LMFDB - Embedded newform 1890.2.g.i.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(379,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1890.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.0917259820$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			379.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	1890.379
Dual form			1890.2.g.i.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(-2.00000 + 1.00000i) q^{10} -1.00000 q^{11} +5.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} -7.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -1.00000i q^{22} +(-3.00000 + 4.00000i) q^{25} -5.00000 q^{26} +1.00000i q^{28} -6.00000 q^{29} +1.00000i q^{32} +4.00000 q^{34} +(2.00000 - 1.00000i) q^{35} +4.00000i q^{37} -7.00000i q^{38} +(2.00000 - 1.00000i) q^{40} +3.00000 q^{41} +11.0000i q^{43} +1.00000 q^{44} +1.00000i q^{47} -1.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -5.00000i q^{52} -1.00000i q^{53} +(-1.00000 - 2.00000i) q^{55} -1.00000 q^{56} -6.00000i q^{58} -2.00000 q^{59} -2.00000 q^{61} -1.00000 q^{64} +(-10.0000 + 5.00000i) q^{65} -15.0000i q^{67} +4.00000i q^{68} +(1.00000 + 2.00000i) q^{70} -16.0000 q^{71} +11.0000i q^{73} -4.00000 q^{74} +7.00000 q^{76} +1.00000i q^{77} -10.0000 q^{79} +(1.00000 + 2.00000i) q^{80} +3.00000i q^{82} -7.00000i q^{83} +(8.00000 - 4.00000i) q^{85} -11.0000 q^{86} +1.00000i q^{88} +1.00000 q^{89} +5.00000 q^{91} -1.00000 q^{94} +(-7.00000 - 14.0000i) q^{95} +14.0000i q^{97} -1.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} + 2 q^{5}+O(q^{10}) $ 2 * q - 2 * q^4 + 2 * q^5	$ 2 q - 2 q^{4} + 2 q^{5} - 4 q^{10} - 2 q^{11} + 2 q^{14} + 2 q^{16} - 14 q^{19} - 2 q^{20} - 6 q^{25} - 10 q^{26} - 12 q^{29} + 8 q^{34} + 4 q^{35} + 4 q^{40} + 6 q^{41} + 2 q^{44} - 2 q^{49} - 8 q^{50} - 2 q^{55} - 2 q^{56} - 4 q^{59} - 4 q^{61} - 2 q^{64} - 20 q^{65} + 2 q^{70} - 32 q^{71} - 8 q^{74} + 14 q^{76} - 20 q^{79} + 2 q^{80} + 16 q^{85} - 22 q^{86} + 2 q^{89} + 10 q^{91} - 2 q^{94} - 14 q^{95}+O(q^{100}) $ 2 * q - 2 * q^4 + 2 * q^5 - 4 * q^10 - 2 * q^11 + 2 * q^14 + 2 * q^16 - 14 * q^19 - 2 * q^20 - 6 * q^25 - 10 * q^26 - 12 * q^29 + 8 * q^34 + 4 * q^35 + 4 * q^40 + 6 * q^41 + 2 * q^44 - 2 * q^49 - 8 * q^50 - 2 * q^55 - 2 * q^56 - 4 * q^59 - 4 * q^61 - 2 * q^64 - 20 * q^65 + 2 * q^70 - 32 * q^71 - 8 * q^74 + 14 * q^76 - 20 * q^79 + 2 * q^80 + 16 * q^85 - 22 * q^86 + 2 * q^89 + 10 * q^91 - 2 * q^94 - 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−2.00000	+	1.00000i	−0.632456	+	0.316228i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$			5.00000i			1.38675i	0.720577	+	0.693375i	$0.243877\pi$
$13$			5.00000i			1.38675i	−0.720577	+	0.693375i	$0.756123\pi$
$14$	1.00000			0.267261
$15$		0			0
$16$	1.00000			0.250000
$17$		−	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
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.00000	−	2.00000i	−0.223607	−	0.447214i
$21$		0			0
$22$		−	1.00000i		−	0.213201i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	−5.00000			−0.980581
$27$		0			0
$28$			1.00000i			0.188982i
$29$	−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
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	4.00000			0.685994
$35$	2.00000	−	1.00000i	0.338062	−	0.169031i
$36$		0			0
$37$			4.00000i			0.657596i	0.944400	+	0.328798i	$0.106644\pi$
$37$			4.00000i			0.657596i	−0.944400	+	0.328798i	$0.893356\pi$
$38$		−	7.00000i		−	1.13555i
$39$		0			0
$40$	2.00000	−	1.00000i	0.316228	−	0.158114i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$			11.0000i			1.67748i	0.544529	+	0.838742i	$0.316708\pi$
$43$			11.0000i			1.67748i	−0.544529	+	0.838742i	$0.683292\pi$
$44$	1.00000			0.150756
$45$		0			0
$46$		0			0
$47$			1.00000i			0.145865i	0.997337	+	0.0729325i	$0.0232358\pi$
$47$			1.00000i			0.145865i	−0.997337	+	0.0729325i	$0.976764\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	−4.00000	−	3.00000i	−0.565685	−	0.424264i
$51$		0			0
$52$		−	5.00000i		−	0.693375i
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$		0			0
$55$	−1.00000	−	2.00000i	−0.134840	−	0.269680i
$56$	−1.00000			−0.133631
$57$		0			0
$58$		−	6.00000i		−	0.787839i
$59$	−2.00000			−0.260378			−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000			−0.260378			−0.130189	+	0.991489i	$0.541558\pi$
$60$		0			0
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.0000	+	5.00000i	−1.24035	+	0.620174i
$66$		0			0
$67$		−	15.0000i		−	1.83254i	−0.400559	−	0.916271i	$-0.631184\pi$
$67$		−	15.0000i		−	1.83254i	0.400559	−	0.916271i	$-0.368816\pi$
$68$			4.00000i			0.485071i
$69$		0			0
$70$	1.00000	+	2.00000i	0.119523	+	0.239046i
$71$	−16.0000			−1.89885			−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000			−1.89885			−0.949425	+	0.313993i	$0.898333\pi$
$72$		0			0
$73$			11.0000i			1.28745i	0.765256	+	0.643726i	$0.222612\pi$
$73$			11.0000i			1.28745i	−0.765256	+	0.643726i	$0.777388\pi$
$74$	−4.00000			−0.464991
$75$		0			0
$76$	7.00000			0.802955
$77$			1.00000i			0.113961i
$78$		0			0
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	1.00000	+	2.00000i	0.111803	+	0.223607i
$81$		0			0
$82$			3.00000i			0.331295i
$83$		−	7.00000i		−	0.768350i	−0.923260	−	0.384175i	$-0.874486\pi$
$83$		−	7.00000i		−	0.768350i	0.923260	−	0.384175i	$-0.125514\pi$
$84$		0			0
$85$	8.00000	−	4.00000i	0.867722	−	0.433861i
$86$	−11.0000			−1.18616
$87$		0			0
$88$			1.00000i			0.106600i
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$		0			0
$91$	5.00000			0.524142
$92$		0			0
$93$		0			0
$94$	−1.00000			−0.103142
$95$	−7.00000	−	14.0000i	−0.718185	−	1.43637i
$96$		0			0
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$		−	1.00000i		−	0.101015i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$	−5.00000			−0.497519			−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000			−0.497519			−0.248759	+	0.968565i	$0.580023\pi$
$102$		0			0
$103$		−	6.00000i		−	0.591198i	−0.955312	−	0.295599i	$-0.904481\pi$
$103$		−	6.00000i		−	0.591198i	0.955312	−	0.295599i	$-0.0955191\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	1.00000			0.0971286
$107$		−	6.00000i		−	0.580042i	−0.957020	−	0.290021i	$-0.906338\pi$
$107$		−	6.00000i		−	0.580042i	0.957020	−	0.290021i	$-0.0936623\pi$
$108$		0			0
$109$	15.0000			1.43674			0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000			1.43674			0.718370	+	0.695662i	$0.244889\pi$
$110$	2.00000	−	1.00000i	0.190693	−	0.0953463i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$			15.0000i			1.41108i	0.708669	+	0.705541i	$0.249296\pi$
$113$			15.0000i			1.41108i	−0.708669	+	0.705541i	$0.750704\pi$
$114$		0			0
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$		−	2.00000i		−	0.184115i
$119$	−4.00000			−0.366679
$120$		0			0
$121$	−10.0000			−0.909091
$122$		−	2.00000i		−	0.181071i
$123$		0			0
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$			9.00000i			0.798621i	0.916816	+	0.399310i	$0.130750\pi$
$127$			9.00000i			0.798621i	−0.916816	+	0.399310i	$0.869250\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	−5.00000	−	10.0000i	−0.438529	−	0.877058i
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$			7.00000i			0.606977i
$134$	15.0000			1.29580
$135$		0			0
$136$	−4.00000			−0.342997
$137$		−	17.0000i		−	1.45241i	−0.687479	−	0.726204i	$-0.741283\pi$
$137$		−	17.0000i		−	1.45241i	0.687479	−	0.726204i	$-0.258717\pi$
$138$		0			0
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$	−2.00000	+	1.00000i	−0.169031	+	0.0845154i
$141$		0			0
$142$		−	16.0000i		−	1.34269i
$143$		−	5.00000i		−	0.418121i
$144$		0			0
$145$	−6.00000	−	12.0000i	−0.498273	−	0.996546i
$146$	−11.0000			−0.910366
$147$		0			0
$148$		−	4.00000i		−	0.328798i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$			7.00000i			0.567775i
$153$		0			0
$154$	−1.00000			−0.0805823
$155$		0			0
$156$		0			0
$157$		−	14.0000i		−	1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$		−	14.0000i		−	1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$		−	10.0000i		−	0.795557i
$159$		0			0
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		0			0
$162$		0			0
$163$			12.0000i			0.939913i	0.882690	+	0.469956i	$0.155730\pi$
$163$			12.0000i			0.939913i	−0.882690	+	0.469956i	$0.844270\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$	7.00000			0.543305
$167$		−	20.0000i		−	1.54765i	−0.633402	−	0.773823i	$-0.718342\pi$
$167$		−	20.0000i		−	1.54765i	0.633402	−	0.773823i	$-0.281658\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	4.00000	+	8.00000i	0.306786	+	0.613572i
$171$		0			0
$172$		−	11.0000i		−	0.838742i
$173$		−	14.0000i		−	1.06440i	−0.846619	−	0.532200i	$-0.821365\pi$
$173$		−	14.0000i		−	1.06440i	0.846619	−	0.532200i	$-0.178635\pi$
$174$		0			0
$175$	4.00000	+	3.00000i	0.302372	+	0.226779i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$			1.00000i			0.0749532i
$179$	7.00000			0.523205			0.261602	−	0.965176i	$-0.415749\pi$
$179$	7.00000			0.523205			0.261602	+	0.965176i	$0.415749\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$			5.00000i			0.370625i
$183$		0			0
$184$		0			0
$185$	−8.00000	+	4.00000i	−0.588172	+	0.294086i
$186$		0			0
$187$			4.00000i			0.292509i
$188$		−	1.00000i		−	0.0729325i
$189$		0			0
$190$	14.0000	−	7.00000i	1.01567	−	0.507833i
$191$	−11.0000			−0.795932			−0.397966	−	0.917400i	$-0.630284\pi$
$191$	−11.0000			−0.795932			−0.397966	+	0.917400i	$0.630284\pi$
$192$		0			0
$193$			18.0000i			1.29567i	0.761781	+	0.647834i	$0.224325\pi$
$193$			18.0000i			1.29567i	−0.761781	+	0.647834i	$0.775675\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	1.00000			0.0714286
$197$			15.0000i			1.06871i	0.845262	+	0.534353i	$0.179445\pi$
$197$			15.0000i			1.06871i	−0.845262	+	0.534353i	$0.820555\pi$
$198$		0			0
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$	4.00000	+	3.00000i	0.282843	+	0.212132i
$201$		0			0
$202$		−	5.00000i		−	0.351799i
$203$			6.00000i			0.421117i
$204$		0			0
$205$	3.00000	+	6.00000i	0.209529	+	0.419058i
$206$	6.00000			0.418040
$207$		0			0
$208$			5.00000i			0.346688i
$209$	7.00000			0.484200
$210$		0			0
$211$	10.0000			0.688428			0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000			0.688428			0.344214	+	0.938891i	$0.388145\pi$
$212$			1.00000i			0.0686803i
$213$		0			0
$214$	6.00000			0.410152
$215$	−22.0000	+	11.0000i	−1.50039	+	0.750194i
$216$		0			0
$217$		0			0
$218$			15.0000i			1.01593i
$219$		0			0
$220$	1.00000	+	2.00000i	0.0674200	+	0.134840i
$221$	20.0000			1.34535
$222$		0			0
$223$			14.0000i			0.937509i	0.883328	+	0.468755i	$0.155297\pi$
$223$			14.0000i			0.937509i	−0.883328	+	0.468755i	$0.844703\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−15.0000			−0.997785
$227$			7.00000i			0.464606i	0.972643	+	0.232303i	$0.0746261\pi$
$227$			7.00000i			0.464606i	−0.972643	+	0.232303i	$0.925374\pi$
$228$		0			0
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$		0			0
$232$			6.00000i			0.393919i
$233$			3.00000i			0.196537i	0.995160	+	0.0982683i	$0.0313303\pi$
$233$			3.00000i			0.196537i	−0.995160	+	0.0982683i	$0.968670\pi$
$234$		0			0
$235$	−2.00000	+	1.00000i	−0.130466	+	0.0652328i
$236$	2.00000			0.130189
$237$		0			0
$238$		−	4.00000i		−	0.259281i
$239$	−4.00000			−0.258738			−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000			−0.258738			−0.129369	+	0.991596i	$0.541295\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		−	10.0000i		−	0.642824i
$243$		0			0
$244$	2.00000			0.128037
$245$	−1.00000	−	2.00000i	−0.0638877	−	0.127775i
$246$		0			0
$247$		−	35.0000i		−	2.22700i
$248$		0			0
$249$		0			0
$250$	2.00000	−	11.0000i	0.126491	−	0.695701i
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$		0			0
$253$		0			0
$254$	−9.00000			−0.564710
$255$		0			0
$256$	1.00000			0.0625000
$257$			28.0000i			1.74659i	0.487190	+	0.873296i	$0.338022\pi$
$257$			28.0000i			1.74659i	−0.487190	+	0.873296i	$0.661978\pi$
$258$		0			0
$259$	4.00000			0.248548
$260$	10.0000	−	5.00000i	0.620174	−	0.310087i
$261$		0			0
$262$		−	4.00000i		−	0.247121i
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$	2.00000	−	1.00000i	0.122859	−	0.0614295i
$266$	−7.00000			−0.429198
$267$		0			0
$268$			15.0000i			0.916271i
$269$	26.0000			1.58525			0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000			1.58525			0.792624	+	0.609711i	$0.208714\pi$
$270$		0			0
$271$	5.00000			0.303728			0.151864	−	0.988401i	$-0.451472\pi$
$271$	5.00000			0.303728			0.151864	+	0.988401i	$0.451472\pi$
$272$		−	4.00000i		−	0.242536i
$273$		0			0
$274$	17.0000			1.02701
$275$	3.00000	−	4.00000i	0.180907	−	0.241209i
$276$		0			0
$277$			8.00000i			0.480673i	0.970690	+	0.240337i	$0.0772579\pi$
$277$			8.00000i			0.480673i	−0.970690	+	0.240337i	$0.922742\pi$
$278$			20.0000i			1.19952i
$279$		0			0
$280$	−1.00000	−	2.00000i	−0.0597614	−	0.119523i
$281$	14.0000			0.835170			0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000			0.835170			0.417585	+	0.908638i	$0.362877\pi$
$282$		0			0
$283$			4.00000i			0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$			4.00000i			0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	16.0000			0.949425
$285$		0			0
$286$	5.00000			0.295656
$287$		−	3.00000i		−	0.177084i
$288$		0			0
$289$	1.00000			0.0588235
$290$	12.0000	−	6.00000i	0.704664	−	0.352332i
$291$		0			0
$292$		−	11.0000i		−	0.643726i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$		0			0
$295$	−2.00000	−	4.00000i	−0.116445	−	0.232889i
$296$	4.00000			0.232495
$297$		0			0
$298$			12.0000i			0.695141i
$299$		0			0
$300$		0			0
$301$	11.0000			0.634029
$302$		−	10.0000i		−	0.575435i
$303$		0			0
$304$	−7.00000			−0.401478
$305$	−2.00000	−	4.00000i	−0.114520	−	0.229039i
$306$		0			0
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$		−	1.00000i		−	0.0569803i
$309$		0			0
$310$		0			0
$311$	14.0000			0.793867			0.396934	−	0.917847i	$-0.370074\pi$
$311$	14.0000			0.793867			0.396934	+	0.917847i	$0.370074\pi$
$312$		0			0
$313$			13.0000i			0.734803i	0.930062	+	0.367402i	$0.119753\pi$
$313$			13.0000i			0.734803i	−0.930062	+	0.367402i	$0.880247\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	10.0000			0.562544
$317$			25.0000i			1.40414i	0.712108	+	0.702070i	$0.247741\pi$
$317$			25.0000i			1.40414i	−0.712108	+	0.702070i	$0.752259\pi$
$318$		0			0
$319$	6.00000			0.335936
$320$	−1.00000	−	2.00000i	−0.0559017	−	0.111803i
$321$		0			0
$322$		0			0
$323$			28.0000i			1.55796i
$324$		0			0
$325$	−20.0000	−	15.0000i	−1.10940	−	0.832050i
$326$	−12.0000			−0.664619
$327$		0			0
$328$		−	3.00000i		−	0.165647i
$329$	1.00000			0.0551318
$330$		0			0
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$			7.00000i			0.384175i
$333$		0			0
$334$	20.0000			1.09435
$335$	30.0000	−	15.0000i	1.63908	−	0.819538i
$336$		0			0
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$		−	12.0000i		−	0.652714i
$339$		0			0
$340$	−8.00000	+	4.00000i	−0.433861	+	0.216930i
$341$		0			0
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	11.0000			0.593080
$345$		0			0
$346$	14.0000			0.752645
$347$			28.0000i			1.50312i	0.659665	+	0.751559i	$0.270698\pi$
$347$			28.0000i			1.50312i	−0.659665	+	0.751559i	$0.729302\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$	−3.00000	+	4.00000i	−0.160357	+	0.213809i
$351$		0			0
$352$		−	1.00000i		−	0.0533002i
$353$		−	6.00000i		−	0.319348i	−0.987170	−	0.159674i	$-0.948956\pi$
$353$		−	6.00000i		−	0.319348i	0.987170	−	0.159674i	$-0.0510443\pi$
$354$		0			0
$355$	−16.0000	−	32.0000i	−0.849192	−	1.69838i
$356$	−1.00000			−0.0529999
$357$		0			0
$358$			7.00000i			0.369961i
$359$	5.00000			0.263890			0.131945	−	0.991257i	$-0.457878\pi$
$359$	5.00000			0.263890			0.131945	+	0.991257i	$0.457878\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$		−	14.0000i		−	0.735824i
$363$		0			0
$364$	−5.00000			−0.262071
$365$	−22.0000	+	11.0000i	−1.15153	+	0.575766i
$366$		0			0
$367$			2.00000i			0.104399i	0.998637	+	0.0521996i	$0.0166232\pi$
$367$			2.00000i			0.104399i	−0.998637	+	0.0521996i	$0.983377\pi$
$368$		0			0
$369$		0			0
$370$	−4.00000	−	8.00000i	−0.207950	−	0.415900i
$371$	−1.00000			−0.0519174
$372$		0			0
$373$			18.0000i			0.932005i	0.884783	+	0.466002i	$0.154306\pi$
$373$			18.0000i			0.932005i	−0.884783	+	0.466002i	$0.845694\pi$
$374$	−4.00000			−0.206835
$375$		0			0
$376$	1.00000			0.0515711
$377$		−	30.0000i		−	1.54508i
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	7.00000	+	14.0000i	0.359092	+	0.718185i
$381$		0			0
$382$		−	11.0000i		−	0.562809i
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$		0			0
$385$	−2.00000	+	1.00000i	−0.101929	+	0.0509647i
$386$	−18.0000			−0.916176
$387$		0			0
$388$		−	14.0000i		−	0.710742i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$			1.00000i			0.0505076i
$393$		0			0
$394$	−15.0000			−0.755689
$395$	−10.0000	−	20.0000i	−0.503155	−	1.00631i
$396$		0			0
$397$			34.0000i			1.70641i	0.521575	+	0.853206i	$0.325345\pi$
$397$			34.0000i			1.70641i	−0.521575	+	0.853206i	$0.674655\pi$
$398$		−	7.00000i		−	0.350878i
$399$		0			0
$400$	−3.00000	+	4.00000i	−0.150000	+	0.200000i
$401$	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
$404$	5.00000			0.248759
$405$		0			0
$406$	−6.00000			−0.297775
$407$		−	4.00000i		−	0.198273i
$408$		0			0
$409$	−22.0000			−1.08783			−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000			−1.08783			−0.543915	+	0.839140i	$0.683059\pi$
$410$	−6.00000	+	3.00000i	−0.296319	+	0.148159i
$411$		0			0
$412$			6.00000i			0.295599i
$413$			2.00000i			0.0984136i
$414$		0			0
$415$	14.0000	−	7.00000i	0.687233	−	0.343616i
$416$	−5.00000			−0.245145
$417$		0			0
$418$			7.00000i			0.342381i
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$		0			0
$421$	−11.0000			−0.536107			−0.268054	−	0.963404i	$-0.586380\pi$
$421$	−11.0000			−0.536107			−0.268054	+	0.963404i	$0.586380\pi$
$422$			10.0000i			0.486792i
$423$		0			0
$424$	−1.00000			−0.0485643
$425$	16.0000	+	12.0000i	0.776114	+	0.582086i
$426$		0			0
$427$			2.00000i			0.0967868i
$428$			6.00000i			0.290021i
$429$		0			0
$430$	−11.0000	−	22.0000i	−0.530467	−	1.06093i
$431$	−3.00000			−0.144505			−0.0722525	−	0.997386i	$-0.523019\pi$
$431$	−3.00000			−0.144505			−0.0722525	+	0.997386i	$0.523019\pi$
$432$		0			0
$433$			17.0000i			0.816968i	0.912766	+	0.408484i	$0.133942\pi$
$433$			17.0000i			0.816968i	−0.912766	+	0.408484i	$0.866058\pi$
$434$		0			0
$435$		0			0
$436$	−15.0000			−0.718370
$437$		0			0
$438$		0			0
$439$	3.00000			0.143182			0.0715911	−	0.997434i	$-0.477192\pi$
$439$	3.00000			0.143182			0.0715911	+	0.997434i	$0.477192\pi$
$440$	−2.00000	+	1.00000i	−0.0953463	+	0.0476731i
$441$		0			0
$442$			20.0000i			0.951303i
$443$			36.0000i			1.71041i	0.518289	+	0.855206i	$0.326569\pi$
$443$			36.0000i			1.71041i	−0.518289	+	0.855206i	$0.673431\pi$
$444$		0			0
$445$	1.00000	+	2.00000i	0.0474045	+	0.0948091i
$446$	−14.0000			−0.662919
$447$		0			0
$448$			1.00000i			0.0472456i
$449$	−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
$451$	−3.00000			−0.141264
$452$		−	15.0000i		−	0.705541i
$453$		0			0
$454$	−7.00000			−0.328526
$455$	5.00000	+	10.0000i	0.234404	+	0.468807i
$456$		0			0
$457$			22.0000i			1.02912i	0.857455	+	0.514558i	$0.172044\pi$
$457$			22.0000i			1.02912i	−0.857455	+	0.514558i	$0.827956\pi$
$458$		−	14.0000i		−	0.654177i
$459$		0			0
$460$		0			0
$461$	15.0000			0.698620			0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000			0.698620			0.349310	+	0.937007i	$0.386416\pi$
$462$		0			0
$463$			21.0000i			0.975953i	0.872857	+	0.487976i	$0.162265\pi$
$463$			21.0000i			0.975953i	−0.872857	+	0.487976i	$0.837735\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−3.00000			−0.138972
$467$			28.0000i			1.29569i	0.761774	+	0.647843i	$0.224329\pi$
$467$			28.0000i			1.29569i	−0.761774	+	0.647843i	$0.775671\pi$
$468$		0			0
$469$	−15.0000			−0.692636
$470$	−1.00000	−	2.00000i	−0.0461266	−	0.0922531i
$471$		0			0
$472$			2.00000i			0.0920575i
$473$		−	11.0000i		−	0.505781i
$474$		0			0
$475$	21.0000	−	28.0000i	0.963546	−	1.28473i
$476$	4.00000			0.183340
$477$		0			0
$478$		−	4.00000i		−	0.182956i
$479$	14.0000			0.639676			0.319838	−	0.947472i	$-0.396371\pi$
$479$	14.0000			0.639676			0.319838	+	0.947472i	$0.396371\pi$
$480$		0			0
$481$	−20.0000			−0.911922
$482$		−	10.0000i		−	0.455488i
$483$		0			0
$484$	10.0000			0.454545
$485$	−28.0000	+	14.0000i	−1.27141	+	0.635707i
$486$		0			0
$487$			33.0000i			1.49537i	0.664052	+	0.747686i	$0.268835\pi$
$487$			33.0000i			1.49537i	−0.664052	+	0.747686i	$0.731165\pi$
$488$			2.00000i			0.0905357i
$489$		0			0
$490$	2.00000	−	1.00000i	0.0903508	−	0.0451754i
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$		0			0
$493$			24.0000i			1.08091i
$494$	35.0000			1.57472
$495$		0			0
$496$		0			0
$497$			16.0000i			0.717698i
$498$		0			0
$499$	40.0000			1.79065			0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000			1.79065			0.895323	+	0.445418i	$0.146945\pi$
$500$	11.0000	+	2.00000i	0.491935	+	0.0894427i
$501$		0			0
$502$			24.0000i			1.07117i
$503$		−	39.0000i		−	1.73892i	−0.494000	−	0.869462i	$-0.664466\pi$
$503$		−	39.0000i		−	1.73892i	0.494000	−	0.869462i	$-0.335534\pi$
$504$		0			0
$505$	−5.00000	−	10.0000i	−0.222497	−	0.444994i
$506$		0			0
$507$		0			0
$508$		−	9.00000i		−	0.399310i
$509$	38.0000			1.68432			0.842160	−	0.539227i	$-0.181284\pi$
$509$	38.0000			1.68432			0.842160	+	0.539227i	$0.181284\pi$
$510$		0			0
$511$	11.0000			0.486611
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−28.0000			−1.23503
$515$	12.0000	−	6.00000i	0.528783	−	0.264392i
$516$		0			0
$517$		−	1.00000i		−	0.0439799i
$518$			4.00000i			0.175750i
$519$		0			0
$520$	5.00000	+	10.0000i	0.219265	+	0.438529i
$521$	−33.0000			−1.44576			−0.722878	−	0.690976i	$-0.757181\pi$
$521$	−33.0000			−1.44576			−0.722878	+	0.690976i	$0.757181\pi$
$522$		0			0
$523$		−	12.0000i		−	0.524723i	−0.964970	−	0.262362i	$-0.915499\pi$
$523$		−	12.0000i		−	0.524723i	0.964970	−	0.262362i	$-0.0845013\pi$
$524$	4.00000			0.174741
$525$		0			0
$526$	−12.0000			−0.523225
$527$		0			0
$528$		0			0
$529$	23.0000			1.00000
$530$	1.00000	+	2.00000i	0.0434372	+	0.0868744i
$531$		0			0
$532$		−	7.00000i		−	0.303488i
$533$			15.0000i			0.649722i
$534$		0			0
$535$	12.0000	−	6.00000i	0.518805	−	0.259403i
$536$	−15.0000			−0.647901
$537$		0			0
$538$			26.0000i			1.12094i
$539$	1.00000			0.0430730
$540$		0			0
$541$	−17.0000			−0.730887			−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000			−0.730887			−0.365444	+	0.930834i	$0.619083\pi$
$542$			5.00000i			0.214768i
$543$		0			0
$544$	4.00000			0.171499
$545$	15.0000	+	30.0000i	0.642529	+	1.28506i
$546$		0			0
$547$		−	32.0000i		−	1.36822i	−0.729378	−	0.684111i	$-0.760191\pi$
$547$		−	32.0000i		−	1.36822i	0.729378	−	0.684111i	$-0.239809\pi$
$548$			17.0000i			0.726204i
$549$		0			0
$550$	4.00000	+	3.00000i	0.170561	+	0.127920i
$551$	42.0000			1.78926
$552$		0			0
$553$			10.0000i			0.425243i
$554$	−8.00000			−0.339887
$555$		0			0
$556$	−20.0000			−0.848189
$557$		−	30.0000i		−	1.27114i	−0.772043	−	0.635570i	$-0.780765\pi$
$557$		−	30.0000i		−	1.27114i	0.772043	−	0.635570i	$-0.219235\pi$
$558$		0			0
$559$	−55.0000			−2.32625
$560$	2.00000	−	1.00000i	0.0845154	−	0.0422577i
$561$		0			0
$562$			14.0000i			0.590554i
$563$			21.0000i			0.885044i	0.896758	+	0.442522i	$0.145916\pi$
$563$			21.0000i			0.885044i	−0.896758	+	0.442522i	$0.854084\pi$
$564$		0			0
$565$	−30.0000	+	15.0000i	−1.26211	+	0.631055i
$566$	−4.00000			−0.168133
$567$		0			0
$568$			16.0000i			0.671345i
$569$	−42.0000			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$570$		0			0
$571$	10.0000			0.418487			0.209243	−	0.977864i	$-0.432900\pi$
$571$	10.0000			0.418487			0.209243	+	0.977864i	$0.432900\pi$
$572$			5.00000i			0.209061i
$573$		0			0
$574$	3.00000			0.125218
$575$		0			0
$576$		0			0
$577$		−	9.00000i		−	0.374675i	−0.982296	−	0.187337i	$-0.940014\pi$
$577$		−	9.00000i		−	0.374675i	0.982296	−	0.187337i	$-0.0599858\pi$
$578$			1.00000i			0.0415945i
$579$		0			0
$580$	6.00000	+	12.0000i	0.249136	+	0.498273i
$581$	−7.00000			−0.290409
$582$		0			0
$583$			1.00000i			0.0414158i
$584$	11.0000			0.455183
$585$		0			0
$586$	26.0000			1.07405
$587$			4.00000i			0.165098i	0.996587	+	0.0825488i	$0.0263060\pi$
$587$			4.00000i			0.165098i	−0.996587	+	0.0825488i	$0.973694\pi$
$588$		0			0
$589$		0			0
$590$	4.00000	−	2.00000i	0.164677	−	0.0823387i
$591$		0			0
$592$			4.00000i			0.164399i
$593$		−	34.0000i		−	1.39621i	−0.715994	−	0.698106i	$-0.754026\pi$
$593$		−	34.0000i		−	1.39621i	0.715994	−	0.698106i	$-0.245974\pi$
$594$		0			0
$595$	−4.00000	−	8.00000i	−0.163984	−	0.327968i
$596$	−12.0000			−0.491539
$597$		0			0
$598$		0			0
$599$	−19.0000			−0.776319			−0.388159	−	0.921592i	$-0.626889\pi$
$599$	−19.0000			−0.776319			−0.388159	+	0.921592i	$0.626889\pi$
$600$		0			0
$601$	−12.0000			−0.489490			−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000			−0.489490			−0.244745	+	0.969587i	$0.578704\pi$
$602$			11.0000i			0.448327i
$603$		0			0
$604$	10.0000			0.406894
$605$	−10.0000	−	20.0000i	−0.406558	−	0.813116i
$606$		0			0
$607$		−	20.0000i		−	0.811775i	−0.913923	−	0.405887i	$-0.866962\pi$
$607$		−	20.0000i		−	0.811775i	0.913923	−	0.405887i	$-0.133038\pi$
$608$		−	7.00000i		−	0.283887i
$609$		0			0
$610$	4.00000	−	2.00000i	0.161955	−	0.0809776i
$611$	−5.00000			−0.202278
$612$		0			0
$613$			44.0000i			1.77714i	0.458738	+	0.888572i	$0.348302\pi$
$613$			44.0000i			1.77714i	−0.458738	+	0.888572i	$0.651698\pi$
$614$	22.0000			0.887848
$615$		0			0
$616$	1.00000			0.0402911
$617$		−	6.00000i		−	0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$		−	6.00000i		−	0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$		0			0
$619$	−33.0000			−1.32638			−0.663191	−	0.748450i	$-0.730798\pi$
$619$	−33.0000			−1.32638			−0.663191	+	0.748450i	$0.730798\pi$
$620$		0			0
$621$		0			0
$622$			14.0000i			0.561349i
$623$		−	1.00000i		−	0.0400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−13.0000			−0.519584
$627$		0			0
$628$			14.0000i			0.558661i
$629$	16.0000			0.637962
$630$		0			0
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$			10.0000i			0.397779i
$633$		0			0
$634$	−25.0000			−0.992877
$635$	−18.0000	+	9.00000i	−0.714308	+	0.357154i
$636$		0			0
$637$		−	5.00000i		−	0.198107i
$638$			6.00000i			0.237542i
$639$		0			0
$640$	2.00000	−	1.00000i	0.0790569	−	0.0395285i
$641$	42.0000			1.65890			0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000			1.65890			0.829450	+	0.558581i	$0.188654\pi$
$642$		0			0
$643$		−	14.0000i		−	0.552106i	−0.961142	−	0.276053i	$-0.910973\pi$
$643$		−	14.0000i		−	0.552106i	0.961142	−	0.276053i	$-0.0890266\pi$
$644$		0			0
$645$		0			0
$646$	−28.0000			−1.10165
$647$		−	23.0000i		−	0.904223i	−0.891961	−	0.452112i	$-0.850671\pi$
$647$		−	23.0000i		−	0.904223i	0.891961	−	0.452112i	$-0.149329\pi$
$648$		0			0
$649$	2.00000			0.0785069
$650$	15.0000	−	20.0000i	0.588348	−	0.784465i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$			2.00000i			0.0782660i	0.999234	+	0.0391330i	$0.0124596\pi$
$653$			2.00000i			0.0782660i	−0.999234	+	0.0391330i	$0.987540\pi$
$654$		0			0
$655$	−4.00000	−	8.00000i	−0.156293	−	0.312586i
$656$	3.00000			0.117130
$657$		0			0
$658$			1.00000i			0.0389841i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$		0			0
$661$	40.0000			1.55582			0.777910	−	0.628376i	$-0.216280\pi$
$661$	40.0000			1.55582			0.777910	+	0.628376i	$0.216280\pi$
$662$			12.0000i			0.466393i
$663$		0			0
$664$	−7.00000			−0.271653
$665$	−14.0000	+	7.00000i	−0.542897	+	0.271448i
$666$		0			0
$667$		0			0
$668$			20.0000i			0.773823i
$669$		0			0
$670$	15.0000	+	30.0000i	0.579501	+	1.15900i
$671$	2.00000			0.0772091
$672$		0			0
$673$		−	12.0000i		−	0.462566i	−0.972887	−	0.231283i	$-0.925708\pi$
$673$		−	12.0000i		−	0.462566i	0.972887	−	0.231283i	$-0.0742923\pi$
$674$	2.00000			0.0770371
$675$		0			0
$676$	12.0000			0.461538
$677$		−	12.0000i		−	0.461197i	−0.973049	−	0.230599i	$-0.925932\pi$
$677$		−	12.0000i		−	0.461197i	0.973049	−	0.230599i	$-0.0740685\pi$
$678$		0			0
$679$	14.0000			0.537271
$680$	−4.00000	−	8.00000i	−0.153393	−	0.306786i
$681$		0			0
$682$		0			0
$683$		−	28.0000i		−	1.07139i	−0.844411	−	0.535695i	$-0.820050\pi$
$683$		−	28.0000i		−	1.07139i	0.844411	−	0.535695i	$-0.179950\pi$
$684$		0			0
$685$	34.0000	−	17.0000i	1.29907	−	0.649537i
$686$	−1.00000			−0.0381802
$687$		0			0
$688$			11.0000i			0.419371i
$689$	5.00000			0.190485
$690$		0			0
$691$	7.00000			0.266293			0.133146	−	0.991096i	$-0.457492\pi$
$691$	7.00000			0.266293			0.133146	+	0.991096i	$0.457492\pi$
$692$			14.0000i			0.532200i
$693$		0			0
$694$	−28.0000			−1.06287
$695$	20.0000	+	40.0000i	0.758643	+	1.51729i
$696$		0			0
$697$		−	12.0000i		−	0.454532i
$698$		0			0
$699$		0			0
$700$	−4.00000	−	3.00000i	−0.151186	−	0.113389i
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$		0			0
$703$		−	28.0000i		−	1.05604i
$704$	1.00000			0.0376889
$705$		0			0
$706$	6.00000			0.225813
$707$			5.00000i			0.188044i
$708$		0			0
$709$	17.0000			0.638448			0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000			0.638448			0.319224	+	0.947679i	$0.396578\pi$
$710$	32.0000	−	16.0000i	1.20094	−	0.600469i
$711$		0			0
$712$		−	1.00000i		−	0.0374766i
$713$		0			0
$714$		0			0
$715$	10.0000	−	5.00000i	0.373979	−	0.186989i
$716$	−7.00000			−0.261602
$717$		0			0
$718$			5.00000i			0.186598i
$719$	−50.0000			−1.86469			−0.932343	−	0.361576i	$-0.882239\pi$
$719$	−50.0000			−1.86469			−0.932343	+	0.361576i	$0.882239\pi$
$720$		0			0
$721$	−6.00000			−0.223452
$722$			30.0000i			1.11648i
$723$		0			0
$724$	14.0000			0.520306
$725$	18.0000	−	24.0000i	0.668503	−	0.891338i
$726$		0			0
$727$		−	22.0000i		−	0.815935i	−0.912996	−	0.407967i	$-0.866238\pi$
$727$		−	22.0000i		−	0.815935i	0.912996	−	0.407967i	$-0.133762\pi$
$728$		−	5.00000i		−	0.185312i
$729$		0			0
$730$	−11.0000	−	22.0000i	−0.407128	−	0.814257i
$731$	44.0000			1.62740
$732$		0			0
$733$			21.0000i			0.775653i	0.921732	+	0.387826i	$0.126774\pi$
$733$			21.0000i			0.775653i	−0.921732	+	0.387826i	$0.873226\pi$
$734$	−2.00000			−0.0738213
$735$		0			0
$736$		0			0
$737$			15.0000i			0.552532i
$738$		0			0
$739$	52.0000			1.91285			0.956425	−	0.291977i	$-0.0943129\pi$
$739$	52.0000			1.91285			0.956425	+	0.291977i	$0.0943129\pi$
$740$	8.00000	−	4.00000i	0.294086	−	0.147043i
$741$		0			0
$742$		−	1.00000i		−	0.0367112i
$743$			26.0000i			0.953847i	0.878945	+	0.476924i	$0.158248\pi$
$743$			26.0000i			0.953847i	−0.878945	+	0.476924i	$0.841752\pi$
$744$		0			0
$745$	12.0000	+	24.0000i	0.439646	+	0.879292i
$746$	−18.0000			−0.659027
$747$		0			0
$748$		−	4.00000i		−	0.146254i
$749$	−6.00000			−0.219235
$750$		0			0
$751$	−50.0000			−1.82453			−0.912263	−	0.409605i	$-0.865667\pi$
$751$	−50.0000			−1.82453			−0.912263	+	0.409605i	$0.865667\pi$
$752$			1.00000i			0.0364662i
$753$		0			0
$754$	30.0000			1.09254
$755$	−10.0000	−	20.0000i	−0.363937	−	0.727875i
$756$		0			0
$757$		−	8.00000i		−	0.290765i	−0.989376	−	0.145382i	$-0.953559\pi$
$757$		−	8.00000i		−	0.290765i	0.989376	−	0.145382i	$-0.0464413\pi$
$758$			10.0000i			0.363216i
$759$		0			0
$760$	−14.0000	+	7.00000i	−0.507833	+	0.253917i
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$		0			0
$763$		−	15.0000i		−	0.543036i
$764$	11.0000			0.397966
$765$		0			0
$766$		0			0
$767$		−	10.0000i		−	0.361079i
$768$		0			0
$769$	−6.00000			−0.216366			−0.108183	−	0.994131i	$-0.534503\pi$
$769$	−6.00000			−0.216366			−0.108183	+	0.994131i	$0.534503\pi$
$770$	−1.00000	−	2.00000i	−0.0360375	−	0.0720750i
$771$		0			0
$772$		−	18.0000i		−	0.647834i
$773$			50.0000i			1.79838i	0.437564	+	0.899188i	$0.355842\pi$
$773$			50.0000i			1.79838i	−0.437564	+	0.899188i	$0.644158\pi$
$774$		0			0
$775$		0			0
$776$	14.0000			0.502571
$777$		0			0
$778$		−	6.00000i		−	0.215110i
$779$	−21.0000			−0.752403
$780$		0			0
$781$	16.0000			0.572525
$782$		0			0
$783$		0			0
$784$	−1.00000			−0.0357143
$785$	28.0000	−	14.0000i	0.999363	−	0.499681i
$786$		0			0
$787$		−	22.0000i		−	0.784215i	−0.919919	−	0.392108i	$-0.871746\pi$
$787$		−	22.0000i		−	0.784215i	0.919919	−	0.392108i	$-0.128254\pi$
$788$		−	15.0000i		−	0.534353i
$789$		0			0
$790$	20.0000	−	10.0000i	0.711568	−	0.355784i
$791$	15.0000			0.533339
$792$		0			0
$793$		−	10.0000i		−	0.355110i
$794$	−34.0000			−1.20661
$795$		0			0
$796$	7.00000			0.248108
$797$		−	48.0000i		−	1.70025i	−0.526583	−	0.850124i	$-0.676527\pi$
$797$		−	48.0000i		−	1.70025i	0.526583	−	0.850124i	$-0.323473\pi$
$798$		0			0
$799$	4.00000			0.141510
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$		0			0
$802$			30.0000i			1.05934i
$803$		−	11.0000i		−	0.388182i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$			5.00000i			0.175899i
$809$	12.0000			0.421898			0.210949	−	0.977497i	$-0.432345\pi$
$809$	12.0000			0.421898			0.210949	+	0.977497i	$0.432345\pi$
$810$		0			0
$811$	−37.0000			−1.29925			−0.649623	−	0.760257i	$-0.725073\pi$
$811$	−37.0000			−1.29925			−0.649623	+	0.760257i	$0.725073\pi$
$812$		−	6.00000i		−	0.210559i
$813$		0			0
$814$	4.00000			0.140200
$815$	−24.0000	+	12.0000i	−0.840683	+	0.420342i
$816$		0			0
$817$		−	77.0000i		−	2.69389i
$818$		−	22.0000i		−	0.769212i
$819$		0			0
$820$	−3.00000	−	6.00000i	−0.104765	−	0.209529i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$		0			0
$823$			17.0000i			0.592583i	0.955098	+	0.296291i	$0.0957499\pi$
$823$			17.0000i			0.592583i	−0.955098	+	0.296291i	$0.904250\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	−2.00000			−0.0695889
$827$			6.00000i			0.208640i	0.994544	+	0.104320i	$0.0332667\pi$
$827$			6.00000i			0.208640i	−0.994544	+	0.104320i	$0.966733\pi$
$828$		0			0
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	7.00000	+	14.0000i	0.242974	+	0.485947i
$831$		0			0
$832$		−	5.00000i		−	0.173344i
$833$			4.00000i			0.138592i
$834$		0			0
$835$	40.0000	−	20.0000i	1.38426	−	0.692129i
$836$	−7.00000			−0.242100
$837$		0			0
$838$			18.0000i			0.621800i
$839$	−46.0000			−1.58810			−0.794048	−	0.607855i	$-0.792030\pi$
$839$	−46.0000			−1.58810			−0.794048	+	0.607855i	$0.792030\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		−	11.0000i		−	0.379085i
$843$		0			0
$844$	−10.0000			−0.344214
$845$	−12.0000	−	24.0000i	−0.412813	−	0.825625i
$846$		0			0
$847$			10.0000i			0.343604i
$848$		−	1.00000i		−	0.0343401i
$849$		0			0
$850$	−12.0000	+	16.0000i	−0.411597	+	0.548795i
$851$		0			0
$852$		0			0
$853$		−	26.0000i		−	0.890223i	−0.895475	−	0.445112i	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	−2.00000			−0.0684386
$855$		0			0
$856$	−6.00000			−0.205076
$857$		−	52.0000i		−	1.77629i	−0.459567	−	0.888143i	$-0.651995\pi$
$857$		−	52.0000i		−	1.77629i	0.459567	−	0.888143i	$-0.348005\pi$
$858$		0			0
$859$	−15.0000			−0.511793			−0.255897	−	0.966704i	$-0.582371\pi$
$859$	−15.0000			−0.511793			−0.255897	+	0.966704i	$0.582371\pi$
$860$	22.0000	−	11.0000i	0.750194	−	0.375097i
$861$		0			0
$862$		−	3.00000i		−	0.102180i
$863$			6.00000i			0.204242i	0.994772	+	0.102121i	$0.0325630\pi$
$863$			6.00000i			0.204242i	−0.994772	+	0.102121i	$0.967437\pi$
$864$		0			0
$865$	28.0000	−	14.0000i	0.952029	−	0.476014i
$866$	−17.0000			−0.577684
$867$		0			0
$868$		0			0
$869$	10.0000			0.339227
$870$		0			0
$871$	75.0000			2.54128
$872$		−	15.0000i		−	0.507964i
$873$		0			0
$874$		0			0
$875$	−2.00000	+	11.0000i	−0.0676123	+	0.371868i
$876$		0			0
$877$			18.0000i			0.607817i	0.952701	+	0.303908i	$0.0982917\pi$
$877$			18.0000i			0.607817i	−0.952701	+	0.303908i	$0.901708\pi$
$878$			3.00000i			0.101245i
$879$		0			0
$880$	−1.00000	−	2.00000i	−0.0337100	−	0.0674200i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$		−	20.0000i		−	0.673054i	−0.941674	−	0.336527i	$-0.890748\pi$
$883$		−	20.0000i		−	0.673054i	0.941674	−	0.336527i	$-0.109252\pi$
$884$	−20.0000			−0.672673
$885$		0			0
$886$	−36.0000			−1.20944
$887$		−	15.0000i		−	0.503651i	−0.967773	−	0.251825i	$-0.918969\pi$
$887$		−	15.0000i		−	0.503651i	0.967773	−	0.251825i	$-0.0810309\pi$
$888$		0			0
$889$	9.00000			0.301850
$890$	−2.00000	+	1.00000i	−0.0670402	+	0.0335201i
$891$		0			0
$892$		−	14.0000i		−	0.468755i
$893$		−	7.00000i		−	0.234246i
$894$		0			0
$895$	7.00000	+	14.0000i	0.233984	+	0.467968i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$		−	18.0000i		−	0.600668i
$899$		0			0
$900$		0			0
$901$	−4.00000			−0.133259
$902$		−	3.00000i		−	0.0998891i
$903$		0			0
$904$	15.0000			0.498893
$905$	−14.0000	−	28.0000i	−0.465376	−	0.930751i
$906$		0			0
$907$		−	31.0000i		−	1.02934i	−0.857389	−	0.514669i	$-0.827915\pi$
$907$		−	31.0000i		−	1.02934i	0.857389	−	0.514669i	$-0.172085\pi$
$908$		−	7.00000i		−	0.232303i
$909$		0			0
$910$	−10.0000	+	5.00000i	−0.331497	+	0.165748i
$911$	27.0000			0.894550			0.447275	−	0.894397i	$-0.352395\pi$
$911$	27.0000			0.894550			0.447275	+	0.894397i	$0.352395\pi$
$912$		0			0
$913$			7.00000i			0.231666i
$914$	−22.0000			−0.727695
$915$		0			0
$916$	14.0000			0.462573
$917$			4.00000i			0.132092i
$918$		0			0
$919$	46.0000			1.51740			0.758700	−	0.651440i	$-0.225835\pi$
$919$	46.0000			1.51740			0.758700	+	0.651440i	$0.225835\pi$
$920$		0			0
$921$		0			0
$922$			15.0000i			0.493999i
$923$		−	80.0000i		−	2.63323i
$924$		0			0
$925$	−16.0000	−	12.0000i	−0.526077	−	0.394558i
$926$	−21.0000			−0.690103
$927$		0			0
$928$		−	6.00000i		−	0.196960i
$929$	−45.0000			−1.47640			−0.738201	−	0.674581i	$-0.764324\pi$
$929$	−45.0000			−1.47640			−0.738201	+	0.674581i	$0.764324\pi$
$930$		0			0
$931$	7.00000			0.229416
$932$		−	3.00000i		−	0.0982683i
$933$		0			0
$934$	−28.0000			−0.916188
$935$	−8.00000	+	4.00000i	−0.261628	+	0.130814i
$936$		0			0
$937$			29.0000i			0.947389i	0.880689	+	0.473694i	$0.157080\pi$
$937$			29.0000i			0.947389i	−0.880689	+	0.473694i	$0.842920\pi$
$938$		−	15.0000i		−	0.489767i
$939$		0			0
$940$	2.00000	−	1.00000i	0.0652328	−	0.0326164i
$941$	33.0000			1.07577			0.537885	−	0.843018i	$-0.319224\pi$
$941$	33.0000			1.07577			0.537885	+	0.843018i	$0.319224\pi$
$942$		0			0
$943$		0			0
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	11.0000			0.357641
$947$			30.0000i			0.974869i	0.873160	+	0.487435i	$0.162067\pi$
$947$			30.0000i			0.974869i	−0.873160	+	0.487435i	$0.837933\pi$
$948$		0			0
$949$	−55.0000			−1.78538
$950$	28.0000	+	21.0000i	0.908440	+	0.681330i
$951$		0			0
$952$			4.00000i			0.129641i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$		0			0
$955$	−11.0000	−	22.0000i	−0.355952	−	0.711903i
$956$	4.00000			0.129369
$957$		0			0
$958$			14.0000i			0.452319i
$959$	−17.0000			−0.548959
$960$		0			0
$961$	−31.0000			−1.00000
$962$		−	20.0000i		−	0.644826i
$963$		0			0
$964$	10.0000			0.322078
$965$	−36.0000	+	18.0000i	−1.15888	+	0.579441i
$966$		0			0
$967$			3.00000i			0.0964735i	0.998836	+	0.0482367i	$0.0153602\pi$
$967$			3.00000i			0.0964735i	−0.998836	+	0.0482367i	$0.984640\pi$
$968$			10.0000i			0.321412i
$969$		0			0
$970$	−14.0000	−	28.0000i	−0.449513	−	0.899026i
$971$	30.0000			0.962746			0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000			0.962746			0.481373	+	0.876516i	$0.340138\pi$
$972$		0			0
$973$		−	20.0000i		−	0.641171i
$974$	−33.0000			−1.05739
$975$		0			0
$976$	−2.00000			−0.0640184
$977$			33.0000i			1.05576i	0.849318	+	0.527882i	$0.177014\pi$
$977$			33.0000i			1.05576i	−0.849318	+	0.527882i	$0.822986\pi$
$978$		0			0
$979$	−1.00000			−0.0319601
$980$	1.00000	+	2.00000i	0.0319438	+	0.0638877i
$981$		0			0
$982$			36.0000i			1.14881i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		0			0
$985$	−30.0000	+	15.0000i	−0.955879	+	0.477940i
$986$	−24.0000			−0.764316
$987$		0			0
$988$			35.0000i			1.11350i
$989$		0			0
$990$		0			0
$991$	60.0000			1.90596			0.952981	−	0.303029i	$-0.0979978\pi$
$991$	60.0000			1.90596			0.952981	+	0.303029i	$0.0979978\pi$
$992$		0			0
$993$		0			0
$994$	−16.0000			−0.507489
$995$	−7.00000	−	14.0000i	−0.221915	−	0.443830i
$996$		0			0
$997$			2.00000i			0.0633406i	0.999498	+	0.0316703i	$0.0100827\pi$
$997$			2.00000i			0.0633406i	−0.999498	+	0.0316703i	$0.989917\pi$
$998$			40.0000i			1.26618i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.g.i.379.2	yes	2
3.2	odd	2		1890.2.g.d.379.1	✓	2
5.2	odd	4		9450.2.a.bk.1.1		1
5.3	odd	4		9450.2.a.ci.1.1		1
5.4	even	2	inner	1890.2.g.i.379.1	yes	2
15.2	even	4		9450.2.a.dq.1.1		1
15.8	even	4		9450.2.a.q.1.1		1
15.14	odd	2		1890.2.g.d.379.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.g.d.379.1	✓	2	3.2	odd	2
1890.2.g.d.379.2	yes	2	15.14	odd	2
1890.2.g.i.379.1	yes	2	5.4	even	2	inner
1890.2.g.i.379.2	yes	2	1.1	even	1	trivial
9450.2.a.q.1.1		1	15.8	even	4
9450.2.a.bk.1.1		1	5.2	odd	4
9450.2.a.ci.1.1		1	5.3	odd	4
9450.2.a.dq.1.1		1	15.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.00000 + 2.00000i) q^{5} -1.00000i q^{7} -1.00000i q^{8} +(-2.00000 + 1.00000i) q^{10} -1.00000 q^{11} +5.00000i q^{13} +1.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} -7.00000 q^{19} +(-1.00000 - 2.00000i) q^{20} -1.00000i q^{22} +(-3.00000 + 4.00000i) q^{25} -5.00000 q^{26} +1.00000i q^{28} -6.00000 q^{29} +1.00000i q^{32} +4.00000 q^{34} +(2.00000 - 1.00000i) q^{35} +4.00000i q^{37} -7.00000i q^{38} +(2.00000 - 1.00000i) q^{40} +3.00000 q^{41} +11.0000i q^{43} +1.00000 q^{44} +1.00000i q^{47} -1.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} -5.00000i q^{52} -1.00000i q^{53} +(-1.00000 - 2.00000i) q^{55} -1.00000 q^{56} -6.00000i q^{58} -2.00000 q^{59} -2.00000 q^{61} -1.00000 q^{64} +(-10.0000 + 5.00000i) q^{65} -15.0000i q^{67} +4.00000i q^{68} +(1.00000 + 2.00000i) q^{70} -16.0000 q^{71} +11.0000i q^{73} -4.00000 q^{74} +7.00000 q^{76} +1.00000i q^{77} -10.0000 q^{79} +(1.00000 + 2.00000i) q^{80} +3.00000i q^{82} -7.00000i q^{83} +(8.00000 - 4.00000i) q^{85} -11.0000 q^{86} +1.00000i q^{88} +1.00000 q^{89} +5.00000 q^{91} -1.00000 q^{94} +(-7.00000 - 14.0000i) q^{95} +14.0000i q^{97} -1.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} + 2 q^{5}+O(q^{10}) \) 2 * q - 2 * q^4 + 2 * q^5	\( 2 q - 2 q^{4} + 2 q^{5} - 4 q^{10} - 2 q^{11} + 2 q^{14} + 2 q^{16} - 14 q^{19} - 2 q^{20} - 6 q^{25} - 10 q^{26} - 12 q^{29} + 8 q^{34} + 4 q^{35} + 4 q^{40} + 6 q^{41} + 2 q^{44} - 2 q^{49} - 8 q^{50} - 2 q^{55} - 2 q^{56} - 4 q^{59} - 4 q^{61} - 2 q^{64} - 20 q^{65} + 2 q^{70} - 32 q^{71} - 8 q^{74} + 14 q^{76} - 20 q^{79} + 2 q^{80} + 16 q^{85} - 22 q^{86} + 2 q^{89} + 10 q^{91} - 2 q^{94} - 14 q^{95}+O(q^{100}) \) 2 * q - 2 * q^4 + 2 * q^5 - 4 * q^10 - 2 * q^11 + 2 * q^14 + 2 * q^16 - 14 * q^19 - 2 * q^20 - 6 * q^25 - 10 * q^26 - 12 * q^29 + 8 * q^34 + 4 * q^35 + 4 * q^40 + 6 * q^41 + 2 * q^44 - 2 * q^49 - 8 * q^50 - 2 * q^55 - 2 * q^56 - 4 * q^59 - 4 * q^61 - 2 * q^64 - 20 * q^65 + 2 * q^70 - 32 * q^71 - 8 * q^74 + 14 * q^76 - 20 * q^79 + 2 * q^80 + 16 * q^85 - 22 * q^86 + 2 * q^89 + 10 * q^91 - 2 * q^94 - 14 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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