LMFDB - Embedded newform 140.3.x.a.103.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.36
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60772 - 1.18964i) q^{2} +(-0.453487 + 1.69244i) q^{3} +(1.16952 - 3.82521i) q^{4} +(0.126349 + 4.99840i) q^{5} +(1.28431 + 3.26045i) q^{6} +(6.79301 - 1.68968i) q^{7} +(-2.67037 - 7.54116i) q^{8} +(5.13554 + 2.96500i) q^{9} +O(q^{10})$	\(q+(1.60772 - 1.18964i) q^{2} +(-0.453487 + 1.69244i) q^{3} +(1.16952 - 3.82521i) q^{4} +(0.126349 + 4.99840i) q^{5} +(1.28431 + 3.26045i) q^{6} +(6.79301 - 1.68968i) q^{7} +(-2.67037 - 7.54116i) q^{8} +(5.13554 + 2.96500i) q^{9} +(6.14943 + 7.88572i) q^{10} +(9.11627 - 5.26328i) q^{11} +(5.94356 + 3.71402i) q^{12} +(-2.37683 + 2.37683i) q^{13} +(8.91113 - 10.7978i) q^{14} +(-8.51678 - 2.05287i) q^{15} +(-13.2645 - 8.94730i) q^{16} +(-3.75985 + 14.0320i) q^{17} +(11.7838 - 1.34255i) q^{18} +(-14.4979 - 8.37036i) q^{19} +(19.2677 + 5.36241i) q^{20} +(-0.220859 + 12.2630i) q^{21} +(8.39499 - 19.3070i) q^{22} +(-6.75377 - 25.2054i) q^{23} +(13.9739 - 1.09960i) q^{24} +(-24.9681 + 1.26309i) q^{25} +(-0.993705 + 6.64886i) q^{26} +(-18.4975 + 18.4975i) q^{27} +(1.48115 - 27.9608i) q^{28} +33.6212i q^{29} +(-16.1348 + 6.83145i) q^{30} +(-3.74694 - 6.48989i) q^{31} +(-31.9696 + 1.39519i) q^{32} +(4.77366 + 17.8155i) q^{33} +(10.6482 + 27.0323i) q^{34} +(9.30401 + 33.7407i) q^{35} +(17.3479 - 16.1769i) q^{36} +(-11.6689 - 43.5489i) q^{37} +(-33.2662 + 3.79008i) q^{38} +(-2.94478 - 5.10051i) q^{39} +(37.3564 - 14.3004i) q^{40} -47.3330i q^{41} +(14.2334 + 19.9782i) q^{42} +(-23.1058 + 23.1058i) q^{43} +(-9.47152 - 41.0272i) q^{44} +(-14.1714 + 26.0441i) q^{45} +(-40.8435 - 32.4886i) q^{46} +(-0.0871637 - 0.325299i) q^{47} +(21.1580 - 18.3918i) q^{48} +(43.2899 - 22.9561i) q^{49} +(-38.6390 + 31.7337i) q^{50} +(-22.0431 - 12.7266i) q^{51} +(6.31214 + 11.8716i) q^{52} +(-19.2790 + 71.9501i) q^{53} +(-7.73343 + 51.7442i) q^{54} +(27.4598 + 44.9018i) q^{55} +(-30.8820 - 46.7151i) q^{56} +(20.7409 - 20.7409i) q^{57} +(39.9971 + 54.0534i) q^{58} +(42.5843 - 24.5861i) q^{59} +(-17.8132 + 30.1776i) q^{60} +(-46.7908 - 27.0147i) q^{61} +(-13.7447 - 5.97641i) q^{62} +(39.8957 + 11.4639i) q^{63} +(-49.7383 + 40.2753i) q^{64} +(-12.1807 - 11.5801i) q^{65} +(28.8688 + 22.9634i) q^{66} +(-21.9640 + 81.9706i) q^{67} +(49.2779 + 30.7928i) q^{68} +45.7213 q^{69} +(55.0975 + 43.1771i) q^{70} -43.1950i q^{71} +(8.64582 - 46.6456i) q^{72} +(-60.2824 - 16.1526i) q^{73} +(-70.5678 - 56.1326i) q^{74} +(9.18500 - 42.8297i) q^{75} +(-48.9739 + 45.6682i) q^{76} +(53.0336 - 51.1571i) q^{77} +(-10.8021 - 4.69695i) q^{78} +(45.3425 - 78.5355i) q^{79} +(43.0462 - 67.4316i) q^{80} +(3.76754 + 6.52557i) q^{81} +(-56.3092 - 76.0982i) q^{82} +(6.44249 + 6.44249i) q^{83} +(46.6502 + 15.1866i) q^{84} +(-70.6124 - 17.0203i) q^{85} +(-9.66004 + 64.6351i) q^{86} +(-56.9017 - 15.2468i) q^{87} +(-64.0351 - 54.6924i) q^{88} +(77.4380 - 134.127i) q^{89} +(8.19945 + 58.7305i) q^{90} +(-12.1298 + 20.1620i) q^{91} +(-104.315 - 3.64357i) q^{92} +(12.6829 - 3.39838i) q^{93} +(-0.527124 - 0.419296i) q^{94} +(40.0066 - 73.5239i) q^{95} +(12.1365 - 54.7392i) q^{96} +(111.262 + 111.262i) q^{97} +(42.2886 - 88.4063i) q^{98} +62.4226 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.60772	−	1.18964i	0.803859	−	0.594820i
$2$	1.60772	−	1.18964i	0.803859	−	0.594820i
$3$	−0.453487	+	1.69244i	−0.151162	+	0.564145i	0.848241	+	0.529610i	$0.177662\pi$
$3$	−0.453487	+	1.69244i	−0.151162	+	0.564145i	−0.999403	+	0.0345353i	$0.989005\pi$
$4$	1.16952	−	3.82521i	0.292379	−	0.956302i
$5$	0.126349	+	4.99840i	0.0252698	+	0.999681i
$5$	0.126349	+	4.99840i	0.0252698	+	0.999681i
$6$	1.28431	+	3.26045i	0.214052	+	0.543408i
$7$	6.79301	−	1.68968i	0.970430	−	0.241383i
$7$	6.79301	−	1.68968i	0.970430	−	0.241383i
$8$	−2.67037	−	7.54116i	−0.333796	−	0.942645i
$9$	5.13554	+	2.96500i	0.570615	+	0.329445i
$10$	6.14943	+	7.88572i	0.614943	+	0.788572i
$11$	9.11627	−	5.26328i	0.828752	−	0.478480i	−0.0246731	−	0.999696i	$-0.507854\pi$
$11$	9.11627	−	5.26328i	0.828752	−	0.478480i	0.853425	+	0.521215i	$0.174521\pi$
$12$	5.94356	+	3.71402i	0.495297	+	0.309501i
$13$	−2.37683	+	2.37683i	−0.182833	+	0.182833i	−0.792589	−	0.609756i	$-0.791267\pi$
$13$	−2.37683	+	2.37683i	−0.182833	+	0.182833i	0.609756	+	0.792589i	$0.291267\pi$
$14$	8.91113	−	10.7978i	0.636509	−	0.771269i
$15$	−8.51678	−	2.05287i	−0.567785	−	0.136858i
$16$	−13.2645	−	8.94730i	−0.829029	−	0.559206i
$17$	−3.75985	+	14.0320i	−0.221168	+	0.825409i	0.762736	+	0.646710i	$0.223856\pi$
$17$	−3.75985	+	14.0320i	−0.221168	+	0.825409i	−0.983904	+	0.178699i	$0.942811\pi$
$18$	11.7838	−	1.34255i	0.654655	−	0.0745859i
$19$	−14.4979	−	8.37036i	−0.763047	−	0.440545i	0.0673417	−	0.997730i	$-0.478548\pi$
$19$	−14.4979	−	8.37036i	−0.763047	−	0.440545i	−0.830389	+	0.557185i	$0.811882\pi$
$20$	19.2677	+	5.36241i	0.963385	+	0.268120i
$21$	−0.220859	+	12.2630i	−0.0105171	+	0.583952i
$22$	8.39499	−	19.3070i	0.381591	−	0.877589i
$23$	−6.75377	−	25.2054i	−0.293642	−	1.09589i	−0.942290	−	0.334798i	$-0.891332\pi$
$23$	−6.75377	−	25.2054i	−0.293642	−	1.09589i	0.648648	−	0.761089i	$-0.275335\pi$
$24$	13.9739	−	1.09960i	0.582246	−	0.0458168i
$25$	−24.9681	+	1.26309i	−0.998723	+	0.0505235i
$26$	−0.993705	+	6.64886i	−0.0382194	+	0.255725i
$27$	−18.4975	+	18.4975i	−0.685094	+	0.685094i
$28$	1.48115	−	27.9608i	0.0528981	−	0.998600i
$29$			33.6212i			1.15935i	0.814847	+	0.579676i	$0.196821\pi$
$29$			33.6212i			1.15935i	−0.814847	+	0.579676i	$0.803179\pi$
$30$	−16.1348	+	6.83145i	−0.537825	+	0.227715i
$31$	−3.74694	−	6.48989i	−0.120869	−	0.209351i	0.799242	−	0.601010i	$-0.205235\pi$
$31$	−3.74694	−	6.48989i	−0.120869	−	0.209351i	−0.920111	+	0.391659i	$0.871901\pi$
$32$	−31.9696	+	1.39519i	−0.999049	+	0.0435996i
$33$	4.77366	+	17.8155i	0.144656	+	0.539865i
$34$	10.6482	+	27.0323i	0.313182	+	0.795067i
$35$	9.30401	+	33.7407i	0.265829	+	0.964020i
$36$	17.3479	−	16.1769i	0.481885	−	0.449358i
$37$	−11.6689	−	43.5489i	−0.315376	−	1.17700i	−0.923639	−	0.383263i	$-0.874800\pi$
$37$	−11.6689	−	43.5489i	−0.315376	−	1.17700i	0.608263	−	0.793735i	$-0.291866\pi$
$38$	−33.2662	+	3.79008i	−0.875427	+	0.0997388i
$39$	−2.94478	−	5.10051i	−0.0755071	−	0.130782i
$40$	37.3564	−	14.3004i	0.933909	−	0.357510i
$41$		−	47.3330i		−	1.15446i	−0.816580	−	0.577232i	$-0.804133\pi$
$41$		−	47.3330i		−	1.15446i	0.816580	−	0.577232i	$-0.195867\pi$
$42$	14.2334	+	19.9782i	0.338892	+	0.475671i
$43$	−23.1058	+	23.1058i	−0.537343	+	0.537343i	−0.922748	−	0.385404i	$-0.874062\pi$
$43$	−23.1058	+	23.1058i	−0.537343	+	0.537343i	0.385404	+	0.922748i	$0.374062\pi$
$44$	−9.47152	−	41.0272i	−0.215262	−	0.932435i
$45$	−14.1714	+	26.0441i	−0.314920	+	0.578758i
$46$	−40.8435	−	32.4886i	−0.887902	−	0.706275i
$47$	−0.0871637	−	0.325299i	−0.00185455	−	0.00692126i	0.964992	−	0.262278i	$-0.0844737\pi$
$47$	−0.0871637	−	0.325299i	−0.00185455	−	0.00692126i	−0.966847	+	0.255357i	$0.917807\pi$
$48$	21.1580	−	18.3918i	0.440791	−	0.383162i
$49$	43.2899	−	22.9561i	0.883468	−	0.468491i
$50$	−38.6390	+	31.7337i	−0.772780	+	0.634674i
$51$	−22.0431	−	12.7266i	−0.432218	−	0.249541i
$52$	6.31214	+	11.8716i	0.121387	+	0.228301i
$53$	−19.2790	+	71.9501i	−0.363754	+	1.35755i	0.505347	+	0.862916i	$0.331364\pi$
$53$	−19.2790	+	71.9501i	−0.363754	+	1.35755i	−0.869101	+	0.494634i	$0.835302\pi$
$54$	−7.73343	+	51.7442i	−0.143212	+	0.958226i
$55$	27.4598	+	44.9018i	0.499270	+	0.816396i
$56$	−30.8820	−	46.7151i	−0.551464	−	0.834199i
$57$	20.7409	−	20.7409i	0.363876	−	0.363876i
$58$	39.9971	+	54.0534i	0.689605	+	0.931955i
$59$	42.5843	−	24.5861i	0.721768	−	0.416713i	−0.0936352	−	0.995607i	$-0.529849\pi$
$59$	42.5843	−	24.5861i	0.721768	−	0.416713i	0.815403	+	0.578894i	$0.196515\pi$
$60$	−17.8132	+	30.1776i	−0.296886	+	0.502960i
$61$	−46.7908	−	27.0147i	−0.767063	−	0.442864i	0.0647630	−	0.997901i	$-0.479371\pi$
$61$	−46.7908	−	27.0147i	−0.767063	−	0.442864i	−0.831826	+	0.555037i	$0.812704\pi$
$62$	−13.7447	−	5.97641i	−0.221688	−	0.0963937i
$63$	39.8957	+	11.4639i	0.633265	+	0.181966i
$64$	−49.7383	+	40.2753i	−0.777161	+	0.629302i
$65$	−12.1807	−	11.5801i	−0.187395	−	0.178155i
$66$	28.8688	+	22.9634i	0.437406	+	0.347931i
$67$	−21.9640	+	81.9706i	−0.327820	+	1.22344i	0.583626	+	0.812023i	$0.301634\pi$
$67$	−21.9640	+	81.9706i	−0.327820	+	1.22344i	−0.911446	+	0.411419i	$0.865033\pi$
$68$	49.2779	+	30.7928i	0.724676	+	0.452836i
$69$	45.7213			0.662627
$70$	55.0975	+	43.1771i	0.787107	+	0.616816i
$71$		−	43.1950i		−	0.608380i	−0.952611	−	0.304190i	$-0.901614\pi$
$71$		−	43.1950i		−	0.608380i	0.952611	−	0.304190i	$-0.0983859\pi$
$72$	8.64582	−	46.6456i	0.120081	−	0.647855i
$73$	−60.2824	−	16.1526i	−0.825786	−	0.221269i	−0.178912	−	0.983865i	$-0.557258\pi$
$73$	−60.2824	−	16.1526i	−0.825786	−	0.221269i	−0.646875	+	0.762596i	$0.723924\pi$
$74$	−70.5678	−	56.1326i	−0.953619	−	0.758549i
$75$	9.18500	−	42.8297i	0.122467	−	0.571062i
$76$	−48.9739	+	45.6682i	−0.644394	+	0.600897i
$77$	53.0336	−	51.1571i	0.688749	−	0.664378i
$78$	−10.8021	−	4.69695i	−0.138489	−	0.0602173i
$79$	45.3425	−	78.5355i	0.573956	−	0.994120i	−0.422199	−	0.906503i	$-0.638741\pi$
$79$	45.3425	−	78.5355i	0.573956	−	0.994120i	0.996154	−	0.0876171i	$-0.0279252\pi$
$80$	43.0462	−	67.4316i	0.538078	−	0.842895i
$81$	3.76754	+	6.52557i	0.0465128	+	0.0805626i
$82$	−56.3092	−	76.0982i	−0.686698	−	0.928026i
$83$	6.44249	+	6.44249i	0.0776203	+	0.0776203i	0.744851	−	0.667231i	$-0.232521\pi$
$83$	6.44249	+	6.44249i	0.0776203	+	0.0776203i	−0.667231	+	0.744851i	$0.732521\pi$
$84$	46.6502	+	15.1866i	0.555359	+	0.180793i
$85$	−70.6124	−	17.0203i	−0.830734	−	0.200239i
$86$	−9.66004	+	64.6351i	−0.112326	+	0.751571i
$87$	−56.9017	−	15.2468i	−0.654043	−	0.175250i
$88$	−64.0351	−	54.6924i	−0.727671	−	0.621505i
$89$	77.4380	−	134.127i	0.870090	−	1.50704i	0.00818644	−	0.999966i	$-0.497394\pi$
$89$	77.4380	−	134.127i	0.870090	−	1.50704i	0.861903	−	0.507073i	$-0.169273\pi$
$90$	8.19945	+	58.7305i	0.0911050	+	0.652561i
$91$	−12.1298	+	20.1620i	−0.133294	+	0.221560i
$92$	−104.315	−	3.64357i	−1.13385	−	0.0396040i
$93$	12.6829	−	3.39838i	0.136375	−	0.0365417i
$94$	−0.527124	−	0.419296i	−0.00560770	−	0.00446060i
$95$	40.0066	−	73.5239i	0.421123	−	0.773936i
$96$	12.1365	−	54.7392i	0.126422	−	0.570200i
$97$	111.262	+	111.262i	1.14703	+	1.14703i	0.987134	+	0.159897i	$0.0511163\pi$
$97$	111.262	+	111.262i	1.14703	+	1.14703i	0.159897	+	0.987134i	$0.448884\pi$
$98$	42.2886	−	88.4063i	0.431516	−	0.902105i
$99$	62.4226			0.630532
$100$	−24.3690	+	96.9853i	−0.243690	+	0.969853i
$101$	61.9518	−	35.7679i	0.613384	−	0.354138i	−0.160905	−	0.986970i	$-0.551441\pi$
$101$	61.9518	−	35.7679i	0.613384	−	0.354138i	0.774289	+	0.632832i	$0.218108\pi$
$102$	−50.5792	+	5.76257i	−0.495875	+	0.0564958i
$103$	−170.659	+	45.7279i	−1.65688	+	0.443960i	−0.961528	−	0.274709i	$-0.911419\pi$
$103$	−170.659	+	45.7279i	−1.65688	+	0.443960i	−0.695353	+	0.718668i	$0.744752\pi$
$104$	24.2711	+	11.5771i	0.233376	+	0.111318i
$105$	−61.3232	+	0.445475i	−0.584031	+	0.00424262i
$106$	54.5995	+	138.611i	0.515090	+	1.30765i
$107$	86.7811	−	23.2529i	0.811038	−	0.217317i	0.170614	−	0.985338i	$-0.445425\pi$
$107$	86.7811	−	23.2529i	0.811038	−	0.217317i	0.640425	+	0.768021i	$0.278758\pi$
$108$	49.1237	+	92.3901i	0.454849	+	0.855464i
$109$	84.4829	−	48.7762i	0.775073	−	0.447488i	−0.0596086	−	0.998222i	$-0.518985\pi$
$109$	84.4829	−	48.7762i	0.775073	−	0.447488i	0.834681	+	0.550733i	$0.185652\pi$
$110$	97.5646	+	39.5221i	0.886951	+	0.359292i
$111$	78.9955			0.711671
$112$	−105.224	−	38.3663i	−0.939497	−	0.342556i
$113$	126.524	+	126.524i	1.11968	+	1.11968i	0.991788	+	0.127893i	$0.0408215\pi$
$113$	126.524	+	126.524i	1.11968	+	1.11968i	0.127893	+	0.991788i	$0.459179\pi$
$114$	8.67134	−	58.0197i	0.0760644	−	0.508945i
$115$	125.133	−	36.9427i	1.08812	−	0.321241i
$116$	128.608	+	39.3206i	1.10869	+	0.338970i
$117$	−19.2537	+	5.15900i	−0.164561	+	0.0440940i
$118$	39.2150	−	90.1874i	0.332331	−	0.764300i
$119$	−1.83114	+	101.672i	−0.0153877	+	0.854388i
$120$	7.26186	+	69.7083i	0.0605155	+	0.580903i
$121$	−5.09572	+	8.82604i	−0.0421134	+	0.0729425i
$122$	−107.364	+	12.2322i	−0.880035	+	0.100264i
$123$	80.1081	+	21.4649i	0.651286	+	0.174511i
$124$	−29.2073	+	6.74279i	−0.235543	+	0.0543774i
$125$	−9.46811	−	124.641i	−0.0757449	−	0.997127i
$126$	77.7789	−	29.0308i	0.617293	−	0.230403i
$127$	−116.148	−	116.148i	−0.914552	−	0.914552i	0.0820746	−	0.996626i	$-0.473845\pi$
$127$	−116.148	−	116.148i	−0.914552	−	0.914552i	−0.996626	+	0.0820746i	$0.973845\pi$
$128$	−32.0521	+	123.922i	−0.250407	+	0.968141i
$129$	−28.6269	−	49.5832i	−0.221914	−	0.384366i
$130$	−33.3592	−	4.12686i	−0.256609	−	0.0317451i
$131$	−115.560	+	200.156i	−0.882140	+	1.52791i	−0.0331824	+	0.999449i	$0.510564\pi$
$131$	−115.560	+	200.156i	−0.882140	+	1.52791i	−0.848957	+	0.528461i	$0.822769\pi$
$132$	73.7311	+	2.57533i	0.558569	+	0.0195101i
$133$	−112.628	−	32.3631i	−0.846824	−	0.243331i
$134$	62.2036	+	157.915i	0.464206	+	1.17847i
$135$	−94.7952	−	90.1209i	−0.702187	−	0.667563i
$136$	115.857	−	9.11679i	0.851893	−	0.0670352i
$137$	6.66523	+	1.78594i	0.0486513	+	0.0130361i	0.283063	−	0.959101i	$-0.408650\pi$
$137$	6.66523	+	1.78594i	0.0486513	+	0.0130361i	−0.234411	+	0.972138i	$0.575316\pi$
$138$	73.5069	−	54.3918i	0.532659	−	0.394144i
$139$			173.318i			1.24690i	0.781865	+	0.623448i	$0.214269\pi$
$139$			173.318i			1.24690i	−0.781865	+	0.623448i	$0.785731\pi$
$140$	139.946	+	3.87054i	0.999618	+	0.0276467i
$141$	0.590076			0.00418494
$142$	−51.3865	−	69.4454i	−0.361877	−	0.489052i
$143$	−9.15792	+	34.1778i	−0.0640414	+	0.239006i
$144$	−41.5914	−	85.2784i	−0.288829	−	0.592211i
$145$	−168.052	+	4.24801i	−1.15898	+	0.0292966i
$146$	−116.133	+	45.7454i	−0.795431	+	0.313325i
$147$	19.2203	+	83.6757i	0.130750	+	0.569223i
$148$	−180.231	−	6.29522i	−1.21778	−	0.0425353i
$149$	−44.3502	−	25.6056i	−0.297652	−	0.171850i	0.343736	−	0.939066i	$-0.388308\pi$
$149$	−44.3502	−	25.6056i	−0.297652	−	0.171850i	−0.641388	+	0.767217i	$0.721641\pi$
$150$	−36.1850	−	79.7849i	−0.241233	−	0.531899i
$151$	146.607	−	84.6434i	0.970905	−	0.560552i	0.0713932	−	0.997448i	$-0.477255\pi$
$151$	146.607	−	84.6434i	0.970905	−	0.560552i	0.899512	+	0.436896i	$0.143922\pi$
$152$	−24.4076	+	131.683i	−0.160576	+	0.866335i
$153$	−60.9136	+	60.9136i	−0.398128	+	0.398128i
$154$	24.4046	−	145.337i	0.158472	−	0.943748i
$155$	31.9657	−	19.5487i	0.206230	−	0.126121i
$156$	−22.9545	+	5.29927i	−0.147144	+	0.0339697i
$157$	5.92043	−	22.0953i	0.0377097	−	0.140735i	−0.944504	−	0.328499i	$-0.893457\pi$
$157$	5.92043	−	22.0953i	0.0377097	−	0.140735i	0.982214	+	0.187764i	$0.0601240\pi$
$158$	−20.5310	−	180.204i	−0.129943	−	1.14053i
$159$	−113.028	−	65.2569i	−0.710870	−	0.410421i
$160$	−11.0130	−	159.621i	−0.0688315	−	0.997628i
$161$	−88.4675	−	159.809i	−0.549488	−	0.992601i
$162$	13.8202	+	6.00927i	0.0853100	+	0.0370942i
$163$	−56.0754	−	209.276i	−0.344021	−	1.28390i	−0.893752	−	0.448562i	$-0.851936\pi$
$163$	−56.0754	−	209.276i	−0.344021	−	1.28390i	0.549731	−	0.835342i	$-0.314730\pi$
$164$	−181.059	−	55.3568i	−1.10402	−	0.337541i
$165$	−88.4461	+	26.1117i	−0.536037	+	0.158252i
$166$	18.0219	+	2.69347i	0.108566	+	0.0162257i
$167$	35.3746	−	35.3746i	0.211824	−	0.211824i	−0.593218	−	0.805042i	$-0.702143\pi$
$167$	35.3746	−	35.3746i	0.211824	−	0.211824i	0.805042	+	0.593218i	$0.202143\pi$
$168$	93.0669	−	31.0811i	0.553970	−	0.185007i
$169$			157.701i			0.933144i
$170$	−133.773	+	56.6394i	−0.786899	+	0.333173i
$171$	−49.6363	−	85.9726i	−0.290271	−	0.502764i
$172$	61.3618	+	115.407i	0.356755	+	0.670971i
$173$	56.9375	+	212.494i	0.329118	+	1.22829i	0.910106	+	0.414375i	$0.136000\pi$
$173$	56.9375	+	212.494i	0.329118	+	1.22829i	−0.580988	+	0.813912i	$0.697334\pi$
$174$	−109.620	+	43.1800i	−0.630001	+	0.248161i
$175$	−167.474	+	50.7683i	−0.956995	+	0.290105i
$176$	−168.015	−	11.7514i	−0.954628	−	0.0667693i
$177$	22.2989	+	83.2207i	0.125983	+	0.470173i
$178$	−35.0637	−	307.761i	−0.196987	−	1.72899i
$179$	80.0123	+	138.585i	0.446996	+	0.774219i	0.998189	−	0.0601583i	$-0.0191605\pi$
$179$	80.0123	+	138.585i	0.446996	+	0.774219i	−0.551193	+	0.834378i	$0.685827\pi$
$180$	83.0505	+	84.6677i	0.461392	+	0.470376i
$181$			146.042i			0.806862i	0.915010	+	0.403431i	$0.132183\pi$
$181$			146.042i			0.806862i	−0.915010	+	0.403431i	$0.867817\pi$
$182$	4.48422	+	46.8448i	0.0246386	+	0.257389i
$183$	66.9397	−	66.9397i	0.365791	−	0.365791i
$184$	−172.043	+	118.239i	−0.935016	+	0.642603i
$185$	216.201	−	63.8282i	1.16865	−	0.345018i
$186$	16.3477	−	20.5517i	0.0878909	−	0.110493i
$187$	39.5783	+	147.708i	0.211649	+	0.789884i
$188$	−1.34628	−	0.0470237i	−0.00716105	−	0.000250126i
$189$	−94.3989	+	156.909i	−0.499465	+	0.830205i
$190$	−23.1475	−	165.799i	−0.121829	−	0.872627i
$191$	−130.788	−	75.5107i	−0.684756	−	0.395344i	0.116889	−	0.993145i	$-0.462708\pi$
$191$	−130.788	−	75.5107i	−0.684756	−	0.395344i	−0.801644	+	0.597801i	$0.796041\pi$
$192$	−45.6078	−	102.443i	−0.237540	−	0.533559i
$193$	−53.3668	+	199.168i	−0.276512	+	1.03196i	0.678309	+	0.734777i	$0.262713\pi$
$193$	−53.3668	+	199.168i	−0.276512	+	1.03196i	−0.954821	+	0.297181i	$0.903954\pi$
$194$	311.240	+	46.5163i	1.60433	+	0.239775i
$195$	25.1223	−	15.3636i	0.128832	−	0.0787879i
$196$	−37.1835	−	192.441i	−0.189712	−	0.981840i
$197$	−49.2339	+	49.2339i	−0.249918	+	0.249918i	−0.820937	−	0.571019i	$-0.806548\pi$
$197$	−49.2339	+	49.2339i	−0.249918	+	0.249918i	0.571019	+	0.820937i	$0.306548\pi$
$198$	100.358	−	74.2604i	0.506859	−	0.375053i
$199$	−239.628	+	138.349i	−1.20416	+	0.695223i	−0.961478	−	0.274883i	$-0.911361\pi$
$199$	−239.628	+	138.349i	−1.20416	+	0.695223i	−0.242683	+	0.970106i	$0.578028\pi$
$200$	76.1990	+	184.915i	0.380995	+	0.924577i
$201$	−128.770	−	74.3452i	−0.640645	−	0.369877i
$202$	57.0502	−	131.205i	0.282427	−	0.649530i
$203$	56.8092	+	228.389i	0.279848	+	1.12507i
$204$	−74.4618	+	69.4356i	−0.365009	+	0.340371i
$205$	236.590	−	5.98048i	1.15410	−	0.0291731i
$206$	−219.971	+	276.540i	−1.06782	+	1.34243i
$207$	40.0499	−	149.468i	0.193478	−	0.722069i
$208$	52.7937	−	10.2612i	0.253816	−	0.0493326i
$209$	−176.222			−0.843169
$210$	−98.0606	+	73.6687i	−0.466955	+	0.350804i
$211$			50.6381i			0.239991i	0.992774	+	0.119995i	$0.0382880\pi$
$211$			50.6381i			0.239991i	−0.992774	+	0.119995i	$0.961712\pi$
$212$	252.677	+	157.893i	1.19187	+	0.744779i
$213$	73.1048	+	19.5884i	0.343215	+	0.0919642i
$214$	111.857	−	140.622i	0.522696	−	0.657114i
$215$	−118.411	−	112.573i	−0.550750	−	0.523593i
$216$	188.888	+	90.0977i	0.874482	+	0.417119i
$217$	−36.4189	−	37.7547i	−0.167829	−	0.173985i
$218$	77.7986	−	178.923i	0.356874	−	0.820746i
$219$	54.6746	−	94.6991i	0.249656	−	0.432416i
$220$	203.874	−	52.5262i	0.926698	−	0.238756i
$221$	−24.4151	−	42.2882i	−0.110475	−	0.191349i
$222$	127.003	−	93.9761i	0.572083	−	0.423316i
$223$	−181.271	−	181.271i	−0.812873	−	0.812873i	0.172191	−	0.985064i	$-0.444916\pi$
$223$	−181.271	−	181.271i	−0.812873	−	0.812873i	−0.985064	+	0.172191i	$0.944916\pi$
$224$	−214.812	+	63.4960i	−0.958983	+	0.283464i
$225$	−131.970	−	67.5438i	−0.586531	−	0.300195i
$226$	353.933	+	52.8970i	1.56607	+	0.234058i
$227$	154.967	+	41.5232i	0.682673	+	0.182922i	0.583457	−	0.812144i	$-0.301700\pi$
$227$	154.967	+	41.5232i	0.682673	+	0.182922i	0.0992161	+	0.995066i	$0.468366\pi$
$228$	−55.0815	−	103.595i	−0.241585	−	0.454365i
$229$	103.636	−	179.502i	0.452558	−	0.783853i	−0.545986	−	0.837794i	$-0.683845\pi$
$229$	103.636	−	179.502i	0.452558	−	0.783853i	0.998544	+	0.0539410i	$0.0171783\pi$
$230$	157.231	−	208.257i	0.683612	−	0.905466i
$231$	62.5301	+	112.955i	0.270693	+	0.488983i
$232$	253.543	−	89.7809i	1.09286	−	0.386986i
$233$	201.573	−	54.0113i	0.865119	−	0.231808i	0.201143	−	0.979562i	$-0.435534\pi$
$233$	201.573	−	54.0113i	0.865119	−	0.231808i	0.663976	+	0.747754i	$0.268868\pi$
$234$	−24.8171	+	31.1991i	−0.106056	+	0.133330i
$235$	1.61496	−	0.476781i	0.00687219	−	0.00202885i
$236$	−44.2438	−	191.648i	−0.187474	−	0.812066i
$237$	112.354	+	112.354i	0.474068	+	0.474068i
$238$	118.009	+	165.639i	0.495837	+	0.695960i
$239$	117.166			0.490235			0.245118	−	0.969493i	$-0.421173\pi$
$239$	117.166			0.490235			0.245118	+	0.969493i	$0.421173\pi$
$240$	94.6028	+	103.432i	0.394178	+	0.430968i
$241$	−85.0989	+	49.1319i	−0.353107	+	0.203867i	−0.666053	−	0.745904i	$-0.732018\pi$
$241$	−85.0989	+	49.1319i	−0.353107	+	0.203867i	0.312946	+	0.949771i	$0.398684\pi$
$242$	2.30733	+	20.2518i	0.00953440	+	0.0836853i
$243$	−240.165	+	64.3521i	−0.988335	+	0.264824i
$244$	−158.060	+	147.391i	−0.647785	+	0.604060i
$245$	120.213	+	213.480i	0.490667	+	0.871347i
$246$	154.327	−	60.7902i	0.627345	−	0.247115i
$247$	54.3541	−	14.5641i	0.220057	−	0.0589641i
$248$	−38.9356	+	45.5867i	−0.156999	+	0.183817i
$249$	−13.8251	+	7.98192i	−0.0555224	+	0.0320559i
$250$	−163.500	−	189.124i	−0.653999	−	0.756495i
$251$	237.666			0.946875			0.473438	−	0.880827i	$-0.343013\pi$
$251$	237.666			0.946875			0.473438	+	0.880827i	$0.343013\pi$
$252$	90.5104	−	139.202i	0.359168	−	0.552389i
$253$	−194.232	−	194.232i	−0.767717	−	0.767717i
$254$	−324.908	−	48.5591i	−1.27916	−	0.191177i
$255$	60.8276	−	111.789i	0.238540	−	0.438386i
$256$	95.8918	+	237.362i	0.374577	+	0.927196i
$257$	184.491	−	49.4343i	0.717864	−	0.192351i	0.118646	−	0.992937i	$-0.462145\pi$
$257$	184.491	−	49.4343i	0.717864	−	0.192351i	0.599219	+	0.800585i	$0.295478\pi$
$258$	−105.010	−	45.6602i	−0.407016	−	0.176977i
$259$	−152.851	−	276.112i	−0.590158	−	1.06607i
$260$	−58.5417	+	33.0506i	−0.225160	+	0.127118i
$261$	−99.6870	+	172.663i	−0.381942	+	0.661544i
$262$	52.3254	+	459.270i	0.199715	+	1.75294i
$263$	233.848	+	62.6594i	0.889156	+	0.238249i	0.674353	−	0.738409i	$-0.264422\pi$
$263$	233.848	+	62.6594i	0.889156	+	0.238249i	0.214803	+	0.976657i	$0.431089\pi$
$264$	121.602	−	83.5730i	0.460616	−	0.316564i
$265$	−362.072	−	87.2733i	−1.36631	−	0.329333i
$266$	−219.574	+	81.9554i	−0.825465	+	0.308103i
$267$	191.883	+	191.883i	0.718665	+	0.718665i
$268$	287.868	+	179.883i	1.07413	+	0.671205i
$269$	−6.09856	−	10.5630i	−0.0226712	−	0.0392677i	0.854467	−	0.519505i	$-0.173884\pi$
$269$	−6.09856	−	10.5630i	−0.0226712	−	0.0392677i	−0.877138	+	0.480238i	$0.840550\pi$
$270$	−259.615	−	32.1170i	−0.961539	−	0.118952i
$271$	222.268	−	384.979i	0.820177	−	1.42059i	−0.0853731	−	0.996349i	$-0.527208\pi$
$271$	222.268	−	384.979i	0.820177	−	1.42059i	0.905550	−	0.424239i	$-0.139458\pi$
$272$	175.420	−	152.486i	0.644928	−	0.560609i
$273$	−28.6221	−	29.6720i	−0.104843	−	0.108689i
$274$	12.8404	−	5.05792i	0.0468629	−	0.0184596i
$275$	−220.968	+	142.929i	−0.803519	+	0.519741i
$276$	53.4718	−	174.893i	0.193738	−	0.633672i
$277$	48.0799	+	12.8830i	0.173574	+	0.0465089i	0.344559	−	0.938765i	$-0.388028\pi$
$277$	48.0799	+	12.8830i	0.173574	+	0.0465089i	−0.170985	+	0.985274i	$0.554695\pi$
$278$	206.186	+	278.647i	0.741678	+	1.00233i
$279$		−	44.4388i		−	0.159279i
$280$	229.599	−	160.263i	0.819997	−	0.572368i
$281$	483.043			1.71901			0.859507	−	0.511123i	$-0.170770\pi$
$281$	483.043			1.71901			0.859507	+	0.511123i	$0.170770\pi$
$282$	0.948676	−	0.701978i	0.00336410	−	0.00248928i
$283$	41.4899	−	154.842i	0.146607	−	0.547147i	−0.853071	−	0.521795i	$-0.825263\pi$
$283$	41.4899	−	154.842i	0.146607	−	0.547147i	0.999679	−	0.0253519i	$-0.00807062\pi$
$284$	−165.230	−	50.5173i	−0.581796	−	0.177878i
$285$	106.292	+	101.051i	0.372954	+	0.354564i
$286$	25.9359	+	65.8429i	0.0906850	+	0.230220i
$287$	−79.9778	−	321.534i	−0.278668	−	1.12033i
$288$	−168.318	−	87.6249i	−0.584436	−	0.304253i
$289$	67.5222	+	38.9840i	0.233641	+	0.134893i
$290$	−265.127	+	206.751i	−0.914231	+	0.712935i
$291$	−238.760	+	137.848i	−0.820480	+	0.473704i
$292$	−132.288	+	211.702i	−0.453043	+	0.725007i
$293$	265.859	−	265.859i	0.907370	−	0.907370i	−0.0886894	−	0.996059i	$-0.528268\pi$
$293$	265.859	−	265.859i	0.907370	−	0.907370i	0.996059	+	0.0886894i	$0.0282679\pi$
$294$	130.445	+	111.662i	0.443690	+	0.379802i
$295$	128.272	+	209.747i	0.434819	+	0.711007i
$296$	−297.249	+	204.289i	−1.00422	+	0.690164i
$297$	−71.2708	+	265.986i	−0.239969	+	0.895576i
$298$	−101.764	+	11.5941i	−0.341490	+	0.0389065i
$299$	75.9617	+	43.8565i	0.254052	+	0.146677i
$300$	−153.090	−	85.2246i	−0.510301	−	0.284082i
$301$	−117.916	+	195.999i	−0.391748	+	0.651160i
$302$	135.007	−	310.492i	0.447044	−	1.02812i
$303$	32.4405	+	121.070i	0.107065	+	0.399570i
$304$	117.415	+	240.745i	0.386232	+	0.791925i
$305$	129.118	−	237.293i	0.423339	−	0.778009i
$306$	−25.4667	+	170.397i	−0.0832246	+	0.556854i
$307$	−162.456	+	162.456i	−0.529171	+	0.529171i	−0.920325	−	0.391154i	$-0.872076\pi$
$307$	−162.456	+	162.456i	−0.529171	+	0.529171i	0.391154	+	0.920325i	$0.372076\pi$
$308$	−133.663	−	262.694i	−0.433971	−	0.852902i
$309$		−	309.566i		−	1.00183i
$310$	28.1359	−	69.4564i	0.0907609	−	0.224053i
$311$	−0.385824	−	0.668266i	−0.00124059	−	0.00214877i	0.865404	−	0.501074i	$-0.167062\pi$
$311$	−0.385824	−	0.668266i	−0.00124059	−	0.00214877i	−0.866645	+	0.498925i	$0.833728\pi$
$312$	−30.6001	+	35.8273i	−0.0980773	+	0.114831i
$313$	−30.3992	−	113.451i	−0.0971219	−	0.362464i	0.900211	−	0.435455i	$-0.143412\pi$
$313$	−30.3992	−	113.451i	−0.0971219	−	0.362464i	−0.997333	+	0.0729906i	$0.976746\pi$
$314$	−16.7671	−	42.5663i	−0.0533984	−	0.135561i
$315$	−52.2602	+	200.863i	−0.165906	+	0.637661i
$316$	−247.386	−	265.293i	−0.782867	−	0.839535i
$317$	−117.458	−	438.359i	−0.370529	−	1.38283i	−0.859768	−	0.510685i	$-0.829392\pi$
$317$	−117.458	−	438.359i	−0.370529	−	1.38283i	0.489239	−	0.872150i	$-0.337275\pi$
$318$	−259.350	+	29.5481i	−0.815566	+	0.0929187i
$319$	176.958	+	306.500i	0.554727	+	0.960815i
$320$	−207.597	−	243.523i	−0.648740	−	0.761010i
$321$			157.416i			0.490394i
$322$	−332.346	−	151.683i	−1.03213	−	0.471065i
$323$	171.962	−	171.962i	0.532391	−	0.532391i
$324$	29.3679	−	6.77986i	0.0906416	−	0.0209255i
$325$	56.3428	−	62.3471i	0.173363	−	0.191837i
$326$	−339.117	−	269.748i	−1.04024	−	0.827448i
$327$	44.2388	+	165.101i	0.135287	+	0.504897i
$328$	−356.946	+	126.396i	−1.08825	+	0.385355i
$329$	−1.14176	−	2.06248i	−0.00347039	−	0.00626894i
$330$	−111.133	+	147.199i	−0.336767	+	0.446058i
$331$	31.6732	+	18.2865i	0.0956894	+	0.0552463i	0.547081	−	0.837080i	$-0.315739\pi$
$331$	31.6732	+	18.2865i	0.0956894	+	0.0552463i	−0.451392	+	0.892326i	$0.649072\pi$
$332$	32.1785	−	17.1093i	0.0969231	−	0.0515339i
$333$	69.1967	−	258.246i	0.207798	−	0.775512i
$334$	14.7894	−	98.9553i	0.0442796	−	0.296273i
$335$	−412.497	−	99.4278i	−1.23134	−	0.296799i
$336$	112.650	−	160.686i	0.335268	−	0.478231i
$337$	95.9045	−	95.9045i	0.284583	−	0.284583i	−0.550351	−	0.834934i	$-0.685506\pi$
$337$	95.9045	−	95.9045i	0.284583	−	0.284583i	0.834934	+	0.550351i	$0.185506\pi$
$338$	187.608	+	253.539i	0.555052	+	0.750116i
$339$	−271.511	+	156.757i	−0.800917	+	0.462409i
$340$	−147.689	+	250.202i	−0.434379	+	0.735887i
$341$	−68.3163	−	39.4424i	−0.200341	−	0.115667i
$342$	−182.078	−	79.1705i	−0.532391	−	0.231493i
$343$	255.280	−	229.087i	0.744258	−	0.667892i
$344$	235.945	+	112.544i	0.685887	+	0.327161i
$345$	5.77684	+	228.533i	0.0167445	+	0.662416i
$346$	344.330	+	273.895i	0.995174	+	0.791604i
$347$	11.6583	−	43.5093i	0.0335973	−	0.125387i	−0.947090	−	0.320967i	$-0.895992\pi$
$347$	11.6583	−	43.5093i	0.0335973	−	0.125387i	0.980688	+	0.195580i	$0.0626589\pi$
$348$	−124.870	+	199.830i	−0.358821	+	0.574223i
$349$	−353.335			−1.01242			−0.506210	−	0.862410i	$-0.668954\pi$
$349$	−353.335			−1.01242			−0.506210	+	0.862410i	$0.668954\pi$
$350$	−208.855	+	280.855i	−0.596729	+	0.802443i
$351$		−	87.9311i		−	0.250516i
$352$	−284.100	+	180.984i	−0.807102	+	0.514159i
$353$	−378.316	−	101.369i	−1.07172	−	0.287166i	−0.320519	−	0.947242i	$-0.603857\pi$
$353$	−378.316	−	101.369i	−1.07172	−	0.287166i	−0.751198	+	0.660077i	$0.770524\pi$
$354$	134.853	+	107.268i	0.380941	+	0.303016i
$355$	215.906	−	5.45765i	0.608186	−	0.0153737i
$356$	−422.497	−	453.080i	−1.18679	−	1.27270i
$357$	−171.243	−	49.2061i	−0.479673	−	0.137832i
$358$	293.504	+	127.620i	0.819843	+	0.356482i
$359$	8.07257	−	13.9821i	0.0224863	−	0.0389473i	−0.854563	−	0.519347i	$-0.826175\pi$
$359$	8.07257	−	13.9821i	0.0224863	−	0.0389473i	0.877050	+	0.480400i	$0.159508\pi$
$360$	234.246	+	37.3217i	0.650683	+	0.103671i
$361$	−40.3741	−	69.9300i	−0.111840	−	0.193712i
$362$	173.737	+	234.795i	0.479938	+	0.648604i
$363$	−12.6267	−	12.6267i	−0.0347842	−	0.0347842i
$364$	62.9378	+	69.9786i	0.172906	+	0.192249i
$365$	73.1207	−	303.357i	0.200331	−	0.831114i
$366$	27.9861	−	187.254i	0.0764647	−	0.511624i
$367$	132.704	+	35.5580i	0.361592	+	0.0968882i	0.435041	−	0.900411i	$-0.356734\pi$
$367$	132.704	+	35.5580i	0.361592	+	0.0968882i	−0.0734491	+	0.997299i	$0.523401\pi$
$368$	−135.935	+	394.764i	−0.369389	+	1.07273i
$369$	140.343	−	243.081i	0.380332	−	0.658755i
$370$	271.657	−	359.819i	0.734209	−	0.972483i
$371$	−9.38932	+	521.333i	−0.0253082	+	1.40521i
$372$	1.83338	−	52.4893i	0.00492844	−	0.141100i
$373$	272.538	−	73.0264i	0.730666	−	0.195781i	0.125740	−	0.992063i	$-0.459869\pi$
$373$	272.538	−	73.0264i	0.730666	−	0.195781i	0.604926	+	0.796282i	$0.293203\pi$
$374$	239.350	+	190.389i	0.639974	+	0.509062i
$375$	215.240	+	40.4988i	0.573975	+	0.107997i
$376$	−2.22038	+	1.52598i	−0.00590526	+	0.00405847i
$377$	−79.9120	−	79.9120i	−0.211968	−	0.211968i
$378$	34.8981	+	364.566i	0.0923229	+	0.964460i
$379$	23.8839			0.0630182			0.0315091	−	0.999503i	$-0.489969\pi$
$379$	23.8839			0.0630182			0.0315091	+	0.999503i	$0.489969\pi$
$380$	−234.456	−	239.021i	−0.616989	−	0.629003i
$381$	249.245	−	143.902i	0.654186	−	0.377694i
$382$	−300.101	+	34.1910i	−0.785605	+	0.0895053i
$383$	−478.096	+	128.106i	−1.24829	+	0.334479i	−0.821677	−	0.569954i	$-0.806961\pi$
$383$	−478.096	+	128.106i	−1.24829	+	0.334479i	−0.426616	+	0.904433i	$0.640295\pi$
$384$	−195.195	−	110.443i	−0.508320	−	0.287612i
$385$	262.405	+	258.620i	0.681571	+	0.671740i
$386$	151.139	+	383.693i	0.391552	+	0.994023i
$387$	−187.169	+	50.1518i	−0.483641	+	0.129591i
$388$	555.723	−	295.478i	1.43228	−	0.761541i
$389$	−208.369	+	120.302i	−0.535653	+	0.309260i	−0.743316	−	0.668941i	$-0.766748\pi$
$389$	−208.369	+	120.302i	−0.535653	+	0.309260i	0.207662	+	0.978201i	$0.433415\pi$
$390$	22.1124	−	54.5869i	0.0566985	−	0.139966i
$391$	379.074			0.969499
$392$	−288.715	−	265.155i	−0.736519	−	0.676417i
$393$	−286.347	−	286.347i	−0.728618	−	0.728618i
$394$	−20.5837	+	137.725i	−0.0522429	+	0.349556i
$395$	398.281	+	216.717i	1.00831	+	0.548651i
$396$	73.0043	−	238.780i	0.184354	−	0.602979i
$397$	−232.801	+	62.3789i	−0.586401	+	0.157126i	−0.539808	−	0.841788i	$-0.681503\pi$
$397$	−232.801	+	62.3789i	−0.586401	+	0.157126i	−0.0465934	+	0.998914i	$0.514837\pi$
$398$	−220.669	+	507.498i	−0.554444	+	1.27512i
$399$	105.848	−	175.939i	0.265282	−	0.440949i
$400$	342.489	+	206.643i	0.856223	+	0.516606i
$401$	−93.4299	+	161.825i	−0.232992	+	0.403555i	−0.958687	−	0.284462i	$-0.908185\pi$
$401$	−93.4299	+	161.825i	−0.232992	+	0.403555i	0.725695	+	0.688017i	$0.241518\pi$
$402$	−295.469	+	33.6633i	−0.734999	+	0.0837396i
$403$	24.3313	+	6.51954i	0.0603753	+	0.0161775i
$404$	−64.3660	−	278.810i	−0.159322	−	0.690123i
$405$	−32.1414	+	19.6562i	−0.0793615	+	0.0485338i
$406$	363.034	+	299.603i	0.894172	+	0.737938i
$407$	−335.587	−	335.587i	−0.824539	−	0.824539i
$408$	−37.1102	+	200.216i	−0.0909564	+	0.490725i
$409$	247.169	+	428.109i	0.604325	+	1.04672i	0.992158	+	0.124992i	$0.0398906\pi$
$409$	247.169	+	428.109i	0.604325	+	1.04672i	−0.387832	+	0.921730i	$0.626776\pi$
$410$	373.255	−	291.071i	0.910377	−	0.709930i
$411$	−6.04519	+	10.4706i	−0.0147085	+	0.0254758i
$412$	−24.6696	+	706.285i	−0.0598777	+	1.71428i
$413$	247.733	−	238.967i	0.599837	−	0.578613i
$414$	−113.424	−	287.948i	−0.273972	−	0.695526i
$415$	−31.3881	+	33.0162i	−0.0756341	+	0.0795570i
$416$	72.6703	−	79.3025i	0.174688	−	0.190631i
$417$	−293.330	−	78.5977i	−0.703430	−	0.188484i
$418$	−283.316	+	209.641i	−0.677789	+	0.501533i
$419$		−	661.743i		−	1.57934i	−0.613532	−	0.789670i	$-0.710252\pi$
$419$		−	661.743i		−	1.57934i	0.613532	−	0.789670i	$-0.289748\pi$
$420$	−70.0146	+	235.095i	−0.166701	+	0.559751i
$421$	116.266			0.276166			0.138083	−	0.990421i	$-0.455906\pi$
$421$	116.266			0.276166			0.138083	+	0.990421i	$0.455906\pi$
$422$	60.2410	+	81.4118i	0.142751	+	0.192919i
$423$	0.516881	−	1.92903i	0.00122194	−	0.00456035i
$424$	594.070	−	46.7472i	1.40111	−	0.110253i
$425$	76.1526	−	355.100i	0.179183	−	0.835529i
$426$	140.835	−	55.4758i	0.330599	−	0.130225i
$427$	−363.497	−	104.449i	−0.851281	−	0.244612i
$428$	12.5447	−	359.151i	0.0293099	−	0.839137i
$429$	−53.6908	−	30.9984i	−0.125153	−	0.0722573i
$430$	−324.293	−	40.1182i	−0.754169	−	0.0932981i
$431$	−641.674	+	370.471i	−1.48880	+	0.859560i	−0.999918	−	0.0127885i	$-0.995929\pi$
$431$	−641.674	+	370.471i	−1.48880	+	0.859560i	−0.488884	+	0.872349i	$0.662596\pi$
$432$	410.863	−	79.8568i	0.951071	−	0.184854i
$433$	−110.428	+	110.428i	−0.255031	+	0.255031i	−0.823030	−	0.567999i	$-0.807718\pi$
$433$	−110.428	+	110.428i	−0.255031	+	0.255031i	0.567999	+	0.823030i	$0.307718\pi$
$434$	−103.466	−	17.3737i	−0.238400	−	0.0400315i
$435$	69.0200	−	286.344i	0.158667	−	0.658262i
$436$	−87.7751	−	380.209i	−0.201319	−	0.872040i
$437$	−113.063	+	421.957i	−0.258725	+	0.965576i
$438$	−24.7565	−	217.293i	−0.0565217	−	0.496102i
$439$	252.643	+	145.864i	0.575498	+	0.332264i	0.759342	−	0.650692i	$-0.225521\pi$
$439$	252.643	+	145.864i	0.575498	+	0.332264i	−0.183844	+	0.982955i	$0.558854\pi$
$440$	265.284	−	326.983i	0.602918	−	0.743144i
$441$	290.382	+	10.4631i	0.658463	+	0.0237258i
$442$	−89.5602	−	38.9423i	−0.202625	−	0.0881048i
$443$	174.274	+	650.399i	0.393394	+	1.46817i	0.824498	+	0.565866i	$0.191458\pi$
$443$	174.274	+	650.399i	0.393394	+	1.46817i	−0.431103	+	0.902303i	$0.641875\pi$
$444$	92.3866	−	302.174i	0.208078	−	0.680573i
$445$	680.203	+	370.119i	1.52855	+	0.831729i
$446$	−507.079	−	75.7855i	−1.13695	−	0.169923i
$447$	63.4480	−	63.4480i	0.141942	−	0.141942i
$448$	−269.820	+	357.633i	−0.602277	+	0.798287i
$449$			372.887i			0.830483i	0.909711	+	0.415242i	$0.136303\pi$
$449$			372.887i			0.830483i	−0.909711	+	0.415242i	$0.863697\pi$
$450$	−292.523	+	48.4047i	−0.650050	+	0.107566i
$451$	−249.127	−	431.501i	−0.552388	−	0.956764i
$452$	631.953	−	336.009i	1.39813	−	0.743382i
$453$	76.7694	+	286.507i	0.169469	+	0.632466i
$454$	298.540	−	117.597i	0.657578	−	0.259024i
$455$	−102.310	−	58.0820i	−0.224858	−	0.127653i
$456$	−211.796	−	101.025i	−0.464466	−	0.221546i
$457$	−40.5657	−	151.393i	−0.0887653	−	0.331277i	0.907235	−	0.420624i	$-0.138189\pi$
$457$	−40.5657	−	151.393i	−0.0887653	−	0.331277i	−0.996001	+	0.0893470i	$0.971522\pi$
$458$	−46.9260	−	411.878i	−0.102458	−	0.899298i
$459$	−190.008	−	329.104i	−0.413962	−	0.717003i
$460$	5.03199	−	521.867i	0.0109391	−	1.13449i
$461$		−	444.474i		−	0.964152i	−0.876129	−	0.482076i	$-0.839883\pi$
$461$		−	444.474i		−	0.964152i	0.876129	−	0.482076i	$-0.160117\pi$
$462$	234.907	+	107.212i	0.508456	+	0.232060i
$463$	−226.193	+	226.193i	−0.488539	+	0.488539i	−0.907845	−	0.419306i	$-0.862273\pi$
$463$	−226.193	+	226.193i	−0.488539	+	0.488539i	0.419306	+	0.907845i	$0.362273\pi$
$464$	300.819	−	445.967i	0.648316	−	0.961136i
$465$	18.5889	+	62.9650i	0.0399762	+	0.135409i
$466$	259.818	−	326.634i	0.557550	−	0.700931i
$467$	−10.6405	−	39.7108i	−0.0227847	−	0.0850338i	0.953597	−	0.301085i	$-0.0973488\pi$
$467$	−10.6405	−	39.7108i	−0.0227847	−	0.0850338i	−0.976382	+	0.216051i	$0.930682\pi$
$468$	−2.78321	+	79.6828i	−0.00594704	+	0.170262i
$469$	−10.6970	+	593.939i	−0.0228080	+	1.26640i
$470$	2.02921	−	2.68775i	0.00431747	−	0.00571862i
$471$	34.7101	+	20.0399i	0.0736945	+	0.0425476i
$472$	−299.123	−	255.481i	−0.633735	−	0.541274i
$473$	−89.0263	+	332.251i	−0.188216	+	0.702433i
$474$	314.295	+	46.9729i	0.663069	+	0.0990990i
$475$	372.557	+	190.680i	0.784330	+	0.401431i
$476$	386.776	+	125.912i	0.812554	+	0.264520i
$477$	−312.340	+	312.340i	−0.654802	+	0.654802i
$478$	188.370	−	139.386i	0.394080	−	0.291602i
$479$	−92.9235	+	53.6494i	−0.193995	+	0.112003i	−0.593851	−	0.804575i	$-0.702393\pi$
$479$	−92.9235	+	53.6494i	−0.193995	+	0.112003i	0.399857	+	0.916578i	$0.369060\pi$
$480$	275.142	+	53.7470i	0.573212	+	0.111973i
$481$	131.244	+	75.7736i	0.272856	+	0.157533i
$482$	−78.3658	+	180.227i	−0.162585	+	0.373915i
$483$	310.585	−	77.2545i	0.643033	−	0.159947i
$484$	27.8019	+	29.8144i	0.0574420	+	0.0616000i
$485$	−542.075	+	570.190i	−1.11768	+	1.17565i
$486$	−309.563	+	389.170i	−0.636960	+	0.800762i
$487$	113.593	−	423.935i	0.233251	−	0.870504i	−0.745679	−	0.666306i	$-0.767875\pi$
$487$	113.593	−	423.935i	0.233251	−	0.870504i	0.978930	−	0.204198i	$-0.0654588\pi$
$488$	−78.7736	+	424.996i	−0.161421	+	0.870894i
$489$	379.616			0.776312
$490$	447.234	+	200.205i	0.912721	+	0.408582i
$491$		−	169.706i		−	0.345632i	−0.984954	−	0.172816i	$-0.944713\pi$
$491$		−	169.706i		−	0.345632i	0.984954	−	0.172816i	$-0.0552867\pi$
$492$	175.796	−	281.327i	0.357308	−	0.571802i
$493$	−471.771	−	126.411i	−0.956939	−	0.256411i
$494$	70.0600	−	88.0767i	0.141822	−	0.178293i
$495$	7.88704	+	312.013i	0.0159334	+	0.630330i
$496$	−8.36584	+	119.610i	−0.0168666	+	0.241149i
$497$	−72.9859	−	293.424i	−0.146853	−	0.590391i
$498$	−12.7312	+	29.2795i	−0.0255647	+	0.0587942i
$499$	209.694	−	363.200i	0.420228	−	0.727856i	−0.575733	−	0.817637i	$-0.695283\pi$
$499$	209.694	−	363.200i	0.420228	−	0.727856i	0.995962	+	0.0897811i	$0.0286167\pi$
$500$	−487.851	−	109.552i	−0.975701	−	0.219104i
$501$	43.8273	+	75.9111i	0.0874797	+	0.151519i
$502$	382.099	−	282.736i	0.761154	−	0.563220i
$503$	145.988	+	145.988i	0.290234	+	0.290234i	0.837173	−	0.546939i	$-0.184207\pi$
$503$	145.988	+	145.988i	0.290234	+	0.290234i	−0.546939	+	0.837173i	$0.684207\pi$
$504$	−20.0851	−	331.473i	−0.0398515	−	0.657684i
$505$	186.610	+	305.141i	0.369525	+	0.604239i
$506$	−543.337	−	81.2045i	−1.07379	−	0.160483i
$507$	−266.899	−	71.5155i	−0.526429	−	0.141056i
$508$	−580.128	+	308.454i	−1.14198	+	0.607192i
$509$	−385.049	+	666.924i	−0.756481	+	1.31026i	0.188153	+	0.982140i	$0.439750\pi$
$509$	−385.049	+	666.924i	−0.756481	+	1.31026i	−0.944635	+	0.328124i	$0.893584\pi$
$510$	−35.1943	−	252.087i	−0.0690085	−	0.494289i
$511$	−436.792	−	7.86671i	−0.854778	−	0.0153947i
$512$	436.542	+	267.535i	0.852622	+	0.522529i
$513$	423.006	−	113.344i	0.824573	−	0.220944i
$514$	237.801	−	298.954i	0.462648	−	0.581623i
$515$	−250.129	−	847.243i	−0.485687	−	1.64513i
$516$	−223.146	+	51.5154i	−0.432453	+	0.0998361i
$517$	−2.50675	−	2.50675i	−0.00484865	−	0.00484865i
$518$	−574.214	−	262.072i	−1.10852	−	0.505931i
$519$	−385.452			−0.742683
$520$	−54.8003	+	122.780i	−0.105385	+	0.236115i
$521$	−29.7155	+	17.1563i	−0.0570355	+	0.0329295i	−0.528247	−	0.849091i	$-0.677150\pi$
$521$	−29.7155	+	17.1563i	−0.0570355	+	0.0329295i	0.471211	+	0.882020i	$0.343817\pi$
$522$	45.1380	+	396.185i	0.0864712	+	0.758975i
$523$	902.781	−	241.899i	1.72616	−	0.462523i	0.746866	−	0.664975i	$-0.231558\pi$
$523$	902.781	−	241.899i	1.72616	−	0.462523i	0.979292	+	0.202452i	$0.0648910\pi$
$524$	630.490	+	676.129i	1.20323	+	1.29032i
$525$	−9.97480	−	306.462i	−0.0189996	−	0.583737i
$526$	450.504	−	177.456i	0.856471	−	0.337369i
$527$	105.154	−	28.1759i	0.199533	−	0.0534646i
$528$	96.0809	−	279.025i	0.181971	−	0.528456i
$529$	−131.571	+	75.9627i	−0.248717	+	0.143597i
$530$	−685.933	+	290.424i	−1.29421	+	0.547970i
$531$	291.591			0.549136
$532$	−255.515	+	392.975i	−0.480292	+	0.738675i
$533$	112.503	+	112.503i	0.211075	+	0.211075i
$534$	536.767	+	80.2225i	1.00518	+	0.150229i
$535$	127.192	+	430.829i	0.237742	+	0.805288i
$536$	676.806	−	53.2577i	1.26270	−	0.0993614i
$537$	−270.831	+	72.5690i	−0.504341	+	0.135138i
$538$	−22.3710	−	9.72728i	−0.0415817	−	0.0180804i
$539$	273.819	−	437.121i	0.508012	−	0.810985i
$540$	−455.596	+	257.214i	−0.843697	+	0.476322i
$541$	−29.7770	+	51.5753i	−0.0550407	+	0.0953333i	−0.892233	−	0.451575i	$-0.850862\pi$
$541$	−29.7770	+	51.5753i	−0.0550407	+	0.0953333i	0.837192	+	0.546909i	$0.184196\pi$
$542$	−100.642	−	883.357i	−0.185687	−	1.62981i
$543$	−247.167	−	66.2282i	−0.455188	−	0.121967i
$544$	100.624	−	453.841i	0.184970	−	0.834267i
$545$	254.478	+	416.117i	0.466931	+	0.763517i
$546$	−81.3154	−	13.6543i	−0.148929	−	0.0250078i
$547$	220.745	+	220.745i	0.403557	+	0.403557i	0.879484	−	0.475928i	$-0.157888\pi$
$547$	220.745	+	220.745i	0.403557	+	0.403557i	−0.475928	+	0.879484i	$0.657888\pi$
$548$	14.6267	−	23.4072i	0.0266911	−	0.0427139i
$549$	−160.197	−	277.470i	−0.291799	−	0.505410i
$550$	−185.220	+	492.661i	−0.336764	+	0.895747i
$551$	281.421	−	487.436i	0.510747	−	0.884639i
$552$	−122.093	−	344.792i	−0.221182	−	0.624623i
$553$	175.312	−	610.107i	0.317020	−	1.10327i
$554$	92.6250	−	36.4855i	0.167193	−	0.0658584i
$555$	9.98101	+	394.851i	0.0179838	+	0.711444i
$556$	662.979	+	202.699i	1.19241	+	0.364566i
$557$	100.097	+	26.8208i	0.179707	+	0.0481523i	0.347550	−	0.937661i	$-0.387014\pi$
$557$	100.097	+	26.8208i	0.179707	+	0.0481523i	−0.167843	+	0.985814i	$0.553680\pi$
$558$	−52.8661	−	71.4450i	−0.0947421	−	0.128038i
$559$		−	109.837i		−	0.196489i
$560$	178.475	−	530.798i	0.318706	−	0.947854i
$561$	−267.935			−0.477603
$562$	776.597	−	574.647i	1.38185	−	1.02250i
$563$	20.7573	−	77.4674i	0.0368691	−	0.137597i	−0.945038	−	0.326960i	$-0.893976\pi$
$563$	20.7573	−	77.4674i	0.0368691	−	0.137597i	0.981907	+	0.189363i	$0.0606423\pi$
$564$	0.690104	−	2.25716i	0.00122359	−	0.00400206i
$565$	−616.432	+	648.404i	−1.09103	+	1.14762i
$566$	−117.503	−	298.301i	−0.207602	−	0.527034i
$567$	36.6191	+	37.9623i	0.0645839	+	0.0669529i
$568$	−325.741	+	115.346i	−0.573487	+	0.203075i
$569$	−297.622	−	171.832i	−0.523061	−	0.301989i	0.215125	−	0.976586i	$-0.430984\pi$
$569$	−297.622	−	171.832i	−0.523061	−	0.301989i	−0.738186	+	0.674597i	$0.764317\pi$
$570$	291.102	+	36.0121i	0.510705	+	0.0631792i
$571$	−910.707	+	525.797i	−1.59493	+	0.920835i	−0.602490	+	0.798126i	$0.705825\pi$
$571$	−910.707	+	525.797i	−1.59493	+	0.920835i	−0.992443	+	0.122709i	$0.960842\pi$
$572$	120.027	+	75.0025i	0.209837	+	0.131123i
$573$	187.108	−	187.108i	0.326541	−	0.326541i
$574$	−511.091	−	421.791i	−0.890402	−	0.734827i
$575$	200.465	+	620.800i	0.348635	+	1.07965i
$576$	−374.849	+	59.3612i	−0.650780	+	0.103058i
$577$	238.355	−	889.552i	0.413093	−	1.54169i	−0.375531	−	0.926810i	$-0.622540\pi$
$577$	238.355	−	889.552i	0.413093	−	1.54169i	0.788624	−	0.614875i	$-0.210794\pi$
$578$	154.933	−	17.6518i	0.268051	−	0.0305395i
$579$	−312.878	−	180.640i	−0.540376	−	0.311986i
$580$	−180.290	+	647.803i	−0.310846	+	1.11690i
$581$	54.6496	+	32.8781i	0.0940613	+	0.0565888i
$582$	−219.869	+	505.659i	−0.377782	+	0.868829i
$583$	202.941	+	757.388i	0.348099	+	1.29912i
$584$	39.1665	+	497.733i	0.0670659	+	0.852282i
$585$	−28.2194	−	95.5857i	−0.0482384	−	0.163394i
$586$	111.150	−	743.704i	0.189676	−	1.26912i
$587$	−600.742	+	600.742i	−1.02341	+	1.02341i	−0.0236912	+	0.999719i	$0.507542\pi$
$587$	−600.742	+	600.742i	−1.02341	+	1.02341i	−0.999719	+	0.0236912i	$0.992458\pi$
$588$	342.556	+	24.3387i	0.582578	+	0.0413923i
$589$			125.453i			0.212993i
$590$	455.748	+	184.617i	0.772454	+	0.312911i
$591$	−60.9984	−	105.652i	−0.103212	−	0.178769i
$592$	−234.864	+	682.058i	−0.396729	+	1.15213i
$593$	−17.9331	−	66.9271i	−0.0302412	−	0.112862i	0.949155	−	0.314808i	$-0.101940\pi$
$593$	−17.9331	−	66.9271i	−0.0302412	−	0.112862i	−0.979397	+	0.201946i	$0.935273\pi$
$594$	201.844	+	512.417i	0.339805	+	0.862656i
$595$	−508.430	+	3.69342i	−0.854504	+	0.00620743i
$596$	−149.815	+	139.703i	−0.251367	+	0.234400i
$597$	−125.479	−	468.295i	−0.210183	−	0.784413i
$598$	174.298	−	19.8581i	0.291469	−	0.0332075i
$599$	523.387	+	906.533i	0.873768	+	1.51341i	0.858069	+	0.513534i	$0.171664\pi$
$599$	523.387	+	906.533i	0.873768	+	1.51341i	0.0156994	+	0.999877i	$0.495003\pi$
$600$	−347.513	+	45.1053i	−0.579188	+	0.0751755i
$601$			73.3536i			0.122053i	0.998136	+	0.0610263i	$0.0194373\pi$
$601$			73.3536i			0.122053i	−0.998136	+	0.0610263i	$0.980563\pi$
$602$	43.5921	+	455.389i	0.0724122	+	0.756460i
$603$	−355.840	+	355.840i	−0.590116	+	0.590116i
$604$	−152.320	−	659.793i	−0.252185	−	1.09237i
$605$	−44.7599	−	24.3553i	−0.0739834	−	0.0402567i
$606$	196.185	+	156.054i	0.323737	+	0.257514i
$607$	80.3797	+	299.981i	0.132421	+	0.494203i	0.999995	−	0.00310540i	$-0.000988480\pi$
$607$	80.3797	+	299.981i	0.132421	+	0.494203i	−0.867574	+	0.497308i	$0.834322\pi$
$608$	475.170	+	247.370i	0.781529	+	0.406858i
$609$	−412.296	−	7.42554i	−0.677005	−	0.0121930i
$610$	−74.7067	−	535.104i	−0.122470	−	0.877220i
$611$	0.980356	+	0.566009i	0.00160451	+	0.000926365i
$612$	161.768	+	304.247i	0.264327	+	0.497136i
$613$	90.4898	−	337.712i	0.147618	−	0.550918i	−0.852007	−	0.523530i	$-0.824615\pi$
$613$	90.4898	−	337.712i	0.147618	−	0.550918i	0.999625	−	0.0273872i	$-0.00871870\pi$
$614$	−67.9193	+	454.447i	−0.110618	+	0.740141i
$615$	−97.1687	+	403.125i	−0.157998	+	0.655487i
$616$	−527.404	−	263.327i	−0.856175	−	0.427479i
$617$	−553.688	+	553.688i	−0.897387	+	0.897387i	−0.995204	−	0.0978174i	$-0.968814\pi$
$617$	−553.688	+	553.688i	−0.897387	+	0.897387i	0.0978174	+	0.995204i	$0.468814\pi$
$618$	−368.272	−	497.695i	−0.595909	−	0.805332i
$619$	−656.271	+	378.898i	−1.06021	+	0.612114i	−0.925491	−	0.378770i	$-0.876347\pi$
$619$	−656.271	+	378.898i	−1.06021	+	0.612114i	−0.134721	+	0.990884i	$0.543014\pi$
$620$	−37.3935	−	145.138i	−0.0603121	−	0.234093i
$621$	591.165	+	341.310i	0.951957	+	0.549613i
$622$	−1.41529	−	0.615393i	−0.00227539	−	0.000989378i
$623$	299.405	−	1041.97i	0.480587	−	1.67250i
$624$	−6.57484	+	94.0032i	−0.0105366	+	0.150646i
$625$	621.809	−	63.0737i	0.994895	−	0.100918i
$626$	−183.839	−	146.234i	−0.293673	−	0.233600i
$627$	79.9145	−	298.245i	0.127455	−	0.475670i
$628$	−77.5953	−	48.4878i	−0.123559	−	0.0772098i
$629$	654.950			1.04126
$630$	154.935	+	385.102i	0.245928	+	0.611273i
$631$			315.333i			0.499735i	0.968280	+	0.249868i	$0.0803871\pi$
$631$			315.333i			0.499735i	−0.968280	+	0.249868i	$0.919613\pi$
$632$	−713.330	−	132.217i	−1.12869	−	0.209204i
$633$	−85.7017	−	22.9637i	−0.135390	−	0.0362776i
$634$	−710.328	−	565.025i	−1.12039	−	0.891206i
$635$	565.880	−	595.230i	0.891149	−	0.937370i
$636$	−381.810	+	356.038i	−0.600330	+	0.559808i
$637$	−48.3302	+	157.456i	−0.0758716	+	0.247183i
$638$	649.123	+	282.250i	1.01743	+	0.442398i
$639$	128.073	−	221.830i	0.200428	−	0.347151i
$640$	−623.462	−	144.552i	−0.974159	−	0.225862i
$641$	−307.468	−	532.550i	−0.479669	−	0.830811i	0.520059	−	0.854130i	$-0.325910\pi$
$641$	−307.468	−	532.550i	−0.479669	−	0.830811i	−0.999728	+	0.0233191i	$0.992577\pi$
$642$	187.269	+	253.081i	0.291696	+	0.394207i
$643$	−713.395	−	713.395i	−1.10948	−	1.10948i	−0.993219	−	0.116260i	$-0.962909\pi$
$643$	−713.395	−	713.395i	−1.10948	−	1.10948i	−0.116260	−	0.993219i	$-0.537091\pi$
$644$	−714.766	+	151.508i	−1.10989	+	0.235261i
$645$	244.220	−	149.353i	0.378635	−	0.231556i
$646$	71.8939	−	481.040i	0.111291	−	0.744644i
$647$	473.853	+	126.969i	0.732385	+	0.196242i	0.605691	−	0.795700i	$-0.292897\pi$
$647$	473.853	+	126.969i	0.732385	+	0.196242i	0.126694	+	0.991942i	$0.459563\pi$
$648$	39.1497	−	45.8373i	0.0604162	−	0.0707366i
$649$	258.807	−	448.266i	0.398778	−	0.690703i
$650$	16.4128	−	167.264i	0.0252505	−	0.257330i
$651$	80.4130	−	44.5153i	0.123522	−	0.0683799i
$652$	−866.107	−	30.2520i	−1.32839	−	0.0463987i
$653$	−895.837	+	240.039i	−1.37188	+	0.367594i	−0.868164	−	0.496277i	$-0.834700\pi$
$653$	−895.837	+	240.039i	−1.37188	+	0.367594i	−0.503714	+	0.863870i	$0.668033\pi$
$654$	267.534	+	212.808i	0.409074	+	0.325395i
$655$	−1015.06	−	552.327i	−1.54971	−	0.843248i
$656$	−423.503	+	627.847i	−0.645583	+	0.957084i
$657$	−261.690	−	261.690i	−0.398311	−	0.398311i
$658$	−4.28923	−	1.95761i	−0.00651859	−	0.00297509i
$659$	−1066.67			−1.61862			−0.809310	−	0.587382i	$-0.800159\pi$
$659$	−1066.67			−1.61862			−0.809310	+	0.587382i	$0.800159\pi$
$660$	−3.55668	+	368.863i	−0.00538891	+	0.558883i
$661$	352.316	−	203.410i	0.533004	−	0.307730i	−0.209235	−	0.977865i	$-0.567097\pi$
$661$	352.316	−	203.410i	0.533004	−	0.307730i	0.742239	+	0.670135i	$0.233764\pi$
$662$	72.6760	−	8.28009i	0.109782	−	0.0125077i
$663$	82.6420	−	22.1438i	0.124649	−	0.0333995i
$664$	31.3801	−	65.7876i	0.0472591	−	0.0990778i
$665$	147.533	−	567.047i	0.221855	−	0.852702i
$666$	−195.970	−	497.505i	−0.294250	−	0.747005i
$667$	847.435	−	227.070i	1.27052	−	0.340434i
$668$	−93.9440	−	176.686i	−0.140635	−	0.264501i
$669$	388.993	−	224.585i	0.581454	−	0.335703i
$670$	−781.463	+	330.871i	−1.16636	+	0.493837i
$671$	−568.744			−0.847607
$672$	−10.0484	−	392.351i	−0.0149530	−	0.583855i
$673$	14.4452	+	14.4452i	0.0214639	+	0.0214639i	0.717757	−	0.696293i	$-0.245169\pi$
$673$	14.4452	+	14.4452i	0.0214639	+	0.0214639i	−0.696293	+	0.717757i	$0.745169\pi$
$674$	40.0957	−	268.279i	0.0594891	−	0.398040i
$675$	438.484	−	485.212i	0.649605	−	0.718832i
$676$	603.241	+	184.434i	0.892368	+	0.272832i
$677$	766.816	−	205.468i	1.13267	−	0.303497i	0.356669	−	0.934231i	$-0.383913\pi$
$677$	766.816	−	205.468i	1.13267	−	0.303497i	0.776000	+	0.630733i	$0.217246\pi$
$678$	−250.029	+	575.021i	−0.368774	+	0.848113i
$679$	943.801	+	567.806i	1.38999	+	0.836239i
$680$	60.2079	+	577.950i	0.0885410	+	0.849927i
$681$	−140.551	+	243.441i	−0.206389	+	0.357476i
$682$	−156.756	+	17.8594i	−0.229847	+	0.0261868i
$683$	604.321	+	161.927i	0.884804	+	0.237082i	0.672478	−	0.740117i	$-0.265230\pi$
$683$	604.321	+	161.927i	0.884804	+	0.237082i	0.212325	+	0.977199i	$0.431896\pi$
$684$	−386.914	+	89.3229i	−0.565663	+	0.130589i
$685$	−8.08472	+	33.5411i	−0.0118025	+	0.0489652i
$686$	137.888	−	671.999i	0.201003	−	0.979591i
$687$	256.799	+	256.799i	0.373797	+	0.373797i
$688$	513.220	−	99.7514i	0.745959	−	0.144987i
$689$	−125.191	−	216.837i	−0.181699	−	0.314712i
$690$	281.160	+	360.545i	0.407478	+	0.522529i
$691$	481.932	−	834.730i	0.697441	−	1.20800i	−0.271910	−	0.962323i	$-0.587655\pi$
$691$	481.932	−	834.730i	0.697441	−	1.20800i	0.969351	−	0.245681i	$-0.0790115\pi$
$692$	879.422	+	30.7171i	1.27084	+	0.0443888i
$693$	424.037	−	105.474i	0.611887	−	0.152200i
$694$	−33.0171	−	83.8198i	−0.0475751	−	0.120778i
$695$	−866.316	+	21.8986i	−1.24650	+	0.0315088i
$696$	36.9700	+	469.820i	0.0531178	+	0.675028i
$697$	664.175	+	177.965i	0.952905	+	0.255330i
$698$	−568.063	+	420.341i	−0.813844	+	0.602208i
$699$			365.642i			0.523094i
$700$	−1.66442	+	699.998i	−0.00237774	+	0.999997i
$701$	−558.023			−0.796039			−0.398020	−	0.917377i	$-0.630302\pi$
$701$	−558.023			−0.796039			−0.398020	+	0.917377i	$0.630302\pi$
$702$	−104.606	−	141.368i	−0.149012	−	0.201380i
$703$	−195.346	+	729.041i	−0.277875	+	1.03704i
$704$	−241.447	+	628.948i	−0.342965	+	0.893391i
$705$	0.0745556	+	2.94944i	0.000105753	+	0.00418360i
$706$	−728.819	+	287.086i	−1.03232	+	0.406637i
$707$	360.403	−	347.651i	0.509763	−	0.491726i
$708$	344.415	+	12.0300i	0.486463	+	0.0169915i
$709$	−960.924	−	554.790i	−1.35532	−	0.782496i	−0.366334	−	0.930484i	$-0.619387\pi$
$709$	−960.924	−	554.790i	−1.35532	−	0.782496i	−0.988989	+	0.147988i	$0.952720\pi$
$710$	340.624	−	265.625i	0.479752	−	0.374119i
$711$	465.716	−	268.881i	0.655016	−	0.378174i
$712$	−1218.26	−	225.806i	−1.71104	−	0.317143i
$713$	−138.274	+	138.274i	−0.193933	+	0.193933i
$714$	−333.848	+	124.608i	−0.467575	+	0.174521i
$715$	−171.992	−	41.4566i	−0.240548	−	0.0579813i
$716$	623.693	−	143.986i	0.871080	−	0.201097i
$717$	−53.1334	+	198.296i	−0.0741051	+	0.276564i
$718$	−3.65524	−	32.0827i	−0.00509086	−	0.0446835i
$719$	1017.38	+	587.382i	1.41499	+	0.816944i	0.995853	−	0.0909802i	$-0.0290000\pi$
$719$	1017.38	+	587.382i	1.41499	+	0.816944i	0.419135	+	0.907924i	$0.362333\pi$
$720$	421.001	−	218.665i	0.584723	−	0.303702i
$721$	−1082.02	+	598.989i	−1.50072	+	0.830775i
$722$	−148.102	−	64.3971i	−0.205127	−	0.0891927i
$723$	−44.5613	−	166.305i	−0.0616339	−	0.230021i
$724$	558.642	+	170.799i	0.771604	+	0.235910i
$725$	−42.4665	−	839.456i	−0.0585745	−	1.15787i
$726$	−35.3213	−	5.27895i	−0.0486519	−	0.00727128i
$727$	−163.053	+	163.053i	−0.224282	+	0.224282i	−0.810299	−	0.586017i	$-0.800695\pi$
$727$	−163.053	+	163.053i	−0.224282	+	0.224282i	0.586017	+	0.810299i	$0.300695\pi$
$728$	184.436	+	37.6327i	0.253345	+	0.0516933i
$729$		−	367.832i		−	0.504570i
$730$	−243.327	−	574.699i	−0.333325	−	0.787259i
$731$	−237.345	−	411.093i	−0.324685	−	0.562371i
$732$	−177.771	−	334.345i	−0.242857	−	0.456756i
$733$	−134.703	−	502.720i	−0.183770	−	0.685839i	−0.994891	−	0.100960i	$-0.967809\pi$
$733$	−134.703	−	502.720i	−0.183770	−	0.685839i	0.811121	−	0.584879i	$-0.198858\pi$
$734$	255.652	−	100.703i	0.348300	−	0.137197i
$735$	−415.817	+	106.643i	−0.565737	+	0.145093i
$736$	251.081	+	796.383i	0.341143	+	1.08204i
$737$	231.205	+	862.869i	0.313711	+	1.17079i
$738$	−63.5467	−	557.762i	−0.0861067	−	0.755775i
$739$	−574.570	−	995.185i	−0.777497	−	1.34666i	−0.933380	−	0.358889i	$-0.883156\pi$
$739$	−574.570	−	995.185i	−0.777497	−	1.34666i	0.155883	−	0.987776i	$-0.450178\pi$
$740$	8.69408	−	901.662i	0.0117488	−	1.21846i
$741$			98.5954i			0.133057i
$742$	605.103	+	849.327i	0.815503	+	1.14465i
$743$	74.1649	−	74.1649i	0.0998182	−	0.0998182i	−0.655434	−	0.755252i	$-0.727514\pi$
$743$	74.1649	−	74.1649i	0.0998182	−	0.0998182i	0.755252	+	0.655434i	$0.227514\pi$
$744$	−59.4957	−	86.5690i	−0.0799674	−	0.116356i
$745$	122.383	−	224.915i	0.164273	−	0.301900i
$746$	351.290	−	441.628i	0.470898	−	0.591995i
$747$	13.9836	+	52.1876i	0.0187197	+	0.0698630i
$748$	611.302	+	21.3520i	0.817249	+	0.0285454i
$749$	550.215	−	304.590i	0.734599	−	0.406662i
$750$	394.225	−	190.948i	0.525633	−	0.254597i
$751$	1054.92	+	609.059i	1.40469	+	0.810998i	0.994869	−	0.101169i	$-0.0322583\pi$
$751$	1054.92	+	609.059i	1.40469	+	0.810998i	0.409820	+	0.912167i	$0.365592\pi$
$752$	−1.75437	+	5.09480i	−0.00233294	+	0.00677500i
$753$	−107.778	+	402.234i	−0.143132	+	0.534175i
$754$	−223.542	−	33.4095i	−0.296475	−	0.0443097i
$755$	441.606	+	722.105i	0.584908	+	0.956430i
$756$	489.808	+	544.603i	0.647894	+	0.720374i
$757$	478.837	−	478.837i	0.632546	−	0.632546i	−0.316160	−	0.948706i	$-0.602394\pi$
$757$	478.837	−	478.837i	0.632546	−	0.632546i	0.948706	+	0.316160i	$0.102394\pi$
$758$	38.3986	−	28.4132i	0.0506578	−	0.0374845i
$759$	416.808	−	240.644i	0.549154	−	0.317054i
$760$	−661.288	−	105.361i	−0.870116	−	0.138633i
$761$	576.622	+	332.913i	0.757716	+	0.437468i	0.828475	−	0.560026i	$-0.189209\pi$
$761$	576.622	+	332.913i	0.757716	+	0.437468i	−0.0707590	+	0.997493i	$0.522542\pi$
$762$	229.525	−	527.865i	0.301213	−	0.692736i
$763$	491.477	−	474.087i	0.644137	−	0.621346i
$764$	−441.803	+	411.982i	−0.578277	+	0.539243i
$765$	−312.167	−	296.775i	−0.408062	−	0.387941i
$766$	−616.245	+	774.720i	−0.804497	+	1.01138i
$767$	−42.7788	+	159.653i	−0.0557742	+	0.208152i
$768$	−445.206	+	54.6501i	−0.579695	+	0.0711590i
$769$	961.397			1.25019			0.625095	−	0.780548i	$-0.285060\pi$
$769$	961.397			1.25019			0.625095	+	0.780548i	$0.285060\pi$
$770$	729.537	+	103.621i	0.947451	+	0.134573i
$771$			334.657i			0.434056i
$772$	699.445	+	437.069i	0.906017	+	0.566152i
$773$	−166.826	−	44.7009i	−0.215816	−	0.0578278i	0.149291	−	0.988793i	$-0.452301\pi$
$773$	−166.826	−	44.7009i	−0.215816	−	0.0578278i	−0.365107	+	0.930966i	$0.618968\pi$
$774$	−241.253	+	303.294i	−0.311696	+	0.391853i
$775$	101.751	+	157.307i	0.131292	+	0.202977i
$776$	541.935	−	1136.16i	0.698370	−	1.46412i
$777$	536.617	−	133.477i	0.690627	−	0.171786i
$778$	−191.883	+	441.296i	−0.246636	+	0.567218i
$779$	−396.194	+	686.229i	−0.508594	+	0.880910i
$780$	−29.3881	−	114.066i	−0.0376771	−	0.146239i
$781$	−227.348	−	393.778i	−0.291098	−	0.504197i
$782$	609.444	−	450.961i	0.779341	−	0.576677i
$783$	−621.909	−	621.909i	−0.794264	−	0.794264i
$784$	−779.612	−	82.8280i	−0.994404	−	0.105648i
$785$	111.189	+	26.8010i	0.141643	+	0.0341414i
$786$	−801.014	−	119.716i	−1.01910	−	0.152310i
$787$	−83.0453	−	22.2519i	−0.105521	−	0.0282743i	0.205672	−	0.978621i	$-0.434062\pi$
$787$	−83.0453	−	22.2519i	−0.105521	−	0.0282743i	−0.311193	+	0.950347i	$0.600729\pi$
$788$	130.750	+	245.910i	0.165927	+	0.312069i
$789$	−212.094	+	367.358i	−0.268814	+	0.465599i
$790$	898.139	−	125.391i	1.13689	−	0.158722i
$791$	1073.26	+	645.693i	1.35684	+	0.816300i
$792$	−166.691	−	470.739i	−0.210469	−	0.594368i
$793$	175.424	−	47.0046i	0.221215	−	0.0592744i
$794$	−300.071	+	377.237i	−0.377923	+	0.475110i
$795$	311.899	−	573.206i	0.392326	−	0.721014i
$796$	248.966	+	1078.43i	0.312771	+	1.35481i
$797$	389.330	+	389.330i	0.488494	+	0.488494i	0.907831	−	0.419337i	$-0.137737\pi$
$797$	389.330	+	389.330i	0.488494	+	0.488494i	−0.419337	+	0.907831i	$0.637737\pi$
$798$	−39.1305	−	408.780i	−0.0490357	−	0.512256i
$799$	4.89231			0.00612304
$800$	796.456	−	75.2155i	0.995570	−	0.0940194i
$801$	795.371	−	459.208i	0.992973	−	0.573293i
$802$	42.3048	+	371.318i	0.0527491	+	0.462989i
$803$	−634.567	+	170.032i	−0.790245	+	0.211745i
$804$	−434.984	+	405.623i	−0.541025	+	0.504506i
$805$	787.611	−	462.388i	0.978399	−	0.574395i
$806$	46.8737	−	18.4638i	0.0581560	−	0.0229080i
$807$	20.6429	−	5.53124i	0.0255798	−	0.00685408i
$808$	−435.165	−	371.675i	−0.538571	−	0.459994i
$809$	−946.759	+	546.611i	−1.17028	+	0.675663i	−0.953747	−	0.300612i	$-0.902809\pi$
$809$	−946.759	+	546.611i	−1.17028	+	0.675663i	−0.216536	+	0.976275i	$0.569476\pi$
$810$	−28.2906	+	69.8383i	−0.0349266	+	0.0862201i
$811$	851.794			1.05030			0.525151	−	0.851009i	$-0.324009\pi$
$811$	851.794			1.05030			0.525151	+	0.851009i	$0.324009\pi$
$812$	940.075	+	49.7979i	1.15773	+	0.0613274i
$813$	550.758	+	550.758i	0.677439	+	0.677439i
$814$	−938.758	−	140.302i	−1.15326	−	0.172361i
$815$	1038.96	−	306.730i	1.27480	−	0.376355i
$816$	178.522	+	366.038i	0.218776	+	0.448576i
$817$	528.388	−	141.581i	0.646742	−	0.173294i
$818$	906.674	+	394.237i	1.10840	+	0.481953i
$819$	−122.073	+	67.5777i	−0.149051	+	0.0825125i
$820$	253.819	−	911.999i	0.309535	−	1.11219i
$821$	−140.942	+	244.118i	−0.171671	+	0.297343i	−0.939004	−	0.343906i	$-0.888250\pi$
$821$	−140.942	+	244.118i	−0.171671	+	0.297343i	0.767333	+	0.641248i	$0.221583\pi$
$822$	2.73724	+	24.0253i	0.00332998	+	0.0292279i
$823$	−83.2983	−	22.3197i	−0.101213	−	0.0271199i	0.207857	−	0.978159i	$-0.433351\pi$
$823$	−83.2983	−	22.3197i	−0.101213	−	0.0271199i	−0.309070	+	0.951039i	$0.600018\pi$
$824$	800.562	+	1164.86i	0.971556	+	1.41366i
$825$	−141.692	−	438.790i	−0.171747	−	0.531867i
$826$	114.000	−	678.905i	0.138014	−	0.821919i
$827$	−767.051	−	767.051i	−0.927510	−	0.927510i	0.0700345	−	0.997545i	$-0.477689\pi$
$827$	−767.051	−	767.051i	−0.927510	−	0.927510i	−0.997545	+	0.0700345i	$0.977689\pi$
$828$	−524.908	−	328.005i	−0.633947	−	0.396141i
$829$	206.230	+	357.202i	0.248770	+	0.430883i	0.963185	−	0.268840i	$-0.0866403\pi$
$829$	206.230	+	357.202i	0.248770	+	0.430883i	−0.714415	+	0.699723i	$0.753307\pi$
$830$	−11.1860	+	90.4212i	−0.0134771	+	0.108941i
$831$	−43.6072	+	75.5299i	−0.0524756	+	0.0908904i
$832$	22.4919	−	213.947i	0.0270336	−	0.257148i
$833$	159.355	+	693.754i	0.191302	+	0.832838i
$834$	−565.096	+	222.595i	−0.677573	+	0.266900i
$835$	181.286	+	172.347i	0.217109	+	0.206403i
$836$	−206.095	+	674.087i	−0.246525	+	0.806324i
$837$	189.356	+	50.7378i	0.226232	+	0.0606186i
$838$	−787.236	−	1063.90i	−0.939422	−	1.26957i
$839$			21.4545i			0.0255715i	0.999918	+	0.0127858i	$0.00406995\pi$
$839$			21.4545i			0.0255715i	−0.999918	+	0.0127858i	$0.995930\pi$
$840$	167.115	+	461.259i	0.198946	+	0.549118i
$841$	−289.384			−0.344095
$842$	186.923	−	138.314i	0.221998	−	0.164269i
$843$	−219.054	+	817.520i	−0.259850	+	0.969774i
$844$	193.701	+	59.2221i	0.229504	+	0.0701684i
$845$	−788.255	+	19.9254i	−0.932846	+	0.0235804i
$846$	−1.46385	−	3.71624i	−0.00173032	−	0.00439271i
$847$	−19.7020	+	68.5655i	−0.0232610	+	0.0809510i
$848$	899.485	−	781.885i	1.06071	−	0.922034i
$849$	243.246	+	140.438i	0.286509	+	0.165416i
$850$	−300.009	−	661.495i	−0.352951	−	0.778229i
$851$	−1018.86	+	588.239i	−1.19725	+	0.691232i
$852$	160.427	−	256.732i	0.188295	−	0.301329i
$853$	−162.145	+	162.145i	−0.190088	+	0.190088i	−0.795734	−	0.605646i	$-0.792915\pi$
$853$	−162.145	+	162.145i	−0.190088	+	0.190088i	0.605646	+	0.795734i	$0.292915\pi$
$854$	−708.658	+	264.505i	−0.829810	+	0.309725i
$855$	423.454	−	258.965i	0.495268	−	0.302883i
$856$	−407.091	−	592.337i	−0.475574	−	0.691982i
$857$	−383.577	+	1431.53i	−0.447582	+	1.67040i	0.261448	+	0.965218i	$0.415800\pi$
$857$	−383.577	+	1431.53i	−0.447582	+	1.67040i	−0.709029	+	0.705179i	$0.750867\pi$
$858$	−123.197	+	14.0360i	−0.143586	+	0.0163590i
$859$	−831.162	−	479.872i	−0.967593	−	0.558640i	−0.0690915	−	0.997610i	$-0.522010\pi$
$859$	−831.162	−	479.872i	−0.967593	−	0.558640i	−0.898502	+	0.438970i	$0.855343\pi$
$860$	−569.098	+	321.293i	−0.661742	+	0.373596i
$861$	580.444	+	10.4539i	0.674151	+	0.0121416i
$862$	−590.904	+	1358.97i	−0.685504	+	1.57653i
$863$	−363.011	−	1354.78i	−0.420639	−	1.56984i	−0.773266	−	0.634081i	$-0.781378\pi$
$863$	−363.011	−	1354.78i	−0.420639	−	1.56984i	0.352628	−	0.935764i	$-0.385288\pi$
$864$	565.550	−	617.165i	0.654572	−	0.714312i
$865$	−1054.93	+	311.445i	−1.21958	+	0.360052i
$866$	−46.1678	+	308.908i	−0.0533116	+	0.356706i
$867$	−96.5983	+	96.5983i	−0.111417	+	0.111417i
$868$	−187.012	+	95.1550i	−0.215452	+	0.109626i
$869$		−	954.602i		−	1.09851i
$870$	−229.681	−	542.470i	−0.264002	−	0.623528i
$871$	−142.626	−	247.035i	−0.163750	−	0.283623i
$872$	−593.430	−	506.849i	−0.680539	−	0.581249i
$873$	241.498	+	901.283i	0.276630	+	1.03240i
$874$	320.203	+	812.891i	0.366365	+	0.930082i
$875$	−274.921	−	830.689i	−0.314195	−	0.949358i
$876$	−298.301	−	319.894i	−0.340527	−	0.365176i
$877$	−199.587	−	744.869i	−0.227579	−	0.849338i	−0.981355	−	0.192206i	$-0.938436\pi$
$877$	−199.587	−	744.869i	−0.227579	−	0.849338i	0.753775	−	0.657132i	$-0.228231\pi$
$878$	579.705	−	66.0467i	0.660256	−	0.0752240i
$879$	329.386	+	570.514i	0.374728	+	0.649049i
$880$	37.5097	−	841.289i	0.0426247	−	0.956011i
$881$			128.770i			0.146164i	0.997326	+	0.0730819i	$0.0232835\pi$
$881$			128.770i			0.146164i	−0.997326	+	0.0730819i	$0.976717\pi$
$882$	479.300	−	328.628i	0.543424	−	0.372594i
$883$	−231.507	+	231.507i	−0.262183	+	0.262183i	−0.825940	−	0.563757i	$-0.809355\pi$
$883$	−231.507	+	231.507i	−0.262183	+	0.262183i	0.563757	+	0.825940i	$0.309355\pi$
$884$	−190.315	+	43.9361i	−0.215288	+	0.0497015i
$885$	−413.153	+	121.974i	−0.466840	+	0.137824i
$886$	1053.92	+	838.335i	1.18953	+	0.946202i
$887$	−39.5724	−	147.686i	−0.0446138	−	0.166501i	0.940025	−	0.341106i	$-0.110802\pi$
$887$	−39.5724	−	147.686i	−0.0446138	−	0.166501i	−0.984638	+	0.174606i	$0.944135\pi$
$888$	−210.947	−	595.718i	−0.237553	−	0.670854i
$889$	−985.248	−	592.741i	−1.10827	−	0.666751i
$890$	1533.88	−	214.148i	1.72346	−	0.240615i
$891$	68.6918	+	39.6593i	0.0770952	+	0.0445109i
$892$	−905.398	+	481.399i	−1.01502	+	0.539685i
$893$	−1.45918	+	5.44575i	−0.00163402	+	0.00609826i
$894$	26.5263	−	177.487i	0.0296715	−	0.198531i
$895$	−682.596	+	417.444i	−0.762677	+	0.466417i
$896$	−8.34099	+	895.961i	−0.00930915	+	0.999957i
$897$	−108.672	+	108.672i	−0.121150	+	0.121150i
$898$	443.601	+	599.497i	0.493988	+	0.667592i
$899$	218.198	−	125.977i	0.242712	−	0.140130i
$900$	−412.710	+	425.818i	−0.458567	+	0.473131i
$901$	−937.115	−	541.043i	−1.04008	−	0.600492i
$902$	−913.856	−	397.360i	−1.01314	−	0.440533i
$903$	−278.243	−	288.449i	−0.308131	−	0.319434i
$904$	616.273	−	1292.00i	0.681718	−	1.42921i
$905$	−729.977	+	18.4523i	−0.806605	+	0.0203893i
$906$	464.264	+	369.295i	0.512432	+	0.407610i
$907$	−74.3974	+	277.655i	−0.0820258	+	0.306124i	−0.994734	−	0.102487i	$-0.967320\pi$
$907$	−74.3974	+	277.655i	−0.0820258	+	0.306124i	0.912709	+	0.408611i	$0.133987\pi$
$908$	340.071	−	544.218i	0.374528	−	0.599359i
$909$	424.208			0.466675
$910$	−233.583	+	28.3327i	−0.256684	+	0.0311349i
$911$		−	567.171i		−	0.622580i	−0.950315	−	0.311290i	$-0.899239\pi$
$911$		−	567.171i		−	0.622580i	0.950315	−	0.311290i	$-0.100761\pi$
$912$	−460.692	+	89.5419i	−0.505145	+	0.0981819i
$913$	92.6401	+	24.8228i	0.101468	+	0.0271882i
$914$	−245.322	−	195.139i	−0.268405	−	0.213500i
$915$	343.049	+	326.134i	0.374917	+	0.356430i
$916$	−565.430	−	606.359i	−0.617282	−	0.661964i
$917$	−446.801	+	1554.92i	−0.487242	+	1.69566i
$918$	−696.995	−	303.066i	−0.759254	−	0.330137i
$919$	−331.250	+	573.742i	−0.360446	+	0.624311i	−0.988034	−	0.154234i	$-0.950709\pi$
$919$	−331.250	+	573.742i	−0.360446	+	0.624311i	0.627588	+	0.778546i	$0.284042\pi$
$920$	−612.743	−	845.001i	−0.666025	−	0.918479i
$921$	−201.274	−	348.617i	−0.218539	−	0.378520i
$922$	−528.764	−	714.589i	−0.573497	−	0.775043i
$923$	102.667	+	102.667i	0.111232	+	0.111232i
$924$	505.207	−	107.088i	0.546761	−	0.115896i
$925$	346.356	+	1072.59i	0.374439	+	1.15956i
$926$	−94.5667	+	632.744i	−0.102124	+	0.683309i
$927$	−1012.01	−	271.167i	−1.09170	−	0.292521i
$928$	−46.9079	−	1074.85i	−0.0505473	−	1.15825i
$929$	355.672	−	616.042i	0.382855	−	0.663124i	−0.608614	−	0.793466i	$-0.708274\pi$
$929$	355.672	−	616.042i	0.382855	−	0.663124i	0.991469	+	0.130342i	$0.0416076\pi$
$930$	104.791	+	79.1158i	0.112679	+	0.0850707i
$931$	−819.763	−	29.5378i	−0.880519	−	0.0317270i
$932$	29.1384	−	834.225i	0.0312644	−	0.895091i
$933$	1.30596	−	0.349932i	0.00139975	−	0.000375061i
$934$	−64.3484	−	51.1855i	−0.0688955	−	0.0548024i
$935$	−733.305	+	216.491i	−0.784283	+	0.231541i
$936$	90.3191	+	131.419i	0.0964948	+	0.140404i
$937$	−865.992	−	865.992i	−0.924218	−	0.924218i	0.0731064	−	0.997324i	$-0.476709\pi$
$937$	−865.992	−	865.992i	−0.924218	−	0.924218i	−0.997324	+	0.0731064i	$0.976709\pi$
$938$	689.376	+	967.613i	0.734942	+	1.03157i
$939$	205.795			0.219164
$940$	0.0649425	−	6.73518i	6.90878e−5	−	0.00716509i
$941$	−433.572	+	250.323i	−0.460757	+	0.266018i	−0.712363	−	0.701812i	$-0.752375\pi$
$941$	−433.572	+	250.323i	−0.460757	+	0.266018i	0.251605	+	0.967830i	$0.419041\pi$
$942$	79.6443	−	9.07401i	0.0845481	−	0.00963271i
$943$	−1193.05	+	319.676i	−1.26516	+	0.338999i
$944$	−784.836	−	54.8936i	−0.831395	−	0.0581500i
$945$	−796.221	−	452.018i	−0.842562	−	0.478326i
$946$	252.129	+	640.075i	0.266521	+	0.676612i
$947$	−1437.86	+	385.273i	−1.51833	+	0.406836i	−0.919192	−	0.393809i	$-0.871157\pi$
$947$	−1437.86	+	385.273i	−1.51833	+	0.406836i	−0.599139	+	0.800645i	$0.704490\pi$
$948$	561.178	−	298.378i	0.591960	−	0.314745i
$949$	181.673	−	104.889i	0.191437	−	0.110526i
$950$	825.807	−	136.649i	0.869270	−	0.143841i
$951$	795.160			0.836130
$952$	771.616	−	257.693i	0.810521	−	0.270686i
$953$	−41.5839	−	41.5839i	−0.0436347	−	0.0436347i	0.684953	−	0.728587i	$-0.259823\pi$
$953$	−41.5839	−	41.5839i	−0.0436347	−	0.0436347i	−0.728587	+	0.684953i	$0.759823\pi$
$954$	−130.583	+	873.728i	−0.136880	+	0.915857i
$955$	360.908	−	663.273i	0.377914	−	0.694527i
$956$	137.028	−	448.186i	0.143335	−	0.468813i
$957$	−598.980	+	160.496i	−0.625893	+	0.167708i
$958$	−85.5713	+	196.798i	−0.0893229	+	0.205426i
$959$	48.2946	+	0.869796i	0.0503594	+	0.000906983i
$960$	506.290	−	240.910i	0.527386	−	0.250947i
$961$	452.421	−	783.616i	0.470781	−	0.815417i
$962$	301.146	−	34.3101i	0.313042	−	0.0356653i
$963$	514.613	+	137.890i	0.534385	+	0.143188i
$964$	88.4151	+	382.982i	0.0917169	+	0.397284i
$965$	−1002.26	−	241.584i	−1.03861	−	0.250346i
$966$	407.428	−	493.688i	0.421768	−	0.511064i
$967$	940.905	+	940.905i	0.973015	+	0.973015i	0.999645	−	0.0266304i	$-0.00847772\pi$
$967$	940.905	+	940.905i	0.973015	+	0.973015i	−0.0266304	+	0.999645i	$0.508478\pi$
$968$	80.1660	+	14.8589i	0.0828161	+	0.0153501i
$969$	213.053	+	369.018i	0.219869	+	0.380824i
$970$	−193.183	+	1561.58i	−0.199157	+	1.60987i
$971$	−40.1834	+	69.5997i	−0.0413835	+	0.0716784i	−0.885975	−	0.463732i	$-0.846510\pi$
$971$	−40.1834	+	69.5997i	−0.0413835	+	0.0716784i	0.844592	+	0.535411i	$0.179843\pi$
$972$	−34.7172	+	993.944i	−0.0357172	+	1.02258i
$973$	292.853	+	1177.35i	0.300980	+	1.21002i
$974$	−321.704	−	816.704i	−0.330292	−	0.838505i
$975$	79.9678	+	123.630i	0.0820183	+	0.126800i
$976$	378.947	+	776.987i	0.388265	+	0.796093i
$977$	−620.653	−	166.303i	−0.635264	−	0.170218i	−0.0732066	−	0.997317i	$-0.523323\pi$
$977$	−620.653	−	166.303i	−0.635264	−	0.170218i	−0.562057	+	0.827098i	$0.689990\pi$
$978$	610.316	−	451.607i	0.624045	−	0.461765i
$979$		−	1630.31i		−	1.66528i
$980$	957.198	−	210.173i	0.976732	−	0.214462i
$981$	578.487			0.589691
$982$	−201.888	−	272.839i	−0.205589	−	0.277840i
$983$	−306.861	+	1145.22i	−0.312168	+	1.16503i	0.614429	+	0.788972i	$0.289386\pi$
$983$	−306.861	+	1145.22i	−0.312168	+	1.16503i	−0.926597	+	0.376055i	$0.877280\pi$
$984$	−52.0476	−	661.428i	−0.0528939	−	0.672183i
$985$	−252.312	−	239.870i	−0.256154	−	0.243523i
$986$	−908.858	+	358.004i	−0.921762	+	0.363088i
$987$	4.00839	−	0.997042i	0.00406119	−	0.00101017i
$988$	7.85716	−	224.949i	0.00795259	−	0.227681i
$989$	738.441	+	426.339i	0.746654	+	0.431081i
$990$	383.864	+	492.247i	0.387741	+	0.497219i
$991$	76.1131	−	43.9439i	0.0768043	−	0.0443430i	−0.461106	−	0.887345i	$-0.652547\pi$
$991$	76.1131	−	43.9439i	0.0768043	−	0.0443430i	0.537910	+	0.843002i	$0.319214\pi$
$992$	128.843	+	202.251i	0.129882	+	0.203882i
$993$	−45.3122	+	45.3122i	−0.0456316	+	0.0456316i
$994$	−466.410	−	384.916i	−0.469225	−	0.387240i
$995$	−721.802	−	1180.28i	−0.725430	−	1.18621i
$996$	14.3638	+	62.2188i	0.0144215	+	0.0624687i
$997$	234.979	−	876.954i	0.235686	−	0.879593i	−0.742152	−	0.670231i	$-0.766195\pi$
$997$	234.979	−	876.954i	0.235686	−	0.879593i	0.977838	−	0.209361i	$-0.0671385\pi$
$998$	−94.9488	−	833.384i	−0.0951390	−	0.835054i
$999$	1021.39	+	589.702i	1.02242	+	0.590292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.36	yes	176
4.3	odd	2	inner	140.3.x.a.103.2	yes	176
5.2	odd	4	inner	140.3.x.a.47.32	yes	176
7.3	odd	6	inner	140.3.x.a.3.24	✓	176
20.7	even	4	inner	140.3.x.a.47.24	yes	176
28.3	even	6	inner	140.3.x.a.3.32	yes	176
35.17	even	12	inner	140.3.x.a.87.2	yes	176
140.87	odd	12	inner	140.3.x.a.87.36	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.24	✓	176	7.3	odd	6	inner
140.3.x.a.3.32	yes	176	28.3	even	6	inner
140.3.x.a.47.24	yes	176	20.7	even	4	inner
140.3.x.a.47.32	yes	176	5.2	odd	4	inner
140.3.x.a.87.2	yes	176	35.17	even	12	inner
140.3.x.a.87.36	yes	176	140.87	odd	12	inner
140.3.x.a.103.2	yes	176	4.3	odd	2	inner
140.3.x.a.103.36	yes	176	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.60772 - 1.18964i) q^{2} +(-0.453487 + 1.69244i) q^{3} +(1.16952 - 3.82521i) q^{4} +(0.126349 + 4.99840i) q^{5} +(1.28431 + 3.26045i) q^{6} +(6.79301 - 1.68968i) q^{7} +(-2.67037 - 7.54116i) q^{8} +(5.13554 + 2.96500i) q^{9} +O(q^{10})\)	\(q+(1.60772 - 1.18964i) q^{2} +(-0.453487 + 1.69244i) q^{3} +(1.16952 - 3.82521i) q^{4} +(0.126349 + 4.99840i) q^{5} +(1.28431 + 3.26045i) q^{6} +(6.79301 - 1.68968i) q^{7} +(-2.67037 - 7.54116i) q^{8} +(5.13554 + 2.96500i) q^{9} +(6.14943 + 7.88572i) q^{10} +(9.11627 - 5.26328i) q^{11} +(5.94356 + 3.71402i) q^{12} +(-2.37683 + 2.37683i) q^{13} +(8.91113 - 10.7978i) q^{14} +(-8.51678 - 2.05287i) q^{15} +(-13.2645 - 8.94730i) q^{16} +(-3.75985 + 14.0320i) q^{17} +(11.7838 - 1.34255i) q^{18} +(-14.4979 - 8.37036i) q^{19} +(19.2677 + 5.36241i) q^{20} +(-0.220859 + 12.2630i) q^{21} +(8.39499 - 19.3070i) q^{22} +(-6.75377 - 25.2054i) q^{23} +(13.9739 - 1.09960i) q^{24} +(-24.9681 + 1.26309i) q^{25} +(-0.993705 + 6.64886i) q^{26} +(-18.4975 + 18.4975i) q^{27} +(1.48115 - 27.9608i) q^{28} +33.6212i q^{29} +(-16.1348 + 6.83145i) q^{30} +(-3.74694 - 6.48989i) q^{31} +(-31.9696 + 1.39519i) q^{32} +(4.77366 + 17.8155i) q^{33} +(10.6482 + 27.0323i) q^{34} +(9.30401 + 33.7407i) q^{35} +(17.3479 - 16.1769i) q^{36} +(-11.6689 - 43.5489i) q^{37} +(-33.2662 + 3.79008i) q^{38} +(-2.94478 - 5.10051i) q^{39} +(37.3564 - 14.3004i) q^{40} -47.3330i q^{41} +(14.2334 + 19.9782i) q^{42} +(-23.1058 + 23.1058i) q^{43} +(-9.47152 - 41.0272i) q^{44} +(-14.1714 + 26.0441i) q^{45} +(-40.8435 - 32.4886i) q^{46} +(-0.0871637 - 0.325299i) q^{47} +(21.1580 - 18.3918i) q^{48} +(43.2899 - 22.9561i) q^{49} +(-38.6390 + 31.7337i) q^{50} +(-22.0431 - 12.7266i) q^{51} +(6.31214 + 11.8716i) q^{52} +(-19.2790 + 71.9501i) q^{53} +(-7.73343 + 51.7442i) q^{54} +(27.4598 + 44.9018i) q^{55} +(-30.8820 - 46.7151i) q^{56} +(20.7409 - 20.7409i) q^{57} +(39.9971 + 54.0534i) q^{58} +(42.5843 - 24.5861i) q^{59} +(-17.8132 + 30.1776i) q^{60} +(-46.7908 - 27.0147i) q^{61} +(-13.7447 - 5.97641i) q^{62} +(39.8957 + 11.4639i) q^{63} +(-49.7383 + 40.2753i) q^{64} +(-12.1807 - 11.5801i) q^{65} +(28.8688 + 22.9634i) q^{66} +(-21.9640 + 81.9706i) q^{67} +(49.2779 + 30.7928i) q^{68} +45.7213 q^{69} +(55.0975 + 43.1771i) q^{70} -43.1950i q^{71} +(8.64582 - 46.6456i) q^{72} +(-60.2824 - 16.1526i) q^{73} +(-70.5678 - 56.1326i) q^{74} +(9.18500 - 42.8297i) q^{75} +(-48.9739 + 45.6682i) q^{76} +(53.0336 - 51.1571i) q^{77} +(-10.8021 - 4.69695i) q^{78} +(45.3425 - 78.5355i) q^{79} +(43.0462 - 67.4316i) q^{80} +(3.76754 + 6.52557i) q^{81} +(-56.3092 - 76.0982i) q^{82} +(6.44249 + 6.44249i) q^{83} +(46.6502 + 15.1866i) q^{84} +(-70.6124 - 17.0203i) q^{85} +(-9.66004 + 64.6351i) q^{86} +(-56.9017 - 15.2468i) q^{87} +(-64.0351 - 54.6924i) q^{88} +(77.4380 - 134.127i) q^{89} +(8.19945 + 58.7305i) q^{90} +(-12.1298 + 20.1620i) q^{91} +(-104.315 - 3.64357i) q^{92} +(12.6829 - 3.39838i) q^{93} +(-0.527124 - 0.419296i) q^{94} +(40.0066 - 73.5239i) q^{95} +(12.1365 - 54.7392i) q^{96} +(111.262 + 111.262i) q^{97} +(42.2886 - 88.4063i) q^{98} +62.4226 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

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