LMFDB - Embedded newform 684.3.s.a.445.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.28
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56710 + 2.55816i) q^{3} +(1.49069 + 2.58196i) q^{5} +(4.88733 + 8.46511i) q^{7} +(-4.08840 + 8.01779i) q^{9} +O(q^{10})$	\(q+(1.56710 + 2.55816i) q^{3} +(1.49069 + 2.58196i) q^{5} +(4.88733 + 8.46511i) q^{7} +(-4.08840 + 8.01779i) q^{9} +(4.58601 + 7.94321i) q^{11} +4.00160i q^{13} +(-4.26900 + 7.85963i) q^{15} +(5.36153 - 9.28644i) q^{17} +(-18.8357 - 2.49349i) q^{19} +(-13.9962 + 25.7683i) q^{21} +14.0694 q^{23} +(8.05566 - 13.9528i) q^{25} +(-26.9177 + 2.10590i) q^{27} +(-6.82419 - 3.93995i) q^{29} +(7.00436 + 4.04397i) q^{31} +(-13.1333 + 24.1796i) q^{33} +(-14.5710 + 25.2378i) q^{35} -64.7492i q^{37} +(-10.2368 + 6.27091i) q^{39} +(-23.0753 + 13.3225i) q^{41} +48.0387 q^{43} +(-26.7962 + 1.39601i) q^{45} +(-46.2868 + 80.1710i) q^{47} +(-23.2720 + 40.3083i) q^{49} +(32.1583 - 0.837116i) q^{51} +(65.3126 - 37.7082i) q^{53} +(-13.6727 + 23.6818i) q^{55} +(-23.1386 - 52.0923i) q^{57} +(27.7279 - 16.0087i) q^{59} +(-31.1994 + 54.0389i) q^{61} +(-87.8528 + 4.57692i) q^{63} +(-10.3320 + 5.96517i) q^{65} -62.3517i q^{67} +(22.0482 + 35.9918i) q^{69} +(-4.44971 - 2.56904i) q^{71} +(-21.4020 + 37.0694i) q^{73} +(48.3176 - 1.25776i) q^{75} +(-44.8267 + 77.6422i) q^{77} +10.6718i q^{79} +(-47.5700 - 65.5598i) q^{81} +(-8.68524 - 15.0433i) q^{83} +31.9696 q^{85} +(-0.615159 - 23.6317i) q^{87} +(-86.5155 + 49.9498i) q^{89} +(-33.8740 + 19.5572i) q^{91} +(0.631400 + 24.2556i) q^{93} +(-21.6401 - 52.3500i) q^{95} -101.970i q^{97} +(-82.4364 + 4.29474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	1.56710	+	2.55816i	0.522367	+	0.852721i
$3$	1.56710	+	2.55816i	0.522367	+	0.852721i
$4$		0			0
$5$	1.49069	+	2.58196i	0.298139	+	0.516392i	0.975710	−	0.219065i	$-0.0703008\pi$
$5$	1.49069	+	2.58196i	0.298139	+	0.516392i	−0.677571	+	0.735457i	$0.736967\pi$
$6$		0			0
$7$	4.88733	+	8.46511i	0.698190	+	1.20930i	0.969093	+	0.246694i	$0.0793443\pi$
$7$	4.88733	+	8.46511i	0.698190	+	1.20930i	−0.270903	+	0.962607i	$0.587322\pi$
$8$		0			0
$9$	−4.08840	+	8.01779i	−0.454266	+	0.890866i
$10$		0			0
$11$	4.58601	+	7.94321i	0.416910	+	0.722110i	0.995627	−	0.0934189i	$-0.0297796\pi$
$11$	4.58601	+	7.94321i	0.416910	+	0.722110i	−0.578717	+	0.815529i	$0.696446\pi$
$12$		0			0
$13$			4.00160i			0.307816i	0.988085	+	0.153908i	$0.0491859\pi$
$13$			4.00160i			0.307816i	−0.988085	+	0.153908i	$0.950814\pi$
$14$		0			0
$15$	−4.26900	+	7.85963i	−0.284600	+	0.523975i
$16$		0			0
$17$	5.36153	−	9.28644i	0.315384	−	0.546261i	−0.664135	−	0.747613i	$-0.731200\pi$
$17$	5.36153	−	9.28644i	0.315384	−	0.546261i	0.979519	+	0.201352i	$0.0645333\pi$
$18$		0			0
$19$	−18.8357	−	2.49349i	−0.991351	−	0.131237i
$19$	−18.8357	−	2.49349i	−0.991351	−	0.131237i
$20$		0			0
$21$	−13.9962	+	25.7683i	−0.666485	+	1.22706i
$22$		0			0
$23$	14.0694			0.611713			0.305857	−	0.952078i	$-0.401057\pi$
$23$	14.0694			0.611713			0.305857	+	0.952078i	$0.401057\pi$
$24$		0			0
$25$	8.05566	−	13.9528i	0.322226	−	0.558112i
$26$		0			0
$27$	−26.9177	+	2.10590i	−0.996954	+	0.0779964i
$28$		0			0
$29$	−6.82419	−	3.93995i	−0.235317	−	0.135860i	0.377706	−	0.925926i	$-0.376713\pi$
$29$	−6.82419	−	3.93995i	−0.235317	−	0.135860i	−0.613022	+	0.790066i	$0.710046\pi$
$30$		0			0
$31$	7.00436	+	4.04397i	0.225947	+	0.130451i	0.608701	−	0.793400i	$-0.291691\pi$
$31$	7.00436	+	4.04397i	0.225947	+	0.130451i	−0.382754	+	0.923850i	$0.625024\pi$
$32$		0			0
$33$	−13.1333	+	24.1796i	−0.397978	+	0.732714i
$34$		0			0
$35$	−14.5710	+	25.2378i	−0.416315	+	0.721079i
$36$		0			0
$37$		−	64.7492i		−	1.74998i	−0.484143	−	0.874989i	$-0.660869\pi$
$37$		−	64.7492i		−	1.74998i	0.484143	−	0.874989i	$-0.339131\pi$
$38$		0			0
$39$	−10.2368	+	6.27091i	−0.262481	+	0.160793i
$40$		0			0
$41$	−23.0753	+	13.3225i	−0.562811	+	0.324939i	−0.754273	−	0.656561i	$-0.772011\pi$
$41$	−23.0753	+	13.3225i	−0.562811	+	0.324939i	0.191462	+	0.981500i	$0.438677\pi$
$42$		0			0
$43$	48.0387			1.11718			0.558590	−	0.829444i	$-0.311343\pi$
$43$	48.0387			1.11718			0.558590	+	0.829444i	$0.311343\pi$
$44$		0			0
$45$	−26.7962	+	1.39601i	−0.595470	+	0.0310225i
$46$		0			0
$47$	−46.2868	+	80.1710i	−0.984825	+	1.70577i	−0.342112	+	0.939659i	$0.611142\pi$
$47$	−46.2868	+	80.1710i	−0.984825	+	1.70577i	−0.642713	+	0.766107i	$0.722191\pi$
$48$		0			0
$49$	−23.2720	+	40.3083i	−0.474939	+	0.822619i
$50$		0			0
$51$	32.1583	−	0.837116i	0.630554	−	0.0164140i
$52$		0			0
$53$	65.3126	−	37.7082i	1.23231	−	0.711476i	0.264801	−	0.964303i	$-0.414694\pi$
$53$	65.3126	−	37.7082i	1.23231	−	0.711476i	0.967512	+	0.252827i	$0.0813604\pi$
$54$		0			0
$55$	−13.6727	+	23.6818i	−0.248594	+	0.430578i
$56$		0			0
$57$	−23.1386	−	52.0923i	−0.405941	−	0.913899i
$58$		0			0
$59$	27.7279	−	16.0087i	0.469964	−	0.271334i	−0.246261	−	0.969204i	$-0.579202\pi$
$59$	27.7279	−	16.0087i	0.469964	−	0.271334i	0.716225	+	0.697870i	$0.245869\pi$
$60$		0			0
$61$	−31.1994	+	54.0389i	−0.511465	+	0.885883i	0.488447	+	0.872594i	$0.337564\pi$
$61$	−31.1994	+	54.0389i	−0.511465	+	0.885883i	−0.999912	+	0.0132895i	$0.995770\pi$
$62$		0			0
$63$	−87.8528	+	4.57692i	−1.39449	+	0.0726494i
$64$		0			0
$65$	−10.3320	+	5.96517i	−0.158953	+	0.0917718i
$66$		0			0
$67$		−	62.3517i		−	0.930622i	−0.885147	−	0.465311i	$-0.845942\pi$
$67$		−	62.3517i		−	0.930622i	0.885147	−	0.465311i	$-0.154058\pi$
$68$		0			0
$69$	22.0482	+	35.9918i	0.319539	+	0.521621i
$70$		0			0
$71$	−4.44971	−	2.56904i	−0.0626720	−	0.0361837i	0.468337	−	0.883550i	$-0.344853\pi$
$71$	−4.44971	−	2.56904i	−0.0626720	−	0.0361837i	−0.531009	+	0.847366i	$0.678187\pi$
$72$		0			0
$73$	−21.4020	+	37.0694i	−0.293178	+	0.507800i	−0.974559	−	0.224129i	$-0.928046\pi$
$73$	−21.4020	+	37.0694i	−0.293178	+	0.507800i	0.681381	+	0.731929i	$0.261380\pi$
$74$		0			0
$75$	48.3176	−	1.25776i	0.644235	−	0.0167701i
$76$		0			0
$77$	−44.8267	+	77.6422i	−0.582165	+	1.00834i
$78$		0			0
$79$			10.6718i			0.135086i	0.997716	+	0.0675428i	$0.0215159\pi$
$79$			10.6718i			0.135086i	−0.997716	+	0.0675428i	$0.978484\pi$
$80$		0			0
$81$	−47.5700	−	65.5598i	−0.587285	−	0.809381i
$82$		0			0
$83$	−8.68524	−	15.0433i	−0.104641	−	0.181244i	0.808950	−	0.587877i	$-0.200036\pi$
$83$	−8.68524	−	15.0433i	−0.104641	−	0.181244i	−0.913592	+	0.406633i	$0.866703\pi$
$84$		0			0
$85$	31.9696			0.376113
$86$		0			0
$87$	−0.615159	−	23.6317i	−0.00707079	−	0.271628i
$88$		0			0
$89$	−86.5155	+	49.9498i	−0.972085	+	0.561233i	−0.899871	−	0.436156i	$-0.856340\pi$
$89$	−86.5155	+	49.9498i	−0.972085	+	0.561233i	−0.0722134	+	0.997389i	$0.523006\pi$
$90$		0			0
$91$	−33.8740	+	19.5572i	−0.372242	+	0.214914i
$92$		0			0
$93$	0.631400	+	24.2556i	0.00678925	+	0.260813i
$94$		0			0
$95$	−21.6401	−	52.3500i	−0.227791	−	0.551052i
$96$		0			0
$97$		−	101.970i		−	1.05123i	−0.850721	−	0.525617i	$-0.823834\pi$
$97$		−	101.970i		−	1.05123i	0.850721	−	0.525617i	$-0.176166\pi$
$98$		0			0
$99$	−82.4364	+	4.29474i	−0.832691	+	0.0433812i
$100$		0			0
$101$	−68.6890	+	118.973i	−0.680089	+	1.17795i	0.294864	+	0.955539i	$0.404726\pi$
$101$	−68.6890	+	118.973i	−0.680089	+	1.17795i	−0.974953	+	0.222409i	$0.928608\pi$
$102$		0			0
$103$	76.8246	+	44.3547i	0.745870	+	0.430628i	0.824200	−	0.566299i	$-0.191625\pi$
$103$	76.8246	+	44.3547i	0.745870	+	0.430628i	−0.0783298	+	0.996927i	$0.524959\pi$
$104$		0			0
$105$	−87.3966	+	2.27503i	−0.832349	+	0.0216670i
$106$		0			0
$107$			76.1669i			0.711840i	0.934516	+	0.355920i	$0.115832\pi$
$107$			76.1669i			0.711840i	−0.934516	+	0.355920i	$0.884168\pi$
$108$		0			0
$109$	27.7998	+	16.0502i	0.255044	+	0.147250i	0.622072	−	0.782960i	$-0.286291\pi$
$109$	27.7998	+	16.0502i	0.255044	+	0.147250i	−0.367028	+	0.930210i	$0.619625\pi$
$110$		0			0
$111$	165.639	−	101.468i	1.49224	−	0.914130i
$112$		0			0
$113$	23.1688	+	13.3765i	0.205034	+	0.118376i	0.599001	−	0.800748i	$-0.295564\pi$
$113$	23.1688	+	13.3765i	0.205034	+	0.118376i	−0.393968	+	0.919124i	$0.628898\pi$
$114$		0			0
$115$	20.9732	+	36.3266i	0.182376	+	0.315884i
$116$		0			0
$117$	−32.0840	−	16.3601i	−0.274223	−	0.139830i
$118$		0			0
$119$	104.814			0.880792
$120$		0			0
$121$	18.4370	−	31.9338i	0.152372	−	0.263915i
$122$		0			0
$123$	−70.2424	−	38.1526i	−0.571076	−	0.310184i
$124$		0			0
$125$	122.569			0.980551
$126$		0			0
$127$	39.4611	−	22.7829i	0.310717	−	0.179393i	−0.336530	−	0.941673i	$-0.609253\pi$
$127$	39.4611	−	22.7829i	0.310717	−	0.179393i	0.647247	+	0.762280i	$0.275920\pi$
$128$		0			0
$129$	75.2815	+	122.891i	0.583577	+	0.952642i
$130$		0			0
$131$	−7.27585	−	12.6021i	−0.0555408	−	0.0961996i	0.836918	−	0.547328i	$-0.184355\pi$
$131$	−7.27585	−	12.6021i	−0.0555408	−	0.0961996i	−0.892459	+	0.451128i	$0.851022\pi$
$132$		0			0
$133$	−70.9485	−	171.632i	−0.533447	−	1.29047i
$134$		0			0
$135$	−45.5635	−	66.3613i	−0.337507	−	0.491565i
$136$		0			0
$137$	2.33265	−	4.04027i	0.0170267	−	0.0294910i	−0.857387	−	0.514673i	$-0.827913\pi$
$137$	2.33265	−	4.04027i	0.0170267	−	0.0294910i	0.874413	+	0.485182i	$0.161247\pi$
$138$		0			0
$139$	35.1589			0.252942			0.126471	−	0.991970i	$-0.459635\pi$
$139$	35.1589			0.252942			0.126471	+	0.991970i	$0.459635\pi$
$140$		0			0
$141$	−277.627	+	7.22693i	−1.96898	+	0.0512548i
$142$		0			0
$143$	−31.7856	+	18.3514i	−0.222277	+	0.128332i
$144$		0			0
$145$		−	23.4930i		−	0.162021i
$146$		0			0
$147$	−139.585	+	3.63355i	−0.949556	+	0.0247180i
$148$		0			0
$149$	65.0176	+	112.614i	0.436360	+	0.755797i	0.997406	−	0.0719877i	$-0.0229342\pi$
$149$	65.0176	+	112.614i	0.436360	+	0.755797i	−0.561046	+	0.827785i	$0.689601\pi$
$150$		0			0
$151$	192.280	−	111.013i	1.27338	−	0.735183i	0.297753	−	0.954643i	$-0.403763\pi$
$151$	192.280	−	111.013i	1.27338	−	0.735183i	0.975622	+	0.219459i	$0.0704293\pi$
$152$		0			0
$153$	52.5367	+	80.9543i	0.343377	+	0.529113i
$154$		0			0
$155$			24.1133i			0.155570i
$156$		0			0
$157$	−56.6694	−	98.1543i	−0.360952	−	0.625187i	0.627166	−	0.778886i	$-0.284215\pi$
$157$	−56.6694	−	98.1543i	−0.360952	−	0.625187i	−0.988118	+	0.153699i	$0.950881\pi$
$158$		0			0
$159$	198.815	+	107.988i	1.25041	+	0.679167i
$160$		0			0
$161$	68.7618	+	119.099i	0.427092	+	0.739745i
$162$		0			0
$163$	108.098			0.663179			0.331589	−	0.943424i	$-0.392415\pi$
$163$	108.098			0.663179			0.331589	+	0.943424i	$0.392415\pi$
$164$		0			0
$165$	−82.0084	+	2.13477i	−0.497020	+	0.0129380i
$166$		0			0
$167$		−	40.6098i		−	0.243172i	−0.992581	−	0.121586i	$-0.961202\pi$
$167$		−	40.6098i		−	0.243172i	0.992581	−	0.121586i	$-0.0387981\pi$
$168$		0			0
$169$	152.987			0.905250
$170$		0			0
$171$	97.0000	−	140.826i	0.567251	−	0.823545i
$172$		0			0
$173$			137.307i			0.793682i	0.917887	+	0.396841i	$0.129894\pi$
$173$			137.307i			0.793682i	−0.917887	+	0.396841i	$0.870106\pi$
$174$		0			0
$175$	157.483			0.899901
$176$		0			0
$177$	84.4052	+	45.8452i	0.476865	+	0.259012i
$178$		0			0
$179$			318.985i			1.78204i	0.453965	+	0.891020i	$0.350009\pi$
$179$			318.985i			1.78204i	−0.453965	+	0.891020i	$0.649991\pi$
$180$		0			0
$181$	−187.463	+	108.232i	−1.03571	+	0.597965i	−0.918614	−	0.395156i	$-0.870690\pi$
$181$	−187.463	+	108.232i	−1.03571	+	0.597965i	−0.117091	+	0.993121i	$0.537357\pi$
$182$		0			0
$183$	−187.133	+	4.87127i	−1.02258	+	0.0266190i
$184$		0			0
$185$	167.180	−	96.5212i	0.903674	−	0.521736i
$186$		0			0
$187$	98.3521			0.525947
$188$		0			0
$189$	−149.383	−	217.569i	−0.790384	−	1.15116i
$190$		0			0
$191$	−64.0496	−	110.937i	−0.335338	−	0.580823i	0.648212	−	0.761460i	$-0.275517\pi$
$191$	−64.0496	−	110.937i	−0.335338	−	0.580823i	−0.983550	+	0.180637i	$0.942184\pi$
$192$		0			0
$193$	−82.0676	+	47.3818i	−0.425221	+	0.245501i	−0.697309	−	0.716771i	$-0.745619\pi$
$193$	−82.0676	+	47.3818i	−0.425221	+	0.245501i	0.272088	+	0.962272i	$0.412286\pi$
$194$		0			0
$195$	−31.4511	−	17.0829i	−0.161288	−	0.0876044i
$196$		0			0
$197$	385.551			1.95711			0.978555	−	0.205988i	$-0.0660407\pi$
$197$	385.551			1.95711			0.978555	+	0.205988i	$0.0660407\pi$
$198$		0			0
$199$	−172.799	−	299.296i	−0.868334	−	1.50400i	−0.863698	−	0.504010i	$-0.831858\pi$
$199$	−172.799	−	299.296i	−0.868334	−	1.50400i	−0.00463619	−	0.999989i	$-0.501476\pi$
$200$		0			0
$201$	159.506	−	97.7114i	0.793561	−	0.486126i
$202$		0			0
$203$		−	77.0233i		−	0.379425i
$204$		0			0
$205$	−68.7963	−	39.7196i	−0.335592	−	0.193754i
$206$		0			0
$207$	−57.5213	+	112.806i	−0.277881	+	0.544955i
$208$		0			0
$209$	−66.5743	−	161.051i	−0.318537	−	0.770578i
$210$		0			0
$211$	160.375	−	92.5928i	0.760073	−	0.438828i	−0.0692489	−	0.997599i	$-0.522060\pi$
$211$	160.375	−	92.5928i	0.760073	−	0.438828i	0.829322	+	0.558771i	$0.188727\pi$
$212$		0			0
$213$	−0.401114	−	15.4090i	−0.00188317	−	0.0723429i
$214$		0			0
$215$	71.6110	+	124.034i	0.333075	+	0.576902i
$216$		0			0
$217$			79.0569i			0.364317i
$218$		0			0
$219$	−128.369	+	3.34158i	−0.586158	+	0.0152583i
$220$		0			0
$221$	37.1606	+	21.4547i	0.168148	+	0.0970801i
$222$		0			0
$223$		−	282.493i		−	1.26678i	−0.773831	−	0.633392i	$-0.781662\pi$
$223$		−	282.493i		−	1.26678i	0.773831	−	0.633392i	$-0.218338\pi$
$224$		0			0
$225$	78.9361	+	121.633i	0.350827	+	0.540592i
$226$		0			0
$227$	307.382	−	177.467i	1.35411	−	0.781794i	0.365286	−	0.930895i	$-0.380971\pi$
$227$	307.382	−	177.467i	1.35411	−	0.781794i	0.988822	+	0.149101i	$0.0476380\pi$
$228$		0			0
$229$	166.122	−	287.731i	0.725423	−	1.25647i	−0.233377	−	0.972386i	$-0.574978\pi$
$229$	166.122	−	287.731i	0.725423	−	1.25647i	0.958800	−	0.284083i	$-0.0916891\pi$
$230$		0			0
$231$	−268.869	+	6.99897i	−1.16394	+	0.0302986i
$232$		0			0
$233$	−202.365	+	350.507i	−0.868519	+	1.50432i	−0.00500979	+	0.999987i	$0.501595\pi$
$233$	−202.365	+	350.507i	−0.868519	+	1.50432i	−0.863510	+	0.504332i	$0.831739\pi$
$234$		0			0
$235$	−275.998			−1.17446
$236$		0			0
$237$	−27.3001	+	16.7237i	−0.115190	+	0.0705642i
$238$		0			0
$239$	12.3824	−	21.4469i	0.0518091	−	0.0897359i	−0.838958	−	0.544196i	$-0.816835\pi$
$239$	12.3824	−	21.4469i	0.0518091	−	0.0897359i	0.890767	+	0.454461i	$0.150168\pi$
$240$		0			0
$241$	−85.5583	−	49.3971i	−0.355014	−	0.204967i	0.311878	−	0.950122i	$-0.399042\pi$
$241$	−85.5583	−	49.3971i	−0.355014	−	0.204967i	−0.666891	+	0.745155i	$0.732375\pi$
$242$		0			0
$243$	93.1657	−	224.431i	0.383398	−	0.923583i
$244$		0			0
$245$	−138.766			−0.566391
$246$		0			0
$247$	9.97798	−	75.3729i	0.0403967	−	0.305153i
$248$		0			0
$249$	24.8725	−	45.7926i	0.0998896	−	0.183906i
$250$		0			0
$251$	78.5808	+	136.106i	0.313071	+	0.542255i	0.979026	−	0.203738i	$-0.0653089\pi$
$251$	78.5808	+	136.106i	0.313071	+	0.542255i	−0.665955	+	0.745992i	$0.731976\pi$
$252$		0			0
$253$	64.5225	+	111.756i	0.255030	+	0.441724i
$254$		0			0
$255$	50.0996	+	81.7835i	0.196469	+	0.320719i
$256$		0			0
$257$		−	326.792i		−	1.27156i	−0.771869	−	0.635782i	$-0.780678\pi$
$257$		−	326.792i		−	1.27156i	0.771869	−	0.635782i	$-0.219322\pi$
$258$		0			0
$259$	548.109	−	316.451i	2.11625	−	1.22182i
$260$		0			0
$261$	59.4897	−	38.6069i	0.227930	−	0.147919i
$262$		0			0
$263$	279.340			1.06213			0.531064	−	0.847332i	$-0.321792\pi$
$263$	279.340			1.06213			0.531064	+	0.847332i	$0.321792\pi$
$264$		0			0
$265$	194.722	+	112.423i	0.734801	+	0.424237i
$266$		0			0
$267$	−263.358	−	143.045i	−0.986360	−	0.535747i
$268$		0			0
$269$	332.826	+	192.157i	1.23727	+	0.714338i	0.968535	−	0.248876i	$-0.0800611\pi$
$269$	332.826	+	192.157i	1.23727	+	0.714338i	0.268735	+	0.963214i	$0.413394\pi$
$270$		0			0
$271$	222.947	−	386.155i	0.822681	−	1.42493i	−0.0809979	−	0.996714i	$-0.525811\pi$
$271$	222.947	−	386.155i	0.822681	−	1.42493i	0.903679	−	0.428211i	$-0.140856\pi$
$272$		0			0
$273$	−103.114	−	56.0072i	−0.377708	−	0.205155i
$274$		0			0
$275$	147.773			0.537358
$276$		0			0
$277$	−235.314	−	407.576i	−0.849509	−	1.47139i	−0.881647	−	0.471909i	$-0.843565\pi$
$277$	−235.314	−	407.576i	−0.849509	−	1.47139i	0.0321383	−	0.999483i	$-0.489768\pi$
$278$		0			0
$279$	−61.0603	+	39.6262i	−0.218854	+	0.142029i
$280$		0			0
$281$	−197.313	−	113.919i	−0.702181	−	0.405404i	0.105978	−	0.994368i	$-0.466203\pi$
$281$	−197.313	−	113.919i	−0.702181	−	0.405404i	−0.808159	+	0.588964i	$0.799536\pi$
$282$		0			0
$283$	−7.02897	−	12.1745i	−0.0248373	−	0.0430195i	0.853340	−	0.521356i	$-0.174573\pi$
$283$	−7.02897	−	12.1745i	−0.0248373	−	0.0430195i	−0.878177	+	0.478336i	$0.841240\pi$
$284$		0			0
$285$	100.007	−	137.397i	0.350903	−	0.482093i
$286$		0			0
$287$	−225.553	−	130.223i	−0.785899	−	0.453739i
$288$		0			0
$289$	87.0080	+	150.702i	0.301066	+	0.521461i
$290$		0			0
$291$	260.855	−	159.797i	0.896410	−	0.549130i
$292$		0			0
$293$	−325.662	−	188.021i	−1.11148	−	0.641711i	−0.172265	−	0.985051i	$-0.555108\pi$
$293$	−325.662	−	188.021i	−1.11148	−	0.641711i	−0.939211	+	0.343340i	$0.888442\pi$
$294$		0			0
$295$	82.6675	+	47.7281i	0.280229	+	0.161790i
$296$		0			0
$297$	−140.173	−	204.156i	−0.471962	−	0.687392i
$298$		0			0
$299$			56.3002i			0.188295i
$300$		0			0
$301$	234.781	+	406.653i	0.780004	+	1.35101i
$302$		0			0
$303$	−411.994	+	10.7247i	−1.35972	+	0.0353950i
$304$		0			0
$305$	−186.035			−0.609950
$306$		0			0
$307$	251.370	+	145.129i	0.818796	+	0.472732i	0.850001	−	0.526781i	$-0.176601\pi$
$307$	251.370	+	145.129i	0.818796	+	0.472732i	−0.0312054	+	0.999513i	$0.509935\pi$
$308$		0			0
$309$	6.92527	+	266.038i	0.0224119	+	0.860965i
$310$		0			0
$311$	169.025	−	292.759i	0.543488	−	0.941348i	−0.455213	−	0.890383i	$-0.650437\pi$
$311$	169.025	−	292.759i	0.543488	−	0.941348i	0.998700	−	0.0509656i	$-0.0162299\pi$
$312$		0			0
$313$	−235.488	+	407.877i	−0.752357	+	1.30312i	0.194321	+	0.980938i	$0.437750\pi$
$313$	−235.488	+	407.877i	−0.752357	+	1.30312i	−0.946678	+	0.322182i	$0.895584\pi$
$314$		0			0
$315$	−142.779	−	220.010i	−0.453267	−	0.698443i
$316$		0			0
$317$	157.842	+	91.1302i	0.497925	+	0.287477i	0.727856	−	0.685730i	$-0.240517\pi$
$317$	157.842	+	91.1302i	0.497925	+	0.287477i	−0.229931	+	0.973207i	$0.573850\pi$
$318$		0			0
$319$		−	72.2746i		−	0.226566i
$320$		0			0
$321$	−194.847	+	119.361i	−0.607001	+	0.371841i
$322$		0			0
$323$	−124.144	+	161.547i	−0.384346	+	0.500147i
$324$		0			0
$325$	55.8336	+	32.2356i	0.171796	+	0.0991863i
$326$		0			0
$327$	2.50598	+	96.2687i	0.00766356	+	0.294400i
$328$		0			0
$329$	−904.875			−2.75038
$330$		0			0
$331$	−41.3761	+	23.8885i	−0.125003	+	0.0721708i	−0.561198	−	0.827682i	$-0.689659\pi$
$331$	−41.3761	+	23.8885i	−0.125003	+	0.0721708i	0.436194	+	0.899852i	$0.356326\pi$
$332$		0			0
$333$	519.146	+	264.720i	1.55900	+	0.794956i
$334$		0			0
$335$	160.990	−	92.9473i	0.480566	−	0.277455i
$336$		0			0
$337$	−220.786	+	127.471i	−0.655151	+	0.378252i	−0.790427	−	0.612556i	$-0.790141\pi$
$337$	−220.786	+	127.471i	−0.655151	+	0.378252i	0.135276	+	0.990808i	$0.456808\pi$
$338$		0			0
$339$	2.08853	+	80.2319i	0.00616085	+	0.236672i
$340$		0			0
$341$			74.1828i			0.217545i
$342$		0			0
$343$	24.0063			0.0699893
$344$		0			0
$345$	−60.0623	+	110.580i	−0.174094	+	0.320523i
$346$		0			0
$347$	−158.134	−	273.896i	−0.455717	−	0.789325i	0.543012	−	0.839725i	$-0.317284\pi$
$347$	−158.134	−	273.896i	−0.455717	−	0.789325i	−0.998729	+	0.0503996i	$0.983950\pi$
$348$		0			0
$349$	−1.03185	−	1.78722i	−0.00295660	−	0.00512097i	0.864543	−	0.502558i	$-0.167608\pi$
$349$	−1.03185	−	1.78722i	−0.00295660	−	0.00512097i	−0.867500	+	0.497437i	$0.834274\pi$
$350$		0			0
$351$	−8.42699	−	107.714i	−0.0240085	−	0.306878i
$352$		0			0
$353$	−53.9798	−	93.4957i	−0.152917	−	0.264860i	0.779381	−	0.626550i	$-0.215533\pi$
$353$	−53.9798	−	93.4957i	−0.152917	−	0.264860i	−0.932299	+	0.361689i	$0.882200\pi$
$354$		0			0
$355$		−	15.3186i		−	0.0431511i
$356$		0			0
$357$	164.254	+	268.132i	0.460096	+	0.751070i
$358$		0			0
$359$	−67.2021	+	116.397i	−0.187192	+	0.324227i	−0.944313	−	0.329048i	$-0.893272\pi$
$359$	−67.2021	+	116.397i	−0.187192	+	0.324227i	0.757121	+	0.653275i	$0.226605\pi$
$360$		0			0
$361$	348.565	+	93.9333i	0.965554	+	0.260203i
$362$		0			0
$363$	110.584	−	2.87863i	0.304640	−	0.00793012i
$364$		0			0
$365$	−127.615			−0.349631
$366$		0			0
$367$	−212.307	+	367.727i	−0.578493	+	1.00198i	0.417159	+	0.908833i	$0.363026\pi$
$367$	−212.307	+	367.727i	−0.578493	+	1.00198i	−0.995652	+	0.0931463i	$0.970308\pi$
$368$		0			0
$369$	−12.4763	−	239.480i	−0.0338112	−	0.648998i
$370$		0			0
$371$	638.408	+	368.585i	1.72078	+	0.993491i
$372$		0			0
$373$	183.007	+	105.659i	0.490635	+	0.283268i	0.724838	−	0.688919i	$-0.241915\pi$
$373$	183.007	+	105.659i	0.490635	+	0.283268i	−0.234203	+	0.972188i	$0.575248\pi$
$374$		0			0
$375$	192.078	+	313.551i	0.512207	+	0.836136i
$376$		0			0
$377$	15.7661	−	27.3077i	0.0418199	−	0.0724342i
$378$		0			0
$379$		−	454.378i		−	1.19889i	−0.800417	−	0.599443i	$-0.795389\pi$
$379$		−	454.378i		−	1.19889i	0.800417	−	0.599443i	$-0.204611\pi$
$380$		0			0
$381$	120.122	+	65.2448i	0.315280	+	0.171246i
$382$		0			0
$383$	−387.148	+	223.520i	−1.01083	+	0.583603i	−0.911435	−	0.411444i	$-0.865024\pi$
$383$	−387.148	+	223.520i	−1.01083	+	0.583603i	−0.0993961	+	0.995048i	$0.531691\pi$
$384$		0			0
$385$	−267.292			−0.694264
$386$		0			0
$387$	−196.401	+	385.164i	−0.507497	+	0.995257i
$388$		0			0
$389$	93.9634	−	162.749i	0.241551	−	0.418379i	−0.719605	−	0.694383i	$-0.755677\pi$
$389$	93.9634	−	162.749i	0.241551	−	0.418379i	0.961156	+	0.276005i	$0.0890105\pi$
$390$		0			0
$391$	75.4335	−	130.655i	0.192925	−	0.334155i
$392$		0			0
$393$	20.8363	−	38.3616i	0.0530187	−	0.0976123i
$394$		0			0
$395$	−27.5540	+	15.9083i	−0.0697571	+	0.0402743i
$396$		0			0
$397$	−185.471	+	321.245i	−0.467181	+	0.809180i	−0.999297	−	0.0374907i	$-0.988064\pi$
$397$	−185.471	+	321.245i	−0.467181	+	0.809180i	0.532116	+	0.846671i	$0.321397\pi$
$398$		0			0
$399$	327.881	−	450.463i	0.821756	−	1.12898i
$400$		0			0
$401$	−102.627	+	59.2516i	−0.255927	+	0.147760i	−0.622475	−	0.782640i	$-0.713873\pi$
$401$	−102.627	+	59.2516i	−0.255927	+	0.147760i	0.366548	+	0.930399i	$0.380539\pi$
$402$		0			0
$403$	−16.1824	+	28.0287i	−0.0401548	+	0.0695501i
$404$		0			0
$405$	98.3603	−	220.554i	0.242865	−	0.544577i
$406$		0			0
$407$	514.316	−	296.941i	1.26368	−	0.729584i
$408$		0			0
$409$			595.804i			1.45673i	0.685187	+	0.728367i	$0.259720\pi$
$409$			595.804i			1.45673i	−0.685187	+	0.728367i	$0.740280\pi$
$410$		0			0
$411$	13.9912	−	0.364206i	0.0340418	−	0.000886146i
$412$		0			0
$413$	271.030	+	156.480i	0.656248	+	0.378885i
$414$		0			0
$415$	25.8941	−	44.8498i	0.0623953	−	0.108072i
$416$		0			0
$417$	55.0975	+	89.9421i	0.132128	+	0.215689i
$418$		0			0
$419$	−337.434	+	584.453i	−0.805331	+	1.39487i	0.110736	+	0.993850i	$0.464679\pi$
$419$	−337.434	+	584.453i	−0.805331	+	1.39487i	−0.916067	+	0.401025i	$0.868654\pi$
$420$		0			0
$421$			35.0015i			0.0831390i	0.999136	+	0.0415695i	$0.0132358\pi$
$421$			35.0015i			0.0831390i	−0.999136	+	0.0415695i	$0.986764\pi$
$422$		0			0
$423$	−453.556	−	698.889i	−1.07224	−	1.65222i
$424$		0			0
$425$	−86.3813	−	149.617i	−0.203250	−	0.352039i
$426$		0			0
$427$	−609.926			−1.42840
$428$		0			0
$429$	−96.7571	−	52.5542i	−0.225541	−	0.122504i
$430$		0			0
$431$	−151.908	+	87.7042i	−0.352455	+	0.203490i	−0.665766	−	0.746161i	$-0.731895\pi$
$431$	−151.908	+	87.7042i	−0.352455	+	0.203490i	0.313311	+	0.949651i	$0.398562\pi$
$432$		0			0
$433$	−528.173	+	304.941i	−1.21980	+	0.704252i	−0.964875	−	0.262709i	$-0.915384\pi$
$433$	−528.173	+	304.941i	−1.21980	+	0.704252i	−0.254925	+	0.966961i	$0.582051\pi$
$434$		0			0
$435$	60.0990	−	36.8159i	0.138159	−	0.0846343i
$436$		0			0
$437$	−265.007	−	35.0820i	−0.606423	−	0.0802791i
$438$		0			0
$439$			134.936i			0.307372i	0.988120	+	0.153686i	$0.0491144\pi$
$439$			134.936i			0.307372i	−0.988120	+	0.153686i	$0.950886\pi$
$440$		0			0
$441$	−228.039	−	351.386i	−0.517094	−	0.796795i
$442$		0			0
$443$	−29.7718	+	51.5663i	−0.0672050	+	0.116402i	−0.897670	−	0.440668i	$-0.854741\pi$
$443$	−29.7718	+	51.5663i	−0.0672050	+	0.116402i	0.830465	+	0.557071i	$0.188075\pi$
$444$		0			0
$445$	−257.936	−	148.920i	−0.579632	−	0.334651i
$446$		0			0
$447$	−186.195	+	342.803i	−0.416544	+	0.766896i
$448$		0			0
$449$			483.031i			1.07579i	0.843011	+	0.537897i	$0.180781\pi$
$449$			483.031i			1.07579i	−0.843011	+	0.537897i	$0.819219\pi$
$450$		0			0
$451$	−211.647	−	122.194i	−0.469284	−	0.270941i
$452$		0			0
$453$	585.310	+	317.915i	1.29208	+	0.701798i
$454$		0			0
$455$	−100.992	−	58.3075i	−0.221959	−	0.128148i
$456$		0			0
$457$	354.029	+	613.196i	0.774680	+	1.34179i	0.934974	+	0.354716i	$0.115423\pi$
$457$	354.029	+	613.196i	0.774680	+	1.34179i	−0.160294	+	0.987069i	$0.551244\pi$
$458$		0			0
$459$	−124.764	+	261.261i	−0.271817	+	0.569196i
$460$		0			0
$461$	−344.655			−0.747624			−0.373812	−	0.927505i	$-0.621949\pi$
$461$	−344.655			−0.747624			−0.373812	+	0.927505i	$0.621949\pi$
$462$		0			0
$463$	−76.7214	+	132.885i	−0.165705	+	0.287009i	−0.936905	−	0.349583i	$-0.886323\pi$
$463$	−76.7214	+	132.885i	−0.165705	+	0.287009i	0.771200	+	0.636592i	$0.219657\pi$
$464$		0			0
$465$	−61.6857	+	37.7879i	−0.132658	+	0.0812644i
$466$		0			0
$467$	−80.3876			−0.172136			−0.0860681	−	0.996289i	$-0.527430\pi$
$467$	−80.3876			−0.172136			−0.0860681	+	0.996289i	$0.527430\pi$
$468$		0			0
$469$	527.814	−	304.733i	1.12540	−	0.649751i
$470$		0			0
$471$	162.288	−	298.787i	0.344561	−	0.634368i
$472$		0			0
$473$	220.306	+	381.581i	0.465764	+	0.806726i
$474$		0			0
$475$	−186.525	+	242.724i	−0.392684	+	0.510998i
$476$		0			0
$477$	35.3132	+	677.829i	0.0740319	+	1.42102i
$478$		0			0
$479$	90.2177	−	156.262i	0.188346	−	0.326225i	−0.756353	−	0.654164i	$-0.773021\pi$
$479$	90.2177	−	156.262i	0.188346	−	0.326225i	0.944699	+	0.327939i	$0.106354\pi$
$480$		0			0
$481$	259.101			0.538671
$482$		0			0
$483$	−196.918	+	362.544i	−0.407698	+	0.750609i
$484$		0			0
$485$	263.282	−	152.006i	0.542849	−	0.313414i
$486$		0			0
$487$		−	537.817i		−	1.10435i	−0.833729	−	0.552174i	$-0.813798\pi$
$487$		−	537.817i		−	1.10435i	0.833729	−	0.552174i	$-0.186202\pi$
$488$		0			0
$489$	169.401	+	276.533i	0.346423	+	0.565507i
$490$		0			0
$491$	282.194	+	488.774i	0.574733	+	0.995467i	0.996071	+	0.0885630i	$0.0282275\pi$
$491$	282.194	+	488.774i	0.574733	+	0.995467i	−0.421337	+	0.906904i	$0.638439\pi$
$492$		0			0
$493$	−73.1762	+	42.2483i	−0.148430	+	0.0856963i
$494$		0			0
$495$	−133.976	−	206.445i	−0.270659	−	0.417061i
$496$		0			0
$497$		−	50.2230i		−	0.101052i
$498$		0			0
$499$	−65.1014	−	112.759i	−0.130464	−	0.225970i	0.793392	−	0.608712i	$-0.208313\pi$
$499$	−65.1014	−	112.759i	−0.130464	−	0.225970i	−0.923855	+	0.382742i	$0.874980\pi$
$500$		0			0
$501$	103.887	−	63.6396i	0.207358	−	0.127025i
$502$		0			0
$503$	197.284	+	341.706i	0.392215	+	0.679336i	0.992741	−	0.120269i	$-0.0383757\pi$
$503$	197.284	+	341.706i	0.392215	+	0.679336i	−0.600527	+	0.799605i	$0.705042\pi$
$504$		0			0
$505$	−409.577			−0.811044
$506$		0			0
$507$	239.746	+	391.366i	0.472872	+	0.771925i
$508$		0			0
$509$		−	892.594i		−	1.75362i	−0.480834	−	0.876812i	$-0.659666\pi$
$509$		−	892.594i		−	1.75362i	0.480834	−	0.876812i	$-0.340334\pi$
$510$		0			0
$511$	−418.395			−0.818777
$512$		0			0
$513$	512.265	+	27.4531i	0.998567	+	0.0535149i
$514$		0			0
$515$			264.477i			0.513548i
$516$		0			0
$517$	−849.087			−1.64233
$518$		0			0
$519$	−351.254	+	215.174i	−0.676790	+	0.414593i
$520$		0			0
$521$		−	98.8257i		−	0.189685i	−0.995492	−	0.0948423i	$-0.969765\pi$
$521$		−	98.8257i		−	0.189685i	0.995492	−	0.0948423i	$-0.0302347\pi$
$522$		0			0
$523$	244.833	−	141.354i	0.468132	−	0.270276i	−0.247326	−	0.968932i	$-0.579552\pi$
$523$	244.833	−	141.354i	0.468132	−	0.270276i	0.715457	+	0.698656i	$0.246218\pi$
$524$		0			0
$525$	246.791	+	402.866i	0.470078	+	0.767365i
$526$		0			0
$527$	75.1082	−	43.3637i	0.142520	−	0.0822841i
$528$		0			0
$529$	−331.052			−0.625807
$530$		0			0
$531$	14.9919	+	287.766i	0.0282333	+	0.541932i
$532$		0			0
$533$	−53.3114	−	92.3381i	−0.100021	−	0.173242i
$534$		0			0
$535$	−196.660	+	113.542i	−0.367588	+	0.212227i
$536$		0			0
$537$	−816.016	+	499.881i	−1.51958	+	0.930878i
$538$		0			0
$539$	−426.903			−0.792028
$540$		0			0
$541$	−2.13015	−	3.68953i	−0.00393743	−	0.00681982i	0.864050	−	0.503406i	$-0.167920\pi$
$541$	−2.13015	−	3.68953i	−0.00393743	−	0.00681982i	−0.867987	+	0.496586i	$0.834587\pi$
$542$		0			0
$543$	−570.647	−	309.950i	−1.05091	−	0.570811i
$544$		0			0
$545$			95.7039i			0.175604i
$546$		0			0
$547$	−735.241	−	424.492i	−1.34413	−	0.776036i	−0.356722	−	0.934210i	$-0.616106\pi$
$547$	−735.241	−	424.492i	−1.34413	−	0.776036i	−0.987411	+	0.158175i	$0.949439\pi$
$548$		0			0
$549$	−305.717	−	471.082i	−0.556862	−	0.858073i
$550$		0			0
$551$	118.714	+	91.2276i	0.215452	+	0.165567i
$552$		0			0
$553$	−90.3376	+	52.1564i	−0.163359	+	0.0943154i
$554$		0			0
$555$	508.904	+	276.414i	0.916945	+	0.498044i
$556$		0			0
$557$	−334.625	−	579.587i	−0.600762	−	1.04055i	−0.992706	−	0.120562i	$-0.961530\pi$
$557$	−334.625	−	579.587i	−0.600762	−	1.04055i	0.391943	−	0.919989i	$-0.371803\pi$
$558$		0			0
$559$			192.232i			0.343885i
$560$		0			0
$561$	154.128	+	251.601i	0.274737	+	0.448486i
$562$		0			0
$563$	588.362	+	339.691i	1.04505	+	0.603359i	0.921259	−	0.388950i	$-0.127162\pi$
$563$	588.362	+	339.691i	1.04505	+	0.603359i	0.123789	+	0.992309i	$0.460495\pi$
$564$		0			0
$565$			79.7612i			0.141170i
$566$		0			0
$567$	322.480	−	723.098i	0.568748	−	1.27531i
$568$		0			0
$569$	158.505	−	91.5129i	0.278568	−	0.160831i	−0.354207	−	0.935167i	$-0.615249\pi$
$569$	158.505	−	91.5129i	0.278568	−	0.160831i	0.632775	+	0.774336i	$0.281916\pi$
$570$		0			0
$571$	−117.920	+	204.243i	−0.206514	+	0.357694i	−0.950614	−	0.310375i	$-0.899545\pi$
$571$	−117.920	+	204.243i	−0.206514	+	0.357694i	0.744100	+	0.668069i	$0.232879\pi$
$572$		0			0
$573$	183.423	−	337.699i	0.320110	−	0.589352i
$574$		0			0
$575$	113.338	−	196.308i	0.197110	−	0.341405i
$576$		0			0
$577$	56.3366			0.0976371			0.0488186	−	0.998808i	$-0.484454\pi$
$577$	56.3366			0.0976371			0.0488186	+	0.998808i	$0.484454\pi$
$578$		0			0
$579$	−249.818	−	135.690i	−0.431465	−	0.234353i
$580$		0			0
$581$	84.8952	−	147.043i	0.146119	−	0.253086i
$582$		0			0
$583$	599.049	+	345.861i	1.02753	+	0.593243i
$584$		0			0
$585$	−5.58629	−	107.228i	−0.00954922	−	0.183295i
$586$		0			0
$587$	628.218			1.07022			0.535109	−	0.844783i	$-0.320271\pi$
$587$	628.218			1.07022			0.535109	+	0.844783i	$0.320271\pi$
$588$		0			0
$589$	−121.848	−	93.6362i	−0.206873	−	0.158975i
$590$		0			0
$591$	604.196	+	986.301i	1.02233	+	1.66887i
$592$		0			0
$593$	−545.345	−	944.565i	−0.919638	−	1.59286i	−0.799966	−	0.600045i	$-0.795149\pi$
$593$	−545.345	−	944.565i	−0.919638	−	1.59286i	−0.119672	−	0.992814i	$-0.538184\pi$
$594$		0			0
$595$	156.246	+	270.626i	0.262598	+	0.454834i
$596$		0			0
$597$	494.855	−	911.073i	0.828903	−	1.52609i
$598$		0			0
$599$		−	396.916i		−	0.662631i	−0.943520	−	0.331315i	$-0.892508\pi$
$599$		−	396.916i		−	0.662631i	0.943520	−	0.331315i	$-0.107492\pi$
$600$		0			0
$601$	149.620	−	86.3834i	0.248952	−	0.143733i	−0.370332	−	0.928899i	$-0.620756\pi$
$601$	149.620	−	86.3834i	0.248952	−	0.143733i	0.619284	+	0.785167i	$0.287423\pi$
$602$		0			0
$603$	499.923	+	254.918i	0.829060	+	0.422750i
$604$		0			0
$605$	109.936			0.181712
$606$		0			0
$607$	−796.780	−	460.021i	−1.31265	−	0.757861i	−0.330118	−	0.943940i	$-0.607089\pi$
$607$	−796.780	−	460.021i	−1.31265	−	0.757861i	−0.982535	+	0.186079i	$0.940422\pi$
$608$		0			0
$609$	197.038	−	120.703i	0.323544	−	0.198199i
$610$		0			0
$611$	−320.813	−	185.221i	−0.525062	−	0.303144i
$612$		0			0
$613$	−201.095	+	348.307i	−0.328050	+	0.568200i	−0.982125	−	0.188230i	$-0.939725\pi$
$613$	−201.095	+	348.307i	−0.328050	+	0.568200i	0.654075	+	0.756430i	$0.273058\pi$
$614$		0			0
$615$	−6.20157	−	238.237i	−0.0100839	−	0.387377i
$616$		0			0
$617$	−970.713			−1.57328			−0.786639	−	0.617413i	$-0.788181\pi$
$617$	−970.713			−1.57328			−0.786639	+	0.617413i	$0.788181\pi$
$618$		0			0
$619$	142.293	+	246.459i	0.229876	+	0.398157i	0.957771	−	0.287531i	$-0.0928345\pi$
$619$	142.293	+	246.459i	0.229876	+	0.398157i	−0.727895	+	0.685689i	$0.759501\pi$
$620$		0			0
$621$	−378.717	+	29.6288i	−0.609850	+	0.0477114i
$622$		0			0
$623$	−845.660	−	488.242i	−1.35740	−	0.783695i
$624$		0			0
$625$	−18.6788	−	32.3526i	−0.0298861	−	0.0517642i
$626$		0			0
$627$	307.666	−	422.691i	0.490695	−	0.674148i
$628$		0			0
$629$	−601.289	−	347.155i	−0.955945	−	0.551915i
$630$		0			0
$631$	131.123	+	227.112i	0.207802	+	0.359924i	0.951022	−	0.309123i	$-0.100036\pi$
$631$	131.123	+	227.112i	0.207802	+	0.359924i	−0.743220	+	0.669047i	$0.766702\pi$
$632$		0			0
$633$	488.192	+	265.164i	0.771235	+	0.418901i
$634$		0			0
$635$	117.649	+	67.9245i	0.185274	+	0.106968i
$636$		0			0
$637$	−161.298	−	93.1254i	−0.253215	−	0.146194i
$638$		0			0
$639$	38.7902	−	25.1736i	0.0607046	−	0.0393953i
$640$		0			0
$641$		−	839.693i		−	1.30997i	−0.755640	−	0.654987i	$-0.772674\pi$
$641$		−	839.693i		−	1.30997i	0.755640	−	0.654987i	$-0.227326\pi$
$642$		0			0
$643$	215.765	+	373.715i	0.335559	+	0.581205i	0.983592	−	0.180407i	$-0.0577414\pi$
$643$	215.765	+	373.715i	0.335559	+	0.581205i	−0.648033	+	0.761612i	$0.724408\pi$
$644$		0			0
$645$	−205.077	+	377.566i	−0.317949	+	0.585374i
$646$		0			0
$647$	−576.599			−0.891189			−0.445594	−	0.895235i	$-0.647008\pi$
$647$	−576.599			−0.891189			−0.445594	+	0.895235i	$0.647008\pi$
$648$		0			0
$649$	254.321	+	146.832i	0.391865	+	0.226244i
$650$		0			0
$651$	−202.240	+	123.890i	−0.310661	+	0.190307i
$652$		0			0
$653$	434.186	−	752.033i	0.664910	−	1.15166i	−0.314400	−	0.949291i	$-0.601803\pi$
$653$	434.186	−	752.033i	0.664910	−	1.15166i	0.979310	−	0.202367i	$-0.0648635\pi$
$654$		0			0
$655$	21.6921	−	37.5719i	0.0331178	−	0.0573617i
$656$		0			0
$657$	−209.715	−	323.151i	−0.319200	−	0.491859i
$658$		0			0
$659$	78.2098	+	45.1544i	0.118679	+	0.0685196i	0.558165	−	0.829730i	$-0.311506\pi$
$659$	78.2098	+	45.1544i	0.118679	+	0.0685196i	−0.439485	+	0.898250i	$0.644839\pi$
$660$		0			0
$661$		−	626.707i		−	0.948119i	−0.880493	−	0.474060i	$-0.842788\pi$
$661$		−	626.707i		−	0.948119i	0.880493	−	0.474060i	$-0.157212\pi$
$662$		0			0
$663$	3.34981	+	128.685i	0.00505250	+	0.194095i
$664$		0			0
$665$	337.385	−	439.038i	0.507347	−	0.660207i
$666$		0			0
$667$	−96.0123	−	55.4327i	−0.143946	−	0.0831075i
$668$		0			0
$669$	722.663	−	442.695i	1.08021	−	0.661726i
$670$		0			0
$671$	−572.323			−0.852940
$672$		0			0
$673$	443.722	−	256.183i	0.659319	−	0.380658i	−0.132699	−	0.991156i	$-0.542364\pi$
$673$	443.722	−	256.183i	0.659319	−	0.380658i	0.792017	+	0.610499i	$0.209031\pi$
$674$		0			0
$675$	−187.457	+	392.543i	−0.277714	+	0.581545i
$676$		0			0
$677$	956.991	−	552.519i	1.41358	−	0.816129i	0.417853	−	0.908514i	$-0.362783\pi$
$677$	956.991	−	552.519i	1.41358	−	0.816129i	0.995723	+	0.0923856i	$0.0294492\pi$
$678$		0			0
$679$	863.185	−	498.360i	1.27126	−	0.733962i
$680$		0			0
$681$	935.689	+	508.225i	1.37399	+	0.746293i
$682$		0			0
$683$			1057.53i			1.54835i	0.632969	+	0.774177i	$0.281836\pi$
$683$			1057.53i			1.54835i	−0.632969	+	0.774177i	$0.718164\pi$
$684$		0			0
$685$	13.9091			0.0203052
$686$		0			0
$687$	996.394	−	25.9372i	1.45035	−	0.0377543i
$688$		0			0
$689$	150.893	+	261.355i	0.219003	+	0.379325i
$690$		0			0
$691$	441.920	+	765.428i	0.639537	+	1.10771i	0.985535	+	0.169475i	$0.0542071\pi$
$691$	441.920	+	765.428i	0.639537	+	1.10771i	−0.345998	+	0.938235i	$0.612460\pi$
$692$		0			0
$693$	−439.250	−	676.843i	−0.633838	−	0.976686i
$694$		0			0
$695$	52.4111	+	90.7788i	0.0754117	+	0.130617i
$696$		0			0
$697$			285.716i			0.409923i
$698$		0			0
$699$	−1213.78	+	31.5960i	−1.73645	+	0.0452017i
$700$		0			0
$701$	548.525	−	950.074i	0.782490	−	1.35531i	−0.147997	−	0.988988i	$-0.547283\pi$
$701$	548.525	−	950.074i	0.782490	−	1.35531i	0.930487	−	0.366324i	$-0.119384\pi$
$702$		0			0
$703$	−161.452	+	1219.59i	−0.229661	+	1.73484i
$704$		0			0
$705$	−432.516	−	706.047i	−0.613498	−	1.00149i
$706$		0			0
$707$	−1342.82			−1.89933
$708$		0			0
$709$	−275.515	+	477.206i	−0.388597	+	0.673070i	−0.992261	−	0.124169i	$-0.960373\pi$
$709$	−275.515	+	477.206i	−0.388597	+	0.673070i	0.603664	+	0.797239i	$0.293707\pi$
$710$		0			0
$711$	−85.5640	−	43.6304i	−0.120343	−	0.0613648i
$712$		0			0
$713$	98.5472	+	56.8963i	0.138215	+	0.0797984i
$714$		0			0
$715$	−94.7651	−	54.7127i	−0.132539	−	0.0765212i
$716$		0			0
$717$	74.2690	−	1.93331i	0.103583	−	0.00269638i
$718$		0			0
$719$	−210.261	+	364.183i	−0.292435	+	0.506513i	−0.974385	−	0.224886i	$-0.927799\pi$
$719$	−210.261	+	364.183i	−0.292435	+	0.506513i	0.681950	+	0.731399i	$0.261132\pi$
$720$		0			0
$721$			867.104i			1.20264i
$722$		0			0
$723$	−7.71256	−	296.282i	−0.0106674	−	0.409796i
$724$		0			0
$725$	−109.947	+	63.4778i	−0.151651	+	0.0875555i
$726$		0			0
$727$	−172.723			−0.237584			−0.118792	−	0.992919i	$-0.537902\pi$
$727$	−172.723			−0.237584			−0.118792	+	0.992919i	$0.537902\pi$
$728$		0			0
$729$	720.130	−	113.372i	0.987833	−	0.155518i
$730$		0			0
$731$	257.561	−	446.109i	0.352340	−	0.610272i
$732$		0			0
$733$	331.859	−	574.796i	0.452740	−	0.784169i	−0.545815	−	0.837906i	$-0.683780\pi$
$733$	331.859	−	574.796i	0.452740	−	0.784169i	0.998555	+	0.0537367i	$0.0171132\pi$
$734$		0			0
$735$	−217.460	−	354.986i	−0.295864	−	0.482974i
$736$		0			0
$737$	495.273	−	285.946i	0.672012	−	0.387986i
$738$		0			0
$739$	256.958	−	445.064i	0.347711	−	0.602252i	−0.638132	−	0.769927i	$-0.720293\pi$
$739$	256.958	−	445.064i	0.347711	−	0.602252i	0.985842	+	0.167675i	$0.0536259\pi$
$740$		0			0
$741$	208.453	−	92.5916i	0.281313	−	0.124955i
$742$		0			0
$743$	−298.354	+	172.255i	−0.401553	+	0.231837i	−0.687154	−	0.726512i	$-0.741140\pi$
$743$	−298.354	+	172.255i	−0.401553	+	0.231837i	0.285601	+	0.958349i	$0.407807\pi$
$744$		0			0
$745$	−193.843	+	335.745i	−0.260192	+	0.450665i
$746$		0			0
$747$	156.123	−	8.13360i	0.208999	−	0.0108884i
$748$		0			0
$749$	−644.761	+	372.253i	−0.860829	+	0.497000i
$750$		0			0
$751$			576.022i			0.767007i	0.923539	+	0.383504i	$0.125283\pi$
$751$			576.022i			0.767007i	−0.923539	+	0.383504i	$0.874717\pi$
$752$		0			0
$753$	−225.037	+	414.314i	−0.298854	+	0.550218i
$754$		0			0
$755$	573.260	+	330.972i	0.759285	+	0.438374i
$756$		0			0
$757$	−148.034	+	256.402i	−0.195553	+	0.338708i	−0.947082	−	0.320993i	$-0.895983\pi$
$757$	−148.034	+	256.402i	−0.195553	+	0.338708i	0.751529	+	0.659700i	$0.229317\pi$
$758$		0			0
$759$	−184.777	+	340.192i	−0.243449	+	0.448211i
$760$		0			0
$761$	98.9438	−	171.376i	0.130018	−	0.225198i	−0.793665	−	0.608355i	$-0.791830\pi$
$761$	98.9438	−	171.376i	0.130018	−	0.225198i	0.923683	+	0.383157i	$0.125163\pi$
$762$		0			0
$763$			313.771i			0.411233i
$764$		0			0
$765$	−130.704	+	256.326i	−0.170855	+	0.335066i
$766$		0			0
$767$	64.0604	+	110.956i	0.0835208	+	0.144662i
$768$		0			0
$769$	−799.737			−1.03997			−0.519985	−	0.854175i	$-0.674062\pi$
$769$	−799.737			−1.03997			−0.519985	+	0.854175i	$0.674062\pi$
$770$		0			0
$771$	835.987	−	512.116i	1.08429	−	0.664223i
$772$		0			0
$773$	733.291	−	423.366i	0.948630	−	0.547692i	0.0559748	−	0.998432i	$-0.482173\pi$
$773$	733.291	−	423.366i	0.948630	−	0.547692i	0.892655	+	0.450741i	$0.148840\pi$
$774$		0			0
$775$	112.850	−	65.1537i	0.145612	−	0.0840693i
$776$		0			0
$777$	1668.47	+	906.241i	2.14733	+	1.16633i
$778$		0			0
$779$	467.858	−	193.400i	0.600588	−	0.248268i
$780$		0			0
$781$		−	47.1266i		−	0.0603414i
$782$		0			0
$783$	191.989	+	91.6834i	0.245197	+	0.117093i
$784$		0			0
$785$	168.954	−	292.636i	0.215227	−	0.372785i
$786$		0			0
$787$	280.142	+	161.740i	0.355962	+	0.205515i	0.667308	−	0.744782i	$-0.267446\pi$
$787$	280.142	+	161.740i	0.355962	+	0.205515i	−0.311346	+	0.950297i	$0.600780\pi$
$788$		0			0
$789$	437.753	+	714.596i	0.554820	+	0.905699i
$790$		0			0
$791$			261.502i			0.330597i
$792$		0			0
$793$	−216.242	−	124.847i	−0.272689	−	0.157437i
$794$		0			0
$795$	17.5530	+	674.309i	0.0220793	+	0.848187i
$796$		0			0
$797$	−1045.19	−	603.440i	−1.31140	−	0.757139i	−0.329075	−	0.944304i	$-0.606737\pi$
$797$	−1045.19	−	603.440i	−1.31140	−	0.757139i	−0.982328	+	0.187165i	$0.940070\pi$
$798$		0			0
$799$	496.336	+	859.678i	0.621196	+	1.07594i
$800$		0			0
$801$	−46.7772	−	897.878i	−0.0583985	−	1.12095i
$802$		0			0
$803$	−392.600			−0.488916
$804$		0			0
$805$	−205.006	+	355.080i	−0.254666	+	0.441094i
$806$		0			0
$807$	30.0022	+	1152.55i	0.0371775	+	1.42819i
$808$		0			0
$809$	−1306.49			−1.61495			−0.807473	−	0.589904i	$-0.799166\pi$
$809$	−1306.49			−1.61495			−0.807473	+	0.589904i	$0.799166\pi$
$810$		0			0
$811$	916.637	−	529.221i	1.13026	−	0.652553i	0.186256	−	0.982501i	$-0.440365\pi$
$811$	916.637	−	529.221i	1.13026	−	0.652553i	0.943999	+	0.329948i	$0.107031\pi$
$812$		0			0
$813$	1337.23	−	34.8095i	1.64480	−	0.0428161i
$814$		0			0
$815$	161.141	+	279.105i	0.197719	+	0.342460i
$816$		0			0
$817$	−904.841	−	119.784i	−1.10752	−	0.146615i
$818$		0			0
$819$	−18.3150	−	351.552i	−0.0223626	−	0.429246i
$820$		0			0
$821$	475.120	−	822.932i	0.578709	−	1.00235i	−0.416919	−	0.908944i	$-0.636890\pi$
$821$	475.120	−	822.932i	0.578709	−	1.00235i	0.995628	−	0.0934094i	$-0.0297765\pi$
$822$		0			0
$823$	941.577			1.14408			0.572040	−	0.820226i	$-0.306152\pi$
$823$	941.577			1.14408			0.572040	+	0.820226i	$0.306152\pi$
$824$		0			0
$825$	231.576	+	378.029i	0.280698	+	0.458216i
$826$		0			0
$827$	−146.968	+	84.8517i	−0.177712	+	0.102602i	−0.586217	−	0.810154i	$-0.699383\pi$
$827$	−146.968	+	84.8517i	−0.177712	+	0.102602i	0.408505	+	0.912756i	$0.366050\pi$
$828$		0			0
$829$		−	203.755i		−	0.245784i	−0.992420	−	0.122892i	$-0.960783\pi$
$829$		−	203.755i		−	0.245784i	0.992420	−	0.122892i	$-0.0392168\pi$
$830$		0			0
$831$	673.885	−	1240.68i	0.810932	−	1.49300i
$832$		0			0
$833$	249.547	+	432.228i	0.299576	+	0.518881i
$834$		0			0
$835$	104.853	−	60.5368i	0.125572	−	0.0724992i
$836$		0			0
$837$	−197.058	−	94.1041i	−0.235434	−	0.112430i
$838$		0			0
$839$		−	920.114i		−	1.09668i	−0.836256	−	0.548340i	$-0.815260\pi$
$839$		−	920.114i		−	1.09668i	0.836256	−	0.548340i	$-0.184740\pi$
$840$		0			0
$841$	−389.454	−	674.553i	−0.463084	−	0.802085i
$842$		0			0
$843$	−17.7865	−	683.280i	−0.0210991	−	0.810534i
$844$		0			0
$845$	228.057	+	395.007i	0.269890	+	0.467463i
$846$		0			0
$847$	360.430			0.425538
$848$		0			0
$849$	20.1293	−	37.0599i	0.0237095	−	0.0436513i
$850$		0			0
$851$		−	910.982i		−	1.07048i
$852$		0			0
$853$	650.510			0.762615			0.381307	−	0.924448i	$-0.375474\pi$
$853$	650.510			0.762615			0.381307	+	0.924448i	$0.375474\pi$
$854$		0			0
$855$	508.205	+	40.5212i	0.594391	+	0.0473932i
$856$		0			0
$857$			658.782i			0.768707i	0.923186	+	0.384353i	$0.125576\pi$
$857$			658.782i			0.768707i	−0.923186	+	0.384353i	$0.874424\pi$
$858$		0			0
$859$	−1307.68			−1.52233			−0.761165	−	0.648559i	$-0.775372\pi$
$859$	−1307.68			−1.52233			−0.761165	+	0.648559i	$0.775372\pi$
$860$		0			0
$861$	−20.3322	−	781.074i	−0.0236147	−	0.907170i
$862$		0			0
$863$			754.521i			0.874300i	0.899389	+	0.437150i	$0.144012\pi$
$863$			754.521i			0.874300i	−0.899389	+	0.437150i	$0.855988\pi$
$864$		0			0
$865$	−354.521	+	204.683i	−0.409851	+	0.236628i
$866$		0			0
$867$	−249.171	+	458.746i	−0.287394	+	0.529119i
$868$		0			0
$869$	−84.7680	+	48.9408i	−0.0975466	+	0.0563186i
$870$		0			0
$871$	249.507			0.286460
$872$		0			0
$873$	817.573	+	416.893i	0.936509	+	0.477540i
$874$		0			0
$875$	599.034	+	1037.56i	0.684611	+	1.18578i
$876$		0			0
$877$	944.294	−	545.188i	1.07673	−	0.621651i	0.146719	−	0.989178i	$-0.453129\pi$
$877$	944.294	−	545.188i	1.07673	−	0.621651i	0.930013	+	0.367527i	$0.119795\pi$
$878$		0			0
$879$	−29.3565	−	1127.75i	−0.0333976	−	1.28299i
$880$		0			0
$881$	−951.353			−1.07986			−0.539928	−	0.841711i	$-0.681548\pi$
$881$	−951.353			−1.07986			−0.539928	+	0.841711i	$0.681548\pi$
$882$		0			0
$883$	493.901	+	855.462i	0.559345	+	0.968813i	0.997551	+	0.0699390i	$0.0222805\pi$
$883$	493.901	+	855.462i	0.559345	+	0.968813i	−0.438207	+	0.898874i	$0.644386\pi$
$884$		0			0
$885$	7.45197	+	286.272i	0.00842031	+	0.323471i
$886$		0			0
$887$		−	821.819i		−	0.926516i	−0.886224	−	0.463258i	$-0.846680\pi$
$887$		−	821.819i		−	0.926516i	0.886224	−	0.463258i	$-0.153320\pi$
$888$		0			0
$889$	385.719	+	222.695i	0.433879	+	0.250500i
$890$		0			0
$891$	302.598	−	678.517i	0.339617	−	0.761523i
$892$		0			0
$893$	1071.75	−	1394.66i	1.20017	−	1.56177i
$894$		0			0
$895$	−823.606	+	475.509i	−0.920230	+	0.531295i
$896$		0			0
$897$	−144.025	+	88.2280i	−0.160563	+	0.0983590i
$898$		0			0
$899$	−31.8661	−	55.1936i	−0.0354461	−	0.0613945i
$900$		0			0
$901$		−	808.695i		−	0.897553i
$902$		0			0
$903$	−672.359	+	1237.87i	−0.744583	+	1.37085i
$904$		0			0
$905$	−558.899	−	322.681i	−0.617568	−	0.356553i
$906$		0			0
$907$		−	1001.10i		−	1.10375i	−0.833927	−	0.551875i	$-0.813912\pi$
$907$		−	1001.10i		−	1.10375i	0.833927	−	0.551875i	$-0.186088\pi$
$908$		0			0
$909$	−673.072	−	1037.14i	−0.740453	−	1.14097i
$910$		0			0
$911$	1212.33	−	699.940i	1.33077	−	0.768320i	0.345352	−	0.938473i	$-0.387759\pi$
$911$	1212.33	−	699.940i	1.33077	−	0.768320i	0.985418	+	0.170153i	$0.0544261\pi$
$912$		0			0
$913$	79.6612	−	137.977i	0.0872521	−	0.151125i
$914$		0			0
$915$	−291.535	−	475.907i	−0.318618	−	0.520117i
$916$		0			0
$917$	71.1190	−	123.182i	0.0775561	−	0.134331i
$918$		0			0
$919$	−1085.36			−1.18103			−0.590513	−	0.807028i	$-0.701075\pi$
$919$	−1085.36			−1.18103			−0.590513	+	0.807028i	$0.701075\pi$
$920$		0			0
$921$	22.6595	+	870.477i	0.0246031	+	0.945144i
$922$		0			0
$923$	10.2803	−	17.8060i	0.0111379	−	0.0192914i
$924$		0			0
$925$	−903.433	−	521.597i	−0.976684	−	0.563889i
$926$		0			0
$927$	−669.716	+	434.624i	−0.722455	+	0.468850i
$928$		0			0
$929$	260.538			0.280450			0.140225	−	0.990120i	$-0.455217\pi$
$929$	260.538			0.280450			0.140225	+	0.990120i	$0.455217\pi$
$930$		0			0
$931$	538.852	−	701.205i	0.578789	−	0.753174i
$932$		0			0
$933$	1013.80	−	26.3905i	1.08661	−	0.0282856i
$934$		0			0
$935$	146.613	+	253.941i	0.156805	+	0.271595i
$936$		0			0
$937$	−307.877	−	533.259i	−0.328578	−	0.569113i	0.653652	−	0.756795i	$-0.273236\pi$
$937$	−307.877	−	533.259i	−0.328578	−	0.569113i	−0.982230	+	0.187682i	$0.939903\pi$
$938$		0			0
$939$	−1412.45	+	36.7676i	−1.50420	+	0.0391561i
$940$		0			0
$941$			456.461i			0.485080i	0.970141	+	0.242540i	$0.0779806\pi$
$941$			456.461i			0.485080i	−0.970141	+	0.242540i	$0.922019\pi$
$942$		0			0
$943$	−324.655	+	187.440i	−0.344279	+	0.198770i
$944$		0			0
$945$	339.071	−	710.029i	0.358805	−	0.751354i
$946$		0			0
$947$	−197.883			−0.208958			−0.104479	−	0.994527i	$-0.533317\pi$
$947$	−197.883			−0.208958			−0.104479	+	0.994527i	$0.533317\pi$
$948$		0			0
$949$	−148.337	−	85.6424i	−0.156309	−	0.0902449i
$950$		0			0
$951$	14.2285	+	546.596i	0.0149616	+	0.574759i
$952$		0			0
$953$	1404.18	+	810.701i	1.47343	+	0.850683i	0.999553	−	0.0299091i	$-0.00952180\pi$
$953$	1404.18	+	810.701i	1.47343	+	0.850683i	0.473874	+	0.880593i	$0.342855\pi$
$954$		0			0
$955$	190.957	−	330.747i	0.199955	−	0.346332i
$956$		0			0
$957$	184.890	−	113.262i	0.193198	−	0.118351i
$958$		0			0
$959$	45.6018			0.0475514
$960$		0			0
$961$	−447.793	−	775.600i	−0.465965	−	0.807075i
$962$		0			0
$963$	−610.690	−	311.400i	−0.634154	−	0.323365i
$964$		0			0
$965$	−244.675	−	141.263i	−0.253550	−	0.146387i
$966$		0			0
$967$	−166.109	−	287.710i	−0.171778	−	0.297528i	0.767264	−	0.641332i	$-0.221618\pi$
$967$	−166.109	−	287.710i	−0.171778	−	0.297528i	−0.939042	+	0.343804i	$0.888285\pi$
$968$		0			0
$969$	−607.810	−	64.4188i	−0.627255	−	0.0664797i
$970$		0			0
$971$	−633.796	−	365.923i	−0.652726	−	0.376851i	0.136774	−	0.990602i	$-0.456327\pi$
$971$	−633.796	−	365.923i	−0.652726	−	0.376851i	−0.789500	+	0.613751i	$0.789660\pi$
$972$		0			0
$973$	171.833	+	297.624i	0.176601	+	0.305882i
$974$		0			0
$975$	5.03306	+	193.348i	0.00516211	+	0.198305i
$976$		0			0
$977$	557.500	+	321.873i	0.570624	+	0.329450i	0.757399	−	0.652953i	$-0.226470\pi$
$977$	557.500	+	321.873i	0.570624	+	0.329450i	−0.186775	+	0.982403i	$0.559803\pi$
$978$		0			0
$979$	−793.523	−	458.140i	−0.810544	−	0.467968i
$980$		0			0
$981$	−242.344	+	157.273i	−0.247038	+	0.160320i
$982$		0			0
$983$		−	1656.38i		−	1.68503i	−0.538673	−	0.842515i	$-0.681074\pi$
$983$		−	1656.38i		−	1.68503i	0.538673	−	0.842515i	$-0.318926\pi$
$984$		0			0
$985$	574.738	+	995.475i	0.583490	+	1.01063i
$986$		0			0
$987$	−1418.03	−	2314.82i	−1.43671	−	2.34531i
$988$		0			0
$989$	675.876			0.683393
$990$		0			0
$991$	−1476.45	−	852.430i	−1.48986	−	0.860171i	−0.489927	−	0.871763i	$-0.662977\pi$
$991$	−1476.45	−	852.430i	−1.48986	−	0.860171i	−0.999933	+	0.0115922i	$0.996310\pi$
$992$		0			0
$993$	−125.951	−	68.4112i	−0.126839	−	0.0688934i
$994$		0			0
$995$	515.180	−	892.317i	0.517768	−	0.896801i
$996$		0			0
$997$	−417.113	+	722.461i	−0.418368	+	0.724634i	−0.995775	−	0.0918216i	$-0.970731\pi$
$997$	−417.113	+	722.461i	−0.418368	+	0.724634i	0.577408	+	0.816456i	$0.304064\pi$
$998$		0			0
$999$	136.355	+	1742.90i	0.136492	+	1.74465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.28	✓	80
3.2	odd	2		2052.3.s.a.901.15		80
9.2	odd	6		2052.3.bl.a.1585.26		80
9.7	even	3		684.3.bl.a.673.39	yes	80
19.12	odd	6		684.3.bl.a.373.39	yes	80
57.50	even	6		2052.3.bl.a.145.26		80
171.88	odd	6	inner	684.3.s.a.601.28	yes	80
171.164	even	6		2052.3.s.a.829.15		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.28	✓	80	1.1	even	1	trivial
684.3.s.a.601.28	yes	80	171.88	odd	6	inner
684.3.bl.a.373.39	yes	80	19.12	odd	6
684.3.bl.a.673.39	yes	80	9.7	even	3
2052.3.s.a.829.15		80	171.164	even	6
2052.3.s.a.901.15		80	3.2	odd	2
2052.3.bl.a.145.26		80	57.50	even	6
2052.3.bl.a.1585.26		80	9.2	odd	6

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56710 + 2.55816i) q^{3} +(1.49069 + 2.58196i) q^{5} +(4.88733 + 8.46511i) q^{7} +(-4.08840 + 8.01779i) q^{9} +O(q^{10})\)	\(q+(1.56710 + 2.55816i) q^{3} +(1.49069 + 2.58196i) q^{5} +(4.88733 + 8.46511i) q^{7} +(-4.08840 + 8.01779i) q^{9} +(4.58601 + 7.94321i) q^{11} +4.00160i q^{13} +(-4.26900 + 7.85963i) q^{15} +(5.36153 - 9.28644i) q^{17} +(-18.8357 - 2.49349i) q^{19} +(-13.9962 + 25.7683i) q^{21} +14.0694 q^{23} +(8.05566 - 13.9528i) q^{25} +(-26.9177 + 2.10590i) q^{27} +(-6.82419 - 3.93995i) q^{29} +(7.00436 + 4.04397i) q^{31} +(-13.1333 + 24.1796i) q^{33} +(-14.5710 + 25.2378i) q^{35} -64.7492i q^{37} +(-10.2368 + 6.27091i) q^{39} +(-23.0753 + 13.3225i) q^{41} +48.0387 q^{43} +(-26.7962 + 1.39601i) q^{45} +(-46.2868 + 80.1710i) q^{47} +(-23.2720 + 40.3083i) q^{49} +(32.1583 - 0.837116i) q^{51} +(65.3126 - 37.7082i) q^{53} +(-13.6727 + 23.6818i) q^{55} +(-23.1386 - 52.0923i) q^{57} +(27.7279 - 16.0087i) q^{59} +(-31.1994 + 54.0389i) q^{61} +(-87.8528 + 4.57692i) q^{63} +(-10.3320 + 5.96517i) q^{65} -62.3517i q^{67} +(22.0482 + 35.9918i) q^{69} +(-4.44971 - 2.56904i) q^{71} +(-21.4020 + 37.0694i) q^{73} +(48.3176 - 1.25776i) q^{75} +(-44.8267 + 77.6422i) q^{77} +10.6718i q^{79} +(-47.5700 - 65.5598i) q^{81} +(-8.68524 - 15.0433i) q^{83} +31.9696 q^{85} +(-0.615159 - 23.6317i) q^{87} +(-86.5155 + 49.9498i) q^{89} +(-33.8740 + 19.5572i) q^{91} +(0.631400 + 24.2556i) q^{93} +(-21.6401 - 52.3500i) q^{95} -101.970i q^{97} +(-82.4364 + 4.29474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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