LMFDB - Embedded newform 547.2.f.a.46.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(46,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([14]))

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

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

chi := DirichletCharacter("547.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.f (of order $13$, degree $12$, 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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$528$
Relative dimension:	$44$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			46.4
Character	$\chi$	$=$	547.46
Dual form			547.2.f.a.440.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.304286 + 2.50602i) q^{2} -1.95070 q^{3} +(-4.24565 - 1.04646i) q^{4} +(-1.15766 - 3.05250i) q^{5} +(0.593571 - 4.88850i) q^{6} +(0.109988 + 0.905836i) q^{7} +(2.12398 - 5.60049i) q^{8} +0.805247 q^{9} +O(q^{10})$	\(q+(-0.304286 + 2.50602i) q^{2} -1.95070 q^{3} +(-4.24565 - 1.04646i) q^{4} +(-1.15766 - 3.05250i) q^{5} +(0.593571 - 4.88850i) q^{6} +(0.109988 + 0.905836i) q^{7} +(2.12398 - 5.60049i) q^{8} +0.805247 q^{9} +(8.00187 - 1.97228i) q^{10} +(0.167724 - 0.242990i) q^{11} +(8.28200 + 2.04133i) q^{12} -0.961079 q^{13} -2.30351 q^{14} +(2.25825 + 5.95452i) q^{15} +(5.64493 + 2.96269i) q^{16} +(3.03133 + 4.39165i) q^{17} +(-0.245025 + 2.01796i) q^{18} +(2.64658 - 1.38903i) q^{19} +(1.72070 + 14.1713i) q^{20} +(-0.214555 - 1.76702i) q^{21} +(0.557900 + 0.494256i) q^{22} +(-3.07691 + 2.72590i) q^{23} +(-4.14327 + 10.9249i) q^{24} +(-4.23501 + 3.75189i) q^{25} +(0.292442 - 2.40848i) q^{26} +4.28131 q^{27} +(0.480947 - 3.96096i) q^{28} +(-1.23855 - 1.09726i) q^{29} +(-15.6093 + 3.84734i) q^{30} +(2.45838 + 1.29026i) q^{31} +(-2.33712 + 3.38591i) q^{32} +(-0.327179 + 0.474001i) q^{33} +(-11.9279 + 6.26026i) q^{34} +(2.63773 - 1.38439i) q^{35} +(-3.41879 - 0.842657i) q^{36} +(-0.0175350 - 0.0155346i) q^{37} +(2.67562 + 7.05503i) q^{38} +1.87478 q^{39} -19.5543 q^{40} +1.84622 q^{41} +4.49346 q^{42} +(5.52096 + 1.36079i) q^{43} +(-0.966373 + 0.856132i) q^{44} +(-0.932201 - 2.45801i) q^{45} +(-5.89490 - 8.54024i) q^{46} +(9.41162 + 8.33797i) q^{47} +(-11.0116 - 5.77933i) q^{48} +(5.98815 - 1.47595i) q^{49} +(-8.11365 - 11.7546i) q^{50} +(-5.91324 - 8.56680i) q^{51} +(4.08040 + 1.00573i) q^{52} +(-2.64015 - 6.96150i) q^{53} +(-1.30274 + 10.7290i) q^{54} +(-0.935891 - 0.230677i) q^{55} +(5.30674 + 1.30799i) q^{56} +(-5.16269 + 2.70959i) q^{57} +(3.12661 - 2.76994i) q^{58} +(-10.5329 - 5.52809i) q^{59} +(-3.35658 - 27.6439i) q^{60} +(-0.353301 + 2.90970i) q^{61} +(-3.98146 + 5.76814i) q^{62} +(0.0885678 + 0.729421i) q^{63} +(1.76978 + 1.56789i) q^{64} +(1.11260 + 2.93369i) q^{65} +(-1.08830 - 0.964148i) q^{66} +(7.98562 + 1.96828i) q^{67} +(-8.27430 - 21.8175i) q^{68} +(6.00214 - 5.31743i) q^{69} +(2.66668 + 7.03145i) q^{70} +(13.7258 - 7.20387i) q^{71} +(1.71033 - 4.50977i) q^{72} +(-5.10925 + 13.4720i) q^{73} +(0.0442657 - 0.0392160i) q^{74} +(8.26125 - 7.31883i) q^{75} +(-12.6900 + 3.12780i) q^{76} +(0.238556 + 0.125204i) q^{77} +(-0.570469 + 4.69823i) q^{78} +(10.7533 + 2.65045i) q^{79} +(2.50869 - 20.6609i) q^{80} -10.7673 q^{81} +(-0.561777 + 4.62665i) q^{82} +(-0.347546 - 0.916402i) q^{83} +(-0.938186 + 7.72666i) q^{84} +(9.89623 - 14.3372i) q^{85} +(-5.09012 + 13.4216i) q^{86} +(2.41604 + 2.14042i) q^{87} +(-1.00462 - 1.45544i) q^{88} +(-0.405151 - 3.33672i) q^{89} +(6.44348 - 1.58817i) q^{90} +(-0.105708 - 0.870580i) q^{91} +(15.9160 - 8.35336i) q^{92} +(-4.79558 - 2.51691i) q^{93} +(-23.7589 + 21.0486i) q^{94} +(-7.30384 - 6.47064i) q^{95} +(4.55904 - 6.60490i) q^{96} +(-2.55643 - 3.70363i) q^{97} +(1.87664 + 15.4555i) q^{98} +(0.135059 - 0.195666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 528 q - 8 q^{2} - 46 q^{3} - 50 q^{4} - 9 q^{5} - 21 q^{6} - 3 q^{7} + 14 q^{8} + 466 q^{9}+O(q^{10}) $ 528 * q - 8 * q^2 - 46 * q^3 - 50 * q^4 - 9 * q^5 - 21 * q^6 - 3 * q^7 + 14 * q^8 + 466 * q^9	\( 528 q - 8 q^{2} - 46 q^{3} - 50 q^{4} - 9 q^{5} - 21 q^{6} - 3 q^{7} + 14 q^{8} + 466 q^{9} + 7 q^{10} - 16 q^{11} - 53 q^{12} - 12 q^{13} - 38 q^{15} - 38 q^{16} + 7 q^{17} - 23 q^{18} + 5 q^{19} + 45 q^{20} + 4 q^{21} + 43 q^{22} + 2 q^{23} - 51 q^{24} - 69 q^{25} - 4 q^{26} - 142 q^{27} - 2 q^{28} - 72 q^{29} - 50 q^{30} + 25 q^{31} + 66 q^{32} - 4 q^{34} + 33 q^{35} - 55 q^{36} + 21 q^{37} + 40 q^{38} - 142 q^{39} + 78 q^{40} - 140 q^{41} - 248 q^{42} + 23 q^{43} + 64 q^{44} - 163 q^{45} + 14 q^{46} + 37 q^{47} - 35 q^{48} + q^{49} + 70 q^{50} - 72 q^{51} - 74 q^{52} - 17 q^{53} - 76 q^{54} + 6 q^{55} - 38 q^{56} + 5 q^{57} + 29 q^{58} + 30 q^{59} - 108 q^{60} - 94 q^{61} - 75 q^{62} - 77 q^{63} - 252 q^{64} - 122 q^{65} + 79 q^{66} + 43 q^{67} - 193 q^{68} + 14 q^{69} - 267 q^{70} + 61 q^{71} + 49 q^{72} + 11 q^{73} + 85 q^{74} + 120 q^{75} - 23 q^{76} + 31 q^{77} - 90 q^{78} + 65 q^{79} + 58 q^{80} + 280 q^{81} + 10 q^{82} - 8 q^{83} - 136 q^{84} + 33 q^{85} + 91 q^{86} - 70 q^{87} - 198 q^{88} + 41 q^{89} - 68 q^{90} + 38 q^{91} + 43 q^{92} + 132 q^{93} + 8 q^{94} - 49 q^{95} + 262 q^{96} - 14 q^{97} + 41 q^{98} - 36 q^{99}+O(q^{100}) \) 528 * q - 8 * q^2 - 46 * q^3 - 50 * q^4 - 9 * q^5 - 21 * q^6 - 3 * q^7 + 14 * q^8 + 466 * q^9 + 7 * q^10 - 16 * q^11 - 53 * q^12 - 12 * q^13 - 38 * q^15 - 38 * q^16 + 7 * q^17 - 23 * q^18 + 5 * q^19 + 45 * q^20 + 4 * q^21 + 43 * q^22 + 2 * q^23 - 51 * q^24 - 69 * q^25 - 4 * q^26 - 142 * q^27 - 2 * q^28 - 72 * q^29 - 50 * q^30 + 25 * q^31 + 66 * q^32 - 4 * q^34 + 33 * q^35 - 55 * q^36 + 21 * q^37 + 40 * q^38 - 142 * q^39 + 78 * q^40 - 140 * q^41 - 248 * q^42 + 23 * q^43 + 64 * q^44 - 163 * q^45 + 14 * q^46 + 37 * q^47 - 35 * q^48 + q^49 + 70 * q^50 - 72 * q^51 - 74 * q^52 - 17 * q^53 - 76 * q^54 + 6 * q^55 - 38 * q^56 + 5 * q^57 + 29 * q^58 + 30 * q^59 - 108 * q^60 - 94 * q^61 - 75 * q^62 - 77 * q^63 - 252 * q^64 - 122 * q^65 + 79 * q^66 + 43 * q^67 - 193 * q^68 + 14 * q^69 - 267 * q^70 + 61 * q^71 + 49 * q^72 + 11 * q^73 + 85 * q^74 + 120 * q^75 - 23 * q^76 + 31 * q^77 - 90 * q^78 + 65 * q^79 + 58 * q^80 + 280 * q^81 + 10 * q^82 - 8 * q^83 - 136 * q^84 + 33 * q^85 + 91 * q^86 - 70 * q^87 - 198 * q^88 + 41 * q^89 - 68 * q^90 + 38 * q^91 + 43 * q^92 + 132 * q^93 + 8 * q^94 - 49 * q^95 + 262 * q^96 - 14 * q^97 + 41 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{13}\right)$

Coefficient data

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

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

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

$2$	−0.304286	+	2.50602i	−0.215162	+	1.77202i	0.340142	+	0.940374i	$0.389525\pi$
$2$	−0.304286	+	2.50602i	−0.215162	+	1.77202i	−0.555304	+	0.831647i	$0.687398\pi$
$3$	−1.95070			−1.12624			−0.563120	−	0.826375i	$-0.690399\pi$
$3$	−1.95070			−1.12624			−0.563120	+	0.826375i	$0.690399\pi$
$4$	−4.24565	−	1.04646i	−2.12282	−	0.523229i
$5$	−1.15766	−	3.05250i	−0.517721	−	1.36512i	−0.897898	−	0.440204i	$-0.854906\pi$
$5$	−1.15766	−	3.05250i	−0.517721	−	1.36512i	0.380177	−	0.924914i	$-0.375863\pi$
$6$	0.593571	−	4.88850i	0.242324	−	1.99572i
$7$	0.109988	+	0.905836i	0.0415717	+	0.342374i	0.998623	+	0.0524560i	$0.0167049\pi$
$7$	0.109988	+	0.905836i	0.0415717	+	0.342374i	−0.957052	+	0.289918i	$0.906372\pi$
$8$	2.12398	−	5.60049i	0.750942	−	1.98007i
$9$	0.805247			0.268416
$10$	8.00187	−	1.97228i	2.53041	−	0.623691i
$11$	0.167724	−	0.242990i	0.0505706	−	0.0732641i	−0.796883	−	0.604134i	$-0.793519\pi$
$11$	0.167724	−	0.242990i	0.0505706	−	0.0732641i	0.847453	+	0.530870i	$0.178135\pi$
$12$	8.28200	+	2.04133i	2.39081	+	0.589281i
$13$	−0.961079			−0.266555			−0.133278	−	0.991079i	$-0.542550\pi$
$13$	−0.961079			−0.266555			−0.133278	+	0.991079i	$0.542550\pi$
$14$	−2.30351			−0.615639
$15$	2.25825	+	5.95452i	0.583078	+	1.53745i
$16$	5.64493	+	2.96269i	1.41123	+	0.740673i
$17$	3.03133	+	4.39165i	0.735207	+	1.06513i	0.995040	+	0.0994771i	$0.0317170\pi$
$17$	3.03133	+	4.39165i	0.735207	+	1.06513i	−0.259833	+	0.965653i	$0.583668\pi$
$18$	−0.245025	+	2.01796i	−0.0577529	+	0.475638i
$19$	2.64658	−	1.38903i	0.607166	−	0.318665i	−0.132972	−	0.991120i	$-0.542452\pi$
$19$	2.64658	−	1.38903i	0.607166	−	0.318665i	0.740139	+	0.672454i	$0.234760\pi$
$20$	1.72070	+	14.1713i	0.384761	+	3.16879i
$21$	−0.214555	−	1.76702i	−0.0468197	−	0.385595i
$22$	0.557900	+	0.494256i	0.118945	+	0.105376i
$23$	−3.07691	+	2.72590i	−0.641580	+	0.568390i	−0.919927	−	0.392091i	$-0.871752\pi$
$23$	−3.07691	+	2.72590i	−0.641580	+	0.568390i	0.278347	+	0.960481i	$0.410213\pi$
$24$	−4.14327	+	10.9249i	−0.845741	+	2.23003i
$25$	−4.23501	+	3.75189i	−0.847002	+	0.750378i
$26$	0.292442	−	2.40848i	0.0573527	−	0.472342i
$27$	4.28131			0.823939
$28$	0.480947	−	3.96096i	0.0908905	−	0.748551i
$29$	−1.23855	−	1.09726i	−0.229992	−	0.203755i	0.540254	−	0.841502i	$-0.318328\pi$
$29$	−1.23855	−	1.09726i	−0.229992	−	0.203755i	−0.770246	+	0.637747i	$0.779867\pi$
$30$	−15.6093	+	3.84734i	−2.84985	+	0.702425i
$31$	2.45838	+	1.29026i	0.441539	+	0.231737i	0.670816	−	0.741624i	$-0.265944\pi$
$31$	2.45838	+	1.29026i	0.441539	+	0.231737i	−0.229277	+	0.973361i	$0.573636\pi$
$32$	−2.33712	+	3.38591i	−0.413149	+	0.598549i
$33$	−0.327179	+	0.474001i	−0.0569546	+	0.0825129i
$34$	−11.9279	+	6.26026i	−2.04562	+	1.07363i
$35$	2.63773	−	1.38439i	0.445858	−	0.234004i
$36$	−3.41879	−	0.842657i	−0.569799	−	0.140443i
$37$	−0.0175350	−	0.0155346i	−0.00288273	−	0.00255388i	0.661680	−	0.749786i	$-0.269844\pi$
$37$	−0.0175350	−	0.0155346i	−0.00288273	−	0.00255388i	−0.664563	+	0.747232i	$0.731382\pi$
$38$	2.67562	+	7.05503i	0.434043	+	1.14448i
$39$	1.87478			0.300205
$40$	−19.5543			−3.09181
$41$	1.84622			0.288330			0.144165	−	0.989554i	$-0.453950\pi$
$41$	1.84622			0.288330			0.144165	+	0.989554i	$0.453950\pi$
$42$	4.49346			0.693356
$43$	5.52096	+	1.36079i	0.841939	+	0.207519i	0.636622	−	0.771176i	$-0.280331\pi$
$43$	5.52096	+	1.36079i	0.841939	+	0.207519i	0.205317	+	0.978696i	$0.434177\pi$
$44$	−0.966373	+	0.856132i	−0.145686	+	0.129067i
$45$	−0.932201	−	2.45801i	−0.138964	−	0.366419i
$46$	−5.89490	−	8.54024i	−0.869155	−	1.25919i
$47$	9.41162	+	8.33797i	1.37283	+	1.21622i	0.950866	+	0.309604i	$0.100196\pi$
$47$	9.41162	+	8.33797i	1.37283	+	1.21622i	0.421960	+	0.906614i	$0.361342\pi$
$48$	−11.0116	−	5.77933i	−1.58939	−	0.834175i
$49$	5.98815	−	1.47595i	0.855450	−	0.210850i
$50$	−8.11365	−	11.7546i	−1.14744	−	1.66236i
$51$	−5.91324	−	8.56680i	−0.828019	−	1.19959i
$52$	4.08040	+	1.00573i	0.565850	+	0.139470i
$53$	−2.64015	−	6.96150i	−0.362652	−	0.956236i	−0.984855	−	0.173380i	$-0.944531\pi$
$53$	−2.64015	−	6.96150i	−0.362652	−	0.956236i	0.622203	−	0.782856i	$-0.286238\pi$
$54$	−1.30274	+	10.7290i	−0.177281	+	1.46004i
$55$	−0.935891	−	0.230677i	−0.126196	−	0.0311044i
$56$	5.30674	+	1.30799i	0.709143	+	0.174788i
$57$	−5.16269	+	2.70959i	−0.683815	+	0.358894i
$58$	3.12661	−	2.76994i	0.410545	−	0.363711i
$59$	−10.5329	−	5.52809i	−1.37127	−	0.719696i	−0.391564	−	0.920151i	$-0.628066\pi$
$59$	−10.5329	−	5.52809i	−1.37127	−	0.719696i	−0.979703	+	0.200454i	$0.935758\pi$
$60$	−3.35658	−	27.6439i	−0.433333	−	3.56882i
$61$	−0.353301	+	2.90970i	−0.0452356	+	0.372549i	0.952458	+	0.304670i	$0.0985462\pi$
$61$	−0.353301	+	2.90970i	−0.0452356	+	0.372549i	−0.997694	+	0.0678787i	$0.978377\pi$
$62$	−3.98146	+	5.76814i	−0.505646	+	0.732555i
$63$	0.0885678	+	0.729421i	0.0111585	+	0.0918985i
$64$	1.76978	+	1.56789i	0.221223	+	0.195986i
$65$	1.11260	+	2.93369i	0.138001	+	0.363880i
$66$	−1.08830	−	0.964148i	−0.133960	−	0.118678i
$67$	7.98562	+	1.96828i	0.975598	+	0.240463i	0.694720	−	0.719280i	$-0.255528\pi$
$67$	7.98562	+	1.96828i	0.975598	+	0.240463i	0.280878	+	0.959743i	$0.409374\pi$
$68$	−8.27430	−	21.8175i	−1.00341	−	2.64577i
$69$	6.00214	−	5.31743i	0.722572	−	0.640143i
$70$	2.66668	+	7.03145i	0.318729	+	0.840419i
$71$	13.7258	−	7.20387i	1.62896	−	0.854942i	0.632171	−	0.774829i	$-0.282164\pi$
$71$	13.7258	−	7.20387i	1.62896	−	0.854942i	0.996786	−	0.0801136i	$-0.0255283\pi$
$72$	1.71033	−	4.50977i	0.201565	−	0.531482i
$73$	−5.10925	+	13.4720i	−0.597993	+	1.57678i	0.203695	+	0.979034i	$0.434705\pi$
$73$	−5.10925	+	13.4720i	−0.597993	+	1.57678i	−0.801688	+	0.597743i	$0.796064\pi$
$74$	0.0442657	−	0.0392160i	0.00514578	−	0.00455877i
$75$	8.26125	−	7.31883i	0.953927	−	0.845105i
$76$	−12.6900	+	3.12780i	−1.45564	+	0.358783i
$77$	0.238556	+	0.125204i	0.0271860	+	0.0142683i
$78$	−0.570469	+	4.69823i	−0.0645929	+	0.531970i
$79$	10.7533	+	2.65045i	1.20984	+	0.298199i	0.792113	−	0.610374i	$-0.208981\pi$
$79$	10.7533	+	2.65045i	1.20984	+	0.298199i	0.417726	+	0.908573i	$0.362827\pi$
$80$	2.50869	−	20.6609i	0.280480	−	2.30996i
$81$	−10.7673			−1.19637
$82$	−0.561777	+	4.62665i	−0.0620378	+	0.510928i
$83$	−0.347546	−	0.916402i	−0.0381481	−	0.100588i	0.914589	−	0.404386i	$-0.132515\pi$
$83$	−0.347546	−	0.916402i	−0.0381481	−	0.100588i	−0.952737	+	0.303797i	$0.901745\pi$
$84$	−0.938186	+	7.72666i	−0.102365	+	0.843048i
$85$	9.89623	−	14.3372i	1.07340	−	1.55508i
$86$	−5.09012	+	13.4216i	−0.548882	+	1.44728i
$87$	2.41604	+	2.14042i	0.259026	+	0.229477i
$88$	−1.00462	−	1.45544i	−0.107093	−	0.155150i
$89$	−0.405151	−	3.33672i	−0.0429460	−	0.353692i	−0.998303	−	0.0582373i	$-0.981452\pi$
$89$	−0.405151	−	3.33672i	−0.0429460	−	0.353692i	0.955357	−	0.295455i	$-0.0954711\pi$
$90$	6.44348	−	1.58817i	0.679202	−	0.167408i
$91$	−0.105708	−	0.870580i	−0.0110812	−	0.0912616i
$92$	15.9160	−	8.35336i	1.65936	−	0.870898i
$93$	−4.79558	−	2.51691i	−0.497278	−	0.260992i
$94$	−23.7589	+	21.0486i	−2.45054	+	2.17099i
$95$	−7.30384	−	6.47064i	−0.749359	−	0.663874i
$96$	4.55904	−	6.60490i	0.465305	−	0.674110i
$97$	−2.55643	−	3.70363i	−0.259566	−	0.376046i	0.671435	−	0.741064i	$-0.265678\pi$
$97$	−2.55643	−	3.70363i	−0.259566	−	0.376046i	−0.931001	+	0.365017i	$0.881063\pi$
$98$	1.87664	+	15.4555i	0.189569	+	1.56124i
$99$	0.135059	−	0.195666i	0.0135739	−	0.0196652i
$100$	21.9065	−	11.4974i	2.19065	−	1.14974i
$101$	−2.64685	+	6.97917i	−0.263371	+	0.694453i	0.736467	+	0.676473i	$0.236493\pi$
$101$	−2.64685	+	6.97917i	−0.263371	+	0.694453i	−0.999838	+	0.0179796i	$0.994277\pi$
$102$	23.2679	−	12.2119i	2.30386	−	1.20916i
$103$	2.29976	+	3.33177i	0.226602	+	0.328289i	0.919749	−	0.392506i	$-0.128392\pi$
$103$	2.29976	+	3.33177i	0.226602	+	0.328289i	−0.693147	+	0.720796i	$0.743777\pi$
$104$	−2.04132	+	5.38251i	−0.200168	+	0.527799i
$105$	−5.14544	+	2.70053i	−0.502143	+	0.263545i
$106$	18.2490	−	4.49797i	1.77250	−	0.436882i
$107$	−1.53070	+	2.21761i	−0.147979	+	0.214384i	−0.889963	−	0.456034i	$-0.849270\pi$
$107$	−1.53070	+	2.21761i	−0.147979	+	0.214384i	0.741984	+	0.670418i	$0.233885\pi$
$108$	−18.1769	−	4.48022i	−1.74908	−	0.431109i
$109$	6.37743	+	3.34714i	0.610847	+	0.320597i	0.741625	−	0.670814i	$-0.234055\pi$
$109$	6.37743	+	3.34714i	0.610847	+	0.320597i	−0.130778	+	0.991412i	$0.541748\pi$
$110$	0.862857	−	2.27517i	0.0822702	−	0.216929i
$111$	0.0342056	+	0.0303035i	0.00324665	+	0.00287628i
$112$	−2.06283	+	5.43925i	−0.194920	+	0.513961i
$113$	−5.62056	−	2.94990i	−0.528738	−	0.277503i	0.179157	−	0.983820i	$-0.442663\pi$
$113$	−5.62056	−	2.94990i	−0.528738	−	0.277503i	−0.707895	+	0.706317i	$0.750355\pi$
$114$	−5.21934	−	13.7623i	−0.488836	−	1.28895i
$115$	11.8828	+	6.23658i	1.10808	+	0.581565i
$116$	4.11020	+	5.95465i	0.381622	+	0.552875i
$117$	−0.773906			−0.0715476
$118$	17.0585	−	24.7135i	1.57036	−	2.27506i
$119$	−3.64470	+	3.22892i	−0.334109	+	0.295995i
$120$	38.1447			3.48212
$121$	3.86974	+	10.2037i	0.351795	+	0.927606i
$122$	−7.18425	−	1.77076i	−0.650431	−	0.160317i
$123$	−3.60142			−0.324729
$124$	−9.08723	−	8.05058i	−0.816057	−	0.722964i
$125$	1.90183	+	0.998155i	0.170104	+	0.0892777i
$126$	−1.85489			−0.165247
$127$	15.9232	−	3.92471i	1.41295	−	0.348262i	0.542310	−	0.840178i	$-0.317550\pi$
$127$	15.9232	−	3.92471i	1.41295	−	0.348262i	0.870642	+	0.491917i	$0.163704\pi$
$128$	−10.6267	+	9.41444i	−0.939277	+	0.832126i
$129$	−10.7698	−	2.65451i	−0.948225	−	0.233716i
$130$	−7.69043	+	1.89552i	−0.674495	+	0.166248i
$131$	−0.0701873	+	0.101684i	−0.00613229	+	0.00888416i	−0.826038	−	0.563614i	$-0.809410\pi$
$131$	−0.0701873	+	0.101684i	−0.00613229	+	0.00888416i	0.819906	+	0.572499i	$0.194026\pi$
$132$	1.88511	−	1.67006i	0.164078	−	0.145360i
$133$	1.54933	+	2.24459i	0.134344	+	0.194630i
$134$	−7.36244	+	19.4132i	−0.636018	+	1.67704i
$135$	−4.95630	−	13.0687i	−0.426571	−	1.12477i
$136$	31.0339	−	7.64916i	2.66113	−	0.655910i
$137$	6.59842	−	1.62636i	0.563741	−	0.138950i	0.0528612	−	0.998602i	$-0.483166\pi$
$137$	6.59842	−	1.62636i	0.563741	−	0.138950i	0.510880	+	0.859652i	$0.329320\pi$
$138$	11.4992	+	16.6595i	0.978877	+	1.41815i
$139$	5.67276	−	1.39821i	0.481157	−	0.118595i	0.00872539	−	0.999962i	$-0.497223\pi$
$139$	5.67276	−	1.39821i	0.481157	−	0.118595i	0.472431	+	0.881367i	$0.343376\pi$
$140$	−12.6476	+	3.11735i	−1.06892	+	0.263464i
$141$	−18.3593	−	16.2649i	−1.54613	−	1.36975i
$142$	13.8765	+	36.5892i	1.16449	+	3.07050i
$143$	−0.161196	+	0.233532i	−0.0134799	+	0.0195289i
$144$	4.54556	+	2.38570i	0.378797	+	0.198808i
$145$	−1.91556	+	5.05091i	−0.159078	+	0.419455i
$146$	−32.2064	−	16.9032i	−2.66542	−	1.39892i
$147$	−11.6811	+	2.87914i	−0.963442	+	0.237467i
$148$	0.0581910	+	0.0843042i	0.00478327	+	0.00692976i
$149$	−12.7421	+	6.68757i	−1.04387	+	0.547867i	−0.897340	−	0.441339i	$-0.854504\pi$
$149$	−12.7421	+	6.68757i	−1.04387	+	0.547867i	−0.146533	+	0.989206i	$0.546811\pi$
$150$	15.8273	+	22.9298i	1.29230	+	1.87221i
$151$	−9.51764	+	8.43189i	−0.774534	+	0.686178i	−0.954737	−	0.297452i	$-0.903863\pi$
$151$	−9.51764	+	8.43189i	−0.774534	+	0.686178i	0.180202	+	0.983630i	$0.442325\pi$
$152$	−2.15796	−	17.7724i	−0.175034	−	1.44153i
$153$	2.44097	+	3.53636i	0.197341	+	0.285898i
$154$	−0.386353	+	0.559728i	−0.0311332	+	0.0451042i
$155$	1.09254	−	8.99789i	0.0877551	−	0.722728i
$156$	−7.95966	−	1.96188i	−0.637283	−	0.157076i
$157$	11.6100	−	2.86160i	0.926576	−	0.228381i	0.252973	−	0.967473i	$-0.418592\pi$
$157$	11.6100	−	2.86160i	0.926576	−	0.228381i	0.673604	+	0.739093i	$0.264746\pi$
$158$	−9.91413	+	26.1414i	−0.788726	+	2.07970i
$159$	5.15015	+	13.5798i	0.408433	+	1.07695i
$160$	13.0411	+	3.21433i	1.03099	+	0.254115i
$161$	−2.80765	−	2.48736i	−0.221273	−	0.196031i
$162$	3.27634	−	26.9831i	0.257414	−	2.11999i
$163$	17.8875	−	15.8470i	1.40106	−	1.24123i	0.466932	−	0.884293i	$-0.345359\pi$
$163$	17.8875	−	15.8470i	1.40106	−	1.24123i	0.934128	−	0.356937i	$-0.116179\pi$
$164$	−7.83838	−	1.93199i	−0.612074	−	0.150863i
$165$	1.82565	+	0.449982i	0.142126	+	0.0350310i
$166$	2.40227	−	0.592107i	0.186453	−	0.0459564i
$167$	1.39139	+	2.01578i	0.107669	+	0.155986i	0.873114	−	0.487515i	$-0.162097\pi$
$167$	1.39139	+	2.01578i	0.107669	+	0.155986i	−0.765445	+	0.643501i	$0.777481\pi$
$168$	−10.3519	−	2.55151i	−0.798665	−	0.196853i
$169$	−12.0763			−0.928948
$170$	32.9179	+	29.1627i	2.52469	+	2.23668i
$171$	2.13115	−	1.11851i	0.162973	−	0.0855348i
$172$	−22.0160	−	11.5549i	−1.67871	−	0.881054i
$173$	0.725439	−	5.97452i	0.0551541	−	0.454235i	−0.938802	−	0.344457i	$-0.888063\pi$
$173$	0.725439	−	5.97452i	0.0551541	−	0.454235i	0.993956	−	0.109778i	$-0.0350139\pi$
$174$	−6.09910	+	5.40333i	−0.462372	+	0.409625i
$175$	−3.86440	−	3.42356i	−0.292121	−	0.258797i
$176$	1.66669	−	0.874747i	0.125632	−	0.0659365i
$177$	20.5466	+	10.7837i	1.54438	+	0.810551i
$178$	8.48516			0.635990
$179$	−14.7989	+	3.64759i	−1.10612	+	0.272634i	−0.749756	−	0.661714i	$-0.769829\pi$
$179$	−14.7989	+	3.64759i	−1.10612	+	0.272634i	−0.356363	+	0.934348i	$0.615983\pi$
$180$	1.38559	+	11.4114i	0.103276	+	0.850553i
$181$	11.9080	+	2.93506i	0.885116	+	0.218161i	0.655568	−	0.755136i	$-0.272429\pi$
$181$	11.9080	+	2.93506i	0.885116	+	0.218161i	0.229548	+	0.973297i	$0.426275\pi$
$182$	2.21385			0.164102
$183$	0.689186	−	5.67596i	0.0509461	−	0.419579i
$184$	8.73108	+	23.0220i	0.643664	+	1.69720i
$185$	−0.0271199	+	0.0715093i	−0.00199389	+	0.00525747i
$186$	7.76666	−	11.2519i	0.569479	−	0.825032i
$187$	1.57555			0.115216
$188$	−31.2331	−	45.2489i	−2.27791	−	3.30012i
$189$	0.470895	+	3.87817i	0.0342526	+	0.282095i
$190$	18.4380	−	16.3346i	1.33763	−	1.18504i
$191$	2.99150	−	24.6372i	0.216457	−	1.78269i	−0.328783	−	0.944405i	$-0.606639\pi$
$191$	2.99150	−	24.6372i	0.216457	−	1.78269i	0.545240	−	0.838280i	$-0.316438\pi$
$192$	−3.45232	−	3.05849i	−0.249150	−	0.220728i
$193$	11.1356	−	16.1326i	0.801555	−	1.16125i	−0.182468	−	0.983212i	$-0.558409\pi$
$193$	11.1356	−	16.1326i	0.801555	−	1.16125i	0.984023	−	0.178041i	$-0.0569761\pi$
$194$	10.0592	−	5.27950i	0.722211	−	0.379046i
$195$	−2.17036	−	5.72276i	−0.155423	−	0.409816i
$196$	−26.9681			−1.92629
$197$	15.8930	−	14.0800i	1.13233	−	1.00316i	0.132403	−	0.991196i	$-0.457731\pi$
$197$	15.8930	−	14.0800i	1.13233	−	1.00316i	0.999928	−	0.0119626i	$-0.00380792\pi$
$198$	0.449247	+	0.397998i	0.0319266	+	0.0282845i
$199$	−14.4831	−	20.9824i	−1.02668	−	1.48741i	−0.865773	−	0.500437i	$-0.833173\pi$
$199$	−14.4831	−	20.9824i	−1.02668	−	1.48741i	−0.160910	−	0.986969i	$-0.551443\pi$
$200$	12.0173	+	31.6871i	0.849753	+	2.24061i
$201$	−15.5776	−	3.83953i	−1.09876	−	0.270819i
$202$	−16.6845	−	8.75671i	−1.17392	−	0.616120i
$203$	0.857709	−	1.24261i	0.0601993	−	0.0872138i
$204$	16.1407	+	42.5596i	1.13008	+	2.97977i
$205$	−2.13729	−	5.63557i	−0.149275	−	0.393605i
$206$	−9.04926	+	4.74942i	−0.630492	+	0.330908i
$207$	−2.47767	+	2.19502i	−0.172210	+	0.152565i
$208$	−5.42523	−	2.84738i	−0.376172	−	0.197430i
$209$	0.106373	−	0.876063i	0.00735800	−	0.0605986i
$210$	−5.20190	−	13.7163i	−0.358965	−	0.946513i
$211$	−5.36258	+	14.1400i	−0.369176	+	0.973436i	0.613761	+	0.789492i	$0.289656\pi$
$211$	−5.36258	+	14.1400i	−0.369176	+	0.973436i	−0.982937	+	0.183944i	$0.941113\pi$
$212$	3.92422	+	32.3189i	0.269517	+	2.21967i
$213$	−26.7750	+	14.0526i	−1.83460	+	0.962870i
$214$	−5.09159	−	4.51075i	−0.348054	−	0.308349i
$215$	−2.23757	−	18.4281i	−0.152601	−	1.25678i
$216$	9.09345	−	23.9775i	0.618731	−	1.63146i
$217$	−0.898370	+	2.36881i	−0.0609853	+	0.160805i
$218$	−10.3285	+	14.9635i	−0.699537	+	1.01345i
$219$	9.96664	−	26.2799i	0.673483	−	1.77583i
$220$	3.73207	+	1.95874i	0.251616	+	0.132058i
$221$	−2.91335	−	4.22072i	−0.195973	−	0.283916i
$222$	−0.0863493	+	0.0764988i	−0.00579538	+	0.00513426i
$223$	26.8943	+	6.62886i	1.80098	+	0.443901i	0.989987	−	0.141157i	$-0.0450821\pi$
$223$	26.8943	+	6.62886i	1.80098	+	0.443901i	0.810991	+	0.585058i	$0.198928\pi$
$224$	−3.32413	−	1.74464i	−0.222103	−	0.116569i
$225$	−3.41023	+	3.02120i	−0.227348	+	0.201413i
$226$	9.10275	−	13.1876i	0.605506	−	0.877227i
$227$	−1.18026	+	3.11208i	−0.0783363	+	0.206556i	−0.968463	−	0.249157i	$-0.919846\pi$
$227$	−1.18026	+	3.11208i	−0.0783363	+	0.206556i	0.890127	+	0.455713i	$0.150616\pi$
$228$	24.7544	−	6.10142i	1.63940	−	0.404076i
$229$	5.22357	−	1.28749i	0.345183	−	0.0850800i	−0.0629129	−	0.998019i	$-0.520039\pi$
$229$	5.22357	−	1.28749i	0.345183	−	0.0850800i	0.408096	+	0.912939i	$0.366193\pi$
$230$	−19.2448	+	27.8808i	−1.26896	+	1.83841i
$231$	−0.465353	−	0.244236i	−0.0306180	−	0.0160695i
$232$	−8.77582	+	4.60591i	−0.576161	+	0.302393i
$233$	3.27126	+	26.9412i	0.214307	+	1.76498i	0.561779	+	0.827287i	$0.310117\pi$
$233$	3.27126	+	26.9412i	0.214307	+	1.76498i	−0.347472	+	0.937690i	$0.612960\pi$
$234$	0.235488	−	1.93942i	0.0153944	−	0.126784i
$235$	14.5562	−	38.3815i	0.949540	−	2.50373i
$236$	38.9341	+	34.4926i	2.53439	+	2.24528i
$237$	−20.9765	−	5.17024i	−1.36257	−	0.335843i
$238$	−6.98270	−	10.1162i	−0.452621	−	0.655735i
$239$	−10.6616	−	9.44535i	−0.689641	−	0.610969i	0.243746	−	0.969839i	$-0.421624\pi$
$239$	−10.6616	−	9.44535i	−0.689641	−	0.610969i	−0.933387	+	0.358870i	$0.883162\pi$
$240$	−4.89371	+	40.3034i	−0.315888	+	2.60157i
$241$	−11.7453	+	6.16439i	−0.756578	+	0.397083i	−0.798466	−	0.602039i	$-0.794355\pi$
$241$	−11.7453	+	6.16439i	−0.756578	+	0.397083i	0.0418880	+	0.999122i	$0.486663\pi$
$242$	−26.7481	+	6.59281i	−1.71943	+	0.423802i
$243$	8.15991			0.523458
$244$	4.54487	−	11.9838i	0.290955	−	0.767186i
$245$	−11.4376	−	16.5702i	−0.730719	−	1.05863i
$246$	1.09586	−	9.02522i	0.0698695	−	0.575427i
$247$	−2.54357	+	1.33497i	−0.161843	+	0.0849420i
$248$	12.4477	−	11.0277i	0.790427	−	0.700257i
$249$	0.677959	+	1.78763i	0.0429639	+	0.113286i
$250$	−3.08009	+	4.46228i	−0.194802	+	0.282220i
$251$	16.7619	−	8.79733i	1.05800	−	0.555282i	0.156331	−	0.987705i	$-0.450033\pi$
$251$	16.7619	−	8.79733i	1.05800	−	0.555282i	0.901671	+	0.432423i	$0.142341\pi$
$252$	0.387281	−	3.18955i	0.0243964	−	0.200923i
$253$	0.146296	+	1.20485i	0.00919754	+	0.0757485i
$254$	4.99020	+	41.0980i	0.313113	+	2.57872i
$255$	−19.3046	+	27.9676i	−1.20890	+	1.75140i
$256$	−17.6729	−	25.6036i	−1.10456	−	1.60023i
$257$	−12.1933	−	6.39955i	−0.760598	−	0.399193i	0.0393779	−	0.999224i	$-0.487462\pi$
$257$	−12.1933	−	6.39955i	−0.760598	−	0.399193i	−0.799976	+	0.600032i	$0.795155\pi$
$258$	9.92932	−	26.1815i	0.618173	−	1.62999i
$259$	0.0121432	−	0.0175924i	0.000754541	−	0.00109314i
$260$	−1.65373	−	13.6197i	−0.102560	−	0.844658i
$261$	−0.997335	−	0.883562i	−0.0617335	−	0.0546911i
$262$	−0.233464	−	0.206831i	−0.0144235	−	0.0127781i
$263$	−8.96222	+	2.20899i	−0.552634	+	0.136212i	−0.505737	−	0.862688i	$-0.668779\pi$
$263$	−8.96222	+	2.20899i	−0.552634	+	0.136212i	−0.0468972	+	0.998900i	$0.514933\pi$
$264$	1.95971	+	2.83913i	0.120612	+	0.174737i
$265$	−18.1936	+	16.1181i	−1.11762	+	0.990127i
$266$	−6.09641	+	3.19964i	−0.373795	+	0.196183i
$267$	0.790331	+	6.50896i	0.0483674	+	0.398342i
$268$	−31.8444	−	16.7132i	−1.94521	−	1.02092i
$269$	3.43933	+	28.3254i	0.209700	+	1.72703i	0.594556	+	0.804055i	$0.297328\pi$
$269$	3.43933	+	28.3254i	0.209700	+	1.72703i	−0.384856	+	0.922977i	$0.625749\pi$
$270$	34.2585	−	8.44396i	2.08491	−	0.513883i
$271$	−23.7459	+	12.4628i	−1.44246	+	0.757062i	−0.990826	−	0.135141i	$-0.956851\pi$
$271$	−23.7459	+	12.4628i	−1.44246	+	0.757062i	−0.451635	+	0.892203i	$0.649159\pi$
$272$	4.10060	+	33.7715i	0.248635	+	2.04770i
$273$	0.206204	+	1.69824i	0.0124800	+	0.102782i
$274$	2.06789	+	17.0306i	0.124926	+	1.02886i
$275$	0.201359	+	1.65834i	0.0121424	+	0.100002i
$276$	−31.0474	+	16.2949i	−1.86884	+	0.980840i
$277$	−21.2272	+	5.23204i	−1.27542	+	0.314363i	−0.818170	−	0.574976i	$-0.805011\pi$
$277$	−21.2272	+	5.23204i	−1.27542	+	0.314363i	−0.457249	+	0.889339i	$0.651165\pi$
$278$	1.77780	+	14.6415i	0.106625	+	0.878137i
$279$	1.97961	+	1.03898i	0.118516	+	0.0622019i
$280$	−2.15075	−	17.7130i	−0.128532	−	1.05855i
$281$	−5.61793	+	2.94852i	−0.335137	+	0.175894i	−0.623894	−	0.781509i	$-0.714450\pi$
$281$	−5.61793	+	2.94852i	−0.335137	+	0.175894i	0.288757	+	0.957402i	$0.406758\pi$
$282$	46.3466	−	41.0595i	2.75990	−	2.44506i
$283$	8.10431	+	11.7411i	0.481751	+	0.697937i	0.986210	−	0.165498i	$-0.0529233\pi$
$283$	8.10431	+	11.7411i	0.481751	+	0.697937i	−0.504459	+	0.863436i	$0.668308\pi$
$284$	−65.8136	+	16.2216i	−3.90532	+	0.962575i
$285$	14.2476	+	12.6223i	0.843957	+	0.747681i
$286$	−0.536186	−	0.475019i	−0.0317053	−	0.0280885i
$287$	0.203062	+	1.67237i	0.0119864	+	0.0987168i
$288$	−1.88196	+	2.72649i	−0.110896	+	0.160660i
$289$	−4.06928	+	10.7298i	−0.239370	+	0.631166i
$290$	−12.0748	−	6.33733i	−0.709056	−	0.372141i
$291$	4.98684	+	7.22468i	0.292334	+	0.423518i
$292$	35.7900	−	51.8507i	2.09445	−	3.03433i
$293$	−0.0826357	−	0.680567i	−0.00482763	−	0.0397591i	0.990096	−	0.140392i	$-0.0448363\pi$
$293$	−0.0826357	−	0.680567i	−0.00482763	−	0.0397591i	−0.994924	+	0.100633i	$0.967913\pi$
$294$	−3.66077	−	30.1491i	−0.213500	−	1.75833i
$295$	−4.68098	+	38.5513i	−0.272537	+	2.24454i
$296$	−0.124246	+	0.0652091i	−0.00722163	+	0.00379020i
$297$	0.718077	−	1.04031i	0.0416671	−	0.0603652i
$298$	−12.8819	−	33.9668i	−0.746230	−	1.96765i
$299$	2.95715	−	2.61981i	0.171017	−	0.151507i
$300$	−42.7332	+	22.4281i	−2.46720	+	1.29489i
$301$	−0.625415	+	5.15076i	−0.0360483	+	0.296885i
$302$	−18.2344	−	26.4171i	−1.04927	−	1.52013i
$303$	5.16322	−	13.6143i	0.296619	−	0.782120i
$304$	19.0550			1.09288
$305$	9.29085	−	2.28999i	0.531992	−	0.131124i
$306$	−9.60493	+	5.04105i	−0.549077	+	0.288178i
$307$	−0.0820101	+	0.675414i	−0.00468056	+	0.0385479i	−0.994862	−	0.101240i	$-0.967719\pi$
$307$	−0.0820101	+	0.675414i	−0.00468056	+	0.0385479i	0.990181	+	0.139788i	$0.0446421\pi$
$308$	−0.881805	−	0.781211i	−0.0502455	−	0.0445136i
$309$	−4.48615	−	6.49930i	−0.255208	−	0.369732i
$310$	22.2164	+	5.47586i	1.26181	+	0.311008i
$311$	−2.83185	−	2.50880i	−0.160580	−	0.142261i	0.579007	−	0.815323i	$-0.303440\pi$
$311$	−2.83185	−	2.50880i	−0.160580	−	0.142261i	−0.739586	+	0.673062i	$0.764979\pi$
$312$	3.98201	−	10.4997i	0.225437	−	0.594428i
$313$	−1.61166	+	13.2732i	−0.0910965	+	0.750247i	0.873556	+	0.486723i	$0.161808\pi$
$313$	−1.61166	+	13.2732i	−0.0910965	+	0.750247i	−0.964653	+	0.263524i	$0.915115\pi$
$314$	3.63847	+	29.9655i	0.205331	+	1.69105i
$315$	2.12403	−	1.11477i	0.119675	−	0.0628104i
$316$	−42.8811	−	22.5057i	−2.41225	−	1.26605i
$317$	7.83115	−	11.3454i	0.439841	−	0.637220i	−0.538888	−	0.842378i	$-0.681155\pi$
$317$	7.83115	−	11.3454i	0.439841	−	0.637220i	0.978729	+	0.205158i	$0.0657707\pi$
$318$	−35.5984	+	8.77422i	−1.99626	+	0.492034i
$319$	−0.474355	+	0.116918i	−0.0265588	+	0.00654615i
$320$	2.73718	−	7.21734i	0.153013	−	0.403461i
$321$	2.98595	−	4.32589i	0.166659	−	0.241448i
$322$	7.08768	−	6.27914i	0.394981	−	0.349923i
$323$	14.1228	+	7.41221i	0.785813	+	0.412426i
$324$	45.7142	+	11.2675i	2.53968	+	0.625975i
$325$	4.07018	−	3.60586i	0.225773	−	0.200017i
$326$	34.2699	+	49.6485i	1.89803	+	2.74977i
$327$	−12.4405	−	6.52927i	−0.687960	−	0.361069i
$328$	3.92133	−	10.3397i	0.216519	−	0.570915i
$329$	−6.51766	+	9.44247i	−0.359330	+	0.520580i
$330$	−1.68318	+	4.43818i	−0.0926560	+	0.244314i
$331$	−0.151137	+	0.398517i	−0.00830727	+	0.0219045i	−0.939106	−	0.343628i	$-0.888344\pi$
$331$	−0.151137	+	0.398517i	−0.00830727	+	0.0219045i	0.930798	+	0.365533i	$0.119113\pi$
$332$	0.516579	+	4.25441i	0.0283510	+	0.233491i
$333$	−0.0141200	−	0.0125092i	−0.000773770	−	0.000685501i
$334$	−5.47495	+	2.87348i	−0.299576	+	0.157230i
$335$	−3.23646	−	26.6547i	−0.176827	−	1.45630i
$336$	4.02398	−	10.6104i	0.219526	−	0.578843i
$337$	11.2155	+	29.5728i	0.610946	+	1.61093i	0.780321	+	0.625379i	$0.215056\pi$
$337$	11.2155	+	29.5728i	0.610946	+	1.61093i	−0.169375	+	0.985552i	$0.554175\pi$
$338$	3.67465	−	30.2635i	0.199875	−	1.64612i
$339$	10.9641	+	5.75438i	0.595486	+	0.312535i
$340$	−57.0192	+	50.5146i	−3.09230	+	2.73954i
$341$	0.725848	−	0.380955i	0.0393069	−	0.0206298i
$342$	2.15453	+	5.68104i	0.116504	+	0.307195i
$343$	4.26060	+	11.2343i	0.230051	+	0.606595i
$344$	19.3476	−	28.0298i	1.04315	−	1.51126i
$345$	−23.1799	−	12.1657i	−1.24796	−	0.654981i
$346$	14.7515	+	3.63592i	0.793046	+	0.195468i
$347$	9.38106	+	24.7358i	0.503602	+	1.32789i	0.910157	+	0.414263i	$0.135961\pi$
$347$	9.38106	+	24.7358i	0.503602	+	1.32789i	−0.406555	+	0.913626i	$0.633270\pi$
$348$	−8.01778	−	11.6158i	−0.429798	−	0.622670i
$349$	5.04566	+	4.47006i	0.270088	+	0.239277i	0.787285	−	0.616589i	$-0.211486\pi$
$349$	5.04566	+	4.47006i	0.270088	+	0.239277i	−0.517197	+	0.855866i	$0.673025\pi$
$350$	9.75538	−	8.64251i	0.521447	−	0.461962i
$351$	−4.11468			−0.219625
$352$	0.430749	+	1.13579i	0.0229590	+	0.0605380i
$353$	−9.90020	+	5.19602i	−0.526934	+	0.276556i	−0.707141	−	0.707072i	$-0.750016\pi$
$353$	−9.90020	+	5.19602i	−0.526934	+	0.276556i	0.180207	+	0.983629i	$0.442323\pi$
$354$	−33.2761	+	48.2087i	−1.76860	+	2.56227i
$355$	−37.8796	−	33.5584i	−2.01044	−	1.78110i
$356$	−1.77161	+	14.5905i	−0.0938951	+	0.773296i
$357$	7.10973	−	6.29867i	0.376287	−	0.333361i
$358$	−4.63785	−	38.1961i	−0.245118	−	2.01873i
$359$	4.46722	+	6.47189i	0.235771	+	0.341573i	0.922953	−	0.384912i	$-0.125768\pi$
$359$	4.46722	+	6.47189i	0.235771	+	0.341573i	−0.687182	+	0.726485i	$0.741153\pi$
$360$	−15.7461			−0.829890
$361$	−5.71827	+	8.28434i	−0.300962	+	0.436018i
$362$	−10.9788	+	28.9486i	−0.577030	+	1.52150i
$363$	−7.54872	−	19.9043i	−0.396205	−	1.04471i
$364$	−0.462229	+	3.80679i	−0.0242274	+	0.199530i
$365$	47.0380			2.46208
$366$	14.0143	+	3.45422i	0.732541	+	0.180555i
$367$	2.29429	+	18.8951i	0.119761	+	0.986318i	0.921428	+	0.388548i	$0.127023\pi$
$367$	2.29429	+	18.8951i	0.119761	+	0.986318i	−0.801668	+	0.597770i	$0.796054\pi$
$368$	−25.4449	+	6.27162i	−1.32641	+	0.326931i
$369$	1.48666			0.0773924
$370$	−0.170951	−	0.0897222i	−0.00888733	−	0.00466443i
$371$	6.01559	−	3.15723i	0.312314	−	0.163915i
$372$	17.7265	+	15.7043i	0.919076	+	0.814230i
$373$	10.3007	−	9.12560i	0.533349	−	0.472506i	−0.352936	−	0.935648i	$-0.614817\pi$
$373$	10.3007	−	9.12560i	0.533349	−	0.472506i	0.886284	+	0.463142i	$0.153278\pi$
$374$	−0.479417	+	3.94835i	−0.0247901	+	0.204165i
$375$	−3.70990	−	1.94711i	−0.191578	−	0.100548i
$376$	66.6868	−	35.0000i	3.43911	−	1.80498i
$377$	1.19034	+	1.05455i	0.0613057	+	0.0543121i
$378$	−9.86204			−0.507249
$379$	26.0898	+	6.43055i	1.34014	+	0.330315i	0.843261	−	0.537504i	$-0.180633\pi$
$379$	26.0898	+	6.43055i	1.34014	+	0.330315i	0.496880	+	0.867819i	$0.334479\pi$
$380$	24.2383	+	35.1152i	1.24340	+	1.80137i
$381$	−31.0614	+	7.65594i	−1.59132	+	0.392226i
$382$	60.8310	+	14.9935i	3.11238	+	0.767133i
$383$	−13.8251	−	3.40759i	−0.706431	−	0.174120i	−0.130297	−	0.991475i	$-0.541593\pi$
$383$	−13.8251	−	3.40759i	−0.706431	−	0.174120i	−0.576134	+	0.817355i	$0.695439\pi$
$384$	20.7295	−	18.3648i	1.05785	−	0.937174i
$385$	0.106018	−	0.873136i	0.00540317	−	0.0444991i
$386$	37.0403	+	32.8148i	1.88530	+	1.67023i
$387$	4.44574	+	1.09578i	0.225989	+	0.0557014i
$388$	6.97801	+	18.3995i	0.354255	+	0.934093i
$389$	2.62465	−	6.92063i	0.133075	−	0.350890i	−0.851871	−	0.523751i	$-0.824532\pi$
$389$	2.62465	−	6.92063i	0.133075	−	0.350890i	0.984946	+	0.172861i	$0.0553013\pi$
$390$	15.0017	−	3.69760i	0.759643	−	0.187235i
$391$	−21.2983	−	5.24957i	−1.07710	−	0.265482i
$392$	4.45272	−	36.6715i	0.224896	−	1.85219i
$393$	0.136915	−	0.198355i	0.00690643	−	0.0100057i
$394$	30.4487	+	44.1126i	1.53398	+	2.22236i
$395$	−4.35816	−	35.8927i	−0.219283	−	1.80596i
$396$	−0.778169	+	0.689397i	−0.0391045	+	0.0346435i
$397$	0.126009	+	0.182555i	0.00632421	+	0.00916220i	0.826133	−	0.563475i	$-0.190536\pi$
$397$	0.126009	+	0.182555i	0.00632421	+	0.00916220i	−0.819809	+	0.572637i	$0.805920\pi$
$398$	56.9894	−	29.9103i	2.85662	−	1.49927i
$399$	−3.02228	−	4.37853i	−0.151303	−	0.219200i
$400$	−35.0220	+	8.63216i	−1.75110	+	0.431608i
$401$	15.7264	+	8.25387i	0.785341	+	0.412179i	0.809198	−	0.587537i	$-0.199902\pi$
$401$	15.7264	+	8.25387i	0.785341	+	0.412179i	−0.0238566	+	0.999715i	$0.507595\pi$
$402$	14.3619	−	37.8693i	0.716309	−	1.88875i
$403$	−2.36270	−	1.24004i	−0.117695	−	0.0617709i
$404$	18.5410	−	26.8613i	0.922449	−	1.33640i
$405$	12.4649	+	32.8672i	0.619385	+	1.63318i
$406$	2.85300	+	2.52754i	0.141592	+	0.125440i
$407$	−0.00671578	+	0.00165529i	−0.000332889	+	8.20498e-5i
$408$	−60.5379	+	14.9213i	−2.99707	+	0.738712i
$409$	5.74056	+	8.31664i	0.283853	+	0.411231i	0.938811	−	0.344434i	$-0.111929\pi$
$409$	5.74056	+	8.31664i	0.283853	+	0.411231i	−0.654958	+	0.755665i	$0.727314\pi$
$410$	14.7732	−	3.64126i	0.729595	−	0.179829i
$411$	−12.8716	+	3.17256i	−0.634907	+	0.156491i
$412$	−6.27740	−	16.5521i	−0.309265	−	0.815465i
$413$	3.84905	−	10.1491i	0.189399	−	0.499405i
$414$	−4.74685	−	6.87700i	−0.233295	−	0.337986i
$415$	−2.39498	+	2.12176i	−0.117565	+	0.104153i
$416$	2.24616	−	3.25412i	0.110127	−	0.159547i
$417$	−11.0659	+	2.72749i	−0.541898	+	0.133566i
$418$	2.16306	+	0.533147i	0.105799	+	0.0260771i
$419$	−0.637907	+	0.565136i	−0.0311638	+	0.0276087i	−0.678561	−	0.734544i	$-0.737396\pi$
$419$	−0.637907	+	0.565136i	−0.0311638	+	0.0276087i	0.647397	+	0.762153i	$0.275858\pi$
$420$	24.6717	−	6.08103i	1.20386	−	0.296724i
$421$	20.9682			1.02193			0.510963	−	0.859603i	$-0.329289\pi$
$421$	20.9682			1.02193			0.510963	+	0.859603i	$0.329289\pi$
$422$	−33.8033	−	17.7413i	−1.64552	−	0.863634i
$423$	7.57868	+	6.71412i	0.368488	+	0.326452i
$424$	−44.5954			−2.16575
$425$	−29.3147	−	7.22542i	−1.42197	−	0.350485i
$426$	−27.0689	−	71.3747i	−1.31149	−	3.45812i
$427$	−2.67457			−0.129431
$428$	8.81945	−	7.81335i	0.426304	−	0.377673i
$429$	0.314445	−	0.455552i	0.0151815	−	0.0219943i
$430$	46.8619			2.25988
$431$	5.61613	+	8.13636i	0.270519	+	0.391915i	0.934574	−	0.355769i	$-0.115781\pi$
$431$	5.61613	+	8.13636i	0.270519	+	0.391915i	−0.664055	+	0.747684i	$0.731166\pi$
$432$	24.1677	+	12.6842i	1.16277	+	0.610269i
$433$	−4.36102	−	11.4991i	−0.209577	−	0.552610i	0.788470	−	0.615073i	$-0.210874\pi$
$433$	−4.36102	−	11.4991i	−0.209577	−	0.552610i	−0.998047	+	0.0624631i	$0.980104\pi$
$434$	−5.66291	−	2.97212i	−0.271828	−	0.142666i
$435$	3.73668	−	9.85283i	0.179160	−	0.472407i
$436$	−23.5737	−	20.8845i	−1.12898	−	1.00018i
$437$	−4.35691	+	11.4882i	−0.208419	+	0.549556i
$438$	62.8251	+	32.9732i	3.00190	+	1.57552i
$439$	5.50636	+	1.35720i	0.262804	+	0.0647754i	0.368516	−	0.929621i	$-0.379866\pi$
$439$	5.50636	+	1.35720i	0.262804	+	0.0647754i	−0.105712	+	0.994397i	$0.533712\pi$
$440$	−3.27972	+	4.75150i	−0.156355	+	0.226519i
$441$	4.82194	−	1.18850i	0.229616	−	0.0565953i
$442$	11.4637	−	6.01661i	0.545272	−	0.286181i
$443$	5.19789	−	13.7057i	0.246959	−	0.651177i	−0.753018	−	0.658000i	$-0.771403\pi$
$443$	5.19789	−	13.7057i	0.246959	−	0.651177i	0.999977	+	0.00682284i	$0.00217180\pi$
$444$	−0.113513	−	0.164453i	−0.00538711	−	0.00780457i
$445$	−9.71631	+	5.09951i	−0.460597	+	0.241740i
$446$	−24.7956	+	65.3806i	−1.17411	+	3.09586i
$447$	24.8561	−	13.0455i	1.17565	−	0.617029i
$448$	−1.22560	+	1.77558i	−0.0579040	+	0.0838884i
$449$	−3.95932	−	32.6080i	−0.186852	−	1.53887i	−0.720678	−	0.693270i	$-0.756169\pi$
$449$	−3.95932	−	32.6080i	−0.186852	−	1.53887i	0.533826	−	0.845595i	$-0.320754\pi$
$450$	−6.53349	−	9.46539i	−0.307992	−	0.446203i
$451$	0.309654	−	0.448611i	0.0145810	−	0.0211243i
$452$	20.7760	+	18.4059i	0.977220	+	0.865741i
$453$	18.5661	−	16.4481i	0.872311	−	0.772800i
$454$	−7.43979	−	3.90470i	−0.349166	−	0.183257i
$455$	−2.53507	+	1.33051i	−0.118846	+	0.0623751i
$456$	4.20954	+	34.6687i	0.197130	+	1.62351i
$457$	−31.7928	+	7.83621i	−1.48720	+	0.366563i	−0.897484	−	0.441046i	$-0.854607\pi$
$457$	−31.7928	+	7.83621i	−1.48720	+	0.366563i	−0.589718	+	0.807609i	$0.700761\pi$
$458$	1.63703	+	13.4821i	0.0764932	+	0.629978i
$459$	12.9781	+	18.8020i	0.605766	+	0.877603i
$460$	−43.9239	−	38.9132i	−2.04796	−	1.81434i
$461$	−10.5713	+	27.8743i	−0.492357	+	1.29824i	0.426800	+	0.904346i	$0.359641\pi$
$461$	−10.5713	+	27.8743i	−0.492357	+	1.29824i	−0.919157	+	0.393892i	$0.871128\pi$
$462$	0.753660	−	1.09186i	0.0350634	−	0.0507981i
$463$	4.27550	−	35.2119i	0.198699	−	1.63644i	−0.462780	−	0.886473i	$-0.653148\pi$
$463$	4.27550	−	35.2119i	0.198699	−	1.63644i	0.661479	−	0.749963i	$-0.269929\pi$
$464$	−3.74068	−	9.86337i	−0.173657	−	0.457895i
$465$	−2.13123	+	17.5522i	−0.0988332	+	0.813965i
$466$	−68.5105			−3.17369
$467$	−1.66863	+	13.7424i	−0.0772150	+	0.635923i	0.901803	+	0.432148i	$0.142244\pi$
$467$	−1.66863	+	13.7424i	−0.0772150	+	0.635923i	−0.979018	+	0.203775i	$0.934679\pi$
$468$	3.28573	+	0.809860i	0.151883	+	0.0374358i
$469$	−0.904612	+	7.45015i	−0.0417711	+	0.344016i
$470$	91.7554	+	48.1569i	4.23236	+	2.22131i
$471$	−22.6476	+	5.58213i	−1.04355	+	0.257211i
$472$	−53.3317	+	47.2478i	−2.45479	+	2.17476i
$473$	1.25665	−	1.11330i	0.0577810	−	0.0511895i
$474$	19.3395	−	50.9942i	0.888295	−	2.34224i
$475$	−5.99678	+	15.8122i	−0.275151	+	0.725514i
$476$	18.8530	−	9.89484i	0.864128	−	0.453529i
$477$	−2.12597	−	5.60573i	−0.0973415	−	0.256669i
$478$	26.9144	−	23.8441i	1.23103	−	1.09060i
$479$	−1.38719	−	3.65771i	−0.0633822	−	0.167125i	0.899584	−	0.436748i	$-0.143870\pi$
$479$	−1.38719	−	3.65771i	−0.0633822	−	0.167125i	−0.962966	+	0.269623i	$0.913101\pi$
$480$	−25.4393	−	6.27021i	−1.16114	−	0.286195i
$481$	0.0168525	+	0.0149300i	0.000768408	+	0.000680750i
$482$	−11.8741	−	31.3095i	−0.540852	−	1.42611i
$483$	5.47689	+	4.85210i	0.249207	+	0.220778i
$484$	−5.75184	−	47.3707i	−0.261447	−	2.15321i
$485$	−8.34584	+	12.0910i	−0.378965	+	0.549025i
$486$	−2.48294	+	20.4489i	−0.112629	+	0.927579i
$487$	−3.56301	−	29.3440i	−0.161455	−	1.32971i	−0.817913	−	0.575342i	$-0.804869\pi$
$487$	−3.56301	−	29.3440i	−0.161455	−	1.32971i	0.656457	−	0.754363i	$-0.272054\pi$
$488$	15.5453	+	8.15881i	0.703704	+	0.369332i
$489$	−34.8933	+	30.9128i	−1.57793	+	1.39792i
$490$	45.0054	−	23.6207i	2.03314	−	1.06707i
$491$	5.25886	+	1.29619i	0.237329	+	0.0584963i	0.356186	−	0.934415i	$-0.384077\pi$
$491$	5.25886	+	1.29619i	0.237329	+	0.0584963i	−0.118857	+	0.992911i	$0.537923\pi$
$492$	15.2904	+	3.76873i	0.689342	+	0.169908i
$493$	1.06431	−	8.76541i	0.0479343	−	0.394774i
$494$	−2.57148	−	6.78044i	−0.115696	−	0.305066i
$495$	−0.753623	−	0.185751i	−0.0338729	−	0.00834891i
$496$	10.0548	+	14.5669i	0.451473	+	0.654071i
$497$	8.03521	+	11.6410i	0.360428	+	0.522171i
$498$	−4.68612	+	1.15503i	−0.209990	+	0.0517579i
$499$	8.61826	+	4.52321i	0.385806	+	0.202487i	0.646464	−	0.762944i	$-0.276247\pi$
$499$	8.61826	+	4.52321i	0.385806	+	0.202487i	−0.260658	+	0.965431i	$0.583939\pi$
$500$	−7.02995	−	6.22800i	−0.314389	−	0.278524i
$501$	−2.71419	−	3.93219i	−0.121261	−	0.175677i
$502$	16.9458	+	44.6825i	0.756330	+	1.99428i
$503$	−2.01016	+	1.78085i	−0.0896286	+	0.0794040i	−0.706747	−	0.707466i	$-0.749838\pi$
$503$	−2.01016	+	1.78085i	−0.0896286	+	0.0794040i	0.617119	+	0.786870i	$0.288300\pi$
$504$	4.27323	+	1.05326i	0.190345	+	0.0469158i
$505$	24.3680			1.08436
$506$	−3.06390			−0.136207
$507$	23.5573			1.04622
$508$	−71.7112			−3.18167
$509$	−8.14955	−	21.4886i	−0.361223	−	0.952466i	−0.985259	−	0.171070i	$-0.945277\pi$
$509$	−8.14955	−	21.4886i	−0.361223	−	0.952466i	0.624036	−	0.781395i	$-0.285492\pi$
$510$	−64.2131	−	56.8878i	−2.84340	−	2.51904i
$511$	−12.7654	−	3.14638i	−0.564707	−	0.139188i
$512$	44.3989	−	23.3023i	1.96217	−	1.02983i
$513$	11.3308	−	5.94688i	0.500268	−	0.262561i
$514$	19.7476	−	28.6094i	0.871030	−	1.26191i
$515$	7.50789	−	10.8771i	0.330837	−	0.479300i
$516$	42.9468	+	22.5402i	1.89063	+	0.992277i
$517$	3.60459	−	0.888452i	0.158530	−	0.0390741i
$518$	0.0403920	+	0.0357842i	0.00177472	+	0.00157227i
$519$	−1.41512	+	11.6545i	−0.0621167	+	0.511577i
$520$	18.7933			0.824139
$521$	−1.48963	+	12.2682i	−0.0652619	+	0.537480i	0.923010	+	0.384776i	$0.125721\pi$
$521$	−1.48963	+	12.2682i	−0.0652619	+	0.537480i	−0.988272	+	0.152704i	$0.951202\pi$
$522$	2.51770	−	2.23048i	0.110197	−	0.0976256i
$523$	−12.5208	+	33.0145i	−0.547495	+	1.44363i	0.320594	+	0.947217i	$0.396117\pi$
$523$	−12.5208	+	33.0145i	−0.547495	+	1.44363i	−0.868089	+	0.496408i	$0.834652\pi$
$524$	0.404398	−	0.358266i	0.0176662	−	0.0156509i
$525$	7.53830	+	6.67835i	0.328998	+	0.291467i
$526$	−2.80869	−	23.1316i	−0.122465	−	1.00859i
$527$	1.78582	+	14.7076i	0.0777916	+	0.640671i
$528$	−3.25122	+	1.70637i	−0.141491	+	0.0742603i
$529$	−0.735526	+	6.05760i	−0.0319794	+	0.263374i
$530$	−34.8562	−	50.4979i	−1.51406	−	2.19349i
$531$	−8.48158	−	4.45148i	−0.368069	−	0.193178i
$532$	−4.22903	−	11.1510i	−0.183352	−	0.483458i
$533$	−1.77436			−0.0768560
$534$	−16.5520			−0.716277
$535$	8.54126	+	2.10523i	0.369271	+	0.0910171i
$536$	27.9846	−	40.5428i	1.20875	−	1.75118i
$537$	28.8682	−	7.11537i	1.24576	−	0.307051i
$538$	−72.0305			−3.10546
$539$	0.645714	−	1.70261i	0.0278129	−	0.0733366i
$540$	7.36687	+	60.6716i	0.317020	+	2.61089i
$541$	3.62909	−	29.8882i	0.156027	−	1.28500i	−0.678735	−	0.734383i	$-0.737471\pi$
$541$	3.62909	−	29.8882i	0.156027	−	1.28500i	0.834761	−	0.550612i	$-0.185605\pi$
$542$	−24.0065	−	63.2999i	−1.03117	−	2.71896i
$543$	−23.2290	−	5.72544i	−0.996852	−	0.245702i
$544$	−21.9543			−0.941283
$545$	2.83422	−	23.3419i	0.121405	−	0.999859i
$546$	−4.31857			−0.184818
$547$	−1.39080	+	23.3466i	−0.0594662	+	0.998230i
$547$	−1.39080	+	23.3466i	−0.0594662	+	0.998230i
$548$	−29.7165			−1.26942
$549$	−0.284495	+	2.34302i	−0.0121419	+	0.0999978i
$550$	−4.21711			−0.179818
$551$	−4.80203	−	1.18359i	−0.204573	−	0.0504228i
$552$	−17.0318	−	44.9090i	−0.724919	−	1.91146i
$553$	−1.21813	+	10.0322i	−0.0518003	+	0.426614i
$554$	−6.65244	−	54.7878i	−0.282635	−	2.32771i
$555$	0.0529029	−	0.139493i	0.00224560	−	0.00592117i
$556$	−25.5477			−1.08346
$557$	0.0231878	−	0.00571527i	0.000982498	−	0.000242164i	−0.238824	−	0.971063i	$-0.576762\pi$
$557$	0.0231878	−	0.00571527i	0.000982498	−	0.000242164i	0.239807	+	0.970821i	$0.422916\pi$
$558$	−3.20606	+	4.64478i	−0.135723	+	0.196629i
$559$	−5.30608	−	1.30783i	−0.224423	−	0.0553154i
$560$	18.9913			0.802531
$561$	−3.07343			−0.129760
$562$	−5.67958	−	14.9758i	−0.239578	−	0.631717i
$563$	38.4964	+	20.2045i	1.62243	+	0.851517i	0.997487	+	0.0708458i	$0.0225698\pi$
$563$	38.4964	+	20.2045i	1.62243	+	0.851517i	0.624942	+	0.780671i	$0.285122\pi$
$564$	60.9265	+	88.2673i	2.56547	+	3.71672i
$565$	−2.49786	+	20.5717i	−0.105086	+	0.865459i
$566$	−31.8895	+	16.7369i	−1.34041	+	0.703504i
$567$	−1.18428	−	9.75343i	−0.0497351	−	0.409605i
$568$	−11.1917	−	92.1723i	−0.469595	−	3.86746i
$569$	−1.97080	−	1.74598i	−0.0826204	−	0.0731953i	0.620802	−	0.783968i	$-0.286807\pi$
$569$	−1.97080	−	1.74598i	−0.0826204	−	0.0731953i	−0.703422	+	0.710772i	$0.748346\pi$
$570$	−35.9671	+	31.8640i	−1.50649	+	1.33464i
$571$	−8.44321	+	22.2629i	−0.353337	+	0.931674i	0.634042	+	0.773299i	$0.281395\pi$
$571$	−8.44321	+	22.2629i	−0.353337	+	0.931674i	−0.987379	+	0.158375i	$0.949374\pi$
$572$	0.928761	−	0.822811i	0.0388335	−	0.0344034i
$573$	−5.83553	+	48.0599i	−0.243783	+	2.00773i
$574$	−4.25277			−0.177507
$575$	2.80344	−	23.0884i	0.116912	−	0.962854i
$576$	1.42511	+	1.26254i	0.0593796	+	0.0526058i
$577$	10.3732	−	2.55677i	0.431843	−	0.106440i	−0.0174015	−	0.999849i	$-0.505539\pi$
$577$	10.3732	−	2.55677i	0.431843	−	0.106440i	0.449245	+	0.893409i	$0.351693\pi$
$578$	−25.6509	−	13.4626i	−1.06694	−	0.559971i
$579$	−21.7222	+	31.4700i	−0.902743	+	1.30785i
$580$	13.4183	−	19.4398i	0.557166	−	0.807195i
$581$	0.791884	−	0.415613i	0.0328529	−	0.0172425i
$582$	−19.6226	+	10.2987i	−0.813383	+	0.426896i
$583$	−2.13439	−	0.526079i	−0.0883973	−	0.0217880i
$584$	64.5978	+	57.2286i	2.67307	+	2.36814i
$585$	0.895919	+	2.36234i	0.0370417	+	0.0976709i
$586$	1.73066			0.0714927
$587$	−5.00526			−0.206589			−0.103295	−	0.994651i	$-0.532938\pi$
$587$	−5.00526			−0.206589			−0.103295	+	0.994651i	$0.532938\pi$
$588$	52.6068			2.16947
$589$	8.29851			0.341934
$590$	−95.1859	−	23.4612i	−3.91874	−	0.965883i
$591$	−31.0026	+	27.4659i	−1.27528	+	1.12980i
$592$	−0.0529595	−	0.139643i	−0.00217662	−	0.00573928i
$593$	−1.08078	−	1.56579i	−0.0443825	−	0.0642991i	0.800164	−	0.599781i	$-0.204746\pi$
$593$	−1.08078	−	1.56579i	−0.0443825	−	0.0642991i	−0.844547	+	0.535482i	$0.820130\pi$
$594$	2.38855	+	2.11607i	0.0980032	+	0.0868233i
$595$	14.0756	+	7.38744i	0.577043	+	0.302856i
$596$	61.0967	−	15.0590i	2.50262	−	0.616840i
$597$	28.2523	+	40.9306i	1.15629	+	1.67518i
$598$	5.66546	+	8.20784i	0.231678	+	0.335644i
$599$	44.1521	+	10.8825i	1.80401	+	0.444648i	0.990570	−	0.137006i	$-0.0437478\pi$
$599$	44.1521	+	10.8825i	1.80401	+	0.444648i	0.813437	+	0.581653i	$0.197594\pi$
$600$	−23.4422	−	61.8121i	−0.957025	−	2.52347i
$601$	4.23323	−	34.8638i	0.172677	−	1.42212i	−0.606382	−	0.795174i	$-0.707380\pi$
$601$	4.23323	−	34.8638i	0.172677	−	1.42212i	0.779059	−	0.626951i	$-0.215697\pi$
$602$	−12.7176	−	3.13460i	−0.518330	−	0.127757i
$603$	6.43039	+	1.58495i	0.261866	+	0.0645441i
$604$	49.2322	−	25.8390i	2.00323	−	1.05138i
$605$	26.6668	−	23.6247i	1.08416	−	0.960482i
$606$	32.5465	+	17.0817i	1.32211	+	0.693898i
$607$	−0.905589	−	7.45820i	−0.0367567	−	0.302719i	−0.999480	−	0.0322321i	$-0.989738\pi$
$607$	−0.905589	−	7.45820i	−0.0367567	−	0.302719i	0.962724	−	0.270487i	$-0.0871846\pi$
$608$	−1.48225	+	12.2074i	−0.0601130	+	0.495075i
$609$	−1.67314	+	2.42396i	−0.0677989	+	0.0982236i
$610$	2.91168	+	23.9798i	0.117890	+	0.970915i
$611$	−9.04531	−	8.01345i	−0.365934	−	0.324189i
$612$	−6.66285	−	17.5685i	−0.269330	−	0.710165i
$613$	−20.0045	−	17.7224i	−0.807973	−	0.715801i	0.154260	−	0.988030i	$-0.450701\pi$
$613$	−20.0045	−	17.7224i	−0.807973	−	0.715801i	−0.962232	+	0.272229i	$0.912239\pi$
$614$	−1.66764	−	0.411037i	−0.0673007	−	0.0165881i
$615$	4.16922	+	10.9933i	0.168119	+	0.443294i
$616$	1.20789	−	1.07010i	0.0486674	−	0.0431156i
$617$	−0.523950	−	1.38154i	−0.0210934	−	0.0556188i	0.924056	−	0.382257i	$-0.124853\pi$
$617$	−0.523950	−	1.38154i	−0.0210934	−	0.0556188i	−0.945149	+	0.326639i	$0.894084\pi$
$618$	17.6524	−	9.26471i	0.710085	−	0.372681i
$619$	5.92494	−	15.6228i	0.238143	−	0.627933i	−0.761655	−	0.647982i	$-0.775613\pi$
$619$	5.92494	−	15.6228i	0.238143	−	0.627933i	0.999799	+	0.0200494i	$0.00638235\pi$
$620$	−14.0545	+	37.0586i	−0.564441	+	1.48831i
$621$	−13.1732	+	11.6704i	−0.528623	+	0.468319i
$622$	7.14879	−	6.33327i	0.286640	−	0.253941i
$623$	2.97796	−	0.734002i	0.119310	−	0.0294072i
$624$	10.5830	+	5.55440i	0.423660	+	0.222354i
$625$	−2.56473	+	21.1225i	−0.102589	+	0.844898i
$626$	−32.7725	−	8.07770i	−1.30985	−	0.322850i
$627$	−0.207503	+	1.70894i	−0.00828687	+	0.0682485i
$628$	−52.2864			−2.08645
$629$	0.0150682	−	0.124098i	0.000600810	−	0.00494812i
$630$	2.14733	+	5.66205i	0.0855518	+	0.225582i
$631$	−1.83439	+	15.1076i	−0.0730260	+	0.601423i	0.909554	+	0.415585i	$0.136423\pi$
$631$	−1.83439	+	15.1076i	−0.0730260	+	0.601423i	−0.982580	+	0.185838i	$0.940500\pi$
$632$	37.6836	−	54.5941i	1.49897	−	2.17164i
$633$	10.4608	−	27.5829i	0.415780	−	1.09632i
$634$	26.0488	+	23.0772i	1.03453	+	0.916514i
$635$	−30.4138	−	44.0619i	−1.20693	−	1.74854i
$636$	−7.65500	−	63.0446i	−0.303540	−	2.49988i
$637$	−5.75509	+	1.41850i	−0.228025	+	0.0562031i
$638$	−0.148659	−	1.22432i	−0.00588547	−	0.0484712i
$639$	11.0527	−	5.80089i	0.437237	−	0.229480i
$640$	41.0396	+	21.5393i	1.62223	+	0.851414i
$641$	−17.5205	+	15.5218i	−0.692017	+	0.613073i	−0.934028	−	0.357200i	$-0.883731\pi$
$641$	−17.5205	+	15.5218i	−0.692017	+	0.613073i	0.242011	+	0.970273i	$0.422193\pi$
$642$	9.93218	+	8.79914i	0.391992	+	0.347274i
$643$	−12.7999	+	18.5439i	−0.504779	+	0.731299i	−0.989684	−	0.143268i	$-0.954239\pi$
$643$	−12.7999	+	18.5439i	−0.504779	+	0.731299i	0.484905	+	0.874567i	$0.338854\pi$
$644$	9.31736	+	13.4985i	0.367155	+	0.531916i
$645$	4.36484	+	35.9477i	0.171865	+	1.41544i
$646$	−22.8725	+	33.1365i	−0.899906	+	1.30374i
$647$	22.5999	−	11.8613i	0.888493	−	0.466317i	0.0422453	−	0.999107i	$-0.486549\pi$
$647$	22.5999	−	11.8613i	0.888493	−	0.466317i	0.846247	+	0.532790i	$0.178857\pi$
$648$	−22.8696	+	60.3022i	−0.898404	+	2.36890i
$649$	−3.10988	+	1.63219i	−0.122074	+	0.0640692i
$650$	7.79786	+	11.2971i	0.305857	+	0.443111i
$651$	1.75245	−	4.62084i	0.0686841	−	0.181105i
$652$	−92.5274	+	48.5621i	−3.62365	+	1.90184i
$653$	13.0793	−	3.22375i	0.511831	−	0.126155i	0.0250622	−	0.999686i	$-0.492022\pi$
$653$	13.0793	−	3.22375i	0.511831	−	0.126155i	0.486769	+	0.873531i	$0.338175\pi$
$654$	20.1479	−	29.1893i	0.787846	−	1.14139i
$655$	0.391643	+	0.0965312i	0.0153027	+	0.00377179i
$656$	10.4218	+	5.46976i	0.406902	+	0.213558i
$657$	−4.11421	+	10.8483i	−0.160511	+	0.423232i
$658$	−21.6797	−	19.2066i	−0.845165	−	0.748751i
$659$	7.39345	−	19.4949i	0.288008	−	0.759414i	−0.710442	−	0.703756i	$-0.751505\pi$
$659$	7.39345	−	19.4949i	0.288008	−	0.759414i	0.998450	−	0.0556585i	$-0.0177258\pi$
$660$	−7.28017	−	3.82093i	−0.283380	−	0.148729i
$661$	−15.2088	−	40.1024i	−0.591556	−	1.55980i	−0.811538	−	0.584300i	$-0.801369\pi$
$661$	−15.2088	−	40.1024i	−0.591556	−	1.55980i	0.219982	−	0.975504i	$-0.429400\pi$
$662$	−0.952701	−	0.500016i	−0.0370278	−	0.0194337i
$663$	5.68309	+	8.23338i	0.220713	+	0.319758i
$664$	−5.87048			−0.227819
$665$	5.05800	−	7.32778i	0.196141	−	0.284159i
$666$	0.0356448	−	0.0315785i	0.00138121	−	0.00122364i
$667$	6.80191			0.263371
$668$	−3.79793	−	10.0143i	−0.146946	−	0.387465i
$669$	−52.4629	−	12.9309i	−2.02833	−	0.499939i
$670$	67.7818			2.61864
$671$	0.647769	+	0.573873i	0.0250068	+	0.0221541i
$672$	6.48440	+	3.40328i	0.250141	+	0.131284i
$673$	40.6795			1.56808			0.784039	−	0.620712i	$-0.213156\pi$
$673$	40.6795			1.56808			0.784039	+	0.620712i	$0.213156\pi$
$674$	−77.5225	+	19.1076i	−2.98606	+	0.735997i
$675$	−18.1314	+	16.0630i	−0.697878	+	0.618266i
$676$	51.2718	+	12.6374i	1.97199	+	0.486053i
$677$	−28.8086	+	7.10069i	−1.10721	+	0.272902i	−0.750207	−	0.661203i	$-0.770046\pi$
$677$	−28.8086	+	7.10069i	−1.10721	+	0.272902i	−0.356998	+	0.934105i	$0.616200\pi$
$678$	−17.7568	+	25.7251i	−0.681945	+	0.987968i
$679$	3.07370	−	2.72306i	0.117958	−	0.104502i
$680$	−59.2757	−	85.8757i	−2.27312	−	3.29318i
$681$	2.30233	−	6.07074i	0.0882255	−	0.232631i
$682$	0.733813	+	1.93491i	0.0280992	+	0.0740914i
$683$	−16.3468	+	4.02913i	−0.625494	+	0.154170i	−0.539308	−	0.842109i	$-0.681314\pi$
$683$	−16.3468	+	4.02913i	−0.625494	+	0.154170i	−0.0861860	+	0.996279i	$0.527468\pi$
$684$	−10.2186	+	2.51865i	−0.390717	+	0.0963031i
$685$	−12.6032	−	18.2589i	−0.481543	−	0.697636i
$686$	−29.4498	+	7.25872i	−1.12440	+	0.277139i
$687$	−10.1896	+	2.51152i	−0.388759	+	0.0958205i
$688$	27.1339	+	24.0385i	1.03447	+	0.916459i
$689$	2.53739	+	6.69055i	0.0966670	+	0.254890i
$690$	37.5408	−	54.3873i	1.42915	−	2.07049i
$691$	−22.9908	−	12.0665i	−0.874610	−	0.459031i	−0.0332131	−	0.999448i	$-0.510574\pi$
$691$	−22.9908	−	12.0665i	−0.874610	−	0.459031i	−0.841397	+	0.540417i	$0.818266\pi$
$692$	−9.33204	+	24.6066i	−0.354751	+	0.935402i
$693$	0.192097	+	0.100820i	0.00729715	+	0.00382984i
$694$	−64.8429	+	15.9823i	−2.46140	+	0.606682i
$695$	−10.8351	−	15.6974i	−0.411000	−	0.595437i
$696$	17.1190	−	8.98476i	0.648895	−	0.340567i
$697$	5.59650	+	8.10792i	0.211982	+	0.307110i
$698$	−12.7374	+	11.2843i	−0.482117	+	0.427118i
$699$	−6.38125	−	52.5543i	−0.241361	−	1.98779i
$700$	12.8243	+	18.5792i	0.484712	+	0.702226i
$701$	22.5429	−	32.6590i	0.851433	−	1.23351i	−0.119181	−	0.992873i	$-0.538027\pi$
$701$	22.5429	−	32.6590i	0.851433	−	1.23351i	0.970614	−	0.240642i	$-0.0773578\pi$
$702$	1.25204	−	10.3115i	0.0472551	−	0.389181i
$703$	−0.0679857	−	0.0167570i	−0.00256413	−	0.000632001i
$704$	0.677815	−	0.167066i	0.0255461	−	0.00629655i
$705$	−28.3948	+	74.8709i	−1.06941	+	2.81980i
$706$	−10.0088	−	26.3911i	−0.376688	−	0.993244i
$707$	−6.61310	−	1.62998i	−0.248711	−	0.0613018i
$708$	−75.9488	−	67.2848i	−2.85433	−	2.52872i
$709$	5.03187	−	41.4412i	0.188976	−	1.55636i	−0.521879	−	0.853019i	$-0.674769\pi$
$709$	5.03187	−	41.4412i	0.188976	−	1.55636i	0.710855	−	0.703338i	$-0.248308\pi$
$710$	95.6242	−	84.7157i	3.58871	−	3.17932i
$711$	8.65905	+	2.13426i	0.324740	+	0.0800411i
$712$	−19.5478	−	4.81810i	−0.732585	−	0.180566i
$713$	−11.0813	+	2.73131i	−0.415000	+	0.102288i
$714$	13.6212	+	19.7337i	0.509760	+	0.738515i
$715$	0.899466	+	0.221698i	0.0336381	+	0.00829105i
$716$	66.6478			2.49075
$717$	20.7976	+	18.4251i	0.776701	+	0.688097i
$718$	−17.5780	+	9.22563i	−0.656004	+	0.344297i
$719$	1.71264	+	0.898865i	0.0638708	+	0.0335220i	0.496356	−	0.868119i	$-0.334671\pi$
$719$	1.71264	+	0.898865i	0.0638708	+	0.0335220i	−0.432485	+	0.901641i	$0.642363\pi$
$720$	2.02012	−	16.6371i	0.0752852	−	0.620030i
$721$	−2.76509	+	2.44966i	−0.102977	+	0.0912301i
$722$	−19.0207	−	16.8509i	−0.707878	−	0.627125i
$723$	22.9115	−	12.0249i	0.852089	−	0.447211i
$724$	−47.4858	−	24.9225i	−1.76480	−	0.926236i
$725$	9.36204			0.347697
$726$	52.1776	−	12.8606i	1.93649	−	0.477302i
$727$	−4.70632	−	38.7600i	−0.174548	−	1.43753i	−0.771998	−	0.635625i	$-0.780743\pi$
$727$	−4.70632	−	38.7600i	−0.174548	−	1.43753i	0.597450	−	0.801906i	$-0.296180\pi$
$728$	−5.10020	−	1.25709i	−0.189026	−	0.0465907i
$729$	16.3844			0.606829
$730$	−14.3130	+	117.878i	−0.529747	+	4.36286i
$731$	10.7598	+	28.3711i	0.397964	+	1.04934i
$732$	−8.86569	+	23.3769i	−0.327686	+	0.864036i
$733$	15.7222	−	22.7776i	0.580714	−	0.841309i	−0.416999	−	0.908907i	$-0.636918\pi$
$733$	15.7222	−	22.7776i	0.580714	−	0.841309i	0.997713	+	0.0675979i	$0.0215335\pi$
$734$	−48.0497			−1.77355
$735$	22.3113	+	32.3235i	0.822965	+	1.19227i
$736$	−2.03854	−	16.7889i	−0.0751416	−	0.618847i
$737$	1.81765	−	1.61029i	0.0669539	−	0.0593160i
$738$	−0.452369	+	3.72559i	−0.0166519	+	0.137141i
$739$	12.9726	+	11.4927i	0.477206	+	0.422768i	0.867132	−	0.498079i	$-0.165961\pi$
$739$	12.9726	+	11.4927i	0.477206	+	0.422768i	−0.389926	+	0.920846i	$0.627499\pi$
$740$	0.189973	−	0.275223i	0.00698355	−	0.0101174i
$741$	4.96175	−	2.60413i	0.182274	−	0.0956650i
$742$	6.08161	+	16.0359i	0.223263	+	0.588696i
$743$	34.5224			1.26650			0.633252	−	0.773946i	$-0.281720\pi$
$743$	34.5224			1.26650			0.633252	+	0.773946i	$0.281720\pi$
$744$	−24.2817	+	21.5117i	−0.890210	+	0.788657i
$745$	35.1648	+	31.1533i	1.28834	+	1.14137i
$746$	19.7346	+	28.5904i	0.722533	+	1.04677i
$747$	−0.279860	−	0.737930i	−0.0102395	−	0.0269994i
$748$	−6.68923	−	1.64875i	−0.244582	−	0.0602842i
$749$	−2.17715	−	1.14265i	−0.0795512	−	0.0417517i
$750$	6.00835	−	8.70459i	0.219394	−	0.317847i
$751$	17.9802	+	47.4100i	0.656108	+	1.73002i	0.683043	+	0.730378i	$0.260656\pi$
$751$	17.9802	+	47.4100i	0.656108	+	1.73002i	−0.0269348	+	0.999637i	$0.508575\pi$
$752$	28.4252	+	74.9510i	1.03656	+	2.73318i
$753$	−32.6975	+	17.1610i	−1.19156	+	0.625381i
$754$	−3.00492	+	2.66213i	−0.109433	+	0.0969491i
$755$	36.7565	+	19.2913i	1.33771	+	0.702082i
$756$	2.05909	−	16.9581i	0.0748883	−	0.616760i
$757$	−15.5671	−	41.0471i	−0.565796	−	1.49188i	−0.846660	−	0.532134i	$-0.821390\pi$
$757$	−15.5671	−	41.0471i	−0.565796	−	1.49188i	0.280865	−	0.959747i	$-0.409379\pi$
$758$	−24.0538	+	63.4247i	−0.873674	+	2.30369i
$759$	−0.285380	−	2.35031i	−0.0103586	−	0.0853110i
$760$	−51.7520	+	27.1615i	−1.87724	+	0.985253i
$761$	5.32591	+	4.71834i	0.193064	+	0.171040i	0.754117	−	0.656740i	$-0.228065\pi$
$761$	5.32591	+	4.71834i	0.193064	+	0.171040i	−0.561053	+	0.827780i	$0.689604\pi$
$762$	−9.73439	−	80.1700i	−0.352640	−	2.90425i
$763$	−2.33051	+	6.14506i	−0.0843702	+	0.222466i
$764$	−38.4826	+	101.470i	−1.39225	+	3.67107i
$765$	7.96891	−	11.5450i	0.288116	−	0.417409i
$766$	12.7463	−	33.6091i	0.460541	−	1.21435i
$767$	10.1230	+	5.31294i	0.365519	+	0.191839i
$768$	34.4746	+	49.9451i	1.24400	+	1.80224i
$769$	31.3896	−	27.8088i	1.13194	−	1.00281i	0.132005	−	0.991249i	$-0.457858\pi$
$769$	31.3896	−	27.8088i	1.13194	−	1.00281i	0.999933	−	0.0115610i	$-0.00368006\pi$
$770$	2.15583	+	0.531365i	0.0776909	+	0.0191491i
$771$	23.7856	+	12.4836i	0.856616	+	0.449587i
$772$	−64.1598	+	56.8406i	−2.30916	+	2.04574i
$773$	−25.1328	+	36.4112i	−0.903965	+	1.30962i	0.0465424	+	0.998916i	$0.485180\pi$
$773$	−25.1328	+	36.4112i	−0.903965	+	1.30962i	−0.950507	+	0.310703i	$0.899436\pi$
$774$	−4.09880	+	10.8077i	−0.147328	+	0.388473i
$775$	−15.2522	+	3.75933i	−0.547875	+	0.135039i
$776$	−26.1719	+	6.45080i	−0.939518	+	0.231570i
$777$	−0.0236878	+	0.0343177i	−0.000849794	+	0.00123114i
$778$	16.5446	+	8.68327i	0.593152	+	0.311310i
$779$	4.88615	−	2.56445i	0.175064	−	0.0918809i
$780$	3.22594	+	26.5680i	0.115507	+	0.951288i
$781$	0.551680	−	4.54349i	0.0197407	−	0.162579i
$782$	19.6363	−	51.7766i	0.702192	−	1.85153i
$783$	−5.30261	−	4.69770i	−0.189500	−	0.167882i
$784$	38.1755	+	9.40941i	1.36341	+	0.336051i
$785$	−22.1754	−	32.1266i	−0.791474	−	1.14665i
$786$	0.455420	+	0.403467i	0.0162443	+	0.0143912i
$787$	−3.01472	+	24.8285i	−0.107463	+	0.885039i	0.834890	+	0.550418i	$0.185531\pi$
$787$	−3.01472	+	24.8285i	−0.107463	+	0.885039i	−0.942353	+	0.334621i	$0.891392\pi$
$788$	−82.2103	+	43.1473i	−2.92862	+	1.53706i
$789$	17.4826	−	4.30909i	0.622399	−	0.153408i
$790$	91.2738			3.24738
$791$	2.05393	−	5.41576i	0.0730293	−	0.192562i
$792$	−0.808965	−	1.17199i	−0.0287453	−	0.0416448i
$793$	0.339551	−	2.79645i	0.0120578	−	0.0993049i
$794$	−0.495830	+	0.260232i	−0.0175963	+	0.00923527i
$795$	35.4903	−	31.4416i	1.25871	−	1.11512i
$796$	39.5330	+	104.240i	1.40121	+	3.69469i
$797$	−16.9922	+	24.6175i	−0.601895	+	0.871995i	−0.998951	−	0.0457994i	$-0.985416\pi$
$797$	−16.9922	+	24.6175i	−0.601895	+	0.871995i	0.397056	+	0.917794i	$0.370032\pi$
$798$	11.8923	−	6.24156i	0.420983	−	0.220949i
$799$	−8.08764	+	66.6077i	−0.286120	+	2.35641i
$800$	−2.80582	−	23.1080i	−0.0992006	−	0.816990i
$801$	−0.326247	−	2.68688i	−0.0115274	−	0.0949364i
$802$	−25.4697	+	36.8992i	−0.899365	+	1.30296i
$803$	2.41661	+	3.50107i	0.0852803	+	0.123550i
$804$	62.1190	+	32.6026i	2.19077	+	1.14980i
$805$	−4.34235	+	11.4498i	−0.153048	+	0.403554i
$806$	3.82650	−	5.54364i	0.134783	−	0.195267i
$807$	−6.70911	−	55.2545i	−0.236172	−	1.94505i
$808$	33.4649	+	29.6473i	1.17729	+	1.04299i
$809$	−20.9095	−	18.5242i	−0.735140	−	0.651277i	0.210090	−	0.977682i	$-0.432624\pi$
$809$	−20.9095	−	18.5242i	−0.735140	−	0.651277i	−0.945230	+	0.326405i	$0.894163\pi$
$810$	−86.1586	+	21.2362i	−3.02731	+	0.746164i
$811$	22.0659	+	31.9679i	0.774838	+	1.12255i	0.989312	+	0.145817i	$0.0465810\pi$
$811$	22.0659	+	31.9679i	0.774838	+	1.12255i	−0.214474	+	0.976730i	$0.568804\pi$
$812$	−4.94186	+	4.37811i	−0.173425	+	0.153641i
$813$	46.3212	−	24.3113i	1.62456	−	0.852633i
$814$	−0.00210467	−	0.0173335i	−7.37688e−5	−	0.000607540i
$815$	−69.0805	−	36.2562i	−2.41978	−	1.27000i
$816$	−7.99905	−	65.8781i	−0.280023	−	2.30620i
$817$	16.5018	−	4.06734i	0.577326	−	0.142298i
$818$	−22.5884	+	11.8553i	−0.789785	+	0.414511i
$819$	−0.0851207	−	0.701032i	−0.00297436	−	0.0244960i
$820$	3.17679	+	26.1632i	0.110938	+	0.913659i
$821$	−0.752539	−	6.19772i	−0.0262638	−	0.216302i	0.973668	−	0.227970i	$-0.0732089\pi$
$821$	−0.752539	−	6.19772i	−0.0262638	−	0.216302i	−0.999932	+	0.0116683i	$0.996286\pi$
$822$	−4.03385	−	33.2217i	−0.140697	−	1.15874i
$823$	11.5966	−	6.08634i	0.404230	−	0.212157i	−0.250339	−	0.968158i	$-0.580542\pi$
$823$	11.5966	−	6.08634i	0.404230	−	0.212157i	0.654570	+	0.756002i	$0.272850\pi$
$824$	23.5442	−	5.80313i	0.820201	−	0.202161i
$825$	−0.392792	−	3.23494i	−0.0136753	−	0.112626i
$826$	24.2626	+	12.7340i	0.844205	+	0.443073i
$827$	2.89844	+	23.8708i	0.100789	+	0.830069i	0.952180	+	0.305538i	$0.0988363\pi$
$827$	2.89844	+	23.8708i	0.100789	+	0.830069i	−0.851391	+	0.524531i	$0.824241\pi$
$828$	12.8163	−	6.72652i	0.445398	−	0.233763i
$829$	15.7163	−	13.9235i	0.545851	−	0.483582i	−0.344544	−	0.938770i	$-0.611967\pi$
$829$	15.7163	−	13.9235i	0.545851	−	0.483582i	0.890395	+	0.455188i	$0.150428\pi$
$830$	−4.58842	−	6.64747i	−0.159266	−	0.230737i
$831$	41.4080	−	10.2062i	1.43643	−	0.354048i
$832$	−1.70090	−	1.50687i	−0.0589681	−	0.0522412i
$833$	24.6339	+	21.8238i	0.853515	+	0.756148i
$834$	−3.46796	−	28.5612i	−0.120085	−	0.988993i
$835$	4.54240	−	6.58080i	0.157196	−	0.227738i
$836$	−1.36839	+	3.60814i	−0.0473267	+	0.124790i
$837$	10.5251	+	5.52401i	0.363801	+	0.190938i
$838$	−1.22214	−	1.77057i	−0.0422180	−	0.0611633i
$839$	1.98732	−	2.87914i	0.0686100	−	0.0993988i	−0.787177	−	0.616727i	$-0.788458\pi$
$839$	1.98732	−	2.87914i	0.0686100	−	0.0993988i	0.855787	+	0.517329i	$0.173073\pi$
$840$	4.19548	+	34.5528i	0.144758	+	1.19219i
$841$	−3.16554	−	26.0706i	−0.109156	−	0.898985i
$842$	−6.38031	+	52.5465i	−0.219880	+	1.81087i
$843$	10.9589	−	5.75168i	0.377445	−	0.198098i
$844$	37.5645	−	54.4216i	1.29302	−	1.87327i
$845$	13.9803	+	36.8629i	0.480936	+	1.26812i
$846$	−19.1318	+	16.9493i	−0.657764	+	0.582728i
$847$	−8.81722	+	4.62764i	−0.302963	+	0.159007i
$848$	5.72130	−	47.1192i	0.196470	−	1.61808i
$849$	−15.8091	−	22.9035i	−0.542567	−	0.786045i
$850$	27.0271	−	71.2645i	0.927021	−	2.44435i
$851$	0.0962994			0.00330110
$852$	128.383	−	31.6435i	4.39832	−	1.08409i
$853$	−21.5274	+	11.2985i	−0.737086	+	0.386852i	−0.791099	−	0.611688i	$-0.790491\pi$
$853$	−21.5274	+	11.2985i	−0.737086	+	0.386852i	0.0540136	+	0.998540i	$0.482799\pi$
$854$	0.813832	−	6.70251i	0.0278488	−	0.229355i
$855$	−5.88140	−	5.21046i	−0.201139	−	0.178194i
$856$	9.16848	+	13.2828i	0.313372	+	0.453998i
$857$	47.3471	+	11.6700i	1.61735	+	0.398640i	0.941125	−	0.338059i	$-0.109770\pi$
$857$	47.3471	+	11.6700i	1.61735	+	0.398640i	0.676221	+	0.736699i	$0.263616\pi$
$858$	1.04594	+	0.926622i	0.0357078	+	0.0316344i
$859$	−5.70185	+	15.0345i	−0.194545	+	0.512972i	−0.996422	−	0.0845167i	$-0.973065\pi$
$859$	−5.70185	+	15.0345i	−0.194545	+	0.512972i	0.801878	+	0.597488i	$0.203835\pi$
$860$	−9.78425	+	80.5805i	−0.333640	+	2.74777i
$861$	−0.396114	−	3.26230i	−0.0134995	−	0.111179i
$862$	−22.0988	+	11.5983i	−0.752687	+	0.395041i
$863$	−10.0012	−	5.24903i	−0.340444	−	0.178679i	0.285833	−	0.958280i	$-0.407730\pi$
$863$	−10.0012	−	5.24903i	−0.340444	−	0.178679i	−0.626277	+	0.779600i	$0.715422\pi$
$864$	−10.0060	+	14.4961i	−0.340410	+	0.493168i
$865$	−19.0770	+	4.70206i	−0.648638	+	0.159875i
$866$	30.1439	−	7.42980i	1.02433	−	0.252475i
$867$	7.93797	−	20.9307i	0.269588	−	0.710844i
$868$	6.29302	−	9.11701i	0.213599	−	0.309451i
$869$	2.44761	−	2.16839i	0.0830295	−	0.0735577i
$870$	23.5543	+	12.3623i	0.798567	+	0.419120i
$871$	−7.67481	−	1.89167i	−0.260051	−	0.0640968i
$872$	32.2912	−	28.6075i	1.09352	−	0.968771i
$873$	−2.05856	−	2.98233i	−0.0696716	−	0.100937i
$874$	−27.4639	−	14.4142i	−0.928982	−	0.487567i
$875$	−0.694986	+	1.83253i	−0.0234948	+	0.0619508i
$876$	−69.8156	+	101.145i	−2.35885	+	3.41739i
$877$	5.27218	−	13.9016i	0.178029	−	0.469424i	−0.816063	−	0.577963i	$-0.803848\pi$
$877$	5.27218	−	13.9016i	0.178029	−	0.469424i	0.994092	+	0.108539i	$0.0346172\pi$
$878$	−5.07666	+	13.3861i	−0.171329	+	0.451758i
$879$	0.161198	+	1.32758i	0.00543707	+	0.0447783i
$880$	−4.59962	−	4.07491i	−0.155053	−	0.137365i
$881$	16.0523	−	8.42488i	0.540815	−	0.283842i	−0.172115	−	0.985077i	$-0.555060\pi$
$881$	16.0523	−	8.42488i	0.540815	−	0.283842i	0.712930	+	0.701235i	$0.247368\pi$
$882$	1.51116	+	12.4455i	0.0508833	+	0.419062i
$883$	−9.60057	+	25.3146i	−0.323085	+	0.851905i	0.670816	+	0.741624i	$0.265944\pi$
$883$	−9.60057	+	25.3146i	−0.323085	+	0.851905i	−0.993901	+	0.110281i	$0.964825\pi$
$884$	7.95226	+	20.9684i	0.267463	+	0.705243i
$885$	9.13120	−	75.2022i	0.306942	−	2.52789i
$886$	32.7651	+	17.1964i	1.10076	+	0.577726i
$887$	−30.4870	+	27.0091i	−1.02365	+	0.906877i	−0.995691	−	0.0927322i	$-0.970440\pi$
$887$	−30.4870	+	27.0091i	−1.02365	+	0.906877i	−0.0279612	+	0.999609i	$0.508901\pi$
$888$	0.242366	−	0.127204i	0.00813328	−	0.00426868i
$889$	5.30651	+	13.9921i	0.177975	+	0.469280i
$890$	−9.82293	−	25.9009i	−0.329265	−	0.868201i
$891$	−1.80593	+	2.61635i	−0.0605010	+	0.0876509i
$892$	−107.247	−	56.2876i	−3.59090	−	1.88465i
$893$	36.4903	+	8.99404i	1.22110	+	0.300974i
$894$	25.1288	+	66.2592i	0.840433	+	2.21604i
$895$	28.2663	+	40.9508i	0.944839	+	1.36883i
$896$	−9.69675	−	8.59057i	−0.323946	−	0.286991i
$897$	−5.76853	+	5.11047i	−0.192606	+	0.170634i
$898$	82.9209			2.76711
$899$	−1.62908	−	4.29552i	−0.0543328	−	0.143264i
$900$	17.6402	−	9.25828i	0.588006	−	0.308609i
$901$	22.5693	−	32.6972i	0.751892	−	1.08930i
$902$	1.03000	+	0.912503i	0.0342954	+	0.0303830i
$903$	1.22000	−	10.0476i	0.0405991	−	0.334363i
$904$	−28.4589	+	25.2124i	−0.946528	+	0.838550i
$905$	−4.82616	−	39.7470i	−0.160427	−	1.32123i
$906$	35.5699	+	51.5319i	1.18173	+	1.71203i
$907$	−9.56147			−0.317483			−0.158742	−	0.987320i	$-0.550744\pi$
$907$	−9.56147			−0.317483			−0.158742	+	0.987320i	$0.550744\pi$
$908$	8.26761	−	11.9777i	0.274370	−	0.397494i
$909$	−2.13137	+	5.61995i	−0.0706929	+	0.186402i
$910$	−2.56289	−	6.75778i	−0.0849589	−	0.224018i
$911$	−1.15669	+	9.52619i	−0.0383228	+	0.315617i	0.960924	+	0.276812i	$0.0892780\pi$
$911$	−1.15669	+	9.52619i	−0.0383228	+	0.315617i	−0.999247	+	0.0388044i	$0.987645\pi$
$912$	−37.1707			−1.23084
$913$	−0.280968	−	0.0692523i	−0.00929867	−	0.00229192i
$914$	−9.96360	−	82.0576i	−0.329567	−	2.71423i
$915$	−18.1237	+	4.46709i	−0.599151	+	0.147677i
$916$	−23.5247			−0.777279
$917$	−0.0998287	−	0.0523941i	−0.00329663	−	0.00173021i
$918$	−51.0672	+	26.8021i	−1.68547	+	0.884603i
$919$	−38.3853	−	34.0064i	−1.26621	−	1.12177i	−0.986860	−	0.161579i	$-0.948341\pi$
$919$	−38.3853	−	34.0064i	−1.26621	−	1.12177i	−0.279354	−	0.960188i	$-0.590120\pi$
$920$	60.1669	−	53.3032i	1.98364	−	1.75735i
$921$	0.159977	−	1.31753i	0.00527144	−	0.0434142i
$922$	−66.6369	−	34.9737i	−2.19457	−	1.15180i
$923$	−13.1916	+	6.92349i	−0.434207	+	0.227890i
$924$	1.72014	+	1.52391i	0.0565885	+	0.0501330i
$925$	0.132545			0.00435805
$926$	86.9407	+	21.4290i	2.85705	+	0.704199i
$927$	1.85187	+	2.68290i	0.0608234	+	0.0881180i
$928$	6.60984	−	1.62918i	0.216979	−	0.0534805i
$929$	−48.8721	−	12.0459i	−1.60344	−	0.395212i	−0.666725	−	0.745304i	$-0.732304\pi$
$929$	−48.8721	−	12.0459i	−1.60344	−	0.395212i	−0.936715	+	0.350092i	$0.886150\pi$
$930$	−43.3377	−	10.6818i	−1.42110	−	0.350269i
$931$	13.7980	−	12.2239i	0.452210	−	0.400623i
$932$	14.3043	−	117.806i	0.468551	−	3.85887i
$933$	5.52410	+	4.89393i	0.180851	+	0.160220i
$934$	−33.9310	−	8.36323i	−1.11026	−	0.273653i
$935$	−1.82395	−	4.80936i	−0.0596496	−	0.157283i
$936$	−1.64376	+	4.33425i	−0.0537281	+	0.141669i
$937$	−33.6752	+	8.30020i	−1.10012	+	0.271156i	−0.747268	−	0.664523i	$-0.768635\pi$
$937$	−33.6752	+	8.30020i	−1.10012	+	0.271156i	−0.352854	+	0.935679i	$0.614789\pi$
$938$	−18.3949	−	4.53394i	−0.600616	−	0.148039i
$939$	3.14387	−	25.8921i	0.102596	−	0.844958i
$940$	−101.965	+	147.722i	−3.32573	+	4.81815i
$941$	−1.26900	−	1.83847i	−0.0413683	−	0.0599323i	0.801754	−	0.597654i	$-0.203900\pi$
$941$	−1.26900	−	1.83847i	−0.0413683	−	0.0599323i	−0.843122	+	0.537722i	$0.819285\pi$
$942$	−7.09758	−	58.4539i	−0.231252	−	1.90453i
$943$	−5.68063	+	5.03260i	−0.184987	+	0.163884i
$944$	−43.0795	−	62.4115i	−1.40212	−	2.03132i
$945$	11.2930	−	5.92700i	0.367360	−	0.192805i
$946$	2.40756	+	3.48796i	0.0782766	+	0.113403i
$947$	17.2353	−	4.24811i	0.560071	−	0.138045i	0.0508893	−	0.998704i	$-0.483794\pi$
$947$	17.2353	−	4.24811i	0.560071	−	0.138045i	0.509181	+	0.860659i	$0.329948\pi$
$948$	83.6483	+	43.9020i	2.71677	+	1.42587i
$949$	4.91040	−	12.9477i	0.159398	−	0.420299i
$950$	−37.8009	−	19.8395i	−1.22642	−	0.643677i
$951$	−15.2763	+	22.1315i	−0.495366	+	0.717662i
$952$	10.3423	+	27.2703i	0.335194	+	0.883835i
$953$	−37.5970	−	33.3081i	−1.21789	−	1.07895i	−0.994555	−	0.104212i	$-0.966768\pi$
$953$	−37.5970	−	33.3081i	−1.21789	−	1.07895i	−0.223332	−	0.974742i	$-0.571693\pi$
$954$	14.6949	−	3.62198i	0.475766	−	0.117266i
$955$	−78.6681	+	19.3899i	−2.54564	+	0.627444i
$956$	35.3812	+	51.2585i	1.14431	+	1.65782i
$957$	0.925327	−	0.228072i	0.0299116	−	0.00737254i
$958$	9.58839	−	2.36332i	0.309787	−	0.0763556i
$959$	2.19897	+	5.79820i	0.0710084	+	0.187234i
$960$	−5.33942	+	14.0789i	−0.172329	+	0.454394i
$961$	−13.2311	−	19.1686i	−0.426810	−	0.618342i
$962$	−0.0425428	+	0.0376897i	−0.00137164	+	0.00121516i
$963$	−1.23259	+	1.78572i	−0.0397198	+	0.0575440i
$964$	56.3170	−	13.8809i	1.81385	−	0.447073i
$965$	−62.1360	−	15.3152i	−2.00023	−	0.493012i
$966$	−13.8260	+	12.2487i	−0.444843	+	0.394097i
$967$	−17.0593	+	4.20474i	−0.548590	+	0.135215i	−0.503862	−	0.863784i	$-0.668088\pi$
$967$	−17.0593	+	4.20474i	−0.548590	+	0.135215i	−0.0447276	+	0.998999i	$0.514242\pi$
$968$	65.3648			2.10090
$969$	−27.5494	−	14.4590i	−0.885014	−	0.464491i
$970$	−27.7608	−	24.5939i	−0.891346	−	0.789664i
$971$	−20.7338			−0.665378			−0.332689	−	0.943037i	$-0.607956\pi$
$971$	−20.7338			−0.665378			−0.332689	+	0.943037i	$0.607956\pi$
$972$	−34.6441	−	8.53900i	−1.11121	−	0.273889i
$973$	1.89049	+	4.98480i	0.0606062	+	0.159805i
$974$	74.6208			2.39101
$975$	−7.93971	+	7.03397i	−0.254274	+	0.225267i
$976$	−10.6149	+	15.3783i	−0.339775	+	0.492248i
$977$	41.7123			1.33449			0.667247	−	0.744836i	$-0.267472\pi$
$977$	41.7123			1.33449			0.667247	+	0.744836i	$0.267472\pi$
$978$	−66.8504	−	96.8495i	−2.13764	−	3.09690i
$979$	−0.878742	−	0.461199i	−0.0280847	−	0.0147400i
$980$	31.2199	+	82.3200i	0.997282	+	2.62962i
$981$	5.13541	+	2.69527i	0.163961	+	0.0860533i
$982$	−4.84847	+	12.7844i	−0.154721	+	0.407966i
$983$	23.6954	+	20.9923i	0.755765	+	0.669550i	0.950296	−	0.311347i	$-0.100780\pi$
$983$	23.6954	+	20.9923i	0.755765	+	0.669550i	−0.194531	+	0.980896i	$0.562318\pi$
$984$	−7.64936	+	20.1697i	−0.243853	+	0.642987i
$985$	−61.3779	−	32.2136i	−1.95566	−	1.02641i
$986$	21.6424	+	5.33437i	0.689235	+	0.169881i
$987$	12.7140	−	18.4195i	0.404692	−	0.586298i
$988$	12.1961	−	3.00607i	0.388009	−	0.0956357i
$989$	−20.6969	+	10.8626i	−0.658123	+	0.345409i
$990$	0.694813	−	1.83207i	0.0220826	−	0.0582271i
$991$	15.2863	+	22.1460i	0.485585	+	0.703492i	0.986820	−	0.161819i	$-0.0517362\pi$
$991$	15.2863	+	22.1460i	0.485585	+	0.703492i	−0.501235	+	0.865311i	$0.667121\pi$
$992$	−10.1142	+	5.30836i	−0.321128	+	0.168541i
$993$	0.294825	−	0.777388i	0.00935597	−	0.0246697i
$994$	−31.6176	+	16.5942i	−1.00285	+	0.526336i
$995$	−47.2823	+	68.5003i	−1.49895	+	2.17160i
$996$	−1.00769	−	8.29910i	−0.0319300	−	0.262967i
$997$	−18.1150	−	26.2442i	−0.573709	−	0.831161i	0.423494	−	0.905899i	$-0.360803\pi$
$997$	−18.1150	−	26.2442i	−0.573709	−	0.831161i	−0.997203	+	0.0747377i	$0.976188\pi$
$998$	−13.9577	+	20.2212i	−0.441822	+	0.640090i
$999$	−0.0750728	−	0.0665087i	−0.00237520	−	0.00210424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.f.a.46.4	✓	528
547.440	even	13	inner	547.2.f.a.440.4	yes	528

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.f.a.46.4	✓	528	1.1	even	1	trivial
547.2.f.a.440.4	yes	528	547.440	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.f (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.304286 + 2.50602i) q^{2} -1.95070 q^{3} +(-4.24565 - 1.04646i) q^{4} +(-1.15766 - 3.05250i) q^{5} +(0.593571 - 4.88850i) q^{6} +(0.109988 + 0.905836i) q^{7} +(2.12398 - 5.60049i) q^{8} +0.805247 q^{9} +O(q^{10})\)	\(q+(-0.304286 + 2.50602i) q^{2} -1.95070 q^{3} +(-4.24565 - 1.04646i) q^{4} +(-1.15766 - 3.05250i) q^{5} +(0.593571 - 4.88850i) q^{6} +(0.109988 + 0.905836i) q^{7} +(2.12398 - 5.60049i) q^{8} +0.805247 q^{9} +(8.00187 - 1.97228i) q^{10} +(0.167724 - 0.242990i) q^{11} +(8.28200 + 2.04133i) q^{12} -0.961079 q^{13} -2.30351 q^{14} +(2.25825 + 5.95452i) q^{15} +(5.64493 + 2.96269i) q^{16} +(3.03133 + 4.39165i) q^{17} +(-0.245025 + 2.01796i) q^{18} +(2.64658 - 1.38903i) q^{19} +(1.72070 + 14.1713i) q^{20} +(-0.214555 - 1.76702i) q^{21} +(0.557900 + 0.494256i) q^{22} +(-3.07691 + 2.72590i) q^{23} +(-4.14327 + 10.9249i) q^{24} +(-4.23501 + 3.75189i) q^{25} +(0.292442 - 2.40848i) q^{26} +4.28131 q^{27} +(0.480947 - 3.96096i) q^{28} +(-1.23855 - 1.09726i) q^{29} +(-15.6093 + 3.84734i) q^{30} +(2.45838 + 1.29026i) q^{31} +(-2.33712 + 3.38591i) q^{32} +(-0.327179 + 0.474001i) q^{33} +(-11.9279 + 6.26026i) q^{34} +(2.63773 - 1.38439i) q^{35} +(-3.41879 - 0.842657i) q^{36} +(-0.0175350 - 0.0155346i) q^{37} +(2.67562 + 7.05503i) q^{38} +1.87478 q^{39} -19.5543 q^{40} +1.84622 q^{41} +4.49346 q^{42} +(5.52096 + 1.36079i) q^{43} +(-0.966373 + 0.856132i) q^{44} +(-0.932201 - 2.45801i) q^{45} +(-5.89490 - 8.54024i) q^{46} +(9.41162 + 8.33797i) q^{47} +(-11.0116 - 5.77933i) q^{48} +(5.98815 - 1.47595i) q^{49} +(-8.11365 - 11.7546i) q^{50} +(-5.91324 - 8.56680i) q^{51} +(4.08040 + 1.00573i) q^{52} +(-2.64015 - 6.96150i) q^{53} +(-1.30274 + 10.7290i) q^{54} +(-0.935891 - 0.230677i) q^{55} +(5.30674 + 1.30799i) q^{56} +(-5.16269 + 2.70959i) q^{57} +(3.12661 - 2.76994i) q^{58} +(-10.5329 - 5.52809i) q^{59} +(-3.35658 - 27.6439i) q^{60} +(-0.353301 + 2.90970i) q^{61} +(-3.98146 + 5.76814i) q^{62} +(0.0885678 + 0.729421i) q^{63} +(1.76978 + 1.56789i) q^{64} +(1.11260 + 2.93369i) q^{65} +(-1.08830 - 0.964148i) q^{66} +(7.98562 + 1.96828i) q^{67} +(-8.27430 - 21.8175i) q^{68} +(6.00214 - 5.31743i) q^{69} +(2.66668 + 7.03145i) q^{70} +(13.7258 - 7.20387i) q^{71} +(1.71033 - 4.50977i) q^{72} +(-5.10925 + 13.4720i) q^{73} +(0.0442657 - 0.0392160i) q^{74} +(8.26125 - 7.31883i) q^{75} +(-12.6900 + 3.12780i) q^{76} +(0.238556 + 0.125204i) q^{77} +(-0.570469 + 4.69823i) q^{78} +(10.7533 + 2.65045i) q^{79} +(2.50869 - 20.6609i) q^{80} -10.7673 q^{81} +(-0.561777 + 4.62665i) q^{82} +(-0.347546 - 0.916402i) q^{83} +(-0.938186 + 7.72666i) q^{84} +(9.89623 - 14.3372i) q^{85} +(-5.09012 + 13.4216i) q^{86} +(2.41604 + 2.14042i) q^{87} +(-1.00462 - 1.45544i) q^{88} +(-0.405151 - 3.33672i) q^{89} +(6.44348 - 1.58817i) q^{90} +(-0.105708 - 0.870580i) q^{91} +(15.9160 - 8.35336i) q^{92} +(-4.79558 - 2.51691i) q^{93} +(-23.7589 + 21.0486i) q^{94} +(-7.30384 - 6.47064i) q^{95} +(4.55904 - 6.60490i) q^{96} +(-2.55643 - 3.70363i) q^{97} +(1.87664 + 15.4555i) q^{98} +(0.135059 - 0.195666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 528 q - 8 q^{2} - 46 q^{3} - 50 q^{4} - 9 q^{5} - 21 q^{6} - 3 q^{7} + 14 q^{8} + 466 q^{9}+O(q^{10}) \) 528 * q - 8 * q^2 - 46 * q^3 - 50 * q^4 - 9 * q^5 - 21 * q^6 - 3 * q^7 + 14 * q^8 + 466 * q^9	\( 528 q - 8 q^{2} - 46 q^{3} - 50 q^{4} - 9 q^{5} - 21 q^{6} - 3 q^{7} + 14 q^{8} + 466 q^{9} + 7 q^{10} - 16 q^{11} - 53 q^{12} - 12 q^{13} - 38 q^{15} - 38 q^{16} + 7 q^{17} - 23 q^{18} + 5 q^{19} + 45 q^{20} + 4 q^{21} + 43 q^{22} + 2 q^{23} - 51 q^{24} - 69 q^{25} - 4 q^{26} - 142 q^{27} - 2 q^{28} - 72 q^{29} - 50 q^{30} + 25 q^{31} + 66 q^{32} - 4 q^{34} + 33 q^{35} - 55 q^{36} + 21 q^{37} + 40 q^{38} - 142 q^{39} + 78 q^{40} - 140 q^{41} - 248 q^{42} + 23 q^{43} + 64 q^{44} - 163 q^{45} + 14 q^{46} + 37 q^{47} - 35 q^{48} + q^{49} + 70 q^{50} - 72 q^{51} - 74 q^{52} - 17 q^{53} - 76 q^{54} + 6 q^{55} - 38 q^{56} + 5 q^{57} + 29 q^{58} + 30 q^{59} - 108 q^{60} - 94 q^{61} - 75 q^{62} - 77 q^{63} - 252 q^{64} - 122 q^{65} + 79 q^{66} + 43 q^{67} - 193 q^{68} + 14 q^{69} - 267 q^{70} + 61 q^{71} + 49 q^{72} + 11 q^{73} + 85 q^{74} + 120 q^{75} - 23 q^{76} + 31 q^{77} - 90 q^{78} + 65 q^{79} + 58 q^{80} + 280 q^{81} + 10 q^{82} - 8 q^{83} - 136 q^{84} + 33 q^{85} + 91 q^{86} - 70 q^{87} - 198 q^{88} + 41 q^{89} - 68 q^{90} + 38 q^{91} + 43 q^{92} + 132 q^{93} + 8 q^{94} - 49 q^{95} + 262 q^{96} - 14 q^{97} + 41 q^{98} - 36 q^{99}+O(q^{100}) \) 528 * q - 8 * q^2 - 46 * q^3 - 50 * q^4 - 9 * q^5 - 21 * q^6 - 3 * q^7 + 14 * q^8 + 466 * q^9 + 7 * q^10 - 16 * q^11 - 53 * q^12 - 12 * q^13 - 38 * q^15 - 38 * q^16 + 7 * q^17 - 23 * q^18 + 5 * q^19 + 45 * q^20 + 4 * q^21 + 43 * q^22 + 2 * q^23 - 51 * q^24 - 69 * q^25 - 4 * q^26 - 142 * q^27 - 2 * q^28 - 72 * q^29 - 50 * q^30 + 25 * q^31 + 66 * q^32 - 4 * q^34 + 33 * q^35 - 55 * q^36 + 21 * q^37 + 40 * q^38 - 142 * q^39 + 78 * q^40 - 140 * q^41 - 248 * q^42 + 23 * q^43 + 64 * q^44 - 163 * q^45 + 14 * q^46 + 37 * q^47 - 35 * q^48 + q^49 + 70 * q^50 - 72 * q^51 - 74 * q^52 - 17 * q^53 - 76 * q^54 + 6 * q^55 - 38 * q^56 + 5 * q^57 + 29 * q^58 + 30 * q^59 - 108 * q^60 - 94 * q^61 - 75 * q^62 - 77 * q^63 - 252 * q^64 - 122 * q^65 + 79 * q^66 + 43 * q^67 - 193 * q^68 + 14 * q^69 - 267 * q^70 + 61 * q^71 + 49 * q^72 + 11 * q^73 + 85 * q^74 + 120 * q^75 - 23 * q^76 + 31 * q^77 - 90 * q^78 + 65 * q^79 + 58 * q^80 + 280 * q^81 + 10 * q^82 - 8 * q^83 - 136 * q^84 + 33 * q^85 + 91 * q^86 - 70 * q^87 - 198 * q^88 + 41 * q^89 - 68 * q^90 + 38 * q^91 + 43 * q^92 + 132 * q^93 + 8 * q^94 - 49 * q^95 + 262 * q^96 - 14 * q^97 + 41 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

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Database

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