LMFDB - Embedded newform 961.2.c.l.521.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16,0,16,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.8
Character	$\chi$	$=$	961.521
Dual form			961.2.c.l.439.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.31607 q^{2} +(0.617233 + 1.06908i) q^{3} -0.267953 q^{4} +(-0.00363912 + 0.00630315i) q^{5} +(-0.812323 - 1.40699i) q^{6} +(0.397459 + 0.688419i) q^{7} +2.98479 q^{8} +(0.738047 - 1.27834i) q^{9} +(0.00478935 - 0.00829540i) q^{10} +(-1.98883 + 3.44475i) q^{11} +(-0.165390 - 0.286463i) q^{12} +(3.15487 - 5.46439i) q^{13} +(-0.523084 - 0.906009i) q^{14} -0.00898475 q^{15} -3.39229 q^{16} +(-3.14043 - 5.43938i) q^{17} +(-0.971323 + 1.68238i) q^{18} +(-1.86730 - 3.23426i) q^{19} +(0.000975115 - 0.00168895i) q^{20} +(-0.490649 + 0.849829i) q^{21} +(2.61744 - 4.53354i) q^{22} +0.483672 q^{23} +(1.84231 + 3.19098i) q^{24} +(2.49997 + 4.33008i) q^{25} +(-4.15203 + 7.19153i) q^{26} +5.52559 q^{27} +(-0.106500 - 0.184464i) q^{28} -1.62052 q^{29} +0.0118246 q^{30} -1.50508 q^{32} -4.91028 q^{33} +(4.13303 + 7.15861i) q^{34} -0.00578561 q^{35} +(-0.197762 + 0.342534i) q^{36} +(-3.74519 - 6.48685i) q^{37} +(2.45750 + 4.25652i) q^{38} +7.78915 q^{39} +(-0.0108620 + 0.0188136i) q^{40} +(2.01443 - 3.48910i) q^{41} +(0.645730 - 1.11844i) q^{42} +(-0.350752 - 0.607520i) q^{43} +(0.532913 - 0.923032i) q^{44} +(0.00537169 + 0.00930404i) q^{45} -0.636548 q^{46} +4.30532 q^{47} +(-2.09384 - 3.62663i) q^{48} +(3.18405 - 5.51494i) q^{49} +(-3.29015 - 5.69870i) q^{50} +(3.87675 - 6.71472i) q^{51} +(-0.845357 + 1.46420i) q^{52} +(2.03984 - 3.53311i) q^{53} -7.27207 q^{54} +(-0.0144752 - 0.0250717i) q^{55} +(1.18633 + 2.05479i) q^{56} +(2.30512 - 3.99258i) q^{57} +2.13272 q^{58} +(6.85180 + 11.8677i) q^{59} +0.00240749 q^{60} -5.02369 q^{61} +1.17337 q^{63} +8.76538 q^{64} +(0.0229619 + 0.0397712i) q^{65} +6.46228 q^{66} +(7.26276 - 12.5795i) q^{67} +(0.841487 + 1.45750i) q^{68} +(0.298538 + 0.517084i) q^{69} +0.00761428 q^{70} +(4.70662 - 8.15211i) q^{71} +(2.20292 - 3.81556i) q^{72} +(-2.21159 + 3.83059i) q^{73} +(4.92894 + 8.53717i) q^{74} +(-3.08613 + 5.34534i) q^{75} +(0.500349 + 0.866630i) q^{76} -3.16191 q^{77} -10.2511 q^{78} +(5.22943 + 9.05763i) q^{79} +(0.0123450 - 0.0213821i) q^{80} +(1.19643 + 2.07228i) q^{81} +(-2.65114 + 4.59190i) q^{82} +(1.00406 - 1.73908i) q^{83} +(0.131471 - 0.227715i) q^{84} +0.0457136 q^{85} +(0.461615 + 0.799541i) q^{86} +(-1.00024 - 1.73246i) q^{87} +(-5.93623 + 10.2819i) q^{88} -1.12238 q^{89} +(-0.00706953 - 0.0122448i) q^{90} +5.01572 q^{91} -0.129602 q^{92} -5.66611 q^{94} +0.0271813 q^{95} +(-0.928983 - 1.60905i) q^{96} +7.27529 q^{97} +(-4.19044 + 7.25806i) q^{98} +(2.93570 + 5.08477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 16 q^{4} + 16 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} - 16 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 16 q^{32} - 64 q^{33} - 32 q^{35} + 40 q^{36} + 24 q^{38} - 64 q^{39}+ \cdots - 16 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 + 16 * q^4 + 16 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 - 16 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 16 * q^32 - 64 * q^33 - 32 * q^35 + 40 * q^36 + 24 * q^38 - 64 * q^39 + 32 * q^41 + 16 * q^45 - 64 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 + 48 * q^56 + 64 * q^59 - 32 * q^63 - 32 * q^64 - 16 * q^67 + 32 * q^69 + 176 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 + 64 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 + 32 * q^87 - 40 * q^90 - 64 * q^94 - 96 * q^95 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.31607			−0.930604			−0.465302	−	0.885152i	$-0.654054\pi$
$2$	−1.31607			−0.930604			−0.465302	+	0.885152i	$0.654054\pi$
$3$	0.617233	+	1.06908i	0.356360	+	0.617233i	0.987350	−	0.158558i	$-0.0506845\pi$
$3$	0.617233	+	1.06908i	0.356360	+	0.617233i	−0.630990	+	0.775791i	$0.717351\pi$
$4$	−0.267953			−0.133977
$5$	−0.00363912	+	0.00630315i	−0.00162747	+	0.00281885i	−0.866838	−	0.498590i	$-0.833851\pi$
$5$	−0.00363912	+	0.00630315i	−0.00162747	+	0.00281885i	0.865211	+	0.501409i	$0.167185\pi$
$6$	−0.812323	−	1.40699i	−0.331630	−	0.574399i
$7$	0.397459	+	0.688419i	0.150225	+	0.260198i	0.931310	−	0.364227i	$-0.118667\pi$
$7$	0.397459	+	0.688419i	0.150225	+	0.260198i	−0.781085	+	0.624425i	$0.785333\pi$
$8$	2.98479			1.05528
$9$	0.738047	−	1.27834i	0.246016	−	0.426112i
$10$	0.00478935	−	0.00829540i	0.00151453	−	0.00262324i
$11$	−1.98883	+	3.44475i	−0.599654	+	1.03863i	0.393218	+	0.919445i	$0.371362\pi$
$11$	−1.98883	+	3.44475i	−0.599654	+	1.03863i	−0.992872	+	0.119186i	$0.961972\pi$
$12$	−0.165390	−	0.286463i	−0.0477439	−	0.0826948i
$13$	3.15487	−	5.46439i	0.875002	−	1.51555i	0.0182420	−	0.999834i	$-0.494193\pi$
$13$	3.15487	−	5.46439i	0.875002	−	1.51555i	0.856760	−	0.515715i	$-0.172474\pi$
$14$	−0.523084	−	0.906009i	−0.139800	−	0.242141i
$15$	−0.00898475			−0.00231985
$16$	−3.39229			−0.848074
$17$	−3.14043	−	5.43938i	−0.761665	−	1.31924i	−0.941992	−	0.335636i	$-0.891049\pi$
$17$	−3.14043	−	5.43938i	−0.761665	−	1.31924i	0.180327	−	0.983607i	$-0.442284\pi$
$18$	−0.971323	+	1.68238i	−0.228943	+	0.396541i
$19$	−1.86730	−	3.23426i	−0.428388	−	0.741989i	0.568342	−	0.822792i	$-0.307585\pi$
$19$	−1.86730	−	3.23426i	−0.428388	−	0.741989i	−0.996730	+	0.0808028i	$0.974252\pi$
$20$	0.000975115	−	0.00168895i	0.000218042	−	0.000377661i
$21$	−0.490649	+	0.849829i	−0.107068	+	0.185448i
$22$	2.61744	−	4.53354i	0.558040	−	0.966554i
$23$	0.483672			0.100853			0.0504263	−	0.998728i	$-0.483942\pi$
$23$	0.483672			0.100853			0.0504263	+	0.998728i	$0.483942\pi$
$24$	1.84231	+	3.19098i	0.376060	+	0.651355i
$25$	2.49997	+	4.33008i	0.499995	+	0.866016i
$26$	−4.15203	+	7.19153i	−0.814280	+	1.41038i
$27$	5.52559			1.06340
$28$	−0.106500	−	0.184464i	−0.0201267	−	0.0348604i
$29$	−1.62052			−0.300922			−0.150461	−	0.988616i	$-0.548076\pi$
$29$	−1.62052			−0.300922			−0.150461	+	0.988616i	$0.548076\pi$
$30$	0.0118246			0.00215886
$31$		0			0
$31$		0			0
$32$	−1.50508			−0.266062
$33$	−4.91028			−0.854769
$34$	4.13303	+	7.15861i	0.708808	+	1.22769i
$35$	−0.00578561			−0.000977946
$36$	−0.197762	+	0.342534i	−0.0329604	+	0.0570890i
$37$	−3.74519	−	6.48685i	−0.615705	−	1.06643i	−0.990260	−	0.139228i	$-0.955538\pi$
$37$	−3.74519	−	6.48685i	−0.615705	−	1.06643i	0.374556	−	0.927204i	$-0.377795\pi$
$38$	2.45750	+	4.25652i	0.398659	+	0.690498i
$39$	7.78915			1.24726
$40$	−0.0108620	+	0.0188136i	−0.00171744	+	0.00297469i
$41$	2.01443	−	3.48910i	0.314601	−	0.544905i	−0.664751	−	0.747065i	$-0.731463\pi$
$41$	2.01443	−	3.48910i	0.314601	−	0.544905i	0.979353	+	0.202159i	$0.0647959\pi$
$42$	0.645730	−	1.11844i	0.0996383	−	0.172579i
$43$	−0.350752	−	0.607520i	−0.0534892	−	0.0926460i	0.838041	−	0.545607i	$-0.183701\pi$
$43$	−0.350752	−	0.607520i	−0.0534892	−	0.0926460i	−0.891530	+	0.452961i	$0.850368\pi$
$44$	0.532913	−	0.923032i	0.0803396	−	0.139152i
$45$	0.00537169	+	0.00930404i	0.000800764	+	0.00138696i
$46$	−0.636548			−0.0938538
$47$	4.30532			0.627995			0.313997	−	0.949424i	$-0.398332\pi$
$47$	4.30532			0.627995			0.313997	+	0.949424i	$0.398332\pi$
$48$	−2.09384	−	3.62663i	−0.302219	−	0.523459i
$49$	3.18405	−	5.51494i	0.454865	−	0.787849i
$50$	−3.29015	−	5.69870i	−0.465297	−	0.805918i
$51$	3.87675	−	6.71472i	0.542853	−	0.940249i
$52$	−0.845357	+	1.46420i	−0.117230	+	0.203048i
$53$	2.03984	−	3.53311i	0.280194	−	0.485310i	−0.691238	−	0.722627i	$-0.742935\pi$
$53$	2.03984	−	3.53311i	0.280194	−	0.485310i	0.971432	+	0.237316i	$0.0762678\pi$
$54$	−7.27207			−0.989603
$55$	−0.0144752	−	0.0250717i	−0.00195183	−	0.00338067i
$56$	1.18633	+	2.05479i	0.158530	+	0.274582i
$57$	2.30512	−	3.99258i	0.305320	−	0.528830i
$58$	2.13272			0.280039
$59$	6.85180	+	11.8677i	0.892028	+	1.54504i	0.837440	+	0.546530i	$0.184051\pi$
$59$	6.85180	+	11.8677i	0.892028	+	1.54504i	0.0545886	+	0.998509i	$0.482615\pi$
$60$	0.00240749			0.000310806
$61$	−5.02369			−0.643218			−0.321609	−	0.946873i	$-0.604224\pi$
$61$	−5.02369			−0.643218			−0.321609	+	0.946873i	$0.604224\pi$
$62$		0			0
$63$	1.17337			0.147831
$64$	8.76538			1.09567
$65$	0.0229619	+	0.0397712i	0.00284807	+	0.00493301i
$66$	6.46228			0.795452
$67$	7.26276	−	12.5795i	0.887287	−	1.53683i	0.0442180	−	0.999022i	$-0.485920\pi$
$67$	7.26276	−	12.5795i	0.887287	−	1.53683i	0.843069	−	0.537805i	$-0.180746\pi$
$68$	0.841487	+	1.45750i	0.102045	+	0.176748i
$69$	0.298538	+	0.517084i	0.0359398	+	0.0622496i
$70$	0.00761428			0.000910080
$71$	4.70662	−	8.15211i	0.558574	−	0.967478i	−0.439042	−	0.898466i	$-0.644682\pi$
$71$	4.70662	−	8.15211i	0.558574	−	0.967478i	0.997616	−	0.0690113i	$-0.0219845\pi$
$72$	2.20292	−	3.81556i	0.259616	−	0.449668i
$73$	−2.21159	+	3.83059i	−0.258847	+	0.448337i	−0.965933	−	0.258791i	$-0.916676\pi$
$73$	−2.21159	+	3.83059i	−0.258847	+	0.448337i	0.707086	+	0.707127i	$0.250009\pi$
$74$	4.92894	+	8.53717i	0.572977	+	0.992426i
$75$	−3.08613	+	5.34534i	−0.356356	+	0.617226i
$76$	0.500349	+	0.866630i	0.0573940	+	0.0994093i
$77$	−3.16191			−0.360333
$78$	−10.2511			−1.16071
$79$	5.22943	+	9.05763i	0.588356	+	1.01906i	0.994448	+	0.105231i	$0.0335581\pi$
$79$	5.22943	+	9.05763i	0.588356	+	1.01906i	−0.406092	+	0.913832i	$0.633109\pi$
$80$	0.0123450	−	0.0213821i	0.00138021	−	0.00239060i
$81$	1.19643	+	2.07228i	0.132937	+	0.230253i
$82$	−2.65114	+	4.59190i	−0.292769	+	0.507091i
$83$	1.00406	−	1.73908i	0.110210	−	0.190889i	−0.805645	−	0.592399i	$-0.798181\pi$
$83$	1.00406	−	1.73908i	0.110210	−	0.190889i	0.915855	+	0.401510i	$0.131514\pi$
$84$	0.131471	−	0.227715i	0.0143447	−	0.0248457i
$85$	0.0457136			0.00495834
$86$	0.461615	+	0.799541i	0.0497772	+	0.0862167i
$87$	−1.00024	−	1.73246i	−0.107237	−	0.185739i
$88$	−5.93623	+	10.2819i	−0.632804	+	1.09605i
$89$	−1.12238			−0.118972			−0.0594859	−	0.998229i	$-0.518946\pi$
$89$	−1.12238			−0.118972			−0.0594859	+	0.998229i	$0.518946\pi$
$90$	−0.00706953	−	0.0122448i	−0.000745194	−	0.00129071i
$91$	5.01572			0.525790
$92$	−0.129602			−0.0135119
$93$		0			0
$94$	−5.66611			−0.584414
$95$	0.0271813			0.00278875
$96$	−0.928983	−	1.60905i	−0.0948139	−	0.164222i
$97$	7.27529			0.738694			0.369347	−	0.929292i	$-0.379581\pi$
$97$	7.27529			0.738694			0.369347	+	0.929292i	$0.379581\pi$
$98$	−4.19044	+	7.25806i	−0.423299	+	0.733175i
$99$	2.93570	+	5.08477i	0.295048	+	0.511039i
$100$	−0.669876	−	1.16026i	−0.0669876	−	0.116026i
$101$	−6.43242			−0.640050			−0.320025	−	0.947409i	$-0.603691\pi$
$101$	−6.43242			−0.640050			−0.320025	+	0.947409i	$0.603691\pi$
$102$	−5.10208	+	8.83706i	−0.505181	+	0.875000i
$103$	4.26771	−	7.39190i	0.420510	−	0.728345i	−0.575479	−	0.817817i	$-0.695184\pi$
$103$	4.26771	−	7.39190i	0.420510	−	0.728345i	0.995989	+	0.0894712i	$0.0285177\pi$
$104$	9.41661	−	16.3101i	0.923375	−	1.59933i
$105$	−0.00357107	−	0.00618527i	−0.000348500	−	0.000603621i
$106$	−2.68458	+	4.64983i	−0.260750	+	0.451632i
$107$	6.75737	+	11.7041i	0.653259	+	1.13148i	0.982327	+	0.187172i	$0.0599322\pi$
$107$	6.75737	+	11.7041i	0.653259	+	1.13148i	−0.329068	+	0.944306i	$0.606734\pi$
$108$	−1.48060			−0.142471
$109$	10.2309			0.979944			0.489972	−	0.871738i	$-0.337007\pi$
$109$	10.2309			0.979944			0.489972	+	0.871738i	$0.337007\pi$
$110$	0.0190504	+	0.0329962i	0.00181638	+	0.00314607i
$111$	4.62330	−	8.00780i	0.438825	−	0.760067i
$112$	−1.34830	−	2.33532i	−0.127402	−	0.220667i
$113$	4.16219	−	7.20912i	0.391546	−	0.678177i	−0.601108	−	0.799168i	$-0.705274\pi$
$113$	4.16219	−	7.20912i	0.391546	−	0.678177i	0.992654	+	0.120991i	$0.0386072\pi$
$114$	−3.03370	+	5.25452i	−0.284132	+	0.492131i
$115$	−0.00176014	+	0.00304866i	−0.000164134	+	0.000284289i
$116$	0.434223			0.0403166
$117$	−4.65688	−	8.06595i	−0.430529	−	0.745697i
$118$	−9.01747	−	15.6187i	−0.830125	−	1.43782i
$119$	2.49638	−	4.32385i	0.228843	−	0.396367i
$120$	−0.0268176			−0.00244810
$121$	−2.41086	−	4.17573i	−0.219169	−	0.379612i
$122$	6.61154			0.598581
$123$	4.97349			0.448445
$124$		0			0
$125$	−0.0727821			−0.00650983
$126$	−1.54424			−0.137572
$127$	−5.62318	−	9.73963i	−0.498976	−	0.864252i	0.501023	−	0.865434i	$-0.332957\pi$
$127$	−5.62318	−	9.73963i	−0.498976	−	0.864252i	−0.999999	+	0.00118170i	$0.999624\pi$
$128$	−8.52572			−0.753574
$129$	0.432991	−	0.749963i	0.0381228	−	0.0660306i
$130$	−0.0302195	−	0.0523418i	−0.00265043	−	0.00459068i
$131$	−0.322789	−	0.559087i	−0.0282022	−	0.0488476i	0.851580	−	0.524225i	$-0.175645\pi$
$131$	−0.322789	−	0.559087i	−0.0282022	−	0.0488476i	−0.879782	+	0.475377i	$0.842312\pi$
$132$	1.31572			0.114519
$133$	1.48435	−	2.57097i	0.128709	−	0.222931i
$134$	−9.55832	+	16.5555i	−0.825713	+	1.43018i
$135$	−0.0201083	+	0.0348286i	−0.00173065	+	0.00299757i
$136$	−9.37351	−	16.2354i	−0.803772	−	1.39217i
$137$	−1.44198	+	2.49758i	−0.123196	+	0.213382i	−0.921027	−	0.389500i	$-0.872648\pi$
$137$	−1.44198	+	2.49758i	−0.123196	+	0.213382i	0.797830	+	0.602882i	$0.205981\pi$
$138$	−0.392898	−	0.680520i	−0.0334457	−	0.0579297i
$139$	3.37884			0.286589			0.143295	−	0.989680i	$-0.454230\pi$
$139$	3.37884			0.286589			0.143295	+	0.989680i	$0.454230\pi$
$140$	0.00155027			0.000131022
$141$	2.65738	+	4.60272i	0.223792	+	0.387619i
$142$	−6.19426	+	10.7288i	−0.519811	+	0.900338i
$143$	12.5490	+	21.7354i	1.04940	+	1.81761i
$144$	−2.50367	+	4.33649i	−0.208639	+	0.361374i
$145$	0.00589726	−	0.0102144i	0.000489741	−	0.000848256i
$146$	2.91062	−	5.04133i	0.240884	−	0.417224i
$147$	7.86121			0.648382
$148$	1.00353	+	1.73817i	0.0824901	+	0.142877i
$149$	5.88496	+	10.1931i	0.482115	+	0.835047i	0.999789	−	0.0205303i	$-0.00653545\pi$
$149$	5.88496	+	10.1931i	0.482115	+	0.835047i	−0.517674	+	0.855578i	$0.673202\pi$
$150$	4.06157	−	7.03485i	0.331626	−	0.574393i
$151$	−17.8685			−1.45412			−0.727061	−	0.686573i	$-0.759114\pi$
$151$	−17.8685			−1.45412			−0.727061	+	0.686573i	$0.759114\pi$
$152$	−5.57350	−	9.65358i	−0.452070	−	0.783009i
$153$	−9.27113			−0.749526
$154$	4.16130			0.335327
$155$		0			0
$156$	−2.08713			−0.167104
$157$	2.66095			0.212367			0.106184	−	0.994347i	$-0.466137\pi$
$157$	2.66095			0.212367			0.106184	+	0.994347i	$0.466137\pi$
$158$	−6.88230	−	11.9205i	−0.547527	−	0.948344i
$159$	5.03623			0.399399
$160$	0.00547716	−	0.00948672i	0.000433008	−	0.000749991i
$161$	0.192240	+	0.332969i	0.0151506	+	0.0262416i
$162$	−1.57459	−	2.72727i	−0.123712	−	0.214275i
$163$	−16.9049			−1.32410			−0.662048	−	0.749461i	$-0.730312\pi$
$163$	−16.9049			−1.32410			−0.662048	+	0.749461i	$0.730312\pi$
$164$	−0.539773	+	0.934915i	−0.0421492	+	0.0730046i
$165$	0.0178691	−	0.0309502i	0.00139111	−	0.00240947i
$166$	−1.32142	+	2.28876i	−0.102562	+	0.177642i
$167$	7.74128	+	13.4083i	0.599039	+	1.03757i	0.992963	+	0.118422i	$0.0377837\pi$
$167$	7.74128	+	13.4083i	0.599039	+	1.03757i	−0.393925	+	0.919143i	$0.628883\pi$
$168$	−1.46449	+	2.53656i	−0.112987	+	0.195700i
$169$	−13.4064	−	23.2205i	−1.03126	−	1.78619i
$170$	−0.0601624			−0.00461425
$171$	−5.51262			−0.421560
$172$	0.0939852	+	0.162787i	0.00716630	+	0.0124124i
$173$	−3.45532	+	5.98479i	−0.262703	+	0.455015i	−0.966959	−	0.254931i	$-0.917947\pi$
$173$	−3.45532	+	5.98479i	−0.262703	+	0.455015i	0.704256	+	0.709946i	$0.251281\pi$
$174$	1.31638	+	2.28004i	0.0997948	+	0.172850i
$175$	−1.98727	+	3.44206i	−0.150224	+	0.260195i
$176$	6.74668	−	11.6856i	0.508551	−	0.880835i
$177$	−8.45831	+	14.6502i	−0.635766	+	1.10118i
$178$	1.47713			0.110716
$179$	−7.24054	−	12.5410i	−0.541184	−	0.937358i	−0.998836	−	0.0482266i	$-0.984643\pi$
$179$	−7.24054	−	12.5410i	−0.541184	−	0.937358i	0.457653	−	0.889131i	$-0.348690\pi$
$180$	−0.00143936	−	0.00249305i	−0.000107284	−	0.000185821i
$181$	8.67667	−	15.0284i	0.644932	−	1.11706i	−0.339385	−	0.940647i	$-0.610219\pi$
$181$	8.67667	−	15.0284i	0.644932	−	1.11706i	0.984317	−	0.176408i	$-0.0564477\pi$
$182$	−6.60104			−0.489302
$183$	−3.10079	−	5.37072i	−0.229217	−	0.397015i
$184$	1.44366			0.106428
$185$	0.0545168			0.00400815
$186$		0			0
$187$	24.9830			1.82694
$188$	−1.15362			−0.0841367
$189$	2.19619	+	3.80392i	0.159749	+	0.276694i
$190$	−0.0357726			−0.00259522
$191$	−7.45255	+	12.9082i	−0.539248	+	0.934005i	0.459697	+	0.888076i	$0.347958\pi$
$191$	−7.45255	+	12.9082i	−0.539248	+	0.934005i	−0.998945	+	0.0459289i	$0.985375\pi$
$192$	5.41028	+	9.37088i	0.390453	+	0.676285i
$193$	−5.13775	−	8.89885i	−0.369824	−	0.640553i	0.619714	−	0.784828i	$-0.287249\pi$
$193$	−5.13775	−	8.89885i	−0.369824	−	0.640553i	−0.989538	+	0.144274i	$0.953915\pi$
$194$	−9.57481			−0.687432
$195$	−0.0283457	+	0.0490962i	−0.00202988	+	0.00351585i
$196$	−0.853178	+	1.47775i	−0.0609413	+	0.105553i
$197$	−7.30260	+	12.6485i	−0.520289	+	0.901167i	0.479433	+	0.877579i	$0.340842\pi$
$197$	−7.30260	+	12.6485i	−0.520289	+	0.901167i	−0.999722	+	0.0235882i	$0.992491\pi$
$198$	−3.86359	−	6.69193i	−0.274573	−	0.475575i
$199$	5.29589	−	9.17274i	0.375415	−	0.650239i	−0.614974	−	0.788548i	$-0.710833\pi$
$199$	5.29589	−	9.17274i	0.375415	−	0.650239i	0.990389	+	0.138309i	$0.0441667\pi$
$200$	7.46190	+	12.9244i	0.527636	+	0.913892i
$201$	17.9313			1.26477
$202$	8.46553			0.595633
$203$	−0.644088	−	1.11559i	−0.0452061	−	0.0782993i
$204$	−1.03879	+	1.79923i	−0.0727297	+	0.125971i
$205$	0.0146615	+	0.0253945i	0.00102401	+	0.00177363i
$206$	−5.61662	+	9.72827i	−0.391329	+	0.677801i
$207$	0.356973	−	0.618295i	0.0248113	−	0.0429745i
$208$	−10.7022	+	18.5368i	−0.742066	+	1.28530i
$209$	14.8549			1.02754
$210$	0.00469978	+	0.00814026i	0.000324316	+	0.000561732i
$211$	−8.28017	−	14.3417i	−0.570030	−	0.987322i	−0.996562	−	0.0828491i	$-0.973598\pi$
$211$	−8.28017	−	14.3417i	−0.570030	−	0.987322i	0.426532	−	0.904473i	$-0.359735\pi$
$212$	−0.546583	+	0.946709i	−0.0375395	+	0.0650203i
$213$	11.6203			0.796212
$214$	−8.89319	−	15.4035i	−0.607926	−	1.05296i
$215$	0.00510572			0.000348207
$216$	16.4927			1.12219
$217$		0			0
$218$	−13.4646			−0.911940
$219$	−5.46027			−0.368971
$220$	0.00387867	+	0.00671805i	0.000261500	+	0.000452931i
$221$	−39.6305			−2.66583
$222$	−6.08460	+	10.5388i	−0.408372	+	0.707321i
$223$	0.402597	+	0.697318i	0.0269599	+	0.0466959i	0.879191	−	0.476470i	$-0.158084\pi$
$223$	0.402597	+	0.697318i	0.0269599	+	0.0466959i	−0.852231	+	0.523166i	$0.824751\pi$
$224$	−0.598206	−	1.03612i	−0.0399693	−	0.0692289i
$225$	7.38039			0.492026
$226$	−5.47774	+	9.48772i	−0.364374	+	0.631114i
$227$	−6.73730	+	11.6694i	−0.447171	+	0.774522i	−0.998201	−	0.0599633i	$-0.980902\pi$
$227$	−6.73730	+	11.6694i	−0.447171	+	0.774522i	0.551030	+	0.834485i	$0.314235\pi$
$228$	−0.617664	+	1.06982i	−0.0409058	+	0.0708509i
$229$	−6.47476	−	11.2146i	−0.427864	−	0.741082i	0.568819	−	0.822463i	$-0.307400\pi$
$229$	−6.47476	−	11.2146i	−0.427864	−	0.741082i	−0.996683	+	0.0813805i	$0.974067\pi$
$230$	0.00231648	−	0.00401225i	0.000152744	−	0.000264560i
$231$	−1.95163	−	3.38033i	−0.128408	−	0.222409i
$232$	−4.83690			−0.317558
$233$	12.3559			0.809465			0.404732	−	0.914435i	$-0.367365\pi$
$233$	12.3559			0.809465			0.404732	+	0.914435i	$0.367365\pi$
$234$	6.12879	+	10.6154i	0.400652	+	0.693949i
$235$	−0.0156676	+	0.0271371i	−0.00102204	+	0.00177023i
$236$	−1.83596	−	3.17998i	−0.119511	−	0.206999i
$237$	−6.45555	+	11.1813i	−0.419333	+	0.726306i
$238$	−3.28542	+	5.69051i	−0.212962	+	0.368861i
$239$	−7.96656	+	13.7985i	−0.515314	+	0.892550i	0.484528	+	0.874776i	$0.338991\pi$
$239$	−7.96656	+	13.7985i	−0.515314	+	0.892550i	−0.999842	+	0.0177745i	$0.994342\pi$
$240$	0.0304789			0.00196741
$241$	10.2609	+	17.7723i	0.660961	+	1.14482i	0.980364	+	0.197199i	$0.0631844\pi$
$241$	10.2609	+	17.7723i	0.660961	+	1.14482i	−0.319403	+	0.947619i	$0.603482\pi$
$242$	3.17287	+	5.49557i	0.203960	+	0.353269i
$243$	6.81142	−	11.7977i	0.436953	−	0.756825i
$244$	1.34612			0.0861762
$245$	0.0231743	+	0.0401391i	0.00148055	+	0.00256439i
$246$	−6.54548			−0.417324
$247$	−23.5643			−1.49936
$248$		0			0
$249$	2.47896			0.157097
$250$	0.0957865			0.00605807
$251$	2.11472	+	3.66280i	0.133480	+	0.231194i	0.925016	−	0.379929i	$-0.124052\pi$
$251$	2.11472	+	3.66280i	0.133480	+	0.231194i	−0.791536	+	0.611123i	$0.790718\pi$
$252$	−0.314409			−0.0198059
$253$	−0.961940	+	1.66613i	−0.0604767	+	0.104749i
$254$	7.40051	+	12.8181i	0.464349	+	0.804276i
$255$	0.0282159	+	0.0488714i	0.00176695	+	0.00306045i
$256$	−6.31029			−0.394393
$257$	−9.27384	+	16.0628i	−0.578486	+	1.00197i	0.417167	+	0.908830i	$0.363023\pi$
$257$	−9.27384	+	16.0628i	−0.578486	+	1.00197i	−0.995653	+	0.0931375i	$0.970310\pi$
$258$	−0.569848	+	0.987006i	−0.0354772	+	0.0614483i
$259$	2.97711	−	5.15651i	0.184989	−	0.320410i
$260$	−0.00615272	−	0.0106568i	−0.000381575	−	0.000660908i
$261$	−1.19602	+	2.07156i	−0.0740316	+	0.128227i
$262$	0.424813	+	0.735798i	0.0262451	+	0.0454578i
$263$	−14.4865			−0.893278			−0.446639	−	0.894714i	$-0.647379\pi$
$263$	−14.4865			−0.893278			−0.446639	+	0.894714i	$0.647379\pi$
$264$	−14.6561			−0.902024
$265$	0.0148465	+	0.0257149i	0.000912013	+	0.00157965i
$266$	−1.95351	+	3.38358i	−0.119777	+	0.207461i
$267$	−0.692768	−	1.19991i	−0.0423967	−	0.0734333i
$268$	−1.94608	+	3.37071i	−0.118876	+	0.205899i
$269$	7.52060	−	13.0261i	0.458539	−	0.794212i	−0.540345	−	0.841443i	$-0.681706\pi$
$269$	7.52060	−	13.0261i	0.458539	−	0.794212i	0.998884	+	0.0472309i	$0.0150397\pi$
$270$	0.0264640	−	0.0458369i	0.00161055	−	0.00278955i
$271$	−22.9151			−1.39199			−0.695996	−	0.718046i	$-0.745037\pi$
$271$	−22.9151			−1.39199			−0.695996	+	0.718046i	$0.745037\pi$
$272$	10.6532	+	18.4520i	0.645948	+	1.11881i
$273$	3.09586	+	5.36219i	0.187370	+	0.324535i
$274$	1.89775	−	3.28699i	0.114647	−	0.198575i
$275$	−19.8881			−1.19929
$276$	−0.0799943	−	0.138554i	−0.00481509	−	0.00833999i
$277$	−14.4506			−0.868255			−0.434127	−	0.900851i	$-0.642943\pi$
$277$	−14.4506			−0.868255			−0.434127	+	0.900851i	$0.642943\pi$
$278$	−4.44679			−0.266701
$279$		0			0
$280$	−0.0172688			−0.00103201
$281$	−5.81764			−0.347051			−0.173526	−	0.984829i	$-0.555516\pi$
$281$	−5.81764			−0.347051			−0.173526	+	0.984829i	$0.555516\pi$
$282$	−3.49731	−	6.05752i	−0.208262	−	0.360720i
$283$	2.58301			0.153544			0.0767721	−	0.997049i	$-0.475539\pi$
$283$	2.58301			0.153544			0.0767721	+	0.997049i	$0.475539\pi$
$284$	−1.26116	+	2.18439i	−0.0748358	+	0.129619i
$285$	0.0167772	+	0.0290590i	0.000993797	+	0.00172131i
$286$	−16.5153	−	28.6054i	−0.976573	−	1.69147i
$287$	3.20261			0.189044
$288$	−1.11082	+	1.92399i	−0.0654555	+	0.113372i
$289$	−11.2245	+	19.4415i	−0.660267	+	1.14362i
$290$	−0.00776122	+	0.0134428i	−0.000455755	+	0.000789390i
$291$	4.49055	+	7.77786i	0.263241	+	0.455946i
$292$	0.592603	−	1.02642i	0.0346795	−	0.0600666i
$293$	−9.22516	−	15.9785i	−0.538940	−	0.933471i	−0.998961	−	0.0455634i	$-0.985492\pi$
$293$	−9.22516	−	15.9785i	−0.538940	−	0.933471i	0.460022	−	0.887908i	$-0.347842\pi$
$294$	−10.3459			−0.603386
$295$	−0.0997382			−0.00580698
$296$	−11.1786	−	19.3619i	−0.649743	−	1.12539i
$297$	−10.9894	+	19.0343i	−0.637671	+	1.10448i
$298$	−7.74504	−	13.4148i	−0.448658	−	0.777098i
$299$	1.52592	−	2.64297i	0.0882463	−	0.152847i
$300$	0.826939	−	1.43230i	0.0477434	−	0.0826939i
$301$	0.278819	−	0.482929i	0.0160709	−	0.0278355i
$302$	23.5163			1.35321
$303$	−3.97030	−	6.87677i	−0.228088	−	0.395060i
$304$	6.33443	+	10.9716i	0.363304	+	0.629262i
$305$	0.0182818	−	0.0316651i	0.00104682	−	0.00181314i
$306$	12.2015			0.697512
$307$	−0.822872	−	1.42526i	−0.0469638	−	0.0813437i	0.841588	−	0.540120i	$-0.181621\pi$
$307$	−0.822872	−	1.42526i	−0.0469638	−	0.0813437i	−0.888552	+	0.458776i	$0.848288\pi$
$308$	0.847243			0.0482762
$309$	10.5367			0.599412
$310$		0			0
$311$	−19.2427			−1.09115			−0.545576	−	0.838061i	$-0.683689\pi$
$311$	−19.2427			−1.09115			−0.545576	+	0.838061i	$0.683689\pi$
$312$	23.2490			1.31621
$313$	7.70151	+	13.3394i	0.435315	+	0.753987i	0.997321	−	0.0731454i	$-0.0233037\pi$
$313$	7.70151	+	13.3394i	0.435315	+	0.753987i	−0.562006	+	0.827133i	$0.689970\pi$
$314$	−3.50201			−0.197630
$315$	−0.00427005	+	0.00739594i	−0.000240590	+	0.000416714i
$316$	−1.40124	−	2.42702i	−0.0788260	−	0.136531i
$317$	14.4629	+	25.0505i	0.812319	+	1.40698i	0.911237	+	0.411882i	$0.135128\pi$
$317$	14.4629	+	25.0505i	0.812319	+	1.40698i	−0.0989183	+	0.995096i	$0.531538\pi$
$318$	−6.62805			−0.371683
$319$	3.22293	−	5.58227i	0.180449	−	0.312547i
$320$	−0.0318983	+	0.0552495i	−0.00178317	+	0.00308854i
$321$	−8.34174	+	14.4483i	−0.465591	+	0.806426i
$322$	−0.253001	−	0.438211i	−0.0140992	−	0.0244206i
$323$	−11.7282	+	20.3139i	−0.652576	+	1.13029i
$324$	−0.320588	−	0.555274i	−0.0178104	−	0.0308486i
$325$	31.5483			1.74999
$326$	22.2481			1.23221
$327$	6.31486	+	10.9377i	0.349213	+	0.604854i
$328$	6.01265	−	10.4142i	0.331993	−	0.575029i
$329$	1.71119	+	2.96386i	0.0943407	+	0.163403i
$330$	−0.0235170	+	0.0407327i	−0.00129457	+	0.00224226i
$331$	−0.923554	+	1.59964i	−0.0507631	+	0.0879243i	−0.890290	−	0.455393i	$-0.849499\pi$
$331$	−0.923554	+	1.59964i	−0.0507631	+	0.0879243i	0.839527	+	0.543318i	$0.182832\pi$
$332$	−0.269041	+	0.465993i	−0.0147656	+	0.0255747i
$333$	−11.0565			−0.605892
$334$	−10.1881	−	17.6463i	−0.557468	−	0.965562i
$335$	0.0528602	+	0.0915565i	0.00288806	+	0.00500227i
$336$	1.66443	−	2.88287i	0.0908019	−	0.157274i
$337$	18.4735			1.00632			0.503158	−	0.864194i	$-0.332171\pi$
$337$	18.4735			1.00632			0.503158	+	0.864194i	$0.332171\pi$
$338$	17.6437	+	30.5598i	0.959693	+	1.66224i
$339$	10.2762			0.558124
$340$	−0.0122491			−0.000664301
$341$		0			0
$342$	7.25501			0.392306
$343$	10.6265			0.573779
$344$	−1.04692	−	1.81332i	−0.0564462	−	0.0977677i
$345$	−0.00434567			−0.000233963
$346$	4.54745	−	7.87642i	0.244473	−	0.423439i
$347$	−6.06471	−	10.5044i	−0.325571	−	0.563905i	0.656057	−	0.754712i	$-0.272223\pi$
$347$	−6.06471	−	10.5044i	−0.325571	−	0.563905i	−0.981628	+	0.190806i	$0.938890\pi$
$348$	0.268017	+	0.464218i	0.0143672	+	0.0248847i
$349$	1.08075			0.0578512			0.0289256	−	0.999582i	$-0.490791\pi$
$349$	1.08075			0.0578512			0.0289256	+	0.999582i	$0.490791\pi$
$350$	2.61539	−	4.53000i	0.139799	−	0.242138i
$351$	17.4325	−	30.1939i	0.930477	−	1.61163i
$352$	2.99334	−	5.18461i	0.159545	−	0.276341i
$353$	9.18678	+	15.9120i	0.488963	+	0.846909i	0.999919	−	0.0126980i	$-0.00404202\pi$
$353$	9.18678	+	15.9120i	0.488963	+	0.846909i	−0.510957	+	0.859607i	$0.670709\pi$
$354$	11.1318	−	19.2808i	0.591646	−	1.02476i
$355$	0.0342560	+	0.0593331i	0.00181812	+	0.00314907i
$356$	0.300745			0.0159394
$357$	6.16339			0.326201
$358$	9.52908	+	16.5049i	0.503628	+	0.872308i
$359$	13.8469	−	23.9835i	0.730810	−	1.26580i	−0.225728	−	0.974190i	$-0.572476\pi$
$359$	13.8469	−	23.9835i	0.730810	−	1.26580i	0.956538	−	0.291609i	$-0.0941906\pi$
$360$	0.0160334	+	0.0277706i	0.000845033	+	0.00146364i
$361$	2.52639	−	4.37583i	0.132968	−	0.230307i
$362$	−11.4191	+	19.7785i	−0.600176	+	1.03954i
$363$	2.97613	−	5.15480i	0.156206	−	0.270557i
$364$	−1.34398			−0.0704436
$365$	−0.0160965	−	0.0278800i	−0.000842530	−	0.00145931i
$366$	4.08086	+	7.06826i	0.213310	+	0.369464i
$367$	−2.76280	+	4.78532i	−0.144217	+	0.249791i	−0.929081	−	0.369877i	$-0.879400\pi$
$367$	−2.76280	+	4.78532i	−0.144217	+	0.249791i	0.784863	+	0.619669i	$0.212733\pi$
$368$	−1.64076			−0.0855304
$369$	−2.97349	−	5.15023i	−0.154794	−	0.268111i
$370$	−0.0717481			−0.00373000
$371$	3.24301			0.168369
$372$		0			0
$373$	5.64476			0.292274			0.146137	−	0.989264i	$-0.453316\pi$
$373$	5.64476			0.292274			0.146137	+	0.989264i	$0.453316\pi$
$374$	−32.8795			−1.70016
$375$	−0.0449235	−	0.0778098i	−0.00231984	−	0.00401808i
$376$	12.8505			0.662712
$377$	−5.11251	+	8.85513i	−0.263308	+	0.456062i
$378$	−2.89035	−	5.00623i	−0.148663	−	0.257493i
$379$	5.58627	+	9.67570i	0.286947	+	0.497007i	0.973080	−	0.230469i	$-0.0740262\pi$
$379$	5.58627	+	9.67570i	0.286947	+	0.497007i	−0.686132	+	0.727477i	$0.740693\pi$
$380$	−0.00728333			−0.000373627
$381$	6.94162	−	12.0232i	0.355630	−	0.615969i
$382$	9.80810	−	16.9881i	0.501826	−	0.869188i
$383$	9.26025	−	16.0392i	0.473177	−	0.819566i	−0.526352	−	0.850267i	$-0.676440\pi$
$383$	9.26025	−	16.0392i	0.473177	−	0.819566i	0.999529	+	0.0307005i	$0.00977382\pi$
$384$	−5.26236	−	9.11467i	−0.268543	−	0.465131i
$385$	0.0115066	−	0.0199300i	0.000586429	−	0.00101572i
$386$	6.76166	+	11.7115i	0.344159	+	0.596101i
$387$	−1.03549			−0.0526367
$388$	−1.94944			−0.0989678
$389$	−11.7929	−	20.4260i	−0.597926	−	1.03564i	−0.993127	−	0.117043i	$-0.962658\pi$
$389$	−11.7929	−	20.4260i	−0.597926	−	1.03564i	0.395201	−	0.918595i	$-0.370675\pi$
$390$	0.0373050	−	0.0646141i	0.00188901	−	0.00327186i
$391$	−1.51894	−	2.63088i	−0.0768159	−	0.133049i
$392$	9.50373	−	16.4609i	0.480011	−	0.831403i
$393$	0.398472	−	0.690173i	0.0201002	−	0.0348146i
$394$	9.61075	−	16.6463i	0.484183	−	0.838629i
$395$	−0.0761221			−0.00383012
$396$	−0.786629	−	1.36248i	−0.0395296	−	0.0684673i
$397$	−5.45457	−	9.44759i	−0.273757	−	0.474161i	0.696064	−	0.717980i	$-0.254933\pi$
$397$	−5.45457	−	9.44759i	−0.273757	−	0.474161i	−0.969821	+	0.243819i	$0.921600\pi$
$398$	−6.96977	+	12.0720i	−0.349363	+	0.605114i
$399$	3.66476			0.183467
$400$	−8.48065	−	14.6889i	−0.424032	−	0.734446i
$401$	10.6709			0.532879			0.266440	−	0.963852i	$-0.414153\pi$
$401$	10.6709			0.532879			0.266440	+	0.963852i	$0.414153\pi$
$402$	−23.5988			−1.17700
$403$		0			0
$404$	1.72359			0.0857517
$405$	−0.0174159			−0.000865401
$406$	0.847667	+	1.46820i	0.0420690	+	0.0728657i
$407$	29.7941			1.47684
$408$	11.5713	−	20.0420i	0.572864	−	0.992229i
$409$	−4.71296	−	8.16309i	−0.233041	−	0.403639i	0.725661	−	0.688053i	$-0.241534\pi$
$409$	−4.71296	−	8.16309i	−0.233041	−	0.403639i	−0.958702	+	0.284414i	$0.908201\pi$
$410$	−0.0192956	−	0.0334210i	−0.000952944	−	0.00165055i
$411$	−3.56014			−0.175609
$412$	−1.14355	+	1.98068i	−0.0563386	+	0.0975813i
$413$	−5.44662	+	9.43381i	−0.268010	+	0.464208i
$414$	−0.469802	+	0.813721i	−0.0230895	+	0.0399922i
$415$	0.00730780	+	0.0126575i	0.000358726	+	0.000621331i
$416$	−4.74831	+	8.22432i	−0.232805	+	0.403231i
$417$	2.08553	+	3.61224i	0.102129	+	0.176892i
$418$	−19.5502			−0.956230
$419$	−29.2065			−1.42683			−0.713416	−	0.700740i	$-0.752853\pi$
$419$	−29.2065			−1.42683			−0.713416	+	0.700740i	$0.752853\pi$
$420$	0.000956879		0.00165736i	4.66909e−5		8.08711e-5i
$421$	−0.298328	+	0.516719i	−0.0145396	+	0.0251833i	−0.873204	−	0.487355i	$-0.837962\pi$
$421$	−0.298328	+	0.516719i	−0.0145396	+	0.0251833i	0.858664	+	0.512539i	$0.171295\pi$
$422$	10.8973	+	18.8747i	0.530472	+	0.918805i
$423$	3.17753	−	5.50364i	0.154497	−	0.267596i
$424$	6.08851	−	10.5456i	0.295684	−	0.512140i
$425$	15.7020	−	27.1966i	0.761657	−	1.31923i
$426$	−15.2932			−0.740958
$427$	−1.99671	−	3.45840i	−0.0966276	−	0.167364i
$428$	−1.81066	−	3.13615i	−0.0875215	−	0.151592i
$429$	−15.4913	+	26.8317i	−0.747925	+	1.29544i
$430$	−0.00671950			−0.000324043
$431$	12.0022	+	20.7885i	0.578127	+	1.00134i	0.995694	+	0.0926988i	$0.0295494\pi$
$431$	12.0022	+	20.7885i	0.578127	+	1.00134i	−0.417568	+	0.908646i	$0.637117\pi$
$432$	−18.7444			−0.901841
$433$	12.5443			0.602840			0.301420	−	0.953492i	$-0.402539\pi$
$433$	12.5443			0.602840			0.301420	+	0.953492i	$0.402539\pi$
$434$		0			0
$435$	0.0145599			0.000698096
$436$	−2.74141			−0.131290
$437$	−0.903161	−	1.56432i	−0.0432040	−	0.0748316i
$438$	7.18611			0.343366
$439$	19.5586	−	33.8765i	0.933482	−	1.61684i	0.156163	−	0.987731i	$-0.450088\pi$
$439$	19.5586	−	33.8765i	0.933482	−	1.61684i	0.777319	−	0.629106i	$-0.216579\pi$
$440$	−0.0432054	−	0.0748339i	−0.00205974	−	0.00356757i
$441$	−4.69996	−	8.14057i	−0.223808	−	0.387646i
$442$	52.1566			2.48084
$443$	3.74603	−	6.48832i	0.177979	−	0.308270i	−0.763209	−	0.646152i	$-0.776377\pi$
$443$	3.74603	−	6.48832i	0.177979	−	0.308270i	0.941188	+	0.337882i	$0.109711\pi$
$444$	−1.23883	+	2.14572i	−0.0587923	+	0.101831i
$445$	0.00408447	−	0.00707451i	0.000193622	−	0.000335364i
$446$	−0.529846	−	0.917721i	−0.0250890	−	0.0434553i
$447$	−7.26478	+	12.5830i	−0.343613	+	0.595154i
$448$	3.48388	+	6.03425i	0.164598	+	0.285092i
$449$	−17.5141			−0.826541			−0.413271	−	0.910608i	$-0.635614\pi$
$449$	−17.5141			−0.826541			−0.413271	+	0.910608i	$0.635614\pi$
$450$	−9.71313			−0.457881
$451$	8.01271	+	13.8784i	0.377304	+	0.653509i
$452$	−1.11527	+	1.93171i	−0.0524580	+	0.0908598i
$453$	−11.0291	−	19.1029i	−0.518190	−	0.897531i
$454$	8.86678	−	15.3577i	0.416139	−	0.720773i
$455$	−0.0182528	+	0.0316148i	−0.000855705	+	0.00148212i
$456$	6.88029	−	11.9170i	0.322199	−	0.558065i
$457$	4.89406			0.228934			0.114467	−	0.993427i	$-0.463484\pi$
$457$	4.89406			0.228934			0.114467	+	0.993427i	$0.463484\pi$
$458$	8.52125	+	14.7592i	0.398172	+	0.689654i
$459$	−17.3527	−	30.0557i	−0.809954	−	1.40288i
$460$	0.000471636	0	0.000816898i	2.19902e−5	0	3.80881e-5i
$461$	−20.2773			−0.944406			−0.472203	−	0.881490i	$-0.656541\pi$
$461$	−20.2773			−0.944406			−0.472203	+	0.881490i	$0.656541\pi$
$462$	2.56849	+	4.44875i	0.119497	+	0.206975i
$463$	22.9558			1.06685			0.533423	−	0.845848i	$-0.320905\pi$
$463$	22.9558			1.06685			0.533423	+	0.845848i	$0.320905\pi$
$464$	5.49727			0.255204
$465$		0			0
$466$	−16.2613			−0.753291
$467$	27.2874			1.26271			0.631355	−	0.775494i	$-0.282499\pi$
$467$	27.2874			1.26271			0.631355	+	0.775494i	$0.282499\pi$
$468$	1.24783	+	2.16130i	0.0576808	+	0.0999060i
$469$	11.5466			0.533172
$470$	0.0206197	−	0.0357143i	0.000951115	−	0.00164738i
$471$	1.64243	+	2.84477i	0.0756791	+	0.131080i
$472$	20.4512	+	35.4225i	0.941342	+	1.63045i
$473$	2.79034			0.128300
$474$	8.49597	−	14.7154i	0.390233	−	0.675903i
$475$	9.33640	−	16.1711i	0.428383	−	0.741982i
$476$	−0.668913	+	1.15859i	−0.0306596	+	0.0531039i
$477$	−3.01100	−	5.21521i	−0.137864	−	0.238788i
$478$	10.4846	−	18.1598i	0.479553	−	0.830611i
$479$	17.1961	+	29.7845i	0.785708	+	1.36089i	0.928575	+	0.371145i	$0.121035\pi$
$479$	17.1961	+	29.7845i	0.785708	+	1.36089i	−0.142867	+	0.989742i	$0.545632\pi$
$480$	0.0135227			0.000617226
$481$	−47.2622			−2.15497
$482$	−13.5040	−	23.3897i	−0.615093	−	1.06537i
$483$	−0.237313	+	0.411039i	−0.0107981	+	0.0187029i
$484$	0.645998	+	1.11890i	0.0293636	+	0.0508592i
$485$	−0.0264757	+	0.0458573i	−0.00120220	+	0.00208227i
$486$	−8.96433	+	15.5267i	−0.406630	+	0.704304i
$487$	13.6539	−	23.6492i	0.618717	−	1.07165i	−0.371003	−	0.928632i	$-0.620986\pi$
$487$	13.6539	−	23.6492i	0.618717	−	1.07165i	0.989720	−	0.143018i	$-0.0456807\pi$
$488$	−14.9947			−0.678777
$489$	−10.4343	−	18.0727i	−0.471854	−	0.817276i
$490$	−0.0304991	−	0.0528260i	−0.00137781	−	0.00238644i
$491$	−17.7513	+	30.7461i	−0.801103	+	1.38755i	0.117787	+	0.993039i	$0.462420\pi$
$491$	−17.7513	+	30.7461i	−0.801103	+	1.38755i	−0.918891	+	0.394512i	$0.870913\pi$
$492$	−1.33266			−0.0600811
$493$	5.08911	+	8.81460i	0.229202	+	0.396990i
$494$	31.0123			1.39531
$495$	−0.0427334			−0.00192073
$496$		0			0
$497$	7.48275			0.335647
$498$	−3.26248			−0.146195
$499$	−5.60388	−	9.70620i	−0.250864	−	0.434509i	0.712900	−	0.701266i	$-0.247381\pi$
$499$	−5.60388	−	9.70620i	−0.250864	−	0.434509i	−0.963764	+	0.266756i	$0.914048\pi$
$500$	0.0195022			0.000872165
$501$	−9.55635	+	16.5521i	−0.426946	+	0.739493i
$502$	−2.78312	−	4.82051i	−0.124217	−	0.215150i
$503$	0.849673	+	1.47168i	0.0378851	+	0.0656188i	0.884346	−	0.466832i	$-0.154605\pi$
$503$	0.849673	+	1.47168i	0.0378851	+	0.0656188i	−0.846461	+	0.532450i	$0.821271\pi$
$504$	3.50227			0.156004
$505$	0.0234084	−	0.0405445i	0.00104166	−	0.00180421i
$506$	1.26598	−	2.19275i	0.0562798	−	0.0974795i
$507$	16.5497	−	28.6649i	0.734997	−	1.27305i
$508$	1.50675	+	2.60977i	0.0668512	+	0.115790i
$509$	20.7540	−	35.9470i	0.919905	−	1.59332i	0.120348	−	0.992732i	$-0.461599\pi$
$509$	20.7540	−	35.9470i	0.919905	−	1.59332i	0.799557	−	0.600590i	$-0.205068\pi$
$510$	−0.0371342	−	0.0643184i	−0.00164433	−	0.00284806i
$511$	−3.51607			−0.155542
$512$	25.3562			1.12060
$513$	−10.3179	−	17.8712i	−0.455547	−	0.789031i
$514$	12.2050	−	21.1398i	0.538341	−	0.932434i
$515$	0.0310615	+	0.0538001i	0.00136873	+	0.00237071i
$516$	−0.116021	+	0.200955i	−0.00510756	+	0.00884656i
$517$	−8.56253	+	14.8307i	−0.376580	+	0.652255i
$518$	−3.91810	+	6.78634i	−0.172151	+	0.298175i
$519$	−8.53095			−0.374467
$520$	0.0685365	+	0.118709i	0.00300552	+	0.00520572i
$521$	16.2836	+	28.2041i	0.713399	+	1.23564i	0.963574	+	0.267443i	$0.0861787\pi$
$521$	16.2836	+	28.2041i	0.713399	+	1.23564i	−0.250175	+	0.968201i	$0.580488\pi$
$522$	1.57405	−	2.72633i	0.0688941	−	0.119328i
$523$	14.5341			0.635533			0.317766	−	0.948169i	$-0.397067\pi$
$523$	14.5341			0.635533			0.317766	+	0.948169i	$0.397067\pi$
$524$	0.0864923	+	0.149809i	0.00377843	+	0.00654444i
$525$	−4.90644			−0.214135
$526$	19.0653			0.831288
$527$		0			0
$528$	16.6571			0.724907
$529$	−22.7661			−0.989829
$530$	−0.0195391	−	0.0338426i	−0.000848723	−	0.00147003i
$531$	20.2278			0.877812
$532$	−0.397736	+	0.688899i	−0.0172440	+	0.0298676i
$533$	−12.7105	−	22.0153i	−0.550554	−	0.953587i
$534$	0.911733	+	1.57917i	0.0394546	+	0.0683373i
$535$	−0.0983636			−0.00425263
$536$	21.6778	−	37.5471i	0.936339	−	1.62179i
$537$	8.93820	−	15.4814i	0.385712	−	0.668073i
$538$	−9.89765	+	17.1432i	−0.426718	+	0.739097i
$539$	12.6651	+	21.9365i	0.545523	+	0.944873i
$540$	0.00538808	−	0.00933243i	0.000231866	−	0.000401604i
$541$	4.19908	+	7.27302i	0.180532	+	0.312691i	0.942062	−	0.335439i	$-0.108885\pi$
$541$	4.19908	+	7.27302i	0.180532	+	0.312691i	−0.761530	+	0.648130i	$0.775551\pi$
$542$	30.1579			1.29539
$543$	21.4221			0.919311
$544$	4.72658	+	8.18668i	0.202650	+	0.351001i
$545$	−0.0372316	+	0.0644870i	−0.00159483	+	0.00276232i
$546$	−4.07438	−	7.05704i	−0.174367	−	0.302013i
$547$	−6.24636	+	10.8190i	−0.267075	+	0.462588i	−0.968105	−	0.250544i	$-0.919391\pi$
$547$	−6.24636	+	10.8190i	−0.267075	+	0.462588i	0.701030	+	0.713132i	$0.252724\pi$
$548$	0.386383	−	0.669234i	0.0165054	−	0.0285883i
$549$	−3.70772	+	6.42196i	−0.158242	+	0.274083i
$550$	26.1741			1.11607
$551$	3.02599	+	5.24117i	0.128911	+	0.223281i
$552$	0.891075	+	1.54339i	0.0379267	+	0.0656909i
$553$	−4.15696	+	7.20007i	−0.176772	+	0.306178i
$554$	19.0181			0.808001
$555$	0.0336496	+	0.0582828i	0.00142834	+	0.00247397i
$556$	−0.905370			−0.0383962
$557$	−16.8308			−0.713144			−0.356572	−	0.934268i	$-0.616054\pi$
$557$	−16.8308			−0.713144			−0.356572	+	0.934268i	$0.616054\pi$
$558$		0			0
$559$	−4.42630			−0.187213
$560$	0.0196265			0.000829370
$561$	15.4204	+	26.7088i	0.651048	+	1.12765i
$562$	7.65644			0.322967
$563$	8.36744	−	14.4928i	0.352645	−	0.610800i	−0.634067	−	0.773278i	$-0.718616\pi$
$563$	8.36744	−	14.4928i	0.352645	−	0.610800i	0.986712	+	0.162479i	$0.0519488\pi$
$564$	−0.712055	−	1.23331i	−0.0299829	−	0.0519319i
$565$	0.0302934	+	0.0524698i	0.00127445	+	0.00220742i
$566$	−3.39943			−0.142889
$567$	−0.951065	+	1.64729i	−0.0399410	+	0.0691798i
$568$	14.0483	−	24.3323i	0.589453	−	1.02096i
$569$	−2.66914	+	4.62308i	−0.111896	+	0.193810i	−0.916535	−	0.399955i	$-0.869026\pi$
$569$	−2.66914	+	4.62308i	−0.111896	+	0.193810i	0.804639	+	0.593765i	$0.202359\pi$
$570$	−0.0220800	−	0.0382437i	−0.000924831	−	0.00160185i
$571$	−18.0003	+	31.1775i	−0.753290	+	1.30474i	0.192930	+	0.981212i	$0.438201\pi$
$571$	−18.0003	+	31.1775i	−0.753290	+	1.30474i	−0.946220	+	0.323524i	$0.895132\pi$
$572$	−3.36254	−	5.82408i	−0.140595	−	0.243517i
$573$	−18.3998			−0.768665
$574$	−4.21487			−0.175925
$575$	1.20917	+	2.09434i	0.0504258	+	0.0873400i
$576$	6.46926	−	11.2051i	0.269553	−	0.466879i
$577$	−1.14463	−	1.98255i	−0.0476514	−	0.0825347i	0.841216	−	0.540699i	$-0.181840\pi$
$577$	−1.14463	−	1.98255i	−0.0476514	−	0.0825347i	−0.888867	+	0.458165i	$0.848507\pi$
$578$	14.7723	−	25.5864i	0.614447	−	1.06425i
$579$	6.34238	−	10.9853i	0.263580	−	0.456535i
$580$	−0.00158019	+	0.00273697i	−6.56139e−5	+	0.000113647i
$581$	1.59629			0.0662252
$582$	−5.90989	−	10.2362i	−0.244973	−	0.424305i
$583$	8.11379	+	14.0535i	0.336039	+	0.582036i
$584$	−6.60114	+	11.4335i	−0.273157	+	0.473122i
$585$	0.0677879			0.00280268
$586$	12.1410	+	21.0288i	0.501539	+	0.868692i
$587$	2.09767			0.0865799			0.0432900	−	0.999063i	$-0.486216\pi$
$587$	2.09767			0.0865799			0.0432900	+	0.999063i	$0.486216\pi$
$588$	−2.10644			−0.0868680
$589$		0			0
$590$	0.131263			0.00540400
$591$	−18.0296			−0.741640
$592$	12.7048	+	22.0053i	0.522163	+	0.904413i
$593$	−6.64085			−0.272707			−0.136354	−	0.990660i	$-0.543538\pi$
$593$	−6.64085			−0.272707			−0.136354	+	0.990660i	$0.543538\pi$
$594$	14.4629	−	25.0505i	0.593419	−	1.02783i
$595$	0.0181693	+	0.0314701i	0.000744867	+	0.00129015i
$596$	−1.57689	−	2.73126i	−0.0645921	−	0.111877i
$597$	13.0752			0.535132
$598$	−2.00822	+	3.47834i	−0.0821223	+	0.142240i
$599$	−15.3614	+	26.6067i	−0.627650	+	1.08712i	0.360372	+	0.932809i	$0.382650\pi$
$599$	−15.3614	+	26.6067i	−0.627650	+	1.08712i	−0.988022	+	0.154313i	$0.950683\pi$
$600$	−9.21146	+	15.9547i	−0.376056	+	0.651348i
$601$	−8.48015	−	14.6881i	−0.345913	−	0.599138i	0.639607	−	0.768702i	$-0.279097\pi$
$601$	−8.48015	−	14.6881i	−0.345913	−	0.599138i	−0.985519	+	0.169564i	$0.945764\pi$
$602$	−0.366946	+	0.635569i	−0.0149556	+	0.0259039i
$603$	−10.7205	−	18.5685i	−0.436573	−	0.756167i
$604$	4.78793			0.194818
$605$	0.0350937			0.00142676
$606$	5.22521	+	9.05032i	0.212259	+	0.367644i
$607$	−8.95830	+	15.5162i	−0.363606	+	0.629785i	−0.988551	−	0.150884i	$-0.951788\pi$
$607$	−8.95830	+	15.5162i	−0.363606	+	0.629785i	0.624945	+	0.780669i	$0.285121\pi$
$608$	2.81043	+	4.86780i	0.113978	+	0.197416i
$609$	0.795105	−	1.37716i	0.0322193	−	0.0558054i
$610$	−0.0240602	+	0.0416735i	−0.000974170	+	0.00168731i
$611$	13.5827	−	23.5259i	0.549497	−	0.951757i
$612$	2.48423			0.100419
$613$	8.82723	+	15.2892i	0.356529	+	0.617525i	0.987378	−	0.158379i	$-0.0506269\pi$
$613$	8.82723	+	15.2892i	0.356529	+	0.617525i	−0.630850	+	0.775905i	$0.717294\pi$
$614$	1.08296	+	1.87574i	0.0437047	+	0.0756987i
$615$	−0.0180992	+	0.0313487i	−0.000729828	+	0.00126410i
$616$	−9.43763			−0.380253
$617$	−10.1711	−	17.6169i	−0.409474	−	0.709230i	0.585356	−	0.810776i	$-0.300955\pi$
$617$	−10.1711	−	17.6169i	−0.409474	−	0.709230i	−0.994831	+	0.101546i	$0.967621\pi$
$618$	−13.8671			−0.557815
$619$	16.4294			0.660354			0.330177	−	0.943919i	$-0.392892\pi$
$619$	16.4294			0.660354			0.330177	+	0.943919i	$0.392892\pi$
$620$		0			0
$621$	2.67257			0.107247
$622$	25.3247			1.01543
$623$	−0.446099	−	0.772665i	−0.0178726	−	0.0309562i
$624$	−26.4231			−1.05777
$625$	−12.4996	+	21.6499i	−0.499984	+	0.865998i
$626$	−10.1357	−	17.5556i	−0.405106	−	0.701664i
$627$	9.16896	+	15.8811i	0.366173	+	0.634230i
$628$	−0.713012			−0.0284523
$629$	−23.5230	+	40.7430i	−0.937922	+	1.62453i
$630$	0.00561970	−	0.00973360i	0.000223894	−	0.000387796i
$631$	−5.20796	+	9.02045i	−0.207326	+	0.359098i	−0.950871	−	0.309587i	$-0.899809\pi$
$631$	−5.20796	+	9.02045i	−0.207326	+	0.359098i	0.743546	+	0.668685i	$0.233143\pi$
$632$	15.6087	+	27.0351i	0.620882	+	1.07540i
$633$	10.2216	−	17.7043i	0.406272	−	0.703683i
$634$	−19.0343	−	32.9683i	−0.755947	−	1.30934i
$635$	0.0818538			0.00324827
$636$	−1.34948			−0.0535102
$637$	−20.0905	−	34.7978i	−0.796015	−	1.37874i
$638$	−4.24160	+	7.34667i	−0.167927	+	0.290858i
$639$	−6.94742	−	12.0333i	−0.274836	−	0.476029i
$640$	0.0310262	−	0.0537389i	0.00122642	−	0.00212422i
$641$	11.4068	−	19.7572i	0.450543	−	0.780364i	−0.547877	−	0.836559i	$-0.684564\pi$
$641$	11.4068	−	19.7572i	0.450543	−	0.780364i	0.998420	+	0.0561954i	$0.0178970\pi$
$642$	10.9783	−	19.0150i	0.433280	−	0.750464i
$643$	−23.9877			−0.945982			−0.472991	−	0.881067i	$-0.656826\pi$
$643$	−23.9877			−0.945982			−0.472991	+	0.881067i	$0.656826\pi$
$644$	−0.0515113	−	0.0892201i	−0.00202983	−	0.00351577i
$645$	0.00315142	+	0.00545842i	0.000124087	+	0.000214925i
$646$	15.4352	−	26.7345i	0.607290	−	1.05186i
$647$	19.6935			0.774232			0.387116	−	0.922031i	$-0.373471\pi$
$647$	19.6935			0.774232			0.387116	+	0.922031i	$0.373471\pi$
$648$	3.57110	+	6.18532i	0.140286	+	0.242982i
$649$	−54.5082			−2.13963
$650$	−41.5199			−1.62854
$651$		0			0
$652$	4.52973			0.177398
$653$	−4.96806			−0.194415			−0.0972076	−	0.995264i	$-0.530991\pi$
$653$	−4.96806			−0.194415			−0.0972076	+	0.995264i	$0.530991\pi$
$654$	−8.31081	−	14.3947i	−0.324978	−	0.562879i
$655$	0.00469867			0.000183592
$656$	−6.83354	+	11.8360i	−0.266805	+	0.462120i
$657$	3.26452	+	5.65431i	0.127361	+	0.220596i
$658$	−2.25204	−	3.90065i	−0.0877938	−	0.152063i
$659$	1.54371			0.0601343			0.0300671	−	0.999548i	$-0.490428\pi$
$659$	1.54371			0.0601343			0.0300671	+	0.999548i	$0.490428\pi$
$660$	−0.00478809	+	0.00829321i	−0.000186376	+	0.000322813i
$661$	−8.01834	+	13.8882i	−0.311877	+	0.540187i	−0.978769	−	0.204968i	$-0.934291\pi$
$661$	−8.01834	+	13.8882i	−0.311877	+	0.540187i	0.666892	+	0.745155i	$0.267624\pi$
$662$	1.21546	−	2.10525i	0.0472403	−	0.0818227i
$663$	−24.4612	−	42.3681i	−0.949996	−	1.64544i
$664$	2.99691	−	5.19080i	0.116303	−	0.201442i
$665$	0.0108035	+	0.0187121i	0.000418940	+	0.000725626i
$666$	14.5511			0.563846
$667$	−0.783799			−0.0303488
$668$	−2.07430	−	3.59280i	−0.0802572	−	0.139009i
$669$	−0.496992	+	0.860815i	−0.0192148	+	0.0332810i
$670$	−0.0695678	−	0.120495i	−0.00268764	−	0.00465513i
$671$	9.99125	−	17.3054i	0.385708	−	0.668066i
$672$	0.738465	−	1.27906i	0.0284869	−	0.0493407i
$673$	−20.0365	+	34.7043i	−0.772351	+	1.33775i	0.163920	+	0.986474i	$0.447586\pi$
$673$	−20.0365	+	34.7043i	−0.772351	+	1.33775i	−0.936271	+	0.351278i	$0.885747\pi$
$674$	−24.3125			−0.936482
$675$	13.8138	+	23.9262i	0.531694	+	0.920921i
$676$	3.59228	+	6.22201i	0.138164	+	0.239308i
$677$	18.2734	−	31.6504i	0.702303	−	1.21642i	−0.265354	−	0.964151i	$-0.585489\pi$
$677$	18.2734	−	31.6504i	0.702303	−	1.21642i	0.967656	−	0.252273i	$-0.0811779\pi$
$678$	−13.5242			−0.519392
$679$	2.89163	+	5.00845i	0.110971	+	0.192207i
$680$	0.136446			0.00523245
$681$	−16.6339			−0.637414
$682$		0			0
$683$	−37.5447			−1.43661			−0.718303	−	0.695730i	$-0.755081\pi$
$683$	−37.5447			−1.43661			−0.718303	+	0.695730i	$0.755081\pi$
$684$	1.47712			0.0564793
$685$	−0.0104951	−	0.0181780i	−0.000400996	−	0.000694545i
$686$	−13.9853			−0.533961
$687$	7.99287	−	13.8441i	0.304947	−	0.528183i
$688$	1.18985	+	2.06089i	0.0453628	+	0.0785706i
$689$	−12.8709	−	22.2930i	−0.490341	−	0.849295i
$690$	0.00571922			0.000217727
$691$	−0.929630	+	1.61017i	−0.0353648	+	0.0612536i	−0.883166	−	0.469060i	$-0.844593\pi$
$691$	−0.929630	+	1.61017i	−0.0353648	+	0.0612536i	0.847801	+	0.530314i	$0.177926\pi$
$692$	0.925864	−	1.60364i	0.0351961	−	0.0609614i
$693$	−2.33364	+	4.04197i	−0.0886475	+	0.153542i
$694$	7.98160	+	13.8245i	0.302978	+	0.524772i
$695$	−0.0122960	+	0.0212973i	−0.000466414	+	0.000807853i
$696$	−2.98550	−	5.17103i	−0.113165	−	0.196007i
$697$	−25.3047			−0.958483
$698$	−1.42234			−0.0538365
$699$	7.62649	+	13.2095i	0.288461	+	0.499628i
$700$	0.532496	−	0.922310i	0.0201265	−	0.0348601i
$701$	−21.5960	−	37.4054i	−0.815670	−	1.41278i	−0.908846	−	0.417133i	$-0.863035\pi$
$701$	−21.5960	−	37.4054i	−0.815670	−	1.41278i	0.0931754	−	0.995650i	$-0.470298\pi$
$702$	−22.9424	+	39.7374i	−0.865905	+	1.49979i
$703$	−13.9868	+	24.2258i	−0.527521	+	0.913693i
$704$	−17.4328	+	30.1945i	−0.657024	+	1.13800i
$705$	−0.0386822			−0.00145686
$706$	−12.0905	−	20.9413i	−0.455031	−	0.788136i
$707$	−2.55662	−	4.42820i	−0.0961517	−	0.166540i
$708$	2.26643	−	3.92558i	0.0851778	−	0.147532i
$709$	48.5108			1.82186			0.910930	−	0.412561i	$-0.135366\pi$
$709$	48.5108			1.82186			0.910930	+	0.412561i	$0.135366\pi$
$710$	−0.0450834	−	0.0780867i	−0.00169195	−	0.00293054i
$711$	15.4382			0.578980
$712$	−3.35006			−0.125549
$713$		0			0
$714$	−8.11147			−0.303564
$715$	−0.182669			−0.00683143
$716$	1.94013	+	3.36040i	0.0725060	+	0.125584i
$717$	−19.6689			−0.734549
$718$	−18.2235	+	31.5640i	−0.680094	+	1.17796i
$719$	13.3329	+	23.0932i	0.497233	+	0.861233i	0.999995	−	0.00319224i	$-0.00101612\pi$
$719$	13.3329	+	23.0932i	0.497233	+	0.861233i	−0.502762	+	0.864425i	$0.667683\pi$
$720$	−0.0182224	−	0.0315620i	−0.000679107	−	0.00117625i
$721$	6.78496			0.252685
$722$	−3.32491	+	5.75891i	−0.123740	+	0.214324i
$723$	−12.6667	+	21.9394i	−0.471079	+	0.815933i
$724$	−2.32494	+	4.02692i	−0.0864058	+	0.149659i
$725$	−4.05125	−	7.01697i	−0.150460	−	0.260604i
$726$	−3.91680	+	6.78409i	−0.145366	+	0.251781i
$727$	18.3835	+	31.8412i	0.681807	+	1.18092i	0.974429	+	0.224696i	$0.0721390\pi$
$727$	18.3835	+	31.8412i	0.681807	+	1.18092i	−0.292622	+	0.956228i	$0.594528\pi$
$728$	14.9709			0.554857
$729$	23.9955			0.888723
$730$	0.0211842	+	0.0366921i	0.000784062	+	0.00135803i
$731$	−2.20302	+	3.81575i	−0.0814817	+	0.141130i
$732$	0.830867	+	1.43910i	0.0307097	+	0.0531908i
$733$	−24.7944	+	42.9452i	−0.915803	+	1.58622i	−0.110082	+	0.993923i	$0.535111\pi$
$733$	−24.7944	+	42.9452i	−0.915803	+	1.58622i	−0.805721	+	0.592295i	$0.798222\pi$
$734$	3.63605	−	6.29782i	0.134209	−	0.232457i
$735$	−0.0286079	+	0.0495504i	−0.00105522	+	0.00182769i
$736$	−0.727964			−0.0268331
$737$	28.8887	+	50.0368i	1.06413	+	1.84313i
$738$	3.91333	+	6.77808i	0.144052	+	0.249505i
$739$	−15.4840	+	26.8190i	−0.569587	+	0.986554i	0.427020	+	0.904242i	$0.359564\pi$
$739$	−15.4840	+	26.8190i	−0.569587	+	0.986554i	−0.996607	+	0.0823114i	$0.973770\pi$
$740$	−0.0146080			−0.000536999
$741$	−14.5447	−	25.1921i	−0.534312	−	0.925455i
$742$	−4.26804			−0.156685
$743$	45.6267			1.67388			0.836940	−	0.547294i	$-0.184342\pi$
$743$	45.6267			1.67388			0.836940	+	0.547294i	$0.184342\pi$
$744$		0			0
$745$	−0.0856644			−0.00313850
$746$	−7.42891			−0.271992
$747$	−1.48209	−	2.56705i	−0.0542267	−	0.0939234i
$748$	−6.69429			−0.244767
$749$	−5.37155	+	9.30380i	−0.196272	+	0.339953i
$750$	0.0591226	+	0.102403i	0.00215885	+	0.00373924i
$751$	−14.2947	−	24.7592i	−0.521621	−	0.903475i	−0.999684	−	0.0251487i	$-0.991994\pi$
$751$	−14.2947	−	24.7592i	−0.521621	−	0.903475i	0.478062	−	0.878326i	$-0.341339\pi$
$752$	−14.6049			−0.532586
$753$	−2.61055	+	4.52160i	−0.0951337	+	0.164776i
$754$	6.72844	−	11.6540i	0.245035	−	0.424413i
$755$	0.0650258	−	0.112628i	0.00236653	−	0.00409896i
$756$	−0.588477	−	1.01927i	−0.0214027	−	0.0370706i
$757$	3.95708	−	6.85387i	0.143823	−	0.249108i	−0.785110	−	0.619356i	$-0.787394\pi$
$757$	3.95708	−	6.85387i	0.143823	−	0.249108i	0.928933	+	0.370248i	$0.120727\pi$
$758$	−7.35193	−	12.7339i	−0.267034	−	0.462517i
$759$	−2.37496			−0.0862057
$760$	0.0811306			0.00294292
$761$	11.4353	+	19.8065i	0.414528	+	0.717984i	0.995379	−	0.0960263i	$-0.0306133\pi$
$761$	11.4353	+	19.8065i	0.414528	+	0.717984i	−0.580851	+	0.814010i	$0.697280\pi$
$762$	−9.13567	+	15.8235i	−0.330951	+	0.573223i
$763$	4.06637	+	7.04316i	0.147212	+	0.254979i
$764$	1.99694	−	3.45880i	0.0722466	−	0.125135i
$765$	0.0337388	−	0.0584373i	0.00121983	−	0.00211280i
$766$	−12.1872	+	21.1088i	−0.440340	+	0.762692i
$767$	86.4660			3.12211
$768$	−3.89492	−	6.74620i	−0.140546	−	0.243432i
$769$	11.6069	+	20.1037i	0.418555	+	0.724959i	0.995794	−	0.0916164i	$-0.0292034\pi$
$769$	11.6069	+	20.1037i	0.418555	+	0.724959i	−0.577239	+	0.816575i	$0.695870\pi$
$770$	−0.0151435	+	0.0262293i	−0.000545733	+	0.000945237i
$771$	−22.8965			−0.824596
$772$	1.37668	+	2.38448i	0.0495477	+	0.0858192i
$773$	22.3694			0.804572			0.402286	−	0.915514i	$-0.368216\pi$
$773$	22.3694			0.804572			0.402286	+	0.915514i	$0.368216\pi$
$774$	1.36277			0.0489839
$775$		0			0
$776$	21.7152			0.779531
$777$	7.35029			0.263690
$778$	15.5204	+	26.8821i	0.556432	+	0.963769i
$779$	−15.0462			−0.539085
$780$	0.00759532	−	0.0131555i	0.000271956	−	0.000471042i
$781$	18.7213	+	32.4263i	0.669901	+	1.16030i
$782$	1.99903	+	3.46242i	0.0714852	+	0.123816i
$783$	−8.95430			−0.320001
$784$	−10.8012	+	18.7083i	−0.385759	+	0.668154i
$785$	−0.00968355	+	0.0167724i	−0.000345621	+	0.000598632i
$786$	−0.524418	+	0.908318i	−0.0187054	+	0.0323986i
$787$	5.73159	+	9.92740i	0.204309	+	0.353874i	0.949912	−	0.312516i	$-0.101172\pi$
$787$	5.73159	+	9.92740i	0.204309	+	0.353874i	−0.745603	+	0.666390i	$0.767839\pi$
$788$	1.95676	−	3.38920i	0.0697066	−	0.120735i
$789$	−8.94157	−	15.4873i	−0.318328	−	0.551361i
$790$	0.100182			0.00356432
$791$	6.61719			0.235280
$792$	8.76244	+	15.1770i	0.311360	+	0.539291i
$793$	−15.8491	+	27.4514i	−0.562817	+	0.974828i
$794$	7.17861	+	12.4337i	0.254759	+	0.441256i
$795$	−0.0183275	+	0.0317441i	−0.000650009	+	0.00112585i
$796$	−1.41905	+	2.45787i	−0.0502969	+	0.0871168i
$797$	−17.6951	+	30.6489i	−0.626794	+	1.08564i	0.361397	+	0.932412i	$0.382300\pi$
$797$	−17.6951	+	30.6489i	−0.626794	+	1.08564i	−0.988191	+	0.153227i	$0.951033\pi$
$798$	−4.82308			−0.170735
$799$	−13.5205	−	23.4182i	−0.478322	−	0.828478i
$800$	−3.76265	−	6.51710i	−0.133030	−	0.230414i
$801$	−0.828367	+	1.43477i	−0.0292689	+	0.0506953i
$802$	−14.0437			−0.495900
$803$	−8.79695	−	15.2368i	−0.310437	−	0.537693i
$804$	−4.80474			−0.169450
$805$	−0.00279834			−9.86284e−5
$806$		0			0
$807$	18.5678			0.653619
$808$	−19.1994			−0.675434
$809$	5.43003	+	9.40509i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$809$	5.43003	+	9.40509i	0.190910	+	0.330665i	−0.754642	+	0.656137i	$0.772190\pi$
$810$	0.0229205			0.000805345
$811$	−20.6303	+	35.7328i	−0.724429	+	1.25475i	0.234779	+	0.972049i	$0.424563\pi$
$811$	−20.6303	+	35.7328i	−0.724429	+	1.25475i	−0.959209	+	0.282699i	$0.908770\pi$
$812$	0.172586	+	0.298927i	0.00605657	+	0.0104903i
$813$	−14.1439	−	24.4980i	−0.496050	−	0.859183i
$814$	−39.2112			−1.37435
$815$	0.0615191	−	0.106554i	0.00215492	−	0.00373243i
$816$	−13.1511	+	22.7783i	−0.460380	+	0.797401i
$817$	−1.30992	+	2.26884i	−0.0458282	+	0.0793768i
$818$	6.20260	+	10.7432i	0.216869	+	0.375628i
$819$	3.70183	−	6.41176i	0.129353	−	0.224045i
$820$	−0.00392861	−	0.00680454i	−0.000137193	−	0.000237625i
$821$	5.91019			0.206267			0.103134	−	0.994668i	$-0.467113\pi$
$821$	5.91019			0.206267			0.103134	+	0.994668i	$0.467113\pi$
$822$	4.68541			0.163422
$823$	−5.55396	−	9.61975i	−0.193599	−	0.335323i	0.752841	−	0.658202i	$-0.228683\pi$
$823$	−5.55396	−	9.61975i	−0.193599	−	0.335323i	−0.946440	+	0.322879i	$0.895349\pi$
$824$	12.7382	−	22.0633i	0.443757	−	0.768610i
$825$	−12.2756	−	21.2619i	−0.427380	−	0.740244i
$826$	7.16814	−	12.4156i	0.249412	−	0.431993i
$827$	2.74241	−	4.74999i	0.0953629	−	0.165173i	−0.814397	−	0.580308i	$-0.802932\pi$
$827$	2.74241	−	4.74999i	0.0953629	−	0.165173i	0.909760	+	0.415135i	$0.136266\pi$
$828$	−0.0956520	+	0.165674i	−0.00332414	+	0.00575758i
$829$	−37.1412			−1.28997			−0.644983	−	0.764197i	$-0.723136\pi$
$829$	−37.1412			−1.28997			−0.644983	+	0.764197i	$0.723136\pi$
$830$	−0.00961759	−	0.0166582i	−0.000333832	−	0.000578213i
$831$	−8.91941	−	15.4489i	−0.309411	−	0.535915i
$832$	27.6536	−	47.8974i	0.958716	−	1.66054i
$833$	−39.9971			−1.38582
$834$	−2.74471	−	4.75397i	−0.0950414	−	0.164617i
$835$	−0.112686			−0.00389966
$836$	−3.98043			−0.137666
$837$		0			0
$838$	38.4379			1.32782
$839$	36.2002			1.24977			0.624886	−	0.780716i	$-0.285146\pi$
$839$	36.2002			1.24977			0.624886	+	0.780716i	$0.285146\pi$
$840$	−0.0106589	−	0.0184617i	−0.000367767	−	0.000636990i
$841$	−26.3739			−0.909446
$842$	0.392621	−	0.680040i	0.0135306	−	0.0234357i
$843$	−3.59084	−	6.21952i	−0.123675	−	0.214212i
$844$	2.21870	+	3.84290i	0.0763708	+	0.132278i
$845$	0.195150			0.00671335
$846$	−4.18185	+	7.24318i	−0.143775	+	0.249026i
$847$	1.91644	−	3.31936i	0.0658495	−	0.114055i
$848$	−6.91975	+	11.9854i	−0.237625	+	0.411579i
$849$	1.59432	+	2.76145i	0.0547170	+	0.0947726i
$850$	−20.6649	+	35.7927i	−0.708801	+	1.22768i
$851$	−1.81144	−	3.13751i	−0.0620954	−	0.107552i
$852$	−3.11371			−0.106674
$853$	−11.1741			−0.382593			−0.191296	−	0.981532i	$-0.561269\pi$
$853$	−11.1741			−0.382593			−0.191296	+	0.981532i	$0.561269\pi$
$854$	2.62782	+	4.55151i	0.0899220	+	0.155749i
$855$	0.0200611	−	0.0347469i	0.000686075	−	0.00118832i
$856$	20.1693	+	34.9343i	0.689374	+	1.19403i
$857$	−27.4330	+	47.5154i	−0.937095	+	1.62310i	−0.166240	+	0.986085i	$0.553163\pi$
$857$	−27.4330	+	47.5154i	−0.937095	+	1.62310i	−0.770855	+	0.637011i	$0.780171\pi$
$858$	20.3876	−	35.3124i	0.696022	−	1.20555i
$859$	−9.95544	+	17.2433i	−0.339675	+	0.588335i	−0.984372	−	0.176104i	$-0.943650\pi$
$859$	−9.95544	+	17.2433i	−0.339675	+	0.588335i	0.644696	+	0.764439i	$0.276984\pi$
$860$	−0.00136810			−4.66517e−5
$861$	1.97676	+	3.42384i	0.0673677	+	0.116684i
$862$	−15.7958	−	27.3591i	−0.538007	−	0.931855i
$863$	5.58861	−	9.67975i	0.190238	−	0.329503i	−0.755091	−	0.655620i	$-0.772407\pi$
$863$	5.58861	−	9.67975i	0.190238	−	0.329503i	0.945329	+	0.326118i	$0.105741\pi$
$864$	−8.31643			−0.282931
$865$	−0.0251487	−	0.0435588i	−0.000855081	−	0.00148104i
$866$	−16.5092			−0.561005
$867$	−27.7126			−0.941170
$868$		0			0
$869$	−41.6017			−1.41124
$870$	−0.0191619			−0.000649650
$871$	−45.8261	−	79.3731i	−1.55276	−	2.68945i
$872$	30.5372			1.03412
$873$	5.36951	−	9.30026i	0.181730	−	0.314766i
$874$	1.18862	+	2.05876i	0.0402058	+	0.0696386i
$875$	−0.0289279	−	0.0501046i	−0.000977941	−	0.00169384i
$876$	1.46310			0.0494335
$877$	13.7743	−	23.8577i	0.465124	−	0.805618i	−0.534083	−	0.845432i	$-0.679343\pi$
$877$	13.7743	−	23.8577i	0.465124	−	0.805618i	0.999207	+	0.0398136i	$0.0126764\pi$
$878$	−25.7406	+	44.5839i	−0.868702	+	1.50464i
$879$	11.3881	−	19.7249i	0.384113	−	0.665303i
$880$	0.0491041	+	0.0850507i	0.00165530	+	0.00286706i
$881$	7.13122	−	12.3516i	0.240257	−	0.416137i	−0.720530	−	0.693423i	$-0.756102\pi$
$881$	7.13122	−	12.3516i	0.240257	−	0.416137i	0.960787	+	0.277286i	$0.0894350\pi$
$882$	6.18549	+	10.7136i	0.208276	+	0.360745i
$883$	18.6749			0.628459			0.314229	−	0.949347i	$-0.398254\pi$
$883$	18.6749			0.628459			0.314229	+	0.949347i	$0.398254\pi$
$884$	10.6191			0.357160
$885$	−0.0615617	−	0.106628i	−0.00206937	−	0.00358426i
$886$	−4.93005	+	8.53910i	−0.165628	+	0.286877i
$887$	17.3692	+	30.0844i	0.583202	+	1.01014i	0.995097	+	0.0989042i	$0.0315337\pi$
$887$	17.3692	+	30.0844i	0.583202	+	1.01014i	−0.411895	+	0.911231i	$0.635133\pi$
$888$	13.7996	−	23.9016i	0.463084	−	0.802085i
$889$	4.46996	−	7.74220i	0.149918	−	0.259665i
$890$	−0.00537546	+	0.00931057i	−0.000180186	+	0.000312091i
$891$	−9.51798			−0.318864
$892$	−0.107877	−	0.186849i	−0.00361199	−	0.00625615i
$893$	−8.03931	−	13.9245i	−0.269025	−	0.465966i
$894$	9.56098	−	16.5601i	0.319767	−	0.553853i
$895$	0.105397			0.00352303
$896$	−3.38862	−	5.86927i	−0.113206	−	0.196078i
$897$	3.76739			0.125790
$898$	23.0498			0.769183
$899$		0			0
$900$	−1.97760			−0.0659200
$901$	−25.6239			−0.853656
$902$	−10.5453	−	18.2650i	−0.351120	−	0.608158i
$903$	0.688385			0.0229080
$904$	12.4233	−	21.5177i	0.413191	−	0.715668i
$905$	0.0631510	+	0.109381i	0.00209921	+	0.00363594i
$906$	14.5150	+	25.1408i	0.482230	+	0.835246i
$907$	−6.36985			−0.211507			−0.105754	−	0.994392i	$-0.533725\pi$
$907$	−6.36985			−0.211507			−0.105754	+	0.994392i	$0.533725\pi$
$908$	1.80528	−	3.12684i	0.0599104	−	0.103768i
$909$	−4.74743	+	8.22279i	−0.157462	+	0.272733i
$910$	0.0240220	−	0.0416074i	0.000796322	−	0.00137927i
$911$	−27.1710	−	47.0615i	−0.900214	−	1.55922i	−0.827216	−	0.561885i	$-0.810076\pi$
$911$	−27.1710	−	47.0615i	−0.900214	−	1.55922i	−0.0729986	−	0.997332i	$-0.523257\pi$
$912$	−7.81964	+	13.5440i	−0.258934	+	0.448487i
$913$	3.99380	+	6.91747i	0.132176	+	0.228935i
$914$	−6.44093			−0.213047
$915$	0.0451366			0.00149217
$916$	1.73493	+	3.00499i	0.0573238	+	0.0992877i
$917$	0.256590	−	0.444428i	0.00847336	−	0.0146763i
$918$	22.8374	+	39.5555i	0.753746	+	1.30553i
$919$	22.3484	−	38.7085i	0.737204	−	1.27688i	−0.216545	−	0.976273i	$-0.569479\pi$
$919$	22.3484	−	38.7085i	0.737204	−	1.27688i	0.953749	−	0.300603i	$-0.0971878\pi$
$920$	−0.00525366	+	0.00909961i	−0.000173208	+	0.000300005i
$921$	1.01581	−	1.75943i	0.0334720	−	0.0579752i
$922$	26.6863			0.878868
$923$	−29.6975	−	51.4376i	−0.977506	−	1.69309i
$924$	0.522946	+	0.905770i	0.0172037	+	0.0297976i
$925$	18.7257	−	32.4339i	0.615698	−	1.06642i
$926$	−30.2115			−0.992812
$927$	−6.29955	−	10.9111i	−0.206904	−	0.358369i
$928$	2.43900			0.0800641
$929$	15.4573			0.507139			0.253569	−	0.967317i	$-0.418395\pi$
$929$	15.4573			0.507139			0.253569	+	0.967317i	$0.418395\pi$
$930$		0			0
$931$	−23.7823			−0.779434
$932$	−3.31082			−0.108449
$933$	−11.8772	−	20.5719i	−0.388842	−	0.673495i
$934$	−35.9122			−1.17508
$935$	−0.0909164	+	0.157472i	−0.00297328	+	0.00514988i
$936$	−13.8998	−	24.0752i	−0.454329	−	0.786922i
$937$	2.65896	+	4.60546i	0.0868645	+	0.150454i	0.906184	−	0.422883i	$-0.138982\pi$
$937$	2.65896	+	4.60546i	0.0868645	+	0.150454i	−0.819320	+	0.573337i	$0.805649\pi$
$938$	−15.1961			−0.496172
$939$	−9.50725	+	16.4670i	−0.310257	+	0.537381i
$940$	0.00419818	−	0.00727146i	0.000136930	−	0.000237169i
$941$	−6.68942	+	11.5864i	−0.218069	+	0.377706i	−0.954217	−	0.299114i	$-0.903309\pi$
$941$	−6.68942	+	11.5864i	−0.218069	+	0.377706i	0.736149	+	0.676820i	$0.236642\pi$
$942$	−2.16156	−	3.74392i	−0.0704273	−	0.121984i
$943$	0.974324	−	1.68758i	0.0317284	−	0.0549551i
$944$	−23.2433	−	40.2586i	−0.756506	−	1.31031i
$945$	−0.0319689			−0.00103995
$946$	−3.67229			−0.119396
$947$	3.35884	+	5.81769i	0.109148	+	0.189049i	0.915425	−	0.402488i	$-0.131855\pi$
$947$	3.35884	+	5.81769i	0.109148	+	0.189049i	−0.806278	+	0.591537i	$0.798521\pi$
$948$	1.72978	−	2.99608i	0.0561808	−	0.0973080i
$949$	13.9546	+	24.1700i	0.452984	+	0.784591i
$950$	−12.2874	+	21.2824i	−0.398655	+	0.690491i
$951$	−17.8540	+	30.9240i	−0.578955	+	1.00278i
$952$	7.45117	−	12.9058i	0.241494	−	0.418279i
$953$	20.6118			0.667682			0.333841	−	0.942629i	$-0.391655\pi$
$953$	20.6118			0.667682			0.333841	+	0.942629i	$0.391655\pi$
$954$	3.96270	+	6.86359i	0.128297	+	0.222217i
$955$	−0.0542416	−	0.0939491i	−0.00175522	−	0.00304012i
$956$	2.13467	−	3.69735i	0.0690401	−	0.119581i
$957$	7.95718			0.257219
$958$	−22.6313	−	39.1985i	−0.731183	−	1.26645i
$959$	−2.29251			−0.0740289
$960$	−0.0787547			−0.00254180
$961$		0			0
$962$	62.2005			2.00543
$963$	19.9490			0.642848
$964$	−2.74943	−	4.76216i	−0.0885533	−	0.153379i
$965$	0.0747877			0.00240750
$966$	0.312322	−	0.540957i	0.0100488	−	0.0174050i
$967$	29.5645	+	51.2072i	0.950731	+	1.64671i	0.743849	+	0.668348i	$0.232998\pi$
$967$	29.5645	+	51.2072i	0.950731	+	1.64671i	0.206881	+	0.978366i	$0.433669\pi$
$968$	−7.19592	−	12.4637i	−0.231286	−	0.400598i
$969$	−28.9562			−0.930207
$970$	0.0348439	−	0.0603515i	0.00111877	−	0.00193777i
$971$	22.8908	−	39.6481i	0.734602	−	1.27237i	−0.220295	−	0.975433i	$-0.570702\pi$
$971$	22.8908	−	39.6481i	0.734602	−	1.27237i	0.954898	−	0.296935i	$-0.0959645\pi$
$972$	−1.82514	+	3.16124i	−0.0585415	+	0.101397i
$973$	1.34295	+	2.32605i	0.0430529	+	0.0745699i
$974$	−17.9695	+	31.1241i	−0.575781	+	0.997281i
$975$	19.4727	+	33.7276i	0.623624	+	1.08015i
$976$	17.0418			0.545496
$977$	7.43684			0.237926			0.118963	−	0.992899i	$-0.462043\pi$
$977$	7.43684			0.237926			0.118963	+	0.992899i	$0.462043\pi$
$978$	13.7323	+	23.7850i	0.439109	+	0.760560i
$979$	2.23221	−	3.86631i	0.0713419	−	0.123568i
$980$	−0.00620964	−	0.0107554i	−0.000198360	−	0.000343569i
$981$	7.55090	−	13.0785i	0.241082	−	0.417566i
$982$	23.3619	−	40.4641i	0.745510	−	1.29126i
$983$	13.6051	−	23.5646i	0.433934	−	0.751595i	−0.563274	−	0.826270i	$-0.690459\pi$
$983$	13.6051	−	23.5646i	0.433934	−	0.751595i	0.997208	+	0.0746748i	$0.0237919\pi$
$984$	14.8448			0.473236
$985$	−0.0531502	−	0.0920588i	−0.00169350	−	0.00293324i
$986$	−6.69764	−	11.6007i	−0.213296	−	0.369440i
$987$	−2.11240	+	3.65878i	−0.0672384	+	0.116460i
$988$	6.31414			0.200879
$989$	−0.169649	−	0.293841i	−0.00539453	−	0.00934359i
$990$	0.0562403			0.00178743
$991$	17.2059			0.546563			0.273282	−	0.961934i	$-0.411891\pi$
$991$	17.2059			0.546563			0.273282	+	0.961934i	$0.411891\pi$
$992$		0			0
$993$	−2.28019			−0.0723597
$994$	−9.84785			−0.312355
$995$	0.0385448	+	0.0667615i	0.00122195	+	0.00211648i
$996$	−0.664244			−0.0210474
$997$	−14.7528	+	25.5527i	−0.467227	+	0.809261i	−0.999299	−	0.0374383i	$-0.988080\pi$
$997$	−14.7528	+	25.5527i	−0.467227	+	0.809261i	0.532072	+	0.846699i	$0.321414\pi$
$998$	7.37511	+	12.7741i	0.233455	+	0.404356i
$999$	−20.6943	−	35.8437i	−0.654740	−	1.13404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.l.521.8		32
31.2	even	5		961.2.g.w.844.8		128
31.3	odd	30		961.2.d.s.628.8		64
31.4	even	5		961.2.g.w.338.10		128
31.5	even	3	inner	961.2.c.l.439.8		32
31.6	odd	6		961.2.a.l.1.8	yes	16
31.7	even	15		961.2.d.s.388.10		64
31.8	even	5		961.2.g.w.732.9		128
31.9	even	15		961.2.g.w.816.10		128
31.10	even	15		961.2.g.w.547.7		128
31.11	odd	30		961.2.g.w.235.10		128
31.12	odd	30		961.2.d.s.531.8		64
31.13	odd	30		961.2.g.w.846.7		128
31.14	even	15		961.2.d.s.374.10		64
31.15	odd	10		961.2.g.w.448.8		128
31.16	even	5		961.2.g.w.448.7		128
31.17	odd	30		961.2.d.s.374.9		64
31.18	even	15		961.2.g.w.846.8		128
31.19	even	15		961.2.d.s.531.7		64
31.20	even	15		961.2.g.w.235.9		128
31.21	odd	30		961.2.g.w.547.8		128
31.22	odd	30		961.2.g.w.816.9		128
31.23	odd	10		961.2.g.w.732.10		128
31.24	odd	30		961.2.d.s.388.9		64
31.25	even	3		961.2.a.l.1.7	✓	16
31.26	odd	6	inner	961.2.c.l.439.7		32
31.27	odd	10		961.2.g.w.338.9		128
31.28	even	15		961.2.d.s.628.7		64
31.29	odd	10		961.2.g.w.844.7		128
31.30	odd	2	inner	961.2.c.l.521.7		32
93.56	odd	6		8649.2.a.bs.1.9		16
93.68	even	6		8649.2.a.bs.1.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.7	✓	16	31.25	even	3
961.2.a.l.1.8	yes	16	31.6	odd	6
961.2.c.l.439.7		32	31.26	odd	6	inner
961.2.c.l.439.8		32	31.5	even	3	inner
961.2.c.l.521.7		32	31.30	odd	2	inner
961.2.c.l.521.8		32	1.1	even	1	trivial
961.2.d.s.374.9		64	31.17	odd	30
961.2.d.s.374.10		64	31.14	even	15
961.2.d.s.388.9		64	31.24	odd	30
961.2.d.s.388.10		64	31.7	even	15
961.2.d.s.531.7		64	31.19	even	15
961.2.d.s.531.8		64	31.12	odd	30
961.2.d.s.628.7		64	31.28	even	15
961.2.d.s.628.8		64	31.3	odd	30
961.2.g.w.235.9		128	31.20	even	15
961.2.g.w.235.10		128	31.11	odd	30
961.2.g.w.338.9		128	31.27	odd	10
961.2.g.w.338.10		128	31.4	even	5
961.2.g.w.448.7		128	31.16	even	5
961.2.g.w.448.8		128	31.15	odd	10
961.2.g.w.547.7		128	31.10	even	15
961.2.g.w.547.8		128	31.21	odd	30
961.2.g.w.732.9		128	31.8	even	5
961.2.g.w.732.10		128	31.23	odd	10
961.2.g.w.816.9		128	31.22	odd	30
961.2.g.w.816.10		128	31.9	even	15
961.2.g.w.844.7		128	31.29	odd	10
961.2.g.w.844.8		128	31.2	even	5
961.2.g.w.846.7		128	31.13	odd	30
961.2.g.w.846.8		128	31.18	even	15
8649.2.a.bs.1.9		16	93.56	odd	6
8649.2.a.bs.1.10		16	93.68	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.31607 q^{2} +(0.617233 + 1.06908i) q^{3} -0.267953 q^{4} +(-0.00363912 + 0.00630315i) q^{5} +(-0.812323 - 1.40699i) q^{6} +(0.397459 + 0.688419i) q^{7} +2.98479 q^{8} +(0.738047 - 1.27834i) q^{9} +(0.00478935 - 0.00829540i) q^{10} +(-1.98883 + 3.44475i) q^{11} +(-0.165390 - 0.286463i) q^{12} +(3.15487 - 5.46439i) q^{13} +(-0.523084 - 0.906009i) q^{14} -0.00898475 q^{15} -3.39229 q^{16} +(-3.14043 - 5.43938i) q^{17} +(-0.971323 + 1.68238i) q^{18} +(-1.86730 - 3.23426i) q^{19} +(0.000975115 - 0.00168895i) q^{20} +(-0.490649 + 0.849829i) q^{21} +(2.61744 - 4.53354i) q^{22} +0.483672 q^{23} +(1.84231 + 3.19098i) q^{24} +(2.49997 + 4.33008i) q^{25} +(-4.15203 + 7.19153i) q^{26} +5.52559 q^{27} +(-0.106500 - 0.184464i) q^{28} -1.62052 q^{29} +0.0118246 q^{30} -1.50508 q^{32} -4.91028 q^{33} +(4.13303 + 7.15861i) q^{34} -0.00578561 q^{35} +(-0.197762 + 0.342534i) q^{36} +(-3.74519 - 6.48685i) q^{37} +(2.45750 + 4.25652i) q^{38} +7.78915 q^{39} +(-0.0108620 + 0.0188136i) q^{40} +(2.01443 - 3.48910i) q^{41} +(0.645730 - 1.11844i) q^{42} +(-0.350752 - 0.607520i) q^{43} +(0.532913 - 0.923032i) q^{44} +(0.00537169 + 0.00930404i) q^{45} -0.636548 q^{46} +4.30532 q^{47} +(-2.09384 - 3.62663i) q^{48} +(3.18405 - 5.51494i) q^{49} +(-3.29015 - 5.69870i) q^{50} +(3.87675 - 6.71472i) q^{51} +(-0.845357 + 1.46420i) q^{52} +(2.03984 - 3.53311i) q^{53} -7.27207 q^{54} +(-0.0144752 - 0.0250717i) q^{55} +(1.18633 + 2.05479i) q^{56} +(2.30512 - 3.99258i) q^{57} +2.13272 q^{58} +(6.85180 + 11.8677i) q^{59} +0.00240749 q^{60} -5.02369 q^{61} +1.17337 q^{63} +8.76538 q^{64} +(0.0229619 + 0.0397712i) q^{65} +6.46228 q^{66} +(7.26276 - 12.5795i) q^{67} +(0.841487 + 1.45750i) q^{68} +(0.298538 + 0.517084i) q^{69} +0.00761428 q^{70} +(4.70662 - 8.15211i) q^{71} +(2.20292 - 3.81556i) q^{72} +(-2.21159 + 3.83059i) q^{73} +(4.92894 + 8.53717i) q^{74} +(-3.08613 + 5.34534i) q^{75} +(0.500349 + 0.866630i) q^{76} -3.16191 q^{77} -10.2511 q^{78} +(5.22943 + 9.05763i) q^{79} +(0.0123450 - 0.0213821i) q^{80} +(1.19643 + 2.07228i) q^{81} +(-2.65114 + 4.59190i) q^{82} +(1.00406 - 1.73908i) q^{83} +(0.131471 - 0.227715i) q^{84} +0.0457136 q^{85} +(0.461615 + 0.799541i) q^{86} +(-1.00024 - 1.73246i) q^{87} +(-5.93623 + 10.2819i) q^{88} -1.12238 q^{89} +(-0.00706953 - 0.0122448i) q^{90} +5.01572 q^{91} -0.129602 q^{92} -5.66611 q^{94} +0.0271813 q^{95} +(-0.928983 - 1.60905i) q^{96} +7.27529 q^{97} +(-4.19044 + 7.25806i) q^{98} +(2.93570 + 5.08477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 16 q^{4} + 16 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} - 16 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 16 q^{32} - 64 q^{33} - 32 q^{35} + 40 q^{36} + 24 q^{38} - 64 q^{39}+ \cdots - 16 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 + 16 * q^4 + 16 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 - 16 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 16 * q^32 - 64 * q^33 - 32 * q^35 + 40 * q^36 + 24 * q^38 - 64 * q^39 + 32 * q^41 + 16 * q^45 - 64 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 + 48 * q^56 + 64 * q^59 - 32 * q^63 - 32 * q^64 - 16 * q^67 + 32 * q^69 + 176 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 + 64 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 + 32 * q^87 - 40 * q^90 - 64 * q^94 - 96 * q^95 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

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