LMFDB - Embedded newform 624.2.bc.a.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [624,2,Mod(31,624)] 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("624.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(624, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$1$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	624.31
Dual form			624.2.bc.a.463.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{3} +(-2.00000 + 2.00000i) q^{7} -1.00000 q^{9} +(-3.00000 + 3.00000i) q^{11} +(-3.00000 - 2.00000i) q^{13} -6.00000i q^{17} +(-4.00000 - 4.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} -6.00000 q^{23} +5.00000i q^{25} +1.00000i q^{27} -6.00000 q^{29} +(4.00000 + 4.00000i) q^{31} +(3.00000 + 3.00000i) q^{33} +(7.00000 + 7.00000i) q^{37} +(-2.00000 + 3.00000i) q^{39} +(6.00000 - 6.00000i) q^{41} -8.00000 q^{43} +(-3.00000 + 3.00000i) q^{47} -1.00000i q^{49} -6.00000 q^{51} -6.00000 q^{53} +(-4.00000 + 4.00000i) q^{57} +(9.00000 - 9.00000i) q^{59} +(2.00000 - 2.00000i) q^{63} +(-2.00000 - 2.00000i) q^{67} +6.00000i q^{69} +(3.00000 + 3.00000i) q^{71} +(1.00000 + 1.00000i) q^{73} +5.00000 q^{75} -12.0000i q^{77} +8.00000i q^{79} +1.00000 q^{81} +(-3.00000 - 3.00000i) q^{83} +6.00000i q^{87} +(10.0000 - 2.00000i) q^{91} +(4.00000 - 4.00000i) q^{93} +(-7.00000 + 7.00000i) q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{13} - 8 q^{19} + 4 q^{21} - 12 q^{23} - 12 q^{29} + 8 q^{31} + 6 q^{33} + 14 q^{37} - 4 q^{39} + 12 q^{41} - 16 q^{43} - 6 q^{47} - 12 q^{51} - 12 q^{53} - 8 q^{57}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - 4 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^13 - 8 * q^19 + 4 * q^21 - 12 * q^23 - 12 * q^29 + 8 * q^31 + 6 * q^33 + 14 * q^37 - 4 * q^39 + 12 * q^41 - 16 * q^43 - 6 * q^47 - 12 * q^51 - 12 * q^53 - 8 * q^57 + 18 * q^59 + 4 * q^63 - 4 * q^67 + 6 * q^71 + 2 * q^73 + 10 * q^75 + 2 * q^81 - 6 * q^83 + 20 * q^91 + 8 * q^93 - 14 * q^97 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$		0			0
$5$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$5$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$		0			0
$9$	−1.00000			−0.333333
$10$		0			0
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	−0.995824	−	0.0912903i	$-0.970901\pi$
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	0.0912903	+	0.995824i	$0.470901\pi$
$12$		0			0
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.00000i		−	1.45521i	−0.685994	−	0.727607i	$-0.740633\pi$
$17$		−	6.00000i		−	1.45521i	0.685994	−	0.727607i	$-0.259367\pi$
$18$		0			0
$19$	−4.00000	−	4.00000i	−0.917663	−	0.917663i	0.0791961	−	0.996859i	$-0.474765\pi$
$19$	−4.00000	−	4.00000i	−0.917663	−	0.917663i	−0.996859	+	0.0791961i	$0.974765\pi$
$20$		0			0
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	4.00000	+	4.00000i	0.718421	+	0.718421i	0.968282	−	0.249861i	$-0.0803848\pi$
$31$	4.00000	+	4.00000i	0.718421	+	0.718421i	−0.249861	+	0.968282i	$0.580385\pi$
$32$		0			0
$33$	3.00000	+	3.00000i	0.522233	+	0.522233i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.00000	+	7.00000i	1.15079	+	1.15079i	0.986394	+	0.164399i	$0.0525685\pi$
$37$	7.00000	+	7.00000i	1.15079	+	1.15079i	0.164399	+	0.986394i	$0.447432\pi$
$38$		0			0
$39$	−2.00000	+	3.00000i	−0.320256	+	0.480384i
$40$		0			0
$41$	6.00000	−	6.00000i	0.937043	−	0.937043i	−0.0610897	−	0.998132i	$-0.519458\pi$
$41$	6.00000	−	6.00000i	0.937043	−	0.937043i	0.998132	+	0.0610897i	$0.0194576\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	+	3.00000i	−0.437595	+	0.437595i	−0.891202	−	0.453607i	$-0.850137\pi$
$47$	−3.00000	+	3.00000i	−0.437595	+	0.437595i	0.453607	+	0.891202i	$0.350137\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−6.00000			−0.840168
$52$		0			0
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.00000	+	4.00000i	−0.529813	+	0.529813i
$58$		0			0
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.189896	−	0.981804i	$-0.439185\pi$
$59$	9.00000	−	9.00000i	1.17170	−	1.17170i	0.981804	−	0.189896i	$-0.0608151\pi$
$60$		0			0
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$		0			0
$63$	2.00000	−	2.00000i	0.251976	−	0.251976i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.00000	−	2.00000i	−0.244339	−	0.244339i	0.574304	−	0.818642i	$-0.305273\pi$
$67$	−2.00000	−	2.00000i	−0.244339	−	0.244339i	−0.818642	+	0.574304i	$0.805273\pi$
$68$		0			0
$69$			6.00000i			0.722315i
$70$		0			0
$71$	3.00000	+	3.00000i	0.356034	+	0.356034i	0.862349	−	0.506314i	$-0.168992\pi$
$71$	3.00000	+	3.00000i	0.356034	+	0.356034i	−0.506314	+	0.862349i	$0.668992\pi$
$72$		0			0
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	0.763202	−	0.646160i	$-0.223626\pi$
$73$	1.00000	+	1.00000i	0.117041	+	0.117041i	−0.646160	+	0.763202i	$0.723626\pi$
$74$		0			0
$75$	5.00000			0.577350
$76$		0			0
$77$		−	12.0000i		−	1.36753i
$78$		0			0
$79$			8.00000i			0.900070i	0.893011	+	0.450035i	$0.148589\pi$
$79$			8.00000i			0.900070i	−0.893011	+	0.450035i	$0.851411\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−3.00000	−	3.00000i	−0.329293	−	0.329293i	0.523025	−	0.852318i	$-0.324804\pi$
$83$	−3.00000	−	3.00000i	−0.329293	−	0.329293i	−0.852318	+	0.523025i	$0.824804\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			6.00000i			0.643268i
$88$		0			0
$89$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$89$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$90$		0			0
$91$	10.0000	−	2.00000i	1.04828	−	0.209657i
$92$		0			0
$93$	4.00000	−	4.00000i	0.414781	−	0.414781i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	−0.966691	−	0.255948i	$-0.917612\pi$
$97$	−7.00000	+	7.00000i	−0.710742	+	0.710742i	0.255948	+	0.966691i	$0.417612\pi$
$98$		0			0
$99$	3.00000	−	3.00000i	0.301511	−	0.301511i
$100$		0			0
$101$		−	18.0000i		−	1.79107i	−0.444994	−	0.895533i	$-0.646794\pi$
$101$		−	18.0000i		−	1.79107i	0.444994	−	0.895533i	$-0.353206\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	18.0000i		−	1.74013i	−0.492941	−	0.870063i	$-0.664078\pi$
$107$		−	18.0000i		−	1.74013i	0.492941	−	0.870063i	$-0.335922\pi$
$108$		0			0
$109$	−5.00000	+	5.00000i	−0.478913	+	0.478913i	−0.904784	−	0.425871i	$-0.859968\pi$
$109$	−5.00000	+	5.00000i	−0.478913	+	0.478913i	0.425871	+	0.904784i	$0.359968\pi$
$110$		0			0
$111$	7.00000	−	7.00000i	0.664411	−	0.664411i
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$		0			0
$119$	12.0000	+	12.0000i	1.10004	+	1.10004i
$120$		0			0
$121$		−	7.00000i		−	0.636364i
$122$		0			0
$123$	−6.00000	−	6.00000i	−0.541002	−	0.541002i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$		0			0
$129$			8.00000i			0.704361i
$130$		0			0
$131$			18.0000i			1.57267i	0.617802	+	0.786334i	$0.288023\pi$
$131$			18.0000i			1.57267i	−0.617802	+	0.786334i	$0.711977\pi$
$132$		0			0
$133$	16.0000			1.38738
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	−	6.00000i	−0.512615	−	0.512615i	0.402712	−	0.915327i	$-0.368068\pi$
$137$	−6.00000	−	6.00000i	−0.512615	−	0.512615i	−0.915327	+	0.402712i	$0.868068\pi$
$138$		0			0
$139$		−	12.0000i		−	1.01783i	−0.860818	−	0.508913i	$-0.830047\pi$
$139$		−	12.0000i		−	1.01783i	0.860818	−	0.508913i	$-0.169953\pi$
$140$		0			0
$141$	3.00000	+	3.00000i	0.252646	+	0.252646i
$142$		0			0
$143$	15.0000	−	3.00000i	1.25436	−	0.250873i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.00000			−0.0824786
$148$		0			0
$149$	−6.00000	+	6.00000i	−0.491539	+	0.491539i	−0.908791	−	0.417252i	$-0.862993\pi$
$149$	−6.00000	+	6.00000i	−0.491539	+	0.491539i	0.417252	+	0.908791i	$0.362993\pi$
$150$		0			0
$151$	4.00000	−	4.00000i	0.325515	−	0.325515i	−0.525363	−	0.850878i	$-0.676070\pi$
$151$	4.00000	−	4.00000i	0.325515	−	0.325515i	0.850878	+	0.525363i	$0.176070\pi$
$152$		0			0
$153$			6.00000i			0.485071i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	4.00000			0.319235			0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000			0.319235			0.159617	+	0.987179i	$0.448974\pi$
$158$		0			0
$159$			6.00000i			0.475831i
$160$		0			0
$161$	12.0000	−	12.0000i	0.945732	−	0.945732i
$162$		0			0
$163$	16.0000	−	16.0000i	1.25322	−	1.25322i	0.298947	−	0.954270i	$-0.403365\pi$
$163$	16.0000	−	16.0000i	1.25322	−	1.25322i	0.954270	−	0.298947i	$-0.0966354\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	−0.813588	−	0.581441i	$-0.802489\pi$
$167$	−3.00000	+	3.00000i	−0.232147	+	0.232147i	0.581441	+	0.813588i	$0.302489\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	4.00000	+	4.00000i	0.305888	+	0.305888i
$172$		0			0
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$		0			0
$175$	−10.0000	−	10.0000i	−0.755929	−	0.755929i
$176$		0			0
$177$	−9.00000	−	9.00000i	−0.676481	−	0.676481i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$			6.00000i			0.445976i	0.974821	+	0.222988i	$0.0715812\pi$
$181$			6.00000i			0.445976i	−0.974821	+	0.222988i	$0.928419\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	18.0000	+	18.0000i	1.31629	+	1.31629i
$188$		0			0
$189$	−2.00000	−	2.00000i	−0.145479	−	0.145479i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	0.408768	−	0.912639i	$-0.365959\pi$
$193$	−7.00000	−	7.00000i	−0.503871	−	0.503871i	−0.912639	+	0.408768i	$0.865959\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.0000	+	12.0000i	−0.854965	+	0.854965i	−0.990740	−	0.135775i	$-0.956648\pi$
$197$	−12.0000	+	12.0000i	−0.854965	+	0.854965i	0.135775	+	0.990740i	$0.456648\pi$
$198$		0			0
$199$	−24.0000			−1.70131			−0.850657	−	0.525720i	$-0.823796\pi$
$199$	−24.0000			−1.70131			−0.850657	+	0.525720i	$0.823796\pi$
$200$		0			0
$201$	−2.00000	+	2.00000i	−0.141069	+	0.141069i
$202$		0			0
$203$	12.0000	−	12.0000i	0.842235	−	0.842235i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	6.00000			0.417029
$208$		0			0
$209$	24.0000			1.66011
$210$		0			0
$211$			4.00000i			0.275371i	0.990476	+	0.137686i	$0.0439664\pi$
$211$			4.00000i			0.275371i	−0.990476	+	0.137686i	$0.956034\pi$
$212$		0			0
$213$	3.00000	−	3.00000i	0.205557	−	0.205557i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−16.0000			−1.08615
$218$		0			0
$219$	1.00000	−	1.00000i	0.0675737	−	0.0675737i
$220$		0			0
$221$	−12.0000	+	18.0000i	−0.807207	+	1.21081i
$222$		0			0
$223$	8.00000	+	8.00000i	0.535720	+	0.535720i	0.922269	−	0.386549i	$-0.126333\pi$
$223$	8.00000	+	8.00000i	0.535720	+	0.535720i	−0.386549	+	0.922269i	$0.626333\pi$
$224$		0			0
$225$		−	5.00000i		−	0.333333i
$226$		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
$229$	−17.0000	−	17.0000i	−1.12339	−	1.12339i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−17.0000	−	17.0000i	−1.12339	−	1.12339i	−0.132164	−	0.991228i	$-0.542192\pi$
$230$		0			0
$231$	−12.0000			−0.789542
$232$		0			0
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.00000			0.519656
$238$		0			0
$239$	9.00000	+	9.00000i	0.582162	+	0.582162i	0.935497	−	0.353335i	$-0.114952\pi$
$239$	9.00000	+	9.00000i	0.582162	+	0.582162i	−0.353335	+	0.935497i	$0.614952\pi$
$240$		0			0
$241$	11.0000	+	11.0000i	0.708572	+	0.708572i	0.966235	−	0.257663i	$-0.0829523\pi$
$241$	11.0000	+	11.0000i	0.708572	+	0.708572i	−0.257663	+	0.966235i	$0.582952\pi$
$242$		0			0
$243$		−	1.00000i		−	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000	+	20.0000i	0.254514	+	1.27257i
$248$		0			0
$249$	−3.00000	+	3.00000i	−0.190117	+	0.190117i
$250$		0			0
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$		0			0
$253$	18.0000	−	18.0000i	1.13165	−	1.13165i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			6.00000i			0.374270i	0.982334	+	0.187135i	$0.0599201\pi$
$257$			6.00000i			0.374270i	−0.982334	+	0.187135i	$0.940080\pi$
$258$		0			0
$259$	−28.0000			−1.73984
$260$		0			0
$261$	6.00000			0.371391
$262$		0			0
$263$		−	30.0000i		−	1.84988i	−0.380114	−	0.924940i	$-0.624115\pi$
$263$		−	30.0000i		−	1.84988i	0.380114	−	0.924940i	$-0.375885\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$	−10.0000	+	10.0000i	−0.607457	+	0.607457i	−0.942281	−	0.334824i	$-0.891323\pi$
$271$	−10.0000	+	10.0000i	−0.607457	+	0.607457i	0.334824	+	0.942281i	$0.391323\pi$
$272$		0			0
$273$	−2.00000	−	10.0000i	−0.121046	−	0.605228i
$274$		0			0
$275$	−15.0000	−	15.0000i	−0.904534	−	0.904534i
$276$		0			0
$277$			24.0000i			1.44202i	0.692925	+	0.721010i	$0.256322\pi$
$277$			24.0000i			1.44202i	−0.692925	+	0.721010i	$0.743678\pi$
$278$		0			0
$279$	−4.00000	−	4.00000i	−0.239474	−	0.239474i
$280$		0			0
$281$	18.0000	+	18.0000i	1.07379	+	1.07379i	0.997051	+	0.0767387i	$0.0244507\pi$
$281$	18.0000	+	18.0000i	1.07379	+	1.07379i	0.0767387	+	0.997051i	$0.475549\pi$
$282$		0			0
$283$	−24.0000			−1.42665			−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			24.0000i			1.41668i
$288$		0			0
$289$	−19.0000			−1.11765
$290$		0			0
$291$	7.00000	+	7.00000i	0.410347	+	0.410347i
$292$		0			0
$293$	−6.00000	−	6.00000i	−0.350524	−	0.350524i	0.509781	−	0.860304i	$-0.329727\pi$
$293$	−6.00000	−	6.00000i	−0.350524	−	0.350524i	−0.860304	+	0.509781i	$0.829727\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.00000	−	3.00000i	−0.174078	−	0.174078i
$298$		0			0
$299$	18.0000	+	12.0000i	1.04097	+	0.693978i
$300$		0			0
$301$	16.0000	−	16.0000i	0.922225	−	0.922225i
$302$		0			0
$303$	−18.0000			−1.03407
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−10.0000	+	10.0000i	−0.570730	+	0.570730i	−0.932332	−	0.361602i	$-0.882230\pi$
$307$	−10.0000	+	10.0000i	−0.570730	+	0.570730i	0.361602	+	0.932332i	$0.382230\pi$
$308$		0			0
$309$		−	4.00000i		−	0.227552i
$310$		0			0
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	−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
$317$	−12.0000	+	12.0000i	−0.673987	+	0.673987i	−0.958633	−	0.284646i	$-0.908124\pi$
$317$	−12.0000	+	12.0000i	−0.673987	+	0.673987i	0.284646	+	0.958633i	$0.408124\pi$
$318$		0			0
$319$	18.0000	−	18.0000i	1.00781	−	1.00781i
$320$		0			0
$321$	−18.0000			−1.00466
$322$		0			0
$323$	−24.0000	+	24.0000i	−1.33540	+	1.33540i
$324$		0			0
$325$	10.0000	−	15.0000i	0.554700	−	0.832050i
$326$		0			0
$327$	5.00000	+	5.00000i	0.276501	+	0.276501i
$328$		0			0
$329$		−	12.0000i		−	0.661581i
$330$		0			0
$331$	−2.00000	−	2.00000i	−0.109930	−	0.109930i	0.650002	−	0.759932i	$-0.274768\pi$
$331$	−2.00000	−	2.00000i	−0.109930	−	0.109930i	−0.759932	+	0.650002i	$0.774768\pi$
$332$		0			0
$333$	−7.00000	−	7.00000i	−0.383598	−	0.383598i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	32.0000i		−	1.74315i	−0.490261	−	0.871576i	$-0.663099\pi$
$337$		−	32.0000i		−	1.74315i	0.490261	−	0.871576i	$-0.336901\pi$
$338$		0			0
$339$			6.00000i			0.325875i
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$		0			0
$349$	−7.00000	−	7.00000i	−0.374701	−	0.374701i	0.494485	−	0.869186i	$-0.335357\pi$
$349$	−7.00000	−	7.00000i	−0.374701	−	0.374701i	−0.869186	+	0.494485i	$0.835357\pi$
$350$		0			0
$351$	2.00000	−	3.00000i	0.106752	−	0.160128i
$352$		0			0
$353$	−18.0000	+	18.0000i	−0.958043	+	0.958043i	−0.999155	−	0.0411112i	$-0.986910\pi$
$353$	−18.0000	+	18.0000i	−0.958043	+	0.958043i	0.0411112	+	0.999155i	$0.486910\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	12.0000	−	12.0000i	0.635107	−	0.635107i
$358$		0			0
$359$	−9.00000	+	9.00000i	−0.475002	+	0.475002i	−0.903529	−	0.428527i	$-0.859033\pi$
$359$	−9.00000	+	9.00000i	−0.475002	+	0.475002i	0.428527	+	0.903529i	$0.359033\pi$
$360$		0			0
$361$			13.0000i			0.684211i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	36.0000i		−	1.87918i	−0.342296	−	0.939592i	$-0.611204\pi$
$367$		−	36.0000i		−	1.87918i	0.342296	−	0.939592i	$-0.388796\pi$
$368$		0			0
$369$	−6.00000	+	6.00000i	−0.312348	+	0.312348i
$370$		0			0
$371$	12.0000	−	12.0000i	0.623009	−	0.623009i
$372$		0			0
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.0000	+	12.0000i	0.927047	+	0.618031i
$378$		0			0
$379$	16.0000	+	16.0000i	0.821865	+	0.821865i	0.986375	−	0.164511i	$-0.0526045\pi$
$379$	16.0000	+	16.0000i	0.821865	+	0.821865i	−0.164511	+	0.986375i	$0.552604\pi$
$380$		0			0
$381$		−	12.0000i		−	0.614779i
$382$		0			0
$383$	−21.0000	−	21.0000i	−1.07305	−	1.07305i	−0.997113	−	0.0759373i	$-0.975805\pi$
$383$	−21.0000	−	21.0000i	−1.07305	−	1.07305i	−0.0759373	−	0.997113i	$-0.524195\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.00000			0.406663
$388$		0			0
$389$		−	6.00000i		−	0.304212i	−0.988364	−	0.152106i	$-0.951394\pi$
$389$		−	6.00000i		−	0.304212i	0.988364	−	0.152106i	$-0.0486055\pi$
$390$		0			0
$391$			36.0000i			1.82060i
$392$		0			0
$393$	18.0000			0.907980
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7.00000	−	7.00000i	−0.351320	−	0.351320i	0.509281	−	0.860601i	$-0.329912\pi$
$397$	−7.00000	−	7.00000i	−0.351320	−	0.351320i	−0.860601	+	0.509281i	$0.829912\pi$
$398$		0			0
$399$		−	16.0000i		−	0.801002i
$400$		0			0
$401$	24.0000	+	24.0000i	1.19850	+	1.19850i	0.974615	+	0.223888i	$0.0718750\pi$
$401$	24.0000	+	24.0000i	1.19850	+	1.19850i	0.223888	+	0.974615i	$0.428125\pi$
$402$		0			0
$403$	−4.00000	−	20.0000i	−0.199254	−	0.996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−42.0000			−2.08186
$408$		0			0
$409$	1.00000	−	1.00000i	0.0494468	−	0.0494468i	−0.681951	−	0.731398i	$-0.738868\pi$
$409$	1.00000	−	1.00000i	0.0494468	−	0.0494468i	0.731398	+	0.681951i	$0.238868\pi$
$410$		0			0
$411$	−6.00000	+	6.00000i	−0.295958	+	0.295958i
$412$		0			0
$413$			36.0000i			1.77144i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−12.0000			−0.587643
$418$		0			0
$419$			30.0000i			1.46560i	0.680446	+	0.732798i	$0.261786\pi$
$419$			30.0000i			1.46560i	−0.680446	+	0.732798i	$0.738214\pi$
$420$		0			0
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	−0.922383	−	0.386276i	$-0.873761\pi$
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	0.386276	+	0.922383i	$0.373761\pi$
$422$		0			0
$423$	3.00000	−	3.00000i	0.145865	−	0.145865i
$424$		0			0
$425$	30.0000			1.45521
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−3.00000	−	15.0000i	−0.144841	−	0.724207i
$430$		0			0
$431$	15.0000	+	15.0000i	0.722525	+	0.722525i	0.969119	−	0.246594i	$-0.0793115\pi$
$431$	15.0000	+	15.0000i	0.722525	+	0.722525i	−0.246594	+	0.969119i	$0.579311\pi$
$432$		0			0
$433$			2.00000i			0.0961139i	0.998845	+	0.0480569i	$0.0153029\pi$
$433$			2.00000i			0.0961139i	−0.998845	+	0.0480569i	$0.984697\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	24.0000	+	24.0000i	1.14808	+	1.14808i
$438$		0			0
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$		0			0
$441$			1.00000i			0.0476190i
$442$		0			0
$443$			6.00000i			0.285069i	0.989790	+	0.142534i	$0.0455251\pi$
$443$			6.00000i			0.285069i	−0.989790	+	0.142534i	$0.954475\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.00000	+	6.00000i	0.283790	+	0.283790i
$448$		0			0
$449$	12.0000	+	12.0000i	0.566315	+	0.566315i	0.931094	−	0.364779i	$-0.118855\pi$
$449$	12.0000	+	12.0000i	0.566315	+	0.566315i	−0.364779	+	0.931094i	$0.618855\pi$
$450$		0			0
$451$			36.0000i			1.69517i
$452$		0			0
$453$	−4.00000	−	4.00000i	−0.187936	−	0.187936i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.00000	+	1.00000i	−0.0467780	+	0.0467780i	−0.730109	−	0.683331i	$-0.760531\pi$
$457$	−1.00000	+	1.00000i	−0.0467780	+	0.0467780i	0.683331	+	0.730109i	$0.260531\pi$
$458$		0			0
$459$	6.00000			0.280056
$460$		0			0
$461$	−12.0000	+	12.0000i	−0.558896	+	0.558896i	−0.928993	−	0.370097i	$-0.879324\pi$
$461$	−12.0000	+	12.0000i	−0.558896	+	0.558896i	0.370097	+	0.928993i	$0.379324\pi$
$462$		0			0
$463$	14.0000	−	14.0000i	0.650635	−	0.650635i	−0.302511	−	0.953146i	$-0.597825\pi$
$463$	14.0000	−	14.0000i	0.650635	−	0.650635i	0.953146	+	0.302511i	$0.0978248\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$		0			0
$469$	8.00000			0.369406
$470$		0			0
$471$		−	4.00000i		−	0.184310i
$472$		0			0
$473$	24.0000	−	24.0000i	1.10352	−	1.10352i
$474$		0			0
$475$	20.0000	−	20.0000i	0.917663	−	0.917663i
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	21.0000	−	21.0000i	0.959514	−	0.959514i	−0.0396973	−	0.999212i	$-0.512639\pi$
$479$	21.0000	−	21.0000i	0.959514	−	0.959514i	0.999212	+	0.0396973i	$0.0126394\pi$
$480$		0			0
$481$	−7.00000	−	35.0000i	−0.319173	−	1.59586i
$482$		0			0
$483$	−12.0000	−	12.0000i	−0.546019	−	0.546019i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	0.0896838	−	0.995970i	$-0.471414\pi$
$487$	−20.0000	−	20.0000i	−0.906287	−	0.906287i	−0.995970	+	0.0896838i	$0.971414\pi$
$488$		0			0
$489$	−16.0000	−	16.0000i	−0.723545	−	0.723545i
$490$		0			0
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$		0			0
$493$			36.0000i			1.62136i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.0000			−0.538274
$498$		0			0
$499$	2.00000	+	2.00000i	0.0895323	+	0.0895323i	0.750454	−	0.660922i	$-0.229835\pi$
$499$	2.00000	+	2.00000i	0.0895323	+	0.0895323i	−0.660922	+	0.750454i	$0.729835\pi$
$500$		0			0
$501$	3.00000	+	3.00000i	0.134030	+	0.134030i
$502$		0			0
$503$		−	30.0000i		−	1.33763i	−0.743427	−	0.668817i	$-0.766801\pi$
$503$		−	30.0000i		−	1.33763i	0.743427	−	0.668817i	$-0.233199\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.0000	−	5.00000i	0.532939	−	0.222058i
$508$		0			0
$509$	−12.0000	+	12.0000i	−0.531891	+	0.531891i	−0.921135	−	0.389244i	$-0.872736\pi$
$509$	−12.0000	+	12.0000i	−0.531891	+	0.531891i	0.389244	+	0.921135i	$0.372736\pi$
$510$		0			0
$511$	−4.00000			−0.176950
$512$		0			0
$513$	4.00000	−	4.00000i	0.176604	−	0.176604i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	18.0000i		−	0.791639i
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$		0			0
$525$	−10.0000	+	10.0000i	−0.436436	+	0.436436i
$526$		0			0
$527$	24.0000	−	24.0000i	1.04546	−	1.04546i
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$	−9.00000	+	9.00000i	−0.390567	+	0.390567i
$532$		0			0
$533$	−30.0000	+	6.00000i	−1.29944	+	0.259889i
$534$		0			0
$535$		0			0
$536$		0			0
$537$			12.0000i			0.517838i
$538$		0			0
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	7.00000	+	7.00000i	0.300954	+	0.300954i	0.841387	−	0.540433i	$-0.181740\pi$
$541$	7.00000	+	7.00000i	0.300954	+	0.300954i	−0.540433	+	0.841387i	$0.681740\pi$
$542$		0			0
$543$	6.00000			0.257485
$544$		0			0
$545$		0			0
$546$		0			0
$547$			36.0000i			1.53925i	0.638497	+	0.769624i	$0.279557\pi$
$547$			36.0000i			1.53925i	−0.638497	+	0.769624i	$0.720443\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	24.0000	+	24.0000i	1.02243	+	1.02243i
$552$		0			0
$553$	−16.0000	−	16.0000i	−0.680389	−	0.680389i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.00000	−	6.00000i	−0.254228	−	0.254228i	0.568473	−	0.822702i	$-0.307534\pi$
$557$	−6.00000	−	6.00000i	−0.254228	−	0.254228i	−0.822702	+	0.568473i	$0.807534\pi$
$558$		0			0
$559$	24.0000	+	16.0000i	1.01509	+	0.676728i
$560$		0			0
$561$	18.0000	−	18.0000i	0.759961	−	0.759961i
$562$		0			0
$563$	−12.0000			−0.505740			−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000			−0.505740			−0.252870	+	0.967500i	$0.581374\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.00000	+	2.00000i	−0.0839921	+	0.0839921i
$568$		0			0
$569$		−	30.0000i		−	1.25767i	−0.777541	−	0.628833i	$-0.783533\pi$
$569$		−	30.0000i		−	1.25767i	0.777541	−	0.628833i	$-0.216467\pi$
$570$		0			0
$571$	12.0000			0.502184			0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000			0.502184			0.251092	+	0.967963i	$0.419210\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	30.0000i		−	1.25109i
$576$		0			0
$577$	1.00000	−	1.00000i	0.0416305	−	0.0416305i	−0.685985	−	0.727616i	$-0.740628\pi$
$577$	1.00000	−	1.00000i	0.0416305	−	0.0416305i	0.727616	+	0.685985i	$0.240628\pi$
$578$		0			0
$579$	−7.00000	+	7.00000i	−0.290910	+	0.290910i
$580$		0			0
$581$	12.0000			0.497844
$582$		0			0
$583$	18.0000	−	18.0000i	0.745484	−	0.745484i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.00000	+	3.00000i	0.123823	+	0.123823i	0.766303	−	0.642480i	$-0.222094\pi$
$587$	3.00000	+	3.00000i	0.123823	+	0.123823i	−0.642480	+	0.766303i	$0.722094\pi$
$588$		0			0
$589$		−	32.0000i		−	1.31854i
$590$		0			0
$591$	12.0000	+	12.0000i	0.493614	+	0.493614i
$592$		0			0
$593$	24.0000	+	24.0000i	0.985562	+	0.985562i	0.999897	−	0.0143354i	$-0.00456325\pi$
$593$	24.0000	+	24.0000i	0.985562	+	0.985562i	−0.0143354	+	0.999897i	$0.504563\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			24.0000i			0.982255i
$598$		0			0
$599$		−	18.0000i		−	0.735460i	−0.929933	−	0.367730i	$-0.880135\pi$
$599$		−	18.0000i		−	0.735460i	0.929933	−	0.367730i	$-0.119865\pi$
$600$		0			0
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$		0			0
$603$	2.00000	+	2.00000i	0.0814463	+	0.0814463i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			12.0000i			0.487065i	0.969893	+	0.243532i	$0.0783062\pi$
$607$			12.0000i			0.487065i	−0.969893	+	0.243532i	$0.921694\pi$
$608$		0			0
$609$	−12.0000	−	12.0000i	−0.486265	−	0.486265i
$610$		0			0
$611$	15.0000	−	3.00000i	0.606835	−	0.121367i
$612$		0			0
$613$	1.00000	−	1.00000i	0.0403896	−	0.0403896i	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	1.00000	−	1.00000i	0.0403896	−	0.0403896i	0.727013	+	0.686624i	$0.240908\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00000	+	6.00000i	−0.241551	+	0.241551i	−0.817492	−	0.575941i	$-0.804636\pi$
$617$	−6.00000	+	6.00000i	−0.241551	+	0.241551i	0.575941	+	0.817492i	$0.304636\pi$
$618$		0			0
$619$	22.0000	−	22.0000i	0.884255	−	0.884255i	−0.109709	−	0.993964i	$-0.534992\pi$
$619$	22.0000	−	22.0000i	0.884255	−	0.884255i	0.993964	+	0.109709i	$0.0349919\pi$
$620$		0			0
$621$		−	6.00000i		−	0.240772i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−25.0000			−1.00000
$626$		0			0
$627$		−	24.0000i		−	0.958468i
$628$		0			0
$629$	42.0000	−	42.0000i	1.67465	−	1.67465i
$630$		0			0
$631$	−4.00000	+	4.00000i	−0.159237	+	0.159237i	−0.782229	−	0.622991i	$-0.785917\pi$
$631$	−4.00000	+	4.00000i	−0.159237	+	0.159237i	0.622991	+	0.782229i	$0.285917\pi$
$632$		0			0
$633$	4.00000			0.158986
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.00000	+	3.00000i	−0.0792429	+	0.118864i
$638$		0			0
$639$	−3.00000	−	3.00000i	−0.118678	−	0.118678i
$640$		0			0
$641$			18.0000i			0.710957i	0.934684	+	0.355479i	$0.115682\pi$
$641$			18.0000i			0.710957i	−0.934684	+	0.355479i	$0.884318\pi$
$642$		0			0
$643$	−2.00000	−	2.00000i	−0.0788723	−	0.0788723i	0.666570	−	0.745442i	$-0.267762\pi$
$643$	−2.00000	−	2.00000i	−0.0788723	−	0.0788723i	−0.745442	+	0.666570i	$0.767762\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$		0			0
$649$			54.0000i			2.11969i
$650$		0			0
$651$			16.0000i			0.627089i
$652$		0			0
$653$	−30.0000			−1.17399			−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000			−1.17399			−0.586995	+	0.809590i	$0.699689\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.00000	−	1.00000i	−0.0390137	−	0.0390137i
$658$		0			0
$659$		−	12.0000i		−	0.467454i	−0.972302	−	0.233727i	$-0.924908\pi$
$659$		−	12.0000i		−	0.467454i	0.972302	−	0.233727i	$-0.0750921\pi$
$660$		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
$663$	18.0000	+	12.0000i	0.699062	+	0.466041i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	36.0000			1.39393
$668$		0			0
$669$	8.00000	−	8.00000i	0.309298	−	0.309298i
$670$		0			0
$671$		0			0
$672$		0			0
$673$			30.0000i			1.15642i	0.815890	+	0.578208i	$0.196248\pi$
$673$			30.0000i			1.15642i	−0.815890	+	0.578208i	$0.803752\pi$
$674$		0			0
$675$	−5.00000			−0.192450
$676$		0			0
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$		0			0
$679$		−	28.0000i		−	1.07454i
$680$		0			0
$681$	−9.00000	+	9.00000i	−0.344881	+	0.344881i
$682$		0			0
$683$	15.0000	−	15.0000i	0.573959	−	0.573959i	−0.359273	−	0.933232i	$-0.616975\pi$
$683$	15.0000	−	15.0000i	0.573959	−	0.573959i	0.933232	+	0.359273i	$0.116975\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−17.0000	+	17.0000i	−0.648590	+	0.648590i
$688$		0			0
$689$	18.0000	+	12.0000i	0.685745	+	0.457164i
$690$		0			0
$691$	2.00000	+	2.00000i	0.0760836	+	0.0760836i	0.744125	−	0.668041i	$-0.232867\pi$
$691$	2.00000	+	2.00000i	0.0760836	+	0.0760836i	−0.668041	+	0.744125i	$0.732867\pi$
$692$		0			0
$693$			12.0000i			0.455842i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−36.0000	−	36.0000i	−1.36360	−	1.36360i
$698$		0			0
$699$	−6.00000			−0.226941
$700$		0			0
$701$		−	30.0000i		−	1.13308i	−0.824033	−	0.566542i	$-0.808281\pi$
$701$		−	30.0000i		−	1.13308i	0.824033	−	0.566542i	$-0.191719\pi$
$702$		0			0
$703$		−	56.0000i		−	2.11208i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	36.0000	+	36.0000i	1.35392	+	1.35392i
$708$		0			0
$709$	29.0000	+	29.0000i	1.08912	+	1.08912i	0.995619	+	0.0934984i	$0.0298050\pi$
$709$	29.0000	+	29.0000i	1.08912	+	1.08912i	0.0934984	+	0.995619i	$0.470195\pi$
$710$		0			0
$711$		−	8.00000i		−	0.300023i
$712$		0			0
$713$	−24.0000	−	24.0000i	−0.898807	−	0.898807i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.00000	−	9.00000i	0.336111	−	0.336111i
$718$		0			0
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	−8.00000	+	8.00000i	−0.297936	+	0.297936i
$722$		0			0
$723$	11.0000	−	11.0000i	0.409094	−	0.409094i
$724$		0			0
$725$		−	30.0000i		−	1.11417i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$			48.0000i			1.77534i
$732$		0			0
$733$	5.00000	−	5.00000i	0.184679	−	0.184679i	−0.608712	−	0.793391i	$-0.708314\pi$
$733$	5.00000	−	5.00000i	0.184679	−	0.184679i	0.793391	+	0.608712i	$0.208314\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.0000			0.442026
$738$		0			0
$739$	−38.0000	+	38.0000i	−1.39785	+	1.39785i	−0.591679	+	0.806174i	$0.701535\pi$
$739$	−38.0000	+	38.0000i	−1.39785	+	1.39785i	−0.806174	+	0.591679i	$0.798465\pi$
$740$		0			0
$741$	20.0000	−	4.00000i	0.734718	−	0.146944i
$742$		0			0
$743$	21.0000	+	21.0000i	0.770415	+	0.770415i	0.978179	−	0.207764i	$-0.0666185\pi$
$743$	21.0000	+	21.0000i	0.770415	+	0.770415i	−0.207764	+	0.978179i	$0.566619\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.00000	+	3.00000i	0.109764	+	0.109764i
$748$		0			0
$749$	36.0000	+	36.0000i	1.31541	+	1.31541i
$750$		0			0
$751$	−4.00000			−0.145962			−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000			−0.145962			−0.0729810	+	0.997333i	$0.523251\pi$
$752$		0			0
$753$			6.00000i			0.218652i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	36.0000			1.30844			0.654221	−	0.756303i	$-0.272997\pi$
$757$	36.0000			1.30844			0.654221	+	0.756303i	$0.272997\pi$
$758$		0			0
$759$	−18.0000	−	18.0000i	−0.653359	−	0.653359i
$760$		0			0
$761$	−18.0000	−	18.0000i	−0.652499	−	0.652499i	0.301095	−	0.953594i	$-0.402648\pi$
$761$	−18.0000	−	18.0000i	−0.652499	−	0.652499i	−0.953594	+	0.301095i	$0.902648\pi$
$762$		0			0
$763$		−	20.0000i		−	0.724049i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−45.0000	+	9.00000i	−1.62486	+	0.324971i
$768$		0			0
$769$	1.00000	−	1.00000i	0.0360609	−	0.0360609i	−0.688846	−	0.724907i	$-0.741883\pi$
$769$	1.00000	−	1.00000i	0.0360609	−	0.0360609i	0.724907	+	0.688846i	$0.241883\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$		0			0
$773$	−30.0000	+	30.0000i	−1.07903	+	1.07903i	−0.0824280	+	0.996597i	$0.526267\pi$
$773$	−30.0000	+	30.0000i	−1.07903	+	1.07903i	−0.996597	+	0.0824280i	$0.973733\pi$
$774$		0			0
$775$	−20.0000	+	20.0000i	−0.718421	+	0.718421i
$776$		0			0
$777$			28.0000i			1.00449i
$778$		0			0
$779$	−48.0000			−1.71978
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$		−	6.00000i		−	0.214423i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	2.00000	−	2.00000i	0.0712923	−	0.0712923i	−0.670562	−	0.741854i	$-0.733947\pi$
$787$	2.00000	−	2.00000i	0.0712923	−	0.0712923i	0.741854	+	0.670562i	$0.233947\pi$
$788$		0			0
$789$	−30.0000			−1.06803
$790$		0			0
$791$	12.0000	−	12.0000i	0.426671	−	0.426671i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	6.00000i		−	0.212531i	−0.994338	−	0.106265i	$-0.966111\pi$
$797$		−	6.00000i		−	0.212531i	0.994338	−	0.106265i	$-0.0338893\pi$
$798$		0			0
$799$	18.0000	+	18.0000i	0.636794	+	0.636794i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.00000			−0.211735
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	18.0000i		−	0.633630i
$808$		0			0
$809$	−42.0000			−1.47664			−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000			−1.47664			−0.738321	+	0.674450i	$0.764381\pi$
$810$		0			0
$811$	−4.00000	−	4.00000i	−0.140459	−	0.140459i	0.633381	−	0.773840i	$-0.281667\pi$
$811$	−4.00000	−	4.00000i	−0.140459	−	0.140459i	−0.773840	+	0.633381i	$0.781667\pi$
$812$		0			0
$813$	10.0000	+	10.0000i	0.350715	+	0.350715i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	32.0000	+	32.0000i	1.11954	+	1.11954i
$818$		0			0
$819$	−10.0000	+	2.00000i	−0.349428	+	0.0698857i
$820$		0			0
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	−0.594612	−	0.804013i	$-0.702694\pi$
$821$	6.00000	−	6.00000i	0.209401	−	0.209401i	0.804013	+	0.594612i	$0.202694\pi$
$822$		0			0
$823$	−40.0000			−1.39431			−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000			−1.39431			−0.697156	+	0.716919i	$0.745552\pi$
$824$		0			0
$825$	−15.0000	+	15.0000i	−0.522233	+	0.522233i
$826$		0			0
$827$	9.00000	−	9.00000i	0.312961	−	0.312961i	−0.533095	−	0.846055i	$-0.678971\pi$
$827$	9.00000	−	9.00000i	0.312961	−	0.312961i	0.846055	+	0.533095i	$0.178971\pi$
$828$		0			0
$829$		−	2.00000i		−	0.0694629i	−0.999397	−	0.0347314i	$-0.988942\pi$
$829$		−	2.00000i		−	0.0694629i	0.999397	−	0.0347314i	$-0.0110576\pi$
$830$		0			0
$831$	24.0000			0.832551
$832$		0			0
$833$	−6.00000			−0.207888
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.00000	+	4.00000i	−0.138260	+	0.138260i
$838$		0			0
$839$	−15.0000	+	15.0000i	−0.517858	+	0.517858i	−0.916923	−	0.399065i	$-0.869335\pi$
$839$	−15.0000	+	15.0000i	−0.517858	+	0.517858i	0.399065	+	0.916923i	$0.369335\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	18.0000	−	18.0000i	0.619953	−	0.619953i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	14.0000	+	14.0000i	0.481046	+	0.481046i
$848$		0			0
$849$			24.0000i			0.823678i
$850$		0			0
$851$	−42.0000	−	42.0000i	−1.43974	−	1.43974i
$852$		0			0
$853$	13.0000	+	13.0000i	0.445112	+	0.445112i	0.893726	−	0.448614i	$-0.148082\pi$
$853$	13.0000	+	13.0000i	0.445112	+	0.445112i	−0.448614	+	0.893726i	$0.648082\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	54.0000i		−	1.84460i	−0.386469	−	0.922302i	$-0.626305\pi$
$857$		−	54.0000i		−	1.84460i	0.386469	−	0.922302i	$-0.373695\pi$
$858$		0			0
$859$			40.0000i			1.36478i	0.730987	+	0.682391i	$0.239060\pi$
$859$			40.0000i			1.36478i	−0.730987	+	0.682391i	$0.760940\pi$
$860$		0			0
$861$	24.0000			0.817918
$862$		0			0
$863$	−27.0000	−	27.0000i	−0.919091	−	0.919091i	0.0778726	−	0.996963i	$-0.475187\pi$
$863$	−27.0000	−	27.0000i	−0.919091	−	0.919091i	−0.996963	+	0.0778726i	$0.975187\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			19.0000i			0.645274i
$868$		0			0
$869$	−24.0000	−	24.0000i	−0.814144	−	0.814144i
$870$		0			0
$871$	2.00000	+	10.0000i	0.0677674	+	0.338837i
$872$		0			0
$873$	7.00000	−	7.00000i	0.236914	−	0.236914i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	19.0000	−	19.0000i	0.641584	−	0.641584i	−0.309360	−	0.950945i	$-0.600115\pi$
$877$	19.0000	−	19.0000i	0.641584	−	0.641584i	0.950945	+	0.309360i	$0.100115\pi$
$878$		0			0
$879$	−6.00000	+	6.00000i	−0.202375	+	0.202375i
$880$		0			0
$881$		−	18.0000i		−	0.606435i	−0.952921	−	0.303218i	$-0.901939\pi$
$881$		−	18.0000i		−	0.606435i	0.952921	−	0.303218i	$-0.0980609\pi$
$882$		0			0
$883$	−24.0000			−0.807664			−0.403832	−	0.914833i	$-0.632322\pi$
$883$	−24.0000			−0.807664			−0.403832	+	0.914833i	$0.632322\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			48.0000i			1.61168i	0.592132	+	0.805841i	$0.298286\pi$
$887$			48.0000i			1.61168i	−0.592132	+	0.805841i	$0.701714\pi$
$888$		0			0
$889$	−24.0000	+	24.0000i	−0.804934	+	0.804934i
$890$		0			0
$891$	−3.00000	+	3.00000i	−0.100504	+	0.100504i
$892$		0			0
$893$	24.0000			0.803129
$894$		0			0
$895$		0			0
$896$		0			0
$897$	12.0000	−	18.0000i	0.400668	−	0.601003i
$898$		0			0
$899$	−24.0000	−	24.0000i	−0.800445	−	0.800445i
$900$		0			0
$901$			36.0000i			1.19933i
$902$		0			0
$903$	−16.0000	−	16.0000i	−0.532447	−	0.532447i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$		0			0
$909$			18.0000i			0.597022i
$910$		0			0
$911$			24.0000i			0.795155i	0.917568	+	0.397578i	$0.130149\pi$
$911$			24.0000i			0.795155i	−0.917568	+	0.397578i	$0.869851\pi$
$912$		0			0
$913$	18.0000			0.595713
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−36.0000	−	36.0000i	−1.18882	−	1.18882i
$918$		0			0
$919$		−	16.0000i		−	0.527791i	−0.964551	−	0.263896i	$-0.914993\pi$
$919$		−	16.0000i		−	0.527791i	0.964551	−	0.263896i	$-0.0850075\pi$
$920$		0			0
$921$	10.0000	+	10.0000i	0.329511	+	0.329511i
$922$		0			0
$923$	−3.00000	−	15.0000i	−0.0987462	−	0.493731i
$924$		0			0
$925$	−35.0000	+	35.0000i	−1.15079	+	1.15079i
$926$		0			0
$927$	−4.00000			−0.131377
$928$		0			0
$929$	30.0000	−	30.0000i	0.984268	−	0.984268i	−0.0156101	−	0.999878i	$-0.504969\pi$
$929$	30.0000	−	30.0000i	0.984268	−	0.984268i	0.999878	+	0.0156101i	$0.00496905\pi$
$930$		0			0
$931$	−4.00000	+	4.00000i	−0.131095	+	0.131095i
$932$		0			0
$933$			18.0000i			0.589294i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$			6.00000i			0.195803i
$940$		0			0
$941$	−6.00000	+	6.00000i	−0.195594	+	0.195594i	−0.798108	−	0.602514i	$-0.794166\pi$
$941$	−6.00000	+	6.00000i	−0.195594	+	0.195594i	0.602514	+	0.798108i	$0.294166\pi$
$942$		0			0
$943$	−36.0000	+	36.0000i	−1.17232	+	1.17232i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.00000	+	3.00000i	−0.0974869	+	0.0974869i	−0.754168	−	0.656681i	$-0.771960\pi$
$947$	−3.00000	+	3.00000i	−0.0974869	+	0.0974869i	0.656681	+	0.754168i	$0.271960\pi$
$948$		0			0
$949$	−1.00000	−	5.00000i	−0.0324614	−	0.162307i
$950$		0			0
$951$	12.0000	+	12.0000i	0.389127	+	0.389127i
$952$		0			0
$953$		−	42.0000i		−	1.36051i	−0.732974	−	0.680257i	$-0.761868\pi$
$953$		−	42.0000i		−	1.36051i	0.732974	−	0.680257i	$-0.238132\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−18.0000	−	18.0000i	−0.581857	−	0.581857i
$958$		0			0
$959$	24.0000			0.775000
$960$		0			0
$961$			1.00000i			0.0322581i
$962$		0			0
$963$			18.0000i			0.580042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−16.0000	−	16.0000i	−0.514525	−	0.514525i	0.401384	−	0.915910i	$-0.368529\pi$
$967$	−16.0000	−	16.0000i	−0.514525	−	0.514525i	−0.915910	+	0.401384i	$0.868529\pi$
$968$		0			0
$969$	24.0000	+	24.0000i	0.770991	+	0.770991i
$970$		0			0
$971$			60.0000i			1.92549i	0.270408	+	0.962746i	$0.412841\pi$
$971$			60.0000i			1.92549i	−0.270408	+	0.962746i	$0.587159\pi$
$972$		0			0
$973$	24.0000	+	24.0000i	0.769405	+	0.769405i
$974$		0			0
$975$	−15.0000	−	10.0000i	−0.480384	−	0.320256i
$976$		0			0
$977$	−24.0000	+	24.0000i	−0.767828	+	0.767828i	−0.977724	−	0.209896i	$-0.932688\pi$
$977$	−24.0000	+	24.0000i	−0.767828	+	0.767828i	0.209896	+	0.977724i	$0.432688\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	5.00000	−	5.00000i	0.159638	−	0.159638i
$982$		0			0
$983$	9.00000	−	9.00000i	0.287055	−	0.287055i	−0.548859	−	0.835915i	$-0.684938\pi$
$983$	9.00000	−	9.00000i	0.287055	−	0.287055i	0.835915	+	0.548859i	$0.184938\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−12.0000			−0.381964
$988$		0			0
$989$	48.0000			1.52631
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	−2.00000	+	2.00000i	−0.0634681	+	0.0634681i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−26.0000			−0.823428			−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000			−0.823428			−0.411714	+	0.911313i	$0.635070\pi$
$998$		0			0
$999$	−7.00000	+	7.00000i	−0.221470	+	0.221470i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bc.a.31.1	✓	2
3.2	odd	2		1872.2.bf.c.1279.1		2
4.3	odd	2		624.2.bc.b.31.1	yes	2
12.11	even	2		1872.2.bf.d.1279.1		2
13.8	odd	4		624.2.bc.b.463.1	yes	2
39.8	even	4		1872.2.bf.d.1711.1		2
52.47	even	4	inner	624.2.bc.a.463.1	yes	2
156.47	odd	4		1872.2.bf.c.1711.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.bc.a.31.1	✓	2	1.1	even	1	trivial
624.2.bc.a.463.1	yes	2	52.47	even	4	inner
624.2.bc.b.31.1	yes	2	4.3	odd	2
624.2.bc.b.463.1	yes	2	13.8	odd	4
1872.2.bf.c.1279.1		2	3.2	odd	2
1872.2.bf.c.1711.1		2	156.47	odd	4
1872.2.bf.d.1279.1		2	12.11	even	2
1872.2.bf.d.1711.1		2	39.8	even	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{3} +(-2.00000 + 2.00000i) q^{7} -1.00000 q^{9} +(-3.00000 + 3.00000i) q^{11} +(-3.00000 - 2.00000i) q^{13} -6.00000i q^{17} +(-4.00000 - 4.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} -6.00000 q^{23} +5.00000i q^{25} +1.00000i q^{27} -6.00000 q^{29} +(4.00000 + 4.00000i) q^{31} +(3.00000 + 3.00000i) q^{33} +(7.00000 + 7.00000i) q^{37} +(-2.00000 + 3.00000i) q^{39} +(6.00000 - 6.00000i) q^{41} -8.00000 q^{43} +(-3.00000 + 3.00000i) q^{47} -1.00000i q^{49} -6.00000 q^{51} -6.00000 q^{53} +(-4.00000 + 4.00000i) q^{57} +(9.00000 - 9.00000i) q^{59} +(2.00000 - 2.00000i) q^{63} +(-2.00000 - 2.00000i) q^{67} +6.00000i q^{69} +(3.00000 + 3.00000i) q^{71} +(1.00000 + 1.00000i) q^{73} +5.00000 q^{75} -12.0000i q^{77} +8.00000i q^{79} +1.00000 q^{81} +(-3.00000 - 3.00000i) q^{83} +6.00000i q^{87} +(10.0000 - 2.00000i) q^{91} +(4.00000 - 4.00000i) q^{93} +(-7.00000 + 7.00000i) q^{97} +(3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{7} - 2 q^{9} - 6 q^{11} - 6 q^{13} - 8 q^{19} + 4 q^{21} - 12 q^{23} - 12 q^{29} + 8 q^{31} + 6 q^{33} + 14 q^{37} - 4 q^{39} + 12 q^{41} - 16 q^{43} - 6 q^{47} - 12 q^{51} - 12 q^{53} - 8 q^{57}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - 4 * q^7 - 2 * q^9 - 6 * q^11 - 6 * q^13 - 8 * q^19 + 4 * q^21 - 12 * q^23 - 12 * q^29 + 8 * q^31 + 6 * q^33 + 14 * q^37 - 4 * q^39 + 12 * q^41 - 16 * q^43 - 6 * q^47 - 12 * q^51 - 12 * q^53 - 8 * q^57 + 18 * q^59 + 4 * q^63 - 4 * q^67 + 6 * q^71 + 2 * q^73 + 10 * q^75 + 2 * q^81 - 6 * q^83 + 20 * q^91 + 8 * q^93 - 14 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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