LMFDB - Embedded newform 425.2.q.a.84.2

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			84.2
Character	$\chi$	$=$	425.84
Dual form			425.2.q.a.339.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-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} +(4.03362 + 0.854352i) 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} +(-8.40222 + 7.57630i) 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} +(-3.09263 + 8.68537i) 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	$0.197573\pi$
$3$	0.861202	+	2.65051i	0.497215	+	1.53027i	−0.316260	+	0.948672i	$0.602427\pi$
$4$	−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	$-0.617308\pi$
$7$	−1.90625			−0.720494			−0.360247	+	0.932857i	$0.617308\pi$
$8$	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	$0.436965\pi$
$11$	−2.64178	+	3.63610i	−0.796527	+	1.09633i	−0.993264	+	0.115869i	$0.963035\pi$
$12$	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
$17$	4.03362	+	0.854352i	0.978296	+	0.207211i
$17$	4.03362	+	0.854352i	0.978296	+	0.207211i
$18$		−	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	0.459663	−	0.888093i	$-0.347970\pi$
$23$	−1.16500	−	0.846425i	−0.242920	−	0.176492i	−0.702583	+	0.711602i	$0.747970\pi$
$24$			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	−0.610473	−	0.792037i	$-0.709021\pi$
$29$	−3.44009	+	1.11775i	−0.638809	+	0.207561i	−0.0283354	+	0.999598i	$0.509021\pi$
$30$	7.39938	−	15.4157i	1.35093	−	2.81451i
$31$	5.87547	+	1.90906i	1.05527	+	0.342876i	0.784733	−	0.619834i	$-0.212800\pi$
$31$	5.87547	+	1.90906i	1.05527	+	0.342876i	0.270533	+	0.962711i	$0.412800\pi$
$32$		−	23.2024i		−	4.10164i
$33$	−11.9126	−	3.87065i	−2.07372	−	0.673793i
$34$	−8.40222	+	7.57630i	−1.44097	+	1.29933i
$35$	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	−0.402359	−	0.915482i	$-0.631810\pi$
$37$	2.09235	−	1.52018i	0.343980	−	0.249916i	0.746339	+	0.665566i	$0.231810\pi$
$38$	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	0.885673	−	0.464310i	$-0.153698\pi$
$41$	1.09109	+	1.50176i	0.170400	+	0.234536i	−0.715273	+	0.698845i	$0.753698\pi$
$42$	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	$-0.582515\pi$
$61$	5.79643	−	7.97811i	0.742157	−	1.02149i	0.998492	−	0.0549038i	$-0.0174852\pi$
$62$	−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	−0.853149	−	0.521668i	$-0.825310\pi$
$71$	−10.4209	+	3.38595i	−1.23673	+	0.401838i	−0.383583	+	0.923506i	$0.625310\pi$
$72$	−43.9038	+	14.2652i	−5.17411	+	1.68117i
$73$	1.80355	+	1.31036i	0.211090	+	0.153366i	0.688307	−	0.725420i	$-0.258354\pi$
$73$	1.80355	+	1.31036i	0.211090	+	0.153366i	−0.477217	+	0.878786i	$0.658354\pi$
$74$			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	−0.792886	−	0.609370i	$-0.791422\pi$
$79$	−9.56517	+	3.10791i	−1.07617	+	0.349667i	−0.283279	+	0.959037i	$0.591422\pi$
$80$	−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
$85$	−3.09263	+	8.68537i	−0.335443	+	0.942061i
$86$	−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	$0.0582691\pi$
$97$	2.90335	+	8.93560i	0.294791	+	0.907273i	−0.688501	+	0.725235i	$0.741731\pi$
$98$	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	$0.454374\pi$
$102$	−27.3171	−	15.7454i	−2.70479	−	1.55903i
$103$	−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	$-0.596379\pi$
$107$	−6.16879			−0.596359			−0.298180	+	0.954510i	$0.596379\pi$
$108$	−8.41349	+	25.8941i	−0.809589	+	2.49166i
$109$	−3.01721	−	4.15284i	−0.288997	−	0.397770i	0.639691	−	0.768632i	$-0.279062\pi$
$109$	−3.01721	−	4.15284i	−0.288997	−	0.397770i	−0.928688	+	0.370862i	$0.879062\pi$
$110$	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	−0.555219	−	0.831704i	$-0.687366\pi$
$113$	0.682524	−	0.495882i	0.0642064	−	0.0466487i	0.619426	+	0.785055i	$0.287366\pi$
$114$	−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
$119$	−7.68908	−	1.62861i	−0.704857	−	0.149294i
$120$	−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	−0.118468	−	0.992958i	$-0.537798\pi$
$131$	−9.13304	−	2.96750i	−0.797957	−	0.259272i	−0.679489	+	0.733686i	$0.737798\pi$
$132$			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
$136$	34.5937	+	19.9397i	2.96639	+	1.70981i
$137$	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	−0.367436	−	0.930049i	$-0.619764\pi$
$139$	7.43510	−	10.2335i	0.630637	−	0.867998i	0.998073	+	0.0620512i	$0.0197642\pi$
$140$	−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
$153$	−17.9493	+	8.00698i	−1.45112	+	0.647326i
$154$	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	−0.953459	−	0.301522i	$-0.902505\pi$
$163$	−12.2734	+	8.91718i	−0.961330	+	0.698447i	−0.00787112	+	0.999969i	$0.502505\pi$
$164$	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	−0.992070	−	0.125690i	$-0.959886\pi$
$167$	−1.49375	+	4.59729i	−0.115590	+	0.355749i	0.876480	+	0.481439i	$0.159886\pi$
$168$		−	51.4476i		−	3.96927i
$169$	3.97414	−	12.2311i	0.305703	−	0.940857i
$170$	−14.2927	−	20.8736i	−1.09620	−	1.60093i
$171$	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	0.949911	−	0.312521i	$-0.101173\pi$
$173$	12.4456	+	9.04229i	0.946225	+	0.687473i	−0.00368601	+	0.999993i	$0.501173\pi$
$174$	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	0.187671	−	0.982232i	$-0.439906\pi$
$181$	−3.19982	−	1.03968i	−0.237841	−	0.0772791i	−0.425512	+	0.904953i	$0.639906\pi$
$182$	−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
$187$	−13.7624	+	12.4096i	−1.00641	+	0.907482i
$188$	−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	$-0.164830\pi$
$193$	24.1422			1.73779			0.868897	+	0.494994i	$0.164830\pi$
$194$	−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	$-0.777915\pi$
$197$	−7.35443	−	22.6346i	−0.523981	−	1.61265i	0.242341	−	0.970191i	$-0.422085\pi$
$198$	47.5604	+	34.5546i	3.37997	+	2.45569i
$199$		−	0.808544i		−	0.0573162i	−0.999589	−	0.0286581i	$-0.990877\pi$
$199$		−	0.808544i		−	0.0573162i	0.999589	−	0.0286581i	$-0.00912340\pi$
$200$	−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
$204$	58.0240	−	25.8838i	4.06249	−	1.81223i
$205$	−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	$0.422917\pi$
$211$	−11.0049	+	15.1469i	−0.757607	+	1.04276i	−0.997409	+	0.0719344i	$0.977083\pi$
$212$	−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
$221$	−0.627168	−	1.40593i	−0.0421879	−	0.0945731i
$222$	−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	0.809727	−	0.586806i	$-0.199615\pi$
$227$	7.56129	+	5.49360i	0.501861	+	0.364623i	−0.307867	+	0.951430i	$0.599615\pi$
$228$	−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	$0.424596\pi$
$233$	−8.03745	+	24.7367i	−0.526551	+	1.62056i	−0.761229	+	0.648483i	$0.775404\pi$
$234$	−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
$238$	16.0167	−	14.4423i	1.03821	−	0.936157i
$239$	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	$0.0351019\pi$
$241$	12.2866	+	16.9111i	0.791452	+	1.08934i	−0.202474	+	0.979288i	$0.564898\pi$
$242$	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
$255$	−25.6840	−	0.717183i	−1.60840	−	0.0449118i
$256$	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	0.557040	−	0.830486i	$-0.311937\pi$
$269$	8.52121	+	2.76871i	0.519547	+	0.168811i	−0.0374926	+	0.999297i	$0.511937\pi$
$270$	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	$0.672128\pi$
$272$	−58.4185	+	26.0598i	−3.54214	+	1.58011i
$273$	−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	0.184356	−	0.982860i	$-0.440980\pi$
$277$	−11.5410	−	8.38501i	−0.693430	−	0.503807i	−0.877786	+	0.479053i	$0.840980\pi$
$278$	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	$0.234596\pi$
$283$	−4.26646	+	13.1308i	−0.253615	+	0.780546i	−0.994099	+	0.108473i	$0.965404\pi$
$284$	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
$289$	15.5402	+	6.89226i	0.914127	+	0.405427i
$290$	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
$306$	11.1750	−	52.7599i	0.638830	−	3.01608i
$307$			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	−0.692792	−	0.721137i	$-0.743620\pi$
$311$	3.65286	−	5.02773i	0.207135	−	0.285096i	0.899927	+	0.436041i	$0.143620\pi$
$312$	8.15251	−	5.92314i	0.461545	−	0.335332i
$313$	0.569420	−	0.413708i	0.0321855	−	0.0233841i	−0.571576	−	0.820549i	$-0.693668\pi$
$313$	0.569420	−	0.413708i	0.0321855	−	0.0233841i	0.603762	+	0.797165i	$0.293668\pi$
$314$	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	−0.914011	−	0.405688i	$-0.867032\pi$
$317$	1.13765	−	3.50133i	0.0638969	−	0.196655i	0.977908	+	0.209034i	$0.0670319\pi$
$318$	−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
$323$	13.5263	−	23.4670i	0.752623	−	1.30574i
$324$	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	−0.716169	−	0.697927i	$-0.754106\pi$
$337$	−5.02463	+	3.65061i	−0.273709	+	0.198861i	0.442460	+	0.896788i	$0.354106\pi$
$338$	20.7423	+	28.5493i	1.12823	+	1.55288i
$339$	1.90213	+	1.38198i	0.103310	+	0.0750588i
$340$	50.9576	+	1.42291i	2.76356	+	0.0771679i
$341$	−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	$0.297610\pi$
$347$	10.9222	+	33.6151i	0.586334	+	1.80455i	−0.00750959	+	0.999972i	$0.502390\pi$
$348$	−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	$-0.711290\pi$
$367$	6.61522	−	20.3596i	0.345312	−	1.06276i	0.961417	−	0.275096i	$-0.0887096\pi$
$368$	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	−0.907825	−	0.419350i	$-0.862258\pi$
$379$	−27.1730	+	8.82904i	−1.39578	+	0.453517i	−0.487958	+	0.872867i	$0.662258\pi$
$380$	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
$391$	−3.97604	−	4.40948i	−0.201077	−	0.222997i
$392$	−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	0.995401	−	0.0957940i	$-0.0305390\pi$
$397$	2.66591	+	8.20484i	0.133798	+	0.411789i	−0.861603	+	0.507583i	$0.830539\pi$
$398$	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	$-0.963026\pi$
$401$		−	4.64168i		−	0.231794i	0.993261	−	0.115897i	$-0.0369743\pi$
$402$	−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
$408$	−23.0580	+	108.863i	−1.14154	+	5.38952i
$409$	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	0.476394	−	0.879232i	$-0.341944\pi$
$419$	7.06209	+	2.29461i	0.345006	+	0.112099i	−0.131389	+	0.991331i	$0.541944\pi$
$420$	−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
$425$	−18.3292	−	9.43611i	−0.889097	−	0.457719i
$426$	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	0.942925	−	0.333004i	$-0.108062\pi$
$431$	31.3491	+	10.1859i	1.51003	+	0.490640i	0.567108	+	0.823643i	$0.308062\pi$
$432$	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	$0.458993\pi$
$439$	−17.9018	+	24.6397i	−0.854404	+	1.17599i	−0.982875	+	0.184273i	$0.941007\pi$
$440$	−46.2297	−	85.6448i	−2.20392	−	4.08296i
$441$	12.9817	−	9.43177i	0.618177	−	0.449132i
$442$	4.13256	+	0.875309i	0.196566	+	0.0416342i
$443$		−	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	$-0.878103\pi$
$449$		−	15.8354i		−	0.747317i	0.927566	−	0.373658i	$-0.121897\pi$
$450$	−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
$459$	−13.5958	−	15.0780i	−0.634600	−	0.703779i
$460$	−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	−0.855994	−	0.516986i	$-0.827054\pi$
$479$	−27.2401	+	8.85084i	−1.24463	+	0.404405i	−0.388637	+	0.921391i	$0.627054\pi$
$480$	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	0.200667	−	0.979660i	$-0.435689\pi$
$487$	26.3578	−	19.1501i	1.19439	−	0.867773i	0.993721	+	0.111886i	$0.0356892\pi$
$488$	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	$-0.784006\pi$
$499$		−	28.0425i		−	1.25535i	0.778474	−	0.627677i	$-0.215994\pi$
$500$	−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	$-0.921999\pi$
$503$	−7.35347	−	22.6317i	−0.327875	−	1.00910i	0.642251	−	0.766494i	$-0.278001\pi$
$504$	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	$0.0425225\pi$
$510$	43.0167	−	55.8594i	1.90481	−	2.47349i
$511$	−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	0.645447	−	0.763805i	$-0.276671\pi$
$521$	36.8991	−	11.9892i	1.61658	−	0.525258i	0.971131	+	0.238547i	$0.0766711\pi$
$522$	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
$527$	22.0684	+	12.7201i	0.961315	+	0.554097i
$528$	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	0.885356	−	0.464913i	$-0.153914\pi$
$541$	3.94498	+	5.42979i	0.169608	+	0.233445i	−0.715749	+	0.698358i	$0.753914\pi$
$542$	−56.3882	−	18.3216i	−2.42208	−	0.786982i
$543$		−	9.37653i		−	0.402385i
$544$	19.8230	−	93.5895i	0.849904	−	4.01262i
$545$	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	0.818020	−	0.575190i	$-0.195072\pi$
$547$	−4.25335	−	13.0905i	−0.181860	−	0.559708i	−0.999880	+	0.0154820i	$0.995072\pi$
$548$	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
$561$	−44.7441	−	25.7903i	−1.88910	−	1.08887i
$562$	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	0.247181	−	0.968969i	$-0.420496\pi$
$571$	24.2947	−	7.89382i	1.01670	−	0.330346i	0.769520	+	0.638623i	$0.220496\pi$
$572$	−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	$0.260311\pi$
$578$	−40.3642	+	23.3815i	−1.67893	+	0.972541i
$579$	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
$595$	5.89532	−	16.5565i	0.241685	−	0.678749i
$596$	−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	$-0.790777\pi$
$601$		−	29.9565i		−	1.22195i	0.791649	−	0.610976i	$-0.209223\pi$
$602$	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	$-0.467760\pi$
$607$	4.98230			0.202225			0.101113	+	0.994875i	$0.467760\pi$
$608$	−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
$612$	72.7749	+	80.7084i	2.94175	+	3.26244i
$613$	−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	−0.866255	−	0.499602i	$-0.833479\pi$
$617$	3.18489	−	9.80209i	0.128219	−	0.394617i	0.994474	+	0.104985i	$0.0334795\pi$
$618$	51.5515			2.07370
$619$	27.4630	+	8.92326i	1.10383	+	0.358656i	0.803575	−	0.595203i	$-0.202928\pi$
$619$	27.4630	+	8.92326i	1.10383	+	0.358656i	0.300254	+	0.953859i	$0.402928\pi$
$620$	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
$629$	9.73850	−	4.34422i	0.388299	−	0.173216i
$630$	−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	0.951700	−	0.307030i	$-0.0993353\pi$
$641$	9.25639	+	12.7403i	0.365605	+	0.503213i	−0.586094	+	0.810243i	$0.699335\pi$
$642$	44.8648	+	14.5775i	1.77067	+	0.575326i
$643$	39.0707			1.54080			0.770399	−	0.637562i	$-0.220057\pi$
$643$	39.0707			1.54080			0.770399	+	0.637562i	$0.220057\pi$
$644$	4.69029	−	14.4352i	0.184824	−	0.568828i
$645$	−13.7671	−	75.3109i	−0.542078	−	2.96536i
$646$	30.2786	+	67.8760i	1.19130	+	2.67055i
$647$	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	$-0.862265\pi$
$653$	−10.7290	−	33.0203i	−0.419856	−	1.29218i	0.487978	−	0.872856i	$-0.337735\pi$
$654$	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
$663$	3.18631	−	2.87310i	0.123746	−	0.111582i
$664$	−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	0.980836	−	0.194837i	$-0.0624178\pi$
$673$	28.5009	+	20.7071i	1.09863	+	0.798201i	0.117794	+	0.993038i	$0.462418\pi$
$674$		−	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	$-0.959029\pi$
$677$	−36.9542	−	26.8488i	−1.42027	−	1.03188i	−0.428539	−	0.903523i	$-0.640971\pi$
$678$	−6.13573	+	1.99362i	−0.235641	+	0.0765644i
$679$	−5.53451	−	17.0335i	−0.212395	−	0.653685i
$680$	−54.4754	+	70.7391i	−2.08904	+	2.71272i
$681$	−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	$0.219444\pi$
$683$	−5.91968	+	18.2189i	−0.226510	+	0.697127i	−0.998135	+	0.0610485i	$0.980556\pi$
$684$	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	0.466398	−	0.884575i	$-0.345551\pi$
$691$	−13.6431	−	18.7781i	−0.519008	−	0.714353i	−0.985406	+	0.170222i	$0.945551\pi$
$692$	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
$697$	3.11802	+	6.98971i	0.118104	+	0.264754i
$698$	−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	0.621200	−	0.783652i	$-0.286645\pi$
$709$	−8.41571	−	11.5832i	−0.316059	−	0.435018i	−0.937259	+	0.348634i	$0.886645\pi$
$710$	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
$714$	52.0731	+	30.0147i	1.94879	+	1.12327i
$715$	−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	−0.0213116	−	0.999773i	$-0.506784\pi$
$719$	−16.7912	−	5.45578i	−0.626205	−	0.203466i	−0.604893	+	0.796307i	$0.706784\pi$
$720$	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
$731$	−10.4960	+	49.5545i	−0.388209	+	1.83284i
$732$		−	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	$-0.811762\pi$
$743$	−45.2581			−1.66036			−0.830180	+	0.557496i	$0.811762\pi$
$744$	−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
$748$	88.7731	+	51.1684i	3.24587	+	1.87090i
$749$	11.7592			0.429673
$750$	−56.0032	+	64.6027i	−2.04495	+	2.35896i
$751$			32.5605i			1.18815i	0.804410	+	0.594075i	$0.202482\pi$
$751$			32.5605i			1.18815i	−0.804410	+	0.594075i	$0.797518\pi$
$752$	−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
$765$	−12.4088	−	42.1601i	−0.448642	−	1.52430i
$766$	−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	−

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} +(4.03362 + 0.854352i) 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} +(-8.40222 + 7.57630i) 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} +(-3.09263 + 8.68537i) 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

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