LMFDB - Embedded newform 3024.2.q.i.2305.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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, 2, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (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:	$\Z[a_1, \ldots, a_{7}]$
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			2305.1
Root			$0.247934 + 0.429435i$ of defining polynomial
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.i.2881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.84629 - 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +O(q^{10})$	$q+(-1.84629 - 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +(0.446284 - 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(0.124991 + 0.216492i) q^{17} +(-1.40414 + 2.43204i) q^{19} +(-1.23886 - 2.14576i) q^{23} +(-4.31757 + 7.47825i) q^{25} +(-2.07128 - 3.58755i) q^{29} -3.58515 q^{31} +(9.63571 - 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(2.39093 - 4.14121i) q^{41} +(4.98928 + 8.64169i) q^{43} -10.1731 q^{47} +(-5.28267 - 4.59275i) q^{49} +(4.94465 + 8.56438i) q^{53} -3.29588 q^{55} +1.81237 q^{59} +10.8041 q^{61} -4.41895 q^{65} -1.02937 q^{67} -4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(1.50205 + 1.82225i) q^{77} +1.79912 q^{79} +(6.16156 + 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(1.20370 - 2.08488i) q^{89} +(2.01387 + 2.44318i) q^{91} +10.3698 q^{95} +(5.52210 + 9.56456i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) $ 10 * q - 4 * q^5 + 4 * q^7	$ 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.84629	−	3.19787i	−0.825686	−	1.43013i	−0.901394	−	0.433000i	$-0.857455\pi$
$5$	−1.84629	−	3.19787i	−0.825686	−	1.43013i	0.0757082	−	0.997130i	$-0.475878\pi$
$6$		0			0
$7$	−0.926641	+	2.47817i	−0.350238	+	0.936661i
$7$	−0.926641	+	2.47817i	−0.350238	+	0.936661i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.446284	−	0.772987i	0.134560	−	0.233064i	−0.790869	−	0.611985i	$-0.790371\pi$
$11$	0.446284	−	0.772987i	0.134560	−	0.233064i	0.925429	+	0.378921i	$0.123705\pi$
$12$		0			0
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	−0.771040	−	0.636787i	$-0.780263\pi$
$13$	0.598355	−	1.03638i	0.165954	−	0.287441i	0.936994	+	0.349346i	$0.113596\pi$
$14$		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
$23$	−1.23886	−	2.14576i	−0.258320	−	0.447423i	0.707472	−	0.706741i	$-0.249835\pi$
$23$	−1.23886	−	2.14576i	−0.258320	−	0.447423i	−0.965792	+	0.259318i	$0.916502\pi$
$24$		0			0
$25$	−4.31757	+	7.47825i	−0.863514	+	1.49565i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	0.607091	−	0.794632i	$-0.292336\pi$
$29$	−2.07128	−	3.58755i	−0.384626	−	0.666192i	−0.991717	+	0.128440i	$0.959003\pi$
$30$		0			0
$31$	−3.58515			−0.643912			−0.321956	−	0.946755i	$-0.604340\pi$
$31$	−3.58515			−0.643912			−0.321956	+	0.946755i	$0.604340\pi$
$32$		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	−0.616686	−	0.787209i	$-0.711525\pi$
$41$	2.39093	−	4.14121i	0.373400	−	0.646748i	0.990086	+	0.140461i	$0.0448584\pi$
$42$		0			0
$43$	4.98928	+	8.64169i	0.760859	+	1.31785i	0.942408	+	0.334464i	$0.108555\pi$
$43$	4.98928	+	8.64169i	0.760859	+	1.31785i	−0.181550	+	0.983382i	$0.558111\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.1731			−1.48389			−0.741947	−	0.670459i	$-0.766097\pi$
$47$	−10.1731			−1.48389			−0.741947	+	0.670459i	$0.766097\pi$
$48$		0			0
$49$	−5.28267	−	4.59275i	−0.754667	−	0.656108i
$50$		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
$59$	1.81237			0.235951			0.117975	−	0.993017i	$-0.462360\pi$
$59$	1.81237			0.235951			0.117975	+	0.993017i	$0.462360\pi$
$60$		0			0
$61$	10.8041			1.38332			0.691662	−	0.722221i	$-0.256879\pi$
$61$	10.8041			1.38332			0.691662	+	0.722221i	$0.256879\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.41895			−0.548103
$66$		0			0
$67$	−1.02937			−0.125757			−0.0628787	−	0.998021i	$-0.520028\pi$
$67$	−1.02937			−0.125757			−0.0628787	+	0.998021i	$0.520028\pi$
$68$		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
$77$	1.50205	+	1.82225i	0.171174	+	0.207665i
$78$		0			0
$79$	1.79912			0.202417			0.101209	−	0.994865i	$-0.467729\pi$
$79$	1.79912			0.202417			0.101209	+	0.994865i	$0.467729\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.16156	+	10.6721i	0.676319	+	1.17142i	0.976082	+	0.217405i	$0.0697591\pi$
$83$	6.16156	+	10.6721i	0.676319	+	1.17142i	−0.299763	+	0.954014i	$0.596908\pi$
$84$		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
$95$	10.3698			1.06392
$96$		0			0
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	0.997437	+	0.0715522i	$0.0227952\pi$
$97$	5.52210	+	9.56456i	0.560684	+	0.971134i	−0.436752	+	0.899582i	$0.643871\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.29982	+	2.25136i	−0.129337	+	0.224018i	−0.923420	−	0.383791i	$-0.874618\pi$
$101$	−1.29982	+	2.25136i	−0.129337	+	0.224018i	0.794083	+	0.607810i	$0.207952\pi$
$102$		0			0
$103$	4.85578	+	8.41045i	0.478454	+	0.828706i	0.999695	−	0.0247032i	$-0.00786408\pi$
$103$	4.85578	+	8.41045i	0.478454	+	0.828706i	−0.521241	+	0.853409i	$0.674531\pi$
$104$		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	0.206061	+	0.978539i	$0.433935\pi$
$113$	−7.91318	+	13.7060i	−0.744409	+	1.28935i	−0.950470	+	0.310816i	$0.899398\pi$
$114$		0			0
$115$	−4.57458	+	7.92341i	−0.426582	+	0.738861i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.652326	+	0.109140i	−0.0597986	+	0.0100049i
$120$		0			0
$121$	5.10166	+	8.83634i	0.463787	+	0.803303i
$122$		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
$131$	7.51444	+	13.0154i	0.656540	+	1.13716i	0.981505	+	0.191435i	$0.0613140\pi$
$131$	7.51444	+	13.0154i	0.656540	+	1.13716i	−0.324965	+	0.945726i	$0.605353\pi$
$132$		0			0
$133$	−4.72587	−	5.73332i	−0.409785	−	0.497142i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.244246	+	0.423047i	−0.0208674	+	0.0361433i	−0.876271	−	0.481819i	$-0.839976\pi$
$137$	−0.244246	+	0.423047i	−0.0208674	+	0.0361433i	0.855403	+	0.517963i	$0.173309\pi$
$138$		0			0
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	−0.577226	−	0.816585i	$-0.695865\pi$
$139$	4.93487	−	8.54745i	0.418570	−	0.724985i	0.995796	+	0.0915997i	$0.0291980\pi$
$140$		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
$149$	10.5120	+	18.2073i	0.861175	+	1.49160i	0.870796	+	0.491645i	$0.163604\pi$
$149$	10.5120	+	18.2073i	0.861175	+	1.49160i	−0.00962096	+	0.999954i	$0.503062\pi$
$150$		0			0
$151$	0.749191	−	1.29764i	0.0609683	−	0.105600i	−0.833930	−	0.551870i	$-0.813914\pi$
$151$	0.749191	−	1.29764i	0.0609683	−	0.105600i	0.894898	+	0.446270i	$0.147248\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.61922	+	11.4648i	0.531669	+	0.920877i
$156$		0			0
$157$	−16.6796			−1.33118			−0.665590	−	0.746317i	$-0.731820\pi$
$157$	−16.6796			−1.33118			−0.665590	+	0.746317i	$0.731820\pi$
$158$		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	−0.292156	−	0.956371i	$-0.594373\pi$
$167$	8.81549	−	15.2689i	0.682163	−	1.18154i	0.974319	−	0.225170i	$-0.0722939\pi$
$168$		0			0
$169$	5.78394	+	10.0181i	0.444919	+	0.770622i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.88685			0.295511			0.147756	−	0.989024i	$-0.452795\pi$
$173$	3.88685			0.295511			0.147756	+	0.989024i	$0.452795\pi$
$174$		0			0
$175$	−14.5316	−	17.6293i	−1.09848	−	1.33265i
$176$		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
$185$	17.4709			1.28449
$186$		0			0
$187$	0.223127			0.0163167
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−23.8459			−1.72543			−0.862715	−	0.505690i	$-0.831238\pi$
$191$	−23.8459			−1.72543			−0.862715	+	0.505690i	$0.831238\pi$
$192$		0			0
$193$	5.93456			0.427179			0.213589	−	0.976924i	$-0.431485\pi$
$193$	5.93456			0.427179			0.213589	+	0.976924i	$0.431485\pi$
$194$		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
$203$	10.8099	−	1.80860i	0.758707	−	0.126939i
$204$		0			0
$205$	−17.6574			−1.23325
$206$		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	−0.891372	−	0.453273i	$-0.850256\pi$
$211$	−0.771898	+	1.33697i	−0.0531397	+	0.0920406i	0.838232	+	0.545314i	$0.183590\pi$
$212$		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
$221$	0.299157			0.0201235
$222$		0			0
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	0.942649	−	0.333784i	$-0.108326\pi$
$223$	2.72171	+	4.71414i	0.182259	+	0.315682i	−0.760390	+	0.649466i	$0.774992\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.03818	−	13.9225i	0.533513	−	0.924072i	−0.465721	−	0.884932i	$-0.654205\pi$
$227$	8.03818	−	13.9225i	0.533513	−	0.924072i	0.999234	−	0.0391399i	$-0.0124618\pi$
$228$		0			0
$229$	4.98420	+	8.63289i	0.329365	+	0.570477i	0.982386	−	0.186863i	$-0.0598319\pi$
$229$	4.98420	+	8.63289i	0.329365	+	0.570477i	−0.653021	+	0.757340i	$0.726499\pi$
$230$		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	0.251687	+	0.967809i	$0.419015\pi$
$239$	−11.0119	+	19.0732i	−0.712303	+	1.23375i	−0.963990	+	0.265937i	$0.914319\pi$
$240$		0			0
$241$	−8.36004	+	14.4800i	−0.538517	+	0.932739i	0.460467	+	0.887677i	$0.347682\pi$
$241$	−8.36004	+	14.4800i	−0.538517	+	0.932739i	−0.998984	+	0.0450623i	$0.985651\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.93368	+	25.3728i	−0.315201	+	1.62101i
$246$		0			0
$247$	1.68035	+	2.91045i	0.106918	+	0.185187i
$248$		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
$257$	−8.55986	−	14.8261i	−0.533950	−	0.924828i	−0.999213	−	0.0396557i	$-0.987374\pi$
$257$	−8.55986	−	14.8261i	−0.533950	−	0.924828i	0.465264	−	0.885172i	$-0.345959\pi$
$258$		0			0
$259$	−7.96211	−	9.65945i	−0.494741	−	0.600209i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.2763	+	17.7991i	−0.633666	+	1.09754i	0.353130	+	0.935574i	$0.385117\pi$
$263$	−10.2763	+	17.7991i	−0.633666	+	1.09754i	−0.986796	+	0.161967i	$0.948216\pi$
$264$		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
$275$	3.85373	+	6.67485i	0.232388	+	0.402509i
$276$		0			0
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	−0.201536	−	0.979481i	$-0.564593\pi$
$277$	12.4407	−	21.5479i	0.747487	−	1.29469i	0.949024	−	0.315205i	$-0.102073\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	0.994652	−	0.103282i	$-0.0329346\pi$
$281$	6.83733	+	11.8426i	0.407881	+	0.706470i	−0.586771	+	0.809753i	$0.699601\pi$
$282$		0			0
$283$	−6.32179			−0.375791			−0.187896	−	0.982189i	$-0.560167\pi$
$283$	−6.32179			−0.375791			−0.187896	+	0.982189i	$0.560167\pi$
$284$		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	−0.825052	−	0.565057i	$-0.808854\pi$
$293$	1.31508	−	2.27778i	0.0768277	−	0.133069i	0.901880	+	0.431987i	$0.142188\pi$
$294$		0			0
$295$	−3.34616	−	5.79573i	−0.194821	−	0.337440i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.96511			−0.171477
$300$		0			0
$301$	−26.0389	+	4.35655i	−1.50086	+	0.251108i
$302$		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
$311$	−15.1003			−0.856258			−0.428129	−	0.903718i	$-0.640827\pi$
$311$	−15.1003			−0.856258			−0.428129	+	0.903718i	$0.640827\pi$
$312$		0			0
$313$	−25.4785			−1.44013			−0.720064	−	0.693908i	$-0.755888\pi$
$313$	−25.4785			−1.44013			−0.720064	+	0.693908i	$0.755888\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−32.5209			−1.82656			−0.913278	−	0.407337i	$-0.866457\pi$
$317$	−32.5209			−1.82656			−0.913278	+	0.407337i	$0.866457\pi$
$318$		0			0
$319$	−3.69751			−0.207021
$320$		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
$329$	9.42678	−	25.2106i	0.519715	−	1.38991i
$330$		0			0
$331$	−18.0948			−0.994582			−0.497291	−	0.867584i	$-0.665672\pi$
$331$	−18.0948			−0.994582			−0.497291	+	0.867584i	$0.665672\pi$
$332$		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	0.293168	+	0.956061i	$0.405290\pi$
$337$	−12.5086	+	21.6656i	−0.681389	+	1.18020i	−0.974557	+	0.224139i	$0.928043\pi$
$338$		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
$347$	10.7489			0.577030			0.288515	−	0.957475i	$-0.406838\pi$
$347$	10.7489			0.577030			0.288515	+	0.957475i	$0.406838\pi$
$348$		0			0
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	0.818695	−	0.574228i	$-0.194698\pi$
$349$	−1.64301	−	2.84577i	−0.0879482	−	0.152331i	−0.906644	+	0.421897i	$0.861364\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.40960	−	14.5658i	0.447598	−	0.775262i	−0.550631	−	0.834748i	$-0.685613\pi$
$353$	8.40960	−	14.5658i	0.447598	−	0.775262i	0.998229	+	0.0594866i	$0.0189463\pi$
$354$		0			0
$355$	9.13051	+	15.8145i	0.484597	+	0.839347i
$356$		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
$367$	−0.344992	+	0.597544i	−0.0180084	+	0.0311915i	−0.874889	−	0.484323i	$-0.839066\pi$
$367$	−0.344992	+	0.597544i	−0.0180084	+	0.0311915i	0.856881	+	0.515515i	$0.172399\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−25.8059	+	4.31757i	−1.33978	+	0.224157i
$372$		0			0
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	0.910585	−	0.413321i	$-0.135631\pi$
$373$	1.88006	+	3.25636i	0.0973457	+	0.168608i	−0.813239	+	0.581929i	$0.802298\pi$
$374$		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
$383$	0.536335	+	0.928960i	0.0274055	+	0.0474676i	0.879403	−	0.476078i	$-0.157942\pi$
$383$	0.536335	+	0.928960i	0.0274055	+	0.0474676i	−0.851997	+	0.523546i	$0.824609\pi$
$384$		0			0
$385$	3.05410	−	8.16775i	0.155651	−	0.416267i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−11.8718	+	20.5626i	−0.601925	+	1.04256i	0.390605	+	0.920559i	$0.372266\pi$
$389$	−11.8718	+	20.5626i	−0.601925	+	1.04256i	−0.992529	+	0.122006i	$0.961067\pi$
$390$		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
$401$	12.2628	+	21.2398i	0.612374	+	1.06066i	0.990839	+	0.135048i	$0.0431188\pi$
$401$	12.2628	+	21.2398i	0.612374	+	1.06066i	−0.378465	+	0.925616i	$0.623548\pi$
$402$		0			0
$403$	−2.14519	+	3.71558i	−0.106860	+	0.185086i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.11153	+	3.65728i	0.104665	+	0.181284i
$408$		0			0
$409$	26.7897			1.32467			0.662333	−	0.749210i	$-0.269567\pi$
$409$	26.7897			1.32467			0.662333	+	0.749210i	$0.269567\pi$
$410$		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	0.485624	+	0.874168i	$0.338593\pi$
$419$	−10.5262	+	18.2320i	−0.514240	+	0.890689i	−0.999864	+	0.0165215i	$0.994741\pi$
$420$		0			0
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	0.625568	−	0.780170i	$-0.284867\pi$
$421$	−7.44533	−	12.8957i	−0.362863	−	0.628498i	−0.988431	+	0.151672i	$0.951534\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.15864			−0.104709
$426$		0			0
$427$	−10.0115	+	26.7744i	−0.484492	+	1.29571i
$428$		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
$437$	6.95811			0.332851
$438$		0			0
$439$	15.5447			0.741909			0.370954	−	0.928651i	$-0.379031\pi$
$439$	15.5447			0.741909			0.370954	+	0.928651i	$0.379031\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.79005			0.0850480			0.0425240	−	0.999095i	$-0.486460\pi$
$443$	1.79005			0.0850480			0.0425240	+	0.999095i	$0.486460\pi$
$444$		0			0
$445$	−8.88955			−0.421405
$446$		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
$455$	4.09478	−	10.9509i	0.191966	−	0.513387i
$456$		0			0
$457$	2.56917			0.120181			0.0600905	−	0.998193i	$-0.480861\pi$
$457$	2.56917			0.120181			0.0600905	+	0.998193i	$0.480861\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	−0.887608	−	0.460600i	$-0.847634\pi$
$461$	−18.0934	−	31.3388i	−0.842695	−	1.45959i	0.0449122	−	0.998991i	$-0.485699\pi$
$462$		0			0
$463$	−8.19224	+	14.1894i	−0.380726	+	0.659436i	−0.991166	−	0.132626i	$-0.957659\pi$
$463$	−8.19224	+	14.1894i	−0.380726	+	0.659436i	0.610440	+	0.792062i	$0.290992\pi$
$464$		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
$473$	8.90655			0.409524
$474$		0			0
$475$	−12.1249	−	21.0010i	−0.556330	−	0.963591i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.88370	−	15.3870i	0.405907	−	0.703051i	−0.588520	−	0.808483i	$-0.700289\pi$
$479$	8.88370	−	15.3870i	0.405907	−	0.703051i	0.994427	+	0.105432i	$0.0336224\pi$
$480$		0			0
$481$	2.83103	+	4.90349i	0.129084	+	0.223580i
$482$		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	−0.929326	−	0.369260i	$-0.879611\pi$
$491$	−3.21021	+	5.56025i	−0.144875	+	0.250930i	0.784451	+	0.620190i	$0.212945\pi$
$492$		0			0
$493$	0.517784	−	0.896827i	0.0233198	−	0.0403911i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.58255	−	12.2554i	0.205555	−	0.549729i
$498$		0			0
$499$	5.57296	+	9.65264i	0.249480	+	0.432112i	0.963382	−	0.268134i	$-0.0864071\pi$
$499$	5.57296	+	9.65264i	0.249480	+	0.432112i	−0.713902	+	0.700246i	$0.753074\pi$
$500$		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
$509$	15.5411	+	26.9180i	0.688848	+	1.19312i	0.972211	+	0.234107i	$0.0752167\pi$
$509$	15.5411	+	26.9180i	0.688848	+	1.19312i	−0.283362	+	0.959013i	$0.591450\pi$
$510$		0			0
$511$	4.77672	−	0.799190i	0.211310	−	0.0353541i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	17.9303	−	31.0563i	0.790105	−	1.36850i
$516$		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
$527$	−0.448113	−	0.776154i	−0.0195201	−	0.0338098i
$528$		0			0
$529$	8.43046	−	14.6020i	0.366542	−	0.634869i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.86125	−	4.95583i	−0.123935	−	0.214661i
$534$		0			0
$535$	40.2510			1.74020
$536$		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	0.967336	−	0.253499i	$-0.0815814\pi$
$547$	6.17751	+	10.6998i	0.264131	+	0.457489i	−0.703204	+	0.710988i	$0.748248\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	11.6334			0.495600
$552$		0			0
$553$	−1.66714	+	4.45854i	−0.0708941	+	0.189596i
$554$		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
$563$	45.2127			1.90549			0.952744	−	0.303774i	$-0.0982467\pi$
$563$	45.2127			1.90549			0.952744	+	0.303774i	$0.0982467\pi$
$564$		0			0
$565$	58.4401			2.45859
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−22.4299			−0.940309			−0.470155	−	0.882584i	$-0.655802\pi$
$569$	−22.4299			−0.940309			−0.470155	+	0.882584i	$0.655802\pi$
$570$		0			0
$571$	21.8269			0.913426			0.456713	−	0.889614i	$-0.349027\pi$
$571$	21.8269			0.913426			0.456713	+	0.889614i	$0.349027\pi$
$572$		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
$581$	−32.1569	+	5.38016i	−1.33409	+	0.223207i
$582$		0			0
$583$	8.82687			0.365571
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.72304	−	16.8408i	−0.401313	−	0.695094i	0.592572	−	0.805518i	$-0.298113\pi$
$587$	−9.72304	−	16.8408i	−0.401313	−	0.695094i	−0.993885	+	0.110424i	$0.964779\pi$
$588$		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
$599$	−46.9989			−1.92032			−0.960161	−	0.279447i	$-0.909849\pi$
$599$	−46.9989			−1.92032			−0.960161	+	0.279447i	$0.909849\pi$
$600$		0			0
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	0.661665	−	0.749799i	$-0.269850\pi$
$601$	−7.80843	−	13.5246i	−0.318512	−	0.551680i	−0.980178	+	0.198119i	$0.936517\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	18.8383	−	32.6289i	0.765885	−	1.32655i
$606$		0			0
$607$	−14.3266	−	24.8144i	−0.581500	−	1.00719i	−0.995302	−	0.0968200i	$-0.969133\pi$
$607$	−14.3266	−	24.8144i	−0.581500	−	1.00719i	0.413802	−	0.910367i	$-0.364200\pi$
$608$		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	−0.904577	−	0.426310i	$-0.859813\pi$
$617$	−2.06401	+	3.57497i	−0.0830938	+	0.143923i	0.821484	+	0.570232i	$0.193147\pi$
$618$		0			0
$619$	11.3565	−	19.6700i	0.456456	−	0.790605i	−0.542315	−	0.840175i	$-0.682452\pi$
$619$	11.3565	−	19.6700i	0.456456	−	0.790605i	0.998771	+	0.0495708i	$0.0157853\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.05128	+	4.91492i	0.162311	+	0.196912i
$624$		0			0
$625$	−3.19498	−	5.53387i	−0.127799	−	0.221355i
$626$		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
$635$	−2.34380	−	4.05958i	−0.0930107	−	0.161099i
$636$		0			0
$637$	−7.92076	+	2.72677i	−0.313832	+	0.108038i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.2363	+	24.6580i	−0.562301	+	0.973933i	0.434995	+	0.900433i	$0.356750\pi$
$641$	−14.2363	+	24.6580i	−0.562301	+	0.973933i	−0.997295	+	0.0735002i	$0.976583\pi$
$642$		0			0
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	−0.647640	−	0.761947i	$-0.724244\pi$
$643$	8.52125	−	14.7592i	0.336045	−	0.582048i	0.983685	+	0.179899i	$0.0575771\pi$
$644$		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
$653$	−9.17255	−	15.8873i	−0.358950	−	0.621719i	0.628836	−	0.777538i	$-0.283532\pi$
$653$	−9.17255	−	15.8873i	−0.358950	−	0.621719i	−0.987786	+	0.155819i	$0.950198\pi$
$654$		0			0
$655$	27.7477	−	48.0604i	1.08419	−	1.87787i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.9248	−	24.1184i	−0.542432	−	0.939519i	−0.998764	−	0.0497098i	$-0.984170\pi$
$659$	−13.9248	−	24.1184i	−0.542432	−	0.939519i	0.456332	−	0.889810i	$-0.349163\pi$
$660$		0			0
$661$	39.0141			1.51747			0.758737	−	0.651397i	$-0.225817\pi$
$661$	39.0141			1.51747			0.758737	+	0.651397i	$0.225817\pi$
$662$		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	0.747841	+	0.663878i	$0.231090\pi$
$673$	24.6154	+	42.6352i	0.948856	+	1.64347i	0.201014	+	0.979588i	$0.435576\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.3915			0.899010			0.449505	−	0.893278i	$-0.351600\pi$
$677$	23.3915			0.899010			0.449505	+	0.893278i	$0.351600\pi$
$678$		0			0
$679$	−28.8196	+	4.82180i	−1.10600	+	0.185044i
$680$		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
$689$	11.8346			0.450863
$690$		0			0
$691$	4.11330			0.156477			0.0782387	−	0.996935i	$-0.475070\pi$
$691$	4.11330			0.156477			0.0782387	+	0.996935i	$0.475070\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−36.4448			−1.38243
$696$		0			0
$697$	1.19538			0.0452784
$698$		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
$707$	−4.37478	−	5.30738i	−0.164531	−	0.199605i
$708$		0			0
$709$	−42.4617			−1.59468			−0.797342	−	0.603528i	$-0.793761\pi$
$709$	−42.4617			−1.59468			−0.797342	+	0.603528i	$0.793761\pi$
$710$		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
$725$	35.7715			1.32852
$726$		0			0
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	0.999308	+	0.0372089i	$0.0118467\pi$
$727$	14.3410	+	24.8393i	0.531878	+	0.921239i	−0.467430	+	0.884030i	$0.654820\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.24724	+	2.16028i	−0.0461307	+	0.0799007i
$732$		0			0
$733$	12.5264	+	21.6964i	0.462674	+	0.801375i	0.999093	−	0.0425768i	$-0.0135567\pi$
$733$	12.5264	+	21.6964i	0.462674	+	0.801375i	−0.536419	+	0.843952i	$0.680223\pi$
$734$		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	−0.965444	−	0.260609i	$-0.916077\pi$
$743$	−7.00608	+	12.1349i	−0.257028	+	0.445186i	0.708416	+	0.705795i	$0.249410\pi$
$744$		0			0
$745$	38.8163	−	67.2318i	1.42212	−	2.46318i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−18.3438	−	22.2543i	−0.670268	−	0.813153i
$750$		0			0
$751$	−26.1297	−	45.2580i	−0.953486	−	1.65149i	−0.737795	−	0.675025i	$-0.764133\pi$
$751$	−26.1297	−	45.2580i	−0.953486	−	1.65149i	−0.215692	−	0.976461i	$-0.569201\pi$
$752$		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
$761$	−8.62550	−	14.9398i	−0.312674	−	0.541568i	0.666266	−	0.745714i	$-0.267891\pi$
$761$	−8.62550	−	14.9398i	−0.312674	−	0.541568i	−0.978940	+	0.204146i	$0.934558\pi$
$762$		0			0
$763$	5.53713	−	0.926414i	0.200457	−	0.0335384i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.08444	−	1.87831i	0.0391570	−	0.0678218i
$768$		0			0
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	−0.991751	−	0.128182i	$-0.959086\pi$
$769$	−10.6727	+	18.4856i	−0.384867	+	0.666609i	0.606884	+	0.794790i	$0.292419\pi$
$770$		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
$779$	6.71439	+	11.6297i	0.240568	+	0.416676i
$780$		0			0
$781$	−2.20702	+	3.82268i	−0.0789735	+	0.136786i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	30.7954	+	53.3393i	1.09914	+	1.90376i
$786$		0			0
$787$	28.1301			1.00273			0.501364	−	0.865236i	$-0.332832\pi$
$787$	28.1301			1.00273			0.501364	+	0.865236i	$0.332832\pi$
$788$		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	−0.998735	−	0.0502873i	$-0.983986\pi$
$797$	−12.8683	+	22.2885i	−0.455817	+	0.789499i	0.542917	+	0.839786i	$0.317320\pi$
$798$		0			0
$799$	−1.27155	−	2.20238i	−0.0449841	−	0.0779147i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.63387			−0.0576580
$804$		0			0
$805$	−15.3966	−	18.6788i	−0.542658	−	0.658340i
$806$		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
$815$	−24.6764			−0.864375
$816$		0			0
$817$	−28.0226			−0.980385
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.3935			0.572139			0.286069	−	0.958209i	$-0.407651\pi$
$821$	16.3935			0.572139			0.286069	+	0.958209i	$0.407651\pi$
$822$		0			0
$823$	26.3780			0.919478			0.459739	−	0.888054i	$-0.347943\pi$
$823$	26.3780			0.919478			0.459739	+	0.888054i	$0.347943\pi$
$824$		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
$833$	0.334004	−	1.71771i	0.0115725	−	0.0595151i
$834$		0			0
$835$	−65.1038			−2.25301
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−12.8405	−	22.2404i	−0.443303	−	0.767824i	0.554629	−	0.832098i	$-0.312860\pi$
$839$	−12.8405	−	22.2404i	−0.443303	−	0.767824i	−0.997932	+	0.0642741i	$0.979527\pi$
$840$		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
$851$	11.7230			0.401858
$852$		0			0
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	0.999990	−	0.00457743i	$-0.00145705\pi$
$853$	14.4872	+	25.0925i	0.496031	+	0.859150i	−0.503959	+	0.863728i	$0.668124\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.6934	+	21.9856i	−0.433598	+	0.751015i	−0.997180	−	0.0750458i	$-0.976090\pi$
$857$	−12.6934	+	21.9856i	−0.433598	+	0.751015i	0.563582	+	0.826060i	$0.309423\pi$
$858$		0			0
$859$	−2.97891	−	5.15963i	−0.101639	−	0.176044i	0.810721	−	0.585433i	$-0.199075\pi$
$859$	−2.97891	−	5.15963i	−0.101639	−	0.176044i	−0.912360	+	0.409388i	$0.865742\pi$
$860$		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
$871$	−0.615929	+	1.06682i	−0.0208700	+	0.0361478i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−12.4384	+	33.2646i	−0.420493	+	1.12455i
$876$		0			0
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	−0.993516	−	0.113695i	$-0.963731\pi$
$877$	−17.6270	−	30.5308i	−0.595220	−	1.03095i	0.398295	−	0.917257i	$-0.369602\pi$
$878$		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
$887$	7.95282	+	13.7747i	0.267030	+	0.462509i	0.968093	−	0.250590i	$-0.0806245\pi$
$887$	7.95282	+	13.7747i	0.267030	+	0.462509i	−0.701064	+	0.713099i	$0.747291\pi$
$888$		0			0
$889$	−1.17634	+	3.14595i	−0.0394531	+	0.105512i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	14.2844	−	24.7413i	0.478009	−	0.827935i
$894$		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
$905$	−20.7829	−	35.9970i	−0.690846	−	1.19658i
$906$		0			0
$907$	−8.54624	+	14.8025i	−0.283773	+	0.491510i	−0.972311	−	0.233691i	$-0.924920\pi$
$907$	−8.54624	+	14.8025i	−0.283773	+	0.491510i	0.688538	+	0.725201i	$0.258253\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	14.9435	+	25.8829i	0.495099	+	0.857537i	0.999984	−	0.00564955i	$-0.00179832\pi$
$911$	14.9435	+	25.8829i	0.495099	+	0.857537i	−0.504885	+	0.863187i	$0.668465\pi$
$912$		0			0
$913$	10.9992			0.364021
$914$		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
$929$	−12.6176			−0.413970			−0.206985	−	0.978344i	$-0.566365\pi$
$929$	−12.6176			−0.413970			−0.206985	+	0.978344i	$0.566365\pi$
$930$		0			0
$931$	18.5873	−	6.39880i	0.609176	−	0.209712i
$932$		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
$941$	−50.9397			−1.66059			−0.830294	−	0.557326i	$-0.811827\pi$
$941$	−50.9397			−1.66059			−0.830294	+	0.557326i	$0.811827\pi$
$942$		0			0
$943$	−11.8481			−0.385827
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.6798			0.899474			0.449737	−	0.893161i	$-0.351518\pi$
$947$	27.6798			0.899474			0.449737	+	0.893161i	$0.351518\pi$
$948$		0			0
$949$	−2.19061			−0.0711102
$950$		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
$959$	−0.822054	−	0.997297i	−0.0265455	−	0.0322044i
$960$		0			0
$961$	−18.1467			−0.585378
$962$		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	−0.974362	−	0.224986i	$-0.927766\pi$
$967$	−9.09069	+	15.7455i	−0.292337	+	0.506342i	0.682025	+	0.731329i	$0.261100\pi$
$968$		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
$977$	−11.9156			−0.381215			−0.190608	−	0.981666i	$-0.561046\pi$
$977$	−11.9156			−0.381215			−0.190608	+	0.981666i	$0.561046\pi$
$978$		0			0
$979$	−1.07439	−	1.86090i	−0.0343376	−	0.0594745i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.23896	−	16.0024i	0.294677	−	0.510396i	−0.680233	−	0.732996i	$-0.738121\pi$
$983$	9.23896	−	16.0024i	0.294677	−	0.510396i	0.974910	+	0.222601i	$0.0714546\pi$
$984$		0			0
$985$	−28.5588	−	49.4653i	−0.909959	−	1.57609i
$986$		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
$997$	−20.9767	+	36.3327i	−0.664338	+	1.15067i	0.315127	+	0.949050i	$0.397953\pi$
$997$	−20.9767	+	36.3327i	−0.664338	+	1.15067i	−0.979464	+	0.201617i	$0.935380\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.3	✓	10	84.11	even	6
63.2.g.b.16.3	yes	10	36.11	even	6
63.2.h.b.25.3	yes	10	252.11	even	6
63.2.h.b.58.3	yes	10	12.11	even	2
189.2.g.b.100.3		10	36.7	odd	6
189.2.g.b.172.3		10	28.11	odd	6
189.2.h.b.37.3		10	4.3	odd	2
189.2.h.b.46.3		10	252.151	odd	6
441.2.f.e.148.3		10	84.23	even	6
441.2.f.e.295.3		10	252.191	even	6
441.2.f.f.148.3		10	84.47	odd	6
441.2.f.f.295.3		10	252.47	odd	6
441.2.g.f.67.3		10	84.59	odd	6
441.2.g.f.79.3		10	252.83	odd	6
441.2.h.f.214.3		10	252.227	odd	6
441.2.h.f.373.3		10	84.83	odd	2
567.2.e.e.163.3		10	36.31	odd	6
567.2.e.e.487.3		10	252.67	odd	6
567.2.e.f.163.3		10	36.23	even	6
567.2.e.f.487.3		10	252.95	even	6
1008.2.q.i.529.3		10	63.11	odd	6
1008.2.q.i.625.3		10	3.2	odd	2
1008.2.t.i.193.1		10	21.11	odd	6
1008.2.t.i.961.1		10	9.2	odd	6
1323.2.f.e.442.3		10	28.23	odd	6
1323.2.f.e.883.3		10	252.79	odd	6
1323.2.f.f.442.3		10	28.19	even	6
1323.2.f.f.883.3		10	252.187	even	6
1323.2.g.f.361.3		10	28.3	even	6
1323.2.g.f.667.3		10	252.223	even	6
1323.2.h.f.226.3		10	28.27	even	2
1323.2.h.f.802.3		10	252.115	even	6
3024.2.q.i.2305.1		10	1.1	even	1	trivial
3024.2.q.i.2881.1		10	63.25	even	3	inner
3024.2.t.i.289.5		10	9.7	even	3
3024.2.t.i.1873.5		10	7.4	even	3
3969.2.a.z.1.3		5	252.23	even	6
3969.2.a.ba.1.3		5	252.131	odd	6
3969.2.a.bb.1.3		5	252.103	even	6
3969.2.a.bc.1.3		5	252.247	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.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.84629 - 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +O(q^{10})\)	\(q+(-1.84629 - 3.19787i) q^{5} +(-0.926641 + 2.47817i) q^{7} +(0.446284 - 0.772987i) q^{11} +(0.598355 - 1.03638i) q^{13} +(0.124991 + 0.216492i) q^{17} +(-1.40414 + 2.43204i) q^{19} +(-1.23886 - 2.14576i) q^{23} +(-4.31757 + 7.47825i) q^{25} +(-2.07128 - 3.58755i) q^{29} -3.58515 q^{31} +(9.63571 - 1.61215i) q^{35} +(-2.36568 + 4.09747i) q^{37} +(2.39093 - 4.14121i) q^{41} +(4.98928 + 8.64169i) q^{43} -10.1731 q^{47} +(-5.28267 - 4.59275i) q^{49} +(4.94465 + 8.56438i) q^{53} -3.29588 q^{55} +1.81237 q^{59} +10.8041 q^{61} -4.41895 q^{65} -1.02937 q^{67} -4.94533 q^{71} +(-0.915262 - 1.58528i) q^{73} +(1.50205 + 1.82225i) q^{77} +1.79912 q^{79} +(6.16156 + 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(1.20370 - 2.08488i) q^{89} +(2.01387 + 2.44318i) q^{91} +10.3698 q^{95} +(5.52210 + 9.56456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{5} + 4 q^{7}+O(q^{10}) \) 10 * q - 4 * q^5 + 4 * q^7	\( 10 q - 4 q^{5} + 4 q^{7} + 4 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} + 3 q^{23} - q^{25} - 7 q^{29} - 6 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} - 54 q^{47} - 8 q^{49} + 21 q^{53} - 4 q^{55} - 60 q^{59} + 28 q^{61} - 22 q^{65} - 4 q^{67} - 6 q^{71} + 15 q^{73} - 11 q^{77} - 8 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} + 28 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q - 4 * q^5 + 4 * q^7 + 4 * q^11 - 8 * q^13 - 12 * q^17 - q^19 + 3 * q^23 - q^25 - 7 * q^29 - 6 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 - 54 * q^47 - 8 * q^49 + 21 * q^53 - 4 * q^55 - 60 * q^59 + 28 * q^61 - 22 * q^65 - 4 * q^67 - 6 * q^71 + 15 * q^73 - 11 * q^77 - 8 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 + 28 * q^95 - 12 * q^97

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