LMFDB - Embedded newform 320.2.q.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [320,2,Mod(49,320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("320.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(320, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	320.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.55521286468$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	320.49
Dual form			320.2.q.a.209.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{9} +(3.00000 + 3.00000i) q^{11} +(3.00000 + 3.00000i) q^{13} +(1.00000 - 3.00000i) q^{15} -4.00000i q^{17} +(1.00000 - 1.00000i) q^{19} +8.00000 q^{23} +(-3.00000 + 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +(3.00000 - 3.00000i) q^{29} -6.00000i q^{33} +(3.00000 - 3.00000i) q^{37} -6.00000i q^{39} +(-3.00000 + 3.00000i) q^{43} +(2.00000 - 1.00000i) q^{45} +2.00000i q^{47} -7.00000 q^{49} +(-4.00000 + 4.00000i) q^{51} +(-9.00000 + 9.00000i) q^{53} +(-3.00000 + 9.00000i) q^{55} -2.00000 q^{57} +(-9.00000 - 9.00000i) q^{59} +(-5.00000 + 5.00000i) q^{61} +(-3.00000 + 9.00000i) q^{65} +(3.00000 + 3.00000i) q^{67} +(-8.00000 - 8.00000i) q^{69} -6.00000i q^{71} +6.00000 q^{73} +(7.00000 - 1.00000i) q^{75} -8.00000 q^{79} +5.00000 q^{81} +(-9.00000 - 9.00000i) q^{83} +(8.00000 - 4.00000i) q^{85} -6.00000 q^{87} -12.0000i q^{89} +(3.00000 + 1.00000i) q^{95} +12.0000i q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{5} + 6 q^{11} + 6 q^{13} + 2 q^{15} + 2 q^{19} + 16 q^{23} - 6 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{37} - 6 q^{43} + 4 q^{45} - 14 q^{49} - 8 q^{51} - 18 q^{53} - 6 q^{55} - 4 q^{57}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^5 + 6 * q^11 + 6 * q^13 + 2 * q^15 + 2 * q^19 + 16 * q^23 - 6 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^37 - 6 * q^43 + 4 * q^45 - 14 * q^49 - 8 * q^51 - 18 * q^53 - 6 * q^55 - 4 * q^57 - 18 * q^59 - 10 * q^61 - 6 * q^65 + 6 * q^67 - 16 * q^69 + 12 * q^73 + 14 * q^75 - 16 * q^79 + 10 * q^81 - 18 * q^83 + 16 * q^85 - 12 * q^87 + 6 * q^95 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$		0			0
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	3.00000	+	3.00000i	0.904534	+	0.904534i	0.995824	−	0.0912903i	$-0.0290991\pi$
$11$	3.00000	+	3.00000i	0.904534	+	0.904534i	−0.0912903	+	0.995824i	$0.529099\pi$
$12$		0			0
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	0.987797	−	0.155747i	$-0.0497784\pi$
$13$	3.00000	+	3.00000i	0.832050	+	0.832050i	−0.155747	+	0.987797i	$0.549778\pi$
$14$		0			0
$15$	1.00000	−	3.00000i	0.258199	−	0.774597i
$16$		0			0
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		0			0
$19$	1.00000	−	1.00000i	0.229416	−	0.229416i	−0.583033	−	0.812449i	$-0.698134\pi$
$19$	1.00000	−	1.00000i	0.229416	−	0.229416i	0.812449	+	0.583033i	$0.198134\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	−0.371391	−	0.928477i	$-0.621119\pi$
$29$	3.00000	−	3.00000i	0.557086	−	0.557086i	0.928477	+	0.371391i	$0.121119\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$		−	6.00000i		−	1.04447i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$		0			0
$39$		−	6.00000i		−	0.960769i
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	−0.897833	−	0.440337i	$-0.854859\pi$
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	0.440337	+	0.897833i	$0.354859\pi$
$44$		0			0
$45$	2.00000	−	1.00000i	0.298142	−	0.149071i
$46$		0			0
$47$			2.00000i			0.291730i	0.989305	+	0.145865i	$0.0465965\pi$
$47$			2.00000i			0.291730i	−0.989305	+	0.145865i	$0.953403\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$	−4.00000	+	4.00000i	−0.560112	+	0.560112i
$52$		0			0
$53$	−9.00000	+	9.00000i	−1.23625	+	1.23625i	−0.274721	+	0.961524i	$0.588586\pi$
$53$	−9.00000	+	9.00000i	−1.23625	+	1.23625i	−0.961524	+	0.274721i	$0.911414\pi$
$54$		0			0
$55$	−3.00000	+	9.00000i	−0.404520	+	1.21356i
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	−9.00000	−	9.00000i	−1.17170	−	1.17170i	−0.981804	−	0.189896i	$-0.939185\pi$
$59$	−9.00000	−	9.00000i	−1.17170	−	1.17170i	−0.189896	−	0.981804i	$-0.560815\pi$
$60$		0			0
$61$	−5.00000	+	5.00000i	−0.640184	+	0.640184i	−0.950601	−	0.310416i	$-0.899532\pi$
$61$	−5.00000	+	5.00000i	−0.640184	+	0.640184i	0.310416	+	0.950601i	$0.399532\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.00000	+	9.00000i	−0.372104	+	1.11631i
$66$		0			0
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	0.866202	−	0.499694i	$-0.166554\pi$
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	−0.499694	+	0.866202i	$0.666554\pi$
$68$		0			0
$69$	−8.00000	−	8.00000i	−0.963087	−	0.963087i
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$		0			0
$73$	6.00000			0.702247			0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000			0.702247			0.351123	+	0.936329i	$0.385800\pi$
$74$		0			0
$75$	7.00000	−	1.00000i	0.808290	−	0.115470i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−9.00000	−	9.00000i	−0.987878	−	0.987878i	0.0120491	−	0.999927i	$-0.496165\pi$
$83$	−9.00000	−	9.00000i	−0.987878	−	0.987878i	−0.999927	+	0.0120491i	$0.996165\pi$
$84$		0			0
$85$	8.00000	−	4.00000i	0.867722	−	0.433861i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.00000	+	1.00000i	0.307794	+	0.102598i
$96$		0			0
$97$			12.0000i			1.21842i	0.793011	+	0.609208i	$0.208512\pi$
$97$			12.0000i			1.21842i	−0.793011	+	0.609208i	$0.791488\pi$
$98$		0			0
$99$	3.00000	−	3.00000i	0.301511	−	0.301511i
$100$		0			0
$101$	3.00000	+	3.00000i	0.298511	+	0.298511i	0.840431	−	0.541919i	$-0.182302\pi$
$101$	3.00000	+	3.00000i	0.298511	+	0.298511i	−0.541919	+	0.840431i	$0.682302\pi$
$102$		0			0
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.00000	−	9.00000i	0.870063	−	0.870063i	−0.122416	−	0.992479i	$-0.539064\pi$
$107$	9.00000	−	9.00000i	0.870063	−	0.870063i	0.992479	+	0.122416i	$0.0390642\pi$
$108$		0			0
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	−0.753374	−	0.657592i	$-0.771575\pi$
$109$	−1.00000	+	1.00000i	−0.0957826	+	0.0957826i	0.657592	+	0.753374i	$0.271575\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$		−	8.00000i		−	0.752577i	−0.926503	−	0.376288i	$-0.877200\pi$
$113$		−	8.00000i		−	0.752577i	0.926503	−	0.376288i	$-0.122800\pi$
$114$		0			0
$115$	8.00000	+	16.0000i	0.746004	+	1.49201i
$116$		0			0
$117$	3.00000	−	3.00000i	0.277350	−	0.277350i
$118$		0			0
$119$		0			0
$120$		0			0
$121$			7.00000i			0.636364i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$		−	6.00000i		−	0.532414i	−0.963916	−	0.266207i	$-0.914230\pi$
$127$		−	6.00000i		−	0.532414i	0.963916	−	0.266207i	$-0.0857705\pi$
$128$		0			0
$129$	6.00000			0.528271
$130$		0			0
$131$	9.00000	−	9.00000i	0.786334	−	0.786334i	−0.194557	−	0.980891i	$-0.562327\pi$
$131$	9.00000	−	9.00000i	0.786334	−	0.786334i	0.980891	+	0.194557i	$0.0623271\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−12.0000	−	4.00000i	−1.03280	−	0.344265i
$136$		0			0
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$	7.00000	+	7.00000i	0.593732	+	0.593732i	0.938638	−	0.344905i	$-0.112089\pi$
$139$	7.00000	+	7.00000i	0.593732	+	0.593732i	−0.344905	+	0.938638i	$0.612089\pi$
$140$		0			0
$141$	2.00000	−	2.00000i	0.168430	−	0.168430i
$142$		0			0
$143$			18.0000i			1.50524i
$144$		0			0
$145$	9.00000	+	3.00000i	0.747409	+	0.249136i
$146$		0			0
$147$	7.00000	+	7.00000i	0.577350	+	0.577350i
$148$		0			0
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	0.819232	−	0.573462i	$-0.194400\pi$
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	−0.573462	+	0.819232i	$0.694400\pi$
$150$		0			0
$151$			18.0000i			1.46482i	0.680864	+	0.732410i	$0.261604\pi$
$151$			18.0000i			1.46482i	−0.680864	+	0.732410i	$0.738396\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.00000	−	9.00000i	−0.718278	−	0.718278i	0.249974	−	0.968252i	$-0.419578\pi$
$157$	−9.00000	−	9.00000i	−0.718278	−	0.718278i	−0.968252	+	0.249974i	$0.919578\pi$
$158$		0			0
$159$	18.0000			1.42749
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−9.00000	−	9.00000i	−0.704934	−	0.704934i	0.260531	−	0.965465i	$-0.416102\pi$
$163$	−9.00000	−	9.00000i	−0.704934	−	0.704934i	−0.965465	+	0.260531i	$0.916102\pi$
$164$		0			0
$165$	12.0000	−	6.00000i	0.934199	−	0.467099i
$166$		0			0
$167$	−8.00000			−0.619059			−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000			−0.619059			−0.309529	+	0.950890i	$0.600171\pi$
$168$		0			0
$169$			5.00000i			0.384615i
$170$		0			0
$171$	−1.00000	−	1.00000i	−0.0764719	−	0.0764719i
$172$		0			0
$173$	−9.00000	−	9.00000i	−0.684257	−	0.684257i	0.276699	−	0.960957i	$-0.410759\pi$
$173$	−9.00000	−	9.00000i	−0.684257	−	0.684257i	−0.960957	+	0.276699i	$0.910759\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			18.0000i			1.35296i
$178$		0			0
$179$	−3.00000	+	3.00000i	−0.224231	+	0.224231i	−0.810277	−	0.586047i	$-0.800683\pi$
$179$	−3.00000	+	3.00000i	−0.224231	+	0.224231i	0.586047	+	0.810277i	$0.300683\pi$
$180$		0			0
$181$	−1.00000	−	1.00000i	−0.0743294	−	0.0743294i	0.668965	−	0.743294i	$-0.266738\pi$
$181$	−1.00000	−	1.00000i	−0.0743294	−	0.0743294i	−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	9.00000	+	3.00000i	0.661693	+	0.220564i
$186$		0			0
$187$	12.0000	−	12.0000i	0.877527	−	0.877527i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$		0			0
$193$		−	12.0000i		−	0.863779i	−0.901927	−	0.431889i	$-0.857847\pi$
$193$		−	12.0000i		−	0.863779i	0.901927	−	0.431889i	$-0.142153\pi$
$194$		0			0
$195$	12.0000	−	6.00000i	0.859338	−	0.429669i
$196$		0			0
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	−0.862423	−	0.506188i	$-0.831054\pi$
$197$	−5.00000	+	5.00000i	−0.356235	+	0.356235i	0.506188	+	0.862423i	$0.331054\pi$
$198$		0			0
$199$			2.00000i			0.141776i	0.997484	+	0.0708881i	$0.0225833\pi$
$199$			2.00000i			0.141776i	−0.997484	+	0.0708881i	$0.977417\pi$
$200$		0			0
$201$		−	6.00000i		−	0.423207i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	8.00000i		−	0.556038i
$208$		0			0
$209$	6.00000			0.415029
$210$		0			0
$211$	−11.0000	+	11.0000i	−0.757271	+	0.757271i	−0.975825	−	0.218554i	$-0.929866\pi$
$211$	−11.0000	+	11.0000i	−0.757271	+	0.757271i	0.218554	+	0.975825i	$0.429866\pi$
$212$		0			0
$213$	−6.00000	+	6.00000i	−0.411113	+	0.411113i
$214$		0			0
$215$	−9.00000	−	3.00000i	−0.613795	−	0.204598i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−6.00000	−	6.00000i	−0.405442	−	0.405442i
$220$		0			0
$221$	12.0000	−	12.0000i	0.807207	−	0.807207i
$222$		0			0
$223$		−	6.00000i		−	0.401790i	−0.979613	−	0.200895i	$-0.935615\pi$
$223$		−	6.00000i		−	0.401790i	0.979613	−	0.200895i	$-0.0643850\pi$
$224$		0			0
$225$	4.00000	+	3.00000i	0.266667	+	0.200000i
$226$		0			0
$227$	−9.00000	−	9.00000i	−0.597351	−	0.597351i	0.342256	−	0.939607i	$-0.388809\pi$
$227$	−9.00000	−	9.00000i	−0.597351	−	0.597351i	−0.939607	+	0.342256i	$0.888809\pi$
$228$		0			0
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	0.899498	−	0.436925i	$-0.143932\pi$
$229$	7.00000	+	7.00000i	0.462573	+	0.462573i	−0.436925	+	0.899498i	$0.643932\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	22.0000			1.44127			0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$		0			0
$235$	−4.00000	+	2.00000i	−0.260931	+	0.130466i
$236$		0			0
$237$	8.00000	+	8.00000i	0.519656	+	0.519656i
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$		0			0
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$		0			0
$245$	−7.00000	−	14.0000i	−0.447214	−	0.894427i
$246$		0			0
$247$	6.00000			0.381771
$248$		0			0
$249$			18.0000i			1.14070i
$250$		0			0
$251$	−9.00000	−	9.00000i	−0.568075	−	0.568075i	0.363514	−	0.931589i	$-0.381577\pi$
$251$	−9.00000	−	9.00000i	−0.568075	−	0.568075i	−0.931589	+	0.363514i	$0.881577\pi$
$252$		0			0
$253$	24.0000	+	24.0000i	1.50887	+	1.50887i
$254$		0			0
$255$	−12.0000	−	4.00000i	−0.751469	−	0.250490i
$256$		0			0
$257$		−	8.00000i		−	0.499026i	−0.968371	−	0.249513i	$-0.919729\pi$
$257$		−	8.00000i		−	0.499026i	0.968371	−	0.249513i	$-0.0802706\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	−	3.00000i	−0.185695	−	0.185695i
$262$		0			0
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	−27.0000	−	9.00000i	−1.65860	−	0.552866i
$266$		0			0
$267$	−12.0000	+	12.0000i	−0.734388	+	0.734388i
$268$		0			0
$269$	−9.00000	+	9.00000i	−0.548740	+	0.548740i	−0.926076	−	0.377337i	$-0.876840\pi$
$269$	−9.00000	+	9.00000i	−0.548740	+	0.548740i	0.377337	+	0.926076i	$0.376840\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−21.0000	+	3.00000i	−1.26635	+	0.180907i
$276$		0			0
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	−0.611213	−	0.791466i	$-0.709318\pi$
$277$	3.00000	−	3.00000i	0.180253	−	0.180253i	0.791466	+	0.611213i	$0.209318\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$		0			0
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	−0.994679	−	0.103022i	$-0.967149\pi$
$283$	−15.0000	+	15.0000i	−0.891657	+	0.891657i	0.103022	+	0.994679i	$0.467149\pi$
$284$		0			0
$285$	−2.00000	−	4.00000i	−0.118470	−	0.236940i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.00000			0.0588235
$290$		0			0
$291$	12.0000	−	12.0000i	0.703452	−	0.703452i
$292$		0			0
$293$	−9.00000	+	9.00000i	−0.525786	+	0.525786i	−0.919313	−	0.393527i	$-0.871255\pi$
$293$	−9.00000	+	9.00000i	−0.525786	+	0.525786i	0.393527	+	0.919313i	$0.371255\pi$
$294$		0			0
$295$	9.00000	−	27.0000i	0.524000	−	1.57200i
$296$		0			0
$297$	−24.0000			−1.39262
$298$		0			0
$299$	24.0000	+	24.0000i	1.38796	+	1.38796i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		−	6.00000i		−	0.344691i
$304$		0			0
$305$	−15.0000	−	5.00000i	−0.858898	−	0.286299i
$306$		0			0
$307$	3.00000	+	3.00000i	0.171219	+	0.171219i	0.787515	−	0.616296i	$-0.211367\pi$
$307$	3.00000	+	3.00000i	0.171219	+	0.171219i	−0.616296	+	0.787515i	$0.711367\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.00000	+	7.00000i	0.393159	+	0.393159i	0.875812	−	0.482653i	$-0.160327\pi$
$317$	7.00000	+	7.00000i	0.393159	+	0.393159i	−0.482653	+	0.875812i	$0.660327\pi$
$318$		0			0
$319$	18.0000			1.00781
$320$		0			0
$321$	−18.0000			−1.00466
$322$		0			0
$323$	−4.00000	−	4.00000i	−0.222566	−	0.222566i
$324$		0			0
$325$	−21.0000	+	3.00000i	−1.16487	+	0.166410i
$326$		0			0
$327$	2.00000			0.110600
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.00000	−	5.00000i	−0.274825	−	0.274825i	0.556214	−	0.831039i	$-0.312253\pi$
$331$	−5.00000	−	5.00000i	−0.274825	−	0.274825i	−0.831039	+	0.556214i	$0.812253\pi$
$332$		0			0
$333$	−3.00000	−	3.00000i	−0.164399	−	0.164399i
$334$		0			0
$335$	−3.00000	+	9.00000i	−0.163908	+	0.491723i
$336$		0			0
$337$		−	24.0000i		−	1.30736i	−0.756770	−	0.653682i	$-0.773224\pi$
$337$		−	24.0000i		−	1.30736i	0.756770	−	0.653682i	$-0.226776\pi$
$338$		0			0
$339$	−8.00000	+	8.00000i	−0.434500	+	0.434500i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	8.00000	−	24.0000i	0.430706	−	1.29212i
$346$		0			0
$347$	−19.0000	+	19.0000i	−1.01997	+	1.01997i	−0.0201770	+	0.999796i	$0.506423\pi$
$347$	−19.0000	+	19.0000i	−1.01997	+	1.01997i	−0.999796	+	0.0201770i	$0.993577\pi$
$348$		0			0
$349$	−5.00000	+	5.00000i	−0.267644	+	0.267644i	−0.828150	−	0.560506i	$-0.810607\pi$
$349$	−5.00000	+	5.00000i	−0.267644	+	0.267644i	0.560506	+	0.828150i	$0.310607\pi$
$350$		0			0
$351$	−24.0000			−1.28103
$352$		0			0
$353$		−	16.0000i		−	0.851594i	−0.904819	−	0.425797i	$-0.859994\pi$
$353$		−	16.0000i		−	0.851594i	0.904819	−	0.425797i	$-0.140006\pi$
$354$		0			0
$355$	12.0000	−	6.00000i	0.636894	−	0.318447i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			18.0000i			0.950004i	0.879985	+	0.475002i	$0.157553\pi$
$359$			18.0000i			0.950004i	−0.879985	+	0.475002i	$0.842447\pi$
$360$		0			0
$361$			17.0000i			0.894737i
$362$		0			0
$363$	7.00000	−	7.00000i	0.367405	−	0.367405i
$364$		0			0
$365$	6.00000	+	12.0000i	0.314054	+	0.628109i
$366$		0			0
$367$			18.0000i			0.939592i	0.882775	+	0.469796i	$0.155673\pi$
$367$			18.0000i			0.939592i	−0.882775	+	0.469796i	$0.844327\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	3.00000	−	3.00000i	0.155334	−	0.155334i	−0.625161	−	0.780496i	$-0.714967\pi$
$373$	3.00000	−	3.00000i	0.155334	−	0.155334i	0.780496	+	0.625161i	$0.214967\pi$
$374$		0			0
$375$	9.00000	+	13.0000i	0.464758	+	0.671317i
$376$		0			0
$377$	18.0000			0.927047
$378$		0			0
$379$	−1.00000	−	1.00000i	−0.0513665	−	0.0513665i	0.680957	−	0.732323i	$-0.261564\pi$
$379$	−1.00000	−	1.00000i	−0.0513665	−	0.0513665i	−0.732323	+	0.680957i	$0.761564\pi$
$380$		0			0
$381$	−6.00000	+	6.00000i	−0.307389	+	0.307389i
$382$		0			0
$383$			10.0000i			0.510976i	0.966812	+	0.255488i	$0.0822362\pi$
$383$			10.0000i			0.510976i	−0.966812	+	0.255488i	$0.917764\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.00000	+	3.00000i	0.152499	+	0.152499i
$388$		0			0
$389$	15.0000	+	15.0000i	0.760530	+	0.760530i	0.976418	−	0.215888i	$-0.0692646\pi$
$389$	15.0000	+	15.0000i	0.760530	+	0.760530i	−0.215888	+	0.976418i	$0.569265\pi$
$390$		0			0
$391$		−	32.0000i		−	1.61831i
$392$		0			0
$393$	−18.0000			−0.907980
$394$		0			0
$395$	−8.00000	−	16.0000i	−0.402524	−	0.805047i
$396$		0			0
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	0.444220	−	0.895918i	$-0.353481\pi$
$397$	−9.00000	−	9.00000i	−0.451697	−	0.451697i	−0.895918	+	0.444220i	$0.853481\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	30.0000			1.49813			0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000			1.49813			0.749064	+	0.662497i	$0.230503\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	5.00000	+	10.0000i	0.248452	+	0.496904i
$406$		0			0
$407$	18.0000			0.892227
$408$		0			0
$409$		0			0		1.00000			$0$
$409$		0			0		−1.00000			$\pi$
$410$		0			0
$411$	−2.00000	−	2.00000i	−0.0986527	−	0.0986527i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	9.00000	−	27.0000i	0.441793	−	1.32538i
$416$		0			0
$417$		−	14.0000i		−	0.685583i
$418$		0			0
$419$	−15.0000	+	15.0000i	−0.732798	+	0.732798i	−0.971173	−	0.238375i	$-0.923385\pi$
$419$	−15.0000	+	15.0000i	−0.732798	+	0.732798i	0.238375	+	0.971173i	$0.423385\pi$
$420$		0			0
$421$	−5.00000	−	5.00000i	−0.243685	−	0.243685i	0.574688	−	0.818373i	$-0.305124\pi$
$421$	−5.00000	−	5.00000i	−0.243685	−	0.243685i	−0.818373	+	0.574688i	$0.805124\pi$
$422$		0			0
$423$	2.00000			0.0972433
$424$		0			0
$425$	16.0000	+	12.0000i	0.776114	+	0.582086i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	18.0000	−	18.0000i	0.869048	−	0.869048i
$430$		0			0
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$			36.0000i			1.73005i	0.501729	+	0.865025i	$0.332697\pi$
$433$			36.0000i			1.73005i	−0.501729	+	0.865025i	$0.667303\pi$
$434$		0			0
$435$	−6.00000	−	12.0000i	−0.287678	−	0.575356i
$436$		0			0
$437$	8.00000	−	8.00000i	0.382692	−	0.382692i
$438$		0			0
$439$			10.0000i			0.477274i	0.971109	+	0.238637i	$0.0767006\pi$
$439$			10.0000i			0.477274i	−0.971109	+	0.238637i	$0.923299\pi$
$440$		0			0
$441$			7.00000i			0.333333i
$442$		0			0
$443$	9.00000	−	9.00000i	0.427603	−	0.427603i	−0.460208	−	0.887811i	$-0.652225\pi$
$443$	9.00000	−	9.00000i	0.427603	−	0.427603i	0.887811	+	0.460208i	$0.152225\pi$
$444$		0			0
$445$	24.0000	−	12.0000i	1.13771	−	0.568855i
$446$		0			0
$447$		−	6.00000i		−	0.283790i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	18.0000	−	18.0000i	0.845714	−	0.845714i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.0000			0.842004			0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000			0.842004			0.421002	+	0.907060i	$0.361678\pi$
$458$		0			0
$459$	16.0000	+	16.0000i	0.746816	+	0.746816i
$460$		0			0
$461$	3.00000	−	3.00000i	0.139724	−	0.139724i	−0.633785	−	0.773509i	$-0.718500\pi$
$461$	3.00000	−	3.00000i	0.139724	−	0.139724i	0.773509	+	0.633785i	$0.218500\pi$
$462$		0			0
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.00000	−	5.00000i	−0.231372	−	0.231372i	0.581893	−	0.813265i	$-0.302312\pi$
$467$	−5.00000	−	5.00000i	−0.231372	−	0.231372i	−0.813265	+	0.581893i	$0.802312\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$			18.0000i			0.829396i
$472$		0			0
$473$	−18.0000			−0.827641
$474$		0			0
$475$	1.00000	+	7.00000i	0.0458831	+	0.321182i
$476$		0			0
$477$	9.00000	+	9.00000i	0.412082	+	0.412082i
$478$		0			0
$479$	24.0000			1.09659			0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000			1.09659			0.548294	+	0.836286i	$0.315277\pi$
$480$		0			0
$481$	18.0000			0.820729
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−24.0000	+	12.0000i	−1.08978	+	0.544892i
$486$		0			0
$487$	−24.0000			−1.08754			−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000			−1.08754			−0.543772	+	0.839233i	$0.683004\pi$
$488$		0			0
$489$			18.0000i			0.813988i
$490$		0			0
$491$	15.0000	+	15.0000i	0.676941	+	0.676941i	0.959307	−	0.282366i	$-0.0911193\pi$
$491$	15.0000	+	15.0000i	0.676941	+	0.676941i	−0.282366	+	0.959307i	$0.591119\pi$
$492$		0			0
$493$	−12.0000	−	12.0000i	−0.540453	−	0.540453i
$494$		0			0
$495$	9.00000	+	3.00000i	0.404520	+	0.134840i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	29.0000	−	29.0000i	1.29822	−	1.29822i	0.368650	−	0.929568i	$-0.379820\pi$
$499$	29.0000	−	29.0000i	1.29822	−	1.29822i	0.929568	−	0.368650i	$-0.120180\pi$
$500$		0			0
$501$	8.00000	+	8.00000i	0.357414	+	0.357414i
$502$		0			0
$503$	−32.0000			−1.42681			−0.713405	−	0.700752i	$-0.752848\pi$
$503$	−32.0000			−1.42681			−0.713405	+	0.700752i	$0.752848\pi$
$504$		0			0
$505$	−3.00000	+	9.00000i	−0.133498	+	0.400495i
$506$		0			0
$507$	5.00000	−	5.00000i	0.222058	−	0.222058i
$508$		0			0
$509$	−9.00000	+	9.00000i	−0.398918	+	0.398918i	−0.877851	−	0.478933i	$-0.841024\pi$
$509$	−9.00000	+	9.00000i	−0.398918	+	0.398918i	0.478933	+	0.877851i	$0.341024\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			8.00000i			0.353209i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−6.00000	+	6.00000i	−0.263880	+	0.263880i
$518$		0			0
$519$			18.0000i			0.790112i
$520$		0			0
$521$		−	24.0000i		−	1.05146i	−0.850652	−	0.525730i	$-0.823792\pi$
$521$		−	24.0000i		−	1.05146i	0.850652	−	0.525730i	$-0.176208\pi$
$522$		0			0
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	−0.482405	−	0.875948i	$-0.660237\pi$
$523$	9.00000	−	9.00000i	0.393543	−	0.393543i	0.875948	+	0.482405i	$0.160237\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	41.0000			1.78261
$530$		0			0
$531$	−9.00000	+	9.00000i	−0.390567	+	0.390567i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	27.0000	+	9.00000i	1.16731	+	0.389104i
$536$		0			0
$537$	6.00000			0.258919
$538$		0			0
$539$	−21.0000	−	21.0000i	−0.904534	−	0.904534i
$540$		0			0
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	−0.728277	−	0.685283i	$-0.759678\pi$
$541$	−1.00000	+	1.00000i	−0.0429934	+	0.0429934i	0.685283	+	0.728277i	$0.259678\pi$
$542$		0			0
$543$			2.00000i			0.0858282i
$544$		0			0
$545$	−3.00000	−	1.00000i	−0.128506	−	0.0428353i
$546$		0			0
$547$	3.00000	+	3.00000i	0.128271	+	0.128271i	0.768328	−	0.640057i	$-0.221089\pi$
$547$	3.00000	+	3.00000i	0.128271	+	0.128271i	−0.640057	+	0.768328i	$0.721089\pi$
$548$		0			0
$549$	5.00000	+	5.00000i	0.213395	+	0.213395i
$550$		0			0
$551$		−	6.00000i		−	0.255609i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−6.00000	−	12.0000i	−0.254686	−	0.509372i
$556$		0			0
$557$	−9.00000	−	9.00000i	−0.381342	−	0.381342i	0.490243	−	0.871586i	$-0.336908\pi$
$557$	−9.00000	−	9.00000i	−0.381342	−	0.381342i	−0.871586	+	0.490243i	$0.836908\pi$
$558$		0			0
$559$	−18.0000			−0.761319
$560$		0			0
$561$	−24.0000			−1.01328
$562$		0			0
$563$	19.0000	+	19.0000i	0.800755	+	0.800755i	0.983213	−	0.182459i	$-0.0584057\pi$
$563$	19.0000	+	19.0000i	0.800755	+	0.800755i	−0.182459	+	0.983213i	$0.558406\pi$
$564$		0			0
$565$	16.0000	−	8.00000i	0.673125	−	0.336563i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	11.0000	+	11.0000i	0.460336	+	0.460336i	0.898765	−	0.438430i	$-0.144465\pi$
$571$	11.0000	+	11.0000i	0.460336	+	0.460336i	−0.438430	+	0.898765i	$0.644465\pi$
$572$		0			0
$573$	−24.0000	−	24.0000i	−1.00261	−	1.00261i
$574$		0			0
$575$	−24.0000	+	32.0000i	−1.00087	+	1.33449i
$576$		0			0
$577$			24.0000i			0.999133i	0.866276	+	0.499567i	$0.166507\pi$
$577$			24.0000i			0.999133i	−0.866276	+	0.499567i	$0.833493\pi$
$578$		0			0
$579$	−12.0000	+	12.0000i	−0.498703	+	0.498703i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−54.0000			−2.23645
$584$		0			0
$585$	9.00000	+	3.00000i	0.372104	+	0.124035i
$586$		0			0
$587$	9.00000	−	9.00000i	0.371470	−	0.371470i	−0.496543	−	0.868012i	$-0.665397\pi$
$587$	9.00000	−	9.00000i	0.371470	−	0.371470i	0.868012	+	0.496543i	$0.165397\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	10.0000			0.411345
$592$		0			0
$593$			32.0000i			1.31408i	0.753855	+	0.657041i	$0.228192\pi$
$593$			32.0000i			1.31408i	−0.753855	+	0.657041i	$0.771808\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.00000	−	2.00000i	0.0818546	−	0.0818546i
$598$		0			0
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$		0			0
$601$		−	36.0000i		−	1.46847i	−0.678895	−	0.734235i	$-0.737541\pi$
$601$		−	36.0000i		−	1.46847i	0.678895	−	0.734235i	$-0.262459\pi$
$602$		0			0
$603$	3.00000	−	3.00000i	0.122169	−	0.122169i
$604$		0			0
$605$	−14.0000	+	7.00000i	−0.569181	+	0.284590i
$606$		0			0
$607$			42.0000i			1.70473i	0.522949	+	0.852364i	$0.324832\pi$
$607$			42.0000i			1.70473i	−0.522949	+	0.852364i	$0.675168\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.00000	+	6.00000i	−0.242734	+	0.242734i
$612$		0			0
$613$	27.0000	−	27.0000i	1.09052	−	1.09052i	0.0950469	−	0.995473i	$-0.469700\pi$
$613$	27.0000	−	27.0000i	1.09052	−	1.09052i	0.995473	−	0.0950469i	$-0.0303001\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.0000			−0.402585			−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000			−0.402585			−0.201292	+	0.979531i	$0.564514\pi$
$618$		0			0
$619$	−13.0000	−	13.0000i	−0.522514	−	0.522514i	0.395816	−	0.918330i	$-0.370462\pi$
$619$	−13.0000	−	13.0000i	−0.522514	−	0.522514i	−0.918330	+	0.395816i	$0.870462\pi$
$620$		0			0
$621$	−32.0000	+	32.0000i	−1.28412	+	1.28412i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$	−6.00000	−	6.00000i	−0.239617	−	0.239617i
$628$		0			0
$629$	−12.0000	−	12.0000i	−0.478471	−	0.478471i
$630$		0			0
$631$			2.00000i			0.0796187i	0.999207	+	0.0398094i	$0.0126751\pi$
$631$			2.00000i			0.0796187i	−0.999207	+	0.0398094i	$0.987325\pi$
$632$		0			0
$633$	22.0000			0.874421
$634$		0			0
$635$	12.0000	−	6.00000i	0.476205	−	0.238103i
$636$		0			0
$637$	−21.0000	−	21.0000i	−0.832050	−	0.832050i
$638$		0			0
$639$	−6.00000			−0.237356
$640$		0			0
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	27.0000	+	27.0000i	1.06478	+	1.06478i	0.997751	+	0.0670247i	$0.0213506\pi$
$643$	27.0000	+	27.0000i	1.06478	+	1.06478i	0.0670247	+	0.997751i	$0.478649\pi$
$644$		0			0
$645$	6.00000	+	12.0000i	0.236250	+	0.472500i
$646$		0			0
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$		0			0
$649$		−	54.0000i		−	2.11969i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.00000	−	9.00000i	−0.352197	−	0.352197i	0.508729	−	0.860927i	$-0.330115\pi$
$653$	−9.00000	−	9.00000i	−0.352197	−	0.352197i	−0.860927	+	0.508729i	$0.830115\pi$
$654$		0			0
$655$	27.0000	+	9.00000i	1.05498	+	0.351659i
$656$		0			0
$657$		−	6.00000i		−	0.234082i
$658$		0			0
$659$	21.0000	−	21.0000i	0.818044	−	0.818044i	−0.167781	−	0.985824i	$-0.553660\pi$
$659$	21.0000	−	21.0000i	0.818044	−	0.818044i	0.985824	+	0.167781i	$0.0536600\pi$
$660$		0			0
$661$	−29.0000	−	29.0000i	−1.12797	−	1.12797i	−0.990507	−	0.137462i	$-0.956105\pi$
$661$	−29.0000	−	29.0000i	−1.12797	−	1.12797i	−0.137462	−	0.990507i	$-0.543895\pi$
$662$		0			0
$663$	−24.0000			−0.932083
$664$		0			0
$665$		0			0
$666$		0			0
$667$	24.0000	−	24.0000i	0.929284	−	0.929284i
$668$		0			0
$669$	−6.00000	+	6.00000i	−0.231973	+	0.231973i
$670$		0			0
$671$	−30.0000			−1.15814
$672$		0			0
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$		0			0
$675$	−4.00000	−	28.0000i	−0.153960	−	1.07772i
$676$		0			0
$677$	−9.00000	+	9.00000i	−0.345898	+	0.345898i	−0.858579	−	0.512681i	$-0.828652\pi$
$677$	−9.00000	+	9.00000i	−0.345898	+	0.345898i	0.512681	+	0.858579i	$0.328652\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$			18.0000i			0.689761i
$682$		0			0
$683$	13.0000	−	13.0000i	0.497431	−	0.497431i	−0.413206	−	0.910637i	$-0.635591\pi$
$683$	13.0000	−	13.0000i	0.497431	−	0.497431i	0.910637	+	0.413206i	$0.135591\pi$
$684$		0			0
$685$	2.00000	+	4.00000i	0.0764161	+	0.152832i
$686$		0			0
$687$		−	14.0000i		−	0.534133i
$688$		0			0
$689$	−54.0000			−2.05724
$690$		0			0
$691$	5.00000	−	5.00000i	0.190209	−	0.190209i	−0.605577	−	0.795786i	$-0.707058\pi$
$691$	5.00000	−	5.00000i	0.190209	−	0.190209i	0.795786	+	0.605577i	$0.207058\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.00000	+	21.0000i	−0.265525	+	0.796575i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−22.0000	−	22.0000i	−0.832116	−	0.832116i
$700$		0			0
$701$	3.00000	−	3.00000i	0.113308	−	0.113308i	−0.648179	−	0.761488i	$-0.724469\pi$
$701$	3.00000	−	3.00000i	0.113308	−	0.113308i	0.761488	+	0.648179i	$0.224469\pi$
$702$		0			0
$703$		−	6.00000i		−	0.226294i
$704$		0			0
$705$	6.00000	+	2.00000i	0.225973	+	0.0753244i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−13.0000	−	13.0000i	−0.488225	−	0.488225i	0.419521	−	0.907746i	$-0.362198\pi$
$709$	−13.0000	−	13.0000i	−0.488225	−	0.488225i	−0.907746	+	0.419521i	$0.862198\pi$
$710$		0			0
$711$			8.00000i			0.300023i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−36.0000	+	18.0000i	−1.34632	+	0.673162i
$716$		0			0
$717$	24.0000	+	24.0000i	0.896296	+	0.896296i
$718$		0			0
$719$	−24.0000			−0.895049			−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	18.0000	+	18.0000i	0.669427	+	0.669427i
$724$		0			0
$725$	3.00000	+	21.0000i	0.111417	+	0.779920i
$726$		0			0
$727$	−24.0000			−0.890111			−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000			−0.890111			−0.445055	+	0.895503i	$0.646816\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	12.0000	+	12.0000i	0.443836	+	0.443836i
$732$		0			0
$733$	3.00000	+	3.00000i	0.110808	+	0.110808i	0.760337	−	0.649529i	$-0.225034\pi$
$733$	3.00000	+	3.00000i	0.110808	+	0.110808i	−0.649529	+	0.760337i	$0.725034\pi$
$734$		0			0
$735$	−7.00000	+	21.0000i	−0.258199	+	0.774597i
$736$		0			0
$737$			18.0000i			0.663039i
$738$		0			0
$739$	−19.0000	+	19.0000i	−0.698926	+	0.698926i	−0.964179	−	0.265253i	$-0.914545\pi$
$739$	−19.0000	+	19.0000i	−0.698926	+	0.698926i	0.265253	+	0.964179i	$0.414545\pi$
$740$		0			0
$741$	−6.00000	−	6.00000i	−0.220416	−	0.220416i
$742$		0			0
$743$	8.00000			0.293492			0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000			0.293492			0.146746	+	0.989174i	$0.453120\pi$
$744$		0			0
$745$	−3.00000	+	9.00000i	−0.109911	+	0.329734i
$746$		0			0
$747$	−9.00000	+	9.00000i	−0.329293	+	0.329293i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$		0			0
$753$			18.0000i			0.655956i
$754$		0			0
$755$	−36.0000	+	18.0000i	−1.31017	+	0.655087i
$756$		0			0
$757$	−33.0000	+	33.0000i	−1.19941	+	1.19941i	−0.225061	+	0.974345i	$0.572258\pi$
$757$	−33.0000	+	33.0000i	−1.19941	+	1.19941i	−0.974345	+	0.225061i	$0.927742\pi$
$758$		0			0
$759$		−	48.0000i		−	1.74229i
$760$		0			0
$761$			48.0000i			1.74000i	0.493053	+	0.869999i	$0.335881\pi$
$761$			48.0000i			1.74000i	−0.493053	+	0.869999i	$0.664119\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−4.00000	−	8.00000i	−0.144620	−	0.289241i
$766$		0			0
$767$		−	54.0000i		−	1.94983i
$768$		0			0
$769$	−18.0000			−0.649097			−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000			−0.649097			−0.324548	+	0.945869i	$0.605212\pi$
$770$		0			0
$771$	−8.00000	+	8.00000i	−0.288113	+	0.288113i
$772$		0			0
$773$	23.0000	−	23.0000i	0.827253	−	0.827253i	−0.159883	−	0.987136i	$-0.551112\pi$
$773$	23.0000	−	23.0000i	0.827253	−	0.827253i	0.987136	+	0.159883i	$0.0511118\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	18.0000	−	18.0000i	0.644091	−	0.644091i
$782$		0			0
$783$			24.0000i			0.857690i
$784$		0			0
$785$	9.00000	−	27.0000i	0.321224	−	0.963671i
$786$		0			0
$787$	−33.0000	−	33.0000i	−1.17632	−	1.17632i	−0.980674	−	0.195649i	$-0.937319\pi$
$787$	−33.0000	−	33.0000i	−1.17632	−	1.17632i	−0.195649	−	0.980674i	$-0.562681\pi$
$788$		0			0
$789$	−16.0000	−	16.0000i	−0.569615	−	0.569615i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−30.0000			−1.06533
$794$		0			0
$795$	18.0000	+	36.0000i	0.638394	+	1.27679i
$796$		0			0
$797$	19.0000	+	19.0000i	0.673015	+	0.673015i	0.958410	−	0.285395i	$-0.0921249\pi$
$797$	19.0000	+	19.0000i	0.673015	+	0.673015i	−0.285395	+	0.958410i	$0.592125\pi$
$798$		0			0
$799$	8.00000			0.283020
$800$		0			0
$801$	−12.0000			−0.423999
$802$		0			0
$803$	18.0000	+	18.0000i	0.635206	+	0.635206i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	18.0000			0.633630
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$	−37.0000	−	37.0000i	−1.29925	−	1.29925i	−0.928890	−	0.370356i	$-0.879236\pi$
$811$	−37.0000	−	37.0000i	−1.29925	−	1.29925i	−0.370356	−	0.928890i	$-0.620764\pi$
$812$		0			0
$813$	16.0000	+	16.0000i	0.561144	+	0.561144i
$814$		0			0
$815$	9.00000	−	27.0000i	0.315256	−	0.945769i
$816$		0			0
$817$			6.00000i			0.209913i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	39.0000	+	39.0000i	1.36111	+	1.36111i	0.872506	+	0.488603i	$0.162493\pi$
$821$	39.0000	+	39.0000i	1.36111	+	1.36111i	0.488603	+	0.872506i	$0.337507\pi$
$822$		0			0
$823$	24.0000			0.836587			0.418294	−	0.908312i	$-0.362628\pi$
$823$	24.0000			0.836587			0.418294	+	0.908312i	$0.362628\pi$
$824$		0			0
$825$	24.0000	+	18.0000i	0.835573	+	0.626680i
$826$		0			0
$827$	−31.0000	+	31.0000i	−1.07798	+	1.07798i	−0.0812847	+	0.996691i	$0.525902\pi$
$827$	−31.0000	+	31.0000i	−1.07798	+	1.07798i	−0.996691	+	0.0812847i	$0.974098\pi$
$828$		0			0
$829$	35.0000	−	35.0000i	1.21560	−	1.21560i	0.246443	−	0.969157i	$-0.420738\pi$
$829$	35.0000	−	35.0000i	1.21560	−	1.21560i	0.969157	−	0.246443i	$-0.0792618\pi$
$830$		0			0
$831$	−6.00000			−0.208138
$832$		0			0
$833$			28.0000i			0.970143i
$834$		0			0
$835$	−8.00000	−	16.0000i	−0.276851	−	0.553703i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			42.0000i			1.45000i	0.688748	+	0.725001i	$0.258161\pi$
$839$			42.0000i			1.45000i	−0.688748	+	0.725001i	$0.741839\pi$
$840$		0			0
$841$			11.0000i			0.379310i
$842$		0			0
$843$	−12.0000	+	12.0000i	−0.413302	+	0.413302i
$844$		0			0
$845$	−10.0000	+	5.00000i	−0.344010	+	0.172005i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	30.0000			1.02960
$850$		0			0
$851$	24.0000	−	24.0000i	0.822709	−	0.822709i
$852$		0			0
$853$	15.0000	−	15.0000i	0.513590	−	0.513590i	−0.402034	−	0.915625i	$-0.631697\pi$
$853$	15.0000	−	15.0000i	0.513590	−	0.513590i	0.915625	+	0.402034i	$0.131697\pi$
$854$		0			0
$855$	1.00000	−	3.00000i	0.0341993	−	0.102598i
$856$		0			0
$857$	−38.0000			−1.29806			−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000			−1.29806			−0.649028	+	0.760765i	$0.724824\pi$
$858$		0			0
$859$	7.00000	+	7.00000i	0.238837	+	0.238837i	0.816368	−	0.577531i	$-0.195984\pi$
$859$	7.00000	+	7.00000i	0.238837	+	0.238837i	−0.577531	+	0.816368i	$0.695984\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	22.0000i		−	0.748889i	−0.927249	−	0.374444i	$-0.877833\pi$
$863$		−	22.0000i		−	0.748889i	0.927249	−	0.374444i	$-0.122167\pi$
$864$		0			0
$865$	9.00000	−	27.0000i	0.306009	−	0.918028i
$866$		0			0
$867$	−1.00000	−	1.00000i	−0.0339618	−	0.0339618i
$868$		0			0
$869$	−24.0000	−	24.0000i	−0.814144	−	0.814144i
$870$		0			0
$871$			18.0000i			0.609907i
$872$		0			0
$873$	12.0000			0.406138
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.00000	+	3.00000i	0.101303	+	0.101303i	0.755942	−	0.654639i	$-0.227179\pi$
$877$	3.00000	+	3.00000i	0.101303	+	0.101303i	−0.654639	+	0.755942i	$0.727179\pi$
$878$		0			0
$879$	18.0000			0.607125
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	0.259135	−	0.965841i	$-0.416563\pi$
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	−0.965841	+	0.259135i	$0.916563\pi$
$884$		0			0
$885$	−36.0000	+	18.0000i	−1.21013	+	0.605063i
$886$		0			0
$887$	8.00000			0.268614			0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000			0.268614			0.134307	+	0.990940i	$0.457119\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	15.0000	+	15.0000i	0.502519	+	0.502519i
$892$		0			0
$893$	2.00000	+	2.00000i	0.0669274	+	0.0669274i
$894$		0			0
$895$	−9.00000	−	3.00000i	−0.300837	−	0.100279i
$896$		0			0
$897$		−	48.0000i		−	1.60267i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	36.0000	+	36.0000i	1.19933	+	1.19933i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.00000	−	3.00000i	0.0332411	−	0.0997234i
$906$		0			0
$907$	21.0000	−	21.0000i	0.697294	−	0.697294i	−0.266532	−	0.963826i	$-0.585878\pi$
$907$	21.0000	−	21.0000i	0.697294	−	0.697294i	0.963826	+	0.266532i	$0.0858779\pi$
$908$		0			0
$909$	3.00000	−	3.00000i	0.0995037	−	0.0995037i
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$		−	54.0000i		−	1.78714i
$914$		0			0
$915$	10.0000	+	20.0000i	0.330590	+	0.661180i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		−	54.0000i		−	1.78130i	−0.454694	−	0.890648i	$-0.650251\pi$
$919$		−	54.0000i		−	1.78130i	0.454694	−	0.890648i	$-0.349749\pi$
$920$		0			0
$921$		−	6.00000i		−	0.197707i
$922$		0			0
$923$	18.0000	−	18.0000i	0.592477	−	0.592477i
$924$		0			0
$925$	3.00000	+	21.0000i	0.0986394	+	0.690476i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	30.0000			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$930$		0			0
$931$	−7.00000	+	7.00000i	−0.229416	+	0.229416i
$932$		0			0
$933$	−6.00000	+	6.00000i	−0.196431	+	0.196431i
$934$		0			0
$935$	36.0000	+	12.0000i	1.17733	+	0.392442i
$936$		0			0
$937$	54.0000			1.76410			0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000			1.76410			0.882052	+	0.471153i	$0.156162\pi$
$938$		0			0
$939$	6.00000	+	6.00000i	0.195803	+	0.195803i
$940$		0			0
$941$	27.0000	−	27.0000i	0.880175	−	0.880175i	−0.113377	−	0.993552i	$-0.536167\pi$
$941$	27.0000	−	27.0000i	0.880175	−	0.880175i	0.993552	+	0.113377i	$0.0361668\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.0000	+	27.0000i	0.877382	+	0.877382i	0.993263	−	0.115881i	$-0.0369691\pi$
$947$	27.0000	+	27.0000i	0.877382	+	0.877382i	−0.115881	+	0.993263i	$0.536969\pi$
$948$		0			0
$949$	18.0000	+	18.0000i	0.584305	+	0.584305i
$950$		0			0
$951$		−	14.0000i		−	0.453981i
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$		0			0
$955$	24.0000	+	48.0000i	0.776622	+	1.55324i
$956$		0			0
$957$	−18.0000	−	18.0000i	−0.581857	−	0.581857i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	−9.00000	−	9.00000i	−0.290021	−	0.290021i
$964$		0			0
$965$	24.0000	−	12.0000i	0.772587	−	0.386294i
$966$		0			0
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$		0			0
$969$			8.00000i			0.256997i
$970$		0			0
$971$	−9.00000	−	9.00000i	−0.288824	−	0.288824i	0.547791	−	0.836615i	$-0.315469\pi$
$971$	−9.00000	−	9.00000i	−0.288824	−	0.288824i	−0.836615	+	0.547791i	$0.815469\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	24.0000	+	18.0000i	0.768615	+	0.576461i
$976$		0			0
$977$		−	28.0000i		−	0.895799i	−0.894084	−	0.447900i	$-0.852172\pi$
$977$		−	28.0000i		−	0.895799i	0.894084	−	0.447900i	$-0.147828\pi$
$978$		0			0
$979$	36.0000	−	36.0000i	1.15056	−	1.15056i
$980$		0			0
$981$	1.00000	+	1.00000i	0.0319275	+	0.0319275i
$982$		0			0
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		0			0
$985$	−15.0000	−	5.00000i	−0.477940	−	0.159313i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.0000	+	24.0000i	−0.763156	+	0.763156i
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$			10.0000i			0.317340i
$994$		0			0
$995$	−4.00000	+	2.00000i	−0.126809	+	0.0634043i
$996$		0			0
$997$	−9.00000	+	9.00000i	−0.285033	+	0.285033i	−0.835112	−	0.550079i	$-0.814597\pi$
$997$	−9.00000	+	9.00000i	−0.285033	+	0.285033i	0.550079	+	0.835112i	$0.314597\pi$
$998$		0			0
$999$			24.0000i			0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.2.q.a.49.1		2
4.3	odd	2		80.2.q.a.69.1	yes	2
5.2	odd	4		1600.2.l.b.1201.1		2
5.3	odd	4		1600.2.l.c.1201.1		2
5.4	even	2		320.2.q.b.49.1		2
8.3	odd	2		640.2.q.b.609.1		2
8.5	even	2		640.2.q.d.609.1		2
12.11	even	2		720.2.bm.b.469.1		2
16.3	odd	4		80.2.q.b.29.1	yes	2
16.5	even	4		640.2.q.a.289.1		2
16.11	odd	4		640.2.q.c.289.1		2
16.13	even	4		320.2.q.b.209.1		2
20.3	even	4		400.2.l.a.101.1		2
20.7	even	4		400.2.l.b.101.1		2
20.19	odd	2		80.2.q.b.69.1	yes	2
40.19	odd	2		640.2.q.c.609.1		2
40.29	even	2		640.2.q.a.609.1		2
48.35	even	4		720.2.bm.a.109.1		2
60.59	even	2		720.2.bm.a.469.1		2
80.3	even	4		400.2.l.a.301.1		2
80.13	odd	4		1600.2.l.c.401.1		2
80.19	odd	4		80.2.q.a.29.1	✓	2
80.29	even	4	inner	320.2.q.a.209.1		2
80.59	odd	4		640.2.q.b.289.1		2
80.67	even	4		400.2.l.b.301.1		2
80.69	even	4		640.2.q.d.289.1		2
80.77	odd	4		1600.2.l.b.401.1		2
240.179	even	4		720.2.bm.b.109.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.a.29.1	✓	2	80.19	odd	4
80.2.q.a.69.1	yes	2	4.3	odd	2
80.2.q.b.29.1	yes	2	16.3	odd	4
80.2.q.b.69.1	yes	2	20.19	odd	2
320.2.q.a.49.1		2	1.1	even	1	trivial
320.2.q.a.209.1		2	80.29	even	4	inner
320.2.q.b.49.1		2	5.4	even	2
320.2.q.b.209.1		2	16.13	even	4
400.2.l.a.101.1		2	20.3	even	4
400.2.l.a.301.1		2	80.3	even	4
400.2.l.b.101.1		2	20.7	even	4
400.2.l.b.301.1		2	80.67	even	4
640.2.q.a.289.1		2	16.5	even	4
640.2.q.a.609.1		2	40.29	even	2
640.2.q.b.289.1		2	80.59	odd	4
640.2.q.b.609.1		2	8.3	odd	2
640.2.q.c.289.1		2	16.11	odd	4
640.2.q.c.609.1		2	40.19	odd	2
640.2.q.d.289.1		2	80.69	even	4
640.2.q.d.609.1		2	8.5	even	2
720.2.bm.a.109.1		2	48.35	even	4
720.2.bm.a.469.1		2	60.59	even	2
720.2.bm.b.109.1		2	240.179	even	4
720.2.bm.b.469.1		2	12.11	even	2
1600.2.l.b.401.1		2	80.77	odd	4
1600.2.l.b.1201.1		2	5.2	odd	4
1600.2.l.c.401.1		2	80.13	odd	4
1600.2.l.c.1201.1		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{3} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{9} +(3.00000 + 3.00000i) q^{11} +(3.00000 + 3.00000i) q^{13} +(1.00000 - 3.00000i) q^{15} -4.00000i q^{17} +(1.00000 - 1.00000i) q^{19} +8.00000 q^{23} +(-3.00000 + 4.00000i) q^{25} +(-4.00000 + 4.00000i) q^{27} +(3.00000 - 3.00000i) q^{29} -6.00000i q^{33} +(3.00000 - 3.00000i) q^{37} -6.00000i q^{39} +(-3.00000 + 3.00000i) q^{43} +(2.00000 - 1.00000i) q^{45} +2.00000i q^{47} -7.00000 q^{49} +(-4.00000 + 4.00000i) q^{51} +(-9.00000 + 9.00000i) q^{53} +(-3.00000 + 9.00000i) q^{55} -2.00000 q^{57} +(-9.00000 - 9.00000i) q^{59} +(-5.00000 + 5.00000i) q^{61} +(-3.00000 + 9.00000i) q^{65} +(3.00000 + 3.00000i) q^{67} +(-8.00000 - 8.00000i) q^{69} -6.00000i q^{71} +6.00000 q^{73} +(7.00000 - 1.00000i) q^{75} -8.00000 q^{79} +5.00000 q^{81} +(-9.00000 - 9.00000i) q^{83} +(8.00000 - 4.00000i) q^{85} -6.00000 q^{87} -12.0000i q^{89} +(3.00000 + 1.00000i) q^{95} +12.0000i q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5} + 6 q^{11} + 6 q^{13} + 2 q^{15} + 2 q^{19} + 16 q^{23} - 6 q^{25} - 8 q^{27} + 6 q^{29} + 6 q^{37} - 6 q^{43} + 4 q^{45} - 14 q^{49} - 8 q^{51} - 18 q^{53} - 6 q^{55} - 4 q^{57}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^5 + 6 * q^11 + 6 * q^13 + 2 * q^15 + 2 * q^19 + 16 * q^23 - 6 * q^25 - 8 * q^27 + 6 * q^29 + 6 * q^37 - 6 * q^43 + 4 * q^45 - 14 * q^49 - 8 * q^51 - 18 * q^53 - 6 * q^55 - 4 * q^57 - 18 * q^59 - 10 * q^61 - 6 * q^65 + 6 * q^67 - 16 * q^69 + 12 * q^73 + 14 * q^75 - 16 * q^79 + 10 * q^81 - 18 * q^83 + 16 * q^85 - 12 * q^87 + 6 * q^95 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more