LMFDB - Embedded newform 156.2.p.b.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(35,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("156.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.p (of order $6$, degree $2$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.8
Character	$\chi$	$=$	156.35
Dual form			156.2.p.b.107.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.475386 - 1.33192i) q^{2} +(-0.564863 + 1.63735i) q^{3} +(-1.54802 + 1.26635i) q^{4} -3.40345i q^{5} +(2.44935 - 0.0260236i) q^{6} +(2.05768 - 1.18800i) q^{7} +(2.42258 + 1.45983i) q^{8} +(-2.36186 - 1.84976i) q^{9} +O(q^{10})$	\(q+(-0.475386 - 1.33192i) q^{2} +(-0.564863 + 1.63735i) q^{3} +(-1.54802 + 1.26635i) q^{4} -3.40345i q^{5} +(2.44935 - 0.0260236i) q^{6} +(2.05768 - 1.18800i) q^{7} +(2.42258 + 1.45983i) q^{8} +(-2.36186 - 1.84976i) q^{9} +(-4.53312 + 1.61795i) q^{10} +(1.63272 - 2.82796i) q^{11} +(-1.19905 - 3.24997i) q^{12} +(2.06220 - 2.95759i) q^{13} +(-2.56051 - 2.17590i) q^{14} +(5.57266 + 1.92249i) q^{15} +(0.792707 - 3.92067i) q^{16} +(-0.380349 + 0.219594i) q^{17} +(-1.34094 + 4.02516i) q^{18} +(-2.98978 + 1.72615i) q^{19} +(4.30997 + 5.26860i) q^{20} +(0.782871 + 4.04020i) q^{21} +(-4.54278 - 0.830282i) q^{22} +(-3.46429 + 6.00032i) q^{23} +(-3.75868 + 3.14203i) q^{24} -6.58350 q^{25} +(-4.91961 - 1.34068i) q^{26} +(4.36284 - 2.82234i) q^{27} +(-1.68089 + 4.44478i) q^{28} +(7.57617 + 4.37410i) q^{29} +(-0.0885701 - 8.33625i) q^{30} +0.323641i q^{31} +(-5.59885 + 0.808008i) q^{32} +(3.70810 + 4.27075i) q^{33} +(0.473295 + 0.402202i) q^{34} +(-4.04330 - 7.00320i) q^{35} +(5.99865 - 0.127482i) q^{36} +(1.58418 - 2.74389i) q^{37} +(3.72039 + 3.16155i) q^{38} +(3.67777 + 5.04718i) q^{39} +(4.96845 - 8.24515i) q^{40} +(1.42562 + 0.823079i) q^{41} +(5.00905 - 2.96338i) q^{42} +(-0.845293 + 0.488030i) q^{43} +(1.05371 + 6.44532i) q^{44} +(-6.29558 + 8.03848i) q^{45} +(9.63882 + 1.76168i) q^{46} -2.05940 q^{47} +(5.97175 + 3.51258i) q^{48} +(-0.677315 + 1.17314i) q^{49} +(3.12970 + 8.76869i) q^{50} +(-0.144709 - 0.746807i) q^{51} +(0.553036 + 7.18986i) q^{52} -5.71107i q^{53} +(-5.83316 - 4.46925i) q^{54} +(-9.62482 - 5.55689i) q^{55} +(6.71916 + 0.125821i) q^{56} +(-1.13750 - 5.87036i) q^{57} +(2.22434 - 12.1702i) q^{58} +(-2.43459 - 4.21683i) q^{59} +(-11.0611 + 4.08091i) q^{60} +(6.60487 + 11.4400i) q^{61} +(0.431063 - 0.153854i) q^{62} +(-7.05746 - 1.00032i) q^{63} +(3.73782 + 7.07310i) q^{64} +(-10.0660 - 7.01859i) q^{65} +(3.92552 - 6.96915i) q^{66} +(3.51711 + 2.03060i) q^{67} +(0.310702 - 0.821591i) q^{68} +(-7.86780 - 9.06163i) q^{69} +(-7.40557 + 8.71457i) q^{70} +(-0.174835 - 0.302822i) q^{71} +(-3.02147 - 7.92911i) q^{72} -5.87640 q^{73} +(-4.40773 - 0.805598i) q^{74} +(3.71878 - 10.7795i) q^{75} +(2.44231 - 6.45821i) q^{76} -7.75869i q^{77} +(4.97408 - 7.29785i) q^{78} +13.0762i q^{79} +(-13.3438 - 2.69794i) q^{80} +(2.15676 + 8.73776i) q^{81} +(0.418557 - 2.29008i) q^{82} +1.55571 q^{83} +(-6.32821 - 5.26291i) q^{84} +(0.747380 + 1.29450i) q^{85} +(1.05186 + 0.893859i) q^{86} +(-11.4415 + 9.93410i) q^{87} +(8.08373 - 4.46747i) q^{88} +(10.7309 + 6.19551i) q^{89} +(13.6994 + 4.56382i) q^{90} +(0.729715 - 8.53565i) q^{91} +(-2.23574 - 13.6756i) q^{92} +(-0.529914 - 0.182813i) q^{93} +(0.979010 + 2.74295i) q^{94} +(5.87487 + 10.1756i) q^{95} +(1.83959 - 9.62372i) q^{96} +(0.991051 + 1.71655i) q^{97} +(1.88452 + 0.344432i) q^{98} +(-9.08731 + 3.65909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) $ 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9	$ 40 q + 6 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{10} - 16 q^{12} + 16 q^{13} + 18 q^{16} - 20 q^{18} - 60 q^{21} + 20 q^{22} - 20 q^{24} - 32 q^{25} - 24 q^{28} - 26 q^{30} - 2 q^{33} - 28 q^{34} + 6 q^{36} + 16 q^{37} + 20 q^{40} - 4 q^{42} + 28 q^{45} + 48 q^{46} - 24 q^{48} - 28 q^{49} + 12 q^{52} - 4 q^{54} + 44 q^{57} - 50 q^{58} - 12 q^{60} - 12 q^{61} + 12 q^{64} + 24 q^{66} - 6 q^{69} + 48 q^{72} - 16 q^{73} + 30 q^{78} - 14 q^{81} - 2 q^{82} - 6 q^{84} + 52 q^{85} - 12 q^{88} + 156 q^{90} + 40 q^{93} - 8 q^{94} + 128 q^{96} - 56 q^{97}+O(q^{100}) $ 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^10 - 16 * q^12 + 16 * q^13 + 18 * q^16 - 20 * q^18 - 60 * q^21 + 20 * q^22 - 20 * q^24 - 32 * q^25 - 24 * q^28 - 26 * q^30 - 2 * q^33 - 28 * q^34 + 6 * q^36 + 16 * q^37 + 20 * q^40 - 4 * q^42 + 28 * q^45 + 48 * q^46 - 24 * q^48 - 28 * q^49 + 12 * q^52 - 4 * q^54 + 44 * q^57 - 50 * q^58 - 12 * q^60 - 12 * q^61 + 12 * q^64 + 24 * q^66 - 6 * q^69 + 48 * q^72 - 16 * q^73 + 30 * q^78 - 14 * q^81 - 2 * q^82 - 6 * q^84 + 52 * q^85 - 12 * q^88 + 156 * q^90 + 40 * q^93 - 8 * q^94 + 128 * q^96 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.475386	−	1.33192i	−0.336149	−	0.941809i
$2$	−0.475386	−	1.33192i	−0.336149	−	0.941809i
$3$	−0.564863	+	1.63735i	−0.326124	+	0.945327i
$3$	−0.564863	+	1.63735i	−0.326124	+	0.945327i
$4$	−1.54802	+	1.26635i	−0.774008	+	0.633176i
$5$		−	3.40345i		−	1.52207i	−0.648710	−	0.761035i	$-0.724691\pi$
$5$		−	3.40345i		−	1.52207i	0.648710	−	0.761035i	$-0.275309\pi$
$6$	2.44935	−	0.0260236i	0.999944	−	0.0106241i
$7$	2.05768	−	1.18800i	0.777728	−	0.449022i	−0.0578964	−	0.998323i	$-0.518439\pi$
$7$	2.05768	−	1.18800i	0.777728	−	0.449022i	0.835625	+	0.549301i	$0.185106\pi$
$8$	2.42258	+	1.45983i	0.856512	+	0.516126i
$9$	−2.36186	−	1.84976i	−0.787286	−	0.616588i
$10$	−4.53312	+	1.61795i	−1.43350	+	0.511642i
$11$	1.63272	−	2.82796i	0.492284	−	0.852661i	−0.507676	−	0.861548i	$-0.669495\pi$
$11$	1.63272	−	2.82796i	0.492284	−	0.852661i	0.999961	+	0.00888660i	$0.00282873\pi$
$12$	−1.19905	−	3.24997i	−0.346136	−	0.938184i
$13$	2.06220	−	2.95759i	0.571950	−	0.820288i
$13$	2.06220	−	2.95759i	0.571950	−	0.820288i
$14$	−2.56051	−	2.17590i	−0.684325	−	0.581533i
$15$	5.57266	+	1.92249i	1.43885	+	0.496384i
$16$	0.792707	−	3.92067i	0.198177	−	0.980166i
$17$	−0.380349	+	0.219594i	−0.0922481	+	0.0532595i	−0.545414	−	0.838167i	$-0.683628\pi$
$17$	−0.380349	+	0.219594i	−0.0922481	+	0.0532595i	0.453166	+	0.891426i	$0.350294\pi$
$18$	−1.34094	+	4.02516i	−0.316062	+	0.948738i
$19$	−2.98978	+	1.72615i	−0.685902	+	0.396006i	−0.802075	−	0.597223i	$-0.796271\pi$
$19$	−2.98978	+	1.72615i	−0.685902	+	0.396006i	0.116173	+	0.993229i	$0.462937\pi$
$20$	4.30997	+	5.26860i	0.963738	+	1.17810i
$21$	0.782871	+	4.04020i	0.170836	+	0.881644i
$22$	−4.54278	−	0.830282i	−0.968525	−	0.177017i
$23$	−3.46429	+	6.00032i	−0.722354	+	1.25115i	0.237700	+	0.971339i	$0.423606\pi$
$23$	−3.46429	+	6.00032i	−0.722354	+	1.25115i	−0.960054	+	0.279815i	$0.909727\pi$
$24$	−3.75868	+	3.14203i	−0.767237	+	0.641363i
$25$	−6.58350			−1.31670
$26$	−4.91961	−	1.34068i	−0.964815	−	0.262929i
$27$	4.36284	−	2.82234i	0.839630	−	0.543159i
$28$	−1.68089	+	4.44478i	−0.317658	+	0.839985i
$29$	7.57617	+	4.37410i	1.40686	+	0.812250i	0.995084	−	0.0990350i	$-0.0315756\pi$
$29$	7.57617	+	4.37410i	1.40686	+	0.812250i	0.411775	+	0.911285i	$0.364909\pi$
$30$	−0.0885701	−	8.33625i	−0.0161706	−	1.52198i
$31$			0.323641i			0.0581276i	0.999578	+	0.0290638i	$0.00925259\pi$
$31$			0.323641i			0.0581276i	−0.999578	+	0.0290638i	$0.990747\pi$
$32$	−5.59885	+	0.808008i	−0.989746	+	0.142837i
$33$	3.70810	+	4.27075i	0.645498	+	0.743443i
$34$	0.473295	+	0.402202i	0.0811693	+	0.0689770i
$35$	−4.04330	−	7.00320i	−0.683443	−	1.18376i
$36$	5.99865	−	0.127482i	0.999774	−	0.0212470i
$37$	1.58418	−	2.74389i	0.260438	−	0.451092i	−0.705920	−	0.708291i	$-0.749466\pi$
$37$	1.58418	−	2.74389i	0.260438	−	0.451092i	0.966358	+	0.257199i	$0.0827997\pi$
$38$	3.72039	+	3.16155i	0.603527	+	0.512872i
$39$	3.67777	+	5.04718i	0.588914	+	0.808196i
$40$	4.96845	−	8.24515i	0.785581	−	1.30367i
$41$	1.42562	+	0.823079i	0.222644	+	0.128543i	0.607174	−	0.794569i	$-0.292303\pi$
$41$	1.42562	+	0.823079i	0.222644	+	0.128543i	−0.384530	+	0.923112i	$0.625637\pi$
$42$	5.00905	−	2.96338i	0.772914	−	0.457259i
$43$	−0.845293	+	0.488030i	−0.128906	+	0.0744239i	−0.563066	−	0.826412i	$-0.690378\pi$
$43$	−0.845293	+	0.488030i	−0.128906	+	0.0744239i	0.434160	+	0.900836i	$0.357045\pi$
$44$	1.05371	+	6.44532i	0.158853	+	0.971669i
$45$	−6.29558	+	8.03848i	−0.938490	+	1.19831i
$46$	9.63882	+	1.76168i	1.42117	+	0.259746i
$47$	−2.05940			−0.300394			−0.150197	−	0.988656i	$-0.547991\pi$
$47$	−2.05940			−0.300394			−0.150197	+	0.988656i	$0.547991\pi$
$48$	5.97175	+	3.51258i	0.861947	+	0.506998i
$49$	−0.677315	+	1.17314i	−0.0967593	+	0.167592i
$50$	3.12970	+	8.76869i	0.442607	+	1.24008i
$51$	−0.144709	−	0.746807i	−0.0202633	−	0.104574i
$52$	0.553036	+	7.18986i	0.0766923	+	0.997055i
$53$		−	5.71107i		−	0.784476i	−0.919864	−	0.392238i	$-0.871701\pi$
$53$		−	5.71107i		−	0.784476i	0.919864	−	0.392238i	$-0.128299\pi$
$54$	−5.83316	−	4.46925i	−0.793793	−	0.608189i
$55$	−9.62482	−	5.55689i	−1.29781	−	0.749291i
$56$	6.71916	+	0.125821i	0.897886	+	0.0168135i
$57$	−1.13750	−	5.87036i	−0.150666	−	0.777548i
$58$	2.22434	−	12.1702i	0.292071	−	1.59803i
$59$	−2.43459	−	4.21683i	−0.316956	−	0.548984i	0.662895	−	0.748712i	$-0.269328\pi$
$59$	−2.43459	−	4.21683i	−0.316956	−	0.548984i	−0.979851	+	0.199728i	$0.935994\pi$
$60$	−11.0611	+	4.08091i	−1.42798	+	0.526843i
$61$	6.60487	+	11.4400i	0.845667	+	1.46474i	0.885041	+	0.465514i	$0.154130\pi$
$61$	6.60487	+	11.4400i	0.845667	+	1.46474i	−0.0393736	+	0.999225i	$0.512536\pi$
$62$	0.431063	−	0.153854i	0.0547451	−	0.0195395i
$63$	−7.05746	−	1.00032i	−0.889156	−	0.126029i
$64$	3.73782	+	7.07310i	0.467227	+	0.884137i
$65$	−10.0660	−	7.01859i	−1.24854	−	0.870549i
$66$	3.92552	−	6.96915i	0.483198	−	0.857843i
$67$	3.51711	+	2.03060i	0.429683	+	0.248077i	0.699211	−	0.714915i	$-0.253535\pi$
$67$	3.51711	+	2.03060i	0.429683	+	0.248077i	−0.269529	+	0.962992i	$0.586868\pi$
$68$	0.310702	−	0.821591i	0.0376782	−	0.0996325i
$69$	−7.86780	−	9.06163i	−0.947172	−	1.09089i
$70$	−7.40557	+	8.71457i	−0.885135	+	1.04159i
$71$	−0.174835	−	0.302822i	−0.0207490	−	0.0359384i	0.855464	−	0.517862i	$-0.173272\pi$
$71$	−0.174835	−	0.302822i	−0.0207490	−	0.0359384i	−0.876213	+	0.481923i	$0.839938\pi$
$72$	−3.02147	−	7.92911i	−0.356083	−	0.934454i
$73$	−5.87640			−0.687781			−0.343890	−	0.939010i	$-0.611745\pi$
$73$	−5.87640			−0.687781			−0.343890	+	0.939010i	$0.611745\pi$
$74$	−4.40773	−	0.805598i	−0.512389	−	0.0936489i
$75$	3.71878	−	10.7795i	0.429407	−	1.24471i
$76$	2.44231	−	6.45821i	0.280152	−	0.740808i
$77$		−	7.75869i		−	0.884185i
$78$	4.97408	−	7.29785i	0.563203	−	0.826318i
$79$			13.0762i			1.47119i	0.677423	+	0.735594i	$0.263097\pi$
$79$			13.0762i			1.47119i	−0.677423	+	0.735594i	$0.736903\pi$
$80$	−13.3438	−	2.69794i	−1.49188	−	0.301639i
$81$	2.15676	+	8.73776i	0.239640	+	0.970862i
$82$	0.418557	−	2.29008i	0.0462219	−	0.252898i
$83$	1.55571			0.170762			0.0853809	−	0.996348i	$-0.472789\pi$
$83$	1.55571			0.170762			0.0853809	+	0.996348i	$0.472789\pi$
$84$	−6.32821	−	5.26291i	−0.690464	−	0.574230i
$85$	0.747380	+	1.29450i	0.0810647	+	0.140408i
$86$	1.05186	+	0.893859i	0.113425	+	0.0963873i
$87$	−11.4415	+	9.93410i	−1.22665	+	1.06505i
$88$	8.08373	−	4.46747i	0.861729	−	0.476234i
$89$	10.7309	+	6.19551i	1.13748	+	0.656723i	0.945805	−	0.324736i	$-0.105275\pi$
$89$	10.7309	+	6.19551i	1.13748	+	0.656723i	0.191673	+	0.981459i	$0.438609\pi$
$90$	13.6994	+	4.56382i	1.44405	+	0.481069i
$91$	0.729715	−	8.53565i	0.0764949	−	0.894779i
$92$	−2.23574	−	13.6756i	−0.233092	−	1.42578i
$93$	−0.529914	−	0.182813i	−0.0549496	−	0.0189568i
$94$	0.979010	+	2.74295i	0.100977	+	0.282914i
$95$	5.87487	+	10.1756i	0.602749	+	1.04399i
$96$	1.83959	−	9.62372i	0.187752	−	0.982216i
$97$	0.991051	+	1.71655i	0.100626	+	0.174289i	0.911943	−	0.410317i	$-0.134582\pi$
$97$	0.991051	+	1.71655i	0.100626	+	0.174289i	−0.811317	+	0.584607i	$0.801249\pi$
$98$	1.88452	+	0.344432i	0.190365	+	0.0347929i
$99$	−9.08731	+	3.65909i	−0.913309	+	0.367752i
$100$	10.1914	−	8.33702i	1.01914	−	0.833702i
$101$	0.317245	+	0.183162i	0.0315671	+	0.0182253i	0.515701	−	0.856769i	$-0.327532\pi$
$101$	0.317245	+	0.183162i	0.0315671	+	0.0182253i	−0.484133	+	0.874994i	$0.660865\pi$
$102$	−0.925893	+	0.547762i	−0.0916771	+	0.0542365i
$103$		−	17.6947i		−	1.74351i	−0.489938	−	0.871757i	$-0.662981\pi$
$103$		−	17.6947i		−	1.74351i	0.489938	−	0.871757i	$-0.337019\pi$
$104$	9.31341	−	4.15456i	0.913255	−	0.407388i
$105$	13.7506	−	2.66447i	1.34192	−	0.260025i
$106$	−7.60669	+	2.71497i	−0.738827	+	0.263701i
$107$	3.78720	−	6.55962i	0.366122	−	0.634143i	−0.622833	−	0.782355i	$-0.714018\pi$
$107$	3.78720	−	6.55962i	0.366122	−	0.634143i	0.988956	+	0.148212i	$0.0473518\pi$
$108$	−3.17968	+	9.89392i	−0.305965	+	0.952043i
$109$	1.23103			0.117911			0.0589557	−	0.998261i	$-0.481223\pi$
$109$	1.23103			0.117911			0.0589557	+	0.998261i	$0.481223\pi$
$110$	−2.82583	+	15.4612i	−0.269432	+	1.47416i
$111$	3.59787	+	4.14379i	0.341494	+	0.393311i
$112$	−3.02661	−	9.00919i	−0.285988	−	0.851289i
$113$	−9.45501	+	5.45885i	−0.889453	+	0.513526i	−0.873763	−	0.486351i	$-0.838328\pi$
$113$	−9.45501	+	5.45885i	−0.889453	+	0.513526i	−0.0156893	+	0.999877i	$0.504994\pi$
$114$	−7.27809	+	4.30575i	−0.681656	+	0.403270i
$115$	20.4218	+	11.7905i	1.90434	+	1.09947i
$116$	−17.2672	+	2.82291i	−1.60322	+	0.262101i
$117$	−10.3415	+	3.17084i	−0.956068	+	0.293144i
$118$	−4.45911	+	5.24729i	−0.410494	+	0.483053i
$119$	−0.521756	+	0.903708i	−0.0478293	+	0.0828428i
$120$	10.6937	+	12.7925i	0.976200	+	1.16779i
$121$	0.168437	+	0.291741i	0.0153125	+	0.0265220i
$122$	12.0973	−	14.2356i	1.09523	−	1.28883i
$123$	−2.15295	+	1.86931i	−0.194125	+	0.168550i
$124$	−0.409843	−	0.501001i	−0.0368050	−	0.0449912i
$125$			5.38936i			0.482039i
$126$	2.02267	+	9.87550i	0.180193	+	0.879779i
$127$	4.03746	+	2.33103i	0.358266	+	0.206845i	0.668320	−	0.743874i	$-0.267014\pi$
$127$	4.03746	+	2.33103i	0.358266	+	0.206845i	−0.310054	+	0.950719i	$0.600347\pi$
$128$	7.64389	−	8.34092i	0.675631	−	0.737240i
$129$	−0.321603	−	1.65971i	−0.0283156	−	0.146130i
$130$	−4.56295	+	16.7437i	−0.400197	+	1.46852i
$131$	6.68043			0.583672			0.291836	−	0.956468i	$-0.405734\pi$
$131$	6.68043			0.583672			0.291836	+	0.956468i	$0.405734\pi$
$132$	−11.1485	−	1.91543i	−0.970351	−	0.166717i
$133$	−4.10133	+	7.10370i	−0.355630	+	0.615969i
$134$	1.03261	−	5.64982i	0.0892042	−	0.488070i
$135$	−9.60570	−	14.8487i	−0.826727	−	1.27798i
$136$	−1.24200	−	0.0232572i	−0.106500	−	0.00199429i
$137$	8.20245	−	4.73569i	0.700783	−	0.404597i	−0.106856	−	0.994274i	$-0.534078\pi$
$137$	8.20245	−	4.73569i	0.700783	−	0.404597i	0.807639	+	0.589677i	$0.200745\pi$
$138$	−8.32911	+	14.7870i	−0.709021	+	1.25876i
$139$	10.9252	−	6.30764i	0.926660	−	0.535007i	0.0409063	−	0.999163i	$-0.486975\pi$
$139$	10.9252	−	6.30764i	0.926660	−	0.535007i	0.885754	+	0.464156i	$0.153642\pi$
$140$	15.1276	+	5.72083i	1.27852	+	0.483498i
$141$	1.16328	−	3.37197i	0.0979658	−	0.283971i
$142$	−0.320221	+	0.376823i	−0.0268723	+	0.0316223i
$143$	−4.99695	−	10.6607i	−0.417866	−	0.891495i
$144$	−9.12456	+	7.79374i	−0.760380	+	0.649478i
$145$	14.8871	−	25.7851i	1.23630	−	2.14134i
$146$	2.79356	+	7.82689i	0.231197	+	0.647758i
$147$	−1.53826	−	1.77167i	−0.126874	−	0.146125i
$148$	1.02238	+	6.25371i	0.0840394	+	0.514052i
$149$	−11.1392	+	6.43120i	−0.912556	+	0.526864i	−0.881253	−	0.472646i	$-0.843299\pi$
$149$	−11.1392	+	6.43120i	−0.912556	+	0.526864i	−0.0313031	+	0.999510i	$0.509966\pi$
$150$	−16.1253	+	0.171326i	−1.31663	+	0.0139887i
$151$			9.19065i			0.747924i	0.927444	+	0.373962i	$0.122001\pi$
$151$			9.19065i			0.747924i	−0.927444	+	0.373962i	$0.877999\pi$
$152$	−9.76286	−	0.182816i	−0.791872	−	0.0148283i
$153$	1.30453	+	0.184904i	0.105465	+	0.0149486i
$154$	−10.3339	+	3.68837i	−0.832733	+	0.297218i
$155$	1.10150			0.0884743
$156$	−12.0847	−	3.15577i	−0.967554	−	0.252664i
$157$	−5.71635			−0.456215			−0.228107	−	0.973636i	$-0.573254\pi$
$157$	−5.71635			−0.456215			−0.228107	+	0.973636i	$0.573254\pi$
$158$	17.4164	−	6.21624i	1.38558	−	0.494538i
$159$	9.35105	+	3.22598i	0.741587	+	0.255837i
$160$	2.75002	+	19.0554i	0.217408	+	1.50646i
$161$			16.4623i			1.29741i
$162$	10.6127	−	7.02643i	0.833812	−	0.552049i
$163$	−12.9200	+	7.45935i	−1.01197	+	0.584262i	−0.911768	−	0.410706i	$-0.865282\pi$
$163$	−12.9200	+	7.45935i	−1.01197	+	0.584262i	−0.100203	+	0.994967i	$0.531949\pi$
$164$	−3.24918	+	0.531190i	−0.253719	+	0.0414790i
$165$	14.5353	−	12.6204i	1.13157	−	0.982494i
$166$	−0.739564	−	2.07208i	−0.0574013	−	0.160825i
$167$	−8.66562	+	15.0093i	−0.670565	+	1.16145i	0.307179	+	0.951652i	$0.400615\pi$
$167$	−8.66562	+	15.0093i	−0.670565	+	1.16145i	−0.977744	+	0.209802i	$0.932718\pi$
$168$	−4.00142	+	10.9306i	−0.308716	+	0.843312i
$169$	−4.49469	−	12.1983i	−0.345745	−	0.938328i
$170$	1.36887	−	1.61084i	0.104988	−	0.123545i
$171$	10.2544	+	1.45346i	0.784173	+	0.111149i
$172$	0.690509	−	1.82592i	0.0526508	−	0.139225i
$173$	8.80380	−	5.08287i	0.669340	−	0.386444i	−0.126486	−	0.991968i	$-0.540370\pi$
$173$	8.80380	−	5.08287i	0.669340	−	0.386444i	0.795827	+	0.605525i	$0.207037\pi$
$174$	18.6705	+	10.5166i	1.41541	+	0.797258i
$175$	−13.5467	+	7.82119i	−1.02403	+	0.591227i
$176$	−9.79320	−	8.64310i	−0.738191	−	0.651498i
$177$	8.27965	−	1.60435i	0.622337	−	0.120590i
$178$	3.15058	−	17.2380i	0.236146	−	1.29204i
$179$	−5.04401	+	8.73648i	−0.377007	+	0.652995i	−0.990625	−	0.136608i	$-0.956380\pi$
$179$	−5.04401	+	8.73648i	−0.377007	+	0.652995i	0.613618	+	0.789603i	$0.289713\pi$
$180$	−0.433878	−	20.4161i	−0.0323394	−	1.52173i
$181$	−10.2537			−0.762153			−0.381076	−	0.924544i	$-0.624446\pi$
$181$	−10.2537			−0.762153			−0.381076	+	0.924544i	$0.624446\pi$
$182$	−11.7157	+	3.08581i	−0.868425	+	0.228735i
$183$	−22.4621	+	4.35250i	−1.66045	+	0.321746i
$184$	−17.1519	+	9.47902i	−1.26446	+	0.698803i
$185$	−9.33869	−	5.39170i	−0.686594	−	0.396405i
$186$	0.00842229	+	0.792710i	0.000617552	+	0.0581243i
$187$			1.43415i			0.104875i
$188$	3.18798	−	2.60792i	0.232508	−	0.190202i
$189$	5.62438	−	10.9905i	0.409114	−	0.799442i
$190$	10.7602	−	12.6622i	0.780627	−	0.918610i
$191$	10.4501	+	18.1001i	0.756144	+	1.30968i	0.944804	+	0.327637i	$0.106252\pi$
$191$	10.4501	+	18.1001i	0.756144	+	1.30968i	−0.188659	+	0.982043i	$0.560414\pi$
$192$	−13.6925	+	2.12480i	−0.988173	+	0.153344i
$193$	−7.06574	+	12.2382i	−0.508603	+	0.880927i	0.491347	+	0.870964i	$0.336505\pi$
$193$	−7.06574	+	12.2382i	−0.508603	+	0.880927i	−0.999950	+	0.00996281i	$0.996829\pi$
$194$	1.81518	−	2.13602i	0.130322	−	0.153358i
$195$	17.1778	−	12.5171i	1.23013	−	0.896369i
$196$	−0.437118	−	2.67377i	−0.0312227	−	0.190983i
$197$	−4.34412	−	2.50808i	−0.309506	−	0.178693i	0.337199	−	0.941433i	$-0.390520\pi$
$197$	−4.34412	−	2.50808i	−0.309506	−	0.178693i	−0.646705	+	0.762740i	$0.723854\pi$
$198$	9.19359	+	10.3641i	0.653360	+	0.736543i
$199$	21.3324	−	12.3163i	1.51221	−	0.873078i	0.512317	−	0.858796i	$-0.328787\pi$
$199$	21.3324	−	12.3163i	1.51221	−	0.873078i	0.999898	−	0.0142813i	$-0.00454603\pi$
$200$	−15.9491	−	9.61076i	−1.12777	−	0.679583i
$201$	−5.31150	+	4.61174i	−0.374644	+	0.325287i
$202$	0.0931425	−	0.509618i	0.00655348	−	0.0358566i
$203$	20.7857			1.45887
$204$	1.16973	+	0.972816i	0.0818976	+	0.0681108i
$205$	2.80131	−	4.85202i	0.195652	−	0.338879i
$206$	−23.5680	+	8.41183i	−1.64206	+	0.586080i
$207$	19.2813	−	7.76381i	1.34014	−	0.539622i
$208$	−9.96101	−	10.4297i	−0.690671	−	0.723169i
$209$			11.2733i			0.779789i
$210$	−10.0857	−	17.0481i	−0.695980	−	1.17643i
$211$	−21.7380	−	12.5505i	−1.49651	−	0.864010i	−0.496517	−	0.868027i	$-0.665388\pi$
$211$	−21.7380	−	12.5505i	−1.49651	−	0.864010i	−0.999992	+	0.00401730i	$0.998721\pi$
$212$	7.23223	+	8.84084i	0.496712	+	0.607191i
$213$	0.594585	−	0.115213i	0.0407403	−	0.00789426i
$214$	−10.5373	−	1.92589i	−0.720313	−	0.131651i
$215$	1.66099	+	2.87692i	0.113278	+	0.196204i
$216$	14.6895	−	0.468354i	0.999492	−	0.0318675i
$217$	0.384485	+	0.665947i	0.0261005	+	0.0452074i
$218$	−0.585215	−	1.63963i	−0.0396357	−	0.111050i
$219$	3.31936	−	9.62175i	0.224302	−	0.650178i
$220$	21.9364	−	3.58625i	1.47895	−	0.241785i
$221$	−0.134883	+	1.57776i	−0.00907324	+	0.106132i
$222$	3.80882	−	6.76197i	0.255631	−	0.453834i
$223$	2.87420	+	1.65942i	0.192471	+	0.111123i	0.593139	−	0.805100i	$-0.297889\pi$
$223$	2.87420	+	1.65942i	0.192471	+	0.111123i	−0.400668	+	0.916223i	$0.631222\pi$
$224$	−10.5607	+	8.31405i	−0.705617	+	0.555506i
$225$	15.5493	+	12.1779i	1.03662	+	0.811861i
$226$	11.7655	+	9.99825i	0.782632	+	0.665073i
$227$	−9.53374	−	16.5129i	−0.632776	−	1.09600i	−0.986982	−	0.160833i	$-0.948582\pi$
$227$	−9.53374	−	16.5129i	−0.632776	−	1.09600i	0.354205	−	0.935168i	$-0.384751\pi$
$228$	9.19481	+	7.64694i	0.608941	+	0.506431i
$229$	26.8999			1.77759			0.888797	−	0.458301i	$-0.151542\pi$
$229$	26.8999			1.77759			0.888797	+	0.458301i	$0.151542\pi$
$230$	5.99580	−	32.8053i	0.395351	−	2.16312i
$231$	12.7037	+	4.38260i	0.835844	+	0.288354i
$232$	11.9685	+	21.6565i	0.785768	+	1.42182i
$233$		−	0.796033i		−	0.0521499i	−0.999660	−	0.0260749i	$-0.991699\pi$
$233$		−	0.796033i		−	0.0521499i	0.999660	−	0.0260749i	$-0.00830085\pi$
$234$	9.13949	+	12.2666i	0.597467	+	0.801894i
$235$			7.00907i			0.457222i
$236$	9.10877	+	3.44468i	0.592930	+	0.224229i
$237$	−21.4104	−	7.38627i	−1.39075	−	0.479789i
$238$	1.45170	+	0.265327i	0.0940998	+	0.0171986i
$239$	7.71543			0.499070			0.249535	−	0.968366i	$-0.419722\pi$
$239$	7.71543			0.499070			0.249535	+	0.968366i	$0.419722\pi$
$240$	11.9549	−	20.3246i	0.771686	−	1.31195i
$241$	−5.43397	−	9.41191i	−0.350033	−	0.606275i	0.636222	−	0.771506i	$-0.280496\pi$
$241$	−5.43397	−	9.41191i	−0.350033	−	0.606275i	−0.986255	+	0.165231i	$0.947163\pi$
$242$	0.308503	−	0.363034i	0.0198313	−	0.0233367i
$243$	−15.5251	−	1.40426i	−0.995934	−	0.0900835i
$244$	−24.7115	−	9.34517i	−1.58199	−	0.598263i
$245$	3.99274	+	2.30521i	0.255087	+	0.147275i
$246$	3.51325	+	1.97891i	0.223997	+	0.126171i
$247$	−1.06027	+	12.4022i	−0.0674632	+	0.789133i
$248$	−0.472459	+	0.784046i	−0.0300012	+	0.0497870i
$249$	−0.878765	+	2.54725i	−0.0556895	+	0.161426i
$250$	7.17820	−	2.56203i	0.453989	−	0.162037i
$251$	−9.04025	−	15.6582i	−0.570615	−	0.988335i	−0.996503	−	0.0835588i	$-0.973371\pi$
$251$	−9.04025	−	15.6582i	−0.570615	−	0.988335i	0.425887	−	0.904776i	$-0.359962\pi$
$252$	12.1918	−	7.38870i	0.768012	−	0.465445i
$253$	11.3124	+	19.5937i	0.711207	+	1.23185i
$254$	1.18539	−	6.48570i	0.0743778	−	0.406949i
$255$	−2.54172	+	0.492510i	−0.159169	+	0.0308422i
$256$	−14.7432	−	6.21588i	−0.921452	−	0.388493i
$257$	−13.8627	−	8.00364i	−0.864732	−	0.499253i	0.000862203	−	1.00000i	$-0.499726\pi$
$257$	−13.8627	−	8.00364i	−0.864732	−	0.499253i	−0.865594	+	0.500747i	$0.833059\pi$
$258$	−2.05772	+	1.21735i	−0.128108	+	0.0757892i
$259$		−	7.52803i		−	0.467769i
$260$	24.4704	−	1.88223i	1.51759	−	0.116731i
$261$	−9.80279	−	24.3451i	−0.606777	−	1.50693i
$262$	−3.17579	−	8.89780i	−0.196201	−	0.549708i
$263$	6.27681	−	10.8718i	0.387045	−	0.670381i	−0.605006	−	0.796221i	$-0.706829\pi$
$263$	6.27681	−	10.8718i	0.387045	−	0.670381i	0.992051	+	0.125840i	$0.0401626\pi$
$264$	2.74863	+	15.7594i	0.169167	+	0.969927i
$265$	−19.4374			−1.19403
$266$	11.4113	+	2.08563i	0.699670	+	0.127878i
$267$	−16.2058	+	14.0707i	−0.991777	+	0.861115i
$268$	−8.01599	+	1.31049i	−0.489655	+	0.0800508i
$269$	−14.9461	+	8.62916i	−0.911282	+	0.526129i	−0.880843	−	0.473408i	$-0.843024\pi$
$269$	−14.9461	+	8.62916i	−0.911282	+	0.526129i	−0.0304388	+	0.999537i	$0.509690\pi$
$270$	−15.2109	+	19.8529i	−0.925706	+	1.20821i
$271$	−13.6221	−	7.86470i	−0.827482	−	0.477747i	0.0255080	−	0.999675i	$-0.491880\pi$
$271$	−13.6221	−	7.86470i	−0.827482	−	0.477747i	−0.852990	+	0.521928i	$0.825213\pi$
$272$	0.559451	+	1.66529i	0.0339217	+	0.100973i
$273$	13.5637	+	6.01628i	0.820912	+	0.364122i
$274$	−10.2069	−	8.67372i	−0.616620	−	0.523998i
$275$	−10.7490	+	18.6179i	−0.648191	+	1.12270i
$276$	23.6547	+	4.06414i	1.42385	+	0.244632i
$277$	−0.265729	−	0.460255i	−0.0159661	−	0.0276541i	0.857932	−	0.513763i	$-0.171749\pi$
$277$	−0.265729	−	0.460255i	−0.0159661	−	0.0276541i	−0.873898	+	0.486109i	$0.838416\pi$
$278$	−13.5949	−	11.5529i	−0.815370	−	0.692895i
$279$	0.598658	−	0.764394i	0.0358407	−	0.0457630i
$280$	0.428225	−	22.8684i	0.0255913	−	1.36665i
$281$			1.81900i			0.108512i	0.998527	+	0.0542562i	$0.0172788\pi$
$281$			1.81900i			0.108512i	−0.998527	+	0.0542562i	$0.982721\pi$
$282$	−5.04419	+	0.0535930i	−0.300377	+	0.00319141i
$283$	−22.5951	−	13.0453i	−1.34314	−	0.775461i	−0.355871	−	0.934535i	$-0.615816\pi$
$283$	−22.5951	−	13.0453i	−1.34314	−	0.775461i	−0.987267	+	0.159074i	$0.949149\pi$
$284$	0.654126	+	0.247372i	0.0388152	+	0.0146788i
$285$	−19.9795	+	3.87143i	−1.18348	+	0.229324i
$286$	−11.8237	+	11.7235i	−0.699153	+	0.693225i
$287$	3.91127			0.230875
$288$	14.7183	+	8.44814i	0.867285	+	0.497812i
$289$	−8.40356	+	14.5554i	−0.494327	+	0.856199i
$290$	−41.4208	−	7.57046i	−2.43231	−	0.444552i
$291$	−3.37041	+	0.653086i	−0.197577	+	0.0382846i
$292$	9.09676	−	7.44159i	0.532348	−	0.435486i
$293$	−13.3597	+	7.71324i	−0.780483	+	0.450612i	−0.836601	−	0.547812i	$-0.815461\pi$
$293$	−13.3597	+	7.71324i	−0.780483	+	0.450612i	0.0561184	+	0.998424i	$0.482128\pi$
$294$	−1.62845	+	2.89107i	−0.0949734	+	0.168611i
$295$	−14.3518	+	8.28601i	−0.835593	+	0.482430i
$296$	7.84341	−	4.33466i	0.455889	−	0.251947i
$297$	−0.858139	−	16.9460i	−0.0497943	−	0.983309i
$298$	13.8612	+	11.7792i	0.802960	+	0.682348i
$299$	10.6025	+	22.6198i	0.613156	+	1.30814i
$300$	7.89394	+	21.3961i	0.455757	+	1.23531i
$301$	−1.15956	+	2.00841i	−0.0668358	+	0.115763i
$302$	12.2412	−	4.36911i	0.704402	−	0.251414i
$303$	−0.479101	+	0.415982i	−0.0275236	+	0.0238975i
$304$	4.39763	+	13.0902i	0.252221	+	0.750777i
$305$	38.9354	−	22.4794i	2.22944	−	1.28717i
$306$	−0.373878	−	1.82543i	−0.0213732	−	0.104353i
$307$		−	18.4001i		−	1.05015i	−0.851057	−	0.525074i	$-0.824038\pi$
$307$		−	18.4001i		−	1.05015i	0.851057	−	0.525074i	$-0.175962\pi$
$308$	9.82523	+	12.0106i	0.559844	+	0.684366i
$309$	28.9726	+	9.99511i	1.64819	+	0.568602i
$310$	−0.523636	−	1.46710i	−0.0297405	−	0.0833259i
$311$	−18.8323			−1.06788			−0.533942	−	0.845521i	$-0.679290\pi$
$311$	−18.8323			−1.06788			−0.533942	+	0.845521i	$0.679290\pi$
$312$	1.54169	+	17.5961i	0.0872808	+	0.996184i
$313$	15.9701			0.902682			0.451341	−	0.892352i	$-0.350946\pi$
$313$	15.9701			0.902682			0.451341	+	0.892352i	$0.350946\pi$
$314$	2.71747	+	7.61372i	0.153356	+	0.429667i
$315$	−3.40455	+	24.0197i	−0.191825	+	1.35336i
$316$	−16.5591	−	20.2422i	−0.931520	−	1.13871i
$317$			6.01383i			0.337770i	0.985636	+	0.168885i	$0.0540167\pi$
$317$			6.01383i			0.337770i	−0.985636	+	0.168885i	$0.945983\pi$
$318$	−0.148623	−	13.9884i	−0.00833434	−	0.784432i
$319$	24.7396	−	14.2834i	1.38515	−	0.799716i
$320$	24.0730	−	12.7215i	1.34572	−	0.711153i
$321$	8.60118	+	9.90628i	0.480071	+	0.552915i
$322$	21.9264	−	7.82594i	1.22191	−	0.436123i
$323$	0.758105	−	1.31308i	0.0421821	−	0.0730615i
$324$	−14.4038	−	10.7950i	−0.800209	−	0.599721i
$325$	−13.5765	+	19.4713i	−0.753087	+	1.08007i
$326$	16.0772	+	13.6623i	0.890435	+	0.756684i
$327$	−0.695364	+	2.01563i	−0.0384537	+	0.111465i
$328$	2.25212	+	4.07513i	0.124352	+	0.225011i
$329$	−4.23758	+	2.44657i	−0.233625	+	0.134884i
$330$	−23.7192	−	13.3603i	−1.30570	−	0.735461i
$331$	−18.8173	+	10.8641i	−1.03429	+	0.597147i	−0.918211	−	0.396093i	$-0.870366\pi$
$331$	−18.8173	+	10.8641i	−1.03429	+	0.597147i	−0.116079	+	0.993240i	$0.537033\pi$
$332$	−2.40827	+	1.97008i	−0.132171	+	0.108122i
$333$	−8.81716	+	3.55031i	−0.483177	+	0.194556i
$334$	24.1107	+	4.40669i	1.31928	+	0.241123i
$335$	6.91106	−	11.9703i	0.377591	−	0.654008i
$336$	16.4609	+	0.133322i	0.898014	+	0.00727333i
$337$	12.3866			0.674739			0.337370	−	0.941372i	$-0.390463\pi$
$337$	12.3866			0.674739			0.337370	+	0.941372i	$0.390463\pi$
$338$	−14.1104	+	11.7854i	−0.767504	+	0.641044i
$339$	−3.59729	−	18.5647i	−0.195378	−	1.00830i
$340$	−2.79625	−	1.05746i	−0.151648	−	0.0573489i
$341$	0.915242	+	0.528415i	0.0495631	+	0.0286153i
$342$	−2.93891	−	14.3490i	−0.158918	−	0.775904i
$343$			19.8506i			1.07183i
$344$	−2.76023	−	0.0516871i	−0.148822	−	0.00278678i
$345$	−30.8408	+	26.7777i	−1.66041	+	1.44166i
$346$	−10.9552	−	9.30962i	−0.588954	−	0.500488i
$347$	−5.08375	−	8.80531i	−0.272910	−	0.472694i	0.696696	−	0.717367i	$-0.254653\pi$
$347$	−5.08375	−	8.80531i	−0.272910	−	0.472694i	−0.969606	+	0.244673i	$0.921319\pi$
$348$	5.13149	−	29.8671i	0.275077	−	1.60104i
$349$	10.3188	−	17.8726i	0.552350	−	0.956699i	−0.445754	−	0.895156i	$-0.647064\pi$
$349$	10.3188	−	17.8726i	0.552350	−	0.956699i	0.998104	−	0.0615436i	$-0.0196023\pi$
$350$	16.8571	+	14.3250i	0.901050	+	0.765705i
$351$	0.649723	−	18.7237i	0.0346796	−	0.999398i
$352$	−6.85635	+	17.1526i	−0.365445	+	0.914235i
$353$	−3.96487	−	2.28912i	−0.211029	−	0.121838i	0.390761	−	0.920492i	$-0.372212\pi$
$353$	−3.96487	−	2.28912i	−0.211029	−	0.121838i	−0.601789	+	0.798655i	$0.705545\pi$
$354$	−6.07290	−	10.2651i	−0.322771	−	0.545586i
$355$	−1.03064	+	0.595041i	−0.0547008	+	0.0315815i
$356$	−24.4574	+	3.99839i	−1.29624	+	0.211914i
$357$	−1.18497	−	1.36477i	−0.0627152	−	0.0722313i
$358$	14.0341	+	2.56501i	0.741727	+	0.135565i
$359$	3.72963			0.196842			0.0984211	−	0.995145i	$-0.468621\pi$
$359$	3.72963			0.196842			0.0984211	+	0.995145i	$0.468621\pi$
$360$	−26.9863	+	10.2834i	−1.42231	+	0.541984i
$361$	−3.54082	+	6.13289i	−0.186359	+	0.322784i
$362$	4.87447	+	13.6571i	0.256197	+	0.717802i
$363$	−0.572828	+	0.110997i	−0.0300657	+	0.00582584i
$364$	9.67952	+	14.1374i	0.507345	+	0.741001i
$365$			20.0001i			1.04685i
$366$	16.4754	+	27.8486i	0.861181	+	1.45567i
$367$	−3.96123	−	2.28702i	−0.206775	−	0.119381i	0.393037	−	0.919523i	$-0.371424\pi$
$367$	−3.96123	−	2.28702i	−0.206775	−	0.119381i	−0.599812	+	0.800141i	$0.704758\pi$
$368$	20.7791	+	18.3388i	1.08318	+	0.955977i
$369$	−1.84460	−	4.58105i	−0.0960261	−	0.238480i
$370$	−2.74182	+	15.0015i	−0.142540	+	0.779892i
$371$	−6.78475	−	11.7515i	−0.352247	−	0.610109i
$372$	1.05182	−	0.388061i	0.0545344	−	0.0201200i
$373$	1.43650	+	2.48810i	0.0743794	+	0.128829i	0.900816	−	0.434201i	$-0.142969\pi$
$373$	1.43650	+	2.48810i	0.0743794	+	0.128829i	−0.826437	+	0.563029i	$0.809636\pi$
$374$	1.91017	−	0.681774i	0.0987724	−	0.0352537i
$375$	−8.82430	−	3.04425i	−0.455685	−	0.157205i
$376$	−4.98907	−	3.00637i	−0.257292	−	0.155041i
$377$	28.5604	−	13.3869i	1.47093	−	0.689463i
$378$	−17.3122	−	2.26648i	−0.890445	−	0.116575i
$379$	29.9026	+	17.2643i	1.53599	+	0.886806i	0.999067	+	0.0431758i	$0.0137475\pi$
$379$	29.9026	+	17.2643i	1.53599	+	0.886806i	0.536925	+	0.843630i	$0.319586\pi$
$380$	−21.9802	−	8.31229i	−1.12756	−	0.426412i
$381$	−6.09733	+	5.29403i	−0.312375	+	0.271222i
$382$	19.1401	−	22.5233i	0.979291	−	1.15239i
$383$	−4.03832	−	6.99457i	−0.206348	−	0.357406i	0.744213	−	0.667942i	$-0.232825\pi$
$383$	−4.03832	−	6.99457i	−0.206348	−	0.357406i	−0.950562	+	0.310536i	$0.899491\pi$
$384$	9.33929	+	17.2272i	0.476594	+	0.879124i
$385$	−26.4063			−1.34579
$386$	19.6593	+	3.59311i	1.00063	+	0.182885i
$387$	2.89920	+	0.410933i	0.147375	+	0.0208889i
$388$	−3.70792	−	1.40223i	−0.188241	−	0.0711874i
$389$			12.7968i			0.648822i	0.945916	+	0.324411i	$0.105166\pi$
$389$			12.7968i			0.648822i	−0.945916	+	0.324411i	$0.894834\pi$
$390$	−24.8379	−	16.9290i	−1.25772	−	0.857235i
$391$		−	3.04295i		−	0.153889i
$392$	−3.35344	+	1.85328i	−0.169374	+	0.0936047i
$393$	−3.77353	+	10.9382i	−0.190349	+	0.551761i
$394$	−1.27542	+	6.97832i	−0.0642549	+	0.351563i
$395$	44.5043			2.23925
$396$	9.43361	−	17.1721i	0.474057	−	0.862928i
$397$	6.70688	+	11.6167i	0.336609	+	0.583023i	0.983793	−	0.179311i	$-0.0573867\pi$
$397$	6.70688	+	11.6167i	0.336609	+	0.583023i	−0.647184	+	0.762334i	$0.724053\pi$
$398$	−26.5454	−	22.5581i	−1.33060	−	1.13073i
$399$	−9.31459	−	10.7279i	−0.466313	−	0.537069i
$400$	−5.21879	+	25.8117i	−0.260939	+	1.29058i
$401$	−26.9891	−	15.5822i	−1.34777	−	0.778136i	−0.359838	−	0.933015i	$-0.617168\pi$
$401$	−26.9891	−	15.5822i	−1.34777	−	0.778136i	−0.987933	+	0.154879i	$0.950501\pi$
$402$	8.66747	+	4.88213i	0.432294	+	0.243498i
$403$	0.957197	+	0.667411i	0.0476814	+	0.0332461i
$404$	−0.723048	+	0.118207i	−0.0359730	+	0.00588102i
$405$	29.7386	−	7.34042i	1.47772	−	0.364749i
$406$	−9.88124	−	27.6849i	−0.490398	−	1.37398i
$407$	−5.17306	−	8.96001i	−0.256419	−	0.444131i
$408$	0.739638	−	2.02045i	0.0366175	−	0.100027i
$409$	−13.0906	−	22.6736i	−0.647288	−	1.12114i	−0.983768	−	0.179445i	$-0.942570\pi$
$409$	−13.0906	−	22.6736i	−0.647288	−	1.12114i	0.336480	−	0.941691i	$-0.390764\pi$
$410$	−7.79420	−	1.42454i	−0.384928	−	0.0703530i
$411$	3.12074	+	16.1053i	0.153935	+	0.794417i
$412$	22.4078	+	27.3917i	1.10395	+	1.34949i
$413$	−10.0192	−	5.78458i	−0.493012	−	0.284640i
$414$	−19.5068	−	21.9904i	−0.958709	−	1.08077i
$415$		−	5.29480i		−	0.259911i
$416$	−9.15617	+	18.2254i	−0.448918	+	0.893573i
$417$	4.15663	+	21.4513i	0.203551	+	1.05048i
$418$	15.0151	−	5.35916i	0.734412	−	0.262125i
$419$	−15.9736	+	27.6671i	−0.780363	+	1.35163i	0.151367	+	0.988478i	$0.451632\pi$
$419$	−15.9736	+	27.6671i	−0.780363	+	1.35163i	−0.931730	+	0.363151i	$0.881701\pi$
$420$	−17.9121	+	21.5378i	−0.874019	+	1.05094i
$421$	9.17039			0.446937			0.223469	−	0.974711i	$-0.428262\pi$
$421$	9.17039			0.446937			0.223469	+	0.974711i	$0.428262\pi$
$422$	−6.38224	+	34.9196i	−0.310683	+	1.69986i
$423$	4.86401	+	3.80940i	0.236496	+	0.185219i
$424$	8.33718	−	13.8356i	0.404889	−	0.671914i
$425$	2.50403	−	1.44570i	0.121463	−	0.0701267i
$426$	−0.436112	−	0.737168i	−0.0211297	−	0.0357159i
$427$	27.1814	+	15.6932i	1.31540	+	0.759445i
$428$	2.44414	+	14.9503i	0.118142	+	0.722651i
$429$	20.2780	−	2.15992i	0.979030	−	0.104282i
$430$	3.04221	−	3.57995i	0.146708	−	0.172640i
$431$	3.41352	−	5.91239i	0.164424	−	0.284790i	−0.772027	−	0.635590i	$-0.780757\pi$
$431$	3.41352	−	5.91239i	0.164424	−	0.284790i	0.936450	+	0.350800i	$0.114090\pi$
$432$	−7.60698	−	19.3425i	−0.365991	−	0.930618i
$433$	−12.1540	−	21.0513i	−0.584082	−	1.01166i	−0.994989	−	0.0999825i	$-0.968121\pi$
$433$	−12.1540	−	21.0513i	−0.584082	−	1.01166i	0.410907	−	0.911677i	$-0.365212\pi$
$434$	0.704209	−	0.828685i	0.0338031	−	0.0397781i
$435$	33.8103	+	38.9405i	1.62108	+	1.86705i
$436$	−1.90565	+	1.55892i	−0.0912643	+	0.0746586i
$437$		−	23.9195i		−	1.14422i
$438$	−14.3934	+	0.152925i	−0.687742	+	0.00730704i
$439$	12.7472	+	7.35961i	0.608391	+	0.351255i	0.772336	−	0.635215i	$-0.219088\pi$
$439$	12.7472	+	7.35961i	0.608391	+	0.351255i	−0.163944	+	0.986470i	$0.552422\pi$
$440$	−15.2048	−	27.5126i	−0.724862	−	1.31161i
$441$	3.76976	−	1.51793i	0.179513	−	0.0722824i
$442$	2.16557	−	0.570393i	0.103006	−	0.0271308i
$443$	−0.455670			−0.0216495			−0.0108248	−	0.999941i	$-0.503446\pi$
$443$	−0.455670			−0.0216495			−0.0108248	+	0.999941i	$0.503446\pi$
$444$	−10.8171	−	1.85849i	−0.513355	−	0.0882000i
$445$	21.0861	−	36.5223i	0.999579	−	1.73132i
$446$	0.843858	−	4.61706i	0.0399578	−	0.218624i
$447$	−4.23805	−	21.8715i	−0.200453	−	1.03449i
$448$	16.0940	+	10.1136i	0.760372	+	0.477823i
$449$	16.1586	−	9.32918i	0.762572	−	0.440271i	−0.0676464	−	0.997709i	$-0.521549\pi$
$449$	16.1586	−	9.32918i	0.762572	−	0.440271i	0.830218	+	0.557438i	$0.188216\pi$
$450$	8.82807	−	26.4996i	0.416159	−	1.24920i
$451$	4.65527	−	2.68772i	0.219208	−	0.126560i
$452$	7.72368	−	20.4238i	0.363291	−	0.960653i
$453$	−15.0483	−	5.19146i	−0.707033	−	0.243916i
$454$	−17.4617	+	20.5482i	−0.819517	+	0.964374i
$455$	−29.0507	−	2.48355i	−1.36192	−	0.116431i
$456$	5.81401	−	15.8820i	0.272266	−	0.743742i
$457$	−11.0743	+	19.1813i	−0.518035	+	0.897264i	0.481745	+	0.876311i	$0.340003\pi$
$457$	−11.0743	+	19.1813i	−0.518035	+	0.897264i	−0.999780	+	0.0209522i	$0.993330\pi$
$458$	−12.7878	−	35.8285i	−0.597536	−	1.67415i
$459$	−1.03963	+	2.03153i	−0.0485259	+	0.0948237i
$460$	−46.5443	+	7.60925i	−2.17014	+	0.354783i
$461$	30.5380	−	17.6311i	1.42230	−	0.821163i	0.425802	−	0.904817i	$-0.359992\pi$
$461$	30.5380	−	17.6311i	1.42230	−	0.821163i	0.996495	+	0.0836531i	$0.0266588\pi$
$462$	−0.201909	−	19.0038i	−0.00939365	−	0.884135i
$463$		−	2.08649i		−	0.0969674i	−0.998824	−	0.0484837i	$-0.984561\pi$
$463$		−	2.08649i		−	0.0969674i	0.998824	−	0.0484837i	$-0.0154389\pi$
$464$	23.1551	−	26.2362i	1.07495	−	1.21799i
$465$	−0.622195	+	1.80354i	−0.0288536	+	0.0836371i
$466$	−1.06025	+	0.378423i	−0.0491152	+	0.0175301i
$467$	−10.1330			−0.468900			−0.234450	−	0.972128i	$-0.575329\pi$
$467$	−10.1330			−0.468900			−0.234450	+	0.972128i	$0.575329\pi$
$468$	11.9933	−	18.0044i	0.554393	−	0.832255i
$469$	9.64941			0.445568
$470$	9.33552	−	3.33202i	0.430615	−	0.153694i
$471$	3.22896	−	9.35969i	0.148782	−	0.431272i
$472$	0.257846	−	13.7697i	0.0118683	−	0.633801i
$473$			3.18727i			0.146551i
$474$	0.340290	+	32.0282i	0.0156300	+	1.47110i
$475$	19.6832	−	11.3641i	0.903127	−	0.521420i
$476$	−0.336725	−	2.05968i	−0.0154338	−	0.0944053i
$477$	−10.5641	+	13.4888i	−0.483698	+	0.617608i
$478$	−3.66781	−	10.2763i	−0.167762	−	0.470028i
$479$	20.1079	−	34.8280i	0.918755	−	1.59133i	0.117446	−	0.993079i	$-0.462529\pi$
$479$	20.1079	−	34.8280i	0.918755	−	1.59133i	0.801309	−	0.598250i	$-0.204137\pi$
$480$	−32.7539	−	6.26096i	−1.49500	−	0.285772i
$481$	−4.84839	−	10.3438i	−0.221068	−	0.471637i
$482$	−9.95267	+	11.7119i	−0.453332	+	0.533462i
$483$	−26.9546	−	9.29894i	−1.22648	−	0.423116i
$484$	−0.630191	−	0.238320i	−0.0286450	−	0.0108327i
$485$	5.84220	−	3.37300i	0.265281	−	0.153160i
$486$	5.51004	+	21.3457i	0.249941	+	0.968261i
$487$	27.4616	−	15.8550i	1.24441	−	0.718458i	0.274418	−	0.961611i	$-0.411515\pi$
$487$	27.4616	−	15.8550i	1.24441	−	0.718458i	0.969988	+	0.243153i	$0.0781816\pi$
$488$	−0.699520	+	37.3562i	−0.0316658	+	1.69104i
$489$	−4.91558	−	25.3681i	−0.222290	−	1.14718i
$490$	1.17226	−	6.41388i	0.0529573	−	0.289749i
$491$	−10.5967	+	18.3540i	−0.478222	+	0.828305i	−0.999688	−	0.0249673i	$-0.992052\pi$
$491$	−10.5967	+	18.3540i	−0.478222	+	0.828305i	0.521466	+	0.853272i	$0.325385\pi$
$492$	0.965598	−	5.62011i	0.0435325	−	0.253374i
$493$	−3.84211			−0.173040
$494$	17.0228	−	4.48364i	0.765890	−	0.201729i
$495$	12.4535	+	30.9282i	0.559745	+	1.39012i
$496$	1.26889	+	0.256552i	0.0569747	+	0.0115195i
$497$	−0.719505	−	0.415407i	−0.0322742	−	0.0186335i
$498$	3.81049	−	0.0404852i	0.170752	−	0.00181419i
$499$			30.2884i			1.35590i	0.735110	+	0.677948i	$0.237131\pi$
$499$			30.2884i			1.35590i	−0.735110	+	0.677948i	$0.762869\pi$
$500$	−6.82483	−	8.34282i	−0.305216	−	0.373102i
$501$	−19.6806	−	22.6669i	−0.879266	−	1.01268i
$502$	−16.5578	+	19.4846i	−0.739011	+	0.869638i
$503$	4.19340	+	7.26318i	0.186974	+	0.323849i	0.944240	−	0.329258i	$-0.106798\pi$
$503$	4.19340	+	7.26318i	0.186974	+	0.323849i	−0.757266	+	0.653107i	$0.773465\pi$
$504$	−15.6370	−	12.7260i	−0.696526	−	0.566862i
$505$	0.623383	−	1.07973i	0.0277402	−	0.0480474i
$506$	20.7195	−	24.3818i	0.921093	−	1.08390i
$507$	22.5118	−	0.469045i	0.999783	−	0.0208310i
$508$	−9.20194	+	1.50437i	−0.408270	+	0.0667457i
$509$	−8.38001	−	4.83820i	−0.371437	−	0.214449i	0.302649	−	0.953102i	$-0.402129\pi$
$509$	−8.38001	−	4.83820i	−0.371437	−	0.214449i	−0.674086	+	0.738653i	$0.735462\pi$
$510$	1.86428	+	3.15123i	0.0825518	+	0.139539i
$511$	−12.0917	+	6.98116i	−0.534906	+	0.308828i
$512$	−1.27032	+	22.5917i	−0.0561409	+	0.998423i
$513$	−8.17216	+	15.9691i	−0.360809	+	0.705052i
$514$	−4.07006	+	22.2688i	−0.179523	+	0.982235i
$515$	−60.2232			−2.65375
$516$	2.59963	+	2.16200i	0.114442	+	0.0951768i
$517$	−3.36243	+	5.82390i	−0.147879	+	0.256135i
$518$	−10.0267	+	3.57872i	−0.440549	+	0.157240i
$519$	3.34953	+	17.2861i	0.147028	+	0.758774i
$520$	−14.1399	−	31.6978i	−0.620074	−	1.39004i
$521$			15.2734i			0.669138i	0.942371	+	0.334569i	$0.108591\pi$
$521$			15.2734i			0.669138i	−0.942371	+	0.334569i	$0.891409\pi$
$522$	−27.7656	+	24.6299i	−1.21527	+	1.07802i
$523$	7.73177	+	4.46394i	0.338087	+	0.195194i	0.659426	−	0.751770i	$-0.270800\pi$
$523$	7.73177	+	4.46394i	0.338087	+	0.195194i	−0.321339	+	0.946964i	$0.604133\pi$
$524$	−10.3414	+	8.45978i	−0.451767	+	0.369567i
$525$	−5.15403	−	26.5987i	−0.224940	−	1.16086i
$526$	−17.4642	−	3.19192i	−0.761475	−	0.139174i
$527$	−0.0710697	−	0.123096i	−0.00309584	−	0.00536216i
$528$	19.6836	−	11.1528i	0.856620	−	0.485362i
$529$	−12.5026	−	21.6551i	−0.543590	−	0.941526i
$530$	9.24026	+	25.8890i	0.401371	+	1.12455i
$531$	−2.04998	+	14.4630i	−0.0889616	+	0.627639i
$532$	−2.64687	−	16.1904i	−0.114756	−	0.701942i
$533$	5.37423	−	2.51904i	0.232784	−	0.109112i
$534$	26.4451	+	14.8957i	1.14439	+	0.644601i
$535$	−22.3254	−	12.8896i	−0.965210	−	0.557264i
$536$	5.55615	+	10.0537i	0.239989	+	0.434252i
$537$	−11.4555	−	13.1937i	−0.494343	−	0.569352i
$538$	18.5985	+	15.8049i	0.801839	+	0.681396i
$539$	2.21174	+	3.83084i	0.0952662	+	0.165006i
$540$	33.6735	+	10.8219i	1.44908	+	0.465700i
$541$	16.8992			0.726554			0.363277	−	0.931681i	$-0.381658\pi$
$541$	16.8992			0.726554			0.363277	+	0.931681i	$0.381658\pi$
$542$	−3.99941	+	21.8823i	−0.171789	+	0.939924i
$543$	5.79195	−	16.7890i	0.248556	−	0.720483i
$544$	1.95208	−	1.53680i	0.0836948	−	0.0658898i
$545$		−	4.18976i		−	0.179469i
$546$	1.56520	−	20.9258i	0.0669844	−	0.895541i
$547$		−	34.2378i		−	1.46390i	−0.681358	−	0.731951i	$-0.738610\pi$
$547$		−	34.2378i		−	1.46390i	0.681358	−	0.731951i	$-0.261390\pi$
$548$	−6.70048	+	17.7181i	−0.286230	+	0.756880i
$549$	5.56146	−	39.2370i	0.237357	−	1.67460i
$550$	29.9074	+	5.46616i	1.27526	+	0.233078i
$551$	−30.2014			−1.28662
$552$	−5.83201	−	33.4382i	−0.248227	−	1.42322i
$553$	15.5345	+	26.9066i	0.660595	+	1.14418i
$554$	−0.486699	+	0.572728i	−0.0206779	+	0.0243329i
$555$	14.1032	−	12.2452i	0.598647	−	0.519779i
$556$	−8.92463	+	23.5994i	−0.378489	+	1.00084i
$557$	13.6598	+	7.88649i	0.578784	+	0.334161i	0.760650	−	0.649162i	$-0.224880\pi$
$557$	13.6598	+	7.88649i	0.578784	+	0.334161i	−0.181866	+	0.983323i	$0.558214\pi$
$558$	−1.30270	−	0.433982i	−0.0551479	−	0.0183719i
$559$	−0.299767	+	3.50644i	−0.0126788	+	0.148307i
$560$	−30.6624	+	10.3009i	−1.29572	+	0.435294i
$561$	−2.34821	−	0.810097i	−0.0991414	−	0.0342023i
$562$	2.42276	−	0.864728i	0.102198	−	0.0364763i
$563$	15.8941	+	27.5293i	0.669854	+	1.16022i	0.977945	+	0.208865i	$0.0669768\pi$
$563$	15.8941	+	27.5293i	0.669854	+	1.16022i	−0.308090	+	0.951357i	$0.599690\pi$
$564$	2.46932	+	6.69298i	0.103977	+	0.281825i
$565$	18.5790	+	32.1797i	0.781623	+	1.35381i
$566$	−6.63386	+	36.2963i	−0.278842	+	1.52565i
$567$	14.8184	+	15.4172i	0.622312	+	0.647463i
$568$	0.0185167	−	0.988840i	0.000776942	−	0.0414908i
$569$	−14.9900	−	8.65451i	−0.628416	−	0.362816i	0.151723	−	0.988423i	$-0.451518\pi$
$569$	−14.9900	−	8.65451i	−0.628416	−	0.362816i	−0.780138	+	0.625607i	$0.784851\pi$
$570$	14.6544	+	24.7707i	0.613806	+	1.03753i
$571$			12.6645i			0.529995i	0.964249	+	0.264997i	$0.0853711\pi$
$571$			12.6645i			0.529995i	−0.964249	+	0.264997i	$0.914629\pi$
$572$	21.2356	+	10.1751i	0.887904	+	0.425442i
$573$	−35.5392	+	6.88645i	−1.48467	+	0.287685i
$574$	−1.85936	−	5.20950i	−0.0776083	−	0.217440i
$575$	22.8071	−	39.5031i	0.951123	−	1.64739i
$576$	4.25536	−	23.6197i	0.177307	−	0.984156i
$577$	28.5689			1.18934			0.594669	−	0.803971i	$-0.297283\pi$
$577$	28.5689			1.18934			0.594669	+	0.803971i	$0.297283\pi$
$578$	23.3815	+	4.27343i	0.972543	+	0.177751i
$579$	−16.0471	−	18.4820i	−0.666896	−	0.768088i
$580$	9.60765	+	58.7681i	0.398936	+	2.44021i
$581$	3.20115	−	1.84819i	0.132806	−	0.0766757i
$582$	2.47210	+	4.17865i	0.102472	+	0.173210i
$583$	−16.1507	−	9.32460i	−0.668893	−	0.386185i
$584$	−14.2361	−	8.57852i	−0.589093	−	0.354982i
$585$	10.7918	+	35.1967i	0.446186	+	1.45520i
$586$	16.6244	+	14.1273i	0.686749	+	0.583593i
$587$	3.14691	−	5.45061i	0.129887	−	0.224971i	−0.793746	−	0.608250i	$-0.791872\pi$
$587$	3.14691	−	5.45061i	0.129887	−	0.224971i	0.923633	+	0.383279i	$0.125205\pi$
$588$	4.62482	+	0.794594i	0.190724	+	0.0327685i
$589$	−0.558652	−	0.967613i	−0.0230188	−	0.0398698i
$590$	17.8589	+	15.1764i	0.735240	+	0.624801i
$591$	6.56045	−	5.69614i	0.269861	−	0.234308i
$592$	−9.50206	−	8.38615i	−0.390532	−	0.344669i
$593$			20.9050i			0.858466i	0.903194	+	0.429233i	$0.141216\pi$
$593$			20.9050i			0.858466i	−0.903194	+	0.429233i	$0.858784\pi$
$594$	−22.1628	+	9.19888i	−0.909350	+	0.377435i
$595$	3.07573	+	1.77577i	0.126093	+	0.0727996i
$596$	9.09944	−	24.0617i	0.372728	−	0.985605i
$597$	8.11621	+	41.8857i	0.332174	+	1.71427i
$598$	25.0875	−	24.8747i	1.02590	−	1.01720i
$599$	−10.0615			−0.411102			−0.205551	−	0.978646i	$-0.565899\pi$
$599$	−10.0615			−0.411102			−0.205551	+	0.978646i	$0.565899\pi$
$600$	24.7453	−	20.6855i	1.01022	−	0.844483i
$601$	0.611503	−	1.05915i	0.0249437	−	0.0432038i	−0.853284	−	0.521446i	$-0.825393\pi$
$601$	0.611503	−	1.05915i	0.0249437	−	0.0432038i	0.878228	+	0.478243i	$0.158726\pi$
$602$	3.22628	+	0.589666i	0.131493	+	0.0240330i
$603$	−4.55078	−	11.3018i	−0.185322	−	0.460245i
$604$	−11.6386	−	14.2273i	−0.473567	−	0.578899i
$605$	0.992929	−	0.573268i	0.0403683	−	0.0233066i
$606$	0.781812	+	0.440372i	0.0317589	+	0.0178889i
$607$	13.8018	−	7.96848i	0.560198	−	0.323430i	−0.193027	−	0.981193i	$-0.561830\pi$
$607$	13.8018	−	7.96848i	0.560198	−	0.323430i	0.753225	+	0.657763i	$0.228497\pi$
$608$	15.3446	−	12.0802i	0.622304	−	0.489917i
$609$	−11.7411	+	34.0336i	−0.475773	+	1.37911i
$610$	−48.4501	−	41.1724i	−1.96169	−	1.66702i
$611$	−4.24689	+	6.09086i	−0.171811	+	0.246410i
$612$	−2.25358	+	1.36576i	−0.0910957	+	0.0552074i
$613$	−20.1949	+	34.9787i	−0.815666	+	1.41277i	0.0931830	+	0.995649i	$0.470296\pi$
$613$	−20.1949	+	34.9787i	−0.815666	+	1.41277i	−0.908849	+	0.417126i	$0.863037\pi$
$614$	−24.5074	+	8.74714i	−0.989038	+	0.353006i
$615$	6.36211	+	7.32747i	0.256545	+	0.295472i
$616$	11.3263	−	18.7961i	0.456351	−	0.757315i
$617$	−0.788983	+	0.455519i	−0.0317632	+	0.0183385i	−0.515798	−	0.856711i	$-0.672504\pi$
$617$	−0.788983	+	0.455519i	−0.0317632	+	0.0183385i	0.484034	+	0.875049i	$0.339171\pi$
$618$	−0.460481	−	43.3406i	−0.0185232	−	1.74342i
$619$		−	10.0964i		−	0.405810i	−0.979198	−	0.202905i	$-0.934962\pi$
$619$		−	10.0964i		−	0.405810i	0.979198	−	0.202905i	$-0.0650383\pi$
$620$	−1.70513	+	1.39488i	−0.0684798	+	0.0560198i
$621$	1.82079	+	35.9559i	0.0730657	+	1.44286i
$622$	8.95263	+	25.0831i	0.358968	+	1.00574i
$623$	29.4411			1.17953
$624$	22.7037	−	10.4183i	0.908875	−	0.417068i
$625$	−14.5750			−0.583002
$626$	−7.59195	−	21.2708i	−0.303435	−	0.850154i
$627$	−18.4584	−	6.36786i	−0.737156	−	0.254308i
$628$	8.84900	−	7.23891i	0.353114	−	0.288864i
$629$			1.39151i			0.0554832i
$630$	33.6108	−	6.88405i	1.33909	−	0.274267i
$631$	−22.2827	+	12.8649i	−0.887061	+	0.512145i	−0.872980	−	0.487756i	$-0.837816\pi$
$631$	−22.2827	+	12.8649i	−0.887061	+	0.512145i	−0.0140809	+	0.999901i	$0.504482\pi$
$632$	−19.0890	+	31.6782i	−0.759319	+	1.26009i
$633$	32.8286	−	28.5036i	1.30482	−	1.13292i
$634$	8.00993	−	2.85889i	0.318115	−	0.113541i
$635$	7.93354	−	13.7413i	0.314833	−	0.545307i
$636$	−18.5608	+	6.84786i	−0.735984	+	0.271535i
$637$	2.07292	+	4.42248i	0.0821323	+	0.175225i
$638$	−30.7852	−	26.1610i	−1.21880	−	1.03572i
$639$	−0.147215	+	1.03863i	−0.00582373	+	0.0410874i
$640$	−28.3879	−	26.0156i	−1.12213	−	1.02836i
$641$	−28.5900	+	16.5064i	−1.12924	+	0.651964i	−0.943743	−	0.330681i	$-0.892722\pi$
$641$	−28.5900	+	16.5064i	−1.12924	+	0.651964i	−0.185493	+	0.982646i	$0.559388\pi$
$642$	9.10548	−	16.1654i	0.359365	−	0.637997i
$643$	−0.377149	+	0.217747i	−0.0148733	+	0.00858710i	−0.507418	−	0.861700i	$-0.669400\pi$
$643$	−0.377149	+	0.217747i	−0.0148733	+	0.00858710i	0.492545	+	0.870287i	$0.336067\pi$
$644$	−20.8470	−	25.4839i	−0.821488	−	1.00421i
$645$	−5.64876	+	1.09456i	−0.222420	+	0.0430983i
$646$	−2.10930	−	0.385516i	−0.0829895	−	0.0151679i
$647$	−10.8633	+	18.8158i	−0.427080	+	0.739725i	−0.996612	−	0.0822444i	$-0.973791\pi$
$647$	−10.8633	+	18.8158i	−0.427080	+	0.739725i	0.569532	+	0.821969i	$0.307125\pi$
$648$	−7.53068	+	24.3164i	−0.295833	+	0.955240i
$649$	−15.9000			−0.624130
$650$	32.3883	+	8.82637i	1.27037	+	0.346199i
$651$	−1.30757	+	0.253369i	−0.0512478	+	0.00993031i
$652$	10.5542	−	27.9084i	0.413333	−	1.09298i
$653$	33.5589	+	19.3752i	1.31326	+	0.758212i	0.982635	−	0.185550i	$-0.0594066\pi$
$653$	33.5589	+	19.3752i	1.31326	+	0.758212i	0.330627	+	0.943762i	$0.392740\pi$
$654$	3.01523	−	0.0320358i	0.117905	−	0.00125270i
$655$		−	22.7366i		−	0.888391i
$656$	4.35711	−	4.93690i	0.170117	−	0.192754i
$657$	13.8792	+	10.8699i	0.541480	+	0.424077i
$658$	5.27311	+	4.48104i	0.205567	+	0.174689i
$659$	13.5023	+	23.3866i	0.525974	+	0.911013i	0.999542	+	0.0302561i	$0.00963229\pi$
$659$	13.5023	+	23.3866i	0.525974	+	0.911013i	−0.473569	+	0.880757i	$0.657034\pi$
$660$	−6.51908	+	37.9433i	−0.253755	+	1.47694i
$661$	−7.17061	+	12.4199i	−0.278905	+	0.483077i	−0.971113	−	0.238621i	$-0.923305\pi$
$661$	−7.17061	+	12.4199i	−0.278905	+	0.483077i	0.692208	+	0.721698i	$0.256638\pi$
$662$	23.4156	+	19.8984i	0.910074	+	0.773373i
$663$	−2.50717	−	1.11207i	−0.0973703	−	0.0431893i
$664$	3.76884	+	2.27107i	0.146260	+	0.0881346i
$665$	24.1771	+	13.9587i	0.937549	+	0.541294i
$666$	8.92028	+	10.0560i	0.345654	+	0.389661i
$667$	−52.4920	+	30.3063i	−2.03250	+	1.17346i
$668$	−5.59252	−	34.2083i	−0.216381	−	1.32356i
$669$	−4.34059	+	3.76874i	−0.167817	+	0.145708i
$670$	−19.2289	−	3.51445i	−0.742877	−	0.135775i
$671$	43.1357			1.66523
$672$	−7.64769	−	21.9879i	−0.295016	−	0.848202i
$673$	11.8171	−	20.4678i	0.455515	−	0.788975i	−0.543203	−	0.839602i	$-0.682788\pi$
$673$	11.8171	−	20.4678i	0.455515	−	0.788975i	0.998718	+	0.0506263i	$0.0161217\pi$
$674$	−5.88840	−	16.4979i	−0.226813	−	0.635476i
$675$	−28.7228	+	18.5809i	−1.10554	+	0.715177i
$676$	22.4051	+	13.1913i	0.861736	+	0.507356i
$677$			15.9779i			0.614082i	0.951696	+	0.307041i	$0.0993389\pi$
$677$			15.9779i			0.614082i	−0.951696	+	0.307041i	$0.900661\pi$
$678$	−23.0166	+	13.6167i	−0.883947	+	0.522946i
$679$	4.07852	+	2.35474i	0.156519	+	0.0903665i
$680$	−0.0791548	+	4.22708i	−0.00303545	+	0.162101i
$681$	32.4228	−	6.28257i	1.24244	−	0.240749i
$682$	0.268713	−	1.47023i	0.0102895	−	0.0562980i
$683$	2.73349	+	4.73455i	0.104594	+	0.181162i	0.913572	−	0.406676i	$-0.133312\pi$
$683$	2.73349	+	4.73455i	0.104594	+	0.181162i	−0.808978	+	0.587839i	$0.799979\pi$
$684$	−17.7146	+	10.7357i	−0.677333	+	0.410489i
$685$	−16.1177	−	27.9167i	−0.615825	−	1.06664i
$686$	26.4394	−	9.43670i	1.00946	−	0.360295i
$687$	−15.1948	+	44.0446i	−0.579716	+	1.68041i
$688$	1.24333	+	3.70098i	0.0474016	+	0.141098i
$689$	−16.8910	−	11.7774i	−0.643497	−	0.448682i
$690$	50.3270	+	28.3477i	1.91592	+	1.07918i
$691$	−30.9581	−	17.8737i	−1.17770	−	0.679946i	−0.222220	−	0.974997i	$-0.571330\pi$
$691$	−30.9581	−	17.8737i	−1.17770	−	0.679946i	−0.955482	+	0.295050i	$0.904664\pi$
$692$	−7.19171	+	19.0171i	−0.273388	+	0.722921i
$693$	−14.3517	+	18.3249i	−0.545177	+	0.696107i
$694$	−9.31122	+	10.9571i	−0.353449	+	0.415925i
$695$	−21.4678	−	37.1833i	−0.814319	−	1.41044i
$696$	−42.2199	+	7.36366i	−1.60034	+	0.279119i
$697$	−0.722975			−0.0273846
$698$	−28.7103	−	5.24736i	−1.08670	−	0.198615i
$699$	1.30339	+	0.449650i	0.0492987	+	0.0170073i
$700$	11.0661	−	29.2622i	0.418261	−	1.10601i
$701$		−	52.7217i		−	1.99127i	−0.0933231	−	0.995636i	$-0.529749\pi$
$701$		−	52.7217i		−	1.99127i	0.0933231	−	0.995636i	$-0.470251\pi$
$702$	−25.2474	+	8.03562i	−0.952900	+	0.303285i
$703$			10.9381i			0.412540i
$704$	26.1052	+	0.978018i	0.983878	+	0.0368604i
$705$	−11.4763	−	3.95917i	−0.432224	−	0.149111i
$706$	−1.16408	+	6.36911i	−0.0438106	+	0.239704i
$707$	0.870384			0.0327342
$708$	−10.7854	+	12.9685i	−0.405339	+	0.487386i
$709$	−5.86991	−	10.1670i	−0.220449	−	0.381829i	0.734495	−	0.678614i	$-0.237419\pi$
$709$	−5.86991	−	10.1670i	−0.220449	−	0.381829i	−0.954944	+	0.296785i	$0.904086\pi$
$710$	1.28250	+	1.08986i	0.0481313	+	0.0409016i
$711$	24.1879	−	30.8841i	0.907116	−	1.15825i
$712$	16.9522	+	30.6745i	0.635312	+	1.14957i
$713$	−1.94195	−	1.12118i	−0.0727265	−	0.0419887i
$714$	−1.25445	+	2.22708i	−0.0469465	+	0.0833463i
$715$	−36.2833	+	17.0069i	−1.35692	+	0.636021i
$716$	−3.25525	−	19.9117i	−0.121654	−	0.744135i
$717$	−4.35816	+	12.6329i	−0.162759	+	0.471784i
$718$	−1.77301	−	4.96756i	−0.0661683	−	0.185388i
$719$	−12.8225	−	22.2092i	−0.478197	−	0.828262i	0.521490	−	0.853257i	$-0.325376\pi$
$719$	−12.8225	−	22.2092i	−0.478197	−	0.828262i	−0.999688	+	0.0249952i	$0.992043\pi$
$720$	26.5256	+	31.0550i	0.988552	+	1.15735i
$721$	−21.0213	−	36.4100i	−0.782876	−	1.35598i
$722$	9.85177	+	1.80060i	0.366645	+	0.0670114i
$723$	18.4801	−	3.58089i	0.687282	−	0.133175i
$724$	15.8729	−	12.9848i	0.589912	−	0.482577i
$725$	−49.8777	−	28.7969i	−1.85241	−	1.06949i
$726$	0.420154	+	0.710194i	0.0155934	+	0.0263578i
$727$			25.0087i			0.927521i	0.885961	+	0.463760i	$0.153500\pi$
$727$			25.0087i			0.927521i	−0.885961	+	0.463760i	$0.846500\pi$
$728$	14.2284	−	19.6131i	0.527338	−	0.726908i
$729$	11.0688	−	24.6268i	0.409956	−	0.912105i
$730$	26.6385	−	9.50775i	0.985933	−	0.351898i
$731$	0.214337	−	0.371243i	0.00792755	−	0.0137309i
$732$	29.2600	−	35.1827i	1.08148	−	1.30039i
$733$	−49.5229			−1.82917			−0.914585	−	0.404394i	$-0.867482\pi$
$733$	−49.5229			−1.82917			−0.914585	+	0.404394i	$0.867482\pi$
$734$	−1.16301	+	6.36326i	−0.0429274	+	0.234872i
$735$	−6.02980	+	5.23541i	−0.222413	+	0.193111i
$736$	14.5477	−	36.3941i	0.536236	−	1.34150i
$737$	11.4849	−	6.63082i	0.423052	−	0.244249i
$738$	−5.22469	+	4.63462i	−0.192323	+	0.170603i
$739$	−42.0666	−	24.2872i	−1.54745	−	0.893418i	−0.998336	−	0.0576672i	$-0.981634\pi$
$739$	−42.0666	−	24.2872i	−1.54745	−	0.893418i	−0.549109	−	0.835751i	$-0.685033\pi$
$740$	21.2842	−	3.47963i	0.782424	−	0.127914i
$741$	−19.7079	−	8.74158i	−0.723987	−	0.321130i
$742$	−12.4267	+	14.6233i	−0.456199	+	0.536837i
$743$	19.6550	−	34.0435i	0.721072	−	1.24893i	−0.239498	−	0.970897i	$-0.576983\pi$
$743$	19.6550	−	34.0435i	0.721072	−	1.24893i	0.960570	−	0.278037i	$-0.0896838\pi$
$744$	−1.01689	−	1.21646i	−0.0372809	−	0.0445976i
$745$	21.8883	+	37.9116i	0.801925	+	1.38897i
$746$	2.63105	−	3.09611i	0.0963296	−	0.113357i
$747$	−3.67438	−	2.87770i	−0.134438	−	0.105290i
$748$	−1.81613	−	2.22008i	−0.0664044	−	0.0811743i
$749$		−	17.9968i		−	0.657587i
$750$	0.140251	+	13.2004i	0.00512123	+	0.482012i
$751$	4.11090	+	2.37343i	0.150009	+	0.0866077i	0.573126	−	0.819467i	$-0.305731\pi$
$751$	4.11090	+	2.37343i	0.150009	+	0.0866077i	−0.423117	+	0.906075i	$0.639064\pi$
$752$	−1.63250	+	8.07422i	−0.0595312	+	0.294436i
$753$	30.7445	−	5.95737i	1.12039	−	0.217099i
$754$	−31.4075	−	31.6761i	−1.14379	−	1.15358i
$755$	31.2799			1.13839
$756$	5.21122	+	24.1359i	0.189530	+	0.877815i
$757$	−8.27842	+	14.3386i	−0.300884	+	0.521147i	−0.976337	−	0.216257i	$-0.930615\pi$
$757$	−8.27842	+	14.3386i	−0.300884	+	0.521147i	0.675452	+	0.737404i	$0.263949\pi$
$758$	8.77933	−	48.0350i	0.318880	−	1.74471i
$759$	−38.4718	+	7.45470i	−1.39644	+	0.270588i
$760$	−0.622205	+	33.2274i	−0.0225698	+	1.20529i
$761$	−1.78128	+	1.02842i	−0.0645713	+	0.0372802i	−0.531938	−	0.846783i	$-0.678536\pi$
$761$	−1.78128	+	1.02842i	−0.0645713	+	0.0372802i	0.467367	+	0.884064i	$0.345203\pi$
$762$	9.94981	+	5.60443i	0.360444	+	0.203027i
$763$	2.53306	−	1.46246i	0.0917029	−	0.0529447i
$764$	−39.0981	−	14.7858i	−1.41452	−	0.534931i
$765$	0.629311	−	4.43990i	0.0227528	−	0.160525i
$766$	−7.39644	+	8.70383i	−0.267244	+	0.314482i
$767$	−17.4923	−	1.49542i	−0.631609	−	0.0539964i
$768$	18.5055	−	20.6288i	0.667760	−	0.744377i
$769$	−4.14393	+	7.17750i	−0.149434	+	0.258827i	−0.931018	−	0.364972i	$-0.881078\pi$
$769$	−4.14393	+	7.17750i	−0.149434	+	0.258827i	0.781584	+	0.623799i	$0.214412\pi$
$770$	12.5532	+	35.1711i	0.452386	+	1.26748i
$771$	20.9353	−	18.1772i	0.753967	−	0.654636i
$772$	−4.56001	−	27.8927i	−0.164118	−	1.00388i
$773$	−25.9732	+	14.9956i	−0.934189	+	0.539354i	−0.888134	−	0.459584i	$-0.847998\pi$
$773$	−25.9732	+	14.9956i	−0.934189	+	0.539354i	−0.0460553	+	0.998939i	$0.514665\pi$
$774$	−0.830911	−	4.05685i	−0.0298665	−	0.145821i
$775$		−	2.13069i		−	0.0765366i
$776$	−0.104962	+	5.60525i	−0.00376791	+	0.201217i
$777$	12.3261	+	4.25231i	0.442195	+	0.152551i
$778$	17.0442	−	6.08340i	0.611066	−	0.218101i
$779$	−5.68303			−0.203616
$780$	−10.7405	+	41.1299i	−0.384573	+	1.47269i
$781$	−1.14182			−0.0408577
$782$	−4.05297	+	1.44658i	−0.144934	+	0.0517295i
$783$	45.3988	−	2.29898i	1.62242	−	0.0821587i
$784$	4.06259	+	3.58549i	0.145093	+	0.128053i
$785$			19.4553i			0.694391i
$786$	16.3627	−	0.173849i	0.583639	−	0.00620098i
$787$	14.5480	−	8.39932i	0.518582	−	0.299403i	−0.217772	−	0.976000i	$-0.569879\pi$
$787$	14.5480	−	8.39932i	0.518582	−	0.299403i	0.736354	+	0.676596i	$0.236546\pi$
$788$	9.90088	−	1.61864i	0.352704	−	0.0576616i
$789$	14.2554	+	16.4184i	0.507505	+	0.584511i
$790$	−21.1567	−	59.2761i	−0.752722	−	2.10895i
$791$	−12.9702	+	22.4651i	−0.461168	+	0.798767i
$792$	−27.3564	−	4.40144i	−0.972067	−	0.156398i
$793$	47.4553	+	4.05697i	1.68519	+	0.144067i
$794$	12.2841	−	14.4554i	0.435946	−	0.513004i
$795$	10.9795	−	31.8259i	0.389401	−	1.12875i
$796$	−17.4262	+	46.0801i	−0.617655	+	1.63327i
$797$	9.05500	−	5.22791i	0.320745	−	0.185182i	−0.330980	−	0.943638i	$-0.607379\pi$
$797$	9.05500	−	5.22791i	0.320745	−	0.185182i	0.651724	+	0.758456i	$0.274046\pi$
$798$	−9.86072	+	17.5062i	−0.349066	+	0.619713i
$799$	0.783290	−	0.452233i	0.0277108	−	0.0159988i
$800$	36.8600	−	5.31952i	1.30320	−	0.188073i
$801$	−13.8847	−	34.4826i	−0.490593	−	1.21838i
$802$	−7.92393	+	43.3548i	−0.279804	+	1.53091i
$803$	−9.59453	+	16.6182i	−0.338584	+	0.586444i
$804$	2.38221	−	13.8653i	0.0840139	−	0.488990i
$805$	56.0286			1.97475
$806$	0.433899	−	1.59219i	0.0152834	−	0.0560824i
$807$	−5.68647	−	29.3464i	−0.200173	−	1.03304i
$808$	0.501169	+	0.906848i	0.0176311	+	0.0319028i
$809$	−24.9906	−	14.4283i	−0.878624	−	0.507274i	−0.00841945	−	0.999965i	$-0.502680\pi$
$809$	−24.9906	−	14.4283i	−0.878624	−	0.507274i	−0.870204	+	0.492691i	$0.836013\pi$
$810$	−23.9141	−	36.1198i	−0.840257	−	1.26912i
$811$		−	41.7971i		−	1.46769i	−0.679315	−	0.733847i	$-0.737723\pi$
$811$		−	41.7971i		−	1.46769i	0.679315	−	0.733847i	$-0.262277\pi$
$812$	−32.1766	+	26.3220i	−1.12918	+	0.923722i
$813$	20.5719	−	17.8617i	0.721488	−	0.626436i
$814$	−9.47480	+	11.1496i	−0.332092	+	0.390792i
$815$	25.3876	+	43.9725i	0.889287	+	1.54029i
$816$	−3.04269	−	0.0246438i	−0.106515	−	0.000862707i
$817$	1.68482	−	2.91820i	0.0589445	−	0.102095i
$818$	−23.9763	+	28.2143i	−0.838310	+	0.986490i
$819$	−17.5124	+	18.8102i	−0.611933	+	0.657282i
$820$	1.80788	+	11.0584i	0.0631339	+	0.386178i
$821$	−2.77218	−	1.60052i	−0.0967496	−	0.0558584i	0.450845	−	0.892602i	$-0.351123\pi$
$821$	−2.77218	−	1.60052i	−0.0967496	−	0.0558584i	−0.547594	+	0.836744i	$0.684456\pi$
$822$	19.9674	−	11.8128i	0.696445	−	0.412019i
$823$	32.1367	−	18.5541i	1.12021	−	0.646756i	0.178759	−	0.983893i	$-0.442792\pi$
$823$	32.1367	−	18.5541i	1.12021	−	0.646756i	0.941456	+	0.337137i	$0.109458\pi$
$824$	25.8312	−	42.8670i	0.899874	−	1.49334i
$825$	−24.4123	−	28.1165i	−0.849927	−	0.978891i
$826$	−2.94161	+	16.0946i	−0.102352	+	0.560004i
$827$	−17.0816			−0.593987			−0.296993	−	0.954880i	$-0.595984\pi$
$827$	−17.0816			−0.593987			−0.296993	+	0.954880i	$0.595984\pi$
$828$	−20.0161	+	36.4354i	−0.695608	+	1.26622i
$829$	11.3042	−	19.5794i	0.392610	−	0.680021i	−0.600183	−	0.799863i	$-0.704906\pi$
$829$	11.3042	−	19.5794i	0.392610	−	0.680021i	0.992793	+	0.119842i	$0.0382388\pi$
$830$	−7.05224	+	2.51707i	−0.244787	+	0.0873689i
$831$	0.903702	−	0.175111i	0.0313491	−	0.00607452i
$832$	28.6274	+	3.53119i	0.992478	+	0.122422i
$833$		−	0.594939i		−	0.0206134i
$834$	26.5954	−	15.7339i	0.920924	−	0.544822i
$835$	51.0834	+	29.4930i	1.76781	+	1.02065i
$836$	−14.2759	−	17.4512i	−0.493744	−	0.603563i
$837$	0.913423	+	1.41199i	0.0315725	+	0.0488056i
$838$	44.4440	+	8.12301i	1.53529	+	0.280605i
$839$	26.3560	+	45.6499i	0.909910	+	1.57601i	0.814188	+	0.580602i	$0.197183\pi$
$839$	26.3560	+	45.6499i	0.909910	+	1.57601i	0.0957218	+	0.995408i	$0.469484\pi$
$840$	37.2017	+	13.6186i	1.28358	+	0.469888i
$841$	23.7655	+	41.1631i	0.819502	+	1.41942i
$842$	−4.35948	−	12.2142i	−0.150237	−	0.420930i
$843$	−2.97835	−	1.02749i	−0.102580	−	0.0353885i
$844$	49.5441	−	8.09968i	1.70538	−	0.278803i
$845$	−41.5162	+	15.2975i	−1.42820	+	0.526249i
$846$	2.76153	−	8.28941i	0.0949433	−	0.284996i
$847$	0.693177	+	0.400206i	0.0238179	+	0.0137512i
$848$	−22.3912	−	4.52721i	−0.768917	−	0.155465i
$849$	34.1229	−	29.6273i	1.17109	−	1.01681i
$850$	−3.11593	−	2.64789i	−0.106876	−	0.0908220i
$851$	10.9761	+	19.0112i	0.376257	+	0.651696i
$852$	−0.774527	+	0.931305i	−0.0265349	+	0.0319060i
$853$	−11.6372			−0.398451			−0.199225	−	0.979954i	$-0.563843\pi$
$853$	−11.6372			−0.398451			−0.199225	+	0.979954i	$0.563843\pi$
$854$	7.98038	−	43.6637i	0.273083	−	1.49414i
$855$	4.94678	−	34.9004i	0.169176	−	1.19357i
$856$	18.7507	−	10.3626i	0.640886	−	0.354186i
$857$			35.3115i			1.20622i	0.797659	+	0.603109i	$0.206072\pi$
$857$			35.3115i			1.20622i	−0.797659	+	0.603109i	$0.793928\pi$
$858$	−12.5167	−	25.9818i	−0.427314	−	0.887005i
$859$			18.0670i			0.616439i	0.951315	+	0.308220i	$0.0997332\pi$
$859$			18.0670i			0.616439i	−0.951315	+	0.308220i	$0.900267\pi$
$860$	−6.21442	−	2.35012i	−0.211910	−	0.0801383i
$861$	−2.20933	+	6.40414i	−0.0752939	+	0.218252i
$862$	−9.49757	−	1.73587i	−0.323489	−	0.0591238i
$863$	−52.4103			−1.78407			−0.892034	−	0.451968i	$-0.850722\pi$
$863$	−52.4103			−1.78407			−0.892034	+	0.451968i	$0.850722\pi$
$864$	−22.1464	+	19.3271i	−0.753437	+	0.657520i
$865$	−17.2993	−	29.9633i	−0.588195	−	1.01878i
$866$	−22.2608	+	26.1956i	−0.756452	+	0.890162i
$867$	−19.0855	−	21.9814i	−0.648176	−	0.746528i
$868$	−1.43851	−	0.544004i	−0.0488263	−	0.0184647i
$869$	36.9789	+	21.3498i	1.25442	+	0.724242i
$870$	35.7926	−	63.5443i	1.21348	−	2.15435i
$871$	13.2587	−	6.21466i	0.449252	−	0.210576i
$872$	2.98227	+	1.79709i	0.100993	+	0.0608571i
$873$	0.834489	−	5.88746i	0.0282432	−	0.199260i
$874$	−31.8588	+	11.3710i	−1.07764	+	0.384630i
$875$	6.40256	+	11.0896i	0.216446	+	0.374896i
$876$	7.04609	+	19.0981i	0.238065	+	0.645265i
$877$	−26.8382	−	46.4851i	−0.906261	−	1.56969i	−0.819216	−	0.573485i	$-0.805591\pi$
$877$	−26.8382	−	46.4851i	−0.906261	−	1.56969i	−0.0870445	−	0.996204i	$-0.527742\pi$
$878$	3.74255	−	20.4769i	0.126305	−	0.691062i
$879$	−5.08289	−	26.2315i	−0.171442	−	0.884767i
$880$	−29.4164	+	33.3307i	−0.991626	+	1.12358i
$881$	38.9529	+	22.4895i	1.31236	+	0.757690i	0.982486	−	0.186336i	$-0.0596612\pi$
$881$	38.9529	+	22.4895i	1.31236	+	0.757690i	0.329872	+	0.944026i	$0.392995\pi$
$882$	−3.81385	−	4.29942i	−0.128419	−	0.144769i
$883$			25.2476i			0.849650i	0.905276	+	0.424825i	$0.139664\pi$
$883$			25.2476i			0.849650i	−0.905276	+	0.424825i	$0.860336\pi$
$884$	−1.78920	−	2.61321i	−0.0601773	−	0.0878918i
$885$	−5.46033	−	28.1794i	−0.183547	−	0.947241i
$886$	0.216619	+	0.606915i	0.00727746	+	0.0203897i
$887$	−3.42157	+	5.92633i	−0.114885	+	0.198987i	−0.917734	−	0.397196i	$-0.869983\pi$
$887$	−3.42157	+	5.92633i	−0.114885	+	0.198987i	0.802849	+	0.596183i	$0.203317\pi$
$888$	2.66692	+	15.2909i	0.0894960	+	0.513130i
$889$	11.0770			0.371512
$890$	−58.6688	−	10.7229i	−1.96658	−	0.359431i
$891$	28.2314	+	8.16711i	0.945787	+	0.273609i
$892$	−6.55071	+	1.07094i	−0.219334	+	0.0358577i
$893$	6.15715	−	3.55483i	0.206041	−	0.118958i
$894$	−27.1164	+	16.0421i	−0.906907	+	0.536530i
$895$	29.7342	+	17.1671i	0.993905	+	0.573831i
$896$	5.81963	−	26.2438i	0.194420	−	0.876745i
$897$	−43.0255	+	4.58289i	−1.43658	+	0.153018i
$898$	−20.1073	−	17.0870i	−0.670989	−	0.570201i
$899$	−1.41564	+	2.45196i	−0.0472141	+	0.0817773i
$900$	−39.4921	+	0.839276i	−1.31640	+	0.0279759i
$901$	1.25412	+	2.17220i	0.0417808	+	0.0723665i
$902$	−5.79287	−	4.92273i	−0.192882	−	0.163909i
$903$	−2.63349	−	3.03309i	−0.0876372	−	0.100935i
$904$	−30.8745	−	0.578146i	−1.02687	−	0.0192288i
$905$			34.8980i			1.16005i
$906$	0.239174	+	22.5111i	0.00794601	+	0.747882i
$907$	−12.6969	−	7.33055i	−0.421593	−	0.243407i	0.274166	−	0.961682i	$-0.411598\pi$
$907$	−12.6969	−	7.33055i	−0.421593	−	0.243407i	−0.695759	+	0.718276i	$0.744932\pi$
$908$	35.6695	+	13.4892i	1.18374	+	0.447655i
$909$	−0.410483	−	1.01943i	−0.0136149	−	0.0338124i
$910$	10.5024	+	39.8738i	0.348151	+	1.32180i
$911$	10.0500			0.332970			0.166485	−	0.986044i	$-0.446758\pi$
$911$	10.0500			0.332970			0.166485	+	0.986044i	$0.446758\pi$
$912$	−23.9174	−	0.193716i	−0.791985	−	0.00641457i
$913$	2.54005	−	4.39949i	0.0840633	−	0.145602i
$914$	30.8125	+	5.63159i	1.01919	+	0.186276i
$915$	14.8135	+	76.4488i	0.489720	+	2.52732i
$916$	−41.6414	+	34.0647i	−1.37587	+	1.12553i
$917$	13.7462	−	7.93635i	0.453938	−	0.262081i
$918$	3.20006	+	0.418946i	0.105618	+	0.0138273i
$919$	−12.5091	+	7.22212i	−0.412637	+	0.238236i	−0.691922	−	0.721972i	$-0.743236\pi$
$919$	−12.5091	+	7.22212i	−0.412637	+	0.238236i	0.279285	+	0.960208i	$0.409902\pi$
$920$	32.2614	+	58.3759i	1.06363	+	1.92460i
$921$	30.1274	+	10.3935i	0.992733	+	0.342478i
$922$	−38.0006	−	32.2926i	−1.25148	−	1.06350i
$923$	−1.25617	−	0.107390i	−0.0413473	−	0.00353479i
$924$	−25.2155	+	9.30305i	−0.829529	+	0.306048i
$925$	−10.4295	+	18.0644i	−0.342919	+	0.593953i
$926$	−2.77904	+	0.991888i	−0.0913248	+	0.0325955i
$927$	−32.7311	+	41.7925i	−1.07503	+	1.37265i
$928$	−45.9521	−	18.3683i	−1.50845	−	0.602970i
$929$	0.734614	−	0.424129i	0.0241019	−	0.0139152i	−0.487901	−	0.872899i	$-0.662237\pi$
$929$	0.734614	−	0.424129i	0.0241019	−	0.0139152i	0.512003	+	0.858984i	$0.328904\pi$
$930$	2.69795	−	0.0286649i	0.0884693	−	0.000939958i
$931$		−	4.67659i		−	0.153269i
$932$	1.00806	+	1.23227i	0.0330200	+	0.0403644i
$933$	10.6377	−	30.8352i	0.348262	−	1.00950i
$934$	4.81710	+	13.4964i	0.157620	+	0.441614i
$935$	4.88105			0.159627
$936$	−29.6819	−	7.41511i	−0.970184	−	0.242370i
$937$	−36.6383			−1.19692			−0.598461	−	0.801152i	$-0.704221\pi$
$937$	−36.6383			−1.19692			−0.598461	+	0.801152i	$0.704221\pi$
$938$	−4.58720	−	12.8522i	−0.149777	−	0.419640i
$939$	−9.02090	+	26.1487i	−0.294386	+	0.853329i
$940$	−8.87595	−	10.8502i	−0.289502	−	0.353893i
$941$			40.0532i			1.30570i	0.757489	+	0.652848i	$0.226426\pi$
$941$			40.0532i			1.30570i	−0.757489	+	0.652848i	$0.773574\pi$
$942$	−14.0014	+	0.148760i	−0.456189	+	0.00484686i
$943$	−9.87748	+	5.70277i	−0.321655	+	0.185708i
$944$	−18.4627	+	6.20249i	−0.600909	+	0.201874i
$945$	−37.4057	−	19.1423i	−1.21681	−	0.622700i
$946$	4.24518	−	1.51518i	0.138023	−	0.0492629i
$947$	21.9067	−	37.9435i	0.711873	−	1.23300i	−0.252281	−	0.967654i	$-0.581181\pi$
$947$	21.9067	−	37.9435i	0.711873	−	1.23300i	0.964153	−	0.265345i	$-0.0854860\pi$
$948$	42.4972	−	15.6790i	1.38025	−	0.509230i
$949$	−12.1183	+	17.3800i	−0.393376	+	0.564178i
$950$	−24.4932	−	20.8141i	−0.794663	−	0.675298i
$951$	−9.84677	−	3.39699i	−0.319303	−	0.110155i
$952$	−2.58325	+	1.42763i	−0.0837237	+	0.0462699i
$953$	−31.3295	+	18.0881i	−1.01486	+	0.585931i	−0.912612	−	0.408828i	$-0.865938\pi$
$953$	−31.3295	+	18.0881i	−1.01486	+	0.585931i	−0.102251	+	0.994759i	$0.532604\pi$
$954$	22.9880	+	7.65820i	0.744263	+	0.247943i
$955$	61.6030	−	35.5665i	1.99343	−	1.15090i
$956$	−11.9436	+	9.77045i	−0.386284	+	0.315999i
$957$	9.41251	+	48.5756i	0.304263	+	1.57023i
$958$	−55.9470	−	10.2254i	−1.80757	−	0.330368i
$959$	11.2520	−	19.4890i	0.363346	−	0.629333i
$960$	7.23165	+	46.6019i	0.233400	+	1.50407i
$961$	30.8953			0.996621
$962$	−11.4722	+	11.3750i	−0.369880	+	0.366744i
$963$	−21.0786	+	8.48748i	−0.679248	+	0.273505i
$964$	20.3307	+	7.68847i	0.654807	+	0.247629i
$965$	41.6522	+	24.0479i	1.34083	+	0.774130i
$966$	0.428408	+	40.3219i	0.0137838	+	1.29734i
$967$			32.8181i			1.05536i	0.849444	+	0.527679i	$0.176938\pi$
$967$			32.8181i			1.05536i	−0.849444	+	0.527679i	$0.823062\pi$
$968$	−0.0178391	+	0.952657i	−0.000573371	+	0.0306195i
$969$	1.72175	+	1.98300i	0.0553105	+	0.0637030i
$970$	−7.26986	−	6.17786i	−0.233421	−	0.198359i
$971$	−9.83311	−	17.0315i	−0.315560	−	0.546565i	0.663997	−	0.747736i	$-0.268859\pi$
$971$	−9.83311	−	17.0315i	−0.315560	−	0.546565i	−0.979556	+	0.201170i	$0.935526\pi$
$972$	25.8114	−	17.4864i	0.827900	−	0.560876i
$973$	14.9870	−	25.9582i	0.480460	−	0.832181i
$974$	−34.1724	−	29.0394i	−1.09496	−	0.930484i
$975$	−24.2126	−	33.2281i	−0.775423	−	1.06415i
$976$	50.0880	−	16.8269i	1.60328	−	0.538617i
$977$	−15.8633	−	9.15867i	−0.507511	−	0.293012i	0.224299	−	0.974520i	$-0.427991\pi$
$977$	−15.8633	−	9.15867i	−0.507511	−	0.293012i	−0.731810	+	0.681509i	$0.761324\pi$
$978$	−31.4514	+	18.6068i	−1.00571	+	0.594980i
$979$	35.0413	−	20.2311i	1.11992	−	0.646589i
$980$	−9.10004	+	1.48771i	−0.290690	+	0.0475232i
$981$	−2.90752	−	2.27711i	−0.0928300	−	0.0727026i
$982$	29.4836	+	5.38869i	0.940858	+	0.171960i
$983$	21.2629			0.678181			0.339090	−	0.940754i	$-0.389881\pi$
$983$	21.2629			0.678181			0.339090	+	0.940754i	$0.389881\pi$
$984$	−7.94457	+	1.38563i	−0.253264	+	0.0441722i
$985$	−8.53613	+	14.7850i	−0.271984	+	0.471090i
$986$	1.82649	+	5.11739i	0.0581672	+	0.162971i
$987$	−1.61224	−	8.32039i	−0.0513183	−	0.264841i
$988$	−14.0642	−	20.5415i	−0.447443	−	0.653511i
$989$		−	6.76270i		−	0.215042i
$990$	35.2737	−	31.2900i	1.12107	−	0.994460i
$991$	28.6598	+	16.5467i	0.910407	+	0.525624i	0.880562	−	0.473931i	$-0.157165\pi$
$991$	28.6598	+	16.5467i	0.910407	+	0.525624i	0.0298451	+	0.999555i	$0.490499\pi$
$992$	−0.261504	−	1.81202i	−0.00830276	−	0.0575315i
$993$	−7.15928	−	36.9473i	−0.227193	−	1.17249i
$994$	−0.211245	+	1.15580i	−0.00670029	+	0.0366598i
$995$	−41.9179	−	72.6039i	−1.32889	−	2.30170i
$996$	−1.86538	−	5.05602i	−0.0591067	−	0.160206i
$997$	−16.1863	−	28.0356i	−0.512627	−	0.887896i	−0.999893	−	0.0146420i	$-0.995339\pi$
$997$	−16.1863	−	28.0356i	−0.512627	−	0.887896i	0.487266	−	0.873254i	$-0.337994\pi$
$998$	40.3417	−	14.3987i	1.27700	−	0.455783i
$999$	−0.832628	−	16.4422i	−0.0263432	−	0.520210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.p.b.35.8	yes	40
3.2	odd	2	inner	156.2.p.b.35.13	yes	40
4.3	odd	2	inner	156.2.p.b.35.2	✓	40
12.11	even	2	inner	156.2.p.b.35.19	yes	40
13.3	even	3	inner	156.2.p.b.107.19	yes	40
39.29	odd	6	inner	156.2.p.b.107.2	yes	40
52.3	odd	6	inner	156.2.p.b.107.13	yes	40
156.107	even	6	inner	156.2.p.b.107.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.p.b.35.2	✓	40	4.3	odd	2	inner
156.2.p.b.35.8	yes	40	1.1	even	1	trivial
156.2.p.b.35.13	yes	40	3.2	odd	2	inner
156.2.p.b.35.19	yes	40	12.11	even	2	inner
156.2.p.b.107.2	yes	40	39.29	odd	6	inner
156.2.p.b.107.8	yes	40	156.107	even	6	inner
156.2.p.b.107.13	yes	40	52.3	odd	6	inner
156.2.p.b.107.19	yes	40	13.3	even	3	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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.475386 - 1.33192i) q^{2} +(-0.564863 + 1.63735i) q^{3} +(-1.54802 + 1.26635i) q^{4} -3.40345i q^{5} +(2.44935 - 0.0260236i) q^{6} +(2.05768 - 1.18800i) q^{7} +(2.42258 + 1.45983i) q^{8} +(-2.36186 - 1.84976i) q^{9} +O(q^{10})\)	\(q+(-0.475386 - 1.33192i) q^{2} +(-0.564863 + 1.63735i) q^{3} +(-1.54802 + 1.26635i) q^{4} -3.40345i q^{5} +(2.44935 - 0.0260236i) q^{6} +(2.05768 - 1.18800i) q^{7} +(2.42258 + 1.45983i) q^{8} +(-2.36186 - 1.84976i) q^{9} +(-4.53312 + 1.61795i) q^{10} +(1.63272 - 2.82796i) q^{11} +(-1.19905 - 3.24997i) q^{12} +(2.06220 - 2.95759i) q^{13} +(-2.56051 - 2.17590i) q^{14} +(5.57266 + 1.92249i) q^{15} +(0.792707 - 3.92067i) q^{16} +(-0.380349 + 0.219594i) q^{17} +(-1.34094 + 4.02516i) q^{18} +(-2.98978 + 1.72615i) q^{19} +(4.30997 + 5.26860i) q^{20} +(0.782871 + 4.04020i) q^{21} +(-4.54278 - 0.830282i) q^{22} +(-3.46429 + 6.00032i) q^{23} +(-3.75868 + 3.14203i) q^{24} -6.58350 q^{25} +(-4.91961 - 1.34068i) q^{26} +(4.36284 - 2.82234i) q^{27} +(-1.68089 + 4.44478i) q^{28} +(7.57617 + 4.37410i) q^{29} +(-0.0885701 - 8.33625i) q^{30} +0.323641i q^{31} +(-5.59885 + 0.808008i) q^{32} +(3.70810 + 4.27075i) q^{33} +(0.473295 + 0.402202i) q^{34} +(-4.04330 - 7.00320i) q^{35} +(5.99865 - 0.127482i) q^{36} +(1.58418 - 2.74389i) q^{37} +(3.72039 + 3.16155i) q^{38} +(3.67777 + 5.04718i) q^{39} +(4.96845 - 8.24515i) q^{40} +(1.42562 + 0.823079i) q^{41} +(5.00905 - 2.96338i) q^{42} +(-0.845293 + 0.488030i) q^{43} +(1.05371 + 6.44532i) q^{44} +(-6.29558 + 8.03848i) q^{45} +(9.63882 + 1.76168i) q^{46} -2.05940 q^{47} +(5.97175 + 3.51258i) q^{48} +(-0.677315 + 1.17314i) q^{49} +(3.12970 + 8.76869i) q^{50} +(-0.144709 - 0.746807i) q^{51} +(0.553036 + 7.18986i) q^{52} -5.71107i q^{53} +(-5.83316 - 4.46925i) q^{54} +(-9.62482 - 5.55689i) q^{55} +(6.71916 + 0.125821i) q^{56} +(-1.13750 - 5.87036i) q^{57} +(2.22434 - 12.1702i) q^{58} +(-2.43459 - 4.21683i) q^{59} +(-11.0611 + 4.08091i) q^{60} +(6.60487 + 11.4400i) q^{61} +(0.431063 - 0.153854i) q^{62} +(-7.05746 - 1.00032i) q^{63} +(3.73782 + 7.07310i) q^{64} +(-10.0660 - 7.01859i) q^{65} +(3.92552 - 6.96915i) q^{66} +(3.51711 + 2.03060i) q^{67} +(0.310702 - 0.821591i) q^{68} +(-7.86780 - 9.06163i) q^{69} +(-7.40557 + 8.71457i) q^{70} +(-0.174835 - 0.302822i) q^{71} +(-3.02147 - 7.92911i) q^{72} -5.87640 q^{73} +(-4.40773 - 0.805598i) q^{74} +(3.71878 - 10.7795i) q^{75} +(2.44231 - 6.45821i) q^{76} -7.75869i q^{77} +(4.97408 - 7.29785i) q^{78} +13.0762i q^{79} +(-13.3438 - 2.69794i) q^{80} +(2.15676 + 8.73776i) q^{81} +(0.418557 - 2.29008i) q^{82} +1.55571 q^{83} +(-6.32821 - 5.26291i) q^{84} +(0.747380 + 1.29450i) q^{85} +(1.05186 + 0.893859i) q^{86} +(-11.4415 + 9.93410i) q^{87} +(8.08373 - 4.46747i) q^{88} +(10.7309 + 6.19551i) q^{89} +(13.6994 + 4.56382i) q^{90} +(0.729715 - 8.53565i) q^{91} +(-2.23574 - 13.6756i) q^{92} +(-0.529914 - 0.182813i) q^{93} +(0.979010 + 2.74295i) q^{94} +(5.87487 + 10.1756i) q^{95} +(1.83959 - 9.62372i) q^{96} +(0.991051 + 1.71655i) q^{97} +(1.88452 + 0.344432i) q^{98} +(-9.08731 + 3.65909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{4} + 2 q^{6} - 10 q^{9}+O(q^{10}) \) 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9	\( 40 q + 6 q^{4} + 2 q^{6} - 10 q^{9} + 6 q^{10} - 16 q^{12} + 16 q^{13} + 18 q^{16} - 20 q^{18} - 60 q^{21} + 20 q^{22} - 20 q^{24} - 32 q^{25} - 24 q^{28} - 26 q^{30} - 2 q^{33} - 28 q^{34} + 6 q^{36} + 16 q^{37} + 20 q^{40} - 4 q^{42} + 28 q^{45} + 48 q^{46} - 24 q^{48} - 28 q^{49} + 12 q^{52} - 4 q^{54} + 44 q^{57} - 50 q^{58} - 12 q^{60} - 12 q^{61} + 12 q^{64} + 24 q^{66} - 6 q^{69} + 48 q^{72} - 16 q^{73} + 30 q^{78} - 14 q^{81} - 2 q^{82} - 6 q^{84} + 52 q^{85} - 12 q^{88} + 156 q^{90} + 40 q^{93} - 8 q^{94} + 128 q^{96} - 56 q^{97}+O(q^{100}) \) 40 * q + 6 * q^4 + 2 * q^6 - 10 * q^9 + 6 * q^10 - 16 * q^12 + 16 * q^13 + 18 * q^16 - 20 * q^18 - 60 * q^21 + 20 * q^22 - 20 * q^24 - 32 * q^25 - 24 * q^28 - 26 * q^30 - 2 * q^33 - 28 * q^34 + 6 * q^36 + 16 * q^37 + 20 * q^40 - 4 * q^42 + 28 * q^45 + 48 * q^46 - 24 * q^48 - 28 * q^49 + 12 * q^52 - 4 * q^54 + 44 * q^57 - 50 * q^58 - 12 * q^60 - 12 * q^61 + 12 * q^64 + 24 * q^66 - 6 * q^69 + 48 * q^72 - 16 * q^73 + 30 * q^78 - 14 * q^81 - 2 * q^82 - 6 * q^84 + 52 * q^85 - 12 * q^88 + 156 * q^90 + 40 * q^93 - 8 * q^94 + 128 * q^96 - 56 * q^97

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