LMFDB - Embedded newform 2940.2.q.g.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(361,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2940, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2940.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.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:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2940.361
Dual form			2940.2.q.g.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -4.00000 q^{13} -1.00000 q^{15} +(1.00000 - 1.73205i) q^{17} +(1.00000 + 1.73205i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(1.00000 + 1.73205i) q^{33} +(-5.00000 - 8.66025i) q^{37} +(2.00000 - 3.46410i) q^{39} +10.0000 q^{41} +12.0000 q^{43} +(0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(1.00000 + 1.73205i) q^{51} +2.00000 q^{55} -2.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(6.00000 - 10.3923i) q^{67} +4.00000 q^{69} -10.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +2.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(1.00000 + 1.73205i) q^{89} +(-1.00000 - 1.73205i) q^{93} +(-1.00000 + 1.73205i) q^{95} +8.00000 q^{97} -2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + q^{5} - q^{9}+O(q^{10}) $ 2 * q - q^3 + q^5 - q^9	$ 2 q - q^{3} + q^{5} - q^{9} + 2 q^{11} - 8 q^{13} - 2 q^{15} + 2 q^{17} + 2 q^{19} - 4 q^{23} - q^{25} + 2 q^{27} + 12 q^{29} - 2 q^{31} + 2 q^{33} - 10 q^{37} + 4 q^{39} + 20 q^{41} + 24 q^{43} + q^{45} - 8 q^{47} + 2 q^{51} + 4 q^{55} - 4 q^{57} - 8 q^{59} - 2 q^{61} - 4 q^{65} + 12 q^{67} + 8 q^{69} - 20 q^{71} + 4 q^{73} - q^{75} - q^{81} + 24 q^{83} + 4 q^{85} - 6 q^{87} + 2 q^{89} - 2 q^{93} - 2 q^{95} + 16 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - q^3 + q^5 - q^9 + 2 * q^11 - 8 * q^13 - 2 * q^15 + 2 * q^17 + 2 * q^19 - 4 * q^23 - q^25 + 2 * q^27 + 12 * q^29 - 2 * q^31 + 2 * q^33 - 10 * q^37 + 4 * q^39 + 20 * q^41 + 24 * q^43 + q^45 - 8 * q^47 + 2 * q^51 + 4 * q^55 - 4 * q^57 - 8 * q^59 - 2 * q^61 - 4 * q^65 + 12 * q^67 + 8 * q^69 - 20 * q^71 + 4 * q^73 - q^75 - q^81 + 24 * q^83 + 4 * q^85 - 6 * q^87 + 2 * q^89 - 2 * q^93 - 2 * q^95 + 16 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		0			0
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$		0			0
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	12.0000			1.82998			0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000			1.82998			0.914991	+	0.403473i	$0.132197\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$		0			0
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	0.478953	+	0.877841i	$0.341016\pi$
$59$	−4.00000	+	6.92820i	−0.520756	+	0.901975i	−0.999709	+	0.0241347i	$0.992317\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	−0.222571	−	0.974916i	$-0.571445\pi$
$67$	6.00000	−	10.3923i	0.733017	−	1.26962i	0.955588	−	0.294706i	$-0.0952216\pi$
$68$		0			0
$69$	4.00000			0.481543
$70$		0			0
$71$	−10.0000			−1.18678			−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000			−1.18678			−0.593391	+	0.804914i	$0.702211\pi$
$72$		0			0
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$		0			0
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	0.914146	−	0.405385i	$-0.132862\pi$
$89$	1.00000	+	1.73205i	0.106000	+	0.183597i	−0.808146	+	0.588982i	$0.799529\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$		0			0
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	0.753010	−	0.658009i	$-0.228601\pi$
$107$	−2.00000	−	3.46410i	−0.193347	−	0.334887i	−0.946357	+	0.323122i	$0.895268\pi$
$108$		0			0
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	−0.307290	−	0.951616i	$-0.599422\pi$
$109$	7.00000	−	12.1244i	0.670478	−	1.16130i	0.977769	−	0.209687i	$-0.0672444\pi$
$110$		0			0
$111$	10.0000			0.949158
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	2.00000	−	3.46410i	0.186501	−	0.323029i
$116$		0			0
$117$	2.00000	+	3.46410i	0.184900	+	0.320256i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−5.00000	+	8.66025i	−0.450835	+	0.780869i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	−6.00000	+	10.3923i	−0.528271	+	0.914991i
$130$		0			0
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	−0.643013	−	0.765855i	$-0.722316\pi$
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	0.984757	+	0.173939i	$0.0556494\pi$
$138$		0			0
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	8.00000			0.673722
$142$		0			0
$143$	−4.00000	+	6.92820i	−0.334497	+	0.579365i
$144$		0			0
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	2.00000	−	3.46410i	0.162758	−	0.281905i	0.935857	+	0.352381i	$0.114628\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−2.00000			−0.160644
$156$		0			0
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	−0.661094	−	0.750303i	$-0.729907\pi$
$157$	4.00000	−	6.92820i	0.319235	−	0.552931i	0.980329	+	0.197372i	$0.0632408\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	0.529454	−	0.848339i	$-0.322397\pi$
$163$	−6.00000	−	10.3923i	−0.469956	−	0.813988i	−0.999410	+	0.0343508i	$0.989064\pi$
$164$		0			0
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$		0			0
$167$	16.0000			1.23812			0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000			1.23812			0.619059	+	0.785345i	$0.287514\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	1.00000	−	1.73205i	0.0764719	−	0.132453i
$172$		0			0
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	0.901533	−	0.432710i	$-0.142443\pi$
$173$	1.00000	+	1.73205i	0.0760286	+	0.131685i	−0.825505	+	0.564396i	$0.809109\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−4.00000	−	6.92820i	−0.300658	−	0.520756i
$178$		0			0
$179$	−11.0000	+	19.0526i	−0.822179	+	1.42406i	0.0818780	+	0.996642i	$0.473908\pi$
$179$	−11.0000	+	19.0526i	−0.822179	+	1.42406i	−0.904057	+	0.427413i	$0.859425\pi$
$180$		0			0
$181$	22.0000			1.63525			0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000			1.63525			0.817624	+	0.575753i	$0.195291\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	5.00000	−	8.66025i	0.367607	−	0.636715i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0000	+	19.0526i	0.795932	+	1.37859i	0.922246	+	0.386604i	$0.126352\pi$
$191$	11.0000	+	19.0526i	0.795932	+	1.37859i	−0.126314	+	0.991990i	$0.540315\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$		0			0
$195$	4.00000			0.286446
$196$		0			0
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$		0			0
$201$	6.00000	+	10.3923i	0.423207	+	0.733017i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	5.00000	+	8.66025i	0.349215	+	0.604858i
$206$		0			0
$207$	−2.00000	+	3.46410i	−0.139010	+	0.240772i
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$		0			0
$213$	5.00000	−	8.66025i	0.342594	−	0.593391i
$214$		0			0
$215$	6.00000	+	10.3923i	0.409197	+	0.708749i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$		0			0
$221$	−4.00000	+	6.92820i	−0.269069	+	0.466041i
$222$		0			0
$223$	−12.0000			−0.803579			−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000			−0.803579			−0.401790	+	0.915732i	$0.631612\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$		0			0
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	−0.872823	−	0.488037i	$-0.837713\pi$
$229$	−13.0000	−	22.5167i	−0.859064	−	1.48794i	0.0137585	−	0.999905i	$-0.495620\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	0.793047	−	0.609160i	$-0.208493\pi$
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	−0.924072	+	0.382219i	$0.875160\pi$
$234$		0			0
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	14.0000			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$240$		0			0
$241$	15.0000	−	25.9808i	0.966235	−	1.67357i	0.259975	−	0.965615i	$-0.416286\pi$
$241$	15.0000	−	25.9808i	0.966235	−	1.67357i	0.706260	−	0.707953i	$-0.250381\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.00000	−	6.92820i	−0.254514	−	0.440831i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	−16.0000			−1.00991			−0.504956	−	0.863145i	$-0.668491\pi$
$251$	−16.0000			−1.00991			−0.504956	+	0.863145i	$0.668491\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$		0			0
$255$	−1.00000	+	1.73205i	−0.0626224	+	0.108465i
$256$		0			0
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.00000			−0.122398
$268$		0			0
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$		0			0
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$		0			0
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	−0.319447	−	0.947604i	$-0.603497\pi$
$277$	11.0000	−	19.0526i	0.660926	−	1.14476i	0.980373	−	0.197153i	$-0.0631696\pi$
$278$		0			0
$279$	2.00000			0.119737
$280$		0			0
$281$	−26.0000			−1.55103			−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000			−1.55103			−0.775515	+	0.631329i	$0.782510\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$		0			0
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$		0			0
$293$	30.0000			1.75262			0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000			1.75262			0.876309	+	0.481749i	$0.159998\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$		0			0
$299$	8.00000	+	13.8564i	0.462652	+	0.801337i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$		0			0
$305$	1.00000	−	1.73205i	0.0572598	−	0.0991769i
$306$		0			0
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$		0			0
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.829222	−	0.558920i	$-0.811216\pi$
$317$	−16.0000	−	27.7128i	−0.898650	−	1.55651i	−0.0694277	−	0.997587i	$-0.522117\pi$
$318$		0			0
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	4.00000			0.223258
$322$		0			0
$323$	4.00000			0.222566
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$		0			0
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$	−5.00000	+	8.66025i	−0.273998	+	0.474579i
$334$		0			0
$335$	12.0000			0.655630
$336$		0			0
$337$	2.00000			0.108947			0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000			0.108947			0.0544735	+	0.998515i	$0.482652\pi$
$338$		0			0
$339$	−2.00000	+	3.46410i	−0.108625	+	0.188144i
$340$		0			0
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.00000	+	3.46410i	0.107676	+	0.186501i
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	−0.920677	+	0.390324i	$0.872363\pi$
$354$		0			0
$355$	−5.00000	−	8.66025i	−0.265372	−	0.459639i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	−10.0000	+	17.3205i	−0.521996	+	0.904123i	0.477677	+	0.878536i	$0.341479\pi$
$367$	−10.0000	+	17.3205i	−0.521996	+	0.904123i	−0.999673	+	0.0255875i	$0.991854\pi$
$368$		0			0
$369$	−5.00000	−	8.66025i	−0.260290	−	0.450835i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.851089	+	0.525022i	$0.175943\pi$
$373$	17.0000	+	29.4449i	0.880227	+	1.52460i	0.0291379	+	0.999575i	$0.490724\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	−24.0000			−1.23606
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.00000	−	10.3923i	−0.304997	−	0.528271i
$388$		0			0
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		0			0
$393$	−12.0000			−0.605320
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	−0.999998	−	0.00217869i	$-0.999307\pi$
$397$	−10.0000	−	17.3205i	−0.501886	−	0.869291i	0.498112	−	0.867113i	$-0.334027\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	0.948272	+	0.317460i	$0.102830\pi$
$401$	15.0000	+	25.9808i	0.749064	+	1.29742i	−0.199207	+	0.979957i	$0.563837\pi$
$402$		0			0
$403$	4.00000	−	6.92820i	0.199254	−	0.345118i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−20.0000			−0.991363
$408$		0			0
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$		0			0
$411$	4.00000	+	6.92820i	0.197305	+	0.341743i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$		0			0
$417$	1.00000	−	1.73205i	0.0489702	−	0.0848189i
$418$		0			0
$419$	−36.0000			−1.75872			−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000			−1.75872			−0.879358	+	0.476162i	$0.842028\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$		0			0
$423$	−4.00000	+	6.92820i	−0.194487	+	0.336861i
$424$		0			0
$425$	1.00000	+	1.73205i	0.0485071	+	0.0840168i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	−24.0000			−1.15337			−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−24.0000			−1.15337			−0.576683	+	0.816968i	$0.695653\pi$
$434$		0			0
$435$	−6.00000			−0.287678
$436$		0			0
$437$	4.00000	−	6.92820i	0.191346	−	0.331421i
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.00000	+	13.8564i	0.380091	+	0.658338i	0.991075	−	0.133306i	$-0.0425592\pi$
$443$	8.00000	+	13.8564i	0.380091	+	0.658338i	−0.610984	+	0.791643i	$0.709226\pi$
$444$		0			0
$445$	−1.00000	+	1.73205i	−0.0474045	+	0.0821071i
$446$		0			0
$447$	18.0000			0.851371
$448$		0			0
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$		0			0
$451$	10.0000	−	17.3205i	0.470882	−	0.815591i
$452$		0			0
$453$	2.00000	+	3.46410i	0.0939682	+	0.162758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	−0.999857	−	0.0168929i	$-0.994623\pi$
$457$	−11.0000	−	19.0526i	−0.514558	−	0.891241i	0.485299	−	0.874348i	$-0.338711\pi$
$458$		0			0
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$		0			0
$461$	10.0000			0.465746			0.232873	−	0.972507i	$-0.425187\pi$
$461$	10.0000			0.465746			0.232873	+	0.972507i	$0.425187\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$		0			0
$465$	1.00000	−	1.73205i	0.0463739	−	0.0803219i
$466$		0			0
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	0.536352	−	0.843995i	$-0.319802\pi$
$467$	−10.0000	−	17.3205i	−0.462745	−	0.801498i	−0.999097	+	0.0424970i	$0.986469\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4.00000	+	6.92820i	0.184310	+	0.319235i
$472$		0			0
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	20.0000	+	34.6410i	0.911922	+	1.57949i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$		0			0
$487$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$487$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	30.0000			1.35388			0.676941	−	0.736038i	$-0.263305\pi$
$491$	30.0000			1.35388			0.676941	+	0.736038i	$0.263305\pi$
$492$		0			0
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$		0			0
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−20.0000	−	34.6410i	−0.895323	−	1.55074i	−0.833404	−	0.552664i	$-0.813611\pi$
$499$	−20.0000	−	34.6410i	−0.895323	−	1.55074i	−0.0619186	−	0.998081i	$-0.519722\pi$
$500$		0			0
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$		0			0
$503$	8.00000			0.356702			0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000			0.356702			0.178351	+	0.983967i	$0.442924\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	−1.50000	+	2.59808i	−0.0666173	+	0.115385i
$508$		0			0
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	0.512331	−	0.858788i	$-0.328782\pi$
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	−0.999898	+	0.0142980i	$0.995449\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$		0			0
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$	−16.0000			−0.703679
$518$		0			0
$519$	−2.00000			−0.0877903
$520$		0			0
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$		0			0
$523$	−20.0000	−	34.6410i	−0.874539	−	1.51475i	−0.857253	−	0.514895i	$-0.827831\pi$
$523$	−20.0000	−	34.6410i	−0.874539	−	1.51475i	−0.0172859	−	0.999851i	$-0.505503\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.00000	+	3.46410i	0.0871214	+	0.150899i
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	8.00000			0.347170
$532$		0			0
$533$	−40.0000			−1.73259
$534$		0			0
$535$	2.00000	−	3.46410i	0.0864675	−	0.149766i
$536$		0			0
$537$	−11.0000	−	19.0526i	−0.474685	−	0.822179i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$		0			0
$543$	−11.0000	+	19.0526i	−0.472055	+	0.817624i
$544$		0			0
$545$	14.0000			0.599694
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		0			0
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	6.00000	+	10.3923i	0.255609	+	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	5.00000	+	8.66025i	0.212238	+	0.367607i
$556$		0			0
$557$	−20.0000	+	34.6410i	−0.847427	+	1.46779i	0.0360693	+	0.999349i	$0.488516\pi$
$557$	−20.0000	+	34.6410i	−0.847427	+	1.46779i	−0.883497	+	0.468438i	$0.844817\pi$
$558$		0			0
$559$	−48.0000			−2.03018
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	2.00000	+	3.46410i	0.0841406	+	0.145736i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	0.648655	+	0.761083i	$0.275332\pi$
$572$		0			0
$573$	−22.0000			−0.919063
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	16.0000	−	27.7128i	0.666089	−	1.15370i	−0.312900	−	0.949786i	$-0.601301\pi$
$577$	16.0000	−	27.7128i	0.666089	−	1.15370i	0.978989	−	0.203913i	$-0.0653661\pi$
$578$		0			0
$579$	7.00000	+	12.1244i	0.290910	+	0.503871i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$		0			0
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$		0			0
$589$	−4.00000			−0.164817
$590$		0			0
$591$	−6.00000	+	10.3923i	−0.246807	+	0.427482i
$592$		0			0
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	0.869638	+	0.493689i	$0.164352\pi$
$593$	21.0000	+	36.3731i	0.862367	+	1.49366i	−0.00727173	+	0.999974i	$0.502315\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.00000	−	8.66025i	−0.204636	−	0.354441i
$598$		0			0
$599$	−13.0000	+	22.5167i	−0.531166	+	0.920006i	0.468173	+	0.883637i	$0.344912\pi$
$599$	−13.0000	+	22.5167i	−0.531166	+	0.920006i	−0.999338	+	0.0363689i	$0.988421\pi$
$600$		0			0
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	−18.0000	−	31.1769i	−0.730597	−	1.26543i	−0.956628	−	0.291312i	$-0.905908\pi$
$607$	−18.0000	−	31.1769i	−0.730597	−	1.26543i	0.226031	−	0.974120i	$-0.427425\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	16.0000	+	27.7128i	0.647291	+	1.12114i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$		0			0
$615$	−10.0000			−0.403239
$616$		0			0
$617$	−20.0000			−0.805170			−0.402585	−	0.915383i	$-0.631888\pi$
$617$	−20.0000			−0.805170			−0.402585	+	0.915383i	$0.631888\pi$
$618$		0			0
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−2.00000	+	3.46410i	−0.0798723	+	0.138343i
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	5.00000	+	8.66025i	0.197797	+	0.342594i
$640$		0			0
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	−16.0000			−0.630978			−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000			−0.630978			−0.315489	+	0.948929i	$0.602169\pi$
$644$		0			0
$645$	−12.0000			−0.472500
$646$		0			0
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	0.358723	+	0.933444i	$0.383212\pi$
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	−0.987748	+	0.156059i	$0.950121\pi$
$648$		0			0
$649$	8.00000	+	13.8564i	0.314027	+	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.0000	−	38.1051i	−0.860927	−	1.49117i	−0.871036	−	0.491220i	$-0.836551\pi$
$653$	−22.0000	−	38.1051i	−0.860927	−	1.49117i	0.0101092	−	0.999949i	$-0.496782\pi$
$654$		0			0
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	−38.0000			−1.48027			−0.740135	−	0.672458i	$-0.765238\pi$
$659$	−38.0000			−1.48027			−0.740135	+	0.672458i	$0.765238\pi$
$660$		0			0
$661$	19.0000	−	32.9090i	0.739014	−	1.28001i	−0.213925	−	0.976850i	$-0.568625\pi$
$661$	19.0000	−	32.9090i	0.739014	−	1.28001i	0.952940	−	0.303160i	$-0.0980418\pi$
$662$		0			0
$663$	−4.00000	−	6.92820i	−0.155347	−	0.269069i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$		0			0
$669$	6.00000	−	10.3923i	0.231973	−	0.401790i
$670$		0			0
$671$	−4.00000			−0.154418
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	−0.995877	−	0.0907112i	$-0.971086\pi$
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	0.419380	−	0.907811i	$-0.362247\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−6.00000	−	10.3923i	−0.229920	−	0.398234i
$682$		0			0
$683$	8.00000	−	13.8564i	0.306111	−	0.530201i	−0.671397	−	0.741098i	$-0.734305\pi$
$683$	8.00000	−	13.8564i	0.306111	−	0.530201i	0.977508	+	0.210898i	$0.0676386\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$		0			0
$687$	26.0000			0.991962
$688$		0			0
$689$		0			0
$690$		0			0
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.00000	−	1.73205i	−0.0379322	−	0.0657004i
$696$		0			0
$697$	10.0000	−	17.3205i	0.378777	−	0.656061i
$698$		0			0
$699$	4.00000			0.151294
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	10.0000	−	17.3205i	0.377157	−	0.653255i
$704$		0			0
$705$	4.00000	+	6.92820i	0.150649	+	0.260931i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.00000			0.299602
$714$		0			0
$715$	−8.00000			−0.299183
$716$		0			0
$717$	−7.00000	+	12.1244i	−0.261420	+	0.452792i
$718$		0			0
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	0.955947	−	0.293538i	$-0.0948328\pi$
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	−0.732185	+	0.681106i	$0.761499\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	15.0000	+	25.9808i	0.557856	+	0.966235i
$724$		0			0
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		0			0
$727$	−12.0000			−0.445055			−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000			−0.445055			−0.222528	+	0.974926i	$0.571431\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$		0			0
$733$	6.00000	+	10.3923i	0.221615	+	0.383849i	0.955299	−	0.295643i	$-0.0955338\pi$
$733$	6.00000	+	10.3923i	0.221615	+	0.383849i	−0.733683	+	0.679491i	$0.762200\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$		0			0
$739$	12.0000	−	20.7846i	0.441427	−	0.764574i	−0.556369	−	0.830936i	$-0.687806\pi$
$739$	12.0000	−	20.7846i	0.441427	−	0.764574i	0.997796	+	0.0663614i	$0.0211390\pi$
$740$		0			0
$741$	8.00000			0.293887
$742$		0			0
$743$	48.0000			1.76095			0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000			1.76095			0.880475	+	0.474093i	$0.157224\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$		0			0
$753$	8.00000	−	13.8564i	0.291536	−	0.504956i
$754$		0			0
$755$	4.00000			0.145575
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$	4.00000	−	6.92820i	0.145191	−	0.251478i
$760$		0			0
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	0.594822	−	0.803857i	$-0.297222\pi$
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	−0.993572	+	0.113203i	$0.963889\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.00000	−	1.73205i	−0.0361551	−	0.0626224i
$766$		0			0
$767$	16.0000	−	27.7128i	0.577727	−	1.00065i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$		0			0
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	−0.761987	−	0.647592i	$-0.775776\pi$
$773$	5.00000	−	8.66025i	0.179838	−	0.311488i	0.941825	+	0.336104i	$0.109109\pi$
$774$		0			0
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	10.0000	+	17.3205i	0.358287	+	0.620572i
$780$		0			0
$781$	−10.0000	+	17.3205i	−0.357828	+	0.619777i
$782$		0			0
$783$	6.00000			0.214423
$784$		0			0
$785$	8.00000			0.285532
$786$		0			0
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	0.250832	+	0.968031i	$0.419296\pi$
$787$	−20.0000	+	34.6410i	−0.712923	+	1.23482i	−0.963755	+	0.266788i	$0.914038\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$		0			0
$801$	1.00000	−	1.73205i	0.0353333	−	0.0611990i
$802$		0			0
$803$	−4.00000	−	6.92820i	−0.141157	−	0.244491i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.00000	+	15.5885i	0.316815	+	0.548740i
$808$		0			0
$809$	13.0000	−	22.5167i	0.457056	−	0.791644i	−0.541748	−	0.840541i	$-0.682237\pi$
$809$	13.0000	−	22.5167i	0.457056	−	0.791644i	0.998804	+	0.0488972i	$0.0155707\pi$
$810$		0			0
$811$	54.0000			1.89620			0.948098	−	0.317978i	$-0.103004\pi$
$811$	54.0000			1.89620			0.948098	+	0.317978i	$0.103004\pi$
$812$		0			0
$813$	6.00000			0.210429
$814$		0			0
$815$	6.00000	−	10.3923i	0.210171	−	0.364027i
$816$		0			0
$817$	12.0000	+	20.7846i	0.419827	+	0.727161i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.859396	+	0.511311i	$0.170840\pi$
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.0131101	+	0.999914i	$0.495827\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$		0			0
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.00453881	−	0.999990i	$-0.498555\pi$
$829$	25.0000	−	43.3013i	0.868286	−	1.50392i	0.863747	−	0.503926i	$-0.168111\pi$
$830$		0			0
$831$	11.0000	+	19.0526i	0.381586	+	0.660926i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$		0			0
$837$	−1.00000	+	1.73205i	−0.0345651	+	0.0598684i
$838$		0			0
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	13.0000	−	22.5167i	0.447744	−	0.775515i
$844$		0			0
$845$	1.50000	+	2.59808i	0.0516016	+	0.0893765i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$		0			0
$851$	−20.0000	+	34.6410i	−0.685591	+	1.18748i
$852$		0			0
$853$	−28.0000			−0.958702			−0.479351	−	0.877623i	$-0.659128\pi$
$853$	−28.0000			−0.958702			−0.479351	+	0.877623i	$0.659128\pi$
$854$		0			0
$855$	2.00000			0.0683986
$856$		0			0
$857$	−17.0000	+	29.4449i	−0.580709	+	1.00582i	0.414687	+	0.909964i	$0.363891\pi$
$857$	−17.0000	+	29.4449i	−0.580709	+	1.00582i	−0.995395	+	0.0958531i	$0.969442\pi$
$858$		0			0
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	−0.995475	−	0.0950262i	$-0.969707\pi$
$859$	−17.0000	−	29.4449i	−0.580033	−	1.00465i	0.415442	−	0.909620i	$-0.363627\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	0.745649	−	0.666339i	$-0.232140\pi$
$863$	−6.00000	−	10.3923i	−0.204242	−	0.353758i	−0.949891	+	0.312581i	$0.898806\pi$
$864$		0			0
$865$	−1.00000	+	1.73205i	−0.0340010	+	0.0588915i
$866$		0			0
$867$	−13.0000			−0.441503
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−24.0000	+	41.5692i	−0.813209	+	1.40852i
$872$		0			0
$873$	−4.00000	−	6.92820i	−0.135379	−	0.234484i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	0.989788	−	0.142548i	$-0.0455296\pi$
$877$	11.0000	+	19.0526i	0.371444	+	0.643359i	−0.618344	+	0.785907i	$0.712196\pi$
$878$		0			0
$879$	−15.0000	+	25.9808i	−0.505937	+	0.876309i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$	4.00000	−	6.92820i	0.134459	−	0.232889i
$886$		0			0
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	0.791026	−	0.611783i	$-0.209547\pi$
$887$	−4.00000	−	6.92820i	−0.134307	−	0.232626i	−0.925332	+	0.379157i	$0.876214\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	8.00000	−	13.8564i	0.267710	−	0.463687i
$894$		0			0
$895$	−22.0000			−0.735379
$896$		0			0
$897$	−16.0000			−0.534224
$898$		0			0
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.0000	+	19.0526i	0.365652	+	0.633328i
$906$		0			0
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	12.0000	−	20.7846i	0.397142	−	0.687870i
$914$		0			0
$915$	1.00000	+	1.73205i	0.0330590	+	0.0572598i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$		0			0
$921$	16.0000	−	27.7128i	0.527218	−	0.913168i
$922$		0			0
$923$	40.0000			1.31662
$924$		0			0
$925$	10.0000			0.328798
$926$		0			0
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$		0			0
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	0.728046	−	0.685529i	$-0.240429\pi$
$929$	−7.00000	−	12.1244i	−0.229663	−	0.397787i	−0.957708	+	0.287742i	$0.907096\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	4.00000	+	6.92820i	0.130954	+	0.226819i
$934$		0			0
$935$	2.00000	−	3.46410i	0.0654070	−	0.113288i
$936$		0			0
$937$	12.0000			0.392023			0.196011	−	0.980602i	$-0.437201\pi$
$937$	12.0000			0.392023			0.196011	+	0.980602i	$0.437201\pi$
$938$		0			0
$939$	8.00000			0.261070
$940$		0			0
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	−0.510934	−	0.859620i	$-0.670700\pi$
$941$	15.0000	−	25.9808i	0.488986	−	0.846949i	0.999920	+	0.0126715i	$0.00403357\pi$
$942$		0			0
$943$	−20.0000	−	34.6410i	−0.651290	−	1.12807i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	0.992442	−	0.122714i	$-0.0391598\pi$
$947$	12.0000	+	20.7846i	0.389948	+	0.675409i	−0.602494	+	0.798123i	$0.705826\pi$
$948$		0			0
$949$	−8.00000	+	13.8564i	−0.259691	+	0.449798i
$950$		0			0
$951$	32.0000			1.03767
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	−11.0000	+	19.0526i	−0.355952	+	0.616526i
$956$		0			0
$957$	6.00000	+	10.3923i	0.193952	+	0.335936i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−2.00000	+	3.46410i	−0.0644491	+	0.111629i
$964$		0			0
$965$	14.0000			0.450676
$966$		0			0
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$		0			0
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.00000	+	3.46410i	0.0640513	+	0.110940i
$976$		0			0
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$		0			0
$979$	4.00000			0.127841
$980$		0			0
$981$	−14.0000			−0.446986
$982$		0			0
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	−0.489608	−	0.871943i	$-0.662860\pi$
$983$	16.0000	−	27.7128i	0.510321	−	0.883901i	0.999928	−	0.0119587i	$-0.00380665\pi$
$984$		0			0
$985$	6.00000	+	10.3923i	0.191176	+	0.331126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.0000	−	41.5692i	−0.763156	−	1.32182i
$990$		0			0
$991$	28.0000	−	48.4974i	0.889449	−	1.54057i	0.0489218	−	0.998803i	$-0.484422\pi$
$991$	28.0000	−	48.4974i	0.889449	−	1.54057i	0.840528	−	0.541769i	$-0.182245\pi$
$992$		0			0
$993$	−20.0000			−0.634681
$994$		0			0
$995$	−10.0000			−0.317021
$996$		0			0
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$		0			0
$999$	−5.00000	−	8.66025i	−0.158193	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.g.361.1		2
7.2	even	3	inner	2940.2.q.g.961.1		2
7.3	odd	6		420.2.a.b.1.1	✓	1
7.4	even	3		2940.2.a.g.1.1		1
7.5	odd	6		2940.2.q.k.961.1		2
7.6	odd	2		2940.2.q.k.361.1		2
21.11	odd	6		8820.2.a.x.1.1		1
21.17	even	6		1260.2.a.e.1.1		1
28.3	even	6		1680.2.a.r.1.1		1
35.3	even	12		2100.2.k.c.1849.1		2
35.17	even	12		2100.2.k.c.1849.2		2
35.24	odd	6		2100.2.a.k.1.1		1
56.3	even	6		6720.2.a.d.1.1		1
56.45	odd	6		6720.2.a.bt.1.1		1
84.59	odd	6		5040.2.a.c.1.1		1
105.17	odd	12		6300.2.k.m.6049.2		2
105.38	odd	12		6300.2.k.m.6049.1		2
105.59	even	6		6300.2.a.l.1.1		1
140.59	even	6		8400.2.a.bc.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.a.b.1.1	✓	1	7.3	odd	6
1260.2.a.e.1.1		1	21.17	even	6
1680.2.a.r.1.1		1	28.3	even	6
2100.2.a.k.1.1		1	35.24	odd	6
2100.2.k.c.1849.1		2	35.3	even	12
2100.2.k.c.1849.2		2	35.17	even	12
2940.2.a.g.1.1		1	7.4	even	3
2940.2.q.g.361.1		2	1.1	even	1	trivial
2940.2.q.g.961.1		2	7.2	even	3	inner
2940.2.q.k.361.1		2	7.6	odd	2
2940.2.q.k.961.1		2	7.5	odd	6
5040.2.a.c.1.1		1	84.59	odd	6
6300.2.a.l.1.1		1	105.59	even	6
6300.2.k.m.6049.1		2	105.38	odd	12
6300.2.k.m.6049.2		2	105.17	odd	12
6720.2.a.d.1.1		1	56.3	even	6
6720.2.a.bt.1.1		1	56.45	odd	6
8400.2.a.bc.1.1		1	140.59	even	6
8820.2.a.x.1.1		1	21.11	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:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} -4.00000 q^{13} -1.00000 q^{15} +(1.00000 - 1.73205i) q^{17} +(1.00000 + 1.73205i) q^{19} +(-2.00000 - 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +6.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(1.00000 + 1.73205i) q^{33} +(-5.00000 - 8.66025i) q^{37} +(2.00000 - 3.46410i) q^{39} +10.0000 q^{41} +12.0000 q^{43} +(0.500000 - 0.866025i) q^{45} +(-4.00000 - 6.92820i) q^{47} +(1.00000 + 1.73205i) q^{51} +2.00000 q^{55} -2.00000 q^{57} +(-4.00000 + 6.92820i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(6.00000 - 10.3923i) q^{67} +4.00000 q^{69} -10.0000 q^{71} +(2.00000 - 3.46410i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +2.00000 q^{85} +(-3.00000 + 5.19615i) q^{87} +(1.00000 + 1.73205i) q^{89} +(-1.00000 - 1.73205i) q^{93} +(-1.00000 + 1.73205i) q^{95} +8.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + q^{5} - q^{9}+O(q^{10}) \) 2 * q - q^3 + q^5 - q^9	\( 2 q - q^{3} + q^{5} - q^{9} + 2 q^{11} - 8 q^{13} - 2 q^{15} + 2 q^{17} + 2 q^{19} - 4 q^{23} - q^{25} + 2 q^{27} + 12 q^{29} - 2 q^{31} + 2 q^{33} - 10 q^{37} + 4 q^{39} + 20 q^{41} + 24 q^{43} + q^{45} - 8 q^{47} + 2 q^{51} + 4 q^{55} - 4 q^{57} - 8 q^{59} - 2 q^{61} - 4 q^{65} + 12 q^{67} + 8 q^{69} - 20 q^{71} + 4 q^{73} - q^{75} - q^{81} + 24 q^{83} + 4 q^{85} - 6 q^{87} + 2 q^{89} - 2 q^{93} - 2 q^{95} + 16 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - q^3 + q^5 - q^9 + 2 * q^11 - 8 * q^13 - 2 * q^15 + 2 * q^17 + 2 * q^19 - 4 * q^23 - q^25 + 2 * q^27 + 12 * q^29 - 2 * q^31 + 2 * q^33 - 10 * q^37 + 4 * q^39 + 20 * q^41 + 24 * q^43 + q^45 - 8 * q^47 + 2 * q^51 + 4 * q^55 - 4 * q^57 - 8 * q^59 - 2 * q^61 - 4 * q^65 + 12 * q^67 + 8 * q^69 - 20 * q^71 + 4 * q^73 - q^75 - q^81 + 24 * q^83 + 4 * q^85 - 6 * q^87 + 2 * q^89 - 2 * q^93 - 2 * q^95 + 16 * q^97 - 4 * q^99

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