LMFDB - Embedded newform 220.2.l.c.23.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.12
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.12

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20596 + 0.738695i) q^{2} +(-2.25953 + 2.25953i) q^{3} +(0.908659 + 1.78167i) q^{4} +(1.86216 + 1.23788i) q^{5} +(-4.39400 + 1.05579i) q^{6} +(-0.985925 - 0.985925i) q^{7} +(-0.220306 + 2.81983i) q^{8} -7.21094i q^{9} +(1.33127 + 2.86840i) q^{10} -1.00000i q^{11} +(-6.07887 - 1.97259i) q^{12} +(-0.233723 - 0.233723i) q^{13} +(-0.460684 - 1.91728i) q^{14} +(-7.00464 + 1.41058i) q^{15} +(-2.34868 + 3.23786i) q^{16} +(-4.05653 + 4.05653i) q^{17} +(5.32669 - 8.69608i) q^{18} +6.98049 q^{19} +(-0.513424 + 4.44257i) q^{20} +4.45545 q^{21} +(0.738695 - 1.20596i) q^{22} +(3.47359 - 3.47359i) q^{23} +(-5.87371 - 6.86929i) q^{24} +(1.93530 + 4.61027i) q^{25} +(-0.109209 - 0.454509i) q^{26} +(9.51475 + 9.51475i) q^{27} +(0.860721 - 2.65246i) q^{28} -1.44023i q^{29} +(-9.48927 - 3.47320i) q^{30} +2.12239i q^{31} +(-5.22419 + 2.16976i) q^{32} +(2.25953 + 2.25953i) q^{33} +(-7.88854 + 1.89546i) q^{34} +(-0.615493 - 3.05641i) q^{35} +(12.8475 - 6.55229i) q^{36} +(5.15870 - 5.15870i) q^{37} +(8.41816 + 5.15645i) q^{38} +1.05621 q^{39} +(-3.90087 + 4.97828i) q^{40} -2.85197 q^{41} +(5.37308 + 3.29122i) q^{42} +(-2.37819 + 2.37819i) q^{43} +(1.78167 - 0.908659i) q^{44} +(8.92630 - 13.4279i) q^{45} +(6.75491 - 1.62307i) q^{46} +(2.14093 + 2.14093i) q^{47} +(-2.00913 - 12.6229i) q^{48} -5.05590i q^{49} +(-1.07171 + 6.98938i) q^{50} -18.3317i q^{51} +(0.204042 - 0.628790i) q^{52} +(5.39174 + 5.39174i) q^{53} +(4.44587 + 18.5029i) q^{54} +(1.23788 - 1.86216i) q^{55} +(2.99735 - 2.56294i) q^{56} +(-15.7726 + 15.7726i) q^{57} +(1.06389 - 1.73685i) q^{58} +2.81550 q^{59} +(-8.87801 - 11.1982i) q^{60} +2.97170 q^{61} +(-1.56780 + 2.55951i) q^{62} +(-7.10945 + 7.10945i) q^{63} +(-7.90293 - 1.24245i) q^{64} +(-0.145908 - 0.724550i) q^{65} +(1.05579 + 4.39400i) q^{66} +(-5.64026 - 5.64026i) q^{67} +(-10.9134 - 3.54139i) q^{68} +15.6973i q^{69} +(1.51550 - 4.14056i) q^{70} -2.91802i q^{71} +(20.3337 + 1.58862i) q^{72} +(-2.55895 - 2.55895i) q^{73} +(10.0319 - 2.41046i) q^{74} +(-14.7899 - 6.04419i) q^{75} +(6.34288 + 12.4369i) q^{76} +(-0.985925 + 0.985925i) q^{77} +(1.27374 + 0.780214i) q^{78} -11.0758 q^{79} +(-8.38170 + 3.12203i) q^{80} -21.3649 q^{81} +(-3.43935 - 2.10674i) q^{82} +(-0.848203 + 0.848203i) q^{83} +(4.04849 + 7.93814i) q^{84} +(-12.5754 + 2.53241i) q^{85} +(-4.62475 + 1.11123i) q^{86} +(3.25424 + 3.25424i) q^{87} +(2.81983 + 0.220306i) q^{88} -0.00599269i q^{89} +(20.6839 - 9.59970i) q^{90} +0.460866i q^{91} +(9.34508 + 3.03247i) q^{92} +(-4.79561 - 4.79561i) q^{93} +(1.00037 + 4.16337i) q^{94} +(12.9988 + 8.64102i) q^{95} +(6.90158 - 16.7068i) q^{96} +(10.1908 - 10.1908i) q^{97} +(3.73477 - 6.09720i) q^{98} -7.21094 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100})$ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	1.20596	+	0.738695i	0.852740	+	0.522336i
$2$	1.20596	+	0.738695i	0.852740	+	0.522336i
$3$	−2.25953	+	2.25953i	−1.30454	+	1.30454i	−0.379242	+	0.925297i	$0.623815\pi$
$3$	−2.25953	+	2.25953i	−1.30454	+	1.30454i	−0.925297	+	0.379242i	$0.876185\pi$
$4$	0.908659	+	1.78167i	0.454330	+	0.890834i
$5$	1.86216	+	1.23788i	0.832784	+	0.553598i
$5$	1.86216	+	1.23788i	0.832784	+	0.553598i
$6$	−4.39400	+	1.05579i	−1.79384	+	0.431024i
$7$	−0.985925	−	0.985925i	−0.372645	−	0.372645i	0.495795	−	0.868440i	$-0.334877\pi$
$7$	−0.985925	−	0.985925i	−0.372645	−	0.372645i	−0.868440	+	0.495795i	$0.834877\pi$
$8$	−0.220306	+	2.81983i	−0.0778900	+	0.996962i
$9$		−	7.21094i		−	2.40365i
$10$	1.33127	+	2.86840i	0.420984	+	0.907068i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−6.07887	−	1.97259i	−1.75482	−	0.569437i
$13$	−0.233723	−	0.233723i	−0.0648230	−	0.0648230i	0.673952	−	0.738775i	$-0.264595\pi$
$13$	−0.233723	−	0.233723i	−0.0648230	−	0.0648230i	−0.738775	+	0.673952i	$0.764595\pi$
$14$	−0.460684	−	1.91728i	−0.123123	−	0.512415i
$15$	−7.00464	+	1.41058i	−1.80859	+	0.364210i
$16$	−2.34868	+	3.23786i	−0.587169	+	0.809464i
$17$	−4.05653	+	4.05653i	−0.983854	+	0.983854i	−0.999872	−	0.0160178i	$-0.994901\pi$
$17$	−4.05653	+	4.05653i	−0.983854	+	0.983854i	0.0160178	+	0.999872i	$0.494901\pi$
$18$	5.32669	−	8.69608i	1.25551	−	2.04969i
$19$	6.98049			1.60143			0.800717	−	0.599043i	$-0.204452\pi$
$19$	6.98049			1.60143			0.800717	+	0.599043i	$0.204452\pi$
$20$	−0.513424	+	4.44257i	−0.114805	+	0.993388i
$21$	4.45545			0.972260
$22$	0.738695	−	1.20596i	0.157490	−	0.257111i
$23$	3.47359	−	3.47359i	0.724293	−	0.724293i	−0.245184	−	0.969477i	$-0.578848\pi$
$23$	3.47359	−	3.47359i	0.724293	−	0.724293i	0.969477	+	0.245184i	$0.0788483\pi$
$24$	−5.87371	−	6.86929i	−1.19897	−	1.40219i
$25$	1.93530	+	4.61027i	0.387059	+	0.922055i
$26$	−0.109209	−	0.454509i	−0.0214177	−	0.0891365i
$27$	9.51475	+	9.51475i	1.83111	+	1.83111i
$28$	0.860721	−	2.65246i	0.162661	−	0.501268i
$29$		−	1.44023i		−	0.267444i	−0.991019	−	0.133722i	$-0.957307\pi$
$29$		−	1.44023i		−	0.267444i	0.991019	−	0.133722i	$-0.0426929\pi$
$30$	−9.48927	−	3.47320i	−1.73250	−	0.634116i
$31$			2.12239i			0.381193i	0.981668	+	0.190596i	$0.0610422\pi$
$31$			2.12239i			0.381193i	−0.981668	+	0.190596i	$0.938958\pi$
$32$	−5.22419	+	2.16976i	−0.923515	+	0.383562i
$33$	2.25953	+	2.25953i	0.393334	+	0.393334i
$34$	−7.88854	+	1.89546i	−1.35287	+	0.325069i
$35$	−0.615493	−	3.05641i	−0.104037	−	0.516628i
$36$	12.8475	−	6.55229i	2.14125	−	1.09205i
$37$	5.15870	−	5.15870i	0.848086	−	0.848086i	−0.141809	−	0.989894i	$-0.545292\pi$
$37$	5.15870	−	5.15870i	0.848086	−	0.848086i	0.989894	+	0.141809i	$0.0452917\pi$
$38$	8.41816	+	5.15645i	1.36561	+	0.836487i
$39$	1.05621			0.169128
$40$	−3.90087	+	4.97828i	−0.616782	+	0.787134i
$41$	−2.85197			−0.445403			−0.222702	−	0.974887i	$-0.571488\pi$
$41$	−2.85197			−0.445403			−0.222702	+	0.974887i	$0.571488\pi$
$42$	5.37308	+	3.29122i	0.829084	+	0.507847i
$43$	−2.37819	+	2.37819i	−0.362670	+	0.362670i	−0.864795	−	0.502125i	$-0.832552\pi$
$43$	−2.37819	+	2.37819i	−0.362670	+	0.362670i	0.502125	+	0.864795i	$0.332552\pi$
$44$	1.78167	−	0.908659i	0.268596	−	0.136986i
$45$	8.92630	−	13.4279i	1.33065	−	2.00172i
$46$	6.75491	−	1.62307i	0.995957	−	0.239309i
$47$	2.14093	+	2.14093i	0.312287	+	0.312287i	0.845795	−	0.533508i	$-0.179127\pi$
$47$	2.14093	+	2.14093i	0.312287	+	0.312287i	−0.533508	+	0.845795i	$0.679127\pi$
$48$	−2.00913	−	12.6229i	−0.289992	−	1.82196i
$49$		−	5.05590i		−	0.722272i
$50$	−1.07171	+	6.98938i	−0.151562	+	0.988448i
$51$		−	18.3317i		−	2.56695i
$52$	0.204042	−	0.628790i	0.0282955	−	0.0871975i
$53$	5.39174	+	5.39174i	0.740612	+	0.740612i	0.972696	−	0.232084i	$-0.0745544\pi$
$53$	5.39174	+	5.39174i	0.740612	+	0.740612i	−0.232084	+	0.972696i	$0.574554\pi$
$54$	4.44587	+	18.5029i	0.605006	+	2.51792i
$55$	1.23788	−	1.86216i	0.166916	−	0.251094i
$56$	2.99735	−	2.56294i	0.400538	−	0.342487i
$57$	−15.7726	+	15.7726i	−2.08913	+	2.08913i
$58$	1.06389	−	1.73685i	0.139696	−	0.228060i
$59$	2.81550			0.366547			0.183274	−	0.983062i	$-0.441331\pi$
$59$	2.81550			0.366547			0.183274	+	0.983062i	$0.441331\pi$
$60$	−8.87801	−	11.1982i	−1.14615	−	1.44568i
$61$	2.97170			0.380487			0.190243	−	0.981737i	$-0.439072\pi$
$61$	2.97170			0.380487			0.190243	+	0.981737i	$0.439072\pi$
$62$	−1.56780	+	2.55951i	−0.199111	+	0.325058i
$63$	−7.10945	+	7.10945i	−0.895707	+	0.895707i
$64$	−7.90293	−	1.24245i	−0.987866	−	0.155307i
$65$	−0.145908	−	0.724550i	−0.0180977	−	0.0898694i
$66$	1.05579	+	4.39400i	0.129959	+	0.540863i
$67$	−5.64026	−	5.64026i	−0.689068	−	0.689068i	0.272958	−	0.962026i	$-0.411998\pi$
$67$	−5.64026	−	5.64026i	−0.689068	−	0.689068i	−0.962026	+	0.272958i	$0.911998\pi$
$68$	−10.9134	−	3.54139i	−1.32344	−	0.429456i
$69$			15.6973i			1.88974i
$70$	1.51550	−	4.14056i	0.181137	−	0.494892i
$71$		−	2.91802i		−	0.346305i	−0.984895	−	0.173152i	$-0.944605\pi$
$71$		−	2.91802i		−	0.346305i	0.984895	−	0.173152i	$-0.0553953\pi$
$72$	20.3337	+	1.58862i	2.39635	+	0.187220i
$73$	−2.55895	−	2.55895i	−0.299502	−	0.299502i	0.541317	−	0.840819i	$-0.317926\pi$
$73$	−2.55895	−	2.55895i	−0.299502	−	0.299502i	−0.840819	+	0.541317i	$0.817926\pi$
$74$	10.0319	−	2.41046i	1.16618	−	0.280210i
$75$	−14.7899	−	6.04419i	−1.70779	−	0.697923i
$76$	6.34288	+	12.4369i	0.727579	+	1.42661i
$77$	−0.985925	+	0.985925i	−0.112357	+	0.112357i
$78$	1.27374	+	0.780214i	0.144222	+	0.0883418i
$79$	−11.0758			−1.24613			−0.623064	−	0.782171i	$-0.714112\pi$
$79$	−11.0758			−1.24613			−0.623064	+	0.782171i	$0.714112\pi$
$80$	−8.38170	+	3.12203i	−0.937103	+	0.349053i
$81$	−21.3649			−2.37387
$82$	−3.43935	−	2.10674i	−0.379813	−	0.232650i
$83$	−0.848203	+	0.848203i	−0.0931023	+	0.0931023i	−0.752124	−	0.659022i	$-0.770971\pi$
$83$	−0.848203	+	0.848203i	−0.0931023	+	0.0931023i	0.659022	+	0.752124i	$0.270971\pi$
$84$	4.04849	+	7.93814i	0.441726	+	0.866122i
$85$	−12.5754	+	2.53241i	−1.36400	+	0.274679i
$86$	−4.62475	+	1.11123i	−0.498699	+	0.119827i
$87$	3.25424	+	3.25424i	0.348891	+	0.348891i
$88$	2.81983	+	0.220306i	0.300595	+	0.0234847i
$89$		−	0.00599269i		−	0.000635224i	−1.00000		0.000317612i	$-0.999899\pi$
$89$		−	0.00599269i		−	0.000635224i	1.00000		0.000317612i	$-0.000101099\pi$
$90$	20.6839	−	9.59970i	2.18027	−	1.01190i
$91$			0.460866i			0.0483119i
$92$	9.34508	+	3.03247i	0.974292	+	0.316157i
$93$	−4.79561	−	4.79561i	−0.497281	−	0.497281i
$94$	1.00037	+	4.16337i	0.103181	+	0.429419i
$95$	12.9988	+	8.64102i	1.33365	+	0.886550i
$96$	6.90158	−	16.7068i	0.704390	−	1.70513i
$97$	10.1908	−	10.1908i	1.03472	−	1.03472i	0.0353404	−	0.999375i	$-0.488748\pi$
$97$	10.1908	−	10.1908i	1.03472	−	1.03472i	0.999375	−	0.0353404i	$-0.0112516\pi$
$98$	3.73477	−	6.09720i	0.377269	−	0.615910i
$99$	−7.21094			−0.724727
$100$	−6.45545	+	7.63722i	−0.645545	+	0.763722i
$101$	−0.180674			−0.0179777			−0.00898886	−	0.999960i	$-0.502861\pi$
$101$	−0.180674			−0.0179777			−0.00898886	+	0.999960i	$0.502861\pi$
$102$	13.5415	−	22.1072i	1.34081	−	2.18894i
$103$	8.81537	−	8.81537i	0.868604	−	0.868604i	−0.123714	−	0.992318i	$-0.539480\pi$
$103$	8.81537	−	8.81537i	0.868604	−	0.868604i	0.992318	+	0.123714i	$0.0394804\pi$
$104$	0.710549	−	0.607568i	0.0696751	−	0.0595770i
$105$	8.29678	+	5.51533i	0.809683	+	0.538241i
$106$	2.51935	+	10.4850i	0.244701	+	1.01840i
$107$	−5.69731	−	5.69731i	−0.550780	−	0.550780i	0.375886	−	0.926666i	$-0.377338\pi$
$107$	−5.69731	−	5.69731i	−0.550780	−	0.550780i	−0.926666	+	0.375886i	$0.877338\pi$
$108$	−8.30646	+	25.5978i	−0.799289	+	2.46315i
$109$		−	18.8642i		−	1.80687i	−0.428728	−	0.903434i	$-0.641038\pi$
$109$		−	18.8642i		−	1.80687i	0.428728	−	0.903434i	$-0.358962\pi$
$110$	2.86840	−	1.33127i	0.273491	−	0.126931i
$111$			23.3125i			2.21272i
$112$	5.50791	−	0.876664i	0.520448	−	0.0828370i
$113$	−1.56803	−	1.56803i	−0.147508	−	0.147508i	0.629496	−	0.777004i	$-0.283261\pi$
$113$	−1.56803	−	1.56803i	−0.147508	−	0.147508i	−0.777004	+	0.629496i	$0.783261\pi$
$114$	−30.6722	+	7.36992i	−2.87272	+	0.690257i
$115$	10.7683	−	2.16849i	1.00415	−	0.202213i
$116$	2.56601	−	1.30868i	0.238248	−	0.121508i
$117$	−1.68536	+	1.68536i	−0.155812	+	0.155812i
$118$	3.39537	+	2.07980i	0.312569	+	0.191461i
$119$	7.99888			0.733256
$120$	−2.43443	−	20.0627i	−0.222232	−	1.83146i
$121$	−1.00000			−0.0909091
$122$	3.58374	+	2.19518i	0.324456	+	0.198742i
$123$	6.44412	−	6.44412i	0.581046	−	0.581046i
$124$	−3.78140	+	1.92853i	−0.339579	+	0.173187i
$125$	−2.10314	+	10.9807i	−0.188111	+	0.982148i
$126$	−13.8254	+	3.32197i	−1.23166	+	0.295944i
$127$	−11.9375	−	11.9375i	−1.05929	−	1.05929i	−0.998128	−	0.0611574i	$-0.980521\pi$
$127$	−11.9375	−	11.9375i	−1.05929	−	1.05929i	−0.0611574	−	0.998128i	$-0.519479\pi$
$128$	−8.61279	−	7.33620i	−0.761270	−	0.648435i
$129$		−	10.7472i		−	0.946236i
$130$	0.359263	−	0.981557i	0.0315094	−	0.0860883i
$131$			6.05700i			0.529202i	0.964358	+	0.264601i	$0.0852403\pi$
$131$			6.05700i			0.529202i	−0.964358	+	0.264601i	$0.914760\pi$
$132$	−1.97259	+	6.07887i	−0.171692	+	0.529098i
$133$	−6.88224	−	6.88224i	−0.596766	−	0.596766i
$134$	−2.63547	−	10.9683i	−0.227670	−	0.947520i
$135$	5.93987	+	29.4961i	0.511222	+	2.53862i
$136$	−10.5451	−	12.3324i	−0.904233	−	1.05750i
$137$	−8.32573	+	8.32573i	−0.711315	+	0.711315i	−0.966810	−	0.255495i	$-0.917762\pi$
$137$	−8.32573	+	8.32573i	−0.711315	+	0.711315i	0.255495	+	0.966810i	$0.417762\pi$
$138$	−11.5955	+	18.9303i	−0.987078	+	1.61145i
$139$	1.02548			0.0869797			0.0434899	−	0.999054i	$-0.486152\pi$
$139$	1.02548			0.0869797			0.0434899	+	0.999054i	$0.486152\pi$
$140$	4.88624	−	3.87384i	0.412962	−	0.327399i
$141$	−9.67500			−0.814782
$142$	2.15552	−	3.51900i	0.180888	−	0.295308i
$143$	−0.233723	+	0.233723i	−0.0195449	+	0.0195449i
$144$	23.3480	+	16.9362i	1.94567	+	1.41135i
$145$	1.78283	−	2.68194i	0.148056	−	0.222723i
$146$	−1.19569	−	4.97626i	−0.0989564	−	0.411838i
$147$	11.4240	+	11.4240i	0.942232	+	0.942232i
$148$	13.8786	+	4.50359i	1.14081	+	0.370193i
$149$			6.43582i			0.527243i	0.964626	+	0.263622i	$0.0849170\pi$
$149$			6.43582i			0.527243i	−0.964626	+	0.263622i	$0.915083\pi$
$150$	−13.3712	−	18.2143i	−1.09175	−	1.48719i
$151$			8.72410i			0.709957i	0.934874	+	0.354979i	$0.115512\pi$
$151$			8.72410i			0.709957i	−0.934874	+	0.354979i	$0.884488\pi$
$152$	−1.53785	+	19.6838i	−0.124736	+	1.59657i
$153$	29.2514	+	29.2514i	2.36484	+	2.36484i
$154$	−1.91728	+	0.460684i	−0.154499	+	0.0371230i
$155$	−2.62727	+	3.95224i	−0.211028	+	0.317451i
$156$	0.959731	+	1.88181i	0.0768400	+	0.150665i
$157$	−8.84400	+	8.84400i	−0.705828	+	0.705828i	−0.965655	−	0.259827i	$-0.916334\pi$
$157$	−8.84400	+	8.84400i	−0.705828	+	0.705828i	0.259827	+	0.965655i	$0.416334\pi$
$158$	−13.3570	−	8.18166i	−1.06262	−	0.650898i
$159$	−24.3656			−1.93232
$160$	−12.4142	−	2.42650i	−0.981428	−	0.191831i
$161$	−6.84939			−0.539808
$162$	−25.7651	−	15.7821i	−2.02430	−	1.23996i
$163$	14.6827	−	14.6827i	1.15004	−	1.15004i	0.163496	−	0.986544i	$-0.447723\pi$
$163$	14.6827	−	14.6827i	1.15004	−	1.15004i	0.986544	−	0.163496i	$-0.0522771\pi$
$164$	−2.59147	−	5.08127i	−0.202360	−	0.396780i
$165$	1.41058	+	7.00464i	0.109813	+	0.545311i
$166$	−1.64946	+	0.396332i	−0.128023	+	0.0307613i
$167$	−1.57457	−	1.57457i	−0.121844	−	0.121844i	0.643556	−	0.765399i	$-0.277459\pi$
$167$	−1.57457	−	1.57457i	−0.121844	−	0.121844i	−0.765399	+	0.643556i	$0.777459\pi$
$168$	−0.981564	+	12.5636i	−0.0757293	+	0.969306i
$169$		−	12.8907i		−	0.991596i
$170$	−17.0361	−	6.23543i	−1.30661	−	0.478236i
$171$		−	50.3359i		−	3.84928i
$172$	−6.39810	−	2.07618i	−0.487851	−	0.158307i
$173$	8.97062	+	8.97062i	0.682024	+	0.682024i	0.960456	−	0.278432i	$-0.0898147\pi$
$173$	8.97062	+	8.97062i	0.682024	+	0.682024i	−0.278432	+	0.960456i	$0.589815\pi$
$174$	1.52058	+	6.32836i	0.115275	+	0.479752i
$175$	2.63733	−	6.45344i	0.199363	−	0.487834i
$176$	3.23786	+	2.34868i	0.244063	+	0.177038i
$177$	−6.36171	+	6.36171i	−0.478176	+	0.478176i
$178$	0.00442677	−	0.00722692i	0.000331800	−	0.000541680i
$179$	8.59206			0.642201			0.321101	−	0.947045i	$-0.395947\pi$
$179$	8.59206			0.642201			0.321101	+	0.947045i	$0.395947\pi$
$180$	32.0351	+	3.70227i	2.38775	+	0.275951i
$181$	−1.00309			−0.0745590			−0.0372795	−	0.999305i	$-0.511869\pi$
$181$	−1.00309			−0.0745590			−0.0372795	+	0.999305i	$0.511869\pi$
$182$	−0.340439	+	0.555784i	−0.0252350	+	0.0411974i
$183$	−6.71464	+	6.71464i	−0.496360	+	0.496360i
$184$	9.02968	+	10.5602i	0.665677	+	0.778508i
$185$	15.9922	−	3.22047i	1.17577	−	0.236774i
$186$	−2.24080	−	9.32578i	−0.164303	−	0.683799i
$187$	4.05653	+	4.05653i	0.296643	+	0.296643i
$188$	−1.86905	+	5.75981i	−0.136315	+	0.420077i
$189$		−	18.7617i		−	1.36471i
$190$	9.29290	+	20.0228i	0.674178	+	1.45261i
$191$			13.4528i			0.973410i	0.873566	+	0.486705i	$0.161801\pi$
$191$			13.4528i			0.973410i	−0.873566	+	0.486705i	$0.838199\pi$
$192$	20.6643	−	15.0495i	1.49131	−	1.08611i
$193$	−16.3719	−	16.3719i	−1.17847	−	1.17847i	−0.980133	−	0.198340i	$-0.936445\pi$
$193$	−16.3719	−	16.3719i	−1.17847	−	1.17847i	−0.198340	−	0.980133i	$-0.563555\pi$
$194$	19.8175	−	4.76175i	1.42281	−	0.341873i
$195$	1.96683	+	1.30746i	0.140847	+	0.0936290i
$196$	9.00794	−	4.59409i	0.643424	−	0.328149i
$197$	10.1591	−	10.1591i	0.723809	−	0.723809i	−0.245570	−	0.969379i	$-0.578975\pi$
$197$	10.1591	−	10.1591i	0.723809	−	0.723809i	0.969379	+	0.245570i	$0.0789751\pi$
$198$	−8.69608	−	5.32669i	−0.618003	−	0.378551i
$199$	1.67028			0.118403			0.0592015	−	0.998246i	$-0.481145\pi$
$199$	1.67028			0.118403			0.0592015	+	0.998246i	$0.481145\pi$
$200$	−13.4266	+	4.44154i	−0.949402	+	0.314064i
$201$	25.4887			1.79783
$202$	−0.217885	−	0.133463i	−0.0153303	−	0.00939042i
$203$	−1.41996	+	1.41996i	−0.0996615	+	0.0996615i
$204$	32.6610	−	16.6573i	2.28673	−	1.16624i
$205$	−5.31084	−	3.53041i	−0.370925	−	0.246574i
$206$	17.1428	−	4.11908i	1.19440	−	0.286990i
$207$	−25.0478	−	25.0478i	−1.74094	−	1.74094i
$208$	1.30570	−	0.207821i	0.0905339	−	0.0144098i
$209$		−	6.98049i		−	0.482850i
$210$	5.93140	+	12.7800i	0.409306	+	0.881906i
$211$			21.9300i			1.50973i	0.655882	+	0.754863i	$0.272297\pi$
$211$			21.9300i			1.50973i	−0.655882	+	0.754863i	$0.727703\pi$
$212$	−4.70703	+	14.5055i	−0.323280	+	0.996244i
$213$	6.59334	+	6.59334i	0.451768	+	0.451768i
$214$	−2.66213	−	11.0793i	−0.181979	−	0.757364i
$215$	−7.37249	+	1.48465i	−0.502800	+	0.101253i
$216$	−28.9262	+	24.7339i	−1.96818	+	1.68293i
$217$	2.09252	−	2.09252i	0.142050	−	0.142050i
$218$	13.9349	−	22.7495i	0.943792	−	1.54079i
$219$	11.5640			0.781424
$220$	4.44257	+	0.513424i	0.299518	+	0.0346150i
$221$	1.89621			0.127553
$222$	−17.2208	+	28.1138i	−1.15579	+	1.88688i
$223$	−16.9116	+	16.9116i	−1.13249	+	1.13249i	−0.142725	+	0.989762i	$0.545586\pi$
$223$	−16.9116	+	16.9116i	−1.13249	+	1.13249i	−0.989762	+	0.142725i	$0.954414\pi$
$224$	7.28988	+	3.01144i	0.487075	+	0.201211i
$225$	33.2444	−	13.9553i	2.21630	−	0.930354i
$226$	−0.732678	−	3.04927i	−0.0487370	−	0.202834i
$227$	−15.9508	−	15.9508i	−1.05869	−	1.05869i	−0.998167	−	0.0605244i	$-0.980723\pi$
$227$	−15.9508	−	15.9508i	−1.05869	−	1.05869i	−0.0605244	−	0.998167i	$-0.519277\pi$
$228$	−42.4335	−	13.7696i	−2.81023	−	0.911916i
$229$			25.4401i			1.68113i	0.541709	+	0.840566i	$0.317777\pi$
$229$			25.4401i			1.68113i	−0.541709	+	0.840566i	$0.682223\pi$
$230$	14.5879	+	5.33937i	0.961898	+	0.352067i
$231$		−	4.45545i		−	0.293147i
$232$	4.06121	+	0.317292i	0.266631	+	0.0208312i
$233$	9.10777	+	9.10777i	0.596670	+	0.596670i	0.939425	−	0.342755i	$-0.111360\pi$
$233$	9.10777	+	9.10777i	0.596670	+	0.596670i	−0.342755	+	0.939425i	$0.611360\pi$
$234$	−3.27744	+	0.787502i	−0.214253	+	0.0514806i
$235$	1.33654	+	6.63699i	0.0871864	+	0.432949i
$236$	2.55833	+	5.01629i	0.166533	+	0.326533i
$237$	25.0262	−	25.0262i	1.62562	−	1.62562i
$238$	9.64629	+	5.90873i	0.625276	+	0.383006i
$239$	13.2529			0.857258			0.428629	−	0.903481i	$-0.358997\pi$
$239$	13.2529			0.857258			0.428629	+	0.903481i	$0.358997\pi$
$240$	11.8844	−	25.9930i	0.767134	−	1.67784i
$241$	−20.7972			−1.33967			−0.669833	−	0.742512i	$-0.733634\pi$
$241$	−20.7972			−1.33967			−0.669833	+	0.742512i	$0.733634\pi$
$242$	−1.20596	−	0.738695i	−0.0775218	−	0.0474851i
$243$	19.7303	−	19.7303i	1.26570	−	1.26570i
$244$	2.70026	+	5.29458i	0.172866	+	0.338951i
$245$	6.25861	−	9.41491i	0.399848	−	0.601497i
$246$	12.5316	−	3.01108i	0.798983	−	0.191980i
$247$	−1.63150	−	1.63150i	−0.103810	−	0.103810i
$248$	−5.98479	−	0.467576i	−0.380035	−	0.0296911i
$249$		−	3.83308i		−	0.242911i
$250$	−10.6477	+	11.6887i	−0.673421	+	0.739259i
$251$			3.91835i			0.247324i	0.992324	+	0.123662i	$0.0394639\pi$
$251$			3.91835i			0.247324i	−0.992324	+	0.123662i	$0.960536\pi$
$252$	−19.1267	−	6.20661i	−1.20487	−	0.390980i
$253$	−3.47359	−	3.47359i	−0.218382	−	0.218382i
$254$	−5.57794	−	23.2144i	−0.349991	−	1.45660i
$255$	22.6925	−	34.1366i	1.42106	−	2.13772i
$256$	−4.96743	−	15.2094i	−0.310464	−	0.950585i
$257$	8.68561	−	8.68561i	0.541794	−	0.541794i	−0.382261	−	0.924054i	$-0.624854\pi$
$257$	8.68561	−	8.68561i	0.541794	−	0.541794i	0.924054	+	0.382261i	$0.124854\pi$
$258$	7.93888	−	12.9606i	0.494253	−	0.806892i
$259$	−10.1722			−0.632069
$260$	1.15833	−	0.918329i	0.0718364	−	0.0569523i
$261$	−10.3854			−0.642841
$262$	−4.47427	+	7.30447i	−0.276422	+	0.451272i
$263$	−17.1486	+	17.1486i	−1.05743	+	1.05743i	−0.0591800	+	0.998247i	$0.518849\pi$
$263$	−17.1486	+	17.1486i	−1.05743	+	1.05743i	−0.998247	+	0.0591800i	$0.981151\pi$
$264$	−6.86929	+	5.87371i	−0.422775	+	0.361502i
$265$	3.36595	+	16.7146i	0.206769	+	1.02677i
$266$	−3.21580	−	13.3836i	−0.197173	−	0.820598i
$267$	0.0135407	+	0.0135407i	0.000828675	+	0.000828675i
$268$	4.92400	−	15.1741i	0.300781	−	0.926909i
$269$			18.2144i			1.11055i	0.831667	+	0.555275i	$0.187387\pi$
$269$			18.2144i			1.11055i	−0.831667	+	0.555275i	$0.812613\pi$
$270$	−14.6254	+	39.9588i	−0.890076	+	2.43181i
$271$			0.351541i			0.0213546i	0.999943	+	0.0106773i	$0.00339876\pi$
$271$			0.351541i			0.0213546i	−0.999943	+	0.0106773i	$0.996601\pi$
$272$	−3.60698	−	22.6620i	−0.218706	−	1.37408i
$273$	−1.04134	−	1.04134i	−0.0630248	−	0.0630248i
$274$	−16.1906	+	3.89029i	−0.978113	+	0.235021i
$275$	4.61027	−	1.93530i	0.278010	−	0.116703i
$276$	−27.9674	+	14.2635i	−1.68344	+	0.858563i
$277$	6.63217	−	6.63217i	0.398489	−	0.398489i	−0.479211	−	0.877700i	$-0.659077\pi$
$277$	6.63217	−	6.63217i	0.398489	−	0.398489i	0.877700	+	0.479211i	$0.159077\pi$
$278$	1.23668	+	0.757514i	0.0741711	+	0.0454327i
$279$	15.3044			0.916253
$280$	8.75417	−	1.06224i	0.523162	−	0.0634811i
$281$	8.44017			0.503498			0.251749	−	0.967793i	$-0.418994\pi$
$281$	8.44017			0.503498			0.251749	+	0.967793i	$0.418994\pi$
$282$	−11.6676	−	7.14688i	−0.694797	−	0.425590i
$283$	9.73908	−	9.73908i	0.578928	−	0.578928i	−0.355680	−	0.934608i	$-0.615751\pi$
$283$	9.73908	−	9.73908i	0.578928	−	0.578928i	0.934608	+	0.355680i	$0.115751\pi$
$284$	5.19893	−	2.65148i	0.308500	−	0.157336i
$285$	−48.8958	+	9.84652i	−2.89634	+	0.583258i
$286$	−0.454509	+	0.109209i	−0.0268757	+	0.00645768i
$287$	2.81183	+	2.81183i	0.165977	+	0.165977i
$288$	15.6460	+	37.6713i	0.921948	+	2.21980i
$289$		−	15.9109i		−	0.935937i
$290$	4.13116	−	1.91733i	0.242590	−	0.112590i
$291$			46.0527i			2.69966i
$292$	2.23398	−	6.88440i	0.130734	−	0.402879i
$293$	−9.88983	−	9.88983i	−0.577770	−	0.577770i	0.356518	−	0.934288i	$-0.383964\pi$
$293$	−9.88983	−	9.88983i	−0.577770	−	0.577770i	−0.934288	+	0.356518i	$0.883964\pi$
$294$	5.33797	+	22.2156i	0.311317	+	1.29564i
$295$	5.24292	+	3.48526i	0.305255	+	0.202920i
$296$	13.4102	+	15.6832i	0.779452	+	0.911566i
$297$	9.51475	−	9.51475i	0.552102	−	0.552102i
$298$	−4.75411	+	7.76132i	−0.275398	+	0.449601i
$299$	−1.62371			−0.0939016
$300$	−2.67024	−	31.8428i	−0.154166	−	1.83845i
$301$	4.68943			0.270294
$302$	−6.44445	+	10.5209i	−0.370837	+	0.605409i
$303$	0.408238	−	0.408238i	0.0234527	−	0.0234527i
$304$	−16.3949	+	22.6018i	−0.940313	+	1.29630i
$305$	5.53378	+	3.67861i	0.316864	+	0.210637i
$306$	13.6680	+	56.8838i	0.781350	+	3.25183i
$307$	0.352645	+	0.352645i	0.0201265	+	0.0201265i	0.717098	−	0.696972i	$-0.245470\pi$
$307$	0.352645	+	0.352645i	0.0201265	+	0.0201265i	−0.696972	+	0.717098i	$0.745470\pi$
$308$	−2.65246	−	0.860721i	−0.151138	−	0.0490441i
$309$			39.8372i			2.26626i
$310$	−6.08787	+	2.82547i	−0.345768	+	0.160476i
$311$			4.16072i			0.235933i	0.993018	+	0.117967i	$0.0376376\pi$
$311$			4.16072i			0.235933i	−0.993018	+	0.117967i	$0.962362\pi$
$312$	−0.232689	+	2.97832i	−0.0131734	+	0.168614i
$313$	−21.9529	−	21.9529i	−1.24085	−	1.24085i	−0.959648	−	0.281206i	$-0.909266\pi$
$313$	−21.9529	−	21.9529i	−1.24085	−	1.24085i	−0.281206	−	0.959648i	$-0.590734\pi$
$314$	−17.1985	+	4.13245i	−0.970567	+	0.233208i
$315$	−22.0396	+	4.43829i	−1.24179	+	0.250069i
$316$	−10.0642	−	19.7334i	−0.566153	−	1.11009i
$317$	−20.1839	+	20.1839i	−1.13364	+	1.13364i	−0.144076	+	0.989567i	$0.546021\pi$
$317$	−20.1839	+	20.1839i	−1.13364	+	1.13364i	−0.989567	+	0.144076i	$0.953979\pi$
$318$	−29.3838	−	17.9987i	−1.64776	−	1.00932i
$319$	−1.44023			−0.0806374
$320$	−13.1785	−	12.0965i	−0.736702	−	0.676218i
$321$	25.7465			1.43703
$322$	−8.26007	−	5.05961i	−0.460315	−	0.281961i
$323$	−28.3166	+	28.3166i	−1.57558	+	1.57558i
$324$	−19.4134	−	38.0651i	−1.07852	−	2.11473i
$325$	0.625203	−	1.52985i	0.0346800	−	0.0848606i
$326$	28.5528	−	6.86066i	1.58139	−	0.379977i
$327$	42.6243	+	42.6243i	2.35713	+	2.35713i
$328$	0.628308	−	8.04209i	0.0346925	−	0.444050i
$329$		−	4.22160i		−	0.232744i
$330$	−3.47320	+	9.48927i	−0.191193	+	0.522367i
$331$		−	9.56340i		−	0.525652i	−0.964843	−	0.262826i	$-0.915346\pi$
$331$		−	9.56340i		−	0.525652i	0.964843	−	0.262826i	$-0.0846545\pi$
$332$	−2.28194	−	0.740488i	−0.125238	−	0.0406396i
$333$	−37.1991	−	37.1991i	−2.03850	−	2.03850i
$334$	−0.735734	−	3.06198i	−0.0402576	−	0.167544i
$335$	−3.52110	−	17.4851i	−0.192378	−	0.955311i
$336$	−10.4644	+	14.4261i	−0.570881	+	0.787009i
$337$	−0.0148998	+	0.0148998i	−0.000811646	+	0.000811646i	−0.707512	−	0.706701i	$-0.750183\pi$
$337$	−0.0148998	+	0.0148998i	−0.000811646	+	0.000811646i	0.706701	+	0.707512i	$0.250183\pi$
$338$	9.52233	−	15.5457i	0.517947	−	0.845573i
$339$	7.08601			0.384859
$340$	−15.9387	−	20.1041i	−0.864397	−	1.09030i
$341$	2.12239			0.114934
$342$	37.1829	−	60.7029i	2.01062	−	3.28244i
$343$	−11.8862	+	11.8862i	−0.641796	+	0.641796i
$344$	−6.18217	−	7.23003i	−0.333320	−	0.389817i
$345$	−19.4315	+	29.2310i	−1.04615	+	1.57374i
$346$	4.19162	+	17.4447i	0.225343	+	0.937834i
$347$	−2.24537	−	2.24537i	−0.120538	−	0.120538i	0.644265	−	0.764802i	$-0.277163\pi$
$347$	−2.24537	−	2.24537i	−0.120538	−	0.120538i	−0.764802	+	0.644265i	$0.777163\pi$
$348$	−2.84098	+	8.75497i	−0.152292	+	0.469316i
$349$			15.1840i			0.812779i	0.913700	+	0.406389i	$0.133212\pi$
$349$			15.1840i			0.812779i	−0.913700	+	0.406389i	$0.866788\pi$
$350$	7.94763	−	5.83438i	0.424819	−	0.311861i
$351$		−	4.44762i		−	0.237397i
$352$	2.16976	+	5.22419i	0.115648	+	0.278450i
$353$	1.26856	+	1.26856i	0.0675186	+	0.0675186i	0.740060	−	0.672541i	$-0.234797\pi$
$353$	1.26856	+	1.26856i	0.0675186	+	0.0675186i	−0.672541	+	0.740060i	$0.734797\pi$
$354$	−12.3713	+	2.97258i	−0.657528	+	0.157991i
$355$	3.61216	−	5.43382i	0.191714	−	0.288397i
$356$	0.0106770	−	0.00544531i	0.000565879	−	0.000288601i
$357$	−18.0737	+	18.0737i	−0.956562	+	0.956562i
$358$	10.3617	+	6.34692i	0.547630	+	0.335445i
$359$	6.54287			0.345319			0.172660	−	0.984982i	$-0.444764\pi$
$359$	6.54287			0.345319			0.172660	+	0.984982i	$0.444764\pi$
$360$	35.8981	+	28.1289i	1.89199	+	1.48253i
$361$	29.7272			1.56459
$362$	−1.20968	−	0.740977i	−0.0635794	−	0.0389449i
$363$	2.25953	−	2.25953i	0.118595	−	0.118595i
$364$	−0.821110	+	0.418770i	−0.0430378	+	0.0219495i
$365$	−1.59750	−	7.93284i	−0.0836169	−	0.415224i
$366$	−13.0576	+	3.13749i	−0.682533	+	0.163999i
$367$	−5.88547	−	5.88547i	−0.307219	−	0.307219i	0.536611	−	0.843830i	$-0.319704\pi$
$367$	−5.88547	−	5.88547i	−0.307219	−	0.307219i	−0.843830	+	0.536611i	$0.819704\pi$
$368$	3.08864	+	19.4053i	0.161006	+	1.01157i
$369$			20.5654i			1.07059i
$370$	21.6648	+	7.92962i	1.12630	+	0.412241i
$371$		−	10.6317i		−	0.551970i
$372$	4.18660	−	12.9017i	0.217065	−	0.668924i
$373$	23.2730	+	23.2730i	1.20503	+	1.20503i	0.972617	+	0.232414i	$0.0746623\pi$
$373$	23.2730	+	23.2730i	1.20503	+	1.20503i	0.232414	+	0.972617i	$0.425338\pi$
$374$	1.89546	+	7.88854i	0.0980118	+	0.407907i
$375$	−20.0592	−	29.5634i	−1.03585	−	1.52665i
$376$	−6.50874	+	5.56542i	−0.335663	+	0.287014i
$377$	−0.336614	+	0.336614i	−0.0173365	+	0.0173365i
$378$	13.8591	−	22.6257i	0.712838	−	1.16374i
$379$	5.39863			0.277309			0.138654	−	0.990341i	$-0.455722\pi$
$379$	5.39863			0.277309			0.138654	+	0.990341i	$0.455722\pi$
$380$	−3.58395	+	31.0113i	−0.183853	+	1.59084i
$381$	53.9464			2.76376
$382$	−9.93751	+	16.2235i	−0.508447	+	0.830065i
$383$	−9.81025	+	9.81025i	−0.501281	+	0.501281i	−0.911836	−	0.410555i	$-0.865335\pi$
$383$	−9.81025	+	9.81025i	−0.501281	+	0.501281i	0.410555	+	0.911836i	$0.365335\pi$
$384$	36.0372	−	2.88449i	1.83902	−	0.147198i
$385$	−3.05641	+	0.615493i	−0.155769	+	0.0313684i
$386$	−7.64994	−	31.8376i	−0.389371	−	1.62049i
$387$	17.1490	+	17.1490i	0.871732	+	0.871732i
$388$	27.4165	+	8.89663i	1.39186	+	0.451658i
$389$			5.54498i			0.281142i	0.990071	+	0.140571i	$0.0448938\pi$
$389$			5.54498i			0.281142i	−0.990071	+	0.140571i	$0.955106\pi$
$390$	1.40609	+	3.02962i	0.0712003	+	0.153411i
$391$			28.1814i			1.42520i
$392$	14.2568	+	1.11385i	0.720078	+	0.0562578i
$393$	−13.6860	−	13.6860i	−0.690365	−	0.690365i
$394$	19.7560	−	4.74697i	0.995292	−	0.239149i
$395$	−20.6250	−	13.7106i	−1.03776	−	0.689854i
$396$	−6.55229	−	12.8475i	−0.329265	−	0.645611i
$397$	−5.04348	+	5.04348i	−0.253125	+	0.253125i	−0.822251	−	0.569126i	$-0.807282\pi$
$397$	−5.04348	+	5.04348i	−0.253125	+	0.253125i	0.569126	+	0.822251i	$0.307282\pi$
$398$	2.01428	+	1.23383i	0.100967	+	0.0618462i
$399$	31.1012			1.55701
$400$	−19.4728	−	4.56184i	−0.973640	−	0.228092i
$401$	−28.1263			−1.40456			−0.702281	−	0.711900i	$-0.747835\pi$
$401$	−28.1263			−1.40456			−0.702281	+	0.711900i	$0.747835\pi$
$402$	30.7382	+	18.8284i	1.53308	+	0.939073i
$403$	0.496051	−	0.496051i	0.0247100	−	0.0247100i
$404$	−0.164171	−	0.321901i	−0.00816781	−	0.0160152i
$405$	−39.7849	−	26.4472i	−1.97693	−	1.31417i
$406$	−2.76132	+	0.663491i	−0.137042	+	0.0329285i
$407$	−5.15870	−	5.15870i	−0.255707	−	0.255707i
$408$	51.6924	+	4.03859i	2.55915	+	0.199940i
$409$		−	29.4667i		−	1.45703i	−0.685029	−	0.728516i	$-0.740210\pi$
$409$		−	29.4667i		−	1.45703i	0.685029	−	0.728516i	$-0.259790\pi$
$410$	−3.79674	−	8.18060i	−0.187508	−	0.404011i
$411$		−	37.6245i		−	1.85588i
$412$	23.7162	+	7.69589i	1.16841	+	0.379149i
$413$	−2.77588	−	2.77588i	−0.136592	−	0.136592i
$414$	−11.7039	−	48.7093i	−0.575214	−	2.39393i
$415$	−2.62947	+	0.529516i	−0.129075	+	0.0259929i
$416$	1.72813	+	0.713890i	0.0847286	+	0.0350013i
$417$	−2.31709	+	2.31709i	−0.113469	+	0.113469i
$418$	5.15645	−	8.41816i	0.252210	−	0.411746i
$419$	−37.1639			−1.81557			−0.907787	−	0.419432i	$-0.862229\pi$
$419$	−37.1639			−1.81557			−0.907787	+	0.419432i	$0.862229\pi$
$420$	−2.28754	+	19.7936i	−0.111620	+	0.965831i
$421$	2.51184			0.122420			0.0612099	−	0.998125i	$-0.480504\pi$
$421$	2.51184			0.122420			0.0612099	+	0.998125i	$0.480504\pi$
$422$	−16.1996	+	26.4467i	−0.788585	+	1.28740i
$423$	15.4382	−	15.4382i	0.750629	−	0.750629i
$424$	−16.3916	+	14.0160i	−0.796048	+	0.680676i
$425$	−26.5523	−	10.8511i	−1.28798	−	0.526358i
$426$	3.08081	+	12.8217i	0.149266	+	0.621216i
$427$	−2.92987	−	2.92987i	−0.141786	−	0.141786i
$428$	4.97380	−	15.3276i	0.240418	−	0.740889i
$429$		−	1.05621i		−	0.0509941i
$430$	−9.98760	−	3.65559i	−0.481645	−	0.176288i
$431$		−	33.8843i		−	1.63215i	−0.577947	−	0.816074i	$-0.696146\pi$
$431$		−	33.8843i		−	1.63215i	0.577947	−	0.816074i	$-0.303854\pi$
$432$	−53.1545	+	8.46032i	−2.55740	+	0.407047i
$433$	9.47738	+	9.47738i	0.455454	+	0.455454i	0.897160	−	0.441706i	$-0.145627\pi$
$433$	9.47738	+	9.47738i	0.455454	+	0.455454i	−0.441706	+	0.897160i	$0.645627\pi$
$434$	4.06922	−	0.977752i	0.195329	−	0.0469336i
$435$	2.03156	+	10.0883i	0.0974057	+	0.483696i
$436$	33.6098	−	17.1412i	1.60962	−	0.820913i
$437$	24.2473	−	24.2473i	1.15991	−	1.15991i
$438$	13.9457	+	8.54229i	0.666351	+	0.408166i
$439$	11.8365			0.564924			0.282462	−	0.959278i	$-0.408849\pi$
$439$	11.8365			0.564924			0.282462	+	0.959278i	$0.408849\pi$
$440$	4.97828	+	3.90087i	0.237330	+	0.185967i
$441$	−36.4578			−1.73609
$442$	2.28674	+	1.40072i	0.108769	+	0.0666254i
$443$	15.2136	−	15.2136i	0.722821	−	0.722821i	−0.246358	−	0.969179i	$-0.579234\pi$
$443$	15.2136	−	15.2136i	0.722821	−	0.722821i	0.969179	+	0.246358i	$0.0792340\pi$
$444$	−41.5351	+	21.1831i	−1.97117	+	1.00531i
$445$	0.00741824	−	0.0111594i	0.000351658	−	0.000529004i
$446$	−32.8872	+	7.90215i	−1.55726	+	0.374177i
$447$	−14.5419	−	14.5419i	−0.687810	−	0.687810i
$448$	6.56673	+	9.01667i	0.310249	+	0.425997i
$449$			2.10304i			0.0992484i	0.998768	+	0.0496242i	$0.0158024\pi$
$449$			2.10304i			0.0992484i	−0.998768	+	0.0496242i	$0.984198\pi$
$450$	50.4000	+	7.72802i	2.37588	+	0.364302i
$451$			2.85197i			0.134294i
$452$	1.36890	−	4.21851i	0.0643877	−	0.198422i
$453$	−19.7124	−	19.7124i	−0.926168	−	0.926168i
$454$	−7.45318	−	31.0187i	−0.349795	−	1.45578i
$455$	−0.570498	+	0.858207i	−0.0267453	+	0.0402334i
$456$	−41.0013	−	47.9510i	−1.92006	−	2.24551i
$457$	−19.2880	+	19.2880i	−0.902256	+	0.902256i	−0.995631	−	0.0933746i	$-0.970235\pi$
$457$	−19.2880	+	19.2880i	−0.902256	+	0.902256i	0.0933746	+	0.995631i	$0.470235\pi$
$458$	−18.7925	+	30.6797i	−0.878116	+	1.43357i
$459$	−77.1938			−3.60310
$460$	13.6482	+	17.2151i	0.636351	+	0.802656i
$461$	−36.5493			−1.70227			−0.851136	−	0.524945i	$-0.824086\pi$
$461$	−36.5493			−1.70227			−0.851136	+	0.524945i	$0.824086\pi$
$462$	3.29122	−	5.37308i	0.153122	−	0.249978i
$463$	−6.96766	+	6.96766i	−0.323815	+	0.323815i	−0.850228	−	0.526414i	$-0.823536\pi$
$463$	−6.96766	+	6.96766i	−0.323815	+	0.323815i	0.526414	+	0.850228i	$0.323536\pi$
$464$	4.66326	+	3.38263i	0.216486	+	0.157035i
$465$	−2.99380	−	14.8666i	−0.138834	−	0.689422i
$466$	4.25570	+	17.7114i	0.197142	+	0.820466i
$467$	12.5061	+	12.5061i	0.578715	+	0.578715i	0.934549	−	0.355834i	$-0.115803\pi$
$467$	12.5061	+	12.5061i	0.578715	+	0.578715i	−0.355834	+	0.934549i	$0.615803\pi$
$468$	−4.53417	−	1.47133i	−0.209592	−	0.0680124i
$469$			11.1218i			0.513555i
$470$	−3.29090	+	8.99121i	−0.151798	+	0.414734i
$471$		−	39.9666i		−	1.84156i
$472$	−0.620273	+	7.93925i	−0.0285504	+	0.365434i
$473$	2.37819	+	2.37819i	0.109349	+	0.109349i
$474$	48.6671	−	11.6937i	2.23536	−	0.537111i
$475$	13.5093	+	32.1820i	0.619849	+	1.47661i
$476$	7.26825	+	14.2513i	0.333140	+	0.653209i
$477$	38.8795	−	38.8795i	1.78017	−	1.78017i
$478$	15.9824	+	9.78984i	0.731018	+	0.447777i
$479$	19.3221			0.882850			0.441425	−	0.897298i	$-0.354473\pi$
$479$	19.3221			0.882850			0.441425	+	0.897298i	$0.354473\pi$
$480$	33.5330	−	22.5675i	1.53056	−	1.03006i
$481$	−2.41141			−0.109951
$482$	−25.0805	−	15.3628i	−1.14239	−	0.699756i
$483$	15.4764	−	15.4764i	0.704201	−	0.704201i
$484$	−0.908659	−	1.78167i	−0.0413027	−	0.0809849i
$485$	31.5918	−	6.36189i	1.43451	−	0.288879i
$486$	38.3686	−	9.21920i	1.74043	−	0.418191i
$487$	−4.35742	−	4.35742i	−0.197454	−	0.197454i	0.601454	−	0.798908i	$-0.294588\pi$
$487$	−4.35742	−	4.35742i	−0.197454	−	0.197454i	−0.798908	+	0.601454i	$0.794588\pi$
$488$	−0.654684	+	8.37970i	−0.0296361	+	0.379331i
$489$			66.3521i			3.00055i
$490$	14.5024	−	6.73076i	0.655150	−	0.304065i
$491$			3.27844i			0.147954i	0.997260	+	0.0739771i	$0.0235692\pi$
$491$			3.27844i			0.147954i	−0.997260	+	0.0739771i	$0.976431\pi$
$492$	17.3368	+	5.62577i	0.781602	+	0.253629i
$493$	5.84234	+	5.84234i	0.263126	+	0.263126i
$494$	−0.762334	−	3.17269i	−0.0342990	−	0.142746i
$495$	−13.4279	−	8.92630i	−0.603541	−	0.401207i
$496$	−6.87200	−	4.98481i	−0.308562	−	0.223825i
$497$	−2.87695	+	2.87695i	−0.129049	+	0.129049i
$498$	2.83148	−	4.62252i	0.126881	−	0.207140i
$499$	19.3590			0.866627			0.433313	−	0.901243i	$-0.357344\pi$
$499$	19.3590			0.866627			0.433313	+	0.901243i	$0.357344\pi$
$500$	−21.4751	+	6.23065i	−0.960395	+	0.278643i
$501$	7.11556			0.317900
$502$	−2.89447	+	4.72536i	−0.129186	+	0.210903i
$503$	−10.7102	+	10.7102i	−0.477542	+	0.477542i	−0.904345	−	0.426803i	$-0.859640\pi$
$503$	−10.7102	+	10.7102i	−0.477542	+	0.477542i	0.426803	+	0.904345i	$0.359640\pi$
$504$	−18.4812	−	21.6137i	−0.823219	−	0.962752i
$505$	−0.336444	−	0.223653i	−0.0149716	−	0.00995243i
$506$	−1.62307	−	6.75491i	−0.0721543	−	0.300292i
$507$	29.1270	+	29.1270i	1.29358	+	1.29358i
$508$	10.4216	−	32.1159i	0.462383	−	1.42491i
$509$			4.64711i			0.205979i	0.994682	+	0.102990i	$0.0328409\pi$
$509$			4.64711i			0.205979i	−0.994682	+	0.102990i	$0.967159\pi$
$510$	52.5827	−	24.4044i	2.32840	−	1.08065i
$511$			5.04586i			0.223216i
$512$	5.24458	−	22.0112i	0.231780	−	0.972768i
$513$	66.4176	+	66.4176i	2.93241	+	2.93241i
$514$	16.8905	−	4.05845i	0.745007	−	0.179010i
$515$	27.3280	−	5.50326i	1.20422	−	0.242503i
$516$	19.1479	−	9.76551i	0.842938	−	0.429903i
$517$	2.14093	−	2.14093i	0.0941582	−	0.0941582i
$518$	−12.2672	−	7.51415i	−0.538990	−	0.330153i
$519$	−40.5388			−1.77945
$520$	2.07526	−	0.251814i	0.0910060	−	0.0110428i
$521$	−22.7241			−0.995559			−0.497779	−	0.867304i	$-0.665851\pi$
$521$	−22.7241			−0.995559			−0.497779	+	0.867304i	$0.665851\pi$
$522$	−12.5243	−	7.67165i	−0.548176	−	0.335779i
$523$	19.6005	−	19.6005i	0.857071	−	0.857071i	−0.133921	−	0.990992i	$-0.542757\pi$
$523$	19.6005	−	19.6005i	0.857071	−	0.857071i	0.990992	+	0.133921i	$0.0427568\pi$
$524$	−10.7916	+	5.50374i	−0.471431	+	0.240432i
$525$	8.62262	+	20.5409i	0.376322	+	0.896477i
$526$	−33.3480	+	8.01286i	−1.45404	+	0.349377i
$527$	−8.60955	−	8.60955i	−0.375038	−	0.375038i
$528$	−12.6229	+	2.00913i	−0.549343	+	0.0874360i
$529$		−	1.13160i		−	0.0492000i
$530$	−8.28782	+	22.6435i	−0.360000	+	0.983571i
$531$		−	20.3024i		−	0.881051i
$532$	6.00825	−	18.5155i	0.260491	−	0.802747i
$533$	0.666570	+	0.666570i	0.0288724	+	0.0288724i
$534$	0.00632702	+	0.0263318i	0.000273797	+	0.00113949i
$535$	−3.55672	−	17.6619i	−0.153770	−	0.763591i
$536$	17.1472	−	14.6620i	0.740646	−	0.633303i
$537$	−19.4140	+	19.4140i	−0.837777	+	0.837777i
$538$	−13.4549	+	21.9657i	−0.580081	+	0.947011i
$539$	−5.05590			−0.217773
$540$	−47.1550	+	37.3848i	−2.02923	+	1.60879i
$541$	31.7244			1.36394			0.681969	−	0.731382i	$-0.261124\pi$
$541$	31.7244			1.36394			0.681969	+	0.731382i	$0.261124\pi$
$542$	−0.259682	+	0.423943i	−0.0111543	+	0.0182099i
$543$	2.26651	−	2.26651i	0.0972652	−	0.0972652i
$544$	12.3904	−	29.9938i	0.531235	−	1.28597i
$545$	23.3517	−	35.1283i	1.00028	−	1.50473i
$546$	−0.486577	−	2.02504i	−0.0208236	−	0.0866638i
$547$	−2.37992	−	2.37992i	−0.101758	−	0.101758i	0.654395	−	0.756153i	$-0.272923\pi$
$547$	−2.37992	−	2.37992i	−0.101758	−	0.101758i	−0.756153	+	0.654395i	$0.772923\pi$
$548$	−22.3989	−	7.26843i	−0.956835	−	0.310492i
$549$		−	21.4287i		−	0.914557i
$550$	6.98938	+	1.07171i	0.298028	+	0.0456977i
$551$		−	10.0535i		−	0.428294i
$552$	−44.2639	−	3.45822i	−1.88400	−	0.147192i
$553$	10.9199	+	10.9199i	0.464363	+	0.464363i
$554$	12.8973	−	3.09895i	0.547952	−	0.131662i
$555$	−28.8581	+	43.4116i	−1.22496	+	1.84272i
$556$	0.931808	+	1.82706i	0.0395175	+	0.0774845i
$557$	−8.85191	+	8.85191i	−0.375068	+	0.375068i	−0.869319	−	0.494251i	$-0.835442\pi$
$557$	−8.85191	+	8.85191i	−0.375068	+	0.375068i	0.494251	+	0.869319i	$0.335442\pi$
$558$	18.4565	+	11.3053i	0.781325	+	0.478592i
$559$	1.11167			0.0470187
$560$	11.3418	+	5.18565i	0.479279	+	0.219134i
$561$	−18.3317			−0.773965
$562$	10.1785	+	6.23471i	0.429353	+	0.262995i
$563$	−14.5178	+	14.5178i	−0.611854	+	0.611854i	−0.943429	−	0.331575i	$-0.892420\pi$
$563$	−14.5178	+	14.5178i	−0.611854	+	0.611854i	0.331575	+	0.943429i	$0.392420\pi$
$564$	−8.79128	−	17.2376i	−0.370180	−	0.725836i
$565$	−0.978888	−	4.86096i	−0.0411821	−	0.204502i
$566$	18.9391	−	4.55069i	0.796070	−	0.191280i
$567$	21.0642	+	21.0642i	0.884612	+	0.884612i
$568$	8.22832	+	0.642857i	0.345253	+	0.0269737i
$569$		−	9.77585i		−	0.409825i	−0.978780	−	0.204912i	$-0.934309\pi$
$569$		−	9.77585i		−	0.409825i	0.978780	−	0.204912i	$-0.0656910\pi$
$570$	−66.2398	−	24.2446i	−2.77448	−	1.01550i
$571$			22.3186i			0.934006i	0.884256	+	0.467003i	$0.154666\pi$
$571$			22.3186i			0.934006i	−0.884256	+	0.467003i	$0.845334\pi$
$572$	−0.628790	−	0.204042i	−0.0262910	−	0.00853141i
$573$	−30.3970	−	30.3970i	−1.26985	−	1.26985i
$574$	1.31386	+	5.46803i	0.0548394	+	0.228231i
$575$	22.7366	+	9.29177i	0.948182	+	0.387494i
$576$	−8.95927	+	56.9876i	−0.373303	+	2.37448i
$577$	11.7451	−	11.7451i	0.488955	−	0.488955i	−0.419021	−	0.907976i	$-0.637627\pi$
$577$	11.7451	−	11.7451i	0.488955	−	0.488955i	0.907976	+	0.419021i	$0.137627\pi$
$578$	11.7533	−	19.1879i	0.488874	−	0.798111i
$579$	73.9855			3.07473
$580$	6.39831	+	0.739448i	0.265676	+	0.0307039i
$581$	1.67253			0.0693882
$582$	−34.0189	+	55.5375i	−1.41013	+	2.30210i
$583$	5.39174	−	5.39174i	0.223303	−	0.223303i
$584$	7.77955	−	6.65205i	0.321920	−	0.275264i
$585$	−5.22469	+	1.05214i	−0.216014	+	0.0435005i
$586$	−4.62113	−	19.2323i	−0.190897	−	0.794477i
$587$	8.44304	+	8.44304i	0.348482	+	0.348482i	0.859544	−	0.511062i	$-0.170748\pi$
$587$	8.44304	+	8.44304i	0.348482	+	0.348482i	−0.511062	+	0.859544i	$0.670748\pi$
$588$	−9.97321	+	30.7342i	−0.411288	+	1.26746i
$589$			14.8153i			0.610455i
$590$	3.74819	+	8.07600i	0.154311	+	0.332483i
$591$			45.9097i			1.88847i
$592$	4.58701	+	28.8193i	0.188525	+	1.18446i
$593$	−25.7919	−	25.7919i	−1.05914	−	1.05914i	−0.998137	−	0.0610072i	$-0.980569\pi$
$593$	−25.7919	−	25.7919i	−1.05914	−	1.05914i	−0.0610072	−	0.998137i	$-0.519431\pi$
$594$	18.5029	−	4.44587i	0.759182	−	0.182416i
$595$	14.8952	+	9.90167i	0.610644	+	0.405929i
$596$	−11.4665	+	5.84797i	−0.469686	+	0.239542i
$597$	−3.77405	+	3.77405i	−0.154461	+	0.154461i
$598$	−1.95812	−	1.19943i	−0.0800736	−	0.0490482i
$599$	47.8167			1.95374			0.976868	−	0.213844i	$-0.0685985\pi$
$599$	47.8167			1.95374			0.976868	+	0.213844i	$0.0685985\pi$
$600$	20.3019	−	40.3735i	0.828823	−	1.64824i
$601$	−22.7524			−0.928090			−0.464045	−	0.885812i	$-0.653602\pi$
$601$	−22.7524			−0.928090			−0.464045	+	0.885812i	$0.653602\pi$
$602$	5.65525	+	3.46406i	0.230491	+	0.141185i
$603$	−40.6716	+	40.6716i	−1.65628	+	1.65628i
$604$	−15.5434	+	7.92723i	−0.632454	+	0.322555i
$605$	−1.86216	−	1.23788i	−0.0757077	−	0.0503271i
$606$	0.793880	−	0.190754i	0.0322492	−	0.00774883i
$607$	−4.82956	−	4.82956i	−0.196026	−	0.196026i	0.602268	−	0.798294i	$-0.294264\pi$
$607$	−4.82956	−	4.82956i	−0.196026	−	0.196026i	−0.798294	+	0.602268i	$0.794264\pi$
$608$	−36.4674	+	15.1459i	−1.47895	+	0.614249i
$609$		−	6.41688i		−	0.260025i
$610$	3.95613	+	8.52402i	0.160179	+	0.345128i
$611$		−	1.00077i		−	0.0404868i
$612$	−25.5367	+	78.6959i	−1.03226	+	3.18109i
$613$	26.6613	+	26.6613i	1.07684	+	1.07684i	0.996791	+	0.0800507i	$0.0255082\pi$
$613$	26.6613	+	26.6613i	1.07684	+	1.07684i	0.0800507	+	0.996791i	$0.474492\pi$
$614$	0.164777	+	0.685771i	0.00664986	+	0.0276755i
$615$	19.9770	−	4.02293i	0.805552	−	0.162220i
$616$	−2.56294	−	2.99735i	−0.103264	−	0.120767i
$617$	33.6638	−	33.6638i	1.35525	−	1.35525i	0.475585	−	0.879670i	$-0.342237\pi$
$617$	33.6638	−	33.6638i	1.35525	−	1.35525i	0.879670	−	0.475585i	$-0.157763\pi$
$618$	−29.4275	+	48.0419i	−1.18375	+	1.93253i
$619$	−37.3190			−1.49998			−0.749989	−	0.661450i	$-0.769941\pi$
$619$	−37.3190			−1.49998			−0.749989	+	0.661450i	$0.769941\pi$
$620$	−9.42887	−	1.08969i	−0.378672	−	0.0437629i
$621$	66.1006			2.65253
$622$	−3.07351	+	5.01765i	−0.123236	+	0.201189i
$623$	−0.00590834	+	0.00590834i	−0.000236713	+	0.000236713i
$624$	−2.48069	+	3.41984i	−0.0993069	+	0.136903i
$625$	−17.5093	+	17.8445i	−0.700371	+	0.713779i
$626$	−10.2577	−	42.6908i	−0.409982	−	1.70627i
$627$	15.7726	+	15.7726i	0.629898	+	0.629898i
$628$	−23.7932	−	7.72089i	−0.949454	−	0.308097i
$629$			41.8529i			1.66878i
$630$	−29.8573	−	10.9282i	−1.18955	−	0.435389i
$631$		−	30.0189i		−	1.19503i	−0.801856	−	0.597517i	$-0.796154\pi$
$631$		−	30.0189i		−	1.19503i	0.801856	−	0.597517i	$-0.203846\pi$
$632$	2.44008	−	31.2320i	0.0970610	−	1.24234i
$633$	−49.5516	−	49.5516i	−1.96950	−	1.96950i
$634$	−39.2507	+	9.43116i	−1.55884	+	0.374559i
$635$	−7.45237	−	37.0069i	−0.295738	−	1.46857i
$636$	−22.1400	−	43.4113i	−0.877908	−	1.72137i
$637$	−1.18168	+	1.18168i	−0.0468198	+	0.0468198i
$638$	−1.73685	−	1.06389i	−0.0687627	−	0.0421198i
$639$	−21.0416			−0.832395
$640$	−6.95706	−	24.3228i	−0.275002	−	0.961444i
$641$	−20.1082			−0.794225			−0.397112	−	0.917770i	$-0.629988\pi$
$641$	−20.1082			−0.794225			−0.397112	+	0.917770i	$0.629988\pi$
$642$	31.0491	+	19.0188i	1.22541	+	0.750612i
$643$	23.8112	−	23.8112i	0.939023	−	0.939023i	−0.0592221	−	0.998245i	$-0.518862\pi$
$643$	23.8112	−	23.8112i	0.939023	−	0.939023i	0.998245	+	0.0592221i	$0.0188620\pi$
$644$	−6.22376	−	12.2033i	−0.245251	−	0.480879i
$645$	13.3037	−	20.0130i	0.523834	−	0.788010i
$646$	−55.0659	+	13.2312i	−2.16654	+	0.520576i
$647$	−1.29811	−	1.29811i	−0.0510341	−	0.0510341i	0.681129	−	0.732163i	$-0.261489\pi$
$647$	−1.29811	−	1.29811i	−0.0510341	−	0.0510341i	−0.732163	+	0.681129i	$0.761489\pi$
$648$	4.70682	−	60.2454i	0.184901	−	2.36666i
$649$		−	2.81550i		−	0.110518i
$650$	1.88406	−	1.38309i	0.0738988	−	0.0542494i
$651$			9.45622i			0.370618i
$652$	39.5013	+	12.8181i	1.54699	+	0.501997i
$653$	25.0283	+	25.0283i	0.979435	+	0.979435i	0.999793	−	0.0203580i	$-0.00648060\pi$
$653$	25.0283	+	25.0283i	0.979435	+	0.979435i	−0.0203580	+	0.999793i	$0.506481\pi$
$654$	19.9167	+	82.8894i	0.778803	+	3.24123i
$655$	−7.49785	+	11.2791i	−0.292965	+	0.440711i
$656$	6.69836	−	9.23428i	0.261527	−	0.360538i
$657$	−18.4524	+	18.4524i	−0.719897	+	0.719897i
$658$	3.11848	−	5.09106i	0.121571	−	0.198470i
$659$	−45.0742			−1.75584			−0.877921	−	0.478806i	$-0.841070\pi$
$659$	−45.0742			−1.75584			−0.877921	+	0.478806i	$0.841070\pi$
$660$	−11.1982	+	8.87801i	−0.435890	+	0.345576i
$661$	17.0030			0.661339			0.330670	−	0.943747i	$-0.392725\pi$
$661$	17.0030			0.661339			0.330670	+	0.943747i	$0.392725\pi$
$662$	7.06443	−	11.5330i	0.274567	−	0.448244i
$663$	−4.28453	+	4.28453i	−0.166397	+	0.166397i
$664$	−2.20493	−	2.57866i	−0.0855677	−	0.100071i
$665$	−4.29644	−	21.3352i	−0.166609	−	0.827345i
$666$	−17.3817	−	72.3393i	−0.673527	−	2.80309i
$667$	−5.00276	−	5.00276i	−0.193708	−	0.193708i
$668$	1.37461	−	4.23610i	0.0531853	−	0.163900i
$669$		−	76.4247i		−	2.95475i
$670$	8.66984	−	23.6872i	0.334945	−	0.915118i
$671$		−	2.97170i		−	0.114721i
$672$	−23.2761	+	9.66724i	−0.897896	+	0.372922i
$673$	12.8409	+	12.8409i	0.494979	+	0.494979i	0.909871	−	0.414892i	$-0.136181\pi$
$673$	12.8409	+	12.8409i	0.494979	+	0.494979i	−0.414892	+	0.909871i	$0.636181\pi$
$674$	−0.0289750	+	0.00696211i	−0.00111607	+	0.000268170i
$675$	−25.4518	+	62.2795i	−0.979639	+	2.39714i
$676$	22.9670	−	11.7133i	0.883347	−	0.450511i
$677$	6.11728	−	6.11728i	0.235106	−	0.235106i	−0.579714	−	0.814820i	$-0.696836\pi$
$677$	6.11728	−	6.11728i	0.235106	−	0.235106i	0.814820	+	0.579714i	$0.196836\pi$
$678$	8.54541	+	5.23440i	0.328185	+	0.201026i
$679$	−20.0947			−0.771163
$680$	−4.37054	−	36.0185i	−0.167602	−	1.38125i
$681$	72.0825			2.76221
$682$	2.55951	+	1.56780i	0.0980087	+	0.0600342i
$683$	10.7880	−	10.7880i	0.412791	−	0.412791i	−0.469918	−	0.882710i	$-0.655717\pi$
$683$	10.7880	−	10.7880i	0.412791	−	0.412791i	0.882710	+	0.469918i	$0.155717\pi$
$684$	89.6818	−	45.7382i	3.42907	−	1.74884i
$685$	−25.8101	+	5.19759i	−0.986155	+	0.198590i
$686$	−23.1145	+	5.55396i	−0.882518	+	0.212051i
$687$	−57.4827	−	57.4827i	−2.19310	−	2.19310i
$688$	−2.11463	−	13.2858i	−0.0806197	−	0.506517i
$689$		−	2.52034i		−	0.0960173i
$690$	−45.0263	+	20.8974i	−1.71412	+	0.795549i
$691$		−	8.07888i		−	0.307335i	−0.988123	−	0.153667i	$-0.950892\pi$
$691$		−	8.07888i		−	0.307335i	0.988123	−	0.153667i	$-0.0491085\pi$
$692$	−7.83143	+	24.1339i	−0.297706	+	0.917433i
$693$	7.10945	+	7.10945i	0.270066	+	0.270066i
$694$	−1.04917	−	4.36645i	−0.0398260	−	0.165748i
$695$	1.90960	+	1.26942i	0.0724354	+	0.0481518i
$696$	−9.89335	+	8.45949i	−0.375006	+	0.320656i
$697$	11.5691	−	11.5691i	0.438212	−	0.438212i
$698$	−11.2163	+	18.3112i	−0.424544	+	0.693089i
$699$	−41.1585			−1.55676
$700$	13.8943	−	1.16513i	0.525156	−	0.0440379i
$701$	14.4120			0.544334			0.272167	−	0.962250i	$-0.412260\pi$
$701$	14.4120			0.544334			0.272167	+	0.962250i	$0.412260\pi$
$702$	3.28544	−	5.36364i	0.124001	−	0.202437i
$703$	36.0103	−	36.0103i	1.35815	−	1.35815i
$704$	−1.24245	+	7.90293i	−0.0468268	+	0.297853i
$705$	−18.0164	−	11.9765i	−0.678538	−	0.451062i
$706$	0.592748	+	2.46690i	0.0223084	+	0.0928432i
$707$	0.178131	+	0.178131i	0.00669930	+	0.00669930i
$708$	−17.1151	−	5.55383i	−0.643224	−	0.208726i
$709$		−	45.0167i		−	1.69064i	−0.534261	−	0.845319i	$-0.679410\pi$
$709$		−	45.0167i		−	1.69064i	0.534261	−	0.845319i	$-0.320590\pi$
$710$	8.37004	−	3.88466i	0.314122	−	0.145789i
$711$			79.8672i			2.99525i
$712$	0.0168984	+	0.00132023i	0.000633294	+	4.94776e-5i
$713$	7.37231	+	7.37231i	0.276095	+	0.276095i
$714$	−35.1470	+	8.44513i	−1.31534	+	0.316051i
$715$	−0.724550	+	0.145908i	−0.0270966	+	0.00545666i
$716$	7.80726	+	15.3082i	0.291771	+	0.572094i
$717$	−29.9453	+	29.9453i	−1.11833	+	1.11833i
$718$	7.89041	+	4.83318i	0.294467	+	0.180373i
$719$	−30.8823			−1.15171			−0.575857	−	0.817550i	$-0.695332\pi$
$719$	−30.8823			−1.15171			−0.575857	+	0.817550i	$0.695332\pi$
$720$	22.5128	+	60.4400i	0.839001	+	2.25247i
$721$	−17.3826			−0.647362
$722$	35.8497	+	21.9593i	1.33419	+	0.817242i
$723$	46.9919	−	46.9919i	1.74765	−	1.74765i
$724$	−0.911466	−	1.78717i	−0.0338744	−	0.0664197i
$725$	6.63985	−	2.78727i	0.246598	−	0.103517i
$726$	4.39400	−	1.05579i	0.163076	−	0.0391840i
$727$	20.3550	+	20.3550i	0.754924	+	0.754924i	0.975394	−	0.220470i	$-0.0707590\pi$
$727$	20.3550	+	20.3550i	0.754924	+	0.754924i	−0.220470	+	0.975394i	$0.570759\pi$
$728$	−1.29957	−	0.101532i	−0.0481651	−	0.00376301i
$729$			25.0678i			0.928437i
$730$	3.93344	−	10.7467i	0.145583	−	0.397754i
$731$		−	19.2944i		−	0.713629i
$732$	−18.0646	−	5.86194i	−0.667686	−	0.216663i
$733$	−19.0629	−	19.0629i	−0.704106	−	0.704106i	0.261184	−	0.965289i	$-0.415887\pi$
$733$	−19.0629	−	19.0629i	−0.704106	−	0.704106i	−0.965289	+	0.261184i	$0.915887\pi$
$734$	−2.75005	−	11.4452i	−0.101506	−	0.422450i
$735$	7.13175	+	35.4148i	0.263058	+	1.30629i
$736$	−10.6098	+	25.6835i	−0.391084	+	0.946707i
$737$	−5.64026	+	5.64026i	−0.207762	+	0.207762i
$738$	−15.1916	+	24.8010i	−0.559209	+	0.912937i
$739$	19.7529			0.726621			0.363310	−	0.931668i	$-0.381646\pi$
$739$	19.7529			0.726621			0.363310	+	0.931668i	$0.381646\pi$
$740$	20.2693	+	25.5665i	0.745113	+	0.939843i
$741$	7.37283			0.270848
$742$	7.85358	−	12.8214i	0.288314	−	0.470687i
$743$	23.9280	−	23.9280i	0.877834	−	0.877834i	−0.115476	−	0.993310i	$-0.536839\pi$
$743$	23.9280	−	23.9280i	0.877834	−	0.877834i	0.993310	+	0.115476i	$0.0368395\pi$
$744$	14.5793	−	12.4663i	0.534504	−	0.457037i
$745$	−7.96679	+	11.9845i	−0.291881	+	0.439080i
$746$	10.8746	+	45.2579i	0.398146	+	1.65701i
$747$	6.11634	+	6.11634i	0.223785	+	0.223785i
$748$	−3.54139	+	10.9134i	−0.129486	+	0.399033i
$749$			11.2342i			0.410491i
$750$	−2.35215	−	50.4698i	−0.0858883	−	1.84290i
$751$		−	14.8424i		−	0.541605i	−0.962635	−	0.270803i	$-0.912711\pi$
$751$		−	14.8424i		−	0.541605i	0.962635	−	0.270803i	$-0.0872891\pi$
$752$	−11.9604	+	1.90367i	−0.436151	+	0.0694198i
$753$	−8.85363	−	8.85363i	−0.322644	−	0.322644i
$754$	−0.654597	+	0.157287i	−0.0238390	+	0.00572804i
$755$	−10.7994	+	16.2457i	−0.393031	+	0.591241i
$756$	33.4270	−	17.0480i	1.21573	−	0.620028i
$757$	31.8932	−	31.8932i	1.15918	−	1.15918i	0.174525	−	0.984653i	$-0.444161\pi$
$757$	31.8932	−	31.8932i	1.15918	−	1.15918i	0.984653	−	0.174525i	$-0.0558389\pi$
$758$	6.51051	+	3.98794i	0.236472	+	0.144849i
$759$	15.6973			0.569777
$760$	−27.2300	+	34.7508i	−0.987735	+	1.26054i
$761$	31.1600			1.12955			0.564775	−	0.825245i	$-0.308963\pi$
$761$	31.1600			1.12955			0.564775	+	0.825245i	$0.308963\pi$
$762$	65.0570	+	39.8500i	2.35677	+	1.44361i
$763$	−18.5987	+	18.5987i	−0.673320	+	0.673320i
$764$	−23.9684	+	12.2240i	−0.867146	+	0.442249i
$765$	18.2611	+	90.6807i	0.660231	+	3.27857i
$766$	−19.0775	+	4.58395i	−0.689299	+	0.165625i
$767$	−0.658047	−	0.658047i	−0.0237607	−	0.0237607i
$768$	45.5900	+	23.1419i	1.64509	+	0.835063i
$769$		−	5.25240i		−	0.189406i	−0.995506	−	0.0947031i	$-0.969810\pi$
$769$		−	5.25240i		−	0.189406i	0.995506	−	0.0947031i	$-0.0301902\pi$
$770$	−4.14056	−	1.51550i	−0.149215	−	0.0546148i
$771$			39.2508i			1.41358i
$772$	14.2928	−	44.0457i	0.514409	−	1.58524i
$773$	6.89506	+	6.89506i	0.247998	+	0.247998i	0.820149	−	0.572151i	$-0.193891\pi$
$773$	6.89506	+	6.89506i	0.247998	+	0.247998i	−0.572151	+	0.820149i	$0.693891\pi$
$774$	8.01304	+	33.3488i	0.288023	+	1.19870i
$775$	−9.78481	+	4.10745i	−0.351481	+	0.147544i
$776$	26.4912	+	30.9814i	0.950978	+	1.11217i
$777$	22.9844	−	22.9844i	0.824559	−	0.824559i
$778$	−4.09605	+	6.68700i	−0.146851	+	0.239741i
$779$	−19.9082			−0.713284
$780$	−0.542281	+	4.69226i	−0.0194168	+	0.168010i
$781$	−2.91802			−0.104415
$782$	−20.8175	+	33.9856i	−0.744432	+	1.21532i
$783$	13.7034	−	13.7034i	0.489720	−	0.489720i
$784$	16.3703	+	11.8747i	0.584653	+	0.424096i
$785$	−27.4168	+	5.52113i	−0.978547	+	0.197058i
$786$	−6.39491	−	26.6144i	−0.228099	−	0.949305i
$787$	−18.4001	−	18.4001i	−0.655893	−	0.655893i	0.298513	−	0.954406i	$-0.403509\pi$
$787$	−18.4001	−	18.4001i	−0.655893	−	0.655893i	−0.954406	+	0.298513i	$0.903509\pi$
$788$	27.3314	+	8.86901i	0.973641	+	0.315946i
$789$		−	77.4955i		−	2.75891i
$790$	−14.7449	−	31.7699i	−0.524600	−	1.13032i
$791$			3.09192i			0.109936i
$792$	1.58862	−	20.3337i	0.0564490	−	0.722525i
$793$	−0.694553	−	0.694553i	−0.0246643	−	0.0246643i
$794$	−9.80780	+	2.35662i	−0.348066	+	0.0836333i
$795$	−45.3726	−	30.1617i	−1.60920	−	1.06973i
$796$	1.51771	+	2.97588i	0.0537940	+	0.105477i
$797$	20.1658	−	20.1658i	0.714311	−	0.714311i	−0.253123	−	0.967434i	$-0.581458\pi$
$797$	20.1658	−	20.1658i	0.714311	−	0.714311i	0.967434	+	0.253123i	$0.0814578\pi$
$798$	37.5067	+	22.9743i	1.32772	+	0.813283i
$799$	−17.3695			−0.614490
$800$	−20.1135	−	19.8858i	−0.711120	−	0.703070i
$801$	−0.0432129			−0.00152685
$802$	−33.9191	−	20.7768i	−1.19773	−	0.733654i
$803$	−2.55895	+	2.55895i	−0.0903032	+	0.0903032i
$804$	23.1605	+	45.4123i	0.816808	+	1.60157i
$805$	−12.7547	−	8.47874i	−0.449543	−	0.298836i
$806$	0.964646	−	0.231785i	0.0339782	−	0.00816428i
$807$	−41.1559	−	41.1559i	−1.44876	−	1.44876i
$808$	0.0398036	−	0.509470i	0.00140029	−	0.0179231i
$809$			24.1778i			0.850046i	0.905183	+	0.425023i	$0.139734\pi$
$809$			24.1778i			0.850046i	−0.905183	+	0.425023i	$0.860266\pi$
$810$	−28.4424	−	61.2830i	−0.999363	−	2.15327i
$811$		−	0.0123408i		−	0.000433344i	−1.00000		0.000216672i	$-0.999931\pi$
$811$		−	0.0123408i		−	0.000433344i	1.00000		0.000216672i	$-6.89689e-5\pi$
$812$	−3.82015	−	1.23964i	−0.134061	−	0.0435027i
$813$	−0.794318	−	0.794318i	−0.0278579	−	0.0278579i
$814$	−2.41046	−	10.0319i	−0.0844866	−	0.351617i
$815$	45.5171	−	9.16613i	1.59439	−	0.321076i
$816$	59.3555	+	43.0553i	2.07786	+	1.50724i
$817$	−16.6009	+	16.6009i	−0.580792	+	0.580792i
$818$	21.7669	−	35.5355i	0.761061	−	1.24247i
$819$	3.32328			0.116125
$820$	1.46427	−	12.6701i	0.0511346	−	0.442458i
$821$	−36.0595			−1.25849			−0.629243	−	0.777209i	$-0.716635\pi$
$821$	−36.0595			−1.25849			−0.629243	+	0.777209i	$0.716635\pi$
$822$	27.7930	−	45.3735i	0.969393	−	1.58258i
$823$	3.12980	−	3.12980i	0.109098	−	0.109098i	−0.650451	−	0.759549i	$-0.725420\pi$
$823$	3.12980	−	3.12980i	0.109098	−	0.109098i	0.759549	+	0.650451i	$0.225420\pi$
$824$	22.9158	+	26.8000i	0.798310	+	0.933621i
$825$	−6.04419	+	14.7899i	−0.210432	+	0.514918i
$826$	−1.29706	−	5.39811i	−0.0451304	−	0.187824i
$827$	−8.81282	−	8.81282i	−0.306452	−	0.306452i	0.537080	−	0.843531i	$-0.319527\pi$
$827$	−8.81282	−	8.81282i	−0.306452	−	0.306452i	−0.843531	+	0.537080i	$0.819527\pi$
$828$	21.8670	−	67.3868i	0.759930	−	2.34185i
$829$			50.9263i			1.76874i	0.466784	+	0.884371i	$0.345412\pi$
$829$			50.9263i			1.76874i	−0.466784	+	0.884371i	$0.654588\pi$
$830$	−3.56217	−	1.30380i	−0.123645	−	0.0452556i
$831$			29.9712i			1.03969i
$832$	1.55670	+	2.13748i	0.0539690	+	0.0741039i
$833$	20.5094	+	20.5094i	0.710610	+	0.710610i
$834$	−4.50594	+	1.08269i	−0.156028	+	0.0374904i
$835$	−0.982971	−	4.88123i	−0.0340171	−	0.168922i
$836$	12.4369	−	6.34288i	0.430139	−	0.219373i
$837$	−20.1940	+	20.1940i	−0.698008	+	0.698008i
$838$	−44.8180	−	27.4528i	−1.54821	−	0.948340i
$839$	30.5168			1.05356			0.526779	−	0.850002i	$-0.323400\pi$
$839$	30.5168			1.05356			0.526779	+	0.850002i	$0.323400\pi$
$840$	−17.3801	+	22.1805i	−0.599672	+	0.765299i
$841$	26.9257			0.928474
$842$	3.02917	+	1.85549i	0.104392	+	0.0639443i
$843$	−19.0708	+	19.0708i	−0.656834	+	0.656834i
$844$	−39.0720	+	19.9269i	−1.34492	+	0.685913i
$845$	15.9572	−	24.0047i	0.548945	−	0.825785i
$846$	30.0218	−	7.21364i	1.03217	−	0.248010i
$847$	0.985925	+	0.985925i	0.0338768	+	0.0338768i
$848$	−30.1211	+	4.79422i	−1.03436	+	0.164634i
$849$			44.0115i			1.51047i
$850$	−24.0052	−	32.7001i	−0.823373	−	1.12160i
$851$		−	35.8384i		−	1.22852i
$852$	−5.75604	+	17.7382i	−0.197199	+	0.607702i
$853$	25.5043	+	25.5043i	0.873250	+	0.873250i	0.992825	−	0.119575i	$-0.0381532\pi$
$853$	25.5043	+	25.5043i	0.873250	+	0.873250i	−0.119575	+	0.992825i	$0.538153\pi$
$854$	−1.36901	−	5.69758i	−0.0468467	−	0.194967i
$855$	62.3099	−	93.7336i	2.13095	−	3.20562i
$856$	17.3206	−	14.8103i	0.592007	−	0.506206i
$857$	10.1886	−	10.1886i	0.348035	−	0.348035i	−0.511342	−	0.859377i	$-0.670852\pi$
$857$	10.1886	−	10.1886i	0.348035	−	0.348035i	0.859377	+	0.511342i	$0.170852\pi$
$858$	0.780214	−	1.27374i	0.0266361	−	0.0434847i
$859$	−23.0026			−0.784840			−0.392420	−	0.919786i	$-0.628362\pi$
$859$	−23.0026			−0.784840			−0.392420	+	0.919786i	$0.628362\pi$
$860$	−9.34424	−	11.7863i	−0.318636	−	0.401909i
$861$	−12.7068			−0.433048
$862$	25.0301	−	40.8629i	0.852530	−	1.39180i
$863$	5.71361	−	5.71361i	0.194494	−	0.194494i	−0.603141	−	0.797635i	$-0.706084\pi$
$863$	5.71361	−	5.71361i	0.194494	−	0.194494i	0.797635	+	0.603141i	$0.206084\pi$
$864$	−70.3515	−	29.0622i	−2.39341	−	0.988715i
$865$	5.60018	+	27.8093i	0.190412	+	0.945545i
$866$	4.42841	+	18.4302i	0.150483	+	0.626283i
$867$	35.9512	+	35.9512i	1.22097	+	1.22097i
$868$	5.62956	+	1.82679i	0.191080	+	0.0620052i
$869$			11.0758i			0.375722i
$870$	−5.00220	+	13.6667i	−0.169591	+	0.463346i
$871$			2.63651i			0.0893348i
$872$	53.1941	+	4.15591i	1.80138	+	0.140737i
$873$	−73.4851	−	73.4851i	−2.48709	−	2.48709i
$874$	47.1526	−	11.3298i	1.59496	−	0.383237i
$875$	12.8997	−	8.75265i	0.436091	−	0.295894i
$876$	10.5078	+	20.6032i	0.355024	+	0.696119i
$877$	−25.4273	+	25.4273i	−0.858619	+	0.858619i	−0.991175	−	0.132557i	$-0.957681\pi$
$877$	−25.4273	+	25.4273i	−0.858619	+	0.858619i	0.132557	+	0.991175i	$0.457681\pi$
$878$	14.2743	+	8.74355i	0.481733	+	0.295080i
$879$	44.6927			1.50745
$880$	3.12203	+	8.38170i	0.105244	+	0.282547i
$881$	−6.30487			−0.212416			−0.106208	−	0.994344i	$-0.533871\pi$
$881$	−6.30487			−0.212416			−0.106208	+	0.994344i	$0.533871\pi$
$882$	−43.9665	−	26.9312i	−1.48043	−	0.906821i
$883$	−4.07678	+	4.07678i	−0.137194	+	0.137194i	−0.772369	−	0.635174i	$-0.780928\pi$
$883$	−4.07678	+	4.07678i	−0.137194	+	0.137194i	0.635174	+	0.772369i	$0.280928\pi$
$884$	1.72301	+	3.37841i	0.0579509	+	0.113628i
$885$	−19.7216	+	3.97149i	−0.662934	+	0.133500i
$886$	29.5852	−	7.10872i	0.993933	−	0.238822i
$887$	36.1576	+	36.1576i	1.21405	+	1.21405i	0.969682	+	0.244370i	$0.0785810\pi$
$887$	36.1576	+	36.1576i	1.21405	+	1.21405i	0.244370	+	0.969682i	$0.421419\pi$
$888$	−65.7373	−	5.13589i	−2.20600	−	0.172349i
$889$			23.5390i			0.789474i
$890$	0.0171894	−	0.00797787i	0.000576191	−	0.000267419i
$891$			21.3649i			0.715750i
$892$	−45.4978	−	14.7640i	−1.52338	−	0.494335i
$893$	14.9448	+	14.9448i	0.500107	+	0.500107i
$894$	−6.79487	−	28.2790i	−0.227255	−	0.945791i
$895$	15.9998	+	10.6360i	0.534815	+	0.355521i
$896$	1.25862	+	15.7245i	0.0420476	+	0.525319i
$897$	3.66882	−	3.66882i	0.122498	−	0.122498i
$898$	−1.55350	+	2.53617i	−0.0518411	+	0.0846331i
$899$	3.05673			0.101948
$900$	55.0716	+	46.5499i	1.83572	+	1.55166i
$901$	−43.7435			−1.45731
$902$	−2.10674	+	3.43935i	−0.0701467	+	0.114518i
$903$	−10.5959	+	10.5959i	−0.352610	+	0.352610i
$904$	4.76702	−	4.07613i	0.158549	−	0.135570i
$905$	−1.86791	−	1.24171i	−0.0620916	−	0.0412757i
$906$	−9.21081	−	38.3337i	−0.306009	−	1.27355i
$907$	15.4572	+	15.4572i	0.513250	+	0.513250i	0.915521	−	0.402271i	$-0.131779\pi$
$907$	15.4572	+	15.4572i	0.513250	+	0.513250i	−0.402271	+	0.915521i	$0.631779\pi$
$908$	13.9252	−	42.9128i	0.462123	−	1.42411i
$909$			1.30283i			0.0432121i
$910$	−1.32195	+	0.613536i	−0.0438222	+	0.0203385i
$911$			39.0494i			1.29376i	0.762590	+	0.646882i	$0.223927\pi$
$911$			39.0494i			1.29376i	−0.762590	+	0.646882i	$0.776073\pi$
$912$	−14.0247	−	88.1142i	−0.464403	−	2.91775i
$913$	0.848203	+	0.848203i	0.0280714	+	0.0280714i
$914$	−37.5085	+	9.01254i	−1.24067	+	0.298108i
$915$	−20.8157	+	4.19181i	−0.688145	+	0.138577i
$916$	−45.3259	+	23.1164i	−1.49761	+	0.763788i
$917$	5.97175	−	5.97175i	0.197204	−	0.197204i
$918$	−93.0923	−	57.0227i	−3.07250	−	1.88203i
$919$	−27.2993			−0.900520			−0.450260	−	0.892897i	$-0.648669\pi$
$919$	−27.2993			−0.900520			−0.450260	+	0.892897i	$0.648669\pi$
$920$	3.74246	+	30.8425i	0.123385	+	1.01685i
$921$	−1.59362			−0.0525117
$922$	−44.0769	−	26.9988i	−1.45159	−	0.889158i
$923$	−0.682006	+	0.682006i	−0.0224485	+	0.0224485i
$924$	7.93814	−	4.04849i	0.261146	−	0.133185i
$925$	33.7666	+	13.7994i	1.11024	+	0.453722i
$926$	−13.5497	+	3.25571i	−0.445270	+	0.106989i
$927$	−63.5671	−	63.5671i	−2.08782	−	2.08782i
$928$	3.12495	+	7.52403i	0.102581	+	0.246988i
$929$			7.40140i			0.242832i	0.992602	+	0.121416i	$0.0387435\pi$
$929$			7.40140i			0.242832i	−0.992602	+	0.121416i	$0.961256\pi$
$930$	7.37149	−	20.1400i	0.241721	−	0.660415i
$931$		−	35.2927i		−	1.15667i
$932$	−7.95116	+	24.5029i	−0.260449	+	0.802618i
$933$	−9.40128	−	9.40128i	−0.307784	−	0.307784i
$934$	5.84363	+	24.3201i	0.191209	+	0.795778i
$935$	2.53241	+	12.5754i	0.0828187	+	0.411261i
$936$	−4.38114	−	5.12373i	−0.143202	−	0.167474i
$937$	−21.0398	+	21.0398i	−0.687342	+	0.687342i	−0.961644	−	0.274302i	$-0.911553\pi$
$937$	−21.0398	+	21.0398i	−0.687342	+	0.687342i	0.274302	+	0.961644i	$0.411553\pi$
$938$	−8.21559	+	13.4123i	−0.268248	+	0.437929i
$939$	99.2066			3.23748
$940$	−10.6104	+	8.41203i	−0.346075	+	0.274370i
$941$	−46.4937			−1.51565			−0.757826	−	0.652456i	$-0.773739\pi$
$941$	−46.4937			−1.51565			−0.757826	+	0.652456i	$0.773739\pi$
$942$	29.5231	−	48.1979i	0.961914	−	1.57037i
$943$	−9.90657	+	9.90657i	−0.322602	+	0.322602i
$944$	−6.61271	+	9.11620i	−0.215225	+	0.296707i
$945$	23.2247	−	34.9373i	0.755501	−	1.13651i
$946$	1.11123	+	4.62475i	0.0361293	+	0.150363i
$947$	15.6887	+	15.6887i	0.509813	+	0.509813i	0.914469	−	0.404656i	$-0.132609\pi$
$947$	15.6887	+	15.6887i	0.509813	+	0.509813i	−0.404656	+	0.914469i	$0.632609\pi$
$948$	67.3285	+	21.8480i	2.18673	+	0.709592i
$949$			1.19617i			0.0388292i
$950$	−7.48104	+	48.7893i	−0.242717	+	1.58293i
$951$		−	91.2124i		−	2.95776i
$952$	−1.76220	+	22.5555i	−0.0571133	+	0.731028i
$953$	−3.36250	−	3.36250i	−0.108922	−	0.108922i	0.650545	−	0.759467i	$-0.274540\pi$
$953$	−3.36250	−	3.36250i	−0.108922	−	0.108922i	−0.759467	+	0.650545i	$0.774540\pi$
$954$	75.6071	−	18.1669i	2.44787	−	0.588174i
$955$	−16.6530	+	25.0513i	−0.538878	+	0.810640i
$956$	12.0424	+	23.6122i	0.389478	+	0.763674i
$957$	3.25424	−	3.25424i	0.105195	−	0.105195i
$958$	23.3016	+	14.2731i	0.752841	+	0.461144i
$959$	16.4171			0.530136
$960$	57.1098	−	2.44476i	1.84321	−	0.0789042i
$961$	26.4955			0.854692
$962$	−2.90805	−	1.78130i	−0.0937594	−	0.0574313i
$963$	−41.0830	+	41.0830i	−1.32388	+	1.32388i
$964$	−18.8976	−	37.0537i	−0.608650	−	1.19342i
$965$	−10.2206	−	50.7535i	−0.329014	−	1.63381i
$966$	30.0962	−	7.23151i	0.968329	−	0.232670i
$967$	−27.3155	−	27.3155i	−0.878409	−	0.878409i	0.114961	−	0.993370i	$-0.463326\pi$
$967$	−27.3155	−	27.3155i	−0.878409	−	0.878409i	−0.993370	+	0.114961i	$0.963326\pi$
$968$	0.220306	−	2.81983i	0.00708091	−	0.0906329i
$969$		−	127.964i		−	4.11080i
$970$	42.7979	+	15.6646i	1.37416	+	0.502959i
$971$		−	6.88941i		−	0.221092i	−0.993871	−	0.110546i	$-0.964740\pi$
$971$		−	6.88941i		−	0.221092i	0.993871	−	0.110546i	$-0.0352599\pi$
$972$	53.0810	+	17.2247i	1.70257	+	0.552483i
$973$	−1.01104	−	1.01104i	−0.0324125	−	0.0324125i
$974$	−2.03605	−	8.47366i	−0.0652393	−	0.271514i
$975$	2.04407	+	4.86940i	0.0654626	+	0.155946i
$976$	−6.97956	+	9.62193i	−0.223410	+	0.307991i
$977$	4.12063	−	4.12063i	0.131831	−	0.131831i	−0.638112	−	0.769943i	$-0.720285\pi$
$977$	4.12063	−	4.12063i	0.131831	−	0.131831i	0.769943	+	0.638112i	$0.220285\pi$
$978$	−49.0140	+	80.0177i	−1.56729	+	2.55868i
$979$	−0.00599269			−0.000191527
$980$	22.4612	+	2.59582i	0.717496	+	0.0829205i
$981$	−136.029			−4.34307
$982$	−2.42177	+	3.95366i	−0.0772818	+	0.126166i
$983$	−3.44593	+	3.44593i	−0.109908	+	0.109908i	−0.759922	−	0.650014i	$-0.774763\pi$
$983$	−3.44593	+	3.44593i	−0.109908	+	0.109908i	0.650014	+	0.759922i	$0.274763\pi$
$984$	16.7517	+	19.5910i	0.534023	+	0.624539i
$985$	31.4938	−	6.34215i	1.00348	−	0.202078i
$986$	2.72990	+	11.3613i	0.0869376	+	0.361818i
$987$	9.53883	+	9.53883i	0.303624	+	0.303624i
$988$	1.42431	−	4.38926i	0.0453134	−	0.139641i
$989$			16.5217i			0.525359i
$990$	−9.59970	−	20.6839i	−0.305098	−	0.657377i
$991$		−	19.8268i		−	0.629819i	−0.949122	−	0.314909i	$-0.898026\pi$
$991$		−	19.8268i		−	0.629819i	0.949122	−	0.314909i	$-0.101974\pi$
$992$	−4.60507	−	11.0878i	−0.146211	−	0.352037i
$993$	21.6088	+	21.6088i	0.685734	+	0.685734i
$994$	−5.59466	+	1.34428i	−0.177452	+	0.0426381i
$995$	3.11033	+	2.06761i	0.0986041	+	0.0655476i
$996$	6.82927	−	3.48296i	0.216394	−	0.110362i
$997$	−37.6367	+	37.6367i	−1.19197	+	1.19197i	−0.215451	+	0.976515i	$0.569122\pi$
$997$	−37.6367	+	37.6367i	−1.19197	+	1.19197i	−0.976515	+	0.215451i	$0.930878\pi$
$998$	23.3461	+	14.3004i	0.739007	+	0.452671i
$999$	98.1675			3.10588

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.12	✓	28
4.3	odd	2		220.2.l.d.23.4	yes	28
5.2	odd	4		220.2.l.d.67.4	yes	28
20.7	even	4	inner	220.2.l.c.67.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.12	✓	28	1.1	even	1	trivial
220.2.l.c.67.12	yes	28	20.7	even	4	inner
220.2.l.d.23.4	yes	28	4.3	odd	2
220.2.l.d.67.4	yes	28	5.2	odd	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	220.2.l.c.23.12

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$