LMFDB - Embedded newform 187.2.j.a.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(16,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("187.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.j (of order $10$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	187.16
Dual form			187.2.j.a.152.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.609729 - 1.87655i) q^{2} +(1.09362 - 1.50523i) q^{3} +(-1.53164 + 1.11281i) q^{4} +(2.63951 + 0.857628i) q^{5} +(-3.49146 - 1.13444i) q^{6} +(-1.01174 - 1.39254i) q^{7} +(-0.170457 - 0.123844i) q^{8} +(-0.142682 - 0.439131i) q^{9} +O(q^{10})$	\(q+(-0.609729 - 1.87655i) q^{2} +(1.09362 - 1.50523i) q^{3} +(-1.53164 + 1.11281i) q^{4} +(2.63951 + 0.857628i) q^{5} +(-3.49146 - 1.13444i) q^{6} +(-1.01174 - 1.39254i) q^{7} +(-0.170457 - 0.123844i) q^{8} +(-0.142682 - 0.439131i) q^{9} -5.47610i q^{10} +(0.792359 - 3.22058i) q^{11} +3.52247i q^{12} +(1.73570 + 5.34194i) q^{13} +(-1.99628 + 2.74765i) q^{14} +(4.17754 - 3.03516i) q^{15} +(-1.29854 + 3.99649i) q^{16} +(-2.02765 + 3.59007i) q^{17} +(-0.737054 + 0.535501i) q^{18} +(-5.72692 - 4.16085i) q^{19} +(-4.99716 + 1.62368i) q^{20} -3.20255 q^{21} +(-6.52672 + 0.476780i) q^{22} +4.09281i q^{23} +(-0.372828 + 0.121139i) q^{24} +(2.18639 + 1.58851i) q^{25} +(8.96611 - 6.51426i) q^{26} +(4.49149 + 1.45937i) q^{27} +(3.09925 + 1.00701i) q^{28} +(3.82688 + 5.26725i) q^{29} +(-8.24281 - 5.98875i) q^{30} +(-0.631400 + 0.205154i) q^{31} +7.87000 q^{32} +(-3.98120 - 4.71477i) q^{33} +(7.97328 + 1.61603i) q^{34} +(-1.47621 - 4.54331i) q^{35} +(0.707205 + 0.513815i) q^{36} +(-5.21012 - 7.17111i) q^{37} +(-4.31619 + 13.2839i) q^{38} +(9.93906 + 3.22940i) q^{39} +(-0.343710 - 0.473076i) q^{40} +(4.35281 - 5.99113i) q^{41} +(1.95269 + 6.00975i) q^{42} +1.63319 q^{43} +(2.37027 + 5.81453i) q^{44} -1.28146i q^{45} +(7.68038 - 2.49551i) q^{46} +(1.44404 + 1.04916i) q^{47} +(4.59556 + 6.32524i) q^{48} +(1.24757 - 3.83963i) q^{49} +(1.64781 - 5.07144i) q^{50} +(3.18642 + 6.97826i) q^{51} +(-8.60301 - 6.25045i) q^{52} +(1.28988 + 3.96984i) q^{53} -9.31835i q^{54} +(4.85350 - 7.82121i) q^{55} +0.362665i q^{56} +(-12.5261 + 4.06998i) q^{57} +(7.55091 - 10.3929i) q^{58} +(-2.72175 + 1.97747i) q^{59} +(-3.02097 + 9.29758i) q^{60} +(4.16797 + 1.35426i) q^{61} +(0.769965 + 1.05977i) q^{62} +(-0.467149 + 0.642975i) q^{63} +(-2.20148 - 6.77547i) q^{64} +15.5887i q^{65} +(-6.42007 + 10.3457i) q^{66} -5.26475 q^{67} +(-0.889404 - 7.75510i) q^{68} +(6.16065 + 4.47597i) q^{69} +(-7.62567 + 5.54037i) q^{70} +(-4.74346 - 1.54124i) q^{71} +(-0.0300626 + 0.0925231i) q^{72} +(-5.51482 - 7.59050i) q^{73} +(-10.2802 + 14.1495i) q^{74} +(4.78215 - 1.55382i) q^{75} +13.4018 q^{76} +(-5.28644 + 2.15500i) q^{77} -20.6202i q^{78} +(1.35533 - 0.440374i) q^{79} +(-6.85501 + 9.43512i) q^{80} +(8.22932 - 5.97895i) q^{81} +(-13.8967 - 4.51531i) q^{82} +(-2.96551 + 9.12692i) q^{83} +(4.90517 - 3.56381i) q^{84} +(-8.43096 + 7.73705i) q^{85} +(-0.995804 - 3.06477i) q^{86} +12.1136 q^{87} +(-0.533913 + 0.450841i) q^{88} +15.2855 q^{89} +(-2.40472 + 0.781341i) q^{90} +(5.68277 - 7.82167i) q^{91} +(-4.55450 - 6.26874i) q^{92} +(-0.381704 + 1.17476i) q^{93} +(1.08833 - 3.34953i) q^{94} +(-11.5478 - 15.8942i) q^{95} +(8.60676 - 11.8462i) q^{96} +(-6.13630 + 1.99380i) q^{97} -7.96595 q^{98} +(-1.52731 + 0.111571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9}+O(q^{10}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36} - 60 q^{38} - 10 q^{42} + 32 q^{43} + 16 q^{47} - 18 q^{49} + 4 q^{50} - 2 q^{51} + 44 q^{52} - 16 q^{53} + 22 q^{55} - 50 q^{59} + 68 q^{60} - 80 q^{64} - 172 q^{66} + 40 q^{67} + 18 q^{68} + 6 q^{69} + 128 q^{70} + 186 q^{72} - 116 q^{76} - 30 q^{77} + 48 q^{81} - 12 q^{83} + 68 q^{84} - 108 q^{85} - 16 q^{86} + 92 q^{87} - 40 q^{89} - 80 q^{93} - 188 q^{94} + 72 q^{98}+O(q^{100}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.609729	−	1.87655i	−0.431143	−	1.32692i	−0.896987	−	0.442056i	$-0.854249\pi$
$2$	−0.609729	−	1.87655i	−0.431143	−	1.32692i	0.465844	−	0.884867i	$-0.345751\pi$
$3$	1.09362	−	1.50523i	0.631400	−	0.869048i	−0.366720	−	0.930331i	$-0.619519\pi$
$3$	1.09362	−	1.50523i	0.631400	−	0.869048i	0.998120	+	0.0612836i	$0.0195194\pi$
$4$	−1.53164	+	1.11281i	−0.765822	+	0.556403i
$5$	2.63951	+	0.857628i	1.18042	+	0.383543i	0.832524	−	0.553989i	$-0.186895\pi$
$5$	2.63951	+	0.857628i	1.18042	+	0.383543i	0.347900	+	0.937532i	$0.386895\pi$
$6$	−3.49146	−	1.13444i	−1.42538	−	0.463135i
$7$	−1.01174	−	1.39254i	−0.382401	−	0.526330i	0.573818	−	0.818983i	$-0.305462\pi$
$7$	−1.01174	−	1.39254i	−0.382401	−	0.526330i	−0.956219	+	0.292653i	$0.905462\pi$
$8$	−0.170457	−	0.123844i	−0.0602655	−	0.0437855i
$9$	−0.142682	−	0.439131i	−0.0475607	−	0.146377i
$10$		−	5.47610i		−	1.73169i
$11$	0.792359	−	3.22058i	0.238905	−	0.971043i
$11$	0.792359	−	3.22058i	0.238905	−	0.971043i
$12$			3.52247i			1.01685i
$13$	1.73570	+	5.34194i	0.481397	+	1.48159i	0.837133	+	0.547000i	$0.184230\pi$
$13$	1.73570	+	5.34194i	0.481397	+	1.48159i	−0.355736	+	0.934586i	$0.615770\pi$
$14$	−1.99628	+	2.74765i	−0.533529	+	0.734340i
$15$	4.17754	−	3.03516i	1.07864	−	0.783676i
$16$	−1.29854	+	3.99649i	−0.324635	+	0.999124i
$17$	−2.02765	+	3.59007i	−0.491778	+	0.870720i
$17$	−2.02765	+	3.59007i	−0.491778	+	0.870720i
$18$	−0.737054	+	0.535501i	−0.173725	+	0.126219i
$19$	−5.72692	−	4.16085i	−1.31385	−	0.954565i	−0.999987	−	0.00509576i	$-0.998378\pi$
$19$	−5.72692	−	4.16085i	−1.31385	−	0.954565i	−0.313859	−	0.949469i	$-0.601622\pi$
$20$	−4.99716	+	1.62368i	−1.11740	+	0.363065i
$21$	−3.20255			−0.698854
$22$	−6.52672	+	0.476780i	−1.39150	+	0.101650i
$23$			4.09281i			0.853411i	0.904391	+	0.426705i	$0.140326\pi$
$23$			4.09281i			0.853411i	−0.904391	+	0.426705i	$0.859674\pi$
$24$	−0.372828	+	0.121139i	−0.0761033	+	0.0247275i
$25$	2.18639	+	1.58851i	0.437279	+	0.317702i
$26$	8.96611	−	6.51426i	1.75840	−	1.27755i
$27$	4.49149	+	1.45937i	0.864388	+	0.280857i
$28$	3.09925	+	1.00701i	0.585702	+	0.190306i
$29$	3.82688	+	5.26725i	0.710634	+	0.978104i	0.999783	+	0.0208199i	$0.00662766\pi$
$29$	3.82688	+	5.26725i	0.710634	+	0.978104i	−0.289149	+	0.957284i	$0.593372\pi$
$30$	−8.24281	−	5.98875i	−1.50492	−	1.09339i
$31$	−0.631400	+	0.205154i	−0.113403	+	0.0368468i	−0.365169	−	0.930941i	$-0.618989\pi$
$31$	−0.631400	+	0.205154i	−0.113403	+	0.0368468i	0.251766	+	0.967788i	$0.418989\pi$
$32$	7.87000			1.39123
$33$	−3.98120	−	4.71477i	−0.693038	−	0.820737i
$34$	7.97328	+	1.61603i	1.36741	+	0.277147i
$35$	−1.47621	−	4.54331i	−0.249525	−	0.767959i
$36$	0.707205	+	0.513815i	0.117868	+	0.0856358i
$37$	−5.21012	−	7.17111i	−0.856538	−	1.17892i	−0.982384	−	0.186874i	$-0.940164\pi$
$37$	−5.21012	−	7.17111i	−0.856538	−	1.17892i	0.125846	−	0.992050i	$-0.459836\pi$
$38$	−4.31619	+	13.2839i	−0.700178	+	2.15493i
$39$	9.93906	+	3.22940i	1.59152	+	0.517117i
$40$	−0.343710	−	0.473076i	−0.0543453	−	0.0747998i
$41$	4.35281	−	5.99113i	0.679795	−	0.935658i	−0.320136	−	0.947371i	$-0.603729\pi$
$41$	4.35281	−	5.99113i	0.679795	−	0.935658i	0.999931	+	0.0117139i	$0.00372875\pi$
$42$	1.95269	+	6.00975i	0.301306	+	0.927325i
$43$	1.63319			0.249060			0.124530	−	0.992216i	$-0.460258\pi$
$43$	1.63319			0.249060			0.124530	+	0.992216i	$0.460258\pi$
$44$	2.37027	+	5.81453i	0.357332	+	0.876574i
$45$		−	1.28146i		−	0.191028i
$46$	7.68038	−	2.49551i	1.13241	−	0.367942i
$47$	1.44404	+	1.04916i	0.210635	+	0.153036i	0.688101	−	0.725615i	$-0.258445\pi$
$47$	1.44404	+	1.04916i	0.210635	+	0.153036i	−0.477466	+	0.878650i	$0.658445\pi$
$48$	4.59556	+	6.32524i	0.663312	+	0.912970i
$49$	1.24757	−	3.83963i	0.178224	−	0.548519i
$50$	1.64781	−	5.07144i	0.233036	−	0.717210i
$51$	3.18642	+	6.97826i	0.446189	+	0.977152i
$52$	−8.60301	−	6.25045i	−1.19302	−	0.866782i
$53$	1.28988	+	3.96984i	0.177179	+	0.545300i	0.999726	−	0.0233964i	$-0.00744800\pi$
$53$	1.28988	+	3.96984i	0.177179	+	0.545300i	−0.822548	+	0.568696i	$0.807448\pi$
$54$		−	9.31835i		−	1.26807i
$55$	4.85350	−	7.82121i	0.654446	−	1.05461i
$56$			0.362665i			0.0484631i
$57$	−12.5261	+	4.06998i	−1.65913	+	0.539082i
$58$	7.55091	−	10.3929i	0.991483	−	1.36466i
$59$	−2.72175	+	1.97747i	−0.354342	+	0.257444i	−0.750688	−	0.660657i	$-0.770278\pi$
$59$	−2.72175	+	1.97747i	−0.354342	+	0.257444i	0.396347	+	0.918101i	$0.370278\pi$
$60$	−3.02097	+	9.29758i	−0.390005	+	1.20031i
$61$	4.16797	+	1.35426i	0.533654	+	0.173395i	0.563433	−	0.826162i	$-0.309480\pi$
$61$	4.16797	+	1.35426i	0.533654	+	0.173395i	−0.0297788	+	0.999557i	$0.509480\pi$
$62$	0.769965	+	1.05977i	0.0977857	+	0.134590i
$63$	−0.467149	+	0.642975i	−0.0588552	+	0.0810073i
$64$	−2.20148	−	6.77547i	−0.275185	−	0.846934i
$65$			15.5887i			1.93354i
$66$	−6.42007	+	10.3457i	−0.790255	+	1.27346i
$67$	−5.26475			−0.643191			−0.321596	−	0.946877i	$-0.604219\pi$
$67$	−5.26475			−0.643191			−0.321596	+	0.946877i	$0.604219\pi$
$68$	−0.889404	−	7.75510i	−0.107856	−	0.940444i
$69$	6.16065	+	4.47597i	0.741655	+	0.538844i
$70$	−7.62567	+	5.54037i	−0.911442	+	0.662201i
$71$	−4.74346	−	1.54124i	−0.562945	−	0.182912i	0.0137010	−	0.999906i	$-0.495639\pi$
$71$	−4.74346	−	1.54124i	−0.562945	−	0.182912i	−0.576646	+	0.816994i	$0.695639\pi$
$72$	−0.0300626	+	0.0925231i	−0.00354291	+	0.0109039i
$73$	−5.51482	−	7.59050i	−0.645461	−	0.888400i	0.353431	−	0.935460i	$-0.385015\pi$
$73$	−5.51482	−	7.59050i	−0.645461	−	0.888400i	−0.998892	+	0.0470602i	$0.985015\pi$
$74$	−10.2802	+	14.1495i	−1.19505	+	1.64485i
$75$	4.78215	−	1.55382i	0.552196	−	0.179419i
$76$	13.4018			1.53730
$77$	−5.28644	+	2.15500i	−0.602446	+	0.245585i
$78$		−	20.6202i		−	2.33478i
$79$	1.35533	−	0.440374i	0.152487	−	0.0495459i	−0.231779	−	0.972768i	$-0.574455\pi$
$79$	1.35533	−	0.440374i	0.152487	−	0.0495459i	0.384266	+	0.923223i	$0.374455\pi$
$80$	−6.85501	+	9.43512i	−0.766414	+	1.05488i
$81$	8.22932	−	5.97895i	0.914368	−	0.664328i
$82$	−13.8967	−	4.51531i	−1.53463	−	0.498633i
$83$	−2.96551	+	9.12692i	−0.325508	+	1.00181i	0.645703	+	0.763588i	$0.276564\pi$
$83$	−2.96551	+	9.12692i	−0.325508	+	1.00181i	−0.971211	+	0.238221i	$0.923436\pi$
$84$	4.90517	−	3.56381i	0.535198	−	0.388844i
$85$	−8.43096	+	7.73705i	−0.914466	+	0.839201i
$86$	−0.995804	−	3.06477i	−0.107380	−	0.330483i
$87$	12.1136			1.29871
$88$	−0.533913	+	0.450841i	−0.0569153	+	0.0480598i
$89$	15.2855			1.62026			0.810128	−	0.586253i	$-0.199398\pi$
$89$	15.2855			1.62026			0.810128	+	0.586253i	$0.199398\pi$
$90$	−2.40472	+	0.781341i	−0.253480	+	0.0823606i
$91$	5.68277	−	7.82167i	0.595716	−	0.819933i
$92$	−4.55450	−	6.26874i	−0.474840	−	0.653561i
$93$	−0.381704	+	1.17476i	−0.0395809	+	0.121817i
$94$	1.08833	−	3.34953i	0.112252	−	0.345477i
$95$	−11.5478	−	15.8942i	−1.18478	−	1.63071i
$96$	8.60676	−	11.8462i	0.878424	−	1.20905i
$97$	−6.13630	+	1.99380i	−0.623047	+	0.202440i	−0.603493	−	0.797369i	$-0.706225\pi$
$97$	−6.13630	+	1.99380i	−0.623047	+	0.202440i	−0.0195543	+	0.999809i	$0.506225\pi$
$98$	−7.96595			−0.804682
$99$	−1.52731	+	0.111571i	−0.153501	+	0.0112133i
$100$	−5.11648			−0.511648
$101$	−1.51827	−	4.67277i	−0.151074	−	0.464958i	0.846668	−	0.532122i	$-0.178605\pi$
$101$	−1.51827	−	4.67277i	−0.151074	−	0.464958i	−0.997742	+	0.0671636i	$0.978605\pi$
$102$	11.1522	−	10.2343i	1.10423	−	1.01335i
$103$	−8.49758	+	6.17386i	−0.837292	+	0.608328i	−0.921613	−	0.388111i	$-0.873128\pi$
$103$	−8.49758	+	6.17386i	−0.837292	+	0.608328i	0.0843210	+	0.996439i	$0.473128\pi$
$104$	0.365705	−	1.12552i	0.0358603	−	0.110367i
$105$	−8.45316	−	2.74660i	−0.824944	−	0.268040i
$106$	6.66314	−	4.84105i	0.647181	−	0.470205i
$107$	−8.89265	+	12.2397i	−0.859685	+	1.18326i	0.121959	+	0.992535i	$0.461082\pi$
$107$	−8.89265	+	12.2397i	−0.859685	+	1.18326i	−0.981644	+	0.190720i	$0.938918\pi$
$108$	−8.50337	+	2.76291i	−0.818237	+	0.265861i
$109$			0.415860i			0.0398321i	0.999802	+	0.0199161i	$0.00633990\pi$
$109$			0.415860i			0.0398321i	−0.999802	+	0.0199161i	$0.993660\pi$
$110$	−17.6362	−	4.33903i	−1.68155	−	0.413711i
$111$	−16.4921			−1.56536
$112$	6.87905	−	2.23514i	0.650009	−	0.211201i
$113$	−2.65402	+	3.65294i	−0.249669	+	0.343640i	−0.915395	−	0.402556i	$-0.868122\pi$
$113$	−2.65402	+	3.65294i	−0.249669	+	0.343640i	0.665726	+	0.746196i	$0.268122\pi$
$114$	15.2751	+	21.0243i	1.43064	+	1.96911i
$115$	−3.51011	+	10.8030i	−0.327320	+	1.00739i
$116$	−11.7228	−	3.80898i	−1.08844	−	0.353655i
$117$	2.09815	−	1.52440i	0.193974	−	0.140931i
$118$	5.37035	+	3.90179i	0.494381	+	0.359189i
$119$	7.05076	−	0.808626i	0.646343	−	0.0741267i
$120$	−1.08798			−0.0993182
$121$	−9.74433	−	5.10372i	−0.885849	−	0.463974i
$122$		−	8.64715i		−	0.782876i
$123$	−4.25775	−	13.1040i	−0.383908	−	1.18155i
$124$	0.738783	−	1.01685i	0.0663447	−	0.0913157i
$125$	−3.74788	−	5.15851i	−0.335220	−	0.461391i
$126$	1.49141	+	0.484589i	0.132865	+	0.0431706i
$127$	0.542194	−	1.66870i	0.0481119	−	0.148073i	−0.924114	−	0.382116i	$-0.875196\pi$
$127$	0.542194	−	1.66870i	0.0481119	−	0.148073i	0.972226	+	0.234043i	$0.0751955\pi$
$128$	1.36171	−	0.989340i	0.120359	−	0.0874461i
$129$	1.78609	−	2.45834i	0.157256	−	0.216445i
$130$	29.2530	−	9.50486i	2.56565	−	0.833631i
$131$		−	12.9515i		−	1.13158i	−0.824550	−	0.565789i	$-0.808572\pi$
$131$		−	12.9515i		−	1.13158i	0.824550	−	0.565789i	$-0.191428\pi$
$132$	11.3444	+	2.79106i	0.987404	+	0.242930i
$133$			12.1846i			1.05654i
$134$	3.21007	+	9.87958i	0.277308	+	0.853465i
$135$	10.6037	+	7.70406i	0.912624	+	0.663060i
$136$	0.790236	−	0.360839i	0.0677622	−	0.0309417i
$137$	1.15458	−	3.55344i	0.0986425	−	0.303590i	−0.889543	−	0.456851i	$-0.848977\pi$
$137$	1.15458	−	3.55344i	0.0986425	−	0.303590i	0.988186	+	0.153260i	$0.0489773\pi$
$138$	4.64307	−	14.2899i	0.395244	−	1.21644i
$139$	11.3282	+	15.5920i	0.960848	+	1.32249i	0.946537	+	0.322596i	$0.104555\pi$
$139$	11.3282	+	15.5920i	0.960848	+	1.32249i	0.0143110	+	0.999898i	$0.495445\pi$
$140$	7.31685	+	5.31600i	0.618387	+	0.449284i
$141$	3.15846	−	1.02625i	0.265990	−	0.0864255i
$142$			9.84109i			0.825846i
$143$	18.5795	−	1.35724i	1.55369	−	0.113498i
$144$	1.94026			0.161689
$145$	5.58374	+	17.1850i	0.463705	+	1.42714i
$146$	−10.8814	+	14.9770i	−0.900552	+	1.23950i
$147$	−4.41518	−	6.07697i	−0.364158	−	0.501220i
$148$	15.9601	+	5.18575i	1.31191	+	0.426266i
$149$	−4.51085	+	13.8830i	−0.369543	+	1.13734i	0.577543	+	0.816360i	$0.304011\pi$
$149$	−4.51085	+	13.8830i	−0.369543	+	1.13734i	−0.947087	+	0.320978i	$0.895989\pi$
$150$	−5.83163	−	8.02655i	−0.476151	−	0.655365i
$151$	−9.22766	−	6.70428i	−0.750936	−	0.545587i	0.145181	−	0.989405i	$-0.453624\pi$
$151$	−9.22766	−	6.70428i	−0.750936	−	0.545587i	−0.896117	+	0.443818i	$0.853624\pi$
$152$	0.460895	+	1.41849i	0.0373835	+	0.115055i
$153$	1.86582	+	0.378166i	0.150843	+	0.0305729i
$154$	7.26726	+	8.60633i	0.585613	+	0.693517i
$155$	−1.84253			−0.147996
$156$	−18.8168	+	6.11395i	−1.50655	+	0.489507i
$157$	3.58712	+	2.60620i	0.286284	+	0.207997i	0.721653	−	0.692254i	$-0.243382\pi$
$157$	3.58712	+	2.60620i	0.286284	+	0.207997i	−0.435370	+	0.900252i	$0.643382\pi$
$158$	−1.65277	−	2.27484i	−0.131487	−	0.180977i
$159$	7.38618	+	2.39992i	0.585762	+	0.190326i
$160$	20.7729	+	6.74953i	1.64224	+	0.533597i
$161$	5.69940	−	4.14085i	0.449175	−	0.326345i
$162$	−16.2375	−	11.7972i	−1.27574	−	0.926876i
$163$	−16.3599	+	5.31564i	−1.28140	+	0.416353i	−0.869074	−	0.494682i	$-0.835284\pi$
$163$	−16.3599	+	5.31564i	−1.28140	+	0.416353i	−0.412329	+	0.911035i	$0.635284\pi$
$164$			14.0201i			1.09479i
$165$	−6.46489	−	15.8591i	−0.503291	−	1.23463i
$166$	18.9353			1.46966
$167$	9.39223	−	3.05172i	0.726793	−	0.236149i	0.0778269	−	0.996967i	$-0.475202\pi$
$167$	9.39223	−	3.05172i	0.726793	−	0.236149i	0.648966	+	0.760818i	$0.275202\pi$
$168$	0.545896	+	0.396616i	0.0421168	+	0.0305996i
$169$	−15.0064	+	10.9028i	−1.15434	+	0.838676i
$170$	19.6596	+	11.1036i	1.50782	+	0.851610i
$171$	−1.01003	+	3.10855i	−0.0772388	+	0.237717i
$172$	−2.50147	+	1.81742i	−0.190735	+	0.138577i
$173$	11.3967	−	15.6862i	0.866476	−	1.19260i	−0.113510	−	0.993537i	$-0.536209\pi$
$173$	11.3967	−	15.6862i	0.866476	−	1.19260i	0.979986	−	0.199065i	$-0.0637905\pi$
$174$	−7.38601	−	22.7318i	−0.559932	−	1.72329i
$175$		−	4.65179i		−	0.351642i
$176$	11.8421	+	7.34872i	0.892635	+	0.553930i
$177$			6.25946i			0.470490i
$178$	−9.31998	−	28.6840i	−0.698562	−	2.14995i
$179$	0.377663	+	0.274388i	0.0282279	+	0.0205088i	0.601810	−	0.798639i	$-0.294447\pi$
$179$	0.377663	+	0.274388i	0.0282279	+	0.0205088i	−0.573582	+	0.819148i	$0.694447\pi$
$180$	1.42601	+	1.96274i	0.106289	+	0.146294i
$181$	−16.4158	−	5.33383i	−1.22018	−	0.396461i	−0.373033	−	0.927818i	$-0.621682\pi$
$181$	−16.4158	−	5.33383i	−1.22018	−	0.396461i	−0.847148	+	0.531358i	$0.821682\pi$
$182$	−18.1427	−	5.89492i	−1.34483	−	0.436961i
$183$	6.59664	−	4.79274i	0.487638	−	0.354290i
$184$	0.506870	−	0.697647i	0.0373670	−	0.0514312i
$185$	−7.60200	−	23.3966i	−0.558910	−	1.72015i
$186$	2.43724			0.178707
$187$	9.95550	+	9.37486i	0.728018	+	0.685558i
$188$	−3.37927			−0.246459
$189$	−2.51198	−	7.73108i	−0.182720	−	0.562353i
$190$	−22.7852	+	31.3612i	−1.65301	+	2.27518i
$191$	6.41790	−	4.66288i	0.464383	−	0.337394i	−0.330865	−	0.943678i	$-0.607341\pi$
$191$	6.41790	−	4.66288i	0.464383	−	0.337394i	0.795248	+	0.606284i	$0.207341\pi$
$192$	−12.6062	−	4.09602i	−0.909778	−	0.295605i
$193$	−19.4040	−	6.30476i	−1.39673	−	0.453826i	−0.488600	−	0.872508i	$-0.662492\pi$
$193$	−19.4040	−	6.30476i	−1.39673	−	0.453826i	−0.908133	+	0.418681i	$0.862492\pi$
$194$	7.48296	+	10.2994i	0.537245	+	0.739454i
$195$	23.4646	+	17.0480i	1.68034	+	1.22083i
$196$	2.36192	+	7.26925i	0.168709	+	0.519232i
$197$		−	9.06164i		−	0.645615i	−0.946465	−	0.322807i	$-0.895373\pi$
$197$		−	9.06164i		−	0.645615i	0.946465	−	0.322807i	$-0.104627\pi$
$198$	1.14062	+	2.79805i	0.0810600	+	0.198849i
$199$		−	12.6546i		−	0.897059i	−0.893768	−	0.448529i	$-0.851948\pi$
$199$		−	12.6546i		−	0.897059i	0.893768	−	0.448529i	$-0.148052\pi$
$200$	−0.175958	−	0.541543i	−0.0124421	−	0.0382929i
$201$	−5.75762	+	7.92468i	−0.406111	+	0.558964i
$202$	−7.84296	+	5.69824i	−0.551829	+	0.400927i
$203$	3.46304	−	10.6582i	0.243058	−	0.748056i
$204$	−12.6459	−	7.14235i	−0.885391	−	0.500064i
$205$	16.6274	−	12.0805i	1.16131	−	0.843742i
$206$	16.7668	+	12.1818i	1.16820	+	0.848745i
$207$	1.79728	−	0.583972i	0.124920	−	0.0405888i
$208$	−23.6029			−1.63657
$209$	−17.9382	+	15.1472i	−1.24081	+	1.04775i
$210$			17.5375i			1.21020i
$211$	−1.60030	+	0.519969i	−0.110169	+	0.0357962i	−0.363583	−	0.931562i	$-0.618447\pi$
$211$	−1.60030	+	0.519969i	−0.110169	+	0.0357962i	0.253414	+	0.967358i	$0.418447\pi$
$212$	−6.39330	−	4.64500i	−0.439094	−	0.319020i
$213$	−7.50746	+	5.45449i	−0.514403	+	0.373735i
$214$	28.3905	+	9.22464i	1.94074	+	0.630583i
$215$	4.31083	+	1.40067i	0.293996	+	0.0955250i
$216$	−0.584870	−	0.805005i	−0.0397954	−	0.0547736i
$217$	0.924496	+	0.671686i	0.0627589	+	0.0455970i
$218$	0.780383	−	0.253562i	0.0528542	−	0.0171734i
$219$	−17.4566			−1.17961
$220$	1.26964	+	17.3803i	0.0855992	+	1.17178i
$221$	−22.6973	−	4.60031i	−1.52679	−	0.309450i
$222$	10.0557	+	30.9483i	0.674894	+	2.07711i
$223$	17.4087	+	12.6482i	1.16578	+	0.846985i	0.990497	−	0.137534i	$-0.0439176\pi$
$223$	17.4087	+	12.6482i	1.16578	+	0.846985i	0.175278	+	0.984519i	$0.443918\pi$
$224$	−7.96237	−	10.9593i	−0.532008	−	0.732247i
$225$	0.385603	−	1.18676i	0.0257069	−	0.0791176i
$226$	8.47317	+	2.75310i	0.563627	+	0.183133i
$227$	−8.08289	−	11.1251i	−0.536480	−	0.738402i	0.451620	−	0.892210i	$-0.350846\pi$
$227$	−8.08289	−	11.1251i	−0.536480	−	0.738402i	−0.988101	+	0.153808i	$0.950846\pi$
$228$	14.6565	−	20.1729i	0.970648	−	1.33598i
$229$	−0.720066	−	2.21614i	−0.0475833	−	0.146446i	0.924442	−	0.381323i	$-0.124531\pi$
$229$	−0.720066	−	2.21614i	−0.0475833	−	0.146446i	−0.972025	+	0.234877i	$0.924531\pi$
$230$	22.4126			1.47785
$231$	−2.53757	+	10.3141i	−0.166960	+	0.678617i
$232$		−	1.37177i		−	0.0900614i
$233$	6.83581	−	2.22109i	0.447829	−	0.145508i	−0.0764160	−	0.997076i	$-0.524348\pi$
$233$	6.83581	−	2.22109i	0.447829	−	0.145508i	0.524245	+	0.851568i	$0.324348\pi$
$234$	−4.13992	−	3.00783i	−0.270635	−	0.196628i
$235$	2.91178	+	4.00772i	0.189943	+	0.261435i
$236$	1.96822	−	6.05755i	0.128120	−	0.394313i
$237$	0.819348	−	2.52169i	0.0532224	−	0.163802i
$238$	−5.81648	−	12.7381i	−0.377027	−	0.825687i
$239$	15.2993	+	11.1156i	0.989632	+	0.719010i	0.959840	−	0.280546i	$-0.0905157\pi$
$239$	15.2993	+	11.1156i	0.989632	+	0.719010i	0.0297915	+	0.999556i	$0.490516\pi$
$240$	6.70531	+	20.6368i	0.432826	+	1.33210i
$241$			11.7200i			0.754953i	0.926019	+	0.377477i	$0.123208\pi$
$241$			11.7200i			0.754953i	−0.926019	+	0.377477i	$0.876792\pi$
$242$	−3.63599	+	21.3976i	−0.233731	+	1.37549i
$243$		−	4.75782i		−	0.305214i
$244$	−7.89088	+	2.56390i	−0.505162	+	0.164137i
$245$	6.58595	−	9.06478i	0.420761	−	0.579128i
$246$	−21.9943	+	15.9798i	−1.40230	+	1.01883i
$247$	12.2868	−	37.8148i	0.781790	−	2.40610i
$248$	0.133033	+	0.0432252i	0.00844763	+	0.00274480i
$249$	10.4950	+	14.4451i	0.665094	+	0.915424i
$250$	−7.39502	+	10.1784i	−0.467702	+	0.643737i
$251$	−8.50112	−	26.1638i	−0.536586	−	1.65144i	−0.740197	−	0.672390i	$-0.765268\pi$
$251$	−8.50112	−	26.1638i	−0.536586	−	1.65144i	0.203611	−	0.979052i	$-0.434732\pi$
$252$		−	1.50466i		−	0.0947844i
$253$	13.1813	+	3.24298i	0.828698	+	0.203884i
$254$	−3.46199			−0.217225
$255$	2.42584	+	21.1519i	0.151912	+	1.32459i
$256$	−14.2139	−	10.3270i	−0.888371	−	0.645439i
$257$	0.0684122	−	0.0497044i	0.00426744	−	0.00310047i	−0.585649	−	0.810564i	$-0.699160\pi$
$257$	0.0684122	−	0.0497044i	0.00426744	−	0.00310047i	0.589917	+	0.807464i	$0.299160\pi$
$258$	−5.70223	−	1.85277i	−0.355005	−	0.115348i
$259$	−4.71477	+	14.5106i	−0.292962	+	0.901643i
$260$	−17.3471	−	23.8763i	−1.07582	−	1.48075i
$261$	1.76698	−	2.43204i	0.109374	−	0.150540i
$262$	−24.3042	+	7.89690i	−1.50152	+	0.487872i
$263$	−13.7258			−0.846369			−0.423185	−	0.906043i	$-0.639088\pi$
$263$	−13.7258			−0.846369			−0.423185	+	0.906043i	$0.639088\pi$
$264$	0.0947255	+	1.29671i	0.00582995	+	0.0798071i
$265$			11.5847i			0.711641i
$266$	22.8651	−	7.42933i	1.40195	−	0.455521i
$267$	16.7164	−	23.0082i	1.02303	−	1.40808i
$268$	8.06373	−	5.85864i	0.492570	−	0.357873i
$269$	−13.1480	−	4.27205i	−0.801649	−	0.260471i	−0.120592	−	0.992702i	$-0.538479\pi$
$269$	−13.1480	−	4.27205i	−0.801649	−	0.260471i	−0.681057	+	0.732231i	$0.738479\pi$
$270$	7.99168	−	24.5959i	0.486358	−	1.49686i
$271$	4.03204	−	2.92945i	0.244929	−	0.177951i	−0.458548	−	0.888670i	$-0.651630\pi$
$271$	4.03204	−	2.92945i	0.244929	−	0.177951i	0.703476	+	0.710719i	$0.251630\pi$
$272$	−11.7147	−	12.7654i	−0.710309	−	0.774014i
$273$	−5.55866	−	17.1078i	−0.336426	−	1.03541i
$274$	−7.37219			−0.445370
$275$	6.84833	−	5.78280i	0.412970	−	0.348716i
$276$	−14.4168			−0.867790
$277$	28.9671	−	9.41197i	1.74046	−	0.565510i	0.745568	−	0.666430i	$-0.232178\pi$
$277$	28.9671	−	9.41197i	1.74046	−	0.565510i	0.994895	+	0.100919i	$0.0321784\pi$
$278$	22.3520	−	30.7649i	1.34058	−	1.84515i
$279$	0.180179	+	0.247995i	0.0107870	+	0.0148471i
$280$	−0.311032	+	0.957257i	−0.0185877	+	0.0572070i
$281$	−4.15948	+	12.8016i	−0.248134	+	0.763677i	0.746972	+	0.664856i	$0.231507\pi$
$281$	−4.15948	+	12.8016i	−0.248134	+	0.763677i	−0.995105	+	0.0988210i	$0.968493\pi$
$282$	−3.85161	−	5.30129i	−0.229360	−	0.315687i
$283$	−0.487102	+	0.670439i	−0.0289552	+	0.0398535i	−0.823249	−	0.567680i	$-0.807841\pi$
$283$	−0.487102	+	0.670439i	−0.0289552	+	0.0398535i	0.794294	+	0.607534i	$0.207841\pi$
$284$	8.98039	−	2.91791i	0.532888	−	0.173146i
$285$	−36.5533			−2.16523
$286$	−13.8754	−	34.0378i	−0.820467	−	2.01270i
$287$	−12.7468			−0.752419
$288$	−1.12291	−	3.45596i	−0.0661680	−	0.203644i
$289$	−8.77723	−	14.5589i	−0.516308	−	0.856403i
$290$	28.8440	−	20.9564i	1.69378	−	1.23060i
$291$	−3.70962	+	11.4170i	−0.217462	+	0.669278i
$292$	16.8935	+	5.48903i	0.988616	+	0.321221i
$293$	−19.8017	+	14.3868i	−1.15683	+	0.840486i	−0.989374	−	0.145393i	$-0.953555\pi$
$293$	−19.8017	+	14.3868i	−1.15683	+	0.840486i	−0.167456	+	0.985880i	$0.553555\pi$
$294$	−8.71169	+	11.9906i	−0.508076	+	0.699307i
$295$	−8.88001	+	2.88529i	−0.517014	+	0.167988i
$296$			1.86761i			0.108552i
$297$	8.25892	−	13.3089i	0.479231	−	0.772260i
$298$	28.8025			1.66849
$299$	−21.8635	+	7.10390i	−1.26440	+	0.410829i
$300$	−5.59547	+	7.70150i	−0.323054	+	0.444646i
$301$	−1.65236	−	2.27428i	−0.0952406	−	0.131087i
$302$	−6.95457	+	21.4040i	−0.400191	+	1.23166i
$303$	−8.69403	−	2.82486i	−0.499459	−	0.162284i
$304$	24.0655	−	17.4846i	1.38025	−	1.00281i
$305$	9.83995	+	7.14914i	0.563434	+	0.409359i
$306$	−0.427997	−	3.73189i	−0.0244669	−	0.213338i
$307$	−8.21980			−0.469129			−0.234564	−	0.972101i	$-0.575366\pi$
$307$	−8.21980			−0.469129			−0.234564	+	0.972101i	$0.575366\pi$
$308$	5.69886	−	9.18347i	0.324723	−	0.523277i
$309$			19.5427i			1.11174i
$310$	1.12344	+	3.45761i	0.0638073	+	0.196379i
$311$	12.2970	−	16.9254i	0.697299	−	0.959749i	−0.302679	−	0.953093i	$-0.597881\pi$
$311$	12.2970	−	16.9254i	0.697299	−	0.959749i	0.999978	−	0.00665688i	$-0.00211897\pi$
$312$	−1.29424	−	1.78136i	−0.0732717	−	0.100850i
$313$	−6.77982	−	2.20290i	−0.383218	−	0.124515i	0.111072	−	0.993812i	$-0.464572\pi$
$313$	−6.77982	−	2.20290i	−0.383218	−	0.124515i	−0.494290	+	0.869297i	$0.664572\pi$
$314$	2.70349	−	8.32050i	0.152567	−	0.469553i
$315$	−1.78448	+	1.29650i	−0.100544	+	0.0730494i
$316$	−1.58584	+	2.18272i	−0.0892103	+	0.122787i
$317$	−1.59680	+	0.518832i	−0.0896852	+	0.0291405i	−0.353516	−	0.935429i	$-0.615014\pi$
$317$	−1.59680	+	0.518832i	−0.0896852	+	0.0291405i	0.263831	+	0.964569i	$0.415014\pi$
$318$		−	15.3238i		−	0.859319i
$319$	19.9959	−	8.15124i	1.11956	−	0.456382i
$320$		−	19.7720i		−	1.10529i
$321$	8.69844	+	26.7711i	0.485500	+	1.49421i
$322$	−11.2456	−	8.17042i	−0.626694	−	0.455320i
$323$	26.5500	−	12.1233i	1.47728	−	0.674558i
$324$	−5.95099	+	18.3152i	−0.330610	+	1.01751i
$325$	−4.69078	+	14.4367i	−0.260198	+	0.800807i
$326$	19.9501	+	27.4590i	1.10494	+	1.52081i
$327$	0.625967	+	0.454791i	0.0346160	+	0.0251500i
$328$	−1.48393	+	0.482158i	−0.0819364	+	0.0266227i
$329$		−	3.07236i		−	0.169385i
$330$	−25.8185	+	21.8014i	−1.42126	+	1.20013i
$331$	9.33395			0.513041			0.256520	−	0.966539i	$-0.417424\pi$
$331$	9.33395			0.513041			0.256520	+	0.966539i	$0.417424\pi$
$332$	−5.61436	−	17.2792i	−0.308128	−	0.948321i
$333$	−2.40566	+	3.31111i	−0.131830	+	0.181448i
$334$	−11.4534	−	15.7643i	−0.626704	−	0.862584i
$335$	−13.8963	−	4.51520i	−0.759239	−	0.246692i
$336$	4.15864	−	12.7990i	0.226872	−	0.698241i
$337$	14.3636	+	19.7697i	0.782433	+	1.07693i	0.995009	+	0.0997819i	$0.0318145\pi$
$337$	14.3636	+	19.7697i	0.782433	+	1.07693i	−0.212577	+	0.977144i	$0.568185\pi$
$338$	29.6095	+	21.5125i	1.61054	+	1.17013i
$339$	2.59606	+	7.98984i	0.140998	+	0.433949i
$340$	4.30340	−	21.2324i	0.233385	−	1.15149i
$341$	0.160421	+	2.19603i	0.00868730	+	0.118922i
$342$	6.44920			0.348733
$343$	−18.0682	+	5.87072i	−0.975593	+	0.316989i
$344$	−0.278388	−	0.202261i	−0.0150097	−	0.0109052i
$345$	12.4224	+	17.0979i	0.668797	+	0.920520i
$346$	−36.3849	−	11.8222i	−1.95607	−	0.635564i
$347$	28.8622	+	9.37789i	1.54940	+	0.503432i	0.953952	−	0.299960i	$-0.0969732\pi$
$347$	28.8622	+	9.37789i	1.54940	+	0.503432i	0.595452	+	0.803391i	$0.296973\pi$
$348$	−18.5537	+	13.4801i	−0.994584	+	0.722607i
$349$	−3.25522	−	2.36506i	−0.174248	−	0.126599i	0.497243	−	0.867611i	$-0.334346\pi$
$349$	−3.25522	−	2.36506i	−0.174248	−	0.126599i	−0.671491	+	0.741013i	$0.734346\pi$
$350$	−8.72932	+	2.83633i	−0.466602	+	0.151608i
$351$			26.5263i			1.41587i
$352$	6.23586	−	25.3460i	0.332373	−	1.35095i
$353$	6.53194			0.347660			0.173830	−	0.984776i	$-0.444386\pi$
$353$	6.53194			0.347660			0.173830	+	0.984776i	$0.444386\pi$
$354$	11.7462	−	3.81657i	0.624304	−	0.202849i
$355$	−11.1986	−	8.13625i	−0.594359	−	0.431827i
$356$	−23.4119	+	17.0097i	−1.24083	+	0.901514i
$357$	6.49366	−	11.4974i	0.343681	−	0.608506i
$358$	0.284632	−	0.876008i	0.0150433	−	0.0462984i
$359$	−6.03700	+	4.38614i	−0.318621	+	0.231492i	−0.735587	−	0.677431i	$-0.763093\pi$
$359$	−6.03700	+	4.38614i	−0.318621	+	0.231492i	0.416966	+	0.908922i	$0.363093\pi$
$360$	−0.158701	+	0.218433i	−0.00836427	+	0.0115124i
$361$	9.61363	+	29.5877i	0.505980	+	1.55725i
$362$			34.0574i			1.79002i
$363$	−18.3389	+	9.08600i	−0.962541	+	0.476891i
$364$			18.3038i			0.959381i
$365$	−8.04658	−	24.7648i	−0.421177	−	1.29625i
$366$	−13.0160	−	9.45667i	−0.680357	−	0.494308i
$367$	17.3365	+	23.8617i	0.904960	+	1.24557i	0.968859	+	0.247614i	$0.0796464\pi$
$367$	17.3365	+	23.8617i	0.904960	+	1.24557i	−0.0638992	+	0.997956i	$0.520354\pi$
$368$	−16.3569	−	5.31468i	−0.852663	−	0.277047i
$369$	−3.25196	−	1.05663i	−0.169290	−	0.0550057i
$370$	−39.2697	+	28.5311i	−2.04153	+	1.48326i
$371$	4.22313	−	5.81265i	0.219254	−	0.301778i
$372$	−0.722649	−	2.22408i	−0.0374676	−	0.115313i
$373$	37.6341			1.94862			0.974311	−	0.225208i	$-0.0723061\pi$
$373$	37.6341			1.94862			0.974311	+	0.225208i	$0.0723061\pi$
$374$	11.5223	−	24.3981i	0.595802	−	1.26160i
$375$	−11.8635			−0.612629
$376$	−0.116215	−	0.357672i	−0.00599332	−	0.0184455i
$377$	−21.4950	+	29.5853i	−1.10705	+	1.52372i
$378$	−12.9761	+	9.42772i	−0.667421	+	0.484910i
$379$	2.23572	+	0.726429i	0.114841	+	0.0373141i	0.365874	−	0.930664i	$-0.380770\pi$
$379$	2.23572	+	0.726429i	0.114841	+	0.0373141i	−0.251033	+	0.967979i	$0.580770\pi$
$380$	35.3742	+	11.4938i	1.81466	+	0.589619i
$381$	−1.91883	−	2.64105i	−0.0983048	−	0.135305i
$382$	−12.6633	−	9.20043i	−0.647911	−	0.470735i
$383$	8.26950	+	25.4509i	0.422552	+	1.30048i	0.905319	+	0.424732i	$0.139632\pi$
$383$	8.26950	+	25.4509i	0.422552	+	1.30048i	−0.482768	+	0.875748i	$0.660368\pi$
$384$		−	3.13165i		−	0.159811i
$385$	−15.8018	+	1.15433i	−0.805334	+	0.0588301i
$386$			40.2569i			2.04902i
$387$	−0.233028	−	0.717185i	−0.0118455	−	0.0364566i
$388$	7.17992	−	9.88231i	0.364505	−	0.501698i
$389$	13.3753	−	9.71771i	0.678154	−	0.492707i	−0.194591	−	0.980884i	$-0.562338\pi$
$389$	13.3753	−	9.71771i	0.678154	−	0.492707i	0.872745	+	0.488177i	$0.162338\pi$
$390$	17.6845	−	54.4272i	0.895488	−	2.75603i
$391$	−14.6935	−	8.29881i	−0.743082	−	0.419689i
$392$	−0.688172	+	0.499986i	−0.0347579	+	0.0252531i
$393$	−19.4950	−	14.1640i	−0.983395	−	0.714478i
$394$	−17.0046	+	5.52514i	−0.856681	+	0.278353i
$395$	3.95509			0.199002
$396$	2.21514	−	1.87049i	0.111315	−	0.0939956i
$397$		−	32.2354i		−	1.61785i	−0.587914	−	0.808924i	$-0.700051\pi$
$397$		−	32.2354i		−	1.61785i	0.587914	−	0.808924i	$-0.299949\pi$
$398$	−23.7470	+	7.71586i	−1.19033	+	0.386761i
$399$	18.3408	+	13.3253i	0.918186	+	0.667101i
$400$	−9.18758	+	6.67517i	−0.459379	+	0.333758i
$401$	1.71770	+	0.558114i	0.0857777	+	0.0278709i	0.351591	−	0.936154i	$-0.385641\pi$
$401$	1.71770	+	0.558114i	0.0857777	+	0.0278709i	−0.265814	+	0.964024i	$0.585641\pi$
$402$	18.3817	+	5.97257i	0.916794	+	0.297884i
$403$	−2.19184	−	3.01681i	−0.109183	−	0.150278i
$404$	7.52534	+	5.46748i	0.374400	+	0.272017i
$405$	26.8491	−	8.72379i	1.33414	−	0.433489i
$406$	−22.1121			−1.09741
$407$	−27.2235	+	11.0975i	−1.34942	+	0.550084i
$408$	0.321068	−	1.58411i	0.0158953	−	0.0784251i
$409$	−1.39681	−	4.29893i	−0.0690677	−	0.212568i	0.910565	−	0.413365i	$-0.135647\pi$
$409$	−1.39681	−	4.29893i	−0.0690677	−	0.212568i	−0.979633	+	0.200797i	$0.935647\pi$
$410$	−32.8080	−	23.8364i	−1.62027	−	1.17720i
$411$	−4.08608	−	5.62401i	−0.201552	−	0.277412i
$412$	6.14498	−	18.9123i	0.302742	−	0.931743i
$413$	5.50739	+	1.78946i	0.271001	+	0.0880536i
$414$	−2.19171	−	3.01663i	−0.107717	−	0.148259i
$415$	−15.6550	+	21.5473i	−0.768474	+	1.05771i
$416$	13.6600	+	42.0410i	0.669734	+	2.06123i
$417$	35.8583			1.75599
$418$	39.3618	+	24.4262i	1.92525	+	1.19473i
$419$		−	15.8899i		−	0.776274i	−0.921602	−	0.388137i	$-0.873119\pi$
$419$		−	15.8899i		−	0.776274i	0.921602	−	0.388137i	$-0.126881\pi$
$420$	16.0037	−	5.19990i	0.780899	−	0.253729i
$421$	13.8601	+	10.0699i	0.675498	+	0.490778i	0.871861	−	0.489753i	$-0.162913\pi$
$421$	13.8601	+	10.0699i	0.675498	+	0.490778i	−0.196363	+	0.980531i	$0.562913\pi$
$422$	1.95150	+	2.68601i	0.0949975	+	0.130753i
$423$	0.254679	−	0.783820i	0.0123829	−	0.0381107i
$424$	0.271773	−	0.836430i	0.0131984	−	0.0406206i
$425$	−10.1361	+	4.62836i	−0.491673	+	0.224509i
$426$	14.8131	+	10.7624i	0.717699	+	0.521439i
$427$	−2.33104	−	7.17421i	−0.112807	−	0.347184i
$428$		−	28.6426i		−	1.38449i
$429$	18.2758	−	29.4507i	0.882366	−	1.42190i
$430$		−	8.94352i		−	0.431295i
$431$	22.6608	−	7.36295i	1.09153	−	0.354661i	0.292695	−	0.956206i	$-0.405448\pi$
$431$	22.6608	−	7.36295i	1.09153	−	0.354661i	0.798839	+	0.601545i	$0.205448\pi$
$432$	−11.6648	+	16.0552i	−0.561221	+	0.772455i
$433$	−26.1427	+	18.9938i	−1.25634	+	0.912784i	−0.998572	−	0.0534230i	$-0.982987\pi$
$433$	−26.1427	+	18.9938i	−1.25634	+	0.912784i	−0.257767	+	0.966207i	$0.582987\pi$
$434$	0.696761	−	2.14441i	0.0334456	−	0.102935i
$435$	31.9739	+	10.3890i	1.53303	+	0.498112i
$436$	−0.462771	−	0.636949i	−0.0221627	−	0.0305043i
$437$	17.0296	−	23.4392i	0.814636	−	1.12125i
$438$	10.6438	+	32.7582i	0.508579	+	1.56525i
$439$		−	23.8682i		−	1.13917i	−0.821933	−	0.569585i	$-0.807104\pi$
$439$		−	23.8682i		−	1.13917i	0.821933	−	0.569585i	$-0.192896\pi$
$440$	−1.79592	+	0.732100i	−0.0856172	+	0.0349015i
$441$	−1.86411			−0.0887669
$442$	5.20649	+	45.3977i	0.247648	+	2.15935i
$443$	−0.576124	−	0.418579i	−0.0273725	−	0.0198873i	0.574015	−	0.818845i	$-0.305385\pi$
$443$	−0.576124	−	0.418579i	−0.0273725	−	0.0198873i	−0.601387	+	0.798958i	$0.705385\pi$
$444$	25.2600	−	18.3525i	1.19879	−	0.870970i
$445$	40.3461	+	13.1092i	1.91259	+	0.621438i
$446$	13.1204	−	40.3804i	0.621268	−	1.91207i
$447$	15.9640	+	21.9725i	0.755071	+	1.03927i
$448$	−7.20777	+	9.92064i	−0.340535	+	0.468706i
$449$	12.3223	−	4.00377i	0.581527	−	0.188949i	−0.00345771	−	0.999994i	$-0.501101\pi$
$449$	12.3223	−	4.00377i	0.581527	−	0.188949i	0.584984	+	0.811045i	$0.301101\pi$
$450$	−2.46214			−0.116066
$451$	−15.8460	−	18.7657i	−0.746157	−	0.883644i
$452$		−	8.54842i		−	0.402084i
$453$	−20.1830	+	6.55787i	−0.948282	+	0.308116i
$454$	−15.9485	+	21.9513i	−0.748502	+	1.03023i
$455$	21.7078	−	15.7716i	1.01768	−	0.739386i
$456$	2.63920	+	0.857529i	0.123592	+	0.0401575i
$457$	−7.37269	+	22.6908i	−0.344880	+	1.06143i	0.616768	+	0.787145i	$0.288442\pi$
$457$	−7.37269	+	22.6908i	−0.344880	+	1.06143i	−0.961648	+	0.274286i	$0.911558\pi$
$458$	−3.71965	+	2.70248i	−0.173808	+	0.126279i
$459$	−14.3465	+	13.1657i	−0.669635	+	0.614521i
$460$	−6.64541	−	20.4525i	−0.309844	−	0.953601i
$461$	25.1167			1.16980			0.584902	−	0.811104i	$-0.301133\pi$
$461$	25.1167			1.16980			0.584902	+	0.811104i	$0.301133\pi$
$462$	20.9021	−	1.52691i	0.972456	−	0.0710384i
$463$	−9.14027			−0.424784			−0.212392	−	0.977185i	$-0.568125\pi$
$463$	−9.14027			−0.424784			−0.212392	+	0.977185i	$0.568125\pi$
$464$	−26.0199	+	8.45438i	−1.20794	+	0.392485i
$465$	−2.01502	+	2.77344i	−0.0934445	+	0.128615i
$466$	−8.33598	−	11.4735i	−0.386157	−	0.531499i
$467$	4.41597	−	13.5910i	0.204347	−	0.628915i	−0.795393	−	0.606094i	$-0.792735\pi$
$467$	4.41597	−	13.5910i	0.204347	−	0.628915i	0.999740	−	0.0228204i	$-0.00726459\pi$
$468$	−1.51727	+	4.66967i	−0.0701358	+	0.215856i
$469$	5.32655	+	7.33136i	0.245957	+	0.338531i
$470$	5.74530	−	7.90772i	0.265011	−	0.364756i
$471$	7.84588	−	2.54928i	0.361519	−	0.117465i
$472$	0.708838			0.0326269
$473$	1.29407	−	5.25984i	0.0595016	−	0.241847i
$474$	−5.23167			−0.240298
$475$	−5.91176	−	18.1945i	−0.271250	−	0.834822i
$476$	−9.89942	+	9.08465i	−0.453739	+	0.416394i
$477$	1.55924	−	1.13285i	0.0713926	−	0.0518697i
$478$	11.5306	−	35.4875i	0.527397	−	1.62316i
$479$	−6.12204	−	1.98917i	−0.279723	−	0.0908875i	0.165796	−	0.986160i	$-0.446981\pi$
$479$	−6.12204	−	1.98917i	−0.279723	−	0.0908875i	−0.445519	+	0.895273i	$0.646981\pi$
$480$	32.8772	−	23.8867i	1.50063	−	1.09027i
$481$	29.2644	−	40.2790i	1.33434	−	1.83657i
$482$	21.9932	−	7.14604i	1.00176	−	0.325493i
$483$		−	13.1074i		−	0.596409i
$484$	20.6043	−	3.02646i	0.936559	−	0.137566i
$485$	−17.9068			−0.813104
$486$	−8.92830	+	2.90098i	−0.404996	+	0.131591i
$487$	0.0753012	−	0.103643i	0.00341222	−	0.00469652i	−0.807307	−	0.590131i	$-0.799076\pi$
$487$	0.0753012	−	0.103643i	0.00341222	−	0.00469652i	0.810720	+	0.585435i	$0.199076\pi$
$488$	−0.542742	−	0.747020i	−0.0245688	−	0.0338160i
$489$	−9.89013	+	30.4387i	−0.447247	+	1.37648i
$490$	−21.0262	−	6.83182i	−0.949866	−	0.308630i
$491$	−9.96691	+	7.24138i	−0.449800	+	0.326799i	−0.789517	−	0.613729i	$-0.789669\pi$
$491$	−9.96691	+	7.24138i	−0.449800	+	0.326799i	0.339717	+	0.940528i	$0.389669\pi$
$492$	21.1036	+	15.3326i	0.951422	+	0.691249i
$493$	−26.6694	+	3.05862i	−1.20113	+	0.137753i
$494$	−78.4531			−3.52977
$495$	−4.12704	−	1.01537i	−0.185497	−	0.0456377i
$496$		−	2.78979i		−	0.125265i
$497$	2.65290	+	8.16478i	0.118999	+	0.366240i
$498$	20.7080	−	28.5021i	0.927946	−	1.27721i
$499$	2.54379	+	3.50122i	0.113876	+	0.156736i	0.862150	−	0.506653i	$-0.169117\pi$
$499$	2.54379	+	3.50122i	0.113876	+	0.156736i	−0.748275	+	0.663389i	$0.769117\pi$
$500$	11.4808	+	3.73035i	0.513438	+	0.166826i
$501$	5.67795	−	17.4749i	0.253672	−	0.780722i
$502$	−43.9143	+	31.9056i	−1.95999	+	1.42402i
$503$	−18.2028	+	25.0541i	−0.811625	+	1.11711i	0.179446	+	0.983768i	$0.442570\pi$
$503$	−18.2028	+	25.0541i	−0.811625	+	1.11711i	−0.991071	+	0.133338i	$0.957430\pi$
$504$	0.159257	−	0.0517458i	0.00709388	−	0.00230494i
$505$		−	13.6359i		−	0.606791i
$506$	−1.95137	−	26.7127i	−0.0867491	−	1.18752i
$507$			34.5116i			1.53272i
$508$	1.02649	+	3.15921i	0.0455431	+	0.140167i
$509$	−12.1400	−	8.82026i	−0.538098	−	0.390951i	0.285280	−	0.958444i	$-0.407913\pi$
$509$	−12.1400	−	8.82026i	−0.538098	−	0.390951i	−0.823378	+	0.567493i	$0.807913\pi$
$510$	38.2136	−	17.4492i	1.69213	−	0.772662i
$511$	−4.99050	+	15.3592i	−0.220767	+	0.679450i
$512$	−9.67231	+	29.7683i	−0.427460	+	1.31559i
$513$	−19.6502	−	27.0462i	−0.867577	−	1.19412i
$514$	−0.134986	−	0.0980729i	−0.00595397	−	0.00432581i
$515$	−27.7243	+	9.00818i	−1.22168	+	0.396948i
$516$			5.75287i			0.253256i
$517$	4.52311	−	3.81936i	0.198926	−	0.167975i
$518$	30.1046			1.32272
$519$	−11.1478	−	34.3095i	−0.489335	−	1.50602i
$520$	1.93056	−	2.65719i	0.0846608	−	0.116526i
$521$	9.32624	+	12.8365i	0.408590	+	0.562376i	0.962874	−	0.269952i	$-0.0870078\pi$
$521$	9.32624	+	12.8365i	0.408590	+	0.562376i	−0.554284	+	0.832328i	$0.687008\pi$
$522$	−5.64124	−	1.83295i	−0.246910	−	0.0802260i
$523$	2.47713	−	7.62381i	0.108317	−	0.333366i	−0.882177	−	0.470917i	$-0.843923\pi$
$523$	2.47713	−	7.62381i	0.108317	−	0.333366i	0.990495	+	0.137551i	$0.0439231\pi$
$524$	14.4125	+	19.8371i	0.629613	+	0.866587i
$525$	−7.00203	−	5.08727i	−0.305594	−	0.222027i
$526$	8.36902	+	25.7572i	0.364906	+	1.12307i
$527$	0.543742	−	2.68275i	0.0236858	−	0.116863i
$528$	24.0123	−	9.78852i	1.04500	−	0.425991i
$529$	6.24887			0.271690
$530$	21.7392	−	7.06351i	0.944292	−	0.306819i
$531$	1.25671	+	0.913055i	0.0545366	+	0.0396232i
$532$	−13.5591	−	18.6626i	−0.587863	−	0.809124i
$533$	39.5594	+	12.8536i	1.71351	+	0.556753i
$534$	−53.3686	−	17.3405i	−2.30948	−	0.750397i
$535$	−33.9693	+	24.6802i	−1.46862	+	1.06702i
$536$	0.897411	+	0.652007i	0.0387623	+	0.0281624i
$537$	0.826038	−	0.268396i	0.0356462	−	0.0115821i
$538$			27.2777i			1.17603i
$539$	−11.3773	−	7.06027i	−0.490056	−	0.304108i
$540$	−24.8143			−1.06784
$541$	−3.34886	+	1.08811i	−0.143979	+	0.0467815i	−0.380120	−	0.924937i	$-0.624117\pi$
$541$	−3.34886	+	1.08811i	−0.143979	+	0.0467815i	0.236141	+	0.971719i	$0.424117\pi$
$542$	−7.95571	−	5.78016i	−0.341727	−	0.248279i
$543$	−25.9813	+	18.8765i	−1.11496	+	0.810069i
$544$	−15.9576	+	28.2539i	−0.684178	+	1.21137i
$545$	−0.356653	+	1.09767i	−0.0152773	+	0.0470188i
$546$	−28.7144	+	20.8622i	−1.22886	+	0.892822i
$547$	8.68497	−	11.9538i	0.371343	−	0.511109i	−0.581923	−	0.813244i	$-0.697699\pi$
$547$	8.68497	−	11.9538i	0.371343	−	0.511109i	0.953265	+	0.302135i	$0.0976993\pi$
$548$	2.18587	+	6.72743i	0.0933759	+	0.287381i
$549$		−	2.02351i		−	0.0863614i
$550$	−15.0273	−	9.32532i	−0.640768	−	0.397633i
$551$		−	46.0882i		−	1.96342i
$552$	−0.495801	−	1.52592i	−0.0211027	−	0.0649474i
$553$	−1.98448	−	1.44181i	−0.0843886	−	0.0613119i
$554$	−35.3241	−	48.6195i	−1.50078	−	2.06564i
$555$	−43.5310	−	14.1441i	−1.84779	−	0.600383i
$556$	−34.7016	−	11.2752i	−1.47168	−	0.478177i
$557$	27.8054	−	20.2018i	1.17815	−	0.855977i	0.186190	−	0.982514i	$-0.440386\pi$
$557$	27.8054	−	20.2018i	1.17815	−	0.855977i	0.991962	+	0.126536i	$0.0403860\pi$
$558$	0.355516	−	0.489325i	0.0150502	−	0.0207148i
$559$	2.83473	+	8.72441i	0.119896	+	0.369003i
$560$	20.0742			0.848291
$561$	24.9989	−	4.73286i	1.05545	−	0.199822i
$562$	26.5589			1.12032
$563$	0.708455	+	2.18040i	0.0298578	+	0.0918929i	0.964875	−	0.262710i	$-0.0846162\pi$
$563$	0.708455	+	2.18040i	0.0298578	+	0.0918929i	−0.935017	+	0.354603i	$0.884616\pi$
$564$	−3.69563	+	5.08660i	−0.155614	+	0.214184i
$565$	−10.1382	+	7.36581i	−0.426516	+	0.309882i
$566$	1.55511	+	0.505287i	0.0653663	+	0.0212388i
$567$	−16.6518	−	5.41050i	−0.699311	−	0.227220i
$568$	0.617680	+	0.850164i	0.0259173	+	0.0356721i
$569$	4.84795	+	3.52225i	0.203237	+	0.147660i	0.684748	−	0.728780i	$-0.259912\pi$
$569$	4.84795	+	3.52225i	0.203237	+	0.147660i	−0.481512	+	0.876440i	$0.659912\pi$
$570$	22.2876	+	68.5942i	0.933526	+	2.87310i
$571$		−	5.39894i		−	0.225939i	−0.993598	−	0.112969i	$-0.963964\pi$
$571$		−	5.39894i		−	0.225939i	0.993598	−	0.112969i	$-0.0360362\pi$
$572$	−26.9468	+	22.7541i	−1.12670	+	0.951398i
$573$		−	14.7598i		−	0.616601i
$574$	7.77208	+	23.9200i	0.324400	+	0.998401i
$575$	−6.50147	+	8.94850i	−0.271130	+	0.373178i
$576$	−2.66120	+	1.93348i	−0.110883	+	0.0805616i
$577$	12.8482	−	39.5426i	0.534877	−	1.64618i	−0.209039	−	0.977907i	$-0.567034\pi$
$577$	12.8482	−	39.5426i	0.534877	−	1.64618i	0.743916	−	0.668274i	$-0.232966\pi$
$578$	−21.9687	+	25.3479i	−0.913778	+	1.05433i
$579$	−30.7107	+	22.3126i	−1.27629	+	0.927282i
$580$	−27.6759	−	20.1077i	−1.14918	−	0.834926i
$581$	15.7099	−	5.10445i	0.651756	−	0.211768i
$582$	23.6865			0.981838
$583$	13.8073	−	1.00863i	0.571838	−	0.0417731i
$584$			1.97683i			0.0818017i
$585$	6.84546	−	2.22423i	0.283025	−	0.0919604i
$586$	39.0713	+	28.3869i	1.61402	+	1.17265i
$587$	6.53751	−	4.74978i	0.269832	−	0.196044i	−0.444638	−	0.895710i	$-0.646668\pi$
$587$	6.53751	−	4.74978i	0.269832	−	0.196044i	0.714470	+	0.699666i	$0.246668\pi$
$588$	13.5250	+	4.39453i	0.557760	+	0.181227i
$589$	4.46959	+	1.45226i	0.184166	+	0.0598393i
$590$	10.8288	+	14.9046i	0.445815	+	0.613611i
$591$	−13.6399	−	9.90996i	−0.561070	−	0.407641i
$592$	35.4249	−	11.5102i	1.45595	−	0.473068i
$593$	31.4679			1.29223			0.646115	−	0.763240i	$-0.276392\pi$
$593$	31.4679			1.29223			0.646115	+	0.763240i	$0.276392\pi$
$594$	−30.0105	−	7.38347i	−1.23135	−	0.302948i
$595$	19.3041	+	3.91256i	0.791389	+	0.160399i
$596$	−8.54002	−	26.2835i	−0.349813	−	1.07661i
$597$	−19.0481	−	13.8393i	−0.779587	−	0.566403i
$598$	26.6617	+	36.6966i	1.09028	+	1.50064i
$599$	−1.46424	+	4.50645i	−0.0598270	+	0.184129i	−0.976504	−	0.215501i	$-0.930861\pi$
$599$	−1.46424	+	4.50645i	−0.0598270	+	0.184129i	0.916676	+	0.399630i	$0.130861\pi$
$600$	−1.00758	−	0.327383i	−0.0411343	−	0.0133653i
$601$	−22.5017	−	30.9709i	−0.917864	−	1.26333i	−0.964409	−	0.264415i	$-0.914821\pi$
$601$	−22.5017	−	30.9709i	−0.917864	−	1.26333i	0.0465455	−	0.998916i	$-0.485179\pi$
$602$	−3.26032	+	4.48744i	−0.132881	+	0.182894i
$603$	0.751186	+	2.31191i	0.0305907	+	0.0941484i
$604$	21.5941			0.878650
$605$	−21.3432	−	21.8283i	−0.867723	−	0.887448i
$606$			18.0372i			0.732711i
$607$	−18.6264	+	6.05209i	−0.756024	+	0.245647i	−0.661571	−	0.749882i	$-0.730110\pi$
$607$	−18.6264	+	6.05209i	−0.756024	+	0.245647i	−0.0944524	+	0.995529i	$0.530110\pi$
$608$	−45.0709	−	32.7459i	−1.82786	−	1.32802i
$609$	−12.2558	−	16.8686i	−0.496629	−	0.683551i
$610$	7.41604	−	22.8242i	0.300267	−	0.924126i
$611$	−3.09811	+	9.53502i	−0.125336	+	0.385745i
$612$	−3.27860	+	1.49708i	−0.132530	+	0.0605158i
$613$	−9.58273	−	6.96226i	−0.387043	−	0.281203i	0.377200	−	0.926132i	$-0.376887\pi$
$613$	−9.58273	−	6.96226i	−0.387043	−	0.281203i	−0.764243	+	0.644929i	$0.776887\pi$
$614$	5.01185	+	15.4249i	0.202262	+	0.622498i
$615$		−	38.2397i		−	1.54197i
$616$	1.16799	+	0.287361i	0.0470598	+	0.0115781i
$617$			42.8634i			1.72562i	0.505533	+	0.862808i	$0.331296\pi$
$617$			42.8634i			1.72562i	−0.505533	+	0.862808i	$0.668704\pi$
$618$	36.6729	−	11.9157i	1.47520	−	0.479321i
$619$	−26.3107	+	36.2135i	−1.05752	+	1.45555i	−0.175409	+	0.984496i	$0.556125\pi$
$619$	−26.3107	+	36.2135i	−1.05752	+	1.45555i	−0.882107	+	0.471049i	$0.843875\pi$
$620$	2.82210	−	2.05038i	0.113338	−	0.0823452i
$621$	−5.97295	+	18.3828i	−0.239686	+	0.737678i
$622$	−39.2592	−	12.7561i	−1.57415	−	0.511472i
$623$	−15.4649	−	21.2856i	−0.619587	−	0.852789i
$624$	−25.8125	+	35.5279i	−1.03333	+	1.42225i
$625$	−9.64411	−	29.6815i	−0.385764	−	1.18726i
$626$			14.0659i			0.562184i
$627$	3.18254	+	43.5663i	0.127099	+	1.73987i
$628$	−8.39439			−0.334973
$629$	36.3091	−	4.16416i	1.44774	−	0.166036i
$630$	3.52100	+	2.55815i	0.140280	+	0.101919i
$631$	25.4607	−	18.4982i	1.01357	−	0.736404i	0.0486171	−	0.998817i	$-0.484519\pi$
$631$	25.4607	−	18.4982i	1.01357	−	0.736404i	0.964955	+	0.262414i	$0.0845186\pi$
$632$	−0.285563	−	0.0927850i	−0.0113591	−	0.00369079i
$633$	−0.967440	+	2.97747i	−0.0384523	+	0.118344i
$634$	1.94723	+	2.68013i	0.0773344	+	0.106442i
$635$	2.86225	−	3.93955i	0.113585	−	0.156336i
$636$	−13.9836	+	4.54356i	−0.554487	+	0.180164i
$637$	22.6765			0.898474
$638$	−27.4883	−	32.5533i	−1.08827	−	1.28880i
$639$			2.30291i			0.0911015i
$640$	4.44273	−	1.44353i	0.175614	−	0.0570605i
$641$	0.708603	−	0.975308i	0.0279881	−	0.0385224i	−0.794794	−	0.606880i	$-0.792421\pi$
$641$	0.708603	−	0.975308i	0.0279881	−	0.0385224i	0.822782	+	0.568357i	$0.192421\pi$
$642$	44.9336	−	32.6462i	1.77339	−	1.28844i
$643$	18.0352	+	5.85999i	0.711239	+	0.231096i	0.642221	−	0.766520i	$-0.278013\pi$
$643$	18.0352	+	5.85999i	0.711239	+	0.231096i	0.0690183	+	0.997615i	$0.478013\pi$
$644$	−4.12149	+	12.6846i	−0.162409	+	0.499845i
$645$	6.82273	−	4.95700i	0.268645	−	0.195182i
$646$	−38.9383	−	42.4305i	−1.53201	−	1.66941i
$647$	−7.39114	−	22.7476i	−0.290576	−	0.894300i	−0.984672	−	0.174418i	$-0.944196\pi$
$647$	−7.39114	−	22.7476i	−0.290576	−	0.894300i	0.694096	−	0.719882i	$-0.255804\pi$
$648$	−2.14320			−0.0841928
$649$	4.21200	+	10.3325i	0.165335	+	0.405586i
$650$	29.9514			1.17479
$651$	2.02209	−	0.657017i	0.0792519	−	0.0257505i
$652$	19.1422	−	26.3470i	0.749667	−	1.03183i
$653$	−0.449448	−	0.618612i	−0.0175883	−	0.0242082i	0.800132	−	0.599824i	$-0.204763\pi$
$653$	−0.449448	−	0.618612i	−0.0175883	−	0.0242082i	−0.817721	+	0.575615i	$0.804763\pi$
$654$	0.471770	−	1.45196i	0.0184477	−	0.0567761i
$655$	11.1076	−	34.1856i	0.434009	−	1.33574i
$656$	18.2912	+	25.1757i	0.714152	+	0.982946i
$657$	−2.54635	+	3.50475i	−0.0993427	+	0.136733i
$658$	−5.76544	+	1.87331i	−0.224760	+	0.0730291i
$659$	5.53669			0.215679			0.107839	−	0.994168i	$-0.465607\pi$
$659$	5.53669			0.215679			0.107839	+	0.994168i	$0.465607\pi$
$660$	27.5500	+	17.0963i	1.07238	+	0.665473i
$661$	−22.3444			−0.869095			−0.434547	−	0.900649i	$-0.643092\pi$
$661$	−22.3444			−0.869095			−0.434547	+	0.900649i	$0.643092\pi$
$662$	−5.69118	−	17.5157i	−0.221194	−	0.680765i
$663$	−31.7467	+	29.1338i	−1.23294	+	1.13146i
$664$	1.63581	−	1.18848i	0.0634816	−	0.0461220i
$665$	−10.4499	+	32.1615i	−0.405230	+	1.24717i
$666$	7.68028	+	2.49547i	0.297605	+	0.0966977i
$667$	−21.5579	+	15.6627i	−0.834724	+	0.606463i
$668$	−10.9896	+	15.1259i	−0.425200	+	0.585238i
$669$	38.0770	−	12.3720i	1.47214	−	0.478328i
$670$			28.8303i			1.11381i
$671$	7.66403	−	12.3503i	0.295867	−	0.476776i
$672$	−25.2041			−0.972267
$673$	−15.4724	+	5.02729i	−0.596417	+	0.193788i	−0.591642	−	0.806201i	$-0.701520\pi$
$673$	−15.4724	+	5.02729i	−0.596417	+	0.193788i	−0.00477548	+	0.999989i	$0.501520\pi$
$674$	28.3411	−	39.0081i	1.09166	−	1.50254i
$675$	7.50194	+	10.3255i	0.288750	+	0.397430i
$676$	10.8518	−	33.3984i	0.417377	−	1.28455i
$677$	4.80281	+	1.56053i	0.184587	+	0.0599760i	0.399852	−	0.916580i	$-0.369062\pi$
$677$	4.80281	+	1.56053i	0.184587	+	0.0599760i	−0.215265	+	0.976556i	$0.569062\pi$
$678$	13.4105	−	9.74327i	0.515026	−	0.374188i
$679$	8.98478	+	6.52782i	0.344804	+	0.250515i
$680$	2.39530	−	0.274708i	0.0918556	−	0.0105346i
$681$	−25.5855			−0.980440
$682$	4.02316	−	1.64002i	0.154055	−	0.0627997i
$683$		−	18.3403i		−	0.701771i	−0.936418	−	0.350885i	$-0.885881\pi$
$683$		−	18.3403i		−	0.701771i	0.936418	−	0.350885i	$-0.114119\pi$
$684$	−1.91220	−	5.88516i	−0.0731149	−	0.225025i
$685$	6.09505	−	8.38912i	0.232880	−	0.320532i
$686$	22.0334	+	30.3264i	0.841240	+	1.15787i
$687$	−4.12328	−	1.33974i	−0.157313	−	0.0511141i
$688$	−2.12077	+	6.52705i	−0.0808534	+	0.248841i
$689$	−18.9678	+	13.7809i	−0.722616	+	0.525011i
$690$	24.5108	−	33.7363i	0.933112	−	1.28432i
$691$	1.64793	−	0.535446i	0.0626903	−	0.0203693i	−0.277504	−	0.960724i	$-0.589507\pi$
$691$	1.64793	−	0.535446i	0.0626903	−	0.0203693i	0.340194	+	0.940355i	$0.389507\pi$
$692$			36.7081i			1.39543i
$693$	1.70061	+	2.01396i	0.0646007	+	0.0765040i
$694$		−	59.8794i		−	2.27299i
$695$	16.5288	+	50.8705i	0.626975	+	1.92963i
$696$	−2.06484	−	1.50020i	−0.0782676	−	0.0568648i
$697$	12.6826	+	27.7749i	0.480388	+	1.05205i
$698$	−2.45335	+	7.55064i	−0.0928607	+	0.285796i
$699$	4.13250	−	12.7185i	0.156305	−	0.481058i
$700$	5.17653	+	7.12489i	0.195655	+	0.269295i
$701$	31.6496	+	22.9948i	1.19539	+	0.868502i	0.993823	−	0.110973i	$-0.0353966\pi$
$701$	31.6496	+	22.9948i	1.19539	+	0.868502i	0.201567	+	0.979475i	$0.435397\pi$
$702$	49.7780	−	16.1739i	1.87875	−	0.610443i
$703$			62.7470i			2.36655i
$704$	−23.5653	+	1.72146i	−0.888152	+	0.0648800i
$705$	9.21693			0.347129
$706$	−3.98271	−	12.2575i	−0.149891	−	0.461318i
$707$	−4.97091	+	6.84187i	−0.186950	+	0.257315i
$708$	−6.96556	−	9.58727i	−0.261782	−	0.360312i
$709$	12.8206	+	4.16567i	0.481488	+	0.156445i	0.539697	−	0.841860i	$-0.318539\pi$
$709$	12.8206	+	4.16567i	0.481488	+	0.156445i	−0.0582089	+	0.998304i	$0.518539\pi$
$710$	−8.43999	+	25.9756i	−0.316747	+	0.974848i
$711$	−0.386764	−	0.532334i	−0.0145048	−	0.0199641i
$712$	−2.60551	−	1.89301i	−0.0976455	−	0.0709436i
$713$	−0.839658	−	2.58420i	−0.0314454	−	0.0967791i
$714$	−25.5348	−	5.17541i	−0.955616	−	0.193685i
$715$	50.2046	+	12.3518i	1.87755	+	0.461932i
$716$	−0.883787			−0.0330287
$717$	33.4632	−	10.8729i	1.24971	−	0.406055i
$718$	11.9118	+	8.65439i	0.444543	+	0.322979i
$719$	−23.7593	−	32.7018i	−0.886071	−	1.21957i	−0.974702	−	0.223508i	$-0.928249\pi$
$719$	−23.7593	−	32.7018i	−0.886071	−	1.21957i	0.0886308	−	0.996065i	$-0.471751\pi$
$720$	5.12134	+	1.66402i	0.190861	+	0.0620145i
$721$	17.1947	+	5.58688i	0.640362	+	0.208066i
$722$	49.6612	−	36.0809i	1.84820	−	1.34279i
$723$	17.6414	+	12.8172i	0.656090	+	0.476678i
$724$	31.0788	−	10.0981i	1.15503	−	0.375293i
$725$			17.5953i			0.653474i
$726$	28.2321	+	28.8738i	1.04779	+	1.07161i
$727$	−8.17676			−0.303259			−0.151630	−	0.988437i	$-0.548452\pi$
$727$	−8.17676			−0.303259			−0.151630	+	0.988437i	$0.548452\pi$
$728$	−1.93733	+	0.629477i	−0.0718023	+	0.0233300i
$729$	17.5263	+	12.7336i	0.649123	+	0.471615i
$730$	−41.5663	+	30.1997i	−1.53844	+	1.11774i
$731$	−3.31155	+	5.86328i	−0.122482	+	0.216861i
$732$	−4.77032	+	14.6815i	−0.176316	+	0.542646i
$733$	−6.47281	+	4.70277i	−0.239079	+	0.173701i	−0.700873	−	0.713286i	$-0.747206\pi$
$733$	−6.47281	+	4.70277i	−0.239079	+	0.173701i	0.461794	+	0.886987i	$0.347206\pi$
$734$	34.2071	−	47.0821i	1.26261	−	1.73783i
$735$	−6.44212	−	19.8268i	−0.237621	−	0.731323i
$736$			32.2104i			1.18729i
$737$	−4.17157	+	16.9556i	−0.153662	+	0.624566i
$738$			6.74672i			0.248350i
$739$	−13.3284	−	41.0207i	−0.490295	−	1.50897i	−0.824163	−	0.566352i	$-0.808354\pi$
$739$	−13.3284	−	41.0207i	−0.490295	−	1.50897i	0.333869	−	0.942620i	$-0.391646\pi$
$740$	37.6794	+	27.3757i	1.38512	+	1.00635i
$741$	−43.4832	−	59.8495i	−1.59739	−	2.19862i
$742$	−13.4827	−	4.38079i	−0.494965	−	0.160824i
$743$	−5.32708	−	1.73087i	−0.195432	−	0.0634996i	0.209666	−	0.977773i	$-0.432762\pi$
$743$	−5.32708	−	1.73087i	−0.195432	−	0.0634996i	−0.405097	+	0.914274i	$0.632762\pi$
$744$	0.210552	−	0.152975i	0.00771920	−	0.00560832i
$745$	−23.8129	+	32.7756i	−0.872436	+	1.20080i
$746$	−22.9466	−	70.6224i	−0.840135	−	2.58567i
$747$	4.43104			0.162123
$748$	−25.6807	−	3.28042i	−0.938979	−	0.119944i
$749$	26.0413			0.951527
$750$	7.23352	+	22.2625i	0.264131	+	0.812911i
$751$	18.6009	−	25.6019i	0.678756	−	0.934227i	−0.321163	−	0.947024i	$-0.604074\pi$
$751$	18.6009	−	25.6019i	0.678756	−	0.934227i	0.999918	+	0.0127972i	$0.00407360\pi$
$752$	−6.06811	+	4.40874i	−0.221281	+	0.160770i
$753$	−48.6796	−	15.8170i	−1.77398	−	0.576402i
$754$	68.6245	+	22.2975i	2.49916	+	0.812026i
$755$	−18.6067	−	25.6099i	−0.677167	−	0.932040i
$756$	12.4506	+	9.04592i	0.452826	+	0.328997i
$757$	5.29889	+	16.3083i	0.192591	+	0.592735i	0.999996	+	0.00273759i	$0.000871403\pi$
$757$	5.29889	+	16.3083i	0.192591	+	0.592735i	−0.807405	+	0.589998i	$0.799129\pi$
$758$		−	4.63836i		−	0.168473i
$759$	19.2967	−	16.2943i	0.700425	−	0.591446i
$760$			4.13939i			0.150152i
$761$	9.10345	+	28.0176i	0.330000	+	1.01564i	0.969133	+	0.246539i	$0.0792934\pi$
$761$	9.10345	+	28.0176i	0.330000	+	1.01564i	−0.639133	+	0.769096i	$0.720707\pi$
$762$	−3.78610	+	5.21111i	−0.137156	+	0.188779i
$763$	0.579100	−	0.420741i	0.0209648	−	0.0152318i
$764$	−4.64107	+	14.2837i	−0.167908	+	0.516768i
$765$	4.60052	+	2.59835i	0.166332	+	0.0939437i
$766$	42.7178	−	31.0363i	1.54346	−	1.12139i
$767$	−15.2876	−	11.1071i	−0.552005	−	0.401055i
$768$	−31.0892	+	10.1015i	−1.12183	+	0.364506i
$769$	−28.6996			−1.03494			−0.517468	−	0.855703i	$-0.673125\pi$
$769$	−28.6996			−1.03494			−0.517468	+	0.855703i	$0.673125\pi$
$770$	11.8010	+	28.9491i	0.425278	+	1.04325i
$771$		−	0.157334i		−	0.00566625i
$772$	36.7361	−	11.9363i	1.32216	−	0.429596i
$773$	−41.7689	−	30.3468i	−1.50232	−	1.09150i	−0.969446	−	0.245307i	$-0.921111\pi$
$773$	−41.7689	−	30.3468i	−1.50232	−	1.09150i	−0.532876	−	0.846194i	$-0.678889\pi$
$774$	−1.20375	+	0.874577i	−0.0432680	+	0.0314360i
$775$	−1.70638	−	0.554436i	−0.0612949	−	0.0199159i
$776$	1.29289	+	0.420087i	0.0464122	+	0.0150802i
$777$	16.6857	+	22.9658i	0.598595	+	0.823895i
$778$	−26.3911	−	19.1742i	−0.946166	−	0.687430i
$779$	−49.8564	+	16.1993i	−1.78629	+	0.580402i
$780$	−54.9106			−1.96611
$781$	−8.72222	+	14.0555i	−0.312106	+	0.502945i
$782$	−6.61411	+	32.6331i	−0.236520	+	1.16696i
$783$	9.50152	+	29.2427i	0.339557	+	1.04505i
$784$	13.7250	+	9.97183i	0.490180	+	0.356137i
$785$	7.23309	+	9.95550i	0.258160	+	0.355327i
$786$	−14.6928	+	45.2196i	−0.524073	+	1.61293i
$787$	19.5331	+	6.34669i	0.696280	+	0.226235i	0.635709	−	0.771929i	$-0.280708\pi$
$787$	19.5331	+	6.34669i	0.696280	+	0.226235i	0.0605712	+	0.998164i	$0.480708\pi$
$788$	10.0838	+	13.8792i	0.359222	+	0.494426i
$789$	−15.0108	+	20.6606i	−0.534398	+	0.735535i
$790$	−2.41153	−	7.42193i	−0.0857984	−	0.264060i
$791$	7.77203			0.276342
$792$	0.274158	+	0.170131i	0.00974178	+	0.00604533i
$793$			24.6156i			0.874127i
$794$	−60.4914	+	19.6548i	−2.14676	+	0.697524i
$795$	17.4376	+	12.6692i	0.618450	+	0.449330i
$796$	14.0821	+	19.3823i	0.499126	+	0.686988i
$797$	4.61207	−	14.1945i	0.163368	−	0.502795i	−0.835544	−	0.549423i	$-0.814848\pi$
$797$	4.61207	−	14.1945i	0.163368	−	0.502795i	0.998912	+	0.0466281i	$0.0148476\pi$
$798$	13.8228	−	42.5422i	0.489322	−	1.50598i
$799$	−6.69458	+	3.05689i	−0.236837	+	0.108145i
$800$	17.2069	+	12.5015i	0.608356	+	0.441997i
$801$	−2.18096	−	6.71232i	−0.0770606	−	0.237168i
$802$		−	3.56365i		−	0.125837i
$803$	−28.8155	+	11.7465i	−1.01688	+	0.414526i
$804$		−	18.5449i		−	0.654028i
$805$	18.5949	−	6.04186i	0.655385	−	0.212947i
$806$	−4.32477	+	5.95254i	−0.152334	+	0.209669i
$807$	−20.8093	+	15.1189i	−0.732523	+	0.532209i
$808$	−0.319894	+	0.984534i	−0.0112538	+	0.0346358i
$809$	−13.0082	−	4.22662i	−0.457344	−	0.148600i	0.0712797	−	0.997456i	$-0.477292\pi$
$809$	−13.0082	−	4.22662i	−0.457344	−	0.148600i	−0.528624	+	0.848856i	$0.677292\pi$
$810$	−32.7413	−	45.0645i	−1.15041	−	1.58341i
$811$	−2.02111	+	2.78182i	−0.0709707	+	0.0976828i	−0.843027	−	0.537872i	$-0.819228\pi$
$811$	−2.02111	+	2.78182i	−0.0709707	+	0.0976828i	0.772056	+	0.635555i	$0.219228\pi$
$812$	6.55629	+	20.1782i	0.230081	+	0.708116i
$813$		−	9.27285i		−	0.325213i
$814$	37.4240	+	44.3198i	1.31171	+	1.55341i
$815$	−47.7408			−1.67229
$816$	−32.0263	+	3.67298i	−1.12114	+	0.128580i
$817$	−9.35317	−	6.79547i	−0.327226	−	0.237744i
$818$	−7.21549	+	5.24236i	−0.252284	+	0.183295i
$819$	−4.24556	−	1.37947i	−0.148352	−	0.0482025i
$820$	−12.0240	+	37.0062i	−0.419898	+	1.29231i
$821$	−20.6370	−	28.4045i	−0.720238	−	0.991322i	−0.999516	−	0.0311121i	$-0.990095\pi$
$821$	−20.6370	−	28.4045i	−0.720238	−	0.991322i	0.279278	−	0.960210i	$-0.409905\pi$
$822$	−8.06235	+	11.0969i	−0.281207	+	0.387048i
$823$	49.2440	−	16.0003i	1.71654	−	0.557737i	0.725138	−	0.688604i	$-0.241776\pi$
$823$	49.2440	−	16.0003i	1.71654	−	0.557737i	0.991400	+	0.130867i	$0.0417761\pi$
$824$	2.21306			0.0770957
$825$	−1.21501	−	16.6325i	−0.0423014	−	0.579070i
$826$		−	11.4260i		−	0.397561i
$827$	−45.0804	+	14.6475i	−1.56760	+	0.509344i	−0.958825	−	0.283999i	$-0.908339\pi$
$827$	−45.0804	+	14.6475i	−1.56760	+	0.509344i	−0.608775	+	0.793343i	$0.708339\pi$
$828$	−2.10295	+	2.89446i	−0.0730825	+	0.100589i
$829$	−1.80874	+	1.31412i	−0.0628200	+	0.0456414i	−0.618752	−	0.785586i	$-0.712361\pi$
$829$	−1.80874	+	1.31412i	−0.0628200	+	0.0456414i	0.555932	+	0.831228i	$0.312361\pi$
$830$	49.9799	+	16.2394i	1.73483	+	0.563679i
$831$	17.5117	−	53.8953i	0.607472	−	1.86961i
$832$	32.3730	−	23.5204i	1.12233	−	0.815422i
$833$	11.2549	+	12.2643i	0.389959	+	0.424933i
$834$	−21.8638	−	67.2900i	−0.757083	−	2.33006i
$835$	27.4081			0.948497
$836$	10.6191	−	43.1617i	0.367268	−	1.49278i
$837$	−3.13533			−0.108373
$838$	−29.8183	+	9.68854i	−1.03006	+	0.334685i
$839$	−20.0783	+	27.6355i	−0.693181	+	0.954082i	0.306816	+	0.951769i	$0.400736\pi$
$839$	−20.0783	+	27.6355i	−0.693181	+	0.954082i	−0.999997	+	0.00231312i	$0.999264\pi$
$840$	1.10075	+	1.51505i	0.0379794	+	0.0522741i
$841$	−4.13742	+	12.7337i	−0.142670	+	0.439092i
$842$	10.4459	−	32.1491i	0.359988	−	1.10793i
$843$	14.7205	+	20.2610i	0.507000	+	0.697826i
$844$	1.87247	−	2.57723i	0.0644530	−	0.0887119i
$845$	−48.9601	+	15.9081i	−1.68428	+	0.547255i
$846$	−1.62616			−0.0559087
$847$	2.75159	+	18.7330i	0.0945458	+	0.643673i
$848$	−17.5404			−0.602340
$849$	0.476464	+	1.46641i	0.0163522	+	0.0503269i
$850$	14.8656	+	16.1989i	0.509887	+	0.555617i
$851$	29.3500	−	21.3240i	1.00611	−	0.730979i
$852$	5.42898	−	16.7087i	0.185994	−	0.572430i
$853$	−8.88566	−	2.88713i	−0.304239	−	0.0988533i	0.152919	−	0.988239i	$-0.451133\pi$
$853$	−8.88566	−	2.88713i	−0.304239	−	0.0988533i	−0.457158	+	0.889385i	$0.651133\pi$
$854$	−12.0415	+	8.74865i	−0.412051	+	0.299373i
$855$	−5.33196	+	7.33881i	−0.182349	+	0.250982i
$856$	3.03162	−	0.985034i	0.103619	−	0.0336678i
$857$		−	24.2764i		−	0.829267i	−0.909989	−	0.414633i	$-0.863910\pi$
$857$		−	24.2764i		−	0.829267i	0.909989	−	0.414633i	$-0.136090\pi$
$858$	−66.4092	−	16.3386i	−2.26717	−	0.557791i
$859$	51.4888			1.75677			0.878387	−	0.477949i	$-0.158620\pi$
$859$	51.4888			1.75677			0.878387	+	0.477949i	$0.158620\pi$
$860$	−8.16133	+	2.65178i	−0.278299	+	0.0904248i
$861$	−13.9401	+	19.1869i	−0.475077	+	0.653888i
$862$	−27.6339	−	38.0348i	−0.941216	−	1.29547i
$863$	−11.6065	+	35.7211i	−0.395089	+	1.21596i	0.533803	+	0.845609i	$0.320763\pi$
$863$	−11.6065	+	35.7211i	−0.395089	+	1.21596i	−0.928892	+	0.370351i	$0.879237\pi$
$864$	35.3480	+	11.4853i	1.20256	+	0.390737i
$865$	43.5347	−	31.6298i	1.48022	−	1.07545i
$866$	51.5828	+	37.4771i	1.75286	+	1.27352i
$867$	−31.5134	−	2.71001i	−1.07025	−	0.0920368i
$868$	−2.16345			−0.0734324
$869$	−0.344353	−	4.71390i	−0.0116814	−	0.159908i
$870$		−	66.3352i		−	2.24897i
$871$	−9.13802	−	28.1239i	−0.309630	−	0.952944i
$872$	0.0515017	−	0.0708861i	0.00174407	−	0.00240050i
$873$	1.75108	+	2.41016i	0.0592651	+	0.0815715i
$874$	−54.3684	−	17.6654i	−1.83904	−	0.597540i
$875$	−3.39155	+	10.4381i	−0.114655	+	0.352873i
$876$	26.7373	−	19.4258i	0.903369	−	0.656336i
$877$	13.5794	−	18.6905i	0.458545	−	0.631133i	−0.515661	−	0.856793i	$-0.672454\pi$
$877$	13.5794	−	18.6905i	0.458545	−	0.631133i	0.974206	+	0.225659i	$0.0724536\pi$
$878$	−44.7900	+	14.5532i	−1.51159	+	0.491145i
$879$			45.5399i			1.53602i
$880$	24.9550	+	29.5532i	0.841232	+	0.996237i
$881$			49.1061i			1.65443i	0.561888	+	0.827213i	$0.310075\pi$
$881$			49.1061i			1.65443i	−0.561888	+	0.827213i	$0.689925\pi$
$882$	1.13660	+	3.49809i	0.0382713	+	0.117787i
$883$	35.1311	+	25.5242i	1.18226	+	0.858959i	0.992424	−	0.122857i	$-0.0392058\pi$
$883$	35.1311	+	25.5242i	1.18226	+	0.858959i	0.189832	+	0.981817i	$0.439206\pi$
$884$	39.8835	−	18.2117i	1.34143	−	0.612525i
$885$	−5.36829	+	16.5219i	−0.180453	+	0.555378i
$886$	−0.434205	+	1.33635i	−0.0145874	+	0.0448954i
$887$	−6.42628	−	8.84502i	−0.215773	−	0.296987i	0.687386	−	0.726293i	$-0.258758\pi$
$887$	−6.42628	−	8.84502i	−0.215773	−	0.296987i	−0.903159	+	0.429306i	$0.858758\pi$
$888$	2.81118	+	2.04245i	0.0943372	+	0.0685400i
$889$	−2.87229	+	0.933262i	−0.0963334	+	0.0313006i
$890$		−	83.7046i		−	2.80579i
$891$	−12.7351	−	31.2407i	−0.426643	−	1.04660i
$892$	−40.7390			−1.36404
$893$	−3.90453	−	12.0169i	−0.130660	−	0.402131i
$894$	31.4989	−	43.3546i	1.05348	−	1.44999i
$895$	0.761522	+	1.04815i	0.0254549	+	0.0350356i
$896$	−2.75539	−	0.895279i	−0.0920510	−	0.0299092i
$897$	−13.2173	+	40.6787i	−0.441313	+	1.35822i
$898$	−15.0266	−	20.6823i	−0.501443	−	0.690177i
$899$	−3.49689	−	2.54064i	−0.116628	−	0.0847351i
$900$	0.730030	+	2.24680i	0.0243343	+	0.0748934i
$901$	−16.8675	−	3.41871i	−0.561936	−	0.113894i
$902$	−25.5531	+	41.1778i	−0.850826	+	1.37107i
$903$	−5.23038			−0.174056
$904$	0.904790	−	0.293984i	0.0300929	−	0.00977777i
$905$	−38.7553	−	28.1574i	−1.28827	−	0.935983i
$906$	24.6124	+	33.8760i	0.817691	+	1.12546i
$907$	−16.8103	−	5.46200i	−0.558178	−	0.181363i	0.0163234	−	0.999867i	$-0.494804\pi$
$907$	−16.8103	−	5.46200i	−0.558178	−	0.181363i	−0.574501	+	0.818504i	$0.694804\pi$
$908$	24.7602	+	8.04509i	0.821697	+	0.266986i
$909$	−1.83533	+	1.33344i	−0.0608739	+	0.0442275i
$910$	−42.8322	−	31.1194i	−1.41987	−	1.03160i
$911$	−14.5330	+	4.72205i	−0.481499	+	0.156448i	−0.539702	−	0.841856i	$-0.681463\pi$
$911$	−14.5330	+	4.72205i	−0.481499	+	0.156448i	0.0582030	+	0.998305i	$0.481463\pi$
$912$		−	55.3456i		−	1.83268i
$913$	27.0443	+	16.7825i	0.895034	+	0.555419i
$914$	47.0758			1.55713
$915$	21.5223	−	6.99301i	0.711505	−	0.231182i
$916$	3.56901	+	2.59304i	0.117924	+	0.0856765i
$917$	−18.0354	+	13.1035i	−0.595583	+	0.432716i
$918$	33.4535	+	18.8944i	1.10413	+	0.623608i
$919$	−4.67145	+	14.3772i	−0.154097	+	0.474261i	−0.998068	−	0.0621268i	$-0.980212\pi$
$919$	−4.67145	+	14.3772i	−0.154097	+	0.474261i	0.843971	+	0.536388i	$0.180212\pi$
$920$	1.93621	−	1.40674i	0.0638350	−	0.0463788i
$921$	−8.98932	+	12.3727i	−0.296208	+	0.407695i
$922$	−15.3144	−	47.1329i	−0.504353	−	1.55224i
$923$		−	28.0144i		−	0.922104i
$924$	−7.59091	−	18.6213i	−0.249723	−	0.612597i
$925$		−	23.9552i		−	0.787642i
$926$	5.57309	+	17.1522i	0.183143	+	0.563656i
$927$	3.92358	+	2.85065i	0.128867	+	0.0936277i
$928$	30.1175	+	41.4532i	0.988657	+	1.36077i
$929$	57.6865	+	18.7435i	1.89263	+	0.614954i	0.977129	+	0.212649i	$0.0682090\pi$
$929$	57.6865	+	18.7435i	1.89263	+	0.614954i	0.915505	+	0.402306i	$0.131791\pi$
$930$	6.43313	+	2.09025i	0.210950	+	0.0685420i
$931$	−23.1209	+	16.7983i	−0.757756	+	0.550542i
$932$	−7.99839	+	11.0088i	−0.261996	+	0.360607i
$933$	−12.0284	−	37.0197i	−0.393793	−	1.21197i
$934$	−28.1967			−0.922624
$935$	18.2375	+	33.2831i	0.596430	+	1.08848i
$936$	−0.546432			−0.0178607
$937$	−6.01624	−	18.5161i	−0.196542	−	0.604894i	−0.999955	−	0.00947222i	$-0.996985\pi$
$937$	−6.01624	−	18.5161i	−0.196542	−	0.604894i	0.803413	−	0.595422i	$-0.203015\pi$
$938$	10.5099	−	14.4657i	0.343161	−	0.472321i
$939$	−10.7304	+	7.79609i	−0.350173	+	0.254416i
$940$	−8.91962	−	2.89816i	−0.290926	−	0.0945275i
$941$	10.6184	+	3.45013i	0.346151	+	0.112471i	0.476932	−	0.878940i	$-0.341749\pi$
$941$	10.6184	+	3.45013i	0.346151	+	0.112471i	−0.130782	+	0.991411i	$0.541749\pi$
$942$	−9.56771	−	13.1688i	−0.311733	−	0.429064i
$943$	24.5206	+	17.8152i	0.798500	+	0.580144i
$944$	−4.36864	−	13.4453i	−0.142187	−	0.437607i
$945$		−	22.5606i		−	0.733896i
$946$	−10.6594	+	0.778674i	−0.346567	+	0.0253169i
$947$		−	20.0175i		−	0.650482i	−0.945631	−	0.325241i	$-0.894555\pi$
$947$		−	20.0175i		−	0.650482i	0.945631	−	0.325241i	$-0.105445\pi$
$948$	1.55120	+	4.77411i	0.0503807	+	0.155056i
$949$	30.9759	−	42.6346i	1.00552	−	1.38398i
$950$	−30.5384	+	22.1874i	−0.990797	+	0.719856i
$951$	−0.965324	+	2.97096i	−0.0313028	+	0.0963401i
$952$	−1.30199	−	0.735359i	−0.0421978	−	0.0238331i
$953$	20.8057	−	15.1162i	0.673961	−	0.489662i	−0.197388	−	0.980326i	$-0.563246\pi$
$953$	20.8057	−	15.1162i	0.673961	−	0.489662i	0.871349	+	0.490664i	$0.163246\pi$
$954$	−3.07657	−	2.23526i	−0.0996075	−	0.0723691i
$955$	20.9391	−	6.80353i	0.677574	−	0.220157i
$956$	−35.8027			−1.15794
$957$	9.59831	−	39.0129i	0.310269	−	1.26111i
$958$			12.7012i			0.410356i
$959$	−6.11643	+	1.98735i	−0.197510	+	0.0641748i
$960$	−29.7614	−	21.6230i	−0.960546	−	0.697878i
$961$	−24.7229	+	17.9623i	−0.797514	+	0.579428i
$962$	−93.4290	−	30.3569i	−3.01227	−	0.978747i
$963$	6.64365	+	2.15865i	0.214088	+	0.0695616i
$964$	−13.0421	−	17.9509i	−0.420058	−	0.578160i
$965$	−45.8100	−	33.2829i	−1.47468	−	1.07141i
$966$	−24.5968	+	7.99198i	−0.791389	+	0.257138i
$967$	−0.904186			−0.0290767			−0.0145383	−	0.999894i	$-0.504628\pi$
$967$	−0.904186			−0.0290767			−0.0145383	+	0.999894i	$0.504628\pi$
$968$	1.02892	+	2.07674i	0.0330708	+	0.0667489i
$969$	10.7871	−	53.2222i	0.346532	−	1.70974i
$970$	10.9183	+	33.6030i	0.350564	+	1.07893i
$971$	24.4838	+	17.7885i	0.785721	+	0.570860i	0.906691	−	0.421796i	$-0.138600\pi$
$971$	24.4838	+	17.7885i	0.785721	+	0.570860i	−0.120970	+	0.992656i	$0.538600\pi$
$972$	5.29453	+	7.28729i	0.169822	+	0.233740i
$973$	10.2512	−	31.5500i	0.328639	−	1.01145i
$974$	−0.240405	−	0.0781124i	−0.00770308	−	0.00250288i
$975$	16.6008	+	22.8490i	0.531650	+	0.731754i
$976$	−10.8246	+	14.8987i	−0.346486	+	0.476897i
$977$	14.6733	+	45.1598i	0.469441	+	1.44479i	0.853311	+	0.521403i	$0.174591\pi$
$977$	14.6733	+	45.1598i	0.469441	+	1.44479i	−0.383870	+	0.923387i	$0.625409\pi$
$978$	63.1501			2.01932
$979$	12.1116	−	49.2281i	0.387088	−	1.57334i
$980$			21.2129i			0.677621i
$981$	0.182617	−	0.0593358i	0.00583051	−	0.00189445i
$982$	19.6659	+	14.2881i	0.627565	+	0.455953i
$983$	−1.94084	−	2.67134i	−0.0619032	−	0.0852025i	0.776943	−	0.629571i	$-0.216769\pi$
$983$	−1.94084	−	2.67134i	−0.0619032	−	0.0852025i	−0.838846	+	0.544369i	$0.816769\pi$
$984$	−0.897091	+	2.76096i	−0.0285982	+	0.0880162i
$985$	7.77152	−	23.9183i	0.247621	−	0.762099i
$986$	22.0008	+	48.1816i	0.700647	+	1.53441i
$987$	−4.62462	−	3.35998i	−0.147203	−	0.106949i
$988$	23.2616	+	71.5917i	0.740049	+	2.27764i
$989$			6.68435i			0.212550i
$990$	0.610974	+	8.36371i	0.0194180	+	0.265816i
$991$			36.9483i			1.17370i	0.809695	+	0.586851i	$0.199633\pi$
$991$			36.9483i			1.17370i	−0.809695	+	0.586851i	$0.800367\pi$
$992$	−4.96911	+	1.61456i	−0.157770	+	0.0512624i
$993$	10.2078	−	14.0498i	0.323934	−	0.445857i
$994$	13.7041	−	9.95660i	0.434667	−	0.315804i
$995$	10.8529	−	33.4018i	0.344061	−	1.05891i
$996$	−32.1493	−	10.4459i	−1.01869	−	0.330992i
$997$	8.70699	+	11.9841i	0.275753	+	0.379542i	0.924321	−	0.381615i	$-0.124632\pi$
$997$	8.70699	+	11.9841i	0.275753	+	0.379542i	−0.648568	+	0.761156i	$0.724632\pi$
$998$	5.01921	−	6.90834i	0.158880	−	0.218680i
$999$	−12.9359	−	39.8125i	−0.409273	−	1.25961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.j.a.16.4	yes	64
11.9	even	5	inner	187.2.j.a.152.3	yes	64
17.16	even	2	inner	187.2.j.a.16.3	✓	64
187.152	even	10	inner	187.2.j.a.152.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.j.a.16.3	✓	64	17.16	even	2	inner
187.2.j.a.16.4	yes	64	1.1	even	1	trivial
187.2.j.a.152.3	yes	64	11.9	even	5	inner
187.2.j.a.152.4	yes	64	187.152	even	10	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.609729 - 1.87655i) q^{2} +(1.09362 - 1.50523i) q^{3} +(-1.53164 + 1.11281i) q^{4} +(2.63951 + 0.857628i) q^{5} +(-3.49146 - 1.13444i) q^{6} +(-1.01174 - 1.39254i) q^{7} +(-0.170457 - 0.123844i) q^{8} +(-0.142682 - 0.439131i) q^{9} +O(q^{10})\)	\(q+(-0.609729 - 1.87655i) q^{2} +(1.09362 - 1.50523i) q^{3} +(-1.53164 + 1.11281i) q^{4} +(2.63951 + 0.857628i) q^{5} +(-3.49146 - 1.13444i) q^{6} +(-1.01174 - 1.39254i) q^{7} +(-0.170457 - 0.123844i) q^{8} +(-0.142682 - 0.439131i) q^{9} -5.47610i q^{10} +(0.792359 - 3.22058i) q^{11} +3.52247i q^{12} +(1.73570 + 5.34194i) q^{13} +(-1.99628 + 2.74765i) q^{14} +(4.17754 - 3.03516i) q^{15} +(-1.29854 + 3.99649i) q^{16} +(-2.02765 + 3.59007i) q^{17} +(-0.737054 + 0.535501i) q^{18} +(-5.72692 - 4.16085i) q^{19} +(-4.99716 + 1.62368i) q^{20} -3.20255 q^{21} +(-6.52672 + 0.476780i) q^{22} +4.09281i q^{23} +(-0.372828 + 0.121139i) q^{24} +(2.18639 + 1.58851i) q^{25} +(8.96611 - 6.51426i) q^{26} +(4.49149 + 1.45937i) q^{27} +(3.09925 + 1.00701i) q^{28} +(3.82688 + 5.26725i) q^{29} +(-8.24281 - 5.98875i) q^{30} +(-0.631400 + 0.205154i) q^{31} +7.87000 q^{32} +(-3.98120 - 4.71477i) q^{33} +(7.97328 + 1.61603i) q^{34} +(-1.47621 - 4.54331i) q^{35} +(0.707205 + 0.513815i) q^{36} +(-5.21012 - 7.17111i) q^{37} +(-4.31619 + 13.2839i) q^{38} +(9.93906 + 3.22940i) q^{39} +(-0.343710 - 0.473076i) q^{40} +(4.35281 - 5.99113i) q^{41} +(1.95269 + 6.00975i) q^{42} +1.63319 q^{43} +(2.37027 + 5.81453i) q^{44} -1.28146i q^{45} +(7.68038 - 2.49551i) q^{46} +(1.44404 + 1.04916i) q^{47} +(4.59556 + 6.32524i) q^{48} +(1.24757 - 3.83963i) q^{49} +(1.64781 - 5.07144i) q^{50} +(3.18642 + 6.97826i) q^{51} +(-8.60301 - 6.25045i) q^{52} +(1.28988 + 3.96984i) q^{53} -9.31835i q^{54} +(4.85350 - 7.82121i) q^{55} +0.362665i q^{56} +(-12.5261 + 4.06998i) q^{57} +(7.55091 - 10.3929i) q^{58} +(-2.72175 + 1.97747i) q^{59} +(-3.02097 + 9.29758i) q^{60} +(4.16797 + 1.35426i) q^{61} +(0.769965 + 1.05977i) q^{62} +(-0.467149 + 0.642975i) q^{63} +(-2.20148 - 6.77547i) q^{64} +15.5887i q^{65} +(-6.42007 + 10.3457i) q^{66} -5.26475 q^{67} +(-0.889404 - 7.75510i) q^{68} +(6.16065 + 4.47597i) q^{69} +(-7.62567 + 5.54037i) q^{70} +(-4.74346 - 1.54124i) q^{71} +(-0.0300626 + 0.0925231i) q^{72} +(-5.51482 - 7.59050i) q^{73} +(-10.2802 + 14.1495i) q^{74} +(4.78215 - 1.55382i) q^{75} +13.4018 q^{76} +(-5.28644 + 2.15500i) q^{77} -20.6202i q^{78} +(1.35533 - 0.440374i) q^{79} +(-6.85501 + 9.43512i) q^{80} +(8.22932 - 5.97895i) q^{81} +(-13.8967 - 4.51531i) q^{82} +(-2.96551 + 9.12692i) q^{83} +(4.90517 - 3.56381i) q^{84} +(-8.43096 + 7.73705i) q^{85} +(-0.995804 - 3.06477i) q^{86} +12.1136 q^{87} +(-0.533913 + 0.450841i) q^{88} +15.2855 q^{89} +(-2.40472 + 0.781341i) q^{90} +(5.68277 - 7.82167i) q^{91} +(-4.55450 - 6.26874i) q^{92} +(-0.381704 + 1.17476i) q^{93} +(1.08833 - 3.34953i) q^{94} +(-11.5478 - 15.8942i) q^{95} +(8.60676 - 11.8462i) q^{96} +(-6.13630 + 1.99380i) q^{97} -7.96595 q^{98} +(-1.52731 + 0.111571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9}+O(q^{10}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36} - 60 q^{38} - 10 q^{42} + 32 q^{43} + 16 q^{47} - 18 q^{49} + 4 q^{50} - 2 q^{51} + 44 q^{52} - 16 q^{53} + 22 q^{55} - 50 q^{59} + 68 q^{60} - 80 q^{64} - 172 q^{66} + 40 q^{67} + 18 q^{68} + 6 q^{69} + 128 q^{70} + 186 q^{72} - 116 q^{76} - 30 q^{77} + 48 q^{81} - 12 q^{83} + 68 q^{84} - 108 q^{85} - 16 q^{86} + 92 q^{87} - 40 q^{89} - 80 q^{93} - 188 q^{94} + 72 q^{98}+O(q^{100}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Introduction

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