LMFDB - Embedded newform 210.2.x.a.53.2

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			53.2
Character	$\chi$	$=$	210.53
Dual form			210.2.x.a.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.53276 - 0.806628i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.13148 + 0.675868i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-2.45002 + 0.998710i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.69870 + 2.47273i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.53276 - 0.806628i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.13148 + 0.675868i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-2.45002 + 0.998710i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.69870 + 2.47273i) q^{9} +(-1.20451 + 1.88392i) q^{10} +(5.16739 + 2.98339i) q^{11} +(0.924094 + 1.46494i) q^{12} +(2.36809 + 2.36809i) q^{13} +(-0.330568 - 2.62502i) q^{14} +(-2.72187 - 2.75525i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.914934 + 0.245156i) q^{17} +(-2.82813 + 1.00083i) 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} +(0.208474 + 0.0558604i) q^{23} +(-1.65420 + 0.513452i) q^{24} +(4.08640 + 2.88120i) q^{25} +(-2.90030 + 1.67449i) q^{26} +(-0.609122 - 5.16033i) q^{27} +(2.62113 + 0.360100i) q^{28} +2.38403 q^{29} +(3.36584 - 1.91601i) q^{30} +(1.28677 - 2.22875i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-5.51387 - 8.74099i) q^{33} -0.947209i q^{34} +(-5.89715 + 0.472840i) q^{35} +(-0.234751 - 2.99080i) q^{36} +(1.31630 + 0.352701i) q^{37} +(-1.26414 - 4.71784i) q^{38} +(-1.71954 - 5.53987i) q^{39} +(1.98509 - 1.02927i) q^{40} -4.15479i q^{41} +(-1.61073 + 4.29017i) q^{42} +(-6.02072 - 6.02072i) q^{43} +(-2.98339 - 5.16739i) q^{44} +(1.94950 + 6.41868i) q^{45} +(-0.107914 + 0.186912i) q^{46} +(0.969620 - 3.61867i) q^{47} +(-0.0678189 - 1.73072i) q^{48} +(5.00516 - 4.89371i) q^{49} +(-3.84066 + 3.20145i) q^{50} +(1.60012 + 0.362247i) q^{51} +(-0.866780 - 3.23487i) q^{52} +(1.60355 + 5.98451i) q^{53} +(5.14215 + 0.747224i) q^{54} +(8.99780 + 9.85151i) q^{55} +(-1.02623 + 2.43862i) q^{56} +(8.45331 - 0.331246i) q^{57} +(-0.617033 + 2.30280i) q^{58} +(2.02618 - 3.50944i) q^{59} +(0.979581 + 3.74706i) q^{60} +(-6.70029 - 11.6052i) q^{61} +(1.81977 + 1.81977i) q^{62} +(-6.63139 - 4.36173i) q^{63} -1.00000i q^{64} +(3.44701 + 6.64804i) q^{65} +(9.87024 - 3.06366i) q^{66} +(2.48740 + 9.28310i) q^{67} +(0.914934 + 0.245156i) q^{68} +(-0.274482 - 0.253781i) q^{69} +(1.06957 - 5.81859i) q^{70} +10.7537i q^{71} +(2.94965 + 0.547324i) q^{72} +(-12.8131 + 3.43327i) q^{73} +(-0.681365 + 1.18016i) q^{74} +(-3.93942 - 7.71239i) q^{75} +4.88427 q^{76} +(-15.6397 - 2.14864i) q^{77} +(5.79616 - 0.227124i) q^{78} +(-0.874016 + 0.504613i) q^{79} +(0.480420 + 2.18385i) q^{80} +(-3.22883 + 8.40087i) q^{81} +(4.01322 + 1.07534i) 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} +(-3.65415 - 1.92303i) q^{87} +(5.76347 - 1.54432i) q^{88} +(0.188917 + 0.327214i) q^{89} +(-6.70454 + 0.221800i) q^{90} +(-8.16688 - 3.43682i) q^{91} +(-0.152613 - 0.152613i) q^{92} +(-3.77008 + 2.37819i) q^{93} +(3.24441 + 1.87316i) q^{94} +(-10.6665 + 2.34650i) q^{95} +(1.68930 + 0.382436i) q^{96} +(3.42689 - 3.42689i) q^{97} +(3.43153 + 6.10120i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.53276	−	0.806628i	−0.884939	−	0.465707i
$3$	−1.53276	−	0.806628i	−0.884939	−	0.465707i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.13148	+	0.675868i	0.953226	+	0.302257i
$5$	2.13148	+	0.675868i	0.953226	+	0.302257i
$6$	1.17585	−	1.27176i	0.480039	−	0.519194i
$7$	−2.45002	+	0.998710i	−0.926019	+	0.377477i
$7$	−2.45002	+	0.998710i	−0.926019	+	0.377477i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.69870	+	2.47273i	0.566234	+	0.824245i
$10$	−1.20451	+	1.88392i	−0.380898	+	0.595749i
$11$	5.16739	+	2.98339i	1.55803	+	0.899527i	0.997446	+	0.0714273i	$0.0227554\pi$
$11$	5.16739	+	2.98339i	1.55803	+	0.899527i	0.560581	+	0.828100i	$0.310578\pi$
$12$	0.924094	+	1.46494i	0.266763	+	0.422892i
$13$	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
$15$	−2.72187	−	2.75525i	−0.702784	−	0.711404i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.914934	+	0.245156i	−0.221904	+	0.0594590i	−0.368058	−	0.929803i	$-0.619977\pi$
$17$	−0.914934	+	0.245156i	−0.221904	+	0.0594590i	0.146154	+	0.989262i	$0.453311\pi$
$18$	−2.82813	+	1.00083i	−0.666598	+	0.235898i
$19$	−4.22990	+	2.44213i	−0.970406	+	0.560264i	−0.899360	−	0.437209i	$-0.855967\pi$
$19$	−4.22990	+	2.44213i	−0.970406	+	0.560264i	−0.0710458	+	0.997473i	$0.522634\pi$
$20$	−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
$23$	0.208474	+	0.0558604i	0.0434698	+	0.0116477i	0.280488	−	0.959857i	$-0.409504\pi$
$23$	0.208474	+	0.0558604i	0.0434698	+	0.0116477i	−0.237019	+	0.971505i	$0.576170\pi$
$24$	−1.65420	+	0.513452i	−0.337662	+	0.104808i
$25$	4.08640	+	2.88120i	0.817281	+	0.576240i
$26$	−2.90030	+	1.67449i	−0.568796	+	0.328395i
$27$	−0.609122	−	5.16033i	−0.117226	−	0.993105i
$28$	2.62113	+	0.360100i	0.495347	+	0.0680526i
$29$	2.38403			0.442704			0.221352	−	0.975194i	$-0.428953\pi$
$29$	2.38403			0.442704			0.221352	+	0.975194i	$0.428953\pi$
$30$	3.36584	−	1.91601i	0.614516	−	0.349814i
$31$	1.28677	−	2.22875i	0.231110	−	0.400295i	−0.727025	−	0.686611i	$-0.759097\pi$
$31$	1.28677	−	2.22875i	0.231110	−	0.400295i	0.958135	+	0.286316i	$0.0924308\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−5.51387	−	8.74099i	−0.959842	−	1.52161i
$34$		−	0.947209i		−	0.162445i
$35$	−5.89715	+	0.472840i	−0.996801	+	0.0799246i
$36$	−0.234751	−	2.99080i	−0.0391252	−	0.498467i
$37$	1.31630	+	0.352701i	0.216398	+	0.0579836i	0.365389	−	0.930855i	$-0.380936\pi$
$37$	1.31630	+	0.352701i	0.216398	+	0.0579836i	−0.148991	+	0.988839i	$0.547603\pi$
$38$	−1.26414	−	4.71784i	−0.205071	−	0.765335i
$39$	−1.71954	−	5.53987i	−0.275347	−	0.887090i
$40$	1.98509	−	1.02927i	0.313871	−	0.162742i
$41$		−	4.15479i		−	0.648869i	−0.945908	−	0.324435i	$-0.894826\pi$
$41$		−	4.15479i		−	0.648869i	0.945908	−	0.324435i	$-0.105174\pi$
$42$	−1.61073	+	4.29017i	−0.248541	+	0.661987i
$43$	−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
$45$	1.94950	+	6.41868i	0.290615	+	0.956840i
$46$	−0.107914	+	0.186912i	−0.0159110	+	0.0275587i
$47$	0.969620	−	3.61867i	0.141434	−	0.527838i	−0.858455	−	0.512890i	$-0.828575\pi$
$47$	0.969620	−	3.61867i	0.141434	−	0.527838i	0.999888	−	0.0149481i	$-0.00475829\pi$
$48$	−0.0678189	−	1.73072i	−0.00978882	−	0.249808i
$49$	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
$52$	−0.866780	−	3.23487i	−0.120201	−	0.448595i
$53$	1.60355	+	5.98451i	0.220264	+	0.822036i	0.984247	+	0.176800i	$0.0565745\pi$
$53$	1.60355	+	5.98451i	0.220264	+	0.822036i	−0.763983	+	0.645236i	$0.776759\pi$
$54$	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
$57$	8.45331	−	0.331246i	1.11967	−	0.0438746i
$58$	−0.617033	+	2.30280i	−0.0810204	+	0.302372i
$59$	2.02618	−	3.50944i	0.263786	−	0.456890i	−0.703459	−	0.710736i	$-0.748362\pi$
$59$	2.02618	−	3.50944i	0.263786	−	0.456890i	0.967245	+	0.253846i	$0.0816955\pi$
$60$	0.979581	+	3.74706i	0.126463	+	0.483743i
$61$	−6.70029	−	11.6052i	−0.857884	−	1.48590i	−0.873943	−	0.486028i	$-0.838445\pi$
$61$	−6.70029	−	11.6052i	−0.857884	−	1.48590i	0.0160589	−	0.999871i	$-0.494888\pi$
$62$	1.81977	+	1.81977i	0.231110	+	0.231110i
$63$	−6.63139	−	4.36173i	−0.835476	−	0.549526i
$64$		−	1.00000i		−	0.125000i
$65$	3.44701	+	6.64804i	0.427549	+	0.824588i
$66$	9.87024	−	3.06366i	1.21494	−	0.377110i
$67$	2.48740	+	9.28310i	0.303884	+	1.13411i	0.933902	+	0.357530i	$0.116381\pi$
$67$	2.48740	+	9.28310i	0.303884	+	1.13411i	−0.630017	+	0.776581i	$0.716952\pi$
$68$	0.914934	+	0.245156i	0.110952	+	0.0297295i
$69$	−0.274482	−	0.253781i	−0.0330437	−	0.0305517i
$70$	1.06957	−	5.81859i	0.127838	−	0.695455i
$71$			10.7537i			1.27623i	0.769943	+	0.638113i	$0.220285\pi$
$71$			10.7537i			1.27623i	−0.769943	+	0.638113i	$0.779715\pi$
$72$	2.94965	+	0.547324i	0.347620	+	0.0645027i
$73$	−12.8131	+	3.43327i	−1.49967	+	0.401834i	−0.912988	−	0.407987i	$-0.866231\pi$
$73$	−12.8131	+	3.43327i	−1.49967	+	0.401834i	−0.586677	+	0.809821i	$0.699564\pi$
$74$	−0.681365	+	1.18016i	−0.0792071	+	0.137191i
$75$	−3.93942	−	7.71239i	−0.454885	−	0.890550i
$76$	4.88427			0.560264
$77$	−15.6397	−	2.14864i	−1.78231	−	0.244860i
$78$	5.79616	−	0.227124i	0.656286	−	0.0257168i
$79$	−0.874016	+	0.504613i	−0.0983345	+	0.0567734i	−0.548361	−	0.836242i	$-0.684748\pi$
$79$	−0.874016	+	0.504613i	−0.0983345	+	0.0567734i	0.450026	+	0.893015i	$0.351415\pi$
$80$	0.480420	+	2.18385i	0.0537126	+	0.244162i
$81$	−3.22883	+	8.40087i	−0.358759	+	0.933430i
$82$	4.01322	+	1.07534i	0.443186	+	0.118751i
$83$	7.84434	−	7.84434i	0.861028	−	0.861028i	−0.130429	−	0.991458i	$-0.541636\pi$
$83$	7.84434	−	7.84434i	0.861028	−	0.861028i	0.991458	+	0.130429i	$0.0416356\pi$
$84$	−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
$87$	−3.65415	−	1.92303i	−0.391766	−	0.206170i
$88$	5.76347	−	1.54432i	0.614388	−	0.164625i
$89$	0.188917	+	0.327214i	0.0200252	+	0.0346846i	0.875864	−	0.482557i	$-0.160292\pi$
$89$	0.188917	+	0.327214i	0.0200252	+	0.0346846i	−0.855839	+	0.517242i	$0.826959\pi$
$90$	−6.70454	+	0.221800i	−0.706720	+	0.0233797i
$91$	−8.16688	−	3.43682i	−0.856122	−	0.360277i
$92$	−0.152613	−	0.152613i	−0.0159110	−	0.0159110i
$93$	−3.77008	+	2.37819i	−0.390939	+	0.246607i
$94$	3.24441	+	1.87316i	0.334636	+	0.193202i
$95$	−10.6665	+	2.34650i	−1.09436	+	0.240746i
$96$	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	$0.170872\pi$
$98$	3.43153	+	6.10120i	0.346637	+	0.616314i
$99$	1.40071	+	17.8455i	0.140777	+	1.79354i
$100$	−2.09833	−	4.53839i	−0.209833	−	0.453839i
$101$	−3.73396	−	2.15580i	−0.371543	−	0.214510i	0.302589	−	0.953121i	$-0.402149\pi$
$101$	−3.73396	−	2.15580i	−0.371543	−	0.214510i	−0.674132	+	0.738611i	$0.735482\pi$
$102$	−0.764046	+	1.45184i	−0.0756518	+	0.143754i
$103$	−3.45971	+	12.9118i	−0.340896	+	1.27224i	0.556438	+	0.830889i	$0.312167\pi$
$103$	−3.45971	+	12.9118i	−0.340896	+	1.27224i	−0.897334	+	0.441352i	$0.854499\pi$
$104$	3.34898			0.328395
$105$	9.42032	+	4.03206i	0.919329	+	0.393489i
$106$	−6.19562			−0.601772
$107$	4.07291	−	15.2003i	0.393743	−	1.46947i	−0.430168	−	0.902749i	$-0.641546\pi$
$107$	4.07291	−	15.2003i	0.393743	−	1.46947i	0.823911	−	0.566720i	$-0.191788\pi$
$108$	−2.05265	+	4.77354i	−0.197516	+	0.459334i
$109$	−9.16343	−	5.29051i	−0.877698	−	0.506739i	−0.00779912	−	0.999970i	$-0.502483\pi$
$109$	−9.16343	−	5.29051i	−0.877698	−	0.506739i	−0.869899	+	0.493231i	$0.835816\pi$
$110$	−11.8446	+	6.14145i	−1.12934	+	0.585564i
$111$	−1.73307	−	1.60237i	−0.164495	−	0.152090i
$112$	−2.08992	−	1.62242i	−0.197478	−	0.153304i
$113$	5.87797	−	5.87797i	0.552953	−	0.552953i	−0.374339	−	0.927292i	$-0.622130\pi$
$113$	5.87797	−	5.87797i	0.552953	−	0.552953i	0.927292	+	0.374339i	$0.122130\pi$
$114$	−1.86792	+	8.25101i	−0.174947	+	0.772778i
$115$	0.406603	+	0.259966i	0.0379159	+	0.0242420i
$116$	−2.06463	−	1.19202i	−0.191696	−	0.110676i
$117$	−1.83298	+	9.87832i	−0.169459	+	0.913251i
$118$	2.86545	+	2.86545i	0.263786	+	0.263786i
$119$	1.99676	−	1.51439i	0.183043	−	0.138824i
$120$	−3.87291	−	0.0236070i	−0.353547	−	0.00215501i
$121$	12.3013	+	21.3064i	1.11830	+	1.93695i
$122$	12.9440	−	3.46833i	1.17189	−	0.314007i
$123$	−3.35137	+	6.36829i	−0.302183	+	0.574210i
$124$	−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	$0.00526612\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	4.37183	+	14.0848i	0.384918	+	1.24010i
$130$	−7.31367	+	1.60892i	−0.641451	+	0.141112i
$131$	−3.73610	+	2.15704i	−0.326424	+	0.188461i	−0.654252	−	0.756276i	$-0.727017\pi$
$131$	−3.73610	+	2.15704i	−0.326424	+	0.188461i	0.327828	+	0.944737i	$0.393683\pi$
$132$	0.404661	+	10.3269i	0.0352212	+	0.898837i
$133$	7.92434	−	10.2077i	0.687128	−	0.885121i
$134$	−9.61057			−0.830227
$135$	2.18937	−	11.4108i	0.188431	−	0.982086i
$136$	−0.473605	+	0.820307i	−0.0406113	+	0.0703408i
$137$	7.85237	−	2.10404i	0.670874	−	0.179760i	0.0927253	−	0.995692i	$-0.470442\pi$
$137$	7.85237	−	2.10404i	0.670874	−	0.179760i	0.578148	+	0.815932i	$0.303775\pi$
$138$	0.316175	−	0.199445i	0.0269146	−	0.0169779i
$139$		−	10.9242i		−	0.926578i	−0.886207	−	0.463289i	$-0.846669\pi$
$139$		−	10.9242i		−	0.926578i	0.886207	−	0.463289i	$-0.153331\pi$
$140$	5.34351	+	2.53909i	0.451609	+	0.214592i
$141$	−4.40512	+	4.76443i	−0.370978	+	0.401237i
$142$	−10.3873	−	2.78326i	−0.871679	−	0.233566i
$143$	5.17189	+	19.3018i	0.432495	+	1.61409i
$144$	−1.29210	+	2.70749i	−0.107675	+	0.225624i
$145$	5.08152	+	1.61129i	0.421997	+	0.133811i
$146$		−	13.2651i		−	1.09783i
$147$	−11.6191	+	3.46357i	−0.958328	+	0.285671i
$148$	−0.963596	−	0.963596i	−0.0792071	−	0.0792071i
$149$	−5.86144	−	10.1523i	−0.480188	−	0.831710i	0.519553	−	0.854438i	$-0.326098\pi$
$149$	−5.86144	−	10.1523i	−0.480188	−	0.831710i	−0.999742	+	0.0227275i	$0.992765\pi$
$150$	8.46919	−	1.80907i	0.691507	−	0.147710i
$151$	8.24246	−	14.2764i	0.670762	−	1.16179i	−0.306927	−	0.951733i	$-0.599301\pi$
$151$	8.24246	−	14.2764i	0.670762	−	1.16179i	0.977688	−	0.210060i	$-0.0673660\pi$
$152$	−1.26414	+	4.71784i	−0.102535	+	0.382667i
$153$	−2.16040	−	1.84594i	−0.174658	−	0.149236i
$154$	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
$157$	−0.651278	−	2.43060i	−0.0519776	−	0.193983i	0.935055	−	0.354503i	$-0.115350\pi$
$157$	−0.651278	−	2.43060i	−0.0519776	−	0.193983i	−0.987033	+	0.160519i	$0.948683\pi$
$158$	−0.261207	−	0.974838i	−0.0207805	−	0.0775540i
$159$	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
$162$	−7.27894	−	5.29311i	−0.571887	−	0.415866i
$163$	1.30371	−	4.86553i	0.102115	−	0.381097i	−0.895887	−	0.444282i	$-0.853459\pi$
$163$	1.30371	−	4.86553i	0.102115	−	0.381097i	0.998002	+	0.0631843i	$0.0201256\pi$
$164$	−2.07740	+	3.59815i	−0.162217	+	0.280969i
$165$	−5.84495	−	22.3579i	−0.455029	−	1.74056i
$166$	5.54679	+	9.60731i	0.430514	+	0.745672i
$167$	13.6846	+	13.6846i	1.05894	+	1.05894i	0.998150	+	0.0607934i	$0.0193631\pi$
$167$	13.6846	+	13.6846i	1.05894	+	1.05894i	0.0607934	+	0.998150i	$0.480637\pi$
$168$	3.54002	−	2.91003i	0.273118	−	0.224514i
$169$		−	1.78432i		−	0.137256i
$170$	0.640189	−	2.01896i	0.0491002	−	0.154847i
$171$	−13.2241	−	6.31096i	−1.01127	−	0.482611i
$172$	2.20373	+	8.22445i	0.168033	+	0.627108i
$173$	13.7236	+	3.67722i	1.04338	+	0.279574i	0.739515	−	0.673140i	$-0.235055\pi$
$173$	13.7236	+	3.67722i	1.04338	+	0.279574i	0.303869	+	0.952714i	$0.401722\pi$
$174$	2.80327	−	3.03192i	0.212515	−	0.229849i
$175$	−12.8892	−	2.97785i	−0.974335	−	0.225104i
$176$			5.96679i			0.449764i
$177$	−5.93646	+	3.74476i	−0.446211	+	0.281473i
$178$	−0.364960	+	0.0977906i	−0.0273549	+	0.00732972i
$179$	4.32841	−	7.49703i	0.323521	−	0.560354i	−0.657691	−	0.753288i	$-0.728467\pi$
$179$	4.32841	−	7.49703i	0.323521	−	0.560354i	0.981212	+	0.192934i	$0.0618002\pi$
$180$	1.52102	−	6.53349i	0.113370	−	0.486978i
$181$	−11.7154			−0.870801			−0.435400	−	0.900237i	$-0.643393\pi$
$181$	−11.7154			−0.870801			−0.435400	+	0.900237i	$0.643393\pi$
$182$	5.43346	−	6.99909i	0.402755	−	0.518807i
$183$	0.908813	+	23.1927i	0.0671814	+	1.71445i
$184$	0.186912	−	0.107914i	0.0137794	−	0.00795552i
$185$	2.56728	+	1.64142i	0.188750	+	0.120679i
$186$	−1.32139	−	4.25714i	−0.0968888	−	0.312148i
$187$	−5.45922	−	1.46279i	−0.399217	−	0.106970i
$188$	−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	−0.659790	+	0.751450i	$0.729355\pi$
$191$	−22.6716	+	13.0895i	−1.64046	+	0.947120i	−0.980670	+	0.195670i	$0.937312\pi$
$192$	−0.806628	+	1.53276i	−0.0582134	+	0.110617i
$193$	20.5578	−	5.50843i	1.47978	−	0.396506i	0.573508	−	0.819200i	$-0.305582\pi$
$193$	20.5578	−	5.50843i	1.47978	−	0.396506i	0.906272	+	0.422694i	$0.138916\pi$
$194$	2.42318	+	4.19707i	0.173974	+	0.301332i
$195$	0.0790593	−	12.9703i	0.00566155	−	0.928823i
$196$	−6.78145	+	1.73550i	−0.484389	+	0.123964i
$197$	−8.39658	−	8.39658i	−0.598231	−	0.598231i	0.341610	−	0.939842i	$-0.389028\pi$
$197$	−8.39658	−	8.39658i	−0.598231	−	0.598231i	−0.939842	+	0.341610i	$0.889028\pi$
$198$	−17.5999	−	3.26576i	−1.25077	−	0.232088i
$199$	16.5482	+	9.55411i	1.17307	+	0.677273i	0.954401	−	0.298527i	$-0.0964951\pi$
$199$	16.5482	+	9.55411i	1.17307	+	0.677273i	0.218669	+	0.975799i	$0.429828\pi$
$200$	4.92684	−	0.852210i	0.348380	−	0.0602603i
$201$	3.67543	−	16.2352i	0.259245	−	1.14514i
$202$	3.04877	−	3.04877i	0.214510	−	0.214510i
$203$	−5.84092	+	2.38096i	−0.409952	+	0.167110i
$204$	−1.20462	−	1.11378i	−0.0843405	−	0.0779799i
$205$	2.80809	−	8.85585i	0.196126	−	0.618519i
$206$	−11.5764	−	6.68365i	−0.806568	−	0.465672i
$207$	0.216007	+	0.610390i	0.0150135	+	0.0424251i
$208$	−0.866780	+	3.23487i	−0.0601004	+	0.224298i
$209$	−29.1434			−2.01589
$210$	−6.33283	+	8.05576i	−0.437007	+	0.555900i
$211$	−6.45261			−0.444216			−0.222108	−	0.975022i	$-0.571294\pi$
$211$	−6.45261			−0.444216			−0.222108	+	0.975022i	$0.571294\pi$
$212$	1.60355	−	5.98451i	0.110132	−	0.411018i
$213$	8.67422	−	16.4828i	0.594348	−	1.12938i
$214$	13.6282	+	7.86826i	0.931606	+	0.537863i
$215$	−8.76382	−	16.9022i	−0.597687	−	1.15272i
$216$	−4.07962	−	3.21819i	−0.277583	−	0.218970i
$217$	−0.926731	+	6.74558i	−0.0629106	+	0.457920i
$218$	7.48191	−	7.48191i	0.506739	−	0.506739i
$219$	22.4088	+	5.07307i	1.51425	+	0.342806i
$220$	−2.86657	−	13.0306i	−0.193264	−	0.878520i
$221$	−2.74719	−	1.58609i	−0.184796	−	0.106692i
$222$	1.99632	−	1.25929i	0.133984	−	0.0845181i
$223$	−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
$225$	−0.182855	+	14.9989i	−0.0121904	+	0.999926i
$226$	4.15635	+	7.19901i	0.276476	+	0.478871i
$227$	9.48829	−	2.54238i	0.629760	−	0.168744i	0.0701991	−	0.997533i	$-0.477637\pi$
$227$	9.48829	−	2.54238i	0.629760	−	0.168744i	0.559561	+	0.828789i	$0.310970\pi$
$228$	−7.48641	−	3.93979i	−0.495799	−	0.260919i
$229$	−7.87583	+	4.54711i	−0.520449	+	0.300482i	−0.737118	−	0.675764i	$-0.763814\pi$
$229$	−7.87583	+	4.54711i	−0.520449	+	0.300482i	0.216669	+	0.976245i	$0.430481\pi$
$230$	−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
$233$	−18.0676	−	4.84119i	−1.18364	−	0.317157i	−0.387274	−	0.921965i	$-0.626583\pi$
$233$	−18.0676	−	4.84119i	−1.18364	−	0.317157i	−0.796371	+	0.604808i	$0.793250\pi$
$234$	−9.06732	−	4.32722i	−0.592749	−	0.282879i
$235$	4.51247	−	7.05779i	0.294361	−	0.460399i
$236$	−3.50944	+	2.02618i	−0.228445	+	0.131893i
$237$	1.74669	−	0.0684447i	0.113460	−	0.00444596i
$238$	0.945987	+	2.32068i	0.0613192	+	0.150427i
$239$	8.87693			0.574201			0.287100	−	0.957900i	$-0.407309\pi$
$239$	8.87693			0.574201			0.287100	+	0.957900i	$0.407309\pi$
$240$	1.02519	−	3.73484i	0.0661755	−	0.241083i
$241$	2.06335	−	3.57384i	0.132912	−	0.230211i	−0.791886	−	0.610669i	$-0.790900\pi$
$241$	2.06335	−	3.57384i	0.132912	−	0.230211i	0.924798	+	0.380458i	$0.124234\pi$
$242$	−23.7642	+	6.36761i	−1.52762	+	0.409325i
$243$	11.7254	−	10.2721i	0.752185	−	0.658952i
$244$			13.4006i			0.857884i
$245$	13.9759	−	7.04801i	0.892887	−	0.450281i
$246$	−5.28390	−	4.88541i	−0.336889	−	0.311483i
$247$	−15.8000	−	4.23359i	−1.00533	−	0.269377i
$248$	−0.666080	−	2.48585i	−0.0422961	−	0.157851i
$249$	−18.3509	+	5.69602i	−1.16294	+	0.360970i
$250$	−10.3501	+	4.22805i	−0.654595	+	0.267405i
$251$		−	9.72407i		−	0.613778i	−0.951745	−	0.306889i	$-0.900712\pi$
$251$		−	9.72407i		−	0.613778i	0.951745	−	0.306889i	$-0.0992880\pi$
$252$	3.56209	+	7.09306i	0.224390	+	0.446821i
$253$	0.910612	+	0.910612i	0.0572497	+	0.0572497i
$254$	7.83577	+	13.5720i	0.491660	+	0.851580i
$255$	3.16580	+	1.85359i	0.198250	+	0.116077i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.62796	−	6.07565i	0.101550	−	0.378988i	−0.896381	−	0.443284i	$-0.853813\pi$
$257$	1.62796	−	6.07565i	0.101550	−	0.378988i	0.997931	+	0.0642955i	$0.0204800\pi$
$258$	−14.7364	+	0.577449i	−0.917446	+	0.0359504i
$259$	−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
$262$	−1.11656	−	4.16707i	−0.0689816	−	0.257443i
$263$	3.36362	+	12.5532i	0.207410	+	0.774064i	0.988701	+	0.149898i	$0.0478945\pi$
$263$	3.36362	+	12.5532i	0.207410	+	0.774064i	−0.781292	+	0.624166i	$0.785439\pi$
$264$	−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
$267$	−0.0256243	−	0.653926i	−0.00156818	−	0.0400196i
$268$	2.48740	−	9.28310i	0.151942	−	0.567056i
$269$	−5.49814	+	9.52306i	−0.335228	+	0.580631i	−0.983529	−	0.180753i	$-0.942147\pi$
$269$	−5.49814	+	9.52306i	−0.335228	+	0.580631i	0.648301	+	0.761384i	$0.275480\pi$
$270$	10.4553	+	5.06810i	0.636292	+	0.308435i
$271$	9.59447	+	16.6181i	0.582823	+	1.00948i	0.995143	+	0.0984394i	$0.0313851\pi$
$271$	9.59447	+	16.6181i	0.582823	+	1.00948i	−0.412321	+	0.911039i	$0.635282\pi$
$272$	−0.669778	−	0.669778i	−0.0406113	−	0.0406113i
$273$	9.74563	+	11.8555i	0.589832	+	0.717525i
$274$			8.12938i			0.491114i
$275$	12.5203	+	27.0796i	0.755002	+	1.63296i
$276$	0.110817	+	0.357022i	0.00667042	+	0.0214902i
$277$	−0.445276	−	1.66179i	−0.0267540	−	0.0998475i	0.951258	−	0.308397i	$-0.0997925\pi$
$277$	−0.445276	−	1.66179i	−0.0267540	−	0.0998475i	−0.978012	+	0.208549i	$0.933126\pi$
$278$	10.5520	+	2.82739i	0.632864	+	0.169575i
$279$	7.69694	−	0.604141i	0.460804	−	0.0361690i
$280$	−3.83557	+	4.50427i	−0.229219	+	0.269181i
$281$		−	17.7331i		−	1.05787i	−0.848664	−	0.528933i	$-0.822592\pi$
$281$		−	17.7331i		−	1.05787i	0.848664	−	0.528933i	$-0.177408\pi$
$282$	−3.46196	−	5.48814i	−0.206157	−	0.326814i
$283$	−16.0784	+	4.30819i	−0.955760	+	0.256095i	−0.702805	−	0.711383i	$-0.748069\pi$
$283$	−16.0784	+	4.30819i	−0.955760	+	0.256095i	−0.252955	+	0.967478i	$0.581402\pi$
$284$	5.37684	−	9.31295i	0.319057	−	0.552622i
$285$	18.2419	+	5.00728i	1.08056	+	0.296606i
$286$	−19.9827			−1.18160
$287$	4.14943	+	10.1793i	0.244933	+	0.600865i
$288$	−2.28081	−	1.94882i	−0.134398	−	0.114835i
$289$	−13.9454	+	8.05140i	−0.820319	+	0.473612i
$290$	−2.87158	+	4.49134i	−0.168625	+	0.263740i
$291$	−8.01682	+	2.48837i	−0.469955	+	0.145871i
$292$	12.8131	+	3.43327i	0.749833	+	0.200917i
$293$	−5.73680	+	5.73680i	−0.335148	+	0.335148i	−0.854537	−	0.519390i	$-0.826159\pi$
$293$	−5.73680	+	5.73680i	−0.335148	+	0.335148i	0.519390	+	0.854537i	$0.326159\pi$
$294$	−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
$297$	12.2477	−	28.4827i	0.710684	−	1.65273i
$298$	11.3234	−	3.03411i	0.655949	−	0.175761i
$299$	0.361402	+	0.625966i	0.0209004	+	0.0362006i
$300$	−0.444560	+	8.64884i	−0.0256667	+	0.499341i
$301$	20.7638	+	8.73790i	1.19681	+	0.503644i
$302$	11.6566	+	11.6566i	0.670762	+	0.670762i
$303$	3.98433	+	6.31624i	0.228894	+	0.362859i
$304$	−4.22990	−	2.44213i	−0.242601	−	0.140066i
$305$	−6.43791	−	29.2648i	−0.368634	−	1.67570i
$306$	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	$0.229638\pi$
$308$	12.4701	+	9.68064i	0.710549	+	0.551606i
$309$	15.7180	−	17.0000i	0.894163	−	0.967097i
$310$	2.64887	+	5.10871i	0.150446	+	0.290155i
$311$	−5.20473	−	3.00495i	−0.295133	−	0.170395i	0.345121	−	0.938558i	$-0.387838\pi$
$311$	−5.20473	−	3.00495i	−0.295133	−	0.170395i	−0.640254	+	0.768163i	$0.721171\pi$
$312$	−5.13318	−	2.70138i	−0.290609	−	0.152936i
$313$	0.831951	−	3.10488i	0.0470246	−	0.175498i	−0.938419	−	0.345498i	$-0.887710\pi$
$313$	0.831951	−	3.10488i	0.0470246	−	0.175498i	0.985444	+	0.170000i	$0.0543767\pi$
$314$	2.51634			0.142006
$315$	−11.1867	−	13.7789i	−0.630300	−	0.776352i
$316$	1.00923			0.0567734
$317$	0.203652	−	0.760038i	0.0114382	−	0.0426880i	−0.959971	−	0.280100i	$-0.909632\pi$
$317$	0.203652	−	0.760038i	0.0114382	−	0.0426880i	0.971409	+	0.237412i	$0.0762991\pi$
$318$	9.49640	+	4.99757i	0.532532	+	0.280250i
$319$	12.3192	+	7.11251i	0.689744	+	0.398224i
$320$	0.675868	−	2.13148i	0.0377822	−	0.119153i
$321$	−18.5038	+	20.0131i	−1.03278	+	1.11702i
$322$	0.0777197	−	0.565713i	0.00433115	−	0.0315260i
$323$	3.27138	−	3.27138i	0.182024	−	0.182024i
$324$	6.99668	−	5.66096i	0.388705	−	0.314498i
$325$	2.85403	+	16.4999i	0.158313	+	0.915249i
$326$	4.36231	+	2.51858i	0.241606	+	0.139491i
$327$	9.77786	+	15.5006i	0.540717	+	0.857183i
$328$	−2.93788	−	2.93788i	−0.162217	−	0.162217i
$329$	1.23842	+	9.83417i	0.0682761	+	0.542176i
$330$	23.1088	+	0.140858i	1.27210	+	0.00775396i
$331$	−10.7885	−	18.6862i	−0.592989	−	1.02709i	−0.993827	−	0.110939i	$-0.964614\pi$
$331$	−10.7885	−	18.6862i	−0.592989	−	1.02709i	0.400838	−	0.916149i	$-0.368719\pi$
$332$	−10.7156	+	2.87123i	−0.588093	+	0.157579i
$333$	1.36386	+	3.85398i	0.0747390	+	0.211197i
$334$	−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	$0.263399\pi$
$338$	1.72352	+	0.461817i	0.0937474	+	0.0251195i
$339$	−13.7509	+	4.26818i	−0.746844	+	0.231815i
$340$	1.78447	+	1.14092i	0.0967764	+	0.0618750i
$341$	13.2985	−	7.67787i	0.720152	−	0.415780i
$342$	9.51857	−	11.1401i	0.514705	−	0.602387i
$343$	−7.37533	+	16.9884i	−0.398230	+	0.917286i
$344$	−8.51458			−0.459075
$345$	−0.413529	−	0.726443i	−0.0222636	−	0.0391104i
$346$	−7.10384	+	12.3042i	−0.381905	+	0.661479i
$347$	−15.6111	+	4.18299i	−0.838050	+	0.224555i	−0.652222	−	0.758028i	$-0.726163\pi$
$347$	−15.6111	+	4.18299i	−0.838050	+	0.224555i	−0.185827	+	0.982582i	$0.559497\pi$
$348$	2.20307	+	3.49247i	0.118097	+	0.187216i
$349$			23.5711i			1.26173i	0.775892	+	0.630866i	$0.217300\pi$
$349$			23.5711i			1.26173i	−0.775892	+	0.630866i	$0.782700\pi$
$350$	6.21236	−	11.6793i	0.332065	−	0.624286i
$351$	10.7776	−	13.6626i	0.575268	−	0.729253i
$352$	−5.76347	−	1.54432i	−0.307194	−	0.0823124i
$353$	−7.00188	−	26.1314i	−0.372672	−	1.39083i	−0.856716	−	0.515788i	$-0.827499\pi$
$353$	−7.00188	−	26.1314i	−0.372672	−	1.39083i	0.484044	−	0.875044i	$-0.339168\pi$
$354$	−2.08069	−	6.70339i	−0.110587	−	0.356281i
$355$	−7.26807	+	22.9212i	−0.385749	+	1.21653i
$356$		−	0.377834i		−	0.0200252i
$357$	−4.28211	+	0.710547i	−0.226633	+	0.0376062i
$358$	6.12130	+	6.12130i	0.323521	+	0.323521i
$359$	3.59250	+	6.22240i	0.189605	+	0.328405i	0.945119	−	0.326727i	$-0.105946\pi$
$359$	3.59250	+	6.22240i	0.189605	+	0.328405i	−0.755514	+	0.655133i	$0.772613\pi$
$360$	5.91720	+	3.16018i	0.311864	+	0.166556i
$361$	2.42804	−	4.20549i	0.127791	−	0.221341i
$362$	3.03218	−	11.3162i	0.159368	−	0.594768i
$363$	−1.66852	−	42.5802i	−0.0875745	−	2.23488i
$364$	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
$367$	3.86571	+	14.4270i	0.201788	+	0.753084i	0.990405	+	0.138198i	$0.0441312\pi$
$367$	3.86571	+	14.4270i	0.201788	+	0.753084i	−0.788616	+	0.614886i	$0.789202\pi$
$368$	0.0558604	+	0.208474i	0.00291192	+	0.0108674i
$369$	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
$372$	4.45408	−	0.174534i	0.230933	−	0.00904919i
$373$	−2.02154	+	7.54451i	−0.104672	+	0.390640i	−0.998308	−	0.0581526i	$-0.981479\pi$
$373$	−2.02154	+	7.54451i	−0.104672	+	0.390640i	0.893636	+	0.448792i	$0.148146\pi$
$374$	2.82590	−	4.89460i	0.146124	−	0.253094i
$375$	−3.18423	−	19.1013i	−0.164433	−	0.986388i
$376$	−1.87316	−	3.24441i	−0.0966010	−	0.167318i
$377$	5.64560	+	5.64560i	0.290763	+	0.290763i
$378$	−13.3446	+	3.30480i	−0.686372	+	0.169981i
$379$			17.2301i			0.885050i	0.896756	+	0.442525i	$0.145917\pi$
$379$			17.2301i			0.885050i	−0.896756	+	0.442525i	$0.854083\pi$
$380$	10.4107	+	3.30112i	0.534058	+	0.169344i
$381$	−25.9238	+	8.04658i	−1.32812	+	0.412239i
$382$	−6.77560	−	25.2869i	−0.346670	−	1.29379i
$383$	5.27933	+	1.41459i	0.269761	+	0.0722823i	0.391164	−	0.920321i	$-0.372073\pi$
$383$	5.27933	+	1.41459i	0.269761	+	0.0722823i	−0.121403	+	0.992603i	$0.538739\pi$
$384$	−1.27176	−	1.17585i	−0.0648993	−	0.0600049i
$385$	−31.8836	−	15.1502i	−1.62494	−	0.772125i
$386$			21.2830i			1.08327i
$387$	4.66023	−	25.1150i	0.236893	−	1.27667i
$388$	−4.68122	+	1.25433i	−0.237653	+	0.0636789i
$389$	2.33417	−	4.04291i	0.118347	−	0.204983i	−0.800766	−	0.598978i	$-0.795574\pi$
$389$	2.33417	−	4.04291i	0.118347	−	0.204983i	0.919113	+	0.393994i	$0.128907\pi$
$390$	12.5079	+	3.43333i	0.633362	+	0.173853i
$391$	−0.204434			−0.0103387
$392$	0.0788068	−	6.99956i	0.00398035	−	0.353531i
$393$	7.46646	−	0.292576i	0.376633	−	0.0147585i
$394$	10.2837	−	5.93728i	0.518084	−	0.299116i
$395$	−2.20400	+	0.484853i	−0.110895	+	0.0243956i
$396$	7.70969	−	16.1550i	0.387426	−	0.811819i
$397$	−0.0492850	−	0.0132059i	−0.00247354	−	0.000662783i	0.257582	−	0.966256i	$-0.417074\pi$
$397$	−0.0492850	−	0.0132059i	−0.00247354	−	0.000662783i	−0.260056	+	0.965594i	$0.583741\pi$
$398$	−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	−0.501383	−	0.865225i	$-0.667175\pi$
$401$	−0.0554200	+	0.0319968i	−0.00276754	+	0.00159784i	0.498616	+	0.866823i	$0.333842\pi$
$402$	14.7307	+	7.75216i	0.734700	+	0.386643i
$403$	8.32505	−	2.23069i	0.414700	−	0.111119i
$404$	2.15580	+	3.73396i	0.107255	+	0.185771i
$405$	−12.5601	+	15.7240i	−0.624114	+	0.781333i
$406$	−0.788086	−	6.25813i	−0.0391121	−	0.310586i
$407$	5.74957	+	5.74957i	0.284996	+	0.284996i
$408$	1.38760	−	0.875311i	0.0686967	−	0.0433343i
$409$	−29.6265	−	17.1049i	−1.46494	−	0.845781i	−0.465702	−	0.884942i	$-0.654198\pi$
$409$	−29.6265	−	17.1049i	−1.46494	−	0.845781i	−0.999233	+	0.0391609i	$0.987532\pi$
$410$	7.82731	+	5.00447i	0.386563	+	0.247153i
$411$	−13.7330	−	3.10897i	−0.677398	−	0.153354i
$412$	9.45212	−	9.45212i	0.465672	−	0.465672i
$413$	−1.45925	+	10.6217i	−0.0718052	+	0.522662i
$414$	−0.645498	+	0.0506659i	−0.0317245	+	0.00249009i
$415$	22.0218	−	11.4183i	1.08101	−	0.560502i
$416$	−2.90030	−	1.67449i	−0.142199	−	0.0820987i
$417$	−8.81176	+	16.7441i	−0.431514	+	0.819965i
$418$	7.54286	−	28.1504i	0.368934	−	1.37688i
$419$	−18.1904			−0.888658			−0.444329	−	0.895864i	$-0.646558\pi$
$419$	−18.1904			−0.888658			−0.444329	+	0.895864i	$0.646558\pi$
$420$	−6.14221	−	8.20203i	−0.299709	−	0.400218i
$421$	−2.01328			−0.0981212			−0.0490606	−	0.998796i	$-0.515623\pi$
$421$	−2.01328			−0.0981212			−0.0490606	+	0.998796i	$0.515623\pi$
$422$	1.67006	−	6.23274i	0.0812972	−	0.303405i
$423$	10.5951	−	3.74943i	0.515152	−	0.182304i
$424$	5.36557	+	3.09781i	0.260575	+	0.150443i
$425$	−4.44513	−	1.63430i	−0.215621	−	0.0792752i
$426$	13.6761	+	12.6447i	0.662609	+	0.612638i
$427$	28.0061	+	21.7414i	1.35531	+	1.05214i
$428$	−11.1274	+	11.1274i	−0.537863	+	0.537863i
$429$	7.64209	−	33.7568i	0.368963	−	1.62979i
$430$	18.5946	−	4.09058i	0.896709	−	0.197265i
$431$	35.3759	+	20.4243i	1.70400	+	0.983804i	0.941624	+	0.336667i	$0.109300\pi$
$431$	35.3759	+	20.4243i	1.70400	+	0.983804i	0.762374	+	0.647136i	$0.224034\pi$
$432$	4.16441	−	3.10768i	0.200360	−	0.149518i
$433$	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
$435$	−6.48903	−	6.56862i	−0.311125	−	0.314941i
$436$	5.29051	+	9.16343i	0.253370	+	0.438849i
$437$	−1.01824	+	0.272837i	−0.0487091	+	0.0130516i
$438$	−10.7000	+	20.3323i	−0.511268	+	0.971514i
$439$	15.7197	−	9.07578i	0.750261	−	0.433163i	−0.0755273	−	0.997144i	$-0.524064\pi$
$439$	15.7197	−	9.07578i	0.750261	−	0.433163i	0.825788	+	0.563980i	$0.190731\pi$
$440$	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
$443$	−8.03323	−	2.15250i	−0.381670	−	0.102268i	0.0628823	−	0.998021i	$-0.479971\pi$
$443$	−8.03323	−	2.15250i	−0.381670	−	0.102268i	−0.444553	+	0.895753i	$0.646637\pi$
$444$	0.699697	+	2.25422i	0.0332061	+	0.106981i
$445$	0.181519	+	0.825132i	0.00860483	+	0.0391150i
$446$	8.01090	−	4.62509i	0.379327	−	0.219004i
$447$	0.795034	+	20.2891i	0.0376038	+	0.959640i
$448$	0.998710	+	2.45002i	0.0471846	+	0.115752i
$449$	12.4820			0.589061			0.294531	−	0.955642i	$-0.404837\pi$
$449$	12.4820			0.589061			0.294531	+	0.955642i	$0.404837\pi$
$450$	−14.4405	−	4.05862i	−0.680731	−	0.191325i
$451$	12.3954	−	21.4694i	0.583676	−	1.01096i
$452$	−8.02946	+	2.15149i	−0.377674	+	0.101197i
$453$	−24.1494	+	15.2336i	−1.13464	+	0.715738i
$454$			9.82300i			0.461016i
$455$	−15.0847	−	12.8452i	−0.707182	−	0.602195i
$456$	5.74317	−	6.21162i	0.268949	−	0.290886i
$457$	−30.5582	−	8.18804i	−1.42945	−	0.383021i	−0.540625	−	0.841264i	$-0.681812\pi$
$457$	−30.5582	−	8.18804i	−1.42945	−	0.383021i	−0.888827	+	0.458243i	$0.848479\pi$
$458$	−2.35376	−	8.78434i	−0.109984	−	0.410465i
$459$	1.82239	+	4.57203i	0.0850619	+	0.213404i
$460$	−0.222146	−	0.428439i	−0.0103576	−	0.0199761i
$461$			13.2219i			0.615807i	0.951418	+	0.307904i	$0.0996274\pi$
$461$			13.2219i			0.615807i	−0.951418	+	0.307904i	$0.900373\pi$
$462$	−21.1225	+	17.3635i	−0.982710	+	0.807824i
$463$	−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
$465$	−9.64318	+	2.52099i	−0.447192	+	0.116908i
$466$	9.35245	−	16.1989i	0.433244	−	0.750401i
$467$	−3.37796	+	12.6067i	−0.156313	+	0.583369i	0.842676	+	0.538421i	$0.180979\pi$
$467$	−3.37796	+	12.6067i	−0.156313	+	0.583369i	−0.998989	+	0.0449484i	$0.985688\pi$
$468$	6.52657	−	7.63839i	0.301691	−	0.353085i
$469$	−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
$472$	−1.04883	−	3.91427i	−0.0482761	−	0.180169i
$473$	−13.1492	−	49.0735i	−0.604602	−	2.25640i
$474$	−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
$477$	−12.0742	+	14.1310i	−0.552838	+	0.647016i
$478$	−2.29752	+	8.57446i	−0.105086	+	0.392187i
$479$	15.7131	−	27.2159i	0.717951	−	1.24353i	−0.243859	−	0.969811i	$-0.578414\pi$
$479$	15.7131	−	27.2159i	0.717951	−	1.24353i	0.961810	−	0.273717i	$-0.0882532\pi$
$480$	3.34224	+	1.95690i	0.152552	+	0.0893199i
$481$	2.28188	+	3.95233i	0.104045	+	0.180211i
$482$	2.91802	+	2.91802i	0.132912	+	0.132912i
$483$	0.925938	+	0.347641i	0.0421316	+	0.0158182i
$484$		−	24.6026i		−	1.11830i
$485$	9.62047	−	4.98822i	0.436843	−	0.226503i
$486$	6.88728	+	13.9845i	0.312414	+	0.634348i
$487$	6.88945	+	25.7118i	0.312191	+	1.16511i	0.926577	+	0.376106i	$0.122737\pi$
$487$	6.88945	+	25.7118i	0.312191	+	1.16511i	−0.614386	+	0.789006i	$0.710596\pi$
$488$	−12.9440	−	3.46833i	−0.585946	−	0.157004i
$489$	−5.92295	+	6.40607i	−0.267845	+	0.289692i
$490$	3.19063	+	15.3238i	0.144138	+	0.692260i
$491$		−	17.2123i		−	0.776779i	−0.921495	−	0.388389i	$-0.873032\pi$
$491$		−	17.2123i		−	0.776779i	0.921495	−	0.388389i	$-0.126968\pi$
$492$	6.08652	−	3.83942i	0.274402	−	0.173094i
$493$	−2.18123	+	0.584460i	−0.0982378	+	0.0263227i
$494$	8.17866	−	14.1659i	0.367975	−	0.637352i
$495$	−9.07560	+	38.9839i	−0.407918	+	1.75220i
$496$	2.57354			0.115555
$497$	−10.7398	−	26.3467i	−0.481746	−	1.18181i
$498$	−0.752354	−	19.1999i	−0.0337138	−	0.860368i
$499$	34.9854	−	20.1988i	1.56616	−	0.904224i	0.569551	−	0.821956i	$-0.307117\pi$
$499$	34.9854	−	20.1988i	1.56616	−	0.904224i	0.996610	−	0.0822678i	$-0.0262163\pi$
$500$	−1.40519	−	11.0917i	−0.0628422	−	0.496035i
$501$	−9.93679	−	32.0135i	−0.443943	−	1.43026i
$502$	9.39273	+	2.51677i	0.419218	+	0.112329i
$503$	−3.72801	+	3.72801i	−0.166224	+	0.166224i	−0.785317	−	0.619094i	$-0.787500\pi$
$503$	−3.72801	+	3.72801i	−0.166224	+	0.166224i	0.619094	+	0.785317i	$0.287500\pi$
$504$	−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
$507$	−1.43929	+	2.73494i	−0.0639210	+	0.121463i
$508$	−15.1375	+	4.05609i	−0.671620	+	0.179960i
$509$	4.53149	+	7.84877i	0.200855	+	0.347891i	0.948804	−	0.315865i	$-0.102295\pi$
$509$	4.53149	+	7.84877i	0.200855	+	0.347891i	−0.747949	+	0.663756i	$0.768961\pi$
$510$	−2.60980	+	2.57818i	−0.115564	+	0.114164i
$511$	27.9636	−	21.2082i	1.23704	−	0.938195i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	15.1787	+	20.3401i	0.670158	+	0.898038i
$514$	5.44728	+	3.14499i	0.240269	+	0.138719i
$515$	−16.1010	+	25.1830i	−0.709495	+	1.10969i
$516$	3.25628	−	14.3837i	0.143350	−	0.633207i
$517$	15.8063	−	15.8063i	0.695162	−	0.695162i
$518$	0.490720	−	3.57189i	0.0215610	−	0.156940i
$519$	−18.0688	−	16.7061i	−0.793131	−	0.733317i
$520$	7.13828	+	2.26347i	0.313034	+	0.0992597i
$521$	28.4540	+	16.4279i	1.24659	+	0.719721i	0.970428	−	0.241389i	$-0.0776030\pi$
$521$	28.4540	+	16.4279i	1.24659	+	0.719721i	0.276165	+	0.961110i	$0.410936\pi$
$522$	−6.74237	+	2.38601i	−0.295105	+	0.104433i
$523$	−3.01831	+	11.2645i	−0.131981	+	0.492561i	−0.999992	−	0.00398437i	$-0.998732\pi$
$523$	−3.01831	+	11.2645i	−0.131981	+	0.492561i	0.868011	+	0.496545i	$0.165398\pi$
$524$	4.31407			0.188461
$525$	17.3541	+	14.9612i	0.757394	+	0.652958i
$526$	−12.9960			−0.566654
$527$	−0.630917	+	2.35462i	−0.0274832	+	0.102569i
$528$	4.81298	−	9.14565i	0.209458	−	0.398013i
$529$	−19.8782	−	11.4767i	−0.864271	−	0.498987i
$530$	−13.2058	−	4.18743i	−0.573625	−	0.181890i
$531$	12.1198	−	0.951296i	0.525954	−	0.0412827i
$532$	−11.9665	+	4.87797i	−0.518815	+	0.211487i
$533$	9.83891	−	9.83891i	0.426170	−	0.426170i
$534$	0.638276	+	0.144497i	0.0276209	+	0.00625301i
$535$	18.9547	−	29.6464i	0.819484	−	1.28172i
$536$	8.32300	+	4.80529i	0.359499	+	0.207557i
$537$	−12.6817	+	7.99972i	−0.547257	+	0.345213i
$538$	−7.77555	−	7.77555i	−0.335228	−	0.335228i
$539$	40.4635	−	10.3553i	1.74288	−	0.446036i
$540$	−7.60146	+	8.78737i	−0.327115	+	0.378148i
$541$	−1.99471	−	3.45495i	−0.0857595	−	0.148540i	0.819955	−	0.572428i	$-0.193998\pi$
$541$	−1.99471	−	3.45495i	−0.0857595	−	0.148540i	−0.905715	+	0.423888i	$0.860665\pi$
$542$	−18.5351	+	4.96646i	−0.796150	+	0.213328i
$543$	17.9569	+	9.45000i	0.770606	+	0.405538i
$544$	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	$0.344319\pi$
$548$	−7.85237	−	2.10404i	−0.335437	−	0.0898800i
$549$	17.3149	−	36.2819i	0.738981	−	1.54847i
$550$	−29.3974	+	5.08495i	−1.25351	+	0.216823i
$551$	−10.0842	+	5.82213i	−0.429602	+	0.248031i
$552$	−0.373538	+	0.0146372i	−0.0158988	+	0.000623001i
$553$	1.63739	−	2.10920i	0.0696290	−	0.0896923i
$554$	1.72041			0.0730934
$555$	−2.61101	−	4.58674i	−0.110831	−	0.194696i
$556$	−5.46209	+	9.46062i	−0.231644	+	0.401220i
$557$	−4.54267	+	1.21720i	−0.192479	+	0.0515746i	−0.353771	−	0.935332i	$-0.615101\pi$
$557$	−4.54267	+	1.21720i	−0.192479	+	0.0515746i	0.161292	+	0.986907i	$0.448434\pi$
$558$	−1.40856	+	7.59103i	−0.0596290	+	0.321354i
$559$		−	28.5152i		−	1.20606i
$560$	−3.35807	−	4.87066i	−0.141904	−	0.205823i
$561$	7.18773	+	6.64567i	0.303466	+	0.280580i
$562$	17.1288	+	4.58965i	0.722536	+	0.193603i
$563$	6.89278	+	25.7242i	0.290496	+	1.08415i	0.944729	+	0.327853i	$0.106325\pi$
$563$	6.89278	+	25.7242i	0.290496	+	1.08415i	−0.654233	+	0.756293i	$0.727008\pi$
$564$	6.19716	−	1.92356i	0.260947	−	0.0809964i
$565$	16.5015	−	8.55604i	0.694223	−	0.359955i
$566$		−	16.6455i		−	0.699665i
$567$	−0.479352	−	23.8069i	−0.0201309	−	0.999797i
$568$	7.60399	+	7.60399i	0.319057	+	0.319057i
$569$	2.30517	+	3.99267i	0.0966376	+	0.167381i	0.910291	−	0.413969i	$-0.135858\pi$
$569$	2.30517	+	3.99267i	0.0966376	+	0.167381i	−0.813653	+	0.581350i	$0.802525\pi$
$570$	−9.55802	+	16.3244i	−0.400342	+	0.683753i
$571$	−2.42916	+	4.20743i	−0.101657	+	0.176075i	−0.912368	−	0.409372i	$-0.865748\pi$
$571$	−2.42916	+	4.20743i	−0.101657	+	0.176075i	0.810710	+	0.585447i	$0.199081\pi$
$572$	5.17189	−	19.3018i	0.216248	−	0.807047i
$573$	45.3084	−	1.77543i	1.89279	−	0.0741695i
$574$	−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
$577$	3.50264	+	13.0720i	0.145817	+	0.544196i	0.999718	+	0.0237602i	$0.00756383\pi$
$577$	3.50264	+	13.0720i	0.145817	+	0.544196i	−0.853901	+	0.520436i	$0.825770\pi$
$578$	−4.16771	−	15.5541i	−0.173354	−	0.646965i
$579$	−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
$582$	−0.328674	−	8.38770i	−0.0136240	−	0.347681i
$583$	−9.56802	+	35.7083i	−0.396267	+	1.47889i
$584$	−6.63257	+	11.4880i	−0.274458	+	0.475375i
$585$	−10.5834	+	19.8166i	−0.437570	+	0.819315i
$586$	−4.05653	−	7.02612i	−0.167574	−	0.290246i
$587$	20.4866	+	20.4866i	0.845574	+	0.845574i	0.989577	−	0.144004i	$-0.0459977\pi$
$587$	20.4866	+	20.4866i	0.845574	+	0.845574i	−0.144004	+	0.989577i	$0.545998\pi$
$588$	11.7942	+	2.81001i	0.486386	+	0.115883i
$589$			12.5698i			0.517931i
$590$	4.17097	+	8.04430i	0.171716	+	0.331179i
$591$	6.09701	+	19.6428i	0.250798	+	0.807999i
$592$	0.352701	+	1.31630i	0.0144959	+	0.0540994i
$593$	33.0195	+	8.84754i	1.35595	+	0.363325i	0.862326	−	0.506353i	$-0.169007\pi$
$593$	33.0195	+	8.84754i	1.35595	+	0.363325i	0.493620	+	0.869678i	$0.335673\pi$
$594$	24.3422	+	19.2022i	0.998773	+	0.787877i
$595$	5.27959	−	1.87834i	0.216442	−	0.0770044i
$596$			11.7229i			0.480188i
$597$	−17.6578	−	27.9924i	−0.722685	−	1.14565i
$598$	−0.698175	+	0.187075i	−0.0285505	+	0.00765008i
$599$	−20.2161	+	35.0153i	−0.826006	+	1.43068i	0.0751420	+	0.997173i	$0.476059\pi$
$599$	−20.2161	+	35.0153i	−0.826006	+	1.43068i	−0.901148	+	0.433512i	$0.857274\pi$
$600$	−8.23907	−	2.66790i	−0.336359	−	0.108916i
$601$	20.3443			0.829861			0.414931	−	0.909853i	$-0.363806\pi$
$601$	20.3443			0.829861			0.414931	+	0.909853i	$0.363806\pi$
$602$	−13.8142	+	17.7948i	−0.563026	+	0.725260i
$603$	−18.7293	+	21.9199i	−0.762716	+	0.892647i
$604$	−14.2764	+	8.24246i	−0.580897	+	0.335381i
$605$	11.8196	+	53.7283i	0.480534	+	2.18436i
$606$	−7.13224	+	2.21380i	−0.289728	+	0.0899296i
$607$	−44.5671	−	11.9417i	−1.80892	−	0.484699i	−0.813609	−	0.581413i	$-0.802500\pi$
$607$	−44.5671	−	11.9417i	−1.80892	−	0.484699i	−0.995312	+	0.0967136i	$0.969167\pi$
$608$	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
$612$	0.947994	+	2.67883i	0.0383204	+	0.108285i
$613$	−14.9181	+	3.99730i	−0.602538	+	0.161450i	−0.547177	−	0.837017i	$-0.684298\pi$
$613$	−14.9181	+	3.99730i	−0.602538	+	0.161450i	−0.0553608	+	0.998466i	$0.517631\pi$
$614$	1.12009	+	1.94006i	0.0452032	+	0.0782943i
$615$	−11.4475	+	11.3088i	−0.461608	+	0.456015i
$616$	−12.5783	+	9.53964i	−0.506793	+	0.384363i
$617$	2.50025	+	2.50025i	0.100656	+	0.100656i	0.755642	−	0.654985i	$-0.227325\pi$
$617$	2.50025	+	2.50025i	0.100656	+	0.100656i	−0.654985	+	0.755642i	$0.727325\pi$
$618$	12.3527	+	19.5823i	0.496897	+	0.787716i
$619$	−4.86025	−	2.80606i	−0.195350	−	0.112785i	0.399135	−	0.916892i	$-0.369311\pi$
$619$	−4.86025	−	2.80606i	−0.195350	−	0.112785i	−0.594485	+	0.804107i	$0.702644\pi$
$620$	−5.62022	+	1.23638i	−0.225713	+	0.0496542i
$621$	0.161272	−	1.10982i	0.00647161	−	0.0445355i
$622$	4.24964	−	4.24964i	0.170395	−	0.170395i
$623$	−0.789641	−	0.613006i	−0.0316363	−	0.0245596i
$624$	3.93790	−	4.25910i	0.157642	−	0.170501i
$625$	8.39740	+	23.5475i	0.335896	+	0.941899i
$626$	2.78376	+	1.60721i	0.111261	+	0.0642369i
$627$	44.6698	+	23.5079i	1.78394	+	0.938815i
$628$	−0.651278	+	2.43060i	−0.0259888	+	0.0969916i
$629$	−1.29079			−0.0514672
$630$	16.2047	−	7.23930i	0.645611	−	0.288420i
$631$	20.0318			0.797455			0.398727	−	0.917069i	$-0.369452\pi$
$631$	20.0318			0.797455			0.398727	+	0.917069i	$0.369452\pi$
$632$	−0.261207	+	0.974838i	−0.0103903	+	0.0387770i
$633$	9.89030	+	5.20486i	0.393104	+	0.206875i
$634$	0.681432	+	0.393425i	0.0270631	+	0.0156249i
$635$	31.1095	−	16.1303i	1.23454	−	0.640111i
$636$	−7.28513	+	7.87935i	−0.288874	+	0.312437i
$637$	23.4414	+	0.263923i	0.928781	+	0.0104570i
$638$	−10.0586	+	10.0586i	−0.398224	+	0.398224i
$639$	−26.5910	+	18.2673i	−1.05192	+	0.722642i
$640$	1.88392	+	1.20451i	0.0744686	+	0.0476123i
$641$	32.1479	+	18.5606i	1.26977	+	0.733100i	0.974944	−	0.222452i	$-0.0714059\pi$
$641$	32.1479	+	18.5606i	1.26977	+	0.733100i	0.294823	+	0.955552i	$0.404739\pi$
$642$	−14.5420	−	23.0530i	−0.573928	−	0.909831i
$643$	−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
$645$	−0.201003	+	32.9762i	−0.00791450	+	1.29844i
$646$	2.31321	+	4.00660i	0.0910121	+	0.157638i
$647$	−23.0376	+	6.17291i	−0.905702	+	0.242682i	−0.681464	−	0.731852i	$-0.738656\pi$
$647$	−23.0376	+	6.17291i	−0.905702	+	0.242682i	−0.224239	+	0.974534i	$0.571990\pi$
$648$	3.65719	+	8.22344i	0.143668	+	0.323047i
$649$	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
$653$	−19.9547	−	5.34683i	−0.780886	−	0.209238i	−0.153711	−	0.988116i	$-0.549122\pi$
$653$	−19.9547	−	5.34683i	−0.780886	−	0.209238i	−0.627175	+	0.778878i	$0.715789\pi$
$654$	−17.5031	+	5.43285i	−0.684425	+	0.212441i
$655$	−9.42128	+	2.07257i	−0.368120	+	0.0809819i
$656$	3.59815	−	2.07740i	0.140484	−	0.0811087i
$657$	−30.2553	−	25.8514i	−1.18037	−	1.00856i
$658$	−9.81961	−	1.34905i	−0.382808	−	0.0525916i
$659$	−15.8694			−0.618184			−0.309092	−	0.951032i	$-0.600025\pi$
$659$	−15.8694			−0.618184			−0.309092	+	0.951032i	$0.600025\pi$
$660$	−6.11707	+	22.2850i	−0.238106	+	0.867441i
$661$	−2.27276	+	3.93654i	−0.0884003	+	0.153114i	−0.906835	−	0.421486i	$-0.861509\pi$
$661$	−2.27276	+	3.93654i	−0.0884003	+	0.153114i	0.818435	+	0.574599i	$0.194842\pi$
$662$	20.8418	−	5.58454i	0.810039	−	0.217049i
$663$	2.93140	+	4.64706i	0.113846	+	0.180477i
$664$		−	11.0936i		−	0.430514i
$665$	23.7896	−	16.4017i	0.922522	−	0.636031i
$666$	−4.07565	+	0.319903i	−0.157928	+	0.0123960i
$667$	0.497008	+	0.133173i	0.0192442	+	0.00515648i
$668$	−5.00890	−	18.6935i	−0.193800	−	0.723272i
$669$	4.74953	+	15.3016i	0.183627	+	0.591595i
$670$	−20.4847	−	6.49548i	−0.791394	−	0.250942i
$671$		−	79.9584i		−	3.08676i
$672$	−4.52076	+	0.750148i	−0.174392	+	0.0289376i
$673$	−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
$675$	12.3788	−	22.8422i	0.476460	−	0.879196i
$676$	−0.892162	+	1.54527i	−0.0343139	+	0.0594335i
$677$	−10.0418	+	37.4764i	−0.385936	+	1.44033i	0.450750	+	0.892650i	$0.351157\pi$
$677$	−10.0418	+	37.4764i	−0.385936	+	1.44033i	−0.836686	+	0.547683i	$0.815510\pi$
$678$	−0.563759	−	14.3870i	−0.0216510	−	0.552529i
$679$	−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
$682$	3.97436	+	14.8325i	0.152186	+	0.567966i
$683$	−2.44140	−	9.11142i	−0.0934175	−	0.348639i	0.903357	−	0.428889i	$-0.141095\pi$
$683$	−2.44140	−	9.11142i	−0.0934175	−	0.348639i	−0.996775	+	0.0802500i	$0.974428\pi$
$684$	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
$687$	15.7396	−	0.616760i	0.600502	−	0.0235309i
$688$	2.20373	−	8.22445i	0.0840166	−	0.313554i
$689$	−10.3745	+	17.9692i	−0.395238	+	0.684571i
$690$	0.808719	−	0.211421i	0.0307874	−	0.00804865i
$691$	−5.48550	−	9.50117i	−0.208678	−	0.361441i	0.742620	−	0.669713i	$-0.233583\pi$
$691$	−5.48550	−	9.50117i	−0.208678	−	0.361441i	−0.951298	+	0.308271i	$0.900250\pi$
$692$	−10.0464	−	10.0464i	−0.381905	−	0.381905i
$693$	−21.2542	−	42.3228i	−0.807381	−	1.60771i
$694$		−	16.1618i		−	0.613495i
$695$	7.38331	−	23.2847i	0.280065	−	0.883238i
$696$	−3.94366	+	1.22409i	−0.149484	+	0.0463989i
$697$	1.01857	+	3.80136i	0.0385811	+	0.143987i
$698$	−22.7679	−	6.10064i	−0.861778	−	0.230913i
$699$	23.7882	+	21.9942i	0.899751	+	0.831896i
$700$	9.67348	+	9.02351i	0.365623	+	0.341057i
$701$		−	10.6209i		−	0.401147i	−0.979679	−	0.200574i	$-0.935719\pi$
$701$		−	10.6209i		−	0.401147i	0.979679	−	0.200574i	$-0.0642806\pi$
$702$	10.4076	+	13.9465i	0.392808	+	0.526378i
$703$	−6.42914	+	1.72268i	−0.242480	+	0.0649723i
$704$	2.98339	−	5.16739i	0.112441	−	0.194753i
$705$	−12.6095	+	7.17800i	−0.474903	+	0.270339i
$706$	27.0532			1.01816
$707$	11.3013	+	1.55261i	0.425028	+	0.0583919i
$708$	7.01350	−	0.274826i	0.263583	−	0.0103286i
$709$	−8.79213	+	5.07614i	−0.330196	+	0.190638i	−0.655928	−	0.754824i	$-0.727722\pi$
$709$	−8.79213	+	5.07614i	−0.330196	+	0.190638i	0.325732	+	0.945462i	$0.394389\pi$
$710$	−20.2591	−	12.9529i	−0.760310	−	0.486112i
$711$	−2.73247	−	1.30402i	−0.102476	−	0.0489046i
$712$	0.364960	+	0.0977906i	0.0136774	+	0.00366486i
$713$	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
$717$	−13.6062	−	7.16038i	−0.508133	−	0.267409i
$718$	−6.94018	+	1.85962i	−0.259005	+	0.0694002i
$719$	−14.4032	−	24.9471i	−0.537150	−	0.930370i	−0.999056	−	0.0434417i	$-0.986168\pi$
$719$	−14.4032	−	24.9471i	−0.537150	−	0.930370i	0.461906	−	0.886929i	$-0.347166\pi$
$720$	−4.58399	+	4.89766i	−0.170835	+	0.182525i
$721$	−4.41881	−	35.0894i	−0.164565	−	1.30680i
$722$	3.43376	+	3.43376i	0.127791	+	0.127791i
$723$	−6.04538	+	3.81347i	−0.224830	+	0.141824i
$724$	10.1459	+	5.85771i	0.377068	+	0.217700i
$725$	9.74212	+	6.86887i	0.361813	+	0.255103i
$726$	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	$0.248731\pi$
$728$	−8.20506	+	3.34466i	−0.304100	+	0.123961i
$729$	−26.2579	+	6.28654i	−0.972516	+	0.232835i
$730$	8.96549	−	28.2744i	0.331828	−	1.04648i
$731$	6.98457	+	4.03254i	0.258334	+	0.149149i
$732$	10.8093	−	20.5399i	0.399523	−	0.759175i
$733$	8.85810	−	33.0589i	0.327181	−	1.22106i	−0.584919	−	0.811091i	$-0.698874\pi$
$733$	8.85810	−	33.0589i	0.327181	−	1.22106i	0.912101	−	0.409966i	$-0.134459\pi$
$734$	−14.9359			−0.551296
$735$	−27.1068	−	0.470450i	−0.999849	−	0.0173528i
$736$	−0.215828			−0.00795552
$737$	−14.8418	+	55.3903i	−0.546704	+	2.04033i
$738$	4.15823	+	11.7503i	0.153067	+	0.432535i
$739$	−28.3705	−	16.3797i	−1.04362	−	0.602537i	−0.122767	−	0.992436i	$-0.539177\pi$
$739$	−28.3705	−	16.3797i	−1.04362	−	0.602537i	−0.920858	+	0.389899i	$0.872510\pi$
$740$	−1.40262	−	2.70515i	−0.0515613	−	0.0994432i
$741$	20.8026	+	19.2338i	0.764203	+	0.706570i
$742$	15.1794	−	6.18763i	0.557253	−	0.227155i
$743$	0.701038	−	0.701038i	0.0257186	−	0.0257186i	−0.694131	−	0.719849i	$-0.744211\pi$
$743$	0.701038	−	0.701038i	0.0257186	−	0.0257186i	0.719849	+	0.694131i	$0.244211\pi$
$744$	−0.984213	+	4.34748i	−0.0360830	+	0.159386i
$745$	−5.63191	−	25.6010i	−0.206337	−	0.937949i
$746$	−6.76422	−	3.90532i	−0.247656	−	0.142984i
$747$	32.7222	+	6.07178i	1.19724	+	0.222155i
$748$	3.99642	+	3.99642i	0.146124	+	0.146124i
$749$	5.20199	+	41.3086i	0.190077	+	1.50938i
$750$	19.2746	+	1.86806i	0.703809	+	0.0682120i
$751$	−0.934185	−	1.61806i	−0.0340889	−	0.0590437i	0.848478	−	0.529231i	$-0.177520\pi$
$751$	−0.934185	−	1.61806i	−0.0340889	−	0.0590437i	−0.882567	+	0.470188i	$0.844186\pi$
$752$	3.61867	−	0.969620i	0.131959	−	0.0353584i
$753$	−7.84371	+	14.9047i	−0.285841	+	0.543156i
$754$	−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	$0.122358\pi$
$758$	−16.6430	−	4.45947i	−0.604500	−	0.161975i
$759$	−0.661223	−	2.13027i	−0.0240009	−	0.0773240i
$760$	−5.88313	+	9.20158i	−0.213404	+	0.333777i
$761$	−43.5861	+	25.1645i	−1.58000	+	0.912211i	−0.585138	+	0.810934i	$0.698960\pi$
$761$	−43.5861	+	25.1645i	−1.58000	+	0.912211i	−0.994858	+	0.101277i	$0.967707\pi$
$762$	−1.06283	−	27.1231i	−0.0385022	−	0.982566i
$763$	27.7342	+	3.81023i	1.00405	+	0.137940i
$764$	26.1789			0.947120
$765$	−3.35724	−	5.39473i	−0.121381	−	0.195047i
$766$	−2.73278	+	4.73332i	−0.0987395	+	0.171022i
$767$	13.1088	−	3.51250i	0.473332	−	0.126829i
$768$	1.46494	−	0.924094i	0.0528615	−	0.0333454i
$769$			5.32307i			0.191955i	0.995384	+	0.0959775i	$0.0305977\pi$
$769$			5.32307i			0.191955i	−0.995384	+	0.0959775i	$0.969402\pi$
$770$	22.8860	−	26.8760i	0.824755	−	0.968544i
$771$	−7.39607	+	7.99934i	−0.266363	+	0.288089i
$772$	−20.5578	−	5.50843i	−0.739890	−	0.198253i
$773$	−5.08164	−	18.9649i	−0.182774	−	0.682121i	−0.995096	−	0.0989124i	$-0.968464\pi$
$773$	−5.08164	−	18.9649i	−0.182774	−	0.682121i	0.812322	−	0.583209i	$-0.198203\pi$
$774$	23.0531	+	11.0017i	0.828626	+	0.395447i
$775$	11.6797	−	5.40013i	0.419548	−	0.193978i
$776$		−	4.84635i		−	0.173974i
$777$	5.84634	+	2.19499i	0.209736	+	0.0787450i
$778$	3.30102	+	3.30102i	0.118347	+	0.118347i
$779$	10.1466	+	17.5744i	0.363538	+	0.629667i
$780$	−6.55362	+	11.1931i	−0.234657	+	0.400777i
$781$	−32.0824	+	55.5684i	−1.14800	+	1.98839i
$782$	0.0529115	−	0.197468i	0.00189211	−	0.00706145i
$783$	−1.45217	−	12.3024i	−0.0518963	−	0.439652i
$784$	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
$787$	−5.74540	−	21.4421i	−0.204801	−	0.764329i	−0.989510	−	0.144464i	$-0.953854\pi$
$787$	−5.74540	−	21.4421i	−0.204801	−	0.764329i	0.784709	−	0.619865i	$-0.212813\pi$
$788$	3.07336	+	11.4699i	0.109484	+	0.408600i
$789$	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
$792$	13.6091	+	11.6282i	0.483579	+	0.413190i
$793$	11.6154	−	43.3491i	0.412473	−	1.53937i
$794$	0.0255118	−	0.0441877i	0.000905379	−	0.00156816i
$795$	12.1242	−	20.7072i	0.430002	−	0.734410i
$796$	−9.55411	−	16.5482i	−0.338636	−	0.586535i
$797$	−0.507697	−	0.507697i	−0.0179836	−	0.0179836i	0.698058	−	0.716041i	$-0.254048\pi$
$797$	−0.507697	−	0.507697i	−0.0179836	−	0.0179836i	−0.716041	+	0.698058i	$0.754048\pi$
$798$	−3.66393	−	22.0806i	−0.129702	−	0.781645i
$799$			3.54855i			0.125539i
$800$	−4.69287	−	1.72538i	−0.165918	−	0.0610015i
$801$	−0.488199	+	1.02298i	−0.0172497	+	0.0361452i
$802$	−0.0165627	−	0.0618130i	−0.000584851	−	0.00218269i
$803$	−76.4533	−	20.4856i	−2.69798	−	0.722921i
$804$	−11.3006	+	12.2224i	−0.398541	+	0.431049i
$805$	−1.25581	−	0.230842i	−0.0442617	−	0.00813613i
$806$			8.61873i			0.303582i
$807$	16.1089	−	10.1616i	0.567060	−	0.357705i
$808$	−4.16469	+	1.11593i	−0.146513	+	0.0392581i
$809$	22.9981	−	39.8339i	0.808571	−	1.40049i	−0.105283	−	0.994442i	$-0.533575\pi$
$809$	22.9981	−	39.8339i	0.808571	−	1.40049i	0.913854	−	0.406044i	$-0.133092\pi$
$810$	−11.9375	−	16.2018i	−0.419439	−	0.569272i
$811$	−45.3779			−1.59343			−0.796717	−	0.604352i	$-0.793432\pi$
$811$	−45.3779			−1.59343			−0.796717	+	0.604352i	$0.793432\pi$
$812$	6.24886	+	0.858491i	0.219292	+	0.0301271i
$813$	−1.30137	−	33.2107i	−0.0456411	−	1.16475i
$814$	−7.04176	+	4.06556i	−0.246813	+	0.142498i
$815$	6.06729	−	9.48963i	0.212528	−	0.332407i
$816$	0.486346	+	1.56687i	0.0170255	+	0.0548514i
$817$	40.1704	+	10.7636i	1.40539	+	0.376572i
$818$	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	0.211508	−	0.977376i	$-0.432163\pi$
$821$	33.3434	−	19.2508i	1.16369	−	0.671859i	0.952187	+	0.305517i	$0.0988293\pi$
$822$	6.55739	−	12.4604i	0.228715	−	0.434606i
$823$	−2.93058	+	0.785245i	−0.102153	+	0.0273719i	−0.309534	−	0.950888i	$-0.600173\pi$
$823$	−2.93058	+	0.785245i	−0.102153	+	0.0273719i	0.207380	+	0.978260i	$0.433506\pi$
$824$	6.68365	+	11.5764i	0.232836	+	0.403284i
$825$	2.65259	−	51.6058i	0.0923515	−	1.79668i
$826$	−9.88214	−	4.15864i	−0.343844	−	0.144698i
$827$	−30.2271	−	30.2271i	−1.05110	−	1.05110i	−0.998622	−	0.0524756i	$-0.983289\pi$
$827$	−30.2271	−	30.2271i	−1.05110	−	1.05110i	−0.0524756	−	0.998622i	$-0.516711\pi$
$828$	0.118128	−	0.636617i	0.00410522	−	0.0221240i
$829$	46.3527	+	26.7617i	1.60990	+	0.929473i	0.989392	+	0.145270i	$0.0464049\pi$
$829$	46.3527	+	26.7617i	1.60990	+	0.929473i	0.620503	+	0.784204i	$0.286928\pi$
$830$	5.32958	+	24.2267i	0.184992	+	0.840920i
$831$	−0.657948	+	2.90630i	−0.0228240	+	0.100818i
$832$	2.36809	−	2.36809i	0.0820987	−	0.0820987i
$833$	−3.37967	+	5.70446i	−0.117099	+	0.197648i
$834$	−13.8930	−	12.8452i	−0.481074	−	0.444793i
$835$	19.9194	+	38.4173i	0.689339	+	1.32949i
$836$	25.2389	+	14.5717i	0.872906	+	0.503973i
$837$	−12.2849	−	5.28256i	−0.424627	−	0.182592i
$838$	4.70802	−	17.5706i	0.162636	−	0.606965i
$839$	−9.47997			−0.327285			−0.163643	−	0.986520i	$-0.552324\pi$
$839$	−9.47997			−0.327285			−0.163643	+	0.986520i	$0.552324\pi$
$840$	9.51227	−	3.81008i	0.328205	−	0.131460i
$841$	−23.3164			−0.804013
$842$	0.521075	−	1.94468i	0.0179574	−	0.0670181i
$843$	−14.3040	+	27.1805i	−0.492656	+	0.936147i
$844$	5.58813	+	3.22631i	0.192351	+	0.111054i
$845$	1.20597	−	3.80325i	0.0414866	−	0.130836i
$846$	0.879455	+	11.2045i	0.0302363	+	0.385219i
$847$	−51.4173	−	39.9157i	−1.76672	−	1.37152i
$848$	−4.38097	+	4.38097i	−0.150443	+	0.150443i
$849$	28.1194	+	6.36586i	0.965054	+	0.218476i
$850$	2.72910	−	3.87068i	0.0936073	−	0.132763i
$851$	0.254711	+	0.147058i	0.00873139	+	0.00504107i
$852$	−15.7535	+	9.93741i	−0.539706	+	0.340450i
$853$	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
$855$	−23.9215	−	22.3894i	−0.818097	−	0.765702i
$856$	−7.86826	−	13.6282i	−0.268931	−	0.465803i
$857$	42.0461	−	11.2662i	1.43627	−	0.384846i	0.545042	−	0.838409i	$-0.316514\pi$
$857$	42.0461	−	11.2662i	1.43627	−	0.384846i	0.891225	+	0.453562i	$0.149847\pi$
$858$	30.6286	+	16.1186i	1.04564	+	0.550279i
$859$	30.1458	−	17.4047i	1.02856	−	0.593841i	0.111990	−	0.993709i	$-0.464277\pi$
$859$	30.1458	−	17.4047i	1.02856	−	0.593841i	0.916573	+	0.399868i	$0.130944\pi$
$860$	−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
$863$	16.6883	+	4.47160i	0.568075	+	0.152215i	0.531413	−	0.847113i	$-0.321661\pi$
$863$	16.6883	+	4.47160i	0.568075	+	0.152215i	0.0366613	+	0.999328i	$0.488328\pi$
$864$	1.92396	+	4.82684i	0.0654544	+	0.164212i
$865$	26.7662	+	17.1132i	0.910078	+	0.581868i
$866$	−8.66531	+	5.00292i	−0.294459	+	0.170006i
$867$	27.8695	−	1.09207i	0.946497	−	0.0370888i
$868$	4.17536	−	5.37848i	0.141721	−	0.182557i
$869$	−6.02184			−0.204277
$870$	8.02428	−	4.56784i	0.272049	−	0.154864i
$871$	−16.0928	+	27.8736i	−0.545284	+	0.944460i
$872$	−10.2205	+	2.73857i	−0.346109	+	0.0927397i
$873$	14.2951	+	2.65253i	0.483814	+	0.0897744i
$874$		−	1.05416i		−	0.0356575i
$875$	−25.4605	−	15.0586i	−0.860722	−	0.509075i
$876$	−16.8701	−	15.5978i	−0.569988	−	0.527002i
$877$	7.67812	+	2.05735i	0.259272	+	0.0694717i	0.386113	−	0.922451i	$-0.373817\pi$
$877$	7.67812	+	2.05735i	0.259272	+	0.0694717i	−0.126842	+	0.991923i	$0.540484\pi$
$878$	4.69797	+	17.5331i	0.158549	+	0.591712i
$879$	13.4206	−	4.16567i	0.452666	−	0.140505i
$880$	−4.03276	+	12.7181i	−0.135944	+	0.428726i
$881$			5.56368i			0.187445i	0.995598	+	0.0937226i	$0.0298767\pi$
$881$			5.56368i			0.187445i	−0.995598	+	0.0937226i	$0.970123\pi$
$882$	−9.25749	+	18.8494i	−0.311716	+	0.634691i
$883$	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
$885$	−15.1844	+	3.96961i	−0.510418	+	0.133437i
$886$	4.15831	−	7.20240i	0.139701	−	0.241969i
$887$	0.789926	−	2.94804i	0.0265231	−	0.0989856i	−0.951395	−	0.307972i	$-0.900350\pi$
$887$	0.789926	−	2.94804i	0.0265231	−	0.0989856i	0.977919	+	0.208986i	$0.0670164\pi$
$888$	−2.35851	+	0.0924189i	−0.0791463	+	0.00310137i
$889$	−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
$892$	2.39412	+	8.93499i	0.0801612	+	0.299166i
$893$	4.73589	+	17.6746i	0.158480	+	0.591457i
$894$	−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
$897$	−0.0490198	−	1.25097i	−0.00163672	−	0.0417688i
$898$	−3.23058	+	12.0567i	−0.107806	+	0.402336i
$899$	3.06770	−	5.31341i	0.102313	−	0.177212i
$900$	7.65780	−	12.8980i	0.255260	−	0.429933i
$901$	−2.93428	−	5.08232i	−0.0977549	−	0.169316i
$902$	17.5297	+	17.5297i	0.583676	+	0.583676i
$903$	−24.7777	−	30.1418i	−0.824549	−	1.00306i
$904$		−	8.31271i		−	0.276476i
$905$	−24.9712	−	7.91809i	−0.830070	−	0.263206i
$906$	−8.46421	−	27.2693i	−0.281205	−	0.905962i
$907$	−9.00978	−	33.6250i	−0.299165	−	1.11650i	−0.937853	−	0.347033i	$-0.887189\pi$
$907$	−9.00978	−	33.6250i	−0.299165	−	1.11650i	0.638688	−	0.769466i	$-0.279477\pi$
$908$	−9.48829	−	2.54238i	−0.314880	−	0.0843718i
$909$	−1.01216	−	12.8952i	−0.0335711	−	0.427705i
$910$	16.3118	−	11.2461i	0.540730	−	0.372805i
$911$		−	13.5125i		−	0.447688i	−0.974625	−	0.223844i	$-0.928139\pi$
$911$		−	13.5125i		−	0.447688i	0.974625	−	0.223844i	$-0.0718605\pi$
$912$	4.51352	+	7.15516i	0.149458	+	0.236931i
$913$	63.9375	−	17.1320i	2.11602	−	0.566987i
$914$	15.8181	−	27.3977i	0.523216	−	0.906236i
$915$	−13.7381	+	50.0490i	−0.454167	+	1.65457i
$916$	9.09422			0.300482
$917$	6.99924	−	9.01605i	0.231135	−	0.297736i
$918$	−4.88791	+	0.576966i	−0.161325	+	0.0190427i
$919$	−23.3642	+	13.4893i	−0.770714	+	0.444972i	−0.833129	−	0.553078i	$-0.813453\pi$
$919$	−23.3642	+	13.4893i	−0.770714	+	0.444972i	0.0624154	+	0.998050i	$0.480120\pi$
$920$	0.471336	−	0.103688i	0.0155395	−	0.00341850i
$921$	−3.70570	+	1.15023i	−0.122107	+	0.0379012i
$922$	−12.7714	−	3.42209i	−0.420604	−	0.112701i
$923$	−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
$927$	−37.8045	+	13.3784i	−1.24166	+	0.439404i
$928$	−2.30280	+	0.617033i	−0.0755931	+	0.0202551i
$929$	24.7230	+	42.8215i	0.811135	+	1.40493i	0.912071	+	0.410033i	$0.134483\pi$
$929$	24.7230	+	42.8215i	0.811135	+	1.40493i	−0.100936	+	0.994893i	$0.532184\pi$
$930$	0.0607534	−	9.96708i	0.00199218	−	0.326833i
$931$	−9.22023	+	32.9232i	−0.302181	+	1.07901i
$932$	13.2264	+	13.2264i	0.433244	+	0.433244i
$933$	5.55371	+	8.80414i	0.181820	+	0.288235i
$934$	−11.3029	−	6.52572i	−0.369841	−	0.213528i
$935$	−10.6475	−	6.80762i	−0.348212	−	0.222633i
$936$	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	$0.335542\pi$
$938$	23.5461	−	9.59817i	0.768806	−	0.313391i
$939$	−3.77967	+	4.08796i	−0.123345	+	0.133406i
$940$	−7.43681	+	3.85599i	−0.242562	+	0.125768i
$941$	−29.1043	−	16.8034i	−0.948774	−	0.547775i	−0.0560744	−	0.998427i	$-0.517858\pi$
$941$	−29.1043	−	16.8034i	−0.948774	−	0.547775i	−0.892700	+	0.450651i	$0.851192\pi$
$942$	−3.85695	−	2.02975i	−0.125666	−	0.0661330i
$943$	0.232088	−	0.866165i	0.00755783	−	0.0282062i
$944$	4.05235			0.131893
$945$	6.03210	+	30.1432i	0.196224	+	0.980559i
$946$	50.8047			1.65180
$947$	13.1124	−	48.9361i	0.426095	−	1.59021i	−0.335424	−	0.942067i	$-0.608880\pi$
$947$	13.1124	−	48.9361i	0.426095	−	1.59021i	0.761520	−	0.648142i	$-0.224454\pi$
$948$	−1.54690	−	0.814071i	−0.0502410	−	0.0264398i
$949$	−38.4729	−	22.2124i	−1.24888	−	0.721044i
$950$	8.42724	−	22.9212i	0.273416	−	0.743663i
$951$	−0.925217	+	1.00068i	−0.0300022	+	0.0324494i
$952$	0.341090	−	2.48276i	0.0110548	−	0.0804667i
$953$	−26.3451	+	26.3451i	−0.853401	+	0.853401i	−0.990550	−	0.137149i	$-0.956206\pi$
$953$	−26.3451	+	26.3451i	−0.853401	+	0.853401i	0.137149	+	0.990550i	$0.456206\pi$
$954$	−10.5245	−	15.3201i	−0.340744	−	0.496008i
$955$	−57.1708	+	12.5769i	−1.85000	+	0.406979i
$956$	−7.68765	−	4.43847i	−0.248636	−	0.143550i
$957$	−13.1453	−	20.8388i	−0.424926	−	0.673623i
$958$	22.2217	+	22.2217i	0.717951	+	0.717951i
$959$	−17.1371	+	12.9972i	−0.553387	+	0.419700i
$960$	−2.75525	+	2.72187i	−0.0889255	+	0.0878480i
$961$	12.1885	+	21.1110i	0.393176	+	0.681001i
$962$	−4.40825	+	1.18119i	−0.142128	+	0.0380830i
$963$	44.5050	−	15.7496i	1.43415	−	0.507522i
$964$	−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	$0.903226\pi$
$968$	23.7642	+	6.36761i	0.763812	+	0.204663i
$969$	−7.65302	+	2.37545i	−0.245850	+	0.0763103i
$970$	2.32829	+	10.5837i	0.0747568	+	0.339822i
$971$	−8.61828	+	4.97576i	−0.276574	+	0.159680i	−0.631871	−	0.775073i	$-0.717713\pi$
$971$	−8.61828	+	4.97576i	−0.276574	+	0.159680i	0.355298	+	0.934753i	$0.384380\pi$
$972$	−15.2905	+	3.03316i	−0.490444	+	0.0972886i
$973$	10.9101	+	26.7644i	0.349761	+	0.858028i
$974$	−26.6188			−0.852921
$975$	8.93473	−	27.5925i	0.286140	−	0.883667i
$976$	6.70029	−	11.6052i	0.214471	−	0.371475i
$977$	−24.4082	+	6.54016i	−0.780888	+	0.209238i	−0.627176	−	0.778877i	$-0.715789\pi$
$977$	−24.4082	+	6.54016i	−0.780888	+	0.209238i	−0.153712	+	0.988116i	$0.549123\pi$
$978$	−4.65481	−	7.37914i	−0.148844	−	0.235959i
$979$			2.25446i			0.0720527i
$980$	−15.6275	−	0.884191i	−0.499202	−	0.0282444i
$981$	−2.48391	−	31.6457i	−0.0793051	−	1.01037i
$982$	16.6258	+	4.45486i	0.530550	+	0.142160i
$983$	−5.90862	−	22.0513i	−0.188456	−	0.703326i	−0.993864	−	0.110606i	$-0.964721\pi$
$983$	−5.90862	−	22.0513i	−0.188456	−	0.703326i	0.805409	−	0.592720i	$-0.201946\pi$
$984$	2.13329	+	6.87284i	0.0680067	+	0.219098i
$985$	−12.2221	−	23.5721i	−0.389430	−	0.751070i
$986$		−	2.25818i		−	0.0719151i
$987$	6.03433	−	16.0724i	0.192075	−	0.511589i
$988$	11.5664	+	11.5664i	0.367975	+	0.367975i
$989$	−0.918842	−	1.59148i	−0.0292175	−	0.0506061i
$990$	−35.3067	−	18.8561i	−1.12212	−	0.599288i
$991$	−19.6593	+	34.0510i	−0.624500	+	1.08166i	0.364138	+	0.931345i	$0.381364\pi$
$991$	−19.6593	+	34.0510i	−0.624500	+	1.08166i	−0.988637	+	0.150320i	$0.951970\pi$
$992$	−0.666080	+	2.48585i	−0.0211481	+	0.0789257i
$993$	1.46333	+	37.3438i	0.0464373	+	1.18507i
$994$	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
$997$	2.97640	+	11.1081i	0.0942636	+	0.351797i	0.996907	−	0.0785932i	$-0.0250428\pi$
$997$	2.97640	+	11.1081i	0.0942636	+	0.351797i	−0.902643	+	0.430390i	$0.858376\pi$
$998$	10.4557	+	39.0211i	0.330969	+	1.23519i
$999$	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.53.2	yes	64
3.2	odd	2	inner	210.2.x.a.53.11	yes	64
5.2	odd	4	inner	210.2.x.a.137.3	yes	64
7.2	even	3	inner	210.2.x.a.23.15	yes	64
15.2	even	4	inner	210.2.x.a.137.15	yes	64
21.2	odd	6	inner	210.2.x.a.23.3	✓	64
35.2	odd	12	inner	210.2.x.a.107.11	yes	64
105.2	even	12	inner	210.2.x.a.107.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.3	✓	64	21.2	odd	6	inner
210.2.x.a.23.15	yes	64	7.2	even	3	inner
210.2.x.a.53.2	yes	64	1.1	even	1	trivial
210.2.x.a.53.11	yes	64	3.2	odd	2	inner
210.2.x.a.107.2	yes	64	105.2	even	12	inner
210.2.x.a.107.11	yes	64	35.2	odd	12	inner
210.2.x.a.137.3	yes	64	5.2	odd	4	inner
210.2.x.a.137.15	yes	64	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.53276 - 0.806628i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.13148 + 0.675868i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-2.45002 + 0.998710i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.69870 + 2.47273i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.53276 - 0.806628i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.13148 + 0.675868i) q^{5} +(1.17585 - 1.27176i) q^{6} +(-2.45002 + 0.998710i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.69870 + 2.47273i) q^{9} +(-1.20451 + 1.88392i) q^{10} +(5.16739 + 2.98339i) q^{11} +(0.924094 + 1.46494i) q^{12} +(2.36809 + 2.36809i) q^{13} +(-0.330568 - 2.62502i) q^{14} +(-2.72187 - 2.75525i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.914934 + 0.245156i) q^{17} +(-2.82813 + 1.00083i) 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} +(0.208474 + 0.0558604i) q^{23} +(-1.65420 + 0.513452i) q^{24} +(4.08640 + 2.88120i) q^{25} +(-2.90030 + 1.67449i) q^{26} +(-0.609122 - 5.16033i) q^{27} +(2.62113 + 0.360100i) q^{28} +2.38403 q^{29} +(3.36584 - 1.91601i) q^{30} +(1.28677 - 2.22875i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-5.51387 - 8.74099i) q^{33} -0.947209i q^{34} +(-5.89715 + 0.472840i) q^{35} +(-0.234751 - 2.99080i) q^{36} +(1.31630 + 0.352701i) q^{37} +(-1.26414 - 4.71784i) q^{38} +(-1.71954 - 5.53987i) q^{39} +(1.98509 - 1.02927i) q^{40} -4.15479i q^{41} +(-1.61073 + 4.29017i) q^{42} +(-6.02072 - 6.02072i) q^{43} +(-2.98339 - 5.16739i) q^{44} +(1.94950 + 6.41868i) q^{45} +(-0.107914 + 0.186912i) q^{46} +(0.969620 - 3.61867i) q^{47} +(-0.0678189 - 1.73072i) q^{48} +(5.00516 - 4.89371i) q^{49} +(-3.84066 + 3.20145i) q^{50} +(1.60012 + 0.362247i) q^{51} +(-0.866780 - 3.23487i) q^{52} +(1.60355 + 5.98451i) q^{53} +(5.14215 + 0.747224i) q^{54} +(8.99780 + 9.85151i) q^{55} +(-1.02623 + 2.43862i) q^{56} +(8.45331 - 0.331246i) q^{57} +(-0.617033 + 2.30280i) q^{58} +(2.02618 - 3.50944i) q^{59} +(0.979581 + 3.74706i) q^{60} +(-6.70029 - 11.6052i) q^{61} +(1.81977 + 1.81977i) q^{62} +(-6.63139 - 4.36173i) q^{63} -1.00000i q^{64} +(3.44701 + 6.64804i) q^{65} +(9.87024 - 3.06366i) q^{66} +(2.48740 + 9.28310i) q^{67} +(0.914934 + 0.245156i) q^{68} +(-0.274482 - 0.253781i) q^{69} +(1.06957 - 5.81859i) q^{70} +10.7537i q^{71} +(2.94965 + 0.547324i) q^{72} +(-12.8131 + 3.43327i) q^{73} +(-0.681365 + 1.18016i) q^{74} +(-3.93942 - 7.71239i) q^{75} +4.88427 q^{76} +(-15.6397 - 2.14864i) q^{77} +(5.79616 - 0.227124i) q^{78} +(-0.874016 + 0.504613i) q^{79} +(0.480420 + 2.18385i) q^{80} +(-3.22883 + 8.40087i) q^{81} +(4.01322 + 1.07534i) 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} +(-3.65415 - 1.92303i) q^{87} +(5.76347 - 1.54432i) q^{88} +(0.188917 + 0.327214i) q^{89} +(-6.70454 + 0.221800i) q^{90} +(-8.16688 - 3.43682i) q^{91} +(-0.152613 - 0.152613i) q^{92} +(-3.77008 + 2.37819i) q^{93} +(3.24441 + 1.87316i) q^{94} +(-10.6665 + 2.34650i) q^{95} +(1.68930 + 0.382436i) q^{96} +(3.42689 - 3.42689i) q^{97} +(3.43153 + 6.10120i) 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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