LMFDB - Embedded newform 2268.2.i.m.2053.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(865,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2268.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.i (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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2053.1
Root			$0.882007 + 1.52768i$ of defining polynomial
Character	$\chi$	$=$	2268.2053
Dual form			2268.2.i.m.865.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25300 - 2.17026i) q^{5} +(1.71031 + 2.01862i) q^{7} +O(q^{10})$	$q+(-1.25300 - 2.17026i) q^{5} +(1.71031 + 2.01862i) q^{7} +(-0.542689 + 0.939965i) q^{11} +(-0.457311 + 0.792086i) q^{13} +(-1.39302 - 2.41278i) q^{17} +(0.667623 - 1.15636i) q^{19} +(-3.06064 - 5.30119i) q^{23} +(-0.640021 + 1.10855i) q^{25} +(0.414622 + 0.718147i) q^{29} +2.61529 q^{31} +(2.23791 - 6.24116i) q^{35} +(3.14602 - 5.44907i) q^{37} +(0.817290 - 1.41559i) q^{41} +(0.795689 + 1.37817i) q^{43} +6.59138 q^{47} +(-1.14967 + 6.90495i) q^{49} +(-3.95967 - 6.85835i) q^{53} +2.71996 q^{55} -5.07809 q^{59} -11.6393 q^{61} +2.29204 q^{65} +15.8954 q^{67} +9.64658 q^{71} +(-5.03904 - 8.72788i) q^{73} +(-2.82560 + 0.512149i) q^{77} -9.34725 q^{79} +(-4.09733 - 7.09679i) q^{83} +(-3.49091 + 6.04644i) q^{85} +(6.36829 - 11.0302i) q^{89} +(-2.38107 + 0.431576i) q^{91} -3.34613 q^{95} +(-8.46931 - 14.6693i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{5} + q^{7}+O(q^{10}) $ 8 * q + 2 * q^5 + q^7	$ 8 q + 2 q^{5} + q^{7} - 5 q^{11} - 3 q^{13} - 2 q^{17} - 8 q^{19} - 2 q^{23} - 8 q^{25} + 2 q^{29} - 11 q^{35} + 4 q^{37} + 3 q^{41} - 5 q^{43} + 30 q^{47} - 19 q^{49} + 24 q^{53} + 16 q^{55} + 20 q^{59} + 24 q^{61} - 24 q^{65} + 14 q^{67} + 22 q^{71} - 10 q^{73} + 11 q^{77} - 35 q^{83} + 13 q^{85} + 18 q^{89} - 9 q^{91} - 20 q^{95} - 19 q^{97}+O(q^{100}) $ 8 * q + 2 * q^5 + q^7 - 5 * q^11 - 3 * q^13 - 2 * q^17 - 8 * q^19 - 2 * q^23 - 8 * q^25 + 2 * q^29 - 11 * q^35 + 4 * q^37 + 3 * q^41 - 5 * q^43 + 30 * q^47 - 19 * q^49 + 24 * q^53 + 16 * q^55 + 20 * q^59 + 24 * q^61 - 24 * q^65 + 14 * q^67 + 22 * q^71 - 10 * q^73 + 11 * q^77 - 35 * q^83 + 13 * q^85 + 18 * q^89 - 9 * q^91 - 20 * q^95 - 19 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−1.25300	−	2.17026i	−0.560359	−	0.970570i	−0.997465	−	0.0711601i	$-0.977330\pi$
$5$	−1.25300	−	2.17026i	−0.560359	−	0.970570i	0.437106	−	0.899410i	$-0.356003\pi$
$6$		0			0
$7$	1.71031	+	2.01862i	0.646437	+	0.762967i
$7$	1.71031	+	2.01862i	0.646437	+	0.762967i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.542689	+	0.939965i	−0.163627	+	0.283410i	−0.936167	−	0.351556i	$-0.885653\pi$
$11$	−0.542689	+	0.939965i	−0.163627	+	0.283410i	0.772540	+	0.634966i	$0.218986\pi$
$12$		0			0
$13$	−0.457311	+	0.792086i	−0.126835	+	0.219685i	−0.922449	−	0.386119i	$-0.873815\pi$
$13$	−0.457311	+	0.792086i	−0.126835	+	0.219685i	0.795614	+	0.605804i	$0.207149\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.39302	−	2.41278i	−0.337857	−	0.585186i	0.646172	−	0.763192i	$-0.276369\pi$
$17$	−1.39302	−	2.41278i	−0.337857	−	0.585186i	−0.984029	+	0.178006i	$0.943035\pi$
$18$		0			0
$19$	0.667623	−	1.15636i	0.153163	−	0.265286i	−0.779225	−	0.626744i	$-0.784387\pi$
$19$	0.667623	−	1.15636i	0.153163	−	0.265286i	0.932389	+	0.361457i	$0.117721\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.06064	−	5.30119i	−0.638189	−	1.10537i	−0.985830	−	0.167747i	$-0.946351\pi$
$23$	−3.06064	−	5.30119i	−0.638189	−	1.10537i	0.347641	−	0.937628i	$-0.386983\pi$
$24$		0			0
$25$	−0.640021	+	1.10855i	−0.128004	+	0.221710i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.414622	+	0.718147i	0.0769934	+	0.133357i	0.901951	−	0.431838i	$-0.142135\pi$
$29$	0.414622	+	0.718147i	0.0769934	+	0.133357i	−0.824958	+	0.565194i	$0.808801\pi$
$30$		0			0
$31$	2.61529			0.469720			0.234860	−	0.972029i	$-0.424537\pi$
$31$	2.61529			0.469720			0.234860	+	0.972029i	$0.424537\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.23791	−	6.24116i	0.378276	−	1.05495i
$36$		0			0
$37$	3.14602	−	5.44907i	0.517203	−	0.895822i	−0.482597	−	0.875842i	$-0.660307\pi$
$37$	3.14602	−	5.44907i	0.517203	−	0.895822i	0.999800	−	0.0199794i	$-0.00636008\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.817290	−	1.41559i	0.127639	−	0.221078i	−0.795122	−	0.606449i	$-0.792593\pi$
$41$	0.817290	−	1.41559i	0.127639	−	0.221078i	0.922762	+	0.385371i	$0.125927\pi$
$42$		0			0
$43$	0.795689	+	1.37817i	0.121342	+	0.210170i	0.920297	−	0.391221i	$-0.127947\pi$
$43$	0.795689	+	1.37817i	0.121342	+	0.210170i	−0.798955	+	0.601390i	$0.794614\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.59138			0.961451			0.480726	−	0.876871i	$-0.340373\pi$
$47$	6.59138			0.961451			0.480726	+	0.876871i	$0.340373\pi$
$48$		0			0
$49$	−1.14967	+	6.90495i	−0.164238	+	0.986421i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.95967	−	6.85835i	−0.543902	−	0.942066i	−0.998675	−	0.0514588i	$-0.983613\pi$
$53$	−3.95967	−	6.85835i	−0.543902	−	0.942066i	0.454773	−	0.890607i	$-0.349720\pi$
$54$		0			0
$55$	2.71996			0.366759
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5.07809			−0.661111			−0.330555	−	0.943787i	$-0.607236\pi$
$59$	−5.07809			−0.661111			−0.330555	+	0.943787i	$0.607236\pi$
$60$		0			0
$61$	−11.6393			−1.49026			−0.745129	−	0.666920i	$-0.767612\pi$
$61$	−11.6393			−1.49026			−0.745129	+	0.666920i	$0.767612\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.29204			0.284293
$66$		0			0
$67$	15.8954			1.94194			0.970968	−	0.239211i	$-0.0768887\pi$
$67$	15.8954			1.94194			0.970968	+	0.239211i	$0.0768887\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	9.64658			1.14484			0.572419	−	0.819961i	$-0.306005\pi$
$71$	9.64658			1.14484			0.572419	+	0.819961i	$0.306005\pi$
$72$		0			0
$73$	−5.03904	−	8.72788i	−0.589776	−	1.02152i	−0.994262	−	0.106977i	$-0.965883\pi$
$73$	−5.03904	−	8.72788i	−0.589776	−	1.02152i	0.404486	−	0.914544i	$-0.367450\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.82560	+	0.512149i	−0.322007	+	0.0583648i
$78$		0			0
$79$	−9.34725			−1.05165			−0.525824	−	0.850594i	$-0.676243\pi$
$79$	−9.34725			−1.05165			−0.525824	+	0.850594i	$0.676243\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.09733	−	7.09679i	−0.449741	−	0.778974i	0.548628	−	0.836066i	$-0.315150\pi$
$83$	−4.09733	−	7.09679i	−0.449741	−	0.778974i	−0.998369	+	0.0570928i	$0.981817\pi$
$84$		0			0
$85$	−3.49091	+	6.04644i	−0.378643	+	0.655829i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.36829	−	11.0302i	0.675037	−	1.16920i	−0.301421	−	0.953491i	$-0.597461\pi$
$89$	6.36829	−	11.0302i	0.675037	−	1.16920i	0.976458	−	0.215708i	$-0.0692058\pi$
$90$		0			0
$91$	−2.38107	+	0.431576i	−0.249604	+	0.0452415i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.34613			−0.343305
$96$		0			0
$97$	−8.46931	−	14.6693i	−0.859929	−	1.48944i	−0.871996	−	0.489513i	$-0.837175\pi$
$97$	−8.46931	−	14.6693i	−0.859929	−	1.48944i	0.0120677	−	0.999927i	$-0.496159\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.56064	−	2.70312i	0.155290	−	0.268970i	−0.777875	−	0.628420i	$-0.783702\pi$
$101$	1.56064	−	2.70312i	0.155290	−	0.268970i	0.933165	+	0.359449i	$0.117035\pi$
$102$		0			0
$103$	−2.40867	−	4.17194i	−0.237333	−	0.411073i	0.722615	−	0.691251i	$-0.242940\pi$
$103$	−2.40867	−	4.17194i	−0.237333	−	0.411073i	−0.959948	+	0.280178i	$0.909607\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.12729	−	12.3448i	0.689021	−	1.19342i	−0.283134	−	0.959080i	$-0.591374\pi$
$107$	7.12729	−	12.3448i	0.689021	−	1.19342i	0.972155	−	0.234339i	$-0.0752927\pi$
$108$		0			0
$109$	−2.94767	−	5.10551i	−0.282335	−	0.489019i	0.689624	−	0.724167i	$-0.257776\pi$
$109$	−2.94767	−	5.10551i	−0.282335	−	0.489019i	−0.971959	+	0.235149i	$0.924442\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.58173	+	7.93579i	−0.431013	+	0.746537i	−0.996961	−	0.0779045i	$-0.975177\pi$
$113$	−4.58173	+	7.93579i	−0.431013	+	0.746537i	0.565948	+	0.824441i	$0.308510\pi$
$114$		0			0
$115$	−7.66998	+	13.2848i	−0.715229	+	1.23881i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.48800	−	6.93860i	0.228074	−	0.636060i
$120$		0			0
$121$	4.91098	+	8.50606i	0.446453	+	0.773278i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.32222			−0.833805
$126$		0			0
$127$	−5.48671			−0.486867			−0.243433	−	0.969918i	$-0.578274\pi$
$127$	−5.48671			−0.486867			−0.243433	+	0.969918i	$0.578274\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−10.8587	−	18.8078i	−0.948728	−	1.64325i	−0.748109	−	0.663576i	$-0.769038\pi$
$131$	−10.8587	−	18.8078i	−0.948728	−	1.64325i	−0.200620	−	0.979669i	$-0.564296\pi$
$132$		0			0
$133$	3.47609	−	0.630053i	0.301415	−	0.0546325i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.2012	+	17.6690i	−0.871550	+	1.50957i	−0.0111561	+	0.999938i	$0.503551\pi$
$137$	−10.2012	+	17.6690i	−0.871550	+	1.50957i	−0.860393	+	0.509630i	$0.829782\pi$
$138$		0			0
$139$	2.41698	−	4.18633i	0.205005	−	0.355080i	−0.745129	−	0.666920i	$-0.767612\pi$
$139$	2.41698	−	4.18633i	0.205005	−	0.355080i	0.950134	+	0.311840i	$0.100945\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.496355	−	0.859713i	−0.0415073	−	0.0718928i
$144$		0			0
$145$	1.03904	−	1.79968i	0.0862879	−	0.149455i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.90867	−	5.03796i	−0.238287	−	0.412726i	0.721936	−	0.691960i	$-0.243253\pi$
$149$	−2.90867	−	5.03796i	−0.238287	−	0.412726i	−0.960223	+	0.279234i	$0.909919\pi$
$150$		0			0
$151$	4.30769	−	7.46114i	0.350555	−	0.607179i	−0.635792	−	0.771861i	$-0.719326\pi$
$151$	4.30769	−	7.46114i	0.350555	−	0.607179i	0.986347	+	0.164682i	$0.0526596\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.27696	−	5.67586i	−0.263212	−	0.455896i
$156$		0			0
$157$	−8.26187			−0.659369			−0.329685	−	0.944091i	$-0.606942\pi$
$157$	−8.26187			−0.659369			−0.329685	+	0.944091i	$0.606942\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.46644	−	15.2450i	0.430816	−	1.20147i
$162$		0			0
$163$	1.02160	−	1.76946i	0.0800179	−	0.138595i	−0.823239	−	0.567694i	$-0.807836\pi$
$163$	1.02160	−	1.76946i	0.0800179	−	0.138595i	0.903257	+	0.429099i	$0.141169\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.31965	−	14.4101i	0.643794	−	1.11508i	−0.340785	−	0.940141i	$-0.610693\pi$
$167$	8.31965	−	14.4101i	0.643794	−	1.11508i	0.984579	−	0.174942i	$-0.0559738\pi$
$168$		0			0
$169$	6.08173	+	10.5339i	0.467826	+	0.810298i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	20.4685			1.55619			0.778097	−	0.628144i	$-0.216185\pi$
$173$	20.4685			1.55619			0.778097	+	0.628144i	$0.216185\pi$
$174$		0			0
$175$	−3.33238	+	0.604004i	−0.251904	+	0.0456584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.624422	−	1.08153i	−0.0466715	−	0.0808374i	0.841746	−	0.539874i	$-0.181528\pi$
$179$	−0.624422	−	1.08153i	−0.0466715	−	0.0808374i	−0.888417	+	0.459036i	$0.848195\pi$
$180$		0			0
$181$	14.6153			1.08635			0.543173	−	0.839621i	$-0.317223\pi$
$181$	14.6153			1.08635			0.543173	+	0.839621i	$0.317223\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−15.7679			−1.15928
$186$		0			0
$187$	3.02391			0.221130
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−17.9495			−1.29878			−0.649390	−	0.760455i	$-0.724976\pi$
$191$	−17.9495			−1.29878			−0.649390	+	0.760455i	$0.724976\pi$
$192$		0			0
$193$	23.1812			1.66862			0.834310	−	0.551296i	$-0.185866\pi$
$193$	23.1812			1.66862			0.834310	+	0.551296i	$0.185866\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.31134			0.449664			0.224832	−	0.974398i	$-0.427817\pi$
$197$	6.31134			0.449664			0.224832	+	0.974398i	$0.427817\pi$
$198$		0			0
$199$	3.82873	+	6.63156i	0.271412	+	0.470099i	0.969224	−	0.246182i	$-0.0791762\pi$
$199$	3.82873	+	6.63156i	0.271412	+	0.470099i	−0.697812	+	0.716281i	$0.745843\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.740534	+	2.06522i	−0.0519753	+	0.144950i
$204$		0			0
$205$	−4.09626			−0.286095
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.724623	+	1.25508i	0.0501232	+	0.0868160i
$210$		0			0
$211$	−2.73740	+	4.74132i	−0.188450	+	0.326406i	−0.944734	−	0.327838i	$-0.893680\pi$
$211$	−2.73740	+	4.74132i	−0.188450	+	0.326406i	0.756283	+	0.654244i	$0.227013\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.99400	−	3.45371i	0.135990	−	0.235541i
$216$		0			0
$217$	4.47296	+	5.27928i	0.303644	+	0.358381i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.54818			0.171409
$222$		0			0
$223$	3.93807	+	6.82093i	0.263712	+	0.456763i	0.967225	−	0.253919i	$-0.0817197\pi$
$223$	3.93807	+	6.82093i	0.263712	+	0.456763i	−0.703513	+	0.710682i	$0.748386\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.0913311	+	0.158190i	−0.00606186	+	0.0104994i	−0.869040	−	0.494741i	$-0.835263\pi$
$227$	−0.0913311	+	0.158190i	−0.00606186	+	0.0104994i	0.862979	+	0.505241i	$0.168596\pi$
$228$		0			0
$229$	−7.32329	−	12.6843i	−0.483937	−	0.838203i	0.515893	−	0.856653i	$-0.327460\pi$
$229$	−7.32329	−	12.6843i	−0.483937	−	0.838203i	−0.999830	+	0.0184500i	$0.994127\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.4693	+	18.1334i	−0.685868	+	1.18796i	0.287296	+	0.957842i	$0.407244\pi$
$233$	−10.4693	+	18.1334i	−0.685868	+	1.18796i	−0.973163	+	0.230116i	$0.926090\pi$
$234$		0			0
$235$	−8.25900	−	14.3050i	−0.538758	−	0.933156i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.16398	−	14.1404i	0.528084	−	0.914668i	−0.471380	−	0.881930i	$-0.656244\pi$
$239$	8.16398	−	14.1404i	0.528084	−	0.914668i	0.999464	−	0.0327379i	$-0.0104227\pi$
$240$		0			0
$241$	0.152536	−	0.264200i	0.00982571	−	0.0170186i	−0.861071	−	0.508485i	$-0.830206\pi$
$241$	0.152536	−	0.264200i	0.00982571	−	0.0170186i	0.870896	+	0.491467i	$0.163539\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	16.4261	−	6.15682i	1.04942	−	0.393345i
$246$		0			0
$247$	0.610623	+	1.05763i	0.0388530	+	0.0672954i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−28.2619			−1.78387			−0.891937	−	0.452160i	$-0.850654\pi$
$251$	−28.2619			−1.78387			−0.891937	+	0.452160i	$0.850654\pi$
$252$		0			0
$253$	6.64391			0.417699
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.1208	+	17.5297i	0.631317	+	1.09347i	0.987283	+	0.158974i	$0.0508185\pi$
$257$	10.1208	+	17.5297i	0.631317	+	1.09347i	−0.355966	+	0.934499i	$0.615848\pi$
$258$		0			0
$259$	16.3803	−	2.96898i	1.01782	−	0.184483i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.81078	+	11.7966i	−0.419970	+	0.727410i	−0.995936	−	0.0900638i	$-0.971293\pi$
$263$	−6.81078	+	11.7966i	−0.419970	+	0.727410i	0.575966	+	0.817474i	$0.304626\pi$
$264$		0			0
$265$	−9.92293	+	17.1870i	−0.609561	+	1.05579i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.30169	+	2.25459i	0.0793655	+	0.137465i	0.902976	−	0.429690i	$-0.141377\pi$
$269$	1.30169	+	2.25459i	0.0793655	+	0.137465i	−0.823611	+	0.567155i	$0.808044\pi$
$270$		0			0
$271$	−0.362288	+	0.627501i	−0.0220074	+	0.0381179i	−0.876819	−	0.480820i	$-0.840339\pi$
$271$	−0.362288	+	0.627501i	−0.0220074	+	0.0381179i	0.854812	+	0.518938i	$0.173672\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.694665	−	1.20319i	−0.0418899	−	0.0725554i
$276$		0			0
$277$	−7.46331	+	12.9268i	−0.448427	+	0.776698i	−0.998284	−	0.0585606i	$-0.981349\pi$
$277$	−7.46331	+	12.9268i	−0.448427	+	0.776698i	0.549857	+	0.835259i	$0.314682\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.67311	+	16.7543i	0.577049	+	0.999479i	0.995816	+	0.0913849i	$0.0291294\pi$
$281$	9.67311	+	16.7543i	0.577049	+	0.999479i	−0.418766	+	0.908094i	$0.637537\pi$
$282$		0			0
$283$	1.38471			0.0823126			0.0411563	−	0.999153i	$-0.486896\pi$
$283$	1.38471			0.0823126			0.0411563	+	0.999153i	$0.486896\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.25536	−	0.771297i	0.251186	−	0.0455282i
$288$		0			0
$289$	4.61898	−	8.00031i	0.271705	−	0.470606i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.61220	+	11.4527i	−0.386289	+	0.669072i	−0.991947	−	0.126653i	$-0.959577\pi$
$293$	−6.61220	+	11.4527i	−0.386289	+	0.669072i	0.605658	+	0.795725i	$0.292910\pi$
$294$		0			0
$295$	6.36285	+	11.0208i	0.370459	+	0.641654i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.59867			0.323779
$300$		0			0
$301$	−1.42114	+	3.96330i	−0.0819129	+	0.228441i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.5840	+	25.2603i	0.835080	+	1.44640i
$306$		0			0
$307$	13.3342			0.761024			0.380512	−	0.924776i	$-0.375748\pi$
$307$	13.3342			0.761024			0.380512	+	0.924776i	$0.375748\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	25.2427			1.43138			0.715690	−	0.698418i	$-0.246112\pi$
$311$	25.2427			1.43138			0.715690	+	0.698418i	$0.246112\pi$
$312$		0			0
$313$	12.7933			0.723122			0.361561	−	0.932348i	$-0.382244\pi$
$313$	12.7933			0.723122			0.361561	+	0.932348i	$0.382244\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.8028			0.775240			0.387620	−	0.921819i	$-0.373297\pi$
$317$	13.8028			0.775240			0.387620	+	0.921819i	$0.373297\pi$
$318$		0			0
$319$	−0.900044			−0.0503928
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.72005			−0.206989
$324$		0			0
$325$	−0.585378	−	1.01390i	−0.0324709	−	0.0562413i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.2733	+	13.3055i	0.621518	+	0.733556i
$330$		0			0
$331$	−12.4951			−0.686794			−0.343397	−	0.939190i	$-0.611578\pi$
$331$	−12.4951			−0.686794			−0.343397	+	0.939190i	$0.611578\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−19.9170	−	34.4972i	−1.08818	−	1.88478i
$336$		0			0
$337$	3.56716	−	6.17850i	0.194315	−	0.336564i	−0.752360	−	0.658752i	$-0.771085\pi$
$337$	3.56716	−	6.17850i	0.194315	−	0.336564i	0.946676	+	0.322187i	$0.104418\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.41929	+	2.45828i	−0.0768587	+	0.133123i
$342$		0			0
$343$	−15.9048	+	9.48887i	−0.858776	+	0.512351i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.10200			0.273890			0.136945	−	0.990579i	$-0.456272\pi$
$347$	5.10200			0.273890			0.136945	+	0.990579i	$0.456272\pi$
$348$		0			0
$349$	−15.7764	−	27.3256i	−0.844494	−	1.46271i	−0.886060	−	0.463570i	$-0.846568\pi$
$349$	−15.7764	−	27.3256i	−0.844494	−	1.46271i	0.0415664	−	0.999136i	$-0.486765\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.52082	+	13.0265i	−0.400293	+	0.693328i	−0.993761	−	0.111530i	$-0.964425\pi$
$353$	−7.52082	+	13.0265i	−0.400293	+	0.693328i	0.593468	+	0.804858i	$0.297758\pi$
$354$		0			0
$355$	−12.0872	−	20.9356i	−0.641521	−	1.11115i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.49322	+	12.9786i	−0.395477	+	0.684987i	−0.993162	−	0.116745i	$-0.962754\pi$
$359$	−7.49322	+	12.9786i	−0.395477	+	0.684987i	0.597685	+	0.801731i	$0.296087\pi$
$360$		0			0
$361$	8.60856	+	14.9105i	0.453082	+	0.784761i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.6279	+	21.8721i	−0.660972	+	1.14484i
$366$		0			0
$367$	8.73006	−	15.1209i	0.455706	−	0.789305i	−0.543023	−	0.839718i	$-0.682720\pi$
$367$	8.73006	−	15.1209i	0.455706	−	0.789305i	0.998728	+	0.0504126i	$0.0160536\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.07214	−	19.7230i	0.367167	−	1.02397i
$372$		0			0
$373$	−5.56716	−	9.64260i	−0.288257	−	0.499275i	0.685137	−	0.728414i	$-0.259742\pi$
$373$	−5.56716	−	9.64260i	−0.288257	−	0.499275i	−0.973394	+	0.229139i	$0.926409\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.758446			−0.0390619
$378$		0			0
$379$	−30.0958			−1.54592			−0.772959	−	0.634455i	$-0.781224\pi$
$379$	−30.0958			−1.54592			−0.772959	+	0.634455i	$0.781224\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.07029	+	8.78200i	0.259080	+	0.448739i	0.965996	−	0.258558i	$-0.0832474\pi$
$383$	5.07029	+	8.78200i	0.259080	+	0.448739i	−0.706916	+	0.707298i	$0.749914\pi$
$384$		0			0
$385$	4.65198	+	5.49057i	0.237087	+	0.279825i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.64367	+	14.9713i	−0.438251	+	0.759073i	−0.997555	−	0.0698895i	$-0.977735\pi$
$389$	−8.64367	+	14.9713i	−0.438251	+	0.759073i	0.559303	+	0.828963i	$0.311069\pi$
$390$		0			0
$391$	−8.52709	+	14.7694i	−0.431233	+	0.746918i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	11.7121	+	20.2860i	0.589300	+	1.02070i
$396$		0			0
$397$	−12.5666	+	21.7661i	−0.630702	+	1.09241i	0.356707	+	0.934216i	$0.383900\pi$
$397$	−12.5666	+	21.7661i	−0.630702	+	1.09241i	−0.987408	+	0.158191i	$0.949434\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.9956	+	20.7770i	0.599031	+	1.03755i	0.992964	+	0.118413i	$0.0377806\pi$
$401$	11.9956	+	20.7770i	0.599031	+	1.03755i	−0.393934	+	0.919139i	$0.628886\pi$
$402$		0			0
$403$	−1.19600	+	2.07153i	−0.0595770	+	0.103190i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.41462	+	5.91430i	0.169257	+	0.293161i
$408$		0			0
$409$	31.5898			1.56202			0.781008	−	0.624521i	$-0.214706\pi$
$409$	31.5898			1.56202			0.781008	+	0.624521i	$0.214706\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.68511	−	10.2507i	−0.427367	−	0.504406i
$414$		0			0
$415$	−10.2679	+	17.7846i	−0.504032	+	0.873010i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.12729	−	7.14868i	0.201631	−	0.349236i	−0.747423	−	0.664349i	$-0.768709\pi$
$419$	4.12729	−	7.14868i	0.201631	−	0.349236i	0.949054	+	0.315113i	$0.102042\pi$
$420$		0			0
$421$	−15.5557	−	26.9433i	−0.758139	−	1.31314i	−0.943799	−	0.330521i	$-0.892775\pi$
$421$	−15.5557	−	26.9433i	−0.758139	−	1.31314i	0.185660	−	0.982614i	$-0.440558\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.56625			0.172989
$426$		0			0
$427$	−19.9068	−	23.4953i	−0.963359	−	1.13702i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.0078	+	29.4585i	0.819239	+	1.41896i	0.906244	+	0.422756i	$0.138937\pi$
$431$	17.0078	+	29.4585i	0.819239	+	1.41896i	−0.0870045	+	0.996208i	$0.527729\pi$
$432$		0			0
$433$	−5.46751			−0.262752			−0.131376	−	0.991333i	$-0.541940\pi$
$433$	−5.46751			−0.262752			−0.131376	+	0.991333i	$0.541940\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.17343			−0.390988
$438$		0			0
$439$	22.9303			1.09440			0.547202	−	0.837001i	$-0.315693\pi$
$439$	22.9303			1.09440			0.547202	+	0.837001i	$0.315693\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−35.5045			−1.68687			−0.843436	−	0.537230i	$-0.819471\pi$
$443$	−35.5045			−1.68687			−0.843436	+	0.537230i	$0.819471\pi$
$444$		0			0
$445$	−31.9179			−1.51305
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.82093			0.463478			0.231739	−	0.972778i	$-0.425558\pi$
$449$	9.82093			0.463478			0.231739	+	0.972778i	$0.425558\pi$
$450$		0			0
$451$	0.887068	+	1.53645i	0.0417704	+	0.0723485i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.92011	+	4.62677i	0.183778	+	0.216906i
$456$		0			0
$457$	22.0350			1.03075			0.515377	−	0.856964i	$-0.327652\pi$
$457$	22.0350			1.03075			0.515377	+	0.856964i	$0.327652\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−21.1026	−	36.5507i	−0.982844	−	1.70234i	−0.651150	−	0.758949i	$-0.725713\pi$
$461$	−21.1026	−	36.5507i	−0.982844	−	1.70234i	−0.331694	−	0.943387i	$-0.607620\pi$
$462$		0			0
$463$	17.7637	−	30.7677i	0.825550	−	1.42989i	−0.0759485	−	0.997112i	$-0.524198\pi$
$463$	17.7637	−	30.7677i	0.825550	−	1.42989i	0.901498	−	0.432783i	$-0.142468\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.39015	−	9.33602i	0.249427	−	0.432019i	−0.713940	−	0.700207i	$-0.753091\pi$
$467$	5.39015	−	9.33602i	0.249427	−	0.432019i	0.963367	+	0.268187i	$0.0864246\pi$
$468$		0			0
$469$	27.1861	+	32.0869i	1.25534	+	1.48163i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.72725			−0.0794189
$474$		0			0
$475$	0.854586	+	1.48019i	0.0392111	+	0.0679156i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.4844	+	19.8916i	−0.524738	+	0.908873i	0.474847	+	0.880068i	$0.342503\pi$
$479$	−11.4844	+	19.8916i	−0.524738	+	0.908873i	−0.999585	+	0.0288044i	$0.990830\pi$
$480$		0			0
$481$	2.87742	+	4.98384i	0.131199	+	0.227244i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.2241	+	36.7612i	−0.963737	+	1.66924i
$486$		0			0
$487$	−14.5432	−	25.1896i	−0.659018	−	1.14145i	−0.980870	−	0.194662i	$-0.937639\pi$
$487$	−14.5432	−	25.1896i	−0.659018	−	1.14145i	0.321853	−	0.946790i	$-0.395694\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.81005	−	16.9915i	0.442721	−	0.766816i	−0.555169	−	0.831738i	$-0.687346\pi$
$491$	9.81005	−	16.9915i	0.442721	−	0.766816i	0.997890	+	0.0649218i	$0.0206798\pi$
$492$		0			0
$493$	1.15516	−	2.00079i	0.0520256	−	0.0901110i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.4987	+	19.4728i	0.740066	+	0.873474i
$498$		0			0
$499$	−1.29805	−	2.24828i	−0.0581085	−	0.100647i	0.835508	−	0.549479i	$-0.185174\pi$
$499$	−1.29805	−	2.24828i	−0.0581085	−	0.100647i	−0.893616	+	0.448832i	$0.851840\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−36.0865			−1.60902			−0.804509	−	0.593941i	$-0.797571\pi$
$503$	−36.0865			−1.60902			−0.804509	+	0.593941i	$0.797571\pi$
$504$		0			0
$505$	−7.82196			−0.348072
$506$		0			0
$507$		0			0
$508$		0			0
$509$	17.3826	+	30.1076i	0.770472	+	1.33450i	0.937304	+	0.348512i	$0.113313\pi$
$509$	17.3826	+	30.1076i	0.770472	+	1.33450i	−0.166832	+	0.985985i	$0.553354\pi$
$510$		0			0
$511$	8.99995	−	25.0993i	0.398134	−	1.11033i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.03613	+	10.4549i	−0.265984	+	0.460697i
$516$		0			0
$517$	−3.57707	+	6.19566i	−0.157319	+	0.272485i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.37609	+	11.0437i	0.279341	+	0.483834i	0.971221	−	0.238179i	$-0.0765505\pi$
$521$	6.37609	+	11.0437i	0.279341	+	0.483834i	−0.691880	+	0.722013i	$0.743217\pi$
$522$		0			0
$523$	−19.0906	+	33.0659i	−0.834774	+	1.44587i	0.0594407	+	0.998232i	$0.481068\pi$
$523$	−19.0906	+	33.0659i	−0.834774	+	1.44587i	−0.894214	+	0.447639i	$0.852265\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.64315	−	6.31013i	−0.158698	−	0.274873i
$528$		0			0
$529$	−7.23509	+	12.5315i	−0.314569	+	0.544850i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.747512	+	1.29473i	0.0323783	+	0.0560809i
$534$		0			0
$535$	−35.7220			−1.54440
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.86649	−	4.82788i	−0.252688	−	0.207952i
$540$		0			0
$541$	7.26136	−	12.5770i	0.312190	−	0.540729i	−0.666646	−	0.745374i	$-0.732271\pi$
$541$	7.26136	−	12.5770i	0.312190	−	0.540729i	0.978836	+	0.204645i	$0.0656041\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.38685	+	12.7944i	−0.316418	+	0.548052i
$546$		0			0
$547$	13.2907	+	23.0202i	0.568270	+	0.984272i	0.996737	+	0.0807148i	$0.0257203\pi$
$547$	13.2907	+	23.0202i	0.568270	+	0.984272i	−0.428468	+	0.903557i	$0.640946\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.10725			0.0471703
$552$		0			0
$553$	−15.9867	−	18.8686i	−0.679824	−	0.802373i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.3017	+	23.0392i	0.563611	+	0.976202i	0.997177	+	0.0750809i	$0.0239215\pi$
$557$	13.3017	+	23.0392i	0.563611	+	0.976202i	−0.433567	+	0.901121i	$0.642745\pi$
$558$		0			0
$559$	−1.45551			−0.0615615
$560$		0			0
$561$		0			0
$562$		0			0
$563$	25.8220			1.08827			0.544133	−	0.838999i	$-0.316859\pi$
$563$	25.8220			1.08827			0.544133	+	0.838999i	$0.316859\pi$
$564$		0			0
$565$	22.9637			0.966088
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.7152			−0.491129			−0.245564	−	0.969380i	$-0.578973\pi$
$569$	−11.7152			−0.491129			−0.245564	+	0.969380i	$0.578973\pi$
$570$		0			0
$571$	10.0973			0.422558			0.211279	−	0.977426i	$-0.432237\pi$
$571$	10.0973			0.422558			0.211279	+	0.977426i	$0.432237\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7.83551			0.326763
$576$		0			0
$577$	4.92842	+	8.53628i	0.205173	+	0.355370i	0.950188	−	0.311678i	$-0.100891\pi$
$577$	4.92842	+	8.53628i	0.205173	+	0.355370i	−0.745015	+	0.667048i	$0.767558\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	7.31801	−	20.4087i	0.303602	−	0.846695i
$582$		0			0
$583$	8.59547			0.355988
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.2506	−	17.7546i	−0.423089	−	0.732812i	0.573151	−	0.819450i	$-0.305721\pi$
$587$	−10.2506	−	17.7546i	−0.423089	−	0.732812i	−0.996240	+	0.0866378i	$0.972388\pi$
$588$		0			0
$589$	1.74603	−	3.02421i	0.0719438	−	0.124610i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.94458	+	8.56427i	−0.203050	+	0.351692i	−0.949510	−	0.313738i	$-0.898419\pi$
$593$	−4.94458	+	8.56427i	−0.203050	+	0.351692i	0.746460	+	0.665430i	$0.231752\pi$
$594$		0			0
$595$	−18.1760	+	3.29446i	−0.745145	+	0.135060i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.34263			−0.259153			−0.129576	−	0.991569i	$-0.541362\pi$
$599$	−6.34263			−0.259153			−0.129576	+	0.991569i	$0.541362\pi$
$600$		0			0
$601$	−7.74469	−	13.4142i	−0.315913	−	0.547177i	0.663719	−	0.747982i	$-0.268977\pi$
$601$	−7.74469	−	13.4142i	−0.315913	−	0.547177i	−0.979631	+	0.200806i	$0.935644\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	12.3069	−	21.3162i	0.500347	−	0.866627i
$606$		0			0
$607$	1.07942	+	1.86962i	0.0438125	+	0.0758854i	0.887100	−	0.461577i	$-0.152716\pi$
$607$	1.07942	+	1.86962i	0.0438125	+	0.0758854i	−0.843288	+	0.537463i	$0.819383\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.01431	+	5.22094i	−0.121946	+	0.211217i
$612$		0			0
$613$	0.944844	+	1.63652i	0.0381619	+	0.0660983i	0.884476	−	0.466587i	$-0.154516\pi$
$613$	0.944844	+	1.63652i	0.0381619	+	0.0660983i	−0.846314	+	0.532685i	$0.821183\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.91093	+	13.7021i	−0.318482	+	0.551627i	−0.980172	−	0.198151i	$-0.936506\pi$
$617$	−7.91093	+	13.7021i	−0.318482	+	0.551627i	0.661689	+	0.749778i	$0.269840\pi$
$618$		0			0
$619$	3.87742	−	6.71589i	0.155847	−	0.269935i	−0.777520	−	0.628858i	$-0.783523\pi$
$619$	3.87742	−	6.71589i	0.155847	−	0.269935i	0.933367	+	0.358923i	$0.116856\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	33.1576	−	6.00992i	1.32843	−	0.240782i
$624$		0			0
$625$	14.8809	+	25.7744i	0.595234	+	1.03098i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−17.5299			−0.698963
$630$		0			0
$631$	39.7148			1.58102			0.790511	−	0.612448i	$-0.209815\pi$
$631$	39.7148			1.58102			0.790511	+	0.612448i	$0.209815\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.87485	+	11.9076i	0.272820	+	0.472538i
$636$		0			0
$637$	−4.94356	−	4.06834i	−0.195871	−	0.161194i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.4289	+	26.7237i	−0.609406	+	1.05552i	0.381932	+	0.924190i	$0.375259\pi$
$641$	−15.4289	+	26.7237i	−0.609406	+	1.05552i	−0.991338	+	0.131332i	$0.958075\pi$
$642$		0			0
$643$	−8.93807	+	15.4812i	−0.352483	+	0.610518i	−0.986684	−	0.162650i	$-0.947996\pi$
$643$	−8.93807	+	15.4812i	−0.352483	+	0.610518i	0.634201	+	0.773168i	$0.281329\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.3928	+	23.1969i	0.526524	+	0.911966i	0.999522	+	0.0309026i	$0.00983818\pi$
$647$	13.3928	+	23.1969i	0.526524	+	0.911966i	−0.472999	+	0.881063i	$0.656828\pi$
$648$		0			0
$649$	2.75582	−	4.77322i	0.108175	−	0.187365i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.2093	+	22.8792i	0.516919	+	0.895331i	0.999807	+	0.0196482i	$0.00625463\pi$
$653$	13.2093	+	22.8792i	0.516919	+	0.895331i	−0.482888	+	0.875682i	$0.660412\pi$
$654$		0			0
$655$	−27.2119	+	47.1324i	−1.06326	+	1.84161i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	19.3473	+	33.5105i	0.753664	+	1.30538i	0.946036	+	0.324062i	$0.105049\pi$
$659$	19.3473	+	33.5105i	0.753664	+	1.30538i	−0.192372	+	0.981322i	$0.561618\pi$
$660$		0			0
$661$	−7.90004			−0.307276			−0.153638	−	0.988127i	$-0.549099\pi$
$661$	−7.90004			−0.307276			−0.153638	+	0.988127i	$0.549099\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.72292	−	6.75457i	−0.221925	−	0.261931i
$666$		0			0
$667$	2.53802	−	4.39599i	0.0982727	−	0.170213i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.31651	−	10.9405i	0.243846	−	0.422354i
$672$		0			0
$673$	0.777686	+	1.34699i	0.0299776	+	0.0519227i	0.880625	−	0.473814i	$-0.157123\pi$
$673$	0.777686	+	1.34699i	0.0299776	+	0.0519227i	−0.850647	+	0.525737i	$0.823790\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.1811			1.12152			0.560761	−	0.827978i	$-0.310509\pi$
$677$	29.1811			1.12152			0.560761	+	0.827978i	$0.310509\pi$
$678$		0			0
$679$	15.1266	−	42.1854i	0.580504	−	1.61893i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	17.9993	+	31.1757i	0.688723	+	1.19290i	0.972251	+	0.233939i	$0.0751617\pi$
$683$	17.9993	+	31.1757i	0.688723	+	1.19290i	−0.283528	+	0.958964i	$0.591505\pi$
$684$		0			0
$685$	51.1286			1.95352
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.24320			0.275944
$690$		0			0
$691$	43.8664			1.66876			0.834378	−	0.551193i	$-0.185827\pi$
$691$	43.8664			1.66876			0.834378	+	0.551193i	$0.185827\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.1139			−0.459507
$696$		0			0
$697$	−4.55401			−0.172495
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−46.5873			−1.75958			−0.879790	−	0.475363i	$-0.842317\pi$
$701$	−46.5873			−1.75958			−0.879790	+	0.475363i	$0.842317\pi$
$702$		0			0
$703$	−4.20071	−	7.27585i	−0.158433	−	0.274414i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.12576	−	1.47282i	0.305601	−	0.0553911i
$708$		0			0
$709$	18.4805			0.694051			0.347026	−	0.937856i	$-0.387192\pi$
$709$	18.4805			0.694051			0.347026	+	0.937856i	$0.387192\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−8.00447	−	13.8641i	−0.299770	−	0.519216i
$714$		0			0
$715$	−1.24387	+	2.15444i	−0.0465180	+	0.0805715i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	19.7978	−	34.2908i	0.738333	−	1.27883i	−0.214913	−	0.976633i	$-0.568947\pi$
$719$	19.7978	−	34.2908i	0.738333	−	1.27883i	0.953246	−	0.302197i	$-0.0977199\pi$
$720$		0			0
$721$	4.30199	−	11.9975i	0.160214	−	0.446810i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.06147			−0.0394219
$726$		0			0
$727$	11.9170	+	20.6409i	0.441978	+	0.765528i	0.997836	−	0.0657487i	$-0.0209436\pi$
$727$	11.9170	+	20.6409i	0.441978	+	0.765528i	−0.555858	+	0.831277i	$0.687610\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.21683	−	3.83965i	0.0819923	−	0.142015i
$732$		0			0
$733$	8.02036	+	13.8917i	0.296239	+	0.513101i	0.975272	−	0.221007i	$-0.0709343\pi$
$733$	8.02036	+	13.8917i	0.296239	+	0.513101i	−0.679034	+	0.734107i	$0.737601\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.62627	+	14.9411i	−0.317753	+	0.550364i
$738$		0			0
$739$	2.74335	+	4.75163i	0.100916	+	0.174792i	0.912062	−	0.410052i	$-0.134489\pi$
$739$	2.74335	+	4.75163i	0.100916	+	0.174792i	−0.811146	+	0.584843i	$0.801156\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.182662	−	0.316380i	0.00670122	−	0.0116069i	−0.862655	−	0.505792i	$-0.831200\pi$
$743$	0.182662	−	0.316380i	0.00670122	−	0.0116069i	0.869357	+	0.494185i	$0.164534\pi$
$744$		0			0
$745$	−7.28913	+	12.6251i	−0.267053	+	0.462549i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	37.1094	−	6.72620i	1.35595	−	0.245770i
$750$		0			0
$751$	5.67855	+	9.83554i	0.207213	+	0.358904i	0.950836	−	0.309696i	$-0.100227\pi$
$751$	5.67855	+	9.83554i	0.207213	+	0.358904i	−0.743622	+	0.668600i	$0.766894\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21.5902			−0.785746
$756$		0			0
$757$	−27.4794			−0.998757			−0.499378	−	0.866384i	$-0.666438\pi$
$757$	−27.4794			−0.998757			−0.499378	+	0.866384i	$0.666438\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.0210882	−	0.0365259i	−0.000764448	−	0.00132406i	0.865643	−	0.500662i	$-0.166910\pi$
$761$	−0.0210882	−	0.0365259i	−0.000764448	−	0.00132406i	−0.866407	+	0.499338i	$0.833577\pi$
$762$		0			0
$763$	5.26466	−	14.6822i	0.190593	−	0.531532i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.32227	−	4.02228i	0.0838522	−	0.145236i
$768$		0			0
$769$	−13.3233	+	23.0766i	−0.480450	+	0.832164i	−0.999748	−	0.0224290i	$-0.992860\pi$
$769$	−13.3233	+	23.0766i	−0.480450	+	0.832164i	0.519298	+	0.854593i	$0.326193\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−22.6206	−	39.1800i	−0.813605	−	1.40921i	−0.910325	−	0.413894i	$-0.864169\pi$
$773$	−22.6206	−	39.1800i	−0.813605	−	1.40921i	0.0967202	−	0.995312i	$-0.469165\pi$
$774$		0			0
$775$	−1.67384	+	2.89918i	−0.0601261	+	0.104141i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.09128	−	1.89016i	−0.0390993	−	0.0677219i
$780$		0			0
$781$	−5.23509	+	9.06745i	−0.187326	+	0.324459i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.3521	+	17.9304i	0.369483	+	0.639964i
$786$		0			0
$787$	36.2843			1.29340			0.646698	−	0.762746i	$-0.276149\pi$
$787$	36.2843			1.29340			0.646698	+	0.762746i	$0.276149\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.8556	+	4.32390i	−0.848206	+	0.153740i
$792$		0			0
$793$	5.32278	−	9.21932i	0.189017	−	0.327388i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.35398	−	11.0054i	0.225069	−	0.389832i	−0.731271	−	0.682087i	$-0.761072\pi$
$797$	6.35398	−	11.0054i	0.225069	−	0.389832i	0.956340	+	0.292256i	$0.0944058\pi$
$798$		0			0
$799$	−9.18193	−	15.9036i	−0.324833	−	0.562628i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10.9385			0.386012
$804$		0			0
$805$	−39.9350	+	7.23835i	−1.40752	+	0.255118i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	21.6398	+	37.4812i	0.760815	+	1.31777i	0.942431	+	0.334401i	$0.108534\pi$
$809$	21.6398	+	37.4812i	0.760815	+	1.31777i	−0.181616	+	0.983370i	$0.558133\pi$
$810$		0			0
$811$	15.4941			0.544071			0.272036	−	0.962287i	$-0.412303\pi$
$811$	15.4941			0.544071			0.272036	+	0.962287i	$0.412303\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.12026			−0.179355
$816$		0			0
$817$	2.12488			0.0743402
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−36.7704			−1.28330			−0.641649	−	0.766999i	$-0.721749\pi$
$821$	−36.7704			−1.28330			−0.641649	+	0.766999i	$0.721749\pi$
$822$		0			0
$823$	7.13422			0.248683			0.124342	−	0.992239i	$-0.460318\pi$
$823$	7.13422			0.248683			0.124342	+	0.992239i	$0.460318\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	40.7236			1.41610			0.708050	−	0.706162i	$-0.249575\pi$
$827$	40.7236			1.41610			0.708050	+	0.706162i	$0.249575\pi$
$828$		0			0
$829$	−15.0794	−	26.1183i	−0.523730	−	0.907127i	−0.999618	−	0.0276214i	$-0.991207\pi$
$829$	−15.0794	−	26.1183i	−0.523730	−	0.907127i	0.475888	−	0.879506i	$-0.342127\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	18.2617	−	6.84484i	0.632729	−	0.237160i
$834$		0			0
$835$	−41.6981			−1.44302
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.37871	−	7.58415i	−0.151170	−	0.261834i	0.780488	−	0.625171i	$-0.214971\pi$
$839$	−4.37871	−	7.58415i	−0.151170	−	0.261834i	−0.931658	+	0.363337i	$0.881637\pi$
$840$		0			0
$841$	14.1562	−	24.5192i	0.488144	−	0.845490i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	15.2408	−	26.3979i	0.524301	−	0.908115i
$846$		0			0
$847$	−8.77122	+	24.4614i	−0.301383	+	0.840505i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−38.5154			−1.32029
$852$		0			0
$853$	−22.8129	−	39.5130i	−0.781098	−	1.35290i	−0.931303	−	0.364246i	$-0.881327\pi$
$853$	−22.8129	−	39.5130i	−0.781098	−	1.35290i	0.150205	−	0.988655i	$-0.452007\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−28.3497	+	49.1030i	−0.968406	+	1.67733i	−0.268233	+	0.963354i	$0.586440\pi$
$857$	−28.3497	+	49.1030i	−0.968406	+	1.67733i	−0.700172	+	0.713974i	$0.746893\pi$
$858$		0			0
$859$	5.29287	+	9.16752i	0.180590	+	0.312792i	0.942082	−	0.335383i	$-0.108866\pi$
$859$	5.29287	+	9.16752i	0.180590	+	0.312792i	−0.761491	+	0.648175i	$0.775533\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	20.3124	−	35.1821i	0.691442	−	1.19761i	−0.279923	−	0.960022i	$-0.590309\pi$
$863$	20.3124	−	35.1821i	0.691442	−	1.19761i	0.971365	−	0.237591i	$-0.0763577\pi$
$864$		0			0
$865$	−25.6471	−	44.4221i	−0.872027	−	1.51040i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	5.07265	−	8.78608i	0.172078	−	0.298047i
$870$		0			0
$871$	−7.26916	+	12.5905i	−0.246306	+	0.426614i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.9439	−	18.8180i	−0.539002	−	0.636166i
$876$		0			0
$877$	−6.01744	−	10.4225i	−0.203195	−	0.351943i	0.746361	−	0.665541i	$-0.231799\pi$
$877$	−6.01744	−	10.4225i	−0.203195	−	0.351943i	−0.949556	+	0.313597i	$0.898466\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.07911			−0.204811			−0.102405	−	0.994743i	$-0.532654\pi$
$881$	−6.07911			−0.204811			−0.102405	+	0.994743i	$0.532654\pi$
$882$		0			0
$883$	11.6345			0.391532			0.195766	−	0.980651i	$-0.437281\pi$
$883$	11.6345			0.391532			0.195766	+	0.980651i	$0.437281\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.243915	−	0.422473i	−0.00818986	−	0.0141853i	0.861901	−	0.507076i	$-0.169274\pi$
$887$	−0.243915	−	0.422473i	−0.00818986	−	0.0141853i	−0.870091	+	0.492891i	$0.835940\pi$
$888$		0			0
$889$	−9.38398	−	11.0756i	−0.314729	−	0.371463i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.40056	−	7.62199i	0.147259	−	0.255060i
$894$		0			0
$895$	−1.56480	+	2.71032i	−0.0523056	+	0.0905959i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.08436	+	1.87816i	0.0361653	+	0.0626402i
$900$		0			0
$901$	−11.0318	+	19.1076i	−0.367523	+	0.636568i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.3130	−	31.7190i	−0.608744	−	1.05437i
$906$		0			0
$907$	8.02889	−	13.9064i	0.266595	−	0.461756i	−0.701385	−	0.712782i	$-0.747435\pi$
$907$	8.02889	−	13.9064i	0.266595	−	0.461756i	0.967980	+	0.251027i	$0.0807681\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−19.9439	−	34.5438i	−0.660769	−	1.14449i	−0.980414	−	0.196949i	$-0.936897\pi$
$911$	−19.9439	−	34.5438i	−0.660769	−	1.14449i	0.319645	−	0.947538i	$-0.396437\pi$
$912$		0			0
$913$	8.89431			0.294359
$914$		0			0
$915$		0			0
$916$		0			0
$917$	19.3941	−	54.0868i	0.640449	−	1.78610i
$918$		0			0
$919$	−8.47711	+	14.6828i	−0.279634	+	0.484340i	−0.971294	−	0.237883i	$-0.923546\pi$
$919$	−8.47711	+	14.6828i	−0.279634	+	0.484340i	0.691660	+	0.722224i	$0.256880\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.41149	+	7.64092i	−0.145206	+	0.251504i
$924$		0			0
$925$	4.02704	+	6.97504i	0.132408	+	0.229338i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.7179			0.515688			0.257844	−	0.966187i	$-0.416988\pi$
$929$	15.7179			0.515688			0.257844	+	0.966187i	$0.416988\pi$
$930$		0			0
$931$	7.21704	+	5.93933i	0.236529	+	0.194654i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.78896	−	6.56267i	−0.123912	−	0.214622i
$936$		0			0
$937$	−21.0501			−0.687675			−0.343838	−	0.939029i	$-0.611727\pi$
$937$	−21.0501			−0.687675			−0.343838	+	0.939029i	$0.611727\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−31.3571			−1.02221			−0.511106	−	0.859518i	$-0.670764\pi$
$941$	−31.3571			−1.02221			−0.511106	+	0.859518i	$0.670764\pi$
$942$		0			0
$943$	−10.0057			−0.325832
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.6365			0.508119			0.254059	−	0.967189i	$-0.418234\pi$
$947$	15.6365			0.508119			0.254059	+	0.967189i	$0.418234\pi$
$948$		0			0
$949$	9.21764			0.299217
$950$		0			0
$951$		0			0
$952$		0			0
$953$	27.7543			0.899051			0.449525	−	0.893268i	$-0.351593\pi$
$953$	27.7543			0.899051			0.449525	+	0.893268i	$0.351593\pi$
$954$		0			0
$955$	22.4907	+	38.9551i	0.727783	+	1.26056i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−53.1144	+	9.62715i	−1.71515	+	0.310877i
$960$		0			0
$961$	−24.1603			−0.779363
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−29.0461	−	50.3093i	−0.935026	−	1.61951i
$966$		0			0
$967$	13.6893	−	23.7105i	0.440217	−	0.762479i	−0.557488	−	0.830185i	$-0.688235\pi$
$967$	13.6893	−	23.7105i	0.440217	−	0.762479i	0.997705	+	0.0677063i	$0.0215681\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.88209	−	6.72398i	0.124582	−	0.215783i	−0.796987	−	0.603996i	$-0.793574\pi$
$971$	3.88209	−	6.72398i	0.124582	−	0.215783i	0.921570	+	0.388213i	$0.126908\pi$
$972$		0			0
$973$	12.5844	−	2.28096i	0.403437	−	0.0731244i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.3134			−0.585897			−0.292948	−	0.956128i	$-0.594636\pi$
$977$	−18.3134			−0.585897			−0.292948	+	0.956128i	$0.594636\pi$
$978$		0			0
$979$	6.91200	+	11.9719i	0.220908	+	0.382625i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−8.09420	+	14.0196i	−0.258165	+	0.447155i	−0.965750	−	0.259473i	$-0.916451\pi$
$983$	−8.09420	+	14.0196i	−0.258165	+	0.447155i	0.707585	+	0.706628i	$0.249784\pi$
$984$		0			0
$985$	−7.90811	−	13.6972i	−0.251973	−	0.436431i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.87065	−	8.43621i	0.154878	−	0.268256i
$990$		0			0
$991$	−19.1897	−	33.2376i	−0.609582	−	1.05583i	−0.991309	−	0.131552i	$-0.958004\pi$
$991$	−19.1897	−	33.2376i	−0.609582	−	1.05583i	0.381727	−	0.924275i	$-0.375329\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.59481	−	16.6187i	0.304176	−	0.526848i
$996$		0			0
$997$	11.5661	−	20.0331i	0.366303	−	0.634456i	−0.622681	−	0.782476i	$-0.713957\pi$
$997$	11.5661	−	20.0331i	0.366303	−	0.634456i	0.988984	+	0.148020i	$0.0472900\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.i.m.2053.1		8
3.2	odd	2		2268.2.i.l.2053.4		8
7.4	even	3		2268.2.l.l.109.4		8
9.2	odd	6		2268.2.l.m.541.1		8
9.4	even	3		2268.2.k.d.1297.1	yes	8
9.5	odd	6		2268.2.k.c.1297.4	✓	8
9.7	even	3		2268.2.l.l.541.4		8
21.11	odd	6		2268.2.l.m.109.1		8
63.4	even	3		2268.2.k.d.1621.1	yes	8
63.11	odd	6		2268.2.i.l.865.4		8
63.25	even	3	inner	2268.2.i.m.865.1		8
63.32	odd	6		2268.2.k.c.1621.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2268.2.i.l.865.4		8	63.11	odd	6
2268.2.i.l.2053.4		8	3.2	odd	2
2268.2.i.m.865.1		8	63.25	even	3	inner
2268.2.i.m.2053.1		8	1.1	even	1	trivial
2268.2.k.c.1297.4	✓	8	9.5	odd	6
2268.2.k.c.1621.4	yes	8	63.32	odd	6
2268.2.k.d.1297.1	yes	8	9.4	even	3
2268.2.k.d.1621.1	yes	8	63.4	even	3
2268.2.l.l.109.4		8	7.4	even	3
2268.2.l.l.541.4		8	9.7	even	3
2268.2.l.m.109.1		8	21.11	odd	6
2268.2.l.m.541.1		8	9.2	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.25300 - 2.17026i) q^{5} +(1.71031 + 2.01862i) q^{7} +O(q^{10})\)	\(q+(-1.25300 - 2.17026i) q^{5} +(1.71031 + 2.01862i) q^{7} +(-0.542689 + 0.939965i) q^{11} +(-0.457311 + 0.792086i) q^{13} +(-1.39302 - 2.41278i) q^{17} +(0.667623 - 1.15636i) q^{19} +(-3.06064 - 5.30119i) q^{23} +(-0.640021 + 1.10855i) q^{25} +(0.414622 + 0.718147i) q^{29} +2.61529 q^{31} +(2.23791 - 6.24116i) q^{35} +(3.14602 - 5.44907i) q^{37} +(0.817290 - 1.41559i) q^{41} +(0.795689 + 1.37817i) q^{43} +6.59138 q^{47} +(-1.14967 + 6.90495i) q^{49} +(-3.95967 - 6.85835i) q^{53} +2.71996 q^{55} -5.07809 q^{59} -11.6393 q^{61} +2.29204 q^{65} +15.8954 q^{67} +9.64658 q^{71} +(-5.03904 - 8.72788i) q^{73} +(-2.82560 + 0.512149i) q^{77} -9.34725 q^{79} +(-4.09733 - 7.09679i) q^{83} +(-3.49091 + 6.04644i) q^{85} +(6.36829 - 11.0302i) q^{89} +(-2.38107 + 0.431576i) q^{91} -3.34613 q^{95} +(-8.46931 - 14.6693i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{5} + q^{7}+O(q^{10}) \) 8 * q + 2 * q^5 + q^7	\( 8 q + 2 q^{5} + q^{7} - 5 q^{11} - 3 q^{13} - 2 q^{17} - 8 q^{19} - 2 q^{23} - 8 q^{25} + 2 q^{29} - 11 q^{35} + 4 q^{37} + 3 q^{41} - 5 q^{43} + 30 q^{47} - 19 q^{49} + 24 q^{53} + 16 q^{55} + 20 q^{59} + 24 q^{61} - 24 q^{65} + 14 q^{67} + 22 q^{71} - 10 q^{73} + 11 q^{77} - 35 q^{83} + 13 q^{85} + 18 q^{89} - 9 q^{91} - 20 q^{95} - 19 q^{97}+O(q^{100}) \) 8 * q + 2 * q^5 + q^7 - 5 * q^11 - 3 * q^13 - 2 * q^17 - 8 * q^19 - 2 * q^23 - 8 * q^25 + 2 * q^29 - 11 * q^35 + 4 * q^37 + 3 * q^41 - 5 * q^43 + 30 * q^47 - 19 * q^49 + 24 * q^53 + 16 * q^55 + 20 * q^59 + 24 * q^61 - 24 * q^65 + 14 * q^67 + 22 * q^71 - 10 * q^73 + 11 * q^77 - 35 * q^83 + 13 * q^85 + 18 * q^89 - 9 * q^91 - 20 * q^95 - 19 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more