LMFDB - Embedded newform 980.2.i.k.361.2

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			361.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	980.361
Dual form			980.2.i.k.961.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +(1.91421 - 3.31552i) q^{11} +3.58579 q^{13} +0.414214 q^{15} +(-3.20711 + 5.55487i) q^{17} +(-1.82843 - 3.16693i) q^{19} +(-0.292893 - 0.507306i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.41421 q^{27} +6.65685 q^{29} +(-2.29289 + 3.97141i) q^{31} +(-0.792893 - 1.37333i) q^{33} +(1.70711 + 2.95680i) q^{37} +(0.742641 - 1.28629i) q^{39} +0.585786 q^{41} +11.6569 q^{43} +(-1.41421 + 2.44949i) q^{45} +(4.44975 + 7.70719i) q^{47} +(1.32843 + 2.30090i) q^{51} +(1.87868 - 3.25397i) q^{53} +3.82843 q^{55} -1.51472 q^{57} +(-1.70711 + 2.95680i) q^{59} +(-2.58579 - 4.47871i) q^{61} +(1.79289 + 3.10538i) q^{65} +(5.53553 - 9.58783i) q^{67} -0.242641 q^{69} +6.48528 q^{71} +(-2.58579 + 4.47871i) q^{73} +(0.207107 + 0.358719i) q^{75} +(-6.57107 - 11.3814i) q^{79} +(-3.74264 + 6.48244i) q^{81} -8.00000 q^{83} -6.41421 q^{85} +(1.37868 - 2.38794i) q^{87} +(-8.48528 - 14.6969i) q^{89} +(0.949747 + 1.64501i) q^{93} +(1.82843 - 3.16693i) q^{95} +15.7279 q^{97} +10.8284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$		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
$11$	1.91421	−	3.31552i	0.577157	−	0.999665i	−0.418646	−	0.908149i	$-0.637495\pi$
$11$	1.91421	−	3.31552i	0.577157	−	0.999665i	0.995804	−	0.0915161i	$-0.0291713\pi$
$12$		0			0
$13$	3.58579			0.994518			0.497259	−	0.867602i	$-0.334340\pi$
$13$	3.58579			0.994518			0.497259	+	0.867602i	$0.334340\pi$
$14$		0			0
$15$	0.414214			0.106949
$16$		0			0
$17$	−3.20711	+	5.55487i	−0.777838	+	1.34725i	0.155348	+	0.987860i	$0.450350\pi$
$17$	−3.20711	+	5.55487i	−0.777838	+	1.34725i	−0.933186	+	0.359395i	$0.882983\pi$
$18$		0			0
$19$	−1.82843	−	3.16693i	−0.419470	−	0.726543i	0.576416	−	0.817156i	$-0.304451\pi$
$19$	−1.82843	−	3.16693i	−0.419470	−	0.726543i	−0.995886	+	0.0906130i	$0.971117\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.292893	−	0.507306i	−0.0610725	−	0.105781i	0.833873	−	0.551957i	$-0.186119\pi$
$23$	−0.292893	−	0.507306i	−0.0610725	−	0.105781i	−0.894945	+	0.446176i	$0.852785\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.41421			0.464616
$28$		0			0
$29$	6.65685			1.23615			0.618073	−	0.786120i	$-0.287913\pi$
$29$	6.65685			1.23615			0.618073	+	0.786120i	$0.287913\pi$
$30$		0			0
$31$	−2.29289	+	3.97141i	−0.411816	+	0.713286i	−0.995088	−	0.0989906i	$-0.968439\pi$
$31$	−2.29289	+	3.97141i	−0.411816	+	0.713286i	0.583273	+	0.812276i	$0.301772\pi$
$32$		0			0
$33$	−0.792893	−	1.37333i	−0.138025	−	0.239066i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.70711	+	2.95680i	0.280647	+	0.486094i	0.971544	−	0.236858i	$-0.0761178\pi$
$37$	1.70711	+	2.95680i	0.280647	+	0.486094i	−0.690898	+	0.722953i	$0.742784\pi$
$38$		0			0
$39$	0.742641	−	1.28629i	0.118918	−	0.205971i
$40$		0			0
$41$	0.585786			0.0914845			0.0457422	−	0.998953i	$-0.485435\pi$
$41$	0.585786			0.0914845			0.0457422	+	0.998953i	$0.485435\pi$
$42$		0			0
$43$	11.6569			1.77765			0.888827	−	0.458243i	$-0.151521\pi$
$43$	11.6569			1.77765			0.888827	+	0.458243i	$0.151521\pi$
$44$		0			0
$45$	−1.41421	+	2.44949i	−0.210819	+	0.365148i
$46$		0			0
$47$	4.44975	+	7.70719i	0.649062	+	1.12421i	0.983347	+	0.181737i	$0.0581719\pi$
$47$	4.44975	+	7.70719i	0.649062	+	1.12421i	−0.334285	+	0.942472i	$0.608495\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.32843	+	2.30090i	0.186017	+	0.322191i
$52$		0			0
$53$	1.87868	−	3.25397i	0.258056	−	0.446967i	−0.707665	−	0.706548i	$-0.750251\pi$
$53$	1.87868	−	3.25397i	0.258056	−	0.446967i	0.965721	+	0.259581i	$0.0835846\pi$
$54$		0			0
$55$	3.82843			0.516225
$56$		0			0
$57$	−1.51472			−0.200629
$58$		0			0
$59$	−1.70711	+	2.95680i	−0.222246	+	0.384942i	−0.955490	−	0.295024i	$-0.904672\pi$
$59$	−1.70711	+	2.95680i	−0.222246	+	0.384942i	0.733243	+	0.679966i	$0.238006\pi$
$60$		0			0
$61$	−2.58579	−	4.47871i	−0.331076	−	0.573441i	0.651647	−	0.758522i	$-0.274078\pi$
$61$	−2.58579	−	4.47871i	−0.331076	−	0.573441i	−0.982723	+	0.185082i	$0.940745\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.79289	+	3.10538i	0.222381	+	0.385175i
$66$		0			0
$67$	5.53553	−	9.58783i	0.676273	−	1.17134i	−0.299822	−	0.953995i	$-0.596927\pi$
$67$	5.53553	−	9.58783i	0.676273	−	1.17134i	0.976095	−	0.217344i	$-0.0697394\pi$
$68$		0			0
$69$	−0.242641			−0.0292105
$70$		0			0
$71$	6.48528			0.769661			0.384831	−	0.922987i	$-0.374260\pi$
$71$	6.48528			0.769661			0.384831	+	0.922987i	$0.374260\pi$
$72$		0			0
$73$	−2.58579	+	4.47871i	−0.302643	+	0.524194i	−0.976734	−	0.214455i	$-0.931202\pi$
$73$	−2.58579	+	4.47871i	−0.302643	+	0.524194i	0.674090	+	0.738649i	$0.264536\pi$
$74$		0			0
$75$	0.207107	+	0.358719i	0.0239146	+	0.0414214i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−6.57107	−	11.3814i	−0.739303	−	1.28051i	−0.952810	−	0.303569i	$-0.901822\pi$
$79$	−6.57107	−	11.3814i	−0.739303	−	1.28051i	0.213507	−	0.976942i	$-0.431511\pi$
$80$		0			0
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$		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
$85$	−6.41421			−0.695719
$86$		0			0
$87$	1.37868	−	2.38794i	0.147810	−	0.256014i
$88$		0			0
$89$	−8.48528	−	14.6969i	−0.899438	−	1.55787i	−0.828214	−	0.560412i	$-0.810643\pi$
$89$	−8.48528	−	14.6969i	−0.899438	−	1.55787i	−0.0712241	−	0.997460i	$-0.522691\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.949747	+	1.64501i	0.0984842	+	0.170580i
$94$		0			0
$95$	1.82843	−	3.16693i	0.187593	−	0.324920i
$96$		0			0
$97$	15.7279			1.59693			0.798464	−	0.602042i	$-0.205646\pi$
$97$	15.7279			1.59693			0.798464	+	0.602042i	$0.205646\pi$
$98$		0			0
$99$	10.8284			1.08830
$100$		0			0
$101$	2.41421	−	4.18154i	0.240223	−	0.416079i	−0.720555	−	0.693398i	$-0.756113\pi$
$101$	2.41421	−	4.18154i	0.240223	−	0.416079i	0.960778	+	0.277319i	$0.0894460\pi$
$102$		0			0
$103$	−0.792893	−	1.37333i	−0.0781261	−	0.135318i	0.824315	−	0.566131i	$-0.191560\pi$
$103$	−0.792893	−	1.37333i	−0.0781261	−	0.135318i	−0.902441	+	0.430813i	$0.858227\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.41421	+	14.5738i	0.813433	+	1.40891i	0.910448	+	0.413624i	$0.135737\pi$
$107$	8.41421	+	14.5738i	0.813433	+	1.40891i	−0.0970151	+	0.995283i	$0.530930\pi$
$108$		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
$113$	−5.07107			−0.477046			−0.238523	−	0.971137i	$-0.576663\pi$
$113$	−5.07107			−0.477046			−0.238523	+	0.971137i	$0.576663\pi$
$114$		0			0
$115$	0.292893	−	0.507306i	0.0273124	−	0.0473065i
$116$		0			0
$117$	5.07107	+	8.78335i	0.468820	+	0.812021i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−1.82843	−	3.16693i	−0.166221	−	0.287903i
$122$		0			0
$123$	0.121320	−	0.210133i	0.0109391	−	0.0189471i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−21.8995			−1.94327			−0.971633	−	0.236494i	$-0.924002\pi$
$127$	−21.8995			−1.94327			−0.971633	+	0.236494i	$0.924002\pi$
$128$		0			0
$129$	2.41421	−	4.18154i	0.212560	−	0.368164i
$130$		0			0
$131$	5.87868	+	10.1822i	0.513623	+	0.889620i	0.999875	+	0.0158021i	$0.00503019\pi$
$131$	5.87868	+	10.1822i	0.513623	+	0.889620i	−0.486253	+	0.873818i	$0.661636\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	1.20711	+	2.09077i	0.103891	+	0.179945i
$136$		0			0
$137$	−6.48528	+	11.2328i	−0.554075	+	0.959686i	0.443900	+	0.896076i	$0.353595\pi$
$137$	−6.48528	+	11.2328i	−0.554075	+	0.959686i	−0.997975	+	0.0636096i	$0.979739\pi$
$138$		0			0
$139$	−13.8995			−1.17894			−0.589470	−	0.807790i	$-0.700663\pi$
$139$	−13.8995			−1.17894			−0.589470	+	0.807790i	$0.700663\pi$
$140$		0			0
$141$	3.68629			0.310442
$142$		0			0
$143$	6.86396	−	11.8887i	0.573993	−	0.994185i
$144$		0			0
$145$	3.32843	+	5.76500i	0.276411	+	0.478758i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.75736	−	3.04384i	−0.143968	−	0.249361i	0.785019	−	0.619472i	$-0.212653\pi$
$149$	−1.75736	−	3.04384i	−0.143968	−	0.249361i	−0.928988	+	0.370111i	$0.879320\pi$
$150$		0			0
$151$	5.91421	−	10.2437i	0.481292	−	0.833622i	−0.518478	−	0.855091i	$-0.673501\pi$
$151$	5.91421	−	10.2437i	0.481292	−	0.833622i	0.999770	+	0.0214692i	$0.00683439\pi$
$152$		0			0
$153$	−18.1421			−1.46670
$154$		0			0
$155$	−4.58579			−0.368339
$156$		0			0
$157$	−5.24264	+	9.08052i	−0.418408	+	0.724704i	−0.995780	−	0.0917773i	$-0.970745\pi$
$157$	−5.24264	+	9.08052i	−0.418408	+	0.724704i	0.577371	+	0.816482i	$0.304079\pi$
$158$		0			0
$159$	−0.778175	−	1.34784i	−0.0617133	−	0.106891i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.7782	−	18.6683i	−0.844212	−	1.46222i	−0.886304	−	0.463104i	$-0.846736\pi$
$163$	−10.7782	−	18.6683i	−0.844212	−	1.46222i	0.0420922	−	0.999114i	$-0.486598\pi$
$164$		0			0
$165$	0.792893	−	1.37333i	0.0617267	−	0.106914i
$166$		0			0
$167$	2.41421			0.186817			0.0934087	−	0.995628i	$-0.470224\pi$
$167$	2.41421			0.186817			0.0934087	+	0.995628i	$0.470224\pi$
$168$		0			0
$169$	−0.142136			−0.0109335
$170$		0			0
$171$	5.17157	−	8.95743i	0.395480	−	0.684992i
$172$		0			0
$173$	−9.27817	−	16.0703i	−0.705407	−	1.22180i	−0.966545	−	0.256499i	$-0.917431\pi$
$173$	−9.27817	−	16.0703i	−0.705407	−	1.22180i	0.261138	−	0.965301i	$-0.415902\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.707107	+	1.22474i	0.0531494	+	0.0920575i
$178$		0			0
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	−0.961388	−	0.275197i	$-0.911257\pi$
$179$	−3.24264	+	5.61642i	−0.242366	+	0.419791i	0.719022	+	0.694988i	$0.244590\pi$
$180$		0			0
$181$	1.75736			0.130623			0.0653117	−	0.997865i	$-0.479196\pi$
$181$	1.75736			0.130623			0.0653117	+	0.997865i	$0.479196\pi$
$182$		0			0
$183$	−2.14214			−0.158351
$184$		0			0
$185$	−1.70711	+	2.95680i	−0.125509	+	0.217388i
$186$		0			0
$187$	12.2782	+	21.2664i	0.897869	+	1.55515i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.32843	−	14.4253i	−0.602624	−	1.04378i	−0.992422	−	0.122875i	$-0.960789\pi$
$191$	−8.32843	−	14.4253i	−0.602624	−	1.04378i	0.389798	−	0.920900i	$-0.372545\pi$
$192$		0			0
$193$	−2.82843	+	4.89898i	−0.203595	+	0.352636i	−0.949684	−	0.313210i	$-0.898596\pi$
$193$	−2.82843	+	4.89898i	−0.203595	+	0.352636i	0.746089	+	0.665846i	$0.231929\pi$
$194$		0			0
$195$	1.48528			0.106363
$196$		0			0
$197$	−27.5563			−1.96331			−0.981654	−	0.190669i	$-0.938934\pi$
$197$	−27.5563			−1.96331			−0.981654	+	0.190669i	$0.938934\pi$
$198$		0			0
$199$	13.3640	−	23.1471i	0.947346	−	1.64085i	0.196362	−	0.980532i	$-0.437087\pi$
$199$	13.3640	−	23.1471i	0.947346	−	1.64085i	0.750984	−	0.660320i	$-0.229579\pi$
$200$		0			0
$201$	−2.29289	−	3.97141i	−0.161728	−	0.280121i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.292893	+	0.507306i	0.0204565	+	0.0354318i
$206$		0			0
$207$	0.828427	−	1.43488i	0.0575797	−	0.0997309i
$208$		0			0
$209$	−14.0000			−0.968400
$210$		0			0
$211$	−24.3137			−1.67382			−0.836912	−	0.547337i	$-0.815642\pi$
$211$	−24.3137			−1.67382			−0.836912	+	0.547337i	$0.815642\pi$
$212$		0			0
$213$	1.34315	−	2.32640i	0.0920308	−	0.159402i
$214$		0			0
$215$	5.82843	+	10.0951i	0.397495	+	0.688482i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	1.07107	+	1.85514i	0.0723761	+	0.125359i
$220$		0			0
$221$	−11.5000	+	19.9186i	−0.773574	+	1.33987i
$222$		0			0
$223$	24.0711			1.61192			0.805959	−	0.591971i	$-0.201650\pi$
$223$	24.0711			1.61192			0.805959	+	0.591971i	$0.201650\pi$
$224$		0			0
$225$	−2.82843			−0.188562
$226$		0			0
$227$	−3.86396	+	6.69258i	−0.256460	+	0.444202i	−0.965291	−	0.261176i	$-0.915890\pi$
$227$	−3.86396	+	6.69258i	−0.256460	+	0.444202i	0.708831	+	0.705378i	$0.249223\pi$
$228$		0			0
$229$	−11.9497	−	20.6976i	−0.789662	−	1.36773i	−0.926174	−	0.377096i	$-0.876923\pi$
$229$	−11.9497	−	20.6976i	−0.789662	−	1.36773i	0.136513	−	0.990638i	$-0.456411\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.58579	+	7.94282i	0.300425	+	0.520351i	0.976232	−	0.216727i	$-0.0695382\pi$
$233$	4.58579	+	7.94282i	0.300425	+	0.520351i	−0.675807	+	0.737078i	$0.736205\pi$
$234$		0			0
$235$	−4.44975	+	7.70719i	−0.290270	+	0.502762i
$236$		0			0
$237$	−5.44365			−0.353603
$238$		0			0
$239$	14.1716			0.916683			0.458341	−	0.888776i	$-0.348444\pi$
$239$	14.1716			0.916683			0.458341	+	0.888776i	$0.348444\pi$
$240$		0			0
$241$	1.77817	−	3.07989i	0.114542	−	0.198393i	−0.803054	−	0.595906i	$-0.796793\pi$
$241$	1.77817	−	3.07989i	0.114542	−	0.198393i	0.917597	+	0.397513i	$0.130127\pi$
$242$		0			0
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−6.55635	−	11.3559i	−0.417171	−	0.722561i
$248$		0			0
$249$	−1.65685	+	2.86976i	−0.104999	+	0.181863i
$250$		0			0
$251$	−27.0711			−1.70871			−0.854355	−	0.519689i	$-0.826048\pi$
$251$	−27.0711			−1.70871			−0.854355	+	0.519689i	$0.826048\pi$
$252$		0			0
$253$	−2.24264			−0.140994
$254$		0			0
$255$	−1.32843	+	2.30090i	−0.0831893	+	0.144088i
$256$		0			0
$257$	12.8995	+	22.3426i	0.804648	+	1.39369i	0.916528	+	0.399970i	$0.130980\pi$
$257$	12.8995	+	22.3426i	0.804648	+	1.39369i	−0.111880	+	0.993722i	$0.535687\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	9.41421	+	16.3059i	0.582725	+	1.00931i
$262$		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
$265$	3.75736			0.230813
$266$		0			0
$267$	−7.02944			−0.430195
$268$		0			0
$269$	8.36396	−	14.4868i	0.509960	−	0.883276i	−0.489974	−	0.871737i	$-0.662994\pi$
$269$	8.36396	−	14.4868i	0.509960	−	0.883276i	0.999933	−	0.0115389i	$-0.00367303\pi$
$270$		0			0
$271$	−14.4853	−	25.0892i	−0.879918	−	1.52406i	−0.851430	−	0.524469i	$-0.824264\pi$
$271$	−14.4853	−	25.0892i	−0.879918	−	1.52406i	−0.0284886	−	0.999594i	$-0.509069\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.91421	+	3.31552i	0.115431	+	0.199933i
$276$		0			0
$277$	3.70711	−	6.42090i	0.222738	−	0.385794i	−0.732900	−	0.680336i	$-0.761834\pi$
$277$	3.70711	−	6.42090i	0.222738	−	0.385794i	0.955639	+	0.294542i	$0.0951671\pi$
$278$		0			0
$279$	−12.9706			−0.776527
$280$		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
$283$	9.37868	−	16.2443i	0.557505	−	0.965626i	−0.440199	−	0.897900i	$-0.645092\pi$
$283$	9.37868	−	16.2443i	0.557505	−	0.965626i	0.997704	−	0.0677263i	$-0.0215745\pi$
$284$		0			0
$285$	−0.757359	−	1.31178i	−0.0448621	−	0.0777034i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−12.0711	−	20.9077i	−0.710063	−	1.22986i
$290$		0			0
$291$	3.25736	−	5.64191i	0.190950	−	0.330735i
$292$		0			0
$293$	−14.4142			−0.842087			−0.421044	−	0.907040i	$-0.638336\pi$
$293$	−14.4142			−0.842087			−0.421044	+	0.907040i	$0.638336\pi$
$294$		0			0
$295$	−3.41421			−0.198783
$296$		0			0
$297$	4.62132	−	8.00436i	0.268156	−	0.464460i
$298$		0			0
$299$	−1.05025	−	1.81909i	−0.0607377	−	0.105201i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−1.00000	−	1.73205i	−0.0574485	−	0.0995037i
$304$		0			0
$305$	2.58579	−	4.47871i	0.148062	−	0.256450i
$306$		0			0
$307$	3.58579			0.204652			0.102326	−	0.994751i	$-0.467372\pi$
$307$	3.58579			0.204652			0.102326	+	0.994751i	$0.467372\pi$
$308$		0			0
$309$	−0.656854			−0.0373671
$310$		0			0
$311$	−3.48528	+	6.03668i	−0.197632	+	0.342309i	−0.947760	−	0.318984i	$-0.896658\pi$
$311$	−3.48528	+	6.03668i	−0.197632	+	0.342309i	0.750128	+	0.661293i	$0.229992\pi$
$312$		0			0
$313$	−8.27817	−	14.3382i	−0.467910	−	0.810444i	0.531417	−	0.847110i	$-0.321660\pi$
$313$	−8.27817	−	14.3382i	−0.467910	−	0.810444i	−0.999328	+	0.0366660i	$0.988326\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.48528	+	12.9649i	0.420415	+	0.728181i	0.995980	−	0.0895756i	$-0.0285511\pi$
$317$	7.48528	+	12.9649i	0.420415	+	0.728181i	−0.575565	+	0.817756i	$0.695218\pi$
$318$		0			0
$319$	12.7426	−	22.0709i	0.713451	−	1.23573i
$320$		0			0
$321$	6.97056			0.389059
$322$		0			0
$323$	23.4558			1.30512
$324$		0			0
$325$	−1.79289	+	3.10538i	−0.0994518	+	0.172256i
$326$		0			0
$327$	1.86396	+	3.22848i	0.103077	+	0.178535i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−2.41421	−	4.18154i	−0.132697	−	0.229838i	0.792018	−	0.610497i	$-0.209030\pi$
$331$	−2.41421	−	4.18154i	−0.132697	−	0.229838i	−0.924715	+	0.380659i	$0.875697\pi$
$332$		0			0
$333$	−4.82843	+	8.36308i	−0.264596	+	0.458294i
$334$		0			0
$335$	11.0711			0.604877
$336$		0			0
$337$	−18.7279			−1.02017			−0.510087	−	0.860123i	$-0.670387\pi$
$337$	−18.7279			−1.02017			−0.510087	+	0.860123i	$0.670387\pi$
$338$		0			0
$339$	−1.05025	+	1.81909i	−0.0570419	+	0.0987994i
$340$		0			0
$341$	8.77817	+	15.2042i	0.475365	+	0.823356i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.121320	−	0.210133i	−0.00653167	−	0.0113132i
$346$		0			0
$347$	3.70711	−	6.42090i	0.199008	−	0.344692i	−0.749199	−	0.662345i	$-0.769561\pi$
$347$	3.70711	−	6.42090i	0.199008	−	0.344692i	0.948207	+	0.317653i	$0.102895\pi$
$348$		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
$351$	8.65685			0.462069
$352$		0			0
$353$	1.03553	−	1.79360i	0.0551159	−	0.0954636i	−0.837151	−	0.546972i	$-0.815781\pi$
$353$	1.03553	−	1.79360i	0.0551159	−	0.0954636i	0.892267	+	0.451508i	$0.149114\pi$
$354$		0			0
$355$	3.24264	+	5.61642i	0.172101	+	0.298089i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.65685	−	9.79796i	−0.298557	−	0.517116i	0.677249	−	0.735754i	$-0.263172\pi$
$359$	−5.65685	−	9.79796i	−0.298557	−	0.517116i	−0.975806	+	0.218638i	$0.929839\pi$
$360$		0			0
$361$	2.81371	−	4.87349i	0.148090	−	0.256499i
$362$		0			0
$363$	−1.51472			−0.0795021
$364$		0			0
$365$	−5.17157			−0.270692
$366$		0			0
$367$	−9.86396	+	17.0849i	−0.514895	+	0.891824i	0.484956	+	0.874539i	$0.338836\pi$
$367$	−9.86396	+	17.0849i	−0.514895	+	0.891824i	−0.999851	+	0.0172850i	$0.994498\pi$
$368$		0			0
$369$	0.828427	+	1.43488i	0.0431262	+	0.0746968i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.24264	−	14.2767i	−0.426788	−	0.739218i	0.569798	−	0.821785i	$-0.307022\pi$
$373$	−8.24264	−	14.2767i	−0.426788	−	0.739218i	−0.996586	+	0.0825669i	$0.973688\pi$
$374$		0			0
$375$	−0.207107	+	0.358719i	−0.0106949	+	0.0185242i
$376$		0			0
$377$	23.8701			1.22937
$378$		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
$381$	−4.53553	+	7.85578i	−0.232362	+	0.402464i
$382$		0			0
$383$	1.75736	+	3.04384i	0.0897969	+	0.155533i	0.907425	−	0.420214i	$-0.138045\pi$
$383$	1.75736	+	3.04384i	0.0897969	+	0.155533i	−0.817628	+	0.575746i	$0.804712\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	16.4853	+	28.5533i	0.837994	+	1.45145i
$388$		0			0
$389$	−6.57107	+	11.3814i	−0.333166	+	0.577061i	−0.983131	−	0.182903i	$-0.941450\pi$
$389$	−6.57107	+	11.3814i	−0.333166	+	0.577061i	0.649965	+	0.759965i	$0.274784\pi$
$390$		0			0
$391$	3.75736			0.190018
$392$		0			0
$393$	4.87006			0.245662
$394$		0			0
$395$	6.57107	−	11.3814i	0.330626	−	0.572662i
$396$		0			0
$397$	−7.20711	−	12.4831i	−0.361714	−	0.626508i	0.626529	−	0.779398i	$-0.284475\pi$
$397$	−7.20711	−	12.4831i	−0.361714	−	0.626508i	−0.988243	+	0.152891i	$0.951142\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−0.257359	−	0.445759i	−0.0128519	−	0.0222602i	0.859528	−	0.511089i	$-0.170758\pi$
$401$	−0.257359	−	0.445759i	−0.0128519	−	0.0222602i	−0.872380	+	0.488829i	$0.837424\pi$
$402$		0			0
$403$	−8.22183	+	14.2406i	−0.409558	+	0.709376i
$404$		0			0
$405$	−7.48528			−0.371947
$406$		0			0
$407$	13.0711			0.647909
$408$		0			0
$409$	−16.4142	+	28.4303i	−0.811631	+	1.40579i	0.100092	+	0.994978i	$0.468086\pi$
$409$	−16.4142	+	28.4303i	−0.811631	+	1.40579i	−0.911722	+	0.410807i	$0.865247\pi$
$410$		0			0
$411$	2.68629	+	4.65279i	0.132505	+	0.229505i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−4.00000	−	6.92820i	−0.196352	−	0.340092i
$416$		0			0
$417$	−2.87868	+	4.98602i	−0.140970	+	0.244166i
$418$		0			0
$419$	−9.55635			−0.466858			−0.233429	−	0.972374i	$-0.574995\pi$
$419$	−9.55635			−0.466858			−0.233429	+	0.972374i	$0.574995\pi$
$420$		0			0
$421$	20.3137			0.990030			0.495015	−	0.868885i	$-0.335163\pi$
$421$	20.3137			0.990030			0.495015	+	0.868885i	$0.335163\pi$
$422$		0			0
$423$	−12.5858	+	21.7992i	−0.611942	+	1.05991i
$424$		0			0
$425$	−3.20711	−	5.55487i	−0.155568	−	0.269451i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.84315	−	4.92447i	−0.137268	−	0.237756i
$430$		0			0
$431$	4.91421	−	8.51167i	0.236709	−	0.409993i	−0.723059	−	0.690787i	$-0.757264\pi$
$431$	4.91421	−	8.51167i	0.236709	−	0.409993i	0.959768	+	0.280794i	$0.0905978\pi$
$432$		0			0
$433$	−22.2843			−1.07091			−0.535457	−	0.844563i	$-0.679861\pi$
$433$	−22.2843			−1.07091			−0.535457	+	0.844563i	$0.679861\pi$
$434$		0			0
$435$	2.75736			0.132205
$436$		0			0
$437$	−1.07107	+	1.85514i	−0.0512361	+	0.0887436i
$438$		0			0
$439$	−12.1213	−	20.9947i	−0.578519	−	1.00202i	−0.995649	−	0.0931778i	$-0.970298\pi$
$439$	−12.1213	−	20.9947i	−0.578519	−	1.00202i	0.417130	−	0.908847i	$-0.363036\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.7279	+	30.7057i	0.842279	+	1.45887i	0.887963	+	0.459914i	$0.152120\pi$
$443$	17.7279	+	30.7057i	0.842279	+	1.45887i	−0.0456844	+	0.998956i	$0.514547\pi$
$444$		0			0
$445$	8.48528	−	14.6969i	0.402241	−	0.696702i
$446$		0			0
$447$	−1.45584			−0.0688591
$448$		0			0
$449$	23.8284			1.12453			0.562267	−	0.826956i	$-0.309930\pi$
$449$	23.8284			1.12453			0.562267	+	0.826956i	$0.309930\pi$
$450$		0			0
$451$	1.12132	−	1.94218i	0.0528009	−	0.0914539i
$452$		0			0
$453$	−2.44975	−	4.24309i	−0.115099	−	0.199358i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.53553	+	13.0519i	0.352497	+	0.610543i	0.986686	−	0.162635i	$-0.0519992\pi$
$457$	7.53553	+	13.0519i	0.352497	+	0.610543i	−0.634189	+	0.773178i	$0.718666\pi$
$458$		0			0
$459$	−7.74264	+	13.4106i	−0.361396	+	0.625955i
$460$		0			0
$461$	22.3431			1.04062			0.520312	−	0.853976i	$-0.325816\pi$
$461$	22.3431			1.04062			0.520312	+	0.853976i	$0.325816\pi$
$462$		0			0
$463$	−13.4558			−0.625346			−0.312673	−	0.949861i	$-0.601224\pi$
$463$	−13.4558			−0.625346			−0.312673	+	0.949861i	$0.601224\pi$
$464$		0			0
$465$	−0.949747	+	1.64501i	−0.0440435	+	0.0762856i
$466$		0			0
$467$	−0.449747	−	0.778985i	−0.0208118	−	0.0360471i	0.855432	−	0.517915i	$-0.173292\pi$
$467$	−0.449747	−	0.778985i	−0.0208118	−	0.0360471i	−0.876244	+	0.481868i	$0.839958\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.17157	+	3.76127i	0.100061	+	0.173310i
$472$		0			0
$473$	22.3137	−	38.6485i	1.02599	−	1.77706i
$474$		0			0
$475$	3.65685			0.167788
$476$		0			0
$477$	10.6274			0.486596
$478$		0			0
$479$	−4.70711	+	8.15295i	−0.215073	+	0.372518i	−0.953295	−	0.302040i	$-0.902332\pi$
$479$	−4.70711	+	8.15295i	−0.215073	+	0.372518i	0.738222	+	0.674558i	$0.235666\pi$
$480$		0			0
$481$	6.12132	+	10.6024i	0.279108	+	0.483430i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.86396	+	13.6208i	0.357084	+	0.618488i
$486$		0			0
$487$	3.70711	−	6.42090i	0.167985	−	0.290959i	−0.769726	−	0.638374i	$-0.779607\pi$
$487$	3.70711	−	6.42090i	0.167985	−	0.290959i	0.937711	+	0.347415i	$0.112941\pi$
$488$		0			0
$489$	−8.92893			−0.403780
$490$		0			0
$491$	17.2843			0.780028			0.390014	−	0.920809i	$-0.372470\pi$
$491$	17.2843			0.780028			0.390014	+	0.920809i	$0.372470\pi$
$492$		0			0
$493$	−21.3492	+	36.9780i	−0.961522	+	1.66540i
$494$		0			0
$495$	5.41421	+	9.37769i	0.243351	+	0.421496i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	6.81371	+	11.8017i	0.305023	+	0.528316i	0.977267	−	0.212014i	$-0.0680024\pi$
$499$	6.81371	+	11.8017i	0.305023	+	0.528316i	−0.672243	+	0.740331i	$0.734669\pi$
$500$		0			0
$501$	0.500000	−	0.866025i	0.0223384	−	0.0386912i
$502$		0			0
$503$	39.0416			1.74078			0.870390	−	0.492363i	$-0.163867\pi$
$503$	39.0416			1.74078			0.870390	+	0.492363i	$0.163867\pi$
$504$		0			0
$505$	4.82843			0.214862
$506$		0			0
$507$	−0.0294373	+	0.0509868i	−0.00130735	+	0.00226440i
$508$		0			0
$509$	17.5355	+	30.3724i	0.777249	+	1.34623i	0.933522	+	0.358521i	$0.116719\pi$
$509$	17.5355	+	30.3724i	0.777249	+	1.34623i	−0.156273	+	0.987714i	$0.549948\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−4.41421	−	7.64564i	−0.194892	−	0.337563i
$514$		0			0
$515$	0.792893	−	1.37333i	0.0349390	−	0.0605162i
$516$		0			0
$517$	34.0711			1.49844
$518$		0			0
$519$	−7.68629			−0.337391
$520$		0			0
$521$	−3.34315	+	5.79050i	−0.146466	+	0.253686i	−0.929919	−	0.367765i	$-0.880123\pi$
$521$	−3.34315	+	5.79050i	−0.146466	+	0.253686i	0.783453	+	0.621451i	$0.213457\pi$
$522$		0			0
$523$	−0.928932	−	1.60896i	−0.0406194	−	0.0703548i	0.845001	−	0.534765i	$-0.179600\pi$
$523$	−0.928932	−	1.60896i	−0.0406194	−	0.0703548i	−0.885620	+	0.464410i	$0.846266\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.7071	−	25.4735i	−0.640652	−	1.10964i
$528$		0			0
$529$	11.3284	−	19.6214i	0.492540	−	0.853105i
$530$		0			0
$531$	−9.65685			−0.419072
$532$		0			0
$533$	2.10051			0.0909830
$534$		0			0
$535$	−8.41421	+	14.5738i	−0.363778	+	0.630082i
$536$		0			0
$537$	1.34315	+	2.32640i	0.0579610	+	0.100391i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−7.98528	−	13.8309i	−0.343314	−	0.594637i	0.641732	−	0.766929i	$-0.278216\pi$
$541$	−7.98528	−	13.8309i	−0.343314	−	0.594637i	−0.985046	+	0.172292i	$0.944883\pi$
$542$		0			0
$543$	0.363961	−	0.630399i	0.0156191	−	0.0270530i
$544$		0			0
$545$	−9.00000			−0.385518
$546$		0			0
$547$	7.51472			0.321306			0.160653	−	0.987011i	$-0.448640\pi$
$547$	7.51472			0.321306			0.160653	+	0.987011i	$0.448640\pi$
$548$		0			0
$549$	7.31371	−	12.6677i	0.312141	−	0.540645i
$550$		0			0
$551$	−12.1716	−	21.0818i	−0.518526	−	0.898114i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.707107	+	1.22474i	0.0300150	+	0.0519875i
$556$		0			0
$557$	3.89949	−	6.75412i	0.165227	−	0.286181i	−0.771509	−	0.636218i	$-0.780498\pi$
$557$	3.89949	−	6.75412i	0.165227	−	0.286181i	0.936736	+	0.350037i	$0.113831\pi$
$558$		0			0
$559$	41.7990			1.76791
$560$		0			0
$561$	10.1716			0.429444
$562$		0			0
$563$	10.3137	−	17.8639i	0.434671	−	0.752872i	−0.562598	−	0.826731i	$-0.690198\pi$
$563$	10.3137	−	17.8639i	0.434671	−	0.752872i	0.997269	+	0.0738585i	$0.0235313\pi$
$564$		0			0
$565$	−2.53553	−	4.39167i	−0.106671	−	0.184759i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.8995	+	27.5387i	0.666542	+	1.15448i	0.978865	+	0.204508i	$0.0655594\pi$
$569$	15.8995	+	27.5387i	0.666542	+	1.15448i	−0.312323	+	0.949976i	$0.601107\pi$
$570$		0			0
$571$	−2.41421	+	4.18154i	−0.101032	+	0.174992i	−0.912110	−	0.409946i	$-0.865548\pi$
$571$	−2.41421	+	4.18154i	−0.101032	+	0.174992i	0.811078	+	0.584938i	$0.198881\pi$
$572$		0			0
$573$	−6.89949			−0.288231
$574$		0			0
$575$	0.585786			0.0244290
$576$		0			0
$577$	7.03553	−	12.1859i	0.292893	−	0.507306i	−0.681599	−	0.731725i	$-0.738715\pi$
$577$	7.03553	−	12.1859i	0.292893	−	0.507306i	0.974493	+	0.224420i	$0.0720487\pi$
$578$		0			0
$579$	1.17157	+	2.02922i	0.0486889	+	0.0843317i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−7.19239	−	12.4576i	−0.297878	−	0.515940i
$584$		0			0
$585$	−5.07107	+	8.78335i	−0.209663	+	0.363147i
$586$		0			0
$587$	−30.8284			−1.27243			−0.636213	−	0.771514i	$-0.719500\pi$
$587$	−30.8284			−1.27243			−0.636213	+	0.771514i	$0.719500\pi$
$588$		0			0
$589$	16.7696			0.690977
$590$		0			0
$591$	−5.70711	+	9.88500i	−0.234759	+	0.406615i
$592$		0			0
$593$	−8.86396	−	15.3528i	−0.363999	−	0.630465i	0.624616	−	0.780932i	$-0.285256\pi$
$593$	−8.86396	−	15.3528i	−0.363999	−	0.630465i	−0.988615	+	0.150467i	$0.951922\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−5.53553	−	9.58783i	−0.226554	−	0.392404i
$598$		0			0
$599$	6.39949	−	11.0843i	0.261476	−	0.452890i	−0.705158	−	0.709050i	$-0.749124\pi$
$599$	6.39949	−	11.0843i	0.261476	−	0.452890i	0.966634	+	0.256160i	$0.0824573\pi$
$600$		0			0
$601$	39.6569			1.61764			0.808818	−	0.588058i	$-0.200108\pi$
$601$	39.6569			1.61764			0.808818	+	0.588058i	$0.200108\pi$
$602$		0			0
$603$	31.3137			1.27519
$604$		0			0
$605$	1.82843	−	3.16693i	0.0743361	−	0.128754i
$606$		0			0
$607$	−6.96447	−	12.0628i	−0.282679	−	0.489614i	0.689365	−	0.724414i	$-0.257890\pi$
$607$	−6.96447	−	12.0628i	−0.282679	−	0.489614i	−0.972044	+	0.234800i	$0.924556\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.9558	+	27.6363i	0.645504	+	1.11805i
$612$		0			0
$613$	20.6569	−	35.7787i	0.834322	−	1.44509i	−0.0602584	−	0.998183i	$-0.519192\pi$
$613$	20.6569	−	35.7787i	0.834322	−	1.44509i	0.894581	−	0.446906i	$-0.147474\pi$
$614$		0			0
$615$	0.242641			0.00978422
$616$		0			0
$617$	40.8701			1.64537			0.822683	−	0.568500i	$-0.192476\pi$
$617$	40.8701			1.64537			0.822683	+	0.568500i	$0.192476\pi$
$618$		0			0
$619$	−5.43503	+	9.41375i	−0.218452	+	0.378370i	−0.954335	−	0.298739i	$-0.903434\pi$
$619$	−5.43503	+	9.41375i	−0.218452	+	0.378370i	0.735883	+	0.677109i	$0.236767\pi$
$620$		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
$627$	−2.89949	+	5.02207i	−0.115795	+	0.200562i
$628$		0			0
$629$	−21.8995			−0.873190
$630$		0			0
$631$	−39.4853			−1.57188			−0.785942	−	0.618300i	$-0.787822\pi$
$631$	−39.4853			−1.57188			−0.785942	+	0.618300i	$0.787822\pi$
$632$		0			0
$633$	−5.03553	+	8.72180i	−0.200145	+	0.346660i
$634$		0			0
$635$	−10.9497	−	18.9655i	−0.434527	−	0.752624i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	9.17157	+	15.8856i	0.362822	+	0.628426i
$640$		0			0
$641$	−19.6569	+	34.0467i	−0.776399	+	1.34476i	0.157606	+	0.987502i	$0.449622\pi$
$641$	−19.6569	+	34.0467i	−0.776399	+	1.34476i	−0.934005	+	0.357261i	$0.883711\pi$
$642$		0			0
$643$	4.21320			0.166153			0.0830763	−	0.996543i	$-0.473525\pi$
$643$	4.21320			0.166153			0.0830763	+	0.996543i	$0.473525\pi$
$644$		0			0
$645$	4.82843			0.190119
$646$		0			0
$647$	−17.5563	+	30.4085i	−0.690211	+	1.19548i	0.281557	+	0.959544i	$0.409149\pi$
$647$	−17.5563	+	30.4085i	−0.690211	+	1.19548i	−0.971768	+	0.235937i	$0.924184\pi$
$648$		0			0
$649$	6.53553	+	11.3199i	0.256542	+	0.444344i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.3431	+	23.1110i	0.522158	+	0.904404i	0.999668	+	0.0257773i	$0.00820608\pi$
$653$	13.3431	+	23.1110i	0.522158	+	0.904404i	−0.477510	+	0.878626i	$0.658461\pi$
$654$		0			0
$655$	−5.87868	+	10.1822i	−0.229699	+	0.397850i
$656$		0			0
$657$	−14.6274			−0.570670
$658$		0			0
$659$	−20.6569			−0.804677			−0.402338	−	0.915491i	$-0.631802\pi$
$659$	−20.6569			−0.804677			−0.402338	+	0.915491i	$0.631802\pi$
$660$		0			0
$661$	17.0711	−	29.5680i	0.663988	−	1.15006i	−0.315571	−	0.948902i	$-0.602196\pi$
$661$	17.0711	−	29.5680i	0.663988	−	1.15006i	0.979559	−	0.201158i	$-0.0644706\pi$
$662$		0			0
$663$	4.76346	+	8.25055i	0.184997	+	0.320425i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.94975	−	3.37706i	−0.0754945	−	0.130760i
$668$		0			0
$669$	4.98528	−	8.63476i	0.192742	−	0.333839i
$670$		0			0
$671$	−19.7990			−0.764332
$672$		0			0
$673$	−27.5147			−1.06061			−0.530307	−	0.847806i	$-0.677923\pi$
$673$	−27.5147			−1.06061			−0.530307	+	0.847806i	$0.677923\pi$
$674$		0			0
$675$	−1.20711	+	2.09077i	−0.0464616	+	0.0804738i
$676$		0			0
$677$	5.13604	+	8.89588i	0.197394	+	0.341896i	0.947683	−	0.319214i	$-0.103419\pi$
$677$	5.13604	+	8.89588i	0.197394	+	0.341896i	−0.750289	+	0.661110i	$0.770086\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.60051	+	2.77216i	0.0613315	+	0.106229i
$682$		0			0
$683$	−17.5563	+	30.4085i	−0.671775	+	1.16355i	0.305625	+	0.952152i	$0.401135\pi$
$683$	−17.5563	+	30.4085i	−0.671775	+	1.16355i	−0.977400	+	0.211397i	$0.932199\pi$
$684$		0			0
$685$	−12.9706			−0.495580
$686$		0			0
$687$	−9.89949			−0.377689
$688$		0			0
$689$	6.73654	−	11.6680i	0.256642	−	0.444517i
$690$		0			0
$691$	−1.75736	−	3.04384i	−0.0668531	−	0.115793i	0.830661	−	0.556778i	$-0.187963\pi$
$691$	−1.75736	−	3.04384i	−0.0668531	−	0.115793i	−0.897515	+	0.440985i	$0.854629\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.94975	−	12.0373i	−0.263619	−	0.456601i
$696$		0			0
$697$	−1.87868	+	3.25397i	−0.0711601	+	0.123253i
$698$		0			0
$699$	3.79899			0.143691
$700$		0			0
$701$	0.514719			0.0194407			0.00972033	−	0.999953i	$-0.496906\pi$
$701$	0.514719			0.0194407			0.00972033	+	0.999953i	$0.496906\pi$
$702$		0			0
$703$	6.24264	−	10.8126i	0.235446	−	0.407804i
$704$		0			0
$705$	1.84315	+	3.19242i	0.0694169	+	0.120234i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.81371	−	3.14144i	−0.0681153	−	0.117979i	0.829956	−	0.557828i	$-0.188365\pi$
$709$	−1.81371	−	3.14144i	−0.0681153	−	0.117979i	−0.898072	+	0.439849i	$0.855032\pi$
$710$		0			0
$711$	18.5858	−	32.1915i	0.697021	−	1.20728i
$712$		0			0
$713$	2.68629			0.100602
$714$		0			0
$715$	13.7279			0.513395
$716$		0			0
$717$	2.93503	−	5.08362i	0.109611	−	0.189851i
$718$		0			0
$719$	−7.87868	−	13.6463i	−0.293825	−	0.508920i	0.680886	−	0.732390i	$-0.261595\pi$
$719$	−7.87868	−	13.6463i	−0.293825	−	0.508920i	−0.974711	+	0.223470i	$0.928262\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−0.736544	−	1.27573i	−0.0273924	−	0.0474450i
$724$		0			0
$725$	−3.32843	+	5.76500i	−0.123615	+	0.214107i
$726$		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
$729$	−18.1716			−0.673021
$730$		0			0
$731$	−37.3848	+	64.7523i	−1.38273	+	2.39495i
$732$		0			0
$733$	15.3492	+	26.5857i	0.566937	+	0.981964i	0.996867	+	0.0791015i	$0.0252051\pi$
$733$	15.3492	+	26.5857i	0.566937	+	0.981964i	−0.429929	+	0.902863i	$0.641462\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.1924	−	36.7063i	−0.780632	−	1.35209i
$738$		0			0
$739$	−10.3284	+	17.8894i	−0.379937	+	0.658071i	−0.991053	−	0.133471i	$-0.957388\pi$
$739$	−10.3284	+	17.8894i	−0.379937	+	0.658071i	0.611115	+	0.791541i	$0.290721\pi$
$740$		0			0
$741$	−5.43146			−0.199530
$742$		0			0
$743$	−8.92893			−0.327571			−0.163785	−	0.986496i	$-0.552370\pi$
$743$	−8.92893			−0.327571			−0.163785	+	0.986496i	$0.552370\pi$
$744$		0			0
$745$	1.75736	−	3.04384i	0.0643847	−	0.111518i
$746$		0			0
$747$	−11.3137	−	19.5959i	−0.413947	−	0.716977i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.571068	−	0.989118i	−0.0208386	−	0.0360934i	0.855418	−	0.517938i	$-0.173300\pi$
$751$	−0.571068	−	0.989118i	−0.0208386	−	0.0360934i	−0.876257	+	0.481845i	$0.839967\pi$
$752$		0			0
$753$	−5.60660	+	9.71092i	−0.204316	+	0.353886i
$754$		0			0
$755$	11.8284			0.430481
$756$		0			0
$757$	37.1716			1.35102			0.675512	−	0.737349i	$-0.263923\pi$
$757$	37.1716			1.35102			0.675512	+	0.737349i	$0.263923\pi$
$758$		0			0
$759$	−0.464466	+	0.804479i	−0.0168591	+	0.0292007i
$760$		0			0
$761$	9.43503	+	16.3419i	0.342020	+	0.592395i	0.984808	−	0.173649i	$-0.0555558\pi$
$761$	9.43503	+	16.3419i	0.342020	+	0.592395i	−0.642788	+	0.766044i	$0.722222\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−9.07107	−	15.7116i	−0.327965	−	0.568052i
$766$		0			0
$767$	−6.12132	+	10.6024i	−0.221028	+	0.382832i
$768$		0			0
$769$	28.1421			1.01483			0.507416	−	0.861701i	$-0.330601\pi$
$769$	28.1421			1.01483			0.507416	+	0.861701i	$0.330601\pi$
$770$		0			0
$771$	10.6863			0.384857
$772$		0			0
$773$	21.8640	−	37.8695i	0.786392	−	1.36207i	−0.141772	−	0.989899i	$-0.545280\pi$
$773$	21.8640	−	37.8695i	0.786392	−	1.36207i	0.928164	−	0.372172i	$-0.121387\pi$
$774$		0			0
$775$	−2.29289	−	3.97141i	−0.0823632	−	0.142657i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.07107	−	1.85514i	−0.0383750	−	0.0664674i
$780$		0			0
$781$	12.4142	−	21.5020i	0.444215	−	0.769404i
$782$		0			0
$783$	16.0711			0.574333
$784$		0			0
$785$	−10.4853			−0.374236
$786$		0			0
$787$	21.8640	−	37.8695i	0.779366	−	1.34990i	−0.152942	−	0.988235i	$-0.548875\pi$
$787$	21.8640	−	37.8695i	0.779366	−	1.34990i	0.932308	−	0.361666i	$-0.117792\pi$
$788$		0			0
$789$	2.07107	+	3.58719i	0.0737320	+	0.127708i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−9.27208	−	16.0597i	−0.329261	−	0.570297i
$794$		0			0
$795$	0.778175	−	1.34784i	0.0275990	−	0.0478029i
$796$		0			0
$797$	−35.3848			−1.25339			−0.626697	−	0.779263i	$-0.715593\pi$
$797$	−35.3848			−1.25339			−0.626697	+	0.779263i	$0.715593\pi$
$798$		0			0
$799$	−57.0833			−2.01946
$800$		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
$807$	−3.46447	−	6.00063i	−0.121955	−	0.211232i
$808$		0			0
$809$	−3.01472	+	5.22165i	−0.105992	+	0.183583i	−0.914143	−	0.405392i	$-0.867135\pi$
$809$	−3.01472	+	5.22165i	−0.105992	+	0.183583i	0.808151	+	0.588975i	$0.200468\pi$
$810$		0			0
$811$	−19.5563			−0.686716			−0.343358	−	0.939205i	$-0.611564\pi$
$811$	−19.5563			−0.686716			−0.343358	+	0.939205i	$0.611564\pi$
$812$		0			0
$813$	−12.0000			−0.420858
$814$		0			0
$815$	10.7782	−	18.6683i	0.377543	−	0.653924i
$816$		0			0
$817$	−21.3137	−	36.9164i	−0.745672	−	1.29154i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.9142	−	41.4206i	−0.834612	−	1.44559i	−0.894346	−	0.447376i	$-0.852359\pi$
$821$	−23.9142	−	41.4206i	−0.834612	−	1.44559i	0.0597343	−	0.998214i	$-0.480975\pi$
$822$		0			0
$823$	−18.2635	+	31.6332i	−0.636624	+	1.10267i	0.349545	+	0.936920i	$0.386336\pi$
$823$	−18.2635	+	31.6332i	−0.636624	+	1.10267i	−0.986169	+	0.165745i	$0.946997\pi$
$824$		0			0
$825$	1.58579			0.0552100
$826$		0			0
$827$	−10.0416			−0.349182			−0.174591	−	0.984641i	$-0.555860\pi$
$827$	−10.0416			−0.349182			−0.174591	+	0.984641i	$0.555860\pi$
$828$		0			0
$829$	−11.3640	+	19.6830i	−0.394687	+	0.683617i	−0.993061	−	0.117599i	$-0.962480\pi$
$829$	−11.3640	+	19.6830i	−0.394687	+	0.683617i	0.598374	+	0.801217i	$0.295814\pi$
$830$		0			0
$831$	−1.53553	−	2.65962i	−0.0532671	−	0.0922613i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.20711	+	2.09077i	0.0417737	+	0.0723541i
$836$		0			0
$837$	−5.53553	+	9.58783i	−0.191336	+	0.331404i
$838$		0			0
$839$	22.3848			0.772808			0.386404	−	0.922330i	$-0.373717\pi$
$839$	22.3848			0.772808			0.386404	+	0.922330i	$0.373717\pi$
$840$		0			0
$841$	15.3137			0.528059
$842$		0			0
$843$	−0.207107	+	0.358719i	−0.00713314	+	0.0123550i
$844$		0			0
$845$	−0.0710678	−	0.123093i	−0.00244481	−	0.00423453i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−3.88478	−	6.72863i	−0.133325	−	0.230926i
$850$		0			0
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$		0			0
$853$	−30.2843			−1.03691			−0.518457	−	0.855104i	$-0.673493\pi$
$853$	−30.2843			−1.03691			−0.518457	+	0.855104i	$0.673493\pi$
$854$		0			0
$855$	10.3431			0.353728
$856$		0			0
$857$	10.4142	−	18.0379i	0.355743	−	0.616165i	−0.631502	−	0.775374i	$-0.717561\pi$
$857$	10.4142	−	18.0379i	0.355743	−	0.616165i	0.987245	+	0.159210i	$0.0508946\pi$
$858$		0			0
$859$	22.7279	+	39.3659i	0.775467	+	1.34315i	0.934532	+	0.355880i	$0.115819\pi$
$859$	22.7279	+	39.3659i	0.775467	+	1.34315i	−0.159065	+	0.987268i	$0.550848\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.87868	+	17.1104i	0.336274	+	0.582444i	0.983729	−	0.179660i	$-0.0574998\pi$
$863$	9.87868	+	17.1104i	0.336274	+	0.582444i	−0.647455	+	0.762104i	$0.724166\pi$
$864$		0			0
$865$	9.27817	−	16.0703i	0.315467	−	0.546406i
$866$		0			0
$867$	−10.0000			−0.339618
$868$		0			0
$869$	−50.3137			−1.70678
$870$		0			0
$871$	19.8492	−	34.3799i	0.672566	−	1.16492i
$872$		0			0
$873$	22.2426	+	38.5254i	0.752799	+	1.30389i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.34315	−	9.25460i	−0.180425	−	0.312506i	0.761600	−	0.648047i	$-0.224414\pi$
$877$	−5.34315	−	9.25460i	−0.180425	−	0.312506i	−0.942025	+	0.335542i	$0.891081\pi$
$878$		0			0
$879$	−2.98528	+	5.17066i	−0.100691	+	0.174402i
$880$		0			0
$881$	−56.2843			−1.89627			−0.948133	−	0.317875i	$-0.897031\pi$
$881$	−56.2843			−1.89627			−0.948133	+	0.317875i	$0.897031\pi$
$882$		0			0
$883$	−7.11270			−0.239361			−0.119681	−	0.992812i	$-0.538187\pi$
$883$	−7.11270			−0.239361			−0.119681	+	0.992812i	$0.538187\pi$
$884$		0			0
$885$	−0.707107	+	1.22474i	−0.0237691	+	0.0411693i
$886$		0			0
$887$	−28.7990	−	49.8813i	−0.966975	−	1.67485i	−0.704211	−	0.709991i	$-0.748699\pi$
$887$	−28.7990	−	49.8813i	−0.966975	−	1.67485i	−0.262764	−	0.964860i	$-0.584634\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	14.3284	+	24.8176i	0.480020	+	0.831420i
$892$		0			0
$893$	16.2721	−	28.1841i	0.544524	−	0.943144i
$894$		0			0
$895$	−6.48528			−0.216779
$896$		0			0
$897$	−0.870058			−0.0290504
$898$		0			0
$899$	−15.2635	+	26.4371i	−0.509065	+	0.881726i
$900$		0			0
$901$	12.0503	+	20.8716i	0.401452	+	0.695335i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.878680	+	1.52192i	0.0292083	+	0.0505903i
$906$		0			0
$907$	−11.2635	+	19.5089i	−0.373997	+	0.647782i	−0.990176	−	0.139824i	$-0.955346\pi$
$907$	−11.2635	+	19.5089i	−0.373997	+	0.647782i	0.616179	+	0.787606i	$0.288680\pi$
$908$		0			0
$909$	13.6569			0.452969
$910$		0			0
$911$	−55.5980			−1.84204			−0.921022	−	0.389511i	$-0.872644\pi$
$911$	−55.5980			−1.84204			−0.921022	+	0.389511i	$0.872644\pi$
$912$		0			0
$913$	−15.3137	+	26.5241i	−0.506810	+	0.877820i
$914$		0			0
$915$	−1.07107	−	1.85514i	−0.0354084	−	0.0613292i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	9.25736	+	16.0342i	0.305372	+	0.528920i	0.977344	−	0.211657i	$-0.0678858\pi$
$919$	9.25736	+	16.0342i	0.305372	+	0.528920i	−0.671972	+	0.740577i	$0.734552\pi$
$920$		0			0
$921$	0.742641	−	1.28629i	0.0244708	−	0.0423847i
$922$		0			0
$923$	23.2548			0.765442
$924$		0			0
$925$	−3.41421			−0.112259
$926$		0			0
$927$	2.24264	−	3.88437i	0.0736580	−	0.127579i
$928$		0			0
$929$	10.6360	+	18.4222i	0.348957	+	0.604411i	0.986064	−	0.166364i	$-0.0532025\pi$
$929$	10.6360	+	18.4222i	0.348957	+	0.604411i	−0.637107	+	0.770775i	$0.719869\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.44365	+	2.50048i	0.0472630	+	0.0818619i
$934$		0			0
$935$	−12.2782	+	21.2664i	−0.401539	+	0.695486i
$936$		0			0
$937$	−7.72792			−0.252460			−0.126230	−	0.992001i	$-0.540288\pi$
$937$	−7.72792			−0.252460			−0.126230	+	0.992001i	$0.540288\pi$
$938$		0			0
$939$	−6.85786			−0.223798
$940$		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
$943$	−0.171573	−	0.297173i	−0.00558718	−	0.00967728i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.0208	+	27.7489i	0.520607	+	0.901717i	0.999713	+	0.0239601i	$0.00762748\pi$
$947$	16.0208	+	27.7489i	0.520607	+	0.901717i	−0.479106	+	0.877757i	$0.659039\pi$
$948$		0			0
$949$	−9.27208	+	16.0597i	−0.300984	+	0.521320i
$950$		0			0
$951$	6.20101			0.201082
$952$		0			0
$953$	−38.8701			−1.25912			−0.629562	−	0.776950i	$-0.716766\pi$
$953$	−38.8701			−1.25912			−0.629562	+	0.776950i	$0.716766\pi$
$954$		0			0
$955$	8.32843	−	14.4253i	0.269502	−	0.466790i
$956$		0			0
$957$	−5.27817	−	9.14207i	−0.170619	−	0.295521i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	4.98528	+	8.63476i	0.160816	+	0.278541i
$962$		0			0
$963$	−23.7990	+	41.2211i	−0.766912	+	1.32833i
$964$		0			0
$965$	−5.65685			−0.182101
$966$		0			0
$967$	−7.45584			−0.239764			−0.119882	−	0.992788i	$-0.538252\pi$
$967$	−7.45584			−0.239764			−0.119882	+	0.992788i	$0.538252\pi$
$968$		0			0
$969$	4.85786	−	8.41407i	0.156057	−	0.270299i
$970$		0			0
$971$	11.2635	+	19.5089i	0.361462	+	0.626070i	0.988202	−	0.153159i	$-0.0489446\pi$
$971$	11.2635	+	19.5089i	0.361462	+	0.626070i	−0.626740	+	0.779228i	$0.715611\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.742641	+	1.28629i	0.0237835	+	0.0411943i
$976$		0			0
$977$	4.07107	−	7.05130i	0.130245	−	0.225591i	−0.793526	−	0.608536i	$-0.791757\pi$
$977$	4.07107	−	7.05130i	0.130245	−	0.225591i	0.923771	+	0.382945i	$0.125090\pi$
$978$		0			0
$979$	−64.9706			−2.07647
$980$		0			0
$981$	−25.4558			−0.812743
$982$		0			0
$983$	21.0061	−	36.3836i	0.669990	−	1.16046i	−0.307916	−	0.951414i	$-0.599632\pi$
$983$	21.0061	−	36.3836i	0.669990	−	1.16046i	0.977906	−	0.209044i	$-0.0670351\pi$
$984$		0			0
$985$	−13.7782	−	23.8645i	−0.439009	−	0.760386i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.41421	−	5.91359i	−0.108566	−	0.188041i
$990$		0			0
$991$	−12.6569	+	21.9223i	−0.402058	+	0.696385i	−0.993974	−	0.109614i	$-0.965038\pi$
$991$	−12.6569	+	21.9223i	−0.402058	+	0.696385i	0.591916	+	0.806000i	$0.298372\pi$
$992$		0			0
$993$	−2.00000			−0.0634681
$994$		0			0
$995$	26.7279			0.847332
$996$		0			0
$997$	25.4203	−	44.0293i	0.805069	−	1.39442i	−0.111175	−	0.993801i	$-0.535461\pi$
$997$	25.4203	−	44.0293i	0.805069	−	1.39442i	0.916244	−	0.400620i	$-0.131205\pi$
$998$		0			0
$999$	4.12132	+	7.13834i	0.130393	+	0.225847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.i.k.361.2		4
7.2	even	3	inner	980.2.i.k.961.2		4
7.3	odd	6		980.2.a.j.1.2	✓	2
7.4	even	3		980.2.a.k.1.1	yes	2
7.5	odd	6		980.2.i.l.961.1		4
7.6	odd	2		980.2.i.l.361.1		4
21.11	odd	6		8820.2.a.bl.1.2		2
21.17	even	6		8820.2.a.bg.1.2		2
28.3	even	6		3920.2.a.bx.1.1		2
28.11	odd	6		3920.2.a.bo.1.2		2
35.3	even	12		4900.2.e.q.2549.3		4
35.4	even	6		4900.2.a.x.1.2		2
35.17	even	12		4900.2.e.q.2549.2		4
35.18	odd	12		4900.2.e.r.2549.2		4
35.24	odd	6		4900.2.a.z.1.1		2
35.32	odd	12		4900.2.e.r.2549.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.a.j.1.2	✓	2	7.3	odd	6
980.2.a.k.1.1	yes	2	7.4	even	3
980.2.i.k.361.2		4	1.1	even	1	trivial
980.2.i.k.961.2		4	7.2	even	3	inner
980.2.i.l.361.1		4	7.6	odd	2
980.2.i.l.961.1		4	7.5	odd	6
3920.2.a.bo.1.2		2	28.11	odd	6
3920.2.a.bx.1.1		2	28.3	even	6
4900.2.a.x.1.2		2	35.4	even	6
4900.2.a.z.1.1		2	35.24	odd	6
4900.2.e.q.2549.2		4	35.17	even	12
4900.2.e.q.2549.3		4	35.3	even	12
4900.2.e.r.2549.2		4	35.18	odd	12
4900.2.e.r.2549.3		4	35.32	odd	12
8820.2.a.bg.1.2		2	21.17	even	6
8820.2.a.bl.1.2		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)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.41421 + 2.44949i) q^{9} +(1.91421 - 3.31552i) q^{11} +3.58579 q^{13} +0.414214 q^{15} +(-3.20711 + 5.55487i) q^{17} +(-1.82843 - 3.16693i) q^{19} +(-0.292893 - 0.507306i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.41421 q^{27} +6.65685 q^{29} +(-2.29289 + 3.97141i) q^{31} +(-0.792893 - 1.37333i) q^{33} +(1.70711 + 2.95680i) q^{37} +(0.742641 - 1.28629i) q^{39} +0.585786 q^{41} +11.6569 q^{43} +(-1.41421 + 2.44949i) q^{45} +(4.44975 + 7.70719i) q^{47} +(1.32843 + 2.30090i) q^{51} +(1.87868 - 3.25397i) q^{53} +3.82843 q^{55} -1.51472 q^{57} +(-1.70711 + 2.95680i) q^{59} +(-2.58579 - 4.47871i) q^{61} +(1.79289 + 3.10538i) q^{65} +(5.53553 - 9.58783i) q^{67} -0.242641 q^{69} +6.48528 q^{71} +(-2.58579 + 4.47871i) q^{73} +(0.207107 + 0.358719i) q^{75} +(-6.57107 - 11.3814i) q^{79} +(-3.74264 + 6.48244i) q^{81} -8.00000 q^{83} -6.41421 q^{85} +(1.37868 - 2.38794i) q^{87} +(-8.48528 - 14.6969i) q^{89} +(0.949747 + 1.64501i) q^{93} +(1.82843 - 3.16693i) q^{95} +15.7279 q^{97} +10.8284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 20 q^{13} - 4 q^{15} - 10 q^{17} + 4 q^{19} - 4 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} - 12 q^{31} - 6 q^{33} + 4 q^{37} - 14 q^{39} + 8 q^{41} + 24 q^{43} - 2 q^{47}+ \cdots + 32 q^{99}+O(q^{100}) \) 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

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