959	−	0.00345665i
$503$	16.5617	+	16.5617i	0.738450	+	0.738450i	0.972278	−	0.233828i	$-0.0751253\pi$
$503$	16.5617	+	16.5617i	0.738450	+	0.738450i	−0.233828	+	0.972278i	$0.575125\pi$
$504$	−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
$508$	14.0687	−	14.1816i	0.624196	−	0.629206i
$509$		−	29.2681i		−	1.29728i	−0.761094	−	0.648642i	$-0.775337\pi$
$509$		−	29.2681i		−	1.29728i	0.761094	−	0.648642i	$-0.224663\pi$
$510$	−32.6126	−	26.7283i	−1.44411	−	1.18355i
$511$			7.01293i			0.310234i
$512$	−0.406973	−	22.6238i	−0.0179858	−	0.999838i
$513$	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
$518$	0.0160053	+	8.00849i	0.000703231	+	0.351873i
$519$	16.1432			0.708607
$520$	3.67955	+	35.6549i	0.161359	+	1.56357i
$521$	−18.0489			−0.790737			−0.395369	−	0.918523i	$-0.629383\pi$
$521$	−18.0489			−0.790737			−0.395369	+	0.918523i	$0.629383\pi$
$522$	0.0821222	+	41.0912i	0.00359439	+	1.79851i
$523$	2.57935	+	2.57935i	0.112787	+	0.112787i	0.761248	−	0.648461i	$-0.224587\pi$
$523$	2.57935	+	2.57935i	0.112787	+	0.112787i	−0.648461	+	0.761248i	$0.724587\pi$
$524$	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
$528$	−11.9855	+	12.1787i	−0.521604	+	0.530011i
$529$		−	3.39757i		−	0.147721i
$530$	2.75817	+	27.8150i	0.119807	+	1.20821i
$531$		−	4.10229i		−	0.178024i
$532$	−1.61619	+	1.62916i	−0.0700707	+	0.0706331i
$533$	−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
$538$	23.2573	−	0.0464805i	1.00269	−	0.00200392i
$539$	10.5215			0.453191
$540$	14.7648	−	1.49389i	0.635374	−	0.0642869i
$541$	−6.04328			−0.259821			−0.129910	−	0.991526i	$-0.541469\pi$
$541$	−6.04328			−0.259821			−0.129910	+	0.991526i	$0.541469\pi$
$542$	−40.8582	+	0.0816566i	−1.75501	+	0.00350745i
$543$	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	$-0.772023\pi$
$547$	−2.28661	+	2.28661i	−0.0977683	+	0.0977683i	0.656531	+	0.754299i	$0.272023\pi$
$548$	−18.0068	−	17.8634i	−0.769213	−	0.763088i
$549$		−	7.23833i		−	0.308925i
$550$	−2.18364	−	11.0166i	−0.0931106	−	0.469748i
$551$			12.8487i			0.547371i
$552$	33.6802	−	0.201936i	1.43353	−	0.00859495i
$553$	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	$0.680399\pi$
$558$	−0.0741528	−	37.1035i	−0.00313914	−	1.57072i
$559$	37.5908			1.58992
$560$	−5.45158	+	0.573611i	−0.230371	+	0.0242395i
$561$	21.1784			0.894155
$562$	−0.00769629	−	3.85096i	−0.000324648	−	0.162443i
$563$	23.0929	+	23.0929i	0.973252	+	0.973252i	0.999651	−	0.0263999i	$-0.00840433\pi$
$563$	23.0929	+	23.0929i	0.973252	+	0.973252i	−0.0263999	+	0.999651i	$0.508404\pi$
$564$	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
$568$	−32.6477	+	0.195745i	−1.36987	+	0.00821327i
$569$			11.3100i			0.474140i	0.971493	+	0.237070i	$0.0761870\pi$
$569$			11.3100i			0.474140i	−0.971493	+	0.237070i	$0.923813\pi$
$570$	15.8457	−	1.57127i	0.663702	−	0.0658134i
$571$			20.4162i			0.854391i	0.904159	+	0.427195i	$0.140498\pi$
$571$			20.4162i			0.854391i	−0.904159	+	0.427195i	$0.859502\pi$
$572$	−12.7810	−	12.6792i	−0.534399	−	0.530144i
$573$	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	$0.739223\pi$
$578$	10.7182	−	0.0214207i	0.445818	−	0.000890984i
$579$	3.55678			0.147815
$580$	−19.4074	+	23.7767i	−0.805847	+	0.987274i
$581$	1.88587			0.0782389
$582$	−2.92789	+	0.00585149i	−0.121365	+	0.000242552i
$583$	−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	$-0.890667\pi$
$587$	−14.6537	+	14.6537i	−0.604824	+	0.604824i	0.336765	+	0.941589i	$0.390667\pi$
$588$	−25.0958	+	25.2972i	−1.03493	+	1.04324i
$589$		−	11.6018i		−	0.478043i
$590$	1.94225	−	2.36984i	0.0799611	−	0.0975647i
$591$		−	15.1218i		−	0.622029i
$592$	−26.3425	−	25.9247i	−1.08267	−	1.06550i
$593$	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
$598$	0.0709204	+	35.4861i	0.00290015	+	1.45114i
$599$	−24.3043			−0.993045			−0.496523	−	0.868024i	$-0.665390\pi$
$599$	−24.3043			−0.993045			−0.496523	+	0.868024i	$0.665390\pi$
$600$	31.6961	+	21.0265i	1.29399	+	0.858405i
$601$	32.2891			1.31710			0.658550	−	0.752537i	$-0.271170\pi$
$601$	32.2891			1.31710			0.658550	+	0.752537i	$0.271170\pi$
$602$	0.0114891	+	5.74876i	0.000468261	+	0.234302i
$603$	−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	$-0.602598\pi$
$607$	15.5642	−	15.5642i	0.631732	−	0.631732i	0.948502	+	0.316770i	$0.102598\pi$
$608$	−0.105828	−	10.5902i	−0.00429190	−	0.429491i
$609$		−	11.3124i		−	0.458403i
$610$	3.42702	−	4.18149i	0.138756	−	0.169304i
$611$			67.9924i			2.75068i
$612$	−29.5653	+	29.8026i	−1.19511	+	1.20470i
$613$	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	$0.913088\pi$
$618$	−18.8521	+	0.0376766i	−0.758342	+	0.00151557i
$619$	−29.8732			−1.20070			−0.600352	−	0.799736i	$-0.704973\pi$
$619$	−29.8732			−1.20070			−0.600352	+	0.799736i	$0.704973\pi$
$620$	17.5240	−	21.4693i	0.703781	−	0.862230i
$621$	14.6919			0.589566
$622$	−18.4402	+	0.0368535i	−0.739386	+	0.00147769i
$623$	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
$628$	−17.7266	−	17.5855i	−0.707368	−	0.701736i
$629$			45.8089i			1.82652i
$630$	−8.16530	+	0.809680i	−0.325313	+	0.0322584i
$631$		−	31.7086i		−	1.26230i	−0.775661	−	0.631149i	$-0.782584\pi$
$631$		−	31.7086i		−	1.26230i	0.775661	−	0.631149i	$-0.217416\pi$
$632$	0.0970758	+	16.1910i	0.00386147	+	0.644042i
$633$	−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
$638$	−0.0308079	−	15.4152i	−0.00121969	−	0.610294i
$639$	−48.8702			−1.93327
$640$	15.8003	−	19.7573i	0.624561	−	0.780976i
$641$	−19.2164			−0.759001			−0.379500	−	0.925192i	$-0.623904\pi$
$641$	−19.2164			−0.759001			−0.379500	+	0.925192i	$0.623904\pi$
$642$	−0.0669905	−	33.5197i	−0.00264390	−	1.32292i
$643$	−20.3110	−	20.3110i	−0.800987	−	0.800987i	0.182263	−	0.983250i	$-0.441658\pi$
$643$	−20.3110	−	20.3110i	−0.800987	−	0.800987i	−0.983250	+	0.182263i	$0.941658\pi$
$644$	−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	$-0.400649\pi$
$647$	32.0181	−	32.0181i	1.25876	−	1.25876i	0.951684	−	0.307078i	$-0.0993511\pi$
$648$	0.0640404	+	10.6811i	0.00251575	+	0.419593i
$649$			1.53896i			0.0604094i
$650$	−22.2869	+	33.3063i	−0.874165	+	1.30638i
$651$			10.2146i			0.400343i
$652$	20.3058	+	20.1441i	0.795235	+	0.788903i
$653$	−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
$658$	−10.3981	+	0.0207809i	−0.405359	+	0.000810125i
$659$	1.35246			0.0526844			0.0263422	−	0.999653i	$-0.491614\pi$
$659$	1.35246			0.0526844			0.0263422	+	0.999653i	$0.491614\pi$
$660$	−19.0071	+	1.92313i	−0.739850	+	0.0748578i
$661$	−38.1313			−1.48314			−0.741568	−	0.670877i	$-0.765918\pi$
$661$	−38.1313			−1.48314			−0.741568	+	0.670877i	$0.765918\pi$
$662$	45.3949	−	0.0907235i	1.76432	−	0.00352607i
$663$	−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
$668$	−18.3661	+	18.5135i	−0.710607	+	0.716310i
$669$			23.1589i			0.895376i
$670$	−2.68343	−	27.0614i	−0.103670	−	1.04547i
$671$			2.71543i			0.104828i
$672$	0.0931752	+	9.32404i	0.00359431	+	0.359683i
$673$	−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	$0.722496\pi$
$678$	−0.111313	−	55.6972i	−0.00427494	−	2.13904i
$679$	0.471765			0.0181047
$680$	−31.1897	+	3.21875i	−1.19607	+	0.123433i
$681$	−24.2134			−0.927859
$682$	0.0278182	+	13.9193i	0.00106521	+	0.532996i
$683$	24.2669	+	24.2669i	0.928548	+	0.928548i	0.997612	−	0.0690643i	$-0.0220014\pi$
$683$	24.2669	+	24.2669i	0.928548	+	0.928548i	−0.0690643	+	0.997612i	$0.522001\pi$
$684$	−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
$688$	−18.9096	−	18.6096i	−0.720920	−	0.709485i
$689$			50.0950i			1.90847i
$690$	29.1246	+	23.8696i	1.10875	+	0.908700i
$691$		−	31.7248i		−	1.20687i	−0.797413	−	0.603433i	$-0.793799\pi$
$691$		−	31.7248i		−	1.20687i	0.797413	−	0.603433i	$-0.206201\pi$
$692$	8.45431	−	8.52217i	0.321385	−	0.323964i
$693$	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
$698$	19.8815	−	0.0397339i	0.752525	−	0.00150395i
$699$	71.8686			2.71832
$700$	−5.10034	−	3.39816i	−0.192775	−	0.128438i
$701$	−40.2785			−1.52130			−0.760648	−	0.649164i	$-0.775119\pi$
$701$	−40.2785			−1.52130			−0.760648	+	0.649164i	$0.775119\pi$
$702$	26.5966	−	0.0531544i	1.00383	−	0.00200618i
$703$	−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
$708$	−3.70019	−	3.67073i	−0.139062	−	0.137954i
$709$		−	44.0802i		−	1.65547i	−0.561122	−	0.827733i	$-0.689630\pi$
$709$		−	44.0802i		−	1.65547i	0.561122	−	0.827733i	$-0.310370\pi$
$710$	−28.2317	−	23.1378i	−1.05952	−	0.868347i
$711$			24.2362i			0.908929i
$712$	−7.60355	+	0.0455884i	−0.284955	+	0.00170850i
$713$	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
$718$	−0.0607792	−	30.4118i	−0.00226826	−	1.13496i
$719$	−28.5020			−1.06295			−0.531473	−	0.847075i	$-0.678361\pi$
$719$	−28.5020			−1.06295			−0.531473	+	0.847075i	$0.678361\pi$
$720$	23.8278	−	29.4318i	0.888011	−	1.09686i
$721$	3.03760			0.113126
$722$	0.0437940	+	21.9130i	0.00162984	+	0.815518i
$723$	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	$-0.956819\pi$
$727$	−23.0687	+	23.0687i	−0.855572	+	0.855572i	0.135240	+	0.990813i	$0.456819\pi$
$728$	−9.82415	+	0.0589024i	−0.364107	+	0.00218307i
$729$			42.7634i			1.58383i
$730$	−3.57066	−	36.0087i	−0.132156	−	1.33274i
$731$			32.8832i			1.21623i
$732$	−6.52885	−	6.47686i	−0.241313	−	0.239392i
$733$	−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
$738$	5.98747	−	0.0119662i	0.220402	−	0.000440481i
$739$	35.5923			1.30929			0.654643	−	0.755939i	$-0.272819\pi$
$739$	35.5923			1.30929			0.654643	+	0.755939i	$0.272819\pi$
$740$	−4.15973	−	41.1123i	−0.152915	−	1.51132i
$741$	28.5381			1.04837
$742$	−7.66102	+	0.0153108i	−0.281245	+	0.000562079i
$743$	−35.7641	−	35.7641i	−1.31206	−	1.31206i	−0.919897	−	0.392161i	$-0.871728\pi$
$743$	−35.7641	−	35.7641i	−1.31206	−	1.31206i	−0.392161	−	0.919897i	$-0.628272\pi$
$744$	−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
$748$	11.0913	−	11.1803i	0.405539	−	0.408794i
$749$			5.40097i			0.197347i
$750$	12.2629	+	40.7194i	0.447777	+	1.48686i
$751$			26.4073i			0.963615i	0.876277	+	0.481807i	$0.160020\pi$
$751$			26.4073i			0.963615i	−0.876277	+	0.481807i	$0.839980\pi$
$752$	33.6601	−	34.2027i	1.22746	−	1.24724i
$753$	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	$0.628334\pi$
$758$	0.0283311	+	14.1759i	0.00102903	+	0.514893i
$759$	−18.9133			−0.686510
$760$	7.46901	−	9.18799i	0.270929	−	0.333284i
$761$	−50.5111			−1.83103			−0.915514	−	0.402287i	$-0.868216\pi$
$761$	−50.5111			−1.83103			−0.915514	+	0.402287i	$0.868216\pi$
$762$	−0.0759259	−	37.9908i	−0.00275051	−	1.37626i
$763$	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
$768$	−30.9116	−	29.9386i	−1.11543	−	1.08032i
$769$		−	21.8236i		−	0.786981i	−0.919329	−	0.393490i	$-0.871267\pi$
$769$		−	21.8236i		−	0.786981i	0.919329	−	0.393490i	$-0.128733\pi$
$770$	3.06318	−	0.303749i	0.110389	−	0.0109463i
$771$		−	49.7598i		−	1.79206i
$772$	1.86271	−	1.87766i	0.0670405	−	0.0675786i
$773$	−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
$778$	42.8798	−	0.0856968i	1.53731	−	0.00307238i
$779$	1.87220			0.0670785
$780$	52.8103	+	43.1056i	1.89091	+	1.54343i
$781$	18.3335			0.656023
$782$	−31.0421	+	0.0620387i	−1.11006	+	0.00221850i
$783$	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	$0.744030\pi$
$787$	−39.6667	+	39.6667i	−1.41396	+	1.41396i	−0.720243	+	0.693721i	$0.755970\pi$
$788$	−7.98299	−	7.91943i	−0.284382	−	0.282118i
$789$			55.2583i			1.96725i
$790$	−11.4748	+	14.0009i	−0.408253	+	0.498131i
$791$			8.97437i			0.319092i
$792$	0.114034	+	19.0194i	0.00405202	+	0.675824i
$793$	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	$0.918919\pi$
$798$	0.00872227	+	4.36433i	0.000308765	+	0.154495i
$799$	−59.4774			−2.10416
$800$	27.6997	−	5.72096i	0.979331	−	0.202266i
$801$	−11.3817			−0.402153
$802$	0.0776703	+	38.8636i	0.00274264	+	1.37232i
$803$	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
$808$	0.0412886	+	6.88640i	0.00145253	+	0.242263i
$809$		−	9.82224i		−	0.345332i	−0.984980	−	0.172666i	$-0.944762\pi$
$809$		−	9.82224i		−	0.345332i	0.984980	−	0.172666i	$-0.0552381\pi$
$810$	−7.56983	+	9.23635i	−0.265977	+	0.324532i
$811$			43.9669i			1.54389i	0.635691	+	0.771943i	$0.280715\pi$
$811$			43.9669i			1.54389i	−0.635691	+	0.771943i	$0.719285\pi$
$812$	−5.97197	−	5.92442i	−0.209575	−	0.207906i
$813$	−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
$818$	12.4525	−	0.0248867i	0.435390	−	0.000870143i
$819$	−14.7057			−0.513860
$820$	3.46455	+	2.82788i	0.120987	+	0.0987539i
$821$	−7.17510			−0.250413			−0.125206	−	0.992131i	$-0.539959\pi$
$821$	−7.17510			−0.250413			−0.125206	+	0.992131i	$0.539959\pi$
$822$	−48.2381	+	0.0964056i	−1.68250	+	0.00336253i
$823$	18.9730	+	18.9730i	0.661358	+	0.661358i	0.955700	−	0.294342i	$-0.0951006\pi$
$823$	18.9730	+	18.9730i	0.661358	+	0.661358i	−0.294342	+	0.955700i	$0.595101\pi$
$824$	−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	$-0.733472\pi$
$827$	2.11082	−	2.11082i	0.0734004	−	0.0734004i	0.742854	+	0.669454i	$0.233472\pi$
$828$	26.4032	−	26.6151i	0.917574	−	0.924938i
$829$			20.4182i			0.709154i	0.935027	+	0.354577i	$0.115375\pi$
$829$			20.4182i			0.709154i	−0.935027	+	0.354577i	$0.884625\pi$
$830$	−9.68318	+	0.960195i	−0.336108	+	0.0333289i
$831$			17.9834i			0.623838i
$832$	31.6733	−	32.4422i	1.09808	−	1.12473i
$833$	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
$838$	0.0162826	+	8.14724i	0.000562472	+	0.281442i
$839$	34.8104			1.20179			0.600894	−	0.799329i	$-0.294811\pi$
$839$	34.8104			1.20179			0.600894	+	0.799329i	$0.294811\pi$
$840$	−6.57600	+	8.08946i	−0.226893	+	0.279113i
$841$	−18.0989			−0.624100
$842$	−0.000808120	−	0.404356i	−2.78497e−5	−	0.0139350i
$843$	−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
$848$	24.7999	−	25.1996i	0.851632	−	0.865358i
$849$			45.0784i			1.54709i
$850$	−29.1352	−	19.4958i	−0.999328	−	0.668702i
$851$		−	40.9094i		−	1.40236i
$852$	−43.7290	+	44.0800i	−1.49813	+	1.51016i
$853$	−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	$0.536814\pi$
$858$	−34.2386	+	0.0684272i	−1.16889	+	0.00233607i
$859$	4.87742			0.166416			0.0832078	−	0.996532i	$-0.473483\pi$
$859$	4.87742			0.166416			0.0832078	+	0.996532i	$0.473483\pi$
$860$	−2.98599	−	29.5118i	−0.101822	−	1.00634i
$861$	−1.64836			−0.0561758
$862$	−47.6920	+	0.0953142i	−1.62439	+	0.00324641i
$863$	−35.1734	−	35.1734i	−1.19732	−	1.19732i	−0.974967	−	0.222349i	$-0.928628\pi$
$863$	−35.1734	−	35.1734i	−1.19732	−	1.19732i	−0.222349	−	0.974967i	$-0.571372\pi$
$864$	−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
$868$	5.39243	+	5.34949i	0.183031	+	0.181574i
$869$		−	9.09213i		−	0.308429i
$870$	5.75976	+	58.0849i	0.195274	+	1.96926i
$871$		−	48.7376i		−	1.65141i
$872$	−49.8795	+	0.299061i	−1.68913	+	0.0101275i
$873$	−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	$0.787465\pi$
$878$	0.0959163	+	47.9933i	0.00323702	+	1.61969i
$879$	−16.7160			−0.563816
$880$	−8.93893	+	11.0412i	−0.301331	+	0.372200i
$881$	−46.2874			−1.55946			−0.779731	−	0.626114i	$-0.784644\pi$
$881$	−46.2874			−1.55946			−0.779731	+	0.626114i	$0.784644\pi$
$882$	0.0792686	+	39.6633i	0.00266911	+	1.33553i
$883$	25.5236	+	25.5236i	0.858938	+	0.858938i	0.991213	−	0.132275i	$-0.0422282\pi$
$883$	25.5236	+	25.5236i	0.858938	+	0.858938i	−0.132275	+	0.991213i	$0.542228\pi$
$884$	−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	$-0.592352\pi$
$887$	20.0177	−	20.0177i	0.672128	−	0.672128i	0.958206	+	0.286078i	$0.0923518\pi$
$888$	−70.2892	+	0.421431i	−2.35875	+	0.0141423i
$889$			6.12138i			0.205304i
$890$	−6.57507	−	5.38873i	−0.220397	−	0.180631i
$891$		−	5.99803i		−	0.200942i
$892$	12.2259	+	12.1285i	0.409352	+	0.406093i
$893$	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
$898$	−16.9422	+	0.0338597i	−0.565370	+	0.00112991i
$899$	42.5283			1.41840
$900$	41.5134	−	8.31478i	1.38378	−	0.277159i
$901$	−43.8214			−1.45990
$902$	−2.24618	+	0.00448907i	−0.0747895	+	0.000149470i
$903$	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	$-0.322992\pi$
$907$	41.4762	−	41.4762i	1.37719	−	1.37719i	0.849328	−	0.527866i	$-0.177008\pi$
$908$	−12.6807	+	12.7825i	−0.420825	+	0.424203i
$909$			10.3082i			0.341902i
$910$	−8.49531	−	6.96250i	−0.281617	−	0.230805i
$911$		−	54.9738i		−	1.82136i	−0.413110	−	0.910681i	$-0.635558\pi$
$911$		−	54.9738i		−	1.82136i	0.413110	−	0.910681i	$-0.364442\pi$
$912$	−14.3557	−	14.1280i	−0.475365	−	0.467824i
$913$	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
$918$	0.0464976	+	23.2658i	0.00153465	+	0.767887i
$919$	30.0697			0.991908			0.495954	−	0.868349i	$-0.334818\pi$
$919$	30.0697			0.991908			0.495954	+	0.868349i	$0.334818\pi$
$920$	27.8538	−	2.87449i	0.918313	−	0.0947690i
$921$	20.2468			0.667155
$922$	0.00518448	+	2.59414i	0.000170742	+	0.0854333i
$923$	−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
$928$	38.8203	−	0.387931i	1.27434	−	0.0127345i
$929$			18.1372i			0.595063i	0.954712	+	0.297532i	$0.0961634\pi$
$929$			18.1372i			0.595063i	−0.954712	+	0.297532i	$0.903837\pi$
$930$	−5.20082	−	52.4482i	−0.170542	−	1.71984i
$931$			12.4022i			0.406465i
$932$	37.6381	−	37.9402i	1.23288	−	1.24277i
$933$	−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	$0.871349\pi$
$938$	7.45343	−	0.0148960i	0.243363	−	0.000486370i
$939$	−35.0754			−1.14464
$940$	53.3794	−	5.40091i	1.74104	−	0.176158i
$941$	53.1895			1.73393			0.866964	−	0.498370i	$-0.166068\pi$
$941$	53.1895			1.73393			0.866964	+	0.498370i	$0.166068\pi$
$942$	−47.4874	+	0.0949053i	−1.54722	+	0.00309218i
$943$	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	$-0.868864\pi$
$947$	−15.8764	+	15.8764i	−0.515912	+	0.515912i	0.400420	+	0.916332i	$0.368864\pi$
$948$	21.8606	+	21.6866i	0.710000	+	0.704347i
$949$		−	64.8517i		−	2.10517i
$950$	12.9858	−	2.57397i	0.421315	−	0.0835105i
$951$		−	39.9883i		−	1.29671i
$952$	−0.0515258	−	8.59383i	−0.00166996	−	0.278528i
$953$	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
$958$	−0.0578837	−	28.9630i	−0.00187014	−	0.935753i
$959$	7.77250			0.250987
$960$	−5.22578	−	47.8278i	−0.168661	−	1.54364i
$961$	−7.40118			−0.238748
$962$	−0.148008	−	74.0580i	−0.00477196	−	2.38773i
$963$	−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	$-0.956334\pi$
$967$	−26.5520	+	26.5520i	−0.853856	+	0.853856i	0.136750	+	0.990606i	$0.456334\pi$
$968$	0.143759	+	23.9771i	0.00462059	+	0.770653i
$969$			24.9641i			0.801964i
$970$	−2.42233	+	0.240200i	−0.0777762	+	0.00771237i
$971$		−	47.6809i		−	1.53015i	−0.643940	−	0.765076i	$-0.722701\pi$
$971$		−	47.6809i		−	1.53015i	0.643940	−	0.765076i	$-0.277299\pi$
$972$	28.5561	+	28.3287i	0.915937	+	0.908644i
$973$	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	$0.704743\pi$
$978$	54.3967	−	0.108714i	1.73941	−	0.00347628i
$979$	4.26981			0.136464
$980$	−18.7330	+	22.9505i	−0.598403	+	0.733127i
$981$	−74.6645			−2.38385
$982$	−11.0985	+	0.0221808i	−0.354168	+	0.000707818i
$983$	−26.1154	−	26.1154i	−0.832951	−	0.832951i	0.154968	−	0.987919i	$-0.450473\pi$
$983$	−26.1154	−	26.1154i	−0.832951	−	0.832951i	−0.987919	+	0.154968i	$0.950473\pi$
$984$	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
$988$	14.9456	−	15.0656i	0.475484	−	0.479300i
$989$		−	29.3662i		−	0.933790i
$990$	−13.4793	+	16.4468i	−0.428399	+	0.522712i
$991$			33.6990i			1.07048i	0.844699	+	0.535242i	$0.179780\pi$
$991$			33.6990i			1.07048i	−0.844699	+	0.535242i	$0.820220\pi$
$992$	−35.0530	+	0.350285i	−1.11293	+	0.0111216i
$993$	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	$0.641067\pi$
$998$	−0.0651957	−	32.6217i	−0.00206373	−	1.03262i
$999$	−30.6614			−0.970082

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.00282635 - 1.41421i) 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} +(0.0169580 + 2.82838i) q^{8} +4.23379i q^{9} +(-2.00451 + 2.44580i) q^{10} -1.58829i q^{11} +(3.81880 + 3.78839i) 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} +(5.98747 - 0.0119662i) q^{18} +1.87220 q^{19} +(3.46455 + 2.82788i) q^{20} -1.64836 q^{21} +(-2.24618 + 0.00448907i) 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} +(-0.863257 + 0.870186i) q^{28} +6.86286i q^{29} +(8.46366 - 0.839265i) q^{30} -6.19687i q^{31} +(-0.0565262 - 5.65657i) 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} +(-0.00529150 - 2.64769i) q^{38} +15.2431 q^{39} +(3.98943 - 4.90759i) q^{40} +1.00000 q^{41} +(0.00465883 + 2.33112i) 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} +(-7.66782 - 7.54620i) q^{48} +6.62439i q^{49} +(6.93612 - 1.37484i) q^{50} +13.3341i q^{51} +(7.98292 - 8.04699i) 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} +(9.70554 - 0.0193969i) q^{58} -0.968941 q^{59} +(-1.21082 - 11.9670i) q^{60} -1.70966 q^{61} +(-8.76368 + 0.0175145i) 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} +(7.03923 + 6.98319i) q^{68} -11.9080i q^{69} +(0.191243 + 1.92860i) q^{70} +11.5429i q^{71} +(-11.9747 + 0.0717967i) 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} +(-0.0430823 - 21.5569i) q^{78} +5.72448 q^{79} +(-6.95165 - 5.62802i) q^{80} +3.77641 q^{81} +(-0.00282635 - 1.41421i) 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} +(4.49228 - 0.0269343i) q^{88} +2.68831i q^{89} +(-10.3550 - 8.48665i) q^{90} +3.47342i q^{91} +(-6.28636 - 6.23630i) 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} +(9.36828 - 0.0187229i) 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

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