LMFDB - Embedded newform 980.2.i.k.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(361,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,2,0,0,0,0,0,2] 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	980.361
Dual form			980.2.i.k.961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 + 2.09077i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.41421 - 2.44949i) q^{9} +(-0.914214 + 1.58346i) q^{11} +6.41421 q^{13} -2.41421 q^{15} +(-1.79289 + 3.10538i) q^{17} +(3.82843 + 6.63103i) q^{19} +(-1.70711 - 2.95680i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.414214 q^{27} -4.65685 q^{29} +(-3.70711 + 6.42090i) q^{31} +(-2.20711 - 3.82282i) q^{33} +(0.292893 + 0.507306i) q^{37} +(-7.74264 + 13.4106i) q^{39} +3.41421 q^{41} +0.343146 q^{43} +(1.41421 - 2.44949i) q^{45} +(-5.44975 - 9.43924i) q^{47} +(-4.32843 - 7.49706i) q^{51} +(6.12132 - 10.6024i) q^{53} -1.82843 q^{55} -18.4853 q^{57} +(-0.292893 + 0.507306i) q^{59} +(-5.41421 - 9.37769i) q^{61} +(3.20711 + 5.55487i) q^{65} +(-1.53553 + 2.65962i) q^{67} +8.24264 q^{69} -10.4853 q^{71} +(-5.41421 + 9.37769i) q^{73} +(-1.20711 - 2.09077i) q^{75} +(7.57107 + 13.1135i) q^{79} +(4.74264 - 8.21449i) q^{81} -8.00000 q^{83} -3.58579 q^{85} +(5.62132 - 9.73641i) q^{87} +(8.48528 + 14.6969i) q^{89} +(-8.94975 - 15.5014i) q^{93} +(-3.82843 + 6.63103i) q^{95} -9.72792 q^{97} +5.17157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 20 q^{13} - 4 q^{15} - 10 q^{17} + 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} - 6 q^{33} + 4 q^{37} - 14 q^{39} + 8 q^{41} + 24 q^{43} - 2 q^{47}+ \cdots + 32 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 20 * q^13 - 4 * q^15 - 10 * q^17 + 4 * q^19 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 - 12 * q^31 - 6 * q^33 + 4 * q^37 - 14 * q^39 + 8 * q^41 + 24 * q^43 - 2 * q^47 - 6 * q^51 + 16 * q^53 + 4 * q^55 - 40 * q^57 - 4 * q^59 - 16 * q^61 + 10 * q^65 + 8 * q^67 + 16 * q^69 - 8 * q^71 - 16 * q^73 - 2 * q^75 + 2 * q^79 + 2 * q^81 - 32 * q^83 - 20 * q^85 + 14 * q^87 - 16 * q^93 - 4 * q^95 + 12 * q^97 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	0.272605	+	0.962126i	$0.412115\pi$
$3$	−1.20711	+	2.09077i	−0.696923	+	1.20711i	−0.969528	+	0.244981i	$0.921218\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.41421	−	2.44949i	−0.471405	−	0.816497i
$10$		0			0
$11$	−0.914214	+	1.58346i	−0.275646	+	0.477432i	−0.970298	−	0.241913i	$-0.922225\pi$
$11$	−0.914214	+	1.58346i	−0.275646	+	0.477432i	0.694652	+	0.719346i	$0.255558\pi$
$12$		0			0
$13$	6.41421			1.77898			0.889491	−	0.456952i	$-0.151059\pi$
$13$	6.41421			1.77898			0.889491	+	0.456952i	$0.151059\pi$
$14$		0			0
$15$	−2.41421			−0.623347
$16$		0			0
$17$	−1.79289	+	3.10538i	−0.434840	+	0.753166i	−0.997283	−	0.0736709i	$-0.976529\pi$
$17$	−1.79289	+	3.10538i	−0.434840	+	0.753166i	0.562442	+	0.826837i	$0.309862\pi$
$18$		0			0
$19$	3.82843	+	6.63103i	0.878301	+	1.52126i	0.853204	+	0.521578i	$0.174656\pi$
$19$	3.82843	+	6.63103i	0.878301	+	1.52126i	0.0250976	+	0.999685i	$0.492010\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	0.631325	−	0.775519i	$-0.282511\pi$
$23$	−1.70711	−	2.95680i	−0.355956	−	0.616535i	−0.987281	+	0.158984i	$0.949178\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	−4.65685			−0.864756			−0.432378	−	0.901692i	$-0.642325\pi$
$29$	−4.65685			−0.864756			−0.432378	+	0.901692i	$0.642325\pi$
$30$		0			0
$31$	−3.70711	+	6.42090i	−0.665816	+	1.15323i	0.313247	+	0.949672i	$0.398583\pi$
$31$	−3.70711	+	6.42090i	−0.665816	+	1.15323i	−0.979063	+	0.203556i	$0.934750\pi$
$32$		0			0
$33$	−2.20711	−	3.82282i	−0.384208	−	0.665468i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.292893	+	0.507306i	0.0481513	+	0.0834006i	0.889097	−	0.457720i	$-0.151334\pi$
$37$	0.292893	+	0.507306i	0.0481513	+	0.0834006i	−0.840945	+	0.541120i	$0.818000\pi$
$38$		0			0
$39$	−7.74264	+	13.4106i	−1.23981	+	2.14742i
$40$		0			0
$41$	3.41421			0.533211			0.266605	−	0.963806i	$-0.414098\pi$
$41$	3.41421			0.533211			0.266605	+	0.963806i	$0.414098\pi$
$42$		0			0
$43$	0.343146			0.0523292			0.0261646	−	0.999658i	$-0.491671\pi$
$43$	0.343146			0.0523292			0.0261646	+	0.999658i	$0.491671\pi$
$44$		0			0
$45$	1.41421	−	2.44949i	0.210819	−	0.365148i
$46$		0			0
$47$	−5.44975	−	9.43924i	−0.794927	−	1.37685i	−0.922885	−	0.385075i	$-0.874176\pi$
$47$	−5.44975	−	9.43924i	−0.794927	−	1.37685i	0.127958	−	0.991780i	$-0.459158\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−4.32843	−	7.49706i	−0.606101	−	1.04980i
$52$		0			0
$53$	6.12132	−	10.6024i	0.840828	−	1.45636i	−0.0483676	−	0.998830i	$-0.515402\pi$
$53$	6.12132	−	10.6024i	0.840828	−	1.45636i	0.889196	−	0.457527i	$-0.151265\pi$
$54$		0			0
$55$	−1.82843			−0.246545
$56$		0			0
$57$	−18.4853			−2.44844
$58$		0			0
$59$	−0.292893	+	0.507306i	−0.0381314	+	0.0660456i	−0.884461	−	0.466614i	$-0.845474\pi$
$59$	−0.292893	+	0.507306i	−0.0381314	+	0.0660456i	0.846330	+	0.532659i	$0.178807\pi$
$60$		0			0
$61$	−5.41421	−	9.37769i	−0.693219	−	1.20069i	−0.970777	−	0.239982i	$-0.922859\pi$
$61$	−5.41421	−	9.37769i	−0.693219	−	1.20069i	0.277558	−	0.960709i	$-0.410475\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.20711	+	5.55487i	0.397793	+	0.688997i
$66$		0			0
$67$	−1.53553	+	2.65962i	−0.187595	+	0.324925i	−0.944448	−	0.328661i	$-0.893403\pi$
$67$	−1.53553	+	2.65962i	−0.187595	+	0.324925i	0.756853	+	0.653586i	$0.226736\pi$
$68$		0			0
$69$	8.24264			0.992297
$70$		0			0
$71$	−10.4853			−1.24437			−0.622187	−	0.782869i	$-0.713756\pi$
$71$	−10.4853			−1.24437			−0.622187	+	0.782869i	$0.713756\pi$
$72$		0			0
$73$	−5.41421	+	9.37769i	−0.633686	+	1.09758i	0.353106	+	0.935583i	$0.385125\pi$
$73$	−5.41421	+	9.37769i	−0.633686	+	1.09758i	−0.986792	+	0.161993i	$0.948208\pi$
$74$		0			0
$75$	−1.20711	−	2.09077i	−0.139385	−	0.241421i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	7.57107	+	13.1135i	0.851812	+	1.47538i	0.879572	+	0.475766i	$0.157829\pi$
$79$	7.57107	+	13.1135i	0.851812	+	1.47538i	−0.0277599	+	0.999615i	$0.508837\pi$
$80$		0			0
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$		0			0
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$	−3.58579			−0.388933
$86$		0			0
$87$	5.62132	−	9.73641i	0.602669	−	1.04385i
$88$		0			0
$89$	8.48528	+	14.6969i	0.899438	+	1.55787i	0.828214	+	0.560412i	$0.189357\pi$
$89$	8.48528	+	14.6969i	0.899438	+	1.55787i	0.0712241	+	0.997460i	$0.477309\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−8.94975	−	15.5014i	−0.928046	−	1.60742i
$94$		0			0
$95$	−3.82843	+	6.63103i	−0.392788	+	0.680329i
$96$		0			0
$97$	−9.72792			−0.987721			−0.493860	−	0.869541i	$-0.664415\pi$
$97$	−9.72792			−0.987721			−0.493860	+	0.869541i	$0.664415\pi$
$98$		0			0
$99$	5.17157			0.519763
$100$		0			0
$101$	−0.414214	+	0.717439i	−0.0412158	+	0.0713878i	−0.885897	−	0.463881i	$-0.846456\pi$
$101$	−0.414214	+	0.717439i	−0.0412158	+	0.0713878i	0.844682	+	0.535269i	$0.179790\pi$
$102$		0			0
$103$	−2.20711	−	3.82282i	−0.217473	−	0.376674i	0.736562	−	0.676370i	$-0.236448\pi$
$103$	−2.20711	−	3.82282i	−0.217473	−	0.376674i	−0.954035	+	0.299696i	$0.903115\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.58579	+	9.67487i	0.539998	+	0.935305i	0.998903	+	0.0468193i	$0.0149085\pi$
$107$	5.58579	+	9.67487i	0.539998	+	0.935305i	−0.458905	+	0.888485i	$0.651758\pi$
$108$		0			0
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	−0.996962	−	0.0778949i	$-0.975180\pi$
$109$	−4.50000	+	7.79423i	−0.431022	+	0.746552i	0.565940	+	0.824447i	$0.308513\pi$
$110$		0			0
$111$	−1.41421			−0.134231
$112$		0			0
$113$	9.07107			0.853334			0.426667	−	0.904409i	$-0.359688\pi$
$113$	9.07107			0.853334			0.426667	+	0.904409i	$0.359688\pi$
$114$		0			0
$115$	1.70711	−	2.95680i	0.159189	−	0.275723i
$116$		0			0
$117$	−9.07107	−	15.7116i	−0.838621	−	1.45253i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.82843	+	6.63103i	0.348039	+	0.602821i
$122$		0			0
$123$	−4.12132	+	7.13834i	−0.371607	+	0.643642i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−2.10051			−0.186390			−0.0931948	−	0.995648i	$-0.529708\pi$
$127$	−2.10051			−0.186390			−0.0931948	+	0.995648i	$0.529708\pi$
$128$		0			0
$129$	−0.414214	+	0.717439i	−0.0364695	+	0.0631670i
$130$		0			0
$131$	10.1213	+	17.5306i	0.884304	+	1.53166i	0.846509	+	0.532374i	$0.178700\pi$
$131$	10.1213	+	17.5306i	0.884304	+	1.53166i	0.0377944	+	0.999286i	$0.487967\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.207107	−	0.358719i	−0.0178249	−	0.0308737i
$136$		0			0
$137$	10.4853	−	18.1610i	0.895818	−	1.55160i	0.0630291	−	0.998012i	$-0.479924\pi$
$137$	10.4853	−	18.1610i	0.895818	−	1.55160i	0.832789	−	0.553591i	$-0.186743\pi$
$138$		0			0
$139$	5.89949			0.500389			0.250194	−	0.968196i	$-0.419505\pi$
$139$	5.89949			0.500389			0.250194	+	0.968196i	$0.419505\pi$
$140$		0			0
$141$	26.3137			2.21601
$142$		0			0
$143$	−5.86396	+	10.1567i	−0.490369	+	0.849344i
$144$		0			0
$145$	−2.32843	−	4.03295i	−0.193365	−	0.334919i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.2426	−	17.7408i	−0.839110	−	1.45338i	−0.890640	−	0.454709i	$-0.849743\pi$
$149$	−10.2426	−	17.7408i	−0.839110	−	1.45338i	0.0515300	−	0.998671i	$-0.483590\pi$
$150$		0			0
$151$	3.08579	−	5.34474i	0.251118	−	0.434949i	−0.712716	−	0.701453i	$-0.752535\pi$
$151$	3.08579	−	5.34474i	0.251118	−	0.434949i	0.963834	+	0.266504i	$0.0858685\pi$
$152$		0			0
$153$	10.1421			0.819943
$154$		0			0
$155$	−7.41421			−0.595524
$156$		0			0
$157$	3.24264	−	5.61642i	0.258791	−	0.448239i	−0.707127	−	0.707086i	$-0.750009\pi$
$157$	3.24264	−	5.61642i	0.258791	−	0.448239i	0.965918	+	0.258847i	$0.0833426\pi$
$158$		0			0
$159$	14.7782	+	25.5965i	1.17199	+	2.02994i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	4.77817	+	8.27604i	0.374256	+	0.648230i	0.990215	−	0.139548i	$-0.0445650\pi$
$163$	4.77817	+	8.27604i	0.374256	+	0.648230i	−0.615960	+	0.787778i	$0.711232\pi$
$164$		0			0
$165$	2.20711	−	3.82282i	0.171823	−	0.297606i
$166$		0			0
$167$	−0.414214			−0.0320528			−0.0160264	−	0.999872i	$-0.505102\pi$
$167$	−0.414214			−0.0320528			−0.0160264	+	0.999872i	$0.505102\pi$
$168$		0			0
$169$	28.1421			2.16478
$170$		0			0
$171$	10.8284	−	18.7554i	0.828071	−	1.43426i
$172$		0			0
$173$	6.27817	+	10.8741i	0.477321	+	0.826744i	0.999662	−	0.0259926i	$-0.00827465\pi$
$173$	6.27817	+	10.8741i	0.477321	+	0.826744i	−0.522341	+	0.852736i	$0.674941\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.707107	−	1.22474i	−0.0531494	−	0.0920575i
$178$		0			0
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	−0.600841	−	0.799369i	$-0.705167\pi$
$179$	5.24264	−	9.08052i	0.391853	−	0.678710i	0.992694	+	0.120659i	$0.0385007\pi$
$180$		0			0
$181$	10.2426			0.761329			0.380665	−	0.924713i	$-0.375695\pi$
$181$	10.2426			0.761329			0.380665	+	0.924713i	$0.375695\pi$
$182$		0			0
$183$	26.1421			1.93248
$184$		0			0
$185$	−0.292893	+	0.507306i	−0.0215339	+	0.0372979i
$186$		0			0
$187$	−3.27817	−	5.67796i	−0.239724	−	0.415214i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.67157	−	4.62730i	−0.193308	−	0.334820i	0.753036	−	0.657979i	$-0.228588\pi$
$191$	−2.67157	−	4.62730i	−0.193308	−	0.334820i	−0.946345	+	0.323159i	$0.895255\pi$
$192$		0			0
$193$	2.82843	−	4.89898i	0.203595	−	0.352636i	−0.746089	−	0.665846i	$-0.768071\pi$
$193$	2.82843	−	4.89898i	0.203595	−	0.352636i	0.949684	+	0.313210i	$0.101404\pi$
$194$		0			0
$195$	−15.4853			−1.10892
$196$		0			0
$197$	3.55635			0.253379			0.126690	−	0.991942i	$-0.459565\pi$
$197$	3.55635			0.253379			0.126690	+	0.991942i	$0.459565\pi$
$198$		0			0
$199$	0.636039	−	1.10165i	0.0450876	−	0.0780940i	−0.842601	−	0.538539i	$-0.818977\pi$
$199$	0.636039	−	1.10165i	0.0450876	−	0.0780940i	0.887688	+	0.460445i	$0.152310\pi$
$200$		0			0
$201$	−3.70711	−	6.42090i	−0.261479	−	0.452895i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.70711	+	2.95680i	0.119230	+	0.206512i
$206$		0			0
$207$	−4.82843	+	8.36308i	−0.335599	+	0.581274i
$208$		0			0
$209$	−14.0000			−0.968400
$210$		0			0
$211$	−1.68629			−0.116089			−0.0580445	−	0.998314i	$-0.518487\pi$
$211$	−1.68629			−0.116089			−0.0580445	+	0.998314i	$0.518487\pi$
$212$		0			0
$213$	12.6569	−	21.9223i	0.867233	−	1.50209i
$214$		0			0
$215$	0.171573	+	0.297173i	0.0117012	+	0.0202670i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−13.0711	−	22.6398i	−0.883261	−	1.52985i
$220$		0			0
$221$	−11.5000	+	19.9186i	−0.773574	+	1.33987i
$222$		0			0
$223$	9.92893			0.664890			0.332445	−	0.943123i	$-0.392126\pi$
$223$	9.92893			0.664890			0.332445	+	0.943123i	$0.392126\pi$
$224$		0			0
$225$	2.82843			0.188562
$226$		0			0
$227$	8.86396	−	15.3528i	0.588322	−	1.01900i	−0.406131	−	0.913815i	$-0.633122\pi$
$227$	8.86396	−	15.3528i	0.588322	−	1.01900i	0.994452	−	0.105188i	$-0.0335445\pi$
$228$		0			0
$229$	−2.05025	−	3.55114i	−0.135485	−	0.234666i	0.790298	−	0.612723i	$-0.209926\pi$
$229$	−2.05025	−	3.55114i	−0.135485	−	0.234666i	−0.925782	+	0.378057i	$0.876592\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.41421	+	12.8418i	0.485721	+	0.841294i	0.999865	−	0.0164099i	$-0.00522367\pi$
$233$	7.41421	+	12.8418i	0.485721	+	0.841294i	−0.514144	+	0.857704i	$0.671890\pi$
$234$		0			0
$235$	5.44975	−	9.43924i	0.355502	−	0.615748i
$236$		0			0
$237$	−36.5563			−2.37459
$238$		0			0
$239$	19.8284			1.28259			0.641297	−	0.767293i	$-0.278397\pi$
$239$	19.8284			1.28259			0.641297	+	0.767293i	$0.278397\pi$
$240$		0			0
$241$	−13.7782	+	23.8645i	−0.887530	+	1.53725i	−0.0447444	+	0.998998i	$0.514247\pi$
$241$	−13.7782	+	23.8645i	−0.887530	+	1.53725i	−0.842786	+	0.538249i	$0.819086\pi$
$242$		0			0
$243$	10.8284	+	18.7554i	0.694644	+	1.20316i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	24.5563	+	42.5328i	1.56248	+	2.70630i
$248$		0			0
$249$	9.65685	−	16.7262i	0.611978	−	1.05998i
$250$		0			0
$251$	−12.9289			−0.816067			−0.408033	−	0.912967i	$-0.633785\pi$
$251$	−12.9289			−0.816067			−0.408033	+	0.912967i	$0.633785\pi$
$252$		0			0
$253$	6.24264			0.392471
$254$		0			0
$255$	4.32843	−	7.49706i	0.271057	−	0.469484i
$256$		0			0
$257$	−6.89949	−	11.9503i	−0.430379	−	0.745438i	0.566527	−	0.824043i	$-0.308287\pi$
$257$	−6.89949	−	11.9503i	−0.430379	−	0.745438i	−0.996906	+	0.0786054i	$0.974953\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	6.58579	+	11.4069i	0.407650	+	0.706070i
$262$		0			0
$263$	−5.00000	+	8.66025i	−0.308313	+	0.534014i	−0.977993	−	0.208635i	$-0.933098\pi$
$263$	−5.00000	+	8.66025i	−0.308313	+	0.534014i	0.669680	+	0.742650i	$0.266431\pi$
$264$		0			0
$265$	12.2426			0.752059
$266$		0			0
$267$	−40.9706			−2.50736
$268$		0			0
$269$	−4.36396	+	7.55860i	−0.266075	+	0.460856i	−0.967845	−	0.251548i	$-0.919060\pi$
$269$	−4.36396	+	7.55860i	−0.266075	+	0.460856i	0.701769	+	0.712404i	$0.252394\pi$
$270$		0			0
$271$	2.48528	+	4.30463i	0.150970	+	0.261488i	0.931584	−	0.363525i	$-0.118427\pi$
$271$	2.48528	+	4.30463i	0.150970	+	0.261488i	−0.780614	+	0.625013i	$0.785094\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.914214	−	1.58346i	−0.0551292	−	0.0954865i
$276$		0			0
$277$	2.29289	−	3.97141i	0.137767	−	0.238619i	−0.788884	−	0.614542i	$-0.789341\pi$
$277$	2.29289	−	3.97141i	0.137767	−	0.238619i	0.926651	+	0.375923i	$0.122674\pi$
$278$		0			0
$279$	20.9706			1.25547
$280$		0			0
$281$	−1.00000			−0.0596550			−0.0298275	−	0.999555i	$-0.509496\pi$
$281$	−1.00000			−0.0596550			−0.0298275	+	0.999555i	$0.509496\pi$
$282$		0			0
$283$	13.6213	−	23.5928i	0.809703	−	1.40245i	−0.103366	−	0.994643i	$-0.532961\pi$
$283$	13.6213	−	23.5928i	0.809703	−	1.40245i	0.913069	−	0.407804i	$-0.133705\pi$
$284$		0			0
$285$	−9.24264	−	16.0087i	−0.547487	−	0.948275i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2.07107	+	3.58719i	0.121828	+	0.211011i
$290$		0			0
$291$	11.7426	−	20.3389i	0.688366	−	1.19228i
$292$		0			0
$293$	−11.5858			−0.676849			−0.338424	−	0.940994i	$-0.609894\pi$
$293$	−11.5858			−0.676849			−0.338424	+	0.940994i	$0.609894\pi$
$294$		0			0
$295$	−0.585786			−0.0341058
$296$		0			0
$297$	0.378680	−	0.655892i	0.0219732	−	0.0380587i
$298$		0			0
$299$	−10.9497	−	18.9655i	−0.633240	−	1.09680i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.00000	−	1.73205i	−0.0574485	−	0.0995037i
$304$		0			0
$305$	5.41421	−	9.37769i	0.310017	−	0.536965i
$306$		0			0
$307$	6.41421			0.366079			0.183039	−	0.983106i	$-0.441406\pi$
$307$	6.41421			0.366079			0.183039	+	0.983106i	$0.441406\pi$
$308$		0			0
$309$	10.6569			0.606247
$310$		0			0
$311$	13.4853	−	23.3572i	0.764680	−	1.32446i	−0.175735	−	0.984437i	$-0.556230\pi$
$311$	13.4853	−	23.3572i	0.764680	−	1.32446i	0.940416	−	0.340027i	$-0.110436\pi$
$312$		0			0
$313$	7.27817	+	12.6062i	0.411387	+	0.712543i	0.995042	−	0.0994591i	$-0.0317112\pi$
$313$	7.27817	+	12.6062i	0.411387	+	0.712543i	−0.583655	+	0.812002i	$0.698378\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.48528	−	16.4290i	−0.532746	−	0.922744i	−0.999269	−	0.0382345i	$-0.987827\pi$
$317$	−9.48528	−	16.4290i	−0.532746	−	0.922744i	0.466522	−	0.884509i	$-0.345507\pi$
$318$		0			0
$319$	4.25736	−	7.37396i	0.238366	−	0.412863i
$320$		0			0
$321$	−26.9706			−1.50535
$322$		0			0
$323$	−27.4558			−1.52768
$324$		0			0
$325$	−3.20711	+	5.55487i	−0.177898	+	0.308129i
$326$		0			0
$327$	−10.8640	−	18.8169i	−0.600778	−	1.04058i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.414214	+	0.717439i	0.0227672	+	0.0394340i	0.877185	−	0.480153i	$-0.159419\pi$
$331$	0.414214	+	0.717439i	0.0227672	+	0.0394340i	−0.854417	+	0.519587i	$0.826086\pi$
$332$		0			0
$333$	0.828427	−	1.43488i	0.0453975	−	0.0786308i
$334$		0			0
$335$	−3.07107			−0.167790
$336$		0			0
$337$	6.72792			0.366493			0.183247	−	0.983067i	$-0.441339\pi$
$337$	6.72792			0.366493			0.183247	+	0.983067i	$0.441339\pi$
$338$		0			0
$339$	−10.9497	+	18.9655i	−0.594709	+	1.03007i
$340$		0			0
$341$	−6.77817	−	11.7401i	−0.367059	−	0.635764i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	4.12132	+	7.13834i	0.221884	+	0.384315i
$346$		0			0
$347$	2.29289	−	3.97141i	0.123089	−	0.213196i	−0.797895	−	0.602796i	$-0.794053\pi$
$347$	2.29289	−	3.97141i	0.123089	−	0.213196i	0.920984	+	0.389600i	$0.127387\pi$
$348$		0			0
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		0			0
$351$	−2.65685			−0.141812
$352$		0			0
$353$	−6.03553	+	10.4539i	−0.321239	+	0.556402i	−0.980744	−	0.195298i	$-0.937433\pi$
$353$	−6.03553	+	10.4539i	−0.321239	+	0.556402i	0.659505	+	0.751700i	$0.270766\pi$
$354$		0			0
$355$	−5.24264	−	9.08052i	−0.278250	−	0.481944i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.65685	+	9.79796i	0.298557	+	0.517116i	0.975806	−	0.218638i	$-0.0701613\pi$
$359$	5.65685	+	9.79796i	0.298557	+	0.517116i	−0.677249	+	0.735754i	$0.736828\pi$
$360$		0			0
$361$	−19.8137	+	34.3183i	−1.04283	+	1.80623i
$362$		0			0
$363$	−18.4853			−0.970226
$364$		0			0
$365$	−10.8284			−0.566786
$366$		0			0
$367$	2.86396	−	4.96053i	0.149498	−	0.258937i	−0.781544	−	0.623850i	$-0.785568\pi$
$367$	2.86396	−	4.96053i	0.149498	−	0.258937i	0.931042	+	0.364912i	$0.118901\pi$
$368$		0			0
$369$	−4.82843	−	8.36308i	−0.251358	−	0.435365i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.242641	+	0.420266i	0.0125635	+	0.0217605i	0.872239	−	0.489080i	$-0.162667\pi$
$373$	0.242641	+	0.420266i	0.0125635	+	0.0217605i	−0.859675	+	0.510841i	$0.829334\pi$
$374$		0			0
$375$	1.20711	−	2.09077i	0.0623347	−	0.107967i
$376$		0			0
$377$	−29.8701			−1.53839
$378$		0			0
$379$	14.0000			0.719132			0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000			0.719132			0.359566	+	0.933120i	$0.382925\pi$
$380$		0			0
$381$	2.53553	−	4.39167i	0.129899	−	0.224992i
$382$		0			0
$383$	10.2426	+	17.7408i	0.523374	+	0.906511i	0.999630	+	0.0272042i	$0.00866044\pi$
$383$	10.2426	+	17.7408i	0.523374	+	0.906511i	−0.476255	+	0.879307i	$0.658006\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.485281	−	0.840532i	−0.0246682	−	0.0427266i
$388$		0			0
$389$	7.57107	−	13.1135i	0.383868	−	0.664880i	−0.607743	−	0.794134i	$-0.707925\pi$
$389$	7.57107	−	13.1135i	0.383868	−	0.664880i	0.991611	+	0.129254i	$0.0412583\pi$
$390$		0			0
$391$	12.2426			0.619137
$392$		0			0
$393$	−48.8701			−2.46517
$394$		0			0
$395$	−7.57107	+	13.1135i	−0.380942	+	0.659810i
$396$		0			0
$397$	−5.79289	−	10.0336i	−0.290737	−	0.503571i	0.683247	−	0.730187i	$-0.260567\pi$
$397$	−5.79289	−	10.0336i	−0.290737	−	0.503571i	−0.973984	+	0.226616i	$0.927234\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.74264	−	15.1427i	−0.436587	−	0.756190i	0.560837	−	0.827926i	$-0.310479\pi$
$401$	−8.74264	−	15.1427i	−0.436587	−	0.756190i	−0.997424	+	0.0717360i	$0.977146\pi$
$402$		0			0
$403$	−23.7782	+	41.1850i	−1.18448	+	2.05157i
$404$		0			0
$405$	9.48528			0.471327
$406$		0			0
$407$	−1.07107			−0.0530909
$408$		0			0
$409$	−13.5858	+	23.5313i	−0.671774	+	1.16355i	0.305627	+	0.952151i	$0.401134\pi$
$409$	−13.5858	+	23.5313i	−0.671774	+	1.16355i	−0.977401	+	0.211395i	$0.932199\pi$
$410$		0			0
$411$	25.3137	+	43.8446i	1.24863	+	2.16270i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−4.00000	−	6.92820i	−0.196352	−	0.340092i
$416$		0			0
$417$	−7.12132	+	12.3345i	−0.348733	+	0.604023i
$418$		0			0
$419$	21.5563			1.05310			0.526548	−	0.850145i	$-0.323486\pi$
$419$	21.5563			1.05310			0.526548	+	0.850145i	$0.323486\pi$
$420$		0			0
$421$	−2.31371			−0.112763			−0.0563816	−	0.998409i	$-0.517956\pi$
$421$	−2.31371			−0.112763			−0.0563816	+	0.998409i	$0.517956\pi$
$422$		0			0
$423$	−15.4142	+	26.6982i	−0.749465	+	1.29811i
$424$		0			0
$425$	−1.79289	−	3.10538i	−0.0869681	−	0.150633i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−14.1569	−	24.5204i	−0.683499	−	1.18386i
$430$		0			0
$431$	2.08579	−	3.61269i	0.100469	−	0.174017i	−0.811409	−	0.584479i	$-0.801299\pi$
$431$	2.08579	−	3.61269i	0.100469	−	0.174017i	0.911878	+	0.410462i	$0.134632\pi$
$432$		0			0
$433$	34.2843			1.64760			0.823798	−	0.566883i	$-0.191851\pi$
$433$	34.2843			1.64760			0.823798	+	0.566883i	$0.191851\pi$
$434$		0			0
$435$	11.2426			0.539043
$436$		0			0
$437$	13.0711	−	22.6398i	0.625274	−	1.08301i
$438$		0			0
$439$	−7.87868	−	13.6463i	−0.376029	−	0.651301i	0.614452	−	0.788955i	$-0.289377\pi$
$439$	−7.87868	−	13.6463i	−0.376029	−	0.651301i	−0.990480	+	0.137653i	$0.956044\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.72792	−	13.3852i	−0.367165	−	0.635948i	0.621956	−	0.783052i	$-0.286338\pi$
$443$	−7.72792	−	13.3852i	−0.367165	−	0.635948i	−0.989121	+	0.147104i	$0.953005\pi$
$444$		0			0
$445$	−8.48528	+	14.6969i	−0.402241	+	0.696702i
$446$		0			0
$447$	49.4558			2.33918
$448$		0			0
$449$	18.1716			0.857570			0.428785	−	0.903407i	$-0.358942\pi$
$449$	18.1716			0.857570			0.428785	+	0.903407i	$0.358942\pi$
$450$		0			0
$451$	−3.12132	+	5.40629i	−0.146977	+	0.254572i
$452$		0			0
$453$	7.44975	+	12.9033i	0.350020	+	0.606252i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.464466	+	0.804479i	0.0217268	+	0.0376319i	0.876684	−	0.481066i	$-0.159750\pi$
$457$	0.464466	+	0.804479i	0.0217268	+	0.0376319i	−0.854958	+	0.518698i	$0.826417\pi$
$458$		0			0
$459$	0.742641	−	1.28629i	0.0346635	−	0.0600389i
$460$		0			0
$461$	33.6569			1.56756			0.783778	−	0.621041i	$-0.213290\pi$
$461$	33.6569			1.56756			0.783778	+	0.621041i	$0.213290\pi$
$462$		0			0
$463$	37.4558			1.74072			0.870360	−	0.492415i	$-0.163886\pi$
$463$	37.4558			1.74072			0.870360	+	0.492415i	$0.163886\pi$
$464$		0			0
$465$	8.94975	−	15.5014i	0.415035	−	0.718861i
$466$		0			0
$467$	9.44975	+	16.3674i	0.437282	+	0.757395i	0.997479	−	0.0709647i	$-0.0226078\pi$
$467$	9.44975	+	16.3674i	0.437282	+	0.757395i	−0.560197	+	0.828360i	$0.689274\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	7.82843	+	13.5592i	0.360715	+	0.624777i
$472$		0			0
$473$	−0.313708	+	0.543359i	−0.0144243	+	0.0249837i
$474$		0			0
$475$	−7.65685			−0.351321
$476$		0			0
$477$	−34.6274			−1.58548
$478$		0			0
$479$	−3.29289	+	5.70346i	−0.150456	+	0.260598i	−0.931395	−	0.364010i	$-0.881408\pi$
$479$	−3.29289	+	5.70346i	−0.150456	+	0.260598i	0.780939	+	0.624607i	$0.214741\pi$
$480$		0			0
$481$	1.87868	+	3.25397i	0.0856604	+	0.148368i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.86396	−	8.42463i	−0.220861	−	0.382543i
$486$		0			0
$487$	2.29289	−	3.97141i	0.103901	−	0.179962i	−0.809388	−	0.587275i	$-0.800201\pi$
$487$	2.29289	−	3.97141i	0.103901	−	0.179962i	0.913289	+	0.407313i	$0.133534\pi$
$488$		0			0
$489$	−23.0711			−1.04331
$490$		0			0
$491$	−39.2843			−1.77287			−0.886437	−	0.462849i	$-0.846827\pi$
$491$	−39.2843			−1.77287			−0.886437	+	0.462849i	$0.846827\pi$
$492$		0			0
$493$	8.34924	−	14.4613i	0.376031	−	0.651305i
$494$		0			0
$495$	2.58579	+	4.47871i	0.116222	+	0.201303i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−15.8137	−	27.3901i	−0.707919	−	1.22615i	−0.965628	−	0.259929i	$-0.916301\pi$
$499$	−15.8137	−	27.3901i	−0.707919	−	1.22615i	0.257709	−	0.966223i	$-0.417032\pi$
$500$		0			0
$501$	0.500000	−	0.866025i	0.0223384	−	0.0386912i
$502$		0			0
$503$	−9.04163			−0.403146			−0.201573	−	0.979473i	$-0.564605\pi$
$503$	−9.04163			−0.403146			−0.201573	+	0.979473i	$0.564605\pi$
$504$		0			0
$505$	−0.828427			−0.0368645
$506$		0			0
$507$	−33.9706	+	58.8387i	−1.50869	+	2.61312i
$508$		0			0
$509$	10.4645	+	18.1250i	0.463829	+	0.803376i	0.999148	−	0.0412743i	$-0.0131418\pi$
$509$	10.4645	+	18.1250i	0.463829	+	0.803376i	−0.535319	+	0.844650i	$0.679808\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.58579	−	2.74666i	−0.0700142	−	0.121268i
$514$		0			0
$515$	2.20711	−	3.82282i	0.0972567	−	0.168454i
$516$		0			0
$517$	19.9289			0.876473
$518$		0			0
$519$	−30.3137			−1.33062
$520$		0			0
$521$	−14.6569	+	25.3864i	−0.642128	+	1.11220i	0.342828	+	0.939398i	$0.388615\pi$
$521$	−14.6569	+	25.3864i	−0.642128	+	1.11220i	−0.984957	+	0.172801i	$0.944718\pi$
$522$		0			0
$523$	−15.0711	−	26.1039i	−0.659012	−	1.14144i	−0.980872	−	0.194655i	$-0.937641\pi$
$523$	−15.0711	−	26.1039i	−0.659012	−	1.14144i	0.321860	−	0.946787i	$-0.395692\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.2929	−	23.0240i	−0.579048	−	1.00294i
$528$		0			0
$529$	5.67157	−	9.82345i	0.246590	−	0.427107i
$530$		0			0
$531$	1.65685			0.0719014
$532$		0			0
$533$	21.8995			0.948572
$534$		0			0
$535$	−5.58579	+	9.67487i	−0.241495	+	0.418281i
$536$		0			0
$537$	12.6569	+	21.9223i	0.546184	+	0.946018i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.98528	+	15.5630i	0.386307	+	0.669104i	0.991950	−	0.126633i	$-0.0404171\pi$
$541$	8.98528	+	15.5630i	0.386307	+	0.669104i	−0.605642	+	0.795737i	$0.707084\pi$
$542$		0			0
$543$	−12.3640	+	21.4150i	−0.530588	+	0.919006i
$544$		0			0
$545$	−9.00000			−0.385518
$546$		0			0
$547$	24.4853			1.04692			0.523458	−	0.852052i	$-0.324642\pi$
$547$	24.4853			1.04692			0.523458	+	0.852052i	$0.324642\pi$
$548$		0			0
$549$	−15.3137	+	26.5241i	−0.653573	+	1.13202i
$550$		0			0
$551$	−17.8284	−	30.8797i	−0.759517	−	1.31552i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.707107	−	1.22474i	−0.0300150	−	0.0519875i
$556$		0			0
$557$	−15.8995	+	27.5387i	−0.673683	+	1.16685i	0.303169	+	0.952937i	$0.401955\pi$
$557$	−15.8995	+	27.5387i	−0.673683	+	1.16685i	−0.976852	+	0.213917i	$0.931378\pi$
$558$		0			0
$559$	2.20101			0.0930928
$560$		0			0
$561$	15.8284			0.668277
$562$		0			0
$563$	−12.3137	+	21.3280i	−0.518961	+	0.898867i	0.480796	+	0.876832i	$0.340348\pi$
$563$	−12.3137	+	21.3280i	−0.518961	+	0.898867i	−0.999757	+	0.0220344i	$0.992986\pi$
$564$		0			0
$565$	4.53553	+	7.85578i	0.190811	+	0.330495i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.89949	−	6.75412i	−0.163475	−	0.283148i	0.772637	−	0.634848i	$-0.218937\pi$
$569$	−3.89949	−	6.75412i	−0.163475	−	0.283148i	−0.936113	+	0.351700i	$0.885604\pi$
$570$		0			0
$571$	0.414214	−	0.717439i	0.0173343	−	0.0300239i	−0.857228	−	0.514937i	$-0.827815\pi$
$571$	0.414214	−	0.717439i	0.0173343	−	0.0300239i	0.874562	+	0.484913i	$0.161149\pi$
$572$		0			0
$573$	12.8995			0.538884
$574$		0			0
$575$	3.41421			0.142383
$576$		0			0
$577$	−0.0355339	+	0.0615465i	−0.00147930	+	0.00256222i	−0.866764	−	0.498718i	$-0.833804\pi$
$577$	−0.0355339	+	0.0615465i	−0.00147930	+	0.00256222i	0.865285	+	0.501281i	$0.167138\pi$
$578$		0			0
$579$	6.82843	+	11.8272i	0.283780	+	0.491521i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	11.1924	+	19.3858i	0.463541	+	0.802877i
$584$		0			0
$585$	9.07107	−	15.7116i	0.375042	−	0.649593i
$586$		0			0
$587$	−25.1716			−1.03894			−0.519471	−	0.854488i	$-0.673871\pi$
$587$	−25.1716			−1.03894			−0.519471	+	0.854488i	$0.673871\pi$
$588$		0			0
$589$	−56.7696			−2.33915
$590$		0			0
$591$	−4.29289	+	7.43551i	−0.176586	+	0.305856i
$592$		0			0
$593$	3.86396	+	6.69258i	0.158674	+	0.274831i	0.934391	−	0.356250i	$-0.115945\pi$
$593$	3.86396	+	6.69258i	0.158674	+	0.274831i	−0.775717	+	0.631081i	$0.782611\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.53553	+	2.65962i	0.0628452	+	0.108851i
$598$		0			0
$599$	−13.3995	+	23.2086i	−0.547489	+	0.948278i	0.450957	+	0.892546i	$0.351083\pi$
$599$	−13.3995	+	23.2086i	−0.547489	+	0.948278i	−0.998446	+	0.0557324i	$0.982251\pi$
$600$		0			0
$601$	28.3431			1.15614			0.578071	−	0.815987i	$-0.303806\pi$
$601$	28.3431			1.15614			0.578071	+	0.815987i	$0.303806\pi$
$602$		0			0
$603$	8.68629			0.353733
$604$		0			0
$605$	−3.82843	+	6.63103i	−0.155648	+	0.269590i
$606$		0			0
$607$	−14.0355	−	24.3103i	−0.569685	−	0.986723i	−0.996597	−	0.0824298i	$-0.973732\pi$
$607$	−14.0355	−	24.3103i	−0.569685	−	0.986723i	0.426912	−	0.904293i	$-0.359601\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−34.9558	−	60.5453i	−1.41416	−	2.44940i
$612$		0			0
$613$	9.34315	−	16.1828i	0.377366	−	0.653617i	−0.613312	−	0.789841i	$-0.710163\pi$
$613$	9.34315	−	16.1828i	0.377366	−	0.653617i	0.990678	+	0.136223i	$0.0434965\pi$
$614$		0			0
$615$	−8.24264			−0.332375
$616$		0			0
$617$	−12.8701			−0.518129			−0.259065	−	0.965860i	$-0.583414\pi$
$617$	−12.8701			−0.518129			−0.259065	+	0.965860i	$0.583414\pi$
$618$		0			0
$619$	21.4350	−	37.1266i	0.861547	−	1.49224i	−0.00888927	−	0.999960i	$-0.502830\pi$
$619$	21.4350	−	37.1266i	0.861547	−	1.49224i	0.870436	−	0.492282i	$-0.163837\pi$
$620$		0			0
$621$	0.707107	+	1.22474i	0.0283752	+	0.0491473i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	16.8995	−	29.2708i	0.674901	−	1.16896i
$628$		0			0
$629$	−2.10051			−0.0837526
$630$		0			0
$631$	−22.5147			−0.896297			−0.448148	−	0.893959i	$-0.647916\pi$
$631$	−22.5147			−0.896297			−0.448148	+	0.893959i	$0.647916\pi$
$632$		0			0
$633$	2.03553	−	3.52565i	0.0809052	−	0.140132i
$634$		0			0
$635$	−1.05025	−	1.81909i	−0.0416780	−	0.0721884i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	14.8284	+	25.6836i	0.586604	+	1.01603i
$640$		0			0
$641$	−8.34315	+	14.4508i	−0.329534	+	0.570770i	−0.982420	−	0.186687i	$-0.940225\pi$
$641$	−8.34315	+	14.4508i	−0.329534	+	0.570770i	0.652885	+	0.757457i	$0.273558\pi$
$642$		0			0
$643$	−38.2132			−1.50698			−0.753491	−	0.657458i	$-0.771632\pi$
$643$	−38.2132			−1.50698			−0.753491	+	0.657458i	$0.771632\pi$
$644$		0			0
$645$	−0.828427			−0.0326193
$646$		0			0
$647$	13.5563	−	23.4803i	0.532955	−	0.923105i	−0.466304	−	0.884624i	$-0.654415\pi$
$647$	13.5563	−	23.4803i	0.532955	−	0.923105i	0.999259	−	0.0384809i	$-0.0122519\pi$
$648$		0			0
$649$	−0.535534	−	0.927572i	−0.0210215	−	0.0364104i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	24.6569	+	42.7069i	0.964897	+	1.67125i	0.709891	+	0.704312i	$0.248744\pi$
$653$	24.6569	+	42.7069i	0.964897	+	1.67125i	0.255006	+	0.966939i	$0.417922\pi$
$654$		0			0
$655$	−10.1213	+	17.5306i	−0.395473	+	0.684979i
$656$		0			0
$657$	30.6274			1.19489
$658$		0			0
$659$	−9.34315			−0.363957			−0.181979	−	0.983302i	$-0.558250\pi$
$659$	−9.34315			−0.363957			−0.181979	+	0.983302i	$0.558250\pi$
$660$		0			0
$661$	2.92893	−	5.07306i	0.113922	−	0.197319i	−0.803426	−	0.595404i	$-0.796992\pi$
$661$	2.92893	−	5.07306i	0.113922	−	0.197319i	0.917348	+	0.398085i	$0.130325\pi$
$662$		0			0
$663$	−27.7635	−	48.0877i	−1.07824	−	1.86757i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.94975	+	13.7694i	0.307815	+	0.533152i
$668$		0			0
$669$	−11.9853	+	20.7591i	−0.463378	+	0.802594i
$670$		0			0
$671$	19.7990			0.764332
$672$		0			0
$673$	−44.4853			−1.71478			−0.857391	−	0.514666i	$-0.827916\pi$
$673$	−44.4853			−1.71478			−0.857391	+	0.514666i	$0.827916\pi$
$674$		0			0
$675$	0.207107	−	0.358719i	0.00797154	−	0.0138071i
$676$		0			0
$677$	17.8640	+	30.9413i	0.686568	+	1.18917i	0.972941	+	0.231052i	$0.0742168\pi$
$677$	17.8640	+	30.9413i	0.686568	+	1.18917i	−0.286374	+	0.958118i	$0.592450\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	21.3995	+	37.0650i	0.820030	+	1.42033i
$682$		0			0
$683$	13.5563	−	23.4803i	0.518719	−	0.898448i	−0.481044	−	0.876696i	$-0.659742\pi$
$683$	13.5563	−	23.4803i	0.518719	−	0.898448i	0.999763	−	0.0217518i	$-0.00692435\pi$
$684$		0			0
$685$	20.9706			0.801244
$686$		0			0
$687$	9.89949			0.377689
$688$		0			0
$689$	39.2635	−	68.0063i	1.49582	−	2.59083i
$690$		0			0
$691$	−10.2426	−	17.7408i	−0.389648	−	0.674891i	0.602754	−	0.797927i	$-0.294070\pi$
$691$	−10.2426	−	17.7408i	−0.389648	−	0.674891i	−0.992402	+	0.123036i	$0.960737\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.94975	+	5.10911i	0.111890	+	0.193800i
$696$		0			0
$697$	−6.12132	+	10.6024i	−0.231862	+	0.401596i
$698$		0			0
$699$	−35.7990			−1.35404
$700$		0			0
$701$	17.4853			0.660410			0.330205	−	0.943909i	$-0.392882\pi$
$701$	17.4853			0.660410			0.330205	+	0.943909i	$0.392882\pi$
$702$		0			0
$703$	−2.24264	+	3.88437i	−0.0845828	+	0.146502i
$704$		0			0
$705$	13.1569	+	22.7883i	0.495516	+	0.858259i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	20.8137	+	36.0504i	0.781675	+	1.35390i	0.930965	+	0.365108i	$0.118968\pi$
$709$	20.8137	+	36.0504i	0.781675	+	1.35390i	−0.149290	+	0.988793i	$0.547699\pi$
$710$		0			0
$711$	21.4142	−	37.0905i	0.803096	−	1.39100i
$712$		0			0
$713$	25.3137			0.948006
$714$		0			0
$715$	−11.7279			−0.438599
$716$		0			0
$717$	−23.9350	+	41.4567i	−0.893870	+	1.54823i
$718$		0			0
$719$	−12.1213	−	20.9947i	−0.452049	−	0.782972i	0.546464	−	0.837482i	$-0.315973\pi$
$719$	−12.1213	−	20.9947i	−0.452049	−	0.782972i	−0.998513	+	0.0545107i	$0.982640\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−33.2635	−	57.6140i	−1.23708	−	2.14269i
$724$		0			0
$725$	2.32843	−	4.03295i	0.0864756	−	0.149780i
$726$		0			0
$727$	−18.0000			−0.667583			−0.333792	−	0.942647i	$-0.608328\pi$
$727$	−18.0000			−0.667583			−0.333792	+	0.942647i	$0.608328\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$		0			0
$731$	−0.615224	+	1.06560i	−0.0227549	+	0.0394126i
$732$		0			0
$733$	−14.3492	−	24.8536i	−0.530001	−	0.917989i	−0.999387	−	0.0349962i	$-0.988858\pi$
$733$	−14.3492	−	24.8536i	−0.530001	−	0.917989i	0.469386	−	0.882993i	$-0.344475\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.80761	−	4.86293i	−0.103420	−	0.179128i
$738$		0			0
$739$	−4.67157	+	8.09140i	−0.171847	+	0.297647i	−0.939065	−	0.343738i	$-0.888307\pi$
$739$	−4.67157	+	8.09140i	−0.171847	+	0.297647i	0.767219	+	0.641385i	$0.221640\pi$
$740$		0			0
$741$	−118.569			−4.35572
$742$		0			0
$743$	−23.0711			−0.846395			−0.423198	−	0.906037i	$-0.639092\pi$
$743$	−23.0711			−0.846395			−0.423198	+	0.906037i	$0.639092\pi$
$744$		0			0
$745$	10.2426	−	17.7408i	0.375261	−	0.649972i
$746$		0			0
$747$	11.3137	+	19.5959i	0.413947	+	0.716977i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	13.5711	+	23.5058i	0.495215	+	0.857738i	0.999985	−	0.00551611i	$-0.00175584\pi$
$751$	13.5711	+	23.5058i	0.495215	+	0.857738i	−0.504769	+	0.863254i	$0.668423\pi$
$752$		0			0
$753$	15.6066	−	27.0314i	0.568736	−	0.985080i
$754$		0			0
$755$	6.17157			0.224607
$756$		0			0
$757$	42.8284			1.55663			0.778313	−	0.627877i	$-0.216076\pi$
$757$	42.8284			1.55663			0.778313	+	0.627877i	$0.216076\pi$
$758$		0			0
$759$	−7.53553	+	13.0519i	−0.273523	+	0.473755i
$760$		0			0
$761$	−17.4350	−	30.1984i	−0.632019	−	1.09469i	−0.987138	−	0.159868i	$-0.948893\pi$
$761$	−17.4350	−	30.1984i	−0.632019	−	1.09469i	0.355119	−	0.934821i	$-0.384440\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.07107	+	8.78335i	0.183345	+	0.317563i
$766$		0			0
$767$	−1.87868	+	3.25397i	−0.0678352	+	0.117494i
$768$		0			0
$769$	−0.142136			−0.00512554			−0.00256277	−	0.999997i	$-0.500816\pi$
$769$	−0.142136			−0.00512554			−0.00256277	+	0.999997i	$0.500816\pi$
$770$		0			0
$771$	33.3137			1.19976
$772$		0			0
$773$	9.13604	−	15.8241i	0.328600	−	0.569153i	−0.653634	−	0.756811i	$-0.726756\pi$
$773$	9.13604	−	15.8241i	0.328600	−	0.569153i	0.982234	+	0.187658i	$0.0600897\pi$
$774$		0			0
$775$	−3.70711	−	6.42090i	−0.133163	−	0.230645i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	13.0711	+	22.6398i	0.468320	+	0.811153i
$780$		0			0
$781$	9.58579	−	16.6031i	0.343006	−	0.594105i
$782$		0			0
$783$	1.92893			0.0689344
$784$		0			0
$785$	6.48528			0.231470
$786$		0			0
$787$	9.13604	−	15.8241i	0.325665	−	0.564068i	−0.655982	−	0.754777i	$-0.727745\pi$
$787$	9.13604	−	15.8241i	0.325665	−	0.564068i	0.981647	+	0.190709i	$0.0610786\pi$
$788$		0			0
$789$	−12.0711	−	20.9077i	−0.429741	−	0.744334i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−34.7279	−	60.1505i	−1.23322	−	2.13601i
$794$		0			0
$795$	−14.7782	+	25.5965i	−0.524128	+	0.907816i
$796$		0			0
$797$	1.38478			0.0490513			0.0245256	−	0.999699i	$-0.492192\pi$
$797$	1.38478			0.0490513			0.0245256	+	0.999699i	$0.492192\pi$
$798$		0			0
$799$	39.0833			1.38267
$800$		0			0
$801$	24.0000	−	41.5692i	0.847998	−	1.46878i
$802$		0			0
$803$	−9.89949	−	17.1464i	−0.349346	−	0.605084i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−10.5355	−	18.2481i	−0.370868	−	0.642363i
$808$		0			0
$809$	−19.9853	+	34.6155i	−0.702645	+	1.21702i	0.264890	+	0.964279i	$0.414664\pi$
$809$	−19.9853	+	34.6155i	−0.702645	+	1.21702i	−0.967535	+	0.252738i	$0.918669\pi$
$810$		0			0
$811$	11.5563			0.405798			0.202899	−	0.979200i	$-0.434964\pi$
$811$	11.5563			0.405798			0.202899	+	0.979200i	$0.434964\pi$
$812$		0			0
$813$	−12.0000			−0.420858
$814$		0			0
$815$	−4.77817	+	8.27604i	−0.167372	+	0.289897i
$816$		0			0
$817$	1.31371	+	2.27541i	0.0459608	+	0.0796065i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21.0858	−	36.5217i	−0.735899	−	1.27461i	−0.954328	−	0.298762i	$-0.903426\pi$
$821$	−21.0858	−	36.5217i	−0.735899	−	1.27461i	0.218429	−	0.975853i	$-0.429907\pi$
$822$		0			0
$823$	14.2635	−	24.7050i	0.497193	−	0.861163i	−0.502802	−	0.864402i	$-0.667697\pi$
$823$	14.2635	−	24.7050i	0.497193	−	0.861163i	0.999995	+	0.00323843i	$0.00103082\pi$
$824$		0			0
$825$	4.41421			0.153683
$826$		0			0
$827$	38.0416			1.32284			0.661419	−	0.750017i	$-0.269955\pi$
$827$	38.0416			1.32284			0.661419	+	0.750017i	$0.269955\pi$
$828$		0			0
$829$	1.36396	−	2.36245i	0.0473723	−	0.0820513i	−0.841367	−	0.540464i	$-0.818249\pi$
$829$	1.36396	−	2.36245i	0.0473723	−	0.0820513i	0.888739	+	0.458413i	$0.151582\pi$
$830$		0			0
$831$	5.53553	+	9.58783i	0.192026	+	0.332598i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.207107	−	0.358719i	−0.00716723	−	0.0124140i
$836$		0			0
$837$	1.53553	−	2.65962i	0.0530758	−	0.0919300i
$838$		0			0
$839$	−14.3848			−0.496618			−0.248309	−	0.968681i	$-0.579875\pi$
$839$	−14.3848			−0.496618			−0.248309	+	0.968681i	$0.579875\pi$
$840$		0			0
$841$	−7.31371			−0.252197
$842$		0			0
$843$	1.20711	−	2.09077i	0.0415750	−	0.0720100i
$844$		0			0
$845$	14.0711	+	24.3718i	0.484059	+	0.838416i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	32.8848	+	56.9581i	1.12860	+	1.95480i
$850$		0			0
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$		0			0
$853$	26.2843			0.899956			0.449978	−	0.893040i	$-0.351432\pi$
$853$	26.2843			0.899956			0.449978	+	0.893040i	$0.351432\pi$
$854$		0			0
$855$	21.6569			0.740649
$856$		0			0
$857$	7.58579	−	13.1390i	0.259126	−	0.448819i	−0.706882	−	0.707331i	$-0.749899\pi$
$857$	7.58579	−	13.1390i	0.259126	−	0.448819i	0.966008	+	0.258513i	$0.0832323\pi$
$858$		0			0
$859$	−2.72792	−	4.72490i	−0.0930755	−	0.161211i	0.815728	−	0.578435i	$-0.196336\pi$
$859$	−2.72792	−	4.72490i	−0.0930755	−	0.161211i	−0.908804	+	0.417224i	$0.863003\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	14.1213	+	24.4588i	0.480695	+	0.832589i	0.999755	−	0.0221495i	$-0.00705097\pi$
$863$	14.1213	+	24.4588i	0.480695	+	0.832589i	−0.519059	+	0.854738i	$0.673718\pi$
$864$		0			0
$865$	−6.27817	+	10.8741i	−0.213464	+	0.369731i
$866$		0			0
$867$	−10.0000			−0.339618
$868$		0			0
$869$	−27.6863			−0.939193
$870$		0			0
$871$	−9.84924	+	17.0594i	−0.333729	+	0.578035i
$872$		0			0
$873$	13.7574	+	23.8284i	0.465616	+	0.806471i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.6569	−	28.8505i	−0.562462	−	0.974213i	−0.997281	−	0.0736948i	$-0.976521\pi$
$877$	−16.6569	−	28.8505i	−0.562462	−	0.974213i	0.434819	−	0.900518i	$-0.356812\pi$
$878$		0			0
$879$	13.9853	−	24.2232i	0.471712	−	0.817029i
$880$		0			0
$881$	0.284271			0.00957734			0.00478867	−	0.999989i	$-0.498476\pi$
$881$	0.284271			0.00957734			0.00478867	+	0.999989i	$0.498476\pi$
$882$		0			0
$883$	55.1127			1.85469			0.927345	−	0.374208i	$-0.122085\pi$
$883$	55.1127			1.85469			0.927345	+	0.374208i	$0.122085\pi$
$884$		0			0
$885$	0.707107	−	1.22474i	0.0237691	−	0.0411693i
$886$		0			0
$887$	10.7990	+	18.7044i	0.362595	+	0.628032i	0.988387	−	0.151957i	$-0.0485576\pi$
$887$	10.7990	+	18.7044i	0.362595	+	0.628032i	−0.625792	+	0.779990i	$0.715224\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	8.67157	+	15.0196i	0.290509	+	0.503176i
$892$		0			0
$893$	41.7279	−	72.2749i	1.39637	−	2.41859i
$894$		0			0
$895$	10.4853			0.350484
$896$		0			0
$897$	52.8701			1.76528
$898$		0			0
$899$	17.2635	−	29.9012i	0.575768	−	0.997260i
$900$		0			0
$901$	21.9497	+	38.0181i	0.731252	+	1.26657i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	5.12132	+	8.87039i	0.170238	+	0.294862i
$906$		0			0
$907$	21.2635	−	36.8294i	0.706041	−	1.22290i	−0.260273	−	0.965535i	$-0.583813\pi$
$907$	21.2635	−	36.8294i	0.706041	−	1.22290i	0.966314	−	0.257365i	$-0.0828541\pi$
$908$		0			0
$909$	2.34315			0.0777172
$910$		0			0
$911$	23.5980			0.781836			0.390918	−	0.920426i	$-0.372158\pi$
$911$	23.5980			0.781836			0.390918	+	0.920426i	$0.372158\pi$
$912$		0			0
$913$	7.31371	−	12.6677i	0.242048	−	0.419240i
$914$		0			0
$915$	13.0711	+	22.6398i	0.432116	+	0.748447i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	17.7426	+	30.7312i	0.585276	+	1.01373i	0.994841	+	0.101446i	$0.0323471\pi$
$919$	17.7426	+	30.7312i	0.585276	+	1.01373i	−0.409565	+	0.912281i	$0.634320\pi$
$920$		0			0
$921$	−7.74264	+	13.4106i	−0.255129	+	0.441896i
$922$		0			0
$923$	−67.2548			−2.21372
$924$		0			0
$925$	−0.585786			−0.0192605
$926$		0			0
$927$	−6.24264	+	10.8126i	−0.205035	+	0.355131i
$928$		0			0
$929$	23.3640	+	40.4676i	0.766547	+	1.32770i	0.939425	+	0.342755i	$0.111360\pi$
$929$	23.3640	+	40.4676i	0.766547	+	1.32770i	−0.172878	+	0.984943i	$0.555307\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	32.5563	+	56.3893i	1.06585	+	1.84610i
$934$		0			0
$935$	3.27817	−	5.67796i	0.107208	−	0.185689i
$936$		0			0
$937$	17.7279			0.579146			0.289573	−	0.957156i	$-0.406487\pi$
$937$	17.7279			0.579146			0.289573	+	0.957156i	$0.406487\pi$
$938$		0			0
$939$	−35.1421			−1.14682
$940$		0			0
$941$	2.00000	−	3.46410i	0.0651981	−	0.112926i	−0.831584	−	0.555399i	$-0.812565\pi$
$941$	2.00000	−	3.46410i	0.0651981	−	0.112926i	0.896782	+	0.442473i	$0.145899\pi$
$942$		0			0
$943$	−5.82843	−	10.0951i	−0.189800	−	0.328743i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.02082	−	13.8925i	−0.260641	−	0.451444i	0.705771	−	0.708440i	$-0.250601\pi$
$947$	−8.02082	−	13.8925i	−0.260641	−	0.451444i	−0.966413	+	0.256996i	$0.917267\pi$
$948$		0			0
$949$	−34.7279	+	60.1505i	−1.12732	+	1.95257i
$950$		0			0
$951$	45.7990			1.48513
$952$		0			0
$953$	14.8701			0.481688			0.240844	−	0.970564i	$-0.422576\pi$
$953$	14.8701			0.481688			0.240844	+	0.970564i	$0.422576\pi$
$954$		0			0
$955$	2.67157	−	4.62730i	0.0864501	−	0.149736i
$956$		0			0
$957$	10.2782	+	17.8023i	0.332246	+	0.575467i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−11.9853	−	20.7591i	−0.386622	−	0.669649i
$962$		0			0
$963$	15.7990	−	27.3647i	0.509115	−	0.881814i
$964$		0			0
$965$	5.65685			0.182101
$966$		0			0
$967$	43.4558			1.39745			0.698723	−	0.715392i	$-0.253752\pi$
$967$	43.4558			1.39745			0.698723	+	0.715392i	$0.253752\pi$
$968$		0			0
$969$	33.1421	−	57.4039i	1.06468	−	1.84408i
$970$		0			0
$971$	−21.2635	−	36.8294i	−0.682377	−	1.18191i	−0.974254	−	0.225455i	$-0.927613\pi$
$971$	−21.2635	−	36.8294i	−0.682377	−	1.18191i	0.291877	−	0.956456i	$-0.405720\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−7.74264	−	13.4106i	−0.247963	−	0.429484i
$976$		0			0
$977$	−10.0711	+	17.4436i	−0.322202	+	0.558070i	−0.980942	−	0.194300i	$-0.937756\pi$
$977$	−10.0711	+	17.4436i	−0.322202	+	0.558070i	0.658740	+	0.752371i	$0.271090\pi$
$978$		0			0
$979$	−31.0294			−0.991705
$980$		0			0
$981$	25.4558			0.812743
$982$		0			0
$983$	−20.0061	+	34.6516i	−0.638095	+	1.10521i	0.347755	+	0.937585i	$0.386944\pi$
$983$	−20.0061	+	34.6516i	−0.638095	+	1.10521i	−0.985850	+	0.167628i	$0.946389\pi$
$984$		0			0
$985$	1.77817	+	3.07989i	0.0566574	+	0.0981334i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.585786	−	1.01461i	−0.0186269	−	0.0322628i
$990$		0			0
$991$	−1.34315	+	2.32640i	−0.0426664	+	0.0739004i	−0.886570	−	0.462594i	$-0.846919\pi$
$991$	−1.34315	+	2.32640i	−0.0426664	+	0.0739004i	0.843904	+	0.536495i	$0.180252\pi$
$992$		0			0
$993$	−2.00000			−0.0634681
$994$		0			0
$995$	1.27208			0.0403276
$996$		0			0
$997$	−18.4203	+	31.9049i	−0.583377	+	1.01044i	0.411699	+	0.911320i	$0.364936\pi$
$997$	−18.4203	+	31.9049i	−0.583377	+	1.01044i	−0.995076	+	0.0991186i	$0.968398\pi$
$998$		0			0
$999$	−0.121320	−	0.210133i	−0.00383841	−	0.00664831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.i.k.361.1		4
7.2	even	3	inner	980.2.i.k.961.1		4
7.3	odd	6		980.2.a.j.1.1	✓	2
7.4	even	3		980.2.a.k.1.2	yes	2
7.5	odd	6		980.2.i.l.961.2		4
7.6	odd	2		980.2.i.l.361.2		4
21.11	odd	6		8820.2.a.bl.1.1		2
21.17	even	6		8820.2.a.bg.1.1		2
28.3	even	6		3920.2.a.bx.1.2		2
28.11	odd	6		3920.2.a.bo.1.1		2
35.3	even	12		4900.2.e.q.2549.1		4
35.4	even	6		4900.2.a.x.1.1		2
35.17	even	12		4900.2.e.q.2549.4		4
35.18	odd	12		4900.2.e.r.2549.4		4
35.24	odd	6		4900.2.a.z.1.2		2
35.32	odd	12		4900.2.e.r.2549.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.a.j.1.1	✓	2	7.3	odd	6
980.2.a.k.1.2	yes	2	7.4	even	3
980.2.i.k.361.1		4	1.1	even	1	trivial
980.2.i.k.961.1		4	7.2	even	3	inner
980.2.i.l.361.2		4	7.6	odd	2
980.2.i.l.961.2		4	7.5	odd	6
3920.2.a.bo.1.1		2	28.11	odd	6
3920.2.a.bx.1.2		2	28.3	even	6
4900.2.a.x.1.1		2	35.4	even	6
4900.2.a.z.1.2		2	35.24	odd	6
4900.2.e.q.2549.1		4	35.3	even	12
4900.2.e.q.2549.4		4	35.17	even	12
4900.2.e.r.2549.1		4	35.32	odd	12
4900.2.e.r.2549.4		4	35.18	odd	12
8820.2.a.bg.1.1		2	21.17	even	6
8820.2.a.bl.1.1		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.41421 - 2.44949i) q^{9} +(-0.914214 + 1.58346i) q^{11} +6.41421 q^{13} -2.41421 q^{15} +(-1.79289 + 3.10538i) q^{17} +(3.82843 + 6.63103i) q^{19} +(-1.70711 - 2.95680i) q^{23} +(-0.500000 + 0.866025i) q^{25} -0.414214 q^{27} -4.65685 q^{29} +(-3.70711 + 6.42090i) q^{31} +(-2.20711 - 3.82282i) q^{33} +(0.292893 + 0.507306i) q^{37} +(-7.74264 + 13.4106i) q^{39} +3.41421 q^{41} +0.343146 q^{43} +(1.41421 - 2.44949i) q^{45} +(-5.44975 - 9.43924i) q^{47} +(-4.32843 - 7.49706i) q^{51} +(6.12132 - 10.6024i) q^{53} -1.82843 q^{55} -18.4853 q^{57} +(-0.292893 + 0.507306i) q^{59} +(-5.41421 - 9.37769i) q^{61} +(3.20711 + 5.55487i) q^{65} +(-1.53553 + 2.65962i) q^{67} +8.24264 q^{69} -10.4853 q^{71} +(-5.41421 + 9.37769i) q^{73} +(-1.20711 - 2.09077i) q^{75} +(7.57107 + 13.1135i) q^{79} +(4.74264 - 8.21449i) q^{81} -8.00000 q^{83} -3.58579 q^{85} +(5.62132 - 9.73641i) q^{87} +(8.48528 + 14.6969i) q^{89} +(-8.94975 - 15.5014i) q^{93} +(-3.82843 + 6.63103i) q^{95} -9.72792 q^{97} +5.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 20 q^{13} - 4 q^{15} - 10 q^{17} + 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} - 6 q^{33} + 4 q^{37} - 14 q^{39} + 8 q^{41} + 24 q^{43} - 2 q^{47}+ \cdots + 32 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 + 2 * q^11 + 20 * q^13 - 4 * q^15 - 10 * q^17 + 4 * q^19 - 4 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 - 12 * q^31 - 6 * q^33 + 4 * q^37 - 14 * q^39 + 8 * q^41 + 24 * q^43 - 2 * q^47 - 6 * q^51 + 16 * q^53 + 4 * q^55 - 40 * q^57 - 4 * q^59 - 16 * q^61 + 10 * q^65 + 8 * q^67 + 16 * q^69 - 8 * q^71 - 16 * q^73 - 2 * q^75 + 2 * q^79 + 2 * q^81 - 32 * q^83 - 20 * q^85 + 14 * q^87 - 16 * q^93 - 4 * q^95 + 12 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more