LMFDB - Embedded newform 2940.2.q.s.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(361,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2940, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("2940.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.q (of order $3$, degree $2$, not 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:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2940.361
Dual form			2940.2.q.s.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(0.414214 - 0.717439i) q^{11} +1.00000 q^{15} +(1.41421 - 2.44949i) q^{17} +(-0.707107 - 1.22474i) q^{19} +(-1.70711 - 2.95680i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(2.70711 - 4.68885i) q^{31} +(-0.414214 - 0.717439i) q^{33} +(-1.58579 - 2.74666i) q^{37} -0.343146 q^{41} +5.65685 q^{43} +(0.500000 - 0.866025i) q^{45} +(0.414214 + 0.717439i) q^{47} +(-1.41421 - 2.44949i) q^{51} +(-0.292893 + 0.507306i) q^{53} +0.828427 q^{55} -1.41421 q^{57} +(4.24264 - 7.34847i) q^{59} +(-3.53553 - 6.12372i) q^{61} +(-3.41421 + 5.91359i) q^{67} -3.41421 q^{69} +7.65685 q^{71} +(3.65685 - 6.33386i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-0.171573 - 0.297173i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.82843 q^{83} +2.82843 q^{85} +(-1.00000 + 1.73205i) q^{87} +(-3.24264 - 5.61642i) q^{89} +(-2.70711 - 4.68885i) q^{93} +(0.707107 - 1.22474i) q^{95} +14.8284 q^{97} -0.828427 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9} - 4 q^{11} + 4 q^{15} - 4 q^{23} - 2 q^{25} - 4 q^{27} - 8 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{37} - 24 q^{41} + 2 q^{45} - 4 q^{47} - 4 q^{53} - 8 q^{55} - 8 q^{67} - 8 q^{69} + 8 q^{71} - 8 q^{73} + 2 q^{75} - 12 q^{79} - 2 q^{81} + 8 q^{83} - 4 q^{87} + 4 q^{89} - 8 q^{93} + 48 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9 - 4 * q^11 + 4 * q^15 - 4 * q^23 - 2 * q^25 - 4 * q^27 - 8 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^37 - 24 * q^41 + 2 * q^45 - 4 * q^47 - 4 * q^53 - 8 * q^55 - 8 * q^67 - 8 * q^69 + 8 * q^71 - 8 * q^73 + 2 * q^75 - 12 * q^79 - 2 * q^81 + 8 * q^83 - 4 * q^87 + 4 * q^89 - 8 * q^93 + 48 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	−0.796800	−	0.604243i	$-0.793476\pi$
$11$	0.414214	−	0.717439i	0.124890	−	0.216316i	0.921690	+	0.387927i	$0.126809\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	1.41421	−	2.44949i	0.342997	−	0.594089i	−0.641991	−	0.766712i	$-0.721891\pi$
$17$	1.41421	−	2.44949i	0.342997	−	0.594089i	0.984988	+	0.172624i	$0.0552245\pi$
$18$		0			0
$19$	−0.707107	−	1.22474i	−0.162221	−	0.280976i	0.773444	−	0.633865i	$-0.218533\pi$
$19$	−0.707107	−	1.22474i	−0.162221	−	0.280976i	−0.935665	+	0.352889i	$0.885199\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	0.631325	−	0.775519i	$-0.282511\pi$
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	−0.987281	+	0.158984i	$0.949178\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	2.70711	−	4.68885i	0.486211	−	0.842142i	−0.513664	−	0.857992i	$-0.671712\pi$
$31$	2.70711	−	4.68885i	0.486211	−	0.842142i	0.999874	+	0.0158500i	$0.00504541\pi$
$32$		0			0
$33$	−0.414214	−	0.717439i	−0.0721053	−	0.124890i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.58579	−	2.74666i	−0.260702	−	0.451549i	0.705727	−	0.708484i	$-0.250621\pi$
$37$	−1.58579	−	2.74666i	−0.260702	−	0.451549i	−0.966429	+	0.256935i	$0.917287\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.343146			−0.0535904			−0.0267952	−	0.999641i	$-0.508530\pi$
$41$	−0.343146			−0.0535904			−0.0267952	+	0.999641i	$0.508530\pi$
$42$		0			0
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	0.414214	+	0.717439i	0.0604193	+	0.104649i	0.894653	−	0.446762i	$-0.147423\pi$
$47$	0.414214	+	0.717439i	0.0604193	+	0.104649i	−0.834234	+	0.551411i	$0.814090\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.41421	−	2.44949i	−0.198030	−	0.342997i
$52$		0			0
$53$	−0.292893	+	0.507306i	−0.0402320	+	0.0696838i	−0.885440	−	0.464753i	$-0.846143\pi$
$53$	−0.292893	+	0.507306i	−0.0402320	+	0.0696838i	0.845208	+	0.534437i	$0.179476\pi$
$54$		0			0
$55$	0.828427			0.111705
$56$		0			0
$57$	−1.41421			−0.187317
$58$		0			0
$59$	4.24264	−	7.34847i	0.552345	−	0.956689i	−0.445760	−	0.895152i	$-0.647067\pi$
$59$	4.24264	−	7.34847i	0.552345	−	0.956689i	0.998105	−	0.0615367i	$-0.0196001\pi$
$60$		0			0
$61$	−3.53553	−	6.12372i	−0.452679	−	0.784063i	0.545873	−	0.837868i	$-0.316198\pi$
$61$	−3.53553	−	6.12372i	−0.452679	−	0.784063i	−0.998551	+	0.0538056i	$0.982865\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.41421	+	5.91359i	−0.417113	+	0.722460i	−0.995648	−	0.0931973i	$-0.970291\pi$
$67$	−3.41421	+	5.91359i	−0.417113	+	0.722460i	0.578535	+	0.815657i	$0.303625\pi$
$68$		0			0
$69$	−3.41421			−0.411023
$70$		0			0
$71$	7.65685			0.908701			0.454351	−	0.890823i	$-0.349871\pi$
$71$	7.65685			0.908701			0.454351	+	0.890823i	$0.349871\pi$
$72$		0			0
$73$	3.65685	−	6.33386i	0.428002	−	0.741322i	−0.568693	−	0.822550i	$-0.692551\pi$
$73$	3.65685	−	6.33386i	0.428002	−	0.741322i	0.996696	+	0.0812278i	$0.0258841\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.171573	−	0.297173i	−0.0193035	−	0.0334346i	0.856212	−	0.516624i	$-0.172812\pi$
$79$	−0.171573	−	0.297173i	−0.0193035	−	0.0334346i	−0.875516	+	0.483190i	$0.839478\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.82843			0.529989			0.264994	−	0.964250i	$-0.414630\pi$
$83$	4.82843			0.529989			0.264994	+	0.964250i	$0.414630\pi$
$84$		0			0
$85$	2.82843			0.306786
$86$		0			0
$87$	−1.00000	+	1.73205i	−0.107211	+	0.185695i
$88$		0			0
$89$	−3.24264	−	5.61642i	−0.343719	−	0.595339i	0.641401	−	0.767206i	$-0.278354\pi$
$89$	−3.24264	−	5.61642i	−0.343719	−	0.595339i	−0.985120	+	0.171867i	$0.945020\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.70711	−	4.68885i	−0.280714	−	0.486211i
$94$		0			0
$95$	0.707107	−	1.22474i	0.0725476	−	0.125656i
$96$		0			0
$97$	14.8284			1.50560			0.752799	−	0.658250i	$-0.228703\pi$
$97$	14.8284			1.50560			0.752799	+	0.658250i	$0.228703\pi$
$98$		0			0
$99$	−0.828427			−0.0832601
$100$		0			0
$101$	8.65685	−	14.9941i	0.861389	−	1.49197i	−0.00919913	−	0.999958i	$-0.502928\pi$
$101$	8.65685	−	14.9941i	0.861389	−	1.49197i	0.870588	−	0.492012i	$-0.163738\pi$
$102$		0			0
$103$	−5.41421	−	9.37769i	−0.533478	−	0.924012i	−0.999235	−	0.0390989i	$-0.987551\pi$
$103$	−5.41421	−	9.37769i	−0.533478	−	0.924012i	0.465757	−	0.884913i	$-0.345782\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.12132	−	15.7986i	−0.881791	−	1.52731i	−0.849348	−	0.527834i	$-0.823004\pi$
$107$	−9.12132	−	15.7986i	−0.881791	−	1.52731i	−0.0324436	−	0.999474i	$-0.510329\pi$
$108$		0			0
$109$	−5.82843	+	10.0951i	−0.558262	+	0.966938i	0.439380	+	0.898301i	$0.355198\pi$
$109$	−5.82843	+	10.0951i	−0.558262	+	0.966938i	−0.997642	+	0.0686368i	$0.978135\pi$
$110$		0			0
$111$	−3.17157			−0.301032
$112$		0			0
$113$	−9.07107			−0.853334			−0.426667	−	0.904409i	$-0.640312\pi$
$113$	−9.07107			−0.853334			−0.426667	+	0.904409i	$0.640312\pi$
$114$		0			0
$115$	1.70711	−	2.95680i	0.159189	−	0.275723i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.15685	+	8.93193i	0.468805	+	0.811994i
$122$		0			0
$123$	−0.171573	+	0.297173i	−0.0154702	+	0.0267952i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	9.17157			0.813845			0.406923	−	0.913463i	$-0.366602\pi$
$127$	9.17157			0.813845			0.406923	+	0.913463i	$0.366602\pi$
$128$		0			0
$129$	2.82843	−	4.89898i	0.249029	−	0.431331i
$130$		0			0
$131$	−0.828427	−	1.43488i	−0.0723800	−	0.125366i	0.827564	−	0.561371i	$-0.189726\pi$
$131$	−0.828427	−	1.43488i	−0.0723800	−	0.125366i	−0.899944	+	0.436006i	$0.856393\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	−3.12132	+	5.40629i	−0.266672	+	0.461890i	−0.968000	−	0.250949i	$-0.919258\pi$
$137$	−3.12132	+	5.40629i	−0.266672	+	0.461890i	0.701328	+	0.712839i	$0.252591\pi$
$138$		0			0
$139$	13.4142			1.13778			0.568889	−	0.822414i	$-0.307373\pi$
$139$	13.4142			1.13778			0.568889	+	0.822414i	$0.307373\pi$
$140$		0			0
$141$	0.828427			0.0697661
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.82843	−	6.63103i	−0.313637	−	0.543235i	0.665510	−	0.746389i	$-0.268214\pi$
$149$	−3.82843	−	6.63103i	−0.313637	−	0.543235i	−0.979147	+	0.203154i	$0.934881\pi$
$150$		0			0
$151$	0.656854	−	1.13770i	0.0534540	−	0.0925851i	−0.838060	−	0.545578i	$-0.816310\pi$
$151$	0.656854	−	1.13770i	0.0534540	−	0.0925851i	0.891514	+	0.452993i	$0.149644\pi$
$152$		0			0
$153$	−2.82843			−0.228665
$154$		0			0
$155$	5.41421			0.434880
$156$		0			0
$157$	−3.17157	+	5.49333i	−0.253119	+	0.438415i	−0.964383	−	0.264510i	$-0.914790\pi$
$157$	−3.17157	+	5.49333i	−0.253119	+	0.438415i	0.711264	+	0.702925i	$0.248123\pi$
$158$		0			0
$159$	0.292893	+	0.507306i	0.0232279	+	0.0402320i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.242641	+	0.420266i	0.0190051	+	0.0329178i	0.875372	−	0.483451i	$-0.160617\pi$
$163$	0.242641	+	0.420266i	0.0190051	+	0.0329178i	−0.856366	+	0.516369i	$0.827283\pi$
$164$		0			0
$165$	0.414214	−	0.717439i	0.0322465	−	0.0558525i
$166$		0			0
$167$	11.3137			0.875481			0.437741	−	0.899101i	$-0.355779\pi$
$167$	11.3137			0.875481			0.437741	+	0.899101i	$0.355779\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$	−0.707107	+	1.22474i	−0.0540738	+	0.0936586i
$172$		0			0
$173$	−2.24264	−	3.88437i	−0.170505	−	0.295323i	0.768092	−	0.640340i	$-0.221207\pi$
$173$	−2.24264	−	3.88437i	−0.170505	−	0.295323i	−0.938596	+	0.345017i	$0.887873\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.24264	−	7.34847i	−0.318896	−	0.552345i
$178$		0			0
$179$	−3.82843	+	6.63103i	−0.286150	+	0.495626i	−0.972887	−	0.231279i	$-0.925709\pi$
$179$	−3.82843	+	6.63103i	−0.286150	+	0.495626i	0.686737	+	0.726906i	$0.259042\pi$
$180$		0			0
$181$	4.92893			0.366365			0.183182	−	0.983079i	$-0.441360\pi$
$181$	4.92893			0.366365			0.183182	+	0.983079i	$0.441360\pi$
$182$		0			0
$183$	−7.07107			−0.522708
$184$		0			0
$185$	1.58579	−	2.74666i	0.116589	−	0.201939i
$186$		0			0
$187$	−1.17157	−	2.02922i	−0.0856739	−	0.148392i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.4142	−	18.0379i	−0.753546	−	1.30518i	−0.946094	−	0.323892i	$-0.895008\pi$
$191$	−10.4142	−	18.0379i	−0.753546	−	1.30518i	0.192548	−	0.981288i	$-0.438325\pi$
$192$		0			0
$193$	−8.89949	+	15.4144i	−0.640600	+	1.10955i	0.344699	+	0.938713i	$0.387981\pi$
$193$	−8.89949	+	15.4144i	−0.640600	+	1.10955i	−0.985299	+	0.170838i	$0.945353\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.3848			−0.882379			−0.441189	−	0.897414i	$-0.645443\pi$
$197$	−12.3848			−0.882379			−0.441189	+	0.897414i	$0.645443\pi$
$198$		0			0
$199$	−0.464466	+	0.804479i	−0.0329251	+	0.0570280i	−0.882018	−	0.471215i	$-0.843816\pi$
$199$	−0.464466	+	0.804479i	−0.0329251	+	0.0570280i	0.849093	+	0.528243i	$0.177149\pi$
$200$		0			0
$201$	3.41421	+	5.91359i	0.240820	+	0.417113i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.171573	−	0.297173i	−0.0119832	−	0.0207555i
$206$		0			0
$207$	−1.70711	+	2.95680i	−0.118652	+	0.205512i
$208$		0			0
$209$	−1.17157			−0.0810394
$210$		0			0
$211$	26.6274			1.83311			0.916553	−	0.399912i	$-0.130959\pi$
$211$	26.6274			1.83311			0.916553	+	0.399912i	$0.130959\pi$
$212$		0			0
$213$	3.82843	−	6.63103i	0.262320	−	0.454351i
$214$		0			0
$215$	2.82843	+	4.89898i	0.192897	+	0.334108i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−3.65685	−	6.33386i	−0.247107	−	0.428002i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	14.1421			0.947027			0.473514	−	0.880786i	$-0.342985\pi$
$223$	14.1421			0.947027			0.473514	+	0.880786i	$0.342985\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−7.17157	+	12.4215i	−0.475994	+	0.824446i	−0.999622	−	0.0275014i	$-0.991245\pi$
$227$	−7.17157	+	12.4215i	−0.475994	+	0.824446i	0.523628	+	0.851947i	$0.324578\pi$
$228$		0			0
$229$	−13.7782	−	23.8645i	−0.910487	−	1.57701i	−0.813377	−	0.581737i	$-0.802373\pi$
$229$	−13.7782	−	23.8645i	−0.910487	−	1.57701i	−0.0971103	−	0.995274i	$-0.530960\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.87868	+	4.98602i	0.188589	+	0.326645i	0.944780	−	0.327706i	$-0.106275\pi$
$233$	2.87868	+	4.98602i	0.188589	+	0.326645i	−0.756191	+	0.654351i	$0.772942\pi$
$234$		0			0
$235$	−0.414214	+	0.717439i	−0.0270203	+	0.0468006i
$236$		0			0
$237$	−0.343146			−0.0222897
$238$		0			0
$239$	−13.7990			−0.892582			−0.446291	−	0.894888i	$-0.647255\pi$
$239$	−13.7990			−0.892582			−0.446291	+	0.894888i	$0.647255\pi$
$240$		0			0
$241$	8.12132	−	14.0665i	0.523140	−	0.906105i	−0.476497	−	0.879176i	$-0.658094\pi$
$241$	8.12132	−	14.0665i	0.523140	−	0.906105i	0.999637	−	0.0269294i	$-0.00857294\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	2.41421	−	4.18154i	0.152995	−	0.264994i
$250$		0			0
$251$	−9.17157			−0.578905			−0.289452	−	0.957192i	$-0.593473\pi$
$251$	−9.17157			−0.578905			−0.289452	+	0.957192i	$0.593473\pi$
$252$		0			0
$253$	−2.82843			−0.177822
$254$		0			0
$255$	1.41421	−	2.44949i	0.0885615	−	0.153393i
$256$		0			0
$257$	2.17157	+	3.76127i	0.135459	+	0.234622i	0.925773	−	0.378081i	$-0.123416\pi$
$257$	2.17157	+	3.76127i	0.135459	+	0.234622i	−0.790314	+	0.612702i	$0.790082\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$		0			0
$263$	5.94975	−	10.3053i	0.366877	−	0.635450i	−0.622198	−	0.782860i	$-0.713760\pi$
$263$	5.94975	−	10.3053i	0.366877	−	0.635450i	0.989076	+	0.147410i	$0.0470936\pi$
$264$		0			0
$265$	−0.585786			−0.0359846
$266$		0			0
$267$	−6.48528			−0.396893
$268$		0			0
$269$	−3.58579	+	6.21076i	−0.218629	+	0.378677i	−0.954389	−	0.298566i	$-0.903492\pi$
$269$	−3.58579	+	6.21076i	−0.218629	+	0.378677i	0.735760	+	0.677242i	$0.236825\pi$
$270$		0			0
$271$	4.36396	+	7.55860i	0.265092	+	0.459152i	0.967588	−	0.252535i	$-0.0812644\pi$
$271$	4.36396	+	7.55860i	0.265092	+	0.459152i	−0.702496	+	0.711688i	$0.747931\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.414214	+	0.717439i	0.0249780	+	0.0432632i
$276$		0			0
$277$	−8.65685	+	14.9941i	−0.520140	+	0.900909i	0.479586	+	0.877495i	$0.340787\pi$
$277$	−8.65685	+	14.9941i	−0.520140	+	0.900909i	−0.999726	+	0.0234139i	$0.992546\pi$
$278$		0			0
$279$	−5.41421			−0.324140
$280$		0			0
$281$	6.97056			0.415829			0.207914	−	0.978147i	$-0.433332\pi$
$281$	6.97056			0.415829			0.207914	+	0.978147i	$0.433332\pi$
$282$		0			0
$283$	0.242641	−	0.420266i	0.0144235	−	0.0249822i	−0.858724	−	0.512439i	$-0.828742\pi$
$283$	0.242641	−	0.420266i	0.0144235	−	0.0249822i	0.873147	+	0.487457i	$0.162075\pi$
$284$		0			0
$285$	−0.707107	−	1.22474i	−0.0418854	−	0.0725476i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.50000	+	7.79423i	0.264706	+	0.458484i
$290$		0			0
$291$	7.41421	−	12.8418i	0.434629	−	0.752799i
$292$		0			0
$293$	−28.6274			−1.67243			−0.836216	−	0.548401i	$-0.815237\pi$
$293$	−28.6274			−1.67243			−0.836216	+	0.548401i	$0.815237\pi$
$294$		0			0
$295$	8.48528			0.494032
$296$		0			0
$297$	−0.414214	+	0.717439i	−0.0240351	+	0.0416300i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−8.65685	−	14.9941i	−0.497323	−	0.861389i
$304$		0			0
$305$	3.53553	−	6.12372i	0.202444	−	0.350643i
$306$		0			0
$307$	25.6569			1.46431			0.732157	−	0.681136i	$-0.238514\pi$
$307$	25.6569			1.46431			0.732157	+	0.681136i	$0.238514\pi$
$308$		0			0
$309$	−10.8284			−0.616008
$310$		0			0
$311$	10.8284	−	18.7554i	0.614024	−	1.06352i	−0.376531	−	0.926404i	$-0.622883\pi$
$311$	10.8284	−	18.7554i	0.614024	−	1.06352i	0.990555	−	0.137116i	$-0.0437834\pi$
$312$		0			0
$313$	−7.65685	−	13.2621i	−0.432791	−	0.749616i	0.564321	−	0.825555i	$-0.309138\pi$
$313$	−7.65685	−	13.2621i	−0.432791	−	0.749616i	−0.997112	+	0.0759392i	$0.975805\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.60660	−	13.1750i	−0.427229	−	0.739983i	0.569396	−	0.822063i	$-0.307177\pi$
$317$	−7.60660	−	13.1750i	−0.427229	−	0.739983i	−0.996626	+	0.0820802i	$0.973844\pi$
$318$		0			0
$319$	−0.828427	+	1.43488i	−0.0463830	+	0.0803377i
$320$		0			0
$321$	−18.2426			−1.01820
$322$		0			0
$323$	−4.00000			−0.222566
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.82843	+	10.0951i	0.322313	+	0.558262i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	12.1421	+	21.0308i	0.667392	+	1.15596i	0.978631	+	0.205625i	$0.0659228\pi$
$331$	12.1421	+	21.0308i	0.667392	+	1.15596i	−0.311239	+	0.950332i	$0.600744\pi$
$332$		0			0
$333$	−1.58579	+	2.74666i	−0.0869006	+	0.150516i
$334$		0			0
$335$	−6.82843			−0.373077
$336$		0			0
$337$	−25.7990			−1.40536			−0.702680	−	0.711506i	$-0.748014\pi$
$337$	−25.7990			−1.40536			−0.702680	+	0.711506i	$0.748014\pi$
$338$		0			0
$339$	−4.53553	+	7.85578i	−0.246336	+	0.426667i
$340$		0			0
$341$	−2.24264	−	3.88437i	−0.121446	−	0.210350i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.70711	−	2.95680i	−0.0919075	−	0.159189i
$346$		0			0
$347$	−10.5355	+	18.2481i	−0.565577	+	0.979608i	0.431419	+	0.902152i	$0.358013\pi$
$347$	−10.5355	+	18.2481i	−0.565577	+	0.979608i	−0.996996	+	0.0774564i	$0.975320\pi$
$348$		0			0
$349$	8.92893			0.477955			0.238977	−	0.971025i	$-0.423188\pi$
$349$	8.92893			0.477955			0.238977	+	0.971025i	$0.423188\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.48528	+	9.50079i	−0.291952	+	0.505676i	−0.974271	−	0.225379i	$-0.927638\pi$
$353$	−5.48528	+	9.50079i	−0.291952	+	0.505676i	0.682319	+	0.731054i	$0.260971\pi$
$354$		0			0
$355$	3.82843	+	6.63103i	0.203192	+	0.351939i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6.07107	−	10.5154i	−0.320419	−	0.554981i	0.660156	−	0.751129i	$-0.270490\pi$
$359$	−6.07107	−	10.5154i	−0.320419	−	0.554981i	−0.980574	+	0.196147i	$0.937157\pi$
$360$		0			0
$361$	8.50000	−	14.7224i	0.447368	−	0.774865i
$362$		0			0
$363$	10.3137			0.541329
$364$		0			0
$365$	7.31371			0.382817
$366$		0			0
$367$	−14.7279	+	25.5095i	−0.768791	+	1.33159i	0.169427	+	0.985543i	$0.445808\pi$
$367$	−14.7279	+	25.5095i	−0.768791	+	1.33159i	−0.938219	+	0.346043i	$0.887525\pi$
$368$		0			0
$369$	0.171573	+	0.297173i	0.00893173	+	0.0154702i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6.65685	+	11.5300i	0.344679	+	0.597001i	0.985295	−	0.170860i	$-0.0546545\pi$
$373$	6.65685	+	11.5300i	0.344679	+	0.597001i	−0.640617	+	0.767861i	$0.721321\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	14.0000			0.719132			0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000			0.719132			0.359566	+	0.933120i	$0.382925\pi$
$380$		0			0
$381$	4.58579	−	7.94282i	0.234937	−	0.406923i
$382$		0			0
$383$	12.8995	+	22.3426i	0.659133	+	1.14165i	0.980840	+	0.194813i	$0.0624101\pi$
$383$	12.8995	+	22.3426i	0.659133	+	1.14165i	−0.321707	+	0.946839i	$0.604257\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.82843	−	4.89898i	−0.143777	−	0.249029i
$388$		0			0
$389$	8.89949	−	15.4144i	0.451222	−	0.781540i	−0.547240	−	0.836976i	$-0.684321\pi$
$389$	8.89949	−	15.4144i	0.451222	−	0.781540i	0.998462	+	0.0554358i	$0.0176548\pi$
$390$		0			0
$391$	−9.65685			−0.488368
$392$		0			0
$393$	−1.65685			−0.0835772
$394$		0			0
$395$	0.171573	−	0.297173i	0.00863277	−	0.0149524i
$396$		0			0
$397$	−2.58579	−	4.47871i	−0.129777	−	0.224780i	0.793813	−	0.608162i	$-0.208093\pi$
$397$	−2.58579	−	4.47871i	−0.129777	−	0.224780i	−0.923590	+	0.383382i	$0.874759\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.07107	+	13.9795i	0.403050	+	0.698103i	0.994092	−	0.108538i	$-0.0346168\pi$
$401$	8.07107	+	13.9795i	0.403050	+	0.698103i	−0.591042	+	0.806640i	$0.701283\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−2.62742			−0.130236
$408$		0			0
$409$	−5.29289	+	9.16756i	−0.261717	+	0.453307i	−0.966698	−	0.255919i	$-0.917622\pi$
$409$	−5.29289	+	9.16756i	−0.261717	+	0.453307i	0.704981	+	0.709226i	$0.250955\pi$
$410$		0			0
$411$	3.12132	+	5.40629i	0.153963	+	0.266672i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	2.41421	+	4.18154i	0.118509	+	0.205264i
$416$		0			0
$417$	6.70711	−	11.6170i	0.328448	−	0.568889i
$418$		0			0
$419$	−5.65685			−0.276355			−0.138178	−	0.990407i	$-0.544125\pi$
$419$	−5.65685			−0.276355			−0.138178	+	0.990407i	$0.544125\pi$
$420$		0			0
$421$	16.2843			0.793647			0.396823	−	0.917895i	$-0.370113\pi$
$421$	16.2843			0.793647			0.396823	+	0.917895i	$0.370113\pi$
$422$		0			0
$423$	0.414214	−	0.717439i	0.0201398	−	0.0348831i
$424$		0			0
$425$	1.41421	+	2.44949i	0.0685994	+	0.118818i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.31371	−	4.00746i	0.111447	−	0.193033i	−0.804907	−	0.593401i	$-0.797785\pi$
$431$	2.31371	−	4.00746i	0.111447	−	0.193033i	0.916354	+	0.400369i	$0.131118\pi$
$432$		0			0
$433$	18.3431			0.881515			0.440758	−	0.897626i	$-0.354710\pi$
$433$	18.3431			0.881515			0.440758	+	0.897626i	$0.354710\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$		0			0
$437$	−2.41421	+	4.18154i	−0.115487	+	0.200030i
$438$		0			0
$439$	4.94975	+	8.57321i	0.236239	+	0.409177i	0.959632	−	0.281259i	$-0.0907520\pi$
$439$	4.94975	+	8.57321i	0.236239	+	0.409177i	−0.723393	+	0.690436i	$0.757419\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.22183	+	5.58037i	0.153074	+	0.265131i	0.932356	−	0.361542i	$-0.117750\pi$
$443$	3.22183	+	5.58037i	0.153074	+	0.265131i	−0.779282	+	0.626673i	$0.784416\pi$
$444$		0			0
$445$	3.24264	−	5.61642i	0.153716	−	0.266244i
$446$		0			0
$447$	−7.65685			−0.362157
$448$		0			0
$449$	−12.3431			−0.582509			−0.291255	−	0.956646i	$-0.594073\pi$
$449$	−12.3431			−0.582509			−0.291255	+	0.956646i	$0.594073\pi$
$450$		0			0
$451$	−0.142136	+	0.246186i	−0.00669291	+	0.0115925i
$452$		0			0
$453$	−0.656854	−	1.13770i	−0.0308617	−	0.0534540i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.0711	+	24.3718i	0.658217	+	1.14006i	0.981077	+	0.193618i	$0.0620223\pi$
$457$	14.0711	+	24.3718i	0.658217	+	1.14006i	−0.322860	+	0.946447i	$0.604644\pi$
$458$		0			0
$459$	−1.41421	+	2.44949i	−0.0660098	+	0.114332i
$460$		0			0
$461$	−30.4853			−1.41984			−0.709921	−	0.704282i	$-0.751269\pi$
$461$	−30.4853			−1.41984			−0.709921	+	0.704282i	$0.751269\pi$
$462$		0			0
$463$	11.7990			0.548346			0.274173	−	0.961680i	$-0.411596\pi$
$463$	11.7990			0.548346			0.274173	+	0.961680i	$0.411596\pi$
$464$		0			0
$465$	2.70711	−	4.68885i	0.125539	−	0.217440i
$466$		0			0
$467$	2.48528	+	4.30463i	0.115005	+	0.199195i	0.917782	−	0.397085i	$-0.129978\pi$
$467$	2.48528	+	4.30463i	0.115005	+	0.199195i	−0.802777	+	0.596280i	$0.796645\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	3.17157	+	5.49333i	0.146138	+	0.253119i
$472$		0			0
$473$	2.34315	−	4.05845i	0.107738	−	0.186608i
$474$		0			0
$475$	1.41421			0.0648886
$476$		0			0
$477$	0.585786			0.0268213
$478$		0			0
$479$	−10.4853	+	18.1610i	−0.479085	+	0.829799i	−0.999712	−	0.0239848i	$-0.992365\pi$
$479$	−10.4853	+	18.1610i	−0.479085	+	0.829799i	0.520628	+	0.853784i	$0.325698\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.41421	+	12.8418i	0.336662	+	0.583116i
$486$		0			0
$487$	1.51472	−	2.62357i	0.0686385	−	0.118885i	−0.829664	−	0.558263i	$-0.811468\pi$
$487$	1.51472	−	2.62357i	0.0686385	−	0.118885i	0.898302	+	0.439378i	$0.144801\pi$
$488$		0			0
$489$	0.485281			0.0219452
$490$		0			0
$491$	25.3137			1.14239			0.571196	−	0.820814i	$-0.306480\pi$
$491$	25.3137			1.14239			0.571196	+	0.820814i	$0.306480\pi$
$492$		0			0
$493$	−2.82843	+	4.89898i	−0.127386	+	0.220639i
$494$		0			0
$495$	−0.414214	−	0.717439i	−0.0186175	−	0.0322465i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	19.1421	+	33.1552i	0.856920	+	1.48423i	0.874853	+	0.484389i	$0.160958\pi$
$499$	19.1421	+	33.1552i	0.856920	+	1.48423i	−0.0179329	+	0.999839i	$0.505709\pi$
$500$		0			0
$501$	5.65685	−	9.79796i	0.252730	−	0.437741i
$502$		0			0
$503$	−4.82843			−0.215289			−0.107644	−	0.994189i	$-0.534331\pi$
$503$	−4.82843			−0.215289			−0.107644	+	0.994189i	$0.534331\pi$
$504$		0			0
$505$	17.3137			0.770450
$506$		0			0
$507$	−6.50000	+	11.2583i	−0.288675	+	0.500000i
$508$		0			0
$509$	−1.58579	−	2.74666i	−0.0702887	−	0.121744i	0.828739	−	0.559635i	$-0.189059\pi$
$509$	−1.58579	−	2.74666i	−0.0702887	−	0.121744i	−0.899028	+	0.437892i	$0.855725\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.707107	+	1.22474i	0.0312195	+	0.0540738i
$514$		0			0
$515$	5.41421	−	9.37769i	0.238579	−	0.413231i
$516$		0			0
$517$	0.686292			0.0301831
$518$		0			0
$519$	−4.48528			−0.196882
$520$		0			0
$521$	20.0711	−	34.7641i	0.879329	−	1.52304i	0.0272513	−	0.999629i	$-0.491325\pi$
$521$	20.0711	−	34.7641i	0.879329	−	1.52304i	0.852078	−	0.523415i	$-0.175342\pi$
$522$		0			0
$523$	3.07107	+	5.31925i	0.134288	+	0.232594i	0.925325	−	0.379174i	$-0.123792\pi$
$523$	3.07107	+	5.31925i	0.134288	+	0.232594i	−0.791037	+	0.611768i	$0.790458\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.65685	−	13.2621i	−0.333538	−	0.577704i
$528$		0			0
$529$	5.67157	−	9.82345i	0.246590	−	0.427107i
$530$		0			0
$531$	−8.48528			−0.368230
$532$		0			0
$533$		0			0
$534$		0			0
$535$	9.12132	−	15.7986i	0.394349	−	0.683033i
$536$		0			0
$537$	3.82843	+	6.63103i	0.165209	+	0.286150i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	20.4853	+	35.4815i	0.880731	+	1.52547i	0.850530	+	0.525927i	$0.176282\pi$
$541$	20.4853	+	35.4815i	0.880731	+	1.52547i	0.0302014	+	0.999544i	$0.490385\pi$
$542$		0			0
$543$	2.46447	−	4.26858i	0.105760	−	0.183182i
$544$		0			0
$545$	−11.6569			−0.499325
$546$		0			0
$547$	−1.17157			−0.0500928			−0.0250464	−	0.999686i	$-0.507973\pi$
$547$	−1.17157			−0.0500928			−0.0250464	+	0.999686i	$0.507973\pi$
$548$		0			0
$549$	−3.53553	+	6.12372i	−0.150893	+	0.261354i
$550$		0			0
$551$	1.41421	+	2.44949i	0.0602475	+	0.104352i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.58579	−	2.74666i	−0.0673129	−	0.116589i
$556$		0			0
$557$	1.46447	−	2.53653i	0.0620514	−	0.107476i	−0.833331	−	0.552775i	$-0.813569\pi$
$557$	1.46447	−	2.53653i	0.0620514	−	0.107476i	0.895382	+	0.445298i	$0.146902\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.34315			−0.0989277
$562$		0			0
$563$	−21.3848	+	37.0395i	−0.901261	+	1.56103i	−0.0754017	+	0.997153i	$0.524024\pi$
$563$	−21.3848	+	37.0395i	−0.901261	+	1.56103i	−0.825859	+	0.563876i	$0.809309\pi$
$564$		0			0
$565$	−4.53553	−	7.85578i	−0.190811	−	0.330495i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.24264	−	2.15232i	−0.0520942	−	0.0902298i	0.838802	−	0.544436i	$-0.183256\pi$
$569$	−1.24264	−	2.15232i	−0.0520942	−	0.0902298i	−0.890897	+	0.454206i	$0.849923\pi$
$570$		0			0
$571$	6.82843	−	11.8272i	0.285761	−	0.494952i	−0.687033	−	0.726627i	$-0.741087\pi$
$571$	6.82843	−	11.8272i	0.285761	−	0.494952i	0.972793	+	0.231674i	$0.0744204\pi$
$572$		0			0
$573$	−20.8284			−0.870120
$574$		0			0
$575$	3.41421			0.142383
$576$		0			0
$577$	−17.1716	+	29.7420i	−0.714862	+	1.23818i	0.248151	+	0.968721i	$0.420177\pi$
$577$	−17.1716	+	29.7420i	−0.714862	+	1.23818i	−0.963013	+	0.269456i	$0.913156\pi$
$578$		0			0
$579$	8.89949	+	15.4144i	0.369850	+	0.640600i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.242641	+	0.420266i	0.0100492	+	0.0174056i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.8284			0.859681			0.429841	−	0.902905i	$-0.358570\pi$
$587$	20.8284			0.859681			0.429841	+	0.902905i	$0.358570\pi$
$588$		0			0
$589$	−7.65685			−0.315495
$590$		0			0
$591$	−6.19239	+	10.7255i	−0.254721	+	0.441189i
$592$		0			0
$593$	13.4853	+	23.3572i	0.553774	+	0.959165i	0.997998	+	0.0632490i	$0.0201462\pi$
$593$	13.4853	+	23.3572i	0.553774	+	0.959165i	−0.444224	+	0.895916i	$0.646520\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.464466	+	0.804479i	0.0190093	+	0.0329251i
$598$		0			0
$599$	−17.3848	+	30.1113i	−0.710323	+	1.23032i	0.254413	+	0.967096i	$0.418118\pi$
$599$	−17.3848	+	30.1113i	−0.710323	+	1.23032i	−0.964736	+	0.263219i	$0.915216\pi$
$600$		0			0
$601$	−3.27208			−0.133471			−0.0667354	−	0.997771i	$-0.521258\pi$
$601$	−3.27208			−0.133471			−0.0667354	+	0.997771i	$0.521258\pi$
$602$		0			0
$603$	6.82843			0.278075
$604$		0			0
$605$	−5.15685	+	8.93193i	−0.209656	+	0.363135i
$606$		0			0
$607$	−1.75736	−	3.04384i	−0.0713290	−	0.123545i	0.828155	−	0.560499i	$-0.189391\pi$
$607$	−1.75736	−	3.04384i	−0.0713290	−	0.123545i	−0.899484	+	0.436954i	$0.856057\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	−0.998002	−	0.0631797i	$-0.979876\pi$
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	0.553716	+	0.832705i	$0.313209\pi$
$614$		0			0
$615$	−0.343146			−0.0138370
$616$		0			0
$617$	−35.4142			−1.42572			−0.712861	−	0.701305i	$-0.752601\pi$
$617$	−35.4142			−1.42572			−0.712861	+	0.701305i	$0.752601\pi$
$618$		0			0
$619$	−5.77817	+	10.0081i	−0.232244	+	0.402259i	−0.958468	−	0.285199i	$-0.907940\pi$
$619$	−5.77817	+	10.0081i	−0.232244	+	0.402259i	0.726224	+	0.687458i	$0.241274\pi$
$620$		0			0
$621$	1.70711	+	2.95680i	0.0685038	+	0.118652i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−0.585786	+	1.01461i	−0.0233941	+	0.0405197i
$628$		0			0
$629$	−8.97056			−0.357680
$630$		0			0
$631$	49.5980			1.97446			0.987232	−	0.159288i	$-0.0509198\pi$
$631$	49.5980			1.97446			0.987232	+	0.159288i	$0.0509198\pi$
$632$		0			0
$633$	13.3137	−	23.0600i	0.529172	−	0.916553i
$634$		0			0
$635$	4.58579	+	7.94282i	0.181981	+	0.315201i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3.82843	−	6.63103i	−0.151450	−	0.262320i
$640$		0			0
$641$	19.9706	−	34.5900i	0.788790	−	1.36622i	−0.137919	−	0.990444i	$-0.544041\pi$
$641$	19.9706	−	34.5900i	0.788790	−	1.36622i	0.926709	−	0.375780i	$-0.122625\pi$
$642$		0			0
$643$	12.0000			0.473234			0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$644$		0			0
$645$	5.65685			0.222738
$646$		0			0
$647$	−13.6569	+	23.6544i	−0.536906	+	0.929949i	0.462162	+	0.886795i	$0.347074\pi$
$647$	−13.6569	+	23.6544i	−0.536906	+	0.929949i	−0.999068	+	0.0431536i	$0.986260\pi$
$648$		0			0
$649$	−3.51472	−	6.08767i	−0.137965	−	0.238962i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.7782	+	39.4530i	0.891379	+	1.54391i	0.838223	+	0.545327i	$0.183595\pi$
$653$	22.7782	+	39.4530i	0.891379	+	1.54391i	0.0531556	+	0.998586i	$0.483072\pi$
$654$		0			0
$655$	0.828427	−	1.43488i	0.0323693	−	0.0560653i
$656$		0			0
$657$	−7.31371			−0.285335
$658$		0			0
$659$	−17.3137			−0.674446			−0.337223	−	0.941425i	$-0.609488\pi$
$659$	−17.3137			−0.674446			−0.337223	+	0.941425i	$0.609488\pi$
$660$		0			0
$661$	−8.02082	+	13.8925i	−0.311974	+	0.540354i	−0.978790	−	0.204868i	$-0.934323\pi$
$661$	−8.02082	+	13.8925i	−0.311974	+	0.540354i	0.666816	+	0.745222i	$0.267657\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.41421	+	5.91359i	0.132199	+	0.228975i
$668$		0			0
$669$	7.07107	−	12.2474i	0.273383	−	0.473514i
$670$		0			0
$671$	−5.85786			−0.226140
$672$		0			0
$673$	−24.1421			−0.930611			−0.465305	−	0.885150i	$-0.654056\pi$
$673$	−24.1421			−0.930611			−0.465305	+	0.885150i	$0.654056\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$		0			0
$677$	−16.3137	−	28.2562i	−0.626987	−	1.08597i	−0.988153	−	0.153471i	$-0.950955\pi$
$677$	−16.3137	−	28.2562i	−0.626987	−	1.08597i	0.361166	−	0.932501i	$-0.382379\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	7.17157	+	12.4215i	0.274815	+	0.475994i
$682$		0			0
$683$	20.2929	−	35.1483i	0.776486	−	1.34491i	−0.157470	−	0.987524i	$-0.550334\pi$
$683$	20.2929	−	35.1483i	0.776486	−	1.34491i	0.933955	−	0.357389i	$-0.116333\pi$
$684$		0			0
$685$	−6.24264			−0.238519
$686$		0			0
$687$	−27.5563			−1.05134
$688$		0			0
$689$		0			0
$690$		0			0
$691$	9.77817	+	16.9363i	0.371979	+	0.644287i	0.989870	−	0.141977i	$-0.0453459\pi$
$691$	9.77817	+	16.9363i	0.371979	+	0.644287i	−0.617891	+	0.786264i	$0.712013\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.70711	+	11.6170i	0.254415	+	0.440660i
$696$		0			0
$697$	−0.485281	+	0.840532i	−0.0183813	+	0.0318374i
$698$		0			0
$699$	5.75736			0.217763
$700$		0			0
$701$	38.2843			1.44598			0.722988	−	0.690860i	$-0.242768\pi$
$701$	38.2843			1.44598			0.722988	+	0.690860i	$0.242768\pi$
$702$		0			0
$703$	−2.24264	+	3.88437i	−0.0845828	+	0.146502i
$704$		0			0
$705$	0.414214	+	0.717439i	0.0156002	+	0.0270203i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.31371	−	2.27541i	−0.0493374	−	0.0854548i	0.840302	−	0.542118i	$-0.182378\pi$
$709$	−1.31371	−	2.27541i	−0.0493374	−	0.0854548i	−0.889639	+	0.456664i	$0.849044\pi$
$710$		0			0
$711$	−0.171573	+	0.297173i	−0.00643449	+	0.0111449i
$712$		0			0
$713$	−18.4853			−0.692279
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.89949	+	11.9503i	−0.257666	+	0.446291i
$718$		0			0
$719$	15.4142	+	26.6982i	0.574853	+	0.995675i	0.996058	+	0.0887092i	$0.0282742\pi$
$719$	15.4142	+	26.6982i	0.574853	+	0.995675i	−0.421204	+	0.906966i	$0.638393\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−8.12132	−	14.0665i	−0.302035	−	0.523140i
$724$		0			0
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$		0			0
$727$	−8.28427			−0.307247			−0.153623	−	0.988129i	$-0.549094\pi$
$727$	−8.28427			−0.307247			−0.153623	+	0.988129i	$0.549094\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.00000	−	13.8564i	0.295891	−	0.512498i
$732$		0			0
$733$	−8.48528	−	14.6969i	−0.313411	−	0.542844i	0.665687	−	0.746231i	$-0.268138\pi$
$733$	−8.48528	−	14.6969i	−0.313411	−	0.542844i	−0.979098	+	0.203387i	$0.934805\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.82843	+	4.89898i	0.104186	+	0.180456i
$738$		0			0
$739$	−11.3137	+	19.5959i	−0.416181	+	0.720847i	−0.995552	−	0.0942170i	$-0.969965\pi$
$739$	−11.3137	+	19.5959i	−0.416181	+	0.720847i	0.579370	+	0.815065i	$0.303299\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−20.8701			−0.765648			−0.382824	−	0.923821i	$-0.625048\pi$
$743$	−20.8701			−0.765648			−0.382824	+	0.923821i	$0.625048\pi$
$744$		0			0
$745$	3.82843	−	6.63103i	0.140263	−	0.242942i
$746$		0			0
$747$	−2.41421	−	4.18154i	−0.0883315	−	0.152995i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$		0			0
$753$	−4.58579	+	7.94282i	−0.167115	+	0.289452i
$754$		0			0
$755$	1.31371			0.0478107
$756$		0			0
$757$	−39.4558			−1.43405			−0.717024	−	0.697049i	$-0.754496\pi$
$757$	−39.4558			−1.43405			−0.717024	+	0.697049i	$0.754496\pi$
$758$		0			0
$759$	−1.41421	+	2.44949i	−0.0513327	+	0.0889108i
$760$		0			0
$761$	12.7574	+	22.0964i	0.462454	+	0.800994i	0.999083	−	0.0428248i	$-0.0136357\pi$
$761$	12.7574	+	22.0964i	0.462454	+	0.800994i	−0.536629	+	0.843818i	$0.680302\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.41421	−	2.44949i	−0.0511310	−	0.0885615i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	16.4437			0.592973			0.296487	−	0.955037i	$-0.404185\pi$
$769$	16.4437			0.592973			0.296487	+	0.955037i	$0.404185\pi$
$770$		0			0
$771$	4.34315			0.156415
$772$		0			0
$773$	−22.3848	+	38.7716i	−0.805124	+	1.39452i	0.111083	+	0.993811i	$0.464568\pi$
$773$	−22.3848	+	38.7716i	−0.805124	+	1.39452i	−0.916207	+	0.400705i	$0.868765\pi$
$774$		0			0
$775$	2.70711	+	4.68885i	0.0972421	+	0.168428i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.242641	+	0.420266i	0.00869350	+	0.0150576i
$780$		0			0
$781$	3.17157	−	5.49333i	0.113488	−	0.196567i
$782$		0			0
$783$	2.00000			0.0714742
$784$		0			0
$785$	−6.34315			−0.226397
$786$		0			0
$787$	−4.24264	+	7.34847i	−0.151234	+	0.261945i	−0.931681	−	0.363277i	$-0.881658\pi$
$787$	−4.24264	+	7.34847i	−0.151234	+	0.261945i	0.780447	+	0.625221i	$0.214991\pi$
$788$		0			0
$789$	−5.94975	−	10.3053i	−0.211817	−	0.366877i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.292893	+	0.507306i	−0.0103879	+	0.0179923i
$796$		0			0
$797$	−13.4558			−0.476630			−0.238315	−	0.971188i	$-0.576595\pi$
$797$	−13.4558			−0.476630			−0.238315	+	0.971188i	$0.576595\pi$
$798$		0			0
$799$	2.34315			0.0828945
$800$		0			0
$801$	−3.24264	+	5.61642i	−0.114573	+	0.198446i
$802$		0			0
$803$	−3.02944	−	5.24714i	−0.106907	−	0.185168i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.58579	+	6.21076i	0.126226	+	0.218629i
$808$		0			0
$809$	16.0711	−	27.8359i	0.565029	−	0.978658i	−0.432018	−	0.901865i	$-0.642198\pi$
$809$	16.0711	−	27.8359i	0.565029	−	0.978658i	0.997047	−	0.0767935i	$-0.0244682\pi$
$810$		0			0
$811$	−32.2426			−1.13219			−0.566096	−	0.824339i	$-0.691547\pi$
$811$	−32.2426			−1.13219			−0.566096	+	0.824339i	$0.691547\pi$
$812$		0			0
$813$	8.72792			0.306102
$814$		0			0
$815$	−0.242641	+	0.420266i	−0.00849933	+	0.0147213i
$816$		0			0
$817$	−4.00000	−	6.92820i	−0.139942	−	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−9.58579	−	16.6031i	−0.334546	−	0.579451i	0.648851	−	0.760915i	$-0.275250\pi$
$821$	−9.58579	−	16.6031i	−0.334546	−	0.579451i	−0.983398	+	0.181464i	$0.941916\pi$
$822$		0			0
$823$	12.3848	−	21.4511i	0.431706	−	0.747737i	−0.565314	−	0.824876i	$-0.691245\pi$
$823$	12.3848	−	21.4511i	0.431706	−	0.747737i	0.997020	+	0.0771386i	$0.0245784\pi$
$824$		0			0
$825$	0.828427			0.0288421
$826$		0			0
$827$	−27.0122			−0.939306			−0.469653	−	0.882851i	$-0.655621\pi$
$827$	−27.0122			−0.939306			−0.469653	+	0.882851i	$0.655621\pi$
$828$		0			0
$829$	−23.1924	+	40.1704i	−0.805505	+	1.39518i	0.110445	+	0.993882i	$0.464772\pi$
$829$	−23.1924	+	40.1704i	−0.805505	+	1.39518i	−0.915950	+	0.401293i	$0.868561\pi$
$830$		0			0
$831$	8.65685	+	14.9941i	0.300303	+	0.520140i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	5.65685	+	9.79796i	0.195764	+	0.339072i
$836$		0			0
$837$	−2.70711	+	4.68885i	−0.0935713	+	0.162070i
$838$		0			0
$839$	18.1421			0.626336			0.313168	−	0.949698i	$-0.398610\pi$
$839$	18.1421			0.626336			0.313168	+	0.949698i	$0.398610\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	3.48528	−	6.03668i	0.120039	−	0.207914i
$844$		0			0
$845$	−6.50000	−	11.2583i	−0.223607	−	0.387298i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.242641	−	0.420266i	−0.00832741	−	0.0144235i
$850$		0			0
$851$	−5.41421	+	9.37769i	−0.185597	+	0.321463i
$852$		0			0
$853$	−7.79899			−0.267032			−0.133516	−	0.991047i	$-0.542627\pi$
$853$	−7.79899			−0.267032			−0.133516	+	0.991047i	$0.542627\pi$
$854$		0			0
$855$	−1.41421			−0.0483651
$856$		0			0
$857$	2.72792	−	4.72490i	0.0931840	−	0.161399i	−0.815665	−	0.578524i	$-0.803629\pi$
$857$	2.72792	−	4.72490i	0.0931840	−	0.161399i	0.908849	+	0.417125i	$0.136962\pi$
$858$		0			0
$859$	22.6066	+	39.1558i	0.771327	+	1.33598i	0.936836	+	0.349770i	$0.113740\pi$
$859$	22.6066	+	39.1558i	0.771327	+	1.33598i	−0.165508	+	0.986208i	$0.552927\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.39340	+	4.14549i	0.0814722	+	0.141114i	0.903883	−	0.427781i	$-0.140704\pi$
$863$	2.39340	+	4.14549i	0.0814722	+	0.141114i	−0.822410	+	0.568895i	$0.807371\pi$
$864$		0			0
$865$	2.24264	−	3.88437i	0.0762521	−	0.132072i
$866$		0			0
$867$	9.00000			0.305656
$868$		0			0
$869$	−0.284271			−0.00964324
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−7.41421	−	12.8418i	−0.250933	−	0.434629i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.14214	−	15.8346i	−0.308708	−	0.534698i	0.669372	−	0.742927i	$-0.266563\pi$
$877$	−9.14214	−	15.8346i	−0.308708	−	0.534698i	−0.978080	+	0.208229i	$0.933230\pi$
$878$		0			0
$879$	−14.3137	+	24.7921i	−0.482789	+	0.836216i
$880$		0			0
$881$	20.6274			0.694955			0.347478	−	0.937688i	$-0.387038\pi$
$881$	20.6274			0.694955			0.347478	+	0.937688i	$0.387038\pi$
$882$		0			0
$883$	26.3431			0.886517			0.443259	−	0.896394i	$-0.353822\pi$
$883$	26.3431			0.886517			0.443259	+	0.896394i	$0.353822\pi$
$884$		0			0
$885$	4.24264	−	7.34847i	0.142615	−	0.247016i
$886$		0			0
$887$	16.7574	+	29.0246i	0.562657	+	0.974551i	0.997263	+	0.0739301i	$0.0235542\pi$
$887$	16.7574	+	29.0246i	0.562657	+	0.974551i	−0.434606	+	0.900621i	$0.643112\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.414214	+	0.717439i	0.0138767	+	0.0240351i
$892$		0			0
$893$	0.585786	−	1.01461i	0.0196026	−	0.0339527i
$894$		0			0
$895$	−7.65685			−0.255940
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.41421	+	9.37769i	−0.180574	+	0.312764i
$900$		0			0
$901$	0.828427	+	1.43488i	0.0275989	+	0.0478027i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.46447	+	4.26858i	0.0819216	+	0.141892i
$906$		0			0
$907$	−10.4853	+	18.1610i	−0.348158	+	0.603027i	−0.985922	−	0.167204i	$-0.946526\pi$
$907$	−10.4853	+	18.1610i	−0.348158	+	0.603027i	0.637764	+	0.770232i	$0.279859\pi$
$908$		0			0
$909$	−17.3137			−0.574259
$910$		0			0
$911$	25.7990			0.854759			0.427379	−	0.904072i	$-0.359437\pi$
$911$	25.7990			0.854759			0.427379	+	0.904072i	$0.359437\pi$
$912$		0			0
$913$	2.00000	−	3.46410i	0.0661903	−	0.114645i
$914$		0			0
$915$	−3.53553	−	6.12372i	−0.116881	−	0.202444i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−10.3431	−	17.9149i	−0.341189	−	0.590957i	0.643465	−	0.765476i	$-0.277496\pi$
$919$	−10.3431	−	17.9149i	−0.341189	−	0.590957i	−0.984654	+	0.174519i	$0.944163\pi$
$920$		0			0
$921$	12.8284	−	22.2195i	0.422711	−	0.732157i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	3.17157			0.104281
$926$		0			0
$927$	−5.41421	+	9.37769i	−0.177826	+	0.308004i
$928$		0			0
$929$	−7.92893	−	13.7333i	−0.260140	−	0.450575i	0.706139	−	0.708073i	$-0.250435\pi$
$929$	−7.92893	−	13.7333i	−0.260140	−	0.450575i	−0.966279	+	0.257498i	$0.917102\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−10.8284	−	18.7554i	−0.354507	−	0.614024i
$934$		0			0
$935$	1.17157	−	2.02922i	0.0383145	−	0.0663627i
$936$		0			0
$937$	29.4558			0.962280			0.481140	−	0.876644i	$-0.340223\pi$
$937$	29.4558			0.962280			0.481140	+	0.876644i	$0.340223\pi$
$938$		0			0
$939$	−15.3137			−0.499744
$940$		0			0
$941$	30.3137	−	52.5049i	0.988199	−	1.71161i	0.361444	−	0.932394i	$-0.382284\pi$
$941$	30.3137	−	52.5049i	0.988199	−	1.71161i	0.626755	−	0.779216i	$-0.284383\pi$
$942$		0			0
$943$	0.585786	+	1.01461i	0.0190758	+	0.0330403i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.36396	−	9.29065i	−0.174305	−	0.301906i	0.765615	−	0.643299i	$-0.222435\pi$
$947$	−5.36396	−	9.29065i	−0.174305	−	0.301906i	−0.939921	+	0.341393i	$0.889101\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−15.2132			−0.493322
$952$		0			0
$953$	−16.1005			−0.521547			−0.260773	−	0.965400i	$-0.583977\pi$
$953$	−16.1005			−0.521547			−0.260773	+	0.965400i	$0.583977\pi$
$954$		0			0
$955$	10.4142	−	18.0379i	0.336996	−	0.583694i
$956$		0			0
$957$	0.828427	+	1.43488i	0.0267792	+	0.0463830i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.843146	+	1.46037i	0.0271983	+	0.0471088i
$962$		0			0
$963$	−9.12132	+	15.7986i	−0.293930	+	0.509102i
$964$		0			0
$965$	−17.7990			−0.572970
$966$		0			0
$967$	−13.1716			−0.423569			−0.211785	−	0.977316i	$-0.567928\pi$
$967$	−13.1716			−0.423569			−0.211785	+	0.977316i	$0.567928\pi$
$968$		0			0
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$		0			0
$971$	−16.7279	−	28.9736i	−0.536825	−	0.929807i	−0.999073	−	0.0430568i	$-0.986290\pi$
$971$	−16.7279	−	28.9736i	−0.536825	−	0.929807i	0.462248	−	0.886751i	$-0.347043\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.43503	+	7.68170i	−0.141889	+	0.245759i	−0.928208	−	0.372062i	$-0.878651\pi$
$977$	−4.43503	+	7.68170i	−0.141889	+	0.245759i	0.786319	+	0.617821i	$0.211984\pi$
$978$		0			0
$979$	−5.37258			−0.171708
$980$		0			0
$981$	11.6569			0.372175
$982$		0			0
$983$	−21.6569	+	37.5108i	−0.690746	+	1.19641i	0.280847	+	0.959752i	$0.409385\pi$
$983$	−21.6569	+	37.5108i	−0.690746	+	1.19641i	−0.971594	+	0.236655i	$0.923949\pi$
$984$		0			0
$985$	−6.19239	−	10.7255i	−0.197306	−	0.341744i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.65685	−	16.7262i	−0.307070	−	0.531861i
$990$		0			0
$991$	14.1421	−	24.4949i	0.449240	−	0.778106i	−0.549097	−	0.835759i	$-0.685028\pi$
$991$	14.1421	−	24.4949i	0.449240	−	0.778106i	0.998337	+	0.0576526i	$0.0183616\pi$
$992$		0			0
$993$	24.2843			0.770638
$994$		0			0
$995$	−0.928932			−0.0294491
$996$		0			0
$997$	−17.4142	+	30.1623i	−0.551514	+	0.955250i	0.446652	+	0.894708i	$0.352616\pi$
$997$	−17.4142	+	30.1623i	−0.551514	+	0.955250i	−0.998166	+	0.0605419i	$0.980717\pi$
$998$		0			0
$999$	1.58579	+	2.74666i	0.0501721	+	0.0869006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.s.361.2		4
7.2	even	3	inner	2940.2.q.s.961.2		4
7.3	odd	6		2940.2.a.t.1.1	yes	2
7.4	even	3		2940.2.a.n.1.1	✓	2
7.5	odd	6		2940.2.q.o.961.2		4
7.6	odd	2		2940.2.q.o.361.2		4
21.11	odd	6		8820.2.a.bi.1.2		2
21.17	even	6		8820.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.a.n.1.1	✓	2	7.4	even	3
2940.2.a.t.1.1	yes	2	7.3	odd	6
2940.2.q.o.361.2		4	7.6	odd	2
2940.2.q.o.961.2		4	7.5	odd	6
2940.2.q.s.361.2		4	1.1	even	1	trivial
2940.2.q.s.961.2		4	7.2	even	3	inner
8820.2.a.bd.1.2		2	21.17	even	6
8820.2.a.bi.1.2		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(0.414214 - 0.717439i) q^{11} +1.00000 q^{15} +(1.41421 - 2.44949i) q^{17} +(-0.707107 - 1.22474i) q^{19} +(-1.70711 - 2.95680i) q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(2.70711 - 4.68885i) q^{31} +(-0.414214 - 0.717439i) q^{33} +(-1.58579 - 2.74666i) q^{37} -0.343146 q^{41} +5.65685 q^{43} +(0.500000 - 0.866025i) q^{45} +(0.414214 + 0.717439i) q^{47} +(-1.41421 - 2.44949i) q^{51} +(-0.292893 + 0.507306i) q^{53} +0.828427 q^{55} -1.41421 q^{57} +(4.24264 - 7.34847i) q^{59} +(-3.53553 - 6.12372i) q^{61} +(-3.41421 + 5.91359i) q^{67} -3.41421 q^{69} +7.65685 q^{71} +(3.65685 - 6.33386i) q^{73} +(0.500000 + 0.866025i) q^{75} +(-0.171573 - 0.297173i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.82843 q^{83} +2.82843 q^{85} +(-1.00000 + 1.73205i) q^{87} +(-3.24264 - 5.61642i) q^{89} +(-2.70711 - 4.68885i) q^{93} +(0.707107 - 1.22474i) q^{95} +14.8284 q^{97} -0.828427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{5} - 2 q^{9} - 4 q^{11} + 4 q^{15} - 4 q^{23} - 2 q^{25} - 4 q^{27} - 8 q^{29} + 8 q^{31} + 4 q^{33} - 12 q^{37} - 24 q^{41} + 2 q^{45} - 4 q^{47} - 4 q^{53} - 8 q^{55} - 8 q^{67} - 8 q^{69} + 8 q^{71} - 8 q^{73} + 2 q^{75} - 12 q^{79} - 2 q^{81} + 8 q^{83} - 4 q^{87} + 4 q^{89} - 8 q^{93} + 48 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^5 - 2 * q^9 - 4 * q^11 + 4 * q^15 - 4 * q^23 - 2 * q^25 - 4 * q^27 - 8 * q^29 + 8 * q^31 + 4 * q^33 - 12 * q^37 - 24 * q^41 + 2 * q^45 - 4 * q^47 - 4 * q^53 - 8 * q^55 - 8 * q^67 - 8 * q^69 + 8 * q^71 - 8 * q^73 + 2 * q^75 - 12 * q^79 - 2 * q^81 + 8 * q^83 - 4 * q^87 + 4 * q^89 - 8 * q^93 + 48 * q^97 + 8 * q^99

Introduction

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