LMFDB - Embedded newform 1300.2.i.d.1101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(601,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1300.601");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 260)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1101.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1300.1101
Dual form			1300.2.i.d.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(-1.50000 - 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} -1.00000 q^{21} +(4.50000 - 7.79423i) q^{23} +5.00000 q^{27} +(4.50000 - 7.79423i) q^{29} +8.00000 q^{31} +(1.50000 + 2.59808i) q^{33} +(-3.50000 + 6.06218i) q^{37} +(-3.50000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{49} -3.00000 q^{51} -6.00000 q^{53} -5.00000 q^{57} +(-4.50000 - 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{63} +(2.50000 - 4.33013i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(-4.50000 - 7.79423i) q^{71} -2.00000 q^{73} +3.00000 q^{77} +8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{87} +(-1.50000 + 2.59808i) q^{89} +(-2.50000 + 2.59808i) q^{91} +(4.00000 - 6.92820i) q^{93} +(8.50000 + 14.7224i) q^{97} -6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 - q^7 + 2 * q^9	$ 2 q + q^{3} - q^{7} + 2 q^{9} - 3 q^{11} - 2 q^{13} - 3 q^{17} - 5 q^{19} - 2 q^{21} + 9 q^{23} + 10 q^{27} + 9 q^{29} + 16 q^{31} + 3 q^{33} - 7 q^{37} - 7 q^{39} - 3 q^{41} - q^{43} + 6 q^{49} - 6 q^{51} - 12 q^{53} - 10 q^{57} - 9 q^{59} + q^{61} + 2 q^{63} + 5 q^{67} - 9 q^{69} - 9 q^{71} - 4 q^{73} + 6 q^{77} + 16 q^{79} - q^{81} - 9 q^{87} - 3 q^{89} - 5 q^{91} + 8 q^{93} + 17 q^{97} - 12 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^7 + 2 * q^9 - 3 * q^11 - 2 * q^13 - 3 * q^17 - 5 * q^19 - 2 * q^21 + 9 * q^23 + 10 * q^27 + 9 * q^29 + 16 * q^31 + 3 * q^33 - 7 * q^37 - 7 * q^39 - 3 * q^41 - q^43 + 6 * q^49 - 6 * q^51 - 12 * q^53 - 10 * q^57 - 9 * q^59 + q^61 + 2 * q^63 + 5 * q^67 - 9 * q^69 - 9 * q^71 - 4 * q^73 + 6 * q^77 + 16 * q^79 - q^81 - 9 * q^87 - 3 * q^89 - 5 * q^91 + 8 * q^93 + 17 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$		0			0
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$13$	−1.00000	−	3.46410i	−0.277350	−	0.960769i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$		0			0
$21$	−1.00000			−0.218218
$22$		0			0
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.169701	−	0.985496i	$-0.445720\pi$
$23$	4.50000	−	7.79423i	0.938315	−	1.62521i	0.768613	−	0.639713i	$-0.220947\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	−0.0578882	−	0.998323i	$-0.518437\pi$
$29$	4.50000	−	7.79423i	0.835629	−	1.44735i	0.893517	−	0.449029i	$-0.148230\pi$
$30$		0			0
$31$	8.00000			1.43684			0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000			1.43684			0.718421	+	0.695608i	$0.244865\pi$
$32$		0			0
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$		0			0
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$		0			0
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$		0			0
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$		0			0
$51$	−3.00000			−0.420084
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.00000			−0.662266
$58$		0			0
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$		0			0
$69$	−4.50000	−	7.79423i	−0.541736	−	0.938315i
$70$		0			0
$71$	−4.50000	−	7.79423i	−0.534052	−	0.925005i	−0.999209	−	0.0397765i	$-0.987335\pi$
$71$	−4.50000	−	7.79423i	−0.534052	−	0.925005i	0.465157	−	0.885228i	$-0.345998\pi$
$72$		0			0
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.00000			0.341882
$78$		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
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.50000	−	7.79423i	−0.482451	−	0.835629i
$88$		0			0
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$	−2.50000	+	2.59808i	−0.262071	+	0.272352i
$92$		0			0
$93$	4.00000	−	6.92820i	0.414781	−	0.718421i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	0.868976	+	0.494854i	$0.164778\pi$
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	−0.00593185	+	0.999982i	$0.501888\pi$
$98$		0			0
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	3.50000	+	6.06218i	0.332205	+	0.575396i
$112$		0			0
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.00000	−	5.19615i	0.462250	−	0.480384i
$118$		0			0
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	1.50000	+	2.59808i	0.135250	+	0.234261i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	8.50000	−	14.7224i	0.754253	−	1.30640i	−0.191492	−	0.981494i	$-0.561333\pi$
$127$	8.50000	−	14.7224i	0.754253	−	1.30640i	0.945745	−	0.324910i	$-0.105334\pi$
$128$		0			0
$129$	−1.00000			−0.0880451
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	10.5000	+	2.59808i	0.878054	+	0.217262i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$		0			0
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$		0			0
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$		0			0
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	−9.00000			−0.709299
$162$		0			0
$163$	−0.500000	−	0.866025i	−0.0391630	−	0.0678323i	0.845780	−	0.533533i	$-0.179136\pi$
$163$	−0.500000	−	0.866025i	−0.0391630	−	0.0678323i	−0.884943	+	0.465700i	$0.845802\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	0.415068	+	0.909790i	$0.363758\pi$
$167$	−7.50000	+	12.9904i	−0.580367	+	1.00523i	−0.995436	+	0.0954356i	$0.969576\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	5.00000	−	8.66025i	0.382360	−	0.662266i
$172$		0			0
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	0.920722	+	0.390218i	$0.127601\pi$
$173$	10.5000	+	18.1865i	0.798300	+	1.38270i	−0.122422	+	0.992478i	$0.539066\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.00000			−0.676481
$178$		0			0
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	0.436870	+	0.899525i	$0.356087\pi$
$179$	−7.50000	+	12.9904i	−0.560576	+	0.970947i	−0.997446	+	0.0714220i	$0.977246\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	1.00000			0.0739221
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.00000			0.658145
$188$		0			0
$189$	−2.50000	−	4.33013i	−0.181848	−	0.314970i
$190$		0			0
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	0.915177	−	0.403051i	$-0.132050\pi$
$191$	1.50000	+	2.59808i	0.108536	+	0.187990i	−0.806641	+	0.591041i	$0.798717\pi$
$192$		0			0
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	−0.761911	−	0.647682i	$-0.775738\pi$
$193$	2.50000	−	4.33013i	0.179954	−	0.311689i	0.941865	+	0.335993i	$0.109072\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	−0.914501	−	0.404584i	$-0.867416\pi$
$197$	−1.50000	+	2.59808i	−0.106871	+	0.185105i	0.807630	+	0.589689i	$0.200750\pi$
$198$		0			0
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	0.963001	−	0.269498i	$-0.0868577\pi$
$199$	3.50000	+	6.06218i	0.248108	+	0.429736i	−0.714893	+	0.699234i	$0.753524\pi$
$200$		0			0
$201$	−2.50000	−	4.33013i	−0.176336	−	0.305424i
$202$		0			0
$203$	−9.00000			−0.631676
$204$		0			0
$205$		0			0
$206$		0			0
$207$	18.0000			1.25109
$208$		0			0
$209$	15.0000			1.03757
$210$		0			0
$211$	12.5000	−	21.6506i	0.860535	−	1.49049i	−0.0108774	−	0.999941i	$-0.503462\pi$
$211$	12.5000	−	21.6506i	0.860535	−	1.49049i	0.871413	−	0.490550i	$-0.163204\pi$
$212$		0			0
$213$	−9.00000			−0.616670
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$		0			0
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$		0			0
$221$	−7.50000	+	7.79423i	−0.504505	+	0.524297i
$222$		0			0
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	0.999997	−	0.00254715i	$-0.000810783\pi$
$227$	7.50000	+	12.9904i	0.497792	+	0.862202i	−0.502204	+	0.864749i	$0.667477\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	1.50000	−	2.59808i	0.0986928	−	0.170941i
$232$		0			0
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	−0.952141	−	0.305661i	$-0.901123\pi$
$241$	−11.5000	−	19.9186i	−0.740780	−	1.28307i	0.211360	−	0.977408i	$-0.432211\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−12.5000	+	12.9904i	−0.795356	+	0.826558i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.50000	−	7.79423i	−0.284037	−	0.491967i	0.688338	−	0.725390i	$-0.258341\pi$
$251$	−4.50000	−	7.79423i	−0.284037	−	0.491967i	−0.972375	+	0.233423i	$0.925007\pi$
$252$		0			0
$253$	13.5000	+	23.3827i	0.848738	+	1.47006i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	0.0460033	+	0.998941i	$0.485352\pi$
$257$	−13.5000	+	23.3827i	−0.842107	+	1.45857i	−0.888110	+	0.459631i	$0.847982\pi$
$258$		0			0
$259$	7.00000			0.434959
$260$		0			0
$261$	18.0000			1.11417
$262$		0			0
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	−0.908560	−	0.417755i	$-0.862817\pi$
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	0.816066	+	0.577959i	$0.196151\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.50000	+	2.59808i	0.0917985	+	0.159000i
$268$		0			0
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	−0.598235	−	0.801321i	$-0.704131\pi$
$271$	6.50000	−	11.2583i	0.394847	−	0.683895i	0.993082	+	0.117426i	$0.0374643\pi$
$272$		0			0
$273$	1.00000	+	3.46410i	0.0605228	+	0.209657i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$		0			0
$279$	8.00000	+	13.8564i	0.478947	+	0.829561i
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$		0			0
$283$	8.50000	−	14.7224i	0.505273	−	0.875158i	−0.494709	−	0.869059i	$-0.664725\pi$
$283$	8.50000	−	14.7224i	0.505273	−	0.875158i	0.999981	−	0.00609896i	$-0.00194137\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.00000			0.177084
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	17.0000			0.996558
$292$		0			0
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	0.818878	−	0.573967i	$-0.194596\pi$
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	−0.906509	+	0.422186i	$0.861263\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−7.50000	+	12.9904i	−0.435194	+	0.753778i
$298$		0			0
$299$	−31.5000	−	7.79423i	−1.82169	−	0.450752i
$300$		0			0
$301$	−0.500000	+	0.866025i	−0.0288195	+	0.0499169i
$302$		0			0
$303$	7.50000	+	12.9904i	0.430864	+	0.746278i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$		0			0
$309$	−4.00000	+	6.92820i	−0.227552	+	0.394132i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$		0			0
$321$	1.50000	+	2.59808i	0.0837218	+	0.145010i
$322$		0			0
$323$	−7.50000	+	12.9904i	−0.417311	+	0.722804i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	7.00000	−	12.1244i	0.387101	−	0.670478i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	0.999667	+	0.0257885i	$0.00820965\pi$
$331$	9.50000	+	16.4545i	0.522167	+	0.904420i	−0.477500	+	0.878632i	$0.658457\pi$
$332$		0			0
$333$	−14.0000			−0.767195
$334$		0			0
$335$		0			0
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$		0			0
$339$	−15.0000			−0.814688
$340$		0			0
$341$	−12.0000	+	20.7846i	−0.649836	+	1.12555i
$342$		0			0
$343$	−13.0000			−0.701934
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	0.719590	−	0.694399i	$-0.244330\pi$
$347$	−4.50000	−	7.79423i	−0.241573	−	0.418416i	−0.961162	+	0.275983i	$0.910997\pi$
$348$		0			0
$349$	−17.5000	+	30.3109i	−0.936754	+	1.62250i	−0.165277	+	0.986247i	$0.552852\pi$
$349$	−17.5000	+	30.3109i	−0.936754	+	1.62250i	−0.771477	+	0.636257i	$0.780482\pi$
$350$		0			0
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$		0			0
$353$	−13.5000	+	23.3827i	−0.718532	+	1.24453i	0.243049	+	0.970014i	$0.421853\pi$
$353$	−13.5000	+	23.3827i	−0.718532	+	1.24453i	−0.961581	+	0.274521i	$0.911481\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.50000	+	2.59808i	0.0793884	+	0.137505i
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$		0			0
$371$	3.00000	+	5.19615i	0.155752	+	0.269771i
$372$		0			0
$373$	2.50000	+	4.33013i	0.129445	+	0.224205i	0.923462	−	0.383691i	$-0.125347\pi$
$373$	2.50000	+	4.33013i	0.129445	+	0.224205i	−0.794017	+	0.607896i	$0.792014\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−31.5000	−	7.79423i	−1.62233	−	0.401423i
$378$		0			0
$379$	−5.50000	+	9.52628i	−0.282516	+	0.489332i	−0.972004	−	0.234965i	$-0.924502\pi$
$379$	−5.50000	+	9.52628i	−0.282516	+	0.489332i	0.689488	+	0.724297i	$0.257836\pi$
$380$		0			0
$381$	−8.50000	−	14.7224i	−0.435468	−	0.754253i
$382$		0			0
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.00000	−	1.73205i	0.0508329	−	0.0880451i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	−27.0000			−1.36545
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	0.957839	+	0.287307i	$0.0927599\pi$
$397$	14.5000	+	25.1147i	0.727734	+	1.26047i	−0.230105	+	0.973166i	$0.573907\pi$
$398$		0			0
$399$	2.50000	+	4.33013i	0.125157	+	0.216777i
$400$		0			0
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	−0.990257	−	0.139253i	$-0.955530\pi$
$401$	−7.50000	+	12.9904i	−0.374532	+	0.648709i	0.615725	+	0.787961i	$0.288863\pi$
$402$		0			0
$403$	−8.00000	−	27.7128i	−0.398508	−	1.38047i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.5000	−	18.1865i	−0.520466	−	0.901473i
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$		0			0
$411$	−3.00000			−0.147979
$412$		0			0
$413$	−4.50000	+	7.79423i	−0.221431	+	0.383529i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−5.00000			−0.244851
$418$		0			0
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	−0.486928	−	0.873442i	$-0.661883\pi$
$419$	10.5000	−	18.1865i	0.512959	−	0.888470i	0.999887	−	0.0150285i	$-0.00478389\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.500000	−	0.866025i	0.0241967	−	0.0419099i
$428$		0			0
$429$	7.50000	−	7.79423i	0.362103	−	0.376309i
$430$		0			0
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	−0.899888	−	0.436121i	$-0.856352\pi$
$431$	−1.50000	+	2.59808i	−0.0722525	+	0.125145i	0.827636	+	0.561266i	$0.189685\pi$
$432$		0			0
$433$	2.50000	+	4.33013i	0.120142	+	0.208093i	0.919824	−	0.392332i	$-0.128332\pi$
$433$	2.50000	+	4.33013i	0.120142	+	0.208093i	−0.799681	+	0.600425i	$0.794998\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−45.0000			−2.15264
$438$		0			0
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	−0.853847	−	0.520524i	$-0.825737\pi$
$439$	0.500000	−	0.866025i	0.0238637	−	0.0413331i	0.877711	+	0.479191i	$0.159070\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$	−12.0000			−0.570137			−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000			−0.570137			−0.285069	+	0.958507i	$0.592016\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	9.00000			0.425685
$448$		0			0
$449$	−7.50000	−	12.9904i	−0.353947	−	0.613054i	0.632990	−	0.774160i	$-0.281827\pi$
$449$	−7.50000	−	12.9904i	−0.353947	−	0.613054i	−0.986937	+	0.161106i	$0.948494\pi$
$450$		0			0
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$		0			0
$453$	10.0000	−	17.3205i	0.469841	−	0.813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	20.5000	−	35.5070i	0.958950	−	1.66095i	0.233890	−	0.972263i	$-0.424854\pi$
$457$	20.5000	−	35.5070i	0.958950	−	1.66095i	0.725059	−	0.688686i	$-0.241812\pi$
$458$		0			0
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−5.00000			−0.230879
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$		0			0
$473$	3.00000			0.137940
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.00000	−	10.3923i	−0.274721	−	0.475831i
$478$		0			0
$479$	−7.50000	+	12.9904i	−0.342684	+	0.593546i	−0.984930	−	0.172953i	$-0.944669\pi$
$479$	−7.50000	+	12.9904i	−0.342684	+	0.593546i	0.642246	+	0.766498i	$0.278003\pi$
$480$		0			0
$481$	24.5000	+	6.06218i	1.11710	+	0.276412i
$482$		0			0
$483$	−4.50000	+	7.79423i	−0.204757	+	0.354650i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	17.5000	+	30.3109i	0.793001	+	1.37352i	0.924101	+	0.382148i	$0.124816\pi$
$487$	17.5000	+	30.3109i	0.793001	+	1.37352i	−0.131100	+	0.991369i	$0.541851\pi$
$488$		0			0
$489$	−1.00000			−0.0452216
$490$		0			0
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$		0			0
$493$	−27.0000			−1.21602
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.50000	+	7.79423i	−0.201853	+	0.349619i
$498$		0			0
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$	7.50000	+	12.9904i	0.335075	+	0.580367i
$502$		0			0
$503$	19.5000	+	33.7750i	0.869462	+	1.50595i	0.862547	+	0.505976i	$0.168868\pi$
$503$	19.5000	+	33.7750i	0.869462	+	1.50595i	0.00691465	+	0.999976i	$0.497799\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.500000	+	12.9904i	0.0222058	+	0.576923i
$508$		0			0
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	−0.224957	−	0.974369i	$-0.572224\pi$
$509$	16.5000	−	28.5788i	0.731350	−	1.26673i	0.956306	−	0.292366i	$-0.0944425\pi$
$510$		0			0
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$		0			0
$513$	−12.5000	−	21.6506i	−0.551888	−	0.955899i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	21.0000			0.921798
$520$		0			0
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	2.50000	−	4.33013i	0.109317	−	0.189343i	−0.806177	−	0.591675i	$-0.798467\pi$
$523$	2.50000	−	4.33013i	0.109317	−	0.189343i	0.915494	+	0.402332i	$0.131800\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000	−	20.7846i	−0.522728	−	0.905392i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$		0			0
$531$	9.00000	−	15.5885i	0.390567	−	0.676481i
$532$		0			0
$533$	10.5000	+	2.59808i	0.454805	+	0.112535i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	7.50000	+	12.9904i	0.323649	+	0.560576i
$538$		0			0
$539$	9.00000	+	15.5885i	0.387657	+	0.671442i
$540$		0			0
$541$	2.00000			0.0859867			0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000			0.0859867			0.0429934	+	0.999075i	$0.486311\pi$
$542$		0			0
$543$	−5.00000	+	8.66025i	−0.214571	+	0.371647i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	−45.0000			−1.91706
$552$		0			0
$553$	−4.00000	−	6.92820i	−0.170097	−	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	0.0747252	+	0.997204i	$0.476192\pi$
$557$	−19.5000	+	33.7750i	−0.826242	+	1.43109i	−0.900967	+	0.433888i	$0.857141\pi$
$558$		0			0
$559$	−2.50000	+	2.59808i	−0.105739	+	0.109887i
$560$		0			0
$561$	4.50000	−	7.79423i	0.189990	−	0.329073i
$562$		0			0
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	−0.970048	−	0.242912i	$-0.921897\pi$
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	0.274656	−	0.961542i	$-0.411436\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.00000			0.0419961
$568$		0			0
$569$	16.5000	−	28.5788i	0.691716	−	1.19809i	−0.279559	−	0.960128i	$-0.590188\pi$
$569$	16.5000	−	28.5788i	0.691716	−	1.19809i	0.971275	−	0.237959i	$-0.0764783\pi$
$570$		0			0
$571$	44.0000			1.84134			0.920671	−	0.390339i	$-0.127642\pi$
$571$	44.0000			1.84134			0.920671	+	0.390339i	$0.127642\pi$
$572$		0			0
$573$	3.00000			0.125327
$574$		0			0
$575$		0			0
$576$		0			0
$577$	22.0000			0.915872			0.457936	−	0.888985i	$-0.348589\pi$
$577$	22.0000			0.915872			0.457936	+	0.888985i	$0.348589\pi$
$578$		0			0
$579$	−2.50000	−	4.33013i	−0.103896	−	0.179954i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	0.440524	+	0.897741i	$0.354793\pi$
$587$	−13.5000	+	23.3827i	−0.557205	+	0.965107i	−0.997728	+	0.0673658i	$0.978541\pi$
$588$		0			0
$589$	−20.0000	−	34.6410i	−0.824086	−	1.42736i
$590$		0			0
$591$	1.50000	+	2.59808i	0.0617018	+	0.106871i
$592$		0			0
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.00000			0.286491
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$	10.0000			0.407231
$604$		0			0
$605$		0			0
$606$		0			0
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	0.999279	−	0.0379540i	$-0.0120840\pi$
$607$	11.5000	+	19.9186i	0.466771	+	0.808470i	−0.532509	+	0.846424i	$0.678751\pi$
$608$		0			0
$609$	−4.50000	+	7.79423i	−0.182349	+	0.315838i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	14.5000	−	25.1147i	0.585649	−	1.01437i	−0.409145	−	0.912470i	$-0.634173\pi$
$613$	14.5000	−	25.1147i	0.585649	−	1.01437i	0.994794	−	0.101905i	$-0.0324938\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	−0.998700	−	0.0509678i	$-0.983769\pi$
$617$	−13.5000	−	23.3827i	−0.543490	−	0.941351i	0.455211	−	0.890384i	$-0.349564\pi$
$618$		0			0
$619$	−28.0000			−1.12542			−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000			−1.12542			−0.562708	+	0.826656i	$0.690240\pi$
$620$		0			0
$621$	22.5000	−	38.9711i	0.902894	−	1.56386i
$622$		0			0
$623$	3.00000			0.120192
$624$		0			0
$625$		0			0
$626$		0			0
$627$	7.50000	−	12.9904i	0.299521	−	0.518786i
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	0.927244	−	0.374457i	$-0.122171\pi$
$631$	3.50000	+	6.06218i	0.139333	+	0.241331i	−0.787911	+	0.615789i	$0.788838\pi$
$632$		0			0
$633$	−12.5000	−	21.6506i	−0.496830	−	0.860535i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−21.0000	−	5.19615i	−0.832050	−	0.205879i
$638$		0			0
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$		0			0
$641$	−1.50000	−	2.59808i	−0.0592464	−	0.102618i	0.834881	−	0.550431i	$-0.185536\pi$
$641$	−1.50000	−	2.59808i	−0.0592464	−	0.102618i	−0.894127	+	0.447813i	$0.852203\pi$
$642$		0			0
$643$	−12.5000	−	21.6506i	−0.492952	−	0.853818i	0.507015	−	0.861937i	$-0.330749\pi$
$643$	−12.5000	−	21.6506i	−0.492952	−	0.853818i	−0.999967	+	0.00811944i	$0.997415\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−13.5000	+	23.3827i	−0.530740	+	0.919268i	0.468617	+	0.883402i	$0.344753\pi$
$647$	−13.5000	+	23.3827i	−0.530740	+	0.919268i	−0.999357	+	0.0358667i	$0.988581\pi$
$648$		0			0
$649$	27.0000			1.05984
$650$		0			0
$651$	−8.00000			−0.313545
$652$		0			0
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.00000	−	3.46410i	−0.0780274	−	0.135147i
$658$		0			0
$659$	−22.5000	−	38.9711i	−0.876476	−	1.51810i	−0.855183	−	0.518327i	$-0.826555\pi$
$659$	−22.5000	−	38.9711i	−0.876476	−	1.51810i	−0.0212930	−	0.999773i	$-0.506778\pi$
$660$		0			0
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	0.294105	+	0.955773i	$0.404978\pi$
$661$	−17.5000	+	30.3109i	−0.680671	+	1.17896i	−0.974776	+	0.223184i	$0.928355\pi$
$662$		0			0
$663$	3.00000	+	10.3923i	0.116510	+	0.403604i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−40.5000	−	70.1481i	−1.56817	−	2.71614i
$668$		0			0
$669$	9.50000	+	16.4545i	0.367291	+	0.636167i
$670$		0			0
$671$	−3.00000			−0.115814
$672$		0			0
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	−0.988968	−	0.148132i	$-0.952674\pi$
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	0.622770	+	0.782405i	$0.286007\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.0000			0.691796			0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000			0.691796			0.345898	+	0.938272i	$0.387574\pi$
$678$		0			0
$679$	8.50000	−	14.7224i	0.326200	−	0.564995i
$680$		0			0
$681$	15.0000			0.574801
$682$		0			0
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−11.0000	+	19.0526i	−0.419676	+	0.726900i
$688$		0			0
$689$	6.00000	+	20.7846i	0.228582	+	0.791831i
$690$		0			0
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	−0.997494	−	0.0707446i	$-0.977462\pi$
$691$	−11.5000	+	19.9186i	−0.437481	+	0.757739i	0.560014	+	0.828483i	$0.310796\pi$
$692$		0			0
$693$	3.00000	+	5.19615i	0.113961	+	0.197386i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.00000			0.340899
$698$		0			0
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	35.0000			1.32005
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.0000			0.564133
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$		0			0
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$	36.0000	−	62.3538i	1.34821	−	2.33517i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$		0			0
$719$	−22.5000	−	38.9711i	−0.839108	−	1.45338i	−0.890641	−	0.454707i	$-0.849744\pi$
$719$	−22.5000	−	38.9711i	−0.839108	−	1.45338i	0.0515326	−	0.998671i	$-0.483589\pi$
$720$		0			0
$721$	4.00000	+	6.92820i	0.148968	+	0.258020i
$722$		0			0
$723$	−23.0000			−0.855379
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$		0			0
$733$	34.0000			1.25582			0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000			1.25582			0.627909	+	0.778287i	$0.283911\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.50000	+	12.9904i	0.276266	+	0.478507i
$738$		0			0
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−5.50000	+	9.52628i	−0.202321	+	0.350430i	0.746955	+	0.664875i	$0.231515\pi$
$740$		0			0
$741$	5.00000	+	17.3205i	0.183680	+	0.636285i
$742$		0			0
$743$	16.5000	−	28.5788i	0.605326	−	1.04846i	−0.386674	−	0.922217i	$-0.626376\pi$
$743$	16.5000	−	28.5788i	0.605326	−	1.04846i	0.992000	−	0.126239i	$-0.0402907\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.00000			0.109618
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$	−9.00000			−0.327978
$754$		0			0
$755$		0			0
$756$		0			0
$757$	2.50000	−	4.33013i	0.0908640	−	0.157381i	−0.817011	−	0.576622i	$-0.804370\pi$
$757$	2.50000	−	4.33013i	0.0908640	−	0.157381i	0.907875	+	0.419241i	$0.137704\pi$
$758$		0			0
$759$	27.0000			0.980038
$760$		0			0
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	0.935988	−	0.352032i	$-0.114509\pi$
$761$	4.50000	+	7.79423i	0.163125	+	0.282541i	−0.772863	+	0.634573i	$0.781176\pi$
$762$		0			0
$763$	−7.00000	−	12.1244i	−0.253417	−	0.438931i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−22.5000	+	23.3827i	−0.812428	+	0.844300i
$768$		0			0
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$770$		0			0
$771$	13.5000	+	23.3827i	0.486191	+	0.842107i
$772$		0			0
$773$	−7.50000	−	12.9904i	−0.269756	−	0.467232i	0.699043	−	0.715080i	$-0.253610\pi$
$773$	−7.50000	−	12.9904i	−0.269756	−	0.467232i	−0.968799	+	0.247849i	$0.920276\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.50000	−	6.06218i	0.125562	−	0.217479i
$778$		0			0
$779$	15.0000			0.537431
$780$		0			0
$781$	27.0000			0.966136
$782$		0			0
$783$	22.5000	−	38.9711i	0.804084	−	1.39272i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−24.5000	−	42.4352i	−0.873331	−	1.51265i	−0.858530	−	0.512763i	$-0.828622\pi$
$787$	−24.5000	−	42.4352i	−0.873331	−	1.51265i	−0.0148003	−	0.999890i	$-0.504711\pi$
$788$		0			0
$789$	1.50000	+	2.59808i	0.0534014	+	0.0924940i
$790$		0			0
$791$	−7.50000	+	12.9904i	−0.266669	+	0.461885i
$792$		0			0
$793$	2.50000	−	2.59808i	0.0887776	−	0.0922604i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−6.00000			−0.212000
$802$		0			0
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	21.0000			0.739235
$808$		0			0
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	0.287670	+	0.957730i	$0.407120\pi$
$809$	−19.5000	+	33.7750i	−0.685583	+	1.18747i	−0.973253	+	0.229736i	$0.926214\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		0			0
$813$	−6.50000	−	11.2583i	−0.227965	−	0.394847i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.50000	+	4.33013i	−0.0874639	+	0.151492i
$818$		0			0
$819$	−7.00000	−	1.73205i	−0.244600	−	0.0605228i
$820$		0			0
$821$	10.5000	−	18.1865i	0.366453	−	0.634714i	−0.622556	−	0.782576i	$-0.713906\pi$
$821$	10.5000	−	18.1865i	0.366453	−	0.634714i	0.989008	+	0.147861i	$0.0472389\pi$
$822$		0			0
$823$	23.5000	+	40.7032i	0.819159	+	1.41882i	0.906303	+	0.422628i	$0.138892\pi$
$823$	23.5000	+	40.7032i	0.819159	+	1.41882i	−0.0871445	+	0.996196i	$0.527774\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		0			0
$831$	−19.0000			−0.659103
$832$		0			0
$833$	−18.0000			−0.623663
$834$		0			0
$835$		0			0
$836$		0			0
$837$	40.0000			1.38260
$838$		0			0
$839$	7.50000	+	12.9904i	0.258929	+	0.448478i	0.965955	−	0.258709i	$-0.0832972\pi$
$839$	7.50000	+	12.9904i	0.258929	+	0.448478i	−0.707026	+	0.707187i	$0.749964\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$		0			0
$843$	−9.00000	+	15.5885i	−0.309976	+	0.536895i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1.00000	−	1.73205i	0.0343604	−	0.0595140i
$848$		0			0
$849$	−8.50000	−	14.7224i	−0.291719	−	0.505273i
$850$		0			0
$851$	31.5000	+	54.5596i	1.07981	+	1.87028i
$852$		0			0
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$		0			0
$859$	8.00000			0.272956			0.136478	−	0.990643i	$-0.456422\pi$
$859$	8.00000			0.272956			0.136478	+	0.990643i	$0.456422\pi$
$860$		0			0
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$		0			0
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.00000	−	6.92820i	−0.135847	−	0.235294i
$868$		0			0
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	−17.5000	−	4.33013i	−0.592965	−	0.146721i
$872$		0			0
$873$	−17.0000	+	29.4449i	−0.575363	+	0.996558i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.50000	+	14.7224i	0.287025	+	0.497141i	0.973098	−	0.230391i	$-0.0740005\pi$
$877$	8.50000	+	14.7224i	0.287025	+	0.497141i	−0.686074	+	0.727532i	$0.740667\pi$
$878$		0			0
$879$	−3.00000			−0.101187
$880$		0			0
$881$	−1.50000	+	2.59808i	−0.0505363	+	0.0875314i	−0.890187	−	0.455595i	$-0.849426\pi$
$881$	−1.50000	+	2.59808i	−0.0505363	+	0.0875314i	0.839651	+	0.543127i	$0.182760\pi$
$882$		0			0
$883$	−56.0000			−1.88455			−0.942275	−	0.334840i	$-0.891318\pi$
$883$	−56.0000			−1.88455			−0.942275	+	0.334840i	$0.891318\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	−0.443964	−	0.896045i	$-0.646428\pi$
$887$	16.5000	−	28.5788i	0.554016	−	0.959583i	0.997979	−	0.0635387i	$-0.0202386\pi$
$888$		0			0
$889$	−17.0000			−0.570162
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−22.5000	+	23.3827i	−0.751253	+	0.780725i
$898$		0			0
$899$	36.0000	−	62.3538i	1.20067	−	2.07962i
$900$		0			0
$901$	9.00000	+	15.5885i	0.299833	+	0.519327i
$902$		0			0
$903$	0.500000	+	0.866025i	0.0166390	+	0.0288195i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−27.5000	+	47.6314i	−0.913123	+	1.58157i	−0.103495	+	0.994630i	$0.533003\pi$
$907$	−27.5000	+	47.6314i	−0.913123	+	1.58157i	−0.809627	+	0.586945i	$0.800331\pi$
$908$		0			0
$909$	−30.0000			−0.995037
$910$		0			0
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	0.917961	−	0.396670i	$-0.129834\pi$
$919$	3.50000	+	6.06218i	0.115454	+	0.199973i	−0.802507	+	0.596643i	$0.796501\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$	−22.5000	+	23.3827i	−0.740597	+	0.769650i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−8.00000	−	13.8564i	−0.262754	−	0.455104i
$928$		0			0
$929$	−1.50000	−	2.59808i	−0.0492134	−	0.0852401i	0.840369	−	0.542014i	$-0.182338\pi$
$929$	−1.50000	−	2.59808i	−0.0492134	−	0.0852401i	−0.889583	+	0.456774i	$0.849005\pi$
$930$		0			0
$931$	−30.0000			−0.983210
$932$		0			0
$933$	6.00000	−	10.3923i	0.196431	−	0.340229i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$		0			0
$939$	5.00000	−	8.66025i	0.163169	−	0.282617i
$940$		0			0
$941$	18.0000			0.586783			0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000			0.586783			0.293392	+	0.955992i	$0.405216\pi$
$942$		0			0
$943$	13.5000	+	23.3827i	0.439620	+	0.761445i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.5000	+	44.1673i	−0.828639	+	1.43524i	0.0704677	+	0.997514i	$0.477551\pi$
$947$	−25.5000	+	44.1673i	−0.828639	+	1.43524i	−0.899106	+	0.437730i	$0.855783\pi$
$948$		0			0
$949$	2.00000	+	6.92820i	0.0649227	+	0.224899i
$950$		0			0
$951$	9.00000	−	15.5885i	0.291845	−	0.505490i
$952$		0			0
$953$	10.5000	+	18.1865i	0.340128	+	0.589120i	0.984456	−	0.175630i	$-0.0561961\pi$
$953$	10.5000	+	18.1865i	0.340128	+	0.589120i	−0.644328	+	0.764749i	$0.722863\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	27.0000			0.872786
$958$		0			0
$959$	−1.50000	+	2.59808i	−0.0484375	+	0.0838963i
$960$		0			0
$961$	33.0000			1.06452
$962$		0			0
$963$	−6.00000			−0.193347
$964$		0			0
$965$		0			0
$966$		0			0
$967$	4.00000			0.128631			0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000			0.128631			0.0643157	+	0.997930i	$0.479514\pi$
$968$		0			0
$969$	7.50000	+	12.9904i	0.240935	+	0.417311i
$970$		0			0
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$		0			0
$973$	−2.50000	+	4.33013i	−0.0801463	+	0.138817i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	−0.889022	−	0.457864i	$-0.848615\pi$
$977$	−1.50000	+	2.59808i	−0.0479893	+	0.0831198i	0.841033	+	0.540984i	$0.181948\pi$
$978$		0			0
$979$	−4.50000	−	7.79423i	−0.143821	−	0.249105i
$980$		0			0
$981$	14.0000	+	24.2487i	0.446986	+	0.774202i
$982$		0			0
$983$	48.0000			1.53096			0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000			1.53096			0.765481	+	0.643458i	$0.222501\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.00000			−0.286183
$990$		0			0
$991$	24.5000	−	42.4352i	0.778268	−	1.34800i	−0.154671	−	0.987966i	$-0.549432\pi$
$991$	24.5000	−	42.4352i	0.778268	−	1.34800i	0.932939	−	0.360034i	$-0.117235\pi$
$992$		0			0
$993$	19.0000			0.602947
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.50000	+	4.33013i	0.0791758	+	0.137136i	0.902895	−	0.429862i	$-0.141438\pi$
$997$	2.50000	+	4.33013i	0.0791758	+	0.137136i	−0.823719	+	0.566999i	$0.808104\pi$
$998$		0			0
$999$	−17.5000	+	30.3109i	−0.553675	+	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.i.d.1101.1		2
5.2	odd	4		1300.2.bb.b.1049.1		4
5.3	odd	4		1300.2.bb.b.1049.2		4
5.4	even	2		260.2.i.a.61.1	✓	2
13.3	even	3	inner	1300.2.i.d.601.1		2
15.14	odd	2		2340.2.q.f.1621.1		2
20.19	odd	2		1040.2.q.i.321.1		2
65.3	odd	12		1300.2.bb.b.549.1		4
65.4	even	6		3380.2.a.i.1.1		1
65.9	even	6		3380.2.a.f.1.1		1
65.19	odd	12		3380.2.f.d.3041.2		2
65.29	even	6		260.2.i.a.81.1	yes	2
65.42	odd	12		1300.2.bb.b.549.2		4
65.59	odd	12		3380.2.f.d.3041.1		2
195.29	odd	6		2340.2.q.f.2161.1		2
260.159	odd	6		1040.2.q.i.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.i.a.61.1	✓	2	5.4	even	2
260.2.i.a.81.1	yes	2	65.29	even	6
1040.2.q.i.81.1		2	260.159	odd	6
1040.2.q.i.321.1		2	20.19	odd	2
1300.2.i.d.601.1		2	13.3	even	3	inner
1300.2.i.d.1101.1		2	1.1	even	1	trivial
1300.2.bb.b.549.1		4	65.3	odd	12
1300.2.bb.b.549.2		4	65.42	odd	12
1300.2.bb.b.1049.1		4	5.2	odd	4
1300.2.bb.b.1049.2		4	5.3	odd	4
2340.2.q.f.1621.1		2	15.14	odd	2
2340.2.q.f.2161.1		2	195.29	odd	6
3380.2.a.f.1.1		1	65.9	even	6
3380.2.a.i.1.1		1	65.4	even	6
3380.2.f.d.3041.1		2	65.59	odd	12
3380.2.f.d.3041.2		2	65.19	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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(-1.50000 - 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} -1.00000 q^{21} +(4.50000 - 7.79423i) q^{23} +5.00000 q^{27} +(4.50000 - 7.79423i) q^{29} +8.00000 q^{31} +(1.50000 + 2.59808i) q^{33} +(-3.50000 + 6.06218i) q^{37} +(-3.50000 - 0.866025i) q^{39} +(-1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{43} +(3.00000 - 5.19615i) q^{49} -3.00000 q^{51} -6.00000 q^{53} -5.00000 q^{57} +(-4.50000 - 7.79423i) q^{59} +(0.500000 + 0.866025i) q^{61} +(1.00000 - 1.73205i) q^{63} +(2.50000 - 4.33013i) q^{67} +(-4.50000 - 7.79423i) q^{69} +(-4.50000 - 7.79423i) q^{71} -2.00000 q^{73} +3.00000 q^{77} +8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{87} +(-1.50000 + 2.59808i) q^{89} +(-2.50000 + 2.59808i) q^{91} +(4.00000 - 6.92820i) q^{93} +(8.50000 + 14.7224i) q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 - q^7 + 2 * q^9	\( 2 q + q^{3} - q^{7} + 2 q^{9} - 3 q^{11} - 2 q^{13} - 3 q^{17} - 5 q^{19} - 2 q^{21} + 9 q^{23} + 10 q^{27} + 9 q^{29} + 16 q^{31} + 3 q^{33} - 7 q^{37} - 7 q^{39} - 3 q^{41} - q^{43} + 6 q^{49} - 6 q^{51} - 12 q^{53} - 10 q^{57} - 9 q^{59} + q^{61} + 2 q^{63} + 5 q^{67} - 9 q^{69} - 9 q^{71} - 4 q^{73} + 6 q^{77} + 16 q^{79} - q^{81} - 9 q^{87} - 3 q^{89} - 5 q^{91} + 8 q^{93} + 17 q^{97} - 12 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^7 + 2 * q^9 - 3 * q^11 - 2 * q^13 - 3 * q^17 - 5 * q^19 - 2 * q^21 + 9 * q^23 + 10 * q^27 + 9 * q^29 + 16 * q^31 + 3 * q^33 - 7 * q^37 - 7 * q^39 - 3 * q^41 - q^43 + 6 * q^49 - 6 * q^51 - 12 * q^53 - 10 * q^57 - 9 * q^59 + q^61 + 2 * q^63 + 5 * q^67 - 9 * q^69 - 9 * q^71 - 4 * q^73 + 6 * q^77 + 16 * q^79 - q^81 - 9 * q^87 - 3 * q^89 - 5 * q^91 + 8 * q^93 + 17 * q^97 - 12 * q^99

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