LMFDB - Embedded newform 403.2.h.a.118.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, 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("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.8
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0439466 q^{2} +(0.820034 + 1.42034i) q^{3} -1.99807 q^{4} +(0.865000 - 1.49822i) q^{5} +(0.0360377 + 0.0624192i) q^{6} +(-2.17574 - 3.76849i) q^{7} -0.175702 q^{8} +(0.155089 - 0.268621i) q^{9} +O(q^{10})$	\(q+0.0439466 q^{2} +(0.820034 + 1.42034i) q^{3} -1.99807 q^{4} +(0.865000 - 1.49822i) q^{5} +(0.0360377 + 0.0624192i) q^{6} +(-2.17574 - 3.76849i) q^{7} -0.175702 q^{8} +(0.155089 - 0.268621i) q^{9} +(0.0380138 - 0.0658419i) q^{10} +(0.377951 - 0.654630i) q^{11} +(-1.63848 - 2.83794i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.0956164 - 0.165613i) q^{14} +2.83732 q^{15} +3.98842 q^{16} +(-1.81812 - 3.14907i) q^{17} +(0.00681562 - 0.0118050i) q^{18} +(-1.12974 - 1.95676i) q^{19} +(-1.72833 + 2.99355i) q^{20} +(3.56836 - 6.18059i) q^{21} +(0.0166097 - 0.0287688i) q^{22} -5.51362 q^{23} +(-0.144081 - 0.249556i) q^{24} +(1.00355 + 1.73820i) q^{25} +(0.0219733 - 0.0380589i) q^{26} +5.42892 q^{27} +(4.34728 + 7.52971i) q^{28} +2.34907 q^{29} +0.124691 q^{30} +(4.77204 + 2.86839i) q^{31} +0.526681 q^{32} +1.23973 q^{33} +(-0.0799001 - 0.138391i) q^{34} -7.52806 q^{35} +(-0.309878 + 0.536724i) q^{36} +(0.0716389 + 0.124082i) q^{37} +(-0.0496482 - 0.0859932i) q^{38} +1.64007 q^{39} +(-0.151982 + 0.263240i) q^{40} +(6.10152 - 10.5681i) q^{41} +(0.156817 - 0.271616i) q^{42} +(-2.21430 - 3.83528i) q^{43} +(-0.755171 + 1.30800i) q^{44} +(-0.268303 - 0.464715i) q^{45} -0.242305 q^{46} -3.15867 q^{47} +(3.27064 + 5.66491i) q^{48} +(-5.96770 + 10.3364i) q^{49} +(0.0441026 + 0.0763880i) q^{50} +(2.98184 - 5.16469i) q^{51} +(-0.999034 + 1.73038i) q^{52} +(-4.33685 + 7.51165i) q^{53} +0.238582 q^{54} +(-0.653855 - 1.13251i) q^{55} +(0.382281 + 0.662130i) q^{56} +(1.85285 - 3.20923i) q^{57} +0.103234 q^{58} +(3.89528 + 6.74683i) q^{59} -5.66916 q^{60} -11.8829 q^{61} +(0.209715 + 0.126056i) q^{62} -1.34973 q^{63} -7.95369 q^{64} +(-0.865000 - 1.49822i) q^{65} +0.0544819 q^{66} +(-1.21707 + 2.10804i) q^{67} +(3.63273 + 6.29206i) q^{68} +(-4.52136 - 7.83122i) q^{69} -0.330833 q^{70} +(2.49054 - 4.31375i) q^{71} +(-0.0272493 + 0.0471972i) q^{72} +(6.56356 - 11.3684i) q^{73} +(0.00314829 + 0.00545299i) q^{74} +(-1.64589 + 2.85077i) q^{75} +(2.25730 + 3.90975i) q^{76} -3.28929 q^{77} +0.0720754 q^{78} +(-3.89339 - 6.74354i) q^{79} +(3.44998 - 5.97554i) q^{80} +(3.98663 + 6.90504i) q^{81} +(0.268141 - 0.464434i) q^{82} +(-7.47684 + 12.9503i) q^{83} +(-7.12983 + 12.3492i) q^{84} -6.29069 q^{85} +(-0.0973111 - 0.168548i) q^{86} +(1.92632 + 3.33648i) q^{87} +(-0.0664065 + 0.115020i) q^{88} +1.15254 q^{89} +(-0.0117910 - 0.0204226i) q^{90} -4.35148 q^{91} +11.0166 q^{92} +(-0.160863 + 9.13009i) q^{93} -0.138813 q^{94} -3.90890 q^{95} +(0.431896 + 0.748066i) q^{96} +16.4293 q^{97} +(-0.262260 + 0.454248i) q^{98} +(-0.117232 - 0.203051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.0439466			0.0310749			0.0155375	−	0.999879i	$-0.495054\pi$
$2$	0.0439466			0.0310749			0.0155375	+	0.999879i	$0.495054\pi$
$3$	0.820034	+	1.42034i	0.473447	+	0.820034i	0.999538	−	0.0303942i	$-0.00967627\pi$
$3$	0.820034	+	1.42034i	0.473447	+	0.820034i	−0.526091	+	0.850428i	$0.676343\pi$
$4$	−1.99807			−0.999034
$5$	0.865000	−	1.49822i	0.386840	−	0.670026i	−0.605183	−	0.796087i	$-0.706900\pi$
$5$	0.865000	−	1.49822i	0.386840	−	0.670026i	0.992023	+	0.126060i	$0.0402333\pi$
$6$	0.0360377	+	0.0624192i	0.0147123	+	0.0254825i
$7$	−2.17574	−	3.76849i	−0.822353	−	1.42436i	−0.903926	−	0.427689i	$-0.859328\pi$
$7$	−2.17574	−	3.76849i	−0.822353	−	1.42436i	0.0815731	−	0.996667i	$-0.474006\pi$
$8$	−0.175702			−0.0621199
$9$	0.155089	−	0.268621i	0.0516962	−	0.0895404i
$10$	0.0380138	−	0.0658419i	0.0120210	−	0.0208210i
$11$	0.377951	−	0.654630i	0.113956	−	0.197378i	−0.803406	−	0.595432i	$-0.796981\pi$
$11$	0.377951	−	0.654630i	0.113956	−	0.197378i	0.917362	+	0.398054i	$0.130314\pi$
$12$	−1.63848	−	2.83794i	−0.472990	−	0.819242i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−0.0956164	−	0.165613i	−0.0255546	−	0.0442618i
$15$	2.83732			0.732592
$16$	3.98842			0.997104
$17$	−1.81812	−	3.14907i	−0.440958	−	0.763762i	0.556802	−	0.830645i	$-0.312028\pi$
$17$	−1.81812	−	3.14907i	−0.440958	−	0.763762i	−0.997761	+	0.0668825i	$0.978695\pi$
$18$	0.00681562	−	0.0118050i	0.00160646	−	0.00278246i
$19$	−1.12974	−	1.95676i	−0.259180	−	0.448913i	0.706843	−	0.707371i	$-0.250119\pi$
$19$	−1.12974	−	1.95676i	−0.259180	−	0.448913i	−0.966022	+	0.258458i	$0.916786\pi$
$20$	−1.72833	+	2.99355i	−0.386466	+	0.669379i
$21$	3.56836	−	6.18059i	0.778681	−	1.34871i
$22$	0.0166097	−	0.0287688i	0.00354119	−	0.00613352i
$23$	−5.51362			−1.14967			−0.574835	−	0.818269i	$-0.694934\pi$
$23$	−5.51362			−1.14967			−0.574835	+	0.818269i	$0.694934\pi$
$24$	−0.144081	−	0.249556i	−0.0294105	−	0.0509404i
$25$	1.00355	+	1.73820i	0.200710	+	0.347640i
$26$	0.0219733	−	0.0380589i	0.00430932	−	0.00746396i
$27$	5.42892			1.04480
$28$	4.34728	+	7.52971i	0.821559	+	1.42298i
$29$	2.34907			0.436211			0.218105	−	0.975925i	$-0.430012\pi$
$29$	2.34907			0.436211			0.218105	+	0.975925i	$0.430012\pi$
$30$	0.124691			0.0227653
$31$	4.77204	+	2.86839i	0.857083	+	0.515179i
$31$	4.77204	+	2.86839i	0.857083	+	0.515179i
$32$	0.526681			0.0931048
$33$	1.23973			0.215809
$34$	−0.0799001	−	0.138391i	−0.0137028	−	0.0237339i
$35$	−7.52806			−1.27247
$36$	−0.309878	+	0.536724i	−0.0516463	+	0.0894540i
$37$	0.0716389	+	0.124082i	0.0117774	+	0.0203990i	0.871854	−	0.489766i	$-0.162918\pi$
$37$	0.0716389	+	0.124082i	0.0117774	+	0.0203990i	−0.860077	+	0.510165i	$0.829584\pi$
$38$	−0.0496482	−	0.0859932i	−0.00805400	−	0.0139499i
$39$	1.64007			0.262621
$40$	−0.151982	+	0.263240i	−0.0240304	+	0.0416219i
$41$	6.10152	−	10.5681i	0.952897	−	1.65047i	0.213787	−	0.976880i	$-0.431420\pi$
$41$	6.10152	−	10.5681i	0.952897	−	1.65047i	0.739109	−	0.673585i	$-0.235247\pi$
$42$	0.156817	−	0.271616i	0.0241975	−	0.0419112i
$43$	−2.21430	−	3.83528i	−0.337678	−	0.584875i	0.646318	−	0.763069i	$-0.276308\pi$
$43$	−2.21430	−	3.83528i	−0.337678	−	0.584875i	−0.983996	+	0.178193i	$0.942975\pi$
$44$	−0.755171	+	1.30800i	−0.113846	+	0.197188i
$45$	−0.268303	−	0.464715i	−0.0399963	−	0.0692756i
$46$	−0.242305			−0.0357259
$47$	−3.15867			−0.460739			−0.230369	−	0.973103i	$-0.573993\pi$
$47$	−3.15867			−0.460739			−0.230369	+	0.973103i	$0.573993\pi$
$48$	3.27064	+	5.66491i	0.472076	+	0.817659i
$49$	−5.96770	+	10.3364i	−0.852528	+	1.47662i
$50$	0.0441026	+	0.0763880i	0.00623705	+	0.0108029i
$51$	2.98184	−	5.16469i	0.417541	−	0.723202i
$52$	−0.999034	+	1.73038i	−0.138541	+	0.239960i
$53$	−4.33685	+	7.51165i	−0.595713	+	1.03180i	0.397733	+	0.917501i	$0.369797\pi$
$53$	−4.33685	+	7.51165i	−0.595713	+	1.03180i	−0.993446	+	0.114303i	$0.963536\pi$
$54$	0.238582			0.0324670
$55$	−0.653855	−	1.13251i	−0.0881658	−	0.152708i
$56$	0.382281	+	0.662130i	0.0510845	+	0.0884809i
$57$	1.85285	−	3.20923i	0.245416	−	0.425072i
$58$	0.103234			0.0135552
$59$	3.89528	+	6.74683i	0.507123	+	0.878363i	0.999966	+	0.00824439i	$0.00262430\pi$
$59$	3.89528	+	6.74683i	0.507123	+	0.878363i	−0.492843	+	0.870118i	$0.664042\pi$
$60$	−5.66916			−0.731885
$61$	−11.8829			−1.52145			−0.760726	−	0.649073i	$-0.775157\pi$
$61$	−11.8829			−1.52145			−0.760726	+	0.649073i	$0.775157\pi$
$62$	0.209715	+	0.126056i	0.0266338	+	0.0160091i
$63$	−1.34973			−0.170050
$64$	−7.95369			−0.994211
$65$	−0.865000	−	1.49822i	−0.107290	−	0.185832i
$66$	0.0544819			0.00670626
$67$	−1.21707	+	2.10804i	−0.148689	+	0.257538i	−0.930743	−	0.365673i	$-0.880839\pi$
$67$	−1.21707	+	2.10804i	−0.148689	+	0.257538i	0.782054	+	0.623211i	$0.214172\pi$
$68$	3.63273	+	6.29206i	0.440533	+	0.763025i
$69$	−4.52136	−	7.83122i	−0.544308	−	0.942768i
$70$	−0.330833			−0.0395421
$71$	2.49054	−	4.31375i	0.295573	−	0.511948i	−0.679545	−	0.733634i	$-0.737823\pi$
$71$	2.49054	−	4.31375i	0.295573	−	0.511948i	0.975118	+	0.221686i	$0.0711560\pi$
$72$	−0.0272493	+	0.0471972i	−0.00321136	+	0.00556224i
$73$	6.56356	−	11.3684i	0.768206	−	1.33057i	−0.170329	−	0.985387i	$-0.554483\pi$
$73$	6.56356	−	11.3684i	0.768206	−	1.33057i	0.938535	−	0.345185i	$-0.112184\pi$
$74$	0.00314829	+	0.00545299i	0.000365981	+	0.000633897i
$75$	−1.64589	+	2.85077i	−0.190051	+	0.329178i
$76$	2.25730	+	3.90975i	0.258930	+	0.448479i
$77$	−3.28929			−0.374849
$78$	0.0720754			0.00816094
$79$	−3.89339	−	6.74354i	−0.438040	−	0.758708i	0.559498	−	0.828832i	$-0.310994\pi$
$79$	−3.89339	−	6.74354i	−0.438040	−	0.758708i	−0.997538	+	0.0701239i	$0.977661\pi$
$80$	3.44998	−	5.97554i	0.385719	−	0.668086i
$81$	3.98663	+	6.90504i	0.442959	+	0.767227i
$82$	0.268141	−	0.464434i	0.0296112	−	0.0512881i
$83$	−7.47684	+	12.9503i	−0.820690	+	1.42148i	0.0844800	+	0.996425i	$0.473077\pi$
$83$	−7.47684	+	12.9503i	−0.820690	+	1.42148i	−0.905170	+	0.425051i	$0.860256\pi$
$84$	−7.12983	+	12.3492i	−0.777929	+	1.34741i
$85$	−6.29069			−0.682321
$86$	−0.0973111	−	0.168548i	−0.0104933	−	0.0181750i
$87$	1.92632	+	3.33648i	0.206523	+	0.357708i
$88$	−0.0664065	+	0.115020i	−0.00707896	+	0.0122611i
$89$	1.15254			0.122169			0.0610845	−	0.998133i	$-0.480544\pi$
$89$	1.15254			0.122169			0.0610845	+	0.998133i	$0.480544\pi$
$90$	−0.0117910	−	0.0204226i	−0.00124288	−	0.00215274i
$91$	−4.35148			−0.456159
$92$	11.0166			1.14856
$93$	−0.160863	+	9.13009i	−0.0166807	+	0.946747i
$94$	−0.138813			−0.0143174
$95$	−3.90890			−0.401044
$96$	0.431896	+	0.748066i	0.0440802	+	0.0763491i
$97$	16.4293			1.66814			0.834069	−	0.551660i	$-0.186005\pi$
$97$	16.4293			1.66814			0.834069	+	0.551660i	$0.186005\pi$
$98$	−0.262260	+	0.454248i	−0.0264923	+	0.0458859i
$99$	−0.117232	−	0.203051i	−0.0117822	−	0.0204074i
$100$	−2.00516	−	3.47304i	−0.200516	−	0.347304i
$101$	17.2180			1.71326			0.856629	−	0.515932i	$-0.172554\pi$
$101$	17.2180			1.71326			0.856629	+	0.515932i	$0.172554\pi$
$102$	0.131042	−	0.226971i	0.0129751	−	0.0224735i
$103$	−1.37970	+	2.38971i	−0.135946	+	0.235465i	−0.925958	−	0.377625i	$-0.876741\pi$
$103$	−1.37970	+	2.38971i	−0.135946	+	0.235465i	0.790012	+	0.613091i	$0.210074\pi$
$104$	−0.0878508	+	0.152162i	−0.00861448	+	0.0149207i
$105$	−6.17327	−	10.6924i	−0.602449	−	1.04347i
$106$	−0.190590	+	0.330112i	−0.0185117	+	0.0320633i
$107$	6.80479	+	11.7862i	0.657844	+	1.13942i	0.981173	+	0.193132i	$0.0618646\pi$
$107$	6.80479	+	11.7862i	0.657844	+	1.13942i	−0.323329	+	0.946287i	$0.604802\pi$
$108$	−10.8473			−1.04379
$109$	6.06210			0.580644			0.290322	−	0.956929i	$-0.406238\pi$
$109$	6.06210			0.580644			0.290322	+	0.956929i	$0.406238\pi$
$110$	−0.0287347	−	0.0497700i	−0.00273975	−	0.00474538i
$111$	−0.117493	+	0.203503i	−0.0111519	+	0.0193157i
$112$	−8.67776	−	15.0303i	−0.819971	−	1.42023i
$113$	0.675946	−	1.17077i	0.0635876	−	0.110137i	−0.832479	−	0.554057i	$-0.813079\pi$
$113$	0.675946	−	1.17077i	0.0635876	−	0.110137i	0.896067	+	0.443920i	$0.146412\pi$
$114$	0.0814264	−	0.141035i	0.00762628	−	0.0132091i
$115$	−4.76928	+	8.26064i	−0.444738	+	0.770309i
$116$	−4.69360			−0.435790
$117$	−0.155089	−	0.268621i	−0.0143379	−	0.0248340i
$118$	0.171185	+	0.296500i	0.0157588	+	0.0272951i
$119$	−7.91151	+	13.7031i	−0.725247	+	1.25616i
$120$	−0.498521			−0.0455086
$121$	5.21431	+	9.03144i	0.474028	+	0.821040i
$122$	−0.522214			−0.0472791
$123$	20.0138			1.80458
$124$	−9.53485	−	5.73125i	−0.856255	−	0.514681i
$125$	12.1223			1.08425
$126$	−0.0593161			−0.00528430
$127$	−6.48690	−	11.2356i	−0.575620	−	0.997002i	−0.995974	−	0.0896424i	$-0.971428\pi$
$127$	−6.48690	−	11.2356i	−0.575620	−	0.997002i	0.420354	−	0.907360i	$-0.361906\pi$
$128$	−1.40290			−0.124000
$129$	3.63161	−	6.29013i	0.319745	−	0.553815i
$130$	−0.0380138	−	0.0658419i	−0.00333403	−	0.00577471i
$131$	0.582399	+	1.00874i	0.0508844	+	0.0881344i	0.890346	−	0.455285i	$-0.150463\pi$
$131$	0.582399	+	1.00874i	0.0508844	+	0.0881344i	−0.839461	+	0.543419i	$0.817129\pi$
$132$	−2.47707			−0.215601
$133$	−4.91604	+	8.51482i	−0.426274	+	0.738329i
$134$	−0.0534863	+	0.0926410i	−0.00462051	+	0.00800297i
$135$	4.69601	−	8.13373i	0.404168	−	0.700040i
$136$	0.319446	+	0.553297i	0.0273923	+	0.0474448i
$137$	−3.63265	+	6.29193i	−0.310358	+	0.537556i	−0.978440	−	0.206532i	$-0.933782\pi$
$137$	−3.63265	+	6.29193i	−0.310358	+	0.537556i	0.668082	+	0.744088i	$0.267116\pi$
$138$	−0.198698	−	0.344156i	−0.0169143	−	0.0292965i
$139$	2.87138			0.243547			0.121774	−	0.992558i	$-0.461142\pi$
$139$	2.87138			0.243547			0.121774	+	0.992558i	$0.461142\pi$
$140$	15.0416			1.27125
$141$	−2.59021	−	4.48638i	−0.218135	−	0.377821i
$142$	0.109451	−	0.189575i	0.00918492	−	0.0159088i
$143$	−0.377951	−	0.654630i	−0.0316058	−	0.0547429i
$144$	0.618558	−	1.07137i	0.0515465	−	0.0892811i
$145$	2.03194	−	3.51943i	0.168744	−	0.292273i
$146$	0.288446	−	0.499603i	0.0238720	−	0.0413475i
$147$	−19.5749			−1.61451
$148$	−0.143139	−	0.247925i	−0.0117660	−	0.0203793i
$149$	7.07231	+	12.2496i	0.579387	+	1.00353i	0.995550	+	0.0942370i	$0.0300411\pi$
$149$	7.07231	+	12.2496i	0.579387	+	1.00353i	−0.416163	+	0.909290i	$0.636626\pi$
$150$	−0.0723313	+	0.125281i	−0.00590583	+	0.0102292i
$151$	−13.0516			−1.06213			−0.531063	−	0.847332i	$-0.678207\pi$
$151$	−13.0516			−1.06213			−0.531063	+	0.847332i	$0.678207\pi$
$152$	0.198497	+	0.343807i	0.0161002	+	0.0278864i
$153$	−1.12788			−0.0911835
$154$	−0.144553			−0.0116484
$155$	8.42531	−	4.66842i	0.676737	−	0.374976i
$156$	−3.27697			−0.262367
$157$	−0.335021			−0.0267376			−0.0133688	−	0.999911i	$-0.504256\pi$
$157$	−0.335021			−0.0267376			−0.0133688	+	0.999911i	$0.504256\pi$
$158$	−0.171101	−	0.296356i	−0.0136121	−	0.0235768i
$159$	−14.2255			−1.12815
$160$	0.455579	−	0.789085i	0.0360167	−	0.0623827i
$161$	11.9962	+	20.7781i	0.945434	+	1.63754i
$162$	0.175199	+	0.303453i	0.0137649	+	0.0238415i
$163$	19.5323			1.52989			0.764944	−	0.644097i	$-0.222767\pi$
$163$	19.5323			1.52989			0.764944	+	0.644097i	$0.222767\pi$
$164$	−12.1912	+	21.1159i	−0.951977	+	1.64887i
$165$	1.07237	−	1.85739i	0.0834836	−	0.144598i
$166$	−0.328582	+	0.569120i	−0.0255029	+	0.0441723i
$167$	−1.36041	−	2.35630i	−0.105272	−	0.182336i	0.808577	−	0.588390i	$-0.200238\pi$
$167$	−1.36041	−	2.35630i	−0.105272	−	0.182336i	−0.913849	+	0.406054i	$0.866905\pi$
$168$	−0.626967	+	1.08594i	−0.0483716	+	0.0837820i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	−0.276454			−0.0212031
$171$	−0.700838			−0.0535944
$172$	4.42433	+	7.66316i	0.337352	+	0.584311i
$173$	10.0978	−	17.4899i	0.767722	−	1.32973i	−0.171073	−	0.985258i	$-0.554723\pi$
$173$	10.0978	−	17.4899i	0.767722	−	1.32973i	0.938795	−	0.344475i	$-0.111943\pi$
$174$	0.0846550	+	0.146627i	0.00641768	+	0.0111158i
$175$	4.36693	−	7.56374i	0.330109	−	0.571765i
$176$	1.50742	−	2.61094i	0.113626	−	0.196807i
$177$	−6.38853	+	11.0653i	−0.480191	+	0.831716i
$178$	0.0506503			0.00379640
$179$	4.61947	+	8.00115i	0.345275	+	0.598034i	0.985404	−	0.170234i	$-0.0544522\pi$
$179$	4.61947	+	8.00115i	0.345275	+	0.598034i	−0.640129	+	0.768268i	$0.721119\pi$
$180$	0.536088	+	0.928532i	0.0399577	+	0.0692087i
$181$	0.283609	−	0.491225i	0.0210805	−	0.0365124i	−0.855293	−	0.518145i	$-0.826623\pi$
$181$	0.283609	−	0.491225i	0.0210805	−	0.0365124i	0.876373	+	0.481633i	$0.159956\pi$
$182$	−0.191233			−0.0141751
$183$	−9.74440	−	16.8778i	−0.720327	−	1.24764i
$184$	0.968752			0.0714174
$185$	0.247870			0.0182238
$186$	−0.00706939	+	0.401237i	−0.000518353	+	0.0294201i
$187$	−2.74864			−0.201000
$188$	6.31123			0.460294
$189$	−11.8119	−	20.4588i	−0.859190	−	1.48816i
$190$	−0.171783			−0.0124624
$191$	5.36327	−	9.28945i	0.388072	−	0.672161i	−0.604118	−	0.796895i	$-0.706474\pi$
$191$	5.36327	−	9.28945i	0.388072	−	0.672161i	0.992190	+	0.124734i	$0.0398077\pi$
$192$	−6.52229	−	11.2969i	−0.470706	−	0.815287i
$193$	−3.82645	−	6.62760i	−0.275434	−	0.477065i	0.694811	−	0.719193i	$-0.255488\pi$
$193$	−3.82645	−	6.62760i	−0.275434	−	0.477065i	−0.970244	+	0.242127i	$0.922155\pi$
$194$	0.722010			0.0518373
$195$	1.41866	−	2.45719i	0.101592	−	0.175963i
$196$	11.9239	−	20.6527i	0.851705	−	1.47520i
$197$	5.98737	−	10.3704i	0.426583	−	0.738863i	−0.569984	−	0.821656i	$-0.693051\pi$
$197$	5.98737	−	10.3704i	0.426583	−	0.738863i	0.996567	+	0.0827929i	$0.0263840\pi$
$198$	−0.00515194	−	0.00892341i	−0.000366132	−	0.000634159i
$199$	−1.06264	+	1.84055i	−0.0753289	+	0.130473i	−0.901229	−	0.433343i	$-0.857334\pi$
$199$	−1.06264	+	1.84055i	−0.0753289	+	0.130473i	0.825900	+	0.563816i	$0.190667\pi$
$200$	−0.176325	−	0.305404i	−0.0124681	−	0.0215954i
$201$	−3.99217			−0.281586
$202$	0.756675			0.0532394
$203$	−5.11096	−	8.85245i	−0.358719	−	0.621320i
$204$	−5.95792	+	10.3194i	−0.417138	+	0.722503i
$205$	−10.5556	−	18.2829i	−0.737237	−	1.27693i
$206$	−0.0606332	+	0.105020i	−0.00422452	+	0.00731707i
$207$	−0.855100	+	1.48108i	−0.0594336	+	0.102942i
$208$	1.99421	−	3.45407i	0.138273	−	0.239497i
$209$	−1.70794			−0.118141
$210$	−0.271294	−	0.469895i	−0.0187211	−	0.0324259i
$211$	1.87081	+	3.24035i	0.128792	+	0.223075i	0.923209	−	0.384299i	$-0.125557\pi$
$211$	1.87081	+	3.24035i	0.128792	+	0.223075i	−0.794417	+	0.607373i	$0.792223\pi$
$212$	8.66533	−	15.0088i	0.595137	−	1.03081i
$213$	8.16932			0.559753
$214$	0.299047	+	0.517965i	0.0204425	+	0.0354074i
$215$	−7.66149			−0.522509
$216$	−0.953869			−0.0649026
$217$	0.426808	−	24.2243i	0.0289736	−	1.64445i
$218$	0.266409			0.0180435
$219$	21.5294			1.45482
$220$	1.30645	+	2.26283i	0.0880806	+	0.152560i
$221$	−3.63624			−0.244600
$222$	−0.00516340	+	0.00894327i	−0.000346545	+	0.000600233i
$223$	−11.2498	−	19.4852i	−0.753341	−	1.30482i	−0.946195	−	0.323597i	$-0.895108\pi$
$223$	−11.2498	−	19.4852i	−0.753341	−	1.30482i	0.192854	−	0.981227i	$-0.438226\pi$
$224$	−1.14592	−	1.98479i	−0.0765650	−	0.132615i
$225$	0.622557			0.0415038
$226$	0.0297055	−	0.0514515i	0.00197598	−	0.00342250i
$227$	−6.69909	+	11.6032i	−0.444634	+	0.770129i	−0.998027	−	0.0627918i	$-0.980000\pi$
$227$	−6.69909	+	11.6032i	−0.444634	+	0.770129i	0.553393	+	0.832921i	$0.313333\pi$
$228$	−3.70212	+	6.41226i	−0.245179	+	0.424662i
$229$	−7.18547	−	12.4456i	−0.474829	−	0.822428i	0.524755	−	0.851253i	$-0.324157\pi$
$229$	−7.18547	−	12.4456i	−0.474829	−	0.822428i	−0.999584	+	0.0288250i	$0.990823\pi$
$230$	−0.209594	+	0.363027i	−0.0138202	+	0.0239373i
$231$	−2.69733	−	4.67191i	−0.177471	−	0.307389i
$232$	−0.412735			−0.0270974
$233$	13.5711			0.889072			0.444536	−	0.895761i	$-0.353369\pi$
$233$	13.5711			0.889072			0.444536	+	0.895761i	$0.353369\pi$
$234$	−0.00681562	−	0.0118050i	−0.000445551	−	0.000771717i
$235$	−2.73225	+	4.73239i	−0.178232	+	0.308707i
$236$	−7.78305	−	13.4806i	−0.506633	−	0.877514i
$237$	6.38542	−	11.0599i	0.414777	−	0.718415i
$238$	−0.347684	+	0.602206i	−0.0225370	+	0.0390352i
$239$	−7.91765	+	13.7138i	−0.512150	+	0.887070i	0.487751	+	0.872983i	$0.337817\pi$
$239$	−7.91765	+	13.7138i	−0.512150	+	0.887070i	−0.999901	+	0.0140869i	$0.995516\pi$
$240$	11.3164			0.730471
$241$	8.83712	+	15.3063i	0.569249	+	0.985968i	0.996640	+	0.0819013i	$0.0260992\pi$
$241$	8.83712	+	15.3063i	0.569249	+	0.985968i	−0.427392	+	0.904067i	$0.640567\pi$
$242$	0.229151	+	0.396901i	0.0147304	+	0.0255138i
$243$	1.60503	−	2.77999i	0.102963	−	0.178337i
$244$	23.7429			1.51998
$245$	10.3241	+	17.8819i	0.659583	+	1.14243i
$246$	0.879539			0.0560774
$247$	−2.25948			−0.143767
$248$	−0.838454	−	0.503981i	−0.0532419	−	0.0320028i
$249$	−24.5250			−1.55421
$250$	0.532733			0.0336930
$251$	−1.64983	−	2.85758i	−0.104136	−	0.180369i	0.809249	−	0.587466i	$-0.199874\pi$
$251$	−1.64983	−	2.85758i	−0.104136	−	0.180369i	−0.913385	+	0.407097i	$0.866541\pi$
$252$	2.69685			0.169886
$253$	−2.08388	+	3.60938i	−0.131012	+	0.226920i
$254$	−0.285077	−	0.493769i	−0.0178873	−	0.0309818i
$255$	−5.15858	−	8.93492i	−0.323043	−	0.559526i
$256$	15.8457			0.990357
$257$	−7.87541	+	13.6406i	−0.491254	+	0.850878i	−0.999949	−	0.0100693i	$-0.996795\pi$
$257$	−7.87541	+	13.6406i	−0.491254	+	0.850878i	0.508695	+	0.860947i	$0.330128\pi$
$258$	0.159597	−	0.276430i	0.00993606	−	0.0172098i
$259$	0.311735	−	0.539941i	0.0193703	−	0.0335503i
$260$	1.72833	+	2.99355i	0.107186	+	0.185652i
$261$	0.364314	−	0.631010i	0.0225504	−	0.0390585i
$262$	0.0255945	+	0.0443309i	0.00158123	+	0.00273877i
$263$	25.8207			1.59217			0.796087	−	0.605183i	$-0.206900\pi$
$263$	25.8207			1.59217			0.796087	+	0.605183i	$0.206900\pi$
$264$	−0.217822			−0.0134060
$265$	7.50276	+	12.9952i	0.460891	+	0.798286i
$266$	−0.216043	+	0.374198i	−0.0132465	+	0.0229435i
$267$	0.945122	+	1.63700i	0.0578406	+	0.100183i
$268$	2.43180	−	4.21200i	0.148546	−	0.257289i
$269$	5.58230	−	9.66883i	0.340359	−	0.589519i	−0.644141	−	0.764907i	$-0.722785\pi$
$269$	5.58230	−	9.66883i	0.340359	−	0.589519i	0.984499	+	0.175388i	$0.0561181\pi$
$270$	0.206374	−	0.357450i	0.0125595	−	0.0217537i
$271$	19.9827			1.21386			0.606932	−	0.794754i	$-0.292400\pi$
$271$	19.9827			1.21386			0.606932	+	0.794754i	$0.292400\pi$
$272$	−7.25141	−	12.5598i	−0.439681	−	0.761551i
$273$	−3.56836	−	6.18059i	−0.215967	−	0.374066i
$274$	−0.159643	+	0.276509i	−0.00964436	+	0.0167045i
$275$	1.51717			0.0914888
$276$	9.03398	+	15.6473i	0.543782	+	0.941858i
$277$	7.55938			0.454199			0.227100	−	0.973872i	$-0.427076\pi$
$277$	7.55938			0.454199			0.227100	+	0.973872i	$0.427076\pi$
$278$	0.126188			0.00756823
$279$	1.51060	−	0.837015i	0.0904372	−	0.0501108i
$280$	1.32269			0.0790460
$281$	13.2911			0.792878			0.396439	−	0.918061i	$-0.370246\pi$
$281$	13.2911			0.792878			0.396439	+	0.918061i	$0.370246\pi$
$282$	−0.113831	−	0.197161i	−0.00677854	−	0.0117408i
$283$	−29.9701			−1.78154			−0.890769	−	0.454456i	$-0.849834\pi$
$283$	−29.9701			−1.78154			−0.890769	+	0.454456i	$0.849834\pi$
$284$	−4.97628	+	8.61917i	−0.295288	+	0.511453i
$285$	−3.20543	−	5.55196i	−0.189873	−	0.328870i
$286$	−0.0166097	−	0.0287688i	−0.000982149	−	0.00170113i
$287$	−53.1013			−3.13447
$288$	0.0816821	−	0.141478i	0.00481317	−	0.00833665i
$289$	1.88889	−	3.27166i	0.111111	−	0.192450i
$290$	0.0892971	−	0.154667i	0.00524370	−	0.00908236i
$291$	13.4725	+	23.3351i	0.789775	+	1.36793i
$292$	−13.1144	+	22.7149i	−0.767464	+	1.32929i
$293$	12.3036	+	21.3104i	0.718781	+	1.24497i	0.961483	+	0.274864i	$0.0886330\pi$
$293$	12.3036	+	21.3104i	0.718781	+	1.24497i	−0.242702	+	0.970101i	$0.578034\pi$
$294$	−0.860248			−0.0501707
$295$	13.4777			0.784701
$296$	−0.0125871	−	0.0218014i	−0.000731608	−	0.00126718i
$297$	2.05186	−	3.55393i	0.119061	−	0.206220i
$298$	0.310804	+	0.538329i	0.0180044	+	0.0311845i
$299$	−2.75681	+	4.77494i	−0.159431	+	0.276142i
$300$	3.28860	−	5.69603i	0.189868	−	0.328860i
$301$	−9.63550	+	16.6892i	−0.555381	+	0.961948i
$302$	−0.573575			−0.0330055
$303$	14.1194	+	24.4555i	0.811137	+	1.40493i
$304$	−4.50587	−	7.80439i	−0.258429	−	0.447612i
$305$	−10.2787	+	17.8033i	−0.588558	+	1.01941i
$306$	−0.0495664			−0.00283352
$307$	5.83488	+	10.1063i	0.333014	+	0.576798i	0.983101	−	0.183062i	$-0.0586010\pi$
$307$	5.83488	+	10.1063i	0.333014	+	0.576798i	−0.650087	+	0.759860i	$0.725268\pi$
$308$	6.57223			0.374488
$309$	−4.52561			−0.257453
$310$	0.370264	−	0.205161i	0.0210296	−	0.0116524i
$311$	−19.8416			−1.12511			−0.562557	−	0.826758i	$-0.690182\pi$
$311$	−19.8416			−1.12511			−0.562557	+	0.826758i	$0.690182\pi$
$312$	−0.288163			−0.0163140
$313$	−16.2837	−	28.2042i	−0.920411	−	1.59420i	−0.798781	−	0.601623i	$-0.794521\pi$
$313$	−16.2837	−	28.2042i	−0.920411	−	1.59420i	−0.121630	−	0.992575i	$-0.538812\pi$
$314$	−0.0147230			−0.000830870
$315$	−1.16752	+	2.02220i	−0.0657821	+	0.113938i
$316$	7.77925	+	13.4741i	0.437617	+	0.757975i
$317$	0.765436	+	1.32577i	0.0429911	+	0.0744628i	0.886720	−	0.462306i	$-0.152978\pi$
$317$	0.765436	+	1.32577i	0.0429911	+	0.0744628i	−0.843729	+	0.536769i	$0.819645\pi$
$318$	−0.625161			−0.0350573
$319$	0.887832	−	1.53777i	0.0497090	−	0.0860986i
$320$	−6.87994	+	11.9164i	−0.384600	+	0.666147i
$321$	−11.1603	+	19.3302i	−0.622908	+	1.07891i
$322$	0.527193	+	0.913125i	0.0293793	+	0.0508865i
$323$	−4.10800	+	7.11526i	−0.228575	+	0.395904i
$324$	−7.96556	−	13.7968i	−0.442531	−	0.766486i
$325$	2.00710			0.111334
$326$	0.858379			0.0475412
$327$	4.97113	+	8.61025i	0.274904	+	0.476148i
$328$	−1.07205	+	1.85684i	−0.0591938	+	0.102527i
$329$	6.87244	+	11.9034i	0.378890	+	0.656256i
$330$	0.0471269	−	0.0816261i	0.00259425	−	0.00449337i
$331$	−1.87523	+	3.24799i	−0.103072	+	0.178526i	−0.912949	−	0.408074i	$-0.866201\pi$
$331$	−1.87523	+	3.24799i	−0.103072	+	0.178526i	0.809877	+	0.586600i	$0.199534\pi$
$332$	14.9392	−	25.8755i	0.819897	−	1.42010i
$333$	0.0444415			0.00243538
$334$	−0.0597855	−	0.103552i	−0.00327132	−	0.00566609i
$335$	2.10554	+	3.64690i	0.115038	+	0.199252i
$336$	14.2321	−	24.6507i	0.776425	−	1.34481i
$337$	−30.3844			−1.65514			−0.827572	−	0.561359i	$-0.810279\pi$
$337$	−30.3844			−1.65514			−0.827572	+	0.561359i	$0.810279\pi$
$338$	−0.0219733	−	0.0380589i	−0.00119519	−	0.00207013i
$339$	2.21719			0.120421
$340$	12.5692			0.681662
$341$	3.68133	−	2.03981i	0.199355	−	0.110462i
$342$	−0.0307995			−0.00166544
$343$	21.4763			1.15961
$344$	0.389057	+	0.673866i	0.0209765	+	0.0363324i
$345$	−15.6439			−0.842239
$346$	0.443765	−	0.768623i	0.0238569	−	0.0413214i
$347$	7.46713	+	12.9335i	0.400857	+	0.694304i	0.993830	−	0.110918i	$-0.0353792\pi$
$347$	7.46713	+	12.9335i	0.400857	+	0.694304i	−0.592973	+	0.805223i	$0.702046\pi$
$348$	−3.84891	−	6.66651i	−0.206323	−	0.357362i
$349$	−12.4565			−0.666781			−0.333390	−	0.942789i	$-0.608193\pi$
$349$	−12.4565			−0.666781			−0.333390	+	0.942789i	$0.608193\pi$
$350$	0.191912	−	0.332401i	0.0102581	−	0.0177676i
$351$	2.71446	−	4.70158i	0.144887	−	0.250952i
$352$	0.199059	−	0.344781i	0.0106099	−	0.0183769i
$353$	−1.94912	−	3.37598i	−0.103741	−	0.179685i	0.809482	−	0.587145i	$-0.199748\pi$
$353$	−1.94912	−	3.37598i	−0.103741	−	0.179685i	−0.913223	+	0.407459i	$0.866415\pi$
$354$	−0.280754	+	0.486281i	−0.0149219	+	0.0258455i
$355$	−4.30864	−	7.46279i	−0.228679	−	0.396084i
$356$	−2.30286			−0.122051
$357$	−25.9508			−1.37346
$358$	0.203010	+	0.351624i	0.0107294	+	0.0185839i
$359$	6.53207	−	11.3139i	0.344749	−	0.597123i	−0.640559	−	0.767909i	$-0.721297\pi$
$359$	6.53207	−	11.3139i	0.344749	−	0.597123i	0.985308	+	0.170786i	$0.0546306\pi$
$360$	0.0471413	+	0.0816511i	0.00248457	+	0.00430339i
$361$	6.94738	−	12.0332i	0.365652	−	0.633327i
$362$	0.0124636	−	0.0215877i	0.000655075	−	0.00113462i
$363$	−8.55182	+	14.8122i	−0.448854	+	0.777438i
$364$	8.69456			0.455719
$365$	−11.3550	−	19.6674i	−0.594345	−	1.02944i
$366$	−0.428233	−	0.741722i	−0.0223841	−	0.0387704i
$367$	−16.5851	+	28.7263i	−0.865737	+	1.49950i	0.000577478		1.00000i	$0.499816\pi$
$367$	−16.5851	+	28.7263i	−0.865737	+	1.49950i	−0.866314	+	0.499500i	$0.833517\pi$
$368$	−21.9906			−1.14634
$369$	−1.89255	−	3.27799i	−0.0985223	−	0.170646i
$370$	0.0108931			0.000566304
$371$	37.7435			1.95954
$372$	0.321416	−	18.2426i	0.0166646	−	0.945832i
$373$	−32.0094			−1.65738			−0.828691	−	0.559707i	$-0.810914\pi$
$373$	−32.0094			−1.65738			−0.828691	+	0.559707i	$0.810914\pi$
$374$	−0.120793			−0.00624607
$375$	9.94068	+	17.2178i	0.513335	+	0.889122i
$376$	0.554983			0.0286210
$377$	1.17453	−	2.03435i	0.0604916	−	0.104774i
$378$	−0.519094	−	0.899096i	−0.0266993	−	0.0462445i
$379$	5.01452	+	8.68541i	0.257579	+	0.446139i	0.965593	−	0.260059i	$-0.0837420\pi$
$379$	5.01452	+	8.68541i	0.257579	+	0.446139i	−0.708014	+	0.706198i	$0.750409\pi$
$380$	7.81024			0.400657
$381$	10.6390	−	18.4272i	0.545051	−	0.944055i
$382$	0.235697	−	0.408240i	0.0120593	−	0.0208874i
$383$	6.39526	−	11.0769i	0.326782	−	0.566004i	−0.655089	−	0.755552i	$-0.727369\pi$
$383$	6.39526	−	11.0769i	0.326782	−	0.566004i	0.981871	+	0.189548i	$0.0607023\pi$
$384$	−1.15042	−	1.99259i	−0.0587074	−	0.101684i
$385$	−2.84524	+	4.92809i	−0.145007	+	0.251159i
$386$	−0.168159	−	0.291261i	−0.00855909	−	0.0148248i
$387$	−1.37365			−0.0698267
$388$	−32.8268			−1.66653
$389$	4.89034	+	8.47032i	0.247950	+	0.429462i	0.962957	−	0.269655i	$-0.0869097\pi$
$389$	4.89034	+	8.47032i	0.247950	+	0.429462i	−0.715007	+	0.699118i	$0.753576\pi$
$390$	0.0623453	−	0.107985i	0.00315697	−	0.00546804i
$391$	10.0244	+	17.3628i	0.506957	+	0.878075i
$392$	1.04853	−	1.81611i	0.0529589	−	0.0917276i
$393$	−0.955174	+	1.65441i	−0.0481822	+	0.0834539i
$394$	0.263125	−	0.455745i	0.0132560	−	0.0229601i
$395$	−13.4711			−0.677805
$396$	0.234237	+	0.405710i	0.0117708	+	0.0203877i
$397$	4.14835	+	7.18516i	0.208200	+	0.360613i	0.951148	−	0.308737i	$-0.0999062\pi$
$397$	4.14835	+	7.18516i	0.208200	+	0.360613i	−0.742948	+	0.669350i	$0.766573\pi$
$398$	−0.0466996	+	0.0808861i	−0.00234084	+	0.00405446i
$399$	−16.1253			−0.807273
$400$	4.00257	+	6.93266i	0.200129	+	0.346633i
$401$	16.6296			0.830443			0.415221	−	0.909720i	$-0.363704\pi$
$401$	16.6296			0.830443			0.415221	+	0.909720i	$0.363704\pi$
$402$	−0.175442			−0.00875027
$403$	4.87012	−	2.69851i	0.242598	−	0.134422i
$404$	−34.4028			−1.71160
$405$	13.7937			0.685416
$406$	−0.224610	−	0.389035i	−0.0111472	−	0.0193075i
$407$	0.108304			0.00536842
$408$	−0.523914	+	0.907445i	−0.0259376	+	0.0449252i
$409$	−10.4943	−	18.1767i	−0.518911	−	0.898781i	−0.999758	−	0.0219765i	$-0.993004\pi$
$409$	−10.4943	−	18.1767i	−0.518911	−	0.898781i	0.480847	−	0.876805i	$-0.340329\pi$
$410$	−0.463884	−	0.803470i	−0.0229096	−	0.0396806i
$411$	−11.9156			−0.587752
$412$	2.75674	−	4.77481i	0.135815	−	0.235238i
$413$	16.9503	−	29.3587i	0.834068	−	1.44465i
$414$	−0.0375788	+	0.0650883i	−0.00184689	+	0.00319892i
$415$	12.9349	+	22.4040i	0.634951	+	1.09977i
$416$	0.263340	−	0.456119i	0.0129113	−	0.0223631i
$417$	2.35463	+	4.07834i	0.115307	+	0.199717i
$418$	−0.0750583			−0.00367122
$419$	20.9420			1.02308			0.511542	−	0.859258i	$-0.329074\pi$
$419$	20.9420			1.02308			0.511542	+	0.859258i	$0.329074\pi$
$420$	12.3346	+	21.3642i	0.601867	+	1.04246i
$421$	5.27968	−	9.14468i	0.257316	−	0.445684i	−0.708206	−	0.706006i	$-0.750495\pi$
$421$	5.27968	−	9.14468i	0.257316	−	0.445684i	0.965522	+	0.260321i	$0.0838285\pi$
$422$	0.0822160	+	0.142402i	0.00400221	+	0.00693203i
$423$	−0.489873	+	0.848485i	−0.0238184	+	0.0412547i
$424$	0.761992	−	1.31981i	0.0370056	−	0.0640956i
$425$	3.64915	−	6.32051i	0.177010	−	0.306590i
$426$	0.359014			0.0173943
$427$	25.8542	+	44.7807i	1.25117	+	2.16709i
$428$	−13.5964	−	23.5497i	−0.657208	−	1.13832i
$429$	0.619865	−	1.07364i	0.0299274	−	0.0518357i
$430$	−0.336696			−0.0162369
$431$	−12.7366	−	22.0604i	−0.613499	−	1.06261i	−0.990646	−	0.136458i	$-0.956428\pi$
$431$	−12.7366	−	22.0604i	−0.613499	−	1.06261i	0.377146	−	0.926154i	$-0.376905\pi$
$432$	21.6528			1.04177
$433$	9.03616			0.434250			0.217125	−	0.976144i	$-0.430332\pi$
$433$	9.03616			0.434250			0.217125	+	0.976144i	$0.430332\pi$
$434$	0.0187567	−	1.06457i	0.000900353	−	0.0511012i
$435$	6.66505			0.319565
$436$	−12.1125			−0.580083
$437$	6.22895	+	10.7889i	0.297971	+	0.516101i
$438$	0.946142			0.0452084
$439$	−12.6871	+	21.9746i	−0.605521	+	1.04879i	0.386448	+	0.922311i	$0.373702\pi$
$439$	−12.6871	+	21.9746i	−0.605521	+	1.04879i	−0.991969	+	0.126481i	$0.959632\pi$
$440$	0.114883	+	0.198984i	0.00547685	+	0.00948618i
$441$	1.85104	+	3.20610i	0.0881449	+	0.152671i
$442$	−0.159800			−0.00760092
$443$	−12.2704	+	21.2529i	−0.582984	+	1.00976i	0.412139	+	0.911121i	$0.364782\pi$
$443$	−12.2704	+	21.2529i	−0.582984	+	1.00976i	−0.995123	+	0.0986372i	$0.968552\pi$
$444$	0.234758	−	0.406613i	0.0111411	−	0.0192970i
$445$	0.996948	−	1.72676i	0.0472599	−	0.0818565i
$446$	−0.494390	−	0.856308i	−0.0234100	−	0.0405473i
$447$	−11.5991	+	20.0902i	−0.548617	+	0.950233i
$448$	17.3052	+	29.9734i	0.817592	+	1.41611i
$449$	4.64614			0.219265			0.109632	−	0.993972i	$-0.465033\pi$
$449$	4.64614			0.219265			0.109632	+	0.993972i	$0.465033\pi$
$450$	0.0273593			0.00128973
$451$	−4.61214	−	7.98847i	−0.217177	−	0.376162i
$452$	−1.35059	+	2.33928i	−0.0635262	+	0.110031i
$453$	−10.7028	−	18.5378i	−0.502860	−	0.870980i
$454$	−0.294402	+	0.509920i	−0.0138170	+	0.0239317i
$455$	−3.76403	+	6.51949i	−0.176461	+	0.305639i
$456$	−0.325548	+	0.563866i	−0.0152452	+	0.0264055i
$457$	−4.77391			−0.223314			−0.111657	−	0.993747i	$-0.535616\pi$
$457$	−4.77391			−0.223314			−0.111657	+	0.993747i	$0.535616\pi$
$458$	−0.315777	−	0.546942i	−0.0147553	−	0.0255569i
$459$	−9.87041	−	17.0961i	−0.460711	−	0.797975i
$460$	9.52936	−	16.5053i	0.444309	−	0.769565i
$461$	−38.5083			−1.79351			−0.896755	−	0.442528i	$-0.854082\pi$
$461$	−38.5083			−1.79351			−0.896755	+	0.442528i	$0.854082\pi$
$462$	−0.118539	−	0.205315i	−0.00551491	−	0.00955211i
$463$	−21.3228			−0.990953			−0.495477	−	0.868621i	$-0.665007\pi$
$463$	−21.3228			−0.990953			−0.495477	+	0.868621i	$0.665007\pi$
$464$	9.36906			0.434948
$465$	13.5398	+	8.13854i	0.627892	+	0.377416i
$466$	0.596403			0.0276279
$467$	−12.1756			−0.563421			−0.281710	−	0.959500i	$-0.590902\pi$
$467$	−12.1756			−0.563421			−0.281710	+	0.959500i	$0.590902\pi$
$468$	0.309878	+	0.536724i	0.0143241	+	0.0248101i
$469$	10.5922			0.489100
$470$	−0.120073	+	0.207972i	−0.00553855	+	0.00959305i
$471$	−0.274729	−	0.475844i	−0.0126588	−	0.0219257i
$472$	−0.684408	−	1.18543i	−0.0315024	−	0.0545638i
$473$	−3.34759			−0.153922
$474$	0.280617	−	0.486044i	0.0128892	−	0.0223247i
$475$	2.26750	−	3.92742i	0.104040	−	0.180202i
$476$	15.8077	−	27.3798i	0.724546	−	1.25495i
$477$	1.34519	+	2.32994i	0.0615922	+	0.106681i
$478$	−0.347954	+	0.602674i	−0.0159150	+	0.0275656i
$479$	17.8607	+	30.9356i	0.816075	+	1.41348i	0.908554	+	0.417768i	$0.137188\pi$
$479$	17.8607	+	30.9356i	0.816075	+	1.41348i	−0.0924788	+	0.995715i	$0.529479\pi$
$480$	1.49436			0.0682079
$481$	0.143278			0.00653290
$482$	0.388361	+	0.672662i	0.0176894	+	0.0306389i
$483$	−19.6746	+	34.0774i	−0.895226	+	1.55058i
$484$	−10.4185	−	18.0454i	−0.473570	−	0.820248i
$485$	14.2113	−	24.6147i	0.645302	−	1.11770i
$486$	0.0705356	−	0.122171i	0.00319956	−	0.00554180i
$487$	2.65171	−	4.59289i	0.120160	−	0.208124i	−0.799670	−	0.600439i	$-0.794992\pi$
$487$	2.65171	−	4.59289i	0.120160	−	0.208124i	0.919831	+	0.392315i	$0.128326\pi$
$488$	2.08785			0.0945124
$489$	16.0172	+	27.7425i	0.724321	+	1.25456i
$490$	0.453710	+	0.785848i	0.0204965	+	0.0355010i
$491$	−7.47743	+	12.9513i	−0.337451	+	0.584483i	−0.983953	−	0.178430i	$-0.942898\pi$
$491$	−7.47743	+	12.9513i	−0.337451	+	0.584483i	0.646501	+	0.762913i	$0.276232\pi$
$492$	−39.9890			−1.80284
$493$	−4.27088	−	7.39739i	−0.192351	−	0.333162i
$494$	−0.0992964			−0.00446755
$495$	−0.405622			−0.0182313
$496$	19.0329	+	11.4403i	0.854601	+	0.513687i
$497$	−21.6751			−0.972262
$498$	−1.07779			−0.0482970
$499$	−5.06302	−	8.76941i	−0.226652	−	0.392573i	0.730162	−	0.683274i	$-0.239445\pi$
$499$	−5.06302	−	8.76941i	−0.226652	−	0.392573i	−0.956814	+	0.290701i	$0.906111\pi$
$500$	−24.2212			−1.08320
$501$	2.23117	−	3.86450i	0.0996812	−	0.172653i
$502$	−0.0725042	−	0.125581i	−0.00323602	−	0.00560496i
$503$	0.615504	+	1.06608i	0.0274440	+	0.0475343i	0.879421	−	0.476044i	$-0.157930\pi$
$503$	0.615504	+	1.06608i	0.0274440	+	0.0475343i	−0.851977	+	0.523579i	$0.824597\pi$
$504$	0.237150			0.0105635
$505$	14.8936	−	25.7965i	0.662757	−	1.14793i
$506$	−0.0915794	+	0.158620i	−0.00407120	+	0.00705153i
$507$	0.820034	−	1.42034i	0.0364190	−	0.0630795i
$508$	12.9613	+	22.4496i	0.575064	+	0.996040i
$509$	10.5568	−	18.2849i	0.467922	−	0.810464i	−0.531406	−	0.847117i	$-0.678336\pi$
$509$	10.5568	−	18.2849i	0.467922	−	0.810464i	0.999328	+	0.0366529i	$0.0116696\pi$
$510$	−0.226702	−	0.392660i	−0.0100385	−	0.0173873i
$511$	−57.1224			−2.52695
$512$	3.50216			0.154775
$513$	−6.13325	−	10.6231i	−0.270790	−	0.469022i
$514$	−0.346097	+	0.599458i	−0.0152657	+	0.0264410i
$515$	2.38688	+	4.13420i	0.105179	+	0.182175i
$516$	−7.25620	+	12.5681i	−0.319436	+	0.553280i
$517$	−1.19382	+	2.06776i	−0.0525041	+	0.0909398i
$518$	0.0136997	−	0.0237286i	0.000601930	−	0.00104257i
$519$	33.1222			1.45390
$520$	0.151982	+	0.263240i	0.00666485	+	0.0115439i
$521$	12.8402	+	22.2399i	0.562540	+	0.974348i	0.997274	+	0.0737891i	$0.0235092\pi$
$521$	12.8402	+	22.2399i	0.562540	+	0.974348i	−0.434734	+	0.900559i	$0.643158\pi$
$522$	0.0160104	−	0.0277307i	0.000700754	−	0.00121374i
$523$	24.2801			1.06170			0.530848	−	0.847467i	$-0.321873\pi$
$523$	24.2801			1.06170			0.530848	+	0.847467i	$0.321873\pi$
$524$	−1.16367	−	2.01554i	−0.0508353	−	0.0880493i
$525$	14.3241			0.625156
$526$	1.13473			0.0494767
$527$	0.356654	−	20.2426i	0.0155361	−	0.881780i
$528$	4.94456			0.215184
$529$	7.40004			0.321741
$530$	0.329721	+	0.571093i	0.0143222	+	0.0248067i
$531$	2.41646			0.104865
$532$	9.82258	−	17.0132i	0.425863	−	0.737616i
$533$	−6.10152	−	10.5681i	−0.264286	−	0.457757i
$534$	0.0415349	+	0.0719406i	0.00179739	+	0.00311317i
$535$	23.5446			1.01792
$536$	0.213842	−	0.370385i	0.00923657	−	0.0159982i
$537$	−7.57624	+	13.1224i	−0.326939	+	0.566275i
$538$	0.245323	−	0.424912i	0.0105766	−	0.0183193i
$539$	4.51099	+	7.81326i	0.194302	+	0.336541i
$540$	−9.38295	+	16.2518i	−0.403778	+	0.699364i
$541$	−14.8193	−	25.6677i	−0.637131	−	1.10354i	−0.986059	−	0.166393i	$-0.946788\pi$
$541$	−14.8193	−	25.6677i	−0.637131	−	1.10354i	0.348929	−	0.937149i	$-0.386545\pi$
$542$	0.878173			0.0377208
$543$	0.930275			0.0399219
$544$	−0.957568	−	1.65856i	−0.0410554	−	0.0711100i
$545$	5.24372	−	9.08239i	0.224616	−	0.389047i
$546$	−0.156817	−	0.271616i	−0.00671117	−	0.0116241i
$547$	2.69040	−	4.65991i	0.115033	−	0.199243i	−0.802760	−	0.596303i	$-0.796636\pi$
$547$	2.69040	−	4.65991i	0.115033	−	0.199243i	0.917793	+	0.397059i	$0.129969\pi$
$548$	7.25828	−	12.5717i	0.310058	−	0.537037i
$549$	−1.84291	+	3.19201i	−0.0786533	+	0.136231i
$550$	0.0666745			0.00284301
$551$	−2.65383	−	4.59657i	−0.113057	−	0.195821i
$552$	0.794410	+	1.37596i	0.0338123	+	0.0585647i
$553$	−16.9420	+	29.3444i	−0.720447	+	1.24785i
$554$	0.332209			0.0141142
$555$	0.203262	+	0.352060i	0.00862800	+	0.0149441i
$556$	−5.73722			−0.243312
$557$	−27.2724			−1.15557			−0.577783	−	0.816190i	$-0.696082\pi$
$557$	−27.2724			−1.15557			−0.577783	+	0.816190i	$0.696082\pi$
$558$	0.0663857	−	0.0367840i	0.00281033	−	0.00155719i
$559$	−4.42861			−0.187310
$560$	−30.0250			−1.26879
$561$	−2.25398	−	3.90400i	−0.0951629	−	0.164827i
$562$	0.584097			0.0246386
$563$	7.90531	−	13.6924i	0.333169	−	0.577066i	−0.649962	−	0.759966i	$-0.725215\pi$
$563$	7.90531	−	13.6924i	0.333169	−	0.577066i	0.983131	+	0.182901i	$0.0585487\pi$
$564$	5.17542	+	8.96410i	0.217925	+	0.377457i
$565$	−1.16939	−	2.02544i	−0.0491964	−	0.0852107i
$566$	−1.31709			−0.0553612
$567$	17.3477	−	30.0472i	0.728537	−	1.26186i
$568$	−0.437593	+	0.757933i	−0.0183610	+	0.0318021i
$569$	13.8525	−	23.9932i	0.580727	−	1.00585i	−0.414666	−	0.909974i	$-0.636102\pi$
$569$	13.8525	−	23.9932i	0.580727	−	1.00585i	0.995393	−	0.0958753i	$-0.0305650\pi$
$570$	−0.140868	−	0.243990i	−0.00590030	−	0.0102196i
$571$	7.55877	−	13.0922i	0.316325	−	0.547891i	−0.663393	−	0.748271i	$-0.730884\pi$
$571$	7.55877	−	13.0922i	0.316325	−	0.547891i	0.979718	+	0.200380i	$0.0642177\pi$
$572$	0.755171	+	1.30800i	0.0315753	+	0.0546900i
$573$	17.5922			0.734927
$574$	−2.33362			−0.0974035
$575$	−5.53320	−	9.58378i	−0.230750	−	0.399671i
$576$	−1.23353	+	2.13653i	−0.0513969	+	0.0890221i
$577$	−0.151086	−	0.261689i	−0.00628981	−	0.0108943i	0.862863	−	0.505437i	$-0.168669\pi$
$577$	−0.151086	−	0.261689i	−0.00628981	−	0.0108943i	−0.869153	+	0.494543i	$0.835335\pi$
$578$	0.0830104	−	0.143778i	0.00345278	−	0.00598039i
$579$	6.27563	−	10.8697i	0.260806	−	0.451730i
$580$	−4.05996	+	7.03206i	−0.168581	+	0.291991i
$581$	65.0706			2.69958
$582$	0.592073	+	1.02550i	0.0245422	+	0.0425084i
$583$	3.27823	+	5.67807i	0.135771	+	0.235162i
$584$	−1.15323	+	1.99745i	−0.0477209	+	0.0826550i
$585$	−0.536607			−0.0221859
$586$	0.540699	+	0.936519i	0.0223361	+	0.0386872i
$587$	−7.48002			−0.308733			−0.154367	−	0.988014i	$-0.549334\pi$
$587$	−7.48002			−0.308733			−0.154367	+	0.988014i	$0.549334\pi$
$588$	39.1119			1.61295
$589$	0.221617	−	12.5783i	0.00913156	−	0.518279i
$590$	0.592299			0.0243845
$591$	19.6394			0.807857
$592$	0.285726	+	0.494891i	0.0117432	+	0.0203399i
$593$	−19.5216			−0.801658			−0.400829	−	0.916153i	$-0.631278\pi$
$593$	−19.5216			−0.801658			−0.400829	+	0.916153i	$0.631278\pi$
$594$	0.0901724	−	0.156183i	0.00369982	−	0.00640827i
$595$	13.6869	+	23.7064i	0.561109	+	0.971869i
$596$	−14.1310	−	24.4756i	−0.578827	−	1.00256i
$597$	−3.48562			−0.142657
$598$	−0.121153	+	0.209842i	−0.00495430	+	0.00858109i
$599$	−3.52226	+	6.10074i	−0.143916	+	0.249269i	−0.928968	−	0.370160i	$-0.879303\pi$
$599$	−3.52226	+	6.10074i	−0.143916	+	0.249269i	0.785052	+	0.619430i	$0.212636\pi$
$600$	0.289186	−	0.500884i	0.0118059	−	0.0204485i
$601$	12.2937	+	21.2933i	0.501469	+	0.868570i	0.999999	+	0.00169736i	$0.000540286\pi$
$601$	12.2937	+	21.2933i	0.501469	+	0.868570i	−0.498529	+	0.866873i	$0.666126\pi$
$602$	−0.423447	+	0.733433i	−0.0172584	+	0.0298925i
$603$	0.377509	+	0.653864i	0.0153733	+	0.0266274i
$604$	26.0781			1.06110
$605$	18.0415			0.733491
$606$	0.620499	+	1.07474i	0.0252060	+	0.0436581i
$607$	7.82764	−	13.5579i	0.317714	−	0.550297i	−0.662296	−	0.749242i	$-0.730418\pi$
$607$	7.82764	−	13.5579i	0.317714	−	0.550297i	0.980011	+	0.198945i	$0.0637514\pi$
$608$	−0.595011	−	1.03059i	−0.0241309	−	0.0417959i
$609$	8.38233	−	14.5186i	0.339669	−	0.588324i
$610$	−0.451715	+	0.782394i	−0.0182894	+	0.0316782i
$611$	−1.57933	+	2.73548i	−0.0638930	+	0.110666i
$612$	2.25358			0.0910954
$613$	−4.63643	−	8.03053i	−0.187264	−	0.324350i	0.757073	−	0.653330i	$-0.226629\pi$
$613$	−4.63643	−	8.03053i	−0.187264	−	0.324350i	−0.944337	+	0.328980i	$0.893295\pi$
$614$	0.256423	+	0.444138i	0.0103484	+	0.0179240i
$615$	17.3119	−	29.9852i	0.698085	−	1.20912i
$616$	0.577934			0.0232856
$617$	−2.06877	−	3.58322i	−0.0832856	−	0.144255i	0.821374	−	0.570390i	$-0.193208\pi$
$617$	−2.06877	−	3.58322i	−0.0832856	−	0.144255i	−0.904659	+	0.426135i	$0.859875\pi$
$618$	−0.198885			−0.00800033
$619$	9.83923			0.395472			0.197736	−	0.980255i	$-0.436641\pi$
$619$	9.83923			0.395472			0.197736	+	0.980255i	$0.436641\pi$
$620$	−16.8343	+	9.32782i	−0.676083	+	0.374614i
$621$	−29.9330			−1.20117
$622$	−0.871971			−0.0349629
$623$	−2.50763	−	4.34334i	−0.100466	−	0.174012i
$624$	6.54127			0.261860
$625$	5.46802	−	9.47090i	0.218721	−	0.378836i
$626$	−0.715615	−	1.23948i	−0.0286017	−	0.0495396i
$627$	−1.40057	−	2.42586i	−0.0559334	−	0.0968795i
$628$	0.669395			0.0267118
$629$	0.260496	−	0.451192i	0.0103866	−	0.0179902i
$630$	−0.0513084	+	0.0888688i	−0.00204418	+	0.00354062i
$631$	5.79446	−	10.0363i	0.230674	−	0.399539i	−0.727333	−	0.686285i	$-0.759240\pi$
$631$	5.79446	−	10.0363i	0.230674	−	0.399539i	0.958007	+	0.286746i	$0.0925736\pi$
$632$	0.684074	+	1.18485i	0.0272110	+	0.0471308i
$633$	−3.06826	+	5.31439i	−0.121952	+	0.211228i
$634$	0.0336383	+	0.0582633i	0.00133595	+	0.00231393i
$635$	−22.4447			−0.890690
$636$	28.4235			1.12706
$637$	5.96770	+	10.3364i	0.236449	+	0.409541i
$638$	0.0390172	−	0.0675798i	0.00154471	−	0.00267551i
$639$	−0.772510	−	1.33803i	−0.0305600	−	0.0529315i
$640$	−1.21351	+	2.10186i	−0.0479681	+	0.0830832i
$641$	10.2889	−	17.8209i	0.406388	−	0.703884i	−0.588094	−	0.808792i	$-0.700122\pi$
$641$	10.2889	−	17.8209i	0.406388	−	0.703884i	0.994482	+	0.104908i	$0.0334549\pi$
$642$	−0.490458	+	0.849498i	−0.0193568	+	0.0335270i
$643$	−3.31277			−0.130643			−0.0653215	−	0.997864i	$-0.520807\pi$
$643$	−3.31277			−0.130643			−0.0653215	+	0.997864i	$0.520807\pi$
$644$	−23.9693	−	41.5160i	−0.944521	−	1.63596i
$645$	−6.28268	−	10.8819i	−0.247380	−	0.428475i
$646$	−0.180533	+	0.312692i	−0.00710296	+	0.0123027i
$647$	33.9324			1.33402			0.667011	−	0.745048i	$-0.267573\pi$
$647$	33.9324			1.33402			0.667011	+	0.745048i	$0.267573\pi$
$648$	−0.700457	−	1.21323i	−0.0275166	−	0.0476601i
$649$	5.88890			0.231160
$650$	0.0882053			0.00345969
$651$	34.7567	−	19.2585i	1.36222	−	0.754800i
$652$	−39.0269			−1.52841
$653$	−49.4629			−1.93563			−0.967817	−	0.251656i	$-0.919025\pi$
$653$	−49.4629			−1.93563			−0.967817	+	0.251656i	$0.919025\pi$
$654$	0.218464	+	0.378391i	0.00854263	+	0.0147963i
$655$	2.01510			0.0787365
$656$	24.3354	−	42.1501i	0.950137	−	1.64569i
$657$	−2.03586	−	3.52622i	−0.0794267	−	0.137571i
$658$	0.302020	+	0.523115i	0.0117740	+	0.0203931i
$659$	−46.1754			−1.79874			−0.899370	−	0.437189i	$-0.855974\pi$
$659$	−46.1754			−1.79874			−0.899370	+	0.437189i	$0.855974\pi$
$660$	−2.14266	+	3.71120i	−0.0834030	+	0.144458i
$661$	−9.71865	+	16.8332i	−0.378012	+	0.654736i	−0.990773	−	0.135533i	$-0.956725\pi$
$661$	−9.71865	+	16.8332i	−0.378012	+	0.654736i	0.612761	+	0.790268i	$0.290059\pi$
$662$	−0.0824100	+	0.142738i	−0.00320295	+	0.00554768i
$663$	−2.98184	−	5.16469i	−0.115805	−	0.200580i
$664$	1.31369	−	2.27538i	0.0509811	−	0.0883019i
$665$	8.50474	+	14.7306i	0.329800	+	0.571230i
$666$	0.00195305			7.56792e−5
$667$	−12.9519			−0.501499
$668$	2.71820	+	4.70805i	0.105170	+	0.182160i
$669$	18.4504	−	31.9570i	0.713333	−	1.23553i
$670$	0.0925313	+	0.160269i	0.00357480	+	0.00619173i
$671$	−4.49116	+	7.77892i	−0.173379	+	0.300302i
$672$	1.87939	−	3.25519i	0.0724989	−	0.125572i
$673$	−0.425921	+	0.737717i	−0.0164180	+	0.0284369i	−0.874118	−	0.485714i	$-0.838560\pi$
$673$	−0.425921	+	0.737717i	−0.0164180	+	0.0284369i	0.857700	+	0.514151i	$0.171893\pi$
$674$	−1.33529			−0.0514335
$675$	5.44819	+	9.43654i	0.209701	+	0.363213i
$676$	0.999034	+	1.73038i	0.0384244	+	0.0665530i
$677$	−9.46590	+	16.3954i	−0.363804	+	0.630127i	−0.988583	−	0.150674i	$-0.951856\pi$
$677$	−9.46590	+	16.3954i	−0.363804	+	0.630127i	0.624780	+	0.780801i	$0.285189\pi$
$678$	0.0974382			0.00374209
$679$	−35.7458	−	61.9135i	−1.37180	−	2.37602i
$680$	1.10528			0.0423857
$681$	−21.9739			−0.842042
$682$	0.161782	−	0.0896426i	0.00619495	−	0.00343259i
$683$	13.2726			0.507863			0.253932	−	0.967222i	$-0.418276\pi$
$683$	13.2726			0.507863			0.253932	+	0.967222i	$0.418276\pi$
$684$	1.40032			0.0535427
$685$	6.28448	+	10.8850i	0.240118	+	0.415896i
$686$	0.943809			0.0360348
$687$	11.7847	−	20.4116i	0.449613	−	0.778752i
$688$	−8.83156	−	15.2967i	−0.336700	−	0.583182i
$689$	4.33685	+	7.51165i	0.165221	+	0.286171i
$690$	−0.687496			−0.0261725
$691$	3.71997	−	6.44318i	0.141514	−	0.245110i	−0.786553	−	0.617523i	$-0.788136\pi$
$691$	3.71997	−	6.44318i	0.141514	−	0.245110i	0.928067	+	0.372413i	$0.121470\pi$
$692$	−20.1761	+	34.9461i	−0.766981	+	1.32845i
$693$	−0.510131	+	0.883574i	−0.0193783	+	0.0335642i
$694$	0.328155	+	0.568382i	0.0124566	+	0.0215755i
$695$	2.48375	−	4.30197i	0.0942139	−	0.163183i
$696$	−0.338457	−	0.586224i	−0.0128292	−	0.0222208i
$697$	−44.3731			−1.68075
$698$	−0.547421			−0.0207202
$699$	11.1288	+	19.2756i	0.420928	+	0.729069i
$700$	−8.72542	+	15.1129i	−0.329790	+	0.571213i
$701$	17.4939	+	30.3004i	0.660736	+	1.14443i	0.980422	+	0.196906i	$0.0630893\pi$
$701$	17.4939	+	30.3004i	0.660736	+	1.14443i	−0.319686	+	0.947524i	$0.603577\pi$
$702$	0.119291	−	0.206618i	0.00450236	−	0.00779831i
$703$	0.161866	−	0.280361i	0.00610491	−	0.0105740i
$704$	−3.00610	+	5.20672i	−0.113297	+	0.196236i
$705$	−8.96214			−0.337534
$706$	−0.0856574	−	0.148363i	−0.00322376	−	0.00558371i
$707$	−37.4620	−	64.8861i	−1.40890	−	2.44029i
$708$	12.7647	−	22.1092i	0.479728	−	0.830913i
$709$	−19.6342			−0.737378			−0.368689	−	0.929553i	$-0.620193\pi$
$709$	−19.6342			−0.737378			−0.368689	+	0.929553i	$0.620193\pi$
$710$	−0.189350	−	0.327964i	−0.00710619	−	0.0123083i
$711$	−2.41528			−0.0905800
$712$	−0.202503			−0.00758913
$713$	−26.3112	−	15.8152i	−0.985362	−	0.592285i
$714$	−1.14045			−0.0426803
$715$	−1.30771			−0.0489056
$716$	−9.23001	−	15.9869i	−0.344942	−	0.597457i
$717$	−25.9710			−0.969903
$718$	0.287062	−	0.497206i	0.0107131	−	0.0185556i
$719$	21.4226	+	37.1050i	0.798927	+	1.38378i	0.920316	+	0.391177i	$0.127932\pi$
$719$	21.4226	+	37.1050i	0.798927	+	1.38378i	−0.121389	+	0.992605i	$0.538735\pi$
$720$	−1.07010	−	1.85348i	−0.0398805	−	0.0690750i
$721$	12.0075			0.447182
$722$	0.305314	−	0.528819i	0.0113626	−	0.0196806i
$723$	−14.4935	+	25.1034i	−0.539018	+	0.933607i
$724$	−0.566670	+	0.981501i	−0.0210601	+	0.0364772i
$725$	2.35741	+	4.08315i	0.0875519	+	0.151644i
$726$	−0.375823	+	0.650945i	−0.0139481	+	0.0241588i
$727$	9.98450	+	17.2937i	0.370304	+	0.641386i	0.989612	−	0.143762i	$-0.0459200\pi$
$727$	9.98450	+	17.2937i	0.370304	+	0.641386i	−0.619308	+	0.785148i	$0.712587\pi$
$728$	0.764562			0.0283366
$729$	29.1845			1.08091
$730$	−0.499012	−	0.864313i	−0.0184692	−	0.0319897i
$731$	−8.05173	+	13.9460i	−0.297804	+	0.515812i
$732$	19.4700	+	33.7230i	0.719631	+	1.24644i
$733$	20.1732	−	34.9410i	0.745115	−	1.29058i	−0.205027	−	0.978756i	$-0.565728\pi$
$733$	20.1732	−	34.9410i	0.745115	−	1.29058i	0.950141	−	0.311820i	$-0.100939\pi$
$734$	−0.728860	+	1.26242i	−0.0269027	+	0.0465969i
$735$	−16.9322	+	29.3275i	−0.624555	+	1.08176i
$736$	−2.90392			−0.107040
$737$	0.919989	+	1.59347i	0.0338882	+	0.0586961i
$738$	−0.0831712	−	0.144057i	−0.00306157	−	0.00530280i
$739$	23.5079	−	40.7169i	0.864752	−	1.49779i	−0.00254175	−	0.999997i	$-0.500809\pi$
$739$	23.5079	−	40.7169i	0.864752	−	1.49779i	0.867293	−	0.497797i	$-0.165858\pi$
$740$	−0.495262			−0.0182062
$741$	−1.85285	−	3.20923i	−0.0680661	−	0.117894i
$742$	1.65870			0.0608927
$743$	−27.2643			−1.00023			−0.500115	−	0.865959i	$-0.666709\pi$
$743$	−27.2643			−1.00023			−0.500115	+	0.865959i	$0.666709\pi$
$744$	0.0282639	−	1.60417i	0.00103621	−	0.0588118i
$745$	24.4702			0.896519
$746$	−1.40670			−0.0515030
$747$	2.31914	+	4.01688i	0.0848531	+	0.146970i
$748$	5.49196			0.200806
$749$	29.6109	−	51.2876i	1.08196	−	1.87401i
$750$	0.436859	+	0.756663i	0.0159519	+	0.0276294i
$751$	3.84585	+	6.66120i	0.140337	+	0.243071i	0.927624	−	0.373517i	$-0.121848\pi$
$751$	3.84585	+	6.66120i	0.140337	+	0.243071i	−0.787287	+	0.616587i	$0.788515\pi$
$752$	−12.5981			−0.459404
$753$	2.70583	−	4.68663i	0.0986058	−	0.170790i
$754$	0.0516168	−	0.0894029i	0.00187977	−	0.00325586i
$755$	−11.2897	+	19.5543i	−0.410873	+	0.711652i
$756$	23.6010	+	40.8782i	0.858361	+	1.48672i
$757$	−10.9286	+	18.9290i	−0.397208	+	0.687985i	−0.993380	−	0.114872i	$-0.963354\pi$
$757$	−10.9286	+	18.9290i	−0.397208	+	0.687985i	0.596172	+	0.802857i	$0.296688\pi$
$758$	0.220371	+	0.381694i	0.00800424	+	0.0138638i
$759$	−6.83540			−0.248109
$760$	0.686799			0.0249128
$761$	25.1444	+	43.5515i	0.911485	+	1.57874i	0.811967	+	0.583703i	$0.198397\pi$
$761$	25.1444	+	43.5515i	0.911485	+	1.57874i	0.0995186	+	0.995036i	$0.468270\pi$
$762$	0.467546	−	0.809814i	0.0169374	−	0.0293365i
$763$	−13.1896	−	22.8450i	−0.477494	−	0.827044i
$764$	−10.7162	+	18.5610i	−0.387698	+	0.671512i
$765$	−0.975614	+	1.68981i	−0.0352734	+	0.0610953i
$766$	0.281050	−	0.486793i	0.0101547	−	0.0175885i
$767$	7.79057			0.281301
$768$	12.9940	+	22.5063i	0.468882	+	0.812127i
$769$	24.4573	+	42.3612i	0.881952	+	1.52759i	0.849168	+	0.528123i	$0.177104\pi$
$769$	24.4573	+	42.3612i	0.881952	+	1.52759i	0.0327837	+	0.999462i	$0.489563\pi$
$770$	−0.125039	+	0.216573i	−0.00450608	+	0.00780475i
$771$	−25.8324			−0.930331
$772$	7.64550	+	13.2424i	0.275168	+	0.476604i
$773$	−22.8268			−0.821022			−0.410511	−	0.911856i	$-0.634650\pi$
$773$	−22.8268			−0.821022			−0.410511	+	0.911856i	$0.634650\pi$
$774$	−0.0603674			−0.00216986
$775$	−0.196863	+	11.1733i	−0.00707153	+	0.401358i
$776$	−2.88665			−0.103625
$777$	1.02253			0.0366832
$778$	0.214914	+	0.372242i	0.00770504	+	0.0133455i
$779$	−27.5725			−0.987886
$780$	−2.83458	+	4.90963i	−0.101494	+	0.175793i
$781$	−1.88261	−	3.26077i	−0.0673649	−	0.116679i
$782$	0.440539	+	0.763036i	0.0157537	+	0.0272861i
$783$	12.7529			0.455751
$784$	−23.8017	+	41.2257i	−0.850059	+	1.47235i
$785$	−0.289793	+	0.501937i	−0.0103432	+	0.0179149i
$786$	−0.0419767	+	0.0727057i	−0.00149726	+	0.00259333i
$787$	−12.3698	−	21.4251i	−0.440935	−	0.763721i	0.556824	−	0.830630i	$-0.312020\pi$
$787$	−12.3698	−	21.4251i	−0.440935	−	0.763721i	−0.997759	+	0.0669090i	$0.978686\pi$
$788$	−11.9632	+	20.7208i	−0.426171	+	0.738149i
$789$	21.1739	+	36.6742i	0.753809	+	1.30564i
$790$	−0.592010			−0.0210628
$791$	−5.88273			−0.209166
$792$	0.0205978	+	0.0356764i	0.000731911	+	0.00126771i
$793$	−5.94146	+	10.2909i	−0.210987	+	0.365441i
$794$	0.182306	+	0.315763i	0.00646980	+	0.0112060i
$795$	−12.3050	+	21.3129i	−0.436414	+	0.755892i
$796$	2.12324	−	3.67755i	0.0752561	−	0.130347i
$797$	−27.1116	+	46.9587i	−0.960343	+	1.66336i	−0.238705	+	0.971092i	$0.576723\pi$
$797$	−27.1116	+	46.9587i	−0.960343	+	1.66336i	−0.721638	+	0.692271i	$0.756610\pi$
$798$	−0.708651			−0.0250860
$799$	5.74283	+	9.94687i	0.203167	+	0.351895i
$800$	0.528550	+	0.915476i	0.0186871	+	0.0323670i
$801$	0.178746	−	0.309597i	0.00631568	−	0.0109391i
$802$	0.730815			0.0258060
$803$	−4.96140	−	8.59340i	−0.175084	−	0.303254i
$804$	7.97663			0.281314
$805$	41.5069			1.46293
$806$	0.214025	−	0.118590i	0.00753872	−	0.00417716i
$807$	18.3107			0.644567
$808$	−3.02524			−0.106427
$809$	−15.8851	−	27.5137i	−0.558489	−	0.967331i	−0.997623	−	0.0689098i	$-0.978048\pi$
$809$	−15.8851	−	27.5137i	−0.558489	−	0.967331i	0.439134	−	0.898422i	$-0.355285\pi$
$810$	0.606188			0.0212993
$811$	6.07684	−	10.5254i	0.213387	−	0.369597i	−0.739385	−	0.673282i	$-0.764884\pi$
$811$	6.07684	−	10.5254i	0.213387	−	0.369597i	0.952772	+	0.303685i	$0.0982172\pi$
$812$	10.2121	+	17.6878i	0.358373	+	0.620720i
$813$	16.3865	+	28.3823i	0.574700	+	0.995410i
$814$	0.00475959			0.000166823
$815$	16.8954	−	29.2638i	0.591822	−	1.02507i
$816$	11.8928	−	20.5989i	0.416332	−	0.721107i
$817$	−5.00317	+	8.66574i	−0.175039	+	0.303176i
$818$	−0.461191	−	0.798805i	−0.0161251	−	0.0279296i
$819$	−0.674865	+	1.16890i	−0.0235817	+	0.0408447i
$820$	21.0909	+	36.5304i	0.736525	+	1.27570i
$821$	28.8261			1.00604			0.503019	−	0.864275i	$-0.332222\pi$
$821$	28.8261			1.00604			0.503019	+	0.864275i	$0.332222\pi$
$822$	−0.523649			−0.0182644
$823$	−4.60225	−	7.97132i	−0.160424	−	0.277863i	0.774597	−	0.632456i	$-0.217953\pi$
$823$	−4.60225	−	7.97132i	−0.160424	−	0.277863i	−0.935021	+	0.354593i	$0.884620\pi$
$824$	0.242416	−	0.419876i	0.00844495	−	0.0146271i
$825$	1.24413	+	2.15490i	0.0433151	+	0.0750239i
$826$	0.744906	−	1.29022i	0.0259186	−	0.0448924i
$827$	−0.819749	+	1.41985i	−0.0285055	+	0.0493729i	−0.879926	−	0.475110i	$-0.842408\pi$
$827$	−0.819749	+	1.41985i	−0.0285055	+	0.0493729i	0.851421	+	0.524483i	$0.175741\pi$
$828$	1.70855	−	2.95929i	0.0593762	−	0.102843i
$829$	29.9685			1.04085			0.520424	−	0.853908i	$-0.325774\pi$
$829$	29.9685			1.04085			0.520424	+	0.853908i	$0.325774\pi$
$830$	0.568446	+	0.984578i	0.0197311	+	0.0341752i
$831$	6.19895	+	10.7369i	0.215039	+	0.372459i
$832$	−3.97684	+	6.88809i	−0.137872	+	0.238802i
$833$	43.3999			1.50372
$834$	0.103478	+	0.179229i	0.00358315	+	0.00620620i
$835$	−4.70703			−0.162893
$836$	3.41259			0.118027
$837$	25.9070	+	15.5723i	0.895476	+	0.538256i
$838$	0.920331			0.0317923
$839$	−33.9221			−1.17112			−0.585561	−	0.810628i	$-0.699126\pi$
$839$	−33.9221			−1.17112			−0.585561	+	0.810628i	$0.699126\pi$
$840$	1.08465	+	1.87867i	0.0374241	+	0.0648204i
$841$	−23.4819			−0.809720
$842$	0.232024	−	0.401878i	0.00799608	−	0.0138496i
$843$	10.8991	+	18.8778i	0.375386	+	0.650187i
$844$	−3.73802	−	6.47443i	−0.128668	−	0.222859i
$845$	−1.73000			−0.0595138
$846$	−0.0215283	+	0.0372880i	−0.000740157	+	0.00128199i
$847$	22.6900	−	39.3002i	0.779636	−	1.35037i
$848$	−17.2972	+	29.9596i	−0.593987	+	1.02882i
$849$	−24.5765	−	42.5678i	−0.843464	−	1.46092i
$850$	0.160368	−	0.277765i	0.00550056	−	0.00952725i
$851$	−0.394990	−	0.684142i	−0.0135401	−	0.0234521i
$852$	−16.3229			−0.559212
$853$	29.3081			1.00349			0.501745	−	0.865016i	$-0.332692\pi$
$853$	29.3081			1.00349			0.501745	+	0.865016i	$0.332692\pi$
$854$	1.13620	+	1.96796i	0.0388801	+	0.0673422i
$855$	−0.606225	+	1.05001i	−0.0207325	+	0.0359097i
$856$	−1.19561	−	2.07086i	−0.0408652	−	0.0707806i
$857$	−20.9176	+	36.2304i	−0.714532	+	1.23761i	0.248607	+	0.968604i	$0.420027\pi$
$857$	−20.9176	+	36.2304i	−0.714532	+	1.23761i	−0.963140	+	0.269002i	$0.913306\pi$
$858$	0.0272410	−	0.0471827i	0.000929991	−	0.00161079i
$859$	26.3934	−	45.7147i	0.900531	−	1.55977i	0.0737246	−	0.997279i	$-0.476511\pi$
$859$	26.3934	−	45.7147i	0.900531	−	1.55977i	0.826806	−	0.562487i	$-0.190155\pi$
$860$	15.3082			0.522005
$861$	−43.5448	−	75.4219i	−1.48400	−	2.57037i
$862$	−0.559730	−	0.969480i	−0.0190645	−	0.0330206i
$863$	−11.8456	+	20.5172i	−0.403229	+	0.698413i	−0.994114	−	0.108343i	$-0.965446\pi$
$863$	−11.8456	+	20.5172i	−0.403229	+	0.698413i	0.590884	+	0.806756i	$0.298779\pi$
$864$	2.85930			0.0972755
$865$	−17.4692	−	30.2576i	−0.593971	−	1.02879i
$866$	0.397108			0.0134943
$867$	6.19582			0.210421
$868$	−0.852791	+	48.4017i	−0.0289456	+	1.64286i
$869$	−5.88603			−0.199670
$870$	0.292906			0.00993046
$871$	1.21707	+	2.10804i	0.0412390	+	0.0714281i
$872$	−1.06512			−0.0360695
$873$	2.54799	−	4.41325i	0.0862364	−	0.149366i
$874$	0.273741	+	0.474134i	0.00925944	+	0.0160378i
$875$	−26.3749	−	45.6827i	−0.891636	−	1.54436i
$876$	−43.0171			−1.45341
$877$	25.0998	−	43.4742i	0.847562	−	1.46802i	−0.0358161	−	0.999358i	$-0.511403\pi$
$877$	25.0998	−	43.4742i	0.847562	−	1.46802i	0.883378	−	0.468662i	$-0.155264\pi$
$878$	−0.557554	+	0.965711i	−0.0188165	+	0.0325912i
$879$	−20.1787	+	34.9505i	−0.680609	+	1.17885i
$880$	−2.60784	−	4.51692i	−0.0879104	−	0.152265i
$881$	22.1167	−	38.3073i	0.745132	−	1.29061i	−0.205002	−	0.978762i	$-0.565720\pi$
$881$	22.1167	−	38.3073i	0.745132	−	1.29061i	0.950133	−	0.311844i	$-0.100947\pi$
$882$	0.0813471	+	0.140897i	0.00273910	+	0.00474426i
$883$	−0.925365			−0.0311410			−0.0155705	−	0.999879i	$-0.504956\pi$
$883$	−0.925365			−0.0311410			−0.0155705	+	0.999879i	$0.504956\pi$
$884$	7.26545			0.244364
$885$	11.0522	+	19.1429i	0.371514	+	0.643482i
$886$	−0.539242	+	0.933995i	−0.0181162	+	0.0313782i
$887$	11.3493	+	19.6576i	0.381073	+	0.660038i	0.991216	−	0.132253i	$-0.0422212\pi$
$887$	11.3493	+	19.6576i	0.381073	+	0.660038i	−0.610143	+	0.792292i	$0.708888\pi$
$888$	0.0206436	−	0.0357558i	0.000692755	−	0.00119989i
$889$	−28.2276	+	48.8917i	−0.946725	+	1.63978i
$890$	0.0438125	−	0.0758854i	0.00146860	−	0.00254369i
$891$	6.02700			0.201912
$892$	22.4778	+	38.9327i	0.752613	+	1.30356i
$893$	3.56847	+	6.18076i	0.119414	+	0.206831i
$894$	−0.509740	+	0.882896i	−0.0170483	+	0.0295284i
$895$	15.9834			0.534265
$896$	3.05234	+	5.28681i	0.101972	+	0.176620i
$897$	−9.04272			−0.301928
$898$	0.204182			0.00681364
$899$	11.2098	+	6.73805i	0.373869	+	0.224727i
$900$	−1.24391			−0.0414637
$901$	31.5396			1.05074
$902$	−0.202688	−	0.351066i	−0.00674878	−	0.0116892i
$903$	−31.6057			−1.05177
$904$	−0.118765	+	0.205707i	−0.00395006	+	0.00684170i
$905$	−0.490643	−	0.849819i	−0.0163095	−	0.0282489i
$906$	−0.470351	−	0.814672i	−0.0156264	−	0.0270657i
$907$	−41.0648			−1.36353			−0.681767	−	0.731570i	$-0.738788\pi$
$907$	−41.0648			−1.36353			−0.681767	+	0.731570i	$0.738788\pi$
$908$	13.3852	−	23.1839i	0.444205	−	0.769385i
$909$	2.67032	−	4.62513i	0.0885690	−	0.153406i
$910$	−0.165416	+	0.286510i	−0.00548350	+	0.00949770i
$911$	−2.00154	−	3.46676i	−0.0663138	−	0.114859i	0.830962	−	0.556329i	$-0.187791\pi$
$911$	−2.00154	−	3.46676i	−0.0663138	−	0.114859i	−0.897276	+	0.441470i	$0.854457\pi$
$912$	7.38993	−	12.7997i	0.244705	−	0.423841i
$913$	5.65175	+	9.78912i	0.187046	+	0.323973i
$914$	−0.209797			−0.00693948
$915$	−33.7156			−1.11460
$916$	14.3571	+	24.8672i	0.474371	+	0.821634i
$917$	2.53430	−	4.38953i	0.0836899	−	0.144955i
$918$	−0.433771	−	0.751314i	−0.0143166	−	0.0247970i
$919$	−9.99953	+	17.3197i	−0.329854	+	0.571324i	−0.982483	−	0.186354i	$-0.940333\pi$
$919$	−9.99953	+	17.3197i	−0.329854	+	0.571324i	0.652629	+	0.757678i	$0.273666\pi$
$920$	0.837971	−	1.45141i	0.0276271	−	0.0478515i
$921$	−9.56960	+	16.5750i	−0.315329	+	0.546166i
$922$	−1.69231			−0.0557332
$923$	−2.49054	−	4.31375i	−0.0819773	−	0.141989i
$924$	5.38945	+	9.33480i	0.177300	+	0.307092i
$925$	−0.143786	+	0.249045i	−0.00472767	+	0.00818856i
$926$	−0.937064			−0.0307938
$927$	0.427952	+	0.741234i	0.0140558	+	0.0243453i
$928$	1.23721			0.0406134
$929$	−58.2842			−1.91224			−0.956122	−	0.292970i	$-0.905356\pi$
$929$	−58.2842			−1.91224			−0.956122	+	0.292970i	$0.905356\pi$
$930$	0.595027	+	0.357661i	0.0195117	+	0.0117282i
$931$	26.9677			0.883832
$932$	−27.1160			−0.888213
$933$	−16.2708	−	28.1818i	−0.532682	−	0.922632i
$934$	−0.535077			−0.0175083
$935$	−2.37757	+	4.11807i	−0.0777549	+	0.134675i
$936$	0.0272493	+	0.0471972i	0.000890672	+	0.00154269i
$937$	19.8415	+	34.3665i	0.648194	+	1.12271i	0.983554	+	0.180615i	$0.0578088\pi$
$937$	19.8415	+	34.3665i	0.648194	+	1.12271i	−0.335360	+	0.942090i	$0.608858\pi$
$938$	0.465489			0.0151988
$939$	26.7064	−	46.2569i	0.871531	−	1.50954i
$940$	5.45921	−	9.45564i	0.178060	−	0.308409i
$941$	7.18165	−	12.4390i	0.234115	−	0.405499i	−0.724900	−	0.688854i	$-0.758114\pi$
$941$	7.18165	−	12.4390i	0.234115	−	0.405499i	0.959015	+	0.283355i	$0.0914474\pi$
$942$	−0.0120734	−	0.0209117i	−0.000393373	−	0.000681341i
$943$	−33.6415	+	58.2687i	−1.09552	+	1.89749i
$944$	15.5360	+	26.9092i	0.505654	+	0.875819i
$945$	−40.8692			−1.32948
$946$	−0.147115			−0.00478313
$947$	−15.5904	−	27.0033i	−0.506620	−	0.877491i	−0.999971	−	0.00766052i	$-0.997562\pi$
$947$	−15.5904	−	27.0033i	−0.506620	−	0.877491i	0.493351	−	0.869830i	$-0.335772\pi$
$948$	−12.7585	+	22.0984i	−0.414377	+	0.717722i
$949$	−6.56356	−	11.3684i	−0.213062	−	0.369034i
$950$	0.0996489	−	0.172597i	0.00323304	−	0.00559978i
$951$	−1.25537	+	2.17436i	−0.0407080	+	0.0705084i
$952$	1.39006	−	2.40766i	0.0450522	−	0.0780328i
$953$	−21.8210			−0.706850			−0.353425	−	0.935463i	$-0.614983\pi$
$953$	−21.8210			−0.706850			−0.353425	+	0.935463i	$0.614983\pi$
$954$	0.0591167	+	0.102393i	0.00191397	+	0.00331510i
$955$	−9.27845	−	16.0708i	−0.300244	−	0.520037i
$956$	15.8200	−	27.4010i	0.511655	−	0.886213i
$957$	2.91221			0.0941384
$958$	0.784916	+	1.35951i	0.0253595	+	0.0439239i
$959$	31.6148			1.02090
$960$	−22.5671			−0.728351
$961$	14.5446	+	27.3761i	0.469182	+	0.883101i
$962$	0.00629657			0.000203010
$963$	4.22138			0.136032
$964$	−17.6572	−	30.5831i	−0.568699	−	0.985016i
$965$	−13.2395			−0.426195
$966$	−0.864632	+	1.49759i	−0.0278191	+	0.0481841i
$967$	−6.06579	−	10.5062i	−0.195063	−	0.337858i	0.751859	−	0.659324i	$-0.229158\pi$
$967$	−6.06579	−	10.5062i	−0.195063	−	0.337858i	−0.946921	+	0.321466i	$0.895824\pi$
$968$	−0.916162	−	1.58684i	−0.0294466	−	0.0510029i
$969$	−13.4748			−0.432872
$970$	0.624539	−	1.08173i	0.0200527	−	0.0347324i
$971$	15.8818	−	27.5082i	0.509673	−	0.882779i	−0.490265	−	0.871574i	$-0.663100\pi$
$971$	15.8818	−	27.5082i	0.509673	−	0.882779i	0.999937	−	0.0112051i	$-0.00356678\pi$
$972$	−3.20696	+	5.55462i	−0.102863	+	0.178164i
$973$	−6.24738	−	10.8208i	−0.200282	−	0.346898i
$974$	0.116534	−	0.201842i	0.00373398	−	0.00646744i
$975$	1.64589	+	2.85077i	0.0527107	+	0.0912976i
$976$	−47.3940			−1.51705
$977$	22.6721			0.725346			0.362673	−	0.931916i	$-0.381864\pi$
$977$	22.6721			0.725346			0.362673	+	0.931916i	$0.381864\pi$
$978$	0.703900	+	1.21919i	0.0225082	+	0.0389854i
$979$	0.435604	−	0.754487i	0.0139220	−	0.0241135i
$980$	−20.6283	−	35.7292i	−0.658946	−	1.14133i
$981$	0.940163	−	1.62841i	0.0300171	−	0.0519911i
$982$	−0.328608	+	0.569165i	−0.0104863	+	0.0181628i
$983$	−4.22767	+	7.32253i	−0.134842	+	0.233552i	−0.925537	−	0.378657i	$-0.876386\pi$
$983$	−4.22767	+	7.32253i	−0.134842	+	0.233552i	0.790695	+	0.612210i	$0.209719\pi$
$984$	−3.51646			−0.112101
$985$	−10.3582	−	17.9409i	−0.330038	−	0.571643i
$986$	−0.187691	−	0.325090i	−0.00597730	−	0.0103530i
$987$	−11.2713	+	19.5224i	−0.358768	+	0.621405i
$988$	4.51459			0.143628
$989$	12.2088	+	21.1463i	0.388218	+	0.672414i
$990$	−0.0178257			−0.000566538
$991$	29.0396			0.922474			0.461237	−	0.887277i	$-0.347406\pi$
$991$	29.0396			0.922474			0.461237	+	0.887277i	$0.347406\pi$
$992$	2.51334	+	1.51073i	0.0797986	+	0.0479656i
$993$	−6.15101			−0.195196
$994$	−0.952548			−0.0302130
$995$	1.83838	+	3.18416i	0.0582804	+	0.100945i
$996$	49.0027			1.55271
$997$	−9.22089	+	15.9710i	−0.292028	+	0.505808i	−0.974289	−	0.225301i	$-0.927664\pi$
$997$	−9.22089	+	15.9710i	−0.292028	+	0.505808i	0.682261	+	0.731109i	$0.260997\pi$
$998$	−0.222503	−	0.385386i	−0.00704320	−	0.0121992i
$999$	0.388921	+	0.673631i	0.0123049	+	0.0213128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.8	✓	30
31.5	even	3	inner	403.2.h.a.222.8	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.8	✓	30	1.1	even	1	trivial
403.2.h.a.222.8	yes	30	31.5	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.0439466 q^{2} +(0.820034 + 1.42034i) q^{3} -1.99807 q^{4} +(0.865000 - 1.49822i) q^{5} +(0.0360377 + 0.0624192i) q^{6} +(-2.17574 - 3.76849i) q^{7} -0.175702 q^{8} +(0.155089 - 0.268621i) q^{9} +O(q^{10})\)	\(q+0.0439466 q^{2} +(0.820034 + 1.42034i) q^{3} -1.99807 q^{4} +(0.865000 - 1.49822i) q^{5} +(0.0360377 + 0.0624192i) q^{6} +(-2.17574 - 3.76849i) q^{7} -0.175702 q^{8} +(0.155089 - 0.268621i) q^{9} +(0.0380138 - 0.0658419i) q^{10} +(0.377951 - 0.654630i) q^{11} +(-1.63848 - 2.83794i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.0956164 - 0.165613i) q^{14} +2.83732 q^{15} +3.98842 q^{16} +(-1.81812 - 3.14907i) q^{17} +(0.00681562 - 0.0118050i) q^{18} +(-1.12974 - 1.95676i) q^{19} +(-1.72833 + 2.99355i) q^{20} +(3.56836 - 6.18059i) q^{21} +(0.0166097 - 0.0287688i) q^{22} -5.51362 q^{23} +(-0.144081 - 0.249556i) q^{24} +(1.00355 + 1.73820i) q^{25} +(0.0219733 - 0.0380589i) q^{26} +5.42892 q^{27} +(4.34728 + 7.52971i) q^{28} +2.34907 q^{29} +0.124691 q^{30} +(4.77204 + 2.86839i) q^{31} +0.526681 q^{32} +1.23973 q^{33} +(-0.0799001 - 0.138391i) q^{34} -7.52806 q^{35} +(-0.309878 + 0.536724i) q^{36} +(0.0716389 + 0.124082i) q^{37} +(-0.0496482 - 0.0859932i) q^{38} +1.64007 q^{39} +(-0.151982 + 0.263240i) q^{40} +(6.10152 - 10.5681i) q^{41} +(0.156817 - 0.271616i) q^{42} +(-2.21430 - 3.83528i) q^{43} +(-0.755171 + 1.30800i) q^{44} +(-0.268303 - 0.464715i) q^{45} -0.242305 q^{46} -3.15867 q^{47} +(3.27064 + 5.66491i) q^{48} +(-5.96770 + 10.3364i) q^{49} +(0.0441026 + 0.0763880i) q^{50} +(2.98184 - 5.16469i) q^{51} +(-0.999034 + 1.73038i) q^{52} +(-4.33685 + 7.51165i) q^{53} +0.238582 q^{54} +(-0.653855 - 1.13251i) q^{55} +(0.382281 + 0.662130i) q^{56} +(1.85285 - 3.20923i) q^{57} +0.103234 q^{58} +(3.89528 + 6.74683i) q^{59} -5.66916 q^{60} -11.8829 q^{61} +(0.209715 + 0.126056i) q^{62} -1.34973 q^{63} -7.95369 q^{64} +(-0.865000 - 1.49822i) q^{65} +0.0544819 q^{66} +(-1.21707 + 2.10804i) q^{67} +(3.63273 + 6.29206i) q^{68} +(-4.52136 - 7.83122i) q^{69} -0.330833 q^{70} +(2.49054 - 4.31375i) q^{71} +(-0.0272493 + 0.0471972i) q^{72} +(6.56356 - 11.3684i) q^{73} +(0.00314829 + 0.00545299i) q^{74} +(-1.64589 + 2.85077i) q^{75} +(2.25730 + 3.90975i) q^{76} -3.28929 q^{77} +0.0720754 q^{78} +(-3.89339 - 6.74354i) q^{79} +(3.44998 - 5.97554i) q^{80} +(3.98663 + 6.90504i) q^{81} +(0.268141 - 0.464434i) q^{82} +(-7.47684 + 12.9503i) q^{83} +(-7.12983 + 12.3492i) q^{84} -6.29069 q^{85} +(-0.0973111 - 0.168548i) q^{86} +(1.92632 + 3.33648i) q^{87} +(-0.0664065 + 0.115020i) q^{88} +1.15254 q^{89} +(-0.0117910 - 0.0204226i) q^{90} -4.35148 q^{91} +11.0166 q^{92} +(-0.160863 + 9.13009i) q^{93} -0.138813 q^{94} -3.90890 q^{95} +(0.431896 + 0.748066i) q^{96} +16.4293 q^{97} +(-0.262260 + 0.454248i) q^{98} +(-0.117232 - 0.203051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

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