LMFDB - Embedded newform 2940.2.x.b.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(97,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.x (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	2940.97
Dual form			2940.2.x.b.1273.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.523252 - 2.17398i) q^{5} +1.00000i q^{9} -0.0458357 q^{11} +(0.0340866 + 0.0340866i) q^{13} +(-1.16724 + 1.90723i) q^{15} +(3.13437 - 3.13437i) q^{17} +1.19862 q^{19} +(2.02315 - 2.02315i) q^{23} +(-4.45242 + 2.27508i) q^{25} +(0.707107 - 0.707107i) q^{27} +0.124154i q^{29} -9.44587i q^{31} +(0.0324107 + 0.0324107i) q^{33} +(-1.29997 - 1.29997i) q^{37} -0.0482058i q^{39} +7.53502i q^{41} +(-3.37211 + 3.37211i) q^{43} +(2.17398 - 0.523252i) q^{45} +(7.52769 - 7.52769i) q^{47} -4.43266 q^{51} +(2.27165 - 2.27165i) q^{53} +(0.0239836 + 0.0996461i) q^{55} +(-0.847549 - 0.847549i) q^{57} +2.35705 q^{59} -10.7438i q^{61} +(0.0562679 - 0.0919397i) q^{65} +(0.762769 + 0.762769i) q^{67} -2.86117 q^{69} -8.76668 q^{71} +(-9.05968 - 9.05968i) q^{73} +(4.75706 + 1.53961i) q^{75} -2.94458i q^{79} -1.00000 q^{81} +(7.74538 + 7.74538i) q^{83} +(-8.45412 - 5.17400i) q^{85} +(0.0877900 - 0.0877900i) q^{87} -14.7996 q^{89} +(-6.67924 + 6.67924i) q^{93} +(-0.627178 - 2.60577i) q^{95} +(-5.38300 + 5.38300i) q^{97} -0.0458357i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Character values

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

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−0.523252	−	2.17398i	−0.234005	−	0.972235i
$5$	−0.523252	−	2.17398i	−0.234005	−	0.972235i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−0.0458357			−0.0138200			−0.00690999	−	0.999976i	$-0.502200\pi$
$11$	−0.0458357			−0.0138200			−0.00690999	+	0.999976i	$0.502200\pi$
$12$		0			0
$13$	0.0340866	+	0.0340866i	0.00945393	+	0.00945393i	0.711818	−	0.702364i	$-0.247872\pi$
$13$	0.0340866	+	0.0340866i	0.00945393	+	0.00945393i	−0.702364	+	0.711818i	$0.747872\pi$
$14$		0			0
$15$	−1.16724	+	1.90723i	−0.301381	+	0.492446i
$16$		0			0
$17$	3.13437	−	3.13437i	0.760195	−	0.760195i	−0.216162	−	0.976357i	$-0.569354\pi$
$17$	3.13437	−	3.13437i	0.760195	−	0.760195i	0.976357	+	0.216162i	$0.0693540\pi$
$18$		0			0
$19$	1.19862			0.274981			0.137491	−	0.990503i	$-0.456096\pi$
$19$	1.19862			0.274981			0.137491	+	0.990503i	$0.456096\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.02315	−	2.02315i	0.421857	−	0.421857i	−0.463986	−	0.885843i	$-0.653581\pi$
$23$	2.02315	−	2.02315i	0.421857	−	0.421857i	0.885843	+	0.463986i	$0.153581\pi$
$24$		0			0
$25$	−4.45242	+	2.27508i	−0.890483	+	0.455016i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			0.124154i			0.0230548i	0.999934	+	0.0115274i	$0.00366936\pi$
$29$			0.124154i			0.0230548i	−0.999934	+	0.0115274i	$0.996331\pi$
$30$		0			0
$31$		−	9.44587i		−	1.69653i	−0.529573	−	0.848265i	$-0.677648\pi$
$31$		−	9.44587i		−	1.69653i	0.529573	−	0.848265i	$-0.322352\pi$
$32$		0			0
$33$	0.0324107	+	0.0324107i	0.00564199	+	0.00564199i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.29997	−	1.29997i	−0.213714	−	0.213714i	0.592129	−	0.805843i	$-0.298288\pi$
$37$	−1.29997	−	1.29997i	−0.213714	−	0.213714i	−0.805843	+	0.592129i	$0.798288\pi$
$38$		0			0
$39$		−	0.0482058i		−	0.00771910i
$40$		0			0
$41$			7.53502i			1.17677i	0.808580	+	0.588386i	$0.200237\pi$
$41$			7.53502i			1.17677i	−0.808580	+	0.588386i	$0.799763\pi$
$42$		0			0
$43$	−3.37211	+	3.37211i	−0.514241	+	0.514241i	−0.915823	−	0.401582i	$-0.868461\pi$
$43$	−3.37211	+	3.37211i	−0.514241	+	0.514241i	0.401582	+	0.915823i	$0.368461\pi$
$44$		0			0
$45$	2.17398	−	0.523252i	0.324078	−	0.0780018i
$46$		0			0
$47$	7.52769	−	7.52769i	1.09803	−	1.09803i	0.103385	−	0.994641i	$-0.467033\pi$
$47$	7.52769	−	7.52769i	1.09803	−	1.09803i	0.994641	−	0.103385i	$-0.0329674\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.43266			−0.620697
$52$		0			0
$53$	2.27165	−	2.27165i	0.312036	−	0.312036i	−0.533662	−	0.845698i	$-0.679185\pi$
$53$	2.27165	−	2.27165i	0.312036	−	0.312036i	0.845698	+	0.533662i	$0.179185\pi$
$54$		0			0
$55$	0.0239836	+	0.0996461i	0.00323395	+	0.0134363i
$56$		0			0
$57$	−0.847549	−	0.847549i	−0.112261	−	0.112261i
$58$		0			0
$59$	2.35705			0.306862			0.153431	−	0.988159i	$-0.450968\pi$
$59$	2.35705			0.306862			0.153431	+	0.988159i	$0.450968\pi$
$60$		0			0
$61$		−	10.7438i		−	1.37560i	−0.725900	−	0.687801i	$-0.758576\pi$
$61$		−	10.7438i		−	1.37560i	0.725900	−	0.687801i	$-0.241424\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0562679	−	0.0919397i	0.00697918	−	0.0114037i
$66$		0			0
$67$	0.762769	+	0.762769i	0.0931871	+	0.0931871i	0.752164	−	0.658976i	$-0.229010\pi$
$67$	0.762769	+	0.762769i	0.0931871	+	0.0931871i	−0.658976	+	0.752164i	$0.729010\pi$
$68$		0			0
$69$	−2.86117			−0.344444
$70$		0			0
$71$	−8.76668			−1.04041			−0.520207	−	0.854040i	$-0.674145\pi$
$71$	−8.76668			−1.04041			−0.520207	+	0.854040i	$0.674145\pi$
$72$		0			0
$73$	−9.05968	−	9.05968i	−1.06035	−	1.06035i	−0.998058	−	0.0622972i	$-0.980157\pi$
$73$	−9.05968	−	9.05968i	−1.06035	−	1.06035i	−0.0622972	−	0.998058i	$-0.519843\pi$
$74$		0			0
$75$	4.75706	+	1.53961i	0.549298	+	0.177779i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		−	2.94458i		−	0.331291i	−0.986185	−	0.165646i	$-0.947029\pi$
$79$		−	2.94458i		−	0.331291i	0.986185	−	0.165646i	$-0.0529708\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	7.74538	+	7.74538i	0.850166	+	0.850166i	0.990153	−	0.139988i	$-0.0447063\pi$
$83$	7.74538	+	7.74538i	0.850166	+	0.850166i	−0.139988	+	0.990153i	$0.544706\pi$
$84$		0			0
$85$	−8.45412	−	5.17400i	−0.916978	−	0.561199i
$86$		0			0
$87$	0.0877900	−	0.0877900i	0.00941208	−	0.00941208i
$88$		0			0
$89$	−14.7996			−1.56875			−0.784377	−	0.620285i	$-0.787017\pi$
$89$	−14.7996			−1.56875			−0.784377	+	0.620285i	$0.787017\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−6.67924	+	6.67924i	−0.692605	+	0.692605i
$94$		0			0
$95$	−0.627178	−	2.60577i	−0.0643471	−	0.267347i
$96$		0			0
$97$	−5.38300	+	5.38300i	−0.546561	+	0.546561i	−0.925444	−	0.378884i	$-0.876308\pi$
$97$	−5.38300	+	5.38300i	−0.546561	+	0.546561i	0.378884	+	0.925444i	$0.376308\pi$
$98$		0			0
$99$		−	0.0458357i		−	0.00460666i
$100$		0			0
$101$			2.44577i			0.243363i	0.992569	+	0.121682i	$0.0388287\pi$
$101$			2.44577i			0.243363i	−0.992569	+	0.121682i	$0.961171\pi$
$102$		0			0
$103$	2.73863	+	2.73863i	0.269846	+	0.269846i	0.829038	−	0.559192i	$-0.188889\pi$
$103$	2.73863	+	2.73863i	0.269846	+	0.269846i	−0.559192	+	0.829038i	$0.688889\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.74354	−	6.74354i	−0.651923	−	0.651923i	0.301533	−	0.953456i	$-0.402502\pi$
$107$	−6.74354	−	6.74354i	−0.651923	−	0.651923i	−0.953456	+	0.301533i	$0.902502\pi$
$108$		0			0
$109$			6.11491i			0.585702i	0.956158	+	0.292851i	$0.0946040\pi$
$109$			6.11491i			0.585702i	−0.956158	+	0.292851i	$0.905396\pi$
$110$		0			0
$111$			1.83844i			0.174497i
$112$		0			0
$113$	−6.61480	+	6.61480i	−0.622268	+	0.622268i	−0.946111	−	0.323843i	$-0.895025\pi$
$113$	−6.61480	+	6.61480i	−0.622268	+	0.622268i	0.323843	+	0.946111i	$0.395025\pi$
$114$		0			0
$115$	−5.45692	−	3.33968i	−0.508860	−	0.311427i
$116$		0			0
$117$	−0.0340866	+	0.0340866i	−0.00315131	+	0.00315131i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−10.9979			−0.999809
$122$		0			0
$123$	5.32807	−	5.32807i	0.480415	−	0.480415i
$124$		0			0
$125$	7.27573	+	8.48904i	0.650761	+	0.759283i
$126$		0			0
$127$	−4.52813	−	4.52813i	−0.401806	−	0.401806i	0.477063	−	0.878869i	$-0.341701\pi$
$127$	−4.52813	−	4.52813i	−0.401806	−	0.401806i	−0.878869	+	0.477063i	$0.841701\pi$
$128$		0			0
$129$	4.76888			0.419876
$130$		0			0
$131$		−	11.0156i		−	0.962434i	−0.876602	−	0.481217i	$-0.840195\pi$
$131$		−	11.0156i		−	0.962434i	0.876602	−	0.481217i	$-0.159805\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.90723	−	1.16724i	−0.164149	−	0.100460i
$136$		0			0
$137$	6.90085	+	6.90085i	0.589580	+	0.589580i	0.937518	−	0.347938i	$-0.113118\pi$
$137$	6.90085	+	6.90085i	0.589580	+	0.589580i	−0.347938	+	0.937518i	$0.613118\pi$
$138$		0			0
$139$	−7.70743			−0.653735			−0.326868	−	0.945070i	$-0.605993\pi$
$139$	−7.70743			−0.653735			−0.326868	+	0.945070i	$0.605993\pi$
$140$		0			0
$141$	−10.6458			−0.896535
$142$		0			0
$143$	−0.00156239	−	0.00156239i	−0.000130653	−	0.000130653i
$144$		0			0
$145$	0.269908	−	0.0649637i	0.0224147	−	0.00539494i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			14.2917i			1.17082i	0.810737	+	0.585410i	$0.199067\pi$
$149$			14.2917i			1.17082i	−0.810737	+	0.585410i	$0.800933\pi$
$150$		0			0
$151$	−5.35235			−0.435568			−0.217784	−	0.975997i	$-0.569883\pi$
$151$	−5.35235			−0.435568			−0.217784	+	0.975997i	$0.569883\pi$
$152$		0			0
$153$	3.13437	+	3.13437i	0.253398	+	0.253398i
$154$		0			0
$155$	−20.5352	+	4.94257i	−1.64943	+	0.396997i
$156$		0			0
$157$	10.1755	−	10.1755i	0.812095	−	0.812095i	−0.172852	−	0.984948i	$-0.555298\pi$
$157$	10.1755	−	10.1755i	0.812095	−	0.812095i	0.984948	+	0.172852i	$0.0552983\pi$
$158$		0			0
$159$	−3.21260			−0.254776
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.6938	−	10.6938i	0.837601	−	0.837601i	−0.150941	−	0.988543i	$-0.548230\pi$
$163$	10.6938	−	10.6938i	0.837601	−	0.837601i	0.988543	+	0.150941i	$0.0482305\pi$
$164$		0			0
$165$	0.0535015	−	0.0874194i	0.00416508	−	0.00680559i
$166$		0			0
$167$	−10.7683	+	10.7683i	−0.833278	+	0.833278i	−0.987964	−	0.154685i	$-0.950564\pi$
$167$	−10.7683	+	10.7683i	−0.833278	+	0.833278i	0.154685	+	0.987964i	$0.450564\pi$
$168$		0			0
$169$		−	12.9977i		−	0.999821i
$170$		0			0
$171$			1.19862i			0.0916604i
$172$		0			0
$173$	1.29659	+	1.29659i	0.0985779	+	0.0985779i	0.754676	−	0.656098i	$-0.227794\pi$
$173$	1.29659	+	1.29659i	0.0985779	+	0.0985779i	−0.656098	+	0.754676i	$0.727794\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.66669	−	1.66669i	−0.125276	−	0.125276i
$178$		0			0
$179$		−	13.3905i		−	1.00085i	−0.865780	−	0.500425i	$-0.833177\pi$
$179$		−	13.3905i		−	1.00085i	0.865780	−	0.500425i	$-0.166823\pi$
$180$		0			0
$181$			5.64168i			0.419343i	0.977772	+	0.209671i	$0.0672394\pi$
$181$			5.64168i			0.419343i	−0.977772	+	0.209671i	$0.932761\pi$
$182$		0			0
$183$	−7.59701	+	7.59701i	−0.561587	+	0.561587i
$184$		0			0
$185$	−2.14591	+	3.50633i	−0.157770	+	0.257791i
$186$		0			0
$187$	−0.143666	+	0.143666i	−0.0105059	+	0.0105059i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.71678			−0.486009			−0.243005	−	0.970025i	$-0.578133\pi$
$191$	−6.71678			−0.486009			−0.243005	+	0.970025i	$0.578133\pi$
$192$		0			0
$193$	−15.4467	+	15.4467i	−1.11188	+	1.11188i	−0.118980	+	0.992897i	$0.537963\pi$
$193$	−15.4467	+	15.4467i	−1.11188	+	1.11188i	−0.992897	+	0.118980i	$0.962037\pi$
$194$		0			0
$195$	−0.104799	+	0.0252238i	−0.00750478	+	0.00180631i
$196$		0			0
$197$	−6.31918	−	6.31918i	−0.450223	−	0.450223i	0.445206	−	0.895428i	$-0.353131\pi$
$197$	−6.31918	−	6.31918i	−0.450223	−	0.450223i	−0.895428	+	0.445206i	$0.853131\pi$
$198$		0			0
$199$	−23.4057			−1.65919			−0.829593	−	0.558368i	$-0.811428\pi$
$199$	−23.4057			−1.65919			−0.829593	+	0.558368i	$0.811428\pi$
$200$		0			0
$201$		−	1.07872i		−	0.0760870i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	16.3810	−	3.94271i	1.14410	−	0.275371i
$206$		0			0
$207$	2.02315	+	2.02315i	0.140619	+	0.140619i
$208$		0			0
$209$	−0.0549394			−0.00380024
$210$		0			0
$211$	−2.60777			−0.179526			−0.0897630	−	0.995963i	$-0.528611\pi$
$211$	−2.60777			−0.179526			−0.0897630	+	0.995963i	$0.528611\pi$
$212$		0			0
$213$	6.19898	+	6.19898i	0.424747	+	0.424747i
$214$		0			0
$215$	9.09537	+	5.56645i	0.620299	+	0.379629i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			12.8123i			0.865776i
$220$		0			0
$221$	0.213680			0.0143737
$222$		0			0
$223$	7.97741	+	7.97741i	0.534207	+	0.534207i	0.921822	−	0.387614i	$-0.126701\pi$
$223$	7.97741	+	7.97741i	0.534207	+	0.534207i	−0.387614	+	0.921822i	$0.626701\pi$
$224$		0			0
$225$	−2.27508	−	4.45242i	−0.151672	−	0.296828i
$226$		0			0
$227$	13.9397	−	13.9397i	0.925208	−	0.925208i	−0.0721835	−	0.997391i	$-0.522997\pi$
$227$	13.9397	−	13.9397i	0.925208	−	0.925208i	0.997391	+	0.0721835i	$0.0229967\pi$
$228$		0			0
$229$	−24.0481			−1.58914			−0.794571	−	0.607171i	$-0.792304\pi$
$229$	−24.0481			−1.58914			−0.794571	+	0.607171i	$0.792304\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.54909	+	7.54909i	−0.494557	+	0.494557i	−0.909739	−	0.415181i	$-0.863718\pi$
$233$	−7.54909	+	7.54909i	−0.494557	+	0.494557i	0.415181	+	0.909739i	$0.363718\pi$
$234$		0			0
$235$	−20.3040	−	12.4262i	−1.32448	−	0.810596i
$236$		0			0
$237$	−2.08213	+	2.08213i	−0.135249	+	0.135249i
$238$		0			0
$239$		−	9.26463i		−	0.599279i	−0.954053	−	0.299639i	$-0.903134\pi$
$239$		−	9.26463i		−	0.599279i	0.954053	−	0.299639i	$-0.0968664\pi$
$240$		0			0
$241$		−	23.7693i		−	1.53111i	−0.643369	−	0.765556i	$-0.722464\pi$
$241$		−	23.7693i		−	1.53111i	0.643369	−	0.765556i	$-0.277536\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.0408568	+	0.0408568i	0.00259965	+	0.00259965i
$248$		0			0
$249$		−	10.9536i		−	0.694157i
$250$		0			0
$251$		−	10.4591i		−	0.660173i	−0.943951	−	0.330086i	$-0.892922\pi$
$251$		−	10.4591i		−	0.660173i	0.943951	−	0.330086i	$-0.107078\pi$
$252$		0			0
$253$	−0.0927327	+	0.0927327i	−0.00583005	+	0.00583005i
$254$		0			0
$255$	2.31940	+	9.63654i	0.145246	+	0.603463i
$256$		0			0
$257$	−4.12648	+	4.12648i	−0.257403	+	0.257403i	−0.823997	−	0.566594i	$-0.808261\pi$
$257$	−4.12648	+	4.12648i	−0.257403	+	0.257403i	0.566594	+	0.823997i	$0.308261\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−0.124154			−0.00768493
$262$		0			0
$263$	10.2844	−	10.2844i	0.634163	−	0.634163i	−0.314947	−	0.949109i	$-0.601987\pi$
$263$	10.2844	−	10.2844i	0.634163	−	0.634163i	0.949109	+	0.314947i	$0.101987\pi$
$264$		0			0
$265$	−6.12719	−	3.74989i	−0.376390	−	0.230354i
$266$		0			0
$267$	10.4649	+	10.4649i	0.640441	+	0.640441i
$268$		0			0
$269$	6.92625			0.422301			0.211150	−	0.977454i	$-0.432279\pi$
$269$	6.92625			0.422301			0.211150	+	0.977454i	$0.432279\pi$
$270$		0			0
$271$		−	20.0868i		−	1.22018i	−0.792330	−	0.610092i	$-0.791132\pi$
$271$		−	20.0868i		−	1.22018i	0.792330	−	0.610092i	$-0.208868\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.204080	−	0.104280i	0.0123065	−	0.00628832i
$276$		0			0
$277$	13.7274	+	13.7274i	0.824799	+	0.824799i	0.986792	−	0.161993i	$-0.0517922\pi$
$277$	13.7274	+	13.7274i	0.824799	+	0.824799i	−0.161993	+	0.986792i	$0.551792\pi$
$278$		0			0
$279$	9.44587			0.565510
$280$		0			0
$281$	11.5282			0.687717			0.343859	−	0.939021i	$-0.388266\pi$
$281$	11.5282			0.687717			0.343859	+	0.939021i	$0.388266\pi$
$282$		0			0
$283$	−22.8389	−	22.8389i	−1.35763	−	1.35763i	−0.876826	−	0.480807i	$-0.840344\pi$
$283$	−22.8389	−	22.8389i	−1.35763	−	1.35763i	−0.480807	−	0.876826i	$-0.659656\pi$
$284$		0			0
$285$	−1.39908	+	2.28604i	−0.0828742	+	0.135413i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	2.64849i		−	0.155794i
$290$		0			0
$291$	7.61271			0.446265
$292$		0			0
$293$	−6.98531	−	6.98531i	−0.408086	−	0.408086i	0.472985	−	0.881071i	$-0.343177\pi$
$293$	−6.98531	−	6.98531i	−0.408086	−	0.408086i	−0.881071	+	0.472985i	$0.843177\pi$
$294$		0			0
$295$	−1.23333	−	5.12419i	−0.0718073	−	0.298342i
$296$		0			0
$297$	−0.0324107	+	0.0324107i	−0.00188066	+	0.00188066i
$298$		0			0
$299$	0.137925			0.00797641
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.72942	−	1.72942i	0.0993525	−	0.0993525i
$304$		0			0
$305$	−23.3568	+	5.62171i	−1.33741	+	0.321898i
$306$		0			0
$307$	12.4017	−	12.4017i	0.707803	−	0.707803i	−0.258270	−	0.966073i	$-0.583152\pi$
$307$	12.4017	−	12.4017i	0.707803	−	0.707803i	0.966073	+	0.258270i	$0.0831525\pi$
$308$		0			0
$309$		−	3.87301i		−	0.220328i
$310$		0			0
$311$			2.48996i			0.141193i	0.997505	+	0.0705964i	$0.0224902\pi$
$311$			2.48996i			0.141193i	−0.997505	+	0.0705964i	$0.977510\pi$
$312$		0			0
$313$	1.75770	+	1.75770i	0.0993513	+	0.0993513i	0.755035	−	0.655684i	$-0.227620\pi$
$313$	1.75770	+	1.75770i	0.0993513	+	0.0993513i	−0.655684	+	0.755035i	$0.727620\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.19754	+	4.19754i	0.235757	+	0.235757i	0.815091	−	0.579333i	$-0.196687\pi$
$317$	4.19754	+	4.19754i	0.235757	+	0.235757i	−0.579333	+	0.815091i	$0.696687\pi$
$318$		0			0
$319$		−	0.00569068i		−	0.000318617i
$320$		0			0
$321$			9.53681i			0.532293i
$322$		0			0
$323$	3.75690	−	3.75690i	0.209039	−	0.209039i
$324$		0			0
$325$	−0.229318	−	0.0742180i	−0.0127203	−	0.00411687i
$326$		0			0
$327$	4.32389	−	4.32389i	0.239112	−	0.239112i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	29.0344			1.59588			0.797938	−	0.602739i	$-0.205924\pi$
$331$	29.0344			1.59588			0.797938	+	0.602739i	$0.205924\pi$
$332$		0			0
$333$	1.29997	−	1.29997i	0.0712381	−	0.0712381i
$334$		0			0
$335$	1.25913	−	2.05737i	0.0687935	−	0.112406i
$336$		0			0
$337$	24.4880	+	24.4880i	1.33395	+	1.33395i	0.901806	+	0.432141i	$0.142242\pi$
$337$	24.4880	+	24.4880i	1.33395	+	1.33395i	0.432141	+	0.901806i	$0.357758\pi$
$338$		0			0
$339$	9.35474			0.508080
$340$		0			0
$341$			0.432958i			0.0234460i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.49711	+	6.22014i	0.0806018	+	0.334881i
$346$		0			0
$347$	−11.1260	−	11.1260i	−0.597276	−	0.597276i	0.342311	−	0.939587i	$-0.388790\pi$
$347$	−11.1260	−	11.1260i	−0.597276	−	0.597276i	−0.939587	+	0.342311i	$0.888790\pi$
$348$		0			0
$349$	−12.0448			−0.644744			−0.322372	−	0.946613i	$-0.604480\pi$
$349$	−12.0448			−0.644744			−0.322372	+	0.946613i	$0.604480\pi$
$350$		0			0
$351$	0.0482058			0.00257303
$352$		0			0
$353$	10.5137	+	10.5137i	0.559590	+	0.559590i	0.929191	−	0.369601i	$-0.120506\pi$
$353$	10.5137	+	10.5137i	0.559590	+	0.559590i	−0.369601	+	0.929191i	$0.620506\pi$
$354$		0			0
$355$	4.58718	+	19.0586i	0.243462	+	1.01153i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			21.0390i			1.11040i	0.831718	+	0.555199i	$0.187358\pi$
$359$			21.0390i			1.11040i	−0.831718	+	0.555199i	$0.812642\pi$
$360$		0			0
$361$	−17.5633			−0.924385
$362$		0			0
$363$	7.77669	+	7.77669i	0.408170	+	0.408170i
$364$		0			0
$365$	−14.9551	+	24.4361i	−0.782786	+	1.27904i
$366$		0			0
$367$	−10.6484	+	10.6484i	−0.555841	+	0.555841i	−0.928121	−	0.372280i	$-0.878576\pi$
$367$	−10.6484	+	10.6484i	−0.555841	+	0.555841i	0.372280	+	0.928121i	$0.378576\pi$
$368$		0			0
$369$	−7.53502			−0.392258
$370$		0			0
$371$		0			0
$372$		0			0
$373$	24.9585	−	24.9585i	1.29230	−	1.29230i	0.358942	−	0.933360i	$-0.383138\pi$
$373$	24.9585	−	24.9585i	1.29230	−	1.29230i	0.933360	−	0.358942i	$-0.116862\pi$
$374$		0			0
$375$	0.857943	−	11.1474i	0.0443040	−	0.575648i
$376$		0			0
$377$	−0.00423199	+	0.00423199i	−0.000217958	+	0.000217958i
$378$		0			0
$379$		−	35.5435i		−	1.82575i	−0.408242	−	0.912874i	$-0.633858\pi$
$379$		−	35.5435i		−	1.82575i	0.408242	−	0.912874i	$-0.366142\pi$
$380$		0			0
$381$			6.40374i			0.328074i
$382$		0			0
$383$	25.6453	+	25.6453i	1.31041	+	1.31041i	0.921110	+	0.389303i	$0.127284\pi$
$383$	25.6453	+	25.6453i	1.31041	+	1.31041i	0.389303	+	0.921110i	$0.372716\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.37211	−	3.37211i	−0.171414	−	0.171414i
$388$		0			0
$389$			10.9448i			0.554924i	0.960737	+	0.277462i	$0.0894933\pi$
$389$			10.9448i			0.554924i	−0.960737	+	0.277462i	$0.910507\pi$
$390$		0			0
$391$		−	12.6826i		−	0.641387i
$392$		0			0
$393$	−7.78918	+	7.78918i	−0.392912	+	0.392912i
$394$		0			0
$395$	−6.40147	+	1.54076i	−0.322093	+	0.0775239i
$396$		0			0
$397$	23.6041	−	23.6041i	1.18466	−	1.18466i	0.206131	−	0.978524i	$-0.433913\pi$
$397$	23.6041	−	23.6041i	1.18466	−	1.18466i	0.978524	−	0.206131i	$-0.0660874\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−34.7863			−1.73714			−0.868572	−	0.495563i	$-0.834962\pi$
$401$	−34.7863			−1.73714			−0.868572	+	0.495563i	$0.834962\pi$
$402$		0			0
$403$	0.321978	−	0.321978i	0.0160389	−	0.0160389i
$404$		0			0
$405$	0.523252	+	2.17398i	0.0260006	+	0.108026i
$406$		0			0
$407$	0.0595852	+	0.0595852i	0.00295353	+	0.00295353i
$408$		0			0
$409$	13.4353			0.664334			0.332167	−	0.943221i	$-0.392220\pi$
$409$	13.4353			0.664334			0.332167	+	0.943221i	$0.392220\pi$
$410$		0			0
$411$		−	9.75928i		−	0.481390i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	12.7855	−	20.8911i	0.627618	−	1.02550i
$416$		0			0
$417$	5.44997	+	5.44997i	0.266886	+	0.266886i
$418$		0			0
$419$	3.03643			0.148339			0.0741697	−	0.997246i	$-0.476369\pi$
$419$	3.03643			0.148339			0.0741697	+	0.997246i	$0.476369\pi$
$420$		0			0
$421$	29.2176			1.42398			0.711989	−	0.702191i	$-0.247795\pi$
$421$	29.2176			1.42398			0.711989	+	0.702191i	$0.247795\pi$
$422$		0			0
$423$	7.52769	+	7.52769i	0.366009	+	0.366009i
$424$		0			0
$425$	−6.82456	+	21.0864i	−0.331040	+	1.02284i
$426$		0			0
$427$		0			0
$428$		0			0
$429$			0.00220955i			0.000106678i
$430$		0			0
$431$	37.2744			1.79545			0.897723	−	0.440560i	$-0.145220\pi$
$431$	37.2744			1.79545			0.897723	+	0.440560i	$0.145220\pi$
$432$		0			0
$433$	−9.21959	−	9.21959i	−0.443065	−	0.443065i	0.449975	−	0.893041i	$-0.351433\pi$
$433$	−9.21959	−	9.21959i	−0.443065	−	0.443065i	−0.893041	+	0.449975i	$0.851433\pi$
$434$		0			0
$435$	−0.236790	−	0.144918i	−0.0113532	−	0.00694828i
$436$		0			0
$437$	2.42498	−	2.42498i	0.116003	−	0.116003i
$438$		0			0
$439$	−31.4340			−1.50026			−0.750132	−	0.661288i	$-0.770010\pi$
$439$	−31.4340			−1.50026			−0.750132	+	0.661288i	$0.770010\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.90048	+	7.90048i	−0.375363	+	0.375363i	−0.869426	−	0.494063i	$-0.835511\pi$
$443$	−7.90048	+	7.90048i	−0.375363	+	0.375363i	0.494063	+	0.869426i	$0.335511\pi$
$444$		0			0
$445$	7.74391	+	32.1741i	0.367096	+	1.52520i
$446$		0			0
$447$	10.1058	−	10.1058i	0.477986	−	0.477986i
$448$		0			0
$449$			15.9164i			0.751142i	0.926794	+	0.375571i	$0.122553\pi$
$449$			15.9164i			0.751142i	−0.926794	+	0.375571i	$0.877447\pi$
$450$		0			0
$451$		−	0.345373i		−	0.0162630i
$452$		0			0
$453$	3.78468	+	3.78468i	0.177820	+	0.177820i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−16.7133	−	16.7133i	−0.781815	−	0.781815i	0.198322	−	0.980137i	$-0.436451\pi$
$457$	−16.7133	−	16.7133i	−0.781815	−	0.781815i	−0.980137	+	0.198322i	$0.936451\pi$
$458$		0			0
$459$		−	4.43266i		−	0.206899i
$460$		0			0
$461$		−	30.0417i		−	1.39918i	−0.714544	−	0.699590i	$-0.753366\pi$
$461$		−	30.0417i		−	1.39918i	0.714544	−	0.699590i	$-0.246634\pi$
$462$		0			0
$463$	20.4319	−	20.4319i	0.949551	−	0.949551i	−0.0492361	−	0.998787i	$-0.515679\pi$
$463$	20.4319	−	20.4319i	0.949551	−	0.949551i	0.998787	+	0.0492361i	$0.0156787\pi$
$464$		0			0
$465$	18.0155	+	11.0256i	0.835448	+	0.511302i
$466$		0			0
$467$	22.1617	−	22.1617i	1.02552	−	1.02552i	0.0258557	−	0.999666i	$-0.491769\pi$
$467$	22.1617	−	22.1617i	1.02552	−	1.02552i	0.999666	−	0.0258557i	$-0.00823104\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−14.3904			−0.663073
$472$		0			0
$473$	0.154563	−	0.154563i	0.00710681	−	0.00710681i
$474$		0			0
$475$	−5.33673	+	2.72695i	−0.244866	+	0.125121i
$476$		0			0
$477$	2.27165	+	2.27165i	0.104012	+	0.104012i
$478$		0			0
$479$	−26.9073			−1.22943			−0.614713	−	0.788751i	$-0.710728\pi$
$479$	−26.9073			−1.22943			−0.614713	+	0.788751i	$0.710728\pi$
$480$		0			0
$481$		−	0.0886234i		−	0.00404088i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	14.5192	+	8.88589i	0.659284	+	0.403488i
$486$		0			0
$487$	−8.41141	−	8.41141i	−0.381157	−	0.381157i	0.490362	−	0.871519i	$-0.336865\pi$
$487$	−8.41141	−	8.41141i	−0.381157	−	0.381157i	−0.871519	+	0.490362i	$0.836865\pi$
$488$		0			0
$489$	−15.1233			−0.683899
$490$		0			0
$491$	40.9300			1.84715			0.923573	−	0.383424i	$-0.125255\pi$
$491$	40.9300			1.84715			0.923573	+	0.383424i	$0.125255\pi$
$492$		0			0
$493$	0.389143	+	0.389143i	0.0175261	+	0.0175261i
$494$		0			0
$495$	−0.0996461	+	0.0239836i	−0.00447876	+	0.00107798i
$496$		0			0
$497$		0			0
$498$		0			0
$499$			17.5575i			0.785982i	0.919542	+	0.392991i	$0.128560\pi$
$499$			17.5575i			0.785982i	−0.919542	+	0.392991i	$0.871440\pi$
$500$		0			0
$501$	15.2287			0.680369
$502$		0			0
$503$	−2.87440	−	2.87440i	−0.128163	−	0.128163i	0.640115	−	0.768279i	$-0.278886\pi$
$503$	−2.87440	−	2.87440i	−0.128163	−	0.128163i	−0.768279	+	0.640115i	$0.778886\pi$
$504$		0			0
$505$	5.31706	−	1.27975i	0.236606	−	0.0569482i
$506$		0			0
$507$	−9.19074	+	9.19074i	−0.408175	+	0.408175i
$508$		0			0
$509$	−40.6440			−1.80151			−0.900756	−	0.434325i	$-0.856987\pi$
$509$	−40.6440			−1.80151			−0.900756	+	0.434325i	$0.856987\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.847549	−	0.847549i	0.0374202	−	0.0374202i
$514$		0			0
$515$	4.52075	−	7.38674i	0.199208	−	0.325499i
$516$		0			0
$517$	−0.345037	+	0.345037i	−0.0151747	+	0.0151747i
$518$		0			0
$519$		−	1.83366i		−	0.0804885i
$520$		0			0
$521$			29.9958i			1.31414i	0.753829	+	0.657071i	$0.228205\pi$
$521$			29.9958i			1.31414i	−0.753829	+	0.657071i	$0.771795\pi$
$522$		0			0
$523$	8.26258	+	8.26258i	0.361297	+	0.361297i	0.864290	−	0.502993i	$-0.167768\pi$
$523$	8.26258	+	8.26258i	0.361297	+	0.361297i	−0.502993	+	0.864290i	$0.667768\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−29.6068	−	29.6068i	−1.28969	−	1.28969i
$528$		0			0
$529$			14.8137i			0.644074i
$530$		0			0
$531$			2.35705i			0.102287i
$532$		0			0
$533$	−0.256844	+	0.256844i	−0.0111251	+	0.0111251i
$534$		0			0
$535$	−11.1318	+	18.1889i	−0.481269	+	0.786376i
$536$		0			0
$537$	−9.46849	+	9.46849i	−0.408596	+	0.408596i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−0.571741			−0.0245811			−0.0122905	−	0.999924i	$-0.503912\pi$
$541$	−0.571741			−0.0245811			−0.0122905	+	0.999924i	$0.503912\pi$
$542$		0			0
$543$	3.98927	−	3.98927i	0.171196	−	0.171196i
$544$		0			0
$545$	13.2937	−	3.19964i	0.569440	−	0.137057i
$546$		0			0
$547$	21.6819	+	21.6819i	0.927053	+	0.927053i	0.997514	−	0.0704619i	$-0.0224473\pi$
$547$	21.6819	+	21.6819i	0.927053	+	0.927053i	−0.0704619	+	0.997514i	$0.522447\pi$
$548$		0			0
$549$	10.7438			0.458534
$550$		0			0
$551$			0.148813i			0.00633963i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.99674	−	0.961966i	0.169652	−	0.0408332i
$556$		0			0
$557$	27.0904	+	27.0904i	1.14786	+	1.14786i	0.986973	+	0.160883i	$0.0514343\pi$
$557$	27.0904	+	27.0904i	1.14786	+	1.14786i	0.160883	+	0.986973i	$0.448566\pi$
$558$		0			0
$559$	−0.229888			−0.00972321
$560$		0			0
$561$	0.203174			0.00857802
$562$		0			0
$563$	31.1842	+	31.1842i	1.31426	+	1.31426i	0.918245	+	0.396013i	$0.129606\pi$
$563$	31.1842	+	31.1842i	1.31426	+	1.31426i	0.396013	+	0.918245i	$0.370394\pi$
$564$		0			0
$565$	17.8417	+	10.9193i	0.750605	+	0.459377i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			18.5073i			0.775866i	0.921688	+	0.387933i	$0.126811\pi$
$569$			18.5073i			0.775866i	−0.921688	+	0.387933i	$0.873189\pi$
$570$		0			0
$571$	15.6822			0.656279			0.328139	−	0.944629i	$-0.393578\pi$
$571$	15.6822			0.656279			0.328139	+	0.944629i	$0.393578\pi$
$572$		0			0
$573$	4.74948	+	4.74948i	0.198412	+	0.198412i
$574$		0			0
$575$	−4.40508	+	13.6108i	−0.183704	+	0.567608i
$576$		0			0
$577$	−16.2474	+	16.2474i	−0.676389	+	0.676389i	−0.959181	−	0.282792i	$-0.908739\pi$
$577$	−16.2474	+	16.2474i	−0.676389	+	0.676389i	0.282792	+	0.959181i	$0.408739\pi$
$578$		0			0
$579$	21.8449			0.907844
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.104123	+	0.104123i	−0.00431233	+	0.00431233i
$584$		0			0
$585$	0.0919397	+	0.0562679i	0.00380124	+	0.00232639i
$586$		0			0
$587$	11.5218	−	11.5218i	0.475556	−	0.475556i	−0.428151	−	0.903707i	$-0.640835\pi$
$587$	11.5218	−	11.5218i	0.475556	−	0.475556i	0.903707	+	0.428151i	$0.140835\pi$
$588$		0			0
$589$		−	11.3220i		−	0.466514i
$590$		0			0
$591$			8.93666i			0.367605i
$592$		0			0
$593$	18.9674	+	18.9674i	0.778899	+	0.778899i	0.979644	−	0.200745i	$-0.0643361\pi$
$593$	18.9674	+	18.9674i	0.778899	+	0.778899i	−0.200745	+	0.979644i	$0.564336\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	16.5503	+	16.5503i	0.677360	+	0.677360i
$598$		0			0
$599$		−	33.7970i		−	1.38091i	−0.723377	−	0.690453i	$-0.757411\pi$
$599$		−	33.7970i		−	1.38091i	0.723377	−	0.690453i	$-0.242589\pi$
$600$		0			0
$601$		−	16.5955i		−	0.676945i	−0.940976	−	0.338473i	$-0.890090\pi$
$601$		−	16.5955i		−	0.676945i	0.940976	−	0.338473i	$-0.109910\pi$
$602$		0			0
$603$	−0.762769	+	0.762769i	−0.0310624	+	0.0310624i
$604$		0			0
$605$	5.75467	+	23.9093i	0.233961	+	0.972050i
$606$		0			0
$607$	−13.3517	+	13.3517i	−0.541929	+	0.541929i	−0.924094	−	0.382165i	$-0.875179\pi$
$607$	−13.3517	+	13.3517i	−0.541929	+	0.541929i	0.382165	+	0.924094i	$0.375179\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.513187			0.0207613
$612$		0			0
$613$	−4.58721	+	4.58721i	−0.185276	+	0.185276i	−0.793650	−	0.608374i	$-0.791822\pi$
$613$	−4.58721	+	4.58721i	−0.185276	+	0.185276i	0.608374	+	0.793650i	$0.291822\pi$
$614$		0			0
$615$	−14.3710	−	8.79521i	−0.579497	−	0.354657i
$616$		0			0
$617$	13.5513	+	13.5513i	0.545557	+	0.545557i	0.925152	−	0.379596i	$-0.123937\pi$
$617$	13.5513	+	13.5513i	0.545557	+	0.545557i	−0.379596	+	0.925152i	$0.623937\pi$
$618$		0			0
$619$	−32.5743			−1.30927			−0.654637	−	0.755944i	$-0.727178\pi$
$619$	−32.5743			−1.30927			−0.654637	+	0.755944i	$0.727178\pi$
$620$		0			0
$621$		−	2.86117i		−	0.114815i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.6480	−	20.2592i	0.585920	−	0.810369i
$626$		0			0
$627$	0.0388480	+	0.0388480i	0.00155144	+	0.00155144i
$628$		0			0
$629$	−8.14918			−0.324929
$630$		0			0
$631$	11.4604			0.456230			0.228115	−	0.973634i	$-0.426744\pi$
$631$	11.4604			0.456230			0.228115	+	0.973634i	$0.426744\pi$
$632$		0			0
$633$	1.84397	+	1.84397i	0.0732912	+	0.0732912i
$634$		0			0
$635$	−7.47473	+	12.2134i	−0.296626	+	0.484675i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		−	8.76668i		−	0.346805i
$640$		0			0
$641$	5.15706			0.203692			0.101846	−	0.994800i	$-0.467525\pi$
$641$	5.15706			0.203692			0.101846	+	0.994800i	$0.467525\pi$
$642$		0			0
$643$	−0.200480	−	0.200480i	−0.00790617	−	0.00790617i	0.703143	−	0.711049i	$-0.251780\pi$
$643$	−0.200480	−	0.200480i	−0.00790617	−	0.00790617i	−0.711049	+	0.703143i	$0.751780\pi$
$644$		0			0
$645$	−2.49532	−	10.3675i	−0.0982533	−	0.408219i
$646$		0			0
$647$	0.690375	−	0.690375i	0.0271414	−	0.0271414i	−0.693406	−	0.720547i	$-0.743891\pi$
$647$	0.690375	−	0.690375i	0.0271414	−	0.0271414i	0.720547	+	0.693406i	$0.243891\pi$
$648$		0			0
$649$	−0.108037			−0.00424083
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.9415	−	20.9415i	0.819504	−	0.819504i	−0.166532	−	0.986036i	$-0.553257\pi$
$653$	20.9415	−	20.9415i	0.819504	−	0.819504i	0.986036	+	0.166532i	$0.0532569\pi$
$654$		0			0
$655$	−23.9476	+	5.76391i	−0.935712	+	0.225215i
$656$		0			0
$657$	9.05968	−	9.05968i	0.353452	−	0.353452i
$658$		0			0
$659$		−	26.2044i		−	1.02078i	−0.859944	−	0.510389i	$-0.829502\pi$
$659$		−	26.2044i		−	1.02078i	0.859944	−	0.510389i	$-0.170498\pi$
$660$		0			0
$661$		−	3.59923i		−	0.139994i	−0.997547	−	0.0699970i	$-0.977701\pi$
$661$		−	3.59923i		−	0.139994i	0.997547	−	0.0699970i	$-0.0222990\pi$
$662$		0			0
$663$	−0.151095	−	0.151095i	−0.00586803	−	0.00586803i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	0.251182	+	0.251182i	0.00972581	+	0.00972581i
$668$		0			0
$669$		−	11.2818i		−	0.436178i
$670$		0			0
$671$			0.492449i			0.0190108i
$672$		0			0
$673$	−8.07117	+	8.07117i	−0.311121	+	0.311121i	−0.845344	−	0.534223i	$-0.820604\pi$
$673$	−8.07117	+	8.07117i	−0.311121	+	0.311121i	0.534223	+	0.845344i	$0.320604\pi$
$674$		0			0
$675$	−1.53961	+	4.75706i	−0.0592595	+	0.183099i
$676$		0			0
$677$	19.4229	−	19.4229i	0.746484	−	0.746484i	−0.227333	−	0.973817i	$-0.573001\pi$
$677$	19.4229	−	19.4229i	0.746484	−	0.746484i	0.973817	+	0.227333i	$0.0730005\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−19.7137			−0.755429
$682$		0			0
$683$	−14.9448	+	14.9448i	−0.571845	+	0.571845i	−0.932644	−	0.360799i	$-0.882504\pi$
$683$	−14.9448	+	14.9448i	−0.571845	+	0.571845i	0.360799	+	0.932644i	$0.382504\pi$
$684$		0			0
$685$	11.3915	−	18.6132i	0.435245	−	0.711175i
$686$		0			0
$687$	17.0046	+	17.0046i	0.648765	+	0.648765i
$688$		0			0
$689$	0.154866			0.00589993
$690$		0			0
$691$			5.29183i			0.201311i	0.994921	+	0.100655i	$0.0320940\pi$
$691$			5.29183i			0.201311i	−0.994921	+	0.100655i	$0.967906\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.03292	+	16.7558i	0.152978	+	0.635585i
$696$		0			0
$697$	23.6175	+	23.6175i	0.894577	+	0.894577i
$698$		0			0
$699$	10.6760			0.403804
$700$		0			0
$701$	44.1805			1.66867			0.834337	−	0.551254i	$-0.185851\pi$
$701$	44.1805			1.66867			0.834337	+	0.551254i	$0.185851\pi$
$702$		0			0
$703$	−1.55817	−	1.55817i	−0.0587674	−	0.0587674i
$704$		0			0
$705$	5.57041	+	23.1437i	0.209794	+	0.871643i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		−	14.4584i		−	0.542996i	−0.962439	−	0.271498i	$-0.912481\pi$
$709$		−	14.4584i		−	0.542996i	0.962439	−	0.271498i	$-0.0875191\pi$
$710$		0			0
$711$	2.94458			0.110430
$712$		0			0
$713$	−19.1104	−	19.1104i	−0.715692	−	0.715692i
$714$		0			0
$715$	−0.00257908	+	0.00421412i	−9.64521e−5	+	0.000157599i
$716$		0			0
$717$	−6.55108	+	6.55108i	−0.244655	+	0.244655i
$718$		0			0
$719$	2.04300			0.0761910			0.0380955	−	0.999274i	$-0.487871\pi$
$719$	2.04300			0.0761910			0.0380955	+	0.999274i	$0.487871\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−16.8074	+	16.8074i	−0.625074	+	0.625074i
$724$		0			0
$725$	−0.282460	−	0.552784i	−0.0104903	−	0.0205299i
$726$		0			0
$727$	20.0770	−	20.0770i	0.744613	−	0.744613i	−0.228849	−	0.973462i	$-0.573496\pi$
$727$	20.0770	−	20.0770i	0.744613	−	0.744613i	0.973462	+	0.228849i	$0.0734962\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$			21.1388i			0.781848i
$732$		0			0
$733$	−19.3394	−	19.3394i	−0.714316	−	0.714316i	0.253119	−	0.967435i	$-0.418543\pi$
$733$	−19.3394	−	19.3394i	−0.714316	−	0.714316i	−0.967435	+	0.253119i	$0.918543\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.0349621	−	0.0349621i	−0.00128784	−	0.00128784i
$738$		0			0
$739$		−	51.6192i		−	1.89884i	−0.314003	−	0.949422i	$-0.601670\pi$
$739$		−	51.6192i		−	1.89884i	0.314003	−	0.949422i	$-0.398330\pi$
$740$		0			0
$741$		−	0.0577802i		−	0.00212261i
$742$		0			0
$743$	11.1739	−	11.1739i	0.409931	−	0.409931i	−0.471783	−	0.881715i	$-0.656390\pi$
$743$	11.1739	−	11.1739i	0.409931	−	0.409931i	0.881715	+	0.471783i	$0.156390\pi$
$744$		0			0
$745$	31.0699	−	7.47815i	1.13831	−	0.273978i
$746$		0			0
$747$	−7.74538	+	7.74538i	−0.283389	+	0.283389i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.48533			0.236653			0.118327	−	0.992975i	$-0.462247\pi$
$751$	6.48533			0.236653			0.118327	+	0.992975i	$0.462247\pi$
$752$		0			0
$753$	−7.39571	+	7.39571i	−0.269514	+	0.269514i
$754$		0			0
$755$	2.80063	+	11.6359i	0.101925	+	0.423475i
$756$		0			0
$757$	25.3506	+	25.3506i	0.921384	+	0.921384i	0.997127	−	0.0757432i	$-0.0241329\pi$
$757$	25.3506	+	25.3506i	0.921384	+	0.921384i	−0.0757432	+	0.997127i	$0.524133\pi$
$758$		0			0
$759$	0.131144			0.00476022
$760$		0			0
$761$			22.0871i			0.800656i	0.916372	+	0.400328i	$0.131104\pi$
$761$			22.0871i			0.800656i	−0.916372	+	0.400328i	$0.868896\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.17400	−	8.45412i	0.187066	−	0.305659i
$766$		0			0
$767$	0.0803439	+	0.0803439i	0.00290105	+	0.00290105i
$768$		0			0
$769$	−17.4450			−0.629081			−0.314541	−	0.949244i	$-0.601850\pi$
$769$	−17.4450			−0.629081			−0.314541	+	0.949244i	$0.601850\pi$
$770$		0			0
$771$	5.83572			0.210168
$772$		0			0
$773$	22.8584	+	22.8584i	0.822158	+	0.822158i	0.986417	−	0.164259i	$-0.0525233\pi$
$773$	22.8584	+	22.8584i	0.822158	+	0.822158i	−0.164259	+	0.986417i	$0.552523\pi$
$774$		0			0
$775$	21.4901	+	42.0570i	0.771949	+	1.51073i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			9.03160i			0.323591i
$780$		0			0
$781$	0.401827			0.0143785
$782$		0			0
$783$	0.0877900	+	0.0877900i	0.00313736	+	0.00313736i
$784$		0			0
$785$	−27.4458	−	16.7971i	−0.979583	−	0.599513i
$786$		0			0
$787$	5.57545	−	5.57545i	0.198743	−	0.198743i	−0.600718	−	0.799461i	$-0.705118\pi$
$787$	5.57545	−	5.57545i	0.198743	−	0.198743i	0.799461	+	0.600718i	$0.205118\pi$
$788$		0			0
$789$	−14.5443			−0.517792
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.366220	−	0.366220i	0.0130048	−	0.0130048i
$794$		0			0
$795$	1.68100	+	6.98415i	0.0596189	+	0.247702i
$796$		0			0
$797$	−29.4306	+	29.4306i	−1.04249	+	1.04249i	−0.0434305	+	0.999056i	$0.513829\pi$
$797$	−29.4306	+	29.4306i	−1.04249	+	1.04249i	−0.999056	+	0.0434305i	$0.986171\pi$
$798$		0			0
$799$		−	47.1891i		−	1.66943i
$800$		0			0
$801$		−	14.7996i		−	0.522918i
$802$		0			0
$803$	0.415257	+	0.415257i	0.0146541	+	0.0146541i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.89760	−	4.89760i	−0.172404	−	0.172404i
$808$		0			0
$809$		−	31.4808i		−	1.10681i	−0.832914	−	0.553403i	$-0.813329\pi$
$809$		−	31.4808i		−	1.10681i	0.832914	−	0.553403i	$-0.186671\pi$
$810$		0			0
$811$		−	15.8991i		−	0.558293i	−0.960249	−	0.279146i	$-0.909949\pi$
$811$		−	15.8991i		−	0.558293i	0.960249	−	0.279146i	$-0.0900514\pi$
$812$		0			0
$813$	−14.2035	+	14.2035i	−0.498138	+	0.498138i
$814$		0			0
$815$	−28.8436	−	17.6526i	−1.01035	−	0.618343i
$816$		0			0
$817$	−4.04186	+	4.04186i	−0.141407	+	0.141407i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	50.7344			1.77064			0.885321	−	0.464980i	$-0.153938\pi$
$821$	50.7344			1.77064			0.885321	+	0.464980i	$0.153938\pi$
$822$		0			0
$823$	−26.2589	+	26.2589i	−0.915327	+	0.915327i	−0.996685	−	0.0813582i	$-0.974074\pi$
$823$	−26.2589	+	26.2589i	−0.915327	+	0.915327i	0.0813582	+	0.996685i	$0.474074\pi$
$824$		0			0
$825$	−0.218043	−	0.0705690i	−0.00759129	−	0.00245690i
$826$		0			0
$827$	−5.93552	−	5.93552i	−0.206398	−	0.206398i	0.596336	−	0.802735i	$-0.296622\pi$
$827$	−5.93552	−	5.93552i	−0.206398	−	0.206398i	−0.802735	+	0.596336i	$0.796622\pi$
$828$		0			0
$829$	−29.8523			−1.03681			−0.518407	−	0.855134i	$-0.673475\pi$
$829$	−29.8523			−1.03681			−0.518407	+	0.855134i	$0.673475\pi$
$830$		0			0
$831$		−	19.4135i		−	0.673445i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	29.0447	+	17.7756i	1.00513	+	0.615151i
$836$		0			0
$837$	−6.67924	−	6.67924i	−0.230868	−	0.230868i
$838$		0			0
$839$	51.9753			1.79439			0.897193	−	0.441639i	$-0.145603\pi$
$839$	51.9753			1.79439			0.897193	+	0.441639i	$0.145603\pi$
$840$		0			0
$841$	28.9846			0.999468
$842$		0			0
$843$	−8.15170	−	8.15170i	−0.280759	−	0.280759i
$844$		0			0
$845$	−28.2567	+	6.80106i	−0.972062	+	0.233963i
$846$		0			0
$847$		0			0
$848$		0			0
$849$			32.2991i			1.10850i
$850$		0			0
$851$	−5.26009			−0.180313
$852$		0			0
$853$	−32.2256	−	32.2256i	−1.10338	−	1.10338i	−0.994000	−	0.109384i	$-0.965112\pi$
$853$	−32.2256	−	32.2256i	−1.10338	−	1.10338i	−0.109384	−	0.994000i	$-0.534888\pi$
$854$		0			0
$855$	2.60577	−	0.627178i	0.0891155	−	0.0214490i
$856$		0			0
$857$	27.2233	−	27.2233i	0.929932	−	0.929932i	−0.0677692	−	0.997701i	$-0.521588\pi$
$857$	27.2233	−	27.2233i	0.929932	−	0.929932i	0.997701	+	0.0677692i	$0.0215882\pi$
$858$		0			0
$859$	−15.6467			−0.533860			−0.266930	−	0.963716i	$-0.586009\pi$
$859$	−15.6467			−0.533860			−0.266930	+	0.963716i	$0.586009\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	28.1639	−	28.1639i	0.958710	−	0.958710i	−0.0404706	−	0.999181i	$-0.512886\pi$
$863$	28.1639	−	28.1639i	0.958710	−	0.958710i	0.999181	+	0.0404706i	$0.0128857\pi$
$864$		0			0
$865$	2.14032	−	3.49721i	0.0727732	−	0.118909i
$866$		0			0
$867$	−1.87277	+	1.87277i	−0.0636025	+	0.0636025i
$868$		0			0
$869$			0.134967i			0.00457844i
$870$		0			0
$871$			0.0520005i			0.00176197i
$872$		0			0
$873$	−5.38300	−	5.38300i	−0.182187	−	0.182187i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	20.5589	+	20.5589i	0.694224	+	0.694224i	0.963158	−	0.268935i	$-0.0866716\pi$
$877$	20.5589	+	20.5589i	0.694224	+	0.694224i	−0.268935	+	0.963158i	$0.586672\pi$
$878$		0			0
$879$			9.87872i			0.333201i
$880$		0			0
$881$		−	9.77743i		−	0.329410i	−0.986343	−	0.164705i	$-0.947333\pi$
$881$		−	9.77743i		−	0.329410i	0.986343	−	0.164705i	$-0.0526672\pi$
$882$		0			0
$883$	1.02968	−	1.02968i	0.0346514	−	0.0346514i	−0.689569	−	0.724220i	$-0.742200\pi$
$883$	1.02968	−	1.02968i	0.0346514	−	0.0346514i	0.724220	+	0.689569i	$0.242200\pi$
$884$		0			0
$885$	−2.75125	+	4.49545i	−0.0924824	+	0.151113i
$886$		0			0
$887$	17.6295	−	17.6295i	0.591942	−	0.591942i	−0.346214	−	0.938156i	$-0.612533\pi$
$887$	17.6295	−	17.6295i	0.591942	−	0.591942i	0.938156	+	0.346214i	$0.112533\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.0458357			0.00153555
$892$		0			0
$893$	9.02281	−	9.02281i	0.301937	−	0.301937i
$894$		0			0
$895$	−29.1107	+	7.00659i	−0.973063	+	0.234204i
$896$		0			0
$897$	−0.0975277	−	0.0975277i	−0.00325635	−	0.00325635i
$898$		0			0
$899$	1.17274			0.0391131
$900$		0			0
$901$		−	14.2404i		−	0.474416i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.2649	−	2.95202i	0.407700	−	0.0981284i
$906$		0			0
$907$	−9.77364	−	9.77364i	−0.324528	−	0.324528i	0.525973	−	0.850501i	$-0.323701\pi$
$907$	−9.77364	−	9.77364i	−0.324528	−	0.324528i	−0.850501	+	0.525973i	$0.823701\pi$
$908$		0			0
$909$	−2.44577			−0.0811210
$910$		0			0
$911$	23.8445			0.790005			0.395003	−	0.918680i	$-0.370744\pi$
$911$	23.8445			0.790005			0.395003	+	0.918680i	$0.370744\pi$
$912$		0			0
$913$	−0.355015	−	0.355015i	−0.0117493	−	0.0117493i
$914$		0			0
$915$	20.4909	+	12.5406i	0.677409	+	0.414580i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			35.6567i			1.17621i	0.808786	+	0.588103i	$0.200125\pi$
$919$			35.6567i			1.17621i	−0.808786	+	0.588103i	$0.799875\pi$
$920$		0			0
$921$	−17.5387			−0.577918
$922$		0			0
$923$	−0.298827	−	0.298827i	−0.00983600	−	0.00983600i
$924$		0			0
$925$	8.74556	+	2.83047i	0.287552	+	0.0930654i
$926$		0			0
$927$	−2.73863	+	2.73863i	−0.0899485	+	0.0899485i
$928$		0			0
$929$	−53.0220			−1.73959			−0.869797	−	0.493410i	$-0.835750\pi$
$929$	−53.0220			−1.73959			−0.869797	+	0.493410i	$0.835750\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.76067	−	1.76067i	0.0576417	−	0.0576417i
$934$		0			0
$935$	0.387501	+	0.237154i	0.0126726	+	0.00775576i
$936$		0			0
$937$	24.8353	−	24.8353i	0.811335	−	0.811335i	−0.173499	−	0.984834i	$-0.555507\pi$
$937$	24.8353	−	24.8353i	0.811335	−	0.811335i	0.984834	+	0.173499i	$0.0555073\pi$
$938$		0			0
$939$		−	2.48577i		−	0.0811200i
$940$		0			0
$941$			24.9037i			0.811837i	0.913909	+	0.405918i	$0.133048\pi$
$941$			24.9037i			0.811837i	−0.913909	+	0.405918i	$0.866952\pi$
$942$		0			0
$943$	15.2445	+	15.2445i	0.496429	+	0.496429i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.01374	−	4.01374i	−0.130429	−	0.130429i	0.638879	−	0.769308i	$-0.279399\pi$
$947$	−4.01374	−	4.01374i	−0.130429	−	0.130429i	−0.769308	+	0.638879i	$0.779399\pi$
$948$		0			0
$949$		−	0.617628i		−	0.0200490i
$950$		0			0
$951$		−	5.93622i		−	0.192495i
$952$		0			0
$953$	4.10429	−	4.10429i	0.132951	−	0.132951i	−0.637500	−	0.770451i	$-0.720031\pi$
$953$	4.10429	−	4.10429i	0.132951	−	0.132951i	0.770451	+	0.637500i	$0.220031\pi$
$954$		0			0
$955$	3.51457	+	14.6022i	0.113729	+	0.472515i
$956$		0			0
$957$	−0.00402392	+	0.00402392i	−0.000130075	+	0.000130075i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−58.2245			−1.87821
$962$		0			0
$963$	6.74354	−	6.74354i	0.217308	−	0.217308i
$964$		0			0
$965$	41.6634	+	25.4984i	1.34119	+	0.820821i
$966$		0			0
$967$	−3.40426	−	3.40426i	−0.109474	−	0.109474i	0.650248	−	0.759722i	$-0.274665\pi$
$967$	−3.40426	−	3.40426i	−0.109474	−	0.109474i	−0.759722	+	0.650248i	$0.774665\pi$
$968$		0			0
$969$	−5.31306			−0.170680
$970$		0			0
$971$		−	9.17093i		−	0.294309i	−0.989114	−	0.147155i	$-0.952989\pi$
$971$		−	9.17093i		−	0.294309i	0.989114	−	0.147155i	$-0.0470115\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.109672	+	0.214632i	0.00351232	+	0.00687373i
$976$		0			0
$977$	−19.3548	−	19.3548i	−0.619216	−	0.619216i	0.326114	−	0.945330i	$-0.394261\pi$
$977$	−19.3548	−	19.3548i	−0.619216	−	0.619216i	−0.945330	+	0.326114i	$0.894261\pi$
$978$		0			0
$979$	0.678350			0.0216802
$980$		0			0
$981$	−6.11491			−0.195234
$982$		0			0
$983$	18.6023	+	18.6023i	0.593322	+	0.593322i	0.938527	−	0.345205i	$-0.112191\pi$
$983$	18.6023	+	18.6023i	0.593322	+	0.593322i	−0.345205	+	0.938527i	$0.612191\pi$
$984$		0			0
$985$	−10.4313	+	17.0443i	−0.332368	+	0.543077i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			13.6446i			0.433872i
$990$		0			0
$991$	−6.39207			−0.203051			−0.101525	−	0.994833i	$-0.532372\pi$
$991$	−6.39207			−0.203051			−0.101525	+	0.994833i	$0.532372\pi$
$992$		0			0
$993$	−20.5304	−	20.5304i	−0.651514	−	0.651514i
$994$		0			0
$995$	12.2471	+	50.8836i	0.388258	+	1.61312i
$996$		0			0
$997$	−0.0661915	+	0.0661915i	−0.00209630	+	0.00209630i	−0.708154	−	0.706058i	$-0.750472\pi$
$997$	−0.0661915	+	0.0661915i	−0.00209630	+	0.00209630i	0.706058	+	0.708154i	$0.250472\pi$
$998$		0			0
$999$	−1.83844			−0.0581656

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.x.b.97.4	yes	24
5.3	odd	4		2940.2.x.a.1273.9	yes	24
7.6	odd	2		2940.2.x.a.97.9	✓	24
35.13	even	4	inner	2940.2.x.b.1273.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.x.a.97.9	✓	24	7.6	odd	2
2940.2.x.a.1273.9	yes	24	5.3	odd	4
2940.2.x.b.97.4	yes	24	1.1	even	1	trivial
2940.2.x.b.1273.4	yes	24	35.13	even	4	inner

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:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-0.523252 - 2.17398i) q^{5} +1.00000i q^{9} -0.0458357 q^{11} +(0.0340866 + 0.0340866i) q^{13} +(-1.16724 + 1.90723i) q^{15} +(3.13437 - 3.13437i) q^{17} +1.19862 q^{19} +(2.02315 - 2.02315i) q^{23} +(-4.45242 + 2.27508i) q^{25} +(0.707107 - 0.707107i) q^{27} +0.124154i q^{29} -9.44587i q^{31} +(0.0324107 + 0.0324107i) q^{33} +(-1.29997 - 1.29997i) q^{37} -0.0482058i q^{39} +7.53502i q^{41} +(-3.37211 + 3.37211i) q^{43} +(2.17398 - 0.523252i) q^{45} +(7.52769 - 7.52769i) q^{47} -4.43266 q^{51} +(2.27165 - 2.27165i) q^{53} +(0.0239836 + 0.0996461i) q^{55} +(-0.847549 - 0.847549i) q^{57} +2.35705 q^{59} -10.7438i q^{61} +(0.0562679 - 0.0919397i) q^{65} +(0.762769 + 0.762769i) q^{67} -2.86117 q^{69} -8.76668 q^{71} +(-9.05968 - 9.05968i) q^{73} +(4.75706 + 1.53961i) q^{75} -2.94458i q^{79} -1.00000 q^{81} +(7.74538 + 7.74538i) q^{83} +(-8.45412 - 5.17400i) q^{85} +(0.0877900 - 0.0877900i) q^{87} -14.7996 q^{89} +(-6.67924 + 6.67924i) q^{93} +(-0.627178 - 2.60577i) q^{95} +(-5.38300 + 5.38300i) q^{97} -0.0458357i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Introduction

L-functions

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Database

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