LMFDB - Embedded newform 403.2.k.d.66.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, 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:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			66.6
Character	$\chi$	$=$	403.66
Dual form			403.2.k.d.287.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0757307 - 0.233075i) q^{2} +(0.263551 - 0.811126i) q^{3} +(1.56945 - 1.14027i) q^{4} -2.48983 q^{5} -0.209012 q^{6} +(2.14015 - 1.55491i) q^{7} +(-0.781154 - 0.567542i) q^{8} +(1.83859 + 1.33581i) q^{9} +O(q^{10})$	\(q+(-0.0757307 - 0.233075i) q^{2} +(0.263551 - 0.811126i) q^{3} +(1.56945 - 1.14027i) q^{4} -2.48983 q^{5} -0.209012 q^{6} +(2.14015 - 1.55491i) q^{7} +(-0.781154 - 0.567542i) q^{8} +(1.83859 + 1.33581i) q^{9} +(0.188556 + 0.580316i) q^{10} +(1.22326 - 0.888750i) q^{11} +(-0.511273 - 1.57354i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.524486 - 0.381061i) q^{14} +(-0.656195 + 2.01956i) q^{15} +(1.12583 - 3.46494i) q^{16} +(-1.83185 - 1.33092i) q^{17} +(0.172107 - 0.529690i) q^{18} +(-2.28875 - 7.04404i) q^{19} +(-3.90765 + 2.83907i) q^{20} +(-0.697190 - 2.14573i) q^{21} +(-0.299784 - 0.217806i) q^{22} +(-0.523847 - 0.380597i) q^{23} +(-0.666222 + 0.484038i) q^{24} +1.19923 q^{25} +0.245070 q^{26} +(3.63802 - 2.64318i) q^{27} +(1.58583 - 4.88069i) q^{28} +(2.39997 + 7.38634i) q^{29} +0.520404 q^{30} +(-5.56086 + 0.277118i) q^{31} -2.82397 q^{32} +(-0.398497 - 1.22645i) q^{33} +(-0.171477 + 0.527751i) q^{34} +(-5.32860 + 3.87146i) q^{35} +4.40874 q^{36} +5.03787 q^{37} +(-1.46846 + 1.06690i) q^{38} +(0.689985 + 0.501303i) q^{39} +(1.94494 + 1.41308i) q^{40} +(2.31083 + 7.11202i) q^{41} +(-0.447317 + 0.324995i) q^{42} +(-0.429337 - 1.32136i) q^{43} +(0.906425 - 2.78969i) q^{44} +(-4.57776 - 3.32593i) q^{45} +(-0.0490364 + 0.150919i) q^{46} +(1.81824 - 5.59596i) q^{47} +(-2.51379 - 1.82637i) q^{48} +(-0.000621286 + 0.00191212i) q^{49} +(-0.0908187 - 0.279511i) q^{50} +(-1.56233 + 1.13510i) q^{51} +(0.599475 + 1.84499i) q^{52} +(4.49661 + 3.26698i) q^{53} +(-0.891569 - 0.647763i) q^{54} +(-3.04570 + 2.21283i) q^{55} -2.55426 q^{56} -6.31680 q^{57} +(1.53982 - 1.11875i) q^{58} +(-3.21810 + 9.90429i) q^{59} +(1.27298 + 3.91783i) q^{60} +14.1567 q^{61} +(0.485717 + 1.27511i) q^{62} +6.01191 q^{63} +(-2.03779 - 6.27168i) q^{64} +(0.769399 - 2.36797i) q^{65} +(-0.255676 + 0.185759i) q^{66} +10.3461 q^{67} -4.39260 q^{68} +(-0.446773 + 0.324599i) q^{69} +(1.30588 + 0.948776i) q^{70} +(-4.25850 - 3.09398i) q^{71} +(-0.678090 - 2.08695i) q^{72} +(-3.20708 + 2.33008i) q^{73} +(-0.381521 - 1.17420i) q^{74} +(0.316059 - 0.972729i) q^{75} +(-11.6242 - 8.44544i) q^{76} +(1.23603 - 3.80412i) q^{77} +(0.0645883 - 0.198782i) q^{78} +(12.5917 + 9.14838i) q^{79} +(-2.80311 + 8.62709i) q^{80} +(0.921684 + 2.83665i) q^{81} +(1.48263 - 1.07720i) q^{82} +(-1.88430 - 5.79927i) q^{83} +(-3.54091 - 2.57262i) q^{84} +(4.56099 + 3.31376i) q^{85} +(-0.275463 + 0.200135i) q^{86} +6.62376 q^{87} -1.45996 q^{88} +(-5.48141 + 3.98247i) q^{89} +(-0.428516 + 1.31884i) q^{90} +(0.817465 + 2.51590i) q^{91} -1.25613 q^{92} +(-1.24079 + 4.58359i) q^{93} -1.44198 q^{94} +(5.69858 + 17.5384i) q^{95} +(-0.744259 + 2.29059i) q^{96} +(-14.3951 + 10.4587i) q^{97} +0.000492718 q^{98} +3.43627 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) $ 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.0757307	−	0.233075i	−0.0535497	−	0.164809i	0.920705	−	0.390259i	$-0.127615\pi$
$2$	−0.0757307	−	0.233075i	−0.0535497	−	0.164809i	−0.974255	+	0.225450i	$0.927615\pi$
$3$	0.263551	−	0.811126i	0.152161	−	0.468304i	−0.845701	−	0.533657i	$-0.820817\pi$
$3$	0.263551	−	0.811126i	0.152161	−	0.468304i	0.997862	+	0.0653532i	$0.0208174\pi$
$4$	1.56945	−	1.14027i	0.784723	−	0.570134i
$5$	−2.48983			−1.11348			−0.556742	−	0.830685i	$-0.687949\pi$
$5$	−2.48983			−1.11348			−0.556742	+	0.830685i	$0.687949\pi$
$6$	−0.209012			−0.0853288
$7$	2.14015	−	1.55491i	0.808901	−	0.587701i	−0.104611	−	0.994513i	$-0.533360\pi$
$7$	2.14015	−	1.55491i	0.808901	−	0.587701i	0.913512	+	0.406812i	$0.133360\pi$
$8$	−0.781154	−	0.567542i	−0.276180	−	0.200656i
$9$	1.83859	+	1.33581i	0.612862	+	0.445270i
$10$	0.188556	+	0.580316i	0.0596267	+	0.183512i
$11$	1.22326	−	0.888750i	0.368826	−	0.267968i	−0.387898	−	0.921702i	$-0.626799\pi$
$11$	1.22326	−	0.888750i	0.368826	−	0.267968i	0.756724	+	0.653734i	$0.226799\pi$
$12$	−0.511273	−	1.57354i	−0.147592	−	0.454241i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−0.524486	−	0.381061i	−0.140175	−	0.101843i
$15$	−0.656195	+	2.01956i	−0.169429	+	0.521449i
$16$	1.12583	−	3.46494i	0.281457	−	0.866235i
$17$	−1.83185	−	1.33092i	−0.444289	−	0.322795i	0.343048	−	0.939318i	$-0.388541\pi$
$17$	−1.83185	−	1.33092i	−0.444289	−	0.322795i	−0.787337	+	0.616523i	$0.788541\pi$
$18$	0.172107	−	0.529690i	0.0405660	−	0.124849i
$19$	−2.28875	−	7.04404i	−0.525074	−	1.61601i	−0.764169	−	0.645016i	$-0.776851\pi$
$19$	−2.28875	−	7.04404i	−0.525074	−	1.61601i	0.239094	−	0.970996i	$-0.423149\pi$
$20$	−3.90765	+	2.83907i	−0.873776	+	0.634835i
$21$	−0.697190	−	2.14573i	−0.152139	−	0.468236i
$22$	−0.299784	−	0.217806i	−0.0639141	−	0.0464363i
$23$	−0.523847	−	0.380597i	−0.109230	−	0.0793600i	0.531830	−	0.846851i	$-0.321505\pi$
$23$	−0.523847	−	0.380597i	−0.109230	−	0.0793600i	−0.641059	+	0.767491i	$0.721505\pi$
$24$	−0.666222	+	0.484038i	−0.135992	+	0.0988039i
$25$	1.19923			0.239847
$26$	0.245070			0.0480621
$27$	3.63802	−	2.64318i	0.700138	−	0.508680i
$28$	1.58583	−	4.88069i	0.299694	−	0.922364i
$29$	2.39997	+	7.38634i	0.445663	+	1.37161i	0.881755	+	0.471707i	$0.156362\pi$
$29$	2.39997	+	7.38634i	0.445663	+	1.37161i	−0.436093	+	0.899902i	$0.643638\pi$
$30$	0.520404			0.0950123
$31$	−5.56086	+	0.277118i	−0.998761	+	0.0497718i
$31$	−5.56086	+	0.277118i	−0.998761	+	0.0497718i
$32$	−2.82397			−0.499212
$33$	−0.398497	−	1.22645i	−0.0693694	−	0.213497i
$34$	−0.171477	+	0.527751i	−0.0294080	+	0.0905085i
$35$	−5.32860	+	3.87146i	−0.900698	+	0.654395i
$36$	4.40874			0.734790
$37$	5.03787			0.828220			0.414110	−	0.910227i	$-0.364093\pi$
$37$	5.03787			0.828220			0.414110	+	0.910227i	$0.364093\pi$
$38$	−1.46846	+	1.06690i	−0.238216	+	0.173074i
$39$	0.689985	+	0.501303i	0.110486	+	0.0802728i
$40$	1.94494	+	1.41308i	0.307522	+	0.223428i
$41$	2.31083	+	7.11202i	0.360892	+	1.11071i	0.952514	+	0.304495i	$0.0984877\pi$
$41$	2.31083	+	7.11202i	0.360892	+	1.11071i	−0.591622	+	0.806215i	$0.701512\pi$
$42$	−0.447317	+	0.324995i	−0.0690225	+	0.0501478i
$43$	−0.429337	−	1.32136i	−0.0654733	−	0.201506i	0.912968	−	0.408031i	$-0.133784\pi$
$43$	−0.429337	−	1.32136i	−0.0654733	−	0.201506i	−0.978441	+	0.206525i	$0.933784\pi$
$44$	0.906425	−	2.78969i	0.136649	−	0.420561i
$45$	−4.57776	−	3.32593i	−0.682412	−	0.495801i
$46$	−0.0490364	+	0.150919i	−0.00723003	+	0.0222517i
$47$	1.81824	−	5.59596i	0.265217	−	0.816255i	−0.726426	−	0.687245i	$-0.758820\pi$
$47$	1.81824	−	5.59596i	0.265217	−	0.816255i	0.991643	−	0.129010i	$-0.0411800\pi$
$48$	−2.51379	−	1.82637i	−0.362834	−	0.263614i
$49$	−0.000621286		0.00191212i	−8.87552e−5		0.000273160i
$50$	−0.0908187	−	0.279511i	−0.0128437	−	0.0395289i
$51$	−1.56233	+	1.13510i	−0.218770	+	0.158946i
$52$	0.599475	+	1.84499i	0.0831322	+	0.255855i
$53$	4.49661	+	3.26698i	0.617657	+	0.448754i	0.852102	−	0.523375i	$-0.175327\pi$
$53$	4.49661	+	3.26698i	0.617657	+	0.448754i	−0.234445	+	0.972129i	$0.575327\pi$
$54$	−0.891569	−	0.647763i	−0.121327	−	0.0881494i
$55$	−3.04570	+	2.21283i	−0.410682	+	0.298378i
$56$	−2.55426			−0.341328
$57$	−6.31680			−0.836681
$58$	1.53982	−	1.11875i	0.202188	−	0.146898i
$59$	−3.21810	+	9.90429i	−0.418961	+	1.28943i	0.489699	+	0.871892i	$0.337107\pi$
$59$	−3.21810	+	9.90429i	−0.418961	+	1.28943i	−0.908660	+	0.417537i	$0.862893\pi$
$60$	1.27298	+	3.91783i	0.164341	+	0.505790i
$61$	14.1567			1.81258			0.906288	−	0.422661i	$-0.138904\pi$
$61$	14.1567			1.81258			0.906288	+	0.422661i	$0.138904\pi$
$62$	0.485717	+	1.27511i	0.0616862	+	0.161939i
$63$	6.01191			0.757430
$64$	−2.03779	−	6.27168i	−0.254724	−	0.783960i
$65$	0.769399	−	2.36797i	0.0954321	−	0.293710i
$66$	−0.255676	+	0.185759i	−0.0314715	+	0.0228654i
$67$	10.3461			1.26398			0.631991	−	0.774976i	$-0.282238\pi$
$67$	10.3461			1.26398			0.631991	+	0.774976i	$0.282238\pi$
$68$	−4.39260			−0.532681
$69$	−0.446773	+	0.324599i	−0.0537851	+	0.0390772i
$70$	1.30588	+	0.948776i	0.156082	+	0.113400i
$71$	−4.25850	−	3.09398i	−0.505392	−	0.367188i	0.305681	−	0.952134i	$-0.401116\pi$
$71$	−4.25850	−	3.09398i	−0.505392	−	0.367188i	−0.811073	+	0.584946i	$0.801116\pi$
$72$	−0.678090	−	2.08695i	−0.0799137	−	0.245949i
$73$	−3.20708	+	2.33008i	−0.375361	+	0.272715i	−0.759430	−	0.650589i	$-0.774522\pi$
$73$	−3.20708	+	2.33008i	−0.375361	+	0.272715i	0.384070	+	0.923304i	$0.374522\pi$
$74$	−0.381521	−	1.17420i	−0.0443509	−	0.136498i
$75$	0.316059	−	0.972729i	0.0364953	−	0.112321i
$76$	−11.6242	−	8.44544i	−1.33338	−	0.968759i
$77$	1.23603	−	3.80412i	0.140859	−	0.433519i
$78$	0.0645883	−	0.198782i	0.00731318	−	0.0225077i
$79$	12.5917	+	9.14838i	1.41667	+	1.02927i	0.992309	+	0.123782i	$0.0395022\pi$
$79$	12.5917	+	9.14838i	1.41667	+	1.02927i	0.424364	+	0.905492i	$0.360498\pi$
$80$	−2.80311	+	8.62709i	−0.313398	+	0.964539i
$81$	0.921684	+	2.83665i	0.102409	+	0.315184i
$82$	1.48263	−	1.07720i	0.163729	−	0.118956i
$83$	−1.88430	−	5.79927i	−0.206828	−	0.636552i	−0.999633	−	0.0270769i	$-0.991380\pi$
$83$	−1.88430	−	5.79927i	−0.206828	−	0.636552i	0.792805	−	0.609475i	$-0.208620\pi$
$84$	−3.54091	−	2.57262i	−0.386345	−	0.280696i
$85$	4.56099	+	3.31376i	0.494709	+	0.359427i
$86$	−0.275463	+	0.200135i	−0.0297039	+	0.0215812i
$87$	6.62376			0.710142
$88$	−1.45996			−0.155632
$89$	−5.48141	+	3.98247i	−0.581028	+	0.422141i	−0.839095	−	0.543986i	$-0.816915\pi$
$89$	−5.48141	+	3.98247i	−0.581028	+	0.422141i	0.258067	+	0.966127i	$0.416915\pi$
$90$	−0.428516	+	1.31884i	−0.0451695	+	0.139018i
$91$	0.817465	+	2.51590i	0.0856936	+	0.263738i
$92$	−1.25613			−0.130961
$93$	−1.24079	+	4.58359i	−0.128664	+	0.475297i
$94$	−1.44198			−0.148728
$95$	5.69858	+	17.5384i	0.584662	+	1.79940i
$96$	−0.744259	+	2.29059i	−0.0759607	+	0.233783i
$97$	−14.3951	+	10.4587i	−1.46160	+	1.06192i	−0.478662	+	0.877999i	$0.658878\pi$
$97$	−14.3951	+	10.4587i	−1.46160	+	1.06192i	−0.982942	+	0.183918i	$0.941122\pi$
$98$	0.000492718	0		4.97721e−5	0
$99$	3.43627			0.345358
$100$	1.88213	−	1.36745i	0.188213	−	0.136745i
$101$	9.43891	+	6.85777i	0.939207	+	0.682374i	0.948230	−	0.317586i	$-0.102872\pi$
$101$	9.43891	+	6.85777i	0.939207	+	0.682374i	−0.00902293	+	0.999959i	$0.502872\pi$
$102$	0.382879	+	0.278178i	0.0379107	+	0.0275437i
$103$	2.53498	+	7.80187i	0.249779	+	0.768741i	0.994814	+	0.101715i	$0.0324331\pi$
$103$	2.53498	+	7.80187i	0.249779	+	0.768741i	−0.745034	+	0.667026i	$0.767567\pi$
$104$	0.781154	−	0.567542i	0.0765985	−	0.0556521i
$105$	1.73588	+	5.34249i	0.169405	+	0.521374i
$106$	0.420920	−	1.29546i	0.0408834	−	0.125826i
$107$	−13.9765	−	10.1545i	−1.35116	−	0.981677i	−0.998953	−	0.0457553i	$-0.985431\pi$
$107$	−13.9765	−	10.1545i	−1.35116	−	0.981677i	−0.352209	−	0.935921i	$-0.614569\pi$
$108$	2.69575	−	8.29665i	0.259398	−	0.798346i
$109$	−0.468016	+	1.44041i	−0.0448278	+	0.137966i	−0.970965	−	0.239220i	$-0.923108\pi$
$109$	−0.468016	+	1.44041i	−0.0448278	+	0.137966i	0.926138	+	0.377186i	$0.123108\pi$
$110$	0.746409	+	0.542298i	0.0711673	+	0.0517061i
$111$	1.32773	−	4.08634i	0.126023	−	0.387859i
$112$	−2.97823	−	9.16605i	−0.281416	−	0.866110i
$113$	−4.66722	+	3.39093i	−0.439055	+	0.318992i	−0.785259	−	0.619167i	$-0.787470\pi$
$113$	−4.66722	+	3.39093i	−0.439055	+	0.318992i	0.346204	+	0.938159i	$0.387470\pi$
$114$	0.478376	+	1.47229i	0.0448040	+	0.137892i
$115$	1.30429	+	0.947621i	0.121626	+	0.0883661i
$116$	12.1890	+	8.85585i	1.13172	+	0.822245i
$117$	−1.83859	+	1.33581i	−0.169977	+	0.123496i
$118$	2.55215			0.234945
$119$	−5.98990			−0.549093
$120$	1.65878	−	1.20517i	0.151425	−	0.110017i
$121$	−2.69270	+	8.28728i	−0.244791	+	0.753389i
$122$	−1.07209	−	3.29957i	−0.0970628	−	0.298729i
$123$	6.37776			0.575063
$124$	−8.41148	+	6.77580i	−0.755373	+	0.608485i
$125$	9.46325			0.846419
$126$	−0.455286	−	1.40123i	−0.0405601	−	0.124831i
$127$	−5.00281	+	15.3971i	−0.443927	+	1.36627i	0.439728	+	0.898131i	$0.355075\pi$
$127$	−5.00281	+	15.3971i	−0.443927	+	1.36627i	−0.883656	+	0.468137i	$0.844925\pi$
$128$	−5.87673	+	4.26969i	−0.519434	+	0.377391i
$129$	−1.18494			−0.104328
$130$	−0.610181			−0.0535164
$131$	1.45155	−	1.05461i	0.126822	−	0.0921418i	−0.522566	−	0.852599i	$-0.675025\pi$
$131$	1.45155	−	1.05461i	0.126822	−	0.0921418i	0.649388	+	0.760457i	$0.275025\pi$
$132$	−2.02390	−	1.47045i	−0.176158	−	0.127986i
$133$	−15.8511	−	11.5165i	−1.37447	−	0.998607i
$134$	−0.783520	−	2.41143i	−0.0676858	−	0.208316i
$135$	−9.05805	+	6.58106i	−0.779593	+	0.566407i
$136$	0.675607	+	2.07931i	0.0579329	+	0.178299i
$137$	3.10049	−	9.54232i	0.264892	−	0.815255i	−0.726826	−	0.686822i	$-0.759005\pi$
$137$	3.10049	−	9.54232i	0.264892	−	0.815255i	0.991718	−	0.128433i	$-0.0409948\pi$
$138$	0.109490	+	0.0795494i	0.00932044	+	0.00677170i
$139$	1.45674	−	4.48338i	0.123559	−	0.380275i	−0.870077	−	0.492916i	$-0.835931\pi$
$139$	1.45674	−	4.48338i	0.123559	−	0.380275i	0.993636	+	0.112641i	$0.0359309\pi$
$140$	−3.94845	+	12.1521i	−0.333705	+	1.02704i
$141$	−4.05983	−	2.94964i	−0.341899	−	0.248404i
$142$	−0.398631	+	1.22686i	−0.0334524	+	0.102956i
$143$	0.467243	+	1.43803i	0.0390729	+	0.120254i
$144$	6.69843	−	4.86669i	0.558202	−	0.405558i
$145$	−5.97550	−	18.3907i	−0.496238	−	1.52726i
$146$	0.785958	+	0.571032i	0.0650464	+	0.0472590i
$147$	0.00138723	+	0.00100788i	0.000114417	+	8.31287e-5i
$148$	7.90666	−	5.74452i	0.649923	−	0.472197i
$149$	4.84558			0.396965			0.198483	−	0.980104i	$-0.436399\pi$
$149$	4.84558			0.396965			0.198483	+	0.980104i	$0.436399\pi$
$150$	−0.250654			−0.0204658
$151$	4.50820	−	3.27540i	0.366872	−	0.266548i	−0.389040	−	0.921221i	$-0.627193\pi$
$151$	4.50820	−	3.27540i	0.366872	−	0.266548i	0.755913	+	0.654672i	$0.227193\pi$
$152$	−2.20992	+	6.80144i	−0.179248	+	0.551669i
$153$	−1.59016	−	4.89401i	−0.128557	−	0.395658i
$154$	−0.980250			−0.0789908
$155$	13.8456	−	0.689975i	1.11210	−	0.0554201i
$156$	1.65451			0.132467
$157$	−4.39070	−	13.5132i	−0.350416	−	1.07847i	−0.958620	−	0.284688i	$-0.908110\pi$
$157$	−4.39070	−	13.5132i	−0.350416	−	1.07847i	0.608204	−	0.793781i	$-0.291890\pi$
$158$	1.17868	−	3.62762i	0.0937711	−	0.288598i
$159$	3.83502	−	2.78630i	0.304137	−	0.220968i
$160$	7.03119			0.555865
$161$	−1.71291			−0.134996
$162$	0.591353	−	0.429643i	0.0464611	−	0.0337560i
$163$	7.83707	+	5.69397i	0.613847	+	0.445986i	0.850767	−	0.525543i	$-0.176138\pi$
$163$	7.83707	+	5.69397i	0.613847	+	0.445986i	−0.236920	+	0.971529i	$0.576138\pi$
$164$	11.7363	+	8.52695i	0.916454	+	0.665843i
$165$	0.992188	+	3.05364i	0.0772417	+	0.237726i
$166$	−1.20897	+	0.878365i	−0.0938339	+	0.0681743i
$167$	−5.66569	−	17.4372i	−0.438424	−	1.34933i	−0.889537	−	0.456864i	$-0.848973\pi$
$167$	−5.66569	−	17.4372i	−0.438424	−	1.34933i	0.451112	−	0.892467i	$-0.351027\pi$
$168$	−0.673178	+	2.07183i	−0.0519368	+	0.159845i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	0.426947	−	1.31401i	0.0327453	−	0.100780i
$171$	5.20144	−	16.0084i	0.397764	−	1.22419i
$172$	−2.18053	−	1.58425i	−0.166264	−	0.120798i
$173$	3.48654	−	10.7305i	0.265077	−	0.815823i	−0.726599	−	0.687062i	$-0.758900\pi$
$173$	3.48654	−	10.7305i	0.265077	−	0.815823i	0.991676	−	0.128761i	$-0.0411000\pi$
$174$	−0.501622	−	1.54383i	−0.0380279	−	0.117038i
$175$	2.56654	−	1.86470i	0.194012	−	0.140958i
$176$	−1.70229	−	5.23910i	−0.128315	−	0.394912i
$177$	7.18549	+	5.22057i	0.540095	+	0.392402i
$178$	1.34333	+	0.975984i	0.100687	+	0.0731531i
$179$	4.40018	−	3.19692i	0.328885	−	0.238949i	−0.411072	−	0.911603i	$-0.634846\pi$
$179$	4.40018	−	3.19692i	0.328885	−	0.238949i	0.739957	+	0.672654i	$0.234846\pi$
$180$	−10.9770			−0.818177
$181$	1.45687			0.108289			0.0541443	−	0.998533i	$-0.482757\pi$
$181$	1.45687			0.108289			0.0541443	+	0.998533i	$0.482757\pi$
$182$	0.524486	−	0.381061i	0.0388775	−	0.0282461i
$183$	3.73100	−	11.4828i	0.275803	−	0.848836i
$184$	0.193201	+	0.594610i	0.0142429	+	0.0438353i
$185$	−12.5434			−0.922210
$186$	1.16229	−	0.0579210i	0.0852231	−	0.00424697i
$187$	−3.42368			−0.250365
$188$	−3.52727	−	10.8558i	−0.257253	−	0.791743i
$189$	3.67601	−	11.3136i	0.267391	−	0.822944i
$190$	3.65621	−	2.65639i	0.265249	−	0.192715i
$191$	−1.00172			−0.0724819			−0.0362409	−	0.999343i	$-0.511538\pi$
$191$	−1.00172			−0.0724819			−0.0362409	+	0.999343i	$0.511538\pi$
$192$	−5.62418			−0.405890
$193$	−7.05467	+	5.12552i	−0.507807	+	0.368943i	−0.811991	−	0.583670i	$-0.801616\pi$
$193$	−7.05467	+	5.12552i	−0.507807	+	0.368943i	0.304184	+	0.952613i	$0.401616\pi$
$194$	3.52781	+	2.56310i	0.253282	+	0.184020i
$195$	−1.71794	−	1.24816i	−0.123024	−	0.0893824i
$196$	0.00120526	+	0.00370940i	8.60899e−5	+	0.000264957i
$197$	−3.39733	+	2.46831i	−0.242050	+	0.175859i	−0.702196	−	0.711984i	$-0.747797\pi$
$197$	−3.39733	+	2.46831i	−0.242050	+	0.175859i	0.460146	+	0.887843i	$0.347797\pi$
$198$	−0.260231	−	0.800908i	−0.0184938	−	0.0569181i
$199$	−0.0674306	+	0.207530i	−0.00478003	+	0.0147114i	−0.953418	−	0.301652i	$-0.902462\pi$
$199$	−0.0674306	+	0.207530i	−0.00478003	+	0.0147114i	0.948638	+	0.316363i	$0.102462\pi$
$200$	−0.936786	−	0.680615i	−0.0662408	−	0.0481267i
$201$	2.72673	−	8.39202i	0.192329	−	0.591927i
$202$	0.883560	−	2.71932i	0.0621671	−	0.191331i
$203$	16.6214	+	12.0761i	1.16659	+	0.847579i
$204$	−1.15767	+	3.56295i	−0.0810533	+	0.249456i
$205$	−5.75358	−	17.7077i	−0.401847	−	1.23676i
$206$	1.62645	−	1.18168i	0.113320	−	0.0823317i
$207$	−0.454732	−	1.39952i	−0.0316061	−	0.0972734i
$208$	2.94745	+	2.14145i	0.204369	+	0.148483i
$209$	−9.06011	−	6.58256i	−0.626701	−	0.455325i
$210$	1.11374	−	0.809181i	0.0768555	−	0.0558388i
$211$	−20.4686			−1.40912			−0.704558	−	0.709646i	$-0.748855\pi$
$211$	−20.4686			−1.40912			−0.704558	+	0.709646i	$0.748855\pi$
$212$	10.7824			0.740540
$213$	−3.63194	+	2.63876i	−0.248857	+	0.180805i
$214$	−1.30832	+	4.02659i	−0.0894348	+	0.275252i
$215$	1.06897	+	3.28996i	0.0729034	+	0.224374i
$216$	−4.34197			−0.295434
$217$	−11.4702	+	9.23972i	−0.778647	+	0.627233i
$218$	0.371166			0.0251385
$219$	1.04476	+	3.21544i	0.0705983	+	0.217279i
$220$	−2.25684	+	6.94584i	−0.152156	+	0.468288i
$221$	1.83185	−	1.33092i	0.123224	−	0.0895273i
$222$	−1.05298			−0.0706711
$223$	−4.72073			−0.316123			−0.158062	−	0.987429i	$-0.550524\pi$
$223$	−4.72073			−0.316123			−0.158062	+	0.987429i	$0.550524\pi$
$224$	−6.04372	+	4.39102i	−0.403813	+	0.293387i
$225$	2.20489	+	1.60195i	0.146993	+	0.106797i
$226$	1.14379	+	0.831014i	0.0760840	+	0.0552782i
$227$	4.04013	+	12.4342i	0.268153	+	0.825289i	0.990950	+	0.134230i	$0.0428559\pi$
$227$	4.04013	+	12.4342i	0.268153	+	0.825289i	−0.722797	+	0.691060i	$0.757144\pi$
$228$	−9.91387	+	7.20285i	−0.656562	+	0.477020i
$229$	−1.51768	−	4.67094i	−0.100291	−	0.308665i	0.888305	−	0.459254i	$-0.151883\pi$
$229$	−1.51768	−	4.67094i	−0.100291	−	0.308665i	−0.988596	+	0.150589i	$0.951883\pi$
$230$	0.122092	−	0.375761i	0.00805052	−	0.0247770i
$231$	−2.75986	−	2.00516i	−0.181585	−	0.131930i
$232$	2.31731	−	7.13195i	0.152139	−	0.468236i
$233$	−0.0389178	+	0.119777i	−0.00254959	+	0.00784682i	−0.952323	−	0.305091i	$-0.901313\pi$
$233$	−0.0389178	+	0.119777i	−0.00254959	+	0.00784682i	0.949774	+	0.312938i	$0.101313\pi$
$234$	0.450581	+	0.327367i	0.0294554	+	0.0214006i
$235$	−4.52710	+	13.9330i	−0.295315	+	0.908887i
$236$	6.24292	+	19.2137i	0.406380	+	1.25071i
$237$	10.7390	−	7.80236i	0.697575	−	0.506818i
$238$	0.453619	+	1.39610i	0.0294038	+	0.0904955i
$239$	−21.8303	−	15.8606i	−1.41208	−	1.02594i	−0.993016	−	0.117982i	$-0.962357\pi$
$239$	−21.8303	−	15.8606i	−1.41208	−	1.02594i	−0.419066	−	0.907956i	$-0.637643\pi$
$240$	6.25890	+	4.54735i	0.404010	+	0.293530i
$241$	−7.12028	+	5.17319i	−0.458657	+	0.333234i	−0.793004	−	0.609216i	$-0.791484\pi$
$241$	−7.12028	+	5.17319i	−0.458657	+	0.333234i	0.334347	+	0.942450i	$0.391484\pi$
$242$	2.13548			0.137274
$243$	16.0343			1.02860
$244$	22.2181	−	16.1424i	1.42237	−	1.03341i
$245$	0.00154689	−	0.00476085i	9.88274e−5	−	0.000304160i
$246$	−0.482992	−	1.48650i	−0.0307945	−	0.0947756i
$247$	7.40654			0.471267
$248$	4.50117	+	2.93955i	0.285824	+	0.186662i
$249$	−5.20054			−0.329571
$250$	−0.716658	−	2.20565i	−0.0453254	−	0.139497i
$251$	−7.42058	+	22.8382i	−0.468383	+	1.44153i	0.386295	+	0.922375i	$0.373755\pi$
$251$	−7.42058	+	22.8382i	−0.468383	+	1.44153i	−0.854678	+	0.519159i	$0.826245\pi$
$252$	9.43537	−	6.85520i	0.594372	−	0.431837i
$253$	−0.979057			−0.0615528
$254$	3.96754			0.248945
$255$	3.88993	−	2.82620i	0.243597	−	0.176983i
$256$	−9.22981	−	6.70585i	−0.576863	−	0.419116i
$257$	−24.5051	−	17.8040i	−1.52859	−	1.11058i	−0.957019	−	0.290027i	$-0.906336\pi$
$257$	−24.5051	−	17.8040i	−1.52859	−	1.11058i	−0.571567	−	0.820555i	$-0.693664\pi$
$258$	0.0897366	+	0.276181i	0.00558676	+	0.0171943i
$259$	10.7818	−	7.83343i	0.669948	−	0.486746i
$260$	−1.49259	−	4.59371i	−0.0925664	−	0.284890i
$261$	−5.45420	+	16.7863i	−0.337607	+	1.03905i
$262$	−0.355730	−	0.258453i	−0.0219771	−	0.0159673i
$263$	2.71780	−	8.36454i	0.167587	−	0.515780i	−0.831631	−	0.555329i	$-0.812592\pi$
$263$	2.71780	−	8.36454i	0.167587	−	0.515780i	0.999218	+	0.0395496i	$0.0125923\pi$
$264$	−0.384773	+	1.18421i	−0.0236811	+	0.0728830i
$265$	−11.1958	−	8.13422i	−0.687752	−	0.499681i
$266$	−1.48379	+	4.56665i	−0.0909773	+	0.279999i
$267$	1.78566	+	5.49569i	0.109281	+	0.336331i
$268$	16.2377	−	11.7974i	0.991875	−	0.720640i
$269$	−6.60287	−	20.3215i	−0.402584	−	1.23903i	−0.922896	−	0.385050i	$-0.874184\pi$
$269$	−6.60287	−	20.3215i	−0.402584	−	1.23903i	0.520312	−	0.853976i	$-0.325816\pi$
$270$	2.21985	+	1.61282i	0.135096	+	0.0981529i
$271$	24.8514	+	18.0556i	1.50961	+	1.09680i	0.966349	+	0.257236i	$0.0828116\pi$
$271$	24.8514	+	18.0556i	1.50961	+	1.09680i	0.543264	+	0.839562i	$0.317188\pi$
$272$	−6.67390	+	4.84887i	−0.404665	+	0.294006i
$273$	2.25615			0.136549
$274$	−2.45888			−0.148546
$275$	1.46697	−	1.06582i	0.0884618	−	0.0642712i
$276$	−0.331055	+	1.01888i	−0.0199271	+	0.0613295i
$277$	3.06920	+	9.44601i	0.184410	+	0.567556i	0.999938	−	0.0111623i	$-0.00355314\pi$
$277$	3.06920	+	9.44601i	0.184410	+	0.567556i	−0.815528	+	0.578718i	$0.803553\pi$
$278$	−1.15528			−0.0692893
$279$	−10.5943	−	6.91875i	−0.634264	−	0.414215i
$280$	6.35967			0.380063
$281$	8.12907	+	25.0187i	0.484940	+	1.49249i	0.832068	+	0.554674i	$0.187157\pi$
$281$	8.12907	+	25.0187i	0.484940	+	1.49249i	−0.347128	+	0.937818i	$0.612843\pi$
$282$	−0.380034	+	1.16962i	−0.0226307	+	0.0696501i
$283$	20.8782	−	15.1689i	1.24108	−	0.901698i	0.243411	−	0.969923i	$-0.421734\pi$
$283$	20.8782	−	15.1689i	1.24108	−	0.901698i	0.997670	+	0.0682254i	$0.0217337\pi$
$284$	−10.2115			−0.605939
$285$	15.7277			0.931630
$286$	0.299784	−	0.217806i	0.0177266	−	0.0128791i
$287$	16.0041	+	11.6276i	0.944691	+	0.686358i
$288$	−5.19211	−	3.77229i	−0.305948	−	0.222284i
$289$	−3.66895	−	11.2919i	−0.215821	−	0.664227i
$290$	−3.83389	+	2.78548i	−0.225133	+	0.163569i
$291$	4.68945	+	14.4326i	0.274901	+	0.846057i
$292$	−2.37642	+	7.31387i	−0.139069	+	0.428012i
$293$	−21.6726	−	15.7460i	−1.26612	−	0.919893i	−0.267083	−	0.963674i	$-0.586060\pi$
$293$	−21.6726	−	15.7460i	−1.26612	−	0.919893i	−0.999041	+	0.0437806i	$0.986060\pi$
$294$	0.000129856	0	0.000399657i	7.57337e−6	0	2.33084e-5i
$295$	8.01251	−	24.6600i	0.466506	−	1.43576i
$296$	−3.93535	−	2.85920i	−0.228738	−	0.166188i
$297$	2.10112	−	6.46659i	0.121919	−	0.375229i
$298$	−0.366959	−	1.12938i	−0.0212574	−	0.0654234i
$299$	0.523847	−	0.380597i	0.0302949	−	0.0220105i
$300$	−0.613135	−	1.88704i	−0.0353994	−	0.108948i
$301$	−2.97345	−	2.16034i	−0.171387	−	0.124520i
$302$	−1.10482	−	0.802701i	−0.0635755	−	0.0461903i
$303$	8.05014	−	5.84877i	0.462469	−	0.336003i
$304$	−26.9839			−1.54763
$305$	−35.2476			−2.01827
$306$	−1.02025	+	0.741254i	−0.0583237	+	0.0423747i
$307$	1.48330	−	4.56514i	0.0846567	−	0.260546i	−0.899764	−	0.436377i	$-0.856261\pi$
$307$	1.48330	−	4.56514i	0.0846567	−	0.260546i	0.984420	+	0.175831i	$0.0562612\pi$
$308$	−2.39783	−	7.37976i	−0.136629	−	0.420501i
$309$	6.99640			0.398011
$310$	−1.20935	−	3.17481i	−0.0686865	−	0.180317i
$311$	3.42570			0.194253			0.0971267	−	0.995272i	$-0.469035\pi$
$311$	3.42570			0.194253			0.0971267	+	0.995272i	$0.469035\pi$
$312$	−0.254474	−	0.783190i	−0.0144068	−	0.0443394i
$313$	−1.64452	+	5.06130i	−0.0929536	+	0.286082i	−0.986715	−	0.162461i	$-0.948057\pi$
$313$	−1.64452	+	5.06130i	−0.0929536	+	0.286082i	0.893761	+	0.448543i	$0.148057\pi$
$314$	−2.81707	+	2.04672i	−0.158977	+	0.115503i
$315$	−14.9686			−0.843386
$316$	30.1935			1.69852
$317$	20.4292	−	14.8427i	1.14742	−	0.833647i	0.159281	−	0.987233i	$-0.449082\pi$
$317$	20.4292	−	14.8427i	1.14742	−	0.833647i	0.988135	+	0.153586i	$0.0490823\pi$
$318$	−0.939847	−	0.682839i	−0.0527040	−	0.0382917i
$319$	9.50039	+	6.90244i	0.531920	+	0.386462i
$320$	5.07375	+	15.6154i	0.283631	+	0.872927i
$321$	−11.9201	+	8.66048i	−0.665317	+	0.483381i
$322$	0.129720	+	0.399236i	0.00722899	+	0.0222485i
$323$	−5.18239	+	15.9498i	−0.288356	+	0.887469i
$324$	4.68108	+	3.40100i	0.260060	+	0.188945i
$325$	−0.370583	+	1.14054i	−0.0205563	+	0.0632657i
$326$	0.733615	−	2.25783i	0.0406312	−	0.125050i
$327$	1.04500	+	0.759240i	0.0577889	+	0.0419861i
$328$	2.23125	−	6.86708i	0.123200	−	0.379171i
$329$	−4.80991	−	14.8034i	−0.265179	−	0.816138i
$330$	0.636588	−	0.462509i	0.0350430	−	0.0254603i
$331$	2.56533	+	7.89526i	0.141003	+	0.433963i	0.996475	−	0.0838858i	$-0.0267331\pi$
$331$	2.56533	+	7.89526i	0.141003	+	0.433963i	−0.855472	+	0.517848i	$0.826733\pi$
$332$	−9.57002	−	6.95303i	−0.525223	−	0.381597i
$333$	9.26255	+	6.72964i	0.507585	+	0.368782i
$334$	−3.63511	+	2.64106i	−0.198904	+	0.144513i
$335$	−25.7601			−1.40742
$336$	−8.21973			−0.448423
$337$	20.2669	−	14.7247i	1.10401	−	0.802108i	0.122297	−	0.992494i	$-0.460974\pi$
$337$	20.2669	−	14.7247i	1.10401	−	0.802108i	0.981709	+	0.190386i	$0.0609739\pi$
$338$	−0.0757307	+	0.233075i	−0.00411921	+	0.0126776i
$339$	1.52042	+	4.67938i	0.0825781	+	0.254149i
$340$	10.9368			0.593131
$341$	−6.55609	+	5.28120i	−0.355032	+	0.285993i
$342$	−4.12507			−0.223058
$343$	5.72390	+	17.6163i	0.309061	+	0.951193i
$344$	−0.414550	+	1.27586i	−0.0223511	+	0.0687895i
$345$	1.11239	−	0.808196i	0.0598888	−	0.0435118i
$346$	−2.76505			−0.148650
$347$	9.33445			0.501100			0.250550	−	0.968104i	$-0.419389\pi$
$347$	9.33445			0.501100			0.250550	+	0.968104i	$0.419389\pi$
$348$	10.3956	−	7.55287i	0.557264	−	0.404876i
$349$	−6.61182	−	4.80377i	−0.353922	−	0.257140i	0.396590	−	0.917996i	$-0.370193\pi$
$349$	−6.61182	−	4.80377i	−0.353922	−	0.257140i	−0.750513	+	0.660856i	$0.770193\pi$
$350$	−0.628981	−	0.456981i	−0.0336204	−	0.0244267i
$351$	1.38960	+	4.27675i	0.0741715	+	0.228276i
$352$	−3.45445	+	2.50980i	−0.184123	+	0.133773i
$353$	6.56723	+	20.2119i	0.349539	+	1.07577i	0.959109	+	0.283037i	$0.0913420\pi$
$353$	6.56723	+	20.2119i	0.349539	+	1.07577i	−0.609570	+	0.792732i	$0.708658\pi$
$354$	0.672622	−	2.07012i	0.0357494	−	0.110025i
$355$	10.6029	+	7.70348i	0.562745	+	0.408858i
$356$	−4.06167	+	12.5006i	−0.215268	+	0.662528i
$357$	−1.57864	+	4.85856i	−0.0835506	+	0.257142i
$358$	−1.07835	−	0.783467i	−0.0569926	−	0.0414075i
$359$	−5.53876	+	17.0465i	−0.292325	+	0.899682i	0.691782	+	0.722106i	$0.256826\pi$
$359$	−5.53876	+	17.0465i	−0.292325	+	0.899682i	−0.984107	+	0.177576i	$0.943174\pi$
$360$	1.68833	+	5.19614i	0.0889827	+	0.273860i
$361$	−29.0088	+	21.0761i	−1.52678	+	1.10927i
$362$	−0.110330	−	0.339561i	−0.00579882	−	0.0178469i
$363$	6.01236	+	4.36824i	0.315567	+	0.229273i
$364$	4.15177	+	3.01643i	0.217612	+	0.158104i
$365$	7.98507	−	5.80150i	0.417958	−	0.303664i
$366$	−2.95891			−0.154665
$367$	−18.7677			−0.979666			−0.489833	−	0.871816i	$-0.662942\pi$
$367$	−18.7677			−0.979666			−0.489833	+	0.871816i	$0.662942\pi$
$368$	−1.90851	+	1.38661i	−0.0994878	+	0.0722821i
$369$	−5.25164	+	16.1629i	−0.273389	+	0.841406i
$370$	0.949921	+	2.92356i	0.0493841	+	0.151989i
$371$	14.7033			0.763357
$372$	3.27917	+	8.60854i	0.170017	+	0.446332i
$373$	−21.0459			−1.08972			−0.544859	−	0.838528i	$-0.683417\pi$
$373$	−21.0459			−1.08972			−0.544859	+	0.838528i	$0.683417\pi$
$374$	0.259278	+	0.797975i	0.0134069	+	0.0412623i
$375$	2.49405	−	7.67588i	0.128792	−	0.396381i
$376$	−4.59627	+	3.33938i	−0.237034	+	0.172216i
$377$	−7.76646			−0.399993
$378$	−2.91531			−0.149947
$379$	3.91624	−	2.84531i	0.201164	−	0.146154i	−0.482643	−	0.875817i	$-0.660323\pi$
$379$	3.91624	−	2.84531i	0.201164	−	0.146154i	0.683807	+	0.729663i	$0.260323\pi$
$380$	28.9421	+	21.0277i	1.48470	+	1.07870i
$381$	11.1705	+	8.11581i	0.572280	+	0.415786i
$382$	0.0758609	+	0.233476i	0.00388138	+	0.0119457i
$383$	15.8010	−	11.4801i	0.807392	−	0.586605i	−0.105681	−	0.994400i	$-0.533702\pi$
$383$	15.8010	−	11.4801i	0.807392	−	0.586605i	0.913073	+	0.407795i	$0.133702\pi$
$384$	1.91444	+	5.89205i	0.0976960	+	0.300677i
$385$	−3.07751	+	9.47159i	−0.156844	+	0.482717i
$386$	1.72889	+	1.25611i	0.0879980	+	0.0639343i
$387$	0.975718	−	3.00295i	0.0495985	−	0.152649i
$388$	−10.6667	+	32.8286i	−0.541518	+	1.66662i
$389$	−5.46867	−	3.97322i	−0.277272	−	0.201450i	0.440454	−	0.897775i	$-0.354817\pi$
$389$	−5.46867	−	3.97322i	−0.277272	−	0.201450i	−0.717727	+	0.696325i	$0.754817\pi$
$390$	−0.160814	+	0.494933i	−0.00814311	+	0.0250619i
$391$	0.453067	+	1.39440i	0.0229126	+	0.0705176i
$392$	0.00157053	−	0.00114106i	7.93237e−5	−	5.76321e-5i
$393$	−0.472866	−	1.45533i	−0.0238529	−	0.0734118i
$394$	0.832583	+	0.604907i	0.0419449	+	0.0304748i
$395$	−31.3511	−	22.7779i	−1.57744	−	1.14608i
$396$	5.39303	−	3.91827i	0.271010	−	0.196900i
$397$	−8.32222			−0.417680			−0.208840	−	0.977950i	$-0.566969\pi$
$397$	−8.32222			−0.417680			−0.208840	+	0.977950i	$0.566969\pi$
$398$	0.0534767			0.00268054
$399$	−13.5189	+	9.82206i	−0.676792	+	0.491718i
$400$	1.35013	−	4.15527i	0.0675064	−	0.207763i
$401$	5.55891	+	17.1086i	0.277599	+	0.854361i	0.988520	+	0.151089i	$0.0482782\pi$
$401$	5.55891	+	17.1086i	0.277599	+	0.854361i	−0.710921	+	0.703271i	$0.751722\pi$
$402$	−2.16247			−0.107854
$403$	1.45485	−	5.37433i	0.0724711	−	0.267714i
$404$	22.6336			1.12606
$405$	−2.29483	−	7.06277i	−0.114031	−	0.350952i
$406$	1.55590	−	4.78857i	0.0772180	−	0.237653i
$407$	6.16262	−	4.47740i	0.305470	−	0.221937i
$408$	1.86464			0.0923132
$409$	23.9398			1.18375			0.591874	−	0.806030i	$-0.298388\pi$
$409$	23.9398			1.18375			0.591874	+	0.806030i	$0.298388\pi$
$410$	−3.69150	+	2.68203i	−0.182310	+	0.132456i
$411$	−6.92288	−	5.02977i	−0.341481	−	0.248100i
$412$	12.8747	+	9.35405i	0.634293	+	0.460841i
$413$	8.51307	+	26.2005i	0.418901	+	1.28924i
$414$	−0.291756	+	0.211973i	−0.0143390	+	0.0104179i
$415$	4.69157	+	14.4392i	0.230300	+	0.708791i
$416$	0.872655	−	2.68576i	0.0427854	−	0.131680i
$417$	−3.25266	−	2.36320i	−0.159283	−	0.115726i
$418$	−0.848102	+	2.61019i	−0.0414820	+	0.127668i
$419$	−4.48562	+	13.8053i	−0.219137	+	0.674433i	0.779697	+	0.626157i	$0.215373\pi$
$419$	−4.48562	+	13.8053i	−0.219137	+	0.674433i	−0.998834	+	0.0482767i	$0.984627\pi$
$420$	8.81624	+	6.40538i	0.430189	+	0.312550i
$421$	−4.72853	+	14.5529i	−0.230455	+	0.709266i	0.767237	+	0.641363i	$0.221631\pi$
$421$	−4.72853	+	14.5529i	−0.230455	+	0.709266i	−0.997692	+	0.0679029i	$0.978369\pi$
$422$	1.55010	+	4.77072i	0.0754577	+	0.232235i
$423$	10.8181	−	7.85983i	0.525995	−	0.382158i
$424$	−1.65840	−	5.10403i	−0.0805391	−	0.247874i
$425$	−2.19682	−	1.59608i	−0.106561	−	0.0774213i
$426$	0.890079	+	0.646680i	0.0431245	+	0.0313318i
$427$	30.2974	−	22.0123i	1.46619	−	1.06525i
$428$	−33.5143			−1.61997
$429$	1.28956			0.0622607
$430$	0.685854	−	0.498302i	0.0330748	−	0.0240303i
$431$	−3.72052	+	11.4506i	−0.179211	+	0.551556i	−0.999801	−	0.0199625i	$-0.993645\pi$
$431$	−3.72052	+	11.4506i	−0.179211	+	0.551556i	0.820589	+	0.571518i	$0.193645\pi$
$432$	−5.06267	−	15.5813i	−0.243578	−	0.749655i
$433$	−30.6894			−1.47484			−0.737419	−	0.675436i	$-0.763956\pi$
$433$	−30.6894			−1.47484			−0.737419	+	0.675436i	$0.763956\pi$
$434$	3.02219	+	1.97369i	0.145070	+	0.0947399i
$435$	−16.4920			−0.790732
$436$	0.907924	+	2.79430i	0.0434817	+	0.133823i
$437$	−1.48199	+	4.56109i	−0.0708931	+	0.218186i
$438$	0.670319	−	0.487015i	0.0320291	−	0.0232705i
$439$	−10.2909			−0.491156			−0.245578	−	0.969377i	$-0.578978\pi$
$439$	−10.2909			−0.491156			−0.245578	+	0.969377i	$0.578978\pi$
$440$	3.63504			0.173294
$441$	−0.00369652	+	0.00268568i	−0.000176025	+	0.000127889i
$442$	−0.448931	−	0.326168i	−0.0213535	−	0.0155142i
$443$	−9.85794	−	7.16221i	−0.468365	−	0.340287i	0.328439	−	0.944525i	$-0.393478\pi$
$443$	−9.85794	−	7.16221i	−0.468365	−	0.340287i	−0.796804	+	0.604238i	$0.793478\pi$
$444$	−2.57573	−	7.92727i	−0.122239	−	0.376211i
$445$	13.6477	−	9.91567i	0.646965	−	0.470048i
$446$	0.357504	+	1.10028i	0.0169283	+	0.0520999i
$447$	1.27706	−	3.93037i	0.0604026	−	0.185900i
$448$	−14.1131	−	10.2538i	−0.666781	−	0.484444i
$449$	7.39403	−	22.7565i	0.348946	−	1.07395i	−0.610491	−	0.792023i	$-0.709028\pi$
$449$	7.39403	−	22.7565i	0.348946	−	1.07395i	0.959437	−	0.281922i	$-0.0909721\pi$
$450$	0.206396	−	0.635222i	0.00972961	−	0.0299447i
$451$	9.14755	+	6.64609i	0.430741	+	0.312952i
$452$	−3.45837	+	10.6438i	−0.162668	+	0.500640i
$453$	−1.46862	−	4.51995i	−0.0690019	−	0.212366i
$454$	2.59215	−	1.88331i	0.121656	−	0.0883880i
$455$	−2.03534	−	6.26415i	−0.0954184	−	0.293668i
$456$	4.93440	+	3.58505i	0.231074	+	0.167885i
$457$	−4.41406	−	3.20700i	−0.206481	−	0.150017i	0.479739	−	0.877411i	$-0.340731\pi$
$457$	−4.41406	−	3.20700i	−0.206481	−	0.150017i	−0.686220	+	0.727394i	$0.740731\pi$
$458$	−0.973746	+	0.707468i	−0.0455001	+	0.0330578i
$459$	−10.1822			−0.475264
$460$	3.12755			0.145823
$461$	−20.9538	+	15.2238i	−0.975914	+	0.709043i	−0.956792	−	0.290774i	$-0.906087\pi$
$461$	−20.9538	+	15.2238i	−0.975914	+	0.709043i	−0.0191221	+	0.999817i	$0.506087\pi$
$462$	−0.258346	+	0.795106i	−0.0120193	+	0.0369917i
$463$	−0.986025	−	3.03467i	−0.0458244	−	0.141033i	0.925526	−	0.378683i	$-0.123623\pi$
$463$	−0.986025	−	3.03467i	−0.0458244	−	0.141033i	−0.971351	+	0.237650i	$0.923623\pi$
$464$	28.2952			1.31357
$465$	3.08936	−	11.4124i	0.143265	−	0.529235i
$466$	0.0308642			0.00142976
$467$	−3.56232	−	10.9637i	−0.164845	−	0.507340i	0.834180	−	0.551492i	$-0.185941\pi$
$467$	−3.56232	−	10.9637i	−0.164845	−	0.507340i	−0.999025	+	0.0441523i	$0.985941\pi$
$468$	−1.36238	+	4.19296i	−0.0629758	+	0.193820i
$469$	22.1423	−	16.0873i	1.02244	−	0.742843i
$470$	3.59027			0.165607
$471$	−12.1181			−0.558371
$472$	8.13493	−	5.91037i	0.374441	−	0.272047i
$473$	−1.69955	−	1.23480i	−0.0781455	−	0.0567760i
$474$	−2.63181	−	1.91212i	−0.120883	−	0.0878267i
$475$	−2.74474	−	8.44744i	−0.125937	−	0.387595i
$476$	−9.40082	+	6.83009i	−0.430886	+	0.313057i
$477$	3.90334	+	12.0132i	0.178722	+	0.550049i
$478$	−2.04349	+	6.28922i	−0.0934672	+	0.287662i
$479$	14.0914	+	10.2380i	0.643855	+	0.467788i	0.861172	−	0.508313i	$-0.169731\pi$
$479$	14.0914	+	10.2380i	0.643855	+	0.467788i	−0.217318	+	0.976101i	$0.569731\pi$
$480$	1.85308	−	5.70318i	0.0845810	−	0.260313i
$481$	−1.55679	+	4.79130i	−0.0709834	+	0.218464i
$482$	1.74496	+	1.26779i	0.0794809	+	0.0577463i
$483$	−0.451438	+	1.38938i	−0.0205411	+	0.0632191i
$484$	5.22368	+	16.0768i	0.237440	+	0.730765i
$485$	35.8414	−	26.0403i	1.62747	−	1.18243i
$486$	−1.21429	−	3.73720i	−0.0550813	−	0.169523i
$487$	−18.7521	−	13.6242i	−0.849740	−	0.617372i	0.0753344	−	0.997158i	$-0.475998\pi$
$487$	−18.7521	−	13.6242i	−0.849740	−	0.617372i	−0.925074	+	0.379786i	$0.875998\pi$
$488$	−11.0585	−	8.03450i	−0.500597	−	0.363705i
$489$	6.68399	−	4.85620i	0.302260	−	0.219605i
$490$	−0.00122678			−5.54204e−5
$491$	16.7949			0.757941			0.378971	−	0.925409i	$-0.376278\pi$
$491$	16.7949			0.757941			0.378971	+	0.925409i	$0.376278\pi$
$492$	10.0095	−	7.27236i	0.451265	−	0.327863i
$493$	5.43423	−	16.7248i	0.244746	−	0.753249i
$494$	−0.560902	−	1.72628i	−0.0252362	−	0.0776690i
$495$	−8.55571			−0.384550
$496$	−5.30037	+	19.5800i	−0.237994	+	0.879170i
$497$	−13.9247			−0.624609
$498$	0.393841	+	1.21212i	0.0176484	+	0.0543163i
$499$	6.99497	−	21.5283i	0.313138	−	0.963740i	−0.663376	−	0.748286i	$-0.730877\pi$
$499$	6.99497	−	21.5283i	0.313138	−	0.963740i	0.976514	−	0.215453i	$-0.0691230\pi$
$500$	14.8520	−	10.7906i	0.664204	−	0.482572i
$501$	−15.6370			−0.698608
$502$	5.88498			0.262660
$503$	24.9513	−	18.1282i	1.11252	−	0.808295i	0.129463	−	0.991584i	$-0.458675\pi$
$503$	24.9513	−	18.1282i	1.11252	−	0.808295i	0.983059	+	0.183289i	$0.0586746\pi$
$504$	−4.69623	−	3.41201i	−0.209187	−	0.151983i
$505$	−23.5012	−	17.0747i	−1.04579	−	0.759812i
$506$	0.0741446	+	0.228194i	0.00329613	+	0.0101444i
$507$	−0.689985	+	0.501303i	−0.0306433	+	0.0222637i
$508$	9.70515	+	29.8694i	0.430597	+	1.32524i
$509$	0.573125	−	1.76390i	0.0254033	−	0.0781834i	−0.937551	−	0.347848i	$-0.886913\pi$
$509$	0.573125	−	1.76390i	0.0254033	−	0.0781834i	0.962954	+	0.269664i	$0.0869127\pi$
$510$	−0.953303	−	0.692615i	−0.0422130	−	0.0306695i
$511$	−3.24057	+	9.97345i	−0.143354	+	0.441199i
$512$	−5.35341	+	16.4761i	−0.236589	+	0.728147i
$513$	−26.9452	−	19.5768i	−1.18966	−	0.864337i
$514$	−2.29388	+	7.05983i	−0.101179	+	0.311396i
$515$	−6.31166	−	19.4253i	−0.278125	−	0.855981i
$516$	−1.85970	+	1.35115i	−0.0818689	+	0.0594812i
$517$	−2.74923	−	8.46127i	−0.120911	−	0.372126i
$518$	−2.64229	−	1.91974i	−0.116096	−	0.0843484i
$519$	−7.78489	−	5.65605i	−0.341719	−	0.248273i
$520$	−1.94494	+	1.41308i	−0.0852912	+	0.0619677i
$521$	15.5986			0.683386			0.341693	−	0.939812i	$-0.389000\pi$
$521$	15.5986			0.683386			0.341693	+	0.939812i	$0.389000\pi$
$522$	4.32552			0.189323
$523$	−18.7936	+	13.6543i	−0.821785	+	0.597062i	−0.917223	−	0.398374i	$-0.869575\pi$
$523$	−18.7936	+	13.6543i	−0.821785	+	0.597062i	0.0954383	+	0.995435i	$0.469575\pi$
$524$	1.07558	−	3.31031i	0.0469871	−	0.144612i
$525$	−0.836093	−	2.57323i	−0.0364901	−	0.112305i
$526$	−2.15539			−0.0939793
$527$	10.5555	+	6.89342i	0.459805	+	0.300282i
$528$	−4.69820			−0.204463
$529$	−6.97783	−	21.4756i	−0.303384	−	0.933720i
$530$	−1.04802	+	3.22547i	−0.0455230	+	0.140105i
$531$	−19.1470	+	13.9111i	−0.830909	+	0.603691i
$532$	−38.0093			−1.64791
$533$	−7.47802			−0.323909
$534$	1.14568	−	0.832385i	0.0495784	−	0.0360208i
$535$	34.7991	+	25.2830i	1.50450	+	1.09308i
$536$	−8.08193	−	5.87187i	−0.349086	−	0.253626i
$537$	−1.43343	−	4.41165i	−0.0618571	−	0.190377i
$538$	−4.23640	+	3.07793i	−0.182644	+	0.132699i
$539$	0.000939404		0.00289119i	4.04630e−5		0.000124532i
$540$	−6.71194	+	20.6572i	−0.288836	+	0.888945i
$541$	−8.61616	−	6.26001i	−0.370438	−	0.269139i	0.386955	−	0.922099i	$-0.373527\pi$
$541$	−8.61616	−	6.26001i	−0.370438	−	0.269139i	−0.757392	+	0.652960i	$0.773527\pi$
$542$	2.32629	−	7.15959i	0.0999228	−	0.307531i
$543$	0.383960	−	1.18171i	0.0164773	−	0.0507120i
$544$	5.17310	+	3.75847i	0.221795	+	0.161143i
$545$	1.16528	−	3.58636i	0.0499151	−	0.153623i
$546$	−0.170860	−	0.525853i	−0.00731213	−	0.0225044i
$547$	−1.64486	+	1.19506i	−0.0703291	+	0.0510971i	−0.622394	−	0.782704i	$-0.713840\pi$
$547$	−1.64486	+	1.19506i	−0.0703291	+	0.0510971i	0.552065	+	0.833801i	$0.313840\pi$
$548$	−6.01476	−	18.5115i	−0.256938	−	0.790773i
$549$	26.0282	+	18.9106i	1.11086	+	0.807086i
$550$	−0.359510	−	0.261200i	−0.0153296	−	0.0111376i
$551$	46.5367	−	33.8109i	1.98253	−	1.44039i
$552$	0.533222			0.0226954
$553$	41.1730			1.75085
$554$	1.96920	−	1.43071i	0.0836632	−	0.0607849i
$555$	−3.30583	+	10.1743i	−0.140324	+	0.431874i
$556$	−2.82599	−	8.69749i	−0.119849	−	0.368856i
$557$	3.36977			0.142782			0.0713908	−	0.997448i	$-0.477256\pi$
$557$	3.36977			0.142782			0.0713908	+	0.997448i	$0.477256\pi$
$558$	−0.810276	+	2.99323i	−0.0343017	+	0.126713i
$559$	1.38936			0.0587638
$560$	7.41527	+	22.8219i	0.313353	+	0.964400i
$561$	−0.902314	+	2.77704i	−0.0380957	+	0.117247i
$562$	5.21562	−	3.78937i	0.220008	−	0.159845i
$563$	−44.4785			−1.87454			−0.937272	−	0.348598i	$-0.886658\pi$
$563$	−44.4785			−1.87454			−0.937272	+	0.348598i	$0.886658\pi$
$564$	−9.73506			−0.409920
$565$	11.6206	−	8.44283i	0.488880	−	0.355192i
$566$	−5.11661	−	3.71744i	−0.215067	−	0.156256i
$567$	6.38328	+	4.63773i	0.268073	+	0.194766i
$568$	1.57058	+	4.83376i	0.0659002	+	0.202820i
$569$	21.1992	−	15.4021i	0.888716	−	0.645690i	−0.0468270	−	0.998903i	$-0.514911\pi$
$569$	21.1992	−	15.4021i	0.888716	−	0.645690i	0.935543	+	0.353213i	$0.114911\pi$
$570$	−1.19107	−	3.66574i	−0.0498885	−	0.153541i
$571$	−6.06952	+	18.6801i	−0.254001	+	0.781736i	0.740023	+	0.672581i	$0.234814\pi$
$571$	−6.06952	+	18.6801i	−0.254001	+	0.781736i	−0.994025	+	0.109155i	$0.965186\pi$
$572$	2.37305	+	1.72412i	0.0992222	+	0.0720892i
$573$	−0.264004	+	0.812520i	−0.0110289	+	0.0339435i
$574$	1.49811	−	4.61072i	0.0625301	−	0.192448i
$575$	−0.628215	−	0.456425i	−0.0261984	−	0.0190342i
$576$	4.63112	−	14.2531i	0.192963	−	0.593880i
$577$	−2.62285	−	8.07230i	−0.109191	−	0.336054i	0.881501	−	0.472183i	$-0.156534\pi$
$577$	−2.62285	−	8.07230i	−0.109191	−	0.336054i	−0.990691	+	0.136129i	$0.956534\pi$
$578$	−2.35400	+	1.71028i	−0.0979135	+	0.0711383i
$579$	2.29818	+	7.07306i	0.0955090	+	0.293946i
$580$	−30.3486	−	22.0495i	−1.26016	−	0.915556i
$581$	−13.0500	−	9.48139i	−0.541406	−	0.393354i
$582$	3.00876	−	2.18599i	0.124717	−	0.0906121i
$583$	8.40405			0.348060
$584$	3.82764			0.158389
$585$	4.57776	−	3.32593i	0.189267	−	0.137510i
$586$	−2.02873	+	6.24379i	−0.0838061	+	0.257929i
$587$	−12.2731	−	37.7727i	−0.506565	−	1.55905i	−0.798123	−	0.602495i	$-0.794173\pi$
$587$	−12.2731	−	37.7727i	−0.506565	−	1.55905i	0.291557	−	0.956553i	$-0.405827\pi$
$588$	0.00332644			0.000137180
$589$	14.6794	+	38.5367i	0.604855	+	1.58788i
$590$	−6.35442			−0.261607
$591$	1.10674	+	3.40619i	0.0455251	+	0.140112i
$592$	5.67177	−	17.4559i	0.233108	−	0.717433i
$593$	−26.0991	+	18.9621i	−1.07176	+	0.778681i	−0.976228	−	0.216745i	$-0.930456\pi$
$593$	−26.0991	+	18.9621i	−1.07176	+	0.778681i	−0.0955339	+	0.995426i	$0.530456\pi$
$594$	−1.66632			−0.0683699
$595$	14.9138			0.611406
$596$	7.60487	−	5.52526i	0.311508	−	0.226323i
$597$	0.150562	+	0.109389i	0.00616208	+	0.00447701i
$598$	−0.128379	−	0.0932728i	−0.00524981	−	0.00381421i
$599$	−0.506435	−	1.55865i	−0.0206924	−	0.0636846i	0.940177	−	0.340686i	$-0.110659\pi$
$599$	−0.506435	−	1.55865i	−0.0206924	−	0.0636846i	−0.960869	+	0.277001i	$0.910659\pi$
$600$	−0.798955	+	0.580475i	−0.0326172	+	0.0236978i
$601$	−0.827823	−	2.54778i	−0.0337676	−	0.103926i	0.932752	−	0.360518i	$-0.117400\pi$
$601$	−0.827823	−	2.54778i	−0.0337676	−	0.103926i	−0.966520	+	0.256592i	$0.917400\pi$
$602$	−0.278339	+	0.856640i	−0.0113443	+	0.0349140i
$603$	19.0223	+	13.8205i	0.774646	+	0.562813i
$604$	3.34054	−	10.2811i	0.135925	−	0.418333i
$605$	6.70436	−	20.6339i	0.272571	−	0.838887i
$606$	−1.97285	−	1.43336i	−0.0801414	−	0.0582261i
$607$	−3.37752	+	10.3949i	−0.137089	+	0.421918i	−0.995909	−	0.0903601i	$-0.971198\pi$
$607$	−3.37752	+	10.3949i	−0.137089	+	0.421918i	0.858820	+	0.512278i	$0.171198\pi$
$608$	6.46335	+	19.8921i	0.262123	+	0.806733i
$609$	14.1758	−	10.2994i	0.574434	−	0.417351i
$610$	2.66933	+	8.21535i	0.108078	+	0.332630i
$611$	4.76021	+	3.45849i	0.192577	+	0.139916i
$612$	−8.07616	−	5.86768i	−0.326460	−	0.237187i
$613$	−5.42927	+	3.94460i	−0.219286	+	0.159321i	−0.692005	−	0.721892i	$-0.743273\pi$
$613$	−5.42927	+	3.94460i	−0.219286	+	0.159321i	0.472719	+	0.881213i	$0.343273\pi$
$614$	−1.17635			−0.0474737
$615$	−15.8795			−0.640324
$616$	−3.12453	+	2.27010i	−0.125891	+	0.0914650i
$617$	−3.47234	+	10.6868i	−0.139791	+	0.430233i	−0.996304	−	0.0858918i	$-0.972626\pi$
$617$	−3.47234	+	10.6868i	−0.139791	+	0.430233i	0.856513	+	0.516125i	$0.172626\pi$
$618$	−0.529842	−	1.63069i	−0.0213134	−	0.0655958i
$619$	4.63576			0.186327			0.0931634	−	0.995651i	$-0.470302\pi$
$619$	4.63576			0.186327			0.0931634	+	0.995651i	$0.470302\pi$
$620$	20.9431	−	16.8706i	0.841096	−	0.677538i
$621$	−2.91176			−0.116845
$622$	−0.259430	−	0.798444i	−0.0104022	−	0.0320147i
$623$	−5.53864	+	17.0462i	−0.221901	+	0.682941i
$624$	2.51379	−	1.82637i	0.100632	−	0.0731135i
$625$	−29.5580			−1.18232
$626$	1.30420			0.0521265
$627$	−7.72708	+	5.61405i	−0.308590	+	0.224204i
$628$	−22.2996	−	16.2016i	−0.889851	−	0.646515i
$629$	−9.22863	−	6.70499i	−0.367970	−	0.267346i
$630$	1.13358	+	3.48881i	0.0451631	+	0.138998i
$631$	−8.82355	+	6.41069i	−0.351260	+	0.255205i	−0.749397	−	0.662120i	$-0.769657\pi$
$631$	−8.82355	+	6.41069i	−0.351260	+	0.255205i	0.398137	+	0.917326i	$0.369657\pi$
$632$	−4.64395	−	14.2926i	−0.184726	−	0.568529i
$633$	−5.39451	+	16.6026i	−0.214413	+	0.659894i
$634$	−5.00657	−	3.63749i	−0.198836	−	0.144463i
$635$	12.4561	−	38.3360i	0.494306	−	1.52132i
$636$	2.84172	−	8.74590i	0.112681	−	0.346798i
$637$	−0.00162655	−	0.00118176i	−6.44462e−5	−	4.68229e-5i
$638$	0.889315	−	2.73703i	0.0352083	−	0.108360i
$639$	−3.69665	−	11.3771i	−0.146237	−	0.450071i
$640$	14.6320	−	10.6308i	0.578382	−	0.420219i
$641$	−14.1945	−	43.6861i	−0.560648	−	1.72550i	−0.680541	−	0.732710i	$-0.738255\pi$
$641$	−14.1945	−	43.6861i	−0.560648	−	1.72550i	0.119893	−	0.992787i	$-0.461745\pi$
$642$	2.92126	+	2.12242i	0.115293	+	0.0837653i
$643$	−1.10398	−	0.802087i	−0.0435366	−	0.0316312i	0.565804	−	0.824540i	$-0.308566\pi$
$643$	−1.10398	−	0.802087i	−0.0435366	−	0.0316312i	−0.609341	+	0.792908i	$0.708566\pi$
$644$	−2.68831	+	1.95317i	−0.105934	+	0.0769658i
$645$	2.95030			0.116168
$646$	4.10996			0.161704
$647$	−9.34912	+	6.79254i	−0.367552	+	0.267042i	−0.756195	−	0.654346i	$-0.772944\pi$
$647$	−9.34912	+	6.79254i	−0.367552	+	0.267042i	0.388643	+	0.921388i	$0.372944\pi$
$648$	0.889941	−	2.73896i	0.0349602	−	0.107596i
$649$	4.86587	+	14.9756i	0.191002	+	0.587844i
$650$	0.293896			0.0115275
$651$	4.47160	+	11.7389i	0.175256	+	0.460084i
$652$	18.7925			0.735971
$653$	−0.699916	−	2.15412i	−0.0273898	−	0.0842972i	0.936427	−	0.350862i	$-0.114111\pi$
$653$	−0.699916	−	2.15412i	−0.0273898	−	0.0842972i	−0.963817	+	0.266565i	$0.914111\pi$
$654$	0.0978210	−	0.301062i	0.00382511	−	0.0117725i
$655$	−3.61410	+	2.62580i	−0.141215	+	0.102598i
$656$	27.2443			1.06371
$657$	−9.00904			−0.351476
$658$	−3.08604	+	2.24214i	−0.120307	+	0.0874078i
$659$	−12.4351	−	9.03464i	−0.484404	−	0.351940i	0.318624	−	0.947881i	$-0.396779\pi$
$659$	−12.4351	−	9.03464i	−0.484404	−	0.351940i	−0.803028	+	0.595941i	$0.796779\pi$
$660$	5.03916	+	3.66116i	0.196149	+	0.142510i
$661$	4.61656	+	14.2083i	0.179563	+	0.552639i	0.999812	−	0.0193676i	$-0.00616528\pi$
$661$	4.61656	+	14.2083i	0.179563	+	0.552639i	−0.820249	+	0.572006i	$0.806165\pi$
$662$	1.64591	−	1.19583i	0.0639703	−	0.0464771i
$663$	−0.596756	−	1.83663i	−0.0231761	−	0.0713287i
$664$	−1.81940	+	5.59954i	−0.0706064	+	0.217304i
$665$	39.4665	+	28.6741i	1.53044	+	1.11193i
$666$	0.867051	−	2.66851i	0.0335976	−	0.103403i
$667$	1.55400	−	4.78273i	0.0601713	−	0.185188i
$668$	−28.7751	−	20.9063i	−1.11334	−	0.808890i
$669$	−1.24415	+	3.82910i	−0.0481016	+	0.148042i
$670$	1.95083	+	6.00403i	0.0753671	+	0.231956i
$671$	17.3173	−	12.5817i	0.668526	−	0.485712i
$672$	1.96884	+	6.05947i	0.0759497	+	0.233749i
$673$	30.9925	+	22.5174i	1.19467	+	0.867982i	0.993750	−	0.111625i	$-0.0356057\pi$
$673$	30.9925	+	22.5174i	1.19467	+	0.867982i	0.200924	+	0.979607i	$0.435606\pi$
$674$	−4.96679	−	3.60859i	−0.191314	−	0.138998i
$675$	4.36284	−	3.16979i	0.167926	−	0.122005i
$676$	−1.93994			−0.0746131
$677$	45.6180			1.75324			0.876622	−	0.481180i	$-0.159792\pi$
$677$	45.6180			1.75324			0.876622	+	0.481180i	$0.159792\pi$
$678$	0.975504	−	0.708745i	0.0374640	−	0.0272192i
$679$	−14.5454	+	44.7663i	−0.558203	+	1.71797i
$680$	−1.68214	−	5.17711i	−0.0645073	−	0.198533i
$681$	11.1505			0.427288
$682$	1.72741	+	1.12811i	0.0661461	+	0.0431976i
$683$	−34.5074			−1.32039			−0.660195	−	0.751094i	$-0.729526\pi$
$683$	−34.5074			−1.32039			−0.660195	+	0.751094i	$0.729526\pi$
$684$	−10.0905	−	31.0553i	−0.385819	−	1.18743i
$685$	−7.71967	+	23.7587i	−0.294954	+	0.907774i
$686$	3.67246	−	2.66820i	0.140215	−	0.101872i
$687$	−4.18871			−0.159809
$688$	−5.06180			−0.192979
$689$	−4.49661	+	3.26698i	−0.171307	+	0.124462i
$690$	−0.272612	−	0.198064i	−0.0103782	−	0.00754018i
$691$	−27.7390	−	20.1535i	−1.05524	−	0.766676i	−0.0820377	−	0.996629i	$-0.526143\pi$
$691$	−27.7390	−	20.1535i	−1.05524	−	0.766676i	−0.973202	+	0.229953i	$0.926143\pi$
$692$	−6.76369	−	20.8165i	−0.257117	−	0.791324i
$693$	7.35413	−	5.34309i	0.279360	−	0.202967i
$694$	−0.706904	−	2.17563i	−0.0268337	−	0.0825857i
$695$	−3.62703	+	11.1628i	−0.137581	+	0.423431i
$696$	−5.17418	−	3.75926i	−0.196127	−	0.142494i
$697$	5.23241	−	16.1037i	0.198192	−	0.609971i
$698$	−0.618921	+	1.90484i	−0.0234265	+	0.0720993i
$699$	0.0868971	+	0.0631344i	0.00328675	+	0.00238796i
$700$	1.90178	−	5.85309i	0.0718807	−	0.221226i
$701$	0.130003	+	0.400107i	0.00491013	+	0.0151118i	0.953482	−	0.301451i	$-0.0974711\pi$
$701$	0.130003	+	0.400107i	0.00491013	+	0.0151118i	−0.948571	+	0.316563i	$0.897471\pi$
$702$	0.891569	−	0.647763i	0.0336501	−	0.0244482i
$703$	−11.5304	−	35.4869i	−0.434877	−	1.33841i
$704$	−8.06670	−	5.86080i	−0.304025	−	0.220887i
$705$	10.1083	+	7.34409i	0.380699	+	0.276594i
$706$	4.21354	−	3.06132i	0.158579	−	0.115214i
$707$	30.8639			1.16076
$708$	17.2301			0.647546
$709$	13.0373	−	9.47218i	0.489628	−	0.355735i	−0.315413	−	0.948954i	$-0.602143\pi$
$709$	13.0373	−	9.47218i	0.489628	−	0.355735i	0.805041	+	0.593219i	$0.202143\pi$
$710$	0.992522	−	3.05467i	0.0372487	−	0.114640i
$711$	10.9303	+	33.6402i	0.409920	+	1.26160i
$712$	6.54204			0.245173
$713$	3.01851	+	1.97128i	0.113044	+	0.0738251i
$714$	1.25196			0.0468535
$715$	−1.16335	−	3.58044i	−0.0435070	−	0.133901i
$716$	3.26049	−	10.0348i	0.121850	−	0.375017i
$717$	−18.6183	+	13.5270i	−0.695314	+	0.505175i
$718$	4.39258			0.163930
$719$	−9.96204			−0.371521			−0.185761	−	0.982595i	$-0.559475\pi$
$719$	−9.96204			−0.371521			−0.185761	+	0.982595i	$0.559475\pi$
$720$	−16.6779	+	12.1172i	−0.621549	+	0.451582i
$721$	17.5565	+	12.7555i	0.653837	+	0.475040i
$722$	7.10917	+	5.16511i	0.264576	+	0.192226i
$723$	2.31955	+	7.13884i	0.0862650	+	0.265496i
$724$	2.28648	−	1.66123i	0.0849765	−	0.0617391i
$725$	2.87812	+	8.85794i	0.106891	+	0.328976i
$726$	0.562807	−	1.73214i	0.0208877	−	0.0642858i
$727$	−24.8843	−	18.0795i	−0.922908	−	0.670532i	0.0213382	−	0.999772i	$-0.493207\pi$
$727$	−24.8843	−	18.0795i	−0.922908	−	0.670532i	−0.944246	+	0.329241i	$0.893207\pi$
$728$	0.789311	−	2.42925i	0.0292538	−	0.0900340i
$729$	1.46081	−	4.49590i	0.0541040	−	0.166515i
$730$	−1.95690	−	1.42177i	−0.0724281	−	0.0526221i
$731$	−0.972145	+	2.99195i	−0.0359561	+	0.110661i
$732$	−7.23792	−	22.2760i	−0.267521	−	0.823346i
$733$	15.5837	−	11.3222i	0.575596	−	0.418195i	−0.261538	−	0.965193i	$-0.584230\pi$
$733$	15.5837	−	11.3222i	0.575596	−	0.418195i	0.837134	+	0.546998i	$0.184230\pi$
$734$	1.42129	+	4.37428i	0.0524608	+	0.161458i
$735$	−0.00345396	−	0.00250945i	−0.000127401	−	9.25625e-5i
$736$	1.47933	+	1.07480i	0.0545288	+	0.0396175i
$737$	12.6560	−	9.19513i	0.466190	−	0.338707i
$738$	4.16488			0.153311
$739$	−51.9409			−1.91068			−0.955338	−	0.295515i	$-0.904509\pi$
$739$	−51.9409			−1.91068			−0.955338	+	0.295515i	$0.904509\pi$
$740$	−19.6862	+	14.3029i	−0.723679	+	0.525784i
$741$	1.95200	−	6.00763i	0.0717085	−	0.220696i
$742$	−1.11349	−	3.42697i	−0.0408775	−	0.125808i
$743$	53.8239			1.97461			0.987303	−	0.158848i	$-0.0507780\pi$
$743$	53.8239			1.97461			0.987303	+	0.158848i	$0.0507780\pi$
$744$	3.57063	−	2.87629i	0.130906	−	0.105450i
$745$	−12.0646			−0.442014
$746$	1.59382	+	4.90528i	0.0583540	+	0.179595i
$747$	4.28228	−	13.1795i	0.156681	−	0.482213i
$748$	−5.37328	+	3.90392i	−0.196467	+	0.142741i
$749$	−45.7013			−1.66989
$750$	−1.97793			−0.0722239
$751$	−4.56119	+	3.31390i	−0.166440	+	0.120926i	−0.667887	−	0.744262i	$-0.732801\pi$
$751$	−4.56119	+	3.31390i	−0.166440	+	0.120926i	0.501447	+	0.865188i	$0.332801\pi$
$752$	−17.3426	−	12.6002i	−0.632421	−	0.459481i
$753$	16.5690	+	12.0380i	0.603806	+	0.438691i
$754$	0.588159	+	1.81017i	0.0214195	+	0.0659224i
$755$	−11.2246	+	8.15518i	−0.408506	+	0.296797i
$756$	−7.13125	−	21.9477i	−0.259361	−	0.798231i
$757$	15.9202	−	48.9972i	0.578628	−	1.78083i	−0.0448517	−	0.998994i	$-0.514282\pi$
$757$	15.9202	−	48.9972i	0.578628	−	1.78083i	0.623480	−	0.781840i	$-0.285718\pi$
$758$	−0.959751	−	0.697300i	−0.0348597	−	0.0253271i
$759$	−0.258031	+	0.794138i	−0.00936593	+	0.0288254i
$760$	5.50232	−	16.9344i	0.199590	−	0.614275i
$761$	22.9732	+	16.6910i	0.832777	+	0.605048i	0.920344	−	0.391111i	$-0.127909\pi$
$761$	22.9732	+	16.6910i	0.832777	+	0.605048i	−0.0875664	+	0.996159i	$0.527909\pi$
$762$	1.04565	−	3.21817i	0.0378798	−	0.116582i
$763$	1.23808	+	3.81041i	0.0448214	+	0.137946i
$764$	−1.57214	+	1.14223i	−0.0568782	+	0.0413244i
$765$	3.95923	+	12.1852i	0.143146	+	0.440558i
$766$	−3.87234	−	2.81342i	−0.139913	−	0.101653i
$767$	−8.42509	−	6.12119i	−0.304213	−	0.221023i
$768$	−7.87181	+	5.71921i	−0.284050	+	0.206374i
$769$	−20.6419			−0.744367			−0.372184	−	0.928159i	$-0.621391\pi$
$769$	−20.6419			−0.744367			−0.372184	+	0.928159i	$0.621391\pi$
$770$	2.44065			0.0879550
$771$	−20.8996	+	15.1845i	−0.752681	+	0.546855i
$772$	−5.22745	+	16.0884i	−0.188140	+	0.579036i
$773$	14.8073	+	45.5721i	0.532581	+	1.63912i	0.748819	+	0.662775i	$0.230621\pi$
$773$	14.8073	+	45.5721i	0.532581	+	1.63912i	−0.216237	+	0.976341i	$0.569379\pi$
$774$	−0.773805			−0.0278138
$775$	−6.66877	+	0.332329i	−0.239549	+	0.0119376i
$776$	17.1806			0.616746
$777$	−3.51235	−	10.8099i	−0.126005	−	0.387803i
$778$	−0.511912	+	1.57550i	−0.0183529	+	0.0564846i
$779$	44.8084	−	32.5552i	1.60543	−	1.16641i
$780$	−4.11945			−0.147500
$781$	−7.95903			−0.284797
$782$	0.290688	−	0.211197i	0.0103950	−	0.00755239i
$783$	28.2546	+	20.5281i	1.00974	+	0.733616i
$784$	0.00592592	+	0.00430544i	0.000211640	+	0.000153766i
$785$	10.9321	+	33.6455i	0.390182	+	1.20086i
$786$	−0.303391	+	0.220426i	−0.0108216	+	0.00786235i
$787$	4.73020	+	14.5581i	0.168613	+	0.518939i	0.999284	−	0.0378249i	$-0.0120429\pi$
$787$	4.73020	+	14.5581i	0.168613	+	0.518939i	−0.830671	+	0.556764i	$0.812043\pi$
$788$	−2.51739	+	7.74774i	−0.0896784	+	0.276002i
$789$	−6.06841	−	4.40896i	−0.216041	−	0.156963i
$790$	−2.93472	+	9.03213i	−0.104413	+	0.321349i
$791$	−4.71595	+	14.5142i	−0.167680	+	0.516066i
$792$	−2.68425	−	1.95023i	−0.0953808	−	0.0692982i
$793$	−4.37465	+	13.4638i	−0.155348	+	0.478113i
$794$	0.630247	+	1.93970i	0.0223666	+	0.0688374i
$795$	−9.54853	+	6.93741i	−0.338651	+	0.246045i
$796$	0.130811	+	0.402596i	0.00463649	+	0.0142696i
$797$	12.6400	+	9.18349i	0.447731	+	0.325296i	0.788699	−	0.614779i	$-0.210755\pi$
$797$	12.6400	+	9.18349i	0.447731	+	0.325296i	−0.340968	+	0.940075i	$0.610755\pi$
$798$	3.31307	+	2.40709i	0.117281	+	0.0852100i
$799$	−10.7785	+	7.83105i	−0.381316	+	0.277043i
$800$	−3.38660			−0.119734
$801$	−15.3979			−0.544057
$802$	3.56660	−	2.59129i	0.125941	−	0.0915015i
$803$	−1.85223	+	5.70059i	−0.0653639	+	0.201169i
$804$	−5.28970	−	16.2800i	−0.186553	−	0.574152i
$805$	4.26484			0.150316
$806$	−1.36280	+	0.0679131i	−0.0480025	+	0.00239214i
$807$	−18.2235			−0.641498
$808$	−3.48117	−	10.7140i	−0.122467	−	0.376916i
$809$	14.5214	−	44.6922i	0.510545	−	1.57130i	−0.280700	−	0.959796i	$-0.590567\pi$
$809$	14.5214	−	44.6922i	0.510545	−	1.57130i	0.791245	−	0.611500i	$-0.209433\pi$
$810$	−1.47237	+	1.06974i	−0.0517337	+	0.0375867i
$811$	16.2150			0.569387			0.284693	−	0.958619i	$-0.408108\pi$
$811$	16.2150			0.569387			0.284693	+	0.958619i	$0.408108\pi$
$812$	39.8564			1.39869
$813$	21.1949	−	15.3990i	0.743339	−	0.540067i
$814$	−1.51027	−	1.09728i	−0.0529350	−	0.0384595i
$815$	−19.5129	−	14.1770i	−0.683509	−	0.496598i
$816$	2.17413	+	6.69130i	0.0761099	+	0.234242i
$817$	−8.32509	+	6.04853i	−0.291258	+	0.211611i
$818$	−1.81298	−	5.57978i	−0.0633894	−	0.195092i
$819$	−1.85778	+	5.71767i	−0.0649162	+	0.199792i
$820$	−29.2214	−	21.2306i	−1.02046	−	0.741405i
$821$	−12.8295	+	39.4851i	−0.447752	+	1.37804i	0.431685	+	0.902024i	$0.357919\pi$
$821$	−12.8295	+	39.4851i	−0.447752	+	1.37804i	−0.879437	+	0.476015i	$0.842081\pi$
$822$	−0.648039	+	1.99446i	−0.0226030	+	0.0695648i
$823$	7.25750	+	5.27288i	0.252981	+	0.183801i	0.707047	−	0.707167i	$-0.250027\pi$
$823$	7.25750	+	5.27288i	0.252981	+	0.183801i	−0.454066	+	0.890968i	$0.650027\pi$
$824$	2.44768	−	7.53317i	0.0852689	−	0.262431i
$825$	−0.477891	−	1.47080i	−0.0166380	−	0.0512066i
$826$	5.46199	−	3.96837i	0.190047	−	0.138077i
$827$	−6.84915	−	21.0795i	−0.238168	−	0.733007i	−0.996685	−	0.0813536i	$-0.974076\pi$
$827$	−6.84915	−	21.0795i	−0.238168	−	0.733007i	0.758517	−	0.651653i	$-0.225924\pi$
$828$	−2.30951	−	1.67795i	−0.0802609	−	0.0583130i
$829$	−2.03184	−	1.47622i	−0.0705687	−	0.0512712i	0.551942	−	0.833883i	$-0.313887\pi$
$829$	−2.03184	−	1.47622i	−0.0705687	−	0.0512712i	−0.622510	+	0.782612i	$0.713887\pi$
$830$	3.01011	−	2.18698i	0.104483	−	0.0759110i
$831$	8.47079			0.293849
$832$	6.59444			0.228621
$833$	0.00368298	−	0.00267584i	0.000127608	−	9.27125e-5i
$834$	−0.304476	+	0.937081i	−0.0105431	+	0.0324484i
$835$	14.1066	+	43.4156i	0.488178	+	1.50246i
$836$	−21.7252			−0.751383
$837$	−19.4981	+	15.7065i	−0.673952	+	0.542897i
$838$	3.55737			0.122887
$839$	1.11022	+	3.41689i	0.0383289	+	0.117964i	0.968390	−	0.249440i	$-0.0802466\pi$
$839$	1.11022	+	3.41689i	0.0383289	+	0.117964i	−0.930061	+	0.367404i	$0.880247\pi$
$840$	1.67610	−	5.15849i	0.0578308	−	0.177985i
$841$	−25.3367	+	18.4082i	−0.873679	+	0.634765i
$842$	3.75002			0.129234
$843$	22.4357			0.772728
$844$	−32.1243	+	23.3397i	−1.10577	+	0.803386i
$845$	2.01431	+	1.46348i	0.0692944	+	0.0503453i
$846$	−2.65119	−	1.92621i	−0.0911499	−	0.0662243i
$847$	7.12319	+	21.9229i	0.244756	+	0.753281i
$848$	16.3823	−	11.9024i	0.562571	−	0.408731i
$849$	−6.80142	−	20.9326i	−0.233424	−	0.718406i
$850$	−0.205640	+	0.632896i	−0.00705341	+	0.0217081i
$851$	−2.63907	−	1.91740i	−0.0904663	−	0.0657276i
$852$	−2.69124	+	8.28278i	−0.0922003	+	0.283763i
$853$	1.92717	−	5.93122i	0.0659850	−	0.203081i	−0.912628	−	0.408791i	$-0.865950\pi$
$853$	1.92717	−	5.93122i	0.0659850	−	0.203081i	0.978613	+	0.205710i	$0.0659504\pi$
$854$	−7.42497	−	5.39456i	−0.254077	−	0.184598i
$855$	−12.9507	+	39.8581i	−0.442904	+	1.36312i
$856$	5.15470	+	15.8645i	0.176184	+	0.542238i
$857$	12.3991	−	9.00848i	0.423546	−	0.307724i	−0.355517	−	0.934670i	$-0.615695\pi$
$857$	12.3991	−	9.00848i	0.423546	−	0.307724i	0.779063	+	0.626946i	$0.215695\pi$
$858$	−0.0976595	−	0.300565i	−0.00333404	−	0.0102611i
$859$	17.9228	+	13.0217i	0.611519	+	0.444294i	0.849949	−	0.526865i	$-0.176633\pi$
$859$	17.9228	+	13.0217i	0.611519	+	0.444294i	−0.238430	+	0.971160i	$0.576633\pi$
$860$	5.42914	+	3.94450i	0.185132	+	0.134506i
$861$	13.6494	−	9.91685i	0.465169	−	0.337965i
$862$	2.95061			0.100498
$863$	−23.1408			−0.787721			−0.393860	−	0.919170i	$-0.628861\pi$
$863$	−23.1408			−0.787721			−0.393860	+	0.919170i	$0.628861\pi$
$864$	−10.2737	+	7.46426i	−0.349517	+	0.253939i
$865$	−8.68089	+	26.7170i	−0.295159	+	0.908406i
$866$	2.32413	+	7.15293i	0.0789771	+	0.243067i
$867$	−10.1261			−0.343900
$868$	−7.46608	+	27.5803i	−0.253415	+	0.936137i
$869$	23.5335			0.798319
$870$	1.24895	+	3.84388i	0.0423434	+	0.130320i
$871$	−3.19713	+	9.83976i	−0.108331	+	0.333408i
$872$	1.18308	−	0.859560i	0.0400643	−	0.0291084i
$873$	−40.4375			−1.36860
$874$	1.17531			0.0397554
$875$	20.2528	−	14.7145i	0.684669	−	0.497441i
$876$	5.30616	+	3.85515i	0.179279	+	0.130253i
$877$	10.0767	+	7.32119i	0.340268	+	0.247219i	0.744775	−	0.667316i	$-0.232557\pi$
$877$	10.0767	+	7.32119i	0.340268	+	0.247219i	−0.404507	+	0.914535i	$0.632557\pi$
$878$	0.779334	+	2.39854i	0.0263013	+	0.0809469i
$879$	−18.4838	+	13.4293i	−0.623444	+	0.452959i
$880$	4.23839	+	13.0444i	0.142876	+	0.439728i
$881$	−5.37437	+	16.5406i	−0.181067	+	0.557267i	−0.999858	−	0.0168240i	$-0.994645\pi$
$881$	−5.37437	+	16.5406i	−0.181067	+	0.557267i	0.818791	+	0.574091i	$0.194645\pi$
$882$	0.000905905	0	0.000658178i	3.05034e−5	0	2.21620e-5i
$883$	−8.07150	+	24.8415i	−0.271628	+	0.835983i	0.718465	+	0.695564i	$0.244845\pi$
$883$	−8.07150	+	24.8415i	−0.271628	+	0.835983i	−0.990092	+	0.140420i	$0.955155\pi$
$884$	1.35739	−	4.17761i	0.0456539	−	0.140508i
$885$	−17.8906	−	12.9983i	−0.601387	−	0.436933i
$886$	−0.922785	+	2.84004i	−0.0310016	+	0.0954130i
$887$	17.7144	+	54.5193i	0.594791	+	1.83058i	0.555765	+	0.831340i	$0.312426\pi$
$887$	17.7144	+	54.5193i	0.594791	+	1.83058i	0.0390261	+	0.999238i	$0.487574\pi$
$888$	−3.35634	+	2.43852i	−0.112631	+	0.0818314i
$889$	13.2343	+	40.7309i	0.443864	+	1.36607i
$890$	−3.34465	−	2.43003i	−0.112113	−	0.0814548i
$891$	3.64853	+	2.65081i	0.122230	+	0.0888056i
$892$	−7.40892	+	5.38290i	−0.248069	+	0.180233i
$893$	−43.5796			−1.45834
$894$	−1.01278			−0.0338726
$895$	−10.9557	+	7.95977i	−0.366208	+	0.266066i
$896$	−5.93809	+	18.2756i	−0.198378	+	0.610544i
$897$	−0.170652	−	0.525213i	−0.00569790	−	0.0175363i
$898$	−5.86393			−0.195682
$899$	−15.3928	−	40.4094i	−0.513378	−	1.34773i
$900$	5.28711			0.176237
$901$	−3.88905	−	11.9693i	−0.129563	−	0.398754i
$902$	0.856287	−	2.63538i	0.0285112	−	0.0877485i
$903$	−2.53596	+	1.84248i	−0.0843914	+	0.0613139i
$904$	5.57031			0.185266
$905$	−3.62736			−0.120578
$906$	−0.942269	+	0.684598i	−0.0313048	+	0.0227443i
$907$	1.69521	+	1.23164i	0.0562885	+	0.0408960i	0.615574	−	0.788079i	$-0.288924\pi$
$907$	1.69521	+	1.23164i	0.0562885	+	0.0408960i	−0.559285	+	0.828975i	$0.688924\pi$
$908$	20.5191	+	14.9080i	0.680951	+	0.494740i
$909$	8.19356	+	25.2172i	0.271763	+	0.836401i
$910$	−1.30588	+	0.948776i	−0.0432894	+	0.0314516i
$911$	0.262935	+	0.809230i	0.00871141	+	0.0268110i	0.955318	−	0.295581i	$-0.0955132\pi$
$911$	0.262935	+	0.809230i	0.00871141	+	0.0268110i	−0.946606	+	0.322392i	$0.895513\pi$
$912$	−7.11162	+	21.8873i	−0.235489	+	0.724762i
$913$	−7.45908	−	5.41934i	−0.246860	−	0.179354i
$914$	−0.413192	+	1.27168i	−0.0136672	+	0.0420633i
$915$	−9.28954	+	28.5903i	−0.307103	+	0.945165i
$916$	−7.70805	−	5.60023i	−0.254681	−	0.185037i
$917$	1.46671	−	4.51405i	0.0484349	−	0.149067i
$918$	0.771104	+	2.37321i	0.0254502	+	0.0783277i
$919$	9.66243	−	7.02017i	0.318734	−	0.231574i	−0.416901	−	0.908952i	$-0.636884\pi$
$919$	9.66243	−	7.02017i	0.318734	−	0.231574i	0.735635	+	0.677378i	$0.236884\pi$
$920$	−0.481036	−	1.48048i	−0.0158593	−	0.0488099i
$921$	−3.31198	−	2.40629i	−0.109133	−	0.0792901i
$922$	5.13513	+	3.73089i	0.169116	+	0.122870i
$923$	4.25850	−	3.09398i	0.140170	−	0.101840i
$924$	−6.61786			−0.217712
$925$	6.04158			0.198646
$926$	−0.632634	+	0.459635i	−0.0207896	+	0.0151046i
$927$	−5.76104	+	17.7307i	−0.189217	+	0.582351i
$928$	−6.77744	−	20.8588i	−0.222480	−	0.684724i
$929$	2.04519			0.0671005			0.0335502	−	0.999437i	$-0.489319\pi$
$929$	2.04519			0.0671005			0.0335502	+	0.999437i	$0.489319\pi$
$930$	−2.89389	+	0.144213i	−0.0948945	+	0.00472893i
$931$	0.0148910			0.000488034
$932$	0.0754982	+	0.232359i	0.00247302	+	0.00761119i
$933$	0.902844	−	2.77867i	0.0295578	−	0.0909696i
$934$	−2.28559	+	1.66058i	−0.0747868	+	0.0543358i
$935$	8.52438			0.278777
$936$	2.19435			0.0717245
$937$	−29.1094	+	21.1492i	−0.950962	+	0.690915i	−0.951034	−	0.309085i	$-0.899977\pi$
$937$	−29.1094	+	21.1492i	−0.950962	+	0.690915i	7.19366e−5		1.00000i	$0.499977\pi$
$938$	−5.42640	−	3.94251i	−0.177178	−	0.128728i
$939$	3.67194	+	2.66782i	0.119829	+	0.0870610i
$940$	8.78230	+	27.0291i	0.286447	+	0.881593i
$941$	46.4229	−	33.7282i	1.51334	−	1.09951i	0.548677	−	0.836035i	$-0.315132\pi$
$941$	46.4229	−	33.7282i	1.51334	−	1.09951i	0.964667	−	0.263474i	$-0.0848682\pi$
$942$	0.917709	+	2.82442i	0.0299006	+	0.0920245i
$943$	1.49629	−	4.60511i	0.0487259	−	0.149963i
$944$	30.6947	+	22.3010i	0.999029	+	0.725837i
$945$	−9.15263	+	28.1689i	−0.297735	+	0.916335i
$946$	−0.159092	+	0.489635i	−0.00517253	+	0.0159194i
$947$	−21.2025	−	15.4045i	−0.688988	−	0.500579i	0.187340	−	0.982295i	$-0.440014\pi$
$947$	−21.2025	−	15.4045i	−0.688988	−	0.500579i	−0.876327	+	0.481716i	$0.840014\pi$
$948$	7.95753	−	24.4908i	0.258449	−	0.795423i
$949$	−1.22500	−	3.77015i	−0.0397651	−	0.122384i
$950$	−1.76103	+	1.27946i	−0.0571353	+	0.0415112i
$951$	−6.65514	−	20.4824i	−0.215808	−	0.664188i
$952$	4.67904	+	3.39952i	0.151648	+	0.110179i
$953$	21.9913	+	15.9776i	0.712367	+	0.517565i	0.883936	−	0.467607i	$-0.154884\pi$
$953$	21.9913	+	15.9776i	0.712367	+	0.517565i	−0.171570	+	0.985172i	$0.554884\pi$
$954$	2.50439	−	1.81954i	0.0810825	−	0.0589099i
$955$	2.49411			0.0807074
$956$	−52.3468			−1.69302
$957$	8.10258	−	5.88687i	0.261919	−	0.190295i
$958$	1.31908	−	4.05970i	0.0426174	−	0.131163i
$959$	−8.20194	−	25.2430i	−0.264854	−	0.815138i
$960$	14.0032			0.451953
$961$	30.8464	−	3.08203i	0.995046	−	0.0994203i
$962$	1.23463			0.0398060
$963$	−12.1325	−	37.3400i	−0.390964	−	1.20326i
$964$	−5.27607	+	16.2381i	−0.169931	+	0.522993i
$965$	17.5649	−	12.7617i	0.565435	−	0.410812i
$966$	0.358018			0.0115190
$967$	44.2959			1.42446			0.712230	−	0.701947i	$-0.247686\pi$
$967$	44.2959			1.42446			0.712230	+	0.701947i	$0.247686\pi$
$968$	6.80679	−	4.94542i	0.218779	−	0.158952i
$969$	11.5714	+	8.40715i	0.371728	+	0.270076i
$970$	−8.78363	−	6.38168i	−0.282025	−	0.204903i
$971$	−9.98983	−	30.7455i	−0.320589	−	0.986672i	−0.973392	−	0.229144i	$-0.926407\pi$
$971$	−9.98983	−	30.7455i	−0.320589	−	0.986672i	0.652803	−	0.757527i	$-0.273593\pi$
$972$	25.1650	−	18.2834i	0.807168	−	0.586442i
$973$	−3.85361	−	11.8602i	−0.123541	−	0.380221i
$974$	−1.75535	+	5.40242i	−0.0562452	+	0.173105i
$975$	0.827453	+	0.601179i	0.0264997	+	0.0192532i
$976$	15.9380	−	49.0520i	0.510162	−	1.57012i
$977$	−0.750719	+	2.31048i	−0.0240176	+	0.0739187i	−0.962347	−	0.271824i	$-0.912373\pi$
$977$	−0.750719	+	2.31048i	−0.0240176	+	0.0739187i	0.938329	+	0.345743i	$0.112373\pi$
$978$	−1.63804	−	1.19011i	−0.0523788	−	0.0380554i
$979$	−3.16576	+	9.74320i	−0.101178	+	0.311394i
$980$	−0.00300088	−	0.00923577i	−9.58597e−5	−	0.000295026i
$981$	−2.78460	+	2.02313i	−0.0889053	+	0.0645935i
$982$	−1.27189	−	3.91446i	−0.0405875	−	0.124915i
$983$	46.3098	+	33.6460i	1.47705	+	1.07314i	0.978492	+	0.206286i	$0.0661378\pi$
$983$	46.3098	+	33.6460i	1.47705	+	1.07314i	0.498560	+	0.866855i	$0.333862\pi$
$984$	−4.98202	−	3.61965i	−0.158821	−	0.115390i
$985$	8.45876	−	6.14565i	0.269519	−	0.195817i
$986$	−4.30968			−0.137248
$987$	−13.2751			−0.422550
$988$	11.6242	−	8.44544i	0.369814	−	0.268685i
$989$	−0.278000	+	0.855597i	−0.00883989	+	0.0272064i
$990$	0.647929	+	1.99412i	0.0205925	+	0.0633774i
$991$	16.3359			0.518928			0.259464	−	0.965753i	$-0.416454\pi$
$991$	16.3359			0.518928			0.259464	+	0.965753i	$0.416454\pi$
$992$	15.7037	−	0.782572i	0.498593	−	0.0248467i
$993$	7.08014			0.224681
$994$	1.05453	+	3.24550i	0.0334476	+	0.102941i
$995$	0.167891	−	0.516714i	0.00532249	−	0.0163809i
$996$	−8.16197	+	5.93002i	−0.258622	+	0.187900i
$997$	24.3926			0.772522			0.386261	−	0.922389i	$-0.373766\pi$
$997$	24.3926			0.772522			0.386261	+	0.922389i	$0.373766\pi$
$998$	−5.54745			−0.175601
$999$	18.3279	−	13.3160i	0.579869	−	0.421299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.d.66.6	✓	48
31.8	even	5	inner	403.2.k.d.287.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.d.66.6	✓	48	1.1	even	1	trivial
403.2.k.d.287.6	yes	48	31.8	even	5	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.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0757307 - 0.233075i) q^{2} +(0.263551 - 0.811126i) q^{3} +(1.56945 - 1.14027i) q^{4} -2.48983 q^{5} -0.209012 q^{6} +(2.14015 - 1.55491i) q^{7} +(-0.781154 - 0.567542i) q^{8} +(1.83859 + 1.33581i) q^{9} +O(q^{10})\)	\(q+(-0.0757307 - 0.233075i) q^{2} +(0.263551 - 0.811126i) q^{3} +(1.56945 - 1.14027i) q^{4} -2.48983 q^{5} -0.209012 q^{6} +(2.14015 - 1.55491i) q^{7} +(-0.781154 - 0.567542i) q^{8} +(1.83859 + 1.33581i) q^{9} +(0.188556 + 0.580316i) q^{10} +(1.22326 - 0.888750i) q^{11} +(-0.511273 - 1.57354i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(-0.524486 - 0.381061i) q^{14} +(-0.656195 + 2.01956i) q^{15} +(1.12583 - 3.46494i) q^{16} +(-1.83185 - 1.33092i) q^{17} +(0.172107 - 0.529690i) q^{18} +(-2.28875 - 7.04404i) q^{19} +(-3.90765 + 2.83907i) q^{20} +(-0.697190 - 2.14573i) q^{21} +(-0.299784 - 0.217806i) q^{22} +(-0.523847 - 0.380597i) q^{23} +(-0.666222 + 0.484038i) q^{24} +1.19923 q^{25} +0.245070 q^{26} +(3.63802 - 2.64318i) q^{27} +(1.58583 - 4.88069i) q^{28} +(2.39997 + 7.38634i) q^{29} +0.520404 q^{30} +(-5.56086 + 0.277118i) q^{31} -2.82397 q^{32} +(-0.398497 - 1.22645i) q^{33} +(-0.171477 + 0.527751i) q^{34} +(-5.32860 + 3.87146i) q^{35} +4.40874 q^{36} +5.03787 q^{37} +(-1.46846 + 1.06690i) q^{38} +(0.689985 + 0.501303i) q^{39} +(1.94494 + 1.41308i) q^{40} +(2.31083 + 7.11202i) q^{41} +(-0.447317 + 0.324995i) q^{42} +(-0.429337 - 1.32136i) q^{43} +(0.906425 - 2.78969i) q^{44} +(-4.57776 - 3.32593i) q^{45} +(-0.0490364 + 0.150919i) q^{46} +(1.81824 - 5.59596i) q^{47} +(-2.51379 - 1.82637i) q^{48} +(-0.000621286 + 0.00191212i) q^{49} +(-0.0908187 - 0.279511i) q^{50} +(-1.56233 + 1.13510i) q^{51} +(0.599475 + 1.84499i) q^{52} +(4.49661 + 3.26698i) q^{53} +(-0.891569 - 0.647763i) q^{54} +(-3.04570 + 2.21283i) q^{55} -2.55426 q^{56} -6.31680 q^{57} +(1.53982 - 1.11875i) q^{58} +(-3.21810 + 9.90429i) q^{59} +(1.27298 + 3.91783i) q^{60} +14.1567 q^{61} +(0.485717 + 1.27511i) q^{62} +6.01191 q^{63} +(-2.03779 - 6.27168i) q^{64} +(0.769399 - 2.36797i) q^{65} +(-0.255676 + 0.185759i) q^{66} +10.3461 q^{67} -4.39260 q^{68} +(-0.446773 + 0.324599i) q^{69} +(1.30588 + 0.948776i) q^{70} +(-4.25850 - 3.09398i) q^{71} +(-0.678090 - 2.08695i) q^{72} +(-3.20708 + 2.33008i) q^{73} +(-0.381521 - 1.17420i) q^{74} +(0.316059 - 0.972729i) q^{75} +(-11.6242 - 8.44544i) q^{76} +(1.23603 - 3.80412i) q^{77} +(0.0645883 - 0.198782i) q^{78} +(12.5917 + 9.14838i) q^{79} +(-2.80311 + 8.62709i) q^{80} +(0.921684 + 2.83665i) q^{81} +(1.48263 - 1.07720i) q^{82} +(-1.88430 - 5.79927i) q^{83} +(-3.54091 - 2.57262i) q^{84} +(4.56099 + 3.31376i) q^{85} +(-0.275463 + 0.200135i) q^{86} +6.62376 q^{87} -1.45996 q^{88} +(-5.48141 + 3.98247i) q^{89} +(-0.428516 + 1.31884i) q^{90} +(0.817465 + 2.51590i) q^{91} -1.25613 q^{92} +(-1.24079 + 4.58359i) q^{93} -1.44198 q^{94} +(5.69858 + 17.5384i) q^{95} +(-0.744259 + 2.29059i) q^{96} +(-14.3951 + 10.4587i) q^{97} +0.000492718 q^{98} +3.43627 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9}+O(q^{10}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9	\( 48 q + 7 q^{2} - 2 q^{3} - 7 q^{4} - 12 q^{5} - 10 q^{6} + 25 q^{7} - 14 q^{8} - 8 q^{9} - 19 q^{10} - 9 q^{11} + 15 q^{12} + 12 q^{13} - 25 q^{14} - 30 q^{15} - 21 q^{16} + 11 q^{17} + 17 q^{18} + 36 q^{19} + 30 q^{20} + 11 q^{21} + 15 q^{22} - 7 q^{23} - 20 q^{24} - 16 q^{25} + 8 q^{26} - 5 q^{27} - 9 q^{28} + 12 q^{29} + 18 q^{30} + 22 q^{31} - 76 q^{32} - 49 q^{33} - 26 q^{34} + 8 q^{35} + 2 q^{36} + 64 q^{37} - 27 q^{38} - 3 q^{39} - 24 q^{40} + 46 q^{41} + 20 q^{42} - 28 q^{43} - 23 q^{45} + 34 q^{46} + 5 q^{47} - 20 q^{48} - 11 q^{49} + 9 q^{50} + 59 q^{51} + 17 q^{52} + 23 q^{53} + 41 q^{54} - 10 q^{55} - 60 q^{56} + 24 q^{57} - 37 q^{58} + 71 q^{59} - 72 q^{60} + 22 q^{61} + 43 q^{62} - 106 q^{63} - 52 q^{64} + 2 q^{65} - 21 q^{66} - 56 q^{67} - 104 q^{68} - 12 q^{69} - 32 q^{70} - 36 q^{71} + 147 q^{72} - 12 q^{73} + 10 q^{74} + 34 q^{75} - 49 q^{76} - 30 q^{77} + 5 q^{78} - 70 q^{79} + q^{81} + 130 q^{82} + 11 q^{83} + 77 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} + 96 q^{88} - 40 q^{89} - 48 q^{90} + 10 q^{91} + 112 q^{92} + 50 q^{93} + 78 q^{94} + 41 q^{95} - 75 q^{96} - 47 q^{97} - 46 q^{98} + 46 q^{99}+O(q^{100}) \) 48 * q + 7 * q^2 - 2 * q^3 - 7 * q^4 - 12 * q^5 - 10 * q^6 + 25 * q^7 - 14 * q^8 - 8 * q^9 - 19 * q^10 - 9 * q^11 + 15 * q^12 + 12 * q^13 - 25 * q^14 - 30 * q^15 - 21 * q^16 + 11 * q^17 + 17 * q^18 + 36 * q^19 + 30 * q^20 + 11 * q^21 + 15 * q^22 - 7 * q^23 - 20 * q^24 - 16 * q^25 + 8 * q^26 - 5 * q^27 - 9 * q^28 + 12 * q^29 + 18 * q^30 + 22 * q^31 - 76 * q^32 - 49 * q^33 - 26 * q^34 + 8 * q^35 + 2 * q^36 + 64 * q^37 - 27 * q^38 - 3 * q^39 - 24 * q^40 + 46 * q^41 + 20 * q^42 - 28 * q^43 - 23 * q^45 + 34 * q^46 + 5 * q^47 - 20 * q^48 - 11 * q^49 + 9 * q^50 + 59 * q^51 + 17 * q^52 + 23 * q^53 + 41 * q^54 - 10 * q^55 - 60 * q^56 + 24 * q^57 - 37 * q^58 + 71 * q^59 - 72 * q^60 + 22 * q^61 + 43 * q^62 - 106 * q^63 - 52 * q^64 + 2 * q^65 - 21 * q^66 - 56 * q^67 - 104 * q^68 - 12 * q^69 - 32 * q^70 - 36 * q^71 + 147 * q^72 - 12 * q^73 + 10 * q^74 + 34 * q^75 - 49 * q^76 - 30 * q^77 + 5 * q^78 - 70 * q^79 + q^81 + 130 * q^82 + 11 * q^83 + 77 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 + 96 * q^88 - 40 * q^89 - 48 * q^90 + 10 * q^91 + 112 * q^92 + 50 * q^93 + 78 * q^94 + 41 * q^95 - 75 * q^96 - 47 * q^97 - 46 * q^98 + 46 * q^99

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