LMFDB - Embedded newform 1728.2.bc.e.1585.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(145,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("1728.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.bc (of order $12$, degree $4$, 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:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1585.11
Character	$\chi$	$=$	1728.1585
Dual form			1728.2.bc.e.145.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0468197 - 0.174734i) q^{5} +(-4.04791 - 2.33706i) q^{7} +O(q^{10})$	$q+(0.0468197 - 0.174734i) q^{5} +(-4.04791 - 2.33706i) q^{7} +(-0.598734 + 0.160430i) q^{11} +(-4.41237 - 1.18229i) q^{13} +4.34691 q^{17} +(1.23918 - 1.23918i) q^{19} +(-3.86311 + 2.23037i) q^{23} +(4.30179 + 2.48364i) q^{25} +(2.31752 + 8.64910i) q^{29} +(2.25376 + 3.90364i) q^{31} +(-0.597886 + 0.597886i) q^{35} +(2.79692 + 2.79692i) q^{37} +(-3.67211 + 2.12009i) q^{41} +(0.0131254 - 0.00351694i) q^{43} +(-1.17465 + 2.03456i) q^{47} +(7.42373 + 12.8583i) q^{49} +(0.519418 + 0.519418i) q^{53} +0.112130i q^{55} +(-2.95679 + 11.0349i) q^{59} +(0.588805 + 2.19745i) q^{61} +(-0.413172 + 0.715636i) q^{65} +(-7.04291 - 1.88714i) q^{67} -7.55145i q^{71} -2.92707i q^{73} +(2.79856 + 0.749872i) q^{77} +(-1.45885 + 2.52680i) q^{79} +(1.99394 + 7.44148i) q^{83} +(0.203521 - 0.759552i) q^{85} -3.18821i q^{89} +(15.0978 + 15.0978i) q^{91} +(-0.158508 - 0.274544i) q^{95} +(8.03868 - 13.9234i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{5}+O(q^{10}) $ 72 * q - 4 * q^5	$ 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) $ 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	0.0468197	−	0.174734i	0.0209384	−	0.0781432i	−0.954666	−	0.297679i	$-0.903788\pi$
$5$	0.0468197	−	0.174734i	0.0209384	−	0.0781432i	0.975604	+	0.219536i	$0.0704542\pi$
$6$		0			0
$7$	−4.04791	−	2.33706i	−1.52997	−	0.883327i	−0.999362	−	0.0357075i	$-0.988632\pi$
$7$	−4.04791	−	2.33706i	−1.52997	−	0.883327i	−0.530605	−	0.847619i	$-0.678035\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.598734	+	0.160430i	−0.180525	+	0.0483716i	−0.347949	−	0.937513i	$-0.613122\pi$
$11$	−0.598734	+	0.160430i	−0.180525	+	0.0483716i	0.167424	+	0.985885i	$0.446455\pi$
$12$		0			0
$13$	−4.41237	−	1.18229i	−1.22377	−	0.327909i	−0.411621	−	0.911355i	$-0.635037\pi$
$13$	−4.41237	−	1.18229i	−1.22377	−	0.327909i	−0.812152	+	0.583446i	$0.801704\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.34691			1.05428			0.527141	−	0.849778i	$-0.323264\pi$
$17$	4.34691			1.05428			0.527141	+	0.849778i	$0.323264\pi$
$18$		0			0
$19$	1.23918	−	1.23918i	0.284287	−	0.284287i	−0.550529	−	0.834816i	$-0.685574\pi$
$19$	1.23918	−	1.23918i	0.284287	−	0.284287i	0.834816	+	0.550529i	$0.185574\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.86311	+	2.23037i	−0.805515	+	0.465064i	−0.845396	−	0.534140i	$-0.820635\pi$
$23$	−3.86311	+	2.23037i	−0.805515	+	0.465064i	0.0398812	+	0.999204i	$0.487302\pi$
$24$		0			0
$25$	4.30179	+	2.48364i	0.860357	+	0.496728i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.31752	+	8.64910i	0.430353	+	1.60610i	0.751949	+	0.659221i	$0.229114\pi$
$29$	2.31752	+	8.64910i	0.430353	+	1.60610i	−0.321597	+	0.946877i	$0.604220\pi$
$30$		0			0
$31$	2.25376	+	3.90364i	0.404788	+	0.701114i	0.994297	−	0.106648i	$-0.0340119\pi$
$31$	2.25376	+	3.90364i	0.404788	+	0.701114i	−0.589509	+	0.807762i	$0.700679\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.597886	+	0.597886i	−0.101061	+	0.101061i
$36$		0			0
$37$	2.79692	+	2.79692i	0.459811	+	0.459811i	0.898593	−	0.438783i	$-0.144590\pi$
$37$	2.79692	+	2.79692i	0.459811	+	0.459811i	−0.438783	+	0.898593i	$0.644590\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.67211	+	2.12009i	−0.573487	+	0.331103i	−0.758541	−	0.651626i	$-0.774087\pi$
$41$	−3.67211	+	2.12009i	−0.573487	+	0.331103i	0.185054	+	0.982728i	$0.440754\pi$
$42$		0			0
$43$	0.0131254	−	0.00351694i	0.00200161	−	0.000536329i	−0.257818	−	0.966193i	$-0.583004\pi$
$43$	0.0131254	−	0.00351694i	0.00200161	−	0.000536329i	0.259820	+	0.965657i	$0.416337\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.17465	+	2.03456i	−0.171341	+	0.296771i	−0.938889	−	0.344221i	$-0.888143\pi$
$47$	−1.17465	+	2.03456i	−0.171341	+	0.296771i	0.767548	+	0.640991i	$0.221477\pi$
$48$		0			0
$49$	7.42373	+	12.8583i	1.06053	+	1.83690i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.519418	+	0.519418i	0.0713476	+	0.0713476i	0.741880	−	0.670533i	$-0.233934\pi$
$53$	0.519418	+	0.519418i	0.0713476	+	0.0713476i	−0.670533	+	0.741880i	$0.733934\pi$
$54$		0			0
$55$			0.112130i			0.0151196i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.95679	+	11.0349i	−0.384942	+	1.43662i	0.453317	+	0.891350i	$0.350241\pi$
$59$	−2.95679	+	11.0349i	−0.384942	+	1.43662i	−0.838258	+	0.545273i	$0.816426\pi$
$60$		0			0
$61$	0.588805	+	2.19745i	0.0753887	+	0.281355i	0.993321	−	0.115382i	$-0.0368093\pi$
$61$	0.588805	+	2.19745i	0.0753887	+	0.281355i	−0.917932	+	0.396737i	$0.870143\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.413172	+	0.715636i	−0.0512477	+	0.0887637i
$66$		0			0
$67$	−7.04291	−	1.88714i	−0.860428	−	0.230551i	−0.198484	−	0.980104i	$-0.563602\pi$
$67$	−7.04291	−	1.88714i	−0.860428	−	0.230551i	−0.661944	+	0.749553i	$0.730268\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.55145i		−	0.896193i	−0.893985	−	0.448096i	$-0.852102\pi$
$71$		−	7.55145i		−	0.896193i	0.893985	−	0.448096i	$-0.147898\pi$
$72$		0			0
$73$		−	2.92707i		−	0.342588i	−0.985220	−	0.171294i	$-0.945205\pi$
$73$		−	2.92707i		−	0.342588i	0.985220	−	0.171294i	$-0.0547948\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.79856	+	0.749872i	0.318925	+	0.0854558i
$78$		0			0
$79$	−1.45885	+	2.52680i	−0.164133	+	0.284287i	−0.936347	−	0.351076i	$-0.885816\pi$
$79$	−1.45885	+	2.52680i	−0.164133	+	0.284287i	0.772214	+	0.635362i	$0.219149\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.99394	+	7.44148i	0.218863	+	0.816808i	0.984771	+	0.173858i	$0.0556232\pi$
$83$	1.99394	+	7.44148i	0.218863	+	0.816808i	−0.765908	+	0.642950i	$0.777710\pi$
$84$		0			0
$85$	0.203521	−	0.759552i	0.0220750	−	0.0823850i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	3.18821i		−	0.337950i	−0.985620	−	0.168975i	$-0.945954\pi$
$89$		−	3.18821i		−	0.337950i	0.985620	−	0.168975i	$-0.0540457\pi$
$90$		0			0
$91$	15.0978	+	15.0978i	1.58268	+	1.58268i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.158508	−	0.274544i	−0.0162626	−	0.0281676i
$96$		0			0
$97$	8.03868	−	13.9234i	0.816204	−	1.41371i	−0.0922553	−	0.995735i	$-0.529408\pi$
$97$	8.03868	−	13.9234i	0.816204	−	1.41371i	0.908460	−	0.417972i	$-0.137259\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−17.0308	+	4.56339i	−1.69463	+	0.454074i	−0.971578	−	0.236720i	$-0.923928\pi$
$101$	−17.0308	+	4.56339i	−1.69463	+	0.454074i	−0.723051	+	0.690795i	$0.757261\pi$
$102$		0			0
$103$	8.05916	−	4.65296i	0.794093	−	0.458470i	−0.0473086	−	0.998880i	$-0.515064\pi$
$103$	8.05916	−	4.65296i	0.794093	−	0.458470i	0.841401	+	0.540411i	$0.181731\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.51927	+	9.51927i	0.920263	+	0.920263i	0.997048	−	0.0767848i	$-0.0244654\pi$
$107$	9.51927	+	9.51927i	0.920263	+	0.920263i	−0.0767848	+	0.997048i	$0.524465\pi$
$108$		0			0
$109$	−6.35255	+	6.35255i	−0.608464	+	0.608464i	−0.942544	−	0.334081i	$-0.891574\pi$
$109$	−6.35255	+	6.35255i	−0.608464	+	0.608464i	0.334081	+	0.942544i	$0.391574\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.34598	−	9.25951i	−0.502908	−	0.871062i	−0.999994	−	0.00336088i	$-0.998930\pi$
$113$	−5.34598	−	9.25951i	−0.502908	−	0.871062i	0.497087	−	0.867701i	$-0.334403\pi$
$114$		0			0
$115$	0.208851	+	0.779441i	0.0194754	+	0.0726832i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17.5959	−	10.1590i	−1.61302	−	0.931275i
$120$		0			0
$121$	−9.19353	+	5.30789i	−0.835776	+	0.482535i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.27495	−	1.27495i	0.114035	−	0.114035i
$126$		0			0
$127$	11.5283			1.02297			0.511484	−	0.859293i	$-0.329096\pi$
$127$	11.5283			1.02297			0.511484	+	0.859293i	$0.329096\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.42289	−	0.917160i	−0.299059	−	0.0801327i	0.106169	−	0.994348i	$-0.466141\pi$
$131$	−3.42289	−	0.917160i	−0.299059	−	0.0801327i	−0.405229	+	0.914215i	$0.632808\pi$
$132$		0			0
$133$	−7.91213	+	2.12005i	−0.686069	+	0.183832i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−13.0194	−	7.51678i	−1.11233	−	0.642202i	−0.172895	−	0.984940i	$-0.555312\pi$
$137$	−13.0194	−	7.51678i	−1.11233	−	0.642202i	−0.939431	+	0.342739i	$0.888646\pi$
$138$		0			0
$139$	−2.61562	+	9.76161i	−0.221854	+	0.827969i	0.761787	+	0.647828i	$0.224322\pi$
$139$	−2.61562	+	9.76161i	−0.221854	+	0.827969i	−0.983641	+	0.180142i	$0.942344\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.83152			0.236783
$144$		0			0
$145$	1.61979			0.134517
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.37943	+	5.14811i	−0.113007	+	0.421749i	−0.999130	−	0.0417013i	$-0.986722\pi$
$149$	−1.37943	+	5.14811i	−0.113007	+	0.421749i	0.886123	+	0.463451i	$0.153389\pi$
$150$		0			0
$151$	9.86458	+	5.69532i	0.802768	+	0.463479i	0.844438	−	0.535653i	$-0.179934\pi$
$151$	9.86458	+	5.69532i	0.802768	+	0.463479i	−0.0416699	+	0.999131i	$0.513268\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.787617	−	0.211041i	0.0632629	−	0.0169512i
$156$		0			0
$157$	−5.47145	−	1.46607i	−0.436670	−	0.117005i	0.0337857	−	0.999429i	$-0.489244\pi$
$157$	−5.47145	−	1.46607i	−0.436670	−	0.117005i	−0.470455	+	0.882424i	$0.655910\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	20.8501			1.64321
$162$		0			0
$163$	−15.0117	+	15.0117i	−1.17581	+	1.17581i	−0.195004	+	0.980802i	$0.562472\pi$
$163$	−15.0117	+	15.0117i	−1.17581	+	1.17581i	−0.980802	+	0.195004i	$0.937528\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.81918	−	4.51441i	0.605066	−	0.349335i	−0.165966	−	0.986132i	$-0.553074\pi$
$167$	7.81918	−	4.51441i	0.605066	−	0.349335i	0.771032	+	0.636796i	$0.219741\pi$
$168$		0			0
$169$	6.81291	+	3.93343i	0.524070	+	0.302572i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.34114	+	5.00520i	0.101965	+	0.380539i	0.997983	−	0.0634788i	$-0.0202195\pi$
$173$	1.34114	+	5.00520i	0.101965	+	0.380539i	−0.896018	+	0.444017i	$0.853553\pi$
$174$		0			0
$175$	−11.6088	−	20.1071i	−0.877546	−	1.51995i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.96093	−	1.96093i	0.146566	−	0.146566i	−0.630016	−	0.776582i	$-0.716952\pi$
$179$	1.96093	−	1.96093i	0.146566	−	0.146566i	0.776582	+	0.630016i	$0.216952\pi$
$180$		0			0
$181$	−0.224256	−	0.224256i	−0.0166688	−	0.0166688i	0.698723	−	0.715392i	$-0.253752\pi$
$181$	−0.224256	−	0.224256i	−0.0166688	−	0.0166688i	−0.715392	+	0.698723i	$0.753752\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.619667	−	0.357765i	0.0455588	−	0.0263034i
$186$		0			0
$187$	−2.60265	+	0.697377i	−0.190324	+	0.0509972i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.3893	+	17.9947i	−0.751741	+	1.30205i	0.195237	+	0.980756i	$0.437452\pi$
$191$	−10.3893	+	17.9947i	−0.751741	+	1.30205i	−0.946978	+	0.321298i	$0.895881\pi$
$192$		0			0
$193$	7.69572	+	13.3294i	0.553950	+	0.959469i	0.997984	+	0.0634596i	$0.0202134\pi$
$193$	7.69572	+	13.3294i	0.553950	+	0.959469i	−0.444035	+	0.896010i	$0.646453\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.905158	+	0.905158i	0.0644898	+	0.0644898i	0.738616	−	0.674126i	$-0.235480\pi$
$197$	0.905158	+	0.905158i	0.0644898	+	0.0644898i	−0.674126	+	0.738616i	$0.735480\pi$
$198$		0			0
$199$		−	16.5201i		−	1.17108i	−0.810645	−	0.585538i	$-0.800883\pi$
$199$		−	16.5201i		−	1.17108i	0.810645	−	0.585538i	$-0.199117\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.8324	−	40.4270i	0.760284	−	2.83742i
$204$		0			0
$205$	0.198524	+	0.740902i	0.0138655	+	0.0517469i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.543137	+	0.940741i	−0.0375696	+	0.0650724i
$210$		0			0
$211$	25.2027	+	6.75305i	1.73503	+	0.464899i	0.981331	−	0.192325i	$-0.0616028\pi$
$211$	25.2027	+	6.75305i	1.73503	+	0.464899i	0.753695	+	0.657224i	$0.228270\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	0.00245811i		−	0.000167642i
$216$		0			0
$217$		−	21.0688i		−	1.43024i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−19.1802	−	5.13932i	−1.29020	−	0.345708i
$222$		0			0
$223$	−6.47927	+	11.2224i	−0.433884	+	0.751510i	−0.997204	−	0.0747295i	$-0.976191\pi$
$223$	−6.47927	+	11.2224i	−0.433884	+	0.751510i	0.563320	+	0.826239i	$0.309524\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.52089	+	13.1401i	0.233690	+	0.872142i	0.978735	+	0.205128i	$0.0657611\pi$
$227$	3.52089	+	13.1401i	0.233690	+	0.872142i	−0.745045	+	0.667014i	$0.767572\pi$
$228$		0			0
$229$	4.35071	−	16.2371i	0.287503	−	1.07298i	−0.659488	−	0.751715i	$-0.729227\pi$
$229$	4.35071	−	16.2371i	0.287503	−	1.07298i	0.946991	−	0.321260i	$-0.104106\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			10.0493i			0.658351i	0.944269	+	0.329176i	$0.106771\pi$
$233$			10.0493i			0.658351i	−0.944269	+	0.329176i	$0.893229\pi$
$234$		0			0
$235$	0.300509	+	0.300509i	0.0196030	+	0.0196030i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.38365	−	5.86066i	−0.218870	−	0.379094i	0.735593	−	0.677424i	$-0.236904\pi$
$239$	−3.38365	−	5.86066i	−0.218870	−	0.379094i	−0.954463	+	0.298330i	$0.903570\pi$
$240$		0			0
$241$	−1.07804	+	1.86722i	−0.0694428	+	0.120278i	−0.898656	−	0.438654i	$-0.855455\pi$
$241$	−1.07804	+	1.86722i	−0.0694428	+	0.120278i	0.829213	+	0.558932i	$0.188789\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.59435	−	0.695154i	0.165747	−	0.0444118i
$246$		0			0
$247$	−6.93279	+	4.00265i	−0.441123	+	0.254683i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	3.65289	+	3.65289i	0.230568	+	0.230568i	0.812930	−	0.582362i	$-0.197871\pi$
$251$	3.65289	+	3.65289i	0.230568	+	0.230568i	−0.582362	+	0.812930i	$0.697871\pi$
$252$		0			0
$253$	1.95516	−	1.95516i	0.122920	−	0.122920i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.09689	+	8.82807i	0.317935	+	0.550680i	0.980057	−	0.198716i	$-0.0636772\pi$
$257$	5.09689	+	8.82807i	0.317935	+	0.550680i	−0.662122	+	0.749396i	$0.730344\pi$
$258$		0			0
$259$	−4.78511	−	17.8583i	−0.297332	−	1.10966i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.5937	+	8.42569i	0.899888	+	0.519550i	0.877164	−	0.480191i	$-0.159433\pi$
$263$	14.5937	+	8.42569i	0.899888	+	0.519550i	0.0227239	+	0.999742i	$0.492766\pi$
$264$		0			0
$265$	0.115079	−	0.0664408i	0.00706924	−	0.00408143i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.2219	+	18.2219i	−1.11101	+	1.11101i	−0.117993	+	0.993014i	$0.537646\pi$
$269$	−18.2219	+	18.2219i	−1.11101	+	1.11101i	−0.993014	+	0.117993i	$0.962354\pi$
$270$		0			0
$271$	−9.95663			−0.604822			−0.302411	−	0.953178i	$-0.597792\pi$
$271$	−9.95663			−0.604822			−0.302411	+	0.953178i	$0.597792\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.97408	−	0.796902i	−0.179344	−	0.0480550i
$276$		0			0
$277$	2.63740	−	0.706690i	0.158466	−	0.0424609i	−0.178714	−	0.983901i	$-0.557194\pi$
$277$	2.63740	−	0.706690i	0.158466	−	0.0424609i	0.337180	+	0.941440i	$0.390527\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	21.8517	+	12.6161i	1.30356	+	0.752612i	0.981013	−	0.193941i	$-0.0621271\pi$
$281$	21.8517	+	12.6161i	1.30356	+	0.752612i	0.322549	+	0.946553i	$0.395460\pi$
$282$		0			0
$283$	2.31429	−	8.63704i	0.137570	−	0.513419i	−0.862404	−	0.506221i	$-0.831042\pi$
$283$	2.31429	−	8.63704i	0.137570	−	0.513419i	0.999974	−	0.00719814i	$-0.00229126\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	19.8192			1.16989
$288$		0			0
$289$	1.89565			0.111509
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.38845	−	20.1100i	0.314796	−	1.17484i	−0.609383	−	0.792876i	$-0.708583\pi$
$293$	5.38845	−	20.1100i	0.314796	−	1.17484i	0.924179	−	0.381960i	$-0.124751\pi$
$294$		0			0
$295$	1.78973	+	1.03330i	0.104202	+	0.0601612i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	19.6824	−	5.27390i	1.13827	−	0.304997i
$300$		0			0
$301$	−0.0613498	−	0.0164386i	−0.00353615	−	0.000947507i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.411536			0.0235645
$306$		0			0
$307$	−11.4523	+	11.4523i	−0.653619	+	0.653619i	−0.953863	−	0.300243i	$-0.902932\pi$
$307$	−11.4523	+	11.4523i	−0.653619	+	0.653619i	0.300243	+	0.953863i	$0.402932\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.6387	+	9.02903i	−0.886792	+	0.511989i	−0.872892	−	0.487914i	$-0.837758\pi$
$311$	−15.6387	+	9.02903i	−0.886792	+	0.511989i	−0.0138999	+	0.999903i	$0.504425\pi$
$312$		0			0
$313$	−22.1825	−	12.8070i	−1.25383	−	0.723897i	−0.281959	−	0.959426i	$-0.590984\pi$
$313$	−22.1825	−	12.8070i	−1.25383	−	0.723897i	−0.971867	+	0.235529i	$0.924318\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.887719	+	3.31301i	0.0498593	+	0.186077i	0.986364	−	0.164577i	$-0.0526259\pi$
$317$	0.887719	+	3.31301i	0.0498593	+	0.186077i	−0.936505	+	0.350654i	$0.885959\pi$
$318$		0			0
$319$	−2.77516	−	4.80671i	−0.155379	−	0.269124i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	5.38660	−	5.38660i	0.299719	−	0.299719i
$324$		0			0
$325$	−16.0447	−	16.0447i	−0.890001	−	0.890001i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.50978	−	5.49047i	0.524291	−	0.302700i
$330$		0			0
$331$	−15.2234	+	4.07910i	−0.836753	+	0.224207i	−0.651658	−	0.758513i	$-0.725926\pi$
$331$	−15.2234	+	4.07910i	−0.836753	+	0.224207i	−0.185096	+	0.982721i	$0.559259\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.659494	+	1.14228i	−0.0360320	+	0.0624093i
$336$		0			0
$337$	−8.67225	−	15.0208i	−0.472407	−	0.818233i	0.527094	−	0.849807i	$-0.323282\pi$
$337$	−8.67225	−	15.0208i	−0.472407	−	0.818233i	−0.999501	+	0.0315734i	$0.989948\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.97567	−	1.97567i	−0.106988	−	0.106988i
$342$		0			0
$343$		−	36.6800i		−	1.98053i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.85473	+	6.92193i	−0.0995669	+	0.371589i	−0.997672	−	0.0681917i	$-0.978277\pi$
$347$	−1.85473	+	6.92193i	−0.0995669	+	0.371589i	0.898105	+	0.439780i	$0.144944\pi$
$348$		0			0
$349$	0.294768	+	1.10009i	0.0157786	+	0.0588865i	0.973366	−	0.229256i	$-0.0736291\pi$
$349$	0.294768	+	1.10009i	0.0157786	+	0.0588865i	−0.957588	+	0.288142i	$0.906962\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.2507	−	21.2188i	0.652037	−	1.12936i	−0.330591	−	0.943774i	$-0.607248\pi$
$353$	12.2507	−	21.2188i	0.652037	−	1.12936i	0.982628	−	0.185587i	$-0.0594187\pi$
$354$		0			0
$355$	−1.31949	−	0.353557i	−0.0700314	−	0.0187649i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	11.6859i		−	0.616757i	−0.951264	−	0.308378i	$-0.900214\pi$
$359$		−	11.6859i		−	0.616757i	0.951264	−	0.308378i	$-0.0997863\pi$
$360$		0			0
$361$			15.9289i			0.838362i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.511458	−	0.137045i	−0.0267709	−	0.00717325i
$366$		0			0
$367$	5.61911	−	9.73258i	0.293315	−	0.508037i	−0.681276	−	0.732026i	$-0.738575\pi$
$367$	5.61911	−	9.73258i	0.293315	−	0.508037i	0.974592	+	0.223990i	$0.0719082\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.888646	−	3.31647i	−0.0461362	−	0.172183i
$372$		0			0
$373$	3.09978	−	11.5685i	0.160501	−	0.598996i	−0.838071	−	0.545561i	$-0.816316\pi$
$373$	3.09978	−	11.5685i	0.160501	−	0.598996i	0.998571	−	0.0534347i	$-0.0170169\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	40.9031i		−	2.10661i
$378$		0			0
$379$	−11.6135	−	11.6135i	−0.596544	−	0.596544i	0.342847	−	0.939391i	$-0.388609\pi$
$379$	−11.6135	−	11.6135i	−0.596544	−	0.596544i	−0.939391	+	0.342847i	$0.888609\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−14.5294	−	25.1657i	−0.742418	−	1.28591i	−0.951391	−	0.307985i	$-0.900345\pi$
$383$	−14.5294	−	25.1657i	−0.742418	−	1.28591i	0.208973	−	0.977921i	$-0.432988\pi$
$384$		0			0
$385$	0.262056	−	0.453894i	0.0133556	−	0.0231326i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.6478	−	3.65693i	0.691973	−	0.185414i	0.104341	−	0.994542i	$-0.466727\pi$
$389$	13.6478	−	3.65693i	0.691973	−	0.185414i	0.587632	+	0.809128i	$0.300060\pi$
$390$		0			0
$391$	−16.7926	+	9.69522i	−0.849239	+	0.490308i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.373213	+	0.373213i	0.0187784	+	0.0187784i
$396$		0			0
$397$	−1.83996	+	1.83996i	−0.0923450	+	0.0923450i	−0.751770	−	0.659425i	$-0.770800\pi$
$397$	−1.83996	+	1.83996i	−0.0923450	+	0.0923450i	0.659425	+	0.751770i	$0.270800\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.5786	−	25.2509i	−0.728021	−	1.26097i	−0.957718	−	0.287708i	$-0.907107\pi$
$401$	−14.5786	−	25.2509i	−0.728021	−	1.26097i	0.229697	−	0.973262i	$-0.426226\pi$
$402$		0			0
$403$	−5.32922	−	19.8889i	−0.265467	−	0.990737i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.12332	−	1.22590i	−0.105249	−	0.0607656i
$408$		0			0
$409$	9.18277	−	5.30167i	0.454059	−	0.262151i	−0.255484	−	0.966813i	$-0.582235\pi$
$409$	9.18277	−	5.30167i	0.454059	−	0.262151i	0.709543	+	0.704662i	$0.248901\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	37.7581	−	37.7581i	1.85796	−	1.85796i
$414$		0			0
$415$	1.39363			0.0684107
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.8275	−	3.70507i	−0.675519	−	0.181005i	−0.0952792	−	0.995451i	$-0.530374\pi$
$419$	−13.8275	−	3.70507i	−0.675519	−	0.181005i	−0.580240	+	0.814446i	$0.697041\pi$
$420$		0			0
$421$	−19.2855	+	5.16753i	−0.939918	+	0.251850i	−0.696079	−	0.717966i	$-0.745074\pi$
$421$	−19.2855	+	5.16753i	−0.939918	+	0.251850i	−0.243839	+	0.969816i	$0.578407\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	18.6995	+	10.7962i	0.907059	+	0.523691i
$426$		0			0
$427$	2.75215	−	10.2712i	0.133186	−	0.497056i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.92159			−0.429738			−0.214869	−	0.976643i	$-0.568932\pi$
$431$	−8.92159			−0.429738			−0.214869	+	0.976643i	$0.568932\pi$
$432$		0			0
$433$	−29.8178			−1.43295			−0.716476	−	0.697612i	$-0.754246\pi$
$433$	−29.8178			−1.43295			−0.716476	+	0.697612i	$0.754246\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.02326	+	7.55091i	−0.0967857	+	0.361209i
$438$		0			0
$439$	27.0574	+	15.6216i	1.29138	+	0.745579i	0.978899	−	0.204345i	$-0.0655065\pi$
$439$	27.0574	+	15.6216i	1.29138	+	0.745579i	0.312481	+	0.949924i	$0.398840\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.6006	+	2.84043i	−0.503651	+	0.134953i	−0.501694	−	0.865045i	$-0.667290\pi$
$443$	−10.6006	+	2.84043i	−0.503651	+	0.134953i	−0.00195701	+	0.999998i	$0.500623\pi$
$444$		0			0
$445$	−0.557087	−	0.149271i	−0.0264085	−	0.00707613i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−27.4967			−1.29765			−0.648824	−	0.760938i	$-0.724739\pi$
$449$	−27.4967			−1.29765			−0.648824	+	0.760938i	$0.724739\pi$
$450$		0			0
$451$	1.85849	−	1.85849i	0.0875128	−	0.0875128i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.34497	−	1.93122i	0.156815	−	0.0905370i
$456$		0			0
$457$	16.8184	+	9.71008i	0.786729	+	0.454218i	0.838810	−	0.544424i	$-0.183252\pi$
$457$	16.8184	+	9.71008i	0.786729	+	0.454218i	−0.0520805	+	0.998643i	$0.516585\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.08101	+	4.03437i	0.0503475	+	0.187900i	0.986520	−	0.163642i	$-0.0523242\pi$
$461$	1.08101	+	4.03437i	0.0503475	+	0.187900i	−0.936172	+	0.351542i	$0.885658\pi$
$462$		0			0
$463$	0.773244	+	1.33930i	0.0359357	+	0.0622425i	0.883434	−	0.468556i	$-0.155226\pi$
$463$	0.773244	+	1.33930i	0.0359357	+	0.0622425i	−0.847498	+	0.530798i	$0.821892\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.13196	+	2.13196i	−0.0986553	+	0.0986553i	−0.754712	−	0.656056i	$-0.772223\pi$
$467$	−2.13196	+	2.13196i	−0.0986553	+	0.0986553i	0.656056	+	0.754712i	$0.272223\pi$
$468$		0			0
$469$	24.0987	+	24.0987i	1.11277	+	1.11277i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.00729441	+	0.00421143i	−0.000335397	+	0.000193642i
$474$		0			0
$475$	8.40836	−	2.25301i	0.385802	−	0.103375i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.5113	−	25.1343i	0.663037	−	1.14841i	−0.316777	−	0.948500i	$-0.602601\pi$
$479$	14.5113	−	25.1343i	0.663037	−	1.14841i	0.979814	−	0.199914i	$-0.0640661\pi$
$480$		0			0
$481$	−9.03428	−	15.6478i	−0.411928	−	0.713480i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.05652	−	2.05652i	−0.0933817	−	0.0933817i
$486$		0			0
$487$		−	3.59517i		−	0.162913i	−0.996677	−	0.0814564i	$-0.974043\pi$
$487$		−	3.59517i		−	0.162913i	0.996677	−	0.0814564i	$-0.0259571\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.35801	+	19.9964i	−0.241804	+	0.902424i	0.733159	+	0.680057i	$0.238045\pi$
$491$	−5.35801	+	19.9964i	−0.241804	+	0.902424i	−0.974963	+	0.222367i	$0.928622\pi$
$492$		0			0
$493$	10.0741	+	37.5969i	0.453713	+	1.69328i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.6482	+	30.5676i	−0.791631	+	1.37115i
$498$		0			0
$499$	14.7412	+	3.94988i	0.659905	+	0.176821i	0.573203	−	0.819413i	$-0.305701\pi$
$499$	14.7412	+	3.94988i	0.659905	+	0.176821i	0.0867019	+	0.996234i	$0.472367\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			11.1260i			0.496085i	0.968749	+	0.248042i	$0.0797872\pi$
$503$			11.1260i			0.496085i	−0.968749	+	0.248042i	$0.920213\pi$
$504$		0			0
$505$			3.18951i			0.141931i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	24.1806	+	6.47918i	1.07179	+	0.287185i	0.751227	−	0.660044i	$-0.229462\pi$
$509$	24.1806	+	6.47918i	1.07179	+	0.287185i	0.320560	+	0.947228i	$0.396129\pi$
$510$		0			0
$511$	−6.84076	+	11.8485i	−0.302617	+	0.524149i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.435701	−	1.62606i	−0.0191993	−	0.0716526i
$516$		0			0
$517$	0.376900	−	1.40661i	0.0165760	−	0.0618626i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			44.7974i			1.96261i	0.192458	+	0.981305i	$0.438354\pi$
$521$			44.7974i			1.96261i	−0.192458	+	0.981305i	$0.561646\pi$
$522$		0			0
$523$	−7.02267	−	7.02267i	−0.307080	−	0.307080i	0.536696	−	0.843776i	$-0.319672\pi$
$523$	−7.02267	−	7.02267i	−0.307080	−	0.307080i	−0.843776	+	0.536696i	$0.819672\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.79692	+	16.9688i	0.426761	+	0.739171i
$528$		0			0
$529$	−1.55091	+	2.68626i	−0.0674309	+	0.116794i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.7093	−	5.01314i	0.810389	−	0.217143i
$534$		0			0
$535$	2.10903	−	1.21765i	0.0911812	−	0.0526435i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.50770	−	6.50770i	−0.280306	−	0.280306i
$540$		0			0
$541$	14.9663	−	14.9663i	0.643452	−	0.643452i	−0.307950	−	0.951402i	$-0.599643\pi$
$541$	14.9663	−	14.9663i	0.643452	−	0.643452i	0.951402	+	0.307950i	$0.0996431\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.812579	+	1.40743i	0.0348071	+	0.0602876i
$546$		0			0
$547$	−1.38173	−	5.15670i	−0.0590787	−	0.220485i	0.930075	−	0.367370i	$-0.119742\pi$
$547$	−1.38173	−	5.15670i	−0.0590787	−	0.220485i	−0.989154	+	0.146885i	$0.953075\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	13.5896	+	7.84596i	0.578937	+	0.334249i
$552$		0			0
$553$	11.8106	−	6.81883i	0.502236	−	0.289966i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.66230	+	7.66230i	−0.324662	+	0.324662i	−0.850552	−	0.525890i	$-0.823732\pi$
$557$	−7.66230	+	7.66230i	−0.324662	+	0.324662i	0.525890	+	0.850552i	$0.323732\pi$
$558$		0			0
$559$	−0.0620723			−0.00262538
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−21.3157	−	5.71152i	−0.898349	−	0.240712i	−0.220042	−	0.975490i	$-0.570619\pi$
$563$	−21.3157	−	5.71152i	−0.898349	−	0.240712i	−0.678307	+	0.734779i	$0.737286\pi$
$564$		0			0
$565$	−1.86825	+	0.500595i	−0.0785977	+	0.0210602i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−38.6354	−	22.3061i	−1.61968	−	0.935122i	−0.987002	−	0.160706i	$-0.948623\pi$
$569$	−38.6354	−	22.3061i	−1.61968	−	0.935122i	−0.632676	−	0.774416i	$-0.718044\pi$
$570$		0			0
$571$	2.53873	−	9.47469i	0.106243	−	0.396503i	−0.892240	−	0.451561i	$-0.850867\pi$
$571$	2.53873	−	9.47469i	0.106243	−	0.396503i	0.998483	+	0.0550573i	$0.0175341\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−22.1577			−0.924041
$576$		0			0
$577$	−0.565932			−0.0235600			−0.0117800	−	0.999931i	$-0.503750\pi$
$577$	−0.565932			−0.0235600			−0.0117800	+	0.999931i	$0.503750\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.31992	−	34.7824i	0.386655	−	1.44302i
$582$		0			0
$583$	−0.394324	−	0.227663i	−0.0163312	−	0.00942884i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−39.9093	+	10.6937i	−1.64723	+	0.441375i	−0.958836	−	0.283960i	$-0.908352\pi$
$587$	−39.9093	+	10.6937i	−1.64723	+	0.441375i	−0.688397	+	0.725334i	$0.741685\pi$
$588$		0			0
$589$	7.63012	+	2.04448i	0.314394	+	0.0842415i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12.9281			0.530893			0.265447	−	0.964126i	$-0.414481\pi$
$593$	12.9281			0.530893			0.265447	+	0.964126i	$0.414481\pi$
$594$		0			0
$595$	−2.59896	+	2.59896i	−0.106547	+	0.106547i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	39.9617	−	23.0719i	1.63279	−	0.942692i	0.649563	−	0.760308i	$-0.274952\pi$
$599$	39.9617	−	23.0719i	1.63279	−	0.942692i	0.983227	−	0.182384i	$-0.0583814\pi$
$600$		0			0
$601$	28.4107	+	16.4029i	1.15890	+	0.669090i	0.951040	−	0.309069i	$-0.100017\pi$
$601$	28.4107	+	16.4029i	1.15890	+	0.669090i	0.207858	+	0.978159i	$0.433351\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.497028	+	1.85493i	0.0202071	+	0.0754138i
$606$		0			0
$607$	6.36706	+	11.0281i	0.258431	+	0.447616i	0.965822	−	0.259207i	$-0.0834611\pi$
$607$	6.36706	+	11.0281i	0.258431	+	0.447616i	−0.707391	+	0.706823i	$0.750128\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.58845	−	7.58845i	0.306996	−	0.306996i
$612$		0			0
$613$	29.9303	+	29.9303i	1.20888	+	1.20888i	0.971392	+	0.237483i	$0.0763225\pi$
$613$	29.9303	+	29.9303i	1.20888	+	1.20888i	0.237483	+	0.971392i	$0.423677\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.50740	+	1.44765i	−0.100944	+	0.0582802i	−0.549622	−	0.835413i	$-0.685228\pi$
$617$	−2.50740	+	1.44765i	−0.100944	+	0.0582802i	0.448678	+	0.893693i	$0.351895\pi$
$618$		0			0
$619$	5.55188	−	1.48762i	0.223149	−	0.0597926i	−0.145512	−	0.989356i	$-0.546483\pi$
$619$	5.55188	−	1.48762i	0.223149	−	0.0597926i	0.368661	+	0.929564i	$0.379816\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.45105	+	12.9056i	−0.298520	+	0.517052i
$624$		0			0
$625$	12.2551	+	21.2265i	0.490204	+	0.849059i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	12.1580	+	12.1580i	0.484770	+	0.484770i
$630$		0			0
$631$			33.4420i			1.33130i	0.746262	+	0.665652i	$0.231846\pi$
$631$			33.4420i			1.33130i	−0.746262	+	0.665652i	$0.768154\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.539750	−	2.01438i	0.0214193	−	0.0799381i
$636$		0			0
$637$	−17.5540	−	65.5126i	−0.695516	−	2.59570i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.42170	+	16.3189i	−0.372135	+	0.644557i	−0.989894	−	0.141811i	$-0.954707\pi$
$641$	−9.42170	+	16.3189i	−0.372135	+	0.644557i	0.617759	+	0.786368i	$0.288041\pi$
$642$		0			0
$643$	11.8825	+	3.18391i	0.468601	+	0.125561i	0.485390	−	0.874298i	$-0.338678\pi$
$643$	11.8825	+	3.18391i	0.468601	+	0.125561i	−0.0167890	+	0.999859i	$0.505344\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			8.72393i			0.342973i	0.985186	+	0.171487i	$0.0548570\pi$
$647$			8.72393i			0.342973i	−0.985186	+	0.171487i	$0.945143\pi$
$648$		0			0
$649$		−	7.08134i		−	0.277967i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−18.9252	−	5.07099i	−0.740600	−	0.198443i	−0.131255	−	0.991349i	$-0.541901\pi$
$653$	−18.9252	−	5.07099i	−0.740600	−	0.198443i	−0.609345	+	0.792906i	$0.708567\pi$
$654$		0			0
$655$	−0.320517	+	0.555152i	−0.0125237	+	0.0216916i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−10.0113	−	37.3628i	−0.389986	−	1.45545i	−0.830155	−	0.557533i	$-0.811748\pi$
$659$	−10.0113	−	37.3628i	−0.389986	−	1.45545i	0.440168	−	0.897915i	$-0.354919\pi$
$660$		0			0
$661$	7.13570	−	26.6308i	0.277546	−	1.03582i	−0.676569	−	0.736379i	$-0.736534\pi$
$661$	7.13570	−	26.6308i	0.277546	−	1.03582i	0.954116	−	0.299438i	$-0.0967992\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			1.48177i			0.0574608i
$666$		0			0
$667$	−28.2435	−	28.2435i	−1.09359	−	1.09359i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.705075	−	1.22123i	−0.0272191	−	0.0471449i
$672$		0			0
$673$	10.0608	−	17.4258i	0.387815	−	0.671716i	−0.604340	−	0.796726i	$-0.706563\pi$
$673$	10.0608	−	17.4258i	0.387815	−	0.671716i	0.992155	+	0.125011i	$0.0398965\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.5932	+	5.24998i	−0.753027	+	0.201773i	−0.614860	−	0.788636i	$-0.710788\pi$
$677$	−19.5932	+	5.24998i	−0.753027	+	0.201773i	−0.138167	+	0.990409i	$0.544121\pi$
$678$		0			0
$679$	−65.0798	+	37.5738i	−2.49753	+	1.44195i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−18.4322	−	18.4322i	−0.705287	−	0.705287i	0.260253	−	0.965540i	$-0.416194\pi$
$683$	−18.4322	−	18.4322i	−0.705287	−	0.705287i	−0.965540	+	0.260253i	$0.916194\pi$
$684$		0			0
$685$	−1.92300	+	1.92300i	−0.0734741	+	0.0734741i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.67776	−	2.90597i	−0.0639177	−	0.110709i
$690$		0			0
$691$	4.19392	+	15.6519i	0.159544	+	0.595427i	0.998673	+	0.0514946i	$0.0163985\pi$
$691$	4.19392	+	15.6519i	0.159544	+	0.595427i	−0.839129	+	0.543932i	$0.816935\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.58322	+	0.914072i	0.0600549	+	0.0346727i
$696$		0			0
$697$	−15.9623	+	9.21585i	−0.604616	+	0.349075i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.97647	+	2.97647i	−0.112420	+	0.112420i	−0.761079	−	0.648659i	$-0.775330\pi$
$701$	−2.97647	+	2.97647i	−0.112420	+	0.112420i	0.648659	+	0.761079i	$0.275330\pi$
$702$		0			0
$703$	6.93177			0.261437
$704$		0			0
$705$		0			0
$706$		0			0
$707$	79.6042	+	21.3299i	2.99382	+	0.802192i
$708$		0			0
$709$	−37.3329	+	10.0033i	−1.40207	+	0.375682i	−0.879086	−	0.476663i	$-0.841846\pi$
$709$	−37.3329	+	10.0033i	−1.40207	+	0.375682i	−0.522980	+	0.852345i	$0.675180\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−17.4131	−	10.0535i	−0.652125	−	0.376505i
$714$		0			0
$715$	0.132571	−	0.494761i	0.00495787	−	0.0185030i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	38.3674			1.43086			0.715431	−	0.698683i	$-0.246230\pi$
$719$	38.3674			1.43086			0.715431	+	0.698683i	$0.246230\pi$
$720$		0			0
$721$	−43.4970			−1.61991
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.5118	+	42.9625i	−0.427536	+	1.59559i
$726$		0			0
$727$	−14.8899	−	8.59667i	−0.552235	−	0.318833i	0.197788	−	0.980245i	$-0.436624\pi$
$727$	−14.8899	−	8.59667i	−0.552235	−	0.318833i	−0.750023	+	0.661412i	$0.769958\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.0570550	−	0.0152878i	0.00211026	−	0.000565441i
$732$		0			0
$733$	−12.7311	−	3.41130i	−0.470235	−	0.125999i	0.0159168	−	0.999873i	$-0.494933\pi$
$733$	−12.7311	−	3.41130i	−0.470235	−	0.125999i	−0.486152	+	0.873874i	$0.661600\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	4.51959			0.166481
$738$		0			0
$739$	15.2048	−	15.2048i	0.559316	−	0.559316i	−0.369797	−	0.929113i	$-0.620573\pi$
$739$	15.2048	−	15.2048i	0.559316	−	0.559316i	0.929113	+	0.369797i	$0.120573\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−36.6127	+	21.1384i	−1.34319	+	0.775491i	−0.987274	−	0.159027i	$-0.949164\pi$
$743$	−36.6127	+	21.1384i	−1.34319	+	0.775491i	−0.355916	+	0.934518i	$0.615831\pi$
$744$		0			0
$745$	0.834963	+	0.482066i	0.0305907	+	0.0176615i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.2860	−	60.7803i	−0.595079	−	2.22086i
$750$		0			0
$751$	9.72823	+	16.8498i	0.354988	+	0.614857i	0.987116	−	0.160007i	$-0.0511516\pi$
$751$	9.72823	+	16.8498i	0.354988	+	0.614857i	−0.632128	+	0.774864i	$0.717818\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	1.45702	−	1.45702i	0.0530264	−	0.0530264i
$756$		0			0
$757$	26.9716	+	26.9716i	0.980300	+	0.980300i	0.999810	−	0.0195093i	$-0.00621039\pi$
$757$	26.9716	+	26.9716i	0.980300	+	0.980300i	−0.0195093	+	0.999810i	$0.506210\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.0417	+	8.68435i	−0.545263	+	0.314808i	−0.747209	−	0.664589i	$-0.768607\pi$
$761$	−15.0417	+	8.68435i	−0.545263	+	0.314808i	0.201946	+	0.979397i	$0.435273\pi$
$762$		0			0
$763$	40.5609	−	10.8683i	1.46840	−	0.393457i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	26.0930	−	45.1944i	0.942163	−	1.63187i
$768$		0			0
$769$	15.0664	+	26.0957i	0.543307	+	0.941036i	0.998711	+	0.0507510i	$0.0161615\pi$
$769$	15.0664	+	26.0957i	0.543307	+	0.941036i	−0.455404	+	0.890285i	$0.650505\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	9.37945	+	9.37945i	0.337355	+	0.337355i	0.855371	−	0.518016i	$-0.173329\pi$
$773$	9.37945	+	9.37945i	0.337355	+	0.337355i	−0.518016	+	0.855371i	$0.673329\pi$
$774$		0			0
$775$			22.3901i			0.804278i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.92322	+	7.17757i	−0.0689067	+	0.257163i
$780$		0			0
$781$	1.21148	+	4.52131i	0.0433502	+	0.161785i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.512344	+	0.887406i	−0.0182863	+	0.0316729i
$786$		0			0
$787$	−12.6850	−	3.39895i	−0.452173	−	0.121159i	0.0255430	−	0.999674i	$-0.491869\pi$
$787$	−12.6850	−	3.39895i	−0.452173	−	0.121159i	−0.477716	+	0.878514i	$0.658535\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			49.9756i			1.77693i
$792$		0			0
$793$		−	10.3921i		−	0.369035i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16.0687	+	4.30559i	0.569181	+	0.152512i	0.531921	−	0.846794i	$-0.321470\pi$
$797$	16.0687	+	4.30559i	0.569181	+	0.152512i	0.0372602	+	0.999306i	$0.488137\pi$
$798$		0			0
$799$	−5.10611	+	8.84405i	−0.180641	+	0.312880i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.469592	+	1.75254i	0.0165715	+	0.0618458i
$804$		0			0
$805$	0.976194	−	3.64320i	0.0344063	−	0.128406i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			6.67548i			0.234697i	0.993091	+	0.117349i	$0.0374395\pi$
$809$			6.67548i			0.234697i	−0.993091	+	0.117349i	$0.962560\pi$
$810$		0			0
$811$	18.4521	+	18.4521i	0.647940	+	0.647940i	0.952495	−	0.304555i	$-0.0985076\pi$
$811$	18.4521	+	18.4521i	0.647940	+	0.647940i	−0.304555	+	0.952495i	$0.598508\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.92020	+	3.32589i	0.0672618	+	0.116501i
$816$		0			0
$817$	0.0119066	−	0.0206229i	0.000416560	−	0.000721502i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.3271	+	3.30305i	−0.430220	+	0.115277i	−0.467430	−	0.884030i	$-0.654820\pi$
$821$	−12.3271	+	3.30305i	−0.430220	+	0.115277i	0.0372093	+	0.999307i	$0.488153\pi$
$822$		0			0
$823$	7.14088	−	4.12279i	0.248915	−	0.143711i	−0.370352	−	0.928891i	$-0.620763\pi$
$823$	7.14088	−	4.12279i	0.248915	−	0.143711i	0.619268	+	0.785180i	$0.287430\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.9396	−	24.9396i	−0.867236	−	0.867236i	0.124930	−	0.992166i	$-0.460130\pi$
$827$	−24.9396	−	24.9396i	−0.867236	−	0.867236i	−0.992166	+	0.124930i	$0.960130\pi$
$828$		0			0
$829$	22.7949	−	22.7949i	0.791701	−	0.791701i	−0.190069	−	0.981771i	$-0.560871\pi$
$829$	22.7949	−	22.7949i	0.791701	−	0.791701i	0.981771	+	0.190069i	$0.0608713\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	32.2703	+	55.8938i	1.11810	+	1.93661i
$834$		0			0
$835$	−0.422726	−	1.57764i	−0.0146291	−	0.0545964i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	29.5746	+	17.0749i	1.02103	+	0.589492i	0.914402	−	0.404807i	$-0.132661\pi$
$839$	29.5746	+	17.0749i	1.02103	+	0.589492i	0.106628	+	0.994299i	$0.465995\pi$
$840$		0			0
$841$	−44.3213	+	25.5889i	−1.52832	+	0.882377i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.00628	−	1.00628i	0.0346171	−	0.0346171i
$846$		0			0
$847$	49.6195			1.70495
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−17.0430	−	4.56665i	−0.584225	−	0.156543i
$852$		0			0
$853$	−21.8060	+	5.84290i	−0.746624	+	0.200057i	−0.612020	−	0.790842i	$-0.709643\pi$
$853$	−21.8060	+	5.84290i	−0.746624	+	0.200057i	−0.134604	+	0.990900i	$0.542976\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	44.1400	+	25.4842i	1.50779	+	0.870525i	0.999959	+	0.00907074i	$0.00288735\pi$
$857$	44.1400	+	25.4842i	1.50779	+	0.870525i	0.507835	+	0.861454i	$0.330446\pi$
$858$		0			0
$859$	4.66973	−	17.4277i	0.159329	−	0.594624i	−0.839367	−	0.543566i	$-0.817074\pi$
$859$	4.66973	−	17.4277i	0.159329	−	0.594624i	0.998696	−	0.0510584i	$-0.0162595\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−45.5523			−1.55062			−0.775309	−	0.631583i	$-0.782406\pi$
$863$	−45.5523			−1.55062			−0.775309	+	0.631583i	$0.782406\pi$
$864$		0			0
$865$	0.937369			0.0318715
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.468086	−	1.74692i	0.0158787	−	0.0592603i
$870$		0			0
$871$	28.8448	+	16.6536i	0.977369	+	0.564284i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.14054	+	2.18125i	−0.275201	+	0.0737398i
$876$		0			0
$877$	18.7798	+	5.03203i	0.634148	+	0.169919i	0.561551	−	0.827442i	$-0.310205\pi$
$877$	18.7798	+	5.03203i	0.634148	+	0.169919i	0.0725968	+	0.997361i	$0.476871\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−51.8921			−1.74829			−0.874145	−	0.485666i	$-0.838577\pi$
$881$	−51.8921			−1.74829			−0.874145	+	0.485666i	$0.838577\pi$
$882$		0			0
$883$	1.40472	−	1.40472i	0.0472726	−	0.0472726i	−0.683075	−	0.730348i	$-0.739358\pi$
$883$	1.40472	−	1.40472i	0.0472726	−	0.0472726i	0.730348	+	0.683075i	$0.239358\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.52145	−	3.76516i	0.218969	−	0.126422i	−0.386504	−	0.922288i	$-0.626317\pi$
$887$	6.52145	−	3.76516i	0.218969	−	0.126422i	0.605473	+	0.795866i	$0.292984\pi$
$888$		0			0
$889$	−46.6654	−	26.9423i	−1.56511	−	0.903616i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.06558	+	3.97679i	0.0356582	+	0.133078i
$894$		0			0
$895$	−0.250830	−	0.434449i	−0.00838431	−	0.0145220i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−28.5398	+	28.5398i	−0.951855	+	0.951855i
$900$		0			0
$901$	2.25787	+	2.25787i	0.0752204	+	0.0752204i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.0496848	+	0.0286855i	−0.00165158	+	0.000953539i
$906$		0			0
$907$	−19.2960	+	5.17036i	−0.640714	+	0.171679i	−0.564527	−	0.825415i	$-0.690941\pi$
$907$	−19.2960	+	5.17036i	−0.640714	+	0.171679i	−0.0761873	+	0.997094i	$0.524275\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.6774	+	35.8143i	−0.685073	+	1.18658i	0.288341	+	0.957528i	$0.406896\pi$
$911$	−20.6774	+	35.8143i	−0.685073	+	1.18658i	−0.973414	+	0.229053i	$0.926437\pi$
$912$		0			0
$913$	−2.38768	−	4.13558i	−0.0790206	−	0.136868i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	11.7121	+	11.7121i	0.386767	+	0.386767i
$918$		0			0
$919$			8.25699i			0.272373i	0.990683	+	0.136187i	$0.0434847\pi$
$919$			8.25699i			0.272373i	−0.990683	+	0.136187i	$0.956515\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.92803	+	33.3198i	−0.293870	+	1.09674i
$924$		0			0
$925$	5.08522	+	18.9783i	0.167201	+	0.624002i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	2.79783	−	4.84599i	0.0917939	−	0.158992i	−0.816472	−	0.577385i	$-0.804073\pi$
$929$	2.79783	−	4.84599i	0.0917939	−	0.158992i	0.908266	+	0.418393i	$0.137407\pi$
$930$		0			0
$931$	25.1330	+	6.73438i	0.823702	+	0.220710i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			0.487421i			0.0159404i
$936$		0			0
$937$			3.12869i			0.102210i	0.998693	+	0.0511049i	$0.0162743\pi$
$937$			3.12869i			0.102210i	−0.998693	+	0.0511049i	$0.983726\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−12.9126	−	3.45992i	−0.420939	−	0.112790i	0.0421307	−	0.999112i	$-0.486585\pi$
$941$	−12.9126	−	3.45992i	−0.420939	−	0.112790i	−0.463070	+	0.886322i	$0.653252\pi$
$942$		0			0
$943$	9.45717	−	16.3803i	0.307968	−	0.533416i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.84975	+	21.8316i	0.190091	+	0.709431i	0.993483	+	0.113980i	$0.0363599\pi$
$947$	5.84975	+	21.8316i	0.190091	+	0.709431i	−0.803392	+	0.595451i	$0.796973\pi$
$948$		0			0
$949$	−3.46066	+	12.9154i	−0.112338	+	0.419250i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	13.2051i		−	0.427754i	−0.976861	−	0.213877i	$-0.931391\pi$
$953$		−	13.2051i		−	0.427754i	0.976861	−	0.213877i	$-0.0686092\pi$
$954$		0			0
$955$	2.65786	+	2.65786i	0.0860065	+	0.0860065i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	35.1344	+	60.8545i	1.13455	+	1.96509i
$960$		0			0
$961$	5.34109	−	9.25104i	0.172293	−	0.298421i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.68940	−	0.720623i	0.0865749	−	0.0231977i
$966$		0			0
$967$	26.0110	−	15.0175i	0.836457	−	0.482929i	−0.0196013	−	0.999808i	$-0.506240\pi$
$967$	26.0110	−	15.0175i	0.836457	−	0.482929i	0.856058	+	0.516879i	$0.172906\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	29.4184	+	29.4184i	0.944081	+	0.944081i	0.998517	−	0.0544362i	$-0.0173361\pi$
$971$	29.4184	+	29.4184i	0.944081	+	0.944081i	−0.0544362	+	0.998517i	$0.517336\pi$
$972$		0			0
$973$	33.4013	−	33.4013i	1.07080	−	1.07080i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.26388	+	2.18911i	0.0404352	+	0.0700358i	0.885535	−	0.464573i	$-0.153792\pi$
$977$	1.26388	+	2.18911i	0.0404352	+	0.0700358i	−0.845100	+	0.534609i	$0.820459\pi$
$978$		0			0
$979$	0.511486	+	1.90889i	0.0163472	+	0.0610084i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	17.8779	+	10.3218i	0.570215	+	0.329214i	0.757235	−	0.653142i	$-0.226550\pi$
$983$	17.8779	+	10.3218i	0.570215	+	0.329214i	−0.187020	+	0.982356i	$0.559883\pi$
$984$		0			0
$985$	0.200541	−	0.115782i	0.00638976	−	0.00368913i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.0428609	+	0.0428609i	−0.00136290	+	0.00136290i
$990$		0			0
$991$	−32.9680			−1.04726			−0.523631	−	0.851945i	$-0.675423\pi$
$991$	−32.9680			−1.04726			−0.523631	+	0.851945i	$0.675423\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.88661	−	0.773465i	−0.0915117	−	0.0245205i
$996$		0			0
$997$	−8.34081	+	2.23491i	−0.264156	+	0.0707804i	−0.388466	−	0.921463i	$-0.626995\pi$
$997$	−8.34081	+	2.23491i	−0.264156	+	0.0707804i	0.124310	+	0.992243i	$0.460328\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.e.1585.11		72
3.2	odd	2		576.2.bb.e.241.15		72
4.3	odd	2		432.2.y.e.181.2		72
9.4	even	3	inner	1728.2.bc.e.1009.8		72
9.5	odd	6		576.2.bb.e.49.14		72
12.11	even	2		144.2.x.e.133.17	yes	72
16.3	odd	4		432.2.y.e.397.10		72
16.13	even	4	inner	1728.2.bc.e.721.8		72
36.23	even	6		144.2.x.e.85.9	yes	72
36.31	odd	6		432.2.y.e.37.10		72
48.29	odd	4		576.2.bb.e.529.14		72
48.35	even	4		144.2.x.e.61.9	yes	72
144.13	even	12	inner	1728.2.bc.e.145.11		72
144.67	odd	12		432.2.y.e.253.2		72
144.77	odd	12		576.2.bb.e.337.15		72
144.131	even	12		144.2.x.e.13.17	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.17	✓	72	144.131	even	12
144.2.x.e.61.9	yes	72	48.35	even	4
144.2.x.e.85.9	yes	72	36.23	even	6
144.2.x.e.133.17	yes	72	12.11	even	2
432.2.y.e.37.10		72	36.31	odd	6
432.2.y.e.181.2		72	4.3	odd	2
432.2.y.e.253.2		72	144.67	odd	12
432.2.y.e.397.10		72	16.3	odd	4
576.2.bb.e.49.14		72	9.5	odd	6
576.2.bb.e.241.15		72	3.2	odd	2
576.2.bb.e.337.15		72	144.77	odd	12
576.2.bb.e.529.14		72	48.29	odd	4
1728.2.bc.e.145.11		72	144.13	even	12	inner
1728.2.bc.e.721.8		72	16.13	even	4	inner
1728.2.bc.e.1009.8		72	9.4	even	3	inner
1728.2.bc.e.1585.11		72	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0468197 - 0.174734i) q^{5} +(-4.04791 - 2.33706i) q^{7} +O(q^{10})\)	\(q+(0.0468197 - 0.174734i) q^{5} +(-4.04791 - 2.33706i) q^{7} +(-0.598734 + 0.160430i) q^{11} +(-4.41237 - 1.18229i) q^{13} +4.34691 q^{17} +(1.23918 - 1.23918i) q^{19} +(-3.86311 + 2.23037i) q^{23} +(4.30179 + 2.48364i) q^{25} +(2.31752 + 8.64910i) q^{29} +(2.25376 + 3.90364i) q^{31} +(-0.597886 + 0.597886i) q^{35} +(2.79692 + 2.79692i) q^{37} +(-3.67211 + 2.12009i) q^{41} +(0.0131254 - 0.00351694i) q^{43} +(-1.17465 + 2.03456i) q^{47} +(7.42373 + 12.8583i) q^{49} +(0.519418 + 0.519418i) q^{53} +0.112130i q^{55} +(-2.95679 + 11.0349i) q^{59} +(0.588805 + 2.19745i) q^{61} +(-0.413172 + 0.715636i) q^{65} +(-7.04291 - 1.88714i) q^{67} -7.55145i q^{71} -2.92707i q^{73} +(2.79856 + 0.749872i) q^{77} +(-1.45885 + 2.52680i) q^{79} +(1.99394 + 7.44148i) q^{83} +(0.203521 - 0.759552i) q^{85} -3.18821i q^{89} +(15.0978 + 15.0978i) q^{91} +(-0.158508 - 0.274544i) q^{95} +(8.03868 - 13.9234i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 72 * q - 4 * q^5	\( 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67} + 36 q^{77} - 44 q^{79} + 20 q^{83} - 8 q^{85} + 80 q^{91} + 48 q^{95} + 40 q^{97}+O(q^{100}) \) 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

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Database

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