LMFDB - Embedded newform 225.2.e.d.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(76,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
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:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.3
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.2.e.d.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.448288i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.633975 + 0.633975i) q^{6} +(-1.67303 + 2.89778i) q^{7} +1.93185 q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.448288i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.633975 + 0.633975i) q^{6} +(-1.67303 + 2.89778i) q^{7} +1.93185 q^{8} +(2.59808 + 1.50000i) q^{9} +(-0.633975 + 1.09808i) q^{11} +(-0.776457 - 2.89778i) q^{12} +(1.22474 + 2.12132i) q^{13} +(0.866025 + 1.50000i) q^{14} +(-1.23205 + 2.13397i) q^{16} +5.27792 q^{17} +(1.34486 - 0.776457i) q^{18} -0.732051 q^{19} +(4.09808 - 4.09808i) q^{21} +(0.328169 + 0.568406i) q^{22} +(-0.258819 - 0.448288i) q^{23} +(-3.23205 - 0.866025i) q^{24} +1.26795 q^{26} +(-3.67423 - 3.67423i) q^{27} -5.79555 q^{28} +(0.232051 - 0.401924i) q^{29} +(-0.366025 - 0.633975i) q^{31} +(2.56961 + 4.45069i) q^{32} +(1.55291 - 1.55291i) q^{33} +(1.36603 - 2.36603i) q^{34} +5.19615i q^{36} -4.24264 q^{37} +(-0.189469 + 0.328169i) q^{38} +(-1.09808 - 4.09808i) q^{39} +(-3.86603 - 6.69615i) q^{41} +(-0.776457 - 2.89778i) q^{42} +(0.328169 - 0.568406i) q^{43} -2.19615 q^{44} -0.267949 q^{46} +(1.48356 - 2.56961i) q^{47} +(3.01790 - 3.01790i) q^{48} +(-2.09808 - 3.63397i) q^{49} +(-8.83013 - 2.36603i) q^{51} +(-2.12132 + 3.67423i) q^{52} -1.03528 q^{53} +(-2.59808 + 0.696152i) q^{54} +(-3.23205 + 5.59808i) q^{56} +(1.22474 + 0.328169i) q^{57} +(-0.120118 - 0.208051i) q^{58} +(-4.73205 - 8.19615i) q^{59} +(3.33013 - 5.76795i) q^{61} -0.378937 q^{62} +(-8.69333 + 5.01910i) q^{63} -2.26795 q^{64} +(-0.294229 - 1.09808i) q^{66} +(3.79435 + 6.57201i) q^{67} +(4.57081 + 7.91688i) q^{68} +(0.232051 + 0.866025i) q^{69} +14.1962 q^{71} +(5.01910 + 2.89778i) q^{72} +8.48528 q^{73} +(-1.09808 + 1.90192i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(-2.12132 - 3.67423i) q^{77} +(-2.12132 - 0.568406i) q^{78} +(-3.73205 + 6.46410i) q^{79} +(4.50000 + 7.79423i) q^{81} -4.00240 q^{82} +(3.98382 - 6.90018i) q^{83} +(9.69615 + 2.59808i) q^{84} +(-0.169873 - 0.294229i) q^{86} +(-0.568406 + 0.568406i) q^{87} +(-1.22474 + 2.12132i) q^{88} +13.3923 q^{89} -8.19615 q^{91} +(0.448288 - 0.776457i) q^{92} +(0.328169 + 1.22474i) q^{93} +(-0.767949 - 1.33013i) q^{94} +(-2.30385 - 8.59808i) q^{96} +(7.58871 - 13.1440i) q^{97} -2.17209 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} - 12 q^{11} + 4 q^{16} + 8 q^{19} + 12 q^{21} - 12 q^{24} + 24 q^{26} - 12 q^{29} + 4 q^{31} + 4 q^{34} + 12 q^{39} - 24 q^{41} + 24 q^{44} - 16 q^{46} + 4 q^{49} - 36 q^{51} - 12 q^{56} - 24 q^{59} - 8 q^{61} - 32 q^{64} + 60 q^{66} - 12 q^{69} + 72 q^{71} + 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{81} + 36 q^{84} - 36 q^{86} + 24 q^{89} - 24 q^{91} - 20 q^{94} - 60 q^{96} + 36 q^{99}+O(q^{100}) $ 8 * q - 12 * q^6 - 12 * q^11 + 4 * q^16 + 8 * q^19 + 12 * q^21 - 12 * q^24 + 24 * q^26 - 12 * q^29 + 4 * q^31 + 4 * q^34 + 12 * q^39 - 24 * q^41 + 24 * q^44 - 16 * q^46 + 4 * q^49 - 36 * q^51 - 12 * q^56 - 24 * q^59 - 8 * q^61 - 32 * q^64 + 60 * q^66 - 12 * q^69 + 72 * q^71 + 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^81 + 36 * q^84 - 36 * q^86 + 24 * q^89 - 24 * q^91 - 20 * q^94 - 60 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.258819	−	0.448288i	0.183013	−	0.316987i	−0.759892	−	0.650049i	$-0.774748\pi$
$2$	0.258819	−	0.448288i	0.183013	−	0.316987i	0.942905	+	0.333062i	$0.108082\pi$
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i
$4$	0.866025	+	1.50000i	0.433013	+	0.750000i
$5$		0			0
$5$		0			0
$6$	−0.633975	+	0.633975i	−0.258819	+	0.258819i
$7$	−1.67303	+	2.89778i	−0.632347	+	1.09526i	0.354724	+	0.934971i	$0.384575\pi$
$7$	−1.67303	+	2.89778i	−0.632347	+	1.09526i	−0.987071	+	0.160286i	$0.948758\pi$
$8$	1.93185			0.683013
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$		0			0
$11$	−0.633975	+	1.09808i	−0.191151	+	0.331082i	−0.945632	−	0.325239i	$-0.894555\pi$
$11$	−0.633975	+	1.09808i	−0.191151	+	0.331082i	0.754481	+	0.656322i	$0.227889\pi$
$12$	−0.776457	−	2.89778i	−0.224144	−	0.836516i
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	0.984373	−	0.176096i	$-0.0563468\pi$
$13$	1.22474	+	2.12132i	0.339683	+	0.588348i	−0.644690	+	0.764444i	$0.723014\pi$
$14$	0.866025	+	1.50000i	0.231455	+	0.400892i
$15$		0			0
$16$	−1.23205	+	2.13397i	−0.308013	+	0.533494i
$17$	5.27792			1.28008			0.640041	−	0.768340i	$-0.278917\pi$
$17$	5.27792			1.28008			0.640041	+	0.768340i	$0.278917\pi$
$18$	1.34486	−	0.776457i	0.316987	−	0.183013i
$19$	−0.732051			−0.167944			−0.0839720	−	0.996468i	$-0.526761\pi$
$19$	−0.732051			−0.167944			−0.0839720	+	0.996468i	$0.526761\pi$
$20$		0			0
$21$	4.09808	−	4.09808i	0.894274	−	0.894274i
$22$	0.328169	+	0.568406i	0.0699660	+	0.121185i
$23$	−0.258819	−	0.448288i	−0.0539675	−	0.0934745i	0.837780	−	0.546009i	$-0.183853\pi$
$23$	−0.258819	−	0.448288i	−0.0539675	−	0.0934745i	−0.891747	+	0.452534i	$0.850520\pi$
$24$	−3.23205	−	0.866025i	−0.659740	−	0.176777i
$25$		0			0
$26$	1.26795			0.248665
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$	−5.79555			−1.09526
$29$	0.232051	−	0.401924i	0.0430908	−	0.0746354i	−0.843676	−	0.536853i	$-0.819613\pi$
$29$	0.232051	−	0.401924i	0.0430908	−	0.0746354i	0.886766	+	0.462218i	$0.152946\pi$
$30$		0			0
$31$	−0.366025	−	0.633975i	−0.0657401	−	0.113865i	0.831282	−	0.555851i	$-0.187607\pi$
$31$	−0.366025	−	0.633975i	−0.0657401	−	0.113865i	−0.897022	+	0.441986i	$0.854274\pi$
$32$	2.56961	+	4.45069i	0.454247	+	0.786779i
$33$	1.55291	−	1.55291i	0.270328	−	0.270328i
$34$	1.36603	−	2.36603i	0.234271	−	0.405770i
$35$		0			0
$36$			5.19615i			0.866025i
$37$	−4.24264			−0.697486			−0.348743	−	0.937218i	$-0.613391\pi$
$37$	−4.24264			−0.697486			−0.348743	+	0.937218i	$0.613391\pi$
$38$	−0.189469	+	0.328169i	−0.0307359	+	0.0532361i
$39$	−1.09808	−	4.09808i	−0.175833	−	0.656217i
$40$		0			0
$41$	−3.86603	−	6.69615i	−0.603772	−	1.04576i	−0.992244	−	0.124303i	$-0.960331\pi$
$41$	−3.86603	−	6.69615i	−0.603772	−	1.04576i	0.388473	−	0.921460i	$-0.373003\pi$
$42$	−0.776457	−	2.89778i	−0.119810	−	0.447137i
$43$	0.328169	−	0.568406i	0.0500454	−	0.0866811i	−0.839918	−	0.542714i	$-0.817397\pi$
$43$	0.328169	−	0.568406i	0.0500454	−	0.0866811i	0.889963	+	0.456033i	$0.150730\pi$
$44$	−2.19615			−0.331082
$45$		0			0
$46$	−0.267949			−0.0395070
$47$	1.48356	−	2.56961i	0.216400	−	0.374816i	−0.737305	−	0.675560i	$-0.763902\pi$
$47$	1.48356	−	2.56961i	0.216400	−	0.374816i	0.953705	+	0.300744i	$0.0972351\pi$
$48$	3.01790	−	3.01790i	0.435596	−	0.435596i
$49$	−2.09808	−	3.63397i	−0.299725	−	0.519139i
$50$		0			0
$51$	−8.83013	−	2.36603i	−1.23647	−	0.331310i
$52$	−2.12132	+	3.67423i	−0.294174	+	0.509525i
$53$	−1.03528			−0.142206			−0.0711031	−	0.997469i	$-0.522652\pi$
$53$	−1.03528			−0.142206			−0.0711031	+	0.997469i	$0.522652\pi$
$54$	−2.59808	+	0.696152i	−0.353553	+	0.0947343i
$55$		0			0
$56$	−3.23205	+	5.59808i	−0.431901	+	0.748074i
$57$	1.22474	+	0.328169i	0.162221	+	0.0434671i
$58$	−0.120118	−	0.208051i	−0.0157723	−	0.0273184i
$59$	−4.73205	−	8.19615i	−0.616061	−	1.06705i	−0.990197	−	0.139675i	$-0.955394\pi$
$59$	−4.73205	−	8.19615i	−0.616061	−	1.06705i	0.374137	−	0.927373i	$-0.377939\pi$
$60$		0			0
$61$	3.33013	−	5.76795i	0.426379	−	0.738510i	−0.570169	−	0.821527i	$-0.693122\pi$
$61$	3.33013	−	5.76795i	0.426379	−	0.738510i	0.996548	+	0.0830172i	$0.0264556\pi$
$62$	−0.378937			−0.0481251
$63$	−8.69333	+	5.01910i	−1.09526	+	0.632347i
$64$	−2.26795			−0.283494
$65$		0			0
$66$	−0.294229	−	1.09808i	−0.0362170	−	0.135164i
$67$	3.79435	+	6.57201i	0.463554	+	0.802899i	0.999135	−	0.0415848i	$-0.0132407\pi$
$67$	3.79435	+	6.57201i	0.463554	+	0.802899i	−0.535581	+	0.844484i	$0.679907\pi$
$68$	4.57081	+	7.91688i	0.554292	+	0.960062i
$69$	0.232051	+	0.866025i	0.0279356	+	0.104257i
$70$		0			0
$71$	14.1962			1.68477			0.842387	−	0.538874i	$-0.181150\pi$
$71$	14.1962			1.68477			0.842387	+	0.538874i	$0.181150\pi$
$72$	5.01910	+	2.89778i	0.591506	+	0.341506i
$73$	8.48528			0.993127			0.496564	−	0.868000i	$-0.334595\pi$
$73$	8.48528			0.993127			0.496564	+	0.868000i	$0.334595\pi$
$74$	−1.09808	+	1.90192i	−0.127649	+	0.221094i
$75$		0			0
$76$	−0.633975	−	1.09808i	−0.0727219	−	0.125958i
$77$	−2.12132	−	3.67423i	−0.241747	−	0.418718i
$78$	−2.12132	−	0.568406i	−0.240192	−	0.0643593i
$79$	−3.73205	+	6.46410i	−0.419889	+	0.727268i	−0.995928	−	0.0901537i	$-0.971264\pi$
$79$	−3.73205	+	6.46410i	−0.419889	+	0.727268i	0.576039	+	0.817422i	$0.304597\pi$
$80$		0			0
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−4.00240			−0.441992
$83$	3.98382	−	6.90018i	0.437281	−	0.757393i	−0.560198	−	0.828359i	$-0.689275\pi$
$83$	3.98382	−	6.90018i	0.437281	−	0.757393i	0.997479	+	0.0709657i	$0.0226081\pi$
$84$	9.69615	+	2.59808i	1.05794	+	0.283473i
$85$		0			0
$86$	−0.169873	−	0.294229i	−0.0183179	−	0.0317275i
$87$	−0.568406	+	0.568406i	−0.0609395	+	0.0609395i
$88$	−1.22474	+	2.12132i	−0.130558	+	0.226134i
$89$	13.3923			1.41958			0.709791	−	0.704413i	$-0.248789\pi$
$89$	13.3923			1.41958			0.709791	+	0.704413i	$0.248789\pi$
$90$		0			0
$91$	−8.19615			−0.859190
$92$	0.448288	−	0.776457i	0.0467372	−	0.0809513i
$93$	0.328169	+	1.22474i	0.0340296	+	0.127000i
$94$	−0.767949	−	1.33013i	−0.0792079	−	0.137192i
$95$		0			0
$96$	−2.30385	−	8.59808i	−0.235135	−	0.877537i
$97$	7.58871	−	13.1440i	0.770516	−	1.33457i	−0.166764	−	0.985997i	$-0.553332\pi$
$97$	7.58871	−	13.1440i	0.770516	−	1.33457i	0.937280	−	0.348577i	$-0.113335\pi$
$98$	−2.17209			−0.219414
$99$	−3.29423	+	1.90192i	−0.331082	+	0.191151i
$100$		0			0
$101$	−4.73205	+	8.19615i	−0.470857	+	0.815548i	−0.999444	−	0.0333310i	$-0.989388\pi$
$101$	−4.73205	+	8.19615i	−0.470857	+	0.815548i	0.528588	+	0.848879i	$0.322722\pi$
$102$	−3.34607	+	3.34607i	−0.331310	+	0.331310i
$103$	−0.328169	−	0.568406i	−0.0323355	−	0.0560067i	0.849405	−	0.527742i	$-0.176961\pi$
$103$	−0.328169	−	0.568406i	−0.0323355	−	0.0560067i	−0.881740	+	0.471735i	$0.843628\pi$
$104$	2.36603	+	4.09808i	0.232008	+	0.401849i
$105$		0			0
$106$	−0.267949	+	0.464102i	−0.0260255	+	0.0450775i
$107$	−10.3156			−0.997246			−0.498623	−	0.866819i	$-0.666161\pi$
$107$	−10.3156			−0.997246			−0.498623	+	0.866819i	$0.666161\pi$
$108$	2.32937	−	8.69333i	0.224144	−	0.836516i
$109$	12.6603			1.21263			0.606316	−	0.795224i	$-0.292647\pi$
$109$	12.6603			1.21263			0.606316	+	0.795224i	$0.292647\pi$
$110$		0			0
$111$	7.09808	+	1.90192i	0.673720	+	0.180523i
$112$	−4.12252	−	7.14042i	−0.389542	−	0.674706i
$113$	−8.62398	−	14.9372i	−0.811276	−	1.40517i	−0.911971	−	0.410254i	$-0.865440\pi$
$113$	−8.62398	−	14.9372i	−0.811276	−	1.40517i	0.100695	−	0.994917i	$-0.467893\pi$
$114$	0.464102	−	0.464102i	0.0434671	−	0.0434671i
$115$		0			0
$116$	0.803848			0.0746354
$117$			7.34847i			0.679366i
$118$	−4.89898			−0.450988
$119$	−8.83013	+	15.2942i	−0.809456	+	1.40202i
$120$		0			0
$121$	4.69615	+	8.13397i	0.426923	+	0.739452i
$122$	−1.72380	−	2.98571i	−0.156066	−	0.270314i
$123$	3.46618	+	12.9360i	0.312535	+	1.16640i
$124$	0.633975	−	1.09808i	0.0569326	−	0.0986102i
$125$		0			0
$126$			5.19615i			0.462910i
$127$	17.3867			1.54282			0.771409	−	0.636340i	$-0.219553\pi$
$127$	17.3867			1.54282			0.771409	+	0.636340i	$0.219553\pi$
$128$	−5.72620	+	9.91808i	−0.506130	+	0.876642i
$129$	−0.803848	+	0.803848i	−0.0707748	+	0.0707748i
$130$		0			0
$131$	−6.46410	−	11.1962i	−0.564771	−	0.978212i	−0.997071	−	0.0764824i	$-0.975631\pi$
$131$	−6.46410	−	11.1962i	−0.564771	−	0.978212i	0.432300	−	0.901730i	$-0.357702\pi$
$132$	3.67423	+	0.984508i	0.319801	+	0.0856904i
$133$	1.22474	−	2.12132i	0.106199	−	0.183942i
$134$	3.92820			0.339345
$135$		0			0
$136$	10.1962			0.874313
$137$	−7.86611	+	13.6245i	−0.672047	+	1.16402i	0.305276	+	0.952264i	$0.401251\pi$
$137$	−7.86611	+	13.6245i	−0.672047	+	1.16402i	−0.977323	+	0.211755i	$0.932082\pi$
$138$	0.448288	+	0.120118i	0.0381608	+	0.0102252i
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$	−3.63397	+	3.63397i	−0.306036	+	0.306036i
$142$	3.67423	−	6.36396i	0.308335	−	0.534052i
$143$	−3.10583			−0.259722
$144$	−6.40192	+	3.69615i	−0.533494	+	0.308013i
$145$		0			0
$146$	2.19615	−	3.80385i	0.181755	−	0.314809i
$147$	1.88108	+	7.02030i	0.155149	+	0.579025i
$148$	−3.67423	−	6.36396i	−0.302020	−	0.523114i
$149$	−2.13397	−	3.69615i	−0.174822	−	0.302801i	0.765278	−	0.643700i	$-0.222602\pi$
$149$	−2.13397	−	3.69615i	−0.174822	−	0.302801i	−0.940100	+	0.340900i	$0.889268\pi$
$150$		0			0
$151$	−4.29423	+	7.43782i	−0.349459	+	0.605281i	−0.986154	−	0.165835i	$-0.946968\pi$
$151$	−4.29423	+	7.43782i	−0.349459	+	0.605281i	0.636694	+	0.771116i	$0.280301\pi$
$152$	−1.41421			−0.114708
$153$	13.7124	+	7.91688i	1.10858	+	0.640041i
$154$	−2.19615			−0.176971
$155$		0			0
$156$	5.19615	−	5.19615i	0.416025	−	0.416025i
$157$	−6.45189	−	11.1750i	−0.514917	−	0.891863i	−0.999850	−	0.0173114i	$-0.994489\pi$
$157$	−6.45189	−	11.1750i	−0.514917	−	0.891863i	0.484933	−	0.874551i	$-0.338844\pi$
$158$	1.93185	+	3.34607i	0.153690	+	0.266199i
$159$	1.73205	+	0.464102i	0.137361	+	0.0368057i
$160$		0			0
$161$	1.73205			0.136505
$162$	4.65874			0.366025
$163$	10.4543			0.818844			0.409422	−	0.912345i	$-0.365730\pi$
$163$	10.4543			0.818844			0.409422	+	0.912345i	$0.365730\pi$
$164$	6.69615	−	11.5981i	0.522882	−	0.905658i
$165$		0			0
$166$	−2.06218	−	3.57180i	−0.160056	−	0.277225i
$167$	−4.96833	−	8.60540i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$167$	−4.96833	−	8.60540i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$168$	7.91688	−	7.91688i	0.610800	−	0.610800i
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$		0			0
$171$	−1.90192	−	1.09808i	−0.145444	−	0.0839720i
$172$	1.13681			0.0866811
$173$	−5.27792	+	9.14162i	−0.401273	+	0.695025i	−0.993880	−	0.110467i	$-0.964765\pi$
$173$	−5.27792	+	9.14162i	−0.401273	+	0.695025i	0.592607	+	0.805492i	$0.298099\pi$
$174$	0.107695	+	0.401924i	0.00816435	+	0.0304698i
$175$		0			0
$176$	−1.56218	−	2.70577i	−0.117754	−	0.203955i
$177$	4.24264	+	15.8338i	0.318896	+	1.19014i
$178$	3.46618	−	6.00361i	0.259801	−	0.449989i
$179$	−6.58846			−0.492444			−0.246222	−	0.969213i	$-0.579189\pi$
$179$	−6.58846			−0.492444			−0.246222	+	0.969213i	$0.579189\pi$
$180$		0			0
$181$	1.53590			0.114162			0.0570812	−	0.998370i	$-0.481821\pi$
$181$	1.53590			0.114162			0.0570812	+	0.998370i	$0.481821\pi$
$182$	−2.12132	+	3.67423i	−0.157243	+	0.272352i
$183$	−8.15711	+	8.15711i	−0.602991	+	0.602991i
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$		0			0
$186$	0.633975	+	0.169873i	0.0464853	+	0.0124557i
$187$	−3.34607	+	5.79555i	−0.244689	+	0.423813i
$188$	5.13922			0.374816
$189$	16.7942	−	4.50000i	1.22160	−	0.327327i
$190$		0			0
$191$	−8.83013	+	15.2942i	−0.638926	+	1.10665i	0.346743	+	0.937960i	$0.387287\pi$
$191$	−8.83013	+	15.2942i	−0.638926	+	1.10665i	−0.985669	+	0.168691i	$0.946046\pi$
$192$	3.79435	+	1.01669i	0.273834	+	0.0733736i
$193$	−1.88108	−	3.25813i	−0.135403	−	0.234526i	0.790348	−	0.612658i	$-0.209900\pi$
$193$	−1.88108	−	3.25813i	−0.135403	−	0.234526i	−0.925751	+	0.378133i	$0.876566\pi$
$194$	−3.92820	−	6.80385i	−0.282029	−	0.488488i
$195$		0			0
$196$	3.63397	−	6.29423i	0.259570	−	0.449588i
$197$	−15.9353			−1.13534			−0.567671	−	0.823255i	$-0.692155\pi$
$197$	−15.9353			−1.13534			−0.567671	+	0.823255i	$0.692155\pi$
$198$			1.96902i			0.139932i
$199$	−26.5885			−1.88481			−0.942403	−	0.334480i	$-0.891439\pi$
$199$	−26.5885			−1.88481			−0.942403	+	0.334480i	$0.891439\pi$
$200$		0			0
$201$	−3.40192	−	12.6962i	−0.239953	−	0.895518i
$202$	2.44949	+	4.24264i	0.172345	+	0.298511i
$203$	0.776457	+	1.34486i	0.0544966	+	0.0943909i
$204$	−4.09808	−	15.2942i	−0.286923	−	1.07081i
$205$		0			0
$206$	−0.339746			−0.0236712
$207$		−	1.55291i		−	0.107935i
$208$	−6.03579			−0.418507
$209$	0.464102	−	0.803848i	0.0321026	−	0.0556033i
$210$		0			0
$211$	−5.56218	−	9.63397i	−0.382916	−	0.663230i	0.608562	−	0.793507i	$-0.291747\pi$
$211$	−5.56218	−	9.63397i	−0.382916	−	0.663230i	−0.991478	+	0.130276i	$0.958414\pi$
$212$	−0.896575	−	1.55291i	−0.0615771	−	0.106655i
$213$	−23.7506	−	6.36396i	−1.62737	−	0.436051i
$214$	−2.66987	+	4.62436i	−0.182509	+	0.316114i
$215$		0			0
$216$	−7.09808	−	7.09808i	−0.482963	−	0.482963i
$217$	2.44949			0.166282
$218$	3.27671	−	5.67544i	0.221927	−	0.384389i
$219$	−14.1962	−	3.80385i	−0.959287	−	0.257040i
$220$		0			0
$221$	6.46410	+	11.1962i	0.434823	+	0.753135i
$222$	2.68973	−	2.68973i	0.180523	−	0.180523i
$223$	2.24144	−	3.88229i	0.150098	−	0.259977i	−0.781165	−	0.624324i	$-0.785374\pi$
$223$	2.24144	−	3.88229i	0.150098	−	0.259977i	0.931263	+	0.364347i	$0.118708\pi$
$224$	−17.1962			−1.14897
$225$		0			0
$226$	−8.92820			−0.593895
$227$	13.1948	−	22.8541i	0.875769	−	1.51688i	0.0198279	−	0.999803i	$-0.493688\pi$
$227$	13.1948	−	22.8541i	0.875769	−	1.51688i	0.855941	−	0.517073i	$-0.172979\pi$
$228$	0.568406	+	2.12132i	0.0376436	+	0.140488i
$229$	−3.03590	−	5.25833i	−0.200618	−	0.347480i	0.748110	−	0.663575i	$-0.230962\pi$
$229$	−3.03590	−	5.25833i	−0.200618	−	0.347480i	−0.948728	+	0.316095i	$0.897628\pi$
$230$		0			0
$231$	1.90192	+	7.09808i	0.125137	+	0.467019i
$232$	0.448288	−	0.776457i	0.0294315	−	0.0509769i
$233$	−7.07107			−0.463241			−0.231621	−	0.972806i	$-0.574403\pi$
$233$	−7.07107			−0.463241			−0.231621	+	0.972806i	$0.574403\pi$
$234$	3.29423	+	1.90192i	0.215350	+	0.124333i
$235$		0			0
$236$	8.19615	−	14.1962i	0.533524	−	0.924091i
$237$	9.14162	−	9.14162i	0.593812	−	0.593812i
$238$	4.57081	+	7.91688i	0.296282	+	0.513175i
$239$	0.464102	+	0.803848i	0.0300202	+	0.0519966i	0.880645	−	0.473776i	$-0.157109\pi$
$239$	0.464102	+	0.803848i	0.0300202	+	0.0519966i	−0.850625	+	0.525773i	$0.823776\pi$
$240$		0			0
$241$	−4.86603	+	8.42820i	−0.313448	+	0.542908i	−0.979106	−	0.203348i	$-0.934818\pi$
$241$	−4.86603	+	8.42820i	−0.313448	+	0.542908i	0.665658	+	0.746257i	$0.268151\pi$
$242$	4.86181			0.312529
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$	11.5359			0.738510
$245$		0			0
$246$	6.69615	+	1.79423i	0.426931	+	0.114396i
$247$	−0.896575	−	1.55291i	−0.0570477	−	0.0988096i
$248$	−0.707107	−	1.22474i	−0.0449013	−	0.0777714i
$249$	−9.75833	+	9.75833i	−0.618409	+	0.618409i
$250$		0			0
$251$	−12.5885			−0.794576			−0.397288	−	0.917694i	$-0.630049\pi$
$251$	−12.5885			−0.794576			−0.397288	+	0.917694i	$0.630049\pi$
$252$	−15.0573	−	8.69333i	−0.948520	−	0.547628i
$253$	0.656339			0.0412637
$254$	4.50000	−	7.79423i	0.282355	−	0.489053i
$255$		0			0
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	8.38375	+	14.5211i	0.522964	+	0.905800i	0.999643	+	0.0267223i	$0.00850700\pi$
$257$	8.38375	+	14.5211i	0.522964	+	0.905800i	−0.476679	+	0.879077i	$0.658160\pi$
$258$	0.152304	+	0.568406i	0.00948203	+	0.0353874i
$259$	7.09808	−	12.2942i	0.441053	−	0.763926i
$260$		0			0
$261$	1.20577	−	0.696152i	0.0746354	−	0.0430908i
$262$	−6.69213			−0.413441
$263$	10.8840	−	18.8516i	0.671136	−	1.16244i	−0.306446	−	0.951888i	$-0.599140\pi$
$263$	10.8840	−	18.8516i	0.671136	−	1.16244i	0.977582	−	0.210554i	$-0.0675268\pi$
$264$	3.00000	−	3.00000i	0.184637	−	0.184637i
$265$		0			0
$266$	−0.633975	−	1.09808i	−0.0388715	−	0.0673274i
$267$	−22.4058	−	6.00361i	−1.37121	−	0.367415i
$268$	−6.57201	+	11.3831i	−0.401450	+	0.695331i
$269$	6.80385			0.414838			0.207419	−	0.978252i	$-0.433494\pi$
$269$	6.80385			0.414838			0.207419	+	0.978252i	$0.433494\pi$
$270$		0			0
$271$	21.5167			1.30704			0.653522	−	0.756908i	$-0.273291\pi$
$271$	21.5167			1.30704			0.653522	+	0.756908i	$0.273291\pi$
$272$	−6.50266	+	11.2629i	−0.394282	+	0.682916i
$273$	13.7124	+	3.67423i	0.829914	+	0.222375i
$274$	4.07180	+	7.05256i	0.245986	+	0.426061i
$275$		0			0
$276$	−1.09808	+	1.09808i	−0.0660964	+	0.0660964i
$277$	−6.12372	+	10.6066i	−0.367939	+	0.637289i	−0.989243	−	0.146281i	$-0.953270\pi$
$277$	−6.12372	+	10.6066i	−0.367939	+	0.637289i	0.621304	+	0.783569i	$0.286603\pi$
$278$	4.14110			0.248367
$279$		−	2.19615i		−	0.131480i
$280$		0			0
$281$	9.86603	−	17.0885i	0.588558	−	1.01941i	−0.405864	−	0.913934i	$-0.633029\pi$
$281$	9.86603	−	17.0885i	0.588558	−	1.01941i	0.994422	−	0.105478i	$-0.0336374\pi$
$282$	0.688524	+	2.56961i	0.0410010	+	0.153018i
$283$	8.36516	+	14.4889i	0.497257	+	0.861275i	0.999995	−	0.00316407i	$-0.00100716\pi$
$283$	8.36516	+	14.4889i	0.497257	+	0.861275i	−0.502738	+	0.864439i	$0.667674\pi$
$284$	12.2942	+	21.2942i	0.729528	+	1.26358i
$285$		0			0
$286$	−0.803848	+	1.39230i	−0.0475325	+	0.0823287i
$287$	25.8719			1.52717
$288$			15.4176i			0.908494i
$289$	10.8564			0.638612
$290$		0			0
$291$	−18.5885	+	18.5885i	−1.08967	+	1.08967i
$292$	7.34847	+	12.7279i	0.430037	+	0.744845i
$293$	6.88160	+	11.9193i	0.402027	+	0.696332i	0.993970	−	0.109648i	$-0.0349724\pi$
$293$	6.88160	+	11.9193i	0.402027	+	0.696332i	−0.591943	+	0.805980i	$0.701639\pi$
$294$	3.63397	+	0.973721i	0.211938	+	0.0567885i
$295$		0			0
$296$	−8.19615			−0.476392
$297$	6.36396	−	1.70522i	0.369274	−	0.0989468i
$298$	−2.20925			−0.127979
$299$	0.633975	−	1.09808i	0.0366637	−	0.0635034i
$300$		0			0
$301$	1.09808	+	1.90192i	0.0632921	+	0.109625i
$302$	2.22286	+	3.85010i	0.127911	+	0.221548i
$303$	11.5911	−	11.5911i	0.665892	−	0.665892i
$304$	0.901924	−	1.56218i	0.0517289	−	0.0895970i
$305$		0			0
$306$	7.09808	−	4.09808i	0.405770	−	0.234271i
$307$	−3.82654			−0.218392			−0.109196	−	0.994020i	$-0.534828\pi$
$307$	−3.82654			−0.218392			−0.109196	+	0.994020i	$0.534828\pi$
$308$	3.67423	−	6.36396i	0.209359	−	0.362620i
$309$	0.294229	+	1.09808i	0.0167381	+	0.0624674i
$310$		0			0
$311$	5.02628	+	8.70577i	0.285014	+	0.493659i	0.972613	−	0.232432i	$-0.0746684\pi$
$311$	5.02628	+	8.70577i	0.285014	+	0.493659i	−0.687598	+	0.726091i	$0.741335\pi$
$312$	−2.12132	−	7.91688i	−0.120096	−	0.448205i
$313$	−7.02030	+	12.1595i	−0.396811	+	0.687296i	−0.993330	−	0.115302i	$-0.963216\pi$
$313$	−7.02030	+	12.1595i	−0.396811	+	0.687296i	0.596520	+	0.802598i	$0.296550\pi$
$314$	−6.67949			−0.376946
$315$		0			0
$316$	−12.9282			−0.727268
$317$	2.01978	−	3.49837i	0.113442	−	0.196488i	−0.803714	−	0.595016i	$-0.797146\pi$
$317$	2.01978	−	3.49837i	0.113442	−	0.196488i	0.917156	+	0.398528i	$0.130479\pi$
$318$	0.656339	−	0.656339i	0.0368057	−	0.0368057i
$319$	0.294229	+	0.509619i	0.0164736	+	0.0285332i
$320$		0			0
$321$	17.2583	+	4.62436i	0.963266	+	0.258106i
$322$	0.448288	−	0.776457i	0.0249821	−	0.0432703i
$323$	−3.86370			−0.214982
$324$	−7.79423	+	13.5000i	−0.433013	+	0.750000i
$325$		0			0
$326$	2.70577	−	4.68653i	0.149859	−	0.259563i
$327$	−21.1810	−	5.67544i	−1.17131	−	0.313852i
$328$	−7.46859	−	12.9360i	−0.412384	−	0.714270i
$329$	4.96410	+	8.59808i	0.273680	+	0.474027i
$330$		0			0
$331$	4.19615	−	7.26795i	0.230641	−	0.399483i	−0.727356	−	0.686261i	$-0.759251\pi$
$331$	4.19615	−	7.26795i	0.230641	−	0.399483i	0.957997	+	0.286778i	$0.0925842\pi$
$332$	13.8004			0.757393
$333$	−11.0227	−	6.36396i	−0.604040	−	0.348743i
$334$	−5.14359			−0.281445
$335$		0			0
$336$	3.69615	+	13.7942i	0.201642	+	0.752537i
$337$	−3.34607	−	5.79555i	−0.182272	−	0.315704i	0.760382	−	0.649476i	$-0.225012\pi$
$337$	−3.34607	−	5.79555i	−0.182272	−	0.315704i	−0.942654	+	0.333772i	$0.891678\pi$
$338$	−1.81173	−	3.13801i	−0.0985453	−	0.170685i
$339$	7.73205	+	28.8564i	0.419947	+	1.56726i
$340$		0			0
$341$	0.928203			0.0502650
$342$	−0.984508	+	0.568406i	−0.0532361	+	0.0307359i
$343$	−9.38186			−0.506573
$344$	0.633975	−	1.09808i	0.0341816	−	0.0592043i
$345$		0			0
$346$	2.73205	+	4.73205i	0.146876	+	0.254397i
$347$	4.94975	+	8.57321i	0.265716	+	0.460234i	0.967751	−	0.251909i	$-0.0810582\pi$
$347$	4.94975	+	8.57321i	0.265716	+	0.460234i	−0.702035	+	0.712143i	$0.747725\pi$
$348$	−1.34486	−	0.360355i	−0.0720922	−	0.0193171i
$349$	−14.2321	+	24.6506i	−0.761824	+	1.31952i	0.180085	+	0.983651i	$0.442363\pi$
$349$	−14.2321	+	24.6506i	−0.761824	+	1.31952i	−0.941909	+	0.335867i	$0.890971\pi$
$350$		0			0
$351$	3.29423	−	12.2942i	0.175833	−	0.656217i
$352$	−6.51626			−0.347318
$353$	−10.1769	+	17.6269i	−0.541662	+	0.938185i	0.457147	+	0.889391i	$0.348871\pi$
$353$	−10.1769	+	17.6269i	−0.541662	+	0.938185i	−0.998809	+	0.0487943i	$0.984462\pi$
$354$	8.19615	+	2.19615i	0.435621	+	0.116724i
$355$		0			0
$356$	11.5981	+	20.0885i	0.614697	+	1.06469i
$357$	21.6293	−	21.6293i	1.14474	−	1.14474i
$358$	−1.70522	+	2.95352i	−0.0901236	+	0.156099i
$359$	20.1962			1.06591			0.532956	−	0.846143i	$-0.321081\pi$
$359$	20.1962			1.06591			0.532956	+	0.846143i	$0.321081\pi$
$360$		0			0
$361$	−18.4641			−0.971795
$362$	0.397520	−	0.688524i	0.0208932	−	0.0361880i
$363$	−4.21046	−	15.7136i	−0.220992	−	0.824752i
$364$	−7.09808	−	12.2942i	−0.372040	−	0.644393i
$365$		0			0
$366$	1.54552	+	5.76795i	0.0807855	+	0.301496i
$367$	−17.2987	+	29.9623i	−0.902986	+	1.56402i	−0.0793890	+	0.996844i	$0.525297\pi$
$367$	−17.2987	+	29.9623i	−0.902986	+	1.56402i	−0.823597	+	0.567175i	$0.808036\pi$
$368$	1.27551			0.0664907
$369$		−	23.1962i		−	1.20754i
$370$		0			0
$371$	1.73205	−	3.00000i	0.0899236	−	0.155752i
$372$	−1.55291	+	1.55291i	−0.0805149	+	0.0805149i
$373$	−13.6245	−	23.5983i	−0.705450	−	1.22187i	−0.966529	−	0.256557i	$-0.917412\pi$
$373$	−13.6245	−	23.5983i	−0.705450	−	1.22187i	0.261079	−	0.965317i	$-0.415922\pi$
$374$	1.73205	+	3.00000i	0.0895622	+	0.155126i
$375$		0			0
$376$	2.86603	−	4.96410i	0.147804	−	0.256004i
$377$	1.13681			0.0585488
$378$	2.32937	−	8.69333i	0.119810	−	0.447137i
$379$	19.4641			0.999804			0.499902	−	0.866082i	$-0.333369\pi$
$379$	19.4641			0.999804			0.499902	+	0.866082i	$0.333369\pi$
$380$		0			0
$381$	−29.0885	−	7.79423i	−1.49025	−	0.399310i
$382$	4.57081	+	7.91688i	0.233863	+	0.405063i
$383$	5.32868	+	9.22955i	0.272283	+	0.471608i	0.969446	−	0.245305i	$-0.0788880\pi$
$383$	5.32868	+	9.22955i	0.272283	+	0.471608i	−0.697163	+	0.716913i	$0.745555\pi$
$384$	14.0263	−	14.0263i	0.715776	−	0.715776i
$385$		0			0
$386$	−1.94744			−0.0991221
$387$	1.70522	−	0.984508i	0.0866811	−	0.0500454i
$388$	26.2880			1.33457
$389$	−0.0621778	+	0.107695i	−0.00315254	+	0.00546036i	−0.867597	−	0.497267i	$-0.834337\pi$
$389$	−0.0621778	+	0.107695i	−0.00315254	+	0.00546036i	0.864445	+	0.502728i	$0.167670\pi$
$390$		0			0
$391$	−1.36603	−	2.36603i	−0.0690829	−	0.119655i
$392$	−4.05317	−	7.02030i	−0.204716	−	0.354579i
$393$	5.79555	+	21.6293i	0.292347	+	1.09105i
$394$	−4.12436	+	7.14359i	−0.207782	+	0.359889i
$395$		0			0
$396$	−5.70577	−	3.29423i	−0.286726	−	0.165541i
$397$	−29.3939			−1.47524			−0.737618	−	0.675218i	$-0.764050\pi$
$397$	−29.3939			−1.47524			−0.737618	+	0.675218i	$0.764050\pi$
$398$	−6.88160	+	11.9193i	−0.344943	+	0.597459i
$399$	−3.00000	+	3.00000i	−0.150188	+	0.150188i
$400$		0			0
$401$	8.53590	+	14.7846i	0.426262	+	0.738308i	0.996537	−	0.0831457i	$-0.0264967\pi$
$401$	8.53590	+	14.7846i	0.426262	+	0.738308i	−0.570275	+	0.821454i	$0.693163\pi$
$402$	−6.57201	−	1.76097i	−0.327782	−	0.0878290i
$403$	0.896575	−	1.55291i	0.0446616	−	0.0773562i
$404$	−16.3923			−0.815548
$405$		0			0
$406$	0.803848			0.0398943
$407$	2.68973	−	4.65874i	0.133325	−	0.230925i
$408$	−17.0585	−	4.57081i	−0.844521	−	0.226289i
$409$	8.26795	+	14.3205i	0.408824	+	0.708104i	0.994758	−	0.102255i	$-0.0326057\pi$
$409$	8.26795	+	14.3205i	0.408824	+	0.708104i	−0.585934	+	0.810358i	$0.699272\pi$
$410$		0			0
$411$	19.2679	−	19.2679i	0.950418	−	0.950418i
$412$	0.568406	−	0.984508i	0.0280034	−	0.0485032i
$413$	31.6675			1.55826
$414$	−0.696152	−	0.401924i	−0.0342140	−	0.0197535i
$415$		0			0
$416$	−6.29423	+	10.9019i	−0.308600	+	0.534511i
$417$	−3.58630	−	13.3843i	−0.175622	−	0.655430i
$418$	−0.240237	−	0.416102i	−0.0117504	−	0.0203522i
$419$	−11.0263	−	19.0981i	−0.538669	−	0.933002i	−0.998976	−	0.0452423i	$-0.985594\pi$
$419$	−11.0263	−	19.0981i	−0.538669	−	0.933002i	0.460307	−	0.887760i	$-0.347739\pi$
$420$		0			0
$421$	9.73205	−	16.8564i	0.474311	−	0.821531i	−0.525256	−	0.850944i	$-0.676031\pi$
$421$	9.73205	−	16.8564i	0.474311	−	0.821531i	0.999567	+	0.0294132i	$0.00936385\pi$
$422$	−5.75839			−0.280314
$423$	7.70882	−	4.45069i	0.374816	−	0.216400i
$424$	−2.00000			−0.0971286
$425$		0			0
$426$	−9.00000	+	9.00000i	−0.436051	+	0.436051i
$427$	11.1428	+	19.2999i	0.539239	+	0.933989i
$428$	−8.93357	−	15.4734i	−0.431820	−	0.747935i
$429$	5.19615	+	1.39230i	0.250873	+	0.0672211i
$430$		0			0
$431$	−6.00000			−0.289010			−0.144505	−	0.989504i	$-0.546159\pi$
$431$	−6.00000			−0.289010			−0.144505	+	0.989504i	$0.546159\pi$
$432$	12.3676	−	3.31388i	0.595035	−	0.159439i
$433$	−13.5601			−0.651658			−0.325829	−	0.945429i	$-0.605643\pi$
$433$	−13.5601			−0.651658			−0.325829	+	0.945429i	$0.605643\pi$
$434$	0.633975	−	1.09808i	0.0304318	−	0.0527093i
$435$		0			0
$436$	10.9641	+	18.9904i	0.525085	+	0.909474i
$437$	0.189469	+	0.328169i	0.00906352	+	0.0156985i
$438$	−5.37945	+	5.37945i	−0.257040	+	0.257040i
$439$	12.6603	−	21.9282i	0.604241	−	1.04658i	−0.387930	−	0.921689i	$-0.626810\pi$
$439$	12.6603	−	21.9282i	0.604241	−	1.04658i	0.992171	−	0.124887i	$-0.0398569\pi$
$440$		0			0
$441$		−	12.5885i		−	0.599450i
$442$	6.69213			0.318312
$443$	−0.827225	+	1.43280i	−0.0393027	+	0.0680742i	−0.885008	−	0.465577i	$-0.845847\pi$
$443$	−0.827225	+	1.43280i	−0.0393027	+	0.0680742i	0.845705	+	0.533651i	$0.179180\pi$
$444$	3.29423	+	12.2942i	0.156337	+	0.583458i
$445$		0			0
$446$	−1.16025	−	2.00962i	−0.0549396	−	0.0951582i
$447$	1.91327	+	7.14042i	0.0904945	+	0.337730i
$448$	3.79435	−	6.57201i	0.179266	−	0.310498i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$	9.80385			0.461645
$452$	14.9372	−	25.8719i	0.702586	−	1.21691i
$453$	10.5187	−	10.5187i	0.494210	−	0.494210i
$454$	−6.83013	−	11.8301i	−0.320554	−	0.555215i
$455$		0			0
$456$	2.36603	+	0.633975i	0.110799	+	0.0296886i
$457$	12.3998	−	21.4770i	0.580036	−	1.00465i	−0.415438	−	0.909621i	$-0.636372\pi$
$457$	12.3998	−	21.4770i	0.580036	−	1.00465i	0.995474	−	0.0950304i	$-0.0302948\pi$
$458$	−3.14299			−0.146862
$459$	−19.3923	−	19.3923i	−0.905155	−	0.905155i
$460$		0			0
$461$	18.3564	−	31.7942i	0.854943	−	1.48080i	−0.0217547	−	0.999763i	$-0.506925\pi$
$461$	18.3564	−	31.7942i	0.854943	−	1.48080i	0.876698	−	0.481042i	$-0.159741\pi$
$462$	3.67423	+	0.984508i	0.170941	+	0.0458035i
$463$	17.0585	+	29.5462i	0.792776	+	1.37313i	0.924242	+	0.381807i	$0.124698\pi$
$463$	17.0585	+	29.5462i	0.792776	+	1.37313i	−0.131467	+	0.991321i	$0.541969\pi$
$464$	0.571797	+	0.990381i	0.0265450	+	0.0459773i
$465$		0			0
$466$	−1.83013	+	3.16987i	−0.0847790	+	0.146842i
$467$	25.3543			1.17326			0.586629	−	0.809856i	$-0.300455\pi$
$467$	25.3543			1.17326			0.586629	+	0.809856i	$0.300455\pi$
$468$	−11.0227	+	6.36396i	−0.509525	+	0.294174i
$469$	−25.3923			−1.17251
$470$		0			0
$471$	5.78461	+	21.5885i	0.266541	+	0.994744i
$472$	−9.14162	−	15.8338i	−0.420777	−	0.728807i
$473$	0.416102	+	0.720710i	0.0191324	+	0.0331383i
$474$	−1.73205	−	6.46410i	−0.0795557	−	0.296906i
$475$		0			0
$476$	−30.5885			−1.40202
$477$	−2.68973	−	1.55291i	−0.123154	−	0.0711031i
$478$	0.480473			0.0219763
$479$	−2.07180	+	3.58846i	−0.0946628	+	0.163961i	−0.909468	−	0.415774i	$-0.863511\pi$
$479$	−2.07180	+	3.58846i	−0.0946628	+	0.163961i	0.814805	+	0.579735i	$0.196844\pi$
$480$		0			0
$481$	−5.19615	−	9.00000i	−0.236924	−	0.410365i
$482$	2.51884	+	4.36276i	0.114730	+	0.198718i
$483$	−2.89778	−	0.776457i	−0.131853	−	0.0353300i
$484$	−8.13397	+	14.0885i	−0.369726	+	0.640384i
$485$		0			0
$486$	−7.79423	−	2.08846i	−0.353553	−	0.0947343i
$487$	15.8338			0.717496			0.358748	−	0.933435i	$-0.383204\pi$
$487$	15.8338			0.717496			0.358748	+	0.933435i	$0.383204\pi$
$488$	6.43331	−	11.1428i	0.291222	−	0.504412i
$489$	−17.4904	−	4.68653i	−0.790942	−	0.211932i
$490$		0			0
$491$	−16.8564	−	29.1962i	−0.760719	−	1.31760i	−0.942480	−	0.334261i	$-0.891513\pi$
$491$	−16.8564	−	29.1962i	−0.760719	−	1.31760i	0.181761	−	0.983343i	$-0.441820\pi$
$492$	−16.4022	+	16.4022i	−0.739466	+	0.739466i
$493$	1.22474	−	2.12132i	0.0551597	−	0.0955395i
$494$	−0.928203			−0.0417618
$495$		0			0
$496$	1.80385			0.0809951
$497$	−23.7506	+	41.1373i	−1.06536	+	1.84526i
$498$	1.84890	+	6.90018i	0.0828511	+	0.309205i
$499$	−11.9282	−	20.6603i	−0.533980	−	0.924880i	−0.999212	−	0.0396914i	$-0.987363\pi$
$499$	−11.9282	−	20.6603i	−0.533980	−	0.924880i	0.465232	−	0.885189i	$-0.345971\pi$
$500$		0			0
$501$	4.45448	+	16.6244i	0.199012	+	0.742721i
$502$	−3.25813	+	5.64325i	−0.145418	+	0.251871i
$503$	2.48665			0.110874			0.0554372	−	0.998462i	$-0.482345\pi$
$503$	2.48665			0.110874			0.0554372	+	0.998462i	$0.482345\pi$
$504$	−16.7942	+	9.69615i	−0.748074	+	0.431901i
$505$		0			0
$506$	0.169873	−	0.294229i	0.00755178	−	0.0130801i
$507$	−8.57321	+	8.57321i	−0.380750	+	0.380750i
$508$	15.0573	+	26.0800i	0.668059	+	1.15711i
$509$	−8.42820	−	14.5981i	−0.373574	−	0.647048i	0.616539	−	0.787324i	$-0.288534\pi$
$509$	−8.42820	−	14.5981i	−0.373574	−	0.647048i	−0.990112	+	0.140276i	$0.955201\pi$
$510$		0			0
$511$	−14.1962	+	24.5885i	−0.628001	+	1.08773i
$512$	−22.1841			−0.980408
$513$	2.68973	+	2.68973i	0.118754	+	0.118754i
$514$	8.67949			0.382836
$515$		0			0
$516$	−1.90192	−	0.509619i	−0.0837275	−	0.0224347i
$517$	1.88108	+	3.25813i	0.0827300	+	0.143293i
$518$	−3.67423	−	6.36396i	−0.161437	−	0.279616i
$519$	12.9282	−	12.9282i	0.567485	−	0.567485i
$520$		0			0
$521$	−19.3923			−0.849592			−0.424796	−	0.905289i	$-0.639654\pi$
$521$	−19.3923			−0.849592			−0.424796	+	0.905289i	$0.639654\pi$
$522$		−	0.720710i		−	0.0315446i
$523$	−35.1894			−1.53873			−0.769363	−	0.638812i	$-0.779426\pi$
$523$	−35.1894			−1.53873			−0.769363	+	0.638812i	$0.779426\pi$
$524$	11.1962	−	19.3923i	0.489106	−	0.847157i
$525$		0			0
$526$	−5.63397	−	9.75833i	−0.245653	−	0.425483i
$527$	−1.93185	−	3.34607i	−0.0841528	−	0.145757i
$528$	1.40061	+	5.22715i	0.0609537	+	0.227482i
$529$	11.3660	−	19.6865i	0.494175	−	0.855936i
$530$		0			0
$531$		−	28.3923i		−	1.23212i
$532$	4.24264			0.183942
$533$	9.46979	−	16.4022i	0.410182	−	0.710456i
$534$	−8.49038	+	8.49038i	−0.367415	+	0.367415i
$535$		0			0
$536$	7.33013	+	12.6962i	0.316613	+	0.548390i
$537$	11.0227	+	2.95352i	0.475665	+	0.127454i
$538$	1.76097	−	3.05008i	0.0759206	−	0.131498i
$539$	5.32051			0.229171
$540$		0			0
$541$	0.607695			0.0261269			0.0130634	−	0.999915i	$-0.495842\pi$
$541$	0.607695			0.0261269			0.0130634	+	0.999915i	$0.495842\pi$
$542$	5.56892	−	9.64566i	0.239206	−	0.414316i
$543$	−2.56961	−	0.688524i	−0.110272	−	0.0295474i
$544$	13.5622	+	23.4904i	0.581474	+	1.00714i
$545$		0			0
$546$	5.19615	−	5.19615i	0.222375	−	0.222375i
$547$	13.0239	−	22.5581i	0.556862	−	0.964513i	−0.440894	−	0.897559i	$-0.645339\pi$
$547$	13.0239	−	22.5581i	0.556862	−	0.964513i	0.997756	−	0.0669541i	$-0.0213281\pi$
$548$	−27.2490			−1.16402
$549$	17.3038	−	9.99038i	0.738510	−	0.426379i
$550$		0			0
$551$	−0.169873	+	0.294229i	−0.00723683	+	0.0125346i
$552$	0.448288	+	1.67303i	0.0190804	+	0.0712090i
$553$	−12.4877	−	21.6293i	−0.531030	−	0.919772i
$554$	3.16987	+	5.49038i	0.134675	+	0.233264i
$555$		0			0
$556$	−6.92820	+	12.0000i	−0.293821	+	0.508913i
$557$	−31.1127			−1.31829			−0.659144	−	0.752017i	$-0.729081\pi$
$557$	−31.1127			−1.31829			−0.659144	+	0.752017i	$0.729081\pi$
$558$	−0.984508	−	0.568406i	−0.0416776	−	0.0240625i
$559$	1.60770			0.0679983
$560$		0			0
$561$	8.19615	−	8.19615i	0.346042	−	0.346042i
$562$	−5.10703	−	8.84564i	−0.215427	−	0.373131i
$563$	−4.58939	−	7.94906i	−0.193420	−	0.335013i	0.752962	−	0.658065i	$-0.228625\pi$
$563$	−4.58939	−	7.94906i	−0.193420	−	0.335013i	−0.946381	+	0.323052i	$0.895291\pi$
$564$	−8.59808	−	2.30385i	−0.362044	−	0.0970095i
$565$		0			0
$566$	8.66025			0.364018
$567$	−30.1146			−1.26469
$568$	27.4249			1.15072
$569$	−14.6603	+	25.3923i	−0.614590	+	1.06450i	0.375867	+	0.926674i	$0.377345\pi$
$569$	−14.6603	+	25.3923i	−0.614590	+	1.06450i	−0.990456	+	0.137827i	$0.955988\pi$
$570$		0			0
$571$	0.732051	+	1.26795i	0.0306354	+	0.0530620i	0.880937	−	0.473234i	$-0.156914\pi$
$571$	0.732051	+	1.26795i	0.0306354	+	0.0530620i	−0.850301	+	0.526296i	$0.823580\pi$
$572$	−2.68973	−	4.65874i	−0.112463	−	0.194792i
$573$	21.6293	−	21.6293i	0.903577	−	0.903577i
$574$	6.69615	−	11.5981i	0.279492	−	0.484094i
$575$		0			0
$576$	−5.89230	−	3.40192i	−0.245513	−	0.141747i
$577$	13.8647			0.577196			0.288598	−	0.957450i	$-0.406811\pi$
$577$	13.8647			0.577196			0.288598	+	0.957450i	$0.406811\pi$
$578$	2.80984	−	4.86679i	0.116874	−	0.202432i
$579$	1.68653	+	6.29423i	0.0700899	+	0.261579i
$580$		0			0
$581$	13.3301	+	23.0885i	0.553027	+	0.957871i
$582$	3.52193	+	13.1440i	0.145989	+	0.544837i
$583$	0.656339	−	1.13681i	0.0271828	−	0.0470819i
$584$	16.3923			0.678318
$585$		0			0
$586$	7.12436			0.294304
$587$	−2.43091	+	4.21046i	−0.100334	+	0.173784i	−0.911822	−	0.410585i	$-0.865325\pi$
$587$	−2.43091	+	4.21046i	−0.100334	+	0.173784i	0.811488	+	0.584369i	$0.198658\pi$
$588$	−8.90138	+	8.90138i	−0.367087	+	0.367087i
$589$	0.267949	+	0.464102i	0.0110407	+	0.0191230i
$590$		0			0
$591$	26.6603	+	7.14359i	1.09666	+	0.293848i
$592$	5.22715	−	9.05369i	0.214834	−	0.372104i
$593$	−19.1427			−0.786094			−0.393047	−	0.919518i	$-0.628579\pi$
$593$	−19.1427			−0.786094			−0.393047	+	0.919518i	$0.628579\pi$
$594$	0.882686	−	3.29423i	0.0362170	−	0.135164i
$595$		0			0
$596$	3.69615	−	6.40192i	0.151400	−	0.262233i
$597$	44.4834	+	11.9193i	1.82058	+	0.487824i
$598$	−0.328169	−	0.568406i	−0.0134198	−	0.0232439i
$599$	10.8564	+	18.8038i	0.443581	+	0.768304i	0.997952	−	0.0639650i	$-0.0203746\pi$
$599$	10.8564	+	18.8038i	0.443581	+	0.768304i	−0.554371	+	0.832269i	$0.687041\pi$
$600$		0			0
$601$	1.53590	−	2.66025i	0.0626506	−	0.108514i	−0.832999	−	0.553275i	$-0.813378\pi$
$601$	1.53590	−	2.66025i	0.0626506	−	0.108514i	0.895649	+	0.444761i	$0.146711\pi$
$602$	1.13681			0.0463330
$603$			22.7661i			0.927108i
$604$	−14.8756			−0.605281
$605$		0			0
$606$	−2.19615	−	8.19615i	−0.0892126	−	0.332946i
$607$	−10.4865	−	18.1631i	−0.425633	−	0.737218i	0.570846	−	0.821057i	$-0.306615\pi$
$607$	−10.4865	−	18.1631i	−0.425633	−	0.737218i	−0.996479	+	0.0838387i	$0.973282\pi$
$608$	−1.88108	−	3.25813i	−0.0762880	−	0.132135i
$609$	−0.696152	−	2.59808i	−0.0282095	−	0.105279i
$610$		0			0
$611$	7.26795			0.294030
$612$			27.4249i			1.10858i
$613$	−9.62209			−0.388633			−0.194316	−	0.980939i	$-0.562249\pi$
$613$	−9.62209			−0.388633			−0.194316	+	0.980939i	$0.562249\pi$
$614$	−0.990381	+	1.71539i	−0.0399685	+	0.0692275i
$615$		0			0
$616$	−4.09808	−	7.09808i	−0.165116	−	0.285990i
$617$	−9.00292	−	15.5935i	−0.362444	−	0.627771i	0.625919	−	0.779888i	$-0.284724\pi$
$617$	−9.00292	−	15.5935i	−0.362444	−	0.627771i	−0.988362	+	0.152117i	$0.951391\pi$
$618$	0.568406	+	0.152304i	0.0228646	+	0.00612656i
$619$	−15.0981	+	26.1506i	−0.606843	+	1.05108i	0.384914	+	0.922952i	$0.374231\pi$
$619$	−15.0981	+	26.1506i	−0.606843	+	1.05108i	−0.991757	+	0.128130i	$0.959102\pi$
$620$		0			0
$621$	−0.696152	+	2.59808i	−0.0279356	+	0.104257i
$622$	5.20359			0.208645
$623$	−22.4058	+	38.8079i	−0.897668	+	1.55481i
$624$	10.0981	+	2.70577i	0.404247	+	0.108318i
$625$		0			0
$626$	3.63397	+	6.29423i	0.145243	+	0.251568i
$627$	−1.13681	+	1.13681i	−0.0453999	+	0.0453999i
$628$	11.1750	−	19.3557i	0.445931	−	0.772376i
$629$	−22.3923			−0.892840
$630$		0			0
$631$	1.32051			0.0525686			0.0262843	−	0.999655i	$-0.491632\pi$
$631$	1.32051			0.0525686			0.0262843	+	0.999655i	$0.491632\pi$
$632$	−7.20977	+	12.4877i	−0.286789	+	0.496733i
$633$	4.98691	+	18.6114i	0.198212	+	0.739737i
$634$	−1.04552	−	1.81089i	−0.0415228	−	0.0719196i
$635$		0			0
$636$	0.803848	+	3.00000i	0.0318746	+	0.118958i
$637$	5.13922	−	8.90138i	0.203623	−	0.352686i
$638$	0.304608			0.0120595
$639$	36.8827	+	21.2942i	1.45906	+	0.842387i
$640$		0			0
$641$	−6.52628	+	11.3038i	−0.257773	+	0.446475i	−0.965645	−	0.259865i	$-0.916322\pi$
$641$	−6.52628	+	11.3038i	−0.257773	+	0.446475i	0.707872	+	0.706340i	$0.249655\pi$
$642$	6.53983	−	6.53983i	0.258106	−	0.258106i
$643$	−6.48408	−	11.2308i	−0.255707	−	0.442898i	0.709380	−	0.704826i	$-0.248975\pi$
$643$	−6.48408	−	11.2308i	−0.255707	−	0.442898i	−0.965087	+	0.261928i	$0.915642\pi$
$644$	1.50000	+	2.59808i	0.0591083	+	0.102379i
$645$		0			0
$646$	−1.00000	+	1.73205i	−0.0393445	+	0.0681466i
$647$	−19.4572			−0.764942			−0.382471	−	0.923967i	$-0.624927\pi$
$647$	−19.4572			−0.764942			−0.382471	+	0.923967i	$0.624927\pi$
$648$	8.69333	+	15.0573i	0.341506	+	0.591506i
$649$	12.0000			0.471041
$650$		0			0
$651$	−4.09808	−	1.09808i	−0.160616	−	0.0430370i
$652$	9.05369	+	15.6814i	0.354570	+	0.614133i
$653$	24.2683	+	42.0339i	0.949691	+	1.64491i	0.746076	+	0.665861i	$0.231936\pi$
$653$	24.2683	+	42.0339i	0.949691	+	1.64491i	0.203615	+	0.979051i	$0.434731\pi$
$654$	−8.02628	+	8.02628i	−0.313852	+	0.313852i
$655$		0			0
$656$	19.0526			0.743877
$657$	22.0454	+	12.7279i	0.860073	+	0.496564i
$658$	5.13922			0.200348
$659$	6.12436	−	10.6077i	0.238571	−	0.413217i	−0.721733	−	0.692171i	$-0.756654\pi$
$659$	6.12436	−	10.6077i	0.238571	−	0.413217i	0.960304	+	0.278954i	$0.0899877\pi$
$660$		0			0
$661$	−5.39230	−	9.33975i	−0.209736	−	0.363274i	0.741895	−	0.670516i	$-0.233927\pi$
$661$	−5.39230	−	9.33975i	−0.209736	−	0.363274i	−0.951631	+	0.307242i	$0.900594\pi$
$662$	−2.17209	−	3.76217i	−0.0844206	−	0.146221i
$663$	−5.79555	−	21.6293i	−0.225081	−	0.840013i
$664$	7.69615	−	13.3301i	0.298669	−	0.517309i
$665$		0			0
$666$	−5.70577	+	3.29423i	−0.221094	+	0.127649i
$667$	−0.240237			−0.00930200
$668$	8.60540	−	14.9050i	0.332953	−	0.576691i
$669$	−5.49038	+	5.49038i	−0.212270	+	0.212270i
$670$		0			0
$671$	4.22243	+	7.31347i	0.163005	+	0.282333i
$672$	28.7697	+	7.70882i	1.10982	+	0.297374i
$673$	20.4046	−	35.3417i	0.786538	−	1.36232i	−0.141538	−	0.989933i	$-0.545205\pi$
$673$	20.4046	−	35.3417i	0.786538	−	1.36232i	0.928076	−	0.372391i	$-0.121462\pi$
$674$	−3.46410			−0.133432
$675$		0			0
$676$	12.1244			0.466321
$677$	1.84392	−	3.19376i	0.0708676	−	0.122746i	−0.828414	−	0.560116i	$-0.810757\pi$
$677$	1.84392	−	3.19376i	0.0708676	−	0.122746i	0.899282	+	0.437370i	$0.144090\pi$
$678$	14.9372	+	4.00240i	0.573659	+	0.153711i
$679$	25.3923	+	43.9808i	0.974467	+	1.68783i
$680$		0			0
$681$	−32.3205	+	32.3205i	−1.23852	+	1.23852i
$682$	0.240237	−	0.416102i	0.00919914	−	0.0159334i
$683$	0.101536			0.00388517			0.00194258	−	0.999998i	$-0.499382\pi$
$683$	0.101536			0.00388517			0.00194258	+	0.999998i	$0.499382\pi$
$684$		−	3.80385i		−	0.145444i
$685$		0			0
$686$	−2.42820	+	4.20577i	−0.0927092	+	0.160577i
$687$	2.72191	+	10.1583i	0.103847	+	0.387564i
$688$	0.808643	+	1.40061i	0.0308292	+	0.0533978i
$689$	−1.26795	−	2.19615i	−0.0483050	−	0.0836667i
$690$		0			0
$691$	14.1244	−	24.4641i	0.537316	−	0.930658i	−0.461732	−	0.887020i	$-0.652772\pi$
$691$	14.1244	−	24.4641i	0.537316	−	0.930658i	0.999047	−	0.0436386i	$-0.0138950\pi$
$692$	−18.2832			−0.695025
$693$		−	12.7279i		−	0.483494i
$694$	5.12436			0.194518
$695$		0			0
$696$	−1.09808	+	1.09808i	−0.0416225	+	0.0416225i
$697$	−20.4046	−	35.3417i	−0.772878	−	1.33866i
$698$	7.36705	+	12.7601i	0.278847	+	0.482977i
$699$	11.8301	+	3.16987i	0.447456	+	0.119896i
$700$		0			0
$701$	−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
$703$	3.10583			0.117139
$704$	1.43782	−	2.49038i	0.0541900	−	0.0938598i
$705$		0			0
$706$	5.26795	+	9.12436i	0.198262	+	0.343400i
$707$	−15.8338	−	27.4249i	−0.595489	−	1.03142i
$708$	−20.0764	+	20.0764i	−0.754517	+	0.754517i
$709$	−4.89230	+	8.47372i	−0.183734	+	0.318237i	−0.943149	−	0.332369i	$-0.892152\pi$
$709$	−4.89230	+	8.47372i	−0.183734	+	0.318237i	0.759415	+	0.650607i	$0.225485\pi$
$710$		0			0
$711$	−19.3923	+	11.1962i	−0.727268	+	0.419889i
$712$	25.8719			0.969592
$713$	−0.189469	+	0.328169i	−0.00709566	+	0.0122900i
$714$	−4.09808	−	15.2942i	−0.153367	−	0.572372i
$715$		0			0
$716$	−5.70577	−	9.88269i	−0.213235	−	0.369333i
$717$	−0.416102	−	1.55291i	−0.0155396	−	0.0579946i
$718$	5.22715	−	9.05369i	0.195075	−	0.337881i
$719$	40.3923			1.50638			0.753189	−	0.657804i	$-0.228514\pi$
$719$	40.3923			1.50638			0.753189	+	0.657804i	$0.228514\pi$
$720$		0			0
$721$	2.19615			0.0817890
$722$	−4.77886	+	8.27723i	−0.177851	+	0.308047i
$723$	11.9193	−	11.9193i	0.443283	−	0.443283i
$724$	1.33013	+	2.30385i	0.0494338	+	0.0856218i
$725$		0			0
$726$	−8.13397	−	2.17949i	−0.301880	−	0.0808885i
$727$	−0.688524	+	1.19256i	−0.0255360	+	0.0442296i	−0.878511	−	0.477722i	$-0.841463\pi$
$727$	−0.688524	+	1.19256i	−0.0255360	+	0.0442296i	0.852975	+	0.521952i	$0.174796\pi$
$728$	−15.8338			−0.586838
$729$			27.0000i			1.00000i
$730$		0			0
$731$	1.73205	−	3.00000i	0.0640622	−	0.110959i
$732$	−19.2999	−	5.17140i	−0.713346	−	0.191141i
$733$	3.76217	+	6.51626i	0.138959	+	0.240684i	0.927103	−	0.374807i	$-0.122291\pi$
$733$	3.76217	+	6.51626i	0.138959	+	0.240684i	−0.788144	+	0.615491i	$0.788958\pi$
$734$	8.95448	+	15.5096i	0.330516	+	0.572470i
$735$		0			0
$736$	1.33013	−	2.30385i	0.0490291	−	0.0849209i
$737$	−9.62209			−0.354434
$738$	−10.3986	−	6.00361i	−0.382776	−	0.220996i
$739$	−18.1436			−0.667423			−0.333711	−	0.942675i	$-0.608301\pi$
$739$	−18.1436			−0.667423			−0.333711	+	0.942675i	$0.608301\pi$
$740$		0			0
$741$	0.803848	+	3.00000i	0.0295301	+	0.110208i
$742$	−0.896575	−	1.55291i	−0.0329143	−	0.0570093i
$743$	−16.3328	−	28.2893i	−0.599193	−	1.03783i	−0.992941	−	0.118613i	$-0.962155\pi$
$743$	−16.3328	−	28.2893i	−0.599193	−	1.03783i	0.393748	−	0.919218i	$-0.371178\pi$
$744$	0.633975	+	2.36603i	0.0232426	+	0.0867427i
$745$		0			0
$746$	−14.1051			−0.516425
$747$	20.7005	−	11.9515i	0.757393	−	0.437281i
$748$	−11.5911			−0.423813
$749$	17.2583	−	29.8923i	0.630606	−	1.09224i
$750$		0			0
$751$	12.2224	+	21.1699i	0.446003	+	0.772500i	0.998121	−	0.0612659i	$-0.0195138\pi$
$751$	12.2224	+	21.1699i	0.446003	+	0.772500i	−0.552119	+	0.833766i	$0.686180\pi$
$752$	3.65565	+	6.33178i	0.133308	+	0.230896i
$753$	21.0609	+	5.64325i	0.767502	+	0.205651i
$754$	0.294229	−	0.509619i	0.0107152	−	0.0185592i
$755$		0			0
$756$	21.2942	+	21.2942i	0.774464	+	0.774464i
$757$	−7.34847			−0.267085			−0.133542	−	0.991043i	$-0.542635\pi$
$757$	−7.34847			−0.267085			−0.133542	+	0.991043i	$0.542635\pi$
$758$	5.03768	−	8.72552i	0.182977	−	0.316925i
$759$	−1.09808	−	0.294229i	−0.0398576	−	0.0106798i
$760$		0			0
$761$	−7.96410	−	13.7942i	−0.288698	−	0.500040i	0.684801	−	0.728730i	$-0.259889\pi$
$761$	−7.96410	−	13.7942i	−0.288698	−	0.500040i	−0.973499	+	0.228690i	$0.926556\pi$
$762$	−11.0227	+	11.0227i	−0.399310	+	0.399310i
$763$	−21.1810	+	36.6866i	−0.766804	+	1.32814i
$764$	−30.5885			−1.10665
$765$		0			0
$766$	5.51666			0.199325
$767$	11.5911	−	20.0764i	0.418531	−	0.724916i
$768$	−0.624153	−	2.32937i	−0.0225222	−	0.0840540i
$769$	−20.8205	−	36.0622i	−0.750807	−	1.30044i	−0.947432	−	0.319957i	$-0.896332\pi$
$769$	−20.8205	−	36.0622i	−0.750807	−	1.30044i	0.196625	−	0.980479i	$-0.437002\pi$
$770$		0			0
$771$	−7.51666	−	28.0526i	−0.270706	−	1.01029i
$772$	3.25813	−	5.64325i	0.117263	−	0.203105i
$773$	2.07055			0.0744726			0.0372363	−	0.999306i	$-0.488145\pi$
$773$	2.07055			0.0744726			0.0372363	+	0.999306i	$0.488145\pi$
$774$		−	1.01924i		−	0.0366357i
$775$		0			0
$776$	14.6603	−	25.3923i	0.526272	−	0.911531i
$777$	−17.3867	+	17.3867i	−0.623743	+	0.623743i
$778$	0.0321856	+	0.0557471i	0.00115391	+	0.00199863i
$779$	2.83013	+	4.90192i	0.101400	+	0.175630i
$780$		0			0
$781$	−9.00000	+	15.5885i	−0.322045	+	0.557799i
$782$	−1.41421			−0.0505722
$783$	−2.32937	+	0.624153i	−0.0832449	+	0.0223054i
$784$	10.3397			0.369277
$785$		0			0
$786$	11.1962	+	3.00000i	0.399354	+	0.107006i
$787$	13.0561	+	22.6138i	0.465399	+	0.806095i	0.999219	−	0.0395027i	$-0.0125774\pi$
$787$	13.0561	+	22.6138i	0.465399	+	0.806095i	−0.533820	+	0.845598i	$0.679244\pi$
$788$	−13.8004	−	23.9029i	−0.491618	−	0.851507i
$789$	−26.6603	+	26.6603i	−0.949130	+	0.949130i
$790$		0			0
$791$	57.7128			2.05203
$792$	−6.36396	+	3.67423i	−0.226134	+	0.130558i
$793$	16.3142			0.579335
$794$	−7.60770	+	13.1769i	−0.269987	+	0.467631i
$795$		0			0
$796$	−23.0263	−	39.8827i	−0.816145	−	1.41360i
$797$	26.3388	+	45.6202i	0.932969	+	1.61595i	0.778217	+	0.627996i	$0.216125\pi$
$797$	26.3388	+	45.6202i	0.932969	+	1.61595i	0.154752	+	0.987953i	$0.450542\pi$
$798$	0.568406	+	2.12132i	0.0201214	+	0.0750939i
$799$	7.83013	−	13.5622i	0.277010	−	0.479795i
$800$		0			0
$801$	34.7942	+	20.0885i	1.22939	+	0.709791i
$802$	8.83701			0.312046
$803$	−5.37945	+	9.31749i	−0.189837	+	0.328807i
$804$	16.0981	−	16.0981i	0.567735	−	0.567735i
$805$		0			0
$806$	−0.464102	−	0.803848i	−0.0163473	−	0.0283143i
$807$	−11.3831	−	3.05008i	−0.400703	−	0.107368i
$808$	−9.14162	+	15.8338i	−0.321601	+	0.557029i
$809$	−25.1769			−0.885173			−0.442587	−	0.896726i	$-0.645939\pi$
$809$	−25.1769			−0.885173			−0.442587	+	0.896726i	$0.645939\pi$
$810$		0			0
$811$	−39.5692			−1.38946			−0.694732	−	0.719269i	$-0.744477\pi$
$811$	−39.5692			−1.38946			−0.694732	+	0.719269i	$0.744477\pi$
$812$	−1.34486	+	2.32937i	−0.0471954	+	0.0817449i
$813$	−35.9981	−	9.64566i	−1.26251	−	0.338288i
$814$	−1.39230	−	2.41154i	−0.0488003	−	0.0845245i
$815$		0			0
$816$	15.9282	−	15.9282i	0.557599	−	0.557599i
$817$	−0.240237	+	0.416102i	−0.00840482	+	0.0145576i
$818$	8.55961			0.299280
$819$	−21.2942	−	12.2942i	−0.744081	−	0.429595i
$820$		0			0
$821$	−14.7224	+	25.5000i	−0.513816	+	0.889956i	0.486055	+	0.873928i	$0.338435\pi$
$821$	−14.7224	+	25.5000i	−0.513816	+	0.889956i	−0.999872	+	0.0160280i	$0.994898\pi$
$822$	−3.65067	−	13.6245i	−0.127332	−	0.475209i
$823$	−9.58991	−	16.6102i	−0.334283	−	0.578995i	0.649064	−	0.760734i	$-0.275161\pi$
$823$	−9.58991	−	16.6102i	−0.334283	−	0.578995i	−0.983347	+	0.181739i	$0.941828\pi$
$824$	−0.633975	−	1.09808i	−0.0220856	−	0.0382533i
$825$		0			0
$826$	8.19615	−	14.1962i	0.285181	−	0.493947i
$827$	23.8014			0.827656			0.413828	−	0.910355i	$-0.364192\pi$
$827$	23.8014			0.827656			0.413828	+	0.910355i	$0.364192\pi$
$828$	2.32937	−	1.34486i	0.0809513	−	0.0467372i
$829$	0.411543			0.0142935			0.00714673	−	0.999974i	$-0.497725\pi$
$829$	0.411543			0.0142935			0.00714673	+	0.999974i	$0.497725\pi$
$830$		0			0
$831$	15.0000	−	15.0000i	0.520344	−	0.520344i
$832$	−2.77766	−	4.81105i	−0.0962980	−	0.166793i
$833$	−11.0735	−	19.1798i	−0.383673	−	0.664541i
$834$	−6.92820	−	1.85641i	−0.239904	−	0.0642821i
$835$		0			0
$836$	1.60770			0.0556033
$837$	−0.984508	+	3.67423i	−0.0340296	+	0.127000i
$838$	−11.4152			−0.394333
$839$	−2.36603	+	4.09808i	−0.0816843	+	0.141481i	−0.903974	−	0.427588i	$-0.859363\pi$
$839$	−2.36603	+	4.09808i	−0.0816843	+	0.141481i	0.822289	+	0.569070i	$0.192697\pi$
$840$		0			0
$841$	14.3923	+	24.9282i	0.496286	+	0.859593i
$842$	−5.03768	−	8.72552i	−0.173610	−	0.300701i
$843$	−24.1667	+	24.1667i	−0.832346	+	0.832346i
$844$	9.63397	−	16.6865i	0.331615	−	0.574374i
$845$		0			0
$846$		−	4.60770i		−	0.158416i
$847$	−31.4273			−1.07985
$848$	1.27551	−	2.20925i	0.0438013	−	0.0758661i
$849$	−7.50000	−	27.9904i	−0.257399	−	0.960627i
$850$		0			0
$851$	1.09808	+	1.90192i	0.0376416	+	0.0651971i
$852$	−11.0227	−	41.1373i	−0.377632	−	1.40934i
$853$	−21.7172	+	37.6154i	−0.743584	+	1.28793i	0.207269	+	0.978284i	$0.433542\pi$
$853$	−21.7172	+	37.6154i	−0.743584	+	1.28793i	−0.950853	+	0.309641i	$0.899791\pi$
$854$	11.5359			0.394750
$855$		0			0
$856$	−19.9282			−0.681132
$857$	−6.88160	+	11.9193i	−0.235071	+	0.407155i	−0.959293	−	0.282412i	$-0.908866\pi$
$857$	−6.88160	+	11.9193i	−0.235071	+	0.407155i	0.724222	+	0.689567i	$0.242199\pi$
$858$	1.96902	−	1.96902i	0.0672211	−	0.0672211i
$859$	−18.2224	−	31.5622i	−0.621741	−	1.07689i	−0.989161	−	0.146832i	$-0.953092\pi$
$859$	−18.2224	−	31.5622i	−0.621741	−	1.07689i	0.367420	−	0.930055i	$-0.380241\pi$
$860$		0			0
$861$	−43.2846	−	11.5981i	−1.47514	−	0.395261i
$862$	−1.55291	+	2.68973i	−0.0528925	+	0.0916124i
$863$	44.9131			1.52886			0.764429	−	0.644708i	$-0.223021\pi$
$863$	44.9131			1.52886			0.764429	+	0.644708i	$0.223021\pi$
$864$	6.91154	−	25.7942i	0.235135	−	0.877537i
$865$		0			0
$866$	−3.50962	+	6.07884i	−0.119262	+	0.206567i
$867$	−18.1631	−	4.86679i	−0.616852	−	0.165285i
$868$	2.12132	+	3.67423i	0.0720023	+	0.124712i
$869$	−4.73205	−	8.19615i	−0.160524	−	0.278035i
$870$		0			0
$871$	−9.29423	+	16.0981i	−0.314923	+	0.545463i
$872$	24.4577			0.828243
$873$	39.4321	−	22.7661i	1.33457	−	0.770516i
$874$	0.196152			0.00663495
$875$		0			0
$876$	−6.58846	−	24.5885i	−0.222603	−	0.830767i
$877$	14.6090	+	25.3035i	0.493311	+	0.854440i	0.999970	−	0.00770656i	$-0.00245310\pi$
$877$	14.6090	+	25.3035i	0.493311	+	0.854440i	−0.506659	+	0.862146i	$0.669120\pi$
$878$	−6.55343	−	11.3509i	−0.221168	−	0.383073i
$879$	−6.16987	−	23.0263i	−0.208105	−	0.776657i
$880$		0			0
$881$	−39.5885			−1.33377			−0.666885	−	0.745161i	$-0.732373\pi$
$881$	−39.5885			−1.33377			−0.666885	+	0.745161i	$0.732373\pi$
$882$	−5.64325	−	3.25813i	−0.190018	−	0.109707i
$883$	54.4336			1.83184			0.915919	−	0.401364i	$-0.131464\pi$
$883$	54.4336			1.83184			0.915919	+	0.401364i	$0.131464\pi$
$884$	−11.1962	+	19.3923i	−0.376567	+	0.652234i
$885$		0			0
$886$	0.428203	+	0.741670i	0.0143858	+	0.0249169i
$887$	4.29341	+	7.43640i	0.144159	+	0.249690i	0.929059	−	0.369932i	$-0.120619\pi$
$887$	4.29341	+	7.43640i	0.144159	+	0.249690i	−0.784900	+	0.619622i	$0.787286\pi$
$888$	13.7124	+	3.67423i	0.460159	+	0.123299i
$889$	−29.0885	+	50.3827i	−0.975596	+	1.68978i
$890$		0			0
$891$	−11.4115			−0.382301
$892$	7.76457			0.259977
$893$	−1.08604	+	1.88108i	−0.0363431	+	0.0629481i
$894$	3.69615	+	0.990381i	0.123618	+	0.0331233i
$895$		0			0
$896$	−19.1603	−	33.1865i	−0.640099	−	1.10868i
$897$	−1.55291	+	1.55291i	−0.0518503	+	0.0518503i
$898$	−3.10583	+	5.37945i	−0.103643	+	0.179515i
$899$	−0.339746			−0.0113312
$900$		0			0
$901$	−5.46410			−0.182036
$902$	2.53742	−	4.39494i	0.0844869	−	0.146336i
$903$	−0.984508	−	3.67423i	−0.0327624	−	0.122271i
$904$	−16.6603	−	28.8564i	−0.554112	−	0.959750i
$905$		0			0
$906$	−1.99296	−	7.43782i	−0.0662116	−	0.247105i
$907$	−5.76337	+	9.98245i	−0.191370	+	0.331462i	−0.945704	−	0.325028i	$-0.894626\pi$
$907$	−5.76337	+	9.98245i	−0.191370	+	0.331462i	0.754335	+	0.656490i	$0.227960\pi$
$908$	45.7081			1.51688
$909$	−24.5885	+	14.1962i	−0.815548	+	0.470857i
$910$		0			0
$911$	−24.9282	+	43.1769i	−0.825908	+	1.43051i	0.0753150	+	0.997160i	$0.476004\pi$
$911$	−24.9282	+	43.1769i	−0.825908	+	1.43051i	−0.901223	+	0.433355i	$0.857330\pi$
$912$	−2.20925	+	2.20925i	−0.0731557	+	0.0731557i
$913$	5.05128	+	8.74908i	0.167173	+	0.289552i
$914$	−6.41858	−	11.1173i	−0.212308	−	0.367728i
$915$		0			0
$916$	5.25833	−	9.10770i	0.173740	−	0.300927i
$917$	43.2586			1.42853
$918$	−13.7124	+	3.67423i	−0.452578	+	0.121268i
$919$	47.1769			1.55622			0.778111	−	0.628126i	$-0.216178\pi$
$919$	47.1769			1.55622			0.778111	+	0.628126i	$0.216178\pi$
$920$		0			0
$921$	6.40192	+	1.71539i	0.210951	+	0.0565240i
$922$	−9.50198	−	16.4579i	−0.312931	−	0.542012i
$923$	17.3867	+	30.1146i	0.572289	+	0.991234i
$924$	−9.00000	+	9.00000i	−0.296078	+	0.296078i
$925$		0			0
$926$	17.6603			0.580352
$927$		−	1.96902i		−	0.0646710i
$928$	2.38512			0.0782954
$929$	1.73205	−	3.00000i	0.0568267	−	0.0984268i	−0.836213	−	0.548405i	$-0.815235\pi$
$929$	1.73205	−	3.00000i	0.0568267	−	0.0984268i	0.893039	+	0.449979i	$0.148568\pi$
$930$		0			0
$931$	1.53590	+	2.66025i	0.0503370	+	0.0871863i
$932$	−6.12372	−	10.6066i	−0.200589	−	0.347431i
$933$	−4.50644	−	16.8183i	−0.147534	−	0.550605i
$934$	6.56218	−	11.3660i	0.214721	−	0.371908i
$935$		0			0
$936$			14.1962i			0.464016i
$937$	−28.5617			−0.933069			−0.466535	−	0.884503i	$-0.654498\pi$
$937$	−28.5617			−0.933069			−0.466535	+	0.884503i	$0.654498\pi$
$938$	−6.57201	+	11.3831i	−0.214584	+	0.371670i
$939$	17.1962	−	17.1962i	0.561175	−	0.561175i
$940$		0			0
$941$	−13.1603	−	22.7942i	−0.429012	−	0.743071i	0.567774	−	0.823185i	$-0.307805\pi$
$941$	−13.1603	−	22.7942i	−0.429012	−	0.743071i	−0.996786	+	0.0801141i	$0.974472\pi$
$942$	11.1750	+	2.99433i	0.364101	+	0.0975607i
$943$	−2.00120	+	3.46618i	−0.0651681	+	0.112874i
$944$	23.3205			0.759018
$945$		0			0
$946$	0.430781			0.0140059
$947$	2.38014	−	4.12252i	0.0773441	−	0.133964i	−0.824759	−	0.565484i	$-0.808689\pi$
$947$	2.38014	−	4.12252i	0.0773441	−	0.133964i	0.902103	+	0.431520i	$0.142023\pi$
$948$	21.6293	+	5.79555i	0.702487	+	0.188231i
$949$	10.3923	+	18.0000i	0.337348	+	0.584305i
$950$		0			0
$951$	−4.94744	+	4.94744i	−0.160432	+	0.160432i
$952$	−17.0585	+	29.5462i	−0.552869	+	0.957597i
$953$	−51.1619			−1.65730			−0.828648	−	0.559770i	$-0.810889\pi$
$953$	−51.1619			−1.65730			−0.828648	+	0.559770i	$0.810889\pi$
$954$	−1.39230	+	0.803848i	−0.0450775	+	0.0260255i
$955$		0			0
$956$	−0.803848	+	1.39230i	−0.0259983	+	0.0450304i
$957$	−0.263798	−	0.984508i	−0.00852738	−	0.0318246i
$958$	1.07244	+	1.85752i	0.0346490	+	0.0600138i
$959$	−26.3205	−	45.5885i	−0.849934	−	1.47213i
$960$		0			0
$961$	15.2321	−	26.3827i	0.491356	−	0.851054i
$962$	−5.37945			−0.173441
$963$	−26.8007	−	15.4734i	−0.863641	−	0.498623i
$964$	−16.8564			−0.542908
$965$		0			0
$966$	−1.09808	+	1.09808i	−0.0353300	+	0.0353300i
$967$	27.9611	+	48.4300i	0.899168	+	1.55740i	0.828560	+	0.559900i	$0.189160\pi$
$967$	27.9611	+	48.4300i	0.899168	+	1.55740i	0.0706076	+	0.997504i	$0.477506\pi$
$968$	9.07227	+	15.7136i	0.291594	+	0.505055i
$969$	6.46410	+	1.73205i	0.207657	+	0.0556415i
$970$		0			0
$971$	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
$973$	−26.7685			−0.858159
$974$	4.09808	−	7.09808i	0.131311	−	0.227437i
$975$		0			0
$976$	8.20577	+	14.2128i	0.262660	+	0.454941i
$977$	−7.77817	−	13.4722i	−0.248846	−	0.431014i	0.714360	−	0.699778i	$-0.246718\pi$
$977$	−7.77817	−	13.4722i	−0.248846	−	0.431014i	−0.963206	+	0.268765i	$0.913385\pi$
$978$	−6.62776	+	6.62776i	−0.211932	+	0.211932i
$979$	−8.49038	+	14.7058i	−0.271354	+	0.469998i
$980$		0			0
$981$	32.8923	+	18.9904i	1.05017	+	0.606316i
$982$	−17.4510			−0.556885
$983$	16.7117	−	28.9456i	0.533022	−	0.923221i	−0.466234	−	0.884661i	$-0.654390\pi$
$983$	16.7117	−	28.9456i	0.533022	−	0.923221i	0.999256	−	0.0385597i	$-0.0122770\pi$
$984$	6.69615	+	24.9904i	0.213466	+	0.796664i
$985$		0			0
$986$	−0.633975	−	1.09808i	−0.0201899	−	0.0349699i
$987$	−4.45069	−	16.6102i	−0.141667	−	0.528709i
$988$	1.55291	−	2.68973i	0.0494048	−	0.0855716i
$989$	−0.339746			−0.0108033
$990$		0			0
$991$	38.9282			1.23660			0.618298	−	0.785944i	$-0.287823\pi$
$991$	38.9282			1.23660			0.618298	+	0.785944i	$0.287823\pi$
$992$	1.88108	−	3.25813i	0.0597245	−	0.103446i
$993$	−10.2784	+	10.2784i	−0.326176	+	0.326176i
$994$	12.2942	+	21.2942i	0.389949	+	0.675412i
$995$		0			0
$996$	−23.0885	−	6.18653i	−0.731586	−	0.196028i
$997$	−5.13922	+	8.90138i	−0.162761	+	0.281910i	−0.935858	−	0.352378i	$-0.885373\pi$
$997$	−5.13922	+	8.90138i	−0.162761	+	0.281910i	0.773097	+	0.634288i	$0.218706\pi$
$998$	−12.3490			−0.390900
$999$	15.5885	+	15.5885i	0.493197	+	0.493197i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.2	✓	8	45.22	odd	12
45.2.j.a.4.3	yes	8	45.13	odd	12
45.2.j.a.34.2	yes	8	5.3	odd	4
45.2.j.a.34.3	yes	8	5.2	odd	4
135.2.j.a.19.2		8	15.2	even	4
135.2.j.a.19.3		8	15.8	even	4
135.2.j.a.64.2		8	45.23	even	12
135.2.j.a.64.3		8	45.32	even	12
225.2.e.d.76.2		8	45.4	even	6	inner
225.2.e.d.76.3		8	9.4	even	3	inner
225.2.e.d.151.2		8	5.4	even	2	inner
225.2.e.d.151.3		8	1.1	even	1	trivial
405.2.b.c.244.2		4	45.38	even	12
405.2.b.c.244.3		4	45.2	even	12
405.2.b.d.244.2		4	45.7	odd	12
405.2.b.d.244.3		4	45.43	odd	12
675.2.e.d.226.2		8	9.5	odd	6
675.2.e.d.226.3		8	45.14	odd	6
675.2.e.d.451.2		8	3.2	odd	2
675.2.e.d.451.3		8	15.14	odd	2
720.2.by.d.49.2		8	180.67	even	12
720.2.by.d.49.3		8	180.103	even	12
720.2.by.d.529.2		8	20.3	even	4
720.2.by.d.529.3		8	20.7	even	4
2025.2.a.r.1.2		4	45.29	odd	6
2025.2.a.r.1.3		4	9.2	odd	6
2025.2.a.t.1.2		4	9.7	even	3
2025.2.a.t.1.3		4	45.34	even	6
2160.2.by.c.289.1		8	60.47	odd	4
2160.2.by.c.289.3		8	60.23	odd	4
2160.2.by.c.1009.1		8	180.23	odd	12
2160.2.by.c.1009.3		8	180.167	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.448288i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.633975 + 0.633975i) q^{6} +(-1.67303 + 2.89778i) q^{7} +1.93185 q^{8} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.448288i) q^{2} +(-1.67303 - 0.448288i) q^{3} +(0.866025 + 1.50000i) q^{4} +(-0.633975 + 0.633975i) q^{6} +(-1.67303 + 2.89778i) q^{7} +1.93185 q^{8} +(2.59808 + 1.50000i) q^{9} +(-0.633975 + 1.09808i) q^{11} +(-0.776457 - 2.89778i) q^{12} +(1.22474 + 2.12132i) q^{13} +(0.866025 + 1.50000i) q^{14} +(-1.23205 + 2.13397i) q^{16} +5.27792 q^{17} +(1.34486 - 0.776457i) q^{18} -0.732051 q^{19} +(4.09808 - 4.09808i) q^{21} +(0.328169 + 0.568406i) q^{22} +(-0.258819 - 0.448288i) q^{23} +(-3.23205 - 0.866025i) q^{24} +1.26795 q^{26} +(-3.67423 - 3.67423i) q^{27} -5.79555 q^{28} +(0.232051 - 0.401924i) q^{29} +(-0.366025 - 0.633975i) q^{31} +(2.56961 + 4.45069i) q^{32} +(1.55291 - 1.55291i) q^{33} +(1.36603 - 2.36603i) q^{34} +5.19615i q^{36} -4.24264 q^{37} +(-0.189469 + 0.328169i) q^{38} +(-1.09808 - 4.09808i) q^{39} +(-3.86603 - 6.69615i) q^{41} +(-0.776457 - 2.89778i) q^{42} +(0.328169 - 0.568406i) q^{43} -2.19615 q^{44} -0.267949 q^{46} +(1.48356 - 2.56961i) q^{47} +(3.01790 - 3.01790i) q^{48} +(-2.09808 - 3.63397i) q^{49} +(-8.83013 - 2.36603i) q^{51} +(-2.12132 + 3.67423i) q^{52} -1.03528 q^{53} +(-2.59808 + 0.696152i) q^{54} +(-3.23205 + 5.59808i) q^{56} +(1.22474 + 0.328169i) q^{57} +(-0.120118 - 0.208051i) q^{58} +(-4.73205 - 8.19615i) q^{59} +(3.33013 - 5.76795i) q^{61} -0.378937 q^{62} +(-8.69333 + 5.01910i) q^{63} -2.26795 q^{64} +(-0.294229 - 1.09808i) q^{66} +(3.79435 + 6.57201i) q^{67} +(4.57081 + 7.91688i) q^{68} +(0.232051 + 0.866025i) q^{69} +14.1962 q^{71} +(5.01910 + 2.89778i) q^{72} +8.48528 q^{73} +(-1.09808 + 1.90192i) q^{74} +(-0.633975 - 1.09808i) q^{76} +(-2.12132 - 3.67423i) q^{77} +(-2.12132 - 0.568406i) q^{78} +(-3.73205 + 6.46410i) q^{79} +(4.50000 + 7.79423i) q^{81} -4.00240 q^{82} +(3.98382 - 6.90018i) q^{83} +(9.69615 + 2.59808i) q^{84} +(-0.169873 - 0.294229i) q^{86} +(-0.568406 + 0.568406i) q^{87} +(-1.22474 + 2.12132i) q^{88} +13.3923 q^{89} -8.19615 q^{91} +(0.448288 - 0.776457i) q^{92} +(0.328169 + 1.22474i) q^{93} +(-0.767949 - 1.33013i) q^{94} +(-2.30385 - 8.59808i) q^{96} +(7.58871 - 13.1440i) q^{97} -2.17209 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	\( 8 q - 12 q^{6} - 12 q^{11} + 4 q^{16} + 8 q^{19} + 12 q^{21} - 12 q^{24} + 24 q^{26} - 12 q^{29} + 4 q^{31} + 4 q^{34} + 12 q^{39} - 24 q^{41} + 24 q^{44} - 16 q^{46} + 4 q^{49} - 36 q^{51} - 12 q^{56} - 24 q^{59} - 8 q^{61} - 32 q^{64} + 60 q^{66} - 12 q^{69} + 72 q^{71} + 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{81} + 36 q^{84} - 36 q^{86} + 24 q^{89} - 24 q^{91} - 20 q^{94} - 60 q^{96} + 36 q^{99}+O(q^{100}) \) 8 * q - 12 * q^6 - 12 * q^11 + 4 * q^16 + 8 * q^19 + 12 * q^21 - 12 * q^24 + 24 * q^26 - 12 * q^29 + 4 * q^31 + 4 * q^34 + 12 * q^39 - 24 * q^41 + 24 * q^44 - 16 * q^46 + 4 * q^49 - 36 * q^51 - 12 * q^56 - 24 * q^59 - 8 * q^61 - 32 * q^64 + 60 * q^66 - 12 * q^69 + 72 * q^71 + 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^81 + 36 * q^84 - 36 * q^86 + 24 * q^89 - 24 * q^91 - 20 * q^94 - 60 * q^96 + 36 * q^99

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