LMFDB - Embedded newform 1040.2.q.h.81.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(81,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.81"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,2,0,-3,0,3,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1040.81
Dual form			1040.2.q.h.321.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-3.50000 - 0.866025i) q^{13} +(2.00000 - 3.46410i) q^{17} +(3.50000 - 6.06218i) q^{19} +(-2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(4.00000 + 6.92820i) q^{29} +10.0000 q^{31} +(-1.50000 + 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.00000 + 1.73205i) q^{41} +(3.00000 - 5.19615i) q^{43} +(1.50000 - 2.59808i) q^{45} +1.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} -9.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(7.00000 - 12.1244i) q^{61} +(4.50000 + 7.79423i) q^{63} +(-3.50000 - 0.866025i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{71} +4.00000 q^{73} +9.00000 q^{77} -10.0000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{85} +(-0.500000 - 0.866025i) q^{89} +(7.50000 - 7.79423i) q^{91} +(3.50000 - 6.06218i) q^{95} +(-8.00000 + 13.8564i) q^{97} -9.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{5} - 3 q^{7} + 3 q^{9} - 3 q^{11} - 7 q^{13} + 4 q^{17} + 7 q^{19} - 4 q^{23} + 2 q^{25} + 8 q^{29} + 20 q^{31} - 3 q^{35} - 3 q^{37} + 2 q^{41} + 6 q^{43} + 3 q^{45} + 2 q^{47} - 2 q^{49} - 18 q^{53}+ \cdots - 18 q^{99}+O(q^{100}) $ 2 * q + 2 * q^5 - 3 * q^7 + 3 * q^9 - 3 * q^11 - 7 * q^13 + 4 * q^17 + 7 * q^19 - 4 * q^23 + 2 * q^25 + 8 * q^29 + 20 * q^31 - 3 * q^35 - 3 * q^37 + 2 * q^41 + 6 * q^43 + 3 * q^45 + 2 * q^47 - 2 * q^49 - 18 * q^53 - 3 * q^55 - 4 * q^59 + 14 * q^61 + 9 * q^63 - 7 * q^65 + 4 * q^67 + 6 * q^71 + 8 * q^73 + 18 * q^77 - 20 * q^79 - 9 * q^81 + 4 * q^85 - q^89 + 15 * q^91 + 7 * q^95 - 16 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	0.951224	+	0.308500i	$0.0998271\pi$
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	−0.208443	+	0.978035i	$0.566840\pi$
$30$		0			0
$31$	10.0000			1.79605			0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000			1.79605			0.898027	+	0.439941i	$0.145001\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$		0			0
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$		0			0
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$		0			0
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$		0			0
$47$	1.00000			0.145865			0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000			0.145865			0.0729325	+	0.997337i	$0.476764\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$	4.50000	+	7.79423i	0.566947	+	0.981981i
$64$		0			0
$65$	−3.50000	−	0.866025i	−0.434122	−	0.107417i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.00000			1.02565
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	0.838308	−	0.545197i	$-0.183545\pi$
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	−0.891308	+	0.453398i	$0.850212\pi$
$90$		0			0
$91$	7.50000	−	7.79423i	0.786214	−	0.817057i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.50000	−	6.06218i	0.359092	−	0.621966i
$96$		0			0
$97$	−8.00000	+	13.8564i	−0.812277	+	1.40690i	0.0989899	+	0.995088i	$0.468439\pi$
$97$	−8.00000	+	13.8564i	−0.812277	+	1.40690i	−0.911267	+	0.411816i	$0.864894\pi$
$98$		0			0
$99$	−9.00000			−0.904534
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	1.00000			0.0985329			0.0492665	−	0.998786i	$-0.484312\pi$
$103$	1.00000			0.0985329			0.0492665	+	0.998786i	$0.484312\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.861931	−	0.507026i	$-0.830745\pi$
$107$	−9.00000	−	15.5885i	−0.870063	−	1.50699i	−0.00813215	−	0.999967i	$-0.502589\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$		0			0
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$		0			0
$117$	−7.50000	+	7.79423i	−0.693375	+	0.720577i
$118$		0			0
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	6.50000	+	11.2583i	0.576782	+	0.999015i	0.995846	+	0.0910585i	$0.0290250\pi$
$127$	6.50000	+	11.2583i	0.576782	+	0.999015i	−0.419064	+	0.907957i	$0.637642\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.0000			−1.13582			−0.567908	−	0.823092i	$-0.692247\pi$
$131$	−13.0000			−1.13582			−0.567908	+	0.823092i	$0.692247\pi$
$132$		0			0
$133$	10.5000	+	18.1865i	0.910465	+	1.57697i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.00000	+	10.3923i	0.250873	+	0.869048i
$144$		0			0
$145$	4.00000	+	6.92820i	0.332182	+	0.575356i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		0			0
$153$	−6.00000	−	10.3923i	−0.485071	−	0.840168i
$154$		0			0
$155$	10.0000			0.803219
$156$		0			0
$157$	−3.00000			−0.239426			−0.119713	−	0.992809i	$-0.538197\pi$
$157$	−3.00000			−0.239426			−0.119713	+	0.992809i	$0.538197\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	12.0000			0.945732
$162$		0			0
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.50000	+	16.4545i	0.735132	+	1.27329i	0.954665	+	0.297681i	$0.0962132\pi$
$167$	9.50000	+	16.4545i	0.735132	+	1.27329i	−0.219533	+	0.975605i	$0.570453\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	−10.5000	−	18.1865i	−0.802955	−	1.39076i
$172$		0			0
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	−0.122422	−	0.992478i	$-0.539066\pi$
$173$	10.5000	−	18.1865i	0.798300	−	1.38270i	0.920722	−	0.390218i	$-0.127601\pi$
$174$		0			0
$175$	−1.50000	+	2.59808i	−0.113389	+	0.196396i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$		0			0
$187$	−12.0000			−0.877527
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	12.0000	+	20.7846i	0.863779	+	1.49611i	0.868255	+	0.496119i	$0.165242\pi$
$193$	12.0000	+	20.7846i	0.863779	+	1.49611i	−0.00447566	+	0.999990i	$0.501425\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−6.50000	−	11.2583i	−0.463106	−	0.802123i	0.536008	−	0.844213i	$-0.319932\pi$
$197$	−6.50000	−	11.2583i	−0.463106	−	0.802123i	−0.999114	+	0.0420901i	$0.986598\pi$
$198$		0			0
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	0.347879	+	0.937539i	$0.386902\pi$
$199$	−9.00000	+	15.5885i	−0.637993	+	1.10504i	−0.985873	+	0.167497i	$0.946431\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−24.0000			−1.68447
$204$		0			0
$205$	1.00000	+	1.73205i	0.0698430	+	0.120972i
$206$		0			0
$207$	−12.0000			−0.834058
$208$		0			0
$209$	−21.0000			−1.45260
$210$		0			0
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$		0			0
$217$	−15.0000	+	25.9808i	−1.01827	+	1.76369i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−10.0000	+	10.3923i	−0.672673	+	0.699062i
$222$		0			0
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$		0			0
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$		0			0
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$		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
$231$		0			0
$232$		0			0
$233$	−18.0000			−1.17922			−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000			−1.17922			−0.589610	+	0.807688i	$0.700718\pi$
$234$		0			0
$235$	1.00000			0.0652328
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$		0			0
$247$	−17.5000	+	18.1865i	−1.11350	+	1.15718i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	−0.232740	−	0.972539i	$-0.574769\pi$
$251$	11.5000	−	19.9186i	0.725874	−	1.25725i	0.958613	−	0.284711i	$-0.0918976\pi$
$252$		0			0
$253$	−6.00000	+	10.3923i	−0.377217	+	0.653359i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$	9.00000			0.559233
$260$		0			0
$261$	24.0000			1.48556
$262$		0			0
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	0.984272	−	0.176659i	$-0.0565291\pi$
$263$	5.50000	+	9.52628i	0.339145	+	0.587416i	−0.645128	+	0.764075i	$0.723196\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.50000	−	2.59808i	−0.0904534	−	0.156670i
$276$		0			0
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$		0			0
$279$	15.0000	−	25.9808i	0.898027	−	1.55543i
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$		0			0
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	0.579437	−	0.815017i	$-0.303272\pi$
$283$	−7.00000	−	12.1244i	−0.416107	−	0.720718i	−0.995544	+	0.0942988i	$0.969939\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.00000			−0.354169
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$	−2.00000	+	3.46410i	−0.116445	+	0.201688i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.00000	+	13.8564i	0.231326	+	0.801337i
$300$		0			0
$301$	9.00000	+	15.5885i	0.518751	+	0.898504i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.00000	−	12.1244i	0.400819	−	0.694239i
$306$		0			0
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$		0			0
$315$	4.50000	+	7.79423i	0.253546	+	0.439155i
$316$		0			0
$317$	31.0000			1.74113			0.870567	−	0.492050i	$-0.163752\pi$
$317$	31.0000			1.74113			0.870567	+	0.492050i	$0.163752\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−14.0000	−	24.2487i	−0.778981	−	1.34923i
$324$		0			0
$325$	−3.50000	−	0.866025i	−0.194145	−	0.0480384i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$		0			0
$333$	−9.00000			−0.493197
$334$		0			0
$335$	2.00000	+	3.46410i	0.109272	+	0.189264i
$336$		0			0
$337$	30.0000			1.63420			0.817102	−	0.576493i	$-0.195579\pi$
$337$	30.0000			1.63420			0.817102	+	0.576493i	$0.195579\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.0000	−	25.9808i	−0.812296	−	1.40694i
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	−0.996826	−	0.0796169i	$-0.974630\pi$
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	0.567363	+	0.823468i	$0.307964\pi$
$348$		0			0
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	0.996716	−	0.0809766i	$-0.0258039\pi$
$349$	8.00000	+	13.8564i	0.428230	+	0.741716i	−0.568486	+	0.822693i	$0.692471\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.0000			−0.527780			−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000			−0.527780			−0.263890	+	0.964553i	$0.585006\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$		0			0
$369$	6.00000			0.312348
$370$		0			0
$371$	13.5000	−	23.3827i	0.700885	−	1.21397i
$372$		0			0
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	−0.777847	−	0.628454i	$-0.783688\pi$
$373$	3.00000	−	5.19615i	0.155334	−	0.269047i	0.933181	+	0.359408i	$0.117021\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.00000	−	27.7128i	−0.412021	−	1.42728i
$378$		0			0
$379$	13.5000	+	23.3827i	0.693448	+	1.20109i	0.970701	+	0.240291i	$0.0772428\pi$
$379$	13.5000	+	23.3827i	0.693448	+	1.20109i	−0.277253	+	0.960797i	$0.589424\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	0.247451	+	0.968900i	$0.420407\pi$
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	−0.962818	+	0.270151i	$0.912926\pi$
$384$		0			0
$385$	9.00000			0.458682
$386$		0			0
$387$	−9.00000	−	15.5885i	−0.457496	−	0.792406i
$388$		0			0
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−10.0000			−0.503155
$396$		0			0
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	−0.472526	−	0.881317i	$-0.656658\pi$
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	0.999506	−	0.0314391i	$-0.0100090\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.5000	+	33.7750i	0.973784	+	1.68664i	0.683892	+	0.729583i	$0.260286\pi$
$401$	19.5000	+	33.7750i	0.973784	+	1.68664i	0.289891	+	0.957060i	$0.406381\pi$
$402$		0			0
$403$	−35.0000	−	8.66025i	−1.74347	−	0.431398i
$404$		0			0
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$		0			0
$407$	−4.50000	+	7.79423i	−0.223057	+	0.386346i
$408$		0			0
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.00000	−	10.3923i	−0.295241	−	0.511372i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$		0			0
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$		0			0
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	21.0000	+	36.3731i	1.01626	+	1.76022i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$		0			0
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	−0.991693	−	0.128624i	$-0.958944\pi$
$433$	−8.00000	+	13.8564i	−0.384455	+	0.665896i	0.607238	+	0.794520i	$0.292277\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−28.0000			−1.33942
$438$		0			0
$439$	−3.00000	−	5.19615i	−0.143182	−	0.247999i	0.785511	−	0.618848i	$-0.212400\pi$
$439$	−3.00000	−	5.19615i	−0.143182	−	0.247999i	−0.928693	+	0.370849i	$0.879067\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	18.0000			0.855206			0.427603	−	0.903967i	$-0.359358\pi$
$443$	18.0000			0.855206			0.427603	+	0.903967i	$0.359358\pi$
$444$		0			0
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	−0.632990	−	0.774160i	$-0.718173\pi$
$449$	7.50000	−	12.9904i	0.353947	−	0.613054i	0.986937	+	0.161106i	$0.0515060\pi$
$450$		0			0
$451$	3.00000	−	5.19615i	0.141264	−	0.244677i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.50000	−	7.79423i	0.351605	−	0.365399i
$456$		0			0
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	20.0000	−	34.6410i	0.931493	−	1.61339i	0.150721	−	0.988576i	$-0.451840\pi$
$461$	20.0000	−	34.6410i	0.931493	−	1.61339i	0.780771	−	0.624817i	$-0.214826\pi$
$462$		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
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	−12.0000			−0.554109
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.0000			−0.827641
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$		0			0
$477$	−13.5000	+	23.3827i	−0.618123	+	1.07062i
$478$		0			0
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$		0			0
$481$	3.00000	+	10.3923i	0.136788	+	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.00000	+	13.8564i	−0.363261	+	0.629187i
$486$		0			0
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	9.50000	−	16.4545i	0.430486	−	0.745624i	0.996915	+	0.0784867i	$0.0250088\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−21.5000	−	37.2391i	−0.970281	−	1.68058i	−0.694701	−	0.719299i	$-0.744463\pi$
$491$	−21.5000	−	37.2391i	−0.970281	−	1.68058i	−0.275581	−	0.961278i	$-0.588870\pi$
$492$		0			0
$493$	32.0000			1.44121
$494$		0			0
$495$	−9.00000			−0.404520
$496$		0			0
$497$	9.00000	+	15.5885i	0.403705	+	0.699238i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.5000	−	19.9186i	0.512760	−	0.888126i	−0.487131	−	0.873329i	$-0.661957\pi$
$503$	11.5000	−	19.9186i	0.512760	−	0.888126i	0.999891	−	0.0147968i	$-0.00471014\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.00000			0.0440653
$516$		0			0
$517$	−1.50000	−	2.59808i	−0.0659699	−	0.114263i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−31.0000			−1.35813			−0.679067	−	0.734076i	$-0.737616\pi$
$521$	−31.0000			−1.35813			−0.679067	+	0.734076i	$0.737616\pi$
$522$		0			0
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	0.999762	−	0.0218062i	$-0.00694167\pi$
$523$	11.0000	+	19.0526i	0.480996	+	0.833110i	−0.518766	+	0.854916i	$0.673608\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.0000	−	34.6410i	0.871214	−	1.50899i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	6.00000	+	10.3923i	0.260378	+	0.450988i
$532$		0			0
$533$	−2.00000	−	6.92820i	−0.0866296	−	0.300094i
$534$		0			0
$535$	−9.00000	−	15.5885i	−0.389104	−	0.673948i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	10.0000			0.429934			0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000			0.429934			0.214967	+	0.976621i	$0.431036\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$	−21.0000	−	36.3731i	−0.896258	−	1.55236i
$550$		0			0
$551$	56.0000			2.38568
$552$		0			0
$553$	15.0000	−	25.9808i	0.637865	−	1.10481i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.5000	+	26.8468i	0.656756	+	1.13753i	0.981450	+	0.191716i	$0.0614052\pi$
$557$	15.5000	+	26.8468i	0.656756	+	1.13753i	−0.324694	+	0.945819i	$0.605261\pi$
$558$		0			0
$559$	−15.0000	+	15.5885i	−0.634432	+	0.659321i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$	4.00000	−	6.92820i	0.168281	−	0.291472i
$566$		0			0
$567$	27.0000			1.13389
$568$		0			0
$569$	5.50000	+	9.52628i	0.230572	+	0.399362i	0.957977	−	0.286846i	$-0.0926069\pi$
$569$	5.50000	+	9.52628i	0.230572	+	0.399362i	−0.727405	+	0.686209i	$0.759274\pi$
$570$		0			0
$571$	37.0000			1.54840			0.774201	−	0.632940i	$-0.218152\pi$
$571$	37.0000			1.54840			0.774201	+	0.632940i	$0.218152\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.00000	−	3.46410i	−0.0834058	−	0.144463i
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	13.5000	+	23.3827i	0.559113	+	0.968412i
$584$		0			0
$585$	−7.50000	+	7.79423i	−0.310087	+	0.322252i
$586$		0			0
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	0.844650	−	0.535319i	$-0.179808\pi$
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	−0.885925	+	0.463829i	$0.846475\pi$
$588$		0			0
$589$	35.0000	−	60.6218i	1.44215	−	2.49788i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.0000			0.821302			0.410651	−	0.911793i	$-0.365302\pi$
$593$	20.0000			0.821302			0.410651	+	0.911793i	$0.365302\pi$
$594$		0			0
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.0000			−1.06233			−0.531166	−	0.847268i	$-0.678246\pi$
$599$	−26.0000			−1.06233			−0.531166	+	0.847268i	$0.678246\pi$
$600$		0			0
$601$	−2.50000	−	4.33013i	−0.101977	−	0.176630i	0.810522	−	0.585708i	$-0.199184\pi$
$601$	−2.50000	−	4.33013i	−0.101977	−	0.176630i	−0.912499	+	0.409079i	$0.865850\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$		0			0
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	10.5000	−	18.1865i	0.426182	−	0.738169i	−0.570348	−	0.821403i	$-0.693192\pi$
$607$	10.5000	−	18.1865i	0.426182	−	0.738169i	0.996530	+	0.0832344i	$0.0265250\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.50000	−	0.866025i	−0.141595	−	0.0350356i
$612$		0			0
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	−0.555056	−	0.831813i	$-0.687303\pi$
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	0.997899	+	0.0647859i	$0.0206365\pi$
$618$		0			0
$619$	3.00000			0.120580			0.0602901	−	0.998181i	$-0.480797\pi$
$619$	3.00000			0.120580			0.0602901	+	0.998181i	$0.480797\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.00000			0.120192
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−18.0000	+	31.1769i	−0.716569	+	1.24113i	0.245783	+	0.969325i	$0.420955\pi$
$631$	−18.0000	+	31.1769i	−0.716569	+	1.24113i	−0.962351	+	0.271808i	$0.912378\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.50000	+	11.2583i	0.257945	+	0.446773i
$636$		0			0
$637$	2.00000	+	6.92820i	0.0792429	+	0.274505i
$638$		0			0
$639$	−9.00000	−	15.5885i	−0.356034	−	0.616670i
$640$		0			0
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	−0.763367	−	0.645966i	$-0.776455\pi$
$641$	4.50000	−	7.79423i	0.177739	−	0.307854i	0.941106	+	0.338112i	$0.109788\pi$
$642$		0			0
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.50000	−	6.06218i	−0.137599	−	0.238329i	0.788988	−	0.614408i	$-0.210605\pi$
$647$	−3.50000	−	6.06218i	−0.137599	−	0.238329i	−0.926587	+	0.376080i	$0.877272\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.50000	+	9.52628i	0.215232	+	0.372792i	0.953344	−	0.301885i	$-0.0976160\pi$
$653$	5.50000	+	9.52628i	0.215232	+	0.372792i	−0.738113	+	0.674678i	$0.764283\pi$
$654$		0			0
$655$	−13.0000			−0.507952
$656$		0			0
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$		0			0
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.5000	+	18.1865i	0.407173	+	0.705244i
$666$		0			0
$667$	16.0000	−	27.7128i	0.619522	−	1.07304i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−42.0000			−1.62139
$672$		0			0
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	0.932763	−	0.360489i	$-0.117390\pi$
$673$	4.00000	+	6.92820i	0.154189	+	0.267063i	−0.778575	+	0.627552i	$0.784057\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−50.0000			−1.92166			−0.960828	−	0.277145i	$-0.910612\pi$
$677$	−50.0000			−1.92166			−0.960828	+	0.277145i	$0.910612\pi$
$678$		0			0
$679$	−24.0000	−	41.5692i	−0.921035	−	1.59528i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.00000	+	1.73205i	−0.0382639	+	0.0662751i	−0.884523	−	0.466496i	$-0.845516\pi$
$683$	−1.00000	+	1.73205i	−0.0382639	+	0.0662751i	0.846259	+	0.532771i	$0.178849\pi$
$684$		0			0
$685$	−6.00000	+	10.3923i	−0.229248	+	0.397070i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	31.5000	+	7.79423i	1.20005	+	0.296936i
$690$		0			0
$691$	14.5000	+	25.1147i	0.551606	+	0.955410i	0.998159	+	0.0606524i	$0.0193181\pi$
$691$	14.5000	+	25.1147i	0.551606	+	0.955410i	−0.446553	+	0.894757i	$0.647349\pi$
$692$		0			0
$693$	13.5000	−	23.3827i	0.512823	−	0.888235i
$694$		0			0
$695$	−2.50000	+	4.33013i	−0.0948304	+	0.164251i
$696$		0			0
$697$	8.00000			0.303022
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−40.0000			−1.51078			−0.755390	−	0.655276i	$-0.772552\pi$
$701$	−40.0000			−1.51078			−0.755390	+	0.655276i	$0.772552\pi$
$702$		0			0
$703$	−21.0000			−0.792030
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$		0			0
$711$	−15.0000	+	25.9808i	−0.562544	+	0.974355i
$712$		0			0
$713$	−20.0000	−	34.6410i	−0.749006	−	1.29732i
$714$		0			0
$715$	3.00000	+	10.3923i	0.112194	+	0.388650i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	14.0000	−	24.2487i	0.522112	−	0.904324i	−0.477557	−	0.878601i	$-0.658478\pi$
$719$	14.0000	−	24.2487i	0.522112	−	0.904324i	0.999669	−	0.0257237i	$-0.00818900\pi$
$720$		0			0
$721$	−1.50000	+	2.59808i	−0.0558629	+	0.0967574i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$		0			0
$727$	−35.0000			−1.29808			−0.649039	−	0.760755i	$-0.724829\pi$
$727$	−35.0000			−1.29808			−0.649039	+	0.760755i	$0.724829\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	−1.00000			−0.0369358			−0.0184679	−	0.999829i	$-0.505879\pi$
$733$	−1.00000			−0.0369358			−0.0184679	+	0.999829i	$0.505879\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	19.5000	+	33.7750i	0.717319	+	1.24243i	0.962058	+	0.272844i	$0.0879643\pi$
$739$	19.5000	+	33.7750i	0.717319	+	1.24243i	−0.244739	+	0.969589i	$0.578702\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4.00000	−	6.92820i	−0.146746	−	0.254171i	0.783277	−	0.621673i	$-0.213547\pi$
$743$	−4.00000	−	6.92820i	−0.146746	−	0.254171i	−0.930023	+	0.367502i	$0.880213\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	54.0000			1.97312
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.00000			0.0727875
$756$		0			0
$757$	14.5000	+	25.1147i	0.527011	+	0.912811i	0.999505	+	0.0314762i	$0.0100208\pi$
$757$	14.5000	+	25.1147i	0.527011	+	0.912811i	−0.472493	+	0.881334i	$0.656646\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	−0.991152	−	0.132734i	$-0.957624\pi$
$761$	−10.5000	+	18.1865i	−0.380625	+	0.659261i	0.610527	+	0.791995i	$0.290958\pi$
$762$		0			0
$763$	3.00000	−	5.19615i	0.108607	−	0.188113i
$764$		0			0
$765$	−6.00000	−	10.3923i	−0.216930	−	0.375735i
$766$		0			0
$767$	10.0000	−	10.3923i	0.361079	−	0.375244i
$768$		0			0
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	0.883493	−	0.468445i	$-0.155186\pi$
$769$	1.00000	+	1.73205i	0.0360609	+	0.0624593i	−0.847432	+	0.530904i	$0.821852\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.5000	+	26.8468i	−0.557496	+	0.965612i	0.440208	+	0.897896i	$0.354905\pi$
$773$	−15.5000	+	26.8468i	−0.557496	+	0.965612i	−0.997705	+	0.0677162i	$0.978429\pi$
$774$		0			0
$775$	10.0000			0.359211
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.0000			0.501602
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.00000			−0.107075
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.0000	+	20.7846i	0.426671	+	0.739016i
$792$		0			0
$793$	−35.0000	+	36.3731i	−1.24289	+	1.29165i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$		0			0
$799$	2.00000	−	3.46410i	0.0707549	−	0.122551i
$800$		0			0
$801$	−3.00000			−0.106000
$802$		0			0
$803$	−6.00000	−	10.3923i	−0.211735	−	0.366736i
$804$		0			0
$805$	12.0000			0.422944
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	0.940435	−	0.339975i	$-0.110418\pi$
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	−0.764644	+	0.644453i	$0.777085\pi$
$810$		0			0
$811$	−21.0000			−0.737410			−0.368705	−	0.929547i	$-0.620199\pi$
$811$	−21.0000			−0.737410			−0.368705	+	0.929547i	$0.620199\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$		0			0
$817$	−21.0000	−	36.3731i	−0.734697	−	1.27253i
$818$		0			0
$819$	−9.00000	−	31.1769i	−0.314485	−	1.08941i
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	−18.5000	+	32.0429i	−0.644869	+	1.11695i	0.339462	+	0.940620i	$0.389755\pi$
$823$	−18.5000	+	32.0429i	−0.644869	+	1.11695i	−0.984332	+	0.176327i	$0.943578\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−30.0000			−1.04320			−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000			−1.04320			−0.521601	+	0.853189i	$0.674665\pi$
$828$		0			0
$829$	14.0000	+	24.2487i	0.486240	+	0.842193i	0.999875	−	0.0158163i	$-0.00503471\pi$
$829$	14.0000	+	24.2487i	0.486240	+	0.842193i	−0.513635	+	0.858009i	$0.671701\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.00000			−0.277184
$834$		0			0
$835$	9.50000	+	16.4545i	0.328761	+	0.569431i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−13.0000	+	22.5167i	−0.448810	+	0.777361i	−0.998309	−	0.0581329i	$-0.981485\pi$
$839$	−13.0000	+	22.5167i	−0.448810	+	0.777361i	0.549499	+	0.835494i	$0.314819\pi$
$840$		0			0
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.5000	+	6.06218i	0.395612	+	0.208545i
$846$		0			0
$847$	3.00000	+	5.19615i	0.103081	+	0.178542i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		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
$855$	−10.5000	−	18.1865i	−0.359092	−	0.621966i
$856$		0			0
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$		0			0
$859$	1.00000			0.0341196			0.0170598	−	0.999854i	$-0.494569\pi$
$859$	1.00000			0.0341196			0.0170598	+	0.999854i	$0.494569\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.0000			1.08929			0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000			1.08929			0.544646	+	0.838666i	$0.316664\pi$
$864$		0			0
$865$	10.5000	−	18.1865i	0.357011	−	0.618361i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	15.0000	+	25.9808i	0.508840	+	0.881337i
$870$		0			0
$871$	−4.00000	−	13.8564i	−0.135535	−	0.469506i
$872$		0			0
$873$	24.0000	+	41.5692i	0.812277	+	1.40690i
$874$		0			0
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		0			0
$877$	17.0000	−	29.4449i	0.574049	−	0.994282i	−0.422095	−	0.906552i	$-0.638705\pi$
$877$	17.0000	−	29.4449i	0.574049	−	0.994282i	0.996144	−	0.0877308i	$-0.0279615\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−2.50000	−	4.33013i	−0.0842271	−	0.145886i	0.820834	−	0.571166i	$-0.193509\pi$
$881$	−2.50000	−	4.33013i	−0.0842271	−	0.145886i	−0.905062	+	0.425280i	$0.860175\pi$
$882$		0			0
$883$	26.0000			0.874970			0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000			0.874970			0.437485	+	0.899226i	$0.355869\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.50000	−	11.2583i	−0.218249	−	0.378018i	0.736024	−	0.676955i	$-0.236701\pi$
$887$	−6.50000	−	11.2583i	−0.218249	−	0.378018i	−0.954273	+	0.298938i	$0.903368\pi$
$888$		0			0
$889$	−39.0000			−1.30802
$890$		0			0
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$		0			0
$893$	3.50000	−	6.06218i	0.117123	−	0.202863i
$894$		0			0
$895$	2.00000	+	3.46410i	0.0668526	+	0.115792i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	40.0000	+	69.2820i	1.33407	+	2.31069i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.0000			−0.465376
$906$		0			0
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	0.770996	−	0.636841i	$-0.219759\pi$
$907$	−5.00000	−	8.66025i	−0.166022	−	0.287559i	−0.937018	+	0.349281i	$0.886426\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	19.5000	−	33.7750i	0.643947	−	1.11535i
$918$		0			0
$919$	25.0000	−	43.3013i	0.824674	−	1.42838i	−0.0774944	−	0.996993i	$-0.524692\pi$
$919$	25.0000	−	43.3013i	0.824674	−	1.42838i	0.902168	−	0.431384i	$-0.141975\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−15.0000	+	15.5885i	−0.493731	+	0.513100i
$924$		0			0
$925$	−1.50000	−	2.59808i	−0.0493197	−	0.0854242i
$926$		0			0
$927$	1.50000	−	2.59808i	0.0492665	−	0.0853320i
$928$		0			0
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		0			0
$931$	−14.0000			−0.458831
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−12.0000			−0.392442
$936$		0			0
$937$	14.0000			0.457360			0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000			0.457360			0.228680	+	0.973502i	$0.426559\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.0000			−0.782378			−0.391189	−	0.920310i	$-0.627936\pi$
$941$	−24.0000			−0.782378			−0.391189	+	0.920310i	$0.627936\pi$
$942$		0			0
$943$	4.00000	−	6.92820i	0.130258	−	0.225613i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.0000	+	32.9090i	0.617417	+	1.06940i	0.989955	+	0.141381i	$0.0451542\pi$
$947$	19.0000	+	32.9090i	0.617417	+	1.06940i	−0.372538	+	0.928017i	$0.621512\pi$
$948$		0			0
$949$	−14.0000	−	3.46410i	−0.454459	−	0.112449i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	−0.631019	−	0.775768i	$-0.717363\pi$
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	0.987344	+	0.158595i	$0.0506963\pi$
$954$		0			0
$955$	−3.00000	+	5.19615i	−0.0970777	+	0.168144i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$		0			0
$961$	69.0000			2.22581
$962$		0			0
$963$	−54.0000			−1.74013
$964$		0			0
$965$	12.0000	+	20.7846i	0.386294	+	0.669080i
$966$		0			0
$967$	33.0000			1.06121			0.530604	−	0.847620i	$-0.321965\pi$
$967$	33.0000			1.06121			0.530604	+	0.847620i	$0.321965\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−24.5000	+	42.4352i	−0.786242	+	1.36181i	0.142012	+	0.989865i	$0.454643\pi$
$971$	−24.5000	+	42.4352i	−0.786242	+	1.36181i	−0.928254	+	0.371947i	$0.878690\pi$
$972$		0			0
$973$	−7.50000	−	12.9904i	−0.240439	−	0.416452i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	0.991618	−	0.129205i	$-0.0412426\pi$
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	−0.607704	+	0.794164i	$0.707909\pi$
$978$		0			0
$979$	−1.50000	+	2.59808i	−0.0479402	+	0.0830349i
$980$		0			0
$981$	−3.00000	+	5.19615i	−0.0957826	+	0.165900i
$982$		0			0
$983$	3.00000			0.0956851			0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000			0.0956851			0.0478426	+	0.998855i	$0.484765\pi$
$984$		0			0
$985$	−6.50000	−	11.2583i	−0.207107	−	0.358720i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.00000	+	15.5885i	−0.285319	+	0.494187i
$996$		0			0
$997$	5.50000	−	9.52628i	0.174187	−	0.301700i	−0.765693	−	0.643206i	$-0.777604\pi$
$997$	5.50000	−	9.52628i	0.174187	−	0.301700i	0.939880	+	0.341506i	$0.110937\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.q.h.81.1		2
4.3	odd	2		130.2.e.a.81.1	yes	2
12.11	even	2		1170.2.i.i.991.1		2
13.9	even	3	inner	1040.2.q.h.321.1		2
20.3	even	4		650.2.o.d.549.1		4
20.7	even	4		650.2.o.d.549.2		4
20.19	odd	2		650.2.e.b.601.1		2
52.3	odd	6		1690.2.a.h.1.1		1
52.7	even	12		1690.2.l.e.1161.1		4
52.11	even	12		1690.2.d.c.1351.2		2
52.15	even	12		1690.2.d.c.1351.1		2
52.19	even	12		1690.2.l.e.1161.2		4
52.23	odd	6		1690.2.a.c.1.1		1
52.31	even	4		1690.2.l.e.361.1		4
52.35	odd	6		130.2.e.a.61.1	✓	2
52.43	odd	6		1690.2.e.h.191.1		2
52.47	even	4		1690.2.l.e.361.2		4
52.51	odd	2		1690.2.e.h.991.1		2
156.35	even	6		1170.2.i.i.451.1		2
260.87	even	12		650.2.o.d.399.1		4
260.139	odd	6		650.2.e.b.451.1		2
260.159	odd	6		8450.2.a.g.1.1		1
260.179	odd	6		8450.2.a.q.1.1		1
260.243	even	12		650.2.o.d.399.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.e.a.61.1	✓	2	52.35	odd	6
130.2.e.a.81.1	yes	2	4.3	odd	2
650.2.e.b.451.1		2	260.139	odd	6
650.2.e.b.601.1		2	20.19	odd	2
650.2.o.d.399.1		4	260.87	even	12
650.2.o.d.399.2		4	260.243	even	12
650.2.o.d.549.1		4	20.3	even	4
650.2.o.d.549.2		4	20.7	even	4
1040.2.q.h.81.1		2	1.1	even	1	trivial
1040.2.q.h.321.1		2	13.9	even	3	inner
1170.2.i.i.451.1		2	156.35	even	6
1170.2.i.i.991.1		2	12.11	even	2
1690.2.a.c.1.1		1	52.23	odd	6
1690.2.a.h.1.1		1	52.3	odd	6
1690.2.d.c.1351.1		2	52.15	even	12
1690.2.d.c.1351.2		2	52.11	even	12
1690.2.e.h.191.1		2	52.43	odd	6
1690.2.e.h.991.1		2	52.51	odd	2
1690.2.l.e.361.1		4	52.31	even	4
1690.2.l.e.361.2		4	52.47	even	4
1690.2.l.e.1161.1		4	52.7	even	12
1690.2.l.e.1161.2		4	52.19	even	12
8450.2.a.g.1.1		1	260.159	odd	6
8450.2.a.q.1.1		1	260.179	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(-3.50000 - 0.866025i) q^{13} +(2.00000 - 3.46410i) q^{17} +(3.50000 - 6.06218i) q^{19} +(-2.00000 - 3.46410i) q^{23} +1.00000 q^{25} +(4.00000 + 6.92820i) q^{29} +10.0000 q^{31} +(-1.50000 + 2.59808i) q^{35} +(-1.50000 - 2.59808i) q^{37} +(1.00000 + 1.73205i) q^{41} +(3.00000 - 5.19615i) q^{43} +(1.50000 - 2.59808i) q^{45} +1.00000 q^{47} +(-1.00000 - 1.73205i) q^{49} -9.00000 q^{53} +(-1.50000 - 2.59808i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(7.00000 - 12.1244i) q^{61} +(4.50000 + 7.79423i) q^{63} +(-3.50000 - 0.866025i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{71} +4.00000 q^{73} +9.00000 q^{77} -10.0000 q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{85} +(-0.500000 - 0.866025i) q^{89} +(7.50000 - 7.79423i) q^{91} +(3.50000 - 6.06218i) q^{95} +(-8.00000 + 13.8564i) q^{97} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} - 3 q^{7} + 3 q^{9} - 3 q^{11} - 7 q^{13} + 4 q^{17} + 7 q^{19} - 4 q^{23} + 2 q^{25} + 8 q^{29} + 20 q^{31} - 3 q^{35} - 3 q^{37} + 2 q^{41} + 6 q^{43} + 3 q^{45} + 2 q^{47} - 2 q^{49} - 18 q^{53}+ \cdots - 18 q^{99}+O(q^{100}) \) 2 * q + 2 * q^5 - 3 * q^7 + 3 * q^9 - 3 * q^11 - 7 * q^13 + 4 * q^17 + 7 * q^19 - 4 * q^23 + 2 * q^25 + 8 * q^29 + 20 * q^31 - 3 * q^35 - 3 * q^37 + 2 * q^41 + 6 * q^43 + 3 * q^45 + 2 * q^47 - 2 * q^49 - 18 * q^53 - 3 * q^55 - 4 * q^59 + 14 * q^61 + 9 * q^63 - 7 * q^65 + 4 * q^67 + 6 * q^71 + 8 * q^73 + 18 * q^77 - 20 * q^79 - 9 * q^81 + 4 * q^85 - q^89 + 15 * q^91 + 7 * q^95 - 16 * q^97 - 18 * q^99

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