LMFDB - Embedded newform 810.3.j.g.539.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	810.j (of order $6$, degree $2$, not 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:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.1
Character	$\chi$	$=$	810.539
Dual form			810.3.j.g.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.43710 - 2.30480i) q^{5} +(6.62225 - 3.82336i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.43710 - 2.30480i) q^{5} +(6.62225 - 3.82336i) q^{7} +2.82843 q^{8} +(-5.96030 - 3.80458i) q^{10} +(-9.85044 + 5.68716i) q^{11} +(-12.4560 - 7.19146i) q^{13} +(-9.36528 - 5.40705i) q^{14} +(-2.00000 - 3.46410i) q^{16} -17.3175 q^{17} -31.8326 q^{19} +(-0.445064 + 9.99009i) q^{20} +(13.9306 + 8.04285i) q^{22} +(-8.25743 + 14.3023i) q^{23} +(14.3758 - 20.4533i) q^{25} +20.3405i q^{26} +15.2934i q^{28} +(7.35437 - 4.24605i) q^{29} +(22.9096 - 39.6806i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(12.2453 + 21.2096i) q^{34} +(20.5715 - 32.2276i) q^{35} -31.8348i q^{37} +(22.5090 + 38.9868i) q^{38} +(12.5500 - 6.51897i) q^{40} +(-59.2167 - 34.1888i) q^{41} +(27.1780 - 15.6912i) q^{43} -22.7486i q^{44} +23.3555 q^{46} +(23.0276 + 39.8849i) q^{47} +(4.73615 - 8.20325i) q^{49} +(-35.2153 - 3.14396i) q^{50} +(24.9120 - 14.3829i) q^{52} -53.6946 q^{53} +(-30.5996 + 47.9378i) q^{55} +(18.7306 - 10.8141i) q^{56} +(-10.4006 - 6.00482i) q^{58} +(-56.0926 - 32.3851i) q^{59} +(48.1377 + 83.3769i) q^{61} -64.7981 q^{62} +8.00000 q^{64} +(-71.8434 - 3.20066i) q^{65} +(1.49343 + 0.862231i) q^{67} +(17.3175 - 29.9948i) q^{68} +(-54.0169 - 2.40648i) q^{70} +26.5730i q^{71} -51.4318i q^{73} +(-38.9895 + 22.5106i) q^{74} +(31.8326 - 55.1356i) q^{76} +(-43.4881 + 75.3236i) q^{77} +(-29.6088 - 51.2839i) q^{79} +(-16.8583 - 10.7610i) q^{80} +96.7004i q^{82} +(-3.46413 - 6.00004i) q^{83} +(-76.8396 + 39.9135i) q^{85} +(-38.4355 - 22.1908i) q^{86} +(-27.8613 + 16.0857i) q^{88} -115.787i q^{89} -109.982 q^{91} +(-16.5149 - 28.6046i) q^{92} +(32.5659 - 56.4058i) q^{94} +(-141.244 + 73.3678i) q^{95} +(137.398 - 79.3269i) q^{97} -13.3959 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) $ 24 * q - 24 * q^4 - 24 * q^7	$ 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) $ 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	4.43710	−	2.30480i	0.887420	−	0.460961i
$5$	4.43710	−	2.30480i	0.887420	−	0.460961i
$6$		0			0
$7$	6.62225	−	3.82336i	0.946036	−	0.546194i	0.0541887	−	0.998531i	$-0.482743\pi$
$7$	6.62225	−	3.82336i	0.946036	−	0.546194i	0.891847	+	0.452337i	$0.149409\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	−5.96030	−	3.80458i	−0.596030	−	0.380458i
$11$	−9.85044	+	5.68716i	−0.895495	+	0.517014i	−0.875736	−	0.482791i	$-0.839623\pi$
$11$	−9.85044	+	5.68716i	−0.895495	+	0.517014i	−0.0197591	+	0.999805i	$0.506290\pi$
$12$		0			0
$13$	−12.4560	−	7.19146i	−0.958152	−	0.553190i	−0.0625485	−	0.998042i	$-0.519923\pi$
$13$	−12.4560	−	7.19146i	−0.958152	−	0.553190i	−0.895604	+	0.444852i	$0.853256\pi$
$14$	−9.36528	−	5.40705i	−0.668948	−	0.386218i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−17.3175			−1.01868			−0.509339	−	0.860566i	$-0.670110\pi$
$17$	−17.3175			−1.01868			−0.509339	+	0.860566i	$0.670110\pi$
$18$		0			0
$19$	−31.8326			−1.67540			−0.837699	−	0.546132i	$-0.816100\pi$
$19$	−31.8326			−1.67540			−0.837699	+	0.546132i	$0.816100\pi$
$20$	−0.445064	+	9.99009i	−0.0222532	+	0.499505i
$21$		0			0
$22$	13.9306	+	8.04285i	0.633211	+	0.365584i
$23$	−8.25743	+	14.3023i	−0.359019	+	0.621838i	−0.987797	−	0.155746i	$-0.950222\pi$
$23$	−8.25743	+	14.3023i	−0.359019	+	0.621838i	0.628779	+	0.777584i	$0.283555\pi$
$24$		0			0
$25$	14.3758	−	20.4533i	0.575030	−	0.818132i
$26$			20.3405i			0.782328i
$27$		0			0
$28$			15.2934i			0.546194i
$29$	7.35437	−	4.24605i	0.253599	−	0.146415i	−0.367812	−	0.929900i	$-0.619893\pi$
$29$	7.35437	−	4.24605i	0.253599	−	0.146415i	0.621411	+	0.783485i	$0.286560\pi$
$30$		0			0
$31$	22.9096	−	39.6806i	0.739019	−	1.28002i	−0.213918	−	0.976852i	$-0.568623\pi$
$31$	22.9096	−	39.6806i	0.739019	−	1.28002i	0.952937	−	0.303167i	$-0.0980441\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	12.2453	+	21.2096i	0.360157	+	0.623810i
$35$	20.5715	−	32.2276i	0.587758	−	0.920789i
$36$		0			0
$37$		−	31.8348i		−	0.860400i	−0.902734	−	0.430200i	$-0.858443\pi$
$37$		−	31.8348i		−	0.860400i	0.902734	−	0.430200i	$-0.141557\pi$
$38$	22.5090	+	38.9868i	0.592343	+	1.02597i
$39$		0			0
$40$	12.5500	−	6.51897i	0.313751	−	0.162974i
$41$	−59.2167	−	34.1888i	−1.44431	−	0.833872i	−0.446176	−	0.894945i	$-0.647214\pi$
$41$	−59.2167	−	34.1888i	−1.44431	−	0.833872i	−0.998133	+	0.0610732i	$0.980548\pi$
$42$		0			0
$43$	27.1780	−	15.6912i	0.632047	−	0.364913i	−0.149497	−	0.988762i	$-0.547766\pi$
$43$	27.1780	−	15.6912i	0.632047	−	0.364913i	0.781545	+	0.623849i	$0.214432\pi$
$44$		−	22.7486i		−	0.517014i
$45$		0			0
$46$	23.3555			0.507729
$47$	23.0276	+	39.8849i	0.489948	+	0.848616i	0.999933	−	0.0115679i	$-0.00368225\pi$
$47$	23.0276	+	39.8849i	0.489948	+	0.848616i	−0.509985	+	0.860184i	$0.670349\pi$
$48$		0			0
$49$	4.73615	−	8.20325i	0.0966561	−	0.167413i
$50$	−35.2153	−	3.14396i	−0.704305	−	0.0628792i
$51$		0			0
$52$	24.9120	−	14.3829i	0.479076	−	0.276595i
$53$	−53.6946			−1.01311			−0.506553	−	0.862209i	$-0.669080\pi$
$53$	−53.6946			−1.01311			−0.506553	+	0.862209i	$0.669080\pi$
$54$		0			0
$55$	−30.5996	+	47.9378i	−0.556357	+	0.871597i
$56$	18.7306	−	10.8141i	0.334474	−	0.193109i
$57$		0			0
$58$	−10.4006	−	6.00482i	−0.179322	−	0.103531i
$59$	−56.0926	−	32.3851i	−0.950722	−	0.548900i	−0.0574171	−	0.998350i	$-0.518286\pi$
$59$	−56.0926	−	32.3851i	−0.950722	−	0.548900i	−0.893305	+	0.449451i	$0.851620\pi$
$60$		0			0
$61$	48.1377	+	83.3769i	0.789142	+	1.36683i	0.926493	+	0.376312i	$0.122808\pi$
$61$	48.1377	+	83.3769i	0.789142	+	1.36683i	−0.137351	+	0.990522i	$0.543859\pi$
$62$	−64.7981			−1.04513
$63$		0			0
$64$	8.00000			0.125000
$65$	−71.8434	−	3.20066i	−1.10528	−	0.0492409i
$66$		0			0
$67$	1.49343	+	0.862231i	0.0222900	+	0.0128691i	0.511104	−	0.859519i	$-0.329237\pi$
$67$	1.49343	+	0.862231i	0.0222900	+	0.0128691i	−0.488814	+	0.872388i	$0.662570\pi$
$68$	17.3175	−	29.9948i	0.254669	−	0.441100i
$69$		0			0
$70$	−54.0169	−	2.40648i	−0.771670	−	0.0343783i
$71$			26.5730i			0.374268i	0.982334	+	0.187134i	$0.0599199\pi$
$71$			26.5730i			0.374268i	−0.982334	+	0.187134i	$0.940080\pi$
$72$		0			0
$73$		−	51.4318i		−	0.704545i	−0.935898	−	0.352272i	$-0.885409\pi$
$73$		−	51.4318i		−	0.704545i	0.935898	−	0.352272i	$-0.114591\pi$
$74$	−38.9895	+	22.5106i	−0.526885	+	0.304197i
$75$		0			0
$76$	31.8326	−	55.1356i	0.418850	−	0.725469i
$77$	−43.4881	+	75.3236i	−0.564780	+	0.978228i
$78$		0			0
$79$	−29.6088	−	51.2839i	−0.374795	−	0.649164i	0.615501	−	0.788136i	$-0.288954\pi$
$79$	−29.6088	−	51.2839i	−0.374795	−	0.649164i	−0.990296	+	0.138972i	$0.955620\pi$
$80$	−16.8583	−	10.7610i	−0.210729	−	0.134512i
$81$		0			0
$82$			96.7004i			1.17927i
$83$	−3.46413	−	6.00004i	−0.0417365	−	0.0722897i	0.844403	−	0.535709i	$-0.179956\pi$
$83$	−3.46413	−	6.00004i	−0.0417365	−	0.0722897i	−0.886139	+	0.463419i	$0.846622\pi$
$84$		0			0
$85$	−76.8396	+	39.9135i	−0.903996	+	0.469571i
$86$	−38.4355	−	22.1908i	−0.446925	−	0.258032i
$87$		0			0
$88$	−27.8613	+	16.0857i	−0.316605	+	0.182792i
$89$		−	115.787i		−	1.30097i	−0.759518	−	0.650486i	$-0.774565\pi$
$89$		−	115.787i		−	1.30097i	0.759518	−	0.650486i	$-0.225435\pi$
$90$		0			0
$91$	−109.982			−1.20860
$92$	−16.5149	−	28.6046i	−0.179509	−	0.310919i
$93$		0			0
$94$	32.5659	−	56.4058i	0.346446	−	0.600062i
$95$	−141.244	+	73.3678i	−1.48678	+	0.772293i
$96$		0			0
$97$	137.398	−	79.3269i	1.41648	−	0.817803i	0.420489	−	0.907298i	$-0.361858\pi$
$97$	137.398	−	79.3269i	1.41648	−	0.817803i	0.995987	+	0.0894944i	$0.0285251\pi$
$98$	−13.3959			−0.136692
$99$		0			0
$100$	21.0504	+	45.3528i	0.210504	+	0.453528i
$101$	−94.2918	+	54.4394i	−0.933583	+	0.539004i	−0.887943	−	0.459954i	$-0.847866\pi$
$101$	−94.2918	+	54.4394i	−0.933583	+	0.539004i	−0.0456398	+	0.998958i	$0.514533\pi$
$102$		0			0
$103$	−116.360	−	67.1803i	−1.12971	−	0.652236i	−0.185844	−	0.982579i	$-0.559502\pi$
$103$	−116.360	−	67.1803i	−1.12971	−	0.652236i	−0.943861	+	0.330344i	$0.892835\pi$
$104$	−35.2308	−	20.3405i	−0.338758	−	0.195582i
$105$		0			0
$106$	37.9678	+	65.7622i	0.358187	+	0.620398i
$107$	125.758			1.17531			0.587655	−	0.809111i	$-0.300051\pi$
$107$	125.758			1.17531			0.587655	+	0.809111i	$0.300051\pi$
$108$		0			0
$109$	−63.2406			−0.580189			−0.290094	−	0.956998i	$-0.593687\pi$
$109$	−63.2406			−0.580189			−0.290094	+	0.956998i	$0.593687\pi$
$110$	80.3488	+	3.57958i	0.730444	+	0.0325417i
$111$		0			0
$112$	−26.4890	−	15.2934i	−0.236509	−	0.136549i
$113$	−52.0087	+	90.0818i	−0.460254	+	0.797184i	−0.998973	−	0.0453015i	$-0.985575\pi$
$113$	−52.0087	+	90.0818i	−0.460254	+	0.797184i	0.538719	+	0.842486i	$0.318908\pi$
$114$		0			0
$115$	−3.67508	+	82.4925i	−0.0319573	+	0.717326i
$116$			16.9842i			0.146415i
$117$		0			0
$118$			91.5989i			0.776262i
$119$	−114.681	+	66.2111i	−0.963706	+	0.556396i
$120$		0			0
$121$	4.18750	−	7.25297i	0.0346075	−	0.0599419i
$122$	68.0770	−	117.913i	0.558008	−	0.966498i
$123$		0			0
$124$	45.8192	+	79.3612i	0.369510	+	0.640009i
$125$	16.6458	−	123.887i	0.133167	−	0.991094i
$126$		0			0
$127$		−	142.712i		−	1.12371i	−0.827235	−	0.561857i	$-0.810087\pi$
$127$		−	142.712i		−	1.12371i	0.827235	−	0.561857i	$-0.189913\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	46.8809	+	90.2530i	0.360623	+	0.694254i
$131$	178.736	+	103.193i	1.36440	+	0.787735i	0.990206	−	0.139616i	$-0.0445868\pi$
$131$	178.736	+	103.193i	1.36440	+	0.787735i	0.374192	+	0.927351i	$0.377920\pi$
$132$		0			0
$133$	−210.803	+	121.707i	−1.58499	+	0.915093i
$134$		−	2.43876i		−	0.0181997i
$135$		0			0
$136$	−48.9814			−0.360157
$137$	82.0604	+	142.133i	0.598981	+	1.03747i	0.992972	+	0.118351i	$0.0377609\pi$
$137$	82.0604	+	142.133i	0.598981	+	1.03747i	−0.393991	+	0.919114i	$0.628906\pi$
$138$		0			0
$139$	−15.2790	+	26.4640i	−0.109921	+	0.190389i	−0.915738	−	0.401776i	$-0.868393\pi$
$139$	−15.2790	+	26.4640i	−0.109921	+	0.190389i	0.805817	+	0.592165i	$0.201726\pi$
$140$	35.2484	+	67.8585i	0.251774	+	0.484704i
$141$		0			0
$142$	32.5452	−	18.7900i	0.229191	−	0.132324i
$143$	163.596			1.14403
$144$		0			0
$145$	22.8458	−	35.7905i	0.157557	−	0.246831i
$146$	−62.9908	+	36.3677i	−0.431444	+	0.249094i
$147$		0			0
$148$	55.1395	+	31.8348i	0.372564	+	0.215100i
$149$	67.4833	+	38.9615i	0.452908	+	0.261486i	0.709057	−	0.705151i	$-0.249121\pi$
$149$	67.4833	+	38.9615i	0.452908	+	0.261486i	−0.256150	+	0.966637i	$0.582454\pi$
$150$		0			0
$151$	−21.5215	−	37.2764i	−0.142527	−	0.246863i	0.785921	−	0.618327i	$-0.212189\pi$
$151$	−21.5215	−	37.2764i	−0.142527	−	0.246863i	−0.928447	+	0.371464i	$0.878856\pi$
$152$	−90.0361			−0.592343
$153$		0			0
$154$	123.003			0.798720
$155$	10.1962	−	228.869i	0.0657822	−	1.47657i
$156$		0			0
$157$	51.3798	+	29.6641i	0.327260	+	0.188943i	0.654624	−	0.755955i	$-0.272827\pi$
$157$	51.3798	+	29.6641i	0.327260	+	0.188943i	−0.327364	+	0.944898i	$0.606160\pi$
$158$	−41.8732	+	72.5264i	−0.265020	+	0.459028i
$159$		0			0
$160$	−1.25883	+	28.2562i	−0.00786769	+	0.176602i
$161$			126.284i			0.784375i
$162$		0			0
$163$			79.1245i			0.485426i	0.970098	+	0.242713i	$0.0780374\pi$
$163$			79.1245i			0.485426i	−0.970098	+	0.242713i	$0.921963\pi$
$164$	118.433	−	68.3775i	0.722154	−	0.416936i
$165$		0			0
$166$	−4.89901	+	8.48534i	−0.0295121	+	0.0511165i
$167$	50.7578	−	87.9151i	0.303939	−	0.526438i	−0.673085	−	0.739565i	$-0.735031\pi$
$167$	50.7578	−	87.9151i	0.303939	−	0.526438i	0.977025	+	0.213127i	$0.0683647\pi$
$168$		0			0
$169$	18.9343	+	32.7952i	0.112037	+	0.194054i
$170$	103.218	+	65.8858i	0.607163	+	0.387564i
$171$		0			0
$172$			62.7650i			0.364913i
$173$	−90.6749	−	157.054i	−0.524132	−	0.907824i	−0.999605	−	0.0280937i	$-0.991056\pi$
$173$	−90.6749	−	157.054i	−0.524132	−	0.907824i	0.475473	−	0.879730i	$-0.342277\pi$
$174$		0			0
$175$	16.9995	−	190.411i	0.0971402	−	1.08806i
$176$	39.4018	+	22.7486i	0.223874	+	0.129254i
$177$		0			0
$178$	−141.809	+	81.8734i	−0.796679	+	0.459963i
$179$			90.4200i			0.505140i	0.967579	+	0.252570i	$0.0812758\pi$
$179$			90.4200i			0.505140i	−0.967579	+	0.252570i	$0.918724\pi$
$180$		0			0
$181$	−160.779			−0.888283			−0.444141	−	0.895957i	$-0.646491\pi$
$181$	−160.779			−0.888283			−0.444141	+	0.895957i	$0.646491\pi$
$182$	77.7692	+	134.700i	0.427303	+	0.740111i
$183$		0			0
$184$	−23.3555	+	40.4530i	−0.126932	+	0.219853i
$185$	−73.3730	−	141.254i	−0.396611	−	0.763537i
$186$		0			0
$187$	170.585	−	98.4875i	0.912221	−	0.526671i
$188$	−92.1103			−0.489948
$189$		0			0
$190$	189.732	+	121.109i	0.998588	+	0.637418i
$191$	−147.629	+	85.2335i	−0.772925	+	0.446249i	−0.833917	−	0.551890i	$-0.813907\pi$
$191$	−147.629	+	85.2335i	−0.772925	+	0.446249i	0.0609920	+	0.998138i	$0.480574\pi$
$192$		0			0
$193$	−185.543	−	107.124i	−0.961365	−	0.555044i	−0.0647720	−	0.997900i	$-0.520632\pi$
$193$	−185.543	−	107.124i	−0.961365	−	0.555044i	−0.896593	+	0.442856i	$0.853965\pi$
$194$	−194.310	−	112.185i	−1.00160	−	0.578274i
$195$		0			0
$196$	9.47230	+	16.4065i	0.0483280	+	0.0837066i
$197$	−209.813			−1.06504			−0.532522	−	0.846416i	$-0.678755\pi$
$197$	−209.813			−1.06504			−0.532522	+	0.846416i	$0.678755\pi$
$198$		0			0
$199$	327.667			1.64657			0.823285	−	0.567628i	$-0.192139\pi$
$199$	327.667			1.64657			0.823285	+	0.567628i	$0.192139\pi$
$200$	40.6608	−	57.8507i	0.203304	−	0.289253i
$201$		0			0
$202$	133.349	+	76.9890i	0.660143	+	0.381134i
$203$	32.4683	−	56.2368i	0.159942	−	0.277029i
$204$		0			0
$205$	−341.549	−	15.2162i	−1.66609	−	0.0742253i
$206$			190.014i			0.922400i
$207$		0			0
$208$			57.5317i			0.276595i
$209$	313.565	−	181.037i	1.50031	−	0.866205i
$210$		0			0
$211$	−51.0064	+	88.3457i	−0.241737	+	0.418700i	−0.961209	−	0.275821i	$-0.911050\pi$
$211$	−51.0064	+	88.3457i	−0.241737	+	0.418700i	0.719472	+	0.694521i	$0.244384\pi$
$212$	53.6946	−	93.0018i	0.253276	−	0.438688i
$213$		0			0
$214$	−88.9245	−	154.022i	−0.415535	−	0.719728i
$215$	84.4265	−	132.264i	0.392681	−	0.615180i
$216$		0			0
$217$		−	350.366i		−	1.61459i
$218$	44.7178	+	77.4536i	0.205128	+	0.355292i
$219$		0			0
$220$	−52.4311	−	100.938i	−0.238323	−	0.458809i
$221$	215.707	+	124.538i	0.976049	+	0.563522i
$222$		0			0
$223$	326.928	−	188.752i	1.46604	−	0.846421i	0.466765	−	0.884381i	$-0.345419\pi$
$223$	326.928	−	188.752i	1.46604	−	0.846421i	0.999279	+	0.0379599i	$0.0120859\pi$
$224$			43.2564i			0.193109i
$225$		0			0
$226$	147.103			0.650898
$227$	−134.727	−	233.354i	−0.593512	−	1.02799i	−0.993755	−	0.111584i	$-0.964408\pi$
$227$	−134.727	−	233.354i	−0.593512	−	1.02799i	0.400243	−	0.916409i	$-0.368926\pi$
$228$		0			0
$229$	−211.931	+	367.075i	−0.925463	+	1.60295i	−0.134649	+	0.990893i	$0.542991\pi$
$229$	−211.931	+	367.075i	−0.925463	+	1.60295i	−0.790814	+	0.612056i	$0.790343\pi$
$230$	103.631	−	53.8299i	0.450569	−	0.234043i
$231$		0			0
$232$	20.8013	−	12.0096i	0.0896608	−	0.0517657i
$233$	70.8761			0.304189			0.152095	−	0.988366i	$-0.451398\pi$
$233$	70.8761			0.304189			0.152095	+	0.988366i	$0.451398\pi$
$234$		0			0
$235$	194.103	+	123.899i	0.825969	+	0.527232i
$236$	112.185	−	64.7702i	0.475361	−	0.274450i
$237$		0			0
$238$	162.183	+	93.6367i	0.681443	+	0.393431i
$239$	304.905	+	176.037i	1.27575	+	0.736555i	0.976064	−	0.217482i	$-0.0697844\pi$
$239$	304.905	+	176.037i	1.27575	+	0.736555i	0.299687	+	0.954038i	$0.403118\pi$
$240$		0			0
$241$	−43.7882	−	75.8434i	−0.181694	−	0.314703i	0.760764	−	0.649029i	$-0.224825\pi$
$241$	−43.7882	−	75.8434i	−0.181694	−	0.314703i	−0.942457	+	0.334326i	$0.891491\pi$
$242$	−11.8440			−0.0489423
$243$		0			0
$244$	−192.551			−0.789142
$245$	2.10789	−	47.3146i	0.00860363	−	0.193121i
$246$		0			0
$247$	396.506	+	228.923i	1.60529	+	0.926813i
$248$	64.7981	−	112.234i	0.261283	−	0.452555i
$249$		0			0
$250$	−163.500	+	67.2143i	−0.654000	+	0.268857i
$251$		−	2.67686i		−	0.0106648i	−0.999986	−	0.00533238i	$-0.998303\pi$
$251$		−	2.67686i		−	0.0106648i	0.999986	−	0.00533238i	$-0.00169736\pi$
$252$		0			0
$253$		−	187.845i		−	0.742471i
$254$	−174.785	+	100.912i	−0.688131	+	0.397293i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	195.326	−	338.315i	0.760025	−	1.31640i	−0.182812	−	0.983148i	$-0.558520\pi$
$257$	195.326	−	338.315i	0.760025	−	1.31640i	0.942837	−	0.333254i	$-0.108147\pi$
$258$		0			0
$259$	−121.716	−	210.818i	−0.469945	−	0.813969i
$260$	77.3871	−	121.236i	0.297643	−	0.466291i
$261$		0			0
$262$		−	291.875i		−	1.11403i
$263$	0.415571	+	0.719790i	0.00158012	+	0.00273684i	0.866814	−	0.498631i	$-0.166164\pi$
$263$	0.415571	+	0.719790i	0.00158012	+	0.00273684i	−0.865234	+	0.501368i	$0.832830\pi$
$264$		0			0
$265$	−238.248	+	123.756i	−0.899051	+	0.467002i
$266$	298.121	+	172.120i	1.12076	+	0.647068i
$267$		0			0
$268$	−2.98685	+	1.72446i	−0.0111450	+	0.00643456i
$269$			126.427i			0.469989i	0.971997	+	0.234994i	$0.0755072\pi$
$269$			126.427i			0.469989i	−0.971997	+	0.234994i	$0.924493\pi$
$270$		0			0
$271$	−359.481			−1.32650			−0.663249	−	0.748399i	$-0.730823\pi$
$271$	−359.481			−1.32650			−0.663249	+	0.748399i	$0.730823\pi$
$272$	34.6351	+	59.9897i	0.127335	+	0.220550i
$273$		0			0
$274$	116.051	−	201.006i	0.423544	−	0.733599i
$275$	−25.2864	+	283.231i	−0.0919506	+	1.02993i
$276$		0			0
$277$	367.858	−	212.383i	1.32801	−	0.766726i	0.343016	−	0.939329i	$-0.388551\pi$
$277$	367.858	−	212.383i	1.32801	−	0.766726i	0.984991	+	0.172604i	$0.0552181\pi$
$278$	43.2156			0.155452
$279$		0			0
$280$	58.1850	−	91.1535i	0.207804	−	0.325548i
$281$	322.655	−	186.285i	1.14824	−	0.662935i	0.199780	−	0.979841i	$-0.435977\pi$
$281$	322.655	−	186.285i	1.14824	−	0.662935i	0.948457	+	0.316906i	$0.102644\pi$
$282$		0			0
$283$	392.514	+	226.618i	1.38698	+	0.800771i	0.992973	−	0.118338i	$-0.0377565\pi$
$283$	392.514	+	226.618i	1.38698	+	0.800771i	0.394003	+	0.919109i	$0.371090\pi$
$284$	−46.0258	−	26.5730i	−0.162063	−	0.0935670i
$285$		0			0
$286$	−115.680	−	200.363i	−0.404475	−	0.700571i
$287$	−522.864			−1.82182
$288$		0			0
$289$	10.8967			0.0377048
$290$	−59.9887	−	2.67253i	−0.206857	−	0.00921561i
$291$		0			0
$292$	89.0824	+	51.4318i	0.305077	+	0.176136i
$293$	52.5694	−	91.0528i	0.179418	−	0.310760i	−0.762264	−	0.647267i	$-0.775912\pi$
$293$	52.5694	−	91.0528i	0.179418	−	0.310760i	0.941681	+	0.336506i	$0.109245\pi$
$294$		0			0
$295$	−323.530	−	14.4134i	−1.09671	−	0.0488591i
$296$		−	90.0424i		−	0.304197i
$297$		0			0
$298$		−	110.200i		−	0.369798i
$299$	205.709	−	118.766i	0.687989	−	0.397211i
$300$		0			0
$301$	119.987	−	207.823i	0.398626	−	0.690441i
$302$	−30.4360	+	52.7167i	−0.100782	+	0.174559i
$303$		0			0
$304$	63.6651	+	110.271i	0.209425	+	0.362734i
$305$	405.759	+	259.004i	1.33036	+	0.849193i
$306$		0			0
$307$		−	488.983i		−	1.59278i	−0.604785	−	0.796389i	$-0.706741\pi$
$307$		−	488.983i		−	1.59278i	0.604785	−	0.796389i	$-0.293259\pi$
$308$	−86.9762	−	150.647i	−0.282390	−	0.489114i
$309$		0			0
$310$	−287.516	+	149.347i	−0.927471	+	0.481764i
$311$	−50.1624	−	28.9613i	−0.161294	−	0.0931231i	0.417180	−	0.908824i	$-0.363018\pi$
$311$	−50.1624	−	28.9613i	−0.161294	−	0.0931231i	−0.578474	+	0.815701i	$0.696352\pi$
$312$		0			0
$313$	−395.028	+	228.069i	−1.26207	+	0.728656i	−0.973475	−	0.228795i	$-0.926521\pi$
$313$	−395.028	+	228.069i	−1.26207	+	0.728656i	−0.288595	+	0.957451i	$0.593188\pi$
$314$		−	83.9028i		−	0.267206i
$315$		0			0
$316$	118.435			0.374795
$317$	241.540	+	418.359i	0.761955	+	1.31975i	0.941841	+	0.336058i	$0.109094\pi$
$317$	241.540	+	418.359i	0.761955	+	1.31975i	−0.179886	+	0.983688i	$0.557573\pi$
$318$		0			0
$319$	−48.2959	+	83.6509i	−0.151398	+	0.262229i
$320$	35.4968	−	18.4384i	0.110928	−	0.0576201i
$321$		0			0
$322$	154.666	−	89.2966i	0.480330	−	0.277319i
$323$	551.261			1.70669
$324$		0			0
$325$	−326.153	+	151.383i	−1.00355	+	0.465795i
$326$	96.9073	−	55.9495i	0.297262	−	0.171624i
$327$		0			0
$328$	−167.490	−	96.7004i	−0.510640	−	0.294818i
$329$	304.989	+	176.085i	0.927018	+	0.535214i
$330$		0			0
$331$	42.7004	+	73.9592i	0.129004	+	0.223442i	0.923291	−	0.384101i	$-0.125489\pi$
$331$	42.7004	+	73.9592i	0.129004	+	0.223442i	−0.794287	+	0.607543i	$0.792155\pi$
$332$	13.8565			0.0417365
$333$		0			0
$334$	−143.565			−0.429835
$335$	8.61376	+	0.383748i	0.0257127	+	0.00114552i
$336$		0			0
$337$	−431.904	−	249.360i	−1.28162	−	0.739941i	−0.304472	−	0.952521i	$-0.598480\pi$
$337$	−431.904	−	249.360i	−1.28162	−	0.739941i	−0.977144	+	0.212580i	$0.931813\pi$
$338$	26.7772	−	46.3794i	0.0792224	−	0.137217i
$339$		0			0
$340$	7.70741	−	173.004i	0.0226688	−	0.508834i
$341$			521.162i			1.52833i
$342$		0			0
$343$			302.257i			0.881216i
$344$	76.8711	−	44.3815i	0.223462	−	0.129016i
$345$		0			0
$346$	−128.234	+	222.107i	−0.370618	+	0.641929i
$347$	247.035	−	427.877i	0.711917	−	1.23308i	−0.252220	−	0.967670i	$-0.581161\pi$
$347$	247.035	−	427.877i	0.711917	−	1.23308i	0.964137	−	0.265406i	$-0.0855061\pi$
$348$		0			0
$349$	−185.886	−	321.964i	−0.532624	−	0.922533i	−0.999274	−	0.0380905i	$-0.987872\pi$
$349$	−185.886	−	321.964i	−0.532624	−	0.922533i	0.466650	−	0.884442i	$-0.345461\pi$
$350$	−245.225	+	113.821i	−0.700643	+	0.325202i
$351$		0			0
$352$		−	64.3428i		−	0.182792i
$353$	−147.674	−	255.779i	−0.418340	−	0.724586i	0.577433	−	0.816438i	$-0.304054\pi$
$353$	−147.674	−	255.779i	−0.418340	−	0.724586i	−0.995773	+	0.0918526i	$0.970721\pi$
$354$		0			0
$355$	61.2456	+	117.907i	0.172523	+	0.332133i
$356$	200.548	+	115.787i	0.563337	+	0.325243i
$357$		0			0
$358$	110.741	−	63.9366i	0.309334	−	0.178594i
$359$		−	251.070i		−	0.699359i	−0.936869	−	0.349679i	$-0.886291\pi$
$359$		−	251.070i		−	0.699359i	0.936869	−	0.349679i	$-0.113709\pi$
$360$		0			0
$361$	652.312			1.80696
$362$	113.688	+	196.913i	0.314055	+	0.543960i
$363$		0			0
$364$	109.982	−	190.495i	0.302149	−	0.523337i
$365$	−118.540	−	228.208i	−0.324768	−	0.625227i
$366$		0			0
$367$	548.174	−	316.488i	1.49366	−	0.862366i	0.493687	−	0.869639i	$-0.335649\pi$
$367$	548.174	−	316.488i	1.49366	−	0.862366i	0.999974	+	0.00727397i	$0.00231540\pi$
$368$	66.0594			0.179509
$369$		0			0
$370$	−121.118	+	189.745i	−0.327346	+	0.512824i
$371$	−355.579	+	205.294i	−0.958434	+	0.553352i
$372$		0			0
$373$	158.508	+	91.5148i	0.424955	+	0.245348i	0.697195	−	0.716881i	$-0.254431\pi$
$373$	158.508	+	91.5148i	0.424955	+	0.245348i	−0.272240	+	0.962229i	$0.587764\pi$
$374$	−241.244	−	139.282i	−0.645038	−	0.372413i
$375$		0			0
$376$	65.1318	+	112.812i	0.173223	+	0.300031i
$377$	−122.141			−0.323982
$378$		0			0
$379$	274.778			0.725009			0.362504	−	0.931982i	$-0.381922\pi$
$379$	274.778			0.725009			0.362504	+	0.931982i	$0.381922\pi$
$380$	14.1675	−	318.010i	0.0372830	−	0.836869i
$381$		0			0
$382$	208.778	+	120.538i	0.546541	+	0.315545i
$383$	−187.093	+	324.054i	−0.488492	+	0.846093i	−0.999912	−	0.0132374i	$-0.995786\pi$
$383$	−187.093	+	324.054i	−0.488492	+	0.846093i	0.511420	+	0.859331i	$0.329120\pi$
$384$		0			0
$385$	−19.3550	+	434.450i	−0.0502727	+	1.12844i
$386$			302.991i			0.784951i
$387$		0			0
$388$			317.308i			0.817803i
$389$	−209.217	+	120.792i	−0.537833	+	0.310518i	−0.744200	−	0.667956i	$-0.767169\pi$
$389$	−209.217	+	120.792i	−0.537833	+	0.310518i	0.206367	+	0.978475i	$0.433836\pi$
$390$		0			0
$391$	142.998	−	247.680i	0.365724	−	0.633453i
$392$	13.3959	−	23.2023i	0.0341731	−	0.0591895i
$393$		0			0
$394$	148.361	+	256.968i	0.376550	+	0.652203i
$395$	−249.577	−	159.310i	−0.631840	−	0.403315i
$396$		0			0
$397$			267.415i			0.673590i	0.941578	+	0.336795i	$0.109343\pi$
$397$			267.415i			0.673590i	−0.941578	+	0.336795i	$0.890657\pi$
$398$	−231.696	−	401.309i	−0.582151	−	1.00831i
$399$		0			0
$400$	−99.6038	−	8.89246i	−0.249010	−	0.0222311i
$401$	−596.600	−	344.447i	−1.48778	−	0.858970i	−0.487877	−	0.872912i	$-0.662229\pi$
$401$	−596.600	−	344.447i	−1.48778	−	0.858970i	−0.999903	+	0.0139424i	$0.995562\pi$
$402$		0			0
$403$	−570.723	+	329.507i	−1.41619	+	0.817635i
$404$		−	217.758i		−	0.539004i
$405$		0			0
$406$	−91.8343			−0.226193
$407$	181.050	+	313.587i	0.444839	+	0.770484i
$408$		0			0
$409$	126.664	−	219.388i	0.309691	−	0.536400i	−0.668604	−	0.743619i	$-0.733108\pi$
$409$	126.664	−	219.388i	0.309691	−	0.536400i	0.978295	+	0.207219i	$0.0664411\pi$
$410$	222.876	+	429.070i	0.543599	+	1.04651i
$411$		0			0
$412$	232.719	−	134.361i	0.564853	−	0.326118i
$413$	−495.279			−1.19922
$414$		0			0
$415$	−29.1996	−	18.6387i	−0.0703605	−	0.0449125i
$416$	70.4617	−	40.6811i	0.169379	−	0.0977910i
$417$		0			0
$418$	−443.448	−	256.025i	−1.06088	−	0.612499i
$419$	446.533	+	257.806i	1.06571	+	0.615289i	0.927007	−	0.375045i	$-0.122373\pi$
$419$	446.533	+	257.806i	1.06571	+	0.615289i	0.138705	+	0.990334i	$0.455706\pi$
$420$		0			0
$421$	258.541	+	447.806i	0.614112	+	1.06367i	0.990540	+	0.137227i	$0.0438191\pi$
$421$	258.541	+	447.806i	0.614112	+	1.06367i	−0.376427	+	0.926446i	$0.622848\pi$
$422$	144.268			0.341867
$423$		0			0
$424$	−151.871			−0.358187
$425$	−248.952	+	354.201i	−0.585771	+	0.833413i
$426$		0			0
$427$	637.560	+	368.095i	1.49311	+	0.862050i
$428$	−125.758	+	217.820i	−0.293828	+	0.508924i
$429$		0			0
$430$	−221.688	−	9.87631i	−0.515553	−	0.0229682i
$431$		−	290.795i		−	0.674698i	−0.941380	−	0.337349i	$-0.890470\pi$
$431$		−	290.795i		−	0.674698i	0.941380	−	0.337349i	$-0.109530\pi$
$432$		0			0
$433$			358.909i			0.828889i	0.910075	+	0.414444i	$0.136024\pi$
$433$			358.909i			0.828889i	−0.910075	+	0.414444i	$0.863976\pi$
$434$	−429.109	+	247.746i	−0.988732	+	0.570844i
$435$		0			0
$436$	63.2406	−	109.536i	0.145047	−	0.251229i
$437$	262.855	−	455.278i	0.601499	−	1.04183i
$438$		0			0
$439$	101.819	+	176.355i	0.231933	+	0.401720i	0.958377	−	0.285506i	$-0.0921616\pi$
$439$	101.819	+	176.355i	0.231933	+	0.401720i	−0.726444	+	0.687226i	$0.758828\pi$
$440$	−86.5489	+	135.589i	−0.196702	+	0.308156i
$441$		0			0
$442$		−	352.248i		−	0.796940i
$443$	−10.6134	−	18.3829i	−0.0239580	−	0.0414965i	0.853798	−	0.520605i	$-0.174293\pi$
$443$	−10.6134	−	18.3829i	−0.0239580	−	0.0414965i	−0.877756	+	0.479108i	$0.840960\pi$
$444$		0			0
$445$	−266.865	−	513.757i	−0.599697	−	1.15451i
$446$	−462.346	−	266.936i	−1.03665	−	0.598510i
$447$		0			0
$448$	52.9780	−	30.5869i	0.118255	−	0.0682743i
$449$			650.346i			1.44843i	0.689573	+	0.724216i	$0.257798\pi$
$449$			650.346i			1.44843i	−0.689573	+	0.724216i	$0.742202\pi$
$450$		0			0
$451$	777.747			1.72450
$452$	−104.017	−	180.164i	−0.230127	−	0.398592i
$453$		0			0
$454$	−190.533	+	330.013i	−0.419676	+	0.726901i
$455$	−488.002	+	253.487i	−1.07253	+	0.557115i
$456$		0			0
$457$	134.210	−	77.4859i	0.293675	−	0.169553i	−0.345923	−	0.938263i	$-0.612434\pi$
$457$	134.210	−	77.4859i	0.293675	−	0.169553i	0.639598	+	0.768710i	$0.279101\pi$
$458$	599.432			1.30880
$459$		0			0
$460$	−139.206	−	88.8579i	−0.302622	−	0.193169i
$461$	304.828	−	175.992i	0.661232	−	0.381762i	−0.131514	−	0.991314i	$-0.541984\pi$
$461$	304.828	−	175.992i	0.661232	−	0.381762i	0.792746	+	0.609552i	$0.208651\pi$
$462$		0			0
$463$	−86.8675	−	50.1530i	−0.187619	−	0.108322i	0.403249	−	0.915091i	$-0.367881\pi$
$463$	−86.8675	−	50.1530i	−0.187619	−	0.108322i	−0.590867	+	0.806769i	$0.701214\pi$
$464$	−29.4175	−	16.9842i	−0.0633997	−	0.0366039i
$465$		0			0
$466$	−50.1170	−	86.8052i	−0.107547	−	0.186277i
$467$	31.5687			0.0675989			0.0337994	−	0.999429i	$-0.489239\pi$
$467$	31.5687			0.0675989			0.0337994	+	0.999429i	$0.489239\pi$
$468$		0			0
$469$	13.1865			0.0281161
$470$	14.4939	−	325.336i	0.0308381	−	0.692205i
$471$		0			0
$472$	−158.654	−	91.5989i	−0.336131	−	0.194065i
$473$	−178.477	+	309.131i	−0.377330	+	0.653555i
$474$		0			0
$475$	−457.617	+	651.081i	−0.963405	+	1.37070i
$476$		−	264.844i		−	0.556396i
$477$		0			0
$478$		−	497.907i		−	1.04165i
$479$	549.367	−	317.177i	1.14690	−	0.662166i	0.198774	−	0.980045i	$-0.436304\pi$
$479$	549.367	−	317.177i	1.14690	−	0.662166i	0.948131	+	0.317880i	$0.102971\pi$
$480$		0			0
$481$	−228.939	+	396.534i	−0.475964	+	0.824394i
$482$	−61.9259	+	107.259i	−0.128477	+	0.222529i
$483$		0			0
$484$	8.37500	+	14.5059i	0.0173037	+	0.0299709i
$485$	426.817	−	668.658i	0.880035	−	1.37868i
$486$		0			0
$487$			639.112i			1.31235i	0.754611	+	0.656173i	$0.227826\pi$
$487$			639.112i			1.31235i	−0.754611	+	0.656173i	$0.772174\pi$
$488$	136.154	+	235.825i	0.279004	+	0.483249i
$489$		0			0
$490$	−59.4388	+	30.8748i	−0.121304	+	0.0630098i
$491$	−318.584	−	183.934i	−0.648847	−	0.374612i	0.139167	−	0.990269i	$-0.455557\pi$
$491$	−318.584	−	183.934i	−0.648847	−	0.374612i	−0.788014	+	0.615657i	$0.788891\pi$
$492$		0			0
$493$	−127.359	+	73.5310i	−0.258336	+	0.149150i
$494$		−	647.491i		−	1.31071i
$495$		0			0
$496$	−183.277			−0.369510
$497$	101.598	+	175.973i	0.204423	+	0.354071i
$498$		0			0
$499$	247.272	−	428.287i	0.495534	−	0.858291i	−0.504452	−	0.863439i	$-0.668306\pi$
$499$	247.272	−	428.287i	0.495534	−	0.858291i	0.999987	+	0.00514892i	$0.00163896\pi$
$500$	197.932	+	152.718i	0.395865	+	0.305436i
$501$		0			0
$502$	−3.27847	+	1.89282i	−0.00653081	+	0.00377057i
$503$	−176.118			−0.350135			−0.175067	−	0.984556i	$-0.556014\pi$
$503$	−176.118			−0.350135			−0.175067	+	0.984556i	$0.556014\pi$
$504$		0			0
$505$	−292.910	+	458.878i	−0.580020	+	0.908668i
$506$	−230.062	+	132.827i	−0.454669	+	0.262503i
$507$		0			0
$508$	247.184	+	142.712i	0.486582	+	0.280928i
$509$	−540.931	−	312.307i	−1.06273	−	0.613569i	−0.136546	−	0.990634i	$-0.543600\pi$
$509$	−540.931	−	312.307i	−1.06273	−	0.613569i	−0.926187	+	0.377065i	$0.876933\pi$
$510$		0			0
$511$	−196.642	−	340.594i	−0.384818	−	0.666525i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−552.467			−1.07484
$515$	−671.137	−	29.8995i	−1.30318	−	0.0580573i
$516$		0			0
$517$	−453.664	−	261.923i	−0.877493	−	0.506621i
$518$	−172.132	+	298.142i	−0.332302	+	0.575563i
$519$		0			0
$520$	−203.204	−	9.05284i	−0.390776	−	0.0174093i
$521$		−	908.634i		−	1.74402i	−0.489489	−	0.872009i	$-0.662817\pi$
$521$		−	908.634i		−	1.74402i	0.489489	−	0.872009i	$-0.337183\pi$
$522$		0			0
$523$			534.875i			1.02271i	0.859371	+	0.511353i	$0.170855\pi$
$523$			534.875i			1.02271i	−0.859371	+	0.511353i	$0.829145\pi$
$524$	−357.472	+	206.387i	−0.682199	+	0.393868i
$525$		0			0
$526$	0.587706	−	1.01794i	0.00111731	−	0.00193524i
$527$	−396.737	+	687.169i	−0.752823	+	1.30393i
$528$		0			0
$529$	128.130	+	221.927i	0.242211	+	0.419522i
$530$	320.036	+	204.285i	0.603841	+	0.385444i
$531$		0			0
$532$		−	486.829i		−	0.915093i
$533$	491.734	+	851.709i	0.922579	+	1.59795i
$534$		0			0
$535$	558.002	−	289.848i	1.04299	−	0.541772i
$536$	4.22405	+	2.43876i	0.00788069	+	0.00454992i
$537$		0			0
$538$	154.841	−	89.3974i	0.287808	−	0.166166i
$539$			107.741i			0.199890i
$540$		0			0
$541$	−996.576			−1.84210			−0.921050	−	0.389444i	$-0.872667\pi$
$541$	−996.576			−1.84210			−0.921050	+	0.389444i	$0.872667\pi$
$542$	254.191	+	440.272i	0.468988	+	0.812311i
$543$		0			0
$544$	48.9814	−	84.8382i	0.0900393	−	0.155953i
$545$	−280.605	+	145.757i	−0.514871	+	0.267444i
$546$		0			0
$547$	547.715	−	316.223i	1.00131	−	0.578105i	0.0926721	−	0.995697i	$-0.470459\pi$
$547$	547.715	−	316.223i	1.00131	−	0.578105i	0.908635	+	0.417592i	$0.137126\pi$
$548$	−328.242			−0.598981
$549$		0			0
$550$	364.766	−	169.305i	0.663211	−	0.307828i
$551$	−234.108	+	135.163i	−0.424879	+	0.245304i
$552$		0			0
$553$	−392.154	−	226.410i	−0.709139	−	0.409421i
$554$	−520.230	−	300.355i	−0.939043	−	0.542157i
$555$		0			0
$556$	−30.5580	−	52.9281i	−0.0549605	−	0.0951943i
$557$	−673.973			−1.21001			−0.605003	−	0.796223i	$-0.706828\pi$
$557$	−673.973			−1.21001			−0.605003	+	0.796223i	$0.706828\pi$
$558$		0			0
$559$	−451.372			−0.807463
$560$	−152.783	−	6.80656i	−0.272826	−	0.0121546i
$561$		0			0
$562$	−456.302	−	263.446i	−0.811926	−	0.468766i
$563$	−168.242	+	291.403i	−0.298831	+	0.517590i	−0.975869	−	0.218358i	$-0.929930\pi$
$563$	−168.242	+	291.403i	−0.298831	+	0.517590i	0.677038	+	0.735948i	$0.263263\pi$
$564$		0			0
$565$	−23.1472	+	519.572i	−0.0409685	+	0.919597i
$566$		−	640.973i		−	1.13246i
$567$		0			0
$568$			75.1599i			0.132324i
$569$	−355.756	+	205.396i	−0.625230	+	0.360977i	−0.778902	−	0.627145i	$-0.784223\pi$
$569$	−355.756	+	205.396i	−0.625230	+	0.360977i	0.153672	+	0.988122i	$0.450890\pi$
$570$		0			0
$571$	222.398	−	385.204i	0.389488	−	0.674613i	−0.602893	−	0.797822i	$-0.705985\pi$
$571$	222.398	−	385.204i	0.389488	−	0.674613i	0.992381	+	0.123209i	$0.0393187\pi$
$572$	−163.596	+	283.356i	−0.286007	+	0.495378i
$573$		0			0
$574$	369.720	+	640.375i	0.644112	+	1.11564i
$575$	173.822	+	374.498i	0.302300	+	0.651301i
$576$		0			0
$577$		−	365.707i		−	0.633808i	−0.948458	−	0.316904i	$-0.897357\pi$
$577$		−	365.707i		−	0.633808i	0.948458	−	0.316904i	$-0.102643\pi$
$578$	−7.70512	−	13.3457i	−0.0133307	−	0.0230894i
$579$		0			0
$580$	39.1452	+	75.3606i	0.0674918	+	0.129932i
$581$	−45.8806	−	26.4892i	−0.0789684	−	0.0455924i
$582$		0			0
$583$	528.916	−	305.370i	0.907231	−	0.523790i
$584$		−	145.471i		−	0.249094i
$585$		0			0
$586$	−148.689			−0.253735
$587$	−193.997	−	336.012i	−0.330488	−	0.572422i	0.652120	−	0.758116i	$-0.273880\pi$
$587$	−193.997	−	336.012i	−0.330488	−	0.572422i	−0.982608	+	0.185694i	$0.940547\pi$
$588$		0			0
$589$	−729.271	+	1263.13i	−1.23815	+	2.14454i
$590$	211.117	+	406.434i	0.357826	+	0.688870i
$591$		0			0
$592$	−110.279	+	63.6696i	−0.186282	+	0.107550i
$593$	−657.706			−1.10912			−0.554558	−	0.832145i	$-0.687113\pi$
$593$	−657.706			−1.10912			−0.554558	+	0.832145i	$0.687113\pi$
$594$		0			0
$595$	−356.248	+	558.103i	−0.598736	+	0.937988i
$596$	−134.967	+	77.9229i	−0.226454	+	0.130743i
$597$		0			0
$598$	−290.916	−	167.960i	−0.486482	−	0.280870i
$599$	−462.748	−	267.167i	−0.772534	−	0.446022i	0.0612441	−	0.998123i	$-0.480493\pi$
$599$	−462.748	−	267.167i	−0.772534	−	0.446022i	−0.833778	+	0.552100i	$0.813827\pi$
$600$		0			0
$601$	450.266	+	779.884i	0.749195	+	1.29764i	0.948209	+	0.317647i	$0.102893\pi$
$601$	450.266	+	779.884i	0.749195	+	1.29764i	−0.199014	+	0.979997i	$0.563774\pi$
$602$	−339.373			−0.563743
$603$		0			0
$604$	86.0861			0.142527
$605$	1.86371	−	41.8335i	0.00308051	−	0.0691463i
$606$		0			0
$607$	753.720	+	435.161i	1.24171	+	0.716904i	0.969443	−	0.245317i	$-0.0788919\pi$
$607$	753.720	+	435.161i	1.24171	+	0.716904i	0.272271	+	0.962221i	$0.412225\pi$
$608$	90.0361	−	155.947i	0.148086	−	0.256492i
$609$		0			0
$610$	30.2986	−	680.095i	0.0496698	−	1.11491i
$611$		−	662.408i		−	1.08414i
$612$		0			0
$613$		−	252.101i		−	0.411258i	−0.978630	−	0.205629i	$-0.934076\pi$
$613$		−	252.101i		−	0.411258i	0.978630	−	0.205629i	$-0.0659240\pi$
$614$	−598.879	+	345.763i	−0.975374	+	0.563132i
$615$		0			0
$616$	−123.003	+	213.047i	−0.199680	+	0.345856i
$617$	362.468	−	627.813i	0.587468	−	1.01752i	−0.407094	−	0.913386i	$-0.633458\pi$
$617$	362.468	−	627.813i	0.587468	−	1.01752i	0.994563	−	0.104139i	$-0.0332086\pi$
$618$		0			0
$619$	−146.645	−	253.996i	−0.236906	−	0.410333i	0.722919	−	0.690933i	$-0.242800\pi$
$619$	−146.645	−	253.996i	−0.236906	−	0.410333i	−0.959825	+	0.280600i	$0.909467\pi$
$620$	386.216	+	246.529i	0.622930	+	0.397628i
$621$		0			0
$622$			81.9149i			0.131696i
$623$	−442.693	−	766.767i	−0.710583	−	1.23077i
$624$		0			0
$625$	−211.675	−	588.063i	−0.338681	−	0.940901i
$626$	558.654	+	322.539i	0.892418	+	0.515238i
$627$		0			0
$628$	−102.760	+	59.3282i	−0.163630	+	0.0944717i
$629$			551.300i			0.876471i
$630$		0			0
$631$	397.922			0.630622			0.315311	−	0.948988i	$-0.397891\pi$
$631$	397.922			0.630622			0.315311	+	0.948988i	$0.397891\pi$
$632$	−83.7463	−	145.053i	−0.132510	−	0.229514i
$633$		0			0
$634$	341.589	−	591.649i	0.538784	−	0.933201i
$635$	−328.922	−	633.226i	−0.517988	−	0.997206i
$636$		0			0
$637$	−117.987	+	68.1197i	−0.185223	+	0.106938i
$638$	136.601			0.214109
$639$		0			0
$640$	−47.6824	−	30.4366i	−0.0745038	−	0.0475572i
$641$	229.741	−	132.641i	0.358411	−	0.206928i	−0.309973	−	0.950745i	$-0.600320\pi$
$641$	229.741	−	132.641i	0.358411	−	0.206928i	0.668383	+	0.743817i	$0.266987\pi$
$642$		0			0
$643$	−217.451	−	125.546i	−0.338182	−	0.195250i	0.321286	−	0.946982i	$-0.395885\pi$
$643$	−217.451	−	125.546i	−0.338182	−	0.195250i	−0.659468	+	0.751733i	$0.729218\pi$
$644$	−218.731	−	126.284i	−0.339645	−	0.196094i
$645$		0			0
$646$	−389.801	−	675.154i	−0.603407	−	1.04513i
$647$	−415.167			−0.641680			−0.320840	−	0.947133i	$-0.603965\pi$
$647$	−415.167			−0.641680			−0.320840	+	0.947133i	$0.603965\pi$
$648$		0			0
$649$	736.716			1.13516
$650$	416.031	+	292.410i	0.640048	+	0.449862i
$651$		0			0
$652$	−137.048	−	79.1245i	−0.210196	−	0.121357i
$653$	423.639	−	733.765i	0.648758	−	1.12368i	−0.334661	−	0.942339i	$-0.608622\pi$
$653$	423.639	−	733.765i	0.648758	−	1.12368i	0.983420	−	0.181344i	$-0.0580448\pi$
$654$		0			0
$655$	1030.91	+	45.9276i	1.57391	+	0.0701185i
$656$			273.510i			0.416936i
$657$		0			0
$658$		−	498.045i		−	0.756907i
$659$	124.230	−	71.7242i	0.188513	−	0.108838i	−0.402773	−	0.915300i	$-0.631954\pi$
$659$	124.230	−	71.7242i	0.188513	−	0.108838i	0.591286	+	0.806462i	$0.298620\pi$
$660$		0			0
$661$	151.517	−	262.436i	0.229224	−	0.397028i	−0.728354	−	0.685201i	$-0.759714\pi$
$661$	151.517	−	262.436i	0.229224	−	0.397028i	0.957578	+	0.288173i	$0.0930477\pi$
$662$	60.3875	−	104.594i	0.0912197	−	0.157997i
$663$		0			0
$664$	−9.79803	−	16.9707i	−0.0147561	−	0.0255583i
$665$	−654.844	+	1025.89i	−0.984728	+	1.54269i
$666$		0			0
$667$			140.246i			0.210263i
$668$	101.516	+	175.830i	0.151970	+	0.263219i
$669$		0			0
$670$	−5.62086	−	10.8210i	−0.00838934	−	0.0161508i
$671$	−948.355	−	547.533i	−1.41335	−	0.815996i
$672$		0			0
$673$	−241.209	+	139.262i	−0.358408	+	0.206927i	−0.668382	−	0.743818i	$-0.733013\pi$
$673$	−241.209	+	139.262i	−0.358408	+	0.206927i	0.309974	+	0.950745i	$0.399680\pi$
$674$			705.297i			1.04643i
$675$		0			0
$676$	−75.7373			−0.112037
$677$	406.560	+	704.183i	0.600532	+	1.04015i	0.992740	+	0.120276i	$0.0383780\pi$
$677$	406.560	+	704.183i	0.600532	+	1.04015i	−0.392208	+	0.919877i	$0.628289\pi$
$678$		0			0
$679$	606.590	−	1050.65i	0.893359	−	1.54734i
$680$	−217.335	+	112.892i	−0.319611	+	0.166018i
$681$		0			0
$682$	638.290	−	368.517i	0.935909	−	0.540348i
$683$	1081.42			1.58334			0.791668	−	0.610952i	$-0.209213\pi$
$683$	1081.42			1.58334			0.791668	+	0.610952i	$0.209213\pi$
$684$		0			0
$685$	691.699	+	441.525i	1.00978	+	0.644561i
$686$	370.188	−	213.728i	0.539633	−	0.311557i
$687$		0			0
$688$	−108.712	−	62.7650i	−0.158012	−	0.0912282i
$689$	668.819	+	386.143i	0.970709	+	0.560439i
$690$		0			0
$691$	−529.864	−	917.751i	−0.766807	−	1.32815i	−0.939286	−	0.343135i	$-0.888511\pi$
$691$	−529.864	−	917.751i	−0.766807	−	1.32815i	0.172479	−	0.985013i	$-0.444822\pi$
$692$	362.700			0.524132
$693$		0			0
$694$	−698.721			−1.00680
$695$	−6.80014	+	152.639i	−0.00978437	+	0.219624i
$696$		0			0
$697$	1025.49	+	592.065i	1.47129	+	0.849447i
$698$	−262.882	+	455.326i	−0.376622	+	0.652329i
$699$		0			0
$700$	312.801	+	219.855i	0.446859	+	0.314078i
$701$		−	716.640i		−	1.02231i	−0.859488	−	0.511155i	$-0.829218\pi$
$701$		−	716.640i		−	1.02231i	0.859488	−	0.511155i	$-0.170782\pi$
$702$		0			0
$703$			1013.38i			1.44151i
$704$	−78.8036	+	45.4973i	−0.111937	+	0.0646268i
$705$		0			0
$706$	−208.842	+	361.726i	−0.295811	+	0.512359i
$707$	−416.283	+	721.023i	−0.588802	+	1.01983i
$708$		0			0
$709$	73.2369	+	126.850i	0.103296	+	0.178914i	0.913041	−	0.407868i	$-0.133728\pi$
$709$	73.2369	+	126.850i	0.103296	+	0.178914i	−0.809745	+	0.586782i	$0.800394\pi$
$710$	101.099	−	158.383i	0.142393	−	0.223075i
$711$		0			0
$712$		−	327.494i		−	0.459963i
$713$	378.349	+	655.319i	0.530643	+	0.919101i
$714$		0			0
$715$	725.892	−	377.057i	1.01523	−	0.527352i
$716$	−156.612	−	90.4200i	−0.218732	−	0.126285i
$717$		0			0
$718$	−307.496	+	177.533i	−0.428268	+	0.247261i
$719$			329.272i			0.457958i	0.973431	+	0.228979i	$0.0735388\pi$
$719$			329.272i			0.457958i	−0.973431	+	0.228979i	$0.926461\pi$
$720$		0			0
$721$	−1027.42			−1.42499
$722$	−461.255	−	798.916i	−0.638857	−	1.10653i
$723$		0			0
$724$	160.779	−	278.478i	0.222071	−	0.384638i
$725$	18.8789	−	211.461i	0.0260399	−	0.291671i
$726$		0			0
$727$	287.737	−	166.125i	0.395787	−	0.228507i	−0.288878	−	0.957366i	$-0.593282\pi$
$727$	287.737	−	166.125i	0.395787	−	0.228507i	0.684664	+	0.728859i	$0.259949\pi$
$728$	−311.077			−0.427303
$729$		0			0
$730$	−195.676	+	306.549i	−0.268049	+	0.419930i
$731$	−470.656	+	271.734i	−0.643853	+	0.371728i
$732$		0			0
$733$	−430.286	−	248.426i	−0.587020	−	0.338916i	0.176898	−	0.984229i	$-0.443394\pi$
$733$	−430.286	−	248.426i	−0.587020	−	0.338916i	−0.763918	+	0.645313i	$0.776727\pi$
$734$	−775.234	−	447.582i	−1.05618	−	0.609784i
$735$		0			0
$736$	−46.7111	−	80.9059i	−0.0634661	−	0.109927i
$737$	−19.6146			−0.0266141
$738$		0			0
$739$	493.117			0.667276			0.333638	−	0.942701i	$-0.391724\pi$
$739$	493.117			0.667276			0.333638	+	0.942701i	$0.391724\pi$
$740$	318.033	+	14.1685i	0.429774	+	0.0191467i
$741$		0			0
$742$	502.865	+	290.329i	0.677715	+	0.391279i
$743$	408.424	−	707.410i	0.549695	−	0.952100i	−0.448600	−	0.893733i	$-0.648077\pi$
$743$	408.424	−	707.410i	0.549695	−	0.952100i	0.998295	−	0.0583675i	$-0.0185895\pi$
$744$		0			0
$745$	389.229	+	17.3403i	0.522455	+	0.0232756i
$746$		−	258.843i		−	0.346975i
$747$		0			0
$748$			393.950i			0.526671i
$749$	832.803	−	480.819i	1.11189	−	0.641948i
$750$		0			0
$751$	−291.789	+	505.393i	−0.388533	+	0.672960i	−0.992253	−	0.124237i	$-0.960352\pi$
$751$	−291.789	+	505.393i	−0.388533	+	0.672960i	0.603719	+	0.797197i	$0.293685\pi$
$752$	92.1103	−	159.540i	0.122487	−	0.212154i
$753$		0			0
$754$	86.3669	+	149.592i	0.114545	+	0.198398i
$755$	−181.408	−	115.796i	−0.240275	−	0.153372i
$756$		0			0
$757$		−	633.635i		−	0.837034i	−0.908209	−	0.418517i	$-0.862550\pi$
$757$		−	633.635i		−	0.837034i	0.908209	−	0.418517i	$-0.137450\pi$
$758$	−194.298	−	336.533i	−0.256329	−	0.443975i
$759$		0			0
$760$	−399.499	+	207.516i	−0.525657	+	0.273047i
$761$	−645.786	−	372.845i	−0.848601	−	0.489940i	0.0115773	−	0.999933i	$-0.496315\pi$
$761$	−645.786	−	372.845i	−0.848601	−	0.489940i	−0.860179	+	0.509993i	$0.829648\pi$
$762$		0			0
$763$	−418.795	+	241.791i	−0.548879	+	0.316896i
$764$		−	340.934i		−	0.446249i
$765$		0			0
$766$	529.178			0.690832
$767$	465.792	+	806.776i	0.607291	+	1.05186i
$768$		0			0
$769$	215.709	−	373.619i	0.280506	−	0.485850i	−0.691004	−	0.722851i	$-0.742831\pi$
$769$	215.709	−	373.619i	0.280506	−	0.485850i	0.971509	+	0.237001i	$0.0761645\pi$
$770$	545.776	−	283.498i	0.708800	−	0.368179i
$771$		0			0
$772$	371.087	−	214.247i	0.480682	−	0.277522i
$773$	−248.851			−0.321929			−0.160964	−	0.986960i	$-0.551460\pi$
$773$	−248.851			−0.321929			−0.160964	+	0.986960i	$0.551460\pi$
$774$		0			0
$775$	−482.256	−	1039.02i	−0.622266	−	1.34066i
$776$	388.621	−	224.370i	0.500800	−	0.289137i
$777$		0			0
$778$	295.878	+	170.825i	0.380306	+	0.219570i
$779$	1885.02	+	1088.32i	2.41979	+	1.39707i
$780$		0			0
$781$	−151.125	−	261.756i	−0.193502	−	0.335155i
$782$	−404.460			−0.517212
$783$		0			0
$784$	−37.8892			−0.0483280
$785$	296.347	+	13.2024i	0.377512	+	0.0168184i
$786$		0			0
$787$	−804.916	−	464.718i	−1.02276	−	0.590494i	−0.107861	−	0.994166i	$-0.534400\pi$
$787$	−804.916	−	464.718i	−1.02276	−	0.590494i	−0.914904	+	0.403672i	$0.867734\pi$
$788$	209.813	−	363.408i	0.266261	−	0.461177i
$789$		0			0
$790$	−18.6362	+	418.317i	−0.0235902	+	0.529515i
$791$			795.392i			1.00555i
$792$		0			0
$793$		−	1384.72i		−	1.74618i
$794$	327.515	−	189.091i	0.412488	−	0.238150i
$795$		0			0
$796$	−327.667	+	567.537i	−0.411643	+	0.712986i
$797$	−292.029	+	505.810i	−0.366411	+	0.634642i	−0.989001	−	0.147906i	$-0.952747\pi$
$797$	−292.029	+	505.810i	−0.366411	+	0.634642i	0.622591	+	0.782548i	$0.286080\pi$
$798$		0			0
$799$	−398.781	−	690.708i	−0.499100	−	0.864466i
$800$	59.5396	+	128.277i	0.0744244	+	0.160347i
$801$		0			0
$802$			974.243i			1.21477i
$803$	292.501	+	506.626i	0.364260	+	0.630916i
$804$		0			0
$805$	291.061	+	560.337i	0.361566	+	0.696071i
$806$	807.124	+	465.993i	1.00139	+	0.578156i
$807$		0			0
$808$	−266.698	+	153.978i	−0.330071	+	0.190567i
$809$			363.295i			0.449067i	0.974466	+	0.224533i	$0.0720858\pi$
$809$			363.295i			0.449067i	−0.974466	+	0.224533i	$0.927914\pi$
$810$		0			0
$811$	69.8507			0.0861290			0.0430645	−	0.999072i	$-0.486288\pi$
$811$	69.8507			0.0861290			0.0430645	+	0.999072i	$0.486288\pi$
$812$	64.9366	+	112.474i	0.0799712	+	0.138514i
$813$		0			0
$814$	256.043	−	443.479i	0.314549	−	0.544814i
$815$	182.366	+	351.083i	0.223763	+	0.430777i
$816$		0			0
$817$	−865.147	+	499.493i	−1.05893	+	0.611374i
$818$	−358.259			−0.437969
$819$		0			0
$820$	367.904	−	576.364i	0.448663	−	0.702883i
$821$	−158.892	+	91.7361i	−0.193534	+	0.111737i	−0.593636	−	0.804734i	$-0.702308\pi$
$821$	−158.892	+	91.7361i	−0.193534	+	0.111737i	0.400102	+	0.916471i	$0.368975\pi$
$822$		0			0
$823$	463.264	+	267.465i	0.562896	+	0.324988i	0.754307	−	0.656522i	$-0.227973\pi$
$823$	463.264	+	267.465i	0.562896	+	0.324988i	−0.191411	+	0.981510i	$0.561306\pi$
$824$	−329.115	−	190.014i	−0.399411	−	0.230600i
$825$		0			0
$826$	350.215	+	606.591i	0.423989	+	0.734371i
$827$	640.632			0.774646			0.387323	−	0.921944i	$-0.373400\pi$
$827$	640.632			0.774646			0.387323	+	0.921944i	$0.373400\pi$
$828$		0			0
$829$	910.462			1.09827			0.549133	−	0.835735i	$-0.314958\pi$
$829$	910.462			1.09827			0.549133	+	0.835735i	$0.314958\pi$
$830$	−2.18037	+	48.9416i	−0.00262696	+	0.0589658i
$831$		0			0
$832$	−99.6479	−	57.5317i	−0.119769	−	0.0691487i
$833$	−82.0184	+	142.060i	−0.0984614	+	0.170540i
$834$		0			0
$835$	22.5905	−	507.075i	0.0270545	−	0.607276i
$836$			724.147i			0.866205i
$837$		0			0
$838$		−	729.186i		−	0.870150i
$839$	−35.9684	+	20.7664i	−0.0428706	+	0.0247513i	−0.521282	−	0.853384i	$-0.674546\pi$
$839$	−35.9684	+	20.7664i	−0.0428706	+	0.0247513i	0.478412	+	0.878136i	$0.341213\pi$
$840$		0			0
$841$	−384.442	+	665.873i	−0.457125	+	0.791764i
$842$	365.632	−	633.294i	0.434243	−	0.752131i
$843$		0			0
$844$	−102.013	−	176.691i	−0.120868	−	0.209350i
$845$	159.600	+	101.876i	0.188876	+	0.120563i
$846$		0			0
$847$		−	64.0413i		−	0.0756096i
$848$	107.389	+	186.004i	0.126638	+	0.219344i
$849$		0			0
$850$	609.841	+	54.4456i	0.717460	+	0.0640536i
$851$	455.310	+	262.874i	0.535030	+	0.308900i
$852$		0			0
$853$	368.940	−	213.007i	0.432520	−	0.249716i	−0.267900	−	0.963447i	$-0.586330\pi$
$853$	368.940	−	213.007i	0.432520	−	0.249716i	0.700420	+	0.713731i	$0.252996\pi$
$854$		−	1041.13i		−	1.21912i
$855$		0			0
$856$	355.698			0.415535
$857$	−331.290	−	573.811i	−0.386570	−	0.669558i	0.605416	−	0.795909i	$-0.293007\pi$
$857$	−331.290	−	573.811i	−0.386570	−	0.669558i	−0.991986	+	0.126351i	$0.959673\pi$
$858$		0			0
$859$	−701.088	+	1214.32i	−0.816168	+	1.41364i	0.0923184	+	0.995730i	$0.470572\pi$
$859$	−701.088	+	1214.32i	−0.816168	+	1.41364i	−0.908486	+	0.417915i	$0.862761\pi$
$860$	144.661	+	278.495i	0.168210	+	0.323831i
$861$		0			0
$862$	−356.149	+	205.623i	−0.413166	+	0.238542i
$863$	−54.6082			−0.0632771			−0.0316386	−	0.999499i	$-0.510073\pi$
$863$	−54.6082			−0.0632771			−0.0316386	+	0.999499i	$0.510073\pi$
$864$		0			0
$865$	−764.312	−	487.875i	−0.883597	−	0.564017i
$866$	439.572	−	253.787i	0.507589	−	0.293057i
$867$		0			0
$868$	606.852	+	350.366i	0.699139	+	0.403648i
$869$	583.320	+	336.780i	0.671254	+	0.387549i
$870$		0			0
$871$	−12.4014	−	21.4799i	−0.0142381	−	0.0246611i
$872$	−178.871			−0.205128
$873$		0			0
$874$	−743.467			−0.850648
$875$	−363.431	−	884.052i	−0.415349	−	1.01035i
$876$		0			0
$877$	−757.923	−	437.587i	−0.864223	−	0.498959i	0.00120136	−	0.999999i	$-0.499618\pi$
$877$	−757.923	−	437.587i	−0.864223	−	0.498959i	−0.865424	+	0.501040i	$0.832951\pi$
$878$	143.993	−	249.404i	0.164001	−	0.284059i
$879$		0			0
$880$	227.261	+	10.1246i	0.258251	+	0.0115052i
$881$		−	1103.84i		−	1.25294i	−0.779445	−	0.626471i	$-0.784499\pi$
$881$		−	1103.84i		−	1.25294i	0.779445	−	0.626471i	$-0.215501\pi$
$882$		0			0
$883$		−	455.458i		−	0.515808i	−0.966171	−	0.257904i	$-0.916968\pi$
$883$		−	455.458i		−	0.515808i	0.966171	−	0.257904i	$-0.0830318\pi$
$884$	−431.414	+	249.077i	−0.488024	+	0.281761i
$885$		0			0
$886$	−15.0096	+	25.9974i	−0.0169409	+	0.0293424i
$887$	475.518	−	823.622i	0.536097	−	0.928548i	−0.463012	−	0.886352i	$-0.653231\pi$
$887$	475.518	−	823.622i	0.536097	−	0.928548i	0.999109	−	0.0421957i	$-0.0134353\pi$
$888$		0			0
$889$	−545.638	−	945.072i	−0.613766	−	1.06307i
$890$	−440.518	+	690.123i	−0.494965	+	0.775419i
$891$		0			0
$892$			755.008i			0.846421i
$893$	−733.027	−	1269.64i	−0.820859	−	1.42177i
$894$		0			0
$895$	208.400	+	401.203i	0.232850	+	0.448271i
$896$	−74.9222	−	43.2564i	−0.0836186	−	0.0482772i
$897$		0			0
$898$	796.508	−	459.864i	0.886980	−	0.512098i
$899$		−	389.101i		−	0.432815i
$900$		0			0
$901$	929.857			1.03203
$902$	−549.950	−	952.542i	−0.609701	−	1.05603i
$903$		0			0
$904$	−147.103	+	254.790i	−0.162725	+	0.281847i
$905$	−713.394	+	370.565i	−0.788280	+	0.409464i
$906$		0			0
$907$	−1168.53	+	674.653i	−1.28835	+	0.743829i	−0.978360	−	0.206911i	$-0.933659\pi$
$907$	−1168.53	+	674.653i	−1.28835	+	0.743829i	−0.309990	+	0.950740i	$0.600326\pi$
$908$	538.909			0.593512
$909$		0			0
$910$	655.527	+	418.436i	0.720360	+	0.459819i
$911$	354.356	−	204.587i	0.388975	−	0.224575i	−0.292741	−	0.956192i	$-0.594567\pi$
$911$	354.356	−	204.587i	0.388975	−	0.224575i	0.681716	+	0.731617i	$0.261234\pi$
$912$		0			0
$913$	68.2464	+	39.4021i	0.0747496	+	0.0431567i
$914$	−189.801	−	109.582i	−0.207660	−	0.119892i
$915$		0			0
$916$	−423.862	−	734.151i	−0.462732	−	0.801475i
$917$	1578.18			1.72103
$918$		0			0
$919$	−247.618			−0.269443			−0.134721	−	0.990884i	$-0.543014\pi$
$919$	−247.618			−0.269443			−0.134721	+	0.990884i	$0.543014\pi$
$920$	−10.3947	+	233.324i	−0.0112986	+	0.253613i
$921$		0			0
$922$	−431.092	−	248.891i	−0.467561	−	0.269947i
$923$	191.099	−	330.993i	0.207041	−	0.358606i
$924$		0			0
$925$	−651.127	−	457.649i	−0.703921	−	0.494756i
$926$			141.854i			0.153190i
$927$		0			0
$928$			48.0385i			0.0517657i
$929$	237.623	−	137.192i	0.255784	−	0.147677i	−0.366626	−	0.930368i	$-0.619487\pi$
$929$	237.623	−	137.192i	0.255784	−	0.147677i	0.622410	+	0.782691i	$0.286154\pi$
$930$		0			0
$931$	−150.764	+	261.130i	−0.161937	+	0.280484i
$932$	−70.8761	+	122.761i	−0.0760473	+	0.131718i
$933$		0			0
$934$	−22.3224	−	38.6636i	−0.0238998	−	0.0413957i
$935$	529.910	−	830.165i	0.566749	−	0.887877i
$936$		0			0
$937$		−	313.547i		−	0.334629i	−0.985904	−	0.167315i	$-0.946490\pi$
$937$		−	313.547i		−	0.334629i	0.985904	−	0.167315i	$-0.0535095\pi$
$938$	−9.32424	−	16.1501i	−0.00994056	−	0.0172175i
$939$		0			0
$940$	−408.703	+	212.296i	−0.434790	+	0.225847i
$941$	440.467	+	254.304i	0.468084	+	0.270248i	0.715437	−	0.698677i	$-0.246228\pi$
$941$	440.467	+	254.304i	0.468084	+	0.270248i	−0.247354	+	0.968925i	$0.579561\pi$
$942$		0			0
$943$	977.955	−	564.622i	1.03707	−	0.598751i
$944$			259.081i			0.274450i
$945$		0			0
$946$	504.810			0.533625
$947$	−504.462	−	873.754i	−0.532695	−	0.922655i	−0.999271	−	0.0381739i	$-0.987846\pi$
$947$	−504.462	−	873.754i	−0.532695	−	0.922655i	0.466576	−	0.884481i	$-0.345487\pi$
$948$		0			0
$949$	−369.870	+	640.633i	−0.389747	+	0.675061i
$950$	1120.99	+	100.080i	1.17999	+	0.105348i
$951$		0			0
$952$	−324.367	+	187.273i	−0.340722	+	0.196716i
$953$	−918.564			−0.963865			−0.481933	−	0.876208i	$-0.660065\pi$
$953$	−918.564			−0.963865			−0.481933	+	0.876208i	$0.660065\pi$
$954$		0			0
$955$	−458.597	+	718.445i	−0.480206	+	0.752298i
$956$	−609.809	+	352.073i	−0.637876	+	0.368278i
$957$		0			0
$958$	−776.923	−	448.557i	−0.810984	−	0.468222i
$959$	1086.85	+	627.493i	1.13332	+	0.654320i
$960$		0			0
$961$	−569.199	−	985.882i	−0.592299	−	1.02589i
$962$	647.537			0.673115
$963$		0			0
$964$	175.153			0.181694
$965$	−1070.17	−	47.6768i	−1.10899	−	0.0494060i
$966$		0			0
$967$	26.2085	+	15.1315i	0.0271029	+	0.0156479i	0.513490	−	0.858095i	$-0.328352\pi$
$967$	26.2085	+	15.1315i	0.0271029	+	0.0156479i	−0.486387	+	0.873743i	$0.661686\pi$
$968$	11.8440	−	20.5145i	0.0122356	−	0.0211927i
$969$		0			0
$970$	−1120.74	−	49.9296i	−1.15540	−	0.0514738i
$971$			1003.74i			1.03372i	0.856071	+	0.516858i	$0.172899\pi$
$971$			1003.74i			1.03372i	−0.856071	+	0.516858i	$0.827101\pi$
$972$		0			0
$973$			233.669i			0.240153i
$974$	782.749	−	451.921i	0.803644	−	0.463984i
$975$		0			0
$976$	192.551	−	333.508i	0.197286	−	0.341709i
$977$	392.247	−	679.391i	0.401481	−	0.695385i	−0.592424	−	0.805626i	$-0.701829\pi$
$977$	392.247	−	679.391i	0.401481	−	0.695385i	0.993905	+	0.110241i	$0.0351624\pi$
$978$		0			0
$979$	658.496	+	1140.55i	0.672621	+	1.16501i
$980$	79.8433	+	50.9655i	0.0814728	+	0.0520056i
$981$		0			0
$982$			520.245i			0.529781i
$983$	26.6166	+	46.1013i	0.0270769	+	0.0468986i	0.879246	−	0.476367i	$-0.158047\pi$
$983$	26.6166	+	46.1013i	0.0270769	+	0.0468986i	−0.852169	+	0.523266i	$0.824713\pi$
$984$		0			0
$985$	−930.964	+	483.579i	−0.945141	+	0.490943i
$986$	180.113	+	103.989i	0.182671	+	0.105465i
$987$		0			0
$988$	−793.012	+	457.846i	−0.802643	+	0.463406i
$989$			518.277i			0.524042i
$990$		0			0
$991$	1202.09			1.21300			0.606501	−	0.795082i	$-0.292572\pi$
$991$	1202.09			1.21300			0.606501	+	0.795082i	$0.292572\pi$
$992$	129.596	+	224.467i	0.130641	+	0.226277i
$993$		0			0
$994$	143.682	−	248.864i	0.144549	−	0.250366i
$995$	1453.89	−	755.209i	1.46120	−	0.759004i
$996$		0			0
$997$	−1157.85	+	668.484i	−1.16133	+	0.670495i	−0.951623	−	0.307269i	$-0.900585\pi$
$997$	−1157.85	+	668.484i	−1.16133	+	0.670495i	−0.209709	+	0.977764i	$0.567252\pi$
$998$	−699.390			−0.700791
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.g.539.1		24
3.2	odd	2	inner	810.3.j.g.539.7		24
5.4	even	2		810.3.j.h.539.7		24
9.2	odd	6		810.3.j.h.269.7		24
9.4	even	3		810.3.b.c.809.15	yes	24
9.5	odd	6		810.3.b.c.809.10	yes	24
9.7	even	3		810.3.j.h.269.1		24
15.14	odd	2		810.3.j.h.539.1		24
45.4	even	6		810.3.b.c.809.9	✓	24
45.14	odd	6		810.3.b.c.809.16	yes	24
45.29	odd	6	inner	810.3.j.g.269.1		24
45.34	even	6	inner	810.3.j.g.269.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.9	✓	24	45.4	even	6
810.3.b.c.809.10	yes	24	9.5	odd	6
810.3.b.c.809.15	yes	24	9.4	even	3
810.3.b.c.809.16	yes	24	45.14	odd	6
810.3.j.g.269.1		24	45.29	odd	6	inner
810.3.j.g.269.7		24	45.34	even	6	inner
810.3.j.g.539.1		24	1.1	even	1	trivial
810.3.j.g.539.7		24	3.2	odd	2	inner
810.3.j.h.269.1		24	9.7	even	3
810.3.j.h.269.7		24	9.2	odd	6
810.3.j.h.539.1		24	15.14	odd	2
810.3.j.h.539.7		24	5.4	even	2

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	810.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.43710 - 2.30480i) q^{5} +(6.62225 - 3.82336i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.43710 - 2.30480i) q^{5} +(6.62225 - 3.82336i) q^{7} +2.82843 q^{8} +(-5.96030 - 3.80458i) q^{10} +(-9.85044 + 5.68716i) q^{11} +(-12.4560 - 7.19146i) q^{13} +(-9.36528 - 5.40705i) q^{14} +(-2.00000 - 3.46410i) q^{16} -17.3175 q^{17} -31.8326 q^{19} +(-0.445064 + 9.99009i) q^{20} +(13.9306 + 8.04285i) q^{22} +(-8.25743 + 14.3023i) q^{23} +(14.3758 - 20.4533i) q^{25} +20.3405i q^{26} +15.2934i q^{28} +(7.35437 - 4.24605i) q^{29} +(22.9096 - 39.6806i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(12.2453 + 21.2096i) q^{34} +(20.5715 - 32.2276i) q^{35} -31.8348i q^{37} +(22.5090 + 38.9868i) q^{38} +(12.5500 - 6.51897i) q^{40} +(-59.2167 - 34.1888i) q^{41} +(27.1780 - 15.6912i) q^{43} -22.7486i q^{44} +23.3555 q^{46} +(23.0276 + 39.8849i) q^{47} +(4.73615 - 8.20325i) q^{49} +(-35.2153 - 3.14396i) q^{50} +(24.9120 - 14.3829i) q^{52} -53.6946 q^{53} +(-30.5996 + 47.9378i) q^{55} +(18.7306 - 10.8141i) q^{56} +(-10.4006 - 6.00482i) q^{58} +(-56.0926 - 32.3851i) q^{59} +(48.1377 + 83.3769i) q^{61} -64.7981 q^{62} +8.00000 q^{64} +(-71.8434 - 3.20066i) q^{65} +(1.49343 + 0.862231i) q^{67} +(17.3175 - 29.9948i) q^{68} +(-54.0169 - 2.40648i) q^{70} +26.5730i q^{71} -51.4318i q^{73} +(-38.9895 + 22.5106i) q^{74} +(31.8326 - 55.1356i) q^{76} +(-43.4881 + 75.3236i) q^{77} +(-29.6088 - 51.2839i) q^{79} +(-16.8583 - 10.7610i) q^{80} +96.7004i q^{82} +(-3.46413 - 6.00004i) q^{83} +(-76.8396 + 39.9135i) q^{85} +(-38.4355 - 22.1908i) q^{86} +(-27.8613 + 16.0857i) q^{88} -115.787i q^{89} -109.982 q^{91} +(-16.5149 - 28.6046i) q^{92} +(32.5659 - 56.4058i) q^{94} +(-141.244 + 73.3678i) q^{95} +(137.398 - 79.3269i) q^{97} -13.3959 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 - 24 * q^7	\( 24 q - 24 q^{4} - 24 q^{7} - 12 q^{10} - 48 q^{13} - 48 q^{16} + 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{43} - 36 q^{49} + 96 q^{52} + 216 q^{55} - 396 q^{58} - 60 q^{61} + 192 q^{64} + 1032 q^{67} - 480 q^{70} - 240 q^{79} - 396 q^{85} - 240 q^{88} + 48 q^{91} - 48 q^{94} + 1440 q^{97}+O(q^{100}) \) 24 * q - 24 * q^4 - 24 * q^7 - 12 * q^10 - 48 * q^13 - 48 * q^16 + 120 * q^22 + 24 * q^25 + 60 * q^34 + 24 * q^43 - 36 * q^49 + 96 * q^52 + 216 * q^55 - 396 * q^58 - 60 * q^61 + 192 * q^64 + 1032 * q^67 - 480 * q^70 - 240 * q^79 - 396 * q^85 - 240 * q^88 + 48 * q^91 - 48 * q^94 + 1440 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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