LMFDB - Embedded newform 900.2.w.c.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(109,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("900.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.w (of order $10$, degree $4$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	900.109
Dual form			900.2.w.c.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64247 - 1.51733i) q^{5} +3.78808i q^{7} +O(q^{10})$	$q+(1.64247 - 1.51733i) q^{5} +3.78808i q^{7} +(-0.653426 - 0.474742i) q^{11} +(2.79168 + 3.84242i) q^{13} +(1.09262 + 0.355012i) q^{17} +(-0.00463870 + 0.0142765i) q^{19} +(-3.68422 + 5.07089i) q^{23} +(0.395416 - 4.98434i) q^{25} +(1.14365 + 3.51978i) q^{29} +(-0.488893 + 1.50466i) q^{31} +(5.74777 + 6.22181i) q^{35} +(5.02074 + 6.91045i) q^{37} +(9.30279 - 6.75887i) q^{41} -10.2458i q^{43} +(-0.500524 + 0.162630i) q^{47} -7.34957 q^{49} +(2.80539 - 0.911527i) q^{53} +(-1.79357 + 0.211714i) q^{55} +(-9.25803 + 6.72635i) q^{59} +(-2.54203 - 1.84689i) q^{61} +(10.4155 + 2.07516i) q^{65} +(12.6312 + 4.10412i) q^{67} +(1.51826 + 4.67271i) q^{71} +(2.75001 - 3.78507i) q^{73} +(1.79836 - 2.47523i) q^{77} +(-2.86507 - 8.81777i) q^{79} +(1.35402 + 0.439947i) q^{83} +(2.33326 - 1.07476i) q^{85} +(13.0306 + 9.46730i) q^{89} +(-14.5554 + 10.5751i) q^{91} +(0.0140432 + 0.0304871i) q^{95} +(-7.66744 + 2.49130i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5}+O(q^{10}) $ 24 * q + 2 * q^5	$ 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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
$5$	1.64247	−	1.51733i	0.734535	−	0.678571i
$5$	1.64247	−	1.51733i	0.734535	−	0.678571i
$6$		0			0
$7$			3.78808i			1.43176i	0.698223	+	0.715880i	$0.253974\pi$
$7$			3.78808i			1.43176i	−0.698223	+	0.715880i	$0.746026\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.653426	−	0.474742i	−0.197015	−	0.143140i	0.484904	−	0.874567i	$-0.338855\pi$
$11$	−0.653426	−	0.474742i	−0.197015	−	0.143140i	−0.681919	+	0.731427i	$0.738855\pi$
$12$		0			0
$13$	2.79168	+	3.84242i	0.774274	+	1.06570i	0.995891	+	0.0905626i	$0.0288665\pi$
$13$	2.79168	+	3.84242i	0.774274	+	1.06570i	−0.221617	+	0.975134i	$0.571133\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.09262	+	0.355012i	0.264998	+	0.0861032i	0.438503	−	0.898730i	$-0.355509\pi$
$17$	1.09262	+	0.355012i	0.264998	+	0.0861032i	−0.173504	+	0.984833i	$0.555509\pi$
$18$		0			0
$19$	−0.00463870	+	0.0142765i	−0.00106419	+	0.00327524i	−0.951587	−	0.307379i	$-0.900548\pi$
$19$	−0.00463870	+	0.0142765i	−0.00106419	+	0.00327524i	0.950523	+	0.310654i	$0.100548\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.68422	+	5.07089i	−0.768213	+	1.05735i	0.228274	+	0.973597i	$0.426692\pi$
$23$	−3.68422	+	5.07089i	−0.768213	+	1.05735i	−0.996486	+	0.0837569i	$0.973308\pi$
$24$		0			0
$25$	0.395416	−	4.98434i	0.0790832	−	0.996868i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.14365	+	3.51978i	0.212370	+	0.653607i	0.999330	+	0.0366030i	$0.0116537\pi$
$29$	1.14365	+	3.51978i	0.212370	+	0.653607i	−0.786960	+	0.617004i	$0.788346\pi$
$30$		0			0
$31$	−0.488893	+	1.50466i	−0.0878078	+	0.270245i	−0.985313	−	0.170760i	$-0.945378\pi$
$31$	−0.488893	+	1.50466i	−0.0878078	+	0.270245i	0.897505	+	0.441005i	$0.145378\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.74777	+	6.22181i	0.971551	+	1.05168i
$36$		0			0
$37$	5.02074	+	6.91045i	0.825404	+	1.13607i	0.988761	+	0.149504i	$0.0477678\pi$
$37$	5.02074	+	6.91045i	0.825404	+	1.13607i	−0.163357	+	0.986567i	$0.552232\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	9.30279	−	6.75887i	1.45285	−	1.05556i	0.467697	−	0.883889i	$-0.345084\pi$
$41$	9.30279	−	6.75887i	1.45285	−	1.05556i	0.985155	−	0.171669i	$-0.0549160\pi$
$42$		0			0
$43$		−	10.2458i		−	1.56247i	−0.624238	−	0.781234i	$-0.714591\pi$
$43$		−	10.2458i		−	1.56247i	0.624238	−	0.781234i	$-0.285409\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.500524	+	0.162630i	−0.0730090	+	0.0237221i	−0.345294	−	0.938495i	$-0.612221\pi$
$47$	−0.500524	+	0.162630i	−0.0730090	+	0.0237221i	0.272285	+	0.962217i	$0.412221\pi$
$48$		0			0
$49$	−7.34957			−1.04994
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.80539	−	0.911527i	0.385350	−	0.125208i	−0.109934	−	0.993939i	$-0.535064\pi$
$53$	2.80539	−	0.911527i	0.385350	−	0.125208i	0.495284	+	0.868731i	$0.335064\pi$
$54$		0			0
$55$	−1.79357	+	0.211714i	−0.241845	+	0.0285475i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.25803	+	6.72635i	−1.20529	+	0.875696i	−0.994795	−	0.101898i	$-0.967508\pi$
$59$	−9.25803	+	6.72635i	−1.20529	+	0.875696i	−0.210498	+	0.977594i	$0.567508\pi$
$60$		0			0
$61$	−2.54203	−	1.84689i	−0.325473	−	0.236470i	0.413034	−	0.910716i	$-0.364469\pi$
$61$	−2.54203	−	1.84689i	−0.325473	−	0.236470i	−0.738507	+	0.674245i	$0.764469\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.4155	+	2.07516i	1.29188	+	0.257392i
$66$		0			0
$67$	12.6312	+	4.10412i	1.54314	+	0.501398i	0.952241	−	0.305346i	$-0.0987722\pi$
$67$	12.6312	+	4.10412i	1.54314	+	0.501398i	0.590901	+	0.806744i	$0.298772\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.51826	+	4.67271i	0.180184	+	0.554549i	0.999832	−	0.0183179i	$-0.00583110\pi$
$71$	1.51826	+	4.67271i	0.180184	+	0.554549i	−0.819648	+	0.572867i	$0.805831\pi$
$72$		0			0
$73$	2.75001	−	3.78507i	0.321865	−	0.443009i	−0.617171	−	0.786829i	$-0.711721\pi$
$73$	2.75001	−	3.78507i	0.321865	−	0.443009i	0.939035	+	0.343820i	$0.111721\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.79836	−	2.47523i	0.204942	−	0.282079i
$78$		0			0
$79$	−2.86507	−	8.81777i	−0.322345	−	0.992076i	−0.972625	−	0.232381i	$-0.925348\pi$
$79$	−2.86507	−	8.81777i	−0.322345	−	0.992076i	0.650280	−	0.759695i	$-0.274652\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.35402	+	0.439947i	0.148623	+	0.0482904i	0.382384	−	0.924004i	$-0.375103\pi$
$83$	1.35402	+	0.439947i	0.148623	+	0.0482904i	−0.233761	+	0.972294i	$0.575103\pi$
$84$		0			0
$85$	2.33326	−	1.07476i	0.253078	−	0.116574i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.0306	+	9.46730i	1.38124	+	1.00353i	0.996763	+	0.0803985i	$0.0256193\pi$
$89$	13.0306	+	9.46730i	1.38124	+	1.00353i	0.384480	+	0.923133i	$0.374381\pi$
$90$		0			0
$91$	−14.5554	+	10.5751i	−1.52582	+	1.10857i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.0140432	+	0.0304871i	0.00144080	+	0.00312791i
$96$		0			0
$97$	−7.66744	+	2.49130i	−0.778511	+	0.252954i	−0.671204	−	0.741272i	$-0.734223\pi$
$97$	−7.66744	+	2.49130i	−0.778511	+	0.252954i	−0.107307	+	0.994226i	$0.534223\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.6496			−1.15918			−0.579590	−	0.814908i	$-0.696787\pi$
$101$	−11.6496			−1.15918			−0.579590	+	0.814908i	$0.696787\pi$
$102$		0			0
$103$	17.9216	−	5.82307i	1.76587	−	0.573764i	0.768084	−	0.640349i	$-0.221210\pi$
$103$	17.9216	−	5.82307i	1.76587	−	0.573764i	0.997781	+	0.0665845i	$0.0212102\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			14.3957i			1.39168i	0.718195	+	0.695842i	$0.244969\pi$
$107$			14.3957i			1.39168i	−0.718195	+	0.695842i	$0.755031\pi$
$108$		0			0
$109$	−4.66144	+	3.38673i	−0.446485	+	0.324390i	−0.788206	−	0.615411i	$-0.788990\pi$
$109$	−4.66144	+	3.38673i	−0.446485	+	0.324390i	0.341722	+	0.939801i	$0.388990\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.5368	−	14.5027i	−0.991223	−	1.36430i	−0.930559	−	0.366143i	$-0.880678\pi$
$113$	−10.5368	−	14.5027i	−0.991223	−	1.36430i	−0.0606641	−	0.998158i	$-0.519322\pi$
$114$		0			0
$115$	1.64300	+	13.9190i	0.153211	+	1.29795i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.34482	+	4.13892i	−0.123279	+	0.379414i
$120$		0			0
$121$	−3.19760	−	9.84120i	−0.290691	−	0.894655i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.91343	−	8.78661i	−0.618356	−	0.785898i
$126$		0			0
$127$	−1.34592	+	1.85250i	−0.119431	+	0.164382i	−0.864547	−	0.502553i	$-0.832394\pi$
$127$	−1.34592	+	1.85250i	−0.119431	+	0.164382i	0.745116	+	0.666935i	$0.232394\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.17840	−	6.70444i	0.190328	−	0.585769i	−0.809671	−	0.586883i	$-0.800355\pi$
$131$	2.17840	−	6.70444i	0.190328	−	0.585769i	0.999999	+	0.00111420i	$0.000354661\pi$
$132$		0			0
$133$	−0.0540804	−	0.0175718i	−0.00468937	−	0.00152367i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.8918	−	17.7441i	−1.10142	−	1.51598i	−0.833484	−	0.552544i	$-0.813657\pi$
$137$	−12.8918	−	17.7441i	−1.10142	−	1.51598i	−0.267940	−	0.963436i	$-0.586343\pi$
$138$		0			0
$139$	7.86171	+	5.71187i	0.666822	+	0.484474i	0.868960	−	0.494883i	$-0.164789\pi$
$139$	7.86171	+	5.71187i	0.666822	+	0.484474i	−0.202138	+	0.979357i	$0.564789\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	3.83607i		−	0.320788i
$144$		0			0
$145$	7.21907	+	4.04584i	0.599512	+	0.335989i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−13.9712			−1.14457			−0.572284	−	0.820056i	$-0.693942\pi$
$149$	−13.9712			−1.14457			−0.572284	+	0.820056i	$0.693942\pi$
$150$		0			0
$151$	−20.1871			−1.64280			−0.821400	−	0.570352i	$-0.806807\pi$
$151$	−20.1871			−1.64280			−0.821400	+	0.570352i	$0.806807\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.48007	+	3.21317i	0.118882	+	0.258088i
$156$		0			0
$157$			7.76546i			0.619751i	0.950777	+	0.309876i	$0.100287\pi$
$157$			7.76546i			0.619751i	−0.950777	+	0.309876i	$0.899713\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−19.2090	−	13.9561i	−1.51388	−	1.09990i
$162$		0			0
$163$	−8.16480	−	11.2379i	−0.639517	−	0.880219i	0.359073	−	0.933310i	$-0.383093\pi$
$163$	−8.16480	−	11.2379i	−0.639517	−	0.880219i	−0.998590	+	0.0530901i	$0.983093\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.75604	+	0.895491i	0.213269	+	0.0692952i	0.413703	−	0.910412i	$-0.364235\pi$
$167$	2.75604	+	0.895491i	0.213269	+	0.0692952i	−0.200434	+	0.979707i	$0.564235\pi$
$168$		0			0
$169$	−2.95350	+	9.08992i	−0.227192	+	0.699225i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.95423	−	12.3244i	0.680777	−	0.937009i	−0.319166	−	0.947699i	$-0.603403\pi$
$173$	8.95423	−	12.3244i	0.680777	−	0.937009i	0.999943	+	0.0106895i	$0.00340264\pi$
$174$		0			0
$175$	18.8811	+	1.49787i	1.42728	+	0.113228i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−7.20182	−	22.1649i	−0.538290	−	1.65669i	−0.736432	−	0.676512i	$-0.763491\pi$
$179$	−7.20182	−	22.1649i	−0.538290	−	1.65669i	0.198142	−	0.980173i	$-0.436509\pi$
$180$		0			0
$181$	5.46913	−	16.8322i	0.406517	−	1.25113i	−0.513105	−	0.858326i	$-0.671505\pi$
$181$	5.46913	−	16.8322i	0.406517	−	1.25113i	0.919622	−	0.392805i	$-0.128495\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	18.7319	+	3.73209i	1.37719	+	0.274389i
$186$		0			0
$187$	−0.545404	−	0.750685i	−0.0398839	−	0.0548955i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.57575	−	5.50411i	0.548162	−	0.398263i	−0.278945	−	0.960307i	$-0.589985\pi$
$191$	7.57575	−	5.50411i	0.548162	−	0.398263i	0.827107	+	0.562044i	$0.189985\pi$
$192$		0			0
$193$		−	18.9309i		−	1.36268i	−0.731969	−	0.681338i	$-0.761398\pi$
$193$		−	18.9309i		−	1.36268i	0.731969	−	0.681338i	$-0.238602\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.17436	+	2.33109i	−0.511152	+	0.166083i	−0.553226	−	0.833031i	$-0.686603\pi$
$197$	−7.17436	+	2.33109i	−0.511152	+	0.166083i	0.0420739	+	0.999114i	$0.486603\pi$
$198$		0			0
$199$	−3.58560			−0.254176			−0.127088	−	0.991891i	$-0.540563\pi$
$199$	−3.58560			−0.254176			−0.127088	+	0.991891i	$0.540563\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−13.3332	+	4.33223i	−0.935808	+	0.304063i
$204$		0			0
$205$	5.02411	−	25.2166i	0.350899	−	1.76121i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.00980868	−	0.00712642i	0.000678480	−	0.000492945i
$210$		0			0
$211$	−1.68674	−	1.22549i	−0.116120	−	0.0843663i	0.528210	−	0.849114i	$-0.322864\pi$
$211$	−1.68674	−	1.22549i	−0.116120	−	0.0843663i	−0.644330	+	0.764748i	$0.722864\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.5462	−	16.8284i	−1.06025	−	1.14769i
$216$		0			0
$217$	−5.69977	−	1.85197i	−0.386926	−	0.125720i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.68613	+	5.18938i	0.113421	+	0.349075i
$222$		0			0
$223$	−8.25091	+	11.3564i	−0.552522	+	0.760481i	−0.990352	−	0.138577i	$-0.955747\pi$
$223$	−8.25091	+	11.3564i	−0.552522	+	0.760481i	0.437830	+	0.899058i	$0.355747\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.48995	−	2.05074i	0.0988915	−	0.136112i	−0.756704	−	0.653758i	$-0.773191\pi$
$227$	1.48995	−	2.05074i	0.0988915	−	0.136112i	0.855595	+	0.517646i	$0.173191\pi$
$228$		0			0
$229$	5.10687	+	15.7173i	0.337472	+	1.03863i	0.965492	+	0.260434i	$0.0838656\pi$
$229$	5.10687	+	15.7173i	0.337472	+	1.03863i	−0.628020	+	0.778197i	$0.716134\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	25.2228	+	8.19539i	1.65240	+	0.536898i	0.979259	−	0.202614i	$-0.0649437\pi$
$233$	25.2228	+	8.19539i	1.65240	+	0.536898i	0.673143	+	0.739512i	$0.264944\pi$
$234$		0			0
$235$	−0.575332	+	1.02658i	−0.0375305	+	0.0669664i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.03839	+	4.38714i	0.390591	+	0.283781i	0.765698	−	0.643201i	$-0.222394\pi$
$239$	6.03839	+	4.38714i	0.390591	+	0.283781i	−0.375107	+	0.926982i	$0.622394\pi$
$240$		0			0
$241$	−8.33107	+	6.05288i	−0.536651	+	0.389900i	−0.822840	−	0.568273i	$-0.807612\pi$
$241$	−8.33107	+	6.05288i	−0.536651	+	0.389900i	0.286189	+	0.958173i	$0.407612\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.0714	+	11.1517i	−0.771216	+	0.712458i
$246$		0			0
$247$	−0.0678060	+	0.0220315i	−0.00431439	+	0.00140183i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−19.5809			−1.23593			−0.617967	−	0.786204i	$-0.712044\pi$
$251$	−19.5809			−1.23593			−0.617967	+	0.786204i	$0.712044\pi$
$252$		0			0
$253$	4.81473	−	1.56440i	0.302699	−	0.0983530i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			5.98030i			0.373041i	0.982451	+	0.186520i	$0.0597210\pi$
$257$			5.98030i			0.373041i	−0.982451	+	0.186520i	$0.940279\pi$
$258$		0			0
$259$	−26.1774	+	19.0190i	−1.62658	+	1.18178i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.56808	−	4.91104i	−0.220017	−	0.302827i	0.684713	−	0.728813i	$-0.259928\pi$
$263$	−3.56808	−	4.91104i	−0.220017	−	0.302827i	−0.904730	+	0.425985i	$0.859928\pi$
$264$		0			0
$265$	3.22469	−	5.75386i	0.198091	−	0.353457i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.97152	−	9.14540i	0.181177	−	0.557605i	−0.818685	−	0.574243i	$-0.805296\pi$
$269$	2.97152	−	9.14540i	0.181177	−	0.557605i	0.999862	+	0.0166382i	$0.00529635\pi$
$270$		0			0
$271$	−9.40263	−	28.9383i	−0.571169	−	1.75788i	−0.648868	−	0.760901i	$-0.724757\pi$
$271$	−9.40263	−	28.9383i	−0.571169	−	1.75788i	0.0776990	−	0.996977i	$-0.475243\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.62465	+	3.06918i	−0.158272	+	0.185078i
$276$		0			0
$277$	−4.23436	+	5.82810i	−0.254418	+	0.350176i	−0.917052	−	0.398767i	$-0.869438\pi$
$277$	−4.23436	+	5.82810i	−0.254418	+	0.350176i	0.662634	+	0.748943i	$0.269438\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.20758	+	28.3380i	−0.549278	+	1.69050i	0.161316	+	0.986903i	$0.448426\pi$
$281$	−9.20758	+	28.3380i	−0.549278	+	1.69050i	−0.710594	+	0.703602i	$0.751574\pi$
$282$		0			0
$283$	−8.39215	−	2.72677i	−0.498861	−	0.162090i	0.0487693	−	0.998810i	$-0.484470\pi$
$283$	−8.39215	−	2.72677i	−0.498861	−	0.162090i	−0.547631	+	0.836720i	$0.684470\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	25.6032	+	35.2397i	1.51131	+	2.08014i
$288$		0			0
$289$	−12.6855	−	9.21656i	−0.746207	−	0.542151i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	4.20743i		−	0.245800i	−0.992419	−	0.122900i	$-0.960780\pi$
$293$		−	4.20743i		−	0.245800i	0.992419	−	0.122900i	$-0.0392195\pi$
$294$		0			0
$295$	−4.99993	+	25.0953i	−0.291107	+	1.46111i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−29.7697			−1.72163
$300$		0			0
$301$	38.8119			2.23708
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.97755	+	0.823633i	−0.399533	+	0.0471611i
$306$		0			0
$307$			4.41109i			0.251754i	0.992046	+	0.125877i	$0.0401745\pi$
$307$			4.41109i			0.251754i	−0.992046	+	0.125877i	$0.959825\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.11346	−	3.71514i	−0.289958	−	0.210667i	0.433291	−	0.901254i	$-0.357352\pi$
$311$	−5.11346	−	3.71514i	−0.289958	−	0.210667i	−0.723249	+	0.690587i	$0.757352\pi$
$312$		0			0
$313$	−9.00753	−	12.3978i	−0.509136	−	0.700765i	0.474638	−	0.880181i	$-0.342579\pi$
$313$	−9.00753	−	12.3978i	−0.509136	−	0.700765i	−0.983773	+	0.179416i	$0.942579\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.2723	+	6.58686i	1.13860	+	0.369955i	0.816840	−	0.576864i	$-0.195724\pi$
$317$	20.2723	+	6.58686i	1.13860	+	0.369955i	0.321765	+	0.946820i	$0.395724\pi$
$318$		0			0
$319$	0.923699	−	2.84285i	0.0517172	−	0.159169i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.0101366	+	0.0139519i	−0.000564018	+	0.000776304i
$324$		0			0
$325$	20.2558	−	12.3953i	1.12359	−	0.687570i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.616057	−	1.89603i	−0.0339643	−	0.104531i
$330$		0			0
$331$	6.12237	−	18.8427i	0.336516	−	1.03569i	−0.629454	−	0.777037i	$-0.716722\pi$
$331$	6.12237	−	18.8427i	0.336516	−	1.03569i	0.965970	−	0.258652i	$-0.0832785\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	26.9736	−	12.4248i	1.47373	−	0.678838i
$336$		0			0
$337$	5.89780	+	8.11762i	0.321274	+	0.442195i	0.938856	−	0.344311i	$-0.111888\pi$
$337$	5.89780	+	8.11762i	0.321274	+	0.442195i	−0.617582	+	0.786507i	$0.711888\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.03378	−	0.751085i	0.0559823	−	0.0406735i
$342$		0			0
$343$		−	1.32419i		−	0.0714997i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.1885	−	4.28519i	0.707994	−	0.230041i	0.0671837	−	0.997741i	$-0.478599\pi$
$347$	13.1885	−	4.28519i	0.707994	−	0.230041i	0.640810	+	0.767700i	$0.278599\pi$
$348$		0			0
$349$	−27.2533			−1.45883			−0.729417	−	0.684069i	$-0.760209\pi$
$349$	−27.2533			−1.45883			−0.729417	+	0.684069i	$0.760209\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.8063	−	3.83609i	0.628384	−	0.204174i	0.0225248	−	0.999746i	$-0.492830\pi$
$353$	11.8063	−	3.83609i	0.628384	−	0.204174i	0.605859	+	0.795572i	$0.292830\pi$
$354$		0			0
$355$	9.58374	+	5.37110i	0.508652	+	0.285068i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.3910	−	11.1823i	0.812308	−	0.590177i	−0.102191	−	0.994765i	$-0.532585\pi$
$359$	15.3910	−	11.1823i	0.812308	−	0.590177i	0.914499	+	0.404588i	$0.132585\pi$
$360$		0			0
$361$	15.3711	+	11.1678i	0.809007	+	0.587778i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.22639	−	10.3895i	−0.0641920	−	0.543814i
$366$		0			0
$367$	0.927465	+	0.301352i	0.0484133	+	0.0157304i	0.333124	−	0.942883i	$-0.391897\pi$
$367$	0.927465	+	0.301352i	0.0484133	+	0.0157304i	−0.284710	+	0.958614i	$0.591897\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.45294	+	10.6271i	0.179268	+	0.551729i
$372$		0			0
$373$	−11.0341	+	15.1871i	−0.571324	+	0.786360i	−0.992711	−	0.120521i	$-0.961543\pi$
$373$	−11.0341	+	15.1871i	−0.571324	+	0.786360i	0.421387	+	0.906881i	$0.361543\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.3318	+	14.2205i	−0.532114	+	0.732392i
$378$		0			0
$379$	1.06536	+	3.27883i	0.0547236	+	0.168422i	0.974683	−	0.223592i	$-0.0717784\pi$
$379$	1.06536	+	3.27883i	0.0547236	+	0.168422i	−0.919959	+	0.392014i	$0.871778\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	25.9681	+	8.43755i	1.32691	+	0.431139i	0.884862	−	0.465854i	$-0.154253\pi$
$383$	25.9681	+	8.43755i	1.32691	+	0.431139i	0.442046	+	0.896992i	$0.354253\pi$
$384$		0			0
$385$	−0.801990	−	6.79420i	−0.0408732	−	0.346264i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−7.94232	−	5.77044i	−0.402692	−	0.292573i	0.367945	−	0.929848i	$-0.380062\pi$
$389$	−7.94232	−	5.77044i	−0.402692	−	0.292573i	−0.770637	+	0.637275i	$0.780062\pi$
$390$		0			0
$391$	−5.82567	+	4.23259i	−0.294617	+	0.214051i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−18.0853	−	10.1357i	−0.909968	−	0.509981i
$396$		0			0
$397$	11.0447	−	3.58865i	0.554319	−	0.180109i	−0.0184443	−	0.999830i	$-0.505871\pi$
$397$	11.0447	−	3.58865i	0.554319	−	0.180109i	0.572763	+	0.819721i	$0.305871\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.4145			1.26914			0.634570	−	0.772865i	$-0.281177\pi$
$401$	25.4145			1.26914			0.634570	+	0.772865i	$0.281177\pi$
$402$		0			0
$403$	−7.14637	+	2.32200i	−0.355986	+	0.115667i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	6.89902i		−	0.341972i
$408$		0			0
$409$	13.9568	−	10.1402i	0.690117	−	0.501399i	−0.186582	−	0.982439i	$-0.559741\pi$
$409$	13.9568	−	10.1402i	0.690117	−	0.501399i	0.876699	+	0.481040i	$0.159741\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−25.4800	−	35.0702i	−1.25379	−	1.72569i
$414$		0			0
$415$	2.89148	−	1.33189i	0.141937	−	0.0653800i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.31956	+	19.4496i	−0.308731	+	0.950176i	0.669528	+	0.742787i	$0.266497\pi$
$419$	−6.31956	+	19.4496i	−0.308731	+	0.950176i	−0.978259	+	0.207389i	$0.933503\pi$
$420$		0			0
$421$	−6.46100	−	19.8849i	−0.314890	−	0.969132i	−0.975800	−	0.218666i	$-0.929829\pi$
$421$	−6.46100	−	19.8849i	−0.314890	−	0.969132i	0.660910	−	0.750466i	$-0.270171\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.20154	−	5.30559i	0.106790	−	0.257359i
$426$		0			0
$427$	6.99618	−	9.62941i	0.338569	−	0.466000i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.85900	−	8.79908i	0.137713	−	0.423837i	−0.858289	−	0.513166i	$-0.828472\pi$
$431$	2.85900	−	8.79908i	0.137713	−	0.423837i	0.996002	+	0.0893294i	$0.0284724\pi$
$432$		0			0
$433$	0.223727	+	0.0726932i	0.0107516	+	0.00349341i	0.314388	−	0.949295i	$-0.398201\pi$
$433$	0.223727	+	0.0726932i	0.0107516	+	0.00349341i	−0.303636	+	0.952788i	$0.598201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.0553044	−	0.0761199i	−0.00264557	−	0.00364131i
$438$		0			0
$439$	25.2424	+	18.3396i	1.20475	+	0.875304i	0.994744	−	0.102396i	$-0.0326509\pi$
$439$	25.2424	+	18.3396i	1.20475	+	0.875304i	0.210008	+	0.977700i	$0.432651\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			24.3862i			1.15862i	0.815106	+	0.579311i	$0.196678\pi$
$443$			24.3862i			1.15862i	−0.815106	+	0.579311i	$0.803322\pi$
$444$		0			0
$445$	35.7674	−	4.22200i	1.69554	−	0.200142i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	23.9483			1.13019			0.565096	−	0.825025i	$-0.308839\pi$
$449$	23.9483			1.13019			0.565096	+	0.825025i	$0.308839\pi$
$450$		0			0
$451$	−9.28740			−0.437327
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−7.86087	+	39.4547i	−0.368523	+	1.84967i
$456$		0			0
$457$			3.91244i			0.183016i	0.995804	+	0.0915082i	$0.0291688\pi$
$457$			3.91244i			0.183016i	−0.995804	+	0.0915082i	$0.970831\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.09170	−	1.51971i	−0.0974202	−	0.0707799i	0.538009	−	0.842939i	$-0.319177\pi$
$461$	−2.09170	−	1.51971i	−0.0974202	−	0.0707799i	−0.635429	+	0.772159i	$0.719177\pi$
$462$		0			0
$463$	12.8777	+	17.7247i	0.598478	+	0.823734i	0.995568	−	0.0940453i	$-0.0299799\pi$
$463$	12.8777	+	17.7247i	0.598478	+	0.823734i	−0.397090	+	0.917780i	$0.629980\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.79561	−	2.53295i	−0.360738	−	0.117211i	0.123040	−	0.992402i	$-0.460736\pi$
$467$	−7.79561	−	2.53295i	−0.360738	−	0.117211i	−0.483778	+	0.875191i	$0.660736\pi$
$468$		0			0
$469$	−15.5467	+	47.8479i	−0.717881	+	2.20941i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.86410	+	6.69486i	−0.223652	+	0.307830i
$474$		0			0
$475$	0.0693245	+	0.0287660i	0.00318083	+	0.00131987i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.90100	−	5.85067i	−0.0868588	−	0.267324i	0.898188	−	0.439612i	$-0.144884\pi$
$479$	−1.90100	−	5.85067i	−0.0868588	−	0.267324i	−0.985047	+	0.172288i	$0.944884\pi$
$480$		0			0
$481$	−12.5366	+	38.5836i	−0.571618	+	1.75926i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.81342	+	15.7259i	−0.400197	+	0.714078i
$486$		0			0
$487$	−3.69230	−	5.08201i	−0.167314	−	0.230288i	0.717124	−	0.696945i	$-0.245458\pi$
$487$	−3.69230	−	5.08201i	−0.167314	−	0.230288i	−0.884438	+	0.466658i	$0.845458\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.22591	+	1.61722i	−0.100454	+	0.0729840i	−0.636878	−	0.770964i	$-0.719775\pi$
$491$	−2.22591	+	1.61722i	−0.100454	+	0.0729840i	0.536424	+	0.843948i	$0.319775\pi$
$492$		0			0
$493$			4.25178i			0.191490i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.7006	+	5.75128i	−0.793982	+	0.257980i
$498$		0			0
$499$	16.4263			0.735341			0.367670	−	0.929956i	$-0.380156\pi$
$499$	16.4263			0.735341			0.367670	+	0.929956i	$0.380156\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.6860	−	3.79701i	0.521053	−	0.169300i	−0.0366701	−	0.999327i	$-0.511675\pi$
$503$	11.6860	−	3.79701i	0.521053	−	0.169300i	0.557723	+	0.830027i	$0.311675\pi$
$504$		0			0
$505$	−19.1341	+	17.6763i	−0.851458	+	0.786586i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.50277	−	6.17763i	0.376879	−	0.273818i	−0.383179	−	0.923674i	$-0.625171\pi$
$509$	8.50277	−	6.17763i	0.376879	−	0.273818i	0.760058	+	0.649856i	$0.225171\pi$
$510$		0			0
$511$	14.3382	+	10.4173i	0.634283	+	0.460833i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	20.6001	−	36.7572i	0.907750	−	1.61971i
$516$		0			0
$517$	0.404263	+	0.131353i	0.0177795	+	0.00577690i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.41778	+	7.44115i	0.105925	+	0.326003i	0.989946	−	0.141443i	$-0.0451742\pi$
$521$	2.41778	+	7.44115i	0.105925	+	0.326003i	−0.884022	+	0.467446i	$0.845174\pi$
$522$		0			0
$523$	−12.9592	+	17.8368i	−0.566665	+	0.779947i	−0.992155	−	0.125016i	$-0.960102\pi$
$523$	−12.9592	+	17.8368i	−0.566665	+	0.779947i	0.425490	+	0.904963i	$0.360102\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.06834	+	1.47045i	−0.0465378	+	0.0640538i
$528$		0			0
$529$	−5.03308	−	15.4902i	−0.218830	−	0.673489i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	51.9409	+	16.8766i	2.24981	+	0.731007i
$534$		0			0
$535$	21.8430	+	23.6445i	0.944357	+	1.02224i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.80240	+	3.48915i	0.206854	+	0.150288i
$540$		0			0
$541$	−10.0860	+	7.32791i	−0.433631	+	0.315052i	−0.783099	−	0.621897i	$-0.786362\pi$
$541$	−10.0860	+	7.32791i	−0.433631	+	0.315052i	0.349468	+	0.936948i	$0.386362\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.51748	+	12.6356i	−0.107837	+	0.541248i
$546$		0			0
$547$	−2.39292	+	0.777505i	−0.102314	+	0.0332437i	−0.359726	−	0.933058i	$-0.617130\pi$
$547$	−2.39292	+	0.777505i	−0.102314	+	0.0332437i	0.257413	+	0.966302i	$0.417130\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.0555550			−0.00236672
$552$		0			0
$553$	33.4024	−	10.8531i	1.42042	−	0.461521i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			0.262544i			0.0111244i	0.999985	+	0.00556218i	$0.00177051\pi$
$557$			0.262544i			0.0111244i	−0.999985	+	0.00556218i	$0.998229\pi$
$558$		0			0
$559$	39.3687	−	28.6030i	1.66512	−	1.20978i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−19.0928	−	26.2790i	−0.804666	−	1.10753i	−0.992125	−	0.125255i	$-0.960025\pi$
$563$	−19.0928	−	26.2790i	−0.804666	−	1.10753i	0.187459	−	0.982272i	$-0.439975\pi$
$564$		0			0
$565$	−39.3119	−	7.83241i	−1.65386	−	0.329512i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.9892	+	36.8991i	−0.502615	+	1.54689i	0.302128	+	0.953267i	$0.402303\pi$
$569$	−11.9892	+	36.8991i	−0.502615	+	1.54689i	−0.804743	+	0.593623i	$0.797697\pi$
$570$		0			0
$571$	−11.0258	−	33.9338i	−0.461414	−	1.42009i	−0.863437	−	0.504456i	$-0.831693\pi$
$571$	−11.0258	−	33.9338i	−0.461414	−	1.42009i	0.402023	−	0.915629i	$-0.368307\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	23.8182	+	20.3685i	0.993290	+	0.849425i
$576$		0			0
$577$	−14.8962	+	20.5029i	−0.620139	+	0.853548i	−0.997363	−	0.0725741i	$-0.976879\pi$
$577$	−14.8962	+	20.5029i	−0.620139	+	0.853548i	0.377224	+	0.926122i	$0.376879\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.66655	+	5.12913i	−0.0691403	+	0.212792i
$582$		0			0
$583$	−2.26586	−	0.736221i	−0.0938422	−	0.0304912i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.303103	+	0.417186i	0.0125104	+	0.0172191i	0.815226	−	0.579142i	$-0.196612\pi$
$587$	0.303103	+	0.417186i	0.0125104	+	0.0172191i	−0.802716	+	0.596362i	$0.796612\pi$
$588$		0			0
$589$	−0.0192134	−	0.0139593i	−0.000791673	−	0.000575184i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			7.14389i			0.293364i	0.989184	+	0.146682i	$0.0468595\pi$
$593$			7.14389i			0.293364i	−0.989184	+	0.146682i	$0.953141\pi$
$594$		0			0
$595$	4.07129	+	8.83858i	0.166907	+	0.362347i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.6627			0.966833			0.483417	−	0.875390i	$-0.339396\pi$
$599$	23.6627			0.966833			0.483417	+	0.875390i	$0.339396\pi$
$600$		0			0
$601$	−7.98023			−0.325520			−0.162760	−	0.986666i	$-0.552040\pi$
$601$	−7.98023			−0.325520			−0.162760	+	0.986666i	$0.552040\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−20.1843	−	11.3121i	−0.820610	−	0.459901i
$606$		0			0
$607$		−	17.2004i		−	0.698144i	−0.937096	−	0.349072i	$-0.886497\pi$
$607$		−	17.2004i		−	0.698144i	0.937096	−	0.349072i	$-0.113503\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.02220	−	1.46921i	−0.0818094	−	0.0594380i
$612$		0			0
$613$	8.67810	+	11.9444i	0.350505	+	0.482429i	0.947473	−	0.319836i	$-0.103628\pi$
$613$	8.67810	+	11.9444i	0.350505	+	0.482429i	−0.596968	+	0.802265i	$0.703628\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.7142	−	4.78092i	−0.592370	−	0.192473i	−0.00253529	−	0.999997i	$-0.500807\pi$
$617$	−14.7142	−	4.78092i	−0.592370	−	0.192473i	−0.589834	+	0.807524i	$0.700807\pi$
$618$		0			0
$619$	11.5792	−	35.6370i	0.465406	−	1.43237i	−0.393066	−	0.919510i	$-0.628586\pi$
$619$	11.5792	−	35.6370i	0.465406	−	1.43237i	0.858471	−	0.512861i	$-0.171414\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−35.8629	+	49.3611i	−1.43682	+	1.97761i
$624$		0			0
$625$	−24.6873	−	3.94177i	−0.987492	−	0.157671i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.03244	+	9.33290i	0.120911	+	0.372127i
$630$		0			0
$631$	−0.468691	+	1.44248i	−0.0186583	+	0.0574244i	−0.959952	−	0.280164i	$-0.909611\pi$
$631$	−0.468691	+	1.44248i	−0.0186583	+	0.0574244i	0.941294	+	0.337588i	$0.109611\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.600220	+	5.08487i	0.0238190	+	0.201787i
$636$		0			0
$637$	−20.5177	−	28.2401i	−0.812940	−	1.11892i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.12903	+	2.27338i	−0.123589	+	0.0897930i	−0.647863	−	0.761757i	$-0.724337\pi$
$641$	−3.12903	+	2.27338i	−0.123589	+	0.0897930i	0.524273	+	0.851550i	$0.324337\pi$
$642$		0			0
$643$		−	23.2212i		−	0.915756i	−0.889015	−	0.457878i	$-0.848610\pi$
$643$		−	23.2212i		−	0.915756i	0.889015	−	0.457878i	$-0.151390\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.8795	−	8.08384i	0.978114	−	0.317808i	0.224027	−	0.974583i	$-0.428080\pi$
$647$	24.8795	−	8.08384i	0.978114	−	0.317808i	0.754087	+	0.656775i	$0.228080\pi$
$648$		0			0
$649$	9.24271			0.362808
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.13602	−	2.64355i	0.318387	−	0.103450i	−0.145464	−	0.989364i	$-0.546467\pi$
$653$	8.13602	−	2.64355i	0.318387	−	0.103450i	0.463851	+	0.885913i	$0.346467\pi$
$654$		0			0
$655$	−6.59488	−	14.3172i	−0.257683	−	0.559419i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	33.9288	−	24.6507i	1.32168	−	0.960255i	0.321767	−	0.946819i	$-0.395723\pi$
$659$	33.9288	−	24.6507i	1.32168	−	0.960255i	0.999910	−	0.0134358i	$-0.00427688\pi$
$660$		0			0
$661$	14.1713	+	10.2961i	0.551201	+	0.400471i	0.828228	−	0.560391i	$-0.189349\pi$
$661$	14.1713	+	10.2961i	0.551201	+	0.400471i	−0.277027	+	0.960862i	$0.589349\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.115488	+	0.0531967i	−0.00447842	+	0.00206288i
$666$		0			0
$667$	−22.0619	−	7.16833i	−0.854239	−	0.277559i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.784230	+	2.41361i	0.0302749	+	0.0931765i
$672$		0			0
$673$	17.1017	−	23.5385i	0.659223	−	0.907343i	−0.340232	−	0.940341i	$-0.610506\pi$
$673$	17.1017	−	23.5385i	0.659223	−	0.907343i	0.999455	+	0.0329986i	$0.0105057\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.5667	−	24.1785i	0.675143	−	0.929255i	−0.324720	−	0.945810i	$-0.605270\pi$
$677$	17.5667	−	24.1785i	0.675143	−	0.929255i	0.999863	+	0.0165555i	$0.00527003\pi$
$678$		0			0
$679$	−9.43726	−	29.0449i	−0.362169	−	1.11464i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−35.3984	−	11.5016i	−1.35448	−	0.440097i	−0.460284	−	0.887772i	$-0.652252\pi$
$683$	−35.3984	−	11.5016i	−1.35448	−	0.440097i	−0.894197	+	0.447674i	$0.852252\pi$
$684$		0			0
$685$	−48.0981	−	9.58296i	−1.83773	−	0.366146i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	11.3342	+	8.23481i	0.431800	+	0.313721i
$690$		0			0
$691$	−13.6397	+	9.90980i	−0.518877	+	0.376986i	−0.816181	−	0.577797i	$-0.803913\pi$
$691$	−13.6397	+	9.90980i	−0.518877	+	0.376986i	0.297303	+	0.954783i	$0.403913\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.5794	−	2.54724i	0.818554	−	0.0966225i
$696$		0			0
$697$	12.5639	−	4.08225i	0.475890	−	0.154626i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	23.3495			0.881898			0.440949	−	0.897532i	$-0.354642\pi$
$701$	23.3495			0.881898			0.440949	+	0.897532i	$0.354642\pi$
$702$		0			0
$703$	−0.121947	+	0.0396228i	−0.00459930	+	0.00149440i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	44.1297i		−	1.65967i
$708$		0			0
$709$	15.4019	−	11.1901i	0.578429	−	0.420253i	−0.259728	−	0.965682i	$-0.583633\pi$
$709$	15.4019	−	11.1901i	0.578429	−	0.420253i	0.838157	+	0.545428i	$0.183633\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−5.82877	−	8.02261i	−0.218289	−	0.300449i
$714$		0			0
$715$	−5.82058	−	6.30063i	−0.217677	−	0.235630i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.55488	+	14.0185i	−0.169868	+	0.522801i	−0.999362	−	0.0357149i	$-0.988629\pi$
$719$	−4.55488	+	14.0185i	−0.169868	+	0.522801i	0.829494	+	0.558516i	$0.188629\pi$
$720$		0			0
$721$	22.0583	+	67.8884i	0.821493	+	2.52830i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	17.9960	−	4.30854i	0.668355	−	0.160015i
$726$		0			0
$727$	17.6698	−	24.3204i	0.655336	−	0.901993i	−0.343979	−	0.938977i	$-0.611775\pi$
$727$	17.6698	−	24.3204i	0.655336	−	0.901993i	0.999316	+	0.0369839i	$0.0117750\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.63738	−	11.1947i	0.134533	−	0.414051i
$732$		0			0
$733$	21.5355	+	6.99732i	0.795433	+	0.258452i	0.678416	−	0.734678i	$-0.262667\pi$
$733$	21.5355	+	6.99732i	0.795433	+	0.258452i	0.117017	+	0.993130i	$0.462667\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.30514	−	8.67828i	−0.232253	−	0.319668i
$738$		0			0
$739$	−20.7764	−	15.0949i	−0.764272	−	0.555276i	0.135946	−	0.990716i	$-0.456593\pi$
$739$	−20.7764	−	15.0949i	−0.764272	−	0.555276i	−0.900218	+	0.435440i	$0.856593\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	24.9796i		−	0.916411i	−0.888846	−	0.458205i	$-0.848492\pi$
$743$		−	24.9796i		−	0.916411i	0.888846	−	0.458205i	$-0.151508\pi$
$744$		0			0
$745$	−22.9473	+	21.1990i	−0.840725	+	0.776670i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−54.5321			−1.99256
$750$		0			0
$751$	17.9383			0.654580			0.327290	−	0.944924i	$-0.393865\pi$
$751$	17.9383			0.654580			0.327290	+	0.944924i	$0.393865\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.1567	+	30.6305i	−1.20669	+	1.11476i
$756$		0			0
$757$		−	9.91474i		−	0.360357i	−0.983634	−	0.180179i	$-0.942332\pi$
$757$		−	9.91474i		−	0.360357i	0.983634	−	0.180179i	$-0.0576676\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−25.6076	−	18.6050i	−0.928273	−	0.674430i	0.0172961	−	0.999850i	$-0.494494\pi$
$761$	−25.6076	−	18.6050i	−0.928273	−	0.674430i	−0.945569	+	0.325420i	$0.894494\pi$
$762$		0			0
$763$	−12.8292	−	17.6579i	−0.464449	−	0.639259i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−51.6910	−	16.7954i	−1.86645	−	0.606447i
$768$		0			0
$769$	−6.91430	+	21.2800i	−0.249336	+	0.767377i	0.745557	+	0.666442i	$0.232184\pi$
$769$	−6.91430	+	21.2800i	−0.249336	+	0.767377i	−0.994893	+	0.100935i	$0.967816\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−28.1148	+	38.6967i	−1.01122	+	1.39182i	−0.0930367	+	0.995663i	$0.529657\pi$
$773$	−28.1148	+	38.6967i	−1.01122	+	1.39182i	−0.918182	+	0.396160i	$0.870343\pi$
$774$		0			0
$775$	7.30641	+	3.03178i	0.262454	+	0.108905i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.0533399	+	0.164163i	0.00191110	+	0.00588176i
$780$		0			0
$781$	1.22626	−	3.77405i	0.0438792	−	0.135046i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	11.7828	+	12.7545i	0.420545	+	0.455229i
$786$		0			0
$787$	16.2038	+	22.3026i	0.577603	+	0.795002i	0.993430	−	0.114442i	$-0.0365079\pi$
$787$	16.2038	+	22.3026i	0.577603	+	0.795002i	−0.415827	+	0.909444i	$0.636508\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	54.9375	−	39.9144i	1.95335	−	1.41919i
$792$		0			0
$793$		−	14.9235i		−	0.529948i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.9712	+	7.13887i	−0.778260	+	0.252872i	−0.671097	−	0.741370i	$-0.734177\pi$
$797$	−21.9712	+	7.13887i	−0.778260	+	0.252872i	−0.107163	+	0.994241i	$0.534177\pi$
$798$		0			0
$799$	−0.604617			−0.0213898
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.59386	+	1.16772i	−0.126825	+	0.0412078i
$804$		0			0
$805$	−52.7262	+	6.22382i	−1.85835	+	0.219361i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.36960	−	0.995071i	0.0481525	−	0.0349848i	−0.563449	−	0.826151i	$-0.690526\pi$
$809$	1.36960	−	0.995071i	0.0481525	−	0.0349848i	0.611601	+	0.791166i	$0.290526\pi$
$810$		0			0
$811$	−16.6435	−	12.0922i	−0.584434	−	0.424616i	0.255886	−	0.966707i	$-0.417633\pi$
$811$	−16.6435	−	12.0922i	−0.584434	−	0.424616i	−0.840320	+	0.542091i	$0.817633\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−30.4620	−	6.06919i	−1.06704	−	0.212594i
$816$		0			0
$817$	0.146274	+	0.0475272i	0.00511746	+	0.00166277i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.2235	+	43.7754i	0.496403	+	1.52777i	0.814759	+	0.579800i	$0.196869\pi$
$821$	14.2235	+	43.7754i	0.496403	+	1.52777i	−0.318356	+	0.947971i	$0.603131\pi$
$822$		0			0
$823$	−32.9082	+	45.2942i	−1.14711	+	1.57886i	−0.396605	+	0.917990i	$0.629812\pi$
$823$	−32.9082	+	45.2942i	−1.14711	+	1.57886i	−0.750502	+	0.660868i	$0.770188\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.1319	+	16.6981i	−0.421866	+	0.580648i	−0.966062	−	0.258309i	$-0.916835\pi$
$827$	−12.1319	+	16.6981i	−0.421866	+	0.580648i	0.544196	+	0.838958i	$0.316835\pi$
$828$		0			0
$829$	0.599179	+	1.84408i	0.0208103	+	0.0640476i	0.960922	−	0.276818i	$-0.0892799\pi$
$829$	0.599179	+	1.84408i	0.0208103	+	0.0640476i	−0.940112	+	0.340866i	$0.889280\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−8.03026	−	2.60919i	−0.278232	−	0.0904030i
$834$		0			0
$835$	5.88547	−	2.71100i	0.203675	−	0.0938182i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−42.2783	−	30.7170i	−1.45961	−	1.06047i	−0.983464	−	0.181102i	$-0.942034\pi$
$839$	−42.2783	−	30.7170i	−1.45961	−	1.06047i	−0.476146	−	0.879366i	$-0.657966\pi$
$840$		0			0
$841$	12.3806	−	8.99501i	0.426916	−	0.310173i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.94139	+	19.4114i	0.307593	+	0.667771i
$846$		0			0
$847$	37.2793	−	12.1128i	1.28093	−	0.416200i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−53.5397			−1.83532
$852$		0			0
$853$	−16.7010	+	5.42649i	−0.571832	+	0.185799i	−0.580638	−	0.814162i	$-0.697197\pi$
$853$	−16.7010	+	5.42649i	−0.571832	+	0.185799i	0.00880614	+	0.999961i	$0.497197\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	50.9890i		−	1.74175i	−0.491503	−	0.870876i	$-0.663552\pi$
$857$		−	50.9890i		−	1.74175i	0.491503	−	0.870876i	$-0.336448\pi$
$858$		0			0
$859$	15.0749	−	10.9525i	0.514349	−	0.373696i	−0.300122	−	0.953901i	$-0.597027\pi$
$859$	15.0749	−	10.9525i	0.514349	−	0.373696i	0.814471	+	0.580205i	$0.197027\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.171716	−	0.236347i	−0.00584529	−	0.00804536i	0.806084	−	0.591801i	$-0.201583\pi$
$863$	−0.171716	−	0.236347i	−0.00584529	−	0.00804536i	−0.811930	+	0.583755i	$0.801583\pi$
$864$		0			0
$865$	−3.99319	−	33.8290i	−0.135773	−	1.15022i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.31405	+	7.12192i	−0.0784989	+	0.241595i
$870$		0			0
$871$	19.4925	+	59.9917i	0.660477	+	2.03274i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	33.2844	−	26.1887i	1.12522	−	0.885338i
$876$		0			0
$877$	−22.3126	+	30.7106i	−0.753442	+	1.03702i	0.244289	+	0.969702i	$0.421445\pi$
$877$	−22.3126	+	30.7106i	−0.753442	+	1.03702i	−0.997731	+	0.0673215i	$0.978555\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.3378	−	34.8942i	0.381981	−	1.17562i	−0.556666	−	0.830736i	$-0.687920\pi$
$881$	11.3378	−	34.8942i	0.381981	−	1.17562i	0.938647	−	0.344879i	$-0.112080\pi$
$882$		0			0
$883$	21.5128	+	6.98993i	0.723964	+	0.235230i	0.647741	−	0.761861i	$-0.275714\pi$
$883$	21.5128	+	6.98993i	0.723964	+	0.235230i	0.0762228	+	0.997091i	$0.475714\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.3643	−	19.7708i	−0.482306	−	0.663838i	0.496640	−	0.867957i	$-0.334567\pi$
$887$	−14.3643	−	19.7708i	−0.482306	−	0.663838i	−0.978946	+	0.204119i	$0.934567\pi$
$888$		0			0
$889$	−7.01741	−	5.09845i	−0.235356	−	0.170996i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	0.00790011i		−	0.000264367i
$894$		0			0
$895$	−45.4603	−	25.4777i	−1.51957	−	0.851625i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.85519			−0.195281
$900$		0			0
$901$	3.38882			0.112898
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−16.5572	−	35.9449i	−0.550380	−	1.19485i
$906$		0			0
$907$			32.7792i			1.08842i	0.838950	+	0.544208i	$0.183170\pi$
$907$			32.7792i			1.08842i	−0.838950	+	0.544208i	$0.816830\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	22.0778	+	16.0405i	0.731470	+	0.531444i	0.890028	−	0.455906i	$-0.150685\pi$
$911$	22.0778	+	16.0405i	0.731470	+	0.531444i	−0.158558	+	0.987350i	$0.550685\pi$
$912$		0			0
$913$	−0.675888	−	0.930280i	−0.0223686	−	0.0307878i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.3970	+	8.25197i	0.838681	+	0.272504i
$918$		0			0
$919$	12.8923	−	39.6783i	0.425277	−	1.30887i	−0.477453	−	0.878658i	$-0.658440\pi$
$919$	12.8923	−	39.6783i	0.425277	−	1.30887i	0.902729	−	0.430209i	$-0.141560\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−13.7161	+	18.8785i	−0.451469	+	0.621394i
$924$		0			0
$925$	36.4293	−	22.2926i	1.19779	−	0.732975i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−10.4151	−	32.0542i	−0.341707	−	1.05167i	−0.963323	−	0.268344i	$-0.913524\pi$
$929$	−10.4151	−	32.0542i	−0.341707	−	1.05167i	0.621616	−	0.783322i	$-0.286476\pi$
$930$		0			0
$931$	0.0340925	−	0.104926i	0.00111734	−	0.00343880i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.03485	−	0.405418i	−0.0665466	−	0.0132586i
$936$		0			0
$937$	0.614857	+	0.846278i	0.0200865	+	0.0276467i	0.818942	−	0.573876i	$-0.194561\pi$
$937$	0.614857	+	0.846278i	0.0200865	+	0.0276467i	−0.798856	+	0.601523i	$0.794561\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	4.62928	−	3.36337i	0.150910	−	0.109643i	−0.509768	−	0.860312i	$-0.670269\pi$
$941$	4.62928	−	3.36337i	0.150910	−	0.109643i	0.660678	+	0.750669i	$0.270269\pi$
$942$		0			0
$943$			72.0746i			2.34707i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.9783	−	3.89200i	0.389244	−	0.126473i	−0.107856	−	0.994167i	$-0.534398\pi$
$947$	11.9783	−	3.89200i	0.389244	−	0.126473i	0.497099	+	0.867694i	$0.334398\pi$
$948$		0			0
$949$	22.2210			0.721325
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−54.5813	+	17.7346i	−1.76806	+	0.574479i	−0.997984	−	0.0634695i	$-0.979783\pi$
$953$	−54.5813	+	17.7346i	−1.76806	+	0.574479i	−0.770079	+	0.637948i	$0.779783\pi$
$954$		0			0
$955$	4.09140	−	20.5352i	0.132395	−	0.664505i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	67.2161	−	48.8353i	2.17052	−	1.57698i
$960$		0			0
$961$	23.0545	+	16.7501i	0.743695	+	0.540326i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−28.7244	−	31.0934i	−0.924672	−	1.00093i
$966$		0			0
$967$	8.40935	+	2.73236i	0.270427	+	0.0878669i	0.441091	−	0.897462i	$-0.354591\pi$
$967$	8.40935	+	2.73236i	0.270427	+	0.0878669i	−0.170665	+	0.985329i	$0.554591\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−16.0493	−	49.3945i	−0.515045	−	1.58515i	−0.783200	−	0.621770i	$-0.786414\pi$
$971$	−16.0493	−	49.3945i	−0.515045	−	1.58515i	0.268155	−	0.963376i	$-0.413586\pi$
$972$		0			0
$973$	−21.6370	+	29.7808i	−0.693651	+	0.954729i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.8859	+	30.1234i	−0.700193	+	0.963732i	0.299760	+	0.954015i	$0.403093\pi$
$977$	−21.8859	+	30.1234i	−0.700193	+	0.963732i	−0.999953	+	0.00971780i	$0.996907\pi$
$978$		0			0
$979$	−4.02002	−	12.3724i	−0.128480	−	0.395422i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	34.0107	+	11.0507i	1.08477	+	0.352464i	0.796225	−	0.605001i	$-0.206827\pi$
$983$	34.0107	+	11.0507i	1.08477	+	0.352464i	0.288548	+	0.957465i	$0.406827\pi$
$984$		0			0
$985$	−8.24664	+	14.7146i	−0.262760	+	0.468847i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	51.9553	+	37.7477i	1.65208	+	1.20031i
$990$		0			0
$991$	35.4505	−	25.7563i	1.12612	−	0.818175i	0.140996	−	0.990010i	$-0.454970\pi$
$991$	35.4505	−	25.7563i	1.12612	−	0.818175i	0.985126	+	0.171835i	$0.0549697\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.88924	+	5.44054i	−0.186701	+	0.172477i
$996$		0			0
$997$	−37.5746	+	12.2087i	−1.19000	+	0.386654i	−0.836072	−	0.548619i	$-0.815154\pi$
$997$	−37.5746	+	12.2087i	−1.19000	+	0.386654i	−0.353927	+	0.935273i	$0.615154\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.w.c.109.4		24
3.2	odd	2		300.2.o.a.109.5	✓	24
15.2	even	4		1500.2.m.d.1201.2		24
15.8	even	4		1500.2.m.c.1201.5		24
15.14	odd	2		1500.2.o.c.49.1		24
25.14	even	10	inner	900.2.w.c.289.4		24
75.2	even	20		1500.2.m.d.301.2		24
75.8	even	20		7500.2.a.n.1.9		12
75.11	odd	10		1500.2.o.c.949.1		24
75.14	odd	10		300.2.o.a.289.5	yes	24
75.17	even	20		7500.2.a.m.1.4		12
75.23	even	20		1500.2.m.c.301.5		24
75.44	odd	10		7500.2.d.g.1249.16		24
75.56	odd	10		7500.2.d.g.1249.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.5	✓	24	3.2	odd	2
300.2.o.a.289.5	yes	24	75.14	odd	10
900.2.w.c.109.4		24	1.1	even	1	trivial
900.2.w.c.289.4		24	25.14	even	10	inner
1500.2.m.c.301.5		24	75.23	even	20
1500.2.m.c.1201.5		24	15.8	even	4
1500.2.m.d.301.2		24	75.2	even	20
1500.2.m.d.1201.2		24	15.2	even	4
1500.2.o.c.49.1		24	15.14	odd	2
1500.2.o.c.949.1		24	75.11	odd	10
7500.2.a.m.1.4		12	75.17	even	20
7500.2.a.n.1.9		12	75.8	even	20
7500.2.d.g.1249.9		24	75.56	odd	10
7500.2.d.g.1249.16		24	75.44	odd	10

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64247 - 1.51733i) q^{5} +3.78808i q^{7} +O(q^{10})\)	\(q+(1.64247 - 1.51733i) q^{5} +3.78808i q^{7} +(-0.653426 - 0.474742i) q^{11} +(2.79168 + 3.84242i) q^{13} +(1.09262 + 0.355012i) q^{17} +(-0.00463870 + 0.0142765i) q^{19} +(-3.68422 + 5.07089i) q^{23} +(0.395416 - 4.98434i) q^{25} +(1.14365 + 3.51978i) q^{29} +(-0.488893 + 1.50466i) q^{31} +(5.74777 + 6.22181i) q^{35} +(5.02074 + 6.91045i) q^{37} +(9.30279 - 6.75887i) q^{41} -10.2458i q^{43} +(-0.500524 + 0.162630i) q^{47} -7.34957 q^{49} +(2.80539 - 0.911527i) q^{53} +(-1.79357 + 0.211714i) q^{55} +(-9.25803 + 6.72635i) q^{59} +(-2.54203 - 1.84689i) q^{61} +(10.4155 + 2.07516i) q^{65} +(12.6312 + 4.10412i) q^{67} +(1.51826 + 4.67271i) q^{71} +(2.75001 - 3.78507i) q^{73} +(1.79836 - 2.47523i) q^{77} +(-2.86507 - 8.81777i) q^{79} +(1.35402 + 0.439947i) q^{83} +(2.33326 - 1.07476i) q^{85} +(13.0306 + 9.46730i) q^{89} +(-14.5554 + 10.5751i) q^{91} +(0.0140432 + 0.0304871i) q^{95} +(-7.66744 + 2.49130i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 24 * q + 2 * q^5	\( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more