LMFDB - Embedded newform 45.3.k.a.22.1

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			22.1
Character	$\chi$	$=$	45.22
Dual form			45.3.k.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.930497 + 3.47266i) q^{2} +(0.635068 + 2.93201i) q^{3} +(-7.72947 - 4.46261i) q^{4} +(4.99913 - 0.0933744i) q^{5} +(-10.7728 - 0.522853i) q^{6} +(1.28323 - 4.78910i) 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} +(8.17569 - 25.4969i) q^{12} +(2.45318 + 9.15539i) q^{13} +(15.4369 + 8.91249i) q^{14} +(3.44856 + 14.5982i) q^{15} +(13.9793 + 24.2129i) q^{16} +(9.17504 + 9.17504i) q^{17} +(-5.30846 - 31.9181i) q^{18} -32.1912i q^{19} +(-39.0573 - 21.5874i) q^{20} +(14.8566 + 0.721059i) q^{21} +(-9.56819 + 2.56379i) q^{22} +(0.179412 + 0.669573i) q^{23} +(44.6624 + 28.7594i) q^{24} +(24.9826 - 0.933581i) q^{25} -34.0763 q^{26} +(-16.1223 - 21.6581i) q^{27} +(-31.2906 + 31.2906i) q^{28} +(-30.1349 + 17.3984i) q^{29} +(-53.9035 - 1.60790i) q^{30} +(12.8482 - 22.2537i) q^{31} +(-28.6765 + 7.68384i) q^{32} +(-6.12132 + 5.55463i) 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} +(111.789 + 29.9538i) q^{38} +(-25.2858 + 13.0070i) q^{39} +(61.4236 - 63.7618i) q^{40} +(20.2139 - 35.0116i) q^{41} +(-16.3280 + 50.9211i) q^{42} +(3.68527 + 0.987466i) q^{43} -24.5915i q^{44} +(-40.6120 + 19.3821i) q^{45} -2.49214 q^{46} +(0.993231 - 3.70679i) q^{47} +(-62.1147 + 56.3644i) q^{48} +(21.1465 + 12.2089i) q^{49} +(-20.0042 + 87.6247i) q^{50} +(-21.0745 + 32.7281i) q^{51} +(21.8952 - 81.7139i) 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} +(94.3850 - 20.4436i) q^{57} +(-32.3783 - 120.837i) q^{58} +(-36.8611 - 21.2818i) q^{59} +(38.4905 - 128.226i) q^{60} +(-6.56994 - 11.3795i) q^{61} +(65.3243 + 65.3243i) q^{62} +(7.32081 + 44.0177i) q^{63} +5.10100i q^{64} +(13.1186 + 45.5399i) q^{65} +(-13.5935 - 26.4259i) q^{66} +(-44.9977 + 12.0571i) q^{67} +(-29.9735 - 111.863i) q^{68} +(-1.84926 + 0.951261i) q^{69} +(78.0031 + 43.1133i) q^{70} -114.062 q^{71} +(-55.9592 + 149.215i) q^{72} +(-18.7982 + 18.7982i) q^{73} +(57.3867 - 33.1322i) q^{74} +(18.6029 + 72.6563i) q^{75} +(-143.657 + 248.821i) q^{76} +(13.1953 - 3.53568i) q^{77} +(-21.6407 - 99.9120i) 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} +(-14.7688 - 3.95730i) q^{83} +(-111.616 - 71.8727i) q^{84} +(46.7239 + 45.0105i) q^{85} +(-6.85828 + 11.8789i) q^{86} +(-70.1499 - 77.3067i) q^{87} +(47.1254 + 12.6272i) q^{88} -92.4405i q^{89} +(-29.5180 - 159.067i) q^{90} +46.9941 q^{91} +(1.60129 - 5.97609i) q^{92} +(73.4075 + 23.5384i) q^{93} +(11.9482 + 6.89832i) q^{94} +(-3.00583 - 160.928i) q^{95} +(-40.7406 - 79.2000i) q^{96} +(-40.7091 + 151.928i) 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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.930497	+	3.47266i	−0.465249	+	1.73633i	0.190815	+	0.981626i	$0.438887\pi$
$2$	−0.930497	+	3.47266i	−0.465249	+	1.73633i	−0.656063	+	0.754706i	$0.727780\pi$
$3$	0.635068	+	2.93201i	0.211689	+	0.977337i
$3$	0.635068	+	2.93201i	0.211689	+	0.977337i
$4$	−7.72947	−	4.46261i	−1.93237	−	1.11565i
$5$	4.99913	−	0.0933744i	0.999826	−	0.0186749i
$5$	4.99913	−	0.0933744i	0.999826	−	0.0186749i
$6$	−10.7728	−	0.522853i	−1.79547	−	0.0871422i
$7$	1.28323	−	4.78910i	0.183319	−	0.684157i	−0.811665	−	0.584123i	$-0.801438\pi$
$7$	1.28323	−	4.78910i	0.183319	−	0.684157i	0.994984	−	0.100033i	$-0.0318950\pi$
$8$	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	0.921827	−	0.387602i	$-0.126696\pi$
$11$	1.37764	+	2.38615i	0.125240	+	0.216923i	−0.796587	+	0.604525i	$0.793363\pi$
$12$	8.17569	−	25.4969i	0.681307	−	2.12474i
$13$	2.45318	+	9.15539i	0.188706	+	0.704261i	0.993807	+	0.111123i	$0.0354446\pi$
$13$	2.45318	+	9.15539i	0.188706	+	0.704261i	−0.805101	+	0.593138i	$0.797889\pi$
$14$	15.4369	+	8.91249i	1.10263	+	0.636606i
$15$	3.44856	+	14.5982i	0.229904	+	0.973213i
$16$	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	$0.625362\pi$
$18$	−5.30846	−	31.9181i	−0.294914	−	1.77323i
$19$		−	32.1912i		−	1.69427i	−0.531375	−	0.847137i	$-0.678324\pi$
$19$		−	32.1912i		−	1.69427i	0.531375	−	0.847137i	$-0.321676\pi$
$20$	−39.0573	−	21.5874i	−1.95286	−	1.07937i
$21$	14.8566	+	0.721059i	0.707459	+	0.0343361i
$22$	−9.56819	+	2.56379i	−0.434918	+	0.116536i
$23$	0.179412	+	0.669573i	0.00780050	+	0.0291119i	0.969716	−	0.244234i	$-0.0785364\pi$
$23$	0.179412	+	0.669573i	0.00780050	+	0.0291119i	−0.961916	+	0.273346i	$0.911870\pi$
$24$	44.6624	+	28.7594i	1.86093	+	1.19831i
$25$	24.9826	−	0.933581i	0.999302	−	0.0373432i
$26$	−34.0763			−1.31063
$27$	−16.1223	−	21.6581i	−0.597122	−	0.802150i
$28$	−31.2906	+	31.2906i	−1.11752	+	1.11752i
$29$	−30.1349	+	17.3984i	−1.03913	+	0.599944i	−0.919588	−	0.392884i	$-0.871477\pi$
$29$	−30.1349	+	17.3984i	−1.03913	+	0.599944i	−0.119546	+	0.992829i	$0.538144\pi$
$30$	−53.9035	−	1.60790i	−1.79678	−	0.0535968i
$31$	12.8482	−	22.2537i	0.414457	−	0.717860i	−0.580914	−	0.813965i	$-0.697305\pi$
$31$	12.8482	−	22.2537i	0.414457	−	0.717860i	0.995371	+	0.0961042i	$0.0306382\pi$
$32$	−28.6765	+	7.68384i	−0.896140	+	0.240120i
$33$	−6.12132	+	5.55463i	−0.185494	+	0.168322i
$34$	−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	$0.830127\pi$
$38$	111.789	+	29.9538i	2.94182	+	0.788259i
$39$	−25.2858	+	13.0070i	−0.648353	+	0.333514i
$40$	61.4236	−	63.7618i	1.53559	−	1.59405i
$41$	20.2139	−	35.0116i	0.493023	−	0.853941i	−0.506945	−	0.861979i	$-0.669225\pi$
$41$	20.2139	−	35.0116i	0.493023	−	0.853941i	0.999968	+	0.00803768i	$0.00255850\pi$
$42$	−16.3280	+	50.9211i	−0.388763	+	1.21241i
$43$	3.68527	+	0.987466i	0.0857040	+	0.0229643i	0.301416	−	0.953493i	$-0.402541\pi$
$43$	3.68527	+	0.987466i	0.0857040	+	0.0229643i	−0.215712	+	0.976457i	$0.569207\pi$
$44$		−	24.5915i		−	0.558899i
$45$	−40.6120	+	19.3821i	−0.902489	+	0.430712i
$46$	−2.49214			−0.0541770
$47$	0.993231	−	3.70679i	0.0211326	−	0.0788679i	−0.954554	−	0.298037i	$-0.903668\pi$
$47$	0.993231	−	3.70679i	0.0211326	−	0.0788679i	0.975687	+	0.219169i	$0.0703347\pi$
$48$	−62.1147	+	56.3644i	−1.29406	+	1.17426i
$49$	21.1465	+	12.2089i	0.431561	+	0.249162i
$50$	−20.0042	+	87.6247i	−0.400084	+	1.75249i
$51$	−21.0745	+	32.7281i	−0.413226	+	0.641727i
$52$	21.8952	−	81.7139i	0.421061	−	1.57142i
$53$	−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
$57$	94.3850	−	20.4436i	1.65588	−	0.358659i
$58$	−32.3783	−	120.837i	−0.558247	−	2.08340i
$59$	−36.8611	−	21.2818i	−0.624765	−	0.360708i	0.153957	−	0.988078i	$-0.450798\pi$
$59$	−36.8611	−	21.2818i	−0.624765	−	0.360708i	−0.778722	+	0.627369i	$0.784132\pi$
$60$	38.4905	−	128.226i	0.641509	−	2.13710i
$61$	−6.56994	−	11.3795i	−0.107704	−	0.186549i	0.807136	−	0.590366i	$-0.201017\pi$
$61$	−6.56994	−	11.3795i	−0.107704	−	0.186549i	−0.914840	+	0.403817i	$0.867683\pi$
$62$	65.3243	+	65.3243i	1.05362	+	1.05362i
$63$	7.32081	+	44.0177i	0.116203	+	0.698694i
$64$			5.10100i			0.0797032i
$65$	13.1186	+	45.5399i	0.201825	+	0.700614i
$66$	−13.5935	−	26.4259i	−0.205962	−	0.400392i
$67$	−44.9977	+	12.0571i	−0.671607	+	0.179957i	−0.578479	−	0.815697i	$-0.696353\pi$
$67$	−44.9977	+	12.0571i	−0.671607	+	0.179957i	−0.0931285	+	0.995654i	$0.529687\pi$
$68$	−29.9735	−	111.863i	−0.440787	−	1.64504i
$69$	−1.84926	+	0.951261i	−0.0268008	+	0.0137864i
$70$	78.0031	+	43.1133i	1.11433	+	0.615904i
$71$	−114.062			−1.60651			−0.803254	−	0.595637i	$-0.796900\pi$
$71$	−114.062			−1.60651			−0.803254	+	0.595637i	$0.796900\pi$
$72$	−55.9592	+	149.215i	−0.777212	+	2.07243i
$73$	−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
$75$	18.6029	+	72.6563i	0.248038	+	0.968750i
$76$	−143.657	+	248.821i	−1.89022	+	3.27396i
$77$	13.1953	−	3.53568i	0.171368	−	0.0459179i
$78$	−21.6407	−	99.9120i	−0.277445	−	1.28092i
$79$	−18.3057	+	10.5688i	−0.231717	+	0.133782i	−0.611364	−	0.791350i	$-0.709379\pi$
$79$	−18.3057	+	10.5688i	−0.231717	+	0.133782i	0.379647	+	0.925132i	$0.376046\pi$
$80$	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
$83$	−14.7688	−	3.95730i	−0.177938	−	0.0476783i	0.168750	−	0.985659i	$-0.446027\pi$
$83$	−14.7688	−	3.95730i	−0.177938	−	0.0476783i	−0.346688	+	0.937981i	$0.612694\pi$
$84$	−111.616	−	71.8727i	−1.32876	−	0.855628i
$85$	46.7239	+	45.0105i	0.549693	+	0.529535i
$86$	−6.85828	+	11.8789i	−0.0797474	+	0.138127i
$87$	−70.1499	−	77.3067i	−0.806321	−	0.888582i
$88$	47.1254	+	12.6272i	0.535516	+	0.143491i
$89$		−	92.4405i		−	1.03866i	−0.854575	−	0.519329i	$-0.826182\pi$
$89$		−	92.4405i		−	1.03866i	0.854575	−	0.519329i	$-0.173818\pi$
$90$	−29.5180	−	159.067i	−0.327978	−	1.76741i
$91$	46.9941			0.516418
$92$	1.60129	−	5.97609i	0.0174053	−	0.0649574i
$93$	73.4075	+	23.5384i	0.789328	+	0.253101i
$94$	11.9482	+	6.89832i	0.127109	+	0.0733864i
$95$	−3.00583	−	160.928i	−0.0316404	−	1.69398i
$96$	−40.7406	−	79.2000i	−0.424382	−	0.825000i
$97$	−40.7091	+	151.928i	−0.419681	+	1.56627i	0.355590	+	0.934642i	$0.384280\pi$
$97$	−40.7091	+	151.928i	−0.419681	+	1.56627i	−0.775271	+	0.631629i	$0.782387\pi$
$98$	−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	0.994766	−	0.102178i	$-0.0325813\pi$
$101$	41.2983	+	71.5307i	0.408894	+	0.708225i	−0.585872	+	0.810404i	$0.699248\pi$
$102$	−94.0438	−	103.638i	−0.921998	−	1.01606i
$103$	−12.9609	−	48.3706i	−0.125834	−	0.469617i	0.874034	−	0.485864i	$-0.161495\pi$
$103$	−12.9609	−	48.3706i	−0.125834	−	0.469617i	−0.999868	+	0.0162466i	$0.994828\pi$
$104$	145.348	+	83.9166i	1.39757	+	0.806890i
$105$	74.3375	+	2.21744i	0.707976	+	0.0211184i
$106$	−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	$0.873996\pi$
$108$	27.9654	+	239.353i	0.258939	+	2.21623i
$109$		−	145.852i		−	1.33809i	−0.743220	−	0.669047i	$-0.766702\pi$
$109$		−	145.852i		−	1.33809i	0.743220	−	0.669047i	$-0.233298\pi$
$110$	−47.5932	+	13.7101i	−0.432665	+	0.124638i
$111$	29.9362	−	46.4900i	0.269696	−	0.418829i
$112$	133.897	−	35.8775i	1.19551	−	0.320335i
$113$	14.0319	+	52.3679i	0.124176	+	0.463432i	0.999809	−	0.0195453i	$-0.00622185\pi$
$113$	14.0319	+	52.3679i	0.124176	+	0.463432i	−0.875633	+	0.482978i	$0.839555\pi$
$114$	−16.8313	+	346.790i	−0.147643	+	3.04202i
$115$	0.959422	+	3.33053i	0.00834280	+	0.0289611i
$116$	310.569			2.67732
$117$	−54.1950	−	65.8778i	−0.463205	−	0.563058i
$118$	108.204	−	108.204i	0.916980	−	0.916980i
$119$	55.7139	−	32.1664i	0.468184	−	0.270306i
$120$	225.959	+	139.602i	1.88299	+	1.16335i
$121$	56.7042	−	98.2145i	0.468630	−	0.811690i
$122$	45.6304	−	12.2266i	0.374019	−	0.100218i
$123$	115.492	+	37.0328i	0.938956	+	0.301080i
$124$	−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	$0.659451\pi$
$128$	−132.420	−	35.4818i	−1.03453	−	0.277202i
$129$	−0.554864	+	11.4324i	−0.00430127	+	0.0886230i
$130$	−170.352	+	3.18185i	−1.31040	+	0.0244758i
$131$	−89.6936	+	155.354i	−0.684684	+	1.18591i	0.288852	+	0.957374i	$0.406726\pi$
$131$	−89.6936	+	155.354i	−0.684684	+	1.18591i	−0.973536	+	0.228534i	$0.926607\pi$
$132$	72.1027	−	15.6173i	0.546232	−	0.118313i
$133$	−154.167	−	41.3089i	−1.15915	−	0.310593i
$134$		−	167.481i		−	1.24986i
$135$	−82.6198	−	106.766i	−0.611998	−	0.790859i
$136$	229.756			1.68938
$137$	−36.5154	+	136.277i	−0.266536	+	0.994725i	0.694768	+	0.719234i	$0.255507\pi$
$137$	−36.5154	+	136.277i	−0.266536	+	0.994725i	−0.961304	+	0.275491i	$0.911160\pi$
$138$	−1.58268	−	7.30699i	−0.0114687	−	0.0529492i
$139$	236.063	+	136.291i	1.69829	+	0.980510i	0.947381	+	0.320108i	$0.103719\pi$
$139$	236.063	+	136.291i	1.69829	+	0.980510i	0.750912	+	0.660402i	$0.229614\pi$
$140$	−153.504	+	159.347i	−1.09646	+	1.13820i
$141$	11.4991	+	0.558104i	0.0815540	+	0.00395818i
$142$	106.134	−	396.099i	0.747426	−	2.78943i
$143$	−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
$147$	−22.3673	+	69.7552i	−0.152158	+	0.474525i
$148$	42.5772	+	158.900i	0.287684	+	1.07365i
$149$	174.004	+	100.461i	1.16781	+	0.674235i	0.953163	−	0.302457i	$-0.0978070\pi$
$149$	174.004	+	100.461i	1.16781	+	0.674235i	0.214646	+	0.976692i	$0.431140\pi$
$150$	−269.621	−	3.00491i	−1.79747	−	0.0200327i
$151$	58.6560	+	101.595i	0.388450	+	0.672816i	0.992241	−	0.124327i	$-0.0396771\pi$
$151$	58.6560	+	101.595i	0.388450	+	0.672816i	−0.603791	+	0.797143i	$0.706344\pi$
$152$	−403.057	−	403.057i	−2.65169	−	2.65169i
$153$	−109.343	−	41.0063i	−0.714659	−	0.268015i
$154$			49.1129i			0.318915i
$155$	62.1517	−	112.449i	0.400979	−	0.725475i
$156$	253.491	+	12.3030i	1.62494	+	0.0788657i
$157$	−205.058	+	54.9450i	−1.30610	+	0.349968i	−0.843753	−	0.536731i	$-0.819659\pi$
$157$	−205.058	+	54.9450i	−1.30610	+	0.349968i	−0.462346	+	0.886700i	$0.652992\pi$
$158$	−19.6684	−	73.4036i	−0.124484	−	0.464580i
$159$	−111.378	−	71.7197i	−0.700493	−	0.451067i
$160$	−142.640	+	41.0902i	−0.891500	+	0.256814i
$161$	3.43688			0.0213471
$162$	162.359	+	241.748i	1.00221	+	1.49227i
$163$	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
$165$	−30.0826	+	28.3399i	−0.182319	+	0.171757i
$166$	27.4847	−	47.6049i	0.165571	−	0.286777i
$167$	234.945	−	62.9533i	1.40686	−	0.376966i	0.526054	−	0.850451i	$-0.323671\pi$
$167$	234.945	−	62.9533i	1.40686	−	0.376966i	0.880802	+	0.473486i	$0.157004\pi$
$168$	195.044	−	176.988i	1.16098	−	1.05350i
$169$	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
$173$	−16.3284	−	4.37517i	−0.0943835	−	0.0252900i	0.211318	−	0.977417i	$-0.432224\pi$
$173$	−16.3284	−	4.37517i	−0.0943835	−	0.0252900i	−0.305702	+	0.952127i	$0.598891\pi$
$174$	333.734	−	171.673i	1.91801	−	0.986629i
$175$	27.5875	−	120.842i	0.157643	−	0.690525i
$176$	−38.5171	+	66.7135i	−0.218847	+	0.379054i
$177$	38.9891	−	121.593i	0.220277	−	0.686964i
$178$	321.015	+	86.0157i	1.80345	+	0.483234i
$179$			274.512i			1.53359i	0.641895	+	0.766793i	$0.278149\pi$
$179$			274.512i			1.53359i	−0.641895	+	0.766793i	$0.721851\pi$
$180$	400.404	+	31.4226i	2.22447	+	0.174570i
$181$	−261.649			−1.44557			−0.722787	−	0.691070i	$-0.757139\pi$
$181$	−261.649			−1.44557			−0.722787	+	0.691070i	$0.757139\pi$
$182$	−43.7279	+	163.195i	−0.240263	+	0.896674i
$183$	29.1924	−	26.4899i	0.159521	−	0.144753i
$184$	10.6299	+	6.13718i	0.0577712	+	0.0333542i
$185$	−66.3709	−	63.9370i	−0.358762	−	0.345606i
$186$	−150.046	+	233.017i	−0.806701	+	1.25278i
$187$	−9.25307	+	34.5329i	−0.0494817	+	0.184668i
$188$	−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	0.529291	−	0.848440i	$-0.322458\pi$
$191$	−89.7939	−	155.528i	−0.470125	−	0.814280i	−0.999416	+	0.0341597i	$0.989125\pi$
$192$	−14.9562	+	3.23948i	−0.0778968	+	0.0168723i
$193$	6.95596	+	25.9600i	0.0360412	+	0.134508i	0.981602	−	0.190937i	$-0.0611526\pi$
$193$	6.95596	+	25.9600i	0.0360412	+	0.134508i	−0.945561	+	0.325445i	$0.894486\pi$
$194$	−489.716	−	282.738i	−2.52431	−	1.45741i
$195$	−125.192	+	67.3849i	−0.642012	+	0.345564i
$196$	−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	$0.610044\pi$
$198$	68.8481	−	56.6385i	0.347718	−	0.286053i
$199$		−	23.9129i		−	0.120166i	−0.998193	−	0.0600828i	$-0.980864\pi$
$199$		−	23.9129i		−	0.120166i	0.998193	−	0.0600828i	$-0.0191365\pi$
$200$	301.111	−	324.489i	1.50555	−	1.62244i
$201$	−63.9281	−	124.277i	−0.318050	−	0.618292i
$202$	−286.830	+	76.8559i	−1.41995	+	0.380475i
$203$	44.6524	+	166.645i	0.219963	+	0.820912i
$204$	308.948	−	158.923i	1.51445	−	0.779035i
$205$	97.7829	−	176.915i	0.476990	−	0.862999i
$206$	180.035			0.873956
$207$	−3.96351	−	4.81793i	−0.0191474	−	0.0232750i
$208$	−187.385	+	187.385i	−0.900889	+	0.900889i
$209$	76.8130	−	44.3480i	0.367526	−	0.212191i
$210$	−76.8713	+	256.086i	−0.366054	+	1.21946i
$211$	68.1081	−	117.967i	0.322787	−	0.559084i	−0.658275	−	0.752778i	$-0.728713\pi$
$211$	68.1081	−	117.967i	0.322787	−	0.559084i	0.981062	+	0.193694i	$0.0620468\pi$
$212$	380.685	−	102.004i	1.79568	−	0.481152i
$213$	−72.4371	−	334.431i	−0.340080	−	1.57010i
$214$	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
$218$	506.496	+	135.715i	2.32338	+	0.622547i
$219$	−67.0548	−	43.1785i	−0.306186	−	0.197162i
$220$	−2.29622	−	122.936i	−0.0104374	−	0.558801i
$221$	−61.4931	+	106.509i	−0.278249	+	0.481942i
$222$	133.588	+	147.217i	0.601750	+	0.663141i
$223$	−387.566	−	103.848i	−1.73796	−	0.465686i	−0.755970	−	0.654606i	$-0.772834\pi$
$223$	−387.566	−	103.848i	−1.73796	−	0.465686i	−0.981992	+	0.188921i	$0.939501\pi$
$224$			147.195i			0.657119i
$225$	−201.215	+	100.685i	−0.894288	+	0.447491i
$226$	−194.913			−0.862445
$227$	48.9929	−	182.844i	0.215828	−	0.805480i	−0.770046	−	0.637988i	$-0.779767\pi$
$227$	48.9929	−	182.844i	0.215828	−	0.805480i	0.985874	−	0.167491i	$-0.0535666\pi$
$228$	−820.777	−	263.185i	−3.59990	−	1.15432i
$229$	−128.197	−	74.0143i	−0.559810	−	0.323207i	0.193259	−	0.981148i	$-0.438094\pi$
$229$	−128.197	−	74.0143i	−0.559810	−	0.323207i	−0.753069	+	0.657941i	$0.771428\pi$
$230$	−12.4585	+	0.232702i	−0.0541676	+	0.00101175i
$231$	18.7466	+	36.4435i	0.0811541	+	0.157764i
$232$	−159.470	+	595.151i	−0.687372	+	2.56531i
$233$	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
$237$	−42.6131	−	46.9605i	−0.179802	−	0.198146i
$238$	59.8616	+	223.406i	0.251519	+	0.938682i
$239$	−113.709	−	65.6499i	−0.475770	−	0.274686i	0.242882	−	0.970056i	$-0.421907\pi$
$239$	−113.709	−	65.6499i	−0.475770	−	0.274686i	−0.718652	+	0.695370i	$0.755240\pi$
$240$	−305.256	+	287.573i	−1.27190	+	1.19822i
$241$	106.787	+	184.961i	0.443101	+	0.767473i	0.997918	−	0.0644993i	$-0.0205450\pi$
$241$	106.787	+	184.961i	0.443101	+	0.767473i	−0.554817	+	0.831972i	$0.687212\pi$
$242$	288.303	+	288.303i	1.19133	+	1.19133i
$243$	212.752	+	117.412i	0.875522	+	0.483178i
$244$			117.276i			0.480640i
$245$	106.854	+	59.0594i	0.436139	+	0.241059i
$246$	−236.067	+	366.604i	−0.959622	+	1.49026i
$247$	294.723	−	78.9708i	1.19321	−	0.319720i
$248$	−117.764	−	439.501i	−0.474854	−	1.77218i
$249$	2.22363	−	45.8155i	0.00893025	−	0.183998i
$250$	−91.8216	+	439.915i	−0.367287	+	1.75966i
$251$	48.4611			0.193072			0.0965360	−	0.995329i	$-0.469224\pi$
$251$	48.4611			0.193072			0.0965360	+	0.995329i	$0.469224\pi$
$252$	139.848	−	372.903i	0.554952	−	1.47978i
$253$	−1.35054	+	1.35054i	−0.00533809	+	0.00533809i
$254$	−221.943	+	128.139i	−0.873792	+	0.504484i
$255$	−102.298	+	165.580i	−0.401170	+	0.649332i
$256$	236.231	−	409.164i	0.922777	−	1.59830i
$257$	−450.204	+	120.632i	−1.75177	+	0.469385i	−0.985002	−	0.172542i	$-0.944802\pi$
$257$	−450.204	+	120.632i	−1.75177	+	0.469385i	−0.766766	+	0.641927i	$0.778135\pi$
$258$	−39.1845	−	12.5646i	−0.151878	−	0.0487002i
$259$	−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
$263$	−104.698	−	28.0536i	−0.398090	−	0.106668i	0.0542194	−	0.998529i	$-0.482733\pi$
$263$	−104.698	−	28.0536i	−0.398090	−	0.106668i	−0.452309	+	0.891861i	$0.649400\pi$
$264$	−7.09532	+	146.191i	−0.0268762	+	0.553755i
$265$	−153.177	+	159.008i	−0.578027	+	0.600031i
$266$	286.904	−	496.932i	1.07859	−	1.86816i
$267$	271.037	−	58.7060i	1.01512	−	0.219873i
$268$	401.614	+	107.612i	1.49856	+	0.401538i
$269$			271.965i			1.01102i	0.862821	+	0.505510i	$0.168696\pi$
$269$			271.965i			1.01102i	−0.862821	+	0.505510i	$0.831304\pi$
$270$	447.640	−	187.565i	1.65793	−	0.694686i
$271$	283.330			1.04550			0.522749	−	0.852487i	$-0.324907\pi$
$271$	283.330			1.04550			0.522749	+	0.852487i	$0.324907\pi$
$272$	−93.8935	+	350.415i	−0.345197	+	1.28829i
$273$	29.8444	+	137.787i	0.109320	+	0.504715i
$274$	−439.268	−	253.611i	−1.60317	−	0.925589i
$275$	36.6447	+	58.3260i	0.133254	+	0.212094i
$276$	18.5389	+	0.899774i	0.0671698	+	0.00326005i
$277$	−38.5154	+	143.741i	−0.139045	+	0.518922i	0.860904	+	0.508768i	$0.169899\pi$
$277$	−38.5154	+	143.741i	−0.139045	+	0.518922i	−0.999948	+	0.0101539i	$0.996768\pi$
$278$	−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	0.549080	−	0.835770i	$-0.314978\pi$
$281$	−126.241	−	218.657i	−0.449258	−	0.778137i	−0.998338	+	0.0576326i	$0.981645\pi$
$282$	−12.6380	+	39.4133i	−0.0448156	+	0.139763i
$283$	124.137	+	463.286i	0.438647	+	1.63705i	0.732184	+	0.681107i	$0.238501\pi$
$283$	124.137	+	463.286i	0.438647	+	1.63705i	−0.293537	+	0.955948i	$0.594832\pi$
$284$	881.639	+	509.015i	3.10436	+	1.79230i
$285$	469.934	−	111.013i	1.64889	−	0.389520i
$286$	−46.9450	−	81.3111i	−0.164143	−	0.284304i
$287$	−141.735	−	141.735i	−0.493849	−	0.493849i
$288$	206.342	−	169.749i	0.716467	−	0.589407i
$289$		−	120.637i		−	0.417430i
$290$	−173.146	−	601.059i	−0.597056	−	2.07262i
$291$	−471.308	−	22.8747i	−1.61962	−	0.0786072i
$292$	229.189	−	61.4111i	0.784895	−	0.210312i
$293$	−52.5299	−	196.044i	−0.179283	−	0.669093i	−0.995782	−	0.0917468i	$-0.970755\pi$
$293$	−52.5299	−	196.044i	−0.179283	−	0.669093i	0.816499	−	0.577346i	$-0.195912\pi$
$294$	−221.424	−	142.581i	−0.753142	−	0.484969i
$295$	−186.261	−	102.948i	−0.631392	−	0.348978i
$296$	−326.367			−1.10259
$297$	29.4685	−	68.3073i	0.0992207	−	0.229991i
$298$	−510.777	+	510.777i	−1.71402	+	1.71402i
$299$	−5.69008	+	3.28517i	−0.0190304	+	0.0109872i
$300$	180.446	−	644.612i	0.601487	−	2.14871i
$301$	9.45814	−	16.3820i	0.0314224	−	0.0544252i
$302$	−407.385	+	109.159i	−1.34896	+	0.361452i
$303$	−183.502	+	166.514i	−0.605616	+	0.549551i
$304$	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	$0.432578\pi$
$308$	−117.771	−	31.5567i	−0.382374	−	0.102457i
$309$	133.592	−	68.7200i	0.432337	−	0.222395i
$310$	332.664	+	320.465i	1.07311	+	1.03376i
$311$	−102.480	+	177.501i	−0.329518	+	0.570743i	−0.982416	−	0.186703i	$-0.940220\pi$
$311$	−102.480	+	177.501i	−0.329518	+	0.570743i	0.652898	+	0.757446i	$0.273553\pi$
$312$	−153.739	+	479.454i	−0.492752	+	1.53671i
$313$	343.429	+	92.0214i	1.09722	+	0.293998i	0.761631	−	0.648011i	$-0.224399\pi$
$313$	343.429	+	92.0214i	1.09722	+	0.293998i	0.335586	+	0.942010i	$0.391066\pi$
$314$		−	763.222i		−	2.43064i
$315$	40.7078	+	219.367i	0.129231	+	0.696402i
$316$	188.657			0.597017
$317$	−6.68768	+	24.9588i	−0.0210968	+	0.0787343i	−0.975672	−	0.219237i	$-0.929643\pi$
$317$	−6.68768	+	24.9588i	−0.0210968	+	0.0787343i	0.954575	+	0.297971i	$0.0963099\pi$
$318$	352.696	−	320.045i	1.10911	−	1.00643i
$319$	−83.0303	−	47.9375i	−0.260283	−	0.150274i
$320$	0.476303	+	25.5006i	0.00148845	+	0.0796893i
$321$	131.998	−	204.989i	0.411209	−	0.638595i
$322$	−3.19801	+	11.9351i	−0.00993169	+	0.0370656i
$323$	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
$327$	427.640	−	92.6260i	1.30777	−	0.283260i
$328$	−185.277	−	691.464i	−0.564869	−	2.10812i
$329$	−16.4776	−	9.51337i	−0.0500840	−	0.0289160i
$330$	−70.4231	−	130.837i	−0.213403	−	0.396476i
$331$	96.8582	+	167.763i	0.292623	+	0.506838i	0.974429	−	0.224695i	$-0.0721386\pi$
$331$	96.8582	+	167.763i	0.292623	+	0.506838i	−0.681806	+	0.731533i	$0.738805\pi$
$332$	96.4953	+	96.4953i	0.290649	+	0.290649i
$333$	155.321	+	58.2491i	0.466428	+	0.174922i
$334$			874.462i			2.61815i
$335$	−223.823	+	64.4766i	−0.668129	+	0.192467i
$336$	190.227	+	369.802i	0.566151	+	1.10060i
$337$	88.6729	−	23.7598i	0.263124	−	0.0705039i	−0.124845	−	0.992176i	$-0.539843\pi$
$337$	88.6729	−	23.7598i	0.263124	−	0.0705039i	0.387969	+	0.921672i	$0.373177\pi$
$338$	73.6588	+	274.898i	0.217925	+	0.813309i
$339$	−144.632	+	74.3989i	−0.426643	+	0.219466i
$340$	−160.287	−	556.418i	−0.471431	−	1.63652i
$341$	70.8008			0.207627
$342$	−1027.48	+	170.886i	−3.00433	+	0.499665i
$343$	257.393	−	257.393i	0.750417	−	0.750417i
$344$	58.5061	−	33.7785i	0.170076	−	0.0981933i
$345$	−9.15585	+	4.92815i	−0.0265387	+	0.0142845i
$346$	30.3870	−	52.6318i	0.0878236	−	0.152115i
$347$	5.84253	−	1.56550i	0.0168372	−	0.00451153i	−0.250391	−	0.968145i	$-0.580559\pi$
$347$	5.84253	−	1.56550i	0.0168372	−	0.00451153i	0.267228	+	0.963633i	$0.413892\pi$
$348$	197.232	+	910.591i	0.566759	+	2.61664i
$349$	67.8704	−	39.1850i	0.194471	−	0.112278i	−0.399603	−	0.916688i	$-0.630852\pi$
$349$	67.8704	−	39.1850i	0.194471	−	0.112278i	0.594074	+	0.804410i	$0.297519\pi$
$350$	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
$353$	38.2322	+	10.2443i	0.108307	+	0.0290207i	0.312565	−	0.949896i	$-0.398812\pi$
$353$	38.2322	+	10.2443i	0.108307	+	0.0290207i	−0.204259	+	0.978917i	$0.565478\pi$
$354$	385.971	+	248.538i	1.09031	+	0.702084i
$355$	−570.211	+	10.6505i	−1.60623	+	0.0300013i
$356$	−412.526	+	714.516i	−1.15878	+	2.00707i
$357$	129.694	+	142.926i	0.363290	+	0.400353i
$358$	−953.287	−	255.433i	−2.66281	−	0.713499i
$359$		−	116.601i		−	0.324795i	−0.986725	−	0.162398i	$-0.948077\pi$
$359$		−	116.601i		−	0.324795i	0.986725	−	0.162398i	$-0.0519227\pi$
$360$	−265.815	+	751.169i	−0.738374	+	2.08658i
$361$	−675.274			−1.87056
$362$	243.464	−	908.619i	0.672552	−	2.51000i
$363$	323.977	+	103.884i	0.892499	+	0.286183i
$364$	−363.239	−	209.716i	−0.997910	−	0.576144i
$365$	−92.2195	+	95.7300i	−0.252656	+	0.262274i
$366$	64.8269	+	126.024i	0.177123	+	0.344328i
$367$	112.479	−	419.779i	0.306483	−	1.14381i	−0.625177	−	0.780483i	$-0.714973\pi$
$367$	112.479	−	419.779i	0.306483	−	1.14381i	0.931661	−	0.363329i	$-0.118360\pi$
$368$	−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
$372$	−462.358	−	509.528i	−1.24290	−	1.36970i
$373$	−167.428	−	624.849i	−0.448868	−	1.67520i	−0.705516	−	0.708694i	$-0.749285\pi$
$373$	−167.428	−	624.849i	−0.448868	−	1.67520i	0.256647	−	0.966505i	$-0.417382\pi$
$374$	−111.311	−	64.2656i	−0.297624	−	0.171833i
$375$	99.7824	+	361.481i	0.266086	+	0.963949i
$376$	−33.9757	−	58.8477i	−0.0903610	−	0.156510i
$377$	−233.215	−	233.215i	−0.618608	−	0.618608i
$378$	−55.8510	−	478.023i	−0.147754	−	1.26461i
$379$		−	297.836i		−	0.785846i	−0.919571	−	0.392923i	$-0.871464\pi$
$379$		−	297.836i		−	0.785846i	0.919571	−	0.392923i	$-0.128536\pi$
$380$	−694.925	+	1257.30i	−1.82875	+	3.30869i
$381$	−115.778	+	179.800i	−0.303880	+	0.471916i
$382$	623.648	−	167.106i	1.63259	−	0.437450i
$383$	−111.047	−	414.434i	−0.289941	−	1.08207i	−0.945153	−	0.326629i	$-0.894087\pi$
$383$	−111.047	−	414.434i	−0.289941	−	1.08207i	0.655212	−	0.755445i	$-0.272579\pi$
$384$	19.9375	−	410.790i	0.0519206	−	1.06977i
$385$	65.6351	−	18.9074i	0.170481	−	0.0491102i
$386$	−96.6228			−0.250318
$387$	−33.8722	+	5.63346i	−0.0875251	+	0.0145567i
$388$	992.656	−	992.656i	2.55839	−	2.55839i
$389$	−197.682	+	114.132i	−0.508181	+	0.293398i	−0.732086	−	0.681213i	$-0.761453\pi$
$389$	−197.682	+	114.132i	−0.508181	+	0.293398i	0.223905	+	0.974611i	$0.428120\pi$
$390$	−117.514	−	497.452i	−0.301318	−	1.27552i
$391$	−4.49725	+	7.78947i	−0.0115019	+	0.0199219i
$392$	417.634	−	111.905i	1.06539	−	0.285471i
$393$	−512.461	−	164.322i	−1.30397	−	0.418123i
$394$	−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	$0.681128\pi$
$398$	83.0416	+	22.2509i	0.208647	+	0.0559069i
$399$	23.2117	−	478.253i	0.0581748	−	1.19863i
$400$	371.844	+	591.850i	0.929610	+	1.47962i
$401$	226.669	−	392.602i	0.565259	−	0.979057i	−0.431766	−	0.901985i	$-0.642110\pi$
$401$	226.669	−	392.602i	0.565259	−	0.979057i	0.997026	−	0.0770720i	$-0.0245571\pi$
$402$	491.056	−	106.362i	1.22153	−	0.264581i
$403$	235.260	+	63.0377i	0.583772	+	0.156421i
$404$		−	737.193i		−	1.82473i
$405$	260.570	−	310.046i	0.643382	−	0.765545i
$406$	−620.251			−1.52771
$407$	13.1439	−	49.0538i	0.0322946	−	0.120525i
$408$	145.911	+	673.648i	0.357624	+	1.65110i
$409$	427.158	+	246.620i	1.04440	+	0.602982i	0.921075	−	0.389385i	$-0.127312\pi$
$409$	427.158	+	246.620i	1.04440	+	0.602982i	0.123320	+	0.992367i	$0.460646\pi$
$410$	523.379	+	504.186i	1.27653	+	1.22972i
$411$	−422.756	−	20.5183i	−1.02860	−	0.0499228i
$412$	−115.679	+	431.718i	−0.280773	+	1.04786i
$413$	−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
$417$	−249.691	+	778.693i	−0.598778	+	1.86737i
$418$	82.5314	+	308.011i	0.197444	+	0.736870i
$419$	−22.7963	−	13.1615i	−0.0544066	−	0.0314116i	0.472550	−	0.881304i	$-0.343334\pi$
$419$	−22.7963	−	13.1615i	−0.0544066	−	0.0314116i	−0.526957	+	0.849892i	$0.676667\pi$
$420$	−564.694	−	348.879i	−1.34451	−	0.830664i
$421$	243.419	+	421.613i	0.578192	+	1.00146i	0.995687	+	0.0927780i	$0.0295747\pi$
$421$	243.419	+	421.613i	0.578192	+	1.00146i	−0.417495	+	0.908679i	$0.637092\pi$
$422$	346.284	+	346.284i	0.820579	+	0.820579i
$423$	5.66635	+	34.0700i	0.0133956	+	0.0805437i
$424$			781.894i			1.84409i
$425$	237.782	+	220.650i	0.559486	+	0.519177i
$426$	1228.77	+	59.6377i	2.88444	+	0.139995i
$427$	−62.9281	+	16.8615i	−0.147373	+	0.0394884i
$428$	187.736	+	700.641i	0.438636	+	1.63701i
$429$	−65.8715	−	42.4166i	−0.153547	−	0.0988731i
$430$	−33.1762	+	60.0244i	−0.0771540	+	0.139592i
$431$	73.2818			0.170027			0.0850137	−	0.996380i	$-0.472907\pi$
$431$	73.2818			0.170027			0.0850137	+	0.996380i	$0.472907\pi$
$432$	299.025	−	693.133i	0.692189	−	1.60447i
$433$	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
$435$	−357.907	−	379.916i	−0.822775	−	0.873369i
$436$	−650.882	+	1127.36i	−1.49285	+	2.58569i
$437$	21.5544	−	5.77547i	0.0493235	−	0.0132162i
$438$	212.339	−	192.681i	0.484791	−	0.439911i
$439$	−97.4363	+	56.2549i	−0.221951	+	0.128143i	−0.606853	−	0.794814i	$-0.707568\pi$
$439$	−97.4363	+	56.2549i	−0.221951	+	0.128143i	0.384903	+	0.922957i	$0.374235\pi$
$440$	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
$443$	−154.045	−	41.2762i	−0.347731	−	0.0931742i	0.0807263	−	0.996736i	$-0.474276\pi$
$443$	−154.045	−	41.2762i	−0.347731	−	0.0931742i	−0.428457	+	0.903562i	$0.640943\pi$
$444$	−438.858	+	225.749i	−0.988418	+	0.508444i
$445$	−8.63158	−	462.122i	−0.0193968	−	1.03848i
$446$	721.258	−	1249.25i	1.61717	−	2.80102i
$447$	−184.049	+	573.980i	−0.411742	+	1.28407i
$448$	24.4292	+	6.54578i	0.0545295	+	0.0146111i
$449$			291.806i			0.649901i	0.945731	+	0.324951i	$0.105348\pi$
$449$			291.806i			0.649901i	−0.945731	+	0.324951i	$0.894652\pi$
$450$	−162.417	−	792.439i	−0.360926	−	1.76098i
$451$	111.390			0.246985
$452$	125.238	−	467.395i	0.277075	−	1.03406i
$453$	−260.628	+	236.500i	−0.575337	+	0.522075i
$454$	589.367	+	340.271i	1.29817	+	0.749497i
$455$	234.929	−	4.38804i	0.516328	−	0.00964405i
$456$	925.800	−	1437.74i	2.03026	−	3.15293i
$457$	121.316	−	452.757i	0.265462	−	0.990716i	−0.696506	−	0.717551i	$-0.745263\pi$
$457$	121.316	−	452.757i	0.265462	−	0.990716i	0.961967	−	0.273165i	$-0.0880705\pi$
$458$	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	−0.998924	−	0.0463832i	$-0.985230\pi$
$461$	−248.770	−	430.882i	−0.539631	−	0.934668i	0.459293	−	0.888285i	$-0.348103\pi$
$462$	−144.000	+	31.1900i	−0.311688	+	0.0675109i
$463$	235.850	+	880.204i	0.509395	+	1.90109i	0.426391	+	0.904539i	$0.359785\pi$
$463$	235.850	+	880.204i	0.509395	+	1.90109i	0.0830044	+	0.996549i	$0.473548\pi$
$464$	−842.531	−	486.435i	−1.81580	−	1.04835i
$465$	369.171	+	110.817i	0.793917	+	0.238316i
$466$	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	$0.850404\pi$
$468$	124.911	+	751.052i	0.266904	+	1.60481i
$469$			230.970i			0.492474i
$470$	60.3749	+	33.3699i	0.128457	+	0.0709998i
$471$	−291.325	−	566.337i	−0.618524	−	1.20241i
$472$	−727.991	+	195.065i	−1.54235	+	0.413273i
$473$	2.72075	+	10.1540i	0.00575212	+	0.0214672i
$474$	202.729	−	104.284i	0.427699	−	0.220009i
$475$	−30.0531	−	804.219i	−0.0632697	−	1.69309i
$476$	−574.185			−1.20627
$477$	139.550	−	372.109i	0.292558	−	0.780104i
$478$	333.786	−	333.786i	0.698297	−	0.698297i
$479$	−177.082	+	102.238i	−0.369691	+	0.213441i	−0.673324	−	0.739348i	$-0.735134\pi$
$479$	−177.082	+	102.238i	−0.369691	+	0.213441i	0.303632	+	0.952789i	$0.401801\pi$
$480$	−211.063	−	392.127i	−0.439714	−	0.816931i
$481$	87.3504	−	151.295i	0.181602	−	0.314543i
$482$	−741.673	+	198.731i	−1.53874	+	0.412304i
$483$	2.18265	+	10.0770i	0.00451894	+	0.0208633i
$484$	−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	$-0.513118\pi$
$488$	−224.740	−	60.2188i	−0.460532	−	0.123399i
$489$	218.143	+	140.469i	0.446100	+	0.287257i
$490$	−304.521	+	316.113i	−0.621471	+	0.645129i
$491$	−104.633	+	181.229i	−0.213101	+	0.369102i	−0.952684	−	0.303964i	$-0.901690\pi$
$491$	−104.633	+	181.229i	−0.213101	+	0.369102i	0.739582	+	0.673066i	$0.235023\pi$
$492$	−727.425	−	801.637i	−1.47851	−	1.62934i
$493$	−436.120	−	116.858i	−0.884624	−	0.237034i
$494$			1096.96i			2.22056i
$495$	−102.197	−	70.2048i	−0.206459	−	0.141828i
$496$	718.435			1.44846
$497$	−146.368	+	546.254i	−0.294504	+	1.09910i
$498$	157.033	+	50.3532i	0.315327	+	0.101111i
$499$	−287.007	−	165.704i	−0.575165	−	0.332072i	0.184044	−	0.982918i	$-0.441081\pi$
$499$	−287.007	−	165.704i	−0.575165	−	0.332072i	−0.759210	+	0.650846i	$0.774414\pi$
$500$	−995.905	−	502.846i	−1.99181	−	1.00569i
$501$	333.786	+	648.881i	0.666239	+	1.29517i
$502$	−45.0929	+	168.289i	−0.0898265	+	0.335237i
$503$	−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
$507$	159.587	+	175.868i	0.314768	+	0.346880i
$508$	−164.667	−	614.546i	−0.324148	−	1.20974i
$509$	679.279	+	392.182i	1.33454	+	0.770495i	0.985991	−	0.166797i	$-0.0533423\pi$
$509$	679.279	+	392.182i	1.33454	+	0.770495i	0.348546	+	0.937292i	$0.386676\pi$
$510$	−479.814	−	509.319i	−0.940812	−	0.998666i
$511$	65.9040	+	114.149i	0.128971	+	0.223384i
$512$	813.324	+	813.324i	1.58852	+	1.58852i
$513$	−697.199	+	518.996i	−1.35906	+	1.01169i
$514$		−	1675.66i		−	3.26003i
$515$	−69.3096	−	240.601i	−0.134582	−	0.467186i
$516$	55.3070	−	85.8900i	0.107184	−	0.166453i
$517$	10.2133	−	2.73664i	0.0197549	−	0.00529330i
$518$	−85.0329	−	317.347i	−0.164156	−	0.612639i
$519$	2.45844	−	50.6534i	0.00473687	−	0.0975981i
$520$	734.448	+	405.938i	1.41240	+	0.780650i
$521$	763.749			1.46593			0.732964	−	0.680267i	$-0.238136\pi$
$521$	763.749			1.46593			0.732964	+	0.680267i	$0.238136\pi$
$522$	715.292	+	869.489i	1.37029	+	1.66569i
$523$	−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
$525$	371.830	+	4.14403i	0.708247	+	0.00789338i
$526$	194.842	−	337.476i	0.370421	−	0.641589i
$527$	322.061	−	86.2959i	0.611121	−	0.163749i
$528$	−220.066	−	70.5649i	−0.416791	−	0.133646i
$529$	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
$533$	370.133	+	99.1769i	0.694434	+	0.186073i
$534$	−48.3328	+	995.845i	−0.0905109	+	1.86488i
$535$	−292.650	−	281.918i	−0.547010	−	0.526950i
$536$	−412.440	+	714.367i	−0.769478	+	1.33277i
$537$	−804.872	+	174.334i	−1.49883	+	0.324643i
$538$	−944.442	−	253.062i	−1.75547	−	0.470376i
$539$			67.2782i			0.124820i
$540$	162.152	+	1193.94i	0.300281	+	2.21101i
$541$	120.576			0.222876			0.111438	−	0.993771i	$-0.464454\pi$
$541$	120.576			0.222876			0.111438	+	0.993771i	$0.464454\pi$
$542$	−263.638	+	983.909i	−0.486416	+	1.81533i
$543$	−166.165	−	767.158i	−0.306013	−	1.41281i
$544$	−333.608	−	192.608i	−0.613249	−	0.354060i
$545$	−13.6189	−	729.134i	−0.0249887	−	1.33786i
$546$	−506.259	−	24.5710i	−0.927214	−	0.0450018i
$547$	59.6213	−	222.510i	0.108997	−	0.406782i	−0.889771	−	0.456407i	$-0.849136\pi$
$547$	59.6213	−	222.510i	0.108997	−	0.406782i	0.998768	+	0.0496252i	$0.0158027\pi$
$548$	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
$552$	−11.2436	+	35.0645i	−0.0203688	+	0.0635227i
$553$	27.1244	+	101.230i	0.0490496	+	0.183056i
$554$	−463.327	−	267.502i	−0.836330	−	0.482855i
$555$	145.314	−	235.205i	0.261827	−	0.423792i
$556$	−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	$-0.569492\pi$
$558$	−778.498	−	291.956i	−1.39516	−	0.523219i
$559$			36.1626i			0.0646915i
$560$	666.017	−	191.859i	1.18932	−	0.342605i
$561$	−107.127	−	5.19937i	−0.190958	−	0.00926803i
$562$	876.788	−	234.935i	1.56012	−	0.418033i
$563$	71.6752	+	267.496i	0.127309	+	0.475125i	0.999911	−	0.0133066i	$-0.00423574\pi$
$563$	71.6752	+	267.496i	0.127309	+	0.475125i	−0.872602	+	0.488432i	$0.837569\pi$
$564$	−86.3915	−	55.6299i	−0.153176	−	0.0986346i
$565$	75.0372	+	260.483i	0.132809	+	0.461033i
$566$	−1724.35			−3.04655
$567$	−223.906	−	333.391i	−0.394897	−	0.587991i
$568$	−1428.14	+	1428.14i	−2.51433	+	2.51433i
$569$	830.591	−	479.542i	1.45974	−	0.842780i	0.460740	−	0.887535i	$-0.347584\pi$
$569$	830.591	−	479.542i	1.45974	−	0.842780i	0.998998	+	0.0447548i	$0.0142506\pi$
$570$	−51.7604	+	1735.22i	−0.0908077	+	3.04424i
$571$	−222.371	+	385.158i	−0.389442	+	0.674533i	−0.992375	−	0.123259i	$-0.960665\pi$
$571$	−222.371	+	385.158i	−0.389442	+	0.674533i	0.602933	+	0.797792i	$0.293999\pi$
$572$	225.145	−	60.3275i	0.393611	−	0.105468i
$573$	398.983	−	362.047i	0.696306	−	0.631845i
$574$	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	$0.443115\pi$
$578$	418.933	+	112.253i	0.724797	+	0.194209i
$579$	−71.6975	+	36.8813i	−0.123830	+	0.0636983i
$580$	1552.57	−	28.9992i	2.67685	−	0.0499986i
$581$	−37.9038	+	65.6513i	−0.0652388	+	0.112997i
$582$	517.987	−	1615.41i	0.890013	−	2.77562i
$583$	−117.521	−	31.4895i	−0.201579	−	0.0540129i
$584$			470.735i			0.806053i
$585$	−277.079	−	324.271i	−0.473639	−	0.554310i
$586$	729.675			1.24518
$587$	−116.613	+	435.207i	−0.198660	+	0.741410i	0.792629	+	0.609704i	$0.208712\pi$
$587$	−116.613	+	435.207i	−0.198660	+	0.741410i	−0.991289	+	0.131705i	$0.957955\pi$
$588$	484.177	−	439.354i	0.823431	−	0.747201i
$589$	−716.373	−	413.598i	−1.21625	−	0.702204i
$590$	530.820	−	551.027i	0.899696	−	0.933945i
$591$	−272.389	+	423.011i	−0.460895	+	0.715755i
$592$	133.375	−	497.762i	0.225295	−	0.840814i
$593$	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
$597$	70.1130	−	15.1863i	0.117442	−	0.0254377i
$598$	−6.11368	−	22.8166i	−0.0102235	−	0.0381548i
$599$	−434.899	−	251.089i	−0.726042	−	0.419180i	0.0909308	−	0.995857i	$-0.471016\pi$
$599$	−434.899	−	251.089i	−0.726042	−	0.419180i	−0.816972	+	0.576677i	$0.804349\pi$
$600$	1142.63	+	676.788i	1.90438	+	1.12798i
$601$	−99.8075	−	172.872i	−0.166069	−	0.287640i	0.770965	−	0.636877i	$-0.219774\pi$
$601$	−99.8075	−	172.872i	−0.166069	−	0.287640i	−0.937034	+	0.349237i	$0.886441\pi$
$602$	48.0883	+	48.0883i	0.0798810	+	0.0798810i
$603$	323.782	−	266.362i	0.536952	−	0.441728i
$604$		−	1047.04i		−	1.73350i
$605$	274.301	−	496.282i	0.453390	−	0.820301i
$606$	−407.499	−	792.180i	−0.672440	−	1.30723i
$607$	−837.927	+	224.522i	−1.38044	+	0.369888i	−0.871281	−	0.490785i	$-0.836710\pi$
$607$	−837.927	+	224.522i	−1.38044	+	0.369888i	−0.509159	+	0.860672i	$0.670043\pi$
$608$	247.352	+	923.131i	0.406829	+	1.51831i
$609$	−460.248	+	236.752i	−0.755744	+	0.388756i
$610$	226.970	−	65.3831i	0.372083	−	0.107185i
$611$	36.3737			0.0595314
$612$	662.167	+	804.911i	1.08197	+	1.31521i
$613$	−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
$615$	580.815	+	174.348i	0.944415	+	0.283492i
$616$	120.946	−	209.485i	0.196341	−	0.340072i
$617$	253.302	−	67.8722i	0.410539	−	0.110004i	−0.0476380	−	0.998865i	$-0.515169\pi$
$617$	253.302	−	67.8722i	0.410539	−	0.110004i	0.458177	+	0.888861i	$0.348503\pi$
$618$	114.334	+	527.864i	0.185007	+	0.854149i
$619$	−422.528	+	243.947i	−0.682598	+	0.394098i	−0.800833	−	0.598887i	$-0.795610\pi$
$619$	−422.528	+	243.947i	−0.682598	+	0.394098i	0.118235	+	0.992986i	$0.462276\pi$
$620$	−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
$623$	−442.707	−	118.623i	−0.710605	−	0.190406i
$624$	−668.417	−	430.412i	−1.07118	−	0.689764i
$625$	623.257	−	46.6465i	0.997211	−	0.0746344i
$626$	−639.119	+	1106.99i	−1.02096	+	1.76835i
$627$	178.810	+	197.053i	0.285184	+	0.314278i
$628$	1830.18	+	490.396i	2.91431	+	0.780886i
$629$		−	239.158i		−	0.380219i
$630$	−799.665	−	62.7556i	−1.26931	−	0.0996121i
$631$	263.490			0.417576			0.208788	−	0.977961i	$-0.433048\pi$
$631$	263.490			0.417576			0.208788	+	0.977961i	$0.433048\pi$
$632$	−96.8714	+	361.529i	−0.153277	+	0.572039i
$633$	389.133	+	124.777i	0.614744	+	0.197120i
$634$	−80.4505	−	46.4481i	−0.126894	−	0.0732620i
$635$	256.690	+	247.276i	0.404236	+	0.389412i
$636$	540.838	+	1051.39i	0.850375	+	1.65313i
$637$	−59.9014	+	223.555i	−0.0940367	+	0.350950i
$638$	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	−0.962387	−	0.271682i	$-0.912420\pi$
$641$	−459.262	−	795.464i	−0.716477	−	1.24097i	0.245911	−	0.969293i	$-0.420913\pi$
$642$	589.034	+	649.127i	0.917498	+	1.01110i
$643$	10.9456	+	40.8497i	0.0170228	+	0.0635298i	0.973915	−	0.226914i	$-0.0728637\pi$
$643$	10.9456	+	40.8497i	0.0170228	+	0.0635298i	−0.956892	+	0.290444i	$0.906197\pi$
$644$	−26.5652	−	15.3374i	−0.0412504	−	0.0238159i
$645$	−1.70635	+	57.2037i	−0.00264550	+	0.0886879i
$646$	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	$0.754374\pi$
$648$	−97.1884	−	1430.97i	−0.149982	−	2.20829i
$649$		−	117.275i		−	0.180701i
$650$	−851.313	+	31.8130i	−1.30971	+	0.0489430i
$651$	206.927	−	321.350i	0.317860	−	0.493626i
$652$	−745.601	+	199.783i	−1.14356	+	0.306416i
$653$	137.591	+	513.495i	0.210705	+	0.786363i	0.987634	+	0.156775i	$0.0501096\pi$
$653$	137.591	+	513.495i	0.210705	+	0.786363i	−0.776929	+	0.629588i	$0.783224\pi$
$654$	−76.2593	+	1571.24i	−0.116604	+	2.40251i
$655$	−433.884	+	785.009i	−0.662418	+	1.19849i
$656$	1130.31			1.72303
$657$	84.0155	−	224.027i	0.127877	−	0.340984i
$658$	48.3691	−	48.3691i	0.0735093	−	0.0735093i
$659$	−64.8393	+	37.4350i	−0.0983905	+	0.0568058i	−0.548388	−	0.836224i	$-0.684758\pi$
$659$	−64.8393	+	37.4350i	−0.0983905	+	0.0568058i	0.449997	+	0.893030i	$0.351425\pi$
$660$	358.992	−	84.8054i	0.543928	−	0.128493i
$661$	11.3687	−	19.6912i	0.0171993	−	0.0297900i	−0.857298	−	0.514821i	$-0.827858\pi$
$661$	11.3687	−	19.6912i	0.0171993	−	0.0297900i	0.874497	+	0.485031i	$0.161192\pi$
$662$	−672.712	+	180.253i	−1.01618	+	0.272285i
$663$	−351.338	−	112.658i	−0.529922	−	0.169921i
$664$	−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
$668$	−2096.93	−	561.872i	−3.13912	−	0.841125i
$669$	58.3528	−	1202.30i	0.0872240	−	1.79716i
$670$	−15.6384	−	837.259i	−0.0233409	−	1.24964i
$671$	18.1021	−	31.3537i	0.0269777	−	0.0467268i
$672$	−431.577	+	93.4786i	−0.642227	+	0.139105i
$673$	619.582	+	166.017i	0.920628	+	0.246681i	0.687854	−	0.725849i	$-0.258553\pi$
$673$	619.582	+	166.017i	0.920628	+	0.246681i	0.232774	+	0.972531i	$0.425220\pi$
$674$			330.040i			0.489673i
$675$	−422.996	−	526.022i	−0.626661	−	0.779292i
$676$	−706.526			−1.04516
$677$	−150.613	+	562.095i	−0.222471	+	0.830273i	0.760931	+	0.648833i	$0.224742\pi$
$677$	−150.613	+	562.095i	−0.222471	+	0.830273i	−0.983402	+	0.181440i	$0.941924\pi$
$678$	−123.783	−	571.486i	−0.182570	−	0.842900i
$679$	675.360	+	389.919i	0.994639	+	0.574255i
$680$	1148.58	−	21.4534i	1.68909	−	0.0315490i
$681$	567.214	+	27.5294i	0.832913	+	0.0404250i
$682$	−65.8799	+	245.867i	−0.0965982	+	0.360509i
$683$	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
$687$	135.597	−	422.878i	0.197376	−	0.615543i
$688$	27.6082	+	103.035i	0.0401282	+	0.149761i
$689$	−362.466	−	209.270i	−0.526075	−	0.303730i
$690$	−8.59430	−	36.3808i	−0.0124555	−	0.0527258i
$691$	−348.543	−	603.695i	−0.504404	−	0.873654i	−0.999987	−	0.00509303i	$-0.998379\pi$
$691$	−348.543	−	603.695i	−0.504404	−	0.873654i	0.495583	−	0.868561i	$-0.334955\pi$
$692$	106.685	+	106.685i	0.154169	+	0.154169i
$693$	−94.9474	+	78.1093i	−0.137009	+	0.112712i
$694$			21.7458i			0.0313340i
$695$	1192.83	+	659.293i	1.71631	+	0.948624i
$696$	−1846.26	−	89.6074i	−2.65268	−	0.128746i
$697$	506.696	−	135.769i	0.726967	−	0.194790i
$698$	72.9231	+	272.153i	0.104474	+	0.389904i
$699$	684.413	+	440.713i	0.979131	+	0.630491i
$700$	−752.507	+	810.932i	−1.07501	+	1.15847i
$701$	−643.602			−0.918119			−0.459060	−	0.888405i	$-0.651814\pi$
$701$	−643.602			−0.918119			−0.459060	+	0.888405i	$0.651814\pi$
$702$	549.388	+	738.026i	0.782604	+	1.05132i
$703$	−419.550	+	419.550i	−0.596800	+	0.596800i
$704$	−12.1718	+	7.02736i	−0.0172894	+	0.00998205i
$705$	57.5377	+	1.71631i	0.0816137	+	0.00243448i
$706$	−71.1500	+	123.235i	−0.100779	+	0.174554i
$707$	395.563	−	105.991i	0.559495	−	0.149916i
$708$	−843.985	+	765.853i	−1.19207	+	1.08171i
$709$	−1069.69	+	617.583i	−1.50872	+	0.871062i	−0.508775	+	0.860899i	$0.669902\pi$
$709$	−1069.69	+	617.583i	−1.50872	+	0.871062i	−0.999948	+	0.0101629i	$0.996765\pi$
$710$	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
$713$	17.2056	+	4.61022i	0.0241312	+	0.00646594i
$714$	−617.014	+	317.393i	−0.864165	+	0.444528i
$715$	−90.5922	+	94.0408i	−0.126702	+	0.131526i
$716$	1225.04	−	2121.83i	1.71095	−	2.96345i
$717$	120.273	−	375.088i	0.167745	−	0.523135i
$718$	404.918	+	108.497i	0.563952	+	0.151110i
$719$		−	219.618i		−	0.305449i	−0.988269	−	0.152724i	$-0.951195\pi$
$719$		−	219.618i		−	0.305449i	0.988269	−	0.152724i	$-0.0488047\pi$
$720$	−1037.02	−	712.387i	−1.44031	−	0.989426i
$721$	−248.283			−0.344360
$722$	628.340	−	2345.00i	0.870278	−	3.24792i
$723$	−474.491	+	430.564i	−0.656280	+	0.595525i
$724$	2022.41	+	1167.64i	2.79338	+	1.61276i
$725$	−736.604	+	462.789i	−1.01601	+	0.638330i
$726$	−662.216	+	1028.40i	−0.912143	+	1.41653i
$727$	73.8261	−	275.523i	0.101549	−	0.378986i	−0.896382	−	0.443283i	$-0.853814\pi$
$727$	73.8261	−	275.523i	0.101549	−	0.378986i	0.997931	+	0.0642969i	$0.0204805\pi$
$728$	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
$732$	−343.855	+	74.4783i	−0.469748	+	0.101746i
$733$	−181.709	−	678.149i	−0.247898	−	0.925169i	−0.971905	−	0.235375i	$-0.924368\pi$
$733$	−181.709	−	678.149i	−0.247898	−	0.925169i	0.724006	−	0.689793i	$-0.242299\pi$
$734$	1353.09	+	781.206i	1.84345	+	1.06431i
$735$	−105.303	+	350.804i	−0.143270	+	0.477284i
$736$	−10.2898	−	17.8224i	−0.0139807	−	0.0242153i
$737$	−90.7608	−	90.7608i	−0.123149	−	0.123149i
$738$	−1224.81	−	459.333i	−1.65963	−	0.622402i
$739$			1147.21i			1.55238i	0.630497	+	0.776192i	$0.282851\pi$
$739$			1147.21i			1.55238i	−0.630497	+	0.776192i	$0.717149\pi$
$740$	227.686	+	790.387i	0.307684	+	1.06809i
$741$	418.712	+	813.980i	0.565064	+	1.09849i
$742$	−760.284	+	203.717i	−1.02464	+	0.274552i
$743$	226.953	+	847.001i	0.305455	+	1.13997i	0.932553	+	0.361034i	$0.117576\pi$
$743$	226.953	+	847.001i	0.305455	+	1.13997i	−0.627098	+	0.778941i	$0.715757\pi$
$744$	1213.83	−	624.397i	1.63150	−	0.839244i
$745$	879.246	+	485.970i	1.18020	+	0.652308i
$746$	2325.68			3.11754
$747$	135.744	−	22.5762i	0.181719	−	0.0302225i
$748$	225.628	−	225.628i	0.301642	−	0.301642i
$749$	−348.958	+	201.471i	−0.465899	+	0.268987i
$750$	−1348.15	+	10.1537i	−1.79753	+	0.0135383i
$751$	147.537	−	255.542i	0.196455	−	0.340269i	−0.750922	−	0.660391i	$-0.770391\pi$
$751$	147.537	−	255.542i	0.196455	−	0.340269i	0.947376	+	0.320122i	$0.103724\pi$
$752$	103.637	−	27.7694i	0.137815	−	0.0369274i
$753$	30.7761	+	142.088i	0.0408713	+	0.188696i
$754$	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	$0.723313\pi$
$758$	1034.28	+	277.135i	1.36449	+	0.365614i
$759$	−4.81747	−	3.10210i	−0.00634712	−	0.00408709i
$760$	−2052.57	−	1977.30i	−2.70075	−	2.60171i
$761$	80.6635	−	139.713i	0.105997	−	0.183592i	−0.808148	−	0.588979i	$-0.799530\pi$
$761$	80.6635	−	139.713i	0.105997	−	0.183592i	0.914145	+	0.405387i	$0.132863\pi$
$762$	−516.654	−	569.363i	−0.678023	−	0.747195i
$763$	−698.501	−	187.163i	−0.915466	−	0.245298i
$764$			1602.86i			2.09798i
$765$	−550.448	−	194.786i	−0.719540	−	0.254622i
$766$	1542.52			2.01373
$767$	104.416	−	389.686i	0.136136	−	0.508065i
$768$	1349.70	+	432.785i	1.75742	+	0.563522i
$769$	−129.486	−	74.7588i	−0.168382	−	0.0972156i	0.413440	−	0.910531i	$-0.364327\pi$
$769$	−129.486	−	74.7588i	−0.168382	−	0.0972156i	−0.581823	+	0.813316i	$0.697660\pi$
$770$	4.58589	+	245.522i	0.00595570	+	0.318859i
$771$	−639.604	−	1243.40i	−0.829578	−	1.61270i
$772$	62.0835	−	231.699i	0.0804190	−	0.300128i
$773$	−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
$777$	−184.230	−	203.025i	−0.237104	−	0.261294i
$778$	−212.399	−	792.684i	−0.273006	−	1.01887i
$779$	−1127.06	−	650.711i	−1.44681	−	0.835316i
$780$	1268.38	+	37.8350i	1.62613	+	0.0485064i
$781$	−157.137	−	272.169i	−0.201200	−	0.348488i
$782$	−22.8655	−	22.8655i	−0.0292398	−	0.0292398i
$783$	862.659	+	372.161i	1.10174	+	0.475301i
$784$			682.690i			0.870778i
$785$	−1019.98	+	293.824i	−1.29934	+	0.374298i
$786$	1047.48	−	1626.70i	1.33267	−	2.06960i
$787$	−887.757	+	237.874i	−1.12803	+	0.302254i	−0.774128	−	0.633030i	$-0.781811\pi$
$787$	−887.757	+	237.874i	−1.12803	+	0.302254i	−0.353899	+	0.935284i	$0.615144\pi$
$788$	−387.409	−	1445.83i	−0.491635	−	1.83481i
$789$	15.7635	−	324.790i	0.0199791	−	0.411648i
$790$	−105.179	−	365.118i	−0.133138	−	0.462174i
$791$	268.801			0.339824
$792$	−433.141	+	72.0378i	−0.546895	+	0.0909569i
$793$	88.0662	−	88.0662i	0.111055	−	0.111055i
$794$	−530.725	+	306.414i	−0.668420	+	0.385912i
$795$	−563.492	−	348.136i	−0.708794	−	0.437907i
$796$	−106.714	+	184.834i	−0.134063	+	0.232204i
$797$	860.450	−	230.557i	1.07961	−	0.289281i	0.325175	−	0.945654i	$-0.394577\pi$
$797$	860.450	−	230.557i	1.07961	−	0.289281i	0.754437	+	0.656373i	$0.227910\pi$
$798$	1639.21	+	525.620i	2.05415	+	0.658671i
$799$	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
$803$	−70.7526	−	18.9581i	−0.0881104	−	0.0236091i
$804$	−60.4680	+	1245.88i	−0.0752090	+	1.54960i
$805$	17.1814	−	0.320916i	0.0213433	−	0.000398654i
$806$	−437.818	+	758.323i	−0.543198	+	0.940847i
$807$	−797.403	+	172.716i	−0.988108	+	0.214022i
$808$	1412.70	+	378.532i	1.74839	+	0.468480i
$809$		−	1398.60i		−	1.72880i	−0.502802	−	0.864402i	$-0.667698\pi$
$809$		−	1398.60i		−	1.72880i	0.502802	−	0.864402i	$-0.332302\pi$
$810$	834.225	+	1193.37i	1.02991	+	1.47329i
$811$	−347.451			−0.428423			−0.214211	−	0.976787i	$-0.568718\pi$
$811$	−347.451			−0.428423			−0.214211	+	0.976787i	$0.568718\pi$
$812$	398.533	−	1487.34i	0.490804	−	1.83170i
$813$	179.934	+	830.726i	0.221321	+	1.02180i
$814$	158.117	+	91.2888i	0.194247	+	0.112148i
$815$	300.009	−	311.430i	0.368109	−	0.382122i
$816$	−1087.05	−	52.7594i	−1.33217	−	0.0646561i
$817$	31.7877	−	118.633i	0.0389079	−	0.145206i
$818$	−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	−0.992693	−	0.120665i	$-0.961497\pi$
$821$	−493.294	−	854.410i	−0.600845	−	1.04069i	0.391848	−	0.920030i	$-0.371836\pi$
$822$	464.627	−	1449.00i	0.565239	−	1.76277i
$823$	65.3381	+	243.845i	0.0793902	+	0.296288i	0.994193	−	0.107613i	$-0.0343207\pi$
$823$	65.3381	+	243.845i	0.0793902	+	0.296288i	−0.914803	+	0.403901i	$0.867654\pi$
$824$	−767.914	−	443.356i	−0.931935	−	0.538053i
$825$	−147.741	+	144.484i	−0.179079	+	0.175132i
$826$	−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	$0.392410\pi$
$828$	9.13529	+	54.9276i	0.0110330	+	0.0663377i
$829$		−	819.644i		−	0.988714i	−0.869259	−	0.494357i	$-0.835404\pi$
$829$		−	819.644i		−	0.988714i	0.869259	−	0.494357i	$-0.164596\pi$
$830$	132.955	−	240.550i	0.160186	−	0.289819i
$831$	−445.911	−	21.6420i	−0.536596	−	0.0260434i
$832$	−46.7017	+	12.5137i	−0.0561318	+	0.0150405i
$833$	82.0024	+	306.037i	0.0984423	+	0.367392i
$834$	−2471.80	−	1591.66i	−2.96379	−	1.90847i
$835$	1168.64	−	336.649i	1.39957	−	0.403173i
$836$	−791.631			−0.946928
$837$	−689.113	+	80.5143i	−0.823313	+	0.0961939i
$838$	66.9173	−	66.9173i	0.0798536	−	0.0798536i
$839$	425.345	−	245.573i	0.506966	−	0.292697i	−0.224619	−	0.974447i	$-0.572114\pi$
$839$	425.345	−	245.573i	0.506966	−	0.292697i	0.731586	+	0.681749i	$0.238781\pi$
$840$	958.524	−	902.996i	1.14110	−	1.07499i
$841$	184.907	−	320.269i	0.219866	−	0.380819i
$842$	−1690.62	+	453.001i	−2.00786	+	0.538006i
$843$	560.932	−	509.003i	0.665399	−	0.603799i
$844$	−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
$848$	−1192.51	−	319.533i	−1.40627	−	0.376808i
$849$	−1279.53	+	658.190i	−1.50710	+	0.775253i
$850$	−987.500	+	620.421i	−1.16176	+	0.729907i
$851$	6.38831	−	11.0649i	0.00750682	−	0.0130022i
$852$	−932.536	+	2908.23i	−1.09453	+	3.41342i
$853$	336.484	+	90.1607i	0.394472	+	0.105698i	0.450602	−	0.892725i	$-0.351209\pi$
$853$	336.484	+	90.1607i	0.394472	+	0.105698i	−0.0561301	+	0.998423i	$0.517876\pi$
$854$		−	234.218i		−	0.274260i
$855$	623.932	+	1307.35i	0.729745	+	1.52906i
$856$	−1439.05			−1.68114
$857$	210.885	−	787.034i	0.246074	−	0.918359i	−0.726767	−	0.686884i	$-0.758978\pi$
$857$	210.885	−	787.034i	0.246074	−	0.918359i	0.972841	−	0.231475i	$-0.0743552\pi$
$858$	208.592	−	189.281i	0.243114	−	0.220607i
$859$	101.706	+	58.7201i	0.118401	+	0.0683587i	0.558031	−	0.829820i	$-0.311557\pi$
$859$	101.706	+	58.7201i	0.118401	+	0.0683587i	−0.439630	+	0.898179i	$0.644890\pi$
$860$	−122.620	−	118.123i	−0.142581	−	0.137353i
$861$	325.556	−	505.579i	0.378114	−	0.587199i
$862$	−68.1886	+	254.483i	−0.0791051	+	0.295224i
$863$	−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
$867$	353.710	−	76.6128i	0.407970	−	0.0883654i
$868$	294.304	+	1098.36i	0.339060	+	1.26539i
$869$	−50.4374	−	29.1200i	−0.0580407	−	0.0335098i
$870$	1652.35	−	889.380i	1.89925	−	1.02228i
$871$	−220.775	−	382.393i	−0.253473	−	0.439028i
$872$	−1826.18	−	1826.18i	−2.09424	−	2.09424i
$873$	−232.244	−	1396.41i	−0.266030	−	1.59955i
$874$			80.2251i			0.0917907i
$875$	126.630	−	606.680i	0.144720	−	0.693349i
$876$	325.609	+	632.986i	0.371700	+	0.722587i
$877$	480.790	−	128.827i	0.548221	−	0.146895i	0.0259318	−	0.999664i	$-0.491745\pi$
$877$	480.790	−	128.827i	0.548221	−	0.146895i	0.522289	+	0.852768i	$0.325078\pi$
$878$	−104.690	−	390.709i	−0.119237	−	0.444998i
$879$	541.444	−	278.520i	0.615977	−	0.316860i
$880$	−186.322	+	337.106i	−0.211730	+	0.383075i
$881$	306.447			0.347840			0.173920	−	0.984760i	$-0.444357\pi$
$881$	306.447			0.347840			0.173920	+	0.984760i	$0.444357\pi$
$882$	277.430	−	739.765i	0.314547	−	0.838736i
$883$	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
$885$	183.558	−	611.498i	0.207410	−	0.690958i
$886$	286.676	−	496.538i	0.323563	−	0.560427i
$887$	−130.986	+	35.0975i	−0.147673	+	0.0395688i	−0.331898	−	0.943315i	$-0.607689\pi$
$887$	−130.986	+	35.0975i	−0.147673	+	0.0395688i	0.184225	+	0.982884i	$0.441022\pi$
$888$	−207.265	−	956.911i	−0.233407	−	1.07760i
$889$	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
$893$	−119.326	−	31.9733i	−0.133624	−	0.0358044i
$894$	−1821.98	−	1173.23i	−2.03801	−	1.31233i
$895$	25.6324	+	1372.32i	0.0286395	+	1.53332i
$896$	−339.852	+	588.641i	−0.379299	+	0.656965i
$897$	−13.2457	−	14.5971i	−0.0147667	−	0.0162732i
$898$	−1013.34	−	271.524i	−1.12844	−	0.302366i
$899$			894.149i			0.994604i
$900$	2004.60	+	119.698i	2.22734	+	0.132998i
$901$	−572.962			−0.635918
$902$	−103.649	+	386.822i	−0.114910	+	0.428849i
$903$	54.0387	+	17.3277i	0.0598435	+	0.0191891i
$904$	831.374	+	479.994i	0.919661	+	0.530967i
$905$	−1308.02	+	24.4313i	−1.44532	+	0.0269959i
$906$	−578.771	−	1125.14i	−0.638820	−	1.24187i
$907$	35.1572	−	131.208i	0.0387621	−	0.144662i	−0.943833	−	0.330423i	$-0.892808\pi$
$907$	35.1572	−	131.208i	0.0387621	−	0.144662i	0.982595	+	0.185761i	$0.0594751\pi$
$908$	−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	0.993038	+	0.117795i	$0.0375826\pi$
$911$	545.263	+	944.423i	0.598532	+	1.03669i	−0.394506	+	0.918894i	$0.629084\pi$
$912$	1814.44	+	1999.55i	1.98951	+	2.19249i
$913$	−10.9035	−	40.6924i	−0.0119425	−	0.0445700i
$914$	1459.39	+	842.579i	1.59671	+	0.921859i
$915$	143.463	−	135.152i	0.156790	−	0.147707i
$916$	660.594	+	1144.18i	0.721173	+	1.24911i
$917$	628.907	+	628.907i	0.685831	+	0.685831i
$918$	1156.49	+	498.923i	1.25979	+	0.543489i
$919$		−	367.996i		−	0.400431i	−0.979752	−	0.200215i	$-0.935836\pi$
$919$		−	367.996i		−	0.400431i	0.979752	−	0.200215i	$-0.0641642\pi$
$920$	53.7133	+	29.6880i	0.0583840	+	0.0322695i
$921$	−837.650	+	1300.84i	−0.909501	+	1.41242i
$922$	1727.79	−	462.959i	1.87396	−	0.502125i
$923$	−279.815	−	1044.28i	−0.303158	−	1.13140i
$924$	17.7319	−	365.347i	0.0191904	−	0.395398i
$925$	−337.767	−	313.432i	−0.365153	−	0.338845i
$926$	−3276.11			−3.53792
$927$	286.328	+	348.052i	0.308876	+	0.375460i
$928$	730.476	−	730.476i	0.787151	−	0.787151i
$929$	62.7337	−	36.2193i	0.0675282	−	0.0389874i	−0.465856	−	0.884861i	$-0.654253\pi$
$929$	62.7337	−	36.2193i	0.0675282	−	0.0389874i	0.533384	+	0.845873i	$0.320920\pi$
$930$	−728.343	+	1178.89i	−0.783165	+	1.26763i
$931$	393.020	−	680.731i	0.422148	−	0.731182i
$932$	−2339.28	+	626.810i	−2.50996	+	0.672542i
$933$	−585.517	−	187.748i	−0.627563	−	0.201231i
$934$	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	$0.983730\pi$
$938$	−802.082	−	214.917i	−0.855099	−	0.229123i
$939$	−51.7075	+	1065.38i	−0.0550666	+	1.13459i
$940$	−118.813	+	123.336i	−0.126397	+	0.131208i
$941$	190.349	−	329.694i	0.202284	−	0.350366i	−0.746980	−	0.664846i	$-0.768497\pi$
$941$	190.349	−	329.694i	0.202284	−	0.350366i	0.949264	+	0.314480i	$0.101830\pi$
$942$	2237.78	−	484.698i	2.37556	−	0.514541i
$943$	27.0694	+	7.25323i	0.0287056	+	0.00769165i
$944$		−	1190.02i		−	1.26061i
$945$	−617.333	+	258.668i	−0.653263	+	0.273723i
$946$	−37.7930			−0.0399504
$947$	−139.605	+	521.012i	−0.147418	+	0.550172i	0.852218	+	0.523187i	$0.175257\pi$
$947$	−139.605	+	521.012i	−0.147418	+	0.550172i	−0.999636	+	0.0269844i	$0.991410\pi$
$948$	119.810	+	553.145i	0.126382	+	0.583487i
$949$	−218.221	−	125.990i	−0.229948	−	0.132761i
$950$	2820.75	+	643.959i	2.96921	+	0.677852i
$951$	−77.4265	−	3.75785i	−0.0814159	−	0.00395148i
$952$	294.831	−	1100.33i	0.309697	−	1.15580i
$953$	−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
$957$	87.8236	−	273.889i	0.0917697	−	0.286196i
$958$	−190.265	−	710.080i	−0.198607	−	0.741210i
$959$	605.788	+	349.752i	0.631687	+	0.364705i
$960$	−74.4654	+	17.5911i	−0.0775682	+	0.0183241i
$961$	150.349	+	260.413i	0.156451	+	0.270981i
$962$	444.118	+	444.118i	0.461662	+	0.461662i
$963$	684.858	+	256.838i	0.711171	+	0.266707i
$964$		−	1906.20i		−	1.97739i
$965$	37.1977	+	129.128i	0.0385469	+	0.133811i
$966$	−37.0249	−	1.79698i	−0.0383280	−	0.00186023i
$967$	278.265	−	74.5608i	0.287761	−	0.0771053i	−0.112051	−	0.993702i	$-0.535742\pi$
$967$	278.265	−	74.5608i	0.287761	−	0.0771053i	0.399812	+	0.916597i	$0.369075\pi$
$968$	−519.740	−	1939.70i	−0.536921	−	2.00382i
$969$	1053.56	+	678.415i	1.08726	+	0.700119i
$970$	−2474.55	−	1367.72i	−2.55109	−	1.41002i
$971$	−227.938			−0.234745			−0.117373	−	0.993088i	$-0.537447\pi$
$971$	−227.938			−0.234745			−0.117373	+	0.993088i	$0.537447\pi$
$972$	−1120.49	−	1856.96i	−1.15277	−	1.91046i
$973$	955.634	−	955.634i	0.982152	−	0.982152i
$974$	2230.86	−	1287.99i	2.29041	−	1.32237i
$975$	−619.560	+	348.556i	−0.635447	+	0.357493i
$976$	183.687	−	318.155i	0.188203	−	0.325978i
$977$	613.083	−	164.275i	0.627516	−	0.168142i	0.0689735	−	0.997618i	$-0.478028\pi$
$977$	613.083	−	164.275i	0.627516	−	0.168142i	0.558542	+	0.829476i	$0.311361\pi$
$978$	−690.781	+	626.832i	−0.706320	+	0.640932i
$979$	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
$983$	−1316.59	−	352.779i	−1.33936	−	0.358880i	−0.483163	−	0.875531i	$-0.660512\pi$
$983$	−1316.59	−	352.779i	−1.33936	−	0.358880i	−0.856196	+	0.516651i	$0.827179\pi$
$984$	1909.72	−	982.361i	1.94077	−	0.998334i
$985$	603.908	+	581.761i	0.613104	+	0.590621i
$986$	811.616	−	1405.76i	0.823140	−	1.42572i
$987$	17.4289	−	54.3542i	0.0176584	−	0.0550701i
$988$	−2630.47	−	704.832i	−2.66242	−	0.713393i
$989$			2.64472i			0.00267414i
$990$	338.892	−	289.572i	0.342315	−	0.292497i
$991$	1111.32			1.12141			0.560705	−	0.828016i	$-0.310530\pi$
$991$	1111.32			1.12141			0.560705	+	0.828016i	$0.310530\pi$
$992$	−197.447	+	736.881i	−0.199039	+	0.742823i
$993$	−430.373	+	390.530i	−0.433406	+	0.393283i
$994$	−1760.76	−	1016.58i	−1.77139	−	1.02271i
$995$	−2.23286	−	119.544i	−0.00224408	−	0.120145i
$996$	−221.644	+	344.206i	−0.222534	+	0.345589i
$997$	−164.802	+	615.048i	−0.165297	+	0.616898i	0.832705	+	0.553717i	$0.186791\pi$
$997$	−164.802	+	615.048i	−0.165297	+	0.616898i	−0.998002	+	0.0631810i	$0.979875\pi$
$998$	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.22.1	yes	40
3.2	odd	2		135.3.l.a.37.10		40
5.2	odd	4		225.3.o.b.193.1		40
5.3	odd	4	inner	45.3.k.a.13.10	yes	40
5.4	even	2		225.3.o.b.157.10		40
9.2	odd	6		135.3.l.a.127.1		40
9.4	even	3		405.3.g.h.82.1		20
9.5	odd	6		405.3.g.g.82.10		20
9.7	even	3	inner	45.3.k.a.7.10	✓	40
15.8	even	4		135.3.l.a.118.1		40
45.7	odd	12		225.3.o.b.43.10		40
45.13	odd	12		405.3.g.h.163.1		20
45.23	even	12		405.3.g.g.163.10		20
45.34	even	6		225.3.o.b.7.1		40
45.38	even	12		135.3.l.a.73.10		40
45.43	odd	12	inner	45.3.k.a.43.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.10	✓	40	9.7	even	3	inner
45.3.k.a.13.10	yes	40	5.3	odd	4	inner
45.3.k.a.22.1	yes	40	1.1	even	1	trivial
45.3.k.a.43.1	yes	40	45.43	odd	12	inner
135.3.l.a.37.10		40	3.2	odd	2
135.3.l.a.73.10		40	45.38	even	12
135.3.l.a.118.1		40	15.8	even	4
135.3.l.a.127.1		40	9.2	odd	6
225.3.o.b.7.1		40	45.34	even	6
225.3.o.b.43.10		40	45.7	odd	12
225.3.o.b.157.10		40	5.4	even	2
225.3.o.b.193.1		40	5.2	odd	4
405.3.g.g.82.10		20	9.5	odd	6
405.3.g.g.163.10		20	45.23	even	12
405.3.g.h.82.1		20	9.4	even	3
405.3.g.h.163.1		20	45.13	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+(-0.930497 + 3.47266i) q^{2} +(0.635068 + 2.93201i) q^{3} +(-7.72947 - 4.46261i) q^{4} +(4.99913 - 0.0933744i) q^{5} +(-10.7728 - 0.522853i) q^{6} +(1.28323 - 4.78910i) 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} +(8.17569 - 25.4969i) q^{12} +(2.45318 + 9.15539i) q^{13} +(15.4369 + 8.91249i) q^{14} +(3.44856 + 14.5982i) q^{15} +(13.9793 + 24.2129i) q^{16} +(9.17504 + 9.17504i) q^{17} +(-5.30846 - 31.9181i) q^{18} -32.1912i q^{19} +(-39.0573 - 21.5874i) q^{20} +(14.8566 + 0.721059i) q^{21} +(-9.56819 + 2.56379i) q^{22} +(0.179412 + 0.669573i) q^{23} +(44.6624 + 28.7594i) q^{24} +(24.9826 - 0.933581i) q^{25} -34.0763 q^{26} +(-16.1223 - 21.6581i) q^{27} +(-31.2906 + 31.2906i) q^{28} +(-30.1349 + 17.3984i) q^{29} +(-53.9035 - 1.60790i) q^{30} +(12.8482 - 22.2537i) q^{31} +(-28.6765 + 7.68384i) q^{32} +(-6.12132 + 5.55463i) 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} +(111.789 + 29.9538i) q^{38} +(-25.2858 + 13.0070i) q^{39} +(61.4236 - 63.7618i) q^{40} +(20.2139 - 35.0116i) q^{41} +(-16.3280 + 50.9211i) q^{42} +(3.68527 + 0.987466i) q^{43} -24.5915i q^{44} +(-40.6120 + 19.3821i) q^{45} -2.49214 q^{46} +(0.993231 - 3.70679i) q^{47} +(-62.1147 + 56.3644i) q^{48} +(21.1465 + 12.2089i) q^{49} +(-20.0042 + 87.6247i) q^{50} +(-21.0745 + 32.7281i) q^{51} +(21.8952 - 81.7139i) 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} +(94.3850 - 20.4436i) q^{57} +(-32.3783 - 120.837i) q^{58} +(-36.8611 - 21.2818i) q^{59} +(38.4905 - 128.226i) q^{60} +(-6.56994 - 11.3795i) q^{61} +(65.3243 + 65.3243i) q^{62} +(7.32081 + 44.0177i) q^{63} +5.10100i q^{64} +(13.1186 + 45.5399i) q^{65} +(-13.5935 - 26.4259i) q^{66} +(-44.9977 + 12.0571i) q^{67} +(-29.9735 - 111.863i) q^{68} +(-1.84926 + 0.951261i) q^{69} +(78.0031 + 43.1133i) q^{70} -114.062 q^{71} +(-55.9592 + 149.215i) q^{72} +(-18.7982 + 18.7982i) q^{73} +(57.3867 - 33.1322i) q^{74} +(18.6029 + 72.6563i) q^{75} +(-143.657 + 248.821i) q^{76} +(13.1953 - 3.53568i) q^{77} +(-21.6407 - 99.9120i) 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} +(-14.7688 - 3.95730i) q^{83} +(-111.616 - 71.8727i) q^{84} +(46.7239 + 45.0105i) q^{85} +(-6.85828 + 11.8789i) q^{86} +(-70.1499 - 77.3067i) q^{87} +(47.1254 + 12.6272i) q^{88} -92.4405i q^{89} +(-29.5180 - 159.067i) q^{90} +46.9941 q^{91} +(1.60129 - 5.97609i) q^{92} +(73.4075 + 23.5384i) q^{93} +(11.9482 + 6.89832i) q^{94} +(-3.00583 - 160.928i) q^{95} +(-40.7406 - 79.2000i) q^{96} +(-40.7091 + 151.928i) 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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