LMFDB - Embedded newform 471.2.e.c.169.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.9
Character	$\chi$	$=$	471.169
Dual form			471.2.e.c.301.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.07617 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.841867 q^{4} +(-1.37194 - 2.37626i) q^{5} +(-0.538083 - 0.931987i) q^{6} +3.41476 q^{7} -3.05832 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.07617 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.841867 q^{4} +(-1.37194 - 2.37626i) q^{5} +(-0.538083 - 0.931987i) q^{6} +3.41476 q^{7} -3.05832 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.47643 - 2.55725i) q^{10} +(-1.64212 - 2.84424i) q^{11} +(0.420934 + 0.729078i) q^{12} +(-2.61595 + 4.53096i) q^{13} +3.67484 q^{14} +(-1.37194 + 2.37626i) q^{15} -1.60753 q^{16} +(-3.47562 - 6.01994i) q^{17} +(-0.538083 + 0.931987i) q^{18} +(-1.29190 - 2.23764i) q^{19} +(1.15499 + 2.00050i) q^{20} +(-1.70738 - 2.95726i) q^{21} +(-1.76720 - 3.06087i) q^{22} -8.32320 q^{23} +(1.52916 + 2.64858i) q^{24} +(-1.26442 + 2.19004i) q^{25} +(-2.81520 + 4.87606i) q^{26} +1.00000 q^{27} -2.87477 q^{28} +9.05384 q^{29} +(-1.47643 + 2.55725i) q^{30} +(1.59197 - 2.75737i) q^{31} +4.38668 q^{32} +(-1.64212 + 2.84424i) q^{33} +(-3.74034 - 6.47846i) q^{34} +(-4.68483 - 8.11436i) q^{35} +(0.420934 - 0.729078i) q^{36} +(-0.504276 + 0.873432i) q^{37} +(-1.39030 - 2.40808i) q^{38} +5.23190 q^{39} +(4.19582 + 7.26738i) q^{40} +2.40039 q^{41} +(-1.83742 - 3.18251i) q^{42} +(5.23078 - 9.05997i) q^{43} +(1.38245 + 2.39447i) q^{44} +2.74387 q^{45} -8.95715 q^{46} +(-5.43121 + 9.40713i) q^{47} +(0.803763 + 1.39216i) q^{48} +4.66055 q^{49} +(-1.36073 + 2.35685i) q^{50} +(-3.47562 + 6.01994i) q^{51} +(2.20228 - 3.81447i) q^{52} +(1.71503 - 2.97051i) q^{53} +1.07617 q^{54} +(-4.50577 + 7.80423i) q^{55} -10.4434 q^{56} +(-1.29190 + 2.23764i) q^{57} +9.74343 q^{58} +12.8995 q^{59} +(1.15499 - 2.00050i) q^{60} +(-0.265478 - 0.459821i) q^{61} +(1.71322 - 2.96738i) q^{62} +(-1.70738 + 2.95726i) q^{63} +7.93584 q^{64} +14.3557 q^{65} +(-1.76720 + 3.06087i) q^{66} +11.1797 q^{67} +(2.92601 + 5.06799i) q^{68} +(4.16160 + 7.20810i) q^{69} +(-5.04165 - 8.73240i) q^{70} +(1.54286 - 2.67232i) q^{71} +(1.52916 - 2.64858i) q^{72} +(0.807645 + 1.39888i) q^{73} +(-0.542685 + 0.939958i) q^{74} +2.52884 q^{75} +(1.08761 + 1.88380i) q^{76} +(-5.60745 - 9.71238i) q^{77} +5.63039 q^{78} -12.4770 q^{79} +(2.20542 + 3.81991i) q^{80} +(-0.500000 - 0.866025i) q^{81} +2.58322 q^{82} +(1.94308 - 3.36551i) q^{83} +(1.43739 + 2.48962i) q^{84} +(-9.53665 + 16.5180i) q^{85} +(5.62918 - 9.75003i) q^{86} +(-4.52692 - 7.84085i) q^{87} +(5.02214 + 8.69859i) q^{88} +(-3.52373 - 6.10329i) q^{89} +2.95286 q^{90} +(-8.93283 + 15.4721i) q^{91} +7.00703 q^{92} -3.18393 q^{93} +(-5.84488 + 10.1236i) q^{94} +(-3.54482 + 6.13981i) q^{95} +(-2.19334 - 3.79897i) q^{96} +(-2.91471 + 5.04842i) q^{97} +5.01553 q^{98} +3.28424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.07617			0.760964			0.380482	−	0.924788i	$-0.375758\pi$
$2$	1.07617			0.760964			0.380482	+	0.924788i	$0.375758\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.841867			−0.420934
$5$	−1.37194	−	2.37626i	−0.613549	−	1.06270i	−0.990637	−	0.136520i	$-0.956408\pi$
$5$	−1.37194	−	2.37626i	−0.613549	−	1.06270i	0.377089	−	0.926177i	$-0.376925\pi$
$6$	−0.538083	−	0.931987i	−0.219671	−	0.380482i
$7$	3.41476			1.29066			0.645328	−	0.763905i	$-0.276721\pi$
$7$	3.41476			1.29066			0.645328	+	0.763905i	$0.276721\pi$
$8$	−3.05832			−1.08128
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.47643	−	2.55725i	−0.466889	−	0.808675i
$11$	−1.64212	−	2.84424i	−0.495118	−	0.857570i	0.504866	−	0.863198i	$-0.331542\pi$
$11$	−1.64212	−	2.84424i	−0.495118	−	0.857570i	−0.999984	+	0.00562760i	$0.998209\pi$
$12$	0.420934	+	0.729078i	0.121513	+	0.210467i
$13$	−2.61595	+	4.53096i	−0.725534	+	1.25666i	0.233219	+	0.972424i	$0.425074\pi$
$13$	−2.61595	+	4.53096i	−0.725534	+	1.25666i	−0.958754	+	0.284238i	$0.908259\pi$
$14$	3.67484			0.982143
$15$	−1.37194	+	2.37626i	−0.354233	+	0.613549i
$16$	−1.60753			−0.401881
$17$	−3.47562	−	6.01994i	−0.842961	−	1.46005i	−0.887380	−	0.461038i	$-0.847477\pi$
$17$	−3.47562	−	6.01994i	−0.842961	−	1.46005i	0.0444194	−	0.999013i	$-0.485856\pi$
$18$	−0.538083	+	0.931987i	−0.126827	+	0.219671i
$19$	−1.29190	−	2.23764i	−0.296383	−	0.513351i	0.678923	−	0.734210i	$-0.262447\pi$
$19$	−1.29190	−	2.23764i	−0.296383	−	0.513351i	−0.975306	+	0.220859i	$0.929114\pi$
$20$	1.15499	+	2.00050i	0.258263	+	0.447325i
$21$	−1.70738	−	2.95726i	−0.372580	−	0.645328i
$22$	−1.76720	−	3.06087i	−0.376767	−	0.652580i
$23$	−8.32320			−1.73551			−0.867754	−	0.496994i	$-0.834437\pi$
$23$	−8.32320			−1.73551			−0.867754	+	0.496994i	$0.834437\pi$
$24$	1.52916	+	2.64858i	0.312139	+	0.540640i
$25$	−1.26442	+	2.19004i	−0.252884	+	0.438008i
$26$	−2.81520	+	4.87606i	−0.552106	+	0.956275i
$27$	1.00000			0.192450
$28$	−2.87477			−0.543280
$29$	9.05384			1.68126			0.840628	−	0.541613i	$-0.182186\pi$
$29$	9.05384			1.68126			0.840628	+	0.541613i	$0.182186\pi$
$30$	−1.47643	+	2.55725i	−0.269558	+	0.466889i
$31$	1.59197	−	2.75737i	0.285926	−	0.495238i	−0.686908	−	0.726745i	$-0.741032\pi$
$31$	1.59197	−	2.75737i	0.285926	−	0.495238i	0.972833	+	0.231507i	$0.0743656\pi$
$32$	4.38668			0.775462
$33$	−1.64212	+	2.84424i	−0.285857	+	0.495118i
$34$	−3.74034	−	6.47846i	−0.641463	−	1.11105i
$35$	−4.68483	−	8.11436i	−0.791880	−	1.37158i
$36$	0.420934	−	0.729078i	0.0701556	−	0.121513i
$37$	−0.504276	+	0.873432i	−0.0829025	+	0.143591i	−0.904496	−	0.426483i	$-0.859752\pi$
$37$	−0.504276	+	0.873432i	−0.0829025	+	0.143591i	0.821593	+	0.570075i	$0.193086\pi$
$38$	−1.39030	−	2.40808i	−0.225537	−	0.390641i
$39$	5.23190			0.837775
$40$	4.19582	+	7.26738i	0.663418	+	1.14907i
$41$	2.40039			0.374878			0.187439	−	0.982276i	$-0.439981\pi$
$41$	2.40039			0.374878			0.187439	+	0.982276i	$0.439981\pi$
$42$	−1.83742	−	3.18251i	−0.283520	−	0.491072i
$43$	5.23078	−	9.05997i	0.797686	−	1.38163i	−0.123434	−	0.992353i	$-0.539391\pi$
$43$	5.23078	−	9.05997i	0.797686	−	1.38163i	0.921120	−	0.389280i	$-0.127276\pi$
$44$	1.38245	+	2.39447i	0.208412	+	0.360980i
$45$	2.74387			0.409032
$46$	−8.95715			−1.32066
$47$	−5.43121	+	9.40713i	−0.792223	+	1.37217i	0.132364	+	0.991201i	$0.457743\pi$
$47$	−5.43121	+	9.40713i	−0.792223	+	1.37217i	−0.924588	+	0.380970i	$0.875590\pi$
$48$	0.803763	+	1.39216i	0.116013	+	0.200941i
$49$	4.66055			0.665794
$50$	−1.36073	+	2.35685i	−0.192436	+	0.333308i
$51$	−3.47562	+	6.01994i	−0.486684	+	0.842961i
$52$	2.20228	−	3.81447i	0.305402	−	0.528971i
$53$	1.71503	−	2.97051i	0.235577	−	0.408031i	−0.723863	−	0.689943i	$-0.757635\pi$
$53$	1.71503	−	2.97051i	0.235577	−	0.408031i	0.959440	+	0.281912i	$0.0909687\pi$
$54$	1.07617			0.146448
$55$	−4.50577	+	7.80423i	−0.607559	+	1.05232i
$56$	−10.4434			−1.39556
$57$	−1.29190	+	2.23764i	−0.171117	+	0.296383i
$58$	9.74343			1.27938
$59$	12.8995			1.67938			0.839689	−	0.543067i	$-0.182737\pi$
$59$	12.8995			1.67938			0.839689	+	0.543067i	$0.182737\pi$
$60$	1.15499	−	2.00050i	0.149108	−	0.258263i
$61$	−0.265478	−	0.459821i	−0.0339910	−	0.0588741i	0.848529	−	0.529148i	$-0.177488\pi$
$61$	−0.265478	−	0.459821i	−0.0339910	−	0.0588741i	−0.882520	+	0.470274i	$0.844155\pi$
$62$	1.71322	−	2.96738i	0.217579	−	0.376858i
$63$	−1.70738	+	2.95726i	−0.215109	+	0.372580i
$64$	7.93584			0.991980
$65$	14.3557			1.78060
$66$	−1.76720	+	3.06087i	−0.217527	+	0.376767i
$67$	11.1797			1.36582			0.682909	−	0.730504i	$-0.260715\pi$
$67$	11.1797			1.36582			0.682909	+	0.730504i	$0.260715\pi$
$68$	2.92601	+	5.06799i	0.354830	+	0.614584i
$69$	4.16160	+	7.20810i	0.500998	+	0.867754i
$70$	−5.04165	−	8.73240i	−0.602593	−	1.04372i
$71$	1.54286	−	2.67232i	0.183104	−	0.317146i	−0.759832	−	0.650120i	$-0.774719\pi$
$71$	1.54286	−	2.67232i	0.183104	−	0.317146i	0.942936	+	0.332974i	$0.108052\pi$
$72$	1.52916	−	2.64858i	0.180213	−	0.312139i
$73$	0.807645	+	1.39888i	0.0945276	+	0.163727i	0.909411	−	0.415898i	$-0.136533\pi$
$73$	0.807645	+	1.39888i	0.0945276	+	0.163727i	−0.814884	+	0.579624i	$0.803199\pi$
$74$	−0.542685	+	0.939958i	−0.0630858	+	0.109268i
$75$	2.52884			0.292005
$76$	1.08761	+	1.88380i	0.124758	+	0.216086i
$77$	−5.60745	−	9.71238i	−0.639028	−	1.10683i
$78$	5.63039			0.637517
$79$	−12.4770			−1.40377			−0.701885	−	0.712291i	$-0.747658\pi$
$79$	−12.4770			−1.40377			−0.701885	+	0.712291i	$0.747658\pi$
$80$	2.20542	+	3.81991i	0.246574	+	0.427078i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.58322			0.285269
$83$	1.94308	−	3.36551i	0.213281	−	0.369413i	−0.739459	−	0.673202i	$-0.764918\pi$
$83$	1.94308	−	3.36551i	0.213281	−	0.369413i	0.952739	+	0.303789i	$0.0982518\pi$
$84$	1.43739	+	2.48962i	0.156832	+	0.271640i
$85$	−9.53665	+	16.5180i	−1.03440	+	1.79162i
$86$	5.62918	−	9.75003i	0.607010	−	1.05137i
$87$	−4.52692	−	7.84085i	−0.485337	−	0.840628i
$88$	5.02214	+	8.69859i	0.535361	+	0.927273i
$89$	−3.52373	−	6.10329i	−0.373515	−	0.646947i	0.616588	−	0.787286i	$-0.288514\pi$
$89$	−3.52373	−	6.10329i	−0.373515	−	0.646947i	−0.990104	+	0.140338i	$0.955181\pi$
$90$	2.95286			0.311259
$91$	−8.93283	+	15.4721i	−0.936415	+	1.62192i
$92$	7.00703			0.730533
$93$	−3.18393			−0.330158
$94$	−5.84488	+	10.1236i	−0.602853	+	1.04417i
$95$	−3.54482	+	6.13981i	−0.363691	+	0.629931i
$96$	−2.19334	−	3.79897i	−0.223857	−	0.387731i
$97$	−2.91471	+	5.04842i	−0.295944	+	0.512590i	−0.975204	−	0.221308i	$-0.928967\pi$
$97$	−2.91471	+	5.04842i	−0.295944	+	0.512590i	0.679260	+	0.733898i	$0.262301\pi$
$98$	5.01553			0.506645
$99$	3.28424			0.330079
$100$	1.06447	−	1.84372i	0.106447	−	0.184372i
$101$	−2.03703			−0.202692			−0.101346	−	0.994851i	$-0.532315\pi$
$101$	−2.03703			−0.202692			−0.101346	+	0.994851i	$0.532315\pi$
$102$	−3.74034	+	6.47846i	−0.370349	+	0.641463i
$103$	−2.83762			−0.279599			−0.139799	−	0.990180i	$-0.544646\pi$
$103$	−2.83762			−0.279599			−0.139799	+	0.990180i	$0.544646\pi$
$104$	8.00042	−	13.8571i	0.784505	−	1.35880i
$105$	−4.68483	+	8.11436i	−0.457192	+	0.791880i
$106$	1.84565	−	3.19676i	0.179266	−	0.310497i
$107$	4.71240	−	8.16211i	0.455565	−	0.789061i	−0.543156	−	0.839632i	$-0.682771\pi$
$107$	4.71240	−	8.16211i	0.455565	−	0.789061i	0.998720	+	0.0505708i	$0.0161040\pi$
$108$	−0.841867			−0.0810087
$109$	−5.47026	−	9.47476i	−0.523955	−	0.907517i	−0.999611	−	0.0278859i	$-0.991122\pi$
$109$	−5.47026	−	9.47476i	−0.523955	−	0.907517i	0.475656	−	0.879632i	$-0.342211\pi$
$110$	−4.84896	+	8.39865i	−0.462330	+	0.800780i
$111$	1.00855			0.0957276
$112$	−5.48931			−0.518691
$113$	−6.75192	−	11.6947i	−0.635167	−	1.10014i	−0.986480	−	0.163883i	$-0.947598\pi$
$113$	−6.75192	−	11.6947i	−0.635167	−	1.10014i	0.351313	−	0.936258i	$-0.385735\pi$
$114$	−1.39030	+	2.40808i	−0.130214	+	0.225537i
$115$	11.4189	+	19.7781i	1.06482	+	1.84432i
$116$	−7.62213			−0.707697
$117$	−2.61595	−	4.53096i	−0.241845	−	0.418887i
$118$	13.8821			1.27795
$119$	−11.8684	−	20.5566i	−1.08797	−	1.88442i
$120$	4.19582	−	7.26738i	0.383024	−	0.663418i
$121$	0.106870	−	0.185104i	0.00971546	−	0.0168277i
$122$	−0.285698	−	0.494844i	−0.0258659	−	0.0448011i
$123$	−1.20020	−	2.07880i	−0.108218	−	0.187439i
$124$	−1.34022	+	2.32134i	−0.120356	+	0.208462i
$125$	−6.78055			−0.606471
$126$	−1.83742	+	3.18251i	−0.163691	+	0.283520i
$127$	8.17234	−	14.1549i	0.725178	−	1.25605i	−0.233722	−	0.972303i	$-0.575091\pi$
$127$	8.17234	−	14.1549i	0.725178	−	1.25605i	0.958901	−	0.283742i	$-0.0915760\pi$
$128$	−0.233069			−0.0206006
$129$	−10.4616			−0.921088
$130$	15.4491			1.35497
$131$	−4.63937	+	8.03563i	−0.405344	+	0.702076i	−0.994361	−	0.106044i	$-0.966181\pi$
$131$	−4.63937	+	8.03563i	−0.405344	+	0.702076i	0.589018	+	0.808120i	$0.299515\pi$
$132$	1.38245	−	2.39447i	0.120327	−	0.208412i
$133$	−4.41154	−	7.64100i	−0.382529	−	0.662559i
$134$	12.0312			1.03934
$135$	−1.37194	−	2.37626i	−0.118078	−	0.204516i
$136$	10.6295	+	18.4109i	0.911476	+	1.57872i
$137$	5.25071	+	9.09450i	0.448599	+	0.776996i	0.998295	−	0.0583686i	$-0.0185899\pi$
$137$	5.25071	+	9.09450i	0.448599	+	0.776996i	−0.549696	+	0.835365i	$0.685257\pi$
$138$	4.47857	+	7.75712i	0.381241	+	0.660330i
$139$	4.81405	−	8.33818i	0.408322	−	0.707235i	−0.586380	−	0.810036i	$-0.699447\pi$
$139$	4.81405	−	8.33818i	0.408322	−	0.707235i	0.994702	+	0.102802i	$0.0327807\pi$
$140$	3.94400	+	6.83121i	0.333329	+	0.577343i
$141$	10.8624			0.914780
$142$	1.66038	−	2.87586i	0.139336	−	0.241337i
$143$	17.1828			1.43690
$144$	0.803763	−	1.39216i	0.0669802	−	0.116013i
$145$	−12.4213	−	21.5143i	−1.03153	−	1.78667i
$146$	0.869159	+	1.50543i	0.0719322	+	0.124590i
$147$	−2.33028	−	4.03616i	−0.192198	−	0.332897i
$148$	0.424534	−	0.735314i	0.0348964	−	0.0604424i
$149$	12.1151			0.992505			0.496253	−	0.868178i	$-0.334709\pi$
$149$	12.1151			0.992505			0.496253	+	0.868178i	$0.334709\pi$
$150$	2.72145			0.222206
$151$	10.2935	+	17.8288i	0.837671	+	1.45089i	0.891837	+	0.452357i	$0.149417\pi$
$151$	10.2935	+	17.8288i	0.837671	+	1.45089i	−0.0541654	+	0.998532i	$0.517250\pi$
$152$	3.95106	+	6.84343i	0.320473	+	0.555075i
$153$	6.95123			0.561974
$154$	−6.03454	−	10.4521i	−0.486277	−	0.842257i
$155$	−8.73631			−0.701717
$156$	−4.40457			−0.352647
$157$	−3.17726	+	12.1204i	−0.253573	+	0.967316i
$157$	−3.17726	+	12.1204i	−0.253573	+	0.967316i
$158$	−13.4273			−1.06822
$159$	−3.43005			−0.272021
$160$	−6.01824	−	10.4239i	−0.475784	−	0.824082i
$161$	−28.4217			−2.23994
$162$	−0.538083	−	0.931987i	−0.0422758	−	0.0732238i
$163$	8.97444	+	15.5442i	0.702932	+	1.21751i	0.967433	+	0.253129i	$0.0814597\pi$
$163$	8.97444	+	15.5442i	0.702932	+	1.21751i	−0.264500	+	0.964386i	$0.585207\pi$
$164$	−2.02081			−0.157799
$165$	9.01155			0.701548
$166$	2.09107	−	3.62185i	0.162299	−	0.281110i
$167$	−1.78964	−	3.09974i	−0.138486	−	0.239865i	0.788438	−	0.615115i	$-0.210890\pi$
$167$	−1.78964	−	3.09974i	−0.138486	−	0.239865i	−0.926924	+	0.375250i	$0.877557\pi$
$168$	5.22171	+	9.04426i	0.402864	+	0.697780i
$169$	−7.18640	−	12.4472i	−0.552800	−	0.957478i
$170$	−10.2630	+	17.7761i	−0.787138	+	1.36336i
$171$	2.58381			0.197589
$172$	−4.40362	+	7.62729i	−0.335773	+	0.581575i
$173$	−8.52685			−0.648284			−0.324142	−	0.946008i	$-0.605076\pi$
$173$	−8.52685			−0.648284			−0.324142	+	0.946008i	$0.605076\pi$
$174$	−4.87172	−	8.43806i	−0.369324	−	0.639688i
$175$	−4.31769	+	7.47845i	−0.326386	+	0.565318i
$176$	2.63975	+	4.57219i	0.198979	+	0.344642i
$177$	−6.44977	−	11.1713i	−0.484795	−	0.839689i
$178$	−3.79212	−	6.56815i	−0.284232	−	0.492304i
$179$	−0.710456	−	1.23055i	−0.0531020	−	0.0919754i	0.838253	−	0.545282i	$-0.183578\pi$
$179$	−0.710456	−	1.23055i	−0.0531020	−	0.0919754i	−0.891355	+	0.453307i	$0.850244\pi$
$180$	−2.30998			−0.172175
$181$	0.305866	+	0.529776i	0.0227349	+	0.0393779i	0.877169	−	0.480182i	$-0.159429\pi$
$181$	0.305866	+	0.529776i	0.0227349	+	0.0393779i	−0.854434	+	0.519560i	$0.826096\pi$
$182$	−9.61321	+	16.6506i	−0.712579	+	1.23422i
$183$	−0.265478	+	0.459821i	−0.0196247	+	0.0339910i
$184$	25.4550			1.87657
$185$	2.76734			0.203459
$186$	−3.42644			−0.251239
$187$	−11.4148	+	19.7710i	−0.834731	+	1.44580i
$188$	4.57236	−	7.91955i	0.333473	−	0.577593i
$189$	3.41476			0.248387
$190$	−3.81481	+	6.60745i	−0.276756	+	0.479355i
$191$	8.45427	+	14.6432i	0.611729	+	1.05955i	0.990949	+	0.134240i	$0.0428592\pi$
$191$	8.45427	+	14.6432i	0.611729	+	1.05955i	−0.379219	+	0.925307i	$0.623807\pi$
$192$	−3.96792	−	6.87264i	−0.286360	−	0.495990i
$193$	1.68274	−	2.91459i	0.121126	−	0.209797i	−0.799086	−	0.601217i	$-0.794683\pi$
$193$	1.68274	−	2.91459i	0.121126	−	0.209797i	0.920212	+	0.391420i	$0.128016\pi$
$194$	−3.13671	+	5.43294i	−0.225203	+	0.390063i
$195$	−7.17784	−	12.4324i	−0.514016	−	0.890301i
$196$	−3.92357			−0.280255
$197$	−6.39087	−	11.0693i	−0.455331	−	0.788656i	0.543377	−	0.839489i	$-0.317146\pi$
$197$	−6.39087	−	11.0693i	−0.455331	−	0.788656i	−0.998707	+	0.0508333i	$0.983812\pi$
$198$	3.53439			0.251178
$199$	0.343855	+	0.595574i	0.0243752	+	0.0422191i	0.877956	−	0.478742i	$-0.158907\pi$
$199$	0.343855	+	0.595574i	0.0243752	+	0.0422191i	−0.853580	+	0.520961i	$0.825574\pi$
$200$	3.86700	−	6.69784i	0.273438	−	0.473609i
$201$	−5.58985	−	9.68190i	−0.394277	−	0.682909i
$202$	−2.19218			−0.154241
$203$	30.9166			2.16992
$204$	2.92601	−	5.06799i	0.204861	−	0.354830i
$205$	−3.29318	−	5.70396i	−0.230006	−	0.398382i
$206$	−3.05375			−0.212765
$207$	4.16160	−	7.20810i	0.289251	−	0.500998i
$208$	4.20521	−	7.28364i	0.291579	−	0.505029i
$209$	−4.24293	+	7.34897i	−0.293489	+	0.508339i
$210$	−5.04165	+	8.73240i	−0.347907	+	0.602593i
$211$	−22.4735			−1.54714			−0.773570	−	0.633711i	$-0.781531\pi$
$211$	−22.4735			−1.54714			−0.773570	+	0.633711i	$0.781531\pi$
$212$	−1.44382	+	2.50078i	−0.0991622	+	0.171754i
$213$	−3.08573			−0.211431
$214$	5.07132	−	8.78379i	0.346668	−	0.600447i
$215$	−28.7052			−1.95768
$216$	−3.05832			−0.208092
$217$	5.43618	−	9.41573i	0.369032	−	0.639182i
$218$	−5.88690	−	10.1964i	−0.398711	−	0.690588i
$219$	0.807645	−	1.39888i	0.0545756	−	0.0945276i
$220$	3.79326	−	6.57012i	0.255742	−	0.442958i
$221$	36.3682			2.44639
$222$	1.08537			0.0728453
$223$	−4.34874	+	7.53223i	−0.291213	+	0.504396i	−0.974097	−	0.226131i	$-0.927392\pi$
$223$	−4.34874	+	7.53223i	−0.291213	+	0.504396i	0.682884	+	0.730527i	$0.260725\pi$
$224$	14.9794			1.00086
$225$	−1.26442	−	2.19004i	−0.0842947	−	0.146003i
$226$	−7.26618	−	12.5854i	−0.483339	−	0.837168i
$227$	6.42452	+	11.1276i	0.426411	+	0.738565i	0.996551	−	0.0829824i	$-0.0264445\pi$
$227$	6.42452	+	11.1276i	0.426411	+	0.738565i	−0.570140	+	0.821547i	$0.693111\pi$
$228$	1.08761	−	1.88380i	0.0720288	−	0.124758i
$229$	5.15214	−	8.92378i	0.340463	−	0.589700i	−0.644055	−	0.764979i	$-0.722749\pi$
$229$	5.15214	−	8.92378i	0.340463	−	0.589700i	0.984519	+	0.175279i	$0.0560828\pi$
$230$	12.2886	+	21.2845i	0.810289	+	1.40346i
$231$	−5.60745	+	9.71238i	−0.368943	+	0.639028i
$232$	−27.6895			−1.81791
$233$	−7.74421	−	13.4134i	−0.507340	−	0.878738i	−0.999964	−	0.00849606i	$-0.997296\pi$
$233$	−7.74421	−	13.4134i	−0.507340	−	0.878738i	0.492624	−	0.870242i	$-0.336038\pi$
$234$	−2.81520	−	4.87606i	−0.184035	−	0.318758i
$235$	29.8051			1.94427
$236$	−10.8597			−0.706907
$237$	6.23849	+	10.8054i	0.405233	+	0.701885i
$238$	−12.7723	−	22.1224i	−0.827908	−	1.43398i
$239$	16.6532			1.07721			0.538603	−	0.842560i	$-0.318952\pi$
$239$	16.6532			1.07721			0.538603	+	0.842560i	$0.318952\pi$
$240$	2.20542	−	3.81991i	0.142359	−	0.246574i
$241$	−12.2108	−	21.1498i	−0.786569	−	1.36238i	−0.928057	−	0.372438i	$-0.878522\pi$
$241$	−12.2108	−	21.1498i	−0.786569	−	1.36238i	0.141488	−	0.989940i	$-0.454811\pi$
$242$	0.115010	−	0.199203i	0.00739312	−	0.0128053i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.223497	+	0.387108i	0.0143079	+	0.0247821i
$245$	−6.39399	−	11.0747i	−0.408497	−	0.707537i
$246$	−1.29161	−	2.23713i	−0.0823500	−	0.142634i
$247$	13.5182			0.860144
$248$	−4.86874	+	8.43291i	−0.309166	+	0.535490i
$249$	−3.88616			−0.246275
$250$	−7.29699			−0.461502
$251$	3.57844	−	6.19805i	0.225869	−	0.391217i	−0.730710	−	0.682687i	$-0.760811\pi$
$251$	3.57844	−	6.19805i	0.225869	−	0.391217i	0.956580	+	0.291470i	$0.0941444\pi$
$252$	1.43739	−	2.48962i	0.0905467	−	0.156832i
$253$	13.6677	+	23.6732i	0.859282	+	1.48832i
$254$	8.79480	−	15.2330i	0.551835	−	0.955806i
$255$	19.0733			1.19442
$256$	−16.1225			−1.00766
$257$	−6.82792	+	11.8263i	−0.425914	+	0.737705i	−0.996505	−	0.0835295i	$-0.973381\pi$
$257$	−6.82792	+	11.8263i	−0.425914	+	0.737705i	0.570591	+	0.821234i	$0.306714\pi$
$258$	−11.2584			−0.700915
$259$	−1.72198	+	2.98256i	−0.106999	+	0.185327i
$260$	−12.0856			−0.749515
$261$	−4.52692	+	7.84085i	−0.280209	+	0.485337i
$262$	−4.99273	+	8.64767i	−0.308452	+	0.534255i
$263$	−13.9014	+	24.0779i	−0.857197	+	1.48471i	0.0173948	+	0.999849i	$0.494463\pi$
$263$	−13.9014	+	24.0779i	−0.857197	+	1.48471i	−0.874592	+	0.484860i	$0.838871\pi$
$264$	5.02214	−	8.69859i	0.309091	−	0.535361i
$265$	−9.41163			−0.578152
$266$	−4.74754	−	8.22299i	−0.291091	−	0.504184i
$267$	−3.52373	+	6.10329i	−0.215649	+	0.373515i
$268$	−9.41182			−0.574918
$269$	−23.6455			−1.44169			−0.720847	−	0.693095i	$-0.756247\pi$
$269$	−23.6455			−1.44169			−0.720847	+	0.693095i	$0.756247\pi$
$270$	−1.47643	−	2.55725i	−0.0898528	−	0.155630i
$271$	5.15267	−	8.92469i	0.313003	−	0.542136i	−0.666008	−	0.745944i	$-0.731998\pi$
$271$	5.15267	−	8.92469i	0.313003	−	0.542136i	0.979011	+	0.203808i	$0.0653318\pi$
$272$	5.58714	+	9.67722i	0.338770	+	0.586767i
$273$	17.8657			1.08128
$274$	5.65064	+	9.78720i	0.341368	+	0.591266i
$275$	8.30533			0.500830
$276$	−3.50351	−	6.06827i	−0.210887	−	0.365267i
$277$	−4.39066	+	7.60485i	−0.263809	+	0.456931i	−0.967251	−	0.253822i	$-0.918312\pi$
$277$	−4.39066	+	7.60485i	−0.263809	+	0.456931i	0.703442	+	0.710753i	$0.251646\pi$
$278$	5.18071	−	8.97326i	0.310719	−	0.538180i
$279$	1.59197	+	2.75737i	0.0953085	+	0.165079i
$280$	14.3277	+	24.8163i	0.856244	+	1.48306i
$281$	−5.55377	+	9.61941i	−0.331310	+	0.573846i	−0.982769	−	0.184838i	$-0.940824\pi$
$281$	−5.55377	+	9.61941i	−0.331310	+	0.573846i	0.651459	+	0.758684i	$0.274157\pi$
$282$	11.6898			0.696115
$283$	14.1046	−	24.4298i	0.838430	−	1.45220i	−0.0527770	−	0.998606i	$-0.516807\pi$
$283$	14.1046	−	24.4298i	0.838430	−	1.45220i	0.891207	−	0.453597i	$-0.149859\pi$
$284$	−1.29889	+	2.24974i	−0.0770747	+	0.133497i
$285$	7.08964			0.419954
$286$	18.4916			1.09343
$287$	8.19675			0.483839
$288$	−2.19334	+	3.79897i	−0.129244	+	0.223857i
$289$	−15.6598	+	27.1236i	−0.921166	+	1.59551i
$290$	−13.3674	−	23.1530i	−0.784959	−	1.35959i
$291$	5.82942			0.341727
$292$	−0.679929	−	1.17767i	−0.0397899	−	0.0689180i
$293$	2.42754	+	4.20463i	0.141819	+	0.245637i	0.928181	−	0.372128i	$-0.121372\pi$
$293$	2.42754	+	4.20463i	0.141819	+	0.245637i	−0.786363	+	0.617765i	$0.788038\pi$
$294$	−2.50777	−	4.34358i	−0.146256	−	0.253323i
$295$	−17.6974	−	30.6527i	−1.03038	−	1.78467i
$296$	1.54224	−	2.67124i	0.0896408	−	0.155262i
$297$	−1.64212	−	2.84424i	−0.0952856	−	0.165039i
$298$	13.0378			0.755261
$299$	21.7731	−	37.7121i	1.25917	−	2.18095i
$300$	−2.12895			−0.122915
$301$	17.8618	−	30.9376i	1.02954	−	1.78321i
$302$	11.0775	+	19.1868i	0.637438	+	1.10407i
$303$	1.01851	+	1.76412i	0.0585121	+	0.101346i
$304$	2.07677	+	3.59707i	0.119111	+	0.206306i
$305$	−0.728438	+	1.26169i	−0.0417102	+	0.0722442i
$306$	7.48068			0.427642
$307$	2.37363			0.135470			0.0677351	−	0.997703i	$-0.478423\pi$
$307$	2.37363			0.135470			0.0677351	+	0.997703i	$0.478423\pi$
$308$	4.72072	+	8.17653i	0.268988	+	0.465901i
$309$	1.41881	+	2.45745i	0.0807132	+	0.139799i
$310$	−9.40172			−0.533982
$311$	1.41582	+	2.45227i	0.0802836	+	0.139055i	0.903372	−	0.428858i	$-0.141084\pi$
$311$	1.41582	+	2.45227i	0.0802836	+	0.139055i	−0.823088	+	0.567914i	$0.807751\pi$
$312$	−16.0008			−0.905869
$313$	−28.5540			−1.61397			−0.806983	−	0.590575i	$-0.798901\pi$
$313$	−28.5540			−1.61397			−0.806983	+	0.590575i	$0.798901\pi$
$314$	−3.41926	+	13.0436i	−0.192960	+	0.736093i
$315$	9.36966			0.527920
$316$	10.5040			0.590893
$317$	−1.75538	−	3.04041i	−0.0985920	−	0.170766i	0.812510	−	0.582947i	$-0.198101\pi$
$317$	−1.75538	−	3.04041i	−0.0985920	−	0.170766i	−0.911102	+	0.412181i	$0.864767\pi$
$318$	−3.69130			−0.206998
$319$	−14.8675	−	25.7513i	−0.832421	−	1.44179i
$320$	−10.8875	−	18.8577i	−0.608628	−	1.05418i
$321$	−9.42480			−0.526041
$322$	−30.5865			−1.70452
$323$	−8.98033	+	15.5544i	−0.499679	+	0.865469i
$324$	0.420934	+	0.729078i	0.0233852	+	0.0405043i
$325$	−6.61532	−	11.4581i	−0.366952	−	0.635580i
$326$	9.65798	+	16.7281i	0.534906	+	0.926485i
$327$	−5.47026	+	9.47476i	−0.302506	+	0.523955i
$328$	−7.34116			−0.405348
$329$	−18.5462	+	32.1230i	−1.02249	+	1.77100i
$330$	9.69792			0.533853
$331$	10.6599	+	18.4634i	0.585919	+	1.01484i	0.994760	+	0.102236i	$0.0325997\pi$
$331$	10.6599	+	18.4634i	0.585919	+	1.01484i	−0.408841	+	0.912606i	$0.634067\pi$
$332$	−1.63581	+	2.83331i	−0.0897769	+	0.155498i
$333$	−0.504276	−	0.873432i	−0.0276342	−	0.0478638i
$334$	−1.92595	−	3.33584i	−0.105383	−	0.182529i
$335$	−15.3378	−	26.5659i	−0.837995	−	1.45145i
$336$	2.74465	+	4.75388i	0.149733	+	0.259345i
$337$	5.21636			0.284153			0.142077	−	0.989856i	$-0.454622\pi$
$337$	5.21636			0.284153			0.142077	+	0.989856i	$0.454622\pi$
$338$	−7.73376	−	13.3953i	−0.420661	−	0.728606i
$339$	−6.75192	+	11.6947i	−0.366714	+	0.635167i
$340$	8.02859	−	13.9059i	0.435412	−	0.754155i
$341$	−10.4568			−0.566268
$342$	2.78061			0.150358
$343$	−7.98863			−0.431346
$344$	−15.9974	+	27.7083i	−0.862521	+	1.49393i
$345$	11.4189	−	19.7781i	0.614773	−	1.06482i
$346$	−9.17630			−0.493321
$347$	14.2191	−	24.6281i	0.763319	−	1.32211i	−0.177812	−	0.984064i	$-0.556902\pi$
$347$	14.2191	−	24.6281i	0.763319	−	1.32211i	0.941131	−	0.338042i	$-0.109765\pi$
$348$	3.81106	+	6.60096i	0.204294	+	0.353848i
$349$	−0.681907	−	1.18110i	−0.0365016	−	0.0632227i	0.847197	−	0.531278i	$-0.178288\pi$
$349$	−0.681907	−	1.18110i	−0.0365016	−	0.0632227i	−0.883699	+	0.468055i	$0.844955\pi$
$350$	−4.64655	+	8.04805i	−0.248368	+	0.430187i
$351$	−2.61595	+	4.53096i	−0.139629	+	0.241845i
$352$	−7.20346	−	12.4768i	−0.383946	−	0.665013i
$353$	−13.5233			−0.719771			−0.359885	−	0.932997i	$-0.617184\pi$
$353$	−13.5233			−0.719771			−0.359885	+	0.932997i	$0.617184\pi$
$354$	−6.94103	−	12.0222i	−0.368911	−	0.638973i
$355$	−8.46685			−0.449374
$356$	2.96652	+	5.13816i	0.157225	+	0.272322i
$357$	−11.8684	+	20.5566i	−0.628141	+	1.08797i
$358$	−0.764569	−	1.32427i	−0.0404087	−	0.0699900i
$359$	5.16482			0.272589			0.136294	−	0.990668i	$-0.456481\pi$
$359$	5.16482			0.272589			0.136294	+	0.990668i	$0.456481\pi$
$360$	−8.39164			−0.442278
$361$	6.16197	−	10.6728i	0.324314	−	0.561729i
$362$	0.329163	+	0.570127i	0.0173004	+	0.0299652i
$363$	−0.213740			−0.0112185
$364$	7.52026	−	13.0255i	0.394169	−	0.682720i
$365$	2.21607	−	3.83835i	0.115995	−	0.200909i
$366$	−0.285698	+	0.494844i	−0.0149337	+	0.0258659i
$367$	9.38478	−	16.2549i	0.489881	−	0.848500i	−0.510051	−	0.860144i	$-0.670373\pi$
$367$	9.38478	−	16.2549i	0.489881	−	0.848500i	0.999932	+	0.0116448i	$0.00370672\pi$
$368$	13.3798			0.697468
$369$	−1.20020	+	2.07880i	−0.0624797	+	0.108218i
$370$	2.97812			0.154825
$371$	5.85639	−	10.1436i	0.304049	−	0.526628i
$372$	2.68045			0.138975
$373$	0.219753			0.0113784			0.00568919	−	0.999984i	$-0.498189\pi$
$373$	0.219753			0.0113784			0.00568919	+	0.999984i	$0.498189\pi$
$374$	−12.2842	+	21.2768i	−0.635200	+	1.10020i
$375$	3.39027	+	5.87213i	0.175073	+	0.303235i
$376$	16.6104	−	28.7700i	0.856615	−	1.48370i
$377$	−23.6844	+	41.0226i	−1.21981	+	2.11277i
$378$	3.67484			0.189014
$379$	22.5469			1.15815			0.579077	−	0.815273i	$-0.303413\pi$
$379$	22.5469			1.15815			0.579077	+	0.815273i	$0.303413\pi$
$380$	2.98427	−	5.16890i	0.153090	−	0.265159i
$381$	−16.3447			−0.837364
$382$	9.09820	+	15.7585i	0.465504	+	0.806277i
$383$	0.175994	+	0.304831i	0.00899288	+	0.0155761i	0.870487	−	0.492192i	$-0.163804\pi$
$383$	0.175994	+	0.304831i	0.00899288	+	0.0155761i	−0.861494	+	0.507768i	$0.830471\pi$
$384$	0.116535	+	0.201844i	0.00594688	+	0.0103003i
$385$	−15.3861	+	26.6495i	−0.784149	+	1.35819i
$386$	1.81091	−	3.13658i	0.0921728	−	0.159648i
$387$	5.23078	+	9.05997i	0.265895	+	0.460544i
$388$	2.45380	−	4.25010i	0.124573	−	0.215766i
$389$	24.8761			1.26127			0.630634	−	0.776081i	$-0.282795\pi$
$389$	24.8761			1.26127			0.630634	+	0.776081i	$0.282795\pi$
$390$	−7.72454	−	13.3793i	−0.391147	−	0.677487i
$391$	28.9283	+	50.1052i	1.46297	+	2.53393i
$392$	−14.2535			−0.719909
$393$	9.27874			0.468051
$394$	−6.87764	−	11.9124i	−0.346490	−	0.600139i
$395$	17.1176	+	29.6486i	0.861281	+	1.49178i
$396$	−2.76490			−0.138941
$397$	−11.5669	+	20.0344i	−0.580524	+	1.00550i	0.414893	+	0.909870i	$0.363819\pi$
$397$	−11.5669	+	20.0344i	−0.580524	+	1.00550i	−0.995417	+	0.0956268i	$0.969514\pi$
$398$	0.370045	+	0.640937i	0.0185487	+	0.0321272i
$399$	−4.41154	+	7.64100i	−0.220853	+	0.382529i
$400$	2.03259	−	3.52055i	0.101629	−	0.176027i
$401$	−11.2196	−	19.4330i	−0.560282	−	0.970437i	−0.997472	−	0.0710674i	$-0.977359\pi$
$401$	−11.2196	−	19.4330i	−0.560282	−	0.970437i	0.437190	−	0.899369i	$-0.355974\pi$
$402$	−6.01560	−	10.4193i	−0.300031	−	0.519669i
$403$	8.32901	+	14.4263i	0.414898	+	0.718624i
$404$	1.71491			0.0853198
$405$	−1.37194	+	2.37626i	−0.0681721	+	0.118078i
$406$	33.2714			1.65123
$407$	3.31233			0.164186
$408$	10.6295	−	18.4109i	0.526241	−	0.911476i
$409$	0.530609	−	0.919042i	0.0262369	−	0.0454437i	−0.852609	−	0.522550i	$-0.824981\pi$
$409$	0.530609	−	0.919042i	0.0262369	−	0.0454437i	0.878846	+	0.477106i	$0.158314\pi$
$410$	−3.54401	−	6.13841i	−0.175026	−	0.303154i
$411$	5.25071	−	9.09450i	0.258999	−	0.448599i
$412$	2.38890			0.117693
$413$	44.0488			2.16750
$414$	4.47857	−	7.75712i	0.220110	−	0.381241i
$415$	−10.6631			−0.523432
$416$	−11.4753	+	19.8759i	−0.562624	+	0.974494i
$417$	−9.62810			−0.471490
$418$	−4.56609	+	7.90871i	−0.223335	+	0.386828i
$419$	−12.3988	+	21.4753i	−0.605720	+	1.04914i	0.386217	+	0.922408i	$0.373782\pi$
$419$	−12.3988	+	21.4753i	−0.605720	+	1.04914i	−0.991937	+	0.126730i	$0.959552\pi$
$420$	3.94400	−	6.83121i	0.192448	−	0.333329i
$421$	16.1863	−	28.0355i	0.788873	−	1.36637i	−0.137784	−	0.990462i	$-0.543998\pi$
$421$	16.1863	−	28.0355i	0.788873	−	1.36637i	0.926658	−	0.375907i	$-0.122669\pi$
$422$	−24.1852			−1.17732
$423$	−5.43121	−	9.40713i	−0.264074	−	0.457390i
$424$	−5.24510	+	9.08478i	−0.254724	+	0.441196i
$425$	17.5786			0.852685
$426$	−3.32076			−0.160891
$427$	−0.906542	−	1.57018i	−0.0438706	−	0.0759862i
$428$	−3.96721	+	6.87141i	−0.191762	+	0.332142i
$429$	−8.59142	−	14.8808i	−0.414798	−	0.718451i
$430$	−30.8915			−1.48972
$431$	3.34605	+	5.79552i	0.161173	+	0.279161i	0.935290	−	0.353883i	$-0.115139\pi$
$431$	3.34605	+	5.79552i	0.161173	+	0.279161i	−0.774116	+	0.633043i	$0.781805\pi$
$432$	−1.60753			−0.0773421
$433$	4.54280	+	7.86836i	0.218313	+	0.378129i	0.954292	−	0.298875i	$-0.0966113\pi$
$433$	4.54280	+	7.86836i	0.218313	+	0.378129i	−0.735979	+	0.677004i	$0.763278\pi$
$434$	5.85023	−	10.1329i	0.280820	−	0.486394i
$435$	−12.4213	+	21.5143i	−0.595555	+	1.03153i
$436$	4.60523	+	7.97649i	0.220550	+	0.382005i
$437$	10.7528	+	18.6244i	0.514375	+	0.890924i
$438$	0.869159	−	1.50543i	0.0415300	−	0.0719322i
$439$	28.7684			1.37304			0.686522	−	0.727109i	$-0.259137\pi$
$439$	28.7684			1.37304			0.686522	+	0.727109i	$0.259137\pi$
$440$	13.7801	−	23.8678i	0.656941	−	1.13785i
$441$	−2.33028	+	4.03616i	−0.110966	+	0.192198i
$442$	39.1382			1.86161
$443$	32.6307			1.55033			0.775166	−	0.631757i	$-0.217666\pi$
$443$	32.6307			1.55033			0.775166	+	0.631757i	$0.217666\pi$
$444$	−0.849067			−0.0402949
$445$	−9.66868	+	16.7466i	−0.458339	+	0.793867i
$446$	−4.67996	+	8.10593i	−0.221603	+	0.383827i
$447$	−6.05753	−	10.4920i	−0.286512	−	0.496253i
$448$	27.0990			1.28031
$449$	9.81764	+	17.0047i	0.463323	+	0.802499i	0.999124	−	0.0418451i	$-0.0133236\pi$
$449$	9.81764	+	17.0047i	0.463323	+	0.802499i	−0.535801	+	0.844344i	$0.679990\pi$
$450$	−1.36073	−	2.35685i	−0.0641452	−	0.111103i
$451$	−3.94173	−	6.82728i	−0.185609	−	0.321484i
$452$	5.68422	+	9.84535i	0.267363	+	0.463086i
$453$	10.2935	−	17.8288i	0.483630	−	0.837671i
$454$	6.91385	+	11.9751i	0.324483	+	0.562021i
$455$	49.0211			2.29815
$456$	3.95106	−	6.84343i	0.185025	−	0.320473i
$457$	5.30065			0.247954			0.123977	−	0.992285i	$-0.460435\pi$
$457$	5.30065			0.247954			0.123977	+	0.992285i	$0.460435\pi$
$458$	5.54456	−	9.60346i	0.259080	−	0.448740i
$459$	−3.47562	−	6.01994i	−0.162228	−	0.280987i
$460$	−9.61320	−	16.6506i	−0.448218	−	0.776336i
$461$	−17.4006	−	30.1388i	−0.810429	−	1.40370i	−0.912564	−	0.408933i	$-0.865901\pi$
$461$	−17.4006	−	30.1388i	−0.810429	−	1.40370i	0.102136	−	0.994770i	$-0.467432\pi$
$462$	−6.03454	+	10.4521i	−0.280752	+	0.486277i
$463$	−2.92154			−0.135775			−0.0678876	−	0.997693i	$-0.521626\pi$
$463$	−2.92154			−0.135775			−0.0678876	+	0.997693i	$0.521626\pi$
$464$	−14.5543			−0.675666
$465$	4.36815	+	7.56587i	0.202568	+	0.350859i
$466$	−8.33405	−	14.4350i	−0.386067	−	0.668688i
$467$	−12.0416			−0.557217			−0.278609	−	0.960405i	$-0.589873\pi$
$467$	−12.0416			−0.557217			−0.278609	+	0.960405i	$0.589873\pi$
$468$	2.20228	+	3.81447i	0.101801	+	0.176324i
$469$	38.1759			1.76280
$470$	32.0752			1.47952
$471$	12.0852	−	3.30863i	0.556858	−	0.152454i
$472$	−39.4510			−1.81588
$473$	−34.3583			−1.57980
$474$	6.71365	+	11.6284i	0.308368	+	0.534109i
$475$	6.53404			0.299802
$476$	9.99160	+	17.3060i	0.457964	+	0.793217i
$477$	1.71503	+	2.97051i	0.0785256	+	0.136010i
$478$	17.9216			0.819715
$479$	−1.54787			−0.0707239			−0.0353620	−	0.999375i	$-0.511258\pi$
$479$	−1.54787			−0.0707239			−0.0353620	+	0.999375i	$0.511258\pi$
$480$	−6.01824	+	10.4239i	−0.274694	+	0.475784i
$481$	−2.63832	−	4.56971i	−0.120297	−	0.208361i
$482$	−13.1409	−	22.7607i	−0.598551	−	1.03672i
$483$	14.2108	+	24.6139i	0.646616	+	1.11997i
$484$	−0.0899704	+	0.155833i	−0.00408956	+	0.00708333i
$485$	15.9952			0.726304
$486$	−0.538083	+	0.931987i	−0.0244079	+	0.0422758i
$487$	6.97701			0.316159			0.158079	−	0.987426i	$-0.449470\pi$
$487$	6.97701			0.316159			0.158079	+	0.987426i	$0.449470\pi$
$488$	0.811916	+	1.40628i	0.0367537	+	0.0636593i
$489$	8.97444	−	15.5442i	0.405838	−	0.702932i
$490$	−6.88099	−	11.9182i	−0.310851	−	0.538410i
$491$	−2.16774	−	3.75464i	−0.0978290	−	0.169445i	0.812957	−	0.582324i	$-0.197856\pi$
$491$	−2.16774	−	3.75464i	−0.0978290	−	0.169445i	−0.910786	+	0.412879i	$0.864523\pi$
$492$	1.01040	+	1.75007i	0.0455526	+	0.0788994i
$493$	−31.4677	−	54.5036i	−1.41723	−	2.45472i
$494$	14.5479			0.654539
$495$	−4.50577	−	7.80423i	−0.202520	−	0.350774i
$496$	−2.55913	+	4.43254i	−0.114908	+	0.199027i
$497$	5.26850	−	9.12532i	0.236325	−	0.409326i
$498$	−4.18215			−0.187407
$499$	10.2320			0.458047			0.229023	−	0.973421i	$-0.426447\pi$
$499$	10.2320			0.458047			0.229023	+	0.973421i	$0.426447\pi$
$500$	5.70832			0.255284
$501$	−1.78964	+	3.09974i	−0.0799551	+	0.138486i
$502$	3.85100	−	6.67013i	0.171879	−	0.297702i
$503$	−17.8283			−0.794923			−0.397462	−	0.917619i	$-0.630109\pi$
$503$	−17.8283			−0.794923			−0.397462	+	0.917619i	$0.630109\pi$
$504$	5.22171	−	9.04426i	0.232593	−	0.402864i
$505$	2.79467	+	4.84051i	0.124361	+	0.215400i
$506$	14.7087	+	25.4763i	0.653883	+	1.13256i
$507$	−7.18640	+	12.4472i	−0.319159	+	0.552800i
$508$	−6.88003	+	11.9166i	−0.305252	+	0.528712i
$509$	10.6252	+	18.4034i	0.470954	+	0.815717i	0.999448	−	0.0332206i	$-0.0105764\pi$
$509$	10.6252	+	18.4034i	0.470954	+	0.815717i	−0.528494	+	0.848937i	$0.677243\pi$
$510$	20.5260			0.908908
$511$	2.75791	+	4.77684i	0.122003	+	0.211315i
$512$	−16.8844			−0.746190
$513$	−1.29190	−	2.23764i	−0.0570390	−	0.0987944i
$514$	−7.34798	+	12.7271i	−0.324105	+	0.561367i
$515$	3.89303	+	6.74293i	0.171547	+	0.297129i
$516$	8.80724			0.387717
$517$	35.6748			1.56898
$518$	−1.85314	+	3.20973i	−0.0814221	+	0.141027i
$519$	4.26342	+	7.38447i	0.187144	+	0.324142i
$520$	−43.9043			−1.92533
$521$	2.61505	−	4.52940i	0.114568	−	0.198437i	−0.803039	−	0.595926i	$-0.796785\pi$
$521$	2.61505	−	4.52940i	0.114568	−	0.198437i	0.917607	+	0.397489i	$0.130118\pi$
$522$	−4.87172	+	8.43806i	−0.213229	+	0.369324i
$523$	5.92605	−	10.2642i	0.259128	−	0.448823i	−0.706880	−	0.707333i	$-0.749898\pi$
$523$	5.92605	−	10.2642i	0.259128	−	0.448823i	0.966009	+	0.258510i	$0.0832314\pi$
$524$	3.90573	−	6.76493i	0.170623	−	0.295527i
$525$	8.63537			0.376879
$526$	−14.9602	+	25.9118i	−0.652296	+	1.12981i
$527$	−22.1323			−0.964097
$528$	2.63975	−	4.57219i	0.114881	−	0.198979i
$529$	46.2757			2.01199
$530$	−10.1285			−0.439953
$531$	−6.44977	+	11.1713i	−0.279896	+	0.484795i
$532$	3.71393	+	6.43271i	0.161019	+	0.278893i
$533$	−6.27930	+	10.8761i	−0.271987	+	0.471095i
$534$	−3.79212	+	6.56815i	−0.164101	+	0.284232i
$535$	−25.8604			−1.11804
$536$	−34.1911			−1.47683
$537$	−0.710456	+	1.23055i	−0.0306585	+	0.0531020i
$538$	−25.4465			−1.09708
$539$	−7.65320	−	13.2557i	−0.329647	−	0.570965i
$540$	1.15499	+	2.00050i	0.0497028	+	0.0860877i
$541$	17.8121	+	30.8514i	0.765801	+	1.32641i	0.939822	+	0.341664i	$0.110991\pi$
$541$	17.8121	+	30.8514i	0.765801	+	1.32641i	−0.174021	+	0.984742i	$0.555676\pi$
$542$	5.54513	−	9.60445i	0.238184	−	0.412546i
$543$	0.305866	−	0.529776i	0.0131260	−	0.0227349i
$544$	−15.2464	−	26.4075i	−0.653684	−	1.13221i
$545$	−15.0097	+	25.9975i	−0.642944	+	1.11361i
$546$	19.2264			0.822815
$547$	−9.97314	−	17.2740i	−0.426421	−	0.738582i	0.570131	−	0.821554i	$-0.306892\pi$
$547$	−9.97314	−	17.2740i	−0.426421	−	0.738582i	−0.996552	+	0.0829714i	$0.973559\pi$
$548$	−4.42040	−	7.65636i	−0.188830	−	0.327064i
$549$	0.530956			0.0226606
$550$	8.93791			0.381114
$551$	−11.6967	−	20.2593i	−0.498296	−	0.863074i
$552$	−12.7275	−	22.0447i	−0.541719	−	0.938284i
$553$	−42.6058			−1.81178
$554$	−4.72508	+	8.18408i	−0.200750	+	0.347708i
$555$	−1.38367	−	2.39659i	−0.0587335	−	0.101729i
$556$	−4.05279	+	7.01964i	−0.171877	+	0.297699i
$557$	1.24147	−	2.15028i	0.0526026	−	0.0911104i	−0.838525	−	0.544863i	$-0.816582\pi$
$557$	1.24147	−	2.15028i	0.0526026	−	0.0911104i	0.891128	+	0.453753i	$0.149915\pi$
$558$	1.71322	+	2.96738i	0.0725264	+	0.125619i
$559$	27.3669	+	47.4009i	1.15750	+	2.00484i
$560$	7.53098	+	13.0440i	0.318242	+	0.551211i
$561$	22.8295			0.963864
$562$	−5.97678	+	10.3521i	−0.252115	+	0.436676i
$563$	17.5709			0.740526			0.370263	−	0.928927i	$-0.379268\pi$
$563$	17.5709			0.740526			0.370263	+	0.928927i	$0.379268\pi$
$564$	−9.14471			−0.385062
$565$	−18.5264	+	32.0887i	−0.779412	+	1.34998i
$566$	15.1789	−	26.2906i	0.638015	−	1.10507i
$567$	−1.70738	−	2.95726i	−0.0717031	−	0.124193i
$568$	−4.71857	+	8.17281i	−0.197987	+	0.342923i
$569$	42.6661			1.78866			0.894328	−	0.447411i	$-0.147654\pi$
$569$	42.6661			1.78866			0.894328	+	0.447411i	$0.147654\pi$
$570$	7.62963			0.319570
$571$	−5.01510	+	8.68641i	−0.209875	+	0.363515i	−0.951675	−	0.307107i	$-0.900639\pi$
$571$	−5.01510	+	8.68641i	−0.209875	+	0.363515i	0.741800	+	0.670622i	$0.233973\pi$
$572$	−14.4657			−0.604840
$573$	8.45427	−	14.6432i	0.353182	−	0.611729i
$574$	8.82106			0.368184
$575$	10.5240	−	18.2281i	0.438882	−	0.760166i
$576$	−3.96792	+	6.87264i	−0.165330	+	0.286360i
$577$	22.3532	−	38.7169i	0.930578	−	1.61181i	0.148241	−	0.988951i	$-0.452639\pi$
$577$	22.3532	−	38.7169i	0.930578	−	1.61181i	0.782336	−	0.622856i	$-0.214028\pi$
$578$	−16.8526	+	29.1895i	−0.700974	+	1.21412i
$579$	−3.36548			−0.139865
$580$	10.4571	+	18.1122i	0.434207	+	0.752068i
$581$	6.63514	−	11.4924i	0.275272	−	0.476785i
$582$	6.27342			0.260042
$583$	−11.2651			−0.466554
$584$	−2.47004	−	4.27823i	−0.102211	−	0.177034i
$585$	−7.17784	+	12.4324i	−0.296767	+	0.514016i
$586$	2.61244	+	4.52488i	0.107919	+	0.186921i
$587$	24.8369			1.02513			0.512564	−	0.858649i	$-0.328696\pi$
$587$	24.8369			1.02513			0.512564	+	0.858649i	$0.328696\pi$
$588$	1.96178	+	3.39791i	0.0809026	+	0.140127i
$589$	−8.22667			−0.338974
$590$	−19.0453	−	32.9874i	−0.784083	−	1.35807i
$591$	−6.39087	+	11.0693i	−0.262885	+	0.455331i
$592$	0.810637	−	1.40406i	0.0333170	−	0.0577067i
$593$	11.8270	+	20.4850i	0.485677	+	0.841217i	0.999865	−	0.0164609i	$-0.00523991\pi$
$593$	11.8270	+	20.4850i	0.485677	+	0.841217i	−0.514188	+	0.857678i	$0.671907\pi$
$594$	−1.76720	−	3.06087i	−0.0725089	−	0.125589i
$595$	−32.5653	+	56.4048i	−1.33505	+	2.31237i
$596$	−10.1993			−0.417779
$597$	0.343855	−	0.595574i	0.0140730	−	0.0243752i
$598$	23.4315	−	40.5845i	0.958183	−	1.65962i
$599$	−1.77731			−0.0726191			−0.0363095	−	0.999341i	$-0.511560\pi$
$599$	−1.77731			−0.0726191			−0.0363095	+	0.999341i	$0.511560\pi$
$600$	−7.73400			−0.315739
$601$	11.1772			0.455928			0.227964	−	0.973670i	$-0.426793\pi$
$601$	11.1772			0.455928			0.227964	+	0.973670i	$0.426793\pi$
$602$	19.2223	−	33.2940i	0.783442	−	1.35696i
$603$	−5.58985	+	9.68190i	−0.227636	+	0.394277i
$604$	−8.66574	−	15.0095i	−0.352604	−	0.610728i
$605$	−0.586476			−0.0238436
$606$	1.09609	+	1.89848i	0.0445256	+	0.0771206i
$607$	15.7428	+	27.2674i	0.638981	+	1.10675i	0.985657	+	0.168763i	$0.0539772\pi$
$607$	15.7428	+	27.2674i	0.638981	+	1.10675i	−0.346675	+	0.937985i	$0.612689\pi$
$608$	−5.66716	−	9.81582i	−0.229834	−	0.398084i
$609$	−15.4583	−	26.7746i	−0.626403	−	1.08496i
$610$	−0.783920	+	1.35779i	−0.0317400	+	0.0549753i
$611$	−28.4155	−	49.2172i	−1.14957	−	1.99111i
$612$	−5.85201			−0.236554
$613$	−3.06756	+	5.31318i	−0.123898	+	0.214597i	−0.921302	−	0.388849i	$-0.872873\pi$
$613$	−3.06756	+	5.31318i	−0.123898	+	0.214597i	0.797404	+	0.603446i	$0.206206\pi$
$614$	2.55442			0.103088
$615$	−3.29318	+	5.70396i	−0.132794	+	0.230006i
$616$	17.1494	+	29.7036i	0.690968	+	1.19679i
$617$	−7.99280	−	13.8439i	−0.321778	−	0.557336i	0.659077	−	0.752075i	$-0.270947\pi$
$617$	−7.99280	−	13.8439i	−0.321778	−	0.557336i	−0.980855	+	0.194740i	$0.937614\pi$
$618$	1.52687	+	2.64462i	0.0614199	+	0.106382i
$619$	8.07464	−	13.9857i	0.324547	−	0.562132i	−0.656873	−	0.754001i	$-0.728121\pi$
$619$	8.07464	−	13.9857i	0.324547	−	0.562132i	0.981421	+	0.191868i	$0.0614547\pi$
$620$	7.35481			0.295376
$621$	−8.32320			−0.333999
$622$	1.52365	+	2.63904i	0.0610929	+	0.105816i
$623$	−12.0327	−	20.8412i	−0.482080	−	0.834986i
$624$	−8.41042			−0.336686
$625$	15.6246	+	27.0626i	0.624983	+	1.08250i
$626$	−30.7288			−1.22817
$627$	8.48586			0.338892
$628$	2.67483	−	10.2038i	0.106737	−	0.407176i
$629$	7.01068			0.279534
$630$	10.0833			0.401728
$631$	−0.0237501	−	0.0411364i	−0.000945477	−	0.00163761i	0.865552	−	0.500819i	$-0.166968\pi$
$631$	−0.0237501	−	0.0411364i	−0.000945477	−	0.00163761i	−0.866498	+	0.499181i	$0.833634\pi$
$632$	38.1586			1.51787
$633$	11.2367	+	19.4626i	0.446621	+	0.773570i
$634$	−1.88908	−	3.27198i	−0.0750250	−	0.129947i
$635$	−44.8477			−1.77973
$636$	2.88765			0.114503
$637$	−12.1918	+	21.1168i	−0.483056	+	0.836678i
$638$	−15.9999	−	27.7127i	−0.633442	−	1.09715i
$639$	1.54286	+	2.67232i	0.0610348	+	0.105715i
$640$	0.319756	+	0.553833i	0.0126395	+	0.0218922i
$641$	12.0405	−	20.8547i	0.475571	−	0.823712i	−0.524038	−	0.851695i	$-0.675575\pi$
$641$	12.0405	−	20.8547i	0.475571	−	0.823712i	0.999608	+	0.0279826i	$0.00890831\pi$
$642$	−10.1426			−0.400298
$643$	−6.85507	+	11.8733i	−0.270337	+	0.468238i	−0.968948	−	0.247264i	$-0.920469\pi$
$643$	−6.85507	+	11.8733i	−0.270337	+	0.468238i	0.698611	+	0.715502i	$0.253802\pi$
$644$	23.9273			0.942867
$645$	14.3526	+	24.8594i	0.565133	+	0.978838i
$646$	−9.66432	+	16.7391i	−0.380238	+	0.658591i
$647$	0.779096	+	1.34943i	0.0306294	+	0.0530517i	0.880934	−	0.473240i	$-0.156915\pi$
$647$	0.779096	+	1.34943i	0.0306294	+	0.0530517i	−0.850304	+	0.526291i	$0.823582\pi$
$648$	1.52916	+	2.64858i	0.0600711	+	0.104046i
$649$	−21.1826	−	36.6894i	−0.831491	−	1.44018i
$650$	−7.11918	−	12.3308i	−0.279237	−	0.483653i
$651$	−10.8724			−0.426121
$652$	−7.55528	−	13.0861i	−0.295888	−	0.512493i
$653$	0.801017	−	1.38740i	0.0313462	−	0.0542932i	−0.849927	−	0.526901i	$-0.823354\pi$
$653$	0.801017	−	1.38740i	0.0313462	−	0.0542932i	0.881273	+	0.472608i	$0.156687\pi$
$654$	−5.88690	+	10.1964i	−0.230196	+	0.398711i
$655$	25.4597			0.994792
$656$	−3.85869			−0.150657
$657$	−1.61529			−0.0630184
$658$	−19.9588	+	34.5697i	−0.778077	+	1.34767i
$659$	8.03676	−	13.9201i	0.313068	−	0.542249i	−0.665957	−	0.745990i	$-0.731977\pi$
$659$	8.03676	−	13.9201i	0.313068	−	0.542249i	0.979025	+	0.203741i	$0.0653099\pi$
$660$	−7.58653			−0.295305
$661$	22.9932	−	39.8254i	0.894332	−	1.54903i	0.0597022	−	0.998216i	$-0.480985\pi$
$661$	22.9932	−	39.8254i	0.894332	−	1.54903i	0.834629	−	0.550812i	$-0.185682\pi$
$662$	11.4718	+	19.8697i	0.445863	+	0.772258i
$663$	−18.1841	−	31.4958i	−0.706211	−	1.22319i
$664$	−5.94256	+	10.2928i	−0.230616	+	0.399439i
$665$	−12.1047	+	20.9659i	−0.469400	+	0.813025i
$666$	−0.542685	−	0.939958i	−0.0210286	−	0.0364226i
$667$	−75.3569			−2.91783
$668$	1.50664	+	2.60957i	0.0582935	+	0.100967i
$669$	8.69747			0.336264
$670$	−16.5061	−	28.5893i	−0.637684	−	1.10450i
$671$	−0.871894	+	1.51016i	−0.0336591	+	0.0582993i
$672$	−7.48971	−	12.9726i	−0.288922	−	0.500428i
$673$	−12.3122			−0.474600			−0.237300	−	0.971436i	$-0.576262\pi$
$673$	−12.3122			−0.474600			−0.237300	+	0.971436i	$0.576262\pi$
$674$	5.61367			0.216230
$675$	−1.26442	+	2.19004i	−0.0486676	+	0.0842947i
$676$	6.04999	+	10.4789i	0.232692	+	0.403034i
$677$	−10.6192			−0.408130			−0.204065	−	0.978957i	$-0.565415\pi$
$677$	−10.6192			−0.408130			−0.204065	+	0.978957i	$0.565415\pi$
$678$	−7.26618	+	12.5854i	−0.279056	+	0.483339i
$679$	−9.95302	+	17.2391i	−0.381962	+	0.661577i
$680$	29.1661	−	50.5172i	1.11847	−	1.93725i
$681$	6.42452	−	11.1276i	0.246188	−	0.426411i
$682$	−11.2533			−0.430910
$683$	−5.35275	+	9.27123i	−0.204817	+	0.354754i	−0.950074	−	0.312023i	$-0.898993\pi$
$683$	−5.35275	+	9.27123i	−0.204817	+	0.354754i	0.745257	+	0.666777i	$0.232327\pi$
$684$	−2.17522			−0.0831717
$685$	14.4073	−	24.9542i	0.550474	−	0.953450i
$686$	−8.59709			−0.328239
$687$	−10.3043			−0.393133
$688$	−8.40861	+	14.5641i	−0.320575	+	0.555252i
$689$	8.97285	+	15.5414i	0.341838	+	0.592081i
$690$	12.2886	−	21.2845i	0.467820	−	0.810289i
$691$	−11.1540	+	19.3193i	−0.424319	+	0.734942i	−0.996357	−	0.0852856i	$-0.972820\pi$
$691$	−11.1540	+	19.3193i	−0.424319	+	0.734942i	0.572038	+	0.820227i	$0.306153\pi$
$692$	7.17847			0.272885
$693$	11.2149			0.426018
$694$	15.3021	−	26.5039i	0.580858	−	1.00608i
$695$	−26.4183			−1.00210
$696$	13.8448	+	23.9798i	0.524785	+	0.908954i
$697$	−8.34284	−	14.4502i	−0.316007	−	0.547341i
$698$	−0.733845	−	1.27106i	−0.0277764	−	0.0481102i
$699$	−7.74421	+	13.4134i	−0.292913	+	0.507340i
$700$	3.63492	−	6.29586i	0.137387	−	0.237961i
$701$	4.22768	+	7.32255i	0.159677	+	0.276569i	0.934752	−	0.355300i	$-0.115621\pi$
$701$	4.22768	+	7.32255i	0.159677	+	0.276569i	−0.775075	+	0.631869i	$0.782288\pi$
$702$	−2.81520	+	4.87606i	−0.106253	+	0.184035i
$703$	2.60591			0.0982836
$704$	−13.0316	−	22.5714i	−0.491148	−	0.850693i
$705$	−14.9025	−	25.8120i	−0.561262	−	0.972135i
$706$	−14.5533			−0.547720
$707$	−6.95595			−0.261605
$708$	5.42985	+	9.40478i	0.204066	+	0.353453i
$709$	−18.9976	−	32.9049i	−0.713472	−	1.23577i	−0.963546	−	0.267543i	$-0.913788\pi$
$709$	−18.9976	−	32.9049i	−0.713472	−	1.23577i	0.250074	−	0.968227i	$-0.419545\pi$
$710$	−9.11173			−0.341957
$711$	6.23849	−	10.8054i	0.233962	−	0.405233i
$712$	10.7767	+	18.6658i	0.403874	+	0.699531i
$713$	−13.2503	+	22.9501i	−0.496226	+	0.859489i
$714$	−12.7723	+	22.1224i	−0.477993	+	0.827908i
$715$	−23.5738	−	40.8310i	−0.881609	−	1.52699i
$716$	0.598110	+	1.03596i	0.0223524	+	0.0387155i
$717$	−8.32660	−	14.4221i	−0.310963	−	0.538603i
$718$	5.55820			0.207430
$719$	8.15629	−	14.1271i	0.304178	−	0.526853i	−0.672900	−	0.739734i	$-0.734951\pi$
$719$	8.15629	−	14.1271i	0.304178	−	0.526853i	0.977078	+	0.212881i	$0.0682848\pi$
$720$	−4.41085			−0.164383
$721$	−9.68977			−0.360866
$722$	6.63130	−	11.4857i	0.246791	−	0.427455i
$723$	−12.2108	+	21.1498i	−0.454126	+	0.786569i
$724$	−0.257499	−	0.446001i	−0.00956987	−	0.0165755i
$725$	−11.4479	+	19.8283i	−0.425163	+	0.736403i
$726$	−0.230020			−0.00853684
$727$	20.7895			0.771041			0.385520	−	0.922699i	$-0.374022\pi$
$727$	20.7895			0.771041			0.385520	+	0.922699i	$0.374022\pi$
$728$	27.3195	−	47.3187i	1.01253	−	1.75375i
$729$	1.00000			0.0370370
$730$	2.38486	−	4.13070i	0.0882678	−	0.152884i
$731$	−72.7207			−2.68967
$732$	0.223497	−	0.387108i	0.00826069	−	0.0143079i
$733$	19.8114	−	34.3144i	0.731752	−	1.26743i	−0.224382	−	0.974501i	$-0.572036\pi$
$733$	19.8114	−	34.3144i	0.731752	−	1.26743i	0.956134	−	0.292930i	$-0.0946304\pi$
$734$	10.0996	−	17.4930i	0.372782	−	0.645678i
$735$	−6.39399	+	11.0747i	−0.235846	+	0.408497i
$736$	−36.5112			−1.34582
$737$	−18.3584	−	31.7977i	−0.676241	−	1.17128i
$738$	−1.29161	+	2.23713i	−0.0475448	+	0.0823500i
$739$	−27.3348			−1.00553			−0.502764	−	0.864424i	$-0.667684\pi$
$739$	−27.3348			−1.00553			−0.502764	+	0.864424i	$0.667684\pi$
$740$	−2.32973			−0.0856427
$741$	−6.75911	−	11.7071i	−0.248302	−	0.430072i
$742$	6.30245	−	10.9162i	0.231370	−	0.400745i
$743$	17.9988	+	31.1749i	0.660313	+	1.14370i	0.980533	+	0.196352i	$0.0629096\pi$
$743$	17.9988	+	31.1749i	0.660313	+	1.14370i	−0.320221	+	0.947343i	$0.603757\pi$
$744$	9.73749			0.356994
$745$	−16.6211	−	28.7886i	−0.608950	−	1.05473i
$746$	0.236491			0.00865854
$747$	1.94308	+	3.36551i	0.0710935	+	0.123138i
$748$	9.60972	−	16.6445i	0.351366	−	0.608584i
$749$	16.0917	−	27.8716i	0.587977	−	1.01841i
$750$	3.64850	+	6.31938i	0.133224	+	0.230751i
$751$	7.43023	+	12.8695i	0.271133	+	0.469616i	0.969152	−	0.246463i	$-0.0792683\pi$
$751$	7.43023	+	12.8695i	0.271133	+	0.469616i	−0.698019	+	0.716079i	$0.745935\pi$
$752$	8.73081	−	15.1222i	0.318380	−	0.551450i
$753$	−7.15689			−0.260812
$754$	−25.4883	+	44.1471i	−0.928231	+	1.60774i
$755$	28.2440	−	48.9200i	1.02790	−	1.78038i
$756$	−2.87477			−0.104554
$757$	5.31585			0.193208			0.0966039	−	0.995323i	$-0.469202\pi$
$757$	5.31585			0.193208			0.0966039	+	0.995323i	$0.469202\pi$
$758$	24.2642			0.881314
$759$	13.6677	−	23.6732i	0.496107	−	0.859282i
$760$	10.8412	−	18.7775i	0.393252	−	0.681132i
$761$	−5.97151	−	10.3430i	−0.216467	−	0.374932i	0.737258	−	0.675611i	$-0.236120\pi$
$761$	−5.97151	−	10.3430i	−0.216467	−	0.374932i	−0.953725	+	0.300679i	$0.902787\pi$
$762$	−17.5896			−0.637204
$763$	−18.6796	−	32.3540i	−0.676246	−	1.17129i
$764$	−7.11737	−	12.3276i	−0.257497	−	0.445999i
$765$	−9.53665	−	16.5180i	−0.344798	−	0.597208i
$766$	0.189399	+	0.328049i	0.00684326	+	0.0118529i
$767$	−33.7446	+	58.4473i	−1.21845	+	2.11041i
$768$	8.06125	+	13.9625i	0.290885	+	0.503828i
$769$	−40.8454			−1.47292			−0.736462	−	0.676479i	$-0.763505\pi$
$769$	−40.8454			−1.47292			−0.736462	+	0.676479i	$0.763505\pi$
$770$	−16.5580	+	28.6793i	−0.596709	+	1.03353i
$771$	13.6558			0.491803
$772$	−1.41664	+	2.45370i	−0.0509861	+	0.0883106i
$773$	9.05779	+	15.6886i	0.325786	+	0.564278i	0.981671	−	0.190583i	$-0.0610377\pi$
$773$	9.05779	+	15.6886i	0.325786	+	0.564278i	−0.655885	+	0.754861i	$0.727704\pi$
$774$	5.62918	+	9.75003i	0.202337	+	0.350458i
$775$	4.02583	+	6.97294i	0.144612	+	0.250475i
$776$	8.91411	−	15.4397i	0.319998	−	0.554253i
$777$	3.44396			0.123551
$778$	26.7708			0.959779
$779$	−3.10107	−	5.37122i	−0.111107	−	0.192444i
$780$	6.04279	+	10.4664i	0.216366	+	0.374758i
$781$	−10.1343			−0.362633
$782$	31.1316	+	53.9215i	1.11326	+	1.92823i
$783$	9.05384			0.323558
$784$	−7.49196			−0.267570
$785$	33.1604	−	9.07846i	1.18354	−	0.324024i
$786$	9.98546			0.356170
$787$	13.5963			0.484655			0.242328	−	0.970194i	$-0.422089\pi$
$787$	13.5963			0.484655			0.242328	+	0.970194i	$0.422089\pi$
$788$	5.38026	+	9.31889i	0.191664	+	0.331972i
$789$	27.8028			0.989806
$790$	18.4214	+	31.9068i	0.655404	+	1.13519i
$791$	−23.0561	−	39.9344i	−0.819782	−	1.41990i
$792$	−10.0443			−0.356908
$793$	2.77791			0.0986464
$794$	−12.4479	+	21.5603i	−0.441758	+	0.765147i
$795$	4.70581	+	8.15071i	0.166898	+	0.289076i
$796$	−0.289480	−	0.501394i	−0.0102604	−	0.0177714i
$797$	−14.5325	−	25.1710i	−0.514766	−	0.891601i	−0.999853	−	0.0171351i	$-0.994545\pi$
$797$	−14.5325	−	25.1710i	−0.514766	−	0.891601i	0.485087	−	0.874466i	$-0.338788\pi$
$798$	−4.74754	+	8.22299i	−0.168061	+	0.291091i
$799$	75.5072			2.67125
$800$	−5.54660	+	9.60700i	−0.196102	+	0.339659i
$801$	7.04747			0.249010
$802$	−12.0742	−	20.9131i	−0.426354	−	0.738468i
$803$	2.65250	−	4.59427i	0.0936048	−	0.162128i
$804$	4.70591	+	8.15087i	0.165965	+	0.287459i
$805$	38.9928	+	67.5375i	1.37431	+	2.38038i
$806$	8.96340	+	15.5251i	0.315722	+	0.546847i
$807$	11.8228	+	20.4776i	0.416181	+	0.720847i
$808$	6.22988			0.219166
$809$	7.53535	+	13.0516i	0.264929	+	0.458870i	0.967545	−	0.252699i	$-0.0813182\pi$
$809$	7.53535	+	13.0516i	0.264929	+	0.458870i	−0.702616	+	0.711569i	$0.747985\pi$
$810$	−1.47643	+	2.55725i	−0.0518765	+	0.0898528i
$811$	−12.8122	+	22.1913i	−0.449896	+	0.779242i	−0.998379	−	0.0569196i	$-0.981872\pi$
$811$	−12.8122	+	22.1913i	−0.449896	+	0.779242i	0.548483	+	0.836162i	$0.315205\pi$
$812$	−26.0277			−0.913393
$813$	−10.3053			−0.361424
$814$	3.56462			0.124940
$815$	24.6247	−	42.6513i	0.862566	−	1.49401i
$816$	5.58714	−	9.67722i	0.195589	−	0.338770i
$817$	−27.0306			−0.945682
$818$	0.571024	−	0.989042i	0.0199654	−	0.0345810i
$819$	−8.93283	−	15.4721i	−0.312138	−	0.540640i
$820$	2.77242	+	4.80198i	0.0968172	+	0.167692i
$821$	−11.2893	+	19.5536i	−0.393998	+	0.682424i	−0.992973	−	0.118344i	$-0.962242\pi$
$821$	−11.2893	+	19.5536i	−0.393998	+	0.682424i	0.598975	+	0.800768i	$0.295575\pi$
$822$	5.65064	−	9.78720i	0.197089	−	0.341368i
$823$	24.8590	+	43.0570i	0.866530	+	1.50087i	0.865520	+	0.500874i	$0.166988\pi$
$823$	24.8590	+	43.0570i	0.866530	+	1.50087i	0.00100962	+	0.999999i	$0.499679\pi$
$824$	8.67835			0.302324
$825$	−4.15266	−	7.19263i	−0.144577	−	0.250415i
$826$	47.4038			1.64939
$827$	−9.22579	−	15.9795i	−0.320812	−	0.555663i	0.659844	−	0.751403i	$-0.270622\pi$
$827$	−9.22579	−	15.9795i	−0.320812	−	0.555663i	−0.980656	+	0.195740i	$0.937289\pi$
$828$	−3.50351	+	6.06827i	−0.121756	+	0.210887i
$829$	1.47137	+	2.54849i	0.0511028	+	0.0885126i	0.890445	−	0.455090i	$-0.150393\pi$
$829$	1.47137	+	2.54849i	0.0511028	+	0.0885126i	−0.839342	+	0.543603i	$0.817060\pi$
$830$	−11.4753			−0.398313
$831$	8.78133			0.304621
$832$	−20.7598	+	35.9570i	−0.719716	+	1.24658i
$833$	−16.1983	−	28.0563i	−0.561238	−	0.972093i
$834$	−10.3614			−0.358787
$835$	−4.91054	+	8.50530i	−0.169936	+	0.294338i
$836$	3.57198	−	6.18685i	0.123540	−	0.213977i
$837$	1.59197	−	2.75737i	0.0550264	−	0.0953085i
$838$	−13.3431	+	23.1110i	−0.460931	+	0.798356i
$839$	−46.9193			−1.61983			−0.809917	−	0.586544i	$-0.800488\pi$
$839$	−46.9193			−1.61983			−0.809917	+	0.586544i	$0.800488\pi$
$840$	14.3277	−	24.8163i	0.494353	−	0.856244i
$841$	52.9720			1.82662
$842$	17.4192	−	30.1709i	0.600304	−	1.03976i
$843$	11.1075			0.382564
$844$	18.9197			0.651243
$845$	−19.7186	+	34.1536i	−0.678339	+	1.17492i
$846$	−5.84488	−	10.1236i	−0.200951	−	0.348058i
$847$	0.364935	−	0.632086i	0.0125393	−	0.0217187i
$848$	−2.75695	+	4.77517i	−0.0946740	+	0.163980i
$849$	−28.2091			−0.968136
$850$	18.9174			0.648863
$851$	4.19719	−	7.26975i	0.143878	−	0.249204i
$852$	2.59777			0.0889983
$853$	−3.10750	−	5.38235i	−0.106399	−	0.184288i	0.807910	−	0.589306i	$-0.200599\pi$
$853$	−3.10750	−	5.38235i	−0.106399	−	0.184288i	−0.914309	+	0.405018i	$0.867265\pi$
$854$	−0.975590	−	1.68977i	−0.0333840	−	0.0578228i
$855$	−3.54482	−	6.13981i	−0.121230	−	0.209977i
$856$	−14.4120	+	24.9624i	−0.492593	+	0.853196i
$857$	−5.01604	+	8.68803i	−0.171345	+	0.296777i	−0.938890	−	0.344217i	$-0.888144\pi$
$857$	−5.01604	+	8.68803i	−0.171345	+	0.296777i	0.767546	+	0.640994i	$0.221478\pi$
$858$	−9.24579	−	16.0142i	−0.315646	−	0.546715i
$859$	21.5473	−	37.3210i	0.735184	−	1.27338i	−0.219459	−	0.975622i	$-0.570429\pi$
$859$	21.5473	−	37.3210i	0.735184	−	1.27338i	0.954643	−	0.297754i	$-0.0962375\pi$
$860$	24.1659			0.824052
$861$	−4.09837	−	7.09859i	−0.139672	−	0.241919i
$862$	3.60090	+	6.23694i	0.122647	+	0.212431i
$863$	−33.4257			−1.13783			−0.568913	−	0.822398i	$-0.692636\pi$
$863$	−33.4257			−1.13783			−0.568913	+	0.822398i	$0.692636\pi$
$864$	4.38668			0.149238
$865$	11.6983	+	20.2620i	0.397754	+	0.688930i
$866$	4.88880	+	8.46766i	0.166128	+	0.287743i
$867$	31.3196			1.06367
$868$	−4.57654	+	7.92680i	−0.155338	+	0.269053i
$869$	20.4887	+	35.4875i	0.695032	+	1.20383i
$870$	−13.3674	+	23.1530i	−0.453196	+	0.784959i
$871$	−29.2455	+	50.6548i	−0.990947	+	1.71637i
$872$	16.7298	+	28.9769i	0.566542	+	0.981280i
$873$	−2.91471	−	5.04842i	−0.0986480	−	0.170863i
$874$	11.5718	+	20.0429i	0.391421	+	0.677961i
$875$	−23.1539			−0.782745
$876$	−0.679929	+	1.17767i	−0.0229727	+	0.0397899i
$877$	−20.6867			−0.698540			−0.349270	−	0.937022i	$-0.613570\pi$
$877$	−20.6867			−0.698540			−0.349270	+	0.937022i	$0.613570\pi$
$878$	30.9596			1.04484
$879$	2.42754	−	4.20463i	0.0818790	−	0.141819i
$880$	7.24315	−	12.5455i	0.244167	−	0.422909i
$881$	−20.7651	−	35.9663i	−0.699596	−	1.21174i	−0.968607	−	0.248598i	$-0.920030\pi$
$881$	−20.7651	−	35.9663i	−0.699596	−	1.21174i	0.269011	−	0.963137i	$-0.413303\pi$
$882$	−2.50777	+	4.34358i	−0.0844408	+	0.146256i
$883$	−27.3630			−0.920838			−0.460419	−	0.887702i	$-0.652301\pi$
$883$	−27.3630			−0.920838			−0.460419	+	0.887702i	$0.652301\pi$
$884$	−30.6172			−1.02977
$885$	−17.6974	+	30.6527i	−0.594890	+	1.03038i
$886$	35.1161			1.17975
$887$	−3.13393	+	5.42813i	−0.105227	+	0.182259i	−0.913831	−	0.406095i	$-0.866890\pi$
$887$	−3.13393	+	5.42813i	−0.105227	+	0.182259i	0.808604	+	0.588354i	$0.200224\pi$
$888$	−3.08448			−0.103508
$889$	27.9066	−	48.3356i	0.935956	−	1.62112i
$890$	−10.4051	+	18.0222i	−0.348780	+	0.604104i
$891$	−1.64212	+	2.84424i	−0.0550132	+	0.0952856i
$892$	3.66106	−	6.34114i	0.122581	−	0.212317i
$893$	28.0664			0.939206
$894$	−6.51891	−	11.2911i	−0.218025	−	0.377630i
$895$	−1.94940	+	3.37646i	−0.0651613	+	0.112863i
$896$	−0.795874			−0.0265883
$897$	−43.5462			−1.45396
$898$	10.5654	+	18.2998i	0.352572	+	0.610673i
$899$	14.4134	−	24.9648i	0.480714	−	0.832621i
$900$	1.06447	+	1.84372i	0.0354825	+	0.0614574i
$901$	−23.8431			−0.794328
$902$	−4.24196	−	7.34729i	−0.141242	−	0.244638i
$903$	−35.7236			−1.18881
$904$	20.6495	+	35.7660i	0.686793	+	1.18956i
$905$	0.839258	−	1.45364i	0.0278979	−	0.0483206i
$906$	11.0775	−	19.1868i	0.368025	−	0.637438i
$907$	−15.2617	−	26.4341i	−0.506758	−	0.877730i	−0.999969	−	0.00782091i	$-0.997511\pi$
$907$	−15.2617	−	26.4341i	−0.506758	−	0.877730i	0.493212	−	0.869909i	$-0.335823\pi$
$908$	−5.40859	−	9.36796i	−0.179491	−	0.310887i
$909$	1.01851	−	1.76412i	0.0337820	−	0.0585121i
$910$	52.7549			1.74881
$911$	24.3117	−	42.1091i	0.805483	−	1.39514i	−0.110482	−	0.993878i	$-0.535240\pi$
$911$	24.3117	−	42.1091i	0.805483	−	1.39514i	0.915965	−	0.401259i	$-0.131427\pi$
$912$	2.07677	−	3.59707i	0.0687687	−	0.119111i
$913$	−12.7631			−0.422397
$914$	5.70438			0.188684
$915$	1.45688			0.0481628
$916$	−4.33742	+	7.51263i	−0.143312	+	0.248224i
$917$	−15.8423	+	27.4397i	−0.523159	+	0.906139i
$918$	−3.74034	−	6.47846i	−0.123450	−	0.213821i
$919$	−23.0713			−0.761052			−0.380526	−	0.924770i	$-0.624257\pi$
$919$	−23.0713			−0.761052			−0.380526	+	0.924770i	$0.624257\pi$
$920$	−34.9227	−	60.4878i	−1.15137	−	1.99423i
$921$	−1.18681	−	2.05562i	−0.0391069	−	0.0677351i
$922$	−18.7260	−	32.4343i	−0.616707	−	1.06817i
$923$	8.07212	+	13.9813i	0.265697	+	0.460201i
$924$	4.72072	−	8.17653i	0.155300	−	0.268988i
$925$	−1.27523	−	2.20877i	−0.0419294	−	0.0726239i
$926$	−3.14406			−0.103320
$927$	1.41881	−	2.45745i	0.0465998	−	0.0807132i
$928$	39.7163			1.30375
$929$	27.1324	−	46.9947i	0.890185	−	1.54185i	0.0505320	−	0.998722i	$-0.483908\pi$
$929$	27.1324	−	46.9947i	0.890185	−	1.54185i	0.839653	−	0.543123i	$-0.182758\pi$
$930$	4.70086	+	8.14213i	0.154147	+	0.266991i
$931$	−6.02099	−	10.4287i	−0.197330	−	0.341785i
$932$	6.51959	+	11.2923i	0.213556	+	0.369890i
$933$	1.41582	−	2.45227i	0.0463517	−	0.0802836i
$934$	−12.9587			−0.424023
$935$	62.6414			2.04859
$936$	8.00042	+	13.8571i	0.261502	+	0.452934i
$937$	4.56546	+	7.90761i	0.149147	+	0.258330i	0.930912	−	0.365242i	$-0.119014\pi$
$937$	4.56546	+	7.90761i	0.149147	+	0.258330i	−0.781765	+	0.623573i	$0.785681\pi$
$938$	41.0836			1.34143
$939$	14.2770	+	24.7285i	0.465912	+	0.806983i
$940$	−25.0919			−0.818408
$941$	−26.2318			−0.855131			−0.427565	−	0.903984i	$-0.640629\pi$
$941$	−26.2318			−0.855131			−0.427565	+	0.903984i	$0.640629\pi$
$942$	13.0057	−	3.56063i	0.423749	−	0.116012i
$943$	−19.9789			−0.650604
$944$	−20.7364			−0.674911
$945$	−4.68483	−	8.11436i	−0.152397	−	0.263960i
$946$	−36.9752			−1.20217
$947$	17.0609	+	29.5504i	0.554406	+	0.960259i	0.997950	+	0.0640060i	$0.0203877\pi$
$947$	17.0609	+	29.5504i	0.554406	+	0.960259i	−0.443544	+	0.896253i	$0.646279\pi$
$948$	−5.25198	−	9.09669i	−0.170576	−	0.295447i
$949$	−8.45103			−0.274332
$950$	7.03171			0.228139
$951$	−1.75538	+	3.04041i	−0.0569221	+	0.0985920i
$952$	36.2973	+	62.8688i	1.17640	+	2.03759i
$953$	13.7019	+	23.7323i	0.443847	+	0.768765i	0.997971	−	0.0636685i	$-0.0202800\pi$
$953$	13.7019	+	23.7323i	0.443847	+	0.768765i	−0.554124	+	0.832434i	$0.686947\pi$
$954$	1.84565	+	3.19676i	0.0597552	+	0.103499i
$955$	23.1974	−	40.1791i	0.750652	−	1.30017i
$956$	−14.0198			−0.453432
$957$	−14.8675	+	25.7513i	−0.480598	+	0.832421i
$958$	−1.66576			−0.0538184
$959$	17.9299	+	31.0555i	0.578987	+	1.00283i
$960$	−10.8875	+	18.8577i	−0.351392	+	0.608628i
$961$	10.4313	+	18.0675i	0.336493	+	0.582823i
$962$	−2.83927	−	4.91777i	−0.0915419	−	0.158555i
$963$	4.71240	+	8.16211i	0.151855	+	0.263020i
$964$	10.2799	+	17.8053i	0.331093	+	0.573471i
$965$	−9.23445			−0.297268
$966$	15.2932	+	26.4887i	0.492052	+	0.852258i
$967$	1.13015	−	1.95748i	0.0363432	−	0.0629483i	−0.847282	−	0.531144i	$-0.821762\pi$
$967$	1.13015	−	1.95748i	0.0363432	−	0.0629483i	0.883625	+	0.468196i	$0.155096\pi$
$968$	−0.326843	+	0.566109i	−0.0105051	+	0.0181954i
$969$	17.9607			0.576979
$970$	17.2135			0.552691
$971$	0.319386			0.0102496			0.00512479	−	0.999987i	$-0.498369\pi$
$971$	0.319386			0.0102496			0.00512479	+	0.999987i	$0.498369\pi$
$972$	0.420934	−	0.729078i	0.0135014	−	0.0233852i
$973$	16.4388	−	28.4728i	0.527004	−	0.912797i
$974$	7.50842			0.240585
$975$	−6.61532	+	11.4581i	−0.211860	+	0.366952i
$976$	0.426763	+	0.739174i	0.0136603	+	0.0236604i
$977$	−0.784482	−	1.35876i	−0.0250978	−	0.0434707i	0.853204	−	0.521578i	$-0.174656\pi$
$977$	−0.784482	−	1.35876i	−0.0250978	−	0.0434707i	−0.878302	+	0.478107i	$0.841323\pi$
$978$	9.65798	−	16.7281i	0.308828	−	0.534906i
$979$	−11.5728	+	20.0447i	−0.369868	+	0.640631i
$980$	5.38289	+	9.32343i	0.171950	+	0.297826i
$981$	10.9405			0.349304
$982$	−2.33285	−	4.04062i	−0.0744443	−	0.128941i
$983$	15.2865			0.487565			0.243783	−	0.969830i	$-0.421612\pi$
$983$	15.2865			0.487565			0.243783	+	0.969830i	$0.421612\pi$
$984$	3.67058	+	6.35763i	0.117014	+	0.202674i
$985$	−17.5357	+	30.3728i	−0.558735	+	0.967757i
$986$	−33.8644	−	58.6549i	−1.07846	−	1.86795i
$987$	37.0925			1.18067
$988$	−11.3806			−0.362064
$989$	−43.5368	+	75.4080i	−1.38439	+	2.39783i
$990$	−4.84896	−	8.39865i	−0.154110	−	0.266927i
$991$	−3.63095			−0.115341			−0.0576705	−	0.998336i	$-0.518367\pi$
$991$	−3.63095			−0.115341			−0.0576705	+	0.998336i	$0.518367\pi$
$992$	6.98344	−	12.0957i	0.221724	−	0.384038i
$993$	10.6599	−	18.4634i	0.338281	−	0.585919i
$994$	5.66979	−	9.82036i	0.179835	−	0.311483i
$995$	0.943494	−	1.63418i	0.0299108	−	0.0518070i
$996$	3.27163			0.103665
$997$	−24.2096	+	41.9323i	−0.766727	+	1.32801i	0.172602	+	0.984992i	$0.444783\pi$
$997$	−24.2096	+	41.9323i	−0.766727	+	1.32801i	−0.939329	+	0.343018i	$0.888551\pi$
$998$	11.0113			0.348557
$999$	−0.504276	+	0.873432i	−0.0159546	+	0.0276342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.169.9	✓	28
157.144	even	3	inner	471.2.e.c.301.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.9	✓	28	1.1	even	1	trivial
471.2.e.c.301.9	yes	28	157.144	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.07617 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.841867 q^{4} +(-1.37194 - 2.37626i) q^{5} +(-0.538083 - 0.931987i) q^{6} +3.41476 q^{7} -3.05832 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.07617 q^{2} +(-0.500000 - 0.866025i) q^{3} -0.841867 q^{4} +(-1.37194 - 2.37626i) q^{5} +(-0.538083 - 0.931987i) q^{6} +3.41476 q^{7} -3.05832 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.47643 - 2.55725i) q^{10} +(-1.64212 - 2.84424i) q^{11} +(0.420934 + 0.729078i) q^{12} +(-2.61595 + 4.53096i) q^{13} +3.67484 q^{14} +(-1.37194 + 2.37626i) q^{15} -1.60753 q^{16} +(-3.47562 - 6.01994i) q^{17} +(-0.538083 + 0.931987i) q^{18} +(-1.29190 - 2.23764i) q^{19} +(1.15499 + 2.00050i) q^{20} +(-1.70738 - 2.95726i) q^{21} +(-1.76720 - 3.06087i) q^{22} -8.32320 q^{23} +(1.52916 + 2.64858i) q^{24} +(-1.26442 + 2.19004i) q^{25} +(-2.81520 + 4.87606i) q^{26} +1.00000 q^{27} -2.87477 q^{28} +9.05384 q^{29} +(-1.47643 + 2.55725i) q^{30} +(1.59197 - 2.75737i) q^{31} +4.38668 q^{32} +(-1.64212 + 2.84424i) q^{33} +(-3.74034 - 6.47846i) q^{34} +(-4.68483 - 8.11436i) q^{35} +(0.420934 - 0.729078i) q^{36} +(-0.504276 + 0.873432i) q^{37} +(-1.39030 - 2.40808i) q^{38} +5.23190 q^{39} +(4.19582 + 7.26738i) q^{40} +2.40039 q^{41} +(-1.83742 - 3.18251i) q^{42} +(5.23078 - 9.05997i) q^{43} +(1.38245 + 2.39447i) q^{44} +2.74387 q^{45} -8.95715 q^{46} +(-5.43121 + 9.40713i) q^{47} +(0.803763 + 1.39216i) q^{48} +4.66055 q^{49} +(-1.36073 + 2.35685i) q^{50} +(-3.47562 + 6.01994i) q^{51} +(2.20228 - 3.81447i) q^{52} +(1.71503 - 2.97051i) q^{53} +1.07617 q^{54} +(-4.50577 + 7.80423i) q^{55} -10.4434 q^{56} +(-1.29190 + 2.23764i) q^{57} +9.74343 q^{58} +12.8995 q^{59} +(1.15499 - 2.00050i) q^{60} +(-0.265478 - 0.459821i) q^{61} +(1.71322 - 2.96738i) q^{62} +(-1.70738 + 2.95726i) q^{63} +7.93584 q^{64} +14.3557 q^{65} +(-1.76720 + 3.06087i) q^{66} +11.1797 q^{67} +(2.92601 + 5.06799i) q^{68} +(4.16160 + 7.20810i) q^{69} +(-5.04165 - 8.73240i) q^{70} +(1.54286 - 2.67232i) q^{71} +(1.52916 - 2.64858i) q^{72} +(0.807645 + 1.39888i) q^{73} +(-0.542685 + 0.939958i) q^{74} +2.52884 q^{75} +(1.08761 + 1.88380i) q^{76} +(-5.60745 - 9.71238i) q^{77} +5.63039 q^{78} -12.4770 q^{79} +(2.20542 + 3.81991i) q^{80} +(-0.500000 - 0.866025i) q^{81} +2.58322 q^{82} +(1.94308 - 3.36551i) q^{83} +(1.43739 + 2.48962i) q^{84} +(-9.53665 + 16.5180i) q^{85} +(5.62918 - 9.75003i) q^{86} +(-4.52692 - 7.84085i) q^{87} +(5.02214 + 8.69859i) q^{88} +(-3.52373 - 6.10329i) q^{89} +2.95286 q^{90} +(-8.93283 + 15.4721i) q^{91} +7.00703 q^{92} -3.18393 q^{93} +(-5.84488 + 10.1236i) q^{94} +(-3.54482 + 6.13981i) q^{95} +(-2.19334 - 3.79897i) q^{96} +(-2.91471 + 5.04842i) q^{97} +5.01553 q^{98} +3.28424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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