LMFDB - Embedded newform 228.2.c.a.191.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(191,228)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("228.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.15
Character	$\chi$	$=$	228.191
Dual form			228.2.c.a.191.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.474569 - 1.33221i) q^{2} +(-1.60213 + 0.658173i) q^{3} +(-1.54957 + 1.26445i) q^{4} -0.191837i q^{5} +(1.63714 + 1.82202i) q^{6} +0.733628i q^{7} +(2.41989 + 1.46428i) q^{8} +(2.13362 - 2.10895i) q^{9} +O(q^{10})$	\(q+(-0.474569 - 1.33221i) q^{2} +(-1.60213 + 0.658173i) q^{3} +(-1.54957 + 1.26445i) q^{4} -0.191837i q^{5} +(1.63714 + 1.82202i) q^{6} +0.733628i q^{7} +(2.41989 + 1.46428i) q^{8} +(2.13362 - 2.10895i) q^{9} +(-0.255567 + 0.0910397i) q^{10} +2.95731 q^{11} +(1.65038 - 3.04569i) q^{12} +4.31169 q^{13} +(0.977347 - 0.348157i) q^{14} +(0.126262 + 0.307347i) q^{15} +(0.802324 - 3.91871i) q^{16} +1.98385i q^{17} +(-3.82212 - 1.84158i) q^{18} -1.00000i q^{19} +(0.242568 + 0.297264i) q^{20} +(-0.482854 - 1.17536i) q^{21} +(-1.40345 - 3.93975i) q^{22} +2.69669 q^{23} +(-4.84072 - 0.753256i) q^{24} +4.96320 q^{25} +(-2.04620 - 5.74408i) q^{26} +(-2.03027 + 4.78310i) q^{27} +(-0.927637 - 1.13681i) q^{28} +8.26462i q^{29} +(0.349530 - 0.314064i) q^{30} -4.66570i q^{31} +(-5.60130 + 0.790833i) q^{32} +(-4.73798 + 1.94642i) q^{33} +(2.64291 - 0.941475i) q^{34} +0.140737 q^{35} +(-0.639519 + 5.96582i) q^{36} -5.08273 q^{37} +(-1.33221 + 0.474569i) q^{38} +(-6.90788 + 2.83784i) q^{39} +(0.280903 - 0.464224i) q^{40} -6.49966i q^{41} +(-1.33669 + 1.20105i) q^{42} +4.65023i q^{43} +(-4.58255 + 3.73937i) q^{44} +(-0.404574 - 0.409306i) q^{45} +(-1.27976 - 3.59256i) q^{46} +6.14432 q^{47} +(1.29376 + 6.80633i) q^{48} +6.46179 q^{49} +(-2.35538 - 6.61202i) q^{50} +(-1.30572 - 3.17838i) q^{51} +(-6.68127 + 5.45193i) q^{52} +7.35410i q^{53} +(7.33559 + 0.434838i) q^{54} -0.567319i q^{55} +(-1.07424 + 1.77530i) q^{56} +(0.658173 + 1.60213i) q^{57} +(11.0102 - 3.92213i) q^{58} -9.63156 q^{59} +(-0.584276 - 0.316603i) q^{60} -1.98059 q^{61} +(-6.21570 + 2.21420i) q^{62} +(1.54719 + 1.56528i) q^{63} +(3.71176 + 7.08681i) q^{64} -0.827141i q^{65} +(4.84153 + 5.38827i) q^{66} +0.0795340i q^{67} +(-2.50848 - 3.07411i) q^{68} +(-4.32043 + 1.77489i) q^{69} +(-0.0667893 - 0.187491i) q^{70} +8.52131 q^{71} +(8.25122 - 1.97922i) q^{72} -5.26155 q^{73} +(2.41211 + 6.77127i) q^{74} +(-7.95167 + 3.26664i) q^{75} +(1.26445 + 1.54957i) q^{76} +2.16956i q^{77} +(7.05886 + 7.85600i) q^{78} -15.3553i q^{79} +(-0.751752 - 0.153915i) q^{80} +(0.104648 - 8.99939i) q^{81} +(-8.65891 + 3.08454i) q^{82} -0.0511504 q^{83} +(2.23441 + 1.21076i) q^{84} +0.380575 q^{85} +(6.19508 - 2.20685i) q^{86} +(-5.43954 - 13.2410i) q^{87} +(7.15636 + 4.33033i) q^{88} -10.6913i q^{89} +(-0.353283 + 0.733222i) q^{90} +3.16318i q^{91} +(-4.17870 + 3.40983i) q^{92} +(3.07084 + 7.47505i) q^{93} +(-2.91590 - 8.18553i) q^{94} -0.191837 q^{95} +(8.45349 - 4.95364i) q^{96} -12.3555 q^{97} +(-3.06657 - 8.60846i) q^{98} +(6.30976 - 6.23681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{6}+O(q^{10}) $ 36 * q - 6 * q^6	$ 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) $ 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.474569	−	1.33221i	−0.335571	−	0.942015i
$2$	−0.474569	−	1.33221i	−0.335571	−	0.942015i
$3$	−1.60213	+	0.658173i	−0.924988	+	0.379996i
$3$	−1.60213	+	0.658173i	−0.924988	+	0.379996i
$4$	−1.54957	+	1.26445i	−0.774784	+	0.632226i
$5$		−	0.191837i		−	0.0857920i	−0.999080	−	0.0428960i	$-0.986342\pi$
$5$		−	0.191837i		−	0.0857920i	0.999080	−	0.0428960i	$-0.0136584\pi$
$6$	1.63714	+	1.82202i	0.668361	+	0.743837i
$7$			0.733628i			0.277285i	0.990342	+	0.138643i	$0.0442740\pi$
$7$			0.733628i			0.277285i	−0.990342	+	0.138643i	$0.955726\pi$
$8$	2.41989	+	1.46428i	0.855561	+	0.517702i
$9$	2.13362	−	2.10895i	0.711206	−	0.702984i
$10$	−0.255567	+	0.0910397i	−0.0808173	+	0.0287893i
$11$	2.95731			0.891661			0.445831	−	0.895117i	$-0.352908\pi$
$11$	2.95731			0.891661			0.445831	+	0.895117i	$0.352908\pi$
$12$	1.65038	−	3.04569i	0.476423	−	0.879216i
$13$	4.31169			1.19585			0.597924	−	0.801552i	$-0.295992\pi$
$13$	4.31169			1.19585			0.597924	+	0.801552i	$0.295992\pi$
$14$	0.977347	−	0.348157i	0.261207	−	0.0930489i
$15$	0.126262	+	0.307347i	0.0326006	+	0.0793565i
$16$	0.802324	−	3.91871i	0.200581	−	0.979677i
$17$			1.98385i			0.481155i	0.970630	+	0.240577i	$0.0773368\pi$
$17$			1.98385i			0.481155i	−0.970630	+	0.240577i	$0.922663\pi$
$18$	−3.82212	−	1.84158i	−0.900881	−	0.434066i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	0.242568	+	0.297264i	0.0542399	+	0.0664702i
$21$	−0.482854	−	1.17536i	−0.105367	−	0.256486i
$22$	−1.40345	−	3.93975i	−0.299216	−	0.839958i
$23$	2.69669			0.562298			0.281149	−	0.959664i	$-0.409284\pi$
$23$	2.69669			0.562298			0.281149	+	0.959664i	$0.409284\pi$
$24$	−4.84072	−	0.753256i	−0.988109	−	0.153758i
$25$	4.96320			0.992640
$26$	−2.04620	−	5.74408i	−0.401292	−	1.12651i
$27$	−2.03027	+	4.78310i	−0.390726	+	0.920507i
$28$	−0.927637	−	1.13681i	−0.175307	−	0.214836i
$29$			8.26462i			1.53470i	0.641228	+	0.767350i	$0.278425\pi$
$29$			8.26462i			1.53470i	−0.641228	+	0.767350i	$0.721575\pi$
$30$	0.349530	−	0.314064i	0.0638152	−	0.0573400i
$31$		−	4.66570i		−	0.837985i	−0.907990	−	0.418993i	$-0.862383\pi$
$31$		−	4.66570i		−	0.837985i	0.907990	−	0.418993i	$-0.137617\pi$
$32$	−5.60130	+	0.790833i	−0.990180	+	0.139801i
$33$	−4.73798	+	1.94642i	−0.824776	+	0.338828i
$34$	2.64291	−	0.941475i	0.453255	−	0.161462i
$35$	0.140737			0.0237889
$36$	−0.639519	+	5.96582i	−0.106587	+	0.994303i
$37$	−5.08273			−0.835596			−0.417798	−	0.908540i	$-0.637198\pi$
$37$	−5.08273			−0.835596			−0.417798	+	0.908540i	$0.637198\pi$
$38$	−1.33221	+	0.474569i	−0.216113	+	0.0769853i
$39$	−6.90788	+	2.83784i	−1.10615	+	0.454418i
$40$	0.280903	−	0.464224i	0.0444146	−	0.0734003i
$41$		−	6.49966i		−	1.01508i	−0.861629	−	0.507538i	$-0.830556\pi$
$41$		−	6.49966i		−	1.01508i	0.861629	−	0.507538i	$-0.169444\pi$
$42$	−1.33669	+	1.20105i	−0.206255	+	0.185327i
$43$			4.65023i			0.709153i	0.935027	+	0.354576i	$0.115375\pi$
$43$			4.65023i			0.709153i	−0.935027	+	0.354576i	$0.884625\pi$
$44$	−4.58255	+	3.73937i	−0.690845	+	0.563731i
$45$	−0.404574	−	0.409306i	−0.0603104	−	0.0610157i
$46$	−1.27976	−	3.59256i	−0.188691	−	0.529693i
$47$	6.14432			0.896241			0.448121	−	0.893973i	$-0.352094\pi$
$47$	6.14432			0.896241			0.448121	+	0.893973i	$0.352094\pi$
$48$	1.29376	+	6.80633i	0.186738	+	0.982410i
$49$	6.46179			0.923113
$50$	−2.35538	−	6.61202i	−0.333101	−	0.935081i
$51$	−1.30572	−	3.17838i	−0.182837	−	0.445062i
$52$	−6.68127	+	5.45193i	−0.926525	+	0.756047i
$53$			7.35410i			1.01016i	0.863072	+	0.505082i	$0.168538\pi$
$53$			7.35410i			1.01016i	−0.863072	+	0.505082i	$0.831462\pi$
$54$	7.33559	+	0.434838i	0.998248	+	0.0591740i
$55$		−	0.567319i		−	0.0764973i
$56$	−1.07424	+	1.77530i	−0.143551	+	0.237235i
$57$	0.658173	+	1.60213i	0.0871771	+	0.212207i
$58$	11.0102	−	3.92213i	1.44571	−	0.515001i
$59$	−9.63156			−1.25392			−0.626961	−	0.779051i	$-0.715702\pi$
$59$	−9.63156			−1.25392			−0.626961	+	0.779051i	$0.715702\pi$
$60$	−0.584276	−	0.316603i	−0.0754297	−	0.0408732i
$61$	−1.98059			−0.253588			−0.126794	−	0.991929i	$-0.540469\pi$
$61$	−1.98059			−0.253588			−0.126794	+	0.991929i	$0.540469\pi$
$62$	−6.21570	+	2.21420i	−0.789395	+	0.281204i
$63$	1.54719	+	1.56528i	0.194927	+	0.197207i
$64$	3.71176	+	7.08681i	0.463970	+	0.885851i
$65$		−	0.827141i		−	0.102594i
$66$	4.84153	+	5.38827i	0.595952	+	0.663250i
$67$			0.0795340i			0.00971662i	0.999988	+	0.00485831i	$0.00154645\pi$
$67$			0.0795340i			0.00971662i	−0.999988	+	0.00485831i	$0.998454\pi$
$68$	−2.50848	−	3.07411i	−0.304198	−	0.372791i
$69$	−4.32043	+	1.77489i	−0.520119	+	0.213671i
$70$	−0.0667893	−	0.187491i	−0.00798285	−	0.0224095i
$71$	8.52131			1.01129			0.505647	−	0.862741i	$-0.331254\pi$
$71$	8.52131			1.01129			0.505647	+	0.862741i	$0.331254\pi$
$72$	8.25122	−	1.97922i	0.972416	−	0.233253i
$73$	−5.26155			−0.615817			−0.307909	−	0.951416i	$-0.599629\pi$
$73$	−5.26155			−0.615817			−0.307909	+	0.951416i	$0.599629\pi$
$74$	2.41211	+	6.77127i	0.280402	+	0.787144i
$75$	−7.95167	+	3.26664i	−0.918180	+	0.377199i
$76$	1.26445	+	1.54957i	0.145043	+	0.177748i
$77$			2.16956i			0.247245i
$78$	7.05886	+	7.85600i	0.799259	+	0.889517i
$79$		−	15.3553i		−	1.72761i	−0.503830	−	0.863803i	$-0.668076\pi$
$79$		−	15.3553i		−	1.72761i	0.503830	−	0.863803i	$-0.331924\pi$
$80$	−0.751752	−	0.153915i	−0.0840484	−	0.0172082i
$81$	0.104648	−	8.99939i	0.0116275	−	0.999932i
$82$	−8.65891	+	3.08454i	−0.956217	+	0.340630i
$83$	−0.0511504			−0.00561448			−0.00280724	−	0.999996i	$-0.500894\pi$
$83$	−0.0511504			−0.00561448			−0.00280724	+	0.999996i	$0.500894\pi$
$84$	2.23441	+	1.21076i	0.243794	+	0.132105i
$85$	0.380575			0.0412792
$86$	6.19508	−	2.20685i	0.668033	−	0.237971i
$87$	−5.43954	−	13.2410i	−0.583180	−	1.41958i
$88$	7.15636	+	4.33033i	0.762871	+	0.461614i
$89$		−	10.6913i		−	1.13328i	−0.823965	−	0.566640i	$-0.808243\pi$
$89$		−	10.6913i		−	1.13328i	0.823965	−	0.566640i	$-0.191757\pi$
$90$	−0.353283	+	0.733222i	−0.0372393	+	0.0772884i
$91$			3.16318i			0.331591i
$92$	−4.17870	+	3.40983i	−0.435660	+	0.355500i
$93$	3.07084	+	7.47505i	0.318431	+	0.775126i
$94$	−2.91590	−	8.18553i	−0.300753	−	0.844273i
$95$	−0.191837			−0.0196820
$96$	8.45349	−	4.95364i	0.862781	−	0.505579i
$97$	−12.3555			−1.25451			−0.627254	−	0.778815i	$-0.715821\pi$
$97$	−12.3555			−1.25451			−0.627254	+	0.778815i	$0.715821\pi$
$98$	−3.06657	−	8.60846i	−0.309770	−	0.869586i
$99$	6.30976	−	6.23681i	0.634155	−	0.626823i
$100$	−7.69082	+	6.27572i	−0.769082	+	0.627572i
$101$		−	7.32537i		−	0.728901i	−0.931223	−	0.364451i	$-0.881257\pi$
$101$		−	7.32537i		−	0.728901i	0.931223	−	0.364451i	$-0.118743\pi$
$102$	−3.61462	+	3.24785i	−0.357901	+	0.321585i
$103$			6.92596i			0.682436i	0.939984	+	0.341218i	$0.110839\pi$
$103$			6.92596i			0.682436i	−0.939984	+	0.341218i	$0.889161\pi$
$104$	10.4338	+	6.31353i	1.02312	+	0.619093i
$105$	−0.225478	+	0.0926291i	−0.0220044	+	0.00903967i
$106$	9.79720	−	3.49003i	0.951589	−	0.338981i
$107$	3.00921			0.290912			0.145456	−	0.989365i	$-0.453535\pi$
$107$	3.00921			0.290912			0.145456	+	0.989365i	$0.453535\pi$
$108$	−2.90195	−	9.97891i	−0.279240	−	0.960221i
$109$	−17.5858			−1.68441			−0.842206	−	0.539156i	$-0.818743\pi$
$109$	−17.5858			−1.68441			−0.842206	+	0.539156i	$0.818743\pi$
$110$	−0.755789	+	0.269232i	−0.0720616	+	0.0256703i
$111$	8.14318	−	3.34531i	0.772916	−	0.317523i
$112$	2.87487	+	0.588608i	0.271650	+	0.0556182i
$113$		−	17.4939i		−	1.64568i	−0.568270	−	0.822842i	$-0.692387\pi$
$113$		−	17.4939i		−	1.64568i	0.568270	−	0.822842i	$-0.307613\pi$
$114$	1.82202	−	1.63714i	0.170648	−	0.153333i
$115$		−	0.517324i		−	0.0482407i
$116$	−10.4502	−	12.8066i	−0.970277	−	1.18906i
$117$	9.19951	−	9.09315i	0.850495	−	0.840662i
$118$	4.57084	+	12.8313i	0.420780	+	1.18121i
$119$	−1.45541			−0.133417
$120$	−0.144502	+	0.928628i	−0.0131912	+	0.0847718i
$121$	−2.25435			−0.204941
$122$	0.939926	+	2.63856i	0.0850969	+	0.238884i
$123$	4.27790	+	10.4133i	0.385725	+	0.938933i
$124$	5.89956	+	7.22983i	0.529796	+	0.649258i
$125$		−	1.91131i		−	0.170952i
$126$	1.35104	−	2.80401i	0.120360	−	0.249801i
$127$			14.9429i			1.32597i	0.748632	+	0.662985i	$0.230711\pi$
$127$			14.9429i			1.32597i	−0.748632	+	0.662985i	$0.769289\pi$
$128$	7.67963	−	8.30803i	0.678790	−	0.734333i
$129$	−3.06065	−	7.45025i	−0.269475	−	0.655958i
$130$	−1.10193	+	0.392536i	−0.0966453	+	0.0344276i
$131$	19.1751			1.67533			0.837666	−	0.546183i	$-0.183920\pi$
$131$	19.1751			1.67533			0.837666	+	0.546183i	$0.183920\pi$
$132$	4.88067	−	9.00705i	0.424808	−	0.783963i
$133$	0.733628			0.0636136
$134$	0.105956	−	0.0377444i	0.00915320	−	0.00326062i
$135$	0.917573	+	0.389480i	0.0789721	+	0.0335211i
$136$	−2.90492	+	4.80071i	−0.249095	+	0.411657i
$137$			14.9263i			1.27524i	0.770352	+	0.637619i	$0.220081\pi$
$137$			14.9263i			1.27524i	−0.770352	+	0.637619i	$0.779919\pi$
$138$	4.41487	+	4.91342i	0.375818	+	0.418258i
$139$		−	19.4651i		−	1.65101i	−0.564393	−	0.825506i	$-0.690890\pi$
$139$		−	19.4651i		−	1.65101i	0.564393	−	0.825506i	$-0.309110\pi$
$140$	−0.218081	+	0.177955i	−0.0184312	+	0.0150399i
$141$	−9.84398	+	4.04402i	−0.829012	+	0.340568i
$142$	−4.04395	−	11.3522i	−0.339361	−	0.952653i
$143$	12.7510			1.06629
$144$	−6.55251	−	10.0531i	−0.546043	−	0.837757i
$145$	1.58546			0.131665
$146$	2.49697	+	7.00949i	0.206650	+	0.580109i
$147$	−10.3526	+	4.25297i	−0.853868	+	0.350779i
$148$	7.87604	−	6.42687i	0.647407	−	0.528285i
$149$			9.53701i			0.781302i	0.920539	+	0.390651i	$0.127750\pi$
$149$			9.53701i			0.781302i	−0.920539	+	0.390651i	$0.872250\pi$
$150$	8.12547	+	9.04305i	0.663442	+	0.738362i
$151$			24.3454i			1.98120i	0.136793	+	0.990600i	$0.456321\pi$
$151$			24.3454i			1.98120i	−0.136793	+	0.990600i	$0.543679\pi$
$152$	1.46428	−	2.41989i	0.118769	−	0.196279i
$153$	4.18385	+	4.23278i	0.338244	+	0.342200i
$154$	2.89031	−	1.02961i	0.232908	−	0.0829681i
$155$	−0.895053			−0.0718924
$156$	7.11592	−	13.1321i	0.569730	−	1.05141i
$157$	6.87668			0.548819			0.274409	−	0.961613i	$-0.411518\pi$
$157$	6.87668			0.548819			0.274409	+	0.961613i	$0.411518\pi$
$158$	−20.4565	+	7.28715i	−1.62743	+	0.579734i
$159$	−4.84027	−	11.7822i	−0.383858	−	0.934389i
$160$	0.151711	+	1.07453i	0.0119938	+	0.0849494i
$161$			1.97837i			0.155917i
$162$	−12.0387	+	4.13142i	−0.945853	+	0.324595i
$163$		−	0.309503i		−	0.0242421i	−0.999927	−	0.0121211i	$-0.996142\pi$
$163$		−	0.309503i		−	0.0242421i	0.999927	−	0.0121211i	$-0.00385835\pi$
$164$	8.21850	+	10.0717i	0.641757	+	0.786465i
$165$	0.373394	+	0.908917i	0.0290687	+	0.0707591i
$166$	0.0242744	+	0.0681431i	0.00188406	+	0.00528893i
$167$	−22.4067			−1.73388			−0.866940	−	0.498412i	$-0.833917\pi$
$167$	−22.4067			−1.73388			−0.866940	+	0.498412i	$0.833917\pi$
$168$	0.552610	−	3.55129i	0.0426348	−	0.273988i
$169$	5.59071			0.430055
$170$	−0.180609	−	0.507006i	−0.0138521	−	0.0388856i
$171$	−2.10895	−	2.13362i	−0.161276	−	0.163162i
$172$	−5.87999	−	7.20584i	−0.448345	−	0.549440i
$173$			10.6578i			0.810294i	0.914252	+	0.405147i	$0.132780\pi$
$173$			10.6578i			0.810294i	−0.914252	+	0.405147i	$0.867220\pi$
$174$	−15.0583	+	13.5304i	−1.14157	+	1.02573i
$175$			3.64114i			0.275244i
$176$	2.37272	−	11.5888i	0.178850	−	0.873540i
$177$	15.4310	−	6.33923i	1.15986	−	0.476486i
$178$	−14.2431	+	5.07378i	−1.06757	+	0.380296i
$179$	2.56983			0.192078			0.0960389	−	0.995378i	$-0.469383\pi$
$179$	2.56983			0.192078			0.0960389	+	0.995378i	$0.469383\pi$
$180$	1.14446	+	0.122683i	0.0853032	+	0.00914427i
$181$	2.97582			0.221191			0.110595	−	0.993866i	$-0.464724\pi$
$181$	2.97582			0.221191			0.110595	+	0.993866i	$0.464724\pi$
$182$	4.21402	−	1.50115i	0.312364	−	0.111272i
$183$	3.17315	−	1.30357i	0.234566	−	0.0963626i
$184$	6.52570	+	3.94871i	0.481081	+	0.291103i
$185$			0.975054i			0.0716874i
$186$	8.50101	−	7.63843i	0.623324	−	0.560077i
$187$			5.86685i			0.429027i
$188$	−9.52104	+	7.76920i	−0.694393	+	0.566627i
$189$	−3.50901	−	1.48946i	−0.255243	−	0.108343i
$190$	0.0910397	+	0.255567i	0.00660472	+	0.0185408i
$191$	−7.12510			−0.515554			−0.257777	−	0.966204i	$-0.582990\pi$
$191$	−7.12510			−0.515554			−0.257777	+	0.966204i	$0.582990\pi$
$192$	−10.6111	−	8.91098i	−0.765787	−	0.643095i
$193$	16.3030			1.17351			0.586757	−	0.809763i	$-0.300405\pi$
$193$	16.3030			1.17351			0.586757	+	0.809763i	$0.300405\pi$
$194$	5.86352	+	16.4601i	0.420976	+	1.18176i
$195$	0.544402	+	1.32518i	0.0389854	+	0.0948984i
$196$	−10.0130	+	8.17062i	−0.715213	+	0.583616i
$197$			7.77505i			0.553949i	0.960877	+	0.276975i	$0.0893318\pi$
$197$			7.77505i			0.553949i	−0.960877	+	0.276975i	$0.910668\pi$
$198$	−11.3032	−	5.44613i	−0.803281	−	0.387039i
$199$			11.7568i			0.833415i	0.909041	+	0.416707i	$0.136816\pi$
$199$			11.7568i			0.833415i	−0.909041	+	0.416707i	$0.863184\pi$
$200$	12.0104	+	7.26752i	0.849264	+	0.513891i
$201$	−0.0523471	−	0.127423i	−0.00369228	−	0.00898776i
$202$	−9.75893	+	3.47639i	−0.686636	+	0.244598i
$203$	−6.06316			−0.425550
$204$	6.04221	+	3.27410i	0.423039	+	0.229233i
$205$	−1.24687			−0.0870853
$206$	9.22684	−	3.28685i	0.642864	−	0.229006i
$207$	5.75370	−	5.68718i	0.399910	−	0.395287i
$208$	3.45938	−	16.8963i	0.239865	−	1.17155i
$209$		−	2.95731i		−	0.204561i
$210$	0.230406	+	0.256425i	0.0158995	+	0.0176950i
$211$		−	23.2554i		−	1.60097i	−0.599355	−	0.800484i	$-0.704576\pi$
$211$		−	23.2554i		−	1.60097i	0.599355	−	0.800484i	$-0.295424\pi$
$212$	−9.29890	−	11.3957i	−0.638651	−	0.782658i
$213$	−13.6522	+	5.60849i	−0.935434	+	0.384288i
$214$	−1.42808	−	4.00891i	−0.0976216	−	0.274043i
$215$	0.892084			0.0608396
$216$	−11.9168	+	8.60169i	−0.810838	+	0.585271i
$217$	3.42289			0.232361
$218$	8.34566	+	23.4279i	0.565240	+	1.58674i
$219$	8.42966	−	3.46301i	0.569624	−	0.234008i
$220$	0.717348	+	0.879100i	0.0483636	+	0.0592689i
$221$			8.55376i			0.575388i
$222$	−8.32116	−	9.26084i	−0.558480	−	0.621547i
$223$			0.454673i			0.0304472i	0.999884	+	0.0152236i	$0.00484601\pi$
$223$			0.454673i			0.0304472i	−0.999884	+	0.0152236i	$0.995154\pi$
$224$	−0.580178	−	4.10927i	−0.0387647	−	0.274562i
$225$	10.5896	−	10.4671i	0.705971	−	0.697810i
$226$	−23.3055	+	8.30205i	−1.55026	+	0.552244i
$227$	−26.0636			−1.72990			−0.864949	−	0.501859i	$-0.832650\pi$
$227$	−26.0636			−1.72990			−0.864949	+	0.501859i	$0.832650\pi$
$228$	−3.04569	−	1.65038i	−0.201706	−	0.109299i
$229$	−22.9804			−1.51859			−0.759293	−	0.650749i	$-0.774455\pi$
$229$	−22.9804			−1.51859			−0.759293	+	0.650749i	$0.774455\pi$
$230$	−0.689184	+	0.245506i	−0.0454434	+	0.0161882i
$231$	−1.42795	−	3.47591i	−0.0939520	−	0.228698i
$232$	−12.1017	+	19.9995i	−0.794517	+	1.31303i
$233$		−	5.12766i		−	0.335924i	−0.985793	−	0.167962i	$-0.946281\pi$
$233$		−	5.12766i		−	0.335924i	0.985793	−	0.167962i	$-0.0537187\pi$
$234$	−16.4798	−	7.94035i	−1.07732	−	0.519077i
$235$		−	1.17871i		−	0.0768903i
$236$	14.9248	−	12.1786i	0.971519	−	0.792762i
$237$	10.1064	+	24.6011i	0.656483	+	1.59801i
$238$	0.690692	+	1.93891i	0.0447709	+	0.125681i
$239$	−15.9279			−1.03029			−0.515145	−	0.857103i	$-0.672262\pi$
$239$	−15.9279			−1.03029			−0.515145	+	0.857103i	$0.672262\pi$
$240$	1.30570	−	0.248191i	0.0842828	−	0.0160207i
$241$	9.04084			0.582372			0.291186	−	0.956667i	$-0.405950\pi$
$241$	9.04084			0.582372			0.291186	+	0.956667i	$0.405950\pi$
$242$	1.06984	+	3.00326i	0.0687721	+	0.193057i
$243$	5.75549	+	14.4870i	0.369215	+	0.929344i
$244$	3.06906	−	2.50436i	0.196476	−	0.160325i
$245$		−	1.23961i		−	0.0791957i
$246$	11.8425	−	10.6409i	0.755051	−	0.678437i
$247$		−	4.31169i		−	0.274347i
$248$	6.83190	−	11.2905i	0.433826	−	0.716948i
$249$	0.0819494	−	0.0336658i	0.00519333	−	0.00213348i
$250$	−2.54626	+	0.907047i	−0.161040	+	0.0573667i
$251$	−1.60174			−0.101101			−0.0505505	−	0.998722i	$-0.516098\pi$
$251$	−1.60174			−0.101101			−0.0505505	+	0.998722i	$0.516098\pi$
$252$	−4.37669	−	0.469169i	−0.275706	−	0.0295549i
$253$	7.97493			0.501380
$254$	19.9071	−	7.09145i	1.24908	−	0.444957i
$255$	−0.609730	+	0.250484i	−0.0381828	+	0.0156859i
$256$	−14.7126	−	6.28815i	−0.919534	−	0.393009i
$257$		−	4.16707i		−	0.259935i	−0.991518	−	0.129967i	$-0.958513\pi$
$257$		−	4.16707i		−	0.259935i	0.991518	−	0.129967i	$-0.0414873\pi$
$258$	−8.47281	+	7.61309i	−0.527494	+	0.473970i
$259$		−	3.72884i		−	0.231699i
$260$	1.04588	+	1.28171i	0.0648627	+	0.0794884i
$261$	17.4297	+	17.6335i	1.07887	+	1.09149i
$262$	−9.09989	−	25.5452i	−0.562193	−	1.57819i
$263$	−24.7297			−1.52490			−0.762450	−	0.647048i	$-0.776004\pi$
$263$	−24.7297			−1.52490			−0.762450	+	0.647048i	$0.776004\pi$
$264$	−14.3155	−	2.22761i	−0.881058	−	0.137100i
$265$	1.41079			0.0866639
$266$	−0.348157	−	0.977347i	−0.0213469	−	0.0599250i
$267$	7.03675	+	17.1289i	0.430642	+	1.04827i
$268$	−0.100567	−	0.123243i	−0.00614310	−	0.00752828i
$269$			6.51095i			0.396980i	0.980103	+	0.198490i	$0.0636037\pi$
$269$			6.51095i			0.396980i	−0.980103	+	0.198490i	$0.936396\pi$
$270$	0.0834179	−	1.40724i	0.00507665	−	0.0856416i
$271$			5.35687i			0.325407i	0.986675	+	0.162703i	$0.0520214\pi$
$271$			5.35687i			0.325407i	−0.986675	+	0.162703i	$0.947979\pi$
$272$	7.77414	+	1.59169i	0.471376	+	0.0965105i
$273$	−2.08192	−	5.06782i	−0.126003	−	0.306718i
$274$	19.8849	−	7.08355i	1.20129	−	0.427933i
$275$	14.6777			0.885098
$276$	4.45055	−	8.21329i	0.267892	−	0.494382i
$277$	10.5863			0.636072			0.318036	−	0.948079i	$-0.396977\pi$
$277$	10.5863			0.636072			0.318036	+	0.948079i	$0.396977\pi$
$278$	−25.9317	+	9.23756i	−1.55528	+	0.554032i
$279$	−9.83974	−	9.95483i	−0.589090	−	0.595980i
$280$	0.340568	+	0.206078i	0.0203528	+	0.0123155i
$281$		−	17.1709i		−	1.02433i	−0.858888	−	0.512164i	$-0.828844\pi$
$281$		−	17.1709i		−	1.02433i	0.858888	−	0.512164i	$-0.171156\pi$
$282$	10.0591	+	11.1951i	0.599013	+	0.666657i
$283$		−	20.5294i		−	1.22035i	−0.792267	−	0.610175i	$-0.791099\pi$
$283$		−	20.5294i		−	1.22035i	0.792267	−	0.610175i	$-0.208901\pi$
$284$	−13.2044	+	10.7748i	−0.783534	+	0.639366i
$285$	0.307347	−	0.126262i	0.0182056	−	0.00747909i
$286$	−6.05123	−	16.9870i	−0.357817	−	1.00446i
$287$	4.76833			0.281466
$288$	−10.2832	+	13.5002i	−0.605944	+	0.795507i
$289$	13.0643			0.768490
$290$	−0.752409	−	2.11216i	−0.0441830	−	0.124030i
$291$	19.7950	−	8.13203i	1.16040	−	0.476708i
$292$	8.15313	−	6.65297i	0.477126	−	0.389336i
$293$		−	6.57254i		−	0.383972i	−0.981398	−	0.191986i	$-0.938507\pi$
$293$		−	6.57254i		−	0.383972i	0.981398	−	0.191986i	$-0.0614928\pi$
$294$	10.5789	+	11.7735i	0.616973	+	0.686645i
$295$			1.84769i			0.107576i
$296$	−12.2997	−	7.44255i	−0.714904	−	0.432589i
$297$	−6.00413	+	14.1451i	−0.348395	+	0.820780i
$298$	12.7053	−	4.52597i	0.735999	−	0.262182i
$299$	11.6273			0.672424
$300$	8.19115	−	15.1164i	0.472916	−	0.872745i
$301$	−3.41154			−0.196638
$302$	32.4332	−	11.5536i	1.86632	−	0.664833i
$303$	4.82136	+	11.7362i	0.276980	+	0.674225i
$304$	−3.91871	−	0.802324i	−0.224753	−	0.0460165i
$305$			0.379949i			0.0217558i
$306$	3.65343	−	7.58251i	0.208853	−	0.433463i
$307$		−	15.1012i		−	0.861870i	−0.902383	−	0.430935i	$-0.858184\pi$
$307$		−	15.1012i		−	0.861870i	0.902383	−	0.430935i	$-0.141816\pi$
$308$	−2.74331	−	3.36189i	−0.156314	−	0.191561i
$309$	−4.55848	−	11.0963i	−0.259323	−	0.631245i
$310$	0.424765	+	1.19240i	0.0241250	+	0.0677237i
$311$	6.42342			0.364239			0.182119	−	0.983276i	$-0.441704\pi$
$311$	6.42342			0.364239			0.182119	+	0.983276i	$0.441704\pi$
$312$	−20.8717	−	3.24781i	−1.18163	−	0.183871i
$313$	−29.4485			−1.66453			−0.832265	−	0.554378i	$-0.812956\pi$
$313$	−29.4485			−1.66453			−0.832265	+	0.554378i	$0.812956\pi$
$314$	−3.26346	−	9.16118i	−0.184168	−	0.516995i
$315$	0.300278	−	0.296807i	0.0169188	−	0.0167232i
$316$	19.4160	+	23.7941i	1.09224	+	1.33852i
$317$		−	11.8086i		−	0.663240i	−0.943413	−	0.331620i	$-0.892405\pi$
$317$		−	11.8086i		−	0.663240i	0.943413	−	0.331620i	$-0.107595\pi$
$318$	−13.3993	+	12.0397i	−0.751397	+	0.675154i
$319$			24.4410i			1.36843i
$320$	1.35951	−	0.712052i	0.0759989	−	0.0398049i
$321$	−4.82114	+	1.98058i	−0.269090	+	0.110545i
$322$	2.63560	−	0.938871i	0.146876	−	0.0523213i
$323$	1.98385			0.110384
$324$	11.2171	+	14.0775i	0.623174	+	0.782083i
$325$	21.3998			1.18705
$326$	−0.412323	+	0.146881i	−0.0228365	+	0.00813496i
$327$	28.1746	−	11.5745i	1.55806	−	0.640070i
$328$	9.51732	−	15.7285i	0.525506	−	0.868459i
$329$			4.50765i			0.248515i
$330$	1.03367	−	0.928784i	0.0569015	−	0.0511279i
$331$			35.5683i			1.95501i	0.210908	+	0.977506i	$0.432358\pi$
$331$			35.5683i			1.95501i	−0.210908	+	0.977506i	$0.567642\pi$
$332$	0.0792610	−	0.0646772i	0.00435001	−	0.00354962i
$333$	−10.8446	+	10.7192i	−0.594281	+	0.587410i
$334$	10.6335	+	29.8504i	0.581840	+	1.63334i
$335$	0.0152575			0.000833608
$336$	−4.99332	+	0.949140i	−0.272408	+	0.0517798i
$337$	21.2214			1.15600			0.578001	−	0.816036i	$-0.303833\pi$
$337$	21.2214			1.15600			0.578001	+	0.816036i	$0.303833\pi$
$338$	−2.65318	−	7.44800i	−0.144314	−	0.405118i
$339$	11.5140	+	28.0274i	0.625354	+	1.52224i
$340$	−0.589728	+	0.481219i	−0.0319825	+	0.0260978i
$341$		−	13.7979i		−	0.747199i
$342$	−1.84158	+	3.82212i	−0.0995815	+	0.206676i
$343$			9.87595i			0.533251i
$344$	−6.80924	+	11.2530i	−0.367130	+	0.606724i
$345$	0.340488	+	0.828818i	0.0183313	+	0.0446220i
$346$	14.1984	−	5.05784i	0.763309	−	0.271911i
$347$	−18.0238			−0.967569			−0.483785	−	0.875187i	$-0.660738\pi$
$347$	−18.0238			−0.967569			−0.483785	+	0.875187i	$0.660738\pi$
$348$	25.1715	+	13.6397i	1.34933	+	0.731166i
$349$	−4.14750			−0.222011			−0.111005	−	0.993820i	$-0.535407\pi$
$349$	−4.14750			−0.222011			−0.111005	+	0.993820i	$0.535407\pi$
$350$	4.85077	−	1.72797i	0.259284	−	0.0923641i
$351$	−8.75391	+	20.6232i	−0.467249	+	1.10079i
$352$	−16.5648	+	2.33874i	−0.882905	+	0.124655i
$353$		−	19.3673i		−	1.03082i	−0.856945	−	0.515409i	$-0.827640\pi$
$353$		−	19.3673i		−	1.03082i	0.856945	−	0.515409i	$-0.172360\pi$
$354$	−15.7683	−	17.5489i	−0.838073	−	0.932714i
$355$		−	1.63470i		−	0.0867608i
$356$	13.5187	+	16.5670i	0.716489	+	0.878048i
$357$	2.33175	−	0.957911i	0.123409	−	0.0506980i
$358$	−1.21956	−	3.42355i	−0.0644557	−	0.180940i
$359$	17.0523			0.899984			0.449992	−	0.893033i	$-0.351427\pi$
$359$	17.0523			0.899984			0.449992	+	0.893033i	$0.351427\pi$
$360$	−0.379687	−	1.58289i	−0.0200113	−	0.0834255i
$361$	−1.00000			−0.0526316
$362$	−1.41223	−	3.96441i	−0.0742252	−	0.208365i
$363$	3.61175	−	1.48375i	0.189568	−	0.0778766i
$364$	−3.99969	−	4.90156i	−0.209641	−	0.256912i
$365$			1.00936i			0.0528322i
$366$	−3.24251	−	3.60867i	−0.169489	−	0.188628i
$367$		−	36.1786i		−	1.88851i	−0.329221	−	0.944253i	$-0.606786\pi$
$367$		−	36.1786i		−	1.88851i	0.329221	−	0.944253i	$-0.393214\pi$
$368$	2.16362	−	10.5675i	0.112786	−	0.550871i
$369$	−13.7075	−	13.8678i	−0.713582	−	0.721928i
$370$	1.29898	−	0.462731i	0.0675306	−	0.0240562i
$371$	−5.39517			−0.280103
$372$	−14.2103	−	7.70017i	−0.736770	−	0.399235i
$373$	17.7370			0.918385			0.459193	−	0.888337i	$-0.348139\pi$
$373$	17.7370			0.918385			0.459193	+	0.888337i	$0.348139\pi$
$374$	7.81588	−	2.78423i	0.404150	−	0.143969i
$375$	1.25797	+	3.06215i	0.0649613	+	0.158129i
$376$	14.8686	+	8.99701i	0.766789	+	0.463985i
$377$			35.6345i			1.83527i
$378$	−0.319010	+	5.38160i	−0.0164081	+	0.276799i
$379$		−	11.0309i		−	0.566617i	−0.959029	−	0.283308i	$-0.908568\pi$
$379$		−	11.0309i		−	0.566617i	0.959029	−	0.283308i	$-0.0914320\pi$
$380$	0.297264	−	0.242568i	0.0152493	−	0.0124435i
$381$	−9.83503	−	23.9405i	−0.503864	−	1.22651i
$382$	3.38135	+	9.49213i	0.173005	+	0.485659i
$383$	−13.6901			−0.699532			−0.349766	−	0.936837i	$-0.613739\pi$
$383$	−13.6901			−0.699532			−0.349766	+	0.936837i	$0.613739\pi$
$384$	−6.83562	+	18.3650i	−0.348829	+	0.937186i
$385$	0.416202			0.0212116
$386$	−7.73688	−	21.7190i	−0.393797	−	1.10547i
$387$	9.80710	+	9.92180i	0.498523	+	0.504354i
$388$	19.1456	−	15.6229i	0.971973	−	0.793132i
$389$		−	19.4353i		−	0.985411i	−0.870196	−	0.492706i	$-0.836008\pi$
$389$		−	19.4353i		−	0.985411i	0.870196	−	0.492706i	$-0.163992\pi$
$390$	1.50707	−	1.35415i	0.0763134	−	0.0685700i
$391$			5.34983i			0.270552i
$392$	15.6368	+	9.46188i	0.789780	+	0.477897i
$393$	−30.7209	+	12.6205i	−1.54966	+	0.636620i
$394$	10.3580	−	3.68980i	0.521829	−	0.185889i
$395$	−2.94571			−0.148215
$396$	−1.89125	+	17.6428i	−0.0950391	+	0.886582i
$397$	−8.01033			−0.402027			−0.201013	−	0.979588i	$-0.564424\pi$
$397$	−8.01033			−0.402027			−0.201013	+	0.979588i	$0.564424\pi$
$398$	15.6625	−	5.57939i	0.785089	−	0.279670i
$399$	−1.17536	+	0.482854i	−0.0588418	+	0.0241729i
$400$	3.98209	−	19.4493i	0.199105	−	0.972466i
$401$		−	35.0912i		−	1.75237i	−0.481973	−	0.876186i	$-0.660080\pi$
$401$		−	35.0912i		−	1.75237i	0.481973	−	0.876186i	$-0.339920\pi$
$402$	−0.144913	+	0.130209i	−0.00722758	+	0.00649421i
$403$		−	20.1171i		−	1.00210i
$404$	9.26257	+	11.3512i	0.460830	+	0.564741i
$405$	−1.72641	−	0.0200753i	−0.0857862	−	0.000997550i
$406$	2.87739	+	8.07740i	0.142802	+	0.400875i
$407$	−15.0312			−0.745068
$408$	1.49435	−	9.60328i	0.0739813	−	0.475433i
$409$	−9.15380			−0.452626			−0.226313	−	0.974055i	$-0.572667\pi$
$409$	−9.15380			−0.452626			−0.226313	+	0.974055i	$0.572667\pi$
$410$	0.591727	+	1.66110i	0.0292233	+	0.0820357i
$411$	−9.82407	−	23.9138i	−0.484586	−	1.17958i
$412$	−8.75755	−	10.7323i	−0.431453	−	0.528740i
$413$		−	7.06598i		−	0.347694i
$414$	−10.3071	−	4.96618i	−0.506564	−	0.244074i
$415$			0.00981252i			0.000481678i
$416$	−24.1511	+	3.40983i	−1.18411	+	0.167181i
$417$	12.8114	+	31.1856i	0.627378	+	1.52717i
$418$	−3.93975	+	1.40345i	−0.192700	+	0.0686448i
$419$	−24.5199			−1.19788			−0.598939	−	0.800795i	$-0.704411\pi$
$419$	−24.5199			−1.19788			−0.598939	+	0.800795i	$0.704411\pi$
$420$	0.232269	−	0.428641i	0.0113336	−	0.0209155i
$421$	−11.0228			−0.537220			−0.268610	−	0.963249i	$-0.586564\pi$
$421$	−11.0228			−0.537220			−0.268610	+	0.963249i	$0.586564\pi$
$422$	−30.9811	+	11.0363i	−1.50813	+	0.537238i
$423$	13.1096	−	12.9581i	0.637412	−	0.630043i
$424$	−10.7685	+	17.7961i	−0.522963	+	0.864256i
$425$			9.84625i			0.477613i
$426$	13.9506	+	15.5260i	0.675909	+	0.752237i
$427$		−	1.45302i		−	0.0703163i
$428$	−4.66298	+	3.80501i	−0.225394	+	0.183922i
$429$	−20.4287	+	8.39236i	−0.986307	+	0.405187i
$430$	−0.423355	−	1.18844i	−0.0204160	−	0.0573118i
$431$	22.7176			1.09427			0.547135	−	0.837044i	$-0.315718\pi$
$431$	22.7176			1.09427			0.547135	+	0.837044i	$0.315718\pi$
$432$	17.1146	+	11.7936i	0.823428	+	0.567421i
$433$	−36.4353			−1.75097			−0.875485	−	0.483246i	$-0.839458\pi$
$433$	−36.4353			−1.75097			−0.875485	+	0.483246i	$0.839458\pi$
$434$	−1.62440	−	4.56001i	−0.0779736	−	0.218888i
$435$	−2.54010	+	1.04350i	−0.121789	+	0.0500322i
$436$	27.2504	−	22.2364i	1.30506	−	1.06493i
$437$		−	2.69669i		−	0.129000i
$438$	−8.61391	−	9.58665i	−0.411588	−	0.458068i
$439$		−	2.72570i		−	0.130091i	−0.997882	−	0.0650454i	$-0.979281\pi$
$439$		−	2.72570i		−	0.130091i	0.997882	−	0.0650454i	$-0.0207192\pi$
$440$	0.830715	−	1.37285i	0.0396028	−	0.0654482i
$441$	13.7870	−	13.6276i	0.656523	−	0.648933i
$442$	11.3954	−	4.05935i	0.542024	−	0.193084i
$443$	3.01125			0.143069			0.0715343	−	0.997438i	$-0.477210\pi$
$443$	3.01125			0.143069			0.0715343	+	0.997438i	$0.477210\pi$
$444$	−8.38842	+	15.4804i	−0.398097	+	0.734670i
$445$	−2.05099			−0.0972264
$446$	0.605721	−	0.215774i	0.0286817	−	0.0102172i
$447$	−6.27700	−	15.2795i	−0.296892	−	0.722695i
$448$	−5.19908	+	2.72305i	−0.245633	+	0.128652i
$449$		−	14.0497i		−	0.663048i	−0.943447	−	0.331524i	$-0.892437\pi$
$449$		−	14.0497i		−	0.663048i	0.943447	−	0.331524i	$-0.107563\pi$
$450$	−18.9699	−	9.14015i	−0.894251	−	0.430871i
$451$		−	19.2215i		−	0.905104i
$452$	22.1201	+	27.1079i	1.04044	+	1.27505i
$453$	−16.0235	−	39.0044i	−0.752848	−	1.83259i
$454$	12.3690	+	34.7221i	0.580504	+	1.62959i
$455$	0.606814			0.0284479
$456$	−0.753256	+	4.84072i	−0.0352745	+	0.226688i
$457$	2.97777			0.139294			0.0696472	−	0.997572i	$-0.477813\pi$
$457$	2.97777			0.139294			0.0696472	+	0.997572i	$0.477813\pi$
$458$	10.9058	+	30.6147i	0.509593	+	1.43053i
$459$	−9.48895	−	4.02776i	−0.442906	−	0.188000i
$460$	0.654131	+	0.801628i	0.0304990	+	0.0373761i
$461$			35.6352i			1.65970i	0.557989	+	0.829848i	$0.311573\pi$
$461$			35.6352i			1.65970i	−0.557989	+	0.829848i	$0.688427\pi$
$462$	−3.95299	+	3.55189i	−0.183910	+	0.165249i
$463$		−	36.4959i		−	1.69611i	−0.529908	−	0.848055i	$-0.677773\pi$
$463$		−	36.4959i		−	1.69611i	0.529908	−	0.848055i	$-0.322227\pi$
$464$	32.3866	+	6.63090i	1.50351	+	0.307832i
$465$	1.43399	−	0.589099i	0.0664996	−	0.0273188i
$466$	−6.83113	+	2.43343i	−0.316446	+	0.112726i
$467$	25.3514			1.17312			0.586561	−	0.809905i	$-0.300481\pi$
$467$	25.3514			1.17312			0.586561	+	0.809905i	$0.300481\pi$
$468$	−2.75741	+	25.7228i	−0.127461	+	1.18904i
$469$	−0.0583484			−0.00269428
$470$	−1.57028	+	0.559377i	−0.0724318	+	0.0258021i
$471$	−11.0173	+	4.52604i	−0.507651	+	0.208549i
$472$	−23.3073	−	14.1033i	−1.07281	−	0.649158i
$473$			13.7521i			0.632324i
$474$	27.9777	−	25.1388i	1.28506	−	1.15466i
$475$		−	4.96320i		−	0.227727i
$476$	2.25526	−	1.84029i	0.103370	−	0.0843498i
$477$	15.5094	+	15.6908i	0.710128	+	0.718434i
$478$	7.55888	+	21.2193i	0.345735	+	0.970548i
$479$	−2.81590			−0.128662			−0.0643308	−	0.997929i	$-0.520491\pi$
$479$	−2.81590			−0.128662			−0.0643308	+	0.997929i	$0.520491\pi$
$480$	−0.950289	−	1.62169i	−0.0433746	−	0.0740196i
$481$	−21.9152			−0.999247
$482$	−4.29050	−	12.0443i	−0.195427	−	0.548603i
$483$	−1.30211	−	3.16959i	−0.0592479	−	0.144221i
$484$	3.49326	−	2.85051i	0.158785	−	0.129569i
$485$			2.37023i			0.107627i
$486$	16.5684	−	14.5426i	0.751558	−	0.659667i
$487$			32.5187i			1.47356i	0.676132	+	0.736781i	$0.263655\pi$
$487$			32.5187i			1.47356i	−0.676132	+	0.736781i	$0.736345\pi$
$488$	−4.79281	−	2.90014i	−0.216960	−	0.131283i
$489$	0.203706	+	0.495863i	0.00921192	+	0.0224237i
$490$	−1.65142	+	0.588280i	−0.0746035	+	0.0265758i
$491$	−4.56679			−0.206096			−0.103048	−	0.994676i	$-0.532860\pi$
$491$	−4.56679			−0.206096			−0.103048	+	0.994676i	$0.532860\pi$
$492$	−19.7960	−	10.7269i	−0.892471	−	0.483605i
$493$	−16.3958			−0.738429
$494$	−5.74408	+	2.04620i	−0.258439	+	0.0920628i
$495$	−1.19645	−	1.21044i	−0.0537764	−	0.0544054i
$496$	−18.2835	−	3.74341i	−0.820955	−	0.168084i
$497$			6.25147i			0.280417i
$498$	−0.0837406	−	0.0931971i	−0.00375250	−	0.00417626i
$499$		−	12.7629i		−	0.571347i	−0.958327	−	0.285674i	$-0.907783\pi$
$499$		−	12.7629i		−	0.571347i	0.958327	−	0.285674i	$-0.0922173\pi$
$500$	2.41675	+	2.96170i	0.108081	+	0.132451i
$501$	35.8983	−	14.7475i	1.60382	−	0.658868i
$502$	0.760136	+	2.13385i	0.0339265	+	0.0952386i
$503$	−18.3385			−0.817675			−0.408837	−	0.912607i	$-0.634066\pi$
$503$	−18.3385			−0.817675			−0.408837	+	0.912607i	$0.634066\pi$
$504$	1.45201	+	6.05333i	0.0646777	+	0.269637i
$505$	−1.40527			−0.0625339
$506$	−3.78465	−	10.6243i	−0.168248	−	0.472307i
$507$	−8.95703	+	3.67965i	−0.397795	+	0.163419i
$508$	−18.8946	−	23.1551i	−0.838313	−	1.02734i
$509$			12.7101i			0.563364i	0.959508	+	0.281682i	$0.0908924\pi$
$509$			12.7101i			0.563364i	−0.959508	+	0.281682i	$0.909108\pi$
$510$	0.623057	+	0.693416i	0.0275894	+	0.0307050i
$511$		−	3.86002i		−	0.170757i
$512$	−1.39502	+	22.5844i	−0.0616516	+	0.998098i
$513$	4.78310	+	2.03027i	0.211179	+	0.0896386i
$514$	−5.55141	+	1.97756i	−0.244862	+	0.0872266i
$515$	1.32865			0.0585475
$516$	14.1632	+	7.67463i	0.623499	+	0.337857i
$517$	18.1706			0.799143
$518$	−4.96759	+	1.76959i	−0.218263	+	0.0777513i
$519$	−7.01464	−	17.0751i	−0.307909	−	0.749512i
$520$	1.21117	−	2.00159i	0.0531132	−	0.0877756i
$521$			33.6566i			1.47452i	0.675608	+	0.737261i	$0.263881\pi$
$521$			33.6566i			1.47452i	−0.675608	+	0.737261i	$0.736119\pi$
$522$	15.2200	−	31.5883i	0.666161	−	1.38258i
$523$		−	6.98539i		−	0.305450i	−0.988269	−	0.152725i	$-0.951195\pi$
$523$		−	6.98539i		−	0.305450i	0.988269	−	0.152725i	$-0.0488048\pi$
$524$	−29.7131	+	24.2459i	−1.29802	+	1.05919i
$525$	−2.39650	−	5.83357i	−0.104592	−	0.254598i
$526$	11.7360	+	32.9452i	0.511712	+	1.43648i
$527$	9.25607			0.403201
$528$	3.82605	+	20.1284i	0.166507	+	0.875976i
$529$	−15.7279			−0.683821
$530$	−0.669515	−	1.87946i	−0.0290819	−	0.0816387i
$531$	−20.5501	+	20.3125i	−0.891797	+	0.881487i
$532$	−1.13681	+	0.927637i	−0.0492868	+	0.0402182i
$533$		−	28.0245i		−	1.21388i
$534$	19.4799	−	17.5033i	0.842976	−	0.757441i
$535$		−	0.577278i		−	0.0249579i
$536$	−0.116460	+	0.192464i	−0.00503031	+	0.00831316i
$537$	−4.11719	+	1.69139i	−0.177670	+	0.0729888i
$538$	8.67396	−	3.08990i	0.373961	−	0.133215i
$539$	19.1095			0.823104
$540$	−1.91432	+	0.556700i	−0.0823793	+	0.0239566i
$541$	−20.7906			−0.893857			−0.446929	−	0.894570i	$-0.647482\pi$
$541$	−20.7906			−0.893857			−0.446929	+	0.894570i	$0.647482\pi$
$542$	7.13648	−	2.54221i	0.306538	−	0.109197i
$543$	−4.76763	+	1.95860i	−0.204599	+	0.0840516i
$544$	−1.56890	−	11.1122i	−0.0672659	−	0.476430i
$545$			3.37360i			0.144509i
$546$	−5.76338	+	5.17858i	−0.246650	+	0.221623i
$547$			32.8567i			1.40485i	0.711757	+	0.702426i	$0.247900\pi$
$547$			32.8567i			1.40485i	−0.711757	+	0.702426i	$0.752100\pi$
$548$	−18.8736	−	23.1293i	−0.806238	−	0.988034i
$549$	−4.22582	+	4.17697i	−0.180354	+	0.178269i
$550$	−6.96558	−	19.5538i	−0.297013	−	0.833776i
$551$	8.26462			0.352085
$552$	−13.0539	−	2.03130i	−0.555612	−	0.0864578i
$553$	11.2651			0.479040
$554$	−5.02395	−	14.1032i	−0.213447	−	0.599189i
$555$	−0.641754	−	1.56216i	−0.0272409	−	0.0663100i
$556$	24.6127	+	30.1626i	1.04381	+	1.27918i
$557$			23.8172i			1.00917i	0.863363	+	0.504584i	$0.168354\pi$
$557$			23.8172i			1.00917i	−0.863363	+	0.504584i	$0.831646\pi$
$558$	−8.59229	+	17.8329i	−0.363741	+	0.754925i
$559$			20.0504i			0.848040i
$560$	0.112917	−	0.551506i	0.00477159	−	0.0233054i
$561$	−3.86140	−	9.39944i	−0.163029	−	0.396845i
$562$	−22.8752	+	8.14876i	−0.964932	+	0.343735i
$563$	3.96274			0.167010			0.0835048	−	0.996507i	$-0.473389\pi$
$563$	3.96274			0.167010			0.0835048	+	0.996507i	$0.473389\pi$
$564$	10.1404	−	18.7137i	0.426990	−	0.787990i
$565$	−3.35596			−0.141186
$566$	−27.3495	+	9.74264i	−1.14959	+	0.409514i
$567$	6.60221	+	0.0767726i	0.277267	+	0.00322415i
$568$	20.6207	+	12.4776i	0.865223	+	0.523548i
$569$			6.89478i			0.289044i	0.989502	+	0.144522i	$0.0461645\pi$
$569$			6.89478i			0.289044i	−0.989502	+	0.144522i	$0.953835\pi$
$570$	−0.314064	−	0.349530i	−0.0131547	−	0.0146402i
$571$			40.0217i			1.67486i	0.546548	+	0.837428i	$0.315942\pi$
$571$			40.0217i			1.67486i	−0.546548	+	0.837428i	$0.684058\pi$
$572$	−19.7585	+	16.1230i	−0.826146	+	0.674137i
$573$	11.4153	−	4.68954i	0.476881	−	0.195908i
$574$	−2.26290	−	6.35242i	−0.0944517	−	0.265145i
$575$	13.3842			0.558160
$576$	22.8652	+	7.29261i	0.952717	+	0.303859i
$577$	21.6884			0.902899			0.451450	−	0.892297i	$-0.350907\pi$
$577$	21.6884			0.902899			0.451450	+	0.892297i	$0.350907\pi$
$578$	−6.19993	−	17.4044i	−0.257883	−	0.723929i
$579$	−26.1194	+	10.7302i	−1.08549	+	0.445930i
$580$	−2.45677	+	2.00473i	−0.102012	+	0.0832420i
$581$		−	0.0375254i		−	0.00155681i
$582$	−20.2277	−	22.5119i	−0.838464	−	0.933149i
$583$			21.7483i			0.900723i
$584$	−12.7324	−	7.70438i	−0.526870	−	0.318810i
$585$	−1.74440	−	1.76480i	−0.0721221	−	0.0729656i
$586$	−8.75601	+	3.11913i	−0.361707	+	0.128850i
$587$	−31.3375			−1.29344			−0.646718	−	0.762729i	$-0.723859\pi$
$587$	−31.3375			−1.29344			−0.646718	+	0.762729i	$0.723859\pi$
$588$	10.6644	−	19.6806i	0.439792	−	0.811616i
$589$	−4.66570			−0.192247
$590$	2.46151	−	0.876855i	0.101339	−	0.0360995i
$591$	−5.11732	−	12.4566i	−0.210499	−	0.512397i
$592$	−4.07800	+	19.9177i	−0.167605	+	0.818614i
$593$			6.22639i			0.255687i	0.991794	+	0.127844i	$0.0408055\pi$
$593$			6.22639i			0.255687i	−0.991794	+	0.127844i	$0.959194\pi$
$594$	21.6936	+	1.28595i	0.890099	+	0.0527632i
$595$			0.279201i			0.0114461i
$596$	−12.0591	−	14.7783i	−0.493960	−	0.605341i
$597$	−7.73798	−	18.8358i	−0.316694	−	0.770898i
$598$	−5.51795	−	15.4900i	−0.225646	−	0.633433i
$599$	19.8716			0.811932			0.405966	−	0.913888i	$-0.366935\pi$
$599$	19.8716			0.811932			0.405966	+	0.913888i	$0.366935\pi$
$600$	−24.0255	−	3.73856i	−0.980836	−	0.152626i
$601$	8.96837			0.365827			0.182914	−	0.983129i	$-0.441447\pi$
$601$	8.96837			0.365827			0.182914	+	0.983129i	$0.441447\pi$
$602$	1.61901	+	4.54488i	0.0659859	+	0.185236i
$603$	0.167733	+	0.169695i	0.00683063	+	0.00691052i
$604$	−30.7836	−	37.7248i	−1.25257	−	1.53500i
$605$			0.432466i			0.0175823i
$606$	13.3470	−	11.9927i	0.542184	−	0.487169i
$607$			28.0176i			1.13720i	0.822615	+	0.568599i	$0.192514\pi$
$607$			28.0176i			1.13720i	−0.822615	+	0.568599i	$0.807486\pi$
$608$	0.790833	+	5.60130i	0.0320725	+	0.227163i
$609$	9.71394	−	3.99060i	0.393629	−	0.161707i
$610$	0.506173	−	0.180312i	0.0204943	−	0.00730063i
$611$	26.4924			1.07177
$612$	−11.8353	−	1.26871i	−0.478414	−	0.0512846i
$613$	8.44438			0.341065			0.170533	−	0.985352i	$-0.445451\pi$
$613$	8.44438			0.341065			0.170533	+	0.985352i	$0.445451\pi$
$614$	−20.1180	+	7.16656i	−0.811895	+	0.289219i
$615$	1.99765	−	0.820657i	0.0805529	−	0.0330921i
$616$	−3.17685	+	5.25011i	−0.127999	+	0.211533i
$617$		−	18.0419i		−	0.726339i	−0.931723	−	0.363169i	$-0.881695\pi$
$617$		−	18.0419i		−	0.726339i	0.931723	−	0.363169i	$-0.118305\pi$
$618$	−12.6193	+	11.3388i	−0.507621	+	0.456113i
$619$		−	6.12362i		−	0.246129i	−0.992399	−	0.123064i	$-0.960728\pi$
$619$		−	6.12362i		−	0.246129i	0.992399	−	0.123064i	$-0.0392722\pi$
$620$	1.38695	−	1.13175i	0.0557011	−	0.0454522i
$621$	−5.47501	+	12.8985i	−0.219704	+	0.517600i
$622$	−3.04836	−	8.55735i	−0.122228	−	0.343118i
$623$	7.84347			0.314242
$624$	5.57831	+	29.3468i	0.223311	+	1.17481i
$625$	24.4493			0.977973
$626$	13.9754	+	39.2316i	0.558568	+	1.56801i
$627$	1.94642	+	4.73798i	0.0777324	+	0.189217i
$628$	−10.6559	+	8.69523i	−0.425216	+	0.346977i
$629$		−	10.0834i		−	0.402051i
$630$	−0.537912	−	0.259179i	−0.0214309	−	0.0103259i
$631$		−	4.13701i		−	0.164692i	−0.996604	−	0.0823458i	$-0.973759\pi$
$631$		−	4.13701i		−	0.164692i	0.996604	−	0.0823458i	$-0.0262412\pi$
$632$	22.4845	−	37.1582i	0.894384	−	1.47807i
$633$	15.3061	+	37.2581i	0.608361	+	1.48088i
$634$	−15.7316	+	5.60402i	−0.624782	+	0.222564i
$635$	2.86660			0.113758
$636$	22.3983	+	12.1370i	0.888152	+	0.481265i
$637$	27.8613			1.10390
$638$	32.5605	−	11.5989i	1.28908	−	0.459206i
$639$	18.1812	−	17.9710i	0.719238	−	0.710923i
$640$	−1.59378	−	1.47323i	−0.0629998	−	0.0582347i
$641$		−	2.36433i		−	0.0933855i	−0.998909	−	0.0466928i	$-0.985132\pi$
$641$		−	2.36433i		−	0.0933855i	0.998909	−	0.0466928i	$-0.0148682\pi$
$642$	4.92652	+	5.48285i	0.194434	+	0.216391i
$643$		−	23.4902i		−	0.926364i	−0.886263	−	0.463182i	$-0.846708\pi$
$643$		−	23.4902i		−	0.926364i	0.886263	−	0.463182i	$-0.153292\pi$
$644$	−2.50155	−	3.06561i	−0.0985748	−	0.120802i
$645$	−1.42923	+	0.587145i	−0.0562759	+	0.0231188i
$646$	−0.941475	−	2.64291i	−0.0370418	−	0.103984i
$647$	21.5692			0.847972			0.423986	−	0.905669i	$-0.360631\pi$
$647$	21.5692			0.847972			0.423986	+	0.905669i	$0.360631\pi$
$648$	13.4309	−	21.6243i	0.527615	−	0.849484i
$649$	−28.4835			−1.11807
$650$	−10.1557	−	28.5090i	−0.398339	−	1.11822i
$651$	−5.48391	+	2.25285i	−0.214931	+	0.0882963i
$652$	0.391352	+	0.479596i	0.0153265	+	0.0187824i
$653$			6.15370i			0.240813i	0.992725	+	0.120406i	$0.0384198\pi$
$653$			6.15370i			0.240813i	−0.992725	+	0.120406i	$0.961580\pi$
$654$	−28.7904	−	32.0416i	−1.12580	−	1.25293i
$655$		−	3.67848i		−	0.143730i
$656$	−25.4703	−	5.21483i	−0.994446	−	0.203605i
$657$	−11.2261	+	11.0963i	−0.437973	+	0.432910i
$658$	6.00513	−	2.13919i	0.234104	−	0.0833943i
$659$	−19.3247			−0.752784			−0.376392	−	0.926460i	$-0.622835\pi$
$659$	−19.3247			−0.752784			−0.376392	+	0.926460i	$0.622835\pi$
$660$	−1.72788	−	0.936291i	−0.0672577	−	0.0364451i
$661$	20.1071			0.782077			0.391038	−	0.920374i	$-0.372116\pi$
$661$	20.1071			0.782077			0.391038	+	0.920374i	$0.372116\pi$
$662$	47.3845	−	16.8796i	1.84165	−	0.656045i
$663$	−5.62985	−	13.7042i	−0.218645	−	0.532227i
$664$	−0.123778	−	0.0748986i	−0.00480354	−	0.00290663i
$665$		−	0.140737i		−	0.00545754i
$666$	19.4268	+	9.36028i	0.752773	+	0.362703i
$667$			22.2871i			0.862960i
$668$	34.7207	−	28.3322i	1.34338	−	1.09620i
$669$	−0.299254	−	0.728444i	−0.0115698	−	0.0281633i
$670$	−0.00724075	−	0.0203262i	−0.000279735	−	0.000785271i
$671$	−5.85720			−0.226115
$672$	3.63413	+	6.20172i	0.140190	+	0.239236i
$673$	34.4661			1.32857			0.664286	−	0.747479i	$-0.268736\pi$
$673$	34.4661			1.32857			0.664286	+	0.747479i	$0.268736\pi$
$674$	−10.0710	−	28.2714i	−0.387921	−	1.08897i
$675$	−10.0766	+	23.7395i	−0.387850	+	0.913732i
$676$	−8.66319	+	7.06918i	−0.333200	+	0.271892i
$677$		−	51.1086i		−	1.96426i	−0.188199	−	0.982131i	$-0.560265\pi$
$677$		−	51.1086i		−	1.96426i	0.188199	−	0.982131i	$-0.439735\pi$
$678$	31.8742	−	28.6400i	1.22412	−	1.09991i
$679$		−	9.06432i		−	0.347857i
$680$	0.920952	+	0.557269i	0.0353169	+	0.0213703i
$681$	41.7571	−	17.1543i	1.60014	−	0.657355i
$682$	−18.3817	+	6.54806i	−0.703872	+	0.250738i
$683$	42.2208			1.61553			0.807767	−	0.589502i	$-0.200676\pi$
$683$	42.2208			1.61553			0.807767	+	0.589502i	$0.200676\pi$
$684$	5.96582	+	0.639519i	0.228109	+	0.0244526i
$685$	2.86341			0.109405
$686$	13.1568	−	4.68682i	0.502330	−	0.178944i
$687$	36.8175	−	15.1251i	1.40467	−	0.577057i
$688$	18.2229	+	3.73099i	0.694741	+	0.142243i
$689$			31.7086i			1.20800i
$690$	0.942574	−	0.846933i	0.0358832	−	0.0322422i
$691$		−	16.3092i		−	0.620431i	−0.950666	−	0.310216i	$-0.899599\pi$
$691$		−	16.3092i		−	0.620431i	0.950666	−	0.310216i	$-0.100401\pi$
$692$	−13.4762	−	16.5149i	−0.512289	−	0.627803i
$693$	4.57550	+	4.62902i	0.173809	+	0.175842i
$694$	8.55355	+	24.0115i	0.324688	+	0.911465i
$695$	−3.73413			−0.141644
$696$	6.22538	−	40.0067i	0.235972	−	1.51645i
$697$	12.8944			0.488408
$698$	1.96827	+	5.52534i	0.0745003	+	0.209137i
$699$	3.37489	+	8.21516i	0.127650	+	0.310726i
$700$	−4.60405	−	5.64220i	−0.174017	−	0.213255i
$701$		−	24.1537i		−	0.912271i	−0.889910	−	0.456136i	$-0.849233\pi$
$701$		−	24.1537i		−	0.912271i	0.889910	−	0.456136i	$-0.150767\pi$
$702$	31.6288	+	1.87489i	1.19375	+	0.0707632i
$703$			5.08273i			0.191699i
$704$	10.9768	+	20.9578i	0.413704	+	0.789879i
$705$	0.775792	+	1.88844i	0.0292180	+	0.0711226i
$706$	−25.8013	+	9.19112i	−0.971045	+	0.345912i
$707$	5.37410			0.202114
$708$	−15.8957	+	29.3348i	−0.597397	+	1.10247i
$709$	−15.7197			−0.590366			−0.295183	−	0.955441i	$-0.595381\pi$
$709$	−15.7197			−0.590366			−0.295183	+	0.955441i	$0.595381\pi$
$710$	−2.17776	+	0.775778i	−0.0817300	+	0.0291144i
$711$	−32.3836	−	32.7623i	−1.21448	−	1.22868i
$712$	15.6551	−	25.8719i	0.586701	−	0.969591i
$713$		−	12.5819i		−	0.471198i
$714$	−2.38271	−	2.65179i	−0.0891709	−	0.0992406i
$715$		−	2.44611i		−	0.0914793i
$716$	−3.98212	+	3.24942i	−0.148819	+	0.121437i
$717$	25.5185	−	10.4833i	0.953005	−	0.391506i
$718$	−8.09248	−	22.7172i	−0.302009	−	0.847799i
$719$	7.42605			0.276945			0.138473	−	0.990366i	$-0.455781\pi$
$719$	7.42605			0.276945			0.138473	+	0.990366i	$0.455781\pi$
$720$	−1.92855	+	1.25701i	−0.0718728	+	0.0468461i
$721$	−5.08108			−0.189229
$722$	0.474569	+	1.33221i	0.0176616	+	0.0495797i
$723$	−14.4846	+	5.95043i	−0.538687	+	0.221299i
$724$	−4.61123	+	3.76277i	−0.171375	+	0.139842i
$725$			41.0189i			1.52341i
$726$	−3.69069	−	4.10747i	−0.136974	−	0.152442i
$727$			11.3503i			0.420960i	0.977598	+	0.210480i	$0.0675026\pi$
$727$			11.3503i			0.420960i	−0.977598	+	0.210480i	$0.932497\pi$
$728$	−4.63179	+	7.65456i	−0.171665	+	0.283697i
$729$	−18.7560	−	19.4220i	−0.694667	−	0.719332i
$730$	1.34468	−	0.479010i	0.0497687	−	0.0177289i
$731$	−9.22536			−0.341212
$732$	−3.26872	+	6.03227i	−0.120815	+	0.222959i
$733$	1.24222			0.0458825			0.0229413	−	0.999737i	$-0.492697\pi$
$733$	1.24222			0.0458825			0.0229413	+	0.999737i	$0.492697\pi$
$734$	−48.1975	+	17.1692i	−1.77900	+	0.633728i
$735$	0.815876	+	1.98601i	0.0300940	+	0.0732550i
$736$	−15.1050	+	2.13263i	−0.556776	+	0.0786098i
$737$			0.235206i			0.00866393i
$738$	−11.9697	+	24.8424i	−0.440609	+	0.914463i
$739$		−	0.217337i		−	0.00799489i	−0.999992	−	0.00399744i	$-0.998728\pi$
$739$		−	0.217337i		−	0.00799489i	0.999992	−	0.00399744i	$-0.00127243\pi$
$740$	−1.23291	−	1.51091i	−0.0453226	−	0.0555423i
$741$	2.83784	+	6.90788i	0.104251	+	0.253767i
$742$	2.56038	+	7.18751i	0.0939946	+	0.263862i
$743$	26.5504			0.974038			0.487019	−	0.873391i	$-0.338084\pi$
$743$	26.5504			0.974038			0.487019	+	0.873391i	$0.338084\pi$
$744$	−3.51447	+	22.5854i	−0.128847	+	0.828020i
$745$	1.82955			0.0670295
$746$	−8.41742	−	23.6294i	−0.308184	−	0.865133i
$747$	−0.109135	+	0.107874i	−0.00399305	+	0.00394689i
$748$	−7.41835	−	9.09109i	−0.271242	−	0.332403i
$749$			2.20764i			0.0806656i
$750$	3.48244	−	3.12908i	0.127161	−	0.114258i
$751$			11.5019i			0.419712i	0.977732	+	0.209856i	$0.0672995\pi$
$751$			11.5019i			0.419712i	−0.977732	+	0.209856i	$0.932700\pi$
$752$	4.92974	−	24.0778i	0.179769	−	0.878027i
$753$	2.56619	−	1.05422i	0.0935172	−	0.0384180i
$754$	47.4727	−	16.9110i	1.72885	−	0.615864i
$755$	4.67034			0.169971
$756$	7.32081	−	2.12895i	0.266255	−	0.0774292i
$757$	−11.3056			−0.410911			−0.205455	−	0.978666i	$-0.565868\pi$
$757$	−11.3056			−0.410911			−0.205455	+	0.978666i	$0.565868\pi$
$758$	−14.6954	+	5.23490i	−0.533762	+	0.190140i
$759$	−12.7768	+	5.24888i	−0.463770	+	0.190522i
$760$	−0.464224	−	0.280903i	−0.0168392	−	0.0101894i
$761$			41.4826i			1.50374i	0.659310	+	0.751872i	$0.270849\pi$
$761$			41.4826i			1.50374i	−0.659310	+	0.751872i	$0.729151\pi$
$762$	−27.2263	+	24.4637i	−0.986306	+	0.886227i
$763$		−	12.9014i		−	0.467063i
$764$	11.0408	−	9.00934i	0.399443	−	0.325946i
$765$	0.812002	−	0.802615i	0.0293580	−	0.0290186i
$766$	6.49690	+	18.2381i	0.234743	+	0.658970i
$767$	−41.5283			−1.49950
$768$	27.7101	+	0.391011i	0.999900	+	0.0141094i
$769$	−31.9561			−1.15237			−0.576183	−	0.817321i	$-0.695459\pi$
$769$	−31.9561			−1.15237			−0.576183	+	0.817321i	$0.695459\pi$
$770$	−0.197516	−	0.554468i	−0.00711800	−	0.0199816i
$771$	2.74265	+	6.67617i	0.0987742	+	0.240437i
$772$	−25.2626	+	20.6143i	−0.909219	+	0.741925i
$773$		−	6.10304i		−	0.219511i	−0.993959	−	0.109756i	$-0.964993\pi$
$773$		−	6.10304i		−	0.219511i	0.993959	−	0.109756i	$-0.0350068\pi$
$774$	8.56378	−	17.7737i	0.307819	−	0.638863i
$775$		−	23.1568i		−	0.831817i
$776$	−29.8989	−	18.0919i	−1.07331	−	0.649461i
$777$	2.45422	+	5.97406i	0.0880446	+	0.214318i
$778$	−25.8920	+	9.22341i	−0.928272	+	0.330675i
$779$	−6.49966			−0.232874
$780$	−2.51922	−	1.36509i	−0.0902025	−	0.0488782i
$781$	25.2001			0.901731
$782$	7.12710	−	2.53886i	0.254864	−	0.0907896i
$783$	−39.5305	−	16.7794i	−1.41270	−	0.599647i
$784$	5.18445	−	25.3219i	0.185159	−	0.904352i
$785$		−	1.31920i		−	0.0470842i
$786$	31.3923	+	34.9373i	1.11973	+	1.24617i
$787$			28.6459i			1.02112i	0.859844	+	0.510558i	$0.170561\pi$
$787$			28.6459i			1.02112i	−0.859844	+	0.510558i	$0.829439\pi$
$788$	−9.83117	−	12.0480i	−0.350221	−	0.429191i
$789$	39.6201	−	16.2764i	1.41051	−	0.579456i
$790$	1.39794	+	3.92430i	0.0497365	+	0.139620i
$791$	12.8340			0.456324
$792$	24.4014	−	5.85316i	0.867065	−	0.207983i
$793$	−8.53969			−0.303253
$794$	3.80146	+	10.6714i	0.134909	+	0.378715i
$795$	−2.26026	+	0.928540i	−0.0801630	+	0.0329319i
$796$	−14.8659	−	18.2179i	−0.526906	−	0.645716i
$797$		−	27.9717i		−	0.990808i	−0.868663	−	0.495404i	$-0.835020\pi$
$797$		−	27.9717i		−	0.990808i	0.868663	−	0.495404i	$-0.164980\pi$
$798$	1.20105	+	1.33669i	0.0425169	+	0.0473182i
$799$			12.1894i			0.431231i
$800$	−27.8004	+	3.92506i	−0.982892	+	0.138772i
$801$	−22.5475	−	22.8112i	−0.796678	−	0.805996i
$802$	−46.7489	+	16.6532i	−1.65076	+	0.588045i
$803$	−15.5600			−0.549100
$804$	0.242236	+	0.131261i	0.00854301	+	0.00462922i
$805$	0.379523			0.0133764
$806$	−26.8002	+	9.54695i	−0.943997	+	0.336277i
$807$	−4.28533	−	10.4314i	−0.150851	−	0.367202i
$808$	10.7264	−	17.7266i	0.377353	−	0.623620i
$809$			22.7426i			0.799588i	0.916605	+	0.399794i	$0.130918\pi$
$809$			22.7426i			0.799588i	−0.916605	+	0.399794i	$0.869082\pi$
$810$	0.792558	+	2.30947i	0.0278476	+	0.0811466i
$811$		−	10.2867i		−	0.361216i	−0.983555	−	0.180608i	$-0.942194\pi$
$811$		−	10.2867i		−	0.361216i	0.983555	−	0.180608i	$-0.0578065\pi$
$812$	9.39527	−	7.66657i	0.329710	−	0.269044i
$813$	−3.52575	−	8.58239i	−0.123653	−	0.300997i
$814$	7.13334	+	20.0247i	0.250023	+	0.701865i
$815$	−0.0593740			−0.00207978
$816$	−13.5028	+	2.56663i	−0.472691	+	0.0898501i
$817$	4.65023			0.162691
$818$	4.34411	+	12.1948i	0.151888	+	0.426380i
$819$	6.67099	+	6.74902i	0.233103	+	0.235830i
$820$	1.93211	−	1.57661i	0.0674723	−	0.0550576i
$821$		−	38.2333i		−	1.33435i	−0.744900	−	0.667176i	$-0.767503\pi$
$821$		−	38.2333i		−	1.33435i	0.744900	−	0.667176i	$-0.232497\pi$
$822$	−27.1960	+	24.4365i	−0.948569	+	0.852320i
$823$		−	1.33165i		−	0.0464185i	−0.999731	−	0.0232093i	$-0.992612\pi$
$823$		−	1.33165i		−	0.0464185i	0.999731	−	0.0232093i	$-0.00738840\pi$
$824$	−10.1416	+	16.7601i	−0.353298	+	0.583865i
$825$	−23.5155	+	9.66046i	−0.818705	+	0.336334i
$826$	−9.41338	+	3.35330i	−0.327533	+	0.116676i
$827$	−41.2763			−1.43532			−0.717659	−	0.696394i	$-0.754786\pi$
$827$	−41.2763			−1.43532			−0.717659	+	0.696394i	$0.754786\pi$
$828$	−1.72458	+	16.0880i	−0.0599334	+	0.559095i
$829$	25.8311			0.897152			0.448576	−	0.893745i	$-0.351931\pi$
$829$	25.8311			0.897152			0.448576	+	0.893745i	$0.351931\pi$
$830$	0.0130723	−	0.00465672i	0.000453748	−	0.000161637i
$831$	−16.9607	+	6.96764i	−0.588359	+	0.241705i
$832$	16.0040	+	30.5561i	0.554838	+	1.05934i
$833$			12.8192i			0.444160i
$834$	35.4659	−	31.8672i	1.22808	−	1.10347i
$835$			4.29842i			0.148753i
$836$	3.73937	+	4.58255i	0.129329	+	0.158491i
$837$	22.3165	+	9.47264i	0.771371	+	0.327422i
$838$	11.6364	+	32.6657i	0.401973	+	1.12842i
$839$	33.4439			1.15461			0.577306	−	0.816528i	$-0.304104\pi$
$839$	33.4439			1.15461			0.577306	+	0.816528i	$0.304104\pi$
$840$	−0.681268	−	0.106011i	−0.0235060	−	0.00365772i
$841$	−39.3039			−1.35531
$842$	5.23110	+	14.6847i	0.180276	+	0.506070i
$843$	11.3014	+	27.5099i	0.389241	+	0.947491i
$844$	29.4053	+	36.0358i	1.01217	+	1.24040i
$845$		−	1.07250i		−	0.0368952i
$846$	−23.4843	−	11.3153i	−0.807407	−	0.389027i
$847$		−	1.65385i		−	0.0568270i
$848$	28.8186	+	5.90037i	0.989634	+	0.202620i
$849$	13.5119	+	32.8908i	0.463728	+	1.12881i
$850$	13.1173	−	4.67273i	0.449919	−	0.160273i
$851$	−13.7065			−0.469854
$852$	14.0634	−	25.9533i	0.481803	−	0.889146i
$853$	−3.80819			−0.130390			−0.0651950	−	0.997873i	$-0.520767\pi$
$853$	−3.80819			−0.130390			−0.0651950	+	0.997873i	$0.520767\pi$
$854$	−1.93572	+	0.689556i	−0.0662391	+	0.0235961i
$855$	−0.409306	+	0.404574i	−0.0139980	+	0.0138361i
$856$	7.28198	+	4.40634i	0.248893	+	0.150605i
$857$			30.3192i			1.03568i	0.855476	+	0.517842i	$0.173265\pi$
$857$			30.3192i			1.03568i	−0.855476	+	0.517842i	$0.826735\pi$
$858$	20.8752	+	23.2326i	0.712668	+	0.793147i
$859$			8.99639i			0.306953i	0.988152	+	0.153476i	$0.0490469\pi$
$859$			8.99639i			0.306953i	−0.988152	+	0.153476i	$0.950953\pi$
$860$	−1.38234	+	1.12800i	−0.0471376	+	0.0384644i
$861$	−7.63947	+	3.13838i	−0.260352	+	0.106956i
$862$	−10.7811	−	30.2647i	−0.367205	−	1.03082i
$863$	−18.5510			−0.631483			−0.315741	−	0.948845i	$-0.602253\pi$
$863$	−18.5510			−0.631483			−0.315741	+	0.948845i	$0.602253\pi$
$864$	7.58953	−	28.3972i	0.258201	−	0.966091i
$865$	2.04455			0.0695167
$866$	17.2911	+	48.5395i	0.587575	+	1.64944i
$867$	−20.9307	+	8.59859i	−0.710844	+	0.292023i
$868$	−5.30401	+	4.32808i	−0.180030	+	0.146905i
$869$		−	45.4103i		−	1.54044i
$870$	2.59562	+	2.88873i	0.0879998	+	0.0979373i
$871$			0.342926i			0.0116196i
$872$	−42.5557	−	25.7505i	−1.44112	−	0.872023i
$873$	−26.3618	+	26.0571i	−0.892213	+	0.881898i
$874$	−3.59256	+	1.27976i	−0.121520	+	0.0432887i
$875$	1.40219			0.0474026
$876$	−8.68353	+	16.0251i	−0.293389	+	0.541437i
$877$	2.97079			0.100316			0.0501582	−	0.998741i	$-0.484027\pi$
$877$	2.97079			0.100316			0.0501582	+	0.998741i	$0.484027\pi$
$878$	−3.63121	+	1.29354i	−0.122547	+	0.0436547i
$879$	4.32587	+	10.5300i	0.145908	+	0.355170i
$880$	−2.22316	−	0.455174i	−0.0749427	−	0.0153439i
$881$			37.1525i			1.25170i	0.779943	+	0.625850i	$0.215248\pi$
$881$			37.1525i			1.25170i	−0.779943	+	0.625850i	$0.784752\pi$
$882$	−24.6977	−	11.8999i	−0.831615	−	0.400691i
$883$		−	35.4963i		−	1.19455i	−0.802038	−	0.597273i	$-0.796251\pi$
$883$		−	35.4963i		−	1.19455i	0.802038	−	0.597273i	$-0.203749\pi$
$884$	−10.8158	−	13.2546i	−0.363775	−	0.445802i
$885$	−1.21610	−	2.96023i	−0.0408786	−	0.0995069i
$886$	−1.42904	−	4.01161i	−0.0480097	−	0.134773i
$887$	11.9230			0.400336			0.200168	−	0.979762i	$-0.435851\pi$
$887$	11.9230			0.400336			0.200168	+	0.979762i	$0.435851\pi$
$888$	24.6041	+	3.82860i	0.825660	+	0.128479i
$889$	−10.9626			−0.367672
$890$	0.973338	+	2.73235i	0.0326263	+	0.0915887i
$891$	0.309476	−	26.6139i	0.0103678	−	0.891601i
$892$	−0.574913	−	0.704548i	−0.0192495	−	0.0235900i
$893$		−	6.14432i		−	0.205612i
$894$	−17.3766	+	15.6135i	−0.581162	+	0.522192i
$895$		−	0.492987i		−	0.0164787i
$896$	6.09500	+	5.63399i	0.203620	+	0.188218i
$897$	−18.6284	+	7.65277i	−0.621984	+	0.255518i
$898$	−18.7172	+	6.66757i	−0.624601	+	0.222500i
$899$	38.5603			1.28606
$900$	−3.17406	+	29.6096i	−0.105802	+	0.986985i
$901$	−14.5894			−0.486045
$902$	−25.6070	+	9.12191i	−0.852621	+	0.303727i
$903$	5.46571	−	2.24538i	0.181888	−	0.0747216i
$904$	25.6159	−	42.3333i	0.851973	−	1.40798i
$905$		−	0.570870i		−	0.0189764i
$906$	−44.3578	+	39.8569i	−1.47369	+	1.32416i
$907$		−	14.4130i		−	0.478575i	−0.970949	−	0.239288i	$-0.923086\pi$
$907$		−	14.4130i		−	0.478575i	0.970949	−	0.239288i	$-0.0769139\pi$
$908$	40.3873	−	32.9561i	1.34030	−	1.09369i
$909$	−15.4488	−	15.6295i	−0.512406	−	0.518399i
$910$	−0.287975	−	0.808404i	−0.00954628	−	0.0267983i
$911$	20.2534			0.671024			0.335512	−	0.942036i	$-0.391091\pi$
$911$	20.2534			0.671024			0.335512	+	0.942036i	$0.391091\pi$
$912$	6.80633	−	1.29376i	0.225380	−	0.0428407i
$913$	−0.151267			−0.00500622
$914$	−1.41316	−	3.96702i	−0.0467432	−	0.131217i
$915$	−0.250072	−	0.608727i	−0.00826714	−	0.0201239i
$916$	35.6097	−	29.0576i	1.17658	−	0.960089i
$917$			14.0674i			0.464545i
$918$	−0.862655	+	14.5527i	−0.0284719	+	0.480312i
$919$			31.6787i			1.04499i	0.852644	+	0.522493i	$0.174998\pi$
$919$			31.6787i			1.04499i	−0.852644	+	0.522493i	$0.825002\pi$
$920$	0.757507	−	1.25187i	0.0249743	−	0.0412728i
$921$	9.93919	+	24.1940i	0.327507	+	0.797220i
$922$	47.4736	−	16.9114i	1.56346	−	0.556946i
$923$	36.7413			1.20935
$924$	6.60782	+	3.58060i	0.217381	+	0.117793i
$925$	−25.2266			−0.829446
$926$	−48.6203	+	17.3198i	−1.59776	+	0.569166i
$927$	14.6065	+	14.7774i	0.479741	+	0.485352i
$928$	−6.53593	−	46.2926i	−0.214553	−	1.51963i
$929$		−	24.3633i		−	0.799335i	−0.916660	−	0.399667i	$-0.869126\pi$
$929$		−	24.3633i		−	0.799335i	0.916660	−	0.399667i	$-0.130874\pi$
$930$	−1.46533	−	1.63081i	−0.0480501	−	0.0534762i
$931$		−	6.46179i		−	0.211777i
$932$	6.48368	+	7.94566i	0.212380	+	0.260269i
$933$	−10.2911	+	4.22772i	−0.336917	+	0.138409i
$934$	−12.0310	−	33.7734i	−0.393666	−	1.10510i
$935$	1.12548			0.0368071
$936$	35.5768	−	8.53379i	1.16286	−	0.278936i
$937$	13.4196			0.438401			0.219200	−	0.975680i	$-0.429655\pi$
$937$	13.4196			0.438401			0.219200	+	0.975680i	$0.429655\pi$
$938$	0.0276903	+	0.0777323i	0.000904121	+	0.00253805i
$939$	47.1803	−	19.3822i	1.53967	−	0.632515i
$940$	1.49042	+	1.82649i	0.0486120	+	0.0595734i
$941$			27.3877i			0.892813i	0.894830	+	0.446406i	$0.147296\pi$
$941$			27.3877i			0.892813i	−0.894830	+	0.446406i	$0.852704\pi$
$942$	11.2581	+	12.5295i	0.366809	+	0.408232i
$943$		−	17.5275i		−	0.570775i
$944$	−7.72763	+	37.7433i	−0.251513	+	1.22844i
$945$	−0.285734	+	0.673157i	−0.00929492	+	0.0218978i
$946$	18.3207	−	6.52634i	0.595659	−	0.212190i
$947$	−29.8326			−0.969430			−0.484715	−	0.874672i	$-0.661077\pi$
$947$	−29.8326			−0.969430			−0.484715	+	0.874672i	$0.661077\pi$
$948$	−46.7675	−	25.3420i	−1.51894	−	0.823070i
$949$	−22.6862			−0.736425
$950$	−6.61202	+	2.35538i	−0.214522	+	0.0764186i
$951$	7.77213	+	18.9189i	0.252029	+	0.613489i
$952$	−3.52193	−	2.13113i	−0.114147	−	0.0690703i
$953$			49.3752i			1.59942i	0.600387	+	0.799710i	$0.295013\pi$
$953$			49.3752i			1.59942i	−0.600387	+	0.799710i	$0.704987\pi$
$954$	13.5432	−	28.1082i	0.438477	−	0.910037i
$955$			1.36685i			0.0442304i
$956$	24.6813	−	20.1400i	0.798252	−	0.651376i
$957$	−16.0864	−	39.1576i	−0.519999	−	1.26578i
$958$	1.33634	+	3.75137i	0.0431751	+	0.121201i
$959$	−10.9503			−0.353605
$960$	−1.70945	+	2.03559i	−0.0551723	+	0.0656983i
$961$	9.23120			0.297781
$962$	10.4003	+	29.1956i	0.335318	+	0.941305i
$963$	6.42051	−	6.34629i	0.206898	−	0.204506i
$964$	−14.0094	+	11.4317i	−0.451212	+	0.368190i
$965$		−	3.12751i		−	0.100678i
$966$	−3.60462	+	3.23887i	−0.115977	+	0.104209i
$967$		−	1.32849i		−	0.0427213i	−0.999772	−	0.0213606i	$-0.993200\pi$
$967$		−	1.32849i		−	0.0427213i	0.999772	−	0.0213606i	$-0.00679982\pi$
$968$	−5.45528	−	3.30100i	−0.175339	−	0.106098i
$969$	−3.17838	+	1.30572i	−0.102104	+	0.0419457i
$970$	3.15765	−	1.12484i	0.101386	−	0.0361164i
$971$	39.9055			1.28063			0.640314	−	0.768114i	$-0.278804\pi$
$971$	39.9055			1.28063			0.640314	+	0.768114i	$0.278804\pi$
$972$	−27.2367	−	15.1711i	−0.873617	−	0.486614i
$973$	14.2802			0.457801
$974$	43.3217	−	15.4324i	1.38812	−	0.494485i
$975$	−34.2852	+	14.0848i	−1.09800	+	0.451073i
$976$	−1.58907	+	7.76135i	−0.0508650	+	0.248435i
$977$		−	3.41931i		−	0.109393i	−0.998503	−	0.0546967i	$-0.982581\pi$
$977$		−	3.41931i		−	0.109393i	0.998503	−	0.0546967i	$-0.0174192\pi$
$978$	0.563921	−	0.506701i	0.0180322	−	0.0162025i
$979$		−	31.6176i		−	1.01050i
$980$	1.56742	+	1.92086i	0.0500695	+	0.0613595i
$981$	−37.5213	+	37.0875i	−1.19796	+	1.18411i
$982$	2.16726	+	6.08393i	0.0691600	+	0.194146i
$983$	−52.3314			−1.66911			−0.834556	−	0.550923i	$-0.814276\pi$
$983$	−52.3314			−1.66911			−0.834556	+	0.550923i	$0.814276\pi$
$984$	−4.89591	+	31.4630i	−0.156076	+	1.00301i
$985$	1.49154			0.0475244
$986$	7.78093	+	21.8426i	0.247795	+	0.695611i
$987$	−2.96681	−	7.22182i	−0.0944346	−	0.229873i
$988$	5.45193	+	6.68127i	0.173449	+	0.212559i
$989$			12.5402i			0.398755i
$990$	−1.04477	+	2.16836i	−0.0332049	+	0.0689150i
$991$			25.3630i			0.805681i	0.915270	+	0.402841i	$0.131977\pi$
$991$			25.3630i			0.805681i	−0.915270	+	0.402841i	$0.868023\pi$
$992$	3.68979	+	26.1340i	0.117151	+	0.829756i
$993$	−23.4101	−	56.9849i	−0.742897	−	1.80836i
$994$	8.32828	−	2.96676i	0.264157	−	0.0940998i
$995$	2.25538			0.0715003
$996$	−0.0844174	+	0.155788i	−0.00267487	+	0.00493635i
$997$	48.3524			1.53134			0.765668	−	0.643236i	$-0.222409\pi$
$997$	48.3524			1.53134			0.765668	+	0.643236i	$0.222409\pi$
$998$	−17.0029	+	6.05689i	−0.538218	+	0.191728i
$999$	10.3193	−	24.3112i	0.326489	−	0.769172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.c.a.191.15	✓	36
3.2	odd	2	inner	228.2.c.a.191.22	yes	36
4.3	odd	2	inner	228.2.c.a.191.21	yes	36
12.11	even	2	inner	228.2.c.a.191.16	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.c.a.191.15	✓	36	1.1	even	1	trivial
228.2.c.a.191.16	yes	36	12.11	even	2	inner
228.2.c.a.191.21	yes	36	4.3	odd	2	inner
228.2.c.a.191.22	yes	36	3.2	odd	2	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.474569 - 1.33221i) q^{2} +(-1.60213 + 0.658173i) q^{3} +(-1.54957 + 1.26445i) q^{4} -0.191837i q^{5} +(1.63714 + 1.82202i) q^{6} +0.733628i q^{7} +(2.41989 + 1.46428i) q^{8} +(2.13362 - 2.10895i) q^{9} +O(q^{10})\)	\(q+(-0.474569 - 1.33221i) q^{2} +(-1.60213 + 0.658173i) q^{3} +(-1.54957 + 1.26445i) q^{4} -0.191837i q^{5} +(1.63714 + 1.82202i) q^{6} +0.733628i q^{7} +(2.41989 + 1.46428i) q^{8} +(2.13362 - 2.10895i) q^{9} +(-0.255567 + 0.0910397i) q^{10} +2.95731 q^{11} +(1.65038 - 3.04569i) q^{12} +4.31169 q^{13} +(0.977347 - 0.348157i) q^{14} +(0.126262 + 0.307347i) q^{15} +(0.802324 - 3.91871i) q^{16} +1.98385i q^{17} +(-3.82212 - 1.84158i) q^{18} -1.00000i q^{19} +(0.242568 + 0.297264i) q^{20} +(-0.482854 - 1.17536i) q^{21} +(-1.40345 - 3.93975i) q^{22} +2.69669 q^{23} +(-4.84072 - 0.753256i) q^{24} +4.96320 q^{25} +(-2.04620 - 5.74408i) q^{26} +(-2.03027 + 4.78310i) q^{27} +(-0.927637 - 1.13681i) q^{28} +8.26462i q^{29} +(0.349530 - 0.314064i) q^{30} -4.66570i q^{31} +(-5.60130 + 0.790833i) q^{32} +(-4.73798 + 1.94642i) q^{33} +(2.64291 - 0.941475i) q^{34} +0.140737 q^{35} +(-0.639519 + 5.96582i) q^{36} -5.08273 q^{37} +(-1.33221 + 0.474569i) q^{38} +(-6.90788 + 2.83784i) q^{39} +(0.280903 - 0.464224i) q^{40} -6.49966i q^{41} +(-1.33669 + 1.20105i) q^{42} +4.65023i q^{43} +(-4.58255 + 3.73937i) q^{44} +(-0.404574 - 0.409306i) q^{45} +(-1.27976 - 3.59256i) q^{46} +6.14432 q^{47} +(1.29376 + 6.80633i) q^{48} +6.46179 q^{49} +(-2.35538 - 6.61202i) q^{50} +(-1.30572 - 3.17838i) q^{51} +(-6.68127 + 5.45193i) q^{52} +7.35410i q^{53} +(7.33559 + 0.434838i) q^{54} -0.567319i q^{55} +(-1.07424 + 1.77530i) q^{56} +(0.658173 + 1.60213i) q^{57} +(11.0102 - 3.92213i) q^{58} -9.63156 q^{59} +(-0.584276 - 0.316603i) q^{60} -1.98059 q^{61} +(-6.21570 + 2.21420i) q^{62} +(1.54719 + 1.56528i) q^{63} +(3.71176 + 7.08681i) q^{64} -0.827141i q^{65} +(4.84153 + 5.38827i) q^{66} +0.0795340i q^{67} +(-2.50848 - 3.07411i) q^{68} +(-4.32043 + 1.77489i) q^{69} +(-0.0667893 - 0.187491i) q^{70} +8.52131 q^{71} +(8.25122 - 1.97922i) q^{72} -5.26155 q^{73} +(2.41211 + 6.77127i) q^{74} +(-7.95167 + 3.26664i) q^{75} +(1.26445 + 1.54957i) q^{76} +2.16956i q^{77} +(7.05886 + 7.85600i) q^{78} -15.3553i q^{79} +(-0.751752 - 0.153915i) q^{80} +(0.104648 - 8.99939i) q^{81} +(-8.65891 + 3.08454i) q^{82} -0.0511504 q^{83} +(2.23441 + 1.21076i) q^{84} +0.380575 q^{85} +(6.19508 - 2.20685i) q^{86} +(-5.43954 - 13.2410i) q^{87} +(7.15636 + 4.33033i) q^{88} -10.6913i q^{89} +(-0.353283 + 0.733222i) q^{90} +3.16318i q^{91} +(-4.17870 + 3.40983i) q^{92} +(3.07084 + 7.47505i) q^{93} +(-2.91590 - 8.18553i) q^{94} -0.191837 q^{95} +(8.45349 - 4.95364i) q^{96} -12.3555 q^{97} +(-3.06657 - 8.60846i) q^{98} +(6.30976 - 6.23681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{6}+O(q^{10}) \) 36 * q - 6 * q^6	\( 36 q - 6 q^{6} + 8 q^{10} + 4 q^{12} - 8 q^{16} + 16 q^{18} + 8 q^{21} - 12 q^{22} - 2 q^{24} - 28 q^{25} + 12 q^{28} - 12 q^{30} - 28 q^{34} - 22 q^{36} - 16 q^{37} - 12 q^{40} + 10 q^{42} + 16 q^{45} - 4 q^{46} + 32 q^{48} - 44 q^{49} - 36 q^{52} - 20 q^{54} - 4 q^{58} - 4 q^{60} + 16 q^{61} + 24 q^{64} + 24 q^{66} - 16 q^{69} + 36 q^{70} - 36 q^{72} - 8 q^{73} - 32 q^{78} - 40 q^{81} + 72 q^{82} - 20 q^{84} + 16 q^{85} - 16 q^{88} - 56 q^{90} + 8 q^{93} - 56 q^{94} + 2 q^{96} + 40 q^{97}+O(q^{100}) \) 36 * q - 6 * q^6 + 8 * q^10 + 4 * q^12 - 8 * q^16 + 16 * q^18 + 8 * q^21 - 12 * q^22 - 2 * q^24 - 28 * q^25 + 12 * q^28 - 12 * q^30 - 28 * q^34 - 22 * q^36 - 16 * q^37 - 12 * q^40 + 10 * q^42 + 16 * q^45 - 4 * q^46 + 32 * q^48 - 44 * q^49 - 36 * q^52 - 20 * q^54 - 4 * q^58 - 4 * q^60 + 16 * q^61 + 24 * q^64 + 24 * q^66 - 16 * q^69 + 36 * q^70 - 36 * q^72 - 8 * q^73 - 32 * q^78 - 40 * q^81 + 72 * q^82 - 20 * q^84 + 16 * q^85 - 16 * q^88 - 56 * q^90 + 8 * q^93 - 56 * q^94 + 2 * q^96 + 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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