LMFDB - Embedded newform 2940.2.bb.h.1549.1

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			1549.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2940.1549
Dual form			2940.2.bb.h.949.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{3} +(0.133975 - 2.23205i) q^{5} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} -6.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(-1.73205 + 1.00000i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-1.73205 - 1.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +1.00000i q^{27} -6.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-3.46410 - 2.00000i) q^{33} +(-3.46410 - 2.00000i) q^{37} +(3.00000 + 5.19615i) q^{39} +8.00000 q^{41} -4.00000i q^{43} +(-1.86603 - 1.23205i) q^{45} +(3.46410 + 2.00000i) q^{47} +(1.00000 - 1.73205i) q^{51} +(5.19615 - 3.00000i) q^{53} +(8.00000 - 4.00000i) q^{55} +6.00000i q^{57} +(2.00000 + 3.46410i) q^{59} +(-7.00000 + 12.1244i) q^{61} +(-13.3923 - 0.803848i) q^{65} +(-3.46410 + 2.00000i) q^{67} +2.00000 q^{69} +(-8.66025 + 5.00000i) q^{73} +(4.59808 - 1.96410i) q^{75} +(-0.500000 - 0.866025i) q^{81} -16.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.19615 - 3.00000i) q^{87} +(4.00000 - 6.92820i) q^{89} +(-1.73205 - 1.00000i) q^{93} +(-11.1962 - 7.39230i) q^{95} -10.0000i q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} + 2 q^{9} + 8 q^{11} + 4 q^{15} + 12 q^{19} - 6 q^{25} - 24 q^{29} + 4 q^{31} + 12 q^{39} + 32 q^{41} - 4 q^{45} + 4 q^{51} + 32 q^{55} + 8 q^{59} - 28 q^{61} - 12 q^{65} + 8 q^{69} + 8 q^{75}+ \cdots + 16 q^{99}+O(q^{100}) $ 4 * q + 4 * q^5 + 2 * q^9 + 8 * q^11 + 4 * q^15 + 12 * q^19 - 6 * q^25 - 24 * q^29 + 4 * q^31 + 12 * q^39 + 32 * q^41 - 4 * q^45 + 4 * q^51 + 32 * q^55 + 8 * q^59 - 28 * q^61 - 12 * q^65 + 8 * q^69 + 8 * q^75 - 2 * q^81 + 8 * q^85 + 16 * q^89 - 24 * q^95 + 16 * q^99

Character values

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

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

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
$3$	−0.866025	+	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	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		0			0
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$		0			0
$15$	1.00000	+	2.00000i	0.258199	+	0.516398i
$16$		0			0
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	−0.695113	−	0.718900i	$-0.744646\pi$
$17$	−1.73205	+	1.00000i	−0.420084	+	0.242536i	0.275029	+	0.961436i	$0.411312\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.73205	−	1.00000i	−0.361158	−	0.208514i	0.308431	−	0.951247i	$-0.400196\pi$
$23$	−1.73205	−	1.00000i	−0.361158	−	0.208514i	−0.669588	+	0.742732i	$0.733529\pi$
$24$		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
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$		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	$-0.439977\pi$
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	−0.756948	+	0.653476i	$0.773310\pi$
$38$		0			0
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$		0			0
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$		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	0.730896	−	0.682489i	$-0.239102\pi$
$47$	3.46410	+	2.00000i	0.505291	+	0.291730i	−0.225605	+	0.974219i	$0.572436\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$		0			0
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	−0.0987002	−	0.995117i	$-0.531468\pi$
$53$	5.19615	−	3.00000i	0.713746	−	0.412082i	0.812447	+	0.583036i	$0.198135\pi$
$54$		0			0
$55$	8.00000	−	4.00000i	1.07872	−	0.539360i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.0640184	+	0.997949i	$0.520392\pi$
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.832240	+	0.554416i	$0.812942\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−13.3923	−	0.803848i	−1.66111	−	0.0997050i
$66$		0			0
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$		0			0
$69$	2.00000			0.240772
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−8.66025	+	5.00000i	−1.01361	+	0.585206i	−0.912245	−	0.409644i	$-0.865653\pi$
$73$	−8.66025	+	5.00000i	−1.01361	+	0.585206i	−0.101361	+	0.994850i	$0.532320\pi$
$74$		0			0
$75$	4.59808	−	1.96410i	0.530940	−	0.226795i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$		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
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	−0.572327	−	0.820025i	$-0.693959\pi$
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	0.996326	+	0.0856373i	$0.0272926\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$		0			0
$95$	−11.1962	−	7.39230i	−1.14870	−	0.758434i
$96$		0			0
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	−8.00000	−	13.8564i	−0.796030	−	1.37876i	−0.922183	−	0.386753i	$-0.873597\pi$
$101$	−8.00000	−	13.8564i	−0.796030	−	1.37876i	0.126153	−	0.992011i	$-0.459737\pi$
$102$		0			0
$103$	−13.8564	−	8.00000i	−1.36531	−	0.788263i	−0.374987	−	0.927030i	$-0.622353\pi$
$103$	−13.8564	−	8.00000i	−1.36531	−	0.788263i	−0.990325	+	0.138767i	$0.955686\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	0.227345	−	0.973814i	$-0.426996\pi$
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	−0.729676	+	0.683793i	$0.760329\pi$
$108$		0			0
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$	−2.46410	+	3.73205i	−0.229779	+	0.348016i
$116$		0			0
$117$	−5.19615	−	3.00000i	−0.480384	−	0.277350i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$	−6.92820	+	4.00000i	−0.624695	+	0.360668i
$124$		0			0
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$		0			0
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.23205	+	0.133975i	0.192104	+	0.0115307i
$136$		0			0
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$		0			0
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−4.00000			−0.336861
$142$		0			0
$143$	20.7846	−	12.0000i	1.73810	−	1.00349i
$144$		0			0
$145$	−0.803848	+	13.3923i	−0.0667559	+	1.11217i
$146$		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
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	−0.982873	−	0.184284i	$-0.941004\pi$
$151$	−8.00000	−	13.8564i	−0.651031	−	1.12762i	0.331842	−	0.943335i	$-0.392330\pi$
$152$		0			0
$153$			2.00000i			0.161690i
$154$		0			0
$155$	4.00000	−	2.00000i	0.321288	−	0.160644i
$156$		0			0
$157$	−8.66025	+	5.00000i	−0.691164	+	0.399043i	−0.804048	−	0.594565i	$-0.797324\pi$
$157$	−8.66025	+	5.00000i	−0.691164	+	0.399043i	0.112884	+	0.993608i	$0.463991\pi$
$158$		0			0
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	0.746156	−	0.665771i	$-0.231897\pi$
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	−0.203497	+	0.979076i	$0.565231\pi$
$164$		0			0
$165$	−4.92820	+	7.46410i	−0.383660	+	0.581080i
$166$		0			0
$167$		−	24.0000i		−	1.85718i	−0.371113	−	0.928588i	$-0.621024\pi$
$167$		−	24.0000i		−	1.85718i	0.371113	−	0.928588i	$-0.378976\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$		0			0
$173$	1.73205	+	1.00000i	0.131685	+	0.0760286i	0.564396	−	0.825505i	$-0.309109\pi$
$173$	1.73205	+	1.00000i	0.131685	+	0.0760286i	−0.432710	+	0.901533i	$0.642443\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.46410	−	2.00000i	−0.260378	−	0.150329i
$178$		0			0
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		−	14.0000i		−	1.03491i
$184$		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
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	6.92820	−	4.00000i	0.498703	−	0.287926i	−0.229475	−	0.973315i	$-0.573701\pi$
$193$	6.92820	−	4.00000i	0.498703	−	0.287926i	0.728178	+	0.685388i	$0.240368\pi$
$194$		0			0
$195$	12.0000	−	6.00000i	0.859338	−	0.429669i
$196$		0			0
$197$		−	10.0000i		−	0.712470i	−0.934396	−	0.356235i	$-0.884060\pi$
$197$		−	10.0000i		−	0.712470i	0.934396	−	0.356235i	$-0.115940\pi$
$198$		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
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.07180	−	17.8564i	0.0748575	−	1.24715i
$206$		0			0
$207$	−1.73205	+	1.00000i	−0.120386	+	0.0695048i
$208$		0			0
$209$	24.0000			1.66011
$210$		0			0
$211$	−24.0000			−1.65223			−0.826114	−	0.563503i	$-0.809453\pi$
$211$	−24.0000			−1.65223			−0.826114	+	0.563503i	$0.809453\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.92820	−	0.535898i	−0.608898	−	0.0365480i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$		−	16.0000i		−	1.07144i	−0.844396	−	0.535720i	$-0.820040\pi$
$223$		−	16.0000i		−	1.07144i	0.844396	−	0.535720i	$-0.179960\pi$
$224$		0			0
$225$	−3.00000	+	4.00000i	−0.200000	+	0.266667i
$226$		0			0
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.948790	−	0.315906i	$-0.897691\pi$
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.200812	+	0.979630i	$0.564358\pi$
$228$		0			0
$229$	1.00000	−	1.73205i	0.0660819	−	0.114457i	−0.831092	−	0.556136i	$-0.812283\pi$
$229$	1.00000	−	1.73205i	0.0660819	−	0.114457i	0.897173	+	0.441679i	$0.145617\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	22.5167	+	13.0000i	1.47512	+	0.851658i	0.999606	−	0.0280525i	$-0.00893057\pi$
$233$	22.5167	+	13.0000i	1.47512	+	0.851658i	0.475509	+	0.879711i	$0.342264\pi$
$234$		0			0
$235$	4.92820	−	7.46410i	0.321481	−	0.486904i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−31.1769	−	18.0000i	−1.98374	−	1.14531i
$248$		0			0
$249$	8.00000	+	13.8564i	0.506979	+	0.878114i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$		0			0
$255$	−3.73205	−	2.46410i	−0.233710	−	0.154308i
$256$		0			0
$257$	5.19615	+	3.00000i	0.324127	+	0.187135i	0.653231	−	0.757159i	$-0.273413\pi$
$257$	5.19615	+	3.00000i	0.324127	+	0.187135i	−0.329104	+	0.944294i	$0.606747\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	−8.66025	+	5.00000i	−0.534014	+	0.308313i	−0.742650	−	0.669680i	$-0.766431\pi$
$263$	−8.66025	+	5.00000i	−0.534014	+	0.308313i	0.208635	+	0.977993i	$0.433098\pi$
$264$		0			0
$265$	−6.00000	−	12.0000i	−0.368577	−	0.737154i
$266$		0			0
$267$			8.00000i			0.489592i
$268$		0			0
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	0.623082	−	0.782157i	$-0.285880\pi$
$269$	−6.00000	−	10.3923i	−0.365826	−	0.633630i	−0.988908	+	0.148527i	$0.952547\pi$
$270$		0			0
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	−0.571221	−	0.820796i	$-0.693530\pi$
$271$	7.00000	−	12.1244i	0.425220	−	0.736502i	0.996441	+	0.0842940i	$0.0268635\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.85641	−	18.3923i	−0.473759	−	1.10910i
$276$		0			0
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.458103	−	0.888899i	$-0.348529\pi$
$277$	24.2487	−	14.0000i	1.45696	−	0.841178i	0.998861	+	0.0477206i	$0.0151957\pi$
$278$		0			0
$279$	2.00000			0.119737
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	24.2487	−	14.0000i	1.44144	−	0.832214i	0.443491	−	0.896279i	$-0.353740\pi$
$283$	24.2487	−	14.0000i	1.44144	−	0.832214i	0.997946	+	0.0640654i	$0.0204066\pi$
$284$		0			0
$285$	13.3923	+	0.803848i	0.793292	+	0.0476158i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−6.50000	+	11.2583i	−0.382353	+	0.662255i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$		0			0
$293$		−	6.00000i		−	0.350524i	−0.984522	−	0.175262i	$-0.943923\pi$
$293$		−	6.00000i		−	0.350524i	0.984522	−	0.175262i	$-0.0560772\pi$
$294$		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
$303$	13.8564	+	8.00000i	0.796030	+	0.459588i
$304$		0			0
$305$	26.1244	+	17.2487i	1.49588	+	0.987658i
$306$		0			0
$307$			12.0000i			0.684876i	0.939540	+	0.342438i	$0.111253\pi$
$307$			12.0000i			0.684876i	−0.939540	+	0.342438i	$0.888747\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−12.1244	−	7.00000i	−0.685309	−	0.395663i	0.116543	−	0.993186i	$-0.462819\pi$
$313$	−12.1244	−	7.00000i	−0.685309	−	0.395663i	−0.801852	+	0.597522i	$0.796152\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.1244	+	7.00000i	0.680972	+	0.393159i	0.800221	−	0.599705i	$-0.204715\pi$
$317$	12.1244	+	7.00000i	0.680972	+	0.393159i	−0.119249	+	0.992864i	$0.538049\pi$
$318$		0			0
$319$	−12.0000	−	20.7846i	−0.671871	−	1.16371i
$320$		0			0
$321$	6.00000			0.334887
$322$		0			0
$323$			12.0000i			0.667698i
$324$		0			0
$325$	−3.58846	+	29.7846i	−0.199052	+	1.65215i
$326$		0			0
$327$	12.1244	+	7.00000i	0.670478	+	0.387101i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$		0			0
$333$	−3.46410	+	2.00000i	−0.189832	+	0.109599i
$334$		0			0
$335$	4.00000	+	8.00000i	0.218543	+	0.437087i
$336$		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
$339$	−9.00000	−	15.5885i	−0.488813	−	0.846649i
$340$		0			0
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.267949	−	4.46410i	0.0144259	−	0.240339i
$346$		0			0
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	−0.856186	−	0.516667i	$-0.827172\pi$
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	0.0193540	+	0.999813i	$0.493839\pi$
$348$		0			0
$349$	−22.0000			−1.17763			−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000			−1.17763			−0.588817	+	0.808267i	$0.700406\pi$
$350$		0			0
$351$	6.00000			0.320256
$352$		0			0
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	−0.545385	−	0.838186i	$-0.683617\pi$
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	0.453197	+	0.891410i	$0.350283\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$		0			0
$363$		−	5.00000i		−	0.262432i
$364$		0			0
$365$	10.0000	+	20.0000i	0.523424	+	1.04685i
$366$		0			0
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	−0.0926670	−	0.995697i	$-0.529539\pi$
$367$	13.8564	−	8.00000i	0.723299	−	0.417597i	0.815966	+	0.578101i	$0.196206\pi$
$368$		0			0
$369$	4.00000	−	6.92820i	0.208232	−	0.360668i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	20.7846	+	12.0000i	1.07619	+	0.621336i	0.929865	−	0.367901i	$-0.119923\pi$
$373$	20.7846	+	12.0000i	1.07619	+	0.621336i	0.146321	+	0.989237i	$0.453257\pi$
$374$		0			0
$375$	−3.76795	−	10.5263i	−0.194576	−	0.543575i
$376$		0			0
$377$			36.0000i			1.85409i
$378$		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
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$		0			0
$383$	−24.2487	−	14.0000i	−1.23905	−	0.715367i	−0.270151	−	0.962818i	$-0.587074\pi$
$383$	−24.2487	−	14.0000i	−1.23905	−	0.715367i	−0.968900	+	0.247451i	$0.920407\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.46410	−	2.00000i	−0.176090	−	0.101666i
$388$		0			0
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	0.890263	−	0.455448i	$-0.150521\pi$
$389$	1.00000	+	1.73205i	0.0507020	+	0.0878185i	−0.839561	+	0.543266i	$0.817187\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		0			0
$393$			12.0000i			0.605320i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.66025	−	5.00000i	−0.434646	−	0.250943i	0.266678	−	0.963786i	$-0.414074\pi$
$397$	−8.66025	−	5.00000i	−0.434646	−	0.250943i	−0.701324	+	0.712843i	$0.747407\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.0000	+	19.0526i	−0.549314	+	0.951439i	0.449008	+	0.893528i	$0.351777\pi$
$401$	−11.0000	+	19.0526i	−0.549314	+	0.951439i	−0.998322	+	0.0579116i	$0.981556\pi$
$402$		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
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−35.7128	−	2.14359i	−1.75307	−	0.105225i
$416$		0			0
$417$	8.66025	−	5.00000i	0.424094	−	0.244851i
$418$		0			0
$419$	40.0000			1.95413			0.977064	−	0.212946i	$-0.0683059\pi$
$419$	40.0000			1.95413			0.977064	+	0.212946i	$0.0683059\pi$
$420$		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
$429$	−12.0000	+	20.7846i	−0.579365	+	1.00349i
$430$		0			0
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$		0			0
$433$		−	10.0000i		−	0.480569i	−0.970702	−	0.240285i	$-0.922759\pi$
$433$		−	10.0000i		−	0.480569i	0.970702	−	0.240285i	$-0.0772408\pi$
$434$		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
$439$	−15.0000	+	25.9808i	−0.715911	+	1.23999i	0.246696	+	0.969093i	$0.420655\pi$
$439$	−15.0000	+	25.9808i	−0.715911	+	1.23999i	−0.962607	+	0.270901i	$0.912678\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.9808	+	15.0000i	1.23438	+	0.712672i	0.967941	−	0.251179i	$-0.0808184\pi$
$443$	25.9808	+	15.0000i	1.23438	+	0.712672i	0.266443	+	0.963851i	$0.414152\pi$
$444$		0			0
$445$	−14.9282	−	9.85641i	−0.707665	−	0.467238i
$446$		0			0
$447$			22.0000i			1.04056i
$448$		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
$451$	16.0000	+	27.7128i	0.753411	+	1.30495i
$452$		0			0
$453$	13.8564	+	8.00000i	0.651031	+	0.375873i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.3205	+	10.0000i	0.810219	+	0.467780i	0.847032	−	0.531542i	$-0.178387\pi$
$457$	17.3205	+	10.0000i	0.810219	+	0.467780i	−0.0368128	+	0.999322i	$0.511721\pi$
$458$		0			0
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$	−2.46410	+	3.73205i	−0.114270	+	0.173070i
$466$		0			0
$467$	10.3923	+	6.00000i	0.480899	+	0.277647i	0.720791	−	0.693153i	$-0.243779\pi$
$467$	10.3923	+	6.00000i	0.480899	+	0.277647i	−0.239892	+	0.970799i	$0.577112\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$		0			0
$473$	13.8564	−	8.00000i	0.637118	−	0.367840i
$474$		0			0
$475$	−18.0000	+	24.0000i	−0.825897	+	1.10120i
$476$		0			0
$477$		−	6.00000i		−	0.274721i
$478$		0			0
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	0.816711	−	0.577047i	$-0.195795\pi$
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	−0.908093	+	0.418769i	$0.862462\pi$
$480$		0			0
$481$	−12.0000	+	20.7846i	−0.547153	+	0.947697i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.3205	−	1.33975i	−1.01352	−	0.0608347i
$486$		0			0
$487$	10.3923	−	6.00000i	0.470920	−	0.271886i	−0.245705	−	0.969345i	$-0.579019\pi$
$487$	10.3923	−	6.00000i	0.470920	−	0.271886i	0.716625	+	0.697459i	$0.245686\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		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
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	0.109965	+	0.993935i	$0.464926\pi$
$499$	−18.0000	+	31.1769i	−0.805791	+	1.39567i	−0.915756	+	0.401735i	$0.868407\pi$
$500$		0			0
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$		0			0
$503$			36.0000i			1.60516i	0.596544	+	0.802580i	$0.296540\pi$
$503$			36.0000i			1.60516i	−0.596544	+	0.802580i	$0.703460\pi$
$504$		0			0
$505$	−32.0000	+	16.0000i	−1.42398	+	0.711991i
$506$		0			0
$507$	19.9186	−	11.5000i	0.884615	−	0.510733i
$508$		0			0
$509$	6.00000	−	10.3923i	0.265945	−	0.460631i	−0.701866	−	0.712309i	$-0.747649\pi$
$509$	6.00000	−	10.3923i	0.265945	−	0.460631i	0.967811	+	0.251679i	$0.0809826\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.19615	+	3.00000i	0.229416	+	0.132453i
$514$		0			0
$515$	−19.7128	+	29.8564i	−0.868650	+	1.31563i
$516$		0			0
$517$			16.0000i			0.703679i
$518$		0			0
$519$	−2.00000			−0.0877903
$520$		0			0
$521$	22.0000	+	38.1051i	0.963837	+	1.66942i	0.712706	+	0.701462i	$0.247469\pi$
$521$	22.0000	+	38.1051i	0.963837	+	1.66942i	0.251131	+	0.967953i	$0.419197\pi$
$522$		0			0
$523$	17.3205	+	10.0000i	0.757373	+	0.437269i	0.828352	−	0.560208i	$-0.189279\pi$
$523$	17.3205	+	10.0000i	0.757373	+	0.437269i	−0.0709788	+	0.997478i	$0.522612\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.46410	−	2.00000i	−0.150899	−	0.0871214i
$528$		0			0
$529$	−9.50000	−	16.4545i	−0.413043	−	0.715412i
$530$		0			0
$531$	4.00000			0.173585
$532$		0			0
$533$		−	48.0000i		−	2.07911i
$534$		0			0
$535$	−7.39230	+	11.1962i	−0.319597	+	0.484052i
$536$		0			0
$537$	−3.46410	−	2.00000i	−0.149487	−	0.0863064i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−5.00000	+	8.66025i	−0.214967	+	0.372333i	−0.953262	−	0.302144i	$-0.902298\pi$
$541$	−5.00000	+	8.66025i	−0.214967	+	0.372333i	0.738296	+	0.674477i	$0.235631\pi$
$542$		0			0
$543$	8.66025	−	5.00000i	0.371647	−	0.214571i
$544$		0			0
$545$	−28.0000	+	14.0000i	−1.19939	+	0.599694i
$546$		0			0
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$		0			0
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$		0			0
$551$	−18.0000	+	31.1769i	−0.766826	+	1.32818i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.535898	−	8.92820i	0.0227476	−	0.378981i
$556$		0			0
$557$	−5.19615	+	3.00000i	−0.220168	+	0.127114i	−0.606028	−	0.795443i	$-0.707238\pi$
$557$	−5.19615	+	3.00000i	−0.220168	+	0.127114i	0.385860	+	0.922557i	$0.373905\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$		0			0
$561$	8.00000			0.337760
$562$		0			0
$563$	34.6410	−	20.0000i	1.45994	−	0.842900i	0.460937	−	0.887433i	$-0.347513\pi$
$563$	34.6410	−	20.0000i	1.45994	−	0.842900i	0.999008	+	0.0445334i	$0.0141801\pi$
$564$		0			0
$565$	40.1769	+	2.41154i	1.69026	+	0.101454i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.00000	+	6.00000i	0.333623	+	0.250217i
$576$		0			0
$577$	−32.9090	+	19.0000i	−1.37002	+	0.790980i	−0.990930	−	0.134380i	$-0.957096\pi$
$577$	−32.9090	+	19.0000i	−1.37002	+	0.790980i	−0.379088	+	0.925361i	$0.623762\pi$
$578$		0			0
$579$	−4.00000	+	6.92820i	−0.166234	+	0.287926i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	20.7846	+	12.0000i	0.860811	+	0.496989i
$584$		0			0
$585$	−7.39230	+	11.1962i	−0.305634	+	0.462904i
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$		0			0
$591$	5.00000	+	8.66025i	0.205673	+	0.356235i
$592$		0			0
$593$	−15.5885	−	9.00000i	−0.640141	−	0.369586i	0.144528	−	0.989501i	$-0.453834\pi$
$593$	−15.5885	−	9.00000i	−0.640141	−	0.369586i	−0.784669	+	0.619915i	$0.787167\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−15.5885	−	9.00000i	−0.637993	−	0.368345i
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$		0			0
$605$	9.33013	+	6.16025i	0.379324	+	0.250450i
$606$		0			0
$607$	34.6410	+	20.0000i	1.40604	+	0.811775i	0.995003	−	0.0998457i	$-0.0318349\pi$
$607$	34.6410	+	20.0000i	1.40604	+	0.811775i	0.411033	+	0.911621i	$0.365168\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.0000	−	20.7846i	0.485468	−	0.840855i
$612$		0			0
$613$	38.1051	−	22.0000i	1.53905	−	0.888572i	0.540157	−	0.841564i	$-0.318365\pi$
$613$	38.1051	−	22.0000i	1.53905	−	0.888572i	0.998895	−	0.0470071i	$-0.0149684\pi$
$614$		0			0
$615$	8.00000	+	16.0000i	0.322591	+	0.645182i
$616$		0			0
$617$			34.0000i			1.36879i	0.729112	+	0.684394i	$0.239933\pi$
$617$			34.0000i			1.36879i	−0.729112	+	0.684394i	$0.760067\pi$
$618$		0			0
$619$	13.0000	+	22.5167i	0.522514	+	0.905021i	0.999657	+	0.0261952i	$0.00833914\pi$
$619$	13.0000	+	22.5167i	0.522514	+	0.905021i	−0.477143	+	0.878826i	$0.658328\pi$
$620$		0			0
$621$	1.00000	−	1.73205i	0.0401286	−	0.0695048i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$		0			0
$627$	−20.7846	+	12.0000i	−0.830057	+	0.479234i
$628$		0			0
$629$	8.00000			0.318981
$630$		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
$633$	20.7846	−	12.0000i	0.826114	−	0.476957i
$634$		0			0
$635$	35.7128	+	2.14359i	1.41722	+	0.0850659i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	0.845601	−	0.533816i	$-0.179242\pi$
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	−0.885098	+	0.465404i	$0.845909\pi$
$642$		0			0
$643$		−	12.0000i		−	0.473234i	−0.971603	−	0.236617i	$-0.923961\pi$
$643$		−	12.0000i		−	0.473234i	0.971603	−	0.236617i	$-0.0760386\pi$
$644$		0			0
$645$	8.00000	−	4.00000i	0.315000	−	0.157500i
$646$		0			0
$647$	20.7846	−	12.0000i	0.817127	−	0.471769i	−0.0322975	−	0.999478i	$-0.510282\pi$
$647$	20.7846	−	12.0000i	0.817127	−	0.471769i	0.849425	+	0.527710i	$0.176949\pi$
$648$		0			0
$649$	−8.00000	+	13.8564i	−0.314027	+	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	29.4449	+	17.0000i	1.15227	+	0.665261i	0.949439	−	0.313953i	$-0.101653\pi$
$653$	29.4449	+	17.0000i	1.15227	+	0.665261i	0.202828	+	0.979214i	$0.434987\pi$
$654$		0			0
$655$	−22.3923	−	14.7846i	−0.874940	−	0.577683i
$656$		0			0
$657$			10.0000i			0.390137i
$658$		0			0
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$		0			0
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.3923	+	6.00000i	0.402392	+	0.232321i
$668$		0			0
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$		0			0
$671$	−56.0000			−2.16186
$672$		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
$677$	32.9090	+	19.0000i	1.26479	+	0.730229i	0.973998	−	0.226556i	$-0.0727465\pi$
$677$	32.9090	+	19.0000i	1.26479	+	0.730229i	0.290796	+	0.956785i	$0.406080\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$		0			0
$683$	22.5167	−	13.0000i	0.861576	−	0.497431i	−0.00296369	−	0.999996i	$-0.500943\pi$
$683$	22.5167	−	13.0000i	0.861576	−	0.497431i	0.864540	+	0.502564i	$0.167610\pi$
$684$		0			0
$685$	18.0000	+	36.0000i	0.687745	+	1.37549i
$686$		0			0
$687$			2.00000i			0.0763048i
$688$		0			0
$689$	−18.0000	−	31.1769i	−0.685745	−	1.18775i
$690$		0			0
$691$	1.00000	−	1.73205i	0.0380418	−	0.0658903i	−0.846378	−	0.532583i	$-0.821221\pi$
$691$	1.00000	−	1.73205i	0.0380418	−	0.0658903i	0.884419	+	0.466693i	$0.154555\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.33975	+	22.3205i	−0.0508195	+	0.846665i
$696$		0			0
$697$	−13.8564	+	8.00000i	−0.524849	+	0.303022i
$698$		0			0
$699$	−26.0000			−0.983410
$700$		0			0
$701$	38.0000			1.43524			0.717620	−	0.696435i	$-0.245231\pi$
$701$	38.0000			1.43524			0.717620	+	0.696435i	$0.245231\pi$
$702$		0			0
$703$	−20.7846	+	12.0000i	−0.783906	+	0.452589i
$704$		0			0
$705$	−0.535898	+	8.92820i	−0.0201831	+	0.336256i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	−0.916845	−	0.399244i	$-0.869273\pi$
$709$	−3.00000	+	5.19615i	−0.112667	+	0.195146i	0.804178	+	0.594389i	$0.202606\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$	−24.0000	−	48.0000i	−0.897549	−	1.79510i
$716$		0			0
$717$	−13.8564	+	8.00000i	−0.517477	+	0.298765i
$718$		0			0
$719$	22.0000	−	38.1051i	0.820462	−	1.42108i	−0.0848774	−	0.996391i	$-0.527050\pi$
$719$	22.0000	−	38.1051i	0.820462	−	1.42108i	0.905339	−	0.424690i	$-0.139617\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	8.66025	+	5.00000i	0.322078	+	0.185952i
$724$		0			0
$725$	29.7846	+	3.58846i	1.10617	+	0.133272i
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	−29.4449	−	17.0000i	−1.08757	−	0.627909i	−0.154642	−	0.987971i	$-0.549422\pi$
$733$	−29.4449	−	17.0000i	−1.08757	−	0.627909i	−0.932929	+	0.360061i	$0.882756\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−13.8564	−	8.00000i	−0.510407	−	0.294684i
$738$		0			0
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$	36.0000			1.32249
$742$		0			0
$743$		−	54.0000i		−	1.98107i	−0.137268	−	0.990534i	$-0.543832\pi$
$743$		−	54.0000i		−	1.98107i	0.137268	−	0.990534i	$-0.456168\pi$
$744$		0			0
$745$	−41.0526	−	27.1051i	−1.50405	−	0.993055i
$746$		0			0
$747$	−13.8564	−	8.00000i	−0.506979	−	0.292705i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$		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
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	12.0000	−	20.7846i	0.435000	−	0.753442i	−0.562296	−	0.826936i	$-0.690082\pi$
$761$	12.0000	−	20.7846i	0.435000	−	0.753442i	0.997296	+	0.0734946i	$0.0234152\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	4.46410	+	0.267949i	0.161400	+	0.00968772i
$766$		0			0
$767$	20.7846	−	12.0000i	0.750489	−	0.433295i
$768$		0			0
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	−5.19615	+	3.00000i	−0.186893	+	0.107903i	−0.590527	−	0.807018i	$-0.701080\pi$
$773$	−5.19615	+	3.00000i	−0.186893	+	0.107903i	0.403634	+	0.914920i	$0.367747\pi$
$774$		0			0
$775$	−3.92820	−	9.19615i	−0.141105	−	0.330336i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	24.0000	−	41.5692i	0.859889	−	1.48937i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	6.00000i		−	0.214423i
$784$		0			0
$785$	10.0000	+	20.0000i	0.356915	+	0.713831i
$786$		0			0
$787$	3.46410	−	2.00000i	0.123482	−	0.0712923i	−0.436987	−	0.899468i	$-0.643954\pi$
$787$	3.46410	−	2.00000i	0.123482	−	0.0712923i	0.560469	+	0.828176i	$0.310621\pi$
$788$		0			0
$789$	5.00000	−	8.66025i	0.178005	−	0.308313i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	72.7461	+	42.0000i	2.58329	+	1.49146i
$794$		0			0
$795$	11.1962	+	7.39230i	0.397087	+	0.262178i
$796$		0			0
$797$			34.0000i			1.20434i	0.798367	+	0.602171i	$0.205697\pi$
$797$			34.0000i			1.20434i	−0.798367	+	0.602171i	$0.794303\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$		0			0
$801$	−4.00000	−	6.92820i	−0.141333	−	0.244796i
$802$		0			0
$803$	−34.6410	−	20.0000i	−1.22245	−	0.705785i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.3923	+	6.00000i	0.365826	+	0.211210i
$808$		0			0
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	0.663316	−	0.748340i	$-0.269149\pi$
$809$	−9.00000	−	15.5885i	−0.316423	−	0.548061i	−0.979739	+	0.200279i	$0.935815\pi$
$810$		0			0
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$		0			0
$813$			14.0000i			0.491001i
$814$		0			0
$815$	9.85641	−	14.9282i	0.345255	−	0.522912i
$816$		0			0
$817$	−20.7846	−	12.0000i	−0.727161	−	0.419827i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	−0.939989	−	0.341206i	$-0.889165\pi$
$821$	−5.00000	+	8.66025i	−0.174501	+	0.302245i	0.765487	+	0.643451i	$0.222498\pi$
$822$		0			0
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	−0.0919029	−	0.995768i	$-0.529295\pi$
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	0.816409	+	0.577474i	$0.195962\pi$
$824$		0			0
$825$	16.0000	+	12.0000i	0.557048	+	0.417786i
$826$		0			0
$827$			22.0000i			0.765015i	0.923952	+	0.382507i	$0.124939\pi$
$827$			22.0000i			0.765015i	−0.923952	+	0.382507i	$0.875061\pi$
$828$		0			0
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	0.913409	−	0.407044i	$-0.133440\pi$
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	−0.809214	+	0.587513i	$0.800107\pi$
$830$		0			0
$831$	−14.0000	+	24.2487i	−0.485655	+	0.841178i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−53.5692	−	3.21539i	−1.85384	−	0.111273i
$836$		0			0
$837$	−1.73205	+	1.00000i	−0.0598684	+	0.0345651i
$838$		0			0
$839$	32.0000			1.10476			0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000			1.10476			0.552381	+	0.833592i	$0.313719\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	5.19615	−	3.00000i	0.178965	−	0.103325i
$844$		0			0
$845$	−3.08142	+	51.3372i	−0.106004	+	1.76605i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.0000	+	24.2487i	−0.480479	+	0.832214i
$850$		0			0
$851$	4.00000	+	6.92820i	0.137118	+	0.237496i
$852$		0			0
$853$		−	2.00000i		−	0.0684787i	−0.999414	−	0.0342393i	$-0.989099\pi$
$853$		−	2.00000i		−	0.0684787i	0.999414	−	0.0342393i	$-0.0109009\pi$
$854$		0			0
$855$	−12.0000	+	6.00000i	−0.410391	+	0.205196i
$856$		0			0
$857$	−5.19615	+	3.00000i	−0.177497	+	0.102478i	−0.586116	−	0.810227i	$-0.699344\pi$
$857$	−5.19615	+	3.00000i	−0.177497	+	0.102478i	0.408619	+	0.912705i	$0.366010\pi$
$858$		0			0
$859$	−23.0000	+	39.8372i	−0.784750	+	1.35923i	0.144399	+	0.989520i	$0.453875\pi$
$859$	−23.0000	+	39.8372i	−0.784750	+	1.35923i	−0.929148	+	0.369707i	$0.879458\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.5885	−	9.00000i	−0.530637	−	0.306364i	0.210639	−	0.977564i	$-0.432446\pi$
$863$	−15.5885	−	9.00000i	−0.530637	−	0.306364i	−0.741276	+	0.671200i	$0.765779\pi$
$864$		0			0
$865$	2.46410	−	3.73205i	0.0837820	−	0.126894i
$866$		0			0
$867$		−	13.0000i		−	0.441503i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	12.0000	+	20.7846i	0.406604	+	0.704260i
$872$		0			0
$873$	−8.66025	−	5.00000i	−0.293105	−	0.169224i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−38.1051	−	22.0000i	−1.28672	−	0.742887i	−0.308651	−	0.951175i	$-0.599877\pi$
$877$	−38.1051	−	22.0000i	−1.28672	−	0.742887i	−0.978068	+	0.208288i	$0.933211\pi$
$878$		0			0
$879$	3.00000	+	5.19615i	0.101187	+	0.175262i
$880$		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
$883$		−	24.0000i		−	0.807664i	−0.914833	−	0.403832i	$-0.867678\pi$
$883$		−	24.0000i		−	0.807664i	0.914833	−	0.403832i	$-0.132322\pi$
$884$		0			0
$885$	−4.92820	+	7.46410i	−0.165660	+	0.250903i
$886$		0			0
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	0.664218	−	0.747539i	$-0.268765\pi$
$887$	10.3923	+	6.00000i	0.348939	+	0.201460i	−0.315279	+	0.948999i	$0.602098\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$		0			0
$893$	20.7846	−	12.0000i	0.695530	−	0.401565i
$894$		0			0
$895$	8.00000	−	4.00000i	0.267411	−	0.133705i
$896$		0			0
$897$		−	12.0000i		−	0.400668i
$898$		0			0
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$		0			0
$901$	−6.00000	+	10.3923i	−0.199889	+	0.346218i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.33975	+	22.3205i	−0.0445347	+	0.741959i
$906$		0			0
$907$	−20.7846	+	12.0000i	−0.690142	+	0.398453i	−0.803665	−	0.595082i	$-0.797120\pi$
$907$	−20.7846	+	12.0000i	−0.690142	+	0.398453i	0.113523	+	0.993535i	$0.463786\pi$
$908$		0			0
$909$	−16.0000			−0.530687
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$		0			0
$913$	55.4256	−	32.0000i	1.83432	−	1.05905i
$914$		0			0
$915$	−31.2487	−	1.87564i	−1.03305	−	0.0620069i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.0000	−	31.1769i	0.593765	−	1.02843i	−0.399955	−	0.916535i	$-0.630974\pi$
$919$	18.0000	−	31.1769i	0.593765	−	1.02843i	0.993720	−	0.111897i	$-0.0356925\pi$
$920$		0			0
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	16.0000	+	12.0000i	0.526077	+	0.394558i
$926$		0			0
$927$	−13.8564	+	8.00000i	−0.455104	+	0.262754i
$928$		0			0
$929$	12.0000	−	20.7846i	0.393707	−	0.681921i	−0.599228	−	0.800578i	$-0.704526\pi$
$929$	12.0000	−	20.7846i	0.393707	−	0.681921i	0.992935	+	0.118657i	$0.0378590\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	10.3923	+	6.00000i	0.340229	+	0.196431i
$934$		0			0
$935$	−9.85641	+	14.9282i	−0.322339	+	0.488204i
$936$		0			0
$937$			14.0000i			0.457360i	0.973502	+	0.228680i	$0.0734410\pi$
$937$			14.0000i			0.457360i	−0.973502	+	0.228680i	$0.926559\pi$
$938$		0			0
$939$	14.0000			0.456873
$940$		0			0
$941$	−22.0000	−	38.1051i	−0.717180	−	1.24219i	−0.962113	−	0.272651i	$-0.912099\pi$
$941$	−22.0000	−	38.1051i	−0.717180	−	1.24219i	0.244933	−	0.969540i	$-0.421234\pi$
$942$		0			0
$943$	−13.8564	−	8.00000i	−0.451227	−	0.260516i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.19615	+	3.00000i	0.168852	+	0.0974869i	0.582045	−	0.813157i	$-0.302253\pi$
$947$	5.19615	+	3.00000i	0.168852	+	0.0974869i	−0.413192	+	0.910644i	$0.635586\pi$
$948$		0			0
$949$	30.0000	+	51.9615i	0.973841	+	1.68674i
$950$		0			0
$951$	−14.0000			−0.453981
$952$		0			0
$953$		−	14.0000i		−	0.453504i	−0.973952	−	0.226752i	$-0.927189\pi$
$953$		−	14.0000i		−	0.453504i	0.973952	−	0.226752i	$-0.0728108\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	20.7846	+	12.0000i	0.671871	+	0.387905i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$	−5.19615	+	3.00000i	−0.167444	+	0.0966736i
$964$		0			0
$965$	−8.00000	−	16.0000i	−0.257529	−	0.515058i
$966$		0			0
$967$			20.0000i			0.643157i	0.946883	+	0.321578i	$0.104213\pi$
$967$			20.0000i			0.643157i	−0.946883	+	0.321578i	$0.895787\pi$
$968$		0			0
$969$	−6.00000	−	10.3923i	−0.192748	−	0.333849i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−11.7846	−	27.5885i	−0.377410	−	0.883538i
$976$		0			0
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	−0.229465	−	0.973317i	$-0.573698\pi$
$977$	15.5885	−	9.00000i	0.498719	−	0.287936i	0.728184	+	0.685381i	$0.240364\pi$
$978$		0			0
$979$	32.0000			1.02272
$980$		0			0
$981$	−14.0000			−0.446986
$982$		0			0
$983$	−6.92820	+	4.00000i	−0.220975	+	0.127580i	−0.606402	−	0.795158i	$-0.707388\pi$
$983$	−6.92820	+	4.00000i	−0.220975	+	0.127580i	0.385426	+	0.922739i	$0.374054\pi$
$984$		0			0
$985$	−22.3205	−	1.33975i	−0.711191	−	0.0426879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$		0			0
$991$	−26.0000	−	45.0333i	−0.825917	−	1.43053i	−0.901216	−	0.433370i	$-0.857324\pi$
$991$	−26.0000	−	45.0333i	−0.825917	−	1.43053i	0.0752991	−	0.997161i	$-0.476009\pi$
$992$		0			0
$993$			8.00000i			0.253872i
$994$		0			0
$995$	36.0000	−	18.0000i	1.14128	−	0.570638i
$996$		0			0
$997$	15.5885	−	9.00000i	0.493691	−	0.285033i	−0.232413	−	0.972617i	$-0.574662\pi$
$997$	15.5885	−	9.00000i	0.493691	−	0.285033i	0.726105	+	0.687584i	$0.241329\pi$
$998$		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.h.1549.1		4
5.4	even	2	inner	2940.2.bb.h.1549.2		4
7.2	even	3		420.2.k.a.169.1	✓	2
7.3	odd	6		2940.2.bb.c.949.1		4
7.4	even	3	inner	2940.2.bb.h.949.2		4
7.5	odd	6		2940.2.k.d.589.2		2
7.6	odd	2		2940.2.bb.c.1549.2		4
21.2	odd	6		1260.2.k.d.1009.1		2
28.23	odd	6		1680.2.t.a.1009.2		2
35.2	odd	12		2100.2.a.e.1.1		1
35.4	even	6	inner	2940.2.bb.h.949.1		4
35.9	even	6		420.2.k.a.169.2	yes	2
35.19	odd	6		2940.2.k.d.589.1		2
35.23	odd	12		2100.2.a.j.1.1		1
35.24	odd	6		2940.2.bb.c.949.2		4
35.34	odd	2		2940.2.bb.c.1549.1		4
84.23	even	6		5040.2.t.o.1009.1		2
105.2	even	12		6300.2.a.bc.1.1		1
105.23	even	12		6300.2.a.n.1.1		1
105.44	odd	6		1260.2.k.d.1009.2		2
140.23	even	12		8400.2.a.bh.1.1		1
140.79	odd	6		1680.2.t.a.1009.1		2
140.107	even	12		8400.2.a.cd.1.1		1
420.359	even	6		5040.2.t.o.1009.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.k.a.169.1	✓	2	7.2	even	3
420.2.k.a.169.2	yes	2	35.9	even	6
1260.2.k.d.1009.1		2	21.2	odd	6
1260.2.k.d.1009.2		2	105.44	odd	6
1680.2.t.a.1009.1		2	140.79	odd	6
1680.2.t.a.1009.2		2	28.23	odd	6
2100.2.a.e.1.1		1	35.2	odd	12
2100.2.a.j.1.1		1	35.23	odd	12
2940.2.k.d.589.1		2	35.19	odd	6
2940.2.k.d.589.2		2	7.5	odd	6
2940.2.bb.c.949.1		4	7.3	odd	6
2940.2.bb.c.949.2		4	35.24	odd	6
2940.2.bb.c.1549.1		4	35.34	odd	2
2940.2.bb.c.1549.2		4	7.6	odd	2
2940.2.bb.h.949.1		4	35.4	even	6	inner
2940.2.bb.h.949.2		4	7.4	even	3	inner
2940.2.bb.h.1549.1		4	1.1	even	1	trivial
2940.2.bb.h.1549.2		4	5.4	even	2	inner
5040.2.t.o.1009.1		2	84.23	even	6
5040.2.t.o.1009.2		2	420.359	even	6
6300.2.a.n.1.1		1	105.23	even	12
6300.2.a.bc.1.1		1	105.2	even	12
8400.2.a.bh.1.1		1	140.23	even	12
8400.2.a.cd.1.1		1	140.107	even	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.133975 - 2.23205i) q^{5} +(0.500000 - 0.866025i) q^{9} +(2.00000 + 3.46410i) q^{11} -6.00000i q^{13} +(1.00000 + 2.00000i) q^{15} +(-1.73205 + 1.00000i) q^{17} +(3.00000 - 5.19615i) q^{19} +(-1.73205 - 1.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +1.00000i q^{27} -6.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-3.46410 - 2.00000i) q^{33} +(-3.46410 - 2.00000i) q^{37} +(3.00000 + 5.19615i) q^{39} +8.00000 q^{41} -4.00000i q^{43} +(-1.86603 - 1.23205i) q^{45} +(3.46410 + 2.00000i) q^{47} +(1.00000 - 1.73205i) q^{51} +(5.19615 - 3.00000i) q^{53} +(8.00000 - 4.00000i) q^{55} +6.00000i q^{57} +(2.00000 + 3.46410i) q^{59} +(-7.00000 + 12.1244i) q^{61} +(-13.3923 - 0.803848i) q^{65} +(-3.46410 + 2.00000i) q^{67} +2.00000 q^{69} +(-8.66025 + 5.00000i) q^{73} +(4.59808 - 1.96410i) q^{75} +(-0.500000 - 0.866025i) q^{81} -16.0000i q^{83} +(2.00000 + 4.00000i) q^{85} +(5.19615 - 3.00000i) q^{87} +(4.00000 - 6.92820i) q^{89} +(-1.73205 - 1.00000i) q^{93} +(-11.1962 - 7.39230i) q^{95} -10.0000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} + 2 q^{9} + 8 q^{11} + 4 q^{15} + 12 q^{19} - 6 q^{25} - 24 q^{29} + 4 q^{31} + 12 q^{39} + 32 q^{41} - 4 q^{45} + 4 q^{51} + 32 q^{55} + 8 q^{59} - 28 q^{61} - 12 q^{65} + 8 q^{69} + 8 q^{75}+ \cdots + 16 q^{99}+O(q^{100}) \) 4 * q + 4 * q^5 + 2 * q^9 + 8 * q^11 + 4 * q^15 + 12 * q^19 - 6 * q^25 - 24 * q^29 + 4 * q^31 + 12 * q^39 + 32 * q^41 - 4 * q^45 + 4 * q^51 + 32 * q^55 + 8 * q^59 - 28 * q^61 - 12 * q^65 + 8 * q^69 + 8 * q^75 - 2 * q^81 + 8 * q^85 + 16 * q^89 - 24 * q^95 + 16 * q^99

Introduction

L-functions

Modular forms

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