LMFDB - Embedded newform 45.2.j.a.4.3

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			4.3
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	45.4
Dual form			45.2.j.a.34.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.448288 - 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(2.09077 - 0.792893i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(-2.89778 + 1.67303i) q^{7} +1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.448288 - 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(2.09077 - 0.792893i) 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} +(-2.26380 - 3.14248i) q^{15} +(-1.23205 - 2.13397i) q^{16} -5.27792i q^{17} +(-0.776457 + 1.34486i) q^{18} +0.732051 q^{19} +(-0.621320 + 3.82282i) 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} +(3.74264 - 3.31552i) q^{25} +1.26795 q^{26} +(3.67423 + 3.67423i) q^{27} -5.79555i q^{28} +(-0.232051 - 0.401924i) q^{29} +(-1.82817 - 0.822821i) 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} +(1.53175 + 4.03906i) 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} +(0.819661 - 2.45497i) 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} +(6.67423 - 0.674235i) q^{60} +(3.33013 + 5.76795i) q^{61} +0.378937i q^{62} +(5.01910 - 8.69333i) q^{63} +2.26795 q^{64} +(5.40629 + 0.878680i) 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} +(-0.621320 + 3.82282i) q^{70} +14.1962 q^{71} +(-2.89778 - 5.01910i) q^{72} +8.48528i q^{73} +(1.09808 + 1.90192i) q^{74} +(-7.22474 - 4.77526i) 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} +(-4.18482 - 11.0349i) q^{85} +(-0.169873 + 0.294229i) q^{86} +(-0.568406 + 0.568406i) q^{87} +(2.12132 - 1.22474i) q^{88} -13.3923 q^{89} +(-0.557061 + 3.42745i) q^{90} -8.19615 q^{91} +(0.776457 - 0.448288i) q^{92} +(1.22474 + 0.328169i) q^{93} +(0.767949 - 1.33013i) q^{94} +(1.53055 - 0.580438i) 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	−0.333062	−	0.942905i	$-0.608082\pi$
$2$	0.448288	−	0.258819i	0.316987	−	0.183013i	0.650049	+	0.759892i	$0.274748\pi$
$3$	−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
$5$	2.09077	−	0.792893i	0.935021	−	0.354593i
$5$	2.09077	−	0.792893i	0.935021	−	0.354593i
$6$	−0.633975	−	0.633975i	−0.258819	−	0.258819i
$7$	−2.89778	+	1.67303i	−1.09526	+	0.632347i	−0.934971	−	0.354724i	$-0.884575\pi$
$7$	−2.89778	+	1.67303i	−1.09526	+	0.632347i	−0.160286	+	0.987071i	$0.551242\pi$
$8$			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	0.764444	−	0.644690i	$-0.223014\pi$
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	−0.176096	+	0.984373i	$0.556347\pi$
$14$	−0.866025	+	1.50000i	−0.231455	+	0.400892i
$15$	−2.26380	−	3.14248i	−0.584511	−	0.811386i
$16$	−1.23205	−	2.13397i	−0.308013	−	0.533494i
$17$		−	5.27792i		−	1.28008i	−0.768340	−	0.640041i	$-0.778917\pi$
$17$		−	5.27792i		−	1.28008i	0.768340	−	0.640041i	$-0.221083\pi$
$18$	−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	$0.473239\pi$
$20$	−0.621320	+	3.82282i	−0.138931	+	0.854809i
$21$	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	0.452534	−	0.891747i	$-0.350520\pi$
$23$	−0.448288	−	0.258819i	−0.0934745	−	0.0539675i	−0.546009	+	0.837780i	$0.683853\pi$
$24$	3.23205	−	0.866025i	0.659740	−	0.176777i
$25$	3.74264	−	3.31552i	0.748528	−	0.663103i
$26$	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	$0.847054\pi$
$30$	−1.82817	−	0.822821i	−0.333777	−	0.150226i
$31$	−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	$0.113391\pi$
$37$			4.24264i			0.697486i	−0.937218	+	0.348743i	$0.886609\pi$
$38$	0.328169	−	0.189469i	0.0532361	−	0.0307359i
$39$	1.09808	−	4.09808i	0.175833	−	0.656217i
$40$	1.53175	+	4.03906i	0.242191	+	0.638631i
$41$	−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	−0.542714	−	0.839918i	$-0.682603\pi$
$43$	−0.568406	+	0.328169i	−0.0866811	+	0.0500454i	0.456033	+	0.889963i	$0.349270\pi$
$44$	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	−0.300744	−	0.953705i	$-0.597235\pi$
$47$	2.56961	−	1.48356i	0.374816	−	0.216400i	0.675560	+	0.737305i	$0.263902\pi$
$48$	−3.01790	+	3.01790i	−0.435596	+	0.435596i
$49$	2.09808	−	3.63397i	0.299725	−	0.519139i
$50$	0.819661	−	2.45497i	0.115918	−	0.347185i
$51$	−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	$-0.977348\pi$
$53$		−	1.03528i		−	0.142206i	0.997469	−	0.0711031i	$-0.0226519\pi$
$54$	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	$-0.0446057\pi$
$60$	6.67423	−	0.674235i	0.861640	−	0.0870433i
$61$	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
$65$	5.40629	+	0.878680i	0.670567	+	0.108987i
$66$	−0.294229	+	1.09808i	−0.0362170	+	0.135164i
$67$	−6.57201	−	3.79435i	−0.802899	−	0.463554i	0.0415848	−	0.999135i	$-0.486759\pi$
$67$	−6.57201	−	3.79435i	−0.802899	−	0.463554i	−0.844484	+	0.535581i	$0.820093\pi$
$68$	7.91688	+	4.57081i	0.960062	+	0.554292i
$69$	−0.232051	+	0.866025i	−0.0279356	+	0.104257i
$70$	−0.621320	+	3.82282i	−0.0742620	+	0.456915i
$71$	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	$0.165405\pi$
$73$			8.48528i			0.993127i	−0.868000	+	0.496564i	$0.834595\pi$
$74$	1.09808	+	1.90192i	0.127649	+	0.221094i
$75$	−7.22474	−	4.77526i	−0.834242	−	0.551399i
$76$	−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	−0.828359	−	0.560198i	$-0.810725\pi$
$83$	−6.90018	+	3.98382i	−0.757393	+	0.437281i	0.0709657	+	0.997479i	$0.477392\pi$
$84$	−9.69615	+	2.59808i	−1.05794	+	0.283473i
$85$	−4.18482	−	11.0349i	−0.453908	−	1.19690i
$86$	−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	$0.751211\pi$
$90$	−0.557061	+	3.42745i	−0.0587193	+	0.361285i
$91$	−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
$95$	1.53055	−	0.580438i	0.157031	−	0.0595517i
$96$	−2.30385	+	8.59808i	−0.235135	+	0.877537i
$97$	13.1440	−	7.58871i	1.33457	−	0.770516i	0.348577	−	0.937280i	$-0.386665\pi$
$97$	13.1440	−	7.58871i	1.33457	−	0.770516i	0.985997	+	0.166764i	$0.0533318\pi$
$98$		−	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	0.471735	−	0.881740i	$-0.343628\pi$
$103$	−0.568406	−	0.328169i	−0.0560067	−	0.0323355i	−0.527742	+	0.849405i	$0.676961\pi$
$104$	−2.36603	+	4.09808i	−0.232008	+	0.401849i
$105$	11.8175	+	5.31880i	1.15327	+	0.519062i
$106$	−0.267949	−	0.464102i	−0.0260255	−	0.0450775i
$107$			10.3156i			0.997246i	0.866819	+	0.498623i	$0.166161\pi$
$107$			10.3156i			0.997246i	−0.866819	+	0.498623i	$0.833839\pi$
$108$	−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	$0.707353\pi$
$110$	−1.44861	−	0.235442i	−0.138120	−	0.0224485i
$111$	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	−0.410254	−	0.911971i	$-0.634560\pi$
$113$	−14.9372	−	8.62398i	−1.40517	−	0.811276i	−0.994917	+	0.100695i	$0.967893\pi$
$114$	−0.464102	−	0.464102i	−0.0434671	−	0.0434671i
$115$	−1.14248	−	0.185687i	−0.106537	−	0.0173154i
$116$	0.803848			0.0746354
$117$	−7.34847			−0.679366
$118$		−	4.89898i		−	0.450988i
$119$	8.83013	+	15.2942i	0.809456	+	1.40202i
$120$	6.07081	−	4.37333i	0.554187	−	0.399229i
$121$	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	$-0.719553\pi$
$127$		−	17.3867i		−	1.54282i	0.636340	−	0.771409i	$-0.280447\pi$
$128$	9.91808	−	5.72620i	0.876642	−	0.506130i
$129$	0.803848	+	0.803848i	0.0707748	+	0.0707748i
$130$	2.65099	−	1.00535i	0.232507	−	0.0881749i
$131$	−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
$135$	10.5953	+	4.76870i	0.911894	+	0.410425i
$136$	10.1962			0.874313
$137$	−13.6245	+	7.86611i	−1.16402	+	0.672047i	−0.952264	−	0.305276i	$-0.901251\pi$
$137$	−13.6245	+	7.86611i	−1.16402	+	0.672047i	−0.211755	+	0.977323i	$0.567918\pi$
$138$	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	$0.276849\pi$
$140$	−4.59526	−	12.1172i	−0.388370	−	1.02409i
$141$	−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	$0.110732\pi$
$150$	−4.47469	−	0.270787i	−0.365357	−	0.0221096i
$151$	−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
$155$	−0.262601	+	1.61571i	−0.0210926	+	0.129777i
$156$	5.19615	+	5.19615i	0.416025	+	0.416025i
$157$	11.1750	+	6.45189i	0.891863	+	0.514917i	0.874551	−	0.484933i	$-0.161156\pi$
$157$	11.1750	+	6.45189i	0.891863	+	0.514917i	0.0173114	+	0.999850i	$0.494489\pi$
$158$	3.34607	+	1.93185i	0.266199	+	0.153690i
$159$	−1.73205	+	0.464102i	−0.137361	+	0.0368057i
$160$	−11.3428	−	1.84354i	−0.896727	−	0.145744i
$161$	1.73205			0.136505
$162$		−	4.65874i		−	0.366025i
$163$			10.4543i			0.818844i	0.912345	+	0.409422i	$0.134270\pi$
$163$			10.4543i			0.818844i	−0.912345	+	0.409422i	$0.865730\pi$
$164$	−6.69615	−	11.5981i	−0.522882	−	0.905658i
$165$	−2.01549	+	4.47808i	−0.156906	+	0.348618i
$166$	−2.06218	+	3.57180i	−0.160056	+	0.277225i
$167$	8.60540	+	4.96833i	0.665906	+	0.384461i	0.794524	−	0.607233i	$-0.207721\pi$
$167$	8.60540	+	4.96833i	0.665906	+	0.384461i	−0.128618	+	0.991694i	$0.541054\pi$
$168$	−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	−0.110467	−	0.993880i	$-0.535235\pi$
$173$	9.14162	−	5.27792i	0.695025	−	0.401273i	0.805492	+	0.592607i	$0.201901\pi$
$174$	−0.107695	+	0.401924i	−0.00816435	+	0.0304698i
$175$	−5.29837	+	15.8692i	−0.400519	+	1.19960i
$176$	−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	$0.420811\pi$
$180$	−4.11999	−	10.8640i	−0.307086	−	0.809752i
$181$	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
$185$	3.36396	+	8.87039i	0.247323	+	0.652164i
$186$	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	0.378133	−	0.925751i	$-0.376566\pi$
$193$	−3.25813	−	1.88108i	−0.234526	−	0.135403i	−0.612658	+	0.790348i	$0.709900\pi$
$194$	3.92820	−	6.80385i	0.282029	−	0.488488i
$195$	−0.953512	−	9.43879i	−0.0682824	−	0.675926i
$196$	3.63397	+	6.29423i	0.259570	+	0.449588i
$197$			15.9353i			1.13534i	0.823255	+	0.567671i	$0.192155\pi$
$197$			15.9353i			1.13534i	−0.823255	+	0.567671i	$0.807845\pi$
$198$	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	$0.108561\pi$
$200$	6.40508	+	7.23023i	0.452908	+	0.511254i
$201$	−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
$205$	−2.77364	+	17.0655i	−0.193719	+	1.19190i
$206$	−0.339746			−0.0236712
$207$	1.55291			0.107935
$208$		−	6.03579i		−	0.418507i
$209$	−0.464102	−	0.803848i	−0.0321026	−	0.0556033i
$210$	6.67423	−	0.674235i	0.460566	−	0.0465266i
$211$	−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
$220$	4.59165	−	1.74131i	0.309569	−	0.117399i
$221$	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	−0.624324	−	0.781165i	$-0.714626\pi$
$223$	−3.88229	+	2.24144i	−0.259977	+	0.150098i	0.364347	+	0.931263i	$0.381292\pi$
$224$	17.1962			1.14897
$225$	−4.75039	+	14.2279i	−0.316693	+	0.948528i
$226$	−8.92820			−0.593895
$227$	22.8541	−	13.1948i	1.51688	−	0.875769i	0.517073	−	0.855941i	$-0.327021\pi$
$227$	22.8541	−	13.1948i	1.51688	−	0.875769i	0.999803	−	0.0198279i	$-0.00631184\pi$
$228$	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	$0.102372\pi$
$230$	−0.560220	+	0.212455i	−0.0369398	+	0.0140089i
$231$	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	$-0.925597\pi$
$233$		−	7.07107i		−	0.463241i	0.972806	−	0.231621i	$-0.0744028\pi$
$234$	−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	$0.176224\pi$
$240$	−3.91686	+	8.70260i	−0.252832	+	0.561750i
$241$	−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
$245$	1.50524	−	9.26136i	0.0961664	−	0.591686i
$246$	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
$250$	−0.232806	−	5.78269i	−0.0147240	−	0.365729i
$251$	−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
$255$	−16.5858	+	11.9482i	−1.03864	+	0.748223i
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	−14.5211	−	8.38375i	−0.905800	−	0.522964i	−0.0267223	−	0.999643i	$-0.508507\pi$
$257$	−14.5211	−	8.38375i	−0.905800	−	0.522964i	−0.879077	+	0.476679i	$0.841840\pi$
$258$	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	−0.951888	−	0.306446i	$-0.900860\pi$
$263$	−18.8516	+	10.8840i	−1.16244	+	0.671136i	−0.210554	+	0.977582i	$0.567527\pi$
$264$	−3.00000	−	3.00000i	−0.184637	−	0.184637i
$265$	−0.820863	−	2.16452i	−0.0504252	−	0.132966i
$266$	−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	$0.566506\pi$
$270$	5.98396	−	0.604502i	0.364172	−	0.0367888i
$271$	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
$275$	−6.01343	−	2.00775i	−0.362623	−	0.121072i
$276$	−1.09808	−	1.09808i	−0.0660964	−	0.0660964i
$277$	−10.6066	+	6.12372i	−0.637289	+	0.367939i	−0.783569	−	0.621304i	$-0.786603\pi$
$277$	−10.6066	+	6.12372i	−0.637289	+	0.367939i	0.146281	+	0.989243i	$0.453270\pi$
$278$			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	0.864439	−	0.502738i	$-0.167674\pi$
$283$	14.4889	+	8.36516i	0.861275	+	0.497257i	−0.00316407	+	0.999995i	$0.501007\pi$
$284$	−12.2942	+	21.2942i	−0.729528	+	1.26358i
$285$	−1.65722	−	2.30046i	−0.0981652	−	0.136267i
$286$	−0.803848	−	1.39230i	−0.0475325	−	0.0823287i
$287$		−	25.8719i		−	1.52717i
$288$	15.4176			0.908494
$289$	−10.8564			−0.638612
$290$	−0.530228	−	0.0861776i	−0.0311361	−	0.00506052i
$291$	−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	0.805980	−	0.591943i	$-0.201639\pi$
$293$	11.9193	+	6.88160i	0.696332	+	0.402027i	−0.109648	+	0.993970i	$0.534972\pi$
$294$	−3.63397	+	0.973721i	−0.211938	+	0.0567885i
$295$	3.39496	−	20.8883i	0.197662	−	1.21616i
$296$	−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
$300$	13.4197	−	6.70163i	0.774786	−	0.386919i
$301$	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	$0.0348276\pi$
$307$			3.82654i			0.218392i	−0.994020	+	0.109196i	$0.965172\pi$
$308$	−6.36396	+	3.67423i	−0.362620	+	0.209359i
$309$	−0.294229	+	1.09808i	−0.0167381	+	0.0624674i
$310$	0.300457	+	0.792271i	0.0170648	+	0.0449980i
$311$	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	−0.115302	−	0.993330i	$-0.536784\pi$
$313$	12.1595	−	7.02030i	0.687296	−	0.396811i	0.802598	+	0.596520i	$0.203450\pi$
$314$	6.67949			0.376946
$315$	3.60090	−	22.1554i	0.202888	−	1.24831i
$316$	−12.9282			−0.727268
$317$	3.49837	−	2.01978i	0.196488	−	0.113442i	−0.398528	−	0.917156i	$-0.630479\pi$
$317$	3.49837	−	2.01978i	0.196488	−	0.113442i	0.595016	+	0.803714i	$0.297146\pi$
$318$	−0.656339	+	0.656339i	−0.0368057	+	0.0368057i
$319$	−0.294229	+	0.509619i	−0.0164736	+	0.0285332i
$320$	4.74176	−	1.79824i	0.265072	−	0.100525i
$321$	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
$330$	0.255493	+	2.52912i	0.0140644	+	0.139223i
$331$	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
$335$	−16.7491	−	2.72222i	−0.915100	−	0.148731i
$336$	3.69615	−	13.7942i	0.201642	−	0.752537i
$337$	5.79555	+	3.34607i	0.315704	+	0.182272i	0.649476	−	0.760382i	$-0.274988\pi$
$337$	5.79555	+	3.34607i	0.315704	+	0.182272i	−0.333772	+	0.942654i	$0.608322\pi$
$338$	−3.13801	−	1.81173i	−0.170685	−	0.0985453i
$339$	−7.73205	+	28.8564i	−0.419947	+	1.56726i
$340$	20.1765	+	3.27928i	1.09423	+	0.177844i
$341$	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
$345$	0.201501	+	1.99465i	0.0108484	+	0.107388i
$346$	2.73205	−	4.73205i	0.146876	−	0.254397i
$347$	−8.57321	−	4.94975i	−0.460234	−	0.265716i	0.251909	−	0.967751i	$-0.418942\pi$
$347$	−8.57321	−	4.94975i	−0.460234	−	0.265716i	−0.712143	+	0.702035i	$0.752275\pi$
$348$	−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	0.0487943	−	0.998809i	$-0.484462\pi$
$353$	17.6269	−	10.1769i	0.938185	−	0.541662i	0.889391	+	0.457147i	$0.151129\pi$
$354$	−8.19615	+	2.19615i	−0.435621	+	0.116724i
$355$	29.6809	−	11.2560i	1.57530	−	0.597408i
$356$	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
$365$	6.72792	+	17.7408i	0.352156	+	0.928595i
$366$	1.54552	−	5.76795i	0.0807855	−	0.301496i
$367$	−29.9623	+	17.2987i	−1.56402	+	0.902986i	−0.567175	+	0.823597i	$0.691964\pi$
$367$	−29.9623	+	17.2987i	−1.56402	+	0.902986i	−0.996844	+	0.0793890i	$0.974703\pi$
$368$			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	−0.256557	−	0.966529i	$-0.582588\pi$
$373$	−23.5983	−	13.6245i	−1.22187	−	0.705450i	−0.965317	+	0.261079i	$0.915922\pi$
$374$	−1.73205	+	3.00000i	−0.0895622	+	0.155126i
$375$	−18.8915	−	4.25551i	−0.975555	−	0.219754i
$376$	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	$0.666631\pi$
$380$	−0.454838	+	2.79850i	−0.0233327	+	0.143560i
$381$	−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	0.716913	−	0.697163i	$-0.245555\pi$
$383$	9.22955	+	5.32868i	0.471608	+	0.272283i	−0.245305	+	0.969446i	$0.578888\pi$
$384$	−14.0263	−	14.0263i	−0.715776	−	0.715776i
$385$	9.36396	+	1.52192i	0.477232	+	0.0775641i
$386$	−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	$0.832330\pi$
$390$	−2.87039	−	3.98451i	−0.145348	−	0.201763i
$391$	−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	$0.264050\pi$
$397$			29.3939i			1.47524i	−0.675218	+	0.737618i	$0.735950\pi$
$398$	11.9193	−	6.88160i	0.597459	−	0.344943i
$399$	3.00000	+	3.00000i	0.150188	+	0.150188i
$400$	−11.6863	−	3.90182i	−0.584317	−	0.195091i
$401$	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
$405$	3.22848	−	19.8640i	0.160424	−	0.987048i
$406$	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	$0.300728\pi$
$410$	3.17348	+	8.36811i	0.156727	+	0.413271i
$411$	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	$-0.0144060\pi$
$420$	−18.2124	+	13.1200i	−0.888676	+	0.640190i
$421$	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
$425$	−17.4990	−	19.7533i	−0.848827	−	0.958178i
$426$	−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
$430$	−0.121873	+	0.749856i	−0.00587726	+	0.0361612i
$431$	−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	$-0.894357\pi$
$433$		−	13.5601i		−	0.651658i	0.945429	−	0.325829i	$-0.105643\pi$
$434$	−0.633975	−	1.09808i	−0.0304318	−	0.0527093i
$435$	−0.737721	+	1.63909i	−0.0353710	+	0.0785884i
$436$	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	−0.465577	−	0.885008i	$-0.654153\pi$
$443$	1.43280	−	0.827225i	0.0680742	−	0.0393027i	0.533651	+	0.845705i	$0.320820\pi$
$444$	−3.29423	+	12.2942i	−0.156337	+	0.583458i
$445$	−28.0002	+	10.6187i	−1.32734	+	0.503373i
$446$	−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
$455$	−17.1363	+	6.49867i	−0.803361	+	0.304663i
$456$	2.36603	−	0.633975i	0.110799	−	0.0296886i
$457$	21.4770	−	12.3998i	1.00465	−	0.580036i	0.0950304	−	0.995474i	$-0.469705\pi$
$457$	21.4770	−	12.3998i	1.00465	−	0.580036i	0.909621	+	0.415438i	$0.136372\pi$
$458$		−	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	0.991321	−	0.131467i	$-0.0419686\pi$
$463$	29.5462	+	17.0585i	1.37313	+	0.792776i	0.381807	+	0.924242i	$0.375302\pi$
$464$	−0.571797	+	0.990381i	−0.0265450	+	0.0459773i
$465$	2.82086	−	0.284965i	0.130814	−	0.0132149i
$466$	−1.83013	−	3.16987i	−0.0847790	−	0.146842i
$467$		−	25.3543i		−	1.17326i	−0.809856	−	0.586629i	$-0.800455\pi$
$467$		−	25.3543i		−	1.17326i	0.809856	−	0.586629i	$-0.199545\pi$
$468$	6.36396	−	11.0227i	0.294174	−	0.509525i
$469$	25.3923			1.17251
$470$	0.550957	−	3.38989i	0.0254137	−	0.156364i
$471$	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
$475$	2.73980	−	2.42713i	0.125711	−	0.111364i
$476$	−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	$0.803156\pi$
$480$	2.00054	+	19.8033i	0.0913118	+	0.903893i
$481$	−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	$-0.883204\pi$
$487$		−	15.8338i		−	0.717496i	0.933435	−	0.358748i	$-0.116796\pi$
$488$	−11.1428	+	6.43331i	−0.504412	+	0.291222i
$489$	17.4904	−	4.68653i	0.790942	−	0.211932i
$490$	−1.72223	−	4.54134i	−0.0778026	−	0.205157i
$491$	−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
$495$	8.39550	+	1.36451i	0.377350	+	0.0613304i
$496$	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	$-0.0126375\pi$
$500$	10.3492	+	16.3674i	0.462832	+	0.731974i
$501$	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	$0.0176553\pi$
$503$			2.48665i			0.110874i	−0.998462	+	0.0554372i	$0.982345\pi$
$504$	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	$0.0447990\pi$
$510$	−4.34278	+	9.64893i	−0.192302	+	0.427262i
$511$	−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
$515$	−1.44861	−	0.235442i	−0.0638334	−	0.0103748i
$516$	−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
$520$	−1.69748	+	10.4441i	−0.0744394	+	0.458006i
$521$	−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	$-0.720574\pi$
$523$		−	35.1894i		−	1.53873i	0.638812	−	0.769363i	$-0.279426\pi$
$524$	−11.1962	−	19.3923i	−0.489106	−	0.847157i
$525$	28.9249	+	1.75039i	1.26238	+	0.0763934i
$526$	−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
$535$	8.17917	+	21.5675i	0.353616	+	0.932446i
$536$	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
$540$	−16.3288	+	11.7631i	−0.702680	+	0.506202i
$541$	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
$545$	−26.4697	+	10.0382i	−1.13384	+	0.429991i
$546$	5.19615	+	5.19615i	0.222375	+	0.222375i
$547$	22.5581	−	13.0239i	0.964513	−	0.556862i	0.0669541	−	0.997756i	$-0.478672\pi$
$547$	22.5581	−	13.0239i	0.964513	−	0.556862i	0.897559	+	0.440894i	$0.145339\pi$
$548$		−	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
$555$	13.3324	−	9.60450i	0.565930	−	0.407688i
$556$	−6.92820	−	12.0000i	−0.293821	−	0.508913i
$557$			31.1127i			1.31829i	0.752017	+	0.659144i	$0.229081\pi$
$557$			31.1127i			1.31829i	−0.752017	+	0.659144i	$0.770919\pi$
$558$	−0.568406	−	0.984508i	−0.0240625	−	0.0416776i
$559$	−1.60770			−0.0679983
$560$	18.1977	+	2.95766i	0.768993	+	0.124984i
$561$	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	0.323052	−	0.946381i	$-0.395291\pi$
$563$	−7.94906	−	4.58939i	−0.335013	−	0.193420i	−0.658065	+	0.752962i	$0.728625\pi$
$564$	8.59808	−	2.30385i	0.362044	−	0.0970095i
$565$	−38.0681	−	6.18718i	−1.60154	−	0.260297i
$566$	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	$0.622655\pi$
$570$	−1.33831	−	0.602347i	−0.0560558	−	0.0252295i
$571$	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	$-0.906811\pi$
$577$		−	13.8647i		−	0.577196i	0.957450	−	0.288598i	$-0.0931892\pi$
$578$	−4.86679	+	2.80984i	−0.202432	+	0.116874i
$579$	−1.68653	+	6.29423i	−0.0700899	+	0.261579i
$580$	1.68066	−	0.637365i	0.0697856	−	0.0264652i
$581$	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
$585$	−15.3640	+	5.82655i	−0.635222	+	0.240898i
$586$	7.12436			0.294304
$587$	−4.21046	+	2.43091i	−0.173784	+	0.100334i	−0.584369	−	0.811488i	$-0.698658\pi$
$587$	−4.21046	+	2.43091i	−0.173784	+	0.100334i	0.410585	+	0.911822i	$0.365325\pi$
$588$	8.90138	−	8.90138i	0.367087	−	0.367087i
$589$	−0.267949	+	0.464102i	−0.0110407	+	0.0191230i
$590$	−3.88437	−	10.2426i	−0.159917	−	0.421683i
$591$	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	$-0.871421\pi$
$593$		−	19.1427i		−	0.786094i	0.919518	−	0.393047i	$-0.128579\pi$
$594$	−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	$0.312959\pi$
$600$	9.22508	−	13.9571i	0.376612	−	0.569798i
$601$	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
$605$	3.36920	−	20.7298i	0.136978	−	0.842787i
$606$	−2.19615	+	8.19615i	−0.0892126	+	0.332946i
$607$	18.1631	+	10.4865i	0.737218	+	0.425633i	0.821057	−	0.570846i	$-0.193385\pi$
$607$	18.1631	+	10.4865i	0.737218	+	0.425633i	−0.0838387	+	0.996479i	$0.526718\pi$
$608$	−3.25813	−	1.88108i	−0.132135	−	0.0762880i
$609$	0.696152	−	2.59808i	0.0282095	−	0.105279i
$610$	7.60922	+	1.23672i	0.308088	+	0.0500734i
$611$	7.26795			0.294030
$612$	−27.4249			−1.10858
$613$		−	9.62209i		−	0.388633i	−0.980939	−	0.194316i	$-0.937751\pi$
$613$		−	9.62209i		−	0.388633i	0.980939	−	0.194316i	$-0.0622488\pi$
$614$	0.990381	+	1.71539i	0.0399685	+	0.0692275i
$615$	29.7945	−	3.00985i	1.20143	−	0.121369i
$616$	−4.09808	+	7.09808i	−0.165116	+	0.285990i
$617$	15.5935	+	9.00292i	0.627771	+	0.362444i	0.779888	−	0.625919i	$-0.215276\pi$
$617$	15.5935	+	9.00292i	0.627771	+	0.362444i	−0.152117	+	0.988362i	$0.548609\pi$
$618$	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
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	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
$630$	−4.11999	−	10.8640i	−0.164144	−	0.432831i
$631$	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
$635$	−13.7858	−	36.3515i	−0.547072	−	1.44257i
$636$	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	0.261928	−	0.965087i	$-0.415642\pi$
$643$	−11.2308	−	6.48408i	−0.442898	−	0.255707i	−0.704826	+	0.709380i	$0.748975\pi$
$644$	−1.50000	+	2.59808i	−0.0591083	+	0.102379i
$645$	2.31803	+	1.04330i	0.0912722	+	0.0410797i
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$			19.4572i			0.764942i	0.923967	+	0.382471i	$0.124927\pi$
$647$			19.4572i			0.764942i	−0.923967	+	0.382471i	$0.875073\pi$
$648$	15.0573	+	8.69333i	0.591506	+	0.341506i
$649$	−12.0000			−0.471041
$650$	4.74548	−	4.20390i	0.186133	−	0.164891i
$651$	−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	$0.0652691\pi$
$653$	42.0339	+	24.2683i	1.64491	+	0.949691i	0.665861	+	0.746076i	$0.268064\pi$
$654$	8.02628	+	8.02628i	0.313852	+	0.313852i
$655$	−4.63760	+	28.5339i	−0.181206	+	1.11491i
$656$	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	$0.910012\pi$
$660$	−4.97166	−	6.90137i	−0.193521	−	0.268635i
$661$	−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
$670$	−8.21297	+	3.11465i	−0.317295	+	0.120329i
$671$	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	−0.989933	−	0.141538i	$-0.954795\pi$
$673$	−35.3417	+	20.4046i	−1.36232	+	0.786538i	−0.372391	+	0.928076i	$0.621462\pi$
$674$	3.46410			0.133432
$675$	25.9333	+	1.56936i	0.998174	+	0.0604047i
$676$	12.1244			0.466321
$677$	3.19376	−	1.84392i	0.122746	−	0.0708676i	−0.437370	−	0.899282i	$-0.644090\pi$
$677$	3.19376	−	1.84392i	0.122746	−	0.0708676i	0.560116	+	0.828414i	$0.310757\pi$
$678$	4.00240	+	14.9372i	0.153711	+	0.573659i
$679$	−25.3923	+	43.9808i	−0.974467	+	1.68783i
$680$	21.3178	−	8.08446i	0.817501	−	0.310025i
$681$	−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	$0.000618344\pi$
$683$			0.101536i			0.00388517i	−0.999998	+	0.00194258i	$0.999382\pi$
$684$		−	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
$690$	0.606584	+	0.842026i	0.0230923	+	0.0320554i
$691$	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
$695$	−2.86976	+	17.6569i	−0.108856	+	0.669763i
$696$	−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
$700$	−19.2153	−	21.6907i	−0.726268	−	0.819831i
$701$	−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
$705$	−10.4792	−	4.71645i	−0.394668	−	0.177632i
$706$	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
$715$	−2.46259	−	6.49357i	−0.0920957	−	0.242846i
$716$	−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	$0.771486\pi$
$720$	16.3156	+	2.65176i	0.608047	+	0.0988254i
$721$	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
$725$	−2.20107	−	0.734888i	−0.0817456	−	0.0272931i
$726$	−8.13397	+	2.17949i	−0.301880	+	0.0808885i
$727$	−1.19256	+	0.688524i	−0.0442296	+	0.0255360i	−0.521952	−	0.852975i	$-0.674796\pi$
$727$	−1.19256	+	0.688524i	−0.0442296	+	0.0255360i	0.477722	+	0.878511i	$0.341463\pi$
$728$		−	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	0.615491	−	0.788144i	$-0.288958\pi$
$733$	6.51626	+	3.76217i	0.240684	+	0.138959i	−0.374807	+	0.927103i	$0.622291\pi$
$734$	−8.95448	+	15.5096i	−0.330516	+	0.572470i
$735$	−16.1693	+	1.63343i	−0.596415	+	0.0602501i
$736$	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	$0.391699\pi$
$740$	−16.2189	−	2.63604i	−0.596217	−	0.0969027i
$741$	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	−0.118613	−	0.992941i	$-0.537845\pi$
$743$	−28.2893	−	16.3328i	−1.03783	−	0.599193i	−0.919218	+	0.393748i	$0.871178\pi$
$744$	−0.633975	+	2.36603i	−0.0232426	+	0.0867427i
$745$	1.53100	−	9.41982i	0.0560914	−	0.345115i
$746$	−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
$750$	−9.57026	+	2.98180i	−0.349456	+	0.108880i
$751$	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	$0.0426352\pi$
$757$			7.34847i			0.267085i	−0.991043	+	0.133542i	$0.957365\pi$
$758$	−8.72552	+	5.03768i	−0.316925	+	0.182977i
$759$	1.09808	−	0.294229i	0.0398576	−	0.0106798i
$760$	1.12132	+	2.95680i	0.0406746	+	0.107254i
$761$	−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
$768$	−2.32937	−	0.624153i	−0.0840540	−	0.0225222i
$769$	20.8205	−	36.0622i	0.750807	−	1.30044i	−0.196625	−	0.980479i	$-0.562998\pi$
$769$	20.8205	−	36.0622i	0.750807	−	1.30044i	0.947432	−	0.319957i	$-0.103668\pi$
$770$	4.59165	−	1.74131i	0.165472	−	0.0627526i
$771$	−7.51666	+	28.0526i	−0.270706	+	1.01029i
$772$	5.64325	−	3.25813i	0.203105	−	0.117263i
$773$			2.07055i			0.0744726i	0.999306	+	0.0372363i	$0.0118554\pi$
$773$			2.07055i			0.0744726i	−0.999306	+	0.0372363i	$0.988145\pi$
$774$		−	1.01924i		−	0.0366357i
$775$	0.732051	+	3.58630i	0.0262960	+	0.128824i
$776$	14.6603	+	25.3923i	0.526272	+	0.911531i
$777$	−17.3867	+	17.3867i	−0.623743	+	0.623743i
$778$	0.0557471	+	0.0321856i	0.00199863	+	0.00115391i
$779$	−2.83013	+	4.90192i	−0.101400	+	0.175630i
$780$	14.9840	+	6.74397i	0.536512	+	0.241473i
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$			1.41421i			0.0505722i
$783$	0.624153	−	2.32937i	0.0223054	−	0.0832449i
$784$	−10.3397			−0.369277
$785$	28.4800	+	4.62884i	1.01650	+	0.165210i
$786$	11.1962	−	3.00000i	0.399354	−	0.107006i
$787$	−22.6138	−	13.0561i	−0.806095	−	0.465399i	0.0395027	−	0.999219i	$-0.487423\pi$
$787$	−22.6138	−	13.0561i	−0.806095	−	0.465399i	−0.845598	+	0.533820i	$0.820756\pi$
$788$	−23.9029	−	13.8004i	−0.851507	−	0.491618i
$789$	26.6603	+	26.6603i	0.949130	+	0.949130i
$790$	8.52761	+	1.38599i	0.303399	+	0.0493112i
$791$	57.7128			2.05203
$792$	−3.67423	+	6.36396i	−0.130558	+	0.226134i
$793$			16.3142i			0.579335i
$794$	7.60770	+	13.1769i	0.269987	+	0.467631i
$795$	−3.25334	+	2.34366i	−0.115384	+	0.0831211i
$796$	−23.0263	+	39.8827i	−0.816145	+	1.41360i
$797$	−45.6202	−	26.3388i	−1.61595	−	0.932969i	−0.987953	−	0.154752i	$-0.950542\pi$
$797$	−45.6202	−	26.3388i	−1.61595	−	0.932969i	−0.627996	−	0.778217i	$-0.716125\pi$
$798$	2.12132	+	0.568406i	0.0750939	+	0.0201214i
$799$	−7.83013	−	13.5622i	−0.277010	−	0.479795i
$800$	−25.1769	+	5.13922i	−0.890138	+	0.181699i
$801$	34.7942	−	20.0885i	1.22939	−	0.709791i
$802$		−	8.83701i		−	0.312046i
$803$	9.31749	−	5.37945i	0.328807	−	0.189837i
$804$	−16.0981	−	16.0981i	−0.567735	−	0.567735i
$805$	3.62132	−	1.37333i	0.127635	−	0.0484036i
$806$	−0.464102	+	0.803848i	−0.0163473	+	0.0283143i
$807$	3.05008	+	11.3831i	0.107368	+	0.400703i
$808$	15.8338	−	9.14162i	0.557029	−	0.321601i
$809$	25.1769			0.885173			0.442587	−	0.896726i	$-0.354061\pi$
$809$	25.1769			0.885173			0.442587	+	0.896726i	$0.354061\pi$
$810$	−3.69389	−	9.74036i	−0.129790	−	0.342241i
$811$	−39.5692			−1.38946			−0.694732	−	0.719269i	$-0.744477\pi$
$811$	−39.5692			−1.38946			−0.694732	+	0.719269i	$0.744477\pi$
$812$	−2.32937	+	1.34486i	−0.0817449	+	0.0471954i
$813$	−9.64566	−	35.9981i	−0.338288	−	1.26251i
$814$	1.39230	−	2.41154i	0.0488003	−	0.0845245i
$815$	8.28914	+	21.8575i	0.290356	+	0.765636i
$816$	15.9282	+	15.9282i	0.557599	+	0.557599i
$817$	−0.416102	+	0.240237i	−0.0145576	+	0.00840482i
$818$			8.55961i			0.299280i
$819$	21.2942	−	12.2942i	0.744081	−	0.429595i
$820$	−23.1962	−	18.9396i	−0.810045	−	0.661399i
$821$	−14.7224	−	25.5000i	−0.513816	−	0.889956i	−0.999872	−	0.0160280i	$-0.994898\pi$
$821$	−14.7224	−	25.5000i	−0.513816	−	0.889956i	0.486055	−	0.873928i	$-0.338435\pi$
$822$	13.6245	+	3.65067i	0.475209	+	0.127332i
$823$	−16.6102	−	9.58991i	−0.578995	−	0.334283i	0.181739	−	0.983347i	$-0.441828\pi$
$823$	−16.6102	−	9.58991i	−0.578995	−	0.334283i	−0.760734	+	0.649064i	$0.775161\pi$
$824$	0.633975	−	1.09808i	0.0220856	−	0.0382533i
$825$	−0.663289	+	10.9607i	−0.0230928	+	0.381603i
$826$	8.19615	+	14.1962i	0.285181	+	0.493947i
$827$		−	23.8014i		−	0.827656i	−0.910355	−	0.413828i	$-0.864192\pi$
$827$		−	23.8014i		−	0.827656i	0.910355	−	0.413828i	$-0.135808\pi$
$828$	−1.34486	+	2.32937i	−0.0467372	+	0.0809513i
$829$	−0.411543			−0.0142935			−0.00714673	−	0.999974i	$-0.502275\pi$
$829$	−0.411543			−0.0142935			−0.00714673	+	0.999974i	$0.502275\pi$
$830$	−1.47949	+	9.10289i	−0.0513537	+	0.315966i
$831$	15.0000	+	15.0000i	0.520344	+	0.520344i
$832$	4.81105	+	2.77766i	0.166793	+	0.0962980i
$833$	−19.1798	−	11.0735i	−0.664541	−	0.383673i
$834$	6.92820	−	1.85641i	0.239904	−	0.0642821i
$835$	21.9313	+	3.56447i	0.758963	+	0.123354i
$836$	1.60770			0.0556033
$837$	−3.67423	+	0.984508i	−0.127000	+	0.0340296i
$838$		−	11.4152i		−	0.394333i
$839$	2.36603	+	4.09808i	0.0816843	+	0.141481i	0.903974	−	0.427588i	$-0.140637\pi$
$839$	2.36603	+	4.09808i	0.0816843	+	0.141481i	−0.822289	+	0.569070i	$0.807303\pi$
$840$	−10.2751	+	22.8296i	−0.354526	+	0.787696i
$841$	14.3923	−	24.9282i	0.496286	−	0.859593i
$842$	8.72552	+	5.03768i	0.300701	+	0.173610i
$843$	24.1667	−	24.1667i	0.832346	−	0.832346i
$844$	−9.63397	−	16.6865i	−0.331615	−	0.574374i
$845$	−12.1244	−	9.89949i	−0.417091	−	0.340553i
$846$			4.60770i			0.158416i
$847$			31.4273i			1.07985i
$848$	−2.20925	+	1.27551i	−0.0758661	+	0.0438013i
$849$	7.50000	−	27.9904i	0.257399	−	0.960627i
$850$	−12.9571	−	4.32611i	−0.444426	−	0.148384i
$851$	1.09808	−	1.90192i	0.0376416	−	0.0651971i
$852$	41.1373	+	11.0227i	1.40934	+	0.377632i
$853$	37.6154	−	21.7172i	1.28793	−	0.743584i	0.309641	−	0.950853i	$-0.399791\pi$
$853$	37.6154	−	21.7172i	1.28793	−	0.743584i	0.978284	+	0.207269i	$0.0664576\pi$
$854$	−11.5359			−0.394750
$855$	−3.10583	+	3.80385i	−0.106217	+	0.130089i
$856$	−19.9282			−0.681132
$857$	−11.9193	+	6.88160i	−0.407155	+	0.235071i	−0.689567	−	0.724222i	$-0.742199\pi$
$857$	−11.9193	+	6.88160i	−0.407155	+	0.235071i	0.282412	+	0.959293i	$0.408866\pi$
$858$	−1.96902	+	1.96902i	−0.0672211	+	0.0672211i
$859$	18.2224	−	31.5622i	0.621741	−	1.07689i	−0.367420	−	0.930055i	$-0.619759\pi$
$859$	18.2224	−	31.5622i	0.621741	−	1.07689i	0.989161	−	0.146832i	$-0.0469078\pi$
$860$	−0.901371	−	2.37681i	−0.0307365	−	0.0810487i
$861$	−43.2846	+	11.5981i	−1.47514	+	0.395261i
$862$	−2.68973	+	1.55291i	−0.0916124	+	0.0528925i
$863$			44.9131i			1.52886i	0.644708	+	0.764429i	$0.276979\pi$
$863$			44.9131i			1.52886i	−0.644708	+	0.764429i	$0.723021\pi$
$864$	−6.91154	−	25.7942i	−0.235135	−	0.877537i
$865$	14.9282	−	18.2832i	0.507574	−	0.621649i
$866$	−3.50962	−	6.07884i	−0.119262	−	0.206567i
$867$	4.86679	+	18.1631i	0.165285	+	0.616852i
$868$	3.67423	+	2.12132i	0.124712	+	0.0720023i
$869$	4.73205	−	8.19615i	0.160524	−	0.278035i
$870$	0.0935168	+	0.925721i	0.00317052	+	0.0313849i
$871$	−9.29423	−	16.0981i	−0.314923	−	0.545463i
$872$		−	24.4577i		−	0.828243i
$873$	−22.7661	+	39.4321i	−0.770516	+	1.33457i
$874$	−0.196152			−0.00663495
$875$	1.50488	+	37.3799i	0.0508744	+	1.26367i
$876$	−6.58846	+	24.5885i	−0.222603	+	0.830767i
$877$	−25.3035	−	14.6090i	−0.854440	−	0.493311i	0.00770656	−	0.999970i	$-0.497547\pi$
$877$	−25.3035	−	14.6090i	−0.854440	−	0.493311i	−0.862146	+	0.506659i	$0.830880\pi$
$878$	−11.3509	−	6.55343i	−0.383073	−	0.221168i
$879$	6.16987	−	23.0263i	0.208105	−	0.776657i
$880$	−1.12077	+	6.89579i	−0.0377811	+	0.232457i
$881$	−39.5885			−1.33377			−0.666885	−	0.745161i	$-0.732373\pi$
$881$	−39.5885			−1.33377			−0.666885	+	0.745161i	$0.732373\pi$
$882$	3.25813	+	5.64325i	0.109707	+	0.190018i
$883$			54.4336i			1.83184i	0.401364	+	0.915919i	$0.368536\pi$
$883$			54.4336i			1.83184i	−0.401364	+	0.915919i	$0.631464\pi$
$884$	11.1962	+	19.3923i	0.376567	+	0.652234i
$885$	−36.4687	+	3.68409i	−1.22588	+	0.123839i
$886$	0.428203	−	0.741670i	0.0143858	−	0.0249169i
$887$	−7.43640	−	4.29341i	−0.249690	−	0.144159i	0.369932	−	0.929059i	$-0.379381\pi$
$887$	−7.43640	−	4.29341i	−0.249690	−	0.144159i	−0.619622	+	0.784900i	$0.712714\pi$
$888$	3.67423	+	13.7124i	0.123299	+	0.460159i
$889$	29.0885	+	50.3827i	0.975596	+	1.68978i
$890$	−9.80385	+	12.0072i	−0.328626	+	0.402483i
$891$	−11.4115			−0.382301
$892$		−	7.76457i		−	0.259977i
$893$	1.88108	−	1.08604i	0.0629481	−	0.0363431i
$894$	−3.69615	+	0.990381i	−0.123618	+	0.0331233i
$895$	13.7750	−	5.22394i	0.460446	−	0.174617i
$896$	−19.1603	+	33.1865i	−0.640099	+	1.10868i
$897$	−1.55291	+	1.55291i	−0.0518503	+	0.0518503i
$898$	5.37945	−	3.10583i	0.179515	−	0.103643i
$899$	0.339746			0.0113312
$900$	−17.2279	−	19.4473i	−0.574264	−	0.648244i
$901$	−5.46410			−0.182036
$902$	4.39494	−	2.53742i	0.146336	−	0.0844869i
$903$	−3.67423	−	0.984508i	−0.122271	−	0.0327624i
$904$	16.6603	−	28.8564i	0.554112	−	0.959750i
$905$	3.21121	−	1.21780i	0.106744	−	0.0404812i
$906$	−1.99296	+	7.43782i	−0.0662116	+	0.247105i
$907$	−9.98245	+	5.76337i	−0.331462	+	0.191370i	−0.656490	−	0.754335i	$-0.727960\pi$
$907$	−9.98245	+	5.76337i	−0.331462	+	0.191370i	0.325028	+	0.945704i	$0.394626\pi$
$908$			45.7081i			1.51688i
$909$	24.5885	+	14.1962i	0.815548	+	0.470857i
$910$	−6.00000	+	7.34847i	−0.198898	+	0.243599i
$911$	−24.9282	−	43.1769i	−0.825908	−	1.43051i	−0.901223	−	0.433355i	$-0.857330\pi$
$911$	−24.9282	−	43.1769i	−0.825908	−	1.43051i	0.0753150	−	0.997160i	$-0.476004\pi$
$912$	−2.20925	+	2.20925i	−0.0731557	+	0.0731557i
$913$	8.74908	+	5.05128i	0.289552	+	0.167173i
$914$	6.41858	−	11.1173i	0.212308	−	0.367728i
$915$	10.5869	−	23.5224i	0.349993	−	0.777625i
$916$	5.25833	+	9.10770i	0.173740	+	0.300927i
$917$		−	43.2586i		−	1.42853i
$918$	3.67423	−	13.7124i	0.121268	−	0.452578i
$919$	−47.1769			−1.55622			−0.778111	−	0.628126i	$-0.783822\pi$
$919$	−47.1769			−1.55622			−0.778111	+	0.628126i	$0.783822\pi$
$920$	0.358719	−	2.20711i	0.0118266	−	0.0727662i
$921$	6.40192	−	1.71539i	0.210951	−	0.0565240i
$922$	16.4579	+	9.50198i	0.542012	+	0.312931i
$923$	30.1146	+	17.3867i	0.991234	+	0.572289i
$924$	9.00000	+	9.00000i	0.296078	+	0.296078i
$925$	14.0665	+	15.8787i	0.462505	+	0.522088i
$926$	17.6603			0.580352
$927$	1.96902			0.0646710
$928$			2.38512i			0.0782954i
$929$	−1.73205	−	3.00000i	−0.0568267	−	0.0984268i	0.836213	−	0.548405i	$-0.184765\pi$
$929$	−1.73205	−	3.00000i	−0.0568267	−	0.0984268i	−0.893039	+	0.449979i	$0.851432\pi$
$930$	1.19080	−	0.857840i	0.0390480	−	0.0281297i
$931$	1.53590	−	2.66025i	0.0503370	−	0.0871863i
$932$	10.6066	+	6.12372i	0.347431	+	0.200589i
$933$	−16.8183	−	4.50644i	−0.550605	−	0.147534i
$934$	−6.56218	−	11.3660i	−0.214721	−	0.371908i
$935$	−9.46410	+	11.5911i	−0.309509	+	0.379070i
$936$		−	14.1962i		−	0.464016i
$937$			28.5617i			0.933069i	0.884503	+	0.466535i	$0.154498\pi$
$937$			28.5617i			0.933069i	−0.884503	+	0.466535i	$0.845502\pi$
$938$	11.3831	−	6.57201i	0.371670	−	0.214584i
$939$	−17.1962	−	17.1962i	−0.561175	−	0.561175i
$940$	4.07485	+	10.7449i	0.132907	+	0.350461i
$941$	−13.1603	+	22.7942i	−0.429012	+	0.743071i	−0.996786	−	0.0801141i	$-0.974472\pi$
$941$	−13.1603	+	22.7942i	−0.429012	+	0.743071i	0.567774	+	0.823185i	$0.307805\pi$
$942$	−2.99433	−	11.1750i	−0.0975607	−	0.364101i
$943$	3.46618	−	2.00120i	0.112874	−	0.0651681i
$944$	−23.3205			−0.759018
$945$	−38.6809	+	3.90756i	−1.25829	+	0.127113i
$946$	0.430781			0.0140059
$947$	4.12252	−	2.38014i	0.133964	−	0.0773441i	−0.431520	−	0.902103i	$-0.642023\pi$
$947$	4.12252	−	2.38014i	0.133964	−	0.0773441i	0.565484	+	0.824759i	$0.308689\pi$
$948$	5.79555	+	21.6293i	0.188231	+	0.702487i
$949$	−10.3923	+	18.0000i	−0.337348	+	0.584305i
$950$	0.600034	−	1.79716i	0.0194677	−	0.0583077i
$951$	−4.94744	−	4.94744i	−0.160432	−	0.160432i
$952$	−29.5462	+	17.0585i	−0.957597	+	0.552869i
$953$		−	51.1619i		−	1.65730i	−0.559770	−	0.828648i	$-0.689111\pi$
$953$		−	51.1619i		−	1.65730i	0.559770	−	0.828648i	$-0.310889\pi$
$954$	1.39230	+	0.803848i	0.0450775	+	0.0260255i
$955$	−30.5885	−	24.9754i	−0.989819	−	0.808184i
$956$	−0.803848	−	1.39230i	−0.0259983	−	0.0450304i
$957$	0.984508	+	0.263798i	0.0318246	+	0.00852738i
$958$	1.85752	+	1.07244i	0.0600138	+	0.0346490i
$959$	26.3205	−	45.5885i	0.849934	−	1.47213i
$960$	−5.13419	−	7.12699i	−0.165705	−	0.230023i
$961$	15.2321	+	26.3827i	0.491356	+	0.851054i
$962$			5.37945i			0.173441i
$963$	−15.4734	−	26.8007i	−0.498623	−	0.863641i
$964$	16.8564			0.542908
$965$	−8.30351	−	1.34956i	−0.267299	−	0.0434440i
$966$	−1.09808	−	1.09808i	−0.0353300	−	0.0353300i
$967$	−48.4300	−	27.9611i	−1.55740	−	0.899168i	−0.997504	−	0.0706076i	$-0.977506\pi$
$967$	−48.4300	−	27.9611i	−1.55740	−	0.899168i	−0.559900	−	0.828560i	$-0.689160\pi$
$968$	15.7136	+	9.07227i	0.505055	+	0.291594i
$969$	−6.46410	+	1.73205i	−0.207657	+	0.0556415i
$970$	2.81825	−	17.3399i	0.0904884	−	0.556752i
$971$	38.1962			1.22577			0.612886	−	0.790171i	$-0.290008\pi$
$971$	38.1962			1.22577			0.612886	+	0.790171i	$0.290008\pi$
$972$	19.0919	−	19.0919i	0.612372	−	0.612372i
$973$		−	26.7685i		−	0.858159i
$974$	−4.09808	−	7.09808i	−0.131311	−	0.227437i
$975$	−9.47753	−	18.9783i	−0.303524	−	0.607793i
$976$	8.20577	−	14.2128i	0.262660	−	0.454941i
$977$	13.4722	+	7.77817i	0.431014	+	0.248846i	0.699778	−	0.714360i	$-0.253282\pi$
$977$	13.4722	+	7.77817i	0.431014	+	0.248846i	−0.268765	+	0.963206i	$0.586615\pi$
$978$	6.62776	−	6.62776i	0.211932	−	0.211932i
$979$	8.49038	+	14.7058i	0.271354	+	0.469998i
$980$	12.5885	+	10.2784i	0.402124	+	0.328332i
$981$	32.8923	−	18.9904i	1.05017	−	0.606316i
$982$			17.4510i			0.556885i
$983$	−28.9456	+	16.7117i	−0.923221	+	0.533022i	−0.884661	−	0.466234i	$-0.845610\pi$
$983$	−28.9456	+	16.7117i	−0.923221	+	0.533022i	−0.0385597	+	0.999256i	$0.512277\pi$
$984$	−6.69615	+	24.9904i	−0.213466	+	0.796664i
$985$	12.6350	+	33.3170i	0.402584	+	1.06157i
$986$	−0.633975	+	1.09808i	−0.0201899	+	0.0349699i
$987$	16.6102	+	4.45069i	0.528709	+	0.141667i
$988$	−2.68973	+	1.55291i	−0.0855716	+	0.0494048i
$989$	0.339746			0.0108033
$990$	4.11676	−	1.56122i	0.130839	−	0.0496188i
$991$	38.9282			1.23660			0.618298	−	0.785944i	$-0.287823\pi$
$991$	38.9282			1.23660			0.618298	+	0.785944i	$0.287823\pi$
$992$	3.25813	−	1.88108i	0.103446	−	0.0597245i
$993$	10.2784	−	10.2784i	0.326176	−	0.326176i
$994$	−12.2942	+	21.2942i	−0.389949	+	0.675412i
$995$	55.5904	−	21.0818i	1.76233	−	0.668338i
$996$	−23.0885	+	6.18653i	−0.731586	+	0.196028i
$997$	−8.90138	+	5.13922i	−0.281910	+	0.162761i	−0.634288	−	0.773097i	$-0.718706\pi$
$997$	−8.90138	+	5.13922i	−0.281910	+	0.162761i	0.352378	+	0.935858i	$0.385373\pi$
$998$		−	12.3490i		−	0.390900i
$999$	−15.5885	+	15.5885i	−0.493197	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.2.j.a.4.3	yes	8
3.2	odd	2		135.2.j.a.64.2		8
4.3	odd	2		720.2.by.d.49.3		8
5.2	odd	4		225.2.e.d.76.3		8
5.3	odd	4		225.2.e.d.76.2		8
5.4	even	2	inner	45.2.j.a.4.2	✓	8
9.2	odd	6		135.2.j.a.19.3		8
9.4	even	3		405.2.b.d.244.3		4
9.5	odd	6		405.2.b.c.244.2		4
9.7	even	3	inner	45.2.j.a.34.2	yes	8
12.11	even	2		2160.2.by.c.1009.1		8
15.2	even	4		675.2.e.d.226.2		8
15.8	even	4		675.2.e.d.226.3		8
15.14	odd	2		135.2.j.a.64.3		8
20.19	odd	2		720.2.by.d.49.2		8
36.7	odd	6		720.2.by.d.529.2		8
36.11	even	6		2160.2.by.c.289.3		8
45.2	even	12		675.2.e.d.451.2		8
45.4	even	6		405.2.b.d.244.2		4
45.7	odd	12		225.2.e.d.151.3		8
45.13	odd	12		2025.2.a.t.1.3		4
45.14	odd	6		405.2.b.c.244.3		4
45.22	odd	12		2025.2.a.t.1.2		4
45.23	even	12		2025.2.a.r.1.2		4
45.29	odd	6		135.2.j.a.19.2		8
45.32	even	12		2025.2.a.r.1.3		4
45.34	even	6	inner	45.2.j.a.34.3	yes	8
45.38	even	12		675.2.e.d.451.3		8
45.43	odd	12		225.2.e.d.151.2		8
60.59	even	2		2160.2.by.c.1009.3		8
180.79	odd	6		720.2.by.d.529.3		8
180.119	even	6		2160.2.by.c.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.2	✓	8	5.4	even	2	inner
45.2.j.a.4.3	yes	8	1.1	even	1	trivial
45.2.j.a.34.2	yes	8	9.7	even	3	inner
45.2.j.a.34.3	yes	8	45.34	even	6	inner
135.2.j.a.19.2		8	45.29	odd	6
135.2.j.a.19.3		8	9.2	odd	6
135.2.j.a.64.2		8	3.2	odd	2
135.2.j.a.64.3		8	15.14	odd	2
225.2.e.d.76.2		8	5.3	odd	4
225.2.e.d.76.3		8	5.2	odd	4
225.2.e.d.151.2		8	45.43	odd	12
225.2.e.d.151.3		8	45.7	odd	12
405.2.b.c.244.2		4	9.5	odd	6
405.2.b.c.244.3		4	45.14	odd	6
405.2.b.d.244.2		4	45.4	even	6
405.2.b.d.244.3		4	9.4	even	3
675.2.e.d.226.2		8	15.2	even	4
675.2.e.d.226.3		8	15.8	even	4
675.2.e.d.451.2		8	45.2	even	12
675.2.e.d.451.3		8	45.38	even	12
720.2.by.d.49.2		8	20.19	odd	2
720.2.by.d.49.3		8	4.3	odd	2
720.2.by.d.529.2		8	36.7	odd	6
720.2.by.d.529.3		8	180.79	odd	6
2025.2.a.r.1.2		4	45.23	even	12
2025.2.a.r.1.3		4	45.32	even	12
2025.2.a.t.1.2		4	45.22	odd	12
2025.2.a.t.1.3		4	45.13	odd	12
2160.2.by.c.289.1		8	180.119	even	6
2160.2.by.c.289.3		8	36.11	even	6
2160.2.by.c.1009.1		8	12.11	even	2
2160.2.by.c.1009.3		8	60.59	even	2

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)

\(f(q)\)	\(=\)	\(q+(0.448288 - 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(2.09077 - 0.792893i) q^{5} +(-0.633975 - 0.633975i) q^{6} +(-2.89778 + 1.67303i) q^{7} +1.93185i q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.448288 - 0.258819i) q^{2} +(-0.448288 - 1.67303i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(2.09077 - 0.792893i) 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} +(-2.26380 - 3.14248i) q^{15} +(-1.23205 - 2.13397i) q^{16} -5.27792i q^{17} +(-0.776457 + 1.34486i) q^{18} +0.732051 q^{19} +(-0.621320 + 3.82282i) 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} +(3.74264 - 3.31552i) q^{25} +1.26795 q^{26} +(3.67423 + 3.67423i) q^{27} -5.79555i q^{28} +(-0.232051 - 0.401924i) q^{29} +(-1.82817 - 0.822821i) 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} +(1.53175 + 4.03906i) 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} +(0.819661 - 2.45497i) 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} +(6.67423 - 0.674235i) q^{60} +(3.33013 + 5.76795i) q^{61} +0.378937i q^{62} +(5.01910 - 8.69333i) q^{63} +2.26795 q^{64} +(5.40629 + 0.878680i) 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} +(-0.621320 + 3.82282i) q^{70} +14.1962 q^{71} +(-2.89778 - 5.01910i) q^{72} +8.48528i q^{73} +(1.09808 + 1.90192i) q^{74} +(-7.22474 - 4.77526i) 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} +(-4.18482 - 11.0349i) q^{85} +(-0.169873 + 0.294229i) q^{86} +(-0.568406 + 0.568406i) q^{87} +(2.12132 - 1.22474i) q^{88} -13.3923 q^{89} +(-0.557061 + 3.42745i) q^{90} -8.19615 q^{91} +(0.776457 - 0.448288i) q^{92} +(1.22474 + 0.328169i) q^{93} +(0.767949 - 1.33013i) q^{94} +(1.53055 - 0.580438i) 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

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