LMFDB - Embedded newform 45.3.k.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(7,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("45.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	45.7
Dual form			45.3.k.a.13.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.47266 - 0.930497i) q^{2} +(-2.93201 - 0.635068i) q^{3} +(7.72947 - 4.46261i) q^{4} +(-2.41870 + 4.37606i) q^{5} +(-10.7728 + 0.522853i) q^{6} +(-4.78910 + 1.28323i) q^{7} +(12.5207 - 12.5207i) q^{8} +(8.19338 + 3.72405i) q^{9} +(-4.32742 + 17.4472i) q^{10} +(1.37764 - 2.38615i) q^{11} +(-25.4969 + 8.17569i) q^{12} +(-9.15539 - 2.45318i) q^{13} +(-15.4369 + 8.91249i) q^{14} +(9.87075 - 11.2946i) q^{15} +(13.9793 - 24.2129i) q^{16} +(9.17504 + 9.17504i) q^{17} +(31.9181 + 5.30846i) q^{18} -32.1912i q^{19} +(0.833387 + 44.6183i) q^{20} +(14.8566 - 0.721059i) q^{21} +(2.56379 - 9.56819i) q^{22} +(-0.669573 - 0.179412i) q^{23} +(-44.6624 + 28.7594i) q^{24} +(-13.2998 - 21.1687i) q^{25} -34.0763 q^{26} +(-21.6581 - 16.1223i) q^{27} +(-31.2906 + 31.2906i) q^{28} +(30.1349 + 17.3984i) q^{29} +(23.7682 - 48.4071i) q^{30} +(12.8482 + 22.2537i) q^{31} +(7.68384 - 28.6765i) q^{32} +(-5.55463 + 6.12132i) q^{33} +(40.3992 + 23.3245i) q^{34} +(5.96788 - 24.0611i) q^{35} +(79.9494 - 7.77893i) q^{36} +(-13.0331 - 13.0331i) q^{37} +(-29.9538 - 111.789i) q^{38} +(25.2858 + 13.0070i) q^{39} +(24.5076 + 85.0753i) q^{40} +(20.2139 + 35.0116i) q^{41} +(50.9211 - 16.3280i) q^{42} +(-0.987466 - 3.68527i) q^{43} -24.5915i q^{44} +(-36.1140 + 26.8474i) q^{45} -2.49214 q^{46} +(-3.70679 + 0.993231i) q^{47} +(-56.3644 + 62.1147i) q^{48} +(-21.1465 + 12.2089i) q^{49} +(-65.8831 - 61.1365i) q^{50} +(-21.0745 - 32.7281i) q^{51} +(-81.7139 + 21.8952i) q^{52} +(-31.2240 + 31.2240i) q^{53} +(-90.2129 - 35.8346i) q^{54} +(7.10982 + 11.8000i) q^{55} +(-43.8959 + 76.0300i) q^{56} +(-20.4436 + 94.3850i) q^{57} +(120.837 + 32.3783i) q^{58} +(36.8611 - 21.2818i) q^{59} +(25.8921 - 131.351i) q^{60} +(-6.56994 + 11.3795i) q^{61} +(65.3243 + 65.3243i) q^{62} +(-44.0177 - 7.32081i) q^{63} +5.10100i q^{64} +(32.8794 - 34.1310i) q^{65} +(-13.5935 + 26.4259i) q^{66} +(12.0571 - 44.9977i) q^{67} +(111.863 + 29.9735i) q^{68} +(1.84926 + 0.951261i) q^{69} +(-1.66440 - 89.1093i) q^{70} -114.062 q^{71} +(149.215 - 55.9592i) q^{72} +(-18.7982 + 18.7982i) q^{73} +(-57.3867 - 33.1322i) q^{74} +(25.5515 + 70.5133i) q^{75} +(-143.657 - 248.821i) q^{76} +(-3.53568 + 13.1953i) q^{77} +(99.9120 + 21.6407i) q^{78} +(18.3057 + 10.5688i) q^{79} +(72.1453 + 119.738i) q^{80} +(53.2629 + 61.0251i) q^{81} +(102.774 + 102.774i) q^{82} +(3.95730 + 14.7688i) q^{83} +(111.616 - 71.8727i) q^{84} +(-62.3422 + 17.9589i) q^{85} +(-6.85828 - 11.8789i) q^{86} +(-77.3067 - 70.1499i) q^{87} +(-12.6272 - 47.1254i) q^{88} -92.4405i q^{89} +(-100.430 + 126.836i) q^{90} +46.9941 q^{91} +(-5.97609 + 1.60129i) q^{92} +(-23.5384 - 73.4075i) q^{93} +(-11.9482 + 6.89832i) q^{94} +(140.871 + 77.8609i) q^{95} +(-40.7406 + 79.2000i) q^{96} +(151.928 - 40.7091i) q^{97} +(-62.0742 + 62.0742i) q^{98} +(20.1737 - 14.4202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	3.47266	−	0.930497i	1.73633	−	0.465249i	0.754706	−	0.656063i	$-0.227780\pi$
$2$	3.47266	−	0.930497i	1.73633	−	0.465249i	0.981626	+	0.190815i	$0.0611130\pi$
$3$	−2.93201	−	0.635068i	−0.977337	−	0.211689i
$3$	−2.93201	−	0.635068i	−0.977337	−	0.211689i
$4$	7.72947	−	4.46261i	1.93237	−	1.11565i
$5$	−2.41870	+	4.37606i	−0.483740	+	0.875212i
$5$	−2.41870	+	4.37606i	−0.483740	+	0.875212i
$6$	−10.7728	+	0.522853i	−1.79547	+	0.0871422i
$7$	−4.78910	+	1.28323i	−0.684157	+	0.183319i	−0.584123	−	0.811665i	$-0.698562\pi$
$7$	−4.78910	+	1.28323i	−0.684157	+	0.183319i	−0.100033	+	0.994984i	$0.531895\pi$
$8$	12.5207	−	12.5207i	1.56509	−	1.56509i
$9$	8.19338	+	3.72405i	0.910375	+	0.413783i
$10$	−4.32742	+	17.4472i	−0.432742	+	1.74472i
$11$	1.37764	−	2.38615i	0.125240	−	0.216923i	−0.796587	−	0.604525i	$-0.793363\pi$
$11$	1.37764	−	2.38615i	0.125240	−	0.216923i	0.921827	+	0.387602i	$0.126696\pi$
$12$	−25.4969	+	8.17569i	−2.12474	+	0.681307i
$13$	−9.15539	−	2.45318i	−0.704261	−	0.188706i	−0.111123	−	0.993807i	$-0.535445\pi$
$13$	−9.15539	−	2.45318i	−0.704261	−	0.188706i	−0.593138	+	0.805101i	$0.702111\pi$
$14$	−15.4369	+	8.91249i	−1.10263	+	0.636606i
$15$	9.87075	−	11.2946i	0.658050	−	0.752974i
$16$	13.9793	−	24.2129i	0.873708	−	1.51331i
$17$	9.17504	+	9.17504i	0.539708	+	0.539708i	0.923443	−	0.383735i	$-0.125362\pi$
$17$	9.17504	+	9.17504i	0.539708	+	0.539708i	−0.383735	+	0.923443i	$0.625362\pi$
$18$	31.9181	+	5.30846i	1.77323	+	0.294914i
$19$		−	32.1912i		−	1.69427i	−0.531375	−	0.847137i	$-0.678324\pi$
$19$		−	32.1912i		−	1.69427i	0.531375	−	0.847137i	$-0.321676\pi$
$20$	0.833387	+	44.6183i	0.0416693	+	2.23092i
$21$	14.8566	−	0.721059i	0.707459	−	0.0343361i
$22$	2.56379	−	9.56819i	0.116536	−	0.434918i
$23$	−0.669573	−	0.179412i	−0.0291119	−	0.00780050i	0.244234	−	0.969716i	$-0.421464\pi$
$23$	−0.669573	−	0.179412i	−0.0291119	−	0.00780050i	−0.273346	+	0.961916i	$0.588130\pi$
$24$	−44.6624	+	28.7594i	−1.86093	+	1.19831i
$25$	−13.2998	−	21.1687i	−0.531991	−	0.846750i
$26$	−34.0763			−1.31063
$27$	−21.6581	−	16.1223i	−0.802150	−	0.597122i
$28$	−31.2906	+	31.2906i	−1.11752	+	1.11752i
$29$	30.1349	+	17.3984i	1.03913	+	0.599944i	0.919588	−	0.392884i	$-0.128523\pi$
$29$	30.1349	+	17.3984i	1.03913	+	0.599944i	0.119546	+	0.992829i	$0.461856\pi$
$30$	23.7682	−	48.4071i	0.792272	−	1.61357i
$31$	12.8482	+	22.2537i	0.414457	+	0.717860i	0.995371	−	0.0961042i	$-0.0306382\pi$
$31$	12.8482	+	22.2537i	0.414457	+	0.717860i	−0.580914	+	0.813965i	$0.697305\pi$
$32$	7.68384	−	28.6765i	0.240120	−	0.896140i
$33$	−5.55463	+	6.12132i	−0.168322	+	0.185494i
$34$	40.3992	+	23.3245i	1.18821	+	0.686014i
$35$	5.96788	−	24.0611i	0.170511	−	0.687461i
$36$	79.9494	−	7.77893i	2.22082	−	0.216081i
$37$	−13.0331	−	13.0331i	−0.352245	−	0.352245i	0.508699	−	0.860944i	$-0.330127\pi$
$37$	−13.0331	−	13.0331i	−0.352245	−	0.352245i	−0.860944	+	0.508699i	$0.830127\pi$
$38$	−29.9538	−	111.789i	−0.788259	−	2.94182i
$39$	25.2858	+	13.0070i	0.648353	+	0.333514i
$40$	24.5076	+	85.0753i	0.612689	+	2.12688i
$41$	20.2139	+	35.0116i	0.493023	+	0.853941i	0.999968	−	0.00803768i	$-0.00255850\pi$
$41$	20.2139	+	35.0116i	0.493023	+	0.853941i	−0.506945	+	0.861979i	$0.669225\pi$
$42$	50.9211	−	16.3280i	1.21241	−	0.388763i
$43$	−0.987466	−	3.68527i	−0.0229643	−	0.0857040i	0.953493	−	0.301416i	$-0.0974594\pi$
$43$	−0.987466	−	3.68527i	−0.0229643	−	0.0857040i	−0.976457	+	0.215712i	$0.930793\pi$
$44$		−	24.5915i		−	0.558899i
$45$	−36.1140	+	26.8474i	−0.802533	+	0.596608i
$46$	−2.49214			−0.0541770
$47$	−3.70679	+	0.993231i	−0.0788679	+	0.0211326i	−0.298037	−	0.954554i	$-0.596332\pi$
$47$	−3.70679	+	0.993231i	−0.0788679	+	0.0211326i	0.219169	+	0.975687i	$0.429665\pi$
$48$	−56.3644	+	62.1147i	−1.17426	+	1.29406i
$49$	−21.1465	+	12.2089i	−0.431561	+	0.249162i
$50$	−65.8831	−	61.1365i	−1.31766	−	1.22273i
$51$	−21.0745	−	32.7281i	−0.413226	−	0.641727i
$52$	−81.7139	+	21.8952i	−1.57142	+	0.421061i
$53$	−31.2240	+	31.2240i	−0.589132	+	0.589132i	−0.937396	−	0.348265i	$-0.886771\pi$
$53$	−31.2240	+	31.2240i	−0.589132	+	0.589132i	0.348265	+	0.937396i	$0.386771\pi$
$54$	−90.2129	−	35.8346i	−1.67061	−	0.663603i
$55$	7.10982	+	11.8000i	0.129269	+	0.214546i
$56$	−43.8959	+	76.0300i	−0.783856	+	1.35768i
$57$	−20.4436	+	94.3850i	−0.358659	+	1.65588i
$58$	120.837	+	32.3783i	2.08340	+	0.558247i
$59$	36.8611	−	21.2818i	0.624765	−	0.360708i	−0.153957	−	0.988078i	$-0.549202\pi$
$59$	36.8611	−	21.2818i	0.624765	−	0.360708i	0.778722	+	0.627369i	$0.215868\pi$
$60$	25.8921	−	131.351i	0.431536	−	2.18918i
$61$	−6.56994	+	11.3795i	−0.107704	+	0.186549i	−0.914840	−	0.403817i	$-0.867683\pi$
$61$	−6.56994	+	11.3795i	−0.107704	+	0.186549i	0.807136	+	0.590366i	$0.201017\pi$
$62$	65.3243	+	65.3243i	1.05362	+	1.05362i
$63$	−44.0177	−	7.32081i	−0.698694	−	0.116203i
$64$			5.10100i			0.0797032i
$65$	32.8794	−	34.1310i	0.505837	−	0.525093i
$66$	−13.5935	+	26.4259i	−0.205962	+	0.400392i
$67$	12.0571	−	44.9977i	0.179957	−	0.671607i	−0.815697	−	0.578479i	$-0.803647\pi$
$67$	12.0571	−	44.9977i	0.179957	−	0.671607i	0.995654	−	0.0931285i	$-0.0296867\pi$
$68$	111.863	+	29.9735i	1.64504	+	0.440787i
$69$	1.84926	+	0.951261i	0.0268008	+	0.0137864i
$70$	−1.66440	−	89.1093i	−0.0237771	−	1.27299i
$71$	−114.062			−1.60651			−0.803254	−	0.595637i	$-0.796900\pi$
$71$	−114.062			−1.60651			−0.803254	+	0.595637i	$0.796900\pi$
$72$	149.215	−	55.9592i	2.07243	−	0.777212i
$73$	−18.7982	+	18.7982i	−0.257510	+	0.257510i	−0.824041	−	0.566531i	$-0.808285\pi$
$73$	−18.7982	+	18.7982i	−0.257510	+	0.257510i	0.566531	+	0.824041i	$0.308285\pi$
$74$	−57.3867	−	33.1322i	−0.775496	−	0.447733i
$75$	25.5515	+	70.5133i	0.340687	+	0.940177i
$76$	−143.657	−	248.821i	−1.89022	−	3.27396i
$77$	−3.53568	+	13.1953i	−0.0459179	+	0.171368i
$78$	99.9120	+	21.6407i	1.28092	+	0.277445i
$79$	18.3057	+	10.5688i	0.231717	+	0.133782i	0.611364	−	0.791350i	$-0.290621\pi$
$79$	18.3057	+	10.5688i	0.231717	+	0.133782i	−0.379647	+	0.925132i	$0.623954\pi$
$80$	72.1453	+	119.738i	0.901816	+	1.49673i
$81$	53.2629	+	61.0251i	0.657567	+	0.753396i
$82$	102.774	+	102.774i	1.25335	+	1.25335i
$83$	3.95730	+	14.7688i	0.0476783	+	0.177938i	0.985659	−	0.168750i	$-0.0539730\pi$
$83$	3.95730	+	14.7688i	0.0476783	+	0.177938i	−0.937981	+	0.346688i	$0.887306\pi$
$84$	111.616	−	71.8727i	1.32876	−	0.855628i
$85$	−62.3422	+	17.9589i	−0.733437	+	0.211281i
$86$	−6.85828	−	11.8789i	−0.0797474	−	0.138127i
$87$	−77.3067	−	70.1499i	−0.888582	−	0.806321i
$88$	−12.6272	−	47.1254i	−0.143491	−	0.535516i
$89$		−	92.4405i		−	1.03866i	−0.854575	−	0.519329i	$-0.826182\pi$
$89$		−	92.4405i		−	1.03866i	0.854575	−	0.519329i	$-0.173818\pi$
$90$	−100.430	+	126.836i	−1.11589	+	1.40929i
$91$	46.9941			0.516418
$92$	−5.97609	+	1.60129i	−0.0649574	+	0.0174053i
$93$	−23.5384	−	73.4075i	−0.253101	−	0.789328i
$94$	−11.9482	+	6.89832i	−0.127109	+	0.0733864i
$95$	140.871	+	77.8609i	1.48285	+	0.819588i
$96$	−40.7406	+	79.2000i	−0.424382	+	0.825000i
$97$	151.928	−	40.7091i	1.56627	−	0.419681i	0.631629	−	0.775271i	$-0.282387\pi$
$97$	151.928	−	40.7091i	1.56627	−	0.419681i	0.934642	+	0.355590i	$0.115720\pi$
$98$	−62.0742	+	62.0742i	−0.633411	+	0.633411i
$99$	20.1737	−	14.4202i	0.203775	−	0.145659i
$100$	−197.268	−	104.271i	−1.97268	−	1.04271i
$101$	41.2983	−	71.5307i	0.408894	−	0.708225i	−0.585872	−	0.810404i	$-0.699248\pi$
$101$	41.2983	−	71.5307i	0.408894	−	0.708225i	0.994766	+	0.102178i	$0.0325813\pi$
$102$	−103.638	−	94.0438i	−1.01606	−	0.921998i
$103$	48.3706	+	12.9609i	0.469617	+	0.125834i	0.485864	−	0.874034i	$-0.338505\pi$
$103$	48.3706	+	12.9609i	0.469617	+	0.125834i	−0.0162466	+	0.999868i	$0.505172\pi$
$104$	−145.348	+	83.9166i	−1.39757	+	0.806890i
$105$	−32.7783	+	66.7575i	−0.312175	+	0.635786i
$106$	−79.3765	+	137.484i	−0.748835	+	1.29702i
$107$	−57.4669	−	57.4669i	−0.537074	−	0.537074i	0.385595	−	0.922668i	$-0.373996\pi$
$107$	−57.4669	−	57.4669i	−0.537074	−	0.537074i	−0.922668	+	0.385595i	$0.873996\pi$
$108$	−239.353	−	27.9654i	−2.21623	−	0.258939i
$109$		−	145.852i		−	1.33809i	−0.743220	−	0.669047i	$-0.766702\pi$
$109$		−	145.852i		−	1.33809i	0.743220	−	0.669047i	$-0.233298\pi$
$110$	35.6699	+	34.3619i	0.324272	+	0.312380i
$111$	29.9362	+	46.4900i	0.269696	+	0.418829i
$112$	−35.8775	+	133.897i	−0.320335	+	1.19551i
$113$	−52.3679	−	14.0319i	−0.463432	−	0.124176i	0.0195453	−	0.999809i	$-0.493778\pi$
$113$	−52.3679	−	14.0319i	−0.463432	−	0.124176i	−0.482978	+	0.875633i	$0.660445\pi$
$114$	16.8313	+	346.790i	0.147643	+	3.04202i
$115$	2.40461	−	2.49615i	0.0209097	−	0.0217056i
$116$	310.569			2.67732
$117$	−65.8778	−	54.1950i	−0.563058	−	0.463205i
$118$	108.204	−	108.204i	0.916980	−	0.916980i
$119$	−55.7139	−	32.1664i	−0.468184	−	0.270306i
$120$	−17.8279	−	265.006i	−0.148566	−	2.20838i
$121$	56.7042	+	98.2145i	0.468630	+	0.811690i
$122$	−12.2266	+	45.6304i	−0.100218	+	0.374019i
$123$	−37.0328	−	115.492i	−0.301080	−	0.938956i
$124$	198.619	+	114.673i	1.60177	+	0.924780i
$125$	124.804	−	6.99982i	0.998431	−	0.0559986i
$126$	−159.671	+	15.5357i	−1.26723	+	0.123299i
$127$	50.4054	+	50.4054i	0.396893	+	0.396893i	0.877136	−	0.480243i	$-0.159451\pi$
$127$	50.4054	+	50.4054i	0.396893	+	0.396893i	−0.480243	+	0.877136i	$0.659451\pi$
$128$	35.4818	+	132.420i	0.277202	+	1.03453i
$129$	0.554864	+	11.4324i	0.00430127	+	0.0886230i
$130$	82.4203	−	149.120i	0.634002	−	1.14708i
$131$	−89.6936	−	155.354i	−0.684684	−	1.18591i	−0.973536	−	0.228534i	$-0.926607\pi$
$131$	−89.6936	−	155.354i	−0.684684	−	1.18591i	0.288852	−	0.957374i	$-0.406726\pi$
$132$	−15.6173	+	72.1027i	−0.118313	+	0.546232i
$133$	41.3089	+	154.167i	0.310593	+	1.15915i
$134$		−	167.481i		−	1.24986i
$135$	122.936	−	55.7819i	0.910641	−	0.413199i
$136$	229.756			1.68938
$137$	136.277	−	36.5154i	0.994725	−	0.266536i	0.275491	−	0.961304i	$-0.411160\pi$
$137$	136.277	−	36.5154i	0.994725	−	0.266536i	0.719234	+	0.694768i	$0.244493\pi$
$138$	7.30699	+	1.58268i	0.0529492	+	0.0114687i
$139$	−236.063	+	136.291i	−1.69829	+	0.980510i	−0.750912	+	0.660402i	$0.770386\pi$
$139$	−236.063	+	136.291i	−1.69829	+	0.980510i	−0.947381	+	0.320108i	$0.896281\pi$
$140$	−61.2469	−	212.612i	−0.437478	−	1.51866i
$141$	11.4991	−	0.558104i	0.0815540	−	0.00395818i
$142$	−396.099	+	106.134i	−2.78943	+	0.747426i
$143$	−18.4665	+	18.4665i	−0.129137	+	0.129137i
$144$	204.708	−	146.326i	1.42158	−	1.01615i
$145$	−149.024	+	89.7906i	−1.02775	+	0.619245i
$146$	−47.7882	+	82.7716i	−0.327317	+	0.566929i
$147$	69.7552	−	22.3673i	0.474525	−	0.152158i
$148$	−158.900	−	42.5772i	−1.07365	−	0.287684i
$149$	−174.004	+	100.461i	−1.16781	+	0.674235i	−0.953163	−	0.302457i	$-0.902193\pi$
$149$	−174.004	+	100.461i	−1.16781	+	0.674235i	−0.214646	+	0.976692i	$0.568860\pi$
$150$	154.344	+	221.093i	1.02896	+	1.47395i
$151$	58.6560	−	101.595i	0.388450	−	0.672816i	−0.603791	−	0.797143i	$-0.706344\pi$
$151$	58.6560	−	101.595i	0.388450	−	0.672816i	0.992241	+	0.124327i	$0.0396771\pi$
$152$	−403.057	−	403.057i	−2.65169	−	2.65169i
$153$	41.0063	+	109.343i	0.268015	+	0.714659i
$154$			49.1129i			0.318915i
$155$	−128.459	+	2.39938i	−0.828769	+	0.0154799i
$156$	253.491	−	12.3030i	1.62494	−	0.0788657i
$157$	54.9450	−	205.058i	0.349968	−	1.30610i	−0.536731	−	0.843753i	$-0.680341\pi$
$157$	54.9450	−	205.058i	0.349968	−	1.30610i	0.886700	−	0.462346i	$-0.152992\pi$
$158$	73.4036	+	19.6684i	0.464580	+	0.124484i
$159$	111.378	−	71.7197i	0.700493	−	0.451067i
$160$	106.905	+	102.985i	0.668157	+	0.643655i
$161$	3.43688			0.0213471
$162$	241.748	+	162.359i	1.49227	+	1.00221i
$163$	61.1545	−	61.1545i	0.375181	−	0.375181i	−0.494179	−	0.869360i	$-0.664531\pi$
$163$	61.1545	−	61.1545i	0.375181	−	0.375181i	0.869360	+	0.494179i	$0.164531\pi$
$164$	312.486	+	180.414i	1.90540	+	1.10008i
$165$	−13.3523	−	39.1130i	−0.0809228	−	0.237049i
$166$	27.4847	+	47.6049i	0.165571	+	0.286777i
$167$	−62.9533	+	234.945i	−0.376966	+	1.40686i	0.473486	+	0.880802i	$0.342996\pi$
$167$	−62.9533	+	234.945i	−0.376966	+	1.40686i	−0.850451	+	0.526054i	$0.823671\pi$
$168$	176.988	−	195.044i	1.05350	−	1.16098i
$169$	−68.5552	−	39.5803i	−0.405652	−	0.234203i
$170$	−199.783	+	120.374i	−1.17519	+	0.708084i
$171$	119.882	−	263.755i	0.701062	−	1.54243i
$172$	−24.0785	−	24.0785i	−0.139991	−	0.139991i
$173$	4.37517	+	16.3284i	0.0252900	+	0.0943835i	0.977417	−	0.211318i	$-0.0677756\pi$
$173$	4.37517	+	16.3284i	0.0252900	+	0.0943835i	−0.952127	+	0.305702i	$0.901109\pi$
$174$	−333.734	−	171.673i	−1.91801	−	0.986629i
$175$	90.8584	+	84.3124i	0.519191	+	0.481785i
$176$	−38.5171	−	66.7135i	−0.218847	−	0.379054i
$177$	−121.593	+	38.9891i	−0.686964	+	0.220277i
$178$	−86.0157	−	321.015i	−0.483234	−	1.80345i
$179$			274.512i			1.53359i	0.641895	+	0.766793i	$0.278149\pi$
$179$			274.512i			1.53359i	−0.641895	+	0.766793i	$0.721851\pi$
$180$	−159.333	+	368.678i	−0.885181	+	2.04821i
$181$	−261.649			−1.44557			−0.722787	−	0.691070i	$-0.757139\pi$
$181$	−261.649			−1.44557			−0.722787	+	0.691070i	$0.757139\pi$
$182$	163.195	−	43.7279i	0.896674	−	0.240263i
$183$	26.4899	−	29.1924i	0.144753	−	0.159521i
$184$	−10.6299	+	6.13718i	−0.0577712	+	0.0333542i
$185$	88.5565	−	25.5104i	0.478684	−	0.137894i
$186$	−150.046	−	233.017i	−0.806701	−	1.25278i
$187$	34.5329	−	9.25307i	0.184668	−	0.0494817i
$188$	−24.2191	+	24.2191i	−0.128825	+	0.128825i
$189$	124.411	+	49.4189i	0.658261	+	0.261476i
$190$	561.646	+	139.305i	2.95603	+	0.733183i
$191$	−89.7939	+	155.528i	−0.470125	+	0.814280i	−0.999416	−	0.0341597i	$-0.989125\pi$
$191$	−89.7939	+	155.528i	−0.470125	+	0.814280i	0.529291	+	0.848440i	$0.322458\pi$
$192$	3.23948	−	14.9562i	0.0168723	−	0.0778968i
$193$	−25.9600	−	6.95596i	−0.134508	−	0.0360412i	0.190937	−	0.981602i	$-0.438847\pi$
$193$	−25.9600	−	6.95596i	−0.134508	−	0.0360412i	−0.325445	+	0.945561i	$0.605514\pi$
$194$	489.716	−	282.738i	2.52431	−	1.45741i
$195$	−118.078	+	79.1919i	−0.605530	+	0.406113i
$196$	−108.967	+	188.737i	−0.555956	+	0.962944i
$197$	118.588	+	118.588i	0.601967	+	0.601967i	0.940834	−	0.338867i	$-0.110044\pi$
$197$	118.588	+	118.588i	0.601967	+	0.601967i	−0.338867	+	0.940834i	$0.610044\pi$
$198$	56.6385	−	68.8481i	0.286053	−	0.347718i
$199$		−	23.9129i		−	0.120166i	−0.998193	−	0.0600828i	$-0.980864\pi$
$199$		−	23.9129i		−	0.120166i	0.998193	−	0.0600828i	$-0.0191365\pi$
$200$	−431.571	−	98.5251i	−2.15785	−	0.492625i
$201$	−63.9281	+	124.277i	−0.318050	+	0.618292i
$202$	76.8559	−	286.830i	0.380475	−	1.41995i
$203$	−166.645	−	44.6524i	−0.820912	−	0.219963i
$204$	−308.948	−	158.923i	−1.51445	−	0.779035i
$205$	−202.104	+	3.77493i	−0.985874	+	0.0184143i
$206$	180.035			0.873956
$207$	−4.81793	−	3.96351i	−0.0232750	−	0.0191474i
$208$	−187.385	+	187.385i	−0.900889	+	0.900889i
$209$	−76.8130	−	44.3480i	−0.367526	−	0.212191i
$210$	−51.7104	+	262.327i	−0.246240	+	1.24917i
$211$	68.1081	+	117.967i	0.322787	+	0.559084i	0.981062	−	0.193694i	$-0.0620468\pi$
$211$	68.1081	+	117.967i	0.322787	+	0.559084i	−0.658275	+	0.752778i	$0.728713\pi$
$212$	−102.004	+	380.685i	−0.481152	+	1.79568i
$213$	334.431	+	72.4371i	1.57010	+	0.340080i
$214$	−253.036	−	146.090i	−1.18241	−	0.682665i
$215$	18.5154	+	4.59236i	0.0861180	+	0.0213598i
$216$	−473.037	+	69.3116i	−2.18999	+	0.320887i
$217$	−90.0878	−	90.0878i	−0.415151	−	0.415151i
$218$	−135.715	−	506.496i	−0.622547	−	2.32338i
$219$	67.0548	−	43.1785i	0.306186	−	0.197162i
$220$	107.614	+	59.4796i	0.489155	+	0.270362i
$221$	−61.4931	−	106.509i	−0.278249	−	0.481942i
$222$	147.217	+	133.588i	0.663141	+	0.601750i
$223$	103.848	+	387.566i	0.465686	+	1.73796i	0.654606	+	0.755970i	$0.272834\pi$
$223$	103.848	+	387.566i	0.465686	+	1.73796i	−0.188921	+	0.981992i	$0.560499\pi$
$224$			147.195i			0.657119i
$225$	−30.1367	−	222.973i	−0.133941	−	0.990989i
$226$	−194.913			−0.862445
$227$	−182.844	+	48.9929i	−0.805480	+	0.215828i	−0.637988	−	0.770046i	$-0.720233\pi$
$227$	−182.844	+	48.9929i	−0.805480	+	0.215828i	−0.167491	+	0.985874i	$0.553567\pi$
$228$	263.185	+	820.777i	1.15432	+	3.59990i
$229$	128.197	−	74.0143i	0.559810	−	0.323207i	−0.193259	−	0.981148i	$-0.561906\pi$
$229$	128.197	−	74.0143i	0.559810	−	0.323207i	0.753069	+	0.657941i	$0.228572\pi$
$230$	6.02775	−	10.9058i	0.0262076	−	0.0474164i
$231$	18.7466	−	36.4435i	0.0811541	−	0.157764i
$232$	595.151	−	159.470i	2.56531	−	0.687372i
$233$	191.869	−	191.869i	0.823473	−	0.823473i	−0.163131	−	0.986604i	$-0.552159\pi$
$233$	191.869	−	191.869i	0.823473	−	0.823473i	0.986604	+	0.163131i	$0.0521593\pi$
$234$	−279.200	−	126.902i	−1.19316	−	0.542315i
$235$	4.61917	−	18.6235i	0.0196561	−	0.0792488i
$236$	189.945	−	328.994i	0.804850	−	1.39404i
$237$	−46.9605	−	42.6131i	−0.198146	−	0.179802i
$238$	−223.406	−	59.8616i	−0.938682	−	0.251519i
$239$	113.709	−	65.6499i	0.475770	−	0.274686i	−0.242882	−	0.970056i	$-0.578093\pi$
$239$	113.709	−	65.6499i	0.475770	−	0.274686i	0.718652	+	0.695370i	$0.244760\pi$
$240$	−135.489	−	396.891i	−0.564538	−	1.65371i
$241$	106.787	−	184.961i	0.443101	−	0.767473i	−0.554817	−	0.831972i	$-0.687212\pi$
$241$	106.787	−	184.961i	0.443101	−	0.767473i	0.997918	+	0.0644993i	$0.0205450\pi$
$242$	288.303	+	288.303i	1.19133	+	1.19133i
$243$	−117.412	−	212.752i	−0.483178	−	0.875522i
$244$			117.276i			0.480640i
$245$	−2.28000	−	122.068i	−0.00930613	−	0.498237i
$246$	−236.067	−	366.604i	−0.959622	−	1.49026i
$247$	−78.9708	+	294.723i	−0.319720	+	1.19321i
$248$	439.501	+	117.764i	1.77218	+	0.474854i
$249$	−2.22363	−	45.8155i	−0.00893025	−	0.183998i
$250$	426.889	−	140.438i	1.70755	−	0.561751i
$251$	48.4611			0.193072			0.0965360	−	0.995329i	$-0.469224\pi$
$251$	48.4611			0.193072			0.0965360	+	0.995329i	$0.469224\pi$
$252$	−372.903	+	139.848i	−1.47978	+	0.554952i
$253$	−1.35054	+	1.35054i	−0.00533809	+	0.00533809i
$254$	221.943	+	128.139i	0.873792	+	0.504484i
$255$	194.193	−	13.0641i	0.761541	−	0.0512316i
$256$	236.231	+	409.164i	0.922777	+	1.59830i
$257$	120.632	−	450.204i	0.469385	−	1.75177i	−0.172542	−	0.985002i	$-0.555198\pi$
$257$	120.632	−	450.204i	0.469385	−	1.75177i	0.641927	−	0.766766i	$-0.278135\pi$
$258$	12.5646	+	39.1845i	0.0487002	+	0.151878i
$259$	79.1411	+	45.6921i	0.305564	+	0.176418i
$260$	101.827	−	410.543i	0.391641	−	1.57901i
$261$	182.114	+	254.775i	0.697755	+	0.976151i
$262$	−456.032	−	456.032i	−1.74058	−	1.74058i
$263$	28.0536	+	104.698i	0.106668	+	0.398090i	0.998529	−	0.0542194i	$-0.0172671\pi$
$263$	28.0536	+	104.698i	0.106668	+	0.398090i	−0.891861	+	0.452309i	$0.850600\pi$
$264$	7.09532	+	146.191i	0.0268762	+	0.553755i
$265$	−61.1165	−	212.159i	−0.230628	−	0.800601i
$266$	286.904	+	496.932i	1.07859	+	1.86816i
$267$	−58.7060	+	271.037i	−0.219873	+	1.01512i
$268$	−107.612	−	401.614i	−0.401538	−	1.49856i
$269$			271.965i			1.01102i	0.862821	+	0.505510i	$0.168696\pi$
$269$			271.965i			1.01102i	−0.862821	+	0.505510i	$0.831304\pi$
$270$	375.012	−	308.104i	1.38893	−	1.14113i
$271$	283.330			1.04550			0.522749	−	0.852487i	$-0.324907\pi$
$271$	283.330			1.04550			0.522749	+	0.852487i	$0.324907\pi$
$272$	350.415	−	93.8935i	1.28829	−	0.345197i
$273$	−137.787	−	29.8444i	−0.504715	−	0.109320i
$274$	439.268	−	253.611i	1.60317	−	0.925589i
$275$	−68.8341	+	2.57228i	−0.250306	+	0.00935376i
$276$	18.5389	−	0.899774i	0.0671698	−	0.00326005i
$277$	143.741	−	38.5154i	0.518922	−	0.139045i	0.0101539	−	0.999948i	$-0.496768\pi$
$277$	143.741	−	38.5154i	0.518922	−	0.139045i	0.508768	+	0.860904i	$0.330101\pi$
$278$	−692.948	+	692.948i	−2.49262	+	2.49262i
$279$	22.3961	+	230.180i	0.0802727	+	0.825018i
$280$	−226.541	−	375.985i	−0.809074	−	1.34280i
$281$	−126.241	+	218.657i	−0.449258	+	0.778137i	−0.998338	−	0.0576326i	$-0.981645\pi$
$281$	−126.241	+	218.657i	−0.449258	+	0.778137i	0.549080	+	0.835770i	$0.314978\pi$
$282$	39.4133	−	12.6380i	0.139763	−	0.0448156i
$283$	−463.286	−	124.137i	−1.63705	−	0.438647i	−0.681107	−	0.732184i	$-0.738501\pi$
$283$	−463.286	−	124.137i	−1.63705	−	0.438647i	−0.955948	+	0.293537i	$0.905168\pi$
$284$	−881.639	+	509.015i	−3.10436	+	1.79230i
$285$	−363.587	−	317.751i	−1.27574	−	1.11492i
$286$	−46.9450	+	81.3111i	−0.164143	+	0.284304i
$287$	−141.735	−	141.735i	−0.493849	−	0.493849i
$288$	169.749	−	206.342i	0.589407	−	0.716467i
$289$		−	120.637i		−	0.417430i
$290$	−433.959	+	450.478i	−1.49641	+	1.55337i
$291$	−471.308	+	22.8747i	−1.61962	+	0.0786072i
$292$	−61.4111	+	229.189i	−0.210312	+	0.784895i
$293$	196.044	+	52.5299i	0.669093	+	0.179283i	0.577346	−	0.816499i	$-0.304088\pi$
$293$	196.044	+	52.5299i	0.669093	+	0.179283i	0.0917468	+	0.995782i	$0.470755\pi$
$294$	221.424	−	142.581i	0.753142	−	0.484969i
$295$	3.97435	+	212.781i	0.0134724	+	0.721290i
$296$	−326.367			−1.10259
$297$	−68.3073	+	29.4685i	−0.229991	+	0.0992207i
$298$	−510.777	+	510.777i	−1.71402	+	1.71402i
$299$	5.69008	+	3.28517i	0.0190304	+	0.0109872i
$300$	512.173	+	431.003i	1.70724	+	1.43668i
$301$	9.45814	+	16.3820i	0.0314224	+	0.0544252i
$302$	109.159	−	407.385i	0.361452	−	1.34896i
$303$	−166.514	+	183.502i	−0.549551	+	0.605616i
$304$	−779.443	−	450.011i	−2.56396	−	1.48030i
$305$	−33.9065	−	56.2739i	−0.111169	−	0.184505i
$306$	244.144	+	341.555i	0.797857	+	1.11619i
$307$	364.680	+	364.680i	1.18788	+	1.18788i	0.977652	+	0.210232i	$0.0674220\pi$
$307$	364.680	+	364.680i	1.18788	+	1.18788i	0.210232	+	0.977652i	$0.432578\pi$
$308$	31.5567	+	117.771i	0.102457	+	0.382374i
$309$	−133.592	−	68.7200i	−0.432337	−	0.222395i
$310$	−443.863	+	127.863i	−1.43182	+	0.412462i
$311$	−102.480	−	177.501i	−0.329518	−	0.570743i	0.652898	−	0.757446i	$-0.273553\pi$
$311$	−102.480	−	177.501i	−0.329518	−	0.570743i	−0.982416	+	0.186703i	$0.940220\pi$
$312$	479.454	−	153.739i	1.53671	−	0.492752i
$313$	−92.0214	−	343.429i	−0.293998	−	1.09722i	−0.942010	−	0.335586i	$-0.891066\pi$
$313$	−92.0214	−	343.429i	−0.293998	−	1.09722i	0.648011	−	0.761631i	$-0.275601\pi$
$314$		−	763.222i		−	2.43064i
$315$	138.502	−	174.917i	0.439689	−	0.555293i
$316$	188.657			0.597017
$317$	24.9588	−	6.68768i	0.0787343	−	0.0210968i	−0.219237	−	0.975672i	$-0.570357\pi$
$317$	24.9588	−	6.68768i	0.0787343	−	0.0210968i	0.297971	+	0.954575i	$0.403690\pi$
$318$	320.045	−	352.696i	1.00643	−	1.10911i
$319$	83.0303	−	47.9375i	0.260283	−	0.150274i
$320$	−22.3223	−	12.3378i	−0.0697571	−	0.0385556i
$321$	131.998	+	204.989i	0.411209	+	0.638595i
$322$	11.9351	−	3.19801i	0.0370656	−	0.00993169i
$323$	295.356	−	295.356i	0.914414	−	0.914414i
$324$	684.025	+	234.000i	2.11119	+	0.722222i
$325$	69.8340	+	226.435i	0.214874	+	0.696723i
$326$	155.465	−	269.273i	0.476886	−	0.825992i
$327$	−92.6260	+	427.640i	−0.283260	+	1.30777i
$328$	691.464	+	185.277i	2.10812	+	0.564869i
$329$	16.4776	−	9.51337i	0.0500840	−	0.0289160i
$330$	−82.7625	−	123.402i	−0.250795	−	0.373946i
$331$	96.8582	−	167.763i	0.292623	−	0.506838i	−0.681806	−	0.731533i	$-0.738805\pi$
$331$	96.8582	−	167.763i	0.292623	−	0.506838i	0.974429	+	0.224695i	$0.0721386\pi$
$332$	96.4953	+	96.4953i	0.290649	+	0.290649i
$333$	−58.2491	−	155.321i	−0.174922	−	0.466428i
$334$			874.462i			2.61815i
$335$	167.750	+	161.598i	0.500746	+	0.482383i
$336$	190.227	−	369.802i	0.566151	−	1.10060i
$337$	−23.7598	+	88.6729i	−0.0705039	+	0.263124i	−0.992176	−	0.124845i	$-0.960157\pi$
$337$	−23.7598	+	88.6729i	−0.0705039	+	0.263124i	0.921672	+	0.387969i	$0.126823\pi$
$338$	−274.898	−	73.6588i	−0.813309	−	0.217925i
$339$	144.632	+	74.3989i	0.426643	+	0.219466i
$340$	−401.728	+	417.021i	−1.18155	+	1.22653i
$341$	70.8008			0.207627
$342$	170.886	−	1027.48i	0.499665	−	3.00433i
$343$	257.393	−	257.393i	0.750417	−	0.750417i
$344$	−58.5061	−	33.7785i	−0.170076	−	0.0981933i
$345$	−8.63557	+	5.79164i	−0.0250306	+	0.0167874i
$346$	30.3870	+	52.6318i	0.0878236	+	0.152115i
$347$	−1.56550	+	5.84253i	−0.00451153	+	0.0168372i	−0.968145	−	0.250391i	$-0.919441\pi$
$347$	−1.56550	+	5.84253i	−0.00451153	+	0.0168372i	0.963633	+	0.267228i	$0.0861076\pi$
$348$	−910.591	−	197.232i	−2.61664	−	0.566759i
$349$	−67.8704	−	39.1850i	−0.194471	−	0.112278i	0.399603	−	0.916688i	$-0.369148\pi$
$349$	−67.8704	−	39.1850i	−0.194471	−	0.112278i	−0.594074	+	0.804410i	$0.702481\pi$
$350$	393.973	+	208.245i	1.12564	+	0.594986i
$351$	158.737	+	200.737i	0.452242	+	0.571901i
$352$	−57.8408	−	57.8408i	−0.164320	−	0.164320i
$353$	−10.2443	−	38.2322i	−0.0290207	−	0.108307i	0.949896	−	0.312565i	$-0.101188\pi$
$353$	−10.2443	−	38.2322i	−0.0290207	−	0.108307i	−0.978917	+	0.204259i	$0.934522\pi$
$354$	−385.971	+	248.538i	−1.09031	+	0.702084i
$355$	275.882	−	499.142i	0.777132	−	1.40603i
$356$	−412.526	−	714.516i	−1.15878	−	2.00707i
$357$	142.926	+	129.694i	0.400353	+	0.363290i
$358$	255.433	+	953.287i	0.713499	+	2.66281i
$359$		−	116.601i		−	0.324795i	−0.986725	−	0.162398i	$-0.948077\pi$
$359$		−	116.601i		−	0.324795i	0.986725	−	0.162398i	$-0.0519227\pi$
$360$	−116.025	+	788.322i	−0.322292	+	2.18978i
$361$	−675.274			−1.87056
$362$	−908.619	+	243.464i	−2.51000	+	0.672552i
$363$	−103.884	−	323.977i	−0.286183	−	0.892499i
$364$	363.239	−	209.716i	0.997910	−	0.576144i
$365$	−36.7949	−	127.729i	−0.100808	−	0.349944i
$366$	64.8269	−	126.024i	0.177123	−	0.344328i
$367$	−419.779	+	112.479i	−1.14381	+	0.306483i	−0.780483	−	0.625177i	$-0.785027\pi$
$367$	−419.779	+	112.479i	−1.14381	+	0.306483i	−0.363329	+	0.931661i	$0.618360\pi$
$368$	−13.7043	+	13.7043i	−0.0372398	+	0.0372398i
$369$	35.2356	+	362.141i	0.0954895	+	0.981411i
$370$	283.790	−	170.991i	0.766999	−	0.462137i
$371$	109.467	−	189.602i	0.295059	−	0.511058i
$372$	−509.528	−	462.358i	−1.36970	−	1.24290i
$373$	624.849	+	167.428i	1.67520	+	0.448868i	0.966505	−	0.256647i	$-0.0826179\pi$
$373$	624.849	+	167.428i	1.67520	+	0.448868i	0.708694	+	0.705516i	$0.249285\pi$
$374$	111.311	−	64.2656i	0.297624	−	0.171833i
$375$	−370.372	−	58.7353i	−0.987658	−	0.156628i
$376$	−33.9757	+	58.8477i	−0.0903610	+	0.156510i
$377$	−233.215	−	233.215i	−0.618608	−	0.618608i
$378$	478.023	+	55.8510i	1.26461	+	0.147754i
$379$		−	297.836i		−	0.785846i	−0.919571	−	0.392923i	$-0.871464\pi$
$379$		−	297.836i		−	0.785846i	0.919571	−	0.392923i	$-0.128536\pi$
$380$	1436.32	−	26.8277i	3.77978	−	0.0705993i
$381$	−115.778	−	179.800i	−0.303880	−	0.471916i
$382$	−167.106	+	623.648i	−0.437450	+	1.63259i
$383$	414.434	+	111.047i	1.08207	+	0.289941i	0.755445	−	0.655212i	$-0.227421\pi$
$383$	414.434	+	111.047i	1.08207	+	0.289941i	0.326629	+	0.945153i	$0.394087\pi$
$384$	−19.9375	−	410.790i	−0.0519206	−	1.06977i
$385$	−49.1918	−	47.3879i	−0.127771	−	0.123085i
$386$	−96.6228			−0.250318
$387$	5.63346	−	33.8722i	0.0145567	−	0.0875251i
$388$	992.656	−	992.656i	2.55839	−	2.55839i
$389$	197.682	+	114.132i	0.508181	+	0.293398i	0.732086	−	0.681213i	$-0.238547\pi$
$389$	197.682	+	114.132i	0.508181	+	0.293398i	−0.223905	+	0.974611i	$0.571880\pi$
$390$	−336.358	+	384.879i	−0.862457	+	0.986868i
$391$	−4.49725	−	7.78947i	−0.0115019	−	0.0199219i
$392$	−111.905	+	417.634i	−0.285471	+	1.06539i
$393$	164.322	+	512.461i	0.418123	+	1.30397i
$394$	522.160	+	301.469i	1.32528	+	0.765151i
$395$	−90.5255	+	54.5440i	−0.229178	+	0.138086i
$396$	91.5801	−	201.488i	0.231263	−	0.508808i
$397$	120.533	+	120.533i	0.303609	+	0.303609i	0.842424	−	0.538815i	$-0.181128\pi$
$397$	120.533	+	120.533i	0.303609	+	0.303609i	−0.538815	+	0.842424i	$0.681128\pi$
$398$	−22.2509	−	83.0416i	−0.0559069	−	0.208647i
$399$	−23.2117	−	478.253i	−0.0581748	−	1.19863i
$400$	−698.479	+	26.1017i	−1.74620	+	0.0652542i
$401$	226.669	+	392.602i	0.565259	+	0.979057i	0.997026	+	0.0770720i	$0.0245571\pi$
$401$	226.669	+	392.602i	0.565259	+	0.979057i	−0.431766	+	0.901985i	$0.642110\pi$
$402$	−106.362	+	491.056i	−0.264581	+	1.22153i
$403$	−63.0377	−	235.260i	−0.156421	−	0.583772i
$404$		−	737.193i		−	1.82473i
$405$	−395.876	+	85.4802i	−0.977473	+	0.211062i
$406$	−620.251			−1.52771
$407$	−49.0538	+	13.1439i	−0.120525	+	0.0322946i
$408$	−673.648	−	145.911i	−1.65110	−	0.357624i
$409$	−427.158	+	246.620i	−1.04440	+	0.602982i	−0.921075	−	0.389385i	$-0.872688\pi$
$409$	−427.158	+	246.620i	−1.04440	+	0.602982i	−0.123320	+	0.992367i	$0.539354\pi$
$410$	−698.327	+	201.166i	−1.70324	+	0.490650i
$411$	−422.756	+	20.5183i	−1.02860	+	0.0499228i
$412$	431.718	−	115.679i	1.04786	−	0.280773i
$413$	−149.222	+	149.222i	−0.361312	+	0.361312i
$414$	−20.4191	−	9.28087i	−0.0493214	−	0.0224176i
$415$	−74.2008	−	18.4040i	−0.178797	−	0.0443470i
$416$	−140.697	+	243.695i	−0.338214	+	0.585805i
$417$	778.693	−	249.691i	1.86737	−	0.598778i
$418$	−308.011	−	82.5314i	−0.736870	−	0.197444i
$419$	22.7963	−	13.1615i	0.0544066	−	0.0314116i	−0.472550	−	0.881304i	$-0.656666\pi$
$419$	22.7963	−	13.1615i	0.0544066	−	0.0314116i	0.526957	+	0.849892i	$0.323333\pi$
$420$	44.5537	+	662.277i	0.106080	+	1.57685i
$421$	243.419	−	421.613i	0.578192	−	1.00146i	−0.417495	−	0.908679i	$-0.637092\pi$
$421$	243.419	−	421.613i	0.578192	−	1.00146i	0.995687	−	0.0927780i	$-0.0295747\pi$
$422$	346.284	+	346.284i	0.820579	+	0.820579i
$423$	−34.0700	−	5.66635i	−0.0805437	−	0.0133956i
$424$			781.894i			1.84409i
$425$	72.1980	−	316.250i	0.169878	−	0.744118i
$426$	1228.77	−	59.6377i	2.88444	−	0.139995i
$427$	16.8615	−	62.9281i	0.0394884	−	0.147373i
$428$	−700.641	−	187.736i	−1.63701	−	0.438636i
$429$	65.8715	−	42.4166i	0.153547	−	0.0988731i
$430$	68.5708	−	1.28077i	0.159467	−	0.00297855i
$431$	73.2818			0.170027			0.0850137	−	0.996380i	$-0.472907\pi$
$431$	73.2818			0.170027			0.0850137	+	0.996380i	$0.472907\pi$
$432$	−693.133	+	299.025i	−1.60447	+	0.692189i
$433$	79.7731	−	79.7731i	0.184234	−	0.184234i	−0.608964	−	0.793198i	$-0.708415\pi$
$433$	79.7731	−	79.7731i	0.184234	−	0.184234i	0.793198	+	0.608964i	$0.208415\pi$
$434$	−396.671	−	229.018i	−0.913989	−	0.527692i
$435$	493.962	−	168.627i	1.13554	−	0.387648i
$436$	−650.882	−	1127.36i	−1.49285	−	2.58569i
$437$	−5.77547	+	21.5544i	−0.0132162	+	0.0493235i
$438$	192.681	−	212.339i	0.439911	−	0.484791i
$439$	97.4363	+	56.2549i	0.221951	+	0.128143i	0.606853	−	0.794814i	$-0.292432\pi$
$439$	97.4363	+	56.2549i	0.221951	+	0.128143i	−0.384903	+	0.922957i	$0.625765\pi$
$440$	236.765	+	58.7248i	0.538102	+	0.133465i
$441$	−218.728	+	21.2818i	−0.495981	+	0.0482581i
$442$	−312.651	−	312.651i	−0.707356	−	0.707356i
$443$	41.2762	+	154.045i	0.0931742	+	0.347731i	0.996736	−	0.0807263i	$-0.0257240\pi$
$443$	41.2762	+	154.045i	0.0931742	+	0.347731i	−0.903562	+	0.428457i	$0.859057\pi$
$444$	438.858	+	225.749i	0.988418	+	0.508444i
$445$	404.525	+	223.586i	0.909045	+	0.502440i
$446$	721.258	+	1249.25i	1.61717	+	2.80102i
$447$	573.980	−	184.049i	1.28407	−	0.411742i
$448$	−6.54578	−	24.4292i	−0.0146111	−	0.0545295i
$449$			291.806i			0.649901i	0.945731	+	0.324951i	$0.105348\pi$
$449$			291.806i			0.649901i	−0.945731	+	0.324951i	$0.894652\pi$
$450$	−312.130	−	746.267i	−0.693623	−	1.65837i
$451$	111.390			0.246985
$452$	−467.395	+	125.238i	−1.03406	+	0.277075i
$453$	−236.500	+	260.628i	−0.522075	+	0.575337i
$454$	−589.367	+	340.271i	−1.29817	+	0.749497i
$455$	−113.665	+	205.649i	−0.249812	+	0.451976i
$456$	925.800	+	1437.74i	2.03026	+	3.15293i
$457$	−452.757	+	121.316i	−0.990716	+	0.265462i	−0.717551	−	0.696506i	$-0.754737\pi$
$457$	−452.757	+	121.316i	−0.990716	+	0.265462i	−0.273165	+	0.961967i	$0.588070\pi$
$458$	376.313	−	376.313i	0.821645	−	0.821645i
$459$	−50.7907	−	346.636i	−0.110655	−	0.755199i
$460$	7.44703	−	30.0247i	0.0161892	−	0.0652712i
$461$	−248.770	+	430.882i	−0.539631	+	0.934668i	0.459293	+	0.888285i	$0.348103\pi$
$461$	−248.770	+	430.882i	−0.539631	+	0.934668i	−0.998924	+	0.0463832i	$0.985230\pi$
$462$	31.1900	−	144.000i	0.0675109	−	0.311688i
$463$	−880.204	−	235.850i	−1.90109	−	0.509395i	−0.996549	−	0.0830044i	$-0.973548\pi$
$463$	−880.204	−	235.850i	−1.90109	−	0.509395i	−0.904539	−	0.426391i	$-0.859785\pi$
$464$	842.531	−	486.435i	1.81580	−	1.04835i
$465$	378.168	+	74.5453i	0.813264	+	0.160312i
$466$	487.764	−	844.831i	1.04670	−	1.81294i
$467$	−204.884	−	204.884i	−0.438724	−	0.438724i	0.452859	−	0.891582i	$-0.350404\pi$
$467$	−204.884	−	204.884i	−0.438724	−	0.438724i	−0.891582	+	0.452859i	$0.850404\pi$
$468$	−751.052	−	124.911i	−1.60481	−	0.266904i
$469$			230.970i			0.492474i
$470$	−1.28825	−	68.9711i	−0.00274096	−	0.146747i
$471$	−291.325	+	566.337i	−0.618524	+	1.20241i
$472$	195.065	−	727.991i	0.413273	−	1.54235i
$473$	−10.1540	−	2.72075i	−0.0214672	−	0.00575212i
$474$	−202.729	−	104.284i	−0.427699	−	0.220009i
$475$	−681.447	+	428.136i	−1.43463	+	0.901339i
$476$	−574.185			−1.20627
$477$	−372.109	+	139.550i	−0.780104	+	0.292558i
$478$	333.786	−	333.786i	0.698297	−	0.698297i
$479$	177.082	+	102.238i	0.369691	+	0.213441i	0.673324	−	0.739348i	$-0.264866\pi$
$479$	177.082	+	102.238i	0.369691	+	0.213441i	−0.303632	+	0.952789i	$0.598199\pi$
$480$	−248.045	−	369.844i	−0.516760	−	0.770509i
$481$	87.3504	+	151.295i	0.181602	+	0.314543i
$482$	198.731	−	741.673i	0.412304	−	1.53874i
$483$	−10.0770	−	2.18265i	−0.0208633	−	0.00451894i
$484$	876.586	+	506.097i	1.81113	+	1.04566i
$485$	−189.324	+	763.310i	−0.390358	+	1.57384i
$486$	−605.699	−	629.564i	−1.24629	−	1.29540i
$487$	−506.650	−	506.650i	−1.04035	−	1.04035i	−0.999151	−	0.0411985i	$-0.986882\pi$
$487$	−506.650	−	506.650i	−1.04035	−	1.04035i	−0.0411985	−	0.999151i	$-0.513118\pi$
$488$	60.2188	+	224.740i	0.123399	+	0.460532i
$489$	−218.143	+	140.469i	−0.446100	+	0.287257i
$490$	−121.502	−	421.779i	−0.247962	−	0.860774i
$491$	−104.633	−	181.229i	−0.213101	−	0.369102i	0.739582	−	0.673066i	$-0.235023\pi$
$491$	−104.633	−	181.229i	−0.213101	−	0.369102i	−0.952684	+	0.303964i	$0.901690\pi$
$492$	−801.637	−	727.425i	−1.62934	−	1.47851i
$493$	116.858	+	436.120i	0.237034	+	0.884624i
$494$			1096.96i			2.22056i
$495$	14.3096	+	123.159i	0.0289082	+	0.248807i
$496$	718.435			1.44846
$497$	546.254	−	146.368i	1.09910	−	0.294504i
$498$	−50.3532	−	157.033i	−0.101111	−	0.315327i
$499$	287.007	−	165.704i	0.575165	−	0.332072i	−0.184044	−	0.982918i	$-0.558919\pi$
$499$	287.007	−	165.704i	0.575165	−	0.332072i	0.759210	+	0.650846i	$0.225586\pi$
$500$	933.430	−	611.056i	1.86686	−	1.22211i
$501$	333.786	−	648.881i	0.666239	−	1.29517i
$502$	168.289	−	45.0929i	0.335237	−	0.0898265i
$503$	−278.209	+	278.209i	−0.553100	+	0.553100i	−0.927334	−	0.374234i	$-0.877906\pi$
$503$	−278.209	+	278.209i	−0.553100	+	0.553100i	0.374234	+	0.927334i	$0.377906\pi$
$504$	−642.796	+	459.472i	−1.27539	+	0.911651i
$505$	213.135	+	353.735i	0.422049	+	0.700466i
$506$	−3.43329	+	5.94663i	−0.00678515	+	0.0117522i
$507$	175.868	+	159.587i	0.346880	+	0.314768i
$508$	614.546	+	164.667i	1.20974	+	0.324148i
$509$	−679.279	+	392.182i	−1.33454	+	0.770495i	−0.985991	−	0.166797i	$-0.946658\pi$
$509$	−679.279	+	392.182i	−1.33454	+	0.770495i	−0.348546	+	0.937292i	$0.613324\pi$
$510$	662.211	−	226.063i	1.29845	−	0.443261i
$511$	65.9040	−	114.149i	0.128971	−	0.223384i
$512$	813.324	+	813.324i	1.58852	+	1.58852i
$513$	−518.996	+	697.199i	−1.01169	+	1.35906i
$514$		−	1675.66i		−	3.26003i
$515$	−173.711	+	180.324i	−0.337304	+	0.350144i
$516$	55.3070	+	85.8900i	0.107184	+	0.166453i
$517$	−2.73664	+	10.2133i	−0.00529330	+	0.0197549i
$518$	317.347	+	85.0329i	0.612639	+	0.164156i
$519$	−2.45844	−	50.6534i	−0.00473687	−	0.0975981i
$520$	−15.6713	−	839.019i	−0.0301371	−	1.61350i
$521$	763.749			1.46593			0.732964	−	0.680267i	$-0.238136\pi$
$521$	763.749			1.46593			0.732964	+	0.680267i	$0.238136\pi$
$522$	869.489	+	715.292i	1.66569	+	1.37029i
$523$	−284.699	+	284.699i	−0.544358	+	0.544358i	−0.924803	−	0.380445i	$-0.875771\pi$
$523$	−284.699	+	284.699i	−0.544358	+	0.544358i	0.380445	+	0.924803i	$0.375771\pi$
$524$	−1386.57	−	800.535i	−2.64612	−	1.52774i
$525$	−212.854	−	304.906i	−0.405436	−	0.580774i
$526$	194.842	+	337.476i	0.370421	+	0.641589i
$527$	−86.2959	+	322.061i	−0.163749	+	0.611121i
$528$	70.5649	+	220.066i	0.133646	+	0.416791i
$529$	−457.711	−	264.260i	−0.865239	−	0.499546i
$530$	−409.651	−	679.889i	−0.772926	−	1.28281i
$531$	381.272	−	37.0970i	0.718026	−	0.0698625i
$532$	1007.28	+	1007.28i	1.89339	+	1.89339i
$533$	−99.1769	−	370.133i	−0.186073	−	0.694434i
$534$	48.3328	+	995.845i	0.0905109	+	1.86488i
$535$	390.474	−	112.483i	0.729857	−	0.210249i
$536$	−412.440	−	714.367i	−0.769478	−	1.33277i
$537$	174.334	−	804.872i	0.324643	−	1.49883i
$538$	253.062	+	944.442i	0.470376	+	1.75547i
$539$			67.2782i			0.124820i
$540$	701.300	−	979.782i	1.29870	−	1.81441i
$541$	120.576			0.222876			0.111438	−	0.993771i	$-0.464454\pi$
$541$	120.576			0.222876			0.111438	+	0.993771i	$0.464454\pi$
$542$	983.909	−	263.638i	1.81533	−	0.486416i
$543$	767.158	+	166.165i	1.41281	+	0.306013i
$544$	333.608	−	192.608i	0.613249	−	0.354060i
$545$	638.258	+	352.773i	1.17112	+	0.647289i
$546$	−506.259	+	24.5710i	−0.927214	+	0.0450018i
$547$	−222.510	+	59.6213i	−0.406782	+	0.108997i	−0.456407	−	0.889771i	$-0.650864\pi$
$547$	−222.510	+	59.6213i	−0.406782	+	0.108997i	0.0496252	+	0.998768i	$0.484197\pi$
$548$	890.397	−	890.397i	1.62481	−	1.62481i
$549$	−96.2077	+	68.7695i	−0.175242	+	0.125263i
$550$	−236.644	+	72.9827i	−0.430262	+	0.132696i
$551$	560.075	−	970.078i	1.01647	−	1.76058i
$552$	35.0645	−	11.2436i	0.0635227	−	0.0203688i
$553$	−101.230	−	27.1244i	−0.183056	−	0.0490496i
$554$	463.327	−	267.502i	0.836330	−	0.482855i
$555$	−275.850	+	18.5574i	−0.497026	+	0.0334367i
$556$	−1216.43	+	2106.91i	−2.18782	+	3.78941i
$557$	−664.417	−	664.417i	−1.19285	−	1.19285i	−0.976264	−	0.216586i	$-0.930508\pi$
$557$	−664.417	−	664.417i	−1.19285	−	1.19285i	−0.216586	−	0.976264i	$-0.569492\pi$
$558$	291.956	+	778.498i	0.523219	+	1.39516i
$559$			36.1626i			0.0646915i
$560$	−499.163	−	480.858i	−0.891363	−	0.858675i
$561$	−107.127	+	5.19937i	−0.190958	+	0.00926803i
$562$	−234.935	+	876.788i	−0.418033	+	1.56012i
$563$	−267.496	−	71.6752i	−0.475125	−	0.127309i	0.0133066	−	0.999911i	$-0.495764\pi$
$563$	−267.496	−	71.6752i	−0.475125	−	0.127309i	−0.488432	+	0.872602i	$0.662431\pi$
$564$	86.3915	−	55.6299i	0.153176	−	0.0986346i
$565$	188.067	−	195.226i	0.332861	−	0.345533i
$566$	−1724.35			−3.04655
$567$	−333.391	−	223.906i	−0.587991	−	0.394897i
$568$	−1428.14	+	1428.14i	−2.51433	+	2.51433i
$569$	−830.591	−	479.542i	−1.45974	−	0.842780i	−0.460740	−	0.887535i	$-0.652416\pi$
$569$	−830.591	−	479.542i	−1.45974	−	0.842780i	−0.998998	+	0.0447548i	$0.985749\pi$
$570$	−1558.28	−	765.126i	−2.73383	−	1.34233i
$571$	−222.371	−	385.158i	−0.389442	−	0.674533i	0.602933	−	0.797792i	$-0.293999\pi$
$571$	−222.371	−	385.158i	−0.389442	−	0.674533i	−0.992375	+	0.123259i	$0.960665\pi$
$572$	−60.3275	+	225.145i	−0.105468	+	0.393611i
$573$	362.047	−	398.983i	0.631845	−	0.696306i
$574$	−624.080	−	360.313i	−1.08725	−	0.627723i
$575$	5.10726	+	16.5602i	0.00888219	+	0.0288003i
$576$	−18.9964	+	41.7944i	−0.0329798	+	0.0725598i
$577$	670.378	+	670.378i	1.16183	+	1.16183i	0.984074	+	0.177761i	$0.0568852\pi$
$577$	670.378	+	670.378i	1.16183	+	1.16183i	0.177761	+	0.984074i	$0.443115\pi$
$578$	−112.253	−	418.933i	−0.194209	−	0.724797i
$579$	71.6975	+	36.8813i	0.123830	+	0.0636983i
$580$	−751.172	+	1359.07i	−1.29512	+	2.34322i
$581$	−37.9038	−	65.6513i	−0.0652388	−	0.112997i
$582$	−1615.41	+	517.987i	−2.77562	+	0.890013i
$583$	31.4895	+	117.521i	0.0540129	+	0.201579i
$584$			470.735i			0.806053i
$585$	396.499	−	157.204i	0.677776	−	0.268725i
$586$	729.675			1.24518
$587$	435.207	−	116.613i	0.741410	−	0.198660i	0.131705	−	0.991289i	$-0.457955\pi$
$587$	435.207	−	116.613i	0.741410	−	0.198660i	0.609704	+	0.792629i	$0.291288\pi$
$588$	439.354	−	484.177i	0.747201	−	0.823431i
$589$	716.373	−	413.598i	1.21625	−	0.702204i
$590$	211.793	+	735.218i	0.358972	+	1.24613i
$591$	−272.389	−	423.011i	−0.460895	−	0.715755i
$592$	−497.762	+	133.375i	−0.840814	+	0.225295i
$593$	292.884	−	292.884i	0.493902	−	0.493902i	−0.415631	−	0.909533i	$-0.636439\pi$
$593$	292.884	−	292.884i	0.493902	−	0.493902i	0.909533	+	0.415631i	$0.136439\pi$
$594$	−209.788	+	165.894i	−0.353178	+	0.279283i
$595$	275.517	−	166.006i	0.463054	−	0.279002i
$596$	−896.636	+	1553.02i	−1.50442	+	2.60574i
$597$	−15.1863	+	70.1130i	−0.0254377	+	0.117442i
$598$	22.8166	+	6.11368i	0.0381548	+	0.0102235i
$599$	434.899	−	251.089i	0.726042	−	0.419180i	−0.0909308	−	0.995857i	$-0.528984\pi$
$599$	434.899	−	251.089i	0.726042	−	0.419180i	0.816972	+	0.576677i	$0.195651\pi$
$600$	1202.80	+	562.953i	2.00467	+	0.938255i
$601$	−99.8075	+	172.872i	−0.166069	+	0.287640i	−0.937034	−	0.349237i	$-0.886441\pi$
$601$	−99.8075	+	172.872i	−0.166069	+	0.287640i	0.770965	+	0.636877i	$0.219774\pi$
$602$	48.0883	+	48.0883i	0.0798810	+	0.0798810i
$603$	266.362	−	323.782i	0.441728	−	0.536952i
$604$		−	1047.04i		−	1.73350i
$605$	−566.943	+	10.5894i	−0.937096	+	0.0175032i
$606$	−407.499	+	792.180i	−0.672440	+	1.30723i
$607$	224.522	−	837.927i	0.369888	−	1.38044i	−0.490785	−	0.871281i	$-0.663290\pi$
$607$	224.522	−	837.927i	0.369888	−	1.38044i	0.860672	−	0.509159i	$-0.170043\pi$
$608$	−923.131	−	247.352i	−1.51831	−	0.406829i
$609$	460.248	+	236.752i	0.755744	+	0.388756i
$610$	−170.109	−	163.871i	−0.278867	−	0.268640i
$611$	36.3737			0.0595314
$612$	804.911	+	662.167i	1.31521	+	1.08197i
$613$	−31.6781	+	31.6781i	−0.0516771	+	0.0516771i	−0.732473	−	0.680796i	$-0.761634\pi$
$613$	−31.6781	+	31.6781i	−0.0516771	+	0.0516771i	0.680796	+	0.732473i	$0.261634\pi$
$614$	1605.75	+	927.078i	2.61522	+	1.50990i
$615$	594.969	+	117.282i	0.967429	+	0.190702i
$616$	120.946	+	209.485i	0.196341	+	0.340072i
$617$	−67.8722	+	253.302i	−0.110004	+	0.410539i	−0.998865	−	0.0476380i	$-0.984831\pi$
$617$	−67.8722	+	253.302i	−0.110004	+	0.410539i	0.888861	+	0.458177i	$0.151497\pi$
$618$	−527.864	−	114.334i	−0.854149	−	0.185007i
$619$	422.528	+	243.947i	0.682598	+	0.394098i	0.800833	−	0.598887i	$-0.204390\pi$
$619$	422.528	+	243.947i	0.682598	+	0.394098i	−0.118235	+	0.992986i	$0.537724\pi$
$620$	−982.214	+	591.809i	−1.58422	+	0.954531i
$621$	11.6091	+	14.6808i	0.0186942	+	0.0236405i
$622$	−521.044	−	521.044i	−0.837691	−	0.837691i
$623$	118.623	+	442.707i	0.190406	+	0.710605i
$624$	668.417	−	430.412i	1.07118	−	0.689764i
$625$	−271.231	+	563.080i	−0.433970	+	0.900927i
$626$	−639.119	−	1106.99i	−1.02096	−	1.76835i
$627$	197.053	+	178.810i	0.314278	+	0.285184i
$628$	−490.396	−	1830.18i	−0.780886	−	2.91431i
$629$		−	239.158i		−	0.380219i
$630$	318.211	−	736.305i	0.505096	−	1.16874i
$631$	263.490			0.417576			0.208788	−	0.977961i	$-0.433048\pi$
$631$	263.490			0.417576			0.208788	+	0.977961i	$0.433048\pi$
$632$	361.529	−	96.8714i	0.572039	−	0.153277i
$633$	−124.777	−	389.133i	−0.197120	−	0.614744i
$634$	80.4505	−	46.4481i	0.126894	−	0.0732620i
$635$	−342.492	+	98.6615i	−0.539358	+	0.155372i
$636$	540.838	−	1051.39i	0.850375	−	1.65313i
$637$	223.555	−	59.9014i	0.350950	−	0.0940367i
$638$	243.730	−	243.730i	0.382023	−	0.382023i
$639$	−934.554	−	424.773i	−1.46253	−	0.664746i
$640$	−665.298	−	165.014i	−1.03953	−	0.257834i
$641$	−459.262	+	795.464i	−0.716477	+	1.24097i	0.245911	+	0.969293i	$0.420913\pi$
$641$	−459.262	+	795.464i	−0.716477	+	1.24097i	−0.962387	+	0.271682i	$0.912420\pi$
$642$	649.127	+	589.034i	1.01110	+	0.917498i
$643$	−40.8497	−	10.9456i	−0.0635298	−	0.0170228i	0.226914	−	0.973915i	$-0.427136\pi$
$643$	−40.8497	−	10.9456i	−0.0635298	−	0.0170228i	−0.290444	+	0.956892i	$0.593803\pi$
$644$	26.5652	−	15.3374i	0.0412504	−	0.0238159i
$645$	−51.3708	−	25.2234i	−0.0796446	−	0.0391060i
$646$	750.843	−	1300.50i	1.16230	−	2.01316i
$647$	−12.5734	−	12.5734i	−0.0194334	−	0.0194334i	0.697323	−	0.716757i	$-0.254374\pi$
$647$	−12.5734	−	12.5734i	−0.0194334	−	0.0194334i	−0.716757	+	0.697323i	$0.754374\pi$
$648$	1430.97	+	97.1884i	2.20829	+	0.149982i
$649$		−	117.275i		−	0.180701i
$650$	453.207	+	721.352i	0.697242	+	1.10977i
$651$	206.927	+	321.350i	0.317860	+	0.493626i
$652$	199.783	−	745.601i	0.306416	−	1.14356i
$653$	−513.495	−	137.591i	−0.786363	−	0.210705i	−0.156775	−	0.987634i	$-0.550110\pi$
$653$	−513.495	−	137.591i	−0.786363	−	0.210705i	−0.629588	+	0.776929i	$0.716776\pi$
$654$	76.2593	+	1571.24i	0.116604	+	2.40251i
$655$	896.780	−	16.7502i	1.36913	−	0.0255728i
$656$	1130.31			1.72303
$657$	−224.027	+	84.0155i	−0.340984	+	0.127877i
$658$	48.3691	−	48.3691i	0.0735093	−	0.0735093i
$659$	64.8393	+	37.4350i	0.0983905	+	0.0568058i	0.548388	−	0.836224i	$-0.315242\pi$
$659$	64.8393	+	37.4350i	0.0983905	+	0.0568058i	−0.449997	+	0.893030i	$0.648575\pi$
$660$	−277.752	−	242.737i	−0.420836	−	0.367783i
$661$	11.3687	+	19.6912i	0.0171993	+	0.0297900i	0.874497	−	0.485031i	$-0.161192\pi$
$661$	11.3687	+	19.6912i	0.0171993	+	0.0297900i	−0.857298	+	0.514821i	$0.827858\pi$
$662$	180.253	−	672.712i	0.272285	−	1.01618i
$663$	112.658	+	351.338i	0.169921	+	0.529922i
$664$	234.465	+	135.368i	0.353110	+	0.203868i
$665$	−774.557	−	192.113i	−1.16475	−	0.288892i
$666$	−346.805	−	485.176i	−0.520728	−	0.728492i
$667$	−17.0560	−	17.0560i	−0.0255713	−	0.0255713i
$668$	561.872	+	2096.93i	0.841125	+	3.13912i
$669$	−58.3528	−	1202.30i	−0.0872240	−	1.79716i
$670$	732.906	+	405.086i	1.09389	+	0.604606i
$671$	18.1021	+	31.3537i	0.0269777	+	0.0467268i
$672$	93.4786	−	431.577i	0.139105	−	0.642227i
$673$	−166.017	−	619.582i	−0.246681	−	0.920628i	−0.972531	−	0.232774i	$-0.925220\pi$
$673$	−166.017	−	619.582i	−0.246681	−	0.920628i	0.725849	−	0.687854i	$-0.241447\pi$
$674$			330.040i			0.489673i
$675$	−53.2414	+	672.897i	−0.0788762	+	0.996884i
$676$	−706.526			−1.04516
$677$	562.095	−	150.613i	0.830273	−	0.222471i	0.181440	−	0.983402i	$-0.441924\pi$
$677$	562.095	−	150.613i	0.830273	−	0.222471i	0.648833	+	0.760931i	$0.275258\pi$
$678$	571.486	+	123.783i	0.842900	+	0.182570i
$679$	−675.360	+	389.919i	−0.994639	+	0.574255i
$680$	−555.711	+	1005.43i	−0.817223	+	1.47857i
$681$	567.214	−	27.5294i	0.832913	−	0.0404250i
$682$	245.867	−	65.8799i	0.360509	−	0.0965982i
$683$	599.384	−	599.384i	0.877576	−	0.877576i	−0.115708	−	0.993283i	$-0.536914\pi$
$683$	599.384	−	599.384i	0.877576	−	0.877576i	0.993283	+	0.115708i	$0.0369136\pi$
$684$	−250.413	−	2573.67i	−0.366101	−	3.76267i
$685$	−169.820	+	684.677i	−0.247913	+	0.999529i
$686$	654.336	−	1133.34i	0.953842	−	1.65210i
$687$	−422.878	+	135.597i	−0.615543	+	0.197376i
$688$	−103.035	−	27.6082i	−0.149761	−	0.0401282i
$689$	362.466	−	209.270i	0.526075	−	0.303730i
$690$	−24.5993	+	28.1478i	−0.0356512	+	0.0407939i
$691$	−348.543	+	603.695i	−0.504404	+	0.873654i	0.495583	+	0.868561i	$0.334955\pi$
$691$	−348.543	+	603.695i	−0.504404	+	0.873654i	−0.999987	+	0.00509303i	$0.998379\pi$
$692$	106.685	+	106.685i	0.154169	+	0.154169i
$693$	−78.1093	+	94.9474i	−0.112712	+	0.137009i
$694$			21.7458i			0.0313340i
$695$	−25.4522	−	1362.67i	−0.0366218	−	1.96068i
$696$	−1846.26	+	89.6074i	−2.65268	+	0.128746i
$697$	−135.769	+	506.696i	−0.194790	+	0.726967i
$698$	−272.153	−	72.9231i	−0.389904	−	0.104474i
$699$	−684.413	+	440.713i	−0.979131	+	0.630491i
$700$	1078.54	+	246.224i	1.54077	+	0.351749i
$701$	−643.602			−0.918119			−0.459060	−	0.888405i	$-0.651814\pi$
$701$	−643.602			−0.918119			−0.459060	+	0.888405i	$0.651814\pi$
$702$	738.026	+	549.388i	1.05132	+	0.782604i
$703$	−419.550	+	419.550i	−0.596800	+	0.596800i
$704$	12.1718	+	7.02736i	0.0172894	+	0.00998205i
$705$	−25.3706	+	51.6707i	−0.0359867	+	0.0732918i
$706$	−71.1500	−	123.235i	−0.100779	−	0.174554i
$707$	−105.991	+	395.563i	−0.149916	+	0.559495i
$708$	−765.853	+	843.985i	−1.08171	+	1.19207i
$709$	1069.69	+	617.583i	1.50872	+	0.871062i	0.999948	+	0.0101629i	$0.00323499\pi$
$709$	1069.69	+	617.583i	1.50872	+	0.871062i	0.508775	+	0.860899i	$0.330098\pi$
$710$	493.594	−	1990.06i	0.695203	−	2.80290i
$711$	110.627	+	154.765i	0.155593	+	0.217673i
$712$	−1157.42	−	1157.42i	−1.62559	−	1.62559i
$713$	−4.61022	−	17.2056i	−0.00646594	−	0.0241312i
$714$	617.014	+	317.393i	0.864165	+	0.444528i
$715$	−36.1456	−	125.476i	−0.0505533	−	0.175490i
$716$	1225.04	+	2121.83i	1.71095	+	2.96345i
$717$	−375.088	+	120.273i	−0.523135	+	0.167745i
$718$	−108.497	−	404.918i	−0.151110	−	0.563952i
$719$		−	219.618i		−	0.305449i	−0.988269	−	0.152724i	$-0.951195\pi$
$719$		−	219.618i		−	0.305449i	0.988269	−	0.152724i	$-0.0488047\pi$
$720$	145.203	+	1249.73i	0.201671	+	1.73574i
$721$	−248.283			−0.344360
$722$	−2345.00	+	628.340i	−3.24792	+	0.870278i
$723$	−430.564	+	474.491i	−0.595525	+	0.656280i
$724$	−2022.41	+	1167.64i	−2.79338	+	1.61276i
$725$	−32.4856	−	869.312i	−0.0448077	−	1.19905i
$726$	−662.216	−	1028.40i	−0.912143	−	1.41653i
$727$	−275.523	+	73.8261i	−0.378986	+	0.101549i	−0.443283	−	0.896382i	$-0.646186\pi$
$727$	−275.523	+	73.8261i	−0.378986	+	0.101549i	0.0642969	+	0.997931i	$0.479520\pi$
$728$	588.400	−	588.400i	0.808242	−	0.808242i
$729$	209.143	+	698.355i	0.286890	+	0.957964i
$730$	−246.628	−	409.324i	−0.337847	−	0.560718i
$731$	24.7525	−	42.8726i	0.0338611	−	0.0586492i
$732$	74.4783	−	343.855i	0.101746	−	0.469748i
$733$	678.149	+	181.709i	0.925169	+	0.247898i	0.689793	−	0.724006i	$-0.257701\pi$
$733$	678.149	+	181.709i	0.925169	+	0.247898i	0.235375	+	0.971905i	$0.424368\pi$
$734$	−1353.09	+	781.206i	−1.84345	+	1.06431i
$735$	−70.8364	+	359.353i	−0.0963761	+	0.488915i
$736$	−10.2898	+	17.8224i	−0.0139807	+	0.0242153i
$737$	−90.7608	−	90.7608i	−0.123149	−	0.123149i
$738$	459.333	+	1224.81i	0.622402	+	1.65963i
$739$			1147.21i			1.55238i	0.630497	+	0.776192i	$0.282851\pi$
$739$			1147.21i			1.55238i	−0.630497	+	0.776192i	$0.717149\pi$
$740$	570.652	−	592.375i	0.771151	−	0.800507i
$741$	418.712	−	813.980i	0.565064	−	1.09849i
$742$	203.717	−	760.284i	0.274552	−	1.02464i
$743$	−847.001	−	226.953i	−1.13997	−	0.305455i	−0.361034	−	0.932553i	$-0.617576\pi$
$743$	−847.001	−	226.953i	−1.13997	−	0.305455i	−0.778941	+	0.627098i	$0.784243\pi$
$744$	−1213.83	−	624.397i	−1.63150	−	0.839244i
$745$	−18.7610	−	1004.43i	−0.0251825	−	1.34823i
$746$	2325.68			3.11754
$747$	−22.5762	+	135.744i	−0.0302225	+	0.181719i
$748$	225.628	−	225.628i	0.301642	−	0.301642i
$749$	348.958	+	201.471i	0.465899	+	0.268987i
$750$	−1340.83	+	140.662i	−1.78777	+	0.187549i
$751$	147.537	+	255.542i	0.196455	+	0.340269i	0.947376	−	0.320122i	$-0.103724\pi$
$751$	147.537	+	255.542i	0.196455	+	0.340269i	−0.750922	+	0.660391i	$0.770391\pi$
$752$	−27.7694	+	103.637i	−0.0369274	+	0.137815i
$753$	−142.088	−	30.7761i	−0.188696	−	0.0408713i
$754$	−1026.88	−	592.872i	−1.36192	−	0.786303i
$755$	302.715	+	502.410i	0.400947	+	0.665444i
$756$	1182.17	−	173.217i	1.56372	−	0.229123i
$757$	89.6510	+	89.6510i	0.118429	+	0.118429i	0.763838	−	0.645408i	$-0.223313\pi$
$757$	89.6510	+	89.6510i	0.118429	+	0.118429i	−0.645408	+	0.763838i	$0.723313\pi$
$758$	−277.135	−	1034.28i	−0.365614	−	1.36449i
$759$	4.81747	−	3.10210i	0.00634712	−	0.00408709i
$760$	2738.68	−	788.928i	3.60352	−	1.03806i
$761$	80.6635	+	139.713i	0.105997	+	0.183592i	0.914145	−	0.405387i	$-0.132863\pi$
$761$	80.6635	+	139.713i	0.105997	+	0.183592i	−0.808148	+	0.588979i	$0.799530\pi$
$762$	−569.363	−	516.654i	−0.747195	−	0.678023i
$763$	187.163	+	698.501i	0.245298	+	0.915466i
$764$			1602.86i			2.09798i
$765$	−577.673	−	85.0217i	−0.755128	−	0.111139i
$766$	1542.52			2.01373
$767$	−389.686	+	104.416i	−0.508065	+	0.136136i
$768$	−432.785	−	1349.70i	−0.563522	−	1.75742i
$769$	129.486	−	74.7588i	0.168382	−	0.0972156i	−0.413440	−	0.910531i	$-0.635673\pi$
$769$	129.486	−	74.7588i	0.168382	−	0.0972156i	0.581823	+	0.813316i	$0.302340\pi$
$770$	−214.921	−	118.789i	−0.279118	−	0.154272i
$771$	−639.604	+	1243.40i	−0.829578	+	1.61270i
$772$	−231.699	+	62.0835i	−0.300128	+	0.0804190i
$773$	−994.453	+	994.453i	−1.28649	+	1.28649i	−0.349578	+	0.936907i	$0.613675\pi$
$773$	−994.453	+	994.453i	−1.28649	+	1.28649i	−0.936907	+	0.349578i	$0.886325\pi$
$774$	−11.9549	−	122.869i	−0.0154456	−	0.158745i
$775$	300.204	−	567.949i	0.387361	−	0.732837i
$776$	1392.55	−	2411.96i	1.79452	−	3.10819i
$777$	−203.025	−	184.230i	−0.261294	−	0.237104i
$778$	792.684	+	212.399i	1.01887	+	0.273006i
$779$	1127.06	−	650.711i	1.44681	−	0.835316i
$780$	−559.280	+	1139.05i	−0.717025	+	1.46032i
$781$	−157.137	+	272.169i	−0.201200	+	0.348488i
$782$	−22.8655	−	22.8655i	−0.0292398	−	0.0292398i
$783$	−372.161	−	862.659i	−0.475301	−	1.10174i
$784$			682.690i			0.870778i
$785$	764.449	+	736.415i	0.973820	+	0.938109i
$786$	1047.48	+	1626.70i	1.33267	+	2.06960i
$787$	237.874	−	887.757i	0.302254	−	1.12803i	−0.633030	−	0.774128i	$-0.718189\pi$
$787$	237.874	−	887.757i	0.302254	−	1.12803i	0.935284	−	0.353899i	$-0.115144\pi$
$788$	1445.83	+	387.409i	1.83481	+	0.491635i
$789$	−15.7635	−	324.790i	−0.0199791	−	0.411648i
$790$	−263.612	+	273.647i	−0.333686	+	0.346388i
$791$	268.801			0.339824
$792$	72.0378	−	433.141i	0.0909569	−	0.546895i
$793$	88.0662	−	88.0662i	0.111055	−	0.111055i
$794$	530.725	+	306.414i	0.668420	+	0.385912i
$795$	44.4589	+	660.867i	0.0559231	+	0.831279i
$796$	−106.714	−	184.834i	−0.134063	−	0.232204i
$797$	−230.557	+	860.450i	−0.289281	+	1.07961i	0.656373	+	0.754437i	$0.272090\pi$
$797$	−230.557	+	860.450i	−0.289281	+	1.07961i	−0.945654	+	0.325175i	$0.894577\pi$
$798$	−525.620	−	1639.21i	−0.658671	−	2.05415i
$799$	−43.1229	−	24.8970i	−0.0539711	−	0.0311602i
$800$	−709.239	+	218.734i	−0.886549	+	0.273417i
$801$	344.253	−	757.400i	0.429779	−	0.945568i
$802$	1152.46	+	1152.46i	1.43698	+	1.43698i
$803$	18.9581	+	70.7526i	0.0236091	+	0.0881104i
$804$	60.4680	+	1245.88i	0.0752090	+	1.54960i
$805$	−8.31277	+	15.0400i	−0.0103264	+	0.0186832i
$806$	−437.818	−	758.323i	−0.543198	−	0.940847i
$807$	172.716	−	797.403i	0.214022	−	0.988108i
$808$	−378.532	−	1412.70i	−0.468480	−	1.74839i
$809$		−	1398.60i		−	1.72880i	−0.502802	−	0.864402i	$-0.667698\pi$
$809$		−	1398.60i		−	1.72880i	0.502802	−	0.864402i	$-0.332302\pi$
$810$	−1295.21	+	665.206i	−1.59902	+	0.821242i
$811$	−347.451			−0.428423			−0.214211	−	0.976787i	$-0.568718\pi$
$811$	−347.451			−0.428423			−0.214211	+	0.976787i	$0.568718\pi$
$812$	−1487.34	+	398.533i	−1.83170	+	0.490804i
$813$	−830.726	−	179.934i	−1.02180	−	0.221321i
$814$	−158.117	+	91.2888i	−0.194247	+	0.112148i
$815$	119.701	+	415.530i	0.146873	+	0.509853i
$816$	−1087.05	+	52.7594i	−1.33217	+	0.0646561i
$817$	−118.633	+	31.7877i	−0.145206	+	0.0389079i
$818$	−1253.90	+	1253.90i	−1.53288	+	1.53288i
$819$	385.040	+	175.008i	0.470135	+	0.213685i
$820$	−1545.31	+	931.090i	−1.88453	+	1.13548i
$821$	−493.294	+	854.410i	−0.600845	+	1.04069i	0.391848	+	0.920030i	$0.371836\pi$
$821$	−493.294	+	854.410i	−0.600845	+	1.04069i	−0.992693	+	0.120665i	$0.961497\pi$
$822$	−1449.00	+	464.627i	−1.76277	+	0.565239i
$823$	−243.845	−	65.3381i	−0.296288	−	0.0793902i	0.107613	−	0.994193i	$-0.465679\pi$
$823$	−243.845	−	65.3381i	−0.296288	−	0.0793902i	−0.403901	+	0.914803i	$0.632346\pi$
$824$	767.914	−	443.356i	0.931935	−	0.538053i
$825$	203.456	+	36.1724i	0.246613	+	0.0438453i
$826$	−379.347	+	657.049i	−0.459258	+	0.795458i
$827$	1054.44	+	1054.44i	1.27502	+	1.27502i	0.943419	+	0.331604i	$0.107590\pi$
$827$	1054.44	+	1054.44i	1.27502	+	1.27502i	0.331604	+	0.943419i	$0.392410\pi$
$828$	−54.9276	−	9.13529i	−0.0663377	−	0.0110330i
$829$		−	819.644i		−	0.988714i	−0.869259	−	0.494357i	$-0.835404\pi$
$829$		−	819.644i		−	0.988714i	0.869259	−	0.494357i	$-0.164596\pi$
$830$	−274.799	+	5.13274i	−0.331084	+	0.00618402i
$831$	−445.911	+	21.6420i	−0.536596	+	0.0260434i
$832$	12.5137	−	46.7017i	0.0150405	−	0.0561318i
$833$	−306.037	−	82.0024i	−0.367392	−	0.0984423i
$834$	2471.80	−	1591.66i	2.96379	−	1.90847i
$835$	−875.867	−	843.748i	−1.04894	−	1.01048i
$836$	−791.631			−0.946928
$837$	80.5143	−	689.113i	0.0961939	−	0.823313i
$838$	66.9173	−	66.9173i	0.0798536	−	0.0798536i
$839$	−425.345	−	245.573i	−0.506966	−	0.292697i	0.224619	−	0.974447i	$-0.427886\pi$
$839$	−425.345	−	245.573i	−0.506966	−	0.292697i	−0.731586	+	0.681749i	$0.761219\pi$
$840$	425.444	+	1246.26i	0.506481	+	1.48364i
$841$	184.907	+	320.269i	0.219866	+	0.380819i
$842$	453.001	−	1690.62i	0.538006	−	2.00786i
$843$	509.003	−	560.932i	0.603799	−	0.665399i
$844$	1052.88	+	607.880i	1.24749	+	0.720237i
$845$	339.020	−	204.268i	0.401207	−	0.241738i
$846$	−123.586	+	12.0247i	−0.146083	+	0.0142136i
$847$	−397.594	−	397.594i	−0.469415	−	0.469415i
$848$	319.533	+	1192.51i	0.376808	+	1.40627i
$849$	1279.53	+	658.190i	1.50710	+	0.775253i
$850$	−43.5506	−	1165.41i	−0.0512360	−	1.37107i
$851$	6.38831	+	11.0649i	0.00750682	+	0.0130022i
$852$	2908.23	−	932.536i	3.41342	−	1.09453i
$853$	−90.1607	−	336.484i	−0.105698	−	0.394472i	0.892725	−	0.450602i	$-0.148791\pi$
$853$	−90.1607	−	336.484i	−0.105698	−	0.394472i	−0.998423	+	0.0561301i	$0.982124\pi$
$854$		−	234.218i		−	0.274260i
$855$	864.249	+	1162.55i	1.01082	+	1.35971i
$856$	−1439.05			−1.68114
$857$	−787.034	+	210.885i	−0.918359	+	0.246074i	−0.686884	−	0.726767i	$-0.741022\pi$
$857$	−787.034	+	210.885i	−0.918359	+	0.246074i	−0.231475	+	0.972841i	$0.574355\pi$
$858$	189.281	−	208.592i	0.220607	−	0.243114i
$859$	−101.706	+	58.7201i	−0.118401	+	0.0683587i	−0.558031	−	0.829820i	$-0.688443\pi$
$859$	−101.706	+	58.7201i	−0.118401	+	0.0683587i	0.439630	+	0.898179i	$0.355110\pi$
$860$	163.608	−	47.1303i	0.190242	−	0.0548027i
$861$	325.556	+	505.579i	0.378114	+	0.587199i
$862$	254.483	−	68.1886i	0.295224	−	0.0791051i
$863$	−148.570	+	148.570i	−0.172155	+	0.172155i	−0.787926	−	0.615770i	$-0.788845\pi$
$863$	−148.570	+	148.570i	−0.172155	+	0.172155i	0.615770	+	0.787926i	$0.288845\pi$
$864$	−628.748	+	497.196i	−0.727718	+	0.575458i
$865$	−82.0360	−	20.3474i	−0.0948394	−	0.0235230i
$866$	202.797	−	351.254i	0.234176	−	0.405605i
$867$	−76.6128	+	353.710i	−0.0883654	+	0.407970i
$868$	−1098.36	−	294.304i	−1.26539	−	0.339060i
$869$	50.4374	−	29.1200i	0.0580407	−	0.0335098i
$870$	1558.46	−	1045.21i	1.79133	−	1.20140i
$871$	−220.775	+	382.393i	−0.253473	+	0.439028i
$872$	−1826.18	−	1826.18i	−2.09424	−	2.09424i
$873$	1396.41	+	232.244i	1.59955	+	0.266030i
$874$			80.2251i			0.0917907i
$875$	−588.715	+	193.675i	−0.672818	+	0.221343i
$876$	325.609	−	632.986i	0.371700	−	0.722587i
$877$	−128.827	+	480.790i	−0.146895	+	0.548221i	0.852768	+	0.522289i	$0.174922\pi$
$877$	−128.827	+	480.790i	−0.146895	+	0.548221i	−0.999664	+	0.0259318i	$0.991745\pi$
$878$	390.709	+	104.690i	0.444998	+	0.119237i
$879$	−541.444	−	278.520i	−0.615977	−	0.316860i
$880$	385.103	−	7.19301i	0.437618	−	0.00817388i
$881$	306.447			0.347840			0.173920	−	0.984760i	$-0.444357\pi$
$881$	306.447			0.347840			0.173920	+	0.984760i	$0.444357\pi$
$882$	−739.765	+	277.430i	−0.838736	+	0.314547i
$883$	930.058	−	930.058i	1.05329	−	1.05329i	0.0547963	−	0.998498i	$-0.482549\pi$
$883$	930.058	−	930.058i	1.05329	−	1.05329i	0.998498	−	0.0547963i	$-0.0174509\pi$
$884$	−950.617	−	548.839i	−1.07536	−	0.620859i
$885$	123.477	−	626.399i	0.139522	−	0.707796i
$886$	286.676	+	496.538i	0.323563	+	0.560427i
$887$	35.0975	−	130.986i	0.0395688	−	0.147673i	−0.943315	−	0.331898i	$-0.892311\pi$
$887$	35.0975	−	130.986i	0.0395688	−	0.147673i	0.982884	+	0.184225i	$0.0589776\pi$
$888$	956.911	+	207.265i	1.07760	+	0.233407i
$889$	−306.078	−	176.714i	−0.344295	−	0.198779i
$890$	1612.83	+	400.029i	1.81216	+	0.449471i
$891$	218.992	−	43.0224i	0.245783	−	0.0482855i
$892$	2532.24	+	2532.24i	2.83884	+	2.83884i
$893$	31.9733	+	119.326i	0.0358044	+	0.133624i
$894$	1821.98	−	1173.23i	2.03801	−	1.31233i
$895$	−1201.28	−	663.962i	−1.34221	−	0.741856i
$896$	−339.852	−	588.641i	−0.379299	−	0.656965i
$897$	−14.5971	−	13.2457i	−0.0162732	−	0.0147667i
$898$	271.524	+	1013.34i	0.302366	+	1.12844i
$899$			894.149i			0.994604i
$900$	−1227.98	−	1588.97i	−1.36442	−	1.76552i
$901$	−572.962			−0.635918
$902$	386.822	−	103.649i	0.428849	−	0.114910i
$903$	−17.3277	−	54.0387i	−0.0191891	−	0.0598435i
$904$	−831.374	+	479.994i	−0.919661	+	0.530967i
$905$	632.850	−	1144.99i	0.699282	−	1.26518i
$906$	−578.771	+	1125.14i	−0.638820	+	1.24187i
$907$	−131.208	+	35.1572i	−0.144662	+	0.0387621i	−0.330423	−	0.943833i	$-0.607192\pi$
$907$	−131.208	+	35.1572i	−0.144662	+	0.0387621i	0.185761	+	0.982595i	$0.440525\pi$
$908$	−1194.65	+	1194.65i	−1.31569	+	1.31569i
$909$	604.757	−	432.282i	0.665299	−	0.475557i
$910$	−203.363	+	819.914i	−0.223476	+	0.901004i
$911$	545.263	−	944.423i	0.598532	−	1.03669i	−0.394506	−	0.918894i	$-0.629084\pi$
$911$	545.263	−	944.423i	0.598532	−	1.03669i	0.993038	−	0.117795i	$-0.0375826\pi$
$912$	1999.55	+	1814.44i	2.19249	+	1.98951i
$913$	40.6924	+	10.9035i	0.0445700	+	0.0119425i
$914$	−1459.39	+	842.579i	−1.59671	+	0.921859i
$915$	63.6765	+	186.529i	0.0695918	+	0.203857i
$916$	660.594	−	1144.18i	0.721173	−	1.24911i
$917$	628.907	+	628.907i	0.685831	+	0.685831i
$918$	−498.923	−	1156.49i	−0.543489	−	1.25979i
$919$		−	367.996i		−	0.400431i	−0.979752	−	0.200215i	$-0.935836\pi$
$919$		−	367.996i		−	0.400431i	0.979752	−	0.200215i	$-0.0641642\pi$
$920$	−1.14611	−	61.3611i	−0.00124577	−	0.0666968i
$921$	−837.650	−	1300.84i	−0.909501	−	1.41242i
$922$	−462.959	+	1727.79i	−0.502125	+	1.87396i
$923$	1044.28	+	279.815i	1.13140	+	0.303158i
$924$	−17.7319	−	365.347i	−0.0191904	−	0.395398i
$925$	−102.557	+	449.231i	−0.110872	+	0.485655i
$926$	−3276.11			−3.53792
$927$	348.052	+	286.328i	0.375460	+	0.308876i
$928$	730.476	−	730.476i	0.787151	−	0.787151i
$929$	−62.7337	−	36.2193i	−0.0675282	−	0.0389874i	0.465856	−	0.884861i	$-0.345747\pi$
$929$	−62.7337	−	36.2193i	−0.0675282	−	0.0389874i	−0.533384	+	0.845873i	$0.679080\pi$
$930$	1382.61	−	93.0134i	1.48668	−	0.100014i
$931$	393.020	+	680.731i	0.422148	+	0.731182i
$932$	626.810	−	2339.28i	0.672542	−	2.50996i
$933$	187.748	+	585.517i	0.201231	+	0.627563i
$934$	−902.137	−	520.849i	−0.965886	−	0.557655i
$935$	−43.0328	+	173.499i	−0.0460244	+	0.185560i
$936$	−1503.40	+	146.278i	−1.60620	+	0.156280i
$937$	−887.903	−	887.903i	−0.947602	−	0.947602i	0.0510921	−	0.998694i	$-0.483730\pi$
$937$	−887.903	−	887.903i	−0.947602	−	0.947602i	−0.998694	+	0.0510921i	$0.983730\pi$
$938$	214.917	+	802.082i	0.229123	+	0.855099i
$939$	51.7075	+	1065.38i	0.0550666	+	1.13459i
$940$	−47.4055	−	164.563i	−0.0504314	−	0.175067i
$941$	190.349	+	329.694i	0.202284	+	0.350366i	0.949264	−	0.314480i	$-0.101830\pi$
$941$	190.349	+	329.694i	0.202284	+	0.350366i	−0.746980	+	0.664846i	$0.768497\pi$
$942$	−484.698	+	2237.78i	−0.514541	+	2.37556i
$943$	−7.25323	−	27.0694i	−0.00769165	−	0.0287056i
$944$		−	1190.02i		−	1.26061i
$945$	−517.174	+	424.901i	−0.547274	+	0.449631i
$946$	−37.7930			−0.0399504
$947$	521.012	−	139.605i	0.550172	−	0.147418i	0.0269844	−	0.999636i	$-0.491410\pi$
$947$	521.012	−	139.605i	0.550172	−	0.147418i	0.523187	+	0.852218i	$0.324743\pi$
$948$	−553.145	−	119.810i	−0.583487	−	0.126382i
$949$	218.221	−	125.990i	0.229948	−	0.132761i
$950$	−1968.06	+	2120.86i	−2.07164	+	2.23248i
$951$	−77.4265	+	3.75785i	−0.0814159	+	0.00395148i
$952$	−1100.33	+	294.831i	−1.15580	+	0.309697i
$953$	−52.0743	+	52.0743i	−0.0546425	+	0.0546425i	−0.733900	−	0.679258i	$-0.762302\pi$
$953$	−52.0743	+	52.0743i	−0.0546425	+	0.0546425i	0.679258	+	0.733900i	$0.262302\pi$
$954$	−1162.36	+	830.858i	−1.21841	+	0.870920i
$955$	−463.413	−	769.118i	−0.485250	−	0.805359i
$956$	585.940	−	1014.88i	0.612908	−	1.06159i
$957$	−273.889	+	87.8236i	−0.286196	+	0.0917697i
$958$	710.080	+	190.265i	0.741210	+	0.198607i
$959$	−605.788	+	349.752i	−0.631687	+	0.364705i
$960$	57.6139	+	50.3507i	0.0600144	+	0.0524486i
$961$	150.349	−	260.413i	0.156451	−	0.270981i
$962$	444.118	+	444.118i	0.461662	+	0.461662i
$963$	−256.838	−	684.858i	−0.266707	−	0.711171i
$964$		−	1906.20i		−	1.97739i
$965$	93.2291	−	96.7781i	0.0966105	−	0.100288i
$966$	−37.0249	+	1.79698i	−0.0383280	+	0.00186023i
$967$	−74.5608	+	278.265i	−0.0771053	+	0.287761i	−0.993702	−	0.112051i	$-0.964258\pi$
$967$	−74.5608	+	278.265i	−0.0771053	+	0.287761i	0.916597	+	0.399812i	$0.130925\pi$
$968$	1939.70	+	519.740i	2.00382	+	0.536921i
$969$	−1053.56	+	678.415i	−1.08726	+	0.700119i
$970$	52.8009	+	2826.88i	0.0544339	+	2.91431i
$971$	−227.938			−0.234745			−0.117373	−	0.993088i	$-0.537447\pi$
$971$	−227.938			−0.234745			−0.117373	+	0.993088i	$0.537447\pi$
$972$	−1856.96	−	1120.49i	−1.91046	−	1.15277i
$973$	955.634	−	955.634i	0.982152	−	0.982152i
$974$	−2230.86	−	1287.99i	−2.29041	−	1.32237i
$975$	−60.9527	−	708.259i	−0.0625156	−	0.726420i
$976$	183.687	+	318.155i	0.188203	+	0.325978i
$977$	−164.275	+	613.083i	−0.168142	+	0.627516i	0.829476	+	0.558542i	$0.188639\pi$
$977$	−164.275	+	613.083i	−0.168142	+	0.627516i	−0.997618	+	0.0689735i	$0.978028\pi$
$978$	−626.832	+	690.781i	−0.640932	+	0.706320i
$979$	−220.577	−	127.350i	−0.225308	−	0.130082i
$980$	−562.365	−	933.345i	−0.573842	−	0.952393i
$981$	543.161	−	1195.02i	0.553681	−	1.21817i
$982$	−531.988	−	531.988i	−0.541739	−	0.541739i
$983$	352.779	+	1316.59i	0.358880	+	1.33936i	0.875531	+	0.483163i	$0.160512\pi$
$983$	352.779	+	1316.59i	0.358880	+	1.33936i	−0.516651	+	0.856196i	$0.672821\pi$
$984$	−1909.72	−	982.361i	−1.94077	−	0.998334i
$985$	−805.774	+	232.119i	−0.818045	+	0.235653i
$986$	811.616	+	1405.76i	0.823140	+	1.42572i
$987$	−54.3542	+	17.4289i	−0.0550701	+	0.0176584i
$988$	704.832	+	2630.47i	0.713393	+	2.66242i
$989$			2.64472i			0.00267414i
$990$	164.292	+	414.376i	0.165951	+	0.418562i
$991$	1111.32			1.12141			0.560705	−	0.828016i	$-0.310530\pi$
$991$	1111.32			1.12141			0.560705	+	0.828016i	$0.310530\pi$
$992$	736.881	−	197.447i	0.742823	−	0.199039i
$993$	−390.530	+	430.373i	−0.393283	+	0.433406i
$994$	1760.76	−	1016.58i	1.77139	−	1.02271i
$995$	104.644	+	57.8382i	0.105170	+	0.0581289i
$996$	−221.644	−	344.206i	−0.222534	−	0.345589i
$997$	615.048	−	164.802i	0.616898	−	0.165297i	0.0631810	−	0.998002i	$-0.479875\pi$
$997$	615.048	−	164.802i	0.616898	−	0.165297i	0.553717	+	0.832705i	$0.313209\pi$
$998$	842.493	−	842.493i	0.844182	−	0.844182i
$999$	72.1478	+	492.394i	0.0722200	+	0.492887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.7.10	✓	40
3.2	odd	2		135.3.l.a.127.1		40
5.2	odd	4		225.3.o.b.43.10		40
5.3	odd	4	inner	45.3.k.a.43.1	yes	40
5.4	even	2		225.3.o.b.7.1		40
9.2	odd	6		405.3.g.g.82.10		20
9.4	even	3	inner	45.3.k.a.22.1	yes	40
9.5	odd	6		135.3.l.a.37.10		40
9.7	even	3		405.3.g.h.82.1		20
15.8	even	4		135.3.l.a.73.10		40
45.4	even	6		225.3.o.b.157.10		40
45.13	odd	12	inner	45.3.k.a.13.10	yes	40
45.22	odd	12		225.3.o.b.193.1		40
45.23	even	12		135.3.l.a.118.1		40
45.38	even	12		405.3.g.g.163.10		20
45.43	odd	12		405.3.g.h.163.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.10	✓	40	1.1	even	1	trivial
45.3.k.a.13.10	yes	40	45.13	odd	12	inner
45.3.k.a.22.1	yes	40	9.4	even	3	inner
45.3.k.a.43.1	yes	40	5.3	odd	4	inner
135.3.l.a.37.10		40	9.5	odd	6
135.3.l.a.73.10		40	15.8	even	4
135.3.l.a.118.1		40	45.23	even	12
135.3.l.a.127.1		40	3.2	odd	2
225.3.o.b.7.1		40	5.4	even	2
225.3.o.b.43.10		40	5.2	odd	4
225.3.o.b.157.10		40	45.4	even	6
225.3.o.b.193.1		40	45.22	odd	12
405.3.g.g.82.10		20	9.2	odd	6
405.3.g.g.163.10		20	45.38	even	12
405.3.g.h.82.1		20	9.7	even	3
405.3.g.h.163.1		20	45.43	odd	12

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.47266 - 0.930497i) q^{2} +(-2.93201 - 0.635068i) q^{3} +(7.72947 - 4.46261i) q^{4} +(-2.41870 + 4.37606i) q^{5} +(-10.7728 + 0.522853i) q^{6} +(-4.78910 + 1.28323i) q^{7} +(12.5207 - 12.5207i) q^{8} +(8.19338 + 3.72405i) q^{9} +(-4.32742 + 17.4472i) q^{10} +(1.37764 - 2.38615i) q^{11} +(-25.4969 + 8.17569i) q^{12} +(-9.15539 - 2.45318i) q^{13} +(-15.4369 + 8.91249i) q^{14} +(9.87075 - 11.2946i) q^{15} +(13.9793 - 24.2129i) q^{16} +(9.17504 + 9.17504i) q^{17} +(31.9181 + 5.30846i) q^{18} -32.1912i q^{19} +(0.833387 + 44.6183i) q^{20} +(14.8566 - 0.721059i) q^{21} +(2.56379 - 9.56819i) q^{22} +(-0.669573 - 0.179412i) q^{23} +(-44.6624 + 28.7594i) q^{24} +(-13.2998 - 21.1687i) q^{25} -34.0763 q^{26} +(-21.6581 - 16.1223i) q^{27} +(-31.2906 + 31.2906i) q^{28} +(30.1349 + 17.3984i) q^{29} +(23.7682 - 48.4071i) q^{30} +(12.8482 + 22.2537i) q^{31} +(7.68384 - 28.6765i) q^{32} +(-5.55463 + 6.12132i) q^{33} +(40.3992 + 23.3245i) q^{34} +(5.96788 - 24.0611i) q^{35} +(79.9494 - 7.77893i) q^{36} +(-13.0331 - 13.0331i) q^{37} +(-29.9538 - 111.789i) q^{38} +(25.2858 + 13.0070i) q^{39} +(24.5076 + 85.0753i) q^{40} +(20.2139 + 35.0116i) q^{41} +(50.9211 - 16.3280i) q^{42} +(-0.987466 - 3.68527i) q^{43} -24.5915i q^{44} +(-36.1140 + 26.8474i) q^{45} -2.49214 q^{46} +(-3.70679 + 0.993231i) q^{47} +(-56.3644 + 62.1147i) q^{48} +(-21.1465 + 12.2089i) q^{49} +(-65.8831 - 61.1365i) q^{50} +(-21.0745 - 32.7281i) q^{51} +(-81.7139 + 21.8952i) q^{52} +(-31.2240 + 31.2240i) q^{53} +(-90.2129 - 35.8346i) q^{54} +(7.10982 + 11.8000i) q^{55} +(-43.8959 + 76.0300i) q^{56} +(-20.4436 + 94.3850i) q^{57} +(120.837 + 32.3783i) q^{58} +(36.8611 - 21.2818i) q^{59} +(25.8921 - 131.351i) q^{60} +(-6.56994 + 11.3795i) q^{61} +(65.3243 + 65.3243i) q^{62} +(-44.0177 - 7.32081i) q^{63} +5.10100i q^{64} +(32.8794 - 34.1310i) q^{65} +(-13.5935 + 26.4259i) q^{66} +(12.0571 - 44.9977i) q^{67} +(111.863 + 29.9735i) q^{68} +(1.84926 + 0.951261i) q^{69} +(-1.66440 - 89.1093i) q^{70} -114.062 q^{71} +(149.215 - 55.9592i) q^{72} +(-18.7982 + 18.7982i) q^{73} +(-57.3867 - 33.1322i) q^{74} +(25.5515 + 70.5133i) q^{75} +(-143.657 - 248.821i) q^{76} +(-3.53568 + 13.1953i) q^{77} +(99.9120 + 21.6407i) q^{78} +(18.3057 + 10.5688i) q^{79} +(72.1453 + 119.738i) q^{80} +(53.2629 + 61.0251i) q^{81} +(102.774 + 102.774i) q^{82} +(3.95730 + 14.7688i) q^{83} +(111.616 - 71.8727i) q^{84} +(-62.3422 + 17.9589i) q^{85} +(-6.85828 - 11.8789i) q^{86} +(-77.3067 - 70.1499i) q^{87} +(-12.6272 - 47.1254i) q^{88} -92.4405i q^{89} +(-100.430 + 126.836i) q^{90} +46.9941 q^{91} +(-5.97609 + 1.60129i) q^{92} +(-23.5384 - 73.4075i) q^{93} +(-11.9482 + 6.89832i) q^{94} +(140.871 + 77.8609i) q^{95} +(-40.7406 + 79.2000i) q^{96} +(151.928 - 40.7091i) q^{97} +(-62.0742 + 62.0742i) q^{98} +(20.1737 - 14.4202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Introduction

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