LMFDB - Embedded newform 126.3.o.a.13.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,3,Mod(13,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.o (of order $6$, degree $2$, 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:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	126.13
Dual form			126.3.o.a.97.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 1.22474i) q^{2} +(1.75392 + 2.43388i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-8.58770 - 4.95811i) q^{5} +(1.74067 - 3.86912i) q^{6} +(-4.53080 + 5.33591i) q^{7} +2.82843 q^{8} +(-2.84752 + 8.53766i) q^{9} +14.0237i q^{10} +(-6.74260 - 11.6785i) q^{11} +(-5.96952 + 0.604004i) q^{12} +(-10.5236 - 6.07580i) q^{13} +(9.73888 + 1.77601i) q^{14} +(-2.99472 - 29.5976i) q^{15} +(-2.00000 - 3.46410i) q^{16} +20.1850i q^{17} +(12.4700 - 2.54955i) q^{18} -4.66654i q^{19} +(17.1754 - 9.91622i) q^{20} +(-20.9336 - 1.66864i) q^{21} +(-9.53548 + 16.5159i) q^{22} +(-0.0880089 + 0.152436i) q^{23} +(4.96084 + 6.88404i) q^{24} +(36.6657 + 63.5069i) q^{25} +17.1849i q^{26} +(-25.7739 + 8.04388i) q^{27} +(-4.71127 - 13.1835i) q^{28} +(-7.01783 - 12.1552i) q^{29} +(-34.1319 + 24.5964i) q^{30} +(-0.0205898 - 0.0118875i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(16.5981 - 36.8939i) q^{33} +(24.7214 - 14.2729i) q^{34} +(65.3651 - 23.3590i) q^{35} +(-11.9401 - 13.4697i) q^{36} -2.42366 q^{37} +(-5.71533 + 3.29975i) q^{38} +(-3.66981 - 36.2696i) q^{39} +(-24.2897 - 14.0237i) q^{40} +(9.48159 + 5.47420i) q^{41} +(12.7586 + 26.8182i) q^{42} +(-3.53303 - 6.11939i) q^{43} +26.9704 q^{44} +(66.7843 - 59.2006i) q^{45} +0.248927 q^{46} +(39.7838 - 22.9692i) q^{47} +(4.92336 - 10.9435i) q^{48} +(-7.94379 - 48.3518i) q^{49} +(51.8532 - 89.8124i) q^{50} +(-49.1277 + 35.4028i) q^{51} +(21.0472 - 12.1516i) q^{52} -57.1896 q^{53} +(28.0766 + 25.8786i) q^{54} +133.722i q^{55} +(-12.8150 + 15.0922i) q^{56} +(11.3578 - 8.18475i) q^{57} +(-9.92471 + 17.1901i) q^{58} +(-41.9730 - 24.2331i) q^{59} +(54.2592 + 24.4105i) q^{60} +(34.2752 - 19.7888i) q^{61} +0.0336230i q^{62} +(-32.6546 - 53.8765i) q^{63} +8.00000 q^{64} +(60.2489 + 104.354i) q^{65} +(-56.9223 + 5.75947i) q^{66} +(-45.1674 + 78.2322i) q^{67} +(-34.9614 - 20.1850i) q^{68} +(-0.525371 + 0.0531577i) q^{69} +(-74.8289 - 63.5383i) q^{70} -80.6841 q^{71} +(-8.05400 + 24.1481i) q^{72} -17.8424i q^{73} +(1.71379 + 2.96837i) q^{74} +(-90.2592 + 200.626i) q^{75} +(8.08269 + 4.66654i) q^{76} +(92.8649 + 16.9351i) q^{77} +(-41.8260 + 30.1410i) q^{78} +(10.1791 + 17.6308i) q^{79} +39.6649i q^{80} +(-64.7833 - 48.6223i) q^{81} -15.4834i q^{82} +(-25.2325 + 14.5680i) q^{83} +(23.8238 - 34.5894i) q^{84} +(100.079 - 173.342i) q^{85} +(-4.99646 + 8.65413i) q^{86} +(17.2756 - 38.3999i) q^{87} +(-19.0710 - 33.0319i) q^{88} +81.5430i q^{89} +(-119.729 - 39.9326i) q^{90} +(80.1001 - 28.6247i) q^{91} +(-0.176018 - 0.304872i) q^{92} +(-0.00718012 - 0.0709629i) q^{93} +(-56.2627 - 32.4833i) q^{94} +(-23.1372 + 40.0749i) q^{95} +(-16.8844 + 1.70838i) q^{96} +(94.2248 - 54.4007i) q^{97} +(-53.6015 + 43.9190i) q^{98} +(118.907 - 24.3112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$	1.75392	+	2.43388i	0.584641	+	0.811292i
$3$	1.75392	+	2.43388i	0.584641	+	0.811292i
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−8.58770	−	4.95811i	−1.71754	−	0.991622i	−0.923356	−	0.383946i	$-0.874565\pi$
$5$	−8.58770	−	4.95811i	−1.71754	−	0.991622i	−0.794185	−	0.607677i	$-0.792102\pi$
$6$	1.74067	−	3.86912i	0.290111	−	0.644853i
$7$	−4.53080	+	5.33591i	−0.647256	+	0.762272i
$7$	−4.53080	+	5.33591i	−0.647256	+	0.762272i
$8$	2.82843			0.353553
$9$	−2.84752	+	8.53766i	−0.316391	+	0.948629i
$10$			14.0237i			1.40237i
$11$	−6.74260	−	11.6785i	−0.612964	−	1.06168i	−0.990738	−	0.135787i	$-0.956644\pi$
$11$	−6.74260	−	11.6785i	−0.612964	−	1.06168i	0.377774	−	0.925898i	$-0.376690\pi$
$12$	−5.96952	+	0.604004i	−0.497460	+	0.0503337i
$13$	−10.5236	−	6.07580i	−0.809507	−	0.467369i	0.0372779	−	0.999305i	$-0.488131\pi$
$13$	−10.5236	−	6.07580i	−0.809507	−	0.467369i	−0.846785	+	0.531936i	$0.821465\pi$
$14$	9.73888	+	1.77601i	0.695634	+	0.126858i
$15$	−2.99472	−	29.5976i	−0.199648	−	1.97317i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$			20.1850i			1.18735i	0.804705	+	0.593675i	$0.202324\pi$
$17$			20.1850i			1.18735i	−0.804705	+	0.593675i	$0.797676\pi$
$18$	12.4700	−	2.54955i	0.692775	−	0.141642i
$19$		−	4.66654i		−	0.245608i	−0.992431	−	0.122804i	$-0.960811\pi$
$19$		−	4.66654i		−	0.245608i	0.992431	−	0.122804i	$-0.0391886\pi$
$20$	17.1754	−	9.91622i	0.858770	−	0.495811i
$21$	−20.9336	−	1.66864i	−0.996838	−	0.0794589i
$22$	−9.53548	+	16.5159i	−0.433431	+	0.750724i
$23$	−0.0880089	+	0.152436i	−0.00382647	+	0.00662765i	−0.867932	−	0.496683i	$-0.834551\pi$
$23$	−0.0880089	+	0.152436i	−0.00382647	+	0.00662765i	0.864106	+	0.503310i	$0.167885\pi$
$24$	4.96084	+	6.88404i	0.206702	+	0.286835i
$25$	36.6657	+	63.5069i	1.46663	+	2.54028i
$26$			17.1849i			0.660959i
$27$	−25.7739	+	8.04388i	−0.954590	+	0.297921i
$28$	−4.71127	−	13.1835i	−0.168259	−	0.470838i
$29$	−7.01783	−	12.1552i	−0.241994	−	0.419146i	0.719288	−	0.694712i	$-0.244468\pi$
$29$	−7.01783	−	12.1552i	−0.241994	−	0.419146i	−0.961282	+	0.275566i	$0.911135\pi$
$30$	−34.1319	+	24.5964i	−1.13773	+	0.819880i
$31$	−0.0205898	−	0.0118875i	−0.000664188	−	0.000383469i	0.499668	−	0.866217i	$-0.333455\pi$
$31$	−0.0205898	−	0.0118875i	−0.000664188	−	0.000383469i	−0.500332	+	0.865834i	$0.666789\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$	16.5981	−	36.8939i	0.502973	−	1.11800i
$34$	24.7214	−	14.2729i	0.727100	−	0.419792i
$35$	65.3651	−	23.3590i	1.86758	−	0.667399i
$36$	−11.9401	−	13.4697i	−0.331671	−	0.374158i
$37$	−2.42366			−0.0655043			−0.0327522	−	0.999464i	$-0.510427\pi$
$37$	−2.42366			−0.0655043			−0.0327522	+	0.999464i	$0.510427\pi$
$38$	−5.71533	+	3.29975i	−0.150403	+	0.0868354i
$39$	−3.66981	−	36.2696i	−0.0940976	−	0.929989i
$40$	−24.2897	−	14.0237i	−0.607242	−	0.350591i
$41$	9.48159	+	5.47420i	0.231258	+	0.133517i	0.611152	−	0.791513i	$-0.290706\pi$
$41$	9.48159	+	5.47420i	0.231258	+	0.133517i	−0.379894	+	0.925030i	$0.624040\pi$
$42$	12.7586	+	26.8182i	0.303777	+	0.638529i
$43$	−3.53303	−	6.11939i	−0.0821636	−	0.142311i	0.822015	−	0.569465i	$-0.192850\pi$
$43$	−3.53303	−	6.11939i	−0.0821636	−	0.142311i	−0.904179	+	0.427154i	$0.859516\pi$
$44$	26.9704			0.612964
$45$	66.7843	−	59.2006i	1.48410	−	1.31557i
$46$	0.248927			0.00541145
$47$	39.7838	−	22.9692i	0.846463	−	0.488706i	−0.0129929	−	0.999916i	$-0.504136\pi$
$47$	39.7838	−	22.9692i	0.846463	−	0.488706i	0.859456	+	0.511210i	$0.170803\pi$
$48$	4.92336	−	10.9435i	0.102570	−	0.227990i
$49$	−7.94379	−	48.3518i	−0.162118	−	0.986771i
$50$	51.8532	−	89.8124i	1.03706	−	1.79625i
$51$	−49.1277	+	35.4028i	−0.963288	+	0.694173i
$52$	21.0472	−	12.1516i	0.404753	−	0.233684i
$53$	−57.1896			−1.07905			−0.539524	−	0.841970i	$-0.681396\pi$
$53$	−57.1896			−1.07905			−0.539524	+	0.841970i	$0.681396\pi$
$54$	28.0766	+	25.8786i	0.519938	+	0.479234i
$55$			133.722i			2.43131i
$56$	−12.8150	+	15.0922i	−0.228840	+	0.269504i
$57$	11.3578	−	8.18475i	0.199260	−	0.143592i
$58$	−9.92471	+	17.1901i	−0.171116	+	0.296381i
$59$	−41.9730	−	24.2331i	−0.711406	−	0.410730i	0.100175	−	0.994970i	$-0.468060\pi$
$59$	−41.9730	−	24.2331i	−0.711406	−	0.410730i	−0.811581	+	0.584239i	$0.801393\pi$
$60$	54.2592	+	24.4105i	0.904320	+	0.406842i
$61$	34.2752	−	19.7888i	0.561888	−	0.324406i	−0.192015	−	0.981392i	$-0.561502\pi$
$61$	34.2752	−	19.7888i	0.561888	−	0.324406i	0.753903	+	0.656986i	$0.228169\pi$
$62$			0.0336230i			0.000542307i
$63$	−32.6546	−	53.8765i	−0.518328	−	0.855182i
$64$	8.00000			0.125000
$65$	60.2489	+	104.354i	0.926907	+	1.60545i
$66$	−56.9223	+	5.75947i	−0.862458	+	0.0872647i
$67$	−45.1674	+	78.2322i	−0.674140	+	1.16764i	0.302580	+	0.953124i	$0.402152\pi$
$67$	−45.1674	+	78.2322i	−0.674140	+	1.16764i	−0.976720	+	0.214520i	$0.931181\pi$
$68$	−34.9614	−	20.1850i	−0.514138	−	0.296838i
$69$	−0.525371	+	0.0531577i	−0.00761407	+	0.000770402i
$70$	−74.8289	−	63.5383i	−1.06898	−	0.907690i
$71$	−80.6841			−1.13640			−0.568198	−	0.822892i	$-0.692359\pi$
$71$	−80.6841			−1.13640			−0.568198	+	0.822892i	$0.692359\pi$
$72$	−8.05400	+	24.1481i	−0.111861	+	0.335391i
$73$		−	17.8424i		−	0.244417i	−0.992504	−	0.122208i	$-0.961002\pi$
$73$		−	17.8424i		−	0.244417i	0.992504	−	0.122208i	$-0.0389976\pi$
$74$	1.71379	+	2.96837i	0.0231593	+	0.0401130i
$75$	−90.2592	+	200.626i	−1.20346	+	2.67501i
$76$	8.08269	+	4.66654i	0.106351	+	0.0614019i
$77$	92.8649	+	16.9351i	1.20604	+	0.219937i
$78$	−41.8260	+	30.1410i	−0.536231	+	0.386424i
$79$	10.1791	+	17.6308i	0.128850	+	0.223174i	0.923231	−	0.384245i	$-0.125538\pi$
$79$	10.1791	+	17.6308i	0.128850	+	0.223174i	−0.794381	+	0.607419i	$0.792205\pi$
$80$			39.6649i			0.495811i
$81$	−64.7833	−	48.6223i	−0.799794	−	0.600275i
$82$		−	15.4834i		−	0.188822i
$83$	−25.2325	+	14.5680i	−0.304006	+	0.175518i	−0.644241	−	0.764822i	$-0.722827\pi$
$83$	−25.2325	+	14.5680i	−0.304006	+	0.175518i	0.340235	+	0.940340i	$0.389493\pi$
$84$	23.8238	−	34.5894i	0.283616	−	0.411779i
$85$	100.079	−	173.342i	1.17740	−	2.03932i
$86$	−4.99646	+	8.65413i	−0.0580984	+	0.100629i
$87$	17.2756	−	38.3999i	0.198571	−	0.441378i
$88$	−19.0710	−	33.0319i	−0.216715	−	0.375362i
$89$			81.5430i			0.916213i	0.888897	+	0.458107i	$0.151472\pi$
$89$			81.5430i			0.916213i	−0.888897	+	0.458107i	$0.848528\pi$
$90$	−119.729	−	39.9326i	−1.33032	−	0.443696i
$91$	80.1001	−	28.6247i	0.880221	−	0.314557i
$92$	−0.176018	−	0.304872i	−0.00191324	−	0.00331382i
$93$	−0.00718012	−	0.0709629i	−7.72056e−5	−	0.000763042i
$94$	−56.2627	−	32.4833i	−0.598540	−	0.345567i
$95$	−23.1372	+	40.0749i	−0.243550	+	0.421841i
$96$	−16.8844	+	1.70838i	−0.175879	+	0.0177956i
$97$	94.2248	−	54.4007i	0.971390	−	0.560832i	0.0717301	−	0.997424i	$-0.477148\pi$
$97$	94.2248	−	54.4007i	0.971390	−	0.560832i	0.899660	+	0.436592i	$0.143815\pi$
$98$	−53.6015	+	43.9190i	−0.546954	+	0.448153i
$99$	118.907	−	24.3112i	1.20108	−	0.245568i
$100$	−146.663			−1.46663
$101$	−120.353	+	69.4857i	−1.19161	+	0.687977i	−0.958672	−	0.284514i	$-0.908168\pi$
$101$	−120.353	+	69.4857i	−1.19161	+	0.687977i	−0.232939	+	0.972491i	$0.574834\pi$
$102$	78.0980	+	35.1353i	0.765666	+	0.344464i
$103$	−66.0960	−	38.1606i	−0.641709	−	0.370491i	0.143563	−	0.989641i	$-0.454144\pi$
$103$	−66.0960	−	38.1606i	−0.641709	−	0.370491i	−0.785273	+	0.619150i	$0.787477\pi$
$104$	−29.7652	−	17.1849i	−0.286204	−	0.165240i
$105$	171.498	+	118.121i	1.63332	+	1.12496i
$106$	40.4391	+	70.0426i	0.381501	+	0.660779i
$107$	−84.5769			−0.790439			−0.395219	−	0.918587i	$-0.629331\pi$
$107$	−84.5769			−0.790439			−0.395219	+	0.918587i	$0.629331\pi$
$108$	11.8415	−	52.6857i	0.109644	−	0.487830i
$109$	−24.1111			−0.221203			−0.110601	−	0.993865i	$-0.535278\pi$
$109$	−24.1111			−0.221203			−0.110601	+	0.993865i	$0.535278\pi$
$110$	163.776	−	94.5560i	1.48887	−	0.859600i
$111$	−4.25091	−	5.89889i	−0.0382965	−	0.0531432i
$112$	27.5457	+	5.02332i	0.245944	+	0.0448511i
$113$	−72.7392	+	125.988i	−0.643710	+	1.11494i	0.340888	+	0.940104i	$0.389272\pi$
$113$	−72.7392	+	125.988i	−0.643710	+	1.11494i	−0.984598	+	0.174835i	$0.944061\pi$
$114$	−18.0554	−	8.12291i	−0.158381	−	0.0712536i
$115$	1.51159	−	0.872716i	0.0131442	−	0.00758883i
$116$	28.0713			0.241994
$117$	81.8392	−	72.5459i	0.699480	−	0.620050i
$118$			68.5415i			0.580861i
$119$	−107.705	−	91.4539i	−0.905084	−	0.768520i
$120$	−8.47035	−	83.7145i	−0.0705862	−	0.697621i
$121$	−30.4254	+	52.6983i	−0.251450	+	0.435523i
$122$	−48.4724	−	27.9856i	−0.397315	−	0.229390i
$123$	3.30644	+	32.6783i	0.0268816	+	0.265678i
$124$	0.0411797	−	0.0237751i	0.000332094	−	0.000191735i
$125$		−	479.266i		−	3.83413i
$126$	−42.8946	+	78.0900i	−0.340434	+	0.619762i
$127$	−155.852			−1.22718			−0.613590	−	0.789625i	$-0.710275\pi$
$127$	−155.852			−1.22718			−0.613590	+	0.789625i	$0.710275\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$	8.69719	−	19.3319i	0.0674201	−	0.149860i
$130$	85.2049	−	147.579i	0.655422	−	1.13522i
$131$	−86.1056	−	49.7131i	−0.657295	−	0.379489i	0.133951	−	0.990988i	$-0.457234\pi$
$131$	−86.1056	−	49.7131i	−0.657295	−	0.379489i	−0.791245	+	0.611499i	$0.790567\pi$
$132$	47.3040	+	65.6427i	0.358364	+	0.497293i
$133$	24.9002	+	21.1432i	0.187220	+	0.158971i
$134$	127.753			0.953377
$135$	261.221	+	58.7117i	1.93497	+	0.434901i
$136$			57.0917i			0.419792i
$137$	12.3339	+	21.3630i	0.0900287	+	0.155934i	0.907523	−	0.420002i	$-0.137971\pi$
$137$	12.3339	+	21.3630i	0.0900287	+	0.155934i	−0.817494	+	0.575937i	$0.804637\pi$
$138$	0.436598	+	0.605857i	0.00316375	+	0.00439027i
$139$	98.5930	+	56.9227i	0.709302	+	0.409516i	0.810803	−	0.585320i	$-0.199031\pi$
$139$	98.5930	+	56.9227i	0.709302	+	0.409516i	−0.101500	+	0.994835i	$0.532364\pi$
$140$	−24.9062	+	136.575i	−0.177901	+	0.975534i
$141$	125.682	+	56.5427i	0.891360	+	0.401012i
$142$	57.0523	+	98.8175i	0.401777	+	0.695898i
$143$			163.867i			1.14592i
$144$	35.2704	−	7.21123i	0.244933	−	0.0500780i
$145$			139.181i			0.959867i
$146$	−21.8524	+	12.6165i	−0.149674	+	0.0864144i
$147$	103.750	−	104.139i	0.705779	−	0.708432i
$148$	2.42366	−	4.19790i	0.0163761	−	0.0283642i
$149$	−85.7383	+	148.503i	−0.575425	+	0.996665i	0.420571	+	0.907260i	$0.361830\pi$
$149$	−85.7383	+	148.503i	−0.575425	+	0.996665i	−0.995995	+	0.0894051i	$0.971503\pi$
$150$	309.539	−	31.3195i	2.06359	−	0.208797i
$151$	−118.787	−	205.745i	−0.786669	−	1.36255i	−0.927997	−	0.372588i	$-0.878471\pi$
$151$	−118.787	−	205.745i	−0.786669	−	1.36255i	0.141328	−	0.989963i	$-0.454863\pi$
$152$		−	13.1990i		−	0.0868354i
$153$	−172.332	−	57.4770i	−1.12635	−	0.375667i
$154$	−44.9242	−	125.711i	−0.291715	−	0.816304i
$155$	0.117880	+	0.204173i	0.000760513	+	0.00131725i
$156$	66.4906	+	29.9133i	0.426222	+	0.191752i
$157$	67.7529	+	39.1171i	0.431547	+	0.249154i	0.700005	−	0.714137i	$-0.253181\pi$
$157$	67.7529	+	39.1171i	0.431547	+	0.249154i	−0.268458	+	0.963291i	$0.586514\pi$
$158$	14.3955	−	24.9337i	0.0911106	−	0.157808i
$159$	−100.306	−	139.192i	−0.630855	−	0.875424i
$160$	48.5794	−	28.0473i	0.303621	−	0.175296i
$161$	−0.414633	−	1.16026i	−0.00257536	−	0.00720660i
$162$	−13.7412	+	113.724i	−0.0848221	+	0.702001i
$163$	236.898			1.45336			0.726682	−	0.686974i	$-0.241061\pi$
$163$	236.898			1.45336			0.726682	+	0.686974i	$0.241061\pi$
$164$	−18.9632	+	10.9484i	−0.115629	+	0.0667585i
$165$	−325.464	+	234.538i	−1.97251	+	1.42145i
$166$	35.6842	+	20.6023i	0.214965	+	0.124110i
$167$	200.478	+	115.746i	1.20047	+	0.693089i	0.960659	−	0.277732i	$-0.0895826\pi$
$167$	200.478	+	115.746i	1.20047	+	0.693089i	0.239807	+	0.970821i	$0.422916\pi$
$168$	−59.2092	−	4.71962i	−0.352436	−	0.0280930i
$169$	−10.6694	−	18.4800i	−0.0631327	−	0.109349i
$170$	−283.067			−1.66510
$171$	39.8414	+	13.2881i	0.232990	+	0.0777080i
$172$	14.1321			0.0821636
$173$	110.666	−	63.8930i	0.639688	−	0.369324i	−0.144807	−	0.989460i	$-0.546256\pi$
$173$	110.666	−	63.8930i	0.639688	−	0.369324i	0.784494	+	0.620136i	$0.212923\pi$
$174$	−59.2458	+	5.99457i	−0.340493	+	0.0344515i
$175$	−504.992	−	92.0919i	−2.88567	−	0.526239i
$176$	−26.9704	+	46.7141i	−0.153241	+	0.265421i
$177$	−14.6369	−	144.660i	−0.0826943	−	0.817288i
$178$	99.8694	−	57.6596i	0.561064	−	0.323930i
$179$	132.848			0.742165			0.371083	−	0.928600i	$-0.378987\pi$
$179$	132.848			0.742165			0.371083	+	0.928600i	$0.378987\pi$
$180$	35.7541	+	174.874i	0.198634	+	0.971524i
$181$			93.4546i			0.516323i	0.966102	+	0.258162i	$0.0831167\pi$
$181$			93.4546i			0.516323i	−0.966102	+	0.258162i	$0.916883\pi$
$182$	−91.6973	−	77.8615i	−0.503831	−	0.427810i
$183$	108.279	+	48.7136i	0.591691	+	0.266195i
$184$	−0.248927	+	0.431154i	−0.00135286	+	0.00234323i
$185$	20.8137	+	12.0168i	0.112506	+	0.0649556i
$186$	−0.0818344	+	0.0589722i	−0.000439970	+	0.000317055i
$187$	235.731	−	136.099i	1.26059	−	0.727803i
$188$			91.8767i			0.488706i
$189$	73.8551	−	173.972i	0.390768	−	0.920489i
$190$	65.4420			0.344432
$191$	−146.456	−	253.668i	−0.766783	−	1.32811i	−0.939299	−	0.343100i	$-0.888523\pi$
$191$	−146.456	−	253.668i	−0.766783	−	1.32811i	0.172516	−	0.985007i	$-0.444810\pi$
$192$	14.0314	+	19.4710i	0.0730801	+	0.101412i
$193$	129.618	−	224.504i	0.671594	−	1.16323i	−0.305859	−	0.952077i	$-0.598943\pi$
$193$	129.618	−	224.504i	0.671594	−	1.16323i	0.977452	−	0.211157i	$-0.0677232\pi$
$194$	−133.254	−	76.9342i	−0.686876	−	0.396568i
$195$	−148.313	+	329.668i	−0.760582	+	1.69060i
$196$	91.6916	+	34.5927i	0.467814	+	0.176494i
$197$	336.752			1.70940			0.854700	−	0.519123i	$-0.173741\pi$
$197$	336.752			1.70940			0.854700	+	0.519123i	$0.173741\pi$
$198$	−113.855	−	128.440i	−0.575025	−	0.648687i
$199$		−	92.4947i		−	0.464797i	−0.972621	−	0.232399i	$-0.925343\pi$
$199$		−	92.4947i		−	0.464797i	0.972621	−	0.232399i	$-0.0746574\pi$
$200$	103.706	+	179.625i	0.518532	+	0.898124i
$201$	−269.627	+	27.2813i	−1.34143	+	0.135728i
$202$	170.204	+	98.2676i	0.842596	+	0.486473i
$203$	96.6556	+	17.6264i	0.476136	+	0.0868296i
$204$	−12.1918	−	120.494i	−0.0597637	−	0.590659i
$205$	−54.2834	−	94.0215i	−0.264797	−	0.458642i
$206$			107.934i			0.523953i
$207$	−1.05084	−	1.18545i	−0.00507651	−	0.00572683i
$208$			48.6064i			0.233684i
$209$	−54.4984	+	31.4647i	−0.260758	+	0.150549i
$210$	23.4004	−	293.566i	0.111430	−	1.39793i
$211$	−99.0672	+	171.589i	−0.469513	+	0.813220i	−0.999392	−	0.0348530i	$-0.988904\pi$
$211$	−99.0672	+	171.589i	−0.469513	+	0.813220i	0.529880	+	0.848073i	$0.322237\pi$
$212$	57.1896	−	99.0552i	0.269762	−	0.467242i
$213$	−141.514	−	196.375i	−0.664383	−	0.921950i
$214$	59.8049	+	103.585i	0.279462	+	0.484043i
$215$			70.0687i			0.325901i
$216$	−72.8997	+	22.7515i	−0.337499	+	0.105331i
$217$	0.156719	−	0.0560054i	0.000722208	−	0.000258089i
$218$	17.0491	+	29.5299i	0.0782069	+	0.135458i
$219$	43.4263	−	31.2942i	0.198294	−	0.142896i
$220$	−231.614	−	133.722i	−1.05279	−	0.607829i
$221$	122.640	−	212.418i	0.554930	−	0.961168i
$222$	−4.21879	+	9.37743i	−0.0190036	+	0.0422407i
$223$	−150.650	+	86.9779i	−0.675561	+	0.390036i	−0.798181	−	0.602418i	$-0.794204\pi$
$223$	−150.650	+	86.9779i	−0.675561	+	0.390036i	0.122619	+	0.992454i	$0.460871\pi$
$224$	−13.3255	−	37.2885i	−0.0594887	−	0.166466i
$225$	−646.607	+	132.203i	−2.87381	+	0.587567i
$226$	205.738			0.910343
$227$	−178.543	+	103.082i	−0.786535	+	0.454106i	−0.838741	−	0.544530i	$-0.816708\pi$
$227$	−178.543	+	103.082i	−0.786535	+	0.454106i	0.0522063	+	0.998636i	$0.483375\pi$
$228$	2.81861	+	27.8570i	0.0123623	+	0.122180i
$229$	−17.2640	−	9.96735i	−0.0753884	−	0.0435255i	0.461832	−	0.886967i	$-0.347192\pi$
$229$	−17.2640	−	9.96735i	−0.0753884	−	0.0435255i	−0.537220	+	0.843442i	$0.680526\pi$
$230$	−2.13771	−	1.23421i	−0.00929438	−	0.00536611i
$231$	121.660	+	255.725i	0.526665	+	1.10703i
$232$	−19.8494	−	34.3802i	−0.0855579	−	0.148191i
$233$	257.078			1.10334			0.551670	−	0.834062i	$-0.313991\pi$
$233$	257.078			1.10334			0.551670	+	0.834062i	$0.313991\pi$
$234$	−146.719	−	48.9344i	−0.627005	−	0.209122i
$235$	−455.535			−1.93845
$236$	83.9459	−	48.4662i	0.355703	−	0.205365i
$237$	−25.0577	+	55.6978i	−0.105729	+	0.235012i
$238$	−35.8487	+	196.579i	−0.150625	+	0.825961i
$239$	−6.18007	+	10.7042i	−0.0258580	+	0.0447874i	−0.878665	−	0.477439i	$-0.841565\pi$
$239$	−6.18007	+	10.7042i	−0.0258580	+	0.0447874i	0.852807	+	0.522227i	$0.174898\pi$
$240$	−96.5395	+	69.5691i	−0.402248	+	0.289871i
$241$	−257.287	+	148.544i	−1.06758	+	0.616367i	−0.927519	−	0.373776i	$-0.878063\pi$
$241$	−257.287	+	148.544i	−1.06758	+	0.616367i	−0.140060	+	0.990143i	$0.544730\pi$
$242$	86.0560			0.355603
$243$	4.71585	−	242.954i	0.0194068	−	0.999812i
$244$			79.1551i			0.324406i
$245$	−171.515	+	454.617i	−0.700060	+	1.85558i
$246$	37.6846	−	27.1566i	0.153189	−	0.110393i
$247$	−28.3530	+	49.1088i	−0.114789	+	0.198821i
$248$	−0.0582368	−	0.0336230i	−0.000234826	−	0.000135577i
$249$	−79.7126	−	35.8617i	−0.320131	−	0.144023i
$250$	−586.978	+	338.892i	−2.34791	+	1.35557i
$251$		−	349.874i		−	1.39392i	−0.717111	−	0.696959i	$-0.754536\pi$
$251$		−	349.874i		−	1.39392i	0.717111	−	0.696959i	$-0.245464\pi$
$252$	125.971	−	2.68301i	0.499887	−	0.0106469i
$253$	2.37364			0.00938196
$254$	110.204	+	190.879i	0.433874	+	0.751492i
$255$	597.425	−	60.4483i	2.34284	−	0.237052i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	292.983	+	169.154i	1.14001	+	0.658186i	0.946433	−	0.322899i	$-0.104657\pi$
$257$	292.983	+	169.154i	1.14001	+	0.658186i	0.193578	+	0.981085i	$0.437991\pi$
$258$	−29.8265	+	3.01788i	−0.115607	+	0.0116972i
$259$	10.9811	−	12.9324i	0.0423981	−	0.0499321i
$260$	−240.996			−0.926907
$261$	123.761	−	25.3036i	0.474179	−	0.0969486i
$262$			140.610i			0.536679i
$263$	32.7296	+	56.6894i	0.124447	+	0.215549i	0.921517	−	0.388339i	$-0.126951\pi$
$263$	32.7296	+	56.6894i	0.124447	+	0.215549i	−0.797069	+	0.603888i	$0.793618\pi$
$264$	46.9466	−	104.352i	0.177828	−	0.395272i
$265$	491.127	+	283.552i	1.85331	+	1.07001i
$266$	8.28784	−	45.4469i	0.0311573	−	0.170853i
$267$	−198.466	+	143.020i	−0.743317	+	0.535655i
$268$	−90.3347	−	156.464i	−0.337070	−	0.583822i
$269$			248.366i			0.923293i	0.887064	+	0.461646i	$0.152741\pi$
$269$			248.366i			0.923293i	−0.887064	+	0.461646i	$0.847259\pi$
$270$	−112.805	−	361.445i	−0.417795	−	1.33868i
$271$		−	59.5945i		−	0.219906i	−0.993937	−	0.109953i	$-0.964930\pi$
$271$		−	59.5945i		−	0.219906i	0.993937	−	0.109953i	$-0.0350700\pi$
$272$	69.9227	−	40.3699i	0.257069	−	0.148419i
$273$	210.158	+	144.748i	0.769810	+	0.530214i
$274$	17.4428	−	30.2118i	0.0636599	−	0.110262i
$275$	494.445	−	856.404i	1.79798	−	3.11420i
$276$	0.433299	−	0.963127i	0.00156992	−	0.00348959i
$277$	222.096	+	384.682i	0.801791	+	1.38874i	0.918436	+	0.395569i	$0.129453\pi$
$277$	222.096	+	384.682i	0.801791	+	1.38874i	−0.116645	+	0.993174i	$0.537214\pi$
$278$		−	161.002i		−	0.579143i
$279$	0.160122	−	0.141939i	0.000573913	−	0.000508742i
$280$	184.881	−	66.0692i	0.660288	−	0.235961i
$281$	−231.769	−	401.435i	−0.824799	−	1.42859i	−0.902073	−	0.431584i	$-0.857955\pi$
$281$	−231.769	−	401.435i	−0.824799	−	1.42859i	0.0772735	−	0.997010i	$-0.475379\pi$
$282$	−19.6200	−	193.910i	−0.0695746	−	0.687623i
$283$	−88.7084	−	51.2158i	−0.313457	−	0.180975i	0.335015	−	0.942213i	$-0.391259\pi$
$283$	−88.7084	−	51.2158i	−0.313457	−	0.180975i	−0.648472	+	0.761238i	$0.724592\pi$
$284$	80.6841	−	139.749i	0.284099	−	0.492074i
$285$	−138.118	+	13.9750i	−0.484626	+	0.0490351i
$286$	200.695	−	115.871i	0.701730	−	0.405144i
$287$	−72.1689	+	25.7904i	−0.251460	+	0.0898620i
$288$	−33.7718	−	38.0981i	−0.117263	−	0.132285i
$289$	−118.432			−0.409800
$290$	170.461	−	98.4157i	0.587796	−	0.339364i
$291$	297.668	+	133.917i	1.02291	+	0.460196i
$292$	30.9040	+	17.8424i	0.105836	+	0.0611042i
$293$	−288.554	−	166.597i	−0.984825	−	0.568589i	−0.0811016	−	0.996706i	$-0.525844\pi$
$293$	−288.554	−	166.597i	−0.984825	−	0.568589i	−0.903723	+	0.428117i	$0.859177\pi$
$294$	−200.906	−	53.4290i	−0.683355	−	0.181731i
$295$	240.301	+	416.213i	0.814579	+	1.41089i
$296$	−6.85515			−0.0231593
$297$	267.724	+	246.765i	0.901428	+	0.830859i
$298$	242.504			0.813773
$299$	1.85234	−	1.06945i	0.00619511	−	0.00357675i
$300$	−257.235	−	356.960i	−0.857451	−	1.18987i
$301$	48.6600	+	8.87378i	0.161661	+	0.0294810i
$302$	−167.990	+	290.968i	−0.556259	+	0.963469i
$303$	−380.209	−	171.051i	−1.25481	−	0.564526i
$304$	−16.1654	+	9.33309i	−0.0531756	+	0.0307010i
$305$	−392.460			−1.28675
$306$	51.4626	+	251.705i	0.168179	+	0.822567i
$307$		−	323.443i		−	1.05356i	−0.850002	−	0.526780i	$-0.823399\pi$
$307$		−	323.443i		−	1.05356i	0.850002	−	0.526780i	$-0.176601\pi$
$308$	−122.197	+	143.912i	−0.396745	+	0.467245i
$309$	−23.0491	−	227.800i	−0.0745927	−	0.737218i
$310$	0.166707	−	0.288745i	0.000537764	−	0.000931434i
$311$	399.241	+	230.502i	1.28373	+	0.741164i	0.977529	−	0.210801i	$-0.0676072\pi$
$311$	399.241	+	230.502i	1.28373	+	0.741164i	0.306205	+	0.951965i	$0.400941\pi$
$312$	−10.3798	−	102.586i	−0.0332685	−	0.328801i
$313$	237.475	−	137.106i	0.758705	−	0.438039i	−0.0701256	−	0.997538i	$-0.522340\pi$
$313$	237.475	−	137.106i	0.758705	−	0.438039i	0.828831	+	0.559500i	$0.189007\pi$
$314$		−	110.640i		−	0.352357i
$315$	13.3027	+	624.580i	0.0422307	+	1.98279i
$316$	−40.7165			−0.128850
$317$	212.280	+	367.679i	0.669652	+	1.15987i	0.978001	+	0.208598i	$0.0668901\pi$
$317$	212.280	+	367.679i	0.669652	+	1.15987i	−0.308349	+	0.951273i	$0.599777\pi$
$318$	−99.5481	+	221.273i	−0.313044	+	0.695827i
$319$	−94.6369	+	163.916i	−0.296667	+	0.513843i
$320$	−68.7016	−	39.6649i	−0.214693	−	0.123953i
$321$	−148.341	−	205.850i	−0.462122	−	0.641277i
$322$	−1.12784	+	1.32825i	−0.00350260	+	0.00412500i
$323$	94.1940			0.291622
$324$	149.000	−	63.5857i	0.459875	−	0.196252i
$325$		−	891.094i		−	2.74183i
$326$	−167.512	−	290.140i	−0.513842	−	0.890000i
$327$	−42.2889	−	58.6834i	−0.129324	−	0.179460i
$328$	26.8180	+	15.4834i	0.0817621	+	0.0472054i
$329$	−57.6907	+	316.351i	−0.175352	+	0.961553i
$330$	517.387	+	232.766i	1.56784	+	0.705352i
$331$	−123.513	−	213.931i	−0.373152	−	0.646318i	0.616897	−	0.787044i	$-0.288390\pi$
$331$	−123.513	−	213.931i	−0.373152	−	0.646318i	−0.990049	+	0.140726i	$0.955056\pi$
$332$		−	58.2720i		−	0.175518i
$333$	6.90142	−	20.6924i	0.0207250	−	0.0621393i
$334$		−	327.379i		−	0.980176i
$335$	775.768	−	447.890i	2.31572	−	1.33698i
$336$	36.0869	+	75.8534i	0.107401	+	0.225754i
$337$	−57.2883	+	99.2262i	−0.169995	+	0.294440i	−0.938418	−	0.345503i	$-0.887708\pi$
$337$	−57.2883	+	99.2262i	−0.169995	+	0.294440i	0.768423	+	0.639942i	$0.221042\pi$
$338$	−15.0888	+	26.1346i	−0.0446415	+	0.0773214i
$339$	−434.218	+	43.9348i	−1.28088	+	0.129601i
$340$	200.158	+	346.685i	0.588701	+	1.01966i
$341$			0.320612i			0.000940211i
$342$	−11.8976	−	58.1916i	−0.0347883	−	0.170151i
$343$	293.992	+	176.685i	0.857121	+	0.515116i
$344$	−9.99293	−	17.3083i	−0.0290492	−	0.0503147i
$345$	4.77529	+	2.14834i	0.0138414	+	0.00622709i
$346$	−156.505	−	90.3584i	−0.452327	−	0.261151i
$347$	−172.728	+	299.174i	−0.497776	+	0.862173i	−0.999997	−	0.00256650i	$-0.999183\pi$
$347$	−172.728	+	299.174i	−0.497776	+	0.862173i	0.502221	+	0.864739i	$0.332516\pi$
$348$	49.2349	+	68.3222i	0.141480	+	0.196328i
$349$	−584.225	+	337.302i	−1.67400	+	0.966483i	−0.708632	+	0.705578i	$0.750687\pi$
$349$	−584.225	+	337.302i	−1.67400	+	0.966483i	−0.965365	+	0.260905i	$0.915979\pi$
$350$	244.294	+	683.605i	0.697983	+	1.95316i
$351$	320.107	+	71.9467i	0.911986	+	0.204976i
$352$	76.2838			0.216715
$353$	−82.7699	+	47.7872i	−0.234476	+	0.135375i	−0.612635	−	0.790366i	$-0.709890\pi$
$353$	−82.7699	+	47.7872i	−0.234476	+	0.135375i	0.378159	+	0.925740i	$0.376557\pi$
$354$	−166.822	+	120.216i	−0.471248	+	0.339595i
$355$	692.891	+	400.041i	1.95181	+	1.12688i
$356$	−141.237	−	81.5430i	−0.396732	−	0.229053i
$357$	33.6814	−	422.544i	0.0943456	−	1.18360i
$358$	−93.9374	−	162.704i	−0.262395	−	0.454482i
$359$	−27.2256			−0.0758374			−0.0379187	−	0.999281i	$-0.512073\pi$
$359$	−27.2256			−0.0758374			−0.0379187	+	0.999281i	$0.512073\pi$
$360$	188.895	−	167.444i	0.524707	−	0.465124i
$361$	339.223			0.939677
$362$	114.458	−	66.0823i	0.316182	−	0.182548i
$363$	−181.625	+	18.3771i	−0.500344	+	0.0506255i
$364$	−30.5207	+	167.362i	−0.0838480	+	0.459786i
$365$	−88.4647	+	153.225i	−0.242369	+	0.419796i
$366$	−16.9034	−	167.060i	−0.0461841	−	0.456449i
$367$	−130.761	+	75.4949i	−0.356297	+	0.205708i	−0.667455	−	0.744650i	$-0.732616\pi$
$367$	−130.761	+	75.4949i	−0.356297	+	0.205708i	0.311158	+	0.950358i	$0.399283\pi$
$368$	0.704071			0.00191324
$369$	−73.7358	+	65.3627i	−0.199826	+	0.177135i
$370$		−	33.9886i		−	0.0918610i
$371$	259.114	−	305.158i	0.698421	−	0.822529i
$372$	0.130092	+	0.0585266i	0.000349708	+	0.000157330i
$373$	81.4304	−	141.042i	0.218312	−	0.378128i	−0.735980	−	0.677003i	$-0.763278\pi$
$373$	81.4304	−	141.042i	0.218312	−	0.378128i	0.954292	+	0.298876i	$0.0966116\pi$
$374$	−333.373	−	192.473i	−0.891373	−	0.514634i
$375$	1166.47	−	840.595i	3.11060	−	2.24159i
$376$	112.525	−	64.9666i	0.299270	−	0.172784i
$377$			170.556i			0.452402i
$378$	−265.295	+	32.5635i	−0.701840	+	0.0861469i
$379$	−391.275			−1.03239			−0.516194	−	0.856472i	$-0.672651\pi$
$379$	−391.275			−1.03239			−0.516194	+	0.856472i	$0.672651\pi$
$380$	−46.2745	−	80.1498i	−0.121775	−	0.210920i
$381$	−273.352	−	379.324i	−0.717460	−	0.995602i
$382$	−207.119	+	358.741i	−0.542197	+	0.939113i
$383$	−263.816	−	152.314i	−0.688815	−	0.397687i	0.114353	−	0.993440i	$-0.463521\pi$
$383$	−263.816	−	152.314i	−0.688815	−	0.397687i	−0.803168	+	0.595753i	$0.796854\pi$
$384$	13.9254	−	30.9529i	0.0362639	−	0.0806066i
$385$	−713.530	−	605.868i	−1.85332	−	1.57368i
$386$	−366.614			−0.949777
$387$	62.3057	−	12.7388i	0.160997	−	0.0329167i
$388$			217.603i			0.560832i
$389$	−135.460	−	234.623i	−0.348225	−	0.603144i	0.637709	−	0.770277i	$-0.279882\pi$
$389$	−135.460	−	234.623i	−0.348225	−	0.603144i	−0.985934	+	0.167134i	$0.946549\pi$
$390$	508.632	−	51.4641i	1.30419	−	0.131959i
$391$	−3.07691	−	1.77645i	−0.00786934	−	0.00454336i
$392$	−22.4684	−	136.760i	−0.0573174	−	0.348876i
$393$	−30.0269	−	296.763i	−0.0764044	−	0.755123i
$394$	−238.119	−	412.435i	−0.604364	−	1.04679i
$395$		−	201.877i		−	0.511081i
$396$	−76.7987	+	230.264i	−0.193936	+	0.581475i
$397$			455.963i			1.14852i	0.818672	+	0.574261i	$0.194710\pi$
$397$			455.963i			1.14852i	−0.818672	+	0.574261i	$0.805290\pi$
$398$	−113.282	+	65.4036i	−0.284629	+	0.164331i
$399$	−7.78677	+	97.6876i	−0.0195157	+	0.244831i
$400$	146.663	−	254.028i	0.366657	−	0.635069i
$401$	−214.070	+	370.780i	−0.533841	+	0.924640i	0.465378	+	0.885112i	$0.345919\pi$
$401$	−214.070	+	370.780i	−0.533841	+	0.924640i	−0.999218	+	0.0395273i	$0.987415\pi$
$402$	224.068	+	310.934i	0.557383	+	0.773468i
$403$	0.144453	+	0.250199i	0.000358443	+	0.000620842i
$404$		−	277.943i		−	0.687977i
$405$	315.265	+	738.756i	0.778432	+	1.82409i
$406$	−46.7580	−	130.842i	−0.115167	−	0.322271i
$407$	16.3418	+	28.3048i	0.0401518	+	0.0695449i
$408$	−138.954	+	100.134i	−0.340574	+	0.245427i
$409$	−310.087	−	179.029i	−0.758159	−	0.437723i	0.0704753	−	0.997514i	$-0.477548\pi$
$409$	−310.087	−	179.029i	−0.758159	−	0.437723i	−0.828634	+	0.559790i	$0.810882\pi$
$410$	−76.7683	+	132.967i	−0.187240	+	0.324309i
$411$	−30.3622	+	67.4883i	−0.0738738	+	0.164205i
$412$	132.192	−	76.3211i	0.320855	−	0.185245i
$413$	319.476	−	114.169i	0.773551	−	0.276437i
$414$	−0.708823	+	2.12525i	−0.00171213	+	0.00513346i
$415$	288.919			0.696191
$416$	59.5304	−	34.3699i	0.143102	−	0.0826199i
$417$	34.3815	+	339.801i	0.0824497	+	0.814871i
$418$	77.0724	+	44.4977i	0.184384	+	0.106454i
$419$	−396.340	−	228.827i	−0.945919	−	0.546127i	−0.0541082	−	0.998535i	$-0.517232\pi$
$419$	−396.340	−	228.827i	−0.945919	−	0.546127i	−0.891811	+	0.452409i	$0.850565\pi$
$420$	−376.090	+	178.923i	−0.895451	+	0.426007i
$421$	3.35845	+	5.81701i	0.00797732	+	0.0138171i	0.869987	−	0.493076i	$-0.164127\pi$
$421$	3.35845	+	5.81701i	0.00797732	+	0.0138171i	−0.862009	+	0.506893i	$0.830794\pi$
$422$	280.204			0.663991
$423$	82.8180	+	405.065i	0.195787	+	0.957601i
$424$	−161.757			−0.381501
$425$	−1281.88	+	740.096i	−3.01620	+	1.74140i
$426$	−140.444	+	312.176i	−0.329682	+	0.732808i
$427$	−49.7027	+	272.548i	−0.116400	+	0.638286i
$428$	84.5769	−	146.492i	0.197610	−	0.342270i
$429$	−398.831	+	287.409i	−0.929677	+	0.669952i
$430$	85.8163	−	49.5460i	0.199573	−	0.115223i
$431$	−399.366			−0.926602			−0.463301	−	0.886201i	$-0.653335\pi$
$431$	−399.366			−0.926602			−0.463301	+	0.886201i	$0.653335\pi$
$432$	79.4127	+	73.1958i	0.183826	+	0.169435i
$433$			566.950i			1.30935i	0.755909	+	0.654677i	$0.227195\pi$
$433$			566.950i			1.30935i	−0.755909	+	0.654677i	$0.772805\pi$
$434$	−0.179409	−	0.152339i	−0.000413386	−	0.000351012i
$435$	−338.749	+	244.112i	−0.778733	+	0.561177i
$436$	24.1111	−	41.7616i	0.0553006	−	0.0957835i
$437$	0.711349	+	0.410697i	0.00162780	+	0.000939811i
$438$	−69.0345	−	31.0578i	−0.157613	−	0.0709081i
$439$	−170.327	+	98.3382i	−0.387988	+	0.224005i	−0.681288	−	0.732015i	$-0.738580\pi$
$439$	−170.327	+	98.3382i	−0.387988	+	0.224005i	0.293300	+	0.956020i	$0.405247\pi$
$440$			378.224i			0.859600i
$441$	435.431	+	69.8612i	0.987373	+	0.158415i
$442$	−346.877			−0.784790
$443$	89.4345	+	154.905i	0.201884	+	0.349673i	0.949135	−	0.314868i	$-0.101960\pi$
$443$	89.4345	+	154.905i	0.201884	+	0.349673i	−0.747252	+	0.664541i	$0.768627\pi$
$444$	14.4681	−	1.46390i	0.0325858	−	0.00329707i
$445$	404.299	−	700.267i	0.908538	−	1.57363i
$446$	213.052	+	123.005i	0.477694	+	0.275797i
$447$	−511.816	+	51.7863i	−1.14500	+	0.115853i
$448$	−36.2464	+	42.6873i	−0.0809071	+	0.0952840i
$449$	381.811			0.850358			0.425179	−	0.905109i	$-0.360211\pi$
$449$	381.811			0.850358			0.425179	+	0.905109i	$0.360211\pi$
$450$	619.135	+	698.447i	1.37585	+	1.55210i
$451$		−	147.641i		−	0.327364i
$452$	−145.478	−	251.976i	−0.321855	−	0.557469i
$453$	292.415	−	649.974i	0.645508	−	1.43482i
$454$	252.499	+	145.780i	0.556164	+	0.321102i
$455$	−829.800	−	151.325i	−1.82374	−	0.332582i
$456$	32.1247	−	23.1500i	0.0704489	−	0.0507675i
$457$	−284.366	−	492.537i	−0.622245	−	1.07776i	−0.989067	−	0.147469i	$-0.952887\pi$
$457$	−284.366	−	492.537i	−0.622245	−	1.07776i	0.366821	−	0.930291i	$-0.380446\pi$
$458$			28.1919i			0.0615544i
$459$	−162.365	−	520.246i	−0.353737	−	1.13343i
$460$			3.49086i			0.00758883i
$461$	315.707	−	182.273i	0.684830	−	0.395387i	−0.116842	−	0.993150i	$-0.537277\pi$
$461$	315.707	−	182.273i	0.684830	−	0.395387i	0.801672	+	0.597764i	$0.203944\pi$
$462$	227.171	−	329.827i	0.491712	−	0.713911i
$463$	−59.3958	+	102.877i	−0.128285	+	0.222196i	−0.923012	−	0.384771i	$-0.874280\pi$
$463$	−59.3958	+	102.877i	−0.128285	+	0.222196i	0.794727	+	0.606967i	$0.207614\pi$
$464$	−28.0713	+	48.6210i	−0.0604985	+	0.104787i
$465$	−0.290181	+	0.645008i	−0.000624046	+	0.00138711i
$466$	−181.782	−	314.855i	−0.390090	−	0.675655i
$467$			401.009i			0.858692i	0.903140	+	0.429346i	$0.141256\pi$
$467$			401.009i			0.858692i	−0.903140	+	0.429346i	$0.858744\pi$
$468$	43.8140	+	214.295i	0.0936196	+	0.457896i
$469$	−212.795	−	595.463i	−0.453722	−	1.26964i
$470$	322.112	+	557.914i	0.685344	+	1.18705i
$471$	23.6269	+	233.511i	0.0501633	+	0.495776i
$472$	−118.717	−	68.5415i	−0.251520	−	0.145215i
$473$	−47.6437	+	82.5213i	−0.100727	+	0.174464i
$474$	85.9341	−	8.69492i	0.181295	−	0.0183437i
$475$	296.358	−	171.102i	0.623911	−	0.360215i
$476$	266.108	−	95.0967i	0.559050	−	0.199783i
$477$	162.848	−	488.265i	0.341401	−	1.02362i
$478$	17.4799			0.0365688
$479$	103.679	−	59.8591i	0.216449	−	0.124967i	−0.387856	−	0.921720i	$-0.626784\pi$
$479$	103.679	−	59.8591i	0.216449	−	0.124967i	0.604305	+	0.796753i	$0.293451\pi$
$480$	153.468	+	69.0434i	0.319725	+	0.143841i
$481$	25.5056	+	14.7257i	0.0530262	+	0.0306147i
$482$	363.858	+	210.074i	0.754893	+	0.435837i
$483$	2.09670	−	3.04418i	0.00434100	−	0.00630264i
$484$	−60.8508	−	105.397i	−0.125725	−	0.217762i
$485$	−1078.90			−2.22453
$486$	−300.892	+	166.019i	−0.619118	+	0.341603i
$487$	−570.074			−1.17058			−0.585291	−	0.810823i	$-0.699020\pi$
$487$	−570.074			−1.17058			−0.585291	+	0.810823i	$0.699020\pi$
$488$	96.9448	−	55.9711i	0.198657	−	0.114695i
$489$	415.501	+	576.582i	0.849696	+	1.17910i
$490$	678.069	−	111.401i	1.38381	−	0.227349i
$491$	−141.060	+	244.323i	−0.287291	+	0.497602i	−0.973162	−	0.230121i	$-0.926088\pi$
$491$	−141.060	+	244.323i	−0.287291	+	0.497602i	0.685871	+	0.727723i	$0.259421\pi$
$492$	−59.9070	−	26.9514i	−0.121762	−	0.0547793i
$493$	245.353	−	141.655i	0.497673	−	0.287332i
$494$	80.1943			0.162337
$495$	−1141.68	−	380.777i	−2.30642	−	0.769246i
$496$			0.0951003i			0.000191735i
$497$	365.563	−	430.523i	0.735540	−	0.866243i
$498$	12.4439	+	122.986i	0.0249877	+	0.246959i
$499$	30.1314	−	52.1891i	0.0603835	−	0.104587i	−0.834253	−	0.551381i	$-0.814101\pi$
$499$	30.1314	−	52.1891i	0.0603835	−	0.104587i	0.894637	+	0.446794i	$0.147434\pi$
$500$	830.113	+	479.266i	1.66023	+	0.958532i
$501$	69.9110	+	690.947i	0.139543	+	1.37914i
$502$	−428.506	+	247.398i	−0.853597	+	0.492825i
$503$			3.37300i			0.00670576i	0.999994	+	0.00335288i	$0.00106726\pi$
$503$			3.37300i			0.00670576i	−0.999994	+	0.00335288i	$0.998933\pi$
$504$	−92.3613	−	152.386i	−0.183256	−	0.302353i
$505$	1378.07			2.72885
$506$	−1.67841	−	2.90710i	−0.00331702	−	0.00574525i
$507$	26.2647	−	58.3805i	0.0518041	−	0.115149i
$508$	155.852	−	269.943i	0.306795	−	0.531385i
$509$	11.9659	+	6.90849i	0.0235086	+	0.0135727i	0.511708	−	0.859159i	$-0.329013\pi$
$509$	11.9659	+	6.90849i	0.0235086	+	0.0135727i	−0.488200	+	0.872732i	$0.662346\pi$
$510$	−496.477	−	688.950i	−0.973484	−	1.35088i
$511$	95.2055	+	80.8404i	0.186312	+	0.158200i
$512$	22.6274			0.0441942
$513$	37.5371	+	120.275i	0.0731718	+	0.234455i
$514$		−	478.439i		−	0.930816i
$515$	378.409	+	655.423i	0.734774	+	1.27267i
$516$	24.7867	+	34.3959i	0.0480362	+	0.0666587i
$517$	−536.492	−	309.744i	−1.03770	−	0.599118i
$518$	−23.6037	−	4.30445i	−0.0455671	−	0.00830975i
$519$	349.607	+	157.284i	0.673617	+	0.303052i
$520$	170.410	+	295.158i	0.327711	+	0.567612i
$521$		−	163.277i		−	0.313391i	−0.987647	−	0.156695i	$-0.949916\pi$
$521$		−	163.277i		−	0.313391i	0.987647	−	0.156695i	$-0.0500841\pi$
$522$	−118.502	−	133.683i	−0.227016	−	0.256098i
$523$		−	953.671i		−	1.82346i	−0.410787	−	0.911731i	$-0.634746\pi$
$523$		−	953.671i		−	1.82346i	0.410787	−	0.911731i	$-0.365254\pi$
$524$	172.211	−	99.4262i	0.328647	−	0.189745i
$525$	−661.576	−	1390.61i	−1.26014	−	2.64878i
$526$	46.2867	−	80.1709i	0.0879975	−	0.152416i
$527$	0.239949	−	0.415605i	0.000455312	−	0.000788624i
$528$	−161.000	+	16.2902i	−0.304925	+	0.0308527i
$529$	264.485	+	458.101i	0.499971	+	0.865975i
$530$		−	802.007i		−	1.51322i
$531$	326.413	−	289.347i	0.614713	−	0.544909i
$532$	−61.5213	+	21.9853i	−0.115641	+	0.0413258i
$533$	−66.5202	−	115.216i	−0.124803	−	0.216166i
$534$	315.499	+	141.939i	0.590823	+	0.265804i
$535$	726.321	+	419.342i	1.35761	+	0.783817i
$536$	−127.753	+	221.274i	−0.238344	+	0.412825i
$537$	233.004	+	323.335i	0.433900	+	0.602113i
$538$	304.185	−	175.621i	0.565399	−	0.326433i
$539$	−511.116	+	418.789i	−0.948267	+	0.776974i
$540$	−362.913	+	393.737i	−0.672061	+	0.729143i
$541$	296.567			0.548183			0.274092	−	0.961704i	$-0.411623\pi$
$541$	296.567			0.548183			0.274092	+	0.961704i	$0.411623\pi$
$542$	−72.9881	+	42.1397i	−0.134664	+	0.0777485i
$543$	−227.457	+	163.912i	−0.418889	+	0.301864i
$544$	−98.8857	−	57.0917i	−0.181775	−	0.104948i
$545$	207.059	+	119.545i	0.379924	+	0.219349i
$546$	28.6754	−	359.743i	0.0525191	−	0.658870i
$547$	−205.972	−	356.754i	−0.376548	−	0.652201i	0.614009	−	0.789299i	$-0.289556\pi$
$547$	−205.972	−	356.754i	−0.376548	−	0.652201i	−0.990557	+	0.137098i	$0.956223\pi$
$548$	−49.3357			−0.0900287
$549$	71.3507	+	348.979i	0.129965	+	0.635663i
$550$	−1398.50			−2.54273
$551$	−56.7230	+	32.7490i	−0.102945	+	0.0594356i
$552$	−1.48597	+	0.150353i	−0.00269198	+	0.000272378i
$553$	−140.196	−	25.5665i	−0.253519	−	0.0462324i
$554$	314.091	−	544.022i	0.566952	−	0.981989i
$555$	7.25818	+	71.7344i	0.0130778	+	0.129251i
$556$	−197.186	+	113.845i	−0.354651	+	0.204758i
$557$	558.037			1.00186			0.500931	−	0.865487i	$-0.332991\pi$
$557$	558.037			1.00186			0.500931	+	0.865487i	$0.332991\pi$
$558$	−0.287062	−	0.0957422i	−0.000514448	−	0.000171581i
$559$			85.8639i			0.153603i
$560$	−211.648	−	179.713i	−0.377943	−	0.320917i
$561$	744.702	+	335.032i	1.32745	+	0.597205i
$562$	−327.770	+	567.715i	−0.583221	+	1.01017i
$563$	−251.341	−	145.112i	−0.446432	−	0.257748i	0.259890	−	0.965638i	$-0.416314\pi$
$563$	−251.341	−	145.112i	−0.446432	−	0.257748i	−0.706322	+	0.707891i	$0.749647\pi$
$564$	−223.616	+	161.144i	−0.396483	+	0.285717i
$565$	1249.33	−	721.298i	2.21120	−	1.27663i
$566$			144.860i			0.255937i
$567$	552.964	−	125.380i	0.975245	−	0.221129i
$568$	−228.209			−0.401777
$569$	321.956	+	557.644i	0.565828	+	0.980043i	0.996972	+	0.0777596i	$0.0247767\pi$
$569$	321.956	+	557.644i	0.565828	+	0.980043i	−0.431144	+	0.902283i	$0.641890\pi$
$570$	114.780	+	159.278i	0.201369	+	0.279435i
$571$	542.172	−	939.070i	0.949514	−	1.64461i	0.203063	−	0.979166i	$-0.434910\pi$
$571$	542.172	−	939.070i	0.949514	−	1.64461i	0.746451	−	0.665441i	$-0.231756\pi$
$572$	−283.825	−	163.867i	−0.496198	−	0.286480i
$573$	360.526	−	801.369i	0.629191	−	1.39855i
$574$	82.6178	+	70.1520i	0.143933	+	0.122216i
$575$	−12.9076			−0.0224481
$576$	−22.7801	+	68.3013i	−0.0395489	+	0.118579i
$577$			650.622i			1.12759i	0.825913	+	0.563797i	$0.190660\pi$
$577$			650.622i			1.12759i	−0.825913	+	0.563797i	$0.809340\pi$
$578$	83.7443	+	145.049i	0.144886	+	0.250950i
$579$	773.755	−	78.2895i	1.33636	−	0.135215i
$580$	−241.068	−	139.181i	−0.415635	−	0.239967i
$581$	36.5899	−	200.643i	0.0629774	−	0.345341i
$582$	−46.4686	−	459.261i	−0.0798429	−	0.789107i
$583$	385.607	+	667.890i	0.661418	+	1.14561i
$584$		−	50.4660i		−	0.0864144i
$585$	−1062.50	+	217.234i	−1.81624	+	0.371341i
$586$			471.206i			0.804106i
$587$	−199.425	+	115.138i	−0.339736	+	0.196147i	−0.660155	−	0.751129i	$-0.729510\pi$
$587$	−199.425	+	115.138i	−0.339736	+	0.196147i	0.320419	+	0.947276i	$0.396176\pi$
$588$	76.6253	+	283.839i	0.130315	+	0.482719i
$589$	−0.0554737	+	0.0960833i	−9.41829e−5	+	0.000163130i
$590$	339.837	−	588.614i	0.575994	−	0.997651i
$591$	590.636	+	819.612i	0.999384	+	1.38682i
$592$	4.84732	+	8.39581i	0.00818804	+	0.0141821i
$593$		−	715.009i		−	1.20575i	−0.797836	−	0.602875i	$-0.794022\pi$
$593$		−	715.009i		−	1.20575i	0.797836	−	0.602875i	$-0.205978\pi$
$594$	112.915	−	502.383i	0.190092	−	0.845763i
$595$	471.500	+	1319.39i	0.792437	+	2.21747i
$596$	−171.477	−	297.006i	−0.287712	−	0.498332i
$597$	225.121	−	162.228i	0.377087	−	0.271739i
$598$	−2.61960	−	1.51243i	−0.00438060	−	0.00252914i
$599$	433.990	−	751.692i	0.724523	−	1.25491i	−0.234646	−	0.972081i	$-0.575393\pi$
$599$	433.990	−	751.692i	0.724523	−	1.25491i	0.959170	−	0.282831i	$-0.0912734\pi$
$600$	−255.292	+	567.456i	−0.425486	+	0.945760i
$601$	−242.032	+	139.737i	−0.402716	+	0.232508i	−0.687655	−	0.726037i	$-0.741360\pi$
$601$	−242.032	+	139.737i	−0.402716	+	0.232508i	0.284939	+	0.958546i	$0.408027\pi$
$602$	−23.5397	−	65.8707i	−0.0391024	−	0.109420i
$603$	−539.305	−	608.391i	−0.894369	−	1.00894i
$604$	475.148			0.786669
$605$	522.568	−	301.705i	0.863749	−	0.498686i
$606$	59.3540	+	586.610i	0.0979439	+	0.968004i
$607$	−381.944	−	220.515i	−0.629232	−	0.363287i	0.151223	−	0.988500i	$-0.451679\pi$
$607$	−381.944	−	220.515i	−0.629232	−	0.363287i	−0.780454	+	0.625213i	$0.785012\pi$
$608$	22.8613	+	13.1990i	0.0376008	+	0.0217089i
$609$	126.626	+	266.163i	0.207924	+	0.437049i
$610$	277.511	+	480.663i	0.454936	+	0.787973i
$611$	−558.224			−0.913623
$612$	271.885	−	241.011i	0.444257	−	0.393809i
$613$	−249.504			−0.407022			−0.203511	−	0.979073i	$-0.565235\pi$
$613$	−249.504			−0.407022			−0.203511	+	0.979073i	$0.565235\pi$
$614$	−396.135	+	228.709i	−0.645171	+	0.372490i
$615$	133.628	−	297.025i	0.217282	−	0.482968i
$616$	262.662	+	47.8998i	0.426399	+	0.0777594i
$617$	276.294	−	478.555i	0.447802	−	0.775616i	−0.550440	−	0.834874i	$-0.685540\pi$
$617$	276.294	−	478.555i	0.447802	−	0.775616i	0.998243	+	0.0592581i	$0.0188735\pi$
$618$	−262.699	+	189.308i	−0.425079	+	0.306324i
$619$	−855.461	+	493.901i	−1.38201	+	0.797901i	−0.992397	−	0.123079i	$-0.960723\pi$
$619$	−855.461	+	493.901i	−1.38201	+	0.797901i	−0.389609	+	0.920980i	$0.627390\pi$
$620$	−0.471518			−0.000760513
$621$	1.04216	−	4.63680i	0.00167820	−	0.00746667i
$622$		−	651.958i		−	1.04816i
$623$	−435.106	−	369.455i	−0.698404	−	0.593025i
$624$	−118.302	+	85.2518i	−0.189586	+	0.136621i
$625$	−1459.61	+	2528.12i	−2.33538	+	4.04499i
$626$	−335.840	−	193.897i	−0.536485	−	0.309740i
$627$	−172.167	−	77.4558i	−0.274589	−	0.123534i
$628$	−135.506	+	78.2343i	−0.215774	+	0.124577i
$629$		−	48.9215i		−	0.0777766i
$630$	755.545	−	457.937i	1.19928	−	0.726885i
$631$	−236.443			−0.374712			−0.187356	−	0.982292i	$-0.559992\pi$
$631$	−236.443			−0.374712			−0.187356	+	0.982292i	$0.559992\pi$
$632$	28.7909	+	49.8674i	0.0455553	+	0.0789041i
$633$	−591.383	+	59.8370i	−0.934255	+	0.0945292i
$634$	300.209	−	519.977i	0.473516	−	0.820153i
$635$	1338.41	+	772.731i	2.10773	+	1.21690i
$636$	341.394	−	34.5427i	0.536783	−	0.0543125i
$637$	−210.178	+	557.099i	−0.329950	+	0.874567i
$638$	267.674			0.419551
$639$	229.750	−	688.854i	0.359545	−	1.07802i
$640$			112.189i			0.175296i
$641$	122.793	+	212.685i	0.191565	+	0.331801i	0.945769	−	0.324839i	$-0.105310\pi$
$641$	122.793	+	212.685i	0.191565	+	0.331801i	−0.754204	+	0.656640i	$0.771977\pi$
$642$	−147.220	+	327.238i	−0.229315	+	0.509717i
$643$	−1004.04	−	579.685i	−1.56150	−	0.901532i	−0.997106	−	0.0760269i	$-0.975777\pi$
$643$	−1004.04	−	579.685i	−1.56150	−	0.901532i	−0.564394	−	0.825505i	$-0.690890\pi$
$644$	2.42427	+	0.442097i	0.00376439	+	0.000686486i
$645$	−170.539	+	122.895i	−0.264401	+	0.190535i
$646$	−66.6052	−	115.364i	−0.103104	−	0.178581i
$647$			78.1821i			0.120838i	0.998173	+	0.0604189i	$0.0192437\pi$
$647$			78.1821i			0.120838i	−0.998173	+	0.0604189i	$0.980756\pi$
$648$	−183.235	−	137.525i	−0.282770	−	0.212229i
$649$			653.577i			1.00705i
$650$	−1091.36	+	630.099i	−1.67902	+	0.969383i
$651$	0.411183	+	0.283206i	0.000631618	+	0.000435032i
$652$	−236.898	+	410.320i	−0.363341	+	0.629325i
$653$	−615.100	+	1065.38i	−0.941960	+	1.63152i	−0.180233	+	0.983624i	$0.557685\pi$
$653$	−615.100	+	1065.38i	−0.941960	+	1.63152i	−0.761727	+	0.647898i	$0.775648\pi$
$654$	−41.9694	+	93.2886i	−0.0641734	+	0.142643i
$655$	492.966	+	853.843i	0.752620	+	1.30358i
$656$		−	43.7936i		−	0.0667585i
$657$	152.333	+	50.8066i	0.231861	+	0.0773312i
$658$	428.243	−	153.037i	0.650825	−	0.232580i
$659$	59.0656	+	102.305i	0.0896291	+	0.155242i	0.907354	−	0.420367i	$-0.138099\pi$
$659$	59.0656	+	102.305i	0.0896291	+	0.155242i	−0.817725	+	0.575609i	$0.804765\pi$
$660$	−80.7688	−	798.258i	−0.122377	−	1.20948i
$661$	558.811	+	322.629i	0.845402	+	0.488093i	0.859097	−	0.511813i	$-0.171026\pi$
$661$	558.811	+	322.629i	0.845402	+	0.488093i	−0.0136948	+	0.999906i	$0.504359\pi$
$662$	−174.674	+	302.545i	−0.263858	+	0.457016i
$663$	732.100	−	74.0748i	1.10422	−	0.111727i
$664$	−71.3683	+	41.2045i	−0.107482	+	0.0620550i
$665$	−109.006	−	305.029i	−0.163918	−	0.458691i
$666$	−30.2229	+	6.17925i	−0.0453798	+	0.00927816i
$667$	2.47053			0.00370394
$668$	−400.955	+	231.492i	−0.600233	+	0.346545i
$669$	−475.922	−	214.112i	−0.711393	−	0.320047i
$670$	−1097.10	−	633.412i	−1.63746	−	0.945390i
$671$	−462.208	−	266.856i	−0.688834	−	0.397699i
$672$	67.3838	−	97.8337i	0.100273	−	0.145586i
$673$	−429.109	−	743.239i	−0.637607	−	1.10437i	−0.985956	−	0.167002i	$-0.946591\pi$
$673$	−429.109	−	743.239i	−0.637607	−	1.10437i	0.348350	−	0.937365i	$-0.386742\pi$
$674$	162.036			0.240409
$675$	−1455.86	−	1341.89i	−2.15683	−	1.98798i
$676$	42.6777			0.0631327
$677$	88.6309	−	51.1710i	0.130917	−	0.0755850i	−0.433111	−	0.901341i	$-0.642584\pi$
$677$	88.6309	−	51.1710i	0.130917	−	0.0755850i	0.564028	+	0.825756i	$0.309251\pi$
$678$	360.848	+	500.740i	0.532224	+	0.738555i
$679$	−136.636	+	749.253i	−0.201231	+	1.10347i
$680$	283.067	−	490.286i	0.416275	−	0.721009i
$681$	−564.040	−	253.755i	−0.828253	−	0.372621i
$682$	0.392668	−	0.226707i	0.000575759	−	0.000332415i
$683$	1031.39			1.51009			0.755044	−	0.655674i	$-0.227616\pi$
$683$	1031.39			1.51009			0.755044	+	0.655674i	$0.227616\pi$
$684$	−62.8570	+	55.7192i	−0.0918962	+	0.0814608i
$685$		−	244.612i		−	0.357098i
$686$	8.50975	−	485.001i	0.0124049	−	0.706998i
$687$	−6.02032	−	59.5003i	−0.00876320	−	0.0866089i
$688$	−14.1321	+	24.4776i	−0.0205409	+	0.0355779i
$689$	601.839	+	347.472i	0.873497	+	0.504314i
$690$	−0.745466	−	7.36762i	−0.00108038	−	0.0106777i
$691$	−791.470	+	456.956i	−1.14540	+	0.661296i	−0.947762	−	0.318979i	$-0.896660\pi$
$691$	−791.470	+	456.956i	−1.14540	+	0.661296i	−0.197637	+	0.980275i	$0.563327\pi$
$692$			255.572i			0.369324i
$693$	−409.021	+	744.626i	−0.590218	+	1.07450i
$694$	488.549			0.703961
$695$	−564.458	−	977.670i	−0.812170	−	1.40672i
$696$	48.8629	−	108.611i	0.0702053	−	0.156051i
$697$	−110.496	+	191.385i	−0.158531	+	0.274584i
$698$	826.219	+	477.018i	1.18369	+	0.683406i
$699$	450.895	+	625.697i	0.645057	+	0.895132i
$700$	664.500	−	782.580i	0.949285	−	1.11797i
$701$	−194.138			−0.276945			−0.138472	−	0.990366i	$-0.544219\pi$
$701$	−194.138			−0.276945			−0.138472	+	0.990366i	$0.544219\pi$
$702$	−138.234	−	442.924i	−0.196914	−	0.630945i
$703$			11.3101i			0.0160884i
$704$	−53.9408	−	93.4282i	−0.0766205	−	0.132711i
$705$	−798.972	−	1108.72i	−1.13329	−	1.57265i
$706$	117.054	+	67.5813i	0.165799	+	0.0957243i
$707$	174.524	−	957.016i	0.246852	−	1.35363i
$708$	265.195	+	119.308i	0.374570	+	0.168514i
$709$	217.583	+	376.864i	0.306886	+	0.531543i	0.977680	−	0.210102i	$-0.0673795\pi$
$709$	217.583	+	376.864i	0.306886	+	0.531543i	−0.670793	+	0.741645i	$0.734046\pi$
$710$		−	1131.49i		−	1.59364i
$711$	−179.511	+	36.7020i	−0.252477	+	0.0516203i
$712$			230.638i			0.323930i
$713$	0.00362417	−	0.00209242i	5.08299e−6	−	2.93467e-6i
$714$	−541.325	+	257.532i	−0.758158	+	0.360690i
$715$	812.469	−	1407.24i	1.13632	−	1.96817i
$716$	−132.848	+	230.099i	−0.185541	+	0.321367i
$717$	−36.8921	+	3.73279i	−0.0514534	+	0.00520612i
$718$	19.2514	+	33.3445i	0.0268126	+	0.0464408i
$719$			922.050i			1.28241i	0.767371	+	0.641203i	$0.221564\pi$
$719$			922.050i			1.28241i	−0.767371	+	0.641203i	$0.778436\pi$
$720$	−338.645	−	112.946i	−0.470341	−	0.156870i
$721$	503.089	−	179.785i	0.697765	−	0.249354i
$722$	−239.867	−	415.462i	−0.332226	−	0.575432i
$723$	−812.800	−	365.669i	−1.12420	−	0.505766i
$724$	−161.868	−	93.4546i	−0.223575	−	0.129081i
$725$	514.628	−	891.362i	0.709832	−	1.22946i
$726$	150.935	+	209.450i	0.207900	+	0.288498i
$727$	451.861	−	260.882i	0.621542	−	0.358847i	−0.155927	−	0.987769i	$-0.549837\pi$
$727$	451.861	−	260.882i	0.621542	−	0.358847i	0.777469	+	0.628921i	$0.216503\pi$
$728$	226.557	−	80.9628i	0.311205	−	0.111213i
$729$	599.592	−	414.645i	0.822486	−	0.568786i
$730$	250.216			0.342762
$731$	123.520	−	71.3141i	0.168974	−	0.0975569i
$732$	−192.654	+	138.832i	−0.263188	+	0.189661i
$733$	132.926	+	76.7450i	0.181346	+	0.104700i	0.587925	−	0.808916i	$-0.299945\pi$
$733$	132.926	+	76.7450i	0.181346	+	0.104700i	−0.406579	+	0.913616i	$0.633278\pi$
$734$	184.924	+	106.766i	0.251940	+	0.145458i
$735$	−1407.31	+	379.917i	−1.91470	+	0.516894i
$736$	−0.497853	−	0.862307i	−0.000676431	−	0.00117161i
$737$	1218.18			1.65289
$738$	132.192	+	44.0892i	0.179122	+	0.0597414i
$739$	−316.707			−0.428561			−0.214280	−	0.976772i	$-0.568741\pi$
$739$	−316.707			−0.428561			−0.214280	+	0.976772i	$0.568741\pi$
$740$	−41.6273	+	24.0336i	−0.0562532	+	0.0324778i
$741$	−169.254	+	17.1253i	−0.228412	+	0.0231111i
$742$	−556.962	−	101.569i	−0.750623	−	0.136886i
$743$	−658.244	+	1140.11i	−0.885927	+	1.53447i	−0.0412793	+	0.999148i	$0.513143\pi$
$743$	−658.244	+	1140.11i	−0.885927	+	1.53447i	−0.844648	+	0.535323i	$0.820190\pi$
$744$	−0.0203085	−	0.200713i	−2.72963e−5	−	0.000269776i
$745$	1472.59	−	850.200i	1.97663	−	1.14121i
$746$	−230.320			−0.308740
$747$	−52.5266	−	256.909i	−0.0703167	−	0.343921i
$748$			544.396i			0.727803i
$749$	383.201	−	451.295i	0.511616	−	0.602529i
$750$	−1854.34	−	834.243i	−2.47245	−	1.11232i
$751$	423.985	−	734.364i	0.564561	−	0.977848i	−0.432530	−	0.901620i	$-0.642379\pi$
$751$	423.985	−	734.364i	0.564561	−	0.977848i	0.997090	−	0.0762280i	$-0.0242877\pi$
$752$	−159.135	−	91.8767i	−0.211616	−	0.122176i
$753$	851.549	−	613.651i	1.13088	−	0.814941i
$754$	208.887	−	120.601i	0.277039	−	0.159948i
$755$			2355.84i			3.12031i
$756$	227.474	+	301.893i	0.300892	+	0.399330i
$757$	−1170.49			−1.54622			−0.773112	−	0.634269i	$-0.781301\pi$
$757$	−1170.49			−1.54622			−0.773112	+	0.634269i	$0.781301\pi$
$758$	276.673	+	479.212i	0.365004	+	0.632205i
$759$	4.16317	+	5.77714i	0.00548507	+	0.00761151i
$760$	−65.4420	+	113.349i	−0.0861079	+	0.149143i
$761$	−240.508	−	138.858i	−0.316043	−	0.182467i	0.333585	−	0.942720i	$-0.391742\pi$
$761$	−240.508	−	138.858i	−0.316043	−	0.182467i	−0.649627	+	0.760253i	$0.725075\pi$
$762$	−271.287	+	603.009i	−0.356019	+	0.791351i
$763$	109.242	−	128.654i	0.143175	−	0.168617i
$764$	585.822			0.766783
$765$	1194.96	+	1348.04i	1.56204	+	1.76214i
$766$			430.810i			0.562415i
$767$	294.471	+	510.038i	0.383925	+	0.664978i
$768$	−47.7562	+	4.83203i	−0.0621825	+	0.00629171i
$769$	−460.984	−	266.149i	−0.599459	−	0.346098i	0.169370	−	0.985553i	$-0.445827\pi$
$769$	−460.984	−	266.149i	−0.599459	−	0.346098i	−0.768829	+	0.639455i	$0.779160\pi$
$770$	−237.492	+	1302.31i	−0.308432	+	1.69131i
$771$	102.170	+	1009.77i	0.132516	+	1.30968i
$772$	259.235	+	449.008i	0.335797	+	0.581617i
$773$		−	323.697i		−	0.418755i	−0.977835	−	0.209377i	$-0.932856\pi$
$773$		−	323.697i		−	0.418755i	0.977835	−	0.209377i	$-0.0671437\pi$
$774$	−59.6585	−	67.3009i	−0.0770782	−	0.0869521i
$775$		−	1.74346i		−	0.00224963i
$776$	266.508	−	153.868i	0.343438	−	0.198284i
$777$	50.7359	+	4.04421i	0.0652972	+	0.00520490i
$778$	−191.569	+	331.807i	−0.246232	+	0.426487i
$779$	25.5456	−	44.2462i	0.0327928	−	0.0567988i
$780$	−422.688	−	586.554i	−0.541907	−	0.751992i
$781$	544.021	+	942.272i	0.696570	+	1.20649i
$782$			5.02457i			0.00642529i
$783$	278.652	+	256.838i	0.355878	+	0.328018i
$784$	−151.608	+	124.222i	−0.193377	+	0.158446i
$785$	−387.894	−	671.853i	−0.494133	−	0.855863i
$786$	−342.227	+	246.619i	−0.435404	+	0.313764i
$787$	−943.069	−	544.481i	−1.19831	−	0.691844i	−0.238131	−	0.971233i	$-0.576535\pi$
$787$	−943.069	−	544.481i	−1.19831	−	0.691844i	−0.960178	+	0.279389i	$0.909868\pi$
$788$	−336.752	+	583.271i	−0.427350	+	0.740192i
$789$	−80.5698	+	179.089i	−0.102116	+	0.226982i
$790$	−247.248	+	142.749i	−0.312972	+	0.180695i
$791$	−342.694	−	958.956i	−0.433241	−	1.21233i
$792$	336.320	−	68.7625i	0.424646	−	0.0868214i
$793$	−480.930			−0.606470
$794$	558.438	−	322.415i	0.703323	−	0.406064i
$795$	171.267	+	1692.67i	0.215430	+	2.12915i
$796$	160.205	+	92.4947i	0.201263	+	0.116199i
$797$	1.86876	+	1.07893i	0.00234475	+	0.00135374i	0.501172	−	0.865348i	$-0.332902\pi$
$797$	1.86876	+	1.07893i	0.00234475	+	0.00135374i	−0.498827	+	0.866701i	$0.666236\pi$
$798$	125.148	−	59.5387i	0.156828	−	0.0746100i
$799$	463.631	+	803.033i	0.580265	+	1.00505i
$800$	−414.826			−0.518532
$801$	−696.186	−	232.195i	−0.869146	−	0.289882i
$802$	605.482			0.754965
$803$	−208.373	+	120.304i	−0.259494	+	0.149819i
$804$	222.375	−	494.290i	0.276586	−	0.614788i
$805$	−2.19197	+	12.0198i	−0.00272294	+	0.0149314i
$806$	0.204287	−	0.353835i	0.000253458	−	0.000439001i
$807$	−604.492	+	435.614i	−0.749060	+	0.539794i
$808$	−340.409	+	196.535i	−0.421298	+	0.243237i
$809$	−137.194			−0.169585			−0.0847924	−	0.996399i	$-0.527023\pi$
$809$	−137.194			−0.169585			−0.0847924	+	0.996399i	$0.527023\pi$
$810$	681.862	−	908.499i	0.841805	−	1.12160i
$811$		−	724.583i		−	0.893444i	−0.894673	−	0.446722i	$-0.852591\pi$
$811$		−	724.583i		−	0.893444i	0.894673	−	0.446722i	$-0.147409\pi$
$812$	−127.185	+	149.786i	−0.156632	+	0.184465i
$813$	145.046	−	104.524i	0.178408	−	0.128566i
$814$	23.1108	−	40.0290i	0.0283916	−	0.0491757i
$815$	−2034.41	−	1174.57i	−2.49621	−	1.44119i
$816$	220.894	+	99.3777i	0.270704	+	0.121786i
$817$	−28.5564	+	16.4871i	−0.0349528	+	0.0201800i
$818$			506.370i			0.619034i
$819$	16.3014	+	765.377i	0.0199041	+	0.934526i
$820$	217.133			0.264797
$821$	−557.777	−	966.098i	−0.679387	−	1.17673i	−0.975166	−	0.221477i	$-0.928912\pi$
$821$	−557.777	−	966.098i	−0.679387	−	1.17673i	0.295778	−	0.955257i	$-0.404421\pi$
$822$	104.125	−	10.5355i	0.126673	−	0.0128169i
$823$	255.274	−	442.148i	0.310175	−	0.537239i	−0.668225	−	0.743959i	$-0.732946\pi$
$823$	255.274	−	442.148i	0.310175	−	0.537239i	0.978400	+	0.206720i	$0.0662790\pi$
$824$	−186.948	−	107.934i	−0.226878	−	0.130988i
$825$	2951.60	−	298.647i	3.57770	−	0.361996i
$826$	−365.731	−	310.548i	−0.442774	−	0.375966i
$827$	1088.29			1.31594			0.657972	−	0.753042i	$-0.271415\pi$
$827$	1088.29			1.31594			0.657972	+	0.753042i	$0.271415\pi$
$828$	3.10410	−	0.634652i	0.00374892	−	0.000766488i
$829$			1155.53i			1.39388i	0.717128	+	0.696942i	$0.245456\pi$
$829$			1155.53i			1.39388i	−0.717128	+	0.696942i	$0.754544\pi$
$830$	−204.297	−	353.852i	−0.246141	−	0.426328i
$831$	−546.729	+	1215.26i	−0.657917	+	1.46240i
$832$	−84.1887	−	48.6064i	−0.101188	−	0.0584211i
$833$	975.979	−	160.345i	1.17164	−	0.192491i
$834$	391.858	−	282.384i	0.469854	−	0.338590i
$835$	−1147.76	−	1987.98i	−1.37457	−	2.38082i
$836$		−	125.859i		−	0.150549i
$837$	0.626303	+	0.140767i	0.000748271	+	0.000168180i
$838$			647.221i			0.772340i
$839$	−162.598	+	93.8762i	−0.193800	+	0.111891i	−0.593760	−	0.804642i	$-0.702357\pi$
$839$	−162.598	+	93.8762i	−0.193800	+	0.111891i	0.399960	+	0.916533i	$0.369024\pi$
$840$	485.070	+	334.096i	0.577465	+	0.397734i
$841$	322.000	−	557.721i	0.382878	−	0.663164i
$842$	4.74957	−	8.22649i	0.00564082	−	0.00977018i
$843$	570.539	−	1268.18i	0.676797	−	1.50437i
$844$	−198.134	−	343.179i	−0.234756	−	0.406610i
$845$			211.601i			0.250415i
$846$	437.541	−	387.855i	0.517187	−	0.458458i
$847$	−143.342	−	401.112i	−0.169235	−	0.473568i
$848$	114.379	+	198.110i	0.134881	+	0.233621i
$849$	−30.9346	−	305.734i	−0.0364365	−	0.360111i
$850$	1812.86	+	1046.65i	2.13277	+	1.23136i
$851$	0.213304	−	0.369453i	0.000250651	−	0.000434139i
$852$	481.646	−	48.7335i	0.565312	−	0.0571990i
$853$	−659.061	+	380.509i	−0.772639	+	0.446083i	−0.833815	−	0.552044i	$-0.813848\pi$
$853$	−659.061	+	380.509i	−0.772639	+	0.446083i	0.0611763	+	0.998127i	$0.480515\pi$
$854$	368.947	−	131.847i	0.432022	−	0.154388i
$855$	−276.262	−	311.652i	−0.323114	−	0.364505i
$856$	−239.220			−0.279462
$857$	−779.492	+	450.040i	−0.909558	+	0.525134i	−0.880289	−	0.474438i	$-0.842651\pi$
$857$	−779.492	+	450.040i	−0.909558	+	0.525134i	−0.0292694	+	0.999572i	$0.509318\pi$
$858$	634.020	+	285.238i	0.738951	+	0.332445i
$859$	1001.95	+	578.477i	1.16642	+	0.673431i	0.952833	−	0.303494i	$-0.0981531\pi$
$859$	1001.95	+	578.477i	1.16642	+	0.673431i	0.213584	+	0.976925i	$0.431486\pi$
$860$	−121.363	−	70.0687i	−0.141119	−	0.0814752i
$861$	−189.349	−	130.416i	−0.219918	−	0.151470i
$862$	282.394	+	489.121i	0.327603	+	0.567426i
$863$	512.272			0.593594			0.296797	−	0.954941i	$-0.404082\pi$
$863$	512.272			0.593594			0.296797	+	0.954941i	$0.404082\pi$
$864$	33.4929	−	149.018i	0.0387650	−	0.172474i
$865$	−1267.15			−1.46492
$866$	694.369	−	400.894i	0.801812	−	0.462926i
$867$	−207.721	−	288.250i	−0.239586	−	0.332468i
$868$	−0.0597150	+	0.327451i	−6.87960e−5	+	0.000377247i
$869$	137.268	−	237.755i	0.157961	−	0.273596i
$870$	538.507	+	242.268i	0.618973	+	0.278469i
$871$	950.645	−	548.855i	1.09144	−	0.630144i
$872$	−68.1964			−0.0782069
$873$	196.148	+	959.366i	0.224683	+	1.09893i
$874$		−	1.16163i		−	0.00132909i
$875$	2557.32	+	2171.45i	2.92265	+	2.48166i
$876$	10.7769	+	106.511i	0.0123024	+	0.121588i
$877$	644.224	−	1115.83i	0.734577	−	1.27233i	−0.220331	−	0.975425i	$-0.570714\pi$
$877$	644.224	−	1115.83i	0.734577	−	1.27233i	0.954909	−	0.296900i	$-0.0959528\pi$
$878$	240.878	+	139.071i	0.274349	+	0.158395i
$879$	−100.625	−	994.502i	−0.114477	−	1.13140i
$880$	463.228	−	267.445i	0.526395	−	0.303914i
$881$		−	1247.46i		−	1.41596i	−0.706235	−	0.707978i	$-0.749608\pi$
$881$		−	1247.46i		−	1.41596i	0.706235	−	0.707978i	$-0.250392\pi$
$882$	−222.334	−	582.692i	−0.252080	−	0.660648i
$883$	−936.870			−1.06101			−0.530504	−	0.847682i	$-0.677997\pi$
$883$	−936.870			−1.06101			−0.530504	+	0.847682i	$0.677997\pi$
$884$	245.279	+	424.836i	0.277465	+	0.480584i
$885$	−591.543	+	1314.87i	−0.668410	+	1.48573i
$886$	126.479	−	219.069i	0.142753	−	0.247256i
$887$	−1251.49	−	722.546i	−1.41092	−	0.814595i	−0.415445	−	0.909618i	$-0.636374\pi$
$887$	−1251.49	−	722.546i	−1.41092	−	0.814595i	−0.995475	+	0.0950234i	$0.969707\pi$
$888$	−12.0234	−	16.6846i	−0.0135399	−	0.0187889i
$889$	706.133	−	831.611i	0.794301	−	0.935446i
$890$	−1143.53			−1.28487
$891$	−131.029	+	1084.41i	−0.147058	+	1.21708i
$892$		−	347.912i		−	0.390036i
$893$	−107.187	−	185.653i	−0.120030	−	0.207898i
$894$	425.334	+	590.226i	0.475765	+	0.660208i
$895$	−1140.86	−	658.673i	−1.27470	−	0.735948i
$896$	77.9110	+	14.2081i	0.0869543	+	0.0158573i
$897$	5.85176	+	2.63264i	0.00652370	+	0.00293493i
$898$	−269.981	−	467.621i	−0.300647	−	0.520736i
$899$			0.333699i			0.000371189i
$900$	417.625	−	1252.16i	0.464028	−	1.39129i
$901$		−	1154.37i		−	1.28121i
$902$	−180.823	+	104.398i	−0.200469	+	0.115741i
$903$	63.7481	+	133.996i	0.0705959	+	0.148390i
$904$	−205.738	+	356.348i	−0.227586	+	0.394190i
$905$	463.358	−	802.560i	0.511998	−	0.886806i
$906$	−1002.82	+	101.467i	−1.10687	+	0.111994i
$907$	20.3747	+	35.2899i	0.0224638	+	0.0389084i	0.877039	−	0.480420i	$-0.159516\pi$
$907$	20.3747	+	35.2899i	0.0224638	+	0.0389084i	−0.854575	+	0.519328i	$0.826182\pi$
$908$		−	412.328i		−	0.454106i
$909$	−250.539	−	1225.39i	−0.275620	−	1.34807i
$910$	401.423	+	1123.30i	0.441124	+	1.23439i
$911$	−96.3670	−	166.913i	−0.105782	−	0.183219i	0.808276	−	0.588804i	$-0.200401\pi$
$911$	−96.3670	−	166.913i	−0.105782	−	0.183219i	−0.914057	+	0.405585i	$0.867068\pi$
$912$	−51.0684	−	22.9751i	−0.0559961	−	0.0251919i
$913$	340.266	+	196.452i	0.372690	+	0.215172i
$914$	−402.154	+	696.552i	−0.439994	+	0.762092i
$915$	−688.344	−	955.199i	−0.752289	−	1.04393i
$916$	34.5279	−	19.9347i	0.0376942	−	0.0217628i
$917$	655.391	−	234.212i	0.714713	−	0.255411i
$918$	−522.359	+	566.725i	−0.569018	+	0.617348i
$919$	851.690			0.926757			0.463378	−	0.886161i	$-0.346637\pi$
$919$	851.690			0.926757			0.463378	+	0.886161i	$0.346637\pi$
$920$	4.27542	−	2.46841i	0.00464719	−	0.00268306i
$921$	787.221	−	567.294i	0.854746	−	0.615954i
$922$	−446.477	−	257.773i	−0.484248	−	0.279581i
$923$	849.086	+	490.220i	0.919920	+	0.531116i
$924$	−564.588	−	45.0038i	−0.611026	−	0.0487055i
$925$	−88.8653	−	153.919i	−0.0960706	−	0.166399i
$926$	167.997			0.181422
$927$	514.012	−	455.643i	0.554489	−	0.491524i
$928$	79.3977			0.0855579
$929$	1301.36	−	751.342i	1.40082	−	0.808764i	0.406343	−	0.913721i	$-0.366804\pi$
$929$	1301.36	−	751.342i	1.40082	−	0.808764i	0.994477	+	0.104957i	$0.0334704\pi$
$930$	0.995160	−	0.100692i	0.00107006	−	0.000108271i
$931$	−225.636	+	37.0701i	−0.242359	+	0.0398175i
$932$	−257.078	+	445.273i	−0.275835	+	0.477760i
$933$	139.224	+	1375.99i	0.149222	+	1.47480i
$934$	491.134	−	283.556i	0.525840	−	0.303594i
$935$	−2699.18			−2.88682
$936$	231.476	−	205.191i	0.247304	−	0.219221i
$937$		−	1330.62i		−	1.42009i	−0.704158	−	0.710043i	$-0.748675\pi$
$937$		−	1330.62i		−	1.42009i	0.704158	−	0.710043i	$-0.251325\pi$
$938$	−578.821	+	681.676i	−0.617080	+	0.726733i
$939$	750.211	+	337.511i	0.798947	+	0.359437i
$940$	455.535	−	789.009i	0.484611	−	0.839372i
$941$	1089.81	+	629.201i	1.15814	+	0.668651i	0.950857	−	0.309631i	$-0.100205\pi$
$941$	1089.81	+	629.201i	1.15814	+	0.668651i	0.207281	+	0.978282i	$0.433539\pi$
$942$	269.284	−	194.054i	0.285864	−	0.206002i
$943$	−1.66893	+	0.963556i	−0.00176981	+	0.00102180i
$944$			193.865i			0.205365i
$945$	−1496.82	+	1127.84i	−1.58394	+	1.19348i
$946$	134.757			0.142449
$947$	671.501	+	1163.07i	0.709083	+	1.22817i	0.965198	+	0.261521i	$0.0842240\pi$
$947$	671.501	+	1163.07i	0.709083	+	1.22817i	−0.256115	+	0.966646i	$0.582443\pi$
$948$	−71.4136	−	99.0991i	−0.0753308	−	0.104535i
$949$	−108.407	+	187.766i	−0.114233	+	0.197857i
$950$	−419.113	−	241.975i	−0.441172	−	0.254711i
$951$	−522.564	+	1161.54i	−0.549489	+	1.22139i
$952$	−304.636	−	258.671i	−0.319996	−	0.271713i
$953$	−1593.34			−1.67192			−0.835961	−	0.548789i	$-0.815089\pi$
$953$	−1593.34			−1.67192			−0.835961	+	0.548789i	$0.815089\pi$
$954$	−713.151	+	145.808i	−0.747538	+	0.152838i
$955$			2904.57i			3.04144i
$956$	−12.3601	−	21.4084i	−0.0129290	−	0.0223937i
$957$	−564.937	+	57.1611i	−0.590321	+	0.0597294i
$958$	−146.624	−	84.6536i	−0.153053	−	0.0883649i
$959$	−169.873	−	30.9786i	−0.177136	−	0.0323031i
$960$	−23.9578	−	236.780i	−0.0249560	−	0.246646i
$961$	−480.500	−	832.250i	−0.500000	−	0.866025i
$962$		−	41.6505i		−	0.0432957i
$963$	240.834	−	722.089i	0.250088	−	0.749833i
$964$		−	594.178i		−	0.616367i
$965$	−2226.23	+	1285.32i	−2.30698	+	1.33193i
$966$	−5.21093	−	0.415368i	−0.00539434	−	0.000429988i
$967$	−819.205	+	1418.91i	−0.847162	+	1.46733i	0.0365690	+	0.999331i	$0.488357\pi$
$967$	−819.205	+	1418.91i	−0.847162	+	1.46733i	−0.883731	+	0.467996i	$0.844976\pi$
$968$	−86.0560	+	149.053i	−0.0889008	+	0.153981i
$969$	165.209	+	229.257i	0.170494	+	0.236591i
$970$	762.897	+	1321.38i	0.786492	+	1.36224i
$971$			1718.35i			1.76967i	0.465902	+	0.884836i	$0.345730\pi$
$971$			1718.35i			1.76967i	−0.465902	+	0.884836i	$0.654270\pi$
$972$	416.093	+	251.122i	0.428079	+	0.258356i
$973$	−750.439	+	268.178i	−0.771263	+	0.275620i
$974$	403.103	+	698.195i	0.413863	+	0.716832i
$975$	2168.81	−	1562.91i	2.22442	−	1.60298i
$976$	−137.101	−	79.1551i	−0.140472	−	0.0811016i
$977$	−179.274	+	310.512i	−0.183495	+	0.317822i	−0.943068	−	0.332599i	$-0.892074\pi$
$977$	−179.274	+	310.512i	−0.183495	+	0.317822i	0.759573	+	0.650422i	$0.225408\pi$
$978$	412.362	−	916.588i	0.421638	−	0.937206i
$979$	952.302	−	549.812i	0.972730	−	0.561606i
$980$	−615.905	−	751.689i	−0.628475	−	0.767030i
$981$	68.6567	−	205.852i	0.0699865	−	0.209839i
$982$	398.977			0.406290
$983$	924.703	−	533.877i	0.940694	−	0.543110i	0.0505165	−	0.998723i	$-0.483913\pi$
$983$	924.703	−	533.877i	0.940694	−	0.543110i	0.890178	+	0.455613i	$0.150580\pi$
$984$	9.35202	+	92.4283i	0.00950408	+	0.0939312i
$985$	−2891.92	−	1669.65i	−2.93596	−	1.69508i
$986$	−346.981	−	200.330i	−0.351908	−	0.203174i
$987$	−871.144	+	414.443i	−0.882619	+	0.419901i
$988$	−56.7059	−	98.2176i	−0.0573947	−	0.0994105i
$989$	1.24375			0.00125759
$990$	340.932	+	1667.51i	0.344376	+	1.68435i
$991$	431.606			0.435526			0.217763	−	0.976002i	$-0.430124\pi$
$991$	431.606			0.435526			0.217763	+	0.976002i	$0.430124\pi$
$992$	0.116474	−	0.0672461i	0.000117413	−	6.77884e-5i
$993$	304.050	−	675.835i	0.306193	−	0.680599i
$994$	−785.773	−	143.296i	−0.790516	−	0.144161i
$995$	−458.599	+	794.317i	−0.460903	+	0.798308i
$996$	141.827	−	102.205i	0.142396	−	0.102615i
$997$	−123.674	+	71.4033i	−0.124046	+	0.0716181i	−0.560739	−	0.827993i	$-0.689483\pi$
$997$	−123.674	+	71.4033i	−0.124046	+	0.0716181i	0.436693	+	0.899611i	$0.356150\pi$
$998$	−85.2244			−0.0853952
$999$	62.4673	−	19.4956i	0.0625298	−	0.0195151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.o.a.13.5	yes	32
3.2	odd	2		378.3.o.a.307.16		32
7.6	odd	2	inner	126.3.o.a.13.4	✓	32
9.2	odd	6		378.3.o.a.181.9		32
9.4	even	3		1134.3.c.e.811.16		16
9.5	odd	6		1134.3.c.d.811.1		16
9.7	even	3	inner	126.3.o.a.97.4	yes	32
21.20	even	2		378.3.o.a.307.9		32
63.13	odd	6		1134.3.c.e.811.9		16
63.20	even	6		378.3.o.a.181.16		32
63.34	odd	6	inner	126.3.o.a.97.5	yes	32
63.41	even	6		1134.3.c.d.811.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.4	✓	32	7.6	odd	2	inner
126.3.o.a.13.5	yes	32	1.1	even	1	trivial
126.3.o.a.97.4	yes	32	9.7	even	3	inner
126.3.o.a.97.5	yes	32	63.34	odd	6	inner
378.3.o.a.181.9		32	9.2	odd	6
378.3.o.a.181.16		32	63.20	even	6
378.3.o.a.307.9		32	21.20	even	2
378.3.o.a.307.16		32	3.2	odd	2
1134.3.c.d.811.1		16	9.5	odd	6
1134.3.c.d.811.8		16	63.41	even	6
1134.3.c.e.811.9		16	63.13	odd	6
1134.3.c.e.811.16		16	9.4	even	3

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(1.75392 + 2.43388i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-8.58770 - 4.95811i) q^{5} +(1.74067 - 3.86912i) q^{6} +(-4.53080 + 5.33591i) q^{7} +2.82843 q^{8} +(-2.84752 + 8.53766i) q^{9} +14.0237i q^{10} +(-6.74260 - 11.6785i) q^{11} +(-5.96952 + 0.604004i) q^{12} +(-10.5236 - 6.07580i) q^{13} +(9.73888 + 1.77601i) q^{14} +(-2.99472 - 29.5976i) q^{15} +(-2.00000 - 3.46410i) q^{16} +20.1850i q^{17} +(12.4700 - 2.54955i) q^{18} -4.66654i q^{19} +(17.1754 - 9.91622i) q^{20} +(-20.9336 - 1.66864i) q^{21} +(-9.53548 + 16.5159i) q^{22} +(-0.0880089 + 0.152436i) q^{23} +(4.96084 + 6.88404i) q^{24} +(36.6657 + 63.5069i) q^{25} +17.1849i q^{26} +(-25.7739 + 8.04388i) q^{27} +(-4.71127 - 13.1835i) q^{28} +(-7.01783 - 12.1552i) q^{29} +(-34.1319 + 24.5964i) q^{30} +(-0.0205898 - 0.0118875i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(16.5981 - 36.8939i) q^{33} +(24.7214 - 14.2729i) q^{34} +(65.3651 - 23.3590i) q^{35} +(-11.9401 - 13.4697i) q^{36} -2.42366 q^{37} +(-5.71533 + 3.29975i) q^{38} +(-3.66981 - 36.2696i) q^{39} +(-24.2897 - 14.0237i) q^{40} +(9.48159 + 5.47420i) q^{41} +(12.7586 + 26.8182i) q^{42} +(-3.53303 - 6.11939i) q^{43} +26.9704 q^{44} +(66.7843 - 59.2006i) q^{45} +0.248927 q^{46} +(39.7838 - 22.9692i) q^{47} +(4.92336 - 10.9435i) q^{48} +(-7.94379 - 48.3518i) q^{49} +(51.8532 - 89.8124i) q^{50} +(-49.1277 + 35.4028i) q^{51} +(21.0472 - 12.1516i) q^{52} -57.1896 q^{53} +(28.0766 + 25.8786i) q^{54} +133.722i q^{55} +(-12.8150 + 15.0922i) q^{56} +(11.3578 - 8.18475i) q^{57} +(-9.92471 + 17.1901i) q^{58} +(-41.9730 - 24.2331i) q^{59} +(54.2592 + 24.4105i) q^{60} +(34.2752 - 19.7888i) q^{61} +0.0336230i q^{62} +(-32.6546 - 53.8765i) q^{63} +8.00000 q^{64} +(60.2489 + 104.354i) q^{65} +(-56.9223 + 5.75947i) q^{66} +(-45.1674 + 78.2322i) q^{67} +(-34.9614 - 20.1850i) q^{68} +(-0.525371 + 0.0531577i) q^{69} +(-74.8289 - 63.5383i) q^{70} -80.6841 q^{71} +(-8.05400 + 24.1481i) q^{72} -17.8424i q^{73} +(1.71379 + 2.96837i) q^{74} +(-90.2592 + 200.626i) q^{75} +(8.08269 + 4.66654i) q^{76} +(92.8649 + 16.9351i) q^{77} +(-41.8260 + 30.1410i) q^{78} +(10.1791 + 17.6308i) q^{79} +39.6649i q^{80} +(-64.7833 - 48.6223i) q^{81} -15.4834i q^{82} +(-25.2325 + 14.5680i) q^{83} +(23.8238 - 34.5894i) q^{84} +(100.079 - 173.342i) q^{85} +(-4.99646 + 8.65413i) q^{86} +(17.2756 - 38.3999i) q^{87} +(-19.0710 - 33.0319i) q^{88} +81.5430i q^{89} +(-119.729 - 39.9326i) q^{90} +(80.1001 - 28.6247i) q^{91} +(-0.176018 - 0.304872i) q^{92} +(-0.00718012 - 0.0709629i) q^{93} +(-56.2627 - 32.4833i) q^{94} +(-23.1372 + 40.0749i) q^{95} +(-16.8844 + 1.70838i) q^{96} +(94.2248 - 54.4007i) q^{97} +(-53.6015 + 43.9190i) q^{98} +(118.907 - 24.3112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 24 q^{9} - 12 q^{11} - 12 q^{14} + 48 q^{15} - 64 q^{16} - 54 q^{21} + 12 q^{23} + 80 q^{25} + 8 q^{28} - 48 q^{29} - 168 q^{30} + 348 q^{35} - 72 q^{36} - 88 q^{37} + 252 q^{39}+ \cdots - 684 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 24 * q^9 - 12 * q^11 - 12 * q^14 + 48 * q^15 - 64 * q^16 - 54 * q^21 + 12 * q^23 + 80 * q^25 + 8 * q^28 - 48 * q^29 - 168 * q^30 + 348 * q^35 - 72 * q^36 - 88 * q^37 + 252 * q^39 + 32 * q^43 + 48 * q^44 + 48 * q^46 + 50 * q^49 + 48 * q^50 - 372 * q^51 - 864 * q^53 - 24 * q^56 + 372 * q^57 + 48 * q^58 - 24 * q^60 - 114 * q^63 + 256 * q^64 + 120 * q^65 - 140 * q^67 - 108 * q^70 + 552 * q^71 + 96 * q^72 + 144 * q^74 - 258 * q^77 + 288 * q^78 - 176 * q^79 - 360 * q^81 - 60 * q^85 + 96 * q^86 + 372 * q^91 + 24 * q^92 - 456 * q^93 + 528 * q^95 + 624 * q^98 - 684 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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