LMFDB - Embedded newform 3900.2.bw.e.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3900,2,Mod(49,3900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))

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

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

chi := DirichletCharacter("3900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.bw (of order $6$, degree $2$, not 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:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 156)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3900.49
Dual form			3900.2.bw.e.2149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 3.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 3.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-2.59808 - 1.50000i) q^{17} +(3.00000 + 1.73205i) q^{19} +3.46410i q^{21} +(-5.19615 + 3.00000i) q^{23} -1.00000i q^{27} +(4.50000 + 7.79423i) q^{29} +(1.73205 - 3.00000i) q^{33} +(-2.59808 - 4.50000i) q^{37} +(3.50000 + 0.866025i) q^{39} +(-7.50000 + 4.33013i) q^{41} +(1.73205 + 1.00000i) q^{43} -3.46410 q^{47} +(-2.50000 - 4.33013i) q^{49} -3.00000 q^{51} +9.00000i q^{53} +3.46410 q^{57} +(-12.0000 - 6.92820i) q^{59} +(5.50000 - 9.52628i) q^{61} +(1.73205 + 3.00000i) q^{63} +(5.19615 + 9.00000i) q^{67} +(-3.00000 + 5.19615i) q^{69} +(9.00000 + 5.19615i) q^{71} +5.19615 q^{73} +12.0000i q^{77} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -3.46410 q^{83} +(7.79423 + 4.50000i) q^{87} +(6.00000 - 3.46410i) q^{89} +(-12.0000 + 3.46410i) q^{91} +(-3.46410 + 6.00000i) q^{97} -3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^9	$ 4 q + 2 q^{9} + 12 q^{11} + 12 q^{19} + 18 q^{29} + 14 q^{39} - 30 q^{41} - 10 q^{49} - 12 q^{51} - 48 q^{59} + 22 q^{61} - 12 q^{69} + 36 q^{71} + 32 q^{79} - 2 q^{81} + 24 q^{89} - 48 q^{91}+O(q^{100}) $ 4 * q + 2 * q^9 + 12 * q^11 + 12 * q^19 + 18 * q^29 + 14 * q^39 - 30 * q^41 - 10 * q^49 - 12 * q^51 - 48 * q^59 + 22 * q^61 - 12 * q^69 + 36 * q^71 + 32 * q^79 - 2 * q^81 + 24 * q^89 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$-1$

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			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	0.327327	+	0.944911i	$0.393852\pi$
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	−0.981981	+	0.188982i	$0.939481\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.0258656	−	0.999665i	$-0.491766\pi$
$11$	3.00000	−	1.73205i	0.904534	−	0.522233i	0.878668	+	0.477432i	$0.158432\pi$
$12$		0			0
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	0.150675	−	0.988583i	$-0.451855\pi$
$17$	−2.59808	−	1.50000i	−0.630126	−	0.363803i	−0.780801	+	0.624780i	$0.785189\pi$
$18$		0			0
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	3.00000	+	1.73205i	0.688247	+	0.397360i	−0.114708	+	0.993399i	$0.536593\pi$
$20$		0			0
$21$			3.46410i			0.755929i
$22$		0			0
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	0.893517	+	0.449029i	$0.148230\pi$
$29$	4.50000	+	7.79423i	0.835629	+	1.44735i	−0.0578882	+	0.998323i	$0.518437\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$		0			0
$33$	1.73205	−	3.00000i	0.301511	−	0.522233i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.59808	−	4.50000i	−0.427121	−	0.739795i	0.569495	−	0.821995i	$-0.307139\pi$
$37$	−2.59808	−	4.50000i	−0.427121	−	0.739795i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$		0			0
$39$	3.50000	+	0.866025i	0.560449	+	0.138675i
$40$		0			0
$41$	−7.50000	+	4.33013i	−1.17130	+	0.676252i	−0.953987	−	0.299849i	$-0.903064\pi$
$41$	−7.50000	+	4.33013i	−1.17130	+	0.676252i	−0.217317	+	0.976101i	$0.569730\pi$
$42$		0			0
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.46410			−0.505291			−0.252646	−	0.967559i	$-0.581301\pi$
$47$	−3.46410			−0.505291			−0.252646	+	0.967559i	$0.581301\pi$
$48$		0			0
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$		0			0
$51$	−3.00000			−0.420084
$52$		0			0
$53$			9.00000i			1.23625i	0.786082	+	0.618123i	$0.212106\pi$
$53$			9.00000i			1.23625i	−0.786082	+	0.618123i	$0.787894\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.46410			0.458831
$58$		0			0
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.997027	−	0.0770484i	$-0.975450\pi$
$59$	−12.0000	−	6.92820i	−1.56227	−	0.901975i	−0.565240	−	0.824927i	$-0.691216\pi$
$60$		0			0
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	−0.262776	−	0.964857i	$-0.584638\pi$
$61$	5.50000	−	9.52628i	0.704203	−	1.21972i	0.966978	−	0.254858i	$-0.0820288\pi$
$62$		0			0
$63$	1.73205	+	3.00000i	0.218218	+	0.377964i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.19615	+	9.00000i	0.634811	+	1.09952i	0.986555	+	0.163429i	$0.0522554\pi$
$67$	5.19615	+	9.00000i	0.634811	+	1.09952i	−0.351744	+	0.936096i	$0.614411\pi$
$68$		0			0
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$		0			0
$71$	9.00000	+	5.19615i	1.06810	+	0.616670i	0.927663	−	0.373419i	$-0.121815\pi$
$71$	9.00000	+	5.19615i	1.06810	+	0.616670i	0.140441	+	0.990089i	$0.455148\pi$
$72$		0			0
$73$	5.19615			0.608164			0.304082	−	0.952646i	$-0.401650\pi$
$73$	5.19615			0.608164			0.304082	+	0.952646i	$0.401650\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			12.0000i			1.36753i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−3.46410			−0.380235			−0.190117	−	0.981761i	$-0.560887\pi$
$83$	−3.46410			−0.380235			−0.190117	+	0.981761i	$0.560887\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	7.79423	+	4.50000i	0.835629	+	0.482451i
$88$		0			0
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$		0			0
$91$	−12.0000	+	3.46410i	−1.25794	+	0.363137i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.46410	+	6.00000i	−0.351726	+	0.609208i	−0.986552	−	0.163448i	$-0.947739\pi$
$97$	−3.46410	+	6.00000i	−0.351726	+	0.609208i	0.634826	+	0.772655i	$0.281072\pi$
$98$		0			0
$99$		−	3.46410i		−	0.348155i
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$		−	14.0000i		−	1.37946i	−0.724066	−	0.689730i	$-0.757729\pi$
$103$		−	14.0000i		−	1.37946i	0.724066	−	0.689730i	$-0.242271\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.5885	+	9.00000i	−1.50699	+	0.870063i	−0.507026	+	0.861931i	$0.669255\pi$
$107$	−15.5885	+	9.00000i	−1.50699	+	0.870063i	−0.999967	+	0.00813215i	$0.997411\pi$
$108$		0			0
$109$			13.8564i			1.32720i	0.748086	+	0.663602i	$0.230973\pi$
$109$			13.8564i			1.32720i	−0.748086	+	0.663602i	$0.769027\pi$
$110$		0			0
$111$	−4.50000	−	2.59808i	−0.427121	−	0.246598i
$112$		0			0
$113$	2.59808	+	1.50000i	0.244406	+	0.141108i	0.617200	−	0.786806i	$-0.288267\pi$
$113$	2.59808	+	1.50000i	0.244406	+	0.141108i	−0.372794	+	0.927914i	$0.621600\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$		0			0
$119$	9.00000	−	5.19615i	0.825029	−	0.476331i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	−4.33013	+	7.50000i	−0.390434	+	0.676252i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	13.8564	−	8.00000i	1.22956	−	0.709885i	0.262620	−	0.964899i	$-0.415413\pi$
$127$	13.8564	−	8.00000i	1.22956	−	0.709885i	0.966937	+	0.255014i	$0.0820801\pi$
$128$		0			0
$129$	2.00000			0.176090
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	−10.3923	+	6.00000i	−0.901127	+	0.520266i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.79423	+	13.5000i	−0.665906	+	1.15338i	0.313133	+	0.949709i	$0.398621\pi$
$137$	−7.79423	+	13.5000i	−0.665906	+	1.15338i	−0.979039	+	0.203674i	$0.934712\pi$
$138$		0			0
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		0			0
$141$	−3.00000	+	1.73205i	−0.252646	+	0.145865i
$142$		0			0
$143$	12.1244	+	3.00000i	1.01389	+	0.250873i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.33013	−	2.50000i	−0.357143	−	0.206197i
$148$		0			0
$149$	7.50000	+	4.33013i	0.614424	+	0.354738i	0.774695	−	0.632335i	$-0.217903\pi$
$149$	7.50000	+	4.33013i	0.614424	+	0.354738i	−0.160271	+	0.987073i	$0.551237\pi$
$150$		0			0
$151$			17.3205i			1.40952i	0.709444	+	0.704761i	$0.248946\pi$
$151$			17.3205i			1.40952i	−0.709444	+	0.704761i	$0.751054\pi$
$152$		0			0
$153$	−2.59808	+	1.50000i	−0.210042	+	0.121268i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			23.0000i			1.83560i	0.397043	+	0.917800i	$0.370036\pi$
$157$			23.0000i			1.83560i	−0.397043	+	0.917800i	$0.629964\pi$
$158$		0			0
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$		−	20.7846i		−	1.63806i
$162$		0			0
$163$	−6.92820	+	12.0000i	−0.542659	+	0.939913i	0.456091	+	0.889933i	$0.349249\pi$
$163$	−6.92820	+	12.0000i	−0.542659	+	0.939913i	−0.998750	+	0.0499796i	$0.984084\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.46410	+	6.00000i	0.268060	+	0.464294i	0.968361	−	0.249554i	$-0.0802840\pi$
$167$	3.46410	+	6.00000i	0.268060	+	0.464294i	−0.700301	+	0.713848i	$0.746951\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$	3.00000	−	1.73205i	0.229416	−	0.132453i
$172$		0			0
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.957205	−	0.289412i	$-0.0934598\pi$
$173$	15.5885	+	9.00000i	1.18517	+	0.684257i	0.227964	+	0.973670i	$0.426793\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−13.8564			−1.04151
$178$		0			0
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	0.977138	+	0.212607i	$0.0681952\pi$
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	−0.304446	+	0.952529i	$0.598471\pi$
$180$		0			0
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$		−	11.0000i		−	0.813143i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.3923			−0.759961
$188$		0			0
$189$	3.00000	+	1.73205i	0.218218	+	0.125988i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	−0.866025	−	1.50000i	−0.0623379	−	0.107972i	0.833172	−	0.553014i	$-0.186522\pi$
$193$	−0.866025	−	1.50000i	−0.0623379	−	0.107972i	−0.895510	+	0.445041i	$0.853189\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.46410	+	6.00000i	0.246807	+	0.427482i	0.962638	−	0.270791i	$-0.0872853\pi$
$197$	3.46410	+	6.00000i	0.246807	+	0.427482i	−0.715831	+	0.698273i	$0.753952\pi$
$198$		0			0
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$		0			0
$201$	9.00000	+	5.19615i	0.634811	+	0.366508i
$202$		0			0
$203$	−31.1769			−2.18819
$204$		0			0
$205$		0			0
$206$		0			0
$207$			6.00000i			0.417029i
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$		0			0
$213$	10.3923			0.712069
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	4.50000	−	2.59808i	0.304082	−	0.175562i
$220$		0			0
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$		0			0
$223$	−6.92820	−	12.0000i	−0.463947	−	0.803579i	0.535207	−	0.844721i	$-0.320234\pi$
$223$	−6.92820	−	12.0000i	−0.463947	−	0.803579i	−0.999153	+	0.0411418i	$0.986900\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.19615	+	9.00000i	−0.344881	+	0.597351i	−0.985332	−	0.170648i	$-0.945414\pi$
$227$	−5.19615	+	9.00000i	−0.344881	+	0.597351i	0.640451	+	0.767999i	$0.278747\pi$
$228$		0			0
$229$		−	6.92820i		−	0.457829i	−0.973447	−	0.228914i	$-0.926482\pi$
$229$		−	6.92820i		−	0.457829i	0.973447	−	0.228914i	$-0.0735176\pi$
$230$		0			0
$231$	6.00000	+	10.3923i	0.394771	+	0.683763i
$232$		0			0
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.92820	−	4.00000i	0.450035	−	0.259828i
$238$		0			0
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	22.5000	+	12.9904i	1.44935	+	0.836784i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	22.5000	+	12.9904i	1.44935	+	0.836784i	0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.46410	+	12.0000i	0.220416	+	0.763542i
$248$		0			0
$249$	−3.00000	+	1.73205i	−0.190117	+	0.109764i
$250$		0			0
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	−0.186722	−	0.982413i	$-0.559786\pi$
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	0.944156	−	0.329500i	$-0.106880\pi$
$252$		0			0
$253$	−10.3923	+	18.0000i	−0.653359	+	1.13165i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.59808	+	1.50000i	−0.162064	+	0.0935674i	−0.578838	−	0.815442i	$-0.696494\pi$
$257$	−2.59808	+	1.50000i	−0.162064	+	0.0935674i	0.416775	+	0.909010i	$0.363160\pi$
$258$		0			0
$259$	18.0000			1.11847
$260$		0			0
$261$	9.00000			0.557086
$262$		0			0
$263$	−5.19615	+	3.00000i	−0.320408	+	0.184988i	−0.651575	−	0.758585i	$-0.725891\pi$
$263$	−5.19615	+	3.00000i	−0.320408	+	0.184988i	0.331166	+	0.943572i	$0.392558\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.46410	−	6.00000i	0.212000	−	0.367194i
$268$		0			0
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.107031	−	0.994256i	$-0.465866\pi$
$269$	15.0000	−	25.9808i	0.914566	−	1.58408i	0.807535	−	0.589819i	$-0.200801\pi$
$270$		0			0
$271$	6.00000	−	3.46410i	0.364474	−	0.210429i	−0.306568	−	0.951849i	$-0.599181\pi$
$271$	6.00000	−	3.46410i	0.364474	−	0.210429i	0.671042	+	0.741420i	$0.265847\pi$
$272$		0			0
$273$	−8.66025	+	9.00000i	−0.524142	+	0.544705i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.4545	+	9.50000i	0.988654	+	0.570800i	0.904872	−	0.425684i	$-0.139967\pi$
$277$	16.4545	+	9.50000i	0.988654	+	0.570800i	0.0837823	+	0.996484i	$0.473300\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	29.4449i		−	1.75653i	−0.478171	−	0.878267i	$-0.658700\pi$
$281$		−	29.4449i		−	1.75653i	0.478171	−	0.878267i	$-0.341300\pi$
$282$		0			0
$283$	12.1244	−	7.00000i	0.720718	−	0.416107i	−0.0942988	−	0.995544i	$-0.530061\pi$
$283$	12.1244	−	7.00000i	0.720718	−	0.416107i	0.815017	+	0.579437i	$0.196728\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	30.0000i		−	1.77084i
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$		0			0
$291$			6.92820i			0.406138i
$292$		0			0
$293$	0.866025	−	1.50000i	0.0505937	−	0.0876309i	−0.839619	−	0.543175i	$-0.817222\pi$
$293$	0.866025	−	1.50000i	0.0505937	−	0.0876309i	0.890213	+	0.455544i	$0.150555\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.73205	−	3.00000i	−0.100504	−	0.174078i
$298$		0			0
$299$	−21.0000	−	5.19615i	−1.21446	−	0.300501i
$300$		0			0
$301$	−6.00000	+	3.46410i	−0.345834	+	0.199667i
$302$		0			0
$303$	−2.59808	−	1.50000i	−0.149256	−	0.0861727i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−17.3205			−0.988534			−0.494267	−	0.869310i	$-0.664563\pi$
$307$	−17.3205			−0.988534			−0.494267	+	0.869310i	$0.664563\pi$
$308$		0			0
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$			14.0000i			0.791327i	0.918396	+	0.395663i	$0.129485\pi$
$313$			14.0000i			0.791327i	−0.918396	+	0.395663i	$0.870515\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.73205			−0.0972817			−0.0486408	−	0.998816i	$-0.515489\pi$
$317$	−1.73205			−0.0972817			−0.0486408	+	0.998816i	$0.515489\pi$
$318$		0			0
$319$	27.0000	+	15.5885i	1.51171	+	0.872786i
$320$		0			0
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$		0			0
$323$	−5.19615	−	9.00000i	−0.289122	−	0.500773i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	6.92820	+	12.0000i	0.383131	+	0.663602i
$328$		0			0
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$		0			0
$331$	12.0000	+	6.92820i	0.659580	+	0.380808i	0.792117	−	0.610370i	$-0.208979\pi$
$331$	12.0000	+	6.92820i	0.659580	+	0.380808i	−0.132537	+	0.991178i	$0.542312\pi$
$332$		0			0
$333$	−5.19615			−0.284747
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	23.0000i		−	1.25289i	−0.779466	−	0.626445i	$-0.784509\pi$
$337$		−	23.0000i		−	1.25289i	0.779466	−	0.626445i	$-0.215491\pi$
$338$		0			0
$339$	3.00000			0.162938
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−6.92820			−0.374088
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	0.0193540	−	0.999813i	$-0.493839\pi$
$347$	−15.5885	−	9.00000i	−0.836832	−	0.483145i	−0.856186	+	0.516667i	$0.827172\pi$
$348$		0			0
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	−0.143172	−	0.989698i	$-0.545730\pi$
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	0.785517	+	0.618840i	$0.212397\pi$
$350$		0			0
$351$	2.50000	−	2.59808i	0.133440	−	0.138675i
$352$		0			0
$353$	12.9904	+	22.5000i	0.691408	+	1.19755i	0.971377	+	0.237545i	$0.0763427\pi$
$353$	12.9904	+	22.5000i	0.691408	+	1.19755i	−0.279968	+	0.960009i	$0.590324\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.19615	−	9.00000i	0.275010	−	0.476331i
$358$		0			0
$359$			3.46410i			0.182828i	0.995813	+	0.0914141i	$0.0291387\pi$
$359$			3.46410i			0.182828i	−0.995813	+	0.0914141i	$0.970861\pi$
$360$		0			0
$361$	−3.50000	−	6.06218i	−0.184211	−	0.319062i
$362$		0			0
$363$		−	1.00000i		−	0.0524864i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.73205	−	1.00000i	0.0904123	−	0.0521996i	−0.454112	−	0.890945i	$-0.650043\pi$
$367$	1.73205	−	1.00000i	0.0904123	−	0.0521996i	0.544524	+	0.838745i	$0.316710\pi$
$368$		0			0
$369$			8.66025i			0.450835i
$370$		0			0
$371$	−27.0000	−	15.5885i	−1.40177	−	0.809312i
$372$		0			0
$373$	26.8468	+	15.5000i	1.39007	+	0.802560i	0.993323	−	0.115367i	$-0.0368043\pi$
$373$	26.8468	+	15.5000i	1.39007	+	0.802560i	0.396751	+	0.917926i	$0.370138\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.79423	+	31.5000i	−0.401423	+	1.62233i
$378$		0			0
$379$	−12.0000	+	6.92820i	−0.616399	+	0.355878i	−0.775466	−	0.631390i	$-0.782485\pi$
$379$	−12.0000	+	6.92820i	−0.616399	+	0.355878i	0.159067	+	0.987268i	$0.449151\pi$
$380$		0			0
$381$	8.00000	−	13.8564i	0.409852	−	0.709885i
$382$		0			0
$383$	6.92820	−	12.0000i	0.354015	−	0.613171i	−0.632934	−	0.774206i	$-0.718150\pi$
$383$	6.92820	−	12.0000i	0.354015	−	0.613171i	0.986949	+	0.161034i	$0.0514830\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.73205	−	1.00000i	0.0880451	−	0.0508329i
$388$		0			0
$389$	−21.0000			−1.06474			−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000			−1.06474			−0.532371	+	0.846511i	$0.678699\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$	−10.3923	+	6.00000i	−0.524222	+	0.302660i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	13.8564	−	24.0000i	0.695433	−	1.20453i	−0.274601	−	0.961558i	$-0.588546\pi$
$397$	13.8564	−	24.0000i	0.695433	−	1.20453i	0.970034	−	0.242967i	$-0.0781208\pi$
$398$		0			0
$399$	−6.00000	+	10.3923i	−0.300376	+	0.520266i
$400$		0			0
$401$	31.5000	−	18.1865i	1.57303	−	0.908192i	0.577241	−	0.816574i	$-0.304129\pi$
$401$	31.5000	−	18.1865i	1.57303	−	0.908192i	0.995794	−	0.0916181i	$-0.0292039\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.5885	−	9.00000i	−0.772691	−	0.446113i
$408$		0			0
$409$	10.5000	+	6.06218i	0.519192	+	0.299755i	0.736604	−	0.676324i	$-0.236428\pi$
$409$	10.5000	+	6.06218i	0.519192	+	0.299755i	−0.217412	+	0.976080i	$0.569762\pi$
$410$		0			0
$411$			15.5885i			0.768922i
$412$		0			0
$413$	41.5692	−	24.0000i	2.04549	−	1.18096i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			4.00000i			0.195881i
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$			12.1244i			0.590905i	0.955357	+	0.295452i	$0.0954704\pi$
$421$			12.1244i			0.590905i	−0.955357	+	0.295452i	$0.904530\pi$
$422$		0			0
$423$	−1.73205	+	3.00000i	−0.0842152	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	19.0526	+	33.0000i	0.922018	+	1.59698i
$428$		0			0
$429$	12.0000	−	3.46410i	0.579365	−	0.167248i
$430$		0			0
$431$	−27.0000	+	15.5885i	−1.30054	+	0.750870i	−0.980497	−	0.196532i	$-0.937032\pi$
$431$	−27.0000	+	15.5885i	−1.30054	+	0.750870i	−0.320047	+	0.947402i	$0.603699\pi$
$432$		0			0
$433$	−25.1147	−	14.5000i	−1.20694	−	0.696826i	−0.244848	−	0.969561i	$-0.578738\pi$
$433$	−25.1147	−	14.5000i	−1.20694	−	0.696826i	−0.962089	+	0.272736i	$0.912071\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−20.7846			−0.994263
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	−5.00000			−0.238095
$442$		0			0
$443$		−	24.0000i		−	1.14027i	−0.821549	−	0.570137i	$-0.806890\pi$
$443$		−	24.0000i		−	1.14027i	0.821549	−	0.570137i	$-0.193110\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8.66025			0.409616
$448$		0			0
$449$	6.00000	+	3.46410i	0.283158	+	0.163481i	0.634852	−	0.772634i	$-0.281061\pi$
$449$	6.00000	+	3.46410i	0.283158	+	0.163481i	−0.351694	+	0.936115i	$0.614394\pi$
$450$		0			0
$451$	−15.0000	+	25.9808i	−0.706322	+	1.22339i
$452$		0			0
$453$	8.66025	+	15.0000i	0.406894	+	0.704761i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.33013	+	7.50000i	0.202555	+	0.350835i	0.949351	−	0.314218i	$-0.101742\pi$
$457$	4.33013	+	7.50000i	0.202555	+	0.350835i	−0.746796	+	0.665053i	$0.768409\pi$
$458$		0			0
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$		0			0
$461$	4.50000	+	2.59808i	0.209586	+	0.121004i	0.601119	−	0.799160i	$-0.294722\pi$
$461$	4.50000	+	2.59808i	0.209586	+	0.121004i	−0.391533	+	0.920164i	$0.628055\pi$
$462$		0			0
$463$	−3.46410			−0.160990			−0.0804952	−	0.996755i	$-0.525650\pi$
$463$	−3.46410			−0.160990			−0.0804952	+	0.996755i	$0.525650\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	6.00000i		−	0.277647i	−0.990317	−	0.138823i	$-0.955668\pi$
$467$		−	6.00000i		−	0.277647i	0.990317	−	0.138823i	$-0.0443321\pi$
$468$		0			0
$469$	−36.0000			−1.66233
$470$		0			0
$471$	11.5000	+	19.9186i	0.529892	+	0.917800i
$472$		0			0
$473$	6.92820			0.318559
$474$		0			0
$475$		0			0
$476$		0			0
$477$	7.79423	+	4.50000i	0.356873	+	0.206041i
$478$		0			0
$479$	−6.00000	+	3.46410i	−0.274147	+	0.158279i	−0.630771	−	0.775969i	$-0.717261\pi$
$479$	−6.00000	+	3.46410i	−0.274147	+	0.158279i	0.356624	+	0.934248i	$0.383928\pi$
$480$		0			0
$481$	4.50000	−	18.1865i	0.205182	−	0.829235i
$482$		0			0
$483$	−10.3923	−	18.0000i	−0.472866	−	0.819028i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	8.66025	−	15.0000i	0.392434	−	0.679715i	−0.600336	−	0.799748i	$-0.704967\pi$
$487$	8.66025	−	15.0000i	0.392434	−	0.679715i	0.992770	+	0.120033i	$0.0383000\pi$
$488$		0			0
$489$			13.8564i			0.626608i
$490$		0			0
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	−0.975898	−	0.218229i	$-0.929972\pi$
$491$	−15.0000	−	25.9808i	−0.676941	−	1.17250i	0.298957	−	0.954267i	$-0.403361\pi$
$492$		0			0
$493$		−	27.0000i		−	1.21602i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−31.1769	+	18.0000i	−1.39848	+	0.807410i
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	6.00000	+	3.46410i	0.268060	+	0.154765i
$502$		0			0
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	0.611349	−	0.791361i	$-0.290627\pi$
$503$	5.19615	+	3.00000i	0.231685	+	0.133763i	−0.379664	+	0.925124i	$0.623960\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.92820	+	11.0000i	0.307692	+	0.488527i
$508$		0			0
$509$	−1.50000	+	0.866025i	−0.0664863	+	0.0383859i	−0.532875	−	0.846194i	$-0.678888\pi$
$509$	−1.50000	+	0.866025i	−0.0664863	+	0.0383859i	0.466388	+	0.884580i	$0.345555\pi$
$510$		0			0
$511$	−9.00000	+	15.5885i	−0.398137	+	0.689593i
$512$		0			0
$513$	1.73205	−	3.00000i	0.0764719	−	0.132453i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−10.3923	+	6.00000i	−0.457053	+	0.263880i
$518$		0			0
$519$	18.0000			0.790112
$520$		0			0
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$		0			0
$523$	8.66025	−	5.00000i	0.378686	−	0.218635i	−0.298560	−	0.954391i	$-0.596506\pi$
$523$	8.66025	−	5.00000i	0.378686	−	0.218635i	0.677247	+	0.735756i	$0.263173\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	−12.0000	+	6.92820i	−0.520756	+	0.300658i
$532$		0			0
$533$	−30.3109	−	7.50000i	−1.31291	−	0.324861i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	15.5885	+	9.00000i	0.672692	+	0.388379i
$538$		0			0
$539$	−15.0000	−	8.66025i	−0.646096	−	0.373024i
$540$		0			0
$541$		−	1.73205i		−	0.0744667i	−0.999307	−	0.0372333i	$-0.988146\pi$
$541$		−	1.73205i		−	0.0744667i	0.999307	−	0.0372333i	$-0.0118545\pi$
$542$		0			0
$543$	−11.2583	+	6.50000i	−0.483141	+	0.278942i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	34.0000i		−	1.45374i	−0.686778	−	0.726868i	$-0.740975\pi$
$547$		−	34.0000i		−	1.45374i	0.686778	−	0.726868i	$-0.259025\pi$
$548$		0			0
$549$	−5.50000	−	9.52628i	−0.234734	−	0.406572i
$550$		0			0
$551$			31.1769i			1.32818i
$552$		0			0
$553$	−13.8564	+	24.0000i	−0.589234	+	1.02058i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.866025	+	1.50000i	0.0366947	+	0.0635570i	0.883789	−	0.467885i	$-0.154984\pi$
$557$	0.866025	+	1.50000i	0.0366947	+	0.0635570i	−0.847095	+	0.531442i	$0.821650\pi$
$558$		0			0
$559$	2.00000	+	6.92820i	0.0845910	+	0.293032i
$560$		0			0
$561$	−9.00000	+	5.19615i	−0.379980	+	0.219382i
$562$		0			0
$563$	20.7846	+	12.0000i	0.875967	+	0.505740i	0.869326	−	0.494238i	$-0.164553\pi$
$563$	20.7846	+	12.0000i	0.875967	+	0.505740i	0.00664037	+	0.999978i	$0.497886\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	3.46410			0.145479
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−26.0000			−1.08807			−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000			−1.08807			−0.544033	+	0.839064i	$0.683103\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.66025			0.360531			0.180266	−	0.983618i	$-0.442304\pi$
$577$	8.66025			0.360531			0.180266	+	0.983618i	$0.442304\pi$
$578$		0			0
$579$	−1.50000	−	0.866025i	−0.0623379	−	0.0359908i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$		0			0
$583$	15.5885	+	27.0000i	0.645608	+	1.11823i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.3923	+	18.0000i	0.428936	+	0.742940i	0.996779	−	0.0801976i	$-0.0255551\pi$
$587$	10.3923	+	18.0000i	0.428936	+	0.742940i	−0.567843	+	0.823137i	$0.692222\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	6.00000	+	3.46410i	0.246807	+	0.142494i
$592$		0			0
$593$	−12.1244			−0.497888			−0.248944	−	0.968518i	$-0.580083\pi$
$593$	−12.1244			−0.497888			−0.248944	+	0.968518i	$0.580083\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	10.0000i		−	0.409273i
$598$		0			0
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	−0.945558	−	0.325455i	$-0.894483\pi$
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	0.190927	−	0.981604i	$-0.438851\pi$
$602$		0			0
$603$	10.3923			0.423207
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.92820	−	4.00000i	−0.281207	−	0.162355i	0.352763	−	0.935713i	$-0.385242\pi$
$607$	−6.92820	−	4.00000i	−0.281207	−	0.162355i	−0.633970	+	0.773358i	$0.718576\pi$
$608$		0			0
$609$	−27.0000	+	15.5885i	−1.09410	+	0.631676i
$610$		0			0
$611$	−9.00000	−	8.66025i	−0.364101	−	0.350356i
$612$		0			0
$613$	2.59808	+	4.50000i	0.104935	+	0.181753i	0.913712	−	0.406363i	$-0.133203\pi$
$613$	2.59808	+	4.50000i	0.104935	+	0.181753i	−0.808776	+	0.588116i	$0.799870\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.9904	−	22.5000i	0.522973	−	0.905816i	−0.476670	−	0.879083i	$-0.658156\pi$
$617$	12.9904	−	22.5000i	0.522973	−	0.905816i	0.999643	−	0.0267333i	$-0.00851050\pi$
$618$		0			0
$619$			13.8564i			0.556936i	0.960446	+	0.278468i	$0.0898266\pi$
$619$			13.8564i			0.556936i	−0.960446	+	0.278468i	$0.910173\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$		0			0
$623$			24.0000i			0.961540i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	10.3923	−	6.00000i	0.415029	−	0.239617i
$628$		0			0
$629$			15.5885i			0.621552i
$630$		0			0
$631$	24.0000	+	13.8564i	0.955425	+	0.551615i	0.894762	−	0.446543i	$-0.147345\pi$
$631$	24.0000	+	13.8564i	0.955425	+	0.551615i	0.0606630	+	0.998158i	$0.480679\pi$
$632$		0			0
$633$	6.92820	+	4.00000i	0.275371	+	0.158986i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	4.33013	−	17.5000i	0.171566	−	0.693375i
$638$		0			0
$639$	9.00000	−	5.19615i	0.356034	−	0.205557i
$640$		0			0
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	−0.580674	−	0.814136i	$-0.697211\pi$
$641$	10.5000	−	18.1865i	0.414725	−	0.718325i	0.995400	+	0.0958109i	$0.0305444\pi$
$642$		0			0
$643$	−3.46410	+	6.00000i	−0.136611	+	0.236617i	−0.926212	−	0.377004i	$-0.876954\pi$
$643$	−3.46410	+	6.00000i	−0.136611	+	0.236617i	0.789601	+	0.613621i	$0.210288\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$		0			0
$649$	−48.0000			−1.88416
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.19615	+	3.00000i	−0.203341	+	0.117399i	−0.598213	−	0.801337i	$-0.704122\pi$
$653$	−5.19615	+	3.00000i	−0.203341	+	0.117399i	0.394872	+	0.918736i	$0.370789\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.59808	−	4.50000i	0.101361	−	0.175562i
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	−10.5000	+	6.06218i	−0.408403	+	0.235791i	−0.690103	−	0.723711i	$-0.742435\pi$
$661$	−10.5000	+	6.06218i	−0.408403	+	0.235791i	0.281701	+	0.959502i	$0.409102\pi$
$662$		0			0
$663$	−7.79423	−	7.50000i	−0.302703	−	0.291276i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−46.7654	−	27.0000i	−1.81076	−	1.04544i
$668$		0			0
$669$	−12.0000	−	6.92820i	−0.463947	−	0.267860i
$670$		0			0
$671$		−	38.1051i		−	1.47103i
$672$		0			0
$673$	−4.33013	+	2.50000i	−0.166914	+	0.0963679i	−0.581130	−	0.813811i	$-0.697389\pi$
$673$	−4.33013	+	2.50000i	−0.166914	+	0.0963679i	0.414216	+	0.910179i	$0.364056\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	30.0000i		−	1.15299i	−0.817099	−	0.576497i	$-0.804419\pi$
$677$		−	30.0000i		−	1.15299i	0.817099	−	0.576497i	$-0.195581\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$		0			0
$681$			10.3923i			0.398234i
$682$		0			0
$683$	−6.92820	+	12.0000i	−0.265100	+	0.459167i	−0.967590	−	0.252527i	$-0.918738\pi$
$683$	−6.92820	+	12.0000i	−0.265100	+	0.459167i	0.702490	+	0.711694i	$0.252072\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.46410	−	6.00000i	−0.132164	−	0.228914i
$688$		0			0
$689$	−22.5000	+	23.3827i	−0.857182	+	0.890809i
$690$		0			0
$691$	−9.00000	+	5.19615i	−0.342376	+	0.197671i	−0.661322	−	0.750102i	$-0.730004\pi$
$691$	−9.00000	+	5.19615i	−0.342376	+	0.197671i	0.318946	+	0.947773i	$0.396671\pi$
$692$		0			0
$693$	10.3923	+	6.00000i	0.394771	+	0.227921i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	25.9808			0.984092
$698$		0			0
$699$	−9.00000	−	15.5885i	−0.340411	−	0.589610i
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$		−	18.0000i		−	0.678883i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.3923			0.390843
$708$		0			0
$709$	−13.5000	−	7.79423i	−0.507003	−	0.292718i	0.224598	−	0.974452i	$-0.427893\pi$
$709$	−13.5000	−	7.79423i	−0.507003	−	0.292718i	−0.731601	+	0.681733i	$0.761227\pi$
$710$		0			0
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−5.19615	−	9.00000i	−0.194054	−	0.336111i
$718$		0			0
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	42.0000	+	24.2487i	1.56416	+	0.903069i
$722$		0			0
$723$	25.9808			0.966235
$724$		0			0
$725$		0			0
$726$		0			0
$727$			10.0000i			0.370879i	0.982656	+	0.185440i	$0.0593710\pi$
$727$			10.0000i			0.370879i	−0.982656	+	0.185440i	$0.940629\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−3.00000	−	5.19615i	−0.110959	−	0.192187i
$732$		0			0
$733$	36.3731			1.34347			0.671735	−	0.740792i	$-0.265549\pi$
$733$	36.3731			1.34347			0.671735	+	0.740792i	$0.265549\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	31.1769	+	18.0000i	1.14842	+	0.663039i
$738$		0			0
$739$	−24.0000	+	13.8564i	−0.882854	+	0.509716i	−0.871598	−	0.490221i	$-0.836916\pi$
$739$	−24.0000	+	13.8564i	−0.882854	+	0.509716i	−0.0112558	+	0.999937i	$0.503583\pi$
$740$		0			0
$741$	9.00000	+	8.66025i	0.330623	+	0.318142i
$742$		0			0
$743$	−20.7846	−	36.0000i	−0.762513	−	1.32071i	−0.941551	−	0.336870i	$-0.890632\pi$
$743$	−20.7846	−	36.0000i	−0.762513	−	1.32071i	0.179038	−	0.983842i	$-0.442702\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.73205	+	3.00000i	−0.0633724	+	0.109764i
$748$		0			0
$749$		−	62.3538i		−	2.27836i
$750$		0			0
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	0.525193	−	0.850983i	$-0.323993\pi$
$751$	−13.0000	−	22.5167i	−0.474377	−	0.821645i	−0.999570	+	0.0293387i	$0.990660\pi$
$752$		0			0
$753$		−	24.0000i		−	0.874609i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.73205	+	1.00000i	−0.0629525	+	0.0363456i	−0.531146	−	0.847280i	$-0.678238\pi$
$757$	−1.73205	+	1.00000i	−0.0629525	+	0.0363456i	0.468193	+	0.883626i	$0.344905\pi$
$758$		0			0
$759$			20.7846i			0.754434i
$760$		0			0
$761$	18.0000	+	10.3923i	0.652499	+	0.376721i	0.789413	−	0.613862i	$-0.210385\pi$
$761$	18.0000	+	10.3923i	0.652499	+	0.376721i	−0.136914	+	0.990583i	$0.543718\pi$
$762$		0			0
$763$	−41.5692	−	24.0000i	−1.50491	−	0.868858i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−13.8564	−	48.0000i	−0.500326	−	1.73318i
$768$		0			0
$769$	30.0000	−	17.3205i	1.08183	−	0.624593i	0.150439	−	0.988619i	$-0.451931\pi$
$769$	30.0000	−	17.3205i	1.08183	−	0.624593i	0.931389	+	0.364026i	$0.118598\pi$
$770$		0			0
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$		0			0
$773$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$773$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	15.5885	−	9.00000i	0.559233	−	0.322873i
$778$		0			0
$779$	−30.0000			−1.07486
$780$		0			0
$781$	36.0000			1.28818
$782$		0			0
$783$	7.79423	−	4.50000i	0.278543	−	0.160817i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	20.7846	−	36.0000i	0.740891	−	1.28326i	−0.211199	−	0.977443i	$-0.567737\pi$
$787$	20.7846	−	36.0000i	0.740891	−	1.28326i	0.952090	−	0.305818i	$-0.0989300\pi$
$788$		0			0
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$		0			0
$791$	−9.00000	+	5.19615i	−0.320003	+	0.184754i
$792$		0			0
$793$	38.1051	−	11.0000i	1.35315	−	0.390621i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.5885	−	9.00000i	−0.552171	−	0.318796i	0.197826	−	0.980237i	$-0.436612\pi$
$797$	−15.5885	−	9.00000i	−0.552171	−	0.318796i	−0.749997	+	0.661441i	$0.769945\pi$
$798$		0			0
$799$	9.00000	+	5.19615i	0.318397	+	0.183827i
$800$		0			0
$801$		−	6.92820i		−	0.244796i
$802$		0			0
$803$	15.5885	−	9.00000i	0.550105	−	0.317603i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	30.0000i		−	1.05605i
$808$		0			0
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	0.620274	−	0.784385i	$-0.287021\pi$
$809$	−10.5000	−	18.1865i	−0.369160	−	0.639404i	−0.989434	+	0.144981i	$0.953688\pi$
$810$		0			0
$811$		−	6.92820i		−	0.243282i	−0.992574	−	0.121641i	$-0.961184\pi$
$811$		−	6.92820i		−	0.243282i	0.992574	−	0.121641i	$-0.0388157\pi$
$812$		0			0
$813$	3.46410	−	6.00000i	0.121491	−	0.210429i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.46410	+	6.00000i	0.121194	+	0.209913i
$818$		0			0
$819$	−3.00000	+	12.1244i	−0.104828	+	0.423659i
$820$		0			0
$821$	24.0000	−	13.8564i	0.837606	−	0.483592i	−0.0188439	−	0.999822i	$-0.505999\pi$
$821$	24.0000	−	13.8564i	0.837606	−	0.483592i	0.856450	+	0.516231i	$0.172665\pi$
$822$		0			0
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.245295	−	0.969448i	$-0.578885\pi$
$823$	−34.6410	−	20.0000i	−1.20751	−	0.697156i	−0.962215	+	0.272292i	$0.912218\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−27.7128			−0.963669			−0.481834	−	0.876262i	$-0.660029\pi$
$827$	−27.7128			−0.963669			−0.481834	+	0.876262i	$0.660029\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$		0			0
$831$	19.0000			0.659103
$832$		0			0
$833$			15.0000i			0.519719i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−36.0000	−	20.7846i	−1.24286	−	0.717564i	−0.273183	−	0.961962i	$-0.588076\pi$
$839$	−36.0000	−	20.7846i	−1.24286	−	0.717564i	−0.969675	+	0.244398i	$0.921410\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	−14.7224	−	25.5000i	−0.507067	−	0.878267i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.73205	+	3.00000i	0.0595140	+	0.103081i
$848$		0			0
$849$	7.00000	−	12.1244i	0.240239	−	0.416107i
$850$		0			0
$851$	27.0000	+	15.5885i	0.925548	+	0.534365i
$852$		0			0
$853$	43.3013			1.48261			0.741304	−	0.671170i	$-0.234208\pi$
$853$	43.3013			1.48261			0.741304	+	0.671170i	$0.234208\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	3.00000i		−	0.102478i	−0.998686	−	0.0512390i	$-0.983683\pi$
$857$		−	3.00000i		−	0.102478i	0.998686	−	0.0512390i	$-0.0163170\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$		0			0
$861$	−15.0000	−	25.9808i	−0.511199	−	0.885422i
$862$		0			0
$863$	−38.1051			−1.29711			−0.648557	−	0.761166i	$-0.724627\pi$
$863$	−38.1051			−1.29711			−0.648557	+	0.761166i	$0.724627\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.92820	−	4.00000i	−0.235294	−	0.135847i
$868$		0			0
$869$	24.0000	−	13.8564i	0.814144	−	0.470046i
$870$		0			0
$871$	−9.00000	+	36.3731i	−0.304953	+	1.23245i
$872$		0			0
$873$	3.46410	+	6.00000i	0.117242	+	0.203069i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	18.1865	−	31.5000i	0.614116	−	1.06368i	−0.376423	−	0.926448i	$-0.622846\pi$
$877$	18.1865	−	31.5000i	0.614116	−	1.06368i	0.990539	−	0.137232i	$-0.0438205\pi$
$878$		0			0
$879$		−	1.73205i		−	0.0584206i
$880$		0			0
$881$	−4.50000	−	7.79423i	−0.151609	−	0.262594i	0.780210	−	0.625517i	$-0.215112\pi$
$881$	−4.50000	−	7.79423i	−0.151609	−	0.262594i	−0.931819	+	0.362923i	$0.881779\pi$
$882$		0			0
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$			55.4256i			1.85892i
$890$		0			0
$891$	−3.00000	−	1.73205i	−0.100504	−	0.0580259i
$892$		0			0
$893$	−10.3923	−	6.00000i	−0.347765	−	0.200782i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−20.7846	+	6.00000i	−0.693978	+	0.200334i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$		0			0
$903$	−3.46410	+	6.00000i	−0.115278	+	0.199667i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	−0.0401089	−	0.999195i	$-0.512770\pi$
$907$	24.2487	−	14.0000i	0.805165	−	0.464862i	0.845274	+	0.534333i	$0.179437\pi$
$908$		0			0
$909$	−3.00000			−0.0995037
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−10.3923	+	6.00000i	−0.343935	+	0.198571i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	20.7846	−	36.0000i	0.686368	−	1.18882i
$918$		0			0
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	0.471684	+	0.881768i	$0.343646\pi$
$919$	−16.0000	+	27.7128i	−0.527791	+	0.914161i	−0.999475	+	0.0323936i	$0.989687\pi$
$920$		0			0
$921$	−15.0000	+	8.66025i	−0.494267	+	0.285365i
$922$		0			0
$923$	10.3923	+	36.0000i	0.342067	+	1.18495i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−12.1244	−	7.00000i	−0.398216	−	0.229910i
$928$		0			0
$929$	49.5000	+	28.5788i	1.62404	+	0.937641i	0.985823	+	0.167786i	$0.0536619\pi$
$929$	49.5000	+	28.5788i	1.62404	+	0.937641i	0.638219	+	0.769855i	$0.279671\pi$
$930$		0			0
$931$		−	17.3205i		−	0.567657i
$932$		0			0
$933$	−15.5885	+	9.00000i	−0.510343	+	0.294647i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	41.0000i		−	1.33941i	−0.742627	−	0.669706i	$-0.766420\pi$
$937$		−	41.0000i		−	1.33941i	0.742627	−	0.669706i	$-0.233580\pi$
$938$		0			0
$939$	7.00000	+	12.1244i	0.228436	+	0.395663i
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$	25.9808	−	45.0000i	0.846050	−	1.46540i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.92820	−	12.0000i	−0.225136	−	0.389948i	0.731224	−	0.682137i	$-0.238949\pi$
$947$	−6.92820	−	12.0000i	−0.225136	−	0.389948i	−0.956360	+	0.292190i	$0.905616\pi$
$948$		0			0
$949$	13.5000	+	12.9904i	0.438229	+	0.421686i
$950$		0			0
$951$	−1.50000	+	0.866025i	−0.0486408	+	0.0280828i
$952$		0			0
$953$	46.7654	+	27.0000i	1.51488	+	0.874616i	0.999848	+	0.0174443i	$0.00555298\pi$
$953$	46.7654	+	27.0000i	1.51488	+	0.874616i	0.515031	+	0.857171i	$0.327780\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	31.1769			1.00781
$958$		0			0
$959$	−27.0000	−	46.7654i	−0.871875	−	1.51013i
$960$		0			0
$961$	31.0000			1.00000
$962$		0			0
$963$			18.0000i			0.580042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	45.0333			1.44817			0.724087	−	0.689709i	$-0.242261\pi$
$967$	45.0333			1.44817			0.724087	+	0.689709i	$0.242261\pi$
$968$		0			0
$969$	−9.00000	−	5.19615i	−0.289122	−	0.166924i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$		0			0
$973$	−6.92820	−	12.0000i	−0.222108	−	0.384702i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.33013	−	7.50000i	−0.138533	−	0.239946i	0.788409	−	0.615152i	$-0.210905\pi$
$977$	−4.33013	−	7.50000i	−0.138533	−	0.239946i	−0.926942	+	0.375206i	$0.877572\pi$
$978$		0			0
$979$	12.0000	−	20.7846i	0.383522	−	0.664279i
$980$		0			0
$981$	12.0000	+	6.92820i	0.383131	+	0.221201i
$982$		0			0
$983$	20.7846			0.662926			0.331463	−	0.943468i	$-0.392458\pi$
$983$	20.7846			0.662926			0.331463	+	0.943468i	$0.392458\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	12.0000i		−	0.381964i
$988$		0			0
$989$	−12.0000			−0.381578
$990$		0			0
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$		0			0
$993$	13.8564			0.439720
$994$		0			0
$995$		0			0
$996$		0			0
$997$	47.6314	+	27.5000i	1.50850	+	0.870934i	0.999951	+	0.00990158i	$0.00315182\pi$
$997$	47.6314	+	27.5000i	1.50850	+	0.870934i	0.508551	+	0.861032i	$0.330182\pi$
$998$		0			0
$999$	−4.50000	+	2.59808i	−0.142374	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.bw.e.49.2		4
5.2	odd	4		3900.2.cd.a.2701.1		2
5.3	odd	4		156.2.q.a.49.1	✓	2
5.4	even	2	inner	3900.2.bw.e.49.1		4
13.4	even	6	inner	3900.2.bw.e.2149.1		4
15.8	even	4		468.2.t.c.361.1		2
20.3	even	4		624.2.bv.a.49.1		2
60.23	odd	4		1872.2.by.b.1297.1		2
65.3	odd	12		2028.2.b.b.337.1		2
65.4	even	6	inner	3900.2.bw.e.2149.2		4
65.8	even	4		2028.2.i.h.2005.2		4
65.17	odd	12		3900.2.cd.a.901.1		2
65.18	even	4		2028.2.i.h.2005.1		4
65.23	odd	12		2028.2.b.b.337.2		2
65.28	even	12		2028.2.a.h.1.1		2
65.33	even	12		2028.2.i.h.529.2		4
65.38	odd	4		2028.2.q.a.361.1		2
65.43	odd	12		156.2.q.a.121.1	yes	2
65.48	odd	12		2028.2.q.a.1837.1		2
65.58	even	12		2028.2.i.h.529.1		4
65.63	even	12		2028.2.a.h.1.2		2
195.23	even	12		6084.2.b.c.4393.1		2
195.68	even	12		6084.2.b.c.4393.2		2
195.128	odd	12		6084.2.a.u.1.1		2
195.158	odd	12		6084.2.a.u.1.2		2
195.173	even	12		468.2.t.c.433.1		2
260.43	even	12		624.2.bv.a.433.1		2
260.63	odd	12		8112.2.a.bt.1.2		2
260.223	odd	12		8112.2.a.bt.1.1		2
780.563	odd	12		1872.2.by.b.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.q.a.49.1	✓	2	5.3	odd	4
156.2.q.a.121.1	yes	2	65.43	odd	12
468.2.t.c.361.1		2	15.8	even	4
468.2.t.c.433.1		2	195.173	even	12
624.2.bv.a.49.1		2	20.3	even	4
624.2.bv.a.433.1		2	260.43	even	12
1872.2.by.b.433.1		2	780.563	odd	12
1872.2.by.b.1297.1		2	60.23	odd	4
2028.2.a.h.1.1		2	65.28	even	12
2028.2.a.h.1.2		2	65.63	even	12
2028.2.b.b.337.1		2	65.3	odd	12
2028.2.b.b.337.2		2	65.23	odd	12
2028.2.i.h.529.1		4	65.58	even	12
2028.2.i.h.529.2		4	65.33	even	12
2028.2.i.h.2005.1		4	65.18	even	4
2028.2.i.h.2005.2		4	65.8	even	4
2028.2.q.a.361.1		2	65.38	odd	4
2028.2.q.a.1837.1		2	65.48	odd	12
3900.2.bw.e.49.1		4	5.4	even	2	inner
3900.2.bw.e.49.2		4	1.1	even	1	trivial
3900.2.bw.e.2149.1		4	13.4	even	6	inner
3900.2.bw.e.2149.2		4	65.4	even	6	inner
3900.2.cd.a.901.1		2	65.17	odd	12
3900.2.cd.a.2701.1		2	5.2	odd	4
6084.2.a.u.1.1		2	195.128	odd	12
6084.2.a.u.1.2		2	195.158	odd	12
6084.2.b.c.4393.1		2	195.23	even	12
6084.2.b.c.4393.2		2	195.68	even	12
8112.2.a.bt.1.1		2	260.223	odd	12
8112.2.a.bt.1.2		2	260.63	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:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.bw (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 3.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(-1.73205 + 3.00000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(3.00000 - 1.73205i) q^{11} +(2.59808 + 2.50000i) q^{13} +(-2.59808 - 1.50000i) q^{17} +(3.00000 + 1.73205i) q^{19} +3.46410i q^{21} +(-5.19615 + 3.00000i) q^{23} -1.00000i q^{27} +(4.50000 + 7.79423i) q^{29} +(1.73205 - 3.00000i) q^{33} +(-2.59808 - 4.50000i) q^{37} +(3.50000 + 0.866025i) q^{39} +(-7.50000 + 4.33013i) q^{41} +(1.73205 + 1.00000i) q^{43} -3.46410 q^{47} +(-2.50000 - 4.33013i) q^{49} -3.00000 q^{51} +9.00000i q^{53} +3.46410 q^{57} +(-12.0000 - 6.92820i) q^{59} +(5.50000 - 9.52628i) q^{61} +(1.73205 + 3.00000i) q^{63} +(5.19615 + 9.00000i) q^{67} +(-3.00000 + 5.19615i) q^{69} +(9.00000 + 5.19615i) q^{71} +5.19615 q^{73} +12.0000i q^{77} +8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} -3.46410 q^{83} +(7.79423 + 4.50000i) q^{87} +(6.00000 - 3.46410i) q^{89} +(-12.0000 + 3.46410i) q^{91} +(-3.46410 + 6.00000i) q^{97} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^9	\( 4 q + 2 q^{9} + 12 q^{11} + 12 q^{19} + 18 q^{29} + 14 q^{39} - 30 q^{41} - 10 q^{49} - 12 q^{51} - 48 q^{59} + 22 q^{61} - 12 q^{69} + 36 q^{71} + 32 q^{79} - 2 q^{81} + 24 q^{89} - 48 q^{91}+O(q^{100}) \) 4 * q + 2 * q^9 + 12 * q^11 + 12 * q^19 + 18 * q^29 + 14 * q^39 - 30 * q^41 - 10 * q^49 - 12 * q^51 - 48 * q^59 + 22 * q^61 - 12 * q^69 + 36 * q^71 + 32 * q^79 - 2 * q^81 + 24 * q^89 - 48 * q^91

Introduction

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