LMFDB - Embedded newform 209.2.e.b.45.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,2,Mod(45,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, 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("209.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 14 x^{16} - 11 x^{15} + 130 x^{14} - 92 x^{13} + 629 x^{12} - 276 x^{11} + 2060 x^{10} + \cdots + 9 $ x^18 - x^17 + 14x^16 - 11x^15 + 130x^14 - 92x^13 + 629x^12 - 276x^11 + 2060x^10 - 681x^9 + 3955x^8 - 115x^7 + 4735x^6 + 105x^5 + 2904x^4 + 1230x^3 + 639x^2 + 81x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			45.8
Root			$1.00688 + 1.74398i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00688 + 1.74398i) q^{2} +(-1.29029 - 2.23484i) q^{3} +(-1.02763 + 1.77991i) q^{4} +(-1.77613 - 3.07635i) q^{5} +(2.59834 - 4.50045i) q^{6} -4.09817 q^{7} -0.111292 q^{8} +(-1.82967 + 3.16909i) q^{9} +O(q^{10})$	\(q+(1.00688 + 1.74398i) q^{2} +(-1.29029 - 2.23484i) q^{3} +(-1.02763 + 1.77991i) q^{4} +(-1.77613 - 3.07635i) q^{5} +(2.59834 - 4.50045i) q^{6} -4.09817 q^{7} -0.111292 q^{8} +(-1.82967 + 3.16909i) q^{9} +(3.57672 - 6.19505i) q^{10} -1.00000 q^{11} +5.30376 q^{12} +(2.55568 - 4.42656i) q^{13} +(-4.12638 - 7.14710i) q^{14} +(-4.58343 + 7.93873i) q^{15} +(1.94321 + 3.36573i) q^{16} +(0.559554 + 0.969175i) q^{17} -7.36908 q^{18} +(4.34935 + 0.288300i) q^{19} +7.30084 q^{20} +(5.28780 + 9.15875i) q^{21} +(-1.00688 - 1.74398i) q^{22} +(0.629766 - 1.09079i) q^{23} +(0.143598 + 0.248719i) q^{24} +(-3.80928 + 6.59786i) q^{25} +10.2931 q^{26} +1.70149 q^{27} +(4.21141 - 7.29438i) q^{28} +(3.20960 - 5.55920i) q^{29} -18.4599 q^{30} -0.563149 q^{31} +(-4.02446 + 6.97057i) q^{32} +(1.29029 + 2.23484i) q^{33} +(-1.12681 + 1.95170i) q^{34} +(7.27888 + 12.6074i) q^{35} +(-3.76046 - 6.51331i) q^{36} -1.00067 q^{37} +(3.87651 + 7.87545i) q^{38} -13.1902 q^{39} +(0.197669 + 0.342372i) q^{40} +(-2.90088 - 5.02447i) q^{41} +(-10.6484 + 18.4436i) q^{42} +(-3.45596 - 5.98589i) q^{43} +(1.02763 - 1.77991i) q^{44} +12.9989 q^{45} +2.53641 q^{46} +(1.17648 - 2.03773i) q^{47} +(5.01458 - 8.68551i) q^{48} +9.79497 q^{49} -15.3420 q^{50} +(1.44397 - 2.50103i) q^{51} +(5.25259 + 9.09776i) q^{52} +(6.48991 - 11.2408i) q^{53} +(1.71320 + 2.96735i) q^{54} +(1.77613 + 3.07635i) q^{55} +0.456093 q^{56} +(-4.96760 - 10.0921i) q^{57} +12.9268 q^{58} +(3.10390 + 5.37611i) q^{59} +(-9.42016 - 16.3162i) q^{60} +(-2.68195 + 4.64528i) q^{61} +(-0.567026 - 0.982118i) q^{62} +(7.49830 - 12.9874i) q^{63} -8.43585 q^{64} -18.1569 q^{65} +(-2.59834 + 4.50045i) q^{66} +(-5.01943 + 8.69391i) q^{67} -2.30006 q^{68} -3.25031 q^{69} +(-14.6580 + 25.3884i) q^{70} +(-0.778159 - 1.34781i) q^{71} +(0.203628 - 0.352693i) q^{72} +(-3.65200 - 6.32545i) q^{73} +(-1.00756 - 1.74515i) q^{74} +19.6602 q^{75} +(-4.98269 + 7.44520i) q^{76} +4.09817 q^{77} +(-13.2810 - 23.0034i) q^{78} +(7.30677 + 12.6557i) q^{79} +(6.90278 - 11.9560i) q^{80} +(3.29361 + 5.70471i) q^{81} +(5.84170 - 10.1181i) q^{82} +3.84888 q^{83} -21.7357 q^{84} +(1.98768 - 3.44276i) q^{85} +(6.95950 - 12.0542i) q^{86} -16.5652 q^{87} +0.111292 q^{88} +(0.742284 - 1.28567i) q^{89} +(13.0884 + 22.6698i) q^{90} +(-10.4736 + 18.1408i) q^{91} +(1.29434 + 2.24186i) q^{92} +(0.726623 + 1.25855i) q^{93} +4.73833 q^{94} +(-6.83811 - 13.8922i) q^{95} +20.7708 q^{96} +(8.33449 + 14.4358i) q^{97} +(9.86240 + 17.0822i) q^{98} +(1.82967 - 3.16909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) $ 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00688	+	1.74398i	0.711975	+	1.23318i	0.964115	+	0.265486i	$0.0855323\pi$
$2$	1.00688	+	1.74398i	0.711975	+	1.23318i	−0.252140	+	0.967691i	$0.581134\pi$
$3$	−1.29029	−	2.23484i	−0.744947	−	1.29029i	−0.950220	−	0.311581i	$-0.899142\pi$
$3$	−1.29029	−	2.23484i	−0.744947	−	1.29029i	0.205273	−	0.978705i	$-0.434192\pi$
$4$	−1.02763	+	1.77991i	−0.513816	+	0.889956i
$5$	−1.77613	−	3.07635i	−0.794310	−	1.37578i	−0.923277	−	0.384136i	$-0.874499\pi$
$5$	−1.77613	−	3.07635i	−0.794310	−	1.37578i	0.128967	−	0.991649i	$-0.458834\pi$
$6$	2.59834	−	4.50045i	1.06077	−	1.83730i
$7$	−4.09817			−1.54896			−0.774481	−	0.632598i	$-0.781989\pi$
$7$	−4.09817			−1.54896			−0.774481	+	0.632598i	$0.781989\pi$
$8$	−0.111292			−0.0393476
$9$	−1.82967	+	3.16909i	−0.609891	+	1.05636i
$10$	3.57672	−	6.19505i	1.13106	−	1.95905i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	5.30376			1.53106
$13$	2.55568	−	4.42656i	0.708817	−	1.22771i	−0.256479	−	0.966550i	$-0.582562\pi$
$13$	2.55568	−	4.42656i	0.708817	−	1.22771i	0.965296	−	0.261157i	$-0.0841042\pi$
$14$	−4.12638	−	7.14710i	−1.10282	−	1.91014i
$15$	−4.58343	+	7.93873i	−1.18344	+	2.04977i
$16$	1.94321	+	3.36573i	0.485802	+	0.841433i
$17$	0.559554	+	0.969175i	0.135712	+	0.235060i	0.925869	−	0.377844i	$-0.123335\pi$
$17$	0.559554	+	0.969175i	0.135712	+	0.235060i	−0.790157	+	0.612904i	$0.790001\pi$
$18$	−7.36908			−1.73691
$19$	4.34935	+	0.288300i	0.997810	+	0.0661406i
$19$	4.34935	+	0.288300i	0.997810	+	0.0661406i
$20$	7.30084			1.63252
$21$	5.28780	+	9.15875i	1.15389	+	1.99860i
$22$	−1.00688	−	1.74398i	−0.214668	−	0.371817i
$23$	0.629766	−	1.09079i	0.131315	−	0.227445i	−0.792869	−	0.609393i	$-0.791413\pi$
$23$	0.629766	−	1.09079i	0.131315	−	0.227445i	0.924184	+	0.381948i	$0.124747\pi$
$24$	0.143598	+	0.248719i	0.0293119	+	0.0507696i
$25$	−3.80928	+	6.59786i	−0.761855	+	1.31957i
$26$	10.2931			2.01864
$27$	1.70149			0.327451
$28$	4.21141	−	7.29438i	0.795882	−	1.37851i
$29$	3.20960	−	5.55920i	0.596008	−	1.03232i	−0.397395	−	0.917647i	$-0.630086\pi$
$29$	3.20960	−	5.55920i	0.596008	−	1.03232i	0.993404	−	0.114669i	$-0.0365808\pi$
$30$	−18.4599			−3.37031
$31$	−0.563149			−0.101145			−0.0505723	−	0.998720i	$-0.516105\pi$
$31$	−0.563149			−0.101145			−0.0505723	+	0.998720i	$0.516105\pi$
$32$	−4.02446	+	6.97057i	−0.711431	+	1.23223i
$33$	1.29029	+	2.23484i	0.224610	+	0.389036i
$34$	−1.12681	+	1.95170i	−0.193247	+	0.334713i
$35$	7.27888	+	12.6074i	1.23035	+	2.13104i
$36$	−3.76046	−	6.51331i	−0.626744	−	1.08555i
$37$	−1.00067			−0.164509			−0.0822547	−	0.996611i	$-0.526212\pi$
$37$	−1.00067			−0.164509			−0.0822547	+	0.996611i	$0.526212\pi$
$38$	3.87651	+	7.87545i	0.628853	+	1.27757i
$39$	−13.1902			−2.11212
$40$	0.197669	+	0.342372i	0.0312542	+	0.0541338i
$41$	−2.90088	−	5.02447i	−0.453041	−	0.784690i	0.545532	−	0.838090i	$-0.316328\pi$
$41$	−2.90088	−	5.02447i	−0.453041	−	0.784690i	−0.998573	+	0.0533997i	$0.982994\pi$
$42$	−10.6484	+	18.4436i	−1.64309	+	2.84591i
$43$	−3.45596	−	5.98589i	−0.527028	−	0.912840i	−0.999504	−	0.0314961i	$-0.989973\pi$
$43$	−3.45596	−	5.98589i	−0.527028	−	0.912840i	0.472476	−	0.881344i	$-0.343360\pi$
$44$	1.02763	−	1.77991i	0.154921	−	0.268332i
$45$	12.9989			1.93777
$46$	2.53641			0.373973
$47$	1.17648	−	2.03773i	0.171608	−	0.297233i	−0.767375	−	0.641199i	$-0.778437\pi$
$47$	1.17648	−	2.03773i	0.171608	−	0.297233i	0.938982	+	0.343966i	$0.111771\pi$
$48$	5.01458	−	8.68551i	0.723793	−	1.25365i
$49$	9.79497			1.39928
$50$	−15.3420			−2.16969
$51$	1.44397	−	2.50103i	0.202196	−	0.350214i
$52$	5.25259	+	9.09776i	0.728404	+	1.26163i
$53$	6.48991	−	11.2408i	0.891457	−	1.54405i	0.0533285	−	0.998577i	$-0.483017\pi$
$53$	6.48991	−	11.2408i	0.891457	−	1.54405i	0.838129	−	0.545472i	$-0.183650\pi$
$54$	1.71320	+	2.96735i	0.233137	+	0.403805i
$55$	1.77613	+	3.07635i	0.239493	+	0.414815i
$56$	0.456093			0.0609479
$57$	−4.96760	−	10.0921i	−0.657975	−	1.33673i
$58$	12.9268			1.69737
$59$	3.10390	+	5.37611i	0.404093	+	0.699910i	0.994215	−	0.107404i	$-0.0342539\pi$
$59$	3.10390	+	5.37611i	0.404093	+	0.699910i	−0.590122	+	0.807314i	$0.700921\pi$
$60$	−9.42016	−	16.3162i	−1.21614	−	2.10641i
$61$	−2.68195	+	4.64528i	−0.343389	+	0.594767i	−0.985060	−	0.172213i	$-0.944908\pi$
$61$	−2.68195	+	4.64528i	−0.343389	+	0.594767i	0.641671	+	0.766980i	$0.278241\pi$
$62$	−0.567026	−	0.982118i	−0.0720124	−	0.124729i
$63$	7.49830	−	12.9874i	0.944697	−	1.63626i
$64$	−8.43585			−1.05448
$65$	−18.1569			−2.25208
$66$	−2.59834	+	4.50045i	−0.319833	+	0.553967i
$67$	−5.01943	+	8.69391i	−0.613221	+	1.06213i	0.377472	+	0.926021i	$0.376793\pi$
$67$	−5.01943	+	8.69391i	−0.613221	+	1.06213i	−0.990694	+	0.136110i	$0.956540\pi$
$68$	−2.30006			−0.278924
$69$	−3.25031			−0.391291
$70$	−14.6580	+	25.3884i	−1.75196	+	3.03449i
$71$	−0.778159	−	1.34781i	−0.0923504	−	0.159956i	0.816149	−	0.577841i	$-0.196105\pi$
$71$	−0.778159	−	1.34781i	−0.0923504	−	0.159956i	−0.908500	+	0.417885i	$0.862771\pi$
$72$	0.203628	−	0.352693i	0.0239977	−	0.0415653i
$73$	−3.65200	−	6.32545i	−0.427434	−	0.740338i	0.569210	−	0.822192i	$-0.307249\pi$
$73$	−3.65200	−	6.32545i	−0.427434	−	0.740338i	−0.996644	+	0.0818545i	$0.973916\pi$
$74$	−1.00756	−	1.74515i	−0.117127	−	0.202869i
$75$	19.6602			2.27017
$76$	−4.98269	+	7.44520i	−0.571553	+	0.854023i
$77$	4.09817			0.467029
$78$	−13.2810	−	23.0034i	−1.50378	−	2.60462i
$79$	7.30677	+	12.6557i	0.822076	+	1.42388i	0.904133	+	0.427250i	$0.140518\pi$
$79$	7.30677	+	12.6557i	0.822076	+	1.42388i	−0.0820570	+	0.996628i	$0.526149\pi$
$80$	6.90278	−	11.9560i	0.771754	−	1.33672i
$81$	3.29361	+	5.70471i	0.365957	+	0.633856i
$82$	5.84170	−	10.1181i	0.645108	−	1.11736i
$83$	3.84888			0.422469			0.211235	−	0.977435i	$-0.432252\pi$
$83$	3.84888			0.422469			0.211235	+	0.977435i	$0.432252\pi$
$84$	−21.7357			−2.37156
$85$	1.98768	−	3.44276i	0.215594	−	0.373420i
$86$	6.95950	−	12.0542i	0.750462	−	1.29984i
$87$	−16.5652			−1.77598
$88$	0.111292			0.0118638
$89$	0.742284	−	1.28567i	0.0786820	−	0.136281i	−0.824000	−	0.566590i	$-0.808262\pi$
$89$	0.742284	−	1.28567i	0.0786820	−	0.136281i	0.902682	+	0.430309i	$0.141596\pi$
$90$	13.0884	+	22.6698i	1.37964	+	2.38961i
$91$	−10.4736	+	18.1408i	−1.09793	+	1.90167i
$92$	1.29434	+	2.24186i	0.134944	+	0.233730i
$93$	0.726623	+	1.25855i	0.0753473	+	0.130505i
$94$	4.73833			0.488721
$95$	−6.83811	−	13.8922i	−0.701575	−	1.42531i
$96$	20.7708			2.11991
$97$	8.33449	+	14.4358i	0.846240	+	1.46573i	0.884540	+	0.466464i	$0.154472\pi$
$97$	8.33449	+	14.4358i	0.846240	+	1.46573i	−0.0383009	+	0.999266i	$0.512195\pi$
$98$	9.86240	+	17.0822i	0.996253	+	1.72556i
$99$	1.82967	−	3.16909i	0.183889	−	0.318505i
$100$	−7.82908	−	13.5604i	−0.782908	−	1.35604i
$101$	7.74526	−	13.4152i	0.770683	−	1.33486i	−0.166507	−	0.986040i	$-0.553249\pi$
$101$	7.74526	−	13.4152i	0.770683	−	1.33486i	0.937189	−	0.348821i	$-0.113418\pi$
$102$	5.81564			0.575834
$103$	−6.13161			−0.604165			−0.302083	−	0.953282i	$-0.597682\pi$
$103$	−6.13161			−0.604165			−0.302083	+	0.953282i	$0.597682\pi$
$104$	−0.284426	+	0.492640i	−0.0278903	+	0.0483073i
$105$	18.7837	−	32.5342i	1.83310	−	3.17502i
$106$	26.1383			2.53878
$107$	−0.568664			−0.0549749			−0.0274874	−	0.999622i	$-0.508751\pi$
$107$	−0.568664			−0.0549749			−0.0274874	+	0.999622i	$0.508751\pi$
$108$	−1.74850	+	3.02850i	−0.168250	+	0.291417i
$109$	8.99308	+	15.5765i	0.861381	+	1.49196i	0.870596	+	0.491999i	$0.163733\pi$
$109$	8.99308	+	15.5765i	0.861381	+	1.49196i	−0.00921471	+	0.999958i	$0.502933\pi$
$110$	−3.57672	+	6.19505i	−0.341026	+	0.590675i
$111$	1.29115	+	2.23634i	0.122551	+	0.212264i
$112$	−7.96359	−	13.7933i	−0.752488	−	1.30335i
$113$	4.20608			0.395675			0.197838	−	0.980235i	$-0.436608\pi$
$113$	4.20608			0.395675			0.197838	+	0.980235i	$0.436608\pi$
$114$	12.5986	−	18.8250i	1.17996	−	1.76312i
$115$	−4.47418			−0.417220
$116$	6.59659	+	11.4256i	0.612478	+	1.06084i
$117$	9.35210	+	16.1983i	0.864602	+	1.49753i
$118$	−6.25053	+	10.8262i	−0.575408	+	0.996636i
$119$	−2.29314	−	3.97184i	−0.210212	−	0.364098i
$120$	0.510098	−	0.883516i	0.0465654	−	0.0806536i
$121$	1.00000			0.0909091
$122$	−10.8017			−0.977936
$123$	−7.48592	+	12.9660i	−0.674983	+	1.16910i
$124$	0.578710	−	1.00236i	0.0519697	−	0.0900142i
$125$	9.30179			0.831977
$126$	30.1997			2.69040
$127$	5.06726	−	8.77675i	0.449647	−	0.778811i	−0.548716	−	0.836009i	$-0.684883\pi$
$127$	5.06726	−	8.77675i	0.449647	−	0.778811i	0.998363	+	0.0571978i	$0.0182166\pi$
$128$	−0.444997	−	0.770758i	−0.0393326	−	0.0681260i
$129$	−8.91834	+	15.4470i	−0.785216	+	1.36003i
$130$	−18.2819	−	31.6651i	−1.60342	−	2.77721i
$131$	−0.633276	−	1.09687i	−0.0553296	−	0.0958336i	0.837034	−	0.547151i	$-0.184288\pi$
$131$	−0.633276	−	1.09687i	−0.0553296	−	0.0958336i	−0.892364	+	0.451317i	$0.850954\pi$
$132$	−5.30376			−0.461633
$133$	−17.8244	−	1.18150i	−1.54557	−	0.102449i
$134$	−20.2160			−1.74639
$135$	−3.02206	−	5.23436i	−0.260098	−	0.450502i
$136$	−0.0622738	−	0.107861i	−0.00533993	−	0.00924903i
$137$	5.91332	−	10.2422i	0.505209	−	0.875048i	−0.494773	−	0.869022i	$-0.664749\pi$
$137$	5.91332	−	10.2422i	0.505209	−	0.875048i	0.999982	−	0.00602554i	$-0.00191800\pi$
$138$	−3.27269	−	5.66846i	−0.278590	−	0.482531i
$139$	2.08925	−	3.61868i	0.177208	−	0.306932i	−0.763716	−	0.645553i	$-0.776627\pi$
$139$	2.08925	−	3.61868i	0.177208	−	0.306932i	0.940923	+	0.338621i	$0.109960\pi$
$140$	−29.9201			−2.52871
$141$	−6.07199			−0.511354
$142$	1.56703	−	2.71418i	0.131502	−	0.227769i
$143$	−2.55568	+	4.42656i	−0.213716	+	0.370168i
$144$	−14.2217			−1.18514
$145$	−22.8027			−1.89366
$146$	7.35428	−	12.7380i	0.608645	−	1.05420i
$147$	−12.6383	−	21.8902i	−1.04239	−	1.80547i
$148$	1.02832	−	1.78111i	0.0845276	−	0.146406i
$149$	6.43412	+	11.1442i	0.527104	+	0.912971i	0.999501	+	0.0315848i	$0.0100554\pi$
$149$	6.43412	+	11.1442i	0.527104	+	0.912971i	−0.472397	+	0.881386i	$0.656611\pi$
$150$	19.7956	+	34.2869i	1.61630	+	2.79952i
$151$	−9.13232			−0.743178			−0.371589	−	0.928397i	$-0.621187\pi$
$151$	−9.13232			−0.743178			−0.371589	+	0.928397i	$0.621187\pi$
$152$	−0.484048	−	0.0320854i	−0.0392615	−	0.00260247i
$153$	−4.09520			−0.331077
$154$	4.12638	+	7.14710i	0.332513	+	0.575930i
$155$	1.00023	+	1.73244i	0.0803401	+	0.139153i
$156$	13.5547	−	23.4774i	1.08524	−	1.87970i
$157$	0.569186	+	0.985860i	0.0454260	+	0.0786802i	0.887844	−	0.460144i	$-0.152202\pi$
$157$	0.569186	+	0.985860i	0.0454260	+	0.0786802i	−0.842418	+	0.538824i	$0.818869\pi$
$158$	−14.7142	+	25.4857i	−1.17060	+	2.02753i
$159$	−33.4953			−2.65635
$160$	28.5919			2.26039
$161$	−2.58088	+	4.47022i	−0.203402	+	0.352303i
$162$	−6.63258	+	11.4880i	−0.521105	+	0.902580i
$163$	10.7609			0.842856			0.421428	−	0.906862i	$-0.361529\pi$
$163$	10.7609			0.842856			0.421428	+	0.906862i	$0.361529\pi$
$164$	11.9242			0.931120
$165$	4.58343	−	7.93873i	0.356820	−	0.618030i
$166$	3.87537	+	6.71234i	0.300787	+	0.520979i
$167$	8.07362	−	13.9839i	0.624756	−	1.08211i	−0.363833	−	0.931464i	$-0.618532\pi$
$167$	8.07362	−	13.9839i	0.624756	−	1.08211i	0.988588	−	0.150644i	$-0.0481347\pi$
$168$	−0.588490	−	1.01929i	−0.0454030	−	0.0786402i
$169$	−6.56296	−	11.3674i	−0.504843	−	0.874414i
$170$	8.00546			0.613991
$171$	−8.87154	+	13.2560i	−0.678424	+	1.01371i
$172$	14.2058			1.08318
$173$	−11.2891	−	19.5533i	−0.858296	−	1.48661i	−0.873553	−	0.486729i	$-0.838190\pi$
$173$	−11.2891	−	19.5533i	−0.858296	−	1.48661i	0.0152572	−	0.999884i	$-0.495143\pi$
$174$	−16.6793	−	28.8893i	−1.26445	−	2.19009i
$175$	15.6111	−	27.0391i	1.18008	−	2.04397i
$176$	−1.94321	−	3.36573i	−0.146475	−	0.253702i
$177$	8.00983	−	13.8734i	0.602055	−	1.04279i
$178$	2.98958			0.224078
$179$	−24.2041			−1.80910			−0.904549	−	0.426369i	$-0.859793\pi$
$179$	−24.2041			−1.80910			−0.904549	+	0.426369i	$0.859793\pi$
$180$	−13.3581	+	23.1370i	−0.995657	+	1.72453i
$181$	−0.716984	+	1.24185i	−0.0532930	+	0.0923062i	−0.891441	−	0.453136i	$-0.850305\pi$
$181$	−0.716984	+	1.24185i	−0.0532930	+	0.0923062i	0.838148	+	0.545443i	$0.183638\pi$
$182$	−42.1828			−3.12679
$183$	13.8419			1.02322
$184$	−0.0700878	+	0.121396i	−0.00516694	+	0.00894940i
$185$	1.77732	+	3.07841i	0.130671	+	0.226329i
$186$	−1.46325	+	2.53442i	−0.107291	+	0.185833i
$187$	−0.559554	−	0.969175i	−0.0409186	−	0.0708731i
$188$	2.41798	+	4.18807i	0.176350	+	0.305446i
$189$	−6.97298			−0.507209
$190$	17.3424	−	25.9133i	1.25815	−	1.87995i
$191$	0.706099			0.0510915			0.0255458	−	0.999674i	$-0.491868\pi$
$191$	0.706099			0.0510915			0.0255458	+	0.999674i	$0.491868\pi$
$192$	10.8846	+	18.8528i	0.785532	+	1.36058i
$193$	3.46026	+	5.99334i	0.249075	+	0.431410i	0.963269	−	0.268537i	$-0.0865402\pi$
$193$	3.46026	+	5.99334i	0.249075	+	0.431410i	−0.714195	+	0.699947i	$0.753207\pi$
$194$	−16.7837	+	29.0703i	−1.20500	+	2.08713i
$195$	23.4275	+	40.5777i	1.67768	+	2.90583i
$196$	−10.0656	+	17.4342i	−0.718974	+	1.24530i
$197$	−0.315004			−0.0224431			−0.0112215	−	0.999937i	$-0.503572\pi$
$197$	−0.315004			−0.0224431			−0.0112215	+	0.999937i	$0.503572\pi$
$198$	7.36908			0.523697
$199$	−3.03859	+	5.26299i	−0.215400	+	0.373084i	−0.953396	−	0.301721i	$-0.902439\pi$
$199$	−3.03859	+	5.26299i	−0.215400	+	0.373084i	0.737996	+	0.674805i	$0.235772\pi$
$200$	0.423942	−	0.734288i	0.0299772	−	0.0519220i
$201$	25.9060			1.82727
$202$	31.1943			2.19483
$203$	−13.1535	+	22.7825i	−0.923194	+	1.59902i
$204$	2.96774	+	5.14027i	0.207783	+	0.359891i
$205$	−10.3047	+	17.8482i	−0.719710	+	1.24657i
$206$	−6.17382	−	10.6934i	−0.430150	−	0.745042i
$207$	2.30453	+	3.99156i	0.160176	+	0.277433i
$208$	19.8648			1.37738
$209$	−4.34935	−	0.288300i	−0.300851	−	0.0199421i
$210$	75.6519			5.22048
$211$	−0.750068	−	1.29916i	−0.0516368	−	0.0894376i	0.839052	−	0.544052i	$-0.183110\pi$
$211$	−0.750068	−	1.29916i	−0.0516368	−	0.0894376i	−0.890688	+	0.454614i	$0.849777\pi$
$212$	13.3385	+	23.1029i	0.916091	+	1.58672i
$213$	−2.00809	+	3.47812i	−0.137592	+	0.238317i
$214$	−0.572579	−	0.991736i	−0.0391407	−	0.0677937i
$215$	−12.2765	+	21.2634i	−0.837247	+	1.45015i
$216$	−0.189362			−0.0128844
$217$	2.30788			0.156669
$218$	−18.1100	+	31.3674i	−1.22656	+	2.12447i
$219$	−9.42424	+	16.3233i	−0.636831	+	1.10302i
$220$	−7.30084			−0.492222
$221$	5.72015			0.384779
$222$	−2.60008	+	4.50347i	−0.174506	+	0.302253i
$223$	−0.556842	−	0.964479i	−0.0372889	−	0.0645863i	0.846779	−	0.531945i	$-0.178539\pi$
$223$	−0.556842	−	0.964479i	−0.0372889	−	0.0645863i	−0.884068	+	0.467359i	$0.845206\pi$
$224$	16.4929	−	28.5666i	1.10198	−	1.90868i
$225$	−13.9395	−	24.1439i	−0.929297	−	1.60959i
$226$	4.23504	+	7.33531i	0.281711	+	0.487937i
$227$	7.44869			0.494387			0.247193	−	0.968966i	$-0.420492\pi$
$227$	7.44869			0.494387			0.247193	+	0.968966i	$0.420492\pi$
$228$	23.0679	+	1.52907i	1.52771	+	0.101265i
$229$	−8.19763			−0.541715			−0.270857	−	0.962620i	$-0.587307\pi$
$229$	−8.19763			−0.541715			−0.270857	+	0.962620i	$0.587307\pi$
$230$	−4.50499	−	7.80286i	−0.297050	−	0.514506i
$231$	−5.28780	−	9.15875i	−0.347912	−	0.602601i
$232$	−0.357203	+	0.618693i	−0.0234515	+	0.0406192i
$233$	3.85323	+	6.67399i	0.252433	+	0.437227i	0.964195	−	0.265193i	$-0.0854358\pi$
$233$	3.85323	+	6.67399i	0.252433	+	0.437227i	−0.711762	+	0.702421i	$0.752102\pi$
$234$	−18.8330	+	32.6197i	−1.23115	+	2.13241i
$235$	−8.35834			−0.545238
$236$	−12.7587			−0.830518
$237$	18.8556	−	32.6589i	1.22481	−	2.12143i
$238$	4.61786	−	7.99837i	0.299332	−	0.518458i
$239$	11.0555			0.715121			0.357560	−	0.933890i	$-0.383609\pi$
$239$	11.0555			0.715121			0.357560	+	0.933890i	$0.383609\pi$
$240$	−35.6262			−2.29966
$241$	−3.66606	+	6.34980i	−0.236152	+	0.409027i	−0.959607	−	0.281345i	$-0.909220\pi$
$241$	−3.66606	+	6.34980i	−0.236152	+	0.409027i	0.723455	+	0.690371i	$0.242553\pi$
$242$	1.00688	+	1.74398i	0.0647250	+	0.112107i
$243$	11.0516	−	19.1420i	0.708963	−	1.22796i
$244$	−5.51212	−	9.54727i	−0.352877	−	0.611202i
$245$	−17.3971	−	30.1327i	−1.11146	−	1.92511i
$246$	−30.1498			−1.92228
$247$	12.3917	−	18.5159i	0.788466	−	1.17814i
$248$	0.0626739			0.00397980
$249$	−4.96615	−	8.60162i	−0.314717	−	0.545106i
$250$	9.36583	+	16.2221i	0.592347	+	1.02597i
$251$	−5.17437	+	8.96227i	−0.326603	+	0.565693i	−0.981836	−	0.189734i	$-0.939237\pi$
$251$	−5.17437	+	8.96227i	−0.326603	+	0.565693i	0.655232	+	0.755427i	$0.272571\pi$
$252$	15.4110	+	26.6926i	0.970802	+	1.68148i
$253$	−0.629766	+	1.09079i	−0.0395930	+	0.0685771i
$254$	20.4086			1.28055
$255$	−10.2587			−0.642425
$256$	−7.53972	+	13.0592i	−0.471233	+	0.816199i
$257$	−12.5223	+	21.6893i	−0.781122	+	1.35294i	0.150167	+	0.988661i	$0.452019\pi$
$257$	−12.5223	+	21.6893i	−0.781122	+	1.35294i	−0.931289	+	0.364282i	$0.881314\pi$
$258$	−35.9189			−2.23622
$259$	4.10092			0.254819
$260$	18.6586	−	32.3176i	1.15716	−	2.00425i
$261$	11.7450	+	20.3430i	0.727000	+	1.25920i
$262$	1.27527	−	2.20883i	0.0787865	−	0.136462i
$263$	−1.79408	−	3.10744i	−0.110628	−	0.191613i	0.805396	−	0.592737i	$-0.201953\pi$
$263$	−1.79408	−	3.10744i	−0.110628	−	0.191613i	−0.916024	+	0.401124i	$0.868619\pi$
$264$	−0.143598	−	0.248719i	−0.00883786	−	0.0153076i
$265$	−46.1077			−2.83237
$266$	−15.8866	−	32.2749i	−0.974069	−	1.97890i
$267$	−3.83103			−0.234455
$268$	−10.3163	−	17.8683i	−0.630166	−	1.09148i
$269$	3.97289	+	6.88125i	0.242231	+	0.419557i	0.961350	−	0.275331i	$-0.0887873\pi$
$269$	3.97289	+	6.88125i	0.242231	+	0.419557i	−0.719118	+	0.694888i	$0.755454\pi$
$270$	6.08573	−	10.5408i	0.370366	−	0.641493i
$271$	−9.49124	−	16.4393i	−0.576552	−	0.998617i	−0.995871	−	0.0907779i	$-0.971065\pi$
$271$	−9.49124	−	16.4393i	−0.576552	−	0.998617i	0.419320	−	0.907839i	$-0.362269\pi$
$272$	−2.17466	+	3.76662i	−0.131858	+	0.228385i
$273$	54.0557			3.27160
$274$	23.8161			1.43878
$275$	3.80928	−	6.59786i	0.229708	−	0.397866i
$276$	3.34012	−	5.78527i	0.201052	−	0.348232i
$277$	6.53005			0.392353			0.196176	−	0.980569i	$-0.437147\pi$
$277$	6.53005			0.392353			0.196176	+	0.980569i	$0.437147\pi$
$278$	8.41452			0.504669
$279$	1.03038	−	1.78467i	0.0616871	−	0.106845i
$280$	−0.810080	−	1.40310i	−0.0484115	−	0.0838512i
$281$	4.74162	−	8.21273i	0.282862	−	0.489931i	−0.689227	−	0.724546i	$-0.742050\pi$
$281$	4.74162	−	8.21273i	0.282862	−	0.489931i	0.972088	+	0.234615i	$0.0753830\pi$
$282$	−6.11379	−	10.5894i	−0.364071	−	0.630589i
$283$	−3.82158	−	6.61917i	−0.227169	−	0.393469i	0.729799	−	0.683662i	$-0.239614\pi$
$283$	−3.82158	−	6.61917i	−0.227169	−	0.393469i	−0.956968	+	0.290193i	$0.906280\pi$
$284$	3.19864			0.189805
$285$	−22.2237	+	33.2070i	−1.31642	+	1.96701i
$286$	−10.2931			−0.608643
$287$	11.8883	+	20.5911i	0.701743	+	1.21545i
$288$	−14.7269	−	25.5077i	−0.867791	−	1.50306i
$289$	7.87380	−	13.6378i	0.463165	−	0.802225i
$290$	−22.9597	−	39.7673i	−1.34824	−	2.33522i
$291$	21.5077	−	37.2525i	1.26081	−	2.18378i
$292$	15.0117			0.878491
$293$	11.6478			0.680472			0.340236	−	0.940340i	$-0.389493\pi$
$293$	11.6478			0.680472			0.340236	+	0.940340i	$0.389493\pi$
$294$	25.4506	−	44.0818i	1.48431	−	2.57090i
$295$	11.0259	−	19.0973i	0.641950	−	1.11189i
$296$	0.111367			0.00647305
$297$	−1.70149			−0.0987303
$298$	−12.9568	+	22.4419i	−0.750569	+	1.30002i
$299$	−3.21895	−	5.57539i	−0.186157	−	0.322433i
$300$	−20.2035	+	34.9935i	−1.16645	+	2.02035i
$301$	14.1631	+	24.5312i	0.816346	+	1.41395i
$302$	−9.19519	−	15.9265i	−0.529124	−	0.916469i
$303$	−39.9744			−2.29647
$304$	7.48136	+	15.1990i	0.429085	+	0.871722i
$305$	19.0540			1.09103
$306$	−4.12339	−	7.14193i	−0.235719	−	0.408277i
$307$	−7.77605	−	13.4685i	−0.443802	−	0.768688i	0.554166	−	0.832406i	$-0.313037\pi$
$307$	−7.77605	−	13.4685i	−0.443802	−	0.768688i	−0.997968	+	0.0637182i	$0.979704\pi$
$308$	−4.21141	+	7.29438i	−0.239967	+	0.415636i
$309$	7.91152	+	13.7032i	0.450071	+	0.779545i
$310$	−2.01422	+	3.48874i	−0.114400	+	0.198147i
$311$	33.6852			1.91011			0.955057	−	0.296421i	$-0.0957933\pi$
$311$	33.6852			1.91011			0.955057	+	0.296421i	$0.0957933\pi$
$312$	1.46796			0.0831070
$313$	−13.1265	+	22.7358i	−0.741954	+	1.28510i	0.209650	+	0.977777i	$0.432768\pi$
$313$	−13.1265	+	22.7358i	−0.741954	+	1.28510i	−0.951604	+	0.307326i	$0.900566\pi$
$314$	−1.14621	+	1.98529i	−0.0646844	+	0.112037i
$315$	−53.2718			−3.00153
$316$	−30.0347			−1.68959
$317$	−13.9300	+	24.1275i	−0.782389	+	1.35514i	0.148157	+	0.988964i	$0.452666\pi$
$317$	−13.9300	+	24.1275i	−0.782389	+	1.35514i	−0.930546	+	0.366174i	$0.880667\pi$
$318$	−33.7259	−	58.4150i	−1.89126	−	3.27575i
$319$	−3.20960	+	5.55920i	−0.179703	+	0.311255i
$320$	14.9832	+	25.9516i	0.837584	+	1.45074i
$321$	0.733739	+	1.27087i	0.0409533	+	0.0709333i
$322$	−10.3946			−0.579269
$323$	2.15428	+	4.37661i	0.119868	+	0.243521i
$324$	−13.5385			−0.752139
$325$	19.4706	+	33.7240i	1.08003	+	1.87067i
$326$	10.8350	+	18.7667i	0.600093	+	1.03939i
$327$	23.2073	−	40.1962i	1.28337	−	2.22286i
$328$	0.322844	+	0.559182i	0.0178261	+	0.0308757i
$329$	−4.82142	+	8.35094i	−0.265813	+	0.460402i
$330$	18.4599			1.01619
$331$	−18.6253			−1.02374			−0.511870	−	0.859063i	$-0.671047\pi$
$331$	−18.6253			−1.02374			−0.511870	+	0.859063i	$0.671047\pi$
$332$	−3.95523	+	6.85066i	−0.217071	+	0.375979i
$333$	1.83090	−	3.17121i	0.100333	−	0.173781i
$334$	32.5168			1.77924
$335$	35.6607			1.94835
$336$	−20.5506	+	35.5947i	−1.12113	+	1.94185i
$337$	−7.41548	−	12.8440i	−0.403947	−	0.699657i	0.590251	−	0.807220i	$-0.299029\pi$
$337$	−7.41548	−	12.8440i	−0.403947	−	0.699657i	−0.994198	+	0.107563i	$0.965695\pi$
$338$	13.2163	−	22.8913i	0.718872	−	1.24512i
$339$	−5.42705	−	9.39992i	−0.294757	−	0.510534i
$340$	4.08521	+	7.07579i	0.221552	+	0.383739i
$341$	0.563149			0.0304962
$342$	−32.0507	−	2.12450i	−1.73310	−	0.114880i
$343$	−11.4542			−0.618471
$344$	0.384620	+	0.666181i	0.0207373	+	0.0359181i
$345$	5.77297	+	9.99908i	0.310806	+	0.538333i
$346$	22.7337	−	39.3759i	1.22217	−	2.11686i
$347$	−5.26910	−	9.12636i	−0.282860	−	0.489928i	0.689228	−	0.724545i	$-0.257950\pi$
$347$	−5.26910	−	9.12636i	−0.282860	−	0.489928i	−0.972088	+	0.234616i	$0.924617\pi$
$348$	17.0230	−	29.4846i	0.912526	−	1.58054i
$349$	18.8702			1.01010			0.505048	−	0.863091i	$-0.331475\pi$
$349$	18.8702			1.01010			0.505048	+	0.863091i	$0.331475\pi$
$350$	62.8741			3.36076
$351$	4.34845	−	7.53174i	0.232103	−	0.402014i
$352$	4.02446	−	6.97057i	0.214505	−	0.371533i
$353$	6.66031			0.354493			0.177246	−	0.984167i	$-0.443281\pi$
$353$	6.66031			0.354493			0.177246	+	0.984167i	$0.443281\pi$
$354$	32.2599			1.71459
$355$	−2.76422	+	4.78777i	−0.146710	+	0.254109i
$356$	1.52559	+	2.64240i	0.0808562	+	0.140047i
$357$	−5.91762	+	10.2496i	−0.313194	+	0.542467i
$358$	−24.3707	−	42.2113i	−1.28803	−	2.23094i
$359$	13.5684	+	23.5012i	0.716114	+	1.24035i	0.962528	+	0.271181i	$0.0874142\pi$
$359$	13.5684	+	23.5012i	0.716114	+	1.24035i	−0.246415	+	0.969165i	$0.579252\pi$
$360$	−1.44668			−0.0762466
$361$	18.8338	+	2.50784i	0.991251	+	0.131991i
$362$	−2.88768			−0.151773
$363$	−1.29029	−	2.23484i	−0.0677224	−	0.117299i
$364$	−21.5260	−	37.2841i	−1.12827	−	1.95422i
$365$	−12.9728	+	22.4696i	−0.679030	+	1.17611i
$366$	13.9372	+	24.1400i	0.728510	+	1.26182i
$367$	10.4742	−	18.1418i	0.546747	−	0.946993i	−0.451748	−	0.892146i	$-0.649199\pi$
$367$	10.4742	−	18.1418i	0.546747	−	0.946993i	0.998495	−	0.0548476i	$-0.0174673\pi$
$368$	4.89506			0.255173
$369$	21.2306			1.10522
$370$	−3.57912	+	6.19921i	−0.186069	+	0.322282i
$371$	−26.5967	+	46.0669i	−1.38083	+	2.39167i
$372$	−2.98681			−0.154859
$373$	12.4492			0.644598			0.322299	−	0.946638i	$-0.395544\pi$
$373$	12.4492			0.644598			0.322299	+	0.946638i	$0.395544\pi$
$374$	1.12681	−	1.95170i	0.0582661	−	0.100920i
$375$	−12.0020	−	20.7880i	−0.619779	−	1.07349i
$376$	−0.130933	+	0.226782i	−0.00675235	+	0.0116954i
$377$	−16.4054	−	28.4150i	−0.844922	−	1.46345i
$378$	−7.02098	−	12.1607i	−0.361120	−	0.625479i
$379$	−2.36527			−0.121496			−0.0607478	−	0.998153i	$-0.519349\pi$
$379$	−2.36527			−0.121496			−0.0607478	+	0.998153i	$0.519349\pi$
$380$	31.7539	+	2.10483i	1.62894	+	0.107976i
$381$	−26.1528			−1.33985
$382$	0.710960	+	1.23142i	0.0363759	+	0.0630049i
$383$	−2.03738	−	3.52885i	−0.104105	−	0.180316i	0.809267	−	0.587441i	$-0.199865\pi$
$383$	−2.03738	−	3.52885i	−0.104105	−	0.180316i	−0.913372	+	0.407125i	$0.866531\pi$
$384$	−1.14835	+	1.98900i	−0.0586014	+	0.101501i
$385$	−7.27888	−	12.6074i	−0.370966	−	0.642532i
$386$	−6.96815	+	12.0692i	−0.354670	+	0.614306i
$387$	25.2931			1.28572
$388$	−34.2592			−1.73925
$389$	15.3012	−	26.5024i	0.775800	−	1.34372i	−0.158544	−	0.987352i	$-0.550680\pi$
$389$	15.3012	−	26.5024i	0.775800	−	1.34372i	0.934344	−	0.356373i	$-0.115987\pi$
$390$	−47.1776	+	81.7140i	−2.38893	+	4.13775i
$391$	1.40955			0.0712841
$392$	−1.09010			−0.0550584
$393$	−1.63421	+	2.83054i	−0.0824351	+	0.142782i
$394$	−0.317172	−	0.549359i	−0.0159789	−	0.0276763i
$395$	25.9556	−	44.9564i	1.30597	−	2.26200i
$396$	3.76046	+	6.51331i	0.188970	+	0.327306i
$397$	16.4053	+	28.4148i	0.823359	+	1.42610i	0.903167	+	0.429290i	$0.141236\pi$
$397$	16.4053	+	28.4148i	0.823359	+	1.42610i	−0.0798075	+	0.996810i	$0.525431\pi$
$398$	−12.2380			−0.613438
$399$	20.3581	+	41.3591i	1.01918	+	2.07054i
$400$	−29.6089			−1.48044
$401$	−8.70563	−	15.0786i	−0.434738	−	0.752989i	0.562536	−	0.826773i	$-0.309826\pi$
$401$	−8.70563	−	15.0786i	−0.434738	−	0.752989i	−0.997274	+	0.0737838i	$0.976493\pi$
$402$	26.0844	+	45.1794i	1.30097	+	2.25335i
$403$	−1.43923	+	2.49281i	−0.0716930	+	0.124176i
$404$	15.9186	+	27.5718i	0.791979	+	1.37175i
$405$	11.6998	−	20.2646i	0.581367	−	1.00696i
$406$	−52.9762			−2.62916
$407$	1.00067			0.0496014
$408$	−0.160702	+	0.278344i	−0.00795593	+	0.0137801i
$409$	1.11047	−	1.92340i	0.0549094	−	0.0951059i	−0.837264	−	0.546799i	$-0.815846\pi$
$409$	1.11047	−	1.92340i	0.0549094	−	0.0951059i	0.892174	+	0.451693i	$0.149180\pi$
$410$	−41.5025			−2.04966
$411$	−30.5195			−1.50542
$412$	6.30104	−	10.9137i	0.310430	−	0.537680i
$413$	−12.7203	−	22.0322i	−0.625924	−	1.08413i
$414$	−4.64079	+	8.03809i	−0.228082	+	0.395050i
$415$	−6.83610	−	11.8405i	−0.335571	−	0.581226i
$416$	20.5704	+	35.6291i	1.00855	+	1.74686i
$417$	−10.7829			−0.528041
$418$	−3.87651	−	7.87545i	−0.189606	−	0.385201i
$419$	15.3405			0.749434			0.374717	−	0.927139i	$-0.377740\pi$
$419$	15.3405			0.749434			0.374717	+	0.927139i	$0.377740\pi$
$420$	38.6054	+	66.8665i	1.88375	+	3.26275i
$421$	13.5100	+	23.4000i	0.658437	+	1.14045i	0.981020	+	0.193905i	$0.0621154\pi$
$421$	13.5100	+	23.4000i	0.658437	+	1.14045i	−0.322583	+	0.946541i	$0.604551\pi$
$422$	1.51046	−	2.61620i	0.0735282	−	0.127355i
$423$	4.30515	+	7.45674i	0.209324	+	0.362559i
$424$	−0.722274	+	1.25101i	−0.0350767	+	0.0607547i
$425$	−8.52598			−0.413571
$426$	−8.08767			−0.391849
$427$	10.9911	−	19.0371i	0.531896	−	0.921270i
$428$	0.584378	−	1.01217i	0.0282470	−	0.0489252i
$429$	13.1902			0.636829
$430$	−49.4439			−2.38440
$431$	−2.43725	+	4.22143i	−0.117398	+	0.203339i	−0.918736	−	0.394873i	$-0.870789\pi$
$431$	−2.43725	+	4.22143i	−0.117398	+	0.203339i	0.801338	+	0.598212i	$0.204122\pi$
$432$	3.30634	+	5.72675i	0.159076	+	0.275528i
$433$	−5.95500	+	10.3144i	−0.286179	+	0.495677i	−0.972894	−	0.231250i	$-0.925719\pi$
$433$	−5.95500	+	10.3144i	−0.286179	+	0.495677i	0.686715	+	0.726926i	$0.259052\pi$
$434$	2.32377	+	4.02488i	0.111544	+	0.193201i
$435$	29.4220	+	50.9604i	1.41068	+	2.44336i
$436$	−36.9664			−1.77037
$437$	3.05355	−	4.56265i	0.146071	−	0.218261i
$438$	−37.9565			−1.81363
$439$	−8.36704	−	14.4921i	−0.399337	−	0.691672i	0.594307	−	0.804238i	$-0.297426\pi$
$439$	−8.36704	−	14.4921i	−0.399337	−	0.691672i	−0.993644	+	0.112566i	$0.964093\pi$
$440$	−0.197669	−	0.342372i	−0.00942349	−	0.0163220i
$441$	−17.9216	+	31.0411i	−0.853409	+	1.47815i
$442$	5.75953	+	9.97580i	0.273953	+	0.474501i
$443$	11.3895	−	19.7272i	0.541132	−	0.937268i	−0.457708	−	0.889103i	$-0.651329\pi$
$443$	11.3895	−	19.7272i	0.541132	−	0.937268i	0.998839	−	0.0481649i	$-0.0153373\pi$
$444$	−5.30732			−0.251874
$445$	−5.27357			−0.249991
$446$	1.12135	−	1.94224i	0.0530975	−	0.0919676i
$447$	16.6037	−	28.7585i	0.785328	−	1.36023i
$448$	34.5715			1.63335
$449$	−21.0257			−0.992264			−0.496132	−	0.868247i	$-0.665247\pi$
$449$	−21.0257			−0.992264			−0.496132	+	0.868247i	$0.665247\pi$
$450$	28.0709	−	48.6201i	1.32327	−	2.29198i
$451$	2.90088	+	5.02447i	0.136597	+	0.236593i
$452$	−4.32231	+	7.48646i	−0.203304	+	0.352133i
$453$	11.7833	+	20.4093i	0.553628	+	0.958911i
$454$	7.49997	+	12.9903i	0.351991	+	0.609666i
$455$	74.4098			3.48839
$456$	0.552854	+	1.12317i	0.0258898	+	0.0525972i
$457$	−33.8141			−1.58175			−0.790877	−	0.611975i	$-0.790375\pi$
$457$	−33.8141			−1.58175			−0.790877	+	0.611975i	$0.790375\pi$
$458$	−8.25407	−	14.2965i	−0.385687	−	0.668030i
$459$	0.952073	+	1.64904i	0.0444390	+	0.0769706i
$460$	4.59782	−	7.96365i	0.214374	−	0.371307i
$461$	−10.1323	−	17.5497i	−0.471909	−	0.817370i	0.527575	−	0.849509i	$-0.323102\pi$
$461$	−10.1323	−	17.5497i	−0.471909	−	0.817370i	−0.999483	+	0.0321386i	$0.989768\pi$
$462$	10.6484	−	18.4436i	0.495409	−	0.858074i
$463$	−17.8047			−0.827456			−0.413728	−	0.910401i	$-0.635774\pi$
$463$	−17.8047			−0.827456			−0.413728	+	0.910401i	$0.635774\pi$
$464$	24.9477			1.15817
$465$	2.58115	−	4.47069i	0.119698	−	0.207323i
$466$	−7.75951	+	13.4399i	−0.359452	+	0.622590i
$467$	−16.8853			−0.781361			−0.390680	−	0.920526i	$-0.627760\pi$
$467$	−16.8853			−0.781361			−0.390680	+	0.920526i	$0.627760\pi$
$468$	−38.4421			−1.77699
$469$	20.5705	−	35.6291i	0.949856	−	1.64520i
$470$	−8.41588	−	14.5767i	−0.388196	−	0.672375i
$471$	1.46883	−	2.54408i	0.0676799	−	0.117225i
$472$	−0.345438	−	0.598317i	−0.0159001	−	0.0275398i
$473$	3.45596	+	5.98589i	0.158905	+	0.275232i
$474$	75.9418			3.48812
$475$	−18.4701	+	27.5982i	−0.847465	+	1.26629i
$476$	9.42604			0.432042
$477$	23.7488	+	41.1341i	1.08738	+	1.88340i
$478$	11.1316	+	19.2805i	0.509148	+	0.881870i
$479$	−20.4174	+	35.3639i	−0.932893	+	1.61582i	−0.154545	+	0.987986i	$0.549391\pi$
$479$	−20.4174	+	35.3639i	−0.932893	+	1.61582i	−0.778348	+	0.627833i	$0.783942\pi$
$480$	−36.8917	−	63.8983i	−1.68387	−	2.91654i
$481$	−2.55739	+	4.42953i	−0.116607	+	0.201969i
$482$	−14.7652			−0.672536
$483$	13.3203			0.606095
$484$	−1.02763	+	1.77991i	−0.0467106	+	0.0809051i
$485$	29.6063	−	51.2796i	1.34435	−	2.32849i
$486$	44.5109			2.01905
$487$	37.0637			1.67952			0.839759	−	0.542959i	$-0.182696\pi$
$487$	37.0637			1.67952			0.839759	+	0.542959i	$0.182696\pi$
$488$	0.298479	−	0.516981i	0.0135115	−	0.0234026i
$489$	−13.8846	−	24.0488i	−0.627883	−	1.08753i
$490$	35.0338	−	60.6804i	1.58267	−	2.74126i
$491$	13.1133	+	22.7129i	0.591796	+	1.02502i	0.993991	+	0.109466i	$0.0349141\pi$
$491$	13.1133	+	22.7129i	0.591796	+	1.02502i	−0.402195	+	0.915554i	$0.631753\pi$
$492$	−15.3856	−	26.6486i	−0.693634	−	1.20141i
$493$	7.18378			0.323541
$494$	44.7683	+	2.96750i	2.01422	+	0.133514i
$495$	−12.9989			−0.584259
$496$	−1.09432	−	1.89541i	−0.0491362	−	0.0851064i
$497$	3.18902	+	5.52355i	0.143047	+	0.247765i
$498$	10.0007	−	17.3217i	0.448141	−	0.776203i
$499$	8.41284	+	14.5715i	0.376611	+	0.652309i	0.990567	−	0.137032i	$-0.0437562\pi$
$499$	8.41284	+	14.5715i	0.376611	+	0.652309i	−0.613956	+	0.789340i	$0.710423\pi$
$500$	−9.55882	+	16.5564i	−0.427484	+	0.740423i
$501$	−41.6691			−1.86164
$502$	−20.8400			−0.930133
$503$	2.56023	−	4.43445i	0.114155	−	0.197722i	−0.803287	−	0.595593i	$-0.796917\pi$
$503$	2.56023	−	4.43445i	0.114155	−	0.197722i	0.917442	+	0.397870i	$0.130251\pi$
$504$	−0.834500	+	1.44540i	−0.0371716	+	0.0643831i
$505$	−55.0264			−2.44864
$506$	−2.53641			−0.112757
$507$	−16.9362	+	29.3343i	−0.752163	+	1.30278i
$508$	10.4146	+	18.0386i	0.462072	+	0.800332i
$509$	−5.24697	+	9.08802i	−0.232568	+	0.402820i	−0.958563	−	0.284880i	$-0.908046\pi$
$509$	−5.24697	+	9.08802i	−0.232568	+	0.402820i	0.725995	+	0.687700i	$0.241379\pi$
$510$	−10.3293	−	17.8909i	−0.457390	−	0.792223i
$511$	14.9665	+	25.9227i	0.662079	+	1.14675i
$512$	−32.1465			−1.42069
$513$	7.40037	+	0.490539i	0.326734	+	0.0216578i
$514$	−50.4342			−2.22456
$515$	10.8905	+	18.8630i	0.479894	+	0.831201i
$516$	−18.3296	−	31.7477i	−0.806914	−	1.39762i
$517$	−1.17648	+	2.03773i	−0.0517416	+	0.0896191i
$518$	4.12915	+	7.15190i	0.181424	+	0.314236i
$519$	−29.1324	+	50.4588i	−1.27877	+	2.21489i
$520$	2.02071			0.0886140
$521$	−3.05739			−0.133946			−0.0669732	−	0.997755i	$-0.521334\pi$
$521$	−3.05739			−0.133946			−0.0669732	+	0.997755i	$0.521334\pi$
$522$	−23.6518	+	40.9661i	−1.03521	+	1.79304i
$523$	−18.8920	+	32.7218i	−0.826088	+	1.43083i	0.0749967	+	0.997184i	$0.476105\pi$
$523$	−18.8920	+	32.7218i	−0.826088	+	1.43083i	−0.901085	+	0.433643i	$0.857228\pi$
$524$	2.60310			0.113717
$525$	−80.5709			−3.51640
$526$	3.61286	−	6.25767i	0.157528	−	0.272847i
$527$	−0.315112	−	0.545790i	−0.0137265	−	0.0237750i
$528$	−5.01458	+	8.68551i	−0.218232	+	0.377988i
$529$	10.7068	+	18.5447i	0.465513	+	0.806292i
$530$	−46.4251	−	80.4107i	−2.01658	−	3.49282i
$531$	−22.7165			−0.985810
$532$	20.4199	−	30.5117i	0.885314	−	1.32285i
$533$	−29.6548			−1.28449
$534$	−3.85741	−	6.68123i	−0.166926	−	0.289125i
$535$	1.01002	+	1.74941i	0.0436671	+	0.0756336i
$536$	0.558622	−	0.967562i	0.0241288	−	0.0417923i
$537$	31.2302	+	54.0923i	1.34768	+	2.33425i
$538$	−8.00049	+	13.8572i	−0.344925	+	0.597428i
$539$	−9.79497			−0.421899
$540$	12.4223			0.534570
$541$	10.3091	−	17.8558i	0.443221	−	0.767682i	−0.554705	−	0.832047i	$-0.687169\pi$
$541$	10.3091	−	17.8558i	0.443221	−	0.767682i	0.997926	+	0.0643653i	$0.0205023\pi$
$542$	19.1132	−	33.1050i	0.820980	−	1.42198i
$543$	3.70046			0.158802
$544$	−9.00761			−0.386198
$545$	31.9458	−	55.3317i	1.36841	−	2.37015i
$546$	54.4278	+	94.2717i	2.32930	+	4.03446i
$547$	1.69198	−	2.93060i	0.0723439	−	0.125303i	−0.827584	−	0.561342i	$-0.810285\pi$
$547$	1.69198	−	2.93060i	0.0723439	−	0.125303i	0.899928	+	0.436038i	$0.143619\pi$
$548$	12.1534	+	21.0504i	0.519169	+	0.899228i
$549$	−9.81418	−	16.9987i	−0.418859	−	0.725485i
$550$	15.3420			0.654185
$551$	15.5624	−	23.2536i	0.662981	−	0.990636i
$552$	0.361733			0.0153964
$553$	−29.9444	−	51.8652i	−1.27336	−	2.20553i
$554$	6.57501	+	11.3882i	0.279345	+	0.483840i
$555$	4.58651	−	7.94406i	0.194686	−	0.337207i
$556$	4.29395	+	7.43735i	0.182104	+	0.315414i
$557$	−3.33704	+	5.77992i	−0.141395	+	0.244903i	−0.928022	−	0.372525i	$-0.878492\pi$
$557$	−3.33704	+	5.77992i	−0.141395	+	0.244903i	0.786627	+	0.617428i	$0.211825\pi$
$558$	4.14989			0.175679
$559$	−35.3292			−1.49427
$560$	−28.2887	+	48.9975i	−1.19542	+	2.07052i
$561$	−1.44397	+	2.50103i	−0.0609644	+	0.105593i
$562$	19.0971			0.805561
$563$	22.1574			0.933823			0.466912	−	0.884304i	$-0.345367\pi$
$563$	22.1574			0.933823			0.466912	+	0.884304i	$0.345367\pi$
$564$	6.23977	−	10.8076i	0.262742	−	0.455082i
$565$	−7.47055	−	12.9394i	−0.314289	−	0.544364i
$566$	7.69578	−	13.3295i	0.323478	−	0.560280i
$567$	−13.4978	−	23.3788i	−0.566853	−	0.981819i
$568$	0.0866027	+	0.150000i	0.00363377	+	0.00629387i
$569$	−14.7481			−0.618271			−0.309136	−	0.951018i	$-0.600040\pi$
$569$	−14.7481			−0.618271			−0.309136	+	0.951018i	$0.600040\pi$
$570$	−80.2888	−	5.32200i	−3.36293	−	0.222914i
$571$	44.9746			1.88213			0.941065	−	0.338226i	$-0.109827\pi$
$571$	44.9746			1.88213			0.941065	+	0.338226i	$0.109827\pi$
$572$	−5.25259	−	9.09776i	−0.219622	−	0.380396i
$573$	−0.911069	−	1.57802i	−0.0380605	−	0.0659226i
$574$	−23.9403	+	41.4657i	−0.999247	+	1.73075i
$575$	4.79790	+	8.31021i	0.200086	+	0.346560i
$576$	15.4348	−	26.7339i	0.643118	−	1.11391i
$577$	3.92477			0.163390			0.0816951	−	0.996657i	$-0.473967\pi$
$577$	3.92477			0.163390			0.0816951	+	0.996657i	$0.473967\pi$
$578$	31.7120			1.31905
$579$	8.92943	−	15.4662i	0.371095	−	0.642755i
$580$	23.4328	−	40.5868i	0.972994	−	1.68527i
$581$	−15.7733			−0.654388
$582$	86.6233			3.59065
$583$	−6.48991	+	11.2408i	−0.268784	+	0.465548i
$584$	0.406438	+	0.703971i	0.0168185	+	0.0291305i
$585$	33.2211	−	57.5406i	1.37352	−	2.37901i
$586$	11.7280	+	20.3135i	0.484479	+	0.839142i
$587$	−5.27535	−	9.13718i	−0.217737	−	0.377132i	0.736379	−	0.676570i	$-0.236534\pi$
$587$	−5.27535	−	9.13718i	−0.217737	−	0.377132i	−0.954116	+	0.299438i	$0.903201\pi$
$588$	51.9501			2.14239
$589$	−2.44933	−	0.162356i	−0.100923	−	0.00668976i
$590$	44.4070			1.82821
$591$	0.406445	+	0.703983i	0.0167189	+	0.0289580i
$592$	−1.94451	−	3.36799i	−0.0799190	−	0.138424i
$593$	3.23898	−	5.61007i	0.133009	−	0.230378i	−0.791826	−	0.610746i	$-0.790869\pi$
$593$	3.23898	−	5.61007i	0.133009	−	0.230378i	0.924835	+	0.380368i	$0.124203\pi$
$594$	−1.71320	−	2.96735i	−0.0702935	−	0.121752i
$595$	−8.14585	+	14.1090i	−0.333947	+	0.578413i
$596$	−26.4477			−1.08334
$597$	15.6826			0.641846
$598$	6.48223	−	11.2276i	0.265078	−	0.459129i
$599$	−9.65323	+	16.7199i	−0.394420	+	0.683156i	−0.993027	−	0.117887i	$-0.962388\pi$
$599$	−9.65323	+	16.7199i	−0.394420	+	0.683156i	0.598607	+	0.801043i	$0.295721\pi$
$600$	−2.18802			−0.0893256
$601$	−35.6734			−1.45515			−0.727573	−	0.686030i	$-0.759352\pi$
$601$	−35.6734			−1.45515			−0.727573	+	0.686030i	$0.759352\pi$
$602$	−28.5212	+	49.4001i	−1.16244	+	2.01340i
$603$	−18.3678	−	31.8140i	−0.747996	−	1.29557i
$604$	9.38467	−	16.2547i	0.381857	−	0.661396i
$605$	−1.77613	−	3.07635i	−0.0722100	−	0.125071i
$606$	−40.2496	−	69.7144i	−1.63503	−	2.83195i
$607$	23.6873			0.961437			0.480718	−	0.876875i	$-0.340376\pi$
$607$	23.6873			0.961437			0.480718	+	0.876875i	$0.340376\pi$
$608$	−19.5134	+	29.1572i	−0.791374	+	1.18248i
$609$	67.8870			2.75092
$610$	19.1852	+	33.2297i	0.776784	+	1.34543i
$611$	−6.01341	−	10.4155i	−0.243277	−	0.421368i
$612$	4.20836	−	7.28910i	0.170113	−	0.294644i
$613$	−10.1824	−	17.6364i	−0.411261	−	0.712325i	0.583767	−	0.811921i	$-0.301578\pi$
$613$	−10.1824	−	17.6364i	−0.411261	−	0.712325i	−0.995028	+	0.0995960i	$0.968245\pi$
$614$	15.6592	−	27.1225i	0.631952	−	1.09457i
$615$	53.1839			2.14458
$616$	−0.456093			−0.0183765
$617$	−18.4839	+	32.0151i	−0.744135	+	1.28888i	0.206463	+	0.978454i	$0.433805\pi$
$617$	−18.4839	+	32.0151i	−0.744135	+	1.28888i	−0.950598	+	0.310425i	$0.899529\pi$
$618$	−15.9320	+	27.5950i	−0.640878	+	1.11003i
$619$	22.3944			0.900106			0.450053	−	0.893002i	$-0.351405\pi$
$619$	22.3944			0.900106			0.450053	+	0.893002i	$0.351405\pi$
$620$	−4.11146			−0.165120
$621$	1.07154	−	1.85596i	0.0429993	−	0.0744770i
$622$	33.9171	+	58.7462i	1.35995	+	2.35551i
$623$	−3.04200	+	5.26891i	−0.121875	+	0.211094i
$624$	−25.6313	−	44.3947i	−1.02607	−	1.77721i
$625$	2.52520	+	4.37377i	0.101008	+	0.174951i
$626$	−52.8675			−2.11301
$627$	4.96760	+	10.0921i	0.198387	+	0.403040i
$628$	−2.33966			−0.0933625
$629$	−0.559929	−	0.969826i	−0.0223258	−	0.0386695i
$630$	−53.6386	−	92.9048i	−2.13701	−	3.70141i
$631$	7.33580	−	12.7060i	0.292033	−	0.505817i	−0.682257	−	0.731112i	$-0.739001\pi$
$631$	7.33580	−	12.7060i	0.292033	−	0.505817i	0.974290	+	0.225296i	$0.0723348\pi$
$632$	−0.813184	−	1.40848i	−0.0323467	−	0.0560262i
$633$	−1.93560	+	3.35256i	−0.0769333	+	0.133252i
$634$	−56.1038			−2.22817
$635$	−36.0005			−1.42863
$636$	34.4209	−	59.6187i	1.36488	−	2.36404i
$637$	25.0328	−	43.3580i	0.991834	−	1.71791i
$638$	−12.9268			−0.511777
$639$	5.69510			0.225295
$640$	−1.58075	+	2.73793i	−0.0624845	+	0.108226i
$641$	13.8311	+	23.9562i	0.546296	+	0.946213i	0.998524	+	0.0543103i	$0.0172960\pi$
$641$	13.8311	+	23.9562i	0.546296	+	0.946213i	−0.452228	+	0.891902i	$0.649371\pi$
$642$	−1.47758	+	2.55925i	−0.0583155	+	0.101005i
$643$	15.8621	+	27.4740i	0.625542	+	1.08347i	0.988436	+	0.151640i	$0.0484553\pi$
$643$	15.8621	+	27.4740i	0.625542	+	1.08347i	−0.362894	+	0.931830i	$0.618211\pi$
$644$	−5.30440	−	9.18750i	−0.209023	−	0.362038i
$645$	63.3605			2.49482
$646$	−5.46358	+	8.16376i	−0.214962	+	0.321199i
$647$	5.52403			0.217172			0.108586	−	0.994087i	$-0.465368\pi$
$647$	5.52403			0.217172			0.108586	+	0.994087i	$0.465368\pi$
$648$	−0.366552	−	0.634887i	−0.0143995	−	0.0249407i
$649$	−3.10390	−	5.37611i	−0.121839	−	0.211031i
$650$	−39.2092	+	67.9123i	−1.53791	+	2.66374i
$651$	−2.97782	−	5.15774i	−0.116710	−	0.202148i
$652$	−11.0582	+	19.1534i	−0.433073	+	0.750105i
$653$	−34.3342			−1.34360			−0.671801	−	0.740731i	$-0.734479\pi$
$653$	−34.3342			−1.34360			−0.671801	+	0.740731i	$0.734479\pi$
$654$	93.4682			3.65490
$655$	−2.24956	+	3.89635i	−0.0878976	+	0.152243i
$656$	11.2740	−	19.5272i	0.440176	−	0.762408i
$657$	26.7278			1.04275
$658$	−19.4184			−0.757010
$659$	2.02403	−	3.50573i	0.0788451	−	0.136564i	−0.823907	−	0.566725i	$-0.808210\pi$
$659$	2.02403	−	3.50573i	0.0788451	−	0.136564i	0.902752	+	0.430162i	$0.141543\pi$
$660$	9.42016	+	16.3162i	0.366679	+	0.635107i
$661$	−5.90898	+	10.2347i	−0.229833	+	0.398082i	−0.957758	−	0.287574i	$-0.907151\pi$
$661$	−5.90898	+	10.2347i	−0.229833	+	0.398082i	0.727926	+	0.685656i	$0.240485\pi$
$662$	−18.7535	−	32.4821i	−0.728877	−	1.26245i
$663$	−7.38063	−	12.7836i	−0.286640	−	0.496475i
$664$	−0.428349			−0.0166231
$665$	28.0237	+	56.9325i	1.08671	+	2.20775i
$666$	7.37402			0.285738
$667$	−4.04260	−	7.00198i	−0.156530	−	0.271118i
$668$	16.5934	+	28.7407i	0.642019	+	1.11201i
$669$	−1.43697	+	2.48891i	−0.0555565	+	0.0962267i
$670$	35.9062	+	62.1913i	1.38718	+	2.40266i
$671$	2.68195	−	4.64528i	0.103536	−	0.179329i
$672$	−85.1223			−3.28366
$673$	38.6295			1.48906			0.744529	−	0.667590i	$-0.232674\pi$
$673$	38.6295			1.48906			0.744529	+	0.667590i	$0.232674\pi$
$674$	14.9331	−	25.8648i	0.575200	−	0.996276i
$675$	−6.48143	+	11.2262i	−0.249471	+	0.432096i
$676$	26.9773			1.03759
$677$	−21.8650			−0.840340			−0.420170	−	0.907445i	$-0.638030\pi$
$677$	−21.8650			−0.840340			−0.420170	+	0.907445i	$0.638030\pi$
$678$	10.9288	−	18.9293i	0.419719	−	0.726975i
$679$	−34.1561	−	59.1602i	−1.31079	−	2.27036i
$680$	−0.221213	+	0.383152i	−0.00848312	+	0.0146932i
$681$	−9.61093	−	16.6466i	−0.368292	−	0.637900i
$682$	0.567026	+	0.982118i	0.0217126	+	0.0376072i
$683$	7.14617			0.273441			0.136720	−	0.990610i	$-0.456344\pi$
$683$	7.14617			0.273441			0.136720	+	0.990610i	$0.456344\pi$
$684$	−14.4778	−	29.4128i	−0.553572	−	1.12463i
$685$	−42.0113			−1.60517
$686$	−11.5331	−	19.9759i	−0.440336	−	0.762684i
$687$	10.5773	+	18.3204i	0.403548	+	0.698966i
$688$	13.4313	−	23.2637i	0.512063	−	0.886919i
$689$	−33.1722	−	57.4559i	−1.26376	−	2.18890i
$690$	−11.6254	+	20.1358i	−0.442573	+	0.766558i
$691$	10.3822			0.394956			0.197478	−	0.980307i	$-0.436725\pi$
$691$	10.3822			0.394956			0.197478	+	0.980307i	$0.436725\pi$
$692$	46.4043			1.76403
$693$	−7.49830	+	12.9874i	−0.284837	+	0.493352i
$694$	10.6108	−	18.3784i	0.402779	−	0.697633i
$695$	−14.8431			−0.563031
$696$	1.84357			0.0698805
$697$	3.24639	−	5.62292i	0.122966	−	0.212983i
$698$	19.0001	+	32.9091i	0.719163	+	1.24563i
$699$	9.94353	−	17.2227i	0.376099	−	0.651422i
$700$	32.0849	+	55.5726i	1.21269	+	2.10045i
$701$	6.09223	+	10.5521i	0.230100	+	0.398546i	0.957837	−	0.287311i	$-0.0927612\pi$
$701$	6.09223	+	10.5521i	0.230100	+	0.398546i	−0.727737	+	0.685856i	$0.759428\pi$
$702$	17.5135			0.661006
$703$	−4.35227	−	0.288494i	−0.164149	−	0.0108807i
$704$	8.43585			0.317938
$705$	10.7846	+	18.6796i	0.406173	+	0.703513i
$706$	6.70617	+	11.6154i	0.252390	+	0.437152i
$707$	−31.7414	+	54.9777i	−1.19376	+	2.06765i
$708$	16.4623	+	28.5136i	0.618692	+	1.07161i
$709$	15.4741	−	26.8019i	0.581142	−	1.00657i	−0.414202	−	0.910185i	$-0.635939\pi$
$709$	15.4741	−	26.8019i	0.581142	−	1.00657i	0.995344	−	0.0963825i	$-0.0307272\pi$
$710$	−11.1330			−0.417814
$711$	−53.4760			−2.00551
$712$	−0.0826102	+	0.143085i	−0.00309595	+	0.00536234i
$713$	−0.354652	+	0.614275i	−0.0132818	+	0.0230048i
$714$	−23.8334			−0.891944
$715$	18.1569			0.679028
$716$	24.8729	−	43.0812i	0.929545	−	1.61002i
$717$	−14.2647	−	24.7073i	−0.532727	−	0.922710i
$718$	−27.3237	+	47.3260i	−1.01971	+	1.76619i
$719$	−12.4152	−	21.5038i	−0.463009	−	0.801956i	0.536100	−	0.844155i	$-0.319897\pi$
$719$	−12.4152	−	21.5038i	−0.463009	−	0.801956i	−0.999109	+	0.0421989i	$0.986564\pi$
$720$	25.2597	+	43.7510i	0.941372	+	1.63050i
$721$	25.1283			0.935828
$722$	14.5898	+	35.3707i	0.542977	+	1.31636i
$723$	18.9210			0.703681
$724$	−1.47359	−	2.55234i	−0.0547657	−	0.0948569i
$725$	24.4525	+	42.3530i	0.908144	+	1.57295i
$726$	2.59834	−	4.50045i	0.0964333	−	0.167027i
$727$	−20.6171	−	35.7099i	−0.764648	−	1.32441i	−0.940433	−	0.339980i	$-0.889580\pi$
$727$	−20.6171	−	35.7099i	−0.764648	−	1.32441i	0.175785	−	0.984429i	$-0.443754\pi$
$728$	1.16562	−	2.01892i	0.0432009	−	0.0748262i
$729$	−37.2774			−1.38064
$730$	−52.2486			−1.93381
$731$	3.86759	−	6.69886i	0.143048	−	0.247766i
$732$	−14.2244	+	24.6374i	−0.525750	+	0.910625i
$733$	−24.6152			−0.909183			−0.454591	−	0.890700i	$-0.650215\pi$
$733$	−24.6152			−0.909183			−0.454591	+	0.890700i	$0.650215\pi$
$734$	42.1851			1.55708
$735$	−44.8945	+	77.7596i	−1.65596	+	2.86821i
$736$	5.06894	+	8.77966i	0.186843	+	0.323622i
$737$	5.01943	−	8.69391i	0.184893	−	0.320244i
$738$	21.3768	+	37.0257i	0.786891	+	1.36293i
$739$	0.581173	+	1.00662i	0.0213788	+	0.0370292i	0.876517	−	0.481371i	$-0.159861\pi$
$739$	0.581173	+	1.00662i	0.0213788	+	0.0370292i	−0.855138	+	0.518400i	$0.826528\pi$
$740$	−7.30574			−0.268564
$741$	−57.3689	−	3.80274i	−2.10750	−	0.139697i
$742$	−107.119			−3.93247
$743$	−11.1098	−	19.2428i	−0.407580	−	0.705950i	0.587038	−	0.809560i	$-0.300294\pi$
$743$	−11.1098	−	19.2428i	−0.407580	−	0.705950i	−0.994618	+	0.103610i	$0.966961\pi$
$744$	−0.0808672	−	0.140066i	−0.00296474	−	0.00513507i
$745$	22.8557	−	39.5872i	0.837367	−	1.45036i
$746$	12.5350	+	21.7112i	0.458937	+	0.794903i
$747$	−7.04218	+	12.1974i	−0.257660	+	0.446280i
$748$	2.30006			0.0840986
$749$	2.33048			0.0851539
$750$	24.1692	−	41.8622i	0.882534	−	1.52859i
$751$	−12.1031	+	20.9632i	−0.441648	+	0.764957i	−0.997812	−	0.0661159i	$-0.978939\pi$
$751$	−12.1031	+	20.9632i	−0.441648	+	0.764957i	0.556164	+	0.831073i	$0.312273\pi$
$752$	9.14459			0.333469
$753$	26.7056			0.973208
$754$	33.0367	−	57.2213i	1.20313	−	2.08388i
$755$	16.2202	+	28.0942i	0.590313	+	1.02245i
$756$	7.16566	−	12.4113i	0.260612	−	0.451394i
$757$	−15.9662	−	27.6543i	−0.580303	−	1.00511i	−0.995443	−	0.0953562i	$-0.969601\pi$
$757$	−15.9662	−	27.6543i	−0.580303	−	1.00511i	0.415141	−	0.909757i	$-0.363732\pi$
$758$	−2.38155	−	4.12497i	−0.0865018	−	0.149826i
$759$	3.25031			0.117979
$760$	0.761026	+	1.54609i	0.0276053	+	0.0560825i
$761$	−20.1507			−0.730463			−0.365231	−	0.930917i	$-0.619010\pi$
$761$	−20.1507			−0.730463			−0.365231	+	0.930917i	$0.619010\pi$
$762$	−26.3329	−	45.6099i	−0.953940	−	1.65227i
$763$	−36.8552	−	63.8350i	−1.33425	−	2.31098i
$764$	−0.725610	+	1.25679i	−0.0262517	+	0.0454692i
$765$	7.27361	+	12.5983i	0.262978	+	0.455491i
$766$	4.10282	−	7.10629i	0.148241	−	0.256761i
$767$	31.7302			1.14571
$768$	38.9136			1.40417
$769$	−5.66959	+	9.82001i	−0.204451	+	0.354119i	−0.949958	−	0.312379i	$-0.898874\pi$
$769$	−5.66959	+	9.82001i	−0.204451	+	0.354119i	0.745507	+	0.666498i	$0.232207\pi$
$770$	14.6580	−	25.3884i	0.528237	−	0.914933i
$771$	64.6296

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00688 + 1.74398i) q^{2} +(-1.29029 - 2.23484i) q^{3} +(-1.02763 + 1.77991i) q^{4} +(-1.77613 - 3.07635i) q^{5} +(2.59834 - 4.50045i) q^{6} -4.09817 q^{7} -0.111292 q^{8} +(-1.82967 + 3.16909i) q^{9} +O(q^{10})\)	\(q+(1.00688 + 1.74398i) q^{2} +(-1.29029 - 2.23484i) q^{3} +(-1.02763 + 1.77991i) q^{4} +(-1.77613 - 3.07635i) q^{5} +(2.59834 - 4.50045i) q^{6} -4.09817 q^{7} -0.111292 q^{8} +(-1.82967 + 3.16909i) q^{9} +(3.57672 - 6.19505i) q^{10} -1.00000 q^{11} +5.30376 q^{12} +(2.55568 - 4.42656i) q^{13} +(-4.12638 - 7.14710i) q^{14} +(-4.58343 + 7.93873i) q^{15} +(1.94321 + 3.36573i) q^{16} +(0.559554 + 0.969175i) q^{17} -7.36908 q^{18} +(4.34935 + 0.288300i) q^{19} +7.30084 q^{20} +(5.28780 + 9.15875i) q^{21} +(-1.00688 - 1.74398i) q^{22} +(0.629766 - 1.09079i) q^{23} +(0.143598 + 0.248719i) q^{24} +(-3.80928 + 6.59786i) q^{25} +10.2931 q^{26} +1.70149 q^{27} +(4.21141 - 7.29438i) q^{28} +(3.20960 - 5.55920i) q^{29} -18.4599 q^{30} -0.563149 q^{31} +(-4.02446 + 6.97057i) q^{32} +(1.29029 + 2.23484i) q^{33} +(-1.12681 + 1.95170i) q^{34} +(7.27888 + 12.6074i) q^{35} +(-3.76046 - 6.51331i) q^{36} -1.00067 q^{37} +(3.87651 + 7.87545i) q^{38} -13.1902 q^{39} +(0.197669 + 0.342372i) q^{40} +(-2.90088 - 5.02447i) q^{41} +(-10.6484 + 18.4436i) q^{42} +(-3.45596 - 5.98589i) q^{43} +(1.02763 - 1.77991i) q^{44} +12.9989 q^{45} +2.53641 q^{46} +(1.17648 - 2.03773i) q^{47} +(5.01458 - 8.68551i) q^{48} +9.79497 q^{49} -15.3420 q^{50} +(1.44397 - 2.50103i) q^{51} +(5.25259 + 9.09776i) q^{52} +(6.48991 - 11.2408i) q^{53} +(1.71320 + 2.96735i) q^{54} +(1.77613 + 3.07635i) q^{55} +0.456093 q^{56} +(-4.96760 - 10.0921i) q^{57} +12.9268 q^{58} +(3.10390 + 5.37611i) q^{59} +(-9.42016 - 16.3162i) q^{60} +(-2.68195 + 4.64528i) q^{61} +(-0.567026 - 0.982118i) q^{62} +(7.49830 - 12.9874i) q^{63} -8.43585 q^{64} -18.1569 q^{65} +(-2.59834 + 4.50045i) q^{66} +(-5.01943 + 8.69391i) q^{67} -2.30006 q^{68} -3.25031 q^{69} +(-14.6580 + 25.3884i) q^{70} +(-0.778159 - 1.34781i) q^{71} +(0.203628 - 0.352693i) q^{72} +(-3.65200 - 6.32545i) q^{73} +(-1.00756 - 1.74515i) q^{74} +19.6602 q^{75} +(-4.98269 + 7.44520i) q^{76} +4.09817 q^{77} +(-13.2810 - 23.0034i) q^{78} +(7.30677 + 12.6557i) q^{79} +(6.90278 - 11.9560i) q^{80} +(3.29361 + 5.70471i) q^{81} +(5.84170 - 10.1181i) q^{82} +3.84888 q^{83} -21.7357 q^{84} +(1.98768 - 3.44276i) q^{85} +(6.95950 - 12.0542i) q^{86} -16.5652 q^{87} +0.111292 q^{88} +(0.742284 - 1.28567i) q^{89} +(13.0884 + 22.6698i) q^{90} +(-10.4736 + 18.1408i) q^{91} +(1.29434 + 2.24186i) q^{92} +(0.726623 + 1.25855i) q^{93} +4.73833 q^{94} +(-6.83811 - 13.8922i) q^{95} +20.7708 q^{96} +(8.33449 + 14.4358i) q^{97} +(9.86240 + 17.0822i) q^{98} +(1.82967 - 3.16909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9}+O(q^{10}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9	\( 18 q + q^{2} - 9 q^{4} - 3 q^{6} - 6 q^{7} - 11 q^{9} + 21 q^{10} - 18 q^{11} + 16 q^{12} + 11 q^{13} + q^{14} + 7 q^{15} - 13 q^{16} + 6 q^{17} - 8 q^{18} + 4 q^{19} + 4 q^{20} + 24 q^{21} - q^{22} - q^{23} - 3 q^{24} - 7 q^{25} - 4 q^{26} + 6 q^{27} - 2 q^{28} + 13 q^{29} - 64 q^{30} - 32 q^{31} - 14 q^{32} + 8 q^{34} - 12 q^{35} + 10 q^{36} - 36 q^{37} - 20 q^{38} + 20 q^{39} + 32 q^{40} + 4 q^{41} + 11 q^{42} + q^{43} + 9 q^{44} + 22 q^{45} - 14 q^{46} - 14 q^{47} + 37 q^{48} - 12 q^{49} + 30 q^{50} - 16 q^{51} + 57 q^{52} - 4 q^{53} - 33 q^{54} - 34 q^{56} - 7 q^{57} + 8 q^{58} + 31 q^{59} + 9 q^{60} + 3 q^{61} + 5 q^{62} + 50 q^{63} + 64 q^{64} - 56 q^{65} + 3 q^{66} - 2 q^{67} - 96 q^{68} - 58 q^{70} - 12 q^{71} + 5 q^{72} - 26 q^{73} + 35 q^{74} + 50 q^{75} - 36 q^{76} + 6 q^{77} + 3 q^{78} + 31 q^{79} + 31 q^{80} - 21 q^{81} + 25 q^{82} + 36 q^{83} - 102 q^{84} - 11 q^{85} + 41 q^{86} - 124 q^{87} - 11 q^{89} + 51 q^{90} - 20 q^{91} - 33 q^{92} + 20 q^{93} - 86 q^{94} + 17 q^{95} + 60 q^{96} + 16 q^{97} + 4 q^{98} + 11 q^{99}+O(q^{100}) \) 18 * q + q^2 - 9 * q^4 - 3 * q^6 - 6 * q^7 - 11 * q^9 + 21 * q^10 - 18 * q^11 + 16 * q^12 + 11 * q^13 + q^14 + 7 * q^15 - 13 * q^16 + 6 * q^17 - 8 * q^18 + 4 * q^19 + 4 * q^20 + 24 * q^21 - q^22 - q^23 - 3 * q^24 - 7 * q^25 - 4 * q^26 + 6 * q^27 - 2 * q^28 + 13 * q^29 - 64 * q^30 - 32 * q^31 - 14 * q^32 + 8 * q^34 - 12 * q^35 + 10 * q^36 - 36 * q^37 - 20 * q^38 + 20 * q^39 + 32 * q^40 + 4 * q^41 + 11 * q^42 + q^43 + 9 * q^44 + 22 * q^45 - 14 * q^46 - 14 * q^47 + 37 * q^48 - 12 * q^49 + 30 * q^50 - 16 * q^51 + 57 * q^52 - 4 * q^53 - 33 * q^54 - 34 * q^56 - 7 * q^57 + 8 * q^58 + 31 * q^59 + 9 * q^60 + 3 * q^61 + 5 * q^62 + 50 * q^63 + 64 * q^64 - 56 * q^65 + 3 * q^66 - 2 * q^67 - 96 * q^68 - 58 * q^70 - 12 * q^71 + 5 * q^72 - 26 * q^73 + 35 * q^74 + 50 * q^75 - 36 * q^76 + 6 * q^77 + 3 * q^78 + 31 * q^79 + 31 * q^80 - 21 * q^81 + 25 * q^82 + 36 * q^83 - 102 * q^84 - 11 * q^85 + 41 * q^86 - 124 * q^87 - 11 * q^89 + 51 * q^90 - 20 * q^91 - 33 * q^92 + 20 * q^93 - 86 * q^94 + 17 * q^95 + 60 * q^96 + 16 * q^97 + 4 * q^98 + 11 * q^99

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