LMFDB - Embedded newform 483.3.g.a.139.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(139,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("483.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.g (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.8
Character	$\chi$	$=$	483.139
Dual form			483.3.g.a.139.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.28514 q^{2} -1.73205i q^{3} +6.79214 q^{4} -3.80523i q^{5} +5.69003i q^{6} +(-0.993207 - 6.92918i) q^{7} -9.17258 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q-3.28514 q^{2} -1.73205i q^{3} +6.79214 q^{4} -3.80523i q^{5} +5.69003i q^{6} +(-0.993207 - 6.92918i) q^{7} -9.17258 q^{8} -3.00000 q^{9} +12.5007i q^{10} +7.79492 q^{11} -11.7643i q^{12} -22.7950i q^{13} +(3.26282 + 22.7633i) q^{14} -6.59085 q^{15} +2.96464 q^{16} +9.89299i q^{17} +9.85542 q^{18} -32.3625i q^{19} -25.8457i q^{20} +(-12.0017 + 1.72029i) q^{21} -25.6074 q^{22} +4.79583 q^{23} +15.8874i q^{24} +10.5202 q^{25} +74.8848i q^{26} +5.19615i q^{27} +(-6.74601 - 47.0640i) q^{28} +11.4297 q^{29} +21.6519 q^{30} +4.16392i q^{31} +26.9511 q^{32} -13.5012i q^{33} -32.4998i q^{34} +(-26.3671 + 3.77938i) q^{35} -20.3764 q^{36} +40.0642 q^{37} +106.315i q^{38} -39.4821 q^{39} +34.9038i q^{40} -17.4931i q^{41} +(39.4272 - 5.65138i) q^{42} +62.2555 q^{43} +52.9442 q^{44} +11.4157i q^{45} -15.7550 q^{46} -32.5512i q^{47} -5.13492i q^{48} +(-47.0271 + 13.7642i) q^{49} -34.5605 q^{50} +17.1352 q^{51} -154.827i q^{52} -57.0429 q^{53} -17.0701i q^{54} -29.6614i q^{55} +(9.11027 + 63.5585i) q^{56} -56.0534 q^{57} -37.5481 q^{58} +69.7638i q^{59} -44.7660 q^{60} +71.8427i q^{61} -13.6791i q^{62} +(2.97962 + 20.7875i) q^{63} -100.397 q^{64} -86.7402 q^{65} +44.3533i q^{66} -76.9997 q^{67} +67.1946i q^{68} -8.30662i q^{69} +(86.6196 - 12.4158i) q^{70} -97.1894 q^{71} +27.5178 q^{72} -69.9330i q^{73} -131.616 q^{74} -18.2216i q^{75} -219.810i q^{76} +(-7.74197 - 54.0124i) q^{77} +129.704 q^{78} -64.5952 q^{79} -11.2811i q^{80} +9.00000 q^{81} +57.4672i q^{82} -85.3491i q^{83} +(-81.5172 + 11.6844i) q^{84} +37.6451 q^{85} -204.518 q^{86} -19.7968i q^{87} -71.4995 q^{88} +11.1608i q^{89} -37.5021i q^{90} +(-157.951 + 22.6402i) q^{91} +32.5740 q^{92} +7.21212 q^{93} +106.935i q^{94} -123.146 q^{95} -46.6806i q^{96} -45.6445i q^{97} +(154.491 - 45.2174i) q^{98} -23.3848 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	$ 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) $ 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−3.28514			−1.64257			−0.821285	−	0.570518i	$-0.806742\pi$
$2$	−3.28514			−1.64257			−0.821285	+	0.570518i	$0.806742\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	6.79214			1.69804
$5$		−	3.80523i		−	0.761045i	−0.924772	−	0.380523i	$-0.875744\pi$
$5$		−	3.80523i		−	0.761045i	0.924772	−	0.380523i	$-0.124256\pi$
$6$			5.69003i			0.948338i
$7$	−0.993207	−	6.92918i	−0.141887	−	0.989883i
$7$	−0.993207	−	6.92918i	−0.141887	−	0.989883i
$8$	−9.17258			−1.14657
$9$	−3.00000			−0.333333
$10$			12.5007i			1.25007i
$11$	7.79492			0.708629			0.354314	−	0.935126i	$-0.384714\pi$
$11$	7.79492			0.708629			0.354314	+	0.935126i	$0.384714\pi$
$12$		−	11.7643i		−	0.980362i
$13$		−	22.7950i		−	1.75346i	−0.480980	−	0.876732i	$-0.659719\pi$
$13$		−	22.7950i		−	1.75346i	0.480980	−	0.876732i	$-0.340281\pi$
$14$	3.26282	+	22.7633i	0.233059	+	1.62595i
$15$	−6.59085			−0.439390
$16$	2.96464			0.185290
$17$			9.89299i			0.581940i	0.956732	+	0.290970i	$0.0939780\pi$
$17$			9.89299i			0.581940i	−0.956732	+	0.290970i	$0.906022\pi$
$18$	9.85542			0.547523
$19$		−	32.3625i		−	1.70329i	−0.524121	−	0.851644i	$-0.675606\pi$
$19$		−	32.3625i		−	1.70329i	0.524121	−	0.851644i	$-0.324394\pi$
$20$		−	25.8457i		−	1.29228i
$21$	−12.0017	+	1.72029i	−0.571509	+	0.0819183i
$22$	−25.6074			−1.16397
$23$	4.79583			0.208514
$23$	4.79583			0.208514
$24$			15.8874i			0.661974i
$25$	10.5202			0.420810
$26$			74.8848i			2.88019i
$27$			5.19615i			0.192450i
$28$	−6.74601	−	47.0640i	−0.240929	−	1.68086i
$29$	11.4297			0.394127			0.197064	−	0.980391i	$-0.436859\pi$
$29$	11.4297			0.394127			0.197064	+	0.980391i	$0.436859\pi$
$30$	21.6519			0.721728
$31$			4.16392i			0.134320i	0.997742	+	0.0671600i	$0.0213938\pi$
$31$			4.16392i			0.134320i	−0.997742	+	0.0671600i	$0.978606\pi$
$32$	26.9511			0.842221
$33$		−	13.5012i		−	0.409127i
$34$		−	32.4998i		−	0.955878i
$35$	−26.3671	+	3.77938i	−0.753346	+	0.107982i
$36$	−20.3764			−0.566012
$37$	40.0642			1.08282			0.541408	−	0.840760i	$-0.317892\pi$
$37$	40.0642			1.08282			0.541408	+	0.840760i	$0.317892\pi$
$38$			106.315i			2.79777i
$39$	−39.4821			−1.01236
$40$			34.9038i			0.872594i
$41$		−	17.4931i		−	0.426661i	−0.976980	−	0.213330i	$-0.931569\pi$
$41$		−	17.4931i		−	0.426661i	0.976980	−	0.213330i	$-0.0684311\pi$
$42$	39.4272	−	5.65138i	0.938744	−	0.134557i
$43$	62.2555			1.44780			0.723901	−	0.689904i	$-0.242347\pi$
$43$	62.2555			1.44780			0.723901	+	0.689904i	$0.242347\pi$
$44$	52.9442			1.20328
$45$			11.4157i			0.253682i
$46$	−15.7550			−0.342500
$47$		−	32.5512i		−	0.692578i	−0.938128	−	0.346289i	$-0.887442\pi$
$47$		−	32.5512i		−	0.692578i	0.938128	−	0.346289i	$-0.112558\pi$
$48$		−	5.13492i		−	0.106977i
$49$	−47.0271	+	13.7642i	−0.959736	+	0.280902i
$50$	−34.5605			−0.691210
$51$	17.1352			0.335983
$52$		−	154.827i		−	2.97744i
$53$	−57.0429			−1.07628			−0.538141	−	0.842855i	$-0.680873\pi$
$53$	−57.0429			−1.07628			−0.538141	+	0.842855i	$0.680873\pi$
$54$		−	17.0701i		−	0.316113i
$55$		−	29.6614i		−	0.539299i
$56$	9.11027	+	63.5585i	0.162683	+	1.13497i
$57$	−56.0534			−0.983393
$58$	−37.5481			−0.647381
$59$			69.7638i			1.18244i	0.806511	+	0.591219i	$0.201353\pi$
$59$			69.7638i			1.18244i	−0.806511	+	0.591219i	$0.798647\pi$
$60$	−44.7660			−0.746100
$61$			71.8427i			1.17775i	0.808225	+	0.588874i	$0.200429\pi$
$61$			71.8427i			1.17775i	−0.808225	+	0.588874i	$0.799571\pi$
$62$		−	13.6791i		−	0.220630i
$63$	2.97962	+	20.7875i	0.0472956	+	0.329961i
$64$	−100.397			−1.56870
$65$	−86.7402			−1.33447
$66$			44.3533i			0.672020i
$67$	−76.9997			−1.14925			−0.574625	−	0.818417i	$-0.694852\pi$
$67$	−76.9997			−1.14925			−0.574625	+	0.818417i	$0.694852\pi$
$68$			67.1946i			0.988156i
$69$		−	8.30662i		−	0.120386i
$70$	86.6196	−	12.4158i	1.23742	−	0.177368i
$71$	−97.1894			−1.36887			−0.684433	−	0.729076i	$-0.739950\pi$
$71$	−97.1894			−1.36887			−0.684433	+	0.729076i	$0.739950\pi$
$72$	27.5178			0.382191
$73$		−	69.9330i		−	0.957986i	−0.877819	−	0.478993i	$-0.841002\pi$
$73$		−	69.9330i		−	0.957986i	0.877819	−	0.478993i	$-0.158998\pi$
$74$	−131.616			−1.77860
$75$		−	18.2216i		−	0.242955i
$76$		−	219.810i		−	2.89224i
$77$	−7.74197	−	54.0124i	−0.100545	−	0.701460i
$78$	129.704			1.66288
$79$	−64.5952			−0.817661			−0.408831	−	0.912610i	$-0.634063\pi$
$79$	−64.5952			−0.817661			−0.408831	+	0.912610i	$0.634063\pi$
$80$		−	11.2811i		−	0.141014i
$81$	9.00000			0.111111
$82$			57.4672i			0.700820i
$83$		−	85.3491i		−	1.02830i	−0.857700	−	0.514151i	$-0.828107\pi$
$83$		−	85.3491i		−	1.02830i	0.857700	−	0.514151i	$-0.171893\pi$
$84$	−81.5172	+	11.6844i	−0.970443	+	0.139100i
$85$	37.6451			0.442883
$86$	−204.518			−2.37812
$87$		−	19.7968i		−	0.227549i
$88$	−71.4995			−0.812495
$89$			11.1608i			0.125403i	0.998032	+	0.0627013i	$0.0199715\pi$
$89$			11.1608i			0.125403i	−0.998032	+	0.0627013i	$0.980028\pi$
$90$		−	37.5021i		−	0.416690i
$91$	−157.951	+	22.6402i	−1.73572	+	0.248793i
$92$	32.5740			0.354065
$93$	7.21212			0.0775497
$94$			106.935i			1.13761i
$95$	−123.146			−1.29628
$96$		−	46.6806i		−	0.486256i
$97$		−	45.6445i		−	0.470562i	−0.971927	−	0.235281i	$-0.924399\pi$
$97$		−	45.6445i		−	0.470562i	0.971927	−	0.235281i	$-0.0756011\pi$
$98$	154.491	−	45.2174i	1.57643	−	0.461402i
$99$	−23.3848			−0.236210
$100$	71.4550			0.714550
$101$			127.283i			1.26022i	0.776504	+	0.630112i	$0.216991\pi$
$101$			127.283i			1.26022i	−0.776504	+	0.630112i	$0.783009\pi$
$102$	−56.2914			−0.551876
$103$			113.919i			1.10601i	0.833179	+	0.553004i	$0.186518\pi$
$103$			113.919i			1.10601i	−0.833179	+	0.553004i	$0.813482\pi$
$104$			209.089i			2.01047i
$105$	6.54608	+	45.6692i	0.0623436	+	0.434944i
$106$	187.394			1.76787
$107$	115.746			1.08174			0.540869	−	0.841107i	$-0.318096\pi$
$107$	115.746			1.08174			0.540869	+	0.841107i	$0.318096\pi$
$108$			35.2930i			0.326787i
$109$	−16.0035			−0.146821			−0.0734106	−	0.997302i	$-0.523388\pi$
$109$	−16.0035			−0.146821			−0.0734106	+	0.997302i	$0.523388\pi$
$110$			97.4419i			0.885836i
$111$		−	69.3932i		−	0.625164i
$112$	−2.94451	−	20.5426i	−0.0262902	−	0.183416i
$113$	42.8195			0.378934			0.189467	−	0.981887i	$-0.439324\pi$
$113$	42.8195			0.378934			0.189467	+	0.981887i	$0.439324\pi$
$114$	184.143			1.61529
$115$		−	18.2492i		−	0.158689i
$116$	77.6321			0.669242
$117$			68.3851i			0.584488i
$118$		−	229.184i		−	1.94224i
$119$	68.5503	−	9.82578i	0.576053	−	0.0825696i
$120$	60.4551			0.503792
$121$	−60.2393			−0.497845
$122$		−	236.013i		−	1.93453i
$123$	−30.2989			−0.246333
$124$			28.2819i			0.228080i
$125$		−	135.163i		−	1.08130i
$126$	−9.78847	−	68.2900i	−0.0776863	−	0.541984i
$127$	−114.716			−0.903279			−0.451640	−	0.892201i	$-0.649161\pi$
$127$	−114.716			−0.903279			−0.451640	+	0.892201i	$0.649161\pi$
$128$	222.013			1.73447
$129$		−	107.830i		−	0.835889i
$130$	284.954			2.19195
$131$			145.038i			1.10716i	0.832796	+	0.553579i	$0.186738\pi$
$131$			145.038i			1.10716i	−0.832796	+	0.553579i	$0.813262\pi$
$132$		−	91.7020i		−	0.694712i
$133$	−224.245	+	32.1426i	−1.68605	+	0.241674i
$134$	252.955			1.88772
$135$	19.7725			0.146463
$136$		−	90.7442i		−	0.667237i
$137$	188.104			1.37303			0.686513	−	0.727118i	$-0.259141\pi$
$137$	188.104			1.37303			0.686513	+	0.727118i	$0.259141\pi$
$138$			27.2884i			0.197742i
$139$		−	107.923i		−	0.776424i	−0.921570	−	0.388212i	$-0.873093\pi$
$139$		−	107.923i		−	0.776424i	0.921570	−	0.388212i	$-0.126907\pi$
$140$	−179.089	+	25.6701i	−1.27921	+	0.183358i
$141$	−56.3803			−0.399860
$142$	319.281			2.24846
$143$		−	177.685i		−	1.24255i
$144$	−8.89393			−0.0617634
$145$		−	43.4925i		−	0.299949i
$146$			229.740i			1.57356i
$147$	23.8403	+	81.4533i	0.162179	+	0.554104i
$148$	272.122			1.83866
$149$	−204.857			−1.37488			−0.687441	−	0.726240i	$-0.741266\pi$
$149$	−204.857			−1.37488			−0.687441	+	0.726240i	$0.741266\pi$
$150$			59.8605i			0.399070i
$151$	236.398			1.56555			0.782774	−	0.622307i	$-0.213804\pi$
$151$	236.398			1.56555			0.782774	+	0.622307i	$0.213804\pi$
$152$			296.847i			1.95294i
$153$		−	29.6790i		−	0.193980i
$154$	25.4334	+	177.438i	0.165152	+	1.15220i
$155$	15.8447			0.102224
$156$	−268.168			−1.71903
$157$			247.573i			1.57690i	0.615099	+	0.788450i	$0.289116\pi$
$157$			247.573i			1.57690i	−0.615099	+	0.788450i	$0.710884\pi$
$158$	212.204			1.34307
$159$			98.8013i			0.621392i
$160$		−	102.555i		−	0.640968i
$161$	−4.76325	−	33.2312i	−0.0295854	−	0.206405i
$162$	−29.5663			−0.182508
$163$	201.319			1.23509			0.617544	−	0.786536i	$-0.288128\pi$
$163$	201.319			1.23509			0.617544	+	0.786536i	$0.288128\pi$
$164$		−	118.816i		−	0.724485i
$165$	−51.3751			−0.311364
$166$			280.384i			1.68906i
$167$			205.877i			1.23279i	0.787436	+	0.616397i	$0.211408\pi$
$167$			205.877i			1.23279i	−0.787436	+	0.616397i	$0.788592\pi$
$168$	110.087	−	15.7795i	0.655277	−	0.0939253i
$169$	−350.613			−2.07463
$170$	−123.669			−0.727466
$171$			97.0874i			0.567762i
$172$	422.848			2.45842
$173$			0.860426i			0.00497356i	0.999997	+	0.00248678i	$0.000791567\pi$
$173$			0.860426i			0.00497356i	−0.999997	+	0.00248678i	$0.999208\pi$
$174$			65.0352i			0.373766i
$175$	−10.4488	−	72.8967i	−0.0597073	−	0.416552i
$176$	23.1092			0.131302
$177$	120.834			0.682681
$178$		−	36.6649i		−	0.205983i
$179$	−46.8028			−0.261468			−0.130734	−	0.991417i	$-0.541733\pi$
$179$	−46.8028			−0.261468			−0.130734	+	0.991417i	$0.541733\pi$
$180$			77.5370i			0.430761i
$181$			72.5862i			0.401029i	0.979691	+	0.200514i	$0.0642613\pi$
$181$			72.5862i			0.401029i	−0.979691	+	0.200514i	$0.935739\pi$
$182$	518.890	−	74.3761i	2.85105	−	0.408660i
$183$	124.435			0.679974
$184$	−43.9902			−0.239077
$185$		−	152.453i		−	0.824072i
$186$	−23.6928			−0.127381
$187$			77.1150i			0.412380i
$188$		−	221.092i		−	1.17602i
$189$	36.0051	−	5.16086i	0.190503	−	0.0273061i
$190$	404.553			2.12923
$191$	120.247			0.629565			0.314782	−	0.949164i	$-0.398068\pi$
$191$	120.247			0.629565			0.314782	+	0.949164i	$0.398068\pi$
$192$			173.892i			0.905687i
$193$	229.423			1.18872			0.594360	−	0.804199i	$-0.297406\pi$
$193$	229.423			1.18872			0.594360	+	0.804199i	$0.297406\pi$
$194$			149.949i			0.772932i
$195$			150.238i			0.770454i
$196$	−319.415	+	93.4886i	−1.62967	+	0.476983i
$197$	−302.951			−1.53782			−0.768910	−	0.639357i	$-0.779201\pi$
$197$	−302.951			−1.53782			−0.768910	+	0.639357i	$0.779201\pi$
$198$	76.8222			0.387991
$199$		−	225.056i		−	1.13093i	−0.824771	−	0.565466i	$-0.808696\pi$
$199$		−	225.056i		−	1.13093i	0.824771	−	0.565466i	$-0.191304\pi$
$200$	−96.4978			−0.482489
$201$			133.367i			0.663519i
$202$		−	418.142i		−	2.07001i
$203$	−11.3520	−	79.1983i	−0.0559214	−	0.390140i
$204$	116.384			0.570512
$205$	−66.5652			−0.324708
$206$		−	374.239i		−	1.81669i
$207$	−14.3875			−0.0695048
$208$		−	67.5791i		−	0.324900i
$209$		−	252.263i		−	1.20700i
$210$	−21.5048	−	150.030i	−0.102404	−	0.714427i
$211$	305.616			1.44842			0.724208	−	0.689582i	$-0.242206\pi$
$211$	305.616			1.44842			0.724208	+	0.689582i	$0.242206\pi$
$212$	−387.444			−1.82757
$213$			168.337i			0.790315i
$214$	−380.241			−1.77683
$215$		−	236.896i		−	1.10184i
$216$		−	47.6621i		−	0.220658i
$217$	28.8526	−	4.13564i	0.132961	−	0.0190582i
$218$	52.5738			0.241164
$219$	−121.127			−0.553094
$220$		−	201.465i		−	0.915749i
$221$	225.511			1.02041
$222$			227.966i			1.02687i
$223$		−	121.390i		−	0.544349i	−0.962248	−	0.272174i	$-0.912257\pi$
$223$		−	121.390i		−	0.544349i	0.962248	−	0.272174i	$-0.0877427\pi$
$224$	−26.7680	−	186.749i	−0.119500	−	0.833700i
$225$	−31.5607			−0.140270
$226$	−140.668			−0.622425
$227$			185.150i			0.815639i	0.913063	+	0.407819i	$0.133711\pi$
$227$			185.150i			0.815639i	−0.913063	+	0.407819i	$0.866289\pi$
$228$	−380.723			−1.66984
$229$			80.2647i			0.350501i	0.984524	+	0.175250i	$0.0560735\pi$
$229$			80.2647i			0.350501i	−0.984524	+	0.175250i	$0.943926\pi$
$230$			59.9513i			0.260658i
$231$	−93.5522	+	13.4095i	−0.404988	+	0.0580497i
$232$	−104.840			−0.451895
$233$	−18.3414			−0.0787185			−0.0393593	−	0.999225i	$-0.512532\pi$
$233$	−18.3414			−0.0787185			−0.0393593	+	0.999225i	$0.512532\pi$
$234$		−	224.654i		−	0.960062i
$235$	−123.865			−0.527084
$236$			473.846i			2.00782i
$237$			111.882i			0.472077i
$238$	−225.197	+	32.2791i	−0.946207	+	0.135626i
$239$	189.325			0.792155			0.396077	−	0.918217i	$-0.370371\pi$
$239$	189.325			0.792155			0.396077	+	0.918217i	$0.370371\pi$
$240$	−19.5395			−0.0814147
$241$		−	106.945i		−	0.443754i	−0.975075	−	0.221877i	$-0.928782\pi$
$241$		−	106.945i		−	0.443754i	0.975075	−	0.221877i	$-0.0712183\pi$
$242$	197.894			0.817746
$243$		−	15.5885i		−	0.0641500i
$244$			487.966i			1.99986i
$245$	52.3760	+	178.949i	0.213780	+	0.730403i
$246$	99.5362			0.404619
$247$	−737.703			−2.98665
$248$		−	38.1939i		−	0.154008i
$249$	−147.829			−0.593691
$250$			444.028i			1.77611i
$251$		−	449.212i		−	1.78969i	−0.446379	−	0.894844i	$-0.647287\pi$
$251$		−	449.212i		−	1.78969i	0.446379	−	0.894844i	$-0.352713\pi$
$252$	20.2380	+	141.192i	0.0803096	+	0.560286i
$253$	37.3831			0.147759
$254$	376.860			1.48370
$255$		−	65.2032i		−	0.255699i
$256$	−327.756			−1.28030
$257$		−	406.702i		−	1.58250i	−0.611494	−	0.791249i	$-0.709431\pi$
$257$		−	406.702i		−	1.58250i	0.611494	−	0.791249i	$-0.290569\pi$
$258$			354.235i			1.37301i
$259$	−39.7920	−	277.612i	−0.153637	−	1.07186i
$260$	−589.152			−2.26597
$261$	−34.2891			−0.131376
$262$		−	476.470i		−	1.81859i
$263$	160.619			0.610717			0.305358	−	0.952237i	$-0.401224\pi$
$263$	160.619			0.610717			0.305358	+	0.952237i	$0.401224\pi$
$264$			123.841i			0.469094i
$265$			217.061i			0.819099i
$266$	736.677	−	105.593i	2.76946	−	0.396966i
$267$	19.3311			0.0724012
$268$	−522.993			−1.95147
$269$		−	2.73332i		−	0.0101611i	−0.999987	−	0.00508053i	$-0.998383\pi$
$269$		−	2.73332i		−	0.0101611i	0.999987	−	0.00508053i	$-0.00161719\pi$
$270$	−64.9556			−0.240576
$271$		−	201.954i		−	0.745217i	−0.927989	−	0.372608i	$-0.878463\pi$
$271$		−	201.954i		−	0.745217i	0.927989	−	0.372608i	$-0.121537\pi$
$272$			29.3292i			0.107828i
$273$	39.2139	+	273.579i	0.143641	+	1.00212i
$274$	−617.949			−2.25529
$275$	82.0044			0.298198
$276$		−	56.4198i		−	0.204420i
$277$	50.8260			0.183487			0.0917437	−	0.995783i	$-0.470756\pi$
$277$	50.8260			0.183487			0.0917437	+	0.995783i	$0.470756\pi$
$278$			354.542i			1.27533i
$279$		−	12.4918i		−	0.0447733i
$280$	241.854	−	34.6667i	0.863766	−	0.123810i
$281$	−429.904			−1.52991			−0.764953	−	0.644086i	$-0.777238\pi$
$281$	−429.904			−1.52991			−0.764953	+	0.644086i	$0.777238\pi$
$282$	185.217			0.656799
$283$			256.809i			0.907452i	0.891141	+	0.453726i	$0.149905\pi$
$283$			256.809i			0.907452i	−0.891141	+	0.453726i	$0.850095\pi$
$284$	−660.125			−2.32438
$285$			213.296i			0.748407i
$286$			583.721i			2.04098i
$287$	−121.213	+	17.3743i	−0.422344	+	0.0605375i
$288$	−80.8532			−0.280740
$289$	191.129			0.661345
$290$			142.879i			0.492687i
$291$	−79.0587			−0.271679
$292$		−	474.995i		−	1.62669i
$293$			480.284i			1.63919i	0.572941	+	0.819596i	$0.305802\pi$
$293$			480.284i			1.63919i	−0.572941	+	0.819596i	$0.694198\pi$
$294$	−78.3188	−	267.585i	−0.266391	−	0.910155i
$295$	265.467			0.899889
$296$	−367.492			−1.24153
$297$			40.5036i			0.136376i
$298$	672.985			2.25834
$299$		−	109.321i		−	0.365622i
$300$		−	123.764i		−	0.412546i
$301$	−61.8326	−	431.379i	−0.205424	−	1.43315i
$302$	−776.599			−2.57152
$303$	220.460			0.727591
$304$		−	95.9432i		−	0.315603i
$305$	273.378			0.896320
$306$			97.4995i			0.318626i
$307$		−	357.607i		−	1.16484i	−0.812887	−	0.582421i	$-0.802105\pi$
$307$		−	357.607i		−	1.16484i	0.812887	−	0.582421i	$-0.197895\pi$
$308$	−52.5845	−	366.860i	−0.170729	−	1.19110i
$309$	197.313			0.638553
$310$	−52.0519			−0.167909
$311$			160.415i			0.515804i	0.966171	+	0.257902i	$0.0830311\pi$
$311$			160.415i			0.515804i	−0.966171	+	0.257902i	$0.916969\pi$
$312$	362.153			1.16075
$313$			80.5821i			0.257451i	0.991680	+	0.128725i	$0.0410886\pi$
$313$			80.5821i			0.257451i	−0.991680	+	0.128725i	$0.958911\pi$
$314$		−	813.313i		−	2.59017i
$315$	79.1013	−	11.3381i	0.251115	−	0.0359941i
$316$	−438.740			−1.38842
$317$	−407.022			−1.28398			−0.641990	−	0.766713i	$-0.721891\pi$
$317$	−407.022			−1.28398			−0.641990	+	0.766713i	$0.721891\pi$
$318$		−	324.576i		−	1.02068i
$319$	89.0934			0.279290
$320$			382.032i			1.19385i
$321$		−	200.478i		−	0.624541i
$322$	15.6480	+	109.169i	0.0485961	+	0.339034i
$323$	320.161			0.991211
$324$	61.1293			0.188671
$325$		−	239.809i		−	0.737874i
$326$	−661.363			−2.02872
$327$			27.7189i			0.0847673i
$328$			160.457i			0.489198i
$329$	−225.553	+	32.3301i	−0.685572	+	0.0982677i
$330$	168.774			0.511438
$331$	85.4818			0.258253			0.129127	−	0.991628i	$-0.458783\pi$
$331$	85.4818			0.258253			0.129127	+	0.991628i	$0.458783\pi$
$332$		−	579.703i		−	1.74609i
$333$	−120.192			−0.360938
$334$		−	676.333i		−	2.02495i
$335$			293.001i			0.874631i
$336$	−35.5808	+	5.10003i	−0.105895	+	0.0151787i
$337$	330.069			0.979432			0.489716	−	0.871882i	$-0.337100\pi$
$337$	330.069			0.979432			0.489716	+	0.871882i	$0.337100\pi$
$338$	1151.81			3.40773
$339$		−	74.1656i		−	0.218778i
$340$	255.691			0.752031
$341$			32.4574i			0.0951830i
$342$		−	318.946i		−	0.932589i
$343$	142.082	+	312.188i	0.414234	+	0.910170i
$344$	−571.043			−1.66001
$345$	−31.6086			−0.0916191
$346$		−	2.82662i		−	0.00816942i
$347$	231.361			0.666747			0.333373	−	0.942795i	$-0.391813\pi$
$347$	231.361			0.666747			0.333373	+	0.942795i	$0.391813\pi$
$348$		−	134.463i		−	0.386387i
$349$			645.510i			1.84960i	0.380456	+	0.924799i	$0.375767\pi$
$349$			645.510i			1.84960i	−0.380456	+	0.924799i	$0.624233\pi$
$350$	34.3257	+	239.476i	0.0980735	+	0.684217i
$351$	118.446			0.337454
$352$	210.081			0.596822
$353$		−	547.067i		−	1.54976i	−0.632106	−	0.774882i	$-0.717809\pi$
$353$		−	547.067i		−	1.54976i	0.632106	−	0.774882i	$-0.282191\pi$
$354$	−396.958			−1.12135
$355$			369.828i			1.04177i
$356$			75.8060i			0.212938i
$357$	−17.0188	−	118.733i	−0.0476716	−	0.332584i
$358$	153.754			0.429479
$359$	274.340			0.764178			0.382089	−	0.924126i	$-0.375205\pi$
$359$	274.340			0.764178			0.382089	+	0.924126i	$0.375205\pi$
$360$		−	104.711i		−	0.290865i
$361$	−686.328			−1.90119
$362$		−	238.456i		−	0.658717i
$363$			104.337i			0.287431i
$364$	−1072.82	+	153.775i	−2.94732	+	0.422460i
$365$	−266.111			−0.729071
$366$	−408.787			−1.11690
$367$			424.086i			1.15555i	0.816197	+	0.577774i	$0.196079\pi$
$367$			424.086i			1.15555i	−0.816197	+	0.577774i	$0.803921\pi$
$368$	14.2179			0.0386357
$369$			52.4793i			0.142220i
$370$			500.830i			1.35360i
$371$	56.6555	+	395.261i	0.152710	+	1.06539i
$372$	48.9858			0.131682
$373$	447.057			1.19854			0.599272	−	0.800545i	$-0.295457\pi$
$373$	447.057			1.19854			0.599272	+	0.800545i	$0.295457\pi$
$374$		−	253.334i		−	0.677362i
$375$	−234.109			−0.624289
$376$			298.578i			0.794092i
$377$		−	260.540i		−	0.691087i
$378$	−118.282	+	16.9541i	−0.312915	+	0.0448522i
$379$	517.130			1.36446			0.682230	−	0.731138i	$-0.261010\pi$
$379$	517.130			1.36446			0.682230	+	0.731138i	$0.261010\pi$
$380$	−836.429			−2.20113
$381$			198.695i			0.521508i
$382$	−395.028			−1.03410
$383$		−	488.095i		−	1.27440i	−0.770699	−	0.637200i	$-0.780093\pi$
$383$		−	488.095i		−	1.27440i	0.770699	−	0.637200i	$-0.219907\pi$
$384$		−	384.537i		−	1.00140i
$385$	−205.529	+	29.4599i	−0.533843	+	0.0765193i
$386$	−753.686			−1.95255
$387$	−186.766			−0.482601
$388$		−	310.024i		−	0.799032i
$389$	−363.416			−0.934232			−0.467116	−	0.884196i	$-0.654707\pi$
$389$	−363.416			−0.934232			−0.467116	+	0.884196i	$0.654707\pi$
$390$		−	493.554i		−	1.26552i
$391$			47.4451i			0.121343i
$392$	431.360	−	126.253i	1.10041	−	0.322075i
$393$	251.213			0.639219
$394$	995.235			2.52598
$395$			245.799i			0.622277i
$396$	−158.833			−0.401092
$397$		−	543.625i		−	1.36933i	−0.728856	−	0.684667i	$-0.759948\pi$
$397$		−	543.625i		−	1.36933i	0.728856	−	0.684667i	$-0.240052\pi$
$398$			739.339i			1.85764i
$399$	55.6726	+	388.404i	0.139530	+	0.973444i
$400$	31.1888			0.0779720
$401$	413.034			1.03001			0.515005	−	0.857187i	$-0.327790\pi$
$401$	413.034			1.03001			0.515005	+	0.857187i	$0.327790\pi$
$402$		−	438.131i		−	1.08988i
$403$	94.9167			0.235525
$404$			864.523i			2.13991i
$405$		−	34.2470i		−	0.0845606i
$406$	37.2930	+	260.178i	0.0918548	+	0.640832i
$407$	312.297			0.767314
$408$	−157.174			−0.385230
$409$			56.2678i			0.137574i	0.997631	+	0.0687870i	$0.0219129\pi$
$409$			56.2678i			0.137574i	−0.997631	+	0.0687870i	$0.978087\pi$
$410$	218.676			0.533356
$411$		−	325.807i		−	0.792717i
$412$			773.752i			1.87804i
$413$	483.406	−	69.2899i	1.17047	−	0.167772i
$414$	47.2649			0.114167
$415$	−324.773			−0.782585
$416$		−	614.350i		−	1.47680i
$417$	−186.928			−0.448269
$418$			828.718i			1.98258i
$419$		−	355.230i		−	0.847805i	−0.905708	−	0.423902i	$-0.860660\pi$
$419$		−	355.230i		−	0.847805i	0.905708	−	0.423902i	$-0.139340\pi$
$420$	44.4619	+	310.192i	0.105862	+	0.738551i
$421$	−17.1544			−0.0407468			−0.0203734	−	0.999792i	$-0.506486\pi$
$421$	−17.1544			−0.0407468			−0.0203734	+	0.999792i	$0.506486\pi$
$422$	−1003.99			−2.37912
$423$			97.6536i			0.230859i
$424$	523.231			1.23404
$425$			104.077i			0.244886i
$426$		−	553.011i		−	1.29815i
$427$	497.811	−	71.3546i	1.16583	−	0.167107i
$428$	786.163			1.83683
$429$	−307.760			−0.717389
$430$			778.237i			1.80985i
$431$	−594.028			−1.37826			−0.689128	−	0.724640i	$-0.742006\pi$
$431$	−594.028			−1.37826			−0.689128	+	0.724640i	$0.742006\pi$
$432$			15.4047i			0.0356591i
$433$			16.3147i			0.0376783i	0.999823	+	0.0188392i	$0.00599704\pi$
$433$			16.3147i			0.0376783i	−0.999823	+	0.0188392i	$0.994003\pi$
$434$	−94.7847	+	13.5861i	−0.218398	+	0.0313045i
$435$	−75.3313			−0.173175
$436$	−108.698			−0.249308
$437$		−	155.205i		−	0.355160i
$438$	397.921			0.908495
$439$			482.624i			1.09937i	0.835371	+	0.549686i	$0.185253\pi$
$439$			482.624i			1.09937i	−0.835371	+	0.549686i	$0.814747\pi$
$440$			272.072i			0.618345i
$441$	141.081	−	41.2927i	0.319912	−	0.0936342i
$442$	−740.835			−1.67610
$443$	685.718			1.54790			0.773948	−	0.633249i	$-0.218279\pi$
$443$	685.718			1.54790			0.773948	+	0.633249i	$0.218279\pi$
$444$		−	471.328i		−	1.06155i
$445$	42.4695			0.0954371
$446$			398.782i			0.894131i
$447$			354.824i			0.793789i
$448$	99.7146	+	695.666i	0.222577	+	1.55283i
$449$	−692.607			−1.54256			−0.771278	−	0.636499i	$-0.780382\pi$
$449$	−692.607			−1.54256			−0.771278	+	0.636499i	$0.780382\pi$
$450$	103.681			0.230403
$451$		−	136.357i		−	0.302344i
$452$	290.836			0.643443
$453$		−	409.453i		−	0.903869i
$454$		−	608.244i		−	1.33974i
$455$	86.1510	+	601.039i	0.189343	+	1.32096i
$456$	514.155			1.12753
$457$	−119.773			−0.262086			−0.131043	−	0.991377i	$-0.541833\pi$
$457$	−119.773			−0.262086			−0.131043	+	0.991377i	$0.541833\pi$
$458$		−	263.681i		−	0.575722i
$459$	−51.4055			−0.111994
$460$		−	123.951i		−	0.269460i
$461$		−	165.948i		−	0.359974i	−0.983669	−	0.179987i	$-0.942394\pi$
$461$		−	165.948i		−	0.359974i	0.983669	−	0.179987i	$-0.0576055\pi$
$462$	307.332	−	44.0520i	0.665221	−	0.0953507i
$463$	499.617			1.07909			0.539544	−	0.841958i	$-0.318597\pi$
$463$	499.617			1.07909			0.539544	+	0.841958i	$0.318597\pi$
$464$	33.8850			0.0730279
$465$		−	27.4438i		−	0.0590188i
$466$	60.2541			0.129301
$467$		−	268.033i		−	0.573948i	−0.957938	−	0.286974i	$-0.907351\pi$
$467$		−	268.033i		−	0.573948i	0.957938	−	0.286974i	$-0.0926493\pi$
$468$			464.481i			0.992481i
$469$	76.4766	+	533.545i	0.163063	+	1.13762i
$470$	406.913			0.865772
$471$	428.810			0.910424
$472$		−	639.914i		−	1.35575i
$473$	485.276			1.02595
$474$		−	367.549i		−	0.775419i
$475$		−	340.461i		−	0.716760i
$476$	465.603	−	66.7381i	0.978158	−	0.140206i
$477$	171.129			0.358761
$478$	−621.959			−1.30117
$479$			239.633i			0.500277i	0.968210	+	0.250138i	$0.0804761\pi$
$479$			239.633i			0.500277i	−0.968210	+	0.250138i	$0.919524\pi$
$480$	−177.630			−0.370063
$481$		−	913.263i		−	1.89868i
$482$			351.328i			0.728896i
$483$	−57.5581	+	8.25020i	−0.119168	+	0.0170812i
$484$	−409.154			−0.845359
$485$	−173.688			−0.358119
$486$			51.2103i			0.105371i
$487$	−335.805			−0.689539			−0.344769	−	0.938687i	$-0.612043\pi$
$487$	−335.805			−0.689539			−0.344769	+	0.938687i	$0.612043\pi$
$488$		−	658.983i		−	1.35037i
$489$		−	348.696i		−	0.713079i
$490$	−172.062	−	587.872i	−0.351148	−	1.19974i
$491$	−187.716			−0.382313			−0.191157	−	0.981560i	$-0.561224\pi$
$491$	−187.716			−0.382313			−0.191157	+	0.981560i	$0.561224\pi$
$492$	−205.795			−0.418282
$493$			113.074i			0.229358i
$494$	2423.46			4.90578
$495$			88.9843i			0.179766i
$496$			12.3445i			0.0248882i
$497$	96.5292	+	673.443i	0.194224	+	1.35502i
$498$	485.639			0.975178
$499$	691.948			1.38667			0.693335	−	0.720616i	$-0.256141\pi$
$499$	691.948			1.38667			0.693335	+	0.720616i	$0.256141\pi$
$500$		−	918.044i		−	1.83609i
$501$	356.589			0.711754
$502$			1475.72i			2.93969i
$503$			217.831i			0.433064i	0.976276	+	0.216532i	$0.0694745\pi$
$503$			217.831i			0.433064i	−0.976276	+	0.216532i	$0.930525\pi$
$504$	−27.3308	−	190.675i	−0.0542278	−	0.378324i
$505$	484.340			0.959088
$506$	−122.809			−0.242705
$507$			607.279i			1.19779i
$508$	−779.171			−1.53380
$509$		−	215.151i		−	0.422694i	−0.977411	−	0.211347i	$-0.932215\pi$
$509$		−	215.151i		−	0.422694i	0.977411	−	0.211347i	$-0.0677850\pi$
$510$			214.201i			0.420003i
$511$	−484.578	+	69.4579i	−0.948294	+	0.135925i
$512$	188.674			0.368504
$513$	168.160			0.327798
$514$			1336.07i			2.59936i
$515$	433.487			0.841722
$516$		−	732.394i		−	1.41937i
$517$		−	253.734i		−	0.490781i
$518$	130.722	+	911.994i	0.252360	+	1.76061i
$519$	1.49030			0.00287149
$520$	795.632			1.53006
$521$			220.894i			0.423981i	0.977272	+	0.211991i	$0.0679946\pi$
$521$			220.894i			0.423981i	−0.977272	+	0.211991i	$0.932005\pi$
$522$	112.644			0.215794
$523$		−	386.113i		−	0.738266i	−0.929377	−	0.369133i	$-0.879655\pi$
$523$		−	386.113i		−	0.738266i	0.929377	−	0.369133i	$-0.120345\pi$
$524$			985.118i			1.88000i
$525$	−126.261	+	18.0978i	−0.240497	+	0.0344720i
$526$	−527.654			−1.00315
$527$	−41.1936			−0.0781662
$528$		−	40.0262i		−	0.0758073i
$529$	23.0000			0.0434783
$530$		−	713.077i		−	1.34543i
$531$		−	209.291i		−	0.394146i
$532$	−1523.11	+	218.317i	−2.86298	+	0.410371i
$533$	−398.755			−0.748134
$534$	−63.5054			−0.118924
$535$		−	440.439i		−	0.823251i
$536$	706.286			1.31770
$537$			81.0648i			0.150959i
$538$			8.97935i			0.0166902i
$539$	−366.572	+	107.291i	−0.680097	+	0.199056i
$540$	134.298			0.248700
$541$	734.540			1.35775			0.678873	−	0.734256i	$-0.262469\pi$
$541$	734.540			1.35775			0.678873	+	0.734256i	$0.262469\pi$
$542$			663.446i			1.22407i
$543$	125.723			0.231534
$544$			266.626i			0.490122i
$545$			60.8970i			0.111738i
$546$	−128.823	−	898.745i	−0.235940	−	1.64605i
$547$	−635.216			−1.16127			−0.580636	−	0.814163i	$-0.697196\pi$
$547$	−635.216			−1.16127			−0.580636	+	0.814163i	$0.697196\pi$
$548$	1277.63			2.33145
$549$		−	215.528i		−	0.392583i
$550$	−269.396			−0.489811
$551$		−	369.893i		−	0.671312i
$552$			76.1932i			0.138031i
$553$	64.1564	+	447.592i	0.116015	+	0.809389i
$554$	−166.971			−0.301391
$555$	−264.057			−0.475778
$556$		−	733.028i		−	1.31840i
$557$	532.642			0.956270			0.478135	−	0.878286i	$-0.341313\pi$
$557$	532.642			0.956270			0.478135	+	0.878286i	$0.341313\pi$
$558$			41.0372i			0.0735433i
$559$		−	1419.11i		−	2.53867i
$560$	−78.1691	+	11.2045i	−0.139588	+	0.0200081i
$561$	133.567			0.238088
$562$	1412.29			2.51298
$563$			92.7109i			0.164673i	0.996605	+	0.0823365i	$0.0262382\pi$
$563$			92.7109i			0.164673i	−0.996605	+	0.0823365i	$0.973762\pi$
$564$	−382.943			−0.678977
$565$		−	162.938i		−	0.288386i
$566$		−	843.653i		−	1.49055i
$567$	−8.93886	−	62.3626i	−0.0157652	−	0.109987i
$568$	891.478			1.56950
$569$	−445.865			−0.783594			−0.391797	−	0.920052i	$-0.628146\pi$
$569$	−445.865			−0.783594			−0.391797	+	0.920052i	$0.628146\pi$
$570$		−	700.707i		−	1.22931i
$571$	271.178			0.474918			0.237459	−	0.971398i	$-0.423685\pi$
$571$	271.178			0.474918			0.237459	+	0.971398i	$0.423685\pi$
$572$		−	1206.86i		−	2.10990i
$573$		−	208.274i		−	0.363479i
$574$	398.201	−	57.0769i	0.693730	−	0.0994371i
$575$	50.4533			0.0877449
$576$	301.190			0.522899
$577$		−	378.809i		−	0.656514i	−0.944588	−	0.328257i	$-0.893539\pi$
$577$		−	378.809i		−	0.656514i	0.944588	−	0.328257i	$-0.106461\pi$
$578$	−627.885			−1.08631
$579$		−	397.372i		−	0.686307i
$580$		−	295.408i		−	0.509324i
$581$	−591.399	+	84.7693i	−1.01790	+	0.145902i
$582$	259.719			0.446252
$583$	−444.645			−0.762684
$584$			641.466i			1.09840i
$585$	260.221			0.444822
$586$		−	1577.80i		−	2.69249i
$587$		−	370.094i		−	0.630484i	−0.949011	−	0.315242i	$-0.897914\pi$
$587$		−	370.094i		−	0.630484i	0.949011	−	0.315242i	$-0.102086\pi$
$588$	161.927	+	553.242i	0.275386	+	0.940889i
$589$	134.755			0.228786
$590$	−872.097			−1.47813
$591$			524.726i			0.887861i
$592$	118.776			0.200635
$593$			83.5371i			0.140872i	0.997516	+	0.0704360i	$0.0224390\pi$
$593$			83.5371i			0.140872i	−0.997516	+	0.0704360i	$0.977561\pi$
$594$		−	133.060i		−	0.224007i
$595$	−37.3893	−	260.849i	−0.0628392	−	0.438402i
$596$	−1391.42			−2.33460
$597$	−389.808			−0.652944
$598$			359.135i			0.600560i
$599$	515.956			0.861363			0.430681	−	0.902504i	$-0.358273\pi$
$599$	515.956			0.861363			0.430681	+	0.902504i	$0.358273\pi$
$600$			167.139i			0.278565i
$601$		−	330.124i		−	0.549291i	−0.961546	−	0.274646i	$-0.911439\pi$
$601$		−	330.124i		−	0.549291i	0.961546	−	0.274646i	$-0.0885605\pi$
$602$	203.129	+	1417.14i	0.337423	+	2.35406i
$603$	230.999			0.383083
$604$	1605.65			2.65836
$605$			229.224i			0.378883i
$606$	−724.242			−1.19512
$607$		−	684.586i		−	1.12782i	−0.825837	−	0.563909i	$-0.809297\pi$
$607$		−	684.586i		−	1.12782i	0.825837	−	0.563909i	$-0.190703\pi$
$608$		−	872.203i		−	1.43454i
$609$	−137.176	+	19.6623i	−0.225247	+	0.0322862i
$610$	−898.084			−1.47227
$611$	−742.005			−1.21441
$612$		−	201.584i		−	0.329385i
$613$	−478.672			−0.780868			−0.390434	−	0.920631i	$-0.627675\pi$
$613$	−478.672			−0.780868			−0.390434	+	0.920631i	$0.627675\pi$
$614$			1174.79i			1.91333i
$615$			115.294i			0.187470i
$616$	71.0138	+	495.433i	0.115282	+	0.804275i
$617$	−1073.40			−1.73971			−0.869855	−	0.493307i	$-0.835788\pi$
$617$	−1073.40			−1.73971			−0.869855	+	0.493307i	$0.835788\pi$
$618$	−648.201			−1.04887
$619$			279.646i			0.451771i	0.974154	+	0.225886i	$0.0725276\pi$
$619$			279.646i			0.451771i	−0.974154	+	0.225886i	$0.927472\pi$
$620$	107.619			0.173579
$621$			24.9199i			0.0401286i
$622$		−	526.986i		−	0.847244i
$623$	77.3354	−	11.0850i	0.124134	−	0.0177930i
$624$	−117.050			−0.187581
$625$	−251.318			−0.402109
$626$		−	264.724i		−	0.422881i
$627$	−436.932			−0.696861
$628$			1681.55i			2.67763i
$629$			396.354i			0.630134i
$630$	−259.859	+	37.2474i	−0.412474	+	0.0591228i
$631$	−131.277			−0.208046			−0.104023	−	0.994575i	$-0.533172\pi$
$631$	−131.277			−0.208046			−0.104023	+	0.994575i	$0.533172\pi$
$632$	592.505			0.937508
$633$		−	529.342i		−	0.836243i
$634$	1337.12			2.10903
$635$			436.522i			0.687436i
$636$			671.072i			1.05515i
$637$	313.756	+	1071.98i	0.492552	+	1.68286i
$638$	−292.684			−0.458753
$639$	291.568			0.456288
$640$		−	844.808i		−	1.32001i
$641$	−942.482			−1.47033			−0.735165	−	0.677888i	$-0.762896\pi$
$641$	−942.482			−1.47033			−0.735165	+	0.677888i	$0.762896\pi$
$642$			658.597i			1.02585i
$643$			341.474i			0.531064i	0.964102	+	0.265532i	$0.0855475\pi$
$643$			341.474i			0.531064i	−0.964102	+	0.265532i	$0.914452\pi$
$644$	−32.3527	−	225.711i	−0.0502371	−	0.350483i
$645$	−410.316			−0.636149
$646$	−1051.77			−1.62813
$647$			920.596i			1.42287i	0.702753	+	0.711434i	$0.251954\pi$
$647$			920.596i			1.42287i	−0.702753	+	0.711434i	$0.748046\pi$
$648$	−82.5533			−0.127397
$649$			543.803i			0.837909i
$650$			787.807i			1.21201i
$651$	−7.16313	−	49.9741i	−0.0110033	−	0.0767651i
$652$	1367.39			2.09723
$653$	−815.859			−1.24940			−0.624701	−	0.780864i	$-0.714779\pi$
$653$	−815.859			−1.24940			−0.624701	+	0.780864i	$0.714779\pi$
$654$		−	91.0604i		−	0.139236i
$655$	551.902			0.842598
$656$		−	51.8608i		−	0.0790561i
$657$			209.799i			0.319329i
$658$	740.973	−	106.209i	1.12610	−	0.161412i
$659$	292.701			0.444159			0.222080	−	0.975029i	$-0.428716\pi$
$659$	292.701			0.444159			0.222080	+	0.975029i	$0.428716\pi$
$660$	−348.947			−0.528708
$661$			399.867i			0.604942i	0.953159	+	0.302471i	$0.0978115\pi$
$661$			399.867i			0.604942i	−0.953159	+	0.302471i	$0.902188\pi$
$662$	−280.820			−0.424199
$663$		−	390.596i		−	0.589135i
$664$			782.872i			1.17902i
$665$	122.310	+	853.304i	0.183925	+	1.28316i
$666$	394.849			0.592867
$667$	54.8148			0.0821812
$668$			1398.34i			2.09333i
$669$	−210.253			−0.314280
$670$		−	962.550i		−	1.43664i
$671$			560.008i			0.834587i
$672$	−323.458	+	46.3635i	−0.481337	+	0.0689933i
$673$	−631.661			−0.938575			−0.469288	−	0.883045i	$-0.655489\pi$
$673$	−631.661			−0.938575			−0.469288	+	0.883045i	$0.655489\pi$
$674$	−1084.32			−1.60879
$675$			54.6648i			0.0809849i
$676$	−2381.41			−3.52280
$677$		−	1182.15i		−	1.74616i	−0.487578	−	0.873079i	$-0.662120\pi$
$677$		−	1182.15i		−	1.74616i	0.487578	−	0.873079i	$-0.337880\pi$
$678$			243.644i			0.359358i
$679$	−316.279	+	45.3345i	−0.465802	+	0.0667665i
$680$	−345.302			−0.507798
$681$	320.689			0.470909
$682$		−	106.627i		−	0.156345i
$683$	1005.50			1.47218			0.736091	−	0.676883i	$-0.236670\pi$
$683$	1005.50			1.47218			0.736091	+	0.676883i	$0.236670\pi$
$684$			659.431i			0.964081i
$685$		−	715.780i		−	1.04493i
$686$	−466.761	−	1025.58i	−0.680409	−	1.49502i
$687$	139.023			0.202362
$688$	184.565			0.268264
$689$			1300.30i			1.88722i
$690$	103.839			0.150491
$691$		−	33.4732i		−	0.0484416i	−0.999707	−	0.0242208i	$-0.992290\pi$
$691$		−	33.4732i		−	0.0484416i	0.999707	−	0.0242208i	$-0.00771048\pi$
$692$			5.84414i			0.00844528i
$693$	23.2259	+	162.037i	0.0335150	+	0.233820i
$694$	−760.054			−1.09518
$695$	−410.671			−0.590894
$696$			181.588i			0.260902i
$697$	173.059			0.248291
$698$		−	2120.59i		−	3.03809i
$699$			31.7683i			0.0454482i
$700$	−70.9696	−	495.125i	−0.101385	−	0.707321i
$701$	783.837			1.11817			0.559085	−	0.829110i	$-0.311152\pi$
$701$	783.837			1.11817			0.559085	+	0.829110i	$0.311152\pi$
$702$	−389.113			−0.554292
$703$		−	1296.57i		−	1.84435i
$704$	−782.583			−1.11162
$705$			214.540i			0.304312i
$706$			1797.19i			2.54560i
$707$	881.965	−	126.418i	1.24748	−	0.178809i
$708$	820.725			1.15922
$709$	−763.770			−1.07725			−0.538625	−	0.842546i	$-0.681056\pi$
$709$	−763.770			−1.07725			−0.538625	+	0.842546i	$0.681056\pi$
$710$		−	1214.94i		−	1.71118i
$711$	193.786			0.272554
$712$		−	102.374i		−	0.143783i
$713$			19.9695i			0.0280077i
$714$	55.9090	+	390.053i	0.0783039	+	0.546293i
$715$	−676.133			−0.945640
$716$	−317.891			−0.443982
$717$		−	327.921i		−	0.457351i
$718$	−901.245			−1.25522
$719$			117.407i			0.163292i	0.996661	+	0.0816462i	$0.0260177\pi$
$719$			117.407i			0.163292i	−0.996661	+	0.0816462i	$0.973982\pi$
$720$			33.8434i			0.0470048i
$721$	789.363	−	113.145i	1.09482	−	0.156928i
$722$	2254.68			3.12283
$723$	−185.234			−0.256201
$724$			493.016i			0.680961i
$725$	120.243			0.165853
$726$		−	342.763i		−	0.472126i
$727$		−	1031.82i		−	1.41929i	−0.704562	−	0.709643i	$-0.748856\pi$
$727$		−	1031.82i		−	1.41929i	0.704562	−	0.709643i	$-0.251144\pi$
$728$	1448.82	−	207.669i	1.99013	−	0.285259i
$729$	−27.0000			−0.0370370
$730$	874.212			1.19755
$731$			615.892i			0.842534i
$732$	845.182			1.15462
$733$		−	80.3824i		−	0.109662i	−0.998496	−	0.0548311i	$-0.982538\pi$
$733$		−	80.3824i		−	0.109662i	0.998496	−	0.0548311i	$-0.0174620\pi$
$734$		−	1393.18i		−	1.89807i
$735$	309.948	−	90.7179i	0.421698	−	0.123426i
$736$	129.253			0.175615
$737$	−600.206			−0.814391
$738$		−	172.402i		−	0.233607i
$739$	−462.402			−0.625713			−0.312857	−	0.949800i	$-0.601286\pi$
$739$	−462.402			−0.625713			−0.312857	+	0.949800i	$0.601286\pi$
$740$		−	1035.48i		−	1.39930i
$741$			1277.74i			1.72434i
$742$	−186.121	−	1298.49i	−0.250837	−	1.74998i
$743$	893.878			1.20307			0.601533	−	0.798848i	$-0.294557\pi$
$743$	893.878			1.20307			0.601533	+	0.798848i	$0.294557\pi$
$744$	−66.1538			−0.0889164
$745$			779.529i			1.04635i
$746$	−1468.65			−1.96869
$747$			256.047i			0.342767i
$748$			523.776i			0.700236i
$749$	−114.960	−	802.024i	−0.153484	−	1.07079i
$750$	769.079			1.02544
$751$	422.444			0.562509			0.281254	−	0.959633i	$-0.409250\pi$
$751$	422.444			0.562509			0.281254	+	0.959633i	$0.409250\pi$
$752$		−	96.5027i		−	0.128328i
$753$	−778.057			−1.03328
$754$			855.910i			1.13516i
$755$		−	899.547i		−	1.19145i
$756$	244.552	−	35.0533i	0.323481	−	0.0463668i
$757$	−912.237			−1.20507			−0.602534	−	0.798093i	$-0.705842\pi$
$757$	−912.237			−1.20507			−0.602534	+	0.798093i	$0.705842\pi$
$758$	−1698.84			−2.24122
$759$		−	64.7494i		−	0.0853089i
$760$	1129.57			1.48628
$761$			99.4923i			0.130739i	0.997861	+	0.0653694i	$0.0208226\pi$
$761$			99.4923i			0.130739i	−0.997861	+	0.0653694i	$0.979177\pi$
$762$		−	652.740i		−	0.856614i
$763$	15.8948	+	110.891i	0.0208320	+	0.145336i
$764$	816.734			1.06902
$765$	−112.935			−0.147628
$766$			1603.46i			2.09329i
$767$	1590.27			2.07336
$768$			567.690i			0.739180i
$769$			872.697i			1.13485i	0.823426	+	0.567423i	$0.192060\pi$
$769$			872.697i			1.13485i	−0.823426	+	0.567423i	$0.807940\pi$
$770$	675.193	−	96.7800i	0.876874	−	0.125688i
$771$	−704.429			−0.913656
$772$	1558.27			2.01849
$773$			366.689i			0.474371i	0.971464	+	0.237186i	$0.0762250\pi$
$773$			366.689i			0.474371i	−0.971464	+	0.237186i	$0.923775\pi$
$774$	613.554			0.792705
$775$			43.8055i			0.0565232i
$776$			418.678i			0.539534i
$777$	−480.838	+	68.9218i	−0.618839	+	0.0887024i
$778$	1193.87			1.53454
$779$	−566.119			−0.726726
$780$			1020.44i			1.30826i
$781$	−757.583			−0.970017
$782$		−	155.864i		−	0.199314i
$783$			59.3904i			0.0758498i
$784$	−139.419	+	40.8060i	−0.177830	+	0.0520485i
$785$	942.073			1.20009
$786$	−825.269			−1.04996
$787$		−	934.682i		−	1.18765i	−0.804594	−	0.593826i	$-0.797617\pi$
$787$		−	934.682i		−	1.18765i	0.804594	−	0.593826i	$-0.202383\pi$
$788$	−2057.68			−2.61127
$789$		−	278.199i		−	0.352598i
$790$		−	807.486i		−	1.02213i
$791$	−42.5287	−	296.704i	−0.0537657	−	0.375100i
$792$	214.499			0.270832
$793$	1637.66			2.06514
$794$			1785.88i			2.24923i
$795$	375.961			0.472907
$796$		−	1528.61i		−	1.92036i
$797$		−	582.598i		−	0.730988i	−0.930814	−	0.365494i	$-0.880900\pi$
$797$		−	582.598i		−	0.730988i	0.930814	−	0.365494i	$-0.119100\pi$
$798$	−182.892	−	1275.96i	−0.229189	−	1.59895i
$799$	322.028			0.403039
$800$	283.532			0.354415
$801$		−	33.4825i		−	0.0418009i
$802$	−1356.88			−1.69186
$803$		−	545.122i		−	0.678857i
$804$			905.851i			1.12668i
$805$	−126.452	+	18.1253i	−0.157083	+	0.0225159i
$806$	−311.814			−0.386867
$807$	−4.73426			−0.00586649
$808$		−	1167.51i		−	1.44494i
$809$	1466.72			1.81300			0.906499	−	0.422208i	$-0.138745\pi$
$809$	1466.72			1.81300			0.906499	+	0.422208i	$0.138745\pi$
$810$			112.506i			0.138897i
$811$			294.587i			0.363239i	0.983369	+	0.181619i	$0.0581339\pi$
$811$			294.587i			0.363239i	−0.983369	+	0.181619i	$0.941866\pi$
$812$	−77.1047	−	537.927i	−0.0949565	−	0.662471i
$813$	−349.794			−0.430251
$814$	−1025.94			−1.26037
$815$		−	766.066i		−	0.939959i
$816$	50.7996			0.0622545
$817$		−	2014.74i		−	2.46602i
$818$		−	184.848i		−	0.225975i
$819$	473.852	−	67.9205i	0.578574	−	0.0829310i
$820$	−452.120			−0.551366
$821$	447.339			0.544871			0.272436	−	0.962174i	$-0.412171\pi$
$821$	447.339			0.544871			0.272436	+	0.962174i	$0.412171\pi$
$822$			1070.32i			1.30209i
$823$	581.369			0.706402			0.353201	−	0.935547i	$-0.385093\pi$
$823$	581.369			0.706402			0.353201	+	0.935547i	$0.385093\pi$
$824$		−	1044.93i		−	1.26812i
$825$		−	142.036i		−	0.172165i
$826$	−1588.06	+	227.627i	−1.92259	+	0.275578i
$827$	713.785			0.863101			0.431551	−	0.902089i	$-0.357967\pi$
$827$	713.785			0.863101			0.431551	+	0.902089i	$0.357967\pi$
$828$	−97.7219			−0.118022
$829$		−	111.361i		−	0.134332i	−0.997742	−	0.0671658i	$-0.978604\pi$
$829$		−	111.361i		−	0.134332i	0.997742	−	0.0671658i	$-0.0213957\pi$
$830$	1066.92			1.28545
$831$		−	88.0332i		−	0.105937i
$832$			2288.54i			2.75065i
$833$	−136.169	−	465.238i	−0.163468	−	0.558509i
$834$	614.085			0.736313
$835$	783.407			0.938212
$836$		−	1713.40i		−	2.04953i
$837$	−21.6364			−0.0258499
$838$			1166.98i			1.39258i
$839$			727.787i			0.867445i	0.901046	+	0.433723i	$0.142800\pi$
$839$			727.787i			0.867445i	−0.901046	+	0.433723i	$0.857200\pi$
$840$	−60.0444	−	418.904i	−0.0714815	−	0.498696i
$841$	−710.362			−0.844664
$842$	56.3546			0.0669295
$843$			744.615i			0.883292i
$844$	2075.79			2.45946
$845$			1334.16i			1.57889i
$846$		−	320.806i		−	0.379203i
$847$	59.8301	+	417.409i	0.0706376	+	0.492808i
$848$	−169.112			−0.199425
$849$	444.806			0.523917
$850$		−	341.906i		−	0.402243i
$851$	192.141			0.225783
$852$			1143.37i			1.34198i
$853$			530.547i			0.621978i	0.950413	+	0.310989i	$0.100660\pi$
$853$			530.547i			0.621978i	−0.950413	+	0.310989i	$0.899340\pi$
$854$	−1635.38	+	234.410i	−1.91496	+	0.274485i
$855$	369.439			0.432093
$856$	−1061.69			−1.24029
$857$			898.515i			1.04844i	0.851582	+	0.524221i	$0.175643\pi$
$857$			898.515i			1.04844i	−0.851582	+	0.524221i	$0.824357\pi$
$858$	1011.03			1.17836
$859$			35.4042i			0.0412156i	0.999788	+	0.0206078i	$0.00656013\pi$
$859$			35.4042i			0.0412156i	−0.999788	+	0.0206078i	$0.993440\pi$
$860$		−	1609.03i		−	1.87097i
$861$	30.0931	+	209.947i	0.0349513	+	0.243840i
$862$	1951.47			2.26388
$863$	−454.442			−0.526584			−0.263292	−	0.964716i	$-0.584808\pi$
$863$	−454.442			−0.526584			−0.263292	+	0.964716i	$0.584808\pi$
$864$			140.042i			0.162085i
$865$	3.27412			0.00378510
$866$		−	53.5961i		−	0.0618893i
$867$		−	331.045i		−	0.381828i
$868$	195.971	−	28.0898i	0.225773	−	0.0323616i
$869$	−503.514			−0.579418
$870$	247.474			0.284453
$871$			1755.21i			2.01517i
$872$	146.794			0.168341
$873$			136.934i			0.156854i
$874$			509.870i			0.583375i
$875$	−936.566	+	134.244i	−1.07036	+	0.153422i
$876$	−822.715			−0.939173
$877$	−1132.67			−1.29153			−0.645766	−	0.763535i	$-0.723462\pi$
$877$	−1132.67			−1.29153			−0.645766	+	0.763535i	$0.723462\pi$
$878$		−	1585.49i		−	1.80580i
$879$	831.875			0.946388
$880$		−	87.9356i		−	0.0999268i
$881$		−	755.817i		−	0.857908i	−0.903326	−	0.428954i	$-0.858882\pi$
$881$		−	755.817i		−	0.857908i	0.903326	−	0.428954i	$-0.141118\pi$
$882$	−463.472	+	135.652i	−0.525478	+	0.153801i
$883$	852.507			0.965466			0.482733	−	0.875768i	$-0.339644\pi$
$883$	852.507			0.965466			0.482733	+	0.875768i	$0.339644\pi$
$884$	1531.70			1.73269
$885$		−	459.803i		−	0.519551i
$886$	−2252.68			−2.54253
$887$			698.752i			0.787770i	0.919160	+	0.393885i	$0.128869\pi$
$887$			698.752i			0.787770i	−0.919160	+	0.393885i	$0.871131\pi$
$888$			636.515i			0.716796i
$889$	113.937	+	794.891i	0.128163	+	0.894140i
$890$	−139.518			−0.156762
$891$	70.1543			0.0787365
$892$		−	824.497i		−	0.924324i
$893$	−1053.44			−1.17966
$894$		−	1165.64i		−	1.30385i
$895$			178.095i			0.198989i
$896$	−220.504	−	1538.37i	−0.246099	−	1.71693i
$897$	−189.350			−0.211092
$898$	2275.31			2.53375
$899$			47.5923i			0.0529392i
$900$	−214.365			−0.238183
$901$		−	564.325i		−	0.626332i
$902$			447.952i			0.496621i
$903$	−747.171	+	107.097i	−0.827432	+	0.118601i
$904$	−392.766			−0.434475
$905$	276.207			0.305201
$906$			1345.11i			1.48467i
$907$	−1570.08			−1.73107			−0.865536	−	0.500847i	$-0.833022\pi$
$907$	−1570.08			−1.73107			−0.865536	+	0.500847i	$0.833022\pi$
$908$			1257.57i			1.38498i
$909$		−	381.848i		−	0.420075i
$910$	−283.018	−	1974.50i	−0.311009	−	2.16978i
$911$	341.481			0.374842			0.187421	−	0.982280i	$-0.439987\pi$
$911$	341.481			0.374842			0.187421	+	0.982280i	$0.439987\pi$
$912$	−166.178			−0.182213
$913$		−	665.289i		−	0.728685i
$914$	393.472			0.430495
$915$		−	473.504i		−	0.517491i
$916$			545.170i			0.595163i
$917$	1004.99	−	144.053i	1.09596	−	0.157091i
$918$	168.874			0.183959
$919$	1380.02			1.50166			0.750830	−	0.660496i	$-0.229654\pi$
$919$	1380.02			1.50166			0.750830	+	0.660496i	$0.229654\pi$
$920$			167.393i			0.181948i
$921$	−619.393			−0.672522
$922$			545.162i			0.591282i
$923$			2215.43i			2.40025i
$924$	−635.420	+	91.0791i	−0.687684	+	0.0985705i
$925$	421.485			0.455659
$926$	−1641.31			−1.77248
$927$		−	341.756i		−	0.368669i
$928$	308.042			0.331942
$929$			1471.28i			1.58373i	0.610699	+	0.791863i	$0.290888\pi$
$929$			1471.28i			1.58373i	−0.610699	+	0.791863i	$0.709112\pi$
$930$			90.1566i			0.0969426i
$931$	445.444	+	1521.91i	0.478458	+	1.63471i
$932$	−124.578			−0.133667
$933$	277.847			0.297800
$934$			880.528i			0.942749i
$935$	293.440			0.313840
$936$		−	627.268i		−	0.670158i
$937$		−	378.847i		−	0.404319i	−0.979353	−	0.202159i	$-0.935204\pi$
$937$		−	378.847i		−	0.404319i	0.979353	−	0.202159i	$-0.0647959\pi$
$938$	−251.236	−	1752.77i	−0.267843	−	1.86862i
$939$	139.572			0.148639
$940$	−841.307			−0.895007
$941$		−	1404.80i		−	1.49288i	−0.665454	−	0.746439i	$-0.731762\pi$
$941$		−	1404.80i		−	1.49288i	0.665454	−	0.746439i	$-0.268238\pi$
$942$	−1408.70			−1.49543
$943$		−	83.8939i		−	0.0889649i
$944$			206.825i			0.219094i
$945$	−19.6382	−	137.008i	−0.0207812	−	0.144981i
$946$	−1594.20			−1.68520
$947$	−988.553			−1.04388			−0.521939	−	0.852983i	$-0.674791\pi$
$947$	−988.553			−1.04388			−0.521939	+	0.852983i	$0.674791\pi$
$948$			759.920i			0.801603i
$949$	−1594.12			−1.67979
$950$			1118.46i			1.17733i
$951$			704.982i			0.741306i
$952$	−628.783	+	90.1278i	−0.660487	+	0.0946721i
$953$	−767.752			−0.805616			−0.402808	−	0.915285i	$-0.631966\pi$
$953$	−767.752			−0.805616			−0.402808	+	0.915285i	$0.631966\pi$
$954$	−562.182			−0.589289
$955$		−	457.567i		−	0.479128i
$956$	1285.92			1.34511
$957$		−	154.314i		−	0.161248i
$958$		−	787.226i		−	0.821739i
$959$	−186.827	−	1303.41i	−0.194814	−	1.35913i
$960$	661.699			0.689269
$961$	943.662			0.981958
$962$			3000.20i			3.11871i
$963$	−347.238			−0.360579
$964$		−	726.383i		−	0.753510i
$965$		−	873.006i		−	0.904669i
$966$	189.086	−	27.1031i	0.195742	−	0.0280570i
$967$	1318.24			1.36322			0.681611	−	0.731714i	$-0.261280\pi$
$967$	1318.24			1.36322			0.681611	+	0.731714i	$0.261280\pi$
$968$	552.550			0.570816
$969$		−	554.536i		−	0.572276i
$970$	570.589			0.588236
$971$			652.422i			0.671907i	0.941879	+	0.335954i	$0.109059\pi$
$971$			652.422i			0.671907i	−0.941879	+	0.335954i	$0.890941\pi$
$972$		−	105.879i		−	0.108929i
$973$	−747.818	+	107.190i	−0.768569	+	0.110164i
$974$	1103.17			1.13262
$975$	−415.362			−0.426012
$976$			212.988i			0.218225i
$977$	−1089.43			−1.11508			−0.557540	−	0.830150i	$-0.688255\pi$
$977$	−1089.43			−1.11508			−0.557540	+	0.830150i	$0.688255\pi$
$978$			1145.51i			1.17128i
$979$			86.9977i			0.0888639i
$980$	355.745	+	1215.45i	0.363005	+	1.24025i
$981$	48.0105			0.0489404
$982$	616.673			0.627976
$983$		−	819.222i		−	0.833390i	−0.909046	−	0.416695i	$-0.863188\pi$
$983$		−	819.222i		−	0.833390i	0.909046	−	0.416695i	$-0.136812\pi$
$984$	277.919			0.282438
$985$			1152.80i			1.17035i
$986$		−	371.463i		−	0.376737i
$987$	55.9973	+	390.669i	0.0567349	+	0.395815i
$988$	−5010.58			−5.07144
$989$	298.567			0.301887
$990$		−	292.326i		−	0.295279i
$991$	−488.012			−0.492444			−0.246222	−	0.969213i	$-0.579189\pi$
$991$	−488.012			−0.492444			−0.246222	+	0.969213i	$0.579189\pi$
$992$			112.222i			0.113127i
$993$		−	148.059i		−	0.149103i
$994$	−317.112	−	2212.35i	−0.319026	−	2.22571i
$995$	−856.388			−0.860691
$996$	−1004.08			−1.00811
$997$			29.2588i			0.0293469i	0.999892	+	0.0146734i	$0.00467087\pi$
$997$			29.2588i			0.0293469i	−0.999892	+	0.0146734i	$0.995329\pi$
$998$	−2273.15			−2.27770
$999$			208.179i			0.208388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.g.a.139.8	yes	60
7.6	odd	2	inner	483.3.g.a.139.7	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.g.a.139.7	✓	60	7.6	odd	2	inner
483.3.g.a.139.8	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.28514 q^{2} -1.73205i q^{3} +6.79214 q^{4} -3.80523i q^{5} +5.69003i q^{6} +(-0.993207 - 6.92918i) q^{7} -9.17258 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q-3.28514 q^{2} -1.73205i q^{3} +6.79214 q^{4} -3.80523i q^{5} +5.69003i q^{6} +(-0.993207 - 6.92918i) q^{7} -9.17258 q^{8} -3.00000 q^{9} +12.5007i q^{10} +7.79492 q^{11} -11.7643i q^{12} -22.7950i q^{13} +(3.26282 + 22.7633i) q^{14} -6.59085 q^{15} +2.96464 q^{16} +9.89299i q^{17} +9.85542 q^{18} -32.3625i q^{19} -25.8457i q^{20} +(-12.0017 + 1.72029i) q^{21} -25.6074 q^{22} +4.79583 q^{23} +15.8874i q^{24} +10.5202 q^{25} +74.8848i q^{26} +5.19615i q^{27} +(-6.74601 - 47.0640i) q^{28} +11.4297 q^{29} +21.6519 q^{30} +4.16392i q^{31} +26.9511 q^{32} -13.5012i q^{33} -32.4998i q^{34} +(-26.3671 + 3.77938i) q^{35} -20.3764 q^{36} +40.0642 q^{37} +106.315i q^{38} -39.4821 q^{39} +34.9038i q^{40} -17.4931i q^{41} +(39.4272 - 5.65138i) q^{42} +62.2555 q^{43} +52.9442 q^{44} +11.4157i q^{45} -15.7550 q^{46} -32.5512i q^{47} -5.13492i q^{48} +(-47.0271 + 13.7642i) q^{49} -34.5605 q^{50} +17.1352 q^{51} -154.827i q^{52} -57.0429 q^{53} -17.0701i q^{54} -29.6614i q^{55} +(9.11027 + 63.5585i) q^{56} -56.0534 q^{57} -37.5481 q^{58} +69.7638i q^{59} -44.7660 q^{60} +71.8427i q^{61} -13.6791i q^{62} +(2.97962 + 20.7875i) q^{63} -100.397 q^{64} -86.7402 q^{65} +44.3533i q^{66} -76.9997 q^{67} +67.1946i q^{68} -8.30662i q^{69} +(86.6196 - 12.4158i) q^{70} -97.1894 q^{71} +27.5178 q^{72} -69.9330i q^{73} -131.616 q^{74} -18.2216i q^{75} -219.810i q^{76} +(-7.74197 - 54.0124i) q^{77} +129.704 q^{78} -64.5952 q^{79} -11.2811i q^{80} +9.00000 q^{81} +57.4672i q^{82} -85.3491i q^{83} +(-81.5172 + 11.6844i) q^{84} +37.6451 q^{85} -204.518 q^{86} -19.7968i q^{87} -71.4995 q^{88} +11.1608i q^{89} -37.5021i q^{90} +(-157.951 + 22.6402i) q^{91} +32.5740 q^{92} +7.21212 q^{93} +106.935i q^{94} -123.146 q^{95} -46.6806i q^{96} -45.6445i q^{97} +(154.491 - 45.2174i) q^{98} -23.3848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9}+O(q^{10}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9	\( 60 q + 128 q^{4} - 16 q^{7} + 24 q^{8} - 180 q^{9} + 28 q^{14} - 48 q^{15} + 192 q^{16} + 48 q^{21} - 8 q^{22} - 292 q^{25} - 128 q^{28} + 136 q^{29} + 96 q^{32} - 88 q^{35} - 384 q^{36} - 200 q^{37} + 48 q^{39} - 60 q^{42} + 72 q^{43} + 352 q^{44} + 132 q^{49} - 376 q^{50} - 112 q^{53} + 260 q^{56} - 240 q^{57} + 32 q^{58} - 216 q^{60} + 48 q^{63} + 536 q^{64} - 8 q^{65} - 408 q^{67} - 112 q^{70} + 456 q^{71} - 72 q^{72} - 120 q^{74} + 104 q^{77} + 48 q^{78} + 192 q^{79} + 540 q^{81} + 24 q^{84} + 488 q^{85} + 72 q^{86} + 432 q^{88} + 88 q^{91} + 48 q^{93} + 880 q^{95} - 16 q^{98}+O(q^{100}) \) 60 * q + 128 * q^4 - 16 * q^7 + 24 * q^8 - 180 * q^9 + 28 * q^14 - 48 * q^15 + 192 * q^16 + 48 * q^21 - 8 * q^22 - 292 * q^25 - 128 * q^28 + 136 * q^29 + 96 * q^32 - 88 * q^35 - 384 * q^36 - 200 * q^37 + 48 * q^39 - 60 * q^42 + 72 * q^43 + 352 * q^44 + 132 * q^49 - 376 * q^50 - 112 * q^53 + 260 * q^56 - 240 * q^57 + 32 * q^58 - 216 * q^60 + 48 * q^63 + 536 * q^64 - 8 * q^65 - 408 * q^67 - 112 * q^70 + 456 * q^71 - 72 * q^72 - 120 * q^74 + 104 * q^77 + 48 * q^78 + 192 * q^79 + 540 * q^81 + 24 * q^84 + 488 * q^85 + 72 * q^86 + 432 * q^88 + 88 * q^91 + 48 * q^93 + 880 * q^95 - 16 * q^98

Introduction

L-functions

Modular forms

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