LMFDB - Embedded newform 810.3.j.h.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.h.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.222532 - 4.99505i) q^{5} +(-6.62225 + 3.82336i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.222532 - 4.99505i) q^{5} +(-6.62225 + 3.82336i) q^{7} +2.82843 q^{8} +(-5.96030 + 3.80458i) q^{10} +(9.85044 - 5.68716i) q^{11} +(12.4560 + 7.19146i) q^{13} +(9.36528 + 5.40705i) q^{14} +(-2.00000 - 3.46410i) q^{16} -17.3175 q^{17} -31.8326 q^{19} +(8.87420 + 4.60961i) q^{20} +(-13.9306 - 8.04285i) q^{22} +(-8.25743 + 14.3023i) q^{23} +(-24.9010 + 2.22311i) q^{25} -20.3405i q^{26} -15.2934i q^{28} +(-7.35437 + 4.24605i) q^{29} +(22.9096 - 39.6806i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(12.2453 + 21.2096i) q^{34} +(20.5715 + 32.2276i) q^{35} +31.8348i q^{37} +(22.5090 + 38.9868i) q^{38} +(-0.629415 - 14.1281i) q^{40} +(59.2167 + 34.1888i) q^{41} +(-27.1780 + 15.6912i) q^{43} +22.7486i q^{44} +23.3555 q^{46} +(23.0276 + 39.8849i) q^{47} +(4.73615 - 8.20325i) q^{49} +(20.3304 + 28.9253i) q^{50} +(-24.9120 + 14.3829i) q^{52} -53.6946 q^{53} +(-30.5996 - 47.9378i) q^{55} +(-18.7306 + 10.8141i) q^{56} +(10.4006 + 6.00482i) q^{58} +(56.0926 + 32.3851i) q^{59} +(48.1377 + 83.3769i) q^{61} -64.7981 q^{62} +8.00000 q^{64} +(33.1498 - 63.8185i) q^{65} +(-1.49343 - 0.862231i) q^{67} +(17.3175 - 29.9948i) q^{68} +(24.9244 - 47.9832i) q^{70} -26.5730i q^{71} +51.4318i q^{73} +(38.9895 - 22.5106i) q^{74} +(31.8326 - 55.1356i) q^{76} +(-43.4881 + 75.3236i) q^{77} +(-29.6088 - 51.2839i) q^{79} +(-16.8583 + 10.7610i) q^{80} -96.7004i q^{82} +(-3.46413 - 6.00004i) q^{83} +(3.85370 + 86.5018i) q^{85} +(38.4355 + 22.1908i) q^{86} +(27.8613 - 16.0857i) q^{88} +115.787i q^{89} -109.982 q^{91} +(-16.5149 - 28.6046i) q^{92} +(32.5659 - 56.4058i) q^{94} +(7.08376 + 159.005i) q^{95} +(-137.398 + 79.3269i) q^{97} -13.3959 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{40} - 24 q^{43} - 36 q^{49} - 96 q^{52} + 216 q^{55} + 396 q^{58} - 60 q^{61} + 192 q^{64} - 1032 q^{67} + 288 q^{70} - 240 q^{79} - 48 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^40 - 24 * q^43 - 36 * q^49 - 96 * q^52 + 216 * q^55 + 396 * q^58 - 60 * q^61 + 192 * q^64 - 1032 * q^67 + 288 * q^70 - 240 * q^79 - 48 * 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
$5$	−0.222532	−	4.99505i	−0.0445064	−	0.999009i
$5$	−0.222532	−	4.99505i	−0.0445064	−	0.999009i
$6$		0			0
$7$	−6.62225	+	3.82336i	−0.946036	+	0.546194i	−0.891847	−	0.452337i	$-0.850591\pi$
$7$	−6.62225	+	3.82336i	−0.946036	+	0.546194i	−0.0541887	+	0.998531i	$0.517257\pi$
$8$	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	0.0197591	−	0.999805i	$-0.493710\pi$
$11$	9.85044	−	5.68716i	0.895495	−	0.517014i	0.875736	+	0.482791i	$0.160377\pi$
$12$		0			0
$13$	12.4560	+	7.19146i	0.958152	+	0.553190i	0.895604	−	0.444852i	$-0.146744\pi$
$13$	12.4560	+	7.19146i	0.958152	+	0.553190i	0.0625485	+	0.998042i	$0.480077\pi$
$14$	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	$0.816100\pi$
$20$	8.87420	+	4.60961i	0.443710	+	0.230480i
$21$		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
$25$	−24.9010	+	2.22311i	−0.996038	+	0.0889246i
$26$		−	20.3405i		−	0.782328i
$27$		0			0
$28$		−	15.2934i		−	0.546194i
$29$	−7.35437	+	4.24605i	−0.253599	+	0.146415i	−0.621411	−	0.783485i	$-0.713440\pi$
$29$	−7.35437	+	4.24605i	−0.253599	+	0.146415i	0.367812	+	0.929900i	$0.380107\pi$
$30$		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	$0.141557\pi$
$37$			31.8348i			0.860400i	−0.902734	+	0.430200i	$0.858443\pi$
$38$	22.5090	+	38.9868i	0.592343	+	1.02597i
$39$		0			0
$40$	−0.629415	−	14.1281i	−0.0157354	−	0.353203i
$41$	59.2167	+	34.1888i	1.44431	+	0.833872i	0.998133	−	0.0610732i	$-0.0194523\pi$
$41$	59.2167	+	34.1888i	1.44431	+	0.833872i	0.446176	+	0.894945i	$0.352786\pi$
$42$		0			0
$43$	−27.1780	+	15.6912i	−0.632047	+	0.364913i	−0.781545	−	0.623849i	$-0.785568\pi$
$43$	−27.1780	+	15.6912i	−0.632047	+	0.364913i	0.149497	+	0.988762i	$0.452234\pi$
$44$			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
$50$	20.3304	+	28.9253i	0.406608	+	0.578507i
$51$		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	0.893305	−	0.449451i	$-0.148380\pi$
$59$	56.0926	+	32.3851i	0.950722	+	0.548900i	0.0574171	+	0.998350i	$0.481714\pi$
$60$		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
$65$	33.1498	−	63.8185i	0.509997	−	0.981823i
$66$		0			0
$67$	−1.49343	−	0.862231i	−0.0222900	−	0.0128691i	0.488814	−	0.872388i	$-0.337430\pi$
$67$	−1.49343	−	0.862231i	−0.0222900	−	0.0128691i	−0.511104	+	0.859519i	$0.670763\pi$
$68$	17.3175	−	29.9948i	0.254669	−	0.441100i
$69$		0			0
$70$	24.9244	−	47.9832i	0.356062	−	0.685475i
$71$		−	26.5730i		−	0.374268i	−0.982334	−	0.187134i	$-0.940080\pi$
$71$		−	26.5730i		−	0.374268i	0.982334	−	0.187134i	$-0.0599199\pi$
$72$		0			0
$73$			51.4318i			0.704545i	0.935898	+	0.352272i	$0.114591\pi$
$73$			51.4318i			0.704545i	−0.935898	+	0.352272i	$0.885409\pi$
$74$	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
$85$	3.85370	+	86.5018i	0.0453377	+	1.01767i
$86$	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	$0.225435\pi$
$89$			115.787i			1.30097i	−0.759518	+	0.650486i	$0.774565\pi$
$90$		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
$95$	7.08376	+	159.005i	0.0745659	+	1.67374i
$96$		0			0
$97$	−137.398	+	79.3269i	−1.41648	+	0.817803i	−0.995987	−	0.0894944i	$-0.971475\pi$
$97$	−137.398	+	79.3269i	−1.41648	+	0.817803i	−0.420489	+	0.907298i	$0.638142\pi$
$98$	−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	0.0456398	−	0.998958i	$-0.485467\pi$
$101$	94.2918	−	54.4394i	0.933583	−	0.539004i	0.887943	+	0.459954i	$0.152134\pi$
$102$		0			0
$103$	116.360	+	67.1803i	1.12971	+	0.652236i	0.943861	−	0.330344i	$-0.107165\pi$
$103$	116.360	+	67.1803i	1.12971	+	0.652236i	0.185844	+	0.982579i	$0.440498\pi$
$104$	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	$0.593687\pi$
$110$	−37.0744	+	71.3739i	−0.337040	+	0.648854i
$111$		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
$115$	73.2781	+	38.0635i	0.637201	+	0.330987i
$116$		−	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	$0.189913\pi$
$127$			142.712i			1.12371i	−0.827235	+	0.561857i	$0.810087\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−101.602	+	4.52642i	−0.781553	+	0.0348186i
$131$	−178.736	−	103.193i	−1.36440	−	0.787735i	−0.374192	−	0.927351i	$-0.622080\pi$
$131$	−178.736	−	103.193i	−1.36440	−	0.787735i	−0.990206	+	0.139616i	$0.955413\pi$
$132$		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	$0.201726\pi$
$140$	−76.3914	+	3.40328i	−0.545653	+	0.0243091i
$141$		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	0.256150	−	0.966637i	$-0.417546\pi$
$149$	−67.4833	−	38.9615i	−0.452908	−	0.261486i	−0.709057	+	0.705151i	$0.750879\pi$
$150$		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
$155$	−203.304	−	105.604i	−1.31164	−	0.681318i
$156$		0			0
$157$	−51.3798	−	29.6641i	−0.327260	−	0.188943i	0.327364	−	0.944898i	$-0.393840\pi$
$157$	−51.3798	−	29.6641i	−0.327260	−	0.188943i	−0.654624	+	0.755955i	$0.727173\pi$
$158$	−41.8732	+	72.5264i	−0.265020	+	0.459028i
$159$		0			0
$160$	25.1000	+	13.0379i	0.156875	+	0.0814871i
$161$		−	126.284i		−	0.784375i
$162$		0			0
$163$		−	79.1245i		−	0.485426i	−0.970098	−	0.242713i	$-0.921963\pi$
$163$		−	79.1245i		−	0.485426i	0.970098	−	0.242713i	$-0.0780374\pi$
$164$	−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
$175$	156.401	−	109.927i	0.893718	−	0.628156i
$176$	−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	$-0.918724\pi$
$179$		−	90.4200i		−	0.505140i	0.967579	−	0.252570i	$-0.0812758\pi$
$180$		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
$185$	159.016	−	7.08426i	0.859548	−	0.0382933i
$186$		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	−0.0609920	−	0.998138i	$-0.519426\pi$
$191$	147.629	−	85.2335i	0.772925	−	0.446249i	0.833917	+	0.551890i	$0.186093\pi$
$192$		0			0
$193$	185.543	+	107.124i	0.961365	+	0.555044i	0.896593	−	0.442856i	$-0.146035\pi$
$193$	185.543	+	107.124i	0.961365	+	0.555044i	0.0647720	+	0.997900i	$0.479368\pi$
$194$	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	$0.192139\pi$
$200$	−70.4305	+	6.28792i	−0.352153	+	0.0314396i
$201$		0			0
$202$	−133.349	−	76.9890i	−0.660143	−	0.381134i
$203$	32.4683	−	56.2368i	0.159942	−	0.277029i
$204$		0			0
$205$	157.597	−	303.398i	0.768765	−	1.47999i
$206$		−	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
$220$	113.630	−	5.06230i	0.516502	−	0.0230104i
$221$	−215.707	−	124.538i	−0.976049	−	0.563522i
$222$		0			0
$223$	−326.928	+	188.752i	−1.46604	+	0.846421i	−0.999279	−	0.0379599i	$-0.987914\pi$
$223$	−326.928	+	188.752i	−1.46604	+	0.846421i	−0.466765	+	0.884381i	$0.654581\pi$
$224$		−	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	$0.790343\pi$
$230$	−5.19735	−	116.662i	−0.0225972	−	0.507226i
$231$		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	−0.299687	−	0.954038i	$-0.596882\pi$
$239$	−304.905	−	176.037i	−1.27575	−	0.736555i	−0.976064	+	0.217482i	$0.930216\pi$
$240$		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
$245$	−42.0295	−	21.8318i	−0.171549	−	0.0891094i
$246$		0			0
$247$	−396.506	−	228.923i	−1.60529	−	0.926813i
$248$	64.7981	−	112.234i	0.261283	−	0.452555i
$249$		0			0
$250$	139.959	−	107.988i	0.559837	−	0.431952i
$251$			2.67686i			0.0106648i	0.999986	+	0.00533238i	$0.00169736\pi$
$251$			2.67686i			0.0106648i	−0.999986	+	0.00533238i	$0.998303\pi$
$252$		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
$265$	11.9488	+	268.207i	0.0450897	+	1.01210i
$266$	−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	$-0.924493\pi$
$269$		−	126.427i		−	0.469989i	0.971997	−	0.234994i	$-0.0755072\pi$
$270$		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
$275$	−232.642	+	163.514i	−0.845972	+	0.594598i
$276$		0			0
$277$	−367.858	+	212.383i	−1.32801	+	0.766726i	−0.984991	−	0.172604i	$-0.944782\pi$
$277$	−367.858	+	212.383i	−1.32801	+	0.766726i	−0.343016	+	0.939329i	$0.611449\pi$
$278$	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	−0.948457	−	0.316906i	$-0.897356\pi$
$281$	−322.655	+	186.285i	−1.14824	+	0.662935i	−0.199780	+	0.979841i	$0.564023\pi$
$282$		0			0
$283$	−392.514	−	226.618i	−1.38698	−	0.800771i	−0.394003	−	0.919109i	$-0.628910\pi$
$283$	−392.514	−	226.618i	−1.38698	−	0.800771i	−0.992973	+	0.118338i	$0.962243\pi$
$284$	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
$290$	27.6799	−	53.2880i	0.0954478	−	0.183752i
$291$		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
$295$	149.283	−	287.392i	0.506043	−	0.974210i
$296$			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	$0.293259\pi$
$307$			488.983i			1.59278i	−0.604785	+	0.796389i	$0.706741\pi$
$308$	−86.9762	−	150.647i	−0.282390	−	0.489114i
$309$		0			0
$310$	14.4197	+	323.670i	0.0465150	+	1.04410i
$311$	50.1624	+	28.9613i	0.161294	+	0.0931231i	0.578474	−	0.815701i	$-0.303648\pi$
$311$	50.1624	+	28.9613i	0.161294	+	0.0931231i	−0.417180	+	0.908824i	$0.636982\pi$
$312$		0			0
$313$	395.028	−	228.069i	1.26207	−	0.728656i	0.288595	−	0.957451i	$-0.406812\pi$
$313$	395.028	−	228.069i	1.26207	−	0.728656i	0.973475	+	0.228795i	$0.0734786\pi$
$314$			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
$320$	−1.78026	−	39.9604i	−0.00556330	−	0.124876i
$321$		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
$335$	−3.97455	+	7.65161i	−0.0118643	+	0.0228406i
$336$		0			0
$337$	431.904	+	249.360i	1.28162	+	0.739941i	0.977144	−	0.212580i	$-0.0681867\pi$
$337$	431.904	+	249.360i	1.28162	+	0.739941i	0.304472	+	0.952521i	$0.401520\pi$
$338$	26.7772	−	46.3794i	0.0792224	−	0.137217i
$339$		0			0
$340$	−153.679	−	79.8270i	−0.451998	−	0.234785i
$341$		−	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
$355$	−132.733	+	5.91335i	−0.373897	+	0.0166573i
$356$	−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	$0.113709\pi$
$359$			251.070i			0.699359i	−0.936869	+	0.349679i	$0.886291\pi$
$360$		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
$365$	256.904	−	11.4452i	0.703847	−	0.0313567i
$366$		0			0
$367$	−548.174	+	316.488i	−1.49366	+	0.862366i	−0.999974	−	0.00727397i	$-0.997685\pi$
$367$	−548.174	+	316.488i	−1.49366	+	0.862366i	−0.493687	+	0.869639i	$0.664351\pi$
$368$	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	0.272240	−	0.962229i	$-0.412236\pi$
$373$	−158.508	−	91.5148i	−0.424955	−	0.245348i	−0.697195	+	0.716881i	$0.745569\pi$
$374$	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	$0.381922\pi$
$380$	−282.489	−	146.736i	−0.743391	−	0.386147i
$381$		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
$385$	385.922	+	200.463i	1.00240	+	0.520683i
$386$		−	302.991i		−	0.784951i
$387$		0			0
$388$		−	317.308i		−	0.817803i
$389$	209.217	−	120.792i	0.537833	−	0.310518i	−0.206367	−	0.978475i	$-0.566164\pi$
$389$	209.217	−	120.792i	0.537833	−	0.310518i	0.744200	+	0.667956i	$0.232831\pi$
$390$		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	$-0.890657\pi$
$397$		−	267.415i		−	0.673590i	0.941578	−	0.336795i	$-0.109343\pi$
$398$	−231.696	−	401.309i	−0.582151	−	1.00831i
$399$		0			0
$400$	57.5030	+	81.8132i	0.143758	+	0.204533i
$401$	596.600	+	344.447i	1.48778	+	0.858970i	0.999903	−	0.0139424i	$-0.00443814\pi$
$401$	596.600	+	344.447i	1.48778	+	0.858970i	0.487877	+	0.872912i	$0.337771\pi$
$402$		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	$0.0664411\pi$
$410$	−483.023	+	21.5189i	−1.17810	+	0.0524852i
$411$		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	−0.138705	−	0.990334i	$-0.544294\pi$
$419$	−446.533	−	257.806i	−1.06571	−	0.615289i	−0.927007	+	0.375045i	$0.877627\pi$
$420$		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
$425$	431.223	−	38.4988i	1.01464	−	0.0905855i
$426$		0			0
$427$	−637.560	−	368.095i	−1.49311	−	0.862050i
$428$	−125.758	+	217.820i	−0.293828	+	0.508924i
$429$		0			0
$430$	102.291	−	196.925i	0.237886	−	0.457966i
$431$			290.795i			0.674698i	0.941380	+	0.337349i	$0.109530\pi$
$431$			290.795i			0.674698i	−0.941380	+	0.337349i	$0.890470\pi$
$432$		0			0
$433$		−	358.909i		−	0.828889i	−0.910075	−	0.414444i	$-0.863976\pi$
$433$		−	358.909i		−	0.828889i	0.910075	−	0.414444i	$-0.136024\pi$
$434$	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
$445$	578.359	−	25.7662i	1.29968	−	0.0579016i
$446$	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	$-0.742202\pi$
$449$		−	650.346i		−	1.44843i	0.689573	−	0.724216i	$-0.257798\pi$
$450$		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
$455$	24.4746	+	549.366i	0.0537902	+	1.20740i
$456$		0			0
$457$	−134.210	+	77.4859i	−0.293675	+	0.169553i	−0.639598	−	0.768710i	$-0.720899\pi$
$457$	−134.210	+	77.4859i	−0.293675	+	0.169553i	0.345923	+	0.938263i	$0.387566\pi$
$458$	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	−0.792746	−	0.609552i	$-0.791349\pi$
$461$	−304.828	+	175.992i	−0.661232	+	0.381762i	0.131514	+	0.991314i	$0.458016\pi$
$462$		0			0
$463$	86.8675	+	50.1530i	0.187619	+	0.108322i	0.590867	−	0.806769i	$-0.298786\pi$
$463$	86.8675	+	50.1530i	0.187619	+	0.108322i	−0.403249	+	0.915091i	$0.632119\pi$
$464$	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
$470$	−288.997	−	150.116i	−0.614886	−	0.319396i
$471$		0			0
$472$	158.654	+	91.5989i	0.336131	+	0.194065i
$473$	−178.477	+	309.131i	−0.377330	+	0.653555i
$474$		0			0
$475$	792.661	−	70.7675i	1.66876	−	0.148984i
$476$			264.844i			0.556396i
$477$		0			0
$478$			497.907i			1.04165i
$479$	−549.367	+	317.177i	−1.14690	+	0.662166i	−0.948131	−	0.317880i	$-0.897029\pi$
$479$	−549.367	+	317.177i	−1.14690	+	0.662166i	−0.198774	+	0.980045i	$0.563696\pi$
$480$		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	$-0.772174\pi$
$487$		−	639.112i		−	1.31235i	0.754611	−	0.656173i	$-0.227826\pi$
$488$	136.154	+	235.825i	0.279004	+	0.483249i
$489$		0			0
$490$	2.98101	+	66.9129i	0.00608368	+	0.136557i
$491$	318.584	+	183.934i	0.648847	+	0.374612i	0.788014	−	0.615657i	$-0.211109\pi$
$491$	318.584	+	183.934i	0.648847	+	0.374612i	−0.139167	+	0.990269i	$0.544443\pi$
$492$		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	$0.00163896\pi$
$500$	−231.224	−	95.0553i	−0.462448	−	0.190111i
$501$		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	0.926187	−	0.377065i	$-0.123067\pi$
$509$	540.931	+	312.307i	1.06273	+	0.613569i	0.136546	+	0.990634i	$0.456400\pi$
$510$		0			0
$511$	−196.642	−	340.594i	−0.384818	−	0.666525i
$512$	22.6274			0.0441942
$513$		0			0
$514$	−552.467			−1.07484
$515$	309.675	−	596.171i	0.601310	−	1.15761i
$516$		0			0
$517$	453.664	+	261.923i	0.877493	+	0.506621i
$518$	−172.132	+	298.142i	−0.332302	+	0.575563i
$519$		0			0
$520$	93.7619	−	180.506i	0.180311	−	0.347127i
$521$			908.634i			1.74402i	0.489489	+	0.872009i	$0.337183\pi$
$521$			908.634i			1.74402i	−0.489489	+	0.872009i	$0.662817\pi$
$522$		0			0
$523$		−	534.875i		−	1.02271i	−0.859371	−	0.511353i	$-0.829145\pi$
$523$		−	534.875i		−	1.02271i	0.859371	−	0.511353i	$-0.170855\pi$
$524$	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
$535$	−27.9852	−	628.168i	−0.0523088	−	1.17415i
$536$	−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
$545$	14.0730	+	315.889i	0.0258221	+	0.579614i
$546$		0			0
$547$	−547.715	+	316.223i	−1.00131	+	0.578105i	−0.908635	−	0.417592i	$-0.862874\pi$
$547$	−547.715	+	316.223i	−1.00131	+	0.578105i	−0.0926721	+	0.995697i	$0.529541\pi$
$548$	−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
$560$	70.4968	−	135.717i	0.125887	−	0.242352i
$561$		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
$565$	461.536	+	239.740i	0.816878	+	0.424319i
$566$			640.973i			1.13246i
$567$		0			0
$568$		−	75.1599i		−	0.132324i
$569$	355.756	−	205.396i	0.625230	−	0.360977i	−0.153672	−	0.988122i	$-0.549110\pi$
$569$	355.756	−	205.396i	0.625230	−	0.360977i	0.778902	+	0.627145i	$0.215777\pi$
$570$		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	$0.102643\pi$
$577$			365.707i			0.633808i	−0.948458	+	0.316904i	$0.897357\pi$
$578$	−7.70512	−	13.3457i	−0.0133307	−	0.0230894i
$579$		0			0
$580$	−84.8368	+	3.77952i	−0.146270	+	0.00651642i
$581$	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
$590$	−457.540	+	20.3837i	−0.775492	+	0.0345486i
$591$		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	0.833778	−	0.552100i	$-0.186173\pi$
$599$	462.748	+	267.167i	0.772534	+	0.446022i	−0.0612441	+	0.998123i	$0.519507\pi$
$600$		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
$605$	−37.1608	−	19.3027i	−0.0614227	−	0.0319054i
$606$		0			0
$607$	−753.720	−	435.161i	−1.24171	−	0.716904i	−0.272271	−	0.962221i	$-0.587775\pi$
$607$	−753.720	−	435.161i	−1.24171	−	0.716904i	−0.969443	+	0.245317i	$0.921108\pi$
$608$	90.0361	−	155.947i	0.148086	−	0.256492i
$609$		0			0
$610$	−604.129	−	313.808i	−0.990375	−	0.514440i
$611$			662.408i			1.08414i
$612$		0			0
$613$			252.101i			0.411258i	0.978630	+	0.205629i	$0.0659240\pi$
$613$			252.101i			0.411258i	−0.978630	+	0.205629i	$0.934076\pi$
$614$	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
$625$	615.116	−	110.715i	0.984185	−	0.177145i
$626$	−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
$635$	712.851	−	31.7579i	1.12260	−	0.0500124i
$636$		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	−0.668383	−	0.743817i	$-0.733013\pi$
$641$	−229.741	+	132.641i	−0.358411	+	0.206928i	0.309973	+	0.950745i	$0.399680\pi$
$642$		0			0
$643$	217.451	+	125.546i	0.338182	+	0.195250i	0.659468	−	0.751733i	$-0.270782\pi$
$643$	217.451	+	125.546i	0.338182	+	0.195250i	−0.321286	+	0.946982i	$0.604115\pi$
$644$	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
$650$	45.2193	+	506.499i	0.0695682	+	0.779229i
$651$		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
$655$	−475.681	+	915.759i	−0.726230	+	1.39811i
$656$		−	273.510i		−	0.416936i
$657$		0			0
$658$			498.045i			0.756907i
$659$	−124.230	+	71.7242i	−0.188513	+	0.108838i	−0.591286	−	0.806462i	$-0.701380\pi$
$659$	−124.230	+	71.7242i	−0.188513	+	0.108838i	0.402773	+	0.915300i	$0.368046\pi$
$660$		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
$670$	12.1817	−	0.542701i	0.0181816	−	0.000810002i
$671$	948.355	+	547.533i	1.41335	+	0.815996i
$672$		0			0
$673$	241.209	−	139.262i	0.358408	−	0.206927i	−0.309974	−	0.950745i	$-0.600320\pi$
$673$	241.209	−	139.262i	0.358408	−	0.206927i	0.668382	+	0.743818i	$0.266987\pi$
$674$		−	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
$680$	10.8999	+	244.664i	0.0160293	+	0.359800i
$681$		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
$695$	135.589	+	70.4303i	0.195092	+	0.101339i
$696$		0			0
$697$	−1025.49	−	592.065i	−1.47129	−	0.849447i
$698$	−262.882	+	455.326i	−0.376622	+	0.652329i
$699$		0			0
$700$	33.9991	+	380.821i	0.0485701	+	0.544030i
$701$			716.640i			1.02231i	0.859488	+	0.511155i	$0.170782\pi$
$701$			716.640i			1.02231i	−0.859488	+	0.511155i	$0.829218\pi$
$702$		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
$715$	−36.4053	−	817.169i	−0.0509165	−	1.14289i
$716$	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	$-0.926461\pi$
$719$		−	329.272i		−	0.457958i	0.973431	−	0.228979i	$-0.0735388\pi$
$720$		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
$725$	173.691	−	122.080i	0.239574	−	0.168387i
$726$		0			0
$727$	−287.737	+	166.125i	−0.395787	+	0.228507i	−0.684664	−	0.728859i	$-0.740051\pi$
$727$	−287.737	+	166.125i	−0.395787	+	0.228507i	0.288878	+	0.957366i	$0.406718\pi$
$728$	−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	0.763918	−	0.645313i	$-0.223273\pi$
$733$	430.286	+	248.426i	0.587020	+	0.338916i	−0.176898	+	0.984229i	$0.556606\pi$
$734$	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	$0.391724\pi$
$740$	−146.746	+	282.509i	−0.198305	+	0.381768i
$741$		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
$745$	−179.597	+	345.752i	−0.241070	+	0.464097i
$746$			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	$0.137450\pi$
$757$			633.635i			0.837034i	−0.908209	+	0.418517i	$0.862550\pi$
$758$	−194.298	−	336.533i	−0.256329	−	0.443975i
$759$		0			0
$760$	20.0359	+	449.734i	0.0263630	+	0.591756i
$761$	645.786	+	372.845i	0.848601	+	0.489940i	0.860179	−	0.509993i	$-0.170352\pi$
$761$	645.786	+	372.845i	0.848601	+	0.489940i	−0.0115773	+	0.999933i	$0.503685\pi$
$762$		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	$0.0761645\pi$
$770$	−27.3721	−	614.405i	−0.0355481	−	0.797929i
$771$		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
$785$	−136.740	+	263.245i	−0.174191	+	0.335345i
$786$		0			0
$787$	804.916	+	464.718i	1.02276	+	0.590494i	0.914904	−	0.403672i	$-0.132266\pi$
$787$	804.916	+	464.718i	1.02276	+	0.590494i	0.107861	+	0.994166i	$0.465600\pi$
$788$	209.813	−	363.408i	0.266261	−	0.461177i
$789$		0			0
$790$	371.591	+	193.019i	0.470368	+	0.244328i
$791$		−	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
$805$	−630.797	+	28.1023i	−0.783598	+	0.0349097i
$806$	−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	$-0.927914\pi$
$809$		−	363.295i		−	0.449067i	0.974466	−	0.224533i	$-0.0720858\pi$
$810$		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
$815$	−395.230	+	17.6077i	−0.484945	+	0.0216046i
$816$		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	−0.400102	−	0.916471i	$-0.631025\pi$
$821$	158.892	−	91.7361i	0.193534	−	0.111737i	0.593636	+	0.804734i	$0.297692\pi$
$822$		0			0
$823$	−463.264	−	267.465i	−0.562896	−	0.324988i	0.191411	−	0.981510i	$-0.438694\pi$
$823$	−463.264	−	267.465i	−0.562896	−	0.324988i	−0.754307	+	0.656522i	$0.772027\pi$
$824$	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	$0.314958\pi$
$830$	43.4749	+	22.5825i	0.0523793	+	0.0272079i
$831$		0			0
$832$	99.6479	+	57.5317i	0.119769	+	0.0691487i
$833$	−82.0184	+	142.060i	−0.0984614	+	0.170540i
$834$		0			0
$835$	−450.435	−	233.974i	−0.539443	−	0.280208i
$836$		−	724.147i		−	0.866205i
$837$		0			0
$838$			729.186i			0.870150i
$839$	35.9684	−	20.7664i	0.0428706	−	0.0247513i	−0.478412	−	0.878136i	$-0.658787\pi$
$839$	35.9684	−	20.7664i	0.0428706	−	0.0247513i	0.521282	+	0.853384i	$0.325454\pi$
$840$		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
$850$	−352.072	−	500.915i	−0.414202	−	0.589312i
$851$	−455.310	−	262.874i	−0.535030	−	0.308900i
$852$		0			0
$853$	−368.940	+	213.007i	−0.432520	+	0.249716i	−0.700420	−	0.713731i	$-0.747004\pi$
$853$	−368.940	+	213.007i	−0.432520	+	0.249716i	0.267900	+	0.963447i	$0.413670\pi$
$854$			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	$0.862761\pi$
$860$	−313.514	+	13.9672i	−0.364551	+	0.0162409i
$861$		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
$875$	−583.896	−	756.766i	−0.667310	−	0.864876i
$876$		0			0
$877$	757.923	+	437.587i	0.864223	+	0.498959i	0.865424	−	0.501040i	$-0.167049\pi$
$877$	757.923	+	437.587i	0.864223	+	0.498959i	−0.00120136	+	0.999999i	$0.500382\pi$
$878$	143.993	−	249.404i	0.164001	−	0.284059i
$879$		0			0
$880$	−104.862	+	201.876i	−0.119162	+	0.229405i
$881$			1103.84i			1.25294i	0.779445	+	0.626471i	$0.215501\pi$
$881$			1103.84i			1.25294i	−0.779445	+	0.626471i	$0.784499\pi$
$882$		0			0
$883$			455.458i			0.515808i	0.966171	+	0.257904i	$0.0830318\pi$
$883$			455.458i			0.515808i	−0.966171	+	0.257904i	$0.916968\pi$
$884$	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
$895$	−451.652	+	20.1213i	−0.504639	+	0.0224820i
$896$	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
$905$	35.7785	+	803.099i	0.0395343	+	0.887403i
$906$		0			0
$907$	1168.53	−	674.653i	1.28835	−	0.743829i	0.309990	−	0.950740i	$-0.399674\pi$
$907$	1168.53	−	674.653i	1.28835	−	0.743829i	0.978360	+	0.206911i	$0.0663410\pi$
$908$	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	−0.681716	−	0.731617i	$-0.738766\pi$
$911$	−354.356	+	204.587i	−0.388975	+	0.224575i	0.292741	+	0.956192i	$0.405433\pi$
$912$		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	$0.543014\pi$
$920$	207.262	+	107.660i	0.225285	+	0.117022i
$921$		0			0
$922$	431.092	+	248.891i	0.467561	+	0.269947i
$923$	191.099	−	330.993i	0.207041	−	0.358606i
$924$		0			0
$925$	−70.7724	−	792.717i	−0.0765107	−	0.856992i
$926$		−	141.854i		−	0.153190i
$927$		0			0
$928$		−	48.0385i		−	0.0517657i
$929$	−237.623	+	137.192i	−0.255784	+	0.147677i	−0.622410	−	0.782691i	$-0.713846\pi$
$929$	−237.623	+	137.192i	−0.255784	+	0.147677i	0.366626	+	0.930368i	$0.380513\pi$
$930$		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	$0.0535095\pi$
$937$			313.547i			0.334629i	−0.985904	+	0.167315i	$0.946490\pi$
$938$	−9.32424	−	16.1501i	−0.00994056	−	0.0172175i
$939$		0			0
$940$	20.4975	+	460.095i	0.0218058	+	0.489463i
$941$	−440.467	−	254.304i	−0.468084	−	0.270248i	0.247354	−	0.968925i	$-0.420439\pi$
$941$	−440.467	−	254.304i	−0.468084	−	0.270248i	−0.715437	+	0.698677i	$0.753772\pi$
$942$		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
$950$	−647.168	−	920.768i	−0.681230	−	0.969229i
$951$		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
$965$	493.798	−	950.636i	0.511707	−	0.985115i
$966$		0			0
$967$	−26.2085	−	15.1315i	−0.0271029	−	0.0156479i	0.486387	−	0.873743i	$-0.338314\pi$
$967$	−26.2085	−	15.1315i	−0.0271029	−	0.0156479i	−0.513490	+	0.858095i	$0.671648\pi$
$968$	11.8440	−	20.5145i	0.0122356	−	0.0211927i
$969$		0			0
$970$	517.130	−	995.554i	0.533124	−	1.02634i
$971$		−	1003.74i		−	1.03372i	−0.856071	−	0.516858i	$-0.827101\pi$
$971$		−	1003.74i		−	1.03372i	0.856071	−	0.516858i	$-0.172899\pi$
$972$		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
$985$	46.6902	+	1048.03i	0.0474012	+	1.06399i
$986$	−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
$995$	−72.9165	−	1636.71i	−0.0732829	−	1.64494i
$996$		0			0
$997$	1157.85	−	668.484i	1.16133	−	0.670495i	0.209709	−	0.977764i	$-0.432748\pi$
$997$	1157.85	−	668.484i	1.16133	−	0.670495i	0.951623	+	0.307269i	$0.0994150\pi$
$998$	−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.h.539.1		24
3.2	odd	2	inner	810.3.j.h.539.7		24
5.4	even	2		810.3.j.g.539.7		24
9.2	odd	6		810.3.j.g.269.7		24
9.4	even	3		810.3.b.c.809.16	yes	24
9.5	odd	6		810.3.b.c.809.9	✓	24
9.7	even	3		810.3.j.g.269.1		24
15.14	odd	2		810.3.j.g.539.1		24
45.4	even	6		810.3.b.c.809.10	yes	24
45.14	odd	6		810.3.b.c.809.15	yes	24
45.29	odd	6	inner	810.3.j.h.269.1		24
45.34	even	6	inner	810.3.j.h.269.7		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.222532 - 4.99505i) q^{5} +(-6.62225 + 3.82336i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-0.222532 - 4.99505i) q^{5} +(-6.62225 + 3.82336i) q^{7} +2.82843 q^{8} +(-5.96030 + 3.80458i) q^{10} +(9.85044 - 5.68716i) q^{11} +(12.4560 + 7.19146i) q^{13} +(9.36528 + 5.40705i) q^{14} +(-2.00000 - 3.46410i) q^{16} -17.3175 q^{17} -31.8326 q^{19} +(8.87420 + 4.60961i) q^{20} +(-13.9306 - 8.04285i) q^{22} +(-8.25743 + 14.3023i) q^{23} +(-24.9010 + 2.22311i) q^{25} -20.3405i q^{26} -15.2934i q^{28} +(-7.35437 + 4.24605i) q^{29} +(22.9096 - 39.6806i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(12.2453 + 21.2096i) q^{34} +(20.5715 + 32.2276i) q^{35} +31.8348i q^{37} +(22.5090 + 38.9868i) q^{38} +(-0.629415 - 14.1281i) q^{40} +(59.2167 + 34.1888i) q^{41} +(-27.1780 + 15.6912i) q^{43} +22.7486i q^{44} +23.3555 q^{46} +(23.0276 + 39.8849i) q^{47} +(4.73615 - 8.20325i) q^{49} +(20.3304 + 28.9253i) q^{50} +(-24.9120 + 14.3829i) q^{52} -53.6946 q^{53} +(-30.5996 - 47.9378i) q^{55} +(-18.7306 + 10.8141i) q^{56} +(10.4006 + 6.00482i) q^{58} +(56.0926 + 32.3851i) q^{59} +(48.1377 + 83.3769i) q^{61} -64.7981 q^{62} +8.00000 q^{64} +(33.1498 - 63.8185i) q^{65} +(-1.49343 - 0.862231i) q^{67} +(17.3175 - 29.9948i) q^{68} +(24.9244 - 47.9832i) q^{70} -26.5730i q^{71} +51.4318i q^{73} +(38.9895 - 22.5106i) q^{74} +(31.8326 - 55.1356i) q^{76} +(-43.4881 + 75.3236i) q^{77} +(-29.6088 - 51.2839i) q^{79} +(-16.8583 + 10.7610i) q^{80} -96.7004i q^{82} +(-3.46413 - 6.00004i) q^{83} +(3.85370 + 86.5018i) q^{85} +(38.4355 + 22.1908i) q^{86} +(27.8613 - 16.0857i) q^{88} +115.787i q^{89} -109.982 q^{91} +(-16.5149 - 28.6046i) q^{92} +(32.5659 - 56.4058i) q^{94} +(7.08376 + 159.005i) q^{95} +(-137.398 + 79.3269i) q^{97} -13.3959 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{7}+O(q^{10}) \) 24 * q - 24 * q^4 + 24 * q^7	\( 24 q - 24 q^{4} + 24 q^{7} - 12 q^{10} + 48 q^{13} - 48 q^{16} - 120 q^{22} + 24 q^{25} + 60 q^{34} + 24 q^{40} - 24 q^{43} - 36 q^{49} - 96 q^{52} + 216 q^{55} + 396 q^{58} - 60 q^{61} + 192 q^{64} - 1032 q^{67} + 288 q^{70} - 240 q^{79} - 48 q^{85} + 240 q^{88} + 48 q^{91} - 48 q^{94} - 1440 q^{97}+O(q^{100}) \) 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^40 - 24 * q^43 - 36 * q^49 - 96 * q^52 + 216 * q^55 + 396 * q^58 - 60 * q^61 + 192 * q^64 - 1032 * q^67 + 288 * q^70 - 240 * q^79 - 48 * 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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