LMFDB - Embedded newform 349.2.c.a.122.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [349,2,Mod(122,349)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(349, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("349.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	349.c (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:	$2.78677903054$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			122.17
Character	$\chi$	$=$	349.122
Dual form			349.2.c.a.226.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.404409 - 0.700458i) q^{2} +(-1.01083 - 1.75081i) q^{3} +(0.672906 + 1.16551i) q^{4} +(-1.32166 - 2.28919i) q^{5} -1.63515 q^{6} +(1.24448 - 2.15550i) q^{7} +2.70616 q^{8} +(-0.543548 + 0.941452i) q^{9} +O(q^{10})$	\(q+(0.404409 - 0.700458i) q^{2} +(-1.01083 - 1.75081i) q^{3} +(0.672906 + 1.16551i) q^{4} +(-1.32166 - 2.28919i) q^{5} -1.63515 q^{6} +(1.24448 - 2.15550i) q^{7} +2.70616 q^{8} +(-0.543548 + 0.941452i) q^{9} -2.13797 q^{10} -2.58351 q^{11} +(1.36039 - 2.35626i) q^{12} +(-1.10242 + 1.90944i) q^{13} +(-1.00656 - 1.74341i) q^{14} +(-2.67195 + 4.62796i) q^{15} +(-0.251418 + 0.435468i) q^{16} -2.51974 q^{17} +(0.439631 + 0.761464i) q^{18} +(-0.928848 - 1.60881i) q^{19} +(1.77871 - 3.08082i) q^{20} -5.03183 q^{21} +(-1.04479 + 1.80964i) q^{22} +(3.60008 - 6.23551i) q^{23} +(-2.73546 - 4.73795i) q^{24} +(-0.993594 + 1.72096i) q^{25} +(0.891656 + 1.54439i) q^{26} -3.86724 q^{27} +3.34967 q^{28} +(-0.786673 - 1.36256i) q^{29} +(2.16112 + 3.74318i) q^{30} -4.74333 q^{31} +(2.90951 + 5.03941i) q^{32} +(2.61148 + 4.52322i) q^{33} +(-1.01901 + 1.76497i) q^{34} -6.57914 q^{35} -1.46303 q^{36} +4.68437 q^{37} -1.50254 q^{38} +4.45742 q^{39} +(-3.57663 - 6.19490i) q^{40} +9.25080 q^{41} +(-2.03492 + 3.52458i) q^{42} +(4.73193 + 8.19593i) q^{43} +(-1.73846 - 3.01110i) q^{44} +2.87355 q^{45} +(-2.91181 - 5.04340i) q^{46} +7.00866 q^{47} +1.01656 q^{48} +(0.402535 + 0.697212i) q^{49} +(0.803638 + 1.39194i) q^{50} +(2.54702 + 4.41157i) q^{51} -2.96730 q^{52} -0.0428653 q^{53} +(-1.56395 + 2.70884i) q^{54} +(3.41453 + 5.91414i) q^{55} +(3.36776 - 5.83313i) q^{56} +(-1.87781 + 3.25247i) q^{57} -1.27255 q^{58} +(-3.08828 - 5.34906i) q^{59} -7.19189 q^{60} -1.94181 q^{61} +(-1.91825 + 3.32250i) q^{62} +(1.35287 + 2.34324i) q^{63} +3.70086 q^{64} +5.82811 q^{65} +4.22443 q^{66} +12.8885 q^{67} +(-1.69555 - 2.93677i) q^{68} -14.5562 q^{69} +(-2.66067 + 4.60841i) q^{70} +(6.71317 - 11.6276i) q^{71} +(-1.47092 + 2.54772i) q^{72} +(-0.561044 - 0.971757i) q^{73} +(1.89440 - 3.28120i) q^{74} +4.01741 q^{75} +(1.25006 - 2.16516i) q^{76} +(-3.21513 + 5.56876i) q^{77} +(1.80262 - 3.12223i) q^{78} +3.98143 q^{79} +1.32916 q^{80} +(5.53975 + 9.59514i) q^{81} +(3.74111 - 6.47980i) q^{82} +(4.03355 - 6.98632i) q^{83} +(-3.38595 - 5.86463i) q^{84} +(3.33025 + 5.76816i) q^{85} +7.65454 q^{86} +(-1.59038 + 2.75462i) q^{87} -6.99137 q^{88} +(-5.34474 - 9.25736i) q^{89} +(1.16209 - 2.01280i) q^{90} +(2.74388 + 4.75253i) q^{91} +9.69005 q^{92} +(4.79469 + 8.30465i) q^{93} +(2.83437 - 4.90927i) q^{94} +(-2.45525 + 4.25262i) q^{95} +(5.88202 - 10.1880i) q^{96} +(-5.02128 + 8.69711i) q^{97} +0.651156 q^{98} +(1.40426 - 2.43225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/349\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.404409	−	0.700458i	0.285961	−	0.495298i	−0.686881	−	0.726770i	$-0.741021\pi$
$2$	0.404409	−	0.700458i	0.285961	−	0.495298i	0.972842	+	0.231472i	$0.0743540\pi$
$3$	−1.01083	−	1.75081i	−0.583602	−	1.01083i	−0.995048	−	0.0993942i	$-0.968310\pi$
$3$	−1.01083	−	1.75081i	−0.583602	−	1.01083i	0.411446	−	0.911434i	$-0.365024\pi$
$4$	0.672906	+	1.16551i	0.336453	+	0.582754i
$5$	−1.32166	−	2.28919i	−0.591066	−	1.02376i	−0.994089	−	0.108567i	$-0.965374\pi$
$5$	−1.32166	−	2.28919i	−0.591066	−	1.02376i	0.403023	−	0.915190i	$-0.367960\pi$
$6$	−1.63515			−0.667549
$7$	1.24448	−	2.15550i	0.470369	−	0.814704i	−0.529056	−	0.848587i	$-0.677454\pi$
$7$	1.24448	−	2.15550i	0.470369	−	0.814704i	0.999426	+	0.0338828i	$0.0107873\pi$
$8$	2.70616			0.956770
$9$	−0.543548	+	0.941452i	−0.181183	+	0.313817i
$10$	−2.13797			−0.676087
$11$	−2.58351			−0.778957			−0.389478	−	0.921036i	$-0.627345\pi$
$11$	−2.58351			−0.778957			−0.389478	+	0.921036i	$0.627345\pi$
$12$	1.36039	−	2.35626i	0.392709	−	0.680193i
$13$	−1.10242	+	1.90944i	−0.305756	+	0.529585i	−0.977429	−	0.211263i	$-0.932242\pi$
$13$	−1.10242	+	1.90944i	−0.305756	+	0.529585i	0.671674	+	0.740847i	$0.265576\pi$
$14$	−1.00656	−	1.74341i	−0.269014	−	0.465946i
$15$	−2.67195	+	4.62796i	−0.689895	+	1.19493i
$16$	−0.251418	+	0.435468i	−0.0628544	+	0.108867i
$17$	−2.51974			−0.611126			−0.305563	−	0.952172i	$-0.598845\pi$
$17$	−2.51974			−0.611126			−0.305563	+	0.952172i	$0.598845\pi$
$18$	0.439631	+	0.761464i	0.103622	+	0.179479i
$19$	−0.928848	−	1.60881i	−0.213092	−	0.369087i	0.739588	−	0.673059i	$-0.235020\pi$
$19$	−0.928848	−	1.60881i	−0.213092	−	0.369087i	−0.952681	+	0.303973i	$0.901687\pi$
$20$	1.77871	−	3.08082i	0.397732	−	0.688892i
$21$	−5.03183			−1.09803
$22$	−1.04479	+	1.80964i	−0.222751	+	0.385816i
$23$	3.60008	−	6.23551i	0.750668	−	1.30019i	−0.196832	−	0.980437i	$-0.563065\pi$
$23$	3.60008	−	6.23551i	0.750668	−	1.30019i	0.947499	−	0.319757i	$-0.103601\pi$
$24$	−2.73546	−	4.73795i	−0.558373	−	0.967131i
$25$	−0.993594	+	1.72096i	−0.198719	+	0.344191i
$26$	0.891656	+	1.54439i	0.174868	+	0.302881i
$27$	−3.86724			−0.744250
$28$	3.34967			0.633029
$29$	−0.786673	−	1.36256i	−0.146081	−	0.253021i	0.783694	−	0.621147i	$-0.213333\pi$
$29$	−0.786673	−	1.36256i	−0.146081	−	0.253021i	−0.929776	+	0.368126i	$0.880000\pi$
$30$	2.16112	+	3.74318i	0.394566	+	0.683408i
$31$	−4.74333			−0.851927			−0.425963	−	0.904740i	$-0.640065\pi$
$31$	−4.74333			−0.851927			−0.425963	+	0.904740i	$0.640065\pi$
$32$	2.90951	+	5.03941i	0.514333	+	0.890851i
$33$	2.61148	+	4.52322i	0.454601	+	0.787392i
$34$	−1.01901	+	1.76497i	−0.174758	+	0.302690i
$35$	−6.57914			−1.11208
$36$	−1.46303			−0.243838
$37$	4.68437			0.770105			0.385053	−	0.922895i	$-0.374183\pi$
$37$	4.68437			0.770105			0.385053	+	0.922895i	$0.374183\pi$
$38$	−1.50254			−0.243744
$39$	4.45742			0.713759
$40$	−3.57663	−	6.19490i	−0.565515	−	0.979500i
$41$	9.25080			1.44473			0.722366	−	0.691511i	$-0.243054\pi$
$41$	9.25080			1.44473			0.722366	+	0.691511i	$0.243054\pi$
$42$	−2.03492	+	3.52458i	−0.313995	+	0.543854i
$43$	4.73193	+	8.19593i	0.721612	+	1.24987i	0.960353	+	0.278785i	$0.0899318\pi$
$43$	4.73193	+	8.19593i	0.721612	+	1.24987i	−0.238742	+	0.971083i	$0.576735\pi$
$44$	−1.73846	−	3.01110i	−0.262082	−	0.453940i
$45$	2.87355			0.428364
$46$	−2.91181	−	5.04340i	−0.429323	−	0.743609i
$47$	7.00866			1.02232			0.511159	−	0.859486i	$-0.329216\pi$
$47$	7.00866			1.02232			0.511159	+	0.859486i	$0.329216\pi$
$48$	1.01656			0.146728
$49$	0.402535	+	0.697212i	0.0575051	+	0.0996017i
$50$	0.803638	+	1.39194i	0.113652	+	0.196850i
$51$	2.54702	+	4.41157i	0.356654	+	0.617743i
$52$	−2.96730			−0.411490
$53$	−0.0428653			−0.00588800			−0.00294400	−	0.999996i	$-0.500937\pi$
$53$	−0.0428653			−0.00588800			−0.00294400	+	0.999996i	$0.500937\pi$
$54$	−1.56395	+	2.70884i	−0.212826	+	0.368626i
$55$	3.41453	+	5.91414i	0.460415	+	0.797463i
$56$	3.36776	−	5.83313i	0.450036	−	0.779485i
$57$	−1.87781	+	3.25247i	−0.248722	+	0.430800i
$58$	−1.27255			−0.167094
$59$	−3.08828	−	5.34906i	−0.402060	−	0.696389i	0.591914	−	0.806001i	$-0.298372\pi$
$59$	−3.08828	−	5.34906i	−0.402060	−	0.696389i	−0.993974	+	0.109612i	$0.965039\pi$
$60$	−7.19189			−0.928469
$61$	−1.94181			−0.248623			−0.124312	−	0.992243i	$-0.539672\pi$
$61$	−1.94181			−0.248623			−0.124312	+	0.992243i	$0.539672\pi$
$62$	−1.91825	+	3.32250i	−0.243618	+	0.421958i
$63$	1.35287	+	2.34324i	0.170445	+	0.295220i
$64$	3.70086			0.462607
$65$	5.82811			0.722888
$66$	4.22443			0.519992
$67$	12.8885			1.57458			0.787289	−	0.616584i	$-0.211484\pi$
$67$	12.8885			1.57458			0.787289	+	0.616584i	$0.211484\pi$
$68$	−1.69555	−	2.93677i	−0.205615	−	0.356136i
$69$	−14.5562			−1.75236
$70$	−2.66067	+	4.60841i	−0.318011	+	0.550810i
$71$	6.71317	−	11.6276i	0.796707	−	1.37994i	−0.125043	−	0.992151i	$-0.539907\pi$
$71$	6.71317	−	11.6276i	0.796707	−	1.37994i	0.921750	−	0.387786i	$-0.126760\pi$
$72$	−1.47092	+	2.54772i	−0.173350	+	0.300251i
$73$	−0.561044	−	0.971757i	−0.0656652	−	0.113736i	0.831324	−	0.555789i	$-0.187584\pi$
$73$	−0.561044	−	0.971757i	−0.0656652	−	0.113736i	−0.896989	+	0.442053i	$0.854250\pi$
$74$	1.89440	−	3.28120i	0.220220	−	0.381432i
$75$	4.01741			0.463891
$76$	1.25006	−	2.16516i	0.143391	−	0.248361i
$77$	−3.21513	+	5.56876i	−0.366398	+	0.634619i
$78$	1.80262	−	3.12223i	0.204107	−	0.353523i
$79$	3.98143			0.447946			0.223973	−	0.974595i	$-0.428097\pi$
$79$	3.98143			0.447946			0.223973	+	0.974595i	$0.428097\pi$
$80$	1.32916			0.148605
$81$	5.53975	+	9.59514i	0.615528	+	1.06613i
$82$	3.74111	−	6.47980i	0.413137	−	0.715574i
$83$	4.03355	−	6.98632i	0.442740	−	0.766848i	−0.555152	−	0.831749i	$-0.687340\pi$
$83$	4.03355	−	6.98632i	0.442740	−	0.766848i	0.997892	+	0.0649008i	$0.0206731\pi$
$84$	−3.38595	−	5.86463i	−0.369437	−	0.639884i
$85$	3.33025	+	5.76816i	0.361216	+	0.625645i
$86$	7.65454			0.825410
$87$	−1.59038	+	2.75462i	−0.170507	+	0.295327i
$88$	−6.99137			−0.745283
$89$	−5.34474	−	9.25736i	−0.566541	−	0.981279i	−0.996904	−	0.0786227i	$-0.974948\pi$
$89$	−5.34474	−	9.25736i	−0.566541	−	0.981279i	0.430363	−	0.902656i	$-0.358386\pi$
$90$	1.16209	−	2.01280i	0.122495	−	0.212168i
$91$	2.74388	+	4.75253i	0.287636	+	0.498201i
$92$	9.69005			1.01026
$93$	4.79469	+	8.30465i	0.497186	+	0.861152i
$94$	2.83437	−	4.90927i	0.292343	−	0.506353i
$95$	−2.45525	+	4.25262i	−0.251903	+	0.436310i
$96$	5.88202	−	10.1880i	0.600332	−	1.03980i
$97$	−5.02128	+	8.69711i	−0.509834	+	0.883058i	0.490101	+	0.871666i	$0.336960\pi$
$97$	−5.02128	+	8.69711i	−0.509834	+	0.883058i	−0.999935	+	0.0113926i	$0.996374\pi$
$98$	0.651156			0.0657767
$99$	1.40426	−	2.43225i	0.141133	−	0.244450i
$100$	−2.67438			−0.267438
$101$	−3.05322			−0.303807			−0.151903	−	0.988395i	$-0.548540\pi$
$101$	−3.05322			−0.303807			−0.151903	+	0.988395i	$0.548540\pi$
$102$	4.12016			0.407956
$103$	8.94343			0.881223			0.440611	−	0.897698i	$-0.354762\pi$
$103$	8.94343			0.881223			0.440611	+	0.897698i	$0.354762\pi$
$104$	−2.98331	+	5.16725i	−0.292538	+	0.506691i
$105$	6.65038	+	11.5188i	0.649011	+	1.12412i
$106$	−0.0173351	+	0.0300253i	−0.00168374	+	0.00291632i
$107$	−5.15382	+	8.92668i	−0.498239	+	0.862975i	−0.999998	−	0.00203231i	$-0.999353\pi$
$107$	−5.15382	+	8.92668i	−0.498239	+	0.862975i	0.501759	+	0.865007i	$0.332686\pi$
$108$	−2.60229	−	4.50729i	−0.250405	−	0.433715i
$109$	4.72571	+	8.18517i	0.452641	+	0.783997i	0.998549	−	0.0538480i	$-0.0171486\pi$
$109$	4.72571	+	8.18517i	0.452641	+	0.783997i	−0.545908	+	0.837845i	$0.683815\pi$
$110$	5.52347			0.526642
$111$	−4.73509	−	8.20142i	−0.449435	−	0.778444i
$112$	0.625769	+	1.08386i	0.0591296	+	0.102415i
$113$	−2.05120	+	3.55277i	−0.192960	+	0.334217i	−0.946230	−	0.323495i	$-0.895142\pi$
$113$	−2.05120	+	3.55277i	−0.192960	+	0.334217i	0.753270	+	0.657712i	$0.228476\pi$
$114$	1.51881	+	2.63066i	0.142250	+	0.246383i
$115$	−19.0324			−1.77478
$116$	1.05871	−	1.83375i	0.0982991	−	0.170259i
$117$	−1.19843	−	2.07575i	−0.110795	−	0.191903i
$118$	−4.99572			−0.459894
$119$	−3.13576	+	5.43130i	−0.287455	+	0.497887i
$120$	−7.23072	+	12.5240i	−0.660071	+	1.14328i
$121$	−4.32549			−0.393226
$122$	−0.785286	+	1.36016i	−0.0710965	+	0.123143i
$123$	−9.35097	−	16.1964i	−0.843149	−	1.46038i
$124$	−3.19181	−	5.52839i	−0.286633	−	0.496464i
$125$	−7.96385			−0.712309
$126$	2.18845			0.194963
$127$	−6.78974			−0.602492			−0.301246	−	0.953547i	$-0.597402\pi$
$127$	−6.78974			−0.602492			−0.301246	+	0.953547i	$0.597402\pi$
$128$	−4.32235	+	7.48653i	−0.382046	+	0.661722i
$129$	9.56633	−	16.5694i	0.842268	−	1.45885i
$130$	2.35694	−	4.08234i	0.206717	−	0.358045i
$131$	13.8401			1.20922			0.604608	−	0.796523i	$-0.293330\pi$
$131$	13.8401			1.20922			0.604608	+	0.796523i	$0.293330\pi$
$132$	−3.51457	+	6.08741i	−0.305904	+	0.529841i
$133$	−4.62373			−0.400929
$134$	5.21222	−	9.02783i	0.450267	−	0.779886i
$135$	5.11119	+	8.85284i	0.439901	+	0.761931i
$136$	−6.81880			−0.584707
$137$	−1.71204	−	2.96533i	−0.146269	−	0.253346i	0.783577	−	0.621295i	$-0.213393\pi$
$137$	−1.71204	−	2.96533i	−0.146269	−	0.253346i	−0.929846	+	0.367950i	$0.880060\pi$
$138$	−5.88668	+	10.1960i	−0.501107	+	0.867943i
$139$	−13.9495			−1.18318			−0.591591	−	0.806238i	$-0.701500\pi$
$139$	−13.9495			−1.18318			−0.591591	+	0.806238i	$0.701500\pi$
$140$	−4.42715	−	7.66804i	−0.374162	−	0.648068i
$141$	−7.08455	−	12.2708i	−0.596627	−	1.03339i
$142$	−5.42974	−	9.40458i	−0.455654	−	0.789215i
$143$	2.84811	−	4.93306i	0.238171	−	0.412524i
$144$	−0.273315	−	0.473395i	−0.0227762	−	0.0394496i
$145$	−2.07944	+	3.60169i	−0.172688	+	0.299104i
$146$	−0.907566			−0.0751107
$147$	0.813788	−	1.40952i	0.0671201	−	0.116255i
$148$	3.15214	+	5.45967i	0.259104	+	0.448782i
$149$	−11.6660	+	20.2062i	−0.955720	+	1.65536i	−0.223007	+	0.974817i	$0.571587\pi$
$149$	−11.6660	+	20.2062i	−0.955720	+	1.65536i	−0.732713	+	0.680538i	$0.761746\pi$
$150$	1.62468	−	2.81403i	0.132654	−	0.229764i
$151$	−7.14132	−	12.3691i	−0.581152	−	1.00659i	−0.995343	−	0.0963953i	$-0.969269\pi$
$151$	−7.14132	−	12.3691i	−0.581152	−	1.00659i	0.414191	−	0.910190i	$-0.364065\pi$
$152$	−2.51361	−	4.35370i	−0.203881	−	0.353131i
$153$	1.36960	−	2.37221i	0.110725	−	0.191782i
$154$	2.60045	+	4.50412i	0.209551	+	0.362952i
$155$	6.26909	+	10.8584i	0.503545	+	0.872166i
$156$	2.99943	+	5.19516i	0.240146	+	0.415946i
$157$	2.83243	+	4.90591i	0.226052	+	0.391534i	0.956635	−	0.291290i	$-0.0940846\pi$
$157$	2.83243	+	4.90591i	0.226052	+	0.391534i	−0.730582	+	0.682825i	$0.760751\pi$
$158$	1.61013	−	2.78882i	0.128095	−	0.221867i
$159$	0.0433294	+	0.0750488i	0.00343625	+	0.00595176i
$160$	7.69078	−	13.3208i	0.608010	−	1.05310i
$161$	−8.96045	−	15.5200i	−0.706182	−	1.22314i
$162$	8.96131			0.704067
$163$	1.66669			0.130545			0.0652725	−	0.997867i	$-0.479208\pi$
$163$	1.66669			0.130545			0.0652725	+	0.997867i	$0.479208\pi$
$164$	6.22492	+	10.7819i	0.486085	+	0.841924i
$165$	6.90301	−	11.9564i	0.537398	−	0.930801i
$166$	−3.26241	−	5.65067i	−0.253212	−	0.438577i
$167$	23.5274			1.82060			0.910302	−	0.413945i	$-0.135849\pi$
$167$	23.5274			1.82060			0.910302	+	0.413945i	$0.135849\pi$
$168$	−13.6169			−1.05057
$169$	4.06935	+	7.04832i	0.313027	+	0.542178i
$170$	5.38713			0.413174
$171$	2.01949			0.154434
$172$	−6.36828	+	11.0302i	−0.485577	+	0.841044i
$173$	−6.76809	+	11.7227i	−0.514568	+	0.891258i	0.485289	+	0.874354i	$0.338714\pi$
$173$	−6.76809	+	11.7227i	−0.514568	+	0.891258i	−0.999857	+	0.0169045i	$0.994619\pi$
$174$	1.28633	+	2.22799i	0.0975165	+	0.168904i
$175$	2.47302	+	4.28339i	0.186943	+	0.323794i
$176$	0.649540	−	1.12504i	0.0489609	−	0.0848027i
$177$	−6.24345	+	10.8140i	−0.469286	+	0.812828i
$178$	−8.64585			−0.648034
$179$	−8.72083			−0.651825			−0.325913	−	0.945400i	$-0.605672\pi$
$179$	−8.72083			−0.651825			−0.325913	+	0.945400i	$0.605672\pi$
$180$	1.93363	+	3.34914i	0.144124	+	0.249630i
$181$	17.9602			1.33497			0.667487	−	0.744622i	$-0.267370\pi$
$181$	17.9602			1.33497			0.667487	+	0.744622i	$0.267370\pi$
$182$	4.43860			0.329011
$183$	1.96284	+	3.39973i	0.145097	+	0.251316i
$184$	9.74236	−	16.8743i	0.718217	−	1.24399i
$185$	−6.19116	−	10.7234i	−0.455183	−	0.788401i
$186$	7.75607			0.568703
$187$	6.50976			0.476041
$188$	4.71617	+	8.16865i	0.343962	+	0.595760i
$189$	−4.81270	+	8.33584i	−0.350073	+	0.606343i
$190$	1.98585	+	3.43960i	0.144069	+	0.249535i
$191$	−7.65028	+	13.2507i	−0.553555	+	0.958785i	0.444460	+	0.895799i	$0.353396\pi$
$191$	−7.65028	+	13.2507i	−0.553555	+	0.958785i	−0.998014	+	0.0629858i	$0.979938\pi$
$192$	−3.74093	−	6.47948i	−0.269978	−	0.467616i
$193$	1.81672	+	3.14665i	0.130770	+	0.226501i	0.923974	−	0.382456i	$-0.124922\pi$
$193$	1.81672	+	3.14665i	0.130770	+	0.226501i	−0.793203	+	0.608957i	$0.791588\pi$
$194$	4.06131	+	7.03439i	0.291585	+	0.505040i
$195$	−5.89122	−	10.2039i	−0.421879	−	0.730715i
$196$	−0.541737	+	0.938316i	−0.0386955	+	0.0670226i
$197$	−8.54736	−	14.8045i	−0.608974	−	1.05477i	−0.991410	−	0.130792i	$-0.958248\pi$
$197$	−8.54736	−	14.8045i	−0.608974	−	1.05477i	0.382436	−	0.923982i	$-0.375085\pi$
$198$	−1.13579	−	1.96725i	−0.0807172	−	0.139806i
$199$	12.5564	−	21.7484i	0.890102	−	1.54170i	0.0503491	−	0.998732i	$-0.483967\pi$
$199$	12.5564	−	21.7484i	0.890102	−	1.54170i	0.839752	−	0.542969i	$-0.182700\pi$
$200$	−2.68882	+	4.65717i	−0.190128	+	0.329312i
$201$	−13.0280	−	22.5652i	−0.918927	−	1.59163i
$202$	−1.23475	+	2.13865i	−0.0868768	+	0.150475i
$203$	−3.91600			−0.274849
$204$	−3.42781	+	5.93715i	−0.239995	+	0.415683i
$205$	−12.2265	−	21.1768i	−0.853933	−	1.47906i
$206$	3.61681	−	6.26449i	0.251995	−	0.436468i
$207$	3.91362	+	6.77860i	0.272016	+	0.471145i
$208$	−0.554335	−	0.960136i	−0.0384362	−	0.0665735i
$209$	2.39969	+	4.15638i	0.165990	+	0.287503i
$210$	10.7579			0.742366
$211$	9.96707	−	17.2635i	0.686162	−	1.18847i	−0.286909	−	0.957958i	$-0.592628\pi$
$211$	9.96707	−	17.2635i	0.686162	−	1.18847i	0.973070	−	0.230509i	$-0.0740391\pi$
$212$	−0.0288443	−	0.0499598i	−0.00198104	−	0.00343125i
$213$	−27.1435			−1.85984
$214$	4.16851	+	7.22007i	0.284953	+	0.493554i
$215$	12.5080	−	21.6646i	0.853041	−	1.47751i
$216$	−10.4653			−0.712076
$217$	−5.90298	+	10.2243i	−0.400720	+	0.694068i
$218$	7.64448			0.517750
$219$	−1.13424	+	1.96456i	−0.0766447	+	0.132753i
$220$	−4.59532	+	7.95932i	−0.309816	+	0.536617i
$221$	2.77780	−	4.81130i	0.186855	−	0.323643i
$222$	−7.65966			−0.514083
$223$	−15.6856			−1.05039			−0.525193	−	0.850983i	$-0.676007\pi$
$223$	−15.6856			−1.05039			−0.525193	+	0.850983i	$0.676007\pi$
$224$	14.4833			0.967706
$225$	−1.08013	−	1.87084i	−0.0720088	−	0.124723i
$226$	1.65905	+	2.87355i	0.110358	+	0.191146i
$227$	−0.284168	+	0.492193i	−0.0188609	+	0.0326680i	−0.875302	−	0.483577i	$-0.839337\pi$
$227$	−0.284168	+	0.492193i	−0.0188609	+	0.0326680i	0.856441	+	0.516245i	$0.172671\pi$
$228$	−5.05436			−0.334733
$229$	−4.89216	+	8.47346i	−0.323283	+	0.559942i	−0.981163	−	0.193180i	$-0.938120\pi$
$229$	−4.89216	+	8.47346i	−0.323283	+	0.559942i	0.657881	+	0.753122i	$0.271453\pi$
$230$	−7.69687	+	13.3314i	−0.507516	+	0.879044i
$231$	12.9998			0.855321
$232$	−2.12886	−	3.68729i	−0.139766	−	0.242083i
$233$	−6.48664	+	11.2352i	−0.424954	+	0.736042i	−0.996416	−	0.0845866i	$-0.973043\pi$
$233$	−6.48664	+	11.2352i	−0.424954	+	0.736042i	0.571462	+	0.820628i	$0.306376\pi$
$234$	−1.93863			−0.126732
$235$	−9.26310	−	16.0442i	−0.604258	−	1.04661i
$236$	4.15625	−	7.19884i	0.270549	−	0.468604i
$237$	−4.02454	−	6.97071i	−0.261422	−	0.452796i
$238$	2.53626	+	4.39294i	0.164402	+	0.284752i
$239$	−0.0388530			−0.00251319			−0.00125659	−	0.999999i	$-0.500400\pi$
$239$	−0.0388530			−0.00251319			−0.00125659	+	0.999999i	$0.500400\pi$
$240$	−1.34355	−	2.32710i	−0.0867259	−	0.150214i
$241$	4.51738	+	7.82433i	0.290990	+	0.504010i	0.974044	−	0.226358i	$-0.0726820\pi$
$241$	4.51738	+	7.82433i	0.290990	+	0.504010i	−0.683054	+	0.730368i	$0.739349\pi$
$242$	−1.74927	+	3.02982i	−0.112447	+	0.194764i
$243$	5.39863	−	9.35069i	0.346322	−	0.599847i
$244$	−1.30666	−	2.26320i	−0.0836501	−	0.144886i
$245$	1.06403	−	1.84296i	0.0679786	−	0.117742i
$246$	−15.1265			−0.964429
$247$	4.09592			0.260617
$248$	−12.8362			−0.815099
$249$	−16.3089			−1.03354
$250$	−3.22066	+	5.57834i	−0.203692	+	0.352805i
$251$	2.91511			0.184000			0.0920000	−	0.995759i	$-0.470674\pi$
$251$	2.91511			0.184000			0.0920000	+	0.995759i	$0.470674\pi$
$252$	−1.82071	+	3.15356i	−0.114694	+	0.198655i
$253$	−9.30082	+	16.1095i	−0.584738	+	1.01280i
$254$	−2.74583	+	4.75592i	−0.172289	+	0.298413i
$255$	6.73262	−	11.6612i	0.421613	−	0.730255i
$256$	7.19686	+	12.4653i	0.449804	+	0.779083i
$257$	11.3215			0.706213			0.353106	−	0.935583i	$-0.385125\pi$
$257$	11.3215			0.706213			0.353106	+	0.935583i	$0.385125\pi$
$258$	−7.73742	−	13.4016i	−0.481711	−	0.834348i
$259$	5.82960	−	10.0972i	0.362234	−	0.627408i
$260$	3.92177	+	6.79270i	0.243218	+	0.421266i
$261$	1.71038			0.105870
$262$	5.59707	−	9.69441i	0.345788	−	0.598923i
$263$	24.2003			1.49225			0.746126	−	0.665805i	$-0.231912\pi$
$263$	24.2003			1.49225			0.746126	+	0.665805i	$0.231912\pi$
$264$	7.06708	+	12.2405i	0.434949	+	0.753353i
$265$	0.0566535	+	0.0981268i	0.00348020	+	0.00602788i
$266$	−1.86988	+	3.23873i	−0.114650	+	0.198579i
$267$	−10.8052	+	18.7152i	−0.661269	+	1.14535i
$268$	8.67273	+	15.0216i	0.529771	+	0.917591i
$269$	−17.9324			−1.09336			−0.546679	−	0.837342i	$-0.684108\pi$
$269$	−17.9324			−1.09336			−0.546679	+	0.837342i	$0.684108\pi$
$270$	8.26805			0.503178
$271$	−3.12529	+	5.41317i	−0.189848	+	0.328826i	−0.945199	−	0.326494i	$-0.894133\pi$
$271$	−3.12529	+	5.41317i	−0.189848	+	0.328826i	0.755351	+	0.655320i	$0.227466\pi$
$272$	0.633506	−	1.09727i	0.0384120	−	0.0665315i
$273$	5.54717	−	9.60799i	0.335730	−	0.581502i
$274$	−2.76945			−0.167309
$275$	2.56696	−	4.44610i	0.154793	−	0.268110i
$276$	−9.79498	−	16.9654i	−0.589588	−	1.02120i
$277$	−3.22340	+	5.58309i	−0.193675	+	0.335456i	−0.946465	−	0.322805i	$-0.895374\pi$
$277$	−3.22340	+	5.58309i	−0.193675	+	0.335456i	0.752790	+	0.658261i	$0.228708\pi$
$278$	−5.64132	+	9.77105i	−0.338344	+	0.586028i
$279$	2.57822	−	4.46562i	0.154354	−	0.267349i
$280$	−17.8042			−1.06400
$281$	11.3271	+	19.6191i	0.675719	+	1.17038i	0.976258	+	0.216610i	$0.0695002\pi$
$281$	11.3271	+	19.6191i	0.675719	+	1.17038i	−0.300539	+	0.953770i	$0.597167\pi$
$282$	−11.4602			−0.682447
$283$	−31.9453			−1.89895			−0.949477	−	0.313837i	$-0.898386\pi$
$283$	−31.9453			−1.89895			−0.949477	+	0.313837i	$0.898386\pi$
$284$	18.0693			1.07222
$285$	9.92735			0.588045
$286$	−2.30360	−	3.98995i	−0.136215	−	0.235931i
$287$	11.5124	−	19.9401i	0.679558	−	1.17703i
$288$	−6.32582			−0.372753
$289$	−10.6509			−0.626525
$290$	1.68189	+	2.91311i	0.0987638	+	0.171064i
$291$	20.3026			1.19016
$292$	0.755060	−	1.30780i	0.0441865	−	0.0765333i
$293$	−8.31171	+	14.3963i	−0.485575	+	0.841041i	−0.999863	−	0.0165770i	$-0.994723\pi$
$293$	−8.31171	+	14.3963i	−0.485575	+	0.841041i	0.514287	+	0.857618i	$0.328056\pi$
$294$	−0.658207	−	1.14005i	−0.0383874	−	0.0664890i
$295$	−8.16335	+	14.1393i	−0.475289	+	0.823224i
$296$	12.6766			0.736814
$297$	9.99104			0.579739
$298$	9.43572	+	16.3431i	0.546596	+	0.946733i
$299$	7.93758	+	13.7483i	0.459042	+	0.795084i
$300$	2.70334	+	4.68232i	0.156077	+	0.270334i
$301$	23.5552			1.35770
$302$	−11.5521			−0.664747
$303$	3.08628	+	5.34560i	0.177302	+	0.307097i
$304$	0.934115			0.0535752
$305$	2.56642	+	4.44517i	0.146953	+	0.254530i
$306$	−1.10776	−	1.91869i	−0.0633262	−	0.109684i
$307$	−4.18425	+	7.24732i	−0.238807	+	0.413627i	−0.960372	−	0.278720i	$-0.910090\pi$
$307$	−4.18425	+	7.24732i	−0.238807	+	0.413627i	0.721565	+	0.692347i	$0.243423\pi$
$308$	−8.65391			−0.493102
$309$	−9.04027	−	15.6582i	−0.514283	−	0.890765i
$310$	10.1411			0.575977
$311$	17.6845			1.00279			0.501397	−	0.865218i	$-0.332820\pi$
$311$	17.6845			1.00279			0.501397	+	0.865218i	$0.332820\pi$
$312$	12.0625			0.682903
$313$	−11.0397			−0.624003			−0.312002	−	0.950082i	$-0.600999\pi$
$313$	−11.0397			−0.624003			−0.312002	+	0.950082i	$0.600999\pi$
$314$	4.58184			0.258568
$315$	3.57608	−	6.19395i	0.201489	−	0.348989i
$316$	2.67913	+	4.64038i	0.150713	+	0.261042i
$317$	−7.41371	−	12.8409i	−0.416396	−	0.721218i	0.579178	−	0.815201i	$-0.303374\pi$
$317$	−7.41371	−	12.8409i	−0.416396	−	0.721218i	−0.995574	+	0.0939827i	$0.970040\pi$
$318$	0.0700913			0.00393053
$319$	2.03238	+	3.52018i	0.113791	+	0.197092i
$320$	−4.89129	−	8.47196i	−0.273431	−	0.473597i
$321$	20.8385			1.16309
$322$	−14.4948			−0.807761
$323$	2.34045	+	4.05378i	0.130226	+	0.225559i
$324$	−7.45547	+	12.9133i	−0.414193	+	0.717403i
$325$	−2.19071	−	3.79443i	−0.121519	−	0.210477i
$326$	0.674024	−	1.16744i	0.0373307	−	0.0646587i
$327$	9.55376	−	16.5476i	0.528324	−	0.915084i
$328$	25.0341			1.38228
$329$	8.72214	−	15.1072i	0.480867	−	0.832887i
$330$	−5.58328	−	9.67053i	−0.307350	−	0.532345i
$331$	6.81088	+	11.7968i	0.374360	+	0.648411i	0.990231	−	0.139436i	$-0.0445291\pi$
$331$	6.81088	+	11.7968i	0.374360	+	0.648411i	−0.615871	+	0.787847i	$0.711196\pi$
$332$	10.8568			0.595845
$333$	−2.54618	+	4.41011i	−0.139530	+	0.241672i
$334$	9.51470	−	16.4799i	0.520621	−	0.901742i
$335$	−17.0342	−	29.5042i	−0.930680	−	1.61198i
$336$	1.26509	−	2.19120i	0.0690163	−	0.119540i
$337$	2.89549	−	5.01513i	0.157727	−	0.273192i	−0.776322	−	0.630337i	$-0.782917\pi$
$337$	2.89549	−	5.01513i	0.157727	−	0.273192i	0.934049	+	0.357146i	$0.116250\pi$
$338$	6.58273			0.358053
$339$	8.29363			0.450448
$340$	−4.48189	+	7.76286i	−0.243064	+	0.421000i
$341$	12.2544			0.663614
$342$	0.816702	−	1.41457i	0.0441622	−	0.0764911i
$343$	19.4265			1.04893
$344$	12.8053	+	22.1795i	0.690417	+	1.19584i
$345$	19.2385	+	33.3220i	1.03576	+	1.79400i
$346$	5.47416	+	9.48152i	0.294292	+	0.509730i
$347$	6.82257	−	11.8170i	0.366255	−	0.634372i	−0.622722	−	0.782443i	$-0.713973\pi$
$347$	6.82257	−	11.8170i	0.366255	−	0.634372i	0.988977	+	0.148071i	$0.0473065\pi$
$348$	−4.28071			−0.229470
$349$	15.2946	−	10.7273i	0.818703	−	0.574217i
$349$	15.2946	−	10.7273i	0.818703	−	0.574217i
$350$	4.00045			0.213833
$351$	4.26331	−	7.38427i	0.227559	−	0.394143i
$352$	−7.51673	−	13.0194i	−0.400643	−	0.693934i
$353$	−0.854330	−	1.47974i	−0.0454714	−	0.0787588i	0.842394	−	0.538862i	$-0.181146\pi$
$353$	−0.854330	−	1.47974i	−0.0454714	−	0.0787588i	−0.887865	+	0.460103i	$0.847812\pi$
$354$	5.04982	+	8.74654i	0.268395	+	0.464873i
$355$	−35.4902			−1.88363
$356$	7.19302	−	12.4587i	0.381229	−	0.660308i
$357$	12.6789			0.671037
$358$	−3.52678	+	6.10857i	−0.186396	+	0.322848i
$359$	−31.5648			−1.66593			−0.832964	−	0.553327i	$-0.813358\pi$
$359$	−31.5648			−1.66593			−0.832964	+	0.553327i	$0.813358\pi$
$360$	7.77627			0.409846
$361$	7.77448	−	13.4658i	0.409183	−	0.708726i
$362$	7.26328	−	12.5804i	0.381750	−	0.661210i
$363$	4.37233	+	7.57309i	0.229488	+	0.397484i
$364$	−3.69274	+	6.39602i	−0.193552	+	0.335242i
$365$	−1.48302	+	2.56867i	−0.0776250	+	0.134450i
$366$	3.17516			0.165968
$367$	12.3780	+	21.4394i	0.646128	+	1.11913i	0.984040	+	0.177949i	$0.0569462\pi$
$367$	12.3780	+	21.4394i	0.646128	+	1.11913i	−0.337911	+	0.941178i	$0.609720\pi$
$368$	1.81025	+	3.13544i	0.0943656	+	0.163446i
$369$	−5.02825	+	8.70919i	−0.261760	+	0.453382i
$370$	−10.0151			−0.520658
$371$	−0.0533450	+	0.0923963i	−0.00276954	+	0.00479698i
$372$	−6.45275	+	11.1765i	−0.334560	+	0.579474i
$373$	2.35529	+	4.07948i	0.121952	+	0.211228i	0.920538	−	0.390654i	$-0.127751\pi$
$373$	2.35529	+	4.07948i	0.121952	+	0.211228i	−0.798585	+	0.601882i	$0.794418\pi$
$374$	2.63261	−	4.55981i	0.136129	−	0.235782i
$375$	8.05009	+	13.9432i	0.415705	+	0.720022i
$376$	18.9665			0.978124
$377$	3.46897			0.178661
$378$	3.89260	+	6.74219i	0.200214	+	0.346781i
$379$	−3.36665	−	5.83122i	−0.172933	−	0.299530i	0.766511	−	0.642232i	$-0.221991\pi$
$379$	−3.36665	−	5.83122i	−0.172933	−	0.299530i	−0.939444	+	0.342702i	$0.888658\pi$
$380$	−6.60861			−0.339015
$381$	6.86326	+	11.8875i	0.351615	+	0.609016i
$382$	6.18769	+	10.7174i	0.316590	+	0.548349i
$383$	4.92086	−	8.52317i	0.251444	−	0.435514i	−0.712480	−	0.701693i	$-0.752428\pi$
$383$	4.92086	−	8.52317i	0.251444	−	0.435514i	0.963924	+	0.266179i	$0.0857612\pi$
$384$	17.4766			0.891850
$385$	16.9973			0.866261
$386$	2.93879			0.149581
$387$	−10.2881			−0.522974
$388$	−13.5154			−0.686141
$389$	−6.55343	−	11.3509i	−0.332272	−	0.575512i	0.650685	−	0.759348i	$-0.274482\pi$
$389$	−6.55343	−	11.3509i	−0.332272	−	0.575512i	−0.982957	+	0.183836i	$0.941149\pi$
$390$	−9.52985			−0.482563
$391$	−9.07124	+	15.7119i	−0.458753	+	0.794583i
$392$	1.08932	+	1.88676i	0.0550192	+	0.0952960i
$393$	−13.9900	−	24.2314i	−0.705701	−	1.22231i
$394$	−13.8265			−0.696570
$395$	−5.26211	−	9.11424i	−0.264766	−	0.458587i
$396$	3.77974			0.189939
$397$	33.2838			1.67047			0.835234	−	0.549895i	$-0.185332\pi$
$397$	33.2838			1.67047			0.835234	+	0.549895i	$0.185332\pi$
$398$	−10.1559	−	17.5905i	−0.509068	−	0.881732i
$399$	4.67380	+	8.09526i	0.233983	+	0.405270i
$400$	−0.499614	−	0.865357i	−0.0249807	−	0.0432679i
$401$	19.1438			0.955993			0.477997	−	0.878362i	$-0.341363\pi$
$401$	19.1438			0.955993			0.477997	+	0.878362i	$0.341363\pi$
$402$	−21.0746			−1.05111
$403$	5.22913	−	9.05712i	0.260482	−	0.451167i
$404$	−2.05453	−	3.55855i	−0.102217	−	0.177045i
$405$	14.6434	−	25.3631i	0.727636	−	1.26030i
$406$	−1.58367	+	2.74299i	−0.0785960	+	0.136132i
$407$	−12.1021			−0.599879
$408$	6.89264	+	11.9384i	0.341236	+	0.591039i
$409$	−33.9789			−1.68015			−0.840074	−	0.542472i	$-0.817488\pi$
$409$	−33.9789			−1.68015			−0.840074	+	0.542472i	$0.817488\pi$
$410$	−19.7780			−0.976765
$411$	−3.46115	+	5.99489i	−0.170726	+	0.295706i
$412$	6.01809	+	10.4236i	0.296490	+	0.513536i
$413$	−15.3732			−0.756468
$414$	6.33083			0.311143
$415$	−21.3240			−1.04676
$416$	−12.8300			−0.629041
$417$	14.1006	+	24.4229i	0.690508	+	1.19599i
$418$	3.88182			0.189866
$419$	−10.8577	+	18.8061i	−0.530433	+	0.918738i	0.468936	+	0.883232i	$0.344637\pi$
$419$	−10.8577	+	18.8061i	−0.530433	+	0.918738i	−0.999369	+	0.0355054i	$0.988696\pi$
$420$	−8.95017	+	15.5021i	−0.436724	+	0.756427i
$421$	−4.08030	+	7.06728i	−0.198862	+	0.344438i	−0.948160	−	0.317795i	$-0.897058\pi$
$421$	−4.08030	+	7.06728i	−0.198862	+	0.344438i	0.749298	+	0.662233i	$0.230391\pi$
$422$	−8.06156	−	13.9630i	−0.392430	−	0.679709i
$423$	−3.80954	+	6.59832i	−0.185226	+	0.320821i
$424$	−0.116000			−0.00563347
$425$	2.50360	−	4.33636i	0.121442	−	0.210344i
$426$	−10.9771	+	19.0128i	−0.531841	+	0.921175i
$427$	−2.41655	+	4.18558i	−0.116945	+	0.202554i
$428$	−13.8722			−0.670536
$429$	−11.5158			−0.555987
$430$	−10.1167	−	17.5227i	−0.487872	−	0.845019i
$431$	−12.7828	+	22.1404i	−0.615724	+	1.06647i	0.374533	+	0.927214i	$0.377803\pi$
$431$	−12.7828	+	22.1404i	−0.615724	+	1.06647i	−0.990257	+	0.139252i	$0.955530\pi$
$432$	0.972292	−	1.68406i	0.0467794	−	0.0810243i
$433$	−0.182228	−	0.315627i	−0.00875730	−	0.0151681i	0.861614	−	0.507565i	$-0.169454\pi$
$433$	−0.182228	−	0.315627i	−0.00875730	−	0.0151681i	−0.870371	+	0.492397i	$0.836121\pi$
$434$	4.77444	+	8.26957i	0.229181	+	0.396952i
$435$	8.40781			0.403124
$436$	−6.35992	+	11.0157i	−0.304585	+	0.527556i
$437$	−13.3757			−0.639846
$438$	0.917393	+	1.58897i	0.0438347	+	0.0759240i
$439$	−0.865804	+	1.49962i	−0.0413226	+	0.0715728i	−0.885947	−	0.463787i	$-0.846490\pi$
$439$	−0.865804	+	1.49962i	−0.0413226	+	0.0715728i	0.844624	+	0.535359i	$0.179824\pi$
$440$	9.24025	+	16.0046i	0.440512	+	0.762989i
$441$	−0.875189			−0.0416757
$442$	−2.24674	−	3.89147i	−0.106867	−	0.185098i
$443$	5.96193	−	10.3264i	0.283260	−	0.490621i	−0.688926	−	0.724832i	$-0.741917\pi$
$443$	5.96193	−	10.3264i	0.283260	−	0.490621i	0.972186	+	0.234211i	$0.0752507\pi$
$444$	6.37254	−	11.0376i	0.302428	−	0.523820i
$445$	−14.1279	+	24.4703i	−0.669727	+	1.16000i
$446$	−6.34340	+	10.9871i	−0.300369	+	0.520254i
$447$	47.1695			2.23104
$448$	4.60564	−	7.97721i	0.217596	−	0.376888i
$449$	−8.54285			−0.403162			−0.201581	−	0.979472i	$-0.564608\pi$
$449$	−8.54285			−0.403162			−0.201581	+	0.979472i	$0.564608\pi$
$450$	−1.74726			−0.0823667
$451$	−23.8995			−1.12538
$452$	−5.52105			−0.259688
$453$	−14.4373	+	25.0061i	−0.678323	+	1.17489i
$454$	0.229840	+	0.398095i	0.0107869	+	0.0186835i
$455$	7.25297	−	12.5625i	0.340024	−	0.588939i
$456$	−5.08165	+	8.80168i	−0.237970	+	0.412176i
$457$	−11.4111	−	19.7647i	−0.533791	−	0.924553i	−0.999221	−	0.0394681i	$-0.987434\pi$
$457$	−11.4111	−	19.7647i	−0.533791	−	0.924553i	0.465430	−	0.885085i	$-0.345900\pi$
$458$	3.95687	+	6.85349i	0.184892	+	0.320243i
$459$	9.74442			0.454831
$460$	−12.8070	−	22.1824i	−0.597129	−	1.03426i
$461$	−2.15348	−	3.72993i	−0.100297	−	0.173720i	0.811510	−	0.584339i	$-0.198646\pi$
$461$	−2.15348	−	3.72993i	−0.100297	−	0.173720i	−0.911807	+	0.410619i	$0.865313\pi$
$462$	5.25722	−	9.10578i	0.244588	−	0.423639i
$463$	18.6806	+	32.3557i	0.868160	+	1.50370i	0.863875	+	0.503706i	$0.168030\pi$
$463$	18.6806	+	32.3557i	0.868160	+	1.50370i	0.00428439	+	0.999991i	$0.498636\pi$
$464$	0.791134			0.0367275
$465$	12.6739	−	21.9519i	0.587740	−	1.01800i
$466$	5.24652	+	9.08723i	0.243040	+	0.420958i
$467$	−27.2838			−1.26254			−0.631272	−	0.775562i	$-0.717467\pi$
$467$	−27.2838			−1.26254			−0.631272	+	0.775562i	$0.717467\pi$
$468$	1.61287	−	2.79357i	0.0745548	−	0.129133i
$469$	16.0395	−	27.7812i	0.740633	−	1.28281i
$470$	−14.9843			−0.691176
$471$	5.72620	−	9.91806i	0.263849	−	0.457000i
$472$	−8.35738	−	14.4754i	−0.384679	−	0.666284i
$473$	−12.2250	−	21.1743i	−0.562104	−	0.973594i
$474$	−6.51025			−0.299025
$475$	3.69159			0.169382
$476$	−8.44030			−0.386861
$477$	0.0232993	−	0.0403556i	0.00106680	−	0.00184776i
$478$	−0.0157125	+	0.0272148i	−0.000718673	+	0.00124478i
$479$	−18.1105	+	31.3683i	−0.827490	+	1.43325i	0.0725121	+	0.997368i	$0.476898\pi$
$479$	−18.1105	+	31.3683i	−0.827490	+	1.43325i	−0.900002	+	0.435886i	$0.856435\pi$
$480$	−31.0962			−1.41934
$481$	−5.16413	+	8.94454i	−0.235464	+	0.407836i
$482$	7.30748			0.332847
$483$	−18.1150	+	31.3760i	−0.824259	+	1.42766i
$484$	−2.91065	−	5.04139i	−0.132302	−	0.229154i
$485$	26.5458			1.20538
$486$	−4.36651	−	7.56302i	−0.198069	−	0.343065i
$487$	21.7331	−	37.6429i	0.984821	−	1.70576i	0.342094	−	0.939666i	$-0.388864\pi$
$487$	21.7331	−	37.6429i	0.984821	−	1.70576i	0.642727	−	0.766095i	$-0.277803\pi$
$488$	−5.25484			−0.237876
$489$	−1.68473	−	2.91804i	−0.0761863	−	0.131959i
$490$	−0.860610	−	1.49062i	−0.0388784	−	0.0673394i
$491$	−14.9912	−	25.9655i	−0.676542	−	1.17181i	−0.976016	−	0.217701i	$-0.930144\pi$
$491$	−14.9912	−	25.9655i	−0.676542	−	1.17181i	0.299473	−	0.954105i	$-0.403189\pi$
$492$	12.5847	−	21.7973i	0.567360	−	0.982696i
$493$	1.98221	+	3.43329i	0.0892742	+	0.154627i
$494$	1.65643	−	2.86902i	0.0745262	−	0.129083i
$495$	−7.42384			−0.333677
$496$	1.19256	−	2.06557i	0.0535474	−	0.0927468i
$497$	−16.7088	−	28.9405i	−0.749493	−	1.29816i
$498$	−6.59548	+	11.4237i	−0.295551	+	0.511909i
$499$	18.3956	−	31.8622i	0.823501	−	1.42635i	−0.0795581	−	0.996830i	$-0.525351\pi$
$499$	18.3956	−	31.8622i	0.823501	−	1.42635i	0.903059	−	0.429516i	$-0.141316\pi$
$500$	−5.35893	−	9.28193i	−0.239658	−	0.415101i
$501$	−23.7821	−	41.1919i	−1.06251	−	1.84032i
$502$	1.17890	−	2.04191i	0.0526167	−	0.0911349i
$503$	16.6348	+	28.8123i	0.741708	+	1.28468i	0.951717	+	0.306976i	$0.0993172\pi$
$503$	16.6348	+	28.8123i	0.741708	+	1.28468i	−0.210010	+	0.977699i	$0.567350\pi$
$504$	3.66107	+	6.34117i	0.163077	+	0.282458i
$505$	4.03533	+	6.98940i	0.179570	+	0.311024i
$506$	7.52268	+	13.0297i	0.334424	+	0.579239i
$507$	8.22683	−	14.2493i	0.365366	−	0.632833i
$508$	−4.56886	−	7.91349i	−0.202710	−	0.351104i
$509$	−14.9333	+	25.8652i	−0.661905	+	1.14645i	0.318209	+	0.948021i	$0.396919\pi$
$509$	−14.9333	+	25.8652i	−0.661905	+	1.14645i	−0.980114	+	0.198433i	$0.936415\pi$
$510$	−5.44547	−	9.43182i	−0.241129	−	0.417648i
$511$	−2.79283			−0.123548
$512$	−5.64751			−0.249587
$513$	3.59208	+	6.22166i	0.158594	+	0.274693i
$514$	4.57850	−	7.93020i	0.201949	−	0.349786i
$515$	−11.8202	−	20.4732i	−0.520861	−	0.902158i
$516$	25.7490			1.13353
$517$	−18.1069			−0.796342
$518$	−4.71509	−	8.16678i	−0.207169	−	0.358828i
$519$	27.3655			1.20121
$520$	15.7718			0.691638
$521$	−6.29142	+	10.8971i	−0.275632	+	0.477409i	−0.970294	−	0.241927i	$-0.922221\pi$
$521$	−6.29142	+	10.8971i	−0.275632	+	0.477409i	0.694662	+	0.719336i	$0.255554\pi$
$522$	0.691692	−	1.19805i	0.0302745	−	0.0524370i
$523$	−9.11923	−	15.7950i	−0.398756	−	0.690666i	0.594817	−	0.803862i	$-0.297225\pi$
$523$	−9.11923	−	15.7950i	−0.398756	−	0.690666i	−0.993573	+	0.113195i	$0.963891\pi$
$524$	9.31310	+	16.1308i	0.406845	+	0.704676i
$525$	4.99959	−	8.65955i	0.218200	−	0.377934i
$526$	9.78681	−	16.9513i	0.426725	−	0.739110i
$527$	11.9519			0.520635
$528$	−2.62629			−0.114295
$529$	−14.4211	−	24.9781i	−0.627004	−	1.08600i
$530$	0.0916449			0.00398080
$531$	6.71452			0.291385
$532$	−3.11134	−	5.38900i	−0.134894	−	0.233643i
$533$	−10.1983	+	17.6639i	−0.441735	+	0.765108i
$534$	8.73947	+	15.1372i	0.378194	+	0.655051i
$535$	27.2465			1.17797
$536$	34.8782			1.50651
$537$	8.81526	+	15.2685i	0.380406	+	0.658883i
$538$	−7.25203	+	12.5609i	−0.312657	+	0.541538i
$539$	−1.03995	−	1.80125i	−0.0447940	−	0.0775854i
$540$	−6.87870	+	11.9143i	−0.296012	+	0.512708i
$541$	−2.06570	−	3.57790i	−0.0888114	−	0.153826i	0.818198	−	0.574937i	$-0.194974\pi$
$541$	−2.06570	−	3.57790i	−0.0888114	−	0.153826i	−0.907009	+	0.421111i	$0.861640\pi$
$542$	2.52780	+	4.37827i	0.108578	+	0.188063i
$543$	−18.1547	−	31.4449i	−0.779093	−	1.34943i
$544$	−7.33119	−	12.6980i	−0.314322	−	0.544422i
$545$	12.4916	−	21.6361i	0.535082	−	0.926788i
$546$	−4.48666	−	7.77112i	−0.192011	−	0.332573i
$547$	11.8435	+	20.5135i	0.506391	+	0.877094i	0.999973	+	0.00739509i	$0.00235395\pi$
$547$	11.8435	+	20.5135i	0.506391	+	0.877094i	−0.493582	+	0.869699i	$0.664313\pi$
$548$	2.30408	−	3.99078i	0.0984254	−	0.170478i
$549$	1.05547	−	1.82812i	0.0450462	−	0.0780223i
$550$	−2.07620	−	3.59609i	−0.0885296	−	0.153338i
$551$	−1.46140	+	2.53122i	−0.0622577	+	0.107834i
$552$	−39.3914			−1.67661
$553$	4.95481	−	8.58198i	0.210700	−	0.364943i
$554$	2.60715	+	4.51571i	0.110767	+	0.191854i
$555$	−12.5164	+	21.6790i	−0.531292	+	0.920224i
$556$	−9.38672	−	16.2583i	−0.398086	−	0.689504i
$557$	−0.385080	−	0.666977i	−0.0163163	−	0.0282607i	0.857752	−	0.514064i	$-0.171861\pi$
$557$	−0.385080	−	0.666977i	−0.0163163	−	0.0282607i	−0.874068	+	0.485803i	$0.838527\pi$
$558$	−2.08532	−	3.61187i	−0.0882785	−	0.152903i
$559$	−20.8662			−0.882548
$560$	1.65411	−	2.86501i	0.0698990	−	0.121069i
$561$	−6.58025	−	11.3973i	−0.277818	−	0.481196i
$562$	18.3232			0.772916
$563$	−0.178418	−	0.309029i	−0.00751943	−	0.0130240i	0.862241	−	0.506498i	$-0.169060\pi$
$563$	−0.178418	−	0.309029i	−0.00751943	−	0.0130240i	−0.869761	+	0.493474i	$0.835727\pi$
$564$	9.53448	−	16.5142i	0.401474	−	0.695373i
$565$	10.8440			0.456209
$566$	−12.9190	+	22.3764i	−0.543026	+	0.940549i
$567$	27.5765			1.15810
$568$	18.1669	−	31.4660i	0.762266	−	1.32028i
$569$	12.7446	−	22.0743i	0.534281	−	0.925402i	−0.464916	−	0.885355i	$-0.653916\pi$
$569$	12.7446	−	22.0743i	0.534281	−	0.925402i	0.999198	−	0.0400478i	$-0.0127510\pi$
$570$	4.01471	−	6.95369i	0.168158	−	0.291258i
$571$	−33.8197			−1.41531			−0.707655	−	0.706558i	$-0.750247\pi$
$571$	−33.8197			−1.41531			−0.707655	+	0.706558i	$0.750247\pi$
$572$	7.66603			0.320533
$573$	30.9325			1.29222
$574$	−9.31148	−	16.1280i	−0.388654	−	0.673168i
$575$	7.15403	+	12.3911i	0.298344	+	0.516746i
$576$	−2.01159	+	3.48418i	−0.0838163	+	0.145174i
$577$	35.1369			1.46277			0.731383	−	0.681967i	$-0.238875\pi$
$577$	35.1369			1.46277			0.731383	+	0.681967i	$0.238875\pi$
$578$	−4.30733	+	7.46052i	−0.179161	+	0.310317i
$579$	3.67278	−	6.36144i	0.152636	−	0.264372i
$580$	−5.59706			−0.232405
$581$	−10.0394	−	17.3887i	−0.416503	−	0.721404i
$582$	8.21057	−	14.2211i	0.340339	−	0.589484i
$583$	0.110743			0.00458650
$584$	−1.51827	−	2.62973i	−0.0628266	−	0.108819i
$585$	−3.16785	+	5.48688i	−0.130975	+	0.226855i
$586$	6.72267	+	11.6440i	0.277711	+	0.481009i
$587$	16.0773	+	27.8466i	0.663580	+	1.14935i	0.979668	+	0.200624i	$0.0642970\pi$
$587$	16.0773	+	27.8466i	0.663580	+	1.14935i	−0.316089	+	0.948730i	$0.602370\pi$
$588$	2.19041			0.0903311
$589$	4.40583	+	7.63112i	0.181539	+	0.314435i
$590$	6.60267	+	11.4362i	0.271828	+	0.470819i
$591$	−17.2798	+	29.9295i	−0.710797	+	1.23114i
$592$	−1.17773	+	2.03989i	−0.0484045	+	0.0838391i
$593$	−21.2061	−	36.7301i	−0.870832	−	1.50833i	−0.861137	−	0.508372i	$-0.830247\pi$
$593$	−21.2061	−	36.7301i	−0.870832	−	1.50833i	−0.00969456	−	0.999953i	$-0.503086\pi$
$594$	4.04047	−	6.99830i	0.165782	−	0.287144i
$595$	16.5777			0.679620
$596$	−31.4006			−1.28622
$597$	−50.7696			−2.07786
$598$	12.8401			0.525072
$599$	−19.9811	+	34.6083i	−0.816405	+	1.41406i	0.0919093	+	0.995767i	$0.470703\pi$
$599$	−19.9811	+	34.6083i	−0.816405	+	1.41406i	−0.908315	+	0.418288i	$0.862630\pi$
$600$	10.8717			0.443837
$601$	6.88561	−	11.9262i	0.280870	−	0.486481i	−0.690729	−	0.723113i	$-0.742710\pi$
$601$	6.88561	−	11.9262i	0.280870	−	0.486481i	0.971599	+	0.236633i	$0.0760438\pi$
$602$	9.52593	−	16.4994i	0.388248	−	0.672465i
$603$	−7.00550	+	12.1339i	−0.285286	+	0.494130i
$604$	9.61088	−	16.6465i	0.391061	−	0.677338i
$605$	5.71684	+	9.90186i	0.232423	+	0.402568i
$606$	4.99249			0.202806
$607$	5.50020	+	9.52662i	0.223246	+	0.386674i	0.955792	−	0.294044i	$-0.0950013\pi$
$607$	5.50020	+	9.52662i	0.223246	+	0.386674i	−0.732546	+	0.680718i	$0.761668\pi$
$608$	5.40498	−	9.36170i	0.219201	−	0.379667i
$609$	3.95840	+	6.85615i	0.160402	+	0.277825i
$610$	4.15154			0.168091
$611$	−7.72648	+	13.3826i	−0.312580	+	0.541404i
$612$	3.68644			0.149016
$613$	−4.04797	−	7.01130i	−0.163496	−	0.283184i	0.772624	−	0.634864i	$-0.218944\pi$
$613$	−4.04797	−	7.01130i	−0.163496	−	0.283184i	−0.936120	+	0.351680i	$0.885610\pi$
$614$	3.38430	+	5.86177i	0.136579	+	0.236562i
$615$	−24.7177	+	42.8123i	−0.996714	+	1.72636i
$616$	−8.70063	+	15.0699i	−0.350558	+	0.607185i
$617$	1.69246	+	2.93142i	0.0681357	+	0.118015i	0.898081	−	0.439831i	$-0.144962\pi$
$617$	1.69246	+	2.93142i	0.0681357	+	0.118015i	−0.829945	+	0.557845i	$0.811628\pi$
$618$	−14.6239			−0.588259
$619$	−23.6224			−0.949466			−0.474733	−	0.880130i	$-0.657455\pi$
$619$	−23.6224			−0.949466			−0.474733	+	0.880130i	$0.657455\pi$
$620$	−8.43702	+	14.6133i	−0.338839	+	0.586886i
$621$	−13.9223	+	24.1142i	−0.558684	+	0.967670i
$622$	7.15176	−	12.3872i	0.286759	−	0.496682i
$623$	−26.6057			−1.06594
$624$	−1.12067	+	1.94107i	−0.0448629	+	0.0777048i
$625$	15.4935	+	26.8356i	0.619740	+	1.07342i
$626$	−4.46457	+	7.73287i	−0.178440	+	0.309068i
$627$	4.85134	−	8.40277i	0.193744	−	0.335574i
$628$	−3.81192	+	6.60243i	−0.152112	+	0.263466i
$629$	−11.8034			−0.470631
$630$	−2.89240	−	5.00978i	−0.115236	−	0.199594i
$631$	7.85450			0.312683			0.156341	−	0.987703i	$-0.450030\pi$
$631$	7.85450			0.312683			0.156341	+	0.987703i	$0.450030\pi$
$632$	10.7744			0.428581
$633$	−40.3000			−1.60178
$634$	−11.9927			−0.476291
$635$	8.97375	+	15.5430i	0.356113	+	0.616805i
$636$	−0.0583133	+	0.101002i	−0.00231227	+	0.00400497i
$637$	−1.77505			−0.0703300
$638$	3.28765			0.130159
$639$	7.29786	+	12.6403i	0.288699	+	0.500041i
$640$	22.8508			0.903257
$641$	−4.18364	+	7.24627i	−0.165244	+	0.286211i	−0.936742	−	0.350021i	$-0.886174\pi$
$641$	−4.18364	+	7.24627i	−0.165244	+	0.286211i	0.771498	+	0.636232i	$0.219508\pi$
$642$	8.42729	−	14.5965i	0.332599	−	0.576078i
$643$	17.8278	+	30.8786i	0.703058	+	1.21773i	0.967388	+	0.253300i	$0.0815160\pi$
$643$	17.8278	+	30.8786i	0.703058	+	1.21773i	−0.264330	+	0.964432i	$0.585151\pi$
$644$	12.0591	−	20.8869i	0.475194	−	0.823061i
$645$	−50.5739			−1.99135
$646$	3.78600			0.148958
$647$	−16.6680	−	28.8698i	−0.655286	−	1.13499i	−0.981822	−	0.189804i	$-0.939215\pi$
$647$	−16.6680	−	28.8698i	−0.655286	−	1.13499i	0.326536	−	0.945185i	$-0.394119\pi$
$648$	14.9914	+	25.9659i	0.588919	+	1.02004i
$649$	7.97861	+	13.8193i	0.313188	+	0.542457i
$650$	−3.54378			−0.138998
$651$	23.8676			0.935445
$652$	1.12152	+	1.94254i	0.0439223	+	0.0760756i
$653$	−13.9268			−0.544999			−0.272499	−	0.962156i	$-0.587850\pi$
$653$	−13.9268			−0.544999			−0.272499	+	0.962156i	$0.587850\pi$
$654$	−7.72726	−	13.3840i	−0.302160	−	0.523356i
$655$	−18.2920	−	31.6827i	−0.714727	−	1.23794i
$656$	−2.32582	+	4.02843i	−0.0908078	+	0.157284i
$657$	1.21982			0.0475896
$658$	−7.05463	−	12.2190i	−0.275018	−	0.476346i
$659$	−4.51462			−0.175865			−0.0879324	−	0.996126i	$-0.528026\pi$
$659$	−4.51462			−0.175865			−0.0879324	+	0.996126i	$0.528026\pi$
$660$	18.5803			0.723237
$661$	35.3097			1.37339			0.686695	−	0.726946i	$-0.259061\pi$
$661$	35.3097			1.37339			0.686695	+	0.726946i	$0.259061\pi$
$662$	11.0175			0.428209
$663$	−11.2315			−0.436196
$664$	10.9154	−	18.9061i	0.423601	−	0.733698i
$665$	6.11103	+	10.5846i	0.236975	+	0.410453i
$666$	2.05939	+	3.56698i	0.0797999	+	0.138218i
$667$	−11.3283			−0.438635
$668$	15.8317	+	27.4213i	0.612548	+	1.06096i
$669$	15.8554	+	27.4624i	0.613007	+	1.06176i
$670$	−27.5552			−1.06455
$671$	5.01668			0.193667
$672$	−14.6401	−	25.3574i	−0.564755	−	0.978185i
$673$	14.1971	−	24.5900i	0.547256	−	0.947875i	−0.451205	−	0.892420i	$-0.649006\pi$
$673$	14.1971	−	24.5900i	0.547256	−	0.947875i	0.998461	−	0.0554551i	$-0.0176610\pi$
$674$	−2.34192	−	4.05633i	−0.0902075	−	0.156244i
$675$	3.84246	−	6.65534i	0.147897	−	0.256164i
$676$	−5.47658	+	9.48571i	−0.210638	+	0.364835i
$677$	−2.35192			−0.0903916			−0.0451958	−	0.998978i	$-0.514391\pi$
$677$	−2.35192			−0.0903916			−0.0451958	+	0.998978i	$0.514391\pi$
$678$	3.35402	−	5.80933i	0.128810	−	0.223106i
$679$	12.4978	+	21.6468i	0.479621	+	0.830727i
$680$	9.01217	+	15.6095i	0.345601	+	0.598598i
$681$	1.14898			0.0440290
$682$	4.95580	−	8.58370i	0.189768	−	0.328687i
$683$	19.2007	−	33.2566i	0.734695	−	1.27253i	−0.220162	−	0.975463i	$-0.570658\pi$
$683$	19.2007	−	33.2566i	0.734695	−	1.27253i	0.954857	−	0.297066i	$-0.0960082\pi$
$684$	1.35893	+	2.35373i	0.0519599	+	0.0899973i
$685$	−4.52548	+	7.83835i	−0.172910	+	0.299488i
$686$	7.85627	−	13.6075i	0.299954	−	0.519535i
$687$	19.7805			0.754674
$688$	−4.75876			−0.181426
$689$	0.0472555	−	0.0818489i	0.00180029	−	0.00311819i
$690$	31.1208			1.18475
$691$	6.47317	−	11.2119i	0.246251	−	0.426519i	−0.716232	−	0.697863i	$-0.754135\pi$
$691$	6.47317	−	11.2119i	0.246251	−	0.426519i	0.962483	+	0.271344i	$0.0874680\pi$
$692$	−18.2172			−0.692512
$693$	−3.49515	−	6.05377i	−0.132770	−	0.229964i
$694$	−5.51823	−	9.55785i	−0.209469	−	0.362811i
$695$	18.4366	+	31.9331i	0.699340	+	1.21129i
$696$	−4.30382	+	7.45444i	−0.163136	+	0.282560i
$697$	−23.3096			−0.882914
$698$	−1.32869	−	15.0514i	−0.0502916	−	0.569706i
$699$	26.2275			0.992016
$700$	−3.32822	+	5.76464i	−0.125795	+	0.217883i
$701$	18.5829	+	32.1866i	0.701867	+	1.21567i	0.967810	+	0.251681i	$0.0809835\pi$
$701$	18.5829	+	32.1866i	0.701867	+	1.21567i	−0.265943	+	0.963989i	$0.585683\pi$
$702$	−3.44825	−	5.97254i	−0.130146	−	0.225419i
$703$	−4.35107	−	7.53627i	−0.164104	−	0.284236i
$704$	−9.56119			−0.360351
$705$	−18.7268	+	32.4358i	−0.705292	+	1.22160i
$706$	−1.38200			−0.0520121
$707$	−3.79967	+	6.58123i	−0.142901	+	0.247513i
$708$	−16.8050			−0.631571
$709$	−6.52029			−0.244875			−0.122437	−	0.992476i	$-0.539071\pi$
$709$	−6.52029			−0.244875			−0.122437	+	0.992476i	$0.539071\pi$
$710$	−14.3526	+	24.8594i	−0.538643	+	0.932957i
$711$	−2.16410	+	3.74832i	−0.0811599	+	0.140573i
$712$	−14.4637	−	25.0519i	−0.542050	−	0.938858i
$713$	−17.0763	+	29.5771i	−0.639514	+	1.10767i
$714$	5.12746	−	8.88101i	0.191890	−	0.332364i
$715$	−15.0570			−0.563098
$716$	−5.86830	−	10.1642i	−0.219309	−	0.379854i
$717$	0.0392737	+	0.0680240i	0.00146670	+	0.00254040i
$718$	−12.7651	+	22.1098i	−0.476390	+	0.825132i
$719$	−31.7730			−1.18493			−0.592466	−	0.805595i	$-0.701846\pi$
$719$	−31.7730			−1.18493			−0.592466	+	0.805595i	$0.701846\pi$
$720$	−0.722461	+	1.25134i	−0.0269245	+	0.0466347i
$721$	11.1299	−	19.2776i	0.414500	−	0.717935i
$722$	−6.28815	−	10.8914i	−0.234021	−	0.405336i
$723$	9.13259	−	15.8181i	0.339645	−	0.588282i
$724$	12.0855	+	20.9328i	0.449156	+	0.777961i
$725$	3.12653			0.116117
$726$	7.07284			0.262498
$727$	10.8283	+	18.7551i	0.401598	+	0.695588i	0.993919	−	0.110114i	$-0.0351215\pi$
$727$	10.8283	+	18.7551i	0.401598	+	0.695588i	−0.592321	+	0.805702i	$0.701788\pi$
$728$	7.42536	+	12.8611i	0.275202	+	0.476664i
$729$	11.4102			0.422600
$730$	1.19950	+	2.07759i	0.0443954	+	0.0768951i
$731$	−11.9232	−	20.6516i	−0.440996	−	0.763827i
$732$	−2.64161	+	4.57540i	−0.0976367	+	0.169112i
$733$	50.7509			1.87453			0.937264	−	0.348621i	$-0.113350\pi$
$733$	50.7509			1.87453			0.937264	+	0.348621i	$0.113350\pi$
$734$	20.0232			0.739069
$735$	−4.30222			−0.158690
$736$	41.8978			1.54437
$737$	−33.2975			−1.22653
$738$	4.06694	+	7.04415i	0.149706	+	0.259299i
$739$	−6.71681			−0.247082			−0.123541	−	0.992339i	$-0.539425\pi$
$739$	−6.71681			−0.247082			−0.123541	+	0.992339i	$0.539425\pi$
$740$	8.33214	−	14.4317i	0.306296	−	0.530520i
$741$	−4.14027	−	7.17115i	−0.152097	−	0.263439i
$742$	0.0431465	+	0.0747319i	0.00158396	+	0.00274349i
$743$	−42.8086			−1.57050			−0.785248	−	0.619181i	$-0.787465\pi$
$743$	−42.8086			−1.57050			−0.785248	+	0.619181i	$0.787465\pi$
$744$	12.9752	+	22.4737i	0.475693	+	0.823925i
$745$	61.6744			2.25957
$746$	3.81001			0.139494
$747$	4.38486	+	7.59480i	0.160434	+	0.277879i
$748$	4.38046	+	7.58718i	0.160165	+	0.277415i
$749$	12.8277	+	22.2182i	0.468713	+	0.811834i
$750$	13.0221			0.475501
$751$	−3.37892			−0.123299			−0.0616493	−	0.998098i	$-0.519636\pi$
$751$	−3.37892			−0.123299			−0.0616493	+	0.998098i	$0.519636\pi$
$752$	−1.76210	+	3.05205i	−0.0642572	+	0.111297i
$753$	−2.94667	−	5.10379i	−0.107383	−	0.185992i
$754$	1.40288	−	2.42987i	0.0510900	−	0.0884905i
$755$	−18.8769	+	32.6957i	−0.686999	+	1.18992i
$756$	−12.9540			−0.471132
$757$	25.3261	+	43.8661i	0.920493	+	1.59434i	0.798653	+	0.601791i	$0.205546\pi$
$757$	25.3261	+	43.8661i	0.920493	+	1.59434i	0.121840	+	0.992550i	$0.461121\pi$
$758$	−5.44603			−0.197809
$759$	37.6061			1.36502
$760$	−6.64429	+	11.5083i	−0.241014	+	0.417448i
$761$	6.45776	+	11.1852i	0.234094	+	0.405462i	0.959009	−	0.283376i	$-0.0914544\pi$
$761$	6.45776	+	11.1852i	0.234094	+	0.405462i	−0.724915	+	0.688838i	$0.758121\pi$
$762$	11.1023			0.402193
$763$	23.5242			0.851634
$764$	−20.5917			−0.744980
$765$	−7.24059			−0.261784
$766$	−3.98008	−	6.89370i	−0.143806	−	0.249080i
$767$	13.6183			0.491729
$768$	14.5496	−	25.2006i	0.525012	−	0.909348i
$769$	2.50012	−	4.33034i	0.0901568	−	0.156156i	−0.817420	−	0.576042i	$-0.804597\pi$
$769$	2.50012	−	4.33034i	0.0901568	−	0.156156i	0.907577	+	0.419886i	$0.137930\pi$
$770$	6.87385	−	11.9059i	0.247717	−	0.429058i
$771$	−11.4440	−	19.8217i	−0.412147	−	0.713860i
$772$	−2.44496	+	4.23480i	−0.0879961	+	0.152414i
$773$	35.3567			1.27169			0.635846	−	0.771816i	$-0.280651\pi$
$773$	35.3567			1.27169			0.635846	+	0.771816i	$0.280651\pi$
$774$	−4.16061	+	7.20638i	−0.149550	+	0.259028i
$775$	4.71294	−	8.16306i	0.169294	−	0.293226i
$776$	−13.5884	+	23.5357i	−0.487794	+	0.844884i
$777$	−23.5709			−0.845602
$778$	−10.6011			−0.380067
$779$	−8.59259	−	14.8828i	−0.307862	−	0.533232i
$780$	7.92847	−	13.7325i	0.283885	−	0.491703i
$781$	−17.3435	+	30.0399i	−0.620600	+	1.07491i
$782$	7.33699	+	12.7080i	0.262370	+	0.454439i
$783$	3.04225	+	5.26933i	0.108721	+	0.188311i
$784$	−0.404818			−0.0144578
$785$	7.48704	−	12.9679i	0.267224	−	0.462845i
$786$	−22.6307			−0.807211
$787$	−0.732688	−	1.26905i	−0.0261175	−	0.0452368i	0.852671	−	0.522448i	$-0.174981\pi$
$787$	−0.732688	−	1.26905i	−0.0261175	−	0.0452368i	−0.878789	+	0.477211i	$0.841648\pi$
$788$	11.5031	−	19.9240i	0.409782	−	0.709764i
$789$	−24.4623	−	42.3700i	−0.870881	−	1.50841i
$790$	−8.51219			−0.302850
$791$	5.10535	+	8.84272i	0.181525	+	0.314411i
$792$	3.80014	−	6.58204i	0.135032	−	0.233883i
$793$	2.14069	−	3.70778i	0.0760180	−	0.131667i
$794$	13.4603	−	23.3139i	0.477688	−	0.827380i
$795$	0.114534	−	0.198379i	0.00406210	−	0.00703577i
$796$	33.7972			1.19791
$797$	17.4300	−	30.1897i	0.617403	−	1.06937i	−0.372555	−	0.928010i	$-0.621518\pi$
$797$	17.4300	−	30.1897i	0.617403	−	1.06937i	0.989958	−	0.141363i	$-0.0451484\pi$
$798$	7.56052			0.267639
$799$	−17.6600			−0.624765
$800$	−11.5635			−0.408831
$801$	11.6205			0.410590
$802$	7.74191	−	13.4094i	0.273376	−	0.473502i
$803$	1.44946	+	2.51054i	0.0511504	+	0.0885951i
$804$	17.5333	−	30.3685i	0.618351	−	1.07102i
$805$	−23.6854	+	41.0243i	−0.834801	+	1.44592i
$806$	−4.22942	−	7.32557i	−0.148975	−	0.258032i
$807$	18.1266	+	31.3962i	0.638086	+	1.10520i
$808$	−8.26249			−0.290673
$809$	−12.0984	−	20.9550i	−0.425356	−	0.736738i	0.571098	−	0.820882i	$-0.306518\pi$
$809$	−12.0984	−	20.9550i	−0.425356	−	0.736738i	−0.996454	+	0.0841440i	$0.973184\pi$
$810$	−11.8439	−	20.5142i	−0.416151	−	0.720794i
$811$	6.93214	−	12.0068i	0.243420	−	0.421616i	−0.718266	−	0.695769i	$-0.755064\pi$
$811$	6.93214	−	12.0068i	0.243420	−	0.421616i	0.961686	+	0.274152i	$0.0883973\pi$
$812$	−2.63510	−	4.56412i	−0.0924738	−	0.160169i
$813$	12.6365			0.443183
$814$	−4.89420	+	8.47701i	−0.171542	+	0.297119i
$815$	−2.20280	−	3.81536i	−0.0771607	−	0.133646i
$816$	−2.56146			−0.0896692
$817$	8.79048	−	15.2256i	0.307540	−	0.532675i
$818$	−13.7414	+	23.8008i	−0.480456	+	0.832174i
$819$	−5.96571			−0.208459
$820$	16.4545	−	28.5001i	0.574617	−	0.995265i
$821$	21.6822	+	37.5546i	0.756714	+	1.31067i	0.944518	+	0.328460i	$0.106530\pi$
$821$	21.6822	+	37.5546i	0.756714	+	1.31067i	−0.187804	+	0.982206i	$0.560137\pi$
$822$	2.79944	+	4.84878i	0.0976418	+	0.169121i
$823$	−30.4141			−1.06017			−0.530084	−	0.847945i	$-0.677840\pi$
$823$	−30.4141			−1.06017			−0.530084	+	0.847945i	$0.677840\pi$
$824$	24.2023			0.843128
$825$	−10.3790			−0.361351
$826$	−6.21708	+	10.7683i	−0.216320	+	0.374677i
$827$	−10.9802	+	19.0182i	−0.381818	+	0.661328i	−0.991322	−	0.131455i	$-0.958035\pi$
$827$	−10.9802	+	19.0182i	−0.381818	+	0.661328i	0.609504	+	0.792783i	$0.291369\pi$
$828$	−5.26700	+	9.12272i	−0.183041	+	0.317036i
$829$	−10.7989			−0.375062			−0.187531	−	0.982259i	$-0.560049\pi$
$829$	−10.7989			−0.375062			−0.187531	+	0.982259i	$0.560049\pi$
$830$	−8.62363	+	14.9366i	−0.299331	+	0.518456i
$831$	13.0332			0.452117
$832$	−4.07989	+	7.06658i	−0.141445	+	0.244990i
$833$	−1.01428	−	1.75679i	−0.0351428	−	0.0608692i
$834$	22.8096			0.789832
$835$	−31.0953	−	53.8587i	−1.07610	−	1.86386i
$836$	−3.22953	+	5.59371i	−0.111696	+	0.193462i
$837$	18.3436			0.634047
$838$	8.78191	+	15.2107i	0.303366	+	0.525445i
$839$	−13.6961	−	23.7224i	−0.472843	−	0.818988i	0.526674	−	0.850067i	$-0.323439\pi$
$839$	−13.6961	−	23.7224i	−0.472843	−	0.818988i	−0.999517	+	0.0310795i	$0.990105\pi$
$840$	17.9970	+	31.1717i	0.620955	+	1.07553i
$841$	13.2623	−	22.9710i	0.457320	−	0.792102i
$842$	3.30022	+	5.71615i	0.113733	+	0.196992i
$843$	22.8995	−	39.6632i	0.788702	−	1.36607i
$844$	26.8276			0.923445
$845$	10.7566	−	18.6310i	0.370039	−	0.640927i
$846$	3.08123	+	5.33684i	0.105935	+	0.183484i
$847$	−5.38299	+	9.32361i	−0.184962	+	0.320363i
$848$	0.0107771	−	0.0186665i	0.000370087	−	0.000641009i
$849$	32.2913	+	55.9301i	1.10823	+	1.91952i
$850$	−2.02496	−	3.50733i	−0.0694554	−	0.120300i
$851$	16.8641	−	29.2094i	0.578093	−	1.00129i
$852$	−18.2650	−	31.6359i	−0.625749	−	1.08383i
$853$	23.1315	+	40.0649i	0.792007	+	1.37180i	0.924722	+	0.380643i	$0.124297\pi$
$853$	23.1315	+	40.0649i	0.792007	+	1.37180i	−0.132715	+	0.991154i	$0.542369\pi$
$854$	1.95455	+	3.38538i	0.0668832	+	0.115845i
$855$	−2.66909	−	4.62300i	−0.0912810	−	0.158103i
$856$	−13.9470	+	24.1570i	−0.476700	+	0.825669i
$857$	−4.10497	−	7.11002i	−0.140223	−	0.242874i	0.787357	−	0.616497i	$-0.211449\pi$
$857$	−4.10497	−	7.11002i	−0.140223	−	0.242874i	−0.927581	+	0.373623i	$0.878115\pi$
$858$	−4.65709	+	8.06632i	−0.158990	+	0.275380i
$859$	−4.41850	−	7.65306i	−0.150757	−	0.261119i	0.780749	−	0.624845i	$-0.214838\pi$
$859$	−4.41850	−	7.65306i	−0.150757	−	0.261119i	−0.931506	+	0.363726i	$0.881504\pi$
$860$	33.6669			1.14803
$861$	−46.5484			−1.58637
$862$	10.3389	+	17.9076i	0.352146	+	0.609934i
$863$	−12.7053	+	22.0062i	−0.432493	+	0.749100i	−0.997087	−	0.0762686i	$-0.975699\pi$
$863$	−12.7053	+	22.0062i	−0.432493	+	0.749100i	0.564594	+	0.825369i	$0.309033\pi$
$864$	−11.2518	−	19.4886i	−0.382792	−	0.663016i
$865$	35.7806			1.21658
$866$	−0.294778			−0.0100170
$867$	10.7663	+	18.6477i	0.365641	+	0.633309i
$868$	−15.8886			−0.539295
$869$	−10.2860			−0.348930
$870$	3.40020	−	5.88931i	0.115277	−	0.199666i
$871$	−14.2085	+	24.6098i	−0.481436	+	0.833872i
$872$	12.7885	+	22.1503i	0.433073	+	0.750105i
$873$	−5.45861	−	9.45459i	−0.184746	−	0.319989i
$874$	−5.40926	+	9.36911i	−0.182971	+	0.316915i
$875$	−9.91086	+	17.1661i	−0.335048	+	0.580321i
$876$	−3.05294			−0.103149
$877$	−48.4021			−1.63442			−0.817211	−	0.576339i	$-0.804481\pi$
$877$	−48.4021			−1.63442			−0.817211	+	0.576339i	$0.804481\pi$
$878$	0.700279	+	1.21292i	0.0236333	+	0.0409340i
$879$	33.6068			1.13353
$880$	−3.43389			−0.115757
$881$	−1.46919	−	2.54471i	−0.0494983	−	0.0857336i	0.840215	−	0.542254i	$-0.182429\pi$
$881$	−1.46919	−	2.54471i	−0.0494983	−	0.0857336i	−0.889713	+	0.456520i	$0.849096\pi$
$882$	−0.353934	+	0.613032i	−0.0119176	+	0.0206419i
$883$	−16.7469	−	29.0066i	−0.563580	−	0.976149i	−0.997180	−	0.0750435i	$-0.976090\pi$
$883$	−16.7469	−	29.0066i	−0.563580	−	0.976149i	0.433601	−	0.901105i	$-0.357243\pi$
$884$	7.47681			0.251472
$885$	33.0070			1.10952
$886$	−4.82212	−	8.35216i	−0.162002	−	0.280596i
$887$	0.541627	−	0.938126i	0.0181861	−	0.0314992i	−0.856789	−	0.515667i	$-0.827544\pi$
$887$	0.541627	−	0.938126i	0.0181861	−	0.0314992i	0.874975	+	0.484168i	$0.160878\pi$
$888$	−12.8139	−	22.1943i	−0.430006	−	0.744792i
$889$	−8.44970	+	14.6353i	−0.283394	+	0.490852i
$890$	11.4269	+	19.7920i	0.383031	+	0.663429i
$891$	−14.3120	−	24.7891i	−0.479470	−	0.830466i
$892$	−10.5549	−	18.2817i	−0.353405	−	0.612116i
$893$	−6.50998	−	11.2756i	−0.217848	−	0.377324i
$894$	19.0758	−	33.0402i	0.637989	−	1.10503i
$895$	11.5260	+	19.9636i	0.385272	+	0.667311i
$896$	10.7582	+	18.6337i	0.359405	+	0.622508i
$897$	16.0471	−	27.7943i	0.535796	−	0.928025i
$898$	−3.45481	+	5.98391i	−0.115288	+	0.199686i
$899$	3.73145	+	6.46306i	0.124451	+	0.215555i
$900$	1.45365	−	2.51780i	0.0484551	−	0.0839268i
$901$	0.108009			0.00359831
$902$	−9.66519	+	16.7406i	−0.321816	+	0.557401i
$903$	−23.8102	−	41.2405i	−0.792354	−	1.37240i
$904$	−5.55085	+	9.61436i	−0.184619	+	0.319769i
$905$	−23.7374	−	41.1144i	−0.789058	−	1.36669i
$906$	11.6772	+	20.2254i	0.387947	+	0.671945i
$907$	−22.9655	−	39.7774i	−0.762557	−	1.32079i	−0.941529	−	0.336933i	$-0.890611\pi$
$907$	−22.9655	−	39.7774i	−0.762557	−	1.32079i	0.178972	−	0.983854i	$-0.442723\pi$
$908$	−0.764873			−0.0253832
$909$	1.65957	−	2.87446i	0.0550445	−	0.0953398i
$910$	−5.86634	−	10.1608i	−0.194467	−	0.336827i
$911$	35.8875			1.18900			0.594502	−	0.804094i	$-0.297349\pi$
$911$	35.8875			1.18900			0.594502	+	0.804094i	$0.297349\pi$
$912$	−0.944230	−	1.63545i	−0.0312666	−	0.0541553i
$913$	−10.4207	+	18.0492i	−0.344875	+	0.597342i
$914$	−18.4591			−0.610573
$915$	5.18842	−	8.98661i	0.171524	−	0.297088i
$916$	−13.1678			−0.435078
$917$	17.2238	−	29.8324i	0.568779	−	0.985154i
$918$	3.94073	−	6.82555i	0.130064	−	0.225277i
$919$	−14.6842	+	25.4337i	−0.484386	+	0.838981i	−0.999839	−	0.0179370i	$-0.994290\pi$
$919$	−14.6842	+	25.4337i	−0.484386	+	0.838981i	0.515453	+	0.856918i	$0.327624\pi$
$920$	−51.5046			−1.69805
$921$	16.9182			0.557474
$922$	−3.48354			−0.114724
$923$	14.8014	+	25.6369i	0.487196	+	0.843847i
$924$	8.74762	+	15.1513i	0.287775	+	0.498442i
$925$	−4.65436	+	8.06159i	−0.153034	+	0.265063i
$926$	30.2184			0.993038
$927$	−4.86118	+	8.41981i	−0.159662	+	0.276543i
$928$	4.57766	−	7.92874i	0.150269	−	0.260274i
$929$	−47.8400			−1.56958			−0.784789	−	0.619763i	$-0.787229\pi$
$929$	−47.8400			−1.56958			−0.784789	+	0.619763i	$0.787229\pi$
$930$	−10.2509	−	17.7551i	−0.336141	−	0.582213i
$931$	0.747789	−	1.29521i	0.0245078	−	0.0424487i
$932$	−17.4596			−0.571908
$933$	−17.8759	−	30.9620i	−0.585232	−	1.01365i
$934$	−11.0338	+	19.1111i	−0.361038	+	0.625336i
$935$	−8.60372	−	14.9021i	−0.281372	−	0.487350i
$936$	−3.24315	−	5.61729i	−0.106006	−	0.183607i
$937$	−12.3589			−0.403746			−0.201873	−	0.979412i	$-0.564703\pi$
$937$	−12.3589			−0.403746			−0.201873	+	0.979412i	$0.564703\pi$
$938$	−12.9730	−	22.4699i	−0.423584	−	0.733669i
$939$	11.1593	+	19.3284i	0.364169	+	0.630760i
$940$	12.4664	−	21.5924i	0.406609	−	0.704267i
$941$	12.9574	−	22.4429i	0.422399	−	0.731617i	−0.573774	−	0.819013i	$-0.694521\pi$
$941$	12.9574	−	22.4429i	0.422399	−	0.731617i	0.996174	+	0.0873964i	$0.0278547\pi$
$942$	−4.63146	−	8.02192i	−0.150901	−	0.261368i
$943$	33.3036	−	57.6835i	1.08451	−	1.87843i
$944$	3.10580			0.101085
$945$	25.4431			0.827664
$946$	−19.7756			−0.642959
$947$	−38.7694			−1.25984			−0.629918	−	0.776662i	$-0.716912\pi$
$947$	−38.7694			−1.25984			−0.629918	+	0.776662i	$0.716912\pi$
$948$	5.41627	−	9.38126i	0.175912	−	0.304689i
$949$	2.47402			0.0803101
$950$	1.49291	−	2.58580i	0.0484365	−	0.0838946i
$951$	−14.9880	+	25.9599i	−0.486019	+	0.841809i
$952$	−8.48587	+	14.6980i	−0.275028	+	0.476363i
$953$	−19.1382	+	33.1483i	−0.619946	+	1.07378i	0.369549	+	0.929211i	$0.379512\pi$
$953$	−19.1382	+	33.1483i	−0.619946	+	1.07378i	−0.989495	+	0.144567i	$0.953821\pi$
$954$	−0.0188449	−	0.0326404i	−0.000610127	−	0.00105677i
$955$	40.4444			1.30875
$956$	−0.0261444	−	0.0452834i	−0.000845570	−	0.00146457i
$957$	4.10876	−	7.11659i	0.132818	−	0.230047i
$958$	14.6481	+	25.3713i	0.473259	+	0.819708i
$959$	−8.52239			−0.275202
$960$	−9.88851	+	17.1274i	−0.319150	+	0.552784i
$961$	−8.50084			−0.274220
$962$	4.17685	+	7.23451i	0.134667	+	0.233250i
$963$	−5.60270	−	9.70415i	−0.180544	−	0.312712i
$964$	−6.07955	+	10.5301i	−0.195809	+	0.339151i
$965$	4.80218	−	8.31763i	0.154588	−	0.267754i
$966$	14.6517	+	25.3775i	0.471411	+	0.816508i
$967$	56.8332			1.82763			0.913817	−	0.406127i	$-0.133121\pi$
$967$	56.8332			1.82763			0.913817	+	0.406127i	$0.133121\pi$
$968$	−11.7054			−0.376227
$969$	4.73159	−	8.19536i	0.152001	−	0.263273i
$970$	10.7354	−	18.5942i	0.344692	−	0.597024i
$971$	23.6441	−	40.9528i	0.758776	−	1.31424i	−0.184699	−	0.982795i	$-0.559131\pi$
$971$	23.6441	−	40.9528i	0.758776	−	1.31424i	0.943475	−	0.331443i	$-0.107536\pi$
$972$	14.5311			0.466084
$973$	−17.3599	+	30.0682i	−0.556533	+	0.963944i
$974$	−17.5781	−	30.4462i	−0.563240	−	0.975561i
$975$	−4.42887	+	7.67102i	−0.141837	+	0.245669i
$976$	0.488206	−	0.845597i	0.0156271	−	0.0270669i
$977$	17.2586	−	29.8928i	0.552153	−	0.956357i	−0.445966	−	0.895050i	$-0.647140\pi$
$977$	17.2586	−	29.8928i	0.552153	−	0.956357i	0.998119	−	0.0613069i	$-0.0195268\pi$
$978$	−2.72529			−0.0871451
$979$	13.8082	+	23.9165i	0.441311	+	0.764374i
$980$	2.86398			0.0914865
$981$	−10.2746			−0.328042
$982$	−24.2503			−0.773858
$983$	1.01451			0.0323579			0.0161790	−	0.999869i	$-0.494850\pi$
$983$	1.01451			0.0323579			0.0161790	+	0.999869i	$0.494850\pi$
$984$	−25.3052	−	43.8299i	−0.806700	−	1.39725i
$985$	−22.5935	+	39.1330i	−0.719888	+	1.24688i
$986$	3.20650			0.102116
$987$	−35.2664			−1.12254
$988$	2.75617	+	4.77382i	0.0876854	+	0.151875i
$989$	68.1412			2.16676
$990$	−3.00227	+	5.20008i	−0.0954184	+	0.165270i
$991$	25.9942	−	45.0233i	0.825733	−	1.43021i	−0.0756244	−	0.997136i	$-0.524095\pi$
$991$	25.9942	−	45.0233i	0.825733	−	1.43021i	0.901358	−	0.433076i	$-0.142572\pi$
$992$	−13.8007	−	23.9036i	−0.438174	−	0.758940i
$993$	13.7693	−	23.8491i	0.436955	−	0.756827i
$994$	−27.0288			−0.857302
$995$	−66.3815			−2.10444
$996$	−10.9744	−	19.0082i	−0.347736	−	0.602297i
$997$	27.5214	+	47.6684i	0.871611	+	1.50967i	0.860329	+	0.509738i	$0.170258\pi$
$997$	27.5214	+	47.6684i	0.871611	+	1.50967i	0.0112817	+	0.999936i	$0.496409\pi$
$998$	−14.8787	−	25.7707i	−0.470978	−	0.815758i
$999$	−18.1156			−0.573151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	349.2.c.a.122.17	✓	56
349.226	even	3	inner	349.2.c.a.226.17	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
349.2.c.a.122.17	✓	56	1.1	even	1	trivial
349.2.c.a.226.17	yes	56	349.226	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	349.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.404409 - 0.700458i) q^{2} +(-1.01083 - 1.75081i) q^{3} +(0.672906 + 1.16551i) q^{4} +(-1.32166 - 2.28919i) q^{5} -1.63515 q^{6} +(1.24448 - 2.15550i) q^{7} +2.70616 q^{8} +(-0.543548 + 0.941452i) q^{9} +O(q^{10})\)	\(q+(0.404409 - 0.700458i) q^{2} +(-1.01083 - 1.75081i) q^{3} +(0.672906 + 1.16551i) q^{4} +(-1.32166 - 2.28919i) q^{5} -1.63515 q^{6} +(1.24448 - 2.15550i) q^{7} +2.70616 q^{8} +(-0.543548 + 0.941452i) q^{9} -2.13797 q^{10} -2.58351 q^{11} +(1.36039 - 2.35626i) q^{12} +(-1.10242 + 1.90944i) q^{13} +(-1.00656 - 1.74341i) q^{14} +(-2.67195 + 4.62796i) q^{15} +(-0.251418 + 0.435468i) q^{16} -2.51974 q^{17} +(0.439631 + 0.761464i) q^{18} +(-0.928848 - 1.60881i) q^{19} +(1.77871 - 3.08082i) q^{20} -5.03183 q^{21} +(-1.04479 + 1.80964i) q^{22} +(3.60008 - 6.23551i) q^{23} +(-2.73546 - 4.73795i) q^{24} +(-0.993594 + 1.72096i) q^{25} +(0.891656 + 1.54439i) q^{26} -3.86724 q^{27} +3.34967 q^{28} +(-0.786673 - 1.36256i) q^{29} +(2.16112 + 3.74318i) q^{30} -4.74333 q^{31} +(2.90951 + 5.03941i) q^{32} +(2.61148 + 4.52322i) q^{33} +(-1.01901 + 1.76497i) q^{34} -6.57914 q^{35} -1.46303 q^{36} +4.68437 q^{37} -1.50254 q^{38} +4.45742 q^{39} +(-3.57663 - 6.19490i) q^{40} +9.25080 q^{41} +(-2.03492 + 3.52458i) q^{42} +(4.73193 + 8.19593i) q^{43} +(-1.73846 - 3.01110i) q^{44} +2.87355 q^{45} +(-2.91181 - 5.04340i) q^{46} +7.00866 q^{47} +1.01656 q^{48} +(0.402535 + 0.697212i) q^{49} +(0.803638 + 1.39194i) q^{50} +(2.54702 + 4.41157i) q^{51} -2.96730 q^{52} -0.0428653 q^{53} +(-1.56395 + 2.70884i) q^{54} +(3.41453 + 5.91414i) q^{55} +(3.36776 - 5.83313i) q^{56} +(-1.87781 + 3.25247i) q^{57} -1.27255 q^{58} +(-3.08828 - 5.34906i) q^{59} -7.19189 q^{60} -1.94181 q^{61} +(-1.91825 + 3.32250i) q^{62} +(1.35287 + 2.34324i) q^{63} +3.70086 q^{64} +5.82811 q^{65} +4.22443 q^{66} +12.8885 q^{67} +(-1.69555 - 2.93677i) q^{68} -14.5562 q^{69} +(-2.66067 + 4.60841i) q^{70} +(6.71317 - 11.6276i) q^{71} +(-1.47092 + 2.54772i) q^{72} +(-0.561044 - 0.971757i) q^{73} +(1.89440 - 3.28120i) q^{74} +4.01741 q^{75} +(1.25006 - 2.16516i) q^{76} +(-3.21513 + 5.56876i) q^{77} +(1.80262 - 3.12223i) q^{78} +3.98143 q^{79} +1.32916 q^{80} +(5.53975 + 9.59514i) q^{81} +(3.74111 - 6.47980i) q^{82} +(4.03355 - 6.98632i) q^{83} +(-3.38595 - 5.86463i) q^{84} +(3.33025 + 5.76816i) q^{85} +7.65454 q^{86} +(-1.59038 + 2.75462i) q^{87} -6.99137 q^{88} +(-5.34474 - 9.25736i) q^{89} +(1.16209 - 2.01280i) q^{90} +(2.74388 + 4.75253i) q^{91} +9.69005 q^{92} +(4.79469 + 8.30465i) q^{93} +(2.83437 - 4.90927i) q^{94} +(-2.45525 + 4.25262i) q^{95} +(5.88202 - 10.1880i) q^{96} +(-5.02128 + 8.69711i) q^{97} +0.651156 q^{98} +(1.40426 - 2.43225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 56 q - 30 q^{4} + 4 q^{5} + 14 q^{6} + 2 q^{7} + 6 q^{8} - 28 q^{9} - 2 q^{10} - 2 q^{11} + 11 q^{12} - 2 q^{13} + 2 q^{14} + 9 q^{15} - 34 q^{16} + 18 q^{18} - 5 q^{19} + 14 q^{20} + 12 q^{21} - 7 q^{22} - 11 q^{23} - 30 q^{24} - 6 q^{25} - 11 q^{26} - 30 q^{27} - 52 q^{28} + 8 q^{29} - 21 q^{30} - 48 q^{31} - 6 q^{32} + 12 q^{33} - 14 q^{34} + 42 q^{35} + 66 q^{36} + 14 q^{37} + 60 q^{38} - 26 q^{39} + 24 q^{40} - 3 q^{42} - 23 q^{43} - 20 q^{44} + 18 q^{45} + 5 q^{46} - 26 q^{47} - 22 q^{48} - 26 q^{49} + 11 q^{50} + 14 q^{51} + 6 q^{52} - 12 q^{53} - 7 q^{54} + 10 q^{55} - 19 q^{56} + 25 q^{57} - 12 q^{58} - 16 q^{59} - 12 q^{60} + 42 q^{61} - 27 q^{62} + 31 q^{63} + 54 q^{64} + 72 q^{65} - 66 q^{66} - 34 q^{67} - 57 q^{68} + 10 q^{69} - 52 q^{70} - 10 q^{71} + 47 q^{72} + 23 q^{73} - 17 q^{74} - 26 q^{75} + 9 q^{76} - 10 q^{77} + 25 q^{78} + 48 q^{79} - 32 q^{80} - 12 q^{81} - 8 q^{82} + 14 q^{83} + 10 q^{84} - 3 q^{85} + 46 q^{86} + 14 q^{87} + 58 q^{88} + 8 q^{89} + 68 q^{90} + 54 q^{91} + 48 q^{92} - 57 q^{93} + 33 q^{94} + 54 q^{95} - 72 q^{96} + 32 q^{98} + 73 q^{99}+O(q^{100}) \) 56 * q - 30 * q^4 + 4 * q^5 + 14 * q^6 + 2 * q^7 + 6 * q^8 - 28 * q^9 - 2 * q^10 - 2 * q^11 + 11 * q^12 - 2 * q^13 + 2 * q^14 + 9 * q^15 - 34 * q^16 + 18 * q^18 - 5 * q^19 + 14 * q^20 + 12 * q^21 - 7 * q^22 - 11 * q^23 - 30 * q^24 - 6 * q^25 - 11 * q^26 - 30 * q^27 - 52 * q^28 + 8 * q^29 - 21 * q^30 - 48 * q^31 - 6 * q^32 + 12 * q^33 - 14 * q^34 + 42 * q^35 + 66 * q^36 + 14 * q^37 + 60 * q^38 - 26 * q^39 + 24 * q^40 - 3 * q^42 - 23 * q^43 - 20 * q^44 + 18 * q^45 + 5 * q^46 - 26 * q^47 - 22 * q^48 - 26 * q^49 + 11 * q^50 + 14 * q^51 + 6 * q^52 - 12 * q^53 - 7 * q^54 + 10 * q^55 - 19 * q^56 + 25 * q^57 - 12 * q^58 - 16 * q^59 - 12 * q^60 + 42 * q^61 - 27 * q^62 + 31 * q^63 + 54 * q^64 + 72 * q^65 - 66 * q^66 - 34 * q^67 - 57 * q^68 + 10 * q^69 - 52 * q^70 - 10 * q^71 + 47 * q^72 + 23 * q^73 - 17 * q^74 - 26 * q^75 + 9 * q^76 - 10 * q^77 + 25 * q^78 + 48 * q^79 - 32 * q^80 - 12 * q^81 - 8 * q^82 + 14 * q^83 + 10 * q^84 - 3 * q^85 + 46 * q^86 + 14 * q^87 + 58 * q^88 + 8 * q^89 + 68 * q^90 + 54 * q^91 + 48 * q^92 - 57 * q^93 + 33 * q^94 + 54 * q^95 - 72 * q^96 + 32 * q^98 + 73 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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