LMFDB - Embedded newform 2940.2.q.l.961.1

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:	$1$
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			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2940.961
Dual form			2940.2.q.l.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -4.00000 q^{13} +1.00000 q^{15} +(1.00000 + 1.73205i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(1.00000 - 1.73205i) q^{33} +(3.00000 - 5.19615i) q^{37} +(-2.00000 - 3.46410i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-1.00000 + 1.73205i) q^{51} +(-4.00000 - 6.92820i) q^{53} -2.00000 q^{55} -2.00000 q^{57} +(-5.00000 + 8.66025i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(6.00000 + 10.3923i) q^{67} -4.00000 q^{69} -14.0000 q^{71} +(2.00000 + 3.46410i) q^{73} +(0.500000 - 0.866025i) q^{75} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +2.00000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(-7.00000 + 12.1244i) q^{89} +(3.00000 - 5.19615i) q^{93} +(1.00000 + 1.73205i) q^{95} -8.00000 q^{97} +2.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 4 q^{29} - 6 q^{31} + 2 q^{33} + 6 q^{37} - 4 q^{39} - 12 q^{41} - 8 q^{43} + q^{45} - 2 q^{51} - 8 q^{53} - 4 q^{55} - 4 q^{57} - 10 q^{61} - 4 q^{65} + 12 q^{67} - 8 q^{69} - 28 q^{71} + 4 q^{73} + q^{75} + 8 q^{79} - q^{81} - 24 q^{83} + 4 q^{85} - 2 q^{87} - 14 q^{89} + 6 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 - 4 * q^29 - 6 * q^31 + 2 * q^33 + 6 * q^37 - 4 * q^39 - 12 * q^41 - 8 * q^43 + q^45 - 2 * q^51 - 8 * q^53 - 4 * q^55 - 4 * q^57 - 10 * q^61 - 4 * q^65 + 12 * q^67 - 8 * q^69 - 28 * q^71 + 4 * q^73 + q^75 + 8 * q^79 - q^81 - 24 * q^83 + 4 * q^85 - 2 * q^87 - 14 * q^89 + 6 * 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 $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

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

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	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		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	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$		0			0
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$		0			0
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$		0			0
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	−0.998313	−	0.0580651i	$-0.981507\pi$
$53$	−4.00000	−	6.92820i	−0.549442	−	0.951662i	0.448871	−	0.893597i	$-0.351826\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−2.00000			−0.264906
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		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	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$	−14.0000			−1.66149			−0.830747	−	0.556650i	$-0.812086\pi$
$71$	−14.0000			−1.66149			−0.830747	+	0.556650i	$0.812086\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$		0			0
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.00000	−	5.19615i	0.311086	−	0.538816i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$		0			0
$99$	2.00000			0.201008
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	6.00000			0.569495
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		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
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$		0			0
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	−0.973910	−	0.226935i	$-0.927130\pi$
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	0.290424	−	0.956898i	$-0.406204\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$		0			0
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.0751583	−	0.997172i	$-0.476054\pi$
$149$	11.0000	−	19.0526i	0.901155	−	1.56085i	0.825997	−	0.563675i	$-0.190613\pi$
$150$		0			0
$151$	10.0000	+	17.3205i	0.813788	+	1.40952i	0.910195	+	0.414181i	$0.135932\pi$
$151$	10.0000	+	17.3205i	0.813788	+	1.40952i	−0.0964061	+	0.995342i	$0.530735\pi$
$152$		0			0
$153$	−2.00000			−0.161690
$154$		0			0
$155$	−6.00000			−0.481932
$156$		0			0
$157$	12.0000	+	20.7846i	0.957704	+	1.65879i	0.728055	+	0.685519i	$0.240425\pi$
$157$	12.0000	+	20.7846i	0.957704	+	1.65879i	0.229650	+	0.973273i	$0.426242\pi$
$158$		0			0
$159$	4.00000	−	6.92820i	0.317221	−	0.549442i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$		0			0
$165$	−1.00000	−	1.73205i	−0.0778499	−	0.134840i
$166$		0			0
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−1.00000	−	1.73205i	−0.0764719	−	0.132453i
$172$		0			0
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	−0.289412	−	0.957205i	$-0.593460\pi$
$173$	9.00000	−	15.5885i	0.684257	−	1.18517i	0.973670	−	0.227964i	$-0.0732068\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	−10.0000			−0.739221
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	0.493469	+	0.869763i	$0.335728\pi$
$191$	−7.00000	+	12.1244i	−0.506502	+	0.877288i	−0.999972	+	0.00752447i	$0.997605\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$	−4.00000			−0.286446
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	0.985873	+	0.167497i	$0.0535685\pi$
$199$	9.00000	+	15.5885i	0.637993	+	1.10504i	−0.347879	+	0.937539i	$0.613098\pi$
$200$		0			0
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$	−2.00000	−	3.46410i	−0.139010	−	0.240772i
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$		0			0
$213$	−7.00000	−	12.1244i	−0.479632	−	0.830747i
$214$		0			0
$215$	−2.00000	+	3.46410i	−0.136399	+	0.236250i
$216$		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
$223$	−20.0000			−1.33930			−0.669650	−	0.742677i	$-0.733556\pi$
$223$	−20.0000			−1.33930			−0.669650	+	0.742677i	$0.733556\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	14.0000	+	24.2487i	0.929213	+	1.60944i	0.784642	+	0.619949i	$0.212847\pi$
$227$	14.0000	+	24.2487i	0.929213	+	1.60944i	0.144571	+	0.989494i	$0.453820\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	−0.793047	−	0.609160i	$-0.791507\pi$
$233$	2.00000	−	3.46410i	0.131024	−	0.226941i	0.924072	+	0.382219i	$0.124840\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	8.00000			0.519656
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	0.832019	−	0.554747i	$-0.187185\pi$
$241$	−1.00000	−	1.73205i	−0.0644157	−	0.111571i	−0.896435	+	0.443176i	$0.853852\pi$
$242$		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
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$		0			0
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$		0			0
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$		0			0
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$		0			0
$265$	−8.00000			−0.491436
$266$		0			0
$267$	−14.0000			−0.856786
$268$		0			0
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.807535	−	0.589819i	$-0.799199\pi$
$269$	−15.0000	−	25.9808i	−0.914566	−	1.58408i	−0.107031	−	0.994256i	$-0.534134\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$		0			0
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	0.675810	−	0.737075i	$-0.263794\pi$
$277$	−5.00000	−	8.66025i	−0.300421	−	0.520344i	−0.976231	+	0.216731i	$0.930460\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$		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
$295$		0			0
$296$		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
$305$	5.00000	+	8.66025i	0.286299	+	0.495885i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$		0			0
$313$	−12.0000	+	20.7846i	−0.678280	+	1.17482i	0.297218	+	0.954810i	$0.403941\pi$
$313$	−12.0000	+	20.7846i	−0.678280	+	1.17482i	−0.975499	+	0.220006i	$0.929392\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.00000	−	6.92820i	0.224662	−	0.389127i	−0.731556	−	0.681782i	$-0.761205\pi$
$317$	4.00000	−	6.92820i	0.224662	−	0.389127i	0.956218	+	0.292655i	$0.0945387\pi$
$318$		0			0
$319$	2.00000	+	3.46410i	0.111979	+	0.193952i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$	−4.00000			−0.222566
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$		0			0
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−18.0000	+	31.1769i	−0.989369	+	1.71364i	−0.368744	+	0.929531i	$0.620212\pi$
$331$	−18.0000	+	31.1769i	−0.989369	+	1.71364i	−0.620625	+	0.784107i	$0.713121\pi$
$332$		0			0
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$		0			0
$335$	12.0000			0.655630
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$		0			0
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$		0			0
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.00000	+	3.46410i	−0.107676	+	0.186501i
$346$		0			0
$347$	−4.00000	−	6.92820i	−0.214731	−	0.371925i	0.738458	−	0.674299i	$-0.235554\pi$
$347$	−4.00000	−	6.92820i	−0.214731	−	0.371925i	−0.953189	+	0.302374i	$0.902221\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	4.00000			0.213504
$352$		0			0
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	0.617388	−	0.786659i	$-0.288191\pi$
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	−0.989960	+	0.141344i	$0.954858\pi$
$354$		0			0
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	−0.524588	−	0.851356i	$-0.675781\pi$
$359$	9.00000	−	15.5885i	0.475002	−	0.822727i	0.999590	+	0.0286287i	$0.00911406\pi$
$360$		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
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$		0			0
$369$	3.00000	−	5.19615i	0.156174	−	0.270501i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.0291379	−	0.999575i	$-0.490724\pi$
$373$	17.0000	−	29.4449i	0.880227	−	1.52460i	0.851089	−	0.525022i	$-0.175943\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	8.00000			0.412021
$378$		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
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$		0			0
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	−0.585973	−	0.810331i	$-0.699287\pi$
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	0.994753	+	0.102302i	$0.0326207\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$		0			0
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	0.987103	−	0.160085i	$-0.0511768\pi$
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	−0.632189	+	0.774814i	$0.717843\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		0			0
$393$	−4.00000			−0.201773
$394$		0			0
$395$	−4.00000	−	6.92820i	−0.201262	−	0.348596i
$396$		0			0
$397$	6.00000	−	10.3923i	0.301131	−	0.521575i	−0.675261	−	0.737579i	$-0.735969\pi$
$397$	6.00000	−	10.3923i	0.301131	−	0.521575i	0.976392	+	0.216004i	$0.0693024\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	0.0332161	+	0.999448i	$0.489425\pi$
$401$	−17.0000	+	29.4449i	−0.848939	+	1.47041i	−0.882156	+	0.470958i	$0.843908\pi$
$402$		0			0
$403$	12.0000	+	20.7846i	0.597763	+	1.03536i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−12.0000			−0.594818
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$	8.00000	−	13.8564i	0.394611	−	0.683486i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	−7.00000	−	12.1244i	−0.342791	−	0.593732i
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$		0			0
$423$		0			0
$424$		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
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$		0			0
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$		0			0
$435$	−2.00000			−0.0958927
$436$		0			0
$437$	−4.00000	−	6.92820i	−0.191346	−	0.331421i
$438$		0			0
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$		0			0
$445$	7.00000	+	12.1244i	0.331832	+	0.574750i
$446$		0			0
$447$	22.0000			1.04056
$448$		0			0
$449$	−22.0000			−1.03824			−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000			−1.03824			−0.519122	+	0.854700i	$0.673741\pi$
$450$		0			0
$451$	6.00000	+	10.3923i	0.282529	+	0.489355i
$452$		0			0
$453$	−10.0000	+	17.3205i	−0.469841	+	0.813788i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	0.991551	−	0.129718i	$-0.0414071\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$	−38.0000			−1.76984			−0.884918	−	0.465746i	$-0.845786\pi$
$461$	−38.0000			−1.76984			−0.884918	+	0.465746i	$0.845786\pi$
$462$		0			0
$463$	−24.0000			−1.11537			−0.557687	−	0.830051i	$-0.688311\pi$
$463$	−24.0000			−1.11537			−0.557687	+	0.830051i	$0.688311\pi$
$464$		0			0
$465$	−3.00000	−	5.19615i	−0.139122	−	0.240966i
$466$		0			0
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	−0.0627555	−	0.998029i	$-0.519989\pi$
$467$	18.0000	−	31.1769i	0.832941	−	1.44270i	0.895696	−	0.444667i	$-0.146678\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−12.0000	+	20.7846i	−0.552931	+	0.957704i
$472$		0			0
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$		0			0
$475$	2.00000			0.0917663
$476$		0			0
$477$	8.00000			0.366295
$478$		0			0
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	0.942821	−	0.333300i	$-0.108162\pi$
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	−0.760056	+	0.649857i	$0.774829\pi$
$480$		0			0
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.00000	+	6.92820i	−0.181631	+	0.314594i
$486$		0			0
$487$	16.0000	+	27.7128i	0.725029	+	1.25579i	0.958962	+	0.283535i	$0.0915071\pi$
$487$	16.0000	+	27.7128i	0.725029	+	1.25579i	−0.233933	+	0.972253i	$0.575160\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	18.0000			0.812329			0.406164	−	0.913800i	$-0.366866\pi$
$491$	18.0000			0.812329			0.406164	+	0.913800i	$0.366866\pi$
$492$		0			0
$493$	−2.00000	−	3.46410i	−0.0900755	−	0.156015i
$494$		0			0
$495$	1.00000	−	1.73205i	0.0449467	−	0.0778499i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	0.461860	+	0.886953i	$0.347182\pi$
$499$	−12.0000	+	20.7846i	−0.537194	+	0.930447i	−0.999054	+	0.0434940i	$0.986151\pi$
$500$		0			0
$501$	4.00000	+	6.92820i	0.178707	+	0.309529i
$502$		0			0
$503$	32.0000			1.42681			0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000			1.42681			0.713405	+	0.700752i	$0.247152\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$		0			0
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		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
$517$		0			0
$518$		0			0
$519$	18.0000			0.790112
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		0			0
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	−0.940129	−	0.340818i	$-0.889296\pi$
$523$	−4.00000	+	6.92820i	−0.174908	+	0.302949i	0.765222	+	0.643767i	$0.222629\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$		0			0
$537$	5.00000	−	8.66025i	0.215766	−	0.373718i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	0.0911008	+	0.995842i	$0.470961\pi$
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	−0.907975	+	0.419025i	$0.862372\pi$
$542$		0			0
$543$	−9.00000	−	15.5885i	−0.386227	−	0.668965i
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$		0			0
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$	2.00000	−	3.46410i	0.0852029	−	0.147576i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$		0			0
$557$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$557$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$	4.00000			0.168880
$562$		0			0
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$		0			0
$565$	6.00000	−	10.3923i	0.252422	−	0.437208i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	0.453619	+	0.891196i	$0.350133\pi$
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	−0.998608	+	0.0527519i	$0.983201\pi$
$570$		0			0
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$	−14.0000			−0.584858
$574$		0			0
$575$	4.00000			0.166812
$576$		0			0
$577$	8.00000	+	13.8564i	0.333044	+	0.576850i	0.983107	−	0.183031i	$-0.0585908\pi$
$577$	8.00000	+	13.8564i	0.333044	+	0.576850i	−0.650063	+	0.759880i	$0.725257\pi$
$578$		0			0
$579$	1.00000	−	1.73205i	0.0415586	−	0.0719816i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−8.00000	+	13.8564i	−0.331326	+	0.573874i
$584$		0			0
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$		0			0
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.00000	+	15.5885i	−0.368345	+	0.637993i
$598$		0			0
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	−12.0000			−0.488678
$604$		0			0
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$		0			0
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	−0.822578	−	0.568652i	$-0.807465\pi$
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	0.903756	+	0.428048i	$0.140799\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$	20.0000			0.805170			0.402585	−	0.915383i	$-0.368112\pi$
$617$	20.0000			0.805170			0.402585	+	0.915383i	$0.368112\pi$
$618$		0			0
$619$	19.0000	+	32.9090i	0.763674	+	1.32272i	0.940945	+	0.338561i	$0.109940\pi$
$619$	19.0000	+	32.9090i	0.763674	+	1.32272i	−0.177270	+	0.984162i	$0.556727\pi$
$620$		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
$629$	12.0000			0.478471
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$		0			0
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	7.00000	−	12.1244i	0.276916	−	0.479632i
$640$		0			0
$641$	−23.0000	−	39.8372i	−0.908445	−	1.57347i	−0.816224	−	0.577735i	$-0.803937\pi$
$641$	−23.0000	−	39.8372i	−0.908445	−	1.57347i	−0.0922210	−	0.995739i	$-0.529397\pi$
$642$		0			0
$643$	16.0000			0.630978			0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000			0.630978			0.315489	+	0.948929i	$0.397831\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$		0			0
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−10.0000	+	17.3205i	−0.391330	+	0.677804i	−0.992625	−	0.121223i	$-0.961318\pi$
$653$	−10.0000	+	17.3205i	−0.391330	+	0.677804i	0.601295	+	0.799027i	$0.294652\pi$
$654$		0			0
$655$	2.00000	+	3.46410i	0.0781465	+	0.135354i
$656$		0			0
$657$	−4.00000			−0.156055
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$		0			0
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	−0.980294	−	0.197542i	$-0.936704\pi$
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	0.319071	−	0.947731i	$-0.396629\pi$
$662$		0			0
$663$	4.00000	−	6.92820i	0.155347	−	0.269069i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$		0			0
$669$	−10.0000	−	17.3205i	−0.386622	−	0.669650i
$670$		0			0
$671$	20.0000			0.772091
$672$		0			0
$673$	6.00000			0.231283			0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000			0.231283			0.115642	+	0.993291i	$0.463108\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$		0			0
$677$	17.0000	−	29.4449i	0.653363	−	1.13166i	−0.328938	−	0.944351i	$-0.606691\pi$
$677$	17.0000	−	29.4449i	0.653363	−	1.13166i	0.982301	−	0.187307i	$-0.0599758\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−14.0000	+	24.2487i	−0.536481	+	0.929213i
$682$		0			0
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$		0			0
$685$	−16.0000			−0.611329
$686$		0			0
$687$	14.0000			0.534133
$688$		0			0
$689$	16.0000	+	27.7128i	0.609551	+	1.05577i
$690$		0			0
$691$	−3.00000	+	5.19615i	−0.114125	+	0.197671i	−0.917430	−	0.397898i	$-0.869740\pi$
$691$	−3.00000	+	5.19615i	−0.114125	+	0.197671i	0.803304	+	0.595569i	$0.203073\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.00000	+	12.1244i	−0.265525	+	0.459903i
$696$		0			0
$697$	−6.00000	−	10.3923i	−0.227266	−	0.393637i
$698$		0			0
$699$	4.00000			0.151294
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$		0			0
$703$	6.00000	+	10.3923i	0.226294	+	0.391953i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$	8.00000			0.299183
$716$		0			0
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$		0			0
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	−0.617079	−	0.786901i	$-0.711684\pi$
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	0.990016	+	0.140955i	$0.0450174\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.00000	−	1.73205i	0.0371904	−	0.0644157i
$724$		0			0
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.00000	−	6.92820i	−0.147945	−	0.256249i
$732$		0			0
$733$	14.0000	−	24.2487i	0.517102	−	0.895647i	−0.482701	−	0.875785i	$-0.660344\pi$
$733$	14.0000	−	24.2487i	0.517102	−	0.895647i	0.999803	−	0.0198613i	$-0.00632248\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	0.954410	+	0.298498i	$0.0964856\pi$
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	−0.218698	+	0.975793i	$0.570181\pi$
$740$		0			0
$741$	8.00000			0.293887
$742$		0			0
$743$	24.0000			0.880475			0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000			0.880475			0.440237	+	0.897881i	$0.354894\pi$
$744$		0			0
$745$	−11.0000	−	19.0526i	−0.403009	−	0.698032i
$746$		0			0
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	0.227153	+	0.973859i	$0.427058\pi$
$751$	−20.0000	+	34.6410i	−0.729810	+	1.26407i	−0.956963	+	0.290209i	$0.906275\pi$
$752$		0			0
$753$	−12.0000	−	20.7846i	−0.437304	−	0.757433i
$754$		0			0
$755$	20.0000			0.727875
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$		0			0
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	−19.0000	+	32.9090i	−0.688749	+	1.19295i	0.283493	+	0.958974i	$0.408507\pi$
$761$	−19.0000	+	32.9090i	−0.688749	+	1.19295i	−0.972243	+	0.233975i	$0.924827\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	26.0000			0.937584			0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000			0.937584			0.468792	+	0.883309i	$0.344689\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$		0			0
$773$	−19.0000	−	32.9090i	−0.683383	−	1.18365i	−0.973942	−	0.226796i	$-0.927175\pi$
$773$	−19.0000	−	32.9090i	−0.683383	−	1.18365i	0.290560	−	0.956857i	$-0.406159\pi$
$774$		0			0
$775$	−3.00000	+	5.19615i	−0.107763	+	0.186651i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	14.0000	+	24.2487i	0.500959	+	0.867687i
$782$		0			0
$783$	2.00000			0.0714742
$784$		0			0
$785$	24.0000			0.856597
$786$		0			0
$787$	4.00000	+	6.92820i	0.142585	+	0.246964i	0.928469	−	0.371409i	$-0.121125\pi$
$787$	4.00000	+	6.92820i	0.142585	+	0.246964i	−0.785885	+	0.618373i	$0.787792\pi$
$788$		0			0
$789$	4.00000	−	6.92820i	0.142404	−	0.246651i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	20.0000	−	34.6410i	0.710221	−	1.23014i
$794$		0			0
$795$	−4.00000	−	6.92820i	−0.141865	−	0.245718i
$796$		0			0
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−7.00000	−	12.1244i	−0.247333	−	0.428393i
$802$		0			0
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.0000	−	25.9808i	0.528025	−	0.914566i
$808$		0			0
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	0.940435	−	0.339975i	$-0.110418\pi$
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	−0.764644	+	0.644453i	$0.777085\pi$
$810$		0			0
$811$	−22.0000			−0.772524			−0.386262	−	0.922389i	$-0.626234\pi$
$811$	−22.0000			−0.772524			−0.386262	+	0.922389i	$0.626234\pi$
$812$		0			0
$813$	−2.00000			−0.0701431
$814$		0			0
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$		0			0
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	0.577474	−	0.816409i	$-0.304038\pi$
$823$	−12.0000	−	20.7846i	−0.418294	−	0.724506i	−0.995768	+	0.0919029i	$0.970705\pi$
$824$		0			0
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−44.0000			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$827$	−44.0000			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$828$		0			0
$829$	−3.00000	−	5.19615i	−0.104194	−	0.180470i	0.809214	−	0.587513i	$-0.199893\pi$
$829$	−3.00000	−	5.19615i	−0.104194	−	0.180470i	−0.913409	+	0.407044i	$0.866560\pi$
$830$		0			0
$831$	5.00000	−	8.66025i	0.173448	−	0.300421i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	4.00000	−	6.92820i	0.138426	−	0.239760i
$836$		0			0
$837$	3.00000	+	5.19615i	0.103695	+	0.179605i
$838$		0			0
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$		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
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		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	−0.995395	−	0.0958531i	$-0.969442\pi$
$857$	−17.0000	−	29.4449i	−0.580709	−	1.00582i	0.414687	−	0.909964i	$-0.363891\pi$
$858$		0			0
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	−0.960381	−	0.278691i	$-0.910099\pi$
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	0.721544	+	0.692369i	$0.243433\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−22.0000	+	38.1051i	−0.748889	+	1.29711i	0.199467	+	0.979905i	$0.436079\pi$
$863$	−22.0000	+	38.1051i	−0.748889	+	1.29711i	−0.948356	+	0.317209i	$0.897254\pi$
$864$		0			0
$865$	−9.00000	−	15.5885i	−0.306009	−	0.530023i
$866$		0			0
$867$	13.0000			0.441503
$868$		0			0
$869$	−16.0000			−0.542763
$870$		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	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$		0			0
$879$	15.0000	+	25.9808i	0.505937	+	0.876309i
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−10.0000			−0.334263
$896$		0			0
$897$	16.0000			0.534224
$898$		0			0
$899$	6.00000	+	10.3923i	0.200111	+	0.346603i
$900$		0			0
$901$	8.00000	−	13.8564i	0.266519	−	0.461624i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.00000	+	15.5885i	−0.299170	+	0.518178i
$906$		0			0
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	0.830909	−	0.556408i	$-0.187821\pi$
$907$	−2.00000	−	3.46410i	−0.0664089	−	0.115024i	−0.897318	+	0.441384i	$0.854488\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	−58.0000			−1.92163			−0.960813	−	0.277198i	$-0.910594\pi$
$911$	−58.0000			−1.92163			−0.960813	+	0.277198i	$0.910594\pi$
$912$		0			0
$913$	12.0000	+	20.7846i	0.397142	+	0.687870i
$914$		0			0
$915$	−5.00000	+	8.66025i	−0.165295	+	0.286299i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	−0.792480	−	0.609898i	$-0.791210\pi$
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	0.924427	+	0.381358i	$0.124544\pi$
$920$		0			0
$921$	8.00000	+	13.8564i	0.263609	+	0.456584i
$922$		0			0
$923$	56.0000			1.84326
$924$		0			0
$925$	−6.00000			−0.197279
$926$		0			0
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		0			0
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	−0.439932	−	0.898031i	$-0.644997\pi$
$929$	17.0000	−	29.4449i	0.557752	−	0.966055i	0.997684	−	0.0680235i	$-0.0216693\pi$
$930$		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
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$		0			0
$939$	−24.0000			−0.783210
$940$		0			0
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	0.999920	−	0.0126715i	$-0.00403357\pi$
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$942$		0			0
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	−0.479801	−	0.877377i	$-0.659291\pi$
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	0.999732	−	0.0231683i	$-0.00737536\pi$
$948$		0			0
$949$	−8.00000	−	13.8564i	−0.259691	−	0.449798i
$950$		0			0
$951$	8.00000			0.259418
$952$		0			0
$953$	−4.00000			−0.129573			−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000			−0.129573			−0.0647864	+	0.997899i	$0.520637\pi$
$954$		0			0
$955$	7.00000	+	12.1244i	0.226515	+	0.392335i
$956$		0			0
$957$	−2.00000	+	3.46410i	−0.0646508	+	0.111979i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$		0			0
$965$	−2.00000			−0.0643823
$966$		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
$971$	−16.0000	+	27.7128i	−0.513464	+	0.889346i	0.486414	+	0.873729i	$0.338305\pi$
$971$	−16.0000	+	27.7128i	−0.513464	+	0.889346i	−0.999878	+	0.0156178i	$0.995028\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$		0			0
$977$	−18.0000	−	31.1769i	−0.575871	−	0.997438i	−0.995946	−	0.0899487i	$-0.971330\pi$
$977$	−18.0000	−	31.1769i	−0.575871	−	0.997438i	0.420075	−	0.907489i	$-0.362004\pi$
$978$		0			0
$979$	28.0000			0.894884
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	0.991453	−	0.130465i	$-0.0416470\pi$
$983$	12.0000	+	20.7846i	0.382741	+	0.662926i	−0.608712	+	0.793391i	$0.708314\pi$
$984$		0			0
$985$	−6.00000	+	10.3923i	−0.191176	+	0.331126i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$		0			0
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	0.710530	−	0.703667i	$-0.248455\pi$
$991$	−8.00000	−	13.8564i	−0.254128	−	0.440163i	−0.964658	+	0.263504i	$0.915122\pi$
$992$		0			0
$993$	−36.0000			−1.14243
$994$		0			0
$995$	18.0000			0.570638
$996$		0			0
$997$	2.00000	+	3.46410i	0.0633406	+	0.109709i	0.895957	−	0.444141i	$-0.146491\pi$
$997$	2.00000	+	3.46410i	0.0633406	+	0.109709i	−0.832616	+	0.553851i	$0.813158\pi$
$998$		0			0
$999$	−3.00000	+	5.19615i	−0.0949158	+	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.l.961.1		2
7.2	even	3		2940.2.a.c.1.1		1
7.3	odd	6		2940.2.q.b.361.1		2
7.4	even	3	inner	2940.2.q.l.361.1		2
7.5	odd	6		420.2.a.d.1.1	✓	1
7.6	odd	2		2940.2.q.b.961.1		2
21.2	odd	6		8820.2.a.s.1.1		1
21.5	even	6		1260.2.a.a.1.1		1
28.19	even	6		1680.2.a.i.1.1		1
35.12	even	12		2100.2.k.h.1849.1		2
35.19	odd	6		2100.2.a.h.1.1		1
35.33	even	12		2100.2.k.h.1849.2		2
56.5	odd	6		6720.2.a.e.1.1		1
56.19	even	6		6720.2.a.bs.1.1		1
84.47	odd	6		5040.2.a.r.1.1		1
105.47	odd	12		6300.2.k.f.6049.1		2
105.68	odd	12		6300.2.k.f.6049.2		2
105.89	even	6		6300.2.a.u.1.1		1
140.19	even	6		8400.2.a.bq.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.a.d.1.1	✓	1	7.5	odd	6
1260.2.a.a.1.1		1	21.5	even	6
1680.2.a.i.1.1		1	28.19	even	6
2100.2.a.h.1.1		1	35.19	odd	6
2100.2.k.h.1849.1		2	35.12	even	12
2100.2.k.h.1849.2		2	35.33	even	12
2940.2.a.c.1.1		1	7.2	even	3
2940.2.q.b.361.1		2	7.3	odd	6
2940.2.q.b.961.1		2	7.6	odd	2
2940.2.q.l.361.1		2	7.4	even	3	inner
2940.2.q.l.961.1		2	1.1	even	1	trivial
5040.2.a.r.1.1		1	84.47	odd	6
6300.2.a.u.1.1		1	105.89	even	6
6300.2.k.f.6049.1		2	105.47	odd	12
6300.2.k.f.6049.2		2	105.68	odd	12
6720.2.a.e.1.1		1	56.5	odd	6
6720.2.a.bs.1.1		1	56.19	even	6
8400.2.a.bq.1.1		1	140.19	even	6
8820.2.a.s.1.1		1	21.2	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{11} -4.00000 q^{13} +1.00000 q^{15} +(1.00000 + 1.73205i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(-2.00000 + 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -2.00000 q^{29} +(-3.00000 - 5.19615i) q^{31} +(1.00000 - 1.73205i) q^{33} +(3.00000 - 5.19615i) q^{37} +(-2.00000 - 3.46410i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(-1.00000 + 1.73205i) q^{51} +(-4.00000 - 6.92820i) q^{53} -2.00000 q^{55} -2.00000 q^{57} +(-5.00000 + 8.66025i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(6.00000 + 10.3923i) q^{67} -4.00000 q^{69} -14.0000 q^{71} +(2.00000 + 3.46410i) q^{73} +(0.500000 - 0.866025i) q^{75} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +2.00000 q^{85} +(-1.00000 - 1.73205i) q^{87} +(-7.00000 + 12.1244i) q^{89} +(3.00000 - 5.19615i) q^{93} +(1.00000 + 1.73205i) q^{95} -8.00000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + q^{5} - q^{9}+O(q^{10}) \) 2 * q + q^3 + q^5 - q^9	\( 2 q + q^{3} + q^{5} - q^{9} - 2 q^{11} - 8 q^{13} + 2 q^{15} + 2 q^{17} - 2 q^{19} - 4 q^{23} - q^{25} - 2 q^{27} - 4 q^{29} - 6 q^{31} + 2 q^{33} + 6 q^{37} - 4 q^{39} - 12 q^{41} - 8 q^{43} + q^{45} - 2 q^{51} - 8 q^{53} - 4 q^{55} - 4 q^{57} - 10 q^{61} - 4 q^{65} + 12 q^{67} - 8 q^{69} - 28 q^{71} + 4 q^{73} + q^{75} + 8 q^{79} - q^{81} - 24 q^{83} + 4 q^{85} - 2 q^{87} - 14 q^{89} + 6 q^{93} + 2 q^{95} - 16 q^{97} + 4 q^{99}+O(q^{100}) \) 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 - 4 * q^29 - 6 * q^31 + 2 * q^33 + 6 * q^37 - 4 * q^39 - 12 * q^41 - 8 * q^43 + q^45 - 2 * q^51 - 8 * q^53 - 4 * q^55 - 4 * q^57 - 10 * q^61 - 4 * q^65 + 12 * q^67 - 8 * q^69 - 28 * q^71 + 4 * q^73 + q^75 + 8 * q^79 - q^81 - 24 * q^83 + 4 * q^85 - 2 * q^87 - 14 * q^89 + 6 * q^93 + 2 * q^95 - 16 * q^97 + 4 * q^99

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