LMFDB - Embedded newform 2940.2.q.p.361.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(361,2940)] 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("2940.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,2,0,0,0,-2,0,4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, \ldots, a_{19}]$
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	$\chi$	$=$	2940.361
Dual form			2940.2.q.p.961.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +2.82843 q^{13} -1.00000 q^{15} +(3.41421 - 5.91359i) q^{17} +(-1.29289 - 2.23936i) q^{19} +(2.29289 + 3.97141i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -7.65685 q^{29} +(2.12132 - 3.67423i) q^{31} +(1.00000 + 1.73205i) q^{33} +(-3.24264 - 5.61642i) q^{37} +(-1.41421 + 2.44949i) q^{39} -2.00000 q^{41} -9.65685 q^{43} +(0.500000 - 0.866025i) q^{45} +(-3.24264 - 5.61642i) q^{47} +(3.41421 + 5.91359i) q^{51} +(3.70711 - 6.42090i) q^{53} +2.00000 q^{55} +2.58579 q^{57} +(1.41421 - 2.44949i) q^{59} +(-4.94975 - 8.57321i) q^{61} +(1.41421 + 2.44949i) q^{65} +(0.585786 - 1.01461i) q^{67} -4.58579 q^{69} +6.48528 q^{71} +(6.24264 - 10.8126i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +0.828427 q^{83} +6.82843 q^{85} +(3.82843 - 6.63103i) q^{87} +(-0.414214 - 0.717439i) q^{89} +(2.12132 + 3.67423i) q^{93} +(1.29289 - 2.23936i) q^{95} +4.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 2 q^{5} - 2 q^{9} + 4 q^{11} - 4 q^{15} + 8 q^{17} - 8 q^{19} + 12 q^{23} - 2 q^{25} + 4 q^{27} - 8 q^{29} + 4 q^{33} + 4 q^{37} - 8 q^{41} - 16 q^{43} + 2 q^{45} + 4 q^{47} + 8 q^{51} + 12 q^{53}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 + 2 * q^5 - 2 * q^9 + 4 * q^11 - 4 * q^15 + 8 * q^17 - 8 * q^19 + 12 * q^23 - 2 * q^25 + 4 * q^27 - 8 * q^29 + 4 * q^33 + 4 * q^37 - 8 * q^41 - 16 * q^43 + 2 * q^45 + 4 * q^47 + 8 * q^51 + 12 * q^53 + 8 * q^55 + 16 * q^57 + 8 * q^67 - 24 * q^69 - 8 * q^71 + 8 * q^73 - 2 * q^75 + 20 * q^79 - 2 * q^81 - 8 * q^83 + 16 * q^85 + 4 * q^87 + 4 * q^89 + 8 * q^95 + 16 * q^97 - 8 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		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
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	2.82843			0.784465			0.392232	−	0.919866i	$-0.371703\pi$
$13$	2.82843			0.784465			0.392232	+	0.919866i	$0.371703\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	−0.0714831	−	0.997442i	$-0.522773\pi$
$17$	3.41421	−	5.91359i	0.828068	−	1.43426i	0.899551	−	0.436815i	$-0.143893\pi$
$18$		0			0
$19$	−1.29289	−	2.23936i	−0.296610	−	0.513744i	0.678748	−	0.734371i	$-0.262523\pi$
$19$	−1.29289	−	2.23936i	−0.296610	−	0.513744i	−0.975358	+	0.220628i	$0.929189\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.29289	+	3.97141i	0.478101	+	0.828096i	0.999685	−	0.0251045i	$-0.00799185\pi$
$23$	2.29289	+	3.97141i	0.478101	+	0.828096i	−0.521584	+	0.853200i	$0.674659\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−7.65685			−1.42184			−0.710921	−	0.703272i	$-0.751722\pi$
$29$	−7.65685			−1.42184			−0.710921	+	0.703272i	$0.751722\pi$
$30$		0			0
$31$	2.12132	−	3.67423i	0.381000	−	0.659912i	−0.610205	−	0.792243i	$-0.708913\pi$
$31$	2.12132	−	3.67423i	0.381000	−	0.659912i	0.991206	+	0.132331i	$0.0422463\pi$
$32$		0			0
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.24264	−	5.61642i	−0.533087	−	0.923334i	−0.999253	−	0.0386365i	$-0.987699\pi$
$37$	−3.24264	−	5.61642i	−0.533087	−	0.923334i	0.466166	−	0.884697i	$-0.345635\pi$
$38$		0			0
$39$	−1.41421	+	2.44949i	−0.226455	+	0.392232i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−9.65685			−1.47266			−0.736328	−	0.676625i	$-0.763442\pi$
$43$	−9.65685			−1.47266			−0.736328	+	0.676625i	$0.763442\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	−3.24264	−	5.61642i	−0.472988	−	0.819239i	0.526534	−	0.850154i	$-0.323491\pi$
$47$	−3.24264	−	5.61642i	−0.472988	−	0.819239i	−0.999522	+	0.0309151i	$0.990158\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.41421	+	5.91359i	0.478086	+	0.828068i
$52$		0			0
$53$	3.70711	−	6.42090i	0.509210	−	0.881978i	−0.490733	−	0.871310i	$-0.663271\pi$
$53$	3.70711	−	6.42090i	0.509210	−	0.881978i	0.999943	−	0.0106680i	$-0.00339578\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$		0			0
$57$	2.58579			0.342496
$58$		0			0
$59$	1.41421	−	2.44949i	0.184115	−	0.318896i	−0.759163	−	0.650901i	$-0.774391\pi$
$59$	1.41421	−	2.44949i	0.184115	−	0.318896i	0.943278	+	0.332004i	$0.107725\pi$
$60$		0			0
$61$	−4.94975	−	8.57321i	−0.633750	−	1.09769i	−0.986778	−	0.162075i	$-0.948181\pi$
$61$	−4.94975	−	8.57321i	−0.633750	−	1.09769i	0.353028	−	0.935613i	$-0.385152\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.41421	+	2.44949i	0.175412	+	0.303822i
$66$		0			0
$67$	0.585786	−	1.01461i	0.0715652	−	0.123955i	−0.828022	−	0.560695i	$-0.810534\pi$
$67$	0.585786	−	1.01461i	0.0715652	−	0.123955i	0.899587	+	0.436741i	$0.143867\pi$
$68$		0			0
$69$	−4.58579			−0.552064
$70$		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
$73$	6.24264	−	10.8126i	0.730646	−	1.26552i	−0.225962	−	0.974136i	$-0.572552\pi$
$73$	6.24264	−	10.8126i	0.730646	−	1.26552i	0.956608	−	0.291380i	$-0.0941142\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	0.828427			0.0909317			0.0454658	−	0.998966i	$-0.485523\pi$
$83$	0.828427			0.0909317			0.0454658	+	0.998966i	$0.485523\pi$
$84$		0			0
$85$	6.82843			0.740647
$86$		0			0
$87$	3.82843	−	6.63103i	0.410450	−	0.710921i
$88$		0			0
$89$	−0.414214	−	0.717439i	−0.0439065	−	0.0760484i	0.843237	−	0.537542i	$-0.180647\pi$
$89$	−0.414214	−	0.717439i	−0.0439065	−	0.0760484i	−0.887144	+	0.461494i	$0.847314\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	2.12132	+	3.67423i	0.219971	+	0.381000i
$94$		0			0
$95$	1.29289	−	2.23936i	0.132648	−	0.229753i
$96$		0			0
$97$	4.00000			0.406138			0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000			0.406138			0.203069	+	0.979164i	$0.434908\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$		0			0
$101$	−0.171573	+	0.297173i	−0.0170721	+	0.0295698i	−0.874435	−	0.485142i	$-0.838768\pi$
$101$	−0.171573	+	0.297173i	−0.0170721	+	0.0295698i	0.857363	+	0.514712i	$0.172101\pi$
$102$		0			0
$103$	1.41421	+	2.44949i	0.139347	+	0.241355i	0.927249	−	0.374444i	$-0.122166\pi$
$103$	1.41421	+	2.44949i	0.139347	+	0.241355i	−0.787903	+	0.615800i	$0.788833\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.53553	+	7.85578i	0.438467	+	0.759446i	0.997571	−	0.0696505i	$-0.0221884\pi$
$107$	4.53553	+	7.85578i	0.438467	+	0.759446i	−0.559105	+	0.829097i	$0.688855\pi$
$108$		0			0
$109$	7.82843	−	13.5592i	0.749827	−	1.29874i	−0.198078	−	0.980186i	$-0.563470\pi$
$109$	7.82843	−	13.5592i	0.749827	−	1.29874i	0.947905	−	0.318553i	$-0.103197\pi$
$110$		0			0
$111$	6.48528			0.615556
$112$		0			0
$113$	2.24264			0.210970			0.105485	−	0.994421i	$-0.466361\pi$
$113$	2.24264			0.210970			0.105485	+	0.994421i	$0.466361\pi$
$114$		0			0
$115$	−2.29289	+	3.97141i	−0.213813	+	0.370336i
$116$		0			0
$117$	−1.41421	−	2.44949i	−0.130744	−	0.226455i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	1.00000	−	1.73205i	0.0901670	−	0.156174i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−14.1421			−1.25491			−0.627456	−	0.778652i	$-0.715904\pi$
$127$	−14.1421			−1.25491			−0.627456	+	0.778652i	$0.715904\pi$
$128$		0			0
$129$	4.82843	−	8.36308i	0.425119	−	0.736328i
$130$		0			0
$131$	5.65685	+	9.79796i	0.494242	+	0.856052i	0.999978	−	0.00663646i	$-0.00211246\pi$
$131$	5.65685	+	9.79796i	0.494242	+	0.856052i	−0.505736	+	0.862688i	$0.668779\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	−5.94975	+	10.3053i	−0.508321	+	0.880438i	0.491632	+	0.870803i	$0.336400\pi$
$137$	−5.94975	+	10.3053i	−0.508321	+	0.880438i	−0.999954	+	0.00963533i	$0.996933\pi$
$138$		0			0
$139$	23.5563			1.99802			0.999012	−	0.0444473i	$-0.0141527\pi$
$139$	23.5563			1.99802			0.999012	+	0.0444473i	$0.0141527\pi$
$140$		0			0
$141$	6.48528			0.546159
$142$		0			0
$143$	2.82843	−	4.89898i	0.236525	−	0.409673i
$144$		0			0
$145$	−3.82843	−	6.63103i	−0.317934	−	0.550677i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.17157	+	7.22538i	0.341749	+	0.591926i	0.984758	−	0.173933i	$-0.0556475\pi$
$149$	4.17157	+	7.22538i	0.341749	+	0.591926i	−0.643009	+	0.765859i	$0.722314\pi$
$150$		0			0
$151$	8.65685	−	14.9941i	0.704485	−	1.22020i	−0.262392	−	0.964961i	$-0.584511\pi$
$151$	8.65685	−	14.9941i	0.704485	−	1.22020i	0.966877	−	0.255242i	$-0.0821552\pi$
$152$		0			0
$153$	−6.82843			−0.552046
$154$		0			0
$155$	4.24264			0.340777
$156$		0			0
$157$	9.07107	−	15.7116i	0.723950	−	1.25392i	−0.235455	−	0.971885i	$-0.575658\pi$
$157$	9.07107	−	15.7116i	0.723950	−	1.25392i	0.959405	−	0.282033i	$-0.0910087\pi$
$158$		0			0
$159$	3.70711	+	6.42090i	0.293993	+	0.509210i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−5.07107	−	8.78335i	−0.397197	−	0.687965i	0.596182	−	0.802849i	$-0.296684\pi$
$163$	−5.07107	−	8.78335i	−0.397197	−	0.687965i	−0.993379	+	0.114884i	$0.963350\pi$
$164$		0			0
$165$	−1.00000	+	1.73205i	−0.0778499	+	0.134840i
$166$		0			0
$167$	−16.0000			−1.23812			−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000			−1.23812			−0.619059	+	0.785345i	$0.712486\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$		0			0
$171$	−1.29289	+	2.23936i	−0.0988700	+	0.171248i
$172$		0			0
$173$	−7.07107	−	12.2474i	−0.537603	−	0.931156i	−0.999032	−	0.0439792i	$-0.985996\pi$
$173$	−7.07107	−	12.2474i	−0.537603	−	0.931156i	0.461429	−	0.887177i	$-0.347337\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.41421	+	2.44949i	0.106299	+	0.184115i
$178$		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
$181$	15.7574			1.17124			0.585618	−	0.810587i	$-0.300852\pi$
$181$	15.7574			1.17124			0.585618	+	0.810587i	$0.300852\pi$
$182$		0			0
$183$	9.89949			0.731792
$184$		0			0
$185$	3.24264	−	5.61642i	0.238404	−	0.412927i
$186$		0			0
$187$	−6.82843	−	11.8272i	−0.499344	−	0.864889i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.48528	+	16.4290i	0.686331	+	1.18876i	0.973017	+	0.230735i	$0.0741131\pi$
$191$	9.48528	+	16.4290i	0.686331	+	1.18876i	−0.286686	+	0.958025i	$0.592554\pi$
$192$		0			0
$193$	−3.58579	+	6.21076i	−0.258111	+	0.447061i	−0.965736	−	0.259527i	$-0.916433\pi$
$193$	−3.58579	+	6.21076i	−0.258111	+	0.447061i	0.707625	+	0.706588i	$0.249767\pi$
$194$		0			0
$195$	−2.82843			−0.202548
$196$		0			0
$197$	−1.07107			−0.0763104			−0.0381552	−	0.999272i	$-0.512148\pi$
$197$	−1.07107			−0.0763104			−0.0381552	+	0.999272i	$0.512148\pi$
$198$		0			0
$199$	0.121320	−	0.210133i	0.00860017	−	0.0148959i	−0.861693	−	0.507429i	$-0.830596\pi$
$199$	0.121320	−	0.210133i	0.00860017	−	0.0148959i	0.870293	+	0.492534i	$0.163929\pi$
$200$		0			0
$201$	0.585786	+	1.01461i	0.0413182	+	0.0715652i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$		0			0
$207$	2.29289	−	3.97141i	0.159367	−	0.276032i
$208$		0			0
$209$	−5.17157			−0.357725
$210$		0			0
$211$	−6.34315			−0.436680			−0.218340	−	0.975873i	$-0.570064\pi$
$211$	−6.34315			−0.436680			−0.218340	+	0.975873i	$0.570064\pi$
$212$		0			0
$213$	−3.24264	+	5.61642i	−0.222182	+	0.384831i
$214$		0			0
$215$	−4.82843	−	8.36308i	−0.329296	−	0.570357i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.24264	+	10.8126i	0.421839	+	0.730646i
$220$		0			0
$221$	9.65685	−	16.7262i	0.649590	−	1.12512i
$222$		0			0
$223$	10.8284			0.725125			0.362563	−	0.931959i	$-0.381902\pi$
$223$	10.8284			0.725125			0.362563	+	0.931959i	$0.381902\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	−0.791989	−	0.610535i	$-0.790954\pi$
$227$	2.00000	−	3.46410i	0.132745	−	0.229920i	0.924734	+	0.380615i	$0.124288\pi$
$228$		0			0
$229$	1.29289	+	2.23936i	0.0854368	+	0.147981i	0.905577	−	0.424181i	$-0.139438\pi$
$229$	1.29289	+	2.23936i	0.0854368	+	0.147981i	−0.820140	+	0.572162i	$0.806105\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.3640	+	19.6830i	0.744478	+	1.28947i	0.950438	+	0.310913i	$0.100635\pi$
$233$	11.3640	+	19.6830i	0.744478	+	1.28947i	−0.205960	+	0.978560i	$0.566032\pi$
$234$		0			0
$235$	3.24264	−	5.61642i	0.211527	−	0.366375i
$236$		0			0
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−8.34315			−0.539673			−0.269837	−	0.962906i	$-0.586970\pi$
$239$	−8.34315			−0.539673			−0.269837	+	0.962906i	$0.586970\pi$
$240$		0			0
$241$	−13.2929	+	23.0240i	−0.856271	+	1.48310i	0.0191908	+	0.999816i	$0.493891\pi$
$241$	−13.2929	+	23.0240i	−0.856271	+	1.48310i	−0.875461	+	0.483288i	$0.839442\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.65685	−	6.33386i	−0.232680	−	0.403014i
$248$		0			0
$249$	−0.414214	+	0.717439i	−0.0262497	+	0.0454658i
$250$		0			0
$251$	28.4853			1.79798			0.898988	−	0.437974i	$-0.144304\pi$
$251$	28.4853			1.79798			0.898988	+	0.437974i	$0.144304\pi$
$252$		0			0
$253$	9.17157			0.576612
$254$		0			0
$255$	−3.41421	+	5.91359i	−0.213806	+	0.370323i
$256$		0			0
$257$	−0.656854	−	1.13770i	−0.0409734	−	0.0709681i	0.844811	−	0.535064i	$-0.179713\pi$
$257$	−0.656854	−	1.13770i	−0.0409734	−	0.0709681i	−0.885785	+	0.464096i	$0.846379\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.82843	+	6.63103i	0.236974	+	0.410450i
$262$		0			0
$263$	1.46447	−	2.53653i	0.0903028	−	0.156409i	−0.817336	−	0.576162i	$-0.804550\pi$
$263$	1.46447	−	2.53653i	0.0903028	−	0.156409i	0.907639	+	0.419753i	$0.137883\pi$
$264$		0			0
$265$	7.41421			0.455452
$266$		0			0
$267$	0.828427			0.0506989
$268$		0			0
$269$	10.4142	−	18.0379i	0.634966	−	1.09979i	−0.351557	−	0.936167i	$-0.614348\pi$
$269$	10.4142	−	18.0379i	0.634966	−	1.09979i	0.986522	−	0.163626i	$-0.0523192\pi$
$270$		0			0
$271$	−5.87868	−	10.1822i	−0.357104	−	0.618523i	0.630371	−	0.776294i	$-0.282903\pi$
$271$	−5.87868	−	10.1822i	−0.357104	−	0.618523i	−0.987476	+	0.157771i	$0.949569\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$		0			0
$277$	8.65685	−	14.9941i	0.520140	−	0.900909i	−0.479586	−	0.877495i	$-0.659213\pi$
$277$	8.65685	−	14.9941i	0.520140	−	0.900909i	0.999726	−	0.0234139i	$-0.00745356\pi$
$278$		0			0
$279$	−4.24264			−0.254000
$280$		0			0
$281$	30.9706			1.84755			0.923774	−	0.382937i	$-0.125087\pi$
$281$	30.9706			1.84755			0.923774	+	0.382937i	$0.125087\pi$
$282$		0			0
$283$	−4.24264	+	7.34847i	−0.252199	+	0.436821i	−0.964131	−	0.265427i	$-0.914487\pi$
$283$	−4.24264	+	7.34847i	−0.252199	+	0.436821i	0.711932	+	0.702248i	$0.247820\pi$
$284$		0			0
$285$	1.29289	+	2.23936i	0.0765844	+	0.132648i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−14.8137	−	25.6581i	−0.871395	−	1.50930i
$290$		0			0
$291$	−2.00000	+	3.46410i	−0.117242	+	0.203069i
$292$		0			0
$293$	7.65685			0.447318			0.223659	−	0.974667i	$-0.428200\pi$
$293$	7.65685			0.447318			0.223659	+	0.974667i	$0.428200\pi$
$294$		0			0
$295$	2.82843			0.164677
$296$		0			0
$297$	1.00000	−	1.73205i	0.0580259	−	0.100504i
$298$		0			0
$299$	6.48528	+	11.2328i	0.375054	+	0.649612i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.171573	−	0.297173i	−0.00985660	−	0.0170721i
$304$		0			0
$305$	4.94975	−	8.57321i	0.283422	−	0.490901i
$306$		0			0
$307$	−9.65685			−0.551146			−0.275573	−	0.961280i	$-0.588868\pi$
$307$	−9.65685			−0.551146			−0.275573	+	0.961280i	$0.588868\pi$
$308$		0			0
$309$	−2.82843			−0.160904
$310$		0			0
$311$	−15.6569	+	27.1185i	−0.887819	+	1.53775i	−0.0453703	+	0.998970i	$0.514447\pi$
$311$	−15.6569	+	27.1185i	−0.887819	+	1.53775i	−0.842448	+	0.538777i	$0.818887\pi$
$312$		0			0
$313$	−5.75736	−	9.97204i	−0.325425	−	0.563653i	0.656173	−	0.754610i	$-0.272174\pi$
$313$	−5.75736	−	9.97204i	−0.325425	−	0.563653i	−0.981598	+	0.190957i	$0.938841\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.94975	−	17.2335i	−0.558833	−	0.967928i	−0.997594	−	0.0693241i	$-0.977916\pi$
$317$	−9.94975	−	17.2335i	−0.558833	−	0.967928i	0.438761	−	0.898604i	$-0.355418\pi$
$318$		0			0
$319$	−7.65685	+	13.2621i	−0.428702	+	0.742533i
$320$		0			0
$321$	−9.07107			−0.506298
$322$		0			0
$323$	−17.6569			−0.982454
$324$		0			0
$325$	−1.41421	+	2.44949i	−0.0784465	+	0.135873i
$326$		0			0
$327$	7.82843	+	13.5592i	0.432913	+	0.749827i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−5.31371	−	9.20361i	−0.292068	−	0.505876i	0.682231	−	0.731137i	$-0.261010\pi$
$331$	−5.31371	−	9.20361i	−0.292068	−	0.505876i	−0.974299	+	0.225261i	$0.927677\pi$
$332$		0			0
$333$	−3.24264	+	5.61642i	−0.177696	+	0.307778i
$334$		0			0
$335$	1.17157			0.0640099
$336$		0			0
$337$	−5.79899			−0.315891			−0.157946	−	0.987448i	$-0.550487\pi$
$337$	−5.79899			−0.315891			−0.157946	+	0.987448i	$0.550487\pi$
$338$		0			0
$339$	−1.12132	+	1.94218i	−0.0609018	+	0.105485i
$340$		0			0
$341$	−4.24264	−	7.34847i	−0.229752	−	0.397942i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−2.29289	−	3.97141i	−0.123445	−	0.213813i
$346$		0			0
$347$	−7.70711	+	13.3491i	−0.413739	+	0.716617i	−0.995295	−	0.0968891i	$-0.969111\pi$
$347$	−7.70711	+	13.3491i	−0.413739	+	0.716617i	0.581556	+	0.813506i	$0.302444\pi$
$348$		0			0
$349$	−13.2132			−0.707287			−0.353643	−	0.935380i	$-0.615057\pi$
$349$	−13.2132			−0.707287			−0.353643	+	0.935380i	$0.615057\pi$
$350$		0			0
$351$	2.82843			0.150970
$352$		0			0
$353$	13.1421	−	22.7628i	0.699485	−	1.21154i	−0.269160	−	0.963096i	$-0.586746\pi$
$353$	13.1421	−	22.7628i	0.699485	−	1.21154i	0.968645	−	0.248449i	$-0.0799207\pi$
$354$		0			0
$355$	3.24264	+	5.61642i	0.172101	+	0.298089i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.48528	+	6.03668i	0.183946	+	0.318604i	0.943221	−	0.332166i	$-0.107779\pi$
$359$	3.48528	+	6.03668i	0.183946	+	0.318604i	−0.759275	+	0.650770i	$0.774446\pi$
$360$		0			0
$361$	6.15685	−	10.6640i	0.324045	−	0.561262i
$362$		0			0
$363$	−7.00000			−0.367405
$364$		0			0
$365$	12.4853			0.653509
$366$		0			0
$367$	12.5858	−	21.7992i	0.656973	−	1.13791i	−0.324423	−	0.945912i	$-0.605170\pi$
$367$	12.5858	−	21.7992i	0.656973	−	1.13791i	0.981395	−	0.191998i	$-0.0614967\pi$
$368$		0			0
$369$	1.00000	+	1.73205i	0.0520579	+	0.0901670i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−12.6569	−	21.9223i	−0.655347	−	1.13509i	−0.981807	−	0.189883i	$-0.939189\pi$
$373$	−12.6569	−	21.9223i	−0.655347	−	1.13509i	0.326460	−	0.945211i	$-0.394144\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	−21.6569			−1.11538
$378$		0			0
$379$	−35.9411			−1.84617			−0.923086	−	0.384594i	$-0.874341\pi$
$379$	−35.9411			−1.84617			−0.923086	+	0.384594i	$0.874341\pi$
$380$		0			0
$381$	7.07107	−	12.2474i	0.362262	−	0.627456i
$382$		0			0
$383$	16.0711	+	27.8359i	0.821193	+	1.42235i	0.904794	+	0.425849i	$0.140025\pi$
$383$	16.0711	+	27.8359i	0.821193	+	1.42235i	−0.0836010	+	0.996499i	$0.526642\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.82843	+	8.36308i	0.245443	+	0.425119i
$388$		0			0
$389$	−6.41421	+	11.1097i	−0.325214	+	0.563286i	−0.981556	−	0.191177i	$-0.938770\pi$
$389$	−6.41421	+	11.1097i	−0.325214	+	0.563286i	0.656342	+	0.754463i	$0.272103\pi$
$390$		0			0
$391$	31.3137			1.58360
$392$		0			0
$393$	−11.3137			−0.570701
$394$		0			0
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	−14.1421	−	24.4949i	−0.709773	−	1.22936i	−0.964941	−	0.262467i	$-0.915464\pi$
$397$	−14.1421	−	24.4949i	−0.709773	−	1.22936i	0.255168	−	0.966897i	$-0.417869\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.7574	−	18.6323i	−0.537197	−	0.930452i	−0.999054	−	0.0434977i	$-0.986150\pi$
$401$	−10.7574	−	18.6323i	−0.537197	−	0.930452i	0.461857	−	0.886955i	$-0.347183\pi$
$402$		0			0
$403$	6.00000	−	10.3923i	0.298881	−	0.517678i
$404$		0			0
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−12.9706			−0.642927
$408$		0			0
$409$	−0.363961	+	0.630399i	−0.0179967	+	0.0311712i	−0.874884	−	0.484333i	$-0.839062\pi$
$409$	−0.363961	+	0.630399i	−0.0179967	+	0.0311712i	0.856887	+	0.515505i	$0.172396\pi$
$410$		0			0
$411$	−5.94975	−	10.3053i	−0.293479	−	0.508321i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.414214	+	0.717439i	0.0203329	+	0.0352177i
$416$		0			0
$417$	−11.7782	+	20.4004i	−0.576780	+	0.999012i
$418$		0			0
$419$	0.970563			0.0474151			0.0237075	−	0.999719i	$-0.492453\pi$
$419$	0.970563			0.0474151			0.0237075	+	0.999719i	$0.492453\pi$
$420$		0			0
$421$	24.2843			1.18354			0.591771	−	0.806106i	$-0.298429\pi$
$421$	24.2843			1.18354			0.591771	+	0.806106i	$0.298429\pi$
$422$		0			0
$423$	−3.24264	+	5.61642i	−0.157663	+	0.273080i
$424$		0			0
$425$	3.41421	+	5.91359i	0.165614	+	0.286851i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	2.82843	+	4.89898i	0.136558	+	0.236525i
$430$		0			0
$431$	−10.7574	+	18.6323i	−0.518164	+	0.897486i	0.481614	+	0.876384i	$0.340051\pi$
$431$	−10.7574	+	18.6323i	−0.518164	+	0.897486i	−0.999777	+	0.0211023i	$0.993282\pi$
$432$		0			0
$433$	18.8284			0.904836			0.452418	−	0.891806i	$-0.350561\pi$
$433$	18.8284			0.904836			0.452418	+	0.891806i	$0.350561\pi$
$434$		0			0
$435$	7.65685			0.367118
$436$		0			0
$437$	5.92893	−	10.2692i	0.283619	−	0.491243i
$438$		0			0
$439$	0.363961	+	0.630399i	0.0173709	+	0.0300873i	0.874580	−	0.484881i	$-0.161137\pi$
$439$	0.363961	+	0.630399i	0.0173709	+	0.0300873i	−0.857209	+	0.514968i	$0.827804\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.7071	+	20.2773i	0.556221	+	0.963404i	0.997807	+	0.0661848i	$0.0210827\pi$
$443$	11.7071	+	20.2773i	0.556221	+	0.963404i	−0.441586	+	0.897219i	$0.645584\pi$
$444$		0			0
$445$	0.414214	−	0.717439i	0.0196356	−	0.0340099i
$446$		0			0
$447$	−8.34315			−0.394617
$448$		0			0
$449$	22.0000			1.03824			0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000			1.03824			0.519122	+	0.854700i	$0.326259\pi$
$450$		0			0
$451$	−2.00000	+	3.46410i	−0.0941763	+	0.163118i
$452$		0			0
$453$	8.65685	+	14.9941i	0.406734	+	0.704485i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.2426	−	22.9369i	−0.619465	−	1.07294i	−0.989584	−	0.143960i	$-0.954016\pi$
$457$	−13.2426	−	22.9369i	−0.619465	−	1.07294i	0.370119	−	0.928984i	$-0.379317\pi$
$458$		0			0
$459$	3.41421	−	5.91359i	0.159362	−	0.276023i
$460$		0			0
$461$	−39.4558			−1.83764			−0.918821	−	0.394675i	$-0.870857\pi$
$461$	−39.4558			−1.83764			−0.918821	+	0.394675i	$0.870857\pi$
$462$		0			0
$463$	−34.1421			−1.58672			−0.793360	−	0.608753i	$-0.791670\pi$
$463$	−34.1421			−1.58672			−0.793360	+	0.608753i	$0.791670\pi$
$464$		0			0
$465$	−2.12132	+	3.67423i	−0.0983739	+	0.170389i
$466$		0			0
$467$	18.9706	+	32.8580i	0.877853	+	1.52049i	0.853692	+	0.520778i	$0.174358\pi$
$467$	18.9706	+	32.8580i	0.877853	+	1.52049i	0.0241607	+	0.999708i	$0.492309\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	9.07107	+	15.7116i	0.417973	+	0.723950i
$472$		0			0
$473$	−9.65685	+	16.7262i	−0.444023	+	0.769070i
$474$		0			0
$475$	2.58579			0.118644
$476$		0			0
$477$	−7.41421			−0.339474
$478$		0			0
$479$	−16.9706	+	29.3939i	−0.775405	+	1.34304i	0.159162	+	0.987252i	$0.449121\pi$
$479$	−16.9706	+	29.3939i	−0.775405	+	1.34304i	−0.934567	+	0.355788i	$0.884213\pi$
$480$		0			0
$481$	−9.17157	−	15.8856i	−0.418188	−	0.724322i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$		0			0
$487$	−18.1421	+	31.4231i	−0.822099	+	1.42392i	0.0820180	+	0.996631i	$0.473864\pi$
$487$	−18.1421	+	31.4231i	−0.822099	+	1.42392i	−0.904117	+	0.427286i	$0.859470\pi$
$488$		0			0
$489$	10.1421			0.458643
$490$		0			0
$491$	33.1127			1.49436			0.747178	−	0.664624i	$-0.231408\pi$
$491$	33.1127			1.49436			0.747178	+	0.664624i	$0.231408\pi$
$492$		0			0
$493$	−26.1421	+	45.2795i	−1.17738	+	2.03929i
$494$		0			0
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−13.1421	−	22.7628i	−0.588323	−	1.01900i	−0.994452	−	0.105189i	$-0.966455\pi$
$499$	−13.1421	−	22.7628i	−0.588323	−	1.01900i	0.406129	−	0.913816i	$-0.366878\pi$
$500$		0			0
$501$	8.00000	−	13.8564i	0.357414	−	0.619059i
$502$		0			0
$503$	−27.1716			−1.21152			−0.605760	−	0.795647i	$-0.707131\pi$
$503$	−27.1716			−1.21152			−0.605760	+	0.795647i	$0.707131\pi$
$504$		0			0
$505$	−0.343146			−0.0152698
$506$		0			0
$507$	2.50000	−	4.33013i	0.111029	−	0.192308i
$508$		0			0
$509$	10.7574	+	18.6323i	0.476812	+	0.825862i	0.999647	−	0.0265718i	$-0.00845907\pi$
$509$	10.7574	+	18.6323i	0.476812	+	0.825862i	−0.522835	+	0.852434i	$0.675126\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.29289	−	2.23936i	−0.0570826	−	0.0988700i
$514$		0			0
$515$	−1.41421	+	2.44949i	−0.0623177	+	0.107937i
$516$		0			0
$517$	−12.9706			−0.570445
$518$		0			0
$519$	14.1421			0.620771
$520$		0			0
$521$	−20.5563	+	35.6046i	−0.900590	+	1.55987i	−0.0738601	+	0.997269i	$0.523532\pi$
$521$	−20.5563	+	35.6046i	−0.900590	+	1.55987i	−0.826730	+	0.562599i	$0.809802\pi$
$522$		0			0
$523$	9.41421	+	16.3059i	0.411655	+	0.713007i	0.995071	−	0.0991664i	$-0.0316176\pi$
$523$	9.41421	+	16.3059i	0.411655	+	0.713007i	−0.583416	+	0.812173i	$0.698284\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.4853	−	25.0892i	−0.630989	−	1.09290i
$528$		0			0
$529$	0.985281	−	1.70656i	0.0428383	−	0.0741981i
$530$		0			0
$531$	−2.82843			−0.122743
$532$		0			0
$533$	−5.65685			−0.245026
$534$		0			0
$535$	−4.53553	+	7.85578i	−0.196088	+	0.339635i
$536$		0			0
$537$	−3.24264	−	5.61642i	−0.139930	−	0.242366i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	10.1421	+	17.5667i	0.436044	+	0.755251i	0.997380	−	0.0723370i	$-0.0230457\pi$
$541$	10.1421	+	17.5667i	0.436044	+	0.755251i	−0.561336	+	0.827588i	$0.689712\pi$
$542$		0			0
$543$	−7.87868	+	13.6463i	−0.338107	+	0.585618i
$544$		0			0
$545$	15.6569			0.670666
$546$		0			0
$547$	−35.1127			−1.50131			−0.750655	−	0.660694i	$-0.770262\pi$
$547$	−35.1127			−1.50131			−0.750655	+	0.660694i	$0.770262\pi$
$548$		0			0
$549$	−4.94975	+	8.57321i	−0.211250	+	0.365896i
$550$		0			0
$551$	9.89949	+	17.1464i	0.421733	+	0.730462i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	3.24264	+	5.61642i	0.137642	+	0.238404i
$556$		0			0
$557$	−13.8492	+	23.9876i	−0.586811	+	1.01639i	0.407836	+	0.913055i	$0.366284\pi$
$557$	−13.8492	+	23.9876i	−0.586811	+	1.01639i	−0.994647	+	0.103332i	$0.967050\pi$
$558$		0			0
$559$	−27.3137			−1.15525
$560$		0			0
$561$	13.6569			0.576593
$562$		0			0
$563$	10.7574	−	18.6323i	0.453369	−	0.785258i	−0.545224	−	0.838290i	$-0.683555\pi$
$563$	10.7574	−	18.6323i	0.453369	−	0.785258i	0.998593	+	0.0530328i	$0.0168888\pi$
$564$		0			0
$565$	1.12132	+	1.94218i	0.0471743	+	0.0817083i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.75736	−	15.1682i	−0.367128	−	0.635884i	0.621988	−	0.783027i	$-0.286325\pi$
$569$	−8.75736	−	15.1682i	−0.367128	−	0.635884i	−0.989115	+	0.147143i	$0.952992\pi$
$570$		0			0
$571$	18.1421	−	31.4231i	0.759225	−	1.31502i	−0.184022	−	0.982922i	$-0.558912\pi$
$571$	18.1421	−	31.4231i	0.759225	−	1.31502i	0.943246	−	0.332094i	$-0.107755\pi$
$572$		0			0
$573$	−18.9706			−0.792507
$574$		0			0
$575$	−4.58579			−0.191241
$576$		0			0
$577$	−1.41421	+	2.44949i	−0.0588745	+	0.101974i	−0.893960	−	0.448146i	$-0.852085\pi$
$577$	−1.41421	+	2.44949i	−0.0588745	+	0.101974i	0.835086	+	0.550119i	$0.185418\pi$
$578$		0			0
$579$	−3.58579	−	6.21076i	−0.149020	−	0.258111i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−7.41421	−	12.8418i	−0.307065	−	0.531853i
$584$		0			0
$585$	1.41421	−	2.44949i	0.0584705	−	0.101274i
$586$		0			0
$587$	11.1716			0.461100			0.230550	−	0.973060i	$-0.425947\pi$
$587$	11.1716			0.461100			0.230550	+	0.973060i	$0.425947\pi$
$588$		0			0
$589$	−10.9706			−0.452034
$590$		0			0
$591$	0.535534	−	0.927572i	0.0220289	−	0.0381552i
$592$		0			0
$593$	−15.4853	−	26.8213i	−0.635904	−	1.10142i	−0.986323	−	0.164825i	$-0.947294\pi$
$593$	−15.4853	−	26.8213i	−0.635904	−	1.10142i	0.350418	−	0.936593i	$-0.386039\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.121320	+	0.210133i	0.00496531	+	0.00860017i
$598$		0			0
$599$	7.00000	−	12.1244i	0.286012	−	0.495388i	−0.686842	−	0.726807i	$-0.741004\pi$
$599$	7.00000	−	12.1244i	0.286012	−	0.495388i	0.972854	+	0.231419i	$0.0743369\pi$
$600$		0			0
$601$	28.2426			1.15204			0.576021	−	0.817435i	$-0.304605\pi$
$601$	28.2426			1.15204			0.576021	+	0.817435i	$0.304605\pi$
$602$		0			0
$603$	−1.17157			−0.0477101
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	14.7279	+	25.5095i	0.597788	+	1.03540i	0.993147	+	0.116872i	$0.0372868\pi$
$607$	14.7279	+	25.5095i	0.597788	+	1.03540i	−0.395359	+	0.918527i	$0.629380\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.17157	−	15.8856i	−0.371042	−	0.642664i
$612$		0			0
$613$	−7.34315	+	12.7187i	−0.296587	+	0.513704i	−0.975353	−	0.220651i	$-0.929182\pi$
$613$	−7.34315	+	12.7187i	−0.296587	+	0.513704i	0.678766	+	0.734355i	$0.262515\pi$
$614$		0			0
$615$	2.00000			0.0806478
$616$		0			0
$617$	−23.6985			−0.954065			−0.477033	−	0.878886i	$-0.658288\pi$
$617$	−23.6985			−0.954065			−0.477033	+	0.878886i	$0.658288\pi$
$618$		0			0
$619$	16.9497	−	29.3578i	0.681268	−	1.17999i	−0.293326	−	0.956012i	$-0.594762\pi$
$619$	16.9497	−	29.3578i	0.681268	−	1.17999i	0.974594	−	0.223978i	$-0.0719044\pi$
$620$		0			0
$621$	2.29289	+	3.97141i	0.0920106	+	0.159367i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	2.58579	−	4.47871i	0.103266	−	0.178863i
$628$		0			0
$629$	−44.2843			−1.76573
$630$		0			0
$631$	29.3137			1.16696			0.583480	−	0.812127i	$-0.301691\pi$
$631$	29.3137			1.16696			0.583480	+	0.812127i	$0.301691\pi$
$632$		0			0
$633$	3.17157	−	5.49333i	0.126059	−	0.218340i
$634$		0			0
$635$	−7.07107	−	12.2474i	−0.280607	−	0.486025i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3.24264	−	5.61642i	−0.128277	−	0.222182i
$640$		0			0
$641$	−21.4853	+	37.2136i	−0.848618	+	1.46985i	0.0338245	+	0.999428i	$0.489231\pi$
$641$	−21.4853	+	37.2136i	−0.848618	+	1.46985i	−0.882442	+	0.470421i	$0.844102\pi$
$642$		0			0
$643$	−24.2843			−0.957678			−0.478839	−	0.877903i	$-0.658942\pi$
$643$	−24.2843			−0.957678			−0.478839	+	0.877903i	$0.658942\pi$
$644$		0			0
$645$	9.65685			0.380238
$646$		0			0
$647$	6.34315	−	10.9867i	0.249375	−	0.431930i	−0.713978	−	0.700168i	$-0.753108\pi$
$647$	6.34315	−	10.9867i	0.249375	−	0.431930i	0.963353	+	0.268239i	$0.0864416\pi$
$648$		0			0
$649$	−2.82843	−	4.89898i	−0.111025	−	0.192302i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.70711	−	16.8132i	−0.379868	−	0.657951i	0.611174	−	0.791496i	$-0.290697\pi$
$653$	−9.70711	−	16.8132i	−0.379868	−	0.657951i	−0.991043	+	0.133545i	$0.957364\pi$
$654$		0			0
$655$	−5.65685	+	9.79796i	−0.221032	+	0.382838i
$656$		0			0
$657$	−12.4853			−0.487097
$658$		0			0
$659$	−29.7990			−1.16080			−0.580402	−	0.814330i	$-0.697105\pi$
$659$	−29.7990			−1.16080			−0.580402	+	0.814330i	$0.697105\pi$
$660$		0			0
$661$	−22.1213	+	38.3153i	−0.860420	+	1.49029i	0.0111047	+	0.999938i	$0.496465\pi$
$661$	−22.1213	+	38.3153i	−0.860420	+	1.49029i	−0.871524	+	0.490352i	$0.836868\pi$
$662$		0			0
$663$	9.65685	+	16.7262i	0.375041	+	0.649590i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−17.5563	−	30.4085i	−0.679785	−	1.17742i
$668$		0			0
$669$	−5.41421	+	9.37769i	−0.209326	+	0.362563i
$670$		0			0
$671$	−19.7990			−0.764332
$672$		0			0
$673$	35.1716			1.35576			0.677882	−	0.735170i	$-0.262898\pi$
$673$	35.1716			1.35576			0.677882	+	0.735170i	$0.262898\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	−4.51472	−	7.81972i	−0.173515	−	0.300536i	0.766132	−	0.642684i	$-0.222179\pi$
$677$	−4.51472	−	7.81972i	−0.173515	−	0.300536i	−0.939646	+	0.342147i	$0.888846\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$		0			0
$683$	16.7782	−	29.0607i	0.641999	−	1.11197i	−0.342987	−	0.939340i	$-0.611439\pi$
$683$	16.7782	−	29.0607i	0.641999	−	1.11197i	0.984986	−	0.172635i	$-0.0552280\pi$
$684$		0			0
$685$	−11.8995			−0.454656
$686$		0			0
$687$	−2.58579			−0.0986539
$688$		0			0
$689$	10.4853	−	18.1610i	0.399457	−	0.691881i
$690$		0			0
$691$	22.3640	+	38.7355i	0.850765	+	1.47357i	0.880519	+	0.474011i	$0.157194\pi$
$691$	22.3640	+	38.7355i	0.850765	+	1.47357i	−0.0297536	+	0.999557i	$0.509472\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.7782	+	20.4004i	0.446772	+	0.773831i
$696$		0			0
$697$	−6.82843	+	11.8272i	−0.258645	+	0.447986i
$698$		0			0
$699$	−22.7279			−0.859649
$700$		0			0
$701$	2.97056			0.112197			0.0560983	−	0.998425i	$-0.482134\pi$
$701$	2.97056			0.112197			0.0560983	+	0.998425i	$0.482134\pi$
$702$		0			0
$703$	−8.38478	+	14.5229i	−0.316238	+	0.547740i
$704$		0			0
$705$	3.24264	+	5.61642i	0.122125	+	0.211527i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−15.6569	−	27.1185i	−0.588006	−	1.01846i	−0.994493	−	0.104799i	$-0.966580\pi$
$709$	−15.6569	−	27.1185i	−0.588006	−	1.01846i	0.406488	−	0.913656i	$-0.366753\pi$
$710$		0			0
$711$	5.00000	−	8.66025i	0.187515	−	0.324785i
$712$		0			0
$713$	19.4558			0.728627
$714$		0			0
$715$	5.65685			0.211554
$716$		0			0
$717$	4.17157	−	7.22538i	0.155790	−	0.269837i
$718$		0			0
$719$	2.24264	+	3.88437i	0.0836364	+	0.144862i	0.904809	−	0.425817i	$-0.140013\pi$
$719$	2.24264	+	3.88437i	0.0836364	+	0.144862i	−0.821173	+	0.570679i	$0.806680\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−13.2929	−	23.0240i	−0.494368	−	0.856271i
$724$		0			0
$725$	3.82843	−	6.63103i	0.142184	−	0.246270i
$726$		0			0
$727$	35.5980			1.32026			0.660128	−	0.751153i	$-0.270502\pi$
$727$	35.5980			1.32026			0.660128	+	0.751153i	$0.270502\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−32.9706	+	57.1067i	−1.21946	+	2.11217i
$732$		0			0
$733$	−3.75736	−	6.50794i	−0.138781	−	0.240376i	0.788254	−	0.615350i	$-0.210985\pi$
$733$	−3.75736	−	6.50794i	−0.138781	−	0.240376i	−0.927036	+	0.374973i	$0.877652\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.17157	−	2.02922i	−0.0431554	−	0.0747474i
$738$		0			0
$739$	−19.3137	+	33.4523i	−0.710466	+	1.23056i	0.254216	+	0.967147i	$0.418183\pi$
$739$	−19.3137	+	33.4523i	−0.710466	+	1.23056i	−0.964682	+	0.263416i	$0.915151\pi$
$740$		0			0
$741$	7.31371			0.268676
$742$		0			0
$743$	30.0416			1.10212			0.551060	−	0.834465i	$-0.314223\pi$
$743$	30.0416			1.10212			0.551060	+	0.834465i	$0.314223\pi$
$744$		0			0
$745$	−4.17157	+	7.22538i	−0.152835	+	0.264717i
$746$		0			0
$747$	−0.414214	−	0.717439i	−0.0151553	−	0.0262497i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.17157	−	2.02922i	−0.0427513	−	0.0740474i	0.843858	−	0.536567i	$-0.180279\pi$
$751$	−1.17157	−	2.02922i	−0.0427513	−	0.0740474i	−0.886609	+	0.462519i	$0.846946\pi$
$752$		0			0
$753$	−14.2426	+	24.6690i	−0.519031	+	0.898988i
$754$		0			0
$755$	17.3137			0.630110
$756$		0			0
$757$	−4.82843			−0.175492			−0.0877461	−	0.996143i	$-0.527966\pi$
$757$	−4.82843			−0.175492			−0.0877461	+	0.996143i	$0.527966\pi$
$758$		0			0
$759$	−4.58579	+	7.94282i	−0.166454	+	0.288306i
$760$		0			0
$761$	5.24264	+	9.08052i	0.190046	+	0.329169i	0.945265	−	0.326303i	$-0.105803\pi$
$761$	5.24264	+	9.08052i	0.190046	+	0.329169i	−0.755220	+	0.655472i	$0.772470\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−3.41421	−	5.91359i	−0.123441	−	0.213806i
$766$		0			0
$767$	4.00000	−	6.92820i	0.144432	−	0.250163i
$768$		0			0
$769$	29.2132			1.05346			0.526728	−	0.850034i	$-0.323419\pi$
$769$	29.2132			1.05346			0.526728	+	0.850034i	$0.323419\pi$
$770$		0			0
$771$	1.31371			0.0473121
$772$		0			0
$773$	6.72792	−	11.6531i	0.241987	−	0.419133i	−0.719294	−	0.694706i	$-0.755534\pi$
$773$	6.72792	−	11.6531i	0.241987	−	0.419133i	0.961280	+	0.275573i	$0.0888677\pi$
$774$		0			0
$775$	2.12132	+	3.67423i	0.0762001	+	0.131982i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.58579	+	4.47871i	0.0926454	+	0.160467i
$780$		0			0
$781$	6.48528	−	11.2328i	0.232062	−	0.401943i
$782$		0			0
$783$	−7.65685			−0.273634
$784$		0			0
$785$	18.1421			0.647521
$786$		0			0
$787$	−11.5563	+	20.0162i	−0.411939	+	0.713500i	−0.995102	−	0.0988557i	$-0.968482\pi$
$787$	−11.5563	+	20.0162i	−0.411939	+	0.713500i	0.583162	+	0.812356i	$0.301815\pi$
$788$		0			0
$789$	1.46447	+	2.53653i	0.0521364	+	0.0903028i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−14.0000	−	24.2487i	−0.497155	−	0.861097i
$794$		0			0
$795$	−3.70711	+	6.42090i	−0.131478	+	0.227726i
$796$		0			0
$797$	−47.1127			−1.66882			−0.834409	−	0.551146i	$-0.814191\pi$
$797$	−47.1127			−1.66882			−0.834409	+	0.551146i	$0.814191\pi$
$798$		0			0
$799$	−44.2843			−1.56666
$800$		0			0
$801$	−0.414214	+	0.717439i	−0.0146355	+	0.0253495i
$802$		0			0
$803$	−12.4853	−	21.6251i	−0.440596	−	0.763135i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.4142	+	18.0379i	0.366598	+	0.634966i
$808$		0			0
$809$	−11.2426	+	19.4728i	−0.395270	+	0.684628i	−0.993136	−	0.116968i	$-0.962682\pi$
$809$	−11.2426	+	19.4728i	−0.395270	+	0.684628i	0.597865	+	0.801596i	$0.296016\pi$
$810$		0			0
$811$	17.8995			0.628536			0.314268	−	0.949334i	$-0.398241\pi$
$811$	17.8995			0.628536			0.314268	+	0.949334i	$0.398241\pi$
$812$		0			0
$813$	11.7574			0.412349
$814$		0			0
$815$	5.07107	−	8.78335i	0.177632	−	0.307667i
$816$		0			0
$817$	12.4853	+	21.6251i	0.436805	+	0.756568i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	22.2132	+	38.4744i	0.775246	+	1.34277i	0.934656	+	0.355553i	$0.115708\pi$
$821$	22.2132	+	38.4744i	0.775246	+	1.34277i	−0.159410	+	0.987212i	$0.550959\pi$
$822$		0			0
$823$	12.7279	−	22.0454i	0.443667	−	0.768455i	−0.554291	−	0.832323i	$-0.687010\pi$
$823$	12.7279	−	22.0454i	0.443667	−	0.768455i	0.997958	+	0.0638684i	$0.0203438\pi$
$824$		0			0
$825$	−2.00000			−0.0696311
$826$		0			0
$827$	−5.75736			−0.200203			−0.100101	−	0.994977i	$-0.531917\pi$
$827$	−5.75736			−0.200203			−0.100101	+	0.994977i	$0.531917\pi$
$828$		0			0
$829$	5.53553	−	9.58783i	0.192257	−	0.332999i	−0.753741	−	0.657172i	$-0.771753\pi$
$829$	5.53553	−	9.58783i	0.192257	−	0.332999i	0.945998	+	0.324173i	$0.105086\pi$
$830$		0			0
$831$	8.65685	+	14.9941i	0.300303	+	0.520140i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−8.00000	−	13.8564i	−0.276851	−	0.479521i
$836$		0			0
$837$	2.12132	−	3.67423i	0.0733236	−	0.127000i
$838$		0			0
$839$	15.5147			0.535628			0.267814	−	0.963471i	$-0.413699\pi$
$839$	15.5147			0.535628			0.267814	+	0.963471i	$0.413699\pi$
$840$		0			0
$841$	29.6274			1.02164
$842$		0			0
$843$	−15.4853	+	26.8213i	−0.533341	+	0.923774i
$844$		0			0
$845$	−2.50000	−	4.33013i	−0.0860026	−	0.148961i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−4.24264	−	7.34847i	−0.145607	−	0.252199i
$850$		0			0
$851$	14.8701	−	25.7557i	0.509739	−	0.882894i
$852$		0			0
$853$	−16.2843			−0.557563			−0.278781	−	0.960355i	$-0.589930\pi$
$853$	−16.2843			−0.557563			−0.278781	+	0.960355i	$0.589930\pi$
$854$		0			0
$855$	−2.58579			−0.0884320
$856$		0			0
$857$	−12.7279	+	22.0454i	−0.434778	+	0.753057i	−0.997277	−	0.0737406i	$-0.976506\pi$
$857$	−12.7279	+	22.0454i	−0.434778	+	0.753057i	0.562500	+	0.826797i	$0.309840\pi$
$858$		0			0
$859$	−14.9497	−	25.8937i	−0.510079	−	0.883482i	−0.999932	−	0.0116774i	$-0.996283\pi$
$859$	−14.9497	−	25.8937i	−0.510079	−	0.883482i	0.489853	−	0.871805i	$-0.337050\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.05025	+	13.9434i	0.274034	+	0.474640i	0.969891	−	0.243540i	$-0.0783087\pi$
$863$	8.05025	+	13.9434i	0.274034	+	0.474640i	−0.695857	+	0.718180i	$0.744975\pi$
$864$		0			0
$865$	7.07107	−	12.2474i	0.240424	−	0.416426i
$866$		0			0
$867$	29.6274			1.00620
$868$		0			0
$869$	20.0000			0.678454
$870$		0			0
$871$	1.65685	−	2.86976i	0.0561404	−	0.0972380i
$872$		0			0
$873$	−2.00000	−	3.46410i	−0.0676897	−	0.117242i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.51472	+	11.2838i	0.219986	+	0.381028i	0.954804	−	0.297238i	$-0.0960654\pi$
$877$	6.51472	+	11.2838i	0.219986	+	0.381028i	−0.734817	+	0.678265i	$0.762732\pi$
$878$		0			0
$879$	−3.82843	+	6.63103i	−0.129130	+	0.223659i
$880$		0			0
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$	16.9706			0.571105			0.285552	−	0.958363i	$-0.407823\pi$
$883$	16.9706			0.571105			0.285552	+	0.958363i	$0.407823\pi$
$884$		0			0
$885$	−1.41421	+	2.44949i	−0.0475383	+	0.0823387i
$886$		0			0
$887$	16.4142	+	28.4303i	0.551135	+	0.954594i	0.998193	+	0.0600893i	$0.0191385\pi$
$887$	16.4142	+	28.4303i	0.551135	+	0.954594i	−0.447058	+	0.894505i	$0.647528\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.00000	+	1.73205i	0.0335013	+	0.0580259i
$892$		0			0
$893$	−8.38478	+	14.5229i	−0.280586	+	0.485989i
$894$		0			0
$895$	−6.48528			−0.216779
$896$		0			0
$897$	−12.9706			−0.433074
$898$		0			0
$899$	−16.2426	+	28.1331i	−0.541722	+	0.938291i
$900$		0			0
$901$	−25.3137	−	43.8446i	−0.843322	−	1.46068i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.87868	+	13.6463i	0.261896	+	0.453617i
$906$		0			0
$907$	−11.1716	+	19.3497i	−0.370946	+	0.642497i	−0.989711	−	0.143079i	$-0.954300\pi$
$907$	−11.1716	+	19.3497i	−0.370946	+	0.642497i	0.618765	+	0.785576i	$0.287633\pi$
$908$		0			0
$909$	0.343146			0.0113814
$910$		0			0
$911$	19.9411			0.660679			0.330339	−	0.943862i	$-0.392837\pi$
$911$	19.9411			0.660679			0.330339	+	0.943862i	$0.392837\pi$
$912$		0			0
$913$	0.828427	−	1.43488i	0.0274169	−	0.0474875i
$914$		0			0
$915$	4.94975	+	8.57321i	0.163634	+	0.283422i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	14.1421	+	24.4949i	0.466506	+	0.808012i	0.999268	−	0.0382530i	$-0.0121793\pi$
$919$	14.1421	+	24.4949i	0.466506	+	0.808012i	−0.532762	+	0.846265i	$0.678846\pi$
$920$		0			0
$921$	4.82843	−	8.36308i	0.159102	−	0.275573i
$922$		0			0
$923$	18.3431			0.603772
$924$		0			0
$925$	6.48528			0.213235
$926$		0			0
$927$	1.41421	−	2.44949i	0.0464489	−	0.0804518i
$928$		0			0
$929$	−12.4142	−	21.5020i	−0.407297	−	0.705459i	0.587289	−	0.809378i	$-0.300195\pi$
$929$	−12.4142	−	21.5020i	−0.407297	−	0.705459i	−0.994586	+	0.103918i	$0.966862\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−15.6569	−	27.1185i	−0.512582	−	0.887819i
$934$		0			0
$935$	6.82843	−	11.8272i	0.223313	−	0.386790i
$936$		0			0
$937$	−6.34315			−0.207222			−0.103611	−	0.994618i	$-0.533040\pi$
$937$	−6.34315			−0.207222			−0.103611	+	0.994618i	$0.533040\pi$
$938$		0			0
$939$	11.5147			0.375769
$940$		0			0
$941$	−19.6274	+	33.9957i	−0.639836	+	1.10823i	0.345633	+	0.938370i	$0.387664\pi$
$941$	−19.6274	+	33.9957i	−0.639836	+	1.10823i	−0.985469	+	0.169858i	$0.945669\pi$
$942$		0			0
$943$	−4.58579	−	7.94282i	−0.149334	−	0.258654i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.5355	−	32.1045i	−0.602324	−	1.04326i	−0.992468	−	0.122502i	$-0.960908\pi$
$947$	−18.5355	−	32.1045i	−0.602324	−	1.04326i	0.390144	−	0.920754i	$-0.372425\pi$
$948$		0			0
$949$	17.6569	−	30.5826i	0.573166	−	0.992752i
$950$		0			0
$951$	19.8995			0.645285
$952$		0			0
$953$	−2.04163			−0.0661349			−0.0330675	−	0.999453i	$-0.510528\pi$
$953$	−2.04163			−0.0661349			−0.0330675	+	0.999453i	$0.510528\pi$
$954$		0			0
$955$	−9.48528	+	16.4290i	−0.306936	+	0.531630i
$956$		0			0
$957$	−7.65685	−	13.2621i	−0.247511	−	0.428702i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	6.50000	+	11.2583i	0.209677	+	0.363172i
$962$		0			0
$963$	4.53553	−	7.85578i	0.146156	−	0.253149i
$964$		0			0
$965$	−7.17157			−0.230861
$966$		0			0
$967$	−59.7990			−1.92301			−0.961503	−	0.274795i	$-0.911390\pi$
$967$	−59.7990			−1.92301			−0.961503	+	0.274795i	$0.911390\pi$
$968$		0			0
$969$	8.82843	−	15.2913i	0.283610	−	0.491227i
$970$		0			0
$971$	−1.75736	−	3.04384i	−0.0563963	−	0.0976813i	0.836449	−	0.548045i	$-0.184628\pi$
$971$	−1.75736	−	3.04384i	−0.0563963	−	0.0976813i	−0.892845	+	0.450364i	$0.851294\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−1.41421	−	2.44949i	−0.0452911	−	0.0784465i
$976$		0			0
$977$	9.02082	−	15.6245i	0.288601	−	0.499872i	−0.684875	−	0.728661i	$-0.740143\pi$
$977$	9.02082	−	15.6245i	0.288601	−	0.499872i	0.973476	+	0.228788i	$0.0734764\pi$
$978$		0			0
$979$	−1.65685			−0.0529533
$980$		0			0
$981$	−15.6569			−0.499885
$982$		0			0
$983$	11.7990	−	20.4364i	0.376329	−	0.651822i	−0.614196	−	0.789154i	$-0.710519\pi$
$983$	11.7990	−	20.4364i	0.376329	−	0.651822i	0.990525	+	0.137332i	$0.0438528\pi$
$984$		0			0
$985$	−0.535534	−	0.927572i	−0.0170635	−	0.0295549i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22.1421	−	38.3513i	−0.704079	−	1.21950i
$990$		0			0
$991$	−5.65685	+	9.79796i	−0.179696	+	0.311242i	−0.941776	−	0.336240i	$-0.890845\pi$
$991$	−5.65685	+	9.79796i	−0.179696	+	0.311242i	0.762080	+	0.647482i	$0.224178\pi$
$992$		0			0
$993$	10.6274			0.337251
$994$		0			0
$995$	0.242641			0.00769223
$996$		0			0
$997$	9.65685	−	16.7262i	0.305836	−	0.529723i	−0.671611	−	0.740904i	$-0.734398\pi$
$997$	9.65685	−	16.7262i	0.305836	−	0.529723i	0.977447	+	0.211181i	$0.0677309\pi$
$998$		0			0
$999$	−3.24264	−	5.61642i	−0.102593	−	0.177696i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.p.361.2		4
7.2	even	3	inner	2940.2.q.p.961.2		4
7.3	odd	6		2940.2.a.o.1.1	✓	2
7.4	even	3		2940.2.a.q.1.2	yes	2
7.5	odd	6		2940.2.q.r.961.1		4
7.6	odd	2		2940.2.q.r.361.1		4
21.11	odd	6		8820.2.a.bm.1.2		2
21.17	even	6		8820.2.a.bh.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.a.o.1.1	✓	2	7.3	odd	6
2940.2.a.q.1.2	yes	2	7.4	even	3
2940.2.q.p.361.2		4	1.1	even	1	trivial
2940.2.q.p.961.2		4	7.2	even	3	inner
2940.2.q.r.361.1		4	7.6	odd	2
2940.2.q.r.961.1		4	7.5	odd	6
8820.2.a.bh.1.1		2	21.17	even	6
8820.2.a.bm.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:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{11} +2.82843 q^{13} -1.00000 q^{15} +(3.41421 - 5.91359i) q^{17} +(-1.29289 - 2.23936i) q^{19} +(2.29289 + 3.97141i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -7.65685 q^{29} +(2.12132 - 3.67423i) q^{31} +(1.00000 + 1.73205i) q^{33} +(-3.24264 - 5.61642i) q^{37} +(-1.41421 + 2.44949i) q^{39} -2.00000 q^{41} -9.65685 q^{43} +(0.500000 - 0.866025i) q^{45} +(-3.24264 - 5.61642i) q^{47} +(3.41421 + 5.91359i) q^{51} +(3.70711 - 6.42090i) q^{53} +2.00000 q^{55} +2.58579 q^{57} +(1.41421 - 2.44949i) q^{59} +(-4.94975 - 8.57321i) q^{61} +(1.41421 + 2.44949i) q^{65} +(0.585786 - 1.01461i) q^{67} -4.58579 q^{69} +6.48528 q^{71} +(6.24264 - 10.8126i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(5.00000 + 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +0.828427 q^{83} +6.82843 q^{85} +(3.82843 - 6.63103i) q^{87} +(-0.414214 - 0.717439i) q^{89} +(2.12132 + 3.67423i) q^{93} +(1.29289 - 2.23936i) q^{95} +4.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 2 q^{5} - 2 q^{9} + 4 q^{11} - 4 q^{15} + 8 q^{17} - 8 q^{19} + 12 q^{23} - 2 q^{25} + 4 q^{27} - 8 q^{29} + 4 q^{33} + 4 q^{37} - 8 q^{41} - 16 q^{43} + 2 q^{45} + 4 q^{47} + 8 q^{51} + 12 q^{53}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 + 2 * q^5 - 2 * q^9 + 4 * q^11 - 4 * q^15 + 8 * q^17 - 8 * q^19 + 12 * q^23 - 2 * q^25 + 4 * q^27 - 8 * q^29 + 4 * q^33 + 4 * q^37 - 8 * q^41 - 16 * q^43 + 2 * q^45 + 4 * q^47 + 8 * q^51 + 12 * q^53 + 8 * q^55 + 16 * q^57 + 8 * q^67 - 24 * q^69 - 8 * q^71 + 8 * q^73 - 2 * q^75 + 20 * q^79 - 2 * q^81 - 8 * q^83 + 16 * q^85 + 4 * q^87 + 4 * q^89 + 8 * q^95 + 16 * q^97 - 8 * q^99

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