LMFDB - Embedded newform 456.2.bk.a.253.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.20
Character	$\chi$	$=$	456.253
Dual form			456.2.bk.a.301.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.116093 + 1.40944i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-1.97305 - 0.327251i) q^{4} +(0.0410365 - 0.00723583i) q^{5} +(-1.28473 - 0.591148i) q^{6} +(-1.18673 + 2.05547i) q^{7} +(0.690297 - 2.74290i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.00543445 + 0.0586785i) q^{10} +(-4.23984 + 2.44787i) q^{11} +(0.982337 - 1.74213i) q^{12} +(-1.16739 - 3.20738i) q^{13} +(-2.75929 - 1.91124i) q^{14} +(-0.00723583 + 0.0410365i) q^{15} +(3.78581 + 1.29136i) q^{16} +(2.30287 - 1.93233i) q^{17} +(0.994903 - 1.00507i) q^{18} +(-4.20938 - 1.13188i) q^{19} +(-0.0833347 + 0.000847406i) q^{20} +(-1.52563 - 1.81817i) q^{21} +(-2.95792 - 6.25998i) q^{22} +(-0.281659 + 1.59737i) q^{23} +(2.34139 + 1.58679i) q^{24} +(-4.69683 + 1.70951i) q^{25} +(4.65614 - 1.27301i) q^{26} +(0.866025 - 0.500000i) q^{27} +(3.01412 - 3.66718i) q^{28} +(-3.88126 + 4.62551i) q^{29} +(-0.0569984 - 0.0149625i) q^{30} +(4.72736 - 8.18803i) q^{31} +(-2.25960 + 5.18596i) q^{32} +(-0.850137 - 4.82137i) q^{33} +(2.45617 + 3.47008i) q^{34} +(-0.0338260 + 0.0929361i) q^{35} +(1.30109 + 1.51894i) q^{36} -5.19065i q^{37} +(2.08399 - 5.80146i) q^{38} +3.41322 q^{39} +(0.00848017 - 0.117554i) q^{40} +(-0.487044 - 0.177269i) q^{41} +(2.73972 - 1.93920i) q^{42} +(-10.2230 + 1.80259i) q^{43} +(9.16646 - 3.44227i) q^{44} +(-0.0360869 - 0.0208348i) q^{45} +(-2.21870 - 0.582424i) q^{46} +(4.77903 + 4.01008i) q^{47} +(-2.50831 + 3.11583i) q^{48} +(0.683363 + 1.18362i) q^{49} +(-1.86418 - 6.81837i) q^{50} +(1.02817 + 2.82488i) q^{51} +(1.25370 + 6.71033i) q^{52} +(2.10907 + 0.371886i) q^{53} +(0.604181 + 1.27866i) q^{54} +(-0.156276 + 0.131131i) q^{55} +(4.81875 + 4.67395i) q^{56} +(2.50331 - 3.56840i) q^{57} +(-6.06880 - 6.00740i) q^{58} +(8.37755 + 9.98398i) q^{59} +(0.0277058 - 0.0785988i) q^{60} +(-0.262558 - 0.0462961i) q^{61} +(10.9917 + 7.61351i) q^{62} +(2.23032 - 0.811768i) q^{63} +(-7.04698 - 3.78683i) q^{64} +(-0.0711136 - 0.123172i) q^{65} +(6.89412 - 0.638493i) q^{66} +(-8.74062 + 10.4167i) q^{67} +(-5.17602 + 3.05897i) q^{68} +(-1.40470 - 0.811005i) q^{69} +(-0.127061 - 0.0584649i) q^{70} +(1.81482 + 10.2924i) q^{71} +(-2.29190 + 1.65747i) q^{72} +(-2.97798 - 1.08389i) q^{73} +(7.31591 + 0.602596i) q^{74} -4.99826i q^{75} +(7.93488 + 3.61077i) q^{76} -11.6198i q^{77} +(-0.396250 + 4.81073i) q^{78} +(-10.9766 - 3.99514i) q^{79} +(0.164700 + 0.0255994i) q^{80} +(0.173648 + 0.984808i) q^{81} +(0.306393 - 0.665880i) q^{82} +(-7.53195 - 4.34857i) q^{83} +(2.41513 + 4.08659i) q^{84} +(0.0805194 - 0.0959593i) q^{85} +(-1.35383 - 14.6180i) q^{86} +(-3.01909 - 5.22921i) q^{87} +(3.78752 + 13.3192i) q^{88} +(-14.5178 + 5.28404i) q^{89} +(0.0335548 - 0.0484435i) q^{90} +(7.97804 + 1.40674i) q^{91} +(1.07847 - 3.05950i) q^{92} +(6.07738 + 7.24274i) q^{93} +(-6.20679 + 6.27022i) q^{94} +(-0.180928 - 0.0159899i) q^{95} +(-4.10038 - 3.89704i) q^{96} +(-4.09249 + 3.43400i) q^{97} +(-1.74757 + 0.825750i) q^{98} +(4.82137 + 0.850137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.116093	+	1.40944i	−0.0820898	+	0.996625i
$2$	−0.116093	+	1.40944i	−0.0820898	+	0.996625i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$3$	−0.342020	+	0.939693i	−0.197465	+	0.542532i
$4$	−1.97305	−	0.327251i	−0.986523	−	0.163626i
$5$	0.0410365	−	0.00723583i	0.0183521	−	0.00323596i	−0.164465	−	0.986383i	$-0.552590\pi$
$5$	0.0410365	−	0.00723583i	0.0183521	−	0.00323596i	0.182817	+	0.983147i	$0.441479\pi$
$6$	−1.28473	−	0.591148i	−0.524491	−	0.241335i
$7$	−1.18673	+	2.05547i	−0.448540	+	0.776895i	−0.998291	−	0.0584340i	$-0.981389\pi$
$7$	−1.18673	+	2.05547i	−0.448540	+	0.776895i	0.549751	+	0.835329i	$0.314723\pi$
$8$	0.690297	−	2.74290i	0.244057	−	0.969761i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	0.00543445	+	0.0586785i	0.00171852	+	0.0185558i
$11$	−4.23984	+	2.44787i	−1.27836	+	0.738061i	−0.976547	−	0.215306i	$-0.930925\pi$
$11$	−4.23984	+	2.44787i	−1.27836	+	0.738061i	−0.301813	+	0.953367i	$0.597592\pi$
$12$	0.982337	−	1.74213i	0.283576	−	0.502909i
$13$	−1.16739	−	3.20738i	−0.323776	−	0.889567i	−0.989650	−	0.143503i	$-0.954163\pi$
$13$	−1.16739	−	3.20738i	−0.323776	−	0.889567i	0.665874	−	0.746064i	$-0.268059\pi$
$14$	−2.75929	−	1.91124i	−0.737452	−	0.510802i
$15$	−0.00723583	+	0.0410365i	−0.00186828	+	0.0105956i
$16$	3.78581	+	1.29136i	0.946453	+	0.322840i
$17$	2.30287	−	1.93233i	0.558527	−	0.468660i	−0.319289	−	0.947657i	$-0.603444\pi$
$17$	2.30287	−	1.93233i	0.558527	−	0.468660i	0.877816	+	0.478997i	$0.159000\pi$
$18$	0.994903	−	1.00507i	0.234501	−	0.236898i
$19$	−4.20938	−	1.13188i	−0.965697	−	0.259670i
$19$	−4.20938	−	1.13188i	−0.965697	−	0.259670i
$20$	−0.0833347		0.000847406i	−0.0186342		0.000189486i
$21$	−1.52563	−	1.81817i	−0.332919	−	0.396757i
$22$	−2.95792	−	6.25998i	−0.630630	−	1.33463i
$23$	−0.281659	+	1.59737i	−0.0587300	+	0.333074i	−0.999989	−	0.00461020i	$-0.998533\pi$
$23$	−0.281659	+	1.59737i	−0.0587300	+	0.333074i	0.941259	+	0.337684i	$0.109644\pi$
$24$	2.34139	+	1.58679i	0.477933	+	0.323903i
$25$	−4.69683	+	1.70951i	−0.939366	+	0.341901i
$26$	4.65614	−	1.27301i	0.913143	−	0.249659i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	3.01412	−	3.66718i	0.569615	−	0.693031i
$29$	−3.88126	+	4.62551i	−0.720733	+	0.858936i	−0.994702	−	0.102803i	$-0.967219\pi$
$29$	−3.88126	+	4.62551i	−0.720733	+	0.858936i	0.273969	+	0.961738i	$0.411663\pi$
$30$	−0.0569984	−	0.0149625i	−0.0104064	−	0.00273177i
$31$	4.72736	−	8.18803i	0.849059	−	1.47061i	−0.0329892	−	0.999456i	$-0.510503\pi$
$31$	4.72736	−	8.18803i	0.849059	−	1.47061i	0.882049	−	0.471158i	$-0.156164\pi$
$32$	−2.25960	+	5.18596i	−0.399445	+	0.916757i
$33$	−0.850137	−	4.82137i	−0.147990	−	0.839292i
$34$	2.45617	+	3.47008i	0.421229	+	0.595114i
$35$	−0.0338260	+	0.0929361i	−0.00571764	+	0.0157091i
$36$	1.30109	+	1.51894i	0.216848	+	0.253156i
$37$		−	5.19065i		−	0.853338i	−0.904408	−	0.426669i	$-0.859687\pi$
$37$		−	5.19065i		−	0.853338i	0.904408	−	0.426669i	$-0.140313\pi$
$38$	2.08399	−	5.80146i	0.338068	−	0.941122i
$39$	3.41322			0.546553
$40$	0.00848017	−	0.117554i	0.00134083	−	0.0185869i
$41$	−0.487044	−	0.177269i	−0.0760635	−	0.0276848i	0.303708	−	0.952765i	$-0.401775\pi$
$41$	−0.487044	−	0.177269i	−0.0760635	−	0.0276848i	−0.379772	+	0.925080i	$0.623997\pi$
$42$	2.73972	−	1.93920i	0.422747	−	0.299225i
$43$	−10.2230	+	1.80259i	−1.55900	+	0.274893i	−0.885621	−	0.464409i	$-0.846267\pi$
$43$	−10.2230	+	1.80259i	−1.55900	+	0.274893i	−0.673375	+	0.739302i	$0.735156\pi$
$44$	9.16646	−	3.44227i	1.38190	−	0.518942i
$45$	−0.0360869	−	0.0208348i	−0.00537951	−	0.00310586i
$46$	−2.21870	−	0.582424i	−0.327129	−	0.0858737i
$47$	4.77903	+	4.01008i	0.697094	+	0.584931i	0.920945	−	0.389692i	$-0.127419\pi$
$47$	4.77903	+	4.01008i	0.697094	+	0.584931i	−0.223852	+	0.974623i	$0.571863\pi$
$48$	−2.50831	+	3.11583i	−0.362043	+	0.449731i
$49$	0.683363	+	1.18362i	0.0976232	+	0.169088i
$50$	−1.86418	−	6.81837i	−0.263635	−	0.964262i
$51$	1.02817	+	2.82488i	0.143973	+	0.395563i
$52$	1.25370	+	6.71033i	0.173856	+	0.930556i
$53$	2.10907	+	0.371886i	0.289703	+	0.0510825i	0.316611	−	0.948555i	$-0.397455\pi$
$53$	2.10907	+	0.371886i	0.289703	+	0.0510825i	−0.0269080	+	0.999638i	$0.508566\pi$
$54$	0.604181	+	1.27866i	0.0822186	+	0.174003i
$55$	−0.156276	+	0.131131i	−0.0210722	+	0.0176817i
$56$	4.81875	+	4.67395i	0.643933	+	0.624583i
$57$	2.50331	−	3.56840i	0.331571	−	0.472646i
$58$	−6.06880	−	6.00740i	−0.796872	−	0.788810i
$59$	8.37755	+	9.98398i	1.09066	+	1.29980i	0.950859	+	0.309624i	$0.100203\pi$
$59$	8.37755	+	9.98398i	1.09066	+	1.29980i	0.139806	+	0.990179i	$0.455352\pi$
$60$	0.0277058	−	0.0785988i	0.00357681	−	0.0101471i
$61$	−0.262558	−	0.0462961i	−0.0336172	−	0.00592761i	0.156814	−	0.987628i	$-0.449878\pi$
$61$	−0.262558	−	0.0462961i	−0.0336172	−	0.00592761i	−0.190431	+	0.981700i	$0.560989\pi$
$62$	10.9917	+	7.61351i	1.39595	+	0.966916i
$63$	2.23032	−	0.811768i	0.280993	−	0.102273i
$64$	−7.04698	−	3.78683i	−0.880873	−	0.473353i
$65$	−0.0711136	−	0.123172i	−0.00882056	−	0.0152777i
$66$	6.89412	−	0.638493i	0.848608	−	0.0785930i
$67$	−8.74062	+	10.4167i	−1.06784	+	1.27260i	−0.107365	+	0.994220i	$0.534241\pi$
$67$	−8.74062	+	10.4167i	−1.06784	+	1.27260i	−0.960472	+	0.278378i	$0.910203\pi$
$68$	−5.17602	+	3.05897i	−0.627684	+	0.370954i
$69$	−1.40470	−	0.811005i	−0.169106	−	0.0976335i
$70$	−0.127061	−	0.0584649i	−0.0151867	−	0.00698789i
$71$	1.81482	+	10.2924i	0.215380	+	1.22148i	0.880246	+	0.474517i	$0.157377\pi$
$71$	1.81482	+	10.2924i	0.215380	+	1.22148i	−0.664867	+	0.746962i	$0.731512\pi$
$72$	−2.29190	+	1.65747i	−0.270103	+	0.195334i
$73$	−2.97798	−	1.08389i	−0.348546	−	0.126860i	0.161814	−	0.986821i	$-0.448266\pi$
$73$	−2.97798	−	1.08389i	−0.348546	−	0.126860i	−0.510360	+	0.859961i	$0.670488\pi$
$74$	7.31591	+	0.602596i	0.850458	+	0.0700503i
$75$		−	4.99826i		−	0.577150i
$76$	7.93488	+	3.61077i	0.910193	+	0.414183i
$77$		−	11.6198i		−	1.32420i
$78$	−0.396250	+	4.81073i	−0.0448664	+	0.544708i
$79$	−10.9766	−	3.99514i	−1.23496	−	0.449488i	−0.359666	−	0.933081i	$-0.617109\pi$
$79$	−10.9766	−	3.99514i	−1.23496	−	0.449488i	−0.875293	+	0.483593i	$0.839332\pi$
$80$	0.164700	+	0.0255994i	0.0184141	+	0.00286210i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	0.306393	−	0.665880i	0.0338354	−	0.0735341i
$83$	−7.53195	−	4.34857i	−0.826739	−	0.477318i	0.0259957	−	0.999662i	$-0.491724\pi$
$83$	−7.53195	−	4.34857i	−0.826739	−	0.477318i	−0.852735	+	0.522344i	$0.825058\pi$
$84$	2.41513	+	4.08659i	0.263512	+	0.445884i
$85$	0.0805194	−	0.0959593i	0.00873356	−	0.0104082i
$86$	−1.35383	−	14.6180i	−0.145988	−	1.57630i
$87$	−3.01909	−	5.22921i	−0.323680	−	0.560630i
$88$	3.78752	+	13.3192i	0.403751	+	1.41983i
$89$	−14.5178	+	5.28404i	−1.53888	+	0.560107i	−0.965777	−	0.259375i	$-0.916484\pi$
$89$	−14.5178	+	5.28404i	−1.53888	+	0.560107i	−0.573105	+	0.819482i	$0.694261\pi$
$90$	0.0335548	−	0.0484435i	0.00353698	−	0.00510639i
$91$	7.97804	+	1.40674i	0.836326	+	0.147467i
$92$	1.07847	−	3.05950i	0.112438	−	0.318975i
$93$	6.07738	+	7.24274i	0.630195	+	0.751037i
$94$	−6.20679	+	6.27022i	−0.640181	+	0.646724i
$95$	−0.180928	−	0.0159899i	−0.0185628	−	0.00164053i
$96$	−4.10038	−	3.89704i	−0.418493	−	0.397739i
$97$	−4.09249	+	3.43400i	−0.415529	+	0.348670i	−0.826459	−	0.562997i	$-0.809648\pi$
$97$	−4.09249	+	3.43400i	−0.415529	+	0.348670i	0.410930	+	0.911667i	$0.365204\pi$
$98$	−1.74757	+	0.825750i	−0.176532	+	0.0834133i
$99$	4.82137	+	0.850137i	0.484566	+	0.0854420i
$100$	9.82650	−	1.83589i	0.982650	−	0.183589i
$101$	0.821669	+	2.25752i	0.0817591	+	0.224631i	0.973836	−	0.227253i	$-0.0729743\pi$
$101$	0.821669	+	2.25752i	0.0817591	+	0.224631i	−0.892077	+	0.451884i	$0.850752\pi$
$102$	−4.10087	+	1.12120i	−0.406047	+	0.111016i
$103$	6.33502	+	10.9726i	0.624208	+	1.08116i	0.988693	+	0.149951i	$0.0479116\pi$
$103$	6.33502	+	10.9726i	0.624208	+	1.08116i	−0.364485	+	0.931209i	$0.618755\pi$
$104$	−9.60336	+	0.987991i	−0.941687	+	0.0968804i
$105$	−0.0757622	−	0.0635721i	−0.00739364	−	0.00620400i
$106$	−0.768998	+	2.92944i	−0.0746917	+	0.284532i
$107$	3.50225	+	2.02202i	0.338575	+	0.195476i	0.659642	−	0.751580i	$-0.270708\pi$
$107$	3.50225	+	2.02202i	0.338575	+	0.195476i	−0.321067	+	0.947057i	$0.604041\pi$
$108$	−1.87233	+	0.703115i	−0.180165	+	0.0676573i
$109$	8.18094	−	1.44252i	0.783592	−	0.138168i	0.232481	−	0.972601i	$-0.425316\pi$
$109$	8.18094	−	1.44252i	0.783592	−	0.138168i	0.551110	+	0.834432i	$0.314204\pi$
$110$	−0.166679	−	0.235484i	−0.0158922	−	0.0224526i
$111$	4.87762	+	1.77531i	0.462963	+	0.168505i
$112$	−7.14708	+	6.24913i	−0.675335	+	0.590488i
$113$	−8.06543			−0.758732			−0.379366	−	0.925247i	$-0.623858\pi$
$113$	−8.06543			−0.758732			−0.379366	+	0.925247i	$0.623858\pi$
$114$	4.73883	+	3.94253i	0.443832	+	0.369252i
$115$			0.0675883i			0.00630264i
$116$	9.17161	−	7.85619i	0.851563	−	0.729429i
$117$	−1.16739	+	3.20738i	−0.107925	+	0.296522i
$118$	−15.0444	+	10.6486i	−1.38495	+	0.980283i
$119$	1.23898	+	7.02662i	0.113577	+	0.644130i
$120$	0.107564	+	0.0481745i	0.00981920	+	0.00439771i
$121$	6.48415	−	11.2309i	0.589469	−	1.02099i
$122$	0.0957327	−	0.364686i	0.00866723	−	0.0330171i
$123$	0.333158	−	0.397042i	0.0300398	−	0.0358000i
$124$	−12.0068	+	14.6083i	−1.07825	+	1.31187i
$125$	−0.360806	+	0.208311i	−0.0322715	+	0.0186319i
$126$	0.885216	+	3.23774i	0.0788613	+	0.288441i
$127$	−12.4309	+	4.52448i	−1.10307	+	0.401483i	−0.828445	−	0.560070i	$-0.810774\pi$
$127$	−12.4309	+	4.52448i	−1.10307	+	0.401483i	−0.274620	+	0.961553i	$0.588552\pi$
$128$	6.15541	−	9.49268i	0.544066	−	0.839042i
$129$	1.80259	−	10.2230i	0.158710	−	0.900087i
$130$	0.181860	−	0.0859310i	0.0159502	−	0.00753665i
$131$	−2.41434	−	2.87730i	−0.210942	−	0.251391i	0.650191	−	0.759771i	$-0.274689\pi$
$131$	−2.41434	−	2.87730i	−0.210942	−	0.251391i	−0.861133	+	0.508380i	$0.830245\pi$
$132$	0.0995616	+	9.79098i	0.00866572	+	0.852196i
$133$	7.32192	−	7.30902i	0.634891	−	0.633772i
$134$	−13.6669	−	13.5287i	−1.18064	−	1.16870i
$135$	0.0319207	−	0.0267846i	0.00274730	−	0.00230525i
$136$	−3.71054	−	7.65041i	−0.318176	−	0.656018i
$137$	−2.02646	+	11.4926i	−0.173132	+	0.981882i	0.767145	+	0.641473i	$0.221677\pi$
$137$	−2.02646	+	11.4926i	−0.173132	+	0.981882i	−0.940278	+	0.340409i	$0.889435\pi$
$138$	1.30614	−	1.88569i	0.111186	−	0.160521i
$139$	−3.35011	−	9.20436i	−0.284153	−	0.780704i	−0.996856	−	0.0792377i	$-0.974751\pi$
$139$	−3.35011	−	9.20436i	−0.284153	−	0.780704i	0.712703	−	0.701466i	$-0.247471\pi$
$140$	0.0971536	−	0.172298i	0.00821098	−	0.0145618i
$141$	−5.40277	+	3.11929i	−0.454996	+	0.262692i
$142$	−14.7172	+	1.36302i	−1.23504	+	0.114382i
$143$	12.8008	+	10.7411i	1.07046	+	0.898220i
$144$	−2.07003	−	3.42271i	−0.172502	−	0.285226i
$145$	−0.125804	+	0.217899i	−0.0104474	+	0.0180955i
$146$	1.87341	−	4.07145i	0.155044	−	0.336956i
$147$	−1.34596	+	0.237329i	−0.111013	+	0.0195746i
$148$	−1.69865	+	10.2414i	−0.139628	+	0.841837i
$149$	2.96694	−	8.15160i	0.243061	−	0.667805i	−0.756838	−	0.653603i	$-0.773257\pi$
$149$	2.96694	−	8.15160i	0.243061	−	0.667805i	0.999899	−	0.0142026i	$-0.00452098\pi$
$150$	7.04476	+	0.580261i	0.575202	+	0.0473781i
$151$	18.4553			1.50187			0.750937	−	0.660374i	$-0.229602\pi$
$151$	18.4553			1.50187			0.750937	+	0.660374i	$0.229602\pi$
$152$	−6.01034	+	10.7646i	−0.487503	+	0.873121i
$153$	−3.00618			−0.243035
$154$	16.3774	+	1.34897i	1.31973	+	0.108703i
$155$	0.134747	−	0.370214i	0.0108231	−	0.0297363i
$156$	−6.73444	−	1.11698i	−0.539187	−	0.0894300i
$157$	17.6276	−	3.10823i	1.40684	−	0.248064i	0.581889	−	0.813269i	$-0.302314\pi$
$157$	17.6276	−	3.10823i	1.40684	−	0.248064i	0.824951	+	0.565205i	$0.191203\pi$
$158$	6.90521	−	15.0070i	0.549349	−	1.19389i
$159$	−1.07080	+	1.85469i	−0.0849202	+	0.147086i
$160$	−0.0552013	+	0.229164i	−0.00436405	+	0.0181170i
$161$	−2.94909	−	2.47458i	−0.232421	−	0.195024i
$162$	−1.40819	+	0.130418i	−0.110638	+	0.0102466i
$163$	4.14121	−	2.39093i	0.324364	−	0.187272i	−0.328972	−	0.944340i	$-0.606702\pi$
$163$	4.14121	−	2.39093i	0.324364	−	0.187272i	0.653336	+	0.757068i	$0.273369\pi$
$164$	0.902948	+	0.509146i	0.0705084	+	0.0397576i
$165$	−0.0697732	−	0.191700i	−0.00543184	−	0.0149239i
$166$	7.00346	−	10.1110i	0.543574	−	0.784766i
$167$	−0.355724	+	2.01741i	−0.0275267	+	0.156112i	−0.995473	−	0.0950460i	$-0.969700\pi$
$167$	−0.355724	+	2.01741i	−0.0275267	+	0.156112i	0.967946	+	0.251158i	$0.0808113\pi$
$168$	−6.04019	+	2.92956i	−0.466011	+	0.226020i
$169$	1.03410	−	0.867710i	0.0795459	−	0.0667470i
$170$	0.125901	+	0.124628i	0.00965618	+	0.00955849i
$171$	2.49701	+	3.57280i	0.190951	+	0.273219i
$172$	20.7604	−	0.211106i	1.58296	−	0.0160967i
$173$	11.6498	+	13.8837i	0.885721	+	1.05556i	0.998083	+	0.0618942i	$0.0197142\pi$
$173$	11.6498	+	13.8837i	0.885721	+	1.05556i	−0.112361	+	0.993667i	$0.535841\pi$
$174$	7.72076	−	3.64815i	0.585309	−	0.276566i
$175$	2.06001	−	11.6829i	0.155722	−	0.883145i
$176$	−19.2123	+	3.79202i	−1.44818	+	0.285834i
$177$	−12.2472	+	4.45760i	−0.920553	+	0.335054i
$178$	−5.76214	−	21.0754i	−0.431890	−	1.57967i
$179$	17.7790	−	10.2647i	1.32886	−	0.767219i	0.343738	−	0.939066i	$-0.388307\pi$
$179$	17.7790	−	10.2647i	1.32886	−	0.767219i	0.985124	+	0.171847i	$0.0549734\pi$
$180$	0.0643828	+	0.0529174i	0.00479881	+	0.00394423i
$181$	−2.62332	+	3.12636i	−0.194990	+	0.232380i	−0.854677	−	0.519161i	$-0.826245\pi$
$181$	−2.62332	+	3.12636i	−0.194990	+	0.232380i	0.659686	+	0.751541i	$0.270689\pi$
$182$	−2.90891	+	11.0813i	−0.215623	+	0.821398i
$183$	0.133304	−	0.230890i	0.00985415	−	0.0170679i
$184$	4.18699	+	1.87522i	0.308669	+	0.138243i
$185$	−0.0375587	−	0.213006i	−0.00276137	−	0.0156605i
$186$	−10.9137	+	7.72488i	−0.800235	+	0.566416i
$187$	−5.03368	+	13.8299i	−0.368099	+	1.01134i
$188$	−8.11694	−	9.47602i	−0.591989	−	0.691110i
$189$			2.37345i			0.172643i
$190$	0.0435412	−	0.253151i	0.00315881	−	0.0183655i
$191$	8.73762			0.632232			0.316116	−	0.948721i	$-0.397621\pi$
$191$	8.73762			0.632232			0.316116	+	0.948721i	$0.397621\pi$
$192$	5.96866	−	5.32683i	0.430751	−	0.384431i
$193$	3.11206	+	1.13270i	0.224011	+	0.0815335i	0.451588	−	0.892227i	$-0.350858\pi$
$193$	3.11206	+	1.13270i	0.224011	+	0.0815335i	−0.227576	+	0.973760i	$0.573080\pi$
$194$	−4.36492	−	6.16678i	−0.313383	−	0.442749i
$195$	0.140067	−	0.0246975i	0.0100304	−	0.00176863i
$196$	−0.960965	−	2.55896i	−0.0686403	−	0.182783i
$197$	−2.18078	−	1.25908i	−0.155374	−	0.0897054i	0.420297	−	0.907387i	$-0.361926\pi$
$197$	−2.18078	−	1.25908i	−0.155374	−	0.0897054i	−0.575671	+	0.817681i	$0.695259\pi$
$198$	−1.75794	+	6.69673i	−0.124932	+	0.475916i
$199$	−13.9606	−	11.7143i	−0.989640	−	0.830406i	−0.00412434	−	0.999991i	$-0.501313\pi$
$199$	−13.9606	−	11.7143i	−0.989640	−	0.830406i	−0.985516	+	0.169585i	$0.945757\pi$
$200$	1.44680	+	14.0630i	0.102304	+	0.994404i
$201$	−6.79899	−	11.7762i	−0.479564	−	0.830629i
$202$	−3.27723	+	0.896013i	−0.230585	+	0.0630432i
$203$	−4.90160	−	13.4670i	−0.344025	−	0.945200i
$204$	−1.10419	−	5.91009i	−0.0773086	−	0.413789i
$205$	−0.0212692	−	0.00375034i	−0.00148551	−	0.000261935i
$206$	−16.2006	+	7.65500i	−1.12875	+	0.533349i
$207$	1.24253	−	1.04261i	0.0863619	−	0.0724662i
$208$	−0.277636	−	13.6501i	−0.0192506	−	0.946462i
$209$	20.6178	−	5.50504i	1.42616	−	0.380792i
$210$	0.0983965	−	0.0994021i	0.00679000	−	0.00685940i
$211$	7.89687	+	9.41113i	0.543643	+	0.647889i	0.966000	−	0.258541i	$-0.0832416\pi$
$211$	7.89687	+	9.41113i	0.543643	+	0.647889i	−0.422357	+	0.906430i	$0.638797\pi$
$212$	−4.03959	−	1.42394i	−0.277440	−	0.0977968i
$213$	−10.2924	−	1.81482i	−0.705221	−	0.124350i
$214$	−3.25651	+	4.70147i	−0.222610	+	0.321386i
$215$	−0.406473	+	0.147944i	−0.0277212	+	0.0100897i
$216$	−0.773635	−	2.72057i	−0.0526392	−	0.185111i
$217$	11.2202	+	19.4339i	0.761675	+	1.31926i
$218$	1.08340	+	11.6980i	0.0733771	+	0.792289i
$219$	2.03706	−	2.42767i	0.137652	−	0.164047i
$220$	0.351251	−	0.207586i	0.0236814	−	0.0139954i
$221$	−8.88607	−	5.13038i	−0.597742	−	0.345107i
$222$	−3.06844	+	6.66861i	−0.205940	+	0.447568i
$223$	−5.00455	−	28.3822i	−0.335130	−	1.90061i	−0.425950	−	0.904747i	$-0.640060\pi$
$223$	−5.00455	−	28.3822i	−0.335130	−	1.90061i	0.0908204	−	0.995867i	$-0.471051\pi$
$224$	−7.97806	−	10.7989i	−0.533056	−	0.721529i
$225$	4.69683	+	1.70951i	0.313122	+	0.113967i
$226$	0.936336	−	11.3677i	0.0622842	−	0.756171i
$227$			6.23350i			0.413732i	0.978369	+	0.206866i	$0.0663264\pi$
$227$			6.23350i			0.413732i	−0.978369	+	0.206866i	$0.933674\pi$
$228$	−6.10690	+	6.22140i	−0.404439	+	0.412022i
$229$		−	3.97342i		−	0.262571i	−0.991345	−	0.131285i	$-0.958090\pi$
$229$		−	3.97342i		−	0.262571i	0.991345	−	0.131285i	$-0.0419104\pi$
$230$	−0.0952617	−	0.00784650i	−0.00628137	−	0.000517383i
$231$	10.9191	+	3.97421i	0.718421	+	0.261484i
$232$	10.0081	+	13.8389i	0.657063	+	0.908567i
$233$	0.542503	+	3.07669i	0.0355405	+	0.201560i	0.997408	−	0.0719563i	$-0.0229242\pi$
$233$	0.542503	+	3.07669i	0.0355405	+	0.201560i	−0.961867	+	0.273517i	$0.911813\pi$
$234$	−4.38508	−	2.01772i	−0.286662	−	0.131903i
$235$	0.225131	+	0.129979i	0.0146859	+	0.00847892i
$236$	−13.2620	−	22.4404i	−0.863284	−	1.46075i
$237$	7.50841	−	8.94817i	0.487723	−	0.581246i
$238$	−10.0474	+	0.930535i	−0.651279	+	0.0603176i
$239$	−3.72390	−	6.44998i	−0.240879	−	0.417214i	0.720086	−	0.693885i	$-0.244102\pi$
$239$	−3.72390	−	6.44998i	−0.240879	−	0.417214i	−0.960965	+	0.276670i	$0.910769\pi$
$240$	−0.0803864	+	0.146012i	−0.00518892	+	0.00942505i
$241$	18.7705	−	6.83191i	1.20912	−	0.440082i	0.342719	−	0.939438i	$-0.388652\pi$
$241$	18.7705	−	6.83191i	1.20912	−	0.440082i	0.866397	+	0.499356i	$0.166430\pi$
$242$	15.0765	+	10.4429i	0.969154	+	0.671292i
$243$	−0.984808	−	0.173648i	−0.0631754	−	0.0111395i
$244$	0.502889	+	0.177267i	0.0321942	+	0.0113484i
$245$	0.0366073	+	0.0436268i	0.00233875	+	0.00278722i
$246$	0.520930	+	0.515659i	0.0332133	+	0.0328772i
$247$	1.28363	+	14.8224i	0.0816753	+	0.943127i
$248$	−19.1957	−	18.6188i	−1.21893	−	1.18230i
$249$	6.66240	−	5.59042i	0.422213	−	0.354278i
$250$	−0.251716	−	0.532718i	−0.0159199	−	0.0336920i
$251$	−7.23276	−	1.27533i	−0.456528	−	0.0804982i	−0.0593446	−	0.998238i	$-0.518901\pi$
$251$	−7.23276	−	1.27533i	−0.456528	−	0.0804982i	−0.397183	+	0.917739i	$0.630012\pi$
$252$	−4.66616	+	0.871783i	−0.293941	+	0.0549171i
$253$	−2.71596	−	7.46205i	−0.170751	−	0.469135i
$254$	−4.93385	−	18.0459i	−0.309577	−	1.13230i
$255$	0.0626330	+	0.108484i	0.00392223	+	0.00679350i
$256$	12.6648	+	9.77771i	0.791548	+	0.611107i
$257$	1.92782	+	1.61764i	0.120254	+	0.100905i	0.700932	−	0.713228i	$-0.252768\pi$
$257$	1.92782	+	1.61764i	0.120254	+	0.100905i	−0.580677	+	0.814134i	$0.697212\pi$
$258$	14.1995	+	3.72746i	0.884020	+	0.232062i
$259$	10.6692	+	6.15988i	0.662953	+	0.382756i
$260$	0.100002	+	0.266297i	0.00620187	+	0.0165150i
$261$	5.94644	−	1.04852i	0.368075	−	0.0649016i
$262$	4.33568	−	3.06884i	0.267859	−	0.189594i
$263$	−25.7079	−	9.35691i	−1.58522	−	0.576972i	−0.608887	−	0.793257i	$-0.708384\pi$
$263$	−25.7079	−	9.35691i	−1.58522	−	0.576972i	−0.976330	+	0.216285i	$0.930606\pi$
$264$	−13.8114	−	0.996334i	−0.850031	−	0.0613201i
$265$	0.0892397			0.00548195
$266$	9.45161	+	11.1683i	0.579515	+	0.684774i
$267$		−	15.4495i		−	0.945494i
$268$	20.6545	−	17.6922i	1.26167	−	1.08072i
$269$	5.31229	−	14.5954i	0.323896	−	0.889897i	−0.665725	−	0.746197i	$-0.731878\pi$
$269$	5.31229	−	14.5954i	0.323896	−	0.889897i	0.989621	−	0.143700i	$-0.0459001\pi$
$270$	0.0340456	+	0.0480998i	0.00207195	+	0.00292726i
$271$	−1.78542	−	10.1256i	−0.108457	−	0.615088i	−0.989783	−	0.142581i	$-0.954460\pi$
$271$	−1.78542	−	10.1256i	−0.108457	−	0.615088i	0.881327	−	0.472508i	$-0.156651\pi$
$272$	11.2136	−	4.34162i	0.679922	−	0.263250i
$273$	−4.05056	+	7.01577i	−0.245151	+	0.424614i
$274$	−15.9629	−	4.19039i	−0.964356	−	0.253150i
$275$	15.7292	−	18.7453i	0.948504	−	1.13038i
$276$	2.50614	+	2.05984i	0.150852	+	0.123988i
$277$	−18.5627	+	10.7172i	−1.11533	+	0.643935i	−0.940204	−	0.340612i	$-0.889366\pi$
$277$	−18.5627	+	10.7172i	−1.11533	+	0.643935i	−0.175123	+	0.984546i	$0.556032\pi$
$278$	13.3619	−	3.65323i	0.801395	−	0.219106i
$279$	−8.88454	+	3.23371i	−0.531903	+	0.193597i
$280$	0.231564	+	0.156935i	0.0138386	+	0.00937864i
$281$	3.25039	−	18.4339i	0.193902	−	1.09967i	−0.720071	−	0.693900i	$-0.755891\pi$
$281$	3.25039	−	18.4339i	0.193902	−	1.09967i	0.913974	−	0.405774i	$-0.132998\pi$
$282$	−3.76924	−	7.97701i	−0.224455	−	0.475024i
$283$	2.71913	+	3.24053i	0.161635	+	0.192629i	0.840783	−	0.541372i	$-0.182095\pi$
$283$	2.71913	+	3.24053i	0.161635	+	0.192629i	−0.679148	+	0.734001i	$0.737651\pi$
$284$	−0.212538	−	20.9012i	−0.0126118	−	1.24026i
$285$	0.0769066	−	0.164548i	0.00455555	−	0.00974697i
$286$	−16.6251	+	16.7950i	−0.983062	+	0.993109i
$287$	0.942359	−	0.790733i	0.0556257	−	0.0466755i
$288$	5.06443	−	2.52023i	0.298424	−	0.148506i
$289$	−1.38274	+	7.84191i	−0.0813377	+	0.461289i
$290$	−0.292510	−	0.202609i	−0.0171768	−	0.0118976i
$291$	−1.82720	−	5.02018i	−0.107112	−	0.294288i
$292$	5.52098	+	3.11312i	0.323091	+	0.182182i
$293$	−28.1669	+	16.2621i	−1.64553	+	0.950045i	−0.666706	+	0.745321i	$0.732296\pi$
$293$	−28.1669	+	16.2621i	−1.64553	+	0.950045i	−0.978820	+	0.204723i	$0.934371\pi$
$294$	−0.178246	−	1.92461i	−0.0103955	−	0.112245i
$295$	0.416027	+	0.349088i	0.0242221	+	0.0203247i
$296$	−14.2374	−	3.58309i	−0.827534	−	0.208263i
$297$	−2.44787	+	4.23984i	−0.142040	+	0.246020i
$298$	11.1448	+	5.12807i	0.645598	+	0.297061i
$299$	5.45217	−	0.961365i	0.315307	−	0.0555971i
$300$	−1.63569	+	9.86180i	−0.0944364	+	0.569371i
$301$	8.42674	−	23.1523i	0.485709	−	1.33448i
$302$	−2.14253	+	26.0117i	−0.123289	+	1.49681i
$303$	−2.40240			−0.138014
$304$	−14.4743	−	9.72090i	−0.830155	−	0.557532i
$305$	−0.0111095			−0.000636126
$306$	0.348995	−	4.23703i	0.0199507	−	0.242215i
$307$	1.48742	−	4.08666i	0.0848917	−	0.233238i	−0.889982	−	0.455995i	$-0.849283\pi$
$307$	1.48742	−	4.08666i	0.0848917	−	0.233238i	0.974874	+	0.222757i	$0.0715057\pi$
$308$	−3.80260	+	22.9264i	−0.216673	+	1.30635i
$309$	−12.4776	+	2.20013i	−0.709823	+	0.125161i
$310$	0.506152	+	0.232897i	0.0287475	+	0.0132277i
$311$	−14.0839	+	24.3940i	−0.798623	+	1.38326i	0.121889	+	0.992544i	$0.461105\pi$
$311$	−14.0839	+	24.3940i	−0.798623	+	1.38326i	−0.920513	+	0.390712i	$0.872229\pi$
$312$	2.35614	−	9.36212i	0.133390	−	0.530026i
$313$	−7.36582	−	6.18066i	−0.416341	−	0.349352i	0.410428	−	0.911893i	$-0.365379\pi$
$313$	−7.36582	−	6.18066i	−0.416341	−	0.349352i	−0.826769	+	0.562541i	$0.809824\pi$
$314$	2.33443	+	25.2060i	0.131739	+	1.42245i
$315$	0.0856504	−	0.0494503i	0.00482585	−	0.00278621i
$316$	20.3498	+	11.4747i	1.14477	+	0.645501i
$317$	0.0166987	+	0.0458793i	0.000937893	+	0.00257684i	0.940161	−	0.340731i	$-0.110675\pi$
$317$	0.0166987	+	0.0458793i	0.000937893	+	0.00257684i	−0.939223	+	0.343308i	$0.888452\pi$
$318$	−2.48976	−	1.72455i	−0.139619	−	0.0967079i
$319$	5.13328	−	29.1123i	0.287408	−	1.62997i
$320$	−0.316584	−	0.104407i	−0.0176976	−	0.00583654i
$321$	−3.09792	+	2.59946i	−0.172909	+	0.145088i
$322$	3.83014	−	3.86928i	0.213445	−	0.215627i
$323$	−11.8808	+	5.52736i	−0.661065	+	0.307551i
$324$	−0.0203364	−	1.99990i	−0.00112980	−	0.111105i
$325$	10.9661	+	13.0689i	0.608288	+	0.724930i
$326$	2.88911	+	6.11436i	0.160013	+	0.338643i
$327$	−1.44252	+	8.18094i	−0.0797715	+	0.452407i
$328$	−0.822437	+	1.21354i	−0.0454115	+	0.0670067i
$329$	−13.9140	+	5.06429i	−0.767104	+	0.279203i
$330$	0.278290	−	0.0760862i	0.0153194	−	0.00418841i
$331$	−18.5772	+	10.7255i	−1.02109	+	0.589529i	−0.914420	−	0.404766i	$-0.867353\pi$
$331$	−18.5772	+	10.7255i	−1.02109	+	0.589529i	−0.106673	+	0.994294i	$0.534020\pi$
$332$	13.4378	+	11.0448i	0.737495	+	0.606161i
$333$	−3.33649	+	3.97627i	−0.182838	+	0.217898i
$334$	−2.80212	−	0.735577i	−0.153325	−	0.0402490i
$335$	−0.283311	+	0.490709i	−0.0154789	+	0.0268103i
$336$	−3.42782	−	8.85339i	−0.187003	−	0.482992i
$337$	−0.765660	−	4.34228i	−0.0417082	−	0.236539i	0.956826	−	0.290661i	$-0.0938751\pi$
$337$	−0.765660	−	4.34228i	−0.0417082	−	0.236539i	−0.998534	+	0.0541220i	$0.982764\pi$
$338$	1.10294	+	1.55823i	0.0599918	+	0.0847567i
$339$	2.75854	−	7.57903i	0.149823	−	0.411636i
$340$	−0.190271	+	0.162982i	−0.0103189	+	0.00883894i
$341$			46.2879i			2.50663i
$342$	−5.32554	+	3.10462i	−0.287972	+	0.167878i
$343$	−19.8580			−1.07223
$344$	−2.11258	+	29.2850i	−0.113903	+	1.57894i
$345$	−0.0635123	−	0.0231166i	−0.00341938	−	0.00124455i
$346$	−20.9208	+	14.8080i	−1.12471	+	0.796081i
$347$	10.9964	−	1.93896i	0.590316	−	0.104089i	0.129492	−	0.991580i	$-0.458665\pi$
$347$	10.9964	−	1.93896i	0.590316	−	0.104089i	0.460823	+	0.887492i	$0.347554\pi$
$348$	4.24553	+	11.3055i	0.227584	+	0.606037i
$349$	20.5782	+	11.8808i	1.10153	+	0.635966i	0.936621	−	0.350343i	$-0.113935\pi$
$349$	20.5782	+	11.8808i	1.10153	+	0.635966i	0.164905	+	0.986310i	$0.447268\pi$
$350$	16.2272	+	4.25976i	0.867381	+	0.227694i
$351$	−2.61468	−	2.19398i	−0.139561	−	0.117106i
$352$	−3.11422	−	27.5189i	−0.165988	−	1.46676i
$353$	0.773591	+	1.33990i	0.0411741	+	0.0713156i	0.885878	−	0.463918i	$-0.153557\pi$
$353$	0.773591	+	1.33990i	0.0411741	+	0.0713156i	−0.844704	+	0.535234i	$0.820224\pi$
$354$	−4.86092	−	17.7791i	−0.258355	−	0.944951i
$355$	0.148948	+	0.409230i	0.00790532	+	0.0217197i
$356$	30.3735	−	5.67469i	1.60979	−	0.300758i
$357$	−7.02662	−	1.23898i	−0.371888	−	0.0655740i
$358$	12.4035	+	26.2500i	0.655543	+	1.38736i
$359$	17.1627	−	14.4012i	0.905812	−	0.760066i	−0.0655058	−	0.997852i	$-0.520866\pi$
$359$	17.1627	−	14.4012i	0.905812	−	0.760066i	0.971318	+	0.237786i	$0.0764216\pi$
$360$	−0.0820582	+	0.0846004i	−0.00432485	+	0.00445883i
$361$	16.4377	+	9.52899i	0.865143	+	0.501526i
$362$	−4.10187	−	4.06037i	−0.215589	−	0.213408i
$363$	8.33587	+	9.93430i	0.437520	+	0.521416i
$364$	−15.2807	−	5.38639i	−0.800925	−	0.282324i
$365$	−0.130048	−	0.0229311i	−0.00680705	−	0.00120027i
$366$	0.309950	+	0.214689i	0.0162014	+	0.0112220i
$367$	−3.97914	+	1.44829i	−0.207709	+	0.0756001i	−0.443780	−	0.896136i	$-0.646363\pi$
$367$	−3.97914	+	1.44829i	−0.207709	+	0.0756001i	0.236070	+	0.971736i	$0.424140\pi$
$368$	−3.12909	+	5.68361i	−0.163115	+	0.296279i
$369$	0.259151	+	0.448862i	0.0134908	+	0.0233668i
$370$	0.304579	−	0.0282083i	0.0158343	−	0.00146648i
$371$	−3.26729	+	3.89380i	−0.169629	+	0.202156i
$372$	−9.62075	−	16.2791i	−0.498813	−	0.844031i
$373$	13.1922	+	7.61650i	0.683064	+	0.394367i	0.801009	−	0.598653i	$-0.204297\pi$
$373$	13.1922	+	7.61650i	0.683064	+	0.394367i	−0.117944	+	0.993020i	$0.537630\pi$
$374$	−18.9081	−	8.70022i	−0.977713	−	0.449877i
$375$	−0.0723458	−	0.410293i	−0.00373592	−	0.0211875i
$376$	14.2982	−	10.3403i	0.737374	−	0.533258i
$377$	19.3667	+	7.04891i	0.997437	+	0.363037i
$378$	−3.34524	−	0.275540i	−0.172061	−	0.0141723i
$379$		−	26.5582i		−	1.36420i	−0.731259	−	0.682100i	$-0.761067\pi$
$379$		−	26.5582i		−	1.36420i	0.731259	−	0.682100i	$-0.238933\pi$
$380$	0.351746	+	0.0907576i	0.0180442	+	0.00465577i
$381$		−	13.2287i		−	0.677727i
$382$	−1.01437	+	12.3152i	−0.0518998	+	0.630098i
$383$	−29.7738	−	10.8368i	−1.52137	−	0.553734i	−0.559882	−	0.828573i	$-0.689153\pi$
$383$	−29.7738	−	10.8368i	−1.52137	−	0.553734i	−0.961490	+	0.274838i	$0.911376\pi$
$384$	6.81493	+	9.03088i	0.347773	+	0.460855i
$385$	−0.0840790	−	0.476836i	−0.00428506	−	0.0243018i
$386$	−1.95776	+	4.25477i	−0.0996473	+	0.216562i
$387$	8.98997	+	5.19036i	0.456986	+	0.263841i
$388$	9.19844	−	5.43617i	0.466980	−	0.275980i
$389$	10.5963	−	12.6282i	0.537253	−	0.640274i	−0.427316	−	0.904102i	$-0.640541\pi$
$389$	10.5963	−	12.6282i	0.537253	−	0.640274i	0.964570	+	0.263829i	$0.0849853\pi$
$390$	0.0185490	+	0.200283i	0.000939265	+	0.0101417i
$391$	2.43803	+	4.22278i	0.123296	+	0.213555i
$392$	3.71827	−	1.05735i	0.187801	−	0.0534040i
$393$	3.52954	−	1.28465i	0.178042	−	0.0648018i
$394$	2.02776	−	2.92751i	0.102157	−	0.147486i
$395$	−0.479347	−	0.0845218i	−0.0241186	−	0.00425275i
$396$	−9.23457	−	3.25516i	−0.464054	−	0.163578i
$397$	6.90727	+	8.23176i	0.346666	+	0.413140i	0.911000	−	0.412406i	$-0.135312\pi$
$397$	6.90727	+	8.23176i	0.346666	+	0.413140i	−0.564334	+	0.825546i	$0.690867\pi$
$398$	18.1314	−	18.3167i	0.908843	−	0.918132i
$399$	4.36399	+	9.38018i	0.218473	+	0.469596i
$400$	−19.9889	+	0.406565i	−0.999446	+	0.0203282i
$401$	−18.2141	+	15.2835i	−0.909570	+	0.763220i	−0.972037	−	0.234827i	$-0.924547\pi$
$401$	−18.2141	+	15.2835i	−0.909570	+	0.763220i	0.0624675	+	0.998047i	$0.480103\pi$
$402$	17.3872	−	8.21565i	0.867193	−	0.409759i
$403$	−31.7808	−	5.60381i	−1.58311	−	0.279146i
$404$	−0.882415	−	4.72307i	−0.0439018	−	0.234982i
$405$	0.0142518	+	0.0391565i	0.000708178	+	0.00194570i
$406$	19.5500	−	5.34509i	0.970251	−	0.265272i
$407$	12.7060	+	22.0075i	0.629815	+	1.09087i
$408$	8.45811	−	0.870168i	0.418739	−	0.0430797i
$409$	23.5162	+	19.7324i	1.16280	+	0.975707i	0.999940	−	0.0109421i	$-0.00348306\pi$
$409$	23.5162	+	19.7324i	1.16280	+	0.975707i	0.162862	+	0.986649i	$0.447928\pi$
$410$	0.00775508	−	0.0295423i	0.000382996	−	0.00145899i
$411$	−10.1065	−	5.83496i	−0.498515	−	0.287818i
$412$	−8.90849	−	23.7225i	−0.438890	−	1.16873i
$413$	−30.4636	+	5.37156i	−1.49902	+	0.264317i
$414$	1.32524	+	1.87231i	0.0651322	+	0.0920192i
$415$	−0.340550	−	0.123950i	−0.0167170	−	0.00608447i
$416$	19.2712	+	1.19336i	0.944848	+	0.0585093i
$417$	9.79508			0.479667
$418$	5.36546	+	29.6986i	0.262433	+	1.45261i
$419$			18.9017i			0.923410i	0.887034	+	0.461705i	$0.152762\pi$
$419$			18.9017i			0.923410i	−0.887034	+	0.461705i	$0.847238\pi$
$420$	0.128678	+	0.150224i	0.00627886	+	0.00733017i
$421$	−3.17715	+	8.72915i	−0.154845	+	0.425433i	−0.992722	−	0.120425i	$-0.961574\pi$
$421$	−3.17715	+	8.72915i	−0.154845	+	0.425433i	0.837877	+	0.545858i	$0.183796\pi$
$422$	−14.1812	+	10.0376i	−0.690330	+	0.488623i
$423$	−1.08332	−	6.14381i	−0.0526728	−	0.298722i
$424$	2.47593	−	5.52825i	0.120242	−	0.268476i
$425$	−7.51284	+	13.0126i	−0.364426	+	0.631205i
$426$	3.75275	−	14.2958i	0.181821	−	0.692633i
$427$	0.406745	−	0.484740i	0.0196838	−	0.0234582i
$428$	−6.24838	−	5.13566i	−0.302027	−	0.248241i
$429$	−14.4715	+	8.35513i	−0.698691	+	0.403389i
$430$	−0.161330	−	0.590075i	−0.00778002	−	0.0284559i
$431$	−5.14174	+	1.87144i	−0.247669	+	0.0901441i	−0.462872	−	0.886425i	$-0.653181\pi$
$431$	−5.14174	+	1.87144i	−0.247669	+	0.0901441i	0.215203	+	0.976569i	$0.430959\pi$
$432$	3.92429	−	0.774555i	0.188808	−	0.0372658i
$433$	−4.13052	+	23.4254i	−0.198500	+	1.12575i	0.708845	+	0.705364i	$0.249217\pi$
$433$	−4.13052	+	23.4254i	−0.198500	+	1.12575i	−0.907345	+	0.420386i	$0.861895\pi$
$434$	−28.6935	+	13.5580i	−1.37733	+	0.650806i
$435$	−0.161730	−	0.192743i	−0.00775438	−	0.00924131i
$436$	−16.6134	+	0.168937i	−0.795639	+	0.00809061i
$437$	2.99363	−	6.40512i	0.143205	−	0.306398i
$438$	3.18517	+	3.15294i	0.152193	+	0.150653i
$439$	−15.2565	+	12.8017i	−0.728153	+	0.610993i	−0.929627	−	0.368501i	$-0.879871\pi$
$439$	−15.2565	+	12.8017i	−0.728153	+	0.610993i	0.201475	+	0.979494i	$0.435427\pi$
$440$	0.251802	+	0.519167i	0.0120042	+	0.0247503i
$441$	0.237329	−	1.34596i	0.0113014	−	0.0640934i
$442$	8.26257	−	11.9288i	0.393010	−	0.567395i
$443$	2.54487	+	6.99196i	0.120910	+	0.332198i	0.985352	−	0.170536i	$-0.0545498\pi$
$443$	2.54487	+	6.99196i	0.120910	+	0.332198i	−0.864441	+	0.502734i	$0.832328\pi$
$444$	−9.04278	−	5.09897i	−0.429152	−	0.241986i
$445$	−0.557524	+	0.321887i	−0.0264292	+	0.0152589i
$446$	40.5840	−	3.75865i	1.92171	−	0.177977i
$447$	6.64525	+	5.57602i	0.314309	+	0.263737i
$448$	16.1465	−	9.99093i	0.762852	−	0.472027i
$449$	1.87400	−	3.24586i	0.0884395	−	0.153182i	−0.818412	−	0.574632i	$-0.805145\pi$
$449$	1.87400	−	3.24586i	0.0884395	−	0.153182i	0.906852	+	0.421450i	$0.138479\pi$
$450$	−2.95472	+	6.42144i	−0.139287	+	0.302710i
$451$	2.49892	−	0.440627i	0.117670	−	0.0207483i
$452$	15.9135	+	2.63942i	0.748506	+	0.124148i
$453$	−6.31210	+	17.3423i	−0.296568	+	0.814814i
$454$	−8.78575	−	0.723663i	−0.412335	−	0.0339632i
$455$	0.337570			0.0158255
$456$	−8.05972	−	9.32957i	−0.377431	−	0.436897i
$457$	4.64905			0.217473			0.108737	−	0.994071i	$-0.465319\pi$
$457$	4.64905			0.217473			0.108737	+	0.994071i	$0.465319\pi$
$458$	5.60030	+	0.461284i	0.261685	+	0.0215544i
$459$	1.02817	−	2.82488i	0.0479910	−	0.131854i
$460$	0.0221183	−	0.133355i	0.00103127	−	0.00621770i
$461$	−6.86149	+	1.20987i	−0.319571	+	0.0563491i	−0.331133	−	0.943584i	$-0.607431\pi$
$461$	−6.86149	+	1.20987i	−0.319571	+	0.0563491i	0.0115616	+	0.999933i	$0.496320\pi$
$462$	−6.86903	+	14.9284i	−0.319576	+	0.694531i
$463$	5.36310	−	9.28916i	0.249244	−	0.431704i	−0.714072	−	0.700072i	$-0.753151\pi$
$463$	5.36310	−	9.28916i	0.249244	−	0.431704i	0.963316	+	0.268368i	$0.0864845\pi$
$464$	−20.6669	+	12.4992i	−0.959439	+	0.580261i
$465$	0.301801	+	0.253241i	0.0139957	+	0.0117438i
$466$	−4.39939	+	0.407445i	−0.203798	+	0.0188745i
$467$	16.7166	−	9.65131i	0.773550	−	0.446609i	−0.0605896	−	0.998163i	$-0.519298\pi$
$467$	16.7166	−	9.65131i	0.773550	−	0.446609i	0.834139	+	0.551554i	$0.185965\pi$
$468$	3.35293	−	5.94627i	0.154989	−	0.274867i
$469$	−11.0384	−	30.3278i	−0.509707	−	1.40041i
$470$	−0.209334	+	0.302219i	−0.00965587	+	0.0139403i
$471$	−3.10823	+	17.6276i	−0.143220	+	0.812239i
$472$	33.1680	−	16.0869i	1.52668	−	0.740458i
$473$	38.9314	−	32.6673i	1.79007	−	1.50205i
$474$	11.7402	+	11.6215i	0.539247	+	0.533792i
$475$	21.7057	−	1.87972i	0.995925	−	0.0862476i
$476$	−0.145100	−	14.2693i	−0.00665066	−	0.654033i
$477$	−1.37660	−	1.64057i	−0.0630301	−	0.0751163i
$478$	9.52318	−	4.49982i	0.435580	−	0.205817i
$479$	6.41906	−	36.4043i	0.293294	−	1.66335i	−0.380761	−	0.924673i	$-0.624338\pi$
$479$	6.41906	−	36.4043i	0.293294	−	1.66335i	0.674055	−	0.738681i	$-0.264551\pi$
$480$	−0.196463	−	0.130251i	−0.00896728	−	0.00594511i
$481$	−16.6484	+	6.05952i	−0.759101	+	0.276290i
$482$	7.45006	+	27.2491i	0.339341	+	1.24116i
$483$	3.33399	−	1.92488i	0.151702	−	0.0875851i
$484$	−16.4688	+	20.0371i	−0.748584	+	0.910777i
$485$	−0.143093	+	0.170532i	−0.00649753	+	0.00774345i
$486$	0.359076	−	1.36787i	0.0162880	−	0.0620478i
$487$	−12.4068	+	21.4892i	−0.562204	+	0.973767i	0.435099	+	0.900382i	$0.356713\pi$
$487$	−12.4068	+	21.4892i	−0.562204	+	0.973767i	−0.997304	+	0.0733842i	$0.976620\pi$
$488$	−0.308229	+	0.688213i	−0.0139529	+	0.0311539i
$489$	0.830361	+	4.70921i	0.0375502	+	0.212958i
$490$	−0.0657392	+	0.0465310i	−0.00296980	+	0.00210206i
$491$	−1.44697	+	3.97552i	−0.0653008	+	0.179413i	−0.968051	−	0.250752i	$-0.919322\pi$
$491$	−1.44697	+	3.97552i	−0.0653008	+	0.179413i	0.902751	+	0.430164i	$0.141544\pi$
$492$	−0.787267	+	0.674355i	−0.0354927	+	0.0304023i
$493$			18.1518i			0.817517i
$494$	−21.0403	+	0.0884259i	−0.946649	+	0.00397847i
$495$	0.204003			0.00916926
$496$	28.4706	−	24.8936i	1.27837	−	1.11776i
$497$	−23.3093	−	8.48391i	−1.04557	−	0.380555i
$498$	7.10591	+	10.0393i	0.318423	+	0.449870i
$499$	−34.1670	+	6.02457i	−1.52953	+	0.269697i	−0.874169	−	0.485622i	$-0.838593\pi$
$499$	−34.1670	+	6.02457i	−1.52953	+	0.269697i	−0.655357	+	0.755319i	$0.727482\pi$
$500$	0.780056	−	0.292934i	0.0348852	−	0.0131004i
$501$	−1.77408	−	1.02427i	−0.0792600	−	0.0457608i
$502$	2.63717	−	10.0461i	0.117703	−	0.448379i
$503$	4.28289	+	3.59378i	0.190965	+	0.160239i	0.733257	−	0.679951i	$-0.237999\pi$
$503$	4.28289	+	3.59378i	0.190965	+	0.160239i	−0.542292	+	0.840190i	$0.682444\pi$
$504$	−0.687019	−	6.67789i	−0.0306023	−	0.297457i
$505$	0.0500534	+	0.0866950i	0.00222735	+	0.00385788i
$506$	10.8326	−	2.96170i	0.481568	−	0.131664i
$507$	0.461699	+	1.26851i	0.0205048	+	0.0563364i
$508$	26.0074	−	4.85898i	1.15389	−	0.215582i
$509$	−24.8024	−	4.37333i	−1.09935	−	0.193844i	−0.405591	−	0.914055i	$-0.632934\pi$
$509$	−24.8024	−	4.37333i	−1.09935	−	0.193844i	−0.693756	+	0.720210i	$0.744045\pi$
$510$	−0.160172	+	0.0756834i	−0.00709255	+	0.00335132i
$511$	5.76196	−	4.83486i	0.254894	−	0.213881i
$512$	−15.2514	+	16.7151i	−0.674022	+	0.738711i
$513$	−4.21137	+	1.12445i	−0.185936	+	0.0496459i
$514$	−2.50377	+	2.52936i	−0.110437	+	0.111565i
$515$	0.339362	+	0.404436i	0.0149541	+	0.0178216i
$516$	−6.90209	+	19.5806i	−0.303848	+	0.861987i
$517$	−30.0785	−	5.30365i	−1.32285	−	0.233254i
$518$	−9.92060	+	14.3225i	−0.435886	+	0.629295i
$519$	−17.0309	+	6.19875i	−0.747575	+	0.272095i
$520$	−0.386939	+	0.110032i	−0.0169684	+	0.00482522i
$521$	−12.5151	−	21.6768i	−0.548298	−	0.949680i	−0.998391	−	0.0566984i	$-0.981943\pi$
$521$	−12.5151	−	21.6768i	−0.548298	−	0.949680i	0.450093	−	0.892981i	$-0.351391\pi$
$522$	0.787486	+	8.50288i	0.0344673	+	0.372161i
$523$	−2.06651	+	2.46277i	−0.0903621	+	0.107689i	−0.809331	−	0.587353i	$-0.800170\pi$
$523$	−2.06651	+	2.46277i	−0.0903621	+	0.107689i	0.718969	+	0.695042i	$0.244614\pi$
$524$	3.82201	+	6.46715i	0.166965	+	0.282519i
$525$	10.2738	+	5.93157i	0.448385	+	0.258875i
$526$	16.1725	−	35.1475i	0.705155	−	1.53250i
$527$	−4.93553	−	27.9908i	−0.214995	−	1.21930i
$528$	3.00767	−	19.3506i	0.130892	−	0.842128i
$529$	19.1407	+	6.96664i	0.832203	+	0.302897i
$530$	−0.0103601	+	0.125778i	−0.000450012	+	0.00546345i
$531$		−	13.0332i		−	0.565591i
$532$	−16.8384	+	12.0249i	−0.730035	+	0.521346i
$533$			1.76908i			0.0766272i
$534$	21.7752	+	1.79357i	0.942303	+	0.0776154i
$535$	0.158351	+	0.0576350i	0.00684610	+	0.00249178i
$536$	22.5382	+	31.1652i	0.973503	+	1.34613i
$537$	3.56489	+	20.2175i	0.153836	+	0.872449i
$538$	19.9546	+	9.18178i	0.860305	+	0.395855i
$539$	−5.79469	−	3.34557i	−0.249595	−	0.144104i
$540$	−0.0717463	+	0.0424012i	−0.00308747	+	0.00182466i
$541$	−10.0026	+	11.9206i	−0.430045	+	0.512508i	−0.936935	−	0.349503i	$-0.886350\pi$
$541$	−10.0026	+	11.9206i	−0.430045	+	0.512508i	0.506890	+	0.862011i	$0.330795\pi$
$542$	14.4788	−	1.34094i	0.621916	−	0.0575981i
$543$	−2.04058	−	3.53440i	−0.0875699	−	0.151675i
$544$	4.81745	+	16.3089i	0.206546	+	0.699238i
$545$	0.325279	−	0.118392i	0.0139334	−	0.00507135i
$546$	−9.41808	−	6.52350i	−0.403056	−	0.279180i
$547$	25.1223	+	4.42973i	1.07415	+	0.189402i	0.682628	−	0.730767i	$-0.260837\pi$
$547$	25.1223	+	4.42973i	1.07415	+	0.189402i	0.391523	+	0.920168i	$0.371948\pi$
$548$	7.75928	−	22.0123i	0.331460	−	0.940320i
$549$	0.171373	+	0.204234i	0.00731402	+	0.00871650i
$550$	24.5943	+	24.3455i	1.04871	+	1.03810i
$551$	21.5732	−	15.0774i	0.919050	−	0.642319i
$552$	−3.19416	+	3.29312i	−0.135953	+	0.140164i
$553$	21.2381	−	17.8208i	0.903134	−	0.757819i
$554$	−12.9503	−	27.4073i	−0.550204	−	1.16442i
$555$	0.213006	+	0.0375587i	0.00904160	+	0.00159428i
$556$	3.59779	+	19.2569i	0.152580	+	0.816677i
$557$	6.93736	+	19.0603i	0.293946	+	0.807609i	0.995480	+	0.0949731i	$0.0302765\pi$
$557$	6.93736	+	19.0603i	0.293946	+	0.807609i	−0.701534	+	0.712636i	$0.747501\pi$
$558$	−3.52629	−	12.8976i	−0.149280	−	0.546000i
$559$	17.7159	+	30.6848i	0.749301	+	1.29783i
$560$	−0.248073	+	0.308157i	−0.0104830	+	0.0130220i
$561$	−11.2742	−	9.46022i	−0.475999	−	0.399411i
$562$	25.6041	+	6.72127i	1.08004	+	0.283520i
$563$	−37.4015	−	21.5938i	−1.57629	−	0.910069i	−0.995371	−	0.0961056i	$-0.969361\pi$
$563$	−37.4015	−	21.5938i	−1.57629	−	0.910069i	−0.580915	−	0.813964i	$-0.697305\pi$
$564$	11.6807	−	4.38644i	0.491846	−	0.184702i
$565$	−0.330977	+	0.0583601i	−0.0139243	+	0.00245523i
$566$	−4.88300	+	3.45625i	−0.205248	+	0.145277i
$567$	−2.23032	−	0.811768i	−0.0936644	−	0.0340911i
$568$	29.4837	+	2.12691i	1.23711	+	0.0892433i
$569$	33.3043			1.39619			0.698095	−	0.716005i	$-0.254031\pi$
$569$	33.3043			1.39619			0.698095	+	0.716005i	$0.254031\pi$
$570$	0.222992	+	0.127498i	0.00934011	+	0.00534030i
$571$		−	12.1571i		−	0.508757i	−0.967105	−	0.254378i	$-0.918129\pi$
$571$		−	12.1571i		−	0.508757i	0.967105	−	0.254378i	$-0.0818709\pi$
$572$	−21.7415	−	25.3818i	−0.909058	−	1.06127i
$573$	−2.98844	+	8.21067i	−0.124844	+	0.343006i
$574$	1.00509	+	1.42000i	0.0419517	+	0.0592696i
$575$	−1.40781	−	7.98406i	−0.0587096	−	0.332958i
$576$	2.96418	+	7.43059i	0.123507	+	0.309608i
$577$	−10.7070	+	18.5451i	−0.445740	+	0.772044i	−0.998103	−	0.0615590i	$-0.980393\pi$
$577$	−10.7070	+	18.5451i	−0.445740	+	0.772044i	0.552363	+	0.833603i	$0.313726\pi$
$578$	−10.8922	−	2.85928i	−0.453055	−	0.118930i
$579$	−2.12878	+	2.53698i	−0.0884690	+	0.105433i
$580$	0.319524	−	0.388754i	0.0132675	−	0.0161422i
$581$	17.8767	−	10.3211i	0.741652	−	0.428193i
$582$	7.28777	−	1.99252i	0.302088	−	0.0825925i
$583$	−9.85245	+	3.58600i	−0.408047	+	0.148517i
$584$	−5.02870	+	7.42008i	−0.208089	+	0.307045i
$585$	−0.0246975	+	0.140067i	−0.00102112	+	0.00579104i
$586$	−19.6506	−	41.5874i	−0.811757	−	1.71796i
$587$	18.8965	+	22.5199i	0.779941	+	0.929497i	0.998931	−	0.0462300i	$-0.0147207\pi$
$587$	18.8965	+	22.5199i	0.779941	+	0.929497i	−0.218990	+	0.975727i	$0.570276\pi$
$588$	2.73331	−	0.0277942i	0.112720	−	0.00114621i
$589$	−29.1671	+	29.1157i	−1.20181	+	1.19969i
$590$	−0.540317	+	0.545839i	−0.0222445	+	0.0224719i
$591$	1.92902	−	1.61864i	0.0793491	−	0.0665818i
$592$	6.70301	−	19.6508i	0.275492	−	0.807644i
$593$	2.44482	−	13.8653i	0.100397	−	0.569378i	−0.892563	−	0.450923i	$-0.851095\pi$
$593$	2.44482	−	13.8653i	0.100397	−	0.569378i	0.992959	−	0.118455i	$-0.0377940\pi$
$594$	−5.69162	−	3.94234i	−0.233530	−	0.161756i
$595$	0.101687	+	0.279383i	0.00416876	+	0.0114536i
$596$	−8.52153	+	15.1125i	−0.349055	+	0.619034i
$597$	15.7827	−	9.11213i	0.645942	−	0.372935i
$598$	0.722030	+	7.79612i	0.0295260	+	0.318807i
$599$	33.8902	+	28.4372i	1.38472	+	1.16191i	0.967430	+	0.253139i	$0.0814629\pi$
$599$	33.8902	+	28.4372i	1.38472	+	1.16191i	0.417285	+	0.908775i	$0.362982\pi$
$600$	−13.7097	−	3.45028i	−0.559697	−	0.140857i
$601$	−21.0133	+	36.3961i	−0.857151	+	1.48463i	0.0174834	+	0.999847i	$0.494435\pi$
$601$	−21.0133	+	36.3961i	−0.857151	+	1.48463i	−0.874635	+	0.484783i	$0.838899\pi$
$602$	31.6535	+	14.5648i	1.29010	+	0.593617i
$603$	13.3914	−	2.36127i	0.545340	−	0.0961582i
$604$	−36.4132	−	6.03953i	−1.48163	−	0.245745i
$605$	0.184822	−	0.507794i	0.00751408	−	0.0206448i
$606$	0.278901	−	3.38604i	0.0113296	−	0.137548i
$607$	−6.29523			−0.255515			−0.127758	−	0.991805i	$-0.540778\pi$
$607$	−6.29523			−0.255515			−0.127758	+	0.991805i	$0.540778\pi$
$608$	15.3814	−	19.2721i	0.623798	−	0.781586i
$609$	14.3313			0.580734
$610$	0.00128973	−	0.0156581i	5.22194e−5	−	0.000633979i
$611$	7.28286	−	20.0095i	0.294633	−	0.809498i
$612$	5.93133	+	0.983775i	0.239760	+	0.0397668i
$613$	−14.6790	+	2.58830i	−0.592879	+	0.104541i	−0.462034	−	0.886862i	$-0.652880\pi$
$613$	−14.6790	+	2.58830i	−0.592879	+	0.104541i	−0.130845	+	0.991403i	$0.541769\pi$
$614$	5.58722	+	2.57086i	0.225482	+	0.103752i
$615$	0.0107987	−	0.0187039i	0.000435445	−	0.000754212i
$616$	−31.8720	−	8.02112i	−1.28416	−	0.323180i
$617$	−36.4509	−	30.5860i	−1.46746	−	1.23134i	−0.918455	−	0.395526i	$-0.870562\pi$
$617$	−36.4509	−	30.5860i	−1.46746	−	1.23134i	−0.549005	−	0.835819i	$-0.684993\pi$
$618$	−1.65240	−	17.8418i	−0.0664693	−	0.717702i
$619$	7.05628	−	4.07394i	0.283616	−	0.163746i	−0.351443	−	0.936209i	$-0.614309\pi$
$619$	7.05628	−	4.07394i	0.283616	−	0.163746i	0.635059	+	0.772463i	$0.280976\pi$
$620$	−0.387015	+	0.686353i	−0.0155429	+	0.0275646i
$621$	0.554760	+	1.52419i	0.0222617	+	0.0611636i
$622$	−32.7468	−	22.6823i	−1.31303	−	0.909479i
$623$	6.36745	−	36.1116i	0.255106	−	1.44678i
$624$	12.9218	+	4.40770i	0.517287	+	0.176449i
$625$	19.1312	−	16.0530i	0.765246	−	0.642118i
$626$	9.56639	−	9.66416i	0.382350	−	0.386258i
$627$	−1.87865	+	21.2572i	−0.0750260	+	0.848931i
$628$	−35.7973	+	0.364012i	−1.42847	+	0.0145257i
$629$	−10.0301	−	11.9534i	−0.399925	−	0.476612i
$630$	0.0597539	+	0.126460i	0.00238065	+	0.00503829i
$631$	7.38602	−	41.8882i	0.294033	−	1.66754i	−0.377074	−	0.926183i	$-0.623070\pi$
$631$	7.38602	−	41.8882i	0.294033	−	1.66754i	0.671107	−	0.741361i	$-0.265819\pi$
$632$	−18.5353	+	27.3497i	−0.737296	+	1.08791i
$633$	−11.5445	+	4.20184i	−0.458851	+	0.167008i
$634$	−0.0666028	+	0.0182096i	−0.00264513	+	0.000723195i
$635$	−0.477382	+	0.275617i	−0.0189443	+	0.0109375i
$636$	2.71969	−	3.30896i	0.107843	−	0.131209i
$637$	2.99856	−	3.57355i	0.118807	−	0.141589i
$638$	40.4361	+	10.6148i	1.60088	+	0.420242i
$639$	5.22557	−	9.05095i	0.206720	−	0.358050i
$640$	0.183909	−	0.434085i	0.00726963	−	0.0171587i
$641$	6.68302	+	37.9013i	0.263963	+	1.49701i	0.771971	+	0.635658i	$0.219271\pi$
$641$	6.68302	+	37.9013i	0.263963	+	1.49701i	−0.508008	+	0.861352i	$0.669618\pi$
$642$	−3.30414	−	4.66811i	−0.130404	−	0.184236i
$643$	−0.989671	+	2.71910i	−0.0390288	+	0.107231i	−0.957676	−	0.287848i	$-0.907060\pi$
$643$	−0.989671	+	2.71910i	−0.0390288	+	0.107231i	0.918647	+	0.395078i	$0.129283\pi$
$644$	5.00888	+	5.84755i	0.197377	+	0.230426i
$645$		−	0.432560i		−	0.0170320i
$646$	−6.41122	−	17.3870i	−0.252246	−	0.684081i
$647$	−25.3253			−0.995639			−0.497820	−	0.867281i	$-0.665866\pi$
$647$	−25.3253			−0.995639			−0.497820	+	0.867281i	$0.665866\pi$
$648$	2.82110	+	0.203510i	0.110823	+	0.00799463i
$649$	−59.9590	−	21.8233i	−2.35360	−	0.856639i
$650$	−19.6929	+	13.9388i	−0.772417	+	0.546726i
$651$	−22.0994	+	3.89672i	−0.866145	+	0.152725i
$652$	−8.95322	+	3.36219i	−0.350635	+	0.131674i
$653$	−6.13708	−	3.54324i	−0.240162	−	0.138658i	0.375089	−	0.926989i	$-0.377612\pi$
$653$	−6.13708	−	3.54324i	−0.240162	−	0.138658i	−0.615251	+	0.788331i	$0.710945\pi$
$654$	−11.3631	−	2.98289i	−0.444331	−	0.116640i
$655$	−0.119896	−	0.100605i	−0.00468472	−	0.00393095i
$656$	−1.61494	−	1.30006i	−0.0630527	−	0.0507588i
$657$	1.58455	+	2.74452i	0.0618191	+	0.107074i
$658$	−5.52250	−	20.1989i	−0.215289	−	0.787435i
$659$	−7.50469	−	20.6190i	−0.292341	−	0.803201i	−0.995723	−	0.0923886i	$-0.970550\pi$
$659$	−7.50469	−	20.6190i	−0.292341	−	0.803201i	0.703382	−	0.710812i	$-0.251672\pi$
$660$	0.0749316	+	0.401067i	0.00291671	+	0.0156115i
$661$	16.6606	+	2.93772i	0.648023	+	0.114264i	0.487992	−	0.872848i	$-0.337729\pi$
$661$	16.6606	+	2.93772i	0.648023	+	0.114264i	0.160031	+	0.987112i	$0.448841\pi$
$662$	−12.9603	−	27.4286i	−0.503717	−	1.06604i
$663$	7.86019	−	6.59549i	0.305265	−	0.256147i
$664$	−17.1270	+	17.6576i	−0.664656	+	0.685247i
$665$	0.247579	−	0.352916i	0.00960069	−	0.0136855i
$666$	−5.21697	−	5.16419i	−0.202154	−	0.200108i
$667$	−6.29545	−	7.50262i	−0.243761	−	0.290503i
$668$	1.36206	−	3.86403i	0.0526996	−	0.149504i
$669$	28.3822	+	5.00455i	1.09732	+	0.193487i
$670$	−0.658734	−	0.456277i	−0.0254491	−	0.0176275i
$671$	1.22653	−	0.446421i	0.0473498	−	0.0172339i
$672$	12.8763	−	3.80349i	0.496713	−	0.146723i
$673$	0.240496	+	0.416552i	0.00927045	+	0.0160569i	0.870623	−	0.491950i	$-0.163716\pi$
$673$	0.240496	+	0.416552i	0.00927045	+	0.0160569i	−0.861353	+	0.508007i	$0.830382\pi$
$674$	6.20907	−	0.575047i	0.239164	−	0.0221500i
$675$	−3.21282	+	3.82889i	−0.123662	+	0.147374i
$676$	−2.32428	+	1.37362i	−0.0893953	+	0.0528316i
$677$	39.8407	+	23.0020i	1.53120	+	0.884040i	0.999307	+	0.0372297i	$0.0118533\pi$
$677$	39.8407	+	23.0020i	1.53120	+	0.884040i	0.531895	+	0.846810i	$0.321480\pi$
$678$	10.3619	+	4.76787i	0.397948	+	0.183109i
$679$	−2.20183	−	12.4872i	−0.0844985	−	0.479215i
$680$	−0.207624	−	0.287097i	−0.00796203	−	0.0110097i
$681$	−5.85757	−	2.13198i	−0.224463	−	0.0816977i
$682$	−65.2401	−	5.37368i	−2.49817	−	0.205769i
$683$		−	24.6012i		−	0.941339i	−0.882310	−	0.470669i	$-0.844012\pi$
$683$		−	24.6012i		−	0.941339i	0.882310	−	0.470669i	$-0.155988\pi$
$684$	−3.75752	−	7.86645i	−0.143672	−	0.300781i
$685$			0.486280i			0.0185798i
$686$	2.30537	−	27.9887i	0.0880194	−	1.06861i
$687$	3.73379	+	1.35899i	0.142453	+	0.0518487i
$688$	−41.0302	−	6.37733i	−1.56426	−	0.243133i
$689$	−1.26933	−	7.19872i	−0.0483576	−	0.274250i
$690$	0.0399547	−	0.0868331i	0.00152105	−	0.00330568i
$691$	1.35596	+	0.782865i	0.0515832	+	0.0297816i	0.525570	−	0.850750i	$-0.323852\pi$
$691$	1.35596	+	0.782865i	0.0515832	+	0.0297816i	−0.473987	+	0.880532i	$0.657185\pi$
$692$	−18.4422	−	31.2057i	−0.701067	−	1.18626i
$693$	−7.46907	+	8.90129i	−0.283727	+	0.338132i
$694$	1.45625	+	15.7238i	0.0552784	+	0.596868i
$695$	−0.204078	−	0.353473i	−0.00774112	−	0.0134080i
$696$	−16.4273	+	4.67134i	−0.622674	+	0.177067i
$697$	−1.46414	+	0.532904i	−0.0554583	+	0.0201852i
$698$	−19.1343	+	27.6245i	−0.724244	+	1.04560i
$699$	−3.07669	−	0.542503i	−0.116371	−	0.0205193i
$700$	−7.88774	+	22.3768i	−0.298129	+	0.845762i
$701$	−15.8308	−	18.8665i	−0.597922	−	0.712576i	0.379185	−	0.925321i	$-0.376204\pi$
$701$	−15.8308	−	18.8665i	−0.597922	−	0.712576i	−0.977108	+	0.212744i	$0.931760\pi$
$702$	3.39582	−	3.43053i	0.128167	−	0.129477i
$703$	−5.87518	+	21.8494i	−0.221587	+	0.824066i
$704$	39.1477	−	1.19457i	1.47544	−	0.0450222i
$705$	−0.199140	+	0.167098i	−0.00750004	+	0.00629328i
$706$	−1.97832	+	0.934778i	−0.0744549	+	0.0351809i
$707$	−5.61535	−	0.990138i	−0.211187	−	0.0372380i
$708$	25.6230	−	4.78715i	0.962970	−	0.179912i
$709$	−9.53648	−	26.2013i	−0.358150	−	0.984009i	−0.979671	−	0.200611i	$-0.935707\pi$
$709$	−9.53648	−	26.2013i	−0.358150	−	0.984009i	0.621521	−	0.783398i	$-0.286515\pi$
$710$	−0.594078	+	0.162424i	−0.0222953	+	0.00609568i
$711$	5.84050	+	10.1160i	0.219036	+	0.379381i
$712$	4.47201	+	43.4684i	0.167596	+	1.62905i
$713$	11.7478	+	9.85757i	0.439958	+	0.369169i
$714$	2.56201	−	9.75977i	0.0958809	−	0.365250i
$715$	0.603021	+	0.348154i	0.0225517	+	0.0130202i
$716$	−38.4378	+	14.4345i	−1.43649	+	0.539443i
$717$	7.33465	−	1.29330i	0.273917	−	0.0482990i
$718$	18.3052	+	25.8617i	0.683143	+	0.965148i
$719$	−25.7009	−	9.35436i	−0.958482	−	0.348859i	−0.185043	−	0.982730i	$-0.559243\pi$
$719$	−25.7009	−	9.35436i	−0.958482	−	0.348859i	−0.773438	+	0.633871i	$0.781465\pi$
$720$	−0.109713	−	0.125478i	−0.00408876	−	0.00467628i
$721$	−30.0717			−1.11993
$722$	−15.3388	+	22.0617i	−0.570853	+	0.821052i
$723$			19.9752i			0.742885i
$724$	6.19904	−	5.30996i	0.230386	−	0.197343i
$725$	10.3223	−	28.3603i	0.383361	−	1.05327i
$726$	−14.9695	+	10.5956i	−0.555572	+	0.393240i
$727$	6.55780	+	37.1911i	0.243215	+	1.37934i	0.824601	+	0.565715i	$0.191400\pi$
$727$	6.55780	+	37.1911i	0.243215	+	1.37934i	−0.581386	+	0.813628i	$0.697489\pi$
$728$	9.36577	−	20.9119i	0.347119	−	0.775046i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	0.0474176	−	0.180633i	0.00175500	−	0.00668555i
$731$	−20.0590	+	23.9054i	−0.741910	+	0.884174i
$732$	−0.338575	+	0.411932i	−0.0125141	+	0.0152255i
$733$	7.47397	−	4.31510i	0.276057	−	0.159382i	−0.355580	−	0.934646i	$-0.615717\pi$
$733$	7.47397	−	4.31510i	0.276057	−	0.159382i	0.631637	+	0.775264i	$0.282383\pi$
$734$	−1.57933	−	5.77650i	−0.0582941	−	0.213214i
$735$	−0.0535162	+	0.0194783i	−0.00197398	+	0.000718468i
$736$	−7.64745	−	5.07009i	−0.281889	−	0.186886i
$737$	11.5602	−	65.5609i	0.425824	−	2.41497i
$738$	−0.662730	+	0.313148i	−0.0243954	+	0.0115271i
$739$	−5.65966	−	6.74492i	−0.208194	−	0.248116i	0.651835	−	0.758360i	$-0.273999\pi$
$739$	−5.65966	−	6.74492i	−0.208194	−	0.248116i	−0.860029	+	0.510245i	$0.829555\pi$
$740$	0.00439859	+	0.432561i	0.000161695	+	0.0159013i
$741$	−14.3675	−	3.86335i	−0.527805	−	0.141924i
$742$	−5.10878	−	5.05709i	−0.187549	−	0.185652i
$743$	−35.4297	+	29.7290i	−1.29979	+	1.09065i	−0.309607	+	0.950865i	$0.600197\pi$
$743$	−35.4297	+	29.7290i	−1.29979	+	1.09065i	−0.990182	+	0.139787i	$0.955358\pi$
$744$	24.0613	−	11.6700i	0.882130	−	0.427843i
$745$	0.0627691	−	0.355981i	0.00229968	−	0.0130421i
$746$	−12.2665	+	17.7093i	−0.449109	+	0.648385i
$747$	2.97460	+	8.17265i	0.108835	+	0.299022i
$748$	14.4575	−	25.6398i	0.528619	−	0.937482i
$749$	−8.31242	+	4.79918i	−0.303729	+	0.175358i
$750$	0.586683	−	0.0543351i	0.0214226	−	0.00198404i
$751$	−12.9771	−	10.8891i	−0.473542	−	0.397349i	0.374542	−	0.927210i	$-0.377800\pi$
$751$	−12.9771	−	10.8891i	−0.473542	−	0.397349i	−0.848085	+	0.529861i	$0.822244\pi$
$752$	12.9141	+	21.3529i	0.470927	+	0.778660i
$753$	3.67217	−	6.36038i	0.133821	−	0.231785i
$754$	−12.1833	+	26.4779i	−0.443691	+	0.964268i
$755$	0.757342	−	0.133540i	0.0275625	−	0.00486001i
$756$	0.776715	−	4.68293i	0.0282488	−	0.170316i
$757$	15.6394	−	42.9689i	0.568424	−	1.56173i	−0.238540	−	0.971133i	$-0.576669\pi$
$757$	15.6394	−	42.9689i	0.568424	−	1.56173i	0.806964	−	0.590600i	$-0.201109\pi$
$758$	37.4321	+	3.08320i	1.35960	+	0.111987i
$759$	7.94094			0.288238
$760$	−0.168753	+	0.485229i	−0.00612130	+	0.0176011i
$761$	22.3198			0.809093			0.404547	−	0.914517i	$-0.367429\pi$
$761$	22.3198			0.809093			0.404547	+	0.914517i	$0.367429\pi$
$762$	18.6451	+	1.53575i	0.675440	+	0.0556345i
$763$	−6.74347	+	18.5275i	−0.244130	+	0.670742i
$764$	−17.2397	−	2.85939i	−0.623711	−	0.103449i
$765$	−0.123363	+	0.0217522i	−0.00446020	+	0.000786453i
$766$	18.7303	−	40.7064i	0.676754	−	1.47078i
$767$	22.2425	−	38.5252i	0.803131	−	1.39106i
$768$	−13.5196	+	8.55682i	−0.487848	+	0.308767i
$769$	−38.4981	−	32.3038i	−1.38828	−	1.16490i	−0.966032	−	0.258423i	$-0.916797\pi$
$769$	−38.4981	−	32.3038i	−1.38828	−	1.16490i	−0.422246	−	0.906481i	$-0.638758\pi$
$770$	0.681833	−	0.0631473i	0.0245715	−	0.00227567i
$771$	−2.17944	+	1.25830i	−0.0784905	+	0.0453165i
$772$	−5.76957	−	3.25329i	−0.207651	−	0.117089i
$773$	6.87035	+	18.8761i	0.247109	+	0.678927i	0.999789	+	0.0205405i	$0.00653871\pi$
$773$	6.87035	+	18.8761i	0.247109	+	0.678927i	−0.752680	+	0.658387i	$0.771239\pi$
$774$	−8.35918	+	12.0683i	−0.300464	+	0.433785i
$775$	−8.20613	+	46.5393i	−0.294773	+	1.67174i
$776$	6.59409	+	13.5958i	0.236714	+	0.488059i
$777$	−9.43748	+	7.91899i	−0.338568	+	0.284092i
$778$	16.5685	+	16.4009i	0.594010	+	0.588000i
$779$	1.84950	+	1.29747i	0.0662653	+	0.0464866i
$780$	−0.284440	+	0.00289238i	−0.0101846	+	0.000103564i
$781$	−32.8889	−	39.1955i	−1.17686	−	1.40253i
$782$	−6.23480	+	2.94602i	−0.222956	+	0.105349i
$783$	−1.04852	+	5.94644i	−0.0374710	+	0.212508i
$784$	1.05860	+	5.36343i	0.0378073	+	0.191551i
$785$	0.700885	−	0.255101i	0.0250157	−	0.00910496i
$786$	1.40088	+	5.12381i	0.0499677	+	0.182760i
$787$	39.5505	−	22.8345i	1.40982	−	0.813961i	0.414451	−	0.910071i	$-0.363974\pi$
$787$	39.5505	−	22.8345i	1.40982	−	0.813961i	0.995371	+	0.0961103i	$0.0306402\pi$
$788$	3.89075	+	3.19788i	0.138602	+	0.113920i
$789$	17.5852	−	20.9573i	0.626051	−	0.746099i
$790$	0.174777	−	0.665799i	0.00621829	−	0.0236881i
$791$	9.57146	−	16.5782i	0.340322	−	0.589455i
$792$	5.66001	−	12.6377i	0.201120	−	0.449060i
$793$	0.158019	+	0.896170i	0.00561142	+	0.0318239i
$794$	−12.4041	+	8.77974i	−0.440204	+	0.311581i
$795$	−0.0305218	+	0.0838578i	−0.00108250	+	0.00297413i
$796$	23.7113	+	27.6815i	0.840426	+	0.981145i
$797$		−	6.54154i		−	0.231713i	−0.993266	−	0.115857i	$-0.963039\pi$
$797$		−	6.54154i		−	0.231713i	0.993266	−	0.115857i	$-0.0369613\pi$
$798$	−13.7274	+	5.06181i	−0.485946	+	0.179186i
$799$	18.7543			0.663479
$800$	1.74754	−	28.2204i	0.0617847	−	0.997742i
$801$	14.5178	+	5.28404i	0.512961	+	0.186702i
$802$	−19.4266	−	27.4460i	−0.685977	−	0.969152i
$803$	15.2794	−	2.69417i	0.539198	−	0.0950751i
$804$	9.56095	+	25.4600i	0.337189	+	0.897903i
$805$	−0.138926	−	0.0802088i	−0.00489649	−	0.00282699i
$806$	11.5878	−	44.1426i	0.408161	−	1.55486i
$807$	11.8983	+	9.98384i	0.418839	+	0.351448i
$808$	6.75933	−	0.695398i	0.237793	−	0.0244640i
$809$	−3.48724	−	6.04008i	−0.122605	−	0.212358i	0.798189	−	0.602407i	$-0.205791\pi$
$809$	−3.48724	−	6.04008i	−0.122605	−	0.212358i	−0.920794	+	0.390049i	$0.872458\pi$
$810$	−0.0568433	+	0.0155413i	−0.00199727	+	0.000546066i
$811$	2.75035	+	7.55654i	0.0965780	+	0.265346i	0.978569	−	0.205921i	$-0.0660190\pi$
$811$	2.75035	+	7.55654i	0.0965780	+	0.265346i	−0.881991	+	0.471267i	$0.843797\pi$
$812$	5.26398	+	28.1751i	0.184729	+	0.988753i
$813$	10.1256	+	1.78542i	0.355121	+	0.0626175i
$814$	−32.4934	+	15.3535i	−1.13889	+	0.538140i
$815$	0.152640	−	0.128080i	0.00534675	−	0.00448646i
$816$	0.244526	+	12.0222i	0.00856013	+	0.420862i
$817$	45.0729	+	3.98340i	1.57690	+	0.139362i
$818$	−30.5418	+	30.8539i	−1.06787	+	1.07878i
$819$	−5.20730	−	6.20582i	−0.181958	−	0.216849i
$820$	0.0407379	+	0.0143600i	0.00142263	+	0.000501472i
$821$	46.3693	+	8.17616i	1.61830	+	0.285350i	0.908133	−	0.418682i	$-0.137508\pi$
$821$	46.3693	+	8.17616i	1.61830	+	0.285350i	0.710168	+	0.704032i	$0.248619\pi$
$822$	9.39732	−	13.5670i	0.327769	−	0.473205i
$823$	−3.65233	+	1.32934i	−0.127312	+	0.0463379i	−0.404891	−	0.914365i	$-0.632690\pi$
$823$	−3.65233	+	1.32934i	−0.127312	+	0.0463379i	0.277578	+	0.960703i	$0.410468\pi$
$824$	34.4697	−	9.80198i	1.20081	−	0.341468i
$825$	12.2351	+	21.1918i	0.425972	+	0.737805i
$826$	−4.03429	−	43.5603i	−0.140371	−	1.51566i
$827$	−16.3014	+	19.4273i	−0.566855	+	0.675552i	−0.970982	−	0.239151i	$-0.923131\pi$
$827$	−16.3014	+	19.4273i	−0.566855	+	0.675552i	0.404127	+	0.914703i	$0.367575\pi$
$828$	−2.79276	+	1.65049i	−0.0970553	+	0.0573586i
$829$	32.7764	+	18.9235i	1.13837	+	0.657240i	0.946027	−	0.324088i	$-0.105057\pi$
$829$	32.7764	+	18.9235i	1.13837	+	0.657240i	0.192345	+	0.981327i	$0.438391\pi$
$830$	0.214236	−	0.465596i	0.00743623	−	0.0161611i
$831$	−3.72205	−	21.1088i	−0.129116	−	0.732255i
$832$	−3.91921	+	27.0230i	−0.135874	+	0.936856i
$833$	3.86084	+	1.40523i	0.133770	+	0.0486884i
$834$	−1.13714	+	13.8056i	−0.0393758	+	0.478048i
$835$			0.0853613i			0.00295405i
$836$	−42.4813	+	4.11451i	−1.46925	+	0.142303i
$837$		−	9.45473i		−	0.326803i
$838$	−26.6409	−	2.19435i	−0.920293	−	0.0758025i
$839$	30.7140	+	11.1790i	1.06037	+	0.385941i	0.812565	−	0.582870i	$-0.198070\pi$
$839$	30.7140	+	11.1790i	1.06037	+	0.385941i	0.247800	+	0.968811i	$0.420293\pi$
$840$	−0.226670	+	0.163925i	−0.00782086	+	0.00565593i
$841$	−1.29534	−	7.34622i	−0.0446668	−	0.253318i
$842$	−11.9344	−	5.49140i	−0.411286	−	0.189246i
$843$	16.2105	+	9.35913i	0.558319	+	0.322346i
$844$	−12.5011	−	21.1528i	−0.430305	−	0.728111i
$845$	0.0361571	−	0.0430903i	0.00124384	−	0.00148235i
$846$	8.78509	−	0.813623i	0.302038	−	0.0279730i
$847$	15.3898	+	26.6560i	0.528801	+	0.915910i
$848$	7.50431	+	4.13146i	0.257699	+	0.141875i
$849$	−3.97510	+	1.44682i	−0.136425	+	0.0496546i
$850$	−17.4683	−	12.0996i	−0.599159	−	0.415012i
$851$	8.29138	+	1.46199i	0.284225	+	0.0501165i
$852$	19.7134	+	6.94891i	0.675370	+	0.238066i
$853$	−8.36191	−	9.96534i	−0.286306	−	0.341207i	0.603652	−	0.797248i	$-0.293711\pi$
$853$	−8.36191	−	9.96534i	−0.286306	−	0.341207i	−0.889959	+	0.456041i	$0.849267\pi$
$854$	0.635992	+	0.629558i	0.0217632	+	0.0215430i
$855$	0.128321	+	0.128547i	0.00438848	+	0.00439622i
$856$	7.96379	−	8.21051i	0.272197	−	0.280630i
$857$	−6.87693	+	5.77043i	−0.234911	+	0.197114i	−0.752643	−	0.658429i	$-0.771221\pi$
$857$	−6.87693	+	5.77043i	−0.234911	+	0.197114i	0.517731	+	0.855543i	$0.326777\pi$
$858$	−10.0960	−	21.3667i	−0.344673	−	0.729447i
$859$	5.81563	+	1.02545i	0.198427	+	0.0349880i	0.271978	−	0.962303i	$-0.412322\pi$
$859$	5.81563	+	1.02545i	0.198427	+	0.0349880i	−0.0735514	+	0.997291i	$0.523433\pi$
$860$	0.850405	−	0.158882i	0.0289986	−	0.00541782i
$861$	0.420740	+	1.15597i	0.0143388	+	0.0393955i
$862$	−2.04077	−	7.46424i	−0.0695088	−	0.254233i
$863$	18.3058	+	31.7067i	0.623138	+	1.07931i	0.988898	+	0.148598i	$0.0474759\pi$
$863$	18.3058	+	31.7067i	0.623138	+	1.07931i	−0.365760	+	0.930709i	$0.619191\pi$
$864$	0.636108	+	5.62098i	0.0216408	+	0.191229i
$865$	0.578529	+	0.485443i	0.0196706	+	0.0165056i
$866$	−32.5371	−	8.54123i	−1.10566	−	0.290243i
$867$	−6.89606	−	3.98144i	−0.234203	−	0.135217i
$868$	−15.7781	−	42.0158i	−0.535545	−	1.42611i
$869$	56.3184	−	9.93046i	1.91047	−	0.336868i
$870$	0.290435	−	0.205573i	0.00984667	−	0.00696959i
$871$	43.6139	+	15.8742i	1.47780	+	0.537875i
$872$	1.69059	−	23.4352i	0.0572505	−	0.793617i
$873$	5.34236			0.180812
$874$	8.68009	+	4.96293i	0.293609	+	0.167874i
$875$		−	0.988834i		−	0.0334287i
$876$	−4.81366	+	4.12327i	−0.162639	+	0.139312i
$877$	−2.42046	+	6.65016i	−0.0817332	+	0.224560i	−0.973827	−	0.227290i	$-0.927014\pi$
$877$	−2.42046	+	6.65016i	−0.0817332	+	0.224560i	0.892094	+	0.451850i	$0.149236\pi$
$878$	−16.2721	−	22.9893i	−0.549157	−	0.775852i
$879$	−5.64778	−	32.0302i	−0.190495	−	1.08035i
$880$	−0.760967	+	0.294628i	−0.0256522	+	0.00993192i
$881$	−13.1328	+	22.7467i	−0.442457	+	0.766357i	−0.997871	−	0.0652164i	$-0.979226\pi$
$881$	−13.1328	+	22.7467i	−0.442457	+	0.766357i	0.555415	+	0.831574i	$0.312560\pi$
$882$	1.86950	+	0.490758i	0.0629494	+	0.0165247i
$883$	−34.0089	+	40.5302i	−1.14449	+	1.36395i	−0.223342	+	0.974740i	$0.571697\pi$
$883$	−34.0089	+	40.5302i	−1.14449	+	1.36395i	−0.921149	+	0.389211i	$0.872748\pi$
$884$	15.8537	+	13.0304i	0.533218	+	0.438261i
$885$	−0.470326	+	0.271543i	−0.0158098	+	0.00912781i
$886$	−10.1502	+	2.77512i	−0.341003	+	0.0932321i
$887$	−10.3417	+	3.76406i	−0.347240	+	0.126385i	−0.509751	−	0.860322i	$-0.670263\pi$
$887$	−10.3417	+	3.76406i	−0.347240	+	0.126385i	0.162512	+	0.986707i	$0.448040\pi$
$888$	8.23649	−	12.1533i	0.276398	−	0.407839i
$889$	5.45215	−	30.9207i	0.182859	−	1.03705i
$890$	−0.388956	−	0.823165i	−0.0130378	−	0.0275926i
$891$	−3.14692	−	3.75036i	−0.105426	−	0.125642i
$892$	0.586095	+	57.6371i	0.0196239	+	1.92983i
$893$	−15.5778	−	22.2892i	−0.521292	−	0.745881i
$894$	−8.63054	+	8.71874i	−0.288648	+	0.291598i
$895$	0.655312	−	0.549872i	0.0219047	−	0.0183802i
$896$	12.2071	+	23.9175i	0.407812	+	0.799026i
$897$	−0.961365	+	5.45217i	−0.0320990	+	0.182043i
$898$	4.35729	+	3.01811i	0.145405	+	0.100716i
$899$	19.5257	+	53.6464i	0.651218	+	1.78921i
$900$	−8.70762	−	4.90998i	−0.290254	−	0.163666i
$901$	5.57552	−	3.21903i	0.185747	−	0.107241i
$902$	0.330932	+	3.57323i	0.0110188	+	0.118976i
$903$	18.8739	+	15.8371i	0.628085	+	0.527026i
$904$	−5.56754	+	22.1227i	−0.185174	+	0.735789i
$905$	−0.0850301	+	0.147277i	−0.00282650	+	0.00489564i
$906$	−23.7102	−	10.9098i	−0.787719	−	0.362455i
$907$	−8.54250	+	1.50627i	−0.283649	+	0.0500150i	−0.313663	−	0.949535i	$-0.601556\pi$
$907$	−8.54250	+	1.50627i	−0.283649	+	0.0500150i	0.0300135	+	0.999549i	$0.490445\pi$
$908$	2.03992	−	12.2990i	0.0676971	−	0.408156i
$909$	0.821669	−	2.25752i	0.0272530	−	0.0748771i
$910$	−0.0391893	+	0.475784i	−0.00129911	+	0.0157721i
$911$	2.69710			0.0893589			0.0446795	−	0.999001i	$-0.485773\pi$
$911$	2.69710			0.0893589			0.0446795	+	0.999001i	$0.485773\pi$
$912$	14.0851	−	10.2766i	0.466406	−	0.340292i
$913$	42.5790			1.40916
$914$	−0.539720	+	6.55256i	−0.0178523	+	0.216739i
$915$	0.00379966	−	0.0104395i	0.000125613	−	0.000345118i
$916$	−1.30031	+	7.83973i	−0.0429633	+	0.259032i
$917$	8.77938	−	1.54804i	0.289921	−	0.0511208i
$918$	3.86214	+	1.77710i	0.127470	+	0.0586530i
$919$	−22.6602	+	39.2487i	−0.747492	+	1.29469i	0.201529	+	0.979483i	$0.435409\pi$
$919$	−22.6602	+	39.2487i	−0.747492	+	1.29469i	−0.949021	+	0.315212i	$0.897924\pi$
$920$	0.185388	+	0.0466560i	0.00611206	+	0.00153820i
$921$	3.33147	+	2.79544i	0.109776	+	0.0921128i
$922$	−0.908666	−	9.81132i	−0.0299253	−	0.323118i
$923$	30.8929	−	17.8360i	1.01685	−	0.587080i
$924$	−20.2432	−	11.4146i	−0.665953	−	0.375512i
$925$	8.87345	+	24.3796i	0.291757	+	0.801597i
$926$	12.4699	+	8.63737i	0.409786	+	0.283842i
$927$	2.20013	−	12.4776i	0.0722617	−	0.409817i
$928$	−15.2176	−	30.5799i	−0.499542	−	1.00383i
$929$	−28.0919	+	23.5719i	−0.921665	+	0.773369i	−0.974302	−	0.225245i	$-0.927682\pi$
$929$	−28.0919	+	23.5719i	−0.921665	+	0.773369i	0.0526369	+	0.998614i	$0.483237\pi$
$930$	−0.391966	+	0.395972i	−0.0128531	+	0.0129844i
$931$	−1.53682	−	5.75578i	−0.0503672	−	0.188638i
$932$	−0.0635338	−	6.24797i	−0.00208112	−	0.204659i
$933$	−18.1059	−	21.5777i	−0.592760	−	0.706424i
$934$	11.6623	+	24.6814i	0.381601	+	0.807601i
$935$	−0.106493	+	0.603953i	−0.00348270	+	0.0197514i
$936$	7.99167	+	5.41608i	0.261216	+	0.177030i
$937$	−26.9092	+	9.79413i	−0.879084	+	0.319960i	−0.741840	−	0.670577i	$-0.766047\pi$
$937$	−26.9092	+	9.79413i	−0.879084	+	0.319960i	−0.137244	+	0.990537i	$0.543824\pi$
$938$	44.0267	−	12.0372i	1.43752	−	0.393027i
$939$	8.32718	−	4.80770i	0.271747	−	0.156893i
$940$	−0.401657	−	0.330129i	−0.0131006	−	0.0107676i
$941$	7.24233	−	8.63107i	0.236093	−	0.281365i	−0.634969	−	0.772538i	$-0.718987\pi$
$941$	7.24233	−	8.63107i	0.236093	−	0.281365i	0.871062	+	0.491173i	$0.163432\pi$
$942$	−24.4843	−	6.42730i	−0.797741	−	0.209413i
$943$	0.420345	−	0.728058i	0.0136883	−	0.0237088i
$944$	18.8229	+	48.6159i	0.612634	+	1.58231i
$945$	0.0171739	+	0.0973981i	0.000558667	+	0.00316836i
$946$	41.5230	+	58.6640i	1.35003	+	1.90733i
$947$	−13.8572	+	38.0724i	−0.450300	+	1.23719i	0.482214	+	0.876053i	$0.339833\pi$
$947$	−13.8572	+	38.0724i	−0.450300	+	1.23719i	−0.932514	+	0.361134i	$0.882390\pi$
$948$	−17.7427	+	15.1980i	−0.576257	+	0.493608i
$949$			10.8168i			0.351129i
$950$	0.129489	+	30.8111i	0.00420119	+	0.999644i
$951$	−0.0488238			−0.00158322
$952$	20.1286	+	1.45205i	0.652371	+	0.0470612i
$953$	−0.176120	−	0.0641025i	−0.00570510	−	0.00207648i	0.339166	−	0.940727i	$-0.389855\pi$
$953$	−0.176120	−	0.0641025i	−0.00570510	−	0.00207648i	−0.344871	+	0.938650i	$0.612077\pi$
$954$	2.47209	−	1.74978i	0.0800369	−	0.0566511i
$955$	0.358561	−	0.0632239i	0.0116028	−	0.00204588i
$956$	5.23666	+	13.9447i	0.169366	+	0.451005i
$957$	25.6009	+	14.7807i	0.827559	+	0.477791i
$958$	50.5645	+	13.2735i	1.63366	+	0.428849i
$959$	−21.2179	−	17.8039i	−0.685162	−	0.574919i
$960$	0.206389	−	0.261782i	0.00666117	−	0.00844899i
$961$	−29.1959	−	50.5688i	−0.941804	−	1.63125i
$962$	−6.60777	−	24.1684i	−0.213043	−	0.779220i
$963$	−1.38315	−	3.80016i	−0.0445712	−	0.122458i
$964$	−39.2708	+	7.33700i	−1.26483	+	0.236309i
$965$	0.135904	+	0.0239636i	0.00437491	+	0.000771414i
$966$	2.32595	+	4.92253i	0.0748363	+	0.158380i
$967$	14.0998	−	11.8311i	0.453419	−	0.380464i	−0.387284	−	0.921961i	$-0.626587\pi$
$967$	14.0998	−	11.8311i	0.453419	−	0.380464i	0.840703	+	0.541497i	$0.182142\pi$
$968$	−26.3292	−	25.5380i	−0.846252	−	0.820823i
$969$	−1.13055	−	13.0548i	−0.0363185	−	0.419380i
$970$	−0.223743	−	0.221479i	−0.00718394	−	0.00711126i
$971$	28.0168	+	33.3891i	0.899103	+	1.07151i	0.997083	+	0.0763204i	$0.0243172\pi$
$971$	28.0168	+	33.3891i	0.899103	+	1.07151i	−0.0979807	+	0.995188i	$0.531238\pi$
$972$	1.88624	+	0.664895i	0.0605013	+	0.0213265i
$973$	22.8950	+	4.03700i	0.733979	+	0.129420i
$974$	−28.8474	−	19.9813i	−0.924329	−	0.640243i
$975$	−16.0313	+	5.83493i	−0.513413	+	0.186867i
$976$	−0.934212	−	0.514327i	−0.0299034	−	0.0164632i
$977$	14.0117	+	24.2690i	0.448275	+	0.776435i	0.998274	−	0.0587302i	$-0.0187052\pi$
$977$	14.0117	+	24.2690i	0.448275	+	0.776435i	−0.549999	+	0.835165i	$0.685372\pi$
$978$	−6.73375	+	0.623640i	−0.215322	+	0.0199418i
$979$	48.6184	−	57.9412i	1.55385	−	1.85181i
$980$	−0.0579508	−	0.0980574i	−0.00185117	−	0.00313233i
$981$	−7.19419	−	4.15357i	−0.229693	−	0.132613i
$982$	−5.43527	−	2.50094i	−0.173446	−	0.0798084i
$983$	−4.89803	−	27.7781i	−0.156223	−	0.885984i	−0.957659	−	0.287904i	$-0.907042\pi$
$983$	−4.89803	−	27.7781i	−0.156223	−	0.885984i	0.801436	−	0.598080i	$-0.204070\pi$
$984$	−0.859067	−	1.18789i	−0.0273861	−	0.0378687i
$985$	−0.0986020	−	0.0358882i	−0.00314172	−	0.00114349i
$986$	−25.5839	−	2.10729i	−0.814758	−	0.0671098i
$987$		−	14.8070i		−	0.471311i
$988$	2.31799	−	29.6654i	0.0737452	−	0.943781i
$989$		−	16.8376i		−	0.535406i
$990$	−0.0236832	+	0.287530i	−0.000752703	+	0.00913832i
$991$	8.86842	+	3.22784i	0.281715	+	0.102536i	0.479013	−	0.877808i	$-0.340995\pi$
$991$	8.86842	+	3.22784i	0.281715	+	0.102536i	−0.197299	+	0.980343i	$0.563217\pi$
$992$	31.7809	+	43.0176i	1.00904	+	1.36581i
$993$	−3.72494	−	21.1252i	−0.118207	−	0.670387i
$994$	14.6636	−	31.8682i	0.465101	−	1.01080i
$995$	−0.657656	−	0.379698i	−0.0208491	−	0.0120372i
$996$	−14.9747	+	8.84987i	−0.474491	+	0.280419i
$997$	9.76136	−	11.6331i	0.309145	−	0.368425i	−0.588993	−	0.808138i	$-0.700475\pi$
$997$	9.76136	−	11.6331i	0.309145	−	0.368425i	0.898138	+	0.439713i	$0.144920\pi$
$998$	−4.52473	−	48.8558i	−0.143228	−	1.54650i
$999$	−2.59533	−	4.49523i	−0.0821125	−	0.142223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.253.20	yes	240
8.5	even	2	inner	456.2.bk.a.253.2	✓	240
19.16	even	9	inner	456.2.bk.a.301.2	yes	240
152.149	even	18	inner	456.2.bk.a.301.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.253.2	✓	240	8.5	even	2	inner
456.2.bk.a.253.20	yes	240	1.1	even	1	trivial
456.2.bk.a.301.2	yes	240	19.16	even	9	inner
456.2.bk.a.301.20	yes	240	152.149	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.116093 + 1.40944i) q^{2} +(-0.342020 + 0.939693i) q^{3} +(-1.97305 - 0.327251i) q^{4} +(0.0410365 - 0.00723583i) q^{5} +(-1.28473 - 0.591148i) q^{6} +(-1.18673 + 2.05547i) q^{7} +(0.690297 - 2.74290i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(0.00543445 + 0.0586785i) q^{10} +(-4.23984 + 2.44787i) q^{11} +(0.982337 - 1.74213i) q^{12} +(-1.16739 - 3.20738i) q^{13} +(-2.75929 - 1.91124i) q^{14} +(-0.00723583 + 0.0410365i) q^{15} +(3.78581 + 1.29136i) q^{16} +(2.30287 - 1.93233i) q^{17} +(0.994903 - 1.00507i) q^{18} +(-4.20938 - 1.13188i) q^{19} +(-0.0833347 + 0.000847406i) q^{20} +(-1.52563 - 1.81817i) q^{21} +(-2.95792 - 6.25998i) q^{22} +(-0.281659 + 1.59737i) q^{23} +(2.34139 + 1.58679i) q^{24} +(-4.69683 + 1.70951i) q^{25} +(4.65614 - 1.27301i) q^{26} +(0.866025 - 0.500000i) q^{27} +(3.01412 - 3.66718i) q^{28} +(-3.88126 + 4.62551i) q^{29} +(-0.0569984 - 0.0149625i) q^{30} +(4.72736 - 8.18803i) q^{31} +(-2.25960 + 5.18596i) q^{32} +(-0.850137 - 4.82137i) q^{33} +(2.45617 + 3.47008i) q^{34} +(-0.0338260 + 0.0929361i) q^{35} +(1.30109 + 1.51894i) q^{36} -5.19065i q^{37} +(2.08399 - 5.80146i) q^{38} +3.41322 q^{39} +(0.00848017 - 0.117554i) q^{40} +(-0.487044 - 0.177269i) q^{41} +(2.73972 - 1.93920i) q^{42} +(-10.2230 + 1.80259i) q^{43} +(9.16646 - 3.44227i) q^{44} +(-0.0360869 - 0.0208348i) q^{45} +(-2.21870 - 0.582424i) q^{46} +(4.77903 + 4.01008i) q^{47} +(-2.50831 + 3.11583i) q^{48} +(0.683363 + 1.18362i) q^{49} +(-1.86418 - 6.81837i) q^{50} +(1.02817 + 2.82488i) q^{51} +(1.25370 + 6.71033i) q^{52} +(2.10907 + 0.371886i) q^{53} +(0.604181 + 1.27866i) q^{54} +(-0.156276 + 0.131131i) q^{55} +(4.81875 + 4.67395i) q^{56} +(2.50331 - 3.56840i) q^{57} +(-6.06880 - 6.00740i) q^{58} +(8.37755 + 9.98398i) q^{59} +(0.0277058 - 0.0785988i) q^{60} +(-0.262558 - 0.0462961i) q^{61} +(10.9917 + 7.61351i) q^{62} +(2.23032 - 0.811768i) q^{63} +(-7.04698 - 3.78683i) q^{64} +(-0.0711136 - 0.123172i) q^{65} +(6.89412 - 0.638493i) q^{66} +(-8.74062 + 10.4167i) q^{67} +(-5.17602 + 3.05897i) q^{68} +(-1.40470 - 0.811005i) q^{69} +(-0.127061 - 0.0584649i) q^{70} +(1.81482 + 10.2924i) q^{71} +(-2.29190 + 1.65747i) q^{72} +(-2.97798 - 1.08389i) q^{73} +(7.31591 + 0.602596i) q^{74} -4.99826i q^{75} +(7.93488 + 3.61077i) q^{76} -11.6198i q^{77} +(-0.396250 + 4.81073i) q^{78} +(-10.9766 - 3.99514i) q^{79} +(0.164700 + 0.0255994i) q^{80} +(0.173648 + 0.984808i) q^{81} +(0.306393 - 0.665880i) q^{82} +(-7.53195 - 4.34857i) q^{83} +(2.41513 + 4.08659i) q^{84} +(0.0805194 - 0.0959593i) q^{85} +(-1.35383 - 14.6180i) q^{86} +(-3.01909 - 5.22921i) q^{87} +(3.78752 + 13.3192i) q^{88} +(-14.5178 + 5.28404i) q^{89} +(0.0335548 - 0.0484435i) q^{90} +(7.97804 + 1.40674i) q^{91} +(1.07847 - 3.05950i) q^{92} +(6.07738 + 7.24274i) q^{93} +(-6.20679 + 6.27022i) q^{94} +(-0.180928 - 0.0159899i) q^{95} +(-4.10038 - 3.89704i) q^{96} +(-4.09249 + 3.43400i) q^{97} +(-1.74757 + 0.825750i) q^{98} +(4.82137 + 0.850137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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