LMFDB - Embedded newform 45.2.j.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,2,Mod(4,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("45.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	45.j (of order $6$, degree $2$, 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:	$0.359326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	45.4
Dual form			45.2.j.a.34.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.448288 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-0.358719 - 2.20711i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(2.89778 - 1.67303i) q^{7} -1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(-0.448288 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-0.358719 - 2.20711i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(2.89778 - 1.67303i) q^{7} -1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +(0.732051 + 0.896575i) q^{10} +(-0.633975 - 1.09808i) q^{11} +(-2.89778 - 0.776457i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(3.53175 - 1.58957i) q^{15} +(-1.23205 - 2.13397i) q^{16} +5.27792i q^{17} +(0.776457 - 1.34486i) q^{18} +0.732051 q^{19} +(3.62132 + 1.37333i) q^{20} +(4.09808 + 4.09808i) q^{21} +(0.568406 + 0.328169i) q^{22} +(0.448288 + 0.258819i) q^{23} +(3.23205 - 0.866025i) q^{24} +(-4.74264 + 1.58346i) q^{25} +1.26795 q^{26} +(-3.67423 - 3.67423i) q^{27} +5.79555i q^{28} +(-0.232051 - 0.401924i) q^{29} +(-1.17183 + 1.62667i) q^{30} +(-0.366025 + 0.633975i) q^{31} +(4.45069 + 2.56961i) q^{32} +(1.55291 - 1.55291i) q^{33} +(-1.36603 - 2.36603i) q^{34} +(-4.73205 - 5.79555i) q^{35} -5.19615i q^{36} -4.24264i q^{37} +(-0.328169 + 0.189469i) q^{38} +(1.09808 - 4.09808i) q^{39} +(-4.26380 + 0.692993i) q^{40} +(-3.86603 + 6.69615i) q^{41} +(-2.89778 - 0.776457i) q^{42} +(0.568406 - 0.328169i) q^{43} +2.19615 q^{44} +(4.24264 + 5.19615i) q^{45} -0.267949 q^{46} +(-2.56961 + 1.48356i) q^{47} +(3.01790 - 3.01790i) q^{48} +(2.09808 - 3.63397i) q^{49} +(1.71624 - 1.93733i) q^{50} +(-8.83013 + 2.36603i) q^{51} +(3.67423 - 2.12132i) q^{52} +1.03528i q^{53} +(2.59808 + 0.696152i) q^{54} +(-2.19615 + 1.79315i) q^{55} +(-3.23205 - 5.59808i) q^{56} +(0.328169 + 1.22474i) q^{57} +(0.208051 + 0.120118i) q^{58} +(4.73205 - 8.19615i) q^{59} +(-0.674235 + 6.67423i) q^{60} +(3.33013 + 5.76795i) q^{61} -0.378937i q^{62} +(-5.01910 + 8.69333i) q^{63} +2.26795 q^{64} +(-1.94218 + 5.12132i) q^{65} +(-0.294229 + 1.09808i) q^{66} +(6.57201 + 3.79435i) q^{67} +(-7.91688 - 4.57081i) q^{68} +(-0.232051 + 0.866025i) q^{69} +(3.62132 + 1.37333i) q^{70} +14.1962 q^{71} +(2.89778 + 5.01910i) q^{72} -8.48528i q^{73} +(1.09808 + 1.90192i) q^{74} +(-4.77526 - 7.22474i) q^{75} +(-0.633975 + 1.09808i) q^{76} +(-3.67423 - 2.12132i) q^{77} +(0.568406 + 2.12132i) q^{78} +(3.73205 + 6.46410i) q^{79} +(-4.26795 + 3.48477i) q^{80} +(4.50000 - 7.79423i) q^{81} -4.00240i q^{82} +(6.90018 - 3.98382i) q^{83} +(-9.69615 + 2.59808i) q^{84} +(11.6489 - 1.89329i) q^{85} +(-0.169873 + 0.294229i) q^{86} +(0.568406 - 0.568406i) q^{87} +(-2.12132 + 1.22474i) q^{88} -13.3923 q^{89} +(-3.24679 - 1.23130i) q^{90} -8.19615 q^{91} +(-0.776457 + 0.448288i) q^{92} +(-1.22474 - 0.328169i) q^{93} +(0.767949 - 1.33013i) q^{94} +(-0.262601 - 1.61571i) q^{95} +(-2.30385 + 8.59808i) q^{96} +(-13.1440 + 7.58871i) q^{97} +2.17209i q^{98} +(3.29423 + 1.90192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{6}+O(q^{10}) $ 8 * q - 12 * q^6	$ 8 q - 12 q^{6} - 8 q^{10} - 12 q^{11} + 12 q^{15} + 4 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{21} + 12 q^{24} - 4 q^{25} + 24 q^{26} + 12 q^{29} - 12 q^{30} + 4 q^{31} - 4 q^{34} - 24 q^{35} - 12 q^{39} - 4 q^{40} - 24 q^{41} - 24 q^{44} - 16 q^{46} - 4 q^{49} + 24 q^{50} - 36 q^{51} + 24 q^{55} - 12 q^{56} + 24 q^{59} + 24 q^{60} - 8 q^{61} + 32 q^{64} + 60 q^{66} + 12 q^{69} + 12 q^{70} + 72 q^{71} - 12 q^{74} - 48 q^{75} - 12 q^{76} + 16 q^{79} - 48 q^{80} + 36 q^{81} - 36 q^{84} + 16 q^{85} - 36 q^{86} - 24 q^{89} - 36 q^{90} - 24 q^{91} + 20 q^{94} + 12 q^{95} - 60 q^{96} - 36 q^{99}+O(q^{100}) $ 8 * q - 12 * q^6 - 8 * q^10 - 12 * q^11 + 12 * q^15 + 4 * q^16 - 8 * q^19 + 12 * q^20 + 12 * q^21 + 12 * q^24 - 4 * q^25 + 24 * q^26 + 12 * q^29 - 12 * q^30 + 4 * q^31 - 4 * q^34 - 24 * q^35 - 12 * q^39 - 4 * q^40 - 24 * q^41 - 24 * q^44 - 16 * q^46 - 4 * q^49 + 24 * q^50 - 36 * q^51 + 24 * q^55 - 12 * q^56 + 24 * q^59 + 24 * q^60 - 8 * q^61 + 32 * q^64 + 60 * q^66 + 12 * q^69 + 12 * q^70 + 72 * q^71 - 12 * q^74 - 48 * q^75 - 12 * q^76 + 16 * q^79 - 48 * q^80 + 36 * q^81 - 36 * q^84 + 16 * q^85 - 36 * q^86 - 24 * q^89 - 36 * q^90 - 24 * q^91 + 20 * q^94 + 12 * q^95 - 60 * q^96 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.448288	+	0.258819i	−0.316987	+	0.183013i	−0.650049	−	0.759892i	$-0.725252\pi$
$2$	−0.448288	+	0.258819i	−0.316987	+	0.183013i	0.333062	+	0.942905i	$0.391918\pi$
$3$	0.448288	+	1.67303i	0.258819	+	0.965926i
$3$	0.448288	+	1.67303i	0.258819	+	0.965926i
$4$	−0.866025	+	1.50000i	−0.433013	+	0.750000i
$5$	−0.358719	−	2.20711i	−0.160424	−	0.987048i
$5$	−0.358719	−	2.20711i	−0.160424	−	0.987048i
$6$	−0.633975	−	0.633975i	−0.258819	−	0.258819i
$7$	2.89778	−	1.67303i	1.09526	−	0.632347i	0.160286	−	0.987071i	$-0.448758\pi$
$7$	2.89778	−	1.67303i	1.09526	−	0.632347i	0.934971	+	0.354724i	$0.115425\pi$
$8$		−	1.93185i		−	0.683013i
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$	0.732051	+	0.896575i	0.231495	+	0.283522i
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$	−2.89778	−	0.776457i	−0.836516	−	0.224144i
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	0.176096	−	0.984373i	$-0.443653\pi$
$13$	−2.12132	−	1.22474i	−0.588348	−	0.339683i	−0.764444	+	0.644690i	$0.776986\pi$
$14$	−0.866025	+	1.50000i	−0.231455	+	0.400892i
$15$	3.53175	−	1.58957i	0.911894	−	0.410425i
$16$	−1.23205	−	2.13397i	−0.308013	−	0.533494i
$17$			5.27792i			1.28008i	0.768340	+	0.640041i	$0.221083\pi$
$17$			5.27792i			1.28008i	−0.768340	+	0.640041i	$0.778917\pi$
$18$	0.776457	−	1.34486i	0.183013	−	0.316987i
$19$	0.732051			0.167944			0.0839720	−	0.996468i	$-0.473239\pi$
$19$	0.732051			0.167944			0.0839720	+	0.996468i	$0.473239\pi$
$20$	3.62132	+	1.37333i	0.809752	+	0.307086i
$21$	4.09808	+	4.09808i	0.894274	+	0.894274i
$22$	0.568406	+	0.328169i	0.121185	+	0.0699660i
$23$	0.448288	+	0.258819i	0.0934745	+	0.0539675i	0.546009	−	0.837780i	$-0.316147\pi$
$23$	0.448288	+	0.258819i	0.0934745	+	0.0539675i	−0.452534	+	0.891747i	$0.649480\pi$
$24$	3.23205	−	0.866025i	0.659740	−	0.176777i
$25$	−4.74264	+	1.58346i	−0.948528	+	0.316693i
$26$	1.26795			0.248665
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$			5.79555i			1.09526i
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	0.843676	−	0.536853i	$-0.180387\pi$
$29$	−0.232051	−	0.401924i	−0.0430908	−	0.0746354i	−0.886766	+	0.462218i	$0.847054\pi$
$30$	−1.17183	+	1.62667i	−0.213946	+	0.296988i
$31$	−0.366025	+	0.633975i	−0.0657401	+	0.113865i	−0.897022	−	0.441986i	$-0.854274\pi$
$31$	−0.366025	+	0.633975i	−0.0657401	+	0.113865i	0.831282	+	0.555851i	$0.187607\pi$
$32$	4.45069	+	2.56961i	0.786779	+	0.454247i
$33$	1.55291	−	1.55291i	0.270328	−	0.270328i
$34$	−1.36603	−	2.36603i	−0.234271	−	0.405770i
$35$	−4.73205	−	5.79555i	−0.799863	−	0.979628i
$36$		−	5.19615i		−	0.866025i
$37$		−	4.24264i		−	0.697486i	−0.937218	−	0.348743i	$-0.886609\pi$
$37$		−	4.24264i		−	0.697486i	0.937218	−	0.348743i	$-0.113391\pi$
$38$	−0.328169	+	0.189469i	−0.0532361	+	0.0307359i
$39$	1.09808	−	4.09808i	0.175833	−	0.656217i
$40$	−4.26380	+	0.692993i	−0.674166	+	0.109572i
$41$	−3.86603	+	6.69615i	−0.603772	+	1.04576i	0.388473	+	0.921460i	$0.373003\pi$
$41$	−3.86603	+	6.69615i	−0.603772	+	1.04576i	−0.992244	+	0.124303i	$0.960331\pi$
$42$	−2.89778	−	0.776457i	−0.447137	−	0.119810i
$43$	0.568406	−	0.328169i	0.0866811	−	0.0500454i	−0.456033	−	0.889963i	$-0.650730\pi$
$43$	0.568406	−	0.328169i	0.0866811	−	0.0500454i	0.542714	+	0.839918i	$0.317397\pi$
$44$	2.19615			0.331082
$45$	4.24264	+	5.19615i	0.632456	+	0.774597i
$46$	−0.267949			−0.0395070
$47$	−2.56961	+	1.48356i	−0.374816	+	0.216400i	−0.675560	−	0.737305i	$-0.736098\pi$
$47$	−2.56961	+	1.48356i	−0.374816	+	0.216400i	0.300744	+	0.953705i	$0.402765\pi$
$48$	3.01790	−	3.01790i	0.435596	−	0.435596i
$49$	2.09808	−	3.63397i	0.299725	−	0.519139i
$50$	1.71624	−	1.93733i	0.242713	−	0.273980i
$51$	−8.83013	+	2.36603i	−1.23647	+	0.331310i
$52$	3.67423	−	2.12132i	0.509525	−	0.294174i
$53$			1.03528i			0.142206i	0.997469	+	0.0711031i	$0.0226519\pi$
$53$			1.03528i			0.142206i	−0.997469	+	0.0711031i	$0.977348\pi$
$54$	2.59808	+	0.696152i	0.353553	+	0.0947343i
$55$	−2.19615	+	1.79315i	−0.296129	+	0.241788i
$56$	−3.23205	−	5.59808i	−0.431901	−	0.748074i
$57$	0.328169	+	1.22474i	0.0434671	+	0.162221i
$58$	0.208051	+	0.120118i	0.0273184	+	0.0157723i
$59$	4.73205	−	8.19615i	0.616061	−	1.06705i	−0.374137	−	0.927373i	$-0.622061\pi$
$59$	4.73205	−	8.19615i	0.616061	−	1.06705i	0.990197	−	0.139675i	$-0.0446057\pi$
$60$	−0.674235	+	6.67423i	−0.0870433	+	0.861640i
$61$	3.33013	+	5.76795i	0.426379	+	0.738510i	0.996548	−	0.0830172i	$-0.0264556\pi$
$61$	3.33013	+	5.76795i	0.426379	+	0.738510i	−0.570169	+	0.821527i	$0.693122\pi$
$62$		−	0.378937i		−	0.0481251i
$63$	−5.01910	+	8.69333i	−0.632347	+	1.09526i
$64$	2.26795			0.283494
$65$	−1.94218	+	5.12132i	−0.240898	+	0.635222i
$66$	−0.294229	+	1.09808i	−0.0362170	+	0.135164i
$67$	6.57201	+	3.79435i	0.802899	+	0.463554i	0.844484	−	0.535581i	$-0.179907\pi$
$67$	6.57201	+	3.79435i	0.802899	+	0.463554i	−0.0415848	+	0.999135i	$0.513241\pi$
$68$	−7.91688	−	4.57081i	−0.960062	−	0.554292i
$69$	−0.232051	+	0.866025i	−0.0279356	+	0.104257i
$70$	3.62132	+	1.37333i	0.432831	+	0.164144i
$71$	14.1962			1.68477			0.842387	−	0.538874i	$-0.181150\pi$
$71$	14.1962			1.68477			0.842387	+	0.538874i	$0.181150\pi$
$72$	2.89778	+	5.01910i	0.341506	+	0.591506i
$73$		−	8.48528i		−	0.993127i	−0.868000	−	0.496564i	$-0.834595\pi$
$73$		−	8.48528i		−	0.993127i	0.868000	−	0.496564i	$-0.165405\pi$
$74$	1.09808	+	1.90192i	0.127649	+	0.221094i
$75$	−4.77526	−	7.22474i	−0.551399	−	0.834242i
$76$	−0.633975	+	1.09808i	−0.0727219	+	0.125958i
$77$	−3.67423	−	2.12132i	−0.418718	−	0.241747i
$78$	0.568406	+	2.12132i	0.0643593	+	0.240192i
$79$	3.73205	+	6.46410i	0.419889	+	0.727268i	0.995928	−	0.0901537i	$-0.0287358\pi$
$79$	3.73205	+	6.46410i	0.419889	+	0.727268i	−0.576039	+	0.817422i	$0.695403\pi$
$80$	−4.26795	+	3.48477i	−0.477171	+	0.389609i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		−	4.00240i		−	0.441992i
$83$	6.90018	−	3.98382i	0.757393	−	0.437281i	−0.0709657	−	0.997479i	$-0.522608\pi$
$83$	6.90018	−	3.98382i	0.757393	−	0.437281i	0.828359	+	0.560198i	$0.189275\pi$
$84$	−9.69615	+	2.59808i	−1.05794	+	0.283473i
$85$	11.6489	−	1.89329i	1.26350	−	0.205356i
$86$	−0.169873	+	0.294229i	−0.0183179	+	0.0317275i
$87$	0.568406	−	0.568406i	0.0609395	−	0.0609395i
$88$	−2.12132	+	1.22474i	−0.226134	+	0.130558i
$89$	−13.3923			−1.41958			−0.709791	−	0.704413i	$-0.751211\pi$
$89$	−13.3923			−1.41958			−0.709791	+	0.704413i	$0.751211\pi$
$90$	−3.24679	−	1.23130i	−0.342241	−	0.129790i
$91$	−8.19615			−0.859190
$92$	−0.776457	+	0.448288i	−0.0809513	+	0.0467372i
$93$	−1.22474	−	0.328169i	−0.127000	−	0.0340296i
$94$	0.767949	−	1.33013i	0.0792079	−	0.137192i
$95$	−0.262601	−	1.61571i	−0.0269423	−	0.165769i
$96$	−2.30385	+	8.59808i	−0.235135	+	0.877537i
$97$	−13.1440	+	7.58871i	−1.33457	+	0.770516i	−0.985997	−	0.166764i	$-0.946668\pi$
$97$	−13.1440	+	7.58871i	−1.33457	+	0.770516i	−0.348577	+	0.937280i	$0.613335\pi$
$98$			2.17209i			0.219414i
$99$	3.29423	+	1.90192i	0.331082	+	0.191151i
$100$	1.73205	−	8.48528i	0.173205	−	0.848528i
$101$	−4.73205	−	8.19615i	−0.470857	−	0.815548i	0.528588	−	0.848879i	$-0.322722\pi$
$101$	−4.73205	−	8.19615i	−0.470857	−	0.815548i	−0.999444	+	0.0333310i	$0.989388\pi$
$102$	3.34607	−	3.34607i	0.331310	−	0.331310i
$103$	0.568406	+	0.328169i	0.0560067	+	0.0323355i	0.527742	−	0.849405i	$-0.323039\pi$
$103$	0.568406	+	0.328169i	0.0560067	+	0.0323355i	−0.471735	+	0.881740i	$0.656372\pi$
$104$	−2.36603	+	4.09808i	−0.232008	+	0.401849i
$105$	7.57483	−	10.5150i	0.739228	−	1.02615i
$106$	−0.267949	−	0.464102i	−0.0260255	−	0.0450775i
$107$		−	10.3156i		−	0.997246i	−0.866819	−	0.498623i	$-0.833839\pi$
$107$		−	10.3156i		−	0.997246i	0.866819	−	0.498623i	$-0.166161\pi$
$108$	8.69333	−	2.32937i	0.836516	−	0.224144i
$109$	−12.6603			−1.21263			−0.606316	−	0.795224i	$-0.707353\pi$
$109$	−12.6603			−1.21263			−0.606316	+	0.795224i	$0.707353\pi$
$110$	0.520407	−	1.37225i	0.0496188	−	0.130839i
$111$	7.09808	−	1.90192i	0.673720	−	0.180523i
$112$	−7.14042	−	4.12252i	−0.674706	−	0.389542i
$113$	14.9372	+	8.62398i	1.40517	+	0.811276i	0.994917	−	0.100695i	$-0.0321067\pi$
$113$	14.9372	+	8.62398i	1.40517	+	0.811276i	0.410254	+	0.911971i	$0.365440\pi$
$114$	−0.464102	−	0.464102i	−0.0434671	−	0.0434671i
$115$	0.410432	−	1.08226i	0.0382730	−	0.100921i
$116$	0.803848			0.0746354
$117$	7.34847			0.679366
$118$			4.89898i			0.450988i
$119$	8.83013	+	15.2942i	0.809456	+	1.40202i
$120$	−3.07081	−	6.82282i	−0.280325	−	0.622836i
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	−2.98571	−	1.72380i	−0.270314	−	0.156066i
$123$	−12.9360	−	3.46618i	−1.16640	−	0.312535i
$124$	−0.633975	−	1.09808i	−0.0569326	−	0.0986102i
$125$	5.19615	+	9.89949i	0.464758	+	0.885438i
$126$		−	5.19615i		−	0.462910i
$127$			17.3867i			1.54282i	0.636340	+	0.771409i	$0.280447\pi$
$127$			17.3867i			1.54282i	−0.636340	+	0.771409i	$0.719553\pi$
$128$	−9.91808	+	5.72620i	−0.876642	+	0.506130i
$129$	0.803848	+	0.803848i	0.0707748	+	0.0707748i
$130$	−0.454838	−	2.79850i	−0.0398919	−	0.245445i
$131$	−6.46410	+	11.1962i	−0.564771	+	0.978212i	0.432300	+	0.901730i	$0.357702\pi$
$131$	−6.46410	+	11.1962i	−0.564771	+	0.978212i	−0.997071	+	0.0764824i	$0.975631\pi$
$132$	0.984508	+	3.67423i	0.0856904	+	0.319801i
$133$	2.12132	−	1.22474i	0.183942	−	0.106199i
$134$	−3.92820			−0.339345
$135$	−6.79141	+	9.42745i	−0.584511	+	0.811386i
$136$	10.1962			0.874313
$137$	13.6245	−	7.86611i	1.16402	−	0.672047i	0.211755	−	0.977323i	$-0.432082\pi$
$137$	13.6245	−	7.86611i	1.16402	−	0.672047i	0.952264	+	0.305276i	$0.0987487\pi$
$138$	−0.120118	−	0.448288i	−0.0102252	−	0.0381608i
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	−0.984297	−	0.176522i	$-0.943515\pi$
$139$	−4.00000	+	6.92820i	−0.339276	+	0.587643i	0.645021	+	0.764165i	$0.276849\pi$
$140$	12.7914	−	2.07898i	1.08107	−	0.175706i
$141$	−3.63397	−	3.63397i	−0.306036	−	0.306036i
$142$	−6.36396	+	3.67423i	−0.534052	+	0.308335i
$143$			3.10583i			0.259722i
$144$	6.40192	+	3.69615i	0.533494	+	0.308013i
$145$	−0.803848	+	0.656339i	−0.0667559	+	0.0545060i
$146$	2.19615	+	3.80385i	0.181755	+	0.314809i
$147$	7.02030	+	1.88108i	0.579025	+	0.155149i
$148$	6.36396	+	3.67423i	0.523114	+	0.302020i
$149$	2.13397	−	3.69615i	0.174822	−	0.302801i	−0.765278	−	0.643700i	$-0.777398\pi$
$149$	2.13397	−	3.69615i	0.174822	−	0.302801i	0.940100	+	0.340900i	$0.110732\pi$
$150$	4.01059	+	2.00284i	0.327463	+	0.163531i
$151$	−4.29423	−	7.43782i	−0.349459	−	0.605281i	0.636694	−	0.771116i	$-0.280301\pi$
$151$	−4.29423	−	7.43782i	−0.349459	−	0.605281i	−0.986154	+	0.165835i	$0.946968\pi$
$152$		−	1.41421i		−	0.114708i
$153$	−7.91688	−	13.7124i	−0.640041	−	1.10858i
$154$	2.19615			0.176971
$155$	1.53055	+	0.580438i	0.122937	+	0.0466219i
$156$	5.19615	+	5.19615i	0.416025	+	0.416025i
$157$	−11.1750	−	6.45189i	−0.891863	−	0.514917i	−0.0173114	−	0.999850i	$-0.505511\pi$
$157$	−11.1750	−	6.45189i	−0.891863	−	0.514917i	−0.874551	+	0.484933i	$0.838844\pi$
$158$	−3.34607	−	1.93185i	−0.266199	−	0.153690i
$159$	−1.73205	+	0.464102i	−0.137361	+	0.0368057i
$160$	4.07485	−	10.7449i	0.322145	−	0.849461i
$161$	1.73205			0.136505
$162$			4.65874i			0.366025i
$163$		−	10.4543i		−	0.818844i	−0.912345	−	0.409422i	$-0.865730\pi$
$163$		−	10.4543i		−	0.818844i	0.912345	−	0.409422i	$-0.134270\pi$
$164$	−6.69615	−	11.5981i	−0.522882	−	0.905658i
$165$	−3.98451	−	2.87039i	−0.310194	−	0.223459i
$166$	−2.06218	+	3.57180i	−0.160056	+	0.277225i
$167$	−8.60540	−	4.96833i	−0.665906	−	0.384461i	0.128618	−	0.991694i	$-0.458946\pi$
$167$	−8.60540	−	4.96833i	−0.665906	−	0.384461i	−0.794524	+	0.607233i	$0.792279\pi$
$168$	7.91688	−	7.91688i	0.610800	−	0.610800i
$169$	−3.50000	−	6.06218i	−0.269231	−	0.466321i
$170$	−4.73205	+	3.86370i	−0.362932	+	0.296333i
$171$	−1.90192	+	1.09808i	−0.145444	+	0.0839720i
$172$			1.13681i			0.0866811i
$173$	−9.14162	+	5.27792i	−0.695025	+	0.401273i	−0.805492	−	0.592607i	$-0.798099\pi$
$173$	−9.14162	+	5.27792i	−0.695025	+	0.401273i	0.110467	+	0.993880i	$0.464765\pi$
$174$	−0.107695	+	0.401924i	−0.00816435	+	0.0304698i
$175$	−11.0939	+	12.5231i	−0.838622	+	0.946659i
$176$	−1.56218	+	2.70577i	−0.117754	+	0.203955i
$177$	15.8338	+	4.24264i	1.19014	+	0.318896i
$178$	6.00361	−	3.46618i	0.449989	−	0.259801i
$179$	6.58846			0.492444			0.246222	−	0.969213i	$-0.420811\pi$
$179$	6.58846			0.492444			0.246222	+	0.969213i	$0.420811\pi$
$180$	−11.4685	+	1.86396i	−0.854809	+	0.138931i
$181$	1.53590			0.114162			0.0570812	−	0.998370i	$-0.481821\pi$
$181$	1.53590			0.114162			0.0570812	+	0.998370i	$0.481821\pi$
$182$	3.67423	−	2.12132i	0.272352	−	0.157243i
$183$	−8.15711	+	8.15711i	−0.602991	+	0.602991i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−9.36396	+	1.52192i	−0.688452	+	0.111894i
$186$	0.633975	−	0.169873i	0.0464853	−	0.0124557i
$187$	5.79555	−	3.34607i	0.423813	−	0.244689i
$188$		−	5.13922i		−	0.374816i
$189$	−16.7942	−	4.50000i	−1.22160	−	0.327327i
$190$	0.535898	+	0.656339i	0.0388782	+	0.0476158i
$191$	−8.83013	−	15.2942i	−0.638926	−	1.10665i	−0.985669	−	0.168691i	$-0.946046\pi$
$191$	−8.83013	−	15.2942i	−0.638926	−	1.10665i	0.346743	−	0.937960i	$-0.387287\pi$
$192$	1.01669	+	3.79435i	0.0733736	+	0.273834i
$193$	3.25813	+	1.88108i	0.234526	+	0.135403i	0.612658	−	0.790348i	$-0.290100\pi$
$193$	3.25813	+	1.88108i	0.234526	+	0.135403i	−0.378133	+	0.925751i	$0.623434\pi$
$194$	3.92820	−	6.80385i	0.282029	−	0.488488i
$195$	−9.43879	−	0.953512i	−0.675926	−	0.0682824i
$196$	3.63397	+	6.29423i	0.259570	+	0.449588i
$197$		−	15.9353i		−	1.13534i	−0.823255	−	0.567671i	$-0.807845\pi$
$197$		−	15.9353i		−	1.13534i	0.823255	−	0.567671i	$-0.192155\pi$
$198$	−1.96902			−0.139932
$199$	26.5885			1.88481			0.942403	−	0.334480i	$-0.108561\pi$
$199$	26.5885			1.88481			0.942403	+	0.334480i	$0.108561\pi$
$200$	3.05902	+	9.16208i	0.216305	+	0.647857i
$201$	−3.40192	+	12.6962i	−0.239953	+	0.895518i
$202$	4.24264	+	2.44949i	0.298511	+	0.172345i
$203$	−1.34486	−	0.776457i	−0.0943909	−	0.0544966i
$204$	4.09808	−	15.2942i	0.286923	−	1.07081i
$205$	16.1659	+	6.13069i	1.12908	+	0.428186i
$206$	−0.339746			−0.0236712
$207$	−1.55291			−0.107935
$208$			6.03579i			0.418507i
$209$	−0.464102	−	0.803848i	−0.0321026	−	0.0556033i
$210$	−0.674235	+	6.67423i	−0.0465266	+	0.460566i
$211$	−5.56218	+	9.63397i	−0.382916	+	0.663230i	−0.991478	−	0.130276i	$-0.958414\pi$
$211$	−5.56218	+	9.63397i	−0.382916	+	0.663230i	0.608562	+	0.793507i	$0.291747\pi$
$212$	−1.55291	−	0.896575i	−0.106655	−	0.0615771i
$213$	6.36396	+	23.7506i	0.436051	+	1.62737i
$214$	2.66987	+	4.62436i	0.182509	+	0.316114i
$215$	−0.928203	−	1.13681i	−0.0633029	−	0.0775299i
$216$	−7.09808	+	7.09808i	−0.482963	+	0.482963i
$217$			2.44949i			0.166282i
$218$	5.67544	−	3.27671i	0.384389	−	0.221927i
$219$	14.1962	−	3.80385i	0.959287	−	0.257040i
$220$	−0.787803	−	4.84714i	−0.0531136	−	0.326794i
$221$	6.46410	−	11.1962i	0.434823	−	0.753135i
$222$	−2.68973	+	2.68973i	−0.180523	+	0.180523i
$223$	3.88229	−	2.24144i	0.259977	−	0.150098i	−0.364347	−	0.931263i	$-0.618708\pi$
$223$	3.88229	−	2.24144i	0.259977	−	0.150098i	0.624324	+	0.781165i	$0.285374\pi$
$224$	17.1962			1.14897
$225$	9.94655	−	11.2279i	0.663103	−	0.748528i
$226$	−8.92820			−0.593895
$227$	−22.8541	+	13.1948i	−1.51688	+	0.875769i	−0.517073	+	0.855941i	$0.672979\pi$
$227$	−22.8541	+	13.1948i	−1.51688	+	0.875769i	−0.999803	+	0.0198279i	$0.993688\pi$
$228$	−2.12132	−	0.568406i	−0.140488	−	0.0376436i
$229$	3.03590	−	5.25833i	0.200618	−	0.347480i	−0.748110	−	0.663575i	$-0.769038\pi$
$229$	3.03590	−	5.25833i	0.200618	−	0.347480i	0.948728	+	0.316095i	$0.102372\pi$
$230$	0.0961186	+	0.591392i	0.00633787	+	0.0389953i
$231$	1.90192	−	7.09808i	0.125137	−	0.467019i
$232$	−0.776457	+	0.448288i	−0.0509769	+	0.0294315i
$233$			7.07107i			0.463241i	0.972806	+	0.231621i	$0.0744028\pi$
$233$			7.07107i			0.463241i	−0.972806	+	0.231621i	$0.925597\pi$
$234$	−3.29423	+	1.90192i	−0.215350	+	0.124333i
$235$	4.19615	+	5.13922i	0.273727	+	0.335245i
$236$	8.19615	+	14.1962i	0.533524	+	0.924091i
$237$	−9.14162	+	9.14162i	−0.593812	+	0.593812i
$238$	−7.91688	−	4.57081i	−0.513175	−	0.296282i
$239$	−0.464102	+	0.803848i	−0.0300202	+	0.0519966i	−0.880645	−	0.473776i	$-0.842891\pi$
$239$	−0.464102	+	0.803848i	−0.0300202	+	0.0519966i	0.850625	+	0.525773i	$0.176224\pi$
$240$	−7.74340	−	5.57824i	−0.499834	−	0.360074i
$241$	−4.86603	−	8.42820i	−0.313448	−	0.542908i	0.665658	−	0.746257i	$-0.268151\pi$
$241$	−4.86603	−	8.42820i	−0.313448	−	0.542908i	−0.979106	+	0.203348i	$0.934818\pi$
$242$			4.86181i			0.312529i
$243$	15.0573	+	4.03459i	0.965926	+	0.258819i
$244$	−11.5359			−0.738510
$245$	−8.77319	−	3.32710i	−0.560499	−	0.212561i
$246$	6.69615	−	1.79423i	0.426931	−	0.114396i
$247$	−1.55291	−	0.896575i	−0.0988096	−	0.0570477i
$248$	1.22474	+	0.707107i	0.0777714	+	0.0449013i
$249$	9.75833	+	9.75833i	0.618409	+	0.618409i
$250$	−4.89155	−	3.09296i	−0.309369	−	0.195616i
$251$	−12.5885			−0.794576			−0.397288	−	0.917694i	$-0.630049\pi$
$251$	−12.5885			−0.794576			−0.397288	+	0.917694i	$0.630049\pi$
$252$	−8.69333	−	15.0573i	−0.547628	−	0.948520i
$253$		−	0.656339i		−	0.0412637i
$254$	−4.50000	−	7.79423i	−0.282355	−	0.489053i
$255$	8.38961	+	18.6403i	0.525378	+	1.16730i
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	14.5211	+	8.38375i	0.905800	+	0.522964i	0.879077	−	0.476679i	$-0.158160\pi$
$257$	14.5211	+	8.38375i	0.905800	+	0.522964i	0.0267223	+	0.999643i	$0.491493\pi$
$258$	−0.568406	−	0.152304i	−0.0353874	−	0.00948203i
$259$	−7.09808	−	12.2942i	−0.441053	−	0.763926i
$260$	−6.00000	−	7.34847i	−0.372104	−	0.455733i
$261$	1.20577	+	0.696152i	0.0746354	+	0.0430908i
$262$		−	6.69213i		−	0.413441i
$263$	18.8516	−	10.8840i	1.16244	−	0.671136i	0.210554	−	0.977582i	$-0.432473\pi$
$263$	18.8516	−	10.8840i	1.16244	−	0.671136i	0.951888	+	0.306446i	$0.0991398\pi$
$264$	−3.00000	−	3.00000i	−0.184637	−	0.184637i
$265$	2.28497	−	0.371374i	0.140364	−	0.0228133i
$266$	−0.633975	+	1.09808i	−0.0388715	+	0.0673274i
$267$	−6.00361	−	22.4058i	−0.367415	−	1.37121i
$268$	−11.3831	+	6.57201i	−0.695331	+	0.401450i
$269$	−6.80385			−0.414838			−0.207419	−	0.978252i	$-0.566506\pi$
$269$	−6.80385			−0.414838			−0.207419	+	0.978252i	$0.566506\pi$
$270$	0.604502	−	5.98396i	0.0367888	−	0.364172i
$271$	21.5167			1.30704			0.653522	−	0.756908i	$-0.273291\pi$
$271$	21.5167			1.30704			0.653522	+	0.756908i	$0.273291\pi$
$272$	11.2629	−	6.50266i	0.682916	−	0.394282i
$273$	−3.67423	−	13.7124i	−0.222375	−	0.829914i
$274$	−4.07180	+	7.05256i	−0.245986	+	0.426061i
$275$	4.74548	+	4.20390i	0.286163	+	0.253505i
$276$	−1.09808	−	1.09808i	−0.0660964	−	0.0660964i
$277$	10.6066	−	6.12372i	0.637289	−	0.367939i	−0.146281	−	0.989243i	$-0.546730\pi$
$277$	10.6066	−	6.12372i	0.637289	−	0.367939i	0.783569	+	0.621304i	$0.213397\pi$
$278$		−	4.14110i		−	0.248367i
$279$		−	2.19615i		−	0.131480i
$280$	−11.1962	+	9.14162i	−0.669098	+	0.546316i
$281$	9.86603	+	17.0885i	0.588558	+	1.01941i	0.994422	+	0.105478i	$0.0336374\pi$
$281$	9.86603	+	17.0885i	0.588558	+	1.01941i	−0.405864	+	0.913934i	$0.633029\pi$
$282$	2.56961	+	0.688524i	0.153018	+	0.0410010i
$283$	−14.4889	−	8.36516i	−0.861275	−	0.497257i	0.00316407	−	0.999995i	$-0.498993\pi$
$283$	−14.4889	−	8.36516i	−0.861275	−	0.497257i	−0.864439	+	0.502738i	$0.832326\pi$
$284$	−12.2942	+	21.2942i	−0.729528	+	1.26358i
$285$	2.58542	−	1.16364i	0.153147	−	0.0689284i
$286$	−0.803848	−	1.39230i	−0.0475325	−	0.0823287i
$287$			25.8719i			1.52717i
$288$	−15.4176			−0.908494
$289$	−10.8564			−0.638612
$290$	0.190482	−	0.502280i	0.0111855	−	0.0294949i
$291$	−18.5885	−	18.5885i	−1.08967	−	1.08967i
$292$	12.7279	+	7.34847i	0.744845	+	0.430037i
$293$	−11.9193	−	6.88160i	−0.696332	−	0.402027i	0.109648	−	0.993970i	$-0.465028\pi$
$293$	−11.9193	−	6.88160i	−0.696332	−	0.402027i	−0.805980	+	0.591943i	$0.798361\pi$
$294$	−3.63397	+	0.973721i	−0.211938	+	0.0567885i
$295$	−19.7873	−	7.50402i	−1.15206	−	0.436901i
$296$	−8.19615			−0.476392
$297$	−1.70522	+	6.36396i	−0.0989468	+	0.369274i
$298$			2.20925i			0.127979i
$299$	−0.633975	−	1.09808i	−0.0366637	−	0.0635034i
$300$	14.9726	−	0.906070i	0.864444	−	0.0523120i
$301$	1.09808	−	1.90192i	0.0632921	−	0.109625i
$302$	3.85010	+	2.22286i	0.221548	+	0.127911i
$303$	11.5911	−	11.5911i	0.665892	−	0.665892i
$304$	−0.901924	−	1.56218i	−0.0517289	−	0.0895970i
$305$	11.5359	−	9.41902i	0.660544	−	0.539332i
$306$	7.09808	+	4.09808i	0.405770	+	0.234271i
$307$		−	3.82654i		−	0.218392i	−0.994020	−	0.109196i	$-0.965172\pi$
$307$		−	3.82654i		−	0.218392i	0.994020	−	0.109196i	$-0.0348276\pi$
$308$	6.36396	−	3.67423i	0.362620	−	0.209359i
$309$	−0.294229	+	1.09808i	−0.0167381	+	0.0624674i
$310$	−0.836355	+	0.135932i	−0.0475018	+	0.00772043i
$311$	5.02628	−	8.70577i	0.285014	−	0.493659i	−0.687598	−	0.726091i	$-0.741335\pi$
$311$	5.02628	−	8.70577i	0.285014	−	0.493659i	0.972613	+	0.232432i	$0.0746684\pi$
$312$	−7.91688	−	2.12132i	−0.448205	−	0.120096i
$313$	−12.1595	+	7.02030i	−0.687296	+	0.396811i	−0.802598	−	0.596520i	$-0.796550\pi$
$313$	−12.1595	+	7.02030i	−0.687296	+	0.396811i	0.115302	+	0.993330i	$0.463216\pi$
$314$	6.67949			0.376946
$315$	20.9876	+	7.95922i	1.18252	+	0.448451i
$316$	−12.9282			−0.727268
$317$	−3.49837	+	2.01978i	−0.196488	+	0.113442i	−0.595016	−	0.803714i	$-0.702854\pi$
$317$	−3.49837	+	2.01978i	−0.196488	+	0.113442i	0.398528	+	0.917156i	$0.369521\pi$
$318$	0.656339	−	0.656339i	0.0368057	−	0.0368057i
$319$	−0.294229	+	0.509619i	−0.0164736	+	0.0285332i
$320$	−0.813558	−	5.00561i	−0.0454792	−	0.279822i
$321$	17.2583	−	4.62436i	0.963266	−	0.258106i
$322$	−0.776457	+	0.448288i	−0.0432703	+	0.0249821i
$323$			3.86370i			0.214982i
$324$	7.79423	+	13.5000i	0.433013	+	0.750000i
$325$	12.0000	+	2.44949i	0.665640	+	0.135873i
$326$	2.70577	+	4.68653i	0.149859	+	0.259563i
$327$	−5.67544	−	21.1810i	−0.313852	−	1.17131i
$328$	12.9360	+	7.46859i	0.714270	+	0.412384i
$329$	−4.96410	+	8.59808i	−0.273680	+	0.474027i
$330$	2.52912	+	0.255493i	0.139223	+	0.0140644i
$331$	4.19615	+	7.26795i	0.230641	+	0.399483i	0.957997	−	0.286778i	$-0.0925842\pi$
$331$	4.19615	+	7.26795i	0.230641	+	0.399483i	−0.727356	+	0.686261i	$0.759251\pi$
$332$			13.8004i			0.757393i
$333$	6.36396	+	11.0227i	0.348743	+	0.604040i
$334$	5.14359			0.281445
$335$	6.01703	−	15.8662i	0.328746	−	0.866865i
$336$	3.69615	−	13.7942i	0.201642	−	0.752537i
$337$	−5.79555	−	3.34607i	−0.315704	−	0.182272i	0.333772	−	0.942654i	$-0.391678\pi$
$337$	−5.79555	−	3.34607i	−0.315704	−	0.182272i	−0.649476	+	0.760382i	$0.725012\pi$
$338$	3.13801	+	1.81173i	0.170685	+	0.0985453i
$339$	−7.73205	+	28.8564i	−0.419947	+	1.56726i
$340$	−7.24833	+	19.1130i	−0.393096	+	1.03655i
$341$	0.928203			0.0502650
$342$	0.568406	−	0.984508i	0.0307359	−	0.0532361i
$343$			9.38186i			0.506573i
$344$	−0.633975	−	1.09808i	−0.0341816	−	0.0592043i
$345$	1.99465	+	0.201501i	0.107388	+	0.0108484i
$346$	2.73205	−	4.73205i	0.146876	−	0.254397i
$347$	8.57321	+	4.94975i	0.460234	+	0.265716i	0.712143	−	0.702035i	$-0.247725\pi$
$347$	8.57321	+	4.94975i	0.460234	+	0.265716i	−0.251909	+	0.967751i	$0.581058\pi$
$348$	0.360355	+	1.34486i	0.0193171	+	0.0720922i
$349$	14.2321	+	24.6506i	0.761824	+	1.31952i	0.941909	+	0.335867i	$0.109029\pi$
$349$	14.2321	+	24.6506i	0.761824	+	1.31952i	−0.180085	+	0.983651i	$0.557637\pi$
$350$	1.73205	−	8.48528i	0.0925820	−	0.453557i
$351$	3.29423	+	12.2942i	0.175833	+	0.656217i
$352$		−	6.51626i		−	0.347318i
$353$	−17.6269	+	10.1769i	−0.938185	+	0.541662i	−0.889391	−	0.457147i	$-0.848871\pi$
$353$	−17.6269	+	10.1769i	−0.938185	+	0.541662i	−0.0487943	+	0.998809i	$0.515538\pi$
$354$	−8.19615	+	2.19615i	−0.435621	+	0.116724i
$355$	−5.09244	−	31.3324i	−0.270278	−	1.66295i
$356$	11.5981	−	20.0885i	0.614697	−	1.06469i
$357$	−21.6293	+	21.6293i	−1.14474	+	1.14474i
$358$	−2.95352	+	1.70522i	−0.156099	+	0.0901236i
$359$	−20.1962			−1.06591			−0.532956	−	0.846143i	$-0.678919\pi$
$359$	−20.1962			−1.06591			−0.532956	+	0.846143i	$0.678919\pi$
$360$	10.0382	−	8.19615i	0.529059	−	0.431975i
$361$	−18.4641			−0.971795
$362$	−0.688524	+	0.397520i	−0.0361880	+	0.0208932i
$363$	15.7136	+	4.21046i	0.824752	+	0.220992i
$364$	7.09808	−	12.2942i	0.372040	−	0.644393i
$365$	−18.7279	+	3.04384i	−0.980264	+	0.159322i
$366$	1.54552	−	5.76795i	0.0807855	−	0.301496i
$367$	29.9623	−	17.2987i	1.56402	−	0.902986i	0.567175	−	0.823597i	$-0.308036\pi$
$367$	29.9623	−	17.2987i	1.56402	−	0.902986i	0.996844	−	0.0793890i	$-0.0252969\pi$
$368$		−	1.27551i		−	0.0664907i
$369$		−	23.1962i		−	1.20754i
$370$	3.80385	−	3.10583i	0.197753	−	0.161464i
$371$	1.73205	+	3.00000i	0.0899236	+	0.155752i
$372$	1.55291	−	1.55291i	0.0805149	−	0.0805149i
$373$	23.5983	+	13.6245i	1.22187	+	0.705450i	0.965317	−	0.261079i	$-0.0840784\pi$
$373$	23.5983	+	13.6245i	1.22187	+	0.705450i	0.256557	+	0.966529i	$0.417412\pi$
$374$	−1.73205	+	3.00000i	−0.0895622	+	0.155126i
$375$	−14.2328	+	13.1312i	−0.734979	+	0.678090i
$376$	2.86603	+	4.96410i	0.147804	+	0.256004i
$377$			1.13681i			0.0585488i
$378$	8.69333	−	2.32937i	0.447137	−	0.119810i
$379$	−19.4641			−0.999804			−0.499902	−	0.866082i	$-0.666631\pi$
$379$	−19.4641			−0.999804			−0.499902	+	0.866082i	$0.666631\pi$
$380$	2.65099	+	1.00535i	0.135993	+	0.0515733i
$381$	−29.0885	+	7.79423i	−1.49025	+	0.399310i
$382$	7.91688	+	4.57081i	0.405063	+	0.233863i
$383$	−9.22955	−	5.32868i	−0.471608	−	0.272283i	0.245305	−	0.969446i	$-0.421112\pi$
$383$	−9.22955	−	5.32868i	−0.471608	−	0.272283i	−0.716913	+	0.697163i	$0.754445\pi$
$384$	−14.0263	−	14.0263i	−0.715776	−	0.715776i
$385$	−3.36396	+	8.87039i	−0.171443	+	0.452077i
$386$	−1.94744			−0.0991221
$387$	−0.984508	+	1.70522i	−0.0500454	+	0.0866811i
$388$		−	26.2880i		−	1.33457i
$389$	0.0621778	+	0.107695i	0.00315254	+	0.00546036i	0.867597	−	0.497267i	$-0.165663\pi$
$389$	0.0621778	+	0.107695i	0.00315254	+	0.00546036i	−0.864445	+	0.502728i	$0.832330\pi$
$390$	4.47808	−	2.01549i	0.226757	−	0.102058i
$391$	−1.36603	+	2.36603i	−0.0690829	+	0.119655i
$392$	−7.02030	−	4.05317i	−0.354579	−	0.204716i
$393$	−21.6293	−	5.79555i	−1.09105	−	0.292347i
$394$	4.12436	+	7.14359i	0.207782	+	0.359889i
$395$	12.9282	−	10.5558i	0.650488	−	0.531122i
$396$	−5.70577	+	3.29423i	−0.286726	+	0.165541i
$397$		−	29.3939i		−	1.47524i	−0.675218	−	0.737618i	$-0.735950\pi$
$397$		−	29.3939i		−	1.47524i	0.675218	−	0.737618i	$-0.264050\pi$
$398$	−11.9193	+	6.88160i	−0.597459	+	0.344943i
$399$	3.00000	+	3.00000i	0.150188	+	0.150188i
$400$	9.22225	+	8.16977i	0.461112	+	0.408488i
$401$	8.53590	−	14.7846i	0.426262	−	0.738308i	−0.570275	−	0.821454i	$-0.693163\pi$
$401$	8.53590	−	14.7846i	0.426262	−	0.738308i	0.996537	+	0.0831457i	$0.0264967\pi$
$402$	−1.76097	−	6.57201i	−0.0878290	−	0.327782i
$403$	1.55291	−	0.896575i	0.0773562	−	0.0446616i
$404$	16.3923			0.815548
$405$	−18.8169	−	7.13604i	−0.935021	−	0.354593i
$406$	0.803848			0.0398943
$407$	−4.65874	+	2.68973i	−0.230925	+	0.133325i
$408$	4.57081	+	17.0585i	0.226289	+	0.844521i
$409$	−8.26795	+	14.3205i	−0.408824	+	0.708104i	−0.994758	−	0.102255i	$-0.967394\pi$
$409$	−8.26795	+	14.3205i	−0.408824	+	0.708104i	0.585934	+	0.810358i	$0.300728\pi$
$410$	−8.83373	+	1.43574i	−0.436267	+	0.0709062i
$411$	19.2679	+	19.2679i	0.950418	+	0.950418i
$412$	−0.984508	+	0.568406i	−0.0485032	+	0.0280034i
$413$		−	31.6675i		−	1.55826i
$414$	0.696152	−	0.401924i	0.0342140	−	0.0197535i
$415$	−11.2679	−	13.8004i	−0.553122	−	0.677433i
$416$	−6.29423	−	10.9019i	−0.308600	−	0.534511i
$417$	−13.3843	−	3.58630i	−0.655430	−	0.175622i
$418$	0.416102	+	0.240237i	0.0203522	+	0.0117504i
$419$	11.0263	−	19.0981i	0.538669	−	0.933002i	−0.460307	−	0.887760i	$-0.652261\pi$
$419$	11.0263	−	19.0981i	0.538669	−	0.933002i	0.998976	−	0.0452423i	$-0.0144060\pi$
$420$	9.21243	+	20.4685i	0.449521	+	0.998759i
$421$	9.73205	+	16.8564i	0.474311	+	0.821531i	0.999567	−	0.0294132i	$-0.00936385\pi$
$421$	9.73205	+	16.8564i	0.474311	+	0.821531i	−0.525256	+	0.850944i	$0.676031\pi$
$422$		−	5.75839i		−	0.280314i
$423$	4.45069	−	7.70882i	0.216400	−	0.374816i
$424$	2.00000			0.0971286
$425$	−8.35739	−	25.0313i	−0.405393	−	1.21419i
$426$	−9.00000	−	9.00000i	−0.436051	−	0.436051i
$427$	19.2999	+	11.1428i	0.933989	+	0.539239i
$428$	15.4734	+	8.93357i	0.747935	+	0.431820i
$429$	−5.19615	+	1.39230i	−0.250873	+	0.0672211i
$430$	0.710331	+	0.269382i	0.0342552	+	0.0129908i
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$	−3.31388	+	12.3676i	−0.159439	+	0.595035i
$433$			13.5601i			0.651658i	0.945429	+	0.325829i	$0.105643\pi$
$433$			13.5601i			0.651658i	−0.945429	+	0.325829i	$0.894357\pi$
$434$	−0.633975	−	1.09808i	−0.0304318	−	0.0527093i
$435$	−1.45843	−	1.05063i	−0.0699264	−	0.0503741i
$436$	10.9641	−	18.9904i	0.525085	−	0.909474i
$437$	0.328169	+	0.189469i	0.0156985	+	0.00906352i
$438$	−5.37945	+	5.37945i	−0.257040	+	0.257040i
$439$	−12.6603	−	21.9282i	−0.604241	−	1.04658i	−0.992171	−	0.124887i	$-0.960143\pi$
$439$	−12.6603	−	21.9282i	−0.604241	−	1.04658i	0.387930	−	0.921689i	$-0.373190\pi$
$440$	3.46410	+	4.24264i	0.165145	+	0.202260i
$441$			12.5885i			0.599450i
$442$			6.69213i			0.318312i
$443$	−1.43280	+	0.827225i	−0.0680742	+	0.0393027i	−0.533651	−	0.845705i	$-0.679180\pi$
$443$	−1.43280	+	0.827225i	−0.0680742	+	0.0393027i	0.465577	+	0.885008i	$0.345847\pi$
$444$	−3.29423	+	12.2942i	−0.156337	+	0.583458i
$445$	4.80408	+	29.5582i	0.227735	+	1.40120i
$446$	−1.16025	+	2.00962i	−0.0549396	+	0.0951582i
$447$	7.14042	+	1.91327i	0.337730	+	0.0904945i
$448$	6.57201	−	3.79435i	0.310498	−	0.179266i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$	−1.55291	+	7.60770i	−0.0732051	+	0.358630i
$451$	9.80385			0.461645
$452$	−25.8719	+	14.9372i	−1.21691	+	0.702586i
$453$	10.5187	−	10.5187i	0.494210	−	0.494210i
$454$	6.83013	−	11.8301i	0.320554	−	0.555215i
$455$	2.94012	+	18.0898i	0.137835	+	0.848062i
$456$	2.36603	−	0.633975i	0.110799	−	0.0296886i
$457$	−21.4770	+	12.3998i	−1.00465	+	0.580036i	−0.909621	−	0.415438i	$-0.863628\pi$
$457$	−21.4770	+	12.3998i	−1.00465	+	0.580036i	−0.0950304	+	0.995474i	$0.530295\pi$
$458$			3.14299i			0.146862i
$459$	19.3923	−	19.3923i	0.905155	−	0.905155i
$460$	1.26795	+	1.55291i	0.0591184	+	0.0724050i
$461$	18.3564	+	31.7942i	0.854943	+	1.48080i	0.876698	+	0.481042i	$0.159741\pi$
$461$	18.3564	+	31.7942i	0.854943	+	1.48080i	−0.0217547	+	0.999763i	$0.506925\pi$
$462$	0.984508	+	3.67423i	0.0458035	+	0.170941i
$463$	−29.5462	−	17.0585i	−1.37313	−	0.792776i	−0.381807	−	0.924242i	$-0.624698\pi$
$463$	−29.5462	−	17.0585i	−1.37313	−	0.792776i	−0.991321	+	0.131467i	$0.958031\pi$
$464$	−0.571797	+	0.990381i	−0.0265450	+	0.0459773i
$465$	−0.284965	+	2.82086i	−0.0132149	+	0.130814i
$466$	−1.83013	−	3.16987i	−0.0847790	−	0.146842i
$467$			25.3543i			1.17326i	0.809856	+	0.586629i	$0.199545\pi$
$467$			25.3543i			1.17326i	−0.809856	+	0.586629i	$0.800455\pi$
$468$	−6.36396	+	11.0227i	−0.294174	+	0.509525i
$469$	25.3923			1.17251
$470$	−3.21121	−	1.21780i	−0.148122	−	0.0561731i
$471$	5.78461	−	21.5885i	0.266541	−	0.994744i
$472$	−15.8338	−	9.14162i	−0.728807	−	0.420777i
$473$	−0.720710	−	0.416102i	−0.0331383	−	0.0191324i
$474$	1.73205	−	6.46410i	0.0795557	−	0.296906i
$475$	−3.47185	+	1.15918i	−0.159300	+	0.0531867i
$476$	−30.5885			−1.40202
$477$	−1.55291	−	2.68973i	−0.0711031	−	0.123154i
$478$		−	0.480473i		−	0.0219763i
$479$	2.07180	+	3.58846i	0.0946628	+	0.163961i	0.909468	−	0.415774i	$-0.136489\pi$
$479$	2.07180	+	3.58846i	0.0946628	+	0.163961i	−0.814805	+	0.579735i	$0.803156\pi$
$480$	19.8033	+	2.00054i	0.903893	+	0.0913118i
$481$	−5.19615	+	9.00000i	−0.236924	+	0.410365i
$482$	4.36276	+	2.51884i	0.198718	+	0.114730i
$483$	0.776457	+	2.89778i	0.0353300	+	0.131853i
$484$	8.13397	+	14.0885i	0.369726	+	0.640384i
$485$	21.4641	+	26.2880i	0.974635	+	1.19368i
$486$	−7.79423	+	2.08846i	−0.353553	+	0.0947343i
$487$			15.8338i			0.717496i	0.933435	+	0.358748i	$0.116796\pi$
$487$			15.8338i			0.717496i	−0.933435	+	0.358748i	$0.883204\pi$
$488$	11.1428	−	6.43331i	0.504412	−	0.291222i
$489$	17.4904	−	4.68653i	0.790942	−	0.211932i
$490$	4.79403	−	0.779170i	0.216572	−	0.0351993i
$491$	−16.8564	+	29.1962i	−0.760719	+	1.31760i	0.181761	+	0.983343i	$0.441820\pi$
$491$	−16.8564	+	29.1962i	−0.760719	+	1.31760i	−0.942480	+	0.334261i	$0.891513\pi$
$492$	16.4022	−	16.4022i	0.739466	−	0.739466i
$493$	2.12132	−	1.22474i	0.0955395	−	0.0551597i
$494$	0.928203			0.0417618
$495$	3.01604	−	7.95297i	0.135561	−	0.357459i
$496$	1.80385			0.0809951
$497$	41.1373	−	23.7506i	1.84526	−	1.06536i
$498$	−6.90018	−	1.84890i	−0.309205	−	0.0828511i
$499$	11.9282	−	20.6603i	0.533980	−	0.924880i	−0.465232	−	0.885189i	$-0.654029\pi$
$499$	11.9282	−	20.6603i	0.533980	−	0.924880i	0.999212	−	0.0396914i	$-0.0126375\pi$
$500$	−19.3492	−	0.778985i	−0.865324	−	0.0348373i
$501$	4.45448	−	16.6244i	0.199012	−	0.742721i
$502$	5.64325	−	3.25813i	0.251871	−	0.145418i
$503$		−	2.48665i		−	0.110874i	−0.998462	−	0.0554372i	$-0.982345\pi$
$503$		−	2.48665i		−	0.110874i	0.998462	−	0.0554372i	$-0.0176553\pi$
$504$	16.7942	+	9.69615i	0.748074	+	0.431901i
$505$	−16.3923	+	13.3843i	−0.729448	+	0.595592i
$506$	0.169873	+	0.294229i	0.00755178	+	0.0130801i
$507$	8.57321	−	8.57321i	0.380750	−	0.380750i
$508$	−26.0800	−	15.0573i	−1.15711	−	0.668059i
$509$	8.42820	−	14.5981i	0.373574	−	0.647048i	−0.616539	−	0.787324i	$-0.711466\pi$
$509$	8.42820	−	14.5981i	0.373574	−	0.647048i	0.990112	+	0.140276i	$0.0447990\pi$
$510$	−8.58542	−	6.18482i	−0.380169	−	0.273869i
$511$	−14.1962	−	24.5885i	−0.628001	−	1.08773i
$512$		−	22.1841i		−	0.980408i
$513$	−2.68973	−	2.68973i	−0.118754	−	0.118754i
$514$	−8.67949			−0.382836
$515$	0.520407	−	1.37225i	0.0229319	−	0.0604687i
$516$	−1.90192	+	0.509619i	−0.0837275	+	0.0224347i
$517$	3.25813	+	1.88108i	0.143293	+	0.0827300i
$518$	6.36396	+	3.67423i	0.279616	+	0.161437i
$519$	−12.9282	−	12.9282i	−0.567485	−	0.567485i
$520$	9.89363	+	3.75201i	0.433864	+	0.164537i
$521$	−19.3923			−0.849592			−0.424796	−	0.905289i	$-0.639654\pi$
$521$	−19.3923			−0.849592			−0.424796	+	0.905289i	$0.639654\pi$
$522$	−0.720710			−0.0315446
$523$			35.1894i			1.53873i	0.638812	+	0.769363i	$0.279426\pi$
$523$			35.1894i			1.53873i	−0.638812	+	0.769363i	$0.720574\pi$
$524$	−11.1962	−	19.3923i	−0.489106	−	0.847157i
$525$	−25.9249	−	12.9465i	−1.13145	−	0.565034i
$526$	−5.63397	+	9.75833i	−0.245653	+	0.425483i
$527$	−3.34607	−	1.93185i	−0.145757	−	0.0841528i
$528$	−5.22715	−	1.40061i	−0.227482	−	0.0609537i
$529$	−11.3660	−	19.6865i	−0.494175	−	0.855936i
$530$	−0.928203	+	0.757875i	−0.0403186	+	0.0329200i
$531$			28.3923i			1.23212i
$532$			4.24264i			0.183942i
$533$	16.4022	−	9.46979i	0.710456	−	0.410182i
$534$	8.49038	+	8.49038i	0.367415	+	0.367415i
$535$	−22.7676	+	3.70041i	−0.984330	+	0.159982i
$536$	7.33013	−	12.6962i	0.316613	−	0.548390i
$537$	2.95352	+	11.0227i	0.127454	+	0.475665i
$538$	3.05008	−	1.76097i	0.131498	−	0.0759206i
$539$	−5.32051			−0.229171
$540$	−8.25964	−	18.3515i	−0.355438	−	0.789724i
$541$	0.607695			0.0261269			0.0130634	−	0.999915i	$-0.495842\pi$
$541$	0.607695			0.0261269			0.0130634	+	0.999915i	$0.495842\pi$
$542$	−9.64566	+	5.56892i	−0.414316	+	0.239206i
$543$	0.688524	+	2.56961i	0.0295474	+	0.110272i
$544$	−13.5622	+	23.4904i	−0.581474	+	1.00714i
$545$	4.54148	+	27.9425i	0.194536	+	1.19693i
$546$	5.19615	+	5.19615i	0.222375	+	0.222375i
$547$	−22.5581	+	13.0239i	−0.964513	+	0.556862i	−0.897559	−	0.440894i	$-0.854661\pi$
$547$	−22.5581	+	13.0239i	−0.964513	+	0.556862i	−0.0669541	+	0.997756i	$0.521328\pi$
$548$			27.2490i			1.16402i
$549$	−17.3038	−	9.99038i	−0.738510	−	0.426379i
$550$	−3.21539	−	0.656339i	−0.137105	−	0.0279864i
$551$	−0.169873	−	0.294229i	−0.00723683	−	0.0125346i
$552$	1.67303	+	0.448288i	0.0712090	+	0.0190804i
$553$	21.6293	+	12.4877i	0.919772	+	0.531030i
$554$	−3.16987	+	5.49038i	−0.134675	+	0.233264i
$555$	−6.74397	−	14.9840i	−0.286265	−	0.636033i
$556$	−6.92820	−	12.0000i	−0.293821	−	0.508913i
$557$		−	31.1127i		−	1.31829i	−0.752017	−	0.659144i	$-0.770919\pi$
$557$		−	31.1127i		−	1.31829i	0.752017	−	0.659144i	$-0.229081\pi$
$558$	0.568406	+	0.984508i	0.0240625	+	0.0416776i
$559$	−1.60770			−0.0679983
$560$	−6.53744	+	17.2385i	−0.276257	+	0.728459i
$561$	8.19615	+	8.19615i	0.346042	+	0.346042i
$562$	−8.84564	−	5.10703i	−0.373131	−	0.215427i
$563$	7.94906	+	4.58939i	0.335013	+	0.193420i	0.658065	−	0.752962i	$-0.271375\pi$
$563$	7.94906	+	4.58939i	0.335013	+	0.193420i	−0.323052	+	0.946381i	$0.604709\pi$
$564$	8.59808	−	2.30385i	0.362044	−	0.0970095i
$565$	13.6758	−	36.0615i	0.575345	−	1.51712i
$566$	8.66025			0.364018
$567$		−	30.1146i		−	1.26469i
$568$		−	27.4249i		−	1.15072i
$569$	14.6603	+	25.3923i	0.614590	+	1.06450i	0.990456	+	0.137827i	$0.0440118\pi$
$569$	14.6603	+	25.3923i	0.614590	+	1.06450i	−0.375867	+	0.926674i	$0.622655\pi$
$570$	−0.857840	+	1.19080i	−0.0359309	+	0.0498773i
$571$	0.732051	−	1.26795i	0.0306354	−	0.0530620i	−0.850301	−	0.526296i	$-0.823580\pi$
$571$	0.732051	−	1.26795i	0.0306354	−	0.0530620i	0.880937	+	0.473234i	$0.156914\pi$
$572$	−4.65874	−	2.68973i	−0.194792	−	0.112463i
$573$	21.6293	−	21.6293i	0.903577	−	0.903577i
$574$	−6.69615	−	11.5981i	−0.279492	−	0.484094i
$575$	−2.53590	−	0.517638i	−0.105754	−	0.0215870i
$576$	−5.89230	+	3.40192i	−0.245513	+	0.141747i
$577$			13.8647i			0.577196i	0.957450	+	0.288598i	$0.0931892\pi$
$577$			13.8647i			0.577196i	−0.957450	+	0.288598i	$0.906811\pi$
$578$	4.86679	−	2.80984i	0.202432	−	0.116874i
$579$	−1.68653	+	6.29423i	−0.0700899	+	0.261579i
$580$	−0.288356	−	1.77418i	−0.0119733	−	0.0736687i
$581$	13.3301	−	23.0885i	0.553027	−	0.957871i
$582$	13.1440	+	3.52193i	0.544837	+	0.145989i
$583$	1.13681	−	0.656339i	0.0470819	−	0.0271828i
$584$	−16.3923			−0.678318
$585$	−2.63604	−	16.2189i	−0.108987	−	0.670567i
$586$	7.12436			0.294304
$587$	4.21046	−	2.43091i	0.173784	−	0.100334i	−0.410585	−	0.911822i	$-0.634675\pi$
$587$	4.21046	−	2.43091i	0.173784	−	0.100334i	0.584369	+	0.811488i	$0.301342\pi$
$588$	−8.90138	+	8.90138i	−0.367087	+	0.367087i
$589$	−0.267949	+	0.464102i	−0.0110407	+	0.0191230i
$590$	10.8126	−	1.75736i	0.445146	−	0.0723493i
$591$	26.6603	−	7.14359i	1.09666	−	0.293848i
$592$	−9.05369	+	5.22715i	−0.372104	+	0.214834i
$593$			19.1427i			0.786094i	0.919518	+	0.393047i	$0.128579\pi$
$593$			19.1427i			0.786094i	−0.919518	+	0.393047i	$0.871421\pi$
$594$	−0.882686	−	3.29423i	−0.0362170	−	0.135164i
$595$	30.5885	−	24.9754i	1.25400	−	1.02389i
$596$	3.69615	+	6.40192i	0.151400	+	0.262233i
$597$	11.9193	+	44.4834i	0.487824	+	1.82058i
$598$	0.568406	+	0.328169i	0.0232439	+	0.0134198i
$599$	−10.8564	+	18.8038i	−0.443581	+	0.768304i	−0.997952	−	0.0639650i	$-0.979625\pi$
$599$	−10.8564	+	18.8038i	−0.443581	+	0.768304i	0.554371	+	0.832269i	$0.312959\pi$
$600$	−13.9571	+	9.22508i	−0.569798	+	0.376612i
$601$	1.53590	+	2.66025i	0.0626506	+	0.108514i	0.895649	−	0.444761i	$-0.146711\pi$
$601$	1.53590	+	2.66025i	0.0626506	+	0.108514i	−0.832999	+	0.553275i	$0.813378\pi$
$602$			1.13681i			0.0463330i
$603$	−22.7661			−0.927108
$604$	14.8756			0.605281
$605$	−19.6372	−	7.44709i	−0.798364	−	0.302767i
$606$	−2.19615	+	8.19615i	−0.0892126	+	0.332946i
$607$	−18.1631	−	10.4865i	−0.737218	−	0.425633i	0.0838387	−	0.996479i	$-0.473282\pi$
$607$	−18.1631	−	10.4865i	−0.737218	−	0.425633i	−0.821057	+	0.570846i	$0.806615\pi$
$608$	3.25813	+	1.88108i	0.132135	+	0.0762880i
$609$	0.696152	−	2.59808i	0.0282095	−	0.105279i
$610$	−2.73358	+	7.20814i	−0.110679	+	0.291849i
$611$	7.26795			0.294030
$612$	27.4249			1.10858
$613$			9.62209i			0.388633i	0.980939	+	0.194316i	$0.0622488\pi$
$613$			9.62209i			0.388633i	−0.980939	+	0.194316i	$0.937751\pi$
$614$	0.990381	+	1.71539i	0.0399685	+	0.0692275i
$615$	−3.00985	+	29.7945i	−0.121369	+	1.20143i
$616$	−4.09808	+	7.09808i	−0.165116	+	0.285990i
$617$	−15.5935	−	9.00292i	−0.627771	−	0.362444i	0.152117	−	0.988362i	$-0.451391\pi$
$617$	−15.5935	−	9.00292i	−0.627771	−	0.362444i	−0.779888	+	0.625919i	$0.784724\pi$
$618$	−0.152304	−	0.568406i	−0.00612656	−	0.0228646i
$619$	15.0981	+	26.1506i	0.606843	+	1.05108i	0.991757	+	0.128130i	$0.0408976\pi$
$619$	15.0981	+	26.1506i	0.606843	+	1.05108i	−0.384914	+	0.922952i	$0.625769\pi$
$620$	−2.19615	+	1.79315i	−0.0881996	+	0.0720147i
$621$	−0.696152	−	2.59808i	−0.0279356	−	0.104257i
$622$			5.20359i			0.208645i
$623$	−38.8079	+	22.4058i	−1.55481	+	0.897668i
$624$	−10.0981	+	2.70577i	−0.404247	+	0.108318i
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	3.63397	−	6.29423i	0.145243	−	0.251568i
$627$	1.13681	−	1.13681i	0.0453999	−	0.0453999i
$628$	19.3557	−	11.1750i	0.772376	−	0.445931i
$629$	22.3923			0.892840
$630$	−11.4685	+	1.86396i	−0.456915	+	0.0742620i
$631$	1.32051			0.0525686			0.0262843	−	0.999655i	$-0.491632\pi$
$631$	1.32051			0.0525686			0.0262843	+	0.999655i	$0.491632\pi$
$632$	12.4877	−	7.20977i	0.496733	−	0.286789i
$633$	−18.6114	−	4.98691i	−0.739737	−	0.198212i
$634$	1.04552	−	1.81089i	0.0415228	−	0.0719196i
$635$	38.3742	−	6.23694i	1.52283	−	0.247505i
$636$	0.803848	−	3.00000i	0.0318746	−	0.118958i
$637$	−8.90138	+	5.13922i	−0.352686	+	0.203623i
$638$		−	0.304608i		−	0.0120595i
$639$	−36.8827	+	21.2942i	−1.45906	+	0.842387i
$640$	16.1962	+	19.8362i	0.640209	+	0.784093i
$641$	−6.52628	−	11.3038i	−0.257773	−	0.446475i	0.707872	−	0.706340i	$-0.249655\pi$
$641$	−6.52628	−	11.3038i	−0.257773	−	0.446475i	−0.965645	+	0.259865i	$0.916322\pi$
$642$	−6.53983	+	6.53983i	−0.258106	+	0.258106i
$643$	11.2308	+	6.48408i	0.442898	+	0.255707i	0.704826	−	0.709380i	$-0.251025\pi$
$643$	11.2308	+	6.48408i	0.442898	+	0.255707i	−0.261928	+	0.965087i	$0.584358\pi$
$644$	−1.50000	+	2.59808i	−0.0591083	+	0.102379i
$645$	1.48582	−	2.06253i	0.0585042	−	0.0812122i
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$		−	19.4572i		−	0.764942i	−0.923967	−	0.382471i	$-0.875073\pi$
$647$		−	19.4572i		−	0.764942i	0.923967	−	0.382471i	$-0.124927\pi$
$648$	−15.0573	−	8.69333i	−0.591506	−	0.341506i
$649$	−12.0000			−0.471041
$650$	−6.01343	+	2.00775i	−0.235866	+	0.0787505i
$651$	−4.09808	+	1.09808i	−0.160616	+	0.0430370i
$652$	15.6814	+	9.05369i	0.614133	+	0.354570i
$653$	−42.0339	−	24.2683i	−1.64491	−	0.949691i	−0.979051	−	0.203615i	$-0.934731\pi$
$653$	−42.0339	−	24.2683i	−1.64491	−	0.949691i	−0.665861	−	0.746076i	$-0.731936\pi$
$654$	8.02628	+	8.02628i	0.313852	+	0.313852i
$655$	27.0299	+	10.2507i	1.05615	+	0.400527i
$656$	19.0526			0.743877
$657$	12.7279	+	22.0454i	0.496564	+	0.860073i
$658$		−	5.13922i		−	0.200348i
$659$	−6.12436	−	10.6077i	−0.238571	−	0.413217i	0.721733	−	0.692171i	$-0.243346\pi$
$659$	−6.12436	−	10.6077i	−0.238571	−	0.413217i	−0.960304	+	0.278954i	$0.910012\pi$
$660$	7.75627	−	3.49093i	0.301912	−	0.135884i
$661$	−5.39230	+	9.33975i	−0.209736	+	0.363274i	−0.951631	−	0.307242i	$-0.900594\pi$
$661$	−5.39230	+	9.33975i	−0.209736	+	0.363274i	0.741895	+	0.670516i	$0.233927\pi$
$662$	−3.76217	−	2.17209i	−0.146221	−	0.0844206i
$663$	21.6293	+	5.79555i	0.840013	+	0.225081i
$664$	−7.69615	−	13.3301i	−0.298669	−	0.517309i
$665$	−3.46410	−	4.24264i	−0.134332	−	0.164523i
$666$	−5.70577	−	3.29423i	−0.221094	−	0.127649i
$667$		−	0.240237i		−	0.00930200i
$668$	14.9050	−	8.60540i	0.576691	−	0.332953i
$669$	5.49038	+	5.49038i	0.212270	+	0.212270i
$670$	1.40912	+	8.66996i	0.0544392	+	0.334950i
$671$	4.22243	−	7.31347i	0.163005	−	0.282333i
$672$	7.70882	+	28.7697i	0.297374	+	1.10982i
$673$	35.3417	−	20.4046i	1.36232	−	0.786538i	0.372391	−	0.928076i	$-0.378538\pi$
$673$	35.3417	−	20.4046i	1.36232	−	0.786538i	0.989933	+	0.141538i	$0.0452047\pi$
$674$	3.46410			0.133432
$675$	23.2436	+	11.6076i	0.894646	+	0.446775i
$676$	12.1244			0.466321
$677$	−3.19376	+	1.84392i	−0.122746	+	0.0708676i	−0.560116	−	0.828414i	$-0.689243\pi$
$677$	−3.19376	+	1.84392i	−0.122746	+	0.0708676i	0.437370	+	0.899282i	$0.355910\pi$
$678$	−4.00240	−	14.9372i	−0.153711	−	0.573659i
$679$	−25.3923	+	43.9808i	−0.974467	+	1.68783i
$680$	−3.65756	−	22.5040i	−0.140261	−	0.862989i
$681$	−32.3205	−	32.3205i	−1.23852	−	1.23852i
$682$	−0.416102	+	0.240237i	−0.0159334	+	0.00919914i
$683$		−	0.101536i		−	0.00388517i	−0.999998	−	0.00194258i	$-0.999382\pi$
$683$		−	0.101536i		−	0.00388517i	0.999998	−	0.00194258i	$-0.000618344\pi$
$684$		−	3.80385i		−	0.145444i
$685$	−22.2487	−	27.2490i	−0.850080	−	1.04113i
$686$	−2.42820	−	4.20577i	−0.0927092	−	0.160577i
$687$	10.1583	+	2.72191i	0.387564	+	0.103847i
$688$	−1.40061	−	0.808643i	−0.0533978	−	0.0308292i
$689$	1.26795	−	2.19615i	0.0483050	−	0.0836667i
$690$	−0.946330	+	0.425924i	−0.0360262	+	0.0162146i
$691$	14.1244	+	24.4641i	0.537316	+	0.930658i	0.999047	+	0.0436386i	$0.0138950\pi$
$691$	14.1244	+	24.4641i	0.537316	+	0.930658i	−0.461732	+	0.887020i	$0.652772\pi$
$692$		−	18.2832i		−	0.695025i
$693$	12.7279			0.483494
$694$	−5.12436			−0.194518
$695$	16.7262	+	6.34315i	0.634459	+	0.240609i
$696$	−1.09808	−	1.09808i	−0.0416225	−	0.0416225i
$697$	−35.3417	−	20.4046i	−1.33866	−	0.772878i
$698$	−12.7601	−	7.36705i	−0.482977	−	0.278847i
$699$	−11.8301	+	3.16987i	−0.447456	+	0.119896i
$700$	−9.17705	−	27.4862i	−0.346860	−	1.03888i
$701$	−12.8038			−0.483595			−0.241797	−	0.970327i	$-0.577737\pi$
$701$	−12.8038			−0.483595			−0.241797	+	0.970327i	$0.577737\pi$
$702$	−4.65874	−	4.65874i	−0.175833	−	0.175833i
$703$		−	3.10583i		−	0.117139i
$704$	−1.43782	−	2.49038i	−0.0541900	−	0.0938598i
$705$	−6.71699	+	9.32415i	−0.252977	+	0.351168i
$706$	5.26795	−	9.12436i	0.198262	−	0.343400i
$707$	−27.4249	−	15.8338i	−1.03142	−	0.595489i
$708$	−20.0764	+	20.0764i	−0.754517	+	0.754517i
$709$	4.89230	+	8.47372i	0.183734	+	0.318237i	0.943149	−	0.332369i	$-0.107848\pi$
$709$	4.89230	+	8.47372i	0.183734	+	0.318237i	−0.759415	+	0.650607i	$0.774515\pi$
$710$	10.3923	+	12.7279i	0.390016	+	0.477670i
$711$	−19.3923	−	11.1962i	−0.727268	−	0.419889i
$712$			25.8719i			0.969592i
$713$	−0.328169	+	0.189469i	−0.0122900	+	0.00709566i
$714$	4.09808	−	15.2942i	0.153367	−	0.572372i
$715$	6.85490	−	1.11412i	0.256359	−	0.0416658i
$716$	−5.70577	+	9.88269i	−0.213235	+	0.369333i
$717$	−1.55291	−	0.416102i	−0.0579946	−	0.0155396i
$718$	9.05369	−	5.22715i	0.337881	−	0.195075i
$719$	−40.3923			−1.50638			−0.753189	−	0.657804i	$-0.771486\pi$
$719$	−40.3923			−1.50638			−0.753189	+	0.657804i	$0.771486\pi$
$720$	5.86131	−	15.4556i	0.218438	−	0.575997i
$721$	2.19615			0.0817890
$722$	8.27723	−	4.77886i	0.308047	−	0.177851i
$723$	11.9193	−	11.9193i	0.443283	−	0.443283i
$724$	−1.33013	+	2.30385i	−0.0494338	+	0.0856218i
$725$	1.73697	+	1.53874i	0.0645093	+	0.0571472i
$726$	−8.13397	+	2.17949i	−0.301880	+	0.0808885i
$727$	1.19256	−	0.688524i	0.0442296	−	0.0255360i	−0.477722	−	0.878511i	$-0.658537\pi$
$727$	1.19256	−	0.688524i	0.0442296	−	0.0255360i	0.521952	+	0.852975i	$0.325204\pi$
$728$			15.8338i			0.586838i
$729$			27.0000i			1.00000i
$730$	7.60770	−	6.21166i	0.281573	−	0.229904i
$731$	1.73205	+	3.00000i	0.0640622	+	0.110959i
$732$	−5.17140	−	19.2999i	−0.191141	−	0.713346i
$733$	−6.51626	−	3.76217i	−0.240684	−	0.138959i	0.374807	−	0.927103i	$-0.377709\pi$
$733$	−6.51626	−	3.76217i	−0.240684	−	0.138959i	−0.615491	+	0.788144i	$0.711042\pi$
$734$	−8.95448	+	15.5096i	−0.330516	+	0.572470i
$735$	1.63343	−	16.1693i	0.0602501	−	0.596415i
$736$	1.33013	+	2.30385i	0.0490291	+	0.0849209i
$737$		−	9.62209i		−	0.354434i
$738$	6.00361	+	10.3986i	0.220996	+	0.382776i
$739$	18.1436			0.667423			0.333711	−	0.942675i	$-0.391699\pi$
$739$	18.1436			0.667423			0.333711	+	0.942675i	$0.391699\pi$
$740$	5.82655	−	15.3640i	0.214188	−	0.564790i
$741$	0.803848	−	3.00000i	0.0295301	−	0.110208i
$742$	−1.55291	−	0.896575i	−0.0570093	−	0.0329143i
$743$	28.2893	+	16.3328i	1.03783	+	0.599193i	0.919218	−	0.393748i	$-0.128822\pi$
$743$	28.2893	+	16.3328i	1.03783	+	0.599193i	0.118613	+	0.992941i	$0.462155\pi$
$744$	−0.633975	+	2.36603i	−0.0232426	+	0.0867427i
$745$	−8.92330	−	3.38403i	−0.326924	−	0.123981i
$746$	−14.1051			−0.516425
$747$	−11.9515	+	20.7005i	−0.437281	+	0.757393i
$748$			11.5911i			0.423813i
$749$	−17.2583	−	29.8923i	−0.630606	−	1.09224i
$750$	2.98180	−	9.57026i	0.108880	−	0.349456i
$751$	12.2224	−	21.1699i	0.446003	−	0.772500i	−0.552119	−	0.833766i	$-0.686180\pi$
$751$	12.2224	−	21.1699i	0.446003	−	0.772500i	0.998121	+	0.0612659i	$0.0195138\pi$
$752$	6.33178	+	3.65565i	0.230896	+	0.133308i
$753$	−5.64325	−	21.0609i	−0.205651	−	0.767502i
$754$	−0.294229	−	0.509619i	−0.0107152	−	0.0185592i
$755$	−14.8756	+	12.1459i	−0.541380	+	0.442035i
$756$	21.2942	−	21.2942i	0.774464	−	0.774464i
$757$		−	7.34847i		−	0.267085i	−0.991043	−	0.133542i	$-0.957365\pi$
$757$		−	7.34847i		−	0.267085i	0.991043	−	0.133542i	$-0.0426352\pi$
$758$	8.72552	−	5.03768i	0.316925	−	0.182977i
$759$	1.09808	−	0.294229i	0.0398576	−	0.0106798i
$760$	−3.12132	+	0.507306i	−0.113222	+	0.0184019i
$761$	−7.96410	+	13.7942i	−0.288698	+	0.500040i	−0.973499	−	0.228690i	$-0.926556\pi$
$761$	−7.96410	+	13.7942i	−0.288698	+	0.500040i	0.684801	+	0.728730i	$0.259889\pi$
$762$	11.0227	−	11.0227i	0.399310	−	0.399310i
$763$	−36.6866	+	21.1810i	−1.32814	+	0.766804i
$764$	30.5885			1.10665
$765$	−27.4249	+	22.3923i	−0.991548	+	0.809595i
$766$	5.51666			0.199325
$767$	−20.0764	+	11.5911i	−0.724916	+	0.418531i

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.448288 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-0.358719 - 2.20711i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(2.89778 - 1.67303i) q^{7} -1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(-0.448288 + 0.258819i) q^{2} +(0.448288 + 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-0.358719 - 2.20711i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(2.89778 - 1.67303i) q^{7} -1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +(0.732051 + 0.896575i) q^{10} +(-0.633975 - 1.09808i) q^{11} +(-2.89778 - 0.776457i) q^{12} +(-2.12132 - 1.22474i) q^{13} +(-0.866025 + 1.50000i) q^{14} +(3.53175 - 1.58957i) q^{15} +(-1.23205 - 2.13397i) q^{16} +5.27792i q^{17} +(0.776457 - 1.34486i) q^{18} +0.732051 q^{19} +(3.62132 + 1.37333i) q^{20} +(4.09808 + 4.09808i) q^{21} +(0.568406 + 0.328169i) q^{22} +(0.448288 + 0.258819i) q^{23} +(3.23205 - 0.866025i) q^{24} +(-4.74264 + 1.58346i) q^{25} +1.26795 q^{26} +(-3.67423 - 3.67423i) q^{27} +5.79555i q^{28} +(-0.232051 - 0.401924i) q^{29} +(-1.17183 + 1.62667i) q^{30} +(-0.366025 + 0.633975i) q^{31} +(4.45069 + 2.56961i) q^{32} +(1.55291 - 1.55291i) q^{33} +(-1.36603 - 2.36603i) q^{34} +(-4.73205 - 5.79555i) q^{35} -5.19615i q^{36} -4.24264i q^{37} +(-0.328169 + 0.189469i) q^{38} +(1.09808 - 4.09808i) q^{39} +(-4.26380 + 0.692993i) q^{40} +(-3.86603 + 6.69615i) q^{41} +(-2.89778 - 0.776457i) q^{42} +(0.568406 - 0.328169i) q^{43} +2.19615 q^{44} +(4.24264 + 5.19615i) q^{45} -0.267949 q^{46} +(-2.56961 + 1.48356i) q^{47} +(3.01790 - 3.01790i) q^{48} +(2.09808 - 3.63397i) q^{49} +(1.71624 - 1.93733i) q^{50} +(-8.83013 + 2.36603i) q^{51} +(3.67423 - 2.12132i) q^{52} +1.03528i q^{53} +(2.59808 + 0.696152i) q^{54} +(-2.19615 + 1.79315i) q^{55} +(-3.23205 - 5.59808i) q^{56} +(0.328169 + 1.22474i) q^{57} +(0.208051 + 0.120118i) q^{58} +(4.73205 - 8.19615i) q^{59} +(-0.674235 + 6.67423i) q^{60} +(3.33013 + 5.76795i) q^{61} -0.378937i q^{62} +(-5.01910 + 8.69333i) q^{63} +2.26795 q^{64} +(-1.94218 + 5.12132i) q^{65} +(-0.294229 + 1.09808i) q^{66} +(6.57201 + 3.79435i) q^{67} +(-7.91688 - 4.57081i) q^{68} +(-0.232051 + 0.866025i) q^{69} +(3.62132 + 1.37333i) q^{70} +14.1962 q^{71} +(2.89778 + 5.01910i) q^{72} -8.48528i q^{73} +(1.09808 + 1.90192i) q^{74} +(-4.77526 - 7.22474i) q^{75} +(-0.633975 + 1.09808i) q^{76} +(-3.67423 - 2.12132i) q^{77} +(0.568406 + 2.12132i) q^{78} +(3.73205 + 6.46410i) q^{79} +(-4.26795 + 3.48477i) q^{80} +(4.50000 - 7.79423i) q^{81} -4.00240i q^{82} +(6.90018 - 3.98382i) q^{83} +(-9.69615 + 2.59808i) q^{84} +(11.6489 - 1.89329i) q^{85} +(-0.169873 + 0.294229i) q^{86} +(0.568406 - 0.568406i) q^{87} +(-2.12132 + 1.22474i) q^{88} -13.3923 q^{89} +(-3.24679 - 1.23130i) q^{90} -8.19615 q^{91} +(-0.776457 + 0.448288i) q^{92} +(-1.22474 - 0.328169i) q^{93} +(0.767949 - 1.33013i) q^{94} +(-0.262601 - 1.61571i) q^{95} +(-2.30385 + 8.59808i) q^{96} +(-13.1440 + 7.58871i) q^{97} +2.17209i q^{98} +(3.29423 + 1.90192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{6}+O(q^{10}) \) 8 * q - 12 * q^6	\( 8 q - 12 q^{6} - 8 q^{10} - 12 q^{11} + 12 q^{15} + 4 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{21} + 12 q^{24} - 4 q^{25} + 24 q^{26} + 12 q^{29} - 12 q^{30} + 4 q^{31} - 4 q^{34} - 24 q^{35} - 12 q^{39} - 4 q^{40} - 24 q^{41} - 24 q^{44} - 16 q^{46} - 4 q^{49} + 24 q^{50} - 36 q^{51} + 24 q^{55} - 12 q^{56} + 24 q^{59} + 24 q^{60} - 8 q^{61} + 32 q^{64} + 60 q^{66} + 12 q^{69} + 12 q^{70} + 72 q^{71} - 12 q^{74} - 48 q^{75} - 12 q^{76} + 16 q^{79} - 48 q^{80} + 36 q^{81} - 36 q^{84} + 16 q^{85} - 36 q^{86} - 24 q^{89} - 36 q^{90} - 24 q^{91} + 20 q^{94} + 12 q^{95} - 60 q^{96} - 36 q^{99}+O(q^{100}) \) 8 * q - 12 * q^6 - 8 * q^10 - 12 * q^11 + 12 * q^15 + 4 * q^16 - 8 * q^19 + 12 * q^20 + 12 * q^21 + 12 * q^24 - 4 * q^25 + 24 * q^26 + 12 * q^29 - 12 * q^30 + 4 * q^31 - 4 * q^34 - 24 * q^35 - 12 * q^39 - 4 * q^40 - 24 * q^41 - 24 * q^44 - 16 * q^46 - 4 * q^49 + 24 * q^50 - 36 * q^51 + 24 * q^55 - 12 * q^56 + 24 * q^59 + 24 * q^60 - 8 * q^61 + 32 * q^64 + 60 * q^66 + 12 * q^69 + 12 * q^70 + 72 * q^71 - 12 * q^74 - 48 * q^75 - 12 * q^76 + 16 * q^79 - 48 * q^80 + 36 * q^81 - 36 * q^84 + 16 * q^85 - 36 * q^86 - 24 * q^89 - 36 * q^90 - 24 * q^91 + 20 * q^94 + 12 * q^95 - 60 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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