LMFDB - Embedded newform 1512.2.t.d.289.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(289,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("1512.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.8
Character	$\chi$	$=$	1512.289
Dual form			1512.2.t.d.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83657 q^{5} +(2.45061 - 0.997255i) q^{7} +O(q^{10})$	$q+1.83657 q^{5} +(2.45061 - 0.997255i) q^{7} +3.09719 q^{11} +(2.40225 + 4.16081i) q^{13} +(-1.87185 - 3.24214i) q^{17} +(-2.71408 + 4.70093i) q^{19} +7.95829 q^{23} -1.62701 q^{25} +(0.325267 - 0.563379i) q^{29} +(-0.518342 + 0.897795i) q^{31} +(4.50072 - 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(-2.52260 - 4.36927i) q^{41} +(-6.09645 + 10.5594i) q^{43} +(-2.30691 - 3.99569i) q^{47} +(5.01096 - 4.88776i) q^{49} +(-4.55082 - 7.88226i) q^{53} +5.68821 q^{55} +(-2.89863 + 5.02058i) q^{59} +(2.40623 + 4.16771i) q^{61} +(4.41190 + 7.64163i) q^{65} +(7.23870 - 12.5378i) q^{67} +5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(7.59000 - 3.08869i) q^{77} +(7.17904 + 12.4345i) q^{79} +(-3.83139 + 6.63616i) q^{83} +(-3.43778 - 5.95441i) q^{85} +(5.76798 - 9.99043i) q^{89} +(10.0364 + 7.80087i) q^{91} +(-4.98461 + 8.63360i) q^{95} +(-1.04480 + 1.80964i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 + 7 * q^7	$ 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 + 7 * q^7 - 6 * q^11 - 3 * q^13 - 7 * q^17 - q^19 + 4 * q^23 + 20 * q^25 - 9 * q^29 - 4 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 - 5 * q^47 - 15 * q^49 - 11 * q^53 + 22 * q^55 + 19 * q^59 - 13 * q^61 - 13 * q^65 + 26 * q^67 + 48 * q^71 - 35 * q^73 + 4 * q^77 + 10 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 - 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	1.83657			0.821340			0.410670	−	0.911784i	$-0.365295\pi$
$5$	1.83657			0.821340			0.410670	+	0.911784i	$0.365295\pi$
$6$		0			0
$7$	2.45061	−	0.997255i	0.926243	−	0.376927i
$7$	2.45061	−	0.997255i	0.926243	−	0.376927i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.09719			0.933838			0.466919	−	0.884300i	$-0.345364\pi$
$11$	3.09719			0.933838			0.466919	+	0.884300i	$0.345364\pi$
$12$		0			0
$13$	2.40225	+	4.16081i	0.666263	+	1.15400i	0.978941	+	0.204143i	$0.0654406\pi$
$13$	2.40225	+	4.16081i	0.666263	+	1.15400i	−0.312678	+	0.949859i	$0.601226\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.87185	−	3.24214i	−0.453990	−	0.786333i	0.544640	−	0.838670i	$-0.316666\pi$
$17$	−1.87185	−	3.24214i	−0.453990	−	0.786333i	−0.998629	+	0.0523367i	$0.983333\pi$
$18$		0			0
$19$	−2.71408	+	4.70093i	−0.622654	+	1.07847i	0.366336	+	0.930483i	$0.380612\pi$
$19$	−2.71408	+	4.70093i	−0.622654	+	1.07847i	−0.988990	+	0.147985i	$0.952721\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.95829			1.65942			0.829709	−	0.558197i	$-0.188507\pi$
$23$	7.95829			1.65942			0.829709	+	0.558197i	$0.188507\pi$
$24$		0			0
$25$	−1.62701			−0.325401
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.325267	−	0.563379i	0.0604006	−	0.104617i	−0.834244	−	0.551396i	$-0.814096\pi$
$29$	0.325267	−	0.563379i	0.0604006	−	0.104617i	0.894645	+	0.446779i	$0.147429\pi$
$30$		0			0
$31$	−0.518342	+	0.897795i	−0.0930970	+	0.161249i	−0.908813	−	0.417204i	$-0.863010\pi$
$31$	−0.518342	+	0.897795i	−0.0930970	+	0.161249i	0.815716	+	0.578453i	$0.196343\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.50072	−	1.83153i	0.760760	−	0.309585i
$36$		0			0
$37$	0.873712	−	1.51331i	0.143637	−	0.248787i	−0.785226	−	0.619209i	$-0.787453\pi$
$37$	0.873712	−	1.51331i	0.143637	−	0.248787i	0.928864	+	0.370422i	$0.120787\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.52260	−	4.36927i	−0.393964	−	0.682365i	0.599005	−	0.800745i	$-0.295563\pi$
$41$	−2.52260	−	4.36927i	−0.393964	−	0.682365i	−0.992968	+	0.118381i	$0.962230\pi$
$42$		0			0
$43$	−6.09645	+	10.5594i	−0.929699	+	1.61029i	−0.145876	+	0.989303i	$0.546600\pi$
$43$	−6.09645	+	10.5594i	−0.929699	+	1.61029i	−0.783824	+	0.620984i	$0.786733\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.30691	−	3.99569i	−0.336498	−	0.582832i	0.647273	−	0.762258i	$-0.275909\pi$
$47$	−2.30691	−	3.99569i	−0.336498	−	0.582832i	−0.983771	+	0.179426i	$0.942576\pi$
$48$		0			0
$49$	5.01096	−	4.88776i	0.715852	−	0.698252i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.55082	−	7.88226i	−0.625104	−	1.08271i	−0.988521	−	0.151085i	$-0.951723\pi$
$53$	−4.55082	−	7.88226i	−0.625104	−	1.08271i	0.363417	−	0.931626i	$-0.381610\pi$
$54$		0			0
$55$	5.68821			0.766998
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.89863	+	5.02058i	−0.377370	+	0.653624i	−0.990679	−	0.136219i	$-0.956505\pi$
$59$	−2.89863	+	5.02058i	−0.377370	+	0.653624i	0.613309	+	0.789843i	$0.289838\pi$
$60$		0			0
$61$	2.40623	+	4.16771i	0.308086	+	0.533620i	0.977944	−	0.208869i	$-0.0669783\pi$
$61$	2.40623	+	4.16771i	0.308086	+	0.533620i	−0.669858	+	0.742489i	$0.733645\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.41190	+	7.64163i	0.547228	+	0.947827i
$66$		0			0
$67$	7.23870	−	12.5378i	0.884348	−	1.53174i	0.0378895	−	0.999282i	$-0.487937\pi$
$67$	7.23870	−	12.5378i	0.884348	−	1.53174i	0.846459	−	0.532454i	$-0.178730\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	5.00714			0.594238			0.297119	−	0.954840i	$-0.403974\pi$
$71$	5.00714			0.594238			0.297119	+	0.954840i	$0.403974\pi$
$72$		0			0
$73$	−1.81364	−	3.14131i	−0.212270	−	0.367662i	0.740155	−	0.672437i	$-0.234752\pi$
$73$	−1.81364	−	3.14131i	−0.212270	−	0.367662i	−0.952425	+	0.304774i	$0.901419\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.59000	−	3.08869i	0.864961	−	0.351989i
$78$		0			0
$79$	7.17904	+	12.4345i	0.807705	+	1.39899i	0.914450	+	0.404699i	$0.132624\pi$
$79$	7.17904	+	12.4345i	0.807705	+	1.39899i	−0.106745	+	0.994286i	$0.534043\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.83139	+	6.63616i	−0.420550	+	0.728414i	−0.995993	−	0.0894279i	$-0.971496\pi$
$83$	−3.83139	+	6.63616i	−0.420550	+	0.728414i	0.575443	+	0.817842i	$0.304829\pi$
$84$		0			0
$85$	−3.43778	−	5.95441i	−0.372880	−	0.645847i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.76798	−	9.99043i	0.611405	−	1.05898i	−0.379599	−	0.925151i	$-0.623938\pi$
$89$	5.76798	−	9.99043i	0.611405	−	1.05898i	0.991004	−	0.133833i	$-0.0427286\pi$
$90$		0			0
$91$	10.0364	+	7.80087i	1.05210	+	0.817753i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.98461	+	8.63360i	−0.511410	+	0.885788i
$96$		0			0
$97$	−1.04480	+	1.80964i	−0.106083	+	0.183741i	−0.914180	−	0.405308i	$-0.867164\pi$
$97$	−1.04480	+	1.80964i	−0.106083	+	0.183741i	0.808097	+	0.589049i	$0.200498\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	16.4532			1.63716			0.818578	−	0.574395i	$-0.194763\pi$
$101$	16.4532			1.63716			0.818578	+	0.574395i	$0.194763\pi$
$102$		0			0
$103$	−7.74692			−0.763327			−0.381663	−	0.924301i	$-0.624649\pi$
$103$	−7.74692			−0.763327			−0.381663	+	0.924301i	$0.624649\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.74746	+	6.49080i	−0.362281	+	0.627489i	−0.988336	−	0.152290i	$-0.951335\pi$
$107$	−3.74746	+	6.49080i	−0.362281	+	0.627489i	0.626055	+	0.779779i	$0.284669\pi$
$108$		0			0
$109$	−4.30644	−	7.45897i	−0.412482	−	0.714440i	0.582678	−	0.812703i	$-0.302005\pi$
$109$	−4.30644	−	7.45897i	−0.412482	−	0.714440i	−0.995160	+	0.0982628i	$0.968671\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.55747	+	2.69762i	0.146514	+	0.253771i	0.929937	−	0.367719i	$-0.119861\pi$
$113$	1.55747	+	2.69762i	0.146514	+	0.253771i	−0.783422	+	0.621490i	$0.786528\pi$
$114$		0			0
$115$	14.6160			1.36295
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.82040	−	6.07850i	−0.716895	−	0.557215i
$120$		0			0
$121$	−1.40741			−0.127946
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1710			−1.08860
$126$		0			0
$127$	10.8866			0.966033			0.483017	−	0.875611i	$-0.339541\pi$
$127$	10.8866			0.966033			0.483017	+	0.875611i	$0.339541\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	16.0558			1.40280			0.701401	−	0.712767i	$-0.252558\pi$
$131$	16.0558			1.40280			0.701401	+	0.712767i	$0.252558\pi$
$132$		0			0
$133$	−1.96313	+	14.2268i	−0.170225	+	1.23362i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.4406			−1.14831			−0.574155	−	0.818747i	$-0.694669\pi$
$137$	−13.4406			−1.14831			−0.574155	+	0.818747i	$0.694669\pi$
$138$		0			0
$139$	−4.06953	−	7.04863i	−0.345173	−	0.597857i	0.640212	−	0.768198i	$-0.278846\pi$
$139$	−4.06953	−	7.04863i	−0.345173	−	0.597857i	−0.985385	+	0.170341i	$0.945513\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.44022	+	12.8868i	0.622182	+	1.07765i
$144$		0			0
$145$	0.597376	−	1.03469i	0.0496094	−	0.0859260i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.52958			−0.616847			−0.308424	−	0.951249i	$-0.599801\pi$
$149$	−7.52958			−0.616847			−0.308424	+	0.951249i	$0.599801\pi$
$150$		0			0
$151$	−5.67232			−0.461607			−0.230803	−	0.973000i	$-0.574135\pi$
$151$	−5.67232			−0.461607			−0.230803	+	0.973000i	$0.574135\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.951973	+	1.64886i	−0.0764643	+	0.132440i
$156$		0			0
$157$	−0.218381	+	0.378248i	−0.0174287	+	0.0301875i	−0.874608	−	0.484830i	$-0.838881\pi$
$157$	−0.218381	+	0.378248i	−0.0174287	+	0.0301875i	0.857179	+	0.515018i	$0.172215\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	19.5026	−	7.93644i	1.53702	−	0.625479i
$162$		0			0
$163$	9.12649	−	15.8076i	0.714842	−	1.23814i	−0.248178	−	0.968714i	$-0.579832\pi$
$163$	9.12649	−	15.8076i	0.714842	−	1.23814i	0.963020	−	0.269429i	$-0.0868348\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.765108	−	1.32521i	−0.0592058	−	0.102548i	0.834903	−	0.550397i	$-0.185523\pi$
$167$	−0.765108	−	1.32521i	−0.0592058	−	0.102548i	−0.894109	+	0.447849i	$0.852190\pi$
$168$		0			0
$169$	−5.04157	+	8.73226i	−0.387813	+	0.671713i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.08474	+	1.87883i	0.0824716	+	0.142845i	0.904311	−	0.426874i	$-0.140385\pi$
$173$	1.08474	+	1.87883i	0.0824716	+	0.142845i	−0.821839	+	0.569719i	$0.807052\pi$
$174$		0			0
$175$	−3.98716	+	1.62254i	−0.301401	+	0.122653i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.08263	+	1.87517i	0.0809195	+	0.140157i	0.903645	−	0.428282i	$-0.140881\pi$
$179$	1.08263	+	1.87517i	0.0809195	+	0.140157i	−0.822726	+	0.568439i	$0.807548\pi$
$180$		0			0
$181$	0.557838			0.0414638			0.0207319	−	0.999785i	$-0.493400\pi$
$181$	0.557838			0.0414638			0.0207319	+	0.999785i	$0.493400\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.60463	−	2.77931i	0.117975	−	0.204339i
$186$		0			0
$187$	−5.79747	−	10.0415i	−0.423953	−	0.734308i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.9998	−	20.7843i	−0.868277	−	1.50390i	−0.863756	−	0.503911i	$-0.831894\pi$
$191$	−11.9998	−	20.7843i	−0.868277	−	1.50390i	−0.00452179	−	0.999990i	$-0.501439\pi$
$192$		0			0
$193$	10.6397	−	18.4285i	0.765862	−	1.32651i	−0.173928	−	0.984758i	$-0.555646\pi$
$193$	10.6397	−	18.4285i	0.765862	−	1.32651i	0.939790	−	0.341753i	$-0.111021\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.8768			1.05993			0.529964	−	0.848020i	$-0.322205\pi$
$197$	14.8768			1.05993			0.529964	+	0.848020i	$0.322205\pi$
$198$		0			0
$199$	6.17884	+	10.7021i	0.438006	+	0.758649i	0.997536	−	0.0701616i	$-0.0223515\pi$
$199$	6.17884	+	10.7021i	0.438006	+	0.758649i	−0.559530	+	0.828810i	$0.689018\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.235270	−	1.70500i	0.0165127	−	0.119667i
$204$		0			0
$205$	−4.63293	−	8.02447i	−0.323578	−	0.560453i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.40604	+	14.5597i	−0.581458	+	1.00711i
$210$		0			0
$211$	8.65802	+	14.9961i	0.596043	+	1.03238i	0.993399	+	0.114712i	$0.0365944\pi$
$211$	8.65802	+	14.9961i	0.596043	+	1.03238i	−0.397356	+	0.917664i	$0.630072\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.1966	+	19.3930i	−0.763599	+	1.32259i
$216$		0			0
$217$	−0.374923	+	2.71706i	−0.0254514	+	0.184446i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	8.99328	−	15.5768i	0.604953	−	1.04781i
$222$		0			0
$223$	1.14489	−	1.98301i	0.0766677	−	0.132792i	−0.825143	−	0.564925i	$-0.808905\pi$
$223$	1.14489	−	1.98301i	0.0766677	−	0.132792i	0.901810	+	0.432132i	$0.142239\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.56026			0.236303			0.118152	−	0.992996i	$-0.462303\pi$
$227$	3.56026			0.236303			0.118152	+	0.992996i	$0.462303\pi$
$228$		0			0
$229$	−26.9597			−1.78155			−0.890775	−	0.454445i	$-0.849837\pi$
$229$	−26.9597			−1.78155			−0.890775	+	0.454445i	$0.849837\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.7321	+	18.5885i	−0.703081	+	1.21777i	0.264298	+	0.964441i	$0.414860\pi$
$233$	−10.7321	+	18.5885i	−0.703081	+	1.21777i	−0.967380	+	0.253332i	$0.918474\pi$
$234$		0			0
$235$	−4.23681	−	7.33837i	−0.276379	−	0.478703i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.65970	−	8.07083i	−0.301411	−	0.522059i	0.675045	−	0.737777i	$-0.264124\pi$
$239$	−4.65970	−	8.07083i	−0.301411	−	0.522059i	−0.976456	+	0.215718i	$0.930791\pi$
$240$		0			0
$241$	−20.2007			−1.30124			−0.650620	−	0.759404i	$-0.725491\pi$
$241$	−20.2007			−1.30124			−0.650620	+	0.759404i	$0.725491\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.20299	−	8.97673i	0.587958	−	0.573502i
$246$		0			0
$247$	−26.0796			−1.65940
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.1837			−1.71582			−0.857910	−	0.513800i	$-0.828238\pi$
$251$	−27.1837			−1.71582			−0.857910	+	0.513800i	$0.828238\pi$
$252$		0			0
$253$	24.6483			1.54963
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−28.4821			−1.77667			−0.888333	−	0.459200i	$-0.848136\pi$
$257$	−28.4821			−1.77667			−0.888333	+	0.459200i	$0.848136\pi$
$258$		0			0
$259$	0.631966	−	4.57985i	0.0392685	−	0.284578i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.59814			−0.221871			−0.110935	−	0.993828i	$-0.535385\pi$
$263$	−3.59814			−0.221871			−0.110935	+	0.993828i	$0.535385\pi$
$264$		0			0
$265$	−8.35791	−	14.4763i	−0.513422	−	0.889274i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−11.2261	−	19.4443i	−0.684470	−	1.18554i	−0.973603	−	0.228248i	$-0.926700\pi$
$269$	−11.2261	−	19.4443i	−0.684470	−	1.18554i	0.289133	−	0.957289i	$-0.406633\pi$
$270$		0			0
$271$	−14.7935	+	25.6231i	−0.898642	+	1.55649i	−0.0694115	+	0.997588i	$0.522112\pi$
$271$	−14.7935	+	25.6231i	−0.898642	+	1.55649i	−0.829231	+	0.558906i	$0.811221\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.03915			−0.303872
$276$		0			0
$277$	−20.3867			−1.22492			−0.612459	−	0.790503i	$-0.709819\pi$
$277$	−20.3867			−1.22492			−0.612459	+	0.790503i	$0.709819\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.23968	−	3.87924i	0.133608	−	0.231416i	−0.791457	−	0.611225i	$-0.790677\pi$
$281$	2.23968	−	3.87924i	0.133608	−	0.231416i	0.925065	+	0.379809i	$0.124010\pi$
$282$		0			0
$283$	−1.03840	+	1.79856i	−0.0617264	+	0.106913i	−0.895237	−	0.445590i	$-0.852994\pi$
$283$	−1.03840	+	1.79856i	−0.0617264	+	0.106913i	0.833511	+	0.552503i	$0.186327\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−10.5392	−	8.19169i	−0.622108	−	0.483540i
$288$		0			0
$289$	1.49237	−	2.58486i	0.0877865	−	0.152051i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.887340	+	1.53692i	0.0518389	+	0.0897877i	0.890780	−	0.454434i	$-0.150158\pi$
$293$	0.887340	+	1.53692i	0.0518389	+	0.0897877i	−0.838942	+	0.544222i	$0.816825\pi$
$294$		0			0
$295$	−5.32355	+	9.22066i	−0.309949	+	0.536847i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.1178	+	33.1129i	1.10561	+	1.91497i
$300$		0			0
$301$	−4.40963	+	31.9566i	−0.254167	+	1.84195i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.41921	+	7.65429i	0.253043	+	0.438283i
$306$		0			0
$307$	19.6315			1.12043			0.560215	−	0.828347i	$-0.310718\pi$
$307$	19.6315			1.12043			0.560215	+	0.828347i	$0.310718\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.65795	+	11.5319i	−0.377538	+	0.653915i	−0.990703	−	0.136040i	$-0.956563\pi$
$311$	−6.65795	+	11.5319i	−0.377538	+	0.653915i	0.613166	+	0.789954i	$0.289896\pi$
$312$		0			0
$313$	−2.32641	−	4.02945i	−0.131496	−	0.227758i	0.792757	−	0.609537i	$-0.208645\pi$
$313$	−2.32641	−	4.02945i	−0.131496	−	0.227758i	−0.924254	+	0.381779i	$0.875311\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.06276	−	3.57281i	−0.115856	−	0.200669i	0.802265	−	0.596967i	$-0.203628\pi$
$317$	−2.06276	−	3.57281i	−0.115856	−	0.200669i	−0.918122	+	0.396299i	$0.870295\pi$
$318$		0			0
$319$	1.00741	−	1.74489i	0.0564044	−	0.0976953i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	20.3214			1.13071
$324$		0			0
$325$	−3.90847	−	6.76967i	−0.216803	−	0.375514i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−9.63807	−	7.49130i	−0.531364	−	0.413009i
$330$		0			0
$331$	−0.0220297	−	0.0381566i	−0.00121086	−	0.00209727i	0.865419	−	0.501048i	$-0.167052\pi$
$331$	−0.0220297	−	0.0381566i	−0.00121086	−	0.00209727i	−0.866630	+	0.498951i	$0.833719\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	13.2944	−	23.0266i	0.726350	−	1.25808i
$336$		0			0
$337$	−13.3351	−	23.0970i	−0.726407	−	1.25817i	−0.958392	−	0.285454i	$-0.907856\pi$
$337$	−13.3351	−	23.0970i	−0.726407	−	1.25817i	0.231986	−	0.972719i	$-0.425478\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.60541	+	2.78064i	−0.0869376	+	0.150580i
$342$		0			0
$343$	7.40556	−	16.9752i	0.399863	−	0.916575i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.41259	−	9.37488i	0.290563	−	0.503270i	−0.683380	−	0.730063i	$-0.739491\pi$
$347$	5.41259	−	9.37488i	0.290563	−	0.503270i	0.973943	+	0.226793i	$0.0728241\pi$
$348$		0			0
$349$	−2.69555	+	4.66884i	−0.144290	+	0.249917i	−0.929108	−	0.369809i	$-0.879423\pi$
$349$	−2.69555	+	4.66884i	−0.144290	+	0.249917i	0.784818	+	0.619726i	$0.212756\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.94614			0.476155			0.238078	−	0.971246i	$-0.423483\pi$
$353$	8.94614			0.476155			0.238078	+	0.971246i	$0.423483\pi$
$354$		0			0
$355$	9.19596			0.488071
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.84157	+	3.18969i	−0.0971942	+	0.168345i	−0.910522	−	0.413460i	$-0.864320\pi$
$359$	−1.84157	+	3.18969i	−0.0971942	+	0.168345i	0.813328	+	0.581805i	$0.197653\pi$
$360$		0			0
$361$	−5.23251	−	9.06297i	−0.275395	−	0.476998i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.33087	−	5.76924i	−0.174346	−	0.301976i
$366$		0			0
$367$	−7.49976			−0.391484			−0.195742	−	0.980655i	$-0.562712\pi$
$367$	−7.49976			−0.391484			−0.195742	+	0.980655i	$0.562712\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.0129	−	14.7780i	−0.987101	−	0.767235i
$372$		0			0
$373$	8.23833			0.426565			0.213282	−	0.976991i	$-0.431585\pi$
$373$	8.23833			0.426565			0.213282	+	0.976991i	$0.431585\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.12549			0.160971
$378$		0			0
$379$	−3.92853			−0.201795			−0.100897	−	0.994897i	$-0.532171\pi$
$379$	−3.92853			−0.201795			−0.100897	+	0.994897i	$0.532171\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−23.9265			−1.22259			−0.611293	−	0.791404i	$-0.709350\pi$
$383$	−23.9265			−1.22259			−0.611293	+	0.791404i	$0.709350\pi$
$384$		0			0
$385$	13.9396	−	5.67260i	0.710427	−	0.289102i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.6575			−0.641761			−0.320881	−	0.947120i	$-0.603979\pi$
$389$	−12.6575			−0.641761			−0.320881	+	0.947120i	$0.603979\pi$
$390$		0			0
$391$	−14.8967	−	25.8018i	−0.753359	−	1.30486i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	13.1848	+	22.8368i	0.663400	+	1.14904i
$396$		0			0
$397$	−17.7703	+	30.7791i	−0.891866	+	1.54476i	−0.0542297	+	0.998528i	$0.517270\pi$
$397$	−17.7703	+	30.7791i	−0.891866	+	1.54476i	−0.837636	+	0.546229i	$0.816063\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.32332			0.165959			0.0829794	−	0.996551i	$-0.473556\pi$
$401$	3.32332			0.165959			0.0829794	+	0.996551i	$0.473556\pi$
$402$		0			0
$403$	−4.98074			−0.248109
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.70605	−	4.68702i	0.134134	−	0.232327i
$408$		0			0
$409$	−11.2564	+	19.4967i	−0.556595	+	0.964051i	0.441182	+	0.897418i	$0.354559\pi$
$409$	−11.2564	+	19.4967i	−0.556595	+	0.964051i	−0.997777	+	0.0666338i	$0.978774\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.09662	+	15.1942i	−0.103168	+	0.747656i
$414$		0			0
$415$	−7.03662	+	12.1878i	−0.345414	+	0.598275i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.59772	+	6.23144i	0.175760	+	0.304426i	0.940424	−	0.340004i	$-0.110428\pi$
$419$	3.59772	+	6.23144i	0.175760	+	0.304426i	−0.764664	+	0.644429i	$0.777095\pi$
$420$		0			0
$421$	16.8121	−	29.1193i	0.819370	−	1.41919i	−0.0867773	−	0.996228i	$-0.527657\pi$
$421$	16.8121	−	29.1193i	0.819370	−	1.41919i	0.906147	−	0.422962i	$-0.139010\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.04551	+	5.27498i	0.147729	+	0.255874i
$426$		0			0
$427$	10.0530	+	7.81380i	0.486498	+	0.378136i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−16.4871	−	28.5565i	−0.794156	−	1.37552i	−0.923373	−	0.383903i	$-0.874580\pi$
$431$	−16.4871	−	28.5565i	−0.794156	−	1.37552i	0.129217	−	0.991616i	$-0.458754\pi$
$432$		0			0
$433$	19.8977			0.956221			0.478110	−	0.878300i	$-0.341322\pi$
$433$	19.8977			0.956221			0.478110	+	0.878300i	$0.341322\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−21.5995	+	37.4114i	−1.03324	+	1.78963i
$438$		0			0
$439$	−14.5634	−	25.2246i	−0.695074	−	1.20390i	−0.970156	−	0.242482i	$-0.922038\pi$
$439$	−14.5634	−	25.2246i	−0.695074	−	1.20390i	0.275082	−	0.961421i	$-0.411295\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.88317	+	11.9220i	0.327029	+	0.566431i	0.981921	−	0.189292i	$-0.0606191\pi$
$443$	6.88317	+	11.9220i	0.327029	+	0.566431i	−0.654892	+	0.755723i	$0.727286\pi$
$444$		0			0
$445$	10.5933	−	18.3481i	0.502171	−	0.869785i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	12.0958			0.570838			0.285419	−	0.958403i	$-0.407867\pi$
$449$	12.0958			0.570838			0.285419	+	0.958403i	$0.407867\pi$
$450$		0			0
$451$	−7.81297	−	13.5325i	−0.367898	−	0.637218i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	18.4325	+	14.3269i	0.864128	+	0.671653i
$456$		0			0
$457$	4.17738	+	7.23544i	0.195410	+	0.338459i	0.947035	−	0.321131i	$-0.104063\pi$
$457$	4.17738	+	7.23544i	0.195410	+	0.338459i	−0.751625	+	0.659591i	$0.770730\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−11.1673	+	19.3423i	−0.520112	+	0.900860i	0.479615	+	0.877479i	$0.340776\pi$
$461$	−11.1673	+	19.3423i	−0.520112	+	0.900860i	−0.999727	+	0.0233807i	$0.992557\pi$
$462$		0			0
$463$	−0.0370790	−	0.0642228i	−0.00172321	−	0.00298469i	0.865163	−	0.501492i	$-0.167215\pi$
$463$	−0.0370790	−	0.0642228i	−0.00172321	−	0.00298469i	−0.866886	+	0.498507i	$0.833882\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.5828	+	25.2581i	−0.674810	+	1.16880i	0.301715	+	0.953398i	$0.402441\pi$
$467$	−14.5828	+	25.2581i	−0.674810	+	1.16880i	−0.976524	+	0.215407i	$0.930892\pi$
$468$		0			0
$469$	5.23584	−	37.9441i	0.241769	−	1.75209i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.8819	+	32.7043i	−0.868189	+	1.50375i
$474$		0			0
$475$	4.41583	−	7.64845i	0.202612	−	0.350935i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−27.9103			−1.27525			−0.637626	−	0.770346i	$-0.720083\pi$
$479$	−27.9103			−1.27525			−0.637626	+	0.770346i	$0.720083\pi$
$480$		0			0
$481$	8.39548			0.382801
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.91884	+	3.32353i	−0.0871301	+	0.150914i
$486$		0			0
$487$	−2.14409	−	3.71367i	−0.0971580	−	0.168283i	0.813349	−	0.581776i	$-0.197642\pi$
$487$	−2.14409	−	3.71367i	−0.0971580	−	0.168283i	−0.910507	+	0.413493i	$0.864309\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.22215	+	9.04503i	0.235672	+	0.408196i	0.959468	−	0.281818i	$-0.0909375\pi$
$491$	5.22215	+	9.04503i	0.235672	+	0.408196i	−0.723796	+	0.690015i	$0.757604\pi$
$492$		0			0
$493$	−2.43540			−0.109685
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.2705	−	4.99339i	0.550409	−	0.223984i
$498$		0			0
$499$	−6.12624			−0.274248			−0.137124	−	0.990554i	$-0.543786\pi$
$499$	−6.12624			−0.274248			−0.137124	+	0.990554i	$0.543786\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	12.4469			0.554982			0.277491	−	0.960728i	$-0.410497\pi$
$503$	12.4469			0.554982			0.277491	+	0.960728i	$0.410497\pi$
$504$		0			0
$505$	30.2175			1.34466
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.8090			−0.523425			−0.261712	−	0.965146i	$-0.584287\pi$
$509$	−11.8090			−0.523425			−0.261712	+	0.965146i	$0.584287\pi$
$510$		0			0
$511$	−7.57720	−	5.88946i	−0.335195	−	0.260534i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−14.2278			−0.626950
$516$		0			0
$517$	−7.14495	−	12.3754i	−0.314235	−	0.544271i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.54828	−	9.60991i	−0.243075	−	0.421018i	0.718514	−	0.695513i	$-0.244823\pi$
$521$	−5.54828	−	9.60991i	−0.243075	−	0.421018i	−0.961589	+	0.274495i	$0.911489\pi$
$522$		0			0
$523$	10.6209	−	18.3960i	0.464421	−	0.804401i	−0.534754	−	0.845008i	$-0.679596\pi$
$523$	10.6209	−	18.3960i	0.464421	−	0.804401i	0.999175	+	0.0406065i	$0.0129290\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.88103			0.169060
$528$		0			0
$529$	40.3343			1.75367
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.1198	−	20.9921i	0.524967	−	0.909269i
$534$		0			0
$535$	−6.88248	+	11.9208i	−0.297556	+	0.515382i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.5199	−	15.1383i	0.668490	−	0.652054i
$540$		0			0
$541$	−6.33567	+	10.9737i	−0.272392	+	0.471796i	−0.969474	−	0.245195i	$-0.921148\pi$
$541$	−6.33567	+	10.9737i	−0.272392	+	0.471796i	0.697082	+	0.716991i	$0.254481\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.90908	−	13.6989i	−0.338788	−	0.586798i
$546$		0			0
$547$	−21.4805	+	37.2053i	−0.918438	+	1.59078i	−0.116651	+	0.993173i	$0.537216\pi$
$547$	−21.4805	+	37.2053i	−0.918438	+	1.59078i	−0.801788	+	0.597609i	$0.796117\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.76560	+	3.05812i	0.0752173	+	0.130280i
$552$		0			0
$553$	29.9933	+	23.3126i	1.27545	+	0.991355i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−16.5129	−	28.6012i	−0.699673	−	1.21187i	−0.968580	−	0.248703i	$-0.919996\pi$
$557$	−16.5129	−	28.6012i	−0.699673	−	1.21187i	0.268906	−	0.963166i	$-0.413338\pi$
$558$		0			0
$559$	−58.5807			−2.47770
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.4066	−	31.8812i	0.775746	−	1.34363i	−0.158629	−	0.987338i	$-0.550707\pi$
$563$	18.4066	−	31.8812i	0.775746	−	1.34363i	0.934374	−	0.356293i	$-0.115959\pi$
$564$		0			0
$565$	2.86040	+	4.95437i	0.120338	+	0.208432i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.1786	+	38.4144i	0.929774	+	1.61042i	0.783698	+	0.621142i	$0.213331\pi$
$569$	22.1786	+	38.4144i	0.929774	+	1.61042i	0.146075	+	0.989273i	$0.453336\pi$
$570$		0			0
$571$	21.2936	−	36.8816i	0.891110	−	1.54345i	0.0525644	−	0.998618i	$-0.483261\pi$
$571$	21.2936	−	36.8816i	0.891110	−	1.54345i	0.838546	−	0.544831i	$-0.183406\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.9482			−0.539977
$576$		0			0
$577$	16.3209	+	28.2687i	0.679450	+	1.17684i	0.975147	+	0.221559i	$0.0711147\pi$
$577$	16.3209	+	28.2687i	0.679450	+	1.17684i	−0.295697	+	0.955282i	$0.595552\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.77129	+	20.0835i	−0.114973	+	0.833205i
$582$		0			0
$583$	−14.0948	−	24.4129i	−0.583746	−	1.01108i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.1270	−	22.7366i	0.541809	−	0.938441i	−0.456991	−	0.889471i	$-0.651073\pi$
$587$	13.1270	−	22.7366i	0.541809	−	0.938441i	0.998800	−	0.0489701i	$-0.0155939\pi$
$588$		0			0
$589$	−2.81365	−	4.87338i	−0.115934	−	0.200804i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.59998	−	4.50330i	0.106768	−	0.184928i	−0.807691	−	0.589606i	$-0.799283\pi$
$593$	2.59998	−	4.50330i	0.106768	−	0.184928i	0.914459	+	0.404678i	$0.132616\pi$
$594$		0			0
$595$	−14.3627	−	11.1636i	−0.588814	−	0.457663i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	13.1837	−	22.8349i	0.538673	−	0.933008i	−0.460303	−	0.887762i	$-0.652259\pi$
$599$	13.1837	−	22.8349i	0.538673	−	0.933008i	0.998976	−	0.0452465i	$-0.0144073\pi$
$600$		0			0
$601$	−15.4505	+	26.7611i	−0.630239	+	1.09161i	0.357263	+	0.934004i	$0.383710\pi$
$601$	−15.4505	+	26.7611i	−0.630239	+	1.09161i	−0.987503	+	0.157603i	$0.949623\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.58480			−0.105087
$606$		0			0
$607$	7.67321			0.311446			0.155723	−	0.987801i	$-0.450229\pi$
$607$	7.67321			0.311446			0.155723	+	0.987801i	$0.450229\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.0836	−	19.1973i	0.448393	−	0.776639i
$612$		0			0
$613$	7.97498	+	13.8131i	0.322106	+	0.557905i	0.980922	−	0.194399i	$-0.0622758\pi$
$613$	7.97498	+	13.8131i	0.322106	+	0.557905i	−0.658816	+	0.752304i	$0.728942\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.67011	+	6.35682i	0.147753	+	0.255916i	0.930397	−	0.366554i	$-0.119463\pi$
$617$	3.67011	+	6.35682i	0.147753	+	0.255916i	−0.782644	+	0.622470i	$0.786129\pi$
$618$		0			0
$619$	20.5684			0.826713			0.413357	−	0.910569i	$-0.364356\pi$
$619$	20.5684			0.826713			0.413357	+	0.910569i	$0.364356\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.17205	−	30.2348i	0.167150	−	1.21133i
$624$		0			0
$625$	−14.2178			−0.568713
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.54182			−0.260840
$630$		0			0
$631$	−5.09394			−0.202787			−0.101393	−	0.994846i	$-0.532330\pi$
$631$	−5.09394			−0.202787			−0.101393	+	0.994846i	$0.532330\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	19.9941			0.793442
$636$		0			0
$637$	32.3746	+	9.10807i	1.28273	+	0.360875i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−12.6372			−0.499140			−0.249570	−	0.968357i	$-0.580289\pi$
$641$	−12.6372			−0.499140			−0.249570	+	0.968357i	$0.580289\pi$
$642$		0			0
$643$	12.4329	+	21.5344i	0.490306	+	0.849235i	0.999938	−	0.0111579i	$-0.00355174\pi$
$643$	12.4329	+	21.5344i	0.490306	+	0.849235i	−0.509632	+	0.860393i	$0.670218\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.12339	−	1.94577i	−0.0441650	−	0.0764960i	0.843098	−	0.537760i	$-0.180729\pi$
$647$	−1.12339	−	1.94577i	−0.0441650	−	0.0764960i	−0.887263	+	0.461264i	$0.847396\pi$
$648$		0			0
$649$	−8.97762	+	15.5497i	−0.352403	+	0.610379i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.05762			−0.0805207			−0.0402604	−	0.999189i	$-0.512819\pi$
$653$	−2.05762			−0.0805207			−0.0402604	+	0.999189i	$0.512819\pi$
$654$		0			0
$655$	29.4876			1.15218
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.16599	−	7.21571i	0.162284	−	0.281084i	−0.773403	−	0.633914i	$-0.781447\pi$
$659$	4.16599	−	7.21571i	0.162284	−	0.281084i	0.935687	+	0.352830i	$0.114781\pi$
$660$		0			0
$661$	−17.0463	+	29.5251i	−0.663024	+	1.14839i	0.316793	+	0.948495i	$0.397394\pi$
$661$	−17.0463	+	29.5251i	−0.663024	+	1.14839i	−0.979817	+	0.199897i	$0.935939\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.60543	+	26.1285i	−0.139812	+	1.01322i
$666$		0			0
$667$	2.58857	−	4.48353i	0.100230	−	0.173603i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	7.45255	+	12.9082i	0.287702	+	0.498315i
$672$		0			0
$673$	0.571008	−	0.989016i	0.0220108	−	0.0381237i	−0.854810	−	0.518941i	$-0.826327\pi$
$673$	0.571008	−	0.989016i	0.0220108	−	0.0381237i	0.876821	+	0.480817i	$0.159660\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	18.1906	+	31.5070i	0.699121	+	1.21091i	0.968772	+	0.247955i	$0.0797584\pi$
$677$	18.1906	+	31.5070i	0.699121	+	1.21091i	−0.269651	+	0.962958i	$0.586908\pi$
$678$		0			0
$679$	−0.755713	+	5.47665i	−0.0290016	+	0.210174i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.11274	−	5.39142i	−0.119106	−	0.206297i	0.800308	−	0.599589i	$-0.204669\pi$
$683$	−3.11274	−	5.39142i	−0.119106	−	0.206297i	−0.919414	+	0.393292i	$0.871336\pi$
$684$		0			0
$685$	−24.6846			−0.943152
$686$		0			0
$687$		0			0
$688$		0			0
$689$	21.8644	−	37.8702i	0.832967	−	1.44274i
$690$		0			0
$691$	19.9130	+	34.4903i	0.757525	+	1.31207i	0.944109	+	0.329633i	$0.106925\pi$
$691$	19.9130	+	34.4903i	0.757525	+	1.31207i	−0.186584	+	0.982439i	$0.559742\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.47398	−	12.9453i	−0.283504	−	0.491044i
$696$		0			0
$697$	−9.44384	+	16.3572i	−0.357711	+	0.619573i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	48.3337			1.82554			0.912769	−	0.408477i	$-0.133940\pi$
$701$	48.3337			1.82554			0.912769	+	0.408477i	$0.133940\pi$
$702$		0			0
$703$	4.74265	+	8.21452i	0.178873	+	0.309816i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	40.3204	−	16.4081i	1.51640	−	0.617088i
$708$		0			0
$709$	8.04198	+	13.9291i	0.302023	+	0.523119i	0.976594	−	0.215091i	$-0.0690048\pi$
$709$	8.04198	+	13.9291i	0.302023	+	0.523119i	−0.674571	+	0.738210i	$0.735671\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.12512	+	7.14491i	−0.154487	+	0.267579i
$714$		0			0
$715$	13.6645	+	23.6676i	0.511023	+	0.885117i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−21.0734	+	36.5002i	−0.785906	+	1.36123i	0.142550	+	0.989788i	$0.454470\pi$
$719$	−21.0734	+	36.5002i	−0.785906	+	1.36123i	−0.928456	+	0.371442i	$0.878864\pi$
$720$		0			0
$721$	−18.9847	+	7.72566i	−0.707026	+	0.287718i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.529212	+	0.916622i	−0.0196544	+	0.0340425i
$726$		0			0
$727$	−12.9548	+	22.4384i	−0.480467	+	0.832192i	−0.999749	−	0.0224103i	$-0.992866\pi$
$727$	−12.9548	+	22.4384i	−0.480467	+	0.832192i	0.519282	+	0.854603i	$0.326199\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	45.6465			1.68830
$732$		0			0
$733$	20.4054			0.753692			0.376846	−	0.926276i	$-0.377009\pi$
$733$	20.4054			0.753692			0.376846	+	0.926276i	$0.377009\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.4196	−	38.8320i	0.825838	−	1.43039i
$738$		0			0
$739$	−11.8953	−	20.6033i	−0.437576	−	0.757903i	0.559926	−	0.828542i	$-0.310829\pi$
$739$	−11.8953	−	20.6033i	−0.437576	−	0.757903i	−0.997502	+	0.0706392i	$0.977496\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.6320	−	37.4678i	−0.793603	−	1.37456i	−0.923723	−	0.383062i	$-0.874870\pi$
$743$	−21.6320	−	37.4678i	−0.793603	−	1.37456i	0.130120	−	0.991498i	$-0.458464\pi$
$744$		0			0
$745$	−13.8286			−0.506641
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.71058	+	19.6436i	−0.0990426	+	0.717761i
$750$		0			0
$751$	−14.3693			−0.524343			−0.262172	−	0.965021i	$-0.584439\pi$
$751$	−14.3693			−0.524343			−0.262172	+	0.965021i	$0.584439\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.4176			−0.379136
$756$		0			0
$757$	39.7854			1.44603			0.723013	−	0.690835i	$-0.242757\pi$
$757$	39.7854			1.44603			0.723013	+	0.690835i	$0.242757\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.3933			0.811756			0.405878	−	0.913927i	$-0.366966\pi$
$761$	22.3933			0.811756			0.405878	+	0.913927i	$0.366966\pi$
$762$		0			0
$763$	−17.9919	−	13.9844i	−0.651350	−	0.506269i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.8529			−1.00571
$768$		0			0
$769$	−1.45546	−	2.52093i	−0.0524853	−	0.0909071i	0.838589	−	0.544764i	$-0.183381\pi$
$769$	−1.45546	−	2.52093i	−0.0524853	−	0.0909071i	−0.891074	+	0.453857i	$0.850048\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.68612	+	11.5807i	0.240483	+	0.416529i	0.960852	−	0.277062i	$-0.0893609\pi$
$773$	6.68612	+	11.5807i	0.240483	+	0.416529i	−0.720369	+	0.693591i	$0.756028\pi$
$774$		0			0
$775$	0.843347	−	1.46072i	0.0302939	−	0.0524706i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	27.3862			0.981211
$780$		0			0
$781$	15.5081			0.554922
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.401073	+	0.694679i	−0.0143149	+	0.0247941i
$786$		0			0
$787$	11.9264	−	20.6571i	0.425130	−	0.736347i	−0.571302	−	0.820740i	$-0.693562\pi$
$787$	11.9264	−	20.6571i	0.425130	−	0.736347i	0.996433	+	0.0843925i	$0.0268950\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.50696	+	5.05761i	0.231361	+	0.179828i
$792$		0			0
$793$	−11.5607	+	20.0237i	−0.410533	+	0.711063i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.10559	+	10.5752i	0.216271	+	0.374593i	0.953665	−	0.300870i	$-0.0972772\pi$
$797$	6.10559	+	10.5752i	0.216271	+	0.374593i	−0.737394	+	0.675463i	$0.763944\pi$
$798$		0			0
$799$	−8.63639	+	14.9587i	−0.305533	+	0.529199i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.61718	−	9.72923i	−0.198226	−	0.343337i
$804$		0			0
$805$	35.8180	−	14.5758i	1.26242	−	0.513731i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−26.7838	−	46.3910i	−0.941669	−	1.63102i	−0.762287	−	0.647240i	$-0.775923\pi$
$809$	−26.7838	−	46.3910i	−0.941669	−	1.63102i	−0.179383	−	0.983779i	$-0.557410\pi$
$810$		0			0
$811$	1.81310			0.0636667			0.0318334	−	0.999493i	$-0.489865\pi$
$811$	1.81310			0.0636667			0.0318334	+	0.999493i	$0.489865\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.7615	−	29.0317i	0.587128	−	1.01694i
$816$		0			0
$817$	−33.0925	−	57.3180i	−1.15776	−	2.00530i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.8371	−	34.3589i	−0.692321	−	1.19913i	−0.971076	−	0.238772i	$-0.923255\pi$
$821$	−19.8371	−	34.3589i	−0.692321	−	1.19913i	0.278755	−	0.960362i	$-0.410078\pi$
$822$		0			0
$823$	−8.40656	+	14.5606i	−0.293034	+	0.507550i	−0.974526	−	0.224276i	$-0.927998\pi$
$823$	−8.40656	+	14.5606i	−0.293034	+	0.507550i	0.681491	+	0.731826i	$0.261332\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.2198			−1.29426			−0.647130	−	0.762379i	$-0.724031\pi$
$827$	−37.2198			−1.29426			−0.647130	+	0.762379i	$0.724031\pi$
$828$		0			0
$829$	−11.4365	−	19.8086i	−0.397206	−	0.687981i	0.596174	−	0.802855i	$-0.296687\pi$
$829$	−11.4365	−	19.8086i	−0.397206	−	0.687981i	−0.993380	+	0.114874i	$0.963354\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−25.2266	−	7.09707i	−0.874048	−	0.245899i
$834$		0			0
$835$	−1.40518	−	2.43384i	−0.0486281	−	0.0842263i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−18.4071	+	31.8820i	−0.635484	+	1.10069i	0.350929	+	0.936402i	$0.385866\pi$
$839$	−18.4071	+	31.8820i	−0.635484	+	1.10069i	−0.986412	+	0.164288i	$0.947467\pi$
$840$		0			0
$841$	14.2884	+	24.7482i	0.492704	+	0.853388i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.25921	+	16.0374i	−0.318527	+	0.551704i
$846$		0			0
$847$	−3.44901	+	1.40354i	−0.118509	+	0.0482264i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.95325	−	12.0434i	0.238354	−	0.412842i
$852$		0			0
$853$	6.98355	−	12.0959i	0.239112	−	0.414155i	−0.721347	−	0.692573i	$-0.756477\pi$
$853$	6.98355	−	12.0959i	0.239112	−	0.414155i	0.960460	+	0.278419i	$0.0898102\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.5677			−0.600102			−0.300051	−	0.953923i	$-0.597004\pi$
$857$	−17.5677			−0.600102			−0.300051	+	0.953923i	$0.597004\pi$
$858$		0			0
$859$	2.84577			0.0970963			0.0485482	−	0.998821i	$-0.484541\pi$
$859$	2.84577			0.0970963			0.0485482	+	0.998821i	$0.484541\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	27.7115	−	47.9977i	0.943310	−	1.63386i	0.184210	−	0.982887i	$-0.441027\pi$
$863$	27.7115	−	47.9977i	0.943310	−	1.63386i	0.759100	−	0.650974i	$-0.225639\pi$
$864$		0			0
$865$	1.99221	+	3.45061i	0.0677372	+	0.117324i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	22.2348	+	38.5119i	0.754265	+	1.30643i
$870$		0			0
$871$	69.5566			2.35684
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−29.8263	+	12.1376i	−1.00831	+	0.410324i
$876$		0			0
$877$	54.8689			1.85279			0.926396	−	0.376552i	$-0.122890\pi$
$877$	54.8689			1.85279			0.926396	+	0.376552i	$0.122890\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	51.1572			1.72353			0.861765	−	0.507307i	$-0.169359\pi$
$881$	51.1572			1.72353			0.861765	+	0.507307i	$0.169359\pi$
$882$		0			0
$883$	38.6438			1.30047			0.650234	−	0.759734i	$-0.274671\pi$
$883$	38.6438			1.30047			0.650234	+	0.759734i	$0.274671\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.8525			0.599429			0.299714	−	0.954029i	$-0.403109\pi$
$887$	17.8525			0.599429			0.299714	+	0.954029i	$0.403109\pi$
$888$		0			0
$889$	26.6789	−	10.8568i	0.894782	−	0.364124i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	25.0446			0.838087
$894$		0			0
$895$	1.98833	+	3.44388i	0.0664624	+	0.115116i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.337199	+	0.584047i	0.0112462	+	0.0194790i
$900$		0			0
$901$	−17.0369	+	29.5088i	−0.567581	+	0.983080i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.02451			0.0340559
$906$		0			0
$907$	−36.4663			−1.21084			−0.605422	−	0.795905i	$-0.706996\pi$
$907$	−36.4663			−1.21084			−0.605422	+	0.795905i	$0.706996\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−18.9847	+	32.8825i	−0.628993	+	1.08945i	0.358762	+	0.933429i	$0.383199\pi$
$911$	−18.9847	+	32.8825i	−0.628993	+	1.08945i	−0.987754	+	0.156018i	$0.950134\pi$
$912$		0			0
$913$	−11.8666	+	20.5535i	−0.392726	+	0.680221i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	39.3465	−	16.0117i	1.29934	−	0.528754i
$918$		0			0
$919$	−1.21770	+	2.10911i	−0.0401681	+	0.0695732i	−0.885411	−	0.464810i	$-0.846123\pi$
$919$	−1.21770	+	2.10911i	−0.0401681	+	0.0695732i	0.845242	+	0.534383i	$0.179456\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	12.0284	+	20.8338i	0.395919	+	0.685752i
$924$		0			0
$925$	−1.42153	+	2.46217i	−0.0467398	+	0.0809557i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−17.7404	−	30.7273i	−0.582044	−	1.00813i	−0.995237	−	0.0974863i	$-0.968920\pi$
$929$	−17.7404	−	30.7273i	−0.582044	−	1.00813i	0.413193	−	0.910644i	$-0.364414\pi$
$930$		0			0
$931$	9.37687	+	36.8220i	0.307314	+	1.20679i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−10.6475	−	18.4420i	−0.348209	−	0.603116i
$936$		0			0
$937$	−30.0427			−0.981452			−0.490726	−	0.871314i	$-0.663268\pi$
$937$	−30.0427			−0.981452			−0.490726	+	0.871314i	$0.663268\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.1250	+	26.1972i	−0.493060	+	0.854004i	−0.999968	−	0.00799565i	$-0.997455\pi$
$941$	−15.1250	+	26.1972i	−0.493060	+	0.854004i	0.506908	+	0.862000i	$0.330788\pi$
$942$		0			0
$943$	−20.0756	−	34.7719i	−0.653750	−	1.13233i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.9944	+	29.4352i	0.552245	+	0.956516i	0.998112	+	0.0614168i	$0.0195619\pi$
$947$	16.9944	+	29.4352i	0.552245	+	0.956516i	−0.445868	+	0.895099i	$0.647105\pi$
$948$		0			0
$949$	8.71360	−	15.0924i	0.282855	−	0.489920i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.4324			0.694265			0.347132	−	0.937816i	$-0.387155\pi$
$953$	21.4324			0.694265			0.347132	+	0.937816i	$0.387155\pi$
$954$		0			0
$955$	−22.0385	−	38.1719i	−0.713151	−	1.23521i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−32.9377	+	13.4037i	−1.06361	+	0.432829i
$960$		0			0
$961$	14.9626	+	25.9161i	0.482666	+	0.836002i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	19.5406	−	33.8452i	0.629033	−	1.08952i
$966$		0			0
$967$	12.4095	+	21.4938i	0.399061	+	0.691194i	0.993610	−	0.112865i	$-0.0360028\pi$
$967$	12.4095	+	21.4938i	0.399061	+	0.691194i	−0.594549	+	0.804059i	$0.702669\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.9437	−	24.1512i	0.447475	−	0.775050i	−0.550746	−	0.834673i	$-0.685657\pi$
$971$	13.9437	−	24.1512i	0.447475	−	0.775050i	0.998221	+	0.0596234i	$0.0189900\pi$
$972$		0			0
$973$	−17.0021	−	13.2151i	−0.545062	−	0.423656i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.6237	−	23.5969i	0.435859	−	0.754930i	−0.561506	−	0.827473i	$-0.689778\pi$
$977$	13.6237	−	23.5969i	0.435859	−	0.754930i	0.997365	+	0.0725422i	$0.0231112\pi$
$978$		0			0
$979$	17.8645	−	30.9423i	0.570953	−	0.988920i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.8908			0.443047			0.221523	−	0.975155i	$-0.428897\pi$
$983$	13.8908			0.443047			0.221523	+	0.975155i	$0.428897\pi$
$984$		0			0
$985$	27.3223			0.870561
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−48.5173	+	84.0344i	−1.54276	+	2.67214i
$990$		0			0
$991$	21.3271	+	36.9397i	0.677479	+	1.17343i	0.975738	+	0.218942i	$0.0702607\pi$
$991$	21.3271	+	36.9397i	0.677479	+	1.17343i	−0.298259	+	0.954485i	$0.596406\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	11.3479	+	19.6551i	0.359752	+	0.623108i
$996$		0			0
$997$	43.1810			1.36756			0.683779	−	0.729690i	$-0.260335\pi$
$997$	43.1810			1.36756			0.683779	+	0.729690i	$0.260335\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.t.d.289.8		22
3.2	odd	2		504.2.t.d.457.1	yes	22
4.3	odd	2		3024.2.t.l.289.8		22
7.4	even	3		1512.2.q.c.1369.4		22
9.4	even	3		1512.2.q.c.793.4		22
9.5	odd	6		504.2.q.d.121.9	yes	22
12.11	even	2		1008.2.t.k.961.11		22
21.11	odd	6		504.2.q.d.25.9	✓	22
28.11	odd	6		3024.2.q.k.2881.4		22
36.23	even	6		1008.2.q.k.625.3		22
36.31	odd	6		3024.2.q.k.2305.4		22
63.4	even	3	inner	1512.2.t.d.361.8		22
63.32	odd	6		504.2.t.d.193.1	yes	22
84.11	even	6		1008.2.q.k.529.3		22
252.67	odd	6		3024.2.t.l.1873.8		22
252.95	even	6		1008.2.t.k.193.11		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.9	✓	22	21.11	odd	6
504.2.q.d.121.9	yes	22	9.5	odd	6
504.2.t.d.193.1	yes	22	63.32	odd	6
504.2.t.d.457.1	yes	22	3.2	odd	2
1008.2.q.k.529.3		22	84.11	even	6
1008.2.q.k.625.3		22	36.23	even	6
1008.2.t.k.193.11		22	252.95	even	6
1008.2.t.k.961.11		22	12.11	even	2
1512.2.q.c.793.4		22	9.4	even	3
1512.2.q.c.1369.4		22	7.4	even	3
1512.2.t.d.289.8		22	1.1	even	1	trivial
1512.2.t.d.361.8		22	63.4	even	3	inner
3024.2.q.k.2305.4		22	36.31	odd	6
3024.2.q.k.2881.4		22	28.11	odd	6
3024.2.t.l.289.8		22	4.3	odd	2
3024.2.t.l.1873.8		22	252.67	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.83657 q^{5} +(2.45061 - 0.997255i) q^{7} +O(q^{10})\)	\(q+1.83657 q^{5} +(2.45061 - 0.997255i) q^{7} +3.09719 q^{11} +(2.40225 + 4.16081i) q^{13} +(-1.87185 - 3.24214i) q^{17} +(-2.71408 + 4.70093i) q^{19} +7.95829 q^{23} -1.62701 q^{25} +(0.325267 - 0.563379i) q^{29} +(-0.518342 + 0.897795i) q^{31} +(4.50072 - 1.83153i) q^{35} +(0.873712 - 1.51331i) q^{37} +(-2.52260 - 4.36927i) q^{41} +(-6.09645 + 10.5594i) q^{43} +(-2.30691 - 3.99569i) q^{47} +(5.01096 - 4.88776i) q^{49} +(-4.55082 - 7.88226i) q^{53} +5.68821 q^{55} +(-2.89863 + 5.02058i) q^{59} +(2.40623 + 4.16771i) q^{61} +(4.41190 + 7.64163i) q^{65} +(7.23870 - 12.5378i) q^{67} +5.00714 q^{71} +(-1.81364 - 3.14131i) q^{73} +(7.59000 - 3.08869i) q^{77} +(7.17904 + 12.4345i) q^{79} +(-3.83139 + 6.63616i) q^{83} +(-3.43778 - 5.95441i) q^{85} +(5.76798 - 9.99043i) q^{89} +(10.0364 + 7.80087i) q^{91} +(-4.98461 + 8.63360i) q^{95} +(-1.04480 + 1.80964i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} + 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 + 7 * q^7	\( 22 q + 6 q^{5} + 7 q^{7} - 6 q^{11} - 3 q^{13} - 7 q^{17} - q^{19} + 4 q^{23} + 20 q^{25} - 9 q^{29} - 4 q^{31} - 14 q^{35} + 2 q^{37} - 16 q^{41} - 5 q^{47} - 15 q^{49} - 11 q^{53} + 22 q^{55} + 19 q^{59} - 13 q^{61} - 13 q^{65} + 26 q^{67} + 48 q^{71} - 35 q^{73} + 4 q^{77} + 10 q^{79} + 28 q^{83} - 20 q^{85} - 6 q^{89} - 37 q^{91} - 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 + 7 * q^7 - 6 * q^11 - 3 * q^13 - 7 * q^17 - q^19 + 4 * q^23 + 20 * q^25 - 9 * q^29 - 4 * q^31 - 14 * q^35 + 2 * q^37 - 16 * q^41 - 5 * q^47 - 15 * q^49 - 11 * q^53 + 22 * q^55 + 19 * q^59 - 13 * q^61 - 13 * q^65 + 26 * q^67 + 48 * q^71 - 35 * q^73 + 4 * q^77 + 10 * q^79 + 28 * q^83 - 20 * q^85 - 6 * q^89 - 37 * q^91 - 12 * q^95 - 29 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more