LMFDB - Embedded newform 810.3.j.g.539.8

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			539.8
Character	$\chi$	$=$	810.539
Dual form			810.3.j.g.269.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-2.51279 + 4.32272i) q^{5} +(5.12645 - 2.95976i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-2.51279 + 4.32272i) q^{5} +(5.12645 - 2.95976i) q^{7} -2.82843 q^{8} +(-7.07104 - 0.0209028i) q^{10} +(3.29935 - 1.90488i) q^{11} +(19.2513 + 11.1148i) q^{13} +(7.24989 + 4.18573i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.20411 q^{17} +29.3606 q^{19} +(-4.97438 - 8.67500i) q^{20} +(4.66598 + 2.69391i) q^{22} +(8.07107 - 13.9795i) q^{23} +(-12.3718 - 21.7242i) q^{25} +31.4373i q^{26} +11.8390i q^{28} +(-39.2196 + 22.6435i) q^{29} +(-21.8878 + 37.9108i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-0.851433 - 1.47473i) q^{34} +(-0.0874935 + 29.5974i) q^{35} +48.4190i q^{37} +(20.7611 + 35.9592i) q^{38} +(7.10724 - 12.2265i) q^{40} +(2.35652 + 1.36054i) q^{41} +(17.3080 - 9.99280i) q^{43} +7.61952i q^{44} +22.8284 q^{46} +(12.1492 + 21.0431i) q^{47} +(-6.97968 + 12.0892i) q^{49} +(17.8584 - 30.5136i) q^{50} +(-38.5027 + 22.2295i) q^{52} -10.8425 q^{53} +(-0.0563102 + 19.0487i) q^{55} +(-14.4998 + 8.37146i) q^{56} +(-55.4649 - 32.0227i) q^{58} +(-16.7913 - 9.69448i) q^{59} +(-9.19954 - 15.9341i) q^{61} -61.9081 q^{62} +8.00000 q^{64} +(-96.4205 + 55.2890i) q^{65} +(71.9917 + 41.5645i) q^{67} +(1.20411 - 2.08558i) q^{68} +(-36.3112 + 20.8214i) q^{70} +121.784i q^{71} -105.116i q^{73} +(-59.3009 + 34.2374i) q^{74} +(-29.3606 + 50.8540i) q^{76} +(11.2760 - 19.5305i) q^{77} +(-47.1052 - 81.5887i) q^{79} +(19.9999 + 0.0591221i) q^{80} +3.84818i q^{82} +(-47.3213 - 81.9629i) q^{83} +(3.02567 - 5.20502i) q^{85} +(24.4773 + 14.1320i) q^{86} +(-9.33197 + 5.38781i) q^{88} +132.665i q^{89} +131.588 q^{91} +(16.1421 + 27.9590i) q^{92} +(-17.1816 + 29.7595i) q^{94} +(-73.7770 + 126.918i) q^{95} +(103.065 - 59.5043i) q^{97} -19.7415 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.51279	+	4.32272i	−0.502558	+	0.864544i
$5$	−2.51279	+	4.32272i	−0.502558	+	0.864544i
$6$		0			0
$7$	5.12645	−	2.95976i	0.732350	−	0.422822i	−0.0869313	−	0.996214i	$-0.527706\pi$
$7$	5.12645	−	2.95976i	0.732350	−	0.422822i	0.819281	+	0.573392i	$0.194373\pi$
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−7.07104	−	0.0209028i	−0.707104	−	0.00209028i
$11$	3.29935	−	1.90488i	0.299941	−	0.173171i	−0.342476	−	0.939527i	$-0.611265\pi$
$11$	3.29935	−	1.90488i	0.299941	−	0.173171i	0.642416	+	0.766356i	$0.277932\pi$
$12$		0			0
$13$	19.2513	+	11.1148i	1.48087	+	0.854982i	0.999765	−	0.0216805i	$-0.00690166\pi$
$13$	19.2513	+	11.1148i	1.48087	+	0.854982i	0.481107	+	0.876662i	$0.340235\pi$
$14$	7.24989	+	4.18573i	0.517850	+	0.298981i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−1.20411			−0.0708299			−0.0354150	−	0.999373i	$-0.511275\pi$
$17$	−1.20411			−0.0708299			−0.0354150	+	0.999373i	$0.511275\pi$
$18$		0			0
$19$	29.3606			1.54529			0.772647	−	0.634836i	$-0.218932\pi$
$19$	29.3606			1.54529			0.772647	+	0.634836i	$0.218932\pi$
$20$	−4.97438	−	8.67500i	−0.248719	−	0.433750i
$21$		0			0
$22$	4.66598	+	2.69391i	0.212090	+	0.122450i
$23$	8.07107	−	13.9795i	0.350916	−	0.607805i	−0.635494	−	0.772106i	$-0.719204\pi$
$23$	8.07107	−	13.9795i	0.350916	−	0.607805i	0.986410	+	0.164301i	$0.0525369\pi$
$24$		0			0
$25$	−12.3718	−	21.7242i	−0.494871	−	0.868966i
$26$			31.4373i			1.20913i
$27$		0			0
$28$			11.8390i			0.422822i
$29$	−39.2196	+	22.6435i	−1.35240	+	0.780809i	−0.988585	−	0.150662i	$-0.951859\pi$
$29$	−39.2196	+	22.6435i	−1.35240	+	0.780809i	−0.363815	+	0.931471i	$0.618526\pi$
$30$		0			0
$31$	−21.8878	+	37.9108i	−0.706059	+	1.22293i	0.260249	+	0.965541i	$0.416195\pi$
$31$	−21.8878	+	37.9108i	−0.706059	+	1.22293i	−0.966308	+	0.257388i	$0.917138\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$	−0.851433	−	1.47473i	−0.0250422	−	0.0433743i
$35$	−0.0874935	+	29.5974i	−0.00249981	+	0.845641i
$36$		0			0
$37$			48.4190i			1.30862i	0.756226	+	0.654311i	$0.227041\pi$
$37$			48.4190i			1.30862i	−0.756226	+	0.654311i	$0.772959\pi$
$38$	20.7611	+	35.9592i	0.546344	+	0.946295i
$39$		0			0
$40$	7.10724	−	12.2265i	0.177681	−	0.305662i
$41$	2.35652	+	1.36054i	0.0574761	+	0.0331838i	0.528463	−	0.848957i	$-0.322769\pi$
$41$	2.35652	+	1.36054i	0.0574761	+	0.0331838i	−0.470987	+	0.882140i	$0.656102\pi$
$42$		0			0
$43$	17.3080	−	9.99280i	0.402513	−	0.232391i	−0.285055	−	0.958511i	$-0.592012\pi$
$43$	17.3080	−	9.99280i	0.402513	−	0.232391i	0.687568	+	0.726120i	$0.258679\pi$
$44$			7.61952i			0.173171i
$45$		0			0
$46$	22.8284			0.496270
$47$	12.1492	+	21.0431i	0.258495	+	0.447726i	0.965839	−	0.259143i	$-0.0834402\pi$
$47$	12.1492	+	21.0431i	0.258495	+	0.447726i	−0.707344	+	0.706869i	$0.750107\pi$
$48$		0			0
$49$	−6.97968	+	12.0892i	−0.142442	+	0.246717i
$50$	17.8584	−	30.5136i	0.357168	−	0.610271i
$51$		0			0
$52$	−38.5027	+	22.2295i	−0.740436	+	0.427491i
$53$	−10.8425			−0.204576			−0.102288	−	0.994755i	$-0.532616\pi$
$53$	−10.8425			−0.204576			−0.102288	+	0.994755i	$0.532616\pi$
$54$		0			0
$55$	−0.0563102	+	19.0487i	−0.00102382	+	0.346340i
$56$	−14.4998	+	8.37146i	−0.258925	+	0.149490i
$57$		0			0
$58$	−55.4649	−	32.0227i	−0.956292	−	0.552115i
$59$	−16.7913	−	9.69448i	−0.284599	−	0.164313i	0.350905	−	0.936411i	$-0.385874\pi$
$59$	−16.7913	−	9.69448i	−0.284599	−	0.164313i	−0.635504	+	0.772098i	$0.719207\pi$
$60$		0			0
$61$	−9.19954	−	15.9341i	−0.150812	−	0.261214i	0.780714	−	0.624888i	$-0.214856\pi$
$61$	−9.19954	−	15.9341i	−0.150812	−	0.261214i	−0.931526	+	0.363674i	$0.881522\pi$
$62$	−61.9081			−0.998518
$63$		0			0
$64$	8.00000			0.125000
$65$	−96.4205	+	55.2890i	−1.48339	+	0.850600i
$66$		0			0
$67$	71.9917	+	41.5645i	1.07450	+	0.620365i	0.929408	−	0.369053i	$-0.120318\pi$
$67$	71.9917	+	41.5645i	1.07450	+	0.620365i	0.145095	+	0.989418i	$0.453651\pi$
$68$	1.20411	−	2.08558i	0.0177075	−	0.0306703i
$69$		0			0
$70$	−36.3112	+	20.8214i	−0.518731	+	0.297448i
$71$			121.784i			1.71527i	0.514258	+	0.857635i	$0.328067\pi$
$71$			121.784i			1.71527i	−0.514258	+	0.857635i	$0.671933\pi$
$72$		0			0
$73$		−	105.116i		−	1.43994i	−0.694003	−	0.719972i	$-0.744155\pi$
$73$		−	105.116i		−	1.43994i	0.694003	−	0.719972i	$-0.255845\pi$
$74$	−59.3009	+	34.2374i	−0.801364	+	0.462668i
$75$		0			0
$76$	−29.3606	+	50.8540i	−0.386324	+	0.669132i
$77$	11.2760	−	19.5305i	0.146441	−	0.253643i
$78$		0			0
$79$	−47.1052	−	81.5887i	−0.596269	−	1.03277i	−0.993366	−	0.114991i	$-0.963316\pi$
$79$	−47.1052	−	81.5887i	−0.596269	−	1.03277i	0.397098	−	0.917776i	$-0.370017\pi$
$80$	19.9999	+	0.0591221i	0.249999	+	0.000739026i
$81$		0			0
$82$			3.84818i			0.0469290i
$83$	−47.3213	−	81.9629i	−0.570136	−	0.987505i	−0.996551	−	0.0829774i	$-0.973557\pi$
$83$	−47.3213	−	81.9629i	−0.570136	−	0.987505i	0.426415	−	0.904528i	$-0.359776\pi$
$84$		0			0
$85$	3.02567	−	5.20502i	0.0355961	−	0.0612356i
$86$	24.4773	+	14.1320i	0.284619	+	0.164325i
$87$		0			0
$88$	−9.33197	+	5.38781i	−0.106045	+	0.0612251i
$89$			132.665i			1.49062i	0.666718	+	0.745310i	$0.267698\pi$
$89$			132.665i			1.49062i	−0.666718	+	0.745310i	$0.732302\pi$
$90$		0			0
$91$	131.588			1.44602
$92$	16.1421	+	27.9590i	0.175458	+	0.303902i
$93$		0			0
$94$	−17.1816	+	29.7595i	−0.182783	+	0.316590i
$95$	−73.7770	+	126.918i	−0.776600	+	1.33597i
$96$		0			0
$97$	103.065	−	59.5043i	1.06252	−	0.613447i	0.136392	−	0.990655i	$-0.456449\pi$
$97$	103.065	−	59.5043i	1.06252	−	0.613447i	0.926129	+	0.377208i	$0.123116\pi$
$98$	−19.7415			−0.201444
$99$		0			0
$100$	49.9991	+	0.295609i	0.499991	+	0.00295609i
$101$	−20.6118	+	11.9002i	−0.204077	+	0.117824i	−0.598556	−	0.801081i	$-0.704259\pi$
$101$	−20.6118	+	11.9002i	−0.204077	+	0.117824i	0.394479	+	0.918905i	$0.370925\pi$
$102$		0			0
$103$	3.57552	+	2.06432i	0.0347137	+	0.0200420i	0.517256	−	0.855830i	$-0.326953\pi$
$103$	3.57552	+	2.06432i	0.0347137	+	0.0200420i	−0.482543	+	0.875872i	$0.660287\pi$
$104$	−54.4510	−	31.4373i	−0.523567	−	0.302282i
$105$		0			0
$106$	−7.66683	−	13.2793i	−0.0723285	−	0.125277i
$107$	117.008			1.09353			0.546765	−	0.837286i	$-0.315859\pi$
$107$	117.008			1.09353			0.546765	+	0.837286i	$0.315859\pi$
$108$		0			0
$109$	−84.3413			−0.773774			−0.386887	−	0.922127i	$-0.626450\pi$
$109$	−84.3413			−0.773774			−0.386887	+	0.922127i	$0.626450\pi$
$110$	−23.3696	+	13.4005i	−0.212451	+	0.121823i
$111$		0			0
$112$	−20.5058	−	11.8390i	−0.183087	−	0.105706i
$113$	−40.0727	+	69.4080i	−0.354626	+	0.614230i	−0.987054	−	0.160389i	$-0.948725\pi$
$113$	−40.0727	+	69.4080i	−0.354626	+	0.614230i	0.632428	+	0.774619i	$0.282058\pi$
$114$		0			0
$115$	40.1486	+	70.0165i	0.349118	+	0.608839i
$116$		−	90.5738i		−	0.780809i
$117$		0			0
$118$		−	27.4201i		−	0.232374i
$119$	−6.17280	+	3.56387i	−0.0518723	+	0.0299485i
$120$		0			0
$121$	−53.2429	+	92.2194i	−0.440024	+	0.762143i
$122$	13.0101	−	22.5342i	0.106640	−	0.184706i
$123$		0			0
$124$	−43.7756	−	75.8216i	−0.353029	−	0.611465i
$125$	124.995	+	1.10853i	0.999961	+	0.00886821i
$126$		0			0
$127$			91.3285i			0.719122i	0.933122	+	0.359561i	$0.117074\pi$
$127$			91.3285i			0.719122i	−0.933122	+	0.359561i	$0.882926\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−135.895	−	78.9953i	−1.04534	−	0.607656i
$131$	197.410	+	113.974i	1.50694	+	0.870034i	0.999967	+	0.00807357i	$0.00256992\pi$
$131$	197.410	+	113.974i	1.50694	+	0.870034i	0.506976	+	0.861960i	$0.330763\pi$
$132$		0			0
$133$	150.516	−	86.9002i	1.13170	−	0.653385i
$134$			117.562i			0.877329i
$135$		0			0
$136$	3.40573			0.0250422
$137$	−61.3594	−	106.278i	−0.447879	−	0.775749i	0.550369	−	0.834922i	$-0.314487\pi$
$137$	−61.3594	−	106.278i	−0.447879	−	0.775749i	−0.998248	+	0.0591727i	$0.981154\pi$
$138$		0			0
$139$	19.2401	−	33.3249i	0.138418	−	0.239747i	−0.788480	−	0.615061i	$-0.789132\pi$
$139$	19.2401	−	33.3249i	0.138418	−	0.239747i	0.926898	+	0.375313i	$0.122465\pi$
$140$	−51.1768	−	29.7490i	−0.365548	−	0.212493i
$141$		0			0
$142$	−149.155	+	86.1145i	−1.05038	+	0.606440i
$143$	84.6891			0.592232
$144$		0			0
$145$	0.669364	−	226.434i	0.00461630	−	1.56161i
$146$	128.740	−	74.3281i	0.881782	−	0.509097i
$147$		0			0
$148$	−83.8642	−	48.4190i	−0.566650	−	0.327155i
$149$	−6.49058	−	3.74734i	−0.0435609	−	0.0251499i	0.478061	−	0.878326i	$-0.341340\pi$
$149$	−6.49058	−	3.74734i	−0.0435609	−	0.0251499i	−0.521622	+	0.853177i	$0.674673\pi$
$150$		0			0
$151$	−108.617	−	188.129i	−0.719315	−	1.24589i	−0.961272	−	0.275603i	$-0.911123\pi$
$151$	−108.617	−	188.129i	−0.719315	−	1.24589i	0.241957	−	0.970287i	$-0.422211\pi$
$152$	−83.0443			−0.546344
$153$		0			0
$154$	31.8932			0.207099
$155$	−108.878	−	189.877i	−0.702441	−	1.22501i
$156$		0			0
$157$	153.578	+	88.6685i	0.978206	+	0.564767i	0.901728	−	0.432304i	$-0.142299\pi$
$157$	153.578	+	88.6685i	0.978206	+	0.564767i	0.0764777	+	0.997071i	$0.475633\pi$
$158$	66.6169	−	115.384i	0.421626	−	0.730277i
$159$		0			0
$160$	14.0697	+	24.5366i	0.0879354	+	0.153354i
$161$		−	95.5537i		−	0.593501i
$162$		0			0
$163$		−	42.6651i		−	0.261749i	−0.991399	−	0.130875i	$-0.958221\pi$
$163$		−	42.6651i		−	0.261749i	0.991399	−	0.130875i	$-0.0417785\pi$
$164$	−4.71304	+	2.72108i	−0.0287381	+	0.0165919i
$165$		0			0
$166$	66.9224	−	115.913i	0.403147	−	0.698271i
$167$	36.9936	−	64.0748i	0.221519	−	0.383681i	−0.733751	−	0.679419i	$-0.762232\pi$
$167$	36.9936	−	64.0748i	0.221519	−	0.383681i	0.955269	+	0.295737i	$0.0955653\pi$
$168$		0			0
$169$	162.576	+	281.590i	0.961987	+	1.66621i
$170$	8.51430	+	0.0251693i	0.0500841	+	0.000148054i
$171$		0			0
$172$			39.9712i			0.232391i
$173$	76.8727	+	133.147i	0.444351	+	0.769638i	0.998007	−	0.0631075i	$-0.0201011\pi$
$173$	76.8727	+	133.147i	0.444351	+	0.769638i	−0.553656	+	0.832745i	$0.686768\pi$
$174$		0			0
$175$	−127.722	−	74.7503i	−0.729837	−	0.427145i
$176$	−13.1974	−	7.61952i	−0.0749852	−	0.0432927i
$177$		0			0
$178$	−162.481	+	93.8084i	−0.912814	+	0.527014i
$179$		−	292.469i		−	1.63390i	−0.576706	−	0.816951i	$-0.695662\pi$
$179$		−	292.469i		−	1.63390i	0.576706	−	0.816951i	$-0.304338\pi$
$180$		0			0
$181$	45.0019			0.248629			0.124315	−	0.992243i	$-0.460327\pi$
$181$	45.0019			0.248629			0.124315	+	0.992243i	$0.460327\pi$
$182$	93.0467	+	161.162i	0.511246	+	0.885504i
$183$		0			0
$184$	−22.8284	+	39.5400i	−0.124068	+	0.214891i
$185$	−209.302	−	121.667i	−1.13136	−	0.657658i
$186$		0			0
$187$	−3.97277	+	2.29368i	−0.0212448	+	0.0122657i
$188$	−48.5970			−0.258495
$189$		0			0
$190$	−207.610	−	0.613719i	−1.09268	−	0.00323010i
$191$	163.433	−	94.3578i	0.855668	−	0.494020i	−0.00689152	−	0.999976i	$-0.502194\pi$
$191$	163.433	−	94.3578i	0.855668	−	0.494020i	0.862559	+	0.505956i	$0.168860\pi$
$192$		0			0
$193$	−78.7052	−	45.4405i	−0.407799	−	0.235443i	0.282045	−	0.959401i	$-0.408987\pi$
$193$	−78.7052	−	45.4405i	−0.407799	−	0.235443i	−0.689844	+	0.723958i	$0.742321\pi$
$194$	145.755	+	84.1518i	0.751316	+	0.433772i
$195$		0			0
$196$	−13.9594	−	24.1783i	−0.0712212	−	0.123359i
$197$	−321.126			−1.63008			−0.815040	−	0.579405i	$-0.803285\pi$
$197$	−321.126			−1.63008			−0.815040	+	0.579405i	$0.803285\pi$
$198$		0			0
$199$	−22.7423			−0.114283			−0.0571414	−	0.998366i	$-0.518199\pi$
$199$	−22.7423			−0.114283			−0.0571414	+	0.998366i	$0.518199\pi$
$200$	34.9927	+	61.4452i	0.174963	+	0.307226i
$201$		0			0
$202$	−29.1495	−	16.8295i	−0.144304	−	0.0833142i
$203$	−134.038	+	232.161i	−0.660287	+	1.14365i
$204$		0			0
$205$	−11.8027	+	6.76783i	−0.0575740	+	0.0330138i
$206$			5.83879i			0.0283437i
$207$		0			0
$208$		−	88.9181i		−	0.427491i
$209$	96.8708	−	55.9284i	0.463497	−	0.267600i
$210$		0			0
$211$	39.9608	−	69.2142i	0.189388	−	0.328029i	−0.755659	−	0.654966i	$-0.772683\pi$
$211$	39.9608	−	69.2142i	0.189388	−	0.328029i	0.945046	+	0.326937i	$0.106016\pi$
$212$	10.8425	−	18.7798i	0.0511440	−	0.0885840i
$213$		0			0
$214$	82.7369	+	143.305i	0.386621	+	0.669647i
$215$	−0.295398	+	99.9276i	−0.00137394	+	0.464779i
$216$		0			0
$217$			259.131i			1.19415i
$218$	−59.6383	−	103.297i	−0.273570	−	0.473838i
$219$		0			0
$220$	−32.9370	−	19.1462i	−0.149714	−	0.0870284i
$221$	−23.1807	−	13.3834i	−0.104890	−	0.0605583i
$222$		0			0
$223$	−56.8626	+	32.8297i	−0.254989	+	0.147218i	−0.622047	−	0.782980i	$-0.713699\pi$
$223$	−56.8626	+	32.8297i	−0.254989	+	0.147218i	0.367057	+	0.930198i	$0.380365\pi$
$224$		−	33.4858i		−	0.149490i
$225$		0			0
$226$	−113.343			−0.501516
$227$	183.852	+	318.441i	0.809921	+	1.40282i	0.912918	+	0.408143i	$0.133824\pi$
$227$	183.852	+	318.441i	0.809921	+	1.40282i	−0.102997	+	0.994682i	$0.532843\pi$
$228$		0			0
$229$	149.821	−	259.497i	0.654238	−	1.13317i	−0.327846	−	0.944731i	$-0.606323\pi$
$229$	149.821	−	259.497i	0.654238	−	1.13317i	0.982084	−	0.188443i	$-0.0603440\pi$
$230$	−57.3631	+	98.6809i	−0.249405	+	0.429047i
$231$		0			0
$232$	110.930	−	64.0454i	0.478146	−	0.276058i
$233$	227.228			0.975229			0.487614	−	0.873059i	$-0.337867\pi$
$233$	227.228			0.975229			0.487614	+	0.873059i	$0.337867\pi$
$234$		0			0
$235$	−121.492	−	0.359144i	−0.516987	−	0.00152827i
$236$	33.5827	−	19.3890i	0.142299	−	0.0821566i
$237$		0			0
$238$	−8.72966	−	5.04007i	−0.0366793	−	0.0211768i
$239$	−164.387	−	94.9090i	−0.687813	−	0.397109i	0.114979	−	0.993368i	$-0.463320\pi$
$239$	−164.387	−	94.9090i	−0.687813	−	0.397109i	−0.802792	+	0.596259i	$0.796653\pi$
$240$		0			0
$241$	−45.4778	−	78.7699i	−0.188705	−	0.326846i	0.756114	−	0.654440i	$-0.227096\pi$
$241$	−45.4778	−	78.7699i	−0.188705	−	0.326846i	−0.944819	+	0.327594i	$0.893762\pi$
$242$	−150.594			−0.622287
$243$		0			0
$244$	36.7982			0.150812
$245$	−34.7195	−	60.5487i	−0.141712	−	0.247137i
$246$		0			0
$247$	565.230	+	326.336i	2.28838	+	1.32120i
$248$	61.9081	−	107.228i	0.249629	−	0.432371i
$249$		0			0
$250$	87.0272	+	153.871i	0.348109	+	0.615484i
$251$		−	386.041i		−	1.53801i	−0.639242	−	0.769005i	$-0.720752\pi$
$251$		−	386.041i		−	1.53801i	0.639242	−	0.769005i	$-0.279248\pi$
$252$		0			0
$253$		−	61.4977i		−	0.243074i
$254$	−111.854	+	64.5790i	−0.440371	+	0.254248i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	173.158	−	299.918i	0.673766	−	1.16700i	−0.303062	−	0.952971i	$-0.598009\pi$
$257$	173.158	−	299.918i	0.673766	−	1.16700i	0.976828	−	0.214026i	$-0.0686579\pi$
$258$		0			0
$259$	143.308	+	248.218i	0.553315	+	0.958369i
$260$	0.657128	−	222.294i	0.00252741	−	0.854978i
$261$		0			0
$262$			322.368i			1.23041i
$263$	−216.736	−	375.397i	−0.824090	−	1.42737i	−0.902613	−	0.430453i	$-0.858354\pi$
$263$	−216.736	−	375.397i	−0.824090	−	1.42737i	0.0785228	−	0.996912i	$-0.474980\pi$
$264$		0			0
$265$	27.2450	−	46.8692i	0.102811	−	0.176865i
$266$	212.861	+	122.895i	0.800230	+	0.462013i
$267$		0			0
$268$	−143.983	+	83.1289i	−0.537252	+	0.310182i
$269$		−	456.780i		−	1.69807i	−0.528340	−	0.849033i	$-0.677185\pi$
$269$		−	456.780i		−	1.69807i	0.528340	−	0.849033i	$-0.322815\pi$
$270$		0			0
$271$	−321.543			−1.18651			−0.593253	−	0.805016i	$-0.702156\pi$
$271$	−321.543			−1.18651			−0.593253	+	0.805016i	$0.702156\pi$
$272$	2.40822	+	4.17116i	0.00885374	+	0.0153351i
$273$		0			0
$274$	86.7753	−	150.299i	0.316698	−	0.548537i
$275$	−82.2007	−	48.1088i	−0.298912	−	0.174941i
$276$		0			0
$277$	287.041	−	165.723i	1.03625	−	0.598278i	0.117480	−	0.993075i	$-0.462518\pi$
$277$	287.041	−	165.723i	1.03625	−	0.598278i	0.918768	+	0.394797i	$0.129185\pi$
$278$	54.4193			0.195753
$279$		0			0
$280$	0.247469	−	83.7142i	0.000883818	−	0.298979i
$281$	409.801	−	236.599i	1.45837	−	0.841989i	0.459437	−	0.888211i	$-0.348051\pi$
$281$	409.801	−	236.599i	1.45837	−	0.841989i	0.998931	+	0.0462214i	$0.0147180\pi$
$282$		0			0
$283$	26.3212	+	15.1965i	0.0930076	+	0.0536980i	0.545782	−	0.837927i	$-0.316233\pi$
$283$	26.3212	+	15.1965i	0.0930076	+	0.0536980i	−0.452775	+	0.891625i	$0.649566\pi$
$284$	−210.936	−	121.784i	−0.742734	−	0.428818i
$285$		0			0
$286$	59.8842	+	103.723i	0.209385	+	0.362666i
$287$	16.1074			0.0561235
$288$		0			0
$289$	−287.550			−0.994983
$290$	277.797	−	159.293i	0.957920	−	0.549286i
$291$		0			0
$292$	182.066	+	105.116i	0.623514	+	0.359986i
$293$	−12.5081	+	21.6647i	−0.0426898	+	0.0739409i	−0.886581	−	0.462574i	$-0.846926\pi$
$293$	−12.5081	+	21.6647i	−0.0426898	+	0.0739409i	0.843891	+	0.536515i	$0.180259\pi$
$294$		0			0
$295$	84.0996	−	48.2240i	0.285083	−	0.163471i
$296$		−	136.950i		−	0.462668i
$297$		0			0
$298$		−	10.5991i		−	0.0355674i
$299$	310.758	−	179.416i	1.03932	−	0.600054i
$300$		0			0
$301$	59.1525	−	102.455i	0.196520	−	0.340383i
$302$	153.607	−	266.055i	0.508632	−	0.880977i
$303$		0			0
$304$	−58.7212	−	101.708i	−0.193162	−	0.334566i
$305$	91.9950	+	0.271948i	0.301623	+	0.000891633i
$306$		0			0
$307$			596.302i			1.94235i	0.238365	+	0.971176i	$0.423389\pi$
$307$			596.302i			1.94235i	−0.238365	+	0.971176i	$0.576611\pi$
$308$	22.5519	+	39.0611i	0.0732205	+	0.126822i
$309$		0			0
$310$	155.562	−	267.611i	0.501813	−	0.863262i
$311$	47.0295	+	27.1525i	0.151220	+	0.0873070i	0.573701	−	0.819065i	$-0.305507\pi$
$311$	47.0295	+	27.1525i	0.151220	+	0.0873070i	−0.422481	+	0.906372i	$0.638841\pi$
$312$		0			0
$313$	139.802	−	80.7145i	0.446650	−	0.257874i	−0.259764	−	0.965672i	$-0.583645\pi$
$313$	139.802	−	80.7145i	0.446650	−	0.257874i	0.706415	+	0.707798i	$0.250311\pi$
$314$			250.792i			0.798702i
$315$		0			0
$316$	188.421			0.596269
$317$	136.292	+	236.064i	0.429942	+	0.744682i	0.996868	−	0.0790874i	$-0.0252006\pi$
$317$	136.292	+	236.064i	0.429942	+	0.744682i	−0.566926	+	0.823769i	$0.691867\pi$
$318$		0			0
$319$	−86.2661	+	149.417i	−0.270427	+	0.468393i
$320$	−20.1023	+	34.5817i	−0.0628197	+	0.108068i
$321$		0			0
$322$	117.029	−	67.5666i	0.363444	−	0.209834i
$323$	−35.3533			−0.109453
$324$		0			0
$325$	3.28562	−	555.728i	0.0101096	−	1.70993i
$326$	52.2539	−	30.1688i	0.160288	−	0.0925423i
$327$		0			0
$328$	−6.66525	−	3.84818i	−0.0203209	−	0.0117323i
$329$	124.565	+	71.9177i	0.378617	+	0.218595i
$330$		0			0
$331$	264.356	+	457.879i	0.798660	+	1.38332i	0.920489	+	0.390769i	$0.127791\pi$
$331$	264.356	+	457.879i	0.798660	+	1.38332i	−0.121829	+	0.992551i	$0.538876\pi$
$332$	189.285			0.570136
$333$		0			0
$334$	104.634			0.313274
$335$	−360.571	+	206.757i	−1.07633	+	0.617186i
$336$		0			0
$337$	337.626	+	194.929i	1.00186	+	0.578423i	0.908798	−	0.417237i	$-0.137002\pi$
$337$	337.626	+	194.929i	1.00186	+	0.578423i	0.0930609	+	0.995660i	$0.470335\pi$
$338$	−229.917	+	398.228i	−0.680228	+	1.17819i
$339$		0			0
$340$	5.98969	+	10.4456i	0.0176167	+	0.0307225i
$341$			166.775i			0.489075i
$342$		0			0
$343$			372.689i			1.08656i
$344$	−48.9545	+	28.2639i	−0.142310	+	0.0821625i
$345$		0			0
$346$	−108.714	+	188.299i	−0.314203	+	0.544216i
$347$	−60.2010	+	104.271i	−0.173490	+	0.300493i	−0.939638	−	0.342171i	$-0.888838\pi$
$347$	−60.2010	+	104.271i	−0.173490	+	0.300493i	0.766148	+	0.642664i	$0.222171\pi$
$348$		0			0
$349$	−274.137	−	474.820i	−0.785494	−	1.36051i	−0.928704	−	0.370823i	$-0.879076\pi$
$349$	−274.137	−	474.820i	−0.785494	−	1.36051i	0.143210	−	0.989692i	$-0.454258\pi$
$350$	1.23734	−	209.283i	0.00353525	−	0.597951i
$351$		0			0
$352$		−	21.5513i		−	0.0612251i
$353$	146.668	+	254.036i	0.415489	+	0.719648i	0.995480	−	0.0949749i	$-0.0302771\pi$
$353$	146.668	+	254.036i	0.415489	+	0.719648i	−0.579991	+	0.814623i	$0.696944\pi$
$354$		0			0
$355$	−526.439	−	306.018i	−1.48293	−	0.862023i
$356$	−229.783	−	132.665i	−0.645457	−	0.372655i
$357$		0			0
$358$	358.199	−	206.807i	1.00056	−	0.577672i
$359$			15.8718i			0.0442110i	0.999756	+	0.0221055i	$0.00703698\pi$
$359$			15.8718i			0.0442110i	−0.999756	+	0.0221055i	$0.992963\pi$
$360$		0			0
$361$	501.044			1.38793
$362$	31.8211	+	55.1158i	0.0879037	+	0.152254i
$363$		0			0
$364$	−131.588	+	227.917i	−0.361505	+	0.626146i
$365$	454.386	+	264.134i	1.24489	+	0.723655i
$366$		0			0
$367$	−513.192	+	296.292i	−1.39834	+	0.807334i	−0.994219	−	0.107370i	$-0.965757\pi$
$367$	−513.192	+	296.292i	−1.39834	+	0.807334i	−0.404125	+	0.914704i	$0.632424\pi$
$368$	−64.5686			−0.175458
$369$		0			0
$370$	1.01209	−	342.373i	0.00273539	−	0.925331i
$371$	−55.5837	+	32.0913i	−0.149821	+	0.0864993i
$372$		0			0
$373$	−328.734	−	189.794i	−0.881323	−	0.508832i	−0.0102288	−	0.999948i	$-0.503256\pi$
$373$	−328.734	−	189.794i	−0.881323	−	0.508832i	−0.871094	+	0.491115i	$0.836589\pi$
$374$	−5.61835	−	3.24376i	−0.0150223	−	0.00867315i
$375$		0			0
$376$	−34.3633	−	59.5189i	−0.0913917	−	0.158295i
$377$	−1006.71			−2.67031
$378$		0			0
$379$	−493.432			−1.30193			−0.650966	−	0.759107i	$-0.725636\pi$
$379$	−493.432			−1.30193			−0.650966	+	0.759107i	$0.725636\pi$
$380$	−146.051	−	254.703i	−0.384344	−	0.670271i
$381$		0			0
$382$	231.128	+	133.442i	0.605048	+	0.349325i
$383$	152.151	−	263.534i	0.397262	−	0.688078i	−0.596125	−	0.802892i	$-0.703294\pi$
$383$	152.151	−	263.534i	0.397262	−	0.688078i	0.993387	+	0.114814i	$0.0366271\pi$
$384$		0			0
$385$	56.0909	+	97.8189i	0.145691	+	0.254075i
$386$		−	128.525i		−	0.332967i
$387$		0			0
$388$			238.017i			0.613447i
$389$	391.427	−	225.990i	1.00624	−	0.580952i	0.0961507	−	0.995367i	$-0.469347\pi$
$389$	391.427	−	225.990i	1.00624	−	0.580952i	0.910088	+	0.414414i	$0.136014\pi$
$390$		0			0
$391$	−9.71845	+	16.8328i	−0.0248554	+	0.0430508i
$392$	19.7415	−	34.1933i	0.0503610	−	0.0872278i
$393$		0			0
$394$	−227.070	−	393.297i	−0.576320	−	0.998216i
$395$	471.050	+	1.39248i	1.19253	+	0.00352526i
$396$		0			0
$397$		−	316.160i		−	0.796373i	−0.917304	−	0.398187i	$-0.869640\pi$
$397$		−	316.160i		−	0.796373i	0.917304	−	0.398187i	$-0.130360\pi$
$398$	−16.0812	−	27.8535i	−0.0404051	−	0.0699836i
$399$		0			0
$400$	−50.5111	+	86.3054i	−0.126278	+	0.215764i
$401$	66.1508	+	38.1922i	0.164964	+	0.0952423i	0.580209	−	0.814467i	$-0.302971\pi$
$401$	66.1508	+	38.1922i	0.164964	+	0.0952423i	−0.415245	+	0.909710i	$0.636304\pi$
$402$		0			0
$403$	−842.739	+	486.556i	−2.09116	+	1.20733i
$404$		−	47.6009i		−	0.117824i
$405$		0			0
$406$	−379.117			−0.933787
$407$	92.2323	+	159.751i	0.226615	+	0.392509i
$408$		0			0
$409$	216.772	−	375.461i	0.530006	−	0.917997i	−0.469382	−	0.882995i	$-0.655523\pi$
$409$	216.772	−	375.461i	0.530006	−	0.917997i	0.999387	−	0.0350014i	$-0.0111436\pi$
$410$	−16.6346	−	9.66967i	−0.0405722	−	0.0235846i
$411$		0			0
$412$	−7.15103	+	4.12865i	−0.0173569	+	0.0100210i
$413$	−114.773			−0.277901
$414$		0			0
$415$	473.211	+	1.39887i	1.14027	+	0.00337076i
$416$	108.902	−	62.8746i	0.261784	−	0.151141i
$417$		0			0
$418$	136.996	+	79.0947i	0.327742	+	0.189222i
$419$	−137.665	−	79.4807i	−0.328555	−	0.189691i	0.326644	−	0.945147i	$-0.394082\pi$
$419$	−137.665	−	79.4807i	−0.328555	−	0.189691i	−0.655200	+	0.755456i	$0.727415\pi$
$420$		0			0
$421$	16.0331	+	27.7702i	0.0380834	+	0.0659625i	0.884439	−	0.466656i	$-0.154541\pi$
$421$	16.0331	+	27.7702i	0.0380834	+	0.0659625i	−0.846355	+	0.532619i	$0.821208\pi$
$422$	113.026			0.267835
$423$		0			0
$424$	30.6673			0.0723285
$425$	14.8970	+	26.1583i	0.0350517	+	0.0615488i
$426$		0			0
$427$	−94.3220	−	54.4568i	−0.220895	−	0.127534i
$428$	−117.008	+	202.663i	−0.273382	+	0.473512i
$429$		0			0
$430$	−122.595	+	70.2977i	−0.285104	+	0.163483i
$431$			636.866i			1.47765i	0.673898	+	0.738824i	$0.264619\pi$
$431$			636.866i			1.47765i	−0.673898	+	0.738824i	$0.735381\pi$
$432$		0			0
$433$		−	594.793i		−	1.37366i	−0.726820	−	0.686828i	$-0.759003\pi$
$433$		−	594.793i		−	1.37366i	0.726820	−	0.686828i	$-0.240997\pi$
$434$	−317.369	+	183.233i	−0.731265	+	0.422196i
$435$		0			0
$436$	84.3413	−	146.083i	0.193443	−	0.335054i
$437$	236.971	−	410.447i	0.542269	−	0.939237i
$438$		0			0
$439$	253.860	+	439.699i	0.578269	+	1.00159i	0.995678	+	0.0928725i	$0.0296049\pi$
$439$	253.860	+	439.699i	0.578269	+	1.00159i	−0.417409	+	0.908719i	$0.637062\pi$
$440$	0.159269	−	53.8779i	0.000361976	−	0.122450i
$441$		0			0
$442$		−	37.8539i		−	0.0856423i
$443$	−340.505	−	589.771i	−0.768633	−	1.33131i	−0.938304	−	0.345811i	$-0.887604\pi$
$443$	−340.505	−	589.771i	−0.768633	−	1.33131i	0.169671	−	0.985501i	$-0.445730\pi$
$444$		0			0
$445$	−573.474	−	333.360i	−1.28871	−	0.749123i
$446$	−80.4159	−	46.4281i	−0.180305	−	0.104099i
$447$		0			0
$448$	41.0116	−	23.6781i	0.0915437	−	0.0528528i
$449$		−	273.889i		−	0.609998i	−0.952353	−	0.304999i	$-0.901344\pi$
$449$		−	273.889i		−	0.609998i	0.952353	−	0.304999i	$-0.0986561\pi$
$450$		0			0
$451$	10.3666			0.0229859
$452$	−80.1454	−	138.816i	−0.177313	−	0.307115i
$453$		0			0
$454$	−260.006	+	450.344i	−0.572701	+	0.991947i
$455$	−330.653	+	568.818i	−0.726710	+	1.25015i
$456$		0			0
$457$	176.210	−	101.735i	0.385580	−	0.222615i	−0.294663	−	0.955601i	$-0.595208\pi$
$457$	176.210	−	101.735i	0.385580	−	0.222615i	0.680243	+	0.732987i	$0.261874\pi$
$458$	423.757			0.925233
$459$		0			0
$460$	−161.421	−	0.477178i	−0.350915	−	0.00103734i
$461$	−732.738	+	423.046i	−1.58945	+	0.917671i	−0.596056	+	0.802943i	$0.703266\pi$
$461$	−732.738	+	423.046i	−1.58945	+	0.917671i	−0.993397	+	0.114728i	$0.963400\pi$
$462$		0			0
$463$	−380.771	−	219.838i	−0.822400	−	0.474813i	0.0288431	−	0.999584i	$-0.490818\pi$
$463$	−380.771	−	219.838i	−0.822400	−	0.474813i	−0.851244	+	0.524771i	$0.824151\pi$
$464$	156.878	+	90.5738i	0.338100	+	0.195202i
$465$		0			0
$466$	160.675	+	278.297i	0.344795	+	0.597203i
$467$	14.0853			0.0301612			0.0150806	−	0.999886i	$-0.495200\pi$
$467$	14.0853			0.0301612			0.0150806	+	0.999886i	$0.495200\pi$
$468$		0			0
$469$	492.083			1.04922
$470$	−85.4679	−	149.051i	−0.181847	−	0.317129i
$471$		0			0
$472$	47.4931	+	27.4201i	0.100621	+	0.0580935i
$473$	38.0702	−	65.9395i	0.0804866	−	0.139407i
$474$		0			0
$475$	−363.243	−	637.834i	−0.764721	−	1.34281i
$476$		−	14.2555i		−	0.0299485i
$477$		0			0
$478$		−	268.443i		−	0.561597i
$479$	−339.132	+	195.798i	−0.708001	+	0.408765i	−0.810320	−	0.585987i	$-0.800707\pi$
$479$	−339.132	+	195.798i	−0.708001	+	0.408765i	0.102319	+	0.994752i	$0.467374\pi$
$480$		0			0
$481$	−538.166	+	932.130i	−1.11885	+	1.93790i
$482$	64.3154	−	111.397i	0.133434	−	0.231115i
$483$		0			0
$484$	−106.486	−	184.439i	−0.220012	−	0.381072i
$485$	−1.75901	+	595.041i	−0.00362682	+	1.22689i
$486$		0			0
$487$			881.169i			1.80938i	0.426069	+	0.904691i	$0.359898\pi$
$487$			881.169i			1.80938i	−0.426069	+	0.904691i	$0.640102\pi$
$488$	26.0202	+	45.0684i	0.0533202	+	0.0923532i
$489$		0			0
$490$	49.6062	−	85.3369i	0.101237	−	0.174157i
$491$	−304.525	−	175.818i	−0.620214	−	0.358081i	0.156738	−	0.987640i	$-0.449902\pi$
$491$	−304.525	−	175.818i	−0.620214	−	0.358081i	−0.776952	+	0.629560i	$0.783235\pi$
$492$		0			0
$493$	47.2247	−	27.2652i	0.0957904	−	0.0553046i
$494$			923.017i			1.86846i
$495$		0			0
$496$	175.103			0.353029
$497$	360.452	+	624.321i	0.725255	+	1.25618i
$498$		0			0
$499$	240.926	−	417.296i	0.482817	−	0.836264i	−0.516988	−	0.855993i	$-0.672947\pi$
$499$	240.926	−	417.296i	0.482817	−	0.836264i	0.999805	+	0.0197284i	$0.00628015\pi$
$500$	−126.915	+	215.389i	−0.253830	+	0.430779i
$501$		0			0
$502$	472.801	−	272.972i	0.941835	−	0.543769i
$503$	670.477			1.33296			0.666478	−	0.745525i	$-0.267801\pi$
$503$	670.477			1.33296			0.666478	+	0.745525i	$0.267801\pi$
$504$		0			0
$505$	0.351783	−	119.002i	0.000696600	−	0.235647i
$506$	75.3190	−	43.4854i	0.148852	−	0.0859396i
$507$		0			0
$508$	−158.186	−	91.3285i	−0.311389	−	0.179781i
$509$	−9.57115	−	5.52591i	−0.0188038	−	0.0108564i	0.490569	−	0.871403i	$-0.336789\pi$
$509$	−9.57115	−	5.52591i	−0.0188038	−	0.0108564i	−0.509372	+	0.860546i	$0.670122\pi$
$510$		0			0
$511$	−311.117	−	538.871i	−0.608840	−	1.05454i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	489.765			0.952849
$515$	−17.9080	+	10.2687i	−0.0347728	+	0.0199393i
$516$		0			0
$517$	80.1692	+	46.2857i	0.155066	+	0.0895275i
$518$	−202.669	+	351.033i	−0.391252	+	0.677669i
$519$		0			0
$520$	272.718	−	156.381i	0.524458	−	0.300733i
$521$			534.980i			1.02683i	0.858140	+	0.513416i	$0.171620\pi$
$521$			534.980i			1.02683i	−0.858140	+	0.513416i	$0.828380\pi$
$522$		0			0
$523$		−	615.393i		−	1.17666i	−0.808621	−	0.588330i	$-0.799786\pi$
$523$		−	615.393i		−	1.17666i	0.808621	−	0.588330i	$-0.200214\pi$
$524$	−394.819	+	227.949i	−0.753472	+	0.435017i
$525$		0			0
$526$	306.511	−	530.892i	0.582720	−	1.00930i
$527$	26.3553	−	45.6488i	0.0500101	−	0.0866200i
$528$		0			0
$529$	134.216	+	232.468i	0.253716	+	0.439448i
$530$	76.6679	+	0.226639i	0.144656	+	0.000427621i
$531$		0			0
$532$			347.601i			0.653385i
$533$	30.2441	+	52.3843i	0.0567432	+	0.0982820i
$534$		0			0
$535$	−294.016	+	505.791i	−0.549562	+	0.945404i
$536$	−203.623	−	117.562i	−0.379894	−	0.219332i
$537$		0			0
$538$	559.439	−	322.992i	1.03985	−	0.600357i
$539$			53.1818i			0.0986675i
$540$		0			0
$541$	−479.872			−0.887010			−0.443505	−	0.896272i	$-0.646265\pi$
$541$	−479.872			−0.887010			−0.443505	+	0.896272i	$0.646265\pi$
$542$	−227.365	−	393.808i	−0.419493	−	0.726583i
$543$		0			0
$544$	−3.40573	+	5.89890i	−0.00626054	+	0.0108436i
$545$	211.932	−	364.584i	0.388866	−	0.668961i
$546$		0			0
$547$	−307.990	+	177.818i	−0.563053	+	0.325079i	−0.754370	−	0.656449i	$-0.772058\pi$
$547$	−307.990	+	177.818i	−0.563053	+	0.325079i	0.191317	+	0.981528i	$0.438724\pi$
$548$	245.438			0.447879
$549$		0			0
$550$	0.796343	−	134.693i	0.00144790	−	0.244896i
$551$	−1151.51	+	664.825i	−2.08986	+	1.20658i
$552$		0			0
$553$	−482.965	−	278.840i	−0.873355	−	0.504232i
$554$	405.937	+	234.368i	0.732738	+	0.423047i
$555$		0			0
$556$	38.4803	+	66.6498i	0.0692091	+	0.119874i
$557$	267.691			0.480595			0.240297	−	0.970699i	$-0.422755\pi$
$557$	267.691			0.480595			0.240297	+	0.970699i	$0.422755\pi$
$558$		0			0
$559$	444.270			0.794759
$560$	102.704	−	58.8918i	0.183399	−	0.105164i
$561$		0			0
$562$	579.547	+	334.601i	1.03122	+	0.595376i
$563$	−120.511	+	208.731i	−0.214052	+	0.370749i	−0.952979	−	0.303037i	$-0.901999\pi$
$563$	−120.511	+	208.731i	−0.214052	+	0.370749i	0.738927	+	0.673785i	$0.235333\pi$
$564$		0			0
$565$	−199.337	−	347.631i	−0.352808	−	0.615275i
$566$			42.9823i			0.0759404i
$567$		0			0
$568$		−	344.458i		−	0.606440i
$569$	−48.7478	+	28.1445i	−0.0856727	+	0.0494632i	−0.542224	−	0.840234i	$-0.682418\pi$
$569$	−48.7478	+	28.1445i	−0.0856727	+	0.0494632i	0.456552	+	0.889697i	$0.349084\pi$
$570$		0			0
$571$	191.424	−	331.556i	0.335243	−	0.580658i	−0.648288	−	0.761395i	$-0.724515\pi$
$571$	191.424	−	331.556i	0.335243	−	0.580658i	0.983531	+	0.180737i	$0.0578482\pi$
$572$	−84.6891	+	146.686i	−0.148058	+	0.256444i
$573$		0			0
$574$	11.3897	+	19.7275i	0.0198427	+	0.0343685i
$575$	−403.547	−	2.38588i	−0.701820	−	0.00414936i
$576$		0			0
$577$		−	114.953i		−	0.199225i	−0.995026	−	0.0996126i	$-0.968240\pi$
$577$		−	114.953i		−	0.199225i	0.995026	−	0.0996126i	$-0.0317603\pi$
$578$	−203.329	−	352.176i	−0.351780	−	0.609300i
$579$		0			0
$580$	391.525	+	227.593i	0.675043	+	0.392402i
$581$	−485.181	−	280.119i	−0.835079	−	0.482133i
$582$		0			0
$583$	−35.7733	+	20.6537i	−0.0613607	+	0.0354266i
$584$			297.313i			0.509097i
$585$		0			0
$586$	−35.3783			−0.0603725
$587$	−243.848	−	422.357i	−0.415414	−	0.719518i	0.580058	−	0.814575i	$-0.303030\pi$
$587$	−243.848	−	422.357i	−0.415414	−	0.719518i	−0.995472	+	0.0950571i	$0.969697\pi$
$588$		0			0
$589$	−642.639	+	1113.08i	−1.09107	+	1.88979i
$590$	118.529	+	68.9010i	0.200897	+	0.116781i
$591$		0			0
$592$	167.728	−	96.8380i	0.283325	−	0.163578i
$593$	−631.323			−1.06463			−0.532313	−	0.846548i	$-0.678677\pi$
$593$	−631.323			−1.06463			−0.532313	+	0.846548i	$0.678677\pi$
$594$		0			0
$595$	0.105352	−	35.6385i	0.000177062	−	0.0598967i
$596$	12.9812	−	7.49468i	0.0217805	−	0.0125750i
$597$		0			0
$598$	439.478	+	253.733i	0.734913	+	0.424302i
$599$	607.509	+	350.745i	1.01421	+	0.585552i	0.912420	−	0.409255i	$-0.134211\pi$
$599$	607.509	+	350.745i	1.01421	+	0.585552i	0.101785	+	0.994806i	$0.467545\pi$
$600$		0			0
$601$	−200.165	−	346.696i	−0.333053	−	0.576865i	0.650056	−	0.759886i	$-0.274745\pi$
$601$	−200.165	−	346.696i	−0.333053	−	0.576865i	−0.983109	+	0.183022i	$0.941412\pi$
$602$	167.309			0.277921
$603$		0			0
$604$	434.466			0.719315
$605$	−264.850	−	461.882i	−0.437769	−	0.763441i
$606$		0			0
$607$	251.522	+	145.216i	0.414368	+	0.239236i	0.692665	−	0.721259i	$-0.256436\pi$
$607$	251.522	+	145.216i	0.414368	+	0.239236i	−0.278297	+	0.960495i	$0.589770\pi$
$608$	83.0443	−	143.837i	0.136586	−	0.236574i
$609$		0			0
$610$	64.7172	+	112.863i	0.106094	+	0.185021i
$611$			540.144i			0.884033i
$612$		0			0
$613$		−	177.921i		−	0.290247i	−0.989414	−	0.145123i	$-0.953642\pi$
$613$		−	177.921i		−	0.290247i	0.989414	−	0.145123i	$-0.0463579\pi$
$614$	−730.318	+	421.649i	−1.18944	+	0.686725i
$615$		0			0
$616$	−31.8932	+	55.2407i	−0.0517747	+	0.0896765i
$617$	232.716	−	403.076i	0.377173	−	0.653284i	−0.613476	−	0.789713i	$-0.710229\pi$
$617$	232.716	−	403.076i	0.377173	−	0.653284i	0.990650	+	0.136429i	$0.0435627\pi$
$618$		0			0
$619$	−282.251	−	488.872i	−0.455978	−	0.789778i	0.542766	−	0.839884i	$-0.317377\pi$
$619$	−282.251	−	488.872i	−0.455978	−	0.789778i	−0.998744	+	0.0501067i	$0.984044\pi$
$620$	437.755	+	1.29405i	0.706056	+	0.00208718i
$621$		0			0
$622$			76.7988i			0.123471i
$623$	392.657	+	680.101i	0.630267	+	1.09166i
$624$		0			0
$625$	−318.878	+	537.533i	−0.510205	+	0.860053i
$626$	197.709	+	114.148i	0.315830	+	0.182344i
$627$		0			0
$628$	−307.157	+	177.337i	−0.489103	+	0.282384i
$629$		−	58.3017i		−	0.0926896i
$630$		0			0
$631$	696.074			1.10313			0.551564	−	0.834133i	$-0.314031\pi$
$631$	696.074			1.10313			0.551564	+	0.834133i	$0.314031\pi$
$632$	133.234	+	230.768i	0.210813	+	0.365139i
$633$		0			0
$634$	−192.745	+	333.845i	−0.304015	+	0.526569i
$635$	−394.787	−	229.489i	−0.621712	−	0.361400i
$636$		0			0
$637$	−268.736	+	155.155i	−0.421878	+	0.243571i
$638$	−243.997			−0.382441
$639$		0			0
$640$	−56.5683	−	0.167222i	−0.0883880	−	0.000261285i
$641$	−282.197	+	162.927i	−0.440245	+	0.254176i	−0.703702	−	0.710495i	$-0.748471\pi$
$641$	−282.197	+	162.927i	−0.440245	+	0.254176i	0.263456	+	0.964671i	$0.415138\pi$
$642$		0			0
$643$	93.9907	+	54.2656i	0.146175	+	0.0843944i	0.571304	−	0.820739i	$-0.306438\pi$
$643$	93.9907	+	54.2656i	0.146175	+	0.0843944i	−0.425129	+	0.905133i	$0.639771\pi$
$644$	165.504	+	95.5537i	0.256993	+	0.148375i
$645$		0			0
$646$	−24.9986	−	43.2988i	−0.0386975	−	0.0670260i
$647$	−895.382			−1.38390			−0.691949	−	0.721946i	$-0.743248\pi$
$647$	−895.382			−1.38390			−0.691949	+	0.721946i	$0.743248\pi$
$648$		0			0
$649$	−73.8673			−0.113817
$650$	682.949	−	388.935i	1.05069	−	0.598362i
$651$		0			0
$652$	73.8981	+	42.6651i	0.113341	+	0.0654373i
$653$	−46.6767	+	80.8464i	−0.0714804	+	0.123808i	−0.899550	−	0.436817i	$-0.856106\pi$
$653$	−46.6767	+	80.8464i	−0.0714804	+	0.123808i	0.828070	+	0.560625i	$0.189439\pi$
$654$		0			0
$655$	−988.728	+	566.952i	−1.50951	+	0.865575i
$656$		−	10.8843i		−	0.0165919i
$657$		0			0
$658$			203.414i			0.309140i
$659$	893.384	−	515.795i	1.35567	−	0.782694i	0.366630	−	0.930367i	$-0.380512\pi$
$659$	893.384	−	515.795i	1.35567	−	0.782694i	0.989036	+	0.147673i	$0.0471783\pi$
$660$		0			0
$661$	432.759	−	749.561i	0.654704	−	1.13398i	−0.327264	−	0.944933i	$-0.606127\pi$
$661$	432.759	−	749.561i	0.654704	−	1.13398i	0.981968	−	0.189048i	$-0.0605401\pi$
$662$	−373.856	+	647.538i	−0.564738	+	0.978155i
$663$		0			0
$664$	133.845	+	231.826i	0.201574	+	0.349136i
$665$	−2.56886	+	868.998i	−0.00386295	+	1.30676i
$666$		0			0
$667$			731.028i			1.09599i
$668$	73.9872	+	128.150i	0.110759	+	0.191841i
$669$		0			0
$670$	−508.187	−	295.409i	−0.758489	−	0.440908i
$671$	−60.7050	−	35.0480i	−0.0904694	−	0.0522326i
$672$		0			0
$673$	594.810	−	343.414i	0.883819	−	0.510273i	0.0119032	−	0.999929i	$-0.496211\pi$
$673$	594.810	−	343.414i	0.883819	−	0.510273i	0.871916	+	0.489656i	$0.162878\pi$
$674$			551.342i			0.818014i
$675$		0			0
$676$	−650.303			−0.961987
$677$	390.040	+	675.569i	0.576130	+	0.997887i	0.995918	+	0.0902643i	$0.0287712\pi$
$677$	390.040	+	675.569i	0.576130	+	0.997887i	−0.419788	+	0.907622i	$0.637895\pi$
$678$		0			0
$679$	352.237	−	610.092i	0.518758	−	0.898515i
$680$	−8.55789	+	14.7220i	−0.0125851	+	0.0216500i
$681$		0			0
$682$	−204.256	+	117.927i	−0.299496	+	0.172914i
$683$	−285.666			−0.418252			−0.209126	−	0.977889i	$-0.567062\pi$
$683$	−285.666			−0.418252			−0.209126	+	0.977889i	$0.567062\pi$
$684$		0			0
$685$	613.591	+	1.81385i	0.895754	+	0.00264795i
$686$	−456.449	+	263.531i	−0.665377	+	0.384156i
$687$		0			0
$688$	−69.2322	−	39.9712i	−0.100628	−	0.0580977i
$689$	−208.733	−	120.512i	−0.302951	−	0.174909i
$690$		0			0
$691$	−32.8975	−	56.9801i	−0.0476085	−	0.0824603i	0.841239	−	0.540663i	$-0.181827\pi$
$691$	−32.8975	−	56.9801i	−0.0476085	−	0.0824603i	−0.888848	+	0.458203i	$0.848493\pi$
$692$	−307.491			−0.444351
$693$		0			0
$694$	−170.274			−0.245352
$695$	95.7077	+	166.908i	0.137709	+	0.240156i
$696$		0			0
$697$	−2.83751	−	1.63824i	−0.00407103	−	0.00235041i
$698$	387.689	−	671.496i	0.555428	−	0.962029i
$699$		0			0
$700$	257.193	−	146.470i	0.367418	−	0.209243i
$701$		−	736.516i		−	1.05067i	−0.850897	−	0.525333i	$-0.823941\pi$
$701$		−	736.516i		−	1.05067i	0.850897	−	0.525333i	$-0.176059\pi$
$702$		0			0
$703$			1421.61i			2.02221i
$704$	26.3948	−	15.2390i	0.0374926	−	0.0216464i
$705$		0			0
$706$	−207.419	+	359.261i	−0.293795	+	0.508868i
$707$	−70.4436	+	122.012i	−0.0996373	+	0.172577i
$708$		0			0
$709$	291.126	+	504.245i	0.410615	+	0.711207i	0.994957	−	0.100301i	$-0.0319806\pi$
$709$	291.126	+	504.245i	0.410615	+	0.711207i	−0.584342	+	0.811508i	$0.698647\pi$
$710$	2.54563	−	861.141i	0.00358540	−	1.21287i
$711$		0			0
$712$		−	375.234i		−	0.527014i
$713$	353.316	+	611.962i	0.495535	+	0.858292i
$714$		0			0
$715$	−212.806	+	366.087i	−0.297631	+	0.512010i
$716$	506.571	+	292.469i	0.707501	+	0.408476i
$717$		0			0
$718$	−19.4389	+	11.2230i	−0.0270736	+	0.0156310i
$719$		−	256.052i		−	0.356123i	−0.984019	−	0.178061i	$-0.943017\pi$
$719$		−	256.052i		−	0.356123i	0.984019	−	0.178061i	$-0.0569826\pi$
$720$		0			0
$721$	24.4396			0.0338968
$722$	354.292	+	613.651i	0.490709	+	0.849932i
$723$		0			0
$724$	−45.0019	+	77.9455i	−0.0621573	+	0.107660i
$725$	977.127	+	571.873i	1.34776	+	0.788791i
$726$		0			0
$727$	−64.1741	+	37.0509i	−0.0882724	+	0.0509641i	−0.543486	−	0.839418i	$-0.682896\pi$
$727$	−64.1741	+	37.0509i	−0.0882724	+	0.0509641i	0.455214	+	0.890382i	$0.349563\pi$
$728$	−372.187			−0.511246
$729$		0			0
$730$	−2.19722	+	743.278i	−0.00300989	+	1.01819i
$731$	−20.8408	+	12.0324i	−0.0285099	+	0.0164602i
$732$		0			0
$733$	202.116	+	116.692i	0.275738	+	0.159197i	0.631492	−	0.775382i	$-0.282443\pi$
$733$	202.116	+	116.692i	0.275738	+	0.159197i	−0.355754	+	0.934579i	$0.615776\pi$
$734$	−725.763	−	419.020i	−0.988779	−	0.570872i
$735$		0			0
$736$	−45.6569	−	79.0800i	−0.0620338	−	0.107446i
$737$	316.701			0.429717
$738$		0			0
$739$	−541.648			−0.732948			−0.366474	−	0.930428i	$-0.619435\pi$
$739$	−541.648			−0.732948			−0.366474	+	0.930428i	$0.619435\pi$
$740$	420.035	−	240.854i	0.567614	−	0.325479i
$741$		0			0
$742$	−78.6072	−	45.3839i	−0.105940	−	0.0611643i
$743$	421.965	−	730.864i	0.567920	−	0.983667i	−0.428851	−	0.903375i	$-0.641082\pi$
$743$	421.965	−	730.864i	0.567920	−	0.983667i	0.996771	−	0.0802915i	$-0.0255851\pi$
$744$		0			0
$745$	32.5081	−	18.6407i	0.0436351	−	0.0250210i
$746$		−	536.820i		−	0.719597i
$747$		0			0
$748$		−	9.17473i		−	0.0122657i
$749$	599.834	−	346.314i	0.800846	−	0.462369i
$750$		0			0
$751$	−50.8153	+	88.0147i	−0.0676635	+	0.117197i	−0.897872	−	0.440256i	$-0.854888\pi$
$751$	−50.8153	+	88.0147i	−0.0676635	+	0.117197i	0.830209	+	0.557452i	$0.188221\pi$
$752$	48.5970	−	84.1725i	0.0646237	−	0.111931i
$753$		0			0
$754$	−711.849	−	1232.96i	−0.944097	−	1.63522i
$755$	1086.16	+	3.21082i	1.43862	+	0.00425274i
$756$		0			0
$757$		−	456.777i		−	0.603404i	−0.953402	−	0.301702i	$-0.902445\pi$
$757$		−	456.777i		−	0.603404i	0.953402	−	0.301702i	$-0.0975547\pi$
$758$	−348.909	−	604.329i	−0.460302	−	0.797267i
$759$		0			0
$760$	208.673	−	358.977i	0.274569	−	0.472338i
$761$	−38.5440	−	22.2534i	−0.0506492	−	0.0292423i	0.474462	−	0.880276i	$-0.342643\pi$
$761$	−38.5440	−	22.2534i	−0.0506492	−	0.0292423i	−0.525111	+	0.851034i	$0.675976\pi$
$762$		0			0
$763$	−432.372	+	249.630i	−0.566673	+	0.327169i
$764$			377.431i			0.494020i
$765$		0			0
$766$	430.349			0.561813
$767$	−215.504	−	373.263i	−0.280970	−	0.486653i
$768$		0			0
$769$	125.075	−	216.637i	0.162647	−	0.281712i	−0.773171	−	0.634198i	$-0.781330\pi$
$769$	125.075	−	216.637i	0.162647	−	0.281712i	0.935817	+	0.352486i	$0.114664\pi$
$770$	−80.1410	+	137.865i	−0.104079	+	0.179046i
$771$		0			0
$772$	157.410	−	90.8810i	0.203900	−	0.117721i
$773$	−1059.49			−1.37063			−0.685313	−	0.728249i	$-0.740334\pi$
$773$	−1059.49			−1.37063			−0.685313	+	0.728249i	$0.740334\pi$
$774$		0			0
$775$	1094.37	+	6.47024i	1.41209	+	0.00834869i
$776$	−291.511	+	168.304i	−0.375658	+	0.216886i
$777$		0			0
$778$	553.561	+	319.599i	0.711518	+	0.410795i
$779$	69.1888	+	39.9462i	0.0888175	+	0.0512788i
$780$		0			0
$781$	231.984	+	401.809i	0.297035	+	0.514480i
$782$	−27.4879			−0.0351508
$783$		0			0
$784$	55.8374			0.0712212
$785$	−769.199	+	441.070i	−0.979871	+	0.561873i
$786$		0			0
$787$	−707.755	−	408.623i	−0.899308	−	0.519216i	−0.0223324	−	0.999751i	$-0.507109\pi$
$787$	−707.755	−	408.623i	−0.899308	−	0.519216i	−0.876976	+	0.480535i	$0.840443\pi$
$788$	321.126	−	556.206i	0.407520	−	0.705845i
$789$		0			0
$790$	331.377	+	577.901i	0.419465	+	0.731520i
$791$			474.422i			0.599775i
$792$		0			0
$793$		−	409.003i		−	0.515767i
$794$	387.216	−	223.559i	0.487677	−	0.281561i
$795$		0			0
$796$	22.7423	−	39.3908i	0.0285707	−	0.0494859i
$797$	532.481	−	922.285i	0.668107	−	1.15720i	−0.310326	−	0.950630i	$-0.600438\pi$
$797$	532.481	−	922.285i	0.668107	−	1.15720i	0.978433	−	0.206565i	$-0.0662286\pi$
$798$		0			0
$799$	−14.6290	−	25.3382i	−0.0183092	−	0.0317124i
$800$	−141.419	−	0.836109i	−0.176774	−	0.00104514i
$801$		0			0
$802$			108.024i			0.134693i
$803$	−200.233	−	346.814i	−0.249356	−	0.431898i
$804$		0			0
$805$	413.051	+	240.106i	0.513107	+	0.298269i
$806$	−1191.81	−	688.094i	−1.47868	−	0.853714i
$807$		0			0
$808$	58.2990	−	33.6589i	0.0721522	−	0.0416571i
$809$		−	417.926i		−	0.516595i	−0.966065	−	0.258298i	$-0.916838\pi$
$809$		−	417.926i		−	0.516595i	0.966065	−	0.258298i	$-0.0831615\pi$
$810$		0			0
$811$	−993.633			−1.22519			−0.612597	−	0.790395i	$-0.709875\pi$
$811$	−993.633			−1.22519			−0.612597	+	0.790395i	$0.709875\pi$
$812$	−268.077	−	464.322i	−0.330144	−	0.571825i
$813$		0			0
$814$	−130.436	+	225.922i	−0.160241	+	0.277546i
$815$	184.429	+	107.208i	0.226294	+	0.131544i
$816$		0			0
$817$	508.174	−	293.394i	0.622000	−	0.359112i
$818$	613.125			0.749541
$819$		0			0
$820$	0.0804378	−	27.2106i	9.80949e−5	−	0.0331837i
$821$	−581.144	+	335.524i	−0.707849	+	0.408677i	−0.810264	−	0.586065i	$-0.800676\pi$
$821$	−581.144	+	335.524i	−0.707849	+	0.408677i	0.102415	+	0.994742i	$0.467343\pi$
$822$		0			0
$823$	595.952	+	344.073i	0.724122	+	0.418072i	0.816268	−	0.577674i	$-0.196039\pi$
$823$	595.952	+	344.073i	0.724122	+	0.418072i	−0.0921460	+	0.995746i	$0.529373\pi$
$824$	−10.1131	−	5.83879i	−0.0122732	−	0.00708591i
$825$		0			0
$826$	−81.1569	−	140.568i	−0.0982529	−	0.170179i
$827$	904.043			1.09316			0.546580	−	0.837407i	$-0.315930\pi$
$827$	904.043			1.09316			0.546580	+	0.837407i	$0.315930\pi$
$828$		0			0
$829$	−1539.16			−1.85664			−0.928321	−	0.371779i	$-0.878748\pi$
$829$	−1539.16			−1.85664			−0.928321	+	0.371779i	$0.878748\pi$
$830$	332.897	+	580.552i	0.401081	+	0.699460i
$831$		0			0
$832$	154.011	+	88.9181i	0.185109	+	0.106873i
$833$	8.40429	−	14.5567i	0.0100892	−	0.0174750i
$834$		0			0
$835$	184.020	+	320.919i	0.220383	+	0.384334i
$836$			223.714i			0.267600i
$837$		0			0
$838$		−	224.805i		−	0.268264i
$839$	767.579	−	443.162i	0.914874	−	0.528203i	0.0328778	−	0.999459i	$-0.489533\pi$
$839$	767.579	−	443.162i	0.914874	−	0.528203i	0.881996	+	0.471257i	$0.156199\pi$
$840$		0			0
$841$	604.952	−	1047.81i	0.719325	−	1.24591i
$842$	−22.6743	+	39.2730i	−0.0269291	+	0.0466425i
$843$		0			0
$844$	79.9216	+	138.428i	0.0946939	+	0.164015i
$845$	−1625.75	−	4.80591i	−1.92397	−	0.00568747i
$846$		0			0
$847$			630.344i			0.744208i
$848$	21.6851	+	37.5596i	0.0255720	+	0.0442920i
$849$		0			0
$850$	−21.5034	+	36.7417i	−0.0252982	+	0.0432255i
$851$	676.874	+	390.793i	0.795386	+	0.459216i
$852$		0			0
$853$	893.181	−	515.678i	1.04711	−	0.604547i	0.125268	−	0.992123i	$-0.460021\pi$
$853$	893.181	−	515.678i	1.04711	−	0.604547i	0.921838	+	0.387576i	$0.126688\pi$
$854$		−	154.027i		−	0.180360i
$855$		0			0
$856$	−330.948			−0.386621
$857$	−271.764	−	470.710i	−0.317111	−	0.549253i	0.662773	−	0.748821i	$-0.269380\pi$
$857$	−271.764	−	470.710i	−0.317111	−	0.549253i	−0.979884	+	0.199568i	$0.936046\pi$
$858$		0			0
$859$	−181.682	+	314.682i	−0.211504	+	0.366335i	−0.952185	−	0.305521i	$-0.901169\pi$
$859$	−181.682	+	314.682i	−0.211504	+	0.366335i	0.740682	+	0.671856i	$0.234503\pi$
$860$	−172.784	−	100.439i	−0.200912	−	0.116790i
$861$		0			0
$862$	−779.999	+	450.332i	−0.904871	+	0.522427i
$863$	693.976			0.804144			0.402072	−	0.915608i	$-0.368290\pi$
$863$	693.976			0.804144			0.402072	+	0.915608i	$0.368290\pi$
$864$		0			0
$865$	−768.723	−	2.27244i	−0.888697	−	0.00262709i
$866$	728.470	−	420.582i	0.841189	−	0.485661i
$867$		0			0
$868$	−448.827	−	259.131i	−0.517082	−	0.298538i
$869$	−310.833	−	179.460i	−0.357691	−	0.206513i
$870$		0			0
$871$	923.958	+	1600.34i	1.06080	+	1.83736i
$872$	238.553			0.273570
$873$		0			0
$874$	670.256			0.766884
$875$	644.062	−	364.272i	0.736071	−	0.416311i
$876$		0			0
$877$	383.390	+	221.350i	0.437161	+	0.252395i	0.702392	−	0.711790i	$-0.252115\pi$
$877$	383.390	+	221.350i	0.437161	+	0.252395i	−0.265232	+	0.964185i	$0.585449\pi$
$878$	−359.012	+	621.828i	−0.408898	+	0.708232i
$879$		0			0
$880$	66.0993	−	37.9024i	0.0751128	−	0.0430709i
$881$		−	1448.18i		−	1.64379i	−0.569642	−	0.821893i	$-0.692918\pi$
$881$		−	1448.18i		−	1.64379i	0.569642	−	0.821893i	$-0.307082\pi$
$882$		0			0
$883$		−	672.798i		−	0.761946i	−0.924586	−	0.380973i	$-0.875589\pi$
$883$		−	672.798i		−	0.761946i	0.924586	−	0.380973i	$-0.124411\pi$
$884$	46.3614	−	26.7668i	0.0524450	−	0.0302791i
$885$		0			0
$886$	481.546	−	834.063i	0.543506	−	0.941380i
$887$	−444.968	+	770.707i	−0.501655	+	0.868891i	0.498344	+	0.866980i	$0.333942\pi$
$887$	−444.968	+	770.707i	−0.501655	+	0.868891i	−0.999998	+	0.00191164i	$0.999392\pi$
$888$		0			0
$889$	270.310	+	468.191i	0.304061	+	0.526649i
$890$	2.77307	−	938.080i	0.00311581	−	1.05402i
$891$		0			0
$892$		−	131.319i		−	0.147218i
$893$	356.709	+	617.838i	0.399450	+	0.691868i
$894$		0			0
$895$	1264.26	+	734.912i	1.41258	+	0.821131i
$896$	57.9992	+	33.4858i	0.0647312	+	0.0373726i
$897$		0			0
$898$	335.444	−	193.669i	0.373546	−	0.215667i
$899$		−	1982.46i		−	2.20519i
$900$		0			0
$901$	13.0556			0.0144901
$902$	7.33032	+	12.6965i	0.00812674	+	0.0140759i
$903$		0			0
$904$	113.343	−	196.315i	0.125379	−	0.217163i
$905$	−113.080	+	194.530i	−0.124951	+	0.214951i
$906$		0			0
$907$	261.396	−	150.917i	0.288199	−	0.166392i	−0.348930	−	0.937149i	$-0.613455\pi$
$907$	261.396	−	150.917i	0.288199	−	0.166392i	0.637129	+	0.770757i	$0.280122\pi$
$908$	−735.409			−0.809921
$909$		0			0
$910$	−930.463	−	2.75056i	−1.02249	−	0.00302259i
$911$	1186.55	−	685.053i	1.30247	−	0.751979i	0.321640	−	0.946862i	$-0.395766\pi$
$911$	1186.55	−	685.053i	1.30247	−	0.751979i	0.980827	+	0.194883i	$0.0624326\pi$
$912$		0			0
$913$	−312.259	−	180.283i	−0.342014	−	0.197462i
$914$	249.198	+	143.875i	0.272646	+	0.157412i
$915$		0			0
$916$	299.641	+	518.994i	0.327119	+	0.566587i
$917$	1349.35			1.47148
$918$		0			0
$919$	−228.522			−0.248664			−0.124332	−	0.992241i	$-0.539679\pi$
$919$	−228.522			−0.248664			−0.124332	+	0.992241i	$0.539679\pi$
$920$	−113.557	−	198.037i	−0.123432	−	0.215257i
$921$		0			0
$922$	−1036.25	−	598.278i	−1.12391	−	0.648891i
$923$	−1353.60	+	2344.51i	−1.46652	+	2.54010i
$924$		0			0
$925$	1051.86	−	599.029i	1.13715	−	0.647599i
$926$		−	621.797i		−	0.671487i
$927$		0			0
$928$			256.181i			0.276058i
$929$	273.889	−	158.130i	0.294821	−	0.170215i	−0.345293	−	0.938495i	$-0.612220\pi$
$929$	273.889	−	158.130i	0.294821	−	0.170215i	0.640114	+	0.768280i	$0.278887\pi$
$930$		0			0
$931$	−204.927	+	354.945i	−0.220115	+	0.381251i
$932$	−227.228	+	393.571i	−0.243807	+	0.422286i
$933$		0			0
$934$	9.95981	+	17.2509i	0.0106636	+	0.0184699i
$935$	0.0678036	−	22.9367i	7.25172e−5	−	0.0245313i
$936$		0			0
$937$		−	1277.28i		−	1.36315i	−0.731746	−	0.681577i	$-0.761294\pi$
$937$		−	1277.28i		−	1.36315i	0.731746	−	0.681577i	$-0.238706\pi$
$938$	347.955	+	602.676i	0.370954	+	0.642512i
$939$		0			0
$940$	122.114	−	210.071i	0.129909	−	0.223480i
$941$	−1393.26	−	804.397i	−1.48061	−	0.854832i	−0.480854	−	0.876801i	$-0.659673\pi$
$941$	−1393.26	−	804.397i	−1.48061	−	0.854832i	−0.999759	+	0.0219687i	$0.993007\pi$
$942$		0			0
$943$	38.0393	−	21.9620i	0.0403386	−	0.0232895i
$944$			77.5558i			0.0821566i
$945$		0			0
$946$	107.679			0.113825
$947$	−793.212	−	1373.88i	−0.837605	−	1.45077i	−0.891892	−	0.452249i	$-0.850622\pi$
$947$	−793.212	−	1373.88i	−0.837605	−	1.45077i	0.0542864	−	0.998525i	$-0.482712\pi$
$948$		0			0
$949$	1168.34	−	2023.62i	1.23113	−	2.13237i
$950$	524.333	−	895.896i	0.551929	−	0.943049i
$951$		0			0
$952$	17.4593	−	10.0801i	0.0183396	−	0.0105884i
$953$	985.215			1.03380			0.516902	−	0.856045i	$-0.327085\pi$
$953$	985.215			1.03380			0.516902	+	0.856045i	$0.327085\pi$
$954$		0			0
$955$	−2.78931	+	943.574i	−0.00292075	+	0.988035i
$956$	328.774	−	189.818i	0.343906	−	0.198554i
$957$		0			0
$958$	−479.606	−	276.901i	−0.500632	−	0.289040i
$959$	−629.112	−	363.218i	−0.656008	−	0.378746i
$960$		0			0
$961$	−477.654	−	827.320i	−0.497038	−	0.860895i
$962$	−1522.16			−1.58229
$963$		0			0
$964$	181.911			0.188705
$965$	394.196	−	226.038i	0.408493	−	0.234236i
$966$		0			0
$967$	−361.961	−	208.979i	−0.374314	−	0.216110i	0.301028	−	0.953615i	$-0.402670\pi$
$967$	−361.961	−	208.979i	−0.374314	−	0.216110i	−0.675341	+	0.737505i	$0.736004\pi$
$968$	150.594	−	260.836i	0.155572	−	0.269458i
$969$		0			0
$970$	−730.017	+	418.603i	−0.752595	+	0.431549i
$971$			685.151i			0.705613i	0.935696	+	0.352807i	$0.114773\pi$
$971$			685.151i			0.705613i	−0.935696	+	0.352807i	$0.885227\pi$
$972$		0			0
$973$		−	227.785i		−	0.234105i
$974$	−1079.21	+	623.080i	−1.10802	+	0.639713i
$975$		0			0
$976$	−36.7982	+	63.7363i	−0.0377030	+	0.0653036i
$977$	−730.930	+	1266.01i	−0.748137	+	1.29581i	0.200578	+	0.979678i	$0.435718\pi$
$977$	−730.930	+	1266.01i	−0.748137	+	1.29581i	−0.948715	+	0.316133i	$0.897615\pi$
$978$		0			0
$979$	252.711	+	437.708i	0.258132	+	0.447097i
$980$	139.593	+	0.412653i	0.142442	+	0.000421074i
$981$		0			0
$982$		−	497.287i		−	0.506402i
$983$	−407.208	−	705.306i	−0.414251	−	0.717503i	0.581099	−	0.813833i	$-0.302623\pi$
$983$	−407.208	−	705.306i	−0.414251	−	0.717503i	−0.995349	+	0.0963298i	$0.969290\pi$
$984$		0			0
$985$	806.921	−	1388.14i	0.819209	−	1.40927i
$986$	66.7858	+	38.5588i	0.0677341	+	0.0391063i
$987$		0			0
$988$	−1130.46	+	652.672i	−1.14419	+	0.660599i
$989$		−	322.610i		−	0.326199i
$990$		0			0
$991$	−594.842			−0.600244			−0.300122	−	0.953901i	$-0.597027\pi$
$991$	−594.842			−0.600244			−0.300122	+	0.953901i	$0.597027\pi$
$992$	123.816	+	214.456i	0.124815	+	0.216185i
$993$		0			0
$994$	−509.756	+	882.923i	−0.512833	+	0.888252i
$995$	57.1465	−	98.3084i	0.0574337	−	0.0988024i
$996$		0			0
$997$	−297.131	+	171.549i	−0.298026	+	0.172065i	−0.641556	−	0.767077i	$-0.721711\pi$
$997$	−297.131	+	171.549i	−0.298026	+	0.172065i	0.343530	+	0.939142i	$0.388377\pi$
$998$	681.441			0.682807
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.g.539.8		24
3.2	odd	2	inner	810.3.j.g.539.2		24
5.4	even	2		810.3.j.h.539.2		24
9.2	odd	6		810.3.j.h.269.2		24
9.4	even	3		810.3.b.c.809.12	yes	24
9.5	odd	6		810.3.b.c.809.13	yes	24
9.7	even	3		810.3.j.h.269.9		24
15.14	odd	2		810.3.j.h.539.8		24
45.4	even	6		810.3.b.c.809.14	yes	24
45.14	odd	6		810.3.b.c.809.11	✓	24
45.29	odd	6	inner	810.3.j.g.269.9		24
45.34	even	6	inner	810.3.j.g.269.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.3.b.c.809.11	✓	24	45.14	odd	6
810.3.b.c.809.12	yes	24	9.4	even	3
810.3.b.c.809.13	yes	24	9.5	odd	6
810.3.b.c.809.14	yes	24	45.4	even	6
810.3.j.g.269.2		24	45.34	even	6	inner
810.3.j.g.269.9		24	45.29	odd	6	inner
810.3.j.g.539.2		24	3.2	odd	2	inner
810.3.j.g.539.8		24	1.1	even	1	trivial
810.3.j.h.269.2		24	9.2	odd	6
810.3.j.h.269.9		24	9.7	even	3
810.3.j.h.539.2		24	5.4	even	2
810.3.j.h.539.8		24	15.14	odd	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-2.51279 + 4.32272i) q^{5} +(5.12645 - 2.95976i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-2.51279 + 4.32272i) q^{5} +(5.12645 - 2.95976i) q^{7} -2.82843 q^{8} +(-7.07104 - 0.0209028i) q^{10} +(3.29935 - 1.90488i) q^{11} +(19.2513 + 11.1148i) q^{13} +(7.24989 + 4.18573i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.20411 q^{17} +29.3606 q^{19} +(-4.97438 - 8.67500i) q^{20} +(4.66598 + 2.69391i) q^{22} +(8.07107 - 13.9795i) q^{23} +(-12.3718 - 21.7242i) q^{25} +31.4373i q^{26} +11.8390i q^{28} +(-39.2196 + 22.6435i) q^{29} +(-21.8878 + 37.9108i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-0.851433 - 1.47473i) q^{34} +(-0.0874935 + 29.5974i) q^{35} +48.4190i q^{37} +(20.7611 + 35.9592i) q^{38} +(7.10724 - 12.2265i) q^{40} +(2.35652 + 1.36054i) q^{41} +(17.3080 - 9.99280i) q^{43} +7.61952i q^{44} +22.8284 q^{46} +(12.1492 + 21.0431i) q^{47} +(-6.97968 + 12.0892i) q^{49} +(17.8584 - 30.5136i) q^{50} +(-38.5027 + 22.2295i) q^{52} -10.8425 q^{53} +(-0.0563102 + 19.0487i) q^{55} +(-14.4998 + 8.37146i) q^{56} +(-55.4649 - 32.0227i) q^{58} +(-16.7913 - 9.69448i) q^{59} +(-9.19954 - 15.9341i) q^{61} -61.9081 q^{62} +8.00000 q^{64} +(-96.4205 + 55.2890i) q^{65} +(71.9917 + 41.5645i) q^{67} +(1.20411 - 2.08558i) q^{68} +(-36.3112 + 20.8214i) q^{70} +121.784i q^{71} -105.116i q^{73} +(-59.3009 + 34.2374i) q^{74} +(-29.3606 + 50.8540i) q^{76} +(11.2760 - 19.5305i) q^{77} +(-47.1052 - 81.5887i) q^{79} +(19.9999 + 0.0591221i) q^{80} +3.84818i q^{82} +(-47.3213 - 81.9629i) q^{83} +(3.02567 - 5.20502i) q^{85} +(24.4773 + 14.1320i) q^{86} +(-9.33197 + 5.38781i) q^{88} +132.665i q^{89} +131.588 q^{91} +(16.1421 + 27.9590i) q^{92} +(-17.1816 + 29.7595i) q^{94} +(-73.7770 + 126.918i) q^{95} +(103.065 - 59.5043i) q^{97} -19.7415 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 24 q^{7}+O(q^{10}) \) 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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