LMFDB - Embedded newform 2940.2.bb.f.949.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(949,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.949"); 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.bb (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,4,0,0,0,2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2940.949
Dual form			2940.2.bb.f.1549.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{3} +(0.133975 + 2.23205i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} -2.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-1.73205 - 1.00000i) q^{17} +(1.00000 + 1.73205i) q^{19} +(-5.19615 + 3.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -1.00000i q^{27} -6.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(3.46410 - 2.00000i) q^{33} +(3.46410 - 2.00000i) q^{37} +(-1.00000 + 1.73205i) q^{39} -4.00000i q^{43} +(-1.86603 + 1.23205i) q^{45} +(3.46410 - 2.00000i) q^{47} +(1.00000 + 1.73205i) q^{51} +(1.73205 + 1.00000i) q^{53} +(-8.00000 - 4.00000i) q^{55} -2.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(4.46410 - 0.267949i) q^{65} +(-10.3923 - 6.00000i) q^{67} +6.00000 q^{69} -8.00000 q^{71} +(12.1244 + 7.00000i) q^{73} +(4.59808 + 1.96410i) q^{75} +(8.00000 + 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{81} -16.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(5.19615 + 3.00000i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(-5.19615 + 3.00000i) q^{93} +(-3.73205 + 2.46410i) q^{95} -14.0000i q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} + 2 q^{9} - 8 q^{11} + 4 q^{15} + 4 q^{19} - 6 q^{25} - 24 q^{29} + 12 q^{31} - 4 q^{39} - 4 q^{45} + 4 q^{51} - 32 q^{55} - 8 q^{59} - 4 q^{61} + 4 q^{65} + 24 q^{69} - 32 q^{71} + 8 q^{75}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^5 + 2 * q^9 - 8 * q^11 + 4 * q^15 + 4 * q^19 - 6 * q^25 - 24 * q^29 + 12 * q^31 - 4 * q^39 - 4 * q^45 + 4 * q^51 - 32 * q^55 - 8 * q^59 - 4 * q^61 + 4 * q^65 + 24 * q^69 - 32 * q^71 + 8 * q^75 + 32 * q^79 - 2 * q^81 + 8 * q^85 - 32 * q^89 - 8 * q^95 - 16 * q^99

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
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$		0			0
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$		−	2.00000i		−	0.554700i	−0.960769	−	0.277350i	$-0.910544\pi$
$13$		−	2.00000i		−	0.554700i	0.960769	−	0.277350i	$-0.0894562\pi$
$14$		0			0
$15$	1.00000	−	2.00000i	0.258199	−	0.516398i
$16$		0			0
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		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
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$		0			0
$33$	3.46410	−	2.00000i	0.603023	−	0.348155i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	−0.187453	−	0.982274i	$-0.560023\pi$
$37$	3.46410	−	2.00000i	0.569495	−	0.328798i	0.756948	+	0.653476i	$0.226690\pi$
$38$		0			0
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		−	4.00000i		−	0.609994i	−0.952353	−	0.304997i	$-0.901344\pi$
$43$		−	4.00000i		−	0.609994i	0.952353	−	0.304997i	$-0.0986555\pi$
$44$		0			0
$45$	−1.86603	+	1.23205i	−0.278171	+	0.183663i
$46$		0			0
$47$	3.46410	−	2.00000i	0.505291	−	0.291730i	−0.225605	−	0.974219i	$-0.572436\pi$
$47$	3.46410	−	2.00000i	0.505291	−	0.291730i	0.730896	+	0.682489i	$0.239102\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$		0			0
$53$	1.73205	+	1.00000i	0.237915	+	0.137361i	0.614218	−	0.789136i	$-0.289471\pi$
$53$	1.73205	+	1.00000i	0.237915	+	0.137361i	−0.376303	+	0.926497i	$0.622805\pi$
$54$		0			0
$55$	−8.00000	−	4.00000i	−1.07872	−	0.539360i
$56$		0			0
$57$		−	2.00000i		−	0.264906i
$58$		0			0
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		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
$65$	4.46410	−	0.267949i	0.553704	−	0.0332350i
$66$		0			0
$67$	−10.3923	−	6.00000i	−1.26962	−	0.733017i	−0.294706	−	0.955588i	$-0.595222\pi$
$67$	−10.3923	−	6.00000i	−1.26962	−	0.733017i	−0.974916	+	0.222571i	$0.928555\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	12.1244	+	7.00000i	1.41905	+	0.819288i	0.996215	−	0.0869195i	$-0.0277023\pi$
$73$	12.1244	+	7.00000i	1.41905	+	0.819288i	0.422833	+	0.906208i	$0.361036\pi$
$74$		0			0
$75$	4.59808	+	1.96410i	0.530940	+	0.226795i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.827401	+	0.561611i	$0.189818\pi$
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.0726692	+	0.997356i	$0.476848\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	16.0000i		−	1.75623i	−0.478451	−	0.878114i	$-0.658802\pi$
$83$		−	16.0000i		−	1.75623i	0.478451	−	0.878114i	$-0.341198\pi$
$84$		0			0
$85$	2.00000	−	4.00000i	0.216930	−	0.433861i
$86$		0			0
$87$	5.19615	+	3.00000i	0.557086	+	0.321634i
$88$		0			0
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−8.00000	−	13.8564i	−0.847998	−	1.46878i	0.0349934	−	0.999388i	$-0.488859\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−5.19615	+	3.00000i	−0.538816	+	0.311086i
$94$		0			0
$95$	−3.73205	+	2.46410i	−0.382900	+	0.252811i
$96$		0			0
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$		0			0
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.5885	+	9.00000i	−1.50699	+	0.870063i	−0.507026	+	0.861931i	$0.669255\pi$
$107$	−15.5885	+	9.00000i	−1.50699	+	0.870063i	−0.999967	+	0.00813215i	$0.997411\pi$
$108$		0			0
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	−0.00790932	−	0.999969i	$-0.502518\pi$
$109$	9.00000	−	15.5885i	0.862044	−	1.49310i	0.869953	−	0.493135i	$-0.164149\pi$
$110$		0			0
$111$	−4.00000			−0.379663
$112$		0			0
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$		0			0
$115$	−7.39230	−	11.1962i	−0.689336	−	1.04405i
$116$		0			0
$117$	1.73205	−	1.00000i	0.160128	−	0.0924500i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$		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	$-0.110758\pi$
$131$	2.00000	+	3.46410i	0.174741	+	0.302660i	−0.765331	+	0.643637i	$0.777425\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.23205	−	0.133975i	0.192104	−	0.0115307i
$136$		0			0
$137$	8.66025	+	5.00000i	0.739895	+	0.427179i	0.822031	−	0.569442i	$-0.192841\pi$
$137$	8.66025	+	5.00000i	0.739895	+	0.427179i	−0.0821359	+	0.996621i	$0.526174\pi$
$138$		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
$141$	−4.00000			−0.336861
$142$		0			0
$143$	6.92820	+	4.00000i	0.579365	+	0.334497i
$144$		0			0
$145$	−0.803848	−	13.3923i	−0.0667559	−	1.11217i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$		0			0
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	12.0000	+	6.00000i	0.963863	+	0.481932i
$156$		0			0
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	0.429289	−	0.903167i	$-0.358764\pi$
$157$	−1.73205	−	1.00000i	−0.138233	−	0.0798087i	−0.567521	+	0.823359i	$0.692098\pi$
$158$		0			0
$159$	−1.00000	−	1.73205i	−0.0793052	−	0.137361i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.643280	+	0.765631i	$0.722427\pi$
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.984696	+	0.174282i	$0.944240\pi$
$164$		0			0
$165$	4.92820	+	7.46410i	0.383660	+	0.581080i
$166$		0			0
$167$		−	8.00000i		−	0.619059i	−0.950890	−	0.309529i	$-0.899829\pi$
$167$		−	8.00000i		−	0.619059i	0.950890	−	0.309529i	$-0.100171\pi$
$168$		0			0
$169$	9.00000			0.692308
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$		0			0
$173$	−12.1244	+	7.00000i	−0.921798	+	0.532200i	−0.884208	−	0.467093i	$-0.845301\pi$
$173$	−12.1244	+	7.00000i	−0.921798	+	0.532200i	−0.0375896	+	0.999293i	$0.511968\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.46410	−	2.00000i	0.260378	−	0.150329i
$178$		0			0
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$			2.00000i			0.147844i
$184$		0			0
$185$	4.92820	+	7.46410i	0.362329	+	0.548772i
$186$		0			0
$187$	6.92820	−	4.00000i	0.506640	−	0.292509i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		0			0
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$	−4.00000	−	2.00000i	−0.286446	−	0.143223i
$196$		0			0
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		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
$205$		0			0
$206$		0			0
$207$	−5.19615	−	3.00000i	−0.361158	−	0.208514i
$208$		0			0
$209$	−8.00000			−0.553372
$210$		0			0
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$		0			0
$213$	6.92820	+	4.00000i	0.474713	+	0.274075i
$214$		0			0
$215$	8.92820	−	0.535898i	0.608898	−	0.0365480i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.00000	−	12.1244i	−0.473016	−	0.819288i
$220$		0			0
$221$	−2.00000	+	3.46410i	−0.134535	+	0.233021i
$222$		0			0
$223$			16.0000i			1.07144i	0.844396	+	0.535720i	$0.179960\pi$
$223$			16.0000i			1.07144i	−0.844396	+	0.535720i	$0.820040\pi$
$224$		0			0
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$		0			0
$227$	−3.46410	−	2.00000i	−0.229920	−	0.132745i	0.380615	−	0.924734i	$-0.375712\pi$
$227$	−3.46410	−	2.00000i	−0.229920	−	0.132745i	−0.610535	+	0.791989i	$0.709046\pi$
$228$		0			0
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	0.831092	−	0.556136i	$-0.187717\pi$
$229$	−1.00000	−	1.73205i	−0.0660819	−	0.114457i	−0.897173	+	0.441679i	$0.854383\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$		0			0
$235$	4.92820	+	7.46410i	0.321481	+	0.486904i
$236$		0			0
$237$		−	16.0000i		−	1.03931i
$238$		0			0
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		0			0
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	−0.0546547	−	0.998505i	$-0.517406\pi$
$241$	13.0000	−	22.5167i	0.837404	−	1.45043i	0.892058	−	0.451920i	$-0.149261\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.46410	−	2.00000i	0.220416	−	0.127257i
$248$		0			0
$249$	−8.00000	+	13.8564i	−0.506979	+	0.878114i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$		−	24.0000i		−	1.50887i
$254$		0			0
$255$	−3.73205	+	2.46410i	−0.233710	+	0.154308i
$256$		0			0
$257$	19.0526	−	11.0000i	1.18847	−	0.686161i	0.230508	−	0.973070i	$-0.425961\pi$
$257$	19.0526	−	11.0000i	1.18847	−	0.686161i	0.957958	+	0.286909i	$0.0926278\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	−25.9808	−	15.0000i	−1.60204	−	0.924940i	−0.991078	−	0.133281i	$-0.957449\pi$
$263$	−25.9808	−	15.0000i	−1.60204	−	0.924940i	−0.610964	−	0.791658i	$-0.709218\pi$
$264$		0			0
$265$	−2.00000	+	4.00000i	−0.122859	+	0.245718i
$266$		0			0
$267$			16.0000i			0.979184i
$268$		0			0
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	−0.798591	−	0.601874i	$-0.794421\pi$
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	0.920534	+	0.390664i	$0.127754\pi$
$270$		0			0
$271$	−11.0000	−	19.0526i	−0.668202	−	1.15736i	−0.978406	−	0.206691i	$-0.933731\pi$
$271$	−11.0000	−	19.0526i	−0.668202	−	1.15736i	0.310204	−	0.950670i	$-0.399603\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.85641	−	18.3923i	0.473759	−	1.10910i
$276$		0			0
$277$	3.46410	+	2.00000i	0.208138	+	0.120168i	0.600446	−	0.799666i	$-0.294990\pi$
$277$	3.46410	+	2.00000i	0.208138	+	0.120168i	−0.392308	+	0.919834i	$0.628323\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	10.0000			0.596550			0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000			0.596550			0.298275	+	0.954480i	$0.403589\pi$
$282$		0			0
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.112728	−	0.993626i	$-0.535959\pi$
$283$	−17.3205	−	10.0000i	−1.02960	−	0.594438i	−0.916869	+	0.399188i	$0.869292\pi$
$284$		0			0
$285$	4.46410	−	0.267949i	0.264431	−	0.0158719i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	−7.00000	+	12.1244i	−0.410347	+	0.710742i
$292$		0			0
$293$			22.0000i			1.28525i	0.766179	+	0.642627i	$0.222155\pi$
$293$			22.0000i			1.28525i	−0.766179	+	0.642627i	$0.777845\pi$
$294$		0			0
$295$	−8.00000	−	4.00000i	−0.465778	−	0.232889i
$296$		0			0
$297$	3.46410	+	2.00000i	0.201008	+	0.116052i
$298$		0			0
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.92820	+	4.00000i	−0.398015	+	0.229794i
$304$		0			0
$305$	3.73205	−	2.46410i	0.213697	−	0.141094i
$306$		0			0
$307$			4.00000i			0.228292i	0.993464	+	0.114146i	$0.0364132\pi$
$307$			4.00000i			0.228292i	−0.993464	+	0.114146i	$0.963587\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	0.429808	+	0.902920i	$0.358581\pi$
$311$	−10.0000	+	17.3205i	−0.567048	+	0.982156i	−0.996856	+	0.0792356i	$0.974752\pi$
$312$		0			0
$313$	−19.0526	+	11.0000i	−1.07691	+	0.621757i	−0.930062	−	0.367402i	$-0.880247\pi$
$313$	−19.0526	+	11.0000i	−1.07691	+	0.621757i	−0.146852	+	0.989158i	$0.546914\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.5167	−	13.0000i	1.26466	−	0.730153i	0.290689	−	0.956818i	$-0.406116\pi$
$317$	22.5167	−	13.0000i	1.26466	−	0.730153i	0.973973	+	0.226665i	$0.0727822\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$		0			0
$321$	18.0000			1.00466
$322$		0			0
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$	1.19615	+	9.92820i	0.0663506	+	0.550718i
$326$		0			0
$327$	−15.5885	+	9.00000i	−0.862044	+	0.497701i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	12.0000	+	20.7846i	0.659580	+	1.14243i	0.980725	+	0.195395i	$0.0625990\pi$
$331$	12.0000	+	20.7846i	0.659580	+	1.14243i	−0.321145	+	0.947030i	$0.604068\pi$
$332$		0			0
$333$	3.46410	+	2.00000i	0.189832	+	0.109599i
$334$		0			0
$335$	12.0000	−	24.0000i	0.655630	−	1.31126i
$336$		0			0
$337$		−	8.00000i		−	0.435788i	−0.975972	−	0.217894i	$-0.930081\pi$
$337$		−	8.00000i		−	0.435788i	0.975972	−	0.217894i	$-0.0699187\pi$
$338$		0			0
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.803848	+	13.3923i	0.0432777	+	0.721017i
$346$		0			0
$347$	8.66025	+	5.00000i	0.464907	+	0.268414i	0.714105	−	0.700038i	$-0.246834\pi$
$347$	8.66025	+	5.00000i	0.464907	+	0.268414i	−0.249198	+	0.968452i	$0.580167\pi$
$348$		0			0
$349$	6.00000			0.321173			0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000			0.321173			0.160586	+	0.987022i	$0.448662\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$		0			0
$353$	25.9808	+	15.0000i	1.38282	+	0.798369i	0.992492	−	0.122308i	$-0.0390296\pi$
$353$	25.9808	+	15.0000i	1.38282	+	0.798369i	0.390324	+	0.920677i	$0.372363\pi$
$354$		0			0
$355$	−1.07180	−	17.8564i	−0.0568851	−	0.947720i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	0.952063	−	0.305903i	$-0.0989582\pi$
$359$	4.00000	+	6.92820i	0.211112	+	0.365657i	−0.740951	+	0.671559i	$0.765625\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$			5.00000i			0.262432i
$364$		0			0
$365$	−14.0000	+	28.0000i	−0.732793	+	1.46559i
$366$		0			0
$367$	−13.8564	−	8.00000i	−0.723299	−	0.417597i	0.0926670	−	0.995697i	$-0.470461\pi$
$367$	−13.8564	−	8.00000i	−0.723299	−	0.417597i	−0.815966	+	0.578101i	$0.803794\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−20.7846	+	12.0000i	−1.07619	+	0.621336i	−0.929865	−	0.367901i	$-0.880077\pi$
$373$	−20.7846	+	12.0000i	−1.07619	+	0.621336i	−0.146321	+	0.989237i	$0.546743\pi$
$374$		0			0
$375$	−3.76795	+	10.5263i	−0.194576	+	0.543575i
$376$		0			0
$377$			12.0000i			0.618031i
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−10.3923	+	6.00000i	−0.531022	+	0.306586i	−0.741433	−	0.671027i	$-0.765853\pi$
$383$	−10.3923	+	6.00000i	−0.531022	+	0.306586i	0.210411	+	0.977613i	$0.432520\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.46410	−	2.00000i	0.176090	−	0.101666i
$388$		0			0
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	0.182047	+	0.983290i	$0.441728\pi$
$389$	−15.0000	+	25.9808i	−0.760530	+	1.31728i	−0.942578	+	0.333987i	$0.891606\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$		−	4.00000i		−	0.201773i
$394$		0			0
$395$	−29.8564	+	19.7128i	−1.50224	+	0.991859i
$396$		0			0
$397$	−29.4449	+	17.0000i	−1.47780	+	0.853206i	−0.999685	−	0.0250943i	$-0.992011\pi$
$397$	−29.4449	+	17.0000i	−1.47780	+	0.853206i	−0.478110	+	0.878300i	$0.658678\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	0.781345	−	0.624099i	$-0.214534\pi$
$401$	−3.00000	−	5.19615i	−0.149813	−	0.259483i	−0.931158	+	0.364615i	$0.881200\pi$
$402$		0			0
$403$	−10.3923	−	6.00000i	−0.517678	−	0.298881i
$404$		0			0
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$		0			0
$407$			16.0000i			0.793091i
$408$		0			0
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$		0			0
$411$	−5.00000	−	8.66025i	−0.246632	−	0.427179i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	35.7128	−	2.14359i	1.75307	−	0.105225i
$416$		0			0
$417$	12.1244	+	7.00000i	0.593732	+	0.342791i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−2.00000			−0.0974740			−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000			−0.0974740			−0.0487370	+	0.998812i	$0.515520\pi$
$422$		0			0
$423$	3.46410	+	2.00000i	0.168430	+	0.0972433i
$424$		0			0
$425$	9.19615	+	3.92820i	0.446079	+	0.190546i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−4.00000	−	6.92820i	−0.193122	−	0.334497i
$430$		0			0
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$		0			0
$433$			34.0000i			1.63394i	0.576683	+	0.816968i	$0.304347\pi$
$433$			34.0000i			1.63394i	−0.576683	+	0.816968i	$0.695653\pi$
$434$		0			0
$435$	−6.00000	+	12.0000i	−0.287678	+	0.575356i
$436$		0			0
$437$	−10.3923	−	6.00000i	−0.497131	−	0.287019i
$438$		0			0
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	0.928693	−	0.370849i	$-0.120933\pi$
$439$	3.00000	+	5.19615i	0.143182	+	0.247999i	−0.785511	+	0.618848i	$0.787600\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.19615	+	3.00000i	−0.246877	+	0.142534i	−0.618333	−	0.785916i	$-0.712192\pi$
$443$	−5.19615	+	3.00000i	−0.246877	+	0.142534i	0.371457	+	0.928450i	$0.378858\pi$
$444$		0			0
$445$	29.8564	−	19.7128i	1.41533	−	0.934477i
$446$		0			0
$447$		−	6.00000i		−	0.283790i
$448$		0			0
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−13.8564	+	8.00000i	−0.651031	+	0.375873i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	24.2487	−	14.0000i	1.13431	−	0.654892i	0.189292	−	0.981921i	$-0.439381\pi$
$457$	24.2487	−	14.0000i	1.13431	−	0.654892i	0.945015	+	0.327028i	$0.106047\pi$
$458$		0			0
$459$	−1.00000	+	1.73205i	−0.0466760	+	0.0808452i
$460$		0			0
$461$	24.0000			1.11779			0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000			1.11779			0.558896	+	0.829238i	$0.311225\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$	−7.39230	−	11.1962i	−0.342810	−	0.519209i
$466$		0			0
$467$	24.2487	−	14.0000i	1.12210	−	0.647843i	0.180161	−	0.983637i	$-0.442338\pi$
$467$	24.2487	−	14.0000i	1.12210	−	0.647843i	0.941935	+	0.335794i	$0.109005\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	1.00000	+	1.73205i	0.0460776	+	0.0798087i
$472$		0			0
$473$	13.8564	+	8.00000i	0.637118	+	0.367840i
$474$		0			0
$475$	−6.00000	−	8.00000i	−0.275299	−	0.367065i
$476$		0			0
$477$			2.00000i			0.0915737i
$478$		0			0
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	−0.816711	−	0.577047i	$-0.804205\pi$
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	0.908093	+	0.418769i	$0.137538\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	31.2487	−	1.87564i	1.41893	−	0.0851686i
$486$		0			0
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	0.245705	−	0.969345i	$-0.420981\pi$
$487$	−10.3923	−	6.00000i	−0.470920	−	0.271886i	−0.716625	+	0.697459i	$0.754314\pi$
$488$		0			0
$489$	24.0000			1.08532
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$		0			0
$493$	10.3923	+	6.00000i	0.468046	+	0.270226i
$494$		0			0
$495$	−0.535898	−	8.92820i	−0.0240868	−	0.401293i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$		0			0
$501$	−4.00000	+	6.92820i	−0.178707	+	0.309529i
$502$		0			0
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$		0			0
$505$	16.0000	+	8.00000i	0.711991	+	0.355995i
$506$		0			0
$507$	−7.79423	−	4.50000i	−0.346154	−	0.199852i
$508$		0			0
$509$	14.0000	+	24.2487i	0.620539	+	1.07481i	0.989385	+	0.145315i	$0.0464195\pi$
$509$	14.0000	+	24.2487i	0.620539	+	1.07481i	−0.368846	+	0.929490i	$0.620247\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	1.73205	−	1.00000i	0.0764719	−	0.0441511i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			16.0000i			0.703679i
$518$		0			0
$519$	14.0000			0.614532
$520$		0			0
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	−0.704137	−	0.710064i	$-0.748666\pi$
$521$	6.00000	−	10.3923i	0.262865	−	0.455295i	0.967002	+	0.254769i	$0.0819994\pi$
$522$		0			0
$523$	−10.3923	+	6.00000i	−0.454424	+	0.262362i	−0.709697	−	0.704507i	$-0.751168\pi$
$523$	−10.3923	+	6.00000i	−0.454424	+	0.262362i	0.255273	+	0.966869i	$0.417835\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.3923	+	6.00000i	−0.452696	+	0.261364i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	−4.00000			−0.173585
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−22.1769	−	33.5885i	−0.958792	−	1.45216i
$536$		0			0
$537$	17.3205	−	10.0000i	0.747435	−	0.431532i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.00000	−	8.66025i	−0.214967	−	0.372333i	0.738296	−	0.674477i	$-0.235631\pi$
$541$	−5.00000	−	8.66025i	−0.214967	−	0.372333i	−0.953262	+	0.302144i	$0.902298\pi$
$542$		0			0
$543$	19.0526	+	11.0000i	0.817624	+	0.472055i
$544$		0			0
$545$	36.0000	+	18.0000i	1.54207	+	0.771035i
$546$		0			0
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$		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
$555$	−0.535898	−	8.92820i	−0.0227476	−	0.378981i
$556$		0			0
$557$	25.9808	+	15.0000i	1.10084	+	0.635570i	0.936442	−	0.350824i	$-0.114098\pi$
$557$	25.9808	+	15.0000i	1.10084	+	0.635570i	0.164399	+	0.986394i	$0.447432\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	20.7846	+	12.0000i	0.875967	+	0.505740i	0.869326	−	0.494238i	$-0.164553\pi$
$563$	20.7846	+	12.0000i	0.875967	+	0.505740i	0.00664037	+	0.999978i	$0.497886\pi$
$564$		0			0
$565$	13.3923	−	0.803848i	0.563418	−	0.0338181i
$566$		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
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$		0			0
$573$			8.00000i			0.334205i
$574$		0			0
$575$	24.0000	−	18.0000i	1.00087	−	0.750652i
$576$		0			0
$577$	15.5885	+	9.00000i	0.648956	+	0.374675i	0.788056	−	0.615603i	$-0.211088\pi$
$577$	15.5885	+	9.00000i	0.648956	+	0.374675i	−0.139100	+	0.990278i	$0.544421\pi$
$578$		0			0
$579$	12.0000	+	20.7846i	0.498703	+	0.863779i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−6.92820	+	4.00000i	−0.286937	+	0.165663i
$584$		0			0
$585$	2.46410	+	3.73205i	0.101878	+	0.154301i
$586$		0			0
$587$			16.0000i			0.660391i	0.943913	+	0.330195i	$0.107115\pi$
$587$			16.0000i			0.660391i	−0.943913	+	0.330195i	$0.892885\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$		0			0
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$		0			0
$593$	12.1244	−	7.00000i	0.497888	−	0.287456i	−0.229953	−	0.973202i	$-0.573857\pi$
$593$	12.1244	−	7.00000i	0.497888	−	0.287456i	0.727841	+	0.685746i	$0.240524\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.66025	−	5.00000i	0.354441	−	0.204636i
$598$		0			0
$599$	4.00000	−	6.92820i	0.163436	−	0.283079i	−0.772663	−	0.634816i	$-0.781076\pi$
$599$	4.00000	−	6.92820i	0.163436	−	0.283079i	0.936099	+	0.351738i	$0.114409\pi$
$600$		0			0
$601$	−30.0000			−1.22373			−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000			−1.22373			−0.611863	+	0.790964i	$0.709580\pi$
$602$		0			0
$603$		−	12.0000i		−	0.488678i
$604$		0			0
$605$	9.33013	−	6.16025i	0.379324	−	0.250450i
$606$		0			0
$607$	6.92820	−	4.00000i	0.281207	−	0.162355i	−0.352763	−	0.935713i	$-0.614758\pi$
$607$	6.92820	−	4.00000i	0.281207	−	0.162355i	0.633970	+	0.773358i	$0.281424\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$		0			0
$613$	3.46410	+	2.00000i	0.139914	+	0.0807792i	0.568323	−	0.822806i	$-0.307592\pi$
$613$	3.46410	+	2.00000i	0.139914	+	0.0807792i	−0.428409	+	0.903585i	$0.640926\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	6.00000i		−	0.241551i	−0.992680	−	0.120775i	$-0.961462\pi$
$617$		−	6.00000i		−	0.241551i	0.992680	−	0.120775i	$-0.0385381\pi$
$618$		0			0
$619$	15.0000	−	25.9808i	0.602901	−	1.04425i	−0.389479	−	0.921036i	$-0.627345\pi$
$619$	15.0000	−	25.9808i	0.602901	−	1.04425i	0.992379	−	0.123219i	$-0.0393219\pi$
$620$		0			0
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		0			0
$627$	6.92820	+	4.00000i	0.276686	+	0.159745i
$628$		0			0
$629$	−8.00000			−0.318981
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	6.92820	+	4.00000i	0.275371	+	0.158986i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−4.00000	−	6.92820i	−0.158238	−	0.274075i
$640$		0			0
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		0			0
$643$		−	4.00000i		−	0.157745i	−0.996885	−	0.0788723i	$-0.974868\pi$
$643$		−	4.00000i		−	0.157745i	0.996885	−	0.0788723i	$-0.0251319\pi$
$644$		0			0
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$		0			0
$647$	−34.6410	−	20.0000i	−1.36188	−	0.786281i	−0.372005	−	0.928231i	$-0.621330\pi$
$647$	−34.6410	−	20.0000i	−1.36188	−	0.786281i	−0.989874	+	0.141950i	$0.954663\pi$
$648$		0			0
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.871036	−	0.491220i	$-0.836551\pi$
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.0101092	+	0.999949i	$0.503218\pi$
$654$		0			0
$655$	−7.46410	+	4.92820i	−0.291647	+	0.192561i
$656$		0			0
$657$			14.0000i			0.546192i
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$		0			0
$663$	3.46410	−	2.00000i	0.134535	−	0.0776736i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	31.1769	−	18.0000i	1.20717	−	0.696963i
$668$		0			0
$669$	8.00000	−	13.8564i	0.309298	−	0.535720i
$670$		0			0
$671$	8.00000			0.308837
$672$		0			0
$673$			12.0000i			0.462566i	0.972887	+	0.231283i	$0.0742923\pi$
$673$			12.0000i			0.462566i	−0.972887	+	0.231283i	$0.925708\pi$
$674$		0			0
$675$	0.598076	+	4.96410i	0.0230200	+	0.191068i
$676$		0			0
$677$	−36.3731	+	21.0000i	−1.39793	+	0.807096i	−0.994176	−	0.107772i	$-0.965628\pi$
$677$	−36.3731	+	21.0000i	−1.39793	+	0.807096i	−0.403755	+	0.914867i	$0.632295\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$		0			0
$683$	12.1244	+	7.00000i	0.463926	+	0.267848i	0.713693	−	0.700458i	$-0.247021\pi$
$683$	12.1244	+	7.00000i	0.463926	+	0.267848i	−0.249768	+	0.968306i	$0.580354\pi$
$684$		0			0
$685$	−10.0000	+	20.0000i	−0.382080	+	0.764161i
$686$		0			0
$687$			2.00000i			0.0763048i
$688$		0			0
$689$	2.00000	−	3.46410i	0.0761939	−	0.131972i
$690$		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
$695$	−1.87564	−	31.2487i	−0.0711472	−	1.18533i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	18.0000			0.680823
$700$		0			0
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$		0			0
$703$	6.92820	+	4.00000i	0.261302	+	0.150863i
$704$		0			0
$705$	−0.535898	−	8.92820i	−0.0201831	−	0.336256i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$		0			0
$711$	−8.00000	+	13.8564i	−0.300023	+	0.519656i
$712$		0			0
$713$			36.0000i			1.34821i
$714$		0			0
$715$	−8.00000	+	16.0000i	−0.299183	+	0.598366i
$716$		0			0
$717$	6.92820	+	4.00000i	0.258738	+	0.149383i
$718$		0			0
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	−0.999669	−	0.0257237i	$-0.991811\pi$
$719$	−14.0000	−	24.2487i	−0.522112	−	0.904324i	0.477557	−	0.878601i	$-0.341522\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−22.5167	+	13.0000i	−0.837404	+	0.483475i
$724$		0			0
$725$	29.7846	−	3.58846i	1.10617	−	0.133272i
$726$		0			0
$727$			16.0000i			0.593407i	0.954970	+	0.296704i	$0.0958873\pi$
$727$			16.0000i			0.593407i	−0.954970	+	0.296704i	$0.904113\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	−36.3731	+	21.0000i	−1.34347	+	0.775653i	−0.987315	−	0.158774i	$-0.949246\pi$
$733$	−36.3731	+	21.0000i	−1.34347	+	0.775653i	−0.356155	+	0.934427i	$0.615912\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	41.5692	−	24.0000i	1.53122	−	0.884051i
$738$		0			0
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$	−4.00000			−0.146944
$742$		0			0
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$		0			0
$745$	−11.1962	+	7.39230i	−0.410195	+	0.270833i
$746$		0			0
$747$	13.8564	−	8.00000i	0.506979	−	0.292705i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$	−10.3923	−	6.00000i	−0.378717	−	0.218652i
$754$		0			0
$755$	32.0000	+	16.0000i	1.16460	+	0.582300i
$756$		0			0
$757$		−	8.00000i		−	0.290765i	−0.989376	−	0.145382i	$-0.953559\pi$
$757$		−	8.00000i		−	0.290765i	0.989376	−	0.145382i	$-0.0464413\pi$
$758$		0			0
$759$	−12.0000	+	20.7846i	−0.435572	+	0.754434i
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	4.46410	−	0.267949i	0.161400	−	0.00968772i
$766$		0			0
$767$	6.92820	+	4.00000i	0.250163	+	0.144432i
$768$		0			0
$769$	30.0000			1.08183			0.540914	−	0.841078i	$-0.318079\pi$
$769$	30.0000			1.08183			0.540914	+	0.841078i	$0.318079\pi$
$770$		0			0
$771$	−22.0000			−0.792311
$772$		0			0
$773$	8.66025	+	5.00000i	0.311488	+	0.179838i	0.647592	−	0.761987i	$-0.275776\pi$
$773$	8.66025	+	5.00000i	0.311488	+	0.179838i	−0.336104	+	0.941825i	$0.609109\pi$
$774$		0			0
$775$	−11.7846	+	27.5885i	−0.423316	+	0.991007i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$		0			0
$783$			6.00000i			0.214423i
$784$		0			0
$785$	2.00000	−	4.00000i	0.0713831	−	0.142766i
$786$		0			0
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$		0			0
$789$	15.0000	+	25.9808i	0.534014	+	0.924940i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−3.46410	+	2.00000i	−0.123014	+	0.0710221i
$794$		0			0
$795$	3.73205	−	2.46410i	0.132362	−	0.0873927i
$796$		0			0
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$		0			0
$801$	8.00000	−	13.8564i	0.282666	−	0.489592i
$802$		0			0
$803$	−48.4974	+	28.0000i	−1.71144	+	0.988099i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.46410	+	2.00000i	−0.121942	+	0.0704033i
$808$		0			0
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$		0			0
$811$	22.0000			0.772524			0.386262	−	0.922389i	$-0.373766\pi$
$811$	22.0000			0.772524			0.386262	+	0.922389i	$0.373766\pi$
$812$		0			0
$813$			22.0000i			0.771574i
$814$		0			0
$815$	−29.5692	−	44.7846i	−1.03576	−	1.56874i
$816$		0			0
$817$	6.92820	−	4.00000i	0.242387	−	0.139942i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	0.374365	−	0.927281i	$-0.377861\pi$
$823$	−6.92820	−	4.00000i	−0.241502	−	0.139431i	−0.615867	+	0.787850i	$0.711194\pi$
$824$		0			0
$825$	−16.0000	+	12.0000i	−0.557048	+	0.417786i
$826$		0			0
$827$			30.0000i			1.04320i	0.853189	+	0.521601i	$0.174665\pi$
$827$			30.0000i			1.04320i	−0.853189	+	0.521601i	$0.825335\pi$
$828$		0			0
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$		0			0
$831$	−2.00000	−	3.46410i	−0.0693792	−	0.120168i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	17.8564	−	1.07180i	0.617946	−	0.0370911i
$836$		0			0
$837$	−5.19615	−	3.00000i	−0.179605	−	0.103695i
$838$		0			0
$839$	−16.0000			−0.552381			−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000			−0.552381			−0.276191	+	0.961103i	$0.589072\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	−8.66025	−	5.00000i	−0.298275	−	0.172209i
$844$		0			0
$845$	1.20577	+	20.0885i	0.0414798	+	0.691064i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	10.0000	+	17.3205i	0.343199	+	0.594438i
$850$		0			0
$851$	−12.0000	+	20.7846i	−0.411355	+	0.712487i
$852$		0			0
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$		0			0
$855$	−4.00000	−	2.00000i	−0.136797	−	0.0683986i
$856$		0			0
$857$	8.66025	+	5.00000i	0.295829	+	0.170797i	0.640567	−	0.767902i	$-0.278699\pi$
$857$	8.66025	+	5.00000i	0.295829	+	0.170797i	−0.344739	+	0.938699i	$0.612033\pi$
$858$		0			0
$859$	3.00000	+	5.19615i	0.102359	+	0.177290i	0.912656	−	0.408729i	$-0.134028\pi$
$859$	3.00000	+	5.19615i	0.102359	+	0.177290i	−0.810297	+	0.586019i	$0.800694\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−46.7654	+	27.0000i	−1.59191	+	0.919091i	−0.598933	+	0.800799i	$0.704408\pi$
$863$	−46.7654	+	27.0000i	−1.59191	+	0.919091i	−0.992979	+	0.118291i	$0.962258\pi$
$864$		0			0
$865$	−17.2487	−	26.1244i	−0.586474	−	0.888255i
$866$		0			0
$867$			13.0000i			0.441503i
$868$		0			0
$869$	−64.0000			−2.17105
$870$		0			0
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$		0			0
$873$	12.1244	−	7.00000i	0.410347	−	0.236914i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−31.1769	+	18.0000i	−1.05277	+	0.607817i	−0.923423	−	0.383783i	$-0.874621\pi$
$877$	−31.1769	+	18.0000i	−1.05277	+	0.607817i	−0.129346	+	0.991600i	$0.541288\pi$
$878$		0			0
$879$	11.0000	−	19.0526i	0.371021	−	0.642627i
$880$		0			0
$881$	36.0000			1.21287			0.606435	−	0.795133i	$-0.292599\pi$
$881$	36.0000			1.21287			0.606435	+	0.795133i	$0.292599\pi$
$882$		0			0
$883$		−	56.0000i		−	1.88455i	−0.334840	−	0.942275i	$-0.608682\pi$
$883$		−	56.0000i		−	1.88455i	0.334840	−	0.942275i	$-0.391318\pi$
$884$		0			0
$885$	4.92820	+	7.46410i	0.165660	+	0.250903i
$886$		0			0
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	−0.315279	−	0.948999i	$-0.602098\pi$
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	0.664218	+	0.747539i	$0.268765\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.00000	−	3.46410i	−0.0670025	−	0.116052i
$892$		0			0
$893$	6.92820	+	4.00000i	0.231843	+	0.133855i
$894$		0			0
$895$	−40.0000	−	20.0000i	−1.33705	−	0.668526i
$896$		0			0
$897$		−	12.0000i		−	0.400668i
$898$		0			0
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	−2.00000	−	3.46410i	−0.0666297	−	0.115406i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.94744	−	49.1051i	−0.0979763	−	1.63231i
$906$		0			0
$907$	−6.92820	−	4.00000i	−0.230047	−	0.132818i	0.380547	−	0.924762i	$-0.375736\pi$
$907$	−6.92820	−	4.00000i	−0.230047	−	0.132818i	−0.610594	+	0.791944i	$0.709069\pi$
$908$		0			0
$909$	8.00000			0.265343
$910$		0			0
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$	55.4256	+	32.0000i	1.83432	+	1.05905i
$914$		0			0
$915$	−4.46410	+	0.267949i	−0.147579	+	0.00885813i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$920$		0			0
$921$	2.00000	−	3.46410i	0.0659022	−	0.114146i
$922$		0			0
$923$			16.0000i			0.526646i
$924$		0			0
$925$	−16.0000	+	12.0000i	−0.526077	+	0.394558i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	−0.927546	−	0.373709i	$-0.878086\pi$
$929$	−24.0000	−	41.5692i	−0.787414	−	1.36384i	0.140132	−	0.990133i	$-0.455247\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	17.3205	−	10.0000i	0.567048	−	0.327385i
$934$		0			0
$935$	9.85641	+	14.9282i	0.322339	+	0.488204i
$936$		0			0
$937$			10.0000i			0.326686i	0.986569	+	0.163343i	$0.0522277\pi$
$937$			10.0000i			0.326686i	−0.986569	+	0.163343i	$0.947772\pi$
$938$		0			0
$939$	22.0000			0.717943
$940$		0			0
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.308215	+	0.951317i	$0.599732\pi$
$941$	−30.0000	+	51.9615i	−0.977972	+	1.69390i	−0.669757	+	0.742581i	$0.733602\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.5885	−	9.00000i	0.506557	−	0.292461i	−0.224860	−	0.974391i	$-0.572193\pi$
$947$	15.5885	−	9.00000i	0.506557	−	0.292461i	0.731417	+	0.681930i	$0.238859\pi$
$948$		0			0
$949$	14.0000	−	24.2487i	0.454459	−	0.787146i
$950$		0			0
$951$	−26.0000			−0.843108
$952$		0			0
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$		0			0
$955$	14.9282	−	9.85641i	0.483065	−	0.318946i
$956$		0			0
$957$	−20.7846	+	12.0000i	−0.671871	+	0.387905i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	−15.5885	−	9.00000i	−0.502331	−	0.290021i
$964$		0			0
$965$	24.0000	−	48.0000i	0.772587	−	1.54517i
$966$		0			0
$967$			36.0000i			1.15768i	0.815440	+	0.578841i	$0.196495\pi$
$967$			36.0000i			1.15768i	−0.815440	+	0.578841i	$0.803505\pi$
$968$		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
$975$	3.92820	−	9.19615i	0.125803	−	0.294513i
$976$		0			0
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.211495	−	0.977379i	$-0.567833\pi$
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.952183	+	0.305530i	$0.901167\pi$
$978$		0			0
$979$	64.0000			2.04545
$980$		0			0
$981$	18.0000			0.574696
$982$		0			0
$983$	−20.7846	−	12.0000i	−0.662926	−	0.382741i	0.130465	−	0.991453i	$-0.458353\pi$
$983$	−20.7846	−	12.0000i	−0.662926	−	0.382741i	−0.793391	+	0.608712i	$0.791686\pi$
$984$		0			0
$985$	40.1769	−	2.41154i	1.28014	−	0.0768381i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	12.0000	+	20.7846i	0.381578	+	0.660912i
$990$		0			0
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	0.424594	+	0.905384i	$0.360417\pi$
$991$	−18.0000	+	31.1769i	−0.571789	+	0.990367i	−0.996382	+	0.0849833i	$0.972916\pi$
$992$		0			0
$993$		−	24.0000i		−	0.761617i
$994$		0			0
$995$	−20.0000	−	10.0000i	−0.634043	−	0.317021i
$996$		0			0
$997$	−19.0526	−	11.0000i	−0.603401	−	0.348373i	0.166978	−	0.985961i	$-0.446599\pi$
$997$	−19.0526	−	11.0000i	−0.603401	−	0.348373i	−0.770378	+	0.637587i	$0.779933\pi$
$998$		0			0
$999$	−2.00000	−	3.46410i	−0.0632772	−	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.bb.f.949.1		4
5.4	even	2	inner	2940.2.bb.f.949.2		4
7.2	even	3	inner	2940.2.bb.f.1549.2		4
7.3	odd	6		420.2.k.b.169.1	✓	2
7.4	even	3		2940.2.k.b.589.2		2
7.5	odd	6		2940.2.bb.a.1549.1		4
7.6	odd	2		2940.2.bb.a.949.2		4
21.17	even	6		1260.2.k.a.1009.1		2
28.3	even	6		1680.2.t.g.1009.2		2
35.3	even	12		2100.2.a.n.1.1		1
35.4	even	6		2940.2.k.b.589.1		2
35.9	even	6	inner	2940.2.bb.f.1549.1		4
35.17	even	12		2100.2.a.i.1.1		1
35.19	odd	6		2940.2.bb.a.1549.2		4
35.24	odd	6		420.2.k.b.169.2	yes	2
35.34	odd	2		2940.2.bb.a.949.1		4
84.59	odd	6		5040.2.t.d.1009.1		2
105.17	odd	12		6300.2.a.r.1.1		1
105.38	odd	12		6300.2.a.b.1.1		1
105.59	even	6		1260.2.k.a.1009.2		2
140.3	odd	12		8400.2.a.o.1.1		1
140.59	even	6		1680.2.t.g.1009.1		2
140.87	odd	12		8400.2.a.bm.1.1		1
420.59	odd	6		5040.2.t.d.1009.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.k.b.169.1	✓	2	7.3	odd	6
420.2.k.b.169.2	yes	2	35.24	odd	6
1260.2.k.a.1009.1		2	21.17	even	6
1260.2.k.a.1009.2		2	105.59	even	6
1680.2.t.g.1009.1		2	140.59	even	6
1680.2.t.g.1009.2		2	28.3	even	6
2100.2.a.i.1.1		1	35.17	even	12
2100.2.a.n.1.1		1	35.3	even	12
2940.2.k.b.589.1		2	35.4	even	6
2940.2.k.b.589.2		2	7.4	even	3
2940.2.bb.a.949.1		4	35.34	odd	2
2940.2.bb.a.949.2		4	7.6	odd	2
2940.2.bb.a.1549.1		4	7.5	odd	6
2940.2.bb.a.1549.2		4	35.19	odd	6
2940.2.bb.f.949.1		4	1.1	even	1	trivial
2940.2.bb.f.949.2		4	5.4	even	2	inner
2940.2.bb.f.1549.1		4	35.9	even	6	inner
2940.2.bb.f.1549.2		4	7.2	even	3	inner
5040.2.t.d.1009.1		2	84.59	odd	6
5040.2.t.d.1009.2		2	420.59	odd	6
6300.2.a.b.1.1		1	105.38	odd	12
6300.2.a.r.1.1		1	105.17	odd	12
8400.2.a.o.1.1		1	140.3	odd	12
8400.2.a.bm.1.1		1	140.87	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(0.133975 + 2.23205i) q^{5} +(0.500000 + 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} -2.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +(-1.73205 - 1.00000i) q^{17} +(1.00000 + 1.73205i) q^{19} +(-5.19615 + 3.00000i) q^{23} +(-4.96410 + 0.598076i) q^{25} -1.00000i q^{27} -6.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(3.46410 - 2.00000i) q^{33} +(3.46410 - 2.00000i) q^{37} +(-1.00000 + 1.73205i) q^{39} -4.00000i q^{43} +(-1.86603 + 1.23205i) q^{45} +(3.46410 - 2.00000i) q^{47} +(1.00000 + 1.73205i) q^{51} +(1.73205 + 1.00000i) q^{53} +(-8.00000 - 4.00000i) q^{55} -2.00000i q^{57} +(-2.00000 + 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(4.46410 - 0.267949i) q^{65} +(-10.3923 - 6.00000i) q^{67} +6.00000 q^{69} -8.00000 q^{71} +(12.1244 + 7.00000i) q^{73} +(4.59808 + 1.96410i) q^{75} +(8.00000 + 13.8564i) q^{79} +(-0.500000 + 0.866025i) q^{81} -16.0000i q^{83} +(2.00000 - 4.00000i) q^{85} +(5.19615 + 3.00000i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(-5.19615 + 3.00000i) q^{93} +(-3.73205 + 2.46410i) q^{95} -14.0000i q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} + 2 q^{9} - 8 q^{11} + 4 q^{15} + 4 q^{19} - 6 q^{25} - 24 q^{29} + 12 q^{31} - 4 q^{39} - 4 q^{45} + 4 q^{51} - 32 q^{55} - 8 q^{59} - 4 q^{61} + 4 q^{65} + 24 q^{69} - 32 q^{71} + 8 q^{75}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^5 + 2 * q^9 - 8 * q^11 + 4 * q^15 + 4 * q^19 - 6 * q^25 - 24 * q^29 + 12 * q^31 - 4 * q^39 - 4 * q^45 + 4 * q^51 - 32 * q^55 - 8 * q^59 - 4 * q^61 + 4 * q^65 + 24 * q^69 - 32 * q^71 + 8 * q^75 + 32 * q^79 - 2 * q^81 + 8 * q^85 - 32 * q^89 - 8 * q^95 - 16 * q^99

Introduction

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