LMFDB - Embedded newform 143.4.b.a.12.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(12,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("143.12");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.b (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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			12.18
Character	$\chi$	$=$	143.12
Dual form			143.4.b.a.12.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.370518i q^{2} -0.548979 q^{3} +7.86272 q^{4} +11.6192i q^{5} +0.203406i q^{6} +19.9902i q^{7} -5.87742i q^{8} -26.6986 q^{9} +O(q^{10})$	\(q-0.370518i q^{2} -0.548979 q^{3} +7.86272 q^{4} +11.6192i q^{5} +0.203406i q^{6} +19.9902i q^{7} -5.87742i q^{8} -26.6986 q^{9} +4.30511 q^{10} +11.0000i q^{11} -4.31646 q^{12} +(-46.8702 - 0.425818i) q^{13} +7.40673 q^{14} -6.37868i q^{15} +60.7240 q^{16} -6.29819 q^{17} +9.89231i q^{18} +71.8312i q^{19} +91.3583i q^{20} -10.9742i q^{21} +4.07569 q^{22} +37.7543 q^{23} +3.22658i q^{24} -10.0053 q^{25} +(-0.157773 + 17.3663i) q^{26} +29.4794 q^{27} +157.177i q^{28} +113.264 q^{29} -2.36341 q^{30} +253.495i q^{31} -69.5187i q^{32} -6.03876i q^{33} +2.33359i q^{34} -232.270 q^{35} -209.924 q^{36} -100.341i q^{37} +26.6147 q^{38} +(25.7308 + 0.233765i) q^{39} +68.2908 q^{40} +25.1578i q^{41} -4.06613 q^{42} +297.870 q^{43} +86.4899i q^{44} -310.216i q^{45} -13.9886i q^{46} -409.760i q^{47} -33.3362 q^{48} -56.6087 q^{49} +3.70715i q^{50} +3.45757 q^{51} +(-368.527 - 3.34809i) q^{52} +385.030 q^{53} -10.9226i q^{54} -127.811 q^{55} +117.491 q^{56} -39.4338i q^{57} -41.9662i q^{58} -416.523i q^{59} -50.1538i q^{60} -460.113 q^{61} +93.9243 q^{62} -533.711i q^{63} +460.034 q^{64} +(4.94765 - 544.594i) q^{65} -2.23747 q^{66} +241.736i q^{67} -49.5209 q^{68} -20.7263 q^{69} +86.0601i q^{70} -554.420i q^{71} +156.919i q^{72} +402.299i q^{73} -37.1781 q^{74} +5.49270 q^{75} +564.788i q^{76} -219.892 q^{77} +(0.0866140 - 9.53370i) q^{78} -490.363 q^{79} +705.564i q^{80} +704.679 q^{81} +9.32143 q^{82} -294.088i q^{83} -86.2870i q^{84} -73.1798i q^{85} -110.366i q^{86} -62.1794 q^{87} +64.6516 q^{88} +396.547i q^{89} -114.941 q^{90} +(8.51219 - 936.946i) q^{91} +296.852 q^{92} -139.163i q^{93} -151.823 q^{94} -834.620 q^{95} +38.1643i q^{96} -852.333i q^{97} +20.9745i q^{98} -293.685i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) $ 36 * q - 152 * q^4 + 360 * q^9	$ 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) $ 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	0.370518i		−	0.130998i	−0.997853	−	0.0654989i	$-0.979136\pi$
$2$		−	0.370518i		−	0.130998i	0.997853	−	0.0654989i	$-0.0208639\pi$
$3$	−0.548979			−0.105651			−0.0528255	−	0.998604i	$-0.516823\pi$
$3$	−0.548979			−0.105651			−0.0528255	+	0.998604i	$0.516823\pi$
$4$	7.86272			0.982840
$5$			11.6192i			1.03925i	0.854394	+	0.519625i	$0.173929\pi$
$5$			11.6192i			1.03925i	−0.854394	+	0.519625i	$0.826071\pi$
$6$			0.203406i			0.0138400i
$7$			19.9902i			1.07937i	0.841867	+	0.539685i	$0.181457\pi$
$7$			19.9902i			1.07937i	−0.841867	+	0.539685i	$0.818543\pi$
$8$		−	5.87742i		−	0.259748i
$9$	−26.6986			−0.988838
$10$	4.30511			0.136140
$11$			11.0000i			0.301511i
$11$			11.0000i			0.301511i
$12$	−4.31646			−0.103838
$13$	−46.8702	−	0.425818i	−0.999959	−	0.00908467i
$13$	−46.8702	−	0.425818i	−0.999959	−	0.00908467i
$14$	7.40673			0.141395
$15$		−	6.37868i		−	0.109798i
$16$	60.7240			0.948813
$17$	−6.29819			−0.0898550			−0.0449275	−	0.998990i	$-0.514306\pi$
$17$	−6.29819			−0.0898550			−0.0449275	+	0.998990i	$0.514306\pi$
$18$			9.89231i			0.129536i
$19$			71.8312i			0.867327i	0.901075	+	0.433663i	$0.142779\pi$
$19$			71.8312i			0.867327i	−0.901075	+	0.433663i	$0.857221\pi$
$20$			91.3583i			1.02142i
$21$		−	10.9742i		−	0.114037i
$22$	4.07569			0.0394973
$23$	37.7543			0.342275			0.171137	−	0.985247i	$-0.445256\pi$
$23$	37.7543			0.342275			0.171137	+	0.985247i	$0.445256\pi$
$24$			3.22658i			0.0274426i
$25$	−10.0053			−0.0800425
$26$	−0.157773	+	17.3663i	−0.00119007	+	0.130992i
$27$	29.4794			0.210123
$28$			157.177i			1.06085i
$29$	113.264			0.725261			0.362630	−	0.931933i	$-0.381879\pi$
$29$	113.264			0.725261			0.362630	+	0.931933i	$0.381879\pi$
$30$	−2.36341			−0.0143833
$31$			253.495i			1.46868i	0.678783	+	0.734339i	$0.262508\pi$
$31$			253.495i			1.46868i	−0.678783	+	0.734339i	$0.737492\pi$
$32$		−	69.5187i		−	0.384040i
$33$		−	6.03876i		−	0.0318550i
$34$			2.33359i			0.0117708i
$35$	−232.270			−1.12174
$36$	−209.924			−0.971869
$37$		−	100.341i		−	0.445837i	−0.974837	−	0.222919i	$-0.928442\pi$
$37$		−	100.341i		−	0.445837i	0.974837	−	0.222919i	$-0.0715584\pi$
$38$	26.6147			0.113618
$39$	25.7308	+	0.233765i	0.105647	+	0.000959804i
$40$	68.2908			0.269943
$41$			25.1578i			0.0958292i	0.998851	+	0.0479146i	$0.0152575\pi$
$41$			25.1578i			0.0958292i	−0.998851	+	0.0479146i	$0.984742\pi$
$42$	−4.06613			−0.0149385
$43$	297.870			1.05639			0.528195	−	0.849123i	$-0.322869\pi$
$43$	297.870			1.05639			0.528195	+	0.849123i	$0.322869\pi$
$44$			86.4899i			0.296337i
$45$		−	310.216i		−	1.02765i
$46$		−	13.9886i		−	0.0448373i
$47$		−	409.760i		−	1.27169i	−0.771815	−	0.635847i	$-0.780651\pi$
$47$		−	409.760i		−	1.27169i	0.771815	−	0.635847i	$-0.219349\pi$
$48$	−33.3362			−0.100243
$49$	−56.6087			−0.165040
$50$			3.70715i			0.0104854i
$51$	3.45757			0.00949327
$52$	−368.527	−	3.34809i	−0.982799	−	0.00892877i
$53$	385.030			0.997884			0.498942	−	0.866635i	$-0.333722\pi$
$53$	385.030			0.997884			0.498942	+	0.866635i	$0.333722\pi$
$54$		−	10.9226i		−	0.0275256i
$55$	−127.811			−0.313346
$56$	117.491			0.280364
$57$		−	39.4338i		−	0.0916339i
$58$		−	41.9662i		−	0.0950075i
$59$		−	416.523i		−	0.919097i	−0.888153	−	0.459549i	$-0.848011\pi$
$59$		−	416.523i		−	0.919097i	0.888153	−	0.459549i	$-0.151989\pi$
$60$		−	50.1538i		−	0.107914i
$61$	−460.113			−0.965761			−0.482881	−	0.875686i	$-0.660410\pi$
$61$	−460.113			−0.965761			−0.482881	+	0.875686i	$0.660410\pi$
$62$	93.9243			0.192393
$63$		−	533.711i		−	1.06732i
$64$	460.034			0.898505
$65$	4.94765	−	544.594i	0.00944125	−	1.03921i
$66$	−2.23747			−0.00417293
$67$			241.736i			0.440788i	0.975411	+	0.220394i	$0.0707343\pi$
$67$			241.736i			0.440788i	−0.975411	+	0.220394i	$0.929266\pi$
$68$	−49.5209			−0.0883131
$69$	−20.7263			−0.0361617
$70$			86.0601i			0.146945i
$71$		−	554.420i		−	0.926727i	−0.886168	−	0.463363i	$-0.846642\pi$
$71$		−	554.420i		−	0.926727i	0.886168	−	0.463363i	$-0.153358\pi$
$72$			156.919i			0.256848i
$73$			402.299i			0.645008i	0.946568	+	0.322504i	$0.104525\pi$
$73$			402.299i			0.645008i	−0.946568	+	0.322504i	$0.895475\pi$
$74$	−37.1781			−0.0584037
$75$	5.49270			0.00845657
$76$			564.788i			0.852443i
$77$	−219.892			−0.325442
$78$	0.0866140	−	9.53370i	0.000125732	−	0.0138395i
$79$	−490.363			−0.698357			−0.349178	−	0.937056i	$-0.613539\pi$
$79$	−490.363			−0.698357			−0.349178	+	0.937056i	$0.613539\pi$
$80$			705.564i			0.986055i
$81$	704.679			0.966638
$82$	9.32143			0.0125534
$83$		−	294.088i		−	0.388920i	−0.980910	−	0.194460i	$-0.937705\pi$
$83$		−	294.088i		−	0.388920i	0.980910	−	0.194460i	$-0.0622954\pi$
$84$		−	86.2870i		−	0.112080i
$85$		−	73.1798i		−	0.0933819i
$86$		−	110.366i		−	0.138385i
$87$	−62.1794			−0.0766245
$88$	64.6516			0.0783168
$89$			396.547i			0.472291i	0.971718	+	0.236146i	$0.0758842\pi$
$89$			396.547i			0.472291i	−0.971718	+	0.236146i	$0.924116\pi$
$90$	−114.941			−0.134620
$91$	8.51219	−	936.946i	0.00980572	−	1.07933i
$92$	296.852			0.336401
$93$		−	139.163i		−	0.155167i
$94$	−151.823			−0.166589
$95$	−834.620			−0.901370
$96$			38.1643i			0.0405742i
$97$		−	852.333i		−	0.892179i	−0.894988	−	0.446089i	$-0.852816\pi$
$97$		−	852.333i		−	0.892179i	0.894988	−	0.446089i	$-0.147184\pi$
$98$			20.9745i			0.0216199i
$99$		−	293.685i		−	0.298146i
$100$	−78.6690			−0.0786690
$101$	−414.163			−0.408028			−0.204014	−	0.978968i	$-0.565399\pi$
$101$	−414.163			−0.408028			−0.204014	+	0.978968i	$0.565399\pi$
$102$		−	1.28109i		−	0.00124360i
$103$	1094.16			1.04671			0.523353	−	0.852116i	$-0.324681\pi$
$103$	1094.16			1.04671			0.523353	+	0.852116i	$0.324681\pi$
$104$	−2.50271	+	275.476i	−0.00235972	+	0.259737i
$105$	127.511			0.118513
$106$		−	142.660i		−	0.130721i
$107$	−1001.90			−0.905207			−0.452603	−	0.891712i	$-0.649505\pi$
$107$	−1001.90			−0.905207			−0.452603	+	0.891712i	$0.649505\pi$
$108$	231.788			0.206517
$109$			1310.76i			1.15182i	0.817514	+	0.575909i	$0.195352\pi$
$109$			1310.76i			1.15182i	−0.817514	+	0.575909i	$0.804648\pi$
$110$			47.3562i			0.0410476i
$111$			55.0851i			0.0471031i
$112$			1213.89i			1.02412i
$113$	1059.52			0.882045			0.441023	−	0.897496i	$-0.354616\pi$
$113$	1059.52			0.882045			0.441023	+	0.897496i	$0.354616\pi$
$114$	−14.6109			−0.0120038
$115$			438.674i			0.355710i
$116$	890.561			0.712815
$117$	1251.37	+	11.3688i	0.988797	+	0.00898326i
$118$	−154.329			−0.120400
$119$		−	125.902i		−	0.0969869i
$120$	−37.4902			−0.0285197
$121$	−121.000			−0.0909091
$122$			170.480i			0.126513i
$123$		−	13.8111i		−	0.0101244i
$124$			1993.16i			1.44347i
$125$			1336.14i			0.956067i
$126$	−197.749			−0.139817
$127$	288.170			0.201346			0.100673	−	0.994920i	$-0.467900\pi$
$127$	288.170			0.201346			0.100673	+	0.994920i	$0.467900\pi$
$128$		−	726.600i		−	0.501742i
$129$	−163.524			−0.111609
$130$	−201.782	−	1.83319i	−0.136134	−	0.00123678i
$131$	−777.678			−0.518672			−0.259336	−	0.965787i	$-0.583504\pi$
$131$	−777.678			−0.518672			−0.259336	+	0.965787i	$0.583504\pi$
$132$		−	47.4811i		−	0.0313083i
$133$	−1435.92			−0.936167
$134$	89.5676			0.0577423
$135$			342.526i			0.218370i
$136$			37.0171i			0.0233396i
$137$			1489.37i			0.928802i	0.885625	+	0.464401i	$0.153730\pi$
$137$			1489.37i			0.928802i	−0.885625	+	0.464401i	$0.846270\pi$
$138$			7.67947i			0.00473710i
$139$	2056.72			1.25503			0.627514	−	0.778605i	$-0.284072\pi$
$139$	2056.72			1.25503			0.627514	+	0.778605i	$0.284072\pi$
$140$	−1826.27			−1.10249
$141$			224.949i			0.134356i
$142$	−205.423			−0.121399
$143$	4.68400	−	515.573i	0.00273913	−	0.301499i
$144$	−1621.25			−0.938222
$145$			1316.03i			0.753728i
$146$	149.059			0.0844946
$147$	31.0769			0.0174366
$148$		−	788.953i		−	0.438186i
$149$		−	799.199i		−	0.439416i	−0.975566	−	0.219708i	$-0.929490\pi$
$149$		−	799.199i		−	0.439416i	0.975566	−	0.219708i	$-0.0705104\pi$
$150$		−	2.03514i		−	0.00110779i
$151$			2561.75i			1.38061i	0.723517	+	0.690306i	$0.242524\pi$
$151$			2561.75i			1.38061i	−0.723517	+	0.690306i	$0.757476\pi$
$152$	422.182			0.225286
$153$	168.153			0.0888521
$154$			81.4740i			0.0426322i
$155$	−2945.40			−1.52632
$156$	202.314	+	1.83803i	0.103834	+	0.000943333i
$157$	895.890			0.455413			0.227706	−	0.973730i	$-0.426877\pi$
$157$	895.890			0.455413			0.227706	+	0.973730i	$0.426877\pi$
$158$			181.688i			0.0914832i
$159$	−211.373			−0.105427
$160$	807.750			0.399114
$161$			754.717i			0.369441i
$162$		−	261.096i		−	0.126627i
$163$		−	841.453i		−	0.404342i	−0.979350	−	0.202171i	$-0.935200\pi$
$163$		−	841.453i		−	0.404342i	0.979350	−	0.202171i	$-0.0647996\pi$
$164$			197.809i			0.0941847i
$165$	70.1655			0.0331053
$166$	−108.965			−0.0509476
$167$		−	4256.21i		−	1.97219i	−0.166184	−	0.986095i	$-0.553144\pi$
$167$		−	4256.21i		−	1.97219i	0.166184	−	0.986095i	$-0.446856\pi$
$168$	−64.4999			−0.0296207
$169$	2196.64	+	39.9164i	0.999835	+	0.0181686i
$170$	−27.1144			−0.0122328
$171$		−	1917.79i		−	0.857646i
$172$	2342.07			1.03826
$173$	−2668.41			−1.17269			−0.586346	−	0.810061i	$-0.699434\pi$
$173$	−2668.41			−1.17269			−0.586346	+	0.810061i	$0.699434\pi$
$174$			23.0386i			0.0100376i
$175$		−	200.008i		−	0.0863955i
$176$			667.965i			0.286078i
$177$			228.662i			0.0971035i
$178$	146.928			0.0618691
$179$	4420.16			1.84569			0.922845	−	0.385173i	$-0.125858\pi$
$179$	4420.16			1.84569			0.922845	+	0.385173i	$0.125858\pi$
$180$		−	2439.14i		−	1.01002i
$181$	−354.730			−0.145673			−0.0728367	−	0.997344i	$-0.523205\pi$
$181$	−354.730			−0.145673			−0.0728367	+	0.997344i	$0.523205\pi$
$182$	−347.155	−	3.15392i	−0.141389	−	0.00128453i
$183$	252.592			0.102034
$184$		−	221.898i		−	0.0889051i
$185$	1165.88			0.463337
$186$	−51.5624			−0.0203266
$187$		−	69.2801i		−	0.0270923i
$188$		−	3221.82i		−	1.24987i
$189$			589.299i			0.226800i
$190$			309.241i			0.118078i
$191$	798.518			0.302507			0.151253	−	0.988495i	$-0.451669\pi$
$191$	798.518			0.302507			0.151253	+	0.988495i	$0.451669\pi$
$192$	−252.549			−0.0949279
$193$		−	2394.76i		−	0.893155i	−0.894745	−	0.446578i	$-0.852643\pi$
$193$		−	2394.76i		−	0.893155i	0.894745	−	0.446578i	$-0.147357\pi$
$194$	−315.805			−0.116873
$195$	−2.71616	+	298.970i	−0.000997477	+	0.109793i
$196$	−445.098			−0.162208
$197$		−	4331.69i		−	1.56660i	−0.621645	−	0.783299i	$-0.713535\pi$
$197$		−	4331.69i		−	1.56660i	0.621645	−	0.783299i	$-0.286465\pi$
$198$	−108.815			−0.0390564
$199$	−4850.75			−1.72794			−0.863971	−	0.503541i	$-0.832030\pi$
$199$	−4850.75			−1.72794			−0.863971	+	0.503541i	$0.832030\pi$
$200$			58.8054i			0.0207909i
$201$		−	132.708i		−	0.0465697i
$202$			153.455i			0.0534507i
$203$			2264.17i			0.782825i
$204$	27.1859			0.00933036
$205$	−292.313			−0.0995905
$206$		−	405.406i		−	0.137116i
$207$	−1007.99			−0.338454
$208$	−2846.15	−	25.8574i	−0.948774	−	0.00861965i
$209$	−790.143			−0.261509
$210$		−	47.2451i		−	0.0155249i
$211$	2211.57			0.721569			0.360784	−	0.932649i	$-0.382509\pi$
$211$	2211.57			0.721569			0.360784	+	0.932649i	$0.382509\pi$
$212$	3027.38			0.980760
$213$			304.365i			0.0979096i
$214$			371.221i			0.118580i
$215$			3461.00i			1.09785i
$216$		−	173.263i		−	0.0545789i
$217$	−5067.41			−1.58525
$218$	485.660			0.150886
$219$		−	220.854i		−	0.0681457i
$220$	−1004.94			−0.307969
$221$	295.198	+	2.68188i	0.0898513	+	0.000816303i
$222$	20.4100			0.00617040
$223$		−	2734.21i		−	0.821059i	−0.911847	−	0.410530i	$-0.865344\pi$
$223$		−	2734.21i		−	0.821059i	0.911847	−	0.410530i	$-0.134656\pi$
$224$	1389.69			0.414521
$225$	267.128			0.0791491
$226$		−	392.570i		−	0.115546i
$227$		−	2762.57i		−	0.807745i	−0.914815	−	0.403873i	$-0.867664\pi$
$227$		−	2762.57i		−	0.807745i	0.914815	−	0.403873i	$-0.132336\pi$
$228$		−	310.057i		−	0.0900614i
$229$			6302.02i			1.81855i	0.416191	+	0.909277i	$0.363365\pi$
$229$			6302.02i			1.81855i	−0.416191	+	0.909277i	$0.636635\pi$
$230$	162.537			0.0465972
$231$	120.716			0.0343833
$232$		−	665.699i		−	0.188385i
$233$	−506.850			−0.142510			−0.0712551	−	0.997458i	$-0.522700\pi$
$233$	−506.850			−0.142510			−0.0712551	+	0.997458i	$0.522700\pi$
$234$	4.21232	−	463.655i	0.00117679	−	0.129530i
$235$	4761.07			1.32161
$236$		−	3275.01i		−	0.903325i
$237$	269.199			0.0737821
$238$	−46.6490			−0.0127051
$239$		−	570.486i		−	0.154400i	−0.997016	−	0.0772001i	$-0.975402\pi$
$239$		−	570.486i		−	0.154400i	0.997016	−	0.0772001i	$-0.0245980\pi$
$240$		−	387.339i		−	0.104178i
$241$			5154.44i			1.37770i	0.724902	+	0.688852i	$0.241885\pi$
$241$			5154.44i			1.37770i	−0.724902	+	0.688852i	$0.758115\pi$
$242$			44.8326i			0.0119089i
$243$	−1182.80			−0.312249
$244$	−3617.74			−0.949188
$245$		−	657.746i		−	0.171518i
$246$	−5.11726			−0.00132628
$247$	30.5870	−	3366.75i	0.00787937	−	0.867291i
$248$	1489.89			0.381485
$249$			161.448i			0.0410897i
$250$	495.065			0.125243
$251$	6819.28			1.71486			0.857429	−	0.514602i	$-0.172060\pi$
$251$	6819.28			1.71486			0.857429	+	0.514602i	$0.172060\pi$
$252$		−	4196.42i		−	1.04901i
$253$			415.298i			0.103200i
$254$		−	106.772i		−	0.0263759i
$255$			40.1741i			0.00986589i
$256$	3411.06			0.832778
$257$	5607.15			1.36095			0.680476	−	0.732771i	$-0.261773\pi$
$257$	5607.15			1.36095			0.680476	+	0.732771i	$0.261773\pi$
$258$			60.5886i			0.0146205i
$259$	2005.84			0.481223
$260$	38.9020	−	4281.99i	0.00927923	−	1.02137i
$261$	−3023.99			−0.717165
$262$			288.144i			0.0679449i
$263$	−3781.28			−0.886555			−0.443278	−	0.896384i	$-0.646184\pi$
$263$	−3781.28			−0.886555			−0.443278	+	0.896384i	$0.646184\pi$
$264$	−35.4923			−0.00827425
$265$			4473.73i			1.03705i
$266$			532.034i			0.122636i
$267$		−	217.696i		−	0.0498980i
$268$			1900.71i			0.433224i
$269$	−4827.98			−1.09430			−0.547151	−	0.837034i	$-0.684288\pi$
$269$	−4827.98			−1.09430			−0.547151	+	0.837034i	$0.684288\pi$
$270$	126.912			0.0286060
$271$			5864.01i			1.31444i	0.753699	+	0.657220i	$0.228268\pi$
$271$			5864.01i			1.31444i	−0.753699	+	0.657220i	$0.771732\pi$
$272$	−382.452			−0.0852557
$273$	−4.67301	+	514.363i	−0.00103598	+	0.114032i
$274$	551.840			0.121671
$275$		−	110.058i		−	0.0241337i
$276$	−162.965			−0.0355411
$277$	−5378.70			−1.16670			−0.583348	−	0.812222i	$-0.698258\pi$
$277$	−5378.70			−1.16670			−0.583348	+	0.812222i	$0.698258\pi$
$278$		−	762.053i		−	0.164406i
$279$		−	6767.96i		−	1.45228i
$280$			1365.15i			0.291368i
$281$			7785.08i			1.65274i	0.563131	+	0.826368i	$0.309597\pi$
$281$			7785.08i			1.65274i	−0.563131	+	0.826368i	$0.690403\pi$
$282$	83.3477			0.0176003
$283$	−5481.62			−1.15141			−0.575704	−	0.817658i	$-0.695272\pi$
$283$	−5481.62			−1.15141			−0.575704	+	0.817658i	$0.695272\pi$
$284$		−	4359.25i		−	0.910824i
$285$	458.188			0.0952306
$286$	−191.029	−	1.73550i	−0.0394957	−	0.000358820i
$287$	−502.911			−0.103435
$288$			1856.05i			0.379753i
$289$	−4873.33			−0.991926
$290$	487.613			0.0987367
$291$			467.913i			0.0942595i
$292$			3163.17i			0.633939i
$293$			6656.08i			1.32714i	0.748114	+	0.663571i	$0.230960\pi$
$293$			6656.08i			1.32714i	−0.748114	+	0.663571i	$0.769040\pi$
$294$		−	11.5146i		−	0.00228416i
$295$	4839.66			0.955173
$296$	−589.746			−0.115805
$297$			324.273i			0.0633544i
$298$	−296.117			−0.0575625
$299$	−1769.55	−	16.0765i	−0.342261	−	0.00310945i
$300$	43.1876			0.00831145
$301$			5954.49i			1.14024i
$302$	949.175			0.180857
$303$	227.367			0.0431085
$304$			4361.88i			0.822931i
$305$		−	5346.14i		−	1.00367i
$306$		−	62.3037i		−	0.0116394i
$307$			6778.67i			1.26019i	0.776517	+	0.630096i	$0.216985\pi$
$307$			6778.67i			1.26019i	−0.776517	+	0.630096i	$0.783015\pi$
$308$	−1728.95			−0.319858
$309$	−600.670			−0.110586
$310$			1091.32i			0.199945i
$311$	−1691.71			−0.308451			−0.154226	−	0.988036i	$-0.549288\pi$
$311$	−1691.71			−0.308451			−0.154226	+	0.988036i	$0.549288\pi$
$312$	1.37393	−	151.230i	0.000249307	−	0.0274415i
$313$	4230.92			0.764043			0.382022	−	0.924153i	$-0.375228\pi$
$313$	4230.92			0.764043			0.382022	+	0.924153i	$0.375228\pi$
$314$		−	331.943i		−	0.0596581i
$315$	6201.29			1.10922
$316$	−3855.59			−0.686373
$317$		−	867.246i		−	0.153657i	−0.997044	−	0.0768287i	$-0.975521\pi$
$317$		−	867.246i		−	0.153657i	0.997044	−	0.0768287i	$-0.0244794\pi$
$318$			78.3174i			0.0138108i
$319$			1245.90i			0.218674i
$320$			5345.22i			0.933772i
$321$	550.020			0.0956360
$322$	279.636			0.0483960
$323$		−	452.407i		−	0.0779337i
$324$	5540.69			0.950050
$325$	468.951	+	4.26044i	0.0800392	+	0.000727159i
$326$	−311.773			−0.0529679
$327$		−	719.580i		−	0.121691i
$328$	147.863			0.0248914
$329$	8191.18			1.37263
$330$		−	25.9976i		−	0.00433672i
$331$		−	3642.56i		−	0.604874i	−0.953169	−	0.302437i	$-0.902200\pi$
$331$		−	3642.56i		−	0.604874i	0.953169	−	0.302437i	$-0.0978002\pi$
$332$		−	2312.33i		−	0.382246i
$333$			2678.97i			0.440861i
$334$	−1577.00			−0.258352
$335$	−2808.78			−0.458090
$336$		−	666.398i		−	0.108199i
$337$	8388.11			1.35587			0.677937	−	0.735120i	$-0.262874\pi$
$337$	8388.11			1.35587			0.677937	+	0.735120i	$0.262874\pi$
$338$	14.7897	−	813.893i	0.00238004	−	0.130976i
$339$	−581.653			−0.0931889
$340$		−	575.392i		−	0.0917795i
$341$	−2788.44			−0.442823
$342$	−710.577			−0.112350
$343$			5725.02i			0.901231i
$344$		−	1750.71i		−	0.274395i
$345$		−	240.823i		−	0.0375811i
$346$			988.695i			0.153620i
$347$	−7895.82			−1.22153			−0.610763	−	0.791813i	$-0.709137\pi$
$347$	−7895.82			−1.22153			−0.610763	+	0.791813i	$0.709137\pi$
$348$	−488.899			−0.0753096
$349$		−	3785.89i		−	0.580670i	−0.956925	−	0.290335i	$-0.906233\pi$
$349$		−	3785.89i		−	0.580670i	0.956925	−	0.290335i	$-0.0937668\pi$
$350$	−74.1066			−0.0113176
$351$	−1381.71	−	12.5529i	−0.210114	−	0.00190889i
$352$	764.705			0.115792
$353$			11750.9i			1.77177i	0.463902	+	0.885886i	$0.346449\pi$
$353$			11750.9i			1.77177i	−0.463902	+	0.885886i	$0.653551\pi$
$354$	84.7235			0.0127203
$355$	6441.91			0.963102
$356$			3117.94i			0.464187i
$357$			69.1176i			0.0102468i
$358$		−	1637.75i		−	0.241781i
$359$		−	12559.3i		−	1.84639i	−0.384332	−	0.923195i	$-0.625568\pi$
$359$		−	12559.3i		−	1.84639i	0.384332	−	0.923195i	$-0.374432\pi$
$360$	−1823.27			−0.266930
$361$	1699.28			0.247744
$362$			131.434i			0.0190829i
$363$	66.4264			0.00960463
$364$	66.9290	−	7366.94i	0.00963745	−	1.06080i
$365$	−4674.39			−0.670325
$366$		−	93.5899i		−	0.0133662i
$367$	−2343.63			−0.333342			−0.166671	−	0.986013i	$-0.553302\pi$
$367$	−2343.63			−0.333342			−0.166671	+	0.986013i	$0.553302\pi$
$368$	2292.60			0.324755
$369$		−	671.680i		−	0.0947595i
$370$		−	431.980i		−	0.0606961i
$371$			7696.82i			1.07709i
$372$		−	1094.20i		−	0.152504i
$373$	6730.50			0.934296			0.467148	−	0.884179i	$-0.345282\pi$
$373$	6730.50			0.934296			0.467148	+	0.884179i	$0.345282\pi$
$374$	−25.6695			−0.00354903
$375$		−	733.514i		−	0.101009i
$376$	−2408.33			−0.330319
$377$	−5308.70	−	48.2298i	−0.725231	−	0.00658875i
$378$	218.346			0.0297103
$379$		−	11278.4i		−	1.52858i	−0.644875	−	0.764288i	$-0.723090\pi$
$379$		−	11278.4i		−	1.52858i	0.644875	−	0.764288i	$-0.276910\pi$
$380$	−6562.38			−0.885902
$381$	−158.199			−0.0212724
$382$		−	295.865i		−	0.0396277i
$383$		−	5394.67i		−	0.719726i	−0.933005	−	0.359863i	$-0.882823\pi$
$383$		−	5394.67i		−	0.719726i	0.933005	−	0.359863i	$-0.117177\pi$
$384$			398.888i			0.0530095i
$385$		−	2554.97i		−	0.338216i
$386$	−887.303			−0.117001
$387$	−7952.72			−1.04460
$388$		−	6701.65i		−	0.876868i
$389$	8909.94			1.16132			0.580658	−	0.814148i	$-0.302795\pi$
$389$	8909.94			1.16132			0.580658	+	0.814148i	$0.302795\pi$
$390$	110.774	+	1.00638i	0.0143827	+	0.000130667i
$391$	−237.784			−0.0307551
$392$			332.713i			0.0428687i
$393$	426.929			0.0547982
$394$	−1604.97			−0.205221
$395$		−	5697.62i		−	0.725768i
$396$		−	2309.16i		−	0.293030i
$397$		−	7513.36i		−	0.949835i	−0.880030	−	0.474918i	$-0.842478\pi$
$397$		−	7513.36i		−	0.949835i	0.880030	−	0.474918i	$-0.157522\pi$
$398$			1797.29i			0.226357i
$399$	788.290			0.0989069
$400$	−607.563			−0.0759454
$401$			4025.54i			0.501311i	0.968076	+	0.250656i	$0.0806462\pi$
$401$			4025.54i			0.501311i	−0.968076	+	0.250656i	$0.919354\pi$
$402$	−49.1707			−0.00610053
$403$	107.943	−	11881.4i	0.0133424	−	1.46862i
$404$	−3256.45			−0.401026
$405$			8187.79i			1.00458i
$406$	838.914			0.102548
$407$	1103.75			0.134425
$408$		−	20.3216i		−	0.00246585i
$409$		−	13707.7i		−	1.65722i	−0.559828	−	0.828609i	$-0.689133\pi$
$409$		−	13707.7i		−	1.65722i	0.559828	−	0.828609i	$-0.310867\pi$
$410$			108.307i			0.0130461i
$411$		−	817.635i		−	0.0981288i
$412$	8603.07			1.02874
$413$	8326.39			0.992046
$414$			373.478i			0.0443368i
$415$	3417.06			0.404185
$416$	−29.6023	+	3258.36i	−0.00348888	+	0.384024i
$417$	−1129.10			−0.132595
$418$			292.762i			0.0342571i
$419$	−6830.53			−0.796404			−0.398202	−	0.917298i	$-0.630366\pi$
$419$	−6830.53			−0.796404			−0.398202	+	0.917298i	$0.630366\pi$
$420$	1002.58			0.116479
$421$			13958.9i			1.61595i	0.589218	+	0.807974i	$0.299436\pi$
$421$			13958.9i			1.61595i	−0.589218	+	0.807974i	$0.700564\pi$
$422$		−	819.427i		−	0.0945239i
$423$			10940.0i			1.25750i
$424$		−	2262.98i		−	0.259198i
$425$	63.0154			0.00719222
$426$	112.773			0.0128259
$427$		−	9197.76i		−	1.04241i
$428$	−7877.64			−0.889673
$429$	−2.57141	+	283.038i	−0.000289392	+	0.0318537i
$430$	1282.36			0.143816
$431$		−	2206.57i		−	0.246604i	−0.992369	−	0.123302i	$-0.960652\pi$
$431$		−	2206.57i		−	0.246604i	0.992369	−	0.123302i	$-0.0393485\pi$
$432$	1790.11			0.199367
$433$	−7897.72			−0.876536			−0.438268	−	0.898844i	$-0.644408\pi$
$433$	−7897.72			−0.876536			−0.438268	+	0.898844i	$0.644408\pi$
$434$			1877.57i			0.207664i
$435$		−	722.473i		−	0.0796321i
$436$			10306.1i			1.13205i
$437$			2711.94i			0.296864i
$438$	−81.8302			−0.00892694
$439$	2111.17			0.229523			0.114762	−	0.993393i	$-0.463390\pi$
$439$	2111.17			0.229523			0.114762	+	0.993393i	$0.463390\pi$
$440$			751.198i			0.0813909i
$441$	1511.37			0.163198
$442$	0.993685	−	109.376i	0.000106934	−	0.0117703i
$443$	−4984.00			−0.534530			−0.267265	−	0.963623i	$-0.586120\pi$
$443$	−4984.00			−0.534530			−0.267265	+	0.963623i	$0.586120\pi$
$444$			433.119i			0.0462948i
$445$	−4607.55			−0.490829
$446$	−1013.07			−0.107557
$447$			438.743i			0.0464247i
$448$			9196.19i			0.969819i
$449$		−	11621.5i		−	1.22150i	−0.791823	−	0.610751i	$-0.790868\pi$
$449$		−	11621.5i		−	1.22150i	0.791823	−	0.610751i	$-0.209132\pi$
$450$		−	98.9757i		−	0.0103684i
$451$	−276.736			−0.0288936
$452$	8330.69			0.866909
$453$		−	1406.35i		−	0.145863i
$454$	−1023.58			−0.105813
$455$	10886.5	+	98.9047i	1.12169	+	0.0101906i
$456$	−231.769			−0.0238017
$457$		−	17200.8i		−	1.76066i	−0.474364	−	0.880329i	$-0.657322\pi$
$457$		−	17200.8i		−	1.76066i	0.474364	−	0.880329i	$-0.342678\pi$
$458$	2335.01			0.238227
$459$	−185.667			−0.0188806
$460$			3449.17i			0.349605i
$461$		−	2531.30i		−	0.255736i	−0.991791	−	0.127868i	$-0.959187\pi$
$461$		−	2531.30i		−	0.255736i	0.991791	−	0.127868i	$-0.0408134\pi$
$462$		−	44.7275i		−	0.00450414i
$463$		−	16502.1i		−	1.65641i	−0.560428	−	0.828203i	$-0.689363\pi$
$463$		−	16502.1i		−	1.65641i	0.560428	−	0.828203i	$-0.310637\pi$
$464$	6877.84			0.688137
$465$	1616.96			0.161258
$466$			187.797i			0.0186685i
$467$	−12689.4			−1.25737			−0.628686	−	0.777659i	$-0.716407\pi$
$467$	−12689.4			−1.25737			−0.628686	+	0.777659i	$0.716407\pi$
$468$	9839.17	+	89.3893i	0.971829	+	0.00882910i
$469$	−4832.36			−0.475774
$470$		−	1764.06i		−	0.173128i
$471$	−491.824			−0.0481148
$472$	−2448.08			−0.238733
$473$			3276.57i			0.318513i
$474$		−	99.7430i		−	0.00966529i
$475$		−	718.694i		−	0.0694230i
$476$		−	989.933i		−	0.0953225i
$477$	−10279.8			−0.986746
$478$	−211.375			−0.0202261
$479$		−	861.353i		−	0.0821633i	−0.999156	−	0.0410817i	$-0.986920\pi$
$479$		−	861.353i		−	0.0821633i	0.999156	−	0.0410817i	$-0.0130804\pi$
$480$	−443.437			−0.0421668
$481$	−42.7270	+	4703.01i	−0.00405028	+	0.445819i
$482$	1909.81			0.180476
$483$		−	414.324i		−	0.0390318i
$484$	−951.389			−0.0893491
$485$	9903.41			0.927197
$486$			438.247i			0.0409039i
$487$		−	10759.2i		−	1.00112i	−0.865702	−	0.500560i	$-0.833127\pi$
$487$		−	10759.2i		−	1.00112i	0.865702	−	0.500560i	$-0.166873\pi$
$488$			2704.28i			0.250854i
$489$			461.940i			0.0427191i
$490$	−243.707			−0.0224685
$491$	−17282.5			−1.58849			−0.794245	−	0.607598i	$-0.792133\pi$
$491$	−17282.5			−1.58849			−0.794245	+	0.607598i	$0.792133\pi$
$492$		−	108.593i		−	0.00995070i
$493$	−713.357			−0.0651683
$494$	−1247.44	−	11.3330i	−0.113613	−	0.00103218i
$495$	3412.38			0.309848
$496$			15393.2i			1.39350i
$497$	11083.0			1.00028
$498$	59.8193			0.00538266
$499$			265.837i			0.0238487i	0.999929	+	0.0119244i	$0.00379573\pi$
$499$			265.837i			0.0238487i	−0.999929	+	0.0119244i	$0.996204\pi$
$500$			10505.7i			0.939660i
$501$			2336.57i			0.208364i
$502$		−	2526.67i		−	0.224643i
$503$	11660.0			1.03358			0.516792	−	0.856111i	$-0.327126\pi$
$503$	11660.0			1.03358			0.516792	+	0.856111i	$0.327126\pi$
$504$	−3136.84			−0.277234
$505$		−	4812.24i		−	0.424043i
$506$	153.875			0.0135189
$507$	−1205.91	−	21.9132i	−0.105634	−	0.00191953i
$508$	2265.80			0.197891
$509$			19777.1i			1.72221i	0.508427	+	0.861105i	$0.330227\pi$
$509$			19777.1i			1.72221i	−0.508427	+	0.861105i	$0.669773\pi$
$510$	14.8852			0.00129241
$511$	−8042.05			−0.696202
$512$		−	7076.66i		−	0.610834i
$513$			2117.54i			0.182245i
$514$		−	2077.55i		−	0.178282i
$515$			12713.2i			1.08779i
$516$	−1285.74			−0.109693
$517$	4507.36			0.383430
$518$		−	743.199i		−	0.0630392i
$519$	1464.90			0.123896
$520$	−3200.80	−	29.0794i	−0.269932	−	0.00245234i
$521$	10244.5			0.861458			0.430729	−	0.902481i	$-0.358256\pi$
$521$	10244.5			0.861458			0.430729	+	0.902481i	$0.358256\pi$
$522$			1120.44i			0.0939470i
$523$	535.008			0.0447309			0.0223654	−	0.999750i	$-0.492880\pi$
$523$	535.008			0.0447309			0.0223654	+	0.999750i	$0.492880\pi$
$524$	−6114.66			−0.509772
$525$			109.800i			0.00912777i
$526$			1401.03i			0.116137i
$527$		−	1596.56i		−	0.131968i
$528$		−	366.698i		−	0.0302244i
$529$	−10741.6			−0.882848
$530$	1657.59			0.135852
$531$			11120.6i			0.908838i
$532$	−11290.2			−0.920102
$533$	10.7127	−	1179.15i	0.000870576	−	0.0958252i
$534$	−80.6602			−0.00653653
$535$		−	11641.2i		−	0.940737i
$536$	1420.79			0.114494
$537$	−2426.57			−0.194999
$538$			1788.85i			0.143351i
$539$		−	622.695i		−	0.0497614i
$540$			2693.19i			0.214623i
$541$			6941.17i			0.551616i	0.961213	+	0.275808i	$0.0889453\pi$
$541$			6941.17i			0.551616i	−0.961213	+	0.275808i	$0.911055\pi$
$542$	2172.72			0.172189
$543$	194.739			0.0153905
$544$			437.842i			0.0345079i
$545$	−15230.0			−1.19703
$546$	190.581	+	1.73143i	0.0149379	+	0.000135712i
$547$	9812.69			0.767020			0.383510	−	0.923537i	$-0.374715\pi$
$547$	9812.69			0.767020			0.383510	+	0.923537i	$0.374715\pi$
$548$			11710.5i			0.912863i
$549$	12284.4			0.954981
$550$	−40.7786			−0.00316146
$551$			8135.88i			0.629038i
$552$			121.817i			0.00939291i
$553$		−	9802.47i		−	0.753785i
$554$			1992.90i			0.152835i
$555$	−640.044			−0.0489520
$556$	16171.4			1.23349
$557$			20923.0i			1.59163i	0.605542	+	0.795813i	$0.292956\pi$
$557$			20923.0i			1.59163i	−0.605542	+	0.795813i	$0.707044\pi$
$558$	−2507.65			−0.190246
$559$	−13961.2	−	126.838i	−1.05635	−	0.00959694i
$560$	−14104.4			−1.06432
$561$			38.0333i			0.00286233i
$562$	2884.51			0.216505
$563$	18951.1			1.41864			0.709319	−	0.704887i	$-0.249002\pi$
$563$	18951.1			1.41864			0.709319	+	0.704887i	$0.249002\pi$
$564$			1768.71i			0.132050i
$565$			12310.7i			0.916666i
$566$			2031.04i			0.150832i
$567$			14086.7i			1.04336i
$568$	−3258.56			−0.240715
$569$	24060.2			1.77268			0.886342	−	0.463031i	$-0.153238\pi$
$569$	24060.2			1.77268			0.886342	+	0.463031i	$0.153238\pi$
$570$		−	169.767i		−	0.0124750i
$571$	−5557.77			−0.407330			−0.203665	−	0.979041i	$-0.565285\pi$
$571$	−5557.77			−0.407330			−0.203665	+	0.979041i	$0.565285\pi$
$572$	36.8289	−	4053.80i	0.00269212	−	0.296325i
$573$	−438.369			−0.0319601
$574$			186.337i			0.0135498i
$575$	−377.744			−0.0273965
$576$	−12282.3			−0.888476
$577$		−	24437.9i		−	1.76319i	−0.472003	−	0.881597i	$-0.656469\pi$
$577$		−	24437.9i		−	1.76319i	0.472003	−	0.881597i	$-0.343531\pi$
$578$			1805.66i			0.129940i
$579$			1314.67i			0.0943627i
$580$			10347.6i			0.740793i
$581$	5878.88			0.419788
$582$	173.370			0.0123478
$583$			4235.32i			0.300873i
$584$	2364.48			0.167539
$585$	−132.096	+	14539.9i	−0.00933586	+	1.02761i
$586$	2466.20			0.173853
$587$		−	5503.17i		−	0.386951i	−0.981105	−	0.193476i	$-0.938024\pi$
$587$		−	5503.17i		−	0.386951i	0.981105	−	0.193476i	$-0.0619760\pi$
$588$	244.349			0.0171374
$589$	−18208.8			−1.27382
$590$		−	1793.18i		−	0.125125i
$591$			2378.00i			0.165513i
$592$		−	6093.12i		−	0.423016i
$593$			2330.82i			0.161409i	0.996738	+	0.0807043i	$0.0257169\pi$
$593$			2330.82i			0.161409i	−0.996738	+	0.0807043i	$0.974283\pi$
$594$	120.149			0.00829928
$595$	1462.88			0.100794
$596$		−	6283.87i		−	0.431875i
$597$	2662.96			0.182559
$598$	−5.95662	+	655.651i	−0.000407331	+	0.0448354i
$599$	3514.35			0.239720			0.119860	−	0.992791i	$-0.461755\pi$
$599$	3514.35			0.239720			0.119860	+	0.992791i	$0.461755\pi$
$600$		−	32.2829i		−	0.00219657i
$601$	5198.76			0.352849			0.176424	−	0.984314i	$-0.443547\pi$
$601$	5198.76			0.352849			0.176424	+	0.984314i	$0.443547\pi$
$602$	2206.24			0.149368
$603$		−	6454.03i		−	0.435868i
$604$			20142.3i			1.35692i
$605$		−	1405.92i		−	0.0944774i
$606$		−	84.2434i		−	0.00564712i
$607$	20939.8			1.40019			0.700097	−	0.714047i	$-0.253140\pi$
$607$	20939.8			1.40019			0.700097	+	0.714047i	$0.253140\pi$
$608$	4993.61			0.333088
$609$		−	1242.98i		−	0.0827062i
$610$	−1980.84			−0.131478
$611$	−174.483	+	19205.5i	−0.0115529	+	1.27164i
$612$	1322.14			0.0873273
$613$		−	20854.6i		−	1.37408i	−0.726622	−	0.687038i	$-0.758911\pi$
$613$		−	20854.6i		−	1.37408i	0.726622	−	0.687038i	$-0.241089\pi$
$614$	2511.62			0.165082
$615$	160.474			0.0105218
$616$			1292.40i			0.0845329i
$617$		−	16354.9i		−	1.06714i	−0.845757	−	0.533569i	$-0.820850\pi$
$617$		−	16354.9i		−	1.06714i	0.845757	−	0.533569i	$-0.179150\pi$
$618$			222.559i			0.0144865i
$619$		−	23288.7i		−	1.51220i	−0.654457	−	0.756099i	$-0.727103\pi$
$619$		−	23288.7i		−	1.51220i	0.654457	−	0.756099i	$-0.272897\pi$
$620$	−23158.8			−1.50013
$621$	1112.97			0.0719197
$622$			626.810i			0.0404064i
$623$	−7927.06			−0.509777
$624$	1562.48	+	14.1952i	0.100239	+	0.000910674i
$625$	−16775.6			−1.07364
$626$		−	1567.63i		−	0.100088i
$627$	433.772			0.0276287
$628$	7044.13			0.447598
$629$			631.967i			0.0400607i
$630$		−	2297.69i		−	0.145305i
$631$		−	25716.8i		−	1.62246i	−0.584728	−	0.811229i	$-0.698799\pi$
$631$		−	25716.8i		−	1.62246i	0.584728	−	0.811229i	$-0.301201\pi$
$632$			2882.07i			0.181396i
$633$	−1214.11			−0.0762344
$634$	−321.330			−0.0201288
$635$			3348.30i			0.209249i
$636$	−1661.97			−0.103618
$637$	2653.26	+	24.1050i	0.165033	+	0.00149933i
$638$	461.629			0.0286458
$639$			14802.3i			0.916382i
$640$	8442.50			0.521436
$641$	−10221.0			−0.629806			−0.314903	−	0.949124i	$-0.601972\pi$
$641$	−10221.0			−0.629806			−0.314903	+	0.949124i	$0.601972\pi$
$642$		−	203.792i		−	0.0125281i
$643$			9836.84i			0.603308i	0.953417	+	0.301654i	$0.0975387\pi$
$643$			9836.84i			0.603308i	−0.953417	+	0.301654i	$0.902461\pi$
$644$			5934.13i			0.363102i
$645$		−	1900.02i		−	0.115989i
$646$	−167.625			−0.0102091
$647$	−27544.5			−1.67370			−0.836851	−	0.547431i	$-0.815606\pi$
$647$	−27544.5			−1.67370			−0.836851	+	0.547431i	$0.815606\pi$
$648$		−	4141.69i		−	0.251082i
$649$	4581.76			0.277118
$650$	1.57857	−	173.755i	9.52563e−5	−	0.0104850i
$651$	2781.90			0.167483
$652$		−	6616.11i		−	0.397403i
$653$	−27098.7			−1.62397			−0.811986	−	0.583677i	$-0.801614\pi$
$653$	−27098.7			−1.62397			−0.811986	+	0.583677i	$0.801614\pi$
$654$	−266.617			−0.0159412
$655$		−	9035.98i		−	0.539031i
$656$			1527.69i			0.0909240i
$657$		−	10740.8i		−	0.637808i
$658$		−	3034.98i		−	0.179811i
$659$	24699.6			1.46003			0.730014	−	0.683432i	$-0.239513\pi$
$659$	24699.6			1.46003			0.730014	+	0.683432i	$0.239513\pi$
$660$	551.691			0.0325372
$661$			5548.01i			0.326464i	0.986588	+	0.163232i	$0.0521919\pi$
$661$			5548.01i			0.326464i	−0.986588	+	0.163232i	$0.947808\pi$
$662$	−1349.63			−0.0792372
$663$	−162.057	−	1.47230i	−0.00949288	−	8.62432e-5i
$664$	−1728.48			−0.101021
$665$		−	16684.2i		−	0.972912i
$666$	992.605			0.0577518
$667$	4276.20			0.248238
$668$		−	33465.4i		−	1.93835i
$669$			1501.02i			0.0867457i
$670$			1040.70i			0.0600087i
$671$		−	5061.24i		−	0.291188i
$672$	−762.912			−0.0437946
$673$	−26941.8			−1.54314			−0.771569	−	0.636146i	$-0.780528\pi$
$673$	−26941.8			−1.54314			−0.771569	+	0.636146i	$0.780528\pi$
$674$		−	3107.94i		−	0.177617i
$675$	−294.951			−0.0168187
$676$	17271.5	+	313.851i	0.982677	+	0.0178568i
$677$	2357.13			0.133814			0.0669069	−	0.997759i	$-0.478687\pi$
$677$	2357.13			0.133814			0.0669069	+	0.997759i	$0.478687\pi$
$678$			215.513i			0.0122075i
$679$	17038.3			0.962991
$680$	−430.108			−0.0242557
$681$			1516.59i			0.0853391i
$682$			1033.17i			0.0580088i
$683$		−	7349.73i		−	0.411756i	−0.978578	−	0.205878i	$-0.933995\pi$
$683$		−	7349.73i		−	0.411756i	0.978578	−	0.205878i	$-0.0660051\pi$
$684$		−	15079.1i		−	0.842928i
$685$	−17305.3			−0.965258
$686$	2121.22			0.118059
$687$		−	3459.67i		−	0.192132i
$688$	18087.9			1.00232
$689$	−18046.4	−	163.952i	−0.997843	−	0.00906544i
$690$	−89.2291			−0.00492304
$691$		−	7901.25i		−	0.434990i	−0.976061	−	0.217495i	$-0.930211\pi$
$691$		−	7901.25i		−	0.434990i	0.976061	−	0.217495i	$-0.0697885\pi$
$692$	−20981.0			−1.15257
$693$	5870.82			0.321810
$694$			2925.54i			0.160017i
$695$			23897.4i			1.30429i
$696$			365.454i			0.0199030i
$697$		−	158.449i		−	0.00861073i
$698$	−1402.74			−0.0760665
$699$	278.250			0.0150563
$700$		−	1572.61i		−	0.0849129i
$701$	22650.1			1.22037			0.610187	−	0.792258i	$-0.291094\pi$
$701$	22650.1			1.22037			0.610187	+	0.792258i	$0.291094\pi$
$702$	−4.65105	+	511.947i	−0.000250061	+	0.0275245i
$703$	7207.62			0.386686
$704$			5060.38i			0.270909i
$705$	−2613.73			−0.139629
$706$	4353.91			0.232098
$707$		−	8279.22i		−	0.440413i
$708$			1797.91i			0.0954372i
$709$			1520.18i			0.0805243i	0.999189	+	0.0402621i	$0.0128193\pi$
$709$			1520.18i			0.0805243i	−0.999189	+	0.0402621i	$0.987181\pi$
$710$		−	2386.84i		−	0.126164i
$711$	13092.0			0.690562
$712$	2330.67			0.122677
$713$			9570.52i			0.502691i
$714$	25.6093			0.00134230
$715$	5990.53	+	54.4242i	0.313333	+	0.00284664i
$716$	34754.5			1.81402
$717$			313.184i			0.0163125i
$718$	−4653.44			−0.241873
$719$	7000.07			0.363085			0.181543	−	0.983383i	$-0.441891\pi$
$719$	7000.07			0.363085			0.181543	+	0.983383i	$0.441891\pi$
$720$		−	18837.6i		−	0.975049i
$721$			21872.5i			1.12978i
$722$		−	629.612i		−	0.0324539i
$723$		−	2829.68i		−	0.145556i
$724$	−2789.14			−0.143174
$725$	−1133.24			−0.0580517
$726$		−	24.6122i		−	0.00125819i
$727$	31551.4			1.60960			0.804798	−	0.593549i	$-0.202274\pi$
$727$	31551.4			1.60960			0.804798	+	0.593549i	$0.202274\pi$
$728$	−5506.82	−	50.0297i	−0.280352	−	0.00254701i
$729$	−18377.0			−0.933649
$730$			1731.94i			0.0878111i
$731$	−1876.04			−0.0949219
$732$	1986.06			0.100283
$733$			16460.8i			0.829458i	0.909945	+	0.414729i	$0.136124\pi$
$733$			16460.8i			0.829458i	−0.909945	+	0.414729i	$0.863876\pi$
$734$			868.357i			0.0436671i
$735$			361.089i			0.0181210i
$736$		−	2624.63i		−	0.131447i
$737$	−2659.10			−0.132903
$738$	−248.869			−0.0124133
$739$			9719.80i			0.483828i	0.970298	+	0.241914i	$0.0777751\pi$
$739$			9719.80i			0.483828i	−0.970298	+	0.241914i	$0.922225\pi$
$740$	9166.99			0.455386
$741$	−16.7916	+	1848.27i	−0.000832464	+	0.0916301i
$742$	2851.81			0.141096
$743$		−	16063.9i		−	0.793174i	−0.917997	−	0.396587i	$-0.870195\pi$
$743$		−	16063.9i		−	0.793174i	0.917997	−	0.396587i	$-0.129805\pi$
$744$	−817.920			−0.0403043
$745$	9286.03			0.456663
$746$		−	2493.77i		−	0.122391i
$747$			7851.74i			0.384578i
$748$		−	544.730i		−	0.0266274i
$749$		−	20028.2i		−	0.977053i
$750$	−271.780			−0.0132320
$751$	−26001.5			−1.26339			−0.631695	−	0.775217i	$-0.717641\pi$
$751$	−26001.5			−1.26339			−0.631695	+	0.775217i	$0.717641\pi$
$752$		−	24882.3i		−	1.20660i
$753$	−3743.64			−0.181176
$754$	−17.8700	+	1966.97i	−0.000863112	+	0.0950036i
$755$	−29765.5			−1.43480
$756$			4633.49i			0.222908i
$757$	9051.63			0.434593			0.217297	−	0.976106i	$-0.430276\pi$
$757$	9051.63			0.434593			0.217297	+	0.976106i	$0.430276\pi$
$758$	−4178.83			−0.200240
$759$		−	227.990i		−	0.0109032i
$760$			4905.41i			0.234129i
$761$		−	9914.92i		−	0.472294i	−0.971717	−	0.236147i	$-0.924115\pi$
$761$		−	9914.92i		−	0.472294i	0.971717	−	0.236147i	$-0.0758847\pi$
$762$			58.6156i			0.00278664i
$763$	−26202.4			−1.24324
$764$	6278.52			0.297315
$765$			1953.80i			0.0923396i
$766$	−1998.82			−0.0942825
$767$	−177.363	+	19522.5i	−0.00834969	+	0.919059i
$768$	−1872.60			−0.0879838
$769$		−	33616.0i		−	1.57636i	−0.615443	−	0.788181i	$-0.711023\pi$
$769$		−	33616.0i		−	1.57636i	0.615443	−	0.788181i	$-0.288977\pi$
$770$	−946.661			−0.0443056
$771$	−3078.21			−0.143786
$772$		−	18829.4i		−	0.877828i
$773$			5047.85i			0.234875i	0.993080	+	0.117438i	$0.0374680\pi$
$773$			5047.85i			0.234875i	−0.993080	+	0.117438i	$0.962532\pi$
$774$			2946.62i			0.136840i
$775$		−	2536.29i		−	0.117557i
$776$	−5009.52			−0.231741
$777$	−1101.16			−0.0508417
$778$		−	3301.29i		−	0.152130i
$779$	−1807.12			−0.0831152
$780$	−21.3564	+	2350.72i	−0.000980360	+	0.107909i
$781$	6098.62			0.279419
$782$			88.1032i			0.00402885i
$783$	3338.95			0.152394
$784$	−3437.51			−0.156592
$785$			10409.5i			0.473288i
$786$		−	158.185i		−	0.00717845i
$787$		−	14751.4i		−	0.668144i	−0.942548	−	0.334072i	$-0.891577\pi$
$787$		−	14751.4i		−	0.668144i	0.942548	−	0.334072i	$-0.108423\pi$
$788$		−	34058.8i		−	1.53971i
$789$	2075.84			0.0936654
$790$	−2111.07			−0.0950740
$791$			21180.0i			0.952053i
$792$	−1726.11			−0.0774427
$793$	21565.6	+	195.924i	0.965721	+	0.00877362i
$794$	−2783.83			−0.124426
$795$		−	2455.98i		−	0.109566i
$796$	−38140.1			−1.69829
$797$	13011.7			0.578293			0.289146	−	0.957285i	$-0.406629\pi$
$797$	13011.7			0.578293			0.289146	+	0.957285i	$0.406629\pi$
$798$		−	292.075i		−	0.0129566i
$799$			2580.74i			0.114268i
$800$			695.556i			0.0307395i
$801$		−	10587.3i		−	0.467019i
$802$	1491.53			0.0656707
$803$	−4425.29			−0.194477
$804$		−	1043.45i		−	0.0457705i
$805$	−8769.19			−0.383942
$806$	−4402.25	−	39.9946i	−0.192386	−	0.00174783i
$807$	2650.46			0.115614
$808$			2434.21i			0.105984i
$809$	−29356.1			−1.27578			−0.637891	−	0.770127i	$-0.720193\pi$
$809$	−29356.1			−1.27578			−0.637891	+	0.770127i	$0.720193\pi$
$810$	3033.72			0.131598
$811$			26529.9i			1.14869i	0.818612	+	0.574347i	$0.194744\pi$
$811$			26529.9i			1.14869i	−0.818612	+	0.574347i	$0.805256\pi$
$812$			17802.5i			0.769391i
$813$		−	3219.22i		−	0.138872i
$814$		−	408.960i		−	0.0176094i
$815$	9776.99			0.420212
$816$	209.958			0.00900734
$817$			21396.4i			0.916235i
$818$	−5078.94			−0.217092
$819$	−227.264	+	25015.2i	−0.00969626	+	1.06728i
$820$	−2298.38			−0.0978815
$821$			36143.0i			1.53642i	0.640198	+	0.768210i	$0.278852\pi$
$821$			36143.0i			1.53642i	−0.640198	+	0.768210i	$0.721148\pi$
$822$	−302.948			−0.0128547
$823$	17671.9			0.748484			0.374242	−	0.927331i	$-0.377903\pi$
$823$	17671.9			0.748484			0.374242	+	0.927331i	$0.377903\pi$
$824$		−	6430.83i		−	0.271879i
$825$			60.4197i			0.00254975i
$826$		−	3085.08i		−	0.129956i
$827$		−	3830.34i		−	0.161057i	−0.996752	−	0.0805284i	$-0.974339\pi$
$827$		−	3830.34i		−	0.161057i	0.996752	−	0.0805284i	$-0.0256608\pi$
$828$	−7925.53			−0.332646
$829$	27299.5			1.14373			0.571863	−	0.820349i	$-0.306221\pi$
$829$	27299.5			1.14373			0.571863	+	0.820349i	$0.306221\pi$
$830$		−	1266.08i		−	0.0529473i
$831$	2952.79			0.123263
$832$	−21561.9	−	195.891i	−0.898468	−	0.00816262i
$833$	356.532			0.0148297
$834$			418.350i			0.0173697i
$835$	49453.7			2.04960
$836$	−6212.67			−0.257021
$837$			7472.87i			0.308602i
$838$			2530.83i			0.104327i
$839$			10105.9i			0.415845i	0.978145	+	0.207922i	$0.0666701\pi$
$839$			10105.9i			0.415845i	−0.978145	+	0.207922i	$0.933330\pi$
$840$		−	749.436i		−	0.0307833i
$841$	−11560.3			−0.473997
$842$	5172.01			0.211686
$843$		−	4273.84i		−	0.174613i
$844$	17389.0			0.709186
$845$	−463.795	+	25523.1i	−0.0188817	+	1.03908i
$846$	4053.47			0.164730
$847$		−	2418.82i		−	0.0981246i
$848$	23380.5			0.946806
$849$	3009.29			0.121647
$850$		−	23.3483i		−	0.000942165i
$851$		−	3788.31i		−	0.152599i
$852$			2393.13i			0.0962294i
$853$		−	1436.66i		−	0.0576672i	−0.999584	−	0.0288336i	$-0.990821\pi$
$853$		−	1436.66i		−	0.0576672i	0.999584	−	0.0288336i	$-0.00917929\pi$
$854$	−3407.93			−0.136554
$855$	22283.2			0.891309
$856$			5888.57i			0.235125i
$857$	17076.2			0.680645			0.340323	−	0.940309i	$-0.389464\pi$
$857$	17076.2			0.680645			0.340323	+	0.940309i	$0.389464\pi$
$858$	104.871	+	0.952754i	0.00417276	+	3.79097e-5i
$859$	−1750.31			−0.0695226			−0.0347613	−	0.999396i	$-0.511067\pi$
$859$	−1750.31			−0.0695226			−0.0347613	+	0.999396i	$0.511067\pi$
$860$			27212.9i			1.07901i
$861$	276.087			0.0109280
$862$	−817.571			−0.0323046
$863$			43005.0i			1.69630i	0.529755	+	0.848151i	$0.322284\pi$
$863$			43005.0i			1.69630i	−0.529755	+	0.848151i	$0.677716\pi$
$864$		−	2049.37i		−	0.0806955i
$865$		−	31004.8i		−	1.21872i
$866$			2926.24i			0.114824i
$867$	2675.36			0.104798
$868$	−39843.6			−1.55804
$869$		−	5394.00i		−	0.210562i
$870$	−267.689			−0.0104316
$871$	102.936	−	11330.2i	0.00400441	−	0.440770i
$872$	7703.89			0.299182
$873$			22756.1i			0.882220i
$874$	1004.82			0.0388886
$875$	−26709.8			−1.03195
$876$		−	1736.51i		−	0.0669763i
$877$			14133.5i			0.544191i	0.962270	+	0.272095i	$0.0877166\pi$
$877$			14133.5i			0.544191i	−0.962270	+	0.272095i	$0.912283\pi$
$878$		−	782.226i		−	0.0300670i
$879$		−	3654.05i		−	0.140214i
$880$	−7761.20			−0.297307
$881$	22316.1			0.853405			0.426703	−	0.904392i	$-0.359675\pi$
$881$	22316.1			0.853405			0.426703	+	0.904392i	$0.359675\pi$
$882$		−	559.991i		−	0.0213785i
$883$	−14579.8			−0.555660			−0.277830	−	0.960630i	$-0.589615\pi$
$883$	−14579.8			−0.555660			−0.277830	+	0.960630i	$0.589615\pi$
$884$	2321.06	+	21.0869i	0.0883095	+	0.000802295i
$885$	−2656.87			−0.100915
$886$			1846.66i			0.0700222i
$887$	−18320.9			−0.693524			−0.346762	−	0.937953i	$-0.612719\pi$
$887$	−18320.9			−0.693524			−0.346762	+	0.937953i	$0.612719\pi$
$888$	323.758			0.0122349
$889$			5760.58i			0.217327i
$890$			1707.18i			0.0642975i
$891$			7751.47i			0.291452i
$892$		−	21498.3i		−	0.806969i
$893$	29433.5			1.10297
$894$	162.562			0.00608153
$895$			51358.6i			1.91813i
$896$	14524.9			0.541566
$897$	971.447	+	8.82564i	0.0361602	+	0.000328517i
$898$	−4305.98			−0.160014
$899$			28711.8i			1.06517i
$900$	2100.35			0.0777908
$901$	−2424.99			−0.0896649
$902$			102.536i			0.00378499i
$903$		−	3268.88i		−	0.120467i
$904$		−	6227.23i		−	0.229109i
$905$		−	4121.68i		−	0.151391i
$906$	−521.077			−0.0191077
$907$	−34884.3			−1.27708			−0.638541	−	0.769588i	$-0.720462\pi$
$907$	−34884.3			−1.27708			−0.638541	+	0.769588i	$0.720462\pi$
$908$		−	21721.3i		−	0.793884i
$909$	11057.6			0.403473
$910$	36.6459	−	4033.66i	0.00133495	−	0.146939i
$911$	−2978.83			−0.108335			−0.0541674	−	0.998532i	$-0.517250\pi$
$911$	−2978.83			−0.108335			−0.0541674	+	0.998532i	$0.517250\pi$
$912$		−	2394.58i		−	0.0869435i
$913$	3234.96			0.117264
$914$	−6373.21			−0.230642
$915$			2934.91i			0.106039i
$916$			49551.0i			1.78735i
$917$		−	15546.0i		−	0.559839i
$918$			68.7929i			0.00247331i
$919$	−37880.6			−1.35970			−0.679850	−	0.733351i	$-0.737955\pi$
$919$	−37880.6			−1.35970			−0.679850	+	0.733351i	$0.737955\pi$
$920$	2578.27			0.0923947
$921$		−	3721.34i		−	0.133141i
$922$	−937.892			−0.0335009
$923$	−236.082	+	25985.8i	−0.00841900	+	0.926688i
$924$	949.157			0.0337933
$925$			1003.94i			0.0356859i
$926$	−6114.31			−0.216986
$927$	−29212.6			−1.03502
$928$		−	7873.95i		−	0.278529i
$929$		−	9454.47i		−	0.333898i	−0.985966	−	0.166949i	$-0.946609\pi$
$929$		−	9454.47i		−	0.333898i	0.985966	−	0.166949i	$-0.0533915\pi$
$930$		−	599.113i		−	0.0211244i
$931$		−	4066.27i		−	0.143144i
$932$	−3985.22			−0.140065
$933$	928.715			0.0325882
$934$			4701.63i			0.164713i
$935$	804.978			0.0281557
$936$	66.8189	−	7354.83i	0.00233338	−	0.256838i
$937$	−5608.48			−0.195540			−0.0977701	−	0.995209i	$-0.531171\pi$
$937$	−5608.48			−0.195540			−0.0977701	+	0.995209i	$0.531171\pi$
$938$			1790.48i			0.0623253i
$939$	−2322.68			−0.0807219
$940$	37434.9			1.29893
$941$		−	44502.3i		−	1.54169i	−0.637020	−	0.770847i	$-0.719833\pi$
$941$		−	44502.3i		−	1.54169i	0.637020	−	0.770847i	$-0.280167\pi$
$942$			182.230i			0.00630293i
$943$			949.818i			0.0327999i
$944$		−	25293.0i		−	0.872051i
$945$	−6847.17			−0.235702
$946$	1214.03			0.0417246
$947$			44740.3i			1.53523i	0.640911	+	0.767615i	$0.278557\pi$
$947$			44740.3i			1.53523i	−0.640911	+	0.767615i	$0.721443\pi$
$948$	2116.64			0.0725159
$949$	171.306	−	18855.9i	0.00585968	−	0.644981i
$950$	−266.289			−0.00909426
$951$			476.099i			0.0162340i
$952$	−739.980			−0.0251921
$953$	10505.5			0.357090			0.178545	−	0.983932i	$-0.442861\pi$
$953$	10505.5			0.357090			0.178545	+	0.983932i	$0.442861\pi$
$954$			3808.83i			0.129262i
$955$			9278.13i			0.314380i
$956$		−	4485.57i		−	0.151751i
$957$		−	683.973i		−	0.0231032i
$958$	−319.147			−0.0107632
$959$	−29772.9			−1.00252
$960$		−	2934.41i		−	0.0986539i
$961$	−34468.5			−1.15701
$962$	1742.55	+	15.8311i	0.0584013	+	0.000530578i
$963$	26749.3			0.895103
$964$			40527.9i			1.35406i
$965$	27825.2			0.928212
$966$	−153.514			−0.00511308
$967$		−	41413.0i		−	1.37720i	−0.725141	−	0.688600i	$-0.758225\pi$
$967$		−	41413.0i		−	1.37720i	0.725141	−	0.688600i	$-0.241775\pi$
$968$			711.167i			0.0236134i
$969$			248.362i			0.00823377i
$970$		−	3669.39i		−	0.121461i
$971$	11424.5			0.377579			0.188789	−	0.982018i	$-0.439544\pi$
$971$	11424.5			0.377579			0.188789	+	0.982018i	$0.439544\pi$
$972$	−9300.00			−0.306891
$973$			41114.3i			1.35464i
$974$	−3986.47			−0.131145
$975$	−257.444	−	2.33889i	−0.00845622	−	7.68251e-5i
$976$	−27939.9			−0.916327
$977$		−	56529.6i		−	1.85112i	−0.378603	−	0.925559i	$-0.623595\pi$
$977$		−	56529.6i		−	1.85112i	0.378603	−	0.925559i	$-0.376405\pi$
$978$	171.157			0.00559611
$979$	−4362.02			−0.142401
$980$		−	5171.67i		−	0.168575i
$981$		−	34995.5i		−	1.13896i
$982$			6403.47i			0.208089i
$983$		−	31465.5i		−	1.02095i	−0.859893	−	0.510474i	$-0.829470\pi$
$983$		−	31465.5i		−	1.02095i	0.859893	−	0.510474i	$-0.170530\pi$
$984$	−81.1737			−0.00262980
$985$	50330.6			1.62809
$986$			264.311i			0.00853691i
$987$	−4496.78			−0.145019
$988$	240.497	−	26471.8i	0.00774416	−	0.852408i
$989$	11245.9			0.361576
$990$		−	1264.35i		−	0.0405894i
$991$	−18338.5			−0.587832			−0.293916	−	0.955831i	$-0.594959\pi$
$991$	−18338.5			−0.587832			−0.293916	+	0.955831i	$0.594959\pi$
$992$	17622.6			0.564031
$993$			1999.69i			0.0639055i
$994$		−	4106.44i		−	0.131035i
$995$		−	56361.7i		−	1.79577i
$996$			1269.42i			0.0403846i
$997$	28193.3			0.895577			0.447789	−	0.894140i	$-0.352212\pi$
$997$	28193.3			0.895577			0.447789	+	0.894140i	$0.352212\pi$
$998$	98.4975			0.00312413
$999$		−	2957.99i		−	0.0936805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.b.a.12.18	✓	36
13.5	odd	4		1859.4.a.j.1.10		18
13.8	odd	4		1859.4.a.k.1.9		18
13.12	even	2	inner	143.4.b.a.12.19	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.b.a.12.18	✓	36	1.1	even	1	trivial
143.4.b.a.12.19	yes	36	13.12	even	2	inner
1859.4.a.j.1.10		18	13.5	odd	4
1859.4.a.k.1.9		18	13.8	odd	4

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.370518i q^{2} -0.548979 q^{3} +7.86272 q^{4} +11.6192i q^{5} +0.203406i q^{6} +19.9902i q^{7} -5.87742i q^{8} -26.6986 q^{9} +O(q^{10})\)	\(q-0.370518i q^{2} -0.548979 q^{3} +7.86272 q^{4} +11.6192i q^{5} +0.203406i q^{6} +19.9902i q^{7} -5.87742i q^{8} -26.6986 q^{9} +4.30511 q^{10} +11.0000i q^{11} -4.31646 q^{12} +(-46.8702 - 0.425818i) q^{13} +7.40673 q^{14} -6.37868i q^{15} +60.7240 q^{16} -6.29819 q^{17} +9.89231i q^{18} +71.8312i q^{19} +91.3583i q^{20} -10.9742i q^{21} +4.07569 q^{22} +37.7543 q^{23} +3.22658i q^{24} -10.0053 q^{25} +(-0.157773 + 17.3663i) q^{26} +29.4794 q^{27} +157.177i q^{28} +113.264 q^{29} -2.36341 q^{30} +253.495i q^{31} -69.5187i q^{32} -6.03876i q^{33} +2.33359i q^{34} -232.270 q^{35} -209.924 q^{36} -100.341i q^{37} +26.6147 q^{38} +(25.7308 + 0.233765i) q^{39} +68.2908 q^{40} +25.1578i q^{41} -4.06613 q^{42} +297.870 q^{43} +86.4899i q^{44} -310.216i q^{45} -13.9886i q^{46} -409.760i q^{47} -33.3362 q^{48} -56.6087 q^{49} +3.70715i q^{50} +3.45757 q^{51} +(-368.527 - 3.34809i) q^{52} +385.030 q^{53} -10.9226i q^{54} -127.811 q^{55} +117.491 q^{56} -39.4338i q^{57} -41.9662i q^{58} -416.523i q^{59} -50.1538i q^{60} -460.113 q^{61} +93.9243 q^{62} -533.711i q^{63} +460.034 q^{64} +(4.94765 - 544.594i) q^{65} -2.23747 q^{66} +241.736i q^{67} -49.5209 q^{68} -20.7263 q^{69} +86.0601i q^{70} -554.420i q^{71} +156.919i q^{72} +402.299i q^{73} -37.1781 q^{74} +5.49270 q^{75} +564.788i q^{76} -219.892 q^{77} +(0.0866140 - 9.53370i) q^{78} -490.363 q^{79} +705.564i q^{80} +704.679 q^{81} +9.32143 q^{82} -294.088i q^{83} -86.2870i q^{84} -73.1798i q^{85} -110.366i q^{86} -62.1794 q^{87} +64.6516 q^{88} +396.547i q^{89} -114.941 q^{90} +(8.51219 - 936.946i) q^{91} +296.852 q^{92} -139.163i q^{93} -151.823 q^{94} -834.620 q^{95} +38.1643i q^{96} -852.333i q^{97} +20.9745i q^{98} -293.685i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 152 q^{4} + 360 q^{9}+O(q^{10}) \) 36 * q - 152 * q^4 + 360 * q^9	\( 36 q - 152 q^{4} + 360 q^{9} - 112 q^{10} - 108 q^{12} - 50 q^{13} + 8 q^{14} + 728 q^{16} + 276 q^{17} + 44 q^{22} - 472 q^{23} - 1172 q^{25} + 152 q^{26} - 12 q^{27} - 572 q^{29} + 712 q^{30} + 68 q^{35} - 430 q^{36} - 50 q^{38} + 640 q^{39} - 216 q^{40} + 1126 q^{42} + 920 q^{43} + 1674 q^{48} - 2164 q^{49} - 340 q^{51} - 800 q^{52} + 2432 q^{53} + 440 q^{55} - 2274 q^{56} - 1844 q^{61} + 2796 q^{62} - 2592 q^{64} + 2264 q^{65} + 1078 q^{66} - 4548 q^{68} - 3288 q^{69} - 4036 q^{74} + 820 q^{75} - 616 q^{77} + 2222 q^{78} + 360 q^{79} + 852 q^{81} + 1948 q^{82} - 2480 q^{87} + 264 q^{88} - 496 q^{90} + 4600 q^{91} + 454 q^{92} - 488 q^{94} + 952 q^{95}+O(q^{100}) \) 36 * q - 152 * q^4 + 360 * q^9 - 112 * q^10 - 108 * q^12 - 50 * q^13 + 8 * q^14 + 728 * q^16 + 276 * q^17 + 44 * q^22 - 472 * q^23 - 1172 * q^25 + 152 * q^26 - 12 * q^27 - 572 * q^29 + 712 * q^30 + 68 * q^35 - 430 * q^36 - 50 * q^38 + 640 * q^39 - 216 * q^40 + 1126 * q^42 + 920 * q^43 + 1674 * q^48 - 2164 * q^49 - 340 * q^51 - 800 * q^52 + 2432 * q^53 + 440 * q^55 - 2274 * q^56 - 1844 * q^61 + 2796 * q^62 - 2592 * q^64 + 2264 * q^65 + 1078 * q^66 - 4548 * q^68 - 3288 * q^69 - 4036 * q^74 + 820 * q^75 - 616 * q^77 + 2222 * q^78 + 360 * q^79 + 852 * q^81 + 1948 * q^82 - 2480 * q^87 + 264 * q^88 - 496 * q^90 + 4600 * q^91 + 454 * q^92 - 488 * q^94 + 952 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more