LMFDB - Embedded newform 354.2.e.c.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	354.49
Dual form			354.2.e.c.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.271121 - 0.319189i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(3.97639 + 2.39251i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})$	\(q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.271121 - 0.319189i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(3.97639 + 2.39251i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(0.196166 + 0.370009i) q^{10} +(0.249248 - 4.59712i) q^{11} +(-0.647386 - 0.762162i) q^{12} +(-4.61848 + 1.01660i) q^{13} +(-3.69440 + 2.80841i) q^{14} +(0.304042 - 0.288004i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(4.87423 - 2.93273i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(-0.702917 + 2.53168i) q^{19} +(-0.416339 + 0.0452796i) q^{20} +(3.69440 + 2.80841i) q^{21} +(4.17836 + 1.93311i) q^{22} +(3.14242 + 4.63472i) q^{23} +(0.947653 - 0.319302i) q^{24} +(0.780535 + 4.76105i) q^{25} +(0.765073 - 4.66674i) q^{26} +(0.947653 + 0.319302i) q^{27} +(-1.24151 - 4.47151i) q^{28} +(0.0677602 + 0.170065i) q^{29} +(0.155012 + 0.389050i) q^{30} +(1.54173 + 5.55282i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(0.744823 - 4.54322i) q^{33} +(0.920297 + 5.61356i) q^{34} +(1.84175 - 0.620556i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(-10.7405 - 4.96909i) q^{37} +(-2.09169 - 1.59006i) q^{38} +(-4.70132 + 0.511299i) q^{39} +(0.112039 - 0.403529i) q^{40} +(-0.365726 + 0.539405i) q^{41} +(-3.97639 + 2.39251i) q^{42} +(-0.567172 - 10.4609i) q^{43} +(-3.34239 + 3.16608i) q^{44} +(0.333399 - 0.253443i) q^{45} +(-5.46868 + 1.20375i) q^{46} +(-5.62826 - 6.62610i) q^{47} +(-0.0541389 + 0.998533i) q^{48} +(6.80867 + 12.8425i) q^{49} +(-4.71182 - 1.03715i) q^{50} +(5.16274 - 2.38854i) q^{51} +(4.05211 + 2.43807i) q^{52} +(-1.09486 + 2.06513i) q^{53} +(-0.647386 + 0.762162i) q^{54} +(-1.39977 - 1.32593i) q^{55} +(4.61346 + 0.501744i) q^{56} +(-0.972519 + 2.44084i) q^{57} -0.183067 q^{58} +(-6.80642 - 3.55987i) q^{59} -0.418794 q^{60} +(0.309567 - 0.776955i) q^{61} +(-5.72909 - 0.623076i) q^{62} +(3.36910 + 3.19138i) q^{63} +(0.647386 - 0.762162i) q^{64} +(-0.927679 + 1.74979i) q^{65} +(3.94486 + 2.37354i) q^{66} +(7.12726 - 3.29742i) q^{67} +(-5.55551 - 1.22286i) q^{68} +(2.62290 + 4.94731i) q^{69} +(-0.105218 + 1.94063i) q^{70} +(-7.34790 - 8.65061i) q^{71} +(0.976621 - 0.214970i) q^{72} +(9.08264 - 6.90445i) q^{73} +(8.59163 - 8.13843i) q^{74} +(0.261199 + 4.81754i) q^{75} +(2.25135 - 1.35459i) q^{76} +(11.9898 - 17.6836i) q^{77} +(1.26515 - 4.55667i) q^{78} +(-0.822754 + 0.0894799i) q^{79} +(0.333399 + 0.253443i) q^{80} +(0.907575 + 0.419889i) q^{81} +(-0.365726 - 0.539405i) q^{82} +(-17.2288 + 5.80506i) q^{83} +(-0.750776 - 4.57953i) q^{84} +(0.385415 - 2.35092i) q^{85} +(9.92784 + 3.34508i) q^{86} +(0.0489757 + 0.176394i) q^{87} +(-1.70407 - 4.27689i) q^{88} +(-0.921762 - 2.31345i) q^{89} +(0.112039 + 0.403529i) q^{90} +(-20.7971 - 7.00735i) q^{91} +(0.905913 - 5.52583i) q^{92} +(0.932329 + 5.68695i) q^{93} +(8.23873 - 2.77595i) q^{94} +(0.617507 + 0.910755i) q^{95} +(-0.907575 - 0.419889i) q^{96} +(-0.133237 - 0.101284i) q^{97} +(-14.4505 + 1.57159i) q^{98} +(1.23167 - 4.43606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{18}{29}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$2$	−0.370138	+	0.928977i	−0.261727	+	0.656886i
$3$	0.994138	+	0.108119i	0.573966	+	0.0624225i
$3$	0.994138	+	0.108119i	0.573966	+	0.0624225i
$4$	−0.725995	−	0.687699i	−0.362998	−	0.343850i
$5$	0.271121	−	0.319189i	0.121249	−	0.142745i	−0.698188	−	0.715914i	$-0.746010\pi$
$5$	0.271121	−	0.319189i	0.121249	−	0.142745i	0.819437	+	0.573169i	$0.194286\pi$
$6$	−0.468408	+	0.883512i	−0.191227	+	0.360692i
$7$	3.97639	+	2.39251i	1.50293	+	0.904284i	0.999182	+	0.0404351i	$0.0128744\pi$
$7$	3.97639	+	2.39251i	1.50293	+	0.904284i	0.503750	+	0.863849i	$0.331953\pi$
$8$	0.907575	−	0.419889i	0.320876	−	0.148453i
$9$	0.976621	+	0.214970i	0.325540	+	0.0716568i
$10$	0.196166	+	0.370009i	0.0620333	+	0.117007i
$11$	0.249248	−	4.59712i	0.0751512	−	1.38608i	−0.681286	−	0.732017i	$-0.738579\pi$
$11$	0.249248	−	4.59712i	0.0751512	−	1.38608i	0.756438	−	0.654066i	$-0.226938\pi$
$12$	−0.647386	−	0.762162i	−0.186884	−	0.220017i
$13$	−4.61848	+	1.01660i	−1.28094	+	0.281955i	−0.802756	−	0.596307i	$-0.796634\pi$
$13$	−4.61848	+	1.01660i	−1.28094	+	0.281955i	−0.478179	+	0.878262i	$0.658703\pi$
$14$	−3.69440	+	2.80841i	−0.987370	+	0.750579i
$15$	0.304042	−	0.288004i	0.0785034	−	0.0743624i
$16$	0.0541389	+	0.998533i	0.0135347	+	0.249633i
$17$	4.87423	−	2.93273i	1.18218	−	0.711291i	0.217842	−	0.975984i	$-0.430098\pi$
$17$	4.87423	−	2.93273i	1.18218	−	0.711291i	0.964333	+	0.264693i	$0.0852706\pi$
$18$	−0.561187	+	0.827689i	−0.132273	+	0.195088i
$19$	−0.702917	+	2.53168i	−0.161260	+	0.580807i	0.838116	+	0.545492i	$0.183657\pi$
$19$	−0.702917	+	2.53168i	−0.161260	+	0.580807i	−0.999376	+	0.0353149i	$0.988757\pi$
$20$	−0.416339	+	0.0452796i	−0.0930962	+	0.0101248i
$21$	3.69440	+	2.80841i	0.806184	+	0.612845i
$22$	4.17836	+	1.93311i	0.890829	+	0.412141i
$23$	3.14242	+	4.63472i	0.655240	+	0.966406i	0.999620	+	0.0275757i	$0.00877874\pi$
$23$	3.14242	+	4.63472i	0.655240	+	0.966406i	−0.344380	+	0.938830i	$0.611911\pi$
$24$	0.947653	−	0.319302i	0.193439	−	0.0651772i
$25$	0.780535	+	4.76105i	0.156107	+	0.952211i
$26$	0.765073	−	4.66674i	0.150043	−	0.915223i
$27$	0.947653	+	0.319302i	0.182376	+	0.0614496i
$28$	−1.24151	−	4.47151i	−0.234623	−	0.845036i
$29$	0.0677602	+	0.170065i	0.0125827	+	0.0315803i	0.935134	−	0.354295i	$-0.115279\pi$
$29$	0.0677602	+	0.170065i	0.0125827	+	0.0315803i	−0.922551	+	0.385875i	$0.873900\pi$
$30$	0.155012	+	0.389050i	0.0283011	+	0.0710304i
$31$	1.54173	+	5.55282i	0.276903	+	0.997315i	0.962933	+	0.269741i	$0.0869382\pi$
$31$	1.54173	+	5.55282i	0.276903	+	0.997315i	−0.686030	+	0.727574i	$0.740648\pi$
$32$	−0.947653	−	0.319302i	−0.167523	−	0.0564451i
$33$	0.744823	−	4.54322i	0.129657	−	0.790873i
$34$	0.920297	+	5.61356i	0.157830	+	0.962718i
$35$	1.84175	−	0.620556i	0.311312	−	0.104893i
$36$	−0.561187	−	0.827689i	−0.0935312	−	0.137948i
$37$	−10.7405	−	4.96909i	−1.76573	−	0.816913i	−0.980179	−	0.198112i	$-0.936519\pi$
$37$	−10.7405	−	4.96909i	−1.76573	−	0.816913i	−0.785548	−	0.618800i	$-0.787619\pi$
$38$	−2.09169	−	1.59006i	−0.339318	−	0.257943i
$39$	−4.70132	+	0.511299i	−0.752813	+	0.0818734i
$40$	0.112039	−	0.403529i	0.0177149	−	0.0638035i
$41$	−0.365726	+	0.539405i	−0.0571168	+	0.0842409i	−0.855175	−	0.518339i	$-0.826550\pi$
$41$	−0.365726	+	0.539405i	−0.0571168	+	0.0842409i	0.798058	+	0.602580i	$0.205861\pi$
$42$	−3.97639	+	2.39251i	−0.613570	+	0.369173i
$43$	−0.567172	−	10.4609i	−0.0864929	−	1.59527i	−0.643953	−	0.765065i	$-0.722707\pi$
$43$	−0.567172	−	10.4609i	−0.0864929	−	1.59527i	0.557460	−	0.830203i	$-0.311776\pi$
$44$	−3.34239	+	3.16608i	−0.503884	+	0.477304i
$45$	0.333399	−	0.253443i	0.0497001	−	0.0377811i
$46$	−5.46868	+	1.20375i	−0.806312	+	0.177483i
$47$	−5.62826	−	6.62610i	−0.820967	−	0.966517i	0.178883	−	0.983870i	$-0.442752\pi$
$47$	−5.62826	−	6.62610i	−0.820967	−	0.966517i	−0.999849	+	0.0173538i	$0.994476\pi$
$48$	−0.0541389	+	0.998533i	−0.00781428	+	0.144126i
$49$	6.80867	+	12.8425i	0.972667	+	1.83464i
$50$	−4.71182	−	1.03715i	−0.666351	−	0.146675i
$51$	5.16274	−	2.38854i	0.722929	−	0.334462i
$52$	4.05211	+	2.43807i	0.561927	+	0.338100i
$53$	−1.09486	+	2.06513i	−0.150391	+	0.283668i	−0.947249	−	0.320500i	$-0.896149\pi$
$53$	−1.09486	+	2.06513i	−0.150391	+	0.283668i	0.796858	+	0.604167i	$0.206494\pi$
$54$	−0.647386	+	0.762162i	−0.0880981	+	0.103717i
$55$	−1.39977	−	1.32593i	−0.188745	−	0.178789i
$56$	4.61346	+	0.501744i	0.616499	+	0.0670484i
$57$	−0.972519	+	2.44084i	−0.128813	+	0.323297i
$58$	−0.183067			−0.0240379
$59$	−6.80642	−	3.55987i	−0.886120	−	0.463455i
$59$	−6.80642	−	3.55987i	−0.886120	−	0.463455i
$60$	−0.418794			−0.0540660
$61$	0.309567	−	0.776955i	0.0396360	−	0.0994789i	−0.907826	−	0.419347i	$-0.862259\pi$
$61$	0.309567	−	0.776955i	0.0396360	−	0.0994789i	0.947462	+	0.319868i	$0.103638\pi$
$62$	−5.72909	−	0.623076i	−0.727595	−	0.0791307i
$63$	3.36910	+	3.19138i	0.424467	+	0.402076i
$64$	0.647386	−	0.762162i	0.0809233	−	0.0952703i
$65$	−0.927679	+	1.74979i	−0.115064	+	0.217035i
$66$	3.94486	+	2.37354i	0.485578	+	0.292163i
$67$	7.12726	−	3.29742i	0.870734	−	0.402844i	0.0669433	−	0.997757i	$-0.478675\pi$
$67$	7.12726	−	3.29742i	0.870734	−	0.402844i	0.803791	+	0.594912i	$0.202813\pi$
$68$	−5.55551	−	1.22286i	−0.673704	−	0.148294i
$69$	2.62290	+	4.94731i	0.315760	+	0.595586i
$70$	−0.105218	+	1.94063i	−0.0125759	+	0.231950i
$71$	−7.34790	−	8.65061i	−0.872035	−	1.02664i	−0.999395	−	0.0347825i	$-0.988926\pi$
$71$	−7.34790	−	8.65061i	−0.872035	−	1.02664i	0.127360	−	0.991857i	$-0.459350\pi$
$72$	0.976621	−	0.214970i	0.115096	−	0.0253345i
$73$	9.08264	−	6.90445i	1.06304	−	0.808104i	0.0809912	−	0.996715i	$-0.474191\pi$
$73$	9.08264	−	6.90445i	1.06304	−	0.808104i	0.982052	+	0.188610i	$0.0603983\pi$
$74$	8.59163	−	8.13843i	0.998757	−	0.946073i
$75$	0.261199	+	4.81754i	0.0301607	+	0.556281i
$76$	2.25135	−	1.35459i	0.258247	−	0.155382i
$77$	11.9898	−	17.6836i	1.36636	−	2.01523i
$78$	1.26515	−	4.55667i	0.143250	−	0.515941i
$79$	−0.822754	+	0.0894799i	−0.0925670	+	0.0100673i	−0.154285	−	0.988026i	$-0.549307\pi$
$79$	−0.822754	+	0.0894799i	−0.0925670	+	0.0100673i	0.0617183	+	0.998094i	$0.480342\pi$
$80$	0.333399	+	0.253443i	0.0372751	+	0.0283358i
$81$	0.907575	+	0.419889i	0.100842	+	0.0466543i
$82$	−0.365726	−	0.539405i	−0.0403876	−	0.0595673i
$83$	−17.2288	+	5.80506i	−1.89111	+	0.637188i	−0.924306	+	0.381651i	$0.875355\pi$
$83$	−17.2288	+	5.80506i	−1.89111	+	0.637188i	−0.966799	+	0.255536i	$0.917748\pi$
$84$	−0.750776	−	4.57953i	−0.0819164	−	0.499668i
$85$	0.385415	−	2.35092i	0.0418041	−	0.254994i
$86$	9.92784	+	3.34508i	1.07055	+	0.360709i
$87$	0.0489757	+	0.176394i	0.00525074	+	0.0189115i
$88$	−1.70407	−	4.27689i	−0.181654	−	0.455918i
$89$	−0.921762	−	2.31345i	−0.0977066	−	0.245225i	0.871996	−	0.489513i	$-0.162825\pi$
$89$	−0.921762	−	2.31345i	−0.0977066	−	0.245225i	−0.969703	+	0.244287i	$0.921446\pi$
$90$	0.112039	+	0.403529i	0.0118100	+	0.0425357i
$91$	−20.7971	−	7.00735i	−2.18013	−	0.734570i
$92$	0.905913	−	5.52583i	0.0944480	−	0.576107i
$93$	0.932329	+	5.68695i	0.0966780	+	0.589710i
$94$	8.23873	−	2.77595i	0.849760	−	0.286318i
$95$	0.617507	+	0.910755i	0.0633549	+	0.0934415i
$96$	−0.907575	−	0.419889i	−0.0926290	−	0.0428548i
$97$	−0.133237	−	0.101284i	−0.0135282	−	0.0102839i	0.598388	−	0.801206i	$-0.295808\pi$
$97$	−0.133237	−	0.101284i	−0.0135282	−	0.0102839i	−0.611916	+	0.790922i	$0.709601\pi$
$98$	−14.4505	+	1.57159i	−1.45973	+	0.158755i
$99$	1.23167	−	4.43606i	0.123787	−	0.445841i
$100$	2.70751	−	3.99328i	0.270751	−	0.399328i
$101$	−11.5522	+	6.95075i	−1.14949	+	0.691625i	−0.957118	−	0.289697i	$-0.906445\pi$
$101$	−11.5522	+	6.95075i	−1.14949	+	0.691625i	−0.192371	+	0.981322i	$0.561618\pi$
$102$	0.307969	+	5.68016i	0.0304935	+	0.562419i
$103$	−4.98640	+	4.72337i	−0.491325	+	0.465408i	−0.892794	−	0.450465i	$-0.851258\pi$
$103$	−4.98640	+	4.72337i	−0.491325	+	0.465408i	0.401469	+	0.915872i	$0.368500\pi$
$104$	−3.76476	+	2.86189i	−0.369165	+	0.280632i
$105$	1.89804	−	0.417791i	0.185230	−	0.0407722i
$106$	−1.51321	−	1.78149i	−0.146976	−	0.173033i
$107$	−0.0196142	+	0.361762i	−0.00189617	+	0.0349729i	−0.999328	−	0.0366442i	$-0.988333\pi$
$107$	−0.0196142	+	0.361762i	−0.00189617	+	0.0349729i	0.997432	+	0.0716170i	$0.0228159\pi$
$108$	−0.468408	−	0.883512i	−0.0450726	−	0.0850160i
$109$	12.5291	+	2.75785i	1.20007	+	0.264154i	0.769644	−	0.638473i	$-0.220434\pi$
$109$	12.5291	+	2.75785i	1.20007	+	0.264154i	0.430422	+	0.902628i	$0.358365\pi$
$110$	1.74987	−	0.809576i	0.166844	−	0.0771900i
$111$	−10.1403	−	6.10121i	−0.962474	−	0.579101i
$112$	−2.17373	+	4.10008i	−0.205398	+	0.387421i
$113$	4.17130	−	4.91084i	0.392403	−	0.461973i	−0.530115	−	0.847926i	$-0.677851\pi$
$113$	4.17130	−	4.91084i	0.392403	−	0.461973i	0.922519	+	0.385953i	$0.126127\pi$
$114$	−1.90752	−	1.80690i	−0.178655	−	0.169231i
$115$	2.33133	+	0.253547i	0.217397	+	0.0236434i
$116$	0.0677602	−	0.170065i	0.00629137	−	0.0157902i
$117$	−4.72904			−0.437200
$118$	5.82635	−	5.00536i	0.536359	−	0.460781i
$119$	26.3984			2.41994
$120$	0.155012	−	0.389050i	0.0141505	−	0.0355152i
$121$	−10.1358	−	1.10234i	−0.921440	−	0.100213i
$122$	0.607190	+	0.575161i	0.0549724	+	0.0520727i
$123$	−0.421902	+	0.496701i	−0.0380416	+	0.0447860i
$124$	2.69938	−	5.09157i	0.242411	−	0.457236i
$125$	3.52553	+	2.12124i	0.315333	+	0.189729i
$126$	−4.21175	+	1.94856i	−0.375213	+	0.173592i
$127$	−11.6866	−	2.57240i	−1.03701	−	0.228264i	−0.336336	−	0.941742i	$-0.609188\pi$
$127$	−11.6866	−	2.57240i	−1.03701	−	0.228264i	−0.700678	+	0.713478i	$0.747119\pi$
$128$	0.468408	+	0.883512i	0.0414018	+	0.0780922i
$129$	0.567172	−	10.4609i	0.0499367	−	0.921029i
$130$	−1.28214	−	1.50946i	−0.112451	−	0.132388i
$131$	−0.349962	+	0.0770324i	−0.0305763	+	0.00673035i	−0.230232	−	0.973136i	$-0.573949\pi$
$131$	−0.349962	+	0.0770324i	−0.0305763	+	0.00673035i	0.199656	+	0.979866i	$0.436018\pi$
$132$	−3.66511	+	2.78614i	−0.319007	+	0.242503i
$133$	−8.85214	+	8.38519i	−0.767578	+	0.727088i
$134$	0.425157	+	7.84156i	0.0367280	+	0.677408i
$135$	0.358846	−	0.215911i	0.0308846	−	0.0185826i
$136$	3.19231	−	4.70831i	0.273739	−	0.403734i
$137$	2.23819	−	8.06124i	0.191222	−	0.688718i	−0.804303	−	0.594219i	$-0.797461\pi$
$137$	2.23819	−	8.06124i	0.191222	−	0.688718i	0.995525	−	0.0944993i	$-0.0301250\pi$
$138$	−5.56677	+	0.605422i	−0.473875	+	0.0515370i
$139$	−11.7101	−	8.90180i	−0.993239	−	0.755040i	−0.0236349	−	0.999721i	$-0.507524\pi$
$139$	−11.7101	−	8.90180i	−0.993239	−	0.755040i	−0.969604	+	0.244680i	$0.921317\pi$
$140$	−1.76385	−	0.816046i	−0.149073	−	0.0689685i
$141$	−4.87886	−	7.19578i	−0.410874	−	0.605994i
$142$	10.7560	−	3.62410i	0.902620	−	0.304128i
$143$	3.52230	+	21.4851i	0.294549	+	1.79667i
$144$	−0.161782	+	0.986827i	−0.0134818	+	0.0822355i
$145$	0.0726541	+	0.0244800i	0.00603360	+	0.00203295i
$146$	3.05224	+	10.9932i	0.252605	+	0.909801i
$147$	5.38024	+	13.5034i	0.443755	+	1.11374i
$148$	4.38032	+	10.9938i	0.360060	+	0.903682i
$149$	2.80556	+	10.1047i	0.229841	+	0.827811i	0.985041	+	0.172318i	$0.0551256\pi$
$149$	2.80556	+	10.1047i	0.229841	+	0.827811i	−0.755201	+	0.655494i	$0.772461\pi$
$150$	−4.57206	−	1.54051i	−0.373307	−	0.125782i
$151$	0.538016	−	3.28175i	0.0437831	−	0.267065i	−0.955859	−	0.293827i	$-0.905071\pi$
$151$	0.538016	−	3.28175i	0.0437831	−	0.267065i	0.999642	+	0.0267613i	$0.00851941\pi$
$152$	0.425074	+	2.59284i	0.0344781	+	0.210307i
$153$	5.39073	−	1.81635i	0.435814	−	0.146843i
$154$	11.9898	+	17.6836i	0.966163	+	1.42498i
$155$	2.19039	+	1.01338i	0.175936	+	0.0813969i
$156$	3.76476	+	2.86189i	0.301422	+	0.229135i
$157$	15.1369	−	1.64623i	1.20805	−	0.131384i	0.518153	−	0.855288i	$-0.326620\pi$
$157$	15.1369	−	1.64623i	1.20805	−	0.131384i	0.689900	+	0.723904i	$0.257654\pi$
$158$	0.221408	−	0.797439i	0.0176143	−	0.0634408i
$159$	−1.31173	+	1.93465i	−0.104027	+	0.153428i
$160$	−0.358846	+	0.215911i	−0.0283693	+	0.0170692i
$161$	1.40684	+	25.9477i	0.110875	+	2.04497i
$162$	−0.725995	+	0.687699i	−0.0570396	+	0.0540308i
$163$	−4.92449	+	3.74350i	−0.385716	+	0.293213i	−0.780005	−	0.625773i	$-0.784784\pi$
$163$	−4.92449	+	3.74350i	−0.385716	+	0.293213i	0.394290	+	0.918986i	$0.370991\pi$
$164$	0.636464	−	0.140096i	0.0496995	−	0.0109397i
$165$	−1.24821	−	1.46950i	−0.0971728	−	0.114401i
$166$	0.984272	−	18.1538i	0.0763943	−	1.40901i
$167$	−2.48950	−	4.69570i	−0.192643	−	0.363364i	0.768308	−	0.640080i	$-0.221099\pi$
$167$	−2.48950	−	4.69570i	−0.192643	−	0.363364i	−0.960952	+	0.276716i	$0.910754\pi$
$168$	4.53217	+	0.997605i	0.349664	+	0.0769669i
$169$	8.49837	−	3.93176i	0.653721	−	0.302443i
$170$	2.04130	+	1.22821i	0.156560	+	0.0941993i
$171$	−1.23072	+	2.32138i	−0.0941155	+	0.177521i
$172$	−6.78217	+	7.98459i	−0.517136	+	0.608819i
$173$	4.74674	+	4.49635i	0.360888	+	0.341851i	0.846563	−	0.532288i	$-0.178668\pi$
$173$	4.74674	+	4.49635i	0.360888	+	0.341851i	−0.485675	+	0.874139i	$0.661426\pi$
$174$	−0.181994	−	0.0197931i	−0.0137969	−	0.00150051i
$175$	−8.28717	+	20.7992i	−0.626451	+	1.57227i
$176$	4.60387			0.347030
$177$	−6.38163	−	4.27490i	−0.479673	−	0.321321i
$178$	2.49032			0.186657
$179$	−4.66259	+	11.7022i	−0.348498	+	0.874665i	0.645347	+	0.763889i	$0.276713\pi$
$179$	−4.66259	+	11.7022i	−0.348498	+	0.874665i	−0.993845	+	0.110775i	$0.964667\pi$
$180$	−0.416339	−	0.0452796i	−0.0310321	−	0.00337494i
$181$	8.36630	+	7.92498i	0.621862	+	0.589059i	0.932367	−	0.361513i	$-0.117740\pi$
$181$	8.36630	+	7.92498i	0.621862	+	0.589059i	−0.310505	+	0.950572i	$0.600498\pi$
$182$	14.2075	−	16.7263i	1.05313	−	1.23984i
$183$	0.391756	−	0.738930i	0.0289594	−	0.0546233i
$184$	4.79805	+	2.88689i	0.353717	+	0.212824i
$185$	−4.49805	+	2.08102i	−0.330704	+	0.153000i
$186$	−5.62814	−	1.23885i	−0.412675	−	0.0908367i
$187$	−12.2672	−	23.1384i	−0.897067	−	1.69205i
$188$	−0.470674	+	8.68108i	−0.0343274	+	0.633133i
$189$	3.00430	+	3.53694i	0.218531	+	0.257274i
$190$	−1.07463	+	0.236545i	−0.0779621	+	0.0171608i
$191$	15.0127	−	11.4124i	1.08628	−	0.825769i	0.100690	−	0.994918i	$-0.467895\pi$
$191$	15.0127	−	11.4124i	1.08628	−	0.825769i	0.985591	+	0.169149i	$0.0541018\pi$
$192$	0.725995	−	0.687699i	0.0523942	−	0.0496304i
$193$	0.418147	+	7.71226i	0.0300989	+	0.555141i	0.974228	+	0.225565i	$0.0724229\pi$
$193$	0.418147	+	7.71226i	0.0300989	+	0.555141i	−0.944129	+	0.329576i	$0.893094\pi$
$194$	0.143407	−	0.0862850i	0.0102960	−	0.00619490i
$195$	−1.11143	+	1.63923i	−0.0795909	+	0.117388i
$196$	3.88873	−	14.0059i	0.277766	−	1.00042i
$197$	−0.707049	+	0.0768962i	−0.0503752	+	0.00547863i	−0.133272	−	0.991080i	$-0.542548\pi$
$197$	−0.707049	+	0.0768962i	−0.0503752	+	0.00547863i	0.0828967	+	0.996558i	$0.473583\pi$
$198$	3.66511	+	2.78614i	0.260468	+	0.198003i
$199$	−12.5746	−	5.81761i	−0.891387	−	0.412400i	−0.0799224	−	0.996801i	$-0.525467\pi$
$199$	−12.5746	−	5.81761i	−0.891387	−	0.412400i	−0.811465	+	0.584402i	$0.801329\pi$
$200$	2.70751	+	3.99328i	0.191450	+	0.282367i
$201$	7.44200	−	2.50750i	0.524918	−	0.176865i
$202$	−2.18116	−	13.3045i	−0.153466	−	0.936101i
$203$	−0.137442	+	0.838362i	−0.00964657	+	0.0588415i
$204$	−5.39073	−	1.81635i	−0.377426	−	0.127170i
$205$	0.0730159	+	0.262980i	0.00509965	+	0.0183673i
$206$	−2.54224	−	6.38055i	−0.177127	−	0.444554i
$207$	2.07262	+	5.20189i	0.144057	+	0.361556i
$208$	−1.26515	−	4.55667i	−0.0877225	−	0.315948i
$209$	11.4632	+	3.86241i	0.792928	+	0.267168i
$210$	−0.314420	+	1.91788i	−0.0216970	+	0.132346i
$211$	3.70978	+	22.6287i	0.255392	+	1.55782i	0.733604	+	0.679577i	$0.237837\pi$
$211$	3.70978	+	22.6287i	0.255392	+	1.55782i	−0.478212	+	0.878244i	$0.658715\pi$
$212$	2.21506	−	0.746339i	0.152131	−	0.0512588i
$213$	−6.36953	−	9.39435i	−0.436433	−	0.643690i
$214$	−0.328809	−	0.152123i	−0.0224769	−	0.0103989i
$215$	−3.49276	−	2.65513i	−0.238205	−	0.181078i
$216$	0.994138	−	0.108119i	0.0676425	−	0.00735657i
$217$	−7.15466	+	25.7687i	−0.485690	+	1.74930i
$218$	−7.19946	+	10.6184i	−0.487609	+	0.719170i
$219$	9.77590	−	5.88197i	0.660594	−	0.397466i
$220$	0.104384	+	1.92524i	0.00703754	+	0.129800i
$221$	−19.5301	+	18.4999i	−1.31374	+	1.24444i
$222$	9.42119	−	7.16180i	0.632309	−	0.480669i
$223$	−7.51338	+	1.65382i	−0.503133	+	0.110748i	−0.459283	−	0.888290i	$-0.651894\pi$
$223$	−7.51338	+	1.65382i	−0.503133	+	0.110748i	−0.0438505	+	0.999038i	$0.513963\pi$
$224$	−3.00430	−	3.53694i	−0.200733	−	0.236322i
$225$	−0.261199	+	4.81754i	−0.0174133	+	0.321169i
$226$	3.01810	+	5.69273i	0.200761	+	0.378675i
$227$	11.9701	+	2.63482i	0.794485	+	0.174879i	0.593626	−	0.804741i	$-0.297696\pi$
$227$	11.9701	+	2.63482i	0.794485	+	0.174879i	0.200859	+	0.979620i	$0.435627\pi$
$228$	2.38461	−	1.10324i	0.157925	−	0.0730637i
$229$	21.4187	+	12.8872i	1.41539	+	0.851610i	0.998358	−	0.0572841i	$-0.0182441\pi$
$229$	21.4187	+	12.8872i	1.41539	+	0.851610i	0.417028	+	0.908894i	$0.363072\pi$
$230$	−1.09845	+	2.07190i	−0.0724298	+	0.136617i
$231$	13.8314	−	16.2836i	0.910040	−	1.07138i
$232$	0.132906	+	0.125895i	0.00872571	+	0.00826543i
$233$	−23.4871	−	2.55438i	−1.53869	−	0.167343i	−0.700872	−	0.713287i	$-0.747206\pi$
$233$	−23.4871	−	2.55438i	−1.53869	−	0.167343i	−0.837822	+	0.545944i	$0.816171\pi$
$234$	1.75040	−	4.39317i	0.114427	−	0.287190i
$235$	−3.64092			−0.237507
$236$	2.49331	+	7.26522i	0.162301	+	0.472925i
$237$	−0.827605			−0.0537587
$238$	−9.77106	+	24.5235i	−0.633364	+	1.58962i
$239$	−0.167170	−	0.0181808i	−0.0108133	−	0.00117602i	0.102711	−	0.994711i	$-0.467248\pi$
$239$	−0.167170	−	0.0181808i	−0.0108133	−	0.00117602i	−0.113524	+	0.993535i	$0.536214\pi$
$240$	0.304042	+	0.288004i	0.0196258	+	0.0185906i
$241$	−1.36322	+	1.60490i	−0.0878125	+	0.103381i	−0.804313	−	0.594205i	$-0.797467\pi$
$241$	−1.36322	+	1.60490i	−0.0878125	+	0.103381i	0.716501	+	0.697586i	$0.245743\pi$
$242$	4.77571	−	9.00794i	0.306994	−	0.579052i
$243$	0.856857	+	0.515554i	0.0549674	+	0.0330728i
$244$	−0.759056	+	0.351177i	−0.0485936	+	0.0224818i
$245$	5.94516	+	1.30863i	0.379822	+	0.0836052i
$246$	−0.305262	−	0.575785i	−0.0194628	−	0.0367107i
$247$	0.672693	−	12.4071i	0.0428024	−	0.789444i
$248$	3.73080	+	4.39224i	0.236906	+	0.278908i
$249$	−17.7554	+	3.90827i	−1.12520	+	0.247676i
$250$	−3.27551	+	2.48998i	−0.207162	+	0.157480i
$251$	13.5817	−	12.8653i	0.857271	−	0.812051i	−0.126409	−	0.991978i	$-0.540345\pi$
$251$	13.5817	−	12.8653i	0.857271	−	0.812051i	0.983680	+	0.179928i	$0.0575864\pi$
$252$	−0.251240	−	4.63386i	−0.0158267	−	0.291906i
$253$	22.0896	−	13.2909i	1.38876	−	0.835590i
$254$	6.71534	−	9.90439i	0.421358	−	0.621457i
$255$	0.637335	−	2.29547i	0.0399115	−	0.143748i
$256$	−0.994138	+	0.108119i	−0.0621336	+	0.00675744i
$257$	−8.07458	−	6.13814i	−0.503679	−	0.382887i	0.322256	−	0.946653i	$-0.395559\pi$
$257$	−8.07458	−	6.13814i	−0.503679	−	0.382887i	−0.825935	+	0.563766i	$0.809352\pi$
$258$	9.50798	+	4.39886i	0.591941	+	0.273861i
$259$	−30.8198	−	45.4558i	−1.91505	−	2.82448i
$260$	1.87682	−	0.632374i	0.116395	−	0.0392182i
$261$	0.0296170	+	0.180656i	0.00183325	+	0.0111823i
$262$	0.0579729	−	0.353619i	0.00358158	−	0.0218466i
$263$	−21.4752	−	7.23582i	−1.32422	−	0.446180i	−0.433669	−	0.901072i	$-0.642781\pi$
$263$	−21.4752	−	7.23582i	−1.32422	−	0.446180i	−0.890546	+	0.454892i	$0.849678\pi$
$264$	−1.23167	−	4.43606i	−0.0758038	−	0.273020i
$265$	0.362326	+	0.909369i	0.0222575	+	0.0558621i
$266$	−4.51313	−	11.3271i	−0.276718	−	0.694510i
$267$	−0.666231	−	2.39955i	−0.0407727	−	0.146850i
$268$	−7.44200	−	2.50750i	−0.454592	−	0.153170i
$269$	−0.598502	+	3.65070i	−0.0364913	+	0.222587i	−0.998776	−	0.0494563i	$-0.984251\pi$
$269$	−0.598502	+	3.65070i	−0.0364913	+	0.222587i	0.962285	+	0.272043i	$0.0876994\pi$
$270$	0.0677533	+	0.413277i	0.00412333	+	0.0251512i
$271$	17.8566	−	6.01660i	1.08471	−	0.365483i	0.280519	−	0.959849i	$-0.409493\pi$
$271$	17.8566	−	6.01660i	1.08471	−	0.365483i	0.804195	+	0.594366i	$0.202597\pi$
$272$	3.19231	+	4.70831i	0.193562	+	0.285483i
$273$	−19.9175	−	9.21484i	−1.20546	−	0.557707i
$274$	6.66027	+	5.06300i	0.402361	+	0.305867i
$275$	22.0817	−	2.40153i	1.33157	−	0.144817i
$276$	1.49805	−	5.39549i	0.0901720	−	0.324770i
$277$	−2.88243	+	4.25126i	−0.173188	+	0.255434i	−0.904370	−	0.426749i	$-0.859659\pi$
$277$	−2.88243	+	4.25126i	−0.173188	+	0.255434i	0.731182	+	0.682183i	$0.238969\pi$
$278$	12.6039	−	7.58353i	0.755933	−	0.454830i
$279$	0.311996	+	5.75442i	0.0186787	+	0.344508i
$280$	1.41096	−	1.33653i	0.0843209	−	0.0798730i
$281$	14.2941	−	10.8661i	0.852713	−	0.648216i	−0.0847110	−	0.996406i	$-0.526997\pi$
$281$	14.2941	−	10.8661i	0.852713	−	0.648216i	0.937424	+	0.348190i	$0.113204\pi$
$282$	8.49057	−	1.86892i	0.505606	−	0.111292i
$283$	7.51574	+	8.84821i	0.446764	+	0.525972i	0.938735	−	0.344640i	$-0.111999\pi$
$283$	7.51574	+	8.84821i	0.446764	+	0.525972i	−0.491970	+	0.870612i	$0.663723\pi$
$284$	−0.614482	+	11.3335i	−0.0364628	+	0.672517i
$285$	0.515417	+	0.972180i	0.0305307	+	0.0575870i
$286$	−21.2629	−	4.68031i	−1.25730	−	0.276753i
$287$	−2.74480	+	1.26988i	−0.162020	+	0.0749586i
$288$	−0.856857	−	0.515554i	−0.0504908	−	0.0303793i
$289$	7.19430	−	13.5699i	0.423194	−	0.798229i
$290$	−0.0496334	+	0.0584330i	−0.00291458	+	0.00343130i
$291$	−0.121505	−	0.115096i	−0.00712277	−	0.00674704i
$292$	−11.3421	−	1.23353i	−0.663749	−	0.0721870i
$293$	−5.51956	+	13.8530i	−0.322456	+	0.809303i	0.674987	+	0.737830i	$0.264149\pi$
$293$	−5.51956	+	13.8530i	−0.322456	+	0.809303i	−0.997443	+	0.0714734i	$0.977230\pi$
$294$	−14.5358			−0.847742
$295$	−2.98163	+	1.20738i	−0.173597	+	0.0702962i
$296$	−11.8343			−0.687854
$297$	1.70407	−	4.27689i	0.0988800	−	0.248170i
$298$	−10.4255	−	1.13384i	−0.603933	−	0.0656817i
$299$	−19.2249	−	18.2108i	−1.11180	−	1.05316i
$300$	3.12339	−	3.67714i	0.180329	−	0.212300i
$301$	22.7725	−	42.9534i	1.31258	−	2.47579i
$302$	2.84953	+	1.71451i	0.163972	+	0.0986588i
$303$	−12.2360	+	5.66098i	−0.702941	+	0.325215i
$304$	−2.56602	−	0.564824i	−0.147171	−	0.0323949i
$305$	−0.164065	−	0.309459i	−0.00939433	−	0.0177196i
$306$	−0.307969	+	5.68016i	−0.0176054	+	0.324713i
$307$	4.29470	+	5.05611i	0.245112	+	0.288568i	0.870936	−	0.491396i	$-0.163513\pi$
$307$	4.29470	+	5.05611i	0.245112	+	0.288568i	−0.625825	+	0.779964i	$0.715237\pi$
$308$	−20.8655	+	4.59284i	−1.18892	+	0.261702i
$309$	−5.46786	+	4.15656i	−0.311056	+	0.236458i
$310$	−1.75216	+	1.65973i	−0.0995158	+	0.0942664i
$311$	1.37621	+	25.3827i	0.0780377	+	1.43932i	0.731231	+	0.682130i	$0.238946\pi$
$311$	1.37621	+	25.3827i	0.0780377	+	1.43932i	−0.653193	+	0.757191i	$0.726571\pi$
$312$	−4.05211	+	2.43807i	−0.229406	+	0.138029i
$313$	4.94144	−	7.28808i	0.279307	−	0.411946i	−0.661998	−	0.749506i	$-0.730291\pi$
$313$	4.94144	−	7.28808i	0.279307	−	0.411946i	0.941304	+	0.337560i	$0.109601\pi$
$314$	−4.07342	+	14.6711i	−0.229876	+	0.827940i
$315$	1.93209	−	0.210127i	0.108861	−	0.0118393i
$316$	0.658851	+	0.500845i	0.0370632	+	0.0281747i
$317$	12.8272	+	5.93449i	0.720446	+	0.333314i	0.745622	−	0.666369i	$-0.232152\pi$
$317$	12.8272	+	5.93449i	0.720446	+	0.333314i	−0.0251756	+	0.999683i	$0.508015\pi$
$318$	−1.31173	−	1.93465i	−0.0735579	−	0.108490i
$319$	0.798699	−	0.269113i	0.0447185	−	0.0150674i
$320$	−0.0677533	−	0.413277i	−0.00378752	−	0.0231029i
$321$	−0.0586126	+	0.357521i	−0.00327143	+	0.0199549i
$322$	−24.6255	−	8.29731i	−1.37233	−	0.462391i
$323$	3.99854	+	14.4015i	0.222485	+	0.801318i
$324$	−0.370138	−	0.928977i	−0.0205632	−	0.0516098i
$325$	−8.44499	−	21.1953i	−0.468444	−	1.17571i
$326$	−1.65488	−	5.96035i	−0.0916554	−	0.330113i
$327$	12.1574	+	4.09632i	0.672308	+	0.226527i
$328$	−0.105433	+	0.643115i	−0.00582158	+	0.0355101i
$329$	−6.52711	−	39.8136i	−0.359851	−	2.19500i
$330$	1.82714	−	0.615636i	0.100581	−	0.0338896i
$331$	2.10381	+	3.10289i	0.115636	+	0.170550i	0.881102	−	0.472926i	$-0.156802\pi$
$331$	2.10381	+	3.10289i	0.115636	+	0.170550i	−0.765467	+	0.643476i	$0.777492\pi$
$332$	16.5002	+	7.63379i	0.905564	+	0.418959i
$333$	−9.42119	−	7.16180i	−0.516278	−	0.392464i
$334$	5.28365	−	0.574632i	0.289109	−	0.0314424i
$335$	0.879853	−	3.16894i	0.0480715	−	0.173138i
$336$	−2.60428	+	3.84103i	−0.142075	+	0.209545i
$337$	−21.7449	+	13.0835i	−1.18452	+	0.712703i	−0.964832	−	0.262867i	$-0.915332\pi$
$337$	−21.7449	+	13.0835i	−1.18452	+	0.712703i	−0.219689	+	0.975570i	$0.570504\pi$
$338$	0.506947	+	9.35008i	0.0275743	+	0.508578i
$339$	4.67781	−	4.43105i	0.254064	−	0.240662i
$340$	−1.89654	+	1.44171i	−0.102854	+	0.0781878i
$341$	25.9112	−	5.70349i	1.40317	−	0.308861i
$342$	−1.70097	−	2.00254i	−0.0919782	−	0.108285i
$343$	−1.89329	+	34.9196i	−0.102228	+	1.88548i
$344$	−4.90716	−	9.25588i	−0.264576	−	0.499044i
$345$	2.29025	+	0.504121i	0.123303	+	0.0271410i
$346$	−5.93395	+	2.74534i	−0.319011	+	0.147590i
$347$	9.73935	+	5.85997i	0.522836	+	0.314580i	0.752392	−	0.658715i	$-0.228900\pi$
$347$	9.73935	+	5.85997i	0.522836	+	0.314580i	−0.229556	+	0.973295i	$0.573727\pi$
$348$	0.0857502	−	0.161742i	0.00459670	−	0.00867029i
$349$	−18.4145	+	21.6792i	−0.985706	+	1.16046i	0.00133611	+	0.999999i	$0.499575\pi$
$349$	−18.4145	+	21.6792i	−0.985706	+	1.16046i	−0.987042	+	0.160463i	$0.948701\pi$
$350$	−16.2546	−	15.3972i	−0.868845	−	0.823014i
$351$	−4.70132	−	0.511299i	−0.250938	−	0.0272911i
$352$	−1.70407	+	4.27689i	−0.0908271	+	0.227959i
$353$	0.856291			0.0455757			0.0227879	−	0.999740i	$-0.492746\pi$
$353$	0.856291			0.0455757			0.0227879	+	0.999740i	$0.492746\pi$
$354$	6.33337	−	4.34608i	0.336615	−	0.230992i
$355$	−4.75335			−0.252282
$356$	−0.921762	+	2.31345i	−0.0488533	+	0.122613i
$357$	26.2437	+	2.85417i	1.38896	+	0.151059i
$358$	−9.14528	−	8.66287i	−0.483343	−	0.457847i
$359$	11.8778	−	13.9837i	0.626888	−	0.738030i	−0.353429	−	0.935461i	$-0.614984\pi$
$359$	11.8778	−	13.9837i	0.626888	−	0.738030i	0.980317	+	0.197432i	$0.0632601\pi$
$360$	0.196166	−	0.370009i	0.0103389	−	0.0195012i
$361$	10.3650	+	6.23640i	0.545525	+	0.328232i
$362$	−10.4588	+	4.83876i	−0.549703	+	0.254319i
$363$	−9.95724	−	2.19175i	−0.522619	−	0.115037i
$364$	10.2796	+	19.3894i	0.538799	+	1.01628i
$365$	0.258677	−	4.77102i	0.0135398	−	0.249727i
$366$	0.541445	+	0.637439i	0.0283018	+	0.0333194i
$367$	17.6749	−	3.89053i	0.922620	−	0.203084i	0.271833	−	0.962344i	$-0.412370\pi$
$367$	17.6749	−	3.89053i	0.922620	−	0.203084i	0.650787	+	0.759260i	$0.274439\pi$
$368$	−4.45780	+	3.38873i	−0.232379	+	0.176650i
$369$	−0.473131	+	0.448174i	−0.0246302	+	0.0233310i
$370$	−0.268319	−	4.94885i	−0.0139492	−	0.257279i
$371$	−9.29445	+	5.59228i	−0.482544	+	0.290337i
$372$	3.23405	−	4.76987i	0.167678	−	0.247306i
$373$	−8.44574	+	30.4188i	−0.437304	+	1.57503i	0.336552	+	0.941665i	$0.390739\pi$
$373$	−8.44574	+	30.4188i	−0.437304	+	1.57503i	−0.773856	+	0.633362i	$0.781675\pi$
$374$	26.0356	−	2.83154i	1.34627	−	0.146415i
$375$	3.27551	+	2.48998i	0.169147	+	0.128582i
$376$	−7.89030	−	3.65044i	−0.406911	−	0.188257i
$377$	−0.485838	−	0.716557i	−0.0250219	−	0.0369046i
$378$	−4.39774	+	1.48177i	−0.226195	+	0.0762141i
$379$	−6.14936	−	37.5094i	−0.315871	−	1.92673i	−0.371840	−	0.928297i	$-0.621273\pi$
$379$	−6.14936	−	37.5094i	−0.315871	−	1.92673i	0.0559686	−	0.998433i	$-0.482175\pi$
$380$	0.178018	−	1.08586i	0.00913215	−	0.0557036i
$381$	−11.3399	−	3.82086i	−0.580962	−	0.195749i
$382$	5.04504	+	18.1706i	0.258127	+	0.929689i
$383$	9.43984	+	23.6922i	0.482353	+	1.21062i	0.945875	+	0.324530i	$0.105206\pi$
$383$	9.43984	+	23.6922i	0.482353	+	1.21062i	−0.463522	+	0.886085i	$0.653415\pi$
$384$	0.370138	+	0.928977i	0.0188885	+	0.0474066i
$385$	−2.39372	−	8.62139i	−0.121995	−	0.439387i
$386$	−7.31929	−	2.46615i	−0.372542	−	0.125524i
$387$	1.69487	−	10.3382i	0.0861549	−	0.525522i
$388$	0.0270764	+	0.165159i	0.00137460	+	0.00838467i
$389$	23.6623	−	7.97275i	1.19972	−	0.404234i	0.352674	−	0.935746i	$-0.385272\pi$
$389$	23.6623	−	7.97275i	1.19972	−	0.404234i	0.847051	+	0.531512i	$0.178376\pi$
$390$	−1.11143	−	1.63923i	−0.0562793	−	0.0830057i
$391$	28.9093	+	13.3748i	1.46200	+	0.676395i
$392$	11.5718	+	8.79666i	0.584465	+	0.444299i
$393$	−0.356239	+	0.0387433i	−0.0179699	+	0.00195434i
$394$	0.190271	−	0.685294i	0.00958572	−	0.0345246i
$395$	−0.194505	+	0.286873i	−0.00978661	+	0.0144342i
$396$	−3.94486	+	2.37354i	−0.198237	+	0.119275i
$397$	−0.207403	−	3.82531i	−0.0104092	−	0.191987i	−0.999113	−	0.0421054i	$-0.986593\pi$
$397$	−0.207403	−	3.82531i	−0.0104092	−	0.191987i	0.988704	−	0.149882i	$-0.0478893\pi$
$398$	10.0588	−	9.52815i	0.504200	−	0.477603i
$399$	−9.70685	+	7.37895i	−0.485950	+	0.369410i
$400$	−4.71182	+	1.03715i	−0.235591	+	0.0518574i
$401$	−25.0943	−	29.5433i	−1.25315	−	1.47532i	−0.818274	−	0.574829i	$-0.805069\pi$
$401$	−25.0943	−	29.5433i	−1.25315	−	1.47532i	−0.434875	−	0.900491i	$-0.643207\pi$
$402$	−0.425157	+	7.84156i	−0.0212049	+	0.391102i
$403$	−12.7655	−	24.0782i	−0.635893	−	1.19942i
$404$	13.1669	+	2.89825i	0.655077	+	0.144193i
$405$	0.380087	−	0.175847i	0.0188867	−	0.00873790i
$406$	−0.727946	−	0.437991i	−0.0361274	−	0.0217371i
$407$	−25.5205	+	48.1368i	−1.26501	+	2.38605i
$408$	3.68266	−	4.33556i	0.182319	−	0.214642i
$409$	8.61969	+	8.16500i	0.426216	+	0.403733i	0.870512	−	0.492147i	$-0.163788\pi$
$409$	8.61969	+	8.16500i	0.426216	+	0.403733i	−0.444296	+	0.895880i	$0.646546\pi$
$410$	−0.271328	−	0.0295087i	−0.0133999	−	0.00145733i
$411$	3.09665	−	7.77199i	0.152746	−	0.383364i
$412$	6.86837			0.338380
$413$	−18.5479	−	30.4398i	−0.912684	−	1.49785i
$414$	−5.59959			−0.275205
$415$	−2.81818	+	7.07311i	−0.138339	+	0.347205i
$416$	4.70132	+	0.511299i	0.230501	+	0.0250685i
$417$	−10.6790	−	10.1157i	−0.522954	−	0.495368i
$418$	−7.83106	+	9.21944i	−0.383030	+	0.450938i
$419$	−5.87640	+	11.0841i	−0.287081	+	0.541492i	−0.984546	−	0.175127i	$-0.943967\pi$
$419$	−5.87640	+	11.0841i	−0.287081	+	0.541492i	0.697465	+	0.716619i	$0.254311\pi$
$420$	−1.66528	−	1.00197i	−0.0812576	−	0.0488911i
$421$	9.92154	−	4.59019i	0.483546	−	0.223712i	−0.162943	−	0.986636i	$-0.552099\pi$
$421$	9.92154	−	4.59019i	0.483546	−	0.223712i	0.646489	+	0.762923i	$0.276237\pi$
$422$	−22.3946	−	4.92943i	−1.09015	−	0.239961i
$423$	−4.07226	−	7.68110i	−0.198000	−	0.373468i
$424$	−0.126545	+	2.33398i	−0.00614556	+	0.113348i
$425$	17.7674	+	20.9174i	0.861845	+	1.01464i
$426$	11.0847	−	2.43994i	0.537057	−	0.118215i
$427$	3.08983	−	2.34883i	0.149527	−	0.113668i
$428$	0.263023	−	0.249149i	0.0127137	−	0.0120431i
$429$	1.17871	+	21.7399i	0.0569084	+	1.04961i
$430$	3.75936	−	2.26193i	0.181292	−	0.109080i
$431$	2.08548	−	3.07586i	0.100454	−	0.148159i	−0.774140	−	0.633014i	$-0.781817\pi$
$431$	2.08548	−	3.07586i	0.100454	−	0.148159i	0.874594	+	0.484855i	$0.161128\pi$
$432$	−0.267528	+	0.963550i	−0.0128715	+	0.0463588i
$433$	−12.7291	+	1.38438i	−0.611723	+	0.0665289i	−0.408736	−	0.912653i	$-0.634030\pi$
$433$	−12.7291	+	1.38438i	−0.611723	+	0.0665289i	−0.202987	+	0.979181i	$0.565065\pi$
$434$	−21.2904	−	16.1845i	−1.02197	−	0.776881i
$435$	0.0695815	+	0.0321918i	0.00333618	+	0.00154348i
$436$	−7.19946	−	10.6184i	−0.344792	−	0.508530i
$437$	−13.9425	+	4.69777i	−0.666959	+	0.224725i
$438$	1.84577	+	11.2587i	0.0881945	+	0.537963i
$439$	0.0478909	−	0.292121i	0.00228571	−	0.0139422i	−0.985659	−	0.168749i	$-0.946027\pi$
$439$	0.0478909	−	0.292121i	0.00228571	−	0.0139422i	0.987945	+	0.154807i	$0.0494755\pi$
$440$	−1.82714	−	0.615636i	−0.0871056	−	0.0293493i
$441$	3.88873	+	14.0059i	0.185177	+	0.666949i
$442$	−9.95714	−	24.9905i	−0.473613	−	1.18868i
$443$	−6.73359	−	16.9000i	−0.319923	−	0.802945i	−0.997707	−	0.0676844i	$-0.978439\pi$
$443$	−6.73359	−	16.9000i	−0.319923	−	0.802945i	0.677784	−	0.735261i	$-0.262940\pi$
$444$	3.16601	+	11.4029i	0.150252	+	0.541159i
$445$	−0.988336	−	0.333009i	−0.0468516	−	0.0157861i
$446$	1.24463	−	7.59190i	0.0589349	−	0.359487i
$447$	1.69660	+	10.3488i	0.0802466	+	0.489483i
$448$	4.39774	−	1.48177i	0.207774	−	0.0700071i
$449$	−2.44372	−	3.60422i	−0.115326	−	0.170094i	0.765645	−	0.643264i	$-0.222420\pi$
$449$	−2.44372	−	3.60422i	−0.115326	−	0.170094i	−0.880971	+	0.473170i	$0.843110\pi$
$450$	−4.37870	−	2.02580i	−0.206414	−	0.0954972i
$451$	2.38855	+	1.81573i	0.112472	+	0.0854994i
$452$	−6.40553	+	0.696643i	−0.301291	+	0.0327673i
$453$	0.889682	−	3.20435i	0.0418009	−	0.150553i
$454$	−6.87829	+	10.1447i	−0.322814	+	0.476115i
$455$	−7.87520	+	4.73835i	−0.369195	+	0.222137i
$456$	0.142247	+	2.62360i	0.00666134	+	0.122861i
$457$	20.9920	−	19.8846i	0.981963	−	0.930165i	−0.0156043	−	0.999878i	$-0.504967\pi$
$457$	20.9920	−	19.8846i	0.981963	−	0.930165i	0.997567	+	0.0697137i	$0.0222086\pi$
$458$	−19.8998	+	15.1274i	−0.929855	+	0.706858i
$459$	5.55551	−	1.22286i	0.259309	−	0.0570782i
$460$	−1.51817	−	1.78733i	−0.0707850	−	0.0833345i
$461$	−1.55836	+	28.7423i	−0.0725803	+	1.33866i	0.704698	+	0.709508i	$0.251083\pi$
$461$	−1.55836	+	28.7423i	−0.0725803	+	1.33866i	−0.777278	+	0.629157i	$0.783400\pi$
$462$	10.0075	+	18.8762i	0.465593	+	0.878202i
$463$	−5.20498	−	1.14570i	−0.241896	−	0.0532453i	0.0923677	−	0.995725i	$-0.470556\pi$
$463$	−5.20498	−	1.14570i	−0.241896	−	0.0532453i	−0.334263	+	0.942480i	$0.608488\pi$
$464$	−0.166147	+	0.0768679i	−0.00771320	+	0.00356850i
$465$	2.06799	+	1.24427i	0.0959005	+	0.0577014i
$466$	11.0664	−	20.8735i	0.512643	−	0.966948i
$467$	19.8371	−	23.3540i	0.917952	−	1.08070i	−0.0785323	−	0.996912i	$-0.525023\pi$
$467$	19.8371	−	23.3540i	0.917952	−	1.08070i	0.996484	−	0.0837846i	$-0.0267008\pi$
$468$	3.43326	+	3.25216i	0.158703	+	0.150331i
$469$	36.2299	+	3.94024i	1.67294	+	0.181943i
$470$	1.34764	−	3.38233i	0.0621621	−	0.156015i
$471$	15.2261			0.701583
$472$	−7.67209	−	0.372906i	−0.353136	−	0.0171644i
$473$	−48.2312			−2.21767
$474$	0.306328	−	0.768826i	0.0140701	−	0.0353133i
$475$	−12.6021	−	1.37056i	−0.578225	−	0.0628857i
$476$	−19.1651	−	18.1542i	−0.878432	−	0.832095i
$477$	−1.51321	+	1.78149i	−0.0692850	+	0.0815687i
$478$	0.0787654	−	0.148567i	0.00360265	−	0.00679531i
$479$	−12.4824	−	7.51041i	−0.570335	−	0.343159i	0.200997	−	0.979592i	$-0.435582\pi$
$479$	−12.4824	−	7.51041i	−0.570335	−	0.343159i	−0.771332	+	0.636432i	$0.780409\pi$
$480$	−0.380087	+	0.175847i	−0.0173485	+	0.00802628i
$481$	54.6564	+	12.0308i	2.49212	+	0.548556i
$482$	−0.986338	−	1.86043i	−0.0449265	−	0.0847403i
$483$	−1.40684	+	25.9477i	−0.0640136	+	1.18066i
$484$	6.60050	+	7.77070i	0.300023	+	0.353214i
$485$	−0.0684522	+	0.0150675i	−0.00310825	+	0.000684178i
$486$	−0.796093	+	0.605174i	−0.0361115	+	0.0274513i
$487$	−4.46218	+	4.22680i	−0.202200	+	0.191534i	−0.782099	−	0.623154i	$-0.785851\pi$
$487$	−4.46218	+	4.22680i	−0.202200	+	0.191534i	0.579898	+	0.814689i	$0.303092\pi$
$488$	−0.0452794	−	0.835129i	−0.00204970	−	0.0378045i
$489$	−5.30036	+	3.18912i	−0.239691	+	0.144217i
$490$	−3.41622	+	5.03854i	−0.154329	+	0.227618i
$491$	4.42702	−	15.9447i	0.199788	−	0.719573i	−0.793964	−	0.607965i	$-0.791986\pi$
$491$	4.42702	−	15.9447i	0.199788	−	0.719573i	0.993752	−	0.111608i	$-0.0356001\pi$
$492$	0.647880	−	0.0704612i	0.0292087	−	0.00317664i
$493$	0.829034	+	0.630215i	0.0373378	+	0.0283835i
$494$	11.2769	+	5.21725i	0.507372	+	0.234735i
$495$	−1.08201	−	1.59584i	−0.0486327	−	0.0717278i
$496$	−5.46120	+	1.84009i	−0.245215	+	0.0826227i
$497$	−8.52138	−	51.9781i	−0.382236	−	2.33154i
$498$	2.94128	−	17.9410i	0.131802	−	0.803955i
$499$	−11.2734	−	3.79846i	−0.504669	−	0.170043i	0.0554397	−	0.998462i	$-0.482344\pi$
$499$	−11.2734	−	3.79846i	−0.504669	−	0.170043i	−0.560108	+	0.828419i	$0.689240\pi$
$500$	−1.10074	−	3.96451i	−0.0492266	−	0.177298i
$501$	−1.96721	−	4.93733i	−0.0878886	−	0.220584i
$502$	6.92445	+	17.3791i	0.309053	+	0.775665i
$503$	−0.174617	−	0.628915i	−0.00778580	−	0.0280419i	0.959555	−	0.281521i	$-0.0908389\pi$
$503$	−0.174617	−	0.628915i	−0.00778580	−	0.0280419i	−0.967341	+	0.253479i	$0.918425\pi$
$504$	4.39774	+	1.48177i	0.195891	+	0.0660033i
$505$	−0.913456	+	5.57184i	−0.0406483	+	0.247943i
$506$	4.17070	+	25.4402i	0.185410	+	1.13095i
$507$	8.87365	−	2.98988i	0.394093	−	0.132785i
$508$	6.71534	+	9.90439i	0.297945	+	0.439436i
$509$	−4.59448	−	2.12563i	−0.203647	−	0.0942169i	0.315415	−	0.948954i	$-0.397856\pi$
$509$	−4.59448	−	2.12563i	−0.203647	−	0.0942169i	−0.519061	+	0.854737i	$0.673718\pi$
$510$	1.89654	+	1.44171i	0.0839802	+	0.0638401i
$511$	52.6351	−	5.72441i	2.32844	−	0.253233i
$512$	0.267528	−	0.963550i	0.0118232	−	0.0425833i
$513$	−1.47449	+	2.17471i	−0.0651003	+	0.0960158i
$514$	8.69090	−	5.22914i	0.383339	−	0.230648i
$515$	0.155727	+	2.87221i	0.00686214	+	0.126565i
$516$	−7.60570	+	7.20450i	−0.334822	+	0.317161i
$517$	−31.8638	+	24.2222i	−1.40137	+	1.06529i
$518$	53.6349	−	11.8059i	2.35658	−	0.518723i
$519$	4.23277	+	4.98321i	0.185798	+	0.218738i
$520$	−0.107222	+	1.97759i	−0.00470198	+	0.0867229i
$521$	11.7256	+	22.1169i	0.513710	+	0.968959i	0.995687	+	0.0927755i	$0.0295739\pi$
$521$	11.7256	+	22.1169i	0.513710	+	0.968959i	−0.481977	+	0.876184i	$0.660081\pi$
$522$	−0.178787	−	0.0393540i	−0.00782531	−	0.00172248i
$523$	28.7442	−	13.2985i	1.25690	−	0.581502i	0.325512	−	0.945538i	$-0.394463\pi$
$523$	28.7442	−	13.2985i	1.25690	−	0.581502i	0.931385	+	0.364036i	$0.118601\pi$
$524$	0.307046	+	0.184743i	0.0134134	+	0.00807055i
$525$	−10.4874	+	19.7813i	−0.457707	+	0.863327i
$526$	14.6707	−	17.2717i	0.639672	−	0.753081i
$527$	23.7997	+	22.5442i	1.03673	+	0.982042i
$528$	4.57688	+	0.497766i	0.199183	+	0.0216625i
$529$	−3.09266	+	7.76200i	−0.134464	+	0.337478i
$530$	−0.978893			−0.0425204
$531$	−5.88202	−	4.93982i	−0.255258	−	0.214370i
$532$	12.1931			0.528638
$533$	1.14073	−	2.86303i	0.0494107	−	0.124012i
$534$	2.47572	+	0.269251i	0.107135	+	0.0116516i
$535$	0.110153	+	0.104342i	0.00476231	+	0.00451110i
$536$	5.08398	−	5.98532i	0.219594	−	0.258526i
$537$	−5.90049	+	11.1295i	−0.254625	+	0.480273i
$538$	−3.16989	−	1.90726i	−0.136663	−	0.0822277i
$539$	60.7356	−	28.0993i	2.61607	−	1.21032i
$540$	−0.409002	−	0.0900283i	−0.0176007	−	0.00387420i
$541$	−2.00066	−	3.77364i	−0.0860149	−	0.162241i	0.836773	−	0.547551i	$-0.184440\pi$
$541$	−2.00066	−	3.77364i	−0.0860149	−	0.162241i	−0.922788	+	0.385309i	$0.874095\pi$
$542$	−1.02014	+	18.8154i	−0.0438188	+	0.808190i
$543$	7.46041	+	8.78308i	0.320157	+	0.376918i
$544$	−5.55551	+	1.22286i	−0.238190	+	0.0524297i
$545$	4.27717	−	3.25142i	0.183214	−	0.139275i
$546$	15.9326	−	15.0922i	0.681853	−	0.645885i
$547$	0.976083	+	18.0028i	0.0417343	+	0.769744i	0.942248	+	0.334916i	$0.108708\pi$
$547$	0.976083	+	18.0028i	0.0417343	+	0.769744i	−0.900514	+	0.434828i	$0.856809\pi$
$548$	−7.16863	+	4.31322i	−0.306229	+	0.184252i
$549$	0.469352	−	0.692242i	0.0200315	−	0.0295442i
$550$	−5.94231	+	21.4023i	−0.253381	+	0.912595i
$551$	−0.478180	+	0.0520052i	−0.0203712	+	0.00221550i
$552$	4.45780	+	3.38873i	0.189736	+	0.144234i
$553$	−3.48567	−	1.61264i	−0.148226	−	0.0685765i
$554$	−2.88243	−	4.25126i	−0.122463	−	0.180619i
$555$	−4.69668	+	1.58250i	−0.199363	+	0.0671733i
$556$	2.37973	+	14.5157i	0.100923	+	0.615603i
$557$	−1.05429	+	6.43088i	−0.0446717	+	0.272485i	−0.999712	−	0.0239901i	$-0.992363\pi$
$557$	−1.05429	+	6.43088i	−0.0446717	+	0.272485i	0.955041	+	0.296475i	$0.0958112\pi$
$558$	−5.46120	−	1.84009i	−0.231191	−	0.0778974i
$559$	13.2540	+	47.7367i	0.560586	+	2.01905i
$560$	0.719356	+	1.80545i	0.0303983	+	0.0762941i
$561$	−9.69359	−	24.3291i	−0.409264	−	1.02717i
$562$	4.80355	+	17.3008i	0.202625	+	0.729791i
$563$	−17.7024	−	5.96464i	−0.746068	−	0.251380i	−0.0795116	−	0.996834i	$-0.525336\pi$
$563$	−17.7024	−	5.96464i	−0.746068	−	0.251380i	−0.666557	+	0.745454i	$0.732233\pi$
$564$	−1.40650	+	8.57930i	−0.0592245	+	0.361254i
$565$	−0.436555	−	2.66287i	−0.0183660	−	0.112028i
$566$	−11.0016	+	3.70689i	−0.462434	+	0.155812i
$567$	2.60428	+	3.84103i	0.109369	+	0.161308i
$568$	−10.3011	−	4.76578i	−0.432223	−	0.199968i
$569$	−3.07544	−	2.33789i	−0.128929	−	0.0980095i	0.538722	−	0.842483i	$-0.318907\pi$
$569$	−3.07544	−	2.33789i	−0.128929	−	0.0980095i	−0.667651	+	0.744474i	$0.732700\pi$
$570$	−1.09391	+	0.118970i	−0.0458188	+	0.00498309i
$571$	−3.76044	+	13.5439i	−0.157370	+	0.566794i	0.842247	+	0.539092i	$0.181233\pi$
$571$	−3.76044	+	13.5439i	−0.157370	+	0.566794i	−0.999616	+	0.0277015i	$0.991181\pi$
$572$	12.2181	−	18.0203i	0.510864	−	0.753468i
$573$	16.1586	−	9.72230i	0.675035	−	0.406155i
$574$	−0.163733	−	3.01989i	−0.00683410	−	0.126048i
$575$	−19.6134	+	18.5788i	−0.817935	+	0.774789i
$576$	0.796093	−	0.605174i	0.0331705	−	0.0252156i
$577$	15.4204	−	3.39429i	0.641959	−	0.141306i	0.117951	−	0.993019i	$-0.462367\pi$
$577$	15.4204	−	3.39429i	0.641959	−	0.141306i	0.524008	+	0.851713i	$0.324436\pi$
$578$	9.94323	+	11.7061i	0.413584	+	0.486909i
$579$	−0.418147	+	7.71226i	−0.0173776	+	0.320511i
$580$	−0.0359117	−	0.0677366i	−0.00149115	−	0.00281261i
$581$	−82.3970	−	18.1369i	−3.41840	−	0.752447i
$582$	0.151895	−	0.0702742i	0.00629626	−	0.00291296i
$583$	9.22076	+	5.54794i	0.381885	+	0.229772i
$584$	5.34408	−	10.0800i	0.221140	−	0.417114i
$585$	−1.28214	+	1.50946i	−0.0530101	+	0.0624083i
$586$	−10.8262	−	10.2551i	−0.447224	−	0.423633i
$587$	−28.4746	−	3.09680i	−1.17527	−	0.127819i	−0.500428	−	0.865778i	$-0.666824\pi$
$587$	−28.4746	−	3.09680i	−1.17527	−	0.127819i	−0.674845	+	0.737960i	$0.735790\pi$
$588$	5.38024	−	13.5034i	0.221877	−	0.556870i
$589$	−15.1417			−0.623901
$590$	−0.0180081	−	3.21676i	−0.000741380	−	0.132432i
$591$	−0.711218			−0.0292556
$592$	4.38032	−	10.9938i	0.180030	−	0.451841i
$593$	−4.59498	−	0.499734i	−0.188693	−	0.0205216i	0.0132845	−	0.999912i	$-0.495771\pi$
$593$	−4.59498	−	0.499734i	−0.188693	−	0.0205216i	−0.201978	+	0.979390i	$0.564737\pi$
$594$	3.34239	+	3.16608i	0.137140	+	0.129906i
$595$	7.15717	−	8.42607i	0.293415	−	0.345435i
$596$	4.91219	−	9.26537i	0.201211	−	0.379524i
$597$	−11.8719	−	7.14306i	−0.485883	−	0.292346i
$598$	24.0332	−	11.1190i	0.982792	−	0.454688i
$599$	30.8558	+	6.79187i	1.26073	+	0.277508i	0.794560	−	0.607185i	$-0.207701\pi$
$599$	30.8558	+	6.79187i	1.26073	+	0.277508i	0.466173	+	0.884694i	$0.345632\pi$
$600$	2.25989	+	4.26260i	0.0922596	+	0.174020i
$601$	−1.13592	+	20.9508i	−0.0463352	+	0.854603i	0.879319	+	0.476233i	$0.157998\pi$
$601$	−1.13592	+	20.9508i	−0.0463352	+	0.854603i	−0.925655	+	0.378370i	$0.876485\pi$
$602$	31.4738	+	37.0538i	1.28278	+	1.51020i
$603$	7.66948	−	1.68818i	0.312325	−	0.0687480i
$604$	−2.64746	+	2.01255i	−0.107724	+	0.0818893i
$605$	−3.09990	+	2.93638i	−0.126029	+	0.119381i
$606$	−0.729906	−	13.4623i	−0.0296504	−	0.546869i
$607$	17.0208	−	10.2411i	0.690852	−	0.415672i	−0.126379	−	0.991982i	$-0.540335\pi$
$607$	17.0208	−	10.2411i	0.690852	−	0.415672i	0.817231	+	0.576310i	$0.195508\pi$
$608$	1.47449	−	2.17471i	0.0597985	−	0.0881962i
$609$	−0.227280	+	0.818587i	−0.00920984	+	0.0331708i
$610$	0.348207	−	0.0378698i	0.0140985	−	0.00153330i
$611$	32.7301	+	24.8808i	1.32412	+	1.00657i
$612$	−5.16274	−	2.38854i	−0.208692	−	0.0965510i
$613$	−14.0334	−	20.6977i	−0.566804	−	0.835973i	0.430991	−	0.902356i	$-0.358164\pi$
$613$	−14.0334	−	20.6977i	−0.566804	−	0.835973i	−0.997794	+	0.0663836i	$0.978854\pi$
$614$	−6.28665	+	2.11822i	−0.253708	+	0.0854843i
$615$	0.0441548	+	0.269332i	0.00178049	+	0.0108605i
$616$	3.45647	−	21.0836i	0.139265	−	0.849481i
$617$	11.6445	+	3.92349i	0.468790	+	0.157954i	0.543775	−	0.839231i	$-0.316994\pi$
$617$	11.6445	+	3.92349i	0.468790	+	0.157954i	−0.0749852	+	0.997185i	$0.523891\pi$
$618$	−1.83748	−	6.61801i	−0.0739144	−	0.266216i
$619$	−3.72645	−	9.35269i	−0.149779	−	0.375916i	0.834874	−	0.550441i	$-0.185540\pi$
$619$	−3.72645	−	9.35269i	−0.149779	−	0.375916i	−0.984653	+	0.174525i	$0.944161\pi$
$620$	−0.893311	−	2.24204i	−0.0358763	−	0.0900426i
$621$	1.49805	+	5.39549i	0.0601147	+	0.216513i
$622$	−24.0893	−	8.11664i	−0.965894	−	0.325448i
$623$	1.86967	−	11.4045i	0.0749068	−	0.456911i
$624$	−0.765073	−	4.66674i	−0.0306275	−	0.186819i
$625$	−21.2274	+	7.15233i	−0.849095	+	0.286093i
$626$	4.94144	+	7.28808i	0.197500	+	0.291290i
$627$	10.9784	+	5.07916i	0.438436	+	0.202842i
$628$	−12.1214	−	9.21446i	−0.483697	−	0.367697i
$629$	−66.9247	+	7.27850i	−2.66846	+	0.290213i
$630$	−0.519936	+	1.87264i	−0.0207147	+	0.0746078i
$631$	1.75939	−	2.59491i	0.0700404	−	0.103302i	−0.791056	−	0.611744i	$-0.790468\pi$
$631$	1.75939	−	2.59491i	0.0700404	−	0.103302i	0.861096	+	0.508442i	$0.169779\pi$
$632$	−0.709139	+	0.426675i	−0.0282080	+	0.0169722i
$633$	1.24145	+	22.8971i	0.0493430	+	0.910078i
$634$	−10.2608	+	9.71958i	−0.407510	+	0.386014i
$635$	−3.98956	+	3.03278i	−0.158321	+	0.120352i
$636$	2.28276	−	0.502474i	0.0905175	−	0.0199244i
$637$	−44.5014	−	52.3911i	−1.76321	−	2.07581i
$638$	−0.0456292	+	0.841582i	−0.00180648	+	0.0333185i
$639$	−5.31648	−	10.0279i	−0.210317	−	0.396700i
$640$	0.409002	+	0.0900283i	0.0161672	+	0.00355868i
$641$	14.5570	−	6.73477i	0.574965	−	0.266007i	−0.110785	−	0.993844i	$-0.535336\pi$
$641$	14.5570	−	6.73477i	0.574965	−	0.266007i	0.685750	+	0.727837i	$0.259474\pi$
$642$	−0.310434	−	0.186782i	−0.0122518	−	0.00737169i
$643$	0.553246	−	1.04353i	0.0218179	−	0.0411529i	−0.872363	−	0.488858i	$-0.837414\pi$
$643$	0.553246	−	1.04353i	0.0218179	−	0.0411529i	0.894181	+	0.447705i	$0.147759\pi$
$644$	16.8229	−	19.8054i	0.662914	−	0.780442i
$645$	−3.18522	−	3.01720i	−0.125418	−	0.118802i
$646$	−14.8586	−	1.61597i	−0.584605	−	0.0635796i
$647$	11.6129	−	29.1462i	0.456551	−	1.14586i	−0.502992	−	0.864291i	$-0.667767\pi$
$647$	11.6129	−	29.1462i	0.456551	−	1.14586i	0.959542	−	0.281564i	$-0.0908533\pi$
$648$	1.00000			0.0392837
$649$	−18.0616	+	30.4026i	−0.708980	+	1.19341i
$650$	22.8158			0.894909
$651$	−9.89881	+	24.8441i	−0.387965	+	0.973718i
$652$	6.14956	+	0.668805i	0.240835	+	0.0261924i
$653$	6.12417	+	5.80112i	0.239657	+	0.227016i	0.798096	−	0.602530i	$-0.205841\pi$
$653$	6.12417	+	5.80112i	0.239657	+	0.227016i	−0.558439	+	0.829546i	$0.688599\pi$
$654$	−8.30531	+	9.77777i	−0.324763	+	0.382341i
$655$	−0.0702942	+	0.132589i	−0.00274662	+	0.00518068i
$656$	−0.558414	−	0.335987i	−0.0218024	−	0.0131181i
$657$	10.3545	−	4.79052i	0.403969	−	0.186896i
$658$	39.4019	+	8.67301i	1.53604	+	0.338109i
$659$	7.11516	+	13.4206i	0.277167	+	0.522793i	0.982542	−	0.186042i	$-0.0595660\pi$
$659$	7.11516	+	13.4206i	0.277167	+	0.522793i	−0.705375	+	0.708835i	$0.749221\pi$
$660$	−0.104384	+	1.92524i	−0.00406313	+	0.0749400i
$661$	1.00318	+	1.18104i	0.0390192	+	0.0459370i	0.781325	−	0.624124i	$-0.214544\pi$
$661$	1.00318	+	1.18104i	0.0390192	+	0.0459370i	−0.742306	+	0.670061i	$0.766268\pi$
$662$	−3.66121	+	0.805893i	−0.142297	+	0.0313219i
$663$	−21.4158	+	16.2799i	−0.831721	+	0.632258i
$664$	−13.1989	+	12.5027i	−0.512219	+	0.485199i
$665$	0.276455	+	5.09891i	0.0107205	+	0.197727i
$666$	10.1403	−	6.10121i	0.392928	−	0.236417i
$667$	−0.575274	+	0.848466i	−0.0222747	+	0.0328527i
$668$	−1.42186	+	5.12108i	−0.0550135	+	0.198141i
$669$	−7.64815	+	0.831786i	−0.295694	+	0.0321587i
$670$	2.61821	+	1.99031i	0.101150	+	0.0768924i
$671$	−3.49459	−	1.61677i	−0.134907	−	0.0624148i
$672$	−2.60428	−	3.84103i	−0.100462	−	0.148171i
$673$	−6.77674	+	2.28335i	−0.261224	+	0.0880166i	−0.446866	−	0.894601i	$-0.647460\pi$
$673$	−6.77674	+	2.28335i	−0.261224	+	0.0880166i	0.185642	+	0.982617i	$0.440563\pi$
$674$	−4.10563	−	25.0432i	−0.158143	−	0.964629i
$675$	−0.780535	+	4.76105i	−0.0300428	+	0.183253i
$676$	−8.87365	−	2.98988i	−0.341294	−	0.114995i
$677$	−3.86296	−	13.9131i	−0.148466	−	0.534725i	−0.999947	−	0.0103396i	$-0.996709\pi$
$677$	−3.86296	−	13.9131i	−0.148466	−	0.534725i	0.851481	−	0.524386i	$-0.175705\pi$
$678$	2.38491	+	5.98568i	0.0915920	+	0.229879i
$679$	−0.287478	−	0.721516i	−0.0110324	−	0.0276893i
$680$	−0.637335	−	2.29547i	−0.0244407	−	0.0880274i
$681$	11.6151	+	3.91358i	0.445091	+	0.149969i
$682$	−4.29232	+	26.1820i	−0.164361	+	1.00256i
$683$	5.29184	+	32.2788i	0.202487	+	1.23511i	0.870951	+	0.491370i	$0.163504\pi$
$683$	5.29184	+	32.2788i	0.202487	+	1.23511i	−0.668464	+	0.743744i	$0.733048\pi$
$684$	2.48991	−	0.838949i	0.0952041	−	0.0320780i
$685$	−1.96623	−	2.89998i	−0.0751260	−	0.110803i
$686$	−31.7387	−	14.6839i	−1.21179	−	0.560634i
$687$	19.8998	+	15.1274i	0.759224	+	0.577147i
$688$	10.4148	−	1.13268i	0.397061	−	0.0431830i
$689$	2.95718	−	10.6508i	0.112660	−	0.405763i
$690$	−1.31602	+	1.94099i	−0.0501002	+	0.0738923i
$691$	8.83634	−	5.31665i	0.336150	−	0.202255i	−0.337463	−	0.941339i	$-0.609569\pi$
$691$	8.83634	−	5.31665i	0.336150	−	0.202255i	0.673613	+	0.739084i	$0.264741\pi$
$692$	−0.353974	−	6.52866i	−0.0134561	−	0.248182i
$693$	15.5109	−	14.6927i	0.589210	−	0.558130i
$694$	−9.04869	+	6.87863i	−0.343483	+	0.261109i
$695$	−6.01621	+	1.32427i	−0.228208	+	0.0502324i
$696$	0.118515	+	0.139527i	0.00449231	+	0.00528875i
$697$	−0.200704	+	3.70176i	−0.00760219	+	0.140214i
$698$	−13.3236	−	25.1310i	−0.504305	−	0.951221i
$699$	−23.0733	−	5.07881i	−0.872712	−	0.192098i
$700$	20.3201	−	9.40106i	0.768026	−	0.355327i
$701$	26.5516	+	15.9756i	1.00284	+	0.603389i	0.919483	−	0.393131i	$-0.128608\pi$
$701$	26.5516	+	15.9756i	1.00284	+	0.603389i	0.0833579	+	0.996520i	$0.473436\pi$
$702$	2.21512	−	4.17816i	0.0836044	−	0.157695i
$703$	20.1298	−	23.6986i	0.759210	−	0.893811i
$704$	−3.34239	−	3.16608i	−0.125971	−	0.119326i
$705$	−3.61958	−	0.393653i	−0.136321	−	0.0148258i
$706$	−0.316946	+	0.795474i	−0.0119284	+	0.0299381i
$707$	−62.5659			−2.35303
$708$	1.69319	+	7.49220i	0.0636339	+	0.281574i
$709$	29.8914			1.12260			0.561298	−	0.827614i	$-0.310302\pi$
$709$	29.8914			1.12260			0.561298	+	0.827614i	$0.310302\pi$
$710$	1.75940	−	4.41575i	0.0660290	−	0.165720i
$711$	−0.822754	−	0.0894799i	−0.0308557	−	0.00335576i
$712$	−1.80796	−	1.71259i	−0.0677562	−	0.0641821i
$713$	−20.8910	+	24.5948i	−0.782373	+	0.921081i
$714$	−12.3652	+	23.3233i	−0.462758	+	0.872853i
$715$	7.81276	+	4.70078i	0.292181	+	0.175799i
$716$	11.4326	−	5.28930i	0.427257	−	0.197670i
$717$	−0.164224	−	0.0361484i	−0.00613306	−	0.00134999i
$718$	8.59406	+	16.2101i	0.320727	+	0.604956i
$719$	0.0301255	−	0.555633i	0.00112349	−	0.0207216i	−0.997918	−	0.0644968i	$-0.979456\pi$
$719$	0.0301255	−	0.555633i	0.00112349	−	0.0207216i	0.999041	+	0.0437752i	$0.0139385\pi$
$720$	0.271121	+	0.319189i	0.0101041	+	0.0118955i
$721$	−31.1286	+	6.85192i	−1.15929	+	0.255179i
$722$	−9.62995	+	7.32050i	−0.358390	+	0.272441i
$723$	−1.52874	+	1.44810i	−0.0568546	+	0.0538556i
$724$	−0.623891	−	11.5070i	−0.0231867	−	0.427654i
$725$	−0.756801	+	0.455352i	−0.0281069	+	0.0169113i
$726$	5.72164	−	8.43879i	0.212350	−	0.313193i
$727$	−1.20076	+	4.32474i	−0.0445336	+	0.160396i	−0.982474	−	0.186402i	$-0.940317\pi$
$727$	−1.20076	+	4.32474i	−0.0445336	+	0.160396i	0.937940	+	0.346798i	$0.112731\pi$
$728$	−21.8172	+	2.37277i	−0.808600	+	0.0879406i
$729$	0.796093	+	0.605174i	0.0294849	+	0.0224139i
$730$	4.33642	+	2.00624i	0.160498	+	0.0742543i
$731$	−33.4434	−	49.3254i	−1.23695	−	1.82436i
$732$	−0.792575	+	0.267050i	−0.0292944	+	0.00987044i
$733$	−2.11712	−	12.9139i	−0.0781978	−	0.476985i	−0.996673	−	0.0815063i	$-0.974027\pi$
$733$	−2.11712	−	12.9139i	−0.0781978	−	0.476985i	0.918475	−	0.395479i	$-0.129421\pi$
$734$	−2.92793	+	17.8596i	−0.108072	+	0.659208i
$735$	5.76882	+	1.94374i	0.212786	+	0.0716960i
$736$	−1.49805	−	5.39549i	−0.0552188	−	0.198880i
$737$	−13.3822	−	33.5867i	−0.492939	−	1.23718i
$738$	−0.241219	−	0.605414i	−0.00887940	−	0.0222856i
$739$	5.41402	+	19.4995i	0.199158	+	0.717302i	0.993893	+	0.110346i	$0.0351958\pi$
$739$	5.41402	+	19.4995i	0.199158	+	0.717302i	−0.794735	+	0.606956i	$0.792390\pi$
$740$	4.69668	+	1.58250i	0.172654	+	0.0581738i
$741$	2.01019	−	12.2616i	0.0738462	−	0.450442i
$742$	−1.75487	−	10.7042i	−0.0644234	−	0.392965i
$743$	−27.9767	+	9.42646i	−1.02637	+	0.345823i	−0.781614	−	0.623762i	$-0.785603\pi$
$743$	−27.9767	+	9.42646i	−1.02637	+	0.345823i	−0.244753	+	0.969586i	$0.578707\pi$
$744$	3.23405	+	4.76987i	0.118566	+	0.174872i
$745$	3.98596	+	1.84410i	0.146034	+	0.0675627i
$746$	−25.1323	−	19.1051i	−0.920158	−	0.699486i
$747$	−18.0739	+	1.96566i	−0.661290	+	0.0719196i
$748$	−7.00633	+	25.2345i	−0.256177	+	0.922665i
$749$	−0.943514	+	1.39158i	−0.0344752	+	0.0508472i
$750$	−3.52553	+	2.12124i	−0.128734	+	0.0774567i
$751$	−2.38322	−	43.9559i	−0.0869650	−	1.60397i	−0.638365	−	0.769734i	$-0.720389\pi$
$751$	−2.38322	−	43.9559i	−0.0869650	−	1.60397i	0.551400	−	0.834241i	$-0.314094\pi$
$752$	6.31168	−	5.97874i	0.230163	−	0.218022i
$753$	14.8931	−	11.3214i	0.542735	−	0.412576i
$754$	0.845492	−	0.186107i	0.0307910	−	0.00677761i
$755$	−0.901631	−	1.06148i	−0.0328137	−	0.0386313i
$756$	0.251240	−	4.63386i	0.00913753	−	0.168532i
$757$	−11.4991	−	21.6895i	−0.417940	−	0.788319i	0.581746	−	0.813371i	$-0.302370\pi$
$757$	−11.4991	−	21.6895i	−0.417940	−	0.788319i	−0.999686	+	0.0250514i	$0.992025\pi$
$758$	37.1215	+	8.17106i	1.34831	+	0.296786i
$759$	23.3971	−	10.8247i	0.849261	−	0.392910i
$760$	0.942851	+	0.567294i	0.0342008	+	0.0205779i
$761$	3.41575	−	6.44278i	0.123821	−	0.233551i	−0.813850	−	0.581074i	$-0.802633\pi$
$761$	3.41575	−	6.44278i	0.123821	−	0.233551i	0.937671	+	0.347524i	$0.112977\pi$
$762$	7.74683	−	9.12027i	0.280638	−	0.330393i
$763$	43.2222	+	40.9422i	1.56475	+	1.48221i
$764$	−18.7474	−	2.03891i	−0.678258	−	0.0737650i
$765$	0.881783	−	2.21311i	0.0318809	−	0.0800151i
$766$	−25.5035			−0.921481
$767$	35.0543	+	9.52173i	1.26574	+	0.343810i
$768$	−1.00000			−0.0360844
$769$	5.29789	−	13.2967i	0.191047	−	0.479491i	−0.801984	−	0.597345i	$-0.796222\pi$
$769$	5.29789	−	13.2967i	0.191047	−	0.479491i	0.993031	+	0.117854i	$0.0376015\pi$
$770$	8.89508	+	0.967398i	0.320556	+	0.0348626i
$771$	−7.36360	−	6.97517i	−0.265194	−	0.251205i
$772$	5.00015	−	5.88663i	0.179959	−	0.211864i
$773$	15.4193	−	29.0839i	0.554594	−	1.04608i	−0.434759	−	0.900547i	$-0.643167\pi$
$773$	15.4193	−	29.0839i	0.554594	−	1.04608i	0.989354	−	0.145529i	$-0.0464886\pi$
$774$	8.97664	+	5.40106i	0.322659	+	0.194137i
$775$	−25.2339	+	11.6744i	−0.906428	+	0.419358i
$776$	−0.163451	−	0.0359782i	−0.00586754	−	0.00129154i
$777$	−25.7245	−	48.5215i	−0.922861	−	1.74070i
$778$	−1.35181	+	24.9327i	−0.0484648	+	0.893881i
$779$	−1.10853	−	1.30506i	−0.0397170	−	0.0467585i
$780$	1.93419	−	0.425747i	0.0692551	−	0.0152442i
$781$	−41.5993	+	31.6230i	−1.48854	+	1.13156i
$782$	−23.1253	+	21.9055i	−0.826960	+	0.783339i
$783$	0.00991106	+	0.182799i	0.000354192	+	0.00653270i
$784$	−12.4551	+	7.49396i	−0.444824	+	0.267642i
$785$	3.57847	−	5.27784i	0.127721	−	0.188374i
$786$	0.0958660	−	0.345278i	0.00341943	−	0.0123157i
$787$	4.42088	−	0.480800i	0.157587	−	0.0171387i	−0.0289852	−	0.999580i	$-0.509228\pi$
$787$	4.42088	−	0.480800i	0.157587	−	0.0171387i	0.186573	+	0.982441i	$0.440262\pi$
$788$	0.566196	+	0.430411i	0.0201699	+	0.0153328i
$789$	−20.5669	−	9.51528i	−0.732203	−	0.338753i
$790$	−0.194505	−	0.286873i	−0.00692018	−	0.0102065i
$791$	28.3360	−	9.54750i	1.00751	−	0.339470i
$792$	−0.744823	−	4.54322i	−0.0264661	−	0.161436i
$793$	−0.639874	+	3.90306i	−0.0227226	+	0.138602i
$794$	3.63040	+	1.22322i	0.128838	+	0.0434105i
$795$	0.261882	+	0.943212i	0.00928798	+	0.0334523i
$796$	5.12831	+	12.8711i	0.181768	+	0.456203i
$797$	6.52044	+	16.3651i	0.230966	+	0.579680i	0.998087	−	0.0618216i	$-0.0196910\pi$
$797$	6.52044	+	16.3651i	0.230966	+	0.579680i	−0.767122	+	0.641502i	$0.778312\pi$
$798$	−3.26200	−	11.7487i	−0.115474	−	0.415898i
$799$	−46.8660	−	15.7910i	−1.65800	−	0.558646i
$800$	0.780535	−	4.76105i	0.0275961	−	0.168329i
$801$	−0.402889	−	2.45751i	−0.0142354	−	0.0868320i
$802$	36.7333	−	12.3769i	1.29710	−	0.437044i
$803$	−29.4767	−	43.4749i	−1.04021	−	1.53420i
$804$	−7.12726	−	3.29742i	−0.251359	−	0.116291i
$805$	8.66364	+	6.58593i	0.305353	+	0.232123i
$806$	27.0931	−	2.94655i	0.954313	−	0.103788i
$807$	−0.989703	+	3.56459i	−0.0348392	+	0.125479i
$808$	−7.56598	+	11.1590i	−0.266170	+	0.392572i
$809$	−23.9384	+	14.4032i	−0.841628	+	0.506391i	−0.869911	−	0.493209i	$-0.835824\pi$
$809$	−23.9384	+	14.4032i	−0.841628	+	0.506391i	0.0282828	+	0.999600i	$0.490996\pi$
$810$	0.0226730	+	0.418179i	0.000796649	+	0.0146933i
$811$	−13.2708	+	12.5708i	−0.466001	+	0.441419i	−0.884320	−	0.466881i	$-0.845378\pi$
$811$	−13.2708	+	12.5708i	−0.466001	+	0.441419i	0.418320	+	0.908300i	$0.362619\pi$
$812$	0.676324	−	0.514128i	0.0237343	−	0.0180424i
$813$	18.4025	−	4.05069i	0.645403	−	0.142064i
$814$	−35.2719	−	41.5252i	−1.23628	−	1.45546i
$815$	−0.140251	+	2.58678i	−0.00491279	+	0.0906110i
$816$	2.66454	+	5.02586i	0.0932776	+	0.175940i
$817$	26.8822	+	5.91723i	0.940491	+	0.207018i
$818$	−10.7756	+	4.98531i	−0.376759	+	0.174307i
$819$	−18.8045	−	11.3143i	−0.657082	−	0.395353i
$820$	0.127842	−	0.241135i	0.00446443	−	0.00842080i
$821$	31.4490	−	37.0246i	1.09758	−	1.29217i	0.144477	−	0.989508i	$-0.453850\pi$
$821$	31.4490	−	37.0246i	1.09758	−	1.29217i	0.953099	−	0.302658i	$-0.0978741\pi$
$822$	6.07382	+	5.75342i	0.211849	+	0.200674i
$823$	−51.0865	−	5.55599i	−1.78076	−	0.193670i	−0.842290	−	0.539025i	$-0.818793\pi$
$823$	−51.0865	−	5.55599i	−1.78076	−	0.193670i	−0.938472	+	0.345355i	$0.887758\pi$
$824$	−2.54224	+	6.38055i	−0.0885633	+	0.222277i
$825$	22.2119			0.773318
$826$	35.1432	−	5.96365i	1.22279	−	0.207502i
$827$	18.9476			0.658873			0.329436	−	0.944178i	$-0.393141\pi$
$827$	18.9476			0.658873			0.329436	+	0.944178i	$0.393141\pi$
$828$	2.07262	−	5.20189i	0.0720286	−	0.180778i
$829$	−43.0558	−	4.68260i	−1.49539	−	0.162633i	−0.676439	−	0.736498i	$-0.736478\pi$
$829$	−43.0558	−	4.68260i	−1.49539	−	0.162633i	−0.818950	+	0.573865i	$0.805443\pi$
$830$	−5.52764	−	5.23606i	−0.191867	−	0.181746i
$831$	−3.32517	+	3.91470i	−0.115349	+	0.135799i
$832$	−2.21512	+	4.17816i	−0.0767955	+	0.144852i
$833$	70.8507	+	42.6294i	2.45483	+	1.47702i
$834$	13.3500	−	6.17635i	0.462271	−	0.213869i
$835$	−2.17377	−	0.478483i	−0.0752264	−	0.0165586i
$836$	−5.66607	−	10.6873i	−0.195965	−	0.369629i
$837$	−0.311996	+	5.75442i	−0.0107841	+	0.198902i
$838$	−8.12177	−	9.56168i	−0.280562	−	0.330303i
$839$	9.47491	−	2.08559i	0.327110	−	0.0720024i	−0.0483793	−	0.998829i	$-0.515406\pi$
$839$	9.47491	−	2.08559i	0.327110	−	0.0720024i	0.375490	+	0.926827i	$0.377475\pi$
$840$	1.54719	−	1.17614i	0.0533832	−	0.0405808i
$841$	21.0295	−	19.9202i	0.725157	−	0.686905i
$842$	0.591842	+	10.9159i	0.0203962	+	0.376186i
$843$	15.3851	−	9.25691i	0.529891	−	0.318825i
$844$	12.8684	−	18.9795i	0.442950	−	0.653302i
$845$	1.04911	−	3.77857i	0.0360906	−	0.129987i
$846$	8.64286	−	0.939968i	0.297148	−	0.0323168i
$847$	−37.6666	−	28.6334i	−1.29424	−	0.983857i
$848$	−2.12138	−	0.981454i	−0.0728484	−	0.0337033i
$849$	6.51502	+	9.60894i	0.223595	+	0.329778i
$850$	−26.0082	+	8.76317i	−0.892073	+	0.300574i
$851$	−10.7208	−	65.3942i	−0.367505	−	2.24168i
$852$	−1.83624	+	11.2006i	−0.0629086	+	0.383726i
$853$	21.0755	+	7.10116i	0.721611	+	0.243139i	0.656059	−	0.754710i	$-0.272222\pi$
$853$	21.0755	+	7.10116i	0.721611	+	0.243139i	0.0655528	+	0.997849i	$0.479119\pi$
$854$	1.03834	+	3.73977i	0.0355314	+	0.127972i
$855$	0.407285	+	1.02221i	0.0139288	+	0.0349588i
$856$	0.134099	+	0.336562i	0.00458340	+	0.0115035i
$857$	11.1902	+	40.3035i	0.382250	+	1.37674i	0.865347	+	0.501174i	$0.167098\pi$
$857$	11.1902	+	40.3035i	0.382250	+	1.37674i	−0.483097	+	0.875567i	$0.660488\pi$
$858$	−20.6322	−	6.95179i	−0.704371	−	0.237330i
$859$	−7.36400	+	44.9184i	−0.251256	+	1.53260i	0.496154	+	0.868234i	$0.334745\pi$
$859$	−7.36400	+	44.9184i	−0.251256	+	1.53260i	−0.747411	+	0.664362i	$0.768703\pi$
$860$	0.709799	+	4.32958i	0.0242040	+	0.147638i
$861$	−2.86601	+	0.965670i	−0.0976733	+	0.0329100i
$862$	2.08548	+	3.07586i	0.0710319	+	0.104764i
$863$	−7.94796	−	3.67712i	−0.270552	−	0.125171i	0.279923	−	0.960023i	$-0.409691\pi$
$863$	−7.94796	−	3.67712i	−0.270552	−	0.125171i	−0.550475	+	0.834852i	$0.685553\pi$
$864$	−0.796093	−	0.605174i	−0.0270836	−	0.0205884i
$865$	2.72213	−	0.296049i	0.0925551	−	0.0100660i
$866$	3.42548	−	12.3375i	0.116403	−	0.419245i
$867$	8.61930	−	12.7125i	0.292727	−	0.431739i
$868$	22.9154	−	13.7877i	0.777799	−	0.467986i
$869$	0.206279	+	3.80460i	0.00699754	+	0.129062i
$870$	−0.0556602	+	0.0527241i	−0.00188706	+	0.00178752i
$871$	−29.5649	+	22.4747i	−1.00177	+	0.761525i
$872$	12.5291	−	2.75785i	0.424287	−	0.0933927i
$873$	−0.108349	−	0.127558i	−0.00366706	−	0.00431719i
$874$	0.796526	−	14.6911i	0.0269429	−	0.496933i
$875$	8.94376	+	16.8697i	0.302354	+	0.570301i
$876$	−11.1423	−	2.45260i	−0.376463	−	0.0828658i
$877$	22.2039	−	10.2726i	0.749774	−	0.346882i	−0.00750705	−	0.999972i	$-0.502390\pi$
$877$	22.2039	−	10.2726i	0.749774	−	0.346882i	0.757281	+	0.653090i	$0.226528\pi$
$878$	0.253648	+	0.152615i	0.00856020	+	0.00515050i
$879$	−6.98498	+	13.1751i	−0.235597	+	0.444384i
$880$	1.24821	−	1.46950i	0.0420770	−	0.0495369i
$881$	29.8995	+	28.3223i	1.00734	+	0.954202i	0.998952	−	0.0457625i	$-0.0145717\pi$
$881$	29.8995	+	28.3223i	1.00734	+	0.954202i	0.00838683	+	0.999965i	$0.497330\pi$
$882$	−14.4505	−	1.57159i	−0.486575	−	0.0529182i
$883$	19.8446	−	49.8063i	0.667826	−	1.67612i	−0.0669071	−	0.997759i	$-0.521313\pi$
$883$	19.8446	−	49.8063i	0.667826	−	1.67612i	0.734733	−	0.678357i	$-0.237308\pi$
$884$	26.9011			0.904783
$885$	−3.09470	+	0.877927i	−0.104027	+	0.0295112i
$886$	18.1921			0.611176
$887$	−18.1617	+	45.5825i	−0.609811	+	1.53051i	0.221766	+	0.975100i	$0.428818\pi$
$887$	−18.1617	+	45.5825i	−0.609811	+	1.53051i	−0.831577	+	0.555409i	$0.812562\pi$
$888$	−11.7649	−	1.27951i	−0.394804	−	0.0429376i
$889$	−40.3157	−	38.1891i	−1.35215	−	1.28082i
$890$	0.675179	−	0.794882i	0.0226320	−	0.0266445i
$891$	2.15649	−	4.06757i	0.0722452	−	0.136269i
$892$	6.59201	+	3.96628i	0.220717	+	0.132801i
$893$	20.7314	−	9.59135i	0.693749	−	0.320962i
$894$	−10.2418	−	2.25439i	−0.342537	−	0.0753981i
$895$	2.47109	+	4.66097i	0.0825993	+	0.155799i
$896$	−0.251240	+	4.63386i	−0.00839335	+	0.154806i
$897$	−17.1432	−	20.1826i	−0.572396	−	0.673877i
$898$	4.25276	−	0.936102i	0.141916	−	0.0312381i
$899$	−0.839873	+	0.638455i	−0.0280113	+	0.0212937i
$900$	3.50265	−	3.31788i	0.116755	−	0.110596i
$901$	0.719851	+	13.2769i	0.0239817	+	0.442317i
$902$	−2.57086	+	1.54684i	−0.0856004	+	0.0515041i
$903$	27.2831	−	40.2395i	0.907923	−	1.33909i
$904$	1.72377	−	6.20844i	0.0573316	−	0.206490i
$905$	4.79784	−	0.521797i	0.159486	−	0.0173451i
$906$	2.64746	+	2.01255i	0.0879559	+	0.0668623i
$907$	9.13077	+	4.22434i	0.303182	+	0.140267i	0.565582	−	0.824692i	$-0.308652\pi$
$907$	9.13077	+	4.22434i	0.303182	+	0.140267i	−0.262399	+	0.964959i	$0.584514\pi$
$908$	−6.87829	−	10.1447i	−0.228264	−	0.336664i
$909$	−12.7763	+	4.30485i	−0.423765	+	0.142783i
$910$	−1.48691	−	9.06972i	−0.0492904	−	0.300658i
$911$	−8.32829	+	50.8003i	−0.275929	+	1.68309i	0.377427	+	0.926039i	$0.376809\pi$
$911$	−8.32829	+	50.8003i	−0.275929	+	1.68309i	−0.653356	+	0.757051i	$0.726639\pi$
$912$	−2.48991	−	0.838949i	−0.0824492	−	0.0277804i
$913$	22.3923	+	80.6497i	0.741076	+	2.66911i
$914$	10.7024	+	26.8611i	0.354005	+	0.888487i
$915$	−0.129645	−	0.325384i	−0.00428592	−	0.0107569i
$916$	−6.68735	−	24.0857i	−0.220956	−	0.795812i
$917$	−1.57588	−	0.530977i	−0.0520403	−	0.0175344i
$918$	−0.920297	+	5.61356i	−0.0303743	+	0.185275i
$919$	1.45388	+	8.86826i	0.0479590	+	0.292537i	0.999906	−	0.0137265i	$-0.00436942\pi$
$919$	1.45388	+	8.86826i	0.0479590	+	0.292537i	−0.951947	+	0.306263i	$0.900921\pi$
$920$	2.22232	−	0.748786i	0.0732676	−	0.0246867i
$921$	3.72286	+	5.49081i	0.122673	+	0.180928i
$922$	−26.1242	−	12.0863i	−0.860353	−	0.398042i
$923$	42.7304	+	32.4828i	1.40649	+	1.06918i
$924$	−21.2398	+	2.30996i	−0.698737	+	0.0759922i
$925$	15.2747	−	55.0147i	0.502231	−	1.80887i
$926$	2.99089	−	4.41123i	0.0982868	−	0.144962i
$927$	−5.88521	+	3.54101i	−0.193296	+	0.116302i
$928$	−0.00991106	−	0.182799i	−0.000325347	−	0.00600066i
$929$	1.90317	−	1.80278i	0.0624409	−	0.0591472i	−0.655843	−	0.754897i	$-0.727687\pi$
$929$	1.90317	−	1.80278i	0.0624409	−	0.0591472i	0.718284	+	0.695750i	$0.244928\pi$
$930$	−1.92133	+	1.46056i	−0.0630030	+	0.0478937i
$931$	−37.2991	+	8.21014i	−1.22243	+	0.269077i
$932$	15.2949	+	18.0066i	0.501002	+	0.589825i
$933$	−1.37621	+	25.3827i	−0.0450551	+	0.830992i
$934$	14.3529	+	27.0724i	0.469641	+	0.885837i
$935$	−10.7114	−	2.35776i	−0.350301	−	0.0771070i
$936$	−4.29196	+	1.98567i	−0.140287	+	0.0649037i
$937$	34.4313	+	20.7166i	1.12482	+	0.676783i	0.951367	−	0.308059i	$-0.0996795\pi$
$937$	34.4313	+	20.7166i	1.12482	+	0.676783i	0.173454	+	0.984842i	$0.444507\pi$
$938$	−17.0704	+	32.1983i	−0.557370	+	1.05131i
$939$	5.70045	−	6.71109i	0.186027	−	0.219008i
$940$	2.64329	+	2.50386i	0.0862146	+	0.0816668i
$941$	−2.57938	−	0.280525i	−0.0840855	−	0.00914485i	0.0659795	−	0.997821i	$-0.478983\pi$
$941$	−2.57938	−	0.280525i	−0.0840855	−	0.00914485i	−0.150065	+	0.988676i	$0.547948\pi$
$942$	−5.63577	+	14.1447i	−0.183623	+	0.460860i
$943$	−3.64925			−0.118836
$944$	3.18615	−	6.98917i	0.103700	−	0.227478i
$945$	1.94348			0.0632214
$946$	17.8522	−	44.8057i	0.580426	−	1.45676i
$947$	−6.62702	−	0.720732i	−0.215349	−	0.0234206i	−0.000191667	−	1.00000i	$-0.500061\pi$
$947$	−6.62702	−	0.720732i	−0.215349	−	0.0234206i	−0.215158	+	0.976579i	$0.569027\pi$
$948$	0.600838	+	0.569144i	0.0195143	+	0.0184849i
$949$	−34.9289	+	41.1215i	−1.13384	+	1.33486i
$950$	5.93774	−	11.1998i	0.192646	−	0.363369i
$951$	12.1104	+	7.28656i	0.392705	+	0.236283i
$952$	23.9586	−	11.0844i	0.776501	−	0.359248i
$953$	−5.59895	−	1.23242i	−0.181368	−	0.0399221i	0.123358	−	0.992362i	$-0.460634\pi$
$953$	−5.59895	−	1.23242i	−0.181368	−	0.0399221i	−0.304726	+	0.952440i	$0.598565\pi$
$954$	−1.09486	−	2.06513i	−0.0354475	−	0.0668611i
$955$	0.427567	−	7.88602i	0.0138358	−	0.255185i
$956$	0.108861	+	0.128162i	0.00352083	+	0.00414504i
$957$	0.823113	−	0.181181i	0.0266075	−	0.00585675i
$958$	11.5972	−	8.81597i	0.374689	−	0.284831i
$959$	28.1865	−	26.6997i	0.910191	−	0.862178i
$960$	−0.0226730	−	0.418179i	−0.000731769	−	0.0134967i
$961$	−1.89425	+	1.13973i	−0.0611048	+	0.0367655i
$962$	−31.4067	+	46.3214i	−1.01259	+	1.49346i
$963$	−0.0969238	+	0.349088i	−0.00312333	+	0.0112492i
$964$	2.09338	−	0.227669i	0.0674232	−	0.00733271i
$965$	2.57504	+	1.95749i	0.0828933	+	0.0630139i
$966$	−23.5841	−	10.9112i	−0.758806	−	0.351061i
$967$	9.75342	+	14.3852i	0.313649	+	0.462597i	0.951538	−	0.307531i	$-0.0995026\pi$
$967$	9.75342	+	14.3852i	0.313649	+	0.462597i	−0.637889	+	0.770128i	$0.720192\pi$
$968$	−9.66190	+	3.25547i	−0.310545	+	0.104635i
$969$	2.41803	+	14.7494i	0.0776784	+	0.473817i
$970$	0.0113394	−	0.0691675i	0.000364087	−	0.00222083i
$971$	44.2107	+	14.8963i	1.41879	+	0.478046i	0.921106	−	0.389312i	$-0.127287\pi$
$971$	44.2107	+	14.8963i	1.41879	+	0.478046i	0.497684	+	0.867358i	$0.334184\pi$
$972$	−0.267528	−	0.963550i	−0.00858098	−	0.0309059i
$973$	−25.2663	−	63.4136i	−0.809999	−	2.03295i
$974$	−2.27498	−	5.70976i	−0.0728949	−	0.182952i
$975$	−6.10387	−	21.9841i	−0.195480	−	0.704056i
$976$	0.792575	+	0.267050i	0.0253697	+	0.00854805i
$977$	2.16312	−	13.1944i	0.0692043	−	0.422127i	−0.929389	−	0.369102i	$-0.879665\pi$
$977$	2.16312	−	13.1944i	0.0692043	−	0.422127i	0.998593	−	0.0530254i	$-0.0168864\pi$
$978$	−1.00075	−	6.10433i	−0.0320006	−	0.195195i
$979$	−10.8649	+	3.66082i	−0.347245	+	0.117000i
$980$	−3.41622	−	5.03854i	−0.109127	−	0.160950i
$981$	11.6433	+	5.38675i	0.371741	+	0.171986i
$982$	13.1736	+	10.0143i	0.420387	+	0.319570i
$983$	7.76613	−	0.844617i	0.247701	−	0.0269391i	0.0165737	−	0.999863i	$-0.494724\pi$
$983$	7.76613	−	0.844617i	0.247701	−	0.0269391i	0.231127	+	0.972924i	$0.425759\pi$
$984$	−0.174348	+	0.627946i	−0.00555802	+	0.0200182i
$985$	−0.167152	+	0.246530i	−0.00532590	+	0.00785511i
$986$	−0.892312	+	0.536887i	−0.0284170	+	0.0170980i
$987$	−2.18424	−	40.2859i	−0.0695251	−	1.28232i
$988$	−9.02072	+	8.54488i	−0.286987	+	0.271849i
$989$	46.7009	−	35.5011i	1.48500	−	1.12887i
$990$	1.88299	−	0.414478i	0.0598455	−	0.0131730i
$991$	6.33049	+	7.45283i	0.201095	+	0.236747i	0.853461	−	0.521157i	$-0.174499\pi$
$991$	6.33049	+	7.45283i	0.201095	+	0.236747i	−0.652366	+	0.757904i	$0.726224\pi$
$992$	0.311996	−	5.75442i	0.00990587	−	0.182703i
$993$	1.75600	+	3.31216i	0.0557248	+	0.105108i
$994$	51.4405	+	11.3229i	1.63159	+	0.359141i
$995$	−5.26615	+	2.43638i	−0.166948	+	0.0772384i
$996$	15.5781	+	9.37302i	0.493610	+	0.296995i
$997$	6.26448	−	11.8161i	0.198398	−	0.374218i	−0.764273	−	0.644893i	$-0.776902\pi$
$997$	6.26448	−	11.8161i	0.198398	−	0.374218i	0.962671	+	0.270675i	$0.0872468\pi$
$998$	7.70142	−	9.06681i	0.243784	−	0.287005i
$999$	−8.59163	−	8.13843i	−0.271827	−	0.257488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.49.2	✓	84
59.53	even	29	inner	354.2.e.c.289.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.49.2	✓	84	1.1	even	1	trivial
354.2.e.c.289.2	yes	84	59.53	even	29	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.271121 - 0.319189i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(3.97639 + 2.39251i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +O(q^{10})\)	\(q+(-0.370138 + 0.928977i) q^{2} +(0.994138 + 0.108119i) q^{3} +(-0.725995 - 0.687699i) q^{4} +(0.271121 - 0.319189i) q^{5} +(-0.468408 + 0.883512i) q^{6} +(3.97639 + 2.39251i) q^{7} +(0.907575 - 0.419889i) q^{8} +(0.976621 + 0.214970i) q^{9} +(0.196166 + 0.370009i) q^{10} +(0.249248 - 4.59712i) q^{11} +(-0.647386 - 0.762162i) q^{12} +(-4.61848 + 1.01660i) q^{13} +(-3.69440 + 2.80841i) q^{14} +(0.304042 - 0.288004i) q^{15} +(0.0541389 + 0.998533i) q^{16} +(4.87423 - 2.93273i) q^{17} +(-0.561187 + 0.827689i) q^{18} +(-0.702917 + 2.53168i) q^{19} +(-0.416339 + 0.0452796i) q^{20} +(3.69440 + 2.80841i) q^{21} +(4.17836 + 1.93311i) q^{22} +(3.14242 + 4.63472i) q^{23} +(0.947653 - 0.319302i) q^{24} +(0.780535 + 4.76105i) q^{25} +(0.765073 - 4.66674i) q^{26} +(0.947653 + 0.319302i) q^{27} +(-1.24151 - 4.47151i) q^{28} +(0.0677602 + 0.170065i) q^{29} +(0.155012 + 0.389050i) q^{30} +(1.54173 + 5.55282i) q^{31} +(-0.947653 - 0.319302i) q^{32} +(0.744823 - 4.54322i) q^{33} +(0.920297 + 5.61356i) q^{34} +(1.84175 - 0.620556i) q^{35} +(-0.561187 - 0.827689i) q^{36} +(-10.7405 - 4.96909i) q^{37} +(-2.09169 - 1.59006i) q^{38} +(-4.70132 + 0.511299i) q^{39} +(0.112039 - 0.403529i) q^{40} +(-0.365726 + 0.539405i) q^{41} +(-3.97639 + 2.39251i) q^{42} +(-0.567172 - 10.4609i) q^{43} +(-3.34239 + 3.16608i) q^{44} +(0.333399 - 0.253443i) q^{45} +(-5.46868 + 1.20375i) q^{46} +(-5.62826 - 6.62610i) q^{47} +(-0.0541389 + 0.998533i) q^{48} +(6.80867 + 12.8425i) q^{49} +(-4.71182 - 1.03715i) q^{50} +(5.16274 - 2.38854i) q^{51} +(4.05211 + 2.43807i) q^{52} +(-1.09486 + 2.06513i) q^{53} +(-0.647386 + 0.762162i) q^{54} +(-1.39977 - 1.32593i) q^{55} +(4.61346 + 0.501744i) q^{56} +(-0.972519 + 2.44084i) q^{57} -0.183067 q^{58} +(-6.80642 - 3.55987i) q^{59} -0.418794 q^{60} +(0.309567 - 0.776955i) q^{61} +(-5.72909 - 0.623076i) q^{62} +(3.36910 + 3.19138i) q^{63} +(0.647386 - 0.762162i) q^{64} +(-0.927679 + 1.74979i) q^{65} +(3.94486 + 2.37354i) q^{66} +(7.12726 - 3.29742i) q^{67} +(-5.55551 - 1.22286i) q^{68} +(2.62290 + 4.94731i) q^{69} +(-0.105218 + 1.94063i) q^{70} +(-7.34790 - 8.65061i) q^{71} +(0.976621 - 0.214970i) q^{72} +(9.08264 - 6.90445i) q^{73} +(8.59163 - 8.13843i) q^{74} +(0.261199 + 4.81754i) q^{75} +(2.25135 - 1.35459i) q^{76} +(11.9898 - 17.6836i) q^{77} +(1.26515 - 4.55667i) q^{78} +(-0.822754 + 0.0894799i) q^{79} +(0.333399 + 0.253443i) q^{80} +(0.907575 + 0.419889i) q^{81} +(-0.365726 - 0.539405i) q^{82} +(-17.2288 + 5.80506i) q^{83} +(-0.750776 - 4.57953i) q^{84} +(0.385415 - 2.35092i) q^{85} +(9.92784 + 3.34508i) q^{86} +(0.0489757 + 0.176394i) q^{87} +(-1.70407 - 4.27689i) q^{88} +(-0.921762 - 2.31345i) q^{89} +(0.112039 + 0.403529i) q^{90} +(-20.7971 - 7.00735i) q^{91} +(0.905913 - 5.52583i) q^{92} +(0.932329 + 5.68695i) q^{93} +(8.23873 - 2.77595i) q^{94} +(0.617507 + 0.910755i) q^{95} +(-0.907575 - 0.419889i) q^{96} +(-0.133237 - 0.101284i) q^{97} +(-14.4505 + 1.57159i) q^{98} +(1.23167 - 4.43606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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