LMFDB - Embedded newform 700.2.c.k.699.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(699,700)] 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("700.699"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,0,0,-32,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.29960650073923649536.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 40x^{8} - 112x^{4} + 256 $ x^16 - 7x^12 + 40x^8 - 112*x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			699.3
Root			$1.38588 + 0.281691i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.k.699.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39897 + 0.207107i) q^{2} -1.47363i q^{3} +(1.91421 - 0.579471i) q^{4} +(0.305198 + 2.06155i) q^{6} +(0.819496 - 2.51564i) q^{7} +(-2.55791 + 1.20711i) q^{8} +0.828427 q^{9} +2.79793i q^{11} +(-0.853923 - 2.82083i) q^{12} +5.83095 q^{13} +(-0.625441 + 3.68901i) q^{14} +(3.32843 - 2.21846i) q^{16} -4.12311 q^{17} +(-1.15894 + 0.171573i) q^{18} +5.64167 q^{19} +(-3.70711 - 1.20763i) q^{21} +(-0.579471 - 3.91421i) q^{22} +3.95687 q^{23} +(1.77882 + 3.76940i) q^{24} +(-8.15731 + 1.20763i) q^{26} -5.64167i q^{27} +(0.110951 - 5.29034i) q^{28} +0.242641 q^{29} -2.08402 q^{31} +(-4.19690 + 3.79289i) q^{32} +4.12311 q^{33} +(5.76809 - 0.853923i) q^{34} +(1.58579 - 0.480049i) q^{36} +6.24264i q^{37} +(-7.89250 + 1.16843i) q^{38} -8.59264i q^{39} -4.12311i q^{41} +(5.43623 + 0.921666i) q^{42} -5.59587 q^{43} +(1.62132 + 5.35584i) q^{44} +(-5.53553 + 0.819496i) q^{46} +6.25206i q^{47} +(-3.26918 - 4.90486i) q^{48} +(-5.65685 - 4.12311i) q^{49} +6.07591i q^{51} +(11.1617 - 3.37887i) q^{52} -12.2426i q^{53} +(1.16843 + 7.89250i) q^{54} +(0.940448 + 7.42399i) q^{56} -8.31371i q^{57} +(-0.339446 + 0.0502525i) q^{58} +2.94725 q^{59} -11.6619i q^{61} +(2.91548 - 0.431615i) q^{62} +(0.678892 - 2.08402i) q^{63} +(5.08579 - 6.17534i) q^{64} +(-5.76809 + 0.853923i) q^{66} -7.43370 q^{67} +(-7.89250 + 2.38922i) q^{68} -5.83095i q^{69} -7.23486i q^{71} +(-2.11904 + 1.00000i) q^{72} +12.3693 q^{73} +(-1.29289 - 8.73324i) q^{74} +(10.7994 - 3.26918i) q^{76} +(7.03858 + 2.29289i) q^{77} +(1.77959 + 12.0208i) q^{78} +7.91375i q^{79} -5.82843 q^{81} +(0.853923 + 5.76809i) q^{82} -1.47363i q^{83} +(-7.79598 - 0.163501i) q^{84} +(7.82843 - 1.15894i) q^{86} -0.357562i q^{87} +(-3.37740 - 7.15685i) q^{88} -12.3693i q^{89} +(4.77844 - 14.6686i) q^{91} +(7.57430 - 2.29289i) q^{92} +3.07107i q^{93} +(-1.29484 - 8.74643i) q^{94} +(5.58931 + 6.18466i) q^{96} -8.24621 q^{97} +(8.76767 + 4.59651i) q^{98} +2.31788i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 32 q^{9} - 24 q^{14} + 8 q^{16} - 48 q^{21} - 64 q^{29} + 48 q^{36} - 8 q^{44} - 32 q^{46} + 40 q^{56} + 104 q^{64} - 32 q^{74} - 48 q^{81} - 40 q^{84} + 80 q^{86}+O(q^{100}) $ 16 * q + 8 * q^4 - 32 * q^9 - 24 * q^14 + 8 * q^16 - 48 * q^21 - 64 * q^29 + 48 * q^36 - 8 * q^44 - 32 * q^46 + 40 * q^56 + 104 * q^64 - 32 * q^74 - 48 * q^81 - 40 * q^84 + 80 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.39897	+	0.207107i	−0.989219	+	0.146447i
$2$	−1.39897	+	0.207107i	−0.989219	+	0.146447i
$3$		−	1.47363i		−	0.850798i	−0.905006	−	0.425399i	$-0.860134\pi$
$3$		−	1.47363i		−	0.850798i	0.905006	−	0.425399i	$-0.139866\pi$
$4$	1.91421	−	0.579471i	0.957107	−	0.289735i
$5$		0			0
$5$		0			0
$6$	0.305198	+	2.06155i	0.124597	+	0.841625i
$7$	0.819496	−	2.51564i	0.309740	−	0.950821i
$7$	0.819496	−	2.51564i	0.309740	−	0.950821i
$8$	−2.55791	+	1.20711i	−0.904357	+	0.426777i
$9$	0.828427			0.276142
$10$		0			0
$11$			2.79793i			0.843608i	0.906687	+	0.421804i	$0.138603\pi$
$11$			2.79793i			0.843608i	−0.906687	+	0.421804i	$0.861397\pi$
$12$	−0.853923	−	2.82083i	−0.246506	−	0.814305i
$13$	5.83095			1.61722			0.808608	−	0.588348i	$-0.200222\pi$
$13$	5.83095			1.61722			0.808608	+	0.588348i	$0.200222\pi$
$14$	−0.625441	+	3.68901i	−0.167156	+	0.985930i
$15$		0			0
$16$	3.32843	−	2.21846i	0.832107	−	0.554615i
$17$	−4.12311			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−4.12311			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$18$	−1.15894	+	0.171573i	−0.273165	+	0.0404401i
$19$	5.64167			1.29429			0.647144	−	0.762368i	$-0.275963\pi$
$19$	5.64167			1.29429			0.647144	+	0.762368i	$0.275963\pi$
$20$		0			0
$21$	−3.70711	−	1.20763i	−0.808957	−	0.263526i
$22$	−0.579471	−	3.91421i	−0.123544	−	0.834513i
$23$	3.95687			0.825065			0.412533	−	0.910943i	$-0.364644\pi$
$23$	3.95687			0.825065			0.412533	+	0.910943i	$0.364644\pi$
$24$	1.77882	+	3.76940i	0.363101	+	0.769425i
$25$		0			0
$26$	−8.15731	+	1.20763i	−1.59978	+	0.236836i
$27$		−	5.64167i		−	1.08574i
$28$	0.110951	−	5.29034i	0.0209678	−	0.999780i
$29$	0.242641			0.0450572			0.0225286	−	0.999746i	$-0.492828\pi$
$29$	0.242641			0.0450572			0.0225286	+	0.999746i	$0.492828\pi$
$30$		0			0
$31$	−2.08402			−0.374301			−0.187151	−	0.982331i	$-0.559925\pi$
$31$	−2.08402			−0.374301			−0.187151	+	0.982331i	$0.559925\pi$
$32$	−4.19690	+	3.79289i	−0.741914	+	0.670495i
$33$	4.12311			0.717741
$34$	5.76809	−	0.853923i	0.989219	−	0.146447i
$35$		0			0
$36$	1.58579	−	0.480049i	0.264298	−	0.0800082i
$37$			6.24264i			1.02628i	0.858304	+	0.513142i	$0.171519\pi$
$37$			6.24264i			1.02628i	−0.858304	+	0.513142i	$0.828481\pi$
$38$	−7.89250	+	1.16843i	−1.28033	+	0.189544i
$39$		−	8.59264i		−	1.37592i
$40$		0			0
$41$		−	4.12311i		−	0.643921i	−0.946753	−	0.321960i	$-0.895658\pi$
$41$		−	4.12311i		−	0.643921i	0.946753	−	0.321960i	$-0.104342\pi$
$42$	5.43623	+	0.921666i	0.838828	+	0.142216i
$43$	−5.59587			−0.853361			−0.426681	−	0.904402i	$-0.640317\pi$
$43$	−5.59587			−0.853361			−0.426681	+	0.904402i	$0.640317\pi$
$44$	1.62132	+	5.35584i	0.244423	+	0.807423i
$45$		0			0
$46$	−5.53553	+	0.819496i	−0.816170	+	0.120828i
$47$			6.25206i			0.911957i	0.889991	+	0.455979i	$0.150711\pi$
$47$			6.25206i			0.911957i	−0.889991	+	0.455979i	$0.849289\pi$
$48$	−3.26918	−	4.90486i	−0.471866	−	0.707955i
$49$	−5.65685	−	4.12311i	−0.808122	−	0.589015i
$50$		0			0
$51$			6.07591i			0.850798i
$52$	11.1617	−	3.37887i	1.54785	−	0.468564i
$53$		−	12.2426i		−	1.68166i	−0.541302	−	0.840828i	$-0.682069\pi$
$53$		−	12.2426i		−	1.68166i	0.541302	−	0.840828i	$-0.317931\pi$
$54$	1.16843	+	7.89250i	0.159003	+	1.07403i
$55$		0			0
$56$	0.940448	+	7.42399i	0.125673	+	0.992072i
$57$		−	8.31371i		−	1.10118i
$58$	−0.339446	+	0.0502525i	−0.0445715	+	0.00659848i
$59$	2.94725			0.383699			0.191850	−	0.981424i	$-0.438551\pi$
$59$	2.94725			0.383699			0.191850	+	0.981424i	$0.438551\pi$
$60$		0			0
$61$		−	11.6619i		−	1.49315i	−0.665299	−	0.746577i	$-0.731696\pi$
$61$		−	11.6619i		−	1.49315i	0.665299	−	0.746577i	$-0.268304\pi$
$62$	2.91548	−	0.431615i	0.370266	−	0.0548152i
$63$	0.678892	−	2.08402i	0.0855324	−	0.262562i
$64$	5.08579	−	6.17534i	0.635723	−	0.771917i
$65$		0			0
$66$	−5.76809	+	0.853923i	−0.710002	+	0.105111i
$67$	−7.43370			−0.908171			−0.454085	−	0.890958i	$-0.650034\pi$
$67$	−7.43370			−0.908171			−0.454085	+	0.890958i	$0.650034\pi$
$68$	−7.89250	+	2.38922i	−0.957107	+	0.289735i
$69$		−	5.83095i		−	0.701964i
$70$		0			0
$71$		−	7.23486i		−	0.858619i	−0.903157	−	0.429310i	$-0.858757\pi$
$71$		−	7.23486i		−	0.858619i	0.903157	−	0.429310i	$-0.141243\pi$
$72$	−2.11904	+	1.00000i	−0.249731	+	0.117851i
$73$	12.3693			1.44772			0.723860	−	0.689947i	$-0.242366\pi$
$73$	12.3693			1.44772			0.723860	+	0.689947i	$0.242366\pi$
$74$	−1.29289	−	8.73324i	−0.150296	−	1.01522i
$75$		0			0
$76$	10.7994	−	3.26918i	1.23877	−	0.375001i
$77$	7.03858	+	2.29289i	0.802121	+	0.261299i
$78$	1.77959	+	12.0208i	0.201499	+	1.36109i
$79$			7.91375i			0.890366i	0.895440	+	0.445183i	$0.146861\pi$
$79$			7.91375i			0.890366i	−0.895440	+	0.445183i	$0.853139\pi$
$80$		0			0
$81$	−5.82843			−0.647603
$82$	0.853923	+	5.76809i	0.0943000	+	0.636979i
$83$		−	1.47363i		−	0.161751i	−0.996724	−	0.0808757i	$-0.974228\pi$
$83$		−	1.47363i		−	0.161751i	0.996724	−	0.0808757i	$-0.0257717\pi$
$84$	−7.79598	−	0.163501i	−0.850611	−	0.0178394i
$85$		0			0
$86$	7.82843	−	1.15894i	0.844161	−	0.124972i
$87$		−	0.357562i		−	0.0383346i
$88$	−3.37740	−	7.15685i	−0.360032	−	0.762923i
$89$		−	12.3693i		−	1.31114i	−0.755132	−	0.655572i	$-0.772427\pi$
$89$		−	12.3693i		−	1.31114i	0.755132	−	0.655572i	$-0.227573\pi$
$90$		0			0
$91$	4.77844	−	14.6686i	0.500916	−	1.53768i
$92$	7.57430	−	2.29289i	0.789676	−	0.239051i
$93$			3.07107i			0.318455i
$94$	−1.29484	−	8.74643i	−0.133553	−	0.902125i
$95$		0			0
$96$	5.58931	+	6.18466i	0.570456	+	0.631219i
$97$	−8.24621			−0.837276			−0.418638	−	0.908153i	$-0.637492\pi$
$97$	−8.24621			−0.837276			−0.418638	+	0.908153i	$0.637492\pi$
$98$	8.76767	+	4.59651i	0.885669	+	0.464318i
$99$			2.31788i			0.232956i
$100$		0			0
$101$			2.41526i			0.240327i	0.992754	+	0.120164i	$0.0383419\pi$
$101$			2.41526i			0.240327i	−0.992754	+	0.120164i	$0.961658\pi$
$102$	−1.25836	−	8.50000i	−0.124597	−	0.841625i
$103$			7.11529i			0.701091i	0.936546	+	0.350545i	$0.114004\pi$
$103$			7.11529i			0.701091i	−0.936546	+	0.350545i	$0.885996\pi$
$104$	−14.9150	+	7.03858i	−1.46254	+	0.690190i
$105$		0			0
$106$	2.53553	+	17.1270i	0.246273	+	1.66353i
$107$	13.0296			1.25962			0.629808	−	0.776751i	$-0.283134\pi$
$107$	13.0296			1.25962			0.629808	+	0.776751i	$0.283134\pi$
$108$	−3.26918	−	10.7994i	−0.314577	−	1.03917i
$109$	−2.82843			−0.270914			−0.135457	−	0.990783i	$-0.543250\pi$
$109$	−2.82843			−0.270914			−0.135457	+	0.990783i	$0.543250\pi$
$110$		0			0
$111$	9.19932			0.873160
$112$	−2.85321	−	10.1911i	−0.269603	−	0.962971i
$113$			18.3137i			1.72281i	0.507920	+	0.861404i	$0.330415\pi$
$113$			18.3137i			1.72281i	−0.507920	+	0.861404i	$0.669585\pi$
$114$	1.72183	+	11.6306i	0.161264	+	1.08931i
$115$		0			0
$116$	0.464466	−	0.140603i	0.0431246	−	0.0130547i
$117$	4.83052			0.446582
$118$	−4.12311	+	0.610396i	−0.379563	+	0.0561915i
$119$	−3.37887	+	10.3722i	−0.309740	+	0.950821i
$120$		0			0
$121$	3.17157			0.288325
$122$	2.41526	+	16.3146i	0.218667	+	1.47706i
$123$	−6.07591			−0.547847
$124$	−3.98926	+	1.20763i	−0.358246	+	0.108448i
$125$		0			0
$126$	−0.518132	+	3.05608i	−0.0461589	+	0.272257i
$127$	−5.59587			−0.496553			−0.248276	−	0.968689i	$-0.579864\pi$
$127$	−5.59587			−0.496553			−0.248276	+	0.968689i	$0.579864\pi$
$128$	−5.83589	+	9.69239i	−0.515825	+	0.856694i
$129$			8.24621i			0.726038i
$130$		0			0
$131$	−13.0098			−1.13667			−0.568336	−	0.822797i	$-0.692412\pi$
$131$	−13.0098			−1.13667			−0.568336	+	0.822797i	$0.692412\pi$
$132$	7.89250	−	2.38922i	0.686954	−	0.207955i
$133$	4.62332	−	14.1924i	0.400893	−	1.23064i
$134$	10.3995	−	1.53957i	0.898380	−	0.132999i
$135$		0			0
$136$	10.5465	−	4.97703i	0.904357	−	0.426777i
$137$			3.48528i			0.297768i	0.988855	+	0.148884i	$0.0475681\pi$
$137$			3.48528i			0.297768i	−0.988855	+	0.148884i	$0.952432\pi$
$138$	1.20763	+	8.15731i	0.102800	+	0.694396i
$139$	−2.69442			−0.228537			−0.114269	−	0.993450i	$-0.536452\pi$
$139$	−2.69442			−0.228537			−0.114269	+	0.993450i	$0.536452\pi$
$140$		0			0
$141$	9.21320			0.775892
$142$	1.49839	+	10.1213i	0.125742	+	0.849362i
$143$			16.3146i			1.36430i
$144$	2.75736	−	1.83783i	0.229780	−	0.153153i
$145$		0			0
$146$	−17.3043	+	2.56177i	−1.43211	+	0.212014i
$147$	−6.07591	+	8.33609i	−0.501133	+	0.687549i
$148$	3.61743	+	11.9497i	0.297351	+	0.982263i
$149$	−2.00000			−0.163846			−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000			−0.163846			−0.0819232	+	0.996639i	$0.526106\pi$
$150$		0			0
$151$			1.63899i			0.133379i	0.997774	+	0.0666896i	$0.0212437\pi$
$151$			1.63899i			0.133379i	−0.997774	+	0.0666896i	$0.978756\pi$
$152$	−14.4309	+	6.81010i	−1.17050	+	0.552372i
$153$	−3.41569			−0.276142
$154$	−10.3216	−	1.74994i	−0.831739	−	0.141014i
$155$		0			0
$156$	−4.97918	−	16.4481i	−0.398654	−	1.31691i
$157$	−22.3234			−1.78160			−0.890800	−	0.454396i	$-0.849855\pi$
$157$	−22.3234			−1.78160			−0.890800	+	0.454396i	$0.849855\pi$
$158$	−1.63899	−	11.0711i	−0.130391	−	0.880767i
$159$	−18.0411			−1.43075
$160$		0			0
$161$	3.24264	−	9.95406i	0.255556	−	0.784490i
$162$	8.15377	−	1.20711i	0.640621	−	0.0948393i
$163$	21.9034			1.71561			0.857804	−	0.513977i	$-0.171828\pi$
$163$	21.9034			1.71561			0.857804	+	0.513977i	$0.171828\pi$
$164$	−2.38922	−	7.89250i	−0.186567	−	0.616301i
$165$		0			0
$166$	0.305198	+	2.06155i	0.0236880	+	0.160008i
$167$			17.1778i			1.32926i	0.747172	+	0.664631i	$0.231411\pi$
$167$			17.1778i			1.32926i	−0.747172	+	0.664631i	$0.768589\pi$
$168$	10.9402	−	1.38587i	0.844053	−	0.106922i
$169$	21.0000			1.61538
$170$		0			0
$171$	4.67371			0.357408
$172$	−10.7117	+	3.24264i	−0.816758	+	0.247249i
$173$	−14.0772			−1.07027			−0.535133	−	0.844768i	$-0.679739\pi$
$173$	−14.0772			−1.07027			−0.535133	+	0.844768i	$0.679739\pi$
$174$	0.0740534	+	0.500217i	0.00561398	+	0.0379213i
$175$		0			0
$176$	6.20711	+	9.31271i	0.467878	+	0.701972i
$177$		−	4.34315i		−	0.326451i
$178$	2.56177	+	17.3043i	0.192013	+	1.29701i
$179$		−	10.7117i		−	0.800629i	−0.916378	−	0.400314i	$-0.868901\pi$
$179$		−	10.7117i		−	0.800629i	0.916378	−	0.400314i	$-0.131099\pi$
$180$		0			0
$181$			19.9081i			1.47976i	0.672740	+	0.739879i	$0.265117\pi$
$181$			19.9081i			1.47976i	−0.672740	+	0.739879i	$0.734883\pi$
$182$	−3.64692	+	21.5105i	−0.270328	+	1.59446i
$183$	−17.1853			−1.27037
$184$	−10.1213	+	4.77637i	−0.746154	+	0.352119i
$185$		0			0
$186$	−0.636039	−	4.29632i	−0.0466366	−	0.315021i
$187$		−	11.5362i		−	0.843608i
$188$	3.62289	+	11.9678i	0.264226	+	0.872841i
$189$	−14.1924	−	4.62332i	−1.03234	−	0.336297i
$190$		0			0
$191$			24.7013i			1.78733i	0.448738	+	0.893663i	$0.351874\pi$
$191$			24.7013i			1.78733i	−0.448738	+	0.893663i	$0.648126\pi$
$192$	−9.10013	−	7.49455i	−0.656746	−	0.540872i
$193$		−	8.31371i		−	0.598434i	−0.954185	−	0.299217i	$-0.903275\pi$
$193$		−	8.31371i		−	0.598434i	0.954185	−	0.299217i	$-0.0967254\pi$
$194$	11.5362	−	1.70785i	0.828249	−	0.122616i
$195$		0			0
$196$	−13.2176	−	4.61452i	−0.944118	−	0.329609i
$197$			2.48528i			0.177069i	0.996073	+	0.0885345i	$0.0282183\pi$
$197$			2.48528i			0.177069i	−0.996073	+	0.0885345i	$0.971782\pi$
$198$	−0.480049	−	3.24264i	−0.0341156	−	0.230444i
$199$	−17.5354			−1.24305			−0.621526	−	0.783394i	$-0.713487\pi$
$199$	−17.5354			−1.24305			−0.621526	+	0.783394i	$0.713487\pi$
$200$		0			0
$201$			10.9545i			0.772670i
$202$	−0.500217	−	3.37887i	−0.0351951	−	0.237736i
$203$	0.198843	−	0.610396i	0.0139560	−	0.0428414i
$204$	3.52082	+	11.6306i	0.246506	+	0.814305i
$205$		0			0
$206$	−1.47363	−	9.95406i	−0.102672	−	0.693532i
$207$	3.27798			0.227835
$208$	19.4079	−	12.9357i	1.34570	−	0.896932i
$209$			15.7850i			1.09187i
$210$		0			0
$211$		−	1.44015i		−	0.0991439i	−0.998771	−	0.0495719i	$-0.984214\pi$
$211$		−	1.44015i		−	0.0991439i	0.998771	−	0.0495719i	$-0.0157857\pi$
$212$	−7.09425	−	23.4350i	−0.487235	−	1.60952i
$213$	−10.6615			−0.730512
$214$	−18.2279	+	2.69851i	−1.24604	+	0.184466i
$215$		0			0
$216$	6.81010	+	14.4309i	0.463368	+	0.981896i
$217$	−1.70785	+	5.24264i	−0.115936	+	0.355894i
$218$	3.95687	−	0.585786i	0.267993	−	0.0396745i
$219$		−	18.2277i		−	1.23172i
$220$		0			0
$221$	−24.0416			−1.61722
$222$	−12.8695	+	1.90524i	−0.863747	+	0.127871i
$223$			0.863230i			0.0578062i	0.999582	+	0.0289031i	$0.00920142\pi$
$223$			0.863230i			0.0578062i	−0.999582	+	0.0289031i	$0.990799\pi$
$224$	6.10220	+	13.6661i	0.407720	+	0.913107i
$225$		0			0
$226$	−3.79289	−	25.6203i	−0.252300	−	1.70423i
$227$		−	7.11529i		−	0.472259i	−0.971722	−	0.236129i	$-0.924121\pi$
$227$		−	7.11529i		−	0.472259i	0.971722	−	0.236129i	$-0.0758789\pi$
$228$	−4.81755	−	15.9142i	−0.319050	−	1.05394i
$229$			14.0772i			0.930245i	0.885246	+	0.465123i	$0.153990\pi$
$229$			14.0772i			0.930245i	−0.885246	+	0.465123i	$0.846010\pi$
$230$		0			0
$231$	3.37887	−	10.3722i	0.222313	−	0.682443i
$232$	−0.620653	+	0.292893i	−0.0407478	+	0.0192294i
$233$			15.7990i			1.03503i	0.855675	+	0.517513i	$0.173142\pi$
$233$			15.7990i			1.03503i	−0.855675	+	0.517513i	$0.826858\pi$
$234$	−6.75773	+	1.00043i	−0.441767	+	0.0654004i
$235$		0			0
$236$	5.64167	−	1.70785i	0.367241	−	0.111171i
$237$	11.6619			0.757522
$238$	2.57876	−	15.2102i	0.167156	−	0.985930i
$239$			16.7876i			1.08590i	0.839765	+	0.542950i	$0.182693\pi$
$239$			16.7876i			1.08590i	−0.839765	+	0.542950i	$0.817307\pi$
$240$		0			0
$241$			15.7850i			1.01680i	0.861120	+	0.508401i	$0.169763\pi$
$241$			15.7850i			1.01680i	−0.861120	+	0.508401i	$0.830237\pi$
$242$	−4.43692	+	0.656854i	−0.285216	+	0.0422242i
$243$		−	8.33609i		−	0.534760i
$244$	−6.75773	−	22.3234i	−0.432620	−	1.42911i
$245$		0			0
$246$	8.50000	−	1.25836i	0.541940	−	0.0802303i
$247$	32.8963			2.09314
$248$	5.33074	−	2.51564i	0.338502	−	0.159743i
$249$	−2.17157			−0.137618
$250$		0			0
$251$	−13.9778			−0.882268			−0.441134	−	0.897441i	$-0.645424\pi$
$251$	−13.9778			−0.882268			−0.441134	+	0.897441i	$0.645424\pi$
$252$	0.0919152	−	4.38266i	0.00579011	−	0.276082i
$253$			11.0711i			0.696032i
$254$	7.82843	−	1.15894i	0.491199	−	0.0727185i
$255$		0			0
$256$	6.15685	−	14.7680i	0.384803	−	0.922999i
$257$	23.3238			1.45490			0.727450	−	0.686161i	$-0.240706\pi$
$257$	23.3238			1.45490			0.727450	+	0.686161i	$0.240706\pi$
$258$	−1.70785	−	11.5362i	−0.106326	−	0.718211i
$259$	15.7042	+	5.11582i	0.975812	+	0.317881i
$260$		0			0
$261$	0.201010			0.0124422
$262$	18.2003	−	2.69442i	1.12442	−	0.166462i
$263$	27.9793			1.72528			0.862640	−	0.505819i	$-0.168810\pi$
$263$	27.9793			1.72528			0.862640	+	0.505819i	$0.168810\pi$
$264$	−10.5465	+	4.97703i	−0.649094	+	0.306315i
$265$		0			0
$266$	−3.52853	+	20.8122i	−0.216348	+	1.27608i
$267$	−18.2277			−1.11552
$268$	−14.2297	+	4.30761i	−0.869217	+	0.263129i
$269$			2.41526i			0.147261i	0.997286	+	0.0736305i	$0.0234585\pi$
$269$			2.41526i			0.147261i	−0.997286	+	0.0736305i	$0.976541\pi$
$270$		0			0
$271$	27.2404			1.65474			0.827368	−	0.561660i	$-0.189837\pi$
$271$	27.2404			1.65474			0.827368	+	0.561660i	$0.189837\pi$
$272$	−13.7235	+	9.14695i	−0.832107	+	0.554615i
$273$	−21.6160	−	7.04163i	−1.30826	−	0.426179i
$274$	−0.721825	−	4.87579i	−0.0436071	−	0.294557i
$275$		0			0
$276$	−3.37887	−	11.1617i	−0.203384	−	0.671855i
$277$			6.10051i			0.366544i	0.983062	+	0.183272i	$0.0586689\pi$
$277$			6.10051i			0.366544i	−0.983062	+	0.183272i	$0.941331\pi$
$278$	3.76940	−	0.558032i	0.226074	−	0.0334685i
$279$	−1.72646			−0.103360
$280$		0			0
$281$	32.9706			1.96686			0.983429	−	0.181291i	$-0.0580277\pi$
$281$	32.9706			1.96686			0.983429	+	0.181291i	$0.0580277\pi$
$282$	−12.8890	+	1.90812i	−0.767526	+	0.113627i
$283$		−	31.6613i		−	1.88207i	−0.338314	−	0.941033i	$-0.609856\pi$
$283$		−	31.6613i		−	1.88207i	0.338314	−	0.941033i	$-0.390144\pi$
$284$	−4.19239	−	13.8491i	−0.248772	−	0.821791i
$285$		0			0
$286$	−3.37887	−	22.8236i	−0.199797	−	1.34959i
$287$	−10.3722	−	3.37887i	−0.612254	−	0.199448i
$288$	−3.47682	+	3.14214i	−0.204874	+	0.185152i
$289$		0			0
$290$		0			0
$291$			12.1518i			0.712353i
$292$	23.6775	−	7.16766i	1.38562	−	0.419455i
$293$	−16.4924			−0.963498			−0.481749	−	0.876309i	$-0.659998\pi$
$293$	−16.4924			−0.963498			−0.481749	+	0.876309i	$0.659998\pi$
$294$	6.77354	−	12.9203i	0.395041	−	0.753525i
$295$		0			0
$296$	−7.53553	−	15.9681i	−0.437994	−	0.928127i
$297$	15.7850			0.915939
$298$	2.79793	−	0.414214i	0.162080	−	0.0239947i
$299$	23.0723			1.33431
$300$		0			0
$301$	−4.58579	+	14.0772i	−0.264320	+	0.811394i
$302$	−0.339446	−	2.29289i	−0.0195329	−	0.131941i
$303$	3.55919			0.204470
$304$	18.7779	−	12.5158i	1.07699	−	0.717832i
$305$		0			0
$306$	4.77844	−	0.707413i	0.273165	−	0.0404401i
$307$		−	18.6515i		−	1.06450i	−0.846589	−	0.532248i	$-0.821348\pi$
$307$		−	18.6515i		−	1.06450i	0.846589	−	0.532248i	$-0.178652\pi$
$308$	14.8020	+	0.310435i	0.843423	+	0.0176887i
$309$	10.4853			0.596487
$310$		0			0
$311$	−11.7890			−0.668493			−0.334247	−	0.942486i	$-0.608482\pi$
$311$	−11.7890			−0.668493			−0.334247	+	0.942486i	$0.608482\pi$
$312$	10.3722	+	21.9792i	0.587212	+	1.24433i
$313$	−4.83052			−0.273037			−0.136519	−	0.990638i	$-0.543591\pi$
$313$	−4.83052			−0.273037			−0.136519	+	0.990638i	$0.543591\pi$
$314$	31.2296	−	4.62332i	1.76239	−	0.260909i
$315$		0			0
$316$	4.58579	+	15.1486i	0.257971	+	0.852176i
$317$		−	25.6569i		−	1.44103i	−0.693438	−	0.720516i	$-0.743905\pi$
$317$		−	25.6569i		−	1.44103i	0.693438	−	0.720516i	$-0.256095\pi$
$318$	25.2389	−	3.73643i	1.41532	−	0.209528i
$319$			0.678892i			0.0380107i
$320$		0			0
$321$		−	19.2007i		−	1.07168i
$322$	−2.47479	+	14.5970i	−0.137915	+	0.813457i
$323$	−23.2612			−1.29429
$324$	−11.1569	+	3.37740i	−0.619825	+	0.187634i
$325$		0			0
$326$	−30.6421	+	4.53635i	−1.69711	+	0.251245i
$327$			4.16804i			0.230493i
$328$	4.97703	+	10.5465i	0.274810	+	0.582334i
$329$	15.7279	+	5.12354i	0.867108	+	0.282470i
$330$		0			0
$331$			28.8571i			1.58613i	0.609139	+	0.793064i	$0.291515\pi$
$331$			28.8571i			1.58613i	−0.609139	+	0.793064i	$0.708485\pi$
$332$	−0.853923	−	2.82083i	−0.0468651	−	0.154813i
$333$			5.17157i			0.283400i
$334$	−3.55765	−	24.0312i	−0.194666	−	1.31493i
$335$		0			0
$336$	−15.0179	+	4.20457i	−0.819294	+	0.229378i
$337$		−	14.7990i		−	0.806152i	−0.915166	−	0.403076i	$-0.867941\pi$
$337$		−	14.7990i		−	0.806152i	0.915166	−	0.403076i	$-0.132059\pi$
$338$	−29.3783	+	4.34924i	−1.59797	+	0.236568i
$339$	26.9876			1.46576
$340$		0			0
$341$		−	5.83095i		−	0.315764i
$342$	−6.53836	+	0.967957i	−0.353554	+	0.0523411i
$343$	−15.0080	+	10.8517i	−0.810356	+	0.585938i
$344$	14.3137	−	6.75481i	0.771743	−	0.364195i
$345$		0			0
$346$	19.6935	−	2.91548i	1.05873	−	0.156737i
$347$	19.9832			1.07276			0.536378	−	0.843978i	$-0.319792\pi$
$347$	19.9832			1.07276			0.536378	+	0.843978i	$0.319792\pi$
$348$	−0.207196	−	0.684449i	−0.0111069	−	0.0366903i
$349$			14.0772i			0.753533i	0.926308	+	0.376767i	$0.122964\pi$
$349$			14.0772i			0.753533i	−0.926308	+	0.376767i	$0.877036\pi$
$350$		0			0
$351$		−	32.8963i		−	1.75587i
$352$	−10.6123	−	11.7426i	−0.565635	−	0.625885i
$353$	−11.6619			−0.620701			−0.310350	−	0.950622i	$-0.600446\pi$
$353$	−11.6619			−0.620701			−0.310350	+	0.950622i	$0.600446\pi$
$354$	0.899495	+	6.07591i	0.0478076	+	0.322931i
$355$		0			0
$356$	−7.16766	−	23.6775i	−0.379885	−	1.25491i
$357$	15.2848	+	4.97918i	0.808957	+	0.263526i
$358$	2.21846	+	14.9853i	0.117249	+	0.791997i
$359$		−	20.4633i		−	1.08001i	−0.841662	−	0.540005i	$-0.818422\pi$
$359$		−	20.4633i		−	1.08001i	0.841662	−	0.540005i	$-0.181578\pi$
$360$		0			0
$361$	12.8284			0.675180
$362$	−4.12311	−	27.8508i	−0.216706	−	1.46380i
$363$		−	4.67371i		−	0.245306i
$364$	0.646952	−	30.8477i	0.0339095	−	1.61686i
$365$		0			0
$366$	24.0416	−	3.55919i	1.25668	−	0.186042i
$367$			15.9570i			0.832951i	0.909147	+	0.416476i	$0.136735\pi$
$367$			15.9570i			0.832951i	−0.909147	+	0.416476i	$0.863265\pi$
$368$	13.1702	−	8.77817i	0.686542	−	0.457594i
$369$		−	3.41569i		−	0.177814i
$370$		0			0
$371$	−30.7980	−	10.0328i	−1.59895	−	0.520876i
$372$	1.77959	+	5.87868i	0.0922677	+	0.304795i
$373$			13.4142i			0.694562i	0.937761	+	0.347281i	$0.112895\pi$
$373$			13.4142i			0.694562i	−0.937761	+	0.347281i	$0.887105\pi$
$374$	2.38922	+	16.1387i	0.123544	+	0.834513i
$375$		0			0
$376$	−7.54691	−	15.9922i	−0.389202	−	0.824735i
$377$	1.41483			0.0728673
$378$	20.8122	+	3.52853i	1.07046	+	0.181488i
$379$			4.15572i			0.213465i	0.994288	+	0.106732i	$0.0340388\pi$
$379$			4.15572i			0.213465i	−0.994288	+	0.106732i	$0.965961\pi$
$380$		0			0
$381$			8.24621i			0.422466i
$382$	−5.11582	−	34.5563i	−0.261748	−	1.76806i
$383$		−	18.3986i		−	0.940126i	−0.882633	−	0.470063i	$-0.844231\pi$
$383$		−	18.3986i		−	0.940126i	0.882633	−	0.470063i	$-0.155769\pi$
$384$	14.2830	+	8.59992i	0.728874	+	0.438863i
$385$		0			0
$386$	1.72183	+	11.6306i	0.0876386	+	0.591982i
$387$	−4.63577			−0.235649
$388$	−15.7850	+	4.77844i	−0.801362	+	0.242588i
$389$	−15.5563			−0.788738			−0.394369	−	0.918952i	$-0.629037\pi$
$389$	−15.5563			−0.788738			−0.394369	+	0.918952i	$0.629037\pi$
$390$		0			0
$391$	−16.3146			−0.825065
$392$	19.4467	+	3.71810i	0.982209	+	0.187792i
$393$			19.1716i			0.967078i
$394$	−0.514719	−	3.47682i	−0.0259311	−	0.175160i
$395$		0			0
$396$	1.34315	+	4.43692i	0.0674956	+	0.222964i
$397$	−18.9077			−0.948949			−0.474475	−	0.880269i	$-0.657362\pi$
$397$	−18.9077			−0.948949			−0.474475	+	0.880269i	$0.657362\pi$
$398$	24.5314	−	3.63170i	1.22965	−	0.182041i
$399$	−20.9143	−	6.81305i	−1.04702	−	0.341079i
$400$		0			0
$401$	−22.4558			−1.12139			−0.560696	−	0.828022i	$-0.689466\pi$
$401$	−22.4558			−1.12139			−0.560696	+	0.828022i	$0.689466\pi$
$402$	−2.26875	−	15.3250i	−0.113155	−	0.764340i
$403$	−12.1518			−0.605326
$404$	1.39957	+	4.62332i	0.0696313	+	0.230019i
$405$		0			0
$406$	−0.151757	+	0.895105i	−0.00753160	+	0.0444233i
$407$	−17.4665			−0.865782
$408$	−7.33428	−	15.5416i	−0.363101	−	0.769425i
$409$			15.7850i			0.780518i	0.920705	+	0.390259i	$0.127615\pi$
$409$			15.7850i			0.780518i	−0.920705	+	0.390259i	$0.872385\pi$
$410$		0			0
$411$	5.13600			0.253340
$412$	4.12311	+	13.6202i	0.203131	+	0.671019i
$413$	2.41526	−	7.41421i	0.118847	−	0.364830i
$414$	−4.58579	+	0.678892i	−0.225379	+	0.0333657i
$415$		0			0
$416$	−24.4719	+	22.1162i	−1.19983	+	1.08433i
$417$			3.97056i			0.194439i
$418$	−3.26918	−	22.0827i	−0.159901	−	1.08010i
$419$	24.5460			1.19915			0.599575	−	0.800319i	$-0.295336\pi$
$419$	24.5460			1.19915			0.599575	+	0.800319i	$0.295336\pi$
$420$		0			0
$421$	−0.686292			−0.0334478			−0.0167239	−	0.999860i	$-0.505324\pi$
$421$	−0.686292			−0.0334478			−0.0167239	+	0.999860i	$0.505324\pi$
$422$	0.298264	+	2.01472i	0.0145193	+	0.0980750i
$423$			5.17938i			0.251830i
$424$	14.7782	+	31.3155i	0.717692	+	1.52082i
$425$		0			0
$426$	14.9150	−	2.20806i	0.722636	−	0.106981i
$427$	−29.3371	−	9.55688i	−1.41972	−	0.462490i
$428$	24.9414	−	7.55025i	1.20559	−	0.364955i
$429$	24.0416			1.16074
$430$		0			0
$431$		−	8.19496i		−	0.394737i	−0.980329	−	0.197369i	$-0.936760\pi$
$431$		−	8.19496i		−	0.394737i	0.980329	−	0.197369i	$-0.0632396\pi$
$432$	−12.5158	−	18.7779i	−0.602168	−	0.903451i
$433$	−4.12311			−0.198144			−0.0990719	−	0.995080i	$-0.531587\pi$
$433$	−4.12311			−0.198144			−0.0990719	+	0.995080i	$0.531587\pi$
$434$	1.30343	−	7.68798i	0.0625668	−	0.369035i
$435$		0			0
$436$	−5.41421	+	1.63899i	−0.259294	+	0.0784934i
$437$	22.3234			1.06787
$438$	3.77509	+	25.5000i	0.180381	+	1.21844i
$439$	−2.94725			−0.140665			−0.0703323	−	0.997524i	$-0.522406\pi$
$439$	−2.94725			−0.140665			−0.0703323	+	0.997524i	$0.522406\pi$
$440$		0			0
$441$	−4.68629	−	3.41569i	−0.223157	−	0.162652i
$442$	33.6334	−	4.97918i	1.59978	−	0.236836i
$443$	−1.83783			−0.0873181			−0.0436591	−	0.999046i	$-0.513902\pi$
$443$	−1.83783			−0.0873181			−0.0436591	+	0.999046i	$0.513902\pi$
$444$	17.6095	−	5.33074i	0.835708	−	0.252986i
$445$		0			0
$446$	−0.178781	−	1.20763i	−0.00846552	−	0.0571829i
$447$			2.94725i			0.139400i
$448$	−11.3671	−	17.8547i	−0.537046	−	0.843553i
$449$	−10.6569			−0.502928			−0.251464	−	0.967867i	$-0.580912\pi$
$449$	−10.6569			−0.502928			−0.251464	+	0.967867i	$0.580912\pi$
$450$		0			0
$451$	11.5362			0.543217
$452$	10.6123	+	35.0563i	0.499159	+	1.64891i
$453$	2.41526			0.113479
$454$	1.47363	+	9.95406i	0.0691607	+	0.467167i
$455$		0			0
$456$	10.0355	+	21.2657i	0.469957	+	0.995858i
$457$			29.4853i			1.37926i	0.724160	+	0.689632i	$0.242228\pi$
$457$			29.4853i			1.37926i	−0.724160	+	0.689632i	$0.757772\pi$
$458$	−2.91548	−	19.6935i	−0.136231	−	0.920216i
$459$			23.2612i			1.08574i
$460$		0			0
$461$			2.41526i			0.112490i	0.998417	+	0.0562449i	$0.0179128\pi$
$461$			2.41526i			0.112490i	−0.998417	+	0.0562449i	$0.982087\pi$
$462$	−2.57876	+	15.2102i	−0.119975	+	0.707642i
$463$	1.35778			0.0631016			0.0315508	−	0.999502i	$-0.489955\pi$
$463$	1.35778			0.0631016			0.0315508	+	0.999502i	$0.489955\pi$
$464$	0.807612	−	0.538289i	0.0374924	−	0.0249894i
$465$		0			0
$466$	−3.27208	−	22.1023i	−0.151576	−	1.02387i
$467$			7.62096i			0.352656i	0.984331	+	0.176328i	$0.0564220\pi$
$467$			7.62096i			0.352656i	−0.984331	+	0.176328i	$0.943578\pi$
$468$	9.24664	−	2.79914i	0.427426	−	0.129391i
$469$	−6.09188	+	18.7005i	−0.281297	+	0.863508i
$470$		0			0
$471$			32.8963i			1.51578i
$472$	−7.53880	+	3.55765i	−0.347001	+	0.163754i
$473$		−	15.6569i		−	0.719903i
$474$	−16.3146	+	2.41526i	−0.749355	+	0.110937i
$475$		0			0
$476$	−0.457464	+	21.8126i	−0.0209678	+	0.999780i
$477$		−	10.1421i		−	0.464376i
$478$	−3.47682	−	23.4853i	−0.159026	−	1.07419i
$479$	−8.84175			−0.403990			−0.201995	−	0.979387i	$-0.564742\pi$
$479$	−8.84175			−0.403990			−0.201995	+	0.979387i	$0.564742\pi$
$480$		0			0
$481$			36.4005i			1.65972i
$482$	−3.26918	−	22.0827i	−0.148907	−	1.00584i
$483$	−14.6686	−	4.77844i	−0.667442	−	0.217426i
$484$	6.07107	−	1.83783i	0.275958	−	0.0835379i
$485$		0			0
$486$	1.72646	+	11.6619i	0.0783138	+	0.528995i
$487$	−3.67567			−0.166560			−0.0832802	−	0.996526i	$-0.526540\pi$
$487$	−3.67567			−0.166560			−0.0832802	+	0.996526i	$0.526540\pi$
$488$	14.0772	+	29.8301i	0.637243	+	1.35034i
$489$		−	32.2774i		−	1.45964i
$490$		0			0
$491$		−	29.3371i		−	1.32397i	−0.749519	−	0.661983i	$-0.769715\pi$
$491$		−	29.3371i		−	1.32397i	0.749519	−	0.661983i	$-0.230285\pi$
$492$	−11.6306	+	3.52082i	−0.524348	+	0.158731i
$493$	−1.00043			−0.0450572
$494$	−46.0208	+	6.81305i	−2.07057	+	0.306533i
$495$		0			0
$496$	−6.93651	+	4.62332i	−0.311459	+	0.207593i
$497$	−18.2003	−	5.92893i	−0.816394	−	0.265949i
$498$	3.03796	−	0.449747i	0.136134	−	0.0201537i
$499$		−	16.7876i		−	0.751516i	−0.926718	−	0.375758i	$-0.877382\pi$
$499$		−	16.7876i		−	0.751516i	0.926718	−	0.375758i	$-0.122618\pi$
$500$		0			0
$501$	25.3137			1.13093
$502$	19.5544	−	2.89489i	0.872756	−	0.129205i
$503$			31.0509i			1.38449i	0.721663	+	0.692245i	$0.243378\pi$
$503$			31.0509i			1.38449i	−0.721663	+	0.692245i	$0.756622\pi$
$504$	0.779092	+	6.15023i	0.0347035	+	0.273953i
$505$		0			0
$506$	−2.29289	−	15.4881i	−0.101932	−	0.688528i
$507$		−	30.9461i		−	1.37437i
$508$	−10.7117	+	3.24264i	−0.475254	+	0.143869i
$509$			8.24621i			0.365507i	0.983159	+	0.182753i	$0.0585010\pi$
$509$			8.24621i			0.365507i	−0.983159	+	0.182753i	$0.941499\pi$
$510$		0			0
$511$	10.1366	−	31.1167i	0.448417	−	1.37652i
$512$	−5.55468	+	21.9350i	−0.245485	+	0.969400i
$513$		−	31.8284i		−	1.40526i
$514$	−32.6292	+	4.83052i	−1.43921	+	0.213065i
$515$		0			0
$516$	4.77844	+	15.7850i	0.210359	+	0.694896i
$517$	−17.4929			−0.769335
$518$	−23.0292	−	3.90440i	−1.01184	−	0.171550i
$519$			20.7445i			0.910581i
$520$		0			0
$521$		−	28.8617i		−	1.26446i	−0.774782	−	0.632228i	$-0.782141\pi$
$521$		−	28.8617i		−	1.26446i	0.774782	−	0.632228i	$-0.217859\pi$
$522$	−0.281206	+	0.0416306i	−0.0123081	+	0.00182212i
$523$		−	4.42088i		−	0.193311i	−0.995318	−	0.0966557i	$-0.969185\pi$
$523$		−	4.42088i		−	0.193311i	0.995318	−	0.0966557i	$-0.0308146\pi$
$524$	−24.9035	+	7.53880i	−1.08792	+	0.329334i
$525$		0			0
$526$	−39.1421	+	5.79471i	−1.70668	+	0.252661i
$527$	8.59264			0.374301
$528$	13.7235	−	9.14695i	0.597237	−	0.398070i
$529$	−7.34315			−0.319267
$530$		0			0
$531$	2.44158			0.105956
$532$	0.625951	−	29.8463i	0.0271384	−	1.29400i
$533$		−	24.0416i		−	1.04136i
$534$	25.5000	−	3.77509i	1.10349	−	0.163364i
$535$		0			0
$536$	19.0147	−	8.97327i	0.821311	−	0.387586i
$537$	−15.7850			−0.681173
$538$	−0.500217	−	3.37887i	−0.0215659	−	0.145673i
$539$	11.5362	−	15.8275i	0.496898	−	0.681739i
$540$		0			0
$541$	10.2426			0.440366			0.220183	−	0.975459i	$-0.429335\pi$
$541$	10.2426			0.440366			0.220183	+	0.975459i	$0.429335\pi$
$542$	−38.1084	+	5.64167i	−1.63690	+	0.242330i
$543$	29.3371			1.25898
$544$	17.3043	−	15.6385i	0.741914	−	0.670495i
$545$		0			0
$546$	31.6984	+	5.37419i	1.35657	+	0.229994i
$547$	13.0296			0.557104			0.278552	−	0.960421i	$-0.410146\pi$
$547$	13.0296			0.557104			0.278552	+	0.960421i	$0.410146\pi$
$548$	2.01962	+	6.67157i	0.0862738	+	0.284995i
$549$		−	9.66104i		−	0.412323i
$550$		0			0
$551$	1.36890			0.0583170
$552$	7.03858	+	14.9150i	0.299582	+	0.634826i
$553$	19.9081	+	6.48528i	0.846579	+	0.275782i
$554$	−1.26346	−	8.53440i	−0.0536791	−	0.362592i
$555$		0			0
$556$	−5.15769	+	1.56134i	−0.218735	+	0.0662154i
$557$		−	10.6863i		−	0.452793i	−0.974035	−	0.226396i	$-0.927306\pi$
$557$		−	10.6863i		−	0.452793i	0.974035	−	0.226396i	$-0.0726945\pi$
$558$	2.41526	−	0.357562i	0.102246	−	0.0151368i
$559$	−32.6292			−1.38007
$560$		0			0
$561$	−17.0000			−0.717741
$562$	−46.1247	+	6.82843i	−1.94565	+	0.288040i
$563$			13.7249i			0.578436i	0.957263	+	0.289218i	$0.0933953\pi$
$563$			13.7249i			0.578436i	−0.957263	+	0.289218i	$0.906605\pi$
$564$	17.6360	−	5.33878i	0.742611	−	0.224803i
$565$		0			0
$566$	6.55726	+	44.2930i	0.275622	+	1.86178i
$567$	−4.77637	+	14.6622i	−0.200589	+	0.615755i
$568$	8.73324	+	18.5061i	0.366439	+	0.776499i
$569$	−3.68629			−0.154537			−0.0772687	−	0.997010i	$-0.524620\pi$
$569$	−3.68629			−0.154537			−0.0772687	+	0.997010i	$0.524620\pi$
$570$		0			0
$571$		−	1.35778i		−	0.0568215i	−0.999596	−	0.0284108i	$-0.990955\pi$
$571$		−	1.35778i		−	0.0568215i	0.999596	−	0.0284108i	$-0.00904464\pi$
$572$	9.45384	+	31.2296i	0.395285	+	1.30578i
$573$	36.4005			1.52065
$574$	15.2102	+	2.57876i	0.634861	+	0.107635i
$575$		0			0
$576$	4.21320	−	5.11582i	0.175550	−	0.213159i
$577$	−7.53880			−0.313844			−0.156922	−	0.987611i	$-0.550157\pi$
$577$	−7.53880			−0.313844			−0.156922	+	0.987611i	$0.550157\pi$
$578$		0			0
$579$	−12.2513			−0.509146
$580$		0			0
$581$	−3.70711	−	1.20763i	−0.153797	−	0.0501009i
$582$	−2.51673	−	17.0000i	−0.104322	−	0.704673i
$583$	34.2541			1.41866
$584$	−31.6396	+	14.9311i	−1.30925	+	0.617853i
$585$		0			0
$586$	23.0723	−	3.41569i	0.953110	−	0.141101i
$587$			0.967957i			0.0399519i	0.999800	+	0.0199759i	$0.00635896\pi$
$587$			0.967957i			0.0399519i	−0.999800	+	0.0199759i	$0.993641\pi$
$588$	−6.80008	+	19.4779i	−0.280431	+	0.803254i
$589$	−11.7574			−0.484454
$590$		0			0
$591$	3.66237			0.150650
$592$	13.8491	+	20.7782i	0.569193	+	0.853978i
$593$	24.0312			0.986844			0.493422	−	0.869790i	$-0.335746\pi$
$593$	24.0312			0.986844			0.493422	+	0.869790i	$0.335746\pi$
$594$	−22.0827	+	3.26918i	−0.906064	+	0.134136i
$595$		0			0
$596$	−3.82843	+	1.15894i	−0.156818	+	0.0474721i
$597$			25.8406i			1.05759i
$598$	−32.2774	+	4.77844i	−1.31992	+	0.195405i
$599$			20.7445i			0.847596i	0.905757	+	0.423798i	$0.139303\pi$
$599$			20.7445i			0.847596i	−0.905757	+	0.423798i	$0.860697\pi$
$600$		0			0
$601$			15.7850i			0.643884i	0.946759	+	0.321942i	$0.104336\pi$
$601$			15.7850i			0.643884i	−0.946759	+	0.321942i	$0.895664\pi$
$602$	3.49988	−	20.6432i	0.142645	−	0.841355i
$603$	−6.15828			−0.250784
$604$	0.949747	+	3.13738i	0.0386447	+	0.127658i
$605$		0			0
$606$	−4.97918	+	0.737132i	−0.202266	+	0.0299439i
$607$		−	16.6722i		−	0.676703i	−0.941020	−	0.338351i	$-0.890131\pi$
$607$		−	16.6722i		−	0.676703i	0.941020	−	0.338351i	$-0.109869\pi$
$608$	−23.6775	+	21.3982i	−0.960250	+	0.867814i
$609$	−0.899495	−	0.293020i	−0.0364494	−	0.0118738i
$610$		0			0
$611$			36.4555i			1.47483i
$612$	−6.53836	+	1.97929i	−0.264298	+	0.0800082i
$613$			17.1127i			0.691175i	0.938386	+	0.345588i	$0.112320\pi$
$613$			17.1127i			0.691175i	−0.938386	+	0.345588i	$0.887680\pi$
$614$	3.86285	+	26.0928i	0.155892	+	1.05302i
$615$		0			0
$616$	−20.7718	+	2.63131i	−0.836920	+	0.106018i
$617$			22.0000i			0.885687i	0.896599	+	0.442843i	$0.146030\pi$
$617$			22.0000i			0.885687i	−0.896599	+	0.442843i	$0.853970\pi$
$618$	−14.6686	+	2.17157i	−0.590056	+	0.0873535i
$619$	−18.9043			−0.759828			−0.379914	−	0.925022i	$-0.624046\pi$
$619$	−18.9043			−0.759828			−0.379914	+	0.925022i	$0.624046\pi$
$620$		0			0
$621$		−	22.3234i		−	0.895806i
$622$	16.4924	−	2.44158i	0.661286	−	0.0978986i
$623$	−31.1167	−	10.1366i	−1.24666	−	0.406114i
$624$	−19.0624	−	28.6000i	−0.763109	−	1.14492i
$625$		0			0
$626$	6.75773	−	1.00043i	0.270093	−	0.0399854i
$627$	23.2612			0.928963
$628$	−42.7317	+	12.9357i	−1.70518	+	0.516192i
$629$		−	25.7391i		−	1.02628i
$630$		0			0
$631$			11.8706i			0.472562i	0.971685	+	0.236281i	$0.0759286\pi$
$631$			11.8706i			0.472562i	−0.971685	+	0.236281i	$0.924071\pi$
$632$	−9.55274	−	20.2426i	−0.379988	−	0.805209i
$633$	−2.12224			−0.0843514
$634$	5.31371	+	35.8931i	0.211034	+	1.42550i
$635$		0			0
$636$	−34.5345	+	10.4543i	−1.36938	+	0.414539i
$637$	−32.9848	−	24.0416i	−1.30691	−	0.952564i
$638$	−0.140603	−	0.949747i	−0.00556653	−	0.0376009i
$639$		−	5.99355i		−	0.237101i
$640$		0			0
$641$	−21.1716			−0.836227			−0.418113	−	0.908395i	$-0.637309\pi$
$641$	−21.1716			−0.836227			−0.418113	+	0.908395i	$0.637309\pi$
$642$	3.97660	+	26.8611i	0.156944	+	1.06012i
$643$		−	25.5139i		−	1.00617i	−0.864237	−	0.503086i	$-0.832198\pi$
$643$		−	25.5139i		−	1.00617i	0.864237	−	0.503086i	$-0.167802\pi$
$644$	0.439021	−	20.9332i	0.0172998	−	0.824884i
$645$		0			0
$646$	32.5416	−	4.81755i	1.28033	−	0.189544i
$647$			46.8598i			1.84225i	0.389268	+	0.921125i	$0.372728\pi$
$647$			46.8598i			1.84225i	−0.389268	+	0.921125i	$0.627272\pi$
$648$	14.9086	−	7.03553i	0.585664	−	0.276382i
$649$			8.24621i			0.323692i
$650$		0			0
$651$	7.72569	+	2.51673i	0.302794	+	0.0986383i
$652$	41.9278	−	12.6924i	1.64202	−	0.497072i
$653$			29.5563i			1.15663i	0.815814	+	0.578315i	$0.196289\pi$
$653$			29.5563i			1.15663i	−0.815814	+	0.578315i	$0.803711\pi$
$654$	−0.863230	−	5.83095i	−0.0337550	−	0.228008i
$655$		0			0
$656$	−9.14695	−	13.7235i	−0.357128	−	0.535811i
$657$	10.2471			0.399777
$658$	−23.0640	−	3.91030i	−0.899126	−	0.152439i
$659$			6.47360i			0.252176i	0.992019	+	0.126088i	$0.0402421\pi$
$659$			6.47360i			0.252176i	−0.992019	+	0.126088i	$0.959758\pi$
$660$		0			0
$661$		−	27.1539i		−	1.05616i	−0.849193	−	0.528082i	$-0.822911\pi$
$661$		−	27.1539i		−	1.05616i	0.849193	−	0.528082i	$-0.177089\pi$
$662$	−5.97649	−	40.3701i	−0.232283	−	1.56903i
$663$			35.4284i			1.37592i
$664$	1.77882	+	3.76940i	0.0690317	+	0.146281i
$665$		0			0
$666$	−1.07107	−	7.23486i	−0.0415030	−	0.280345i
$667$	0.960099			0.0371752
$668$	9.95406	+	32.8821i	0.385134	+	1.27224i
$669$	1.27208			0.0491814
$670$		0			0
$671$	32.6292			1.25964
$672$	20.1388	−	8.99236i	0.776870	−	0.346888i
$673$		−	4.00000i		−	0.154189i	−0.997024	−	0.0770943i	$-0.975436\pi$
$673$		−	4.00000i		−	0.154189i	0.997024	−	0.0770943i	$-0.0245643\pi$
$674$	3.06497	+	20.7033i	0.118058	+	0.797461i
$675$		0			0
$676$	40.1985	−	12.1689i	1.54610	−	0.468034i
$677$	−11.6619			−0.448203			−0.224102	−	0.974566i	$-0.571945\pi$
$677$	−11.6619			−0.448203			−0.224102	+	0.974566i	$0.571945\pi$
$678$	−37.7547	+	5.58931i	−1.44996	+	0.214656i
$679$	−6.75773	+	20.7445i	−0.259338	+	0.796100i
$680$		0			0
$681$	−10.4853			−0.401797
$682$	1.20763	+	8.15731i	0.0462425	+	0.312359i
$683$	26.5392			1.01549			0.507747	−	0.861506i	$-0.330479\pi$
$683$	26.5392			1.01549			0.507747	+	0.861506i	$0.330479\pi$
$684$	8.94648	−	2.70828i	0.342077	−	0.103554i
$685$		0			0
$686$	18.7482	−	18.2895i	0.715811	−	0.698295i
$687$	20.7445			0.791451
$688$	−18.6254	+	12.4142i	−0.710088	+	0.473287i
$689$		−	71.3862i		−	2.71960i
$690$		0			0
$691$	−48.3334			−1.83869			−0.919345	−	0.393452i	$-0.871281\pi$
$691$	−48.3334			−1.83869			−0.919345	+	0.393452i	$0.871281\pi$
$692$	−26.9467	+	8.15731i	−1.02436	+	0.310094i
$693$	5.83095	+	1.89949i	0.221500	+	0.0721558i
$694$	−27.9558	+	4.13866i	−1.06119	+	0.157101i
$695$		0			0
$696$	0.431615	+	0.914610i	0.0163603	+	0.0346682i
$697$			17.0000i			0.643921i
$698$	−2.91548	−	19.6935i	−0.110352	−	0.745409i
$699$	23.2818			0.880598
$700$		0			0
$701$	−16.8284			−0.635601			−0.317800	−	0.948158i	$-0.602944\pi$
$701$	−16.8284			−0.635601			−0.317800	+	0.948158i	$0.602944\pi$
$702$	6.81305	+	46.0208i	0.257142	+	1.73694i
$703$			35.2189i			1.32831i
$704$	17.2782	+	14.2297i	0.651196	+	0.536302i
$705$		0			0
$706$	16.3146	−	2.41526i	0.614008	−	0.0908995i
$707$	6.07591	+	1.97929i	0.228508	+	0.0744390i
$708$	−2.51673	−	8.31371i	−0.0945844	−	0.312448i
$709$	28.0000			1.05156			0.525781	−	0.850620i	$-0.323773\pi$
$709$	28.0000			1.05156			0.525781	+	0.850620i	$0.323773\pi$
$710$		0			0
$711$			6.55596i			0.245868i
$712$	14.9311	+	31.6396i	0.559566	+	1.18574i
$713$	−8.24621			−0.308823
$714$	−22.4141	−	3.80013i	−0.838828	−	0.142216i
$715$		0			0
$716$	−6.20711	−	20.5044i	−0.231970	−	0.766287i
$717$	24.7386			0.923881
$718$	4.23808	+	28.6274i	0.158164	+	1.06837i
$719$	−36.9454			−1.37783			−0.688915	−	0.724842i	$-0.741913\pi$
$719$	−36.9454			−1.37783			−0.688915	+	0.724842i	$0.741913\pi$
$720$		0			0
$721$	17.8995	+	5.83095i	0.666612	+	0.217156i
$722$	−17.9465	+	2.65685i	−0.667901	+	0.0988779i
$723$	23.2612			0.865093
$724$	11.5362	+	38.1084i	0.428738	+	1.41629i
$725$		0			0
$726$	0.967957	+	6.53836i	0.0359243	+	0.242661i
$727$			32.2717i			1.19689i	0.801164	+	0.598445i	$0.204214\pi$
$727$			32.2717i			1.19689i	−0.801164	+	0.598445i	$0.795786\pi$
$728$	5.48371	+	43.2889i	0.203240	+	1.60439i
$729$	−29.7696			−1.10258
$730$		0			0
$731$	23.0723			0.853361
$732$	−32.8963	+	9.95837i	−1.21588	+	0.368072i
$733$	24.7386			0.913742			0.456871	−	0.889533i	$-0.348970\pi$
$733$	24.7386			0.913742			0.456871	+	0.889533i	$0.348970\pi$
$734$	−3.30481	−	22.3234i	−0.121983	−	0.823971i
$735$		0			0
$736$	−16.6066	+	15.0080i	−0.612127	+	0.553202i
$737$		−	20.7990i		−	0.766141i
$738$	0.707413	+	4.77844i	0.0260402	+	0.175897i
$739$		−	18.7078i		−	0.688177i	−0.938937	−	0.344089i	$-0.888188\pi$
$739$		−	18.7078i		−	0.688177i	0.938937	−	0.344089i	$-0.111812\pi$
$740$		0			0
$741$		−	48.4768i		−	1.78084i
$742$	45.1633	+	7.65705i	1.65800	+	0.281099i
$743$	16.5064			0.605561			0.302780	−	0.953060i	$-0.402085\pi$
$743$	16.5064			0.605561			0.302780	+	0.953060i	$0.402085\pi$
$744$	−3.70711	−	7.85551i	−0.135909	−	0.287997i
$745$		0			0
$746$	−2.77817	−	18.7660i	−0.101716	−	0.687073i
$747$		−	1.22079i		−	0.0446664i
$748$	−6.68488	−	22.0827i	−0.244423	−	0.807423i
$749$	10.6777	−	32.7776i	0.390154	−	1.19767i
$750$		0			0
$751$			21.1422i			0.771488i	0.922606	+	0.385744i	$0.126055\pi$
$751$			21.1422i			0.771488i	−0.922606	+	0.385744i	$0.873945\pi$
$752$	13.8700	+	20.8095i	0.505786	+	0.758846i
$753$			20.5980i			0.750632i
$754$	−1.97929	+	0.293020i	−0.0720816	+	0.0106712i
$755$		0			0
$756$	−29.8463	−	0.625951i	−1.08550	−	0.0227656i
$757$			12.5858i			0.457438i	0.973492	+	0.228719i	$0.0734537\pi$
$757$			12.5858i			0.457438i	−0.973492	+	0.228719i	$0.926546\pi$
$758$	−0.860677	−	5.81371i	−0.0312612	−	0.211163i
$759$	16.3146			0.592183
$760$		0			0
$761$		−	39.1088i		−	1.41769i	−0.705363	−	0.708847i	$-0.749216\pi$
$761$		−	39.1088i		−	1.41769i	0.705363	−	0.708847i	$-0.250784\pi$
$762$	−1.70785	−	11.5362i	−0.0618687	−	0.417911i
$763$	−2.31788	+	7.11529i	−0.0839130	+	0.257591i
$764$	14.3137	+	47.2836i	0.517852	+	1.71066i
$765$		0			0
$766$	3.81048	+	25.7391i	0.137678	+	0.929990i
$767$	17.1853			0.620525
$768$	−21.7625	−	9.07290i	−0.785286	−	0.327390i
$769$			40.5236i			1.46132i	0.682742	+	0.730660i	$0.260788\pi$
$769$			40.5236i			1.46132i	−0.682742	+	0.730660i	$0.739212\pi$
$770$		0			0
$771$		−	34.3706i		−	1.23783i
$772$	−4.81755	−	15.9142i	−0.173387	−	0.572765i
$773$	36.4005			1.30924			0.654618	−	0.755960i	$-0.272829\pi$
$773$	36.4005			1.30924			0.654618	+	0.755960i	$0.272829\pi$
$774$	6.48528	−	0.960099i	0.233109	−	0.0345100i
$775$		0			0
$776$	21.0930	−	9.95406i	0.757196	−	0.357330i
$777$	7.53880	−	23.1421i	0.270453	−	0.830219i
$778$	21.7628	−	3.22183i	0.780234	−	0.115508i
$779$		−	23.2612i		−	0.833419i
$780$		0			0
$781$	20.2426			0.724339
$782$	22.8236	−	3.37887i	0.816170	−	0.120828i
$783$		−	1.36890i		−	0.0489204i
$784$	−27.9754	−	1.17394i	−0.999121	−	0.0419265i
$785$		0			0
$786$	−3.97056	−	26.8204i	−0.141625	−	0.956651i
$787$		−	20.6308i		−	0.735407i	−0.929943	−	0.367704i	$-0.880144\pi$
$787$		−	20.6308i		−	0.735407i	0.929943	−	0.367704i	$-0.119856\pi$
$788$	1.44015	+	4.75736i	0.0513032	+	0.169474i
$789$		−	41.2311i		−	1.46786i
$790$		0			0
$791$	46.0706	+	15.0080i	1.63808	+	0.533623i
$792$	−2.79793	−	5.92893i	−0.0994202	−	0.210675i
$793$		−	68.0000i		−	2.41475i
$794$	26.4512	−	3.91591i	0.938718	−	0.138970i
$795$		0			0
$796$	−33.5665	+	10.1613i	−1.18973	+	0.360156i
$797$	26.7395			0.947162			0.473581	−	0.880750i	$-0.342961\pi$
$797$	26.7395			0.947162			0.473581	+	0.880750i	$0.342961\pi$
$798$	30.6694	+	5.19974i	1.08568	+	0.184069i
$799$		−	25.7779i		−	0.911957i
$800$		0			0
$801$		−	10.2471i		−	0.362063i
$802$	31.4150	−	4.65076i	1.10930	−	0.164224i
$803$			34.6085i			1.22131i
$804$	6.34781	+	20.9692i	0.223870	+	0.739528i
$805$		0			0
$806$	17.0000	−	2.51673i	0.598799	−	0.0886479i
$807$	3.55919			0.125289
$808$	−2.91548	−	6.17801i	−0.102566	−	0.217342i
$809$	1.17157			0.0411903			0.0205952	−	0.999788i	$-0.493444\pi$
$809$	1.17157			0.0411903			0.0205952	+	0.999788i	$0.493444\pi$
$810$		0			0
$811$	36.0821			1.26702			0.633508	−	0.773736i	$-0.281615\pi$
$811$	36.0821			1.26702			0.633508	+	0.773736i	$0.281615\pi$
$812$	0.0269213	−	1.28365i	0.000944753	−	0.0450473i
$813$		−	40.1421i		−	1.40785i
$814$	24.4350	−	3.61743i	0.856447	−	0.126791i
$815$		0			0
$816$	13.4792	+	20.2232i	0.471866	+	0.707955i
$817$	−31.5700			−1.10450
$818$	−3.26918	−	22.0827i	−0.114304	−	0.772103i
$819$	3.95859	−	12.1518i	0.138324	−	0.424619i
$820$		0			0
$821$	14.5858			0.509047			0.254524	−	0.967067i	$-0.418081\pi$
$821$	14.5858			0.509047			0.254524	+	0.967067i	$0.418081\pi$
$822$	−7.18509	+	1.06370i	−0.250609	+	0.0371008i
$823$	−49.1215			−1.71227			−0.856134	−	0.516755i	$-0.827140\pi$
$823$	−49.1215			−1.71227			−0.856134	+	0.516755i	$0.827140\pi$
$824$	−8.58892	−	18.2003i	−0.299209	−	0.634036i
$825$		0			0
$826$	−1.84333	+	10.8725i	−0.0641377	+	0.378301i
$827$	−47.0024			−1.63444			−0.817218	−	0.576329i	$-0.804485\pi$
$827$	−47.0024			−1.63444			−0.817218	+	0.576329i	$0.804485\pi$
$828$	6.27476	−	1.89949i	0.218063	−	0.0660120i
$829$		−	26.7395i		−	0.928701i	−0.885651	−	0.464351i	$-0.846288\pi$
$829$		−	26.7395i		−	0.928701i	0.885651	−	0.464351i	$-0.153712\pi$
$830$		0			0
$831$	8.98986			0.311855
$832$	29.6550	−	36.0081i	1.02810	−	1.24836i
$833$	23.3238	+	17.0000i	0.808122	+	0.589015i
$834$	−0.822330	−	5.55468i	−0.0284750	−	0.192343i
$835$		0			0
$836$	9.14695	+	30.2159i	0.316354	+	1.04504i
$837$			11.7574i			0.406394i
$838$	−34.3390	+	5.08364i	−1.18622	+	0.175611i
$839$	−37.6605			−1.30018			−0.650092	−	0.759855i	$-0.725270\pi$
$839$	−37.6605			−1.30018			−0.650092	+	0.759855i	$0.725270\pi$
$840$		0			0
$841$	−28.9411			−0.997970
$842$	0.960099	−	0.142136i	0.0330872	−	0.00489832i
$843$		−	48.5863i		−	1.67340i
$844$	−0.834524	−	2.75675i	−0.0287255	−	0.0948913i
$845$		0			0
$846$	−1.07268	−	7.24578i	−0.0368797	−	0.249115i
$847$	2.59909	−	7.97852i	0.0893058	−	0.274145i
$848$	−27.1598	−	40.7487i	−0.932672	−	1.39932i
$849$	−46.6569			−1.60126
$850$		0			0
$851$			24.7013i			0.846751i
$852$	−20.4083	+	6.17801i	−0.699178	+	0.211655i
$853$	−15.0776			−0.516247			−0.258124	−	0.966112i	$-0.583104\pi$
$853$	−15.0776			−0.516247			−0.258124	+	0.966112i	$0.583104\pi$
$854$	43.0209	+	7.29384i	1.47215	+	0.249590i
$855$		0			0
$856$	−33.3284	+	15.7281i	−1.13914	+	0.537575i
$857$	5.53793			0.189172			0.0945861	−	0.995517i	$-0.469847\pi$
$857$	5.53793			0.189172			0.0945861	+	0.995517i	$0.469847\pi$
$858$	−33.6334	+	4.97918i	−1.14823	+	0.169987i
$859$	36.3350			1.23973			0.619867	−	0.784707i	$-0.287187\pi$
$859$	36.3350			1.23973			0.619867	+	0.784707i	$0.287187\pi$
$860$		0			0
$861$	−4.97918	+	15.2848i	−0.169690	+	0.520904i
$862$	1.69723	+	11.4645i	0.0578079	+	0.390481i
$863$	−12.1518			−0.413653			−0.206827	−	0.978378i	$-0.566314\pi$
$863$	−12.1518			−0.413653			−0.206827	+	0.978378i	$0.566314\pi$
$864$	21.3982	+	23.6775i	0.727983	+	0.805525i
$865$		0			0
$866$	5.76809	−	0.853923i	0.196008	−	0.0290175i
$867$		0			0
$868$	−0.231225	+	11.0252i	−0.00784829	+	0.374219i
$869$	−22.1421			−0.751121
$870$		0			0
$871$	−43.3455			−1.46871
$872$	7.23486	−	3.41421i	0.245003	−	0.115620i
$873$	−6.83139			−0.231207
$874$	−31.2296	+	4.62332i	−1.05636	+	0.156386i
$875$		0			0
$876$	−10.5624	−	34.8918i	−0.356872	−	1.17888i
$877$			4.97056i			0.167844i	0.996472	+	0.0839220i	$0.0267447\pi$
$877$			4.97056i			0.167844i	−0.996472	+	0.0839220i	$0.973255\pi$
$878$	4.12311	−	0.610396i	0.139148	−	0.0205999i
$879$			24.3037i			0.819742i
$880$		0			0
$881$			11.6619i			0.392900i	0.980514	+	0.196450i	$0.0629413\pi$
$881$			11.6619i			0.392900i	−0.980514	+	0.196450i	$0.937059\pi$
$882$	7.26338	+	3.80788i	0.244571	+	0.128218i
$883$	−7.99611			−0.269091			−0.134545	−	0.990907i	$-0.542957\pi$
$883$	−7.99611			−0.269091			−0.134545	+	0.990907i	$0.542957\pi$
$884$	−46.0208	+	13.9314i	−1.54785	+	0.468564i
$885$		0			0
$886$	2.57107	−	0.380628i	0.0863767	−	0.0127874i
$887$		−	10.9258i		−	0.366852i	−0.983034	−	0.183426i	$-0.941281\pi$
$887$		−	10.9258i		−	0.366852i	0.983034	−	0.183426i	$-0.0587187\pi$
$888$	−23.5310	+	11.1046i	−0.789649	+	0.372645i
$889$	−4.58579	+	14.0772i	−0.153802	+	0.472133i
$890$		0			0
$891$		−	16.3075i		−	0.546323i
$892$	0.500217	+	1.65241i	0.0167485	+	0.0553267i
$893$			35.2721i			1.18034i
$894$	−0.610396	−	4.12311i	−0.0204147	−	0.137897i
$895$		0			0
$896$	19.6000	+	22.6238i	0.654791	+	0.755810i
$897$		−	34.0000i		−	1.13523i
$898$	14.9086	−	2.20711i	0.497506	−	0.0736521i
$899$	−0.505668			−0.0168650
$900$		0			0
$901$			50.4777i			1.68166i
$902$	−16.1387	+	2.38922i	−0.537360	+	0.0795523i
$903$	20.7445	+	6.75773i	0.690333	+	0.224883i
$904$	−22.1066	−	46.8448i	−0.735255	−	1.55803i
$905$		0			0
$906$	−3.37887	+	0.500217i	−0.112255	+	0.0166186i
$907$	−39.5687			−1.31386			−0.656929	−	0.753952i	$-0.728145\pi$
$907$	−39.5687			−1.31386			−0.656929	+	0.753952i	$0.728145\pi$
$908$	−4.12311	−	13.6202i	−0.136830	−	0.452002i
$909$			2.00087i			0.0663645i
$910$		0			0
$911$		−	30.2972i		−	1.00379i	−0.864928	−	0.501896i	$-0.832636\pi$
$911$		−	30.2972i		−	1.00379i	0.864928	−	0.501896i	$-0.167364\pi$
$912$	−18.4436	−	27.6716i	−0.610730	−	0.916297i
$913$	4.12311			0.136455
$914$	−6.10660	−	41.2489i	−0.201988	−	1.36439i
$915$		0			0
$916$	8.15731	+	26.9467i	0.269525	+	0.890344i
$917$	−10.6615	+	32.7279i	−0.352073	+	1.08077i
$918$	−4.81755	−	32.5416i	−0.159003	−	1.07403i
$919$			22.7811i			0.751481i	0.926725	+	0.375740i	$0.122612\pi$
$919$			22.7811i			0.751481i	−0.926725	+	0.375740i	$0.877388\pi$
$920$		0			0
$921$	−27.4853			−0.905671
$922$	−0.500217	−	3.37887i	−0.0164738	−	0.111277i
$923$		−	42.1861i		−	1.38857i
$924$	0.457464	−	21.8126i	0.0150495	−	0.717583i
$925$		0			0
$926$	−1.89949	+	0.281206i	−0.0624213	+	0.00924102i
$927$			5.89450i			0.193601i
$928$	−1.01834	+	0.920310i	−0.0334286	+	0.0302107i
$929$			39.8162i			1.30633i	0.757216	+	0.653164i	$0.226559\pi$
$929$			39.8162i			1.30633i	−0.757216	+	0.653164i	$0.773441\pi$
$930$		0			0
$931$	−31.9141	−	23.2612i	−1.04594	−	0.762355i
$932$	9.15505	+	30.2426i	0.299884	+	0.990631i
$933$			17.3726i			0.568753i
$934$	−1.57835	−	10.6615i	−0.0516453	−	0.348854i
$935$		0			0
$936$	−12.3560	+	5.83095i	−0.403869	+	0.190591i
$937$	−10.9545			−0.357868			−0.178934	−	0.983861i	$-0.557265\pi$
$937$	−10.9545			−0.357868			−0.178934	+	0.983861i	$0.557265\pi$
$938$	4.64934	−	27.4230i	0.151806	−	0.895393i
$939$			7.11838i			0.232299i
$940$		0			0
$941$		−	24.7386i		−	0.806456i	−0.915099	−	0.403228i	$-0.867888\pi$
$941$		−	24.7386i		−	0.806456i	0.915099	−	0.403228i	$-0.132112\pi$
$942$	−6.81305	−	46.0208i	−0.221981	−	1.49944i
$943$		−	16.3146i		−	0.531277i
$944$	9.80971	−	6.53836i	0.319279	−	0.212806i
$945$		0			0
$946$	3.24264	+	21.9034i	0.105427	+	0.712141i
$947$	19.5032			0.633768			0.316884	−	0.948464i	$-0.397363\pi$
$947$	19.5032			0.633768			0.316884	+	0.948464i	$0.397363\pi$
$948$	22.3234	−	6.75773i	0.725029	−	0.219481i
$949$	72.1249			2.34127
$950$		0			0
$951$	−37.8086			−1.22603
$952$	−3.87757	−	30.6099i	−0.125673	−	0.992072i
$953$		−	53.7696i		−	1.74177i	−0.491490	−	0.870883i	$-0.663547\pi$
$953$		−	53.7696i		−	1.74177i	0.491490	−	0.870883i	$-0.336453\pi$
$954$	2.10051	+	14.1885i	0.0680064	+	0.459370i
$955$		0			0
$956$	9.72792	+	32.1350i	0.314623	+	1.03932i
$957$	1.00043			0.0323394
$958$	12.3693	−	1.83119i	0.399634	−	0.0591630i
$959$	8.76770	+	2.85617i	0.283124	+	0.0922306i
$960$		0			0
$961$	−26.6569			−0.859899
$962$	−7.53880	−	50.9231i	−0.243061	−	1.64183i
$963$	10.7940			0.347833
$964$	9.14695	+	30.2159i	0.294604	+	0.973188i
$965$		0			0
$966$	21.5105	+	3.64692i	0.692088	+	0.117338i
$967$	−9.55274			−0.307195			−0.153598	−	0.988133i	$-0.549086\pi$
$967$	−9.55274			−0.307195			−0.153598	+	0.988133i	$0.549086\pi$
$968$	−8.11259	+	3.82843i	−0.260749	+	0.123050i
$969$			34.2783i			1.10118i
$970$		0			0
$971$	−4.92655			−0.158100			−0.0790502	−	0.996871i	$-0.525189\pi$
$971$	−4.92655			−0.158100			−0.0790502	+	0.996871i	$0.525189\pi$
$972$	−4.83052	−	15.9570i	−0.154939	−	0.511823i
$973$	−2.20806	+	6.77817i	−0.0707872	+	0.217298i
$974$	5.14214	−	0.761256i	0.164765	−	0.0243922i
$975$		0			0
$976$	−25.8715	−	38.8158i	−0.828126	−	1.24246i
$977$		−	7.28427i		−	0.233044i	−0.993188	−	0.116522i	$-0.962825\pi$
$977$		−	7.28427i		−	0.233044i	0.993188	−	0.116522i	$-0.0371746\pi$
$978$	6.68488	+	45.1550i	0.213759	+	1.44390i
$979$	34.6085			1.10609
$980$		0			0
$981$	−2.34315			−0.0748109
$982$	6.07591	+	41.0416i	0.193890	+	1.30969i
$983$		−	11.6409i		−	0.371287i	−0.982617	−	0.185644i	$-0.940563\pi$
$983$		−	11.6409i		−	0.371287i	0.982617	−	0.185644i	$-0.0594370\pi$
$984$	15.5416	−	7.33428i	0.495449	−	0.233808i
$985$		0			0
$986$	1.39957	−	0.207196i	0.0445715	−	0.00659848i
$987$	7.55018	−	23.1771i	0.240325	−	0.737734i
$988$	62.9705	−	19.0624i	2.00336	−	0.606457i
$989$	−22.1421			−0.704079
$990$		0			0
$991$		−	6.27476i		−	0.199324i	−0.995021	−	0.0996621i	$-0.968224\pi$
$991$		−	6.27476i		−	0.199324i	0.995021	−	0.0996621i	$-0.0317762\pi$
$992$	8.74643	−	7.90447i	0.277699	−	0.250967i
$993$	42.5245			1.34947
$994$	26.6895	+	4.52498i	0.846539	+	0.143524i
$995$		0			0
$996$	−4.15685	+	1.25836i	−0.131715	+	0.0398728i
$997$	2.41526			0.0764920			0.0382460	−	0.999268i	$-0.487823\pi$
$997$	2.41526			0.0764920			0.0382460	+	0.999268i	$0.487823\pi$
$998$	3.47682	+	23.4853i	0.110057	+	0.743414i
$999$	35.2189			1.11428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.c.k.699.3		16
4.3	odd	2	inner	700.2.c.k.699.16		16
5.2	odd	4		700.2.g.k.251.1	yes	8
5.3	odd	4		700.2.g.i.251.8	yes	8
5.4	even	2	inner	700.2.c.k.699.14		16
7.6	odd	2	inner	700.2.c.k.699.4		16
20.3	even	4		700.2.g.i.251.5	✓	8
20.7	even	4		700.2.g.k.251.4	yes	8
20.19	odd	2	inner	700.2.c.k.699.1		16
28.27	even	2	inner	700.2.c.k.699.15		16
35.13	even	4		700.2.g.i.251.7	yes	8
35.27	even	4		700.2.g.k.251.2	yes	8
35.34	odd	2	inner	700.2.c.k.699.13		16
140.27	odd	4		700.2.g.k.251.3	yes	8
140.83	odd	4		700.2.g.i.251.6	yes	8
140.139	even	2	inner	700.2.c.k.699.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.c.k.699.1		16	20.19	odd	2	inner
700.2.c.k.699.2		16	140.139	even	2	inner
700.2.c.k.699.3		16	1.1	even	1	trivial
700.2.c.k.699.4		16	7.6	odd	2	inner
700.2.c.k.699.13		16	35.34	odd	2	inner
700.2.c.k.699.14		16	5.4	even	2	inner
700.2.c.k.699.15		16	28.27	even	2	inner
700.2.c.k.699.16		16	4.3	odd	2	inner
700.2.g.i.251.5	✓	8	20.3	even	4
700.2.g.i.251.6	yes	8	140.83	odd	4
700.2.g.i.251.7	yes	8	35.13	even	4
700.2.g.i.251.8	yes	8	5.3	odd	4
700.2.g.k.251.1	yes	8	5.2	odd	4
700.2.g.k.251.2	yes	8	35.27	even	4
700.2.g.k.251.3	yes	8	140.27	odd	4
700.2.g.k.251.4	yes	8	20.7	even	4

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39897 + 0.207107i) q^{2} -1.47363i q^{3} +(1.91421 - 0.579471i) q^{4} +(0.305198 + 2.06155i) q^{6} +(0.819496 - 2.51564i) q^{7} +(-2.55791 + 1.20711i) q^{8} +0.828427 q^{9} +2.79793i q^{11} +(-0.853923 - 2.82083i) q^{12} +5.83095 q^{13} +(-0.625441 + 3.68901i) q^{14} +(3.32843 - 2.21846i) q^{16} -4.12311 q^{17} +(-1.15894 + 0.171573i) q^{18} +5.64167 q^{19} +(-3.70711 - 1.20763i) q^{21} +(-0.579471 - 3.91421i) q^{22} +3.95687 q^{23} +(1.77882 + 3.76940i) q^{24} +(-8.15731 + 1.20763i) q^{26} -5.64167i q^{27} +(0.110951 - 5.29034i) q^{28} +0.242641 q^{29} -2.08402 q^{31} +(-4.19690 + 3.79289i) q^{32} +4.12311 q^{33} +(5.76809 - 0.853923i) q^{34} +(1.58579 - 0.480049i) q^{36} +6.24264i q^{37} +(-7.89250 + 1.16843i) q^{38} -8.59264i q^{39} -4.12311i q^{41} +(5.43623 + 0.921666i) q^{42} -5.59587 q^{43} +(1.62132 + 5.35584i) q^{44} +(-5.53553 + 0.819496i) q^{46} +6.25206i q^{47} +(-3.26918 - 4.90486i) q^{48} +(-5.65685 - 4.12311i) q^{49} +6.07591i q^{51} +(11.1617 - 3.37887i) q^{52} -12.2426i q^{53} +(1.16843 + 7.89250i) q^{54} +(0.940448 + 7.42399i) q^{56} -8.31371i q^{57} +(-0.339446 + 0.0502525i) q^{58} +2.94725 q^{59} -11.6619i q^{61} +(2.91548 - 0.431615i) q^{62} +(0.678892 - 2.08402i) q^{63} +(5.08579 - 6.17534i) q^{64} +(-5.76809 + 0.853923i) q^{66} -7.43370 q^{67} +(-7.89250 + 2.38922i) q^{68} -5.83095i q^{69} -7.23486i q^{71} +(-2.11904 + 1.00000i) q^{72} +12.3693 q^{73} +(-1.29289 - 8.73324i) q^{74} +(10.7994 - 3.26918i) q^{76} +(7.03858 + 2.29289i) q^{77} +(1.77959 + 12.0208i) q^{78} +7.91375i q^{79} -5.82843 q^{81} +(0.853923 + 5.76809i) q^{82} -1.47363i q^{83} +(-7.79598 - 0.163501i) q^{84} +(7.82843 - 1.15894i) q^{86} -0.357562i q^{87} +(-3.37740 - 7.15685i) q^{88} -12.3693i q^{89} +(4.77844 - 14.6686i) q^{91} +(7.57430 - 2.29289i) q^{92} +3.07107i q^{93} +(-1.29484 - 8.74643i) q^{94} +(5.58931 + 6.18466i) q^{96} -8.24621 q^{97} +(8.76767 + 4.59651i) q^{98} +2.31788i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 32 q^{9} - 24 q^{14} + 8 q^{16} - 48 q^{21} - 64 q^{29} + 48 q^{36} - 8 q^{44} - 32 q^{46} + 40 q^{56} + 104 q^{64} - 32 q^{74} - 48 q^{81} - 40 q^{84} + 80 q^{86}+O(q^{100}) \) 16 * q + 8 * q^4 - 32 * q^9 - 24 * q^14 + 8 * q^16 - 48 * q^21 - 64 * q^29 + 48 * q^36 - 8 * q^44 - 32 * q^46 + 40 * q^56 + 104 * q^64 - 32 * q^74 - 48 * q^81 - 40 * q^84 + 80 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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