LMFDB - Embedded newform 3024.2.t.i.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.5
Root			$0.247934 - 0.429435i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.i.1873.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.69258 q^{5} +(2.60948 - 0.436591i) q^{7} +O(q^{10})$	$q+3.69258 q^{5} +(2.60948 - 0.436591i) q^{7} -0.892568 q^{11} +(0.598355 + 1.03638i) q^{13} +(0.124991 + 0.216492i) q^{17} +(-1.40414 + 2.43204i) q^{19} +2.47772 q^{23} +8.63514 q^{25} +(-2.07128 + 3.58755i) q^{29} +(1.79257 - 3.10483i) q^{31} +(9.63571 - 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(2.39093 + 4.14121i) q^{41} +(4.98928 - 8.64169i) q^{43} +(5.08653 + 8.81013i) q^{47} +(6.61878 - 2.27855i) q^{49} +(4.94465 + 8.56438i) q^{53} -3.29588 q^{55} +(-0.906186 + 1.56956i) q^{59} +(-5.40205 - 9.35663i) q^{61} +(2.20948 + 3.82692i) q^{65} +(0.514685 - 0.891460i) q^{67} -4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(-2.32914 + 0.389687i) q^{77} +(-0.899562 - 1.55809i) q^{79} +(6.16156 - 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(1.20370 - 2.08488i) q^{89} +(2.01387 + 2.44318i) q^{91} +(-5.18489 + 8.98049i) q^{95} +(5.52210 - 9.56456i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{5} + q^{7}+O(q^{10}) $ 10 * q + 8 * q^5 + q^7	$ 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.69258			1.65137			0.825686	−	0.564130i	$-0.190788\pi$
$5$	3.69258			1.65137			0.825686	+	0.564130i	$0.190788\pi$
$6$		0			0
$7$	2.60948	−	0.436591i	0.986291	−	0.165016i
$7$	2.60948	−	0.436591i	0.986291	−	0.165016i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.892568			−0.269119			−0.134560	−	0.990905i	$-0.542962\pi$
$11$	−0.892568			−0.269119			−0.134560	+	0.990905i	$0.542962\pi$
$12$		0			0
$13$	0.598355	+	1.03638i	0.165954	+	0.287441i	0.936994	−	0.349346i	$-0.113596\pi$
$13$	0.598355	+	1.03638i	0.165954	+	0.287441i	−0.771040	+	0.636787i	$0.780263\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	0.880785	−	0.473517i	$-0.157016\pi$
$17$	0.124991	+	0.216492i	0.0303149	+	0.0525069i	−0.850470	+	0.526024i	$0.823682\pi$
$18$		0			0
$19$	−1.40414	+	2.43204i	−0.322131	+	0.557948i	−0.980928	−	0.194374i	$-0.937733\pi$
$19$	−1.40414	+	2.43204i	−0.322131	+	0.557948i	0.658796	+	0.752321i	$0.271066\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.47772			0.516639			0.258320	−	0.966059i	$-0.416831\pi$
$23$	2.47772			0.516639			0.258320	+	0.966059i	$0.416831\pi$
$24$		0			0
$25$	8.63514			1.72703
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.07128	+	3.58755i	−0.384626	+	0.666192i	−0.991717	−	0.128440i	$-0.959003\pi$
$29$	−2.07128	+	3.58755i	−0.384626	+	0.666192i	0.607091	+	0.794632i	$0.292336\pi$
$30$		0			0
$31$	1.79257	−	3.10483i	0.321956	−	0.557644i	−0.658936	−	0.752199i	$-0.728993\pi$
$31$	1.79257	−	3.10483i	0.321956	−	0.557644i	0.980892	+	0.194555i	$0.0623264\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.63571	−	1.61215i	1.62873	−	0.272502i
$36$		0			0
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	−0.992304	−	0.123826i	$-0.960483\pi$
$37$	−2.36568	+	4.09747i	−0.388915	+	0.673621i	0.603389	+	0.797447i	$0.293817\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.39093	+	4.14121i	0.373400	+	0.646748i	0.990086	−	0.140461i	$-0.0448584\pi$
$41$	2.39093	+	4.14121i	0.373400	+	0.646748i	−0.616686	+	0.787209i	$0.711525\pi$
$42$		0			0
$43$	4.98928	−	8.64169i	0.760859	−	1.31785i	−0.181550	−	0.983382i	$-0.558111\pi$
$43$	4.98928	−	8.64169i	0.760859	−	1.31785i	0.942408	−	0.334464i	$-0.108555\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.08653	+	8.81013i	0.741947	+	1.28509i	0.951608	+	0.307316i	$0.0994308\pi$
$47$	5.08653	+	8.81013i	0.741947	+	1.28509i	−0.209661	+	0.977774i	$0.567236\pi$
$48$		0			0
$49$	6.61878	−	2.27855i	0.945540	−	0.325507i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.94465	+	8.56438i	0.679199	+	1.17641i	0.975222	+	0.221227i	$0.0710061\pi$
$53$	4.94465	+	8.56438i	0.679199	+	1.17641i	−0.296023	+	0.955181i	$0.595661\pi$
$54$		0			0
$55$	−3.29588			−0.444416
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.906186	+	1.56956i	−0.117975	+	0.204339i	−0.918965	−	0.394339i	$-0.870974\pi$
$59$	−0.906186	+	1.56956i	−0.117975	+	0.204339i	0.800990	+	0.598678i	$0.204307\pi$
$60$		0			0
$61$	−5.40205	−	9.35663i	−0.691662	−	1.19799i	−0.971293	−	0.237886i	$-0.923545\pi$
$61$	−5.40205	−	9.35663i	−0.691662	−	1.19799i	0.279631	−	0.960108i	$-0.409788\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.20948	+	3.82692i	0.274052	+	0.474671i
$66$		0			0
$67$	0.514685	−	0.891460i	0.0628787	−	0.108909i	−0.832872	−	0.553465i	$-0.813305\pi$
$67$	0.514685	−	0.891460i	0.0628787	−	0.108909i	0.895751	+	0.444556i	$0.146639\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.94533			−0.586903			−0.293451	−	0.955974i	$-0.594804\pi$
$71$	−4.94533			−0.586903			−0.293451	+	0.955974i	$0.594804\pi$
$72$		0			0
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	0.807480	−	0.589894i	$-0.200831\pi$
$73$	−0.915262	−	1.58528i	−0.107123	−	0.185543i	−0.914604	+	0.404351i	$0.867497\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.32914	+	0.389687i	−0.265430	+	0.0444090i
$78$		0			0
$79$	−0.899562	−	1.55809i	−0.101209	−	0.175298i	0.810974	−	0.585082i	$-0.198938\pi$
$79$	−0.899562	−	1.55809i	−0.101209	−	0.175298i	−0.912183	+	0.409783i	$0.865604\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.16156	−	10.6721i	0.676319	−	1.17142i	−0.299763	−	0.954014i	$-0.596908\pi$
$83$	6.16156	−	10.6721i	0.676319	−	1.17142i	0.976082	−	0.217405i	$-0.0697591\pi$
$84$		0			0
$85$	0.461541	+	0.799412i	0.0500611	+	0.0867084i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	−0.795151	−	0.606412i	$-0.792608\pi$
$89$	1.20370	−	2.08488i	0.127592	−	0.220997i	0.922743	+	0.385415i	$0.125942\pi$
$90$		0			0
$91$	2.01387	+	2.44318i	0.211111	+	0.256115i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.18489	+	8.98049i	−0.531958	+	0.921379i
$96$		0			0
$97$	5.52210	−	9.56456i	0.560684	−	0.971134i	−0.436752	−	0.899582i	$-0.643871\pi$
$97$	5.52210	−	9.56456i	0.560684	−	0.971134i	0.997437	−	0.0715522i	$-0.0227952\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.59964			0.258674			0.129337	−	0.991601i	$-0.458715\pi$
$101$	2.59964			0.258674			0.129337	+	0.991601i	$0.458715\pi$
$102$		0			0
$103$	−9.71155			−0.956908			−0.478454	−	0.878113i	$-0.658803\pi$
$103$	−9.71155			−0.956908			−0.478454	+	0.878113i	$0.658803\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.45025	+	9.44012i	−0.526896	+	0.912610i	0.472613	+	0.881270i	$0.343311\pi$
$107$	−5.45025	+	9.44012i	−0.526896	+	0.912610i	−0.999509	+	0.0313403i	$0.990022\pi$
$108$		0			0
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	0.810731	−	0.585419i	$-0.199070\pi$
$109$	−1.06096	−	1.83764i	−0.101622	−	0.176014i	−0.912353	+	0.409404i	$0.865737\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.91318	−	13.7060i	−0.744409	−	1.28935i	−0.950470	−	0.310816i	$-0.899398\pi$
$113$	−7.91318	−	13.7060i	−0.744409	−	1.28935i	0.206061	−	0.978539i	$-0.433935\pi$
$114$		0			0
$115$	9.14916			0.853164
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.420681	+	0.510360i	0.0385638	+	0.0467847i
$120$		0			0
$121$	−10.2033			−0.927575
$122$		0			0
$123$		0			0
$124$		0			0
$125$	13.4230			1.20059
$126$		0			0
$127$	1.26946			0.112647			0.0563233	−	0.998413i	$-0.482062\pi$
$127$	1.26946			0.112647			0.0563233	+	0.998413i	$0.482062\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−15.0289			−1.31308			−0.656540	−	0.754291i	$-0.727981\pi$
$131$	−15.0289			−1.31308			−0.656540	+	0.754291i	$0.727981\pi$
$132$		0			0
$133$	−2.60226	+	6.95939i	−0.225645	+	0.603455i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.488493			0.0417347			0.0208674	−	0.999782i	$-0.493357\pi$
$137$	0.488493			0.0417347			0.0208674	+	0.999782i	$0.493357\pi$
$138$		0			0
$139$	4.93487	+	8.54745i	0.418570	+	0.724985i	0.995796	−	0.0915997i	$-0.0291980\pi$
$139$	4.93487	+	8.54745i	0.418570	+	0.724985i	−0.577226	+	0.816585i	$0.695865\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.534073	−	0.925042i	−0.0446614	−	0.0773559i
$144$		0			0
$145$	−7.64835	+	13.2473i	−0.635161	+	1.10013i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−21.0240			−1.72235			−0.861175	−	0.508309i	$-0.830271\pi$
$149$	−21.0240			−1.72235			−0.861175	+	0.508309i	$0.830271\pi$
$150$		0			0
$151$	−1.49838			−0.121937			−0.0609683	−	0.998140i	$-0.519419\pi$
$151$	−1.49838			−0.121937			−0.0609683	+	0.998140i	$0.519419\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.61922	−	11.4648i	0.531669	−	0.920877i
$156$		0			0
$157$	8.33982	−	14.4450i	0.665590	−	1.15284i	−0.313535	−	0.949577i	$-0.601513\pi$
$157$	8.33982	−	14.4450i	0.665590	−	1.15284i	0.979125	−	0.203259i	$-0.0651534\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.46555	−	1.08175i	0.509557	−	0.0852537i
$162$		0			0
$163$	3.34135	−	5.78738i	0.261714	−	0.453303i	−0.704983	−	0.709224i	$-0.749046\pi$
$163$	3.34135	−	5.78738i	0.261714	−	0.453303i	0.966698	+	0.255921i	$0.0823788\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.81549	+	15.2689i	0.682163	+	1.18154i	0.974319	+	0.225170i	$0.0722939\pi$
$167$	8.81549	+	15.2689i	0.682163	+	1.18154i	−0.292156	+	0.956371i	$0.594373\pi$
$168$		0			0
$169$	5.78394	−	10.0181i	0.444919	−	0.770622i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.94342	−	3.36611i	−0.147756	−	0.255920i	0.782642	−	0.622472i	$-0.213872\pi$
$173$	−1.94342	−	3.36611i	−0.147756	−	0.255920i	−0.930398	+	0.366552i	$0.880538\pi$
$174$		0			0
$175$	22.5332	−	3.77002i	1.70335	−	0.284987i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.66758	+	6.35244i	0.274128	+	0.474804i	0.969915	−	0.243445i	$-0.0782775\pi$
$179$	3.66758	+	6.35244i	0.274128	+	0.474804i	−0.695787	+	0.718248i	$0.744944\pi$
$180$		0			0
$181$	11.2566			0.836693			0.418346	−	0.908288i	$-0.362610\pi$
$181$	11.2566			0.836693			0.418346	+	0.908288i	$0.362610\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.73545	+	15.1302i	−0.642243	+	1.11240i
$186$		0			0
$187$	−0.111563	−	0.193234i	−0.00815833	−	0.0141306i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.9230	+	20.6512i	0.862715	+	1.49427i	0.869298	+	0.494288i	$0.164571\pi$
$191$	11.9230	+	20.6512i	0.862715	+	1.49427i	−0.00658302	+	0.999978i	$0.502095\pi$
$192$		0			0
$193$	−2.96728	+	5.13948i	−0.213589	+	0.369948i	−0.952835	−	0.303488i	$-0.901849\pi$
$193$	−2.96728	+	5.13948i	−0.213589	+	0.369948i	0.739246	+	0.673436i	$0.235182\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.4682			1.10206			0.551032	−	0.834484i	$-0.314234\pi$
$197$	15.4682			1.10206			0.551032	+	0.834484i	$0.314234\pi$
$198$		0			0
$199$	−7.74818	−	13.4202i	−0.549254	−	0.951336i	−0.998326	−	0.0578402i	$-0.981579\pi$
$199$	−7.74818	−	13.4202i	−0.549254	−	0.951336i	0.449072	−	0.893496i	$-0.351755\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3.83866	+	10.2660i	−0.269421	+	0.720529i
$204$		0			0
$205$	8.82870	+	15.2917i	0.616623	+	1.06802i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.25329	−	2.17076i	0.0866918	−	0.150155i
$210$		0			0
$211$	−0.771898	−	1.33697i	−0.0531397	−	0.0920406i	0.838232	−	0.545314i	$-0.183590\pi$
$211$	−0.771898	−	1.33697i	−0.0531397	−	0.0920406i	−0.891372	+	0.453273i	$0.850256\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	18.4233	−	31.9101i	1.25646	−	2.17625i
$216$		0			0
$217$	3.32215	−	8.88461i	0.225522	−	0.603127i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.149579	+	0.259078i	−0.0100617	+	0.0174275i
$222$		0			0
$223$	2.72171	−	4.71414i	0.182259	−	0.315682i	−0.760390	−	0.649466i	$-0.774992\pi$
$223$	2.72171	−	4.71414i	0.182259	−	0.315682i	0.942649	+	0.333784i	$0.108326\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.0764			−1.06703			−0.533513	−	0.845792i	$-0.679128\pi$
$227$	−16.0764			−1.06703			−0.533513	+	0.845792i	$0.679128\pi$
$228$		0			0
$229$	−9.96840			−0.658730			−0.329365	−	0.944203i	$-0.606835\pi$
$229$	−9.96840			−0.658730			−0.329365	+	0.944203i	$0.606835\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.27045	+	14.3248i	−0.541815	+	0.938451i	0.456985	+	0.889474i	$0.348929\pi$
$233$	−8.27045	+	14.3248i	−0.541815	+	0.938451i	−0.998800	+	0.0489765i	$0.984404\pi$
$234$		0			0
$235$	18.7824	+	32.5321i	1.22523	+	2.12216i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−11.0119	−	19.0732i	−0.712303	−	1.23375i	−0.963990	−	0.265937i	$-0.914319\pi$
$239$	−11.0119	−	19.0732i	−0.712303	−	1.23375i	0.251687	−	0.967809i	$-0.419015\pi$
$240$		0			0
$241$	16.7201			1.07703			0.538517	−	0.842615i	$-0.318985\pi$
$241$	16.7201			1.07703			0.538517	+	0.842615i	$0.318985\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	24.4404	−	8.41373i	1.56144	−	0.537533i
$246$		0			0
$247$	−3.36069			−0.213836
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−8.53099			−0.538471			−0.269236	−	0.963074i	$-0.586771\pi$
$251$	−8.53099			−0.538471			−0.269236	+	0.963074i	$0.586771\pi$
$252$		0			0
$253$	−2.21153			−0.139038
$254$		0			0
$255$		0			0
$256$		0			0
$257$	17.1197			1.06790			0.533950	−	0.845516i	$-0.320707\pi$
$257$	17.1197			1.06790			0.533950	+	0.845516i	$0.320707\pi$
$258$		0			0
$259$	−4.38427	+	11.7251i	−0.272425	+	0.728563i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.5527			1.26733			0.633666	−	0.773607i	$-0.281549\pi$
$263$	20.5527			1.26733			0.633666	+	0.773607i	$0.281549\pi$
$264$		0			0
$265$	18.2585	+	31.6246i	1.12161	+	1.94269i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	−0.992052	−	0.125827i	$-0.959842\pi$
$269$	−9.92267	−	17.1866i	−0.604996	−	1.04788i	0.387057	−	0.922056i	$-0.373492\pi$
$270$		0			0
$271$	−5.32056	+	9.21548i	−0.323201	+	0.559801i	−0.981147	−	0.193265i	$-0.938092\pi$
$271$	−5.32056	+	9.21548i	−0.323201	+	0.559801i	0.657946	+	0.753065i	$0.271426\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.70745			−0.464777
$276$		0			0
$277$	−24.8813			−1.49497			−0.747487	−	0.664276i	$-0.768740\pi$
$277$	−24.8813			−1.49497			−0.747487	+	0.664276i	$0.768740\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.83733	−	11.8426i	0.407881	−	0.706470i	−0.586771	−	0.809753i	$-0.699601\pi$
$281$	6.83733	−	11.8426i	0.407881	−	0.706470i	0.994652	+	0.103282i	$0.0329346\pi$
$282$		0			0
$283$	3.16089	−	5.47483i	0.187896	−	0.325445i	−0.756653	−	0.653817i	$-0.773167\pi$
$283$	3.16089	−	5.47483i	0.187896	−	0.325445i	0.944548	+	0.328372i	$0.106500\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.04710	+	9.76255i	0.475005	+	0.576265i
$288$		0			0
$289$	8.46875	−	14.6683i	0.498162	−	0.862842i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.31508	+	2.27778i	0.0768277	+	0.133069i	0.901880	−	0.431987i	$-0.142188\pi$
$293$	1.31508	+	2.27778i	0.0768277	+	0.133069i	−0.825052	+	0.565057i	$0.808854\pi$
$294$		0			0
$295$	−3.34616	+	5.79573i	−0.194821	+	0.337440i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.48255	+	2.56786i	0.0857384	+	0.148503i
$300$		0			0
$301$	9.24656	−	24.7286i	0.532963	−	1.42533i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−19.9475	−	34.5501i	−1.14219	−	1.97833i
$306$		0			0
$307$	2.79496			0.159517			0.0797583	−	0.996814i	$-0.474585\pi$
$307$	2.79496			0.159517			0.0797583	+	0.996814i	$0.474585\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.55013	−	13.0772i	0.428129	−	0.741541i	−0.568578	−	0.822629i	$-0.692506\pi$
$311$	7.55013	−	13.0772i	0.428129	−	0.741541i	0.996707	+	0.0810885i	$0.0258396\pi$
$312$		0			0
$313$	12.7392	+	22.0650i	0.720064	+	1.24719i	0.960974	+	0.276640i	$0.0892209\pi$
$313$	12.7392	+	22.0650i	0.720064	+	1.24719i	−0.240910	+	0.970548i	$0.577446\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.2605	+	28.1639i	0.913278	+	1.58184i	0.809403	+	0.587253i	$0.199791\pi$
$317$	16.2605	+	28.1639i	0.913278	+	1.58184i	0.103875	+	0.994590i	$0.466876\pi$
$318$		0			0
$319$	1.84875	−	3.20214i	0.103510	−	0.179285i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.702021			−0.0390615
$324$		0			0
$325$	5.16688	+	8.94931i	0.286607	+	0.496418i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	17.1196	+	20.7691i	0.943836	+	1.14504i
$330$		0			0
$331$	9.04741	+	15.6706i	0.497291	+	0.861333i	0.999995	−	0.00312545i	$-0.000994863\pi$
$331$	9.04741	+	15.6706i	0.497291	+	0.861333i	−0.502704	+	0.864458i	$0.667662\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.90051	−	3.29179i	0.103836	−	0.179850i
$336$		0			0
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	−0.974557	−	0.224139i	$-0.928043\pi$
$337$	−12.5086	−	21.6656i	−0.681389	−	1.18020i	0.293168	−	0.956061i	$-0.405290\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.59999	+	2.77127i	−0.0866446	+	0.150073i
$342$		0			0
$343$	16.2768	−	8.83553i	0.878863	−	0.477074i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−5.37444	+	9.30881i	−0.288515	+	0.499723i	−0.973456	−	0.228876i	$-0.926495\pi$
$347$	−5.37444	+	9.30881i	−0.288515	+	0.499723i	0.684940	+	0.728599i	$0.259828\pi$
$348$		0			0
$349$	−1.64301	+	2.84577i	−0.0879482	+	0.152331i	−0.906644	−	0.421897i	$-0.861364\pi$
$349$	−1.64301	+	2.84577i	−0.0879482	+	0.152331i	0.818695	+	0.574228i	$0.194698\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16.8192			−0.895195			−0.447598	−	0.894235i	$-0.647720\pi$
$353$	−16.8192			−0.895195			−0.447598	+	0.894235i	$0.647720\pi$
$354$		0			0
$355$	−18.2610			−0.969195
$356$		0			0
$357$		0			0
$358$		0			0
$359$	11.8921	−	20.5978i	0.627642	−	1.08711i	−0.360382	−	0.932805i	$-0.617354\pi$
$359$	11.8921	−	20.5978i	0.627642	−	1.08711i	0.988024	−	0.154303i	$-0.0493131\pi$
$360$		0			0
$361$	5.55680	+	9.62466i	0.292463	+	0.506561i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.37968	−	5.85377i	−0.176900	−	0.306401i
$366$		0			0
$367$	0.689984			0.0360169			0.0180084	−	0.999838i	$-0.494267\pi$
$367$	0.689984			0.0360169			0.0180084	+	0.999838i	$0.494267\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	16.6421	+	20.1898i	0.864014	+	1.04820i
$372$		0			0
$373$	−3.76012			−0.194691			−0.0973457	−	0.995251i	$-0.531035\pi$
$373$	−3.76012			−0.194691			−0.0973457	+	0.995251i	$0.531035\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.95744			−0.255321
$378$		0			0
$379$	−32.8735			−1.68860			−0.844300	−	0.535872i	$-0.819983\pi$
$379$	−32.8735			−1.68860			−0.844300	+	0.535872i	$0.819983\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.07267			−0.0548109			−0.0274055	−	0.999624i	$-0.508725\pi$
$383$	−1.07267			−0.0548109			−0.0274055	+	0.999624i	$0.508725\pi$
$384$		0			0
$385$	−8.60053	+	1.43895i	−0.438324	+	0.0733357i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	23.7436			1.20385			0.601925	−	0.798553i	$-0.294401\pi$
$389$	23.7436			1.20385			0.601925	+	0.798553i	$0.294401\pi$
$390$		0			0
$391$	0.309693	+	0.536405i	0.0156619	+	0.0271271i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.32170	−	5.75336i	−0.167133	−	0.289483i
$396$		0			0
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	−0.866428	−	0.499302i	$-0.833590\pi$
$397$	−0.0160489	+	0.0277975i	−0.000805471	+	0.00139512i	0.865622	+	0.500697i	$0.166923\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−24.5256			−1.22475			−0.612374	−	0.790568i	$-0.709785\pi$
$401$	−24.5256			−1.22475			−0.612374	+	0.790568i	$0.709785\pi$
$402$		0			0
$403$	4.29039			0.213719
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.11153	−	3.65728i	0.104665	−	0.181284i
$408$		0			0
$409$	−13.3948	+	23.2006i	−0.662333	+	1.14719i	0.317669	+	0.948202i	$0.397100\pi$
$409$	−13.3948	+	23.2006i	−0.662333	+	1.14719i	−0.980001	+	0.198992i	$0.936233\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.67942	+	4.49137i	−0.0826388	+	0.221006i
$414$		0			0
$415$	22.7520	−	39.4077i	1.11685	−	1.93445i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.5262	−	18.2320i	−0.514240	−	0.890689i	−0.999864	−	0.0165215i	$-0.994741\pi$
$419$	−10.5262	−	18.2320i	−0.514240	−	0.890689i	0.485624	−	0.874168i	$-0.338593\pi$
$420$		0			0
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	−0.988431	−	0.151672i	$-0.951534\pi$
$421$	−7.44533	+	12.8957i	−0.362863	+	0.628498i	0.625568	+	0.780170i	$0.284867\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.07932	+	1.86944i	0.0523547	+	0.0906809i
$426$		0			0
$427$	−18.1816	−	22.0575i	−0.879868	−	1.06744i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.95192	−	13.7731i	−0.383031	−	0.663428i	0.608463	−	0.793582i	$-0.291786\pi$
$431$	−7.95192	−	13.7731i	−0.383031	−	0.663428i	−0.991494	+	0.130154i	$0.958453\pi$
$432$		0			0
$433$	−16.3658			−0.786490			−0.393245	−	0.919434i	$-0.628648\pi$
$433$	−16.3658			−0.786490			−0.393245	+	0.919434i	$0.628648\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.47905	+	6.02590i	−0.166426	+	0.288258i
$438$		0			0
$439$	−7.77236	−	13.4621i	−0.370954	−	0.642512i	0.618758	−	0.785582i	$-0.287636\pi$
$439$	−7.77236	−	13.4621i	−0.370954	−	0.642512i	−0.989713	+	0.143070i	$0.954303\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.895027	−	1.55023i	−0.0425240	−	0.0736537i	0.843980	−	0.536375i	$-0.180207\pi$
$443$	−0.895027	−	1.55023i	−0.0425240	−	0.0736537i	−0.886504	+	0.462721i	$0.846873\pi$
$444$		0			0
$445$	4.44477	−	7.69857i	0.210702	−	0.364947i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.5666			−0.640250			−0.320125	−	0.947375i	$-0.603725\pi$
$449$	−13.5666			−0.640250			−0.320125	+	0.947375i	$0.603725\pi$
$450$		0			0
$451$	−2.13407	−	3.69631i	−0.100489	−	0.174053i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.43638	+	9.02164i	0.348623	+	0.422941i
$456$		0			0
$457$	−1.28459	−	2.22497i	−0.0600905	−	0.104080i	0.834415	−	0.551136i	$-0.185806\pi$
$457$	−1.28459	−	2.22497i	−0.0600905	−	0.104080i	−0.894506	+	0.447057i	$0.852472\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.0934	+	31.3388i	−0.842695	+	1.45959i	0.0449122	+	0.998991i	$0.485699\pi$
$461$	−18.0934	+	31.3388i	−0.842695	+	1.45959i	−0.887608	+	0.460600i	$0.847634\pi$
$462$		0			0
$463$	−8.19224	−	14.1894i	−0.380726	−	0.659436i	0.610440	−	0.792062i	$-0.290992\pi$
$463$	−8.19224	−	14.1894i	−0.380726	−	0.659436i	−0.991166	+	0.132626i	$0.957659\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.35022	+	7.53480i	−0.201304	+	0.348669i	−0.948949	−	0.315430i	$-0.897851\pi$
$467$	−4.35022	+	7.53480i	−0.201304	+	0.348669i	0.747645	+	0.664099i	$0.231185\pi$
$468$		0			0
$469$	0.953856	−	2.55095i	0.0440450	−	0.117792i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.45328	+	7.71330i	−0.204762	+	0.354658i
$474$		0			0
$475$	−12.1249	+	21.0010i	−0.556330	+	0.963591i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.7674			−0.811813			−0.405907	−	0.913915i	$-0.633044\pi$
$479$	−17.7674			−0.811813			−0.405907	+	0.913915i	$0.633044\pi$
$480$		0			0
$481$	−5.66207			−0.258168
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.3908	−	35.3179i	0.925898	−	1.60370i
$486$		0			0
$487$	−8.32763	−	14.4239i	−0.377361	−	0.653608i	0.613316	−	0.789837i	$-0.289835\pi$
$487$	−8.32763	−	14.4239i	−0.377361	−	0.653608i	−0.990677	+	0.136229i	$0.956502\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.21021	−	5.56025i	−0.144875	−	0.250930i	0.784451	−	0.620190i	$-0.212945\pi$
$491$	−3.21021	−	5.56025i	−0.144875	−	0.250930i	−0.929326	+	0.369260i	$0.879611\pi$
$492$		0			0
$493$	−1.03557			−0.0466396
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−12.9047	+	2.15909i	−0.578857	+	0.0968483i
$498$		0			0
$499$	−11.1459			−0.498960			−0.249480	−	0.968380i	$-0.580260\pi$
$499$	−11.1459			−0.498960			−0.249480	+	0.968380i	$0.580260\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−17.7223			−0.790200			−0.395100	−	0.918638i	$-0.629290\pi$
$503$	−17.7223			−0.790200			−0.395100	+	0.918638i	$0.629290\pi$
$504$		0			0
$505$	9.59939			0.427167
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−31.0823			−1.37770			−0.688848	−	0.724906i	$-0.741883\pi$
$509$	−31.0823			−1.37770			−0.688848	+	0.724906i	$0.741883\pi$
$510$		0			0
$511$	−3.08048	−	3.73716i	−0.136272	−	0.165322i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−35.8607			−1.58021
$516$		0			0
$517$	−4.54008	−	7.86365i	−0.199672	−	0.345843i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	0.913437	−	0.406980i	$-0.133418\pi$
$521$	2.37986	+	4.12203i	0.104263	+	0.180590i	−0.809174	+	0.587570i	$0.800085\pi$
$522$		0			0
$523$	−20.1258	+	34.8588i	−0.880038	+	1.52427i	−0.0287402	+	0.999587i	$0.509150\pi$
$523$	−20.1258	+	34.8588i	−0.880038	+	1.52427i	−0.851298	+	0.524683i	$0.824184\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.896226			0.0390402
$528$		0			0
$529$	−16.8609			−0.733084
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.86125	+	4.95583i	−0.123935	+	0.214661i
$534$		0			0
$535$	−20.1255	+	34.8584i	−0.870101	+	1.50706i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.90771	+	2.03376i	−0.254463	+	0.0876003i
$540$		0			0
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	−0.481502	−	0.876445i	$-0.659908\pi$
$541$	12.0547	−	20.8794i	0.518273	−	0.897675i	0.999775	−	0.0212301i	$-0.00675826\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.91769	−	6.78564i	−0.167815	−	0.290665i
$546$		0			0
$547$	6.17751	−	10.6998i	0.264131	−	0.457489i	−0.703204	−	0.710988i	$-0.748248\pi$
$547$	6.17751	−	10.6998i	0.264131	−	0.457489i	0.967336	+	0.253499i	$0.0815814\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.81671	−	10.0748i	−0.247800	−	0.429203i
$552$		0			0
$553$	−3.02763	−	3.67306i	−0.128748	−	0.156194i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.03845	−	6.99479i	−0.171114	−	0.296379i	0.767695	−	0.640815i	$-0.221403\pi$
$557$	−4.03845	−	6.99479i	−0.171114	−	0.296379i	−0.938810	+	0.344436i	$0.888070\pi$
$558$		0			0
$559$	11.9415			0.505070
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.6064	+	39.1554i	−0.952744	+	1.65020i	−0.213296	+	0.976988i	$0.568420\pi$
$563$	−22.6064	+	39.1554i	−0.952744	+	1.65020i	−0.739448	+	0.673214i	$0.764913\pi$
$564$		0			0
$565$	−29.2200	−	50.6106i	−1.22930	−	2.12920i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.2149	+	19.4248i	0.470155	+	0.814332i	0.999418	−	0.0341263i	$-0.0108648\pi$
$569$	11.2149	+	19.4248i	0.470155	+	0.814332i	−0.529263	+	0.848458i	$0.677532\pi$
$570$		0			0
$571$	−10.9134	+	18.9026i	−0.456713	+	0.791050i	−0.998785	−	0.0492820i	$-0.984307\pi$
$571$	−10.9134	+	18.9026i	−0.456713	+	0.791050i	0.542072	+	0.840332i	$0.317640\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	21.3954			0.892251
$576$		0			0
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	−0.977807	−	0.209508i	$-0.932814\pi$
$577$	−16.1022	−	27.8898i	−0.670342	−	1.16107i	0.307465	−	0.951559i	$-0.400519\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.4191	−	30.5388i	0.473744	−	1.26696i
$582$		0			0
$583$	−4.41343	−	7.64429i	−0.182786	−	0.316594i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.72304	+	16.8408i	−0.401313	+	0.695094i	−0.993885	−	0.110424i	$-0.964779\pi$
$587$	−9.72304	+	16.8408i	−0.401313	+	0.695094i	0.592572	+	0.805518i	$0.298113\pi$
$588$		0			0
$589$	5.03404	+	8.71921i	0.207424	+	0.359269i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	−0.401772	−	0.915740i	$-0.631606\pi$
$593$	14.4202	−	24.9766i	0.592168	−	1.02566i	0.993940	−	0.109925i	$-0.0350611\pi$
$594$		0			0
$595$	1.55340	+	1.88455i	0.0636831	+	0.0772589i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.4994	−	40.7022i	0.960161	−	1.66305i	0.238072	−	0.971247i	$-0.423484\pi$
$599$	23.4994	−	40.7022i	0.960161	−	1.66305i	0.722089	−	0.691800i	$-0.243182\pi$
$600$		0			0
$601$	−7.80843	+	13.5246i	−0.318512	+	0.551680i	−0.980178	−	0.198119i	$-0.936517\pi$
$601$	−7.80843	+	13.5246i	−0.318512	+	0.551680i	0.661665	+	0.749799i	$0.269850\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−37.6766			−1.53177
$606$		0			0
$607$	28.6532			1.16300			0.581500	−	0.813547i	$-0.302466\pi$
$607$	28.6532			1.16300			0.581500	+	0.813547i	$0.302466\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.08711	+	10.5432i	−0.246258	+	0.426531i
$612$		0			0
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	0.993873	+	0.110524i	$0.0352529\pi$
$613$	14.6734	+	25.4151i	0.592653	+	1.02651i	−0.401220	+	0.915982i	$0.631414\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.06401	−	3.57497i	−0.0830938	−	0.143923i	0.821484	−	0.570232i	$-0.193147\pi$
$617$	−2.06401	−	3.57497i	−0.0830938	−	0.143923i	−0.904577	+	0.426310i	$0.859813\pi$
$618$		0			0
$619$	−22.7130			−0.912912			−0.456456	−	0.889746i	$-0.650881\pi$
$619$	−22.7130			−0.912912			−0.456456	+	0.889746i	$0.650881\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.23080	−	5.96597i	0.0893753	−	0.239022i
$624$		0			0
$625$	6.38996			0.255598
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.18276			−0.0471597
$630$		0			0
$631$	38.6411			1.53828			0.769138	−	0.639082i	$-0.220686\pi$
$631$	38.6411			1.53828			0.769138	+	0.639082i	$0.220686\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.68759			0.186021
$636$		0			0
$637$	6.32183	+	5.49620i	0.250480	+	0.217767i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	28.4726			1.12460			0.562301	−	0.826933i	$-0.309916\pi$
$641$	28.4726			1.12460			0.562301	+	0.826933i	$0.309916\pi$
$642$		0			0
$643$	8.52125	+	14.7592i	0.336045	+	0.582048i	0.983685	−	0.179899i	$-0.0575771\pi$
$643$	8.52125	+	14.7592i	0.336045	+	0.582048i	−0.647640	+	0.761947i	$0.724244\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.68809	+	2.92386i	0.0663657	+	0.114949i	0.897299	−	0.441423i	$-0.145526\pi$
$647$	1.68809	+	2.92386i	0.0663657	+	0.114949i	−0.830933	+	0.556372i	$0.812193\pi$
$648$		0			0
$649$	0.808833	−	1.40094i	0.0317495	−	0.0549917i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.3451			0.717899			0.358950	−	0.933357i	$-0.383135\pi$
$653$	18.3451			0.717899			0.358950	+	0.933357i	$0.383135\pi$
$654$		0			0
$655$	−55.4954			−2.16838
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.9248	+	24.1184i	−0.542432	+	0.939519i	0.456332	+	0.889810i	$0.349163\pi$
$659$	−13.9248	+	24.1184i	−0.542432	+	0.939519i	−0.998764	+	0.0497098i	$0.984170\pi$
$660$		0			0
$661$	−19.5071	+	33.7872i	−0.758737	+	1.31417i	0.184758	+	0.982784i	$0.440850\pi$
$661$	−19.5071	+	33.7872i	−0.758737	+	1.31417i	−0.943495	+	0.331387i	$0.892484\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.60906	+	25.6981i	−0.372624	+	0.996529i
$666$		0			0
$667$	−5.13203	+	8.88894i	−0.198713	+	0.344181i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.82170	+	8.35143i	0.186140	+	0.322404i
$672$		0			0
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.201014	−	0.979588i	$-0.435576\pi$
$673$	24.6154	−	42.6352i	0.948856	−	1.64347i	0.747841	−	0.663878i	$-0.231090\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.6958	−	20.2577i	−0.449505	−	0.778565i	0.548849	−	0.835922i	$-0.315066\pi$
$677$	−11.6958	−	20.2577i	−0.449505	−	0.778565i	−0.998354	+	0.0573564i	$0.981733\pi$
$678$		0			0
$679$	10.2340	−	27.3694i	0.392745	−	1.05034i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−15.1632	−	26.2634i	−0.580204	−	1.00494i	−0.995455	−	0.0952356i	$-0.969640\pi$
$683$	−15.1632	−	26.2634i	−0.580204	−	1.00494i	0.415251	−	0.909707i	$-0.363694\pi$
$684$		0			0
$685$	1.80380			0.0689196
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−5.91731	+	10.2491i	−0.225432	+	0.390459i
$690$		0			0
$691$	−2.05665	−	3.56223i	−0.0782387	−	0.135513i	0.824251	−	0.566224i	$-0.191596\pi$
$691$	−2.05665	−	3.56223i	−0.0782387	−	0.135513i	−0.902490	+	0.430711i	$0.858263\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	18.2224	+	31.5621i	0.691215	+	1.19722i
$696$		0			0
$697$	−0.597691	+	1.03523i	−0.0226392	+	0.0392122i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−29.1835			−1.10225			−0.551123	−	0.834424i	$-0.685800\pi$
$701$	−29.1835			−1.10225			−0.551123	+	0.834424i	$0.685800\pi$
$702$		0			0
$703$	−6.64347	−	11.5068i	−0.250563	−	0.433988i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.78372	−	1.13498i	0.255128	−	0.0426853i
$708$		0			0
$709$	21.2309	+	36.7729i	0.797342	+	1.38104i	0.921341	+	0.388755i	$0.127095\pi$
$709$	21.2309	+	36.7729i	0.797342	+	1.38104i	−0.123999	+	0.992282i	$0.539572\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.44149	−	7.69288i	0.166335	−	0.288101i
$714$		0			0
$715$	−1.97211	−	3.41579i	−0.0737526	−	0.127743i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.57126	+	9.64970i	−0.207773	+	0.359873i	−0.951013	−	0.309152i	$-0.899955\pi$
$719$	−5.57126	+	9.64970i	−0.207773	+	0.359873i	0.743240	+	0.669025i	$0.233288\pi$
$720$		0			0
$721$	−25.3421	+	4.23997i	−0.943789	+	0.157905i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−17.8858	+	30.9790i	−0.664260	+	1.15053i
$726$		0			0
$727$	14.3410	−	24.8393i	0.531878	−	0.921239i	−0.467430	−	0.884030i	$-0.654820\pi$
$727$	14.3410	−	24.8393i	0.531878	−	0.921239i	0.999308	−	0.0372089i	$-0.0118467\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.49447			0.0922614
$732$		0			0
$733$	−25.0528			−0.925348			−0.462674	−	0.886529i	$-0.653110\pi$
$733$	−25.0528			−0.925348			−0.462674	+	0.886529i	$0.653110\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.459391	+	0.795689i	−0.0169219	+	0.0293096i
$738$		0			0
$739$	−13.7608	−	23.8344i	−0.506198	−	0.876761i	−0.999974	−	0.00717223i	$-0.997717\pi$
$739$	−13.7608	−	23.8344i	−0.506198	−	0.876761i	0.493776	−	0.869589i	$-0.335616\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7.00608	−	12.1349i	−0.257028	−	0.445186i	0.708416	−	0.705795i	$-0.249410\pi$
$743$	−7.00608	−	12.1349i	−0.257028	−	0.445186i	−0.965444	+	0.260609i	$0.916077\pi$
$744$		0			0
$745$	−77.6326			−2.84424
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.1009	+	27.0133i	−0.369077	+	0.987046i
$750$		0			0
$751$	52.2594			1.90697			0.953486	−	0.301436i	$-0.0974660\pi$
$751$	52.2594			1.90697			0.953486	+	0.301436i	$0.0974660\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.53289			−0.201363
$756$		0			0
$757$	−43.3447			−1.57539			−0.787694	−	0.616066i	$-0.788725\pi$
$757$	−43.3447			−1.57539			−0.787694	+	0.616066i	$0.788725\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.2510			0.625348			0.312674	−	0.949860i	$-0.398775\pi$
$761$	17.2510			0.625348			0.312674	+	0.949860i	$0.398775\pi$
$762$		0			0
$763$	−3.57086	−	4.33209i	−0.129274	−	0.156832i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.16889			−0.0783139
$768$		0			0
$769$	−10.6727	−	18.4856i	−0.384867	−	0.666609i	0.606884	−	0.794790i	$-0.292419\pi$
$769$	−10.6727	−	18.4856i	−0.384867	−	0.666609i	−0.991751	+	0.128182i	$0.959086\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	0.959689	−	0.281065i	$-0.0906877\pi$
$773$	6.57357	+	11.3858i	0.236435	+	0.409517i	−0.723254	+	0.690582i	$0.757354\pi$
$774$		0			0
$775$	15.4791	−	26.8106i	0.556027	−	0.963066i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13.4288			−0.481136
$780$		0			0
$781$	4.41405			0.157947
$782$		0			0
$783$		0			0
$784$		0			0
$785$	30.7954	−	53.3393i	1.09914	−	1.90376i
$786$		0			0
$787$	−14.0650	+	24.3614i	−0.501364	+	0.868389i	0.498634	+	0.866812i	$0.333835\pi$
$787$	−14.0650	+	24.3614i	−0.501364	+	0.868389i	−0.999999	+	0.00157623i	$0.999498\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−26.6332	−	32.3108i	−0.946968	−	1.14884i
$792$		0			0
$793$	6.46470	−	11.1972i	0.229568	−	0.397624i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.8683	−	22.2885i	−0.455817	−	0.789499i	0.542917	−	0.839786i	$-0.317320\pi$
$797$	−12.8683	−	22.2885i	−0.455817	−	0.789499i	−0.998735	+	0.0502873i	$0.983986\pi$
$798$		0			0
$799$	−1.27155	+	2.20238i	−0.0449841	+	0.0779147i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.816934	+	1.41497i	0.0288290	+	0.0499333i
$804$		0			0
$805$	23.8746	−	3.99444i	0.841468	−	0.140786i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.9353	−	27.6007i	−0.560254	−	0.970388i	−0.997474	−	0.0710338i	$-0.977370\pi$
$809$	−15.9353	−	27.6007i	−0.560254	−	0.970388i	0.437220	−	0.899355i	$-0.355963\pi$
$810$		0			0
$811$	−43.3860			−1.52349			−0.761744	−	0.647878i	$-0.775657\pi$
$811$	−43.3860			−1.52349			−0.761744	+	0.647878i	$0.775657\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.3382	−	21.3704i	0.432188	−	0.748571i
$816$		0			0
$817$	14.0113	+	24.2682i	0.490193	+	0.849039i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.19677	−	14.1972i	−0.286069	−	0.495487i	0.686799	−	0.726848i	$-0.259015\pi$
$821$	−8.19677	−	14.1972i	−0.286069	−	0.495487i	−0.972868	+	0.231361i	$0.925682\pi$
$822$		0			0
$823$	−13.1890	+	22.8440i	−0.459739	+	0.796292i	−0.998947	−	0.0458812i	$-0.985390\pi$
$823$	−13.1890	+	22.8440i	−0.459739	+	0.796292i	0.539208	+	0.842173i	$0.318724\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	36.7225			1.27697			0.638484	−	0.769635i	$-0.279562\pi$
$827$	36.7225			1.27697			0.638484	+	0.769635i	$0.279562\pi$
$828$		0			0
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	0.996160	−	0.0875485i	$-0.0279033\pi$
$829$	12.1579	+	21.0581i	0.422261	+	0.731377i	−0.573899	+	0.818926i	$0.694570\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.32058	+	1.14811i	0.0457553	+	0.0397797i
$834$		0			0
$835$	32.5519	+	56.3815i	1.12650	+	1.95116i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.8405	+	22.2404i	−0.443303	+	0.767824i	−0.997932	−	0.0642741i	$-0.979527\pi$
$839$	−12.8405	+	22.2404i	−0.443303	+	0.767824i	0.554629	+	0.832098i	$0.312860\pi$
$840$		0			0
$841$	5.91963	+	10.2531i	0.204125	+	0.353555i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	21.3577	−	36.9926i	0.734726	−	1.27258i
$846$		0			0
$847$	−26.6254	+	4.45468i	−0.914859	+	0.153065i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−5.86148	+	10.1524i	−0.200929	+	0.348019i
$852$		0			0
$853$	14.4872	−	25.0925i	0.496031	−	0.859150i	−0.503959	−	0.863728i	$-0.668124\pi$
$853$	14.4872	−	25.0925i	0.496031	−	0.859150i	0.999990	+	0.00457743i	$0.00145705\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.3868			0.867197			0.433598	−	0.901106i	$-0.357244\pi$
$857$	25.3868			0.867197			0.433598	+	0.901106i	$0.357244\pi$
$858$		0			0
$859$	5.95783			0.203279			0.101639	−	0.994821i	$-0.467591\pi$
$859$	5.95783			0.203279			0.101639	+	0.994821i	$0.467591\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.19545	−	14.1949i	0.278977	−	0.483201i	−0.692154	−	0.721750i	$-0.743338\pi$
$863$	8.19545	−	14.1949i	0.278977	−	0.483201i	0.971131	+	0.238548i	$0.0766715\pi$
$864$		0			0
$865$	−7.17624	−	12.4296i	−0.244000	−	0.422620i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.802920	+	1.39070i	0.0272372	+	0.0471762i
$870$		0			0
$871$	1.23186			0.0417399
$872$		0			0
$873$		0			0
$874$		0			0
$875$	35.0272	−	5.86038i	1.18413	−	0.198117i
$876$		0			0
$877$	35.2539			1.19044			0.595220	−	0.803563i	$-0.297065\pi$
$877$	35.2539			1.19044			0.595220	+	0.803563i	$0.297065\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−26.2582			−0.884661			−0.442331	−	0.896852i	$-0.645848\pi$
$881$	−26.2582			−0.884661			−0.442331	+	0.896852i	$0.645848\pi$
$882$		0			0
$883$	−10.0087			−0.336821			−0.168410	−	0.985717i	$-0.553863\pi$
$883$	−10.0087			−0.336821			−0.168410	+	0.985717i	$0.553863\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.9056			−0.534059			−0.267030	−	0.963688i	$-0.586042\pi$
$887$	−15.9056			−0.534059			−0.267030	+	0.963688i	$0.586042\pi$
$888$		0			0
$889$	3.31264	−	0.554236i	0.111102	−	0.0185885i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−28.5688			−0.956017
$894$		0			0
$895$	13.5428	+	23.4569i	0.452687	+	0.784077i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	7.42583	+	12.8619i	0.247665	+	0.428969i
$900$		0			0
$901$	−1.23608	+	2.14095i	−0.0411797	+	0.0713253i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	41.5657			1.38169
$906$		0			0
$907$	17.0925			0.567547			0.283773	−	0.958891i	$-0.408414\pi$
$907$	17.0925			0.567547			0.283773	+	0.958891i	$0.408414\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	14.9435	−	25.8829i	0.495099	−	0.857537i	−0.504885	−	0.863187i	$-0.668465\pi$
$911$	14.9435	−	25.8829i	0.495099	−	0.857537i	0.999984	+	0.00564955i	$0.00179832\pi$
$912$		0			0
$913$	−5.49961	+	9.52561i	−0.182011	+	0.315252i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−39.2176	+	6.56148i	−1.29508	+	0.216679i
$918$		0			0
$919$	−11.8283	+	20.4873i	−0.390181	+	0.675813i	−0.992473	−	0.122462i	$-0.960921\pi$
$919$	−11.8283	+	20.4873i	−0.390181	+	0.675813i	0.602292	+	0.798276i	$0.294254\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.95907	−	5.12525i	−0.0973989	−	0.168700i
$924$		0			0
$925$	−20.4280	+	35.3823i	−0.671667	+	1.16336i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.30880	+	10.9272i	0.206985	+	0.358509i	0.950763	−	0.309918i	$-0.100302\pi$
$929$	6.30880	+	10.9272i	0.206985	+	0.358509i	−0.743778	+	0.668426i	$0.766968\pi$
$930$		0			0
$931$	−3.75215	+	19.2965i	−0.122972	+	0.632417i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.411957	−	0.713530i	−0.0134724	−	0.0233349i
$936$		0			0
$937$	−26.3440			−0.860622			−0.430311	−	0.902681i	$-0.641596\pi$
$937$	−26.3440			−0.860622			−0.430311	+	0.902681i	$0.641596\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	25.4699	−	44.1151i	0.830294	−	1.43811i	−0.0675118	−	0.997718i	$-0.521506\pi$
$941$	25.4699	−	44.1151i	0.830294	−	1.43811i	0.897805	−	0.440392i	$-0.145161\pi$
$942$		0			0
$943$	5.92404	+	10.2607i	0.192913	+	0.334136i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.8399	−	23.9714i	−0.449737	−	0.778967i	0.548632	−	0.836064i	$-0.315149\pi$
$947$	−13.8399	−	23.9714i	−0.449737	−	0.778967i	−0.998369	+	0.0570968i	$0.981816\pi$
$948$		0			0
$949$	1.09530	−	1.89712i	0.0355551	−	0.0615832i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	27.4017			0.887628			0.443814	−	0.896119i	$-0.353625\pi$
$953$	27.4017			0.887628			0.443814	+	0.896119i	$0.353625\pi$
$954$		0			0
$955$	44.0265	+	76.2561i	1.42466	+	2.46759i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.27471	−	0.213271i	0.0411626	−	0.00688689i
$960$		0			0
$961$	9.07336	+	15.7155i	0.292689	+	0.506952i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−10.9569	+	18.9779i	−0.352715	+	0.610921i
$966$		0			0
$967$	−9.09069	−	15.7455i	−0.292337	−	0.506342i	0.682025	−	0.731329i	$-0.261100\pi$
$967$	−9.09069	−	15.7455i	−0.292337	−	0.506342i	−0.974362	+	0.224986i	$0.927766\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.7416	−	34.1935i	0.633538	−	1.09732i	−0.353285	−	0.935516i	$-0.614935\pi$
$971$	19.7416	−	34.1935i	0.633538	−	1.09732i	0.986823	−	0.161804i	$-0.0517313\pi$
$972$		0			0
$973$	16.6092	+	20.1499i	0.532466	+	0.645975i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.95782	−	10.3193i	0.190608	−	0.330142i	−0.754844	−	0.655904i	$-0.772288\pi$
$977$	5.95782	−	10.3193i	0.190608	−	0.330142i	0.945452	+	0.325762i	$0.105621\pi$
$978$		0			0
$979$	−1.07439	+	1.86090i	−0.0343376	+	0.0594745i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.4779			−0.589354			−0.294677	−	0.955597i	$-0.595212\pi$
$983$	−18.4779			−0.589354			−0.294677	+	0.955597i	$0.595212\pi$
$984$		0			0
$985$	57.1176			1.81992
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.3620	−	21.4117i	0.393090	−	0.680851i
$990$		0			0
$991$	6.34850	+	10.9959i	0.201667	+	0.349297i	0.949066	−	0.315079i	$-0.102031\pi$
$991$	6.34850	+	10.9959i	0.201667	+	0.349297i	−0.747399	+	0.664376i	$0.768698\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−28.6108	−	49.5553i	−0.907023	−	1.57101i
$996$		0			0
$997$	41.9533			1.32868			0.664338	−	0.747432i	$-0.268714\pi$
$997$	41.9533			1.32868			0.664338	+	0.747432i	$0.268714\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.i.289.5		10
3.2	odd	2		1008.2.t.i.961.1		10
4.3	odd	2		189.2.g.b.100.3		10
7.4	even	3		3024.2.q.i.2881.1		10
9.4	even	3		3024.2.q.i.2305.1		10
9.5	odd	6		1008.2.q.i.625.3		10
12.11	even	2		63.2.g.b.16.3	yes	10
21.11	odd	6		1008.2.q.i.529.3		10
28.3	even	6		1323.2.h.f.802.3		10
28.11	odd	6		189.2.h.b.46.3		10
28.19	even	6		1323.2.f.f.883.3		10
28.23	odd	6		1323.2.f.e.883.3		10
28.27	even	2		1323.2.g.f.667.3		10
36.7	odd	6		567.2.e.e.163.3		10
36.11	even	6		567.2.e.f.163.3		10
36.23	even	6		63.2.h.b.58.3	yes	10
36.31	odd	6		189.2.h.b.37.3		10
63.4	even	3	inner	3024.2.t.i.1873.5		10
63.32	odd	6		1008.2.t.i.193.1		10
84.11	even	6		63.2.h.b.25.3	yes	10
84.23	even	6		441.2.f.e.295.3		10
84.47	odd	6		441.2.f.f.295.3		10
84.59	odd	6		441.2.h.f.214.3		10
84.83	odd	2		441.2.g.f.79.3		10
252.11	even	6		567.2.e.f.487.3		10
252.23	even	6		441.2.f.e.148.3		10
252.31	even	6		1323.2.g.f.361.3		10
252.47	odd	6		3969.2.a.ba.1.3		5
252.59	odd	6		441.2.g.f.67.3		10
252.67	odd	6		189.2.g.b.172.3		10
252.79	odd	6		3969.2.a.bc.1.3		5
252.95	even	6		63.2.g.b.4.3	✓	10
252.103	even	6		1323.2.f.f.442.3		10
252.131	odd	6		441.2.f.f.148.3		10
252.139	even	6		1323.2.h.f.226.3		10
252.151	odd	6		567.2.e.e.487.3		10
252.167	odd	6		441.2.h.f.373.3		10
252.187	even	6		3969.2.a.bb.1.3		5
252.191	even	6		3969.2.a.z.1.3		5
252.247	odd	6		1323.2.f.e.442.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	252.95	even	6
63.2.g.b.16.3	yes	10	12.11	even	2
63.2.h.b.25.3	yes	10	84.11	even	6
63.2.h.b.58.3	yes	10	36.23	even	6
189.2.g.b.100.3		10	4.3	odd	2
189.2.g.b.172.3		10	252.67	odd	6
189.2.h.b.37.3		10	36.31	odd	6
189.2.h.b.46.3		10	28.11	odd	6
441.2.f.e.148.3		10	252.23	even	6
441.2.f.e.295.3		10	84.23	even	6
441.2.f.f.148.3		10	252.131	odd	6
441.2.f.f.295.3		10	84.47	odd	6
441.2.g.f.67.3		10	252.59	odd	6
441.2.g.f.79.3		10	84.83	odd	2
441.2.h.f.214.3		10	84.59	odd	6
441.2.h.f.373.3		10	252.167	odd	6
567.2.e.e.163.3		10	36.7	odd	6
567.2.e.e.487.3		10	252.151	odd	6
567.2.e.f.163.3		10	36.11	even	6
567.2.e.f.487.3		10	252.11	even	6
1008.2.q.i.529.3		10	21.11	odd	6
1008.2.q.i.625.3		10	9.5	odd	6
1008.2.t.i.193.1		10	63.32	odd	6
1008.2.t.i.961.1		10	3.2	odd	2
1323.2.f.e.442.3		10	252.247	odd	6
1323.2.f.e.883.3		10	28.23	odd	6
1323.2.f.f.442.3		10	252.103	even	6
1323.2.f.f.883.3		10	28.19	even	6
1323.2.g.f.361.3		10	252.31	even	6
1323.2.g.f.667.3		10	28.27	even	2
1323.2.h.f.226.3		10	252.139	even	6
1323.2.h.f.802.3		10	28.3	even	6
3024.2.q.i.2305.1		10	9.4	even	3
3024.2.q.i.2881.1		10	7.4	even	3
3024.2.t.i.289.5		10	1.1	even	1	trivial
3024.2.t.i.1873.5		10	63.4	even	3	inner
3969.2.a.z.1.3		5	252.191	even	6
3969.2.a.ba.1.3		5	252.47	odd	6
3969.2.a.bb.1.3		5	252.187	even	6
3969.2.a.bc.1.3		5	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.69258 q^{5} +(2.60948 - 0.436591i) q^{7} +O(q^{10})\)	\(q+3.69258 q^{5} +(2.60948 - 0.436591i) q^{7} -0.892568 q^{11} +(0.598355 + 1.03638i) q^{13} +(0.124991 + 0.216492i) q^{17} +(-1.40414 + 2.43204i) q^{19} +2.47772 q^{23} +8.63514 q^{25} +(-2.07128 + 3.58755i) q^{29} +(1.79257 - 3.10483i) q^{31} +(9.63571 - 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(2.39093 + 4.14121i) q^{41} +(4.98928 - 8.64169i) q^{43} +(5.08653 + 8.81013i) q^{47} +(6.61878 - 2.27855i) q^{49} +(4.94465 + 8.56438i) q^{53} -3.29588 q^{55} +(-0.906186 + 1.56956i) q^{59} +(-5.40205 - 9.35663i) q^{61} +(2.20948 + 3.82692i) q^{65} +(0.514685 - 0.891460i) q^{67} -4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(-2.32914 + 0.389687i) q^{77} +(-0.899562 - 1.55809i) q^{79} +(6.16156 - 10.6721i) q^{83} +(0.461541 + 0.799412i) q^{85} +(1.20370 - 2.08488i) q^{89} +(2.01387 + 2.44318i) q^{91} +(-5.18489 + 8.98049i) q^{95} +(5.52210 - 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{5} + q^{7}+O(q^{10}) \) 10 * q + 8 * q^5 + q^7	\( 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

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