LMFDB - Embedded newform 650.2.d.c.51.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(51,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.51"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-6,0,0,0,0,18,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.126157824.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 18x^{4} + 81x^{2} + 4 $ x^6 + 18x^4 + 81x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.4
Root			$-3.10548i$ of defining polynomial
Character	$\chi$	$=$	650.51
Dual form			650.2.d.c.51.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -3.10548 q^{3} -1.00000 q^{4} -3.10548i q^{6} -4.10548i q^{7} -1.00000i q^{8} +6.64402 q^{9} +1.53854i q^{11} +3.10548 q^{12} +(-1.26927 + 3.37475i) q^{13} +4.10548 q^{14} +1.00000 q^{16} +3.00000 q^{17} +6.64402i q^{18} +1.10548i q^{19} +12.7495i q^{21} -1.53854 q^{22} -6.74950 q^{23} +3.10548i q^{24} +(-3.37475 - 1.26927i) q^{26} -11.3164 q^{27} +4.10548i q^{28} -5.56694 q^{29} -8.64402i q^{31} +1.00000i q^{32} -4.77791i q^{33} +3.00000i q^{34} -6.64402 q^{36} +4.53854i q^{37} -1.10548 q^{38} +(3.94170 - 10.4802i) q^{39} +7.85499i q^{41} -12.7495 q^{42} +4.00000 q^{43} -1.53854i q^{44} -6.74950i q^{46} +10.8550i q^{47} -3.10548 q^{48} -9.85499 q^{49} -9.31645 q^{51} +(1.26927 - 3.37475i) q^{52} -0.433057 q^{53} -11.3164i q^{54} -4.10548 q^{56} -3.43306i q^{57} -5.56694i q^{58} +13.7779i q^{59} -14.3164 q^{61} +8.64402 q^{62} -27.2769i q^{63} -1.00000 q^{64} +4.77791 q^{66} +3.74950i q^{67} -3.00000 q^{68} +20.9605 q^{69} -6.64402i q^{72} +10.7779i q^{73} -4.53854 q^{74} -1.10548i q^{76} +6.31645 q^{77} +(10.4802 + 3.94170i) q^{78} -6.53854 q^{79} +15.2110 q^{81} -7.85499 q^{82} +4.46146i q^{83} -12.7495i q^{84} +4.00000i q^{86} +17.2880 q^{87} +1.53854 q^{88} +1.85499i q^{89} +(13.8550 + 5.21097i) q^{91} +6.74950 q^{92} +26.8439i q^{93} -10.8550 q^{94} -3.10548i q^{96} +3.78903i q^{97} -9.85499i q^{98} +10.2221i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 18 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{16} + 18 q^{17} - 6 q^{22} - 12 q^{27} - 18 q^{29} - 18 q^{36} + 12 q^{38} - 12 q^{39} - 36 q^{42} + 24 q^{43} + 6 q^{52} - 18 q^{53} - 6 q^{56} - 30 q^{61}+ \cdots - 6 q^{94}+O(q^{100}) $ 6 * q - 6 * q^4 + 18 * q^9 - 6 * q^13 + 6 * q^14 + 6 * q^16 + 18 * q^17 - 6 * q^22 - 12 * q^27 - 18 * q^29 - 18 * q^36 + 12 * q^38 - 12 * q^39 - 36 * q^42 + 24 * q^43 + 6 * q^52 - 18 * q^53 - 6 * q^56 - 30 * q^61 + 30 * q^62 - 6 * q^64 - 24 * q^66 - 18 * q^68 + 48 * q^69 - 24 * q^74 - 18 * q^77 + 24 * q^78 - 36 * q^79 + 54 * q^81 + 12 * q^82 + 60 * q^87 + 6 * q^88 + 24 * q^91 - 6 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$-1$

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
$3$	−3.10548			−1.79295			−0.896476	−	0.443093i	$-0.853881\pi$
$3$	−3.10548			−1.79295			−0.896476	+	0.443093i	$0.853881\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	3.10548i		−	1.26781i
$7$		−	4.10548i		−	1.55173i	−0.630901	−	0.775863i	$-0.717315\pi$
$7$		−	4.10548i		−	1.55173i	0.630901	−	0.775863i	$-0.282685\pi$
$8$		−	1.00000i		−	0.353553i
$9$	6.64402			2.21467
$10$		0			0
$11$			1.53854i			0.463887i	0.972729	+	0.231944i	$0.0745085\pi$
$11$			1.53854i			0.463887i	−0.972729	+	0.231944i	$0.925492\pi$
$12$	3.10548			0.896476
$13$	−1.26927	+	3.37475i	−0.352032	+	0.935988i
$13$	−1.26927	+	3.37475i	−0.352032	+	0.935988i
$14$	4.10548			1.09724
$15$		0			0
$16$	1.00000			0.250000
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$			6.64402i			1.56601i
$19$			1.10548i			0.253615i	0.991927	+	0.126808i	$0.0404731\pi$
$19$			1.10548i			0.253615i	−0.991927	+	0.126808i	$0.959527\pi$
$20$		0			0
$21$			12.7495i			2.78217i
$22$	−1.53854			−0.328018
$23$	−6.74950			−1.40737			−0.703685	−	0.710513i	$-0.748463\pi$
$23$	−6.74950			−1.40737			−0.703685	+	0.710513i	$0.748463\pi$
$24$			3.10548i			0.633904i
$25$		0			0
$26$	−3.37475	−	1.26927i	−0.661843	−	0.248924i
$27$	−11.3164			−2.17785
$28$			4.10548i			0.775863i
$29$	−5.56694			−1.03376			−0.516878	−	0.856059i	$-0.672906\pi$
$29$	−5.56694			−1.03376			−0.516878	+	0.856059i	$0.672906\pi$
$30$		0			0
$31$		−	8.64402i		−	1.55251i	−0.630418	−	0.776256i	$-0.717116\pi$
$31$		−	8.64402i		−	1.55251i	0.630418	−	0.776256i	$-0.282884\pi$
$32$			1.00000i			0.176777i
$33$		−	4.77791i		−	0.831727i
$34$			3.00000i			0.514496i
$35$		0			0
$36$	−6.64402			−1.10734
$37$			4.53854i			0.746131i	0.927805	+	0.373066i	$0.121693\pi$
$37$			4.53854i			0.746131i	−0.927805	+	0.373066i	$0.878307\pi$
$38$	−1.10548			−0.179333
$39$	3.94170	−	10.4802i	0.631176	−	1.67818i
$40$		0			0
$41$			7.85499i			1.22674i	0.789795	+	0.613371i	$0.210187\pi$
$41$			7.85499i			1.22674i	−0.789795	+	0.613371i	$0.789813\pi$
$42$	−12.7495			−1.96729
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		−	1.53854i		−	0.231944i
$45$		0			0
$46$		−	6.74950i		−	0.995160i
$47$			10.8550i			1.58336i	0.610934	+	0.791681i	$0.290794\pi$
$47$			10.8550i			1.58336i	−0.610934	+	0.791681i	$0.709206\pi$
$48$	−3.10548			−0.448238
$49$	−9.85499			−1.40786
$50$		0			0
$51$	−9.31645			−1.30456
$52$	1.26927	−	3.37475i	0.176016	−	0.467994i
$53$	−0.433057			−0.0594850			−0.0297425	−	0.999558i	$-0.509469\pi$
$53$	−0.433057			−0.0594850			−0.0297425	+	0.999558i	$0.509469\pi$
$54$		−	11.3164i		−	1.53997i
$55$		0			0
$56$	−4.10548			−0.548618
$57$		−	3.43306i		−	0.454720i
$58$		−	5.56694i		−	0.730975i
$59$			13.7779i			1.79373i	0.442304	+	0.896865i	$0.354161\pi$
$59$			13.7779i			1.79373i	−0.442304	+	0.896865i	$0.645839\pi$
$60$		0			0
$61$	−14.3164			−1.83303			−0.916517	−	0.399997i	$-0.869011\pi$
$61$	−14.3164			−1.83303			−0.916517	+	0.399997i	$0.869011\pi$
$62$	8.64402			1.09779
$63$		−	27.2769i		−	3.43657i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.77791			0.588120
$67$			3.74950i			0.458075i	0.973418	+	0.229037i	$0.0735578\pi$
$67$			3.74950i			0.458075i	−0.973418	+	0.229037i	$0.926442\pi$
$68$	−3.00000			−0.363803
$69$	20.9605			2.52334
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		−	6.64402i		−	0.783006i
$73$			10.7779i			1.26146i	0.776003	+	0.630729i	$0.217244\pi$
$73$			10.7779i			1.26146i	−0.776003	+	0.630729i	$0.782756\pi$
$74$	−4.53854			−0.527595
$75$		0			0
$76$		−	1.10548i		−	0.126808i
$77$	6.31645			0.719826
$78$	10.4802	+	3.94170i	1.18665	+	0.446309i
$79$	−6.53854			−0.735643			−0.367822	−	0.929896i	$-0.619896\pi$
$79$	−6.53854			−0.735643			−0.367822	+	0.929896i	$0.619896\pi$
$80$		0			0
$81$	15.2110			1.69011
$82$	−7.85499			−0.867438
$83$			4.46146i			0.489709i	0.969560	+	0.244854i	$0.0787402\pi$
$83$			4.46146i			0.489709i	−0.969560	+	0.244854i	$0.921260\pi$
$84$		−	12.7495i		−	1.39109i
$85$		0			0
$86$			4.00000i			0.431331i
$87$	17.2880			1.85347
$88$	1.53854			0.164009
$89$			1.85499i			0.196628i	0.995155	+	0.0983141i	$0.0313450\pi$
$89$			1.85499i			0.196628i	−0.995155	+	0.0983141i	$0.968655\pi$
$90$		0			0
$91$	13.8550	+	5.21097i	1.45240	+	0.546258i
$92$	6.74950			0.703685
$93$			26.8439i			2.78358i
$94$	−10.8550			−1.11961
$95$		0			0
$96$		−	3.10548i		−	0.316952i
$97$			3.78903i			0.384718i	0.981325	+	0.192359i	$0.0616138\pi$
$97$			3.78903i			0.384718i	−0.981325	+	0.192359i	$0.938386\pi$
$98$		−	9.85499i		−	0.995504i
$99$			10.2221i			1.02736i
$100$		0			0
$101$	7.18256			0.714692			0.357346	−	0.933972i	$-0.383682\pi$
$101$	7.18256			0.714692			0.357346	+	0.933972i	$0.383682\pi$
$102$		−	9.31645i		−	0.922466i
$103$	−12.5385			−1.23546			−0.617730	−	0.786391i	$-0.711947\pi$
$103$	−12.5385			−1.23546			−0.617730	+	0.786391i	$0.711947\pi$
$104$	3.37475	+	1.26927i	0.330922	+	0.124462i
$105$		0			0
$106$		−	0.433057i		−	0.0420622i
$107$	−1.81744			−0.175698			−0.0878492	−	0.996134i	$-0.527999\pi$
$107$	−1.81744			−0.175698			−0.0878492	+	0.996134i	$0.527999\pi$
$108$	11.3164			1.08893
$109$		−	3.67243i		−	0.351755i	−0.984412	−	0.175877i	$-0.943724\pi$
$109$		−	3.67243i		−	0.351755i	0.984412	−	0.175877i	$-0.0562762\pi$
$110$		0			0
$111$		−	14.0944i		−	1.33778i
$112$		−	4.10548i		−	0.387932i
$113$	16.0660			1.51136			0.755679	−	0.654942i	$-0.227307\pi$
$113$	16.0660			1.51136			0.755679	+	0.654942i	$0.227307\pi$
$114$	3.43306			0.321535
$115$		0			0
$116$	5.56694			0.516878
$117$	−8.43306	+	22.4219i	−0.779636	+	2.07291i
$118$	−13.7779			−1.26836
$119$		−	12.3164i		−	1.12905i
$120$		0			0
$121$	8.63290			0.784809
$122$		−	14.3164i		−	1.29615i
$123$		−	24.3935i		−	2.19949i
$124$			8.64402i			0.776256i
$125$		0			0
$126$	27.2769			2.43002
$127$	4.92292			0.436839			0.218419	−	0.975855i	$-0.429910\pi$
$127$	4.92292			0.436839			0.218419	+	0.975855i	$0.429910\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.4219			−1.09369
$130$		0			0
$131$	0.866114			0.0756727			0.0378364	−	0.999284i	$-0.487953\pi$
$131$	0.866114			0.0756727			0.0378364	+	0.999284i	$0.487953\pi$
$132$			4.77791i			0.415864i
$133$	4.53854			0.393541
$134$	−3.74950			−0.323908
$135$		0			0
$136$		−	3.00000i		−	0.257248i
$137$		−	16.7779i		−	1.43343i	−0.697364	−	0.716717i	$-0.745644\pi$
$137$		−	16.7779i		−	1.43343i	0.697364	−	0.716717i	$-0.254356\pi$
$138$			20.9605i			1.78427i
$139$	−4.39353			−0.372654			−0.186327	−	0.982488i	$-0.559658\pi$
$139$	−4.39353			−0.372654			−0.186327	+	0.982488i	$0.559658\pi$
$140$		0			0
$141$		−	33.7100i		−	2.83889i
$142$		0			0
$143$	−5.19219	−	1.95282i	−0.434193	−	0.163303i
$144$	6.64402			0.553669
$145$		0			0
$146$	−10.7779			−0.891986
$147$	30.6045			2.52422
$148$		−	4.53854i		−	0.373066i
$149$			9.70998i			0.795472i	0.917500	+	0.397736i	$0.130204\pi$
$149$			9.70998i			0.795472i	−0.917500	+	0.397736i	$0.869796\pi$
$150$		0			0
$151$			2.48986i			0.202622i	0.994855	+	0.101311i	$0.0323038\pi$
$151$			2.48986i			0.202622i	−0.994855	+	0.101311i	$0.967696\pi$
$152$	1.10548			0.0896665
$153$	19.9321			1.61141
$154$			6.31645i			0.508994i
$155$		0			0
$156$	−3.94170	+	10.4802i	−0.315588	+	0.839090i
$157$	−11.3935			−0.909302			−0.454651	−	0.890670i	$-0.650236\pi$
$157$	−11.3935			−0.909302			−0.454651	+	0.890670i	$0.650236\pi$
$158$		−	6.53854i		−	0.520178i
$159$	1.34485			0.106654
$160$		0			0
$161$			27.7100i			2.18385i
$162$			15.2110i			1.19509i
$163$		−	16.8155i		−	1.31709i	−0.752542	−	0.658544i	$-0.771173\pi$
$163$		−	16.8155i		−	1.31709i	0.752542	−	0.658544i	$-0.228827\pi$
$164$		−	7.85499i		−	0.613371i
$165$		0			0
$166$	−4.46146			−0.346276
$167$		−	1.61562i		−	0.125020i	−0.998044	−	0.0625102i	$-0.980089\pi$
$167$		−	1.61562i		−	0.125020i	0.998044	−	0.0625102i	$-0.0199106\pi$
$168$	12.7495			0.983646
$169$	−9.77791	−	8.56694i	−0.752147	−	0.658996i
$170$		0			0
$171$			7.34485i			0.561675i
$172$	−4.00000			−0.304997
$173$	−12.3164			−0.936402			−0.468201	−	0.883622i	$-0.655098\pi$
$173$	−12.3164			−0.936402			−0.468201	+	0.883622i	$0.655098\pi$
$174$			17.2880i			1.31060i
$175$		0			0
$176$			1.53854i			0.115972i
$177$		−	42.7871i		−	3.21607i
$178$	−1.85499			−0.139037
$179$	10.1826			0.761080			0.380540	−	0.924764i	$-0.375738\pi$
$179$	10.1826			0.761080			0.380540	+	0.924764i	$0.375738\pi$
$180$		0			0
$181$	11.3935			0.846874			0.423437	−	0.905926i	$-0.360823\pi$
$181$	11.3935			0.846874			0.423437	+	0.905926i	$0.360823\pi$
$182$	−5.21097	+	13.8550i	−0.386262	+	1.02700i
$183$	44.4595			3.28654
$184$			6.74950i			0.497580i
$185$		0			0
$186$	−26.8439			−1.96829
$187$			4.61562i			0.337527i
$188$		−	10.8550i		−	0.791681i
$189$			46.4595i			3.37943i
$190$		0			0
$191$	−19.4990			−1.41090			−0.705449	−	0.708760i	$-0.749255\pi$
$191$	−19.4990			−1.41090			−0.705449	+	0.708760i	$0.749255\pi$
$192$	3.10548			0.224119
$193$			2.72110i			0.195869i	0.995193	+	0.0979346i	$0.0312236\pi$
$193$			2.72110i			0.195869i	−0.995193	+	0.0979346i	$0.968776\pi$
$194$	−3.78903			−0.272037
$195$		0			0
$196$	9.85499			0.703928
$197$		−	1.61562i		−	0.115108i	−0.998342	−	0.0575540i	$-0.981670\pi$
$197$		−	1.61562i		−	0.115108i	0.998342	−	0.0575540i	$-0.0183302\pi$
$198$	−10.2221			−0.726452
$199$	−22.2485			−1.57716			−0.788578	−	0.614935i	$-0.789182\pi$
$199$	−22.2485			−1.57716			−0.788578	+	0.614935i	$0.789182\pi$
$200$		0			0
$201$		−	11.6440i		−	0.821306i
$202$			7.18256i			0.505363i
$203$			22.8550i			1.60411i
$204$	9.31645			0.652282
$205$		0			0
$206$		−	12.5385i		−	0.873601i
$207$	−44.8439			−3.11686
$208$	−1.26927	+	3.37475i	−0.0880080	+	0.233997i
$209$	−1.70083			−0.117649
$210$		0			0
$211$	10.2394			0.704907			0.352454	−	0.935829i	$-0.385347\pi$
$211$	10.2394			0.704907			0.352454	+	0.935829i	$0.385347\pi$
$212$	0.433057			0.0297425
$213$		0			0
$214$		−	1.81744i		−	0.124238i
$215$		0			0
$216$			11.3164i			0.769987i
$217$	−35.4879			−2.40907
$218$	3.67243			0.248728
$219$		−	33.4706i		−	2.26173i
$220$		0			0
$221$	−3.80781	+	10.1243i	−0.256141	+	0.681031i
$222$	14.0944			0.945951
$223$			20.9605i			1.40362i	0.712366	+	0.701808i	$0.247624\pi$
$223$			20.9605i			1.40362i	−0.712366	+	0.701808i	$0.752376\pi$
$224$	4.10548			0.274309
$225$		0			0
$226$			16.0660i			1.06869i
$227$		−	4.85499i		−	0.322237i	−0.986935	−	0.161118i	$-0.948490\pi$
$227$		−	4.85499i		−	0.322237i	0.986935	−	0.161118i	$-0.0515101\pi$
$228$			3.43306i			0.227360i
$229$			6.71196i			0.443538i	0.975099	+	0.221769i	$0.0711832\pi$
$229$			6.71196i			0.443538i	−0.975099	+	0.221769i	$0.928817\pi$
$230$		0			0
$231$	−19.6156			−1.29061
$232$			5.56694i			0.365488i
$233$	14.3651			0.941091			0.470545	−	0.882376i	$-0.344057\pi$
$233$	14.3651			0.941091			0.470545	+	0.882376i	$0.344057\pi$
$234$	−22.4219	−	8.43306i	−1.46577	−	0.551286i
$235$		0			0
$236$		−	13.7779i		−	0.896865i
$237$	20.3053			1.31897
$238$	12.3164			0.798357
$239$			1.14501i			0.0740647i	0.999314	+	0.0370324i	$0.0117905\pi$
$239$			1.14501i			0.0740647i	−0.999314	+	0.0370324i	$0.988210\pi$
$240$		0			0
$241$			20.5669i			1.32483i	0.749136	+	0.662417i	$0.230469\pi$
$241$			20.5669i			1.32483i	−0.749136	+	0.662417i	$0.769531\pi$
$242$			8.63290i			0.554944i
$243$	−13.2880			−0.852428
$244$	14.3164			0.916517
$245$		0			0
$246$	24.3935			1.55527
$247$	−3.73073	−	1.40316i	−0.237381	−	0.0892807i
$248$	−8.64402			−0.548896
$249$		−	13.8550i		−	0.878024i
$250$		0			0
$251$	3.31645			0.209332			0.104666	−	0.994507i	$-0.466623\pi$
$251$	3.31645			0.209332			0.104666	+	0.994507i	$0.466623\pi$
$252$			27.2769i			1.71828i
$253$		−	10.3844i		−	0.652860i
$254$			4.92292i			0.308892i
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.4331			0.775553			0.387776	−	0.921753i	$-0.373243\pi$
$257$	12.4331			0.775553			0.387776	+	0.921753i	$0.373243\pi$
$258$		−	12.4219i		−	0.773356i
$259$	18.6329			1.15779
$260$		0			0
$261$	−36.9869			−2.28943
$262$			0.866114i			0.0535087i
$263$	4.38438			0.270353			0.135176	−	0.990822i	$-0.456840\pi$
$263$	4.38438			0.270353			0.135176	+	0.990822i	$0.456840\pi$
$264$	−4.77791			−0.294060
$265$		0			0
$266$			4.53854i			0.278276i
$267$		−	5.76063i		−	0.352545i
$268$		−	3.74950i		−	0.229037i
$269$	−5.56694			−0.339423			−0.169711	−	0.985494i	$-0.554284\pi$
$269$	−5.56694			−0.339423			−0.169711	+	0.985494i	$0.554284\pi$
$270$		0			0
$271$		−	9.39353i		−	0.570616i	−0.958436	−	0.285308i	$-0.907904\pi$
$271$		−	9.39353i		−	0.570616i	0.958436	−	0.285308i	$-0.0920959\pi$
$272$	3.00000			0.181902
$273$	−43.0264	−	16.1826i	−2.60408	−	0.979413i
$274$	16.7779			1.01359
$275$		0			0
$276$	−20.9605			−1.26167
$277$	8.38438			0.503769			0.251884	−	0.967757i	$-0.418950\pi$
$277$	8.38438			0.503769			0.251884	+	0.967757i	$0.418950\pi$
$278$		−	4.39353i		−	0.263506i
$279$		−	57.4311i		−	3.43831i
$280$		0			0
$281$		−	12.6329i		−	0.753615i	−0.926292	−	0.376808i	$-0.877022\pi$
$281$		−	12.6329i		−	0.753615i	0.926292	−	0.376808i	$-0.122978\pi$
$282$	33.7100			2.00740
$283$	−13.4706			−0.800744			−0.400372	−	0.916353i	$-0.631119\pi$
$283$	−13.4706			−0.800744			−0.400372	+	0.916353i	$0.631119\pi$
$284$		0			0
$285$		0			0
$286$	1.95282	−	5.19219i	0.115473	−	0.307021i
$287$	32.2485			1.90357
$288$			6.64402i			0.391503i
$289$	−8.00000			−0.470588
$290$		0			0
$291$		−	11.7668i		−	0.689781i
$292$		−	10.7779i		−	0.630729i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$			30.6045i			1.78489i
$295$		0			0
$296$	4.53854			0.263797
$297$		−	17.4108i		−	1.01028i
$298$	−9.70998			−0.562484
$299$	8.56694	−	22.7779i	0.495439	−	1.31728i
$300$		0			0
$301$		−	16.4219i		−	0.946544i
$302$	−2.48986			−0.143276
$303$	−22.3053			−1.28141
$304$			1.10548i			0.0634038i
$305$		0			0
$306$			19.9321i			1.13944i
$307$			13.8925i			0.792889i	0.918059	+	0.396444i	$0.129756\pi$
$307$			13.8925i			0.792889i	−0.918059	+	0.396444i	$0.870244\pi$
$308$	−6.31645			−0.359913
$309$	38.9382			2.21512
$310$		0			0
$311$	3.51827			0.199503			0.0997513	−	0.995012i	$-0.468195\pi$
$311$	3.51827			0.199503			0.0997513	+	0.995012i	$0.468195\pi$
$312$	−10.4802	−	3.94170i	−0.593326	−	0.223155i
$313$	−24.5650			−1.38849			−0.694247	−	0.719737i	$-0.744262\pi$
$313$	−24.5650			−1.38849			−0.694247	+	0.719737i	$0.744262\pi$
$314$		−	11.3935i		−	0.642974i
$315$		0			0
$316$	6.53854			0.367822
$317$			1.46146i			0.0820838i	0.999157	+	0.0410419i	$0.0130677\pi$
$317$			1.46146i			0.0820838i	−0.999157	+	0.0410419i	$0.986932\pi$
$318$			1.34485i			0.0754155i
$319$		−	8.56496i		−	0.479546i
$320$		0			0
$321$	5.64402			0.315019
$322$	−27.7100			−1.54422
$323$			3.31645i			0.184532i
$324$	−15.2110			−0.845054
$325$		0			0
$326$	16.8155			0.931322
$327$			11.4047i			0.630679i
$328$	7.85499			0.433719
$329$	44.5650			2.45695
$330$		0			0
$331$		−	18.2394i		−	1.00253i	−0.865295	−	0.501263i	$-0.832869\pi$
$331$		−	18.2394i		−	1.00253i	0.865295	−	0.501263i	$-0.167131\pi$
$332$		−	4.46146i		−	0.244854i
$333$			30.1542i			1.65244i
$334$	1.61562			0.0884027
$335$		0			0
$336$			12.7495i			0.695543i
$337$	−19.6329			−1.06947			−0.534736	−	0.845019i	$-0.679589\pi$
$337$	−19.6329			−1.06947			−0.534736	+	0.845019i	$0.679589\pi$
$338$	8.56694	−	9.77791i	0.465980	−	0.531848i
$339$	−49.8925			−2.70979
$340$		0			0
$341$	13.2992			0.720190
$342$	−7.34485			−0.397164
$343$			11.7211i			0.632880i
$344$		−	4.00000i		−	0.215666i
$345$		0			0
$346$		−	12.3164i		−	0.662136i
$347$	−23.6816			−1.27129			−0.635647	−	0.771980i	$-0.719266\pi$
$347$	−23.6816			−1.27129			−0.635647	+	0.771980i	$0.719266\pi$
$348$	−17.2880			−0.926736
$349$			0.154159i			0.00825192i	0.999991	+	0.00412596i	$0.00131334\pi$
$349$			0.154159i			0.00825192i	−0.999991	+	0.00412596i	$0.998687\pi$
$350$		0			0
$351$	14.3636	−	38.1902i	0.766674	−	2.03844i
$352$	−1.53854			−0.0820044
$353$		−	36.6329i		−	1.94977i	−0.222704	−	0.974886i	$-0.571488\pi$
$353$		−	36.6329i		−	1.94977i	0.222704	−	0.974886i	$-0.428512\pi$
$354$	42.7871			2.27411
$355$		0			0
$356$		−	1.85499i		−	0.0983141i
$357$			38.2485i			2.02433i
$358$			10.1826i			0.538165i
$359$			27.2394i			1.43764i	0.695197	+	0.718819i	$0.255317\pi$
$359$			27.2394i			1.43764i	−0.695197	+	0.718819i	$0.744683\pi$
$360$		0			0
$361$	17.7779			0.935679
$362$			11.3935i			0.598830i
$363$	−26.8093			−1.40712
$364$	−13.8550	−	5.21097i	−0.726199	−	0.273129i
$365$		0			0
$366$			44.4595i			2.32393i
$367$	−23.8641			−1.24570			−0.622849	−	0.782342i	$-0.714025\pi$
$367$	−23.8641			−1.24570			−0.622849	+	0.782342i	$0.714025\pi$
$368$	−6.74950			−0.351842
$369$			52.1887i			2.71684i
$370$		0			0
$371$			1.77791i			0.0923044i
$372$		−	26.8439i		−	1.39179i
$373$	−22.3164			−1.15550			−0.577751	−	0.816213i	$-0.696070\pi$
$373$	−22.3164			−1.15550			−0.577751	+	0.816213i	$0.696070\pi$
$374$	−4.61562			−0.238668
$375$		0			0
$376$	10.8550			0.559803
$377$	7.06595	−	18.7871i	0.363915	−	0.967583i
$378$	−46.4595			−2.38962
$379$			9.74950i			0.500798i	0.968143	+	0.250399i	$0.0805619\pi$
$379$			9.74950i			0.500798i	−0.968143	+	0.250399i	$0.919438\pi$
$380$		0			0
$381$	−15.2880			−0.783230
$382$		−	19.4990i		−	0.997656i
$383$			24.7871i			1.26656i	0.773923	+	0.633280i	$0.218292\pi$
$383$			24.7871i			1.26656i	−0.773923	+	0.633280i	$0.781708\pi$
$384$			3.10548i			0.158476i
$385$		0			0
$386$	−2.72110			−0.138500
$387$	26.5761			1.35094
$388$		−	3.78903i		−	0.192359i
$389$	−0.749505			−0.0380014			−0.0190007	−	0.999819i	$-0.506048\pi$
$389$	−0.749505			−0.0380014			−0.0190007	+	0.999819i	$0.506048\pi$
$390$		0			0
$391$	−20.2485			−1.02401
$392$			9.85499i			0.497752i
$393$	−2.68970			−0.135678
$394$	1.61562			0.0813937
$395$		0			0
$396$		−	10.2221i		−	0.513679i
$397$		−	9.67243i		−	0.485445i	−0.970096	−	0.242723i	$-0.921960\pi$
$397$		−	9.67243i		−	0.485445i	0.970096	−	0.242723i	$-0.0780405\pi$
$398$		−	22.2485i		−	1.11522i
$399$	−14.0944			−0.705600
$400$		0			0
$401$			10.9321i			0.545921i	0.962025	+	0.272961i	$0.0880029\pi$
$401$			10.9321i			0.545921i	−0.962025	+	0.272961i	$0.911997\pi$
$402$	11.6440			0.580751
$403$	29.1714	+	10.9716i	1.45313	+	0.546534i
$404$	−7.18256			−0.357346
$405$		0			0
$406$	−22.8550			−1.13427
$407$	−6.98272			−0.346121
$408$			9.31645i			0.461233i
$409$		−	26.5669i		−	1.31365i	−0.754043	−	0.656825i	$-0.771899\pi$
$409$		−	26.5669i		−	1.31365i	0.754043	−	0.656825i	$-0.228101\pi$
$410$		0			0
$411$			52.1035i			2.57008i
$412$	12.5385			0.617730
$413$	56.5650			2.78338
$414$		−	44.8439i		−	2.20396i
$415$		0			0
$416$	−3.37475	−	1.26927i	−0.165461	−	0.0622311i
$417$	13.6440			0.668151
$418$		−	1.70083i		−	0.0831903i
$419$	24.3145			1.18784			0.593920	−	0.804524i	$-0.297580\pi$
$419$	24.3145			1.18784			0.593920	+	0.804524i	$0.297580\pi$
$420$		0			0
$421$		−	6.15416i		−	0.299935i	−0.988691	−	0.149968i	$-0.952083\pi$
$421$		−	6.15416i		−	0.299935i	0.988691	−	0.149968i	$-0.0479170\pi$
$422$			10.2394i			0.498445i
$423$			72.1208i			3.50663i
$424$			0.433057i			0.0210311i
$425$		0			0
$426$		0			0
$427$			58.7759i			2.84437i
$428$	1.81744			0.0878492
$429$	16.1243	+	6.06445i	0.778486	+	0.292795i
$430$		0			0
$431$			0.828565i			0.0399106i	0.999801	+	0.0199553i	$0.00635238\pi$
$431$			0.828565i			0.0399106i	−0.999801	+	0.0199553i	$0.993648\pi$
$432$	−11.3164			−0.544463
$433$	15.7008			0.754534			0.377267	−	0.926105i	$-0.376864\pi$
$433$	15.7008			0.754534			0.377267	+	0.926105i	$0.376864\pi$
$434$		−	35.4879i		−	1.70347i
$435$		0			0
$436$			3.67243i			0.175877i
$437$		−	7.46146i		−	0.356930i
$438$	33.4706			1.59929
$439$	−9.17144			−0.437729			−0.218864	−	0.975755i	$-0.570235\pi$
$439$	−9.17144			−0.437729			−0.218864	+	0.975755i	$0.570235\pi$
$440$		0			0
$441$	−65.4768			−3.11794
$442$	−10.1243	−	3.80781i	−0.481562	−	0.181119i
$443$	15.3164			0.727706			0.363853	−	0.931456i	$-0.381461\pi$
$443$	15.3164			0.727706			0.363853	+	0.931456i	$0.381461\pi$
$444$			14.0944i			0.668889i
$445$		0			0
$446$	−20.9605			−0.992507
$447$		−	30.1542i		−	1.42624i
$448$			4.10548i			0.193966i
$449$		−	23.4108i		−	1.10482i	−0.833571	−	0.552412i	$-0.813708\pi$
$449$		−	23.4108i		−	1.10482i	0.833571	−	0.552412i	$-0.186292\pi$
$450$		0			0
$451$	−12.0852			−0.569070
$452$	−16.0660			−0.755679
$453$		−	7.73223i		−	0.363292i
$454$	4.85499			0.227856
$455$		0			0
$456$	−3.43306			−0.160768
$457$		−	22.9321i		−	1.07272i	−0.843990	−	0.536358i	$-0.819800\pi$
$457$		−	22.9321i		−	1.07272i	0.843990	−	0.536358i	$-0.180200\pi$
$458$	−6.71196			−0.313629
$459$	−33.9493			−1.58462
$460$		0			0
$461$		−	13.4615i		−	0.626963i	−0.949594	−	0.313481i	$-0.898505\pi$
$461$		−	13.4615i		−	0.626963i	0.949594	−	0.313481i	$-0.101495\pi$
$462$		−	19.6156i		−	0.912601i
$463$		−	16.0264i		−	0.744811i	−0.928070	−	0.372406i	$-0.878533\pi$
$463$		−	16.0264i		−	0.744811i	0.928070	−	0.372406i	$-0.121467\pi$
$464$	−5.56694			−0.258439
$465$		0			0
$466$			14.3651i			0.665452i
$467$	−0.866114			−0.0400790			−0.0200395	−	0.999799i	$-0.506379\pi$
$467$	−0.866114			−0.0400790			−0.0200395	+	0.999799i	$0.506379\pi$
$468$	8.43306	−	22.4219i	0.389818	−	1.03645i
$469$	15.3935			0.710807
$470$		0			0
$471$	35.3824			1.63033
$472$	13.7779			0.634180
$473$			6.15416i			0.282969i
$474$			20.3053i			0.932654i
$475$		0			0
$476$			12.3164i			0.564523i
$477$	−2.87724			−0.131740
$478$	−1.14501			−0.0523717
$479$			29.4879i			1.34734i	0.739034	+	0.673668i	$0.235282\pi$
$479$			29.4879i			1.34734i	−0.739034	+	0.673668i	$0.764718\pi$
$480$		0			0
$481$	−15.3164	−	5.76063i	−0.698370	−	0.262662i
$482$	−20.5669			−0.936799
$483$		−	86.0528i		−	3.91554i
$484$	−8.63290			−0.392404
$485$		0			0
$486$		−	13.2880i		−	0.602758i
$487$			35.4503i			1.60641i	0.595704	+	0.803204i	$0.296873\pi$
$487$			35.4503i			1.60641i	−0.595704	+	0.803204i	$0.703127\pi$
$488$			14.3164i			0.648075i
$489$			52.2201i			2.36148i
$490$		0			0
$491$	−32.1319			−1.45009			−0.725046	−	0.688700i	$-0.758182\pi$
$491$	−32.1319			−1.45009			−0.725046	+	0.688700i	$0.758182\pi$
$492$			24.3935i			1.09975i
$493$	−16.7008			−0.752168
$494$	1.40316	−	3.73073i	0.0631310	−	0.167853i
$495$		0			0
$496$		−	8.64402i		−	0.388128i
$497$		0			0
$498$	13.8550			0.620857
$499$		−	27.2769i		−	1.22108i	−0.791984	−	0.610541i	$-0.790952\pi$
$499$		−	27.2769i		−	1.22108i	0.791984	−	0.610541i	$-0.209048\pi$
$500$		0			0
$501$			5.01728i			0.224155i
$502$			3.31645i			0.148020i
$503$	26.9980			1.20378			0.601891	−	0.798578i	$-0.294414\pi$
$503$	26.9980			1.20378			0.601891	+	0.798578i	$0.294414\pi$
$504$	−27.2769			−1.21501
$505$		0			0
$506$	10.3844			0.461642
$507$	30.3651	+	26.6045i	1.34856	+	1.18155i
$508$	−4.92292			−0.218419
$509$			38.8814i			1.72339i	0.507428	+	0.861694i	$0.330596\pi$
$509$			38.8814i			1.72339i	−0.507428	+	0.861694i	$0.669404\pi$
$510$		0			0
$511$	44.2485			1.95744
$512$			1.00000i			0.0441942i
$513$		−	12.5101i		−	0.552336i
$514$			12.4331i			0.548399i
$515$		0			0
$516$	12.4219			0.546845
$517$	−16.7008			−0.734502
$518$			18.6329i			0.818682i
$519$	38.2485			1.67892
$520$		0			0
$521$	4.06595			0.178133			0.0890663	−	0.996026i	$-0.471612\pi$
$521$	4.06595			0.178133			0.0890663	+	0.996026i	$0.471612\pi$
$522$		−	36.9869i		−	1.61887i
$523$	34.8723			1.52486			0.762429	−	0.647072i	$-0.224007\pi$
$523$	34.8723			1.52486			0.762429	+	0.647072i	$0.224007\pi$
$524$	−0.866114			−0.0378364
$525$		0			0
$526$			4.38438i			0.191168i
$527$		−	25.9321i		−	1.12962i
$528$		−	4.77791i		−	0.207932i
$529$	22.5558			0.980688
$530$		0			0
$531$			91.5407i			3.97253i
$532$	−4.53854			−0.196771
$533$	−26.5086	−	9.97010i	−1.14822	−	0.431853i
$534$	5.76063			0.249287
$535$		0			0
$536$	3.74950			0.161954
$537$	−31.6218			−1.36458
$538$		−	5.56694i		−	0.240008i
$539$		−	15.1623i		−	0.653086i
$540$		0			0
$541$		−	37.2282i		−	1.60057i	−0.599622	−	0.800284i	$-0.704682\pi$
$541$		−	37.2282i		−	1.60057i	0.599622	−	0.800284i	$-0.295318\pi$
$542$	9.39353			0.403487
$543$	−35.3824			−1.51840
$544$			3.00000i			0.128624i
$545$		0			0
$546$	16.1826	−	43.0264i	0.692550	−	1.84136i
$547$	−35.9493			−1.53708			−0.768541	−	0.639800i	$-0.779017\pi$
$547$	−35.9493			−1.53708			−0.768541	+	0.639800i	$0.779017\pi$
$548$			16.7779i			0.716717i
$549$	−95.1188			−4.05957
$550$		0			0
$551$		−	6.15416i		−	0.262176i
$552$		−	20.9605i		−	0.892137i
$553$			26.8439i			1.14152i
$554$			8.38438i			0.356218i
$555$		0			0
$556$	4.39353			0.186327
$557$			14.0944i			0.597197i	0.954379	+	0.298599i	$0.0965191\pi$
$557$			14.0944i			0.597197i	−0.954379	+	0.298599i	$0.903481\pi$
$558$	57.4311			2.43125
$559$	−5.07708	+	13.4990i	−0.214738	+	0.570947i
$560$		0			0
$561$		−	14.3337i		−	0.605170i
$562$	12.6329			0.532887
$563$	−28.2678			−1.19134			−0.595672	−	0.803228i	$-0.703114\pi$
$563$	−28.2678			−1.19134			−0.595672	+	0.803228i	$0.703114\pi$
$564$			33.7100i			1.41945i
$565$		0			0
$566$		−	13.4706i		−	0.566212i
$567$		−	62.4484i		−	2.62258i
$568$		0			0
$569$	−26.1339			−1.09559			−0.547795	−	0.836613i	$-0.684533\pi$
$569$	−26.1339			−1.09559			−0.547795	+	0.836613i	$0.684533\pi$
$570$		0			0
$571$	10.7871			0.451424			0.225712	−	0.974194i	$-0.427529\pi$
$571$	10.7871			0.451424			0.225712	+	0.974194i	$0.427529\pi$
$572$	5.19219	+	1.95282i	0.217096	+	0.0816516i
$573$	60.5538			2.52967
$574$			32.2485i			1.34603i
$575$		0			0
$576$	−6.64402			−0.276834
$577$		−	12.1228i		−	0.504677i	−0.967639	−	0.252339i	$-0.918800\pi$
$577$		−	12.1228i		−	0.504677i	0.967639	−	0.252339i	$-0.0811997\pi$
$578$		−	8.00000i		−	0.332756i
$579$		−	8.45033i		−	0.351184i
$580$		0			0
$581$	18.3164			0.759894
$582$	11.7668			0.487749
$583$		−	0.666275i		−	0.0275943i
$584$	10.7779			0.445993
$585$		0			0
$586$	−6.00000			−0.247858
$587$			35.2485i			1.45486i	0.686181	+	0.727431i	$0.259286\pi$
$587$			35.2485i			1.45486i	−0.686181	+	0.727431i	$0.740714\pi$
$588$	−30.6045			−1.26211
$589$	9.55582			0.393741
$590$		0			0
$591$			5.01728i			0.206383i
$592$			4.53854i			0.186533i
$593$		−	11.0862i		−	0.455257i	−0.973748	−	0.227628i	$-0.926903\pi$
$593$		−	11.0862i		−	0.455257i	0.973748	−	0.227628i	$-0.0730971\pi$
$594$	17.4108			0.714374
$595$		0			0
$596$		−	9.70998i		−	0.397736i
$597$	69.0924			2.82776
$598$	22.7779	+	8.56694i	0.931458	+	0.350328i
$599$	31.4990			1.28701			0.643507	−	0.765440i	$-0.277479\pi$
$599$	31.4990			1.28701			0.643507	+	0.765440i	$0.277479\pi$
$600$		0			0
$601$	19.6329			0.800843			0.400421	−	0.916331i	$-0.368864\pi$
$601$	19.6329			0.800843			0.400421	+	0.916331i	$0.368864\pi$
$602$	16.4219			0.669308
$603$			24.9118i			1.01449i
$604$		−	2.48986i		−	0.101311i
$605$		0			0
$606$		−	22.3053i		−	0.906092i
$607$	17.6156			0.714996			0.357498	−	0.933914i	$-0.383630\pi$
$607$	17.6156			0.714996			0.357498	+	0.933914i	$0.383630\pi$
$608$	−1.10548			−0.0448332
$609$		−	70.9758i		−	2.87608i
$610$		0			0
$611$	−36.6329	−	13.7779i	−1.48201	−	0.557395i
$612$	−19.9321			−0.805706
$613$		−	25.4200i		−	1.02670i	−0.858179	−	0.513351i	$-0.828404\pi$
$613$		−	25.4200i		−	1.02670i	0.858179	−	0.513351i	$-0.171596\pi$
$614$	−13.8925			−0.560657
$615$		0			0
$616$		−	6.31645i		−	0.254497i
$617$		−	27.7100i		−	1.11556i	−0.829988	−	0.557781i	$-0.811653\pi$
$617$		−	27.7100i		−	1.11556i	0.829988	−	0.557781i	$-0.188347\pi$
$618$			38.9382i			1.56632i
$619$			20.8439i			0.837786i	0.908036	+	0.418893i	$0.137582\pi$
$619$			20.8439i			0.837786i	−0.908036	+	0.418893i	$0.862418\pi$
$620$		0			0
$621$	76.3804			3.06504
$622$			3.51827i			0.141070i
$623$	7.61562			0.305113
$624$	3.94170	−	10.4802i	0.157794	−	0.419545i
$625$		0			0
$626$		−	24.5650i		−	0.981813i
$627$	5.28189			0.210939
$628$	11.3935			0.454651
$629$			13.6156i			0.542890i
$630$		0			0
$631$			30.7495i			1.22412i	0.790812	+	0.612059i	$0.209659\pi$
$631$			30.7495i			1.22412i	−0.790812	+	0.612059i	$0.790341\pi$
$632$			6.53854i			0.260089i
$633$	−31.7982			−1.26386
$634$	−1.46146			−0.0580420
$635$		0			0
$636$	−1.34485			−0.0533268
$637$	12.5086	−	33.2581i	0.495610	−	1.31774i
$638$	8.56496			0.339090
$639$		0			0
$640$		0			0
$641$	19.0660			0.753060			0.376530	−	0.926404i	$-0.377117\pi$
$641$	19.0660			0.753060			0.376530	+	0.926404i	$0.377117\pi$
$642$			5.64402i			0.222752i
$643$		−	45.8641i		−	1.80870i	−0.426786	−	0.904352i	$-0.640354\pi$
$643$		−	45.8641i		−	1.80870i	0.426786	−	0.904352i	$-0.359646\pi$
$644$		−	27.7100i		−	1.09193i
$645$		0			0
$646$	−3.31645			−0.130484
$647$	11.0173			0.433134			0.216567	−	0.976268i	$-0.430514\pi$
$647$	11.0173			0.433134			0.216567	+	0.976268i	$0.430514\pi$
$648$		−	15.2110i		−	0.597543i
$649$	−21.1979			−0.832089
$650$		0			0
$651$	110.207			4.31935
$652$			16.8155i			0.658544i
$653$	−14.5650			−0.569971			−0.284986	−	0.958532i	$-0.591989\pi$
$653$	−14.5650			−0.569971			−0.284986	+	0.958532i	$0.591989\pi$
$654$	−11.4047			−0.445957
$655$		0			0
$656$			7.85499i			0.306686i
$657$			71.6087i			2.79372i
$658$			44.5650i			1.73732i
$659$	19.8174			0.771978			0.385989	−	0.922503i	$-0.373860\pi$
$659$	19.8174			0.771978			0.385989	+	0.922503i	$0.373860\pi$
$660$		0			0
$661$			13.4615i			0.523590i	0.965123	+	0.261795i	$0.0843145\pi$
$661$			13.4615i			0.523590i	−0.965123	+	0.261795i	$0.915686\pi$
$662$	18.2394			0.708893
$663$	11.8251	−	31.4407i	0.459248	−	1.22106i
$664$	4.46146			0.173138
$665$		0			0
$666$	−30.1542			−1.16845
$667$	37.5741			1.45488
$668$			1.61562i			0.0625102i
$669$		−	65.0924i		−	2.51662i
$670$		0			0
$671$		−	22.0264i		−	0.850321i
$672$	−12.7495			−0.491823
$673$	−0.0679332			−0.00261863			−0.00130932	−	0.999999i	$-0.500417\pi$
$673$	−0.0679332			−0.00261863			−0.00130932	+	0.999999i	$0.500417\pi$
$674$		−	19.6329i		−	0.756231i
$675$		0			0
$676$	9.77791	+	8.56694i	0.376073	+	0.329498i
$677$	−26.1319			−1.00433			−0.502165	−	0.864772i	$-0.667463\pi$
$677$	−26.1319			−1.00433			−0.502165	+	0.864772i	$0.667463\pi$
$678$		−	49.8925i		−	1.91611i
$679$	15.5558			0.596977
$680$		0			0
$681$			15.0771i			0.577755i
$682$			13.2992i			0.509252i
$683$			17.0944i			0.654097i	0.945007	+	0.327049i	$0.106054\pi$
$683$			17.0944i			0.654097i	−0.945007	+	0.327049i	$0.893946\pi$
$684$		−	7.34485i		−	0.280837i
$685$		0			0
$686$	−11.7211			−0.447514
$687$		−	20.8439i		−	0.795243i
$688$	4.00000			0.152499
$689$	0.549666	−	1.46146i	0.0209406	−	0.0556772i
$690$		0			0
$691$		−	25.3844i		−	0.965667i	−0.875712	−	0.482834i	$-0.839608\pi$
$691$		−	25.3844i		−	0.965667i	0.875712	−	0.482834i	$-0.160392\pi$
$692$	12.3164			0.468201
$693$	41.9666			1.59418
$694$		−	23.6816i		−	0.898940i
$695$		0			0
$696$		−	17.2880i		−	0.655302i
$697$			23.5650i			0.892587i
$698$	−0.154159			−0.00583499
$699$	−44.6106			−1.68733
$700$		0			0
$701$	9.43108			0.356207			0.178103	−	0.984012i	$-0.443004\pi$
$701$	9.43108			0.356207			0.178103	+	0.984012i	$0.443004\pi$
$702$	38.1902	+	14.3636i	1.44140	+	0.542120i
$703$	−5.01728			−0.189230
$704$		−	1.53854i		−	0.0579859i
$705$		0			0
$706$	36.6329			1.37870
$707$		−	29.4879i		−	1.10901i
$708$			42.7871i			1.60804i
$709$			20.1734i			0.757629i	0.925473	+	0.378814i	$0.123668\pi$
$709$			20.1734i			0.757629i	−0.925473	+	0.378814i	$0.876332\pi$
$710$		0			0
$711$	−43.4422			−1.62921
$712$	1.85499			0.0695186
$713$			58.3429i			2.18496i
$714$	−38.2485			−1.43141
$715$		0			0
$716$	−10.1826			−0.380540
$717$		−	3.55582i		−	0.132794i
$718$	−27.2394			−1.01656
$719$	−31.4990			−1.17471			−0.587357	−	0.809328i	$-0.699832\pi$
$719$	−31.4990			−1.17471			−0.587357	+	0.809328i	$0.699832\pi$
$720$		0			0
$721$			51.4768i			1.91709i
$722$			17.7779i			0.661625i
$723$		−	63.8703i		−	2.37536i
$724$	−11.3935			−0.423437
$725$		0			0
$726$		−	26.8093i		−	0.994987i
$727$	22.8814			0.848625			0.424312	−	0.905516i	$-0.360516\pi$
$727$	22.8814			0.848625			0.424312	+	0.905516i	$0.360516\pi$
$728$	5.21097	−	13.8550i	0.193131	−	0.513500i
$729$	−4.36710			−0.161745
$730$		0			0
$731$	12.0000			0.443836
$732$	−44.4595			−1.64327
$733$		−	48.1126i		−	1.77708i	−0.458798	−	0.888541i	$-0.651720\pi$
$733$		−	48.1126i		−	1.77708i	0.458798	−	0.888541i	$-0.348280\pi$
$734$		−	23.8641i		−	0.880841i
$735$		0			0
$736$		−	6.74950i		−	0.248790i
$737$	−5.76876			−0.212495
$738$	−52.1887			−1.92109
$739$			19.9321i			0.733213i	0.930376	+	0.366606i	$0.119480\pi$
$739$			19.9321i			0.733213i	−0.930376	+	0.366606i	$0.880520\pi$
$740$		0			0
$741$	11.5857	+	4.35748i	0.425612	+	0.160076i
$742$	−1.77791			−0.0652691
$743$			24.6248i			0.903395i	0.892171	+	0.451698i	$0.149181\pi$
$743$			24.6248i			0.903395i	−0.892171	+	0.451698i	$0.850819\pi$
$744$	26.8439			0.984144
$745$		0			0
$746$		−	22.3164i		−	0.817063i
$747$			29.6420i			1.08455i
$748$		−	4.61562i		−	0.168764i
$749$			7.46146i			0.272636i
$750$		0			0
$751$	−36.7273			−1.34020			−0.670098	−	0.742272i	$-0.733748\pi$
$751$	−36.7273			−1.34020			−0.670098	+	0.742272i	$0.733748\pi$
$752$			10.8550i			0.395841i
$753$	−10.2992			−0.375323
$754$	18.7871	+	7.06595i	0.684184	+	0.257327i
$755$		0			0
$756$		−	46.4595i		−	1.68971i
$757$	37.0091			1.34512			0.672560	−	0.740042i	$-0.265195\pi$
$757$	37.0091			1.34512			0.672560	+	0.740042i	$0.265195\pi$
$758$	−9.74950			−0.354118
$759$			32.2485i			1.17055i
$760$		0			0
$761$			26.6420i			0.965773i	0.875683	+	0.482887i	$0.160412\pi$
$761$			26.6420i			0.965773i	−0.875683	+	0.482887i	$0.839588\pi$
$762$		−	15.2880i		−	0.553827i
$763$	−15.0771			−0.545827
$764$	19.4990			0.705449
$765$		0			0
$766$	−24.7871			−0.895593
$767$	−46.4970	−	17.4879i	−1.67891	−	0.631451i
$768$	−3.10548			−0.112059
$769$		−	37.2972i		−	1.34497i	−0.740110	−	0.672486i	$-0.765227\pi$
$769$		−	37.2972i		−	1.34497i	0.740110	−	0.672486i	$-0.234773\pi$
$770$		0			0
$771$	−38.6106			−1.39053
$772$		−	2.72110i		−	0.0979346i
$773$		−	10.5385i		−	0.379045i	−0.981876	−	0.189522i	$-0.939306\pi$
$773$		−	10.5385i		−	0.379045i	0.981876	−	0.189522i	$-0.0606940\pi$
$774$			26.5761i			0.955258i
$775$		0			0
$776$	3.78903			0.136018
$777$	−57.8641			−2.07586
$778$		−	0.749505i		−	0.0268711i
$779$	−8.68355			−0.311121
$780$		0			0
$781$		0			0
$782$		−	20.2485i		−	0.724085i
$783$	62.9980			2.25137
$784$	−9.85499			−0.351964
$785$		0			0
$786$		−	2.68970i		−	0.0959385i
$787$		−	0.278898i		−	0.00994165i	−0.999988	−	0.00497083i	$-0.998418\pi$
$787$		−	0.278898i		−	0.00994165i	0.999988	−	0.00497083i	$-0.00158227\pi$
$788$			1.61562i			0.0575540i
$789$	−13.6156			−0.484729
$790$		0			0
$791$		−	65.9585i		−	2.34521i
$792$	10.2221			0.363226
$793$	18.1714	−	48.3145i	0.645287	−	1.71570i
$794$	9.67243			0.343262
$795$		0			0
$796$	22.2485			0.788578
$797$	−42.0832			−1.49066			−0.745332	−	0.666693i	$-0.767709\pi$
$797$	−42.0832			−1.49066			−0.745332	+	0.666693i	$0.767709\pi$
$798$		−	14.0944i		−	0.498935i
$799$			32.5650i			1.15207i
$800$		0			0
$801$			12.3246i			0.435468i
$802$	−10.9321			−0.386025
$803$	−16.5822			−0.585175
$804$			11.6440i			0.410653i
$805$		0			0
$806$	−10.9716	+	29.1714i	−0.386458	+	1.02752i
$807$	17.2880			0.608568
$808$		−	7.18256i		−	0.252682i
$809$	−12.6329			−0.444149			−0.222074	−	0.975030i	$-0.571283\pi$
$809$	−12.6329			−0.444149			−0.222074	+	0.975030i	$0.571283\pi$
$810$		0			0
$811$			43.1411i			1.51489i	0.652901	+	0.757444i	$0.273552\pi$
$811$			43.1411i			1.51489i	−0.652901	+	0.757444i	$0.726448\pi$
$812$		−	22.8550i		−	0.802053i
$813$			29.1714i			1.02309i
$814$		−	6.98272i		−	0.244744i
$815$		0			0
$816$	−9.31645			−0.326141
$817$			4.42193i			0.154704i
$818$	26.5669			0.928891
$819$	92.0528	+	34.6218i	3.21659	+	1.20978i
$820$		0			0
$821$			23.0173i			0.803308i	0.915791	+	0.401654i	$0.131565\pi$
$821$			23.0173i			0.803308i	−0.915791	+	0.401654i	$0.868435\pi$
$822$	−52.1035			−1.81732
$823$	4.00000			0.139431			0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000			0.139431			0.0697156	+	0.997567i	$0.477791\pi$
$824$			12.5385i			0.436801i
$825$		0			0
$826$			56.5650i			1.96815i
$827$		−	35.4027i		−	1.23107i	−0.788109	−	0.615536i	$-0.788940\pi$
$827$		−	35.4027i		−	1.23107i	0.788109	−	0.615536i	$-0.211060\pi$
$828$	44.8439			1.55843
$829$	−10.6065			−0.368378			−0.184189	−	0.982891i	$-0.558966\pi$
$829$	−10.6065			−0.368378			−0.184189	+	0.982891i	$0.558966\pi$
$830$		0			0
$831$	−26.0375			−0.903233
$832$	1.26927	−	3.37475i	0.0440040	−	0.116998i
$833$	−29.5650			−1.02437
$834$			13.6440i			0.472454i
$835$		0			0
$836$	1.70083			0.0588244
$837$			97.8196i			3.38114i
$838$			24.3145i			0.839929i
$839$		−	19.4615i		−	0.671884i	−0.941883	−	0.335942i	$-0.890945\pi$
$839$		−	19.4615i		−	0.671884i	0.941883	−	0.335942i	$-0.109055\pi$
$840$		0			0
$841$	1.99085			0.0686501
$842$	6.15416			0.212086
$843$			39.2312i			1.35120i
$844$	−10.2394			−0.352454
$845$		0			0
$846$	−72.1208			−2.47956
$847$		−	35.4422i		−	1.21781i
$848$	−0.433057			−0.0148712
$849$	41.8327			1.43570
$850$		0			0
$851$		−	30.6329i		−	1.05008i
$852$		0			0
$853$			15.9807i			0.547170i	0.961848	+	0.273585i	$0.0882095\pi$
$853$			15.9807i			0.547170i	−0.961848	+	0.273585i	$0.911790\pi$
$854$	−58.7759			−2.01127
$855$		0			0
$856$			1.81744i			0.0621188i
$857$	38.5669			1.31742			0.658711	−	0.752396i	$-0.271102\pi$
$857$	38.5669			1.31742			0.658711	+	0.752396i	$0.271102\pi$
$858$	−6.06445	+	16.1243i	−0.207037	+	0.550473i
$859$	−28.6836			−0.978670			−0.489335	−	0.872096i	$-0.662760\pi$
$859$	−28.6836			−0.978670			−0.489335	+	0.872096i	$0.662760\pi$
$860$		0			0
$861$	−100.147			−3.41301
$862$	−0.828565			−0.0282210
$863$		−	36.4706i		−	1.24147i	−0.784019	−	0.620737i	$-0.786834\pi$
$863$		−	36.4706i		−	1.24147i	0.784019	−	0.620737i	$-0.213166\pi$
$864$		−	11.3164i		−	0.384993i
$865$		0			0
$866$			15.7008i			0.533536i
$867$	24.8439			0.843742
$868$	35.4879			1.20454
$869$		−	10.0598i		−	0.341255i
$870$		0			0
$871$	−12.6537	−	4.75913i	−0.428753	−	0.161257i
$872$	−3.67243			−0.124364
$873$			25.1744i			0.852025i
$874$	7.46146			0.252388
$875$		0			0
$876$			33.4706i			1.13087i
$877$		−	7.02027i		−	0.237058i	−0.992951	−	0.118529i	$-0.962182\pi$
$877$		−	7.02027i		−	0.237058i	0.992951	−	0.118529i	$-0.0378178\pi$
$878$		−	9.17144i		−	0.309521i
$879$		−	18.6329i		−	0.628472i
$880$		0			0
$881$	4.93405			0.166232			0.0831161	−	0.996540i	$-0.473513\pi$
$881$	4.93405			0.166232			0.0831161	+	0.996540i	$0.473513\pi$
$882$		−	65.4768i		−	2.20472i
$883$	−49.9493			−1.68093			−0.840465	−	0.541866i	$-0.817718\pi$
$883$	−49.9493			−1.68093			−0.840465	+	0.541866i	$0.817718\pi$
$884$	3.80781	−	10.1243i	0.128070	−	0.340516i
$885$		0			0
$886$			15.3164i			0.514566i
$887$	−3.86413			−0.129745			−0.0648725	−	0.997894i	$-0.520664\pi$
$887$	−3.86413			−0.129745			−0.0648725	+	0.997894i	$0.520664\pi$
$888$	−14.0944			−0.472976
$889$		−	20.2110i		−	0.677854i
$890$		0			0
$891$			23.4027i			0.784019i
$892$		−	20.9605i		−	0.701808i
$893$	−12.0000			−0.401565
$894$	30.1542			1.00851
$895$		0			0
$896$	−4.10548			−0.137155
$897$	−26.6045	+	70.7364i	−0.888298	+	2.36182i
$898$	23.4108			0.781229
$899$			48.1208i			1.60492i
$900$		0			0
$901$	−1.29917			−0.0432817
$902$		−	12.0852i		−	0.402393i
$903$			50.9980i			1.69711i
$904$		−	16.0660i		−	0.534346i
$905$		0			0
$906$	7.73223			0.256886
$907$	17.5558			0.582931			0.291466	−	0.956581i	$-0.405857\pi$
$907$	17.5558			0.582931			0.291466	+	0.956581i	$0.405857\pi$
$908$			4.85499i			0.161118i
$909$	47.7211			1.58281
$910$		0			0
$911$	−27.9807			−0.927043			−0.463522	−	0.886086i	$-0.653414\pi$
$911$	−27.9807			−0.927043			−0.463522	+	0.886086i	$0.653414\pi$
$912$		−	3.43306i		−	0.113680i
$913$	−6.86413			−0.227170
$914$	22.9321			0.758525
$915$		0			0
$916$		−	6.71196i		−	0.221769i
$917$		−	3.55582i		−	0.117423i
$918$		−	33.9493i		−	1.12050i
$919$	31.0356			1.02377			0.511884	−	0.859054i	$-0.328948\pi$
$919$	31.0356			1.02377			0.511884	+	0.859054i	$0.328948\pi$
$920$		0			0
$921$		−	43.1430i		−	1.42161i
$922$	13.4615			0.443330
$923$		0			0
$924$	19.6156			0.645306
$925$		0			0
$926$	16.0264			0.526661
$927$	−83.3063			−2.73614
$928$		−	5.56694i		−	0.182744i
$929$			24.0000i			0.787414i	0.919236	+	0.393707i	$0.128808\pi$
$929$			24.0000i			0.787414i	−0.919236	+	0.393707i	$0.871192\pi$
$930$		0			0
$931$		−	10.8945i		−	0.357053i
$932$	−14.3651			−0.470545
$933$	−10.9259			−0.357698
$934$		−	0.866114i		−	0.0283401i
$935$		0			0
$936$	22.4219	+	8.43306i	0.732884	+	0.275643i
$937$	60.8987			1.98947			0.994737	−	0.102464i	$-0.0326727\pi$
$937$	60.8987			1.98947			0.994737	+	0.102464i	$0.0326727\pi$
$938$			15.3935i			0.502616i
$939$	76.2861			2.48950
$940$		0			0
$941$			32.2485i			1.05127i	0.850710	+	0.525636i	$0.176173\pi$
$941$			32.2485i			1.05127i	−0.850710	+	0.525636i	$0.823827\pi$
$942$			35.3824i			1.15282i
$943$		−	53.0173i		−	1.72648i
$944$			13.7779i			0.448433i
$945$		0			0
$946$	−6.15416			−0.200089
$947$			20.4108i			0.663262i	0.943409	+	0.331631i	$0.107599\pi$
$947$			20.4108i			0.663262i	−0.943409	+	0.331631i	$0.892401\pi$
$948$	−20.3053			−0.659486
$949$	−36.3728	−	13.6801i	−1.18071	−	0.444074i
$950$		0			0
$951$		−	4.53854i		−	0.147172i
$952$	−12.3164			−0.399178
$953$	−8.36710			−0.271037			−0.135519	−	0.990775i	$-0.543270\pi$
$953$	−8.36710			−0.271037			−0.135519	+	0.990775i	$0.543270\pi$
$954$		−	2.87724i		−	0.0931541i
$955$		0			0
$956$		−	1.14501i		−	0.0370324i
$957$			26.5983i			0.859802i
$958$	−29.4879			−0.952710
$959$	−68.8814			−2.22430
$960$		0			0
$961$	−43.7191			−1.41029
$962$	5.76063	−	15.3164i	0.185730	−	0.493822i
$963$	−12.0751			−0.389115
$964$		−	20.5669i		−	0.662417i
$965$		0			0
$966$	86.0528			2.76870
$967$		−	14.4108i		−	0.463420i	−0.972785	−	0.231710i	$-0.925568\pi$
$967$		−	14.4108i		−	0.463420i	0.972785	−	0.231710i	$-0.0744321\pi$
$968$		−	8.63290i		−	0.277472i
$969$		−	10.2992i		−	0.330857i
$970$		0			0
$971$	25.1806			0.808083			0.404042	−	0.914741i	$-0.367605\pi$
$971$	25.1806			0.808083			0.404042	+	0.914741i	$0.367605\pi$
$972$	13.2880			0.426214
$973$			18.0375i			0.578257i
$974$	−35.4503			−1.13590
$975$		0			0
$976$	−14.3164			−0.458258
$977$			38.1633i			1.22095i	0.792035	+	0.610476i	$0.209022\pi$
$977$			38.1633i			1.22095i	−0.792035	+	0.610476i	$0.790978\pi$
$978$	−52.2201			−1.66982
$979$	−2.85397			−0.0912133
$980$		0			0
$981$		−	24.3997i		−	0.779022i
$982$		−	32.1319i		−	1.02537i
$983$			49.8906i			1.59126i	0.605782	+	0.795631i	$0.292860\pi$
$983$			49.8906i			1.59126i	−0.605782	+	0.795631i	$0.707140\pi$
$984$	−24.3935			−0.777637
$985$		0			0
$986$		−	16.7008i		−	0.531863i
$987$	−138.396			−4.40518
$988$	3.73073	+	1.40316i	0.118690	+	0.0446403i
$989$	−26.9980			−0.858487
$990$		0			0
$991$	−10.6329			−0.337765			−0.168883	−	0.985636i	$-0.554016\pi$
$991$	−10.6329			−0.337765			−0.168883	+	0.985636i	$0.554016\pi$
$992$	8.64402			0.274448
$993$			56.6420i			1.79748i
$994$		0			0
$995$		0			0
$996$			13.8550i			0.439012i
$997$	−2.99085			−0.0947213			−0.0473606	−	0.998878i	$-0.515081\pi$
$997$	−2.99085			−0.0947213			−0.0473606	+	0.998878i	$0.515081\pi$
$998$	27.2769			0.863436
$999$		−	51.3601i		−	1.62496i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.d.c.51.4	yes	6
5.2	odd	4		650.2.c.e.649.6		6
5.3	odd	4		650.2.c.f.649.1		6
5.4	even	2		650.2.d.d.51.3	yes	6
13.5	odd	4		8450.2.a.cd.1.1		3
13.8	odd	4		8450.2.a.br.1.1		3
13.12	even	2	inner	650.2.d.c.51.1	✓	6
65.12	odd	4		650.2.c.f.649.6		6
65.34	odd	4		8450.2.a.ce.1.3		3
65.38	odd	4		650.2.c.e.649.1		6
65.44	odd	4		8450.2.a.bq.1.3		3
65.64	even	2		650.2.d.d.51.6	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.c.e.649.1		6	65.38	odd	4
650.2.c.e.649.6		6	5.2	odd	4
650.2.c.f.649.1		6	5.3	odd	4
650.2.c.f.649.6		6	65.12	odd	4
650.2.d.c.51.1	✓	6	13.12	even	2	inner
650.2.d.c.51.4	yes	6	1.1	even	1	trivial
650.2.d.d.51.3	yes	6	5.4	even	2
650.2.d.d.51.6	yes	6	65.64	even	2
8450.2.a.bq.1.3		3	65.44	odd	4
8450.2.a.br.1.1		3	13.8	odd	4
8450.2.a.cd.1.1		3	13.5	odd	4
8450.2.a.ce.1.3		3	65.34	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -3.10548 q^{3} -1.00000 q^{4} -3.10548i q^{6} -4.10548i q^{7} -1.00000i q^{8} +6.64402 q^{9} +1.53854i q^{11} +3.10548 q^{12} +(-1.26927 + 3.37475i) q^{13} +4.10548 q^{14} +1.00000 q^{16} +3.00000 q^{17} +6.64402i q^{18} +1.10548i q^{19} +12.7495i q^{21} -1.53854 q^{22} -6.74950 q^{23} +3.10548i q^{24} +(-3.37475 - 1.26927i) q^{26} -11.3164 q^{27} +4.10548i q^{28} -5.56694 q^{29} -8.64402i q^{31} +1.00000i q^{32} -4.77791i q^{33} +3.00000i q^{34} -6.64402 q^{36} +4.53854i q^{37} -1.10548 q^{38} +(3.94170 - 10.4802i) q^{39} +7.85499i q^{41} -12.7495 q^{42} +4.00000 q^{43} -1.53854i q^{44} -6.74950i q^{46} +10.8550i q^{47} -3.10548 q^{48} -9.85499 q^{49} -9.31645 q^{51} +(1.26927 - 3.37475i) q^{52} -0.433057 q^{53} -11.3164i q^{54} -4.10548 q^{56} -3.43306i q^{57} -5.56694i q^{58} +13.7779i q^{59} -14.3164 q^{61} +8.64402 q^{62} -27.2769i q^{63} -1.00000 q^{64} +4.77791 q^{66} +3.74950i q^{67} -3.00000 q^{68} +20.9605 q^{69} -6.64402i q^{72} +10.7779i q^{73} -4.53854 q^{74} -1.10548i q^{76} +6.31645 q^{77} +(10.4802 + 3.94170i) q^{78} -6.53854 q^{79} +15.2110 q^{81} -7.85499 q^{82} +4.46146i q^{83} -12.7495i q^{84} +4.00000i q^{86} +17.2880 q^{87} +1.53854 q^{88} +1.85499i q^{89} +(13.8550 + 5.21097i) q^{91} +6.74950 q^{92} +26.8439i q^{93} -10.8550 q^{94} -3.10548i q^{96} +3.78903i q^{97} -9.85499i q^{98} +10.2221i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 18 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{16} + 18 q^{17} - 6 q^{22} - 12 q^{27} - 18 q^{29} - 18 q^{36} + 12 q^{38} - 12 q^{39} - 36 q^{42} + 24 q^{43} + 6 q^{52} - 18 q^{53} - 6 q^{56} - 30 q^{61}+ \cdots - 6 q^{94}+O(q^{100}) \) 6 * q - 6 * q^4 + 18 * q^9 - 6 * q^13 + 6 * q^14 + 6 * q^16 + 18 * q^17 - 6 * q^22 - 12 * q^27 - 18 * q^29 - 18 * q^36 + 12 * q^38 - 12 * q^39 - 36 * q^42 + 24 * q^43 + 6 * q^52 - 18 * q^53 - 6 * q^56 - 30 * q^61 + 30 * q^62 - 6 * q^64 - 24 * q^66 - 18 * q^68 + 48 * q^69 - 24 * q^74 - 18 * q^77 + 24 * q^78 - 36 * q^79 + 54 * q^81 + 12 * q^82 + 60 * q^87 + 6 * q^88 + 24 * q^91 - 6 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more