LMFDB - Embedded newform 425.2.q.a.84.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(84,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7, 5]))

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

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

chi := DirichletCharacter("425.84");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.q (of order $10$, degree $4$, 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			84.1
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61286 + 2.21990i) q^{2} +(-0.861202 - 2.65051i) q^{3} +(-1.70864 - 5.25866i) q^{4} +(0.297302 - 2.21622i) q^{5} +(7.27287 + 2.36310i) q^{6} +1.90625 q^{7} +(9.21020 + 2.99258i) q^{8} +(-3.85647 + 2.80189i) q^{9} +(4.44028 + 4.23442i) q^{10} +(2.64178 - 3.63610i) q^{11} +(-12.4666 + 9.05754i) q^{12} +(-0.219466 - 0.302069i) q^{13} +(-3.07450 + 4.23169i) q^{14} +(-6.13013 + 1.12061i) q^{15} +(-12.5514 + 9.11912i) q^{16} +(3.76544 + 1.67972i) q^{17} -13.0800i q^{18} +(2.03005 - 6.24784i) q^{19} +(-12.1623 + 2.22331i) q^{20} +(-1.64167 - 5.05253i) q^{21} +(3.81099 + 11.7290i) q^{22} +(1.16500 + 0.846425i) q^{23} -26.9889i q^{24} +(-4.82322 - 1.31777i) q^{25} +1.02453 q^{26} +(3.98367 + 2.89430i) q^{27} +(-3.25710 - 10.0243i) q^{28} +(3.44009 - 1.11775i) q^{29} +(7.39938 - 15.4157i) q^{30} +(-5.87547 - 1.90906i) q^{31} -23.2024i q^{32} +(-11.9126 - 3.87065i) q^{33} +(-9.80192 + 5.64978i) q^{34} +(0.566732 - 4.22466i) q^{35} +(21.3235 + 15.4924i) q^{36} +(-2.09235 + 1.52018i) q^{37} +(10.5954 + 14.5834i) q^{38} +(-0.611631 + 0.841838i) q^{39} +(9.37041 - 19.5221i) q^{40} +(-1.09109 - 1.50176i) q^{41} +(13.8639 + 4.50465i) q^{42} +12.2854i q^{43} +(-23.6349 - 7.67943i) q^{44} +(5.06306 + 9.37978i) q^{45} +(-3.75796 + 1.22104i) q^{46} +(0.0802572 - 0.0260771i) q^{47} +(34.9796 + 25.4142i) q^{48} -3.36622 q^{49} +(10.7045 - 8.58172i) q^{50} +(1.20930 - 11.4269i) q^{51} +(-1.21349 + 1.67022i) q^{52} +(0.319741 - 0.103890i) q^{53} +(-12.8502 + 4.17527i) q^{54} +(-7.27298 - 6.93578i) q^{55} +(17.5569 + 5.70460i) q^{56} -18.3082 q^{57} +(-3.06706 + 9.43944i) q^{58} +(-1.06587 + 0.774396i) q^{59} +(16.3671 + 30.3216i) q^{60} +(-5.79643 + 7.97811i) q^{61} +(13.7142 - 9.96395i) q^{62} +(-7.35140 + 5.34110i) q^{63} +(26.4043 + 19.1838i) q^{64} +(-0.734697 + 0.396578i) q^{65} +(27.8058 - 20.2021i) q^{66} +(3.59511 + 1.16812i) q^{67} +(2.39926 - 22.6712i) q^{68} +(1.24015 - 3.81679i) q^{69} +(8.46428 + 8.07185i) q^{70} +(10.4209 - 3.38595i) q^{71} +(-43.9038 + 14.2652i) q^{72} +(-1.80355 - 1.31036i) q^{73} -7.09664i q^{74} +(0.661009 + 13.9189i) q^{75} -36.3239 q^{76} +(5.03589 - 6.93131i) q^{77} +(-0.882327 - 2.71552i) q^{78} +(9.56517 - 3.10791i) q^{79} +(16.4784 + 30.5277i) q^{80} +(-0.178492 + 0.549342i) q^{81} +5.09354 q^{82} +(-1.19600 - 0.388603i) q^{83} +(-23.7645 + 17.2659i) q^{84} +(4.84209 - 7.84565i) q^{85} +(-27.2723 - 19.8145i) q^{86} +(-5.92523 - 8.15537i) q^{87} +(35.2127 - 25.5835i) q^{88} +(-5.55007 - 4.03236i) q^{89} +(-28.9882 - 3.88872i) q^{90} +(-0.418356 - 0.575818i) q^{91} +(2.46048 - 7.57259i) q^{92} +17.2171i q^{93} +(-0.0715544 + 0.220222i) q^{94} +(-13.2430 - 6.35652i) q^{95} +(-61.4981 + 19.9819i) q^{96} +(-2.90335 - 8.93560i) q^{97} +(5.42922 - 7.47268i) q^{98} +21.4245i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) $ 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.61286	+	2.21990i	−1.14046	+	1.56971i	−0.373988	+	0.927434i	$0.622010\pi$
$2$	−1.61286	+	2.21990i	−1.14046	+	1.56971i	−0.766473	+	0.642276i	$0.777990\pi$
$3$	−0.861202	−	2.65051i	−0.497215	−	1.53027i	−0.813476	−	0.581599i	$-0.802427\pi$
$3$	−0.861202	−	2.65051i	−0.497215	−	1.53027i	0.316260	−	0.948672i	$-0.397573\pi$
$4$	−1.70864	−	5.25866i	−0.854321	−	2.62933i
$5$	0.297302	−	2.21622i	0.132957	−	0.991122i
$5$	0.297302	−	2.21622i	0.132957	−	0.991122i
$6$	7.27287	+	2.36310i	2.96914	+	0.964731i
$7$	1.90625			0.720494			0.360247	−	0.932857i	$-0.382692\pi$
$7$	1.90625			0.720494			0.360247	+	0.932857i	$0.382692\pi$
$8$	9.21020	+	2.99258i	3.25630	+	1.05804i
$9$	−3.85647	+	2.80189i	−1.28549	+	0.933964i
$10$	4.44028	+	4.23442i	1.40414	+	1.33904i
$11$	2.64178	−	3.63610i	0.796527	−	1.09633i	−0.196737	−	0.980456i	$-0.563035\pi$
$11$	2.64178	−	3.63610i	0.796527	−	1.09633i	0.993264	−	0.115869i	$-0.0369654\pi$
$12$	−12.4666	+	9.05754i	−3.59881	+	2.61469i
$13$	−0.219466	−	0.302069i	−0.0608688	−	0.0837787i	0.777497	−	0.628886i	$-0.216489\pi$
$13$	−0.219466	−	0.302069i	−0.0608688	−	0.0837787i	−0.838366	+	0.545107i	$0.816489\pi$
$14$	−3.07450	+	4.23169i	−0.821696	+	1.13097i
$15$	−6.13013	+	1.12061i	−1.58279	+	0.289340i
$16$	−12.5514	+	9.11912i	−3.13785	+	2.27978i
$17$	3.76544	+	1.67972i	0.913254	+	0.407391i
$17$	3.76544	+	1.67972i	0.913254	+	0.407391i
$18$		−	13.0800i		−	3.08300i
$19$	2.03005	−	6.24784i	0.465725	−	1.43335i	−0.392344	−	0.919818i	$-0.628336\pi$
$19$	2.03005	−	6.24784i	0.465725	−	1.43335i	0.858069	−	0.513535i	$-0.171664\pi$
$20$	−12.1623	+	2.22331i	−2.71957	+	0.497147i
$21$	−1.64167	−	5.05253i	−0.358241	−	1.10255i
$22$	3.81099	+	11.7290i	0.812505	+	2.50063i
$23$	1.16500	+	0.846425i	0.242920	+	0.176492i	0.702583	−	0.711602i	$-0.252030\pi$
$23$	1.16500	+	0.846425i	0.242920	+	0.176492i	−0.459663	+	0.888093i	$0.652030\pi$
$24$		−	26.9889i		−	5.50909i
$25$	−4.82322	−	1.31777i	−0.964645	−	0.263554i
$26$	1.02453			0.200927
$27$	3.98367	+	2.89430i	0.766657	+	0.557009i
$28$	−3.25710	−	10.0243i	−0.615533	−	1.89442i
$29$	3.44009	−	1.11775i	0.638809	−	0.207561i	0.0283354	−	0.999598i	$-0.490979\pi$
$29$	3.44009	−	1.11775i	0.638809	−	0.207561i	0.610473	+	0.792037i	$0.290979\pi$
$30$	7.39938	−	15.4157i	1.35093	−	2.81451i
$31$	−5.87547	−	1.90906i	−1.05527	−	0.342876i	−0.270533	−	0.962711i	$-0.587200\pi$
$31$	−5.87547	−	1.90906i	−1.05527	−	0.342876i	−0.784733	+	0.619834i	$0.787200\pi$
$32$		−	23.2024i		−	4.10164i
$33$	−11.9126	−	3.87065i	−2.07372	−	0.673793i
$34$	−9.80192	+	5.64978i	−1.68102	+	0.968930i
$35$	0.566732	−	4.22466i	0.0957951	−	0.714098i
$36$	21.3235	+	15.4924i	3.55392	+	2.58207i
$37$	−2.09235	+	1.52018i	−0.343980	+	0.249916i	−0.746339	−	0.665566i	$-0.768190\pi$
$37$	−2.09235	+	1.52018i	−0.343980	+	0.249916i	0.402359	+	0.915482i	$0.368190\pi$
$38$	10.5954	+	14.5834i	1.71881	+	2.36574i
$39$	−0.611631	+	0.841838i	−0.0979393	+	0.134802i
$40$	9.37041	−	19.5221i	1.48159	−	3.08671i
$41$	−1.09109	−	1.50176i	−0.170400	−	0.234536i	0.715273	−	0.698845i	$-0.246302\pi$
$41$	−1.09109	−	1.50176i	−0.170400	−	0.234536i	−0.885673	+	0.464310i	$0.846302\pi$
$42$	13.8639	+	4.50465i	2.13925	+	0.695083i
$43$			12.2854i			1.87350i	0.350000	+	0.936750i	$0.386182\pi$
$43$			12.2854i			1.87350i	−0.350000	+	0.936750i	$0.613818\pi$
$44$	−23.6349	−	7.67943i	−3.56309	−	1.15772i
$45$	5.06306	+	9.37978i	0.754756	+	1.39826i
$46$	−3.75796	+	1.22104i	−0.554082	+	0.180032i
$47$	0.0802572	−	0.0260771i	0.0117067	−	0.00380374i	−0.303158	−	0.952940i	$-0.598041\pi$
$47$	0.0802572	−	0.0260771i	0.0117067	−	0.00380374i	0.314864	+	0.949137i	$0.398041\pi$
$48$	34.9796	+	25.4142i	5.04887	+	3.66822i
$49$	−3.36622			−0.480888
$50$	10.7045	−	8.58172i	1.51384	−	1.21364i
$51$	1.20930	−	11.4269i	0.169335	−	1.60009i
$52$	−1.21349	+	1.67022i	−0.168280	+	0.231618i
$53$	0.319741	−	0.103890i	0.0439198	−	0.0142704i	−0.286975	−	0.957938i	$-0.592650\pi$
$53$	0.319741	−	0.103890i	0.0439198	−	0.0142704i	0.330894	+	0.943668i	$0.392650\pi$
$54$	−12.8502	+	4.17527i	−1.74869	+	0.568182i
$55$	−7.27298	−	6.93578i	−0.980688	−	0.935220i
$56$	17.5569	+	5.70460i	2.34614	+	0.762309i
$57$	−18.3082			−2.42498
$58$	−3.06706	+	9.43944i	−0.402725	+	1.23946i
$59$	−1.06587	+	0.774396i	−0.138764	+	0.100818i	−0.655002	−	0.755627i	$-0.727332\pi$
$59$	−1.06587	+	0.774396i	−0.138764	+	0.100818i	0.516238	+	0.856445i	$0.327332\pi$
$60$	16.3671	+	30.3216i	2.11298	+	3.91450i
$61$	−5.79643	+	7.97811i	−0.742157	+	1.02149i	0.256334	+	0.966588i	$0.417485\pi$
$61$	−5.79643	+	7.97811i	−0.742157	+	1.02149i	−0.998492	+	0.0549038i	$0.982515\pi$
$62$	13.7142	−	9.96395i	1.74171	−	1.26542i
$63$	−7.35140	+	5.34110i	−0.926189	+	0.672916i
$64$	26.4043	+	19.1838i	3.30053	+	2.39798i
$65$	−0.734697	+	0.396578i	−0.0911279	+	0.0491894i
$66$	27.8058	−	20.2021i	3.42266	−	2.48671i
$67$	3.59511	+	1.16812i	0.439213	+	0.142709i	0.520272	−	0.854000i	$-0.325830\pi$
$67$	3.59511	+	1.16812i	0.439213	+	0.142709i	−0.0810596	+	0.996709i	$0.525830\pi$
$68$	2.39926	−	22.6712i	0.290954	−	2.74929i
$69$	1.24015	−	3.81679i	0.149297	−	0.459488i
$70$	8.46428	+	8.07185i	1.01168	+	0.964771i
$71$	10.4209	−	3.38595i	1.23673	−	0.401838i	0.383583	−	0.923506i	$-0.374690\pi$
$71$	10.4209	−	3.38595i	1.23673	−	0.401838i	0.853149	+	0.521668i	$0.174690\pi$
$72$	−43.9038	+	14.2652i	−5.17411	+	1.68117i
$73$	−1.80355	−	1.31036i	−0.211090	−	0.153366i	0.477217	−	0.878786i	$-0.341646\pi$
$73$	−1.80355	−	1.31036i	−0.211090	−	0.153366i	−0.688307	+	0.725420i	$0.741646\pi$
$74$		−	7.09664i		−	0.824968i
$75$	0.661009	+	13.9189i	0.0763268	+	1.60721i
$76$	−36.3239			−4.16664
$77$	5.03589	−	6.93131i	0.573893	−	0.789896i
$78$	−0.882327	−	2.71552i	−0.0999039	−	0.307473i
$79$	9.56517	−	3.10791i	1.07617	−	0.349667i	0.283279	−	0.959037i	$-0.408578\pi$
$79$	9.56517	−	3.10791i	1.07617	−	0.349667i	0.792886	+	0.609370i	$0.208578\pi$
$80$	16.4784	+	30.5277i	1.84234	+	3.41310i
$81$	−0.178492	+	0.549342i	−0.0198325	+	0.0610380i
$82$	5.09354			0.562488
$83$	−1.19600	−	0.388603i	−0.131278	−	0.0426547i	0.242641	−	0.970116i	$-0.421986\pi$
$83$	−1.19600	−	0.388603i	−0.131278	−	0.0426547i	−0.373919	+	0.927461i	$0.621986\pi$
$84$	−23.7645	+	17.2659i	−2.59292	+	1.88387i
$85$	4.84209	−	7.84565i	0.525198	−	0.850980i
$86$	−27.2723	−	19.8145i	−2.94085	−	2.13665i
$87$	−5.92523	−	8.15537i	−0.635251	−	0.874348i
$88$	35.2127	−	25.5835i	3.75368	−	2.72721i
$89$	−5.55007	−	4.03236i	−0.588307	−	0.427430i	0.253403	−	0.967361i	$-0.418450\pi$
$89$	−5.55007	−	4.03236i	−0.588307	−	0.427430i	−0.841709	+	0.539931i	$0.818450\pi$
$90$	−28.9882	−	3.88872i	−3.05563	−	0.409907i
$91$	−0.418356	−	0.575818i	−0.0438556	−	0.0603621i
$92$	2.46048	−	7.57259i	0.256523	−	0.789497i
$93$			17.2171i			1.78533i
$94$	−0.0715544	+	0.220222i	−0.00738028	+	0.0227142i
$95$	−13.2430	−	6.35652i	−1.35871	−	0.652165i
$96$	−61.4981	+	19.9819i	−6.27662	+	2.03940i
$97$	−2.90335	−	8.93560i	−0.294791	−	0.907273i	−0.983292	−	0.182037i	$-0.941731\pi$
$97$	−2.90335	−	8.93560i	−0.294791	−	0.907273i	0.688501	−	0.725235i	$-0.258269\pi$
$98$	5.42922	−	7.47268i	0.548434	−	0.754854i
$99$			21.4245i			2.15324i
$100$	1.31145	+	27.6153i	0.131145	+	2.76153i
$101$	2.87123			0.285698			0.142849	−	0.989744i	$-0.454374\pi$
$101$	2.87123			0.285698			0.142849	+	0.989744i	$0.454374\pi$
$102$	23.4162	+	21.1145i	2.31855	+	2.09064i
$103$	−6.41133	+	2.08317i	−0.631727	+	0.205260i	−0.607340	−	0.794442i	$-0.707763\pi$
$103$	−6.41133	+	2.08317i	−0.631727	+	0.205260i	−0.0243868	+	0.999703i	$0.507763\pi$
$104$	−1.11736	−	3.43888i	−0.109566	−	0.337210i
$105$	−11.6856	+	2.13616i	−1.14039	+	0.208468i
$106$	−0.285069	+	0.877354i	−0.0276884	+	0.0852161i
$107$	6.16879			0.596359			0.298180	−	0.954510i	$-0.403621\pi$
$107$	6.16879			0.596359			0.298180	+	0.954510i	$0.403621\pi$
$108$	8.41349	−	25.8941i	0.809589	−	2.49166i
$109$	3.01721	+	4.15284i	0.288997	+	0.397770i	0.928688	−	0.370862i	$-0.120938\pi$
$109$	3.01721	+	4.15284i	0.288997	+	0.397770i	−0.639691	+	0.768632i	$0.720938\pi$
$110$	27.1270	−	4.95891i	2.58646	−	0.472813i
$111$	5.83118	+	4.23660i	0.553471	+	0.402120i
$112$	−23.9261	+	17.3833i	−2.26080	+	1.64257i
$113$	−0.682524	+	0.495882i	−0.0642064	+	0.0466487i	−0.619426	−	0.785055i	$-0.712634\pi$
$113$	−0.682524	+	0.495882i	−0.0642064	+	0.0466487i	0.555219	+	0.831704i	$0.312634\pi$
$114$	29.5285	−	40.6425i	2.76560	−	3.80652i
$115$	2.22222	−	2.33026i	0.207223	−	0.217297i
$116$	−11.7558	−	16.1804i	−1.09149	−	1.50231i
$117$	1.69273	+	0.550000i	0.156493	+	0.0508475i
$118$		−	3.61511i		−	0.332798i
$119$	7.17787	+	3.20196i	0.657994	+	0.293523i
$120$	−59.8133	−	8.02386i	−5.46018	−	0.732475i
$121$	−2.84303	−	8.74994i	−0.258457	−	0.795449i
$122$	−8.36183	−	25.7351i	−0.757045	−	2.32994i
$123$	−3.04078	+	4.18527i	−0.274178	+	0.377373i
$124$			34.1590i			3.06757i
$125$	−4.35442	+	10.2975i	−0.389471	+	0.921039i
$126$		−	24.9338i		−	2.22128i
$127$	−7.28155	+	10.0222i	−0.646133	+	0.889325i	−0.998924	−	0.0463767i	$-0.985233\pi$
$127$	−7.28155	+	10.0222i	−0.646133	+	0.889325i	0.352791	+	0.935702i	$0.385233\pi$
$128$	−41.0390	+	13.3344i	−3.62737	+	1.17860i
$129$	32.5624	−	10.5802i	2.86696	−	0.931533i
$130$	0.304595	−	2.27058i	0.0267147	−	0.199143i
$131$	9.13304	+	2.96750i	0.797957	+	0.259272i	0.679489	−	0.733686i	$-0.262202\pi$
$131$	9.13304	+	2.96750i	0.797957	+	0.259272i	0.118468	+	0.992958i	$0.462202\pi$
$132$			69.2579i			6.02813i
$133$	3.86977	−	11.9099i	0.335552	−	1.03272i
$134$	−8.39152	+	6.09679i	−0.724917	+	0.526683i
$135$	7.59875	−	7.96818i	0.653997	−	0.685792i
$136$	29.6538	+	26.7389i	2.54279	+	2.29284i
$137$	4.99670	+	6.87737i	0.426897	+	0.587573i	0.967237	−	0.253873i	$-0.0817046\pi$
$137$	4.99670	+	6.87737i	0.426897	+	0.587573i	−0.540341	+	0.841446i	$0.681705\pi$
$138$	6.47273	+	8.90895i	0.550996	+	0.758381i
$139$	−7.43510	+	10.2335i	−0.630637	+	0.867998i	−0.998073	−	0.0620512i	$-0.980236\pi$
$139$	−7.43510	+	10.2335i	−0.630637	+	0.867998i	0.367436	+	0.930049i	$0.380236\pi$
$140$	−23.1844	+	4.23818i	−1.95944	+	0.358192i
$141$	−0.138235	−	0.190265i	−0.0116415	−	0.0160232i
$142$	−9.29089	+	28.5944i	−0.779674	+	2.39959i
$143$	−1.67813			−0.140332
$144$	22.8533	−	70.3353i	1.90444	−	5.86127i
$145$	−1.45444	−	7.95629i	−0.120784	−	0.660734i
$146$	5.81773	−	1.89030i	0.481479	−	0.156442i
$147$	2.89899	+	8.92218i	0.239105	+	0.735889i
$148$	11.5692	+	8.40550i	0.950980	+	0.690928i
$149$	11.4180			0.935402			0.467701	−	0.883887i	$-0.345082\pi$
$149$	11.4180			0.935402			0.467701	+	0.883887i	$0.345082\pi$
$150$	−31.9647	−	20.9817i	−2.60990	−	1.71315i
$151$	8.50567			0.692182			0.346091	−	0.938201i	$-0.387509\pi$
$151$	8.50567			0.692182			0.346091	+	0.938201i	$0.387509\pi$
$152$	37.3943	−	51.4688i	3.03308	−	4.17467i
$153$	−19.2277	+	4.07258i	−1.55447	+	0.329248i
$154$	7.26469	+	22.3584i	0.585405	+	1.80169i
$155$	−5.97767	+	12.4537i	−0.480138	+	1.00031i
$156$	5.47199	+	1.77796i	0.438110	+	0.142351i
$157$		−	9.27211i		−	0.739995i	−0.929033	−	0.369997i	$-0.879359\pi$
$157$		−	9.27211i		−	0.739995i	0.929033	−	0.369997i	$-0.120641\pi$
$158$	−8.52796	+	26.2464i	−0.678448	+	2.08805i
$159$	−0.550723	−	0.758005i	−0.0436752	−	0.0601137i
$160$	−51.4215	−	6.89811i	−4.06522	−	0.545344i
$161$	2.22079	+	1.61350i	0.175023	+	0.127161i
$162$	−0.931606	−	1.28225i	−0.0731939	−	0.100743i
$163$	12.2734	−	8.91718i	0.961330	−	0.698447i	0.00787112	−	0.999969i	$-0.497495\pi$
$163$	12.2734	−	8.91718i	0.961330	−	0.698447i	0.953459	+	0.301522i	$0.0974945\pi$
$164$	−6.03296	+	8.30366i	−0.471095	+	0.648407i
$165$	−12.1198	+	25.2502i	−0.943527	+	1.96572i
$166$	2.79163	−	2.02824i	0.216673	−	0.157422i
$167$	1.49375	−	4.59729i	0.115590	−	0.355749i	−0.876480	−	0.481439i	$-0.840114\pi$
$167$	1.49375	−	4.59729i	0.115590	−	0.355749i	0.992070	+	0.125690i	$0.0401143\pi$
$168$		−	51.4476i		−	3.96927i
$169$	3.97414	−	12.2311i	0.305703	−	0.940857i
$170$	9.60701	+	23.4029i	0.736824	+	1.79492i
$171$	9.67695	+	29.7826i	0.740015	+	2.27753i
$172$	64.6045	−	20.9913i	4.92605	−	1.60057i
$173$	−12.4456	−	9.04229i	−0.946225	−	0.687473i	0.00368601	−	0.999993i	$-0.498827\pi$
$173$	−12.4456	−	9.04229i	−0.946225	−	0.687473i	−0.949911	+	0.312521i	$0.898827\pi$
$174$	27.6607			2.09695
$175$	−9.19426	−	2.51200i	−0.695021	−	0.189889i
$176$			69.7289i			5.25601i
$177$	2.97047	+	2.15817i	0.223274	+	0.162218i
$178$	17.9029	−	5.81702i	1.34188	−	0.436004i
$179$	4.12104	+	12.6833i	0.308021	+	0.947991i	0.978533	+	0.206092i	$0.0660746\pi$
$179$	4.12104	+	12.6833i	0.308021	+	0.947991i	−0.670512	+	0.741899i	$0.733925\pi$
$180$	40.6741	−	42.6516i	3.03167	−	3.17906i
$181$	3.19982	+	1.03968i	0.237841	+	0.0772791i	0.425512	−	0.904953i	$-0.360094\pi$
$181$	3.19982	+	1.03968i	0.237841	+	0.0772791i	−0.187671	+	0.982232i	$0.560094\pi$
$182$	1.95301			0.144767
$183$	26.1379	+	8.49273i	1.93217	+	0.627801i
$184$	8.19693	+	11.2821i	0.604286	+	0.831728i
$185$	2.74699	+	5.08904i	0.201962	+	0.374154i
$186$	−38.2202	−	27.7686i	−2.80244	−	2.03609i
$187$	16.0551	−	9.25408i	1.17406	−	0.676725i
$188$	−0.274261	−	0.377489i	−0.0200026	−	0.0275312i
$189$	7.59386	+	5.51726i	0.552372	+	0.401322i
$190$	35.4699	−	19.1461i	2.57326	−	1.38901i
$191$	−16.2916	+	11.8365i	−1.17882	+	0.856462i	−0.992038	−	0.125940i	$-0.959805\pi$
$191$	−16.2916	+	11.8365i	−1.17882	+	0.856462i	−0.186781	+	0.982402i	$0.559805\pi$
$192$	28.1075	−	86.5059i	2.02848	−	6.24302i
$193$	−24.1422			−1.73779			−0.868897	−	0.494994i	$-0.835170\pi$
$193$	−24.1422			−1.73779			−0.868897	+	0.494994i	$0.835170\pi$
$194$	24.5189	+	7.96666i	1.76035	+	0.571973i
$195$	1.68385	+	1.60579i	0.120583	+	0.114993i
$196$	5.75166	+	17.7018i	0.410833	+	1.26441i
$197$	7.35443	+	22.6346i	0.523981	+	1.61265i	0.766322	+	0.642457i	$0.222085\pi$
$197$	7.35443	+	22.6346i	0.523981	+	1.61265i	−0.242341	+	0.970191i	$0.577915\pi$
$198$	−47.5604	−	34.5546i	−3.37997	−	2.45569i
$199$			0.808544i			0.0573162i	0.999589	+	0.0286581i	$0.00912340\pi$
$199$			0.808544i			0.0573162i	−0.999589	+	0.0286581i	$0.990877\pi$
$200$	−40.4793	−	26.5708i	−2.86232	−	1.87884i
$201$		−	10.5349i		−	0.743072i
$202$	−4.63088	+	6.37386i	−0.325827	+	0.448463i
$203$	6.55767	−	2.13071i	0.460258	−	0.149547i
$204$	−62.1565	+	13.1652i	−4.35182	+	0.921750i
$205$	−3.65261	+	1.97162i	−0.255109	+	0.137704i
$206$	5.71611	−	17.5924i	0.398260	−	1.22572i
$207$	−6.86439			−0.477108
$208$	5.50920	+	1.79005i	0.381994	+	0.124117i
$209$	−17.3548	−	23.8869i	−1.20046	−	1.65229i
$210$	14.1051	−	29.3862i	0.973341	−	2.02784i
$211$	11.0049	−	15.1469i	0.757607	−	1.04276i	−0.239803	−	0.970822i	$-0.577083\pi$
$211$	11.0049	−	15.1469i	0.757607	−	1.04276i	0.997409	−	0.0719344i	$-0.0229172\pi$
$212$	−1.09264	−	1.50390i	−0.0750431	−	0.103288i
$213$	−17.9490	−	24.7047i	−1.22984	−	1.69273i
$214$	−9.94936	+	13.6941i	−0.680124	+	0.936111i
$215$	27.2270	+	3.65246i	1.85687	+	0.249096i
$216$	28.0290	+	38.5786i	1.90713	+	2.62494i
$217$	−11.2001	−	3.63913i	−0.760313	−	0.247041i
$218$	−14.0852			−0.953972
$219$	−1.91989	+	5.90881i	−0.129734	+	0.399280i
$220$	−24.0460	+	50.0968i	−1.62118	+	3.37753i
$221$	−0.318996	−	1.50606i	−0.0214580	−	0.101309i
$222$	−18.8097	+	6.11164i	−1.26242	+	0.410187i
$223$	8.66718	−	11.9293i	0.580397	−	0.798848i	−0.413342	−	0.910576i	$-0.635638\pi$
$223$	8.66718	−	11.9293i	0.580397	−	0.798848i	0.993739	+	0.111728i	$0.0356385\pi$
$224$		−	44.2295i		−	2.95521i
$225$	22.2929	−	8.43220i	1.48619	−	0.562147i
$226$		−	2.31492i		−	0.153986i
$227$	−7.56129	−	5.49360i	−0.501861	−	0.364623i	0.307867	−	0.951430i	$-0.400385\pi$
$227$	−7.56129	−	5.49360i	−0.501861	−	0.364623i	−0.809727	+	0.586806i	$0.800385\pi$
$228$	31.2822	+	96.2767i	2.07171	+	6.37608i
$229$	−4.42778	−	13.6273i	−0.292596	−	0.900517i	−0.984018	−	0.178067i	$-0.943016\pi$
$229$	−4.42778	−	13.6273i	−0.292596	−	0.900517i	0.691423	−	0.722451i	$-0.256984\pi$
$230$	1.58883	+	8.69148i	0.104764	+	0.573099i
$231$	−22.7084	−	7.37841i	−1.49410	−	0.485464i
$232$	35.0289			2.29976
$233$	8.03745	−	24.7367i	0.526551	−	1.62056i	−0.234678	−	0.972073i	$-0.575404\pi$
$233$	8.03745	−	24.7367i	0.526551	−	1.62056i	0.761229	−	0.648483i	$-0.224596\pi$
$234$	−3.95107	+	2.87062i	−0.258290	+	0.187658i
$235$	−0.0339319	−	0.185620i	−0.00221348	−	0.0121085i
$236$	5.89347	+	4.28185i	0.383632	+	0.278725i
$237$	−16.4751	−	22.6760i	−1.07017	−	1.47297i
$238$	−18.6849	+	10.7699i	−1.21116	+	0.698108i
$239$	17.7693	+	12.9102i	1.14940	+	0.835089i	0.988401	−	0.151866i	$-0.0485281\pi$
$239$	17.7693	+	12.9102i	1.14940	+	0.835089i	0.161000	+	0.986954i	$0.448528\pi$
$240$	66.7228	−	69.9667i	4.30694	−	4.51633i
$241$	−12.2866	−	16.9111i	−0.791452	−	1.08934i	−0.993926	−	0.110052i	$-0.964898\pi$
$241$	−12.2866	−	16.9111i	−0.791452	−	1.08934i	0.202474	−	0.979288i	$-0.435102\pi$
$242$	24.0094	+	7.80114i	1.54338	+	0.501476i
$243$	16.3820			1.05091
$244$	51.8582	+	16.8497i	3.31988	+	1.07869i
$245$	−1.00078	+	7.46026i	−0.0639376	+	0.476618i
$246$	−4.38657	−	13.5005i	−0.279678	−	0.860759i
$247$	−2.33280	+	0.757973i	−0.148433	+	0.0482287i
$248$	−48.4013	−	35.1656i	−3.07348	−	2.23302i
$249$			3.50467i			0.222099i
$250$	−15.8365	−	26.2748i	−1.00159	−	1.66177i
$251$	15.4610			0.975889			0.487945	−	0.872875i	$-0.337747\pi$
$251$	15.4610			0.975889			0.487945	+	0.872875i	$0.337747\pi$
$252$	40.6479	+	29.5324i	2.56058	+	1.86037i
$253$	6.15537	−	2.00000i	0.386985	−	0.125739i
$254$	−10.5042	−	32.3287i	−0.659094	−	2.02848i
$255$	−24.9650	−	6.07730i	−1.56337	−	0.380575i
$256$	16.4178	−	50.5289i	1.02612	−	3.15806i
$257$			22.5592i			1.40720i	0.710594	+	0.703602i	$0.248426\pi$
$257$			22.5592i			1.40720i	−0.710594	+	0.703602i	$0.751574\pi$
$258$	−29.0315	+	89.3498i	−1.80742	+	5.56268i
$259$	−3.98853	+	2.89784i	−0.247835	+	0.180063i
$260$	3.34080	+	3.18591i	0.207188	+	0.197582i
$261$	−10.1348	+	13.9493i	−0.627328	+	0.863442i
$262$	−21.3179	+	15.4883i	−1.31702	+	0.956872i
$263$	13.3945	+	18.4359i	0.825940	+	1.13681i	0.988665	+	0.150138i	$0.0479717\pi$
$263$	13.3945	+	18.4359i	0.825940	+	1.13681i	−0.162725	+	0.986671i	$0.552028\pi$
$264$	−98.1345	−	71.2989i	−6.03976	−	4.38814i
$265$	−0.135183	−	0.739501i	−0.00830424	−	0.0454272i
$266$	20.1975	+	27.7995i	1.23839	+	1.70450i
$267$	−5.90808	+	18.1832i	−0.361569	+	1.11279i
$268$		−	20.9014i		−	1.27675i
$269$	−8.52121	−	2.76871i	−0.519547	−	0.168811i	0.0374926	−	0.999297i	$-0.488063\pi$
$269$	−8.52121	−	2.76871i	−0.519547	−	0.168811i	−0.557040	+	0.830486i	$0.688063\pi$
$270$	5.43292	+	29.7200i	0.330637	+	1.80870i
$271$	6.67709	+	20.5500i	0.405605	+	1.24832i	0.920389	+	0.391003i	$0.127872\pi$
$271$	6.67709	+	20.5500i	0.405605	+	1.24832i	−0.514785	+	0.857319i	$0.672128\pi$
$272$	−62.5791	+	13.2547i	−3.79442	+	0.803687i
$273$	−1.16592	+	1.60475i	−0.0705647	+	0.0971240i
$274$	−23.3260			−1.40918
$275$	−17.5334	+	14.0565i	−1.05731	+	0.847636i
$276$	−22.1902			−1.33569
$277$	11.5410	+	8.38501i	0.693430	+	0.503807i	0.877786	−	0.479053i	$-0.159020\pi$
$277$	11.5410	+	8.38501i	0.693430	+	0.503807i	−0.184356	+	0.982860i	$0.559020\pi$
$278$	−10.7257	−	33.0104i	−0.643287	−	1.97984i
$279$	28.0075	−	9.10020i	1.67677	−	0.544815i
$280$	17.8623	−	37.2140i	1.06748	−	2.22396i
$281$	3.84389	−	11.8303i	0.229307	−	0.705734i	−0.768519	−	0.639827i	$-0.779006\pi$
$281$	3.84389	−	11.8303i	0.229307	−	0.705734i	0.997826	−	0.0659072i	$-0.0209941\pi$
$282$	0.645323			0.0384284
$283$	4.26646	−	13.1308i	0.253615	−	0.780546i	−0.740485	−	0.672073i	$-0.765404\pi$
$283$	4.26646	−	13.1308i	0.253615	−	0.780546i	0.994099	−	0.108473i	$-0.0345961\pi$
$284$	−35.6111	−	49.0145i	−2.11313	−	2.90848i
$285$	−5.44307	+	40.5750i	−0.322420	+	2.40346i
$286$	2.70658	−	3.72529i	0.160044	−	0.220281i
$287$	−2.07990	−	2.86273i	−0.122772	−	0.168982i
$288$	65.0105	+	89.4793i	3.83078	+	5.27262i
$289$	11.3571	+	12.6498i	0.668065	+	0.744103i
$290$	20.0080	+	9.60363i	1.17491	+	0.563945i
$291$	−21.1835	+	15.3907i	−1.24180	+	0.902220i
$292$	−3.80909	+	11.7232i	−0.222910	+	0.686048i
$293$		−	21.8734i		−	1.27786i	−0.769265	−	0.638930i	$-0.779377\pi$
$293$		−	21.8734i		−	1.27786i	0.769265	−	0.638930i	$-0.220623\pi$
$294$	−24.4820	−	7.95470i	−1.42782	−	0.463927i
$295$	1.39935	+	2.59242i	0.0814730	+	0.150936i
$296$	−23.8202	+	7.73965i	−1.38452	+	0.449858i
$297$	21.0480	−	6.83890i	1.22133	−	0.396833i
$298$	−18.4157	+	25.3470i	−1.06679	+	1.46831i
$299$		−	0.537672i		−	0.0310944i
$300$	72.0651	−	27.2584i	4.16068	−	1.57376i
$301$			23.4190i			1.34985i
$302$	−13.7184	+	18.8818i	−0.789406	+	1.08652i
$303$	−2.47271	−	7.61022i	−0.142053	−	0.437196i
$304$	31.4949	+	96.9314i	1.80636	+	5.55940i
$305$	15.9579	+	15.2181i	0.913748	+	0.871383i
$306$	21.9708	−	49.2522i	1.25599	−	2.81556i
$307$			5.23617i			0.298844i	0.988774	+	0.149422i	$0.0477413\pi$
$307$			5.23617i			0.298844i	−0.988774	+	0.149422i	$0.952259\pi$
$308$	−45.0539	−	14.6389i	−2.56719	−	0.834129i
$309$	11.0429	+	15.1992i	0.628208	+	0.864655i
$310$	−18.0050	−	33.3559i	−1.02262	−	1.89449i
$311$	−3.65286	+	5.02773i	−0.207135	+	0.285096i	−0.899927	−	0.436041i	$-0.856380\pi$
$311$	−3.65286	+	5.02773i	−0.207135	+	0.285096i	0.692792	+	0.721137i	$0.256380\pi$
$312$	−8.15251	+	5.92314i	−0.461545	+	0.335332i
$313$	−0.569420	+	0.413708i	−0.0321855	+	0.0233841i	−0.603762	−	0.797165i	$-0.706332\pi$
$313$	−0.569420	+	0.413708i	−0.0321855	+	0.0233841i	0.571576	+	0.820549i	$0.306332\pi$
$314$	20.5832	+	14.9546i	1.16158	+	0.843935i
$315$	9.65145	+	17.8802i	0.543798	+	1.00744i
$316$	−32.6869	−	44.9896i	−1.83878	−	2.53086i
$317$	−1.13765	+	3.50133i	−0.0638969	+	0.196655i	−0.977908	−	0.209034i	$-0.932968\pi$
$317$	−1.13765	+	3.50133i	−0.0638969	+	0.196655i	0.914011	+	0.405688i	$0.132968\pi$
$318$	2.57094			0.144171
$319$	5.02370	−	15.4614i	0.281273	−	0.865670i
$320$	50.3655	−	52.8142i	2.81552	−	2.95240i
$321$	−5.31257	−	16.3504i	−0.296519	−	0.912591i
$322$	−7.16362	+	2.32760i	−0.399213	+	0.129712i
$323$	18.1386	−	20.1160i	1.00926	−	1.11928i
$324$	3.19378			0.177432
$325$	0.660475	+	1.74615i	0.0366365	+	0.0968589i
$326$			41.6280i			2.30556i
$327$	8.40870	−	11.5736i	0.465002	−	0.640020i
$328$	−5.55506	−	17.0967i	−0.306727	−	0.944008i
$329$	0.152990	−	0.0497095i	0.00843462	−	0.00274057i
$330$	−36.5055	−	67.6298i	−2.00956	−	3.72290i
$331$	2.82896	−	8.70665i	0.155494	−	0.478561i	−0.842717	−	0.538357i	$-0.819045\pi$
$331$	2.82896	−	8.70665i	0.155494	−	0.478561i	0.998211	+	0.0597963i	$0.0190451\pi$
$332$			6.95333i			0.381613i
$333$	3.80970	−	11.7251i	0.208770	−	0.642529i
$334$	7.79635	+	10.7308i	0.426597	+	0.587161i
$335$	3.65765	−	7.62026i	0.199839	−	0.416339i
$336$	66.6798	+	48.4457i	3.63768	+	2.64293i
$337$	5.02463	−	3.65061i	0.273709	−	0.198861i	−0.442460	−	0.896788i	$-0.645894\pi$
$337$	5.02463	−	3.65061i	0.273709	−	0.198861i	0.716169	+	0.697927i	$0.245894\pi$
$338$	20.7423	+	28.5493i	1.12823	+	1.55288i
$339$	1.90213	+	1.38198i	0.103310	+	0.0750588i
$340$	−49.5310	−	12.0575i	−2.68619	−	0.653909i
$341$	−22.4632	+	16.3205i	−1.21645	+	0.883804i
$342$	−81.7221	−	26.5531i	−4.41902	−	1.43583i
$343$	−19.7606			−1.06697
$344$	−36.7649	+	113.151i	−1.98223	+	6.10067i
$345$	−8.09014	−	3.88318i	−0.435558	−	0.209064i
$346$	40.1461	−	13.0442i	2.15827	−	0.701263i
$347$	−10.9222	−	33.6151i	−0.586334	−	1.80455i	−0.593844	−	0.804580i	$-0.702390\pi$
$347$	−10.9222	−	33.6151i	−0.586334	−	1.80455i	0.00750959	−	0.999972i	$-0.497610\pi$
$348$	−32.7622	+	45.0933i	−1.75624	+	2.41726i
$349$	24.5658			1.31498			0.657488	−	0.753465i	$-0.271619\pi$
$349$	24.5658			1.31498			0.657488	+	0.753465i	$0.271619\pi$
$350$	20.4054	−	16.3589i	1.09072	−	0.874420i
$351$		−	1.83854i		−	0.0981341i
$352$	−84.3662	−	61.2956i	−4.49673	−	3.26707i
$353$	−10.2728	+	3.33783i	−0.546766	+	0.177655i	−0.569358	−	0.822090i	$-0.692808\pi$
$353$	−10.2728	+	3.33783i	−0.546766	+	0.177655i	0.0225920	+	0.999745i	$0.492808\pi$
$354$	−9.58187	+	3.11334i	−0.509271	+	0.165472i
$355$	−4.40585	−	24.1016i	−0.233838	−	1.27918i
$356$	−11.7217	+	36.0758i	−0.621251	+	1.91201i
$357$	2.30522	−	21.7825i	0.122005	−	1.15285i
$358$	−34.8023	−	11.3079i	−1.83936	−	0.597643i
$359$	15.9406	−	11.5815i	0.841313	−	0.611249i	−0.0814244	−	0.996680i	$-0.525947\pi$
$359$	15.9406	−	11.5815i	0.841313	−	0.611249i	0.922737	+	0.385430i	$0.125947\pi$
$360$	18.5621	+	101.541i	0.978307	+	5.35170i
$361$	−19.5431	−	14.1989i	−1.02858	−	0.747310i
$362$	−7.46885	+	5.42644i	−0.392554	+	0.285207i
$363$	−20.7434	+	15.0709i	−1.08874	+	0.791019i
$364$	−2.31321	+	3.18386i	−0.121245	+	0.166880i
$365$	−3.44023	+	3.60749i	−0.180070	+	0.188824i
$366$	−61.0098	+	44.3262i	−3.18903	+	2.31697i
$367$	−6.61522	+	20.3596i	−0.345312	+	1.06276i	0.616105	+	0.787664i	$0.288710\pi$
$367$	−6.61522	+	20.3596i	−0.345312	+	1.06276i	−0.961417	+	0.275096i	$0.911290\pi$
$368$	−22.3411			−1.16461
$369$	8.41554	+	2.73438i	0.438096	+	0.142346i
$370$	−15.7277	−	2.10985i	−0.817643	−	0.109686i
$371$	0.609505	−	0.198040i	0.0316439	−	0.0102817i
$372$	90.5386	−	29.4178i	4.69421	−	1.52524i
$373$	−7.61987	+	10.4878i	−0.394542	+	0.543040i	−0.959364	−	0.282173i	$-0.908945\pi$
$373$	−7.61987	+	10.4878i	−0.394542	+	0.543040i	0.564822	+	0.825213i	$0.308945\pi$
$374$	−5.35136	+	50.5663i	−0.276712	+	2.61472i
$375$	31.0437	+	2.67317i	1.60309	+	0.138042i
$376$	0.817223			0.0421450
$377$	−1.09262	−	0.793834i	−0.0562728	−	0.0408846i
$378$	−24.4956	+	7.95910i	−1.25992	+	0.409372i
$379$	27.1730	−	8.82904i	1.39578	−	0.453517i	0.487958	−	0.872867i	$-0.337742\pi$
$379$	27.1730	−	8.82904i	1.39578	−	0.453517i	0.907825	+	0.419350i	$0.137742\pi$
$380$	−10.7992	+	80.5016i	−0.553985	+	4.12964i
$381$	32.8348	+	10.6687i	1.68218	+	0.546572i
$382$		−	55.2564i		−	2.82716i
$383$	3.37639	+	1.09706i	0.172526	+	0.0560570i	0.394006	−	0.919108i	$-0.371089\pi$
$383$	3.37639	+	1.09706i	0.172526	+	0.0560570i	−0.221480	+	0.975165i	$0.571089\pi$
$384$	70.6858	+	97.2906i	3.60717	+	4.96484i
$385$	−13.8641	−	13.2213i	−0.706580	−	0.673821i
$386$	38.9379	−	53.5934i	1.98189	−	2.72783i
$387$	−34.4222	−	47.3781i	−1.74978	−	2.40837i
$388$	−42.0285	+	30.5355i	−2.13367	+	1.55020i
$389$	−13.1781	−	9.57443i	−0.668155	−	0.485443i	0.201252	−	0.979539i	$-0.435499\pi$
$389$	−13.1781	−	9.57443i	−0.668155	−	0.485443i	−0.869407	+	0.494097i	$0.835499\pi$
$390$	−6.28051	+	1.14810i	−0.318026	+	0.0581362i
$391$	2.96500	+	5.14404i	0.149946	+	0.260145i
$392$	−31.0035	−	10.0737i	−1.56591	−	0.508796i
$393$		−	26.7628i		−	1.35001i
$394$	−62.1083	−	20.1802i	−3.12897	−	1.01666i
$395$	−4.04406	−	22.1225i	−0.203479	−	1.11310i
$396$	112.664	−	36.6068i	5.66159	−	1.83956i
$397$	−2.66591	−	8.20484i	−0.133798	−	0.411789i	0.861603	−	0.507583i	$-0.169461\pi$
$397$	−2.66591	−	8.20484i	−0.133798	−	0.411789i	−0.995401	+	0.0957940i	$0.969461\pi$
$398$	−1.79489	−	1.30406i	−0.0899698	−	0.0653669i
$399$	−34.9001			−1.74719
$400$	72.5551	−	27.4437i	3.62775	−	1.37219i
$401$			4.64168i			0.231794i	0.993261	+	0.115897i	$0.0369743\pi$
$401$			4.64168i			0.231794i	−0.993261	+	0.115897i	$0.963026\pi$
$402$	23.3864	+	16.9912i	1.16641	+	0.847445i
$403$	0.712798	+	2.19377i	0.0355070	+	0.109279i
$404$	−4.90590	−	15.0988i	−0.244078	−	0.751194i
$405$	1.16439	+	0.558898i	0.0578592	+	0.0277718i
$406$	−5.84658	+	17.9939i	−0.290161	+	0.893024i
$407$			11.6240i			0.576179i
$408$	45.3338	−	101.625i	2.24436	−	5.03120i
$409$	1.41593	−	1.02874i	0.0700134	−	0.0508677i	−0.552228	−	0.833693i	$-0.686222\pi$
$409$	1.41593	−	1.02874i	0.0700134	−	0.0508677i	0.622241	+	0.782825i	$0.286222\pi$
$410$	1.51432	−	11.2884i	0.0747870	−	0.557494i
$411$	13.9253	−	19.1666i	0.686887	−	0.945418i
$412$	21.9093	+	30.1556i	1.07939	+	1.48566i
$413$	−2.03180	+	1.47619i	−0.0999786	+	0.0726387i
$414$	11.0713	−	15.2383i	0.544123	−	0.748922i
$415$	−1.21680	+	2.53506i	−0.0597304	+	0.124441i
$416$	−7.00871	+	5.09212i	−0.343630	+	0.249662i
$417$	33.5272	+	10.8937i	1.64183	+	0.533464i
$418$	81.0175			3.96269
$419$	−7.06209	−	2.29461i	−0.345006	−	0.112099i	0.131389	−	0.991331i	$-0.458056\pi$
$419$	−7.06209	−	2.29461i	−0.345006	−	0.112099i	−0.476394	+	0.879232i	$0.658056\pi$
$420$	31.1998	+	57.8004i	1.52239	+	2.82037i
$421$	−5.97208	−	18.3802i	−0.291061	−	0.895794i	−0.984516	−	0.175294i	$-0.943912\pi$
$421$	−5.97208	−	18.3802i	−0.291061	−	0.895794i	0.693455	−	0.720500i	$-0.256088\pi$
$422$	15.8754	+	48.8595i	0.772804	+	2.37845i
$423$	−0.236444	+	0.325438i	−0.0114963	+	0.0158233i
$424$	3.25578			0.158114
$425$	−15.9481	−	13.0636i	−0.773596	−	0.633679i
$426$	83.7911			4.05969
$427$	−11.0494	+	15.2083i	−0.534720	+	0.735979i
$428$	−10.5402	−	32.4395i	−0.509482	−	1.56802i
$429$	1.44521	+	4.44790i	0.0697754	+	0.214747i
$430$	−52.0213	+	54.5505i	−2.50869	+	2.63066i
$431$	−31.3491	−	10.1859i	−1.51003	−	0.490640i	−0.567108	−	0.823643i	$-0.691938\pi$
$431$	−31.3491	−	10.1859i	−1.51003	−	0.490640i	−0.942925	+	0.333004i	$0.891938\pi$
$432$	−76.3941			−3.67551
$433$	15.7734	+	5.12510i	0.758023	+	0.246297i	0.662430	−	0.749124i	$-0.269525\pi$
$433$	15.7734	+	5.12510i	0.758023	+	0.246297i	0.0955930	+	0.995421i	$0.469525\pi$
$434$	26.1427	−	18.9938i	1.25489	−	0.911730i
$435$	−19.8356	+	10.7070i	−0.951046	+	0.513360i
$436$	16.6830	−	22.9622i	0.798971	−	1.09969i
$437$	7.65334	−	5.56048i	0.366109	−	0.265994i
$438$	−10.0205	−	13.7920i	−0.478798	−	0.659008i
$439$	17.9018	−	24.6397i	0.854404	−	1.17599i	−0.128471	−	0.991713i	$-0.541007\pi$
$439$	17.9018	−	24.6397i	0.854404	−	1.17599i	0.982875	−	0.184273i	$-0.0589932\pi$
$440$	−46.2297	−	85.6448i	−2.20392	−	4.08296i
$441$	12.9817	−	9.43177i	0.618177	−	0.449132i
$442$	3.85781	+	1.72092i	0.183497	+	0.0818558i
$443$		−	9.34990i		−	0.444227i	−0.975021	−	0.222114i	$-0.928704\pi$
$443$		−	9.34990i		−	0.444227i	0.975021	−	0.222114i	$-0.0712956\pi$
$444$	12.3154	−	37.9030i	0.584465	−	1.79880i
$445$	−10.5866	+	11.1013i	−0.501855	+	0.526254i
$446$	12.5031	+	38.4806i	0.592040	+	1.82211i
$447$	−9.83324	−	30.2636i	−0.465096	−	1.43142i
$448$	50.3331	+	36.5691i	2.37802	+	1.72773i
$449$			15.8354i			0.747317i	0.927566	+	0.373658i	$0.121897\pi$
$449$			15.8354i			0.747317i	−0.927566	+	0.373658i	$0.878103\pi$
$450$	−17.2365	+	63.0880i	−0.812536	+	2.97400i
$451$	−8.34298			−0.392856
$452$	3.77386	+	2.74187i	0.177508	+	0.128967i
$453$	−7.32510	−	22.5443i	−0.344163	−	1.05923i
$454$	24.3905	−	7.92497i	1.14470	−	0.371937i
$455$	−1.40051	+	0.755976i	−0.0656571	+	0.0354407i
$456$	−168.623	−	54.7888i	−7.89647	−	2.56572i
$457$			31.9613i			1.49509i	0.664213	+	0.747543i	$0.268767\pi$
$457$			31.9613i			1.49509i	−0.664213	+	0.747543i	$0.731233\pi$
$458$	37.3927	+	12.1496i	1.74725	+	0.567714i
$459$	10.1387	+	17.5898i	0.473232	+	0.821020i
$460$	−16.0510	−	7.70431i	−0.748381	−	0.359215i
$461$	2.15838	+	1.56816i	0.100526	+	0.0730363i	0.636913	−	0.770936i	$-0.280211\pi$
$461$	2.15838	+	1.56816i	0.100526	+	0.0730363i	−0.536387	+	0.843972i	$0.680211\pi$
$462$	53.0048	−	38.5102i	2.46601	−	1.79166i
$463$	−11.3085	−	15.5648i	−0.525550	−	0.723358i	0.460894	−	0.887455i	$-0.347529\pi$
$463$	−11.3085	−	15.5648i	−0.525550	−	0.723358i	−0.986444	+	0.164097i	$0.947529\pi$
$464$	−32.9850	+	45.4000i	−1.53129	+	2.10764i
$465$	38.1567	+	5.11867i	1.76948	+	0.237372i
$466$	41.9499	+	57.7391i	1.94329	+	2.67471i
$467$	−10.5821	−	3.43832i	−0.489679	−	0.159106i	0.0537618	−	0.998554i	$-0.482879\pi$
$467$	−10.5821	−	3.43832i	−0.489679	−	0.159106i	−0.543441	+	0.839447i	$0.682879\pi$
$468$		−	9.84122i		−	0.454911i
$469$	6.85318	+	2.22673i	0.316450	+	0.102821i
$470$	0.466786	+	0.224052i	0.0215312	+	0.0103348i
$471$	−24.5758	+	7.98516i	−1.13239	+	0.367937i
$472$	−12.1343	+	3.94267i	−0.558525	+	0.181476i
$473$	44.6708	+	32.4552i	2.05397	+	1.49229i
$474$	76.9105			3.53262
$475$	−18.0246	+	27.4596i	−0.827025	+	1.25993i
$476$	4.57360	−	43.2170i	0.209630	−	1.98085i
$477$	−0.941983	+	1.29653i	−0.0431304	+	0.0593639i
$478$	−57.3187	+	18.6240i	−2.62169	+	0.851840i
$479$	27.2401	−	8.85084i	1.24463	−	0.404405i	0.388637	−	0.921391i	$-0.372946\pi$
$479$	27.2401	−	8.85084i	1.24463	−	0.404405i	0.855994	+	0.516986i	$0.172946\pi$
$480$	26.0008	+	142.234i	1.18677	+	6.49205i
$481$	0.918397	+	0.298405i	0.0418753	+	0.0136061i
$482$	57.3576			2.61257
$483$	2.36404	−	7.27576i	0.107567	−	0.331058i
$484$	−41.1552	+	29.9010i	−1.87069	+	1.35914i
$485$	−20.6664	+	3.77788i	−0.938412	+	0.171545i
$486$	−26.4218	+	36.3665i	−1.19852	+	1.64962i
$487$	−26.3578	+	19.1501i	−1.19439	+	0.867773i	−0.993721	−	0.111886i	$-0.964311\pi$
$487$	−26.3578	+	19.1501i	−1.19439	+	0.867773i	−0.200667	+	0.979660i	$0.564311\pi$
$488$	−77.2614	+	56.1337i	−3.49746	+	2.54105i
$489$	−34.2050	−	24.8514i	−1.54680	−	1.12382i
$490$	−14.9469	−	14.2540i	−0.675234	−	0.643928i
$491$	15.8897	−	11.5445i	0.717092	−	0.520998i	−0.168362	−	0.985725i	$-0.553848\pi$
$491$	15.8897	−	11.5445i	0.717092	−	0.520998i	0.885454	+	0.464727i	$0.153848\pi$
$492$	27.2045	+	8.83928i	1.22647	+	0.398506i
$493$	14.8310	+	1.56954i	0.667953	+	0.0706886i
$494$	2.07984	−	6.40110i	0.0935766	−	0.287999i
$495$	47.4813	+	6.36955i	2.13413	+	0.286290i
$496$	91.1543	−	29.6178i	4.09295	−	1.32988i
$497$	19.8648	−	6.45447i	0.891058	−	0.289522i
$498$	−7.78003	−	5.65252i	−0.348631	−	0.253296i
$499$			28.0425i			1.25535i	0.778474	+	0.627677i	$0.215994\pi$
$499$			28.0425i			1.25535i	−0.778474	+	0.627677i	$0.784006\pi$
$500$	61.5913	+	5.30361i	2.75445	+	0.237185i
$501$	−13.4716			−0.601866
$502$	−24.9363	+	34.3219i	−1.11296	+	1.53186i
$503$	7.35347	+	22.6317i	0.327875	+	1.00910i	0.970126	+	0.242601i	$0.0780007\pi$
$503$	7.35347	+	22.6317i	0.327875	+	1.00910i	−0.642251	+	0.766494i	$0.721999\pi$
$504$	−83.6915	+	27.1930i	−3.72792	+	1.21127i
$505$	0.853622	−	6.36326i	0.0379857	−	0.283162i
$506$	−5.48791	+	16.8900i	−0.243967	+	0.750854i
$507$	−35.8413			−1.59177
$508$	65.1448	+	21.1668i	2.89033	+	0.939126i
$509$	26.4118	−	19.1893i	1.17068	−	0.850550i	0.179591	−	0.983741i	$-0.442523\pi$
$509$	26.4118	−	19.1893i	1.17068	−	0.850550i	0.991090	+	0.133192i	$0.0425225\pi$
$510$	53.7559	−	45.6180i	2.38035	−	2.02000i
$511$	−3.43802	−	2.49787i	−0.152089	−	0.110499i
$512$	34.9628	+	48.1222i	1.54515	+	2.12672i
$513$	26.1702	−	19.0137i	1.15544	−	0.839478i
$514$	−50.0793	−	36.3847i	−2.20890	−	1.60486i
$515$	2.71064	+	14.8282i	0.119445	+	0.653409i
$516$	−111.275	−	153.157i	−4.89861	−	6.74236i
$517$	0.117203	−	0.360713i	0.00515457	−	0.0158641i
$518$		−	13.5280i		−	0.594385i
$519$	−13.2484	+	40.7745i	−0.581542	+	1.78980i
$520$	−7.95349	+	1.45392i	−0.348784	+	0.0637588i
$521$	−36.8991	+	11.9892i	−1.61658	+	0.525258i	−0.971131	−	0.238547i	$-0.923329\pi$
$521$	−36.8991	+	11.9892i	−1.61658	+	0.525258i	−0.645447	+	0.763805i	$0.723329\pi$
$522$	−14.6203	−	44.9965i	−0.639911	−	1.96944i
$523$	15.9294	−	21.9249i	0.696543	−	0.958709i	−0.303440	−	0.952851i	$-0.598135\pi$
$523$	15.9294	−	21.9249i	0.696543	−	0.958709i	0.999983	−	0.00585851i	$-0.00186483\pi$
$524$		−	53.0979i		−	2.31959i
$525$	1.26005	+	26.5328i	0.0549930	+	1.15799i
$526$	−62.5294			−2.72641
$527$	−18.9171	−	17.0576i	−0.824040	−	0.743039i
$528$	184.817	−	60.0507i	8.04312	−	2.61337i
$529$	−6.46659	−	19.9021i	−0.281156	−	0.865310i
$530$	1.85965	+	0.892614i	0.0807782	+	0.0387727i
$531$	1.94071	−	5.97288i	0.0842194	−	0.259201i
$532$	−69.2424			−3.00204
$533$	−0.214177	+	0.659170i	−0.00927705	+	0.0285518i
$534$	−30.8361	−	42.4422i	−1.33441	−	1.83666i
$535$	1.83399	−	13.6714i	0.0792904	−	0.591064i
$536$	29.6160	+	21.5173i	1.27922	+	0.929406i
$537$	30.0680	−	21.8457i	1.29753	−	0.942711i
$538$	19.8897	−	14.4507i	0.857508	−	0.623016i
$539$	−8.89281	+	12.2399i	−0.383040	+	0.527210i
$540$	−54.8855	−	26.3445i	−2.36190	−	1.13369i
$541$	−3.94498	−	5.42979i	−0.169608	−	0.233445i	0.715749	−	0.698358i	$-0.246086\pi$
$541$	−3.94498	−	5.42979i	−0.169608	−	0.233445i	−0.885356	+	0.464913i	$0.846086\pi$
$542$	−56.3882	−	18.3216i	−2.42208	−	0.786982i
$543$		−	9.37653i		−	0.402385i
$544$	38.9734	−	87.3672i	1.67097	−	3.74584i
$545$	10.1006	−	5.45215i	0.432662	−	0.233544i
$546$	−1.68194	−	5.17647i	−0.0719802	−	0.221532i
$547$	4.25335	+	13.0905i	0.181860	+	0.559708i	0.999880	−	0.0154820i	$-0.00492826\pi$
$547$	4.25335	+	13.0905i	0.181860	+	0.559708i	−0.818020	+	0.575190i	$0.804928\pi$
$548$	27.6281	−	38.0269i	1.18022	−	1.62443i
$549$		−	47.0083i		−	2.00627i
$550$	−2.92509	−	61.5936i	−0.124726	−	2.62636i
$551$		−	23.7622i		−	1.01230i
$552$	22.8441	−	31.4422i	0.972309	−	1.33827i
$553$	18.2336	−	5.92445i	0.775371	−	0.251933i
$554$	−37.2279	+	12.0961i	−1.58166	+	0.513913i
$555$	11.1228	−	11.6636i	0.472138	−	0.495092i
$556$	66.5186	+	21.6132i	2.82102	+	0.916604i
$557$			27.8422i			1.17971i	0.807509	+	0.589855i	$0.200815\pi$
$557$			27.8422i			1.17971i	−0.807509	+	0.589855i	$0.799185\pi$
$558$	−24.9705	+	76.8514i	−1.05709	+	3.25338i
$559$	3.71102	−	2.69621i	0.156959	−	0.114038i
$560$	31.4119	+	58.1935i	1.32740	+	2.45912i
$561$	−38.3547	−	34.5845i	−1.61934	−	1.46016i
$562$	20.0624	+	27.6136i	0.846283	+	1.16481i
$563$	24.4626	+	33.6699i	1.03098	+	1.41902i	0.904212	+	0.427085i	$0.140459\pi$
$563$	24.4626	+	33.6699i	1.03098	+	1.41902i	0.126765	+	0.991933i	$0.459541\pi$
$564$	−0.764342	+	1.05203i	−0.0321846	+	0.0442983i
$565$	0.896067	+	1.66005i	0.0376978	+	0.0698387i
$566$	22.2680	+	30.6493i	0.935993	+	1.28828i
$567$	−0.340250	+	1.04718i	−0.0142892	+	0.0439776i
$568$	106.111			4.45233
$569$	0.213861	−	0.658197i	0.00896552	−	0.0275930i	−0.946474	−	0.322781i	$-0.895382\pi$
$569$	0.213861	−	0.658197i	0.00896552	−	0.0275930i	0.955439	+	0.295188i	$0.0953823\pi$
$570$	−81.2937	−	77.5247i	−3.40502	−	3.24715i
$571$	−24.2947	+	7.89382i	−1.01670	+	0.330346i	−0.769520	−	0.638623i	$-0.779504\pi$
$571$	−24.2947	+	7.89382i	−1.01670	+	0.330346i	−0.247181	+	0.968969i	$0.579504\pi$
$572$	2.86733	+	8.82472i	0.119889	+	0.368980i
$573$	45.4032	+	32.9873i	1.89675	+	1.37807i
$574$	9.70956			0.405269
$575$	−4.50368	−	5.61770i	−0.187816	−	0.234274i
$576$	−155.578			−6.48243
$577$	−5.31836	+	7.32010i	−0.221406	+	0.304740i	−0.905242	−	0.424896i	$-0.860311\pi$
$577$	−5.31836	+	7.32010i	−0.221406	+	0.304740i	0.683836	+	0.729636i	$0.260311\pi$
$578$	−46.3986	+	4.80947i	−1.92993	+	0.200048i
$579$	20.7913	+	63.9891i	0.864057	+	2.65930i
$580$	−39.3543	+	21.2428i	−1.63410	+	0.882060i
$581$	−2.27987	−	0.740774i	−0.0945849	−	0.0307325i
$582$		−	71.8484i		−	2.97821i
$583$	0.466930	−	1.43706i	0.0193383	−	0.0595171i
$584$	−12.6897	−	17.4659i	−0.525105	−	0.722745i
$585$	1.72217	−	3.58793i	0.0712030	−	0.148343i
$586$	48.5570	+	35.2787i	2.00587	+	1.45735i
$587$	5.95751	+	8.19981i	0.245893	+	0.338443i	0.914068	−	0.405562i	$-0.132924\pi$
$587$	5.95751	+	8.19981i	0.245893	+	0.338443i	−0.668175	+	0.744004i	$0.732924\pi$
$588$	41.9654	−	30.4896i	1.73062	−	1.25737i
$589$	−23.8550	+	32.8335i	−0.982926	+	1.35288i
$590$	−8.01186	−	1.07478i	−0.329843	−	0.0442480i
$591$	53.6595	−	38.9859i	2.20726	−	1.60367i
$592$	12.3992	−	38.1607i	0.509603	−	1.56840i
$593$			11.2431i			0.461699i	0.972989	+	0.230849i	$0.0741505\pi$
$593$			11.2431i			0.461699i	−0.972989	+	0.230849i	$0.925850\pi$
$594$	−18.7656	+	57.7546i	−0.769962	+	2.36970i
$595$	9.23022	−	14.9558i	0.378402	−	0.613126i
$596$	−19.5093	−	60.0436i	−0.799134	−	2.45948i
$597$	2.14305	−	0.696320i	0.0877093	−	0.0284985i
$598$	1.19358	+	0.867187i	0.0488092	+	0.0354619i
$599$	−12.2896			−0.502139			−0.251070	−	0.967969i	$-0.580782\pi$
$599$	−12.2896			−0.502139			−0.251070	+	0.967969i	$0.580782\pi$
$600$	−35.5652	+	130.174i	−1.45194	+	5.31432i
$601$			29.9565i			1.22195i	0.791649	+	0.610976i	$0.209223\pi$
$601$			29.9565i			1.22195i	−0.791649	+	0.610976i	$0.790777\pi$
$602$	−51.9878	−	37.7714i	−2.11887	−	1.53945i
$603$	−17.1374	+	5.56828i	−0.697889	+	0.226758i
$604$	−14.5331	−	44.7284i	−0.591345	−	1.81997i
$605$	−20.2370	+	3.69939i	−0.822751	+	0.150402i
$606$	20.8821	+	6.78500i	0.848277	+	0.275622i
$607$	−4.98230			−0.202225			−0.101113	−	0.994875i	$-0.532240\pi$
$607$	−4.98230			−0.202225			−0.101113	+	0.994875i	$0.532240\pi$
$608$	−144.965	−	47.1019i	−5.87910	−	1.91023i
$609$	−11.2950	−	15.5462i	−0.457695	−	0.629963i
$610$	−59.5204	+	10.8805i	−2.40991	+	0.440540i
$611$	−0.0254908	−	0.0185201i	−0.00103125	−	0.000749244i
$612$	54.2695	+	94.1534i	2.19372	+	3.80592i
$613$	−2.79094	−	3.84139i	−0.112725	−	0.155152i	0.748927	−	0.662653i	$-0.230570\pi$
$613$	−2.79094	−	3.84139i	−0.112725	−	0.155152i	−0.861651	+	0.507501i	$0.830570\pi$
$614$	−11.6238	−	8.44518i	−0.469098	−	0.340820i
$615$	8.37144	+	7.98331i	0.337569	+	0.321918i
$616$	67.1241	−	48.7685i	2.70451	−	1.96494i
$617$	−3.18489	+	9.80209i	−0.128219	+	0.394617i	−0.994474	−	0.104985i	$-0.966521\pi$
$617$	−3.18489	+	9.80209i	−0.128219	+	0.394617i	0.866255	+	0.499602i	$0.166521\pi$
$618$	−51.5515			−2.07370
$619$	−27.4630	−	8.92326i	−1.10383	−	0.358656i	−0.300254	−	0.953859i	$-0.597072\pi$
$619$	−27.4630	−	8.92326i	−1.10383	−	0.358656i	−0.803575	+	0.595203i	$0.797072\pi$
$620$	75.7036	+	10.1555i	3.04033	+	0.407856i
$621$	2.19118	+	6.74375i	0.0879289	+	0.270617i
$622$	−5.26955	−	16.2180i	−0.211290	−	0.650282i
$623$	−10.5798	−	7.68669i	−0.423872	−	0.307961i
$624$		−	16.1438i		−	0.646268i
$625$	21.5270	+	12.7118i	0.861078	+	0.508472i
$626$		−	1.93131i		−	0.0771906i
$627$	−48.3664	+	66.5706i	−1.93157	+	2.65857i
$628$	−48.7589	+	15.8427i	−1.94569	+	0.632193i
$629$	−10.4321	+	2.20960i	−0.415954	+	0.0881024i
$630$	−55.2587	−	7.41288i	−2.20156	−	0.295336i
$631$	2.74410	−	8.44549i	0.109241	−	0.336209i	−0.881461	−	0.472256i	$-0.843440\pi$
$631$	2.74410	−	8.44549i	0.109241	−	0.336209i	0.990702	+	0.136047i	$0.0434397\pi$
$632$	97.3978			3.87428
$633$	−49.6244	−	16.1240i	−1.97239	−	0.640870i
$634$	−5.93776	−	8.17263i	−0.235819	−	0.324576i
$635$	20.0465	+	19.1171i	0.795522	+	0.758639i
$636$	−3.04510	+	4.19122i	−0.120746	+	0.166193i
$637$	0.738769	+	1.01683i	0.0292711	+	0.0402882i
$638$	26.2203	+	36.0891i	1.03807	+	1.42878i
$639$	−30.7008	+	42.2560i	−1.21450	+	1.67162i
$640$	17.3509	+	94.9156i	0.685854	+	3.75187i
$641$	−9.25639	−	12.7403i	−0.365605	−	0.503213i	0.586094	−	0.810243i	$-0.300665\pi$
$641$	−9.25639	−	12.7403i	−0.365605	−	0.503213i	−0.951700	+	0.307030i	$0.900665\pi$
$642$	44.8648	+	14.5775i	1.77067	+	0.575326i
$643$	−39.0707			−1.54080			−0.770399	−	0.637562i	$-0.779943\pi$
$643$	−39.0707			−1.54080			−0.770399	+	0.637562i	$0.779943\pi$
$644$	4.69029	−	14.4352i	0.184824	−	0.568828i
$645$	−13.7671	−	75.3109i	−0.542078	−	2.96536i
$646$	15.4006	+	72.7102i	0.605928	+	2.86074i
$647$	20.4885	−	6.65711i	0.805485	−	0.261718i	0.122801	−	0.992431i	$-0.460812\pi$
$647$	20.4885	−	6.65711i	0.805485	−	0.261718i	0.682684	+	0.730713i	$0.260812\pi$
$648$	−3.28790	+	4.52540i	−0.129161	+	0.177775i
$649$			5.92138i			0.232434i
$650$	−4.94154	−	1.35010i	−0.193823	−	0.0529551i
$651$			32.8200i			1.28632i
$652$	−67.8633	−	49.3056i	−2.65773	−	1.93096i
$653$	10.7290	+	33.0203i	0.419856	+	1.29218i	0.907834	+	0.419329i	$0.137735\pi$
$653$	10.7290	+	33.0203i	0.419856	+	1.29218i	−0.487978	+	0.872856i	$0.662265\pi$
$654$	12.1302	+	37.3330i	0.474330	+	1.45984i
$655$	9.29190	−	19.3585i	0.363065	−	0.756401i
$656$	27.3895	+	8.89939i	1.06938	+	0.347463i
$657$	10.6268			0.414592
$658$	−0.136401	+	0.419798i	−0.00531745	+	0.0163654i
$659$	−20.1638	+	14.6499i	−0.785470	+	0.570678i	−0.906616	−	0.421957i	$-0.861343\pi$
$659$	−20.1638	+	14.6499i	−0.785470	+	0.570678i	0.121145	+	0.992635i	$0.461343\pi$
$660$	153.491	+	20.5905i	5.97461	+	0.801485i
$661$	2.27790	+	1.65499i	0.0886002	+	0.0643718i	0.631203	−	0.775617i	$-0.282561\pi$
$661$	2.27790	+	1.65499i	0.0886002	+	0.0643718i	−0.542603	+	0.839989i	$0.682561\pi$
$662$	14.7652	+	20.3226i	0.573867	+	0.789860i
$663$	−3.71711	+	2.14252i	−0.144361	+	0.0832087i
$664$	−9.85246	−	7.15823i	−0.382349	−	0.277793i
$665$	−25.2445	−	12.1171i	−0.978940	−	0.469881i
$666$	19.8840	+	27.3680i	0.770490	+	1.06049i
$667$	4.95381	+	1.60959i	0.191812	+	0.0623236i
$668$	−26.7279			−1.03413
$669$	−39.0830	−	12.6988i	−1.51104	−	0.490966i
$670$	11.0170	+	20.4100i	0.425624	+	0.788507i
$671$	13.6963	+	42.1528i	0.528739	+	1.62729i
$672$	−117.231	+	38.0905i	−4.52227	+	1.46937i
$673$	−28.5009	−	20.7071i	−1.09863	−	0.798201i	−0.117794	−	0.993038i	$-0.537582\pi$
$673$	−28.5009	−	20.7071i	−1.09863	−	0.798201i	−0.980836	+	0.194837i	$0.937582\pi$
$674$			17.0421i			0.656438i
$675$	−15.4001	−	19.2094i	−0.592750	−	0.739371i
$676$	−71.1098			−2.73499
$677$	36.9542	+	26.8488i	1.42027	+	1.03188i	0.991728	+	0.128360i	$0.0409715\pi$
$677$	36.9542	+	26.8488i	1.42027	+	1.03188i	0.428539	+	0.903523i	$0.359029\pi$
$678$	−6.13573	+	1.99362i	−0.235641	+	0.0765644i
$679$	−5.53451	−	17.0335i	−0.212395	−	0.653685i
$680$	68.0753	−	57.7697i	2.61057	−	2.21537i
$681$	−8.04903	+	24.7724i	−0.308439	+	0.949279i
$682$		−	76.1888i		−	2.91742i
$683$	5.91968	−	18.2189i	0.226510	−	0.697127i	−0.771625	−	0.636078i	$-0.780556\pi$
$683$	5.91968	−	18.2189i	0.226510	−	0.697127i	0.998135	−	0.0610485i	$-0.0194444\pi$
$684$	140.082	−	101.776i	5.35617	−	3.89149i
$685$	16.7273	−	9.02911i	0.639115	−	0.344984i
$686$	31.8710	−	43.8666i	1.21684	−	1.67484i
$687$	−32.3061	+	23.4717i	−1.23255	+	0.895502i
$688$	−112.032	−	154.198i	−4.27117	−	5.87876i
$689$	−0.101554	−	0.0737833i	−0.00386890	−	0.00281092i
$690$	21.6685	−	11.6963i	0.824906	−	0.445271i
$691$	13.6431	+	18.7781i	0.519008	+	0.714353i	0.985406	−	0.170222i	$-0.0544486\pi$
$691$	13.6431	+	18.7781i	0.519008	+	0.714353i	−0.466398	+	0.884575i	$0.654449\pi$
$692$	−26.2852	+	80.8974i	−0.999212	+	3.07526i
$693$			40.8404i			1.55140i
$694$	92.2382	+	29.9700i	3.50131	+	1.13765i
$695$	20.4693	+	19.5202i	0.776444	+	0.740445i
$696$	−30.1670	−	92.8443i	−1.14348	−	3.51926i
$697$	−1.58592	−	7.48752i	−0.0600708	−	0.283610i
$698$	−39.6211	+	54.5337i	−1.49968	+	2.06413i
$699$	−72.4867			−2.74170
$700$	2.49996	+	52.6416i	0.0944896	+	1.98967i
$701$	41.8959			1.58239			0.791193	−	0.611567i	$-0.209460\pi$
$701$	41.8959			1.58239			0.791193	+	0.611567i	$0.209460\pi$
$702$	4.08139	+	2.96530i	0.154042	+	0.111918i
$703$	5.25028	+	16.1587i	0.198018	+	0.609436i
$704$	139.509	−	45.3291i	5.25793	−	1.70840i
$705$	−0.462765	+	0.249793i	−0.0174287	+	0.00940776i
$706$	9.15886	−	28.1881i	0.344698	−	1.06087i
$707$	5.47328			0.205844
$708$	6.27362	−	19.3082i	0.235777	−	0.725648i
$709$	8.41571	+	11.5832i	0.316059	+	0.435018i	0.937259	−	0.348634i	$-0.113355\pi$
$709$	8.41571	+	11.5832i	0.316059	+	0.435018i	−0.621200	+	0.783652i	$0.713355\pi$
$710$	60.6092	+	29.0918i	2.27462	+	1.09180i
$711$	−28.1798	+	38.7861i	−1.05682	+	1.45459i
$712$	−39.0502	−	53.7479i	−1.46347	−	2.01429i
$713$	−5.22907	−	7.19720i	−0.195830	−	0.269537i
$714$	44.6372	+	40.2494i	1.67050	+	1.50630i
$715$	−0.498912	+	3.71910i	−0.0186582	+	0.139087i
$716$	59.6555	−	43.3423i	2.22943	−	1.61978i
$717$	18.9155	−	58.2160i	0.706413	−	2.17411i
$718$			54.0659i			2.01772i
$719$	16.7912	+	5.45578i	0.626205	+	0.203466i	0.604893	−	0.796307i	$-0.293216\pi$
$719$	16.7912	+	5.45578i	0.626205	+	0.203466i	0.0213116	+	0.999773i	$0.493216\pi$
$720$	−149.084	−	71.5587i	−5.55603	−	2.66684i
$721$	−12.2216	+	3.97103i	−0.455155	+	0.147889i
$722$	63.0404	−	20.4831i	2.34612	−	0.762301i
$723$	−34.2417	+	47.1297i	−1.27346	+	1.75277i
$724$		−	18.6032i		−	0.691383i
$725$	−18.0653	+	0.857923i	−0.670927	+	0.0318624i
$726$		−	70.3556i		−	2.61114i
$727$	4.56755	−	6.28669i	0.169401	−	0.233160i	−0.715873	−	0.698231i	$-0.753971\pi$
$727$	4.56755	−	6.28669i	0.169401	−	0.233160i	0.885274	+	0.465070i	$0.153971\pi$
$728$	−2.12997	−	6.55536i	−0.0789418	−	0.242958i
$729$	−13.5727	−	41.7726i	−0.502694	−	1.54713i
$730$	−2.45968	−	13.4553i	−0.0910368	−	0.498004i
$731$	−20.6359	+	46.2598i	−0.763247	+	1.71098i
$732$		−	151.962i		−	5.61666i
$733$	33.5776	+	10.9100i	1.24022	+	0.402971i	0.854406	−	0.519606i	$-0.173921\pi$
$733$	33.5776	+	10.9100i	1.24022	+	0.402971i	0.385812	+	0.922577i	$0.373921\pi$
$734$	−34.5269	−	47.5222i	−1.27441	−	1.75408i
$735$	20.6354	−	3.77221i	0.761146	−	0.139140i
$736$	19.6391	−	27.0308i	0.723905	−	0.996370i
$737$	13.7449	−	9.98626i	0.506300	−	0.367849i
$738$	−19.6431	+	14.2716i	−0.723073	+	0.525343i
$739$	−8.49165	−	6.16955i	−0.312371	−	0.226951i	0.420542	−	0.907273i	$-0.361840\pi$
$739$	−8.49165	−	6.16955i	−0.312371	−	0.226951i	−0.732913	+	0.680322i	$0.761840\pi$
$740$	22.0679	−	23.1408i	0.811233	−	0.850673i
$741$	4.01803	+	5.53034i	0.147606	+	0.203162i
$742$	−0.543413	+	1.67245i	−0.0199493	+	0.0613977i
$743$	45.2581			1.66036			0.830180	−	0.557496i	$-0.188238\pi$
$743$	45.2581			1.66036			0.830180	+	0.557496i	$0.188238\pi$
$744$	−51.5234	+	158.573i	−1.88894	+	5.81355i
$745$	3.39461	−	25.3048i	0.124369	−	0.927098i
$746$	−10.9923	−	33.8308i	−0.402456	−	1.23863i
$747$	5.70116	−	1.85242i	0.208594	−	0.0677764i
$748$	−76.0964	−	68.6163i	−2.78236	−	2.50886i
$749$	11.7592			0.429673
$750$	−56.0032	+	64.6027i	−2.04495	+	2.35896i
$751$		−	32.5605i		−	1.18815i	−0.804410	−	0.594075i	$-0.797518\pi$
$751$		−	32.5605i		−	1.18815i	0.804410	−	0.594075i	$-0.202482\pi$
$752$	−0.769539	+	1.05918i	−0.0280622	+	0.0386243i
$753$	−13.3150	−	40.9795i	−0.485227	−	1.49338i
$754$	3.52447	−	1.14517i	0.128354	−	0.0417047i
$755$	2.52875	−	18.8504i	0.0920307	−	0.686036i
$756$	16.0382	−	49.3605i	0.583304	−	1.79523i
$757$			11.1766i			0.406222i	0.979156	+	0.203111i	$0.0651052\pi$
$757$			11.1766i			0.406222i	−0.979156	+	0.203111i	$0.934895\pi$
$758$	−24.2265	+	74.5614i	−0.879945	+	2.70819i
$759$	−10.6020	−	14.5925i	−0.384830	−	0.529672i
$760$	−102.949	−	98.1756i	−3.73434	−	3.56120i
$761$	−29.7754	−	21.6331i	−1.07936	−	0.784198i	−0.101786	−	0.994806i	$-0.532456\pi$
$761$	−29.7754	−	21.6331i	−1.07936	−	0.784198i	−0.977571	+	0.210608i	$0.932456\pi$
$762$	−76.6412	+	55.6831i	−2.77642	+	2.01718i
$763$	5.75156	+	7.91634i	0.208220	+	0.286591i
$764$	90.0808	+	65.4475i	3.25901	+	2.36781i
$765$	3.30927	+	43.8235i	0.119647	+	1.58444i
$766$	−7.88099	+	5.72588i	−0.284752	+	0.206884i
$767$	0.467842	+	0.152011i	0.0168928	+	0.00548880i
$768$	−148.066			−5.34289
$769$	−15.7120	+	48.3564i	−0.566587	+	1.74378i	0.0965999	+	0.995323i	$0.469203\pi$
$769$	−15.7120	+	48.3564i	−0.566587	+	1.74378i	−0.663187	+	0.748453i	$0.730797\pi$
$770$	51.7109	−	9.45291i	1.86353	−	0.340659i
$771$	59.7933	−	19.4280i	2.15340	−	0.699683i
$772$	41.2504	+	126.956i

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.q (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61286 + 2.21990i) q^{2} +(-0.861202 - 2.65051i) q^{3} +(-1.70864 - 5.25866i) q^{4} +(0.297302 - 2.21622i) q^{5} +(7.27287 + 2.36310i) q^{6} +1.90625 q^{7} +(9.21020 + 2.99258i) q^{8} +(-3.85647 + 2.80189i) q^{9} +(4.44028 + 4.23442i) q^{10} +(2.64178 - 3.63610i) q^{11} +(-12.4666 + 9.05754i) q^{12} +(-0.219466 - 0.302069i) q^{13} +(-3.07450 + 4.23169i) q^{14} +(-6.13013 + 1.12061i) q^{15} +(-12.5514 + 9.11912i) q^{16} +(3.76544 + 1.67972i) q^{17} -13.0800i q^{18} +(2.03005 - 6.24784i) q^{19} +(-12.1623 + 2.22331i) q^{20} +(-1.64167 - 5.05253i) q^{21} +(3.81099 + 11.7290i) q^{22} +(1.16500 + 0.846425i) q^{23} -26.9889i q^{24} +(-4.82322 - 1.31777i) q^{25} +1.02453 q^{26} +(3.98367 + 2.89430i) q^{27} +(-3.25710 - 10.0243i) q^{28} +(3.44009 - 1.11775i) q^{29} +(7.39938 - 15.4157i) q^{30} +(-5.87547 - 1.90906i) q^{31} -23.2024i q^{32} +(-11.9126 - 3.87065i) q^{33} +(-9.80192 + 5.64978i) q^{34} +(0.566732 - 4.22466i) q^{35} +(21.3235 + 15.4924i) q^{36} +(-2.09235 + 1.52018i) q^{37} +(10.5954 + 14.5834i) q^{38} +(-0.611631 + 0.841838i) q^{39} +(9.37041 - 19.5221i) q^{40} +(-1.09109 - 1.50176i) q^{41} +(13.8639 + 4.50465i) q^{42} +12.2854i q^{43} +(-23.6349 - 7.67943i) q^{44} +(5.06306 + 9.37978i) q^{45} +(-3.75796 + 1.22104i) q^{46} +(0.0802572 - 0.0260771i) q^{47} +(34.9796 + 25.4142i) q^{48} -3.36622 q^{49} +(10.7045 - 8.58172i) q^{50} +(1.20930 - 11.4269i) q^{51} +(-1.21349 + 1.67022i) q^{52} +(0.319741 - 0.103890i) q^{53} +(-12.8502 + 4.17527i) q^{54} +(-7.27298 - 6.93578i) q^{55} +(17.5569 + 5.70460i) q^{56} -18.3082 q^{57} +(-3.06706 + 9.43944i) q^{58} +(-1.06587 + 0.774396i) q^{59} +(16.3671 + 30.3216i) q^{60} +(-5.79643 + 7.97811i) q^{61} +(13.7142 - 9.96395i) q^{62} +(-7.35140 + 5.34110i) q^{63} +(26.4043 + 19.1838i) q^{64} +(-0.734697 + 0.396578i) q^{65} +(27.8058 - 20.2021i) q^{66} +(3.59511 + 1.16812i) q^{67} +(2.39926 - 22.6712i) q^{68} +(1.24015 - 3.81679i) q^{69} +(8.46428 + 8.07185i) q^{70} +(10.4209 - 3.38595i) q^{71} +(-43.9038 + 14.2652i) q^{72} +(-1.80355 - 1.31036i) q^{73} -7.09664i q^{74} +(0.661009 + 13.9189i) q^{75} -36.3239 q^{76} +(5.03589 - 6.93131i) q^{77} +(-0.882327 - 2.71552i) q^{78} +(9.56517 - 3.10791i) q^{79} +(16.4784 + 30.5277i) q^{80} +(-0.178492 + 0.549342i) q^{81} +5.09354 q^{82} +(-1.19600 - 0.388603i) q^{83} +(-23.7645 + 17.2659i) q^{84} +(4.84209 - 7.84565i) q^{85} +(-27.2723 - 19.8145i) q^{86} +(-5.92523 - 8.15537i) q^{87} +(35.2127 - 25.5835i) q^{88} +(-5.55007 - 4.03236i) q^{89} +(-28.9882 - 3.88872i) q^{90} +(-0.418356 - 0.575818i) q^{91} +(2.46048 - 7.57259i) q^{92} +17.2171i q^{93} +(-0.0715544 + 0.220222i) q^{94} +(-13.2430 - 6.35652i) q^{95} +(-61.4981 + 19.9819i) q^{96} +(-2.90335 - 8.93560i) q^{97} +(5.42922 - 7.47268i) q^{98} +21.4245i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 10 q^{2} + 38 q^{4} - 10 q^{8} - 50 q^{9} - 10 q^{13} + 6 q^{15} - 58 q^{16} - 8 q^{19} - 44 q^{21} - 20 q^{25} - 64 q^{26} + 78 q^{30} - 20 q^{33} - 23 q^{34} - 46 q^{35} + 52 q^{36} - 10 q^{38}+ \cdots - 250 q^{98}+O(q^{100}) \) 176 * q - 10 * q^2 + 38 * q^4 - 10 * q^8 - 50 * q^9 - 10 * q^13 + 6 * q^15 - 58 * q^16 - 8 * q^19 - 44 * q^21 - 20 * q^25 - 64 * q^26 + 78 * q^30 - 20 * q^33 - 23 * q^34 - 46 * q^35 + 52 * q^36 - 10 * q^38 - 20 * q^42 + 40 * q^47 + 164 * q^49 + 84 * q^50 + 20 * q^51 - 30 * q^52 - 40 * q^53 - 18 * q^55 - 18 * q^59 - 48 * q^60 + 66 * q^64 + 80 * q^66 - 50 * q^67 + 68 * q^69 - 152 * q^70 + 60 * q^72 - 72 * q^76 - 40 * q^77 - 38 * q^81 + 50 * q^83 - 52 * q^84 + 47 * q^85 - 94 * q^86 - 120 * q^87 + 60 * q^89 + 50 * q^94 - 250 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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