LMFDB - Embedded newform 1728.2.bc.e.1009.17

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			1009.17
Character	$\chi$	$=$	1728.1009
Dual form			1728.2.bc.e.721.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.69708 - 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +O(q^{10})$	$q+(2.69708 - 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +(1.23365 - 4.60405i) q^{11} +(0.398486 + 1.48717i) q^{13} +6.47719 q^{17} +(-0.957336 + 0.957336i) q^{19} +(-3.70277 - 2.13780i) q^{23} +(2.42183 - 1.39824i) q^{25} +(1.07893 + 0.289099i) q^{29} +(-1.89670 + 3.28518i) q^{31} +(6.59588 - 6.59588i) q^{35} +(-6.14639 - 6.14639i) q^{37} +(-5.04156 - 2.91075i) q^{41} +(-1.69287 + 6.31788i) q^{43} +(1.81739 + 3.14781i) q^{47} +(2.08016 - 3.60295i) q^{49} +(-0.762460 - 0.762460i) q^{53} -13.3090i q^{55} +(-8.11476 + 2.17434i) q^{59} +(6.74711 + 1.80788i) q^{61} +(2.14950 + 3.72304i) q^{65} +(0.487339 + 1.81878i) q^{67} +3.98472i q^{71} +5.45461i q^{73} +(-4.12126 - 15.3808i) q^{77} +(2.95225 + 5.11344i) q^{79} +(-10.3428 - 2.77135i) q^{83} +(17.4695 - 4.68093i) q^{85} -2.24307i q^{89} +(3.63698 + 3.63698i) q^{91} +(-1.89016 + 3.27385i) q^{95} +(6.50191 + 11.2616i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.69708	−	0.722679i	1.20617	−	0.323192i	0.400911	−	0.916117i	$-0.368694\pi$
$5$	2.69708	−	0.722679i	1.20617	−	0.323192i	0.805258	+	0.592925i	$0.202027\pi$
$6$		0			0
$7$	2.89314	−	1.67035i	1.09350	−	0.631334i	0.158996	−	0.987279i	$-0.449174\pi$
$7$	2.89314	−	1.67035i	1.09350	−	0.631334i	0.934507	+	0.355945i	$0.115841\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.23365	−	4.60405i	0.371960	−	1.38817i	−0.485777	−	0.874083i	$-0.661463\pi$
$11$	1.23365	−	4.60405i	0.371960	−	1.38817i	0.857737	−	0.514089i	$-0.171870\pi$
$12$		0			0
$13$	0.398486	+	1.48717i	0.110520	+	0.412467i	0.998913	−	0.0466175i	$-0.0148442\pi$
$13$	0.398486	+	1.48717i	0.110520	+	0.412467i	−0.888393	+	0.459084i	$0.848178\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.47719			1.57095			0.785475	−	0.618894i	$-0.212419\pi$
$17$	6.47719			1.57095			0.785475	+	0.618894i	$0.212419\pi$
$18$		0			0
$19$	−0.957336	+	0.957336i	−0.219628	+	0.219628i	−0.808342	−	0.588714i	$-0.799635\pi$
$19$	−0.957336	+	0.957336i	−0.219628	+	0.219628i	0.588714	+	0.808342i	$0.299635\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.70277	−	2.13780i	−0.772081	−	0.445761i	0.0615352	−	0.998105i	$-0.480400\pi$
$23$	−3.70277	−	2.13780i	−0.772081	−	0.445761i	−0.833617	+	0.552343i	$0.813734\pi$
$24$		0			0
$25$	2.42183	−	1.39824i	0.484365	−	0.279648i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.07893	+	0.289099i	0.200353	+	0.0536843i	0.357600	−	0.933875i	$-0.383595\pi$
$29$	1.07893	+	0.289099i	0.200353	+	0.0536843i	−0.157247	+	0.987559i	$0.550262\pi$
$30$		0			0
$31$	−1.89670	+	3.28518i	−0.340657	+	0.590036i	−0.984555	−	0.175076i	$-0.943983\pi$
$31$	−1.89670	+	3.28518i	−0.340657	+	0.590036i	0.643898	+	0.765112i	$0.277316\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.59588	−	6.59588i	1.11491	−	1.11491i
$36$		0			0
$37$	−6.14639	−	6.14639i	−1.01046	−	1.01046i	−0.999945	−	0.0105160i	$-0.996653\pi$
$37$	−6.14639	−	6.14639i	−1.01046	−	1.01046i	−0.0105160	−	0.999945i	$-0.503347\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.04156	−	2.91075i	−0.787359	−	0.454582i	0.0516729	−	0.998664i	$-0.483545\pi$
$41$	−5.04156	−	2.91075i	−0.787359	−	0.454582i	−0.839032	+	0.544082i	$0.816878\pi$
$42$		0			0
$43$	−1.69287	+	6.31788i	−0.258160	+	0.963468i	0.708144	+	0.706068i	$0.249533\pi$
$43$	−1.69287	+	6.31788i	−0.258160	+	0.963468i	−0.966305	+	0.257400i	$0.917134\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.81739	+	3.14781i	0.265093	+	0.459155i	0.967588	−	0.252534i	$-0.0812639\pi$
$47$	1.81739	+	3.14781i	0.265093	+	0.459155i	−0.702495	+	0.711689i	$0.747931\pi$
$48$		0			0
$49$	2.08016	−	3.60295i	0.297166	−	0.514707i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.762460	−	0.762460i	−0.104732	−	0.104732i	0.652799	−	0.757531i	$-0.273595\pi$
$53$	−0.762460	−	0.762460i	−0.104732	−	0.104732i	−0.757531	+	0.652799i	$0.773595\pi$
$54$		0			0
$55$		−	13.3090i		−	1.79458i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.11476	+	2.17434i	−1.05645	+	0.283075i	−0.744915	−	0.667159i	$-0.767510\pi$
$59$	−8.11476	+	2.17434i	−1.05645	+	0.283075i	−0.311536	+	0.950234i	$0.600844\pi$
$60$		0			0
$61$	6.74711	+	1.80788i	0.863879	+	0.231476i	0.663439	−	0.748230i	$-0.269096\pi$
$61$	6.74711	+	1.80788i	0.863879	+	0.231476i	0.200440	+	0.979706i	$0.435763\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.14950	+	3.72304i	0.266612	+	0.461786i
$66$		0			0
$67$	0.487339	+	1.81878i	0.0595380	+	0.222199i	0.989284	−	0.146002i	$-0.0466406\pi$
$67$	0.487339	+	1.81878i	0.0595380	+	0.222199i	−0.929746	+	0.368201i	$0.879974\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			3.98472i			0.472899i	0.971644	+	0.236450i	$0.0759838\pi$
$71$			3.98472i			0.472899i	−0.971644	+	0.236450i	$0.924016\pi$
$72$		0			0
$73$			5.45461i			0.638414i	0.947685	+	0.319207i	$0.103417\pi$
$73$			5.45461i			0.638414i	−0.947685	+	0.319207i	$0.896583\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.12126	−	15.3808i	−0.469662	−	1.75280i
$78$		0			0
$79$	2.95225	+	5.11344i	0.332154	+	0.575307i	0.982934	−	0.183959i	$-0.0588914\pi$
$79$	2.95225	+	5.11344i	0.332154	+	0.575307i	−0.650780	+	0.759266i	$0.725558\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−10.3428	−	2.77135i	−1.13527	−	0.304195i	−0.358223	−	0.933636i	$-0.616617\pi$
$83$	−10.3428	−	2.77135i	−1.13527	−	0.304195i	−0.777048	+	0.629441i	$0.783284\pi$
$84$		0			0
$85$	17.4695	−	4.68093i	1.89483	−	0.507718i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	2.24307i		−	0.237765i	−0.992908	−	0.118883i	$-0.962069\pi$
$89$		−	2.24307i		−	0.237765i	0.992908	−	0.118883i	$-0.0379312\pi$
$90$		0			0
$91$	3.63698	+	3.63698i	0.381259	+	0.381259i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.89016	+	3.27385i	−0.193926	+	0.335890i
$96$		0			0
$97$	6.50191	+	11.2616i	0.660169	+	1.14345i	0.980571	+	0.196165i	$0.0628488\pi$
$97$	6.50191	+	11.2616i	0.660169	+	1.14345i	−0.320402	+	0.947282i	$0.603818\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.36072	−	8.81034i	0.234901	−	0.876662i	−0.743293	−	0.668966i	$-0.766737\pi$
$101$	2.36072	−	8.81034i	0.234901	−	0.876662i	0.978194	−	0.207696i	$-0.0665963\pi$
$102$		0			0
$103$	3.73262	+	2.15503i	0.367786	+	0.212342i	0.672491	−	0.740105i	$-0.265224\pi$
$103$	3.73262	+	2.15503i	0.367786	+	0.212342i	−0.304705	+	0.952447i	$0.598558\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.0516852	+	0.0516852i	0.00499659	+	0.00499659i	0.709601	−	0.704604i	$-0.248875\pi$
$107$	0.0516852	+	0.0516852i	0.00499659	+	0.00499659i	−0.704604	+	0.709601i	$0.748875\pi$
$108$		0			0
$109$	5.73510	−	5.73510i	0.549323	−	0.549323i	−0.376922	−	0.926245i	$-0.623018\pi$
$109$	5.73510	−	5.73510i	0.549323	−	0.549323i	0.926245	+	0.376922i	$0.123018\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.13575	+	12.3595i	−0.671275	+	1.16268i	0.306268	+	0.951945i	$0.400920\pi$
$113$	−7.13575	+	12.3595i	−0.671275	+	1.16268i	−0.977543	+	0.210737i	$0.932414\pi$
$114$		0			0
$115$	−11.5316	−	3.08988i	−1.07533	−	0.288133i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	18.7394	−	10.8192i	1.71784	−	0.991794i
$120$		0			0
$121$	−10.1491	−	5.85956i	−0.922642	−	0.532688i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.35061	+	4.35061i	−0.389131	+	0.389131i
$126$		0			0
$127$	16.2634			1.44315			0.721573	−	0.692338i	$-0.243419\pi$
$127$	16.2634			1.44315			0.721573	+	0.692338i	$0.243419\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.58345	−	17.1057i	−0.400458	−	1.49453i	−0.812281	−	0.583267i	$-0.801774\pi$
$131$	−4.58345	−	17.1057i	−0.400458	−	1.49453i	0.411822	−	0.911264i	$-0.364892\pi$
$132$		0			0
$133$	−1.17061	+	4.36879i	−0.101505	+	0.378822i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.62551	−	5.55729i	0.822363	−	0.474791i	−0.0288677	−	0.999583i	$-0.509190\pi$
$137$	9.62551	−	5.55729i	0.822363	−	0.474791i	0.851231	+	0.524792i	$0.175857\pi$
$138$		0			0
$139$	−6.50347	+	1.74260i	−0.551617	+	0.147805i	−0.523852	−	0.851809i	$-0.675506\pi$
$139$	−6.50347	+	1.74260i	−0.551617	+	0.147805i	−0.0277649	+	0.999614i	$0.508839\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.33859			0.613684
$144$		0			0
$145$	3.11889			0.259009
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.7583	−	2.88268i	0.881354	−	0.236158i	0.210363	−	0.977623i	$-0.432535\pi$
$149$	10.7583	−	2.88268i	0.881354	−	0.236158i	0.670991	+	0.741465i	$0.265869\pi$
$150$		0			0
$151$	18.9045	−	10.9145i	1.53842	−	0.888210i	0.539493	−	0.841990i	$-0.318616\pi$
$151$	18.9045	−	10.9145i	1.53842	−	0.888210i	0.998931	−	0.0462196i	$-0.0147174\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.74141	+	10.2311i	−0.220195	+	0.821780i
$156$		0			0
$157$	−2.18429	−	8.15189i	−0.174326	−	0.650592i	−0.996666	−	0.0815954i	$-0.973998\pi$
$157$	−2.18429	−	8.15189i	−0.174326	−	0.650592i	0.822340	−	0.568996i	$-0.192668\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−14.2835			−1.12570
$162$		0			0
$163$	6.93193	−	6.93193i	0.542950	−	0.542950i	−0.381442	−	0.924393i	$-0.624572\pi$
$163$	6.93193	−	6.93193i	0.542950	−	0.542950i	0.924393	+	0.381442i	$0.124572\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.33544	+	4.23512i	0.567633	+	0.327723i	0.756204	−	0.654336i	$-0.227052\pi$
$167$	7.33544	+	4.23512i	0.567633	+	0.327723i	−0.188570	+	0.982060i	$0.560385\pi$
$168$		0			0
$169$	9.20544	−	5.31477i	0.708111	−	0.408828i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.81815	+	1.55897i	0.442346	+	0.118526i	0.473116	−	0.881000i	$-0.343129\pi$
$173$	5.81815	+	1.55897i	0.442346	+	0.118526i	−0.0307700	+	0.999526i	$0.509796\pi$
$174$		0			0
$175$	4.67112	−	8.09061i	0.353103	−	0.611593i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.34442	+	8.34442i	−0.623692	+	0.623692i	−0.946473	−	0.322782i	$-0.895382\pi$
$179$	−8.34442	+	8.34442i	−0.623692	+	0.623692i	0.322782	+	0.946473i	$0.395382\pi$
$180$		0			0
$181$	−13.3444	−	13.3444i	−0.991880	−	0.991880i	0.00808779	−	0.999967i	$-0.497426\pi$
$181$	−13.3444	−	13.3444i	−0.991880	−	0.991880i	−0.999967	+	0.00808779i	$0.997426\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−21.0192	−	12.1354i	−1.54536	−	0.892214i
$186$		0			0
$187$	7.99059	−	29.8213i	0.584330	−	2.18075i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.892527	−	1.54590i	−0.0645810	−	0.111858i	0.831927	−	0.554885i	$-0.187238\pi$
$191$	−0.892527	−	1.54590i	−0.0645810	−	0.111858i	−0.896508	+	0.443027i	$0.853904\pi$
$192$		0			0
$193$	−8.20588	+	14.2130i	−0.590672	+	1.02307i	0.403470	+	0.914993i	$0.367804\pi$
$193$	−8.20588	+	14.2130i	−0.590672	+	1.02307i	−0.994142	+	0.108081i	$0.965529\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.44937	+	3.44937i	0.245758	+	0.245758i	0.819227	−	0.573469i	$-0.194403\pi$
$197$	3.44937	+	3.44937i	0.245758	+	0.245758i	−0.573469	+	0.819227i	$0.694403\pi$
$198$		0			0
$199$			15.0093i			1.06398i	0.846751	+	0.531990i	$0.178556\pi$
$199$			15.0093i			1.06398i	−0.846751	+	0.531990i	$0.821444\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.60439	−	0.965795i	0.252979	−	0.0677855i
$204$		0			0
$205$	−15.7010	−	4.20707i	−1.09661	−	0.293835i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.22660	+	5.58863i	0.223189	+	0.386574i
$210$		0			0
$211$	3.18415	+	11.8834i	0.219206	+	0.818089i	0.984643	+	0.174578i	$0.0558562\pi$
$211$	3.18415	+	11.8834i	0.219206	+	0.818089i	−0.765437	+	0.643511i	$0.777477\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			18.2632i			1.24554i
$216$		0			0
$217$			12.6726i			0.860274i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.58107	+	9.63269i	0.173622	+	0.647965i
$222$		0			0
$223$	−0.258294	−	0.447379i	−0.0172967	−	0.0299587i	0.857248	−	0.514905i	$-0.172173\pi$
$223$	−0.258294	−	0.447379i	−0.0172967	−	0.0299587i	−0.874544	+	0.484946i	$0.838839\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.84745	+	2.63862i	0.653598	+	0.175131i	0.570355	−	0.821398i	$-0.306806\pi$
$227$	9.84745	+	2.63862i	0.653598	+	0.175131i	0.0832432	+	0.996529i	$0.473472\pi$
$228$		0			0
$229$	−20.6838	+	5.54222i	−1.36683	+	0.366240i	−0.866319	−	0.499491i	$-0.833520\pi$
$229$	−20.6838	+	5.54222i	−1.36683	+	0.366240i	−0.500508	+	0.865732i	$0.666854\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			23.2468i			1.52295i	0.648194	+	0.761476i	$0.275525\pi$
$233$			23.2468i			1.52295i	−0.648194	+	0.761476i	$0.724475\pi$
$234$		0			0
$235$	7.17649	+	7.17649i	0.468142	+	0.468142i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.219358	−	0.379939i	0.0141891	−	0.0245762i	−0.858844	−	0.512238i	$-0.828817\pi$
$239$	0.219358	−	0.379939i	0.0141891	−	0.0245762i	0.873033	+	0.487662i	$0.162150\pi$
$240$		0			0
$241$	7.67406	+	13.2919i	0.494330	+	0.856204i	0.999979	−	0.00653501i	$-0.00208017\pi$
$241$	7.67406	+	13.2919i	0.494330	+	0.856204i	−0.505649	+	0.862739i	$0.668747\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.00658	−	11.2207i	0.192083	−	0.716865i
$246$		0			0
$247$	−1.80521	−	1.04224i	−0.114863	−	0.0663159i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.02147	+	8.02147i	0.506310	+	0.506310i	0.913392	−	0.407081i	$-0.133453\pi$
$251$	8.02147	+	8.02147i	0.506310	+	0.506310i	−0.407081	+	0.913392i	$0.633453\pi$
$252$		0			0
$253$	−14.4104	+	14.4104i	−0.905977	+	0.905977i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.72936	+	8.19149i	−0.295009	+	0.510971i	−0.974987	−	0.222262i	$-0.928656\pi$
$257$	−4.72936	+	8.19149i	−0.295009	+	0.510971i	0.679978	+	0.733233i	$0.261989\pi$
$258$		0			0
$259$	−28.0490	−	7.51571i	−1.74288	−	0.467003i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	16.2413	−	9.37694i	1.00148	−	0.578207i	0.0927966	−	0.995685i	$-0.470419\pi$
$263$	16.2413	−	9.37694i	1.00148	−	0.578207i	0.908687	+	0.417478i	$0.137086\pi$
$264$		0			0
$265$	−2.60743	−	1.50540i	−0.160173	−	0.0924759i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.5606	−	13.5606i	0.826805	−	0.826805i	−0.160269	−	0.987073i	$-0.551236\pi$
$269$	13.5606	−	13.5606i	0.826805	−	0.826805i	0.987073	+	0.160269i	$0.0512361\pi$
$270$		0			0
$271$	−30.6233			−1.86023			−0.930115	−	0.367268i	$-0.880293\pi$
$271$	−30.6233			−1.86023			−0.930115	+	0.367268i	$0.880293\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.44988	−	12.8751i	−0.208036	−	0.776400i
$276$		0			0
$277$	5.40521	−	20.1725i	0.324767	−	1.21205i	−0.589778	−	0.807565i	$-0.700785\pi$
$277$	5.40521	−	20.1725i	0.324767	−	1.21205i	0.914545	−	0.404483i	$-0.132549\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.6538	+	6.15097i	−0.635552	+	0.366936i	−0.782899	−	0.622149i	$-0.786260\pi$
$281$	−10.6538	+	6.15097i	−0.635552	+	0.366936i	0.147347	+	0.989085i	$0.452927\pi$
$282$		0			0
$283$	−12.8013	+	3.43009i	−0.760957	+	0.203898i	−0.618373	−	0.785885i	$-0.712208\pi$
$283$	−12.8013	+	3.43009i	−0.760957	+	0.203898i	−0.142584	+	0.989783i	$0.545541\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−19.4479			−1.14797
$288$		0			0
$289$	24.9540			1.46788
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−21.3351	+	5.71672i	−1.24641	+	0.333974i	−0.820948	−	0.571003i	$-0.806554\pi$
$293$	−21.3351	+	5.71672i	−1.24641	+	0.333974i	−0.425460	+	0.904977i	$0.639888\pi$
$294$		0			0
$295$	−20.3148	+	11.7287i	−1.18277	+	0.682874i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.70377	−	6.35854i	0.0985313	−	0.367724i
$300$		0			0
$301$	5.65539	+	21.1062i	0.325971	+	1.21654i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	19.5040			1.11680
$306$		0			0
$307$	3.59225	−	3.59225i	0.205021	−	0.205021i	−0.597126	−	0.802147i	$-0.703691\pi$
$307$	3.59225	−	3.59225i	0.205021	−	0.205021i	0.802147	+	0.597126i	$0.203691\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.62665	−	4.98060i	−0.489173	−	0.282424i	0.235058	−	0.971981i	$-0.424472\pi$
$311$	−8.62665	−	4.98060i	−0.489173	−	0.282424i	−0.724231	+	0.689557i	$0.757805\pi$
$312$		0			0
$313$	−22.1588	+	12.7934i	−1.25249	+	0.723124i	−0.971603	−	0.236617i	$-0.923961\pi$
$313$	−22.1588	+	12.7934i	−1.25249	+	0.723124i	−0.280885	+	0.959741i	$0.590628\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.8781	−	4.79041i	−1.00413	−	0.269056i	−0.280957	−	0.959720i	$-0.590652\pi$
$317$	−17.8781	−	4.79041i	−1.00413	−	0.269056i	−0.723176	+	0.690664i	$0.757318\pi$
$318$		0			0
$319$	2.66205	−	4.61080i	0.149046	−	0.258155i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−6.20084	+	6.20084i	−0.345024	+	0.345024i
$324$		0			0
$325$	3.04449	+	3.04449i	0.168878	+	0.168878i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	10.5159	+	6.07136i	0.579760	+	0.334725i
$330$		0			0
$331$	−5.10146	+	19.0389i	−0.280402	+	1.04647i	0.671733	+	0.740794i	$0.265550\pi$
$331$	−5.10146	+	19.0389i	−0.280402	+	1.04647i	−0.952134	+	0.305680i	$0.901116\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.62878	+	4.55319i	0.143626	+	0.248767i
$336$		0			0
$337$	3.29609	−	5.70899i	0.179549	−	0.310988i	−0.762177	−	0.647369i	$-0.775869\pi$
$337$	3.29609	−	5.70899i	0.179549	−	0.310988i	0.941726	+	0.336380i	$0.109203\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.7852	+	12.7852i	0.692360	+	0.692360i
$342$		0			0
$343$			9.48653i			0.512224i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.20074	+	0.857635i	−0.171825	+	0.0460403i	−0.343706	−	0.939077i	$-0.611682\pi$
$347$	−3.20074	+	0.857635i	−0.171825	+	0.0460403i	0.171881	+	0.985118i	$0.445016\pi$
$348$		0			0
$349$	−22.0000	−	5.89488i	−1.17763	−	0.315546i	−0.383645	−	0.923480i	$-0.625331\pi$
$349$	−22.0000	−	5.89488i	−1.17763	−	0.315546i	−0.793987	+	0.607935i	$0.791998\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.2071	−	24.6074i	−0.756167	−	1.30972i	−0.944792	−	0.327670i	$-0.893737\pi$
$353$	−14.2071	−	24.6074i	−0.756167	−	1.30972i	0.188626	−	0.982049i	$-0.439597\pi$
$354$		0			0
$355$	2.87967	+	10.7471i	0.152837	+	0.570396i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	7.35521i		−	0.388193i	−0.980982	−	0.194097i	$-0.937823\pi$
$359$		−	7.35521i		−	0.388193i	0.980982	−	0.194097i	$-0.0621775\pi$
$360$		0			0
$361$			17.1670i			0.903527i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.94194	+	14.7115i	0.206330	+	0.770035i
$366$		0			0
$367$	17.0496	+	29.5308i	0.889984	+	1.54150i	0.839893	+	0.542752i	$0.182618\pi$
$367$	17.0496	+	29.5308i	0.889984	+	1.54150i	0.0500906	+	0.998745i	$0.484049\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.47948	−	0.932323i	−0.180646	−	0.0484038i
$372$		0			0
$373$	23.8179	−	6.38198i	1.23324	−	0.330447i	0.417402	−	0.908722i	$-0.362941\pi$
$373$	23.8179	−	6.38198i	1.23324	−	0.330447i	0.815842	+	0.578275i	$0.196274\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			1.71976i			0.0885720i
$378$		0			0
$379$	2.66916	+	2.66916i	0.137106	+	0.137106i	0.772329	−	0.635223i	$-0.219092\pi$
$379$	2.66916	+	2.66916i	0.137106	+	0.137106i	−0.635223	+	0.772329i	$0.719092\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.14570	+	5.44851i	−0.160738	+	0.278406i	−0.935133	−	0.354296i	$-0.884721\pi$
$383$	−3.14570	+	5.44851i	−0.160738	+	0.278406i	0.774396	+	0.632701i	$0.218054\pi$
$384$		0			0
$385$	−22.2307	−	38.5047i	−1.13298	−	1.96238i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.724164	−	2.70262i	0.0367166	−	0.137028i	−0.945135	−	0.326681i	$-0.894070\pi$
$389$	0.724164	−	2.70262i	0.0367166	−	0.137028i	0.981851	+	0.189653i	$0.0607363\pi$
$390$		0			0
$391$	−23.9836	−	13.8469i	−1.21290	−	0.700269i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	11.6578	+	11.6578i	0.586568	+	0.586568i
$396$		0			0
$397$	−4.29700	+	4.29700i	−0.215660	+	0.215660i	−0.806667	−	0.591007i	$-0.798731\pi$
$397$	−4.29700	+	4.29700i	−0.215660	+	0.215660i	0.591007	+	0.806667i	$0.298731\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.63116	−	11.4855i	0.331145	−	0.573559i	−0.651592	−	0.758570i	$-0.725899\pi$
$401$	6.63116	−	11.4855i	0.331145	−	0.573559i	0.982737	+	0.185010i	$0.0592319\pi$
$402$		0			0
$403$	−5.64143	−	1.51162i	−0.281020	−	0.0752990i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−35.8808	+	20.7158i	−1.77854	+	1.02684i
$408$		0			0
$409$	−10.6538	−	6.15100i	−0.526799	−	0.304147i	0.212913	−	0.977071i	$-0.431705\pi$
$409$	−10.6538	−	6.15100i	−0.526799	−	0.304147i	−0.739712	+	0.672924i	$0.765038\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−19.8452	+	19.8452i	−0.976518	+	0.976518i
$414$		0			0
$415$	−29.8981			−1.46764
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.82317	+	29.1965i	0.382187	+	1.42634i	0.842554	+	0.538612i	$0.181051\pi$
$419$	7.82317	+	29.1965i	0.382187	+	1.42634i	−0.460367	+	0.887729i	$0.652282\pi$
$420$		0			0
$421$	−5.75964	+	21.4953i	−0.280708	+	1.04762i	0.671211	+	0.741266i	$0.265774\pi$
$421$	−5.75964	+	21.4953i	−0.280708	+	1.04762i	−0.951919	+	0.306350i	$0.900892\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	15.6866	−	9.05668i	0.760913	−	0.439314i
$426$		0			0
$427$	22.5401	−	6.03961i	1.09079	−	0.292277i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.3940			0.741505			0.370752	−	0.928732i	$-0.379100\pi$
$431$	15.3940			0.741505			0.370752	+	0.928732i	$0.379100\pi$
$432$		0			0
$433$	−17.2454			−0.828763			−0.414382	−	0.910103i	$-0.636002\pi$
$433$	−17.2454			−0.828763			−0.414382	+	0.910103i	$0.636002\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.59138	−	1.49821i	0.267472	−	0.0716690i
$438$		0			0
$439$	4.55070	−	2.62735i	0.217193	−	0.125397i	−0.387457	−	0.921888i	$-0.626646\pi$
$439$	4.55070	−	2.62735i	0.217193	−	0.125397i	0.604650	+	0.796491i	$0.293313\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.35032	−	12.5036i	0.159179	−	0.594062i	−0.839533	−	0.543309i	$-0.817171\pi$
$443$	3.35032	−	12.5036i	0.159179	−	0.594062i	0.998711	−	0.0507532i	$-0.0161622\pi$
$444$		0			0
$445$	−1.62102	−	6.04974i	−0.0768438	−	0.286785i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−27.9740			−1.32018			−0.660088	−	0.751189i	$-0.729481\pi$
$449$	−27.9740			−1.32018			−0.660088	+	0.751189i	$0.729481\pi$
$450$		0			0
$451$	−19.6207	+	19.6207i	−0.923904	+	0.923904i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	12.4376	+	7.18083i	0.583082	+	0.336643i
$456$		0			0
$457$	35.2732	−	20.3650i	1.65001	−	0.952635i	0.672947	−	0.739690i	$-0.265028\pi$
$457$	35.2732	−	20.3650i	1.65001	−	0.952635i	0.977064	−	0.212944i	$-0.0683053\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	36.8721	+	9.87984i	1.71730	+	0.460150i	0.977196	−	0.212339i	$-0.0681082\pi$
$461$	36.8721	+	9.87984i	1.71730	+	0.460150i	0.740107	+	0.672489i	$0.234775\pi$
$462$		0			0
$463$	17.7637	−	30.7676i	0.825549	−	1.42989i	−0.0759497	−	0.997112i	$-0.524199\pi$
$463$	17.7637	−	30.7676i	0.825549	−	1.42989i	0.901499	−	0.432781i	$-0.142468\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.1010	+	17.1010i	−0.791341	+	0.791341i	−0.981712	−	0.190371i	$-0.939031\pi$
$467$	−17.1010	+	17.1010i	−0.791341	+	0.791341i	0.190371	+	0.981712i	$0.439031\pi$
$468$		0			0
$469$	4.44794	+	4.44794i	0.205387	+	0.205387i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	26.9994	+	15.5881i	1.24143	+	0.716742i
$474$		0			0
$475$	−0.979914	+	3.65709i	−0.0449615	+	0.167799i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.76619	−	11.7194i	−0.309155	−	0.535473i	0.669023	−	0.743242i	$-0.266713\pi$
$479$	−6.76619	−	11.7194i	−0.309155	−	0.535473i	−0.978178	+	0.207769i	$0.933380\pi$
$480$		0			0
$481$	6.69148	−	11.5900i	0.305105	−	0.528458i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	25.6747	+	25.6747i	1.16583	+	1.16583i
$486$		0			0
$487$		−	16.1436i		−	0.731536i	−0.930706	−	0.365768i	$-0.880806\pi$
$487$		−	16.1436i		−	0.731536i	0.930706	−	0.365768i	$-0.119194\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−34.9555	+	9.36630i	−1.57752	+	0.422695i	−0.938157	−	0.346209i	$-0.887469\pi$
$491$	−34.9555	+	9.36630i	−1.57752	+	0.422695i	−0.639363	+	0.768905i	$0.720802\pi$
$492$		0			0
$493$	6.98844	+	1.87255i	0.314744	+	0.0843353i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.65589	+	11.5283i	0.298557	+	0.517117i
$498$		0			0
$499$	1.70347	+	6.35742i	0.0762576	+	0.284597i	0.993516	−	0.113696i	$-0.0362691\pi$
$499$	1.70347	+	6.35742i	0.0762576	+	0.284597i	−0.917258	+	0.398294i	$0.869602\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	8.67964i		−	0.387006i	−0.981100	−	0.193503i	$-0.938015\pi$
$503$		−	8.67964i		−	0.387006i	0.981100	−	0.193503i	$-0.0619849\pi$
$504$		0			0
$505$		−	25.4682i		−	1.13332i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.894794	−	3.33942i	−0.0396611	−	0.148017i	0.943256	−	0.332067i	$-0.107746\pi$
$509$	−0.894794	−	3.33942i	−0.0396611	−	0.148017i	−0.982917	+	0.184050i	$0.941079\pi$
$510$		0			0
$511$	9.11113	+	15.7809i	0.403053	+	0.698108i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	11.6246	+	3.11479i	0.512240	+	0.137254i
$516$		0			0
$517$	16.7347	−	4.48404i	0.735990	−	0.197208i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	15.7843i		−	0.691524i	−0.938322	−	0.345762i	$-0.887620\pi$
$521$		−	15.7843i		−	0.691524i	0.938322	−	0.345762i	$-0.112380\pi$
$522$		0			0
$523$	−6.62449	−	6.62449i	−0.289669	−	0.289669i	0.547280	−	0.836949i	$-0.315663\pi$
$523$	−6.62449	−	6.62449i	−0.289669	−	0.289669i	−0.836949	+	0.547280i	$0.815663\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.2853	+	21.2787i	−0.535155	+	0.926916i
$528$		0			0
$529$	−2.35965	−	4.08703i	−0.102593	−	0.177697i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.31978	−	8.65755i	0.100481	−	0.375000i
$534$		0			0
$535$	0.176751	+	0.102047i	0.00764160	+	0.00441188i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−14.0219	−	14.0219i	−0.603967	−	0.603967i
$540$		0			0
$541$	32.2832	−	32.2832i	1.38796	−	1.38796i	0.558377	−	0.829587i	$-0.311424\pi$
$541$	32.2832	−	32.2832i	1.38796	−	1.38796i	0.829587	−	0.558377i	$-0.188576\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.3234	−	19.6126i	0.485040	−	0.840113i
$546$		0			0
$547$	7.43060	+	1.99102i	0.317710	+	0.0851300i	0.414150	−	0.910209i	$-0.364079\pi$
$547$	7.43060	+	1.99102i	0.317710	+	0.0851300i	−0.0964402	+	0.995339i	$0.530746\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.30966	+	0.756135i	−0.0557936	+	0.0322124i
$552$		0			0
$553$	17.0825	+	9.86259i	0.726422	+	0.419400i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−24.4143	+	24.4143i	−1.03447	+	1.03447i	−0.0350828	+	0.999384i	$0.511170\pi$
$557$	−24.4143	+	24.4143i	−1.03447	+	1.03447i	−0.999384	+	0.0350828i	$0.988830\pi$
$558$		0			0
$559$	−10.0704			−0.425931
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.30278	+	12.3261i	0.139196	+	0.519485i	0.999945	+	0.0104567i	$0.00332852\pi$
$563$	3.30278	+	12.3261i	0.139196	+	0.519485i	−0.860750	+	0.509028i	$0.830005\pi$
$564$		0			0
$565$	−10.3137	+	38.4913i	−0.433901	+	1.61934i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.2747	+	12.8603i	−0.933803	+	0.539132i	−0.888012	−	0.459819i	$-0.847914\pi$
$569$	−22.2747	+	12.8603i	−0.933803	+	0.539132i	−0.0457910	+	0.998951i	$0.514581\pi$
$570$		0			0
$571$	−33.6207	+	9.00865i	−1.40698	+	0.377000i	−0.880848	−	0.473400i	$-0.843027\pi$
$571$	−33.6207	+	9.00865i	−1.40698	+	0.377000i	−0.526136	+	0.850400i	$0.676360\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−11.9566			−0.498626
$576$		0			0
$577$	−26.7695			−1.11443			−0.557215	−	0.830369i	$-0.688130\pi$
$577$	−26.7695			−1.11443			−0.557215	+	0.830369i	$0.688130\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−34.5523	+	9.25826i	−1.43347	+	0.384097i
$582$		0			0
$583$	−4.45101	+	2.56979i	−0.184342	+	0.106430i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.79668	−	36.5617i	0.404352	−	1.50906i	−0.400895	−	0.916124i	$-0.631301\pi$
$587$	9.79668	−	36.5617i	0.404352	−	1.50906i	0.805247	−	0.592939i	$-0.202033\pi$
$588$		0			0
$589$	−1.32924	−	4.96080i	−0.0547704	−	0.204406i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	7.98596			0.327944			0.163972	−	0.986465i	$-0.447569\pi$
$593$	7.98596			0.327944			0.163972	+	0.986465i	$0.447569\pi$
$594$		0			0
$595$	42.7228	−	42.7228i	1.75146	−	1.75146i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.64879	+	0.951932i	0.0673679	+	0.0388949i	0.533306	−	0.845923i	$-0.320950\pi$
$599$	1.64879	+	0.951932i	0.0673679	+	0.0388949i	−0.465938	+	0.884818i	$0.654283\pi$
$600$		0			0
$601$	−11.7530	+	6.78561i	−0.479416	+	0.276791i	−0.720173	−	0.693794i	$-0.755938\pi$
$601$	−11.7530	+	6.78561i	−0.479416	+	0.276791i	0.240757	+	0.970585i	$0.422604\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−31.6074	−	8.46917i	−1.28502	−	0.344321i
$606$		0			0
$607$	3.16527	−	5.48241i	0.128474	−	0.222524i	−0.794611	−	0.607119i	$-0.792325\pi$
$607$	3.16527	−	5.48241i	0.128474	−	0.222524i	0.923086	+	0.384594i	$0.125659\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.95712	+	3.95712i	−0.160088	+	0.160088i
$612$		0			0
$613$	−1.83081	−	1.83081i	−0.0739458	−	0.0739458i	0.669167	−	0.743112i	$-0.266651\pi$
$613$	−1.83081	−	1.83081i	−0.0739458	−	0.0739458i	−0.743112	+	0.669167i	$0.766651\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3.82758	−	2.20985i	−0.154092	−	0.0889653i	0.420971	−	0.907074i	$-0.361689\pi$
$617$	−3.82758	−	2.20985i	−0.154092	−	0.0889653i	−0.575064	+	0.818109i	$0.695023\pi$
$618$		0			0
$619$	−3.75899	+	14.0287i	−0.151087	+	0.563863i	0.848322	+	0.529480i	$0.177613\pi$
$619$	−3.75899	+	14.0287i	−0.151087	+	0.563863i	−0.999409	+	0.0343824i	$0.989054\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.74672	−	6.48952i	−0.150109	−	0.259997i
$624$		0			0
$625$	−15.5810	+	26.9872i	−0.623242	+	1.07949i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−39.8114	−	39.8114i	−1.58738	−	1.58738i
$630$		0			0
$631$			33.6255i			1.33861i	0.742987	+	0.669305i	$0.233408\pi$
$631$			33.6255i			1.33861i	−0.742987	+	0.669305i	$0.766592\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	43.8637	−	11.7532i	1.74068	−	0.466413i
$636$		0			0
$637$	6.18711	+	1.65783i	0.245142	+	0.0656857i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	22.9601	+	39.7681i	0.906871	+	1.57075i	0.818386	+	0.574668i	$0.194869\pi$
$641$	22.9601	+	39.7681i	0.906871	+	1.57075i	0.0884843	+	0.996078i	$0.471798\pi$
$642$		0			0
$643$	−6.92565	−	25.8469i	−0.273121	−	1.01930i	−0.957090	−	0.289790i	$-0.906415\pi$
$643$	−6.92565	−	25.8469i	−0.273121	−	1.01930i	0.683969	−	0.729511i	$-0.260252\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	11.4351i		−	0.449559i	−0.974410	−	0.224780i	$-0.927834\pi$
$647$		−	11.4351i		−	0.449559i	0.974410	−	0.224780i	$-0.0721662\pi$
$648$		0			0
$649$			40.0431i			1.57183i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.73613	−	21.4075i	−0.224472	−	0.837741i	−0.982615	−	0.185653i	$-0.940560\pi$
$653$	−5.73613	−	21.4075i	−0.224472	−	0.837741i	0.758143	−	0.652088i	$-0.226107\pi$
$654$		0			0
$655$	−24.7239	−	42.8230i	−0.966041	−	1.67323i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	26.7345	+	7.16348i	1.04143	+	0.279050i	0.738705	−	0.674029i	$-0.235438\pi$
$659$	26.7345	+	7.16348i	1.04143	+	0.279050i	0.302723	+	0.953079i	$0.402104\pi$
$660$		0			0
$661$	9.68293	−	2.59453i	0.376622	−	0.100916i	−0.0655417	−	0.997850i	$-0.520878\pi$
$661$	9.68293	−	2.59453i	0.376622	−	0.100916i	0.442164	+	0.896934i	$0.354211\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			12.6289i			0.489729i
$666$		0			0
$667$	−3.37700	−	3.37700i	−0.130758	−	0.130758i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	16.6472	−	28.8337i	0.642656	−	1.11311i
$672$		0			0
$673$	−16.7789	−	29.0620i	−0.646781	−	1.12026i	−0.983887	−	0.178791i	$-0.942782\pi$
$673$	−16.7789	−	29.0620i	−0.646781	−	1.12026i	0.337106	−	0.941467i	$-0.390552\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.92612	+	25.8486i	−0.266192	+	0.993443i	0.695324	+	0.718696i	$0.255261\pi$
$677$	−6.92612	+	25.8486i	−0.266192	+	0.993443i	−0.961517	+	0.274747i	$0.911406\pi$
$678$		0			0
$679$	37.6218	+	21.7210i	1.44379	+	0.833575i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.62993	−	9.62993i	−0.368479	−	0.368479i	0.498443	−	0.866922i	$-0.333905\pi$
$683$	−9.62993	−	9.62993i	−0.368479	−	0.368479i	−0.866922	+	0.498443i	$0.833905\pi$
$684$		0			0
$685$	21.9446	−	21.9446i	0.838460	−	0.838460i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.830078	−	1.43774i	0.0316235	−	0.0547734i
$690$		0			0
$691$	36.8896	+	9.88454i	1.40335	+	0.376025i	0.879545	−	0.475815i	$-0.157847\pi$
$691$	36.8896	+	9.88454i	1.40335	+	0.376025i	0.523801	+	0.851841i	$0.324514\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.2810	+	9.39985i	−0.617574	+	0.356557i
$696$		0			0
$697$	−32.6551	−	18.8534i	−1.23690	−	0.714125i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	24.7308	−	24.7308i	0.934070	−	0.934070i	−0.0638873	−	0.997957i	$-0.520350\pi$
$701$	24.7308	−	24.7308i	0.934070	−	0.934070i	0.997957	+	0.0638873i	$0.0203498\pi$
$702$		0			0
$703$	11.7683			0.443851
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.88649	−	29.4328i	−0.296602	−	1.10693i
$708$		0			0
$709$	−7.27509	+	27.1510i	−0.273222	+	1.01968i	0.683802	+	0.729668i	$0.260325\pi$
$709$	−7.27509	+	27.1510i	−0.273222	+	1.01968i	−0.957024	+	0.290010i	$0.906341\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.0461	−	8.10951i	0.526030	−	0.303704i
$714$		0			0
$715$	19.7927	−	5.30345i	0.740207	−	0.198338i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	12.7928			0.477091			0.238546	−	0.971131i	$-0.423329\pi$
$719$	12.7928			0.477091			0.238546	+	0.971131i	$0.423329\pi$
$720$		0			0
$721$	14.3987			0.536234
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.01722	−	0.808460i	0.112057	−	0.0300255i
$726$		0			0
$727$	−3.44828	+	1.99086i	−0.127890	+	0.0738371i	−0.562580	−	0.826743i	$-0.690191\pi$
$727$	−3.44828	+	1.99086i	−0.127890	+	0.0738371i	0.434690	+	0.900580i	$0.356858\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.9650	+	40.9221i	−0.405557	+	1.51356i
$732$		0			0
$733$	9.71206	+	36.2459i	0.358723	+	1.33877i	0.875734	+	0.482794i	$0.160378\pi$
$733$	9.71206	+	36.2459i	0.358723	+	1.33877i	−0.517011	+	0.855979i	$0.672955\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.97493			0.330596
$738$		0			0
$739$	−3.06425	+	3.06425i	−0.112720	+	0.112720i	−0.761217	−	0.648497i	$-0.775398\pi$
$739$	−3.06425	+	3.06425i	−0.112720	+	0.112720i	0.648497	+	0.761217i	$0.275398\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−30.1059	−	17.3817i	−1.10448	−	0.637671i	−0.167085	−	0.985943i	$-0.553435\pi$
$743$	−30.1059	−	17.3817i	−1.10448	−	0.637671i	−0.937394	+	0.348272i	$0.886769\pi$
$744$		0			0
$745$	26.9327	−	15.5496i	0.986738	−	0.569693i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.235865	+	0.0631998i	0.00861831	+	0.00230927i
$750$		0			0
$751$	7.10890	−	12.3130i	0.259407	−	0.449307i	−0.706676	−	0.707537i	$-0.749806\pi$
$751$	7.10890	−	12.3130i	0.259407	−	0.449307i	0.966083	+	0.258231i	$0.0831394\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	43.0991	−	43.0991i	1.56854	−	1.56854i
$756$		0			0
$757$	2.11199	+	2.11199i	0.0767615	+	0.0767615i	0.744445	−	0.667684i	$-0.232714\pi$
$757$	2.11199	+	2.11199i	0.0767615	+	0.0767615i	−0.667684	+	0.744445i	$0.732714\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.3519	+	9.44076i	0.592755	+	0.342227i	0.766186	−	0.642619i	$-0.222152\pi$
$761$	16.3519	+	9.44076i	0.592755	+	0.342227i	−0.173431	+	0.984846i	$0.555485\pi$
$762$		0			0
$763$	7.01279	−	26.1721i	0.253880	−	0.947493i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.46724	−	11.2016i	−0.233519	−	0.404466i
$768$		0			0
$769$	3.50579	−	6.07221i	0.126422	−	0.218970i	−0.795866	−	0.605473i	$-0.792984\pi$
$769$	3.50579	−	6.07221i	0.126422	−	0.218970i	0.922288	+	0.386503i	$0.126317\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.54407	−	8.54407i	−0.307309	−	0.307309i	0.536556	−	0.843865i	$-0.319725\pi$
$773$	−8.54407	−	8.54407i	−0.307309	−	0.307309i	−0.843865	+	0.536556i	$0.819725\pi$
$774$		0			0
$775$			10.6082i			0.381057i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.61302	−	2.03990i	0.272765	−	0.0730871i
$780$		0			0
$781$	18.3458	+	4.91575i	0.656465	+	0.175899i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.7824	−	20.4077i	−0.420532	−	0.728383i
$786$		0			0
$787$	6.16205	+	22.9971i	0.219653	+	0.819758i	0.984476	+	0.175517i	$0.0561598\pi$
$787$	6.16205	+	22.9971i	0.219653	+	0.819758i	−0.764823	+	0.644241i	$0.777174\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			47.6769i			1.69519i
$792$		0			0
$793$			10.7545i			0.381904i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.78931	−	6.67778i	−0.0633804	−	0.236539i	0.926968	−	0.375141i	$-0.122406\pi$
$797$	−1.78931	−	6.67778i	−0.0633804	−	0.236539i	−0.990348	+	0.138602i	$0.955739\pi$
$798$		0			0
$799$	11.7716	+	20.3889i	0.416448	+	0.721309i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	25.1133	+	6.72909i	0.886229	+	0.237464i
$804$		0			0
$805$	−38.5237	+	10.3224i	−1.35778	+	0.363817i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	39.0505i		−	1.37294i	−0.727157	−	0.686471i	$-0.759159\pi$
$809$		−	39.0505i		−	1.37294i	0.727157	−	0.686471i	$-0.240841\pi$
$810$		0			0
$811$	2.40853	+	2.40853i	0.0845748	+	0.0845748i	0.748129	−	0.663554i	$-0.230953\pi$
$811$	2.40853	+	2.40853i	0.0845748	+	0.0845748i	−0.663554	+	0.748129i	$0.730953\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.6864	−	23.7055i	0.479413	−	0.830367i
$816$		0			0
$817$	−4.42769	−	7.66898i	−0.154905	−	0.268304i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.66611	+	28.6103i	−0.267549	+	0.998506i	0.693123	+	0.720820i	$0.256234\pi$
$821$	−7.66611	+	28.6103i	−0.267549	+	0.998506i	−0.960672	+	0.277687i	$0.910432\pi$
$822$		0			0
$823$	−22.1086	−	12.7644i	−0.770659	−	0.444940i	0.0624509	−	0.998048i	$-0.480108\pi$
$823$	−22.1086	−	12.7644i	−0.770659	−	0.444940i	−0.833110	+	0.553108i	$0.813442\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.10050	+	5.10050i	0.177362	+	0.177362i	0.790205	−	0.612843i	$-0.209974\pi$
$827$	5.10050	+	5.10050i	0.177362	+	0.177362i	−0.612843	+	0.790205i	$0.709974\pi$
$828$		0			0
$829$	1.30033	−	1.30033i	0.0451624	−	0.0451624i	−0.684165	−	0.729327i	$-0.739833\pi$
$829$	1.30033	−	1.30033i	0.0451624	−	0.0451624i	0.729327	+	0.684165i	$0.239833\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	13.4736	−	23.3370i	0.466833	−	0.808578i
$834$		0			0
$835$	22.8449	+	6.12126i	0.790579	+	0.211835i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−28.6072	+	16.5164i	−0.987631	+	0.570209i	−0.904565	−	0.426335i	$-0.859804\pi$
$839$	−28.6072	+	16.5164i	−0.987631	+	0.570209i	−0.0830657	+	0.996544i	$0.526471\pi$
$840$		0			0
$841$	−24.0342	−	13.8762i	−0.828766	−	0.478488i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	20.9869	−	20.9869i	0.721972	−	0.721972i
$846$		0			0
$847$	−39.1502			−1.34522
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.61896	+	35.8984i	0.329734	+	1.23058i
$852$		0			0
$853$	−4.12451	+	15.3929i	−0.141221	+	0.527043i	0.858674	+	0.512522i	$0.171289\pi$
$853$	−4.12451	+	15.3929i	−0.141221	+	0.527043i	−0.999895	+	0.0145204i	$0.995378\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.6603	−	7.88675i	0.466625	−	0.269406i	−0.248201	−	0.968709i	$-0.579839\pi$
$857$	13.6603	−	7.88675i	0.466625	−	0.269406i	0.714826	+	0.699302i	$0.246506\pi$
$858$		0			0
$859$	31.9956	−	8.57320i	1.09168	−	0.292514i	0.332306	−	0.943172i	$-0.392173\pi$
$859$	31.9956	−	8.57320i	1.09168	−	0.292514i	0.759371	+	0.650658i	$0.225507\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	37.4407			1.27449			0.637247	−	0.770659i	$-0.280073\pi$
$863$	37.4407			1.27449			0.637247	+	0.770659i	$0.280073\pi$
$864$		0			0
$865$	16.8186			0.571850
$866$		0			0
$867$		0			0
$868$		0			0
$869$	27.1845	−	7.28408i	0.922173	−	0.247095i
$870$		0			0
$871$	−2.51063	+	1.44951i	−0.0850695	+	0.0491149i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.31986	+	19.8540i	−0.179844	+	0.671187i
$876$		0			0
$877$	7.55790	+	28.2065i	0.255212	+	0.952465i	0.967972	+	0.251057i	$0.0807781\pi$
$877$	7.55790	+	28.2065i	0.255212	+	0.952465i	−0.712760	+	0.701408i	$0.752555\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.5567			0.389355			0.194678	−	0.980867i	$-0.437634\pi$
$881$	11.5567			0.389355			0.194678	+	0.980867i	$0.437634\pi$
$882$		0			0
$883$	19.2632	−	19.2632i	0.648260	−	0.648260i	−0.304313	−	0.952572i	$-0.598427\pi$
$883$	19.2632	−	19.2632i	0.648260	−	0.648260i	0.952572	+	0.304313i	$0.0984267\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−19.8424	−	11.4560i	−0.666243	−	0.384656i	0.128408	−	0.991721i	$-0.459013\pi$
$887$	−19.8424	−	11.4560i	−0.666243	−	0.384656i	−0.794652	+	0.607066i	$0.792347\pi$
$888$		0			0
$889$	47.0523	−	27.1657i	1.57808	−	0.911107i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.75336	−	1.27366i	−0.159065	−	0.0426214i
$894$		0			0
$895$	−16.4752	+	28.5359i	−0.550705	+	0.953850i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.99615	+	2.99615i	−0.0999272	+	0.0999272i
$900$		0			0
$901$	−4.93860	−	4.93860i	−0.164529	−	0.164529i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−45.6345	−	26.3471i	−1.51694	−	0.875807i
$906$		0			0
$907$	12.7169	−	47.4603i	0.422259	−	1.57589i	−0.347577	−	0.937651i	$-0.612995\pi$
$907$	12.7169	−	47.4603i	0.422259	−	1.57589i	0.769836	−	0.638242i	$-0.220338\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.47683	+	11.2182i	0.214587	+	0.371675i	0.953145	−	0.302515i	$-0.0978262\pi$
$911$	6.47683	+	11.2182i	0.214587	+	0.371675i	−0.738558	+	0.674190i	$0.764493\pi$
$912$		0			0
$913$	−25.5188	+	44.1999i	−0.844550	+	1.46280i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−41.8331	−	41.8331i	−1.38145	−	1.38145i
$918$		0			0
$919$			5.55214i			0.183148i	0.995798	+	0.0915740i	$0.0291898\pi$
$919$			5.55214i			0.183148i	−0.995798	+	0.0915740i	$0.970810\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.92596	+	1.58786i	−0.195055	+	0.0522649i
$924$		0			0
$925$	−23.4796	−	6.29135i	−0.772006	−	0.206858i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.8356	−	49.9447i	−0.946066	−	1.63863i	−0.753603	−	0.657330i	$-0.771686\pi$
$929$	−28.8356	−	49.9447i	−0.946066	−	1.63863i	−0.192462	−	0.981304i	$-0.561647\pi$
$930$		0			0
$931$	1.45782	+	5.44064i	0.0477780	+	0.178310i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	86.2049i		−	2.81920i
$936$		0			0
$937$		−	44.7899i		−	1.46322i	−0.681722	−	0.731612i	$-0.738768\pi$
$937$		−	44.7899i		−	1.46322i	0.681722	−	0.731612i	$-0.261232\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.72682	+	36.3010i	0.317085	+	1.18338i	0.922032	+	0.387113i	$0.126528\pi$
$941$	9.72682	+	36.3010i	0.317085	+	1.18338i	−0.604947	+	0.796266i	$0.706806\pi$
$942$		0			0
$943$	12.4452	+	21.5557i	0.405270	+	0.701949i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−54.8652	−	14.7011i	−1.78288	−	0.477721i	−0.791775	−	0.610813i	$-0.790843\pi$
$947$	−54.8652	−	14.7011i	−1.78288	−	0.477721i	−0.991104	+	0.133093i	$0.957509\pi$
$948$		0			0
$949$	−8.11194	+	2.17359i	−0.263325	+	0.0705577i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	7.26359i		−	0.235291i	−0.993056	−	0.117645i	$-0.962465\pi$
$953$		−	7.26359i		−	0.235291i	0.993056	−	0.117645i	$-0.0375346\pi$
$954$		0			0
$955$	−3.52440	−	3.52440i	−0.114047	−	0.114047i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	18.5653	−	32.1560i	0.599504	−	1.03837i
$960$		0			0
$961$	8.30507	+	14.3848i	0.267905	+	0.464026i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.8604	+	44.2638i	−0.381801	+	1.42490i
$966$		0			0
$967$	−4.17378	−	2.40973i	−0.134220	−	0.0774917i	0.431387	−	0.902167i	$-0.358024\pi$
$967$	−4.17378	−	2.40973i	−0.134220	−	0.0774917i	−0.565606	+	0.824675i	$0.691358\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.69916	+	2.69916i	0.0866202	+	0.0866202i	0.749089	−	0.662469i	$-0.230491\pi$
$971$	2.69916	+	2.69916i	0.0866202	+	0.0866202i	−0.662469	+	0.749089i	$0.730491\pi$
$972$		0			0
$973$	−15.9047	+	15.9047i	−0.509881	+	0.509881i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.16168	−	10.6724i	0.197130	−	0.341439i	−0.750467	−	0.660908i	$-0.770171\pi$
$977$	6.16168	−	10.6724i	0.197130	−	0.341439i	0.947597	+	0.319469i	$0.103505\pi$
$978$		0			0
$979$	−10.3272	−	2.76717i	−0.330059	−	0.0884390i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	42.5445	−	24.5631i	1.35696	−	0.783441i	0.367747	−	0.929926i	$-0.380129\pi$
$983$	42.5445	−	24.5631i	1.35696	−	0.783441i	0.989213	+	0.146485i	$0.0467960\pi$
$984$		0			0
$985$	11.7960	+	6.81043i	0.375852	+	0.216998i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	19.7747	−	19.7747i	0.628798	−	0.628798i
$990$		0			0
$991$	40.4968			1.28642			0.643212	−	0.765688i	$-0.277601\pi$
$991$	40.4968			1.28642			0.643212	+	0.765688i	$0.277601\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	10.8469	+	40.4812i	0.343870	+	1.28334i
$996$		0			0
$997$	6.26425	−	23.3785i	0.198391	−	0.740404i	−0.792972	−	0.609258i	$-0.791467\pi$
$997$	6.26425	−	23.3785i	0.198391	−	0.740404i	0.991363	−	0.131147i	$-0.0418659\pi$
$998$		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.1009.17		72
3.2	odd	2		576.2.bb.e.49.11		72
4.3	odd	2		432.2.y.e.37.13		72
9.2	odd	6		576.2.bb.e.241.3		72
9.7	even	3	inner	1728.2.bc.e.1585.2		72
12.11	even	2		144.2.x.e.85.6	yes	72
16.3	odd	4		432.2.y.e.253.13		72
16.13	even	4	inner	1728.2.bc.e.145.2		72
36.7	odd	6		432.2.y.e.181.13		72
36.11	even	6		144.2.x.e.133.6	yes	72
48.29	odd	4		576.2.bb.e.337.3		72
48.35	even	4		144.2.x.e.13.6	✓	72
144.29	odd	12		576.2.bb.e.529.11		72
144.61	even	12	inner	1728.2.bc.e.721.17		72
144.83	even	12		144.2.x.e.61.6	yes	72
144.115	odd	12		432.2.y.e.397.13		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.6	✓	72	48.35	even	4
144.2.x.e.61.6	yes	72	144.83	even	12
144.2.x.e.85.6	yes	72	12.11	even	2
144.2.x.e.133.6	yes	72	36.11	even	6
432.2.y.e.37.13		72	4.3	odd	2
432.2.y.e.181.13		72	36.7	odd	6
432.2.y.e.253.13		72	16.3	odd	4
432.2.y.e.397.13		72	144.115	odd	12
576.2.bb.e.49.11		72	3.2	odd	2
576.2.bb.e.241.3		72	9.2	odd	6
576.2.bb.e.337.3		72	48.29	odd	4
576.2.bb.e.529.11		72	144.29	odd	12
1728.2.bc.e.145.2		72	16.13	even	4	inner
1728.2.bc.e.721.17		72	144.61	even	12	inner
1728.2.bc.e.1009.17		72	1.1	even	1	trivial
1728.2.bc.e.1585.2		72	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.69708 - 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +O(q^{10})\)	\(q+(2.69708 - 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +(1.23365 - 4.60405i) q^{11} +(0.398486 + 1.48717i) q^{13} +6.47719 q^{17} +(-0.957336 + 0.957336i) q^{19} +(-3.70277 - 2.13780i) q^{23} +(2.42183 - 1.39824i) q^{25} +(1.07893 + 0.289099i) q^{29} +(-1.89670 + 3.28518i) q^{31} +(6.59588 - 6.59588i) q^{35} +(-6.14639 - 6.14639i) q^{37} +(-5.04156 - 2.91075i) q^{41} +(-1.69287 + 6.31788i) q^{43} +(1.81739 + 3.14781i) q^{47} +(2.08016 - 3.60295i) q^{49} +(-0.762460 - 0.762460i) q^{53} -13.3090i q^{55} +(-8.11476 + 2.17434i) q^{59} +(6.74711 + 1.80788i) q^{61} +(2.14950 + 3.72304i) q^{65} +(0.487339 + 1.81878i) q^{67} +3.98472i q^{71} +5.45461i q^{73} +(-4.12126 - 15.3808i) q^{77} +(2.95225 + 5.11344i) q^{79} +(-10.3428 - 2.77135i) q^{83} +(17.4695 - 4.68093i) q^{85} -2.24307i q^{89} +(3.63698 + 3.63698i) q^{91} +(-1.89016 + 3.27385i) q^{95} +(6.50191 + 11.2616i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5}+O(q^{10}) \) 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

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