LMFDB - Embedded newform 209.2.e.b.45.5

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			45.5
Root			$-0.0694302 - 0.120257i$ of defining polynomial
Character	$\chi$	$=$	209.45
Dual form			209.2.e.b.144.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0694302 - 0.120257i) q^{2} +(0.748393 + 1.29625i) q^{3} +(0.990359 - 1.71535i) q^{4} +(1.75825 + 3.04538i) q^{5} +(0.103922 - 0.179998i) q^{6} -1.46902 q^{7} -0.552764 q^{8} +(0.379817 - 0.657862i) q^{9} +O(q^{10})$	\(q+(-0.0694302 - 0.120257i) q^{2} +(0.748393 + 1.29625i) q^{3} +(0.990359 - 1.71535i) q^{4} +(1.75825 + 3.04538i) q^{5} +(0.103922 - 0.179998i) q^{6} -1.46902 q^{7} -0.552764 q^{8} +(0.379817 - 0.657862i) q^{9} +(0.244151 - 0.422882i) q^{10} -1.00000 q^{11} +2.96471 q^{12} +(-1.19628 + 2.07201i) q^{13} +(0.101994 + 0.176659i) q^{14} +(-2.63172 + 4.55828i) q^{15} +(-1.94234 - 3.36423i) q^{16} +(1.62021 + 2.80628i) q^{17} -0.105483 q^{18} +(-1.08996 - 4.22043i) q^{19} +6.96519 q^{20} +(-1.09940 - 1.90422i) q^{21} +(0.0694302 + 0.120257i) q^{22} +(3.69089 - 6.39280i) q^{23} +(-0.413685 - 0.716523i) q^{24} +(-3.68288 + 6.37894i) q^{25} +0.332231 q^{26} +5.62736 q^{27} +(-1.45486 + 2.51989i) q^{28} +(-3.20477 + 5.55082i) q^{29} +0.730884 q^{30} +0.866600 q^{31} +(-0.822478 + 1.42457i) q^{32} +(-0.748393 - 1.29625i) q^{33} +(0.224982 - 0.389681i) q^{34} +(-2.58290 - 4.47372i) q^{35} +(-0.752310 - 1.30304i) q^{36} -2.78244 q^{37} +(-0.431858 + 0.424100i) q^{38} -3.58113 q^{39} +(-0.971897 - 1.68338i) q^{40} +(-4.92679 - 8.53345i) q^{41} +(-0.152664 + 0.264421i) q^{42} +(-3.65252 - 6.32635i) q^{43} +(-0.990359 + 1.71535i) q^{44} +2.67125 q^{45} -1.02504 q^{46} +(-1.67951 + 2.90900i) q^{47} +(2.90726 - 5.03553i) q^{48} -4.84198 q^{49} +1.02281 q^{50} +(-2.42510 + 4.20040i) q^{51} +(2.36948 + 4.10407i) q^{52} +(1.89180 - 3.27669i) q^{53} +(-0.390709 - 0.676728i) q^{54} +(-1.75825 - 3.04538i) q^{55} +0.812022 q^{56} +(4.65503 - 4.57140i) q^{57} +0.890031 q^{58} +(-4.20103 - 7.27640i) q^{59} +(5.21270 + 9.02866i) q^{60} +(0.718836 - 1.24506i) q^{61} +(-0.0601682 - 0.104214i) q^{62} +(-0.557959 + 0.966413i) q^{63} -7.54094 q^{64} -8.41340 q^{65} +(-0.103922 + 0.179998i) q^{66} +(-3.24306 + 5.61714i) q^{67} +6.41834 q^{68} +11.0489 q^{69} +(-0.358663 + 0.621223i) q^{70} +(1.70784 + 2.95807i) q^{71} +(-0.209949 + 0.363643i) q^{72} +(-1.40544 - 2.43430i) q^{73} +(0.193185 + 0.334607i) q^{74} -11.0250 q^{75} +(-8.31897 - 2.31007i) q^{76} +1.46902 q^{77} +(0.248639 + 0.430655i) q^{78} +(8.85942 + 15.3450i) q^{79} +(6.83023 - 11.8303i) q^{80} +(3.07203 + 5.32091i) q^{81} +(-0.684136 + 1.18496i) q^{82} +17.7129 q^{83} -4.35522 q^{84} +(-5.69745 + 9.86827i) q^{85} +(-0.507190 + 0.878479i) q^{86} -9.59370 q^{87} +0.552764 q^{88} +(-6.43621 + 11.1478i) q^{89} +(-0.185466 - 0.321236i) q^{90} +(1.75735 - 3.04382i) q^{91} +(-7.31060 - 12.6623i) q^{92} +(0.648557 + 1.12333i) q^{93} +0.466435 q^{94} +(10.9364 - 10.7399i) q^{95} -2.46215 q^{96} +(7.86297 + 13.6191i) q^{97} +(0.336180 + 0.582280i) q^{98} +(-0.379817 + 0.657862i) 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 $

$2$	−0.0694302	−	0.120257i	−0.0490946	−	0.0850343i	0.840434	−	0.541914i	$-0.182300\pi$
$2$	−0.0694302	−	0.120257i	−0.0490946	−	0.0850343i	−0.889528	+	0.456880i	$0.848967\pi$
$3$	0.748393	+	1.29625i	0.432085	+	0.748393i	0.997053	−	0.0767202i	$-0.0244448\pi$
$3$	0.748393	+	1.29625i	0.432085	+	0.748393i	−0.564968	+	0.825113i	$0.691111\pi$
$4$	0.990359	−	1.71535i	0.495179	−	0.857676i
$5$	1.75825	+	3.04538i	0.786313	+	1.36193i	0.928212	+	0.372053i	$0.121346\pi$
$5$	1.75825	+	3.04538i	0.786313	+	1.36193i	−0.141898	+	0.989881i	$0.545321\pi$
$6$	0.103922	−	0.179998i	0.0424260	−	0.0734840i
$7$	−1.46902			−0.555237			−0.277619	−	0.960691i	$-0.589545\pi$
$7$	−1.46902			−0.555237			−0.277619	+	0.960691i	$0.589545\pi$
$8$	−0.552764			−0.195432
$9$	0.379817	−	0.657862i	0.126606	−	0.219287i
$10$	0.244151	−	0.422882i	0.0772074	−	0.133727i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	2.96471			0.855838
$13$	−1.19628	+	2.07201i	−0.331787	+	0.574672i	−0.982862	−	0.184341i	$-0.940985\pi$
$13$	−1.19628	+	2.07201i	−0.331787	+	0.574672i	0.651075	+	0.759013i	$0.274318\pi$
$14$	0.101994	+	0.176659i	0.0272591	+	0.0472142i
$15$	−2.63172	+	4.55828i	−0.679508	+	1.17694i
$16$	−1.94234	−	3.36423i	−0.485585	−	0.841058i
$17$	1.62021	+	2.80628i	0.392957	+	0.680622i	0.992838	−	0.119467i	$-0.0381186\pi$
$17$	1.62021	+	2.80628i	0.392957	+	0.680622i	−0.599881	+	0.800089i	$0.704785\pi$
$18$	−0.105483			−0.0248626
$19$	−1.08996	−	4.22043i	−0.250054	−	0.968232i
$19$	−1.08996	−	4.22043i	−0.250054	−	0.968232i
$20$	6.96519			1.55746
$21$	−1.09940	−	1.90422i	−0.239910	−	0.415536i
$22$	0.0694302	+	0.120257i	0.0148026	+	0.0256388i
$23$	3.69089	−	6.39280i	0.769603	−	1.33299i	−0.168175	−	0.985757i	$-0.553787\pi$
$23$	3.69089	−	6.39280i	0.769603	−	1.33299i	0.937778	−	0.347234i	$-0.112879\pi$
$24$	−0.413685	−	0.716523i	−0.0844430	−	0.146260i
$25$	−3.68288	+	6.37894i	−0.736576	+	1.27579i
$26$	0.332231			0.0651558
$27$	5.62736			1.08299
$28$	−1.45486	+	2.51989i	−0.274942	+	0.476214i
$29$	−3.20477	+	5.55082i	−0.595111	+	1.03076i	0.398421	+	0.917203i	$0.369558\pi$
$29$	−3.20477	+	5.55082i	−0.595111	+	1.03076i	−0.993531	+	0.113559i	$0.963775\pi$
$30$	0.730884			0.133441
$31$	0.866600			0.155646			0.0778230	−	0.996967i	$-0.475203\pi$
$31$	0.866600			0.155646			0.0778230	+	0.996967i	$0.475203\pi$
$32$	−0.822478	+	1.42457i	−0.145395	+	0.251831i
$33$	−0.748393	−	1.29625i	−0.130278	−	0.225649i
$34$	0.224982	−	0.389681i	0.0385842	−	0.0668297i
$35$	−2.58290	−	4.47372i	−0.436590	−	0.756197i
$36$	−0.752310	−	1.30304i	−0.125385	−	0.217173i
$37$	−2.78244			−0.457430			−0.228715	−	0.973493i	$-0.573452\pi$
$37$	−2.78244			−0.457430			−0.228715	+	0.973493i	$0.573452\pi$
$38$	−0.431858	+	0.424100i	−0.0700566	+	0.0687981i
$39$	−3.58113			−0.573440
$40$	−0.971897	−	1.68338i	−0.153670	−	0.266165i
$41$	−4.92679	−	8.53345i	−0.769435	−	1.33270i	−0.937870	−	0.346988i	$-0.887205\pi$
$41$	−4.92679	−	8.53345i	−0.769435	−	1.33270i	0.168435	−	0.985713i	$-0.446129\pi$
$42$	−0.152664	+	0.264421i	−0.0235565	+	0.0408011i
$43$	−3.65252	−	6.32635i	−0.557004	−	0.964759i	−0.997745	−	0.0671246i	$-0.978618\pi$
$43$	−3.65252	−	6.32635i	−0.557004	−	0.964759i	0.440741	−	0.897634i	$-0.354716\pi$
$44$	−0.990359	+	1.71535i	−0.149302	+	0.258599i
$45$	2.67125			0.398207
$46$	−1.02504			−0.151133
$47$	−1.67951	+	2.90900i	−0.244982	+	0.424321i	−0.962126	−	0.272603i	$-0.912115\pi$
$47$	−1.67951	+	2.90900i	−0.244982	+	0.424321i	0.717145	+	0.696924i	$0.245449\pi$
$48$	2.90726	−	5.03553i	0.419628	−	0.726816i
$49$	−4.84198			−0.691711
$50$	1.02281			0.144648
$51$	−2.42510	+	4.20040i	−0.339582	+	0.588173i
$52$	2.36948	+	4.10407i	0.328588	+	0.569132i
$53$	1.89180	−	3.27669i	0.259859	−	0.450089i	−0.706345	−	0.707868i	$-0.749657\pi$
$53$	1.89180	−	3.27669i	0.259859	−	0.450089i	0.966204	+	0.257779i	$0.0829906\pi$
$54$	−0.390709	−	0.676728i	−0.0531688	−	0.0920910i
$55$	−1.75825	−	3.04538i	−0.237082	−	0.410639i
$56$	0.812022			0.108511
$57$	4.65503	−	4.57140i	0.616573	−	0.605497i
$58$	0.890031			0.116867
$59$	−4.20103	−	7.27640i	−0.546928	−	0.947307i	−0.998483	−	0.0550636i	$-0.982464\pi$
$59$	−4.20103	−	7.27640i	−0.546928	−	0.947307i	0.451555	−	0.892243i	$-0.350869\pi$
$60$	5.21270	+	9.02866i	0.672956	+	1.16559i
$61$	0.718836	−	1.24506i	0.0920375	−	0.159414i	−0.816331	−	0.577585i	$-0.803995\pi$
$61$	0.718836	−	1.24506i	0.0920375	−	0.159414i	0.908368	+	0.418171i	$0.137329\pi$
$62$	−0.0601682	−	0.104214i	−0.00764137	−	0.0132352i
$63$	−0.557959	+	0.966413i	−0.0702962	+	0.121757i
$64$	−7.54094			−0.942617
$65$	−8.41340			−1.04355
$66$	−0.103922	+	0.179998i	−0.0127919	+	0.0221563i
$67$	−3.24306	+	5.61714i	−0.396203	+	0.686243i	−0.993254	−	0.115960i	$-0.963006\pi$
$67$	−3.24306	+	5.61714i	−0.396203	+	0.686243i	0.597051	+	0.802203i	$0.296339\pi$
$68$	6.41834			0.778338
$69$	11.0489			1.33013
$70$	−0.358663	+	0.621223i	−0.0428684	+	0.0742503i
$71$	1.70784	+	2.95807i	0.202683	+	0.351058i	0.949392	−	0.314093i	$-0.101700\pi$
$71$	1.70784	+	2.95807i	0.202683	+	0.351058i	−0.746709	+	0.665151i	$0.768367\pi$
$72$	−0.209949	+	0.363643i	−0.0247428	+	0.0428557i
$73$	−1.40544	−	2.43430i	−0.164495	−	0.284913i	0.771981	−	0.635645i	$-0.219266\pi$
$73$	−1.40544	−	2.43430i	−0.164495	−	0.284913i	−0.936476	+	0.350733i	$0.885933\pi$
$74$	0.193185	+	0.334607i	0.0224573	+	0.0388972i
$75$	−11.0250			−1.27305
$76$	−8.31897	−	2.31007i	−0.954251	−	0.264983i
$77$	1.46902			0.167410
$78$	0.248639	+	0.430655i	0.0281528	+	0.0487621i
$79$	8.85942	+	15.3450i	0.996763	+	1.72644i	0.568005	+	0.823025i	$0.307716\pi$
$79$	8.85942	+	15.3450i	0.996763	+	1.72644i	0.428758	+	0.903419i	$0.358951\pi$
$80$	6.83023	−	11.8303i	0.763643	−	1.32267i
$81$	3.07203	+	5.32091i	0.341336	+	0.591212i
$82$	−0.684136	+	1.18496i	−0.0755502	+	0.130857i
$83$	17.7129			1.94425			0.972124	−	0.234467i	$-0.0753345\pi$
$83$	17.7129			1.94425			0.972124	+	0.234467i	$0.0753345\pi$
$84$	−4.35522			−0.475193
$85$	−5.69745	+	9.86827i	−0.617975	+	1.07036i
$86$	−0.507190	+	0.878479i	−0.0546917	+	0.0947289i
$87$	−9.59370			−1.02855
$88$	0.552764			0.0589249
$89$	−6.43621	+	11.1478i	−0.682236	+	1.18167i	0.292060	+	0.956400i	$0.405659\pi$
$89$	−6.43621	+	11.1478i	−0.682236	+	1.18167i	−0.974297	+	0.225268i	$0.927674\pi$
$90$	−0.185466	−	0.321236i	−0.0195498	−	0.0338612i
$91$	1.75735	−	3.04382i	0.184221	−	0.319079i
$92$	−7.31060	−	12.6623i	−0.762183	−	1.32014i
$93$	0.648557	+	1.12333i	0.0672523	+	0.116484i
$94$	0.466435			0.0481091
$95$	10.9364	−	10.7399i	1.12205	−	1.10189i
$96$	−2.46215			−0.251292
$97$	7.86297	+	13.6191i	0.798364	+	1.38281i	0.920681	+	0.390316i	$0.127634\pi$
$97$	7.86297	+	13.6191i	0.798364	+	1.38281i	−0.122317	+	0.992491i	$0.539032\pi$
$98$	0.336180	+	0.582280i	0.0339593	+	0.0588192i
$99$	−0.379817	+	0.657862i	−0.0381730	+	0.0661177i
$100$	7.29475	+	12.6349i	0.729475	+	1.26349i
$101$	3.91875	−	6.78748i	0.389931	−	0.675380i	−0.602509	−	0.798112i	$-0.705832\pi$
$101$	3.91875	−	6.78748i	0.389931	−	0.675380i	0.992440	+	0.122732i	$0.0391656\pi$
$102$	0.673501			0.0666865
$103$	−7.27715			−0.717039			−0.358519	−	0.933522i	$-0.616718\pi$
$103$	−7.27715			−0.717039			−0.358519	+	0.933522i	$0.616718\pi$
$104$	0.661258	−	1.14533i	0.0648417	−	0.112309i
$105$	3.86605	−	6.69620i	0.377288	−	0.653482i
$106$	−0.525392			−0.0510306
$107$	6.23745			0.602997			0.301498	−	0.953467i	$-0.402513\pi$
$107$	6.23745			0.602997			0.301498	+	0.953467i	$0.402513\pi$
$108$	5.57311	−	9.65291i	0.536273	−	0.928852i
$109$	−1.35921	−	2.35422i	−0.130189	−	0.225493i	0.793561	−	0.608491i	$-0.208225\pi$
$109$	−1.35921	−	2.35422i	−0.130189	−	0.225493i	−0.923749	+	0.382998i	$0.874892\pi$
$110$	−0.244151	+	0.422882i	−0.0232789	+	0.0403203i
$111$	−2.08236	−	3.60675i	−0.197648	−	0.342337i
$112$	2.85334	+	4.94212i	0.269615	+	0.466987i
$113$	0.486637			0.0457789			0.0228895	−	0.999738i	$-0.492713\pi$
$113$	0.486637			0.0457789			0.0228895	+	0.999738i	$0.492713\pi$
$114$	−0.872941	−	0.242405i	−0.0817584	−	0.0227033i
$115$	25.9580			2.42060
$116$	6.34774	+	10.9946i	0.589373	+	1.02082i
$117$	0.908731	+	1.57397i	0.0840123	+	0.145513i
$118$	−0.583357	+	1.01040i	−0.0537024	+	0.0930152i
$119$	−2.38011	−	4.12248i	−0.218185	−	0.377907i
$120$	1.45472	−	2.51965i	0.132797	−	0.230012i
$121$	1.00000			0.0909091
$122$	−0.199636			−0.0180742
$123$	7.37434	−	12.7727i	0.664922	−	1.15168i
$124$	0.858245	−	1.48652i	0.0770727	−	0.133494i
$125$	−8.31921			−0.744093
$126$	0.154957			0.0138046
$127$	−1.84127	+	3.18918i	−0.163386	+	0.282994i	−0.936081	−	0.351784i	$-0.885575\pi$
$127$	−1.84127	+	3.18918i	−0.163386	+	0.282994i	0.772695	+	0.634778i	$0.218908\pi$
$128$	2.16853	+	3.75600i	0.191672	+	0.331986i
$129$	5.46704	−	9.46918i	0.481346	−	0.833715i
$130$	0.584144	+	1.01177i	0.0512328	+	0.0887379i
$131$	−0.0270579	−	0.0468657i	−0.00236406	−	0.00409467i	0.864841	−	0.502046i	$-0.167419\pi$
$131$	−0.0270579	−	0.0468657i	−0.00236406	−	0.00409467i	−0.867205	+	0.497951i	$0.834086\pi$
$132$	−2.96471			−0.258045
$133$	1.60117	+	6.19989i	0.138839	+	0.537599i
$134$	0.900665			0.0778056
$135$	9.89431	+	17.1374i	0.851567	+	1.47496i
$136$	−0.895591	−	1.55121i	−0.0767963	−	0.133015i
$137$	−8.48635	+	14.6988i	−0.725038	+	1.25580i	0.233921	+	0.972256i	$0.424844\pi$
$137$	−8.48635	+	14.6988i	−0.725038	+	1.25580i	−0.958958	+	0.283547i	$0.908489\pi$
$138$	−0.767129	−	1.32871i	−0.0653024	−	0.113107i
$139$	9.01812	−	15.6198i	0.764907	−	1.32486i	−0.175389	−	0.984499i	$-0.556118\pi$
$139$	9.01812	−	15.6198i	0.764907	−	1.32486i	0.940296	−	0.340358i	$-0.110548\pi$
$140$	−10.2320			−0.864763
$141$	−5.02773			−0.423412
$142$	0.237151	−	0.410758i	0.0199013	−	0.0344701i
$143$	1.19628	−	2.07201i	0.100038	−	0.173270i
$144$	−2.95093			−0.245911
$145$	−22.5391			−1.87177
$146$	−0.195160	+	0.338027i	−0.0161516	+	0.0279753i
$147$	−3.62370	−	6.27644i	−0.298878	−	0.517672i
$148$	−2.75561	+	4.77286i	−0.226510	+	0.392327i
$149$	2.65188	+	4.59319i	0.217250	+	0.376288i	0.953966	−	0.299914i	$-0.0969579\pi$
$149$	2.65188	+	4.59319i	0.217250	+	0.376288i	−0.736716	+	0.676202i	$0.763625\pi$
$150$	0.765466	+	1.32583i	0.0625000	+	0.108253i
$151$	−10.8143			−0.880057			−0.440029	−	0.897984i	$-0.645032\pi$
$151$	−10.8143			−0.880057			−0.440029	+	0.897984i	$0.645032\pi$
$152$	0.602490	+	2.33290i	0.0488684	+	0.189223i
$153$	2.46153			0.199003
$154$	−0.101994	−	0.176659i	−0.00821894	−	0.0142356i
$155$	1.52370	+	2.63913i	0.122387	+	0.211980i
$156$	−3.54661	+	6.14291i	−0.283956	+	0.491826i
$157$	−1.59764	−	2.76720i	−0.127506	−	0.220846i	0.795204	−	0.606342i	$-0.207364\pi$
$157$	−1.59764	−	2.76720i	−0.127506	−	0.220846i	−0.922710	+	0.385496i	$0.874030\pi$
$158$	1.23022	−	2.13081i	0.0978713	−	0.169518i
$159$	5.66324			0.449124
$160$	−5.78449			−0.457304
$161$	−5.42199	+	9.39116i	−0.427312	+	0.740127i
$162$	0.426583	−	0.738863i	0.0335155	−	0.0580506i
$163$	−14.3438			−1.12349			−0.561747	−	0.827309i	$-0.689871\pi$
$163$	−14.3438			−1.12349			−0.561747	+	0.827309i	$0.689871\pi$
$164$	−19.5172			−1.52403
$165$	2.63172	−	4.55828i	0.204879	−	0.354861i
$166$	−1.22981	−	2.13010i	−0.0954520	−	0.165328i
$167$	−7.62833	+	13.2127i	−0.590298	+	1.02243i	0.403894	+	0.914806i	$0.367656\pi$
$167$	−7.62833	+	13.2127i	−0.590298	+	1.02243i	−0.994192	+	0.107620i	$0.965677\pi$
$168$	0.607711	+	1.05259i	0.0468859	+	0.0812088i
$169$	3.63785	+	6.30094i	0.279835	+	0.484688i
$170$	1.58230			0.121357
$171$	−3.19044	−	0.885946i	−0.243979	−	0.0677500i
$172$	−14.4692			−1.10327
$173$	10.8374	+	18.7710i	0.823954	+	1.42713i	0.902716	+	0.430237i	$0.141570\pi$
$173$	10.8374	+	18.7710i	0.823954	+	1.42713i	−0.0787615	+	0.996893i	$0.525097\pi$
$174$	0.666093	+	1.15371i	0.0504964	+	0.0874623i
$175$	5.41023	−	9.37079i	0.408975	−	0.708365i
$176$	1.94234	+	3.36423i	0.146409	+	0.253588i
$177$	6.28804	−	10.8912i	0.472638	−	0.818634i
$178$	1.78747			0.133976
$179$	4.19425			0.313493			0.156746	−	0.987639i	$-0.449899\pi$
$179$	4.19425			0.313493			0.156746	+	0.987639i	$0.449899\pi$
$180$	2.64550	−	4.58214i	0.197184	−	0.341532i
$181$	12.4639	−	21.5881i	0.926436	−	1.60463i	0.137200	−	0.990543i	$-0.456190\pi$
$181$	12.4639	−	21.5881i	0.926436	−	1.60463i	0.789236	−	0.614090i	$-0.210477\pi$
$182$	−0.488053			−0.0361769
$183$	2.15189			0.159072
$184$	−2.04019	+	3.53371i	−0.150405	+	0.260509i
$185$	−4.89222	−	8.47357i	−0.359683	−	0.622989i
$186$	0.0900589	−	0.155987i	0.00660344	−	0.0114375i
$187$	−1.62021	−	2.80628i	−0.118481	−	0.205215i
$188$	3.32664	+	5.76190i	0.242620	+	0.420230i
$189$	−8.26671			−0.601315
$190$	−2.05086	−	0.569498i	−0.148785	−	0.0413157i
$191$	−7.74450			−0.560372			−0.280186	−	0.959946i	$-0.590396\pi$
$191$	−7.74450			−0.560372			−0.280186	+	0.959946i	$0.590396\pi$
$192$	−5.64358	−	9.77497i	−0.407290	−	0.705448i
$193$	−6.95480	−	12.0461i	−0.500617	−	0.867095i	−1.00000		0.000712945i	$-0.999773\pi$
$193$	−6.95480	−	12.0461i	−0.500617	−	0.867095i	0.499382	−	0.866382i	$-0.333560\pi$
$194$	1.09186	−	1.89115i	0.0783907	−	0.135777i
$195$	−6.29653	−	10.9059i	−0.450904	−	0.780988i
$196$	−4.79530	+	8.30570i	−0.342521	+	0.593264i
$197$	20.3595			1.45056			0.725279	−	0.688455i	$-0.241711\pi$
$197$	20.3595			1.45056			0.725279	+	0.688455i	$0.241711\pi$
$198$	0.105483			0.00749636
$199$	−1.51713	+	2.62774i	−0.107546	+	0.186276i	−0.914776	−	0.403962i	$-0.867633\pi$
$199$	−1.51713	+	2.62774i	−0.107546	+	0.186276i	0.807229	+	0.590238i	$0.200966\pi$
$200$	2.03577	−	3.52605i	0.143950	−	0.249329i
$201$	−9.70833			−0.684773
$202$	−1.08832			−0.0765739
$203$	4.70787	−	8.15427i	0.330428	−	0.572318i
$204$	4.80344	+	8.31980i	0.336308	+	0.582502i
$205$	17.3250	−	30.0079i	1.21003	−	2.09584i
$206$	0.505254	+	0.875125i	0.0352027	+	0.0609729i
$207$	−2.80372	−	4.85619i	−0.194872	−	0.337529i
$208$	9.29429			0.644443
$209$	1.08996	+	4.22043i	0.0753940	+	0.291933i
$210$	−1.07368			−0.0740912
$211$	−2.50879	−	4.34536i	−0.172712	−	0.299147i	0.766655	−	0.642059i	$-0.221920\pi$
$211$	−2.50879	−	4.34536i	−0.172712	−	0.299147i	−0.939367	+	0.342913i	$0.888586\pi$
$212$	−3.74712	−	6.49021i	−0.257353	−	0.445749i
$213$	−2.55627	+	4.42759i	−0.175153	+	0.303373i
$214$	−0.433067	−	0.750094i	−0.0296039	−	0.0512754i
$215$	12.8441	−	22.2466i	0.875959	−	1.51721i
$216$	−3.11061			−0.211650
$217$	−1.27305			−0.0864205
$218$	−0.188740	+	0.326908i	−0.0127831	+	0.0221410i
$219$	2.10364	−	3.64362i	0.142151	−	0.246213i
$220$	−6.96519			−0.469593
$221$	−7.75285			−0.521513
$222$	−0.289157	+	0.500834i	−0.0194069	+	0.0336138i
$223$	5.93082	+	10.2725i	0.397157	+	0.687896i	0.993374	−	0.114927i	$-0.0366635\pi$
$223$	5.93082	+	10.2725i	0.397157	+	0.687896i	−0.596217	+	0.802823i	$0.703330\pi$
$224$	1.20824	−	2.09273i	0.0807287	−	0.139826i
$225$	2.79764	+	4.84566i	0.186510	+	0.323044i
$226$	−0.0337873	−	0.0585213i	−0.00224750	−	0.00389278i
$227$	−1.40838			−0.0934777			−0.0467388	−	0.998907i	$-0.514883\pi$
$227$	−1.40838			−0.0934777			−0.0467388	+	0.998907i	$0.514883\pi$
$228$	−3.23141	−	12.5123i	−0.214005	−	0.828650i
$229$	11.3642			0.750971			0.375485	−	0.926828i	$-0.377476\pi$
$229$	11.3642			0.750971			0.375485	+	0.926828i	$0.377476\pi$
$230$	−1.80227	−	3.12162i	−0.118838	−	0.205834i
$231$	1.09940	+	1.90422i	0.0723355	+	0.125289i
$232$	1.77148	−	3.06830i	0.116303	−	0.201443i
$233$	6.40005	+	11.0852i	0.419281	+	0.726217i	0.995867	−	0.0908199i	$-0.0289488\pi$
$233$	6.40005	+	11.0852i	0.419281	+	0.726217i	−0.576586	+	0.817036i	$0.695615\pi$
$234$	0.126187	−	0.218562i	0.00824909	−	0.0142878i
$235$	−11.8120			−0.770530
$236$	−16.6421			−1.08331
$237$	−13.2607	+	22.9681i	−0.861372	+	1.49194i
$238$	−0.330504	+	0.572449i	−0.0214234	+	0.0371064i
$239$	−3.62977			−0.234790			−0.117395	−	0.993085i	$-0.537454\pi$
$239$	−3.62977			−0.234790			−0.117395	+	0.993085i	$0.537454\pi$
$240$	20.4468			1.31983
$241$	−9.66079	+	16.7330i	−0.622306	+	1.07787i	0.366749	+	0.930320i	$0.380471\pi$
$241$	−9.66079	+	16.7330i	−0.622306	+	1.07787i	−0.989055	+	0.147546i	$0.952862\pi$
$242$	−0.0694302	−	0.120257i	−0.00446314	−	0.00773039i
$243$	3.84288	−	6.65607i	0.246521	−	0.426987i
$244$	−1.42381	−	2.46611i	−0.0911502	−	0.157877i
$245$	−8.51341	−	14.7457i	−0.543902	−	0.942065i
$246$	−2.04801			−0.130576
$247$	10.0487	+	2.79039i	0.639381	+	0.177548i
$248$	−0.479026			−0.0304182
$249$	13.2562	+	22.9605i	0.840080	+	1.45506i
$250$	0.577604	+	1.00044i	0.0365309	+	0.0632734i
$251$	−9.06491	+	15.7009i	−0.572172	+	0.991031i	0.424170	+	0.905582i	$0.360566\pi$
$251$	−9.06491	+	15.7009i	−0.572172	+	0.991031i	−0.996343	+	0.0854489i	$0.972768\pi$
$252$	1.10516	+	1.91419i	0.0696185	+	0.120583i
$253$	−3.69089	+	6.39280i	−0.232044	+	0.401912i
$254$	0.511360			0.0320856
$255$	−17.0557			−1.06807
$256$	−7.23982	+	12.5397i	−0.452488	+	0.783733i
$257$	−0.779689	+	1.35046i	−0.0486357	+	0.0842394i	−0.889318	−	0.457289i	$-0.848821\pi$
$257$	−0.779689	+	1.35046i	−0.0486357	+	0.0842394i	0.840683	+	0.541528i	$0.182154\pi$
$258$	−1.51831			−0.0945258
$259$	4.08746			0.253982
$260$	−8.33229	+	14.4319i	−0.516747	+	0.895031i
$261$	2.43445	+	4.21659i	0.150689	+	0.261001i
$262$	−0.00375727	+	0.00650779i	−0.000232125	+	0.000402053i
$263$	−8.63606	−	14.9581i	−0.532522	−	0.922355i	−0.999279	−	0.0379695i	$-0.987911\pi$
$263$	−8.63606	−	14.9581i	−0.532522	−	0.922355i	0.466757	−	0.884386i	$-0.345422\pi$
$264$	0.413685	+	0.716523i	0.0254605	+	0.0440989i
$265$	13.3050			0.817321
$266$	0.634408	−	0.623011i	0.0388981	−	0.0381993i
$267$	−19.2672			−1.17914
$268$	6.42359	+	11.1260i	0.392383	+	0.679627i
$269$	6.96546	+	12.0645i	0.424692	+	0.735588i	0.996392	−	0.0848751i	$-0.0270491\pi$
$269$	6.96546	+	12.0645i	0.424692	+	0.735588i	−0.571700	+	0.820463i	$0.693716\pi$
$270$	1.37393	−	2.37971i	0.0836146	−	0.144825i
$271$	−3.07653	−	5.32870i	−0.186886	−	0.323695i	0.757325	−	0.653039i	$-0.226506\pi$
$271$	−3.07653	−	5.32870i	−0.186886	−	0.323695i	−0.944210	+	0.329343i	$0.893173\pi$
$272$	6.29398	−	10.9015i	0.381628	−	0.661000i
$273$	5.26076			0.318396
$274$	2.35684			0.142382
$275$	3.68288	−	6.37894i	0.222086	−	0.384665i
$276$	10.9424	−	18.9528i	0.658655	−	1.14082i
$277$	−18.4147			−1.10643			−0.553215	−	0.833039i	$-0.686599\pi$
$277$	−18.4147			−1.10643			−0.553215	+	0.833039i	$0.686599\pi$
$278$	−2.50452			−0.150211
$279$	0.329150	−	0.570104i	0.0197057	−	0.0341312i
$280$	1.42774	+	2.47291i	0.0853236	+	0.147785i
$281$	−12.4165	+	21.5060i	−0.740706	+	1.28294i	0.211469	+	0.977385i	$0.432175\pi$
$281$	−12.4165	+	21.5060i	−0.740706	+	1.28294i	−0.952174	+	0.305555i	$0.901158\pi$
$282$	0.349077	+	0.604618i	0.0207872	+	0.0360045i
$283$	−8.58804	−	14.8749i	−0.510506	−	0.884222i	−0.999926	−	0.0121742i	$-0.996125\pi$
$283$	−8.58804	−	14.8749i	−0.510506	−	0.884222i	0.489420	−	0.872048i	$-0.337209\pi$
$284$	6.76550			0.401458
$285$	22.1063	+	6.13865i	1.30947	+	0.363622i
$286$	−0.332231			−0.0196452
$287$	7.23755	+	12.5358i	0.427219	+	0.739965i
$288$	0.624782	+	1.08215i	0.0368157	+	0.0637666i
$289$	3.24987	−	5.62894i	0.191169	−	0.331114i
$290$	1.56490	+	2.71048i	0.0918939	+	0.159165i
$291$	−11.7692	+	20.3848i	−0.689922	+	1.19498i
$292$	−5.56757			−0.325817
$293$	23.1770			1.35402			0.677008	−	0.735976i	$-0.263276\pi$
$293$	23.1770			1.35402			0.677008	+	0.735976i	$0.263276\pi$
$294$	−0.503189	+	0.871548i	−0.0293466	+	0.0508297i
$295$	14.7729	−	25.5875i	0.860113	−	1.48976i
$296$	1.53803			0.0893963
$297$	−5.62736			−0.326533
$298$	0.368241	−	0.637812i	0.0213316	−	0.0369474i
$299$	8.83063	+	15.2951i	0.510689	+	0.884539i
$300$	−10.9187	+	18.9117i	−0.630390	+	1.09187i
$301$	5.36562	+	9.29353i	0.309269	+	0.535670i
$302$	0.750841	+	1.30049i	0.0432060	+	0.0748351i
$303$	11.7311			0.673932
$304$	−12.0814	+	11.8644i	−0.692917	+	0.680468i
$305$	5.05557			0.289481
$306$	−0.170904	−	0.296015i	−0.00976995	−	0.0169220i
$307$	−13.1575	−	22.7895i	−0.750940	−	1.30067i	−0.947367	−	0.320148i	$-0.896267\pi$
$307$	−13.1575	−	22.7895i	−0.750940	−	1.30067i	0.196427	−	0.980518i	$-0.437066\pi$
$308$	1.45486	−	2.51989i	0.0828982	−	0.143584i
$309$	−5.44616	−	9.43303i	−0.309821	−	0.536626i
$310$	0.211582	−	0.366470i	0.0120170	−	0.0208141i
$311$	25.2900			1.43407			0.717033	−	0.697039i	$-0.245500\pi$
$311$	25.2900			1.43407			0.717033	+	0.697039i	$0.245500\pi$
$312$	1.97952			0.112068
$313$	13.8440	−	23.9785i	0.782509	−	1.35534i	−0.147967	−	0.988992i	$-0.547273\pi$
$313$	13.8440	−	23.9785i	0.782509	−	1.35534i	0.930476	−	0.366353i	$-0.119394\pi$
$314$	−0.221849	+	0.384254i	−0.0125197	+	0.0216847i
$315$	−3.92412			−0.221099
$316$	35.0960			1.97431
$317$	−5.06181	+	8.76730i	−0.284299	+	0.492421i	−0.972439	−	0.233157i	$-0.925094\pi$
$317$	−5.06181	+	8.76730i	−0.284299	+	0.492421i	0.688140	+	0.725578i	$0.258428\pi$
$318$	−0.393200	−	0.681042i	−0.0220496	−	0.0381909i
$319$	3.20477	−	5.55082i	0.179433	−	0.310786i
$320$	−13.2588	−	22.9650i	−0.741192	−	1.28378i
$321$	4.66806	+	8.08532i	0.260546	+	0.451278i
$322$	1.50580			0.0839149
$323$	10.0777	−	9.89668i	0.560740	−	0.550666i
$324$	12.1696			0.676091
$325$	−8.81148	−	15.2619i	−0.488773	−	0.846580i
$326$	0.995894	+	1.72494i	0.0551575	+	0.0955355i
$327$	2.03444	−	3.52376i	0.112505	−	0.194864i
$328$	2.72335	+	4.71698i	0.150372	+	0.260452i
$329$	2.46724	−	4.27338i	0.136023	−	0.235599i
$330$	−0.730884			−0.0402338
$331$	8.45572			0.464769			0.232384	−	0.972624i	$-0.425347\pi$
$331$	8.45572			0.464769			0.232384	+	0.972624i	$0.425347\pi$
$332$	17.5422	−	30.3839i	0.962752	−	1.66753i
$333$	−1.05682	+	1.83046i	−0.0579132	+	0.100309i
$334$	2.11855			0.115922
$335$	−22.8084			−1.24616
$336$	−4.27083	+	7.39730i	−0.232993	+	0.403556i
$337$	−0.00868906	−	0.0150499i	−0.000473323	−	0.000819820i	0.865789	−	0.500410i	$-0.166817\pi$
$337$	−0.00868906	−	0.0150499i	−0.000473323	−	0.000819820i	−0.866262	+	0.499590i	$0.833484\pi$
$338$	0.505153	−	0.874951i	0.0274767	−	0.0475911i
$339$	0.364195	+	0.630805i	0.0197804	+	0.0342606i
$340$	11.2850	+	19.5463i	0.612017	+	1.06004i
$341$	−0.866600			−0.0469290
$342$	0.114972	+	0.445184i	0.00621699	+	0.0240728i
$343$	17.3961			0.939302
$344$	2.01898	+	3.49698i	0.108856	+	0.188544i
$345$	19.4268	+	33.6482i	1.04590	+	1.81156i
$346$	1.50489	−	2.60655i	0.0809034	−	0.140129i
$347$	−4.31931	−	7.48127i	−0.231873	−	0.401615i	0.726486	−	0.687181i	$-0.241152\pi$
$347$	−4.31931	−	7.48127i	−0.231873	−	0.401615i	−0.958359	+	0.285565i	$0.907819\pi$
$348$	−9.50121	+	16.4566i	−0.509318	+	0.882165i
$349$	−3.41607			−0.182858			−0.0914289	−	0.995812i	$-0.529143\pi$
$349$	−3.41607			−0.182858			−0.0914289	+	0.995812i	$0.529143\pi$
$350$	−1.50253			−0.0803138
$351$	−6.73188	+	11.6600i	−0.359321	+	0.622362i
$352$	0.822478	−	1.42457i	0.0438382	−	0.0759300i
$353$	−10.9807			−0.584443			−0.292221	−	0.956351i	$-0.594394\pi$
$353$	−10.9807			−0.584443			−0.292221	+	0.956351i	$0.594394\pi$
$354$	−1.74632			−0.0928159
$355$	−6.00562	+	10.4020i	−0.318745	+	0.552083i
$356$	12.7483	+	22.0807i	0.675659	+	1.17028i
$357$	3.56252	−	6.17047i	0.188549	−	0.326576i
$358$	−0.291207	−	0.504386i	−0.0153908	−	0.0266576i
$359$	−3.78126	−	6.54933i	−0.199567	−	0.345660i	0.748821	−	0.662772i	$-0.230620\pi$
$359$	−3.78126	−	6.54933i	−0.199567	−	0.345660i	−0.948388	+	0.317112i	$0.897287\pi$
$360$	−1.47657			−0.0778222
$361$	−16.6240	+	9.20018i	−0.874946	+	0.484220i
$362$	−3.46149			−0.181932
$363$	0.748393	+	1.29625i	0.0392804	+	0.0680357i
$364$	−3.48082	−	6.02896i	−0.182445	−	0.316003i
$365$	4.94223	−	8.56020i	0.258688	−	0.448061i
$366$	−0.149406	−	0.258779i	−0.00780957	−	0.0135266i
$367$	−1.48731	+	2.57609i	−0.0776369	+	0.134471i	−0.902230	−	0.431255i	$-0.858071\pi$
$367$	−1.48731	+	2.57609i	−0.0776369	+	0.134471i	0.824593	+	0.565726i	$0.191404\pi$
$368$	−28.6758			−1.49483
$369$	−7.48511			−0.389659
$370$	−0.679335	+	1.17664i	−0.0353170	+	0.0611708i
$371$	−2.77909	+	4.81353i	−0.144283	+	0.249906i
$372$	2.56922			0.133208
$373$	29.9852			1.55258			0.776288	−	0.630378i	$-0.217100\pi$
$373$	29.9852			1.55258			0.776288	+	0.630378i	$0.217100\pi$
$374$	−0.224982	+	0.389681i	−0.0116336	+	0.0201499i
$375$	−6.22603	−	10.7838i	−0.321511	−	0.556873i
$376$	0.928373	−	1.60799i	0.0478772	−	0.0829257i
$377$	−7.66757	−	13.2806i	−0.394900	−	0.683987i
$378$	0.573960	+	0.994127i	0.0295213	+	0.0511324i
$379$	−30.6010			−1.57187			−0.785933	−	0.618312i	$-0.787817\pi$
$379$	−30.6010			−1.57187			−0.785933	+	0.618312i	$0.787817\pi$
$380$	−7.59177	−	29.3961i	−0.389450	−	1.50799i
$381$	−5.51198			−0.282387
$382$	0.537702	+	0.931328i	0.0275112	+	0.0476509i
$383$	0.846790	+	1.46668i	0.0432690	+	0.0749440i	0.886849	−	0.462060i	$-0.152889\pi$
$383$	0.846790	+	1.46668i	0.0432690	+	0.0749440i	−0.843580	+	0.537004i	$0.819556\pi$
$384$	−3.24582	+	5.62192i	−0.165637	+	0.286892i
$385$	2.58290	+	4.47372i	0.131637	+	0.228002i
$386$	−0.965746	+	1.67272i	−0.0491552	+	0.0851393i
$387$	−5.54915			−0.282079
$388$	31.1487			1.58133
$389$	11.5309	−	19.9721i	0.584638	−	1.01262i	−0.410282	−	0.911959i	$-0.634570\pi$
$389$	11.5309	−	19.9721i	0.584638	−	1.01262i	0.994920	−	0.100665i	$-0.0320970\pi$
$390$	−0.874338	+	1.51440i	−0.0442739	+	0.0766846i
$391$	23.9200			1.20969
$392$	2.67647			0.135182
$393$	0.0404999	−	0.0701479i	0.00204295	−	0.00353849i
$394$	−1.41357	−	2.44837i	−0.0712145	−	0.123347i
$395$	−31.1542	+	53.9606i	−1.56754	+	2.71505i
$396$	0.752310	+	1.30304i	0.0378050	+	0.0654802i
$397$	9.51780	+	16.4853i	0.477685	+	0.827374i	0.999673	−	0.0255788i	$-0.00814286\pi$
$397$	9.51780	+	16.4853i	0.477685	+	0.827374i	−0.521988	+	0.852953i	$0.674810\pi$
$398$	0.421338			0.0211198
$399$	−6.83833	+	6.71548i	−0.342345	+	0.336194i
$400$	28.6136			1.43068
$401$	−13.9508	−	24.1634i	−0.696668	−	1.20666i	−0.969615	−	0.244635i	$-0.921332\pi$
$401$	−13.9508	−	24.1634i	−0.696668	−	1.20666i	0.272947	−	0.962029i	$-0.412002\pi$
$402$	0.674051	+	1.16749i	0.0336186	+	0.0582292i
$403$	−1.03669	+	1.79560i	−0.0516413	+	0.0894454i
$404$	−7.76195	−	13.4441i	−0.386171	−	0.668868i
$405$	−10.8028	+	18.7110i	−0.536794	+	0.929755i
$406$	−1.30747			−0.0648888
$407$	2.78244			0.137920
$408$	1.34051	−	2.32183i	0.0663650	−	0.114948i
$409$	3.66019	−	6.33964i	0.180985	−	0.313475i	−0.761231	−	0.648480i	$-0.775405\pi$
$409$	3.66019	−	6.33964i	0.180985	−	0.313475i	0.942216	+	0.335006i	$0.108738\pi$
$410$	−4.81153			−0.237624
$411$	−25.4045			−1.25311
$412$	−7.20699	+	12.4829i	−0.355063	+	0.614987i
$413$	6.17140	+	10.6892i	0.303675	+	0.525980i
$414$	−0.389326	+	0.674333i	−0.0191343	+	0.0331416i
$415$	31.1438	+	53.9426i	1.52879	+	2.64794i
$416$	−1.96782	−	3.40837i	−0.0964803	−	0.167109i
$417$	26.9964			1.32202
$418$	0.431858	−	0.424100i	0.0211229	−	0.0207434i
$419$	−37.5029			−1.83214			−0.916069	−	0.401021i	$-0.868655\pi$
$419$	−37.5029			−1.83214			−0.916069	+	0.401021i	$0.868655\pi$
$420$	−7.65756	−	13.2633i	−0.373651	−	0.647182i
$421$	−18.4265	−	31.9156i	−0.898050	−	1.55547i	−0.829983	−	0.557788i	$-0.811650\pi$
$421$	−18.4265	−	31.9156i	−0.898050	−	1.55547i	−0.0680671	−	0.997681i	$-0.521683\pi$
$422$	−0.348372	+	0.603398i	−0.0169585	+	0.0293729i
$423$	1.27581	+	2.20977i	0.0620322	+	0.107443i
$424$	−1.04572	+	1.81124i	−0.0507846	+	0.0879616i
$425$	−23.8681			−1.15777
$426$	0.709929			0.0343962
$427$	−1.05598	+	1.82902i	−0.0511027	+	0.0885125i
$428$	6.17731	−	10.6994i	0.298592	−	0.517176i
$429$	3.58113			0.172899
$430$	−3.56707			−0.172019
$431$	12.8949	−	22.3346i	0.621124	−	1.07582i	−0.368153	−	0.929765i	$-0.620010\pi$
$431$	12.8949	−	22.3346i	0.621124	−	1.07582i	0.989277	−	0.146053i	$-0.0466569\pi$
$432$	−10.9303	−	18.9318i	−0.525882	−	0.910854i
$433$	15.5014	−	26.8492i	0.744949	−	1.29029i	−0.205270	−	0.978705i	$-0.565807\pi$
$433$	15.5014	−	26.8492i	0.744949	−	1.29029i	0.950219	−	0.311584i	$-0.100860\pi$
$434$	0.0883884	+	0.153093i	0.00424278	+	0.00734871i
$435$	−16.8681	−	29.2164i	−0.808765	−	1.40082i
$436$	−5.38442			−0.257867
$437$	−31.0033	−	8.60922i	−1.48309	−	0.411835i
$438$	−0.584226			−0.0279154
$439$	−9.28895	−	16.0889i	−0.443337	−	0.767883i	0.554597	−	0.832119i	$-0.312872\pi$
$439$	−9.28895	−	16.0889i	−0.443337	−	0.767883i	−0.997935	+	0.0642361i	$0.979539\pi$
$440$	0.971897	+	1.68338i	0.0463334	+	0.0802518i
$441$	−1.83907	+	3.18536i	−0.0875746	+	0.151684i
$442$	0.538282	+	0.932331i	0.0256035	+	0.0443465i
$443$	13.3064	−	23.0474i	0.632208	−	1.09502i	−0.354891	−	0.934908i	$-0.615482\pi$
$443$	13.3064	−	23.0474i	0.632208	−	1.09502i	0.987099	−	0.160109i	$-0.0511845\pi$
$444$	−8.24912			−0.391486
$445$	−45.2658			−2.14581
$446$	0.823556	−	1.42644i	0.0389965	−	0.0675439i
$447$	−3.96929	+	6.87501i	−0.187741	+	0.325177i
$448$	11.0778			0.523376
$449$	7.83267			0.369647			0.184823	−	0.982772i	$-0.440829\pi$
$449$	7.83267			0.369647			0.184823	+	0.982772i	$0.440829\pi$
$450$	0.388482	−	0.672870i	0.0183132	−	0.0317194i
$451$	4.92679	+	8.53345i	0.231993	+	0.401824i
$452$	0.481945	−	0.834753i	0.0226688	−	0.0392635i
$453$	−8.09336	−	14.0181i	−0.380259	−	0.658628i
$454$	0.0977843	+	0.169367i	0.00458925	+	0.00794881i
$455$	12.3595			0.579420
$456$	−2.57313	+	2.52691i	−0.120498	+	0.118333i
$457$	2.02478			0.0947150			0.0473575	−	0.998878i	$-0.484920\pi$
$457$	2.02478			0.0947150			0.0473575	+	0.998878i	$0.484920\pi$
$458$	−0.789022	−	1.36663i	−0.0368686	−	0.0638583i
$459$	9.11749	+	15.7919i	0.425568	+	0.737105i
$460$	25.7077	−	44.5271i	1.19863	−	2.07609i
$461$	19.0709	+	33.0317i	0.888219	+	1.53844i	0.841979	+	0.539510i	$0.181390\pi$
$461$	19.0709	+	33.0317i	0.888219	+	1.53844i	0.0462393	+	0.998930i	$0.485276\pi$
$462$	0.152664	−	0.264421i	0.00710256	−	0.0123020i
$463$	−27.6957			−1.28713			−0.643564	−	0.765393i	$-0.722545\pi$
$463$	−27.6957			−1.28713			−0.643564	+	0.765393i	$0.722545\pi$
$464$	24.8990			1.15591
$465$	−2.28065	+	3.95020i	−0.105763	+	0.183186i
$466$	0.888714	−	1.53930i	0.0411689	−	0.0713066i
$467$	−3.91063			−0.180962			−0.0904811	−	0.995898i	$-0.528840\pi$
$467$	−3.91063			−0.180962			−0.0904811	+	0.995898i	$0.528840\pi$
$468$	3.59988			0.166405
$469$	4.76412	−	8.25170i	0.219987	−	0.381028i
$470$	0.820109	+	1.42047i	0.0378288	+	0.0655214i
$471$	2.39133	−	4.14190i	0.110187	−	0.190849i
$472$	2.32218	+	4.02213i	0.106887	+	0.185134i
$473$	3.65252	+	6.32635i	0.167943	+	0.290886i
$474$	3.68276			0.169155
$475$	30.9360	+	8.59055i	1.41944	+	0.394161i
$476$	−9.42867			−0.432162
$477$	−1.43708	−	2.48909i	−0.0657992	−	0.113968i
$478$	0.252016	+	0.436504i	0.0115269	+	0.0199652i
$479$	−3.38753	+	5.86737i	−0.154780	+	0.268087i	−0.932979	−	0.359931i	$-0.882800\pi$
$479$	−3.38753	+	5.86737i	−0.154780	+	0.268087i	0.778199	+	0.628018i	$0.216134\pi$
$480$	−4.32907	−	7.49816i	−0.197594	−	0.342243i
$481$	3.32856	−	5.76524i	0.151769	−	0.262872i
$482$	2.68300			0.122207
$483$	−16.2311			−0.738541
$484$	0.990359	−	1.71535i	0.0450163	−	0.0779705i
$485$	−27.6501	+	47.8914i	−1.25553	+	2.17464i
$486$	−1.06725			−0.0484114
$487$	15.8303			0.717340			0.358670	−	0.933464i	$-0.383230\pi$
$487$	15.8303			0.717340			0.358670	+	0.933464i	$0.383230\pi$
$488$	−0.397347	+	0.688225i	−0.0179870	+	0.0311545i
$489$	−10.7348	−	18.5932i	−0.485445	−	0.840815i
$490$	−1.18218	+	2.04759i	−0.0534052	+	0.0925006i
$491$	1.33202	+	2.30713i	0.0601132	+	0.104119i	0.894516	−	0.447036i	$-0.147520\pi$
$491$	1.33202	+	2.30713i	0.0601132	+	0.104119i	−0.834403	+	0.551155i	$0.814187\pi$
$492$	−14.6065	−	25.2992i	−0.658512	−	1.14058i
$493$	−20.7695			−0.935413
$494$	−0.362118	−	1.40215i	−0.0162924	−	0.0630859i
$495$	−2.67125			−0.120064
$496$	−1.68323	−	2.91544i	−0.0755793	−	0.130907i
$497$	−2.50885	−	4.34546i	−0.112537	−	0.194920i
$498$	1.84077	−	3.18830i	0.0824867	−	0.142871i
$499$	−5.45825	−	9.45397i	−0.244345	−	0.423218i	0.717602	−	0.696453i	$-0.245240\pi$
$499$	−5.45825	−	9.45397i	−0.244345	−	0.423218i	−0.961947	+	0.273235i	$0.911906\pi$
$500$	−8.23900	+	14.2704i	−0.368459	+	0.638190i
$501$	−22.8359			−1.02023
$502$	2.51752			0.112362
$503$	−15.3259	+	26.5453i	−0.683350	+	1.18360i	0.290603	+	0.956844i	$0.406144\pi$
$503$	−15.3259	+	26.5453i	−0.683350	+	1.18360i	−0.973952	+	0.226753i	$0.927189\pi$
$504$	0.308420	−	0.534198i	0.0137381	−	0.0237951i
$505$	27.5606			1.22643
$506$	1.02504			0.0455684
$507$	−5.44508	+	9.43116i	−0.241825	+	0.418852i
$508$	3.64704	+	6.31686i	0.161811	+	0.280265i
$509$	3.34825	−	5.79933i	0.148408	−	0.257051i	−0.782231	−	0.622989i	$-0.785918\pi$
$509$	3.34825	−	5.79933i	0.148408	−	0.257051i	0.930639	+	0.365938i	$0.119252\pi$
$510$	1.18418	+	2.05106i	0.0524365	+	0.0908226i
$511$	2.06462	+	3.57603i	0.0913335	+	0.158194i
$512$	10.6847			0.472204
$513$	−6.13360	−	23.7499i	−0.270805	−	1.04858i
$514$	0.216536			0.00955099
$515$	−12.7950	−	22.1617i	−0.563817	−	0.976559i
$516$	−10.8287	−	18.7558i	−0.476705	−	0.825677i
$517$	1.67951	−	2.90900i	0.0738648	−	0.127938i
$518$	−0.283793	−	0.491544i	−0.0124691	−	0.0215972i
$519$	−16.2213	+	28.0961i	−0.712036	+	1.23328i
$520$	4.65063			0.203943
$521$	−23.4833			−1.02882			−0.514412	−	0.857543i	$-0.671990\pi$
$521$	−23.4833			−1.02882			−0.514412	+	0.857543i	$0.671990\pi$
$522$	0.338049	−	0.585518i	0.0147960	−	0.0256274i
$523$	−17.5320	+	30.3664i	−0.766622	+	1.32783i	0.172763	+	0.984963i	$0.444731\pi$
$523$	−17.5320	+	30.3664i	−0.766622	+	1.32783i	−0.939385	+	0.342865i	$0.888603\pi$
$524$	−0.107188			−0.00468254
$525$	16.1959			0.706847
$526$	−1.19921	+	2.07709i	−0.0522879	+	0.0905653i
$527$	1.40407	+	2.43192i	0.0611623	+	0.105936i
$528$	−2.90726	+	5.03553i	−0.126522	+	0.219143i
$529$	−15.7453	−	27.2716i	−0.684578	−	1.18572i
$530$	−0.923771	−	1.60002i	−0.0401260	−	0.0695003i
$531$	−6.38249			−0.276977
$532$	12.2207	+	3.39354i	0.529836	+	0.147129i
$533$	23.5752			1.02115
$534$	1.33773	+	2.31701i	0.0578892	+	0.100267i
$535$	10.9670	+	18.9954i	0.474144	+	0.821242i
$536$	1.79265	−	3.10496i	0.0774306	−	0.134114i
$537$	3.13894	+	5.43681i	0.135455	+	0.234616i
$538$	0.967227	−	1.67529i	0.0417001	−	0.0722267i
$539$	4.84198			0.208559
$540$	39.1957			1.68671
$541$	−15.5351	+	26.9076i	−0.667906	+	1.15685i	0.310582	+	0.950547i	$0.399476\pi$
$541$	−15.5351	+	26.9076i	−0.667906	+	1.15685i	−0.978489	+	0.206301i	$0.933857\pi$
$542$	−0.427208	+	0.739946i	−0.0183501	+	0.0317834i
$543$	37.3116			1.60119
$544$	−5.33033			−0.228536
$545$	4.77966	−	8.27861i	0.204738	−	0.354616i
$546$	−0.365256	−	0.632641i	−0.0156315	−	0.0270745i
$547$	9.58969	−	16.6098i	0.410025	−	0.710185i	−0.584867	−	0.811129i	$-0.698853\pi$
$547$	9.58969	−	16.6098i	0.410025	−	0.710185i	0.994892	+	0.100945i	$0.0321865\pi$
$548$	16.8091	+	29.1142i	0.718048	+	1.24369i
$549$	−0.546052	−	0.945791i	−0.0233049	−	0.0403654i
$550$	−1.02281			−0.0436129
$551$	26.9199	+	7.47532i	1.14683	+	0.318459i
$552$	−6.10745			−0.259950
$553$	−13.0147	−	22.5421i	−0.553440	−	0.958587i
$554$	1.27853	+	2.21449i	0.0543197	+	0.0940845i
$555$	7.32260	−	12.6831i	0.310827	−	0.538368i
$556$	−17.8623	−	30.9385i	−0.757532	−	1.31208i
$557$	4.84499	−	8.39177i	0.205289	−	0.355571i	−0.744936	−	0.667136i	$-0.767520\pi$
$557$	4.84499	−	8.39177i	0.205289	−	0.355571i	0.950225	+	0.311565i	$0.100853\pi$
$558$	−0.0914117			−0.00386977
$559$	17.4777			0.739227
$560$	−10.0338	+	17.3790i	−0.424003	+	0.734395i
$561$	2.42510	−	4.20040i	0.102388	−	0.177341i
$562$	3.44832			0.145458
$563$	−24.4092			−1.02873			−0.514363	−	0.857573i	$-0.671972\pi$
$563$	−24.4092			−1.02873			−0.514363	+	0.857573i	$0.671972\pi$
$564$	−4.97926	+	8.62433i	−0.209665	+	0.363150i
$565$	0.855629	+	1.48199i	0.0359966	+	0.0623479i
$566$	−1.19254	+	2.06554i	−0.0501262	+	0.0868210i
$567$	−4.51287	−	7.81652i	−0.189523	−	0.328263i
$568$	−0.944033	−	1.63511i	−0.0396107	−	0.0686078i
$569$	34.3379			1.43952			0.719761	−	0.694222i	$-0.244251\pi$
$569$	34.3379			1.43952			0.719761	+	0.694222i	$0.244251\pi$
$570$	−0.796634	−	3.08464i	−0.0333673	−	0.129201i
$571$	43.4564			1.81859			0.909296	−	0.416149i	$-0.136621\pi$
$571$	43.4564			1.81859			0.909296	+	0.416149i	$0.136621\pi$
$572$	−2.36948	−	4.10407i	−0.0990731	−	0.171600i
$573$	−5.79593	−	10.0388i	−0.242128	−	0.419378i
$574$	1.00501	−	1.74073i	0.0419483	−	0.0726566i
$575$	27.1862	+	47.0879i	1.13374	+	1.96370i
$576$	−2.86418	+	4.96090i	−0.119341	+	0.206704i
$577$	18.1629			0.756131			0.378066	−	0.925779i	$-0.376589\pi$
$577$	18.1629			0.756131			0.378066	+	0.925779i	$0.376589\pi$
$578$	−0.902557			−0.0375414
$579$	10.4098	−	18.0304i	0.432618	−	0.749317i
$580$	−22.3218	+	38.6625i	−0.926864	+	1.60537i
$581$	−26.0207			−1.07952
$582$	3.26855			0.135486
$583$	−1.89180	+	3.27669i	−0.0783504	+	0.135707i
$584$	0.776878	+	1.34559i	0.0321474	+	0.0556810i
$585$	−3.19555	+	5.53486i	−0.132120	+	0.228838i
$586$	−1.60919	−	2.78719i	−0.0664748	−	0.115138i
$587$	5.77889	+	10.0093i	0.238520	+	0.413129i	0.960290	−	0.279004i	$-0.0900044\pi$
$587$	5.77889	+	10.0093i	0.238520	+	0.413129i	−0.721770	+	0.692133i	$0.756671\pi$
$588$	−14.3551			−0.591993
$589$	−0.944559	−	3.65742i	−0.0389199	−	0.150701i
$590$	−4.10275			−0.168908
$591$	15.2369	+	26.3911i	0.626764	+	1.08559i
$592$	5.40444	+	9.36076i	0.222121	+	0.384725i
$593$	−15.4091	+	26.6893i	−0.632776	+	1.09600i	0.354206	+	0.935167i	$0.384751\pi$
$593$	−15.4091	+	26.6893i	−0.632776	+	1.09600i	−0.986982	+	0.160832i	$0.948582\pi$
$594$	0.390709	+	0.676728i	0.0160310	+	0.0277665i
$595$	8.36967	−	14.4967i	0.343123	−	0.594306i
$596$	10.5052			0.430311
$597$	−4.54163			−0.185877
$598$	1.22623	−	2.12388i	0.0501441	−	0.0868521i
$599$	11.4515	−	19.8345i	0.467894	−	0.810416i	−0.531433	−	0.847100i	$-0.678346\pi$
$599$	11.4515	−	19.8345i	0.467894	−	0.810416i	0.999327	+	0.0366844i	$0.0116796\pi$
$600$	6.09421			0.248795
$601$	−5.27555			−0.215194			−0.107597	−	0.994195i	$-0.534316\pi$
$601$	−5.27555			−0.215194			−0.107597	+	0.994195i	$0.534316\pi$
$602$	0.745073	−	1.29050i	0.0303669	−	0.0525970i
$603$	2.46354	+	4.26697i	0.100323	+	0.173765i
$604$	−10.7101	+	18.5504i	−0.435786	+	0.754804i
$605$	1.75825	+	3.04538i	0.0714830	+	0.123812i
$606$	−0.814490	−	1.41074i	−0.0330864	−	0.0573074i
$607$	−22.3060			−0.905372			−0.452686	−	0.891670i	$-0.649534\pi$
$607$	−22.3060			−0.905372			−0.452686	+	0.891670i	$0.649534\pi$
$608$	6.90878	+	1.91848i	0.280188	+	0.0778047i
$609$	14.0933			0.571091
$610$	−0.351010	−	0.607966i	−0.0142120	−	0.0246158i
$611$	−4.01831	−	6.95992i	−0.162564	−	0.281568i
$612$	2.43779	−	4.22238i	0.0985420	−	0.170680i
$613$	−18.8972	−	32.7309i	−0.763249	−	1.32199i	−0.941167	−	0.337941i	$-0.890269\pi$
$613$	−18.8972	−	32.7309i	−0.763249	−	1.32199i	0.177918	−	0.984045i	$-0.443064\pi$
$614$	−1.82706	+	3.16456i	−0.0737342	+	0.127711i
$615$	51.8637			2.09135
$616$	−0.812022			−0.0327173
$617$	−4.84658	+	8.39452i	−0.195116	+	0.337951i	−0.946939	−	0.321415i	$-0.895842\pi$
$617$	−4.84658	+	8.39452i	−0.195116	+	0.337951i	0.751823	+	0.659366i	$0.229175\pi$
$618$	−0.756257	+	1.30987i	−0.0304211	+	0.0526909i
$619$	−18.4686			−0.742314			−0.371157	−	0.928570i	$-0.621039\pi$
$619$	−18.4686			−0.742314			−0.371157	+	0.928570i	$0.621039\pi$
$620$	6.03604			0.242413
$621$	20.7700	−	35.9746i	0.833470	−	1.44361i
$622$	−1.75589	−	3.04129i	−0.0704049	−	0.121945i
$623$	9.45492	−	16.3764i	0.378803	−	0.656106i
$624$	6.95578	+	12.0478i	0.278454	+	0.482296i
$625$	3.78717	+	6.55957i	0.151487	+	0.262383i
$626$	−3.84476			−0.153668
$627$	−4.65503	+	4.57140i	−0.185904	+	0.182564i
$628$	−6.32896			−0.252553
$629$	−4.50812	−	7.80829i	−0.179750	−	0.311337i
$630$	0.272453	+	0.471902i	0.0108548	+	0.0188010i
$631$	−6.41709	+	11.1147i	−0.255460	+	0.442470i	−0.965020	−	0.262175i	$-0.915560\pi$
$631$	−6.41709	+	11.1147i	−0.255460	+	0.442470i	0.709560	+	0.704645i	$0.248894\pi$
$632$	−4.89717	−	8.48215i	−0.194799	−	0.337402i
$633$	3.75512	−	6.50406i	0.149253	−	0.258513i
$634$	1.40577			0.0558302
$635$	−12.9497			−0.513892
$636$	5.60864	−	9.71445i	0.222397	−	0.385203i
$637$	5.79234	−	10.0326i	0.229501	−	0.397507i
$638$	−0.890031			−0.0352367
$639$	2.59467			0.102643
$640$	−7.62562	+	13.2080i	−0.301429	+	0.522090i
$641$	−20.6116	−	35.7004i	−0.814110	−	1.41008i	−0.909966	−	0.414684i	$-0.863892\pi$
$641$	−20.6116	−	35.7004i	−0.814110	−	1.41008i	0.0958560	−	0.995395i	$-0.469441\pi$
$642$	0.648209	−	1.12273i	0.0255828	−	0.0443106i
$643$	7.80162	+	13.5128i	0.307666	+	0.532893i	0.977851	−	0.209301i	$-0.0671188\pi$
$643$	7.80162	+	13.5128i	0.307666	+	0.532893i	−0.670186	+	0.742194i	$0.733785\pi$
$644$	10.7394	+	18.6012i	0.423193	+	0.732991i
$645$	38.4497			1.51395
$646$	−1.88984	−	0.524785i	−0.0743548	−	0.0206474i
$647$	−12.7748			−0.502228			−0.251114	−	0.967958i	$-0.580797\pi$
$647$	−12.7748			−0.502228			−0.251114	+	0.967958i	$0.580797\pi$
$648$	−1.69811	−	2.94121i	−0.0667079	−	0.115542i
$649$	4.20103	+	7.27640i	0.164905	+	0.285624i
$650$	−1.22357	+	2.11928i	−0.0479922	+	0.0831250i
$651$	−0.952744	−	1.65020i	−0.0373410	−	0.0646765i
$652$	−14.2055	+	24.6047i	−0.556331	+	0.963594i
$653$	−5.05990			−0.198009			−0.0990045	−	0.995087i	$-0.531566\pi$
$653$	−5.05990			−0.198009			−0.0990045	+	0.995087i	$0.531566\pi$
$654$	−0.565007			−0.0220935
$655$	0.0951492	−	0.164803i	0.00371779	−	0.00643939i
$656$	−19.1390	+	33.1497i	−0.747252	+	1.29428i
$657$	−2.13524			−0.0833037
$658$	−0.685203			−0.0267120
$659$	14.6898	−	25.4435i	0.572233	−	0.991137i	−0.424103	−	0.905614i	$-0.639410\pi$
$659$	14.6898	−	25.4435i	0.572233	−	0.991137i	0.996336	−	0.0855232i	$-0.0272562\pi$
$660$	−5.21270	−	9.02866i	−0.202904	−	0.351440i
$661$	16.2699	−	28.1804i	0.632827	−	1.09609i	−0.354144	−	0.935191i	$-0.615228\pi$
$661$	16.2699	−	28.1804i	0.632827	−	1.09609i	0.986971	−	0.160898i	$-0.0514389\pi$
$662$	−0.587083	−	1.01686i	−0.0228176	−	0.0395213i
$663$	−5.80217	−	10.0497i	−0.225338	−	0.390296i
$664$	−9.79108			−0.379968
$665$	−16.0657	+	15.7771i	−0.623003	+	0.611811i
$666$	0.293500			0.0113729
$667$	23.6569	+	40.9749i	0.915998	+	1.58656i
$668$	15.1096	+	26.1705i	0.584607	+	1.01257i
$669$	−8.87716	+	15.3757i	−0.343211	+	0.594459i
$670$	1.58359	+	2.74287i	0.0611796	+	0.105966i
$671$	−0.718836	+	1.24506i	−0.0277504	+	0.0480650i
$672$	3.61694			0.139527
$673$	−37.8116			−1.45753			−0.728765	−	0.684764i	$-0.759905\pi$
$673$	−37.8116			−1.45753			−0.728765	+	0.684764i	$0.759905\pi$
$674$	−0.00120657	+	0.00208983i	−4.64752e−5	+	8.04974e-5i
$675$	−20.7249	+	35.8966i	−0.797703	+	1.38166i
$676$	14.4111			0.554273
$677$	−1.66524			−0.0640004			−0.0320002	−	0.999488i	$-0.510188\pi$
$677$	−1.66524			−0.0640004			−0.0320002	+	0.999488i	$0.510188\pi$
$678$	0.0505723	−	0.0875938i	0.00194222	−	0.00336402i
$679$	−11.5509	−	20.0067i	−0.443282	−	0.767786i
$680$	3.14935	−	5.45483i	0.120772	−	0.209183i
$681$	−1.05402	−	1.82562i	−0.0403903	−	0.0699580i
$682$	0.0601682	+	0.104214i	0.00230396	+	0.00399058i
$683$	−22.3652			−0.855779			−0.427890	−	0.903831i	$-0.640743\pi$
$683$	−22.3652			−0.855779			−0.427890	+	0.903831i	$0.640743\pi$
$684$	−4.67939	+	4.59533i	−0.178921	+	0.175707i
$685$	−59.6845			−2.28043
$686$	−1.20782	−	2.09200i	−0.0461146	−	0.0798728i
$687$	8.50492	+	14.7310i	0.324483	+	0.562021i
$688$	−14.1889	+	24.5758i	−0.540945	+	0.936945i
$689$	4.52623	+	7.83966i	0.172436	+	0.298667i
$690$	2.69761	−	4.67240i	0.102696	−	0.177875i
$691$	22.7083			0.863865			0.431932	−	0.901906i	$-0.357832\pi$
$691$	22.7083			0.863865			0.431932	+	0.901906i	$0.357832\pi$
$692$	42.9318			1.63202
$693$	0.557959	−	0.966413i	0.0211951	−	0.0367110i
$694$	−0.599781	+	1.03885i	−0.0227674	+	0.0394343i
$695$	63.4244			2.40582
$696$	5.30305			0.201012
$697$	15.9648	−	27.6519i	0.604710	−	1.04739i
$698$	0.237178	+	0.410805i	0.00897733	+	0.0155492i
$699$	−9.57950	+	16.5922i	−0.362330	+	0.627574i
$700$	−10.7161	−	18.5609i	−0.405032	−	0.701536i
$701$	13.5245	+	23.4252i	0.510814	+	0.884756i	0.999921	+	0.0125325i	$0.00398932\pi$
$701$	13.5245	+	23.4252i	0.510814	+	0.884756i	−0.489107	+	0.872224i	$0.662677\pi$
$702$	1.86958			0.0705629
$703$	3.03274	+	11.7431i	0.114382	+	0.442898i
$704$	7.54094			0.284210
$705$	−8.84001	−	15.3113i	−0.332934	−	0.576659i
$706$	0.762391	+	1.32050i	0.0286930	+	0.0496977i
$707$	−5.75673	+	9.97095i	−0.216504	+	0.374996i
$708$	−12.4548	−	21.5724i	−0.468082	−	0.810741i
$709$	15.6386	−	27.0868i	0.587320	−	1.01727i	−0.407262	−	0.913311i	$-0.633517\pi$
$709$	15.6386	−	27.0868i	0.587320	−	1.01727i	0.994582	−	0.103956i	$-0.0331501\pi$
$710$	1.66788			0.0625946
$711$	13.4598			0.504783
$712$	3.55770	−	6.16212i	0.133331	−	0.230935i
$713$	3.19852	−	5.54001i	0.119786	−	0.207475i
$714$	−0.989386			−0.0370268
$715$	8.41340			0.314643
$716$	4.15381	−	7.19461i	0.155235	−	0.268875i
$717$	−2.71649	−	4.70511i	−0.101449	−	0.175715i
$718$	−0.525067	+	0.909442i	−0.0195953	+	0.0339401i
$719$	5.24510	+	9.08478i	0.195609	+	0.338805i	0.947100	−	0.320938i	$-0.103998\pi$
$719$	5.24510	+	9.08478i	0.195609	+	0.338805i	−0.751491	+	0.659744i	$0.770665\pi$
$720$	−5.18848	−	8.98671i	−0.193363	−	0.334915i
$721$	10.6903			0.398127
$722$	2.26059	+	1.36037i	0.0841304	+	0.0506279i
$723$	−28.9203			−1.07556
$724$	−24.6875	−	42.7600i	−0.917504	−	1.58916i
$725$	−23.6056	−	40.8861i	−0.876689	−	1.51847i
$726$	0.103922	−	0.179998i	0.00385691	−	0.00668037i
$727$	21.7091	+	37.6012i	0.805145	+	1.39455i	0.916193	+	0.400737i	$0.131246\pi$
$727$	21.7091	+	37.6012i	0.805145	+	1.39455i	−0.111048	+	0.993815i	$0.535421\pi$
$728$	−0.971402	+	1.68252i	−0.0360025	+	0.0623582i
$729$	29.9361			1.10874
$730$	−1.37256			−0.0508008
$731$	11.8357	−	20.5000i	0.437758	−	0.758219i
$732$	2.13114	−	3.69124i	0.0787692	−	0.136432i
$733$	37.7254			1.39342			0.696710	−	0.717353i	$-0.254646\pi$
$733$	37.7254			1.39342			0.696710	+	0.717353i	$0.254646\pi$
$734$	0.413057			0.0152462
$735$	12.7427	−	22.0711i	0.470023	−	0.814104i
$736$	6.07135	+	10.5159i	0.223793	+	0.387621i
$737$	3.24306	−	5.61714i	0.119460	−	0.206910i
$738$	0.519693	+	0.900134i	0.0191302	+	0.0331344i
$739$	−5.29522	−	9.17158i	−0.194788	−	0.337382i	0.752043	−	0.659114i	$-0.229068\pi$
$739$	−5.29522	−	9.17158i	−0.194788	−	0.337382i	−0.946831	+	0.321732i	$0.895735\pi$
$740$	−19.3802			−0.712431
$741$	3.90329	+	15.1139i	0.143391	+	0.555223i
$742$	0.771812			0.0283341
$743$	1.16281	+	2.01404i	0.0426593	+	0.0738881i	0.886567	−	0.462601i	$-0.153084\pi$
$743$	1.16281	+	2.01404i	0.0426593	+	0.0738881i	−0.843907	+	0.536489i	$0.819750\pi$
$744$	−0.358499	−	0.620939i	−0.0131432	−	0.0227647i
$745$	−9.32532	+	16.1519i	−0.341653	+	0.591761i
$746$	−2.08188	−	3.60592i	−0.0762231	−	0.132022i
$747$	6.72768	−	11.6527i	0.246153	−	0.426349i
$748$	−6.41834			−0.234678
$749$	−9.16294			−0.334806
$750$	−0.864550	+	1.49744i	−0.0315689	+	0.0546789i
$751$	3.68732	−	6.38662i	0.134552	−	0.233051i	−0.790874	−	0.611979i	$-0.790374\pi$
$751$	3.68732	−	6.38662i	0.134552	−	0.233051i	0.925426	+	0.378928i	$0.123707\pi$
$752$	13.0487			0.475838
$753$	−27.1365			−0.988907
$754$	−1.06472	+	1.84415i	−0.0387749	+	0.0671601i
$755$	−19.0143	−	32.9337i	−0.692001	−	1.19858i
$756$	−8.18701	+	14.1803i	−0.297759	+	0.515733i
$757$	18.1150	+	31.3761i	0.658401	+	1.14038i	0.981029	+	0.193859i	$0.0621003\pi$
$757$	18.1150	+	31.3761i	0.658401	+	1.14038i	−0.322628	+	0.946526i	$0.604566\pi$
$758$	2.12463	+	3.67997i	0.0771701	+	0.133662i
$759$	−11.0489			−0.401051
$760$	−6.04523	+	5.93663i	−0.219284	+	0.215344i
$761$	8.48528			0.307591			0.153796	−	0.988103i	$-0.450850\pi$
$761$	8.48528			0.307591			0.153796	+	0.988103i	$0.450850\pi$
$762$	0.382698	+	0.662852i	0.0138637	+	0.0240126i
$763$	1.99670	+	3.45839i	0.0722856	+	0.125202i
$764$	−7.66983	+	13.2845i	−0.277485	+	0.480618i
$765$	4.32798	+	7.49628i	0.156478	+	0.271028i
$766$	0.117586	−	0.203664i	0.00424854	−	0.00735869i
$767$	20.1024			0.725854
$768$	−21.6729			−0.782053
$769$	4.09326	−	7.08973i	0.147607	−	0.255662i	−0.782736	−	0.622354i	$-0.786176\pi$
$769$	4.09326	−	7.08973i	0.147607	−	0.255662i	0.930342	+	0.366692i	$0.119510\pi$
$770$	0.358663	−	0.621223i	0.0129253	−	0.0223873i

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)

\(f(q)\)	\(=\)	\(q+(-0.0694302 - 0.120257i) q^{2} +(0.748393 + 1.29625i) q^{3} +(0.990359 - 1.71535i) q^{4} +(1.75825 + 3.04538i) q^{5} +(0.103922 - 0.179998i) q^{6} -1.46902 q^{7} -0.552764 q^{8} +(0.379817 - 0.657862i) q^{9} +O(q^{10})\)	\(q+(-0.0694302 - 0.120257i) q^{2} +(0.748393 + 1.29625i) q^{3} +(0.990359 - 1.71535i) q^{4} +(1.75825 + 3.04538i) q^{5} +(0.103922 - 0.179998i) q^{6} -1.46902 q^{7} -0.552764 q^{8} +(0.379817 - 0.657862i) q^{9} +(0.244151 - 0.422882i) q^{10} -1.00000 q^{11} +2.96471 q^{12} +(-1.19628 + 2.07201i) q^{13} +(0.101994 + 0.176659i) q^{14} +(-2.63172 + 4.55828i) q^{15} +(-1.94234 - 3.36423i) q^{16} +(1.62021 + 2.80628i) q^{17} -0.105483 q^{18} +(-1.08996 - 4.22043i) q^{19} +6.96519 q^{20} +(-1.09940 - 1.90422i) q^{21} +(0.0694302 + 0.120257i) q^{22} +(3.69089 - 6.39280i) q^{23} +(-0.413685 - 0.716523i) q^{24} +(-3.68288 + 6.37894i) q^{25} +0.332231 q^{26} +5.62736 q^{27} +(-1.45486 + 2.51989i) q^{28} +(-3.20477 + 5.55082i) q^{29} +0.730884 q^{30} +0.866600 q^{31} +(-0.822478 + 1.42457i) q^{32} +(-0.748393 - 1.29625i) q^{33} +(0.224982 - 0.389681i) q^{34} +(-2.58290 - 4.47372i) q^{35} +(-0.752310 - 1.30304i) q^{36} -2.78244 q^{37} +(-0.431858 + 0.424100i) q^{38} -3.58113 q^{39} +(-0.971897 - 1.68338i) q^{40} +(-4.92679 - 8.53345i) q^{41} +(-0.152664 + 0.264421i) q^{42} +(-3.65252 - 6.32635i) q^{43} +(-0.990359 + 1.71535i) q^{44} +2.67125 q^{45} -1.02504 q^{46} +(-1.67951 + 2.90900i) q^{47} +(2.90726 - 5.03553i) q^{48} -4.84198 q^{49} +1.02281 q^{50} +(-2.42510 + 4.20040i) q^{51} +(2.36948 + 4.10407i) q^{52} +(1.89180 - 3.27669i) q^{53} +(-0.390709 - 0.676728i) q^{54} +(-1.75825 - 3.04538i) q^{55} +0.812022 q^{56} +(4.65503 - 4.57140i) q^{57} +0.890031 q^{58} +(-4.20103 - 7.27640i) q^{59} +(5.21270 + 9.02866i) q^{60} +(0.718836 - 1.24506i) q^{61} +(-0.0601682 - 0.104214i) q^{62} +(-0.557959 + 0.966413i) q^{63} -7.54094 q^{64} -8.41340 q^{65} +(-0.103922 + 0.179998i) q^{66} +(-3.24306 + 5.61714i) q^{67} +6.41834 q^{68} +11.0489 q^{69} +(-0.358663 + 0.621223i) q^{70} +(1.70784 + 2.95807i) q^{71} +(-0.209949 + 0.363643i) q^{72} +(-1.40544 - 2.43430i) q^{73} +(0.193185 + 0.334607i) q^{74} -11.0250 q^{75} +(-8.31897 - 2.31007i) q^{76} +1.46902 q^{77} +(0.248639 + 0.430655i) q^{78} +(8.85942 + 15.3450i) q^{79} +(6.83023 - 11.8303i) q^{80} +(3.07203 + 5.32091i) q^{81} +(-0.684136 + 1.18496i) q^{82} +17.7129 q^{83} -4.35522 q^{84} +(-5.69745 + 9.86827i) q^{85} +(-0.507190 + 0.878479i) q^{86} -9.59370 q^{87} +0.552764 q^{88} +(-6.43621 + 11.1478i) q^{89} +(-0.185466 - 0.321236i) q^{90} +(1.75735 - 3.04382i) q^{91} +(-7.31060 - 12.6623i) q^{92} +(0.648557 + 1.12333i) q^{93} +0.466435 q^{94} +(10.9364 - 10.7399i) q^{95} -2.46215 q^{96} +(7.86297 + 13.6191i) q^{97} +(0.336180 + 0.582280i) q^{98} +(-0.379817 + 0.657862i) 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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