LMFDB - Embedded newform 960.2.cn.a.131.92

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.92
Character	$\chi$	$=$	960.131
Dual form			960.2.cn.a.491.92

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.908567 + 1.08375i) q^{2} +(0.0753215 - 1.73041i) q^{3} +(-0.349011 + 1.96931i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(1.94376 - 1.49057i) q^{6} +(-0.894725 - 2.16006i) q^{7} +(-2.45133 + 1.41101i) q^{8} +(-2.98865 - 0.260675i) q^{9} +O(q^{10})$	\(q+(0.908567 + 1.08375i) q^{2} +(0.0753215 - 1.73041i) q^{3} +(-0.349011 + 1.96931i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(1.94376 - 1.49057i) q^{6} +(-0.894725 - 2.16006i) q^{7} +(-2.45133 + 1.41101i) q^{8} +(-2.98865 - 0.260675i) q^{9} +(-1.40587 + 0.153349i) q^{10} +(-2.78201 + 0.553376i) q^{11} +(3.38143 + 0.752265i) q^{12} +(-1.64171 + 1.09696i) q^{13} +(1.52804 - 2.93221i) q^{14} +(1.39694 + 1.02399i) q^{15} +(-3.75638 - 1.37462i) q^{16} +(2.08673 - 2.08673i) q^{17} +(-2.43289 - 3.47578i) q^{18} +(-5.32408 + 3.55744i) q^{19} +(-1.44352 - 1.38428i) q^{20} +(-3.80518 + 1.38554i) q^{21} +(-3.12736 - 2.51221i) q^{22} +(-2.92055 + 7.05083i) q^{23} +(2.25700 + 4.34810i) q^{24} +(-0.382683 - 0.923880i) q^{25} +(-2.68043 - 0.782541i) q^{26} +(-0.676184 + 5.15197i) q^{27} +(4.56610 - 1.00811i) q^{28} +(1.77935 - 8.94538i) q^{29} +(0.159464 + 2.44429i) q^{30} -5.53553 q^{31} +(-1.92318 - 5.31990i) q^{32} +(0.748024 + 4.85571i) q^{33} +(4.15742 + 0.365551i) q^{34} +(2.29310 + 0.456127i) q^{35} +(1.55642 - 5.79461i) q^{36} +(1.90978 - 2.85818i) q^{37} +(-8.69264 - 2.53778i) q^{38} +(1.77453 + 2.92347i) q^{39} +(0.188674 - 2.82213i) q^{40} +(-0.879720 - 0.364392i) q^{41} +(-4.95884 - 2.86499i) q^{42} +(-9.53263 + 1.89616i) q^{43} +(-0.118817 - 5.67178i) q^{44} +(1.87715 - 2.34015i) q^{45} +(-10.2948 + 3.24102i) q^{46} +(4.63408 + 4.63408i) q^{47} +(-2.66160 + 6.39655i) q^{48} +(1.08443 - 1.08443i) q^{49} +(0.653557 - 1.25414i) q^{50} +(-3.45373 - 3.76808i) q^{51} +(-1.58728 - 3.61590i) q^{52} +(1.07174 + 5.38802i) q^{53} +(-6.19778 + 3.94810i) q^{54} +(1.08549 - 2.62060i) q^{55} +(5.24114 + 4.03255i) q^{56} +(5.75481 + 9.48080i) q^{57} +(11.3112 - 6.19912i) q^{58} +(7.94523 + 5.30883i) q^{59} +(-2.50411 + 2.39362i) q^{60} +(0.364498 - 1.83245i) q^{61} +(-5.02940 - 5.99910i) q^{62} +(2.11095 + 6.68889i) q^{63} +(4.01809 - 6.91773i) q^{64} -1.97447i q^{65} +(-4.58272 + 5.22240i) q^{66} +(-8.67485 - 1.72553i) q^{67} +(3.38113 + 4.83772i) q^{68} +(11.9809 + 5.58483i) q^{69} +(1.58911 + 2.89956i) q^{70} +(8.56335 - 3.54706i) q^{71} +(7.69401 - 3.57803i) q^{72} +(-9.84027 - 4.07597i) q^{73} +(4.83271 - 0.527138i) q^{74} +(-1.62752 + 0.592612i) q^{75} +(-5.14754 - 11.7264i) q^{76} +(3.68446 + 5.51418i) q^{77} +(-1.55601 + 4.57931i) q^{78} +(-5.52976 - 5.52976i) q^{79} +(3.22989 - 2.35962i) q^{80} +(8.86410 + 1.55813i) q^{81} +(-0.404376 - 1.28447i) q^{82} +(-3.20451 - 4.79589i) q^{83} +(-1.40052 - 7.97716i) q^{84} +(0.575728 + 2.89438i) q^{85} +(-10.7160 - 8.60817i) q^{86} +(-15.3452 - 3.75278i) q^{87} +(6.03882 - 5.28196i) q^{88} +(3.13329 - 1.29785i) q^{89} +(4.24165 - 0.0918309i) q^{90} +(3.83837 + 2.56472i) q^{91} +(-12.8660 - 8.21229i) q^{92} +(-0.416944 + 9.57874i) q^{93} +(-0.811793 + 9.23254i) q^{94} -6.40322i q^{95} +(-9.35048 + 2.92719i) q^{96} +5.83577i q^{97} +(2.16053 + 0.189970i) q^{98} +(8.45872 - 0.928651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{16}\right)$

Coefficient data

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

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

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

$2$	0.908567	+	1.08375i	0.642454	+	0.766324i
$2$	0.908567	+	1.08375i	0.642454	+	0.766324i
$3$	0.0753215	−	1.73041i	0.0434869	−	0.999054i
$3$	0.0753215	−	1.73041i	0.0434869	−	0.999054i
$4$	−0.349011	+	1.96931i	−0.174506	+	0.984656i
$5$	−0.555570	+	0.831470i	−0.248459	+	0.371845i
$5$	−0.555570	+	0.831470i	−0.248459	+	0.371845i
$6$	1.94376	−	1.49057i	0.793538	−	0.608521i
$7$	−0.894725	−	2.16006i	−0.338174	−	0.816425i	−0.997891	−	0.0649106i	$-0.979324\pi$
$7$	−0.894725	−	2.16006i	−0.338174	−	0.816425i	0.659717	−	0.751514i	$-0.270676\pi$
$8$	−2.45133	+	1.41101i	−0.866678	+	0.498868i
$9$	−2.98865	−	0.260675i	−0.996218	−	0.0868915i
$10$	−1.40587	+	0.153349i	−0.444577	+	0.0484932i
$11$	−2.78201	+	0.553376i	−0.838808	+	0.166849i	−0.595757	−	0.803164i	$-0.703148\pi$
$11$	−2.78201	+	0.553376i	−0.838808	+	0.166849i	−0.243050	+	0.970014i	$0.578148\pi$
$12$	3.38143	+	0.752265i	0.976136	+	0.217160i
$13$	−1.64171	+	1.09696i	−0.455329	+	0.304241i	−0.762003	−	0.647573i	$-0.775784\pi$
$13$	−1.64171	+	1.09696i	−0.455329	+	0.304241i	0.306674	+	0.951815i	$0.400784\pi$
$14$	1.52804	−	2.93221i	0.408385	−	0.783666i
$15$	1.39694	+	1.02399i	0.360688	+	0.264394i
$16$	−3.75638	−	1.37462i	−0.939096	−	0.343656i
$17$	2.08673	−	2.08673i	0.506107	−	0.506107i	−0.407222	−	0.913329i	$-0.633503\pi$
$17$	2.08673	−	2.08673i	0.506107	−	0.506107i	0.913329	+	0.407222i	$0.133503\pi$
$18$	−2.43289	−	3.47578i	−0.573437	−	0.819250i
$19$	−5.32408	+	3.55744i	−1.22143	+	0.816132i	−0.987729	−	0.156177i	$-0.950083\pi$
$19$	−5.32408	+	3.55744i	−1.22143	+	0.816132i	−0.233699	+	0.972309i	$0.575083\pi$
$20$	−1.44352	−	1.38428i	−0.322782	−	0.309535i
$21$	−3.80518	+	1.38554i	−0.830359	+	0.302351i
$22$	−3.12736	−	2.51221i	−0.666756	−	0.535606i
$23$	−2.92055	+	7.05083i	−0.608977	+	1.47020i	0.255138	+	0.966905i	$0.417879\pi$
$23$	−2.92055	+	7.05083i	−0.608977	+	1.47020i	−0.864115	+	0.503295i	$0.832121\pi$
$24$	2.25700	+	4.34810i	0.460707	+	0.887552i
$25$	−0.382683	−	0.923880i	−0.0765367	−	0.184776i
$26$	−2.68043	−	0.782541i	−0.525676	−	0.153469i
$27$	−0.676184	+	5.15197i	−0.130132	+	0.991497i
$28$	4.56610	−	1.00811i	0.862911	−	0.190515i
$29$	1.77935	−	8.94538i	0.330416	−	1.66112i	−0.356437	−	0.934319i	$-0.616009\pi$
$29$	1.77935	−	8.94538i	0.330416	−	1.66112i	0.686853	−	0.726796i	$-0.258991\pi$
$30$	0.159464	+	2.44429i	0.0291140	+	0.446265i
$31$	−5.53553			−0.994210			−0.497105	−	0.867690i	$-0.665604\pi$
$31$	−5.53553			−0.994210			−0.497105	+	0.867690i	$0.665604\pi$
$32$	−1.92318	−	5.31990i	−0.339974	−	0.940435i
$33$	0.748024	+	4.85571i	0.130214	+	0.845270i
$34$	4.15742	+	0.365551i	0.712992	+	0.0626915i
$35$	2.29310	+	0.456127i	0.387605	+	0.0770995i
$36$	1.55642	−	5.79461i	0.259404	−	0.965769i
$37$	1.90978	−	2.85818i	0.313965	−	0.469883i	−0.640604	−	0.767872i	$-0.721316\pi$
$37$	1.90978	−	2.85818i	0.313965	−	0.469883i	0.954569	+	0.297989i	$0.0963159\pi$
$38$	−8.69264	−	2.53778i	−1.41013	−	0.411682i
$39$	1.77453	+	2.92347i	0.284153	+	0.468129i
$40$	0.188674	−	2.82213i	0.0298321	−	0.446217i
$41$	−0.879720	−	0.364392i	−0.137389	−	0.0569084i	0.312930	−	0.949776i	$-0.398690\pi$
$41$	−0.879720	−	0.364392i	−0.137389	−	0.0569084i	−0.450319	+	0.892868i	$0.648690\pi$
$42$	−4.95884	−	2.86499i	−0.765166	−	0.442078i
$43$	−9.53263	+	1.89616i	−1.45371	+	0.289162i	−0.857840	−	0.513917i	$-0.828194\pi$
$43$	−9.53263	+	1.89616i	−1.45371	+	0.289162i	−0.595873	+	0.803079i	$0.703194\pi$
$44$	−0.118817	−	5.67178i	−0.0179124	−	0.855053i
$45$	1.87715	−	2.34015i	0.279829	−	0.348849i
$46$	−10.2948	+	3.24102i	−1.51789	+	0.477862i
$47$	4.63408	+	4.63408i	0.675950	+	0.675950i	0.959081	−	0.283131i	$-0.0913732\pi$
$47$	4.63408	+	4.63408i	0.675950	+	0.675950i	−0.283131	+	0.959081i	$0.591373\pi$
$48$	−2.66160	+	6.39655i	−0.384169	+	0.923263i
$49$	1.08443	−	1.08443i	0.154919	−	0.154919i
$50$	0.653557	−	1.25414i	0.0924270	−	0.177362i
$51$	−3.45373	−	3.76808i	−0.483619	−	0.527637i
$52$	−1.58728	−	3.61590i	−0.220116	−	0.501435i
$53$	1.07174	+	5.38802i	0.147215	+	0.740102i	0.981904	+	0.189380i	$0.0606477\pi$
$53$	1.07174	+	5.38802i	0.147215	+	0.740102i	−0.834689	+	0.550722i	$0.814352\pi$
$54$	−6.19778	+	3.94810i	−0.843412	+	0.537268i
$55$	1.08549	−	2.62060i	0.146367	−	0.353361i
$56$	5.24114	+	4.03255i	0.700377	+	0.538873i
$57$	5.75481	+	9.48080i	0.762244	+	1.25576i
$58$	11.3112	−	6.19912i	1.48523	−	0.813984i
$59$	7.94523	+	5.30883i	1.03438	+	0.691151i	0.952203	−	0.305467i	$-0.0988124\pi$
$59$	7.94523	+	5.30883i	1.03438	+	0.691151i	0.0821780	+	0.996618i	$0.473812\pi$
$60$	−2.50411	+	2.39362i	−0.323279	+	0.309015i
$61$	0.364498	−	1.83245i	0.0466692	−	0.234622i	−0.950410	−	0.311001i	$-0.899336\pi$
$61$	0.364498	−	1.83245i	0.0466692	−	0.234622i	0.997079	+	0.0763789i	$0.0243359\pi$
$62$	−5.02940	−	5.99910i	−0.638734	−	0.761887i
$63$	2.11095	+	6.68889i	0.265955	+	0.842721i
$64$	4.01809	−	6.91773i	0.502261	−	0.864716i
$65$		−	1.97447i		−	0.244903i
$66$	−4.58272	+	5.22240i	−0.564094	+	0.642833i
$67$	−8.67485	−	1.72553i	−1.05980	−	0.210808i	−0.365735	−	0.930719i	$-0.619182\pi$
$67$	−8.67485	−	1.72553i	−1.05980	−	0.210808i	−0.694066	+	0.719911i	$0.744182\pi$
$68$	3.38113	+	4.83772i	0.410022	+	0.586659i
$69$	11.9809	+	5.58483i	1.44233	+	0.672335i
$70$	1.58911	+	2.89956i	0.189935	+	0.346564i
$71$	8.56335	−	3.54706i	1.01628	−	0.420958i	0.188540	−	0.982066i	$-0.439625\pi$
$71$	8.56335	−	3.54706i	1.01628	−	0.420958i	0.827743	+	0.561107i	$0.189625\pi$
$72$	7.69401	−	3.57803i	0.906747	−	0.421675i
$73$	−9.84027	−	4.07597i	−1.15172	−	0.477057i	−0.276608	−	0.960983i	$-0.589210\pi$
$73$	−9.84027	−	4.07597i	−1.15172	−	0.477057i	−0.875109	+	0.483926i	$0.839210\pi$
$74$	4.83271	−	0.527138i	0.561791	−	0.0612786i
$75$	−1.62752	+	0.592612i	−0.187929	+	0.0684290i
$76$	−5.14754	−	11.7264i	−0.590463	−	1.34511i
$77$	3.68446	+	5.51418i	0.419883	+	0.628399i
$78$	−1.55601	+	4.57931i	−0.176184	+	0.518504i
$79$	−5.52976	−	5.52976i	−0.622147	−	0.622147i	0.323933	−	0.946080i	$-0.394995\pi$
$79$	−5.52976	−	5.52976i	−0.622147	−	0.622147i	−0.946080	+	0.323933i	$0.894995\pi$
$80$	3.22989	−	2.35962i	0.361113	−	0.263813i
$81$	8.86410	+	1.55813i	0.984900	+	0.173126i
$82$	−0.404376	−	1.28447i	−0.0446559	−	0.141846i
$83$	−3.20451	−	4.79589i	−0.351740	−	0.526417i	0.612839	−	0.790207i	$-0.290027\pi$
$83$	−3.20451	−	4.79589i	−0.351740	−	0.526417i	−0.964580	+	0.263791i	$0.915027\pi$
$84$	−1.40052	−	7.97716i	−0.152809	−	0.870380i
$85$	0.575728	+	2.89438i	0.0624464	+	0.313939i
$86$	−10.7160	−	8.60817i	−1.15554	−	0.928243i
$87$	−15.3452	−	3.75278i	−1.64518	−	0.402341i
$88$	6.03882	−	5.28196i	0.643740	−	0.563059i
$89$	3.13329	−	1.29785i	0.332128	−	0.137572i	−0.210387	−	0.977618i	$-0.567472\pi$
$89$	3.13329	−	1.29785i	0.332128	−	0.137572i	0.542515	+	0.840046i	$0.317472\pi$
$90$	4.24165	−	0.0918309i	0.447109	−	0.00967983i
$91$	3.83837	+	2.56472i	0.402371	+	0.268856i
$92$	−12.8660	−	8.21229i	−1.34137	−	0.856191i
$93$	−0.416944	+	9.57874i	−0.0432351	+	0.993269i
$94$	−0.811793	+	9.23254i	−0.0837301	+	0.952263i
$95$		−	6.40322i		−	0.656956i
$96$	−9.35048	+	2.92719i	−0.954330	+	0.298755i
$97$			5.83577i			0.592533i	0.955105	+	0.296267i	$0.0957417\pi$
$97$			5.83577i			0.592533i	−0.955105	+	0.296267i	$0.904258\pi$
$98$	2.16053	+	0.189970i	0.218247	+	0.0191899i
$99$	8.45872	−	0.928651i	0.850133	−	0.0933329i
$100$	1.95297	−	0.431179i	0.195297	−	0.0431179i
$101$	−14.4024	−	9.62335i	−1.43309	−	0.957560i	−0.998375	−	0.0569913i	$-0.981849\pi$
$101$	−14.4024	−	9.62335i	−1.43309	−	0.957560i	−0.434715	−	0.900568i	$-0.643151\pi$
$102$	0.945698	−	7.16652i	0.0936380	−	0.709591i
$103$	7.40217	−	3.06608i	0.729357	−	0.302110i	0.0130694	−	0.999915i	$-0.495840\pi$
$103$	7.40217	−	3.06608i	0.729357	−	0.302110i	0.716288	+	0.697805i	$0.245840\pi$
$104$	2.47657	−	5.00549i	0.242847	−	0.490829i
$105$	0.962007	−	3.93366i	0.0938823	−	0.383886i
$106$	−4.86550	+	6.05688i	−0.472579	+	0.588296i
$107$	3.24475	+	16.3125i	0.313682	+	1.57698i	0.740125	+	0.672470i	$0.234766\pi$
$107$	3.24475	+	16.3125i	0.313682	+	1.57698i	−0.426443	+	0.904514i	$0.640234\pi$
$108$	−9.90984	−	3.12971i	−0.953575	−	0.301157i
$109$	−0.316216	−	0.473250i	−0.0302880	−	0.0453292i	0.816017	−	0.578028i	$-0.196178\pi$
$109$	−0.316216	−	0.473250i	−0.0302880	−	0.0453292i	−0.846305	+	0.532699i	$0.821178\pi$
$110$	3.82630	−	1.20460i	0.364823	−	0.114854i
$111$	−4.80199	−	3.51999i	−0.455785	−	0.334102i
$112$	0.391661	+	9.34391i	0.0370084	+	0.882917i
$113$	3.74686	+	3.74686i	0.352475	+	0.352475i	0.861030	−	0.508555i	$-0.169820\pi$
$113$	3.74686	+	3.74686i	0.352475	+	0.352475i	−0.508555	+	0.861030i	$0.669820\pi$
$114$	−5.04615	+	14.8507i	−0.472615	+	1.39090i
$115$	−4.23998	−	6.34558i	−0.395380	−	0.591728i
$116$	16.9952	+	6.62613i	1.57797	+	0.615221i
$117$	5.19246	−	2.85047i	0.480043	−	0.263526i
$118$	1.46535	+	13.4340i	0.134896	+	1.23670i
$119$	−6.37451	−	2.64041i	−0.584350	−	0.242046i
$120$	−4.86923	−	0.539051i	−0.444498	−	0.0492084i
$121$	−2.72932	+	1.13052i	−0.248120	+	0.102775i
$122$	2.31709	−	1.26988i	0.209779	−	0.114970i
$123$	−0.696810	+	1.49483i	−0.0628292	+	0.134784i
$124$	1.93196	−	10.9012i	0.173495	−	0.978955i
$125$	0.980785	+	0.195090i	0.0877241	+	0.0174494i
$126$	−5.33112	+	8.36504i	−0.474934	+	0.745217i
$127$		−	14.8804i		−	1.32042i	−0.751081	−	0.660210i	$-0.770467\pi$
$127$		−	14.8804i		−	1.32042i	0.751081	−	0.660210i	$-0.229533\pi$
$128$	11.1478	−	1.93064i	0.985332	−	0.170646i
$129$	2.56312	+	16.6382i	0.225671	+	1.46491i
$130$	2.13983	−	1.79394i	0.187675	−	0.157339i
$131$	−1.57847	+	7.93549i	−0.137911	+	0.693327i	0.848521	+	0.529161i	$0.177493\pi$
$131$	−1.57847	+	7.93549i	−0.137911	+	0.693327i	−0.986433	+	0.164166i	$0.947507\pi$
$132$	−9.82347	−	0.221604i	−0.855023	−	0.0192882i
$133$	12.4479	+	8.31739i	1.07937	+	0.721209i
$134$	−6.01164	−	10.9691i	−0.519327	−	0.947586i
$135$	−3.90804	−	3.42451i	−0.336350	−	0.294735i
$136$	−2.17087	+	8.05968i	−0.186151	+	0.691112i
$137$	4.44674	−	10.7354i	0.379911	−	0.917185i	−0.612071	−	0.790803i	$-0.709663\pi$
$137$	4.44674	−	10.7354i	0.379911	−	0.917185i	0.991982	−	0.126383i	$-0.0403367\pi$
$138$	4.83288	+	18.0584i	0.411402	+	1.53723i
$139$	3.24106	+	16.2939i	0.274903	+	1.38203i	0.833466	+	0.552571i	$0.186353\pi$
$139$	3.24106	+	16.2939i	0.274903	+	1.38203i	−0.558563	+	0.829462i	$0.688647\pi$
$140$	−1.69858	+	4.35665i	−0.143556	+	0.368204i
$141$	8.36791	−	7.66982i	0.704705	−	0.645915i
$142$	11.6245	+	6.05776i	0.975505	+	0.508356i
$143$	3.96023	−	3.96023i	0.331171	−	0.331171i
$144$	10.8682	+	5.08747i	0.905683	+	0.423956i
$145$	6.44926	+	6.44926i	0.535582	+	0.535582i
$146$	−4.52323	−	14.3677i	−0.374345	−	1.18908i
$147$	−1.79484	−	1.95820i	−0.148036	−	0.161510i
$148$	4.96212	+	4.75849i	0.407884	+	0.391145i
$149$	9.68876	−	1.92721i	0.793734	−	0.157884i	0.218462	−	0.975845i	$-0.429896\pi$
$149$	9.68876	−	1.92721i	0.793734	−	0.157884i	0.575272	+	0.817962i	$0.304896\pi$
$150$	−2.12095	−	1.22539i	−0.173175	−	0.100052i
$151$	7.90073	+	3.27259i	0.642952	+	0.266319i	0.680245	−	0.732985i	$-0.261873\pi$
$151$	7.90073	+	3.27259i	0.642952	+	0.266319i	−0.0372929	+	0.999304i	$0.511873\pi$
$152$	8.03151	−	16.2328i	0.651442	−	1.31665i
$153$	−6.78047	+	5.69256i	−0.548169	+	0.460216i
$154$	−2.62839	+	9.00302i	−0.211802	+	0.725484i
$155$	3.07537	−	4.60262i	0.247020	−	0.369691i
$156$	−6.37655	+	2.47429i	−0.510532	+	0.198101i
$157$	14.2508	+	2.83467i	1.13734	+	0.226231i	0.727620	−	0.685980i	$-0.240626\pi$
$157$	14.2508	+	2.83467i	1.13734	+	0.226231i	0.409720	+	0.912211i	$0.365626\pi$
$158$	0.968698	−	11.0170i	0.0770655	−	0.876467i
$159$	9.40423	−	1.44873i	0.745804	−	0.114891i
$160$	5.49180	+	1.35651i	0.434165	+	0.107242i
$161$	17.8433			1.40625
$162$	6.36501	+	11.0221i	0.500082	+	0.865978i
$163$	−0.295021	+	1.48317i	−0.0231078	+	0.116171i	−0.990618	−	0.136662i	$-0.956362\pi$
$163$	−0.295021	+	1.48317i	−0.0231078	+	0.116171i	0.967510	+	0.252833i	$0.0813624\pi$
$164$	1.02463	−	1.60527i	0.0800104	−	0.125350i
$165$	−4.45295	−	2.07573i	−0.346662	−	0.161595i
$166$	2.28601	−	7.83026i	0.177429	−	0.607746i
$167$	−2.16672	−	5.23092i	−0.167666	−	0.404781i	0.817606	−	0.575779i	$-0.195301\pi$
$167$	−2.16672	−	5.23092i	−0.167666	−	0.404781i	−0.985271	+	0.170998i	$0.945301\pi$
$168$	7.37275	−	8.76559i	0.568820	−	0.676280i
$169$	−3.48298	+	8.40865i	−0.267921	+	0.646820i
$170$	−2.61368	+	3.25368i	−0.200460	+	0.249546i
$171$	16.8392	−	9.24409i	1.28772	−	0.706913i
$172$	−0.407131	−	19.4345i	−0.0310435	−	1.48187i
$173$	−13.7341	+	9.17683i	−1.04418	+	0.697702i	−0.954483	−	0.298267i	$-0.903591\pi$
$173$	−13.7341	+	9.17683i	−1.04418	+	0.697702i	−0.0897020	+	0.995969i	$0.528591\pi$
$174$	−9.87506	−	20.0399i	−0.748626	−	1.51922i
$175$	−1.65324	+	1.65324i	−0.124973	+	0.124973i
$176$	11.2110	+	1.74553i	0.845059	+	0.131574i
$177$	9.78492	−	13.3487i	0.735479	−	1.00335i
$178$	4.25334	+	2.21651i	0.318802	+	0.166134i
$179$	−9.30247	+	6.21571i	−0.695299	+	0.464584i	−0.852326	−	0.523010i	$-0.824809\pi$
$179$	−9.30247	+	6.21571i	−0.695299	+	0.464584i	0.157027	+	0.987594i	$0.449809\pi$
$180$	3.95334	+	4.51343i	0.294665	+	0.336411i
$181$	−14.0536	+	2.79544i	−1.04460	+	0.207783i	−0.687425	−	0.726256i	$-0.741259\pi$
$181$	−14.0536	+	2.79544i	−1.04460	+	0.207783i	−0.357171	+	0.934039i	$0.616259\pi$
$182$	0.707916	+	6.49004i	0.0524742	+	0.481074i
$183$	−3.14345	−	0.768755i	−0.232370	−	0.0568280i
$184$	−2.78957	−	21.4049i	−0.205650	−	1.57799i
$185$	1.31548	+	3.17584i	0.0967158	+	0.233493i
$186$	−10.7597	+	8.25107i	−0.788943	+	0.604998i
$187$	−4.65056	+	6.96005i	−0.340083	+	0.508969i
$188$	−10.7433	+	7.50860i	−0.783535	+	0.547621i
$189$	11.7335	−	3.14900i	0.853490	−	0.229056i
$190$	6.93946	−	5.81775i	0.503441	−	0.422064i
$191$	24.2396			1.75392			0.876959	−	0.480566i	$-0.159569\pi$
$191$	24.2396			1.75392			0.876959	+	0.480566i	$0.159569\pi$
$192$	−11.6679	−	7.47400i	−0.842056	−	0.539389i
$193$	−12.0578			−0.867937			−0.433969	−	0.900928i	$-0.642887\pi$
$193$	−12.0578			−0.867937			−0.433969	+	0.900928i	$0.642887\pi$
$194$	−6.32450	+	5.30219i	−0.454073	+	0.380675i
$195$	−3.41665	−	0.148720i	−0.244671	−	0.0106501i
$196$	1.75711	+	2.51407i	0.125508	+	0.179576i
$197$	−5.74600	+	8.59949i	−0.409385	+	0.612688i	−0.977671	−	0.210143i	$-0.932607\pi$
$197$	−5.74600	+	8.59949i	−0.409385	+	0.612688i	0.568285	+	0.822832i	$0.307607\pi$
$198$	8.69173	+	8.32336i	0.617695	+	0.591515i
$199$	−0.909145	−	2.19487i	−0.0644476	−	0.155590i	0.888375	−	0.459119i	$-0.151835\pi$
$199$	−0.909145	−	2.19487i	−0.0644476	−	0.155590i	−0.952822	+	0.303529i	$0.901835\pi$
$200$	2.24169	+	1.72477i	0.158511	+	0.121959i
$201$	−3.63929	+	14.8811i	−0.256696	+	1.04963i
$202$	−2.65625	−	24.3520i	−0.186893	−	1.71340i
$203$	−20.9146	+	4.16016i	−1.46791	+	0.291986i
$204$	8.62592	−	5.48637i	0.603935	−	0.384123i
$205$	0.791727	−	0.529015i	0.0552966	−	0.0369480i
$206$	10.0482	+	5.23633i	0.700092	+	0.364833i
$207$	10.5665	−	20.3112i	0.734421	−	1.41172i
$208$	7.67481	−	1.86385i	0.532152	−	0.129235i
$209$	12.8430	−	12.8430i	0.888372	−	0.888372i
$210$	5.13714	−	2.53142i	0.354496	−	0.174685i
$211$	−1.17615	+	0.785878i	−0.0809695	+	0.0541021i	−0.595396	−	0.803432i	$-0.703005\pi$
$211$	−1.17615	+	0.785878i	−0.0809695	+	0.0541021i	0.514427	+	0.857534i	$0.328005\pi$
$212$	−10.9848	+	0.230118i	−0.754436	+	0.0158046i
$213$	−5.49287	−	15.0853i	−0.376365	−	1.03363i
$214$	−14.7305	+	18.3374i	−1.00696	+	1.25352i
$215$	3.71945	−	8.97955i	0.253664	−	0.612400i
$216$	−5.61194	−	13.5833i	−0.381844	−	0.924227i
$217$	4.95277	+	11.9570i	0.336216	+	0.811697i
$218$	0.225580	−	0.772677i	0.0152782	−	0.0523323i
$219$	−7.79430	+	16.7207i	−0.526690	+	1.12988i
$220$	4.78193	+	3.05228i	0.322397	+	0.205785i
$221$	−1.13676	+	5.71487i	−0.0764666	+	0.384424i
$222$	−0.548160	−	8.40228i	−0.0367901	−	0.563924i
$223$	1.97351			0.132156			0.0660779	−	0.997814i	$-0.478951\pi$
$223$	1.97351			0.132156			0.0660779	+	0.997814i	$0.478951\pi$
$224$	−9.77058	+	8.91403i	−0.652824	+	0.595594i
$225$	0.902876	+	2.86091i	0.0601918	+	0.190727i
$226$	−0.656371	+	7.46492i	−0.0436611	+	0.496559i
$227$	−21.1853	−	4.21402i	−1.40612	−	0.279695i	−0.567034	−	0.823694i	$-0.691909\pi$
$227$	−21.1853	−	4.21402i	−1.40612	−	0.279695i	−0.839085	+	0.544000i	$0.816909\pi$
$228$	−20.6792	+	8.02412i	−1.36951	+	0.531410i
$229$	8.94810	−	13.3918i	0.591307	−	0.884954i	−0.408304	−	0.912846i	$-0.633880\pi$
$229$	8.94810	−	13.3918i	0.591307	−	0.884954i	0.999611	+	0.0278924i	$0.00887957\pi$
$230$	3.02469	−	10.3604i	0.199442	−	0.683148i
$231$	9.81933	−	5.96030i	0.646064	−	0.392159i
$232$	8.26027	+	24.4388i	0.542313	+	1.60449i
$233$	20.8761	+	8.64716i	1.36764	+	0.566494i	0.941147	−	0.337998i	$-0.109750\pi$
$233$	20.8761	+	8.64716i	1.36764	+	0.566494i	0.426491	+	0.904492i	$0.359750\pi$
$234$	7.80689	+	3.03746i	0.510352	+	0.198565i
$235$	−6.42765	+	1.27854i	−0.419294	+	0.0834027i
$236$	−13.2277	+	13.7938i	−0.861052	+	0.897900i
$237$	−9.98528	+	9.15226i	−0.648614	+	0.594503i
$238$	−2.93014	−	9.30733i	−0.189933	−	0.603305i
$239$	−8.54796	−	8.54796i	−0.552922	−	0.552922i	0.374361	−	0.927283i	$-0.377862\pi$
$239$	−8.54796	−	8.54796i	−0.552922	−	0.552922i	−0.927283	+	0.374361i	$0.877862\pi$
$240$	−3.83983	−	5.76678i	−0.247860	−	0.372244i
$241$	13.0956	−	13.0956i	0.843564	−	0.843564i	−0.145756	−	0.989321i	$-0.546562\pi$
$241$	13.0956	−	13.0956i	0.843564	−	0.843564i	0.989321	+	0.145756i	$0.0465615\pi$
$242$	−3.70497	−	1.93073i	−0.238164	−	0.124112i
$243$	3.36387	−	15.2212i	0.215792	−	0.976439i
$244$	3.48146	+	1.35736i	0.222878	+	0.0868959i
$245$	0.299195	+	1.50415i	0.0191148	+	0.0960968i
$246$	−2.25312	+	0.602990i	−0.143653	+	0.0384452i
$247$	4.83825	−	11.6806i	0.307851	−	0.743218i
$248$	13.5694	−	7.81070i	0.861659	−	0.495980i
$249$	−8.54023	+	5.18389i	−0.541215	+	0.328515i
$250$	0.679681	+	1.24017i	0.0429868	+	0.0784355i
$251$	7.05364	+	4.71309i	0.445222	+	0.297488i	0.757899	−	0.652372i	$-0.226226\pi$
$251$	7.05364	+	4.71309i	0.445222	+	0.297488i	−0.312677	+	0.949859i	$0.601226\pi$
$252$	−13.9093	+	1.82262i	−0.876201	+	0.114814i
$253$	4.22324	−	21.2316i	0.265513	−	1.33482i
$254$	16.1266	−	13.5198i	1.01187	−	0.848309i
$255$	5.05183	−	0.778237i	0.316358	−	0.0487351i
$256$	12.2208	+	10.3272i	0.763801	+	0.645452i
$257$		−	0.636039i		−	0.0396750i	−0.999803	−	0.0198375i	$-0.993685\pi$
$257$		−	0.636039i		−	0.0396750i	0.999803	−	0.0198375i	$-0.00631489\pi$
$258$	−15.7028	+	17.8947i	−0.977615	+	1.11408i
$259$	−7.88257	−	1.56794i	−0.489799	−	0.0974270i
$260$	3.88835	+	0.689113i	0.241145	+	0.0427370i
$261$	−7.64968	+	26.2708i	−0.473503	+	1.62612i
$262$	−10.0342	+	5.49927i	−0.619915	+	0.339746i
$263$	13.5679	−	5.61999i	0.836630	−	0.346543i	0.0771059	−	0.997023i	$-0.475432\pi$
$263$	13.5679	−	5.61999i	0.836630	−	0.346543i	0.759524	+	0.650480i	$0.225432\pi$
$264$	−8.68512	−	10.8475i	−0.534532	−	0.667617i
$265$	−5.07541	−	2.10230i	−0.311780	−	0.129143i
$266$	2.29577	+	21.0472i	0.140763	+	1.29049i
$267$	−2.00981	−	5.51964i	−0.122999	−	0.337796i
$268$	6.42574	−	16.4813i	0.392514	−	1.00675i
$269$	−9.17908	−	13.7375i	−0.559659	−	0.837588i	0.438469	−	0.898746i	$-0.355521\pi$
$269$	−9.17908	−	13.7375i	−0.559659	−	0.837588i	−0.998128	+	0.0611577i	$0.980521\pi$
$270$	0.160582	−	7.34671i	0.00977270	−	0.447107i
$271$	0.805739	+	0.805739i	0.0489451	+	0.0489451i	0.731156	−	0.682211i	$-0.238981\pi$
$271$	0.805739	+	0.805739i	0.0489451	+	0.0489451i	−0.682211	+	0.731156i	$0.738981\pi$
$272$	−10.7070	+	4.97009i	−0.649209	+	0.301356i
$273$	4.72713	−	6.44879i	0.286099	−	0.390298i
$274$	15.6746	−	4.93468i	0.946937	−	0.298115i
$275$	1.57588	+	2.35847i	0.0950293	+	0.142221i
$276$	−15.1797	+	21.6449i	−0.913713	+	1.30287i
$277$	6.15991	+	30.9680i	0.370113	+	1.86068i	0.495545	+	0.868583i	$0.334969\pi$
$277$	6.15991	+	30.9680i	0.370113	+	1.86068i	−0.125431	+	0.992102i	$0.540031\pi$
$278$	−14.7138	+	18.3166i	−0.882472	+	1.09856i
$279$	16.5438	+	1.44297i	0.990449	+	0.0863884i
$280$	−6.26477	+	2.11748i	−0.374391	+	0.126544i
$281$	−20.8836	+	8.65026i	−1.24581	+	0.516031i	−0.905526	−	0.424291i	$-0.860523\pi$
$281$	−20.8836	+	8.65026i	−1.24581	+	0.516031i	−0.340284	+	0.940323i	$0.610523\pi$
$282$	15.9149	+	2.10015i	0.947721	+	0.125062i
$283$	−27.2969	−	18.2392i	−1.62263	−	1.08421i	−0.932896	−	0.360147i	$-0.882727\pi$
$283$	−27.2969	−	18.2392i	−1.62263	−	1.08421i	−0.689736	−	0.724061i	$-0.742273\pi$
$284$	3.99655	+	18.1019i	0.237152	+	1.07415i
$285$	−11.0802	−	0.482300i	−0.656335	−	0.0285690i
$286$	7.89002	+	0.693749i	0.466547	+	0.0410223i
$287$			2.22628i			0.131413i
$288$	4.36096	+	16.4007i	0.256972	+	0.966419i
$289$			8.29111i			0.487712i
$290$	−1.12977	+	12.8489i	−0.0663426	+	0.754516i
$291$	10.0983	+	0.439559i	0.591973	+	0.0257674i
$292$	11.4612	−	17.9560i	0.670718	−	1.05080i
$293$	−21.9932	−	14.6954i	−1.28486	−	0.858513i	−0.289728	−	0.957109i	$-0.593565\pi$
$293$	−21.9932	−	14.6954i	−1.28486	−	0.858513i	−0.995128	+	0.0985964i	$0.968565\pi$
$294$	0.491461	−	3.72430i	0.0286626	−	0.217206i
$295$	−8.82827	+	3.65679i	−0.514002	+	0.212906i
$296$	−0.648570	+	9.70109i	−0.0376974	+	0.563864i
$297$	−0.969825	−	14.7070i	−0.0562750	−	0.853387i
$298$	10.8915	+	8.74915i	0.630928	+	0.506825i
$299$	−2.93976	−	14.7792i	−0.170011	−	0.854701i
$300$	−0.599016	−	3.41192i	−0.0345842	−	0.196987i
$301$	12.6249	+	18.8945i	0.727687	+	1.08906i
$302$	3.63169	+	11.5357i	0.208980	+	0.663808i
$303$	−17.7372	+	24.1972i	−1.01897	+	1.39009i
$304$	24.8894	−	6.04448i	1.42751	−	0.346675i
$305$	1.32113	+	1.32113i	0.0756474	+	0.0756474i
$306$	−12.3298	−	2.17624i	−0.704848	−	0.124407i
$307$	3.05631	+	4.57409i	0.174433	+	0.261057i	0.908377	−	0.418153i	$-0.137322\pi$
$307$	3.05631	+	4.57409i	0.174433	+	0.261057i	−0.733944	+	0.679210i	$0.762322\pi$
$308$	−12.1451	+	5.33134i	−0.692029	+	0.303781i
$309$	−4.74804	−	13.0397i	−0.270106	−	0.741805i
$310$	7.78226	−	0.848867i	0.442002	−	0.0482124i
$311$	−17.3066	−	7.16865i	−0.981370	−	0.406497i	−0.166437	−	0.986052i	$-0.553226\pi$
$311$	−17.3066	−	7.16865i	−0.981370	−	0.406497i	−0.814933	+	0.579555i	$0.803226\pi$
$312$	−8.47502	−	4.66250i	−0.479804	−	0.263962i
$313$	−16.6132	+	6.88142i	−0.939035	+	0.388961i	−0.799099	−	0.601200i	$-0.794690\pi$
$313$	−16.6132	+	6.88142i	−0.939035	+	0.388961i	−0.139936	+	0.990161i	$0.544690\pi$
$314$	9.87578	+	18.0198i	0.557322	+	1.01691i
$315$	−6.73439	−	1.96096i	−0.379440	−	0.110488i
$316$	12.8198	−	8.95988i	0.721169	−	0.504033i
$317$	6.72320	+	1.33733i	0.377612	+	0.0751118i	0.380248	−	0.924885i	$-0.375839\pi$
$317$	6.72320	+	1.33733i	0.377612	+	0.0751118i	−0.00263511	+	0.999997i	$0.500839\pi$
$318$	10.1144	+	8.87553i	0.567189	+	0.497715i
$319$			25.8708i			1.44849i
$320$	3.51955	+	7.18420i	0.196749	+	0.401609i
$321$	28.4717	−	4.38607i	1.58913	−	0.244807i
$322$	16.2118	+	19.3376i	0.903449	+	1.07764i
$323$	−3.68651	+	18.5333i	−0.205123	+	1.03122i
$324$	−6.16212	+	16.9124i	−0.342340	+	0.939576i
$325$	1.64171	+	1.09696i	0.0910659	+	0.0608483i
$326$	−1.87543	+	1.02783i	−0.103870	+	0.0569263i
$327$	−0.842736	+	0.511538i	−0.0466034	+	0.0282881i
$328$	2.67065	−	0.348049i	0.147462	−	0.0192178i
$329$	5.86365	−	14.1561i	0.323273	−	0.780451i
$330$	−1.79625	−	6.71181i	−0.0988800	−	0.369473i
$331$	1.81830	+	9.14123i	0.0999430	+	0.502447i	0.998036	+	0.0626419i	$0.0199526\pi$
$331$	1.81830	+	9.14123i	0.0999430	+	0.502447i	−0.898093	+	0.439805i	$0.855047\pi$
$332$	10.5630	−	4.63686i	0.579720	−	0.254481i
$333$	−6.45272	+	8.04429i	−0.353607	+	0.440824i
$334$	3.70038	−	7.10082i	0.202476	−	0.388539i
$335$	6.25422	−	6.25422i	0.341704	−	0.341704i
$336$	16.1983	+	0.0260632i	0.883691	+	0.00142186i
$337$	13.3540	+	13.3540i	0.727437	+	0.727437i	0.970108	−	0.242672i	$-0.0780238\pi$
$337$	13.3540	+	13.3540i	0.727437	+	0.727437i	−0.242672	+	0.970108i	$0.578024\pi$
$338$	−12.2774	+	3.86516i	−0.667801	+	0.210237i
$339$	6.76583	−	6.20139i	0.367469	−	0.336813i
$340$	−5.90087	+	0.123617i	−0.320020	+	0.00670405i
$341$	15.3999	−	3.06323i	0.833951	−	0.165883i
$342$	25.3178	+	9.85050i	1.36903	+	0.532654i
$343$	−18.4331	−	7.63524i	−0.995294	−	0.412264i
$344$	20.6922	−	18.0988i	1.11565	−	0.975821i
$345$	−11.2998	+	6.85895i	−0.608362	+	0.369274i
$346$	−22.4237	−	6.54651i	−1.20551	−	0.351943i
$347$	−18.4313	+	27.5843i	−0.989443	+	1.48081i	−0.116376	+	0.993205i	$0.537128\pi$
$347$	−18.4313	+	27.5843i	−0.989443	+	1.48081i	−0.873067	+	0.487600i	$0.837872\pi$
$348$	12.7460	−	28.9097i	0.683260	−	1.54972i
$349$	−6.47517	−	1.28799i	−0.346608	−	0.0689446i	0.0187165	−	0.999825i	$-0.494042\pi$
$349$	−6.47517	−	1.28799i	−0.346608	−	0.0689446i	−0.365325	+	0.930880i	$0.619042\pi$
$350$	−3.29376	−	0.289612i	−0.176059	−	0.0154804i
$351$	−4.54139	−	9.19980i	−0.242401	−	0.491049i
$352$	8.29422	+	13.7358i	0.442083	+	0.732120i
$353$	−13.3220			−0.709057			−0.354529	−	0.935045i	$-0.615359\pi$
$353$	−13.3220			−0.709057			−0.354529	+	0.935045i	$0.615359\pi$
$354$	23.3568	−	1.52378i	1.24140	−	0.0809882i
$355$	−1.80827	+	9.09081i	−0.0959732	+	0.482490i
$356$	1.46232	+	6.62339i	0.0775028	+	0.351039i
$357$	−5.04913	+	10.8316i	−0.267228	+	0.573271i
$358$	−15.1882	−	4.43413i	−0.802720	−	0.234351i
$359$	−9.93681	−	23.9896i	−0.524445	−	1.26612i	−0.935117	−	0.354339i	$-0.884706\pi$
$359$	−9.93681	−	23.9896i	−0.524445	−	1.26612i	0.410672	−	0.911783i	$-0.365294\pi$
$360$	−1.29954	+	8.38518i	−0.0684917	+	0.441938i
$361$	8.41948	−	20.3264i	0.443131	−	1.06981i
$362$	−15.7982	−	12.6907i	−0.830334	−	0.667008i
$363$	1.75069	+	4.80800i	0.0918874	+	0.252355i
$364$	−6.39037	+	6.66384i	−0.334946	+	0.349280i
$365$	8.85601	−	5.91740i	0.463545	−	0.309731i
$366$	−2.02290	−	4.10516i	−0.105739	−	0.214580i
$367$	−22.3949	+	22.3949i	−1.16900	+	1.16900i	−0.186558	+	0.982444i	$0.559733\pi$
$367$	−22.3949	+	22.3949i	−1.16900	+	1.16900i	−0.982444	+	0.186558i	$0.940267\pi$
$368$	20.6629	−	22.4709i	1.07713	−	1.17138i
$369$	2.53419	+	1.31836i	0.131925	+	0.0686312i
$370$	−2.24661	+	4.31111i	−0.116796	+	0.224124i
$371$	10.6795	−	7.13583i	0.554453	−	0.370474i
$372$	−18.7180	−	4.16418i	−0.970484	−	0.215903i
$373$	−22.3534	+	4.44636i	−1.15741	+	0.230224i	−0.736217	−	0.676746i	$-0.763390\pi$
$373$	−22.3534	+	4.44636i	−1.15741	+	0.230224i	−0.421196	+	0.906969i	$0.638390\pi$
$374$	−11.7683	+	1.28365i	−0.608523	+	0.0663760i
$375$	0.411461	−	1.68247i	0.0212478	−	0.0868823i
$376$	−17.8984	−	4.82093i	−0.923041	−	0.248621i
$377$	6.89153	+	16.6376i	0.354932	+	0.856881i
$378$	14.0734	+	9.85511i	0.723859	+	0.506892i
$379$	6.88836	−	10.3092i	0.353831	−	0.529546i	−0.611270	−	0.791422i	$-0.709341\pi$
$379$	6.88836	−	10.3092i	0.353831	−	0.529546i	0.965101	+	0.261876i	$0.0843412\pi$
$380$	12.6099	+	2.23480i	0.646876	+	0.114643i
$381$	−25.7492	−	1.12081i	−1.31917	−	0.0574210i
$382$	22.0233	+	26.2696i	1.12681	+	1.34407i
$383$	−28.8248			−1.47288			−0.736440	−	0.676503i	$-0.763495\pi$
$383$	−28.8248			−1.47288			−0.736440	+	0.676503i	$0.763495\pi$
$384$	−2.50113	−	19.4356i	−0.127635	−	0.991821i
$385$	−6.63185			−0.337990
$386$	−10.9553	−	13.0676i	−0.557610	−	0.665121i
$387$	28.9840	−	3.18205i	1.47334	−	0.161753i
$388$	−11.4925	−	2.03675i	−0.583441	−	0.103400i
$389$	−1.84753	+	2.76502i	−0.0936734	+	0.140192i	−0.875346	−	0.483496i	$-0.839367\pi$
$389$	−1.84753	+	2.76502i	−0.0936734	+	0.140192i	0.781673	+	0.623689i	$0.214367\pi$
$390$	−2.94308	−	3.83790i	−0.149029	−	0.194340i
$391$	8.61878	+	20.8076i	0.435870	+	1.05228i
$392$	−1.12816	+	4.18846i	−0.0569807	+	0.211549i
$393$	13.6128	+	3.32911i	0.686674	+	0.167932i
$394$	−14.5403	+	1.58601i	−0.732529	+	0.0799022i
$395$	7.67000	−	1.52566i	0.385920	−	0.0767642i
$396$	−1.12339	+	16.9820i	−0.0564522	+	0.853376i
$397$	−4.10241	+	2.74115i	−0.205894	+	0.137574i	−0.654243	−	0.756285i	$-0.727012\pi$
$397$	−4.10241	+	2.74115i	−0.205894	+	0.137574i	0.448348	+	0.893859i	$0.352012\pi$
$398$	1.55266	−	2.97947i	0.0778279	−	0.149347i
$399$	15.3301	−	20.9134i	0.767465	−	1.04698i
$400$	0.167517	+	3.99649i	0.00837587	+	0.199825i
$401$	−16.7683	+	16.7683i	−0.837367	+	0.837367i	−0.988512	−	0.151145i	$-0.951704\pi$
$401$	−16.7683	+	16.7683i	−0.837367	+	0.837367i	0.151145	+	0.988512i	$0.451704\pi$
$402$	−19.4339	+	9.57641i	−0.969273	+	0.477628i
$403$	9.08774	−	6.07224i	0.452693	−	0.302480i
$404$	23.9780	−	25.0041i	1.19295	−	1.24400i
$405$	−6.22017	+	6.50458i	−0.309083	+	0.323215i
$406$	−23.5108	−	18.8863i	−1.16682	−	0.937310i
$407$	−3.73137	+	9.00832i	−0.184957	+	0.446526i
$408$	13.7831	+	4.36357i	0.682363	+	0.216029i
$409$	−8.59599	−	20.7526i	−0.425044	−	1.02615i	−0.980838	−	0.194827i	$-0.937585\pi$
$409$	−8.59599	−	20.7526i	−0.425044	−	1.02615i	0.555793	−	0.831321i	$-0.312415\pi$
$410$	1.29266	+	0.377385i	0.0638397	+	0.0186377i
$411$	−18.2417	−	8.50330i	−0.899797	−	0.419437i
$412$	3.45462	+	15.6473i	0.170197	+	0.770886i
$413$	4.35859	−	21.9121i	0.214472	−	1.07822i
$414$	31.6125	−	7.00268i	1.55367	−	0.344163i
$415$	5.76796			0.283138
$416$	8.99302	+	6.62411i	0.440919	+	0.324774i
$417$	28.4393	−	4.38109i	1.39268	−	0.214543i
$418$	25.5874	+	2.24983i	1.25152	+	0.110043i
$419$	17.3857	+	3.45823i	0.849347	+	0.168946i	0.600527	−	0.799604i	$-0.294957\pi$
$419$	17.3857	+	3.45823i	0.849347	+	0.168946i	0.248820	+	0.968550i	$0.419957\pi$
$420$	7.41085	+	3.26739i	0.361613	+	0.159432i
$421$	6.76935	−	10.1311i	0.329918	−	0.493757i	−0.629014	−	0.777394i	$-0.716541\pi$
$421$	6.76935	−	10.1311i	0.329918	−	0.493757i	0.958932	+	0.283637i	$0.0915410\pi$
$422$	−1.92030	−	0.560625i	−0.0934789	−	0.0272908i
$423$	−12.6417	−	15.0576i	−0.614659	−	0.732127i
$424$	−10.2298	−	11.6956i	−0.496802	−	0.567989i
$425$	−2.72644	−	1.12933i	−0.132252	−	0.0547806i
$426$	11.3580	−	19.6589i	0.550297	−	0.952476i
$427$	−4.28433	+	0.852206i	−0.207333	+	0.0412411i
$428$	−33.2568	+	0.696692i	−1.60753	+	0.0336759i
$429$	−6.55454	−	7.15113i	−0.316456	−	0.345260i
$430$	13.1109	−	4.12758i	0.632265	−	0.199050i
$431$	−12.4303	−	12.4303i	−0.598746	−	0.598746i	0.341233	−	0.939979i	$-0.389156\pi$
$431$	−12.4303	−	12.4303i	−0.598746	−	0.598746i	−0.939979	+	0.341233i	$0.889156\pi$
$432$	9.62203	−	18.4233i	0.462940	−	0.886390i
$433$	−3.55902	+	3.55902i	−0.171035	+	0.171035i	−0.787434	−	0.616399i	$-0.788591\pi$
$433$	−3.55902	+	3.55902i	−0.171035	+	0.171035i	0.616399	+	0.787434i	$0.288591\pi$
$434$	−8.45848	+	16.2313i	−0.406020	+	0.779129i
$435$	11.6456	−	10.6741i	0.558366	−	0.511784i
$436$	1.04234	−	0.457558i	0.0499191	−	0.0219130i
$437$	−9.53364	−	47.9288i	−0.456056	−	2.29275i
$438$	−25.2027	+	6.74485i	−1.20423	+	0.322282i
$439$	5.70825	−	13.7809i	0.272440	−	0.657728i	−0.727147	−	0.686482i	$-0.759154\pi$
$439$	5.70825	−	13.7809i	0.272440	−	0.657728i	0.999587	+	0.0287544i	$0.00915406\pi$
$440$	1.03680	+	7.95559i	0.0494277	+	0.379268i
$441$	−3.52368	+	2.95831i	−0.167794	+	0.140872i
$442$	−7.22629	+	3.96038i	−0.343719	+	0.188376i
$443$	−7.82705	−	5.22987i	−0.371874	−	0.248479i	0.355563	−	0.934652i	$-0.384289\pi$
$443$	−7.82705	−	5.22987i	−0.371874	−	0.248479i	−0.727438	+	0.686174i	$0.759289\pi$
$444$	8.60790	−	8.22810i	0.408513	−	0.390488i
$445$	−0.661639	+	3.32628i	−0.0313647	+	0.157681i
$446$	1.79306	+	2.13878i	0.0849040	+	0.101274i
$447$	−2.60510	−	16.9107i	−0.123217	−	0.799849i
$448$	−18.5378	−	2.48983i	−0.875827	−	0.117633i
$449$			18.7544i			0.885077i	0.896750	+	0.442538i	$0.145922\pi$
$449$			18.7544i			0.885077i	−0.896750	+	0.442538i	$0.854078\pi$
$450$	−2.28018	+	3.57782i	−0.107489	+	0.168660i
$451$	2.64904	+	0.526926i	0.124738	+	0.0248120i
$452$	−8.68643	+	6.07104i	−0.408575	+	0.285558i
$453$	6.25802	−	13.4250i	0.294027	−	0.630762i
$454$	−14.6814	−	26.7882i	−0.689031	−	1.25723i
$455$	−4.26497	+	1.76661i	−0.199945	+	0.0828199i
$456$	−27.4845	−	15.1205i	−1.28708	−	0.708083i
$457$	−25.1849	−	10.4319i	−1.17810	−	0.487986i	−0.294239	−	0.955732i	$-0.595066\pi$
$457$	−25.1849	−	10.4319i	−1.17810	−	0.487986i	−0.883863	+	0.467746i	$0.845066\pi$
$458$	22.6432	−	2.46986i	1.05805	−	0.115409i
$459$	9.33975	+	12.1618i	0.435942	+	0.567663i
$460$	13.9762	−	6.13517i	0.651645	−	0.286054i
$461$	1.26474	+	1.89281i	0.0589046	+	0.0881570i	0.859753	−	0.510711i	$-0.170618\pi$
$461$	1.26474	+	1.89281i	0.0589046	+	0.0881570i	−0.800848	+	0.598868i	$0.795618\pi$
$462$	15.3810	+	5.22633i	0.715587	+	0.243151i
$463$	−11.4509	−	11.4509i	−0.532168	−	0.532168i	0.389049	−	0.921217i	$-0.372804\pi$
$463$	−11.4509	−	11.4509i	−0.532168	−	0.532168i	−0.921217	+	0.389049i	$0.872804\pi$
$464$	−18.9804	+	31.1563i	−0.881145	+	1.44640i
$465$	−7.73279	−	5.66834i	−0.358600	−	0.262863i
$466$	9.59600	+	30.4809i	0.444526	+	1.41200i
$467$	−18.0764	−	27.0533i	−0.836477	−	1.25188i	−0.965544	−	0.260240i	$-0.916198\pi$
$467$	−18.0764	−	27.0533i	−0.836477	−	1.25188i	0.129067	−	0.991636i	$-0.458802\pi$
$468$	3.80124	+	11.2204i	0.175713	+	0.518664i
$469$	4.03435	+	20.2820i	0.186289	+	0.936538i
$470$	−7.22556	−	5.80430i	−0.333290	−	0.267733i
$471$	5.97854	−	24.4463i	0.275476	−	1.12643i
$472$	−26.9672	−	1.80291i	−1.24127	−	0.0829855i
$473$	25.4706	−	10.5503i	1.17114	−	0.485102i
$474$	−18.9910	−	2.50607i	−0.872287	−	0.115107i
$475$	5.32408	+	3.55744i	0.244286	+	0.163226i
$476$	7.42456	−	11.6319i	0.340304	−	0.533146i
$477$	−1.79855	−	16.3823i	−0.0823500	−	0.750094i
$478$	1.49742	−	17.0302i	0.0684905	−	0.778944i
$479$			12.5738i			0.574510i	0.957854	+	0.287255i	$0.0927427\pi$
$479$			12.5738i			0.574510i	−0.957854	+	0.287255i	$0.907257\pi$
$480$	2.76098	−	9.40090i	0.126021	−	0.429091i
$481$			6.78726i			0.309473i
$482$	26.0906	+	2.29408i	1.18840	+	0.104493i
$483$	1.34398	−	30.8762i	0.0611533	−	1.40492i
$484$	−1.27379	−	5.76945i	−0.0578993	−	0.262248i
$485$	−4.85227	−	3.24218i	−0.220330	−	0.147220i
$486$	19.5522	−	10.1839i	0.886906	−	0.461951i
$487$	32.4637	−	13.4469i	1.47107	−	0.609337i	0.503968	−	0.863722i	$-0.331873\pi$
$487$	32.4637	−	13.4469i	1.47107	−	0.609337i	0.967103	+	0.254385i	$0.0818730\pi$
$488$	1.69211	+	5.00627i	0.0765982	+	0.226623i
$489$	2.54427	+	0.622222i	0.115056	+	0.0281379i
$490$	−1.35828	+	1.69088i	−0.0613609	+	0.0763860i
$491$	−2.97820	−	14.9724i	−0.134404	−	0.675695i	−0.987962	−	0.154697i	$-0.950560\pi$
$491$	−2.97820	−	14.9724i	−0.134404	−	0.675695i	0.853558	−	0.520998i	$-0.174440\pi$
$492$	−2.70060	−	1.89395i	−0.121752	−	0.0853858i
$493$	−14.9536	−	22.3796i	−0.673475	−	1.00793i
$494$	17.0547	−	5.36915i	0.767326	−	0.241570i
$495$	−3.92727	+	7.54910i	−0.176517	+	0.339307i
$496$	20.7935	+	7.60927i	0.933658	+	0.341666i
$497$	−15.3237	−	15.3237i	−0.687361	−	0.687361i
$498$	−13.3774	−	4.54553i	−0.599455	−	0.203690i
$499$	−21.4993	−	32.1760i	−0.962443	−	1.44040i	−0.896740	−	0.442558i	$-0.854071\pi$
$499$	−21.4993	−	32.1760i	−0.962443	−	1.44040i	−0.0657032	−	0.997839i	$-0.520929\pi$
$500$	−0.726499	+	1.86338i	−0.0324900	+	0.0833331i
$501$	−9.21485	+	3.35532i	−0.411689	+	0.149904i
$502$	1.30091	+	11.9265i	0.0580625	+	0.532307i
$503$	20.1440	+	8.34393i	0.898177	+	0.372037i	0.783519	−	0.621368i	$-0.213423\pi$
$503$	20.1440	+	8.34393i	0.898177	+	0.372037i	0.114658	+	0.993405i	$0.463423\pi$
$504$	−14.6128	−	13.4181i	−0.650904	−	0.597691i
$505$	16.0031	−	6.62868i	0.712127	−	0.294972i
$506$	26.8468	−	14.7135i	1.19349	−	0.654093i
$507$	14.2881	+	6.66034i	0.634557	+	0.295796i
$508$	29.3041	+	5.19342i	1.30016	+	0.230421i
$509$	−5.35675	−	1.06552i	−0.237434	−	0.0472285i	0.0749390	−	0.997188i	$-0.476124\pi$
$509$	−5.35675	−	1.06552i	−0.237434	−	0.0472285i	−0.312373	+	0.949960i	$0.601124\pi$
$510$	5.43334	+	4.76782i	0.240592	+	0.211123i
$511$			24.9024i			1.10162i
$512$	−0.0886687	+	22.6272i	−0.00391864	+	0.999992i
$513$	−14.7277	−	29.8350i	−0.650246	−	1.31725i
$514$	0.689305	−	0.577884i	0.0304039	−	0.0254894i
$515$	−1.56307	+	7.85810i	−0.0688772	+	0.346269i
$516$	−33.6604	−	0.759332i	−1.48182	−	0.0334277i
$517$	−15.4564	−	10.3277i	−0.679774	−	0.454210i
$518$	−5.46259	−	9.96728i	−0.240012	−	0.437937i
$519$	14.8452	+	24.4569i	0.651633	+	1.07354i
$520$	2.78600	+	4.84009i	0.122174	+	0.212252i
$521$	10.5068	−	25.3657i	0.460312	−	1.11129i	−0.507957	−	0.861382i	$-0.669599\pi$
$521$	10.5068	−	25.3657i	0.460312	−	1.11129i	0.968269	−	0.249909i	$-0.0804008\pi$
$522$	−35.4211	+	15.5785i	−1.55034	+	0.681852i
$523$	5.47880	+	27.5438i	0.239571	+	1.20441i	0.893925	+	0.448217i	$0.147941\pi$
$523$	5.47880	+	27.5438i	0.239571	+	1.20441i	−0.654354	+	0.756189i	$0.727059\pi$
$524$	−15.0766	−	5.87807i	−0.658622	−	0.256785i
$525$	2.73626	+	2.98530i	0.119420	+	0.130289i
$526$	18.4179	+	9.59797i	0.803061	+	0.418491i
$527$	−11.5511	+	11.5511i	−0.503176	+	0.503176i
$528$	3.86491	−	19.2681i	0.168199	−	0.838538i
$529$	−24.9211	−	24.9211i	−1.08353	−	1.08353i
$530$	−2.33299	−	7.41053i	−0.101338	−	0.321893i
$531$	−22.3617	−	17.9374i	−0.970413	−	0.778416i
$532$	−20.7240	+	21.6108i	−0.898498	+	0.936949i
$533$	1.84397	−	0.366788i	0.0798712	−	0.0158874i
$534$	4.15584	−	7.19309i	0.179841	−	0.311275i
$535$	−15.3660	−	6.36480i	−0.664330	−	0.275174i
$536$	23.6997	−	8.01046i	1.02367	−	0.345999i
$537$	10.0551	+	16.5653i	0.433908	+	0.714845i
$538$	6.54812	−	22.4292i	0.282309	−	0.966992i
$539$	−2.41681	+	3.61701i	−0.104099	+	0.155795i
$540$	8.10787	−	6.50095i	0.348907	−	0.279757i
$541$	13.0867	+	2.60311i	0.562642	+	0.111916i	0.468214	−	0.883615i	$-0.344898\pi$
$541$	13.0867	+	2.60311i	0.562642	+	0.111916i	0.0944282	+	0.995532i	$0.469898\pi$
$542$	−0.141148	+	1.60528i	−0.00606285	+	0.0689529i
$543$	3.77872	+	24.5291i	0.162160	+	1.05264i
$544$	−15.1144	−	7.08804i	−0.648023	−	0.303897i
$545$	0.569173			0.0243807
$546$	11.2838	−	0.736146i	0.482901	−	0.0315041i
$547$	−2.79220	+	14.0373i	−0.119386	+	0.600194i	0.874053	+	0.485830i	$0.161483\pi$
$547$	−2.79220	+	14.0373i	−0.119386	+	0.600194i	−0.993439	+	0.114363i	$0.963517\pi$
$548$	19.5894	+	12.5038i	0.836816	+	0.534135i
$549$	−1.56703	+	5.38155i	−0.0668793	+	0.229679i
$550$	−1.12419	+	3.85069i	−0.0479357	+	0.164194i
$551$	22.3492	+	53.9558i	0.952109	+	2.29860i
$552$	−37.2494	+	3.21485i	−1.58544	+	0.136833i
$553$	−6.99699	+	16.8922i	−0.297542	+	0.718330i
$554$	−27.9647	+	34.8123i	−1.18811	+	1.47903i
$555$	5.59460	−	2.03711i	0.237478	−	0.0864705i
$556$	−33.2190	+	0.695900i	−1.40880	+	0.0295128i
$557$	3.24308	−	2.16696i	0.137414	−	0.0918169i	−0.484963	−	0.874534i	$-0.661167\pi$
$557$	3.24308	−	2.16696i	0.137414	−	0.0918169i	0.622377	+	0.782718i	$0.286167\pi$
$558$	13.4673	+	19.2403i	0.570117	+	0.814506i
$559$	13.5698	−	13.5698i	0.573943	−	0.573943i
$560$	−7.98677	−	4.86554i	−0.337503	−	0.205607i
$561$	11.6935	+	8.57163i	0.493699	+	0.361894i
$562$	−28.3488	−	14.7732i	−1.19582	−	0.623168i
$563$	−17.9806	+	12.0142i	−0.757791	+	0.506339i	−0.873429	−	0.486952i	$-0.838109\pi$
$563$	−17.9806	+	12.0142i	−0.757791	+	0.506339i	0.115638	+	0.993291i	$0.463109\pi$
$564$	12.1838	+	19.1559i	0.513029	+	0.806608i
$565$	−5.19704	+	1.03376i	−0.218641	+	0.0434904i
$566$	−5.03440	−	46.1544i	−0.211611	−	1.94002i
$567$	−4.56528	−	20.5411i	−0.191724	−	0.862643i
$568$	−15.9867	+	20.7780i	−0.670787	+	0.871826i
$569$	−4.30968	−	10.4045i	−0.180671	−	0.436178i	0.807434	−	0.589958i	$-0.200856\pi$
$569$	−4.30968	−	10.4045i	−0.180671	−	0.436178i	−0.988105	+	0.153779i	$0.950856\pi$
$570$	−9.54442	−	12.4463i	−0.399772	−	0.521319i
$571$	22.8209	−	34.1540i	0.955027	−	1.42930i	0.0525217	−	0.998620i	$-0.483274\pi$
$571$	22.8209	−	34.1540i	0.955027	−	1.42930i	0.902505	−	0.430679i	$-0.141726\pi$
$572$	6.41677	+	9.18110i	0.268299	+	0.383881i
$573$	1.82576	−	41.9445i	0.0762724	−	1.75226i
$574$	−2.41272	+	2.02272i	−0.100705	+	0.0844267i
$575$	7.63176			0.318266
$576$	−13.8119	+	19.6273i	−0.575498	+	0.817803i
$577$	45.3562			1.88820			0.944102	−	0.329654i	$-0.106932\pi$
$577$	45.3562			1.88820			0.944102	+	0.329654i	$0.106932\pi$
$578$	−8.98546	+	7.53303i	−0.373746	+	0.313333i
$579$	−0.908209	+	20.8649i	−0.0377439	+	0.867116i
$580$	−14.9515	+	10.4497i	−0.620826	+	0.433902i
$581$	−7.49223	+	11.2129i	−0.310830	+	0.465190i
$582$	8.69861	+	11.3434i	0.360569	+	0.470197i
$583$	−5.96321	−	14.3965i	−0.246971	−	0.596240i
$584$	29.8731	−	3.89317i	1.23616	−	0.161101i
$585$	−0.514694	+	5.90101i	−0.0212800	+	0.243977i
$586$	−4.05623	−	37.1868i	−0.167561	−	1.53617i
$587$	21.6288	−	4.30223i	0.892714	−	0.177572i	0.272641	−	0.962116i	$-0.412103\pi$
$587$	21.6288	−	4.30223i	0.892714	−	0.177572i	0.620073	+	0.784544i	$0.287103\pi$
$588$	4.48272	−	2.85116i	0.184864	−	0.117580i
$589$	29.4716	−	19.6923i	1.21436	−	0.811406i
$590$	−11.9841	−	6.24516i	−0.493378	−	0.257109i
$591$	14.4479	+	10.5907i	0.594306	+	0.435642i
$592$	−11.1028	+	8.11120i	−0.456322	+	0.333368i
$593$	2.00190	−	2.00190i	0.0822083	−	0.0822083i	−0.664807	−	0.747015i	$-0.731486\pi$
$593$	2.00190	−	2.00190i	0.0822083	−	0.0822083i	0.747015	+	0.664807i	$0.231486\pi$
$594$	15.0575	−	14.4134i	0.617817	−	0.591387i
$595$	5.73690	−	3.83328i	0.235190	−	0.157149i
$596$	0.413799	+	19.7528i	0.0169499	+	0.809107i
$597$	−3.86651	+	1.40787i	−0.158246	+	0.0576205i
$598$	13.3459	−	16.6138i	0.545754	−	0.679389i
$599$	0.869054	−	2.09808i	0.0355086	−	0.0857253i	−0.905130	−	0.425134i	$-0.860227\pi$
$599$	0.869054	−	2.09808i	0.0355086	−	0.0857253i	0.940639	+	0.339409i	$0.110227\pi$
$600$	3.15341	−	3.74914i	0.128737	−	0.153058i
$601$	4.79701	+	11.5810i	0.195674	+	0.472399i	0.991013	−	0.133766i	$-0.0427070\pi$
$601$	4.79701	+	11.5810i	0.195674	+	0.472399i	−0.795339	+	0.606165i	$0.792707\pi$
$602$	−9.00627	+	30.8491i	−0.367068	+	1.25732i
$603$	25.4763	+	7.41834i	1.03748	+	0.302098i
$604$	−9.20219	+	14.4168i	−0.374432	+	0.586612i
$605$	0.576335	−	2.89743i	0.0234313	−	0.117797i
$606$	−42.3390	+	2.76217i	−1.71991	+	0.112206i
$607$	−24.3666			−0.989009			−0.494505	−	0.869175i	$-0.664650\pi$
$607$	−24.3666			−0.989009			−0.494505	+	0.869175i	$0.664650\pi$
$608$	29.1644	+	21.4820i	1.18277	+	0.871210i
$609$	5.62348	+	36.5042i	0.227875	+	1.47922i
$610$	−0.231433	+	2.63210i	−0.00937047	+	0.106570i
$611$	−12.6912	−	2.52444i	−0.513432	−	0.102128i
$612$	−8.84396	−	15.3396i	−0.357496	−	0.620068i
$613$	−17.0366	+	25.4970i	−0.688101	+	1.02982i	0.308798	+	0.951128i	$0.400073\pi$
$613$	−17.0366	+	25.4970i	−0.688101	+	1.02982i	−0.996899	+	0.0786882i	$0.974927\pi$
$614$	−2.18029	+	7.46813i	−0.0879893	+	0.301389i
$615$	−0.855780	−	1.40986i	−0.0345084	−	0.0568510i
$616$	−16.8124	−	8.31829i	−0.677392	−	0.335153i
$617$	23.6399	+	9.79197i	0.951707	+	0.394210i	0.803872	−	0.594802i	$-0.202770\pi$
$617$	23.6399	+	9.79197i	0.951707	+	0.394210i	0.147835	+	0.989012i	$0.452770\pi$
$618$	9.81786	−	16.9931i	0.394932	−	0.683565i
$619$	−31.5326	+	6.27222i	−1.26740	+	0.252102i	−0.782601	−	0.622523i	$-0.786108\pi$
$619$	−31.5326	+	6.27222i	−1.26740	+	0.252102i	−0.484800	+	0.874625i	$0.661108\pi$
$620$	7.99066	+	7.66274i	0.320913	+	0.307743i
$621$	−34.3508	−	19.8142i	−1.37845	−	0.795118i
$622$	−7.95526	−	25.2692i	−0.318977	−	1.01320i
$623$	−5.60686	−	5.60686i	−0.224634	−	0.224634i
$624$	−2.64716	−	13.4210i	−0.105971	−	0.537269i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	−22.5519	−	11.7523i	−0.901357	−	0.469716i
$627$	−21.2564	−	23.1911i	−0.848899	−	0.926164i
$628$	−10.5560	+	27.0750i	−0.421232	+	1.08041i
$629$	−1.97907	−	9.94945i	−0.0789106	−	0.396711i
$630$	−3.99347	−	9.08004i	−0.159104	−	0.361757i
$631$	16.7115	−	40.3452i	0.665275	−	1.60612i	−0.124146	−	0.992264i	$-0.539619\pi$
$631$	16.7115	−	40.3452i	0.665275	−	1.60612i	0.789421	−	0.613852i	$-0.210381\pi$
$632$	21.3579	+	5.75274i	0.849570	+	0.228832i
$633$	1.27130	+	2.09442i	0.0505298	+	0.0832456i
$634$	4.65915	+	8.50129i	0.185039	+	0.337629i
$635$	12.3726	+	8.26710i	0.490991	+	0.328070i
$636$	−0.429189	+	19.0255i	−0.0170184	+	0.754409i
$637$	−0.590751	+	2.96991i	−0.0234064	+	0.117672i
$638$	−28.0374	+	23.5053i	−1.11001	+	0.930586i
$639$	−26.5175	+	8.36867i	−1.04902	+	0.331060i
$640$	−4.58810	+	10.3416i	−0.181361	+	0.408789i
$641$			33.8820i			1.33826i	0.743146	+	0.669129i	$0.233333\pi$
$641$			33.8820i			1.33826i	−0.743146	+	0.669129i	$0.766667\pi$
$642$	30.6218	+	26.8710i	1.20855	+	1.06051i
$643$	−20.1830	−	4.01465i	−0.795940	−	0.158322i	−0.219662	−	0.975576i	$-0.570495\pi$
$643$	−20.1830	−	4.01465i	−0.795940	−	0.158322i	−0.576278	+	0.817254i	$0.695495\pi$
$644$	−6.22751	+	35.1390i	−0.245398	+	1.38467i
$645$	−15.2582	−	7.11253i	−0.600790	−	0.280056i
$646$	−23.4349	+	12.8435i	−0.922032	+	0.505322i
$647$	2.45032	−	1.01496i	0.0963320	−	0.0399020i	−0.333997	−	0.942574i	$-0.608398\pi$
$647$	2.45032	−	1.01496i	0.0963320	−	0.0399020i	0.430329	+	0.902672i	$0.358398\pi$
$648$	−23.9274	+	8.68785i	−0.939958	+	0.341291i
$649$	−25.0415	−	10.3725i	−0.982965	−	0.407157i
$650$	0.302783	+	2.77586i	0.0118761	+	0.108878i
$651$	21.0637	−	7.66971i	0.825551	−	0.300600i
$652$	−2.81786	−	1.09863i	−0.110356	−	0.0430257i
$653$	16.9438	+	25.3581i	0.663060	+	0.992340i	0.998731	+	0.0503604i	$0.0160370\pi$
$653$	16.9438	+	25.3581i	0.663060	+	0.992340i	−0.335671	+	0.941979i	$0.608963\pi$
$654$	−1.32006	−	0.448546i	−0.0516184	−	0.0175395i
$655$	−5.72117	−	5.72117i	−0.223545	−	0.223545i
$656$	2.80366	+	2.57808i	0.109465	+	0.100657i
$657$	28.3467	+	14.7468i	1.10591	+	0.575327i
$658$	20.6691	−	6.50706i	0.805767	−	0.253672i
$659$	16.2483	+	24.3173i	0.632945	+	0.947268i	0.999855	+	0.0170123i	$0.00541545\pi$
$659$	16.2483	+	24.3173i	0.632945	+	0.947268i	−0.366911	+	0.930256i	$0.619585\pi$
$660$	5.64188	−	8.04480i	0.219610	−	0.313143i
$661$	−6.73852	−	33.8769i	−0.262098	−	1.31766i	−0.857606	−	0.514307i	$-0.828049\pi$
$661$	−6.73852	−	33.8769i	−0.262098	−	1.31766i	0.595508	−	0.803350i	$-0.296951\pi$
$662$	−8.25472	+	10.2760i	−0.320829	+	0.399388i
$663$	9.80346	+	2.39751i	0.380735	+	0.0931117i
$664$	14.6224	+	7.23472i	0.567458	+	0.280762i
$665$	−13.8313	+	5.72912i	−0.536355	+	0.222166i
$666$	−14.5807	+	0.315670i	−0.564991	+	0.0122319i
$667$	57.8757	+	38.6713i	2.24095	+	1.49736i
$668$	11.0575	−	2.44129i	0.427829	−	0.0944565i
$669$	0.148647	−	3.41498i	0.00574704	−	0.132031i
$670$	12.4604	+	1.09561i	0.481386	+	0.0423270i
$671$			5.29961i			0.204589i
$672$	14.6890	+	17.5785i	0.566641	+	0.678107i
$673$		−	6.87737i		−	0.265103i	−0.991176	−	0.132552i	$-0.957683\pi$
$673$		−	6.87737i		−	0.265103i	0.991176	−	0.132552i	$-0.0423170\pi$
$674$	−2.33933	+	26.6053i	−0.0901078	+	1.02480i
$675$	5.01856	−	1.34686i	0.193165	−	0.0518407i
$676$	−15.3437	−	9.79379i	−0.590141	−	0.376684i
$677$	−8.92634	−	5.96439i	−0.343067	−	0.229230i	0.372085	−	0.928199i	$-0.378643\pi$
$677$	−8.92634	−	5.96439i	−0.343067	−	0.229230i	−0.715153	+	0.698968i	$0.753643\pi$
$678$	12.8679	+	1.69806i	0.494190	+	0.0652136i
$679$	12.6056	−	5.22141i	0.483759	−	0.200379i
$680$	−5.49531	−	6.28273i	−0.210735	−	0.240932i
$681$	−8.88771	+	36.3419i	−0.340578	+	1.39263i
$682$	17.3116	+	13.9064i	0.662895	+	0.532504i
$683$	3.15726	+	15.8726i	0.120809	+	0.607349i	0.992993	+	0.118171i	$0.0377031\pi$
$683$	3.15726	+	15.8726i	0.120809	+	0.607349i	−0.872184	+	0.489178i	$0.837297\pi$
$684$	12.3274	+	36.3879i	0.471352	+	1.39132i
$685$	6.45567	+	9.66159i	0.246658	+	0.369150i
$686$	−8.47305	−	26.9139i	−0.323503	−	1.02758i
$687$	−22.4993	−	16.4926i	−0.858402	−	0.629232i
$688$	38.4147	+	5.98110i	1.46455	+	0.228027i
$689$	−7.66993	−	7.66993i	−0.292201	−	0.292201i
$690$	−17.7000	−	6.01432i	−0.673828	−	0.228961i
$691$	11.6664	+	17.4600i	0.443810	+	0.664209i	0.984170	−	0.177225i	$-0.0567120\pi$
$691$	11.6664	+	17.4600i	0.443810	+	0.664209i	−0.540360	+	0.841434i	$0.681712\pi$
$692$	−13.2787	−	30.2496i	−0.504780	−	1.14992i
$693$	−9.57416	−	17.4404i	−0.363692	−	0.662507i
$694$	−46.6405	+	5.08741i	−1.77045	+	0.193116i
$695$	−15.3485	−	6.35757i	−0.582203	−	0.241157i
$696$	42.9114	−	12.4529i	1.62655	−	0.472026i
$697$	−2.59613	+	1.07535i	−0.0983353	+	0.0407318i
$698$	−4.48727	−	8.18767i	−0.169846	−	0.309908i
$699$	16.5356	−	35.4729i	0.625432	−	1.34171i
$700$	−2.67874	−	3.83274i	−0.101247	−	0.144864i
$701$	−13.2928	−	2.64410i	−0.502061	−	0.0998661i	−0.0624384	−	0.998049i	$-0.519888\pi$
$701$	−13.2928	−	2.64410i	−0.502061	−	0.0998661i	−0.439622	+	0.898183i	$0.644888\pi$
$702$	5.84409	−	13.2804i	0.220571	−	0.501235i
$703$			22.0111i			0.830165i
$704$	−7.35025	+	21.4687i	−0.277023	+	0.809132i
$705$	1.72826	+	11.2188i	0.0650900	+	0.422524i
$706$	−12.1039	−	14.4376i	−0.455537	−	0.543368i
$707$	−7.90084	+	39.7202i	−0.297142	+	1.49383i
$708$	22.8726	+	23.9284i	0.859606	+	0.899284i
$709$	3.99629	+	2.67023i	0.150084	+	0.100283i	0.628345	−	0.777935i	$-0.283733\pi$
$709$	3.99629	+	2.67023i	0.150084	+	0.100283i	−0.478261	+	0.878218i	$0.658733\pi$
$710$	−11.4951	+	6.29990i	−0.431402	+	0.236431i
$711$	15.0851	+	17.9680i	0.565735	+	0.673853i
$712$	−5.84946	+	7.60258i	−0.219218	+	0.284919i
$713$	16.1668	−	39.0300i	0.605450	−	1.46169i
$714$	−16.3262	+	4.36930i	−0.610994	+	0.163517i
$715$	1.09263	+	5.49300i	0.0408619	+	0.205427i
$716$	−8.99401	−	20.4888i	−0.336122	−	0.765703i
$717$	−15.4353	+	14.1476i	−0.576443	+	0.528354i
$718$	16.9704	−	32.5651i	0.633328	−	1.21532i
$719$	−0.158063	+	0.158063i	−0.00589477	+	0.00589477i	−0.710048	−	0.704153i	$-0.751327\pi$
$719$	−0.158063	+	0.158063i	−0.00589477	+	0.00589477i	0.704153	+	0.710048i	$0.251327\pi$
$720$	−10.2681	+	6.21013i	−0.382670	+	0.231438i
$721$	−13.2458	−	13.2458i	−0.493300	−	0.493300i
$722$	29.6784	−	9.34335i	1.10451	−	0.347723i
$723$	−21.6745	−	23.6472i	−0.806082	−	0.879450i
$724$	−0.600218	−	28.6516i	−0.0223069	−	1.06483i
$725$	−8.94538	+	1.77935i	−0.332223	+	0.0660833i
$726$	−3.62003	+	6.26569i	−0.134352	+	0.232542i
$727$	30.6391	+	12.6911i	1.13634	+	0.470689i	0.869932	−	0.493171i	$-0.164162\pi$
$727$	30.6391	+	12.6911i	1.13634	+	0.470689i	0.266410	+	0.963860i	$0.414162\pi$
$728$	−13.0280	−	0.870991i	−0.482849	−	0.0322811i
$729$	−26.0855	−	6.96736i	−0.966131	−	0.258050i
$730$	14.4592	+	4.22131i	0.535160	+	0.156238i
$731$	−15.9353	+	23.8488i	−0.589387	+	0.882080i
$732$	2.61102	−	5.92212i	0.0965059	−	0.218888i
$733$	−19.3381	−	3.84659i	−0.714269	−	0.142077i	−0.175437	−	0.984491i	$-0.556134\pi$
$733$	−19.3381	−	3.84659i	−0.714269	−	0.142077i	−0.538831	+	0.842414i	$0.681134\pi$
$734$	−44.6176	−	3.92311i	−1.64686	−	0.144805i
$735$	2.62534	−	0.404435i	0.0968372	−	0.0149178i
$736$	43.1265	+	1.97702i	1.58966	+	0.0728738i
$737$	25.0884			0.924143
$738$	0.873712	+	3.94424i	0.0321618	+	0.145189i
$739$	2.98479	−	15.0055i	0.109797	−	0.551988i	−0.886253	−	0.463201i	$-0.846701\pi$
$739$	2.98479	−	15.0055i	0.109797	−	0.551988i	0.996051	−	0.0887870i	$-0.0282990\pi$
$740$	−6.71334	+	1.48218i	−0.246787	+	0.0544860i
$741$	−19.8478	−	9.25197i	−0.729127	−	0.339880i
$742$	17.4365	+	5.09051i	0.640114	+	0.186879i
$743$	18.5689	+	44.8293i	0.681227	+	1.64463i	0.761746	+	0.647875i	$0.224342\pi$
$743$	18.5689	+	44.8293i	0.681227	+	1.64463i	−0.0805192	+	0.996753i	$0.525658\pi$
$744$	−12.4937	−	24.0690i	−0.458040	−	0.882413i
$745$	−3.78037	+	9.12661i	−0.138502	+	0.334373i
$746$	−25.1283	−	20.1856i	−0.920011	−	0.739046i
$747$	8.32700	+	15.1686i	0.304669	+	0.554989i
$748$	−12.0834	−	11.5875i	−0.441814	−	0.423682i
$749$	32.3327	−	21.6040i	1.18141	−	0.789393i
$750$	2.19721	−	1.08272i	0.0802307	−	0.0395352i
$751$	−12.8185	+	12.8185i	−0.467754	+	0.467754i	−0.901186	−	0.433432i	$-0.857302\pi$
$751$	−12.8185	+	12.8185i	−0.467754	+	0.467754i	0.433432	+	0.901186i	$0.357302\pi$
$752$	−11.0372	−	23.7775i	−0.402487	−	0.867076i
$753$	8.68689	−	11.8507i	0.316568	−	0.431864i
$754$	−11.7695	+	22.5851i	−0.428621	+	0.822499i
$755$	−7.11047	+	4.75106i	−0.258776	+	0.172909i
$756$	2.10622	+	24.2060i	0.0766025	+	0.880365i
$757$	3.50753	−	0.697692i	0.127483	−	0.0253580i	−0.130936	−	0.991391i	$-0.541798\pi$
$757$	3.50753	−	0.697692i	0.127483	−	0.0253580i	0.258420	+	0.966033i	$0.416798\pi$
$758$	17.4310	−	1.90133i	0.633124	−	0.0690594i
$759$	−36.4214	−	8.90714i	−1.32201	−	0.323309i
$760$	9.03502	+	15.6964i	0.327735	+	0.569369i
$761$	7.97858	+	19.2620i	0.289223	+	0.698246i	0.999987	−	0.00518470i	$-0.00165035\pi$
$761$	7.97858	+	19.2620i	0.289223	+	0.698246i	−0.710763	+	0.703431i	$0.751650\pi$
$762$	−22.1802	−	28.9239i	−0.803504	−	1.04780i
$763$	−0.739322	+	1.10647i	−0.0267652	+	0.0400570i
$764$	−8.45990	+	47.7354i	−0.306069	+	1.72701i
$765$	−0.966160	−	8.80037i	−0.0349316	−	0.318178i
$766$	−26.1893	−	31.2388i	−0.946258	−	1.12870i
$767$	−18.8674			−0.681261
$768$	18.7909	−	20.3692i	0.678057	−	0.735010i
$769$	4.90893			0.177020			0.0885102	−	0.996075i	$-0.471789\pi$
$769$	4.90893			0.177020			0.0885102	+	0.996075i	$0.471789\pi$
$770$	−6.02548	−	7.18724i	−0.217143	−	0.259010i
$771$	−1.10061	−	0.0479074i	−0.0396375	−	0.00172534i
$772$	4.20830	−	23.7455i	0.151460	−	0.854620i
$773$	−12.4723	+	18.6661i	−0.448597	+	0.671372i	−0.984993	−	0.172594i	$-0.944785\pi$
$773$	−12.4723	+	18.6661i	−0.448597	+	0.671372i	0.536396	+	0.843966i	$0.319785\pi$
$774$	29.7825	+	28.5202i	1.07051	+	1.02514i
$775$	2.11835	+	5.11416i	0.0760935	+	0.183706i
$776$	−8.23435	−	14.3054i	−0.295596	−	0.513535i
$777$	−3.30691	+	13.5220i	−0.118635	+	0.485099i
$778$	−4.67518	+	0.509956i	−0.167613	+	0.0182828i
$779$	5.98000	−	1.18950i	0.214256	−	0.0426181i
$780$	1.48533	−	6.67655i	0.0531832	−	0.239059i
$781$	−21.8605	+	14.6067i	−0.782229	+	0.522669i
$782$	−14.7194	+	28.2457i	−0.526364	+	1.01006i
$783$	44.8831	+	15.2159i	1.60399	+	0.543771i
$784$	−5.56424	+	2.58286i	−0.198723	+	0.0922449i
$785$	−10.2743	+	10.2743i	−0.366705	+	0.366705i
$786$	8.76021	+	17.7775i	0.312466	+	0.634103i
$787$	−12.5880	+	8.41101i	−0.448712	+	0.299820i	−0.759319	−	0.650718i	$-0.774468\pi$
$787$	−12.5880	+	8.41101i	−0.448712	+	0.299820i	0.310607	+	0.950539i	$0.399468\pi$
$788$	−14.9297	−	14.3170i	−0.531847	−	0.510021i
$789$	−8.70295	−	23.9013i	−0.309833	−	0.850908i
$790$	8.62214	+	6.92617i	0.306762	+	0.246422i
$791$	4.74102	−	11.4458i	0.168571	−	0.406967i
$792$	−19.4248	+	14.2118i	−0.690230	+	0.504994i
$793$	1.41172	+	3.40820i	0.0501318	+	0.121029i
$794$	−6.69803	−	1.95546i	−0.237704	−	0.0693967i
$795$	−4.02014	+	8.62420i	−0.142580	+	0.305869i
$796$	4.63969	−	1.02436i	0.164449	−	0.0363073i
$797$	3.19391	−	16.0569i	0.113134	−	0.568764i	−0.882084	−	0.471091i	$-0.843860\pi$
$797$	3.19391	−	16.0569i	0.113134	−	0.568764i	0.995219	−	0.0976727i	$-0.0311398\pi$
$798$	36.5933	−	2.38732i	1.29539	−	0.0845103i
$799$	19.3401			0.684205
$800$	−4.17898	+	3.81263i	−0.147749	+	0.134797i
$801$	−9.70263	+	3.06206i	−0.342826	+	0.108192i
$802$	−33.4076	−	2.93745i	−1.17966	−	0.103725i
$803$	29.6313	+	5.89403i	1.04567	+	0.207996i
$804$	−28.0354	−	12.3606i	−0.988731	−	0.435924i
$805$	−9.91319	+	14.8361i	−0.349394	+	0.522905i
$806$	14.8376	+	4.33177i	0.522632	+	0.152580i
$807$	−24.4629	+	14.8489i	−0.861134	+	0.522705i
$808$	48.8837	+	3.26814i	1.71972	+	0.114973i
$809$	−12.3418	−	5.11214i	−0.433915	−	0.179733i	0.155025	−	0.987911i	$-0.450454\pi$
$809$	−12.3418	−	5.11214i	−0.433915	−	0.179733i	−0.588939	+	0.808177i	$0.700454\pi$
$810$	−12.7007	−	0.831238i	−0.446259	−	0.0292067i
$811$	−0.637014	+	0.126710i	−0.0223686	+	0.00444939i	−0.206262	−	0.978497i	$-0.566130\pi$
$811$	−0.637014	+	0.126710i	−0.0223686	+	0.00444939i	0.183893	+	0.982946i	$0.441130\pi$
$812$	−0.893244	−	42.6392i	−0.0313467	−	1.49634i
$813$	1.45495	−	1.33357i	0.0510273	−	0.0467704i
$814$	−13.1529	+	4.14081i	−0.461010	+	0.145135i
$815$	−1.06931	−	1.06931i	−0.0374561	−	0.0374561i
$816$	7.79383	+	18.9019i	0.272839	+	0.661700i
$817$	44.0070	−	44.0070i	1.53961	−	1.53961i
$818$	14.6805	−	28.1710i	0.513290	−	0.984975i
$819$	−10.8030	−	8.66562i	−0.377488	−	0.302801i
$820$	0.765474	+	1.74379i	0.0267315	+	0.0608958i
$821$	8.68294	+	43.6521i	0.303037	+	1.52347i	0.769337	+	0.638843i	$0.220587\pi$
$821$	8.68294	+	43.6521i	0.303037	+	1.52347i	−0.466301	+	0.884626i	$0.654413\pi$
$822$	−7.35839	−	27.4952i	−0.256653	−	0.959005i
$823$	−5.67881	+	13.7099i	−0.197951	+	0.477895i	−0.991420	−	0.130715i	$-0.958273\pi$
$823$	−5.67881	+	13.7099i	−0.197951	+	0.477895i	0.793469	+	0.608610i	$0.208273\pi$
$824$	−13.8189	+	17.9605i	−0.481405	+	0.625685i
$825$	4.19983	−	2.54928i	0.146219	−	0.0887546i
$826$	27.7072	−	15.1850i	0.964057	−	0.528354i
$827$	−35.9525	−	24.0227i	−1.25019	−	0.835352i	−0.258756	−	0.965943i	$-0.583313\pi$
$827$	−35.9525	−	24.0227i	−1.25019	−	0.835352i	−0.991436	+	0.130591i	$0.958313\pi$
$828$	36.3112	+	27.8975i	1.26190	+	0.969506i
$829$	7.50633	−	37.7369i	0.260706	−	1.31066i	−0.599363	−	0.800477i	$-0.704580\pi$
$829$	7.50633	−	37.7369i	0.260706	−	1.31066i	0.860069	−	0.510178i	$-0.170420\pi$
$830$	5.24058	+	6.25101i	0.181903	+	0.216976i
$831$	54.0513	−	8.32663i	1.87502	−	0.288848i
$832$	0.991912	+	15.7646i	0.0343884	+	0.546539i
$833$		−	4.52584i		−	0.156811i
$834$	30.5870	+	26.8405i	1.05914	+	0.929410i
$835$	5.55312	+	1.10458i	0.192174	+	0.0382257i
$836$	20.8096	+	29.7743i	0.719715	+	1.02977i
$837$	3.74304	−	28.5188i	0.129378	−	0.985756i
$838$	12.0482	+	21.9837i	0.416199	+	0.759415i
$839$	−20.3189	+	8.41635i	−0.701485	+	0.290565i	−0.704776	−	0.709430i	$-0.748952\pi$
$839$	−20.3189	+	8.41635i	−0.701485	+	0.290565i	0.00329085	+	0.999995i	$0.498952\pi$
$840$	3.19224	+	11.0001i	0.110143	+	0.379540i
$841$	−50.0612	−	20.7360i	−1.72625	−	0.715036i
$842$	17.1299	−	1.86848i	0.590336	−	0.0643921i
$843$	13.3955	+	36.7888i	0.461367	+	1.26707i
$844$	−1.13715	−	2.59049i	−0.0391423	−	0.0891682i
$845$	−5.05650	−	7.56759i	−0.173949	−	0.260333i
$846$	4.83285	−	27.3812i	0.166157	−	0.941386i
$847$	4.88398	+	4.88398i	0.167816	+	0.167816i
$848$	3.38063	−	21.7127i	0.116091	−	0.745618i
$849$	−33.6174	+	45.8611i	−1.15375	+	1.57395i
$850$	−1.25325	−	3.98085i	−0.0429861	−	0.136542i
$851$	14.5750	+	21.8130i	0.499623	+	0.747739i
$852$	31.6247	−	5.55223i	1.08345	−	0.190216i
$853$	10.3776	+	52.1715i	0.355321	+	1.78632i	0.582885	+	0.812555i	$0.301924\pi$
$853$	10.3776	+	52.1715i	0.355321	+	1.78632i	−0.227564	+	0.973763i	$0.573076\pi$
$854$	−4.81618	−	3.86884i	−0.164806	−	0.132389i
$855$	−1.66916	+	19.1370i	−0.0570839	+	0.654471i
$856$	−30.9710	−	35.4089i	−1.05857	−	1.21025i
$857$	32.5546	−	13.4845i	1.11204	−	0.460623i	0.250402	−	0.968142i	$-0.419437\pi$
$857$	32.5546	−	13.4845i	1.11204	−	0.460623i	0.861641	+	0.507519i	$0.169437\pi$
$858$	1.79476	−	13.6007i	0.0612721	−	0.464322i
$859$	7.92931	+	5.29820i	0.270545	+	0.180772i	0.683441	−	0.730006i	$-0.260483\pi$
$859$	7.92931	+	5.29820i	0.270545	+	0.180772i	−0.412896	+	0.910778i	$0.635483\pi$
$860$	16.3854	+	10.4587i	0.558737	+	0.356639i
$861$	3.85237	+	0.167686i	0.131289	+	0.00571474i
$862$	2.17753	−	24.7650i	0.0741668	−	0.843501i
$863$			22.2764i			0.758299i	0.925335	+	0.379149i	$0.123783\pi$
$863$			22.2764i			0.758299i	−0.925335	+	0.379149i	$0.876217\pi$
$864$	28.7084	−	6.31093i	0.976680	−	0.214702i
$865$		−	16.5179i		−	0.561624i
$866$	−7.09068	−	0.623465i	−0.240951	−	0.0211862i
$867$	14.3470	+	0.624499i	0.487251	+	0.0212091i
$868$	−25.2757	+	5.58041i	−0.857914	+	0.189411i
$869$	18.4439	+	12.3238i	0.625666	+	0.418057i
$870$	22.1489	+	2.92278i	0.750917	+	0.0990914i
$871$	16.1345	−	6.68311i	0.546695	−	0.226449i
$872$	1.44291	+	0.713911i	0.0488632	+	0.0241761i
$873$	1.52124	−	17.4411i	0.0514861	−	0.590292i
$874$	43.2807	−	53.8786i	1.46399	−	1.82247i
$875$	−0.456127	−	2.29310i	−0.0154199	−	0.0775211i
$876$	−30.2080	−	21.1851i	−1.02063	−	0.715779i
$877$	1.64796	+	2.46634i	0.0556476	+	0.0832825i	0.858250	−	0.513232i	$-0.171552\pi$
$877$	1.64796	+	2.46634i	0.0556476	+	0.0832825i	−0.802602	+	0.596514i	$0.796552\pi$
$878$	20.1213	−	6.33461i	0.679063	−	0.213783i
$879$	−27.0856	+	36.9504i	−0.913575	+	1.24631i
$880$	−7.67984	+	8.35182i	−0.258887	+	0.281540i
$881$	−13.7193	−	13.7193i	−0.462214	−	0.462214i	0.437167	−	0.899381i	$-0.355982\pi$
$881$	−13.7193	−	13.7193i	−0.462214	−	0.462214i	−0.899381	+	0.437167i	$0.855982\pi$
$882$	−6.40756	−	1.13095i	−0.215754	−	0.0380811i
$883$	−21.0584	−	31.5161i	−0.708671	−	1.06060i	−0.994744	−	0.102393i	$-0.967350\pi$
$883$	−21.0584	−	31.5161i	−0.708671	−	1.06060i	0.286073	−	0.958208i	$-0.407650\pi$
$884$	−10.8576	−	4.23319i	−0.365181	−	0.142377i
$885$	5.66279	+	15.5520i	0.190353	+	0.522774i
$886$	−1.44355	−	13.2342i	−0.0484971	−	0.444612i
$887$	13.3383	+	5.52491i	0.447856	+	0.185508i	0.595201	−	0.803577i	$-0.297073\pi$
$887$	13.3383	+	5.52491i	0.447856	+	0.185508i	−0.147344	+	0.989085i	$0.547073\pi$
$888$	16.7380	+	1.85299i	0.561691	+	0.0621824i
$889$	−32.1425	+	13.3138i	−1.07802	+	0.446532i
$890$	−4.20599	+	2.30510i	−0.140985	+	0.0772672i
$891$	−25.5222	+	0.570443i	−0.855027	+	0.0191106i
$892$	−0.688776	+	3.88645i	−0.0230619	+	0.130128i
$893$	−41.1576	−	8.18676i	−1.37729	−	0.273960i
$894$	15.9600	−	18.1878i	0.533782	−	0.608291i
$895$		−	11.1880i		−	0.373973i
$896$	−14.1445	−	22.3524i	−0.472534	−	0.746742i
$897$	−25.7955	+	3.97380i	−0.861285	+	0.132681i
$898$	−20.3250	+	17.0397i	−0.678256	+	0.568621i
$899$	−9.84962	+	49.5174i	−0.328503	+	1.65150i
$900$	−5.94914	+	0.779555i	−0.198305	+	0.0259852i
$901$	13.4798	+	9.00691i	0.449077	+	0.300064i
$902$	1.83577	+	3.34963i	0.0611245	+	0.111530i
$903$	33.6462	−	20.4231i	1.11968	−	0.679639i
$904$	−14.4717	−	3.89794i	−0.481321	−	0.129644i
$905$	5.48344	−	13.2382i	0.182276	−	0.440053i
$906$	20.2351	−	5.41542i	0.672268	−	0.179915i
$907$	4.98149	+	25.0436i	0.165408	+	0.831561i	0.970998	+	0.239088i	$0.0768483\pi$
$907$	4.98149	+	25.0436i	0.165408	+	0.831561i	−0.805590	+	0.592473i	$0.798152\pi$
$908$	15.6927	−	40.2498i	0.520779	−	1.33574i
$909$	40.5351	+	32.5152i	1.34447	+	1.07846i
$910$	−5.78957	−	3.01706i	−0.191922	−	0.100015i
$911$	16.9068	−	16.9068i	0.560146	−	0.560146i	−0.369203	−	0.929349i	$-0.620369\pi$
$911$	16.9068	−	16.9068i	0.560146	−	0.560146i	0.929349	+	0.369203i	$0.120369\pi$
$912$	−8.58473	−	43.5242i	−0.284269	−	1.44123i
$913$	11.5689	+	11.5689i	0.382875	+	0.382875i
$914$	−11.5766	−	36.7722i	−0.382921	−	1.21632i
$915$	2.38560	−	2.18658i	0.0788655	−	0.0722862i
$916$	23.2496	+	22.2955i	0.768189	+	0.736664i
$917$	18.5534	−	3.69050i	0.612687	−	0.121871i
$918$	−4.69449	+	21.1717i	−0.154941	+	0.698771i
$919$	27.3720	+	11.3378i	0.902917	+	0.374001i	0.785341	−	0.619063i	$-0.212488\pi$
$919$	27.3720	+	11.3378i	0.902917	+	0.374001i	0.117576	+	0.993064i	$0.462488\pi$
$920$	19.3473	+	9.57247i	0.637862	+	0.315595i
$921$	8.14527	−	4.94415i	0.268396	−	0.162915i
$922$	−0.902229	+	3.09040i	−0.0297133	+	0.101777i
$923$	−10.1676	+	15.2169i	−0.334671	+	0.500870i
$924$	8.31063	+	21.4175i	0.273400	+	0.704585i
$925$	−3.37146	−	0.670625i	−0.110853	−	0.0220500i
$926$	2.00596	−	22.8138i	0.0659198	−	0.749707i
$927$	−22.9218	+	7.23389i	−0.752849	+	0.237592i
$928$	−51.0106	+	7.73763i	−1.67450	+	0.254000i
$929$	24.7909			0.813362			0.406681	−	0.913570i	$-0.366686\pi$
$929$	24.7909			0.813362			0.406681	+	0.913570i	$0.366686\pi$
$930$	−0.882718	−	13.5304i	−0.0289455	−	0.443681i
$931$	−1.91581	+	9.63142i	−0.0627881	+	0.315657i
$932$	−24.3149	+	38.0936i	−0.796462	+	1.24780i
$933$	−13.7083	+	29.4077i	−0.448789	+	0.962764i
$934$	12.8952	−	44.1700i	0.421945	−	1.44529i
$935$	−3.20336	−	7.73360i	−0.104761	−	0.252916i
$936$	−8.70641	+	14.3141i	−0.284578	+	0.467871i
$937$	−3.45945	+	8.35185i	−0.113015	+	0.272843i	−0.970260	−	0.242067i	$-0.922175\pi$
$937$	−3.45945	+	8.35185i	−0.113015	+	0.272843i	0.857244	+	0.514910i	$0.172175\pi$
$938$	−18.3151	+	22.7998i	−0.598010	+	0.744440i
$939$	10.6564	+	29.2660i	0.347757	+	0.955061i
$940$	−0.274520	−	13.1043i	−0.00895385	−	0.427414i
$941$	−23.6198	+	15.7822i	−0.769983	+	0.514486i	−0.877418	−	0.479726i	$-0.840736\pi$
$941$	−23.6198	+	15.7822i	−0.769983	+	0.514486i	0.107436	+	0.994212i	$0.465736\pi$
$942$	31.9255	−	15.7319i	1.04019	−	0.512573i
$943$	5.13853	−	5.13853i	0.167334	−	0.167334i
$944$	−22.5477	−	30.8637i	−0.733864	−	1.00453i
$945$	−3.90051	+	11.5056i	−0.126884	+	0.374276i
$946$	34.5756	+	18.0180i	1.12415	+	0.585817i
$947$	−17.0966	+	11.4236i	−0.555564	+	0.371216i	−0.801431	−	0.598088i	$-0.795927\pi$
$947$	−17.0966	+	11.4236i	−0.555564	+	0.371216i	0.245867	+	0.969304i	$0.420927\pi$
$948$	−14.5387	−	22.8584i	−0.472194	−	0.742406i
$949$	20.6261	−	4.10278i	0.669551	−	0.133182i
$950$	0.981926	+	9.00212i	0.0318579	+	0.292067i
$951$	2.82053	−	11.5332i	0.0914619	−	0.373989i
$952$	19.3517	−	2.52199i	0.627192	−	0.0817381i
$953$	10.6165	+	25.6304i	0.343901	+	0.830250i	0.997314	+	0.0732481i	$0.0233365\pi$
$953$	10.6165	+	25.6304i	0.343901	+	0.830250i	−0.653413	+	0.757002i	$0.726663\pi$
$954$	16.1202	−	16.8336i	0.521909	−	0.545008i
$955$	−13.4668	+	20.1545i	−0.435776	+	0.652184i
$956$	19.8169	−	13.8503i	0.640926	−	0.447950i
$957$	44.7671	+	1.94863i	1.44712	+	0.0629902i
$958$	−13.6268	+	11.4241i	−0.440261	+	0.369096i
$959$	−27.1676			−0.877289
$960$	12.6967	−	5.54915i	0.409785	−	0.179098i
$961$	−0.357962			−0.0115472
$962$	−7.35567	+	6.16668i	−0.237156	+	0.198822i
$963$	−5.44519	−	49.5981i	−0.175469	−	1.59828i
$964$	21.2189	+	30.3599i	0.683414	+	0.977828i
$965$	6.69894	−	10.0257i	0.215646	−	0.322738i
$966$	34.6831	−	26.5966i	1.11591	−	0.855731i
$967$	−3.61293	−	8.72239i	−0.116184	−	0.280493i	0.855081	−	0.518495i	$-0.173508\pi$
$967$	−3.61293	−	8.72239i	−0.116184	−	0.280493i	−0.971265	+	0.238002i	$0.923508\pi$
$968$	5.09530	−	6.62239i	0.163769	−	0.212852i
$969$	31.7926	+	7.77514i	1.02133	+	0.249773i
$970$	−0.894910	−	8.20437i	−0.0287338	−	0.263426i
$971$	59.0089	−	11.7376i	1.89368	−	0.376677i	0.895962	−	0.444131i	$-0.146488\pi$
$971$	59.0089	−	11.7376i	1.89368	−	0.376677i	0.997722	+	0.0674539i	$0.0214876\pi$
$972$	28.8012	+	11.9369i	0.923800	+	0.382875i
$973$	32.2959	−	21.5795i	1.03536	−	0.691806i
$974$	44.0685	+	22.9650i	1.41205	+	0.735846i
$975$	2.02185	−	2.75822i	0.0647509	−	0.0883336i
$976$	−3.88813	+	6.38235i	−0.124456	+	0.204294i
$977$	−2.81060	+	2.81060i	−0.0899189	+	0.0899189i	−0.750635	−	0.660717i	$-0.770253\pi$
$977$	−2.81060	+	2.81060i	−0.0899189	+	0.0899189i	0.660717	+	0.750635i	$0.270253\pi$
$978$	1.63731	+	3.32268i	0.0523555	+	0.106247i
$979$	−7.99864	+	5.34452i	−0.255638	+	0.170812i
$980$	−3.06657	+	0.0642412i	−0.0979580	+	0.00205211i
$981$	0.821695	+	1.49681i	0.0262347	+	0.0477895i
$982$	13.5204	−	16.8310i	0.431453	−	0.537100i
$983$	12.0188	−	29.0160i	0.383340	−	0.925466i	−0.607975	−	0.793957i	$-0.708018\pi$
$983$	12.0188	−	29.0160i	0.383340	−	0.925466i	0.991315	−	0.131509i	$-0.0419823\pi$
$984$	−0.401112	−	4.64754i	−0.0127870	−	0.148158i
$985$	−3.95791	−	9.55524i	−0.126110	−	0.304455i
$986$	10.6675	−	36.5393i	0.339722	−	1.16365i
$987$	−24.0542	−	11.2128i	−0.765654	−	0.356907i
$988$	21.3141	+	13.6047i	0.678092	+	0.432823i
$989$	14.4710	−	72.7508i	0.460152	−	2.31334i
$990$	−11.7495	+	2.60270i	−0.373423	+	0.0827193i
$991$	11.8197			0.375466			0.187733	−	0.982220i	$-0.439886\pi$
$991$	11.8197			0.375466			0.187733	+	0.982220i	$0.439886\pi$
$992$	10.6458	+	29.4485i	0.338005	+	0.934990i
$993$	15.9550	−	2.45788i	0.506318	−	0.0779986i
$994$	2.68439	−	30.5296i	0.0851436	−	0.968340i
$995$	2.33006	+	0.463478i	0.0738679	+	0.0146932i
$996$	−7.22806	−	18.6276i	−0.229030	−	0.590238i
$997$	−0.270902	+	0.405434i	−0.00857956	+	0.0128402i	−0.835735	−	0.549134i	$-0.814958\pi$
$997$	−0.270902	+	0.405434i	−0.00857956	+	0.0128402i	0.827155	+	0.561974i	$0.189958\pi$
$998$	15.3371	−	52.5339i	0.485486	−	1.66293i
$999$	13.4339	+	11.7718i	0.425030	+	0.372442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.131.92	yes	1024
3.2	odd	2	inner	960.2.cn.a.131.37	✓	1024
64.43	odd	16	inner	960.2.cn.a.491.37	yes	1024
192.107	even	16	inner	960.2.cn.a.491.92	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.131.37	✓	1024	3.2	odd	2	inner
960.2.cn.a.131.92	yes	1024	1.1	even	1	trivial
960.2.cn.a.491.37	yes	1024	64.43	odd	16	inner
960.2.cn.a.491.92	yes	1024	192.107	even	16	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.908567 + 1.08375i) q^{2} +(0.0753215 - 1.73041i) q^{3} +(-0.349011 + 1.96931i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(1.94376 - 1.49057i) q^{6} +(-0.894725 - 2.16006i) q^{7} +(-2.45133 + 1.41101i) q^{8} +(-2.98865 - 0.260675i) q^{9} +O(q^{10})\)	\(q+(0.908567 + 1.08375i) q^{2} +(0.0753215 - 1.73041i) q^{3} +(-0.349011 + 1.96931i) q^{4} +(-0.555570 + 0.831470i) q^{5} +(1.94376 - 1.49057i) q^{6} +(-0.894725 - 2.16006i) q^{7} +(-2.45133 + 1.41101i) q^{8} +(-2.98865 - 0.260675i) q^{9} +(-1.40587 + 0.153349i) q^{10} +(-2.78201 + 0.553376i) q^{11} +(3.38143 + 0.752265i) q^{12} +(-1.64171 + 1.09696i) q^{13} +(1.52804 - 2.93221i) q^{14} +(1.39694 + 1.02399i) q^{15} +(-3.75638 - 1.37462i) q^{16} +(2.08673 - 2.08673i) q^{17} +(-2.43289 - 3.47578i) q^{18} +(-5.32408 + 3.55744i) q^{19} +(-1.44352 - 1.38428i) q^{20} +(-3.80518 + 1.38554i) q^{21} +(-3.12736 - 2.51221i) q^{22} +(-2.92055 + 7.05083i) q^{23} +(2.25700 + 4.34810i) q^{24} +(-0.382683 - 0.923880i) q^{25} +(-2.68043 - 0.782541i) q^{26} +(-0.676184 + 5.15197i) q^{27} +(4.56610 - 1.00811i) q^{28} +(1.77935 - 8.94538i) q^{29} +(0.159464 + 2.44429i) q^{30} -5.53553 q^{31} +(-1.92318 - 5.31990i) q^{32} +(0.748024 + 4.85571i) q^{33} +(4.15742 + 0.365551i) q^{34} +(2.29310 + 0.456127i) q^{35} +(1.55642 - 5.79461i) q^{36} +(1.90978 - 2.85818i) q^{37} +(-8.69264 - 2.53778i) q^{38} +(1.77453 + 2.92347i) q^{39} +(0.188674 - 2.82213i) q^{40} +(-0.879720 - 0.364392i) q^{41} +(-4.95884 - 2.86499i) q^{42} +(-9.53263 + 1.89616i) q^{43} +(-0.118817 - 5.67178i) q^{44} +(1.87715 - 2.34015i) q^{45} +(-10.2948 + 3.24102i) q^{46} +(4.63408 + 4.63408i) q^{47} +(-2.66160 + 6.39655i) q^{48} +(1.08443 - 1.08443i) q^{49} +(0.653557 - 1.25414i) q^{50} +(-3.45373 - 3.76808i) q^{51} +(-1.58728 - 3.61590i) q^{52} +(1.07174 + 5.38802i) q^{53} +(-6.19778 + 3.94810i) q^{54} +(1.08549 - 2.62060i) q^{55} +(5.24114 + 4.03255i) q^{56} +(5.75481 + 9.48080i) q^{57} +(11.3112 - 6.19912i) q^{58} +(7.94523 + 5.30883i) q^{59} +(-2.50411 + 2.39362i) q^{60} +(0.364498 - 1.83245i) q^{61} +(-5.02940 - 5.99910i) q^{62} +(2.11095 + 6.68889i) q^{63} +(4.01809 - 6.91773i) q^{64} -1.97447i q^{65} +(-4.58272 + 5.22240i) q^{66} +(-8.67485 - 1.72553i) q^{67} +(3.38113 + 4.83772i) q^{68} +(11.9809 + 5.58483i) q^{69} +(1.58911 + 2.89956i) q^{70} +(8.56335 - 3.54706i) q^{71} +(7.69401 - 3.57803i) q^{72} +(-9.84027 - 4.07597i) q^{73} +(4.83271 - 0.527138i) q^{74} +(-1.62752 + 0.592612i) q^{75} +(-5.14754 - 11.7264i) q^{76} +(3.68446 + 5.51418i) q^{77} +(-1.55601 + 4.57931i) q^{78} +(-5.52976 - 5.52976i) q^{79} +(3.22989 - 2.35962i) q^{80} +(8.86410 + 1.55813i) q^{81} +(-0.404376 - 1.28447i) q^{82} +(-3.20451 - 4.79589i) q^{83} +(-1.40052 - 7.97716i) q^{84} +(0.575728 + 2.89438i) q^{85} +(-10.7160 - 8.60817i) q^{86} +(-15.3452 - 3.75278i) q^{87} +(6.03882 - 5.28196i) q^{88} +(3.13329 - 1.29785i) q^{89} +(4.24165 - 0.0918309i) q^{90} +(3.83837 + 2.56472i) q^{91} +(-12.8660 - 8.21229i) q^{92} +(-0.416944 + 9.57874i) q^{93} +(-0.811793 + 9.23254i) q^{94} -6.40322i q^{95} +(-9.35048 + 2.92719i) q^{96} +5.83577i q^{97} +(2.16053 + 0.189970i) q^{98} +(8.45872 - 0.928651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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