LMFDB - Embedded newform 210.2.x.a.23.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.3
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.806628 - 1.53276i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.480420 + 2.18385i) q^{5} +(1.17585 + 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.69870 + 2.47273i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.806628 - 1.53276i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.480420 + 2.18385i) q^{5} +(1.17585 + 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.69870 + 2.47273i) q^{9} +(-1.02927 - 1.98509i) q^{10} +(5.16739 - 2.98339i) q^{11} +(-1.46494 - 0.924094i) q^{12} +(2.36809 + 2.36809i) q^{13} +(0.330568 - 2.62502i) q^{14} +(2.95979 - 2.49792i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.245156 + 0.914934i) q^{17} +(1.00083 - 2.82813i) q^{18} +(4.22990 + 2.44213i) q^{19} +(1.50798 + 1.65106i) q^{20} +(4.56087 - 0.445471i) q^{21} +(-4.21916 + 4.21916i) q^{22} +(0.0558604 + 0.208474i) q^{23} +(1.65420 + 0.513452i) q^{24} +(-4.53839 + 2.09833i) q^{25} +(-2.90030 - 1.67449i) q^{26} +(5.16033 + 0.609122i) q^{27} +(0.360100 + 2.62113i) q^{28} -2.38403 q^{29} +(-2.21243 + 3.17886i) q^{30} +(1.28677 + 2.22875i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-8.74099 - 5.51387i) q^{33} -0.947209i q^{34} +(-5.83027 - 1.00399i) q^{35} +(-0.234751 + 2.99080i) q^{36} +(-0.352701 - 1.31630i) q^{37} +(-4.71784 - 1.26414i) q^{38} +(1.71954 - 5.53987i) q^{39} +(-1.88392 - 1.20451i) q^{40} +4.15479i q^{41} +(-4.29017 + 1.61073i) q^{42} +(-6.02072 - 6.02072i) q^{43} +(2.98339 - 5.16739i) q^{44} +(-6.21617 - 2.52176i) q^{45} +(-0.107914 - 0.186912i) q^{46} +(3.61867 - 0.969620i) q^{47} +(-1.73072 - 0.0678189i) q^{48} +(-5.00516 - 4.89371i) q^{49} +(3.84066 - 3.20145i) q^{50} +(1.60012 - 0.362247i) q^{51} +(3.23487 + 0.866780i) q^{52} +(5.98451 + 1.60355i) q^{53} +(-5.14215 + 0.747224i) q^{54} +(8.99780 + 9.85151i) q^{55} +(-1.02623 - 2.43862i) q^{56} +(0.331246 - 8.45331i) q^{57} +(2.30280 - 0.617033i) q^{58} +(-2.02618 - 3.50944i) q^{59} +(1.31429 - 3.64316i) q^{60} +(-6.70029 + 11.6052i) q^{61} +(-1.81977 - 1.81977i) q^{62} +(-4.36173 - 6.63139i) q^{63} -1.00000i q^{64} +(-4.03387 + 6.30922i) q^{65} +(9.87024 + 3.06366i) q^{66} +(-9.28310 - 2.48740i) q^{67} +(0.245156 + 0.914934i) q^{68} +(0.274482 - 0.253781i) q^{69} +(5.89146 - 0.539201i) q^{70} -10.7537i q^{71} +(-0.547324 - 2.94965i) q^{72} +(3.43327 - 12.8131i) q^{73} +(0.681365 + 1.18016i) q^{74} +(6.87703 + 5.26369i) q^{75} +4.88427 q^{76} +(2.14864 + 15.6397i) q^{77} +(-0.227124 + 5.79616i) q^{78} +(0.874016 + 0.504613i) q^{79} +(2.13148 + 0.675868i) q^{80} +(-3.22883 - 8.40087i) q^{81} +(-1.07534 - 4.01322i) q^{82} +(-7.84434 + 7.84434i) q^{83} +(3.72710 - 2.66623i) q^{84} +(-2.11586 - 0.0958303i) q^{85} +(7.37384 + 4.25729i) q^{86} +(1.92303 + 3.65415i) q^{87} +(-1.54432 + 5.76347i) q^{88} +(-0.188917 + 0.327214i) q^{89} +(6.65704 + 0.826966i) q^{90} +(-8.16688 + 3.43682i) q^{91} +(0.152613 + 0.152613i) q^{92} +(2.37819 - 3.77008i) q^{93} +(-3.24441 + 1.87316i) q^{94} +(-3.30112 + 10.4107i) q^{95} +(1.68930 - 0.382436i) q^{96} +(3.42689 - 3.42689i) q^{97} +(6.10120 + 3.43153i) q^{98} +(-1.40071 + 17.8455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.806628	−	1.53276i	−0.465707	−	0.884939i
$3$	−0.806628	−	1.53276i	−0.465707	−	0.884939i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.480420	+	2.18385i	0.214851	+	0.976647i
$5$	0.480420	+	2.18385i	0.214851	+	0.976647i
$6$	1.17585	+	1.27176i	0.480039	+	0.519194i
$7$	−0.998710	+	2.45002i	−0.377477	+	0.926019i
$7$	−0.998710	+	2.45002i	−0.377477	+	0.926019i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.69870	+	2.47273i	−0.566234	+	0.824245i
$10$	−1.02927	−	1.98509i	−0.325484	−	0.627742i
$11$	5.16739	−	2.98339i	1.55803	−	0.899527i	0.560581	−	0.828100i	$-0.310578\pi$
$11$	5.16739	−	2.98339i	1.55803	−	0.899527i	0.997446	−	0.0714273i	$-0.0227554\pi$
$12$	−1.46494	−	0.924094i	−0.422892	−	0.266763i
$13$	2.36809	+	2.36809i	0.656789	+	0.656789i	0.954619	−	0.297830i	$-0.0962628\pi$
$13$	2.36809	+	2.36809i	0.656789	+	0.656789i	−0.297830	+	0.954619i	$0.596263\pi$
$14$	0.330568	−	2.62502i	0.0883481	−	0.701566i
$15$	2.95979	−	2.49792i	0.764215	−	0.644961i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.245156	+	0.914934i	−0.0594590	+	0.221904i	−0.989262	−	0.146154i	$-0.953311\pi$
$17$	−0.245156	+	0.914934i	−0.0594590	+	0.221904i	0.929803	+	0.368058i	$0.119977\pi$
$18$	1.00083	−	2.82813i	0.235898	−	0.666598i
$19$	4.22990	+	2.44213i	0.970406	+	0.560264i	0.899360	−	0.437209i	$-0.144033\pi$
$19$	4.22990	+	2.44213i	0.970406	+	0.560264i	0.0710458	+	0.997473i	$0.477366\pi$
$20$	1.50798	+	1.65106i	0.337195	+	0.369188i
$21$	4.56087	−	0.445471i	0.995264	−	0.0972098i
$22$	−4.21916	+	4.21916i	−0.899527	+	0.899527i
$23$	0.0558604	+	0.208474i	0.0116477	+	0.0434698i	0.971505	−	0.237019i	$-0.0761702\pi$
$23$	0.0558604	+	0.208474i	0.0116477	+	0.0434698i	−0.959857	+	0.280488i	$0.909504\pi$
$24$	1.65420	+	0.513452i	0.337662	+	0.104808i
$25$	−4.53839	+	2.09833i	−0.907678	+	0.419666i
$26$	−2.90030	−	1.67449i	−0.568796	−	0.328395i
$27$	5.16033	+	0.609122i	0.993105	+	0.117226i
$28$	0.360100	+	2.62113i	0.0680526	+	0.495347i
$29$	−2.38403			−0.442704			−0.221352	−	0.975194i	$-0.571047\pi$
$29$	−2.38403			−0.442704			−0.221352	+	0.975194i	$0.571047\pi$
$30$	−2.21243	+	3.17886i	−0.403933	+	0.580378i
$31$	1.28677	+	2.22875i	0.231110	+	0.400295i	0.958135	−	0.286316i	$-0.0924308\pi$
$31$	1.28677	+	2.22875i	0.231110	+	0.400295i	−0.727025	+	0.686611i	$0.759097\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−8.74099	−	5.51387i	−1.52161	−	0.959842i
$34$		−	0.947209i		−	0.162445i
$35$	−5.83027	−	1.00399i	−0.985495	−	0.169706i
$36$	−0.234751	+	2.99080i	−0.0391252	+	0.498467i
$37$	−0.352701	−	1.31630i	−0.0579836	−	0.216398i	0.930855	−	0.365389i	$-0.119064\pi$
$37$	−0.352701	−	1.31630i	−0.0579836	−	0.216398i	−0.988839	+	0.148991i	$0.952397\pi$
$38$	−4.71784	−	1.26414i	−0.765335	−	0.205071i
$39$	1.71954	−	5.53987i	0.275347	−	0.887090i
$40$	−1.88392	−	1.20451i	−0.297874	−	0.190449i
$41$			4.15479i			0.648869i	0.945908	+	0.324435i	$0.105174\pi$
$41$			4.15479i			0.648869i	−0.945908	+	0.324435i	$0.894826\pi$
$42$	−4.29017	+	1.61073i	−0.661987	+	0.248541i
$43$	−6.02072	−	6.02072i	−0.918151	−	0.918151i	0.0787443	−	0.996895i	$-0.474909\pi$
$43$	−6.02072	−	6.02072i	−0.918151	−	0.918151i	−0.996895	+	0.0787443i	$0.974909\pi$
$44$	2.98339	−	5.16739i	0.449764	−	0.779013i
$45$	−6.21617	−	2.52176i	−0.926652	−	0.375921i
$46$	−0.107914	−	0.186912i	−0.0159110	−	0.0275587i
$47$	3.61867	−	0.969620i	0.527838	−	0.141434i	0.0149481	−	0.999888i	$-0.495242\pi$
$47$	3.61867	−	0.969620i	0.527838	−	0.141434i	0.512890	+	0.858455i	$0.328575\pi$
$48$	−1.73072	−	0.0678189i	−0.249808	−	0.00978882i
$49$	−5.00516	−	4.89371i	−0.715023	−	0.699101i
$50$	3.84066	−	3.20145i	0.543152	−	0.452754i
$51$	1.60012	−	0.362247i	0.224062	−	0.0507247i
$52$	3.23487	+	0.866780i	0.448595	+	0.120201i
$53$	5.98451	+	1.60355i	0.822036	+	0.220264i	0.645236	−	0.763983i	$-0.276759\pi$
$53$	5.98451	+	1.60355i	0.822036	+	0.220264i	0.176800	+	0.984247i	$0.443426\pi$
$54$	−5.14215	+	0.747224i	−0.699757	+	0.101684i
$55$	8.99780	+	9.85151i	1.21326	+	1.32838i
$56$	−1.02623	−	2.43862i	−0.137136	−	0.325874i
$57$	0.331246	−	8.45331i	0.0438746	−	1.11967i
$58$	2.30280	−	0.617033i	0.302372	−	0.0810204i
$59$	−2.02618	−	3.50944i	−0.263786	−	0.456890i	0.703459	−	0.710736i	$-0.251638\pi$
$59$	−2.02618	−	3.50944i	−0.263786	−	0.456890i	−0.967245	+	0.253846i	$0.918305\pi$
$60$	1.31429	−	3.64316i	0.169675	−	0.470330i
$61$	−6.70029	+	11.6052i	−0.857884	+	1.48590i	0.0160589	+	0.999871i	$0.494888\pi$
$61$	−6.70029	+	11.6052i	−0.857884	+	1.48590i	−0.873943	+	0.486028i	$0.838445\pi$
$62$	−1.81977	−	1.81977i	−0.231110	−	0.231110i
$63$	−4.36173	−	6.63139i	−0.549526	−	0.835476i
$64$		−	1.00000i		−	0.125000i
$65$	−4.03387	+	6.30922i	−0.500340	+	0.782563i
$66$	9.87024	+	3.06366i	1.21494	+	0.377110i
$67$	−9.28310	−	2.48740i	−1.13411	−	0.303884i	−0.357530	−	0.933902i	$-0.616381\pi$
$67$	−9.28310	−	2.48740i	−1.13411	−	0.303884i	−0.776581	+	0.630017i	$0.783048\pi$
$68$	0.245156	+	0.914934i	0.0297295	+	0.110952i
$69$	0.274482	−	0.253781i	0.0330437	−	0.0305517i
$70$	5.89146	−	0.539201i	0.704164	−	0.0644469i
$71$		−	10.7537i		−	1.27623i	−0.769943	−	0.638113i	$-0.779715\pi$
$71$		−	10.7537i		−	1.27623i	0.769943	−	0.638113i	$-0.220285\pi$
$72$	−0.547324	−	2.94965i	−0.0645027	−	0.347620i
$73$	3.43327	−	12.8131i	0.401834	−	1.49967i	−0.407987	−	0.912988i	$-0.633769\pi$
$73$	3.43327	−	12.8131i	0.401834	−	1.49967i	0.809821	−	0.586677i	$-0.199564\pi$
$74$	0.681365	+	1.18016i	0.0792071	+	0.137191i
$75$	6.87703	+	5.26369i	0.794091	+	0.607798i
$76$	4.88427			0.560264
$77$	2.14864	+	15.6397i	0.244860	+	1.78231i
$78$	−0.227124	+	5.79616i	−0.0257168	+	0.656286i
$79$	0.874016	+	0.504613i	0.0983345	+	0.0567734i	0.548361	−	0.836242i	$-0.315252\pi$
$79$	0.874016	+	0.504613i	0.0983345	+	0.0567734i	−0.450026	+	0.893015i	$0.648585\pi$
$80$	2.13148	+	0.675868i	0.238307	+	0.0755644i
$81$	−3.22883	−	8.40087i	−0.358759	−	0.933430i
$82$	−1.07534	−	4.01322i	−0.118751	−	0.443186i
$83$	−7.84434	+	7.84434i	−0.861028	+	0.861028i	−0.991458	−	0.130429i	$-0.958364\pi$
$83$	−7.84434	+	7.84434i	−0.861028	+	0.861028i	0.130429	+	0.991458i	$0.458364\pi$
$84$	3.72710	−	2.66623i	0.406659	−	0.290909i
$85$	−2.11586	−	0.0958303i	−0.229497	−	0.0103943i
$86$	7.37384	+	4.25729i	0.795142	+	0.459075i
$87$	1.92303	+	3.65415i	0.206170	+	0.391766i
$88$	−1.54432	+	5.76347i	−0.164625	+	0.614388i
$89$	−0.188917	+	0.327214i	−0.0200252	+	0.0346846i	−0.875864	−	0.482557i	$-0.839708\pi$
$89$	−0.188917	+	0.327214i	−0.0200252	+	0.0346846i	0.855839	+	0.517242i	$0.173041\pi$
$90$	6.65704	+	0.826966i	0.701713	+	0.0871698i
$91$	−8.16688	+	3.43682i	−0.856122	+	0.360277i
$92$	0.152613	+	0.152613i	0.0159110	+	0.0159110i
$93$	2.37819	−	3.77008i	0.246607	−	0.390939i
$94$	−3.24441	+	1.87316i	−0.334636	+	0.193202i
$95$	−3.30112	+	10.4107i	−0.338688	+	1.06812i
$96$	1.68930	−	0.382436i	0.172414	−	0.0390322i
$97$	3.42689	−	3.42689i	0.347948	−	0.347948i	−0.511397	−	0.859345i	$-0.670872\pi$
$97$	3.42689	−	3.42689i	0.347948	−	0.347948i	0.859345	+	0.511397i	$0.170872\pi$
$98$	6.10120	+	3.43153i	0.616314	+	0.346637i
$99$	−1.40071	+	17.8455i	−0.140777	+	1.79354i
$100$	−2.88120	+	4.08640i	−0.288120	+	0.408640i
$101$	−3.73396	+	2.15580i	−0.371543	+	0.214510i	−0.674132	−	0.738611i	$-0.735482\pi$
$101$	−3.73396	+	2.15580i	−0.371543	+	0.214510i	0.302589	+	0.953121i	$0.402149\pi$
$102$	−1.45184	+	0.764046i	−0.143754	+	0.0756518i
$103$	12.9118	−	3.45971i	1.27224	−	0.340896i	0.441352	−	0.897334i	$-0.354499\pi$
$103$	12.9118	−	3.45971i	1.27224	−	0.340896i	0.830889	+	0.556438i	$0.187833\pi$
$104$	−3.34898			−0.328395
$105$	3.16398	+	9.74624i	0.308773	+	0.951136i
$106$	−6.19562			−0.601772
$107$	15.2003	−	4.07291i	1.46947	−	0.393743i	0.566720	−	0.823911i	$-0.308212\pi$
$107$	15.2003	−	4.07291i	1.46947	−	0.393743i	0.902749	+	0.430168i	$0.141546\pi$
$108$	4.77354	−	2.05265i	0.459334	−	0.197516i
$109$	9.16343	−	5.29051i	0.877698	−	0.506739i	0.00779912	−	0.999970i	$-0.497517\pi$
$109$	9.16343	−	5.29051i	0.877698	−	0.506739i	0.869899	+	0.493231i	$0.164184\pi$
$110$	−11.2410	−	7.18703i	−1.07178	−	0.685256i
$111$	−1.73307	+	1.60237i	−0.164495	+	0.152090i
$112$	1.62242	+	2.08992i	0.153304	+	0.197478i
$113$	−5.87797	+	5.87797i	−0.552953	+	0.552953i	−0.927292	−	0.374339i	$-0.877870\pi$
$113$	−5.87797	+	5.87797i	−0.552953	+	0.552953i	0.374339	+	0.927292i	$0.377870\pi$
$114$	1.86792	+	8.25101i	0.174947	+	0.772778i
$115$	−0.428439	+	0.222146i	−0.0399521	+	0.0207152i
$116$	−2.06463	+	1.19202i	−0.191696	+	0.110676i
$117$	−9.87832	+	1.83298i	−0.913251	+	0.169459i
$118$	2.86545	+	2.86545i	0.263786	+	0.263786i
$119$	−1.99676	−	1.51439i	−0.183043	−	0.138824i
$120$	−0.326592	+	3.85919i	−0.0298136	+	0.352294i
$121$	12.3013	−	21.3064i	1.11830	−	1.93695i
$122$	3.46833	−	12.9440i	0.314007	−	1.17189i
$123$	6.36829	−	3.35137i	0.574210	−	0.302183i
$124$	2.22875	+	1.28677i	0.200147	+	0.115555i
$125$	−6.76277	−	8.90308i	−0.604881	−	0.796316i
$126$	5.92944	+	5.27653i	0.528236	+	0.470071i
$127$	11.0815	−	11.0815i	0.983320	−	0.983320i	−0.0165433	−	0.999863i	$-0.505266\pi$
$127$	11.0815	−	11.0815i	0.983320	−	0.983320i	0.999863	+	0.0165433i	$0.00526612\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−4.37183	+	14.0848i	−0.384918	+	1.24010i
$130$	2.26347	−	7.13828i	0.198519	−	0.626069i
$131$	−3.73610	−	2.15704i	−0.326424	−	0.188461i	0.327828	−	0.944737i	$-0.393683\pi$
$131$	−3.73610	−	2.15704i	−0.326424	−	0.188461i	−0.654252	+	0.756276i	$0.727017\pi$
$132$	−10.3269	−	0.404661i	−0.898837	−	0.0352212i
$133$	−10.2077	+	7.92434i	−0.885121	+	0.687128i
$134$	9.61057			0.830227
$135$	1.14889	+	11.5620i	0.0988811	+	0.995099i
$136$	−0.473605	−	0.820307i	−0.0406113	−	0.0703408i
$137$	2.10404	−	7.85237i	0.179760	−	0.670874i	−0.815932	−	0.578148i	$-0.803775\pi$
$137$	2.10404	−	7.85237i	0.179760	−	0.670874i	0.995692	−	0.0927253i	$-0.0295578\pi$
$138$	−0.199445	+	0.316175i	−0.0169779	+	0.0269146i
$139$		−	10.9242i		−	0.926578i	−0.886207	−	0.463289i	$-0.846669\pi$
$139$		−	10.9242i		−	0.926578i	0.886207	−	0.463289i	$-0.153331\pi$
$140$	−5.55115	+	2.04565i	−0.469158	+	0.172889i
$141$	−4.40512	−	4.76443i	−0.370978	−	0.401237i
$142$	2.78326	+	10.3873i	0.233566	+	0.871679i
$143$	19.3018	+	5.17189i	1.61409	+	0.432495i
$144$	1.29210	+	2.70749i	0.107675	+	0.225624i
$145$	−1.14534	−	5.20637i	−0.0951152	−	0.432365i
$146$			13.2651i			1.09783i
$147$	−3.46357	+	11.6191i	−0.285671	+	0.958328i
$148$	−0.963596	−	0.963596i	−0.0792071	−	0.0792071i
$149$	5.86144	−	10.1523i	0.480188	−	0.831710i	−0.519553	−	0.854438i	$-0.673902\pi$
$149$	5.86144	−	10.1523i	0.480188	−	0.831710i	0.999742	+	0.0227275i	$0.00723502\pi$
$150$	−8.00505	−	3.30443i	−0.653609	−	0.269805i
$151$	8.24246	+	14.2764i	0.670762	+	1.16179i	0.977688	+	0.210060i	$0.0673660\pi$
$151$	8.24246	+	14.2764i	0.670762	+	1.16179i	−0.306927	+	0.951733i	$0.599301\pi$
$152$	−4.71784	+	1.26414i	−0.382667	+	0.102535i
$153$	−1.84594	−	2.16040i	−0.149236	−	0.174658i
$154$	−6.12329	−	14.5507i	−0.493429	−	1.17253i
$155$	−4.24906	+	3.88084i	−0.341293	+	0.311717i
$156$	−1.28077	−	5.65744i	−0.102544	−	0.452958i
$157$	2.43060	+	0.651278i	0.193983	+	0.0519776i	0.354503	−	0.935055i	$-0.384650\pi$
$157$	2.43060	+	0.651278i	0.193983	+	0.0519776i	−0.160519	+	0.987033i	$0.551317\pi$
$158$	−0.974838	−	0.261207i	−0.0775540	−	0.0207805i
$159$	−2.36943	−	10.4663i	−0.187908	−	0.830030i
$160$	−2.23378	−	0.101171i	−0.176596	−	0.00799829i
$161$	−0.566552	−	0.0713459i	−0.0446506	−	0.00562285i
$162$	5.29311	+	7.27894i	0.415866	+	0.571887i
$163$	−4.86553	+	1.30371i	−0.381097	+	0.102115i	−0.444282	−	0.895887i	$-0.646541\pi$
$163$	−4.86553	+	1.30371i	−0.381097	+	0.102115i	0.0631843	+	0.998002i	$0.479874\pi$
$164$	2.07740	+	3.59815i	0.162217	+	0.280969i
$165$	7.84212	−	21.7380i	0.610508	−	1.69230i
$166$	5.54679	−	9.60731i	0.430514	−	0.745672i
$167$	−13.6846	−	13.6846i	−1.05894	−	1.05894i	−0.998150	−	0.0607934i	$-0.980637\pi$
$167$	−13.6846	−	13.6846i	−1.05894	−	1.05894i	−0.0607934	−	0.998150i	$-0.519363\pi$
$168$	−2.91003	+	3.54002i	−0.224514	+	0.273118i
$169$		−	1.78432i		−	0.137256i
$170$	2.06856	−	0.455059i	0.158651	−	0.0349014i
$171$	−13.2241	+	6.31096i	−1.01127	+	0.482611i
$172$	−8.22445	−	2.20373i	−0.627108	−	0.168033i
$173$	3.67722	+	13.7236i	0.279574	+	1.04338i	0.952714	+	0.303869i	$0.0982785\pi$
$173$	3.67722	+	13.7236i	0.279574	+	1.04338i	−0.673140	+	0.739515i	$0.735055\pi$
$174$	−2.80327	−	3.03192i	−0.212515	−	0.229849i
$175$	−0.608409	−	13.2148i	−0.0459914	−	0.998942i
$176$		−	5.96679i		−	0.449764i
$177$	−3.74476	+	5.93646i	−0.281473	+	0.446211i
$178$	0.0977906	−	0.364960i	0.00732972	−	0.0273549i
$179$	−4.32841	−	7.49703i	−0.323521	−	0.560354i	0.657691	−	0.753288i	$-0.271533\pi$
$179$	−4.32841	−	7.49703i	−0.323521	−	0.560354i	−0.981212	+	0.192934i	$0.938200\pi$
$180$	−6.64424	+	0.924180i	−0.495232	+	0.0688843i
$181$	−11.7154			−0.870801			−0.435400	−	0.900237i	$-0.643393\pi$
$181$	−11.7154			−0.870801			−0.435400	+	0.900237i	$0.643393\pi$
$182$	6.99909	−	5.43346i	0.518807	−	0.402755i
$183$	23.1927	+	0.908813i	1.71445	+	0.0671814i
$184$	−0.186912	−	0.107914i	−0.0137794	−	0.00795552i
$185$	2.70515	−	1.40262i	0.198886	−	0.103123i
$186$	−1.32139	+	4.25714i	−0.0968888	+	0.312148i
$187$	1.46279	+	5.45922i	0.106970	+	0.399217i
$188$	2.64905	−	2.64905i	0.193202	−	0.193202i
$189$	−6.64603	+	12.0345i	−0.483427	+	0.875384i
$190$	0.494147	−	10.9104i	0.0358492	−	0.791522i
$191$	−22.6716	−	13.0895i	−1.64046	−	0.947120i	−0.980670	−	0.195670i	$-0.937312\pi$
$191$	−22.6716	−	13.0895i	−1.64046	−	0.947120i	−0.659790	−	0.751450i	$-0.729355\pi$
$192$	−1.53276	+	0.806628i	−0.110617	+	0.0582134i
$193$	−5.50843	+	20.5578i	−0.396506	+	1.47978i	0.422694	+	0.906272i	$0.361084\pi$
$193$	−5.50843	+	20.5578i	−0.396506	+	1.47978i	−0.819200	+	0.573508i	$0.805582\pi$
$194$	−2.42318	+	4.19707i	−0.173974	+	0.301332i
$195$	12.9244	+	1.09375i	0.925532	+	0.0783250i
$196$	−6.78145	−	1.73550i	−0.484389	−	0.123964i
$197$	8.39658	+	8.39658i	0.598231	+	0.598231i	0.939842	−	0.341610i	$-0.110972\pi$
$197$	8.39658	+	8.39658i	0.598231	+	0.598231i	−0.341610	+	0.939842i	$0.610972\pi$
$198$	−3.26576	−	17.5999i	−0.232088	−	1.25077i
$199$	−16.5482	+	9.55411i	−1.17307	+	0.677273i	−0.954401	−	0.298527i	$-0.903505\pi$
$199$	−16.5482	+	9.55411i	−1.17307	+	0.677273i	−0.218669	+	0.975799i	$0.570172\pi$
$200$	1.72538	−	4.69287i	0.122003	−	0.331836i
$201$	3.67543	+	16.2352i	0.259245	+	1.14514i
$202$	3.04877	−	3.04877i	0.214510	−	0.214510i
$203$	2.38096	−	5.84092i	0.167110	−	0.409952i
$204$	1.20462	−	1.11378i	0.0843405	−	0.0779799i
$205$	−9.07344	+	1.99605i	−0.633716	+	0.139410i
$206$	−11.5764	+	6.68365i	−0.806568	+	0.465672i
$207$	−0.610390	−	0.216007i	−0.0424251	−	0.0150135i
$208$	3.23487	−	0.866780i	0.224298	−	0.0601004i
$209$	29.1434			2.01589
$210$	−5.57868	−	8.59525i	−0.384966	−	0.593129i
$211$	−6.45261			−0.444216			−0.222108	−	0.975022i	$-0.571294\pi$
$211$	−6.45261			−0.444216			−0.222108	+	0.975022i	$0.571294\pi$
$212$	5.98451	−	1.60355i	0.411018	−	0.110132i
$213$	−16.4828	+	8.67422i	−1.12938	+	0.594348i
$214$	−13.6282	+	7.86826i	−0.931606	+	0.537863i
$215$	10.2559	−	16.0408i	0.699444	−	1.09397i
$216$	−4.07962	+	3.21819i	−0.277583	+	0.218970i
$217$	−6.74558	+	0.926731i	−0.457920	+	0.0629106i
$218$	−7.48191	+	7.48191i	−0.506739	+	0.506739i
$219$	−22.4088	+	5.07307i	−1.51425	+	0.342806i
$220$	12.7181	+	4.03276i	0.857453	+	0.271889i
$221$	−2.74719	+	1.58609i	−0.184796	+	0.106692i
$222$	1.25929	−	1.99632i	0.0845181	−	0.133984i
$223$	−6.54087	−	6.54087i	−0.438009	−	0.438009i	0.453333	−	0.891341i	$-0.350235\pi$
$223$	−6.54087	−	6.54087i	−0.438009	−	0.438009i	−0.891341	+	0.453333i	$0.850235\pi$
$224$	−2.10805	−	1.59879i	−0.140850	−	0.106824i
$225$	2.52076	−	14.7867i	0.168051	−	0.985778i
$226$	4.15635	−	7.19901i	0.276476	−	0.478871i
$227$	2.54238	−	9.48829i	0.168744	−	0.629760i	−0.828789	−	0.559561i	$-0.810970\pi$
$227$	2.54238	−	9.48829i	0.168744	−	0.629760i	0.997533	−	0.0701991i	$-0.0223635\pi$
$228$	−3.93979	−	7.48641i	−0.260919	−	0.495799i
$229$	7.87583	+	4.54711i	0.520449	+	0.300482i	0.737118	−	0.675764i	$-0.236186\pi$
$229$	7.87583	+	4.54711i	0.520449	+	0.300482i	−0.216669	+	0.976245i	$0.569519\pi$
$230$	0.356345	−	0.325464i	0.0234967	−	0.0214605i
$231$	22.2388	−	15.9088i	1.46320	−	1.04672i
$232$	1.68577	−	1.68577i	0.110676	−	0.110676i
$233$	−4.84119	−	18.0676i	−0.317157	−	1.18364i	−0.921965	−	0.387274i	$-0.873417\pi$
$233$	−4.84119	−	18.0676i	−0.317157	−	1.18364i	0.604808	−	0.796371i	$-0.293250\pi$
$234$	9.06732	−	4.32722i	0.592749	−	0.282879i
$235$	3.85599	+	7.43681i	0.251537	+	0.485124i
$236$	−3.50944	−	2.02618i	−0.228445	−	0.131893i
$237$	0.0684447	−	1.74669i	0.00444596	−	0.113460i
$238$	2.32068	+	0.945987i	0.150427	+	0.0613192i
$239$	−8.87693			−0.574201			−0.287100	−	0.957900i	$-0.592691\pi$
$239$	−8.87693			−0.574201			−0.287100	+	0.957900i	$0.592691\pi$
$240$	−0.683368	−	3.81222i	−0.0441112	−	0.246078i
$241$	2.06335	+	3.57384i	0.132912	+	0.230211i	0.924798	−	0.380458i	$-0.124234\pi$
$241$	2.06335	+	3.57384i	0.132912	+	0.230211i	−0.791886	+	0.610669i	$0.790900\pi$
$242$	−6.36761	+	23.7642i	−0.409325	+	1.52762i
$243$	−10.2721	+	11.7254i	−0.658952	+	0.752185i
$244$			13.4006i			0.857884i
$245$	8.28254	−	13.2815i	0.529152	−	0.848527i
$246$	−5.28390	+	4.88541i	−0.336889	+	0.311483i
$247$	4.23359	+	15.8000i	0.269377	+	1.00533i
$248$	−2.48585	−	0.666080i	−0.157851	−	0.0422961i
$249$	18.3509	+	5.69602i	1.16294	+	0.360970i
$250$	8.83663	+	6.84938i	0.558877	+	0.433193i
$251$			9.72407i			0.613778i	0.951745	+	0.306889i	$0.0992880\pi$
$251$			9.72407i			0.613778i	−0.951745	+	0.306889i	$0.900712\pi$
$252$	−7.09306	−	3.56209i	−0.446821	−	0.224390i
$253$	0.910612	+	0.910612i	0.0572497	+	0.0572497i
$254$	−7.83577	+	13.5720i	−0.491660	+	0.851580i
$255$	1.55982	+	3.32040i	0.0976800	+	0.207931i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.07565	−	1.62796i	0.378988	−	0.101550i	−0.0642955	−	0.997931i	$-0.520480\pi$
$257$	6.07565	−	1.62796i	0.378988	−	0.101550i	0.443284	+	0.896381i	$0.353813\pi$
$258$	0.577449	−	14.7364i	0.0359504	−	0.917446i
$259$	3.57719	+	0.450476i	0.222276	+	0.0279912i
$260$	−0.338821	+	7.48088i	−0.0210128	+	0.463945i
$261$	4.04976	−	5.89508i	0.250674	−	0.364896i
$262$	4.16707	+	1.11656i	0.257443	+	0.0689816i
$263$	12.5532	+	3.36362i	0.774064	+	0.207410i	0.624166	−	0.781292i	$-0.285439\pi$
$263$	12.5532	+	3.36362i	0.774064	+	0.207410i	0.149898	+	0.988701i	$0.452106\pi$
$264$	10.0797	−	2.28191i	0.620363	−	0.140442i
$265$	−0.626819	+	13.8396i	−0.0385052	+	0.850163i
$266$	7.80892	−	10.2963i	0.478796	−	0.631305i
$267$	0.653926	+	0.0256243i	0.0400196	+	0.00156818i
$268$	−9.28310	+	2.48740i	−0.567056	+	0.151942i
$269$	5.49814	+	9.52306i	0.335228	+	0.580631i	0.983529	−	0.180753i	$-0.0578535\pi$
$269$	5.49814	+	9.52306i	0.335228	+	0.580631i	−0.648301	+	0.761384i	$0.724520\pi$
$270$	−4.10221	−	10.8707i	−0.249653	−	0.661569i
$271$	9.59447	−	16.6181i	0.582823	−	1.00948i	−0.412321	−	0.911039i	$-0.635282\pi$
$271$	9.59447	−	16.6181i	0.582823	−	1.00948i	0.995143	−	0.0984394i	$-0.0313851\pi$
$272$	0.669778	+	0.669778i	0.0406113	+	0.0406113i
$273$	11.8555	+	9.74563i	0.717525	+	0.589832i
$274$			8.12938i			0.491114i
$275$	−17.1915	+	24.3827i	−1.03669	+	1.47033i
$276$	0.110817	−	0.357022i	0.00667042	−	0.0214902i
$277$	1.66179	+	0.445276i	0.0998475	+	0.0267540i	0.308397	−	0.951258i	$-0.400208\pi$
$277$	1.66179	+	0.445276i	0.0998475	+	0.0267540i	−0.208549	+	0.978012i	$0.566874\pi$
$278$	2.82739	+	10.5520i	0.169575	+	0.632864i
$279$	−7.69694	−	0.604141i	−0.460804	−	0.0361690i
$280$	4.83255	−	3.41269i	0.288800	−	0.203947i
$281$			17.7331i			1.05787i	0.848664	+	0.528933i	$0.177408\pi$
$281$			17.7331i			1.05787i	−0.848664	+	0.528933i	$0.822592\pi$
$282$	5.48814	+	3.46196i	0.326814	+	0.206157i
$283$	4.30819	−	16.0784i	0.256095	−	0.955760i	−0.711383	−	0.702805i	$-0.751931\pi$
$283$	4.30819	−	16.0784i	0.256095	−	0.955760i	0.967478	−	0.252955i	$-0.0814025\pi$
$284$	−5.37684	−	9.31295i	−0.319057	−	0.552622i
$285$	18.6199	−	3.33775i	1.10295	−	0.197711i
$286$	−19.9827			−1.18160
$287$	−10.1793	−	4.14943i	−0.600865	−	0.244933i
$288$	−1.94882	−	2.28081i	−0.114835	−	0.134398i
$289$	13.9454	+	8.05140i	0.820319	+	0.473612i
$290$	2.45382	+	4.73253i	0.144093	+	0.277904i
$291$	−8.01682	−	2.48837i	−0.469955	−	0.145871i
$292$	−3.43327	−	12.8131i	−0.200917	−	0.749833i
$293$	5.73680	−	5.73680i	0.335148	−	0.335148i	−0.519390	−	0.854537i	$-0.673841\pi$
$293$	5.73680	−	5.73680i	0.335148	−	0.335148i	0.854537	+	0.519390i	$0.173841\pi$
$294$	0.338310	−	12.1196i	0.0197306	−	0.706831i
$295$	6.69067	−	6.11087i	0.389546	−	0.355789i
$296$	1.18016	+	0.681365i	0.0685953	+	0.0396035i
$297$	28.4827	−	12.2477i	1.65273	−	0.710684i
$298$	−3.03411	+	11.3234i	−0.175761	+	0.655949i
$299$	−0.361402	+	0.625966i	−0.0209004	+	0.0362006i
$300$	8.58753	+	1.11997i	0.495801	+	0.0646616i
$301$	20.7638	−	8.73790i	1.19681	−	0.503644i
$302$	−11.6566	−	11.6566i	−0.670762	−	0.670762i
$303$	6.31624	+	3.98433i	0.362859	+	0.228894i
$304$	4.22990	−	2.44213i	0.242601	−	0.140066i
$305$	−28.5631	−	9.05703i	−1.63552	−	0.518604i
$306$	2.34220	+	1.60903i	0.133894	+	0.0919819i
$307$	1.58405	−	1.58405i	0.0904064	−	0.0904064i	−0.660457	−	0.750864i	$-0.729638\pi$
$307$	1.58405	−	1.58405i	0.0904064	−	0.0904064i	0.750864	+	0.660457i	$0.229638\pi$
$308$	9.68064	+	12.4701i	0.551606	+	0.710549i
$309$	−15.7180	−	17.0000i	−0.894163	−	0.967097i
$310$	3.09984	−	4.84834i	0.176059	−	0.275367i
$311$	−5.20473	+	3.00495i	−0.295133	+	0.170395i	−0.640254	−	0.768163i	$-0.721171\pi$
$311$	−5.20473	+	3.00495i	−0.295133	+	0.170395i	0.345121	+	0.938558i	$0.387838\pi$
$312$	2.70138	+	5.13318i	0.152936	+	0.290609i
$313$	−3.10488	+	0.831951i	−0.175498	+	0.0470246i	−0.345498	−	0.938419i	$-0.612290\pi$
$313$	−3.10488	+	0.831951i	−0.175498	+	0.0470246i	0.170000	+	0.985444i	$0.445623\pi$
$314$	−2.51634			−0.142006
$315$	12.3865	−	12.7112i	0.697900	−	0.716196i
$316$	1.00923			0.0567734
$317$	0.760038	−	0.203652i	0.0426880	−	0.0114382i	−0.237412	−	0.971409i	$-0.576299\pi$
$317$	0.760038	−	0.203652i	0.0426880	−	0.0114382i	0.280100	+	0.959971i	$0.409632\pi$
$318$	4.99757	+	9.49640i	0.280250	+	0.532532i
$319$	−12.3192	+	7.11251i	−0.689744	+	0.398224i
$320$	2.18385	−	0.480420i	0.122081	−	0.0268563i
$321$	−18.5038	−	20.0131i	−1.03278	−	1.11702i
$322$	0.565713	−	0.0777197i	0.0315260	−	0.00433115i
$323$	−3.27138	+	3.27138i	−0.182024	+	0.182024i
$324$	−6.99668	−	5.66096i	−0.388705	−	0.314498i
$325$	−15.7163	−	5.77828i	−0.871786	−	0.320521i
$326$	4.36231	−	2.51858i	0.241606	−	0.139491i
$327$	−15.5006	−	9.77786i	−0.857183	−	0.540717i
$328$	−2.93788	−	2.93788i	−0.162217	−	0.162217i
$329$	−1.23842	+	9.83417i	−0.0682761	+	0.542176i
$330$	−1.94870	+	23.0270i	−0.107273	+	1.26759i
$331$	−10.7885	+	18.6862i	−0.592989	+	1.02709i	0.400838	+	0.916149i	$0.368719\pi$
$331$	−10.7885	+	18.6862i	−0.592989	+	1.02709i	−0.993827	+	0.110939i	$0.964614\pi$
$332$	−2.87123	+	10.7156i	−0.157579	+	0.588093i
$333$	3.85398	+	1.36386i	0.211197	+	0.0747390i
$334$	16.7601	+	9.67645i	0.917072	+	0.529472i
$335$	0.972314	−	21.4679i	0.0531232	−	1.17292i
$336$	1.89465	−	4.17257i	0.103361	−	0.227632i
$337$	−1.09253	+	1.09253i	−0.0595139	+	0.0595139i	−0.736237	−	0.676723i	$-0.763399\pi$
$337$	−1.09253	+	1.09253i	−0.0595139	+	0.0595139i	0.676723	+	0.736237i	$0.263399\pi$
$338$	0.461817	+	1.72352i	0.0251195	+	0.0937474i
$339$	13.7509	+	4.26818i	0.746844	+	0.231815i
$340$	−1.88030	+	0.974936i	−0.101974	+	0.0528733i
$341$	13.2985	+	7.67787i	0.720152	+	0.415780i
$342$	11.1401	−	9.51857i	0.602387	−	0.514705i
$343$	16.9884	−	7.37533i	0.917286	−	0.398230i
$344$	8.51458			0.459075
$345$	0.686087	+	0.477504i	0.0369377	+	0.0257080i
$346$	−7.10384	−	12.3042i	−0.381905	−	0.661479i
$347$	−4.18299	+	15.6111i	−0.224555	+	0.838050i	0.758028	+	0.652222i	$0.226163\pi$
$347$	−4.18299	+	15.6111i	−0.224555	+	0.838050i	−0.982582	+	0.185827i	$0.940503\pi$
$348$	3.49247	+	2.20307i	0.187216	+	0.118097i
$349$			23.5711i			1.26173i	0.775892	+	0.630866i	$0.217300\pi$
$349$			23.5711i			1.26173i	−0.775892	+	0.630866i	$0.782700\pi$
$350$	4.00791	+	12.6070i	0.214232	+	0.673873i
$351$	10.7776	+	13.6626i	0.575268	+	0.729253i
$352$	1.54432	+	5.76347i	0.0823124	+	0.307194i
$353$	−26.1314	−	7.00188i	−1.39083	−	0.372672i	−0.515788	−	0.856716i	$-0.672501\pi$
$353$	−26.1314	−	7.00188i	−1.39083	−	0.372672i	−0.875044	+	0.484044i	$0.839168\pi$
$354$	2.08069	−	6.70339i	0.110587	−	0.356281i
$355$	23.4844	−	5.16628i	1.24642	−	0.274198i
$356$			0.377834i			0.0200252i
$357$	−0.710547	+	4.28211i	−0.0376062	+	0.226633i
$358$	6.12130	+	6.12130i	0.323521	+	0.323521i
$359$	−3.59250	+	6.22240i	−0.189605	+	0.328405i	−0.945119	−	0.326727i	$-0.894054\pi$
$359$	−3.59250	+	6.22240i	−0.189605	+	0.328405i	0.755514	+	0.655133i	$0.227387\pi$
$360$	6.17865	−	2.61234i	0.325643	−	0.137683i
$361$	2.42804	+	4.20549i	0.127791	+	0.221341i
$362$	11.3162	−	3.03218i	0.594768	−	0.159368i
$363$	−42.5802	−	1.66852i	−2.23488	−	0.0875745i
$364$	−5.35432	+	7.05982i	−0.280643	+	0.370035i
$365$	29.6314	+	1.34205i	1.55098	+	0.0702462i
$366$	−22.6376	+	5.12486i	−1.18329	+	0.267881i
$367$	−14.4270	−	3.86571i	−0.753084	−	0.201788i	−0.138198	−	0.990405i	$-0.544131\pi$
$367$	−14.4270	−	3.86571i	−0.753084	−	0.201788i	−0.614886	+	0.788616i	$0.710798\pi$
$368$	0.208474	+	0.0558604i	0.0108674	+	0.00291192i
$369$	−10.2737	−	7.05775i	−0.534827	−	0.367412i
$370$	−2.24995	+	2.05497i	−0.116969	+	0.106833i
$371$	−9.90550	+	13.0607i	−0.514268	+	0.678077i
$372$	0.174534	−	4.45408i	0.00904919	−	0.230933i
$373$	7.54451	−	2.02154i	0.390640	−	0.104672i	−0.0581526	−	0.998308i	$-0.518521\pi$
$373$	7.54451	−	2.02154i	0.390640	−	0.104672i	0.448792	+	0.893636i	$0.351854\pi$
$374$	−2.82590	−	4.89460i	−0.146124	−	0.253094i
$375$	−8.19124	+	17.5472i	−0.422994	+	0.906133i
$376$	−1.87316	+	3.24441i	−0.0966010	+	0.167318i
$377$	−5.64560	−	5.64560i	−0.290763	−	0.290763i
$378$	3.30480	−	13.3446i	0.169981	−	0.686372i
$379$			17.2301i			0.885050i	0.896756	+	0.442525i	$0.145917\pi$
$379$			17.2301i			0.885050i	−0.896756	+	0.442525i	$0.854083\pi$
$380$	2.34650	+	10.6665i	0.120373	+	0.547180i
$381$	−25.9238	−	8.04658i	−1.32812	−	0.412239i
$382$	25.2869	+	6.77560i	1.29379	+	0.346670i
$383$	1.41459	+	5.27933i	0.0722823	+	0.269761i	0.992603	−	0.121403i	$-0.0387392\pi$
$383$	1.41459	+	5.27933i	0.0722823	+	0.269761i	−0.920321	+	0.391164i	$0.872073\pi$
$384$	1.27176	−	1.17585i	0.0648993	−	0.0600049i
$385$	−33.1226	+	12.2060i	−1.68808	+	0.622073i
$386$		−	21.2830i		−	1.08327i
$387$	25.1150	−	4.66023i	1.27667	−	0.236893i
$388$	1.25433	−	4.68122i	0.0636789	−	0.237653i
$389$	−2.33417	−	4.04291i	−0.118347	−	0.204983i	0.800766	−	0.598978i	$-0.204426\pi$
$389$	−2.33417	−	4.04291i	−0.118347	−	0.204983i	−0.919113	+	0.393994i	$0.871093\pi$
$390$	−12.7670	+	2.28859i	−0.646485	+	0.115887i
$391$	−0.204434			−0.0103387
$392$	6.99956	−	0.0788068i	0.353531	−	0.00398035i
$393$	−0.292576	+	7.46646i	−0.0147585	+	0.376633i
$394$	−10.2837	−	5.93728i	−0.518084	−	0.299116i
$395$	−0.682104	+	2.15115i	−0.0343204	+	0.108236i
$396$	7.70969	+	16.1550i	0.387426	+	0.811819i
$397$	0.0132059	+	0.0492850i	0.000662783	+	0.00247354i	0.966256	−	0.257582i	$-0.0829258\pi$
$397$	0.0132059	+	0.0492850i	0.000662783	+	0.00247354i	−0.965594	+	0.260056i	$0.916259\pi$
$398$	13.5115	−	13.5115i	0.677273	−	0.677273i
$399$	20.3799	+	9.25396i	1.02027	+	0.463278i
$400$	−0.451988	+	4.97953i	−0.0225994	+	0.248976i
$401$	−0.0554200	−	0.0319968i	−0.00276754	−	0.00159784i	0.498616	−	0.866823i	$-0.333842\pi$
$401$	−0.0554200	−	0.0319968i	−0.00276754	−	0.00159784i	−0.501383	+	0.865225i	$0.667175\pi$
$402$	−7.75216	−	14.7307i	−0.386643	−	0.734700i
$403$	−2.23069	+	8.32505i	−0.111119	+	0.414700i
$404$	−2.15580	+	3.73396i	−0.107255	+	0.185771i
$405$	16.7950	−	11.0872i	0.834552	−	0.550929i
$406$	−0.788086	+	6.25813i	−0.0391121	+	0.310586i
$407$	−5.74957	−	5.74957i	−0.284996	−	0.284996i
$408$	−0.875311	+	1.38760i	−0.0433343	+	0.0686967i
$409$	29.6265	−	17.1049i	1.46494	−	0.845781i	0.465702	−	0.884942i	$-0.345802\pi$
$409$	29.6265	−	17.1049i	1.46494	−	0.845781i	0.999233	+	0.0391609i	$0.0124685\pi$
$410$	8.24765	−	4.27641i	0.407323	−	0.211197i
$411$	−13.7330	+	3.10897i	−0.677398	+	0.153354i
$412$	9.45212	−	9.45212i	0.465672	−	0.465672i
$413$	10.6217	−	1.45925i	0.522662	−	0.0718052i
$414$	0.645498	+	0.0506659i	0.0317245	+	0.00249009i
$415$	−20.8994	−	13.3623i	−1.02591	−	0.655928i
$416$	−2.90030	+	1.67449i	−0.142199	+	0.0820987i
$417$	−16.7441	+	8.81176i	−0.819965	+	0.431514i
$418$	−28.1504	+	7.54286i	−1.37688	+	0.368934i
$419$	18.1904			0.888658			0.444329	−	0.895864i	$-0.353442\pi$
$419$	18.1904			0.888658			0.444329	+	0.895864i	$0.353442\pi$
$420$	7.61321	+	6.85850i	0.371486	+	0.334661i
$421$	−2.01328			−0.0981212			−0.0490606	−	0.998796i	$-0.515623\pi$
$421$	−2.01328			−0.0981212			−0.0490606	+	0.998796i	$0.515623\pi$
$422$	6.23274	−	1.67006i	0.303405	−	0.0812972i
$423$	−3.74943	+	10.5951i	−0.182304	+	0.515152i
$424$	−5.36557	+	3.09781i	−0.260575	+	0.150443i
$425$	−0.807221	−	4.66675i	−0.0391560	−	0.226370i
$426$	13.6761	−	12.6447i	0.662609	−	0.612638i
$427$	−21.7414	−	28.0061i	−1.05214	−	1.35531i
$428$	11.1274	−	11.1274i	0.537863	−	0.537863i
$429$	−7.64209	−	33.7568i	−0.368963	−	1.62979i
$430$	−5.75473	+	18.1486i	−0.277518	+	0.875205i
$431$	35.3759	−	20.4243i	1.70400	−	0.983804i	0.762374	−	0.647136i	$-0.224034\pi$
$431$	35.3759	−	20.4243i	1.70400	−	0.983804i	0.941624	−	0.336667i	$-0.109300\pi$
$432$	3.10768	−	4.16441i	0.149518	−	0.200360i
$433$	7.07520	+	7.07520i	0.340012	+	0.340012i	0.856372	−	0.516360i	$-0.172713\pi$
$433$	7.07520	+	7.07520i	0.340012	+	0.340012i	−0.516360	+	0.856372i	$0.672713\pi$
$434$	6.27587	−	2.64104i	0.301251	−	0.126774i
$435$	−7.05625	+	5.95513i	−0.338321	+	0.285527i
$436$	5.29051	−	9.16343i	0.253370	−	0.438849i
$437$	−0.272837	+	1.01824i	−0.0130516	+	0.0487091i
$438$	20.3323	−	10.7000i	0.971514	−	0.511268i
$439$	−15.7197	−	9.07578i	−0.750261	−	0.433163i	0.0755273	−	0.997144i	$-0.475936\pi$
$439$	−15.7197	−	9.07578i	−0.750261	−	0.433163i	−0.825788	+	0.563980i	$0.809269\pi$
$440$	−13.3285	−	0.603667i	−0.635410	−	0.0287787i
$441$	20.6031	−	4.06348i	0.981100	−	0.193499i
$442$	2.24307	−	2.24307i	0.106692	−	0.106692i
$443$	−2.15250	−	8.03323i	−0.102268	−	0.381670i	0.895753	−	0.444553i	$-0.146637\pi$
$443$	−2.15250	−	8.03323i	−0.102268	−	0.381670i	−0.998021	+	0.0628823i	$0.979971\pi$
$444$	−0.699697	+	2.25422i	−0.0332061	+	0.106981i
$445$	−0.805345	−	0.255366i	−0.0381770	−	0.0121055i
$446$	8.01090	+	4.62509i	0.379327	+	0.219004i
$447$	−20.2891	−	0.795034i	−0.959640	−	0.0376038i
$448$	2.45002	+	0.998710i	0.115752	+	0.0471846i
$449$	−12.4820			−0.589061			−0.294531	−	0.955642i	$-0.595163\pi$
$449$	−12.4820			−0.589061			−0.294531	+	0.955642i	$0.595163\pi$
$450$	1.39221	+	14.9353i	0.0656293	+	0.704055i
$451$	12.3954	+	21.4694i	0.583676	+	1.01096i
$452$	−2.15149	+	8.02946i	−0.101197	+	0.377674i
$453$	15.2336	−	24.1494i	0.715738	−	1.13464i
$454$			9.82300i			0.461016i
$455$	−11.4290	−	16.1841i	−0.535801	−	0.758723i
$456$	5.74317	+	6.21162i	0.268949	+	0.290886i
$457$	8.18804	+	30.5582i	0.383021	+	1.42945i	0.841264	+	0.540625i	$0.181812\pi$
$457$	8.18804	+	30.5582i	0.383021	+	1.42945i	−0.458243	+	0.888827i	$0.651521\pi$
$458$	−8.78434	−	2.35376i	−0.410465	−	0.109984i
$459$	−1.82239	+	4.57203i	−0.0850619	+	0.213404i
$460$	−0.259966	+	0.406603i	−0.0121210	+	0.0189580i
$461$		−	13.2219i		−	0.615807i	−0.951418	−	0.307904i	$-0.900373\pi$
$461$		−	13.2219i		−	0.615807i	0.951418	−	0.307904i	$-0.0996274\pi$
$462$	−17.3635	+	21.1225i	−0.807824	+	0.982710i
$463$	−16.2332	−	16.2332i	−0.754422	−	0.754422i	0.220879	−	0.975301i	$-0.429107\pi$
$463$	−16.2332	−	16.2332i	−0.754422	−	0.754422i	−0.975301	+	0.220879i	$0.929107\pi$
$464$	−1.19202	+	2.06463i	−0.0553380	+	0.0958482i
$465$	9.37581	+	3.38239i	0.434793	+	0.156854i
$466$	9.35245	+	16.1989i	0.433244	+	0.750401i
$467$	−12.6067	+	3.37796i	−0.583369	+	0.156313i	−0.538421	−	0.842676i	$-0.680979\pi$
$467$	−12.6067	+	3.37796i	−0.583369	+	0.156313i	−0.0449484	+	0.998989i	$0.514312\pi$
$468$	−7.63839	+	6.52657i	−0.353085	+	0.301691i
$469$	15.3653	−	20.2596i	0.709503	−	0.935500i
$470$	−5.64939	−	6.18540i	−0.260587	−	0.285311i
$471$	−0.962341	−	4.25087i	−0.0443423	−	0.195870i
$472$	3.91427	+	1.04883i	0.180169	+	0.0482761i
$473$	−49.0735	−	13.1492i	−2.25640	−	0.604602i
$474$	0.385965	+	1.70489i	0.0177279	+	0.0783082i
$475$	−24.3214	−	2.20763i	−1.11594	−	0.101293i
$476$	−2.48644	−	0.313117i	−0.113966	−	0.0143517i
$477$	−14.1310	+	12.0742i	−0.647016	+	0.552838i
$478$	8.57446	−	2.29752i	0.392187	−	0.105086i
$479$	−15.7131	−	27.2159i	−0.717951	−	1.24353i	−0.961810	−	0.273717i	$-0.911747\pi$
$479$	−15.7131	−	27.2159i	−0.717951	−	1.24353i	0.243859	−	0.969811i	$-0.421586\pi$
$480$	1.64676	+	3.50545i	0.0751639	+	0.160001i
$481$	2.28188	−	3.95233i	0.104045	−	0.180211i
$482$	−2.91802	−	2.91802i	−0.132912	−	0.132912i
$483$	0.347641	+	0.925938i	0.0158182	+	0.0421316i
$484$		−	24.6026i		−	1.11830i
$485$	9.13016	+	5.83746i	0.414579	+	0.265066i
$486$	6.88728	−	13.9845i	0.312414	−	0.634348i
$487$	−25.7118	−	6.88945i	−1.16511	−	0.312191i	−0.376106	−	0.926577i	$-0.622737\pi$
$487$	−25.7118	−	6.88945i	−1.16511	−	0.312191i	−0.789006	+	0.614386i	$0.789404\pi$
$488$	−3.46833	−	12.9440i	−0.157004	−	0.585946i
$489$	5.92295	+	6.40607i	0.267845	+	0.289692i
$490$	−4.56280	+	14.9727i	−0.206126	+	0.676396i
$491$			17.2123i			0.776779i	0.921495	+	0.388389i	$0.126968\pi$
$491$			17.2123i			0.776779i	−0.921495	+	0.388389i	$0.873032\pi$
$492$	3.83942	−	6.08652i	0.173094	−	0.274402i
$493$	0.584460	−	2.18123i	0.0263227	−	0.0982378i
$494$	−8.17866	−	14.1659i	−0.367975	−	0.637352i
$495$	−39.6448	+	5.51439i	−1.78190	+	0.247853i
$496$	2.57354			0.115555
$497$	26.3467	+	10.7398i	1.18181	+	0.481746i
$498$	−19.1999	−	0.752354i	−0.860368	−	0.0337138i
$499$	−34.9854	−	20.1988i	−1.56616	−	0.904224i	−0.996610	−	0.0822678i	$-0.973784\pi$
$499$	−34.9854	−	20.1988i	−1.56616	−	0.904224i	−0.569551	−	0.821956i	$-0.692883\pi$
$500$	−10.3083	−	4.32891i	−0.461000	−	0.193595i
$501$	−9.93679	+	32.0135i	−0.443943	+	1.43026i
$502$	−2.51677	−	9.39273i	−0.112329	−	0.419218i
$503$	3.72801	−	3.72801i	0.166224	−	0.166224i	−0.619094	−	0.785317i	$-0.712500\pi$
$503$	3.72801	−	3.72801i	0.166224	−	0.166224i	0.785317	+	0.619094i	$0.212500\pi$
$504$	7.77331	+	1.60489i	0.346251	+	0.0714875i
$505$	−6.50182	−	7.11871i	−0.289327	−	0.316779i
$506$	−1.11527	−	0.643900i	−0.0495797	−	0.0286248i
$507$	−2.73494	+	1.43929i	−0.121463	+	0.0639210i
$508$	4.05609	−	15.1375i	0.179960	−	0.671620i
$509$	−4.53149	+	7.84877i	−0.200855	+	0.347891i	−0.948804	−	0.315865i	$-0.897705\pi$
$509$	−4.53149	+	7.84877i	−0.200855	+	0.347891i	0.747949	+	0.663756i	$0.231039\pi$
$510$	−2.36606	−	2.80354i	−0.104771	−	0.124143i
$511$	27.9636	+	21.2082i	1.23704	+	0.938195i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	20.3401	+	15.1787i	0.898038	+	0.670158i
$514$	−5.44728	+	3.14499i	−0.240269	+	0.138719i
$515$	13.7586	+	26.5354i	0.606276	+	1.16929i
$516$	3.25628	+	14.3837i	0.143350	+	0.633207i
$517$	15.8063	−	15.8063i	0.695162	−	0.695162i
$518$	−3.57189	+	0.490720i	−0.156940	+	0.0215610i
$519$	18.0688	−	16.7061i	0.793131	−	0.733317i
$520$	−1.60892	−	7.31367i	−0.0705558	−	0.320726i
$521$	28.4540	−	16.4279i	1.24659	−	0.719721i	0.276165	−	0.961110i	$-0.410936\pi$
$521$	28.4540	−	16.4279i	1.24659	−	0.719721i	0.970428	+	0.241389i	$0.0776030\pi$
$522$	−2.38601	+	6.74237i	−0.104433	+	0.295105i
$523$	11.2645	−	3.01831i	0.492561	−	0.131981i	−0.00398437	−	0.999992i	$-0.501268\pi$
$523$	11.2645	−	3.01831i	0.492561	−	0.131981i	0.496545	+	0.868011i	$0.334602\pi$
$524$	−4.31407			−0.188461
$525$	−19.7643	+	11.5919i	−0.862584	+	0.505914i
$526$	−12.9960			−0.566654
$527$	−2.35462	+	0.630917i	−0.102569	+	0.0274832i
$528$	−9.14565	+	4.81298i	−0.398013	+	0.209458i
$529$	19.8782	−	11.4767i	0.864271	−	0.498987i
$530$	−2.97650	−	13.5303i	−0.129291	−	0.587719i
$531$	12.1198	+	0.951296i	0.525954	+	0.0412827i
$532$	−4.87797	+	11.9665i	−0.211487	+	0.518815i
$533$	−9.83891	+	9.83891i	−0.426170	+	0.426170i
$534$	−0.638276	+	0.144497i	−0.0276209	+	0.00625301i
$535$	16.1972	+	31.2385i	0.700264	+	1.35056i
$536$	8.32300	−	4.80529i	0.359499	−	0.207557i
$537$	−7.99972	+	12.6817i	−0.345213	+	0.547257i
$538$	−7.77555	−	7.77555i	−0.335228	−	0.335228i
$539$	−40.4635	−	10.3553i	−1.74288	−	0.446036i
$540$	6.77598	+	9.43855i	0.291592	+	0.406170i
$541$	−1.99471	+	3.45495i	−0.0857595	+	0.148540i	−0.905715	−	0.423888i	$-0.860665\pi$
$541$	−1.99471	+	3.45495i	−0.0857595	+	0.148540i	0.819955	+	0.572428i	$0.193998\pi$
$542$	−4.96646	+	18.5351i	−0.213328	+	0.796150i
$543$	9.45000	+	17.9569i	0.405538	+	0.770606i
$544$	−0.820307	−	0.473605i	−0.0351704	−	0.0203056i
$545$	15.9560	+	17.4699i	0.683479	+	0.748328i
$546$	−13.9738	−	6.34514i	−0.598026	−	0.271547i
$547$	−9.65788	+	9.65788i	−0.412941	+	0.412941i	−0.882762	−	0.469821i	$-0.844319\pi$
$547$	−9.65788	+	9.65788i	−0.412941	+	0.412941i	0.469821	+	0.882762i	$0.344319\pi$
$548$	−2.10404	−	7.85237i	−0.0898800	−	0.335437i
$549$	−17.3149	−	36.2819i	−0.738981	−	1.54847i
$550$	10.2950	−	28.0014i	0.438980	−	1.19398i
$551$	−10.0842	−	5.82213i	−0.429602	−	0.248031i
$552$	−0.0146372	+	0.373538i	−0.000623001	+	0.0158988i
$553$	−2.10920	+	1.63739i	−0.0896923	+	0.0696290i
$554$	−1.72041			−0.0730934
$555$	−4.33193	−	3.01495i	−0.183880	−	0.127977i
$556$	−5.46209	−	9.46062i	−0.231644	−	0.401220i
$557$	−1.21720	+	4.54267i	−0.0515746	+	0.192479i	−0.986907	−	0.161292i	$-0.948434\pi$
$557$	−1.21720	+	4.54267i	−0.0515746	+	0.192479i	0.935332	+	0.353771i	$0.115101\pi$
$558$	7.59103	−	1.40856i	0.321354	−	0.0596290i
$559$		−	28.5152i		−	1.20606i
$560$	−3.78462	+	4.54716i	−0.159929	+	0.192153i
$561$	7.18773	−	6.64567i	0.303466	−	0.280580i
$562$	−4.58965	−	17.1288i	−0.193603	−	0.722536i
$563$	25.7242	+	6.89278i	1.08415	+	0.290496i	0.756293	−	0.654233i	$-0.227008\pi$
$563$	25.7242	+	6.89278i	1.08415	+	0.290496i	0.327853	+	0.944729i	$0.393675\pi$
$564$	−6.19716	−	1.92356i	−0.260947	−	0.0809964i
$565$	−15.6605	−	10.0127i	−0.658842	−	0.421238i
$566$			16.6455i			0.699665i
$567$	23.8069	+	0.479352i	0.999797	+	0.0201309i
$568$	7.60399	+	7.60399i	0.319057	+	0.319057i
$569$	−2.30517	+	3.99267i	−0.0966376	+	0.167381i	−0.910291	−	0.413969i	$-0.864142\pi$
$569$	−2.30517	+	3.99267i	−0.0966376	+	0.167381i	0.813653	+	0.581350i	$0.197475\pi$
$570$	−17.1216	+	8.04321i	−0.717143	+	0.336893i
$571$	−2.42916	−	4.20743i	−0.101657	−	0.176075i	0.810710	−	0.585447i	$-0.199081\pi$
$571$	−2.42916	−	4.20743i	−0.101657	−	0.176075i	−0.912368	+	0.409372i	$0.865748\pi$
$572$	19.3018	−	5.17189i	0.807047	−	0.216248i
$573$	−1.77543	+	45.3084i	−0.0741695	+	1.89279i
$574$	10.9064	+	1.37344i	0.455225	+	0.0573264i
$575$	−0.690963	−	0.828922i	−0.0288152	−	0.0345684i
$576$	2.47273	+	1.69870i	0.103031	+	0.0707792i
$577$	−13.0720	−	3.50264i	−0.544196	−	0.145817i	−0.0237602	−	0.999718i	$-0.507564\pi$
$577$	−13.0720	−	3.50264i	−0.544196	−	0.145817i	−0.520436	+	0.853901i	$0.674230\pi$
$578$	−15.5541	−	4.16771i	−0.646965	−	0.173354i
$579$	35.9534	−	8.13937i	1.49417	−	0.338261i
$580$	−3.59508	−	3.93618i	−0.149277	−	0.163441i
$581$	−11.3845	−	27.0530i	−0.472310	−	1.12235i
$582$	8.38770	+	0.328674i	0.347681	+	0.0136240i
$583$	35.7083	−	9.56802i	1.47889	−	0.396267i
$584$	6.63257	+	11.4880i	0.274458	+	0.475375i
$585$	−8.74869	−	20.6922i	−0.361714	−	0.855516i
$586$	−4.05653	+	7.02612i	−0.167574	+	0.290246i
$587$	−20.4866	−	20.4866i	−0.845574	−	0.845574i	0.144004	−	0.989577i	$-0.454002\pi$
$587$	−20.4866	−	20.4866i	−0.845574	−	0.845574i	−0.989577	+	0.144004i	$0.954002\pi$
$588$	2.81001	+	11.7942i	0.115883	+	0.486386i
$589$			12.5698i			0.517931i
$590$	−4.88108	+	7.63432i	−0.200951	+	0.314300i
$591$	6.09701	−	19.6428i	0.250798	−	0.807999i
$592$	−1.31630	−	0.352701i	−0.0540994	−	0.0144959i
$593$	8.84754	+	33.0195i	0.363325	+	1.35595i	0.869678	+	0.493620i	$0.164327\pi$
$593$	8.84754	+	33.0195i	0.363325	+	1.35595i	−0.506353	+	0.862326i	$0.669007\pi$
$594$	−24.3422	+	19.2022i	−0.998773	+	0.787877i
$595$	2.34791	−	5.08817i	0.0962549	−	0.208595i
$596$		−	11.7229i		−	0.480188i
$597$	27.9924	+	17.6578i	1.14565	+	0.722685i
$598$	0.187075	−	0.698175i	0.00765008	−	0.0285505i
$599$	20.2161	+	35.0153i	0.826006	+	1.43068i	0.901148	+	0.433512i	$0.142726\pi$
$599$	20.2161	+	35.0153i	0.826006	+	1.43068i	−0.0751420	+	0.997173i	$0.523941\pi$
$600$	−8.58479	+	1.14081i	−0.350472	+	0.0465732i
$601$	20.3443			0.829861			0.414931	−	0.909853i	$-0.363806\pi$
$601$	20.3443			0.829861			0.414931	+	0.909853i	$0.363806\pi$
$602$	−17.7948	+	13.8142i	−0.725260	+	0.563026i
$603$	21.9199	−	18.7293i	0.892647	−	0.762716i
$604$	14.2764	+	8.24246i	0.580897	+	0.335381i
$605$	52.4398	+	16.6281i	2.13198	+	0.676028i
$606$	−7.13224	−	2.21380i	−0.289728	−	0.0899296i
$607$	11.9417	+	44.5671i	0.484699	+	1.80892i	0.581413	+	0.813609i	$0.302500\pi$
$607$	11.9417	+	44.5671i	0.484699	+	1.80892i	−0.0967136	+	0.995312i	$0.530833\pi$
$608$	−3.45370	+	3.45370i	−0.140066	+	0.140066i
$609$	−10.8733	+	1.06202i	−0.440607	+	0.0430352i
$610$	29.9339	+	1.35575i	1.21199	+	0.0548928i
$611$	10.8655	+	6.27319i	0.439570	+	0.253786i
$612$	−2.67883	−	0.947994i	−0.108285	−	0.0383204i
$613$	3.99730	−	14.9181i	0.161450	−	0.602538i	−0.837017	−	0.547177i	$-0.815702\pi$
$613$	3.99730	−	14.9181i	0.161450	−	0.602538i	0.998466	−	0.0553608i	$-0.0176309\pi$
$614$	−1.12009	+	1.94006i	−0.0452032	+	0.0782943i
$615$	10.3784	+	12.2973i	0.418495	+	0.495876i
$616$	−12.5783	−	9.53964i	−0.506793	−	0.384363i
$617$	−2.50025	−	2.50025i	−0.100656	−	0.100656i	0.654985	−	0.755642i	$-0.272675\pi$
$617$	−2.50025	−	2.50025i	−0.100656	−	0.100656i	−0.755642	+	0.654985i	$0.772675\pi$
$618$	19.5823	+	12.3527i	0.787716	+	0.496897i
$619$	4.86025	−	2.80606i	0.195350	−	0.112785i	−0.399135	−	0.916892i	$-0.630689\pi$
$619$	4.86025	−	2.80606i	0.195350	−	0.112785i	0.594485	+	0.804107i	$0.297356\pi$
$620$	−1.73937	+	5.48544i	−0.0698548	+	0.220301i
$621$	0.161272	+	1.10982i	0.00647161	+	0.0445355i
$622$	4.24964	−	4.24964i	0.170395	−	0.170395i
$623$	−0.613006	−	0.789641i	−0.0245596	−	0.0316363i
$624$	−3.93790	−	4.25910i	−0.157642	−	0.170501i
$625$	16.1940	−	19.0461i	0.647761	−	0.761844i
$626$	2.78376	−	1.60721i	0.111261	−	0.0642369i
$627$	−23.5079	−	44.6698i	−0.938815	−	1.78394i
$628$	2.43060	−	0.651278i	0.0969916	−	0.0259888i
$629$	1.29079			0.0514672
$630$	−8.67452	+	15.4839i	−0.345601	+	0.616895i
$631$	20.0318			0.797455			0.398727	−	0.917069i	$-0.369452\pi$
$631$	20.0318			0.797455			0.398727	+	0.917069i	$0.369452\pi$
$632$	−0.974838	+	0.261207i	−0.0387770	+	0.0103903i
$633$	5.20486	+	9.89030i	0.206875	+	0.393104i
$634$	−0.681432	+	0.393425i	−0.0270631	+	0.0156249i
$635$	29.5240	+	18.8765i	1.17162	+	0.749090i
$636$	−7.28513	−	7.87935i	−0.288874	−	0.312437i
$637$	−0.263923	−	23.4414i	−0.0104570	−	0.928781i
$638$	10.0586	−	10.0586i	0.398224	−	0.398224i
$639$	26.5910	+	18.2673i	1.05192	+	0.722642i
$640$	−1.98509	+	1.02927i	−0.0784677	+	0.0406856i
$641$	32.1479	−	18.5606i	1.26977	−	0.733100i	0.294823	−	0.955552i	$-0.404739\pi$
$641$	32.1479	−	18.5606i	1.26977	−	0.733100i	0.974944	+	0.222452i	$0.0714059\pi$
$642$	23.0530	+	14.5420i	0.909831	+	0.573928i
$643$	−7.70403	−	7.70403i	−0.303817	−	0.303817i	0.538688	−	0.842505i	$-0.318920\pi$
$643$	−7.70403	−	7.70403i	−0.303817	−	0.303817i	−0.842505	+	0.538688i	$0.818920\pi$
$644$	−0.526322	+	0.221489i	−0.0207400	+	0.00872788i
$645$	−32.8594	−	2.78079i	−1.29384	−	0.109494i
$646$	2.31321	−	4.00660i	0.0910121	−	0.157638i
$647$	−6.17291	+	23.0376i	−0.242682	+	0.905702i	0.731852	+	0.681464i	$0.238656\pi$
$647$	−6.17291	+	23.0376i	−0.242682	+	0.905702i	−0.974534	+	0.224239i	$0.928010\pi$
$648$	8.22344	+	3.65719i	0.323047	+	0.143668i
$649$	−20.9401	−	12.0898i	−0.821970	−	0.474565i
$650$	16.6763	+	1.51370i	0.654100	+	0.0593722i
$651$	6.86163	+	9.59182i	0.268928	+	0.375933i
$652$	−3.56181	+	3.56181i	−0.139491	+	0.139491i
$653$	−5.34683	−	19.9547i	−0.209238	−	0.780886i	−0.988116	−	0.153711i	$-0.950878\pi$
$653$	−5.34683	−	19.9547i	−0.209238	−	0.780886i	0.778878	−	0.627175i	$-0.215789\pi$
$654$	17.5031	+	5.43285i	0.684425	+	0.212441i
$655$	2.91574	−	9.19535i	0.113928	−	0.359292i
$656$	3.59815	+	2.07740i	0.140484	+	0.0811087i
$657$	25.8514	+	30.2553i	1.00856	+	1.18037i
$658$	−1.34905	−	9.81961i	−0.0525916	−	0.382808i
$659$	15.8694			0.618184			0.309092	−	0.951032i	$-0.399975\pi$
$659$	15.8694			0.618184			0.309092	+	0.951032i	$0.399975\pi$
$660$	−4.07751	−	22.7467i	−0.158717	−	0.885414i
$661$	−2.27276	−	3.93654i	−0.0884003	−	0.153114i	0.818435	−	0.574599i	$-0.194842\pi$
$661$	−2.27276	−	3.93654i	−0.0884003	−	0.153114i	−0.906835	+	0.421486i	$0.861509\pi$
$662$	5.58454	−	20.8418i	0.217049	−	0.810039i
$663$	4.64706	+	2.93140i	0.180477	+	0.113846i
$664$		−	11.0936i		−	0.430514i
$665$	−22.2096	−	18.4851i	−0.861250	−	0.716821i
$666$	−4.07565	−	0.319903i	−0.157928	−	0.0123960i
$667$	−0.133173	−	0.497008i	−0.00515648	−	0.0192442i
$668$	−18.6935	−	5.00890i	−0.723272	−	0.193800i
$669$	−4.74953	+	15.3016i	−0.183627	+	0.591595i
$670$	4.61712	+	20.9880i	0.178375	+	0.810839i
$671$			79.9584i			3.08676i
$672$	−0.750148	+	4.52076i	−0.0289376	+	0.174392i
$673$	−8.60027	−	8.60027i	−0.331516	−	0.331516i	0.521646	−	0.853162i	$-0.325318\pi$
$673$	−8.60027	−	8.60027i	−0.331516	−	0.331516i	−0.853162	+	0.521646i	$0.825318\pi$
$674$	0.772535	−	1.33807i	0.0297570	−	0.0515405i
$675$	−24.6977	+	8.06364i	−0.950616	+	0.310370i
$676$	−0.892162	−	1.54527i	−0.0343139	−	0.0594335i
$677$	−37.4764	+	10.0418i	−1.44033	+	0.385936i	−0.892650	−	0.450750i	$-0.851157\pi$
$677$	−37.4764	+	10.0418i	−1.44033	+	0.385936i	−0.547683	+	0.836686i	$0.684490\pi$
$678$	−14.3870	−	0.563759i	−0.552529	−	0.0216510i
$679$	4.97347	+	11.8184i	0.190864	+	0.453549i
$680$	1.56390	−	1.42837i	0.0599727	−	0.0547756i
$681$	−16.5940	+	3.75667i	−0.635884	+	0.143956i
$682$	−14.8325	−	3.97436i	−0.567966	−	0.152186i
$683$	−9.11142	−	2.44140i	−0.348639	−	0.0934175i	0.0802500	−	0.996775i	$-0.474428\pi$
$683$	−9.11142	−	2.44140i	−0.348639	−	0.0934175i	−0.428889	+	0.903357i	$0.641095\pi$
$684$	−8.29691	+	12.0775i	−0.317240	+	0.461795i
$685$	18.1592	+	0.822459i	0.693828	+	0.0314245i
$686$	−14.5006	+	11.5209i	−0.553636	+	0.439871i
$687$	0.616760	−	15.7396i	0.0235309	−	0.600502i
$688$	−8.22445	+	2.20373i	−0.313554	+	0.0840166i
$689$	10.3745	+	17.9692i	0.395238	+	0.684571i
$690$	−0.786296	−	0.283662i	−0.0299338	−	0.0107988i
$691$	−5.48550	+	9.50117i	−0.208678	+	0.361441i	−0.951298	−	0.308271i	$-0.900250\pi$
$691$	−5.48550	+	9.50117i	−0.208678	+	0.361441i	0.742620	+	0.669713i	$0.233583\pi$
$692$	10.0464	+	10.0464i	0.381905	+	0.381905i
$693$	−42.3228	−	21.2542i	−1.60771	−	0.807381i
$694$		−	16.1618i		−	0.613495i
$695$	23.8568	−	5.24820i	0.904939	−	0.199076i
$696$	−3.94366	−	1.22409i	−0.149484	−	0.0463989i
$697$	−3.80136	−	1.01857i	−0.143987	−	0.0385811i
$698$	−6.10064	−	22.7679i	−0.230913	−	0.861778i
$699$	−23.7882	+	21.9942i	−0.899751	+	0.831896i
$700$	−7.13428	−	11.1401i	−0.269650	−	0.421057i
$701$			10.6209i			0.401147i	0.979679	+	0.200574i	$0.0642806\pi$
$701$			10.6209i			0.401147i	−0.979679	+	0.200574i	$0.935719\pi$
$702$	−13.9465	−	10.4076i	−0.526378	−	0.392808i
$703$	1.72268	−	6.42914i	0.0649723	−	0.242480i
$704$	−2.98339	−	5.16739i	−0.112441	−	0.194753i
$705$	8.28849	−	11.9090i	0.312162	−	0.448520i
$706$	27.0532			1.01816
$707$	−1.55261	−	11.3013i	−0.0583919	−	0.425028i
$708$	−0.274826	+	7.01350i	−0.0103286	+	0.263583i
$709$	8.79213	+	5.07614i	0.330196	+	0.190638i	0.655928	−	0.754824i	$-0.272278\pi$
$709$	8.79213	+	5.07614i	0.330196	+	0.190638i	−0.325732	+	0.945462i	$0.605611\pi$
$710$	−21.3471	+	11.0685i	−0.801141	+	0.415392i
$711$	−2.73247	+	1.30402i	−0.102476	+	0.0489046i
$712$	−0.0977906	−	0.364960i	−0.00366486	−	0.0136774i
$713$	−0.392756	+	0.392756i	−0.0147088	+	0.0147088i
$714$	−0.421955	−	4.32010i	−0.0157913	−	0.161676i
$715$	−2.02167	+	44.6368i	−0.0756062	+	1.66932i
$716$	−7.49703	−	4.32841i	−0.280177	−	0.161760i
$717$	7.16038	+	13.6062i	0.267409	+	0.508133i
$718$	1.85962	−	6.94018i	0.0694002	−	0.259005i
$719$	14.4032	−	24.9471i	0.537150	−	0.930370i	−0.461906	−	0.886929i	$-0.652834\pi$
$719$	14.4032	−	24.9471i	0.537150	−	0.930370i	0.999056	−	0.0434417i	$-0.0138323\pi$
$720$	−5.29199	+	4.12248i	−0.197221	+	0.153636i
$721$	−4.41881	+	35.0894i	−0.164565	+	1.30680i
$722$	−3.43376	−	3.43376i	−0.127791	−	0.127791i
$723$	3.81347	−	6.04538i	0.141824	−	0.224830i
$724$	−10.1459	+	5.85771i	−0.377068	+	0.217700i
$725$	10.8197	−	5.00249i	0.401833	−	0.185788i
$726$	41.5612	−	9.40890i	1.54248	−	0.349197i
$727$	0.151969	−	0.151969i	0.00563622	−	0.00563622i	−0.704283	−	0.709919i	$-0.748731\pi$
$727$	0.151969	−	0.151969i	0.00563622	−	0.00563622i	0.709919	+	0.704283i	$0.248731\pi$
$728$	3.34466	−	8.20506i	0.123961	−	0.304100i
$729$	26.2579	+	6.28654i	0.972516	+	0.232835i
$730$	−28.9691	+	6.37285i	−1.07219	+	0.235870i
$731$	6.98457	−	4.03254i	0.258334	−	0.149149i
$732$	20.5399	−	10.8093i	0.759175	−	0.399523i
$733$	−33.0589	+	8.85810i	−1.22106	+	0.327181i	−0.811091	−	0.584919i	$-0.801126\pi$
$733$	−33.0589	+	8.85810i	−1.22106	+	0.327181i	−0.409966	+	0.912101i	$0.634459\pi$
$734$	14.9359			0.551296
$735$	−27.0383	−	1.98187i	−0.997324	−	0.0731023i
$736$	−0.215828			−0.00795552
$737$	−55.3903	+	14.8418i	−2.04033	+	0.546704i
$738$	11.7503	+	4.15823i	0.432535	+	0.153067i
$739$	28.3705	−	16.3797i	1.04362	−	0.602537i	0.122767	−	0.992436i	$-0.460823\pi$
$739$	28.3705	−	16.3797i	1.04362	−	0.602537i	0.920858	+	0.389899i	$0.127490\pi$
$740$	1.64142	−	2.56728i	0.0603397	−	0.0943750i
$741$	20.8026	−	19.2338i	0.764203	−	0.706570i
$742$	6.18763	−	15.1794i	0.227155	−	0.557253i
$743$	−0.701038	+	0.701038i	−0.0257186	+	0.0257186i	−0.719849	−	0.694131i	$-0.755789\pi$
$743$	−0.701038	+	0.701038i	−0.0257186	+	0.0257186i	0.694131	+	0.719849i	$0.255789\pi$
$744$	0.984213	+	4.34748i	0.0360830	+	0.159386i
$745$	24.9871	+	7.92313i	0.915456	+	0.290281i
$746$	−6.76422	+	3.90532i	−0.247656	+	0.142984i
$747$	−6.07178	−	32.7222i	−0.222155	−	1.19724i
$748$	3.99642	+	3.99642i	0.146124	+	0.146124i
$749$	−5.20199	+	41.3086i	−0.190077	+	1.50938i
$750$	3.37058	−	19.0693i	0.123076	−	0.696313i
$751$	−0.934185	+	1.61806i	−0.0340889	+	0.0590437i	−0.882567	−	0.470188i	$-0.844186\pi$
$751$	−0.934185	+	1.61806i	−0.0340889	+	0.0590437i	0.848478	+	0.529231i	$0.177520\pi$
$752$	0.969620	−	3.61867i	0.0353584	−	0.131959i
$753$	14.9047	−	7.84371i	0.543156	−	0.285841i
$754$	6.91442	+	3.99204i	0.251808	+	0.145382i
$755$	−27.2176	+	24.8589i	−0.990548	+	0.904709i
$756$	0.261645	+	13.7452i	0.00951595	+	0.499909i
$757$	15.1882	−	15.1882i	0.552024	−	0.552024i	−0.375001	−	0.927025i	$-0.622358\pi$
$757$	15.1882	−	15.1882i	0.552024	−	0.552024i	0.927025	+	0.375001i	$0.122358\pi$
$758$	−4.45947	−	16.6430i	−0.161975	−	0.604500i
$759$	0.661223	−	2.13027i	0.0240009	−	0.0773240i
$760$	−5.02724	−	9.69573i	−0.182357	−	0.351701i
$761$	−43.5861	−	25.1645i	−1.58000	−	0.912211i	−0.994858	−	0.101277i	$-0.967707\pi$
$761$	−43.5861	−	25.1645i	−1.58000	−	0.912211i	−0.585138	−	0.810934i	$-0.698960\pi$
$762$	27.1231	+	1.06283i	0.982566	+	0.0385022i
$763$	3.81023	+	27.7342i	0.137940	+	1.00405i
$764$	−26.1789			−0.947120
$765$	3.83117	−	5.06916i	0.138516	−	0.183276i
$766$	−2.73278	−	4.73332i	−0.0987395	−	0.171022i
$767$	3.51250	−	13.1088i	0.126829	−	0.473332i
$768$	−0.924094	+	1.46494i	−0.0333454	+	0.0528615i
$769$			5.32307i			0.191955i	0.995384	+	0.0959775i	$0.0305977\pi$
$769$			5.32307i			0.191955i	−0.995384	+	0.0959775i	$0.969402\pi$
$770$	28.8348	−	20.3628i	1.03913	−	0.733824i
$771$	−7.39607	−	7.99934i	−0.266363	−	0.288089i
$772$	5.50843	+	20.5578i	0.198253	+	0.739890i
$773$	−18.9649	−	5.08164i	−0.682121	−	0.182774i	−0.0989124	−	0.995096i	$-0.531536\pi$
$773$	−18.9649	−	5.08164i	−0.682121	−	0.182774i	−0.583209	+	0.812322i	$0.698203\pi$
$774$	−23.0531	+	11.0017i	−0.828626	+	0.395447i
$775$	−10.5165	−	7.41487i	−0.377764	−	0.266350i
$776$			4.84635i			0.173974i
$777$	−2.19499	−	5.84634i	−0.0787450	−	0.209736i
$778$	3.30102	+	3.30102i	0.118347	+	0.118347i
$779$	−10.1466	+	17.5744i	−0.363538	+	0.629667i
$780$	11.7397	−	5.51496i	0.420348	−	0.197467i
$781$	−32.0824	−	55.5684i	−1.14800	−	1.98839i
$782$	0.197468	−	0.0529115i	0.00706145	−	0.00189211i
$783$	−12.3024	−	1.45217i	−0.439652	−	0.0518963i
$784$	−6.74066	+	1.88774i	−0.240738	+	0.0674193i
$785$	−0.254582	+	5.62096i	−0.00908641	+	0.200620i
$786$	−1.64986	−	7.28777i	−0.0588484	−	0.259946i
$787$	21.4421	+	5.74540i	0.764329	+	0.204801i	0.619865	−	0.784709i	$-0.287187\pi$
$787$	21.4421	+	5.74540i	0.764329	+	0.204801i	0.144464	+	0.989510i	$0.453854\pi$
$788$	11.4699	+	3.07336i	0.408600	+	0.109484i
$789$	−4.97015	−	21.9542i	−0.176942	−	0.781592i
$790$	0.102105	−	2.25439i	0.00363272	−	0.0802075i
$791$	−8.53074	−	20.2715i	−0.303318	−	0.720772i
$792$	−11.6282	−	13.6091i	−0.413190	−	0.483579i
$793$	−43.3491	+	11.6154i	−1.53937	+	0.412473i
$794$	−0.0255118	−	0.0441877i	−0.000905379	−	0.00156816i
$795$	21.7185	−	10.2027i	0.770274	−	0.361852i
$796$	−9.55411	+	16.5482i	−0.338636	+	0.586535i
$797$	0.507697	+	0.507697i	0.0179836	+	0.0179836i	0.716041	−	0.698058i	$-0.245952\pi$
$797$	0.507697	+	0.507697i	0.0179836	+	0.0179836i	−0.698058	+	0.716041i	$0.745952\pi$
$798$	−22.0806	−	3.66393i	−0.781645	−	0.129702i
$799$			3.54855i			0.125539i
$800$	−0.852210	−	4.92684i	−0.0301302	−	0.174190i
$801$	−0.488199	−	1.02298i	−0.0172497	−	0.0361452i
$802$	0.0618130	+	0.0165627i	0.00218269	+	0.000584851i
$803$	−20.4856	−	76.4533i	−0.722921	−	2.69798i
$804$	11.3006	+	12.2224i	0.398541	+	0.431049i
$805$	−0.116375	−	1.27154i	−0.00410167	−	0.0448159i
$806$		−	8.61873i		−	0.303582i
$807$	10.1616	−	16.1089i	0.357705	−	0.567060i
$808$	1.11593	−	4.16469i	0.0392581	−	0.146513i
$809$	−22.9981	−	39.8339i	−0.808571	−	1.40049i	−0.913854	−	0.406044i	$-0.866908\pi$
$809$	−22.9981	−	39.8339i	−0.808571	−	1.40049i	0.105283	−	0.994442i	$-0.466425\pi$
$810$	−13.3532	+	15.0563i	−0.469183	+	0.529025i
$811$	−45.3779			−1.59343			−0.796717	−	0.604352i	$-0.793432\pi$
$811$	−45.3779			−1.59343			−0.796717	+	0.604352i	$0.793432\pi$
$812$	−0.858491	−	6.24886i	−0.0301271	−	0.219292i
$813$	−33.2107	−	1.30137i	−1.16475	−	0.0456411i
$814$	7.04176	+	4.06556i	0.246813	+	0.142498i
$815$	−5.18461	−	9.99924i	−0.181609	−	0.350258i
$816$	0.486346	−	1.56687i	0.0170255	−	0.0548514i
$817$	−10.7636	−	40.1704i	−0.376572	−	1.40539i
$818$	−24.1899	+	24.1899i	−0.845781	+	0.845781i
$819$	5.37475	−	26.0327i	0.187809	−	0.909655i
$820$	−6.85980	+	6.26535i	−0.239555	+	0.218795i
$821$	33.3434	+	19.2508i	1.16369	+	0.671859i	0.952187	−	0.305517i	$-0.0988293\pi$
$821$	33.3434	+	19.2508i	1.16369	+	0.671859i	0.211508	+	0.977376i	$0.432163\pi$
$822$	12.4604	−	6.55739i	0.434606	−	0.228715i
$823$	0.785245	−	2.93058i	0.0273719	−	0.102153i	−0.950888	−	0.309534i	$-0.899827\pi$
$823$	0.785245	−	2.93058i	0.0273719	−	0.102153i	0.978260	+	0.207380i	$0.0664937\pi$
$824$	−6.68365	+	11.5764i	−0.232836	+	0.403284i
$825$	51.2400	+	6.68264i	1.78395	+	0.232660i
$826$	−9.88214	+	4.15864i	−0.343844	+	0.144698i
$827$	30.2271	+	30.2271i	1.05110	+	1.05110i	0.998622	+	0.0524756i	$0.0167112\pi$
$827$	30.2271	+	30.2271i	1.05110	+	1.05110i	0.0524756	+	0.998622i	$0.483289\pi$
$828$	−0.636617	+	0.118128i	−0.0221240	+	0.00410522i
$829$	−46.3527	+	26.7617i	−1.60990	+	0.929473i	−0.620503	+	0.784204i	$0.713072\pi$
$829$	−46.3527	+	26.7617i	−1.60990	+	0.929473i	−0.989392	+	0.145270i	$0.953595\pi$
$830$	23.6457	+	7.49779i	0.820755	+	0.260252i
$831$	−0.657948	−	2.90630i	−0.0228240	−	0.100818i
$832$	2.36809	−	2.36809i	0.0820987	−	0.0820987i
$833$	5.70446	−	3.37967i	0.197648	−	0.117099i
$834$	13.8930	−	12.8452i	0.481074	−	0.444793i
$835$	23.3107	−	36.4594i	0.806700	−	1.26173i
$836$	25.2389	−	14.5717i	0.872906	−	0.503973i
$837$	5.28256	+	12.2849i	0.182592	+	0.424627i
$838$	−17.5706	+	4.70802i	−0.606965	+	0.162636i
$839$	9.47997			0.327285			0.163643	−	0.986520i	$-0.447676\pi$
$839$	9.47997			0.327285			0.163643	+	0.986520i	$0.447676\pi$
$840$	−9.12890	−	4.65436i	−0.314977	−	0.160591i
$841$	−23.3164			−0.804013
$842$	1.94468	−	0.521075i	0.0670181	−	0.0179574i
$843$	27.1805	−	14.3040i	0.936147	−	0.492656i
$844$	−5.58813	+	3.22631i	−0.192351	+	0.111054i
$845$	3.89669	−	0.857226i	0.134050	−	0.0294895i
$846$	0.879455	−	11.2045i	0.0302363	−	0.385219i
$847$	39.9157	+	51.4173i	1.37152	+	1.76672i
$848$	4.38097	−	4.38097i	0.150443	−	0.150443i
$849$	−28.1194	+	6.36586i	−0.965054	+	0.218476i
$850$	1.98756	+	4.29881i	0.0681727	+	0.147448i
$851$	0.254711	−	0.147058i	0.00873139	−	0.00504107i
$852$	−9.93741	+	15.7535i	−0.340450	+	0.539706i
$853$	22.4380	+	22.4380i	0.768262	+	0.768262i	0.977800	−	0.209539i	$-0.0671962\pi$
$853$	22.4380	+	22.4380i	0.768262	+	0.768262i	−0.209539	+	0.977800i	$0.567196\pi$
$854$	28.2491	+	21.4247i	0.966664	+	0.733139i
$855$	−20.1353	−	25.8475i	−0.688613	−	0.883966i
$856$	−7.86826	+	13.6282i	−0.268931	+	0.465803i
$857$	11.2662	−	42.0461i	0.384846	−	1.43627i	−0.453562	−	0.891225i	$-0.649847\pi$
$857$	11.2662	−	42.0461i	0.384846	−	1.43627i	0.838409	−	0.545042i	$-0.183486\pi$
$858$	16.1186	+	30.6286i	0.550279	+	1.04564i
$859$	−30.1458	−	17.4047i	−1.02856	−	0.593841i	−0.111990	−	0.993709i	$-0.535723\pi$
$859$	−30.1458	−	17.4047i	−1.02856	−	0.593841i	−0.916573	+	0.399868i	$0.869056\pi$
$860$	0.861430	−	19.0197i	0.0293745	−	0.648566i
$861$	1.85084	+	18.9495i	0.0630765	+	0.645796i
$862$	−28.8843	+	28.8843i	−0.983804	+	0.983804i
$863$	4.47160	+	16.6883i	0.152215	+	0.568075i	0.999328	+	0.0366613i	$0.0116723\pi$
$863$	4.47160	+	16.6883i	0.152215	+	0.568075i	−0.847113	+	0.531413i	$0.821661\pi$
$864$	−1.92396	+	4.82684i	−0.0654544	+	0.164212i
$865$	−28.2036	+	14.6236i	−0.958951	+	0.497217i
$866$	−8.66531	−	5.00292i	−0.294459	−	0.170006i
$867$	1.09207	−	27.8695i	0.0370888	−	0.946497i
$868$	−5.37848	+	4.17536i	−0.182557	+	0.141721i
$869$	6.02184			0.204277
$870$	5.27451	−	7.57851i	0.178823	−	0.256935i
$871$	−16.0928	−	27.8736i	−0.545284	−	0.944460i
$872$	−2.73857	+	10.2205i	−0.0927397	+	0.346109i
$873$	2.65253	+	14.2951i	0.0897744	+	0.483814i
$874$		−	1.05416i		−	0.0356575i
$875$	28.5667	−	7.67731i	0.965732	−	0.259541i
$876$	−16.8701	+	15.5978i	−0.569988	+	0.527002i
$877$	−2.05735	−	7.67812i	−0.0694717	−	0.259272i	0.922451	−	0.386113i	$-0.126183\pi$
$877$	−2.05735	−	7.67812i	−0.0694717	−	0.259272i	−0.991923	+	0.126842i	$0.959516\pi$
$878$	17.5331	+	4.69797i	0.591712	+	0.158549i
$879$	−13.4206	−	4.16567i	−0.452666	−	0.140505i
$880$	13.0306	−	2.86657i	0.439260	−	0.0966319i
$881$		−	5.56368i		−	0.187445i	−0.995598	−	0.0937226i	$-0.970123\pi$
$881$		−	5.56368i		−	0.187445i	0.995598	−	0.0937226i	$-0.0298767\pi$
$882$	−18.8494	+	9.25749i	−0.634691	+	0.311716i
$883$	4.84514	+	4.84514i	0.163052	+	0.163052i	0.783917	−	0.620865i	$-0.213219\pi$
$883$	4.84514	+	4.84514i	0.163052	+	0.163052i	−0.620865	+	0.783917i	$0.713219\pi$
$884$	−1.58609	+	2.74719i	−0.0533461	+	0.0923981i
$885$	−14.7634	−	5.32599i	−0.496266	−	0.179031i
$886$	4.15831	+	7.20240i	0.139701	+	0.241969i
$887$	2.94804	−	0.789926i	0.0989856	−	0.0265231i	−0.208986	−	0.977919i	$-0.567016\pi$
$887$	2.94804	−	0.789926i	0.0989856	−	0.0265231i	0.307972	+	0.951395i	$0.400350\pi$
$888$	0.0924189	−	2.35851i	0.00310137	−	0.0791463i
$889$	16.0826	+	38.2169i	0.539393	+	1.28175i
$890$	0.843997	+	0.0382259i	0.0282909	+	0.00128134i
$891$	−41.7477	−	33.7777i	−1.39860	−	1.13160i
$892$	−8.93499	−	2.39412i	−0.299166	−	0.0801612i
$893$	17.6746	+	4.73589i	0.591457	+	0.158480i
$894$	19.8035	−	4.48325i	0.662328	−	0.149942i
$895$	14.2929	−	13.0543i	0.477759	−	0.436358i
$896$	−2.62502	−	0.330568i	−0.0876957	−	0.0110435i
$897$	1.25097	+	0.0490198i	0.0417688	+	0.00163672i
$898$	12.0567	−	3.23058i	0.402336	−	0.107806i
$899$	−3.06770	−	5.31341i	−0.102313	−	0.177212i
$900$	−5.21030	−	14.0660i	−0.173677	−	0.468867i
$901$	−2.93428	+	5.08232i	−0.0977549	+	0.169316i
$902$	−17.5297	−	17.5297i	−0.583676	−	0.583676i
$903$	−30.1418	−	24.7777i	−1.00306	−	0.824549i
$904$		−	8.31271i		−	0.276476i
$905$	−5.62833	−	25.5847i	−0.187092	−	0.850465i
$906$	−8.46421	+	27.2693i	−0.281205	+	0.905962i
$907$	33.6250	+	9.00978i	1.11650	+	0.299165i	0.769466	−	0.638688i	$-0.220523\pi$
$907$	33.6250	+	9.00978i	1.11650	+	0.299165i	0.347033	+	0.937853i	$0.387189\pi$
$908$	−2.54238	−	9.48829i	−0.0843718	−	0.314880i
$909$	1.01216	−	12.8952i	0.0335711	−	0.427705i
$910$	15.2284	+	12.6746i	0.504815	+	0.420159i
$911$			13.5125i			0.447688i	0.974625	+	0.223844i	$0.0718605\pi$
$911$			13.5125i			0.447688i	−0.974625	+	0.223844i	$0.928139\pi$
$912$	−7.15516	−	4.51352i	−0.236931	−	0.149458i
$913$	−17.1320	+	63.9375i	−0.566987	+	2.11602i
$914$	−15.8181	−	27.3977i	−0.523216	−	0.906236i
$915$	9.15753	+	51.0859i	0.302739	+	1.68885i
$916$	9.09422			0.300482
$917$	9.01605	−	6.99924i	0.297736	−	0.231135i
$918$	0.576966	−	4.88791i	0.0190427	−	0.161325i
$919$	23.3642	+	13.4893i	0.770714	+	0.444972i	0.833129	−	0.553078i	$-0.186547\pi$
$919$	23.3642	+	13.4893i	0.770714	+	0.444972i	−0.0624154	+	0.998050i	$0.519880\pi$
$920$	0.145871	−	0.460033i	0.00480923	−	0.0151668i
$921$	−3.70570	−	1.15023i	−0.122107	−	0.0379012i
$922$	3.42209	+	12.7714i	0.112701	+	0.420604i
$923$	25.4656	−	25.4656i	0.838212	−	0.838212i
$924$	11.3050	−	24.8968i	0.371906	−	0.819045i
$925$	4.36272	+	5.23379i	0.143445	+	0.172086i
$926$	19.8816	+	11.4786i	0.653349	+	0.377211i
$927$	−13.3784	+	37.8045i	−0.439404	+	1.24166i
$928$	0.617033	−	2.30280i	0.0202551	−	0.0755931i
$929$	−24.7230	+	42.8215i	−0.811135	+	1.40493i	0.100936	+	0.994893i	$0.467816\pi$
$929$	−24.7230	+	42.8215i	−0.811135	+	1.40493i	−0.912071	+	0.410033i	$0.865517\pi$
$930$	−9.93176	−	0.840496i	−0.325675	−	0.0275609i
$931$	−9.22023	−	32.9232i	−0.302181	−	1.07901i
$932$	−13.2264	−	13.2264i	−0.433244	−	0.433244i
$933$	8.80414	+	5.55371i	0.288235	+	0.181820i
$934$	11.3029	−	6.52572i	0.369841	−	0.213528i
$935$	−11.2193	+	5.81724i	−0.366912	+	0.190244i
$936$	5.68892	−	8.28114i	0.185948	−	0.270678i
$937$	−11.4941	+	11.4941i	−0.375495	+	0.375495i	−0.869474	−	0.493979i	$-0.835542\pi$
$937$	−11.4941	+	11.4941i	−0.375495	+	0.375495i	0.493979	+	0.869474i	$0.335542\pi$
$938$	−9.59817	+	23.5461i	−0.313391	+	0.768806i
$939$	3.77967	+	4.08796i	0.123345	+	0.133406i
$940$	7.05779	+	4.51247i	0.230200	+	0.147181i
$941$	−29.1043	+	16.8034i	−0.948774	+	0.547775i	−0.892700	−	0.450651i	$-0.851192\pi$
$941$	−29.1043	+	16.8034i	−0.948774	+	0.547775i	−0.0560744	+	0.998427i	$0.517858\pi$
$942$	2.02975	+	3.85695i	0.0661330	+	0.125666i
$943$	−0.866165	+	0.232088i	−0.0282062	+	0.00755783i
$944$	−4.05235			−0.131893
$945$	−29.4745	−	8.73228i	−0.958806	−	0.284061i
$946$	50.8047			1.65180
$947$	48.9361	−	13.1124i	1.59021	−	0.426095i	0.648142	−	0.761520i	$-0.275546\pi$
$947$	48.9361	−	13.1124i	1.59021	−	0.426095i	0.942067	+	0.335424i	$0.108880\pi$
$948$	−0.814071	−	1.54690i	−0.0264398	−	0.0502410i
$949$	38.4729	−	22.2124i	1.24888	−	0.721044i
$950$	24.0640	−	4.16242i	0.780739	−	0.135047i
$951$	−0.925217	−	1.00068i	−0.0300022	−	0.0324494i
$952$	2.48276	−	0.341090i	0.0804667	−	0.0110548i
$953$	26.3451	−	26.3451i	0.853401	−	0.853401i	−0.137149	−	0.990550i	$-0.543794\pi$
$953$	26.3451	−	26.3451i	0.853401	−	0.853401i	0.990550	+	0.137149i	$0.0437939\pi$
$954$	10.5245	−	15.3201i	0.340744	−	0.496008i
$955$	17.6935	−	55.7998i	0.572548	−	1.80564i
$956$	−7.68765	+	4.43847i	−0.248636	+	0.143550i
$957$	20.8388	+	13.1453i	0.673623	+	0.424926i
$958$	22.2217	+	22.2217i	0.717951	+	0.717951i
$959$	17.1371	+	12.9972i	0.553387	+	0.419700i
$960$	−2.49792	−	2.95979i	−0.0806201	−	0.0955269i
$961$	12.1885	−	21.1110i	0.393176	−	0.681001i
$962$	−1.18119	+	4.40825i	−0.0380830	+	0.142128i
$963$	−15.7496	+	44.5050i	−0.507522	+	1.43415i
$964$	3.57384	+	2.06335i	0.115105	+	0.0664562i
$965$	−47.5414	−	2.15322i	−1.53041	−	0.0693147i
$966$	−0.575446	−	0.804411i	−0.0185147	−	0.0258815i
$967$	−38.9797	+	38.9797i	−1.25350	+	1.25350i	−0.299362	+	0.954139i	$0.596774\pi$
$967$	−38.9797	+	38.9797i	−1.25350	+	1.25350i	−0.954139	+	0.299362i	$0.903226\pi$
$968$	6.36761	+	23.7642i	0.204663	+	0.763812i
$969$	7.65302	+	2.37545i	0.245850	+	0.0763103i
$970$	−10.3299	−	3.27550i	−0.331673	−	0.105170i
$971$	−8.61828	−	4.97576i	−0.276574	−	0.159680i	0.355298	−	0.934753i	$-0.384380\pi$
$971$	−8.61828	−	4.97576i	−0.276574	−	0.159680i	−0.631871	+	0.775073i	$0.717713\pi$
$972$	−3.03316	+	15.2905i	−0.0972886	+	0.490444i
$973$	26.7644	+	10.9101i	0.858028	+	0.349761i
$974$	26.6188			0.852921
$975$	3.82054	+	28.7503i	0.122355	+	0.920746i
$976$	6.70029	+	11.6052i	0.214471	+	0.371475i
$977$	−6.54016	+	24.4082i	−0.209238	+	0.780888i	0.778877	+	0.627176i	$0.215789\pi$
$977$	−6.54016	+	24.4082i	−0.209238	+	0.780888i	−0.988116	+	0.153712i	$0.950877\pi$
$978$	−7.37914	−	4.65481i	−0.235959	−	0.148844i
$979$			2.25446i			0.0720527i
$980$	0.532117	−	15.6434i	0.0169978	−	0.499711i
$981$	−2.48391	+	31.6457i	−0.0793051	+	1.01037i
$982$	−4.45486	−	16.6258i	−0.142160	−	0.530550i
$983$	−22.0513	−	5.90862i	−0.703326	−	0.188456i	−0.110606	−	0.993864i	$-0.535279\pi$
$983$	−22.0513	−	5.90862i	−0.703326	−	0.188456i	−0.592720	+	0.805409i	$0.701946\pi$
$984$	−2.13329	+	6.87284i	−0.0680067	+	0.219098i
$985$	−14.3030	+	22.3707i	−0.455730	+	0.712791i
$986$			2.25818i			0.0719151i
$987$	16.0724	−	6.03433i	0.511589	−	0.192075i
$988$	11.5664	+	11.5664i	0.367975	+	0.367975i
$989$	0.918842	−	1.59148i	0.0292175	−	0.0506061i
$990$	36.8667	−	15.5873i	1.17170	−	0.495397i
$991$	−19.6593	−	34.0510i	−0.624500	−	1.08166i	−0.988637	−	0.150320i	$-0.951970\pi$
$991$	−19.6593	−	34.0510i	−0.624500	−	1.08166i	0.364138	−	0.931345i	$-0.381364\pi$
$992$	−2.48585	+	0.666080i	−0.0789257	+	0.0211481i
$993$	37.3438	+	1.46333i	1.18507	+	0.0464373i
$994$	−28.2286	−	3.55482i	−0.895357	−	0.112752i
$995$	−28.8148	−	31.5488i	−0.913491	−	1.00016i
$996$	18.7404	−	4.24258i	0.593812	−	0.134431i
$997$	−11.1081	−	2.97640i	−0.351797	−	0.0942636i	0.0785932	−	0.996907i	$-0.474957\pi$
$997$	−11.1081	−	2.97640i	−0.351797	−	0.0942636i	−0.430390	+	0.902643i	$0.641624\pi$
$998$	39.0211	+	10.4557i	1.23519	+	0.330969i
$999$	−1.01826	−	7.00736i	−0.0322165	−	0.221703i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.23.3	✓	64
3.2	odd	2	inner	210.2.x.a.23.15	yes	64
5.2	odd	4	inner	210.2.x.a.107.2	yes	64
7.4	even	3	inner	210.2.x.a.53.11	yes	64
15.2	even	4	inner	210.2.x.a.107.11	yes	64
21.11	odd	6	inner	210.2.x.a.53.2	yes	64
35.32	odd	12	inner	210.2.x.a.137.15	yes	64
105.32	even	12	inner	210.2.x.a.137.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.3	✓	64	1.1	even	1	trivial
210.2.x.a.23.15	yes	64	3.2	odd	2	inner
210.2.x.a.53.2	yes	64	21.11	odd	6	inner
210.2.x.a.53.11	yes	64	7.4	even	3	inner
210.2.x.a.107.2	yes	64	5.2	odd	4	inner
210.2.x.a.107.11	yes	64	15.2	even	4	inner
210.2.x.a.137.3	yes	64	105.32	even	12	inner
210.2.x.a.137.15	yes	64	35.32	odd	12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.806628 - 1.53276i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.480420 + 2.18385i) q^{5} +(1.17585 + 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.69870 + 2.47273i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.806628 - 1.53276i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.480420 + 2.18385i) q^{5} +(1.17585 + 1.27176i) q^{6} +(-0.998710 + 2.45002i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.69870 + 2.47273i) q^{9} +(-1.02927 - 1.98509i) q^{10} +(5.16739 - 2.98339i) q^{11} +(-1.46494 - 0.924094i) q^{12} +(2.36809 + 2.36809i) q^{13} +(0.330568 - 2.62502i) q^{14} +(2.95979 - 2.49792i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.245156 + 0.914934i) q^{17} +(1.00083 - 2.82813i) q^{18} +(4.22990 + 2.44213i) q^{19} +(1.50798 + 1.65106i) q^{20} +(4.56087 - 0.445471i) q^{21} +(-4.21916 + 4.21916i) q^{22} +(0.0558604 + 0.208474i) q^{23} +(1.65420 + 0.513452i) q^{24} +(-4.53839 + 2.09833i) q^{25} +(-2.90030 - 1.67449i) q^{26} +(5.16033 + 0.609122i) q^{27} +(0.360100 + 2.62113i) q^{28} -2.38403 q^{29} +(-2.21243 + 3.17886i) q^{30} +(1.28677 + 2.22875i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-8.74099 - 5.51387i) q^{33} -0.947209i q^{34} +(-5.83027 - 1.00399i) q^{35} +(-0.234751 + 2.99080i) q^{36} +(-0.352701 - 1.31630i) q^{37} +(-4.71784 - 1.26414i) q^{38} +(1.71954 - 5.53987i) q^{39} +(-1.88392 - 1.20451i) q^{40} +4.15479i q^{41} +(-4.29017 + 1.61073i) q^{42} +(-6.02072 - 6.02072i) q^{43} +(2.98339 - 5.16739i) q^{44} +(-6.21617 - 2.52176i) q^{45} +(-0.107914 - 0.186912i) q^{46} +(3.61867 - 0.969620i) q^{47} +(-1.73072 - 0.0678189i) q^{48} +(-5.00516 - 4.89371i) q^{49} +(3.84066 - 3.20145i) q^{50} +(1.60012 - 0.362247i) q^{51} +(3.23487 + 0.866780i) q^{52} +(5.98451 + 1.60355i) q^{53} +(-5.14215 + 0.747224i) q^{54} +(8.99780 + 9.85151i) q^{55} +(-1.02623 - 2.43862i) q^{56} +(0.331246 - 8.45331i) q^{57} +(2.30280 - 0.617033i) q^{58} +(-2.02618 - 3.50944i) q^{59} +(1.31429 - 3.64316i) q^{60} +(-6.70029 + 11.6052i) q^{61} +(-1.81977 - 1.81977i) q^{62} +(-4.36173 - 6.63139i) q^{63} -1.00000i q^{64} +(-4.03387 + 6.30922i) q^{65} +(9.87024 + 3.06366i) q^{66} +(-9.28310 - 2.48740i) q^{67} +(0.245156 + 0.914934i) q^{68} +(0.274482 - 0.253781i) q^{69} +(5.89146 - 0.539201i) q^{70} -10.7537i q^{71} +(-0.547324 - 2.94965i) q^{72} +(3.43327 - 12.8131i) q^{73} +(0.681365 + 1.18016i) q^{74} +(6.87703 + 5.26369i) q^{75} +4.88427 q^{76} +(2.14864 + 15.6397i) q^{77} +(-0.227124 + 5.79616i) q^{78} +(0.874016 + 0.504613i) q^{79} +(2.13148 + 0.675868i) q^{80} +(-3.22883 - 8.40087i) q^{81} +(-1.07534 - 4.01322i) q^{82} +(-7.84434 + 7.84434i) q^{83} +(3.72710 - 2.66623i) q^{84} +(-2.11586 - 0.0958303i) q^{85} +(7.37384 + 4.25729i) q^{86} +(1.92303 + 3.65415i) q^{87} +(-1.54432 + 5.76347i) q^{88} +(-0.188917 + 0.327214i) q^{89} +(6.65704 + 0.826966i) q^{90} +(-8.16688 + 3.43682i) q^{91} +(0.152613 + 0.152613i) q^{92} +(2.37819 - 3.77008i) q^{93} +(-3.24441 + 1.87316i) q^{94} +(-3.30112 + 10.4107i) q^{95} +(1.68930 - 0.382436i) q^{96} +(3.42689 - 3.42689i) q^{97} +(6.10120 + 3.43153i) q^{98} +(-1.40071 + 17.8455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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