LMFDB - Embedded newform 684.3.s.a.445.17

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			445.17
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.522544 - 2.95414i) q^{3} +(-3.49763 - 6.05807i) q^{5} +(0.133800 + 0.231748i) q^{7} +(-8.45389 + 3.08734i) q^{9} +O(q^{10})$	\(q+(-0.522544 - 2.95414i) q^{3} +(-3.49763 - 6.05807i) q^{5} +(0.133800 + 0.231748i) q^{7} +(-8.45389 + 3.08734i) q^{9} +(9.29330 + 16.0965i) q^{11} +15.0833i q^{13} +(-16.0687 + 13.4981i) q^{15} +(-7.41969 + 12.8513i) q^{17} +(-10.6722 - 15.7196i) q^{19} +(0.614701 - 0.516363i) q^{21} -19.9176 q^{23} +(-11.9668 + 20.7271i) q^{25} +(13.5380 + 23.3607i) q^{27} +(-1.60036 - 0.923966i) q^{29} +(40.4634 + 23.3615i) q^{31} +(42.6951 - 35.8649i) q^{33} +(0.935965 - 1.62114i) q^{35} -19.8245i q^{37} +(44.5582 - 7.88170i) q^{39} +(-15.1351 + 8.73823i) q^{41} +75.1394 q^{43} +(48.2719 + 40.4159i) q^{45} +(-6.27614 + 10.8706i) q^{47} +(24.4642 - 42.3732i) q^{49} +(41.8416 + 15.2034i) q^{51} +(1.06598 - 0.615444i) q^{53} +(65.0090 - 112.599i) q^{55} +(-40.8611 + 39.7413i) q^{57} +(-76.6856 + 44.2745i) q^{59} +(-51.2375 + 88.7460i) q^{61} +(-1.84662 - 1.54609i) q^{63} +(91.3756 - 52.7558i) q^{65} +78.8235i q^{67} +(10.4078 + 58.8395i) q^{69} +(-85.6563 - 49.4537i) q^{71} +(-10.6721 + 18.4847i) q^{73} +(67.4838 + 24.5207i) q^{75} +(-2.48689 + 4.30742i) q^{77} +30.0514i q^{79} +(61.9367 - 52.2001i) q^{81} +(-27.5237 - 47.6725i) q^{83} +103.805 q^{85} +(-1.89327 + 5.21049i) q^{87} +(122.281 - 70.5992i) q^{89} +(-3.49553 + 2.01815i) q^{91} +(47.8694 - 131.742i) q^{93} +(-57.9028 + 119.634i) q^{95} +117.234i q^{97} +(-128.260 - 107.386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.522544	−	2.95414i	−0.174181	−	0.984714i
$3$	−0.522544	−	2.95414i	−0.174181	−	0.984714i
$4$		0			0
$5$	−3.49763	−	6.05807i	−0.699525	−	1.21161i	−0.968631	−	0.248503i	$-0.920062\pi$
$5$	−3.49763	−	6.05807i	−0.699525	−	1.21161i	0.269106	−	0.963111i	$-0.413272\pi$
$6$		0			0
$7$	0.133800	+	0.231748i	0.0191143	+	0.0331069i	0.875424	−	0.483355i	$-0.160582\pi$
$7$	0.133800	+	0.231748i	0.0191143	+	0.0331069i	−0.856310	+	0.516462i	$0.827249\pi$
$8$		0			0
$9$	−8.45389	+	3.08734i	−0.939322	+	0.343038i
$10$		0			0
$11$	9.29330	+	16.0965i	0.844846	+	1.46332i	0.885755	+	0.464153i	$0.153641\pi$
$11$	9.29330	+	16.0965i	0.844846	+	1.46332i	−0.0409092	+	0.999163i	$0.513025\pi$
$12$		0			0
$13$			15.0833i			1.16025i	0.814526	+	0.580127i	$0.196997\pi$
$13$			15.0833i			1.16025i	−0.814526	+	0.580127i	$0.803003\pi$
$14$		0			0
$15$	−16.0687	+	13.4981i	−1.07125	+	0.899873i
$16$		0			0
$17$	−7.41969	+	12.8513i	−0.436452	+	0.755958i	−0.997413	−	0.0718849i	$-0.977099\pi$
$17$	−7.41969	+	12.8513i	−0.436452	+	0.755958i	0.560961	+	0.827842i	$0.310432\pi$
$18$		0			0
$19$	−10.6722	−	15.7196i	−0.561694	−	0.827345i
$19$	−10.6722	−	15.7196i	−0.561694	−	0.827345i
$20$		0			0
$21$	0.614701	−	0.516363i	0.0292715	−	0.0245887i
$22$		0			0
$23$	−19.9176			−0.865984			−0.432992	−	0.901398i	$-0.642542\pi$
$23$	−19.9176			−0.865984			−0.432992	+	0.901398i	$0.642542\pi$
$24$		0			0
$25$	−11.9668	+	20.7271i	−0.478671	+	0.829083i
$26$		0			0
$27$	13.5380	+	23.3607i	0.501406	+	0.865212i
$28$		0			0
$29$	−1.60036	−	0.923966i	−0.0551847	−	0.0318609i	0.472154	−	0.881516i	$-0.343477\pi$
$29$	−1.60036	−	0.923966i	−0.0551847	−	0.0318609i	−0.527339	+	0.849655i	$0.676810\pi$
$30$		0			0
$31$	40.4634	+	23.3615i	1.30527	+	0.753598i	0.981303	−	0.192470i	$-0.0616499\pi$
$31$	40.4634	+	23.3615i	1.30527	+	0.753598i	0.323967	+	0.946068i	$0.394983\pi$
$32$		0			0
$33$	42.6951	−	35.8649i	1.29379	−	1.08681i
$34$		0			0
$35$	0.935965	−	1.62114i	0.0267419	−	0.0463182i
$36$		0			0
$37$		−	19.8245i		−	0.535798i	−0.963447	−	0.267899i	$-0.913671\pi$
$37$		−	19.8245i		−	0.535798i	0.963447	−	0.267899i	$-0.0863293\pi$
$38$		0			0
$39$	44.5582	−	7.88170i	1.14252	−	0.202095i
$40$		0			0
$41$	−15.1351	+	8.73823i	−0.369148	+	0.213127i	−0.673086	−	0.739564i	$-0.735032\pi$
$41$	−15.1351	+	8.73823i	−0.369148	+	0.213127i	0.303938	+	0.952692i	$0.401698\pi$
$42$		0			0
$43$	75.1394			1.74743			0.873713	−	0.486441i	$-0.161705\pi$
$43$	75.1394			1.74743			0.873713	+	0.486441i	$0.161705\pi$
$44$		0			0
$45$	48.2719	+	40.4159i	1.07271	+	0.898131i
$46$		0			0
$47$	−6.27614	+	10.8706i	−0.133535	+	0.231289i	−0.925037	−	0.379877i	$-0.875966\pi$
$47$	−6.27614	+	10.8706i	−0.133535	+	0.231289i	0.791502	+	0.611167i	$0.209299\pi$
$48$		0			0
$49$	24.4642	−	42.3732i	0.499269	−	0.864760i
$50$		0			0
$51$	41.8416	+	15.2034i	0.820424	+	0.298107i
$52$		0			0
$53$	1.06598	−	0.615444i	0.0201128	−	0.0116122i	−0.489910	−	0.871773i	$-0.662970\pi$
$53$	1.06598	−	0.615444i	0.0201128	−	0.0116122i	0.510023	+	0.860161i	$0.329637\pi$
$54$		0			0
$55$	65.0090	−	112.599i	1.18198	−	2.04725i
$56$		0			0
$57$	−40.8611	+	39.7413i	−0.716861	+	0.697216i
$58$		0			0
$59$	−76.6856	+	44.2745i	−1.29976	+	0.750415i	−0.980362	−	0.197207i	$-0.936813\pi$
$59$	−76.6856	+	44.2745i	−1.29976	+	0.750415i	−0.319395	+	0.947622i	$0.603480\pi$
$60$		0			0
$61$	−51.2375	+	88.7460i	−0.839960	+	1.45485i	0.0499676	+	0.998751i	$0.484088\pi$
$61$	−51.2375	+	88.7460i	−0.839960	+	1.45485i	−0.889927	+	0.456102i	$0.849245\pi$
$62$		0			0
$63$	−1.84662	−	1.54609i	−0.0293114	−	0.0245411i
$64$		0			0
$65$	91.3756	−	52.7558i	1.40578	−	0.811627i
$66$		0			0
$67$			78.8235i			1.17647i	0.808690	+	0.588235i	$0.200177\pi$
$67$			78.8235i			1.17647i	−0.808690	+	0.588235i	$0.799823\pi$
$68$		0			0
$69$	10.4078	+	58.8395i	0.150838	+	0.852746i
$70$		0			0
$71$	−85.6563	−	49.4537i	−1.20643	−	0.696531i	−0.244450	−	0.969662i	$-0.578607\pi$
$71$	−85.6563	−	49.4537i	−1.20643	−	0.696531i	−0.961977	+	0.273131i	$0.911941\pi$
$72$		0			0
$73$	−10.6721	+	18.4847i	−0.146194	+	0.253215i	−0.929818	−	0.368021i	$-0.880036\pi$
$73$	−10.6721	+	18.4847i	−0.146194	+	0.253215i	0.783624	+	0.621235i	$0.213369\pi$
$74$		0			0
$75$	67.4838	+	24.5207i	0.899785	+	0.326943i
$76$		0			0
$77$	−2.48689	+	4.30742i	−0.0322973	+	0.0559405i
$78$		0			0
$79$			30.0514i			0.380398i	0.981746	+	0.190199i	$0.0609132\pi$
$79$			30.0514i			0.380398i	−0.981746	+	0.190199i	$0.939087\pi$
$80$		0			0
$81$	61.9367	−	52.2001i	0.764650	−	0.644446i
$82$		0			0
$83$	−27.5237	−	47.6725i	−0.331611	−	0.574368i	0.651217	−	0.758892i	$-0.274259\pi$
$83$	−27.5237	−	47.6725i	−0.331611	−	0.574368i	−0.982828	+	0.184524i	$0.940926\pi$
$84$		0			0
$85$	103.805			1.22124
$86$		0			0
$87$	−1.89327	+	5.21049i	−0.0217617	+	0.0598907i
$88$		0			0
$89$	122.281	−	70.5992i	1.37395	−	0.793249i	0.382526	−	0.923945i	$-0.375054\pi$
$89$	122.281	−	70.5992i	1.37395	−	0.793249i	0.991423	+	0.130695i	$0.0417210\pi$
$90$		0			0
$91$	−3.49553	+	2.01815i	−0.0384124	+	0.0221774i
$92$		0			0
$93$	47.8694	−	131.742i	0.514724	−	1.41658i
$94$		0			0
$95$	−57.9028	+	119.634i	−0.609503	+	1.25930i
$96$		0			0
$97$			117.234i			1.20860i	0.796757	+	0.604300i	$0.206547\pi$
$97$			117.234i			1.20860i	−0.796757	+	0.604300i	$0.793453\pi$
$98$		0			0
$99$	−128.260	−	107.386i	−1.29555	−	1.08471i
$100$		0			0
$101$	−47.6081	+	82.4596i	−0.471367	+	0.816431i	−0.999463	−	0.0327530i	$-0.989573\pi$
$101$	−47.6081	+	82.4596i	−0.471367	+	0.816431i	0.528097	+	0.849184i	$0.322906\pi$
$102$		0			0
$103$	−103.934	−	60.0065i	−1.00907	−	0.582588i	−0.0981518	−	0.995171i	$-0.531293\pi$
$103$	−103.934	−	60.0065i	−1.00907	−	0.582588i	−0.910920	+	0.412584i	$0.864626\pi$
$104$		0			0
$105$	−5.27816	−	1.91785i	−0.0502681	−	0.0182653i
$106$		0			0
$107$			63.7390i			0.595692i	0.954614	+	0.297846i	$0.0962681\pi$
$107$			63.7390i			0.595692i	−0.954614	+	0.297846i	$0.903732\pi$
$108$		0			0
$109$	134.646	+	77.7377i	1.23528	+	0.713190i	0.968126	−	0.250464i	$-0.0805831\pi$
$109$	134.646	+	77.7377i	1.23528	+	0.713190i	0.267155	+	0.963654i	$0.413916\pi$
$110$		0			0
$111$	−58.5644	+	10.3592i	−0.527607	+	0.0933261i
$112$		0			0
$113$	178.339	+	102.964i	1.57823	+	0.911189i	0.995107	+	0.0988014i	$0.0315009\pi$
$113$	178.339	+	102.964i	1.57823	+	0.911189i	0.583118	+	0.812387i	$0.301832\pi$
$114$		0			0
$115$	69.6644	+	120.662i	0.605778	+	1.04924i
$116$		0			0
$117$	−46.5673	−	127.513i	−0.398011	−	1.08985i
$118$		0			0
$119$	−3.97102			−0.0333699
$120$		0			0
$121$	−112.231	+	194.390i	−0.927529	+	1.60653i
$122$		0			0
$123$	33.7227	+	40.1450i	0.274168	+	0.326382i
$124$		0			0
$125$	−7.46006			−0.0596804
$126$		0			0
$127$	−2.83897	+	1.63908i	−0.0223541	+	0.0129061i	−0.511135	−	0.859500i	$-0.670775\pi$
$127$	−2.83897	+	1.63908i	−0.0223541	+	0.0129061i	0.488781	+	0.872406i	$0.337442\pi$
$128$		0			0
$129$	−39.2637	−	221.972i	−0.304369	−	1.72071i
$130$		0			0
$131$	−83.5254	−	144.670i	−0.637599	−	1.10435i	−0.985958	−	0.166992i	$-0.946595\pi$
$131$	−83.5254	−	144.670i	−0.637599	−	1.10435i	0.348360	−	0.937361i	$-0.386739\pi$
$132$		0			0
$133$	2.21504	−	4.57654i	0.0166545	−	0.0344101i
$134$		0			0
$135$	94.1700	−	163.721i	0.697556	−	1.21275i
$136$		0			0
$137$	−6.03580	+	10.4543i	−0.0440570	+	0.0763089i	−0.887213	−	0.461360i	$-0.847362\pi$
$137$	−6.03580	+	10.4543i	−0.0440570	+	0.0763089i	0.843156	+	0.537669i	$0.180695\pi$
$138$		0			0
$139$	−32.9869			−0.237316			−0.118658	−	0.992935i	$-0.537859\pi$
$139$	−32.9869			−0.237316			−0.118658	+	0.992935i	$0.537859\pi$
$140$		0			0
$141$	35.3928	+	12.8602i	0.251013	+	0.0912073i
$142$		0			0
$143$	−242.788	+	140.174i	−1.69782	+	0.980236i
$144$		0			0
$145$			12.9268i			0.0891500i
$146$		0			0
$147$	−137.960	−	50.1288i	−0.938504	−	0.341012i
$148$		0			0
$149$	94.0778	+	162.948i	0.631395	+	1.09361i	0.987267	+	0.159073i	$0.0508505\pi$
$149$	94.0778	+	162.948i	0.631395	+	1.09361i	−0.355872	+	0.934535i	$0.615816\pi$
$150$		0			0
$151$	−146.502	+	84.5828i	−0.970210	+	0.560151i	−0.899300	−	0.437332i	$-0.855924\pi$
$151$	−146.502	+	84.5828i	−0.970210	+	0.560151i	−0.0709097	+	0.997483i	$0.522590\pi$
$152$		0			0
$153$	23.0490	−	131.550i	0.150647	−	0.859807i
$154$		0			0
$155$		−	326.840i		−	2.10864i
$156$		0			0
$157$	38.1750	+	66.1211i	0.243153	+	0.421154i	0.961611	−	0.274417i	$-0.0884849\pi$
$157$	38.1750	+	66.1211i	0.243153	+	0.421154i	−0.718458	+	0.695571i	$0.755152\pi$
$158$		0			0
$159$	−2.37513	−	2.82746i	−0.0149379	−	0.0177828i
$160$		0			0
$161$	−2.66498	−	4.61588i	−0.0165527	−	0.0286701i
$162$		0			0
$163$	119.907			0.735625			0.367813	−	0.929900i	$-0.380107\pi$
$163$	119.907			0.735625			0.367813	+	0.929900i	$0.380107\pi$
$164$		0			0
$165$	−366.603	−	133.208i	−2.22184	−	0.807320i
$166$		0			0
$167$		−	178.351i		−	1.06797i	−0.845494	−	0.533985i	$-0.820694\pi$
$167$		−	178.351i		−	1.06797i	0.845494	−	0.533985i	$-0.179306\pi$
$168$		0			0
$169$	−58.5060			−0.346190
$170$		0			0
$171$	138.753	+	99.9428i	0.811422	+	0.584461i
$172$		0			0
$173$		−	46.6901i		−	0.269885i	−0.990853	−	0.134943i	$-0.956915\pi$
$173$		−	46.6901i		−	0.269885i	0.990853	−	0.134943i	$-0.0430850\pi$
$174$		0			0
$175$	−6.40462			−0.0365978
$176$		0			0
$177$	170.865	+	203.405i	0.965337	+	1.14918i
$178$		0			0
$179$			181.221i			1.01241i	0.862413	+	0.506205i	$0.168952\pi$
$179$			181.221i			1.01241i	−0.862413	+	0.506205i	$0.831048\pi$
$180$		0			0
$181$	58.3219	−	33.6721i	0.322220	−	0.186034i	−0.330162	−	0.943924i	$-0.607103\pi$
$181$	58.3219	−	33.6721i	0.322220	−	0.186034i	0.652382	+	0.757891i	$0.273770\pi$
$182$		0			0
$183$	288.942	+	104.989i	1.57892	+	0.573711i
$184$		0			0
$185$	−120.098	+	69.3388i	−0.649180	+	0.374804i
$186$		0			0
$187$	−275.814			−1.47494
$188$		0			0
$189$	−3.60243	+	6.26307i	−0.0190605	+	0.0331379i
$190$		0			0
$191$	−9.69790	−	16.7973i	−0.0507744	−	0.0879438i	0.839521	−	0.543327i	$-0.182836\pi$
$191$	−9.69790	−	16.7973i	−0.0507744	−	0.0879438i	−0.890296	+	0.455383i	$0.849502\pi$
$192$		0			0
$193$	79.7564	−	46.0474i	0.413246	−	0.238588i	−0.278938	−	0.960309i	$-0.589982\pi$
$193$	79.7564	−	46.0474i	0.413246	−	0.238588i	0.692183	+	0.721722i	$0.256649\pi$
$194$		0			0
$195$	−203.596	−	242.369i	−1.04408	−	1.24292i
$196$		0			0
$197$	−274.390			−1.39284			−0.696421	−	0.717633i	$-0.745225\pi$
$197$	−274.390			−1.39284			−0.696421	+	0.717633i	$0.745225\pi$
$198$		0			0
$199$	163.455	+	283.112i	0.821379	+	1.42267i	0.904655	+	0.426144i	$0.140128\pi$
$199$	163.455	+	283.112i	0.821379	+	1.42267i	−0.0832757	+	0.996527i	$0.526538\pi$
$200$		0			0
$201$	232.856	−	41.1888i	1.15849	−	0.204919i
$202$		0			0
$203$		−	0.494507i		−	0.00243599i
$204$		0			0
$205$	105.873	+	61.1261i	0.516456	+	0.298176i
$206$		0			0
$207$	168.382	−	61.4925i	0.813437	−	0.297065i
$208$		0			0
$209$	153.850	−	317.871i	0.736122	−	1.52091i
$210$		0			0
$211$	−324.585	+	187.399i	−1.53832	+	0.888148i	−0.539380	+	0.842062i	$0.681341\pi$
$211$	−324.585	+	187.399i	−1.53832	+	0.888148i	−0.998937	+	0.0460860i	$0.985325\pi$
$212$		0			0
$213$	−101.334	+	278.883i	−0.475746	+	1.30931i
$214$		0			0
$215$	−262.809	−	455.199i	−1.22237	−	2.11721i
$216$		0			0
$217$			12.5031i			0.0576180i
$218$		0			0
$219$	60.1830	+	21.8679i	0.274808	+	0.0998536i
$220$		0			0
$221$	−193.840	−	111.913i	−0.877103	−	0.506396i
$222$		0			0
$223$		−	410.551i		−	1.84104i	−0.390700	−	0.920518i	$-0.627767\pi$
$223$		−	410.551i		−	1.84104i	0.390700	−	0.920518i	$-0.372233\pi$
$224$		0			0
$225$	37.1744	−	212.170i	0.165219	−	0.942978i
$226$		0			0
$227$	−253.428	+	146.316i	−1.11642	+	0.644566i	−0.940485	−	0.339836i	$-0.889629\pi$
$227$	−253.428	+	146.316i	−1.11642	+	0.644566i	−0.175936	+	0.984402i	$0.556295\pi$
$228$		0			0
$229$	63.7894	−	110.486i	0.278556	−	0.482474i	−0.692470	−	0.721447i	$-0.743477\pi$
$229$	63.7894	−	110.486i	0.278556	−	0.482474i	0.971026	+	0.238973i	$0.0768108\pi$
$230$		0			0
$231$	14.0242	+	5.09580i	0.0607109	+	0.0220597i
$232$		0			0
$233$	−32.8387	+	56.8782i	−0.140938	+	0.244113i	−0.927850	−	0.372953i	$-0.878345\pi$
$233$	−32.8387	+	56.8782i	−0.140938	+	0.244113i	0.786912	+	0.617065i	$0.211679\pi$
$234$		0			0
$235$	87.8064			0.373644
$236$		0			0
$237$	88.7761	−	15.7032i	0.374583	−	0.0662582i
$238$		0			0
$239$	−218.108	+	377.773i	−0.912584	+	1.58064i	−0.102183	+	0.994766i	$0.532583\pi$
$239$	−218.108	+	377.773i	−0.912584	+	1.58064i	−0.810401	+	0.585876i	$0.800751\pi$
$240$		0			0
$241$	207.104	+	119.571i	0.859351	+	0.496146i	0.863795	−	0.503844i	$-0.168081\pi$
$241$	207.104	+	119.571i	0.859351	+	0.496146i	−0.00444396	+	0.999990i	$0.501415\pi$
$242$		0			0
$243$	−186.571	−	155.693i	−0.767782	−	0.640711i
$244$		0			0
$245$	−342.266			−1.39701
$246$		0			0
$247$	237.103	−	160.972i	0.959930	−	0.651708i
$248$		0			0
$249$	−126.449	+	106.220i	−0.507827	+	0.426587i
$250$		0			0
$251$	62.2217	+	107.771i	0.247895	+	0.429367i	0.962942	−	0.269710i	$-0.0869278\pi$
$251$	62.2217	+	107.771i	0.247895	+	0.429367i	−0.715046	+	0.699077i	$0.753594\pi$
$252$		0			0
$253$	−185.101	−	320.604i	−0.731623	−	1.26721i
$254$		0			0
$255$	−54.2428	−	306.655i	−0.212717	−	1.20257i
$256$		0			0
$257$			129.966i			0.505703i	0.967505	+	0.252852i	$0.0813685\pi$
$257$			129.966i			0.505703i	−0.967505	+	0.252852i	$0.918632\pi$
$258$		0			0
$259$	4.59430	−	2.65252i	0.0177386	−	0.0102414i
$260$		0			0
$261$	16.3818	+	2.87027i	0.0627657	+	0.0109972i
$262$		0			0
$263$	−70.6656			−0.268691			−0.134345	−	0.990935i	$-0.542893\pi$
$263$	−70.6656			−0.268691			−0.134345	+	0.990935i	$0.542893\pi$
$264$		0			0
$265$	−7.45681	−	4.30519i	−0.0281389	−	0.0162460i
$266$		0			0
$267$	−272.457	−	324.345i	−1.02044	−	1.21478i
$268$		0			0
$269$	−108.899	−	62.8726i	−0.404827	−	0.233727i	0.283737	−	0.958902i	$-0.408426\pi$
$269$	−108.899	−	62.8726i	−0.404827	−	0.233727i	−0.688565	+	0.725175i	$0.741759\pi$
$270$		0			0
$271$	98.9843	−	171.446i	0.365256	−	0.632642i	−0.623561	−	0.781774i	$-0.714315\pi$
$271$	98.9843	−	171.446i	0.365256	−	0.632642i	0.988817	+	0.149133i	$0.0476482\pi$
$272$		0			0
$273$	7.78846	+	9.27172i	0.0285292	+	0.0339623i
$274$		0			0
$275$	−444.844			−1.61761
$276$		0			0
$277$	−20.6263	−	35.7258i	−0.0744632	−	0.128974i	0.826390	−	0.563099i	$-0.190391\pi$
$277$	−20.6263	−	35.7258i	−0.0744632	−	0.128974i	−0.900853	+	0.434125i	$0.857058\pi$
$278$		0			0
$279$	−414.198	−	72.5718i	−1.48458	−	0.260114i
$280$		0			0
$281$	109.367	+	63.1431i	0.389206	+	0.224708i	0.681816	−	0.731524i	$-0.261190\pi$
$281$	109.367	+	63.1431i	0.389206	+	0.224708i	−0.292610	+	0.956232i	$0.594524\pi$
$282$		0			0
$283$	−95.0596	−	164.648i	−0.335900	−	0.581796i	0.647757	−	0.761847i	$-0.275707\pi$
$283$	−95.0596	−	164.648i	−0.335900	−	0.581796i	−0.983657	+	0.180051i	$0.942374\pi$
$284$		0			0
$285$	383.672	+	108.539i	1.34622	+	0.380838i
$286$		0			0
$287$	−4.05014	−	2.33835i	−0.0141120	−	0.00814756i
$288$		0			0
$289$	34.3964	+	59.5763i	0.119019	+	0.206147i
$290$		0			0
$291$	346.326	−	61.2600i	1.19012	−	0.210516i
$292$		0			0
$293$	−197.636	−	114.105i	−0.674527	−	0.389438i	0.123263	−	0.992374i	$-0.460664\pi$
$293$	−197.636	−	114.105i	−0.674527	−	0.389438i	−0.797790	+	0.602936i	$0.793997\pi$
$294$		0			0
$295$	536.435	+	309.711i	1.81843	+	1.04987i
$296$		0			0
$297$	−250.213	+	435.012i	−0.842467	+	1.46469i
$298$		0			0
$299$		−	300.424i		−	1.00476i
$300$		0			0
$301$	10.0536	+	17.4134i	0.0334008	+	0.0578519i
$302$		0			0
$303$	268.474	+	97.5521i	0.886054	+	0.321954i
$304$		0			0
$305$	716.839			2.35029
$306$		0			0
$307$	−27.2921	−	15.7571i	−0.0888994	−	0.0513261i	0.454891	−	0.890547i	$-0.349678\pi$
$307$	−27.2921	−	15.7571i	−0.0888994	−	0.0513261i	−0.543791	+	0.839221i	$0.683011\pi$
$308$		0			0
$309$	−122.957	+	338.393i	−0.397920	+	1.09512i
$310$		0			0
$311$	−86.5119	+	149.843i	−0.278173	+	0.481810i	−0.970931	−	0.239360i	$-0.923062\pi$
$311$	−86.5119	+	149.843i	−0.278173	+	0.481810i	0.692757	+	0.721171i	$0.256396\pi$
$312$		0			0
$313$	60.7712	−	105.259i	0.194157	−	0.336290i	−0.752467	−	0.658630i	$-0.771136\pi$
$313$	60.7712	−	105.259i	0.194157	−	0.336290i	0.946624	+	0.322340i	$0.104469\pi$
$314$		0			0
$315$	−2.90754	+	16.5946i	−0.00923029	+	0.0526812i
$316$		0			0
$317$	−209.658	−	121.046i	−0.661380	−	0.381848i	0.131422	−	0.991326i	$-0.458046\pi$
$317$	−209.658	−	121.046i	−0.661380	−	0.381848i	−0.792803	+	0.609478i	$0.791379\pi$
$318$		0			0
$319$		−	34.3468i		−	0.107670i
$320$		0			0
$321$	188.294	−	33.3065i	0.586586	−	0.103758i
$322$		0			0
$323$	281.201	−	20.5170i	0.870590	−	0.0635202i
$324$		0			0
$325$	−312.633	−	180.499i	−0.961947	−	0.555380i
$326$		0			0
$327$	159.290	−	438.384i	0.487125	−	1.34062i
$328$		0			0
$329$	−3.35899			−0.0102097
$330$		0			0
$331$	−113.130	+	65.3154i	−0.341781	+	0.197327i	−0.661059	−	0.750334i	$-0.729893\pi$
$331$	−113.130	+	65.3154i	−0.341781	+	0.197327i	0.319278	+	0.947661i	$0.396560\pi$
$332$		0			0
$333$	61.2050	+	167.594i	0.183799	+	0.503287i
$334$		0			0
$335$	477.518	−	275.695i	1.42543	−	0.822971i
$336$		0			0
$337$	220.214	−	127.140i	0.653453	−	0.377271i	−0.136325	−	0.990664i	$-0.543529\pi$
$337$	220.214	−	127.140i	0.653453	−	0.377271i	0.789778	+	0.613393i	$0.210196\pi$
$338$		0			0
$339$	210.981	−	580.643i	0.622362	−	1.71281i
$340$		0			0
$341$			868.424i			2.54670i
$342$		0			0
$343$	26.2056			0.0764013
$344$		0			0
$345$	320.051	−	268.850i	0.927683	−	0.779275i
$346$		0			0
$347$	−332.985	−	576.748i	−0.959612	−	1.66210i	−0.723442	−	0.690385i	$-0.757441\pi$
$347$	−332.985	−	576.748i	−0.959612	−	1.66210i	−0.236170	−	0.971712i	$-0.575892\pi$
$348$		0			0
$349$	96.7248	+	167.532i	0.277149	+	0.480035i	0.970675	−	0.240396i	$-0.0772772\pi$
$349$	96.7248	+	167.532i	0.277149	+	0.480035i	−0.693526	+	0.720431i	$0.743944\pi$
$350$		0			0
$351$	−352.357	+	204.197i	−1.00387	+	0.581759i
$352$		0			0
$353$	167.622	+	290.329i	0.474849	+	0.822462i	0.999585	−	0.0288025i	$-0.00916939\pi$
$353$	167.622	+	290.329i	0.474849	+	0.822462i	−0.524736	+	0.851265i	$0.675836\pi$
$354$		0			0
$355$			691.882i			1.94896i
$356$		0			0
$357$	2.07503	+	11.7309i	0.00581242	+	0.0328598i
$358$		0			0
$359$	−143.086	+	247.832i	−0.398568	+	0.690341i	−0.993550	−	0.113399i	$-0.963826\pi$
$359$	−143.086	+	247.832i	−0.398568	+	0.690341i	0.594981	+	0.803740i	$0.297160\pi$
$360$		0			0
$361$	−133.209	+	335.524i	−0.369000	+	0.929430i
$362$		0			0
$363$	632.900	+	229.969i	1.74353	+	0.633523i
$364$		0			0
$365$	149.309			0.409065
$366$		0			0
$367$	275.548	−	477.264i	0.750813	−	1.30045i	−0.196616	−	0.980481i	$-0.562995\pi$
$367$	275.548	−	477.264i	0.750813	−	1.30045i	0.947429	−	0.319966i	$-0.103671\pi$
$368$		0			0
$369$	100.972	−	120.599i	0.273638	−	0.326827i
$370$		0			0
$371$	0.285257	+	0.164693i	0.000768886	+	0.000443916i
$372$		0			0
$373$	−444.407	−	256.579i	−1.19144	−	0.687878i	−0.232807	−	0.972523i	$-0.574791\pi$
$373$	−444.407	−	256.579i	−1.19144	−	0.687878i	−0.958633	+	0.284645i	$0.908124\pi$
$374$		0			0
$375$	3.89821	+	22.0381i	0.0103952	+	0.0587681i
$376$		0			0
$377$	13.9365	−	24.1387i	0.0369667	−	0.0640283i
$378$		0			0
$379$			647.818i			1.70928i	0.519220	+	0.854641i	$0.326223\pi$
$379$			647.818i			1.70928i	−0.519220	+	0.854641i	$0.673777\pi$
$380$		0			0
$381$	6.32555	+	7.53021i	0.0166025	+	0.0197643i
$382$		0			0
$383$	159.246	−	91.9408i	0.415786	−	0.240054i	−0.277487	−	0.960729i	$-0.589501\pi$
$383$	159.246	−	91.9408i	0.415786	−	0.240054i	0.693273	+	0.720675i	$0.256168\pi$
$384$		0			0
$385$	34.7928			0.0903710
$386$		0			0
$387$	−635.220	+	231.981i	−1.64140	+	0.599433i
$388$		0			0
$389$	301.343	−	521.942i	0.774661	−	1.34175i	−0.160324	−	0.987064i	$-0.551254\pi$
$389$	301.343	−	521.942i	0.774661	−	1.34175i	0.934985	−	0.354688i	$-0.115413\pi$
$390$		0			0
$391$	147.783	−	255.967i	0.377961	−	0.654647i
$392$		0			0
$393$	−383.731	+	322.342i	−0.976414	+	0.820210i
$394$		0			0
$395$	182.053	−	105.109i	0.460895	−	0.266098i
$396$		0			0
$397$	60.0424	−	103.996i	0.151240	−	0.261956i	−0.780443	−	0.625226i	$-0.785007\pi$
$397$	60.0424	−	103.996i	0.151240	−	0.261956i	0.931684	+	0.363271i	$0.118340\pi$
$398$		0			0
$399$	−14.6772	−	4.15211i	−0.0367850	−	0.0104063i
$400$		0			0
$401$	−403.848	+	233.162i	−1.00710	+	0.581450i	−0.910342	−	0.413858i	$-0.864181\pi$
$401$	−403.848	+	233.162i	−1.00710	+	0.581450i	−0.0967597	+	0.995308i	$0.530848\pi$
$402$		0			0
$403$	−352.369	+	610.321i	−0.874365	+	1.51444i
$404$		0			0
$405$	−532.863	−	192.640i	−1.31571	−	0.475654i
$406$		0			0
$407$	319.105	−	184.235i	0.784042	−	0.452667i
$408$		0			0
$409$		−	28.3532i		−	0.0693232i	−0.999399	−	0.0346616i	$-0.988965\pi$
$409$		−	28.3532i		−	0.0693232i	0.999399	−	0.0346616i	$-0.0110353\pi$
$410$		0			0
$411$	34.0375	+	12.3678i	0.0828163	+	0.0300919i
$412$		0			0
$413$	−20.5211	−	11.8479i	−0.0496878	−	0.0286873i
$414$		0			0
$415$	−192.536	+	333.481i	−0.463941	+	0.803570i
$416$		0			0
$417$	17.2371	+	97.4480i	0.0413361	+	0.233688i
$418$		0			0
$419$	−151.556	+	262.502i	−0.361708	+	0.626497i	−0.988242	−	0.152897i	$-0.951140\pi$
$419$	−151.556	+	262.502i	−0.361708	+	0.626497i	0.626534	+	0.779394i	$0.284473\pi$
$420$		0			0
$421$			608.422i			1.44518i	0.691276	+	0.722591i	$0.257049\pi$
$421$			608.422i			1.44518i	−0.691276	+	0.722591i	$0.742951\pi$
$422$		0			0
$423$	19.4966	−	111.275i	0.0460913	−	0.263062i
$424$		0			0
$425$	−177.580	−	307.577i	−0.417834	−	0.723710i
$426$		0			0
$427$	−27.4223			−0.0642209
$428$		0			0
$429$	540.960	+	643.983i	1.26098	+	1.50113i
$430$		0			0
$431$	18.5148	−	10.6895i	0.0429577	−	0.0248016i	−0.478367	−	0.878160i	$-0.658771\pi$
$431$	18.5148	−	10.6895i	0.0429577	−	0.0248016i	0.521325	+	0.853358i	$0.325438\pi$
$432$		0			0
$433$	−107.300	+	61.9498i	−0.247807	+	0.143071i	−0.618760	−	0.785580i	$-0.712364\pi$
$433$	−107.300	+	61.9498i	−0.247807	+	0.143071i	0.370953	+	0.928652i	$0.379031\pi$
$434$		0			0
$435$	38.1875	−	6.75480i	0.0877873	−	0.0155283i
$436$		0			0
$437$	212.565	+	313.096i	0.486418	+	0.716467i
$438$		0			0
$439$		−	552.522i		−	1.25859i	−0.777166	−	0.629296i	$-0.783343\pi$
$439$		−	552.522i		−	1.25859i	0.777166	−	0.629296i	$-0.216657\pi$
$440$		0			0
$441$	−75.9972	+	433.748i	−0.172329	+	0.983556i
$442$		0			0
$443$	−124.222	+	215.159i	−0.280411	+	0.485687i	−0.971486	−	0.237097i	$-0.923804\pi$
$443$	−124.222	+	215.159i	−0.280411	+	0.485687i	0.691075	+	0.722783i	$0.257138\pi$
$444$		0			0
$445$	−855.389	−	493.859i	−1.92222	−	1.10980i
$446$		0			0
$447$	432.210	−	363.066i	0.966913	−	0.812229i
$448$		0			0
$449$		−	105.045i		−	0.233954i	−0.993135	−	0.116977i	$-0.962680\pi$
$449$		−	105.045i		−	0.233954i	0.993135	−	0.116977i	$-0.0373204\pi$
$450$		0			0
$451$	−281.309	−	162.414i	−0.623746	−	0.360120i
$452$		0			0
$453$	326.423	+	388.588i	0.720581	+	0.857811i
$454$		0			0
$455$	24.4521	+	14.1174i	0.0537409	+	0.0310273i
$456$		0			0
$457$	128.074	+	221.830i	0.280249	+	0.485406i	0.971446	−	0.237261i	$-0.0762496\pi$
$457$	128.074	+	221.830i	0.280249	+	0.485406i	−0.691197	+	0.722667i	$0.742916\pi$
$458$		0			0
$459$	−400.663	+	0.650962i	−0.872903	+	0.00141822i
$460$		0			0
$461$	30.3257			0.0657824			0.0328912	−	0.999459i	$-0.489529\pi$
$461$	30.3257			0.0657824			0.0328912	+	0.999459i	$0.489529\pi$
$462$		0			0
$463$	227.150	−	393.435i	0.490604	−	0.849752i	−0.509337	−	0.860567i	$-0.670109\pi$
$463$	227.150	−	393.435i	0.490604	−	0.849752i	0.999942	+	0.0108153i	$0.00344267\pi$
$464$		0			0
$465$	−965.530	+	170.788i	−2.07641	+	0.367287i
$466$		0			0
$467$	−53.0719			−0.113644			−0.0568222	−	0.998384i	$-0.518097\pi$
$467$	−53.0719			−0.113644			−0.0568222	+	0.998384i	$0.518097\pi$
$468$		0			0
$469$	−18.2672	+	10.5466i	−0.0389493	+	0.0224874i
$470$		0			0
$471$	175.383	−	147.326i	0.372363	−	0.312793i
$472$		0			0
$473$	698.293	+	1209.48i	1.47631	+	2.55704i
$474$		0			0
$475$	453.532	−	33.0907i	0.954804	−	0.0696646i
$476$		0			0
$477$	−7.11160	+	8.49395i	−0.0149090	+	0.0178070i
$478$		0			0
$479$	6.77465	−	11.7340i	0.0141433	−	0.0244969i	−0.858867	−	0.512198i	$-0.828831\pi$
$479$	6.77465	−	11.7340i	0.0141433	−	0.0244969i	0.873010	+	0.487702i	$0.162165\pi$
$480$		0			0
$481$	299.019			0.621662
$482$		0			0
$483$	−12.2434	+	10.2847i	−0.0253486	+	0.0212934i
$484$		0			0
$485$	710.212	−	410.041i	1.46435	−	0.845446i
$486$		0			0
$487$		−	318.476i		−	0.653956i	−0.945032	−	0.326978i	$-0.893970\pi$
$487$		−	318.476i		−	0.653956i	0.945032	−	0.326978i	$-0.106030\pi$
$488$		0			0
$489$	−62.6567	−	354.222i	−0.128132	−	0.724380i
$490$		0			0
$491$	222.485	+	385.355i	0.453126	+	0.784837i	0.998578	−	0.0533049i	$-0.0169755\pi$
$491$	222.485	+	385.355i	0.453126	+	0.784837i	−0.545453	+	0.838142i	$0.683642\pi$
$492$		0			0
$493$	23.7483	−	13.7111i	0.0481710	−	0.0278115i
$494$		0			0
$495$	−201.948	+	1152.60i	−0.407976	+	2.32849i
$496$		0			0
$497$		−	26.4676i		−	0.0532548i
$498$		0			0
$499$	407.735	+	706.218i	0.817104	+	1.41527i	0.907807	+	0.419388i	$0.137755\pi$
$499$	407.735	+	706.218i	0.817104	+	1.41527i	−0.0907029	+	0.995878i	$0.528911\pi$
$500$		0			0
$501$	−526.873	+	93.1962i	−1.05164	+	0.186020i
$502$		0			0
$503$	201.885	+	349.675i	0.401361	+	0.695178i	0.993890	−	0.110371i	$-0.0352038\pi$
$503$	201.885	+	349.675i	0.401361	+	0.695178i	−0.592529	+	0.805549i	$0.701871\pi$
$504$		0			0
$505$	666.061			1.31893
$506$		0			0
$507$	30.5720	+	172.835i	0.0602998	+	0.340898i
$508$		0			0
$509$		−	804.565i		−	1.58068i	−0.612670	−	0.790339i	$-0.709904\pi$
$509$		−	804.565i		−	1.58068i	0.612670	−	0.790339i	$-0.290096\pi$
$510$		0			0
$511$	−5.71173			−0.0111776
$512$		0			0
$513$	222.740	−	462.121i	0.434192	−	0.900820i
$514$		0			0
$515$			839.522i			1.63014i
$516$		0			0
$517$	−233.304			−0.451266
$518$		0			0
$519$	−137.929	+	24.3977i	−0.265759	+	0.0470090i
$520$		0			0
$521$			191.360i			0.367294i	0.982992	+	0.183647i	$0.0587903\pi$
$521$			191.360i			0.367294i	−0.982992	+	0.183647i	$0.941210\pi$
$522$		0			0
$523$	353.793	−	204.262i	0.676468	−	0.390559i	−0.122055	−	0.992523i	$-0.538949\pi$
$523$	353.793	−	204.262i	0.676468	−	0.390559i	0.798523	+	0.601965i	$0.205615\pi$
$524$		0			0
$525$	3.34670	+	18.9201i	0.00637466	+	0.0360384i
$526$		0			0
$527$	−600.451	+	346.671i	−1.13938	+	0.657819i
$528$		0			0
$529$	−132.288			−0.250072
$530$		0			0
$531$	511.602	−	611.046i	0.963469	−	1.15075i
$532$		0			0
$533$	−131.801	−	228.287i	−0.247282	−	0.428305i
$534$		0			0
$535$	386.135	−	222.935i	0.721748	−	0.416701i
$536$		0			0
$537$	535.353	−	94.6962i	0.996933	−	0.176343i
$538$		0			0
$539$	909.413			1.68722
$540$		0			0
$541$	28.1693	+	48.7906i	0.0520689	+	0.0901860i	0.890885	−	0.454229i	$-0.150085\pi$
$541$	28.1693	+	48.7906i	0.0520689	+	0.0901860i	−0.838816	+	0.544415i	$0.816752\pi$
$542$		0			0
$543$	−129.948	−	154.696i	−0.239315	−	0.284891i
$544$		0			0
$545$		−	1087.59i		−	1.99558i
$546$		0			0
$547$	−401.186	−	231.625i	−0.733429	−	0.423445i	0.0862464	−	0.996274i	$-0.472513\pi$
$547$	−401.186	−	231.625i	−0.733429	−	0.423445i	−0.819675	+	0.572829i	$0.805846\pi$
$548$		0			0
$549$	159.168	−	908.437i	0.289923	−	1.65471i
$550$		0			0
$551$	2.55496	+	35.0176i	0.00463696	+	0.0635529i
$552$		0			0
$553$	−6.96437	+	4.02088i	−0.0125938	+	0.00727103i
$554$		0			0
$555$	267.593	+	318.555i	0.482150	+	0.573972i
$556$		0			0
$557$	190.449	+	329.868i	0.341920	+	0.592223i	0.984789	−	0.173753i	$-0.0555894\pi$
$557$	190.449	+	329.868i	0.341920	+	0.592223i	−0.642869	+	0.765976i	$0.722256\pi$
$558$		0			0
$559$			1133.35i			2.02746i
$560$		0			0
$561$	144.125	+	814.793i	0.256907	+	1.45239i
$562$		0			0
$563$	−145.097	−	83.7716i	−0.257720	−	0.148795i	0.365574	−	0.930782i	$-0.380873\pi$
$563$	−145.097	−	83.7716i	−0.257720	−	0.148795i	−0.623294	+	0.781987i	$0.714206\pi$
$564$		0			0
$565$		−	1440.52i		−	2.54960i
$566$		0			0
$567$	20.3844	+	7.36935i	0.0359513	+	0.0129971i
$568$		0			0
$569$	−165.234	+	95.3978i	−0.290394	+	0.167659i	−0.638119	−	0.769938i	$-0.720287\pi$
$569$	−165.234	+	95.3978i	−0.290394	+	0.167659i	0.347726	+	0.937596i	$0.386954\pi$
$570$		0			0
$571$	−537.327	+	930.678i	−0.941028	+	1.62991i	−0.177513	+	0.984118i	$0.556805\pi$
$571$	−537.327	+	930.678i	−0.941028	+	1.62991i	−0.763515	+	0.645790i	$0.776528\pi$
$572$		0			0
$573$	−44.5539	+	37.4263i	−0.0777555	+	0.0653164i
$574$		0			0
$575$	238.350	−	412.834i	0.414521	−	0.717972i
$576$		0			0
$577$	−335.073			−0.580716			−0.290358	−	0.956918i	$-0.593774\pi$
$577$	−335.073			−0.580716			−0.290358	+	0.956918i	$0.593774\pi$
$578$		0			0
$579$	−177.707	−	211.550i	−0.306920	−	0.365371i
$580$		0			0
$581$	7.36536	−	12.7572i	0.0126770	−	0.0219573i
$582$		0			0
$583$	19.8130	+	11.4390i	0.0339845	+	0.0196210i
$584$		0			0
$585$	−609.605	+	728.099i	−1.04206	+	1.24461i
$586$		0			0
$587$	707.177			1.20473			0.602365	−	0.798221i	$-0.294225\pi$
$587$	707.177			1.20473			0.602365	+	0.798221i	$0.294225\pi$
$588$		0			0
$589$	−64.5996	−	885.385i	−0.109677	−	1.50320i
$590$		0			0
$591$	143.381	+	810.586i	0.242607	+	1.37155i
$592$		0			0
$593$	517.354	+	896.083i	0.872434	+	1.51110i	0.859471	+	0.511185i	$0.170793\pi$
$593$	517.354	+	896.083i	0.872434	+	1.51110i	0.0129636	+	0.999916i	$0.495873\pi$
$594$		0			0
$595$	13.8891	+	24.0567i	0.0233431	+	0.0404314i
$596$		0			0
$597$	750.939	−	630.806i	1.25785	−	1.05663i
$598$		0			0
$599$		−	584.923i		−	0.976500i	−0.872704	−	0.488250i	$-0.837635\pi$
$599$		−	584.923i		−	0.976500i	0.872704	−	0.488250i	$-0.162365\pi$
$600$		0			0
$601$	71.6749	−	41.3815i	0.119259	−	0.0688544i	−0.439184	−	0.898397i	$-0.644732\pi$
$601$	71.6749	−	41.3815i	0.119259	−	0.0688544i	0.558443	+	0.829543i	$0.311399\pi$
$602$		0			0
$603$	−243.355	−	666.366i	−0.403574	−	1.10508i
$604$		0			0
$605$	1570.17			2.59532
$606$		0			0
$607$	−459.170	−	265.102i	−0.756458	−	0.436741i	0.0715644	−	0.997436i	$-0.477201\pi$
$607$	−459.170	−	265.102i	−0.756458	−	0.436741i	−0.828023	+	0.560695i	$0.810534\pi$
$608$		0			0
$609$	−1.46084	+	0.258402i	−0.00239876	+	0.000424305i
$610$		0			0
$611$	−163.964	−	94.6649i	−0.268354	−	0.154934i
$612$		0			0
$613$	328.438	−	568.872i	0.535788	−	0.928013i	−0.463336	−	0.886183i	$-0.653348\pi$
$613$	328.438	−	568.872i	0.535788	−	0.928013i	0.999125	−	0.0418302i	$-0.0133189\pi$
$614$		0			0
$615$	125.251	−	344.706i	0.203661	−	0.560498i
$616$		0			0
$617$	1105.41			1.79158			0.895792	−	0.444473i	$-0.146609\pi$
$617$	1105.41			1.79158			0.895792	+	0.444473i	$0.146609\pi$
$618$		0			0
$619$	−579.962	−	1004.52i	−0.936933	−	1.62282i	−0.771150	−	0.636654i	$-0.780318\pi$
$619$	−579.962	−	1004.52i	−0.936933	−	1.62282i	−0.165783	−	0.986162i	$-0.553015\pi$
$620$		0			0
$621$	−269.644	−	465.290i	−0.434210	−	0.749259i
$622$		0			0
$623$	32.7225	+	18.8923i	0.0525241	+	0.0303248i
$624$		0			0
$625$	325.262	+	563.370i	0.520419	+	0.901392i
$626$		0			0
$627$	−1019.43	−	288.391i	−1.62588	−	0.459954i
$628$		0			0
$629$	254.770	+	147.092i	0.405040	+	0.233850i
$630$		0			0
$631$	−134.726	−	233.352i	−0.213511	−	0.369812i	0.739300	−	0.673376i	$-0.235157\pi$
$631$	−134.726	−	233.352i	−0.213511	−	0.369812i	−0.952811	+	0.303564i	$0.901823\pi$
$632$		0			0
$633$	723.214	+	860.945i	1.14252	+	1.36010i
$634$		0			0
$635$	19.8593	+	11.4658i	0.0312745	+	0.0180563i
$636$		0			0
$637$	639.128	+	369.001i	1.00334	+	0.579279i
$638$		0			0
$639$	876.810	+	153.626i	1.37216	+	0.240417i
$640$		0			0
$641$		−	908.900i		−	1.41794i	−0.705238	−	0.708970i	$-0.749160\pi$
$641$		−	908.900i		−	1.41794i	0.705238	−	0.708970i	$-0.250840\pi$
$642$		0			0
$643$	−57.6008	−	99.7674i	−0.0895813	−	0.155159i	0.817753	−	0.575569i	$-0.195220\pi$
$643$	−57.6008	−	99.7674i	−0.0895813	−	0.155159i	−0.907334	+	0.420410i	$0.861886\pi$
$644$		0			0
$645$	−1207.39	+	1014.24i	−1.87193	+	1.57246i
$646$		0			0
$647$	1207.11			1.86570			0.932850	−	0.360264i	$-0.117313\pi$
$647$	1207.11			1.86570			0.932850	+	0.360264i	$0.117313\pi$
$648$		0			0
$649$	−1425.33	−	822.912i	−2.19619	−	1.26797i
$650$		0			0
$651$	36.9359	−	6.53342i	0.0567372	−	0.0100360i
$652$		0			0
$653$	293.553	−	508.449i	0.449545	−	0.778635i	−0.548811	−	0.835946i	$-0.684919\pi$
$653$	293.553	−	508.449i	0.449545	−	0.778635i	0.998356	+	0.0573114i	$0.0182528\pi$
$654$		0			0
$655$	−584.281	+	1012.00i	−0.892033	+	1.54505i
$656$		0			0
$657$	33.1526	−	189.216i	0.0504606	−	0.288000i
$658$		0			0
$659$	−591.774	−	341.661i	−0.897988	−	0.518453i	−0.0214408	−	0.999770i	$-0.506825\pi$
$659$	−591.774	−	341.661i	−0.897988	−	0.518453i	−0.876547	+	0.481317i	$0.840159\pi$
$660$		0			0
$661$		−	441.803i		−	0.668386i	−0.942505	−	0.334193i	$-0.891536\pi$
$661$		−	441.803i		−	0.668386i	0.942505	−	0.334193i	$-0.108464\pi$
$662$		0			0
$663$	−229.318	+	631.110i	−0.345880	+	0.951900i
$664$		0			0
$665$	−35.4724	+	2.58814i	−0.0533419	+	0.00389194i
$666$		0			0
$667$	31.8753	+	18.4032i	0.0477891	+	0.0275910i
$668$		0			0
$669$	−1212.83	+	214.531i	−1.81289	+	0.320674i
$670$		0			0
$671$	−1904.66			−2.83855
$672$		0			0
$673$	592.886	−	342.303i	0.880960	−	0.508623i	0.00998520	−	0.999950i	$-0.496822\pi$
$673$	592.886	−	342.303i	0.880960	−	0.508623i	0.870975	+	0.491328i	$0.163488\pi$
$674$		0			0
$675$	−646.205	+	1.04990i	−0.957341	+	0.00155540i
$676$		0			0
$677$	−496.365	+	286.576i	−0.733183	+	0.423303i	−0.819585	−	0.572957i	$-0.805796\pi$
$677$	−496.365	+	286.576i	−0.733183	+	0.423303i	0.0864027	+	0.996260i	$0.472463\pi$
$678$		0			0
$679$	−27.1688	+	15.6859i	−0.0400130	+	0.0231015i
$680$		0			0
$681$	564.667	+	672.204i	0.829173	+	0.987083i
$682$		0			0
$683$		−	313.554i		−	0.459083i	−0.973299	−	0.229542i	$-0.926277\pi$
$683$		−	313.554i		−	0.459083i	0.973299	−	0.229542i	$-0.0737227\pi$
$684$		0			0
$685$	84.4440			0.123276
$686$		0			0
$687$	−359.725	−	130.709i	−0.523618	−	0.190260i
$688$		0			0
$689$	9.28293	+	16.0785i	0.0134731	+	0.0233360i
$690$		0			0
$691$	−326.726	−	565.905i	−0.472830	−	0.818966i	0.526686	−	0.850060i	$-0.323434\pi$
$691$	−326.726	−	565.905i	−0.472830	−	0.818966i	−0.999516	+	0.0310940i	$0.990101\pi$
$692$		0			0
$693$	7.72543	−	44.0923i	0.0111478	−	0.0636253i
$694$		0			0
$695$	115.376	+	199.837i	0.166009	+	0.287535i
$696$		0			0
$697$		−	259.340i		−	0.372080i
$698$		0			0
$699$	185.186	+	67.2886i	0.264930	+	0.0962641i
$700$		0			0
$701$	581.857	−	1007.81i	0.830039	−	1.43767i	−0.0679678	−	0.997688i	$-0.521652\pi$
$701$	581.857	−	1007.81i	0.830039	−	1.43767i	0.898007	−	0.439982i	$-0.145015\pi$
$702$		0			0
$703$	−311.633	+	211.571i	−0.443290	+	0.300954i
$704$		0			0
$705$	−45.8827	−	259.392i	−0.0650819	−	0.367932i
$706$		0			0
$707$	−25.4798			−0.0360394
$708$		0			0
$709$	−37.7280	+	65.3468i	−0.0532129	+	0.0921675i	−0.891405	−	0.453208i	$-0.850280\pi$
$709$	−37.7280	+	65.3468i	−0.0532129	+	0.0921675i	0.838192	+	0.545375i	$0.183613\pi$
$710$		0			0
$711$	−92.7789	−	254.051i	−0.130491	−	0.357316i
$712$		0			0
$713$	−805.934	−	465.306i	−1.13034	−	0.652604i
$714$		0			0
$715$	1698.36	+	980.551i	2.37533	+	1.37140i
$716$		0			0
$717$	1229.97	+	446.917i	1.71543	+	0.623315i
$718$		0			0
$719$	−495.695	+	858.570i	−0.689423	+	1.19412i	0.282601	+	0.959237i	$0.408803\pi$
$719$	−495.695	+	858.570i	−0.689423	+	1.19412i	−0.972025	+	0.234879i	$0.924531\pi$
$720$		0			0
$721$		−	32.1155i		−	0.0445430i
$722$		0			0
$723$	245.010	−	674.294i	0.338879	−	0.932634i
$724$		0			0
$725$	38.3022	−	22.1138i	0.0528307	−	0.0305018i
$726$		0			0
$727$	−1106.15			−1.52153			−0.760763	−	0.649030i	$-0.775175\pi$
$727$	−1106.15			−1.52153			−0.760763	+	0.649030i	$0.775175\pi$
$728$		0			0
$729$	−362.447	+	632.514i	−0.497183	+	0.867646i
$730$		0			0
$731$	−557.511	+	965.637i	−0.762669	+	1.32098i
$732$		0			0
$733$	−283.607	+	491.222i	−0.386913	+	0.670153i	−0.992033	−	0.125982i	$-0.959792\pi$
$733$	−283.607	+	491.222i	−0.386913	+	0.670153i	0.605120	+	0.796134i	$0.293125\pi$
$734$		0			0
$735$	178.849	+	1011.10i	0.243333	+	1.37565i
$736$		0			0
$737$	−1268.78	+	732.531i	−1.72155	+	0.993936i
$738$		0			0
$739$	229.797	−	398.021i	0.310957	−	0.538594i	−0.667613	−	0.744509i	$-0.732684\pi$
$739$	229.797	−	398.021i	0.310957	−	0.538594i	0.978570	+	0.205915i	$0.0660171\pi$
$740$		0			0
$741$	−599.430	−	616.320i	−0.808948	−	0.831741i
$742$		0			0
$743$	−275.505	+	159.063i	−0.370801	+	0.214082i	−0.673808	−	0.738906i	$-0.735343\pi$
$743$	−275.505	+	159.063i	−0.370801	+	0.214082i	0.303007	+	0.952988i	$0.402009\pi$
$744$		0			0
$745$	658.098	−	1139.86i	0.883353	−	1.53001i
$746$		0			0
$747$	379.864	+	318.043i	0.508520	+	0.425761i
$748$		0			0
$749$	−14.7714	+	8.52828i	−0.0197215	+	0.0113862i
$750$		0			0
$751$		−	498.944i		−	0.664373i	−0.943214	−	0.332186i	$-0.892214\pi$
$751$		−	498.944i		−	0.664373i	0.943214	−	0.332186i	$-0.107786\pi$
$752$		0			0
$753$	285.858	−	240.127i	0.379625	−	0.318894i
$754$		0			0
$755$	1024.82	+	591.678i	1.35737	+	0.783679i
$756$		0			0
$757$	63.9290	−	110.728i	0.0844505	−	0.146273i	−0.820706	−	0.571350i	$-0.806420\pi$
$757$	63.9290	−	110.728i	0.0844505	−	0.146273i	0.905157	+	0.425078i	$0.139753\pi$
$758$		0			0
$759$	−850.385	+	714.343i	−1.12040	+	0.941163i
$760$		0			0
$761$	−243.975	+	422.577i	−0.320598	+	0.555292i	−0.980612	−	0.195962i	$-0.937217\pi$
$761$	−243.975	+	422.577i	−0.320598	+	0.555292i	0.660014	+	0.751254i	$0.270550\pi$
$762$		0			0
$763$			41.6052i			0.0545285i
$764$		0			0
$765$	−877.558	+	320.482i	−1.14713	+	0.418931i
$766$		0			0
$767$	−667.805	−	1156.67i	−0.870672	−	1.50805i
$768$		0			0
$769$	−763.452			−0.992786			−0.496393	−	0.868098i	$-0.665342\pi$
$769$	−763.452			−0.992786			−0.496393	+	0.868098i	$0.665342\pi$
$770$		0			0
$771$	383.937	−	67.9129i	0.497973	−	0.0880842i
$772$		0			0
$773$	181.681	−	104.893i	0.235033	−	0.135696i	−0.377859	−	0.925863i	$-0.623339\pi$
$773$	181.681	−	104.893i	0.235033	−	0.135696i	0.612892	+	0.790167i	$0.290006\pi$
$774$		0			0
$775$	−968.432	+	559.125i	−1.24959	+	0.721451i
$776$		0			0
$777$	−10.2366	−	12.1862i	−0.0131746	−	0.0156836i
$778$		0			0
$779$	298.885	+	144.660i	0.383678	+	0.185700i
$780$		0			0
$781$		−	1838.35i		−	2.35385i
$782$		0			0
$783$	−0.0810636	−	49.8941i	−0.000103530	−	0.0637217i
$784$		0			0
$785$	267.044	−	462.534i	0.340184	−	0.589215i
$786$		0			0
$787$	44.6872	+	25.8001i	0.0567816	+	0.0327829i	0.528122	−	0.849168i	$-0.322896\pi$
$787$	44.6872	+	25.8001i	0.0567816	+	0.0327829i	−0.471340	+	0.881951i	$0.656230\pi$
$788$		0			0
$789$	36.9259	+	208.756i	0.0468009	+	0.264583i
$790$		0			0
$791$			55.1065i			0.0696669i
$792$		0			0
$793$	−1338.58	−	772.831i	−1.68800	−	0.974567i
$794$		0			0
$795$	−8.82162	+	24.2781i	−0.0110964	+	0.0305385i
$796$		0			0
$797$	−1186.04	−	684.759i	−1.48813	−	0.859170i	−0.488218	−	0.872721i	$-0.662353\pi$
$797$	−1186.04	−	684.759i	−1.48813	−	0.859170i	−0.999908	+	0.0135512i	$0.995686\pi$
$798$		0			0
$799$	−93.1340	−	161.313i	−0.116563	−	0.201893i
$800$		0			0
$801$	−815.790	+	974.362i	−1.01846	+	1.21643i
$802$		0			0
$803$	−396.718			−0.494045
$804$		0			0
$805$	−18.6422	+	32.2892i	−0.0231580	+	0.0401109i
$806$		0			0
$807$	−128.830	+	354.556i	−0.159641	+	0.439350i
$808$		0			0
$809$	−656.453			−0.811438			−0.405719	−	0.913998i	$-0.632979\pi$
$809$	−656.453			−0.811438			−0.405719	+	0.913998i	$0.632979\pi$
$810$		0			0
$811$	1122.54	−	648.101i	1.38415	−	0.799138i	0.391501	−	0.920178i	$-0.371956\pi$
$811$	1122.54	−	648.101i	1.38415	−	0.799138i	0.992648	+	0.121039i	$0.0386228\pi$
$812$		0			0
$813$	−558.199	−	202.826i	−0.686592	−	0.249478i
$814$		0			0
$815$	−419.390	−	726.404i	−0.514588	−	0.891293i
$816$		0			0
$817$	−801.901	−	1181.16i	−0.981519	−	1.44573i
$818$		0			0
$819$	23.3202	−	27.8531i	0.0284739	−	0.0340087i
$820$		0			0
$821$	−496.761	+	860.416i	−0.605069	+	1.04801i	0.386972	+	0.922091i	$0.373521\pi$
$821$	−496.761	+	860.416i	−0.605069	+	1.04801i	−0.992041	+	0.125918i	$0.959812\pi$
$822$		0			0
$823$	1126.51			1.36878			0.684391	−	0.729115i	$-0.260068\pi$
$823$	1126.51			1.36878			0.684391	+	0.729115i	$0.260068\pi$
$824$		0			0
$825$	232.451	+	1314.13i	0.281758	+	1.59289i
$826$		0			0
$827$	−135.268	+	78.0970i	−0.163565	+	0.0944341i	−0.579548	−	0.814938i	$-0.696771\pi$
$827$	−135.268	+	78.0970i	−0.163565	+	0.0944341i	0.415983	+	0.909372i	$0.363437\pi$
$828$		0			0
$829$			3.38334i			0.00408123i	0.999998	+	0.00204062i	$0.000649549\pi$
$829$			3.38334i			0.00408123i	−0.999998	+	0.00204062i	$0.999350\pi$
$830$		0			0
$831$	−94.7609	+	79.6013i	−0.114032	+	0.0957898i
$832$		0			0
$833$	363.033	+	628.792i	0.435814	+	0.754853i
$834$		0			0
$835$	−1080.46	+	623.805i	−1.29397	+	0.747071i
$836$		0			0
$837$	2.04961	+	1261.52i	0.00244876	+	1.50719i
$838$		0			0
$839$		−	630.796i		−	0.751842i	−0.926652	−	0.375921i	$-0.877326\pi$
$839$		−	630.796i		−	0.751842i	0.926652	−	0.375921i	$-0.122674\pi$
$840$		0			0
$841$	−418.793	−	725.370i	−0.497970	−	0.862509i
$842$		0			0
$843$	129.384	−	356.081i	0.153481	−	0.422397i
$844$		0			0
$845$	204.632	+	354.433i	0.242168	+	0.419448i
$846$		0			0
$847$	−60.0660			−0.0709162
$848$		0			0
$849$	−436.721	+	366.856i	−0.514394	+	0.432103i
$850$		0			0
$851$			394.857i			0.463992i
$852$		0			0
$853$	−1014.79			−1.18967			−0.594834	−	0.803848i	$-0.702782\pi$
$853$	−1014.79			−1.18967			−0.594834	+	0.803848i	$0.702782\pi$
$854$		0			0
$855$	120.153	−	1190.14i	0.140530	−	1.39197i
$856$		0			0
$857$		−	493.374i		−	0.575699i	−0.957676	−	0.287850i	$-0.907060\pi$
$857$		−	493.374i		−	0.575699i	0.957676	−	0.287850i	$-0.0929404\pi$
$858$		0			0
$859$	801.753			0.933356			0.466678	−	0.884427i	$-0.345451\pi$
$859$	801.753			0.933356			0.466678	+	0.884427i	$0.345451\pi$
$860$		0			0
$861$	−4.79143	+	13.1866i	−0.00556496	+	0.0153154i
$862$		0			0
$863$		−	563.699i		−	0.653185i	−0.945165	−	0.326593i	$-0.894099\pi$
$863$		−	563.699i		−	0.653185i	0.945165	−	0.326593i	$-0.105901\pi$
$864$		0			0
$865$	−282.852	+	163.305i	−0.326996	+	0.188791i
$866$		0			0
$867$	158.023	−	132.743i	0.182264	−	0.153106i
$868$		0			0
$869$	−483.722	+	279.277i	−0.556642	+	0.321377i
$870$		0			0
$871$	−1188.92			−1.36500
$872$		0			0
$873$	−361.942	−	991.085i	−0.414595	−	1.13526i
$874$		0			0
$875$	−0.998155	−	1.72886i	−0.00114075	−	0.00197584i
$876$		0			0
$877$	136.491	−	78.8030i	0.155634	−	0.0898552i	−0.420161	−	0.907450i	$-0.638026\pi$
$877$	136.491	−	78.8030i	0.155634	−	0.0898552i	0.575794	+	0.817595i	$0.304693\pi$
$878$		0			0
$879$	−233.810	+	643.471i	−0.265995	+	0.732048i
$880$		0			0
$881$	1304.72			1.48095			0.740476	−	0.672083i	$-0.234600\pi$
$881$	1304.72			1.48095			0.740476	+	0.672083i	$0.234600\pi$
$882$		0			0
$883$	388.325	+	672.599i	0.439779	+	0.761720i	0.997672	−	0.0681929i	$-0.0217233\pi$
$883$	388.325	+	672.599i	0.439779	+	0.761720i	−0.557893	+	0.829913i	$0.688390\pi$
$884$		0			0
$885$	634.619	−	1746.54i	0.717084	−	1.97350i
$886$		0			0
$887$		−	68.6338i		−	0.0773774i	−0.999251	−	0.0386887i	$-0.987682\pi$
$887$		−	68.6338i		−	0.0773774i	0.999251	−	0.0386887i	$-0.0123181\pi$
$888$		0			0
$889$	−0.759707	−	0.438617i	−0.000854564	−	0.000493383i
$890$		0			0
$891$	1415.83	+	511.851i	1.58904	+	0.574468i
$892$		0			0
$893$	237.861	−	17.3549i	0.266362	−	0.0194343i
$894$		0			0
$895$	1097.85	−	633.844i	1.22665	−	0.708206i
$896$		0			0
$897$	−887.494	+	156.985i	−0.989402	+	0.175011i
$898$		0			0
$899$	−43.1706	−	74.7736i	−0.0480206	−	0.0831742i
$900$		0			0
$901$			18.2656i			0.0202726i
$902$		0			0
$903$	46.1882	−	38.7992i	0.0511498	−	0.0429670i
$904$		0			0
$905$	−407.976	−	235.545i	−0.450802	−	0.260271i
$906$		0			0
$907$		−	285.498i		−	0.314771i	−0.987537	−	0.157386i	$-0.949693\pi$
$907$		−	285.498i		−	0.314771i	0.987537	−	0.157386i	$-0.0503066\pi$
$908$		0			0
$909$	147.893	−	844.087i	0.162698	−	0.928588i
$910$		0			0
$911$	327.463	−	189.061i	0.359454	−	0.207531i	−0.309387	−	0.950936i	$-0.600124\pi$
$911$	327.463	−	189.061i	0.359454	−	0.207531i	0.668841	+	0.743405i	$0.266791\pi$
$912$		0			0
$913$	511.573	−	886.071i	0.560321	−	0.970505i
$914$		0			0
$915$	−374.580	−	2117.64i	−0.409377	−	2.31436i
$916$		0			0
$917$	22.3514	−	38.7138i	0.0243745	−	0.0422178i
$918$		0			0
$919$	956.436			1.04074			0.520368	−	0.853942i	$-0.325795\pi$
$919$	956.436			1.04074			0.520368	+	0.853942i	$0.325795\pi$
$920$		0			0
$921$	−32.2874	+	88.8585i	−0.0350569	+	0.0964805i
$922$		0			0
$923$	745.925	−	1291.98i	0.808153	−	1.39976i
$924$		0			0
$925$	410.904	+	237.236i	0.444221	+	0.256471i
$926$		0			0
$927$	1063.91	+	186.408i	1.14769	+	0.201088i
$928$		0			0
$929$	986.885			1.06231			0.531154	−	0.847275i	$-0.321758\pi$
$929$	986.885			1.06231			0.531154	+	0.847275i	$0.321758\pi$
$930$		0			0
$931$	−927.175	+	67.6487i	−0.995891	+	0.0726624i
$932$		0			0
$933$	487.864	+	177.269i	0.522898	+	0.189999i
$934$		0			0
$935$	964.693	+	1670.90i	1.03176	+	1.78706i
$936$		0			0
$937$	−858.403	−	1486.80i	−0.916118	−	1.58676i	−0.805256	−	0.592927i	$-0.797972\pi$
$937$	−858.403	−	1486.80i	−0.916118	−	1.58676i	−0.110862	−	0.993836i	$-0.535361\pi$
$938$		0			0
$939$	−342.705	−	124.524i	−0.364968	−	0.132614i
$940$		0			0
$941$			1159.32i			1.23200i	0.787745	+	0.616002i	$0.211249\pi$
$941$			1159.32i			1.23200i	−0.787745	+	0.616002i	$0.788751\pi$
$942$		0			0
$943$	301.454	−	174.045i	0.319676	−	0.184565i
$944$		0			0
$945$	50.5420	−	0.0821163i	0.0534836	−	8.68955e-5i
$946$		0			0
$947$	1697.33			1.79233			0.896163	−	0.443724i	$-0.146343\pi$
$947$	1697.33			1.79233			0.896163	+	0.443724i	$0.146343\pi$
$948$		0			0
$949$	−278.810	−	160.971i	−0.293794	−	0.169622i
$950$		0			0
$951$	−248.031	+	682.610i	−0.260811	+	0.717781i
$952$		0			0
$953$	895.156	+	516.819i	0.939303	+	0.542307i	0.889742	−	0.456464i	$-0.150884\pi$
$953$	895.156	+	516.819i	0.939303	+	0.542307i	0.0495615	+	0.998771i	$0.484218\pi$
$954$		0			0
$955$	−67.8393	+	117.501i	−0.0710359	+	0.123038i
$956$		0			0
$957$	−101.465	+	17.9477i	−0.106024	+	0.0187542i
$958$		0			0
$959$	−3.23036			−0.00336847
$960$		0			0
$961$	611.023	+	1058.32i	0.635820	+	1.10127i
$962$		0			0
$963$	−196.784	−	538.843i	−0.204345	−	0.559546i
$964$		0			0
$965$	−557.916	−	322.113i	−0.578152	−	0.333796i
$966$		0			0
$967$	767.042	+	1328.56i	0.793219	+	1.37389i	0.923964	+	0.382479i	$0.124930\pi$
$967$	767.042	+	1328.56i	0.793219	+	1.37389i	−0.130746	+	0.991416i	$0.541737\pi$
$968$		0			0
$969$	−207.550	−	819.985i	−0.214190	−	0.846218i
$970$		0			0
$971$	145.053	+	83.7464i	0.149385	+	0.0862475i	0.572829	−	0.819675i	$-0.305846\pi$
$971$	145.053	+	83.7464i	0.149385	+	0.0862475i	−0.423444	+	0.905922i	$0.639179\pi$
$972$		0			0
$973$	−4.41365	−	7.64467i	−0.00453613	−	0.00785680i
$974$		0			0
$975$	−369.854	+	1017.88i	−0.379337	+	1.04398i
$976$		0			0
$977$	265.644	+	153.369i	0.271897	+	0.156980i	0.629750	−	0.776798i	$-0.283158\pi$
$977$	265.644	+	153.369i	0.271897	+	0.156980i	−0.357852	+	0.933778i	$0.616491\pi$
$978$		0			0
$979$	2272.80	+	1312.20i	2.32155	+	1.34035i
$980$		0			0
$981$	−1378.28	−	241.489i	−1.40498	−	0.246167i
$982$		0			0
$983$		−	1636.58i		−	1.66489i	−0.554110	−	0.832444i	$-0.686941\pi$
$983$		−	1636.58i		−	1.66489i	0.554110	−	0.832444i	$-0.313059\pi$
$984$		0			0
$985$	959.713	+	1662.27i	0.974328	+	1.68759i
$986$		0			0
$987$	1.75522	+	9.92293i	0.00177834	+	0.0100536i
$988$		0			0
$989$	−1496.60			−1.51324
$990$		0			0
$991$	468.337	+	270.394i	0.472590	+	0.272850i	0.717323	−	0.696740i	$-0.245367\pi$
$991$	468.337	+	270.394i	0.472590	+	0.272850i	−0.244733	+	0.969590i	$0.578700\pi$
$992$		0			0
$993$	252.066	+	300.070i	0.253843	+	0.302186i
$994$		0			0
$995$	1143.41	−	1980.44i	1.14915	−	1.99039i
$996$		0			0
$997$	−948.639	+	1643.09i	−0.951493	+	1.64803i	−0.209297	+	0.977852i	$0.567118\pi$
$997$	−948.639	+	1643.09i	−0.951493	+	1.64803i	−0.742196	+	0.670183i	$0.766216\pi$
$998$		0			0
$999$	463.115	−	268.384i	0.463579	−	0.268652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.17	✓	80
3.2	odd	2		2052.3.s.a.901.36		80
9.2	odd	6		2052.3.bl.a.1585.5		80
9.7	even	3		684.3.bl.a.673.5	yes	80
19.12	odd	6		684.3.bl.a.373.5	yes	80
57.50	even	6		2052.3.bl.a.145.5		80
171.88	odd	6	inner	684.3.s.a.601.17	yes	80
171.164	even	6		2052.3.s.a.829.36		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.17	✓	80	1.1	even	1	trivial
684.3.s.a.601.17	yes	80	171.88	odd	6	inner
684.3.bl.a.373.5	yes	80	19.12	odd	6
684.3.bl.a.673.5	yes	80	9.7	even	3
2052.3.s.a.829.36		80	171.164	even	6
2052.3.s.a.901.36		80	3.2	odd	2
2052.3.bl.a.145.5		80	57.50	even	6
2052.3.bl.a.1585.5		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)

\(f(q)\)	\(=\)	\(q+(-0.522544 - 2.95414i) q^{3} +(-3.49763 - 6.05807i) q^{5} +(0.133800 + 0.231748i) q^{7} +(-8.45389 + 3.08734i) q^{9} +O(q^{10})\)	\(q+(-0.522544 - 2.95414i) q^{3} +(-3.49763 - 6.05807i) q^{5} +(0.133800 + 0.231748i) q^{7} +(-8.45389 + 3.08734i) q^{9} +(9.29330 + 16.0965i) q^{11} +15.0833i q^{13} +(-16.0687 + 13.4981i) q^{15} +(-7.41969 + 12.8513i) q^{17} +(-10.6722 - 15.7196i) q^{19} +(0.614701 - 0.516363i) q^{21} -19.9176 q^{23} +(-11.9668 + 20.7271i) q^{25} +(13.5380 + 23.3607i) q^{27} +(-1.60036 - 0.923966i) q^{29} +(40.4634 + 23.3615i) q^{31} +(42.6951 - 35.8649i) q^{33} +(0.935965 - 1.62114i) q^{35} -19.8245i q^{37} +(44.5582 - 7.88170i) q^{39} +(-15.1351 + 8.73823i) q^{41} +75.1394 q^{43} +(48.2719 + 40.4159i) q^{45} +(-6.27614 + 10.8706i) q^{47} +(24.4642 - 42.3732i) q^{49} +(41.8416 + 15.2034i) q^{51} +(1.06598 - 0.615444i) q^{53} +(65.0090 - 112.599i) q^{55} +(-40.8611 + 39.7413i) q^{57} +(-76.6856 + 44.2745i) q^{59} +(-51.2375 + 88.7460i) q^{61} +(-1.84662 - 1.54609i) q^{63} +(91.3756 - 52.7558i) q^{65} +78.8235i q^{67} +(10.4078 + 58.8395i) q^{69} +(-85.6563 - 49.4537i) q^{71} +(-10.6721 + 18.4847i) q^{73} +(67.4838 + 24.5207i) q^{75} +(-2.48689 + 4.30742i) q^{77} +30.0514i q^{79} +(61.9367 - 52.2001i) q^{81} +(-27.5237 - 47.6725i) q^{83} +103.805 q^{85} +(-1.89327 + 5.21049i) q^{87} +(122.281 - 70.5992i) q^{89} +(-3.49553 + 2.01815i) q^{91} +(47.8694 - 131.742i) q^{93} +(-57.9028 + 119.634i) q^{95} +117.234i q^{97} +(-128.260 - 107.386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 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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