LMFDB - Embedded newform 175.2.o.c.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(68,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("175.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.o (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	175.157
Dual form			175.2.o.c.68.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(2.38014 + 1.15539i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(-2.00000 + 3.46410i) q^{11} +(-1.67303 - 0.448288i) q^{12} +(-2.44949 - 2.44949i) q^{13} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.896575 + 3.34607i) q^{17} +(-1.73205 - 3.00000i) q^{19} +(-4.50000 - 0.866025i) q^{21} +(-2.82843 - 2.82843i) q^{22} +(6.76148 + 1.81173i) q^{23} +(2.59808 - 4.50000i) q^{24} +(3.00000 - 1.73205i) q^{26} +(3.67423 - 3.67423i) q^{27} +(1.48356 + 2.19067i) q^{28} +1.00000i q^{29} +(9.00000 + 5.19615i) q^{31} +(-4.82963 + 1.29410i) q^{32} +(1.79315 - 6.69213i) q^{33} -3.46410 q^{34} +(1.03528 - 3.86370i) q^{37} +(3.34607 - 0.896575i) q^{38} +(5.19615 + 3.00000i) q^{39} -8.66025i q^{41} +(2.00120 - 4.12252i) q^{42} +(3.53553 - 3.53553i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(-3.50000 + 6.06218i) q^{46} +(-3.34607 - 0.896575i) q^{47} +(1.22474 + 1.22474i) q^{48} +(4.33013 + 5.50000i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-0.896575 - 3.34607i) q^{52} +(0.517638 + 1.93185i) q^{53} +(2.59808 + 4.50000i) q^{54} +(-7.50000 + 2.59808i) q^{56} +(4.24264 + 4.24264i) q^{57} +(-0.965926 - 0.258819i) q^{58} +(1.73205 - 3.00000i) q^{59} +(1.50000 - 0.866025i) q^{61} +(-7.34847 + 7.34847i) q^{62} -7.00000i q^{64} +(6.00000 + 3.46410i) q^{66} +(8.69333 - 2.32937i) q^{67} +(-0.896575 + 3.34607i) q^{68} -12.1244 q^{69} +2.00000 q^{71} +(-10.0382 + 2.68973i) q^{73} +(3.46410 + 2.00000i) q^{74} -3.46410i q^{76} +(-8.76268 + 5.93426i) q^{77} +(-4.24264 + 4.24264i) q^{78} +(1.73205 - 1.00000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(8.36516 + 2.24144i) q^{82} +(3.67423 + 3.67423i) q^{83} +(-3.46410 - 3.00000i) q^{84} +(2.50000 + 4.33013i) q^{86} +(-0.448288 - 1.67303i) q^{87} +(-3.10583 - 11.5911i) q^{88} +(-6.06218 - 10.5000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +(4.94975 + 4.94975i) q^{92} +(-17.3867 - 4.65874i) q^{93} +(1.73205 - 3.00000i) q^{94} +(7.50000 - 4.33013i) q^{96} +(-4.89898 + 4.89898i) q^{97} +(-6.43331 + 2.75908i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{11} - 4 q^{16} - 36 q^{21} + 24 q^{26} + 72 q^{31} - 28 q^{46} - 24 q^{51} - 60 q^{56} + 12 q^{61} + 48 q^{66} + 16 q^{71} - 36 q^{81} + 20 q^{86} - 24 q^{91} + 60 q^{96}+O(q^{100}) $ 8 * q - 16 * q^11 - 4 * q^16 - 36 * q^21 + 24 * q^26 + 72 * q^31 - 28 * q^46 - 24 * q^51 - 60 * q^56 + 12 * q^61 + 48 * q^66 + 16 * q^71 - 36 * q^81 + 20 * q^86 - 24 * q^91 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i	0.812035	+	0.583609i	$0.198360\pi$
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i	−0.995047	+	0.0994033i	$0.968307\pi$
$3$	−1.67303	+	0.448288i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$3$	−1.67303	+	0.448288i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.707107i
$7$	2.38014	+	1.15539i	0.899608	+	0.436698i
$7$	2.38014	+	1.15539i	0.899608	+	0.436698i
$8$	−2.12132	+	2.12132i	−0.750000	+	0.750000i
$9$		0			0
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	−1.67303	−	0.448288i	−0.482963	−	0.129410i
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	0.280491	−	0.959857i	$-0.409503\pi$
$13$	−2.44949	−	2.44949i	−0.679366	−	0.679366i	−0.959857	+	0.280491i	$0.909503\pi$
$14$	−1.73205	+	2.00000i	−0.462910	+	0.534522i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.896575	+	3.34607i	0.217451	+	0.811540i	0.985289	+	0.170896i	$0.0546661\pi$
$17$	0.896575	+	3.34607i	0.217451	+	0.811540i	−0.767838	+	0.640644i	$0.778667\pi$
$18$		0			0
$19$	−1.73205	−	3.00000i	−0.397360	−	0.688247i	0.596040	−	0.802955i	$-0.296740\pi$
$19$	−1.73205	−	3.00000i	−0.397360	−	0.688247i	−0.993399	+	0.114708i	$0.963407\pi$
$20$		0			0
$21$	−4.50000	−	0.866025i	−0.981981	−	0.188982i
$22$	−2.82843	−	2.82843i	−0.603023	−	0.603023i
$23$	6.76148	+	1.81173i	1.40987	+	0.377773i	0.881877	−	0.471479i	$-0.156280\pi$
$23$	6.76148	+	1.81173i	1.40987	+	0.377773i	0.527989	+	0.849251i	$0.322946\pi$
$24$	2.59808	−	4.50000i	0.530330	−	0.918559i
$25$		0			0
$26$	3.00000	−	1.73205i	0.588348	−	0.339683i
$27$	3.67423	−	3.67423i	0.707107	−	0.707107i
$28$	1.48356	+	2.19067i	0.280367	+	0.413998i
$29$			1.00000i			0.185695i	0.995680	+	0.0928477i	$0.0295970\pi$
$29$			1.00000i			0.185695i	−0.995680	+	0.0928477i	$0.970403\pi$
$30$		0			0
$31$	9.00000	+	5.19615i	1.61645	+	0.933257i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	9.00000	+	5.19615i	1.61645	+	0.933257i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−4.82963	+	1.29410i	−0.853766	+	0.228766i
$33$	1.79315	−	6.69213i	0.312148	−	1.16495i
$34$	−3.46410			−0.594089
$35$		0			0
$36$		0			0
$37$	1.03528	−	3.86370i	0.170198	−	0.635189i	−0.827121	−	0.562023i	$-0.810023\pi$
$37$	1.03528	−	3.86370i	0.170198	−	0.635189i	0.997320	−	0.0731657i	$-0.0233102\pi$
$38$	3.34607	−	0.896575i	0.542803	−	0.145444i
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$		0			0
$41$		−	8.66025i		−	1.35250i	−0.736670	−	0.676252i	$-0.763603\pi$
$41$		−	8.66025i		−	1.35250i	0.736670	−	0.676252i	$-0.236397\pi$
$42$	2.00120	−	4.12252i	0.308792	−	0.636119i
$43$	3.53553	−	3.53553i	0.539164	−	0.539164i	−0.384120	−	0.923283i	$-0.625495\pi$
$43$	3.53553	−	3.53553i	0.539164	−	0.539164i	0.923283	+	0.384120i	$0.125495\pi$
$44$	−3.46410	+	2.00000i	−0.522233	+	0.301511i
$45$		0			0
$46$	−3.50000	+	6.06218i	−0.516047	+	0.893819i
$47$	−3.34607	−	0.896575i	−0.488074	−	0.130779i	0.00638578	−	0.999980i	$-0.497967\pi$
$47$	−3.34607	−	0.896575i	−0.488074	−	0.130779i	−0.494460	+	0.869201i	$0.664634\pi$
$48$	1.22474	+	1.22474i	0.176777	+	0.176777i
$49$	4.33013	+	5.50000i	0.618590	+	0.785714i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$	−0.896575	−	3.34607i	−0.124333	−	0.464016i
$53$	0.517638	+	1.93185i	0.0711031	+	0.265360i	0.992321	−	0.123686i	$-0.0394714\pi$
$53$	0.517638	+	1.93185i	0.0711031	+	0.265360i	−0.921218	+	0.389046i	$0.872805\pi$
$54$	2.59808	+	4.50000i	0.353553	+	0.612372i
$55$		0			0
$56$	−7.50000	+	2.59808i	−1.00223	+	0.347183i
$57$	4.24264	+	4.24264i	0.561951	+	0.561951i
$58$	−0.965926	−	0.258819i	−0.126832	−	0.0339846i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$		0			0
$61$	1.50000	−	0.866025i	0.192055	−	0.110883i	−0.400889	−	0.916127i	$-0.631299\pi$
$61$	1.50000	−	0.866025i	0.192055	−	0.110883i	0.592944	+	0.805243i	$0.297965\pi$
$62$	−7.34847	+	7.34847i	−0.933257	+	0.933257i
$63$		0			0
$64$		−	7.00000i		−	0.875000i
$65$		0			0
$66$	6.00000	+	3.46410i	0.738549	+	0.426401i
$67$	8.69333	−	2.32937i	1.06206	−	0.284578i	0.314833	−	0.949147i	$-0.398052\pi$
$67$	8.69333	−	2.32937i	1.06206	−	0.284578i	0.747227	+	0.664569i	$0.231385\pi$
$68$	−0.896575	+	3.34607i	−0.108726	+	0.405770i
$69$	−12.1244			−1.45960
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$		0			0
$73$	−10.0382	+	2.68973i	−1.17488	+	0.314809i	−0.792895	−	0.609359i	$-0.791427\pi$
$73$	−10.0382	+	2.68973i	−1.17488	+	0.314809i	−0.381987	+	0.924168i	$0.624760\pi$
$74$	3.46410	+	2.00000i	0.402694	+	0.232495i
$75$		0			0
$76$		−	3.46410i		−	0.397360i
$77$	−8.76268	+	5.93426i	−0.998600	+	0.676271i
$78$	−4.24264	+	4.24264i	−0.480384	+	0.480384i
$79$	1.73205	−	1.00000i	0.194871	−	0.112509i	−0.399390	−	0.916781i	$-0.630778\pi$
$79$	1.73205	−	1.00000i	0.194871	−	0.112509i	0.594261	+	0.804272i	$0.297445\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	8.36516	+	2.24144i	0.923778	+	0.247525i
$83$	3.67423	+	3.67423i	0.403300	+	0.403300i	0.879394	−	0.476094i	$-0.157948\pi$
$83$	3.67423	+	3.67423i	0.403300	+	0.403300i	−0.476094	+	0.879394i	$0.657948\pi$
$84$	−3.46410	−	3.00000i	−0.377964	−	0.327327i
$85$		0			0
$86$	2.50000	+	4.33013i	0.269582	+	0.466930i
$87$	−0.448288	−	1.67303i	−0.0480615	−	0.179368i
$88$	−3.10583	−	11.5911i	−0.331082	−	1.23562i
$89$	−6.06218	−	10.5000i	−0.642590	−	1.11300i	−0.984853	−	0.173394i	$-0.944527\pi$
$89$	−6.06218	−	10.5000i	−0.642590	−	1.11300i	0.342263	−	0.939604i	$-0.388807\pi$
$90$		0			0
$91$	−3.00000	−	8.66025i	−0.314485	−	0.907841i
$92$	4.94975	+	4.94975i	0.516047	+	0.516047i
$93$	−17.3867	−	4.65874i	−1.80291	−	0.483089i
$94$	1.73205	−	3.00000i	0.178647	−	0.309426i
$95$		0			0
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	−4.89898	+	4.89898i	−0.497416	+	0.497416i	−0.910633	−	0.413217i	$-0.864405\pi$
$97$	−4.89898	+	4.89898i	−0.497416	+	0.497416i	0.413217	+	0.910633i	$0.364405\pi$
$98$	−6.43331	+	2.75908i	−0.649863	+	0.278709i
$99$		0			0
$100$		0			0
$101$	1.50000	+	0.866025i	0.149256	+	0.0861727i	0.572768	−	0.819718i	$-0.305870\pi$
$101$	1.50000	+	0.866025i	0.149256	+	0.0861727i	−0.423512	+	0.905890i	$0.639203\pi$
$102$	5.79555	−	1.55291i	0.573845	−	0.153761i
$103$	−4.03459	+	15.0573i	−0.397540	+	1.48364i	0.419871	+	0.907584i	$0.362075\pi$
$103$	−4.03459	+	15.0573i	−0.397540	+	1.48364i	−0.817411	+	0.576055i	$0.804591\pi$
$104$	10.3923			1.01905
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−0.258819	+	0.965926i	−0.0250210	+	0.0933796i	−0.977307	−	0.211827i	$-0.932059\pi$
$107$	−0.258819	+	0.965926i	−0.0250210	+	0.0933796i	0.952286	+	0.305206i	$0.0987254\pi$
$108$	5.01910	−	1.34486i	0.482963	−	0.129410i
$109$	2.59808	+	1.50000i	0.248851	+	0.143674i	0.619238	−	0.785203i	$-0.287442\pi$
$109$	2.59808	+	1.50000i	0.248851	+	0.143674i	−0.370387	+	0.928877i	$0.620775\pi$
$110$		0			0
$111$			6.92820i			0.657596i
$112$	−0.189469	−	2.63896i	−0.0179031	−	0.249358i
$113$	7.07107	−	7.07107i	0.665190	−	0.665190i	−0.291409	−	0.956599i	$-0.594124\pi$
$113$	7.07107	−	7.07107i	0.665190	−	0.665190i	0.956599	+	0.291409i	$0.0941239\pi$
$114$	−5.19615	+	3.00000i	−0.486664	+	0.280976i
$115$		0			0
$116$	−0.500000	+	0.866025i	−0.0464238	+	0.0804084i
$117$		0			0
$118$	2.44949	+	2.44949i	0.225494	+	0.225494i
$119$	−1.73205	+	9.00000i	−0.158777	+	0.825029i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	0.448288	+	1.67303i	0.0405861	+	0.151469i
$123$	3.88229	+	14.4889i	0.350054	+	1.30642i
$124$	5.19615	+	9.00000i	0.466628	+	0.808224i
$125$		0			0
$126$		0			0
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	−2.89778	−	0.776457i	−0.256130	−	0.0686298i
$129$	−4.33013	+	7.50000i	−0.381246	+	0.660338i
$130$		0			0
$131$	−6.00000	+	3.46410i	−0.524222	+	0.302660i	−0.738661	−	0.674078i	$-0.764541\pi$
$131$	−6.00000	+	3.46410i	−0.524222	+	0.302660i	0.214438	+	0.976738i	$0.431208\pi$
$132$	4.89898	−	4.89898i	0.426401	−	0.426401i
$133$	−0.656339	−	9.14162i	−0.0569118	−	0.792679i
$134$			9.00000i			0.777482i
$135$		0			0
$136$	−9.00000	−	5.19615i	−0.771744	−	0.445566i
$137$	−15.4548	+	4.14110i	−1.32039	+	0.353798i	−0.849125	−	0.528191i	$-0.822870\pi$
$137$	−15.4548	+	4.14110i	−1.32039	+	0.353798i	−0.471268	+	0.881990i	$0.656204\pi$
$138$	3.13801	−	11.7112i	0.267126	−	0.996926i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	−0.517638	+	1.93185i	−0.0434392	+	0.162117i
$143$	13.3843	−	3.58630i	1.11925	−	0.299902i
$144$		0			0
$145$		0			0
$146$		−	10.3923i		−	0.860073i
$147$	−9.71003	−	7.26054i	−0.800869	−	0.598839i
$148$	2.82843	−	2.82843i	0.232495	−	0.232495i
$149$	14.7224	−	8.50000i	1.20611	−	0.696347i	0.244202	−	0.969724i	$-0.421474\pi$
$149$	14.7224	−	8.50000i	1.20611	−	0.696347i	0.961907	+	0.273377i	$0.0881408\pi$
$150$		0			0
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	−0.717752	−	0.696299i	$-0.754829\pi$
$151$	3.00000	−	5.19615i	0.244137	−	0.422857i	0.961888	+	0.273442i	$0.0881622\pi$
$152$	10.0382	+	2.68973i	0.814205	+	0.218166i
$153$		0			0
$154$	−3.46410	−	10.0000i	−0.279145	−	0.805823i
$155$		0			0
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$	−3.58630	−	13.3843i	−0.286218	−	1.06818i	−0.947945	−	0.318435i	$-0.896843\pi$
$157$	−3.58630	−	13.3843i	−0.286218	−	1.06818i	0.661727	−	0.749745i	$-0.269824\pi$
$158$	0.517638	+	1.93185i	0.0411811	+	0.153690i
$159$	−1.73205	−	3.00000i	−0.137361	−	0.237915i
$160$		0			0
$161$	14.0000	+	12.1244i	1.10335	+	0.955533i
$162$	−6.36396	−	6.36396i	−0.500000	−	0.500000i
$163$	11.5911	+	3.10583i	0.907886	+	0.243267i	0.682400	−	0.730979i	$-0.260936\pi$
$163$	11.5911	+	3.10583i	0.907886	+	0.243267i	0.225486	+	0.974246i	$0.427603\pi$
$164$	4.33013	−	7.50000i	0.338126	−	0.585652i
$165$		0			0
$166$	−4.50000	+	2.59808i	−0.349268	+	0.201650i
$167$	13.4722	−	13.4722i	1.04251	−	1.04251i	0.0434542	−	0.999055i	$-0.486164\pi$
$167$	13.4722	−	13.4722i	1.04251	−	1.04251i	0.999055	−	0.0434542i	$-0.0138363\pi$
$168$	11.3831	−	7.70882i	0.878222	−	0.594749i
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$		0			0
$172$	4.82963	−	1.29410i	0.368256	−	0.0986738i
$173$	−1.79315	+	6.69213i	−0.136331	+	0.508793i	0.863658	+	0.504078i	$0.168168\pi$
$173$	−1.79315	+	6.69213i	−0.136331	+	0.508793i	−0.999989	+	0.00471527i	$0.998499\pi$
$174$	1.73205			0.131306
$175$		0			0
$176$	4.00000			0.301511
$177$	−1.55291	+	5.79555i	−0.116724	+	0.435621i
$178$	11.7112	−	3.13801i	0.877794	−	0.235204i
$179$	−19.0526	−	11.0000i	−1.42406	−	0.822179i	−0.427413	−	0.904057i	$-0.640575\pi$
$179$	−19.0526	−	11.0000i	−1.42406	−	0.822179i	−0.996642	+	0.0818780i	$0.973908\pi$
$180$		0			0
$181$			8.66025i			0.643712i	0.946789	+	0.321856i	$0.104307\pi$
$181$			8.66025i			0.643712i	−0.946789	+	0.321856i	$0.895693\pi$
$182$	9.14162	−	0.656339i	0.677622	−	0.0486511i
$183$	−2.12132	+	2.12132i	−0.156813	+	0.156813i
$184$	−18.1865	+	10.5000i	−1.34073	+	0.774070i
$185$		0			0
$186$	9.00000	−	15.5885i	0.659912	−	1.14300i
$187$	−13.3843	−	3.58630i	−0.978754	−	0.262256i
$188$	−2.44949	−	2.44949i	−0.178647	−	0.178647i
$189$	12.9904	−	4.50000i	0.944911	−	0.327327i
$190$		0			0
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$	3.13801	+	11.7112i	0.226467	+	0.845185i
$193$	−2.07055	−	7.72741i	−0.149042	−	0.556231i	−0.999542	−	0.0302567i	$-0.990368\pi$
$193$	−2.07055	−	7.72741i	−0.149042	−	0.556231i	0.850501	−	0.525974i	$-0.176299\pi$
$194$	−3.46410	−	6.00000i	−0.248708	−	0.430775i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−14.1421	−	14.1421i	−1.00759	−	1.00759i	−0.999971	−	0.00761443i	$-0.997576\pi$
$197$	−14.1421	−	14.1421i	−1.00759	−	1.00759i	−0.00761443	−	0.999971i	$-0.502424\pi$
$198$		0			0
$199$	−6.92820	+	12.0000i	−0.491127	+	0.850657i	−0.999948	−	0.0102152i	$-0.996748\pi$
$199$	−6.92820	+	12.0000i	−0.491127	+	0.850657i	0.508821	+	0.860873i	$0.330082\pi$
$200$		0			0
$201$	−13.5000	+	7.79423i	−0.952217	+	0.549762i
$202$	−1.22474	+	1.22474i	−0.0861727	+	0.0861727i
$203$	−1.15539	+	2.38014i	−0.0810928	+	0.167053i
$204$		−	6.00000i		−	0.420084i
$205$		0			0
$206$	−13.5000	−	7.79423i	−0.940590	−	0.543050i
$207$		0			0
$208$	−0.896575	+	3.34607i	−0.0621663	+	0.232008i
$209$	13.8564			0.958468
$210$		0			0
$211$	−18.0000			−1.23917			−0.619586	−	0.784929i	$-0.712699\pi$
$211$	−18.0000			−1.23917			−0.619586	+	0.784929i	$0.712699\pi$
$212$	−0.517638	+	1.93185i	−0.0355515	+	0.132680i
$213$	−3.34607	+	0.896575i	−0.229269	+	0.0614323i
$214$	−0.866025	−	0.500000i	−0.0592003	−	0.0341793i
$215$		0			0
$216$			15.5885i			1.06066i
$217$	15.4176	+	22.7661i	1.04662	+	1.54546i
$218$	−2.12132	+	2.12132i	−0.143674	+	0.143674i
$219$	15.5885	−	9.00000i	1.05337	−	0.608164i
$220$		0			0
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$	−6.69213	−	1.79315i	−0.449146	−	0.120348i
$223$	−2.44949	−	2.44949i	−0.164030	−	0.164030i	0.620319	−	0.784349i	$-0.287003\pi$
$223$	−2.44949	−	2.44949i	−0.164030	−	0.164030i	−0.784349	+	0.620319i	$0.787003\pi$
$224$	−12.9904	−	2.50000i	−0.867956	−	0.167038i
$225$		0			0
$226$	5.00000	+	8.66025i	0.332595	+	0.576072i
$227$	0.896575	+	3.34607i	0.0595078	+	0.222086i	0.989276	−	0.146060i	$-0.0466593\pi$
$227$	0.896575	+	3.34607i	0.0595078	+	0.222086i	−0.929768	+	0.368146i	$0.879993\pi$
$228$	1.55291	+	5.79555i	0.102844	+	0.383820i
$229$	6.92820	+	12.0000i	0.457829	+	0.792982i	0.998846	−	0.0480291i	$-0.0152940\pi$
$229$	6.92820	+	12.0000i	0.457829	+	0.792982i	−0.541017	+	0.841011i	$0.681961\pi$
$230$		0			0
$231$	12.0000	−	13.8564i	0.789542	−	0.911685i
$232$	−2.12132	−	2.12132i	−0.139272	−	0.139272i
$233$	1.93185	+	0.517638i	0.126560	+	0.0339116i	0.321543	−	0.946895i	$-0.395799\pi$
$233$	1.93185	+	0.517638i	0.126560	+	0.0339116i	−0.194983	+	0.980807i	$0.562465\pi$
$234$		0			0
$235$		0			0
$236$	3.00000	−	1.73205i	0.195283	−	0.112747i
$237$	−2.44949	+	2.44949i	−0.159111	+	0.159111i
$238$	−8.24504	−	4.00240i	−0.534447	−	0.259437i
$239$			26.0000i			1.68180i	0.541190	+	0.840900i	$0.317974\pi$
$239$			26.0000i			1.68180i	−0.541190	+	0.840900i	$0.682026\pi$
$240$		0			0
$241$	−6.00000	−	3.46410i	−0.386494	−	0.223142i	0.294146	−	0.955761i	$-0.404965\pi$
$241$	−6.00000	−	3.46410i	−0.386494	−	0.223142i	−0.680640	+	0.732618i	$0.738298\pi$
$242$	4.82963	−	1.29410i	0.310460	−	0.0831876i
$243$		0			0
$244$	1.73205			0.110883
$245$		0			0
$246$	−15.0000			−0.956365
$247$	−3.10583	+	11.5911i	−0.197619	+	0.737525i
$248$	−30.1146	+	8.06918i	−1.91228	+	0.512393i
$249$	−7.79423	−	4.50000i	−0.493939	−	0.285176i
$250$		0			0
$251$			17.3205i			1.09326i	0.837374	+	0.546630i	$0.184090\pi$
$251$			17.3205i			1.09326i	−0.837374	+	0.546630i	$0.815910\pi$
$252$		0			0
$253$	−19.7990	+	19.7990i	−1.24475	+	1.24475i
$254$		0			0
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	13.3843	+	3.58630i	0.834887	+	0.223707i	0.650845	−	0.759211i	$-0.274415\pi$
$257$	13.3843	+	3.58630i	0.834887	+	0.223707i	0.184043	+	0.982918i	$0.441082\pi$
$258$	−6.12372	−	6.12372i	−0.381246	−	0.381246i
$259$	6.92820	−	8.00000i	0.430498	−	0.497096i
$260$		0			0
$261$		0			0
$262$	−1.79315	−	6.69213i	−0.110781	−	0.413441i
$263$	−3.36465	−	12.5570i	−0.207473	−	0.774300i	−0.988681	−	0.150030i	$-0.952063\pi$
$263$	−3.36465	−	12.5570i	−0.207473	−	0.774300i	0.781208	−	0.624270i	$-0.214604\pi$
$264$	10.3923	+	18.0000i	0.639602	+	1.10782i
$265$		0			0
$266$	9.00000	+	1.73205i	0.551825	+	0.106199i
$267$	14.8492	+	14.8492i	0.908759	+	0.908759i
$268$	8.69333	+	2.32937i	0.531030	+	0.142289i
$269$	−11.2583	+	19.5000i	−0.686433	+	1.18894i	0.286552	+	0.958065i	$0.407491\pi$
$269$	−11.2583	+	19.5000i	−0.686433	+	1.18894i	−0.972984	+	0.230871i	$0.925842\pi$
$270$		0			0
$271$	9.00000	−	5.19615i	0.546711	−	0.315644i	−0.201083	−	0.979574i	$-0.564446\pi$
$271$	9.00000	−	5.19615i	0.546711	−	0.315644i	0.747794	+	0.663930i	$0.231113\pi$
$272$	2.44949	−	2.44949i	0.148522	−	0.148522i
$273$	8.90138	+	13.1440i	0.538736	+	0.795513i
$274$		−	16.0000i		−	0.966595i
$275$		0			0
$276$	−10.5000	−	6.06218i	−0.632026	−	0.364900i
$277$	−5.79555	+	1.55291i	−0.348221	+	0.0933056i	−0.428690	−	0.903452i	$-0.641025\pi$
$277$	−5.79555	+	1.55291i	−0.348221	+	0.0933056i	0.0804691	+	0.996757i	$0.474358\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$	−1.55291	+	5.79555i	−0.0924747	+	0.345120i
$283$	−10.0382	+	2.68973i	−0.596709	+	0.159888i	−0.544518	−	0.838749i	$-0.683287\pi$
$283$	−10.0382	+	2.68973i	−0.596709	+	0.159888i	−0.0521913	+	0.998637i	$0.516621\pi$
$284$	1.73205	+	1.00000i	0.102778	+	0.0593391i
$285$		0			0
$286$			13.8564i			0.819346i
$287$	10.0060	−	20.6126i	0.590636	−	1.21672i
$288$		0			0
$289$	4.33013	−	2.50000i	0.254713	−	0.147059i
$290$		0			0
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	−10.0382	−	2.68973i	−0.587441	−	0.157404i
$293$	−14.6969	−	14.6969i	−0.858604	−	0.858604i	0.132569	−	0.991174i	$-0.457677\pi$
$293$	−14.6969	−	14.6969i	−0.858604	−	0.858604i	−0.991174	+	0.132569i	$0.957677\pi$
$294$	9.52628	−	7.50000i	0.555584	−	0.437409i
$295$		0			0
$296$	6.00000	+	10.3923i	0.348743	+	0.604040i
$297$	5.37945	+	20.0764i	0.312148	+	1.16495i
$298$	4.39992	+	16.4207i	0.254881	+	0.951228i
$299$	−12.1244	−	21.0000i	−0.701170	−	1.21446i
$300$		0			0
$301$	12.5000	−	4.33013i	0.720488	−	0.249584i
$302$	4.24264	+	4.24264i	0.244137	+	0.244137i
$303$	−2.89778	−	0.776457i	−0.166473	−	0.0446063i
$304$	−1.73205	+	3.00000i	−0.0993399	+	0.172062i
$305$		0			0
$306$		0			0
$307$	−11.0227	+	11.0227i	−0.629099	+	0.629099i	−0.947841	−	0.318742i	$-0.896740\pi$
$307$	−11.0227	+	11.0227i	−0.629099	+	0.629099i	0.318742	+	0.947841i	$0.396740\pi$
$308$	−10.5558	+	0.757875i	−0.601474	+	0.0431839i
$309$		−	27.0000i		−	1.53598i
$310$		0			0
$311$	−21.0000	−	12.1244i	−1.19080	−	0.687509i	−0.232313	−	0.972641i	$-0.574629\pi$
$311$	−21.0000	−	12.1244i	−1.19080	−	0.687509i	−0.958488	+	0.285132i	$0.907963\pi$
$312$	−17.3867	+	4.65874i	−0.984326	+	0.263749i
$313$	7.17260	−	26.7685i	0.405420	−	1.51305i	−0.397861	−	0.917446i	$-0.630247\pi$
$313$	7.17260	−	26.7685i	0.405420	−	1.51305i	0.803281	−	0.595601i	$-0.203086\pi$
$314$	13.8564			0.781962
$315$		0			0
$316$	2.00000			0.112509
$317$	8.79985	−	32.8415i	0.494249	−	1.84456i	−0.0399492	−	0.999202i	$-0.512720\pi$
$317$	8.79985	−	32.8415i	0.494249	−	1.84456i	0.534198	−	0.845359i	$-0.320614\pi$
$318$	3.34607	−	0.896575i	0.187638	−	0.0502775i
$319$	−3.46410	−	2.00000i	−0.193952	−	0.111979i
$320$		0			0
$321$		−	1.73205i		−	0.0966736i
$322$	−15.3347	+	10.3849i	−0.854569	+	0.578730i
$323$	8.48528	−	8.48528i	0.472134	−	0.472134i
$324$	−7.79423	+	4.50000i	−0.433013	+	0.250000i
$325$		0			0
$326$	−6.00000	+	10.3923i	−0.332309	+	0.575577i
$327$	−5.01910	−	1.34486i	−0.277557	−	0.0743711i
$328$	18.3712	+	18.3712i	1.01438	+	1.01438i
$329$	−6.92820	−	6.00000i	−0.381964	−	0.330791i
$330$		0			0
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	0.936618	−	0.350352i	$-0.113938\pi$
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	−0.771723	+	0.635959i	$0.780605\pi$
$332$	1.34486	+	5.01910i	0.0738090	+	0.275459i
$333$		0			0
$334$	9.52628	+	16.5000i	0.521255	+	0.902840i
$335$		0			0
$336$	1.50000	+	4.33013i	0.0818317	+	0.236228i
$337$	7.07107	+	7.07107i	0.385186	+	0.385186i	0.872966	−	0.487781i	$-0.162193\pi$
$337$	7.07107	+	7.07107i	0.385186	+	0.385186i	−0.487781	+	0.872966i	$0.662193\pi$
$338$	0.965926	+	0.258819i	0.0525394	+	0.0140779i
$339$	−8.66025	+	15.0000i	−0.470360	+	0.814688i
$340$		0			0
$341$	−36.0000	+	20.7846i	−1.94951	+	1.12555i
$342$		0			0
$343$	3.95164	+	18.0938i	0.213368	+	0.976972i
$344$			15.0000i			0.808746i
$345$		0			0
$346$	−6.00000	−	3.46410i	−0.322562	−	0.186231i
$347$	18.3526	−	4.91756i	0.985219	−	0.263989i	0.269978	−	0.962867i	$-0.412984\pi$
$347$	18.3526	−	4.91756i	0.985219	−	0.263989i	0.715241	+	0.698878i	$0.246317\pi$
$348$	0.448288	−	1.67303i	0.0240307	−	0.0896840i
$349$	−25.9808			−1.39072			−0.695359	−	0.718662i	$-0.744755\pi$
$349$	−25.9808			−1.39072			−0.695359	+	0.718662i	$0.744755\pi$
$350$		0			0
$351$	−18.0000			−0.960769
$352$	5.17638	−	19.3185i	0.275902	−	1.02968i
$353$	23.4225	−	6.27603i	1.24665	−	0.334039i	0.425609	−	0.904907i	$-0.360060\pi$
$353$	23.4225	−	6.27603i	1.24665	−	0.334039i	0.821042	+	0.570868i	$0.193393\pi$
$354$	−5.19615	−	3.00000i	−0.276172	−	0.159448i
$355$		0			0
$356$		−	12.1244i		−	0.642590i
$357$	−1.13681	−	15.8338i	−0.0601665	−	0.838011i
$358$	15.5563	−	15.5563i	0.822179	−	0.822179i
$359$	1.73205	−	1.00000i	0.0914141	−	0.0527780i	−0.453596	−	0.891207i	$-0.649859\pi$
$359$	1.73205	−	1.00000i	0.0914141	−	0.0527780i	0.545010	+	0.838429i	$0.316526\pi$
$360$		0			0
$361$	3.50000	−	6.06218i	0.184211	−	0.319062i
$362$	−8.36516	−	2.24144i	−0.439663	−	0.117807i
$363$	6.12372	+	6.12372i	0.321412	+	0.321412i
$364$	1.73205	−	9.00000i	0.0907841	−	0.471728i
$365$		0			0
$366$	−1.50000	−	2.59808i	−0.0784063	−	0.135804i
$367$	−1.34486	−	5.01910i	−0.0702013	−	0.261995i	0.921901	−	0.387425i	$-0.126635\pi$
$367$	−1.34486	−	5.01910i	−0.0702013	−	0.261995i	−0.992102	+	0.125430i	$0.959969\pi$
$368$	−1.81173	−	6.76148i	−0.0944431	−	0.352467i
$369$		0			0
$370$		0			0
$371$	−1.00000	+	5.19615i	−0.0519174	+	0.269771i
$372$	−12.7279	−	12.7279i	−0.659912	−	0.659912i
$373$	11.5911	+	3.10583i	0.600165	+	0.160814i	0.546095	−	0.837723i	$-0.316114\pi$
$373$	11.5911	+	3.10583i	0.600165	+	0.160814i	0.0540702	+	0.998537i	$0.482781\pi$
$374$	6.92820	−	12.0000i	0.358249	−	0.620505i
$375$		0			0
$376$	9.00000	−	5.19615i	0.464140	−	0.267971i
$377$	2.44949	−	2.44949i	0.126155	−	0.126155i
$378$	0.984508	+	13.7124i	0.0506376	+	0.705291i
$379$			6.00000i			0.308199i	0.988055	+	0.154100i	$0.0492477\pi$
$379$			6.00000i			0.308199i	−0.988055	+	0.154100i	$0.950752\pi$
$380$		0			0
$381$		0			0
$382$	3.86370	−	1.03528i	0.197684	−	0.0529693i
$383$	4.93117	−	18.4034i	0.251971	−	0.940368i	−0.717780	−	0.696270i	$-0.754842\pi$
$383$	4.93117	−	18.4034i	0.251971	−	0.940368i	0.969751	−	0.244098i	$-0.0784917\pi$
$384$	5.19615			0.265165
$385$		0			0
$386$	8.00000			0.407189
$387$		0			0
$388$	−6.69213	+	1.79315i	−0.339741	+	0.0910334i
$389$	−1.73205	−	1.00000i	−0.0878185	−	0.0507020i	0.455448	−	0.890263i	$-0.349479\pi$
$389$	−1.73205	−	1.00000i	−0.0878185	−	0.0507020i	−0.543266	+	0.839561i	$0.682813\pi$
$390$		0			0
$391$			24.2487i			1.22631i
$392$	−20.8528	−	2.48168i	−1.05323	−	0.125344i
$393$	8.48528	−	8.48528i	0.428026	−	0.428026i
$394$	17.3205	−	10.0000i	0.872595	−	0.503793i
$395$		0			0
$396$		0			0
$397$	13.3843	+	3.58630i	0.671737	+	0.179991i	0.578537	−	0.815656i	$-0.303624\pi$
$397$	13.3843	+	3.58630i	0.671737	+	0.179991i	0.0931997	+	0.995647i	$0.470290\pi$
$398$	−9.79796	−	9.79796i	−0.491127	−	0.491127i
$399$	5.19615	+	15.0000i	0.260133	+	0.750939i
$400$		0			0
$401$	−9.50000	−	16.4545i	−0.474407	−	0.821698i	0.525163	−	0.851002i	$-0.324004\pi$
$401$	−9.50000	−	16.4545i	−0.474407	−	0.821698i	−0.999571	+	0.0293039i	$0.990671\pi$
$402$	−4.03459	−	15.0573i	−0.201227	−	0.750990i
$403$	−9.31749	−	34.7733i	−0.464137	−	1.73218i
$404$	0.866025	+	1.50000i	0.0430864	+	0.0746278i
$405$		0			0
$406$	−2.00000	−	1.73205i	−0.0992583	−	0.0859602i
$407$	11.3137	+	11.3137i	0.560800	+	0.560800i
$408$	17.3867	+	4.65874i	0.860768	+	0.230642i
$409$	6.06218	−	10.5000i	0.299755	−	0.519192i	−0.676324	−	0.736604i	$-0.736428\pi$
$409$	6.06218	−	10.5000i	0.299755	−	0.519192i	0.976080	+	0.217412i	$0.0697616\pi$
$410$		0			0
$411$	24.0000	−	13.8564i	1.18383	−	0.683486i
$412$	−11.0227	+	11.0227i	−0.543050	+	0.543050i
$413$	7.58871	−	5.13922i	0.373416	−	0.252884i
$414$		0			0
$415$		0			0
$416$	15.0000	+	8.66025i	0.735436	+	0.424604i
$417$		0			0
$418$	−3.58630	+	13.3843i	−0.175412	+	0.654646i
$419$	34.6410			1.69232			0.846162	−	0.532925i	$-0.178907\pi$
$419$	34.6410			1.69232			0.846162	+	0.532925i	$0.178907\pi$
$420$		0			0
$421$	7.00000			0.341159			0.170580	−	0.985344i	$-0.445436\pi$
$421$	7.00000			0.341159			0.170580	+	0.985344i	$0.445436\pi$
$422$	4.65874	−	17.3867i	0.226784	−	0.846370i
$423$		0			0
$424$	−5.19615	−	3.00000i	−0.252347	−	0.145693i
$425$		0			0
$426$		−	3.46410i		−	0.167836i
$427$	4.57081	−	0.328169i	0.221197	−	0.0158812i
$428$	−0.707107	+	0.707107i	−0.0341793	+	0.0341793i
$429$	−20.7846	+	12.0000i	−1.00349	+	0.579365i
$430$		0			0
$431$	8.00000	−	13.8564i	0.385346	−	0.667440i	−0.606471	−	0.795106i	$-0.707415\pi$
$431$	8.00000	−	13.8564i	0.385346	−	0.667440i	0.991817	+	0.127666i	$0.0407486\pi$
$432$	−5.01910	−	1.34486i	−0.241481	−	0.0647048i
$433$	22.0454	+	22.0454i	1.05943	+	1.05943i	0.998118	+	0.0613163i	$0.0195298\pi$
$433$	22.0454	+	22.0454i	1.05943	+	1.05943i	0.0613163	+	0.998118i	$0.480470\pi$
$434$	−25.9808	+	9.00000i	−1.24712	+	0.432014i
$435$		0			0
$436$	1.50000	+	2.59808i	0.0718370	+	0.124425i
$437$	−6.27603	−	23.4225i	−0.300223	−	1.12045i
$438$	4.65874	+	17.3867i	0.222603	+	0.830767i
$439$	−10.3923	−	18.0000i	−0.495998	−	0.859093i	0.503992	−	0.863708i	$-0.331864\pi$
$439$	−10.3923	−	18.0000i	−0.495998	−	0.859093i	−0.999989	+	0.00461537i	$0.998531\pi$
$440$		0			0
$441$		0			0
$442$	8.48528	+	8.48528i	0.403604	+	0.403604i
$443$	−12.5570	−	3.36465i	−0.596603	−	0.159859i	−0.0521336	−	0.998640i	$-0.516602\pi$
$443$	−12.5570	−	3.36465i	−0.596603	−	0.159859i	−0.544469	+	0.838781i	$0.683269\pi$
$444$	−3.46410	+	6.00000i	−0.164399	+	0.284747i
$445$		0			0
$446$	3.00000	−	1.73205i	0.142054	−	0.0820150i
$447$	−20.8207	+	20.8207i	−0.984784	+	0.984784i
$448$	8.08776	−	16.6610i	0.382111	−	0.787157i
$449$			31.0000i			1.46298i	0.681852	+	0.731490i	$0.261175\pi$
$449$			31.0000i			1.46298i	−0.681852	+	0.731490i	$0.738825\pi$
$450$		0			0
$451$	30.0000	+	17.3205i	1.41264	+	0.815591i
$452$	9.65926	−	2.58819i	0.454333	−	0.121738i
$453$	−2.68973	+	10.0382i	−0.126374	+	0.471636i
$454$	−3.46410			−0.162578
$455$		0			0
$456$	−18.0000			−0.842927
$457$	−4.14110	+	15.4548i	−0.193713	+	0.722946i	0.798884	+	0.601486i	$0.205424\pi$
$457$	−4.14110	+	15.4548i	−0.193713	+	0.722946i	−0.992596	+	0.121460i	$0.961242\pi$
$458$	−13.3843	+	3.58630i	−0.625405	+	0.167577i
$459$	15.5885	+	9.00000i	0.727607	+	0.420084i
$460$		0			0
$461$		−	34.6410i		−	1.61339i	−0.590966	−	0.806696i	$-0.701253\pi$
$461$		−	34.6410i		−	1.61339i	0.590966	−	0.806696i	$-0.298747\pi$
$462$	10.2784	+	15.1774i	0.478196	+	0.706117i
$463$	−10.6066	+	10.6066i	−0.492931	+	0.492931i	−0.909228	−	0.416298i	$-0.863327\pi$
$463$	−10.6066	+	10.6066i	−0.492931	+	0.492931i	0.416298	+	0.909228i	$0.363327\pi$
$464$	0.866025	−	0.500000i	0.0402042	−	0.0232119i
$465$		0			0
$466$	−1.00000	+	1.73205i	−0.0463241	+	0.0802357i
$467$	5.01910	+	1.34486i	0.232256	+	0.0622328i	0.373070	−	0.927803i	$-0.378305\pi$
$467$	5.01910	+	1.34486i	0.232256	+	0.0622328i	−0.140814	+	0.990036i	$0.544972\pi$
$468$		0			0
$469$	23.3827	+	4.50000i	1.07971	+	0.207791i
$470$		0			0
$471$	12.0000	+	20.7846i	0.552931	+	0.957704i
$472$	2.68973	+	10.0382i	0.123805	+	0.462045i
$473$	5.17638	+	19.3185i	0.238010	+	0.888266i
$474$	−1.73205	−	3.00000i	−0.0795557	−	0.137795i
$475$		0			0
$476$	−6.00000	+	6.92820i	−0.275010	+	0.317554i
$477$		0			0
$478$	−25.1141	−	6.72930i	−1.14869	−	0.307791i
$479$	19.0526	−	33.0000i	0.870534	−	1.50781i	0.00908799	−	0.999959i	$-0.497107\pi$
$479$	19.0526	−	33.0000i	0.870534	−	1.50781i	0.861446	−	0.507850i	$-0.169560\pi$
$480$		0			0
$481$	−12.0000	+	6.92820i	−0.547153	+	0.315899i
$482$	4.89898	−	4.89898i	0.223142	−	0.223142i
$483$	−28.8577	−	14.0084i	−1.31307	−	0.637405i
$484$		−	5.00000i		−	0.227273i
$485$		0			0
$486$		0			0
$487$	3.86370	−	1.03528i	0.175081	−	0.0469128i	−0.170213	−	0.985407i	$-0.554446\pi$
$487$	3.86370	−	1.03528i	0.175081	−	0.0469128i	0.345294	+	0.938494i	$0.387779\pi$
$488$	−1.34486	+	5.01910i	−0.0608791	+	0.227204i
$489$	−20.7846			−0.939913
$490$		0			0
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$	−3.88229	+	14.4889i	−0.175027	+	0.653209i
$493$	−3.34607	+	0.896575i	−0.150699	+	0.0403797i
$494$	−10.3923	−	6.00000i	−0.467572	−	0.269953i
$495$		0			0
$496$		−	10.3923i		−	0.466628i
$497$	4.76028	+	2.31079i	0.213528	+	0.103653i
$498$	6.36396	−	6.36396i	0.285176	−	0.285176i
$499$	10.3923	−	6.00000i	0.465223	−	0.268597i	−0.249015	−	0.968500i	$-0.580107\pi$
$499$	10.3923	−	6.00000i	0.465223	−	0.268597i	0.714238	+	0.699903i	$0.246773\pi$
$500$		0			0
$501$	−16.5000	+	28.5788i	−0.737166	+	1.27681i
$502$	−16.7303	−	4.48288i	−0.746711	−	0.200081i
$503$	−8.57321	−	8.57321i	−0.382261	−	0.382261i	0.489655	−	0.871916i	$-0.337123\pi$
$503$	−8.57321	−	8.57321i	−0.382261	−	0.382261i	−0.871916	+	0.489655i	$0.837123\pi$
$504$		0			0
$505$		0			0
$506$	−14.0000	−	24.2487i	−0.622376	−	1.07799i
$507$	0.448288	+	1.67303i	0.0199092	+	0.0743020i
$508$		0			0
$509$	2.59808	+	4.50000i	0.115158	+	0.199459i	0.917843	−	0.396944i	$-0.129929\pi$
$509$	2.59808	+	4.50000i	0.115158	+	0.199459i	−0.802685	+	0.596403i	$0.796596\pi$
$510$		0			0
$511$	−27.0000	−	5.19615i	−1.19441	−	0.229864i
$512$	7.77817	+	7.77817i	0.343750	+	0.343750i
$513$	−17.3867	−	4.65874i	−0.767640	−	0.205689i
$514$	−6.92820	+	12.0000i	−0.305590	+	0.529297i
$515$		0			0
$516$	−7.50000	+	4.33013i	−0.330169	+	0.190623i
$517$	9.79796	−	9.79796i	0.430914	−	0.430914i
$518$	5.93426	+	8.76268i	0.260736	+	0.385010i
$519$		−	12.0000i		−	0.526742i
$520$		0			0
$521$	−6.00000	−	3.46410i	−0.262865	−	0.151765i	0.362776	−	0.931876i	$-0.381829\pi$
$521$	−6.00000	−	3.46410i	−0.262865	−	0.151765i	−0.625641	+	0.780111i	$0.715162\pi$
$522$		0			0
$523$	−6.27603	+	23.4225i	−0.274432	+	1.02419i	0.681790	+	0.731548i	$0.261202\pi$
$523$	−6.27603	+	23.4225i	−0.274432	+	1.02419i	−0.956221	+	0.292644i	$0.905465\pi$
$524$	−6.92820			−0.302660
$525$		0			0
$526$	13.0000			0.566827
$527$	−9.31749	+	34.7733i	−0.405876	+	1.51475i
$528$	−6.69213	+	1.79315i	−0.291238	+	0.0780369i
$529$	22.5167	+	13.0000i	0.978985	+	0.565217i
$530$		0			0
$531$		0			0
$532$	4.00240	−	8.24504i	0.173526	−	0.357468i
$533$	−21.2132	+	21.2132i	−0.918846	+	0.918846i
$534$	−18.1865	+	10.5000i	−0.787008	+	0.454379i
$535$		0			0
$536$	−13.5000	+	23.3827i	−0.583111	+	1.00998i
$537$	36.8067	+	9.86233i	1.58833	+	0.425591i
$538$	−15.9217	−	15.9217i	−0.686433	−	0.686433i
$539$	−27.7128	+	4.00000i	−1.19368	+	0.172292i
$540$		0			0
$541$	−9.50000	−	16.4545i	−0.408437	−	0.707433i	0.586278	−	0.810110i	$-0.300593\pi$
$541$	−9.50000	−	16.4545i	−0.408437	−	0.707433i	−0.994715	+	0.102677i	$0.967259\pi$
$542$	2.68973	+	10.0382i	0.115534	+	0.431177i
$543$	−3.88229	−	14.4889i	−0.166605	−	0.621778i
$544$	−8.66025	−	15.0000i	−0.371305	−	0.643120i
$545$		0			0
$546$	−15.0000	+	5.19615i	−0.641941	+	0.222375i
$547$	−31.8198	−	31.8198i	−1.36052	−	1.36052i	−0.873257	−	0.487259i	$-0.837997\pi$
$547$	−31.8198	−	31.8198i	−1.36052	−	1.36052i	−0.487259	−	0.873257i	$-0.662003\pi$
$548$	−15.4548	−	4.14110i	−0.660197	−	0.176899i
$549$		0			0
$550$		0			0
$551$	3.00000	−	1.73205i	0.127804	−	0.0737878i
$552$	25.7196	−	25.7196i	1.09470	−	1.09470i
$553$	5.27792	−	0.378937i	0.224440	−	0.0161141i
$554$		−	6.00000i		−	0.254916i
$555$		0			0
$556$		0			0
$557$	−15.4548	+	4.14110i	−0.654841	+	0.175464i	−0.570917	−	0.821008i	$-0.693412\pi$
$557$	−15.4548	+	4.14110i	−0.654841	+	0.175464i	−0.0839246	+	0.996472i	$0.526745\pi$
$558$		0			0
$559$	−17.3205			−0.732579
$560$		0			0
$561$	24.0000			1.01328
$562$	−5.69402	+	21.2504i	−0.240188	+	0.896393i
$563$	15.0573	−	4.03459i	0.634589	−	0.170038i	0.0728379	−	0.997344i	$-0.476794\pi$
$563$	15.0573	−	4.03459i	0.634589	−	0.170038i	0.561751	+	0.827306i	$0.310128\pi$
$564$	5.19615	+	3.00000i	0.218797	+	0.126323i
$565$		0			0
$566$		−	10.3923i		−	0.436821i
$567$	−19.7160	+	13.3521i	−0.827996	+	0.560734i
$568$	−4.24264	+	4.24264i	−0.178017	+	0.178017i
$569$	1.73205	−	1.00000i	0.0726113	−	0.0419222i	−0.463255	−	0.886225i	$-0.653319\pi$
$569$	1.73205	−	1.00000i	0.0726113	−	0.0419222i	0.535866	+	0.844303i	$0.319985\pi$
$570$		0			0
$571$	−17.0000	+	29.4449i	−0.711428	+	1.23223i	0.252893	+	0.967494i	$0.418618\pi$
$571$	−17.0000	+	29.4449i	−0.711428	+	1.23223i	−0.964321	+	0.264735i	$0.914716\pi$
$572$	13.3843	+	3.58630i	0.559624	+	0.149951i
$573$	4.89898	+	4.89898i	0.204658	+	0.204658i
$574$	17.3205	+	15.0000i	0.722944	+	0.626088i
$575$		0			0
$576$		0			0
$577$	5.37945	+	20.0764i	0.223950	+	0.835791i	0.982823	+	0.184553i	$0.0590836\pi$
$577$	5.37945	+	20.0764i	0.223950	+	0.835791i	−0.758873	+	0.651239i	$0.774250\pi$
$578$	1.29410	+	4.82963i	0.0538273	+	0.200886i
$579$	6.92820	+	12.0000i	0.287926	+	0.498703i
$580$		0			0
$581$	4.50000	+	12.9904i	0.186691	+	0.538932i
$582$	8.48528	+	8.48528i	0.351726	+	0.351726i
$583$	−7.72741	−	2.07055i	−0.320036	−	0.0857535i
$584$	15.5885	−	27.0000i	0.645055	−	1.11727i
$585$		0			0
$586$	18.0000	−	10.3923i	0.743573	−	0.429302i
$587$	7.34847	−	7.34847i	0.303304	−	0.303304i	−0.539001	−	0.842305i	$-0.681198\pi$
$587$	7.34847	−	7.34847i	0.303304	−	0.303304i	0.842305	+	0.539001i	$0.181198\pi$
$588$	−4.77886	−	11.1428i	−0.197077	−	0.459522i
$589$		−	36.0000i		−	1.48335i
$590$		0			0
$591$	30.0000	+	17.3205i	1.23404	+	0.712470i
$592$	−3.86370	+	1.03528i	−0.158797	+	0.0425496i
$593$	−6.27603	+	23.4225i	−0.257726	+	0.961845i	0.708828	+	0.705381i	$0.249224\pi$
$593$	−6.27603	+	23.4225i	−0.257726	+	0.961845i	−0.966554	+	0.256464i	$0.917443\pi$
$594$	−20.7846			−0.852803
$595$		0			0
$596$	17.0000			0.696347
$597$	6.21166	−	23.1822i	0.254226	−	0.948785i
$598$	23.4225	−	6.27603i	0.957815	−	0.256646i
$599$	6.92820	+	4.00000i	0.283079	+	0.163436i	0.634816	−	0.772663i	$-0.281076\pi$
$599$	6.92820	+	4.00000i	0.283079	+	0.163436i	−0.351738	+	0.936099i	$0.614409\pi$
$600$		0			0
$601$		−	34.6410i		−	1.41304i	−0.707695	−	0.706518i	$-0.750265\pi$
$601$		−	34.6410i		−	1.41304i	0.707695	−	0.706518i	$-0.249735\pi$
$602$	0.947343	+	13.1948i	0.0386108	+	0.537780i
$603$		0			0
$604$	5.19615	−	3.00000i	0.211428	−	0.122068i
$605$		0			0
$606$	1.50000	−	2.59808i	0.0609333	−	0.105540i
$607$	−11.7112	−	3.13801i	−0.475344	−	0.127368i	0.0131898	−	0.999913i	$-0.495801\pi$
$607$	−11.7112	−	3.13801i	−0.475344	−	0.127368i	−0.488534	+	0.872545i	$0.662468\pi$
$608$	12.2474	+	12.2474i	0.496700	+	0.496700i
$609$	0.866025	−	4.50000i	0.0350931	−	0.182349i
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$		0			0
$613$	10.8704	+	40.5689i	0.439051	+	1.63856i	0.731181	+	0.682183i	$0.238969\pi$
$613$	10.8704	+	40.5689i	0.439051	+	1.63856i	−0.292130	+	0.956379i	$0.594364\pi$
$614$	−7.79423	−	13.5000i	−0.314549	−	0.544816i
$615$		0			0
$616$	6.00000	−	31.1769i	0.241747	−	1.25615i
$617$	−28.2843	−	28.2843i	−1.13868	−	1.13868i	−0.988687	−	0.149995i	$-0.952074\pi$
$617$	−28.2843	−	28.2843i	−1.13868	−	1.13868i	−0.149995	−	0.988687i	$-0.547926\pi$
$618$	26.0800	+	6.98811i	1.04909	+	0.281103i
$619$	−6.92820	+	12.0000i	−0.278468	+	0.482321i	−0.971004	−	0.239062i	$-0.923160\pi$
$619$	−6.92820	+	12.0000i	−0.278468	+	0.482321i	0.692536	+	0.721383i	$0.256493\pi$
$620$		0			0
$621$	31.5000	−	18.1865i	1.26405	−	0.729800i
$622$	17.1464	−	17.1464i	0.687509	−	0.687509i
$623$	−2.29719	−	31.9957i	−0.0920348	−	1.28188i
$624$		−	6.00000i		−	0.240192i
$625$		0			0
$626$	24.0000	+	13.8564i	0.959233	+	0.553813i
$627$	−23.1822	+	6.21166i	−0.925809	+	0.248070i
$628$	3.58630	−	13.3843i	0.143109	−	0.534090i
$629$	13.8564			0.552491
$630$		0			0
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$	−1.55291	+	5.79555i	−0.0617716	+	0.230535i
$633$	30.1146	−	8.06918i	1.19695	−	0.320721i
$634$	29.4449	+	17.0000i	1.16940	+	0.675156i
$635$		0			0
$636$		−	3.46410i		−	0.137361i
$637$	2.86559	−	24.0788i	0.113539	−	0.954037i
$638$	2.82843	−	2.82843i	0.111979	−	0.111979i
$639$		0			0
$640$		0			0
$641$	−14.5000	+	25.1147i	−0.572716	+	0.991972i	0.423570	+	0.905863i	$0.360777\pi$
$641$	−14.5000	+	25.1147i	−0.572716	+	0.991972i	−0.996286	+	0.0861092i	$0.972557\pi$
$642$	1.67303	+	0.448288i	0.0660293	+	0.0176925i
$643$	−26.9444	−	26.9444i	−1.06258	−	1.06258i	−0.997906	−	0.0646766i	$-0.979398\pi$
$643$	−26.9444	−	26.9444i	−1.06258	−	1.06258i	−0.0646766	−	0.997906i	$-0.520602\pi$
$644$	6.06218	+	17.5000i	0.238883	+	0.689597i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	3.13801	+	11.7112i	0.123368	+	0.460416i	0.999776	−	0.0211531i	$-0.00673374\pi$
$647$	3.13801	+	11.7112i	0.123368	+	0.460416i	−0.876408	+	0.481569i	$0.840067\pi$
$648$	−6.98811	−	26.0800i	−0.274519	−	1.02452i
$649$	6.92820	+	12.0000i	0.271956	+	0.471041i
$650$		0			0
$651$	−36.0000	−	31.1769i	−1.41095	−	1.22192i
$652$	8.48528	+	8.48528i	0.332309	+	0.332309i
$653$	21.2504	+	5.69402i	0.831591	+	0.222824i	0.649408	−	0.760440i	$-0.275017\pi$
$653$	21.2504	+	5.69402i	0.831591	+	0.222824i	0.182183	+	0.983265i	$0.441684\pi$
$654$	2.59808	−	4.50000i	0.101593	−	0.175964i
$655$		0			0
$656$	−7.50000	+	4.33013i	−0.292826	+	0.169063i
$657$		0			0
$658$	7.58871	−	5.13922i	0.295839	−	0.200348i
$659$			26.0000i			1.01282i	0.862294	+	0.506408i	$0.169027\pi$
$659$			26.0000i			1.01282i	−0.862294	+	0.506408i	$0.830973\pi$
$660$		0			0
$661$	1.50000	+	0.866025i	0.0583432	+	0.0336845i	0.528888	−	0.848692i	$-0.322609\pi$
$661$	1.50000	+	0.866025i	0.0583432	+	0.0336845i	−0.470545	+	0.882376i	$0.655943\pi$
$662$	−5.79555	+	1.55291i	−0.225251	+	0.0603557i
$663$	−5.37945	+	20.0764i	−0.208921	+	0.779702i
$664$	−15.5885			−0.604949
$665$		0			0
$666$		0			0
$667$	−1.81173	+	6.76148i	−0.0701506	+	0.261806i
$668$	18.4034	−	4.93117i	0.712047	−	0.190793i
$669$	5.19615	+	3.00000i	0.200895	+	0.115987i
$670$		0			0
$671$			6.92820i			0.267460i
$672$	22.8541	−	1.64085i	0.881614	−	0.0632970i
$673$	28.2843	−	28.2843i	1.09028	−	1.09028i	0.0947803	−	0.995498i	$-0.469785\pi$
$673$	28.2843	−	28.2843i	1.09028	−	1.09028i	0.995498	−	0.0947803i	$-0.0302149\pi$
$674$	−8.66025	+	5.00000i	−0.333581	+	0.192593i
$675$		0			0
$676$	0.500000	−	0.866025i	0.0192308	−	0.0333087i
$677$	−36.8067	−	9.86233i	−1.41460	−	0.379040i	−0.531033	−	0.847351i	$-0.678196\pi$
$677$	−36.8067	−	9.86233i	−1.41460	−	0.379040i	−0.883564	+	0.468311i	$0.844863\pi$
$678$	−12.2474	−	12.2474i	−0.470360	−	0.470360i
$679$	−17.3205	+	6.00000i	−0.664700	+	0.230259i
$680$		0			0
$681$	−3.00000	−	5.19615i	−0.114960	−	0.199117i
$682$	−10.7589	−	40.1528i	−0.411980	−	1.53753i
$683$	4.39992	+	16.4207i	0.168358	+	0.628322i	0.997588	+	0.0694139i	$0.0221129\pi$
$683$	4.39992	+	16.4207i	0.168358	+	0.628322i	−0.829230	+	0.558908i	$0.811220\pi$
$684$		0			0
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	−16.9706	−	16.9706i	−0.647467	−	0.647467i
$688$	−4.82963	−	1.29410i	−0.184128	−	0.0493369i
$689$	3.46410	−	6.00000i	0.131972	−	0.228582i
$690$		0			0
$691$	24.0000	−	13.8564i	0.913003	−	0.527123i	0.0316069	−	0.999500i	$-0.489938\pi$
$691$	24.0000	−	13.8564i	0.913003	−	0.527123i	0.881396	+	0.472378i	$0.156604\pi$
$692$	−4.89898	+	4.89898i	−0.186231	+	0.186231i
$693$		0			0
$694$			19.0000i			0.721230i
$695$		0			0
$696$	4.50000	+	2.59808i	0.170572	+	0.0984798i
$697$	28.9778	−	7.76457i	1.09761	−	0.294104i
$698$	6.72432	−	25.0955i	0.254519	−	0.949878i
$699$	−3.46410			−0.131024
$700$		0			0
$701$	17.0000			0.642081			0.321041	−	0.947065i	$-0.395967\pi$
$701$	17.0000			0.642081			0.321041	+	0.947065i	$0.395967\pi$
$702$	4.65874	−	17.3867i	0.175833	−	0.656217i
$703$	−13.3843	+	3.58630i	−0.504797	+	0.135260i
$704$	24.2487	+	14.0000i	0.913908	+	0.527645i
$705$		0			0
$706$			24.2487i			0.912612i
$707$	2.56961	+	3.79435i	0.0966401	+	0.142701i
$708$	−4.24264	+	4.24264i	−0.159448	+	0.159448i
$709$	−28.5788	+	16.5000i	−1.07330	+	0.619671i	−0.929081	−	0.369875i	$-0.879400\pi$
$709$	−28.5788	+	16.5000i	−1.07330	+	0.619671i	−0.144219	+	0.989546i	$0.546067\pi$
$710$		0			0
$711$		0			0
$712$	35.1337	+	9.41404i	1.31669	+	0.352806i
$713$	51.4393	+	51.4393i	1.92642	+	1.92642i
$714$	15.5885	+	3.00000i	0.583383	+	0.112272i
$715$		0			0
$716$	−11.0000	−	19.0526i	−0.411089	−	0.712028i
$717$	−11.6555	−	43.4988i	−0.435282	−	1.62449i
$718$	0.517638	+	1.93185i	0.0193181	+	0.0720961i
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	0.604554	−	0.796564i	$-0.293351\pi$
$719$	−10.3923	−	18.0000i	−0.387568	−	0.671287i	−0.992122	+	0.125277i	$0.960018\pi$
$720$		0			0
$721$	−27.0000	+	31.1769i	−1.00553	+	1.16109i
$722$	4.94975	+	4.94975i	0.184211	+	0.184211i
$723$	11.5911	+	3.10583i	0.431078	+	0.115507i
$724$	−4.33013	+	7.50000i	−0.160928	+	0.278735i
$725$		0			0
$726$	−7.50000	+	4.33013i	−0.278351	+	0.160706i
$727$	1.22474	−	1.22474i	0.0454233	−	0.0454233i	−0.684030	−	0.729454i	$-0.739774\pi$
$727$	1.22474	−	1.22474i	0.0454233	−	0.0454233i	0.729454	+	0.684030i	$0.239774\pi$
$728$	24.7351	+	12.0072i	0.916745	+	0.445017i
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	15.0000	+	8.66025i	0.554795	+	0.320311i
$732$	−2.89778	+	0.776457i	−0.107105	+	0.0286987i
$733$	7.17260	−	26.7685i	0.264926	−	0.988718i	−0.697369	−	0.716712i	$-0.745646\pi$
$733$	7.17260	−	26.7685i	0.264926	−	0.988718i	0.962296	−	0.272006i	$-0.0876871\pi$
$734$	5.19615			0.191793
$735$		0			0
$736$	−35.0000			−1.29012
$737$	−9.31749	+	34.7733i	−0.343214	+	1.28089i
$738$		0			0
$739$	−27.7128	−	16.0000i	−1.01943	−	0.588570i	−0.105493	−	0.994420i	$-0.533642\pi$
$739$	−27.7128	−	16.0000i	−1.01943	−	0.588570i	−0.913939	+	0.405851i	$0.866975\pi$
$740$		0			0
$741$		−	20.7846i		−	0.763542i
$742$	−4.76028	−	2.31079i	−0.174755	−	0.0848317i
$743$	−3.53553	+	3.53553i	−0.129706	+	0.129706i	−0.768980	−	0.639273i	$-0.779235\pi$
$743$	−3.53553	+	3.53553i	−0.129706	+	0.129706i	0.639273	+	0.768980i	$0.279235\pi$
$744$	46.7654	−	27.0000i	1.71450	−	0.989868i
$745$		0			0
$746$	−6.00000	+	10.3923i	−0.219676	+	0.380489i
$747$		0			0
$748$	−9.79796	−	9.79796i	−0.358249	−	0.358249i
$749$	−1.73205	+	2.00000i	−0.0632878	+	0.0730784i
$750$		0			0
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	0.559640	−	0.828736i	$-0.310939\pi$
$751$	−12.0000	−	20.7846i	−0.437886	−	0.758441i	−0.997526	+	0.0702946i	$0.977606\pi$
$752$	0.896575	+	3.34607i	0.0326947	+	0.122018i
$753$	−7.76457	−	28.9778i	−0.282957	−	1.05601i
$754$	1.73205	+	3.00000i	0.0630776	+	0.109254i
$755$		0			0
$756$	13.5000	+	2.59808i	0.490990	+	0.0944911i
$757$	7.07107	+	7.07107i	0.257002	+	0.257002i	0.823834	−	0.566831i	$-0.191831\pi$
$757$	7.07107	+	7.07107i	0.257002	+	0.257002i	−0.566831	+	0.823834i	$0.691831\pi$
$758$	−5.79555	−	1.55291i	−0.210504	−	0.0564044i
$759$	24.2487	−	42.0000i	0.880172	−	1.52450i
$760$		0			0
$761$	−6.00000	+	3.46410i	−0.217500	+	0.125574i	−0.604792	−	0.796383i	$-0.706744\pi$
$761$	−6.00000	+	3.46410i	−0.217500	+	0.125574i	0.387292	+	0.921957i	$0.373410\pi$
$762$		0			0
$763$	4.45069	+	6.57201i	0.161126	+	0.237923i
$764$		−	4.00000i		−	0.144715i
$765$		0			0
$766$	16.5000	+	9.52628i	0.596169	+	0.344198i
$767$	−11.5911	+	3.10583i	−0.418531	+	0.112145i
$768$	−7.62089	+	28.4416i	−0.274995	+	1.02630i
$769$	−34.6410			−1.24919			−0.624593	−	0.780950i	$-0.714735\pi$
$769$	−34.6410			−1.24919			−0.624593	+	0.780950i	$0.714735\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$	2.07055	−	7.72741i	0.0745208	−	0.278115i
$773$	−43.4988	+	11.6555i	−1.56454	+	0.419219i	−0.934099	−	0.357015i	$-0.883795\pi$
$773$	−43.4988	+	11.6555i	−1.56454	+	0.419219i	−0.630446	+	0.776233i	$0.717128\pi$
$774$		0			0
$775$		0			0
$776$		−	20.7846i		−	0.746124i
$777$	−8.00481	+	16.4901i	−0.287171	+	0.591579i
$778$	1.41421	−	1.41421i	0.0507020	−	0.0507020i
$779$	−25.9808	+	15.0000i	−0.930857	+	0.537431i
$780$		0			0
$781$	−4.00000	+	6.92820i	−0.143131	+	0.247911i
$782$	−23.4225	−	6.27603i	−0.837585	−	0.224430i
$783$	3.67423	+	3.67423i	0.131306	+	0.131306i
$784$	2.59808	−	6.50000i	0.0927884	−	0.232143i
$785$		0			0
$786$	6.00000	+	10.3923i	0.214013	+	0.370681i
$787$	7.62089	+	28.4416i	0.271655	+	1.01383i	0.958050	+	0.286602i	$0.0925258\pi$
$787$	7.62089	+	28.4416i	0.271655	+	1.01383i	−0.686394	+	0.727230i	$0.740808\pi$
$788$	−5.17638	−	19.3185i	−0.184401	−	0.688194i
$789$	11.2583	+	19.5000i	0.400807	+	0.694218i
$790$		0			0
$791$	25.0000	−	8.66025i	0.888898	−	0.307923i
$792$		0			0
$793$	−5.79555	−	1.55291i	−0.205806	−	0.0551456i
$794$	−6.92820	+	12.0000i	−0.245873	+	0.425864i
$795$		0			0
$796$	−12.0000	+	6.92820i	−0.425329	+	0.245564i
$797$	−29.3939	+	29.3939i	−1.04118	+	1.04118i	−0.0420699	+	0.999115i	$0.513395\pi$
$797$	−29.3939	+	29.3939i	−1.04118	+	1.04118i	−0.999115	+	0.0420699i	$0.986605\pi$
$798$	−15.8338	+	1.13681i	−0.560509	+	0.0402427i
$799$		−	12.0000i		−	0.424529i
$800$		0			0
$801$		0			0
$802$	18.3526	−	4.91756i	0.648053	−	0.173645i
$803$	10.7589	−	40.1528i	0.379674	−	1.41696i
$804$	−15.5885			−0.549762
$805$		0			0
$806$	36.0000			1.26805
$807$	10.0939	−	37.6711i	0.355324	−	1.32609i
$808$	−5.01910	+	1.34486i	−0.176571	+	0.0473121i
$809$	−14.7224	−	8.50000i	−0.517613	−	0.298844i	0.218344	−	0.975872i	$-0.429934\pi$
$809$	−14.7224	−	8.50000i	−0.517613	−	0.298844i	−0.735958	+	0.677028i	$0.763268\pi$
$810$		0			0
$811$		−	17.3205i		−	0.608205i	−0.952639	−	0.304103i	$-0.901643\pi$
$811$		−	17.3205i		−	0.608205i	0.952639	−	0.304103i	$-0.0983566\pi$
$812$	−2.19067	+	1.48356i	−0.0768775	+	0.0520629i
$813$	−12.7279	+	12.7279i	−0.446388	+	0.446388i
$814$	−13.8564	+	8.00000i	−0.485667	+	0.280400i
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−16.7303	−	4.48288i	−0.585320	−	0.156836i
$818$	8.57321	+	8.57321i	0.299755	+	0.299755i
$819$		0			0
$820$		0			0
$821$	13.0000	+	22.5167i	0.453703	+	0.785837i	0.998613	−	0.0526580i	$-0.0167693\pi$
$821$	13.0000	+	22.5167i	0.453703	+	0.785837i	−0.544909	+	0.838495i	$0.683436\pi$
$822$	7.17260	+	26.7685i	0.250173	+	0.933659i
$823$	6.98811	+	26.0800i	0.243590	+	0.909092i	0.974087	+	0.226175i	$0.0726221\pi$
$823$	6.98811	+	26.0800i	0.243590	+	0.909092i	−0.730496	+	0.682917i	$0.760711\pi$
$824$	−23.3827	−	40.5000i	−0.814574	−	1.41088i
$825$		0			0
$826$	3.00000	+	8.66025i	0.104383	+	0.301329i
$827$	24.7487	+	24.7487i	0.860598	+	0.860598i	0.991408	−	0.130810i	$-0.0417577\pi$
$827$	24.7487	+	24.7487i	0.860598	+	0.860598i	−0.130810	+	0.991408i	$0.541758\pi$
$828$		0			0
$829$	10.3923	−	18.0000i	0.360940	−	0.625166i	−0.627176	−	0.778878i	$-0.715789\pi$
$829$	10.3923	−	18.0000i	0.360940	−	0.625166i	0.988116	+	0.153712i	$0.0491227\pi$
$830$		0			0
$831$	9.00000	−	5.19615i	0.312207	−	0.180253i
$832$	−17.1464	+	17.1464i	−0.594445	+	0.594445i
$833$	−14.5211	+	19.4201i	−0.503125	+	0.672865i
$834$		0			0
$835$		0			0
$836$	12.0000	+	6.92820i	0.415029	+	0.239617i
$837$	52.1600	−	13.9762i	1.80291	−	0.483089i
$838$	−8.96575	+	33.4607i	−0.309717	+	1.15588i
$839$	34.6410			1.19594			0.597970	−	0.801518i	$-0.295974\pi$
$839$	34.6410			1.19594			0.597970	+	0.801518i	$0.295974\pi$
$840$		0			0
$841$	28.0000			0.965517
$842$	−1.81173	+	6.76148i	−0.0624365	+	0.233016i
$843$	−36.8067	+	9.86233i	−1.26769	+	0.339677i
$844$	−15.5885	−	9.00000i	−0.536577	−	0.309793i
$845$		0			0
$846$		0			0
$847$	−0.947343	−	13.1948i	−0.0325511	−	0.453378i
$848$	1.41421	−	1.41421i	0.0485643	−	0.0485643i
$849$	15.5885	−	9.00000i	0.534994	−	0.308879i
$850$		0			0
$851$	14.0000	−	24.2487i	0.479914	−	0.831235i
$852$	−3.34607	−	0.896575i	−0.114634	−	0.0307162i
$853$	−26.9444	−	26.9444i	−0.922558	−	0.922558i	0.0746514	−	0.997210i	$-0.476216\pi$
$853$	−26.9444	−	26.9444i	−0.922558	−	0.922558i	−0.997210	+	0.0746514i	$0.976216\pi$
$854$	−0.866025	+	4.50000i	−0.0296348	+	0.153987i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	5.37945	+	20.0764i	0.183759	+	0.685796i	0.994893	+	0.100936i	$0.0321839\pi$
$857$	5.37945	+	20.0764i	0.183759	+	0.685796i	−0.811134	+	0.584860i	$0.801149\pi$
$858$	−6.21166	−	23.1822i	−0.212062	−	0.791428i
$859$	24.2487	+	42.0000i	0.827355	+	1.43302i	0.900106	+	0.435671i	$0.143489\pi$
$859$	24.2487	+	42.0000i	0.827355	+	1.43302i	−0.0727505	+	0.997350i	$0.523178\pi$
$860$		0			0
$861$	−7.50000	+	38.9711i	−0.255599	+	1.32813i
$862$	11.3137	+	11.3137i	0.385346	+	0.385346i
$863$	−12.5570	−	3.36465i	−0.427446	−	0.114534i	0.0386808	−	0.999252i	$-0.487684\pi$
$863$	−12.5570	−	3.36465i	−0.427446	−	0.114534i	−0.466127	+	0.884718i	$0.654351\pi$
$864$	−12.9904	+	22.5000i	−0.441942	+	0.765466i
$865$		0			0
$866$	−27.0000	+	15.5885i	−0.917497	+	0.529717i
$867$	−6.12372	+	6.12372i	−0.207973	+	0.207973i
$868$	1.96902	+	27.4249i	0.0668328	+	0.930860i
$869$			8.00000i			0.271381i
$870$		0			0
$871$	−27.0000	−	15.5885i	−0.914860	−	0.528195i
$872$	−8.69333	+	2.32937i	−0.294393	+	0.0788825i
$873$		0			0
$874$	24.2487			0.820225
$875$		0			0
$876$	18.0000			0.608164
$877$	13.9762	−	52.1600i	0.471944	−	1.76132i	−0.160831	−	0.986982i	$-0.551417\pi$
$877$	13.9762	−	52.1600i	0.471944	−	1.76132i	0.632775	−	0.774336i	$-0.281916\pi$
$878$	20.0764	−	5.37945i	0.677545	−	0.181548i
$879$	31.1769	+	18.0000i	1.05157	+	0.607125i
$880$		0			0
$881$		−	8.66025i		−	0.291771i	−0.989301	−	0.145886i	$-0.953397\pi$
$881$		−	8.66025i		−	0.291771i	0.989301	−	0.145886i	$-0.0466032\pi$
$882$		0			0
$883$	−14.1421	+	14.1421i	−0.475921	+	0.475921i	−0.903824	−	0.427904i	$-0.859252\pi$
$883$	−14.1421	+	14.1421i	−0.475921	+	0.475921i	0.427904	+	0.903824i	$0.359252\pi$
$884$	10.3923	−	6.00000i	0.349531	−	0.201802i
$885$		0			0
$886$	6.50000	−	11.2583i	0.218372	−	0.378231i
$887$	21.7494	+	5.82774i	0.730274	+	0.195676i	0.604751	−	0.796414i	$-0.293272\pi$
$887$	21.7494	+	5.82774i	0.730274	+	0.195676i	0.125523	+	0.992091i	$0.459939\pi$
$888$	−14.6969	−	14.6969i	−0.493197	−	0.493197i
$889$		0			0
$890$		0			0
$891$	−18.0000	−	31.1769i	−0.603023	−	1.04447i
$892$	−0.896575	−	3.34607i	−0.0300196	−	0.112035i
$893$	3.10583	+	11.5911i	0.103933	+	0.387882i
$894$	−14.7224	−	25.5000i	−0.492392	−	0.852848i
$895$		0			0
$896$	−6.00000	−	5.19615i	−0.200446	−	0.173591i
$897$	29.6985	+	29.6985i	0.991604	+	0.991604i
$898$	−29.9437	−	8.02339i	−0.999234	−	0.267744i
$899$	−5.19615	+	9.00000i	−0.173301	+	0.300167i
$900$		0			0
$901$	−6.00000	+	3.46410i	−0.199889	+	0.115406i
$902$	−24.4949	+	24.4949i	−0.815591	+	0.815591i
$903$	−18.9718	+	12.8480i	−0.631341	+	0.427556i
$904$			30.0000i			0.997785i
$905$		0			0
$906$	−9.00000	−	5.19615i	−0.299005	−	0.172631i
$907$	−39.6030	+	10.6116i	−1.31499	+	0.352352i	−0.847100	−	0.531433i	$-0.821654\pi$
$907$	−39.6030	+	10.6116i	−1.31499	+	0.352352i	−0.467894	+	0.883784i	$0.654987\pi$
$908$	−0.896575	+	3.34607i	−0.0297539	+	0.111043i
$909$		0			0
$910$		0			0
$911$	−28.0000			−0.927681			−0.463841	−	0.885919i	$-0.653529\pi$
$911$	−28.0000			−0.927681			−0.463841	+	0.885919i	$0.653529\pi$
$912$	1.55291	−	5.79555i	0.0514221	−	0.191910i
$913$	−20.0764	+	5.37945i	−0.664432	+	0.178034i
$914$	−13.8564	−	8.00000i	−0.458329	−	0.264616i
$915$		0			0
$916$			13.8564i			0.457829i
$917$	−18.2832	+	1.31268i	−0.603766	+	0.0433484i
$918$	−12.7279	+	12.7279i	−0.420084	+	0.420084i
$919$	−15.5885	+	9.00000i	−0.514216	+	0.296883i	−0.734565	−	0.678538i	$-0.762614\pi$
$919$	−15.5885	+	9.00000i	−0.514216	+	0.296883i	0.220349	+	0.975421i	$0.429280\pi$
$920$		0			0
$921$	13.5000	−	23.3827i	0.444840	−	0.770486i
$922$	33.4607	+	8.96575i	1.10197	+	0.295271i
$923$	−4.89898	−	4.89898i	−0.161252	−	0.161252i
$924$	17.3205	−	6.00000i	0.569803	−	0.197386i
$925$		0			0
$926$	−7.50000	−	12.9904i	−0.246465	−	0.426890i
$927$		0			0
$928$	−1.29410	−	4.82963i	−0.0424808	−	0.158540i
$929$	11.2583	+	19.5000i	0.369374	+	0.639774i	0.989468	−	0.144753i	$-0.0462389\pi$
$929$	11.2583	+	19.5000i	0.369374	+	0.639774i	−0.620094	+	0.784528i	$0.712906\pi$
$930$		0			0
$931$	9.00000	−	22.5167i	0.294963	−	0.737954i
$932$	1.41421	+	1.41421i	0.0463241	+	0.0463241i
$933$	40.5689	+	10.8704i	1.32817	+	0.355881i
$934$	−2.59808	+	4.50000i	−0.0850117	+	0.147244i
$935$		0			0
$936$		0			0
$937$	19.5959	−	19.5959i	0.640171	−	0.640171i	−0.310427	−	0.950597i	$-0.600472\pi$
$937$	19.5959	−	19.5959i	0.640171	−	0.640171i	0.950597	+	0.310427i	$0.100472\pi$
$938$	−10.3986	+	21.4213i	−0.339525	+	0.699429i
$939$			48.0000i			1.56642i
$940$		0			0
$941$	−36.0000	−	20.7846i	−1.17357	−	0.677559i	−0.219049	−	0.975714i	$-0.570295\pi$
$941$	−36.0000	−	20.7846i	−1.17357	−	0.677559i	−0.954517	+	0.298155i	$0.903629\pi$
$942$	−23.1822	+	6.21166i	−0.755318	+	0.202387i
$943$	15.6901	−	58.5561i	0.510939	−	1.90685i
$944$	−3.46410			−0.112747
$945$		0			0
$946$	−20.0000			−0.650256
$947$	−2.84701	+	10.6252i	−0.0925154	+	0.345272i	−0.996631	−	0.0820157i	$-0.973864\pi$
$947$	−2.84701	+	10.6252i	−0.0925154	+	0.345272i	0.904116	+	0.427288i	$0.140531\pi$
$948$	−3.34607	+	0.896575i	−0.108675	+	0.0291194i
$949$	31.1769	+	18.0000i	1.01205	+	0.584305i
$950$		0			0
$951$			58.8897i			1.90963i
$952$	−15.4176	−	22.7661i	−0.499689	−	0.737854i
$953$	28.2843	−	28.2843i	0.916217	−	0.916217i	−0.0805344	−	0.996752i	$-0.525663\pi$
$953$	28.2843	−	28.2843i	0.916217	−	0.916217i	0.996752	+	0.0805344i	$0.0256627\pi$
$954$		0			0
$955$		0			0
$956$	−13.0000	+	22.5167i	−0.420450	+	0.728241i
$957$	6.69213	+	1.79315i	0.216326	+	0.0579643i
$958$	26.9444	+	26.9444i	0.870534	+	0.870534i
$959$	−41.5692	−	8.00000i	−1.34234	−	0.258333i
$960$		0			0
$961$	38.5000	+	66.6840i	1.24194	+	2.15110i
$962$	−3.58630	−	13.3843i	−0.115627	−	0.431526i
$963$		0			0
$964$	−3.46410	−	6.00000i	−0.111571	−	0.193247i
$965$		0			0
$966$	21.0000	−	24.2487i	0.675664	−	0.780189i
$967$	10.6066	+	10.6066i	0.341085	+	0.341085i	0.856775	−	0.515690i	$-0.172464\pi$
$967$	10.6066	+	10.6066i	0.341085	+	0.341085i	−0.515690	+	0.856775i	$0.672464\pi$
$968$	14.4889	+	3.88229i	0.465690	+	0.124781i
$969$	−10.3923	+	18.0000i	−0.333849	+	0.578243i
$970$		0			0
$971$	24.0000	−	13.8564i	0.770197	−	0.444673i	−0.0627481	−	0.998029i	$-0.519986\pi$
$971$	24.0000	−	13.8564i	0.770197	−	0.444673i	0.832945	+	0.553356i	$0.186653\pi$
$972$		0			0
$973$		0			0
$974$			4.00000i			0.128168i
$975$		0			0
$976$	−1.50000	−	0.866025i	−0.0480138	−	0.0277208i
$977$	3.86370	−	1.03528i	0.123611	−	0.0331214i	−0.196483	−	0.980507i	$-0.562952\pi$
$977$	3.86370	−	1.03528i	0.123611	−	0.0331214i	0.320094	+	0.947386i	$0.396285\pi$
$978$	5.37945	−	20.0764i	0.172016	−	0.641972i
$979$	48.4974			1.54998
$980$		0			0
$981$		0			0
$982$	−0.517638	+	1.93185i	−0.0165185	+	0.0616479i
$983$	−18.4034	+	4.93117i	−0.586976	+	0.157280i	−0.540071	−	0.841620i	$-0.681603\pi$
$983$	−18.4034	+	4.93117i	−0.586976	+	0.157280i	−0.0469052	+	0.998899i	$0.514936\pi$
$984$	−38.9711	−	22.5000i	−1.24235	−	0.717274i
$985$		0			0
$986$		−	3.46410i		−	0.110319i
$987$	14.2808	+	6.93237i	0.454564	+	0.220660i
$988$	−8.48528	+	8.48528i	−0.269953	+	0.269953i
$989$	30.3109	−	17.5000i	0.963830	−	0.556468i
$990$		0			0
$991$	3.00000	−	5.19615i	0.0952981	−	0.165061i	−0.814435	−	0.580255i	$-0.802953\pi$
$991$	3.00000	−	5.19615i	0.0952981	−	0.165061i	0.909733	+	0.415194i	$0.136286\pi$
$992$	−50.1910	−	13.4486i	−1.59357	−	0.426994i
$993$	−7.34847	−	7.34847i	−0.233197	−	0.233197i
$994$	−3.46410	+	4.00000i	−0.109875	+	0.126872i
$995$		0			0
$996$	−4.50000	−	7.79423i	−0.142588	−	0.246970i
$997$	9.86233	+	36.8067i	0.312343	+	1.16568i	0.926438	+	0.376448i	$0.122855\pi$
$997$	9.86233	+	36.8067i	0.312343	+	1.16568i	−0.614095	+	0.789232i	$0.710479\pi$
$998$	3.10583	+	11.5911i	0.0983133	+	0.366910i
$999$	−10.3923	−	18.0000i	−0.328798	−	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.o.c.157.1	yes	8
5.2	odd	4	inner	175.2.o.c.143.1	yes	8
5.3	odd	4	inner	175.2.o.c.143.2	yes	8
5.4	even	2	inner	175.2.o.c.157.2	yes	8
7.5	odd	6	inner	175.2.o.c.82.2	yes	8
35.12	even	12	inner	175.2.o.c.68.2	yes	8
35.19	odd	6	inner	175.2.o.c.82.1	yes	8
35.33	even	12	inner	175.2.o.c.68.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.o.c.68.1	✓	8	35.33	even	12	inner
175.2.o.c.68.2	yes	8	35.12	even	12	inner
175.2.o.c.82.1	yes	8	35.19	odd	6	inner
175.2.o.c.82.2	yes	8	7.5	odd	6	inner
175.2.o.c.143.1	yes	8	5.2	odd	4	inner
175.2.o.c.143.2	yes	8	5.3	odd	4	inner
175.2.o.c.157.1	yes	8	1.1	even	1	trivial
175.2.o.c.157.2	yes	8	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(0.866025 + 0.500000i) q^{4} -1.73205i q^{6} +(2.38014 + 1.15539i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(-2.00000 + 3.46410i) q^{11} +(-1.67303 - 0.448288i) q^{12} +(-2.44949 - 2.44949i) q^{13} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.896575 + 3.34607i) q^{17} +(-1.73205 - 3.00000i) q^{19} +(-4.50000 - 0.866025i) q^{21} +(-2.82843 - 2.82843i) q^{22} +(6.76148 + 1.81173i) q^{23} +(2.59808 - 4.50000i) q^{24} +(3.00000 - 1.73205i) q^{26} +(3.67423 - 3.67423i) q^{27} +(1.48356 + 2.19067i) q^{28} +1.00000i q^{29} +(9.00000 + 5.19615i) q^{31} +(-4.82963 + 1.29410i) q^{32} +(1.79315 - 6.69213i) q^{33} -3.46410 q^{34} +(1.03528 - 3.86370i) q^{37} +(3.34607 - 0.896575i) q^{38} +(5.19615 + 3.00000i) q^{39} -8.66025i q^{41} +(2.00120 - 4.12252i) q^{42} +(3.53553 - 3.53553i) q^{43} +(-3.46410 + 2.00000i) q^{44} +(-3.50000 + 6.06218i) q^{46} +(-3.34607 - 0.896575i) q^{47} +(1.22474 + 1.22474i) q^{48} +(4.33013 + 5.50000i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(-0.896575 - 3.34607i) q^{52} +(0.517638 + 1.93185i) q^{53} +(2.59808 + 4.50000i) q^{54} +(-7.50000 + 2.59808i) q^{56} +(4.24264 + 4.24264i) q^{57} +(-0.965926 - 0.258819i) q^{58} +(1.73205 - 3.00000i) q^{59} +(1.50000 - 0.866025i) q^{61} +(-7.34847 + 7.34847i) q^{62} -7.00000i q^{64} +(6.00000 + 3.46410i) q^{66} +(8.69333 - 2.32937i) q^{67} +(-0.896575 + 3.34607i) q^{68} -12.1244 q^{69} +2.00000 q^{71} +(-10.0382 + 2.68973i) q^{73} +(3.46410 + 2.00000i) q^{74} -3.46410i q^{76} +(-8.76268 + 5.93426i) q^{77} +(-4.24264 + 4.24264i) q^{78} +(1.73205 - 1.00000i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(8.36516 + 2.24144i) q^{82} +(3.67423 + 3.67423i) q^{83} +(-3.46410 - 3.00000i) q^{84} +(2.50000 + 4.33013i) q^{86} +(-0.448288 - 1.67303i) q^{87} +(-3.10583 - 11.5911i) q^{88} +(-6.06218 - 10.5000i) q^{89} +(-3.00000 - 8.66025i) q^{91} +(4.94975 + 4.94975i) q^{92} +(-17.3867 - 4.65874i) q^{93} +(1.73205 - 3.00000i) q^{94} +(7.50000 - 4.33013i) q^{96} +(-4.89898 + 4.89898i) q^{97} +(-6.43331 + 2.75908i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{11} - 4 q^{16} - 36 q^{21} + 24 q^{26} + 72 q^{31} - 28 q^{46} - 24 q^{51} - 60 q^{56} + 12 q^{61} + 48 q^{66} + 16 q^{71} - 36 q^{81} + 20 q^{86} - 24 q^{91} + 60 q^{96}+O(q^{100}) \) 8 * q - 16 * q^11 - 4 * q^16 - 36 * q^21 + 24 * q^26 + 72 * q^31 - 28 * q^46 - 24 * q^51 - 60 * q^56 + 12 * q^61 + 48 * q^66 + 16 * q^71 - 36 * q^81 + 20 * q^86 - 24 * q^91 + 60 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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