LMFDB - Embedded newform 483.2.j.a.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(229,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("483.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.6
Character	$\chi$	$=$	483.229
Dual form			483.2.j.a.367.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.987485 + 1.71037i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.950252 - 1.64589i) q^{4} +(0.274706 - 0.475805i) q^{5} +1.97497i q^{6} +(-2.33704 + 1.24025i) q^{7} -0.196501 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.542536 + 0.939701i) q^{10} +(-1.60616 + 0.927315i) q^{11} +(-1.64589 - 0.950252i) q^{12} +4.79309i q^{13} +(0.186502 - 5.22195i) q^{14} -0.549412i q^{15} +(2.09455 - 3.62786i) q^{16} +(-2.03194 - 3.51943i) q^{17} +(0.987485 + 1.71037i) q^{18} +(-3.79634 + 6.57545i) q^{19} -1.04416 q^{20} +(-1.40381 + 2.24261i) q^{21} -3.66284i q^{22} +(-4.38086 + 1.95143i) q^{23} +(-0.170175 + 0.0982504i) q^{24} +(2.34907 + 4.06871i) q^{25} +(-8.19798 - 4.73311i) q^{26} -1.00000i q^{27} +(4.26209 + 2.66795i) q^{28} -0.625539 q^{29} +(0.939701 + 0.542536i) q^{30} +(-0.455304 + 0.262870i) q^{31} +(3.94016 + 6.82456i) q^{32} +(-0.927315 + 1.60616i) q^{33} +8.02605 q^{34} +(-0.0518827 + 1.45268i) q^{35} -1.90050 q^{36} +(-4.13587 - 2.38785i) q^{37} +(-7.49765 - 12.9863i) q^{38} +(2.39655 + 4.15094i) q^{39} +(-0.0539800 + 0.0934961i) q^{40} +5.16291i q^{41} +(-2.44946 - 4.61559i) q^{42} +5.70566i q^{43} +(3.05251 + 1.76237i) q^{44} +(-0.274706 - 0.475805i) q^{45} +(0.988354 - 9.41991i) q^{46} +(-7.28083 - 4.20359i) q^{47} -4.18909i q^{48} +(3.92355 - 5.79705i) q^{49} -9.27869 q^{50} +(-3.51943 - 2.03194i) q^{51} +(7.88888 - 4.55465i) q^{52} +(3.28289 - 1.89538i) q^{53} +(1.71037 + 0.987485i) q^{54} +1.01896i q^{55} +(0.459231 - 0.243711i) q^{56} +7.59268i q^{57} +(0.617711 - 1.06991i) q^{58} +(9.45730 - 5.46018i) q^{59} +(-0.904270 + 0.522080i) q^{60} +(6.96462 - 12.0631i) q^{61} -1.03832i q^{62} +(-0.0944330 + 2.64407i) q^{63} -7.18522 q^{64} +(2.28058 + 1.31669i) q^{65} +(-1.83142 - 3.17211i) q^{66} +(4.29758 - 2.48121i) q^{67} +(-3.86172 + 6.68869i) q^{68} +(-2.81822 + 3.88042i) q^{69} +(-2.43340 - 1.52324i) q^{70} -9.53344 q^{71} +(-0.0982504 + 0.170175i) q^{72} +(-0.387939 + 0.223977i) q^{73} +(8.16822 - 4.71592i) q^{74} +(4.06871 + 2.34907i) q^{75} +14.4299 q^{76} +(2.60356 - 4.15921i) q^{77} -9.46621 q^{78} +(14.8972 + 8.60088i) q^{79} +(-1.15077 - 1.99319i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.83050 - 5.09829i) q^{82} -6.85884 q^{83} +(5.02506 + 0.179470i) q^{84} -2.23275 q^{85} +(-9.75880 - 5.63425i) q^{86} +(-0.541733 + 0.312770i) q^{87} +(0.315611 - 0.182218i) q^{88} +(-3.88678 + 6.73210i) q^{89} +1.08507 q^{90} +(-5.94464 - 11.2017i) q^{91} +(7.37475 + 5.35604i) q^{92} +(-0.262870 + 0.455304i) q^{93} +(14.3794 - 8.30196i) q^{94} +(2.08576 + 3.61263i) q^{95} +(6.82456 + 3.94016i) q^{96} +5.69409 q^{97} +(6.04066 + 12.4352i) q^{98} +1.85463i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) $ 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.987485	+	1.71037i	−0.698257	+	1.20942i	0.270813	+	0.962632i	$0.412707\pi$
$2$	−0.987485	+	1.71037i	−0.698257	+	1.20942i	−0.969070	+	0.246785i	$0.920626\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.950252	−	1.64589i	−0.475126	−	0.822943i
$5$	0.274706	−	0.475805i	0.122852	−	0.212787i	−0.798039	−	0.602606i	$-0.794129\pi$
$5$	0.274706	−	0.475805i	0.122852	−	0.212787i	0.920891	+	0.389819i	$0.127463\pi$
$6$			1.97497i			0.806278i
$7$	−2.33704	+	1.24025i	−0.883320	+	0.468771i
$7$	−2.33704	+	1.24025i	−0.883320	+	0.468771i
$8$	−0.196501			−0.0694736
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.542536	+	0.939701i	0.171565	+	0.297159i
$11$	−1.60616	+	0.927315i	−0.484274	+	0.279596i	−0.722196	−	0.691688i	$-0.756867\pi$
$11$	−1.60616	+	0.927315i	−0.484274	+	0.279596i	0.237922	+	0.971284i	$0.423534\pi$
$12$	−1.64589	−	0.950252i	−0.475126	−	0.274314i
$13$			4.79309i			1.32936i	0.747126	+	0.664682i	$0.231433\pi$
$13$			4.79309i			1.32936i	−0.747126	+	0.664682i	$0.768567\pi$
$14$	0.186502	−	5.22195i	0.0498448	−	1.39562i
$15$		−	0.549412i		−	0.141858i
$16$	2.09455	−	3.62786i	0.523636	−	0.906965i
$17$	−2.03194	−	3.51943i	−0.492818	−	0.853586i	0.507147	−	0.861859i	$-0.330700\pi$
$17$	−2.03194	−	3.51943i	−0.492818	−	0.853586i	−0.999966	+	0.00827286i	$0.997367\pi$
$18$	0.987485	+	1.71037i	0.232752	+	0.403139i
$19$	−3.79634	+	6.57545i	−0.870940	+	1.50851i	−0.00991372	+	0.999951i	$0.503156\pi$
$19$	−3.79634	+	6.57545i	−0.870940	+	1.50851i	−0.861026	+	0.508561i	$0.830178\pi$
$20$	−1.04416			−0.233481
$21$	−1.40381	+	2.24261i	−0.306337	+	0.489378i
$22$		−	3.66284i		−	0.780920i
$23$	−4.38086	+	1.95143i	−0.913472	+	0.406901i
$23$	−4.38086	+	1.95143i	−0.913472	+	0.406901i
$24$	−0.170175	+	0.0982504i	−0.0347368	+	0.0200553i
$25$	2.34907	+	4.06871i	0.469815	+	0.813743i
$26$	−8.19798	−	4.73311i	−1.60776	−	0.928239i
$27$		−	1.00000i		−	0.192450i
$28$	4.26209	+	2.66795i	0.805460	+	0.504196i
$29$	−0.625539			−0.116160			−0.0580799	−	0.998312i	$-0.518498\pi$
$29$	−0.625539			−0.116160			−0.0580799	+	0.998312i	$0.518498\pi$
$30$	0.939701	+	0.542536i	0.171565	+	0.0990531i
$31$	−0.455304	+	0.262870i	−0.0817750	+	0.0472128i	−0.540330	−	0.841453i	$-0.681701\pi$
$31$	−0.455304	+	0.262870i	−0.0817750	+	0.0472128i	0.458555	+	0.888666i	$0.348367\pi$
$32$	3.94016	+	6.82456i	0.696529	+	1.20642i
$33$	−0.927315	+	1.60616i	−0.161425	+	0.279596i
$34$	8.02605			1.37646
$35$	−0.0518827	+	1.45268i	−0.00876977	+	0.245548i
$36$	−1.90050			−0.316751
$37$	−4.13587	−	2.38785i	−0.679933	−	0.392560i	0.119897	−	0.992786i	$-0.461744\pi$
$37$	−4.13587	−	2.38785i	−0.679933	−	0.392560i	−0.799830	+	0.600227i	$0.795077\pi$
$38$	−7.49765	−	12.9863i	−1.21628	−	2.10666i
$39$	2.39655	+	4.15094i	0.383755	+	0.664682i
$40$	−0.0539800	+	0.0934961i	−0.00853499	+	0.0147830i
$41$			5.16291i			0.806311i	0.915132	+	0.403155i	$0.132087\pi$
$41$			5.16291i			0.806311i	−0.915132	+	0.403155i	$0.867913\pi$
$42$	−2.44946	−	4.61559i	−0.377960	−	0.712201i
$43$			5.70566i			0.870104i	0.900405	+	0.435052i	$0.143270\pi$
$43$			5.70566i			0.870104i	−0.900405	+	0.435052i	$0.856730\pi$
$44$	3.05251	+	1.76237i	0.460183	+	0.265687i
$45$	−0.274706	−	0.475805i	−0.0409508	−	0.0709288i
$46$	0.988354	−	9.41991i	0.145725	−	1.38889i
$47$	−7.28083	−	4.20359i	−1.06202	−	0.613156i	−0.136028	−	0.990705i	$-0.543434\pi$
$47$	−7.28083	−	4.20359i	−1.06202	−	0.613156i	−0.925990	+	0.377549i	$0.876767\pi$
$48$		−	4.18909i		−	0.604643i
$49$	3.92355	−	5.79705i	0.560508	−	0.828149i
$50$	−9.27869			−1.31221
$51$	−3.51943	−	2.03194i	−0.492818	−	0.284529i
$52$	7.88888	−	4.55465i	1.09399	−	0.631616i
$53$	3.28289	−	1.89538i	0.450940	−	0.260350i	−0.257287	−	0.966335i	$-0.582829\pi$
$53$	3.28289	−	1.89538i	0.450940	−	0.260350i	0.708227	+	0.705985i	$0.249495\pi$
$54$	1.71037	+	0.987485i	0.232752	+	0.134380i
$55$			1.01896i			0.137396i
$56$	0.459231	−	0.243711i	0.0613674	−	0.0325672i
$57$			7.59268i			1.00567i
$58$	0.617711	−	1.06991i	0.0811094	−	0.140486i
$59$	9.45730	−	5.46018i	1.23124	−	0.710854i	0.263948	−	0.964537i	$-0.414975\pi$
$59$	9.45730	−	5.46018i	1.23124	−	0.710854i	0.967288	+	0.253682i	$0.0816418\pi$
$60$	−0.904270	+	0.522080i	−0.116741	+	0.0674003i
$61$	6.96462	−	12.0631i	0.891729	−	1.54452i	0.0539272	−	0.998545i	$-0.482826\pi$
$61$	6.96462	−	12.0631i	0.891729	−	1.54452i	0.837802	−	0.545975i	$-0.183841\pi$
$62$		−	1.03832i		−	0.131867i
$63$	−0.0944330	+	2.64407i	−0.0118974	+	0.333121i
$64$	−7.18522			−0.898153
$65$	2.28058	+	1.31669i	0.282871	+	0.163316i
$66$	−1.83142	−	3.17211i	−0.225432	−	0.390460i
$67$	4.29758	−	2.48121i	0.525032	−	0.303128i	−0.213959	−	0.976843i	$-0.568636\pi$
$67$	4.29758	−	2.48121i	0.525032	−	0.303128i	0.738991	+	0.673715i	$0.235302\pi$
$68$	−3.86172	+	6.68869i	−0.468302	+	0.811122i
$69$	−2.81822	+	3.88042i	−0.339274	+	0.467147i
$70$	−2.43340	−	1.52324i	−0.290847	−	0.182062i
$71$	−9.53344			−1.13141			−0.565705	−	0.824607i	$-0.691396\pi$
$71$	−9.53344			−1.13141			−0.565705	+	0.824607i	$0.691396\pi$
$72$	−0.0982504	+	0.170175i	−0.0115789	+	0.0200553i
$73$	−0.387939	+	0.223977i	−0.0454049	+	0.0262145i	−0.522531	−	0.852621i	$-0.675012\pi$
$73$	−0.387939	+	0.223977i	−0.0454049	+	0.0262145i	0.477126	+	0.878835i	$0.341679\pi$
$74$	8.16822	−	4.71592i	0.949536	−	0.548215i
$75$	4.06871	+	2.34907i	0.469815	+	0.271248i
$76$	14.4299			1.65522
$77$	2.60356	−	4.15921i	0.296703	−	0.473986i
$78$	−9.46621			−1.07184
$79$	14.8972	+	8.60088i	1.67606	+	0.967675i	0.964132	+	0.265424i	$0.0855120\pi$
$79$	14.8972	+	8.60088i	1.67606	+	0.967675i	0.711930	+	0.702250i	$0.247821\pi$
$80$	−1.15077	−	1.99319i	−0.128660	−	0.222846i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−8.83050	−	5.09829i	−0.975166	−	0.563012i
$83$	−6.85884			−0.752855			−0.376428	−	0.926446i	$-0.622848\pi$
$83$	−6.85884			−0.752855			−0.376428	+	0.926446i	$0.622848\pi$
$84$	5.02506	+	0.179470i	0.548279	+	0.0195818i
$85$	−2.23275			−0.242176
$86$	−9.75880	−	5.63425i	−1.05232	−	0.607557i
$87$	−0.541733	+	0.312770i	−0.0580799	+	0.0335324i
$88$	0.315611	−	0.182218i	0.0336443	−	0.0194245i
$89$	−3.88678	+	6.73210i	−0.411998	+	0.713601i	−0.995108	−	0.0987918i	$-0.968502\pi$
$89$	−3.88678	+	6.73210i	−0.411998	+	0.713601i	0.583110	+	0.812393i	$0.301836\pi$
$90$	1.08507			0.114377
$91$	−5.94464	−	11.2017i	−0.623168	−	1.17425i
$92$	7.37475	+	5.35604i	0.768871	+	0.558405i
$93$	−0.262870	+	0.455304i	−0.0272583	+	0.0472128i
$94$	14.3794	−	8.30196i	1.48312	−	0.856281i
$95$	2.08576	+	3.61263i	0.213994	+	0.370648i
$96$	6.82456	+	3.94016i	0.696529	+	0.402141i
$97$	5.69409			0.578147			0.289074	−	0.957307i	$-0.406653\pi$
$97$	5.69409			0.578147			0.289074	+	0.957307i	$0.406653\pi$
$98$	6.04066	+	12.4352i	0.610199	+	1.25615i
$99$			1.85463i			0.186397i
$100$	4.46442	−	7.73261i	0.446442	−	0.773261i
$101$	12.1070	−	6.98997i	1.20469	−	0.695528i	0.243096	−	0.970002i	$-0.421837\pi$
$101$	12.1070	−	6.98997i	1.20469	−	0.695528i	0.961594	+	0.274474i	$0.0885038\pi$
$102$	6.95076	−	4.01302i	0.688228	−	0.397349i
$103$	−7.40105	+	12.8190i	−0.729247	+	1.26309i	0.227955	+	0.973672i	$0.426796\pi$
$103$	−7.40105	+	12.8190i	−0.729247	+	1.26309i	−0.957202	+	0.289421i	$0.906537\pi$
$104$		−	0.941847i		−	0.0923557i
$105$	0.681410	+	1.28400i	0.0664988	+	0.125306i
$106$			7.48663i			0.727165i
$107$	3.54020	+	2.04394i	0.342245	+	0.197595i	0.661264	−	0.750153i	$-0.270020\pi$
$107$	3.54020	+	2.04394i	0.342245	+	0.197595i	−0.319020	+	0.947748i	$0.603354\pi$
$108$	−1.64589	+	0.950252i	−0.158375	+	0.0914381i
$109$	−15.2496	+	8.80435i	−1.46065	+	0.843304i	−0.999041	−	0.0437823i	$-0.986059\pi$
$109$	−15.2496	+	8.80435i	−1.46065	+	0.843304i	−0.461604	+	0.887086i	$0.652726\pi$
$110$	−1.74280	−	1.00620i	−0.166169	−	0.0959378i
$111$	−4.77569			−0.453289
$112$	−0.395588	+	11.0762i	−0.0373796	+	1.04661i
$113$			14.7696i			1.38941i	0.719294	+	0.694705i	$0.244465\pi$
$113$			14.7696i			1.38941i	−0.719294	+	0.694705i	$0.755535\pi$
$114$	−12.9863	−	7.49765i	−1.21628	−	0.702219i
$115$	−0.274948	+	2.62050i	−0.0256390	+	0.244363i
$116$	0.594420	+	1.02957i	0.0551905	+	0.0955928i
$117$	4.15094	+	2.39655i	0.383755	+	0.221561i
$118$			21.5674i			1.98544i
$119$	9.11371	+	5.70494i	0.835453	+	0.522971i
$120$			0.107960i			0.00985536i
$121$	−3.78017	+	6.54745i	−0.343652	+	0.595223i
$122$	13.7549	+	23.8242i	1.24531	+	2.15694i
$123$	2.58145	+	4.47121i	0.232762	+	0.403155i
$124$	0.865307	+	0.499585i	0.0777069	+	0.0448641i
$125$	5.32828			0.476576
$126$	−4.42909	−	2.77249i	−0.394575	−	0.246993i
$127$	9.68945			0.859800			0.429900	−	0.902876i	$-0.358549\pi$
$127$	9.68945			0.859800			0.429900	+	0.902876i	$0.358549\pi$
$128$	−0.785031	+	1.35971i	−0.0693876	+	0.120183i
$129$	2.85283	+	4.94124i	0.251177	+	0.435052i
$130$	−4.50407	+	2.60043i	−0.395033	+	0.228073i
$131$	8.68718	+	5.01554i	0.759002	+	0.438210i	0.828937	−	0.559341i	$-0.188946\pi$
$131$	8.68718	+	5.01554i	0.759002	+	0.438210i	−0.0699352	+	0.997552i	$0.522279\pi$
$132$	3.52473			0.306789
$133$	0.716999	−	20.0755i	0.0621717	−	1.74077i
$134$			9.80061i			0.846644i
$135$	−0.475805	−	0.274706i	−0.0409508	−	0.0236429i
$136$	0.399278	+	0.691571i	0.0342378	+	0.0593017i
$137$	4.66989	−	2.69616i	0.398975	−	0.230349i	−0.287066	−	0.957911i	$-0.592680\pi$
$137$	4.66989	−	2.69616i	0.398975	−	0.230349i	0.686042	+	0.727562i	$0.259347\pi$
$138$	−3.85402	−	8.65206i	−0.328076	−	0.736512i
$139$			2.17302i			0.184313i	0.995745	+	0.0921564i	$0.0293760\pi$
$139$			2.17302i			0.184313i	−0.995745	+	0.0921564i	$0.970624\pi$
$140$	2.44025	−	1.29502i	0.206239	−	0.109449i
$141$	−8.40717			−0.708012
$142$	9.41412	−	16.3057i	0.790016	−	1.36835i
$143$	−4.44471	−	7.69846i	−0.371685	−	0.643778i
$144$	−2.09455	−	3.62786i	−0.174545	−	0.302322i
$145$	−0.171840	+	0.297635i	−0.0142705	+	0.0247172i
$146$		−	0.884695i		−	0.0732179i
$147$	0.499374	−	6.98216i	0.0411877	−	0.575879i
$148$			9.07622i			0.746061i
$149$	9.64396	+	5.56794i	0.790064	+	0.456144i	0.839985	−	0.542609i	$-0.182564\pi$
$149$	9.64396	+	5.56794i	0.790064	+	0.456144i	−0.0499209	+	0.998753i	$0.515897\pi$
$150$	−8.03559	+	4.63935i	−0.656103	+	0.378801i
$151$	−4.49218	−	7.78069i	−0.365569	−	0.633184i	0.623299	−	0.781984i	$-0.285792\pi$
$151$	−4.49218	−	7.78069i	−0.365569	−	0.633184i	−0.988867	+	0.148800i	$0.952459\pi$
$152$	0.745984	−	1.29208i	0.0605073	−	0.104802i
$153$	−4.06388			−0.328546
$154$	4.54284	+	8.56021i	0.366072	+	0.689802i
$155$			0.288848i			0.0232008i
$156$	4.55465	−	7.88888i	0.364664	−	0.631616i
$157$	−6.48261	−	11.2282i	−0.517368	−	0.896108i	−0.999797	−	0.0201727i	$-0.993578\pi$
$157$	−6.48261	−	11.2282i	−0.517368	−	0.896108i	0.482428	−	0.875936i	$-0.339755\pi$
$158$	−29.4214	+	16.9865i	−2.34064	+	1.35137i
$159$	1.89538	−	3.28289i	0.150313	−	0.260350i
$160$	4.32955			0.342281
$161$	7.81799	−	9.99395i	0.616144	−	0.787633i
$162$	1.97497			0.155168
$163$	−9.32205	+	16.1463i	−0.730159	+	1.26467i	0.226656	+	0.973975i	$0.427221\pi$
$163$	−9.32205	+	16.1463i	−0.730159	+	1.26467i	−0.956815	+	0.290698i	$0.906113\pi$
$164$	8.49755	−	4.90606i	0.663547	−	0.383099i
$165$	0.509478	+	0.882443i	0.0396628	+	0.0686981i
$166$	6.77300	−	11.7312i	0.525687	−	0.910516i
$167$		−	14.2278i		−	1.10098i	−0.834842	−	0.550490i	$-0.814441\pi$
$167$		−	14.2278i		−	1.10098i	0.834842	−	0.550490i	$-0.185559\pi$
$168$	0.275851	−	0.440675i	0.0212823	−	0.0339988i
$169$	−9.97375			−0.767211
$170$	2.20481	−	3.81883i	0.169101	−	0.292891i
$171$	3.79634	+	6.57545i	0.290313	+	0.502837i
$172$	9.39085	−	5.42181i	0.716046	−	0.413409i
$173$	1.48083	+	0.854960i	0.112586	+	0.0650014i	0.555235	−	0.831693i	$-0.312628\pi$
$173$	1.48083	+	0.854960i	0.112586	+	0.0650014i	−0.442650	+	0.896695i	$0.645961\pi$
$174$		−	1.23542i		−	0.0936571i
$175$	−10.5361	−	6.59532i	−0.796455	−	0.498560i
$176$			7.76922i			0.585627i
$177$	5.46018	−	9.45730i	0.410412	−	0.710854i
$178$	−7.67627	−	13.2957i	−0.575361	−	0.996554i
$179$	−5.87300	−	10.1723i	−0.438968	−	0.760316i	0.558642	−	0.829409i	$-0.311323\pi$
$179$	−5.87300	−	10.1723i	−0.438968	−	0.760316i	−0.997610	+	0.0690934i	$0.977989\pi$
$180$	−0.522080	+	0.904270i	−0.0389136	+	0.0674003i
$181$	12.1844			0.905659			0.452829	−	0.891597i	$-0.350415\pi$
$181$	12.1844			0.905659			0.452829	+	0.891597i	$0.350415\pi$
$182$	25.0293	+	0.893923i	1.85529	+	0.0662620i
$183$		−	13.9292i		−	1.02968i
$184$	0.860843	−	0.383458i	0.0634622	−	0.0282689i
$185$	−2.27230	+	1.31191i	−0.167063	+	0.0964537i
$186$	−0.519160	−	0.899212i	−0.0380667	−	0.0659334i
$187$	6.52724	+	3.76850i	0.477319	+	0.275580i
$188$			15.9779i			1.16531i
$189$	1.24025	+	2.33704i	0.0902150	+	0.169995i
$190$	−8.23861			−0.597691
$191$	23.5627	+	13.6039i	1.70493	+	0.984344i	0.940596	+	0.339528i	$0.110267\pi$
$191$	23.5627	+	13.6039i	1.70493	+	0.984344i	0.764338	+	0.644816i	$0.223066\pi$
$192$	−6.22258	+	3.59261i	−0.449076	+	0.259274i
$193$	−0.692504	−	1.19945i	−0.0498475	−	0.0863384i	0.840025	−	0.542548i	$-0.182540\pi$
$193$	−0.692504	−	1.19945i	−0.0498475	−	0.0863384i	−0.889873	+	0.456209i	$0.849207\pi$
$194$	−5.62283	+	9.73902i	−0.403695	+	0.699221i
$195$	2.63339			0.188581
$196$	−13.2696	−	0.949062i	−0.947831	−	0.0677902i
$197$	−20.9635			−1.49359			−0.746795	−	0.665054i	$-0.768408\pi$
$197$	−20.9635			−1.49359			−0.746795	+	0.665054i	$0.768408\pi$
$198$	−3.17211	−	1.83142i	−0.225432	−	0.130153i
$199$	−5.88147	−	10.1870i	−0.416927	−	0.722138i	0.578702	−	0.815539i	$-0.303559\pi$
$199$	−5.88147	−	10.1870i	−0.416927	−	0.722138i	−0.995629	+	0.0934009i	$0.970226\pi$
$200$	−0.461595	−	0.799506i	−0.0326397	−	0.0565336i
$201$	2.48121	−	4.29758i	0.175011	−	0.303128i
$202$			27.6100i			1.94263i
$203$	1.46191	−	0.775826i	0.102606	−	0.0544523i
$204$			7.72343i			0.540748i
$205$	2.45654	+	1.41828i	0.171572	+	0.0990572i
$206$	−14.6168	−	25.3171i	−1.01840	−	1.76393i
$207$	−0.500440	+	4.76965i	−0.0347830	+	0.331514i
$208$	17.3887	+	10.0394i	1.20569	+	0.696104i
$209$		−	14.0816i		−	0.974045i
$210$	−2.86900	−	0.102467i	−0.197980	−	0.00707087i
$211$	−13.3608			−0.919794			−0.459897	−	0.887972i	$-0.652114\pi$
$211$	−13.3608			−0.919794			−0.459897	+	0.887972i	$0.652114\pi$
$212$	−6.23915	−	3.60217i	−0.428506	−	0.247398i
$213$	−8.25620	+	4.76672i	−0.565705	+	0.326610i
$214$	−6.99180	+	4.03672i	−0.477949	+	0.275944i
$215$	2.71478	+	1.56738i	0.185146	+	0.106894i
$216$			0.196501i			0.0133702i
$217$	0.738041	−	1.17903i	0.0501015	−	0.0800378i
$218$		−	34.7766i		−	2.35537i
$219$	−0.223977	+	0.387939i	−0.0151350	+	0.0262145i
$220$	1.67709	−	0.968266i	0.113069	−	0.0652805i
$221$	16.8689	−	9.73929i	1.13473	−	0.655135i
$222$	4.71592	−	8.16822i	0.316512	−	0.548215i
$223$			9.90651i			0.663389i	0.943387	+	0.331694i	$0.107620\pi$
$223$			9.90651i			0.663389i	−0.943387	+	0.331694i	$0.892380\pi$
$224$	−17.6725	−	11.0625i	−1.18079	−	0.739145i
$225$	4.69815			0.313210
$226$	−25.2616	−	14.5848i	−1.68038	−	0.970166i
$227$	10.3644	+	17.9517i	0.687910	+	1.19149i	0.972513	+	0.232849i	$0.0748048\pi$
$227$	10.3644	+	17.9517i	0.687910	+	1.19149i	−0.284603	+	0.958645i	$0.591862\pi$
$228$	12.4967	−	7.21496i	0.827612	−	0.477822i
$229$	12.7580	−	22.0974i	0.843069	−	1.46024i	−0.0442179	−	0.999022i	$-0.514080\pi$
$229$	12.7580	−	22.0974i	0.843069	−	1.46024i	0.887287	−	0.461217i	$-0.152587\pi$
$230$	−4.21054	−	3.05797i	−0.277635	−	0.201637i
$231$	0.175138	−	4.90376i	0.0115233	−	0.322644i
$232$	0.122919			0.00807003
$233$	1.33553	−	2.31321i	0.0874937	−	0.151544i	−0.818957	−	0.573854i	$-0.805448\pi$
$233$	1.33553	−	2.31321i	0.0874937	−	0.151544i	0.906451	+	0.422311i	$0.138781\pi$
$234$	−8.19798	+	4.73311i	−0.535919	+	0.309413i
$235$	−4.00018	+	2.30950i	−0.260943	+	0.150655i
$236$	−17.9736	−	10.3771i	−1.16998	−	0.675491i
$237$	17.2018			1.11737
$238$	−18.7572	+	9.95432i	−1.21585	+	0.645243i
$239$	−4.87195			−0.315140			−0.157570	−	0.987508i	$-0.550366\pi$
$239$	−4.87195			−0.315140			−0.157570	+	0.987508i	$0.550366\pi$
$240$	−1.99319	−	1.15077i	−0.128660	−	0.0742819i
$241$	8.24289	+	14.2771i	0.530971	+	0.919669i	0.999347	+	0.0361394i	$0.0115060\pi$
$241$	8.24289	+	14.2771i	0.530971	+	0.919669i	−0.468376	+	0.883529i	$0.655161\pi$
$242$	−7.46573	−	12.9310i	−0.479915	−	0.831237i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−26.4726			−1.69473
$245$	−1.68044	−	3.45933i	−0.107359	−	0.221009i
$246$	−10.1966			−0.650111
$247$	−31.5167	−	18.1962i	−2.00536	−	1.15780i
$248$	0.0894677	−	0.0516542i	0.00568120	−	0.00328004i
$249$	−5.93993	+	3.42942i	−0.376428	+	0.217331i
$250$	−5.26160	+	9.11335i	−0.332773	+	0.576379i
$251$	8.27572			0.522359			0.261179	−	0.965290i	$-0.415889\pi$
$251$	8.27572			0.522359			0.261179	+	0.965290i	$0.415889\pi$
$252$	4.44156	−	2.35710i	0.279792	−	0.148484i
$253$	5.22675	−	7.19674i	0.328603	−	0.452455i
$254$	−9.56819	+	16.5726i	−0.600362	+	1.03986i
$255$	−1.93362	+	1.11637i	−0.121088	+	0.0699101i
$256$	−8.73563	−	15.1306i	−0.545977	−	0.945660i
$257$	−1.54317	−	0.890949i	−0.0962602	−	0.0555759i	0.451097	−	0.892475i	$-0.351033\pi$
$257$	−1.54317	−	0.890949i	−0.0962602	−	0.0555759i	−0.547357	+	0.836899i	$0.684366\pi$
$258$	−11.2685			−0.701546
$259$	12.6272	+	0.450983i	0.784619	+	0.0280227i
$260$		−	5.00476i		−	0.310382i
$261$	−0.312770	+	0.541733i	−0.0193600	+	0.0335324i
$262$	−17.1569	+	9.90555i	−1.05996	+	0.611967i
$263$	−4.80860	+	2.77625i	−0.296511	+	0.171191i	−0.640874	−	0.767646i	$-0.721428\pi$
$263$	−4.80860	+	2.77625i	−0.296511	+	0.171191i	0.344363	+	0.938836i	$0.388095\pi$
$264$	0.182218	−	0.315611i	0.0112148	−	0.0194245i
$265$		−	2.08269i		−	0.127939i
$266$	33.6286	+	21.0506i	2.06190	+	1.29070i
$267$			7.77356i			0.475734i
$268$	−8.16756	−	4.71554i	−0.498913	−	0.288048i
$269$	−22.0864	+	12.7516i	−1.34663	+	0.777477i	−0.987771	−	0.155914i	$-0.950168\pi$
$269$	−22.0864	+	12.7516i	−1.34663	+	0.777477i	−0.358860	+	0.933392i	$0.616834\pi$
$270$	0.939701	−	0.542536i	0.0571884	−	0.0330177i
$271$	7.21499	+	4.16558i	0.438279	+	0.253041i	0.702868	−	0.711321i	$-0.251903\pi$
$271$	7.21499	+	4.16558i	0.438279	+	0.253041i	−0.264588	+	0.964362i	$0.585236\pi$
$272$	−17.0240			−1.03223
$273$	−10.7490	−	6.72861i	−0.650562	−	0.407234i
$274$			10.6497i			0.643370i
$275$	−7.54596	−	4.35666i	−0.455038	−	0.262717i
$276$	9.06474	+	0.951089i	0.545633	+	0.0572488i
$277$	−6.08232	−	10.5349i	−0.365451	−	0.632980i	0.623397	−	0.781905i	$-0.285752\pi$
$277$	−6.08232	−	10.5349i	−0.365451	−	0.632980i	−0.988848	+	0.148925i	$0.952419\pi$
$278$	−3.71667	−	2.14582i	−0.222911	−	0.128698i
$279$			0.525740i			0.0314752i
$280$	0.0101950	−	0.285453i	0.000609267	−	0.0170591i
$281$			3.14916i			0.187863i	0.995579	+	0.0939316i	$0.0299435\pi$
$281$			3.14916i			0.187863i	−0.995579	+	0.0939316i	$0.970057\pi$
$282$	8.30196	−	14.3794i	0.494374	−	0.856281i
$283$	−6.09803	−	10.5621i	−0.362490	−	0.627852i	0.625880	−	0.779920i	$-0.284740\pi$
$283$	−6.09803	−	10.5621i	−0.362490	−	0.627852i	−0.988370	+	0.152068i	$0.951407\pi$
$284$	9.05917	+	15.6909i	0.537563	+	0.931086i
$285$	3.61263	+	2.08576i	0.213994	+	0.123549i
$286$	17.5563			1.03813
$287$	−6.40330	−	12.0659i	−0.377975	−	0.712230i
$288$	7.88033			0.464353
$289$	0.242421	−	0.419886i	0.0142601	−	0.0246992i
$290$	−0.339378	−	0.587820i	−0.0199290	−	0.0345180i
$291$	4.93123	−	2.84704i	0.289074	−	0.166897i
$292$	0.737280	+	0.425669i	0.0431461	+	0.0249104i
$293$	−20.1206			−1.17546			−0.587730	−	0.809057i	$-0.699978\pi$
$293$	−20.1206			−1.17546			−0.587730	+	0.809057i	$0.699978\pi$
$294$	11.4490	+	7.74890i	0.667718	+	0.451925i
$295$		−	5.99978i		−	0.349321i
$296$	0.812702	+	0.469214i	0.0472374	+	0.0272725i
$297$	0.927315	+	1.60616i	0.0538083	+	0.0931987i
$298$	−19.0465	+	10.9965i	−1.10334	+	0.637011i
$299$	−9.35339	−	20.9979i	−0.540921	−	1.21434i
$300$		−	8.92885i		−	0.515507i
$301$	−7.07645	−	13.3344i	−0.407880	−	0.768580i
$302$	17.7439			1.02104
$303$	6.98997	−	12.1070i	0.401563	−	0.695528i
$304$	15.9032	+	27.5452i	0.912112	+	1.57982i
$305$	−3.82645	−	6.62761i	−0.219102	−	0.379496i
$306$	4.01302	−	6.95076i	0.229409	−	0.397349i
$307$			4.79221i			0.273506i	0.990605	+	0.136753i	$0.0436666\pi$
$307$			4.79221i			0.273506i	−0.990605	+	0.136753i	$0.956333\pi$
$308$	−9.31962	−	0.332851i	−0.531035	−	0.0189659i
$309$			14.8021i			0.842062i
$310$	−0.494038	−	0.285233i	−0.0280595	−	0.0162001i
$311$	−9.98594	+	5.76539i	−0.566251	+	0.326925i	−0.755651	−	0.654975i	$-0.772679\pi$
$311$	−9.98594	+	5.76539i	−0.566251	+	0.326925i	0.189400	+	0.981900i	$0.439346\pi$
$312$	−0.470924	−	0.815664i	−0.0266608	−	0.0461779i
$313$	3.85716	−	6.68080i	0.218020	−	0.377621i	−0.736183	−	0.676783i	$-0.763374\pi$
$313$	3.85716	−	6.68080i	0.218020	−	0.377621i	0.954202	+	0.299162i	$0.0967070\pi$
$314$	25.6059			1.44502
$315$	1.23212	+	0.771273i	0.0694220	+	0.0434563i
$316$		−	32.6920i		−	1.83907i
$317$	−7.12873	+	12.3473i	−0.400389	+	0.693495i	−0.993773	−	0.111425i	$-0.964458\pi$
$317$	−7.12873	+	12.3473i	−0.400389	+	0.693495i	0.593383	+	0.804920i	$0.297792\pi$
$318$	3.74331	+	6.48361i	0.209915	+	0.363583i
$319$	1.00471	−	0.580072i	0.0562532	−	0.0324778i
$320$	−1.97382	+	3.41877i	−0.110340	+	0.191115i
$321$	4.08788			0.228163
$322$	9.37323	+	23.2406i	0.522350	+	1.29515i
$323$	30.8558			1.71686
$324$	−0.950252	+	1.64589i	−0.0527918	+	0.0914381i
$325$	−19.5017	+	11.2593i	−1.08176	+	0.624555i
$326$	−18.4108	−	31.8884i	−1.01968	−	1.76613i
$327$	−8.80435	+	15.2496i	−0.486882	+	0.843304i
$328$		−	1.01452i		−	0.0560173i
$329$	22.2291	+	0.793914i	1.22553	+	0.0437699i
$330$	−2.01241			−0.110779
$331$	−0.956566	+	1.65682i	−0.0525776	+	0.0910671i	−0.891116	−	0.453775i	$-0.850077\pi$
$331$	−0.956566	+	1.65682i	−0.0525776	+	0.0910671i	0.838539	+	0.544842i	$0.183410\pi$
$332$	6.51763	+	11.2889i	0.357701	+	0.619557i
$333$	−4.13587	+	2.38785i	−0.226644	+	0.130853i
$334$	24.3348	+	14.0497i	1.33154	+	0.768767i
$335$		−	2.72641i		−	0.148960i
$336$	5.19553	+	9.79009i	0.283439	+	0.534093i
$337$		−	5.38333i		−	0.293248i	−0.989192	−	0.146624i	$-0.953159\pi$
$337$		−	5.38333i		−	0.293248i	0.989192	−	0.146624i	$-0.0468408\pi$
$338$	9.84892	−	17.0588i	0.535711	−	0.927878i
$339$	7.38482	+	12.7909i	0.401088	+	0.694705i
$340$	2.12167	+	3.67485i	0.115064	+	0.199297i
$341$	0.487527	−	0.844421i	0.0264010	−	0.0457279i
$342$	−14.9953			−0.810853
$343$	−1.97972	+	18.4141i	−0.106895	+	0.994270i
$344$		−	1.12117i		−	0.0604492i
$345$	1.07214	+	2.40690i	0.0577221	+	0.129583i
$346$	−2.92460	+	1.68852i	−0.157228	+	0.0907754i
$347$	13.3694	+	23.1565i	0.717707	+	1.24311i	0.961906	+	0.273380i	$0.0881417\pi$
$347$	13.3694	+	23.1565i	0.717707	+	1.24311i	−0.244199	+	0.969725i	$0.578525\pi$
$348$	1.02957	+	0.594420i	0.0551905	+	0.0318643i
$349$			14.3883i			0.770189i	0.922877	+	0.385095i	$0.125831\pi$
$349$			14.3883i			0.770189i	−0.922877	+	0.385095i	$0.874169\pi$
$350$	21.6847	−	11.5079i	1.15910	−	0.615124i
$351$	4.79309			0.255836
$352$	−12.6570	−	7.30755i	−0.674623	−	0.389493i
$353$	20.4992	−	11.8352i	1.09106	−	0.629924i	0.157202	−	0.987567i	$-0.449753\pi$
$353$	20.4992	−	11.8352i	1.09106	−	0.629924i	0.933858	+	0.357643i	$0.116419\pi$
$354$	10.7837	+	18.6779i	0.573146	+	0.992718i
$355$	−2.61889	+	4.53606i	−0.138996	+	0.240749i
$356$	14.7737			0.783004
$357$	10.7452	+	0.383765i	0.568695	+	0.0203110i
$358$	23.1980			1.22605
$359$	−14.7992	−	8.54431i	−0.781071	−	0.450951i	0.0557389	−	0.998445i	$-0.482249\pi$
$359$	−14.7992	−	8.54431i	−0.781071	−	0.450951i	−0.836810	+	0.547494i	$0.815582\pi$
$360$	0.0539800	+	0.0934961i	0.00284500	+	0.00492768i
$361$	−19.3244	−	33.4708i	−1.01707	−	1.76162i
$362$	−12.0319	+	20.8399i	−0.632383	+	1.09532i
$363$			7.56035i			0.396815i
$364$	−12.7878	+	20.4286i	−0.670261	+	1.07075i
$365$			0.246111i			0.0128821i
$366$	23.8242	+	13.7549i	1.24531	+	0.718981i
$367$	−2.62399	−	4.54488i	−0.136971	−	0.237241i	0.789378	−	0.613908i	$-0.210403\pi$
$367$	−2.62399	−	4.54488i	−0.136971	−	0.237241i	−0.926349	+	0.376667i	$0.877070\pi$
$368$	−2.09639	+	19.9805i	−0.109282	+	1.04156i
$369$	4.47121	+	2.58145i	0.232762	+	0.134385i
$370$		−	5.18197i		−	0.269398i
$371$	−5.32152	+	8.50119i	−0.276279	+	0.441360i
$372$	0.999171			0.0518046
$373$	22.1467	+	12.7864i	1.14672	+	0.662056i	0.948085	−	0.318018i	$-0.103017\pi$
$373$	22.1467	+	12.7864i	1.14672	+	0.662056i	0.198630	+	0.980074i	$0.436351\pi$
$374$	−12.8911	+	7.44267i	−0.666582	+	0.384852i
$375$	4.61443	−	2.66414i	0.238288	−	0.137576i
$376$	1.43069	+	0.826009i	0.0737821	+	0.0425981i
$377$		−	2.99827i		−	0.154419i
$378$	−5.22195	−	0.186502i	−0.268588	−	0.00959264i
$379$			4.80637i			0.246887i	0.992352	+	0.123443i	$0.0393937\pi$
$379$			4.80637i			0.246887i	−0.992352	+	0.123443i	$0.960606\pi$
$380$	3.96399	−	6.86583i	0.203348	−	0.352210i
$381$	8.39131	−	4.84473i	0.429900	−	0.248203i
$382$	−46.5355	+	26.8673i	−2.38096	+	1.37465i
$383$	−12.4261	+	21.5226i	−0.634942	+	1.09975i	0.351586	+	0.936156i	$0.385642\pi$
$383$	−12.4261	+	21.5226i	−0.634942	+	1.09975i	−0.986528	+	0.163595i	$0.947691\pi$
$384$			1.57006i			0.0801219i
$385$	−1.26376	−	2.38135i	−0.0644073	−	0.121365i
$386$	2.73535			0.139225
$387$	4.94124	+	2.85283i	0.251177	+	0.145017i
$388$	−5.41082	−	9.37182i	−0.274693	−	0.475782i
$389$	−7.86835	+	4.54280i	−0.398941	+	0.230329i	−0.686027	−	0.727576i	$-0.740647\pi$
$389$	−7.86835	+	4.54280i	−0.398941	+	0.230329i	0.287086	+	0.957905i	$0.407314\pi$
$390$	−2.60043	+	4.50407i	−0.131678	+	0.228073i
$391$	15.7696	+	11.4529i	0.797501	+	0.579199i
$392$	−0.770982	+	1.13912i	−0.0389405	+	0.0575345i
$393$	10.0311			0.506001
$394$	20.7012	−	35.8555i	1.04291	−	1.80637i
$395$	8.18469	−	4.72543i	0.411816	−	0.237762i
$396$	3.05251	−	1.76237i	0.153394	−	0.0885622i
$397$	−7.76251	−	4.48169i	−0.389589	−	0.224930i	0.292393	−	0.956298i	$-0.405549\pi$
$397$	−7.76251	−	4.48169i	−0.389589	−	0.224930i	−0.681982	+	0.731369i	$0.738882\pi$
$398$	23.2315			1.16449
$399$	−9.41683	−	17.7444i	−0.471431	−	0.888332i
$400$	19.6810			0.984048
$401$	−8.52567	−	4.92230i	−0.425752	−	0.245808i	0.271784	−	0.962358i	$-0.412387\pi$
$401$	−8.52567	−	4.92230i	−0.425752	−	0.245808i	−0.697535	+	0.716551i	$0.745720\pi$
$402$	4.90031	+	8.48758i	0.244405	+	0.423322i
$403$	−1.25996	−	2.18232i	−0.0627631	−	0.108709i
$404$	−23.0094	−	13.2845i	−1.14476	−	0.660927i
$405$	−0.549412			−0.0273005
$406$	−0.116665	+	3.26653i	−0.00578996	+	0.162115i
$407$	8.85714			0.439032
$408$	0.691571	+	0.399278i	0.0342378	+	0.0197672i
$409$	25.8377	−	14.9174i	1.27759	−	0.737617i	0.301186	−	0.953566i	$-0.402618\pi$
$409$	25.8377	−	14.9174i	1.27759	−	0.737617i	0.976405	+	0.215948i	$0.0692843\pi$
$410$	−4.85159	+	2.80107i	−0.239603	+	0.138335i
$411$	2.69616	−	4.66989i	0.132992	−	0.230349i
$412$	28.1315			1.38594
$413$	−15.3301	+	24.4901i	−0.754347	+	1.20508i
$414$	−7.66371	−	5.56590i	−0.376651	−	0.273549i
$415$	−1.88417	+	3.26347i	−0.0924900	+	0.160197i
$416$	−32.7108	+	18.8856i	−1.60378	+	0.925941i
$417$	1.08651	+	1.88189i	0.0532065	+	0.0921564i
$418$	24.0848	+	13.9054i	1.17803	+	0.680134i
$419$	−9.37803			−0.458147			−0.229073	−	0.973409i	$-0.573570\pi$
$419$	−9.37803			−0.458147			−0.229073	+	0.973409i	$0.573570\pi$
$420$	1.46581	−	2.34165i	0.0715241	−	0.114261i
$421$		−	15.9242i		−	0.776096i	−0.921639	−	0.388048i	$-0.873150\pi$
$421$		−	15.9242i		−	0.776096i	0.921639	−	0.388048i	$-0.126850\pi$
$422$	13.1936	−	22.8519i	0.642253	−	1.11241i
$423$	−7.28083	+	4.20359i	−0.354006	+	0.204385i
$424$	−0.645091	+	0.372443i	−0.0313284	+	0.0180875i
$425$	9.54636	−	16.5348i	0.463067	−	0.802055i
$426$		−	18.8282i		−	0.912232i
$427$	−1.31538	+	36.8298i	−0.0636557	+	1.78232i
$428$		−	7.76903i		−	0.375530i
$429$	−7.69846	−	4.44471i	−0.371685	−	0.214593i
$430$	−5.36161	+	3.09553i	−0.258560	+	0.149279i
$431$	3.29079	−	1.89994i	0.158512	−	0.0915167i	−0.418646	−	0.908150i	$-0.637495\pi$
$431$	3.29079	−	1.89994i	0.158512	−	0.0915167i	0.577158	+	0.816633i	$0.304162\pi$
$432$	−3.62786	−	2.09455i	−0.174545	−	0.100774i
$433$	5.04845			0.242613			0.121307	−	0.992615i	$-0.461292\pi$
$433$	5.04845			0.242613			0.121307	+	0.992615i	$0.461292\pi$
$434$	1.28778	+	2.42660i	0.0618153	+	0.116481i
$435$			0.343679i			0.0164782i
$436$	28.9819	+	16.7327i	1.38798	+	0.801351i
$437$	3.79968	−	36.2144i	0.181763	−	1.73237i
$438$	−0.442348	−	0.766168i	−0.0211362	−	0.0366089i
$439$	−13.2765	−	7.66518i	−0.633652	−	0.365839i	0.148513	−	0.988910i	$-0.452551\pi$
$439$	−13.2765	−	7.66518i	−0.633652	−	0.365839i	−0.782165	+	0.623072i	$0.785885\pi$
$440$		−	0.200226i		−	0.00954540i
$441$	−3.05861	−	6.29642i	−0.145648	−	0.299829i
$442$			38.4696i			1.82981i
$443$	−19.1635	+	33.1921i	−0.910485	+	1.57701i	−0.0971040	+	0.995274i	$0.530958\pi$
$443$	−19.1635	+	33.1921i	−0.910485	+	1.57701i	−0.813381	+	0.581732i	$0.802375\pi$
$444$	4.53811	+	7.86024i	0.215369	+	0.373031i
$445$	2.13545	+	3.69870i	0.101230	+	0.175335i
$446$	−16.9438	−	9.78252i	−0.802314	−	0.463216i
$447$	11.1359			0.526710
$448$	16.7922	−	8.91148i	0.793356	−	0.421028i
$449$	9.06679			0.427888			0.213944	−	0.976846i	$-0.431369\pi$
$449$	9.06679			0.427888			0.213944	+	0.976846i	$0.431369\pi$
$450$	−4.63935	+	8.03559i	−0.218701	+	0.378801i
$451$	−4.78764	−	8.29244i	−0.225441	−	0.390476i
$452$	24.3091	−	14.0349i	1.14341	−	0.660145i
$453$	−7.78069	−	4.49218i	−0.365569	−	0.211061i
$454$	−40.9388			−1.92135
$455$	−6.96284	−	0.248678i	−0.326423	−	0.0116582i
$456$		−	1.49197i		−	0.0698678i
$457$	12.9074	+	7.45211i	0.603784	+	0.348595i	0.770529	−	0.637405i	$-0.219992\pi$
$457$	12.9074	+	7.45211i	0.603784	+	0.348595i	−0.166745	+	0.986000i	$0.553326\pi$
$458$	25.1966	+	43.6417i	1.17736	+	2.03924i
$459$	−3.51943	+	2.03194i	−0.164273	+	0.0948429i
$460$	4.57432	−	2.03761i	0.213279	−	0.0950039i
$461$		−	27.7253i		−	1.29130i	−0.763634	−	0.645649i	$-0.776587\pi$
$461$		−	27.7253i		−	1.29130i	0.763634	−	0.645649i	$-0.223413\pi$
$462$	8.21432	+	5.14194i	0.382165	+	0.239225i
$463$	6.33260			0.294301			0.147150	−	0.989114i	$-0.452990\pi$
$463$	6.33260			0.294301			0.147150	+	0.989114i	$0.452990\pi$
$464$	−1.31022	+	2.26937i	−0.0608255	+	0.105353i
$465$	0.144424	+	0.250150i	0.00669750	+	0.0116004i
$466$	2.63764	+	4.56852i	0.122186	+	0.211633i
$467$	6.13845	−	10.6321i	0.284054	−	0.491995i	−0.688326	−	0.725402i	$-0.741654\pi$
$467$	6.13845	−	10.6321i	0.284054	−	0.491995i	0.972379	+	0.233407i	$0.0749873\pi$
$468$		−	9.10929i		−	0.421077i
$469$	−6.96631	+	11.1288i	−0.321674	+	0.513879i
$470$		−	9.12240i		−	0.420785i
$471$	−11.2282	−	6.48261i	−0.517368	−	0.298703i
$472$	−1.85837	+	1.07293i	−0.0855383	+	0.0493856i
$473$	−5.29094	−	9.16418i	−0.243278	−	0.421369i
$474$	−16.9865	+	29.4214i	−0.780215	+	1.35137i
$475$	−35.6715			−1.63672
$476$	0.729347	−	20.4213i	0.0334295	−	0.936007i
$477$		−	3.79076i		−	0.173567i
$478$	4.81098	−	8.33286i	0.220049	−	0.381136i
$479$	−18.6749	−	32.3459i	−0.853279	−	1.47792i	−0.878232	−	0.478235i	$-0.841277\pi$
$479$	−18.6749	−	32.3459i	−0.853279	−	1.47792i	0.0249527	−	0.999689i	$-0.492056\pi$
$480$	3.74950	−	2.16477i	0.171140	−	0.0988080i
$481$	11.4452	−	19.8236i	0.521855	−	0.903879i
$482$	−32.5589			−1.48302
$483$	1.77361	−	12.5640i	0.0807020	−	0.571682i
$484$	14.3685			0.653112
$485$	1.56420	−	2.70928i	0.0710268	−	0.123022i
$486$	1.71037	−	0.987485i	0.0775841	−	0.0447932i
$487$	13.1104	+	22.7080i	0.594091	+	1.02900i	0.993674	+	0.112299i	$0.0358214\pi$
$487$	13.1104	+	22.7080i	0.594091	+	1.02900i	−0.399584	+	0.916697i	$0.630845\pi$
$488$	−1.36855	+	2.37041i	−0.0619516	+	0.107303i
$489$			18.6441i			0.843115i
$490$	7.57616	+	0.541857i	0.342256	+	0.0244786i
$491$	−28.9901			−1.30830			−0.654152	−	0.756363i	$-0.726974\pi$
$491$	−28.9901			−1.30830			−0.654152	+	0.756363i	$0.726974\pi$
$492$	4.90606	−	8.49755i	0.221182	−	0.383099i
$493$	1.27106	+	2.20154i	0.0572457	+	0.0991524i
$494$	62.2446	−	35.9369i	2.80052	−	1.61688i
$495$	0.882443	+	0.509478i	0.0396628	+	0.0228994i
$496$			2.20237i			0.0988895i
$497$	22.2801	−	11.8239i	0.999398	−	0.530373i
$498$		−	13.5460i		−	0.607011i
$499$	6.07262	−	10.5181i	0.271848	−	0.470854i	−0.697487	−	0.716597i	$-0.745699\pi$
$499$	6.07262	−	10.5181i	0.271848	−	0.470854i	0.969335	+	0.245743i	$0.0790319\pi$
$500$	−5.06321	−	8.76974i	−0.226434	−	0.392195i
$501$	−7.11389	−	12.3216i	−0.317825	−	0.550490i
$502$	−8.17214	+	14.1546i	−0.364741	+	0.631749i
$503$	−25.1221			−1.12014			−0.560068	−	0.828446i	$-0.689225\pi$
$503$	−25.1221			−1.12014			−0.560068	+	0.828446i	$0.689225\pi$
$504$	0.0185562	−	0.519561i	0.000826557	−	0.0231431i
$505$		−	7.68076i		−	0.341789i
$506$	7.14777	+	16.0464i	0.317757	+	0.713348i
$507$	−8.63752	+	4.98687i	−0.383606	+	0.221475i
$508$	−9.20743	−	15.9477i	−0.408513	−	0.707566i
$509$	24.1602	+	13.9489i	1.07088	+	0.618275i	0.928423	−	0.371526i	$-0.121165\pi$
$509$	24.1602	+	13.9489i	1.07088	+	0.618275i	0.142461	+	0.989800i	$0.454499\pi$
$510$		−	4.40961i		−	0.195261i
$511$	0.628844	−	1.00459i	0.0278184	−	0.0444403i
$512$	31.3651			1.38615
$513$	6.57545	+	3.79634i	0.290313	+	0.167612i
$514$	3.04771	−	1.75960i	0.134429	−	0.0776125i
$515$	4.06623	+	7.04291i	0.179179	+	0.310348i
$516$	5.42181	−	9.39085i	0.238682	−	0.413409i
$517$	15.5922			0.685744
$518$	−13.2406	+	21.1520i	−0.581757	+	0.929364i
$519$	1.70992			0.0750572
$520$	−0.448136	−	0.258731i	−0.0196521	−	0.0113461i
$521$	19.1310	+	33.1359i	0.838144	+	1.45171i	0.891445	+	0.453130i	$0.149693\pi$
$521$	19.1310	+	33.1359i	0.838144	+	1.45171i	−0.0533004	+	0.998579i	$0.516974\pi$
$522$	−0.617711	−	1.06991i	−0.0270365	−	0.0468285i
$523$	−5.48359	+	9.49786i	−0.239781	+	0.415312i	−0.960651	−	0.277757i	$-0.910409\pi$
$523$	−5.48359	+	9.49786i	−0.239781	+	0.415312i	0.720871	+	0.693070i	$0.243742\pi$
$524$		−	19.0641i		−	0.832820i
$525$	−12.4222	−	0.443660i	−0.542150	−	0.0193629i
$526$		−	10.9660i		−	0.478140i
$527$	1.85030	+	1.06827i	0.0806005	+	0.0465347i
$528$	3.88461	+	6.72834i	0.169056	+	0.292813i
$529$	15.3838	−	17.0979i	0.668862	−	0.743386i
$530$	3.56218	+	2.05662i	0.154731	+	0.0893340i
$531$		−	10.9204i		−	0.473903i
$532$	−33.7234	+	17.8967i	−1.46209	+	0.775921i
$533$	−24.7463			−1.07188
$534$	−13.2957	−	7.67627i	−0.575361	−	0.332185i
$535$	1.94503	−	1.12297i	0.0840911	−	0.0485500i
$536$	−0.844477	+	0.487559i	−0.0364759	+	0.0210594i
$537$	−10.1723	−	5.87300i	−0.438968	−	0.253439i
$538$		−	50.3680i		−	2.17152i
$539$	−0.926154	+	12.9493i	−0.0398923	+	0.557767i
$540$			1.04416i			0.0449335i
$541$	−8.53068	+	14.7756i	−0.366763	+	0.635252i	−0.989057	−	0.147531i	$-0.952867\pi$
$541$	−8.53068	+	14.7756i	−0.366763	+	0.635252i	0.622295	+	0.782783i	$0.286201\pi$
$542$	−14.2494	+	8.22689i	−0.612064	+	0.353375i
$543$	10.5520	−	6.09220i	0.452829	−	0.261441i
$544$	16.0124	−	27.7342i	0.686525	−	1.18910i
$545$			9.67444i			0.414407i
$546$	22.1230	−	11.7405i	0.946775	−	0.502446i
$547$	−37.0745			−1.58519			−0.792596	−	0.609747i	$-0.791271\pi$
$547$	−37.0745			−1.58519			−0.792596	+	0.609747i	$0.791271\pi$
$548$	−8.87514	−	5.12406i	−0.379127	−	0.218889i
$549$	−6.96462	−	12.0631i	−0.297243	−	0.514840i
$550$	14.9030	−	8.60427i	0.635468	−	0.366887i
$551$	2.37476	−	4.11320i	0.101168	−	0.175228i
$552$	0.553783	−	0.762506i	0.0235705	−	0.0324544i
$553$	−45.4826	−	1.62441i	−1.93412	−	0.0690771i
$554$	24.0248			1.02072
$555$	−1.31191	+	2.27230i	−0.0556876	+	0.0964537i
$556$	3.57654	−	2.06491i	0.151679	−	0.0875719i
$557$	−31.4372	+	18.1503i	−1.33204	+	0.769052i	−0.985612	−	0.169025i	$-0.945938\pi$
$557$	−31.4372	+	18.1503i	−1.33204	+	0.769052i	−0.346426	+	0.938077i	$0.612605\pi$
$558$	−0.899212	−	0.519160i	−0.0380667	−	0.0219778i
$559$	−27.3477			−1.15669
$560$	5.16146	+	3.23093i	0.218111	+	0.136532i
$561$	7.53700			0.318212
$562$	−5.38624	−	3.10975i	−0.227205	−	0.131177i
$563$	2.26992	+	3.93162i	0.0956657	+	0.165698i	0.909886	−	0.414858i	$-0.136169\pi$
$563$	2.26992	+	3.93162i	0.0956657	+	0.165698i	−0.814221	+	0.580556i	$0.802835\pi$
$564$	7.98893	+	13.8372i	0.336395	+	0.582653i
$565$	7.02747	+	4.05731i	0.295648	+	0.170692i
$566$	24.0869			1.01245
$567$	2.24261	+	1.40381i	0.0941808	+	0.0589547i
$568$	1.87333			0.0786031
$569$	24.4352	+	14.1077i	1.02438	+	0.591425i	0.915369	−	0.402616i	$-0.131899\pi$
$569$	24.4352	+	14.1077i	1.02438	+	0.591425i	0.109009	+	0.994041i	$0.465232\pi$
$570$	−7.13484	+	4.11930i	−0.298846	+	0.172539i
$571$	−25.1813	+	14.5384i	−1.05381	+	0.608415i	−0.923712	−	0.383087i	$-0.874861\pi$
$571$	−25.1813	+	14.5384i	−1.05381	+	0.608415i	−0.130093	+	0.991502i	$0.541528\pi$
$572$	−8.44719	+	14.6310i	−0.353195	+	0.611751i
$573$	27.2078			1.13662
$574$	26.9604	+	0.962894i	1.12531	+	0.0401904i
$575$	−18.2308	−	13.2404i	−0.760276	−	0.552163i
$576$	−3.59261	+	6.22258i	−0.149692	+	0.259274i
$577$	31.7048	−	18.3048i	1.31989	−	0.762037i	0.336177	−	0.941799i	$-0.390866\pi$
$577$	31.7048	−	18.3048i	1.31989	−	0.762037i	0.983710	+	0.179761i	$0.0575325\pi$
$578$	0.478775	+	0.829263i	0.0199144	+	0.0344928i
$579$	−1.19945	−	0.692504i	−0.0498475	−	0.0287795i
$580$	0.653164			0.0271211
$581$	16.0294	−	8.50668i	0.665012	−	0.352917i
$582$			11.2457i			0.466147i
$583$	−3.51522	+	6.08855i	−0.145586	+	0.252162i
$584$	0.0762304	−	0.0440117i	0.00315444	−	0.00182122i
$585$	2.28058	−	1.31669i	0.0942903	−	0.0544385i
$586$	19.8688	−	34.4138i	0.820773	−	1.42162i
$587$		−	5.69033i		−	0.234865i	−0.993081	−	0.117432i	$-0.962534\pi$
$587$		−	5.69033i		−	0.234865i	0.993081	−	0.117432i	$-0.0374664\pi$
$588$	−11.9664	+	5.81291i	−0.493485	+	0.239720i
$589$		−	3.99177i		−	0.164478i
$590$	10.2619	+	5.92469i	0.422474	+	0.243916i
$591$	−18.1550	+	10.4818i	−0.746795	+	0.431162i
$592$	−17.3255	+	10.0029i	−0.712075	+	0.411117i
$593$	23.1887	+	13.3880i	0.952244	+	0.549778i	0.893777	−	0.448511i	$-0.148045\pi$
$593$	23.1887	+	13.3880i	0.952244	+	0.549778i	0.0584669	+	0.998289i	$0.481379\pi$
$594$	−3.66284			−0.150288
$595$	5.21803	−	2.76917i	0.213918	−	0.113525i
$596$		−	21.1638i		−	0.866903i
$597$	−10.1870	−	5.88147i	−0.416927	−	0.240713i
$598$	45.1505	+	4.73727i	1.84634	+	0.193722i
$599$	−1.42676	−	2.47121i	−0.0582956	−	0.100971i	0.835405	−	0.549635i	$-0.185233\pi$
$599$	−1.42676	−	2.47121i	−0.0582956	−	0.100971i	−0.893700	+	0.448664i	$0.851900\pi$
$600$	−0.799506	−	0.461595i	−0.0326397	−	0.0188445i
$601$		−	37.0473i		−	1.51119i	−0.655038	−	0.755596i	$-0.727347\pi$
$601$		−	37.0473i		−	1.51119i	0.655038	−	0.755596i	$-0.272653\pi$
$602$	29.7946	+	1.06412i	1.21434	+	0.0433702i
$603$		−	4.96241i		−	0.202085i
$604$	−8.53741	+	14.7872i	−0.347382	+	0.601684i
$605$	2.07687	+	3.59725i	0.0844370	+	0.146249i
$606$	13.8050	+	23.9109i	0.560789	+	0.971315i
$607$	−26.8903	−	15.5251i	−1.09144	−	0.630145i	−0.157482	−	0.987522i	$-0.550338\pi$
$607$	−26.8903	−	15.5251i	−1.09144	−	0.630145i	−0.933960	+	0.357377i	$0.883671\pi$
$608$	−59.8328			−2.42654
$609$	0.878141	−	1.40284i	0.0355841	−	0.0568460i
$610$	15.1142			0.611958
$611$	20.1482	−	34.8977i	0.815108	−	1.41181i
$612$	3.86172	+	6.68869i	0.156101	+	0.270374i
$613$	8.42860	−	4.86625i	0.340428	−	0.196546i	−0.320033	−	0.947406i	$-0.603694\pi$
$613$	8.42860	−	4.86625i	0.340428	−	0.196546i	0.660461	+	0.750860i	$0.270361\pi$
$614$	−8.19647	−	4.73223i	−0.330783	−	0.190977i
$615$	2.83657			0.114381
$616$	−0.511601	+	0.817289i	−0.0206130	+	0.0329295i
$617$		−	4.92512i		−	0.198278i	−0.995074	−	0.0991388i	$-0.968391\pi$
$617$		−	4.92512i		−	0.198278i	0.995074	−	0.0991388i	$-0.0316088\pi$
$618$	−25.3171	−	14.6168i	−1.01840	−	0.587976i
$619$	−13.3087	−	23.0514i	−0.534922	−	0.926512i	−0.999167	−	0.0408055i	$-0.987008\pi$
$619$	−13.3087	−	23.0514i	−0.534922	−	0.926512i	0.464245	−	0.885707i	$-0.346326\pi$
$620$	0.475411	−	0.274478i	0.0190930	−	0.0110233i
$621$	1.95143	+	4.38086i	0.0783082	+	0.175798i
$622$		−	22.7729i		−	0.913111i
$623$	0.734080	−	20.5538i	0.0294103	−	0.823471i
$624$	20.0787			0.803792
$625$	−10.2817	+	17.8083i	−0.411266	+	0.712334i
$626$	7.61777	+	13.1944i	0.304467	+	0.527353i
$627$	−7.04080	−	12.1950i	−0.281183	−	0.487023i
$628$	−12.3202	+	21.3393i	−0.491630	+	0.851529i
$629$			19.4079i			0.773842i
$630$	−2.53586	+	1.34576i	−0.101031	+	0.0536165i
$631$			26.0289i			1.03620i	0.855321	+	0.518098i	$0.173360\pi$
$631$			26.0289i			1.03620i	−0.855321	+	0.518098i	$0.826640\pi$
$632$	−2.92731	−	1.69008i	−0.116442	−	0.0672278i
$633$	−11.5708	+	6.68039i	−0.459897	+	0.265522i
$634$	−14.0790	−	24.3856i	−0.559149	−	0.968475i
$635$	2.66175	−	4.61029i	0.105628	−	0.182954i
$636$	−7.20435			−0.285671
$637$	27.7858	+	18.8060i	1.10091	+	0.745119i
$638$			2.29125i			0.0907114i
$639$	−4.76672	+	8.25620i	−0.188568	+	0.326610i
$640$	0.431306	+	0.747044i	0.0170489	+	0.0295295i
$641$	−10.7634	+	6.21424i	−0.425128	+	0.245448i	−0.697269	−	0.716810i	$-0.745602\pi$
$641$	−10.7634	+	6.21424i	−0.425128	+	0.245448i	0.272141	+	0.962257i	$0.412268\pi$
$642$	−4.03672	+	6.99180i	−0.159316	+	0.275944i
$643$	30.4303			1.20006			0.600028	−	0.799979i	$-0.295156\pi$
$643$	30.4303			1.20006			0.600028	+	0.799979i	$0.295156\pi$
$644$	−23.8780	−	3.37075i	−0.940923	−	0.132826i
$645$	3.13476			0.123431
$646$	−30.4696	+	52.7749i	−1.19881	+	2.07640i
$647$	−8.52489	+	4.92185i	−0.335148	+	0.193498i	−0.658124	−	0.752909i	$-0.728650\pi$
$647$	−8.52489	+	4.92185i	−0.335148	+	0.193498i	0.322976	+	0.946407i	$0.395317\pi$
$648$	0.0982504	+	0.170175i	0.00385964	+	0.00668510i
$649$	−10.1266	+	17.5398i	−0.397504	+	0.688497i
$650$		−	44.4737i		−	1.74440i
$651$	0.0496472	−	1.39009i	0.00194583	−	0.0544820i
$652$	35.4332			1.38767
$653$	−22.7148	+	39.3431i	−0.888898	+	1.53962i	−0.0477175	+	0.998861i	$0.515195\pi$
$653$	−22.7148	+	39.3431i	−0.888898	+	1.53962i	−0.841180	+	0.540755i	$0.818139\pi$
$654$	−17.3883	−	30.1175i	−0.679937	−	1.17769i
$655$	4.77284	−	2.75560i	0.186490	−	0.107670i
$656$	18.7303	+	10.8139i	0.731296	+	0.422214i
$657$			0.447954i			0.0174763i
$658$	−23.3088	+	37.2361i	−0.908672	+	1.45162i
$659$			21.8404i			0.850780i	0.905010	+	0.425390i	$0.139863\pi$
$659$			21.8404i			0.850780i	−0.905010	+	0.425390i	$0.860137\pi$
$660$	0.968266	−	1.67709i	0.0376897	−	0.0652805i
$661$	−10.4776	−	18.1477i	−0.407530	−	0.705862i	0.587082	−	0.809527i	$-0.300276\pi$
$661$	−10.4776	−	18.1477i	−0.407530	−	0.705862i	−0.994612	+	0.103665i	$0.966943\pi$
$662$	−1.88919	−	3.27217i	−0.0734254	−	0.127177i
$663$	9.73929	−	16.8689i	0.378243	−	0.655135i
$664$	1.34777			0.0523035
$665$	−9.35508	−	5.85603i	−0.362774	−	0.227087i
$666$		−	9.43185i		−	0.365477i
$667$	2.74040	−	1.22070i	0.106109	−	0.0472656i
$668$	−23.4173	+	13.5200i	−0.906043	+	0.523104i
$669$	4.95325	+	8.57929i	0.191504	+	0.331694i
$670$	4.66318	+	2.69229i	0.180154	+	0.104012i
$671$			25.8336i			0.997295i
$672$	−20.8361	−	0.744163i	−0.803770	−	0.0287067i
$673$	16.5558			0.638179			0.319090	−	0.947725i	$-0.396623\pi$
$673$	16.5558			0.638179			0.319090	+	0.947725i	$0.396623\pi$
$674$	9.20750	+	5.31595i	0.354660	+	0.204763i
$675$	4.06871	−	2.34907i	0.156605	−	0.0904159i
$676$	9.47757	+	16.4156i	0.364522	+	0.631371i
$677$	−2.74144	+	4.74832i	−0.105362	+	0.182493i	−0.913886	−	0.405971i	$-0.866934\pi$
$677$	−2.74144	+	4.74832i	−0.105362	+	0.182493i	0.808524	+	0.588463i	$0.200267\pi$
$678$	−29.1696			−1.12025
$679$	−13.3073	+	7.06210i	−0.510689	+	0.271019i
$680$	0.438737			0.0168248
$681$	17.9517	+	10.3644i	0.687910	+	0.397165i
$682$	0.962850	+	1.66771i	0.0368694	+	0.0638597i
$683$	9.63701	+	16.6918i	0.368750	+	0.638694i	0.989370	−	0.145417i	$-0.0464525\pi$
$683$	9.63701	+	16.6918i	0.368750	+	0.638694i	−0.620620	+	0.784111i	$0.713119\pi$
$684$	7.21496	−	12.4967i	0.275871	−	0.477822i
$685$		−	2.96261i		−	0.113195i
$686$	−29.5401	−	21.5698i	−1.12785	−	0.823537i
$687$		−	25.5159i		−	0.973493i
$688$	20.6993	+	11.9508i	0.789154	+	0.455618i
$689$	9.08472	+	15.7352i	0.346100	+	0.599463i
$690$	−5.17542	−	0.543014i	−0.197025	−	0.0206722i
$691$	23.4635	+	13.5467i	0.892593	+	0.515339i	0.874790	−	0.484503i	$-0.160999\pi$
$691$	23.4635	+	13.5467i	0.892593	+	0.515339i	0.0178034	+	0.999842i	$0.494333\pi$
$692$		−	3.24971i		−	0.123535i
$693$	−2.30021	−	4.33435i	−0.0873777	−	0.164648i
$694$	−52.8083			−2.00458
$695$	1.03393	+	0.596941i	0.0392193	+	0.0226433i
$696$	0.106451	−	0.0614595i	0.00403502	−	0.00232962i
$697$	18.1705	−	10.4907i	0.688256	−	0.397365i
$698$	−24.6094	−	14.2082i	−0.931480	−	0.537790i
$699$		−	2.67107i		−	0.101029i
$700$	−0.843178	+	23.6085i	−0.0318691	+	0.892316i
$701$			29.2256i			1.10384i	0.833899	+	0.551918i	$0.186104\pi$
$701$			29.2256i			1.10384i	−0.833899	+	0.551918i	$0.813896\pi$
$702$	−4.73311	+	8.19798i	−0.178640	+	0.309413i
$703$	31.4023	−	18.1301i	1.18436	−	0.683791i
$704$	11.5406	−	6.66296i	0.434952	−	0.251120i
$705$	−2.30950	+	4.00018i	−0.0869809	+	0.150655i
$706$			46.7483i			1.75940i
$707$	−19.6252	+	31.3516i	−0.738083	+	1.17910i
$708$	−20.7542			−0.779990
$709$	3.93216	+	2.27023i	0.147675	+	0.0852604i	0.572017	−	0.820242i	$-0.306161\pi$
$709$	3.93216	+	2.27023i	0.147675	+	0.0852604i	−0.424342	+	0.905502i	$0.639494\pi$
$710$	−5.17224	−	8.95858i	−0.194111	−	0.336209i
$711$	14.8972	−	8.60088i	0.558687	−	0.322558i
$712$	0.763756	−	1.32286i	0.0286230	−	0.0495764i
$713$	1.48165	−	2.04009i	0.0554882	−	0.0764020i
$714$	−11.2671	+	17.9993i	−0.421660	+	0.673607i
$715$	−4.88396			−0.182650
$716$	−11.1617	+	19.3326i	−0.417131	+	0.722492i
$717$	−4.21924	+	2.43598i	−0.157570	+	0.0909732i
$718$	29.2279	−	16.8747i	1.09078	−	0.629760i
$719$	0.559250	+	0.322883i	0.0208565	+	0.0120415i	0.510392	−	0.859942i	$-0.329500\pi$
$719$	0.559250	+	0.322883i	0.0208565	+	0.0120415i	−0.489536	+	0.871983i	$0.662834\pi$
$720$	−2.30154			−0.0857733
$721$	1.39781	−	39.1377i	0.0520570	−	1.45756i
$722$	76.3301			2.84071
$723$	14.2771	+	8.24289i	0.530971	+	0.306556i
$724$	−11.5782	−	20.0541i	−0.430302	−	0.745305i
$725$	−1.46944	−	2.54514i	−0.0545736	−	0.0945242i
$726$	−12.9310	−	7.46573i	−0.479915	−	0.277079i
$727$	−19.3355			−0.717112			−0.358556	−	0.933508i	$-0.616731\pi$
$727$	−19.3355			−0.717112			−0.358556	+	0.933508i	$0.616731\pi$
$728$	1.16813	+	2.20114i	0.0432937	+	0.0815796i
$729$	−1.00000			−0.0370370
$730$	−0.420942	−	0.243031i	−0.0155798	−	0.00899499i
$731$	20.0806	−	11.5936i	0.742709	−	0.428803i
$732$	−22.9259	+	13.2363i	−0.847367	+	0.489228i
$733$	1.26377	−	2.18891i	0.0466783	−	0.0808492i	−0.841742	−	0.539880i	$-0.818470\pi$
$733$	1.26377	−	2.18891i	0.0466783	−	0.0808492i	0.888421	+	0.459030i	$0.151803\pi$
$734$	10.3646			0.382564
$735$	−3.18497	−	2.15565i	−0.117479	−	0.0795123i
$736$	−30.5790	−	22.2085i	−1.12716	−	0.818616i
$737$	−4.60172	+	7.97041i	−0.169507	+	0.293594i
$738$	−8.83050	+	5.09829i	−0.325055	+	0.187671i
$739$	11.6108	+	20.1105i	0.427111	+	0.739777i	0.996615	−	0.0822112i	$-0.0261982\pi$
$739$	11.6108	+	20.1105i	0.427111	+	0.739777i	−0.569504	+	0.821988i	$0.692865\pi$
$740$	4.31851	+	2.49330i	0.158752	+	0.0916554i
$741$	−36.3924			−1.33691
$742$	−9.28530	−	17.4966i	−0.340874	−	0.642320i
$743$			10.2312i			0.375347i	0.982231	+	0.187674i	$0.0600947\pi$
$743$			10.2312i			0.375347i	−0.982231	+	0.187674i	$0.939905\pi$
$744$	0.0516542	−	0.0894677i	0.00189373	−	0.00328004i
$745$	5.29851	−	3.05910i	0.194123	−	0.112077i
$746$	−43.7391	+	25.2528i	−1.60140	+	0.924571i
$747$	−3.42942	+	5.93993i	−0.125476	+	0.217331i
$748$		−	14.3241i		−	0.523741i
$749$	−10.8086	−	0.386030i	−0.394938	−	0.0141052i
$750$			10.5232i			0.384253i
$751$	2.82406	+	1.63047i	0.103051	+	0.0594967i	0.550640	−	0.834743i	$-0.314384\pi$
$751$	2.82406	+	1.63047i	0.103051	+	0.0594967i	−0.447589	+	0.894240i	$0.647717\pi$
$752$	−30.5000	+	17.6092i	−1.11222	+	0.642142i
$753$	7.16698	−	4.13786i	0.261179	−	0.150792i
$754$	5.12816	+	2.96075i	0.186757	+	0.107824i
$755$	−4.93612			−0.179644
$756$	2.66795	−	4.26209i	0.0970326	−	0.155011i
$757$		−	30.6098i		−	1.11253i	−0.831004	−	0.556266i	$-0.812234\pi$
$757$		−	30.6098i		−	1.11253i	0.831004	−	0.556266i	$-0.187766\pi$
$758$	−8.22069	−	4.74622i	−0.298589	−	0.172390i
$759$	0.928132	−	8.84594i	0.0336890	−	0.321087i
$760$	−0.409853	−	0.709886i	−0.0148669	−	0.0257503i
$761$	41.2750	+	23.8301i	1.49622	+	0.863841i	0.999991	−	0.00435261i	$-0.00138548\pi$
$761$	41.2750	+	23.8301i	1.49622	+	0.863841i	0.496226	+	0.868194i	$0.334719\pi$
$762$			19.1364i			0.693238i
$763$	24.7193	−	39.4895i	0.894900	−	1.42961i
$764$		−	51.7086i		−	1.87075i
$765$	−1.11637	+	1.93362i	−0.0403626	+	0.0699101i
$766$	−24.5411	−	42.5064i	−0.886705	−	1.53582i
$767$	26.1711	+	45.3297i	0.944985	+	1.63676i
$768$	−15.1306	−	8.73563i	−0.545977	−	0.315220i
$769$	−8.01477			−0.289020			−0.144510	−	0.989503i	$-0.546161\pi$
$769$	−8.01477			−0.289020			−0.144510	+	0.989503i	$0.546161\pi$
$770$	5.32094	+	0.190038i	0.191753	+	0.00684849i
$771$	−1.78190			−0.0641735
$772$	−1.31611	+	2.27956i	−0.0473677	+	0.0820432i
$773$	−8.07480	−	13.9860i	−0.290430	−	0.503040i	0.683481	−	0.729968i	$-0.260465\pi$
$773$	−8.07480	−	13.9860i	−0.290430	−	0.503040i	−0.

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987485 + 1.71037i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.950252 - 1.64589i) q^{4} +(0.274706 - 0.475805i) q^{5} +1.97497i q^{6} +(-2.33704 + 1.24025i) q^{7} -0.196501 q^{8} +(0.500000 - 0.866025i) q^{9} +(0.542536 + 0.939701i) q^{10} +(-1.60616 + 0.927315i) q^{11} +(-1.64589 - 0.950252i) q^{12} +4.79309i q^{13} +(0.186502 - 5.22195i) q^{14} -0.549412i q^{15} +(2.09455 - 3.62786i) q^{16} +(-2.03194 - 3.51943i) q^{17} +(0.987485 + 1.71037i) q^{18} +(-3.79634 + 6.57545i) q^{19} -1.04416 q^{20} +(-1.40381 + 2.24261i) q^{21} -3.66284i q^{22} +(-4.38086 + 1.95143i) q^{23} +(-0.170175 + 0.0982504i) q^{24} +(2.34907 + 4.06871i) q^{25} +(-8.19798 - 4.73311i) q^{26} -1.00000i q^{27} +(4.26209 + 2.66795i) q^{28} -0.625539 q^{29} +(0.939701 + 0.542536i) q^{30} +(-0.455304 + 0.262870i) q^{31} +(3.94016 + 6.82456i) q^{32} +(-0.927315 + 1.60616i) q^{33} +8.02605 q^{34} +(-0.0518827 + 1.45268i) q^{35} -1.90050 q^{36} +(-4.13587 - 2.38785i) q^{37} +(-7.49765 - 12.9863i) q^{38} +(2.39655 + 4.15094i) q^{39} +(-0.0539800 + 0.0934961i) q^{40} +5.16291i q^{41} +(-2.44946 - 4.61559i) q^{42} +5.70566i q^{43} +(3.05251 + 1.76237i) q^{44} +(-0.274706 - 0.475805i) q^{45} +(0.988354 - 9.41991i) q^{46} +(-7.28083 - 4.20359i) q^{47} -4.18909i q^{48} +(3.92355 - 5.79705i) q^{49} -9.27869 q^{50} +(-3.51943 - 2.03194i) q^{51} +(7.88888 - 4.55465i) q^{52} +(3.28289 - 1.89538i) q^{53} +(1.71037 + 0.987485i) q^{54} +1.01896i q^{55} +(0.459231 - 0.243711i) q^{56} +7.59268i q^{57} +(0.617711 - 1.06991i) q^{58} +(9.45730 - 5.46018i) q^{59} +(-0.904270 + 0.522080i) q^{60} +(6.96462 - 12.0631i) q^{61} -1.03832i q^{62} +(-0.0944330 + 2.64407i) q^{63} -7.18522 q^{64} +(2.28058 + 1.31669i) q^{65} +(-1.83142 - 3.17211i) q^{66} +(4.29758 - 2.48121i) q^{67} +(-3.86172 + 6.68869i) q^{68} +(-2.81822 + 3.88042i) q^{69} +(-2.43340 - 1.52324i) q^{70} -9.53344 q^{71} +(-0.0982504 + 0.170175i) q^{72} +(-0.387939 + 0.223977i) q^{73} +(8.16822 - 4.71592i) q^{74} +(4.06871 + 2.34907i) q^{75} +14.4299 q^{76} +(2.60356 - 4.15921i) q^{77} -9.46621 q^{78} +(14.8972 + 8.60088i) q^{79} +(-1.15077 - 1.99319i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-8.83050 - 5.09829i) q^{82} -6.85884 q^{83} +(5.02506 + 0.179470i) q^{84} -2.23275 q^{85} +(-9.75880 - 5.63425i) q^{86} +(-0.541733 + 0.312770i) q^{87} +(0.315611 - 0.182218i) q^{88} +(-3.88678 + 6.73210i) q^{89} +1.08507 q^{90} +(-5.94464 - 11.2017i) q^{91} +(7.37475 + 5.35604i) q^{92} +(-0.262870 + 0.455304i) q^{93} +(14.3794 - 8.30196i) q^{94} +(2.08576 + 3.61263i) q^{95} +(6.82456 + 3.94016i) q^{96} +5.69409 q^{97} +(6.04066 + 12.4352i) q^{98} +1.85463i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{2} - 36 q^{4} - 24 q^{8} + 32 q^{9} - 44 q^{16} - 4 q^{18} - 16 q^{23} - 12 q^{25} + 84 q^{26} + 24 q^{29} - 12 q^{31} + 8 q^{32} + 32 q^{35} - 72 q^{36} - 8 q^{46} - 12 q^{47} + 8 q^{49} - 96 q^{50}+ \cdots + 112 q^{98}+O(q^{100}) \) 64 * q + 4 * q^2 - 36 * q^4 - 24 * q^8 + 32 * q^9 - 44 * q^16 - 4 * q^18 - 16 * q^23 - 12 * q^25 + 84 * q^26 + 24 * q^29 - 12 * q^31 + 8 * q^32 + 32 * q^35 - 72 * q^36 - 8 * q^46 - 12 * q^47 + 8 * q^49 - 96 * q^50 - 108 * q^52 - 24 * q^58 + 36 * q^59 + 168 * q^64 - 40 * q^70 - 16 * q^71 - 12 * q^72 + 48 * q^73 - 48 * q^75 - 32 * q^78 - 32 * q^81 - 24 * q^82 + 88 * q^85 + 36 * q^87 + 152 * q^92 + 24 * q^93 - 108 * q^94 - 44 * q^95 + 60 * q^96 + 112 * q^98

Introduction

L-functions

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