LMFDB - Embedded newform 220.2.l.d.23.4

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			23.4
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.738695 - 1.20596i) 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} +(2.81983 - 0.220306i) q^{8} -7.21094i q^{9} +(0.117261 - 3.16010i) q^{10} +1.00000i q^{11} +(1.97259 + 6.07887i) 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} +(-8.69608 + 5.32669i) q^{18} -6.98049 q^{19} +(-3.89756 + 2.19294i) q^{20} +4.45545 q^{21} +(1.20596 - 0.738695i) 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} +(-2.65246 + 0.860721i) q^{28} -1.44023i q^{29} +(-6.87539 - 7.40530i) q^{30} -2.12239i q^{31} +(-2.16976 + 5.22419i) 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} +(5.15645 + 8.41816i) q^{38} -1.05621 q^{39} +(5.52370 + 3.08038i) q^{40} -2.85197 q^{41} +(-3.29122 - 5.37308i) 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} +(-12.6229 - 2.00913i) q^{48} -5.05590i q^{49} +(4.13019 - 5.73947i) q^{50} +18.3317i q^{51} +(0.628790 - 0.204042i) 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} +(-1.73685 + 1.06389i) q^{58} -2.81550 q^{59} +(-3.85165 + 13.7617i) q^{60} +2.97170 q^{61} +(-2.55951 + 1.56780i) 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} +(-3.54139 - 10.9134i) q^{68} +15.6973i q^{69} +(3.23124 - 3.00001i) q^{70} +2.91802i q^{71} +(-1.58862 - 20.3337i) 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} +(0.780214 + 1.27374i) q^{78} +11.0758 q^{79} +(-0.365533 - 8.93680i) q^{80} -21.3649 q^{81} +(2.10674 + 3.43935i) 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} +(0.220306 + 2.81983i) q^{88} -0.00599269i q^{89} +(-22.7873 - 0.845565i) q^{90} -0.460866i q^{91} +(-3.03247 - 9.34508i) 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} +(-6.09720 + 3.73477i) q^{98} +7.21094 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100})$ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * 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 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * 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

)

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

$2$	−0.738695	−	1.20596i	−0.522336	−	0.852740i
$2$	−0.738695	−	1.20596i	−0.522336	−	0.852740i
$3$	2.25953	−	2.25953i	1.30454	−	1.30454i	0.379242	−	0.925297i	$-0.376185\pi$
$3$	2.25953	−	2.25953i	1.30454	−	1.30454i	0.925297	−	0.379242i	$-0.123815\pi$
$4$	−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	0.868440	−	0.495795i	$-0.165123\pi$
$7$	0.985925	+	0.985925i	0.372645	+	0.372645i	−0.495795	+	0.868440i	$0.665123\pi$
$8$	2.81983	−	0.220306i	0.996962	−	0.0778900i
$9$		−	7.21094i		−	2.40365i
$10$	0.117261	−	3.16010i	0.0370813	−	0.999312i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	1.97259	+	6.07887i	0.569437	+	1.75482i
$13$	−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	$0.494901\pi$
$18$	−8.69608	+	5.32669i	−2.04969	+	1.25551i
$19$	−6.98049			−1.60143			−0.800717	−	0.599043i	$-0.795548\pi$
$19$	−6.98049			−1.60143			−0.800717	+	0.599043i	$0.795548\pi$
$20$	−3.89756	+	2.19294i	−0.871522	+	0.490356i
$21$	4.45545			0.972260
$22$	1.20596	−	0.738695i	0.257111	−	0.157490i
$23$	−3.47359	+	3.47359i	−0.724293	+	0.724293i	−0.969477	−	0.245184i	$-0.921152\pi$
$23$	−3.47359	+	3.47359i	−0.724293	+	0.724293i	0.245184	+	0.969477i	$0.421152\pi$
$24$	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
$28$	−2.65246	+	0.860721i	−0.501268	+	0.162661i
$29$		−	1.44023i		−	0.267444i	−0.991019	−	0.133722i	$-0.957307\pi$
$29$		−	1.44023i		−	0.267444i	0.991019	−	0.133722i	$-0.0426929\pi$
$30$	−6.87539	−	7.40530i	−1.25527	−	1.35202i
$31$		−	2.12239i		−	0.381193i	−0.981668	−	0.190596i	$-0.938958\pi$
$31$		−	2.12239i		−	0.381193i	0.981668	−	0.190596i	$-0.0610422\pi$
$32$	−2.16976	+	5.22419i	−0.383562	+	0.923515i
$33$	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	$0.0452917\pi$
$38$	5.15645	+	8.41816i	0.836487	+	1.36561i
$39$	−1.05621			−0.169128
$40$	5.52370	+	3.08038i	0.873374	+	0.487050i
$41$	−2.85197			−0.445403			−0.222702	−	0.974887i	$-0.571488\pi$
$41$	−2.85197			−0.445403			−0.222702	+	0.974887i	$0.571488\pi$
$42$	−3.29122	−	5.37308i	−0.507847	−	0.829084i
$43$	2.37819	−	2.37819i	0.362670	−	0.362670i	−0.502125	−	0.864795i	$-0.667448\pi$
$43$	2.37819	−	2.37819i	0.362670	−	0.362670i	0.864795	+	0.502125i	$0.167448\pi$
$44$	−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	0.533508	−	0.845795i	$-0.320873\pi$
$47$	−2.14093	−	2.14093i	−0.312287	−	0.312287i	−0.845795	+	0.533508i	$0.820873\pi$
$48$	−12.6229	−	2.00913i	−1.82196	−	0.289992i
$49$		−	5.05590i		−	0.722272i
$50$	4.13019	−	5.73947i	0.584098	−	0.811683i
$51$			18.3317i			2.56695i
$52$	0.628790	−	0.204042i	0.0871975	−	0.0282955i
$53$	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
$58$	−1.73685	+	1.06389i	−0.228060	+	0.139696i
$59$	−2.81550			−0.366547			−0.183274	−	0.983062i	$-0.558669\pi$
$59$	−2.81550			−0.366547			−0.183274	+	0.983062i	$0.558669\pi$
$60$	−3.85165	+	13.7617i	−0.497246	+	1.77662i
$61$	2.97170			0.380487			0.190243	−	0.981737i	$-0.439072\pi$
$61$	2.97170			0.380487			0.190243	+	0.981737i	$0.439072\pi$
$62$	−2.55951	+	1.56780i	−0.325058	+	0.199111i
$63$	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	0.962026	−	0.272958i	$-0.0880021\pi$
$67$	5.64026	+	5.64026i	0.689068	+	0.689068i	−0.272958	+	0.962026i	$0.588002\pi$
$68$	−3.54139	−	10.9134i	−0.429456	−	1.32344i
$69$			15.6973i			1.88974i
$70$	3.23124	−	3.00001i	0.386207	−	0.358570i
$71$			2.91802i			0.346305i	0.984895	+	0.173152i	$0.0553953\pi$
$71$			2.91802i			0.346305i	−0.984895	+	0.173152i	$0.944605\pi$
$72$	−1.58862	−	20.3337i	−0.187220	−	2.39635i
$73$	−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
$78$	0.780214	+	1.27374i	0.0883418	+	0.144222i
$79$	11.0758			1.24613			0.623064	−	0.782171i	$-0.285888\pi$
$79$	11.0758			1.24613			0.623064	+	0.782171i	$0.285888\pi$
$80$	−0.365533	−	8.93680i	−0.0408678	−	0.999165i
$81$	−21.3649			−2.37387
$82$	2.10674	+	3.43935i	0.232650	+	0.379813i
$83$	0.848203	−	0.848203i	0.0931023	−	0.0931023i	−0.659022	−	0.752124i	$-0.729029\pi$
$83$	0.848203	−	0.848203i	0.0931023	−	0.0931023i	0.752124	+	0.659022i	$0.229029\pi$
$84$	−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
$88$	0.220306	+	2.81983i	0.0234847	+	0.300595i
$89$		−	0.00599269i		−	0.000635224i	−1.00000		0.000317612i	$-0.999899\pi$
$89$		−	0.00599269i		−	0.000635224i	1.00000		0.000317612i	$-0.000101099\pi$
$90$	−22.7873	−	0.845565i	−2.40199	−	0.0891304i
$91$		−	0.460866i		−	0.0483119i
$92$	−3.03247	−	9.34508i	−0.316157	−	0.974292i
$93$	−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	$-0.0112516\pi$
$98$	−6.09720	+	3.73477i	−0.615910	+	0.377269i
$99$	7.21094			0.724727
$100$	−9.97250	−	0.741116i	−0.997250	−	0.0741116i
$101$	−0.180674			−0.0179777			−0.00898886	−	0.999960i	$-0.502861\pi$
$101$	−0.180674			−0.0179777			−0.00898886	+	0.999960i	$0.502861\pi$
$102$	22.1072	−	13.5415i	2.18894	−	1.34081i
$103$	−8.81537	+	8.81537i	−0.868604	+	0.868604i	−0.992318	−	0.123714i	$-0.960520\pi$
$103$	−8.81537	+	8.81537i	−0.868604	+	0.868604i	0.123714	+	0.992318i	$0.460520\pi$
$104$	−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	0.926666	−	0.375886i	$-0.122662\pi$
$107$	5.69731	+	5.69731i	0.550780	+	0.550780i	−0.375886	+	0.926666i	$0.622662\pi$
$108$	25.5978	−	8.30646i	2.46315	−	0.799289i
$109$		−	18.8642i		−	1.80687i	−0.428728	−	0.903434i	$-0.641038\pi$
$109$		−	18.8642i		−	1.80687i	0.428728	−	0.903434i	$-0.358962\pi$
$110$	3.16010	+	0.117261i	0.301304	+	0.0111804i
$111$		−	23.3125i		−	2.21272i
$112$	0.876664	−	5.50791i	0.0828370	−	0.520448i
$113$	−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
$118$	2.07980	+	3.39537i	0.191461	+	0.312569i
$119$	−7.99888			−0.733256
$120$	19.4412	−	5.52076i	1.77473	−	0.503974i
$121$	−1.00000			−0.0909091
$122$	−2.19518	−	3.58374i	−0.198742	−	0.324456i
$123$	−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	$0.0194791\pi$
$127$	11.9375	+	11.9375i	1.05929	+	1.05929i	0.0611574	+	0.998128i	$0.480521\pi$
$128$	−7.33620	−	8.61279i	−0.648435	−	0.761270i
$129$		−	10.7472i		−	0.946236i
$130$	−0.765994	+	0.711181i	−0.0671821	+	0.0623747i
$131$		−	6.05700i		−	0.529202i	−0.964358	−	0.264601i	$-0.914760\pi$
$131$		−	6.05700i		−	0.529202i	0.964358	−	0.264601i	$-0.0852403\pi$
$132$	−6.07887	+	1.97259i	−0.529098	+	0.171692i
$133$	−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	$0.417762\pi$
$138$	18.9303	−	11.5955i	1.61145	−	0.987078i
$139$	−1.02548			−0.0869797			−0.0434899	−	0.999054i	$-0.513848\pi$
$139$	−1.02548			−0.0869797			−0.0434899	+	0.999054i	$0.513848\pi$
$140$	−6.00478	−	1.68063i	−0.507497	−	0.142039i
$141$	−9.67500			−0.814782
$142$	3.51900	−	2.15552i	0.295308	−	0.180888i
$143$	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
$148$	4.50359	+	13.8786i	0.370193	+	1.14081i
$149$			6.43582i			0.527243i	0.964626	+	0.263622i	$0.0849170\pi$
$149$			6.43582i			0.527243i	−0.964626	+	0.263622i	$0.915083\pi$
$150$	−3.63620	−	22.3008i	−0.296894	−	1.82085i
$151$		−	8.72410i		−	0.709957i	−0.934874	−	0.354979i	$-0.884488\pi$
$151$		−	8.72410i		−	0.709957i	0.934874	−	0.354979i	$-0.115512\pi$
$152$	−19.6838	+	1.53785i	−1.59657	+	0.124736i
$153$	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	$0.416334\pi$
$158$	−8.18166	−	13.3570i	−0.650898	−	1.06262i
$159$	24.3656			1.93232
$160$	−10.5074	+	7.04239i	−0.830680	+	0.556750i
$161$	−6.84939			−0.539808
$162$	15.7821	+	25.7651i	1.23996	+	2.02430i
$163$	−14.6827	+	14.6827i	−1.15004	+	1.15004i	−0.163496	+	0.986544i	$0.552277\pi$
$163$	−14.6827	+	14.6827i	−1.15004	+	1.15004i	−0.986544	+	0.163496i	$0.947723\pi$
$164$	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	0.765399	−	0.643556i	$-0.222541\pi$
$167$	1.57457	+	1.57457i	0.121844	+	0.121844i	−0.643556	+	0.765399i	$0.722541\pi$
$168$	12.5636	−	0.981564i	0.969306	−	0.0757293i
$169$		−	12.8907i		−	0.991596i
$170$	12.3434	+	13.2947i	0.946695	+	1.01966i
$171$			50.3359i			3.84928i
$172$	2.07618	+	6.39810i	0.158307	+	0.487851i
$173$	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
$178$	−0.00722692	+	0.00442677i	−0.000541680	+	0.000331800i
$179$	−8.59206			−0.642201			−0.321101	−	0.947045i	$-0.604053\pi$
$179$	−8.59206			−0.642201			−0.321101	+	0.947045i	$0.604053\pi$
$180$	15.8132	+	28.1051i	1.17864	+	2.09483i
$181$	−1.00309			−0.0745590			−0.0372795	−	0.999305i	$-0.511869\pi$
$181$	−1.00309			−0.0745590			−0.0372795	+	0.999305i	$0.511869\pi$
$182$	−0.555784	+	0.340439i	−0.0411974	+	0.0252350i
$183$	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
$188$	5.75981	−	1.86905i	0.420077	−	0.136315i
$189$		−	18.7617i		−	1.36471i
$190$	−0.818541	+	22.0591i	−0.0593832	+	1.60033i
$191$		−	13.4528i		−	0.973410i	−0.873566	−	0.486705i	$-0.838199\pi$
$191$		−	13.4528i		−	0.973410i	0.873566	−	0.486705i	$-0.161801\pi$
$192$	15.0495	−	20.6643i	1.08611	−	1.49131i
$193$	−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	$0.0789751\pi$
$198$	−5.32669	−	8.69608i	−0.378551	−	0.618003i
$199$	−1.67028			−0.118403			−0.0592015	−	0.998246i	$-0.518855\pi$
$199$	−1.67028			−0.118403			−0.0592015	+	0.998246i	$0.518855\pi$
$200$	6.47288	+	12.5739i	0.457702	+	0.889106i
$201$	25.4887			1.79783
$202$	0.133463	+	0.217885i	0.00939042	+	0.0153303i
$203$	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
$208$	−0.207821	+	1.30570i	−0.0144098	+	0.0905339i
$209$		−	6.98049i		−	0.482850i
$210$	0.522452	−	14.0797i	0.0360526	−	0.971591i
$211$		−	21.9300i		−	1.50973i	−0.655882	−	0.754863i	$-0.727703\pi$
$211$		−	21.9300i		−	1.50973i	0.655882	−	0.754863i	$-0.272297\pi$
$212$	−14.5055	+	4.70703i	−0.996244	+	0.323280i
$213$	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
$218$	−22.7495	+	13.9349i	−1.54079	+	0.943792i
$219$	−11.5640			−0.781424
$220$	−2.19294	−	3.89756i	−0.147848	−	0.262774i
$221$	1.89621			0.127553
$222$	−28.1138	+	17.2208i	−1.88688	+	1.15579i
$223$	16.9116	−	16.9116i	1.13249	−	1.13249i	0.142725	−	0.989762i	$-0.454414\pi$
$223$	16.9116	−	16.9116i	1.13249	−	1.13249i	0.989762	−	0.142725i	$-0.0455864\pi$
$224$	−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	$0.0192773\pi$
$227$	15.9508	+	15.9508i	1.05869	+	1.05869i	0.0605244	+	0.998167i	$0.480723\pi$
$228$	−13.7696	−	42.4335i	−0.911916	−	2.81023i
$229$			25.4401i			1.68113i	0.541709	+	0.840566i	$0.317777\pi$
$229$			25.4401i			1.68113i	−0.541709	+	0.840566i	$0.682223\pi$
$230$	10.5696	+	11.3842i	0.696937	+	0.750652i
$231$			4.45545i			0.293147i
$232$	−0.317292	−	4.06121i	−0.0208312	−	0.266631i
$233$	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
$238$	5.90873	+	9.64629i	0.383006	+	0.625276i
$239$	−13.2529			−0.857258			−0.428629	−	0.903481i	$-0.641003\pi$
$239$	−13.2529			−0.857258			−0.428629	+	0.903481i	$0.641003\pi$
$240$	−21.0189	−	19.3670i	−1.35676	−	1.25014i
$241$	−20.7972			−1.33967			−0.669833	−	0.742512i	$-0.733634\pi$
$241$	−20.7972			−1.33967			−0.669833	+	0.742512i	$0.733634\pi$
$242$	0.738695	+	1.20596i	0.0474851	+	0.0775218i
$243$	−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
$248$	−0.467576	−	5.98479i	−0.0296911	−	0.380035i
$249$		−	3.83308i		−	0.242911i
$250$	14.7959	−	5.57512i	0.935773	−	0.352602i
$251$		−	3.91835i		−	0.247324i	−0.992324	−	0.123662i	$-0.960536\pi$
$251$		−	3.91835i		−	0.247324i	0.992324	−	0.123662i	$-0.0394639\pi$
$252$	6.20661	+	19.1267i	0.390980	+	1.20487i
$253$	−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	$0.124854\pi$
$258$	−12.9606	+	7.93888i	−0.806892	+	0.494253i
$259$	10.1722			0.632069
$260$	1.42349	+	0.398409i	0.0882810	+	0.0247083i
$261$	−10.3854			−0.642841
$262$	−7.30447	+	4.47427i	−0.451272	+	0.276422i
$263$	17.1486	−	17.1486i	1.05743	−	1.05743i	0.0591800	−	0.998247i	$-0.481151\pi$
$263$	17.1486	−	17.1486i	1.05743	−	1.05743i	0.998247	−	0.0591800i	$-0.0188486\pi$
$264$	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
$268$	−15.1741	+	4.92400i	−0.926909	+	0.300781i
$269$			18.2144i			1.11055i	0.831667	+	0.555275i	$0.187387\pi$
$269$			18.2144i			1.11055i	−0.831667	+	0.555275i	$0.812613\pi$
$270$	−31.1833	+	28.9519i	−1.89776	+	1.76195i
$271$		−	0.351541i		−	0.0213546i	−0.999943	−	0.0106773i	$-0.996601\pi$
$271$		−	0.351541i		−	0.0213546i	0.999943	−	0.0106773i	$-0.00339876\pi$
$272$	22.6620	+	3.60698i	1.37408	+	0.218706i
$273$	−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	$0.159077\pi$
$278$	0.757514	+	1.23668i	0.0454327	+	0.0741711i
$279$	−15.3044			−0.916253
$280$	2.40894	+	8.48298i	0.143961	+	0.506955i
$281$	8.44017			0.503498			0.251749	−	0.967793i	$-0.418994\pi$
$281$	8.44017			0.503498			0.251749	+	0.967793i	$0.418994\pi$
$282$	7.14688	+	11.6676i	0.425590	+	0.694797i
$283$	−9.73908	+	9.73908i	−0.578928	+	0.578928i	−0.934608	−	0.355680i	$-0.884249\pi$
$283$	−9.73908	+	9.73908i	−0.578928	+	0.578928i	0.355680	+	0.934608i	$0.384249\pi$
$284$	−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
$288$	37.6713	+	15.6460i	2.21980	+	0.921948i
$289$		−	15.9109i		−	0.935937i
$290$	−4.55127	−	0.168883i	−0.267260	−	0.00991716i
$291$		−	46.0527i		−	2.69966i
$292$	6.88440	−	2.23398i	0.402879	−	0.130734i
$293$	−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
$298$	7.76132	−	4.75411i	0.449601	−	0.275398i
$299$	1.62371			0.0939016
$300$	−24.2077	+	20.8586i	−1.39763	+	1.20427i
$301$	4.68943			0.270294
$302$	−10.5209	+	6.44445i	−0.605409	+	0.370837i
$303$	−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	0.696972	−	0.717098i	$-0.254530\pi$
$307$	−0.352645	−	0.352645i	−0.0201265	−	0.0201265i	−0.717098	+	0.696972i	$0.754530\pi$
$308$	−0.860721	−	2.65246i	−0.0490441	−	0.151138i
$309$			39.8372i			2.26626i
$310$	−6.70698	−	0.248874i	−0.380931	−	0.0141351i
$311$		−	4.16072i		−	0.235933i	−0.993018	−	0.117967i	$-0.962362\pi$
$311$		−	4.16072i		−	0.235933i	0.993018	−	0.117967i	$-0.0376376\pi$
$312$	−2.97832	+	0.232689i	−0.168614	+	0.0131734i
$313$	−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	$0.953979\pi$
$318$	−17.9987	−	29.3838i	−1.00932	−	1.64776i
$319$	1.44023			0.0806374
$320$	16.2545	+	7.46925i	0.908657	+	0.417544i
$321$	25.7465			1.43703
$322$	5.05961	+	8.26007i	0.281961	+	0.460315i
$323$	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
$328$	−8.04209	+	0.628308i	−0.444050	+	0.0346925i
$329$		−	4.22160i		−	0.232744i
$330$	7.40530	−	6.87539i	0.407648	−	0.378478i
$331$			9.56340i			0.525652i	0.964843	+	0.262826i	$0.0846545\pi$
$331$			9.56340i			0.525652i	−0.964843	+	0.262826i	$0.915346\pi$
$332$	0.740488	+	2.28194i	0.0406396	+	0.125238i
$333$	−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	$0.250183\pi$
$338$	−15.5457	+	9.52233i	−0.845573	+	0.517947i
$339$	−7.08601			−0.384859
$340$	6.91487	−	24.7063i	0.375011	−	1.33989i
$341$	2.12239			0.114934
$342$	60.7029	−	37.1829i	3.28244	−	2.01062i
$343$	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	0.764802	−	0.644265i	$-0.222837\pi$
$347$	2.24537	+	2.24537i	0.120538	+	0.120538i	−0.644265	+	0.764802i	$0.722837\pi$
$348$	8.75497	−	2.84098i	0.469316	−	0.152292i
$349$			15.1840i			0.812779i	0.913700	+	0.406389i	$0.133212\pi$
$349$			15.1840i			0.812779i	−0.913700	+	0.406389i	$0.866788\pi$
$350$	9.73075	−	1.58662i	0.520130	−	0.0848086i
$351$			4.44762i			0.237397i
$352$	−5.22419	−	2.16976i	−0.278450	−	0.115648i
$353$	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
$358$	6.34692	+	10.3617i	0.335445	+	0.547630i
$359$	−6.54287			−0.345319			−0.172660	−	0.984982i	$-0.555236\pi$
$359$	−6.54287			−0.345319			−0.172660	+	0.984982i	$0.555236\pi$
$360$	22.2124	−	39.8311i	1.17070	−	2.09928i
$361$	29.7272			1.56459
$362$	0.740977	+	1.20968i	0.0389449	+	0.0635794i
$363$	−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	0.843830	−	0.536611i	$-0.180296\pi$
$367$	5.88547	+	5.88547i	0.307219	+	0.307219i	−0.536611	+	0.843830i	$0.680296\pi$
$368$	19.4053	+	3.08864i	1.01157	+	0.161006i
$369$			20.5654i			1.07059i
$370$	−15.6971	−	16.9069i	−0.816054	−	0.878950i
$371$			10.6317i			0.551970i
$372$	12.9017	−	4.18660i	0.668924	−	0.217065i
$373$	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
$378$	−22.6257	+	13.8591i	−1.16374	+	0.712838i
$379$	−5.39863			−0.277309			−0.138654	−	0.990341i	$-0.544278\pi$
$379$	−5.39863			−0.277309			−0.138654	+	0.990341i	$0.544278\pi$
$380$	27.2069	−	15.3078i	1.39568	−	0.785273i
$381$	53.9464			2.76376
$382$	−16.2235	+	9.93751i	−0.830065	+	0.508447i
$383$	9.81025	−	9.81025i	0.501281	−	0.501281i	−0.410555	−	0.911836i	$-0.634665\pi$
$383$	9.81025	−	9.81025i	0.501281	−	0.501281i	0.911836	+	0.410555i	$0.134665\pi$
$384$	−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
$388$	8.89663	+	27.4165i	0.451658	+	1.39186i
$389$			5.54498i			0.281142i	0.990071	+	0.140571i	$0.0448938\pi$
$389$			5.54498i			0.281142i	−0.990071	+	0.140571i	$0.955106\pi$
$390$	−0.123852	+	3.33772i	−0.00627149	+	0.169012i
$391$		−	28.1814i		−	1.42520i
$392$	−1.11385	−	14.2568i	−0.0562578	−	0.720078i
$393$	−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	$0.307282\pi$
$398$	1.23383	+	2.01428i	0.0618462	+	0.100967i
$399$	−31.1012			−1.55701
$400$	10.3820	−	17.0943i	0.519101	−	0.854713i
$401$	−28.1263			−1.40456			−0.702281	−	0.711900i	$-0.747835\pi$
$401$	−28.1263			−1.40456			−0.702281	+	0.711900i	$0.747835\pi$
$402$	−18.8284	−	30.7382i	−0.939073	−	1.53308i
$403$	−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
$408$	4.03859	+	51.6924i	0.199940	+	2.55915i
$409$		−	29.4667i		−	1.45703i	−0.685029	−	0.728516i	$-0.740210\pi$
$409$		−	29.4667i		−	1.45703i	0.685029	−	0.728516i	$-0.259790\pi$
$410$	−0.334426	+	9.01253i	−0.0165161	+	0.445097i
$411$			37.6245i			1.85588i
$412$	−7.69589	−	23.7162i	−0.379149	−	1.16841i
$413$	−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
$418$	−8.41816	+	5.15645i	−0.411746	+	0.252210i
$419$	37.1639			1.81557			0.907787	−	0.419432i	$-0.137771\pi$
$419$	37.1639			1.81557			0.907787	+	0.419432i	$0.137771\pi$
$420$	−17.3654	+	9.77055i	−0.847346	+	0.476754i
$421$	2.51184			0.122420			0.0612099	−	0.998125i	$-0.480504\pi$
$421$	2.51184			0.122420			0.0612099	+	0.998125i	$0.480504\pi$
$422$	−26.4467	+	16.1996i	−1.28740	+	0.788585i
$423$	−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
$428$	−15.3276	+	4.97380i	−0.740889	+	0.240418i
$429$		−	1.05621i		−	0.0509941i
$430$	−7.23645	−	7.79419i	−0.348973	−	0.375869i
$431$			33.8843i			1.63215i	0.577947	+	0.816074i	$0.303854\pi$
$431$			33.8843i			1.63215i	−0.577947	+	0.816074i	$0.696146\pi$
$432$	−8.46032	+	53.1545i	−0.407047	+	2.55740i
$433$	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
$438$	8.54229	+	13.9457i	0.408166	+	0.666351i
$439$	−11.8365			−0.564924			−0.282462	−	0.959278i	$-0.591151\pi$
$439$	−11.8365			−0.564924			−0.282462	+	0.959278i	$0.591151\pi$
$440$	−3.08038	+	5.52370i	−0.146851	+	0.263332i
$441$	−36.4578			−1.73609
$442$	−1.40072	−	2.28674i	−0.0666254	−	0.108769i
$443$	−15.2136	+	15.2136i	−0.722821	+	0.722821i	−0.969179	−	0.246358i	$-0.920766\pi$
$443$	−15.2136	+	15.2136i	−0.722821	+	0.722821i	0.246358	+	0.969179i	$0.420766\pi$
$444$	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
$448$	9.01667	+	6.56673i	0.425997	+	0.310249i
$449$			2.10304i			0.0992484i	0.998768	+	0.0496242i	$0.0158024\pi$
$449$			2.10304i			0.0992484i	−0.998768	+	0.0496242i	$0.984198\pi$
$450$	−41.3870	−	29.7826i	−1.95100	−	1.40397i
$451$		−	2.85197i		−	0.134294i
$452$	4.21851	−	1.36890i	0.198422	−	0.0643877i
$453$	−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	$0.470235\pi$
$458$	30.6797	−	18.7925i	1.43357	−	0.878116i
$459$	77.1938			3.60310
$460$	5.92116	−	21.1559i	0.276075	−	0.986399i
$461$	−36.5493			−1.70227			−0.851136	−	0.524945i	$-0.824086\pi$
$461$	−36.5493			−1.70227			−0.851136	+	0.524945i	$0.824086\pi$
$462$	5.37308	−	3.29122i	0.249978	−	0.153122i
$463$	6.96766	−	6.96766i	0.323815	−	0.323815i	−0.526414	−	0.850228i	$-0.676464\pi$
$463$	6.96766	−	6.96766i	0.323815	−	0.323815i	0.850228	+	0.526414i	$0.176464\pi$
$464$	−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	0.355834	−	0.934549i	$-0.384197\pi$
$467$	−12.5061	−	12.5061i	−0.578715	−	0.578715i	−0.934549	+	0.355834i	$0.884197\pi$
$468$	−1.47133	−	4.53417i	−0.0680124	−	0.209592i
$469$			11.1218i			0.513555i
$470$	−7.01662	+	6.51452i	−0.323653	+	0.300492i
$471$			39.9666i			1.84156i
$472$	−7.93925	+	0.620273i	−0.365434	+	0.0285504i
$473$	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
$478$	9.78984	+	15.9824i	0.447777	+	0.731018i
$479$	−19.3221			−0.882850			−0.441425	−	0.897298i	$-0.645527\pi$
$479$	−19.3221			−0.882850			−0.441425	+	0.897298i	$0.645527\pi$
$480$	−7.82923	+	39.6542i	−0.357354	+	1.80996i
$481$	−2.41141			−0.109951
$482$	15.3628	+	25.0805i	0.699756	+	1.14239i
$483$	−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	0.798908	−	0.601454i	$-0.205412\pi$
$487$	4.35742	+	4.35742i	0.197454	+	0.197454i	−0.601454	+	0.798908i	$0.705412\pi$
$488$	8.37970	−	0.654684i	0.379331	−	0.0296361i
$489$			66.3521i			3.00055i
$490$	−15.9772	−	0.592862i	−0.721775	−	0.0267828i
$491$		−	3.27844i		−	0.147954i	−0.997260	−	0.0739771i	$-0.976431\pi$
$491$		−	3.27844i		−	0.147954i	0.997260	−	0.0739771i	$-0.0235692\pi$
$492$	−5.62577	−	17.3368i	−0.253629	−	0.781602i
$493$	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
$498$	−4.62252	+	2.83148i	−0.207140	+	0.126881i
$499$	−19.3590			−0.866627			−0.433313	−	0.901243i	$-0.642656\pi$
$499$	−19.3590			−0.866627			−0.433313	+	0.901243i	$0.642656\pi$
$500$	−17.6530	−	13.7249i	−0.789466	−	0.613794i
$501$	7.11556			0.317900
$502$	−4.72536	+	2.89447i	−0.210903	+	0.129186i
$503$	10.7102	−	10.7102i	0.477542	−	0.477542i	−0.426803	−	0.904345i	$-0.640360\pi$
$503$	10.7102	−	10.7102i	0.477542	−	0.477542i	0.904345	+	0.426803i	$0.140360\pi$
$504$	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
$508$	−32.1159	+	10.4216i	−1.42491	+	0.462383i
$509$			4.64711i			0.205979i	0.994682	+	0.102990i	$0.0328409\pi$
$509$			4.64711i			0.205979i	−0.994682	+	0.102990i	$0.967159\pi$
$510$	57.9301	+	2.14960i	2.56519	+	0.0951859i
$511$		−	5.04586i		−	0.223216i
$512$	22.0112	−	5.24458i	0.972768	−	0.231780i
$513$	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
$518$	−7.51415	−	12.2672i	−0.330153	−	0.538990i
$519$	40.5388			1.77945
$520$	−0.571060	−	2.01097i	−0.0250426	−	0.0881867i
$521$	−22.7241			−0.995559			−0.497779	−	0.867304i	$-0.665851\pi$
$521$	−22.7241			−0.995559			−0.497779	+	0.867304i	$0.665851\pi$
$522$	7.67165	+	12.5243i	0.335779	+	0.548176i
$523$	−19.6005	+	19.6005i	−0.857071	+	0.857071i	−0.990992	−	0.133921i	$-0.957243\pi$
$523$	−19.6005	+	19.6005i	−0.857071	+	0.857071i	0.133921	+	0.990992i	$0.457243\pi$
$524$	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
$528$	2.00913	−	12.6229i	0.0874360	−	0.549343i
$529$		−	1.13160i		−	0.0492000i
$530$	17.6707	−	16.4062i	0.767566	−	0.712640i
$531$			20.3024i			0.881051i
$532$	18.5155	−	6.00825i	0.802747	−	0.260491i
$533$	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
$538$	21.9657	−	13.4549i	0.947011	−	0.580081i
$539$	5.05590			0.217773
$540$	57.9496	+	16.2191i	2.49376	+	0.697958i
$541$	31.7244			1.36394			0.681969	−	0.731382i	$-0.261124\pi$
$541$	31.7244			1.36394			0.681969	+	0.731382i	$0.261124\pi$
$542$	−0.423943	+	0.259682i	−0.0182099	+	0.0111543i
$543$	−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	0.756153	−	0.654395i	$-0.227077\pi$
$547$	2.37992	+	2.37992i	0.101758	+	0.101758i	−0.654395	+	0.756153i	$0.727077\pi$
$548$	−7.26843	−	22.3989i	−0.310492	−	0.956835i
$549$		−	21.4287i		−	0.914557i
$550$	5.73947	+	4.13019i	0.244732	+	0.176112i
$551$			10.0535i			0.428294i
$552$	3.45822	+	44.2639i	0.147192	+	1.88400i
$553$	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	$0.335442\pi$
$558$	11.3053	+	18.4565i	0.478592	+	0.781325i
$559$	−1.11167			−0.0470187
$560$	8.45063	−	9.17140i	0.357104	−	0.387563i
$561$	−18.3317			−0.773965
$562$	−6.23471	−	10.1785i	−0.262995	−	0.429353i
$563$	14.5178	−	14.5178i	0.611854	−	0.611854i	−0.331575	−	0.943429i	$-0.607580\pi$
$563$	14.5178	−	14.5178i	0.611854	−	0.611854i	0.943429	+	0.331575i	$0.107580\pi$
$564$	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
$568$	0.642857	+	8.22832i	0.0269737	+	0.345253i
$569$		−	9.77585i		−	0.409825i	−0.978780	−	0.204912i	$-0.934309\pi$
$569$		−	9.77585i		−	0.409825i	0.978780	−	0.204912i	$-0.0656910\pi$
$570$	47.9936	+	51.6926i	2.01023	+	2.16516i
$571$		−	22.3186i		−	0.934006i	−0.884256	−	0.467003i	$-0.845334\pi$
$571$		−	22.3186i		−	0.934006i	0.884256	−	0.467003i	$-0.154666\pi$
$572$	0.204042	+	0.628790i	0.00853141	+	0.0262910i
$573$	−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	$0.137627\pi$
$578$	−19.1879	+	11.7533i	−0.798111	+	0.488874i
$579$	−73.9855			−3.07473
$580$	3.15834	+	5.61339i	0.131143	+	0.233083i
$581$	1.67253			0.0693882
$582$	−55.5375	+	34.0189i	−2.30210	+	1.41013i
$583$	−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	0.511062	−	0.859544i	$-0.329252\pi$
$587$	−8.44304	−	8.44304i	−0.348482	−	0.348482i	−0.859544	+	0.511062i	$0.829252\pi$
$588$	30.7342	−	9.97321i	1.26746	−	0.411288i
$589$			14.8153i			0.610455i
$590$	−0.330150	+	8.89728i	−0.0135920	+	0.366295i
$591$		−	45.9097i		−	1.88847i
$592$	−28.8193	−	4.58701i	−1.18446	−	0.188525i
$593$	−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
$598$	−1.19943	−	1.95812i	−0.0490482	−	0.0800736i
$599$	−47.8167			−1.95374			−0.976868	−	0.213844i	$-0.931402\pi$
$599$	−47.8167			−1.95374			−0.976868	+	0.213844i	$0.931402\pi$
$600$	43.0367	+	13.7853i	1.75696	+	0.562783i
$601$	−22.7524			−0.928090			−0.464045	−	0.885812i	$-0.653602\pi$
$601$	−22.7524			−0.928090			−0.464045	+	0.885812i	$0.653602\pi$
$602$	−3.46406	−	5.65525i	−0.141185	−	0.230491i
$603$	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	0.798294	−	0.602268i	$-0.205736\pi$
$607$	4.82956	+	4.82956i	0.196026	+	0.196026i	−0.602268	+	0.798294i	$0.705736\pi$
$608$	15.1459	−	36.4674i	0.614249	−	1.47895i
$609$		−	6.41688i		−	0.260025i
$610$	0.348465	−	9.39087i	0.0141089	−	0.380225i
$611$			1.00077i			0.0404868i
$612$	−78.6959	+	25.5367i	−3.18109	+	1.03226i
$613$	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	$-0.157763\pi$
$618$	48.0419	−	29.4275i	1.93253	−	1.18375i
$619$	37.3190			1.49998			0.749989	−	0.661450i	$-0.230059\pi$
$619$	37.3190			1.49998			0.749989	+	0.661450i	$0.230059\pi$
$620$	4.65428	+	8.27216i	0.186920	+	0.332218i
$621$	66.1006			2.65253
$622$	−5.01765	+	3.07351i	−0.201189	+	0.123236i
$623$	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
$628$	−7.72089	−	23.7932i	−0.308097	−	0.949454i
$629$			41.8529i			1.66878i
$630$	−21.6329	−	23.3003i	−0.861877	−	0.928305i
$631$			30.0189i			1.19503i	0.801856	+	0.597517i	$0.203846\pi$
$631$			30.0189i			1.19503i	−0.801856	+	0.597517i	$0.796154\pi$
$632$	31.2320	−	2.44008i	1.24234	−	0.0970610i
$633$	−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
$638$	−1.06389	−	1.73685i	−0.0421198	−	0.0687627i
$639$	21.0416			0.832395
$640$	−2.99958	−	25.1198i	−0.118569	−	0.992946i
$641$	−20.1082			−0.794225			−0.397112	−	0.917770i	$-0.629988\pi$
$641$	−20.1082			−0.794225			−0.397112	+	0.917770i	$0.629988\pi$
$642$	−19.0188	−	31.0491i	−0.750612	−	1.22541i
$643$	−23.8112	+	23.8112i	−0.939023	+	0.939023i	−0.998245	−	0.0592221i	$-0.981138\pi$
$643$	−23.8112	+	23.8112i	−0.939023	+	0.939023i	0.0592221	+	0.998245i	$0.481138\pi$
$644$	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	0.732163	−	0.681129i	$-0.238511\pi$
$647$	1.29811	+	1.29811i	0.0510341	+	0.0510341i	−0.681129	+	0.732163i	$0.738511\pi$
$648$	−60.2454	+	4.70682i	−2.36666	+	0.184901i
$649$		−	2.81550i		−	0.110518i
$650$	−2.30676	+	0.376123i	−0.0904787	+	0.0147528i
$651$		−	9.45622i		−	0.370618i
$652$	−12.8181	−	39.5013i	−0.501997	−	1.54699i
$653$	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
$658$	−5.09106	+	3.11848i	−0.198470	+	0.121571i
$659$	45.0742			1.75584			0.877921	−	0.478806i	$-0.158930\pi$
$659$	45.0742			1.75584			0.877921	+	0.478806i	$0.158930\pi$
$660$	−13.7617	−	3.85165i	−0.535672	−	0.149925i
$661$	17.0030			0.661339			0.330670	−	0.943747i	$-0.392725\pi$
$661$	17.0030			0.661339			0.330670	+	0.943747i	$0.392725\pi$
$662$	11.5330	−	7.06443i	0.448244	−	0.274567i
$663$	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
$668$	−4.23610	+	1.37461i	−0.163900	+	0.0531853i
$669$		−	76.4247i		−	2.95475i
$670$	18.4852	−	17.1624i	0.714145	−	0.663042i
$671$			2.97170i			0.114721i
$672$	−9.66724	+	23.2761i	−0.372922	+	0.897896i
$673$	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	$0.196836\pi$
$678$	5.23440	+	8.54541i	0.201026	+	0.328185i
$679$	20.0947			0.771163
$680$	−34.9027	+	9.91143i	−1.33846	+	0.380086i
$681$	72.0825			2.76221
$682$	−1.56780	−	2.55951i	−0.0600342	−	0.0980087i
$683$	−10.7880	+	10.7880i	−0.412791	+	0.412791i	−0.882710	−	0.469918i	$-0.844283\pi$
$683$	−10.7880	+	10.7880i	−0.412791	+	0.412791i	0.469918	+	0.882710i	$0.344283\pi$
$684$	−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
$688$	−13.2858	−	2.11463i	−0.506517	−	0.0806197i
$689$		−	2.52034i		−	0.0960173i
$690$	49.6052	+	1.84069i	1.88844	+	0.0700739i
$691$			8.07888i			0.307335i	0.988123	+	0.153667i	$0.0491085\pi$
$691$			8.07888i			0.307335i	−0.988123	+	0.153667i	$0.950892\pi$
$692$	−24.1339	+	7.83143i	−0.917433	+	0.297706i
$693$	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
$698$	18.3112	−	11.2163i	0.693089	−	0.424544i
$699$	41.1585			1.55676
$700$	−9.10145	−	10.5628i	−0.344003	−	0.399237i
$701$	14.4120			0.544334			0.272167	−	0.962250i	$-0.412260\pi$
$701$	14.4120			0.544334			0.272167	+	0.962250i	$0.412260\pi$
$702$	5.36364	−	3.28544i	0.202437	−	0.124001i
$703$	−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
$708$	−5.55383	−	17.1151i	−0.208726	−	0.643224i
$709$		−	45.0167i		−	1.69064i	−0.534261	−	0.845319i	$-0.679410\pi$
$709$		−	45.0167i		−	1.69064i	0.534261	−	0.845319i	$-0.320590\pi$
$710$	9.22123	+	0.342170i	0.346067	+	0.0128414i
$711$		−	79.8672i		−	2.99525i
$712$	−0.00132023	−	0.0168984i	−4.94776e−5	−	0.000633294i
$713$	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
$718$	4.83318	+	7.89041i	0.180373	+	0.294467i
$719$	30.8823			1.15171			0.575857	−	0.817550i	$-0.304668\pi$
$719$	30.8823			1.15171			0.575857	+	0.817550i	$0.304668\pi$
$720$	−64.4428	+	2.63584i	−2.40164	+	0.0982319i
$721$	−17.3826			−0.647362
$722$	−21.9593	−	35.8497i	−0.817242	−	1.33419i
$723$	−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	0.220470	−	0.975394i	$-0.429241\pi$
$727$	−20.3550	−	20.3550i	−0.754924	−	0.754924i	−0.975394	+	0.220470i	$0.929241\pi$
$728$	−0.101532	−	1.29957i	−0.00376301	−	0.0481651i
$729$			25.0678i			0.928437i
$730$	−8.38660	+	7.78647i	−0.310402	+	0.288190i
$731$			19.2944i			0.713629i
$732$	5.86194	+	18.0646i	0.216663	+	0.667686i
$733$	−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
$738$	24.8010	−	15.1916i	0.912937	−	0.559209i
$739$	−19.7529			−0.726621			−0.363310	−	0.931668i	$-0.618354\pi$
$739$	−19.7529			−0.726621			−0.363310	+	0.931668i	$0.618354\pi$
$740$	−8.79365	+	31.4191i	−0.323261	+	1.15499i
$741$	7.37283			0.270848
$742$	12.8214	−	7.85358i	0.470687	−	0.288314i
$743$	−23.9280	+	23.9280i	−0.877834	+	0.877834i	−0.993310	−	0.115476i	$-0.963161\pi$
$743$	−23.9280	+	23.9280i	−0.877834	+	0.877834i	0.115476	+	0.993310i	$0.463161\pi$
$744$	−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
$748$	10.9134	−	3.54139i	0.399033	−	0.129486i
$749$			11.2342i			0.410491i
$750$	20.8346	−	46.0289i	0.760771	−	1.68074i
$751$			14.8424i			0.541605i	0.962635	+	0.270803i	$0.0872891\pi$
$751$			14.8424i			0.541605i	−0.962635	+	0.270803i	$0.912711\pi$
$752$	−1.90367	+	11.9604i	−0.0694198	+	0.436151i
$753$	−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	$-0.0558389\pi$
$758$	3.98794	+	6.51051i	0.144849	+	0.236472i
$759$	−15.6973			−0.569777
$760$	−38.5581	−	21.5025i	−1.39865	−	0.779979i
$761$	31.1600			1.12955			0.564775	−	0.825245i	$-0.308963\pi$
$761$	31.1600			1.12955			0.564775	+	0.825245i	$0.308963\pi$
$762$	−39.8500	−	65.0570i	−1.44361	−	2.35677i
$763$	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
$768$	23.1419	+	45.5900i	0.835063	+	1.64509i
$769$		−	5.25240i		−	0.189406i	−0.995506	−	0.0947031i	$-0.969810\pi$
$769$		−	5.25240i		−	0.189406i	0.995506	−	0.0947031i	$-0.0301902\pi$
$770$	3.00001	+	3.23124i	0.108113	+	0.116446i
$771$		−	39.2508i		−	1.41358i
$772$	44.0457	−	14.2928i	1.58524	−	0.514409i
$773$	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
$778$	6.68700	−	4.09605i	0.239741	−	0.146851i
$779$	19.9082			0.713284
$780$	4.11663	−	2.31620i	0.147399	−	0.0829331i
$781$	−2.91802			−0.104415
$782$	−33.9856	+	20.8175i	−1.21532	+	0.744432i
$783$	−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	0.954406	−	0.298513i	$-0.0964906\pi$
$787$	18.4001	+	18.4001i	0.655893	+	0.655893i	−0.298513	+	0.954406i	$0.596491\pi$
$788$	8.86901	+	27.3314i	0.315946	+	0.973641i
$789$		−	77.4955i		−	2.75891i
$790$	1.29877	−	35.0008i	0.0462080	−	1.24527i
$791$		−	3.09192i		−	0.109936i
$792$	20.3337	−	1.58862i	0.722525	−	0.0564490i
$793$	−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	$0.0814578\pi$
$798$	22.9743	+	37.5067i	0.813283	+	1.32772i
$799$	17.3695			0.614490
$800$	−28.2841	+	0.107181i	−0.999993	+	0.00378942i
$801$	−0.0432129			−0.00152685
$802$	20.7768	+	33.9191i	0.733654	+	1.19773i
$803$	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
$808$	−0.509470	+	0.0398036i	−0.0179231	+	0.00140029i
$809$			24.1778i			0.850046i	0.905183	+	0.425023i	$0.139734\pi$
$809$			24.1778i			0.850046i	−0.905183	+	0.425023i	$0.860266\pi$
$810$	−2.50527	+	67.5152i	−0.0880263	+	2.37224i
$811$			0.0123408i			0.000433344i	1.00000		0.000216672i	$6.89689e-5\pi$
$811$			0.0123408i			0.000433344i	−1.00000		0.000216672i	$0.999931\pi$
$812$	1.23964	+	3.82015i	0.0435027	+	0.134061i
$813$	−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
$818$	−35.5355	+	21.7669i	−1.24247	+	0.761061i
$819$	−3.32328			−0.116125
$820$	11.1157	−	6.25421i	0.388179	−	0.218406i
$821$	−36.0595			−1.25849			−0.629243	−	0.777209i	$-0.716635\pi$
$821$	−36.0595			−1.25849			−0.629243	+	0.777209i	$0.716635\pi$
$822$	45.3735	−	27.7930i	1.58258	−	0.969393i
$823$	−3.12980	+	3.12980i	−0.109098	+	0.109098i	−0.759549	−	0.650451i	$-0.774580\pi$
$823$	−3.12980	+	3.12980i	−0.109098	+	0.109098i	0.650451	+	0.759549i	$0.274580\pi$
$824$	−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	0.843531	−	0.537080i	$-0.180473\pi$
$827$	8.81282	+	8.81282i	0.306452	+	0.306452i	−0.537080	+	0.843531i	$0.680473\pi$
$828$	−67.3868	+	21.8670i	−2.34185	+	0.759930i
$829$			50.9263i			1.76874i	0.466784	+	0.884371i	$0.345412\pi$
$829$			50.9263i			1.76874i	−0.466784	+	0.884371i	$0.654588\pi$
$830$	−2.58095	−	2.77987i	−0.0895860	−	0.0964907i
$831$		−	29.9712i		−	1.03969i
$832$	−2.13748	−	1.55670i	−0.0741039	−	0.0539690i
$833$	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
$838$	−27.4528	−	44.8180i	−0.948340	−	1.54821i
$839$	−30.5168			−1.05356			−0.526779	−	0.850002i	$-0.676600\pi$
$839$	−30.5168			−1.05356			−0.526779	+	0.850002i	$0.676600\pi$
$840$	24.6106	+	13.7245i	0.849146	+	0.473539i
$841$	26.9257			0.928474
$842$	−1.85549	−	3.02917i	−0.0639443	−	0.104392i
$843$	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
$848$	4.79422	−	30.1211i	0.164634	−	1.03436i
$849$			44.0115i			1.51047i
$850$	6.52807	+	40.0366i	0.223911	+	1.37324i
$851$			35.8384i			1.22852i
$852$	−17.7382	+	5.75604i	−0.607702	+	0.197199i
$853$	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	$0.170852\pi$
$858$	−1.27374	+	0.780214i	−0.0434847	+	0.0266361i
$859$	23.0026			0.784840			0.392420	−	0.919786i	$-0.371638\pi$
$859$	23.0026			0.784840			0.392420	+	0.919786i	$0.371638\pi$
$860$	−4.05392	+	14.4844i	−0.138237	+	0.493913i
$861$	−12.7068			−0.433048
$862$	40.8629	−	25.0301i	1.39180	−	0.852530i
$863$	−5.71361	+	5.71361i	−0.194494	+	0.194494i	−0.797635	−	0.603141i	$-0.793916\pi$
$863$	−5.71361	+	5.71361i	−0.194494	+	0.194494i	0.603141	+	0.797635i	$0.293916\pi$
$864$	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
$868$	1.82679	+	5.62956i	0.0620052	+	0.191080i
$869$			11.0758i			0.375722i
$870$	−10.6653	+	9.90214i	−0.361589	+	0.335714i
$871$		−	2.63651i		−	0.0893348i
$872$	−4.15591	−	53.1941i	−0.140737	−	1.80138i
$873$	−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	$0.457681\pi$
$878$	8.74355	+	14.2743i	0.295080	+	0.481733i
$879$	−44.6927			−1.50745
$880$	8.93680	−	0.365533i	0.301259	−	0.0123221i
$881$	−6.30487			−0.212416			−0.106208	−	0.994344i	$-0.533871\pi$
$881$	−6.30487			−0.212416			−0.106208	+	0.994344i	$0.533871\pi$
$882$	26.9312	+	43.9665i	0.906821	+	1.48043i
$883$	4.07678	−	4.07678i	0.137194	−	0.137194i	−0.635174	−	0.772369i	$-0.719072\pi$
$883$	4.07678	−	4.07678i	0.137194	−	0.137194i	0.772369	+	0.635174i	$0.219072\pi$
$884$	−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	$-0.921419\pi$
$887$	−36.1576	−	36.1576i	−1.21405	−	1.21405i	−0.244370	−	0.969682i	$-0.578581\pi$
$888$	−5.13589	−	65.7373i	−0.172349	−	2.20600i
$889$			23.5390i			0.789474i
$890$	−0.0189375		0.000702711i	−0.000634787		2.35549e-5i
$891$		−	21.3649i		−	0.715750i
$892$	14.7640	+	45.4978i	0.494335	+	1.52338i
$893$	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
$898$	2.53617	−	1.55350i	0.0846331	−	0.0518411i
$899$	−3.05673			−0.101948
$900$	−5.34414	+	71.9111i	−0.178138	+	2.39704i
$901$	−43.7435			−1.45731
$902$	−3.43935	+	2.10674i	−0.114518	+	0.0701467i
$903$	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	0.402271	−	0.915521i	$-0.368221\pi$
$907$	−15.4572	−	15.4572i	−0.513250	−	0.513250i	−0.915521	+	0.402271i	$0.868221\pi$
$908$	−42.9128	+	13.9252i	−1.42411	+	0.462123i
$909$			1.30283i			0.0432121i
$910$	−1.45638	−	0.0540417i	−0.0482786	−	0.00179147i
$911$		−	39.0494i		−	1.29376i	−0.762590	−	0.646882i	$-0.776073\pi$
$911$		−	39.0494i		−	1.29376i	0.762590	−	0.646882i	$-0.223927\pi$
$912$	88.1142	+	14.0247i	2.91775	+	0.464403i
$913$	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
$918$	−57.0227	−	93.0923i	−1.88203	−	3.07250i
$919$	27.2993			0.900520			0.450260	−	0.892897i	$-0.351331\pi$
$919$	27.2993			0.900520			0.450260	+	0.892897i	$0.351331\pi$
$920$	−29.8870	+	8.48710i	−0.985345	+	0.279811i
$921$	−1.59362			−0.0525117
$922$	26.9988	+	44.0769i	0.889158	+	1.45159i
$923$	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
$928$	7.52403	+	3.12495i	0.246988	+	0.102581i
$929$			7.40140i			0.242832i	0.992602	+	0.121416i	$0.0387435\pi$
$929$			7.40140i			0.242832i	−0.992602	+	0.121416i	$0.961256\pi$
$930$	−15.7169	+	14.5923i	−0.515379	+	0.478499i
$931$			35.2927i			1.15667i
$932$	−24.5029	+	7.95116i	−0.802618	+	0.260449i
$933$	−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	$0.411553\pi$
$938$	13.4123	−	8.21559i	0.437929	−	0.268248i
$939$	−99.2066			−3.23748
$940$	13.0394	+	3.64949i	0.425297	+	0.119033i
$941$	−46.4937			−1.51565			−0.757826	−	0.652456i	$-0.773739\pi$
$941$	−46.4937			−1.51565			−0.757826	+	0.652456i	$0.773739\pi$
$942$	48.1979	−	29.5231i	1.57037	−	0.961914i
$943$	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	0.404656	−	0.914469i	$-0.367391\pi$
$947$	−15.6887	−	15.6887i	−0.509813	−	0.509813i	−0.914469	+	0.404656i	$0.867391\pi$
$948$	21.8480	+	67.3285i	0.709592	+	2.18673i
$949$			1.19617i			0.0388292i
$950$	−28.8308	+	40.0643i	−0.935394	+	1.29986i
$951$			91.2124i			2.95776i
$952$	−22.5555	+	1.76220i	−0.731028	+	0.0571133i
$953$	−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
$958$	14.2731	+	23.3016i	0.461144	+	0.752841i
$959$	−16.4171			−0.530136
$960$	53.6046	−	19.8506i	1.73008	−	0.640677i
$961$	26.4955			0.854692
$962$	1.78130	+	2.90805i	0.0574313	+	0.0937594i
$963$	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	0.993370	−	0.114961i	$-0.0366744\pi$
$967$	27.3155	+	27.3155i	0.878409	+	0.878409i	−0.114961	+	0.993370i	$0.536674\pi$
$968$	−2.81983	+	0.220306i	−0.0906329	+	0.00708091i
$969$		−	127.964i		−	4.11080i
$970$	−31.0089	−	33.3989i	−0.995636	−	1.07237i
$971$			6.88941i			0.221092i	0.993871	+	0.110546i	$0.0352599\pi$
$971$			6.88941i			0.221092i	−0.993871	+	0.110546i	$0.964740\pi$
$972$	−17.2247	−	53.0810i	−0.552483	−	1.70257i
$973$	−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	$0.220285\pi$
$978$	80.0177	−	49.0140i	2.55868	−	1.56729i
$979$	0.00599269			0.000191527
$980$	11.0873	+	19.7057i	0.354171	+	0.629476i
$981$	−136.029			−4.34307
$982$	−3.95366	+	2.42177i	−0.126166	+	0.0772818i
$983$	3.44593	−	3.44593i	0.109908	−	0.109908i	−0.650014	−	0.759922i	$-0.725237\pi$
$983$	3.44593	−	3.44593i	0.109908	−	0.109908i	0.759922	+	0.650014i	$0.225237\pi$
$984$	−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
$988$	−4.38926	+	1.42431i	−0.139641	+	0.0453134i
$989$			16.5217i			0.525359i
$990$	0.845565	−	22.7873i	0.0268738	−	0.724229i
$991$			19.8268i			0.629819i	0.949122	+	0.314909i	$0.101974\pi$
$991$			19.8268i			0.629819i	−0.949122	+	0.314909i	$0.898026\pi$
$992$	11.0878	+	4.60507i	0.352037	+	0.146211i
$993$	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	$0.930878\pi$
$998$	14.3004	+	23.3461i	0.452671	+	0.739007i
$999$	−98.1675			−3.10588

Display

a_p

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

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)

Twists

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

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

Overview	Random
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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

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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.d.23.4

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