LMFDB - Embedded newform 252.2.bi.c.139.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.4
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38071 + 0.306010i) q^{2} +(1.38170 - 1.04446i) q^{3} +(1.81272 - 0.845022i) q^{4} +(-1.82425 - 1.05323i) q^{5} +(-1.58811 + 1.86491i) q^{6} +(2.54762 + 0.713899i) q^{7} +(-2.24425 + 1.72144i) q^{8} +(0.818200 - 2.88627i) q^{9} +O(q^{10})$	\(q+(-1.38071 + 0.306010i) q^{2} +(1.38170 - 1.04446i) q^{3} +(1.81272 - 0.845022i) q^{4} +(-1.82425 - 1.05323i) q^{5} +(-1.58811 + 1.86491i) q^{6} +(2.54762 + 0.713899i) q^{7} +(-2.24425 + 1.72144i) q^{8} +(0.818200 - 2.88627i) q^{9} +(2.84106 + 0.895969i) q^{10} +(1.99265 - 1.15046i) q^{11} +(1.62204 - 3.06088i) q^{12} +(-0.218388 - 0.126086i) q^{13} +(-3.73598 - 0.206091i) q^{14} +(-3.62064 + 0.450108i) q^{15} +(2.57187 - 3.06357i) q^{16} -4.60054i q^{17} +(-0.246468 + 4.23548i) q^{18} -4.87573 q^{19} +(-4.19686 - 0.367678i) q^{20} +(4.26569 - 1.67449i) q^{21} +(-2.39922 + 2.19822i) q^{22} +(4.23165 + 2.44314i) q^{23} +(-1.30290 + 4.72255i) q^{24} +(-0.281399 - 0.487397i) q^{25} +(0.340113 + 0.107259i) q^{26} +(-1.88409 - 4.84254i) q^{27} +(5.22136 - 0.858695i) q^{28} +(1.08689 + 1.88255i) q^{29} +(4.86131 - 1.72942i) q^{30} +(1.78200 - 3.08652i) q^{31} +(-2.61353 + 5.01692i) q^{32} +(1.55164 - 3.67084i) q^{33} +(1.40781 + 6.35201i) q^{34} +(-3.89560 - 3.98557i) q^{35} +(-0.955798 - 5.92338i) q^{36} +10.5786 q^{37} +(6.73197 - 1.49202i) q^{38} +(-0.433439 + 0.0538840i) q^{39} +(5.90715 - 0.776626i) q^{40} +(1.15076 + 0.664389i) q^{41} +(-5.37726 + 3.61733i) q^{42} +(-8.60873 + 4.97025i) q^{43} +(2.63995 - 3.76929i) q^{44} +(-4.53252 + 4.40353i) q^{45} +(-6.59030 - 2.07834i) q^{46} +(5.43270 + 9.40970i) q^{47} +(0.353783 - 6.91916i) q^{48} +(5.98070 + 3.63748i) q^{49} +(0.537678 + 0.586842i) q^{50} +(-4.80509 - 6.35657i) q^{51} +(-0.502420 - 0.0440159i) q^{52} -7.98161 q^{53} +(4.08325 + 6.10959i) q^{54} -4.84680 q^{55} +(-6.94642 + 2.78340i) q^{56} +(-6.73681 + 5.09251i) q^{57} +(-2.07676 - 2.26666i) q^{58} +(-3.69586 + 6.40141i) q^{59} +(-6.18283 + 3.87544i) q^{60} +(-12.5132 + 7.22449i) q^{61} +(-1.51592 + 4.80690i) q^{62} +(4.14497 - 6.76899i) q^{63} +(2.07329 - 7.72667i) q^{64} +(0.265596 + 0.460026i) q^{65} +(-1.01905 + 5.54318i) q^{66} +(7.35240 + 4.24491i) q^{67} +(-3.88756 - 8.33947i) q^{68} +(8.39864 - 1.04410i) q^{69} +(6.59831 + 4.31082i) q^{70} +6.14583i q^{71} +(3.13229 + 7.88598i) q^{72} -2.16000i q^{73} +(-14.6059 + 3.23715i) q^{74} +(-0.897876 - 0.379527i) q^{75} +(-8.83831 + 4.12010i) q^{76} +(5.89782 - 1.50837i) q^{77} +(0.581964 - 0.207035i) q^{78} +(-2.84679 + 1.64360i) q^{79} +(-7.91841 + 2.87994i) q^{80} +(-7.66110 - 4.72309i) q^{81} +(-1.79217 - 0.565185i) q^{82} +(4.56438 + 7.90574i) q^{83} +(6.31749 - 6.63998i) q^{84} +(-4.84544 + 8.39255i) q^{85} +(10.3652 - 9.49684i) q^{86} +(3.46801 + 1.46591i) q^{87} +(-2.49156 + 6.01214i) q^{88} +4.62446i q^{89} +(4.91057 - 7.46699i) q^{90} +(-0.466355 - 0.477126i) q^{91} +(9.73528 + 0.852886i) q^{92} +(-0.761555 - 6.12588i) q^{93} +(-10.3804 - 11.3296i) q^{94} +(8.89457 + 5.13528i) q^{95} +(1.62886 + 9.66162i) q^{96} +(4.34667 - 2.50955i) q^{97} +(-9.37071 - 3.19215i) q^{98} +(-1.69014 - 6.69264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.38071	+	0.306010i	−0.976309	+	0.216382i
$2$	−1.38071	+	0.306010i	−0.976309	+	0.216382i
$3$	1.38170	−	1.04446i	0.797726	−	0.603020i
$3$	1.38170	−	1.04446i	0.797726	−	0.603020i
$4$	1.81272	−	0.845022i	0.906358	−	0.422511i
$5$	−1.82425	−	1.05323i	−0.815831	−	0.471020i	0.0331456	−	0.999451i	$-0.489447\pi$
$5$	−1.82425	−	1.05323i	−0.815831	−	0.471020i	−0.848977	+	0.528430i	$0.822781\pi$
$6$	−1.58811	+	1.86491i	−0.648344	+	0.761347i
$7$	2.54762	+	0.713899i	0.962908	+	0.269829i
$7$	2.54762	+	0.713899i	0.962908	+	0.269829i
$8$	−2.24425	+	1.72144i	−0.793461	+	0.608621i
$9$	0.818200	−	2.88627i	0.272733	−	0.962090i
$10$	2.84106	+	0.895969i	0.898423	+	0.283330i
$11$	1.99265	−	1.15046i	0.600807	−	0.346876i	−0.168552	−	0.985693i	$-0.553909\pi$
$11$	1.99265	−	1.15046i	0.600807	−	0.346876i	0.769359	+	0.638817i	$0.220576\pi$
$12$	1.62204	−	3.06088i	0.468242	−	0.883600i
$13$	−0.218388	−	0.126086i	−0.0605698	−	0.0349700i	0.469409	−	0.882981i	$-0.344467\pi$
$13$	−0.218388	−	0.126086i	−0.0605698	−	0.0349700i	−0.529979	+	0.848011i	$0.677800\pi$
$14$	−3.73598	−	0.206091i	−0.998482	−	0.0550801i
$15$	−3.62064	+	0.450108i	−0.934844	+	0.116218i
$16$	2.57187	−	3.06357i	0.642969	−	0.765892i
$17$		−	4.60054i		−	1.11579i	−0.829910	−	0.557897i	$-0.811608\pi$
$17$		−	4.60054i		−	1.11579i	0.829910	−	0.557897i	$-0.188392\pi$
$18$	−0.246468	+	4.23548i	−0.0580932	+	0.998311i
$19$	−4.87573			−1.11857			−0.559285	−	0.828976i	$-0.688924\pi$
$19$	−4.87573			−1.11857			−0.559285	+	0.828976i	$0.688924\pi$
$20$	−4.19686	−	0.367678i	−0.938446	−	0.0822152i
$21$	4.26569	−	1.67449i	0.930849	−	0.365404i
$22$	−2.39922	+	2.19822i	−0.511516	+	0.468662i
$23$	4.23165	+	2.44314i	0.882359	+	0.509430i	0.871435	−	0.490510i	$-0.163190\pi$
$23$	4.23165	+	2.44314i	0.882359	+	0.509430i	0.0109235	+	0.999940i	$0.496523\pi$
$24$	−1.30290	+	4.72255i	−0.265954	+	0.963986i
$25$	−0.281399	−	0.487397i	−0.0562797	−	0.0974793i
$26$	0.340113	+	0.107259i	0.0667017	+	0.0210353i
$27$	−1.88409	−	4.84254i	−0.362593	−	0.931948i
$28$	5.22136	−	0.858695i	0.986745	−	0.162278i
$29$	1.08689	+	1.88255i	0.201831	+	0.349581i	0.949118	−	0.314920i	$-0.101978\pi$
$29$	1.08689	+	1.88255i	0.201831	+	0.349581i	−0.747288	+	0.664501i	$0.768644\pi$
$30$	4.86131	−	1.72942i	0.887549	−	0.315748i
$31$	1.78200	−	3.08652i	0.320057	−	0.554355i	−0.660442	−	0.750877i	$-0.729631\pi$
$31$	1.78200	−	3.08652i	0.320057	−	0.554355i	0.980500	+	0.196521i	$0.0629645\pi$
$32$	−2.61353	+	5.01692i	−0.462011	+	0.886874i
$33$	1.55164	−	3.67084i	0.270106	−	0.639011i
$34$	1.40781	+	6.35201i	0.241438	+	1.08936i
$35$	−3.89560	−	3.98557i	−0.658476	−	0.673684i
$36$	−0.955798	−	5.92338i	−0.159300	−	0.987230i
$37$	10.5786			1.73911			0.869553	−	0.493839i	$-0.164407\pi$
$37$	10.5786			1.73911			0.869553	+	0.493839i	$0.164407\pi$
$38$	6.73197	−	1.49202i	1.09207	−	0.242038i
$39$	−0.433439	+	0.0538840i	−0.0694057	+	0.00862835i
$40$	5.90715	−	0.776626i	0.934003	−	0.122795i
$41$	1.15076	+	0.664389i	0.179718	+	0.103760i	0.587160	−	0.809471i	$-0.300246\pi$
$41$	1.15076	+	0.664389i	0.179718	+	0.103760i	−0.407442	+	0.913231i	$0.633579\pi$
$42$	−5.37726	+	3.61733i	−0.829729	+	0.558166i
$43$	−8.60873	+	4.97025i	−1.31282	+	0.757957i	−0.982562	−	0.185934i	$-0.940469\pi$
$43$	−8.60873	+	4.97025i	−1.31282	+	0.757957i	−0.330257	+	0.943891i	$0.607136\pi$
$44$	2.63995	−	3.76929i	0.397987	−	0.568242i
$45$	−4.53252	+	4.40353i	−0.675668	+	0.656440i
$46$	−6.59030	−	2.07834i	−0.971686	−	0.306435i
$47$	5.43270	+	9.40970i	0.792440	+	1.37255i	0.924452	+	0.381298i	$0.124523\pi$
$47$	5.43270	+	9.40970i	0.792440	+	1.37255i	−0.132012	+	0.991248i	$0.542144\pi$
$48$	0.353783	−	6.91916i	0.0510642	−	0.998695i
$49$	5.98070	+	3.63748i	0.854385	+	0.519641i
$50$	0.537678	+	0.586842i	0.0760392	+	0.0829920i
$51$	−4.80509	−	6.35657i	−0.672847	−	0.890098i
$52$	−0.502420	−	0.0440159i	−0.0696731	−	0.00610391i
$53$	−7.98161			−1.09636			−0.548179	−	0.836361i	$-0.684679\pi$
$53$	−7.98161			−1.09636			−0.548179	+	0.836361i	$0.684679\pi$
$54$	4.08325	+	6.10959i	0.555659	+	0.831410i
$55$	−4.84680			−0.653543
$56$	−6.94642	+	2.78340i	−0.928254	+	0.371947i
$57$	−6.73681	+	5.09251i	−0.892312	+	0.674520i
$58$	−2.07676	−	2.26666i	−0.272692	−	0.297627i
$59$	−3.69586	+	6.40141i	−0.481160	+	0.833393i	−0.999766	−	0.0216198i	$-0.993118\pi$
$59$	−3.69586	+	6.40141i	−0.481160	+	0.833393i	0.518606	+	0.855013i	$0.326451\pi$
$60$	−6.18283	+	3.87544i	−0.798200	+	0.500317i
$61$	−12.5132	+	7.22449i	−1.60215	+	0.925001i	−0.611092	+	0.791559i	$0.709270\pi$
$61$	−12.5132	+	7.22449i	−1.60215	+	0.925001i	−0.991057	+	0.133442i	$0.957397\pi$
$62$	−1.51592	+	4.80690i	−0.192522	+	0.610477i
$63$	4.14497	−	6.76899i	0.522217	−	0.852813i
$64$	2.07329	−	7.72667i	0.259162	−	0.965834i
$65$	0.265596	+	0.460026i	0.0329432	+	0.0570592i
$66$	−1.01905	+	5.54318i	−0.125437	+	0.682318i
$67$	7.35240	+	4.24491i	0.898239	+	0.518598i	0.876628	−	0.481168i	$-0.159787\pi$
$67$	7.35240	+	4.24491i	0.898239	+	0.518598i	0.0216103	+	0.999766i	$0.493121\pi$
$68$	−3.88756	−	8.33947i	−0.471436	−	1.01131i
$69$	8.39864	−	1.04410i	1.01108	−	0.125695i
$70$	6.59831	+	4.31082i	0.788649	+	0.515241i
$71$			6.14583i			0.729375i	0.931130	+	0.364688i	$0.118824\pi$
$71$			6.14583i			0.729375i	−0.931130	+	0.364688i	$0.881176\pi$
$72$	3.13229	+	7.88598i	0.369144	+	0.929372i
$73$		−	2.16000i		−	0.252809i	−0.991979	−	0.126404i	$-0.959656\pi$
$73$		−	2.16000i		−	0.252809i	0.991979	−	0.126404i	$-0.0403437\pi$
$74$	−14.6059	+	3.23715i	−1.69791	+	0.376311i
$75$	−0.897876	−	0.379527i	−0.103678	−	0.0438240i
$76$	−8.83831	+	4.12010i	−1.01382	+	0.472608i
$77$	5.89782	−	1.50837i	0.672119	−	0.171895i
$78$	0.581964	−	0.207035i	0.0658944	−	0.0234421i
$79$	−2.84679	+	1.64360i	−0.320289	+	0.184919i	−0.651522	−	0.758630i	$-0.725869\pi$
$79$	−2.84679	+	1.64360i	−0.320289	+	0.184919i	0.331232	+	0.943549i	$0.392536\pi$
$80$	−7.91841	+	2.87994i	−0.885305	+	0.321988i
$81$	−7.66110	−	4.72309i	−0.851233	−	0.524788i
$82$	−1.79217	−	0.565185i	−0.197912	−	0.0624143i
$83$	4.56438	+	7.90574i	0.501006	+	0.867768i	0.999999	+	0.00116189i	$0.000369841\pi$
$83$	4.56438	+	7.90574i	0.501006	+	0.867768i	−0.498993	+	0.866606i	$0.666297\pi$
$84$	6.31749	−	6.63998i	0.689295	−	0.724481i
$85$	−4.84544	+	8.39255i	−0.525562	+	0.910300i
$86$	10.3652	−	9.49684i	1.11771	−	1.02407i
$87$	3.46801	+	1.46591i	0.371810	+	0.157162i
$88$	−2.49156	+	6.01214i	−0.265601	+	0.640897i
$89$			4.62446i			0.490191i	0.969499	+	0.245096i	$0.0788194\pi$
$89$			4.62446i			0.490191i	−0.969499	+	0.245096i	$0.921181\pi$
$90$	4.91057	−	7.46699i	0.517619	−	0.787090i
$91$	−0.466355	−	0.477126i	−0.0488873	−	0.0500164i
$92$	9.73528	+	0.852886i	1.01497	+	0.0889195i
$93$	−0.761555	−	6.12588i	−0.0789695	−	0.635225i
$94$	−10.3804	−	11.3296i	−1.07066	−	1.16856i
$95$	8.89457	+	5.13528i	0.912564	+	0.526869i
$96$	1.62886	+	9.66162i	0.166245	+	0.986084i
$97$	4.34667	−	2.50955i	0.441338	−	0.254807i	−0.262827	−	0.964843i	$-0.584655\pi$
$97$	4.34667	−	2.50955i	0.441338	−	0.254807i	0.704165	+	0.710036i	$0.251322\pi$
$98$	−9.37071	−	3.19215i	−0.946584	−	0.322456i
$99$	−1.69014	−	6.69264i	−0.169866	−	0.672635i
$100$	−0.921957	−	0.645724i	−0.0921957	−	0.0645724i
$101$	4.75755	−	2.74677i	0.473394	−	0.273314i	−0.244265	−	0.969708i	$-0.578547\pi$
$101$	4.75755	−	2.74677i	0.473394	−	0.273314i	0.717659	+	0.696394i	$0.245213\pi$
$102$	8.57960	+	7.30617i	0.849507	+	0.723419i
$103$	2.95680	−	5.12133i	0.291342	−	0.504619i	−0.682785	−	0.730619i	$-0.739232\pi$
$103$	2.95680	−	5.12133i	0.291342	−	0.504619i	0.974127	+	0.226000i	$0.0725649\pi$
$104$	0.707165	−	0.0929725i	0.0693433	−	0.00911670i
$105$	−9.54532	−	1.43807i	−0.931528	−	0.140341i
$106$	11.0203	−	2.44245i	1.07038	−	0.237232i
$107$		−	8.51213i		−	0.822899i	−0.911433	−	0.411450i	$-0.865023\pi$
$107$		−	8.51213i		−	0.822899i	0.911433	−	0.411450i	$-0.134977\pi$
$108$	−7.50737	−	7.18605i	−0.722397	−	0.691478i
$109$	−6.38002			−0.611095			−0.305548	−	0.952177i	$-0.598840\pi$
$109$	−6.38002			−0.611095			−0.305548	+	0.952177i	$0.598840\pi$
$110$	6.69203	−	1.48317i	0.638060	−	0.141415i
$111$	14.6164	−	11.0489i	1.38733	−	1.04872i
$112$	8.73923	−	5.96874i	0.825780	−	0.563993i
$113$	5.84315	−	10.1206i	0.549677	−	0.952069i	−0.448619	−	0.893723i	$-0.648084\pi$
$113$	5.84315	−	10.1206i	0.549677	−	0.952069i	0.998296	−	0.0583459i	$-0.0185826\pi$
$114$	7.74321	−	9.09281i	0.725218	−	0.851620i
$115$	−5.14640	−	8.91382i	−0.479904	−	0.831218i
$116$	3.56102	+	2.49408i	0.330633	+	0.231570i
$117$	−0.542603	+	0.527162i	−0.0501637	+	0.0487361i
$118$	3.14401	−	9.96946i	0.289429	−	0.917763i
$119$	3.28432	−	11.7204i	0.301073	−	1.07441i
$120$	7.35077	−	7.24286i	0.671030	−	0.661180i
$121$	−2.85289	+	4.94135i	−0.259354	+	0.449214i
$122$	15.0663	−	13.8041i	1.36404	−	1.24976i
$123$	2.28393	−	0.283932i	0.205935	−	0.0256013i
$124$	0.622087	−	7.10082i	0.0558650	−	0.637672i
$125$			11.7178i			1.04808i
$126$	−3.65161	+	10.6144i	−0.325311	+	0.945607i
$127$			13.8984i			1.23328i	0.787244	+	0.616642i	$0.211507\pi$
$127$			13.8984i			1.23328i	−0.787244	+	0.616642i	$0.788493\pi$
$128$	−0.498174	+	11.3027i	−0.0440328	+	0.999030i
$129$	−6.70346	+	15.8589i	−0.590207	+	1.39630i
$130$	−0.507484	−	0.553887i	−0.0445093	−	0.0485791i
$131$	7.18258	−	12.4406i	0.627545	−	1.08694i	−0.360498	−	0.932760i	$-0.617393\pi$
$131$	7.18258	−	12.4406i	0.627545	−	1.08694i	0.988043	−	0.154180i	$-0.0492735\pi$
$132$	−0.289255	−	7.96536i	−0.0251765	−	0.693295i
$133$	−12.4215	−	3.48078i	−1.07708	−	0.301822i
$134$	−11.4505	−	3.61108i	−0.989174	−	0.311950i
$135$	−1.66327	+	10.8184i	−0.143152	+	0.931101i
$136$	7.91955	+	10.3247i	0.679096	+	0.885340i
$137$	−1.07629	−	1.86419i	−0.0919538	−	0.159269i	0.816379	−	0.577516i	$-0.195978\pi$
$137$	−1.07629	−	1.86419i	−0.0919538	−	0.159269i	−0.908333	+	0.418247i	$0.862645\pi$
$138$	−11.2766	+	4.01166i	−0.959926	+	0.341496i
$139$	−8.26506	+	14.3155i	−0.701033	+	1.21423i	0.267071	+	0.963677i	$0.413944\pi$
$139$	−8.26506	+	14.3155i	−0.701033	+	1.21423i	−0.968104	+	0.250549i	$0.919389\pi$
$140$	−10.4295	−	3.93284i	−0.881454	−	0.332385i
$141$	17.3344	+	7.32716i	1.45982	+	0.617059i
$142$	−1.88069	−	8.48560i	−0.157824	−	0.712096i
$143$	−0.580227			−0.0485210
$144$	−6.73798	−	9.92974i	−0.561498	−	0.827478i
$145$		−	4.57900i		−	0.380265i
$146$	0.660982	+	2.98233i	0.0547033	+	0.246820i
$147$	12.0627	−	1.22069i	0.994919	−	0.100681i
$148$	19.1759	−	8.93913i	1.57625	−	0.734792i
$149$	−4.33757	+	7.51290i	−0.355348	+	0.615480i	−0.987177	−	0.159627i	$-0.948971\pi$
$149$	−4.33757	+	7.51290i	−0.355348	+	0.615480i	0.631830	+	0.775107i	$0.282304\pi$
$150$	1.35584	+	0.249257i	0.110704	+	0.0203517i
$151$	−2.31838	+	1.33852i	−0.188667	+	0.108927i	−0.591359	−	0.806409i	$-0.701408\pi$
$151$	−2.31838	+	1.33852i	−0.188667	+	0.108927i	0.402691	+	0.915336i	$0.368075\pi$
$152$	10.9423	−	8.39327i	0.887541	−	0.680784i
$153$	−13.2784	−	3.76416i	−1.07349	−	0.304314i
$154$	−7.68160	+	3.88742i	−0.619001	+	0.313257i
$155$	−6.50165	+	3.75373i	−0.522225	+	0.301507i
$156$	−0.740168	+	0.463942i	−0.0592608	+	0.0371451i
$157$	15.5179	+	8.95927i	1.23846	+	0.715028i	0.968780	−	0.247921i	$-0.0797474\pi$
$157$	15.5179	+	8.95927i	1.23846	+	0.715028i	0.269684	+	0.962949i	$0.413081\pi$
$158$	3.42764	−	3.14048i	0.272688	−	0.249843i
$159$	−11.0282	+	8.33648i	−0.874593	+	0.661126i
$160$	10.0517	−	6.39948i	0.794659	−	0.505923i
$161$	9.03645	+	9.24516i	0.712172	+	0.728620i
$162$	12.0231	+	4.17684i	0.944621	+	0.328164i
$163$		−	2.86313i		−	0.224258i	−0.993694	−	0.112129i	$-0.964233\pi$
$163$		−	2.86313i		−	0.224258i	0.993694	−	0.112129i	$-0.0357669\pi$
$164$	2.64742	+	0.231934i	0.206728	+	0.0181110i
$165$	−6.69684	+	5.06230i	−0.521348	+	0.394100i
$166$	−8.72132	−	9.51878i	−0.676906	−	0.738801i
$167$	3.53318	−	6.11964i	0.273405	−	0.473552i	−0.696326	−	0.717725i	$-0.745183\pi$
$167$	3.53318	−	6.11964i	0.273405	−	0.473552i	0.969732	+	0.244174i	$0.0785167\pi$
$168$	−6.69072	+	11.1011i	−0.516200	+	0.856468i
$169$	−6.46820	−	11.2033i	−0.497554	−	0.861789i
$170$	4.12194	−	13.0704i	0.316138	−	1.00246i
$171$	−3.98932	+	14.0727i	−0.305071	+	1.07616i
$172$	−11.4052	+	16.2842i	−0.869639	+	1.24166i
$173$	14.4716	−	8.35518i	1.10025	−	0.635232i	0.163967	−	0.986466i	$-0.447571\pi$
$173$	14.4716	−	8.35518i	1.10025	−	0.635232i	0.936288	+	0.351234i	$0.114238\pi$
$174$	−5.23690	−	0.962746i	−0.397008	−	0.0729856i
$175$	−0.368943	−	1.44259i	−0.0278895	−	0.109050i
$176$	1.60034	−	9.06346i	0.120630	−	0.683184i
$177$	1.57946	+	12.7050i	0.118719	+	0.954968i
$178$	−1.41513	−	6.38503i	−0.106069	−	0.478578i
$179$		−	13.2700i		−	0.991844i	−0.868367	−	0.495922i	$-0.834830\pi$
$179$		−	13.2700i		−	0.991844i	0.868367	−	0.495922i	$-0.165170\pi$
$180$	−4.49509	+	11.8124i	−0.335044	+	0.880447i
$181$		−	14.7060i		−	1.09309i	−0.837431	−	0.546543i	$-0.815943\pi$
$181$		−	14.7060i		−	1.09309i	0.837431	−	0.546543i	$-0.184057\pi$
$182$	0.789906	+	0.516063i	0.0585517	+	0.0382531i
$183$	−9.74379	+	23.0516i	−0.720281	+	1.70403i
$184$	−13.7026	+	1.80151i	−1.01017	+	0.132809i
$185$	−19.2980	−	11.1417i	−1.41882	−	0.819155i
$186$	2.92607	+	8.22502i	0.214550	+	0.603088i
$187$	−5.29273	−	9.16727i	−0.387043	−	0.670377i
$188$	17.7993	+	12.4664i	1.29815	+	0.909203i
$189$	−1.34285	−	13.6820i	−0.0976777	−	0.995218i
$190$	−13.8523	−	4.36850i	−1.00495	−	0.316924i
$191$	−13.5569	+	7.82708i	−0.980943	+	0.566348i	−0.902555	−	0.430575i	$-0.858311\pi$
$191$	−13.5569	+	7.82708i	−0.980943	+	0.566348i	−0.0783882	+	0.996923i	$0.524977\pi$
$192$	−5.20554	−	12.8414i	−0.375677	−	0.926750i
$193$	2.25489	−	3.90558i	0.162310	−	0.281130i	−0.773386	−	0.633935i	$-0.781439\pi$
$193$	2.25489	−	3.90558i	0.162310	−	0.281130i	0.935697	+	0.352805i	$0.114772\pi$
$194$	−5.23354	+	4.79509i	−0.375746	+	0.344267i
$195$	0.847455	+	0.358214i	0.0606875	+	0.0256522i
$196$	13.9151	+	1.53990i	0.993932	+	0.109993i
$197$	−7.04052			−0.501616			−0.250808	−	0.968037i	$-0.580696\pi$
$197$	−7.04052			−0.501616			−0.250808	+	0.968037i	$0.580696\pi$
$198$	4.38161	+	8.72338i	0.311388	+	0.619944i
$199$	1.64695			0.116749			0.0583747	−	0.998295i	$-0.481408\pi$
$199$	1.64695			0.116749			0.0583747	+	0.998295i	$0.481408\pi$
$200$	1.47055	+	0.609428i	0.103984	+	0.0430931i
$201$	14.5925	−	1.81410i	1.02927	−	0.127957i
$202$	−5.72825	+	5.24835i	−0.403038	+	0.369273i
$203$	1.42503	+	5.57195i	0.100017	+	0.391074i
$204$	−14.0817	−	7.46225i	−0.985916	−	0.522462i
$205$	−1.39951	−	2.42403i	−0.0977463	−	0.169302i
$206$	−2.51530	+	7.97587i	−0.175249	+	0.555705i
$207$	10.5139	−	10.2147i	0.730766	−	0.709970i
$208$	−0.947939	+	0.344768i	−0.0657278	+	0.0239053i
$209$	−9.71563	+	5.60932i	−0.672045	+	0.388005i
$210$	13.6194	−	0.935414i	0.939827	−	0.0645497i
$211$	−7.67682	−	4.43221i	−0.528494	−	0.305126i	0.211909	−	0.977289i	$-0.432032\pi$
$211$	−7.67682	−	4.43221i	−0.528494	−	0.305126i	−0.740403	+	0.672163i	$0.765365\pi$
$212$	−14.4684	+	6.74463i	−0.993692	+	0.463223i
$213$	6.41908	+	8.49170i	0.439828	+	0.581842i
$214$	2.60480	+	11.7528i	0.178060	+	0.803404i
$215$	20.9394			1.42805
$216$	12.5645	+	7.62452i	0.854906	+	0.518783i
$217$	6.74333	−	6.59110i	0.457767	−	0.447433i
$218$	8.80895	−	1.95235i	0.596618	−	0.132230i
$219$	−2.25604	−	2.98448i	−0.152449	−	0.201672i
$220$	−8.78588	+	4.09566i	−0.592344	+	0.276129i
$221$	−0.580064	+	1.00470i	−0.0390193	+	0.0675835i
$222$	−16.8000	+	19.7281i	−1.12754	+	1.32406i
$223$	8.51444	+	14.7474i	0.570169	+	0.987561i	0.996548	+	0.0830169i	$0.0264555\pi$
$223$	8.51444	+	14.7474i	0.570169	+	0.987561i	−0.426379	+	0.904544i	$0.640211\pi$
$224$	−10.2398	+	10.9154i	−0.684178	+	0.729315i
$225$	−1.63700	+	0.413404i	−0.109133	+	0.0275603i
$226$	−4.97067	+	15.7617i	−0.330644	+	1.04845i
$227$	−3.29592	−	5.70870i	−0.218758	−	0.378900i	0.735671	−	0.677339i	$-0.236867\pi$
$227$	−3.29592	−	5.70870i	−0.218758	−	0.378900i	−0.954429	+	0.298440i	$0.903534\pi$
$228$	−7.90863	+	14.9240i	−0.523762	+	0.988368i
$229$	−15.0244	−	8.67434i	−0.992840	−	0.573217i	−0.0867182	−	0.996233i	$-0.527638\pi$
$229$	−15.0244	−	8.67434i	−0.992840	−	0.573217i	−0.906122	+	0.423016i	$0.860971\pi$
$230$	9.83340	+	10.7325i	0.648395	+	0.707683i
$231$	6.57360	−	8.24417i	0.432511	−	0.542427i
$232$	−5.67995	−	2.35389i	−0.372907	−	0.154541i
$233$	1.69802			0.111241			0.0556204	−	0.998452i	$-0.482286\pi$
$233$	1.69802			0.111241			0.0556204	+	0.998452i	$0.482286\pi$
$234$	0.587860	−	0.893899i	0.0384296	−	0.0584360i
$235$		−	22.8876i		−	1.49302i
$236$	−1.29020	+	14.7270i	−0.0839850	+	0.958648i
$237$	−2.21675	+	5.24433i	−0.143993	+	0.340656i
$238$	−0.948130	+	17.1875i	−0.0614581	+	1.11410i
$239$	−24.4418	−	14.1115i	−1.58101	−	0.912795i	−0.994713	−	0.102698i	$-0.967252\pi$
$239$	−24.4418	−	14.1115i	−1.58101	−	0.912795i	−0.586295	−	0.810097i	$-0.699414\pi$
$240$	−7.93289	+	12.2497i	−0.512066	+	0.790714i
$241$	23.6006	−	13.6258i	1.52025	−	0.877717i	0.520535	−	0.853840i	$-0.325733\pi$
$241$	23.6006	−	13.6258i	1.52025	−	0.877717i	0.999715	−	0.0238762i	$-0.00760075\pi$
$242$	2.42691	−	7.69559i	0.156008	−	0.494691i
$243$	−15.5184	+	1.47582i	−0.995508	+	0.0946738i
$244$	−16.5780	+	23.6699i	−1.06130	+	1.51531i
$245$	−7.07919	−	12.9348i	−0.452273	−	0.826372i
$246$	−3.06656	+	1.09093i	−0.195517	+	0.0695554i
$247$	1.06480	+	0.614762i	0.0677515	+	0.0391164i
$248$	1.31400	+	9.99453i	0.0834392	+	0.634653i
$249$	14.5639	+	6.15605i	0.922947	+	0.390124i
$250$	−3.58578	−	16.1789i	−0.226785	−	1.02325i
$251$	−29.8268			−1.88265			−0.941326	−	0.337498i	$-0.890419\pi$
$251$	−29.8268			−1.88265			−0.941326	+	0.337498i	$0.890419\pi$
$252$	1.79369	−	15.7728i	0.112992	−	0.993596i
$253$	11.2429			0.706837
$254$	−4.25305	−	19.1897i	−0.266860	−	1.20407i
$255$	2.07074	+	16.6569i	0.129675	+	1.04309i
$256$	−2.77092	−	15.7582i	−0.173182	−	0.984890i
$257$	22.9770	+	13.2658i	1.43326	+	0.827496i	0.997368	−	0.0725013i	$-0.0230982\pi$
$257$	22.9770	+	13.2658i	1.43326	+	0.827496i	0.435896	+	0.899997i	$0.356431\pi$
$258$	4.40255	−	23.9479i	0.274091	−	1.49093i
$259$	26.9501	+	7.55204i	1.67460	+	0.469261i
$260$	0.870183	+	0.609462i	0.0539664	+	0.0377972i
$261$	6.32284	−	1.59676i	0.391374	−	0.0988368i
$262$	−6.11011	+	19.3748i	−0.377484	+	1.19698i
$263$	−3.65334	+	2.10926i	−0.225274	+	0.130062i	−0.608390	−	0.793638i	$-0.708184\pi$
$263$	−3.65334	+	2.10926i	−0.225274	+	0.130062i	0.383116	+	0.923700i	$0.374851\pi$
$264$	2.83686	+	10.9093i	0.174597	+	0.671423i
$265$	14.5605	+	8.40649i	0.894443	+	0.516407i
$266$	18.2156	+	1.00484i	1.11687	+	0.0616110i
$267$	4.83007	+	6.38962i	0.295595	+	0.391038i
$268$	16.9149	+	1.48187i	1.03324	+	0.0905198i
$269$		−	28.6035i		−	1.74399i	−0.489519	−	0.871993i	$-0.662828\pi$
$269$		−	28.6035i		−	1.74399i	0.489519	−	0.871993i	$-0.337172\pi$
$270$	−1.01405	−	15.4461i	−0.0617132	−	0.940017i
$271$	1.52227			0.0924715			0.0462357	−	0.998931i	$-0.485277\pi$
$271$	1.52227			0.0924715			0.0462357	+	0.998931i	$0.485277\pi$
$272$	−14.0941	−	11.8320i	−0.854578	−	0.717421i
$273$	−1.14270	−	0.172156i	−0.0691595	−	0.0104193i
$274$	2.05651	+	2.24455i	0.124238	+	0.135598i
$275$	−1.12146	−	0.647475i	−0.0676265	−	0.0390442i
$276$	14.3421	−	8.98969i	0.863290	−	0.541116i
$277$	3.40358	+	5.89517i	0.204501	+	0.354206i	0.949974	−	0.312330i	$-0.101109\pi$
$277$	3.40358	+	5.89517i	0.204501	+	0.354206i	−0.745472	+	0.666536i	$0.767776\pi$
$278$	7.03096	−	22.2947i	0.421689	−	1.33715i
$279$	−7.45049	−	7.66873i	−0.446049	−	0.459115i
$280$	15.6036	+	2.23857i	0.932493	+	0.133780i
$281$	13.4890	+	23.3636i	0.804684	+	1.39375i	0.916504	+	0.400025i	$0.130998\pi$
$281$	13.4890	+	23.3636i	0.804684	+	1.39375i	−0.111821	+	0.993728i	$0.535668\pi$
$282$	−26.1760	−	4.81217i	−1.55876	−	0.286560i
$283$	6.69636	−	11.5984i	0.398057	−	0.689455i	−0.595429	−	0.803408i	$-0.703018\pi$
$283$	6.69636	−	11.5984i	0.398057	−	0.689455i	0.993486	+	0.113953i	$0.0363512\pi$
$284$	5.19336	+	11.1406i	0.308169	+	0.661075i
$285$	17.6532	−	2.19461i	1.04569	−	0.129997i
$286$	0.801125	−	0.177555i	0.0473715	−	0.0104991i
$287$	2.45738	+	2.51413i	0.145054	+	0.148405i
$288$	12.3418	+	11.6482i	0.727247	+	0.686376i
$289$	−4.16495			−0.244997
$290$	1.40122	+	6.32227i	0.0822826	+	0.371256i
$291$	3.38468	−	8.00739i	0.198413	−	0.469401i
$292$	−1.82525	−	3.91547i	−0.106815	−	0.229135i
$293$	−20.0411	−	11.5707i	−1.17081	−	0.675969i	−0.216942	−	0.976185i	$-0.569608\pi$
$293$	−20.0411	−	11.5707i	−1.17081	−	0.675969i	−0.953871	+	0.300215i	$0.902942\pi$
$294$	−16.2816	+	5.37674i	−0.949562	+	0.313578i
$295$	13.4844	−	7.78520i	0.785090	−	0.453272i
$296$	−23.7409	+	18.2104i	−1.37991	+	1.05846i
$297$	−9.32548	−	7.48194i	−0.541119	−	0.434146i
$298$	3.68990	−	11.7005i	0.213750	−	0.677790i
$299$	−0.616092	−	1.06710i	−0.0356295	−	0.0617122i
$300$	−1.94830	+	0.0707510i	−0.112485	+	0.00408481i
$301$	−25.4800	+	6.51653i	−1.46864	+	0.375607i
$302$	2.79141	−	2.55756i	0.160628	−	0.147171i
$303$	3.70462	−	8.76430i	0.212825	−	0.503496i
$304$	−12.5398	+	14.9371i	−0.719205	+	0.856704i
$305$	30.4363			1.74278
$306$	19.4855	+	1.13389i	1.11391	+	0.0648200i
$307$	10.2865			0.587083			0.293542	−	0.955946i	$-0.405166\pi$
$307$	10.2865			0.587083			0.293542	+	0.955946i	$0.405166\pi$
$308$	9.41647	−	7.71804i	0.536553	−	0.439776i
$309$	−1.26361	−	10.1644i	−0.0718845	−	0.578233i
$310$	7.82821	−	7.17238i	0.444613	−	0.407364i
$311$	−0.476652	+	0.825585i	−0.0270284	+	0.0468146i	−0.879223	−	0.476410i	$-0.841938\pi$
$311$	−0.476652	+	0.825585i	−0.0270284	+	0.0468146i	0.852195	+	0.523225i	$0.175271\pi$
$312$	0.879985	−	0.867067i	0.0498194	−	0.0490880i
$313$	−25.2144	+	14.5576i	−1.42520	+	0.822842i	−0.996737	−	0.0807151i	$-0.974280\pi$
$313$	−25.2144	+	14.5576i	−1.42520	+	0.822842i	−0.428467	+	0.903557i	$0.640946\pi$
$314$	−24.1674	−	7.62151i	−1.36384	−	0.430107i
$315$	−14.6908	+	7.98274i	−0.827733	+	0.449777i
$316$	−3.77155	+	5.38498i	−0.212166	+	0.302929i
$317$	0.119800	+	0.207499i	0.00672861	+	0.0116543i	0.869370	−	0.494162i	$-0.164525\pi$
$317$	0.119800	+	0.207499i	0.00672861	+	0.0116543i	−0.862641	+	0.505816i	$0.831192\pi$
$318$	12.6757	−	14.8850i	0.710817	−	0.834709i
$319$	4.33159	+	2.50085i	0.242523	+	0.140021i
$320$	−11.9202	+	11.9117i	−0.666360	+	0.665887i
$321$	−8.89060	−	11.7612i	−0.496225	−	0.656448i
$322$	−15.3058	−	9.99962i	−0.852960	−	0.557257i
$323$			22.4310i			1.24809i
$324$	−17.8785	−	2.08782i	−0.993250	−	0.115990i
$325$			0.141922i			0.00787241i
$326$	0.876147	+	3.95315i	0.0485253	+	0.218945i
$327$	−8.81529	+	6.66369i	−0.487487	+	0.368503i
$328$	−3.72629	+	0.489903i	−0.205750	+	0.0270503i
$329$	7.12284	+	27.8507i	0.392695	+	1.53546i
$330$	7.69727	−	9.03887i	0.423721	−	0.497573i
$331$	−7.65430	+	4.41921i	−0.420718	+	0.242902i	−0.695385	−	0.718638i	$-0.744766\pi$
$331$	−7.65430	+	4.41921i	−0.420718	+	0.242902i	0.274666	+	0.961540i	$0.411433\pi$
$332$	14.9544	+	10.4739i	0.820732	+	0.574827i
$333$	8.65539	−	30.5326i	0.474312	−	1.67318i
$334$	−3.00562	+	9.53063i	−0.164460	+	0.521493i
$335$	−8.94176	−	15.4876i	−0.488541	−	0.846177i
$336$	5.84089	−	17.3748i	0.318647	−	0.947874i
$337$	6.89773	−	11.9472i	0.375743	−	0.650806i	−0.614695	−	0.788765i	$-0.710721\pi$
$337$	6.89773	−	11.9472i	0.375743	−	0.650806i	0.990438	+	0.137959i	$0.0440541\pi$
$338$	12.3590	+	13.4891i	0.672242	+	0.733711i
$339$	−2.49712	−	20.0866i	−0.135625	−	1.09096i
$340$	−1.69151	+	19.3078i	−0.0917353	+	1.04711i
$341$		−	8.20048i		−	0.444081i
$342$	1.20171	−	20.6510i	0.0649812	−	1.11668i
$343$	12.6397	+	13.5365i	0.682481	+	0.730904i
$344$	10.7641	−	25.9739i	0.580363	−	1.40042i
$345$	−16.4209	−	6.94103i	−0.884073	−	0.373692i
$346$	−17.4243	+	15.9645i	−0.936735	+	0.858258i
$347$	−2.29653	−	1.32590i	−0.123284	−	0.0711782i	0.437090	−	0.899418i	$-0.356009\pi$
$347$	−2.29653	−	1.32590i	−0.123284	−	0.0711782i	−0.560374	+	0.828240i	$0.689343\pi$
$348$	7.52525	−	0.273273i	0.403396	−	0.0146490i
$349$	−3.36079	+	1.94035i	−0.179899	+	0.103865i	−0.587245	−	0.809409i	$-0.699788\pi$
$349$	−3.36079	+	1.94035i	−0.179899	+	0.103865i	0.407346	+	0.913274i	$0.366454\pi$
$350$	0.950851	+	1.87890i	0.0508251	+	0.100431i
$351$	−0.199116	+	1.29511i	−0.0106280	+	0.0691278i
$352$	0.563904	+	13.0037i	0.0300562	+	0.693101i
$353$	−27.8946	+	16.1049i	−1.48468	+	0.857180i	−0.999848	−	0.0174283i	$-0.994452\pi$
$353$	−27.8946	+	16.1049i	−1.48468	+	0.857180i	−0.484831	+	0.874608i	$0.661119\pi$
$354$	−6.06864	−	17.0586i	−0.322545	−	0.906655i
$355$	6.47299	−	11.2115i	0.343551	−	0.595047i
$356$	3.90777	+	8.38282i	0.207111	+	0.444289i
$357$	−7.70356	−	19.6245i	−0.407716	−	1.03864i
$358$	4.06074	+	18.3220i	0.214617	+	0.968346i
$359$			16.9972i			0.897079i	0.893763	+	0.448539i	$0.148056\pi$
$359$			16.9972i			0.897079i	−0.893763	+	0.448539i	$0.851944\pi$
$360$	2.59168	−	17.6851i	0.136594	−	0.932085i
$361$	4.77275			0.251197
$362$	4.50018	+	20.3047i	0.236524	+	1.06719i
$363$	1.21921	+	9.80721i	0.0639918	+	0.514745i
$364$	−1.24855	−	0.470813i	−0.0654418	−	0.0246773i
$365$	−2.27499	+	3.94039i	−0.119078	+	0.206249i
$366$	6.39930	−	34.8093i	0.334497	−	1.81951i
$367$	−0.947065	−	1.64036i	−0.0494364	−	0.0856263i	0.840248	−	0.542202i	$-0.182409\pi$
$367$	−0.947065	−	1.64036i	−0.0494364	−	0.0856263i	−0.889685	+	0.456575i	$0.849076\pi$
$368$	18.3680	−	6.68049i	0.957498	−	0.348244i
$369$	2.85915	−	2.77779i	0.148842	−	0.144606i
$370$	30.0544	+	9.47807i	1.56245	+	0.492741i
$371$	−20.3341	−	5.69806i	−1.05569	−	0.295829i
$372$	−6.55699	−	10.4610i	−0.339964	−	0.542375i
$373$	−6.46642	+	11.2002i	−0.334818	+	0.579922i	−0.983450	−	0.181180i	$-0.942008\pi$
$373$	−6.46642	+	11.2002i	−0.334818	+	0.579922i	0.648632	+	0.761103i	$0.275342\pi$
$374$	10.1130	+	11.0377i	0.522931	+	0.570746i
$375$	12.2388	+	16.1906i	0.632011	+	0.836078i
$376$	−28.3905	−	11.7656i	−1.46413	−	0.606767i
$377$		−	0.548168i		−	0.0282321i
$378$	6.04091	+	18.4799i	0.310711	+	0.950505i
$379$		−	19.4116i		−	0.997106i	−0.866859	−	0.498553i	$-0.833865\pi$
$379$		−	19.4116i		−	0.997106i	0.866859	−	0.498553i	$-0.166135\pi$
$380$	20.4628	+	1.79270i	1.04972	+	0.0919634i
$381$	14.5164	+	19.2035i	0.743695	+	0.983823i
$382$	16.3230	−	14.9555i	0.835156	−	0.765188i
$383$	−6.44294	+	11.1595i	−0.329219	+	0.570224i	−0.982357	−	0.187015i	$-0.940119\pi$
$383$	−6.44294	+	11.1595i	−0.329219	+	0.570224i	0.653138	+	0.757239i	$0.273452\pi$
$384$	11.1169	+	16.1373i	0.567309	+	0.823505i
$385$	−12.3478	−	3.46013i	−0.629302	−	0.176345i
$386$	−1.91820	+	6.08249i	−0.0976337	+	0.309591i
$387$	7.30183	+	28.9138i	0.371173	+	1.46977i
$388$	5.75865	−	8.22214i	0.292351	−	0.417416i
$389$	−9.53163	−	16.5093i	−0.483273	−	0.837053i	0.516543	−	0.856261i	$-0.327219\pi$
$389$	−9.53163	−	16.5093i	−0.483273	−	0.837053i	−0.999816	+	0.0192083i	$0.993885\pi$
$390$	−1.27971	−	0.235260i	−0.0648004	−	0.0119128i
$391$	11.2398	−	19.4678i	0.568419	−	0.984531i
$392$	−19.6839	+	2.13199i	−0.994185	+	0.107682i
$393$	−3.06954	−	24.6911i	−0.154838	−	1.24550i
$394$	9.72091	−	2.15447i	0.489732	−	0.108541i
$395$	6.92437			0.348403
$396$	−8.71918	−	10.7036i	−0.438155	−	0.537878i
$397$			2.33175i			0.117027i	0.998287	+	0.0585135i	$0.0186361\pi$
$397$			2.33175i			0.117027i	−0.998287	+	0.0585135i	$0.981364\pi$
$398$	−2.27396	+	0.503984i	−0.113983	+	0.0252625i
$399$	−20.7983	+	8.16437i	−1.04122	+	0.408730i
$400$	−2.21690	−	0.391439i	−0.110845	−	0.0195720i
$401$	8.17411	−	14.1580i	0.408195	−	0.707015i	−0.586492	−	0.809955i	$-0.699492\pi$
$401$	8.17411	−	14.1580i	0.408195	−	0.707015i	0.994688	+	0.102940i	$0.0328249\pi$
$402$	−19.5928	+	6.97019i	−0.977201	+	0.347641i
$403$	−0.778335	+	0.449372i	−0.0387716	+	0.0223848i
$404$	6.30300	−	8.99935i	0.313586	−	0.447735i
$405$	9.00127	+	16.6850i	0.447277	+	0.829086i
$406$	−3.67263	−	7.25717i	−0.182269	−	0.360167i
$407$	21.0794	−	12.1702i	1.04487	−	0.603255i
$408$	21.7263	+	5.99406i	1.07561	+	0.296750i
$409$	16.5082	+	9.53101i	0.816278	+	0.471278i	0.849131	−	0.528182i	$-0.177126\pi$
$409$	16.5082	+	9.53101i	0.816278	+	0.471278i	−0.0328535	+	0.999460i	$0.510459\pi$
$410$	2.67410	+	2.91861i	0.132064	+	0.144140i
$411$	−3.43419	−	1.45161i	−0.169396	−	0.0716028i
$412$	1.03220	−	11.7821i	0.0508529	−	0.580461i
$413$	−13.9856	+	13.6699i	−0.688186	+	0.672651i
$414$	−11.3908	+	17.3209i	−0.559829	+	0.851274i
$415$		−	19.2294i		−	0.943936i
$416$	1.20333	−	0.766103i	0.0589979	−	0.0375613i
$417$	3.53215	+	28.4123i	0.172970	+	1.39136i
$418$	11.6980	−	10.7179i	0.572166	−	0.524231i
$419$	5.27532	−	9.13712i	0.257716	−	0.446377i	−0.707914	−	0.706299i	$-0.750363\pi$
$419$	5.27532	−	9.13712i	0.257716	−	0.446377i	0.965630	+	0.259922i	$0.0836968\pi$
$420$	−18.5182	+	5.45920i	−0.903594	+	0.266382i
$421$	17.6583	+	30.5850i	0.860611	+	1.49062i	0.871340	+	0.490679i	$0.163251\pi$
$421$	17.6583	+	30.5850i	0.860611	+	1.49062i	−0.0107298	+	0.999942i	$0.503415\pi$
$422$	11.9558	+	3.77041i	0.581997	+	0.183541i
$423$	31.6040	−	7.98120i	1.53664	−	0.388059i
$424$	17.9127	−	13.7398i	0.869917	−	0.667266i
$425$	−2.24229	+	1.29459i	−0.108767	+	0.0627966i
$426$	−11.4614	−	9.76026i	−0.555308	−	0.472886i
$427$	−37.0363	+	9.47207i	−1.79231	+	0.458386i
$428$	−7.19294	−	15.4301i	−0.347684	−	0.745841i
$429$	−0.801701	+	0.606025i	−0.0387065	+	0.0292592i
$430$	−28.9112	+	6.40766i	−1.39422	+	0.309005i
$431$			1.78484i			0.0859726i	0.999076	+	0.0429863i	$0.0136872\pi$
$431$			1.78484i			0.0859726i	−0.999076	+	0.0429863i	$0.986313\pi$
$432$	−19.6811	−	6.68237i	−0.946908	−	0.321506i
$433$			6.52824i			0.313727i	0.987620	+	0.156864i	$0.0501383\pi$
$433$			6.52824i			0.313727i	−0.987620	+	0.156864i	$0.949862\pi$
$434$	−7.29363	+	11.1639i	−0.350105	+	0.535885i
$435$	−4.78259	−	6.32682i	−0.229308	−	0.303348i
$436$	−11.5652	+	5.39126i	−0.553871	+	0.258195i
$437$	−20.6324	−	11.9121i	−0.986980	−	0.569833i
$438$	4.02821	+	3.43032i	0.192475	+	0.163907i
$439$	7.67744	+	13.2977i	0.366424	+	0.634665i	0.989004	−	0.147891i	$-0.0472486\pi$
$439$	7.67744	+	13.2977i	0.366424	+	0.634665i	−0.622579	+	0.782557i	$0.713915\pi$
$440$	10.8774	−	8.34348i	0.518561	−	0.397760i
$441$	15.3922	−	14.2857i	0.732960	−	0.680272i
$442$	0.493451	−	1.56470i	0.0234711	−	0.0744254i
$443$	11.2566	−	6.49898i	0.534816	−	0.308776i	−0.208160	−	0.978095i	$-0.566747\pi$
$443$	11.2566	−	6.49898i	0.534816	−	0.308776i	0.742975	+	0.669319i	$0.233414\pi$
$444$	17.1589	−	32.3797i	0.814323	−	1.53667i
$445$	4.87063	−	8.43618i	0.230890	−	0.399913i
$446$	−16.2688	−	17.7564i	−0.770351	−	0.840791i
$447$	1.85370	+	14.9110i	0.0876770	+	0.705267i
$448$	10.7980	−	18.2045i	0.510159	−	0.860080i
$449$	−30.5126			−1.43998			−0.719989	−	0.693985i	$-0.755853\pi$
$449$	−30.5126			−1.43998			−0.719989	+	0.693985i	$0.755853\pi$
$450$	2.13371	−	1.07173i	0.100584	−	0.0505218i
$451$	3.05741			0.143968
$452$	2.03981	−	23.2834i	0.0959445	−	1.09516i
$453$	−1.80528	+	4.27090i	−0.0848196	+	0.200664i
$454$	6.29763	+	6.87347i	0.295562	+	0.322588i
$455$	0.348225	+	1.36158i	0.0163250	+	0.0638318i
$456$	6.35261	−	23.0259i	0.297488	−	1.07828i
$457$	−16.7185	−	28.9573i	−0.782060	−	1.35457i	−0.930740	−	0.365682i	$-0.880836\pi$
$457$	−16.7185	−	28.9573i	−0.782060	−	1.35457i	0.148680	−	0.988885i	$-0.452498\pi$
$458$	23.3988	+	7.37912i	1.09335	+	0.344804i
$459$	−22.2783	+	8.66782i	−1.03986	+	0.404579i
$460$	−16.8613	−	11.8094i	−0.786164	−	0.550616i
$461$	8.42658	−	4.86509i	0.392465	−	0.226590i	−0.290763	−	0.956795i	$-0.593909\pi$
$461$	8.42658	−	4.86509i	0.392465	−	0.226590i	0.683228	+	0.730206i	$0.260576\pi$
$462$	−6.55343	+	13.3944i	−0.304893	+	0.623163i
$463$	−7.80112	−	4.50398i	−0.362549	−	0.209318i	0.307650	−	0.951500i	$-0.400458\pi$
$463$	−7.80112	−	4.50398i	−0.362549	−	0.209318i	−0.670198	+	0.742182i	$0.733791\pi$
$464$	8.56268	+	1.51192i	0.397512	+	0.0701891i
$465$	−5.06272	+	11.9773i	−0.234778	+	0.555432i
$466$	−2.34447	+	0.519610i	−0.108605	+	0.0240705i
$467$	6.77334			0.313433			0.156716	−	0.987644i	$-0.449909\pi$
$467$	6.77334			0.313433			0.156716	+	0.987644i	$0.449909\pi$
$468$	−0.538122	+	1.41411i	−0.0248747	+	0.0653671i
$469$	15.7007	+	16.0633i	0.724989	+	0.741733i
$470$	7.00383	+	31.6011i	0.323063	+	1.45765i
$471$	30.7987	−	3.82882i	1.41913	−	0.176423i
$472$	−2.72523	−	20.7286i	−0.125439	−	0.954109i
$473$	−11.4361	+	19.8080i	−0.525834	+	0.910772i
$474$	1.45586	−	7.91924i	0.0668700	−	0.363743i
$475$	1.37202	+	2.37642i	0.0629528	+	0.109037i
$476$	−3.95046	−	24.0211i	−0.181069	−	1.10100i
$477$	−6.53055	+	23.0371i	−0.299013	+	1.05479i
$478$	38.0653	+	12.0044i	1.74106	+	0.549069i
$479$	−2.68770	−	4.65524i	−0.122804	−	0.212703i	0.798068	−	0.602567i	$-0.205855\pi$
$479$	−2.68770	−	4.65524i	−0.122804	−	0.212703i	−0.920873	+	0.389864i	$0.872522\pi$
$480$	7.20448	−	19.3408i	0.328838	−	0.882783i
$481$	−2.31023	−	1.33381i	−0.105337	−	0.0608166i
$482$	−28.4160	+	26.0353i	−1.29431	+	1.18588i
$483$	22.1419	+	3.33582i	1.00749	+	0.151785i
$484$	−0.995928	+	11.3680i	−0.0452694	+	0.516728i
$485$	−10.5726			−0.480076
$486$	20.9748	−	6.78648i	0.951438	−	0.307841i
$487$		−	14.5792i		−	0.660648i	−0.943868	−	0.330324i	$-0.892842\pi$
$487$		−	14.5792i		−	0.660648i	0.943868	−	0.330324i	$-0.107158\pi$
$488$	15.6462	−	37.7542i	0.708268	−	1.70905i
$489$	−2.99043	−	3.95599i	−0.135232	−	0.178896i
$490$	13.7325	+	15.6928i	0.620370	+	0.708930i
$491$	7.49552	+	4.32754i	0.338268	+	0.195299i	0.659506	−	0.751699i	$-0.270766\pi$
$491$	7.49552	+	4.32754i	0.338268	+	0.195299i	−0.321238	+	0.946999i	$0.604099\pi$
$492$	3.90019	−	2.44466i	0.175834	−	0.110214i
$493$	8.66075	−	5.00029i	0.390061	−	0.225202i
$494$	−1.65830	−	0.522968i	−0.0746105	−	0.0235294i
$495$	−3.96566	+	13.9892i	−0.178243	+	0.628767i
$496$	−4.87268	−	13.3974i	−0.218790	−	0.601563i
$497$	−4.38750	+	15.6572i	−0.196806	+	0.702322i
$498$	−21.9923	−	4.04303i	−0.985497	−	0.181173i
$499$	34.8419	+	20.1160i	1.55974	+	0.900516i	0.997281	+	0.0736908i	$0.0234778\pi$
$499$	34.8419	+	20.1160i	1.55974	+	0.900516i	0.562459	+	0.826825i	$0.309856\pi$
$500$	9.90184	+	21.2411i	0.442824	+	0.949932i
$501$	−1.50993	−	12.1458i	−0.0674588	−	0.542634i
$502$	41.1822	−	9.12731i	1.83805	−	0.407372i
$503$	−3.02477			−0.134868			−0.0674339	−	0.997724i	$-0.521481\pi$
$503$	−3.02477			−0.134868			−0.0674339	+	0.997724i	$0.521481\pi$
$504$	2.35008	+	22.3266i	0.104681	+	0.994506i
$505$	−11.5720			−0.514946
$506$	−15.5232	+	3.44045i	−0.690091	+	0.152947i
$507$	−20.6385	−	8.72377i	−0.916588	−	0.387436i
$508$	11.7445	+	25.1939i	0.521076	+	1.11780i
$509$	8.81165	+	5.08741i	0.390569	+	0.225495i	0.682407	−	0.730973i	$-0.260933\pi$
$509$	8.81165	+	5.08741i	0.390569	+	0.225495i	−0.291837	+	0.956468i	$0.594267\pi$
$510$	−7.95627	−	22.3646i	−0.352309	−	0.990323i
$511$	1.54202	−	5.50285i	0.0682151	−	0.243432i
$512$	8.64801	+	20.9096i	0.382192	+	0.924083i
$513$	9.18631	+	23.6109i	0.405585	+	1.04245i
$514$	−35.7840	−	11.2850i	−1.57836	−	0.497759i
$515$	−10.7879	+	6.22840i	−0.475372	+	0.274456i
$516$	1.24965	+	34.4123i	0.0550129	+	1.51491i
$517$	21.6509	+	12.5002i	0.952207	+	0.549757i
$518$	−39.5213	−	2.18015i	−1.73647	−	0.0957902i
$519$	11.2688	−	26.6594i	0.494644	−	1.17022i
$520$	−1.38797	−	0.575205i	−0.0608666	−	0.0252244i
$521$		−	6.75953i		−	0.296140i	−0.988977	−	0.148070i	$-0.952694\pi$
$521$		−	6.75953i		−	0.296140i	0.988977	−	0.148070i	$-0.0473061\pi$
$522$	−8.24139	+	4.13951i	−0.360716	+	0.181182i
$523$	7.45208			0.325857			0.162928	−	0.986638i	$-0.447906\pi$
$523$	7.45208			0.325857			0.162928	+	0.986638i	$0.447906\pi$
$524$	2.50740	−	28.6207i	0.109536	−	1.25030i
$525$	−2.01650	−	1.60788i	−0.0880073	−	0.0701737i
$526$	4.39874	−	4.03023i	0.191794	−	0.175726i
$527$	−14.1997	−	8.19817i	−0.618547	−	0.357118i
$528$	−7.25524	−	14.1945i	−0.315744	−	0.617736i
$529$	0.437880	+	0.758431i	0.0190383	+	0.0329752i
$530$	−22.6763	−	7.15127i	−0.984993	−	0.310631i
$531$	15.4523	+	15.9049i	0.670571	+	0.690213i
$532$	−25.4580	+	4.18677i	−1.10374	+	0.181519i
$533$	−0.167541	−	0.290189i	−0.00725699	−	0.0125695i
$534$	−8.62421	−	7.34416i	−0.373206	−	0.317813i
$535$	−8.96527	+	15.5283i	−0.387602	+	0.671347i
$536$	−23.8080	+	3.13008i	−1.02835	+	0.135199i
$537$	−13.8600	−	18.3351i	−0.598102	−	0.791219i
$538$	8.75296	+	39.4931i	0.377367	+	1.70267i
$539$	16.1022	+	0.367699i	0.693572	+	0.0158379i
$540$	6.12676	+	21.0162i	0.263654	+	0.904393i
$541$	−23.2824			−1.00099			−0.500494	−	0.865740i	$-0.666848\pi$
$541$	−23.2824			−1.00099			−0.500494	+	0.865740i	$0.666848\pi$
$542$	−2.10182	+	0.465831i	−0.0902807	+	0.0200092i
$543$	−15.3598	−	20.3193i	−0.659153	−	0.871984i
$544$	23.0805	+	12.0236i	0.989569	+	0.515509i
$545$	11.6388	+	6.71965i	0.498551	+	0.287838i
$546$	1.63042	−	0.111982i	0.0697756	−	0.00479237i
$547$	2.95053	−	1.70349i	0.126155	−	0.0728358i	−0.435594	−	0.900143i	$-0.643462\pi$
$547$	2.95053	−	1.70349i	0.126155	−	0.0728358i	0.561750	+	0.827307i	$0.310128\pi$
$548$	−3.52629	−	2.46976i	−0.150636	−	0.105503i
$549$	10.6135	+	42.0275i	0.452975	+	1.79369i
$550$	1.74654	+	0.550796i	0.0744728	+	0.0234860i
$551$	−5.29939	−	9.17881i	−0.225762	−	0.391031i
$552$	−17.0513	+	16.8010i	−0.725750	+	0.715096i
$553$	−8.42590	+	2.15493i	−0.358306	+	0.0916369i
$554$	−6.50333	−	7.09799i	−0.276300	−	0.301565i
$555$	−38.3012	+	4.76151i	−1.62579	+	0.202115i
$556$	−2.88528	+	32.9341i	−0.122363	+	1.39672i
$557$	5.02799			0.213043			0.106521	−	0.994310i	$-0.466029\pi$
$557$	5.02799			0.213043			0.106521	+	0.994310i	$0.466029\pi$
$558$	12.6337	+	8.30836i	0.534826	+	0.351721i
$559$	2.50672			0.106023
$560$	−22.2291	+	1.68405i	−0.939349	+	0.0711639i
$561$	−16.8878	−	7.13839i	−0.713005	−	0.301383i
$562$	−25.7738	−	28.1305i	−1.08720	−	1.18661i
$563$	−11.5220	+	19.9567i	−0.485595	+	0.841076i	−0.999863	−	0.0165541i	$-0.994730\pi$
$563$	−11.5220	+	19.9567i	−0.485595	+	0.841076i	0.514268	+	0.857630i	$0.328064\pi$
$564$	37.6140	−	1.36592i	1.58384	−	0.0575157i
$565$	−21.3188	+	12.3084i	−0.896888	+	0.517818i
$566$	−5.69649	+	18.0632i	−0.239441	+	0.759254i
$567$	−16.1457	−	17.5019i	−0.678057	−	0.735010i
$568$	−10.5797	−	13.7928i	−0.443913	−	0.578731i
$569$	−0.515380	−	0.892665i	−0.0216059	−	0.0374225i	0.855020	−	0.518595i	$-0.173545\pi$
$569$	−0.515380	−	0.892665i	−0.0216059	−	0.0374225i	−0.876626	+	0.481172i	$0.840211\pi$
$570$	−23.7024	+	8.43219i	−0.992786	+	0.353186i
$571$	10.5140	+	6.07026i	0.439997	+	0.254032i	0.703596	−	0.710600i	$-0.251576\pi$
$571$	10.5140	+	6.07026i	0.439997	+	0.254032i	−0.263599	+	0.964632i	$0.584910\pi$
$572$	−1.05179	+	0.490305i	−0.0439774	+	0.0205007i
$573$	−10.5565	+	24.9744i	−0.441005	+	1.04332i
$574$	−4.16227	−	2.71930i	−0.173730	−	0.113502i
$575$		−	2.74999i		−	0.114682i
$576$	−20.6049	−	12.3060i	−0.858537	−	0.512752i
$577$		−	29.8675i		−	1.24340i	−0.783256	−	0.621699i	$-0.786443\pi$
$577$		−	29.8675i		−	1.24340i	0.783256	−	0.621699i	$-0.213557\pi$
$578$	5.75059	−	1.27452i	0.239193	−	0.0530130i
$579$	−0.963646	−	7.75149i	−0.0400478	−	0.322141i
$580$	−3.86936	−	8.30043i	−0.160666	−	0.344657i
$581$	5.98439	+	23.3993i	0.248274	+	0.970766i
$582$	−2.22291	+	12.0916i	−0.0921426	+	0.501214i
$583$	−15.9046	+	9.18250i	−0.658700	+	0.380300i
$584$	3.71831	+	4.84758i	0.153865	+	0.200594i
$585$	1.54507	−	0.390189i	0.0638808	−	0.0161323i
$586$	31.2117	+	9.84303i	1.28934	+	0.406612i
$587$	10.4711	+	18.1365i	0.432189	+	0.748573i	0.997062	−	0.0766048i	$-0.0244080\pi$
$587$	10.4711	+	18.1365i	0.432189	+	0.748573i	−0.564873	+	0.825178i	$0.691075\pi$
$588$	20.8348	−	12.4061i	0.859214	−	0.511617i
$589$	−8.68857	+	15.0490i	−0.358006	+	0.620085i
$590$	−16.2356	+	14.8755i	−0.668411	+	0.612413i
$591$	−9.72790	+	7.35355i	−0.400152	+	0.302485i
$592$	27.2068	−	32.4082i	1.11819	−	1.33197i
$593$			19.8667i			0.815828i	0.913020	+	0.407914i	$0.133744\pi$
$593$			19.8667i			0.815828i	−0.913020	+	0.407914i	$0.866256\pi$
$594$	15.1653	+	7.47669i	0.622241	+	0.306772i
$595$	−18.3358	+	17.9218i	−0.751693	+	0.734724i
$596$	−1.51422	+	17.2841i	−0.0620249	+	0.707984i
$597$	2.27560	−	1.72018i	0.0931340	−	0.0704022i
$598$	1.17719	+	1.28483i	0.0481388	+	0.0525406i
$599$	−18.7134	−	10.8042i	−0.764610	−	0.441448i	0.0663385	−	0.997797i	$-0.478868\pi$
$599$	−18.7134	−	10.8042i	−0.764610	−	0.441448i	−0.830948	+	0.556349i	$0.812202\pi$
$600$	2.66839	−	0.693887i	0.108937	−	0.0283278i
$601$	27.9379	−	16.1299i	1.13961	−	0.657954i	0.193276	−	0.981144i	$-0.438089\pi$
$601$	27.9379	−	16.1299i	1.13961	−	0.657954i	0.946334	+	0.323190i	$0.104755\pi$
$602$	33.1864	−	16.7946i	1.35258	−	0.684496i
$603$	18.2677	−	17.7478i	0.743918	−	0.722747i
$604$	−3.07149	+	4.38544i	−0.124977	+	0.178441i
$605$	10.4088	−	6.00952i	0.423178	−	0.244322i
$606$	−2.43303	+	13.2346i	−0.0988352	+	0.537619i
$607$	−7.23936	+	12.5389i	−0.293837	+	0.508940i	−0.974714	−	0.223458i	$-0.928265\pi$
$607$	−7.23936	+	12.5389i	−0.293837	+	0.508940i	0.680877	+	0.732398i	$0.261599\pi$
$608$	12.7429	−	24.4611i	0.516791	−	0.992030i
$609$	7.78865	+	6.21038i	0.315612	+	0.251657i
$610$	−42.0237	+	9.31382i	−1.70149	+	0.377105i
$611$		−	2.73995i		−	0.110847i
$612$	−27.2507	+	4.39718i	−1.10155	+	0.177746i
$613$	−5.59075			−0.225808			−0.112904	−	0.993606i	$-0.536015\pi$
$613$	−5.59075			−0.225808			−0.112904	+	0.993606i	$0.536015\pi$
$614$	−14.2027	+	3.14778i	−0.573175	+	0.127034i
$615$	−4.46552	−	1.88755i	−0.180067	−	0.0761132i
$616$	−10.6396	+	13.5379i	−0.428682	+	0.545458i
$617$	13.2535	−	22.9557i	0.533564	−	0.924161i	−0.465667	−	0.884960i	$-0.654186\pi$
$617$	13.2535	−	22.9557i	0.533564	−	0.924161i	0.999231	−	0.0392006i	$-0.0124811\pi$
$618$	4.85510	+	13.6474i	0.195301	+	0.548979i
$619$	−0.214256	−	0.371103i	−0.00861169	−	0.0149159i	0.861687	−	0.507439i	$-0.169408\pi$
$619$	−0.214256	−	0.371103i	−0.00861169	−	0.0149159i	−0.870299	+	0.492524i	$0.836075\pi$
$620$	−8.61366	+	12.2985i	−0.345933	+	0.493919i
$621$	3.85822	−	25.0950i	0.154825	−	1.00703i
$622$	0.405480	−	1.28575i	0.0162583	−	0.0515540i
$623$	−3.30140	+	11.7813i	−0.132268	+	0.472009i
$624$	−0.949673	+	1.46645i	−0.0380173	+	0.0587051i
$625$	10.9346	−	18.9393i	0.437385	−	0.757574i
$626$	30.3590	−	27.8156i	1.21339	−	1.11174i
$627$	−7.56539	+	17.8980i	−0.302132	+	0.714778i
$628$	35.7003	+	3.12763i	1.42460	+	0.124806i
$629$		−	48.6671i		−	1.94049i
$630$	17.8409	−	15.5174i	0.710799	−	0.618227i
$631$			23.4474i			0.933428i	0.884408	+	0.466714i	$0.154562\pi$
$631$			23.4474i			0.933428i	−0.884408	+	0.466714i	$0.845438\pi$
$632$	3.55956	−	8.58922i	0.141592	−	0.341661i
$633$	−15.2364	+	1.89414i	−0.605591	+	0.0752855i
$634$	−0.228905	−	0.249836i	−0.00909098	−	0.00992224i
$635$	14.6383	−	25.3542i	0.580902	−	1.00615i
$636$	−12.9465	+	24.4307i	−0.513361	+	0.968742i
$637$	−0.847473	−	1.54846i	−0.0335781	−	0.0613524i
$638$	−6.74596	−	2.12743i	−0.267075	−	0.0842258i
$639$	17.7385	+	5.02851i	0.701724	+	0.198925i
$640$	12.8132	−	20.0944i	0.506487	−	0.794299i
$641$	5.26351	+	9.11666i	0.207896	+	0.360086i	0.951052	−	0.309032i	$-0.100005\pi$
$641$	5.26351	+	9.11666i	0.207896	+	0.360086i	−0.743156	+	0.669119i	$0.766672\pi$
$642$	15.8744	+	13.5182i	0.626512	+	0.533522i
$643$	8.71937	−	15.1024i	0.343858	−	0.595580i	−0.641287	−	0.767301i	$-0.721599\pi$
$643$	8.71937	−	15.1024i	0.343858	−	0.595580i	0.985146	+	0.171721i	$0.0549327\pi$
$644$	24.1929	+	9.12284i	0.953333	+	0.359490i
$645$	28.9319	−	21.8704i	1.13919	−	0.861144i
$646$	−6.86411	−	30.9707i	−0.270065	−	1.21852i
$647$	−2.85701			−0.112321			−0.0561604	−	0.998422i	$-0.517886\pi$
$647$	−2.85701			−0.112321			−0.0561604	+	0.998422i	$0.517886\pi$
$648$	25.3239	−	2.58833i	0.994817	−	0.101679i
$649$			17.0077i			0.667612i
$650$	−0.0434295	−	0.195953i	−0.00170345	−	0.00768590i
$651$	2.43312	−	16.1501i	0.0953614	−	0.632971i
$652$	−2.41941	−	5.19004i	−0.0947514	−	0.203258i
$653$	14.1498	−	24.5081i	0.553724	−	0.959078i	−0.444278	−	0.895889i	$-0.646540\pi$
$653$	14.1498	−	24.5081i	0.553724	−	0.959078i	0.998002	−	0.0631888i	$-0.0201270\pi$
$654$	10.1322	−	11.8982i	0.396200	−	0.465256i
$655$	−26.2057	+	15.1299i	−1.02394	+	0.591173i
$656$	4.99500	−	1.81669i	0.195022	−	0.0709300i
$657$	−6.23434	−	1.76731i	−0.243225	−	0.0689494i
$658$	−18.3572	−	36.2741i	−0.715637	−	1.41411i
$659$	16.3336	−	9.43023i	0.636268	−	0.367350i	−0.146907	−	0.989150i	$-0.546932\pi$
$659$	16.3336	−	9.43023i	0.636268	−	0.367350i	0.783176	+	0.621801i	$0.213599\pi$
$660$	−7.86171	+	14.8355i	−0.306017	+	0.577471i
$661$	−5.06764	−	2.92580i	−0.197108	−	0.113801i	0.398198	−	0.917300i	$-0.369636\pi$
$661$	−5.06764	−	2.92580i	−0.197108	−	0.113801i	−0.595306	+	0.803499i	$0.702969\pi$
$662$	9.21603	−	8.44394i	0.358191	−	0.328183i
$663$	0.247895	+	1.99405i	0.00962746	+	0.0774425i
$664$	−23.8529	−	9.88513i	−0.925670	−	0.383617i
$665$	18.9939	+	19.4326i	0.736551	+	0.753562i
$666$	−2.60728	+	44.8053i	−0.101030	+	1.73617i
$667$			10.6217i			0.411275i
$668$	1.23341	−	14.0788i	0.0477221	−	0.544724i
$669$	27.1675	+	11.4836i	1.05036	+	0.443980i
$670$	17.0853	+	18.6476i	0.660064	+	0.720419i
$671$	−16.6229	+	28.7918i	−0.641722	+	1.11149i
$672$	−2.74770	+	25.7769i	−0.105995	+	0.994367i
$673$	−17.5342	−	30.3701i	−0.675893	−	1.17068i	−0.976207	−	0.216841i	$-0.930425\pi$
$673$	−17.5342	−	30.3701i	−0.675893	−	1.17068i	0.300314	−	0.953840i	$-0.402909\pi$
$674$	−5.86779	+	18.6064i	−0.226019	+	0.716692i
$675$	−1.83006	+	2.28098i	−0.0704390	+	0.0877951i
$676$	−21.1920	−	14.8425i	−0.815078	−	0.570867i
$677$	−16.9051	+	9.76017i	−0.649716	+	0.375114i	−0.788347	−	0.615230i	$-0.789063\pi$
$677$	−16.9051	+	9.76017i	−0.649716	+	0.375114i	0.138631	+	0.990344i	$0.455730\pi$
$678$	9.59451	+	26.9697i	0.368475	+	1.03576i
$679$	12.8652	−	3.29029i	0.493722	−	0.126270i
$680$	−3.57290	−	27.1761i	−0.137014	−	1.04216i
$681$	−10.5165	−	4.44526i	−0.402993	−	0.170343i
$682$	2.50943	+	11.3225i	0.0960911	+	0.433560i
$683$		−	2.90828i		−	0.111282i	−0.998451	−	0.0556411i	$-0.982280\pi$
$683$		−	2.90828i		−	0.111282i	0.998451	−	0.0556411i	$-0.0177203\pi$
$684$	4.66021	+	28.8808i	0.178188	+	1.10429i
$685$			4.53435i			0.173248i
$686$	−21.5941	−	14.8221i	−0.824466	−	0.565911i
$687$	−29.8193	+	3.70705i	−1.13768	+	0.141433i
$688$	−6.91386	+	39.1563i	−0.263589	+	1.49282i
$689$	1.74308	+	1.00637i	0.0664062	+	0.0383396i
$690$	24.7966	+	4.55857i	0.943989	+	0.173542i
$691$	−5.35077	−	9.26780i	−0.203553	−	0.352564i	0.746118	−	0.665814i	$-0.231916\pi$
$691$	−5.35077	−	9.26780i	−0.203553	−	0.352564i	−0.949671	+	0.313250i	$0.898582\pi$
$692$	19.1726	−	27.3744i	0.728832	−	1.04062i
$693$	0.472031	−	18.2569i	0.0179310	−	0.693521i
$694$	3.57658	+	1.12792i	0.135765	+	0.0428154i
$695$	30.1551	−	17.4101i	1.14385	−	0.660402i
$696$	−10.3066	+	2.68011i	−0.390669	+	0.101589i
$697$	3.05655	−	5.29410i	0.115775	−	0.200528i
$698$	4.04650	−	3.70750i	0.153162	−	0.140331i
$699$	2.34615	−	1.77351i	0.0887396	−	0.0670804i
$700$	−1.88781	−	2.30324i	−0.0713525	−	0.0870543i
$701$	20.8466			0.787365			0.393682	−	0.919247i	$-0.371201\pi$
$701$	20.8466			0.787365			0.393682	+	0.919247i	$0.371201\pi$
$702$	−0.121395	−	1.84910i	−0.00458177	−	0.0697898i
$703$	−51.5783			−1.94531
$704$	−4.75786	−	17.7818i	−0.179319	−	0.670177i
$705$	−23.9052	−	31.6238i	−0.900322	−	1.19102i
$706$	33.5860	−	30.7723i	1.26403	−	1.15813i
$707$	14.0813	−	3.60131i	0.529583	−	0.135441i
$708$	13.5991	+	21.6959i	0.511087	+	0.815383i
$709$	25.1621	+	43.5820i	0.944981	+	1.63676i	0.755789	+	0.654815i	$0.227254\pi$
$709$	25.1621	+	43.5820i	0.944981	+	1.63676i	0.189192	+	0.981940i	$0.439413\pi$
$710$	−5.50647	+	17.4607i	−0.206654	+	0.655288i
$711$	2.41462	+	9.56140i	0.0905552	+	0.358581i
$712$	−7.96072	−	10.3784i	−0.298341	−	0.388948i
$713$	15.0816	−	8.70737i	0.564811	−	0.326094i
$714$	16.6417	+	24.7383i	0.622798	+	0.925807i
$715$	1.05848	+	0.611115i	0.0395850	+	0.0228544i
$716$	−11.2134	−	24.0547i	−0.419065	−	0.898965i
$717$	−48.5102	+	6.03066i	−1.81165	+	0.225219i
$718$	−5.20132	−	23.4682i	−0.194112	−	0.875826i
$719$	−3.83545			−0.143038			−0.0715190	−	0.997439i	$-0.522785\pi$
$719$	−3.83545			−0.143038			−0.0715190	+	0.997439i	$0.522785\pi$
$720$	1.83345	+	25.2110i	0.0683288	+	0.939559i
$721$	11.1889	−	10.9363i	0.416696	−	0.407290i
$722$	−6.58978	+	1.46051i	−0.245246	+	0.0543545i
$723$	18.3774	−	43.4768i	0.683462	−	1.61692i
$724$	−12.4269	−	26.6578i	−0.461841	−	0.990728i
$725$	0.611700	−	1.05949i	0.0227180	−	0.0393486i
$726$	−4.68448	−	13.1678i	−0.173857	−	0.488704i
$727$	−26.0730	−	45.1597i	−0.966993	−	1.67488i	−0.704162	−	0.710039i	$-0.748677\pi$
$727$	−26.0730	−	45.1597i	−0.966993	−	1.67488i	−0.262831	−	0.964842i	$-0.584656\pi$
$728$	1.86796	+	0.267987i	0.0692312	+	0.00993225i
$729$	−19.9004	+	18.2476i	−0.737053	+	0.675835i
$730$	1.93529	−	6.13670i	0.0716284	−	0.227130i
$731$	22.8658	+	39.6048i	0.845724	+	1.46484i
$732$	1.81643	+	50.0198i	0.0671371	+	1.84878i
$733$	−31.3189	−	18.0820i	−1.15679	−	0.667874i	−0.206258	−	0.978498i	$-0.566129\pi$
$733$	−31.3189	−	18.0820i	−1.15679	−	0.667874i	−0.950533	+	0.310624i	$0.899462\pi$
$734$	1.80959	+	1.97505i	0.0667932	+	0.0729006i
$735$	−23.2912	−	10.4780i	−0.859108	−	0.386489i
$736$	−23.3166	+	14.8446i	−0.859460	+	0.547179i
$737$	19.5344			0.719558
$738$	−3.09763	+	4.71025i	−0.114025	+	0.173387i
$739$			41.8456i			1.53932i	0.638456	+	0.769658i	$0.279573\pi$
$739$			41.8456i			1.53932i	−0.638456	+	0.769658i	$0.720427\pi$
$740$	−44.3968	−	3.88950i	−1.63206	−	0.142981i
$741$	2.11333	−	0.262724i	0.0776351	−	0.00965140i
$742$	29.8191	+	1.64494i	1.09469	+	0.0603875i
$743$	18.1807	+	10.4967i	0.666987	+	0.385085i	0.794934	−	0.606696i	$-0.207505\pi$
$743$	18.1807	+	10.4967i	0.666987	+	0.385085i	−0.127947	+	0.991781i	$0.540839\pi$
$744$	12.2545	+	12.4370i	0.449270	+	0.455964i
$745$	15.8257	−	9.13695i	0.579808	−	0.334752i
$746$	5.50088	−	17.4430i	0.201401	−	0.638632i
$747$	26.5527	−	6.70555i	0.971511	−	0.245343i
$748$	−17.3408	−	12.1452i	−0.634041	−	0.444072i
$749$	6.07681	−	21.6857i	0.222042	−	0.792376i
$750$	−21.8528	−	18.6093i	−0.797950	−	0.679514i
$751$	−17.9902	−	10.3866i	−0.656470	−	0.379013i	0.134460	−	0.990919i	$-0.457070\pi$
$751$	−17.9902	−	10.3866i	−0.656470	−	0.379013i	−0.790931	+	0.611906i	$0.790403\pi$
$752$	42.7995	+	7.55714i	1.56074	+	0.275581i
$753$	−41.2118	+	31.1530i	−1.50184	+	1.13528i
$754$	0.167745	+	0.756860i	0.00610891	+	0.0275632i
$755$	5.63910			0.205228
$756$	−13.9958	−	23.6668i	−0.509022	−	0.860754i
$757$	16.5395			0.601137			0.300568	−	0.953760i	$-0.402824\pi$
$757$	16.5395			0.601137			0.300568	+	0.953760i	$0.402824\pi$
$758$	5.94014	+	26.8017i	0.215756	+	0.973483i
$759$	15.5344	−	11.7428i	0.563862	−	0.426237i
$760$	−28.8017	+	3.78662i	−1.04475	+	0.137355i
$761$	−6.77126	−	3.90939i	−0.245458	−	0.141715i	0.372225	−	0.928143i	$-0.378595\pi$
$761$	−6.77126	−	3.90939i	−0.245458	−	0.141715i	−0.617683	+	0.786427i	$0.711928\pi$
$762$	−25.9193	−	22.0722i	−0.938958	−	0.799593i
$763$	−16.2538	−	4.55469i	−0.588429	−	0.164891i
$764$	−17.9607	+	25.6442i	−0.649797	+	0.927773i
$765$	20.2586	+	20.8520i	0.732452	+	0.753907i
$766$	5.48090	−	17.3796i	0.198033	−	0.627951i
$767$	1.61426	−	0.931993i	0.0582875	−	0.0336523i
$768$	−20.2875	−	18.8791i	−0.732061	−	0.681240i
$769$	−21.7560	−	12.5608i	−0.784542	−	0.452955i	0.0534956	−	0.998568i	$-0.482964\pi$
$769$	−21.7560	−	12.5608i	−0.784542	−	0.452955i	−0.838038	+	0.545613i	$0.816297\pi$
$770$	18.1076	+	0.998883i	0.652551	+	0.0359972i
$771$	45.6029	−	5.66924i	1.64235	−	0.204173i
$772$	0.787168	−	8.98514i	0.0283308	−	0.323382i
$773$		−	6.00293i		−	0.215910i	−0.994156	−	0.107955i	$-0.965570\pi$
$773$		−	6.00293i		−	0.215910i	0.994156	−	0.107955i	$-0.0344303\pi$
$774$	−18.9296	−	37.6871i	−0.680411	−	1.35463i
$775$	−2.00581			−0.0720509
$776$	−5.43497	+	13.1146i	−0.195104	+	0.470786i
$777$	45.1249	−	17.7137i	1.61885	−	0.635476i
$778$	18.2124	+	19.8777i	0.652947	+	0.712651i
$779$	−5.61078	−	3.23938i	−0.201027	−	0.116063i
$780$	1.83889	−	0.0667779i	0.0658429	−	0.00239103i
$781$	7.07052	+	12.2465i	0.253003	+	0.438214i
$782$	−9.56149	+	30.3189i	−0.341918	+	1.08420i
$783$	7.06853	−	8.81021i	0.252609	−	0.314851i
$784$	26.5253	−	8.96712i	0.947332	−	0.320254i
$785$	−18.8724	−	32.6880i	−0.673585	−	1.16668i
$786$	11.7939	+	33.1519i	0.420674	+	1.18249i
$787$	14.5065	−	25.1260i	0.517100	−	0.895644i	−0.482703	−	0.875784i	$-0.660345\pi$
$787$	14.5065	−	25.1260i	0.517100	−	0.895644i	0.999803	−	0.0198595i	$-0.00632188\pi$
$788$	−12.7625	+	5.94940i	−0.454644	+	0.211938i
$789$	−2.84479	+	6.73013i	−0.101277	+	0.239599i
$790$	−9.56054	+	2.11893i	−0.340149	+	0.0753880i
$791$	22.1112	−	21.6121i	0.786184	−	0.768436i
$792$	15.3141	+	12.1104i	0.544162	+	0.430326i
$793$	3.64363			0.129389
$794$	−0.713538	−	3.21946i	−0.0253225	−	0.114254i
$795$	28.8985	−	3.59259i	1.02492	−	0.127416i
$796$	2.98546	−	1.39171i	0.105817	−	0.0493279i
$797$	13.1794	+	7.60913i	0.466838	+	0.269529i	0.714915	−	0.699211i	$-0.246465\pi$
$797$	13.1794	+	7.60913i	0.466838	+	0.269529i	−0.248077	+	0.968740i	$0.579799\pi$
$798$	26.2181	−	17.6371i	0.928110	−	0.624347i
$799$	43.2897	−	24.9933i	1.53148	−	0.884200i
$800$	3.18067	−	0.137929i	0.112454	−	0.00487654i
$801$	13.3474	+	3.78373i	0.471608	+	0.133692i
$802$	−6.95358	+	22.0494i	−0.245539	+	0.778591i
$803$	−2.48499	−	4.30413i	−0.0876934	−	0.151889i
$804$	24.9190	−	15.6194i	0.878827	−	0.550854i
$805$	−6.74747	−	26.3830i	−0.237817	−	0.929879i
$806$	0.937142	−	0.858630i	0.0330094	−	0.0302440i
$807$	−29.8752	−	39.5215i	−1.05166	−	1.39122i
$808$	−5.94872	+	14.3543i	−0.209275	+	0.504982i
$809$	22.3835			0.786960			0.393480	−	0.919333i	$-0.371271\pi$
$809$	22.3835			0.786960			0.393480	+	0.919333i	$0.371271\pi$
$810$	−17.5339	−	20.2827i	−0.616079	−	0.712662i
$811$	−7.32710			−0.257289			−0.128645	−	0.991691i	$-0.541063\pi$
$811$	−7.32710			−0.257289			−0.128645	+	0.991691i	$0.541063\pi$
$812$	7.29160	+	8.89618i	0.255885	+	0.312195i
$813$	2.10333	−	1.58996i	0.0737669	−	0.0557622i
$814$	−25.3803	+	23.2540i	−0.889580	+	0.815053i
$815$	−3.01555	+	5.22308i	−0.105630	+	0.182956i
$816$	−31.8319	−	1.62759i	−1.11434	−	0.0569772i
$817$	41.9739	−	24.2336i	1.46848	−	0.847827i
$818$	−25.7096	−	8.10788i	−0.898915	−	0.283485i
$819$	−1.75869	+	0.955641i	−0.0614534	+	0.0333928i
$820$	−4.58528	−	3.21145i	−0.160125	−	0.112149i
$821$	6.58917	+	11.4128i	0.229964	+	0.398309i	0.957797	−	0.287445i	$-0.0928059\pi$
$821$	6.58917	+	11.4128i	0.229964	+	0.398309i	−0.727833	+	0.685754i	$0.759473\pi$
$822$	5.18583	+	0.953357i	0.180877	+	0.0332521i
$823$	−6.62089	−	3.82257i	−0.230790	−	0.133246i	0.380147	−	0.924926i	$-0.375874\pi$
$823$	−6.62089	−	3.82257i	−0.230790	−	0.133246i	−0.610936	+	0.791680i	$0.709207\pi$
$824$	2.18026	+	16.5835i	0.0759531	+	0.577713i
$825$	−2.22578	+	0.276704i	−0.0774919	+	0.00963360i
$826$	15.1269	−	23.1539i	0.526333	−	0.805626i
$827$		−	33.7614i		−	1.17400i	−0.809587	−	0.587000i	$-0.800309\pi$
$827$		−	33.7614i		−	1.17400i	0.809587	−	0.587000i	$-0.199691\pi$
$828$	10.4271	−	27.4008i	0.362365	−	0.952244i
$829$		−	16.4004i		−	0.569611i	−0.958585	−	0.284805i	$-0.908071\pi$
$829$		−	16.4004i		−	0.569611i	0.958585	−	0.284805i	$-0.0919290\pi$
$830$	5.88440	+	26.5503i	0.204251	+	0.921573i
$831$	10.8600	+	4.59046i	0.376730	+	0.159241i
$832$	−1.42701	+	1.42600i	−0.0494726	+	0.0494375i
$833$	16.7344	−	27.5144i	0.579812	−	0.953318i
$834$	−13.5713	−	38.1483i	−0.469936	−	1.32097i
$835$	−12.8908	+	7.44252i	−0.446105	+	0.257559i
$836$	−12.8717	+	18.3780i	−0.445176	+	0.635618i
$837$	−18.3041	−	2.81415i	−0.632681	−	0.0972712i
$838$	−4.48763	+	14.2300i	−0.155022	+	0.491567i
$839$	−16.1916	−	28.0447i	−0.558996	−	0.968209i	−0.997581	−	0.0695192i	$-0.977854\pi$
$839$	−16.1916	−	28.0447i	−0.558996	−	0.968209i	0.438585	−	0.898690i	$-0.355480\pi$
$840$	23.8976	−	13.2043i	0.824546	−	0.455592i
$841$	12.1373	−	21.0225i	0.418529	−	0.724913i
$842$	−33.7402	−	36.8254i	−1.16277	−	1.26909i
$843$	43.0401	+	18.1928i	1.48238	+	0.626593i
$844$	−17.6612	−	1.54726i	−0.607924	−	0.0532589i
$845$			27.2501i			0.937433i
$846$	−41.1936	+	20.6909i	−1.41626	+	0.711366i
$847$	−10.7957	+	10.5520i	−0.370945	+	0.362571i
$848$	−20.5277	+	24.4522i	−0.704924	+	0.839692i
$849$	−2.86175	−	23.0197i	−0.0982149	−	0.790033i
$850$	2.69979	−	2.47361i	0.0926020	−	0.0848441i
$851$	44.7648	+	25.8450i	1.53452	+	0.885953i
$852$	18.8116	+	9.96877i	0.644476	+	0.341524i
$853$	−12.4256	+	7.17395i	−0.425446	+	0.245631i	−0.697405	−	0.716678i	$-0.745662\pi$
$853$	−12.4256	+	7.17395i	−0.425446	+	0.245631i	0.271959	+	0.962309i	$0.412329\pi$
$854$	48.2379	−	24.4117i	1.65067	−	0.835350i
$855$	22.0993	−	21.4704i	0.755782	−	0.734273i
$856$	14.6531	+	19.1033i	0.500833	+	0.652939i
$857$	15.0174	−	8.67031i	0.512985	−	0.296172i	−0.221075	−	0.975257i	$-0.570956\pi$
$857$	15.0174	−	8.67031i	0.512985	−	0.296172i	0.734060	+	0.679085i	$0.237623\pi$
$858$	0.921466	−	1.08207i	0.0314583	−	0.0369414i
$859$	−25.4872	+	44.1451i	−0.869612	+	1.50621i	−0.00721838	+	0.999974i	$0.502298\pi$
$859$	−25.4872	+	44.1451i	−0.869612	+	1.50621i	−0.862394	+	0.506238i	$0.831036\pi$
$860$	37.9571	−	17.6942i	1.29433	−	0.603368i
$861$	6.02128	+	0.907146i	0.205205	+	0.0309154i
$862$	−0.546178	−	2.46434i	−0.0186029	−	0.0839358i
$863$			19.5828i			0.666606i	0.942820	+	0.333303i	$0.108163\pi$
$863$			19.5828i			0.666606i	−0.942820	+	0.333303i	$0.891837\pi$
$864$	29.2188	+	3.20380i	0.994042	+	0.108995i
$865$	−35.1998			−1.19683
$866$	−1.99771	−	9.01360i	−0.0678849	−	0.306294i
$867$	−5.75472	+	4.35013i	−0.195441	+	0.147738i
$868$	6.65411	−	17.6460i	0.225855	−	0.598946i
$869$	−3.78178	+	6.55023i	−0.128288	+	0.222201i
$870$	8.53944	+	7.27197i	0.289514	+	0.246543i
$871$	−1.07045	−	1.85407i	−0.0362708	−	0.0628228i
$872$	14.3183	−	10.9828i	0.484880	−	0.371925i
$873$	−3.68680	−	14.5990i	−0.124779	−	0.494101i
$874$	32.1325	+	10.1334i	1.08690	+	0.342768i
$875$	−8.36537	+	29.8526i	−0.282801	+	1.00920i
$876$	−6.61150	−	3.50361i	−0.223382	−	0.118376i
$877$	1.48110	−	2.56533i	0.0500130	−	0.0866251i	−0.839935	−	0.542687i	$-0.817407\pi$
$877$	1.48110	−	2.56533i	0.0500130	−	0.0866251i	0.889948	+	0.456062i	$0.150740\pi$
$878$	−14.6695	−	16.0109i	−0.495073	−	0.540342i
$879$	−39.7760	+	4.94485i	−1.34161	+	0.166786i
$880$	−12.4654	+	14.8485i	−0.420208	+	0.500544i
$881$			27.0811i			0.912384i	0.889881	+	0.456192i	$0.150787\pi$
$881$			27.0811i			0.912384i	−0.889881	+	0.456192i	$0.849213\pi$
$882$	−16.8805	+	24.4346i	−0.568397	+	0.822755i
$883$			24.9046i			0.838107i	0.907962	+	0.419054i	$0.137638\pi$
$883$			24.9046i			0.838107i	−0.907962	+	0.419054i	$0.862362\pi$
$884$	−0.202497	+	2.31140i	−0.00681071	+	0.0777409i
$885$	10.5000	−	24.8407i	0.352955	−	0.835012i
$886$	−13.5533	+	12.4178i	−0.455332	+	0.417185i
$887$	−22.4128	+	38.8200i	−0.752547	+	1.30345i	0.194038	+	0.980994i	$0.437841\pi$
$887$	−22.4128	+	38.8200i	−0.752547	+	1.30345i	−0.946585	+	0.322455i	$0.895492\pi$
$888$	−13.7829	+	49.9578i	−0.462523	+	1.67647i
$889$	−9.92206	+	35.4078i	−0.332775	+	1.18754i
$890$	−4.14337	+	13.1384i	−0.138886	+	0.440399i
$891$	−20.6996	−	0.597704i	−0.693463	−	0.0200238i
$892$	27.8962	+	19.5380i	0.934033	+	0.654181i
$893$	−26.4884	−	45.8792i	−0.886399	−	1.53529i
$894$	−7.12234	−	20.0205i	−0.238207	−	0.669586i
$895$	−13.9764	+	24.2078i	−0.467179	+	0.809177i
$896$	−9.33817	+	28.4394i	−0.311966	+	0.950093i
$897$	−1.96580	−	0.830934i	−0.0656363	−	0.0277441i
$898$	42.1290	−	9.33716i	1.40586	−	0.311585i
$899$	7.74738			0.258390
$900$	−2.61808	+	2.13268i	−0.0872692	+	0.0710895i
$901$			36.7197i			1.22331i
$902$	−4.22139	+	0.935598i	−0.140557	+	0.0311520i
$903$	−28.3995	+	35.6168i	−0.945077	+	1.18525i
$904$	4.30858	+	32.7718i	0.143301	+	1.08997i
$905$	−15.4888	+	26.8274i	−0.514866	+	0.891774i
$906$	1.18563	−	6.44930i	0.0393900	−	0.214264i
$907$	−49.7076	+	28.6987i	−1.65051	+	0.952924i	−0.673651	+	0.739049i	$0.735275\pi$
$907$	−49.7076	+	28.6987i	−1.65051	+	0.952924i	−0.976861	+	0.213874i	$0.931392\pi$
$908$	−10.7985	−	7.56313i	−0.358362	−	0.250991i
$909$	−4.03530	−	15.9790i	−0.133842	−	0.529989i
$910$	−0.897454	−	1.77338i	−0.0297503	−	0.0587871i
$911$	41.7826	−	24.1232i	1.38432	−	0.799237i	0.391652	−	0.920113i	$-0.371904\pi$
$911$	41.7826	−	24.1232i	1.38432	−	0.799237i	0.992668	+	0.120876i	$0.0385703\pi$
$912$	−1.72495	+	33.7360i	−0.0571189	+	1.11711i
$913$	18.1904	+	10.5023i	0.602016	+	0.347574i
$914$	31.9447	+	34.8656i	1.05664	+	1.15325i
$915$	42.0539	−	31.7895i	1.39026	−	1.05093i
$916$	−34.5650	−	3.02816i	−1.14206	−	0.100053i
$917$	27.1798	−	26.5662i	0.897556	−	0.877294i
$918$	28.1074	−	18.7851i	0.927683	−	0.620002i
$919$		−	50.4712i		−	1.66489i	−0.554106	−	0.832446i	$-0.686940\pi$
$919$		−	50.4712i		−	1.66489i	0.554106	−	0.832446i	$-0.313060\pi$
$920$	26.8944	+	11.1456i	0.886682	+	0.367460i
$921$	14.2129	−	10.7439i	0.468332	−	0.354023i
$922$	−10.1459	+	9.29589i	−0.334137	+	0.306144i
$923$	0.774903	−	1.34217i	0.0255063	−	0.0441781i
$924$	4.94955	−	20.4992i	0.162828	−	0.674373i
$925$	−2.97680	−	5.15596i	−0.0978765	−	0.169527i
$926$	12.1493	+	3.83146i	0.399252	+	0.125910i
$927$	−12.3623	−	12.7244i	−0.406030	−	0.417924i
$928$	−12.2852	+	0.532747i	−0.403282	+	0.0174883i
$929$	20.5217	−	11.8482i	0.673295	−	0.388727i	−0.124029	−	0.992279i	$-0.539582\pi$
$929$	20.5217	−	11.8482i	0.673295	−	0.388727i	0.797324	+	0.603552i	$0.206248\pi$
$930$	3.32498	−	18.0864i	0.109030	−	0.593075i
$931$	−29.1603	−	17.7354i	−0.955689	−	0.581254i
$932$	3.07802	−	1.43486i	0.100824	−	0.0470004i
$933$	0.203701	+	1.63856i	0.00666888	+	0.0536439i
$934$	−9.35201	+	2.07271i	−0.306007	+	0.0678211i
$935$			22.2979i			0.729220i
$936$	0.310259	−	2.11714i	0.0101411	−	0.0692009i
$937$			34.0220i			1.11145i	0.831366	+	0.555725i	$0.187559\pi$
$937$			34.0220i			1.11145i	−0.831366	+	0.555725i	$0.812441\pi$
$938$	−26.5936	−	17.3742i	−0.868311	−	0.567286i
$939$	−19.6340	+	46.4497i	−0.640732	+	1.51583i
$940$	−19.3405	−	41.4887i	−0.630818	−	1.35321i
$941$	−14.0890	−	8.13430i	−0.459289	−	0.265171i	0.252456	−	0.967608i	$-0.418762\pi$
$941$	−14.0890	−	8.13430i	−0.459289	−	0.265171i	−0.711745	+	0.702438i	$0.752095\pi$
$942$	−41.3525	+	14.7112i	−1.34734	+	0.479318i
$943$	3.24639	+	5.62292i	0.105717	+	0.183107i
$944$	10.1059	+	27.7862i	0.328919	+	0.904362i
$945$	−11.9606	+	26.3737i	−0.389079	+	0.857938i
$946$	9.72854	−	30.8486i	0.316302	−	1.00298i
$947$	14.2574	−	8.23153i	0.463304	−	0.267489i	−0.250128	−	0.968213i	$-0.580473\pi$
$947$	14.2574	−	8.23153i	0.463304	−	0.267489i	0.713433	+	0.700724i	$0.247140\pi$
$948$	0.413244	+	11.3797i	0.0134215	+	0.369595i
$949$	−0.272346	+	0.471717i	−0.00884073	+	0.0153126i
$950$	−2.62157	−	2.86128i	−0.0850551	−	0.0928323i
$951$	0.382252	+	0.161576i	0.0123954	+	0.00523945i
$952$	12.8051	+	31.9572i	0.415017	+	1.03574i
$953$	−20.7444			−0.671977			−0.335988	−	0.941866i	$-0.609070\pi$
$953$	−20.7444			−0.671977			−0.335988	+	0.941866i	$0.609070\pi$
$954$	1.96721	−	33.8059i	0.0636909	−	1.09451i
$955$	32.9750			1.06704
$956$	−56.2305	−	4.92623i	−1.81863	−	0.159326i
$957$	8.59701	−	1.06876i	0.277902	−	0.0345481i
$958$	5.13549	+	5.60507i	0.165920	+	0.181091i
$959$	−1.41113	−	5.51761i	−0.0455678	−	0.178173i
$960$	−4.02880	+	28.9087i	−0.130029	+	0.933024i
$961$	9.14893	+	15.8464i	0.295127	+	0.511174i
$962$	3.59791	+	1.13465i	0.116001	+	0.0365826i
$963$	−24.5683	−	6.96463i	−0.791703	−	0.224432i
$964$	31.2671	−	44.6428i	1.00705	−	1.43785i
$965$	−8.22698	+	4.74985i	−0.264836	+	0.152903i
$966$	−31.5923	+	2.16984i	−1.01647	+	0.0698135i
$967$	−6.47848	−	3.74035i	−0.208334	−	0.120282i	0.392203	−	0.919879i	$-0.371713\pi$
$967$	−6.47848	−	3.74035i	−0.208334	−	0.120282i	−0.600537	+	0.799597i	$0.705046\pi$
$968$	−2.10365	−	16.0007i	−0.0676137	−	0.514282i
$969$	23.4283	+	30.9929i	0.752625	+	0.995636i
$970$	14.5977	−	3.23532i	0.468703	−	0.103880i
$971$	−57.8577			−1.85674			−0.928371	−	0.371655i	$-0.878790\pi$
$971$	−57.8577			−1.85674			−0.928371	+	0.371655i	$0.878790\pi$
$972$	−26.8834	+	15.7887i	−0.862286	+	0.506422i
$973$	−31.2760	+	30.5700i	−1.00266	+	0.980029i
$974$	4.46139	+	20.1297i	0.142952	+	0.644996i
$975$	0.148232	+	0.196094i	0.00474722	+	0.00628002i
$976$	−10.0496	+	56.9155i	−0.321680	+	1.82182i
$977$	−16.3314	+	28.2869i	−0.522489	+	0.904977i	0.477169	+	0.878812i	$0.341663\pi$
$977$	−16.3314	+	28.2869i	−0.522489	+	0.904977i	−0.999658	+	0.0261653i	$0.991670\pi$
$978$	5.33949	+	4.54697i	0.170738	+	0.145396i
$979$	5.32024	+	9.21493i	0.170036	+	0.294511i
$980$	−23.7627	−	17.4650i	−0.759072	−	0.557898i
$981$	−5.22013	+	18.4145i	−0.166666	+	0.587928i
$982$	−11.6734	−	3.68137i	−0.372513	−	0.117477i
$983$	−15.4395	−	26.7421i	−0.492445	−	0.852939i	0.507518	−	0.861641i	$-0.330563\pi$
$983$	−15.4395	−	26.7421i	−0.492445	−	0.852939i	−0.999962	+	0.00870241i	$0.997230\pi$
$984$	−4.63693	+	4.56886i	−0.147820	+	0.145650i
$985$	12.8437	+	7.41531i	0.409234	+	0.236271i
$986$	−10.4278	+	9.55422i	−0.332090	+	0.304268i
$987$	38.9306	+	31.0418i	1.23918	+	0.988073i
$988$	2.44967	+	0.214610i	0.0779342	+	0.00682765i
$989$	−48.5721			−1.54450
$990$	1.19458	−	20.5285i	0.0379664	−	0.652439i
$991$			8.94754i			0.284228i	0.989850	+	0.142114i	$0.0453900\pi$
$991$			8.94754i			0.284228i	−0.989850	+	0.142114i	$0.954610\pi$
$992$	10.8275	+	17.0069i	0.343774	+	0.539969i
$993$	−5.96026	+	14.1006i	−0.189143	+	0.447471i
$994$	1.26660	−	22.9607i	0.0401741	−	0.728268i
$995$	−3.00446	−	1.73463i	−0.0952478	−	0.0549913i
$996$	31.6021	−	1.14761i	1.00135	−	0.0363633i
$997$	−1.31627	+	0.759946i	−0.0416865	+	0.0240677i	−0.520698	−	0.853741i	$-0.674328\pi$
$997$	−1.31627	+	0.759946i	−0.0416865	+	0.0240677i	0.479012	+	0.877808i	$0.340995\pi$
$998$	−54.2623	−	17.1124i	−1.71764	−	0.541682i
$999$	−19.9310	−	51.2272i	−0.630588	−	1.62076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.4	yes	80
3.2	odd	2		756.2.bi.c.307.38		80
4.3	odd	2	inner	252.2.bi.c.139.29	yes	80
7.6	odd	2	inner	252.2.bi.c.139.3	✓	80
9.2	odd	6		756.2.bi.c.559.11		80
9.7	even	3	inner	252.2.bi.c.223.30	yes	80
12.11	even	2		756.2.bi.c.307.12		80
21.20	even	2		756.2.bi.c.307.37		80
28.27	even	2	inner	252.2.bi.c.139.30	yes	80
36.7	odd	6	inner	252.2.bi.c.223.3	yes	80
36.11	even	6		756.2.bi.c.559.37		80
63.20	even	6		756.2.bi.c.559.12		80
63.34	odd	6	inner	252.2.bi.c.223.29	yes	80
84.83	odd	2		756.2.bi.c.307.11		80
252.83	odd	6		756.2.bi.c.559.38		80
252.223	even	6	inner	252.2.bi.c.223.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.3	✓	80	7.6	odd	2	inner
252.2.bi.c.139.4	yes	80	1.1	even	1	trivial
252.2.bi.c.139.29	yes	80	4.3	odd	2	inner
252.2.bi.c.139.30	yes	80	28.27	even	2	inner
252.2.bi.c.223.3	yes	80	36.7	odd	6	inner
252.2.bi.c.223.4	yes	80	252.223	even	6	inner
252.2.bi.c.223.29	yes	80	63.34	odd	6	inner
252.2.bi.c.223.30	yes	80	9.7	even	3	inner
756.2.bi.c.307.11		80	84.83	odd	2
756.2.bi.c.307.12		80	12.11	even	2
756.2.bi.c.307.37		80	21.20	even	2
756.2.bi.c.307.38		80	3.2	odd	2
756.2.bi.c.559.11		80	9.2	odd	6
756.2.bi.c.559.12		80	63.20	even	6
756.2.bi.c.559.37		80	36.11	even	6
756.2.bi.c.559.38		80	252.83	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38071 + 0.306010i) q^{2} +(1.38170 - 1.04446i) q^{3} +(1.81272 - 0.845022i) q^{4} +(-1.82425 - 1.05323i) q^{5} +(-1.58811 + 1.86491i) q^{6} +(2.54762 + 0.713899i) q^{7} +(-2.24425 + 1.72144i) q^{8} +(0.818200 - 2.88627i) q^{9} +O(q^{10})\)	\(q+(-1.38071 + 0.306010i) q^{2} +(1.38170 - 1.04446i) q^{3} +(1.81272 - 0.845022i) q^{4} +(-1.82425 - 1.05323i) q^{5} +(-1.58811 + 1.86491i) q^{6} +(2.54762 + 0.713899i) q^{7} +(-2.24425 + 1.72144i) q^{8} +(0.818200 - 2.88627i) q^{9} +(2.84106 + 0.895969i) q^{10} +(1.99265 - 1.15046i) q^{11} +(1.62204 - 3.06088i) q^{12} +(-0.218388 - 0.126086i) q^{13} +(-3.73598 - 0.206091i) q^{14} +(-3.62064 + 0.450108i) q^{15} +(2.57187 - 3.06357i) q^{16} -4.60054i q^{17} +(-0.246468 + 4.23548i) q^{18} -4.87573 q^{19} +(-4.19686 - 0.367678i) q^{20} +(4.26569 - 1.67449i) q^{21} +(-2.39922 + 2.19822i) q^{22} +(4.23165 + 2.44314i) q^{23} +(-1.30290 + 4.72255i) q^{24} +(-0.281399 - 0.487397i) q^{25} +(0.340113 + 0.107259i) q^{26} +(-1.88409 - 4.84254i) q^{27} +(5.22136 - 0.858695i) q^{28} +(1.08689 + 1.88255i) q^{29} +(4.86131 - 1.72942i) q^{30} +(1.78200 - 3.08652i) q^{31} +(-2.61353 + 5.01692i) q^{32} +(1.55164 - 3.67084i) q^{33} +(1.40781 + 6.35201i) q^{34} +(-3.89560 - 3.98557i) q^{35} +(-0.955798 - 5.92338i) q^{36} +10.5786 q^{37} +(6.73197 - 1.49202i) q^{38} +(-0.433439 + 0.0538840i) q^{39} +(5.90715 - 0.776626i) q^{40} +(1.15076 + 0.664389i) q^{41} +(-5.37726 + 3.61733i) q^{42} +(-8.60873 + 4.97025i) q^{43} +(2.63995 - 3.76929i) q^{44} +(-4.53252 + 4.40353i) q^{45} +(-6.59030 - 2.07834i) q^{46} +(5.43270 + 9.40970i) q^{47} +(0.353783 - 6.91916i) q^{48} +(5.98070 + 3.63748i) q^{49} +(0.537678 + 0.586842i) q^{50} +(-4.80509 - 6.35657i) q^{51} +(-0.502420 - 0.0440159i) q^{52} -7.98161 q^{53} +(4.08325 + 6.10959i) q^{54} -4.84680 q^{55} +(-6.94642 + 2.78340i) q^{56} +(-6.73681 + 5.09251i) q^{57} +(-2.07676 - 2.26666i) q^{58} +(-3.69586 + 6.40141i) q^{59} +(-6.18283 + 3.87544i) q^{60} +(-12.5132 + 7.22449i) q^{61} +(-1.51592 + 4.80690i) q^{62} +(4.14497 - 6.76899i) q^{63} +(2.07329 - 7.72667i) q^{64} +(0.265596 + 0.460026i) q^{65} +(-1.01905 + 5.54318i) q^{66} +(7.35240 + 4.24491i) q^{67} +(-3.88756 - 8.33947i) q^{68} +(8.39864 - 1.04410i) q^{69} +(6.59831 + 4.31082i) q^{70} +6.14583i q^{71} +(3.13229 + 7.88598i) q^{72} -2.16000i q^{73} +(-14.6059 + 3.23715i) q^{74} +(-0.897876 - 0.379527i) q^{75} +(-8.83831 + 4.12010i) q^{76} +(5.89782 - 1.50837i) q^{77} +(0.581964 - 0.207035i) q^{78} +(-2.84679 + 1.64360i) q^{79} +(-7.91841 + 2.87994i) q^{80} +(-7.66110 - 4.72309i) q^{81} +(-1.79217 - 0.565185i) q^{82} +(4.56438 + 7.90574i) q^{83} +(6.31749 - 6.63998i) q^{84} +(-4.84544 + 8.39255i) q^{85} +(10.3652 - 9.49684i) q^{86} +(3.46801 + 1.46591i) q^{87} +(-2.49156 + 6.01214i) q^{88} +4.62446i q^{89} +(4.91057 - 7.46699i) q^{90} +(-0.466355 - 0.477126i) q^{91} +(9.73528 + 0.852886i) q^{92} +(-0.761555 - 6.12588i) q^{93} +(-10.3804 - 11.3296i) q^{94} +(8.89457 + 5.13528i) q^{95} +(1.62886 + 9.66162i) q^{96} +(4.34667 - 2.50955i) q^{97} +(-9.37071 - 3.19215i) q^{98} +(-1.69014 - 6.69264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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