LMFDB - Embedded newform 43.11.b.b.42.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,11,Mod(42,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	43.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:	$27.3203618650$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.6
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-44.1717i q^{2} -389.187i q^{3} -927.142 q^{4} +5234.98i q^{5} -17191.1 q^{6} +21894.1i q^{7} -4278.39i q^{8} -92417.4 q^{9} +O(q^{10})$	\(q-44.1717i q^{2} -389.187i q^{3} -927.142 q^{4} +5234.98i q^{5} -17191.1 q^{6} +21894.1i q^{7} -4278.39i q^{8} -92417.4 q^{9} +231238. q^{10} +16244.7 q^{11} +360831. i q^{12} +326289. q^{13} +967102. q^{14} +2.03738e6 q^{15} -1.13838e6 q^{16} +287393. q^{17} +4.08224e6i q^{18} +139732. i q^{19} -4.85357e6i q^{20} +8.52091e6 q^{21} -717555. i q^{22} +1.90806e6 q^{23} -1.66509e6 q^{24} -1.76393e7 q^{25} -1.44127e7i q^{26} +1.29865e7i q^{27} -2.02990e7i q^{28} +3.83545e7i q^{29} -8.99948e7i q^{30} +5.40348e7 q^{31} +4.59030e7i q^{32} -6.32221e6i q^{33} -1.26946e7i q^{34} -1.14615e8 q^{35} +8.56840e7 q^{36} +8.73532e7i q^{37} +6.17221e6 q^{38} -1.26987e8i q^{39} +2.23973e7 q^{40} +8.87662e7 q^{41} -3.76384e8i q^{42} +(-6.67162e7 - 1.30998e8i) q^{43} -1.50611e7 q^{44} -4.83803e8i q^{45} -8.42821e7i q^{46} +1.99511e8 q^{47} +4.43041e8i q^{48} -1.96878e8 q^{49} +7.79160e8i q^{50} -1.11849e8i q^{51} -3.02516e8 q^{52} -3.58718e8 q^{53} +5.73638e8 q^{54} +8.50405e7i q^{55} +9.36717e7 q^{56} +5.43819e7 q^{57} +1.69419e9 q^{58} +9.43790e8 q^{59} -1.88894e9 q^{60} +1.50091e9i q^{61} -2.38681e9i q^{62} -2.02340e9i q^{63} +8.61918e8 q^{64} +1.70811e9i q^{65} -2.79263e8 q^{66} -1.23620e9 q^{67} -2.66454e8 q^{68} -7.42590e8i q^{69} +5.06276e9i q^{70} -1.85479e9i q^{71} +3.95398e8i q^{72} +1.84969e9i q^{73} +3.85854e9 q^{74} +6.86500e9i q^{75} -1.29552e8i q^{76} +3.55663e8i q^{77} -5.60925e9 q^{78} -8.05333e8 q^{79} -5.95938e9i q^{80} -4.02965e8 q^{81} -3.92096e9i q^{82} -6.35127e9 q^{83} -7.90010e9 q^{84} +1.50449e9i q^{85} +(-5.78640e9 + 2.94697e9i) q^{86} +1.49271e10 q^{87} -6.95010e7i q^{88} +3.36937e9i q^{89} -2.13704e10 q^{90} +7.14381e9i q^{91} -1.76904e9 q^{92} -2.10296e10i q^{93} -8.81277e9i q^{94} -7.31495e8 q^{95} +1.78649e10 q^{96} +1.34193e10 q^{97} +8.69646e9i q^{98} -1.50129e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	$ 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) $ 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$		−	44.1717i		−	1.38037i	−0.723635	−	0.690183i	$-0.757530\pi$
$2$		−	44.1717i		−	1.38037i	0.723635	−	0.690183i	$-0.242470\pi$
$3$		−	389.187i		−	1.60159i	−0.598937	−	0.800796i	$-0.704410\pi$
$3$		−	389.187i		−	1.60159i	0.598937	−	0.800796i	$-0.295590\pi$
$4$	−927.142			−0.905412
$5$			5234.98i			1.67519i	0.546290	+	0.837596i	$0.316040\pi$
$5$			5234.98i			1.67519i	−0.546290	+	0.837596i	$0.683960\pi$
$6$	−17191.1			−2.21078
$7$			21894.1i			1.30268i	0.758786	+	0.651340i	$0.225793\pi$
$7$			21894.1i			1.30268i	−0.758786	+	0.651340i	$0.774207\pi$
$8$		−	4278.39i		−	0.130566i
$9$	−92417.4			−1.56510
$10$	231238.			2.31238
$11$	16244.7			0.100867			0.0504333	−	0.998727i	$-0.483940\pi$
$11$	16244.7			0.100867			0.0504333	+	0.998727i	$0.483940\pi$
$12$			360831.i			1.45010i
$13$	326289.			0.878790			0.439395	−	0.898294i	$-0.355193\pi$
$13$	326289.			0.878790			0.439395	+	0.898294i	$0.355193\pi$
$14$	967102.			1.79818
$15$	2.03738e6			2.68297
$16$	−1.13838e6			−1.08564
$17$	287393.			0.202410			0.101205	−	0.994866i	$-0.467730\pi$
$17$	287393.			0.202410			0.101205	+	0.994866i	$0.467730\pi$
$18$			4.08224e6i			2.16041i
$19$			139732.i			0.0564324i	0.999602	+	0.0282162i	$0.00898269\pi$
$19$			139732.i			0.0564324i	−0.999602	+	0.0282162i	$0.991017\pi$
$20$		−	4.85357e6i		−	1.51674i
$21$	8.52091e6			2.08636
$22$		−	717555.i		−	0.139233i
$23$	1.90806e6			0.296450			0.148225	−	0.988954i	$-0.452644\pi$
$23$	1.90806e6			0.296450			0.148225	+	0.988954i	$0.452644\pi$
$24$	−1.66509e6			−0.209114
$25$	−1.76393e7			−1.80627
$26$		−	1.44127e7i		−	1.21305i
$27$			1.29865e7i			0.905054i
$28$		−	2.02990e7i		−	1.17946i
$29$			3.83545e7i			1.86994i	0.354733	+	0.934968i	$0.384572\pi$
$29$			3.83545e7i			1.86994i	−0.354733	+	0.934968i	$0.615428\pi$
$30$		−	8.99948e7i		−	3.70349i
$31$	5.40348e7			1.88741			0.943703	−	0.330794i	$-0.107317\pi$
$31$	5.40348e7			1.88741			0.943703	+	0.330794i	$0.107317\pi$
$32$			4.59030e7i			1.36802i
$33$		−	6.32221e6i		−	0.161547i
$34$		−	1.26946e7i		−	0.279399i
$35$	−1.14615e8			−2.18224
$36$	8.56840e7			1.41706
$37$			8.73532e7i			1.25971i	0.776713	+	0.629855i	$0.216886\pi$
$37$			8.73532e7i			1.25971i	−0.776713	+	0.629855i	$0.783114\pi$
$38$	6.17221e6			0.0778974
$39$		−	1.26987e8i		−	1.40746i
$40$	2.23973e7			0.218723
$41$	8.87662e7			0.766176			0.383088	−	0.923712i	$-0.374861\pi$
$41$	8.87662e7			0.766176			0.383088	+	0.923712i	$0.374861\pi$
$42$		−	3.76384e8i		−	2.87994i
$43$	−6.67162e7	−	1.30998e8i	−0.453826	−	0.891091i
$43$	−6.67162e7	−	1.30998e8i	−0.453826	−	0.891091i
$44$	−1.50611e7			−0.0913259
$45$		−	4.83803e8i		−	2.62184i
$46$		−	8.42821e7i		−	0.409210i
$47$	1.99511e8			0.869918			0.434959	−	0.900450i	$-0.356763\pi$
$47$	1.99511e8			0.869918			0.434959	+	0.900450i	$0.356763\pi$
$48$			4.43041e8i			1.73875i
$49$	−1.96878e8			−0.696976
$50$			7.79160e8i			2.49331i
$51$		−	1.11849e8i		−	0.324177i
$52$	−3.02516e8			−0.795667
$53$	−3.58718e8			−0.857776			−0.428888	−	0.903358i	$-0.641094\pi$
$53$	−3.58718e8			−0.857776			−0.428888	+	0.903358i	$0.641094\pi$
$54$	5.73638e8			1.24931
$55$			8.50405e7i			0.168971i
$56$	9.36717e7			0.170086
$57$	5.43819e7			0.0903817
$58$	1.69419e9			2.58120
$59$	9.43790e8			1.32013			0.660063	−	0.751211i	$-0.270530\pi$
$59$	9.43790e8			1.32013			0.660063	+	0.751211i	$0.270530\pi$
$60$	−1.88894e9			−2.42920
$61$			1.50091e9i			1.77708i	0.458803	+	0.888538i	$0.348278\pi$
$61$			1.50091e9i			1.77708i	−0.458803	+	0.888538i	$0.651722\pi$
$62$		−	2.38681e9i		−	2.60531i
$63$		−	2.02340e9i		−	2.03882i
$64$	8.61918e8			0.802723
$65$			1.70811e9i			1.47214i
$66$	−2.79263e8			−0.222994
$67$	−1.23620e9			−0.915616			−0.457808	−	0.889051i	$-0.651365\pi$
$67$	−1.23620e9			−0.915616			−0.457808	+	0.889051i	$0.651365\pi$
$68$	−2.66454e8			−0.183264
$69$		−	7.42590e8i		−	0.474792i
$70$			5.06276e9i			3.01229i
$71$		−	1.85479e9i		−	1.02802i	−0.857783	−	0.514012i	$-0.828159\pi$
$71$		−	1.85479e9i		−	1.02802i	0.857783	−	0.514012i	$-0.171841\pi$
$72$			3.95398e8i			0.204349i
$73$			1.84969e9i			0.892247i	0.894971	+	0.446124i	$0.147196\pi$
$73$			1.84969e9i			0.892247i	−0.894971	+	0.446124i	$0.852804\pi$
$74$	3.85854e9			1.73886
$75$			6.86500e9i			2.89291i
$76$		−	1.29552e8i		−	0.0510946i
$77$			3.55663e8i			0.131397i
$78$	−5.60925e9			−1.94282
$79$	−8.05333e8			−0.261722			−0.130861	−	0.991401i	$-0.541774\pi$
$79$	−8.05333e8			−0.261722			−0.130861	+	0.991401i	$0.541774\pi$
$80$		−	5.95938e9i		−	1.81866i
$81$	−4.02965e8			−0.115569
$82$		−	3.92096e9i		−	1.05760i
$83$	−6.35127e9			−1.61239			−0.806195	−	0.591649i	$-0.798477\pi$
$83$	−6.35127e9			−1.61239			−0.806195	+	0.591649i	$0.798477\pi$
$84$	−7.90010e9			−1.88902
$85$			1.50449e9i			0.339075i
$86$	−5.78640e9	+	2.94697e9i	−1.23003	+	0.626446i
$87$	1.49271e10			2.99487
$88$		−	6.95010e7i		−	0.0131698i
$89$			3.36937e9i			0.603390i	0.953404	+	0.301695i	$0.0975525\pi$
$89$			3.36937e9i			0.603390i	−0.953404	+	0.301695i	$0.902448\pi$
$90$	−2.13704e10			−3.61910
$91$			7.14381e9i			1.14478i
$92$	−1.76904e9			−0.268410
$93$		−	2.10296e10i		−	3.02285i
$94$		−	8.81277e9i		−	1.20081i
$95$	−7.31495e8			−0.0945351
$96$	1.78649e10			2.19100
$97$	1.34193e10			1.56269			0.781343	−	0.624102i	$-0.214535\pi$
$97$	1.34193e10			1.56269			0.781343	+	0.624102i	$0.214535\pi$
$98$			8.69646e9i			0.962082i
$99$	−1.50129e9			−0.157866
$100$	1.63542e10			1.63542
$101$	1.38886e10			1.32145			0.660727	−	0.750626i	$-0.270248\pi$
$101$	1.38886e10			1.32145			0.660727	+	0.750626i	$0.270248\pi$
$102$	−4.94058e9			−0.447484
$103$	1.78504e9			0.153979			0.0769894	−	0.997032i	$-0.475469\pi$
$103$	1.78504e9			0.153979			0.0769894	+	0.997032i	$0.475469\pi$
$104$		−	1.39599e9i		−	0.114740i
$105$			4.46068e10i			3.49506i
$106$			1.58452e10i			1.18404i
$107$	1.17048e10			0.834537			0.417268	−	0.908783i	$-0.362988\pi$
$107$	1.17048e10			0.834537			0.417268	+	0.908783i	$0.362988\pi$
$108$		−	1.20404e10i		−	0.819447i
$109$	−7.22912e9			−0.469843			−0.234921	−	0.972014i	$-0.575483\pi$
$109$	−7.22912e9			−0.469843			−0.234921	+	0.972014i	$0.575483\pi$
$110$	3.75638e9			0.233242
$111$	3.39967e10			2.01754
$112$		−	2.49238e10i		−	1.41424i
$113$		−	5.13237e9i		−	0.278565i	−0.990253	−	0.139282i	$-0.955520\pi$
$113$		−	5.13237e9i		−	0.278565i	0.990253	−	0.139282i	$-0.0444795\pi$
$114$		−	2.40214e9i		−	0.124760i
$115$			9.98863e9i			0.496611i
$116$		−	3.55601e10i		−	1.69306i
$117$	−3.01548e10			−1.37539
$118$		−	4.16888e10i		−	1.82226i
$119$			6.29221e9i			0.263675i
$120$		−	8.71672e9i		−	0.350306i
$121$	−2.56735e10			−0.989826
$122$	6.62979e10			2.45302
$123$		−	3.45467e10i		−	1.22710i
$124$	−5.00979e10			−1.70888
$125$		−	4.12187e10i		−	1.35066i
$126$	−8.93771e10			−2.81432
$127$	−3.96185e9			−0.119917			−0.0599583	−	0.998201i	$-0.519097\pi$
$127$	−3.96185e9			−0.119917			−0.0599583	+	0.998201i	$0.519097\pi$
$128$			8.93230e9i			0.259964i
$129$	−5.09826e10	+	2.59651e10i	−1.42716	+	0.726843i
$130$	7.54503e10			2.03210
$131$			2.31997e10i			0.601349i	0.953727	+	0.300674i	$0.0972117\pi$
$131$			2.31997e10i			0.601349i	−0.953727	+	0.300674i	$0.902788\pi$
$132$			5.86159e9i			0.146267i
$133$	−3.05932e9			−0.0735134
$134$			5.46049e10i			1.26389i
$135$	−6.79842e10			−1.51614
$136$		−	1.22958e9i		−	0.0264278i
$137$		−	3.32676e10i		−	0.689317i	−0.938728	−	0.344658i	$-0.887995\pi$
$137$		−	3.32676e10i		−	0.689317i	0.938728	−	0.344658i	$-0.112005\pi$
$138$	−3.28015e10			−0.655388
$139$	3.77175e10			0.726890			0.363445	−	0.931616i	$-0.381600\pi$
$139$	3.77175e10			0.726890			0.363445	+	0.931616i	$0.381600\pi$
$140$	1.06265e11			1.97583
$141$		−	7.76472e10i		−	1.39325i
$142$	−8.19293e10			−1.41905
$143$	5.30045e9			0.0886406
$144$	1.05206e11			1.69913
$145$	−2.00785e11			−3.13250
$146$	8.17041e10			1.23163
$147$			7.66225e10i			1.11627i
$148$		−	8.09888e10i		−	1.14056i
$149$			4.43509e10i			0.603908i	0.953323	+	0.301954i	$0.0976389\pi$
$149$			4.43509e10i			0.603908i	−0.953323	+	0.301954i	$0.902361\pi$
$150$	3.03239e11			3.99327
$151$			4.70013e10i			0.598722i	0.954140	+	0.299361i	$0.0967735\pi$
$151$			4.70013e10i			0.598722i	−0.954140	+	0.299361i	$0.903226\pi$
$152$	5.97829e8			0.00736816
$153$	−2.65601e10			−0.316790
$154$	1.57103e10			0.181376
$155$			2.82871e11i			3.16177i
$156$			1.17735e11i			1.27433i
$157$		−	1.29297e11i		−	1.35547i	−0.735308	−	0.677733i	$-0.762963\pi$
$157$		−	1.29297e11i		−	1.35547i	0.735308	−	0.677733i	$-0.237037\pi$
$158$			3.55729e10i			0.361272i
$159$			1.39608e11i			1.37381i
$160$	−2.40301e11			−2.29169
$161$			4.17753e10i			0.386180i
$162$			1.77997e10i			0.159528i
$163$		−	4.46002e10i		−	0.387613i	−0.981040	−	0.193807i	$-0.937917\pi$
$163$		−	4.46002e10i		−	0.387613i	0.981040	−	0.193807i	$-0.0620834\pi$
$164$	−8.22989e10			−0.693705
$165$	3.30966e10			0.270623
$166$			2.80547e11i			2.22569i
$167$	−9.28129e9			−0.0714539			−0.0357270	−	0.999362i	$-0.511375\pi$
$167$	−9.28129e9			−0.0714539			−0.0357270	+	0.999362i	$0.511375\pi$
$168$		−	3.64558e10i		−	0.272408i
$169$	−3.13942e10			−0.227727
$170$	6.64561e10			0.468048
$171$		−	1.29137e10i		−	0.0883222i
$172$	6.18554e10	+	1.21454e11i	0.410899	+	0.806804i
$173$	−8.77693e10			−0.566386			−0.283193	−	0.959063i	$-0.591394\pi$
$173$	−8.77693e10			−0.566386			−0.283193	+	0.959063i	$0.591394\pi$
$174$		−	6.59355e11i		−	4.13402i
$175$		−	3.86198e11i		−	2.35299i
$176$	−1.84926e10			−0.109505
$177$		−	3.67311e11i		−	2.11430i
$178$	1.48831e11			0.832900
$179$			3.05725e11i			1.66367i	0.555026	+	0.831833i	$0.312708\pi$
$179$			3.05725e11i			1.66367i	−0.555026	+	0.831833i	$0.687292\pi$
$180$			4.48554e11i			2.37384i
$181$	−5.19389e10			−0.267362			−0.133681	−	0.991024i	$-0.542680\pi$
$181$	−5.19389e10			−0.267362			−0.133681	+	0.991024i	$0.542680\pi$
$182$	3.15555e11			1.58022
$183$	5.84135e11			2.84615
$184$		−	8.16341e9i		−	0.0387064i
$185$	−4.57292e11			−2.11026
$186$	−9.28916e11			−4.17265
$187$	4.66860e9			0.0204164
$188$	−1.84975e11			−0.787635
$189$	−2.84329e11			−1.17900
$190$			3.23114e10i			0.130493i
$191$			4.65718e11i			1.83213i	0.401031	+	0.916064i	$0.368652\pi$
$191$			4.65718e11i			1.83213i	−0.401031	+	0.916064i	$0.631348\pi$
$192$		−	3.35447e11i		−	1.28564i
$193$	−1.21544e11			−0.453888			−0.226944	−	0.973908i	$-0.572873\pi$
$193$	−1.21544e11			−0.453888			−0.226944	+	0.973908i	$0.572873\pi$
$194$		−	5.92754e11i		−	2.15708i
$195$	6.64775e11			2.35777
$196$	1.82534e11			0.631050
$197$	2.78554e11			0.938813			0.469406	−	0.882982i	$-0.344468\pi$
$197$	2.78554e11			0.938813			0.469406	+	0.882982i	$0.344468\pi$
$198$			6.63146e10i			0.217913i
$199$		−	4.27701e11i		−	1.37049i	−0.728314	−	0.685244i	$-0.759696\pi$
$199$		−	4.27701e11i		−	1.37049i	0.728314	−	0.685244i	$-0.240304\pi$
$200$			7.54680e10i			0.235838i
$201$			4.81111e11i			1.46644i
$202$		−	6.13484e11i		−	1.82409i
$203$	−8.39740e11			−2.43593
$204$			1.03700e11i			0.293514i
$205$			4.64689e11i			1.28349i
$206$		−	7.88481e10i		−	0.212547i
$207$	−1.76338e11			−0.463973
$208$	−3.71440e11			−0.954051
$209$			2.26990e9i			0.00569215i
$210$	1.97036e12			4.82446
$211$		−	1.70602e11i		−	0.407917i	−0.978980	−	0.203959i	$-0.934619\pi$
$211$		−	1.70602e11i		−	0.407917i	0.978980	−	0.203959i	$-0.0653808\pi$
$212$	3.32582e11			0.776640
$213$	−7.21860e11			−1.64647
$214$		−	5.17022e11i		−	1.15197i
$215$	6.85770e11	−	3.49258e11i	1.49275	−	0.760245i
$216$	5.55615e10			0.118169
$217$			1.18305e12i			2.45869i
$218$			3.19323e11i			0.648555i
$219$	7.19876e11			1.42902
$220$		−	7.88446e10i		−	0.152988i
$221$	9.37730e10			0.177876
$222$		−	1.50169e12i		−	2.78495i
$223$		−	5.36910e11i		−	0.973593i	−0.873515	−	0.486796i	$-0.838165\pi$
$223$		−	5.36910e11i		−	0.973593i	0.873515	−	0.486796i	$-0.161835\pi$
$224$	−1.00501e12			−1.78209
$225$	1.63018e12			2.82699
$226$	−2.26706e11			−0.384521
$227$			1.51475e11i			0.251311i	0.992074	+	0.125656i	$0.0401034\pi$
$227$			1.51475e11i			0.251311i	−0.992074	+	0.125656i	$0.959897\pi$
$228$	−5.04198e10			−0.0818327
$229$	−4.10757e11			−0.652240			−0.326120	−	0.945328i	$-0.605741\pi$
$229$	−4.10757e11			−0.652240			−0.326120	+	0.945328i	$0.605741\pi$
$230$	4.41215e11			0.685506
$231$	1.38419e11			0.210444
$232$	1.64096e11			0.244150
$233$		−	1.03337e12i		−	1.50479i	−0.658712	−	0.752395i	$-0.728899\pi$
$233$		−	1.03337e12i		−	1.50479i	0.658712	−	0.752395i	$-0.271101\pi$
$234$			1.33199e12i			1.89855i
$235$			1.04444e12i			1.45728i
$236$	−8.75027e11			−1.19526
$237$			3.13425e11i			0.419171i
$238$	2.77938e11			0.363968
$239$	−6.49764e11			−0.833232			−0.416616	−	0.909082i	$-0.636784\pi$
$239$	−6.49764e11			−0.833232			−0.416616	+	0.909082i	$0.636784\pi$
$240$	−2.31931e12			−2.91275
$241$		−	9.03941e11i		−	1.11187i	−0.831225	−	0.555936i	$-0.812360\pi$
$241$		−	9.03941e11i		−	1.11187i	0.831225	−	0.555936i	$-0.187640\pi$
$242$			1.13404e12i			1.36632i
$243$			9.23671e11i			1.09015i
$244$		−	1.39156e12i		−	1.60899i
$245$		−	1.03065e12i		−	1.16757i
$246$	−1.52599e12			−1.69385
$247$			4.55930e10i			0.0495923i
$248$		−	2.31182e11i		−	0.246431i
$249$			2.47183e12i			2.58239i
$250$	−1.82070e12			−1.86440
$251$	1.76657e12			1.77322			0.886611	−	0.462516i	$-0.153053\pi$
$251$	1.76657e12			1.77322			0.886611	+	0.462516i	$0.153053\pi$
$252$			1.87598e12i			1.84597i
$253$	3.09957e10			0.0299019
$254$			1.75002e11i			0.165529i
$255$	5.85529e11			0.543060
$256$	1.27716e12			1.16157
$257$			8.68522e11i			0.774667i	0.921940	+	0.387333i	$0.126604\pi$
$257$			8.68522e11i			0.774667i	−0.921940	+	0.387333i	$0.873396\pi$
$258$	1.14692e12	+	2.25199e12i	1.00331	+	1.97001i
$259$	−1.91252e12			−1.64100
$260$		−	1.58366e12i		−	1.33290i
$261$		−	3.54462e12i		−	2.92663i
$262$	1.02477e12			0.830082
$263$			2.81196e11i			0.223476i	0.993738	+	0.111738i	$0.0356417\pi$
$263$			2.81196e11i			0.223476i	−0.993738	+	0.111738i	$0.964358\pi$
$264$	−2.70489e10			−0.0210926
$265$		−	1.87788e12i		−	1.43694i
$266$			1.35135e11i			0.101475i
$267$	1.31131e12			0.966385
$268$	1.14613e12			0.829010
$269$	1.95784e12			1.39000			0.695002	−	0.719008i	$-0.255403\pi$
$269$	1.95784e12			1.39000			0.695002	+	0.719008i	$0.255403\pi$
$270$			3.00298e12i			2.09283i
$271$	−9.57099e11			−0.654803			−0.327401	−	0.944885i	$-0.606173\pi$
$271$	−9.57099e11			−0.654803			−0.327401	+	0.944885i	$0.606173\pi$
$272$	−3.27161e11			−0.219744
$273$	2.78028e12			1.83348
$274$	−1.46949e12			−0.951510
$275$	−2.86545e11			−0.182192
$276$			6.88487e11i			0.429883i
$277$		−	1.00767e12i		−	0.617900i	−0.951078	−	0.308950i	$-0.900022\pi$
$277$		−	1.00767e12i		−	0.617900i	0.951078	−	0.308950i	$-0.0999775\pi$
$278$		−	1.66605e12i		−	1.00337i
$279$	−4.99376e12			−2.95397
$280$			4.90369e11i			0.284927i
$281$	−1.64012e12			−0.936147			−0.468073	−	0.883690i	$-0.655052\pi$
$281$	−1.64012e12			−0.936147			−0.468073	+	0.883690i	$0.655052\pi$
$282$	−3.42981e12			−1.92320
$283$	−3.07182e12			−1.69225			−0.846124	−	0.532986i	$-0.821070\pi$
$283$	−3.07182e12			−1.69225			−0.846124	+	0.532986i	$0.821070\pi$
$284$			1.71965e12i			0.930785i
$285$			2.84688e11i			0.151407i
$286$		−	2.34130e11i		−	0.122357i
$287$			1.94346e12i			0.998082i
$288$		−	4.24224e12i		−	2.14108i
$289$	−1.93340e12			−0.959030
$290$			8.86902e12i			4.32400i
$291$		−	5.22262e12i		−	2.50278i
$292$		−	1.71493e12i		−	0.807852i
$293$	2.79147e12			1.29269			0.646346	−	0.763045i	$-0.276296\pi$
$293$	2.79147e12			1.29269			0.646346	+	0.763045i	$0.276296\pi$
$294$	3.38455e12			1.54086
$295$			4.94072e12i			2.21146i
$296$	3.73731e11			0.164475
$297$			2.10962e11i			0.0912898i
$298$	1.95905e12			0.833614
$299$	6.22577e11			0.260518
$300$		−	6.36483e12i		−	2.61927i
$301$	2.86809e12	−	1.46069e12i	1.16081	−	0.591190i
$302$	2.07613e12			0.826456
$303$		−	5.40526e12i		−	2.11643i
$304$		−	1.59068e11i		−	0.0612653i
$305$	−7.85724e12			−2.97694
$306$			1.17320e12i			0.437287i
$307$	4.91023e11			0.180057			0.0900284	−	0.995939i	$-0.471304\pi$
$307$	4.91023e11			0.180057			0.0900284	+	0.995939i	$0.471304\pi$
$308$		−	3.29750e11i		−	0.118968i
$309$		−	6.94713e11i		−	0.246611i
$310$	1.24949e13			4.36440
$311$	−1.24650e12			−0.428439			−0.214220	−	0.976785i	$-0.568721\pi$
$311$	−1.24650e12			−0.428439			−0.214220	+	0.976785i	$0.568721\pi$
$312$	−5.43301e11			−0.183767
$313$			5.02951e12i			1.67419i	0.547060	+	0.837093i	$0.315747\pi$
$313$			5.02951e12i			1.67419i	−0.547060	+	0.837093i	$0.684253\pi$
$314$	−5.71125e12			−1.87104
$315$	1.05924e13			3.41542
$316$	7.46658e11			0.236966
$317$	−2.31349e12			−0.722723			−0.361362	−	0.932426i	$-0.617688\pi$
$317$	−2.31349e12			−0.722723			−0.361362	+	0.932426i	$0.617688\pi$
$318$	6.16674e12			1.89636
$319$			6.23057e11i			0.188614i
$320$			4.51212e12i			1.34472i
$321$		−	4.55536e12i		−	1.33659i
$322$	1.84529e12			0.533070
$323$			4.01580e10i			0.0114225i
$324$	3.73606e11			0.104638
$325$	−5.75552e12			−1.58733
$326$	−1.97007e12			−0.535048
$327$			2.81348e12i			0.752497i
$328$		−	3.79777e11i		−	0.100037i
$329$			4.36813e12i			1.13323i
$330$		−	1.46194e12i		−	0.373558i
$331$		−	5.06669e12i		−	1.27522i	−0.770361	−	0.637608i	$-0.779924\pi$
$331$		−	5.06669e12i		−	1.27522i	0.770361	−	0.637608i	$-0.220076\pi$
$332$	5.88853e12			1.45988
$333$		−	8.07296e12i		−	1.97157i
$334$			4.09971e11i			0.0986326i
$335$		−	6.47146e12i		−	1.53383i
$336$	−9.70001e12			−2.26504
$337$	2.41861e12			0.556437			0.278218	−	0.960518i	$-0.410256\pi$
$337$	2.41861e12			0.556437			0.278218	+	0.960518i	$0.410256\pi$
$338$			1.38673e12i			0.314347i
$339$	−1.99745e12			−0.446147
$340$		−	1.39488e12i		−	0.307002i
$341$	8.77778e11			0.190376
$342$	−5.70420e11			−0.121917
$343$			1.87407e12i			0.394743i
$344$	−5.60460e11	+	2.85438e11i	−0.116346	+	0.0592542i
$345$	3.88744e12			0.795369
$346$			3.87692e12i			0.781820i
$347$		−	1.55356e12i		−	0.308803i	−0.988008	−	0.154402i	$-0.950655\pi$
$347$		−	1.55356e12i		−	0.308803i	0.988008	−	0.154402i	$-0.0493449\pi$
$348$	−1.38395e13			−2.71159
$349$		−	5.81530e12i		−	1.12317i	−0.827419	−	0.561585i	$-0.810192\pi$
$349$		−	5.81530e12i		−	1.12317i	0.827419	−	0.561585i	$-0.189808\pi$
$350$	−1.70591e13			−3.24799
$351$			4.23736e12i			0.795353i
$352$			7.45679e11i			0.137987i
$353$	8.34462e12			1.52241			0.761207	−	0.648509i	$-0.224607\pi$
$353$	8.34462e12			1.52241			0.761207	+	0.648509i	$0.224607\pi$
$354$	−1.62247e13			−2.91851
$355$	9.70978e12			1.72214
$356$		−	3.12388e12i		−	0.546317i
$357$	2.44885e12			0.422300
$358$	1.35044e13			2.29647
$359$	5.63916e12			0.945675			0.472838	−	0.881150i	$-0.343230\pi$
$359$	5.63916e12			0.945675			0.472838	+	0.881150i	$0.343230\pi$
$360$	−2.06990e12			−0.342323
$361$	6.11154e12			0.996815
$362$			2.29423e12i			0.369058i
$363$			9.99180e12i			1.58530i
$364$		−	6.62333e12i		−	1.03650i
$365$	−9.68310e12			−1.49469
$366$		−	2.58023e13i		−	3.92873i
$367$	−3.17914e12			−0.477506			−0.238753	−	0.971080i	$-0.576739\pi$
$367$	−3.17914e12			−0.477506			−0.238753	+	0.971080i	$0.576739\pi$
$368$	−2.17209e12			−0.321839
$369$	−8.20354e12			−1.19914
$370$			2.01994e13i			2.91293i
$371$		−	7.85382e12i		−	1.11741i
$372$			1.94975e13i			2.73693i
$373$		−	3.17793e12i		−	0.440149i	−0.975483	−	0.220075i	$-0.929370\pi$
$373$		−	3.17793e12i		−	0.440149i	0.975483	−	0.220075i	$-0.0706301\pi$
$374$		−	2.06220e11i		−	0.0281821i
$375$	−1.60418e13			−2.16320
$376$		−	8.53588e11i		−	0.113582i
$377$			1.25146e13i			1.64328i
$378$			1.25593e13i			1.62745i
$379$	4.13270e12			0.528491			0.264246	−	0.964455i	$-0.414877\pi$
$379$	4.13270e12			0.528491			0.264246	+	0.964455i	$0.414877\pi$
$380$	6.78199e11			0.0855932
$381$			1.54190e12i			0.192057i
$382$	2.05716e13			2.52901
$383$			8.82149e12i			1.07040i	0.844724	+	0.535202i	$0.179765\pi$
$383$			8.82149e12i			1.07040i	−0.844724	+	0.535202i	$0.820235\pi$
$384$	3.47633e12			0.416356
$385$	−1.86189e12			−0.220115
$386$			5.36883e12i			0.626532i
$387$	6.16574e12	+	1.21065e13i	0.710281	+	1.39464i
$388$	−1.24416e13			−1.41487
$389$			9.50961e12i			1.06762i	0.845606	+	0.533808i	$0.179239\pi$
$389$			9.50961e12i			1.06762i	−0.845606	+	0.533808i	$0.820761\pi$
$390$		−	2.93643e13i		−	3.25459i
$391$	5.48361e11			0.0600044
$392$			8.42323e11i			0.0910014i
$393$	9.02903e12			0.963115
$394$		−	1.23042e13i		−	1.29591i
$395$		−	4.21590e12i		−	0.438434i
$396$	1.39191e12			0.142934
$397$	−1.98113e12			−0.200891			−0.100446	−	0.994943i	$-0.532027\pi$
$397$	−1.98113e12			−0.200891			−0.100446	+	0.994943i	$0.532027\pi$
$398$	−1.88923e13			−1.89177
$399$			1.19065e12i			0.117738i
$400$	2.00802e13			1.96096
$401$	6.65423e12			0.641765			0.320883	−	0.947119i	$-0.396021\pi$
$401$	6.65423e12			0.641765			0.320883	+	0.947119i	$0.396021\pi$
$402$	2.12515e13			2.02423
$403$	1.76310e13			1.65863
$404$	−1.28767e13			−1.19646
$405$		−	2.10951e12i		−	0.193601i
$406$			3.70928e13i			3.36247i
$407$			1.41902e12i			0.127063i
$408$	−4.78535e11			−0.0423266
$409$		−	2.33376e12i		−	0.203911i	−0.994789	−	0.101955i	$-0.967490\pi$
$409$		−	2.33376e12i		−	0.203911i	0.994789	−	0.101955i	$-0.0325099\pi$
$410$	2.05261e13			1.77169
$411$	−1.29473e13			−1.10400
$412$	−1.65498e12			−0.139414
$413$			2.06635e13i			1.71970i
$414$			7.78914e12i			0.640453i
$415$		−	3.32488e13i		−	2.70106i
$416$			1.49776e13i			1.20220i
$417$		−	1.46791e13i		−	1.16418i
$418$	1.00266e11			0.00785725
$419$			5.16084e12i			0.399623i	0.979834	+	0.199811i	$0.0640329\pi$
$419$			5.16084e12i			0.399623i	−0.979834	+	0.199811i	$0.935967\pi$
$420$		−	4.13568e13i		−	3.16447i
$421$		−	1.86467e13i		−	1.40991i	−0.709251	−	0.704956i	$-0.750967\pi$
$421$		−	1.86467e13i		−	1.40991i	0.709251	−	0.704956i	$-0.249033\pi$
$422$	−7.53579e12			−0.563075
$423$	−1.84383e13			−1.36151
$424$			1.53474e12i			0.111996i
$425$	−5.06942e12			−0.365606
$426$			3.18858e13i			2.27274i
$427$	−3.28612e13			−2.31496
$428$	−1.08520e13			−0.755600
$429$		−	2.06287e12i		−	0.141966i
$430$	−1.54273e13	−	3.02917e13i	−1.04942	−	2.06054i
$431$	6.14696e12			0.413308			0.206654	−	0.978414i	$-0.433743\pi$
$431$	6.14696e12			0.413308			0.206654	+	0.978414i	$0.433743\pi$
$432$		−	1.47836e13i		−	0.982564i
$433$			3.26476e12i			0.214492i	0.994233	+	0.107246i	$0.0342033\pi$
$433$			3.26476e12i			0.214492i	−0.994233	+	0.107246i	$0.965797\pi$
$434$	5.22572e13			3.39389
$435$			7.81429e13i			5.01699i
$436$	6.70242e12			0.425401
$437$			2.66617e11i			0.0167294i
$438$		−	3.17982e13i		−	1.97257i
$439$	−1.89155e13			−1.16010			−0.580049	−	0.814581i	$-0.696967\pi$
$439$	−1.89155e13			−1.16010			−0.580049	+	0.814581i	$0.696967\pi$
$440$	3.63836e11			0.0220619
$441$	1.81950e13			1.09083
$442$		−	4.14211e12i		−	0.245533i
$443$	−1.44922e13			−0.849405			−0.424703	−	0.905333i	$-0.639621\pi$
$443$	−1.44922e13			−0.849405			−0.424703	+	0.905333i	$0.639621\pi$
$444$	−3.15198e13			−1.82671
$445$	−1.76386e13			−1.01079
$446$	−2.37163e13			−1.34391
$447$	1.72608e13			0.967214
$448$			1.88710e13i			1.04569i
$449$		−	3.15308e13i		−	1.72784i	−0.503629	−	0.863920i	$-0.668002\pi$
$449$		−	3.15308e13i		−	1.72784i	0.503629	−	0.863920i	$-0.331998\pi$
$450$		−	7.20080e13i		−	3.90228i
$451$	1.44198e12			0.0772816
$452$			4.75844e12i			0.252216i
$453$	1.82923e13			0.958909
$454$	6.69092e12			0.346902
$455$	−3.73977e13			−1.91773
$456$		−	2.32667e11i		−	0.0118008i
$457$		−	3.13837e12i		−	0.157443i	−0.996897	−	0.0787214i	$-0.974916\pi$
$457$		−	3.13837e12i		−	0.157443i	0.996897	−	0.0787214i	$-0.0250838\pi$
$458$			1.81438e13i			0.900331i
$459$			3.73223e12i			0.183192i
$460$		−	9.26087e12i		−	0.449638i
$461$	−1.70711e13			−0.819895			−0.409947	−	0.912109i	$-0.634453\pi$
$461$	−1.70711e13			−0.819895			−0.409947	+	0.912109i	$0.634453\pi$
$462$		−	6.11423e12i		−	0.290490i
$463$		−	1.76507e13i		−	0.829576i	−0.909918	−	0.414788i	$-0.863856\pi$
$463$		−	1.76507e13i		−	0.829576i	0.909918	−	0.414788i	$-0.136144\pi$
$464$		−	4.36619e13i		−	2.03008i
$465$	1.10090e14			5.06386
$466$	−4.56457e13			−2.07716
$467$		−	3.03925e13i		−	1.36830i	−0.729340	−	0.684152i	$-0.760173\pi$
$467$		−	3.03925e13i		−	1.36830i	0.729340	−	0.684152i	$-0.239827\pi$
$468$	2.79577e13			1.24530
$469$		−	2.70655e13i		−	1.19276i
$470$	4.61346e13			2.01158
$471$	−5.03205e13			−2.17090
$472$		−	4.03790e12i		−	0.172364i
$473$	−1.08378e12	−	2.12802e12i	−0.0457759	−	0.0898813i
$474$	1.38445e13			0.578610
$475$		−	2.46479e12i		−	0.101932i
$476$		−	5.83378e12i		−	0.238734i
$477$	3.31518e13			1.34250
$478$			2.87012e13i			1.15017i
$479$	4.42392e13			1.75440			0.877201	−	0.480123i	$-0.159408\pi$
$479$	4.42392e13			1.75440			0.877201	+	0.480123i	$0.159408\pi$
$480$			9.35221e13i			3.67035i
$481$			2.85024e13i			1.10702i
$482$	−3.99286e13			−1.53479
$483$	1.62584e13			0.618503
$484$	2.38030e13			0.896200
$485$			7.02498e13i			2.61780i
$486$	4.08001e13			1.50481
$487$	−1.57076e13			−0.573411			−0.286705	−	0.958019i	$-0.592560\pi$
$487$	−1.57076e13			−0.573411			−0.286705	+	0.958019i	$0.592560\pi$
$488$	6.42149e12			0.232026
$489$	−1.73578e13			−0.620798
$490$	−4.55258e13			−1.61167
$491$		−	1.54818e13i		−	0.542519i	−0.962506	−	0.271260i	$-0.912560\pi$
$491$		−	1.54818e13i		−	0.542519i	0.962506	−	0.271260i	$-0.0874402\pi$
$492$			3.20296e13i			1.11103i
$493$			1.10228e13i			0.378493i
$494$	2.01392e12			0.0684555
$495$		−	7.85922e12i		−	0.264456i
$496$	−6.15120e13			−2.04905
$497$	4.06091e13			1.33919
$498$	1.09185e14			3.56465
$499$			2.61506e13i			0.845237i	0.906308	+	0.422618i	$0.138889\pi$
$499$			2.61506e13i			0.845237i	−0.906308	+	0.422618i	$0.861111\pi$
$500$			3.82156e13i			1.22290i
$501$			3.61216e12i			0.114440i
$502$		−	7.80326e13i		−	2.44770i
$503$		−	9.51220e12i		−	0.295421i	−0.989031	−	0.147710i	$-0.952810\pi$
$503$		−	9.51220e12i		−	0.295421i	0.989031	−	0.147710i	$-0.0471904\pi$
$504$	−8.65690e12			−0.266201
$505$			7.27065e13i			2.21369i
$506$		−	1.36914e12i		−	0.0412756i
$507$			1.22182e13i			0.364726i
$508$	3.67320e12			0.108574
$509$	−3.68569e13			−1.07877			−0.539387	−	0.842058i	$-0.681344\pi$
$509$	−3.68569e13			−1.07877			−0.539387	+	0.842058i	$0.681344\pi$
$510$		−	2.58638e13i		−	0.749621i
$511$	−4.04974e13			−1.16231
$512$		−	4.72676e13i		−	1.34343i
$513$	−1.81464e12			−0.0510744
$514$	3.83641e13			1.06932
$515$			9.34462e12i			0.257944i
$516$	4.72681e13	−	2.40733e13i	1.29217	−	0.658093i
$517$	3.24100e12			0.0877457
$518$			8.44795e13i			2.26518i
$519$			3.41587e13i			0.907119i
$520$	7.30798e12			0.192212
$521$		−	3.11431e13i		−	0.811285i	−0.914032	−	0.405643i	$-0.867048\pi$
$521$		−	3.11431e13i		−	0.811285i	0.914032	−	0.405643i	$-0.132952\pi$
$522$	−1.56572e14			−4.03982
$523$		−	6.70568e13i		−	1.71370i	−0.515568	−	0.856849i	$-0.672419\pi$
$523$		−	6.70568e13i		−	1.71370i	0.515568	−	0.856849i	$-0.327581\pi$
$524$		−	2.15094e13i		−	0.544468i
$525$	−1.50303e14			−3.76853
$526$	1.24209e13			0.308479
$527$	1.55292e13			0.382029
$528$			7.19706e12i			0.175382i
$529$	−3.77858e13			−0.912117
$530$	−8.29492e13			−1.98350
$531$	−8.72226e13			−2.06612
$532$	2.83642e12			0.0665599
$533$	2.89634e13			0.673308
$534$		−	5.79230e13i		−	1.33397i
$535$			6.12744e13i			1.39801i
$536$			5.28893e12i			0.119548i
$537$	1.18984e14			2.66451
$538$		−	8.64812e13i		−	1.91872i
$539$	−3.19823e12			−0.0703016
$540$	6.30310e13			1.37273
$541$	−7.26190e12			−0.156698			−0.0783491	−	0.996926i	$-0.524965\pi$
$541$	−7.26190e12			−0.156698			−0.0783491	+	0.996926i	$0.524965\pi$
$542$			4.22767e13i			0.903868i
$543$			2.02139e13i			0.428205i
$544$			1.31922e13i			0.276900i
$545$		−	3.78442e13i		−	0.787077i
$546$		−	1.22810e14i		−	2.53087i
$547$	−2.42391e12			−0.0494971			−0.0247485	−	0.999694i	$-0.507879\pi$
$547$	−2.42391e12			−0.0494971			−0.0247485	+	0.999694i	$0.507879\pi$
$548$			3.08438e13i			0.624116i
$549$		−	1.38710e14i		−	2.78130i
$550$			1.26572e13i			0.251492i
$551$	−5.35936e12			−0.105525
$552$	−3.17709e12			−0.0619918
$553$		−	1.76321e13i		−	0.340940i
$554$	−4.45104e13			−0.852928
$555$			1.77972e14i			3.37977i
$556$	−3.49695e13			−0.658135
$557$	−7.15510e13			−1.33457			−0.667283	−	0.744805i	$-0.732543\pi$
$557$	−7.15510e13			−1.33457			−0.667283	+	0.744805i	$0.732543\pi$
$558$			2.20583e14i			4.07756i
$559$	−2.17687e13	−	4.27431e13i	−0.398818	−	0.783082i
$560$	1.30475e14			2.36913
$561$		−	1.81696e12i		−	0.0326987i
$562$			7.24469e13i			1.29223i
$563$	7.78919e13			1.37705			0.688526	−	0.725212i	$-0.258258\pi$
$563$	7.78919e13			1.37705			0.688526	+	0.725212i	$0.258258\pi$
$564$			7.19900e13i			1.26147i
$565$	2.68678e13			0.466649
$566$			1.35688e14i			2.33592i
$567$		−	8.82257e12i		−	0.150550i
$568$	−7.93552e12			−0.134225
$569$	−5.62609e13			−0.943289			−0.471645	−	0.881789i	$-0.656340\pi$
$569$	−5.62609e13			−0.943289			−0.471645	+	0.881789i	$0.656340\pi$
$570$	1.25752e13			0.208997
$571$		−	9.80201e12i		−	0.161486i	−0.996735	−	0.0807430i	$-0.974271\pi$
$571$		−	9.80201e12i		−	0.161486i	0.996735	−	0.0807430i	$-0.0257293\pi$
$572$	−4.91427e12			−0.0802563
$573$	1.81251e14			2.93432
$574$	8.58460e13			1.37772
$575$	−3.36569e13			−0.535469
$576$	−7.96562e13			−1.25634
$577$		−	8.14357e13i		−	1.27331i	−0.771147	−	0.636657i	$-0.780317\pi$
$577$		−	8.14357e13i		−	1.27331i	0.771147	−	0.636657i	$-0.219683\pi$
$578$			8.54016e13i			1.32381i
$579$			4.73035e13i			0.726943i
$580$	1.86156e14			2.83620
$581$		−	1.39056e14i		−	2.10043i
$582$	−2.30692e14			−3.45476
$583$	−5.82725e12			−0.0865209
$584$	7.91371e12			0.116497
$585$		−	1.57859e14i		−	2.30405i
$586$		−	1.23304e14i		−	1.78439i
$587$			7.99336e13i			1.14693i	0.819228	+	0.573467i	$0.194402\pi$
$587$			7.99336e13i			1.14693i	−0.819228	+	0.573467i	$0.805598\pi$
$588$		−	7.10399e13i		−	1.01069i
$589$			7.55041e12i			0.106511i
$590$	2.18240e14			3.05263
$591$		−	1.08410e14i		−	1.50360i
$592$		−	9.94409e13i		−	1.36759i
$593$		−	3.00724e13i		−	0.410105i	−0.978751	−	0.205052i	$-0.934264\pi$
$593$		−	3.00724e13i		−	0.410105i	0.978751	−	0.205052i	$-0.0657365\pi$
$594$	9.31856e12			0.126013
$595$	−3.29396e13			−0.441706
$596$		−	4.11195e13i		−	0.546785i
$597$	−1.66456e14			−2.19496
$598$		−	2.75003e13i		−	0.359610i
$599$	8.26667e13			1.07200			0.536002	−	0.844217i	$-0.319934\pi$
$599$	8.26667e13			1.07200			0.536002	+	0.844217i	$0.319934\pi$
$600$	2.93712e13			0.377715
$601$			1.17845e13i			0.150293i	0.997172	+	0.0751466i	$0.0239425\pi$
$601$			1.17845e13i			0.150293i	−0.997172	+	0.0751466i	$0.976058\pi$
$602$	−6.45214e13	−	1.26688e14i	−0.816058	−	1.60234i
$603$	1.14246e14			1.43303
$604$		−	4.35769e13i		−	0.542090i
$605$		−	1.34400e14i		−	1.65815i
$606$	−2.38760e14			−2.92145
$607$		−	1.83173e13i		−	0.222289i	−0.993804	−	0.111145i	$-0.964548\pi$
$607$		−	1.83173e13i		−	0.222289i	0.993804	−	0.111145i	$-0.0354517\pi$
$608$	−6.41413e12			−0.0772005
$609$			3.26816e14i			3.90136i
$610$			3.47068e14i			4.10927i
$611$	6.50983e13			0.764476
$612$	2.46250e13			0.286826
$613$	3.12591e13			0.361138			0.180569	−	0.983562i	$-0.442206\pi$
$613$	3.12591e13			0.361138			0.180569	+	0.983562i	$0.442206\pi$
$614$		−	2.16893e13i		−	0.248545i
$615$	1.80851e14			2.05563
$616$	1.52167e12			0.0171560
$617$	−5.75834e13			−0.643979			−0.321990	−	0.946743i	$-0.604352\pi$
$617$	−5.75834e13			−0.643979			−0.321990	+	0.946743i	$0.604352\pi$
$618$	−3.06867e13			−0.340414
$619$	2.57630e13			0.283494			0.141747	−	0.989903i	$-0.454728\pi$
$619$	2.57630e13			0.283494			0.141747	+	0.989903i	$0.454728\pi$
$620$		−	2.62262e14i		−	2.86270i
$621$			2.47790e13i			0.268304i
$622$			5.50600e13i			0.591404i
$623$	−7.37694e13			−0.786025
$624$			1.44559e14i			1.52800i
$625$	4.35199e13			0.456339
$626$	2.22162e14			2.31099
$627$	8.83417e11			0.00911650
$628$			1.19876e14i			1.22726i
$629$			2.51047e13i			0.254977i
$630$		−	4.67887e14i		−	4.71453i
$631$			7.65352e13i			0.765094i	0.923936	+	0.382547i	$0.124953\pi$
$631$			7.65352e13i			0.765094i	−0.923936	+	0.382547i	$0.875047\pi$
$632$			3.44553e12i			0.0341720i
$633$	−6.63961e13			−0.653317
$634$			1.02191e14i			0.997623i
$635$		−	2.07402e13i		−	0.200883i
$636$		−	1.29437e14i		−	1.24386i
$637$	−6.42392e13			−0.612496
$638$	2.75215e13			0.260357
$639$			1.71415e14i			1.60896i
$640$	−4.67604e13			−0.435490
$641$		−	7.91033e13i		−	0.730978i	−0.930816	−	0.365489i	$-0.880902\pi$
$641$		−	7.91033e13i		−	0.730978i	0.930816	−	0.365489i	$-0.119098\pi$
$642$	−2.01218e14			−1.84498
$643$	−7.07860e13			−0.644010			−0.322005	−	0.946738i	$-0.604357\pi$
$643$	−7.07860e13			−0.644010			−0.322005	+	0.946738i	$0.604357\pi$
$644$		−	3.87316e13i		−	0.349652i
$645$	−1.35926e14	−	2.66893e14i	−1.21760	−	2.39077i
$646$	1.77385e12			0.0157672
$647$		−	5.00521e12i		−	0.0441470i	−0.999756	−	0.0220735i	$-0.992973\pi$
$647$		−	5.00521e12i		−	0.0441470i	0.999756	−	0.0220735i	$-0.00702678\pi$
$648$			1.72404e12i			0.0150894i
$649$	1.53316e13			0.133157
$650$			2.54231e14i			2.19110i
$651$	4.60426e14			3.93781
$652$			4.13507e13i			0.350950i
$653$			4.06276e13i			0.342181i	0.985255	+	0.171090i	$0.0547290\pi$
$653$			4.06276e13i			0.342181i	−0.985255	+	0.171090i	$0.945271\pi$
$654$	1.24276e14			1.03872
$655$	−1.21450e14			−1.00737
$656$	−1.01049e14			−0.831792
$657$		−	1.70944e14i		−	1.39645i
$658$	1.92948e14			1.56427
$659$	1.05908e14			0.852123			0.426062	−	0.904694i	$-0.359901\pi$
$659$	1.05908e14			0.852123			0.426062	+	0.904694i	$0.359901\pi$
$660$	−3.06853e13			−0.245025
$661$	4.93221e13			0.390872			0.195436	−	0.980716i	$-0.437388\pi$
$661$	4.93221e13			0.390872			0.195436	+	0.980716i	$0.437388\pi$
$662$	−2.23804e14			−1.76027
$663$		−	3.64952e13i		−	0.284884i
$664$			2.71732e13i			0.210524i
$665$		−	1.60155e13i		−	0.123149i
$666$	−3.56597e14			−2.72149
$667$			7.31826e13i			0.554343i
$668$	8.60508e12			0.0646952
$669$	−2.08958e14			−1.55930
$670$	−2.85856e14			−2.11725
$671$			2.43818e13i			0.179248i
$672$			3.91136e14i			2.85418i
$673$		−	2.16473e14i		−	1.56794i	−0.620801	−	0.783968i	$-0.713193\pi$
$673$		−	2.16473e14i		−	1.56794i	0.620801	−	0.783968i	$-0.286807\pi$
$674$		−	1.06834e14i		−	0.768087i
$675$		−	2.29074e14i		−	1.63477i
$676$	2.91068e13			0.206187
$677$			1.92061e14i			1.35050i	0.737588	+	0.675251i	$0.235964\pi$
$677$			1.92061e14i			1.35050i	−0.737588	+	0.675251i	$0.764036\pi$
$678$			8.82309e13i			0.615846i
$679$			2.93804e14i			2.03568i
$680$	6.43681e12			0.0442717
$681$	5.89521e13			0.402498
$682$		−	3.87730e13i		−	0.262789i
$683$	1.63569e14			1.10052			0.550260	−	0.834994i	$-0.314529\pi$
$683$	1.63569e14			1.10052			0.550260	+	0.834994i	$0.314529\pi$
$684$			1.19728e13i			0.0799679i
$685$	1.74155e14			1.15474
$686$	8.27809e13			0.544891
$687$			1.59861e14i			1.04462i
$688$	7.59482e13	+	1.49125e14i	0.492692	+	0.967405i
$689$	−1.17046e14			−0.753805
$690$		−	1.71715e14i		−	1.09790i
$691$		−	5.58274e13i		−	0.354370i	−0.984178	−	0.177185i	$-0.943301\pi$
$691$		−	5.58274e13i		−	0.354370i	0.984178	−	0.177185i	$-0.0566991\pi$
$692$	8.13746e13			0.512812
$693$		−	3.28695e13i		−	0.205649i
$694$	−6.86236e13			−0.426262
$695$			1.97450e14i			1.21768i
$696$		−	6.38639e13i		−	0.391029i
$697$	2.55108e13			0.155081
$698$	−2.56872e14			−1.55039
$699$	−4.02174e14			−2.41006
$700$			3.58061e14i			2.13043i
$701$	−8.36705e13			−0.494290			−0.247145	−	0.968978i	$-0.579492\pi$
$701$	−8.36705e13			−0.494290			−0.247145	+	0.968978i	$0.579492\pi$
$702$	1.87172e14			1.09788
$703$	−1.22061e13			−0.0710884
$704$	1.40016e13			0.0809680
$705$	4.06481e14			2.33397
$706$		−	3.68596e14i		−	2.10149i
$707$			3.04079e14i			1.72143i
$708$			3.40549e14i			1.91431i
$709$	1.75974e14			0.982241			0.491120	−	0.871092i	$-0.336587\pi$
$709$	1.75974e14			0.982241			0.491120	+	0.871092i	$0.336587\pi$
$710$		−	4.28898e14i		−	2.37718i
$711$	7.44267e13			0.409620
$712$	1.44155e13			0.0787823
$713$	1.03101e14			0.559522
$714$		−	1.08170e14i		−	0.582928i
$715$			2.77477e13i			0.148490i
$716$		−	2.83451e14i		−	1.50630i
$717$			2.52880e14i			1.33450i
$718$		−	2.49091e14i		−	1.30538i
$719$	−1.71319e14			−0.891583			−0.445792	−	0.895137i	$-0.647078\pi$
$719$	−1.71319e14			−0.891583			−0.445792	+	0.895137i	$0.647078\pi$
$720$			5.50750e14i			2.84637i
$721$			3.90818e13i			0.200585i
$722$		−	2.69957e14i		−	1.37597i
$723$	−3.51802e14			−1.78077
$724$	4.81547e13			0.242073
$725$		−	6.76549e14i		−	3.37761i
$726$	4.41355e14			2.18829
$727$		−	2.33883e14i		−	1.15167i	−0.817567	−	0.575833i	$-0.804678\pi$
$727$		−	2.33883e14i		−	1.15167i	0.817567	−	0.575833i	$-0.195322\pi$
$728$	3.05640e13			0.149470
$729$	3.35686e14			1.63040
$730$			4.27719e14i			2.06321i
$731$	−1.91737e13	−	3.76478e13i	−0.0918586	−	0.180365i
$732$	−5.41576e14			−2.57694
$733$		−	1.03433e14i		−	0.488809i	−0.969673	−	0.244405i	$-0.921407\pi$
$733$		−	1.03433e14i		−	0.488809i	0.969673	−	0.244405i	$-0.0785925\pi$
$734$			1.40428e14i			0.659133i
$735$	−4.01117e14			−1.86997
$736$			8.75855e13i			0.405549i
$737$	−2.00816e13			−0.0923551
$738$			3.62365e14i			1.65525i
$739$			1.10575e14i			0.501690i	0.968027	+	0.250845i	$0.0807084\pi$
$739$			1.10575e14i			0.501690i	−0.968027	+	0.250845i	$0.919292\pi$
$740$	4.23975e14			1.91065
$741$	1.77442e13			0.0794266
$742$	−3.46917e14			−1.54243
$743$			6.99827e13i			0.309063i	0.987988	+	0.154531i	$0.0493867\pi$
$743$			6.99827e13i			0.309063i	−0.987988	+	0.154531i	$0.950613\pi$
$744$	−8.99730e13			−0.394682
$745$	−2.32176e14			−1.01166
$746$	−1.40375e14			−0.607567
$747$	5.86968e14			2.52355
$748$	−4.32845e12			−0.0184852
$749$			2.56267e14i			1.08713i
$750$			7.08594e14i			2.98601i
$751$			2.78846e14i			1.16725i	0.812023	+	0.583626i	$0.198367\pi$
$751$			2.78846e14i			1.16725i	−0.812023	+	0.583626i	$0.801633\pi$
$752$	−2.27119e14			−0.944419
$753$		−	6.87527e14i		−	2.83998i
$754$	5.52794e14			2.26833
$755$	−2.46051e14			−1.00297
$756$	2.63613e14			1.06748
$757$		−	2.25706e14i		−	0.907955i	−0.891013	−	0.453977i	$-0.850005\pi$
$757$		−	2.25706e14i		−	0.907955i	0.891013	−	0.453977i	$-0.149995\pi$
$758$		−	1.82548e14i		−	0.729511i
$759$		−	1.20631e13i		−	0.0478907i
$760$			3.12962e12i			0.0123431i
$761$		−	9.98414e13i		−	0.391190i	−0.980685	−	0.195595i	$-0.937336\pi$
$761$		−	9.98414e13i		−	0.391190i	0.980685	−	0.195595i	$-0.0626638\pi$
$762$	6.81084e13			0.265110
$763$		−	1.58275e14i		−	0.612055i
$764$		−	4.31786e14i		−	1.65883i
$765$		−	1.39041e14i		−	0.530685i
$766$	3.89660e14			1.47755
$767$	3.07948e14			1.16011
$768$		−	4.97053e14i		−	1.86036i
$769$	−2.32066e14			−0.862940			−0.431470	−	0.902127i	$-0.642005\pi$
$769$	−2.32066e14			−0.862940			−0.431470	+	0.902127i	$0.642005\pi$
$770$			8.22428e13i			0.303840i
$771$	3.38017e14			1.24070
$772$	1.12689e14			0.410956
$773$			8.76719e13i			0.317660i	0.987306	+	0.158830i	$0.0507722\pi$
$773$			8.76719e13i			0.317660i	−0.987306	+	0.158830i	$0.949228\pi$
$774$	5.34764e14	−	2.72351e14i	1.92512	−	0.980448i
$775$	−9.53139e14			−3.40916
$776$		−	5.74131e13i		−	0.204034i
$777$			7.44329e14i			2.62821i
$778$	4.20056e14			1.47370
$779$			1.24035e13i			0.0432372i
$780$	−6.16341e14			−2.13476
$781$		−	3.01305e13i		−	0.103693i
$782$		−	2.42221e13i		−	0.0828280i
$783$	−4.98092e14			−1.69239
$784$	2.24122e14			0.756666
$785$	6.76864e14			2.27067
$786$		−	3.98828e14i		−	1.32945i
$787$	−3.41632e14			−1.13158			−0.565789	−	0.824550i	$-0.691428\pi$
$787$	−3.41632e14			−1.13158			−0.565789	+	0.824550i	$0.691428\pi$
$788$	−2.58260e14			−0.850012
$789$	1.09438e14			0.357917
$790$	−1.86223e14			−0.605200
$791$	1.12369e14			0.362881
$792$			6.42311e12i			0.0206120i
$793$			4.89731e14i			1.56168i
$794$			8.75101e13i			0.277304i
$795$	−7.30846e14			−2.30139
$796$			3.96540e14i			1.24086i
$797$	1.20344e14			0.374226			0.187113	−	0.982338i	$-0.440087\pi$
$797$	1.20344e14			0.374226			0.187113	+	0.982338i	$0.440087\pi$
$798$	5.25929e13			0.162522
$799$	5.73381e13			0.176080
$800$		−	8.09699e14i		−	2.47101i
$801$		−	3.11388e14i		−	0.944364i
$802$		−	2.93929e14i		−	0.885871i
$803$			3.00477e13i			0.0899980i
$804$		−	4.46059e14i		−	1.32774i
$805$	−2.18692e14			−0.646926
$806$		−	7.78790e14i		−	2.28952i
$807$		−	7.61966e14i		−	2.22622i
$808$		−	5.94209e13i		−	0.172537i
$809$	−4.37310e13			−0.126196			−0.0630982	−	0.998007i	$-0.520098\pi$
$809$	−4.37310e13			−0.126196			−0.0630982	+	0.998007i	$0.520098\pi$
$810$	−9.31808e13			−0.267240
$811$			4.31250e14i			1.22921i	0.788836	+	0.614604i	$0.210684\pi$
$811$			4.31250e14i			1.22921i	−0.788836	+	0.614604i	$0.789316\pi$
$812$	7.78558e14			2.20552
$813$			3.72490e14i			1.04873i
$814$	6.26808e13			0.175393
$815$	2.33481e14			0.649327
$816$			1.27327e14i			0.351940i
$817$	1.83046e13	−	9.32240e12i	0.0502864	−	0.0256105i
$818$	−1.03086e14			−0.281471
$819$		−	6.60213e14i		−	1.79170i
$820$		−	4.30833e14i		−	1.16209i
$821$	−1.52394e14			−0.408556			−0.204278	−	0.978913i	$-0.565485\pi$
$821$	−1.52394e14			−0.408556			−0.204278	+	0.978913i	$0.565485\pi$
$822$			5.71906e14i			1.52393i
$823$	3.56707e14			0.944742			0.472371	−	0.881400i	$-0.343398\pi$
$823$	3.56707e14			0.944742			0.472371	+	0.881400i	$0.343398\pi$
$824$		−	7.63708e12i		−	0.0201044i
$825$			1.11520e14i			0.291798i
$826$	9.12741e14			2.37382
$827$	−2.45422e14			−0.634433			−0.317216	−	0.948353i	$-0.602748\pi$
$827$	−2.45422e14			−0.634433			−0.317216	+	0.948353i	$0.602748\pi$
$828$	1.63490e14			0.420087
$829$			3.39102e14i			0.866080i	0.901375	+	0.433040i	$0.142559\pi$
$829$			3.39102e14i			0.866080i	−0.901375	+	0.433040i	$0.857441\pi$
$830$	−1.46866e15			−3.72846
$831$	−3.92170e14			−0.989623
$832$	2.81234e14			0.705426
$833$	−5.65814e13			−0.141075
$834$	−6.48403e14			−1.60700
$835$		−	4.85873e13i		−	0.119699i
$836$		−	2.10452e12i		−	0.00515374i
$837$			7.01725e14i			1.70820i
$838$	2.27963e14			0.551626
$839$			2.23442e14i			0.537470i	0.963214	+	0.268735i	$0.0866056\pi$
$839$			2.23442e14i			0.537470i	−0.963214	+	0.268735i	$0.913394\pi$
$840$	1.90845e14			0.456336
$841$	−1.05036e15			−2.49666
$842$	−8.23658e14			−1.94619
$843$			6.38313e14i			1.49933i
$844$			1.58172e14i			0.369333i
$845$		−	1.64348e14i		−	0.381487i
$846$			8.14453e14i			1.87938i
$847$		−	5.62100e14i		−	1.28943i
$848$	4.08356e14			0.931236
$849$			1.19551e15i			2.71029i
$850$			2.23925e14i			0.504670i
$851$			1.66675e14i			0.373441i
$852$	6.69267e14			1.49074
$853$	8.56693e14			1.89706			0.948528	−	0.316693i	$-0.102572\pi$
$853$	8.56693e14			1.89706			0.948528	+	0.316693i	$0.102572\pi$
$854$			1.45154e15i			3.19550i
$855$	6.76028e13			0.147957
$856$		−	5.00777e13i		−	0.108962i
$857$	−2.03304e13			−0.0439786			−0.0219893	−	0.999758i	$-0.507000\pi$
$857$	−2.03304e13			−0.0439786			−0.0219893	+	0.999758i	$0.507000\pi$
$858$	−9.11204e13			−0.195965
$859$		−	8.96916e14i		−	1.91772i	−0.283875	−	0.958861i	$-0.591620\pi$
$859$		−	8.96916e14i		−	1.91772i	0.283875	−	0.958861i	$-0.408380\pi$
$860$	−6.35807e14	+	3.23811e14i	−1.35155	+	0.688335i
$861$	7.56370e14			1.59852
$862$		−	2.71522e14i		−	0.570517i
$863$			5.40883e13i			0.112992i	0.998403	+	0.0564962i	$0.0179929\pi$
$863$			5.40883e13i			0.112992i	−0.998403	+	0.0564962i	$0.982007\pi$
$864$	−5.96121e14			−1.23813
$865$		−	4.59470e14i		−	0.948805i
$866$	1.44210e14			0.296078
$867$			7.52454e14i			1.53598i
$868$		−	1.09685e15i		−	2.22612i
$869$	−1.30824e13			−0.0263990
$870$	3.45171e15			6.92528
$871$	−4.03357e14			−0.804635
$872$			3.09290e13i			0.0613456i
$873$	−1.24018e15			−2.44575
$874$	1.17769e13			0.0230927
$875$	9.02449e14			1.75947
$876$	−6.67427e14			−1.29385
$877$	9.25212e14			1.78338			0.891688	−	0.452650i	$-0.149521\pi$
$877$	9.25212e14			1.78338			0.891688	+	0.452650i	$0.149521\pi$
$878$			8.35530e14i			1.60136i
$879$		−	1.08640e15i		−	2.07036i
$880$		−	9.68081e13i		−	0.183442i
$881$	6.38962e14			1.20391			0.601957	−	0.798528i	$-0.294388\pi$
$881$	6.38962e14			1.20391			0.601957	+	0.798528i	$0.294388\pi$
$882$		−	8.03704e14i		−	1.50575i
$883$	3.36107e14			0.626144			0.313072	−	0.949729i	$-0.398642\pi$
$883$	3.36107e14			0.626144			0.313072	+	0.949729i	$0.398642\pi$
$884$	−8.69408e13			−0.161051
$885$	1.92286e15			3.54186
$886$			6.40144e14i			1.17249i
$887$		−	4.56881e14i		−	0.832118i	−0.909338	−	0.416059i	$-0.863411\pi$
$887$		−	4.56881e14i		−	0.832118i	0.909338	−	0.416059i	$-0.136589\pi$
$888$		−	1.45451e14i		−	0.263422i
$889$		−	8.67413e13i		−	0.156213i
$890$			7.79126e14i			1.39527i
$891$	−6.54603e12			−0.0116571
$892$			4.97792e14i			0.881503i
$893$			2.78782e13i			0.0490916i
$894$		−	7.62438e14i		−	1.33511i
$895$	−1.60046e15			−2.78696
$896$	−1.95565e14			−0.338650
$897$		−	2.42299e14i		−	0.417243i
$898$	−1.39277e15			−2.38505
$899$			2.07248e15i			3.52933i
$900$	−1.51141e15			−2.55959
$901$	−1.03093e14			−0.173622
$902$		−	6.36947e13i		−	0.106677i
$903$	−5.68483e14	−	1.11622e15i	−0.946844	−	1.85914i
$904$	−2.19583e13			−0.0363711
$905$		−	2.71899e14i		−	0.447883i
$906$		−	8.08002e14i		−	1.32365i
$907$	1.38257e14			0.225242			0.112621	−	0.993638i	$-0.464075\pi$
$907$	1.38257e14			0.225242			0.112621	+	0.993638i	$0.464075\pi$
$908$		−	1.40439e14i		−	0.227540i
$909$	−1.28355e15			−2.06820
$910$			1.65192e15i			2.64717i
$911$		−	2.12223e13i		−	0.0338221i	−0.999857	−	0.0169111i	$-0.994617\pi$
$911$		−	2.12223e13i		−	0.0338221i	0.999857	−	0.0169111i	$-0.00538321\pi$
$912$	−6.19072e13			−0.0981221
$913$	−1.03174e14			−0.162636
$914$	−1.38627e14			−0.217329
$915$			3.05793e15i			4.76785i
$916$	3.80830e14			0.590546
$917$	−5.07938e14			−0.783365
$918$	1.64859e14			0.252872
$919$	−2.66977e14			−0.407283			−0.203642	−	0.979046i	$-0.565278\pi$
$919$	−2.66977e14			−0.407283			−0.203642	+	0.979046i	$0.565278\pi$
$920$	4.27352e13			0.0648406
$921$		−	1.91100e14i		−	0.288378i
$922$			7.54062e14i			1.13176i
$923$		−	6.05197e14i		−	0.903417i
$924$	−1.28334e14			−0.190539
$925$		−	1.54085e15i		−	2.27537i
$926$	−7.79660e14			−1.14512
$927$	−1.64968e14			−0.240992
$928$	−1.76059e15			−2.55810
$929$		−	3.15131e14i		−	0.455421i	−0.973729	−	0.227710i	$-0.926876\pi$
$929$		−	3.15131e14i		−	0.455421i	0.973729	−	0.227710i	$-0.0731240\pi$
$930$		−	4.86285e15i		−	6.98998i
$931$		−	2.75103e13i		−	0.0393320i
$932$			9.58080e14i			1.36245i
$933$			4.85120e14i			0.686185i
$934$	−1.34249e15			−1.88876
$935$			2.44400e13i			0.0342013i
$936$			1.29014e14i			0.179580i
$937$			8.58525e14i			1.18865i	0.804224	+	0.594326i	$0.202581\pi$
$937$			8.58525e14i			1.18865i	−0.804224	+	0.594326i	$0.797419\pi$
$938$	−1.19553e15			−1.64644
$939$	1.95742e15			2.68136
$940$		−	9.68342e14i		−	1.31944i
$941$	1.09478e15			1.48381			0.741906	−	0.670504i	$-0.233922\pi$
$941$	1.09478e15			1.48381			0.741906	+	0.670504i	$0.233922\pi$
$942$			2.22274e15i			2.99664i
$943$	1.69371e14			0.227133
$944$	−1.07439e15			−1.43318
$945$		−	1.48846e15i		−	1.97505i
$946$	−9.39982e13	+	4.78725e13i	−0.124069	+	0.0631875i
$947$	1.16773e15			1.53317			0.766587	−	0.642140i	$-0.221953\pi$
$947$	1.16773e15			1.53317			0.766587	+	0.642140i	$0.221953\pi$
$948$		−	2.90589e14i		−	0.379523i
$949$			6.03534e14i			0.784098i
$950$	−1.08874e14			−0.140704
$951$			9.00381e14i			1.15751i
$952$	2.69206e13			0.0344270
$953$		−	1.06155e15i		−	1.35044i	−0.737615	−	0.675222i	$-0.764048\pi$
$953$		−	1.06155e15i		−	1.35044i	0.737615	−	0.675222i	$-0.235952\pi$
$954$		−	1.46437e15i		−	1.85314i
$955$	−2.43802e15			−3.06917
$956$	6.02423e14			0.754419
$957$	2.42485e14			0.302083
$958$		−	1.95412e15i		−	2.42172i
$959$	7.28366e14			0.897960
$960$	1.75606e15			2.15369
$961$	2.10013e15			2.56230
$962$	1.25900e15			1.52809
$963$	−1.08173e15			−1.30613
$964$			8.38082e14i			1.00670i
$965$		−	6.36282e14i		−	0.760350i
$966$		−	7.18161e14i		−	0.853761i
$967$	3.84023e14			0.454176			0.227088	−	0.973874i	$-0.427079\pi$
$967$	3.84023e14			0.454176			0.227088	+	0.973874i	$0.427079\pi$
$968$			1.09841e14i			0.129238i
$969$	1.56290e13			0.0182941
$970$	3.10305e15			3.61352
$971$	9.65918e14			1.11904			0.559518	−	0.828818i	$-0.310986\pi$
$971$	9.65918e14			1.11904			0.559518	+	0.828818i	$0.310986\pi$
$972$		−	8.56374e14i		−	0.987034i
$973$			8.25792e14i			0.946905i
$974$			6.93833e14i			0.791517i
$975$			2.23997e15i			2.54226i
$976$		−	1.70860e15i		−	1.92927i
$977$	−4.53688e13			−0.0509664			−0.0254832	−	0.999675i	$-0.508112\pi$
$977$	−4.53688e13			−0.0509664			−0.0254832	+	0.999675i	$0.508112\pi$
$978$			7.66724e14i			0.856929i
$979$			5.47343e13i			0.0608619i
$980$			9.55562e14i			1.05713i
$981$	6.68096e14			0.735350
$982$	−6.83860e14			−0.748876
$983$		−	4.33875e14i		−	0.472712i	−0.971666	−	0.236356i	$-0.924047\pi$
$983$		−	4.33875e14i		−	0.472712i	0.971666	−	0.236356i	$-0.0759532\pi$
$984$	−1.47804e14			−0.160218
$985$			1.45823e15i			1.57269i
$986$	4.86896e14			0.522459
$987$	1.70002e15			1.81496
$988$		−	4.22712e13i		−	0.0449014i
$989$	−1.27298e14	−	2.49951e14i	−0.134537	−	0.264164i
$990$	−3.47155e14			−0.365046
$991$			5.53585e14i			0.579183i	0.957150	+	0.289591i	$0.0935194\pi$
$991$			5.53585e14i			0.579183i	−0.957150	+	0.289591i	$0.906481\pi$
$992$			2.48036e15i			2.58200i
$993$	−1.97189e15			−2.04238
$994$		−	1.79377e15i		−	1.84857i
$995$	2.23900e15			2.29583
$996$		−	2.29174e15i		−	2.33813i
$997$		−	1.16710e14i		−	0.118476i	−0.998244	−	0.0592381i	$-0.981133\pi$
$997$		−	1.16710e14i		−	0.118476i	0.998244	−	0.0592381i	$-0.0188671\pi$
$998$	1.15512e15			1.16674
$999$	−1.13442e15			−1.14011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.6	✓	34
43.42	odd	2	inner	43.11.b.b.42.29	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.6	✓	34	1.1	even	1	trivial
43.11.b.b.42.29	yes	34	43.42	odd	2	inner

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-44.1717i q^{2} -389.187i q^{3} -927.142 q^{4} +5234.98i q^{5} -17191.1 q^{6} +21894.1i q^{7} -4278.39i q^{8} -92417.4 q^{9} +O(q^{10})\)	\(q-44.1717i q^{2} -389.187i q^{3} -927.142 q^{4} +5234.98i q^{5} -17191.1 q^{6} +21894.1i q^{7} -4278.39i q^{8} -92417.4 q^{9} +231238. q^{10} +16244.7 q^{11} +360831. i q^{12} +326289. q^{13} +967102. q^{14} +2.03738e6 q^{15} -1.13838e6 q^{16} +287393. q^{17} +4.08224e6i q^{18} +139732. i q^{19} -4.85357e6i q^{20} +8.52091e6 q^{21} -717555. i q^{22} +1.90806e6 q^{23} -1.66509e6 q^{24} -1.76393e7 q^{25} -1.44127e7i q^{26} +1.29865e7i q^{27} -2.02990e7i q^{28} +3.83545e7i q^{29} -8.99948e7i q^{30} +5.40348e7 q^{31} +4.59030e7i q^{32} -6.32221e6i q^{33} -1.26946e7i q^{34} -1.14615e8 q^{35} +8.56840e7 q^{36} +8.73532e7i q^{37} +6.17221e6 q^{38} -1.26987e8i q^{39} +2.23973e7 q^{40} +8.87662e7 q^{41} -3.76384e8i q^{42} +(-6.67162e7 - 1.30998e8i) q^{43} -1.50611e7 q^{44} -4.83803e8i q^{45} -8.42821e7i q^{46} +1.99511e8 q^{47} +4.43041e8i q^{48} -1.96878e8 q^{49} +7.79160e8i q^{50} -1.11849e8i q^{51} -3.02516e8 q^{52} -3.58718e8 q^{53} +5.73638e8 q^{54} +8.50405e7i q^{55} +9.36717e7 q^{56} +5.43819e7 q^{57} +1.69419e9 q^{58} +9.43790e8 q^{59} -1.88894e9 q^{60} +1.50091e9i q^{61} -2.38681e9i q^{62} -2.02340e9i q^{63} +8.61918e8 q^{64} +1.70811e9i q^{65} -2.79263e8 q^{66} -1.23620e9 q^{67} -2.66454e8 q^{68} -7.42590e8i q^{69} +5.06276e9i q^{70} -1.85479e9i q^{71} +3.95398e8i q^{72} +1.84969e9i q^{73} +3.85854e9 q^{74} +6.86500e9i q^{75} -1.29552e8i q^{76} +3.55663e8i q^{77} -5.60925e9 q^{78} -8.05333e8 q^{79} -5.95938e9i q^{80} -4.02965e8 q^{81} -3.92096e9i q^{82} -6.35127e9 q^{83} -7.90010e9 q^{84} +1.50449e9i q^{85} +(-5.78640e9 + 2.94697e9i) q^{86} +1.49271e10 q^{87} -6.95010e7i q^{88} +3.36937e9i q^{89} -2.13704e10 q^{90} +7.14381e9i q^{91} -1.76904e9 q^{92} -2.10296e10i q^{93} -8.81277e9i q^{94} -7.31495e8 q^{95} +1.78649e10 q^{96} +1.34193e10 q^{97} +8.69646e9i q^{98} -1.50129e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9} - 254122 q^{10} - 218200 q^{11} - 191008 q^{13} - 1380228 q^{14} - 512732 q^{15} + 2224308 q^{16} - 1070678 q^{17} + 17857352 q^{21} + 8915254 q^{23} - 39666730 q^{24} - 82938284 q^{25} - 55042410 q^{31} - 179227232 q^{35} + 394381042 q^{36} + 709061882 q^{38} + 433255366 q^{40} + 80370626 q^{41} + 1585062 q^{43} + 324477888 q^{44} - 544910502 q^{47} - 2479345922 q^{49} - 987059452 q^{52} - 915886820 q^{53} - 297150836 q^{54} + 2172449592 q^{56} - 2398069428 q^{57} + 930519014 q^{58} + 3394816764 q^{59} - 5474941192 q^{60} + 2925325476 q^{64} + 455136192 q^{66} + 3405920388 q^{67} + 664008226 q^{68} + 16264108918 q^{74} - 17800086268 q^{78} - 13853150858 q^{79} + 20444701546 q^{81} + 113867236 q^{83} - 30401949428 q^{84} + 19291204884 q^{86} - 5221634730 q^{87} - 6984391876 q^{90} + 41423783058 q^{92} + 4107406010 q^{95} + 33148445474 q^{96} + 15795117154 q^{97} + 1345877600 q^{99}+O(q^{100}) \) 34 * q - 16156 * q^4 + 12798 * q^6 - 790716 * q^9 - 254122 * q^10 - 218200 * q^11 - 191008 * q^13 - 1380228 * q^14 - 512732 * q^15 + 2224308 * q^16 - 1070678 * q^17 + 17857352 * q^21 + 8915254 * q^23 - 39666730 * q^24 - 82938284 * q^25 - 55042410 * q^31 - 179227232 * q^35 + 394381042 * q^36 + 709061882 * q^38 + 433255366 * q^40 + 80370626 * q^41 + 1585062 * q^43 + 324477888 * q^44 - 544910502 * q^47 - 2479345922 * q^49 - 987059452 * q^52 - 915886820 * q^53 - 297150836 * q^54 + 2172449592 * q^56 - 2398069428 * q^57 + 930519014 * q^58 + 3394816764 * q^59 - 5474941192 * q^60 + 2925325476 * q^64 + 455136192 * q^66 + 3405920388 * q^67 + 664008226 * q^68 + 16264108918 * q^74 - 17800086268 * q^78 - 13853150858 * q^79 + 20444701546 * q^81 + 113867236 * q^83 - 30401949428 * q^84 + 19291204884 * q^86 - 5221634730 * q^87 - 6984391876 * q^90 + 41423783058 * q^92 + 4107406010 * q^95 + 33148445474 * q^96 + 15795117154 * q^97 + 1345877600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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