LMFDB - Embedded newform 2940.2.bb.d.949.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(949,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("2940.949");

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$4$
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 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2940.949
Dual form			2940.2.bb.d.1549.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-2.23205 + 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.866025 + 0.500000i) q^{3} +(-2.23205 + 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(-2.00000 - 1.00000i) q^{15} +(-3.46410 - 2.00000i) q^{17} +(-3.46410 + 2.00000i) q^{23} +(4.96410 - 0.598076i) q^{25} +1.00000i q^{27} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.46410 - 2.00000i) q^{33} +(-6.92820 + 4.00000i) q^{37} -10.0000 q^{41} -4.00000i q^{43} +(-1.23205 - 1.86603i) q^{45} +(-3.46410 + 2.00000i) q^{47} +(-2.00000 - 3.46410i) q^{51} +(-10.3923 - 6.00000i) q^{53} +(-4.00000 + 8.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(3.46410 + 2.00000i) q^{67} -4.00000 q^{69} +(-6.92820 - 4.00000i) q^{73} +(4.59808 + 1.96410i) q^{75} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.00000i q^{83} +(8.00000 + 4.00000i) q^{85} +(5.19615 + 3.00000i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-3.46410 + 2.00000i) q^{93} +8.00000i q^{97} +4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^5 + 2 * q^9	$ 4 q - 2 q^{5} + 2 q^{9} + 8 q^{11} - 8 q^{15} + 6 q^{25} + 24 q^{29} - 8 q^{31} - 40 q^{41} + 2 q^{45} - 8 q^{51} - 16 q^{55} + 8 q^{59} - 4 q^{61} - 16 q^{69} + 8 q^{75} - 24 q^{79} - 2 q^{81} + 32 q^{85} - 20 q^{89} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^5 + 2 * q^9 + 8 * q^11 - 8 * q^15 + 6 * q^25 + 24 * q^29 - 8 * q^31 - 40 * q^41 + 2 * q^45 - 8 * q^51 - 16 * q^55 + 8 * q^59 - 4 * q^61 - 16 * q^69 + 8 * q^75 - 24 * q^79 - 2 * q^81 + 32 * q^85 - 20 * q^89 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$	−2.23205	+	0.133975i	−0.998203	+	0.0599153i
$5$	−2.23205	+	0.133975i	−0.998203	+	0.0599153i
$6$		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	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$	−2.00000	−	1.00000i	−0.516398	−	0.258199i
$16$		0			0
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	0.0171533	−	0.999853i	$-0.494540\pi$
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	−0.857321	+	0.514782i	$0.827873\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	−0.815604	−	0.578610i	$-0.803595\pi$
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	0.0932891	+	0.995639i	$0.470262\pi$
$24$		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	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	3.46410	−	2.00000i	0.603023	−	0.348155i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.946180	−	0.323640i	$-0.895093\pi$
$37$	−6.92820	+	4.00000i	−1.13899	+	0.657596i	−0.192809	+	0.981236i	$0.561760\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$		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
$45$	−1.23205	−	1.86603i	−0.183663	−	0.278171i
$46$		0			0
$47$	−3.46410	+	2.00000i	−0.505291	+	0.291730i	−0.730896	−	0.682489i	$-0.760898\pi$
$47$	−3.46410	+	2.00000i	−0.505291	+	0.291730i	0.225605	+	0.974219i	$0.427564\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.430570	−	0.902557i	$-0.641688\pi$
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.996922	+	0.0783936i	$0.975021\pi$
$54$		0			0
$55$	−4.00000	+	8.00000i	−0.539360	+	1.07872i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		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
$65$		0			0
$66$		0			0
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	0.696449	−	0.717607i	$-0.254762\pi$
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	−0.273241	+	0.961946i	$0.588096\pi$
$68$		0			0
$69$	−4.00000			−0.481543
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−6.92820	−	4.00000i	−0.810885	−	0.468165i	0.0363782	−	0.999338i	$-0.488418\pi$
$73$	−6.92820	−	4.00000i	−0.810885	−	0.468165i	−0.847263	+	0.531174i	$0.821751\pi$
$74$		0			0
$75$	4.59808	+	1.96410i	0.530940	+	0.226795i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	−0.976453	−	0.215728i	$-0.930788\pi$
$79$	−6.00000	−	10.3923i	−0.675053	−	1.16923i	0.301401	−	0.953498i	$-0.402546\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	4.00000i		−	0.439057i	−0.975606	−	0.219529i	$-0.929548\pi$
$83$		−	4.00000i		−	0.439057i	0.975606	−	0.219529i	$-0.0704519\pi$
$84$		0			0
$85$	8.00000	+	4.00000i	0.867722	+	0.433861i
$86$		0			0
$87$	5.19615	+	3.00000i	0.557086	+	0.321634i
$88$		0			0
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	−0.999388	−	0.0349934i	$-0.988859\pi$
$89$	−5.00000	−	8.66025i	−0.529999	−	0.917985i	0.469389	−	0.882992i	$-0.344474\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			8.00000i			0.812277i	0.913812	+	0.406138i	$0.133125\pi$
$97$			8.00000i			0.812277i	−0.913812	+	0.406138i	$0.866875\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	−0.319531	−	0.947576i	$-0.603525\pi$
$103$	3.46410	−	2.00000i	0.341328	−	0.197066i	0.660859	+	0.750510i	$0.270192\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.0950377	−	0.995474i	$-0.469703\pi$
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.909624	+	0.415432i	$0.136370\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$		0			0
$111$	−8.00000			−0.759326
$112$		0			0
$113$		−	12.0000i		−	1.12887i	−0.825479	−	0.564433i	$-0.809095\pi$
$113$		−	12.0000i		−	1.12887i	0.825479	−	0.564433i	$-0.190905\pi$
$114$		0			0
$115$	7.46410	−	4.92820i	0.696031	−	0.459557i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$		0			0
$123$	−8.66025	−	5.00000i	−0.780869	−	0.450835i
$124$		0			0
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$		0			0
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$		0			0
$129$	2.00000	−	3.46410i	0.176090	−	0.304997i
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.133975	−	2.23205i	−0.0115307	−	0.192104i
$136$		0			0
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$	−4.00000			−0.336861
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−13.3923	+	0.803848i	−1.11217	+	0.0667559i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	0.822153	−	0.569267i	$-0.192773\pi$
$149$	−1.00000	−	1.73205i	−0.0819232	−	0.141895i	−0.904076	+	0.427372i	$0.859440\pi$
$150$		0			0
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	−0.0964061	−	0.995342i	$-0.530735\pi$
$151$	10.0000	−	17.3205i	0.813788	−	1.40952i	0.910195	−	0.414181i	$-0.135932\pi$
$152$		0			0
$153$		−	4.00000i		−	0.323381i
$154$		0			0
$155$	4.00000	−	8.00000i	0.321288	−	0.642575i
$156$		0			0
$157$	−6.92820	−	4.00000i	−0.552931	−	0.319235i	0.197372	−	0.980329i	$-0.436759\pi$
$157$	−6.92820	−	4.00000i	−0.552931	−	0.319235i	−0.750303	+	0.661094i	$0.770093\pi$
$158$		0			0
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−17.3205	+	10.0000i	−1.35665	+	0.783260i	−0.989170	−	0.146772i	$-0.953112\pi$
$163$	−17.3205	+	10.0000i	−1.35665	+	0.783260i	−0.367477	+	0.930033i	$0.619778\pi$
$164$		0			0
$165$	−7.46410	+	4.92820i	−0.581080	+	0.383660i
$166$		0			0
$167$			12.0000i			0.928588i	0.885681	+	0.464294i	$0.153692\pi$
$167$			12.0000i			0.928588i	−0.885681	+	0.464294i	$0.846308\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.46410	−	2.00000i	0.263371	−	0.152057i	−0.362500	−	0.931984i	$-0.618077\pi$
$173$	3.46410	−	2.00000i	0.263371	−	0.152057i	0.625871	+	0.779926i	$0.284744\pi$
$174$		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	−0.781551	−	0.623841i	$-0.785571\pi$
$179$	2.00000	−	3.46410i	0.149487	−	0.258919i	0.931038	+	0.364922i	$0.118904\pi$
$180$		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
$183$		−	2.00000i		−	0.147844i
$184$		0			0
$185$	14.9282	−	9.85641i	1.09754	−	0.724657i
$186$		0			0
$187$	−13.8564	+	8.00000i	−1.01328	+	0.585018i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$		0			0
$193$	13.8564	+	8.00000i	0.997406	+	0.575853i	0.907480	−	0.420096i	$-0.138004\pi$
$193$	13.8564	+	8.00000i	0.997406	+	0.575853i	0.0899262	+	0.995948i	$0.471337\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	4.00000i		−	0.284988i	−0.989796	−	0.142494i	$-0.954488\pi$
$197$		−	4.00000i		−	0.284988i	0.989796	−	0.142494i	$-0.0455122\pi$
$198$		0			0
$199$	−6.00000	+	10.3923i	−0.425329	+	0.736691i	−0.996451	−	0.0841740i	$-0.973175\pi$
$199$	−6.00000	+	10.3923i	−0.425329	+	0.736691i	0.571122	+	0.820865i	$0.306508\pi$
$200$		0			0
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	22.3205	−	1.33975i	1.55893	−	0.0935719i
$206$		0			0
$207$	−3.46410	−	2.00000i	−0.240772	−	0.139010i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.535898	+	8.92820i	0.0365480	+	0.608898i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−4.00000	−	6.92820i	−0.270295	−	0.468165i
$220$		0			0
$221$		0			0
$222$		0			0
$223$			20.0000i			1.33930i	0.742677	+	0.669650i	$0.233556\pi$
$223$			20.0000i			1.33930i	−0.742677	+	0.669650i	$0.766444\pi$
$224$		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	$-0.102309\pi$
$227$	17.3205	+	10.0000i	1.14960	+	0.663723i	0.200812	+	0.979630i	$0.435642\pi$
$228$		0			0
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	0.872823	+	0.488037i	$0.162287\pi$
$229$	13.0000	+	22.5167i	0.859064	+	1.48794i	−0.0137585	+	0.999905i	$0.504380\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.3205	+	10.0000i	−1.13470	+	0.655122i	−0.945114	−	0.326741i	$-0.894049\pi$
$233$	−17.3205	+	10.0000i	−1.13470	+	0.655122i	−0.189590	+	0.981863i	$0.560716\pi$
$234$		0			0
$235$	7.46410	−	4.92820i	0.486904	−	0.321481i
$236$		0			0
$237$		−	12.0000i		−	0.779484i
$238$		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
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	−0.832019	−	0.554747i	$-0.812815\pi$
$241$	1.00000	−	1.73205i	0.0644157	−	0.111571i	0.896435	+	0.443176i	$0.146148\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	2.00000	−	3.46410i	0.126745	−	0.219529i
$250$		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
$253$			16.0000i			1.00591i
$254$		0			0
$255$	4.92820	+	7.46410i	0.308616	+	0.467420i
$256$		0			0
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	−0.139533	−	0.990217i	$-0.544560\pi$
$257$	10.3923	−	6.00000i	0.648254	−	0.374270i	0.787787	+	0.615948i	$0.211227\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	3.46410	+	2.00000i	0.213606	+	0.123325i	0.602986	−	0.797752i	$-0.293977\pi$
$263$	3.46410	+	2.00000i	0.213606	+	0.123325i	−0.389380	+	0.921077i	$0.627311\pi$
$264$		0			0
$265$	24.0000	+	12.0000i	1.47431	+	0.737154i
$266$		0			0
$267$		−	10.0000i		−	0.611990i
$268$		0			0
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$		0			0
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	0.798865	−	0.601511i	$-0.205434\pi$
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	−0.920356	+	0.391082i	$0.872101\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.85641	−	18.3923i	0.473759	−	1.10910i
$276$		0			0
$277$	27.7128	+	16.0000i	1.66510	+	0.961347i	0.970221	+	0.242222i	$0.0778761\pi$
$277$	27.7128	+	16.0000i	1.66510	+	0.961347i	0.694881	+	0.719125i	$0.255457\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−24.2487	−	14.0000i	−1.44144	−	0.832214i	−0.443491	−	0.896279i	$-0.646260\pi$
$283$	−24.2487	−	14.0000i	−1.44144	−	0.832214i	−0.997946	+	0.0640654i	$0.979593\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$		0			0
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$		0			0
$295$	−4.00000	+	8.00000i	−0.232889	+	0.465778i
$296$		0			0
$297$	3.46410	+	2.00000i	0.201008	+	0.116052i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.73205	−	1.00000i	0.0995037	−	0.0574485i
$304$		0			0
$305$	2.46410	+	3.73205i	0.141094	+	0.213697i
$306$		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
$309$	4.00000			0.227552
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−13.8564	+	8.00000i	−0.783210	+	0.452187i	−0.837567	−	0.546335i	$-0.816023\pi$
$313$	−13.8564	+	8.00000i	−0.783210	+	0.452187i	0.0543564	+	0.998522i	$0.482689\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.46410	−	2.00000i	0.194563	−	0.112331i	−0.399554	−	0.916710i	$-0.630835\pi$
$317$	3.46410	−	2.00000i	0.194563	−	0.112331i	0.594117	+	0.804379i	$0.297502\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$		0			0
$321$	12.0000			0.669775
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$		0			0
$333$	−6.92820	−	4.00000i	−0.379663	−	0.219199i
$334$		0			0
$335$	−8.00000	−	4.00000i	−0.437087	−	0.218543i
$336$		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
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$		0			0
$341$	8.00000	+	13.8564i	0.433224	+	0.750366i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	8.92820	−	0.535898i	0.480678	−	0.0288518i
$346$		0			0
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−24.2487	−	14.0000i	−1.29063	−	0.745145i	−0.311863	−	0.950127i	$-0.600953\pi$
$353$	−24.2487	−	14.0000i	−1.29063	−	0.745145i	−0.978766	+	0.204982i	$0.934286\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$		0			0
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$		0			0
$363$		−	5.00000i		−	0.262432i
$364$		0			0
$365$	16.0000	+	8.00000i	0.837478	+	0.418739i
$366$		0			0
$367$	−3.46410	−	2.00000i	−0.180825	−	0.104399i	0.406855	−	0.913493i	$-0.366625\pi$
$367$	−3.46410	−	2.00000i	−0.180825	−	0.104399i	−0.587680	+	0.809093i	$0.699959\pi$
$368$		0			0
$369$	−5.00000	−	8.66025i	−0.260290	−	0.450835i
$370$		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
$375$	−10.5263	−	3.76795i	−0.543575	−	0.194576i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	−2.00000	+	3.46410i	−0.102463	+	0.177471i
$382$		0			0
$383$	24.2487	−	14.0000i	1.23905	−	0.715367i	0.270151	−	0.962818i	$-0.412926\pi$
$383$	24.2487	−	14.0000i	1.23905	−	0.715367i	0.968900	+	0.247451i	$0.0795931\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.46410	−	2.00000i	0.176090	−	0.101666i
$388$		0			0
$389$	−17.0000	+	29.4449i	−0.861934	+	1.49291i	0.00812520	+	0.999967i	$0.497414\pi$
$389$	−17.0000	+	29.4449i	−0.861934	+	1.49291i	−0.870059	+	0.492947i	$0.835920\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$		−	12.0000i		−	0.605320i
$394$		0			0
$395$	14.7846	+	22.3923i	0.743894	+	1.12668i
$396$		0			0
$397$	−6.92820	+	4.00000i	−0.347717	+	0.200754i	−0.663679	−	0.748017i	$-0.731006\pi$
$397$	−6.92820	+	4.00000i	−0.347717	+	0.200754i	0.315963	+	0.948772i	$0.397673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.00000	+	12.1244i	0.349563	+	0.605461i	0.986172	−	0.165726i	$-0.0529966\pi$
$401$	7.00000	+	12.1244i	0.349563	+	0.605461i	−0.636609	+	0.771187i	$0.719663\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	1.00000	−	2.00000i	0.0496904	−	0.0993808i
$406$		0			0
$407$			32.0000i			1.58618i
$408$		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
$411$	−6.00000	−	10.3923i	−0.295958	−	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.535898	+	8.92820i	0.0263062	+	0.438268i
$416$		0			0
$417$	−13.8564	−	8.00000i	−0.678551	−	0.391762i
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$		0			0
$423$	−3.46410	−	2.00000i	−0.168430	−	0.0972433i
$424$		0			0
$425$	−18.3923	−	7.85641i	−0.892158	−	0.381092i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	−0.946135	−	0.323772i	$-0.895049\pi$
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	0.753462	+	0.657491i	$0.228382\pi$
$432$		0			0
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$		0			0
$435$	−12.0000	−	6.00000i	−0.575356	−	0.287678i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−6.00000	−	10.3923i	−0.286364	−	0.495998i	0.686575	−	0.727059i	$-0.259113\pi$
$439$	−6.00000	−	10.3923i	−0.286364	−	0.495998i	−0.972939	+	0.231062i	$0.925780\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−31.1769	+	18.0000i	−1.48126	+	0.855206i	−0.999774	−	0.0212481i	$-0.993236\pi$
$443$	−31.1769	+	18.0000i	−1.48126	+	0.855206i	−0.481486	+	0.876454i	$0.659903\pi$
$444$		0			0
$445$	12.3205	+	18.6603i	0.584048	+	0.884581i
$446$		0			0
$447$		−	2.00000i		−	0.0945968i
$448$		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
$451$	−20.0000	+	34.6410i	−0.941763	+	1.63118i
$452$		0			0
$453$	17.3205	−	10.0000i	0.813788	−	0.469841i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	34.6410	−	20.0000i	1.62044	−	0.935561i	0.633636	−	0.773631i	$-0.281562\pi$
$457$	34.6410	−	20.0000i	1.62044	−	0.935561i	0.986802	−	0.161929i	$-0.0517716\pi$
$458$		0			0
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	6.00000			0.279448			0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000			0.279448			0.139724	+	0.990190i	$0.455378\pi$
$462$		0			0
$463$		−	12.0000i		−	0.557687i	−0.960337	−	0.278844i	$-0.910049\pi$
$463$		−	12.0000i		−	0.557687i	0.960337	−	0.278844i	$-0.0899511\pi$
$464$		0			0
$465$	7.46410	−	4.92820i	0.346139	−	0.228540i
$466$		0			0
$467$	10.3923	−	6.00000i	0.480899	−	0.277647i	−0.239892	−	0.970799i	$-0.577112\pi$
$467$	10.3923	−	6.00000i	0.480899	−	0.277647i	0.720791	+	0.693153i	$0.243779\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.00000	−	6.92820i	−0.184310	−	0.319235i
$472$		0			0
$473$	−13.8564	−	8.00000i	−0.637118	−	0.367840i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	12.0000i		−	0.549442i
$478$		0			0
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.07180	−	17.8564i	−0.0486678	−	0.810818i
$486$		0			0
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$		0			0
$489$	−20.0000			−0.904431
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$		0			0
$493$	−20.7846	−	12.0000i	−0.936092	−	0.540453i
$494$		0			0
$495$	−8.92820	+	0.535898i	−0.401293	+	0.0240868i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	12.0000	+	20.7846i	0.537194	+	0.930447i	0.999054	+	0.0434940i	$0.0138489\pi$
$499$	12.0000	+	20.7846i	0.537194	+	0.930447i	−0.461860	+	0.886953i	$0.652818\pi$
$500$		0			0
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$		0			0
$503$		−	36.0000i		−	1.60516i	−0.596544	−	0.802580i	$-0.703460\pi$
$503$		−	36.0000i		−	1.60516i	0.596544	−	0.802580i	$-0.296540\pi$
$504$		0			0
$505$	−2.00000	+	4.00000i	−0.0889988	+	0.177998i
$506$		0			0
$507$	11.2583	+	6.50000i	0.500000	+	0.288675i
$508$		0			0
$509$	21.0000	+	36.3731i	0.930809	+	1.61221i	0.781943	+	0.623350i	$0.214229\pi$
$509$	21.0000	+	36.3731i	0.930809	+	1.61221i	0.148866	+	0.988857i	$0.452438\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.46410	+	4.92820i	−0.328908	+	0.217163i
$516$		0			0
$517$			16.0000i			0.703679i
$518$		0			0
$519$	4.00000			0.175581
$520$		0			0
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	−0.0637207	−	0.997968i	$-0.520297\pi$
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	0.896126	−	0.443800i	$-0.146370\pi$
$522$		0			0
$523$	24.2487	−	14.0000i	1.06032	−	0.612177i	0.134801	−	0.990873i	$-0.456961\pi$
$523$	24.2487	−	14.0000i	1.06032	−	0.612177i	0.925521	+	0.378695i	$0.123627\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.8564	−	8.00000i	0.603595	−	0.348485i
$528$		0			0
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	4.00000			0.173585
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−22.3923	+	14.7846i	−0.968104	+	0.639194i
$536$		0			0
$537$	3.46410	−	2.00000i	0.149487	−	0.0863064i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	0.886721	−	0.462304i	$-0.152977\pi$
$541$	1.00000	+	1.73205i	0.0429934	+	0.0744667i	−0.843728	+	0.536771i	$0.819644\pi$
$542$		0			0
$543$	−8.66025	−	5.00000i	−0.371647	−	0.214571i
$544$		0			0
$545$	2.00000	−	4.00000i	0.0856706	−	0.171341i
$546$		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
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	17.8564	−	1.07180i	0.757962	−	0.0454952i
$556$		0			0
$557$	10.3923	+	6.00000i	0.440336	+	0.254228i	0.703740	−	0.710457i	$-0.251512\pi$
$557$	10.3923	+	6.00000i	0.440336	+	0.254228i	−0.263404	+	0.964686i	$0.584845\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−16.0000			−0.675521
$562$		0			0
$563$	17.3205	+	10.0000i	0.729972	+	0.421450i	0.818412	−	0.574632i	$-0.194855\pi$
$563$	17.3205	+	10.0000i	0.729972	+	0.421450i	−0.0884397	+	0.996082i	$0.528188\pi$
$564$		0			0
$565$	1.60770	+	26.7846i	0.0676362	+	1.12684i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	0.998608	+	0.0527519i	$0.0167993\pi$
$569$	13.0000	+	22.5167i	0.544988	+	0.943948i	−0.453619	+	0.891196i	$0.649867\pi$
$570$		0			0
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	0.0554391	+	0.998462i	$0.482344\pi$
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	−0.892413	+	0.451219i	$0.850989\pi$
$572$		0			0
$573$		−	24.0000i		−	1.00261i
$574$		0			0
$575$	−16.0000	+	12.0000i	−0.667246	+	0.500435i
$576$		0			0
$577$	27.7128	+	16.0000i	1.15370	+	0.666089i	0.949786	−	0.312900i	$-0.101301\pi$
$577$	27.7128	+	16.0000i	1.15370	+	0.666089i	0.203913	+	0.978989i	$0.434634\pi$
$578$		0			0
$579$	8.00000	+	13.8564i	0.332469	+	0.575853i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−41.5692	+	24.0000i	−1.72162	+	0.993978i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	2.00000	−	3.46410i	0.0822690	−	0.142494i
$592$		0			0
$593$	31.1769	−	18.0000i	1.28028	−	0.739171i	0.303383	−	0.952869i	$-0.401884\pi$
$593$	31.1769	−	18.0000i	1.28028	−	0.739171i	0.976900	+	0.213697i	$0.0685507\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−10.3923	+	6.00000i	−0.425329	+	0.245564i
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$		0			0
$603$			4.00000i			0.162893i
$604$		0			0
$605$	6.16025	+	9.33013i	0.250450	+	0.379324i
$606$		0			0
$607$	−24.2487	+	14.0000i	−0.984225	+	0.568242i	−0.903543	−	0.428497i	$-0.859043\pi$
$607$	−24.2487	+	14.0000i	−0.984225	+	0.568242i	−0.0806818	+	0.996740i	$0.525710\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−6.92820	−	4.00000i	−0.279827	−	0.161558i	0.353518	−	0.935428i	$-0.384985\pi$
$613$	−6.92820	−	4.00000i	−0.279827	−	0.161558i	−0.633345	+	0.773869i	$0.718319\pi$
$614$		0			0
$615$	20.0000	+	10.0000i	0.806478	+	0.403239i
$616$		0			0
$617$		−	44.0000i		−	1.77137i	−0.464283	−	0.885687i	$-0.653688\pi$
$617$		−	44.0000i		−	1.77137i	0.464283	−	0.885687i	$-0.346312\pi$
$618$		0			0
$619$	−8.00000	+	13.8564i	−0.321547	+	0.556936i	−0.980807	−	0.194979i	$-0.937536\pi$
$619$	−8.00000	+	13.8564i	−0.321547	+	0.556936i	0.659260	+	0.751915i	$0.270870\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	32.0000			1.27592
$630$		0			0
$631$	−28.0000			−1.11466			−0.557331	−	0.830290i	$-0.688175\pi$
$631$	−28.0000			−1.11466			−0.557331	+	0.830290i	$0.688175\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.535898	−	8.92820i	−0.0212665	−	0.354305i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.00000	+	12.1244i	−0.276483	+	0.478883i	−0.970508	−	0.241068i	$-0.922502\pi$
$641$	−7.00000	+	12.1244i	−0.276483	+	0.478883i	0.694025	+	0.719951i	$0.255836\pi$
$642$		0			0
$643$		−	36.0000i		−	1.41970i	−0.704352	−	0.709851i	$-0.748762\pi$
$643$		−	36.0000i		−	1.41970i	0.704352	−	0.709851i	$-0.251238\pi$
$644$		0			0
$645$	−4.00000	+	8.00000i	−0.157500	+	0.315000i
$646$		0			0
$647$	−10.3923	−	6.00000i	−0.408564	−	0.235884i	0.281609	−	0.959529i	$-0.409132\pi$
$647$	−10.3923	−	6.00000i	−0.408564	−	0.235884i	−0.690172	+	0.723645i	$0.742465\pi$
$648$		0			0
$649$	−8.00000	−	13.8564i	−0.314027	−	0.543912i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.46410	+	2.00000i	−0.135561	+	0.0782660i	−0.566247	−	0.824236i	$-0.691605\pi$
$653$	−3.46410	+	2.00000i	−0.135561	+	0.0782660i	0.430686	+	0.902502i	$0.358272\pi$
$654$		0			0
$655$	14.7846	+	22.3923i	0.577683	+	0.874940i
$656$		0			0
$657$		−	8.00000i		−	0.312110i
$658$		0			0
$659$	−28.0000			−1.09073			−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000			−1.09073			−0.545363	+	0.838200i	$0.683608\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−20.7846	+	12.0000i	−0.804783	+	0.464642i
$668$		0			0
$669$	−10.0000	+	17.3205i	−0.386622	+	0.669650i
$670$		0			0
$671$	−8.00000			−0.308837
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$	0.598076	+	4.96410i	0.0230200	+	0.191068i
$676$		0			0
$677$	3.46410	−	2.00000i	0.133136	−	0.0768662i	−0.431953	−	0.901896i	$-0.642175\pi$
$677$	3.46410	−	2.00000i	0.133136	−	0.0768662i	0.565089	+	0.825030i	$0.308842\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	10.0000	+	17.3205i	0.383201	+	0.663723i
$682$		0			0
$683$	−38.1051	−	22.0000i	−1.45805	−	0.841807i	−0.459136	−	0.888366i	$-0.651841\pi$
$683$	−38.1051	−	22.0000i	−1.45805	−	0.841807i	−0.998916	+	0.0465592i	$0.985174\pi$
$684$		0			0
$685$	24.0000	+	12.0000i	0.916993	+	0.458496i
$686$		0			0
$687$			26.0000i			0.991962i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	35.7128	−	2.14359i	1.35466	−	0.0813111i
$696$		0			0
$697$	34.6410	+	20.0000i	1.31212	+	0.757554i
$698$		0			0
$699$	−20.0000			−0.756469
$700$		0			0
$701$	26.0000			0.982006			0.491003	−	0.871158i	$-0.336630\pi$
$701$	26.0000			0.982006			0.491003	+	0.871158i	$0.336630\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	8.92820	−	0.535898i	0.336256	−	0.0201831i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	0.804178	−	0.594389i	$-0.202606\pi$
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	−0.916845	+	0.399244i	$0.869273\pi$
$710$		0			0
$711$	6.00000	−	10.3923i	0.225018	−	0.389742i
$712$		0			0
$713$		−	16.0000i		−	0.599205i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.92820	−	4.00000i	−0.258738	−	0.149383i
$718$		0			0
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.73205	−	1.00000i	0.0644157	−	0.0371904i
$724$		0			0
$725$	29.7846	−	3.58846i	1.10617	−	0.133272i
$726$		0			0
$727$		−	12.0000i		−	0.445055i	−0.974926	−	0.222528i	$-0.928569\pi$
$727$		−	12.0000i		−	0.445055i	0.974926	−	0.222528i	$-0.0714308\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−8.00000	+	13.8564i	−0.295891	+	0.512498i
$732$		0			0
$733$	13.8564	−	8.00000i	0.511798	−	0.295487i	−0.221774	−	0.975098i	$-0.571185\pi$
$733$	13.8564	−	8.00000i	0.511798	−	0.295487i	0.733572	+	0.679611i	$0.237852\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.8564	−	8.00000i	0.510407	−	0.294684i
$738$		0			0
$739$	20.0000	−	34.6410i	0.735712	−	1.27429i	−0.218698	−	0.975793i	$-0.570181\pi$
$739$	20.0000	−	34.6410i	0.735712	−	1.27429i	0.954410	−	0.298498i	$-0.0964856\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	36.0000i		−	1.32071i	−0.750953	−	0.660356i	$-0.770405\pi$
$743$		−	36.0000i		−	1.32071i	0.750953	−	0.660356i	$-0.229595\pi$
$744$		0			0
$745$	2.46410	+	3.73205i	0.0902777	+	0.136732i
$746$		0			0
$747$	3.46410	−	2.00000i	0.126745	−	0.0731762i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	0.999921	+	0.0125942i	$0.00400897\pi$
$751$	14.0000	+	24.2487i	0.510867	+	0.884848i	−0.489053	+	0.872254i	$0.662658\pi$
$752$		0			0
$753$	−10.3923	−	6.00000i	−0.378717	−	0.218652i
$754$		0			0
$755$	−20.0000	+	40.0000i	−0.727875	+	1.45575i
$756$		0			0
$757$			16.0000i			0.581530i	0.956795	+	0.290765i	$0.0939098\pi$
$757$			16.0000i			0.581530i	−0.956795	+	0.290765i	$0.906090\pi$
$758$		0			0
$759$	−8.00000	+	13.8564i	−0.290382	+	0.502956i
$760$		0			0
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	0.535898	+	8.92820i	0.0193754	+	0.322800i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	18.0000			0.649097			0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000			0.649097			0.324548	+	0.945869i	$0.394788\pi$
$770$		0			0
$771$	12.0000			0.432169
$772$		0			0
$773$	−10.3923	−	6.00000i	−0.373785	−	0.215805i	0.301326	−	0.953521i	$-0.402571\pi$
$773$	−10.3923	−	6.00000i	−0.373785	−	0.215805i	−0.675111	+	0.737716i	$0.735904\pi$
$774$		0			0
$775$	−7.85641	+	18.3923i	−0.282210	+	0.660671i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$			6.00000i			0.214423i
$784$		0			0
$785$	16.0000	+	8.00000i	0.571064	+	0.285532i
$786$		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
$789$	2.00000	+	3.46410i	0.0712019	+	0.123325i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	14.7846	+	22.3923i	0.524356	+	0.794173i
$796$		0			0
$797$			28.0000i			0.991811i	0.868377	+	0.495905i	$0.165164\pi$
$797$			28.0000i			0.991811i	−0.868377	+	0.495905i	$0.834836\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$		0			0
$801$	5.00000	−	8.66025i	0.176666	−	0.305995i
$802$		0			0
$803$	−27.7128	+	16.0000i	−0.977964	+	0.564628i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.19615	−	3.00000i	0.182913	−	0.105605i
$808$		0			0
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$		0			0
$811$	40.0000			1.40459			0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$		0			0
$813$		−	4.00000i		−	0.140286i
$814$		0			0
$815$	37.3205	−	24.6410i	1.30728	−	0.863137i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	0.961935	−	0.273278i	$-0.0881079\pi$
$821$	7.00000	+	12.1244i	0.244302	+	0.423143i	−0.717633	+	0.696421i	$0.754775\pi$
$822$		0			0
$823$	10.3923	+	6.00000i	0.362253	+	0.209147i	0.670069	−	0.742299i	$-0.266265\pi$
$823$	10.3923	+	6.00000i	0.362253	+	0.209147i	−0.307816	+	0.951446i	$0.599598\pi$
$824$		0			0
$825$	16.0000	−	12.0000i	0.557048	−	0.417786i
$826$		0			0
$827$			28.0000i			0.973655i	0.873498	+	0.486828i	$0.161846\pi$
$827$			28.0000i			0.973655i	−0.873498	+	0.486828i	$0.838154\pi$
$828$		0			0
$829$	−9.00000	+	15.5885i	−0.312583	+	0.541409i	−0.978921	−	0.204240i	$-0.934528\pi$
$829$	−9.00000	+	15.5885i	−0.312583	+	0.541409i	0.666338	+	0.745650i	$0.267861\pi$
$830$		0			0
$831$	16.0000	+	27.7128i	0.555034	+	0.961347i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.60770	−	26.7846i	−0.0556366	−	0.926920i
$836$		0			0
$837$	−3.46410	−	2.00000i	−0.119737	−	0.0691301i
$838$		0			0
$839$	56.0000			1.93333			0.966667	−	0.256036i	$-0.0824164\pi$
$839$	56.0000			1.93333			0.966667	+	0.256036i	$0.0824164\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	5.19615	+	3.00000i	0.178965	+	0.103325i
$844$		0			0
$845$	−29.0167	+	1.74167i	−0.998203	+	0.0599153i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−14.0000	−	24.2487i	−0.480479	−	0.832214i
$850$		0			0
$851$	16.0000	−	27.7128i	0.548473	−	0.949983i
$852$		0			0
$853$		−	8.00000i		−	0.273915i	−0.990577	−	0.136957i	$-0.956268\pi$
$853$		−	8.00000i		−	0.273915i	0.990577	−	0.136957i	$-0.0437323\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.3923	+	6.00000i	0.354994	+	0.204956i	0.666883	−	0.745163i	$-0.267628\pi$
$857$	10.3923	+	6.00000i	0.354994	+	0.204956i	−0.311888	+	0.950119i	$0.600962\pi$
$858$		0			0
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	−0.974249	−	0.225475i	$-0.927607\pi$
$859$	−20.0000	−	34.6410i	−0.682391	−	1.18194i	0.291858	−	0.956462i	$-0.405727\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.3923	−	6.00000i	0.353758	−	0.204242i	−0.312581	−	0.949891i	$-0.601194\pi$
$863$	10.3923	−	6.00000i	0.353758	−	0.204242i	0.666339	+	0.745649i	$0.267860\pi$
$864$		0			0
$865$	−7.46410	+	4.92820i	−0.253787	+	0.167564i
$866$		0			0
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	−48.0000			−1.62829
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−6.92820	+	4.00000i	−0.234484	+	0.135379i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	48.4974	−	28.0000i	1.63764	−	0.945493i	0.655999	−	0.754761i	$-0.272247\pi$
$877$	48.4974	−	28.0000i	1.63764	−	0.945493i	0.981642	−	0.190731i	$-0.0610859\pi$
$878$		0			0
$879$	6.00000	−	10.3923i	0.202375	−	0.350524i
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$			12.0000i			0.403832i	0.979403	+	0.201916i	$0.0647168\pi$
$883$			12.0000i			0.403832i	−0.979403	+	0.201916i	$0.935283\pi$
$884$		0			0
$885$	−7.46410	+	4.92820i	−0.250903	+	0.165660i
$886$		0			0
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.921757	−	0.387768i	$-0.873246\pi$
$887$	−31.1769	+	18.0000i	−1.04682	+	0.604381i	−0.125061	+	0.992149i	$0.539913\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−4.00000	+	8.00000i	−0.133705	+	0.267411i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$		0			0
$901$	24.0000	+	41.5692i	0.799556	+	1.38487i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	22.3205	−	1.33975i	0.741959	−	0.0445347i
$906$		0			0
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	0.317441	−	0.948278i	$-0.397176\pi$
$907$	−10.3923	−	6.00000i	−0.345071	−	0.199227i	−0.662512	+	0.749051i	$0.730510\pi$
$908$		0			0
$909$	2.00000			0.0663358
$910$		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
$913$	−13.8564	−	8.00000i	−0.458580	−	0.264761i
$914$		0			0
$915$	0.267949	+	4.46410i	0.00885813	+	0.147579i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−6.00000	−	10.3923i	−0.197922	−	0.342811i	0.749933	−	0.661514i	$-0.230086\pi$
$919$	−6.00000	−	10.3923i	−0.197922	−	0.342811i	−0.947854	+	0.318704i	$0.896753\pi$
$920$		0			0
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−32.0000	+	24.0000i	−1.05215	+	0.789115i
$926$		0			0
$927$	3.46410	+	2.00000i	0.113776	+	0.0656886i
$928$		0			0
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	0.975050	−	0.221985i	$-0.0712536\pi$
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	−0.679770	+	0.733426i	$0.737920\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−20.7846	+	12.0000i	−0.680458	+	0.392862i
$934$		0			0
$935$	29.8564	−	19.7128i	0.976409	−	0.644678i
$936$		0			0
$937$			32.0000i			1.04539i	0.852518	+	0.522697i	$0.175074\pi$
$937$			32.0000i			1.04539i	−0.852518	+	0.522697i	$0.824926\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$		0			0
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	−0.772946	−	0.634472i	$-0.781218\pi$
$941$	5.00000	−	8.66025i	0.162995	−	0.282316i	0.935942	+	0.352155i	$0.114551\pi$
$942$		0			0
$943$	34.6410	−	20.0000i	1.12807	−	0.651290i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	4.00000			0.129709
$952$		0			0
$953$			4.00000i			0.129573i	0.997899	+	0.0647864i	$0.0206366\pi$
$953$			4.00000i			0.129573i	−0.997899	+	0.0647864i	$0.979363\pi$
$954$		0			0
$955$	29.5692	+	44.7846i	0.956837	+	1.44920i
$956$		0			0
$957$	20.7846	−	12.0000i	0.671871	−	0.387905i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	10.3923	+	6.00000i	0.334887	+	0.193347i
$964$		0			0
$965$	−32.0000	−	16.0000i	−1.03012	−	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
$969$		0			0
$970$		0			0
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	0.656941	−	0.753942i	$-0.271850\pi$
$977$	10.3923	+	6.00000i	0.332479	+	0.191957i	−0.324462	+	0.945899i	$0.605183\pi$
$978$		0			0
$979$	−40.0000			−1.27841
$980$		0			0
$981$	−2.00000			−0.0638551
$982$		0			0
$983$	−24.2487	−	14.0000i	−0.773414	−	0.446531i	0.0606773	−	0.998157i	$-0.480674\pi$
$983$	−24.2487	−	14.0000i	−0.773414	−	0.446531i	−0.834091	+	0.551627i	$0.814007\pi$
$984$		0			0
$985$	0.535898	+	8.92820i	0.0170751	+	0.284476i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.00000	+	13.8564i	0.254385	+	0.440608i
$990$		0			0
$991$	−14.0000	+	24.2487i	−0.444725	+	0.770286i	−0.998033	−	0.0626908i	$-0.980032\pi$
$991$	−14.0000	+	24.2487i	−0.444725	+	0.770286i	0.553308	+	0.832977i	$0.313365\pi$
$992$		0			0
$993$			8.00000i			0.253872i
$994$		0			0
$995$	12.0000	−	24.0000i	0.380426	−	0.760851i
$996$		0			0
$997$	20.7846	+	12.0000i	0.658255	+	0.380044i	0.791612	−	0.611024i	$-0.209242\pi$
$997$	20.7846	+	12.0000i	0.658255	+	0.380044i	−0.133357	+	0.991068i	$0.542576\pi$
$998$		0			0
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.bb.d.949.2		4
5.4	even	2	inner	2940.2.bb.d.949.1		4
7.2	even	3	inner	2940.2.bb.d.1549.1		4
7.3	odd	6		2940.2.k.c.589.2		2
7.4	even	3		60.2.d.a.49.1	✓	2
7.5	odd	6		2940.2.bb.e.1549.2		4
7.6	odd	2		2940.2.bb.e.949.1		4
21.11	odd	6		180.2.d.a.109.2		2
28.11	odd	6		240.2.f.b.49.2		2
35.4	even	6		60.2.d.a.49.2	yes	2
35.9	even	6	inner	2940.2.bb.d.1549.2		4
35.18	odd	12		300.2.a.d.1.1		1
35.19	odd	6		2940.2.bb.e.1549.1		4
35.24	odd	6		2940.2.k.c.589.1		2
35.32	odd	12		300.2.a.a.1.1		1
35.34	odd	2		2940.2.bb.e.949.2		4
56.11	odd	6		960.2.f.c.769.1		2
56.53	even	6		960.2.f.f.769.2		2
63.4	even	3		1620.2.r.c.1189.1		4
63.11	odd	6		1620.2.r.d.109.1		4
63.25	even	3		1620.2.r.c.109.2		4
63.32	odd	6		1620.2.r.d.1189.2		4
84.11	even	6		720.2.f.c.289.2		2
105.32	even	12		900.2.a.a.1.1		1
105.53	even	12		900.2.a.h.1.1		1
105.74	odd	6		180.2.d.a.109.1		2
112.11	odd	12		3840.2.d.be.2689.2		2
112.53	even	12		3840.2.d.o.2689.2		2
112.67	odd	12		3840.2.d.b.2689.1		2
112.109	even	12		3840.2.d.r.2689.1		2
140.39	odd	6		240.2.f.b.49.1		2
140.67	even	12		1200.2.a.s.1.1		1
140.123	even	12		1200.2.a.a.1.1		1
168.11	even	6		2880.2.f.p.1729.1		2
168.53	odd	6		2880.2.f.l.1729.1		2
280.53	odd	12		4800.2.a.bj.1.1		1
280.67	even	12		4800.2.a.bf.1.1		1
280.109	even	6		960.2.f.f.769.1		2
280.123	even	12		4800.2.a.bk.1.1		1
280.179	odd	6		960.2.f.c.769.2		2
280.277	odd	12		4800.2.a.bn.1.1		1
315.4	even	6		1620.2.r.c.1189.2		4
315.74	odd	6		1620.2.r.d.109.2		4
315.214	even	6		1620.2.r.c.109.1		4
315.284	odd	6		1620.2.r.d.1189.1		4
420.179	even	6		720.2.f.c.289.1		2
420.263	odd	12		3600.2.a.d.1.1		1
420.347	odd	12		3600.2.a.bm.1.1		1
560.109	even	12		3840.2.d.o.2689.1		2
560.179	odd	12		3840.2.d.be.2689.1		2
560.389	even	12		3840.2.d.r.2689.2		2
560.459	odd	12		3840.2.d.b.2689.2		2
840.179	even	6		2880.2.f.p.1729.2		2
840.389	odd	6		2880.2.f.l.1729.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.d.a.49.1	✓	2	7.4	even	3
60.2.d.a.49.2	yes	2	35.4	even	6
180.2.d.a.109.1		2	105.74	odd	6
180.2.d.a.109.2		2	21.11	odd	6
240.2.f.b.49.1		2	140.39	odd	6
240.2.f.b.49.2		2	28.11	odd	6
300.2.a.a.1.1		1	35.32	odd	12
300.2.a.d.1.1		1	35.18	odd	12
720.2.f.c.289.1		2	420.179	even	6
720.2.f.c.289.2		2	84.11	even	6
900.2.a.a.1.1		1	105.32	even	12
900.2.a.h.1.1		1	105.53	even	12
960.2.f.c.769.1		2	56.11	odd	6
960.2.f.c.769.2		2	280.179	odd	6
960.2.f.f.769.1		2	280.109	even	6
960.2.f.f.769.2		2	56.53	even	6
1200.2.a.a.1.1		1	140.123	even	12
1200.2.a.s.1.1		1	140.67	even	12
1620.2.r.c.109.1		4	315.214	even	6
1620.2.r.c.109.2		4	63.25	even	3
1620.2.r.c.1189.1		4	63.4	even	3
1620.2.r.c.1189.2		4	315.4	even	6
1620.2.r.d.109.1		4	63.11	odd	6
1620.2.r.d.109.2		4	315.74	odd	6
1620.2.r.d.1189.1		4	315.284	odd	6
1620.2.r.d.1189.2		4	63.32	odd	6
2880.2.f.l.1729.1		2	168.53	odd	6
2880.2.f.l.1729.2		2	840.389	odd	6
2880.2.f.p.1729.1		2	168.11	even	6
2880.2.f.p.1729.2		2	840.179	even	6
2940.2.k.c.589.1		2	35.24	odd	6
2940.2.k.c.589.2		2	7.3	odd	6
2940.2.bb.d.949.1		4	5.4	even	2	inner
2940.2.bb.d.949.2		4	1.1	even	1	trivial
2940.2.bb.d.1549.1		4	7.2	even	3	inner
2940.2.bb.d.1549.2		4	35.9	even	6	inner
2940.2.bb.e.949.1		4	7.6	odd	2
2940.2.bb.e.949.2		4	35.34	odd	2
2940.2.bb.e.1549.1		4	35.19	odd	6
2940.2.bb.e.1549.2		4	7.5	odd	6
3600.2.a.d.1.1		1	420.263	odd	12
3600.2.a.bm.1.1		1	420.347	odd	12
3840.2.d.b.2689.1		2	112.67	odd	12
3840.2.d.b.2689.2		2	560.459	odd	12
3840.2.d.o.2689.1		2	560.109	even	12
3840.2.d.o.2689.2		2	112.53	even	12
3840.2.d.r.2689.1		2	112.109	even	12
3840.2.d.r.2689.2		2	560.389	even	12
3840.2.d.be.2689.1		2	560.179	odd	12
3840.2.d.be.2689.2		2	112.11	odd	12
4800.2.a.bf.1.1		1	280.67	even	12
4800.2.a.bj.1.1		1	280.53	odd	12
4800.2.a.bk.1.1		1	280.123	even	12
4800.2.a.bn.1.1		1	280.277	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-2.23205 + 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-2.23205 + 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(-2.00000 - 1.00000i) q^{15} +(-3.46410 - 2.00000i) q^{17} +(-3.46410 + 2.00000i) q^{23} +(4.96410 - 0.598076i) q^{25} +1.00000i q^{27} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.46410 - 2.00000i) q^{33} +(-6.92820 + 4.00000i) q^{37} -10.0000 q^{41} -4.00000i q^{43} +(-1.23205 - 1.86603i) q^{45} +(-3.46410 + 2.00000i) q^{47} +(-2.00000 - 3.46410i) q^{51} +(-10.3923 - 6.00000i) q^{53} +(-4.00000 + 8.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(3.46410 + 2.00000i) q^{67} -4.00000 q^{69} +(-6.92820 - 4.00000i) q^{73} +(4.59808 + 1.96410i) q^{75} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.00000i q^{83} +(8.00000 + 4.00000i) q^{85} +(5.19615 + 3.00000i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-3.46410 + 2.00000i) q^{93} +8.00000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^5 + 2 * q^9	\( 4 q - 2 q^{5} + 2 q^{9} + 8 q^{11} - 8 q^{15} + 6 q^{25} + 24 q^{29} - 8 q^{31} - 40 q^{41} + 2 q^{45} - 8 q^{51} - 16 q^{55} + 8 q^{59} - 4 q^{61} - 16 q^{69} + 8 q^{75} - 24 q^{79} - 2 q^{81} + 32 q^{85} - 20 q^{89} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^5 + 2 * q^9 + 8 * q^11 - 8 * q^15 + 6 * q^25 + 24 * q^29 - 8 * q^31 - 40 * q^41 + 2 * q^45 - 8 * q^51 - 16 * q^55 + 8 * q^59 - 4 * q^61 - 16 * q^69 + 8 * q^75 - 24 * q^79 - 2 * q^81 + 32 * q^85 - 20 * q^89 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more