LMFDB - Embedded newform 3276.2.gv.a.1117.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3276,2,Mod(1117,3276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3276, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("3276.1117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$3276 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3276.gv (of order $6$ , degree $2$ , 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:	$26.1589917022$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - x + 1$ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			1117.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3276.1117
Dual form			3276.2.gv.a.2053.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50000 - 0.866025i) q^{7} +(-2.50000 + 2.59808i) q^{13} +(7.50000 - 4.33013i) q^{19} +(-2.50000 + 4.33013i) q^{25} +(-1.50000 - 0.866025i) q^{31} +(4.50000 - 2.59808i) q^{37} -13.0000 q^{43} +(5.50000 + 4.33013i) q^{49} +(7.00000 + 12.1244i) q^{61} +(13.5000 + 7.79423i) q^{67} +(-1.50000 - 0.866025i) q^{73} +(8.50000 + 14.7224i) q^{79} +(8.50000 - 4.33013i) q^{91} +13.8564i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 5 q^{7} - 5 q^{13} + 15 q^{19} - 5 q^{25} - 3 q^{31} + 9 q^{37} - 26 q^{43} + 11 q^{49} + 14 q^{61} + 27 q^{67} - 3 q^{73} + 17 q^{79} + 17 q^{91}+O(q^{100})$ 2 * q - 5 * q^7 - 5 * q^13 + 15 * q^19 - 5 * q^25 - 3 * q^31 + 9 * q^37 - 26 * q^43 + 11 * q^49 + 14 * q^61 + 27 * q^67 - 3 * q^73 + 17 * q^79 + 17 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3276\mathbb{Z}\right)^\times$ .

$n$	$1639$	$2017$	$2341$	$2549$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$5$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$		0			0
$15$		0			0
$16$		0			0
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	7.50000	−	4.33013i	1.72062	−	0.993399i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.50000	−	4.33013i	1.72062	−	0.993399i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−2.50000	+	4.33013i	−0.500000	+	0.866025i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	−1.50000	−	0.866025i	−0.269408	−	0.155543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	−13.0000			−1.98248			−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−13.0000			−1.98248			−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$53$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		0			0
$66$		0			0
$67$	13.5000	+	7.79423i	1.64929	+	0.952217i	0.977356	+	0.211604i	$0.0678686\pi$
$67$	13.5000	+	7.79423i	1.64929	+	0.952217i	0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	−1.50000	−	0.866025i	−0.175562	−	0.101361i	0.409644	−	0.912245i	$-0.365653\pi$
$73$	−1.50000	−	0.866025i	−0.175562	−	0.101361i	−0.585206	+	0.810885i	$0.698986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.50000	+	14.7224i	0.956325	+	1.65640i	0.731307	+	0.682048i	$0.238911\pi$
$79$	8.50000	+	14.7224i	0.956325	+	1.65640i	0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$89$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$90$		0			0
$91$	8.50000	−	4.33013i	0.891042	−	0.453921i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$			13.8564i			1.40690i	0.710742	+	0.703452i	$0.248359\pi$
$97$			13.8564i			1.40690i	−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	0.985329	+	0.170664i	$0.0545913\pi$
$103$	6.50000	+	11.2583i	0.640464	+	1.10932i	−0.344865	+	0.938652i	$0.612075\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$	7.50000	+	4.33013i	0.718370	+	0.414751i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	7.50000	+	4.33013i	0.718370	+	0.414751i	−0.0957826	+	0.995402i	$0.530535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.00000			0.0887357			0.0443678	−	0.999015i	$-0.485873\pi$
$127$	1.00000			0.0887357			0.0443678	+	0.999015i	$0.485873\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−22.5000	+	4.33013i	−1.95100	+	0.375470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	23.0000			1.95083			0.975417	−	0.220366i	$-0.0707252\pi$
$139$	23.0000			1.95083			0.975417	+	0.220366i	$0.0707252\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$	21.0000	+	12.1244i	1.70896	+	0.986666i	0.935857	+	0.352381i	$0.114628\pi$
$151$	21.0000	+	12.1244i	1.70896	+	0.986666i	0.773099	+	0.634285i	$0.218706\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$	21.0000	−	12.1244i	1.64485	−	0.949653i	0.665771	−	0.746156i	$-0.268103\pi$
$163$	21.0000	−	12.1244i	1.64485	−	0.949653i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	10.0000	−	8.66025i	0.755929	−	0.654654i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	−19.0000			−1.41226			−0.706129	−	0.708083i	$-0.749560\pi$
$181$	−19.0000			−1.41226			−0.706129	+	0.708083i	$0.749560\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−13.5000	−	7.79423i	−0.971751	−	0.561041i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−13.5000	−	7.79423i	−0.971751	−	0.561041i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	−14.0000	+	24.2487i	−0.992434	+	1.71895i	−0.389885	+	0.920864i	$0.627485\pi$
$199$	−14.0000	+	24.2487i	−0.992434	+	1.71895i	−0.602549	+	0.798082i	$0.705848\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.00000	+	3.46410i	0.203653	+	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		−	10.3923i		−	0.695920i	−0.937509	−	0.347960i	$-0.886874\pi$
$223$		−	10.3923i		−	0.695920i	0.937509	−	0.347960i	$-0.113126\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$	−7.50000	+	4.33013i	−0.495614	+	0.286143i	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−7.50000	+	4.33013i	−0.495614	+	0.286143i	0.231287	+	0.972886i	$0.425707\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$233$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	24.0000	+	13.8564i	1.54598	+	0.892570i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$	24.0000	+	13.8564i	1.54598	+	0.892570i	0.547533	+	0.836784i	$0.315567\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.50000	+	30.3109i	−0.477214	+	1.92864i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	−13.5000	+	2.59808i	−0.838849	+	0.161437i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−15.0000	+	8.66025i	−0.911185	+	0.526073i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.50000	+	4.33013i	−0.150210	+	0.260172i	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−2.50000	+	4.33013i	−0.150210	+	0.260172i	0.781094	+	0.624413i	$0.214662\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$		0			0
$283$	−12.5000	+	21.6506i	−0.743048	+	1.28700i	0.208053	+	0.978117i	$0.433287\pi$
$283$	−12.5000	+	21.6506i	−0.743048	+	1.28700i	−0.951101	+	0.308879i	$0.900046\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	32.5000	+	11.2583i	1.87327	+	0.648919i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	29.4449i		−	1.68051i	−0.542194	−	0.840254i	$-0.682406\pi$
$307$		−	29.4449i		−	1.68051i	0.542194	−	0.840254i	$-0.317594\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	0.621757	−	0.783210i	$-0.286419\pi$
$313$	−6.50000	−	11.2583i	−0.367402	−	0.636358i	−0.989158	+	0.146852i	$0.953086\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−5.00000	−	17.3205i	−0.277350	−	0.960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	16.5000	−	9.52628i	0.906922	−	0.523612i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.5000	−	9.52628i	0.906922	−	0.523612i	0.879440	+	0.476011i	$0.157918\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−29.0000			−1.57973			−0.789865	−	0.613280i	$-0.789850\pi$
$337$	−29.0000			−1.57973			−0.789865	+	0.613280i	$0.789850\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$347$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$348$		0			0
$349$			34.6410i			1.85429i	0.374701	+	0.927146i	$0.377745\pi$
$349$			34.6410i			1.85429i	−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$359$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$360$		0			0
$361$	28.0000	−	48.4974i	1.47368	−	2.55250i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	15.5000	−	26.8468i	0.809093	−	1.40139i	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	15.5000	−	26.8468i	0.809093	−	1.40139i	0.913493	−	0.406855i	$-0.133375\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−12.5000	−	21.6506i	−0.647225	−	1.12103i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−12.5000	−	21.6506i	−0.647225	−	1.12103i	0.336557	−	0.941663i	$-0.390737\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	25.9808i		−	1.33454i	−0.744815	−	0.667271i	$-0.767462\pi$
$379$		−	25.9808i		−	1.33454i	0.744815	−	0.667271i	$-0.232538\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−34.5000	+	19.9186i	−1.73151	+	0.999685i	−0.853206	+	0.521575i	$0.825345\pi$
$397$	−34.5000	+	19.9186i	−1.73151	+	0.999685i	−0.878300	+	0.478110i	$0.841322\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$		0			0
$403$	6.00000	−	1.73205i	0.298881	−	0.0862796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$	22.5000	+	12.9904i	1.11255	+	0.642333i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	22.5000	+	12.9904i	1.11255	+	0.642333i	0.173064	+	0.984911i	$0.444633\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		−	1.73205i		−	0.0844150i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$		−	1.73205i		−	0.0844150i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−7.00000	−	36.3731i	−0.338754	−	1.76022i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$431$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$432$		0			0
$433$	37.0000			1.77811			0.889053	−	0.457804i	$-0.151364\pi$
$433$	37.0000			1.77811			0.889053	+	0.457804i	$0.151364\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−25.5000	+	14.7224i	−1.19284	+	0.688686i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−25.5000	+	14.7224i	−1.19284	+	0.688686i	−0.233890	+	0.972263i	$0.575146\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$		0			0
$463$		−	1.73205i		−	0.0804952i	−0.999190	−	0.0402476i	$-0.987185\pi$
$463$		−	1.73205i		−	0.0804952i	0.999190	−	0.0402476i	$-0.0128147\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$	−27.0000	−	31.1769i	−1.24674	−	1.43962i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$			43.3013i			1.98680i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	−4.50000	+	18.1865i	−0.205182	+	0.829235i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	34.5000	+	19.9186i	1.56334	+	0.902597i	0.996915	+	0.0784867i	$0.0250088\pi$
$487$	34.5000	+	19.9186i	1.56334	+	0.902597i	0.566429	+	0.824110i	$0.308325\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−37.5000	+	21.6506i	−1.67873	+	0.969216i	−0.716258	+	0.697835i	$0.754147\pi$
$499$	−37.5000	+	21.6506i	−1.67873	+	0.969216i	−0.962472	+	0.271380i	$0.912520\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$	3.00000	+	3.46410i	0.132712	+	0.153243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$		0			0
$523$	21.5000	+	37.2391i	0.940129	+	1.62835i	0.765222	+	0.643767i	$0.222629\pi$
$523$	21.5000	+	37.2391i	0.940129	+	1.62835i	0.174908	+	0.984585i	$0.444037\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−37.5000	+	21.6506i	−1.61225	+	0.930834i	−0.623404	+	0.781900i	$0.714251\pi$
$541$	−37.5000	+	21.6506i	−1.61225	+	0.930834i	−0.988847	+	0.148933i	$0.952416\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−40.0000			−1.71028			−0.855138	−	0.518400i	$-0.826528\pi$
$547$	−40.0000			−1.71028			−0.855138	+	0.518400i	$0.826528\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−8.50000	−	44.1673i	−0.361457	−	1.87818i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$	32.5000	−	33.7750i	1.37460	−	1.42853i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	23.5000	−	40.7032i	0.983444	−	1.70338i	0.334790	−	0.942293i	$-0.391335\pi$
$571$	23.5000	−	40.7032i	0.983444	−	1.70338i	0.648655	−	0.761083i	$-0.275332\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−40.5000	−	23.3827i	−1.68604	−	0.973434i	−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−40.5000	−	23.3827i	−1.68604	−	0.973434i	−0.728535	−	0.685009i	$-0.759798\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$	−15.0000			−0.618064
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$593$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−23.0000			−0.938190			−0.469095	−	0.883148i	$-0.655420\pi$
$601$	−23.0000			−0.938190			−0.469095	+	0.883148i	$0.655420\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	0.405887	−	0.913923i	$-0.366962\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	42.0000	+	24.2487i	1.69636	+	0.979396i	0.949156	+	0.314806i	$0.101939\pi$
$613$	42.0000	+	24.2487i	1.69636	+	0.979396i	0.747208	+	0.664590i	$0.231394\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$	−40.5000	−	23.3827i	−1.62783	−	0.939829i	−0.984738	−	0.174042i	$-0.944317\pi$
$619$	−40.5000	−	23.3827i	−1.62783	−	0.939829i	−0.643094	−	0.765787i	$-0.722350\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		−	24.2487i		−	0.965326i	−0.875806	−	0.482663i	$-0.839670\pi$
$631$		−	24.2487i		−	0.965326i	0.875806	−	0.482663i	$-0.160330\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−25.0000	+	3.46410i	−0.990536	+	0.137253i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$			19.0526i			0.751360i	0.926750	+	0.375680i	$0.122591\pi$
$643$			19.0526i			0.751360i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	−43.5000	−	25.1147i	−1.69195	−	0.976850i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−43.5000	−	25.1147i	−1.69195	−	0.976850i	−0.739014	−	0.673690i	$-0.764708\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−13.0000			−0.501113			−0.250557	−	0.968102i	$-0.580614\pi$
$673$	−13.0000			−0.501113			−0.250557	+	0.968102i	$0.580614\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$		0			0
$679$	12.0000	−	34.6410i	0.460518	−	1.32940i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$683$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	28.5000	−	16.4545i	1.08419	−	0.625958i	0.152167	−	0.988355i	$-0.451375\pi$
$691$	28.5000	−	16.4545i	1.08419	−	0.625958i	0.932024	+	0.362397i	$0.118041\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	22.5000	−	38.9711i	0.848604	−	1.46982i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	42.0000	−	24.2487i	1.57734	−	0.910679i	0.582115	−	0.813107i	$-0.302225\pi$
$709$	42.0000	−	24.2487i	1.57734	−	0.910679i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−6.50000	−	33.7750i	−0.242073	−	1.25785i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−5.00000			−0.185440			−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	−5.00000			−0.185440			−0.0927199	+	0.995692i	$0.529556\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−28.5000	+	16.4545i	−1.05267	+	0.607760i	−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−28.5000	+	16.4545i	−1.05267	+	0.607760i	−0.129275	+	0.991609i	$0.541265\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−34.5000	−	19.9186i	−1.26910	−	0.732717i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−34.5000	−	19.9186i	−1.26910	−	0.732717i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	0.748056	−	0.663636i	$-0.230988\pi$
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	−0.948753	+	0.316017i	$0.897654\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$		0			0
$763$	−15.0000	−	17.3205i	−0.543036	−	0.627044i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	29.4449i		−	1.06181i	−0.847432	−	0.530904i	$-0.821852\pi$
$769$		−	29.4449i		−	1.06181i	0.847432	−	0.530904i	$-0.178148\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$773$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$774$		0			0
$775$	7.50000	−	4.33013i	0.269408	−	0.155543i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−3.00000	−	1.73205i	−0.106938	−	0.0617409i	0.445577	−	0.895244i	$-0.352999\pi$
$787$	−3.00000	−	1.73205i	−0.106938	−	0.0617409i	−0.552515	+	0.833503i	$0.686332\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−49.0000	−	12.1244i	−1.74004	−	0.430548i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$			10.3923i			0.364923i	0.983213	+	0.182462i	$0.0584065\pi$
$811$			10.3923i			0.364923i	−0.983213	+	0.182462i	$0.941593\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−97.5000	+	56.2917i	−3.41109	+	1.96940i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$		0			0
$823$	26.0000	−	45.0333i	0.906303	−	1.56976i	0.0871445	−	0.996196i	$-0.472226\pi$
$823$	26.0000	−	45.0333i	0.906303	−	1.56976i	0.819159	−	0.573567i	$-0.194441\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$	26.5000	−	45.8993i	0.920383	−	1.59415i	0.121560	−	0.992584i	$-0.461210\pi$
$829$	26.5000	−	45.8993i	0.920383	−	1.59415i	0.798823	−	0.601566i	$-0.205456\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.50000	+	28.5788i	0.188982	+	0.981981i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$			53.6936i			1.83843i	0.393753	+	0.919216i	$0.371177\pi$
$853$			53.6936i			1.83843i	−0.393753	+	0.919216i	$0.628823\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$857$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$858$		0			0
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.733571	+	0.679613i	$0.237852\pi$
$859$	28.0000	+	48.4974i	0.955348	+	1.65471i	0.221777	+	0.975097i	$0.428814\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−54.0000	+	15.5885i	−1.82972	+	0.528195i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	42.0000	−	24.2487i	1.41824	−	0.818821i	0.422095	−	0.906552i	$-0.361295\pi$
$877$	42.0000	−	24.2487i	1.41824	−	0.818821i	0.996144	+	0.0877308i	$0.0279615\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	55.0000			1.85090			0.925449	−	0.378873i	$-0.123688\pi$
$883$	55.0000			1.85090			0.925449	+	0.378873i	$0.123688\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$		0			0
$889$	−2.50000	−	0.866025i	−0.0838473	−	0.0290456i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−9.50000	+	16.4545i	−0.315442	+	0.546362i	−0.979531	−	0.201291i	$-0.935486\pi$
$907$	−9.50000	+	16.4545i	−0.315442	+	0.546362i	0.664089	+	0.747653i	$0.268820\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	26.5000	+	45.8993i	0.874154	+	1.51408i	0.857661	+	0.514216i	$0.171917\pi$
$919$	26.5000	+	45.8993i	0.874154	+	1.51408i	0.0164935	+	0.999864i	$0.494750\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$			25.9808i			0.854242i
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$		0			0
$931$	60.0000	+	8.66025i	1.96642	+	0.283828i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	61.0000			1.99278			0.996392	−	0.0848755i	$-0.0270492\pi$
$937$	61.0000			1.99278			0.996392	+	0.0848755i	$0.0270492\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$941$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$	6.00000	−	1.73205i	0.194768	−	0.0562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	46.7654i		−	1.50387i	−0.659236	−	0.751936i	$-0.729120\pi$
$967$		−	46.7654i		−	1.50387i	0.659236	−	0.751936i	$-0.270880\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$		0			0
$973$	−57.5000	−	19.9186i	−1.84337	−	0.638560i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	30.5000	−	52.8275i	0.968864	−	1.67812i	0.270011	−	0.962857i	$-0.412973\pi$
$991$	30.5000	−	52.8275i	0.968864	−	1.67812i	0.698853	−	0.715265i	$-0.253694\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−29.5000	+	51.0955i	−0.934274	+	1.61821i	−0.158352	+	0.987383i	$0.550618\pi$
$997$	−29.5000	+	51.0955i	−0.934274	+	1.61821i	−0.775923	+	0.630828i	$0.782715\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3276.2.gv.a.1117.1	✓	2
3.2	odd	2	CM	3276.2.gv.a.1117.1	✓	2
7.2	even	3		3276.2.gv.b.2053.1	yes	2
13.12	even	2		3276.2.gv.b.1117.1	yes	2
21.2	odd	6		3276.2.gv.b.2053.1	yes	2
39.38	odd	2		3276.2.gv.b.1117.1	yes	2
91.51	even	6	inner	3276.2.gv.a.2053.1	yes	2
273.233	odd	6	inner	3276.2.gv.a.2053.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3276.2.gv.a.1117.1	✓	2	1.1	even	1	trivial
3276.2.gv.a.1117.1	✓	2	3.2	odd	2	CM
3276.2.gv.a.2053.1	yes	2	91.51	even	6	inner
3276.2.gv.a.2053.1	yes	2	273.233	odd	6	inner
3276.2.gv.b.1117.1	yes	2	13.12	even	2
3276.2.gv.b.1117.1	yes	2	39.38	odd	2
3276.2.gv.b.2053.1	yes	2	7.2	even	3
3276.2.gv.b.2053.1	yes	2	21.2	odd	6

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	3276.2.gv.a.1117.1

Level	$3276$
Weight	$2$
Character	3276.1117
Analytic conductor	$26.159$
Analytic rank	$0$
Dimension	$2$
CM discriminant	-3
Inner twists	$4$