LMFDB - Embedded newform 43.11.b.b.42.19

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			42.19
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.51570i q^{2} +292.852i q^{3} +993.577 q^{4} -3204.10i q^{5} -1615.28 q^{6} +16511.8i q^{7} +11128.3i q^{8} -26713.4 q^{9} +O(q^{10})$	\(q+5.51570i q^{2} +292.852i q^{3} +993.577 q^{4} -3204.10i q^{5} -1615.28 q^{6} +16511.8i q^{7} +11128.3i q^{8} -26713.4 q^{9} +17672.9 q^{10} +31573.6 q^{11} +290971. i q^{12} +240071. q^{13} -91074.0 q^{14} +938328. q^{15} +956042. q^{16} +1.02720e6 q^{17} -147343. i q^{18} +1.67184e6i q^{19} -3.18352e6i q^{20} -4.83551e6 q^{21} +174150. i q^{22} -6.08630e6 q^{23} -3.25896e6 q^{24} -500648. q^{25} +1.32416e6i q^{26} +9.46955e6i q^{27} +1.64057e7i q^{28} +1.23237e7i q^{29} +5.17554e6i q^{30} -5.08085e6 q^{31} +1.66687e7i q^{32} +9.24639e6i q^{33} +5.66573e6i q^{34} +5.29054e7 q^{35} -2.65418e7 q^{36} +2.30677e7i q^{37} -9.22138e6 q^{38} +7.03054e7i q^{39} +3.56564e7 q^{40} -7.74946e7 q^{41} -2.66712e7i q^{42} +(2.90004e7 + 1.44120e8i) q^{43} +3.13708e7 q^{44} +8.55925e7i q^{45} -3.35702e7i q^{46} -2.22341e8 q^{47} +2.79979e8i q^{48} +9.83663e6 q^{49} -2.76142e6i q^{50} +3.00818e8i q^{51} +2.38529e8 q^{52} -1.87870e8 q^{53} -5.22312e7 q^{54} -1.01165e8i q^{55} -1.83749e8 q^{56} -4.89603e8 q^{57} -6.79736e7 q^{58} -5.73654e8 q^{59} +9.32302e8 q^{60} +4.87066e7i q^{61} -2.80245e7i q^{62} -4.41086e8i q^{63} +8.87048e8 q^{64} -7.69213e8i q^{65} -5.10003e7 q^{66} +6.11603e8 q^{67} +1.02060e9 q^{68} -1.78239e9i q^{69} +2.91810e8i q^{70} -2.16541e9i q^{71} -2.97276e8i q^{72} +5.90470e8i q^{73} -1.27234e8 q^{74} -1.46616e8i q^{75} +1.66110e9i q^{76} +5.21336e8i q^{77} -3.87783e8 q^{78} +3.70326e9 q^{79} -3.06326e9i q^{80} -4.35058e9 q^{81} -4.27437e8i q^{82} +4.86372e9 q^{83} -4.80445e9 q^{84} -3.29126e9i q^{85} +(-7.94920e8 + 1.59958e8i) q^{86} -3.60901e9 q^{87} +3.51362e8i q^{88} -6.61537e9i q^{89} -4.72102e8 q^{90} +3.96400e9i q^{91} -6.04721e9 q^{92} -1.48794e9i q^{93} -1.22637e9i q^{94} +5.35675e9 q^{95} -4.88146e9 q^{96} +3.91240e9 q^{97} +5.42559e7i q^{98} -8.43438e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			5.51570i			0.172366i	0.996279	+	0.0861828i	$0.0274669\pi$
$2$			5.51570i			0.172366i	−0.996279	+	0.0861828i	$0.972533\pi$
$3$			292.852i			1.20515i	0.798061	+	0.602577i	$0.205859\pi$
$3$			292.852i			1.20515i	−0.798061	+	0.602577i	$0.794141\pi$
$4$	993.577			0.970290
$5$		−	3204.10i		−	1.02531i	−0.858594	−	0.512656i	$-0.828661\pi$
$5$		−	3204.10i		−	1.02531i	0.858594	−	0.512656i	$-0.171339\pi$
$6$	−1615.28			−0.207727
$7$			16511.8i			0.982434i	0.871037	+	0.491217i	$0.163448\pi$
$7$			16511.8i			0.982434i	−0.871037	+	0.491217i	$0.836552\pi$
$8$			11128.3i			0.339610i
$9$	−26713.4			−0.452394
$10$	17672.9			0.176729
$11$	31573.6			0.196047			0.0980235	−	0.995184i	$-0.468748\pi$
$11$	31573.6			0.196047			0.0980235	+	0.995184i	$0.468748\pi$
$12$			290971.i			1.16935i
$13$	240071.			0.646582			0.323291	−	0.946300i	$-0.395211\pi$
$13$	240071.			0.646582			0.323291	+	0.946300i	$0.395211\pi$
$14$	−91074.0			−0.169338
$15$	938328.			1.23566
$16$	956042.			0.911753
$17$	1.02720e6			0.723454			0.361727	−	0.932284i	$-0.382187\pi$
$17$	1.02720e6			0.723454			0.361727	+	0.932284i	$0.382187\pi$
$18$		−	147343.i		−	0.0779771i
$19$			1.67184e6i			0.675192i	0.941291	+	0.337596i	$0.109614\pi$
$19$			1.67184e6i			0.675192i	−0.941291	+	0.337596i	$0.890386\pi$
$20$		−	3.18352e6i		−	0.994851i
$21$	−4.83551e6			−1.18398
$22$			174150.i			0.0337918i
$23$	−6.08630e6			−0.945615			−0.472807	−	0.881166i	$-0.656759\pi$
$23$	−6.08630e6			−0.945615			−0.472807	+	0.881166i	$0.656759\pi$
$24$	−3.25896e6			−0.409282
$25$	−500648.			−0.0512663
$26$			1.32416e6i			0.111448i
$27$			9.46955e6i			0.659949i
$28$			1.64057e7i			0.953246i
$29$			1.23237e7i			0.600828i	0.953809	+	0.300414i	$0.0971248\pi$
$29$			1.23237e7i			0.600828i	−0.953809	+	0.300414i	$0.902875\pi$
$30$			5.17554e6i			0.212985i
$31$	−5.08085e6			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$31$	−5.08085e6			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$32$			1.66687e7i			0.496765i
$33$			9.24639e6i			0.236267i
$34$			5.66573e6i			0.124699i
$35$	5.29054e7			1.00730
$36$	−2.65418e7			−0.438953
$37$			2.30677e7i			0.332656i	0.986071	+	0.166328i	$0.0531910\pi$
$37$			2.30677e7i			0.332656i	−0.986071	+	0.166328i	$0.946809\pi$
$38$	−9.22138e6			−0.116380
$39$			7.03054e7i			0.779230i
$40$	3.56564e7			0.348207
$41$	−7.74946e7			−0.668886			−0.334443	−	0.942416i	$-0.608548\pi$
$41$	−7.74946e7			−0.668886			−0.334443	+	0.942416i	$0.608548\pi$
$42$		−	2.66712e7i		−	0.204078i
$43$	2.90004e7	+	1.44120e8i	0.197270	+	0.980349i
$43$	2.90004e7	+	1.44120e8i	0.197270	+	0.980349i
$44$	3.13708e7			0.190223
$45$			8.55925e7i			0.463845i
$46$		−	3.35702e7i		−	0.162991i
$47$	−2.22341e8			−0.969460			−0.484730	−	0.874664i	$-0.661082\pi$
$47$	−2.22341e8			−0.969460			−0.484730	+	0.874664i	$0.661082\pi$
$48$			2.79979e8i			1.09880i
$49$	9.83663e6			0.0348230
$50$		−	2.76142e6i		−	0.00883655i
$51$			3.00818e8i			0.871873i
$52$	2.38529e8			0.627372
$53$	−1.87870e8			−0.449240			−0.224620	−	0.974446i	$-0.572114\pi$
$53$	−1.87870e8			−0.449240			−0.224620	+	0.974446i	$0.572114\pi$
$54$	−5.22312e7			−0.113753
$55$		−	1.01165e8i		−	0.201010i
$56$	−1.83749e8			−0.333645
$57$	−4.89603e8			−0.813710
$58$	−6.79736e7			−0.103562
$59$	−5.73654e8			−0.802398			−0.401199	−	0.915991i	$-0.631406\pi$
$59$	−5.73654e8			−0.802398			−0.401199	+	0.915991i	$0.631406\pi$
$60$	9.32302e8			1.19895
$61$			4.87066e7i			0.0576685i	0.999584	+	0.0288343i	$0.00917950\pi$
$61$			4.87066e7i			0.0576685i	−0.999584	+	0.0288343i	$0.990820\pi$
$62$		−	2.80245e7i		−	0.0305900i
$63$		−	4.41086e8i		−	0.444447i
$64$	8.87048e8			0.826128
$65$		−	7.69213e8i		−	0.662948i
$66$	−5.10003e7			−0.0407243
$67$	6.11603e8			0.452997			0.226499	−	0.974012i	$-0.427272\pi$
$67$	6.11603e8			0.452997			0.226499	+	0.974012i	$0.427272\pi$
$68$	1.02060e9			0.701960
$69$		−	1.78239e9i		−	1.13961i
$70$			2.91810e8i			0.173624i
$71$		−	2.16541e9i		−	1.20019i	−0.799930	−	0.600094i	$-0.795130\pi$
$71$		−	2.16541e9i		−	1.20019i	0.799930	−	0.600094i	$-0.204870\pi$
$72$		−	2.97276e8i		−	0.153638i
$73$			5.90470e8i			0.284828i	0.989807	+	0.142414i	$0.0454865\pi$
$73$			5.90470e8i			0.284828i	−0.989807	+	0.142414i	$0.954514\pi$
$74$	−1.27234e8			−0.0573384
$75$		−	1.46616e8i		−	0.0617838i
$76$			1.66110e9i			0.655132i
$77$			5.21336e8i			0.192603i
$78$	−3.87783e8			−0.134312
$79$	3.70326e9			1.20351			0.601753	−	0.798682i	$-0.294469\pi$
$79$	3.70326e9			1.20351			0.601753	+	0.798682i	$0.294469\pi$
$80$		−	3.06326e9i		−	0.934832i
$81$	−4.35058e9			−1.24773
$82$		−	4.27437e8i		−	0.115293i
$83$	4.86372e9			1.23475			0.617374	−	0.786670i	$-0.288196\pi$
$83$	4.86372e9			1.23475			0.617374	+	0.786670i	$0.288196\pi$
$84$	−4.80445e9			−1.14881
$85$		−	3.29126e9i		−	0.741767i
$86$	−7.94920e8	+	1.59958e8i	−0.168978	+	0.0340026i
$87$	−3.60901e9			−0.724089
$88$			3.51362e8i			0.0665796i
$89$		−	6.61537e9i		−	1.18469i	−0.805685	−	0.592345i	$-0.798202\pi$
$89$		−	6.61537e9i		−	1.18469i	0.805685	−	0.592345i	$-0.201798\pi$
$90$	−4.72102e8			−0.0799510
$91$			3.96400e9i			0.635224i
$92$	−6.04721e9			−0.917521
$93$		−	1.48794e9i		−	0.213880i
$94$		−	1.22637e9i		−	0.167102i
$95$	5.35675e9			0.692283
$96$	−4.88146e9			−0.598678
$97$	3.91240e9			0.455601			0.227800	−	0.973708i	$-0.426847\pi$
$97$	3.91240e9			0.455601			0.227800	+	0.973708i	$0.426847\pi$
$98$			5.42559e7i			0.00600228i
$99$	−8.43438e8			−0.0886905
$100$	−4.97432e8			−0.0497432
$101$	3.04443e9			0.289667			0.144834	−	0.989456i	$-0.453735\pi$
$101$	3.04443e9			0.289667			0.144834	+	0.989456i	$0.453735\pi$
$102$	−1.65922e9			−0.150281
$103$	1.78627e10			1.54085			0.770424	−	0.637532i	$-0.220045\pi$
$103$	1.78627e10			1.54085			0.770424	+	0.637532i	$0.220045\pi$
$104$			2.67160e9i			0.219586i
$105$			1.54935e10i			1.21395i
$106$		−	1.03624e9i		−	0.0774336i
$107$	2.44008e10			1.73974			0.869871	−	0.493279i	$-0.164202\pi$
$107$	2.44008e10			1.73974			0.869871	+	0.493279i	$0.164202\pi$
$108$			9.40873e9i			0.640342i
$109$	−1.37165e10			−0.891478			−0.445739	−	0.895163i	$-0.647059\pi$
$109$	−1.37165e10			−0.891478			−0.445739	+	0.895163i	$0.647059\pi$
$110$	5.57996e8			0.0346471
$111$	−6.75541e9			−0.400901
$112$			1.57860e10i			0.895737i
$113$			6.06915e9i			0.329409i	0.986343	+	0.164705i	$0.0526671\pi$
$113$			6.06915e9i			0.329409i	−0.986343	+	0.164705i	$0.947333\pi$
$114$		−	2.70050e9i		−	0.140256i
$115$			1.95011e10i			0.969551i
$116$			1.22445e10i			0.582977i
$117$	−6.41312e9			−0.292509
$118$		−	3.16410e9i		−	0.138306i
$119$			1.69609e10i			0.710746i
$120$			1.04420e10i			0.419642i
$121$	−2.49405e10			−0.961566
$122$	−2.68651e8			−0.00994007
$123$		−	2.26944e10i		−	0.806110i
$124$	−5.04822e9			−0.172199
$125$		−	2.96859e10i		−	0.972749i
$126$	2.43290e9			0.0766074
$127$	−3.99008e10			−1.20771			−0.603855	−	0.797094i	$-0.706369\pi$
$127$	−3.99008e10			−1.20771			−0.603855	+	0.797094i	$0.706369\pi$
$128$			2.19614e10i			0.639161i
$129$	−4.22057e10	+	8.49283e9i	−1.18147	+	0.237741i
$130$	4.24275e9			0.114269
$131$		−	4.31876e10i		−	1.11944i	−0.828680	−	0.559722i	$-0.810908\pi$
$131$		−	4.31876e10i		−	1.11944i	0.828680	−	0.559722i	$-0.189092\pi$
$132$			9.18700e9i			0.229247i
$133$	−2.76051e10			−0.663332
$134$			3.37342e9i			0.0780811i
$135$	3.03414e10			0.676654
$136$			1.14311e10i			0.245692i
$137$		−	7.78479e9i		−	0.161304i	−0.996742	−	0.0806518i	$-0.974300\pi$
$137$		−	7.78479e9i		−	0.161304i	0.996742	−	0.0806518i	$-0.0257002\pi$
$138$	9.83111e9			0.196430
$139$	7.64081e10			1.47253			0.736267	−	0.676691i	$-0.236587\pi$
$139$	7.64081e10			1.47253			0.736267	+	0.676691i	$0.236587\pi$
$140$	5.25656e10			0.977376
$141$		−	6.51130e10i		−	1.16835i
$142$	1.19438e10			0.206871
$143$	7.57991e9			0.126760
$144$	−2.55391e10			−0.412471
$145$	3.94863e10			0.616036
$146$	−3.25685e9			−0.0490946
$147$			2.88068e9i			0.0419670i
$148$			2.29195e10i			0.322772i
$149$			6.05305e10i			0.824220i	0.911134	+	0.412110i	$0.135208\pi$
$149$			6.05305e10i			0.824220i	−0.911134	+	0.412110i	$0.864792\pi$
$150$	8.08689e8			0.0106494
$151$		−	4.49709e10i		−	0.572858i	−0.958101	−	0.286429i	$-0.907532\pi$
$151$		−	4.49709e10i		−	0.572858i	0.958101	−	0.286429i	$-0.0924683\pi$
$152$	−1.86048e10			−0.229302
$153$	−2.74401e10			−0.327286
$154$	−2.87553e9			−0.0331982
$155$			1.62796e10i			0.181964i
$156$			6.98538e10i			0.756079i
$157$		−	1.13946e11i		−	1.19454i	−0.802040	−	0.597270i	$-0.796252\pi$
$157$		−	1.13946e11i		−	1.19454i	0.802040	−	0.597270i	$-0.203748\pi$
$158$			2.04260e10i			0.207443i
$159$		−	5.50182e10i		−	0.541403i
$160$	5.34081e10			0.509340
$161$		−	1.00496e11i		−	0.929004i
$162$		−	2.39965e10i		−	0.215066i
$163$		−	1.77980e11i		−	1.54680i	−0.633919	−	0.773399i	$-0.718555\pi$
$163$		−	1.77980e11i		−	1.54680i	0.633919	−	0.773399i	$-0.281445\pi$
$164$	−7.69968e10			−0.649013
$165$	2.96264e10			0.242247
$166$			2.68268e10i			0.212828i
$167$	1.04020e11			0.800820			0.400410	−	0.916336i	$-0.368868\pi$
$167$	1.04020e11			0.800820			0.400410	+	0.916336i	$0.368868\pi$
$168$		−	5.38112e10i		−	0.402093i
$169$	−8.02243e10			−0.581932
$170$	1.81536e10			0.127855
$171$		−	4.46606e10i		−	0.305453i
$172$	2.88141e10	+	1.43194e11i	0.191409	+	0.951223i
$173$	1.68634e10			0.108822			0.0544109	−	0.998519i	$-0.482672\pi$
$173$	1.68634e10			0.108822			0.0544109	+	0.998519i	$0.482672\pi$
$174$		−	1.99062e10i		−	0.124808i
$175$		−	8.26658e9i		−	0.0503658i
$176$	3.01857e10			0.178746
$177$		−	1.67996e11i		−	0.967012i
$178$	3.64884e10			0.204200
$179$			3.41248e10i			0.185697i	0.995680	+	0.0928484i	$0.0295972\pi$
$179$			3.41248e10i			0.185697i	−0.995680	+	0.0928484i	$0.970403\pi$
$180$			8.50427e10i			0.450064i
$181$	−2.40858e11			−1.23985			−0.619924	−	0.784662i	$-0.712836\pi$
$181$	−2.40858e11			−1.23985			−0.619924	+	0.784662i	$0.712836\pi$
$182$	−2.18642e10			−0.109491
$183$	−1.42638e10			−0.0694994
$184$		−	6.77305e10i		−	0.321140i
$185$	7.39111e10			0.341076
$186$	8.20702e9			0.0368656
$187$	3.24324e10			0.141831
$188$	−2.20913e11			−0.940658
$189$	−1.56359e11			−0.648357
$190$			2.95462e10i			0.119326i
$191$			1.22618e11i			0.482376i	0.970478	+	0.241188i	$0.0775370\pi$
$191$			1.22618e11i			0.482376i	−0.970478	+	0.241188i	$0.922463\pi$
$192$			2.59774e11i			0.995610i
$193$	3.39835e10			0.126906			0.0634530	−	0.997985i	$-0.479789\pi$
$193$	3.39835e10			0.126906			0.0634530	+	0.997985i	$0.479789\pi$
$194$			2.15796e10i			0.0785299i
$195$	2.25266e11			0.798954
$196$	9.77345e9			0.0337884
$197$	−4.27539e10			−0.144094			−0.0720468	−	0.997401i	$-0.522953\pi$
$197$	−4.27539e10			−0.144094			−0.0720468	+	0.997401i	$0.522953\pi$
$198$		−	4.65215e9i		−	0.0152872i
$199$			3.23926e11i			1.03796i	0.854787	+	0.518979i	$0.173688\pi$
$199$			3.23926e11i			1.03796i	−0.854787	+	0.518979i	$0.826312\pi$
$200$		−	5.57138e9i		−	0.0174106i
$201$			1.79109e11i			0.545931i
$202$			1.67922e10i			0.0499287i
$203$	−2.03486e11			−0.590274
$204$			2.98886e11i			0.845970i
$205$			2.48300e11i			0.685817i
$206$			9.85250e10i			0.265589i
$207$	1.62586e11			0.427790
$208$	2.29518e11			0.589523
$209$			5.27860e10i			0.132369i
$210$	−8.54573e10			−0.209244
$211$		−	2.63888e11i		−	0.630967i	−0.948931	−	0.315484i	$-0.897833\pi$
$211$		−	2.63888e11i		−	0.630967i	0.948931	−	0.315484i	$-0.102167\pi$
$212$	−1.86664e11			−0.435894
$213$	6.34146e11			1.44641
$214$			1.34587e11i			0.299872i
$215$	4.61774e11	−	9.29203e10i	1.00516	−	0.202264i
$216$	−1.05380e11			−0.224126
$217$		−	8.38939e10i		−	0.174354i
$218$		−	7.56560e10i		−	0.153660i
$219$	−1.72920e11			−0.343262
$220$		−	1.00515e11i		−	0.195038i
$221$	2.46602e11			0.467772
$222$		−	3.72608e10i		−	0.0691015i
$223$			5.14534e11i			0.933018i	0.884516	+	0.466509i	$0.154488\pi$
$223$			5.14534e11i			0.933018i	−0.884516	+	0.466509i	$0.845512\pi$
$224$	−2.75229e11			−0.488039
$225$	1.33740e10			0.0231926
$226$	−3.34756e10			−0.0567788
$227$		−	1.64053e11i		−	0.272179i	−0.990697	−	0.136089i	$-0.956547\pi$
$227$		−	1.64053e11i		−	0.272179i	0.990697	−	0.136089i	$-0.0434534\pi$
$228$	−4.86458e11			−0.789534
$229$	−1.09291e12			−1.73543			−0.867716	−	0.497060i	$-0.834413\pi$
$229$	−1.09291e12			−1.73543			−0.867716	+	0.497060i	$0.834413\pi$
$230$	−1.07562e11			−0.167117
$231$	−1.52674e11			−0.232117
$232$	−1.37142e11			−0.204047
$233$		−	1.28928e12i		−	1.87744i	−0.344680	−	0.938720i	$-0.612013\pi$
$233$		−	1.28928e12i		−	1.87744i	0.344680	−	0.938720i	$-0.387987\pi$
$234$		−	3.53728e10i		−	0.0504186i
$235$			7.12403e11i			0.994000i
$236$	−5.69969e11			−0.778559
$237$			1.08451e12i			1.45041i
$238$	−9.35513e10			−0.122508
$239$	5.08555e11			0.652152			0.326076	−	0.945344i	$-0.394273\pi$
$239$	5.08555e11			0.652152			0.326076	+	0.945344i	$0.394273\pi$
$240$	8.97082e11			1.12662
$241$		−	1.38456e12i		−	1.70304i	−0.524318	−	0.851522i	$-0.675680\pi$
$241$		−	1.38456e12i		−	1.70304i	0.524318	−	0.851522i	$-0.324320\pi$
$242$		−	1.37564e11i		−	0.165741i
$243$		−	7.14909e11i		−	0.843761i
$244$			4.83938e10i			0.0559552i
$245$		−	3.15176e10i		−	0.0357044i
$246$	1.25176e11			0.138946
$247$			4.01361e11i			0.436567i
$248$		−	5.65415e10i		−	0.0602711i
$249$			1.42435e12i			1.48806i
$250$	1.63739e11			0.167668
$251$	−4.19781e10			−0.0421361			−0.0210680	−	0.999778i	$-0.506707\pi$
$251$	−4.19781e10			−0.0421361			−0.0210680	+	0.999778i	$0.506707\pi$
$252$		−	4.38253e11i		−	0.431243i
$253$	−1.92166e11			−0.185385
$254$		−	2.20081e11i		−	0.208168i
$255$	9.63852e11			0.893943
$256$	7.87205e11			0.715958
$257$		−	5.14381e11i		−	0.458795i	−0.973333	−	0.229398i	$-0.926324\pi$
$257$		−	5.14381e11i		−	0.458795i	0.973333	−	0.229398i	$-0.0736756\pi$
$258$	−4.68439e10	−	2.32794e11i	−0.0409784	−	0.203645i
$259$	−3.80888e11			−0.326812
$260$		−	7.64272e11i		−	0.643252i
$261$		−	3.29207e11i		−	0.271811i
$262$	2.38210e11			0.192954
$263$		−	2.20947e12i		−	1.75594i	−0.478719	−	0.877968i	$-0.658899\pi$
$263$		−	2.20947e12i		−	1.75594i	0.478719	−	0.877968i	$-0.341101\pi$
$264$	−1.02897e11			−0.0802386
$265$			6.01956e11i			0.460612i
$266$		−	1.52261e11i		−	0.114336i
$267$	1.93733e12			1.42773
$268$	6.07674e11			0.439539
$269$	−5.98549e11			−0.424950			−0.212475	−	0.977166i	$-0.568152\pi$
$269$	−5.98549e11			−0.424950			−0.212475	+	0.977166i	$0.568152\pi$
$270$			1.67354e11i			0.116632i
$271$	−8.02913e11			−0.549315			−0.274658	−	0.961542i	$-0.588565\pi$
$271$	−8.02913e11			−0.549315			−0.274658	+	0.961542i	$0.588565\pi$
$272$	9.82048e11			0.659612
$273$	−1.16087e12			−0.765542
$274$	4.29386e10			0.0278032
$275$	−1.58072e10			−0.0100506
$276$		−	1.77094e12i		−	1.10575i
$277$		−	3.55023e11i		−	0.217700i	−0.994058	−	0.108850i	$-0.965283\pi$
$277$		−	3.55023e11i		−	0.217700i	0.994058	−	0.108850i	$-0.0347168\pi$
$278$			4.21444e11i			0.253814i
$279$	1.35727e11			0.0802869
$280$			5.88750e11i			0.342090i
$281$	9.07881e11			0.518200			0.259100	−	0.965851i	$-0.416574\pi$
$281$	9.07881e11			0.518200			0.259100	+	0.965851i	$0.416574\pi$
$282$	3.59144e11			0.201383
$283$	−1.06931e12			−0.589074			−0.294537	−	0.955640i	$-0.595165\pi$
$283$	−1.06931e12			−0.589074			−0.294537	+	0.955640i	$0.595165\pi$
$284$		−	2.15150e12i		−	1.16453i
$285$			1.56874e12i			0.834307i
$286$			4.18085e10i			0.0218491i
$287$		−	1.27957e12i		−	0.657136i
$288$		−	4.45277e11i		−	0.224733i
$289$	−9.60851e11			−0.476614
$290$			2.17795e11i			0.106183i
$291$			1.14575e12i			0.549069i
$292$			5.86677e11i			0.276366i
$293$	−3.17887e12			−1.47209			−0.736046	−	0.676932i	$-0.763309\pi$
$293$	−3.17887e12			−1.47209			−0.736046	+	0.676932i	$0.763309\pi$
$294$	−1.58890e10			−0.00723367
$295$			1.83805e12i			0.822709i
$296$	−2.56705e11			−0.112973
$297$			2.98988e11i			0.129381i
$298$	−3.33868e11			−0.142067
$299$	−1.46115e12			−0.611417
$300$		−	1.45674e11i		−	0.0599482i
$301$	−2.37967e12	+	4.78848e11i	−0.963129	+	0.193805i
$302$	2.48046e11			0.0987411
$303$			8.91569e11i			0.349093i
$304$			1.59835e12i			0.615608i
$305$	1.56061e11			0.0591283
$306$		−	1.51351e11i		−	0.0564129i
$307$	−1.42283e11			−0.0521749			−0.0260875	−	0.999660i	$-0.508305\pi$
$307$	−1.42283e11			−0.0521749			−0.0260875	+	0.999660i	$0.508305\pi$
$308$			5.17987e11i			0.186881i
$309$			5.23112e12i			1.85696i
$310$	−8.97932e10			−0.0313643
$311$	2.92237e12			1.00446			0.502231	−	0.864733i	$-0.332513\pi$
$311$	2.92237e12			1.00446			0.502231	+	0.864733i	$0.332513\pi$
$312$	−7.82383e11			−0.264634
$313$		−	3.24566e11i		−	0.108039i	−0.998540	−	0.0540195i	$-0.982797\pi$
$313$		−	3.24566e11i		−	0.108039i	0.998540	−	0.0540195i	$-0.0172033\pi$
$314$	6.28492e11			0.205898
$315$	−1.41328e12			−0.455697
$316$	3.67947e12			1.16775
$317$	5.95423e12			1.86007			0.930034	−	0.367473i	$-0.119777\pi$
$317$	5.95423e12			1.86007			0.930034	+	0.367473i	$0.119777\pi$
$318$	3.03464e11			0.0933193
$319$			3.89102e11i			0.117791i
$320$		−	2.84219e12i		−	0.847039i
$321$			7.14582e12i			2.09666i
$322$	5.54304e11			0.160128
$323$			1.71732e12i			0.488470i
$324$	−4.32263e12			−1.21066
$325$	−1.20191e11			−0.0331479
$326$	9.81685e11			0.266615
$327$		−	4.01690e12i		−	1.07437i
$328$		−	8.62386e11i		−	0.227160i
$329$		−	3.67124e12i		−	0.952431i
$330$			1.63410e11i			0.0417551i
$331$			4.61496e12i			1.16152i	0.814073	+	0.580762i	$0.197245\pi$
$331$			4.61496e12i			1.16152i	−0.814073	+	0.580762i	$0.802755\pi$
$332$	4.83248e12			1.19806
$333$		−	6.16216e11i		−	0.150491i
$334$			5.73743e11i			0.138034i
$335$		−	1.95964e12i		−	0.464464i
$336$	−4.62295e12			−1.07950
$337$	5.38665e12			1.23928			0.619640	−	0.784886i	$-0.287279\pi$
$337$	5.38665e12			1.23928			0.619640	+	0.784886i	$0.287279\pi$
$338$		−	4.42493e11i		−	0.100305i
$339$	−1.77737e12			−0.396989
$340$		−	3.27012e12i		−	0.719729i
$341$	−1.60421e11			−0.0347927
$342$	2.46334e11			0.0526495
$343$			4.82659e12i			1.01665i
$344$	−1.60381e12	+	3.22727e11i	−0.332937	+	0.0669950i
$345$	−5.71095e12			−1.16846
$346$			9.30137e10i			0.0187571i
$347$			8.09633e12i			1.60931i	0.593740	+	0.804657i	$0.297651\pi$
$347$			8.09633e12i			1.60931i	−0.593740	+	0.804657i	$0.702349\pi$
$348$	−3.58583e12			−0.702577
$349$		−	5.38376e12i		−	1.03982i	−0.854221	−	0.519910i	$-0.825965\pi$
$349$		−	5.38376e12i		−	1.03982i	0.854221	−	0.519910i	$-0.174035\pi$
$350$	4.55960e10			0.00868133
$351$			2.27337e12i			0.426711i
$352$			5.26289e11i			0.0973893i
$353$	4.06273e12			0.741215			0.370608	−	0.928790i	$-0.379149\pi$
$353$	4.06273e12			0.741215			0.370608	+	0.928790i	$0.379149\pi$
$354$	9.26614e11			0.166680
$355$	−6.93820e12			−1.23057
$356$		−	6.57288e12i		−	1.14949i
$357$	−4.96704e12			−0.856558
$358$	−1.88222e11			−0.0320078
$359$	−7.21622e12			−1.21015			−0.605073	−	0.796170i	$-0.706856\pi$
$359$	−7.21622e12			−1.21015			−0.605073	+	0.796170i	$0.706856\pi$
$360$	−9.52503e11			−0.157527
$361$	3.33601e12			0.544116
$362$		−	1.32850e12i		−	0.213707i
$363$		−	7.30389e12i		−	1.15883i
$364$			3.93854e12i			0.616351i
$365$	1.89192e12			0.292038
$366$		−	7.86750e10i		−	0.0119793i
$367$	1.20158e13			1.80477			0.902385	−	0.430931i	$-0.141815\pi$
$367$	1.20158e13			1.80477			0.902385	+	0.430931i	$0.141815\pi$
$368$	−5.81876e12			−0.862167
$369$	2.07014e12			0.302600
$370$			4.07672e11i			0.0587898i
$371$		−	3.10207e12i		−	0.441349i
$372$		−	1.47838e12i		−	0.207526i
$373$			5.46051e12i			0.756291i	0.925746	+	0.378146i	$0.123438\pi$
$373$			5.46051e12i			0.756291i	−0.925746	+	0.378146i	$0.876562\pi$
$374$			1.78887e11i			0.0244468i
$375$	8.69359e12			1.17231
$376$		−	2.47429e12i		−	0.329239i
$377$			2.95856e12i			0.388484i
$378$		−	8.62429e11i		−	0.111754i
$379$	2.08400e12			0.266503			0.133251	−	0.991082i	$-0.457458\pi$
$379$	2.08400e12			0.266503			0.133251	+	0.991082i	$0.457458\pi$
$380$	5.32235e12			0.671715
$381$		−	1.16850e13i		−	1.45547i
$382$	−6.76321e11			−0.0831450
$383$		−	6.42552e12i		−	0.779676i	−0.920883	−	0.389838i	$-0.872531\pi$
$383$		−	6.42552e12i		−	0.779676i	0.920883	−	0.389838i	$-0.127469\pi$
$384$	−6.43145e12			−0.770287
$385$	1.67041e12			0.197479
$386$			1.87443e11i			0.0218742i
$387$	−7.74700e11	−	3.84993e12i	−0.0892439	−	0.443504i
$388$	3.88727e12			0.442065
$389$		−	6.24207e12i		−	0.700779i	−0.936604	−	0.350389i	$-0.886049\pi$
$389$		−	6.24207e12i		−	0.700779i	0.936604	−	0.350389i	$-0.113951\pi$
$390$			1.24250e12i			0.137712i
$391$	−6.25186e12			−0.684109
$392$			1.09465e11i			0.0118262i
$393$	1.26476e13			1.34910
$394$		−	2.35818e11i		−	0.0248368i
$395$		−	1.18656e13i		−	1.23397i
$396$	−8.38020e11			−0.0860555
$397$	−3.04685e12			−0.308958			−0.154479	−	0.987996i	$-0.549370\pi$
$397$	−3.04685e12			−0.308958			−0.154479	+	0.987996i	$0.549370\pi$
$398$	−1.78668e12			−0.178908
$399$		−	8.08421e12i		−	0.799416i
$400$	−4.78641e11			−0.0467422
$401$	−5.06144e12			−0.488149			−0.244074	−	0.969757i	$-0.578484\pi$
$401$	−5.06144e12			−0.488149			−0.244074	+	0.969757i	$0.578484\pi$
$402$	−9.87912e11			−0.0940997
$403$	−1.21977e12			−0.114750
$404$	3.02488e12			0.281061
$405$			1.39397e13i			1.27932i
$406$		−	1.12237e12i		−	0.101743i
$407$			7.28328e11i			0.0652161i
$408$	−3.34761e12			−0.296097
$409$			9.21342e12i			0.805016i	0.915416	+	0.402508i	$0.131861\pi$
$409$			9.21342e12i			0.805016i	−0.915416	+	0.402508i	$0.868139\pi$
$410$	−1.36955e12			−0.118211
$411$	2.27979e12			0.194396
$412$	1.77479e13			1.49507
$413$		−	9.47204e12i		−	0.788303i
$414$			8.96774e11i			0.0737363i
$415$		−	1.55839e13i		−	1.26600i
$416$			4.00167e12i			0.321199i
$417$			2.23763e13i			1.77463i
$418$	−2.91152e11			−0.0228159
$419$		−	1.86619e13i		−	1.44506i	−0.691339	−	0.722531i	$-0.742979\pi$
$419$		−	1.86619e13i		−	1.44506i	0.691339	−	0.722531i	$-0.257021\pi$
$420$			1.53940e13i			1.17789i
$421$			8.57888e12i			0.648665i	0.945943	+	0.324332i	$0.105140\pi$
$421$			8.57888e12i			0.648665i	−0.945943	+	0.324332i	$0.894860\pi$
$422$	1.45552e12			0.108757
$423$	5.93948e12			0.438578
$424$		−	2.09069e12i		−	0.152567i
$425$	−5.14266e11			−0.0370889
$426$			3.49776e12i			0.249311i
$427$	−8.04232e11			−0.0566555
$428$	2.42441e13			1.68805
$429$			2.21979e12i			0.152766i
$430$	5.12520e11	+	2.54701e12i	0.0348633	+	0.173256i
$431$	−2.69197e13			−1.81002			−0.905010	−	0.425390i	$-0.860137\pi$
$431$	−2.69197e13			−1.81002			−0.905010	+	0.425390i	$0.860137\pi$
$432$			9.05329e12i			0.601711i
$433$			1.86409e13i			1.22469i	0.790590	+	0.612346i	$0.209774\pi$
$433$			1.86409e13i			1.22469i	−0.790590	+	0.612346i	$0.790226\pi$
$434$	4.62733e11			0.0300526
$435$			1.15636e13i			0.742418i
$436$	−1.36284e13			−0.864992
$437$		−	1.01753e13i		−	0.638471i
$438$		−	9.53776e11i		−	0.0591665i
$439$	−1.34913e13			−0.827428			−0.413714	−	0.910407i	$-0.635769\pi$
$439$	−1.34913e13			−0.827428			−0.413714	+	0.910407i	$0.635769\pi$
$440$	1.12580e12			0.0682649
$441$	−2.62770e11			−0.0157537
$442$			1.36018e12i			0.0806278i
$443$	−1.26659e13			−0.742367			−0.371184	−	0.928559i	$-0.621048\pi$
$443$	−1.26659e13			−0.742367			−0.371184	+	0.928559i	$0.621048\pi$
$444$	−6.71202e12			−0.388990
$445$	−2.11963e13			−1.21468
$446$	−2.83802e12			−0.160820
$447$	−1.77265e13			−0.993311
$448$			1.46467e13i			0.811616i
$449$		−	2.11844e13i		−	1.16087i	−0.814306	−	0.580436i	$-0.802882\pi$
$449$		−	2.11844e13i		−	1.16087i	0.814306	−	0.580436i	$-0.197118\pi$
$450$			7.37670e10i			0.00399760i
$451$	−2.44678e12			−0.131133
$452$			6.03017e12i			0.319623i
$453$	1.31698e13			0.690382
$454$	9.04866e11			0.0469143
$455$	1.27011e13			0.651303
$456$		−	5.44847e12i		−	0.276344i
$457$		−	1.61516e13i		−	0.810277i	−0.914255	−	0.405138i	$-0.867223\pi$
$457$		−	1.61516e13i		−	0.810277i	0.914255	−	0.405138i	$-0.132777\pi$
$458$		−	6.02817e12i		−	0.299129i
$459$			9.72714e12i			0.477443i
$460$			1.93759e13i			0.940746i
$461$	4.88602e11			0.0234666			0.0117333	−	0.999931i	$-0.496265\pi$
$461$	4.88602e11			0.0234666			0.0117333	+	0.999931i	$0.496265\pi$
$462$		−	8.42105e11i		−	0.0400089i
$463$			2.11110e13i			0.992210i	0.868263	+	0.496105i	$0.165237\pi$
$463$			2.11110e13i			0.992210i	−0.868263	+	0.496105i	$0.834763\pi$
$464$			1.17819e13i			0.547807i
$465$	−4.76751e12			−0.219294
$466$	7.11126e12			0.323606
$467$		−	2.80571e13i		−	1.26316i	−0.775311	−	0.631580i	$-0.782407\pi$
$467$		−	2.80571e13i		−	1.26316i	0.775311	−	0.631580i	$-0.217593\pi$
$468$	−6.37193e12			−0.283819
$469$			1.00986e13i			0.445040i
$470$	−3.92940e12			−0.171331
$471$	3.33693e13			1.43960
$472$		−	6.38382e12i		−	0.272503i
$473$	9.15647e11	+	4.55037e12i	0.0386743	+	0.192195i
$474$	−5.98181e12			−0.250001
$475$		−	8.37004e11i		−	0.0346146i
$476$			1.68520e13i			0.689630i
$477$	5.01866e12			0.203234
$478$			2.80504e12i			0.112409i
$479$	2.61293e13			1.03622			0.518108	−	0.855315i	$-0.326636\pi$
$479$	2.61293e13			1.03622			0.518108	+	0.855315i	$0.326636\pi$
$480$			1.56407e13i			0.613832i
$481$			5.53788e12i			0.215089i
$482$	7.63681e12			0.293546
$483$	2.94304e13			1.11959
$484$	−2.47803e13			−0.932998
$485$		−	1.25357e13i		−	0.467133i
$486$	3.94322e12			0.145435
$487$	−2.80825e13			−1.02516			−0.512579	−	0.858640i	$-0.671310\pi$
$487$	−2.80825e13			−1.02516			−0.512579	+	0.858640i	$0.671310\pi$
$488$	−5.42024e11			−0.0195848
$489$	5.21219e13			1.86413
$490$	1.73841e11			0.00615422
$491$			2.65400e13i			0.930024i	0.885304	+	0.465012i	$0.153950\pi$
$491$			2.65400e13i			0.930024i	−0.885304	+	0.465012i	$0.846050\pi$
$492$		−	2.25487e13i		−	0.782160i
$493$			1.26589e13i			0.434671i
$494$	−2.21379e12			−0.0752491
$495$			2.70246e12i			0.0909355i
$496$	−4.85751e12			−0.161810
$497$	3.57548e13			1.17910
$498$	−7.85630e12			−0.256490
$499$		−	5.01516e13i		−	1.62100i	−0.585741	−	0.810499i	$-0.699196\pi$
$499$		−	5.01516e13i		−	1.62100i	0.585741	−	0.810499i	$-0.300804\pi$
$500$		−	2.94953e13i		−	0.943848i
$501$			3.04625e13i			0.965110i
$502$		−	2.31538e11i		−	0.00726281i
$503$			4.15535e13i			1.29053i	0.763959	+	0.645264i	$0.223253\pi$
$503$			4.15535e13i			1.29053i	−0.763959	+	0.645264i	$0.776747\pi$
$504$	4.90855e12			0.150939
$505$		−	9.75467e12i		−	0.297000i
$506$		−	1.05993e12i		−	0.0319540i
$507$		−	2.34939e13i		−	0.701318i
$508$	−3.96445e13			−1.17183
$509$	−1.85803e13			−0.543831			−0.271916	−	0.962321i	$-0.587657\pi$
$509$	−1.85803e13			−0.543831			−0.271916	+	0.962321i	$0.587657\pi$
$510$			5.31632e12i			0.154085i
$511$	−9.74970e12			−0.279825
$512$			2.68305e13i			0.762568i
$513$	−1.58316e13			−0.445592
$514$	2.83717e12			0.0790805
$515$		−	5.72338e13i		−	1.57985i
$516$	−4.19347e13	+	8.43828e12i	−1.14637	+	0.230678i
$517$	−7.02010e12			−0.190060
$518$		−	2.10086e12i		−	0.0563312i
$519$			4.93850e12i			0.131147i
$520$	8.56007e12			0.225144
$521$		−	4.29356e13i		−	1.11848i	−0.829005	−	0.559241i	$-0.811093\pi$
$521$		−	4.29356e13i		−	1.11848i	0.829005	−	0.559241i	$-0.188907\pi$
$522$	1.81581e12			0.0468508
$523$		−	5.43272e13i		−	1.38838i	−0.719791	−	0.694191i	$-0.755762\pi$
$523$		−	5.43272e13i		−	1.38838i	0.719791	−	0.694191i	$-0.244238\pi$
$524$		−	4.29102e13i		−	1.08619i
$525$	2.42089e12			0.0606985
$526$	1.21868e13			0.302663
$527$	−5.21906e12			−0.128392
$528$			8.83994e12i			0.215417i
$529$	−4.38346e12			−0.105813
$530$	−3.32021e12			−0.0793937
$531$	1.53242e13			0.363000
$532$	−2.74278e13			−0.643624
$533$	−1.86042e13			−0.432489
$534$			1.06857e13i			0.246092i
$535$		−	7.81826e13i		−	1.78378i
$536$			6.80613e12i			0.153842i
$537$	−9.99351e12			−0.223793
$538$		−	3.30141e12i		−	0.0732468i
$539$	3.10577e11			0.00682694
$540$	3.01465e13			0.656551
$541$	2.25829e13			0.487297			0.243648	−	0.969864i	$-0.421656\pi$
$541$	2.25829e13			0.487297			0.243648	+	0.969864i	$0.421656\pi$
$542$		−	4.42862e12i		−	0.0946831i
$543$		−	7.05358e13i		−	1.49421i
$544$			1.71221e13i			0.359387i
$545$			4.39490e13i			0.914043i
$546$		−	6.40299e12i		−	0.131953i
$547$	3.55882e13			0.726724			0.363362	−	0.931648i	$-0.381629\pi$
$547$	3.55882e13			0.726724			0.363362	+	0.931648i	$0.381629\pi$
$548$		−	7.73479e12i		−	0.156511i
$549$		−	1.30112e12i		−	0.0260889i
$550$		−	8.71880e10i		−	0.00173238i
$551$	−2.06032e13			−0.405674
$552$	1.98350e13			0.387023
$553$			6.11473e13i			1.18237i
$554$	1.95820e12			0.0375240
$555$			2.16450e13i			0.411049i
$556$	7.59173e13			1.42878
$557$	−8.95325e13			−1.66995			−0.834977	−	0.550285i	$-0.814519\pi$
$557$	−8.95325e13			−1.66995			−0.834977	+	0.550285i	$0.814519\pi$
$558$			7.48629e11i			0.0138387i
$559$	6.96216e12	+	3.45990e13i	0.127551	+	0.633876i
$560$	5.05798e13			0.918411
$561$			9.49791e12i			0.170928i
$562$			5.00760e12i			0.0893198i
$563$	−3.15967e13			−0.558598			−0.279299	−	0.960204i	$-0.590102\pi$
$563$	−3.15967e13			−0.558598			−0.279299	+	0.960204i	$0.590102\pi$
$564$		−	6.46948e13i		−	1.13364i
$565$	1.94462e13			0.337748
$566$		−	5.89797e12i		−	0.101536i
$567$		−	7.18358e13i		−	1.22582i
$568$	2.40975e13			0.407596
$569$	5.74761e13			0.963665			0.481832	−	0.876263i	$-0.339971\pi$
$569$	5.74761e13			0.963665			0.481832	+	0.876263i	$0.339971\pi$
$570$	−8.65268e12			−0.143806
$571$			4.22519e13i			0.696090i	0.937478	+	0.348045i	$0.113154\pi$
$571$			4.22519e13i			0.696090i	−0.937478	+	0.348045i	$0.886846\pi$
$572$	7.53122e12			0.122994
$573$	−3.59088e13			−0.581337
$574$	7.05774e12			0.113268
$575$	3.04709e12			0.0484782
$576$	−2.36961e13			−0.373735
$577$			8.04729e13i			1.25826i	0.777300	+	0.629131i	$0.216589\pi$
$577$			8.04729e13i			1.25826i	−0.777300	+	0.629131i	$0.783411\pi$
$578$		−	5.29976e12i		−	0.0821518i
$579$			9.95215e12i			0.152941i
$580$	3.92327e13			0.597734
$581$			8.03087e13i			1.21306i
$582$	−6.31964e12			−0.0946405
$583$	−5.93174e12			−0.0880723
$584$	−6.57095e12			−0.0967306
$585$			2.05483e13i			0.299914i
$586$		−	1.75337e13i		−	0.253738i
$587$			1.08267e14i			1.55348i	0.629822	+	0.776739i	$0.283128\pi$
$587$			1.08267e14i			1.55348i	−0.629822	+	0.776739i	$0.716872\pi$
$588$			2.86218e12i			0.0407202i
$589$		−	8.49438e12i		−	0.119827i
$590$	−1.01381e13			−0.141807
$591$		−	1.25206e13i		−	0.173655i
$592$			2.20537e13i			0.303300i
$593$			1.10196e14i			1.50278i	0.659861	+	0.751388i	$0.270615\pi$
$593$			1.10196e14i			1.50278i	−0.659861	+	0.751388i	$0.729385\pi$
$594$	−1.64913e12			−0.0223009
$595$	5.43445e13			0.728737
$596$			6.01417e13i			0.799732i
$597$	−9.48623e13			−1.25090
$598$		−	8.05924e12i		−	0.105387i
$599$	−2.01917e13			−0.261841			−0.130921	−	0.991393i	$-0.541793\pi$
$599$	−2.01917e13			−0.261841			−0.130921	+	0.991393i	$0.541793\pi$
$600$	1.63159e12			0.0209824
$601$		−	6.69262e13i		−	0.853539i	−0.904360	−	0.426770i	$-0.859652\pi$
$601$		−	6.69262e13i		−	0.853539i	0.904360	−	0.426770i	$-0.140348\pi$
$602$	−2.64118e12	−	1.31255e13i	−0.0334053	−	0.166010i
$603$	−1.63380e13			−0.204933
$604$		−	4.46821e13i		−	0.555839i
$605$			7.99120e13i			0.985905i
$606$	−4.91762e12			−0.0601717
$607$		−	1.38942e14i		−	1.68613i	−0.537815	−	0.843063i	$-0.680750\pi$
$607$		−	1.38942e14i		−	1.68613i	0.537815	−	0.843063i	$-0.319250\pi$
$608$	−2.78674e13			−0.335412
$609$		−	5.95912e13i		−	0.711370i
$610$			8.60785e11i			0.0101917i
$611$	−5.33776e13			−0.626835
$612$	−2.72638e13			−0.317563
$613$	−5.52303e13			−0.638080			−0.319040	−	0.947741i	$-0.603360\pi$
$613$	−5.52303e13			−0.638080			−0.319040	+	0.947741i	$0.603360\pi$
$614$		−	7.84791e11i		−	0.00899316i
$615$	−7.27153e13			−0.826514
$616$	−5.80160e12			−0.0654101
$617$	−6.03257e13			−0.674647			−0.337324	−	0.941389i	$-0.609522\pi$
$617$	−6.03257e13			−0.674647			−0.337324	+	0.941389i	$0.609522\pi$
$618$	−2.88533e13			−0.320076
$619$	1.44434e14			1.58934			0.794671	−	0.607041i	$-0.207644\pi$
$619$	1.44434e14			1.58934			0.794671	+	0.607041i	$0.207644\pi$
$620$			1.61750e13i			0.176557i
$621$		−	5.76345e13i		−	0.624058i
$622$			1.61189e13i			0.173135i
$623$	1.09232e14			1.16388
$624$			6.72149e13i			0.710465i
$625$	−1.00006e14			−1.04864
$626$	1.79021e12			0.0186222
$627$	−1.54585e13			−0.159525
$628$		−	1.13214e14i		−	1.15905i
$629$			2.36951e13i			0.240661i
$630$		−	7.79525e12i		−	0.0785466i
$631$			1.75437e14i			1.75378i	0.480692	+	0.876890i	$0.340386\pi$
$631$			1.75437e14i			1.75378i	−0.480692	+	0.876890i	$0.659614\pi$
$632$			4.12111e13i			0.408723i
$633$	7.72801e13			0.760412
$634$			3.28417e13i			0.320612i
$635$			1.27846e14i			1.23828i
$636$		−	5.46649e13i		−	0.525318i
$637$	2.36149e12			0.0225159
$638$	−2.14617e12			−0.0203030
$639$			5.78455e13i			0.542957i
$640$	7.03666e13			0.655340
$641$			1.42208e14i			1.31412i	0.753838	+	0.657060i	$0.228200\pi$
$641$			1.42208e14i			1.31412i	−0.753838	+	0.657060i	$0.771800\pi$
$642$	−3.94142e13			−0.361391
$643$	1.12154e14			1.02037			0.510186	−	0.860064i	$-0.329577\pi$
$643$	1.12154e14			1.02037			0.510186	+	0.860064i	$0.329577\pi$
$644$		−	9.98501e13i		−	0.901404i
$645$	2.72119e13	+	1.35232e14i	0.243759	+	1.21138i
$646$	−9.47221e12			−0.0841955
$647$		−	9.56448e13i		−	0.843607i	−0.906687	−	0.421803i	$-0.861397\pi$
$647$		−	9.56448e13i		−	0.843607i	0.906687	−	0.421803i	$-0.138603\pi$
$648$		−	4.84147e13i		−	0.423743i
$649$	−1.81123e13			−0.157308
$650$		−	6.62938e11i		−	0.00571355i
$651$	2.45685e13			0.210123
$652$		−	1.76837e14i		−	1.50084i
$653$		−	7.62193e13i		−	0.641947i	−0.947088	−	0.320974i	$-0.895990\pi$
$653$		−	7.62193e13i		−	0.641947i	0.947088	−	0.320974i	$-0.104010\pi$
$654$	2.21560e13			0.185184
$655$	−1.38377e14			−1.14778
$656$	−7.40881e13			−0.609858
$657$		−	1.57735e13i		−	0.128855i
$658$	2.02495e13			0.164166
$659$	1.91006e14			1.53681			0.768403	−	0.639967i	$-0.221052\pi$
$659$	1.91006e14			1.53681			0.768403	+	0.639967i	$0.221052\pi$
$660$	2.94361e13			0.235050
$661$	−1.55645e13			−0.123347			−0.0616733	−	0.998096i	$-0.519644\pi$
$661$	−1.55645e13			−0.123347			−0.0616733	+	0.998096i	$0.519644\pi$
$662$	−2.54548e13			−0.200207
$663$			7.22178e13i			0.563737i
$664$			5.41252e13i			0.419333i
$665$			8.84495e13i			0.680122i
$666$	3.39886e12			0.0259395
$667$		−	7.50055e13i		−	0.568152i
$668$	1.03352e14			0.777027
$669$	−1.50682e14			−1.12443
$670$	1.08088e13			0.0800576
$671$			1.53784e12i			0.0113057i
$672$		−	8.06015e13i		−	0.588162i
$673$		−	5.98762e13i		−	0.433690i	−0.976206	−	0.216845i	$-0.930423\pi$
$673$		−	5.98762e13i		−	0.433690i	0.976206	−	0.216845i	$-0.0695766\pi$
$674$			2.97111e13i			0.213609i
$675$		−	4.74091e12i		−	0.0338332i
$676$	−7.97090e13			−0.564643
$677$		−	9.73601e12i		−	0.0684601i	−0.999414	−	0.0342301i	$-0.989102\pi$
$677$		−	9.73601e12i		−	0.0684601i	0.999414	−	0.0342301i	$-0.0108979\pi$
$678$		−	9.80341e12i		−	0.0684272i
$679$			6.46006e13i			0.447598i
$680$	3.66263e13			0.251912
$681$	4.80432e13			0.328017
$682$		−	8.84832e11i		−	0.00599707i
$683$	7.39029e13			0.497231			0.248615	−	0.968602i	$-0.420025\pi$
$683$	7.39029e13			0.497231			0.248615	+	0.968602i	$0.420025\pi$
$684$		−	4.43737e13i		−	0.296378i
$685$	−2.49433e13			−0.165387
$686$	−2.66220e13			−0.175235
$687$		−	3.20062e14i		−	2.09146i
$688$	2.77256e13	+	1.37784e14i	0.179862	+	0.893836i
$689$	−4.51022e13			−0.290471
$690$		−	3.14999e13i		−	0.201402i
$691$		−	2.93000e14i		−	1.85985i	−0.367751	−	0.929924i	$-0.619872\pi$
$691$		−	2.93000e14i		−	1.85985i	0.367751	−	0.929924i	$-0.380128\pi$
$692$	1.67551e13			0.105589
$693$		−	1.39267e13i		−	0.0871326i
$694$	−4.46569e13			−0.277390
$695$		−	2.44819e14i		−	1.50981i
$696$		−	4.01624e13i		−	0.245908i
$697$	−7.96025e13			−0.483908
$698$	2.96952e13			0.179229
$699$	3.77567e14			2.26260
$700$		−	8.21349e12i		−	0.0488694i
$701$	4.69230e13			0.277201			0.138601	−	0.990348i	$-0.455740\pi$
$701$	4.69230e13			0.277201			0.138601	+	0.990348i	$0.455740\pi$
$702$	−1.25392e13			−0.0735503
$703$	−3.85655e13			−0.224606
$704$	2.80073e13			0.161960
$705$	−2.08629e14			−1.19792
$706$			2.24088e13i			0.127760i
$707$			5.02690e13i			0.284579i
$708$		−	1.66917e14i		−	0.938283i
$709$	−9.97058e13			−0.556531			−0.278265	−	0.960504i	$-0.589759\pi$
$709$	−9.97058e13			−0.556531			−0.278265	+	0.960504i	$0.589759\pi$
$710$		−	3.82690e13i		−	0.212107i
$711$	−9.89266e13			−0.544459
$712$	7.36182e13			0.402333
$713$	3.09236e13			0.167819
$714$		−	2.73967e13i		−	0.147641i
$715$		−	2.42868e13i		−	0.129969i
$716$			3.39056e13i			0.180180i
$717$			1.48932e14i			0.785943i
$718$		−	3.98025e13i		−	0.208588i
$719$	−1.78844e14			−0.930741			−0.465371	−	0.885116i	$-0.654079\pi$
$719$	−1.78844e14			−0.930741			−0.465371	+	0.885116i	$0.654079\pi$
$720$			8.18300e13i			0.422912i
$721$			2.94944e14i			1.51378i
$722$			1.84004e13i			0.0937869i
$723$	4.05471e14			2.05243
$724$	−2.39311e14			−1.20301
$725$		−	6.16982e12i		−	0.0308022i
$726$	4.02861e13			0.199743
$727$		−	2.91641e14i		−	1.43607i	−0.696005	−	0.718037i	$-0.745041\pi$
$727$		−	2.91641e14i		−	1.43607i	0.696005	−	0.718037i	$-0.254959\pi$
$728$	−4.41128e13			−0.215729
$729$	−4.75347e13			−0.230873
$730$			1.04353e13i			0.0503373i
$731$	2.97893e13	+	1.48040e14i	0.142716	+	0.709238i
$732$	−1.41722e13			−0.0674346
$733$		−	2.10681e14i		−	0.995648i	−0.867278	−	0.497824i	$-0.834133\pi$
$733$		−	2.10681e14i		−	0.995648i	0.867278	−	0.497824i	$-0.165867\pi$
$734$			6.62755e13i			0.311080i
$735$	9.22999e12			0.0430293
$736$		−	1.01451e14i		−	0.469748i
$737$	1.93105e13			0.0888087
$738$			1.14183e13i			0.0521578i
$739$			5.50708e13i			0.249862i	0.992165	+	0.124931i	$0.0398709\pi$
$739$			5.50708e13i			0.249862i	−0.992165	+	0.124931i	$0.960129\pi$
$740$	7.34364e13			0.330943
$741$	−1.17539e14			−0.526130
$742$	1.71101e13			0.0760734
$743$		−	5.59921e13i		−	0.247276i	−0.992327	−	0.123638i	$-0.960544\pi$
$743$		−	5.59921e13i		−	0.247276i	0.992327	−	0.123638i	$-0.0394562\pi$
$744$	1.65583e13			0.0726359
$745$	1.93946e14			0.845083
$746$	−3.01185e13			−0.130359
$747$	−1.29927e14			−0.558593
$748$	3.22241e13			0.137617
$749$			4.02900e14i			1.70918i
$750$			4.79512e13i			0.202066i
$751$			2.89087e14i			1.21012i	0.796179	+	0.605061i	$0.206851\pi$
$751$			2.89087e14i			1.21012i	−0.796179	+	0.605061i	$0.793149\pi$
$752$	−2.12567e14			−0.883908
$753$		−	1.22934e13i		−	0.0507804i
$754$	−1.63185e13			−0.0669613
$755$	−1.44092e14			−0.587359
$756$	−1.55355e14			−0.629094
$757$			1.01995e14i			0.410297i	0.978731	+	0.205149i	$0.0657678\pi$
$757$			1.01995e14i			0.410297i	−0.978731	+	0.205149i	$0.934232\pi$
$758$			1.14947e13i			0.0459359i
$759$		−	5.62763e13i		−	0.223417i
$760$			5.96118e13i			0.235106i
$761$			1.48371e14i			0.581335i	0.956824	+	0.290667i	$0.0938773\pi$
$761$			1.48371e14i			0.581335i	−0.956824	+	0.290667i	$0.906123\pi$
$762$	6.44511e13			0.250874
$763$		−	2.26484e14i		−	0.875818i
$764$			1.21830e14i			0.468045i
$765$			8.79207e13i			0.335571i
$766$	3.54412e13			0.134389
$767$	−1.37718e14			−0.518816
$768$			2.30535e14i			0.862839i
$769$	4.82893e14			1.79564			0.897820	−	0.440362i	$-0.145150\pi$
$769$	4.82893e14			1.79564			0.897820	+	0.440362i	$0.145150\pi$
$770$			9.21349e12i			0.0340385i
$771$	1.50637e14			0.552919
$772$	3.37653e13			0.123136
$773$			4.77918e13i			0.173163i	0.996245	+	0.0865817i	$0.0275943\pi$
$773$			4.77918e13i			0.173163i	−0.996245	+	0.0865817i	$0.972406\pi$
$774$	2.12350e13	−	4.27301e12i	0.0764448	−	0.0153826i
$775$	2.54372e12			0.00909831
$776$			4.35385e13i			0.154727i
$777$		−	1.11544e14i		−	0.393859i
$778$	3.44294e13			0.120790
$779$		−	1.29559e14i		−	0.451626i
$780$	2.23819e14			0.775217
$781$		−	6.83698e13i		−	0.235293i
$782$		−	3.44834e13i		−	0.117917i
$783$	−1.16700e14			−0.396516
$784$	9.40423e12			0.0317499
$785$	−3.65095e14			−1.22478
$786$			6.97602e13i			0.232539i
$787$	2.33706e14			0.774098			0.387049	−	0.922059i	$-0.373494\pi$
$787$	2.33706e14			0.774098			0.387049	+	0.922059i	$0.373494\pi$
$788$	−4.24793e13			−0.139813
$789$	6.47047e14			2.11617
$790$	6.54471e13			0.212694
$791$	−1.00212e14			−0.323623
$792$		−	9.38607e12i		−	0.0301202i
$793$			1.16931e13i			0.0372874i
$794$		−	1.68055e13i		−	0.0532537i
$795$	−1.76284e14			−0.555108
$796$			3.21845e14i			1.00712i
$797$	3.00140e14			0.933325			0.466663	−	0.884435i	$-0.345456\pi$
$797$	3.00140e14			0.933325			0.466663	+	0.884435i	$0.345456\pi$
$798$	4.45900e13			0.137792
$799$	−2.28389e14			−0.701360
$800$		−	8.34513e12i		−	0.0254673i
$801$			1.76719e14i			0.535946i
$802$		−	2.79174e13i		−	0.0841400i
$803$			1.86432e13i			0.0558398i
$804$			1.77959e14i			0.529711i
$805$	−3.21998e14			−0.952520
$806$		−	6.72786e12i		−	0.0197789i
$807$		−	1.75286e14i		−	0.512130i
$808$			3.38795e13i			0.0983740i
$809$	−2.84113e14			−0.819877			−0.409939	−	0.912113i	$-0.634450\pi$
$809$	−2.84113e14			−0.819877			−0.409939	+	0.912113i	$0.634450\pi$
$810$	−7.68872e13			−0.220510
$811$			2.70701e12i			0.00771589i	0.999993	+	0.00385794i	$0.00122802\pi$
$811$			2.70701e12i			0.00771589i	−0.999993	+	0.00385794i	$0.998772\pi$
$812$	−2.02179e14			−0.572737
$813$		−	2.35135e14i		−	0.662009i
$814$	−4.01724e12			−0.0112410
$815$	−5.70267e14			−1.58595
$816$			2.87595e14i			0.794933i
$817$	−2.40945e14	+	4.84841e13i	−0.661924	+	0.133195i
$818$	−5.08185e13			−0.138757
$819$		−	1.05892e14i		−	0.287371i
$820$			2.46706e14i			0.665441i
$821$	2.40061e13			0.0643584			0.0321792	−	0.999482i	$-0.489755\pi$
$821$	2.40061e13			0.0643584			0.0321792	+	0.999482i	$0.489755\pi$
$822$			1.25747e13i			0.0335071i
$823$	−6.12116e14			−1.62119			−0.810597	−	0.585605i	$-0.800857\pi$
$823$	−6.12116e14			−1.62119			−0.810597	+	0.585605i	$0.800857\pi$
$824$			1.98782e14i			0.523288i
$825$		−	4.62919e12i		−	0.0121125i
$826$	5.22449e13			0.135876
$827$	−1.53725e14			−0.397390			−0.198695	−	0.980061i	$-0.563670\pi$
$827$	−1.53725e14			−0.397390			−0.198695	+	0.980061i	$0.563670\pi$
$828$	1.61542e14			0.415081
$829$		−	1.20932e14i		−	0.308865i	−0.988003	−	0.154432i	$-0.950645\pi$
$829$		−	1.20932e14i		−	0.308865i	0.988003	−	0.154432i	$-0.0493549\pi$
$830$	8.59559e13			0.218215
$831$	1.03969e14			0.262362
$832$	2.12955e14			0.534159
$833$	1.01042e13			0.0251928
$834$	−1.23421e14			−0.305885
$835$		−	3.33291e14i		−	0.821091i
$836$			5.24470e13i			0.128437i
$837$		−	4.81134e13i		−	0.117122i
$838$	1.02934e14			0.249079
$839$		−	1.74692e14i		−	0.420206i	−0.977679	−	0.210103i	$-0.932620\pi$
$839$		−	1.74692e14i		−	0.420206i	0.977679	−	0.210103i	$-0.0673799\pi$
$840$	−1.72417e14			−0.412271
$841$	2.68834e14			0.639006
$842$	−4.73185e13			−0.111807
$843$			2.65875e14i			0.624510i
$844$		−	2.62193e14i		−	0.612221i
$845$			2.57047e14i			0.596663i
$846$			3.27604e13i			0.0755957i
$847$		−	4.11812e14i		−	0.944675i
$848$	−1.79612e14			−0.409596
$849$		−	3.13149e14i		−	0.709925i
$850$		−	2.83654e12i		−	0.00639284i
$851$		−	1.40397e14i		−	0.314564i
$852$	6.30073e14			1.40344
$853$	7.35089e13			0.162778			0.0813888	−	0.996682i	$-0.474064\pi$
$853$	7.35089e13			0.162778			0.0813888	+	0.996682i	$0.474064\pi$
$854$		−	4.43590e12i		−	0.00976546i
$855$	−1.43097e14			−0.313185
$856$			2.71540e14i			0.590834i
$857$	5.75184e14			1.24423			0.622117	−	0.782924i	$-0.286273\pi$
$857$	5.75184e14			1.24423			0.622117	+	0.782924i	$0.286273\pi$
$858$	−1.22437e13			−0.0263315
$859$			9.34183e13i			0.199741i	0.995000	+	0.0998703i	$0.0318428\pi$
$859$			9.34183e13i			0.199741i	−0.995000	+	0.0998703i	$0.968157\pi$
$860$	4.58808e14	−	9.23235e13i	0.975301	−	0.196255i
$861$	3.74726e14			0.791950
$862$		−	1.48481e14i		−	0.311985i
$863$			3.48918e14i			0.728903i	0.931222	+	0.364451i	$0.118744\pi$
$863$			3.48918e14i			0.728903i	−0.931222	+	0.364451i	$0.881256\pi$
$864$	−1.57845e14			−0.327840
$865$		−	5.40322e13i		−	0.111576i
$866$	−1.02818e14			−0.211095
$867$		−	2.81387e14i		−	0.574393i
$868$		−	8.33550e13i		−	0.169174i
$869$	1.16925e14			0.235944
$870$	−6.37816e13			−0.127967
$871$	1.46828e14			0.292900
$872$		−	1.52642e14i		−	0.302755i
$873$	−1.04513e14			−0.206111
$874$	5.61241e13			0.110050
$875$	4.90167e14			0.955662
$876$	−1.71810e14			−0.333063
$877$	9.14192e14			1.76214			0.881068	−	0.472989i	$-0.156825\pi$
$877$	9.14192e14			1.76214			0.881068	+	0.472989i	$0.156825\pi$
$878$		−	7.44138e13i		−	0.142620i
$879$		−	9.30940e14i		−	1.77410i
$880$		−	9.67180e13i		−	0.183271i
$881$	6.90185e14			1.30043			0.650214	−	0.759751i	$-0.274679\pi$
$881$	6.90185e14			1.30043			0.650214	+	0.759751i	$0.274679\pi$
$882$		−	1.44936e12i		−	0.00271540i
$883$	−4.40508e14			−0.820635			−0.410317	−	0.911943i	$-0.634582\pi$
$883$	−4.40508e14			−0.820635			−0.410317	+	0.911943i	$0.634582\pi$
$884$	2.45018e14			0.453875
$885$	−5.38276e14			−0.991490
$886$		−	6.98615e13i		−	0.127959i
$887$			1.15384e14i			0.210149i	0.994464	+	0.105074i	$0.0335081\pi$
$887$			1.15384e14i			0.210149i	−0.994464	+	0.105074i	$0.966492\pi$
$888$		−	7.51766e13i		−	0.136150i
$889$		−	6.58832e14i		−	1.18650i
$890$		−	1.16913e14i		−	0.209369i
$891$	−1.37363e14			−0.244615
$892$			5.11229e14i			0.905298i
$893$		−	3.71719e14i		−	0.654572i
$894$		−	9.77740e13i		−	0.171213i
$895$	1.09339e14			0.190397
$896$	−3.62622e14			−0.627934
$897$		−	4.27900e14i		−	0.736851i
$898$	1.16847e14			0.200094
$899$		−	6.26148e13i		−	0.106630i
$900$	1.32881e13			0.0225035
$901$	−1.92981e14			−0.325005
$902$		−	1.34957e13i		−	0.0226028i
$903$	−1.40232e14	−	6.96892e14i	−0.233565	−	1.16072i
$904$	−6.75397e13			−0.111871
$905$			7.71734e14i			1.27123i
$906$			7.26409e13i			0.118998i
$907$	2.81353e14			0.458369			0.229184	−	0.973383i	$-0.426394\pi$
$907$	2.81353e14			0.458369			0.229184	+	0.973383i	$0.426394\pi$
$908$		−	1.62999e14i		−	0.264092i
$909$	−8.13271e13			−0.131044
$910$			7.00553e13i			0.112262i
$911$			7.11694e14i			1.13423i	0.823638	+	0.567116i	$0.191941\pi$
$911$			7.11694e14i			1.13423i	−0.823638	+	0.567116i	$0.808059\pi$
$912$	−4.68081e14			−0.741902
$913$	1.53565e14			0.242069
$914$	8.90871e13			0.139664
$915$			4.57028e13i			0.0712586i
$916$	−1.08589e15			−1.68387
$917$	7.13104e14			1.09978
$918$	−5.36520e13			−0.0822948
$919$	−1.27393e15			−1.94342			−0.971712	−	0.236167i	$-0.924109\pi$
$919$	−1.27393e15			−1.94342			−0.971712	+	0.236167i	$0.924109\pi$
$920$	−2.17015e14			−0.329269
$921$		−	4.16679e13i		−	0.0628788i
$922$			2.69498e12i			0.00404484i
$923$		−	5.19853e14i		−	0.776019i
$924$	−1.51694e14			−0.225220
$925$		−	1.15488e13i		−	0.0170540i
$926$	−1.16442e14			−0.171023
$927$	−4.77172e14			−0.697070
$928$	−2.05419e14			−0.298470
$929$		−	2.55612e14i		−	0.369405i	−0.982794	−	0.184703i	$-0.940868\pi$
$929$		−	2.55612e14i		−	0.369405i	0.982794	−	0.184703i	$-0.0591322\pi$
$930$		−	2.62961e13i		−	0.0377987i
$931$			1.64453e13i			0.0235122i
$932$		−	1.28099e15i		−	1.82166i
$933$			8.55823e14i			1.21053i
$934$	1.54755e14			0.217725
$935$		−	1.03917e14i		−	0.145421i
$936$		−	7.13674e13i		−	0.0993392i
$937$			8.48209e13i			0.117437i	0.998275	+	0.0587185i	$0.0187014\pi$
$937$			8.48209e13i			0.117437i	−0.998275	+	0.0587185i	$0.981299\pi$
$938$	−5.57011e13			−0.0767095
$939$	9.50498e13			0.130204
$940$			7.07827e14i			0.964468i
$941$	2.82807e14			0.383302			0.191651	−	0.981463i	$-0.438616\pi$
$941$	2.82807e14			0.383302			0.191651	+	0.981463i	$0.438616\pi$
$942$			1.84055e14i			0.248138i
$943$	4.71655e14			0.632508
$944$	−5.48437e14			−0.731589
$945$			5.00990e14i			0.664768i
$946$	−2.50985e13	+	5.05043e12i	−0.0331277	+	0.00666611i
$947$	4.44919e14			0.584159			0.292079	−	0.956394i	$-0.405653\pi$
$947$	4.44919e14			0.584159			0.292079	+	0.956394i	$0.405653\pi$
$948$			1.07754e15i			1.40732i
$949$			1.41755e14i			0.184165i
$950$	4.61666e12			0.00596637
$951$			1.74371e15i			2.24167i
$952$	−1.88747e14			−0.241377
$953$			6.91033e14i			0.879092i	0.898220	+	0.439546i	$0.144861\pi$
$953$			6.91033e14i			0.879092i	−0.898220	+	0.439546i	$0.855139\pi$
$954$			2.76814e13i			0.0350305i
$955$	3.92879e14			0.494586
$956$	5.05289e14			0.632777
$957$	−1.13949e14			−0.141956
$958$			1.44121e14i			0.178608i
$959$	1.28541e14			0.158470
$960$	8.32342e14			1.02081
$961$	−7.93813e14			−0.968504
$962$	−3.05453e13			−0.0370739
$963$	−6.51828e14			−0.787048
$964$		−	1.37567e15i		−	1.65245i
$965$		−	1.08887e14i		−	0.130118i
$966$			1.62329e14i			0.192979i
$967$	1.19497e15			1.41327			0.706637	−	0.707577i	$-0.250212\pi$
$967$	1.19497e15			1.41327			0.706637	+	0.707577i	$0.250212\pi$
$968$		−	2.77547e14i		−	0.326557i
$969$	−5.02921e14			−0.588682
$970$	6.91433e13			0.0805177
$971$	1.50122e14			0.173919			0.0869596	−	0.996212i	$-0.472285\pi$
$971$	1.50122e14			0.173919			0.0869596	+	0.996212i	$0.472285\pi$
$972$		−	7.10317e14i		−	0.818693i
$973$			1.26163e15i			1.44667i
$974$		−	1.54894e14i		−	0.176702i
$975$		−	3.51982e13i		−	0.0399483i
$976$			4.65656e13i			0.0525794i
$977$	−3.65592e14			−0.410699			−0.205349	−	0.978689i	$-0.565833\pi$
$977$	−3.65592e14			−0.410699			−0.205349	+	0.978689i	$0.565833\pi$
$978$			2.87489e14i			0.321312i
$979$		−	2.08871e14i		−	0.232255i
$980$		−	3.13151e13i		−	0.0346437i
$981$	3.66414e14			0.403299
$982$	−1.46387e14			−0.160304
$983$		−	1.72397e15i		−	1.87828i	−0.343531	−	0.939141i	$-0.611623\pi$
$983$		−	1.72397e15i		−	1.87828i	0.343531	−	0.939141i	$-0.388377\pi$
$984$	2.52552e14			0.273763
$985$			1.36988e14i			0.147741i
$986$	−6.98226e13			−0.0749224
$987$	1.07513e15			1.14782
$988$			3.98783e14i			0.423596i
$989$	−1.76505e14	−	8.77155e14i	−0.186542	−	0.927033i
$990$	−1.49060e13			−0.0156741
$991$			1.52002e15i			1.59030i	0.606411	+	0.795151i	$0.292609\pi$
$991$			1.52002e15i			1.59030i	−0.606411	+	0.795151i	$0.707391\pi$
$992$		−	8.46911e13i		−	0.0881616i
$993$	−1.35150e15			−1.39981
$994$			1.97213e14i			0.203237i
$995$	1.03789e15			1.06423
$996$			1.41520e15i			1.44385i
$997$			9.05181e14i			0.918882i	0.888208	+	0.459441i	$0.151950\pi$
$997$			9.05181e14i			0.918882i	−0.888208	+	0.459441i	$0.848050\pi$
$998$	2.76621e14			0.279404
$999$	−2.18440e14			−0.219536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.19	yes	34
43.42	odd	2	inner	43.11.b.b.42.16	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.16	✓	34	43.42	odd	2	inner
43.11.b.b.42.19	yes	34	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+5.51570i q^{2} +292.852i q^{3} +993.577 q^{4} -3204.10i q^{5} -1615.28 q^{6} +16511.8i q^{7} +11128.3i q^{8} -26713.4 q^{9} +O(q^{10})\)	\(q+5.51570i q^{2} +292.852i q^{3} +993.577 q^{4} -3204.10i q^{5} -1615.28 q^{6} +16511.8i q^{7} +11128.3i q^{8} -26713.4 q^{9} +17672.9 q^{10} +31573.6 q^{11} +290971. i q^{12} +240071. q^{13} -91074.0 q^{14} +938328. q^{15} +956042. q^{16} +1.02720e6 q^{17} -147343. i q^{18} +1.67184e6i q^{19} -3.18352e6i q^{20} -4.83551e6 q^{21} +174150. i q^{22} -6.08630e6 q^{23} -3.25896e6 q^{24} -500648. q^{25} +1.32416e6i q^{26} +9.46955e6i q^{27} +1.64057e7i q^{28} +1.23237e7i q^{29} +5.17554e6i q^{30} -5.08085e6 q^{31} +1.66687e7i q^{32} +9.24639e6i q^{33} +5.66573e6i q^{34} +5.29054e7 q^{35} -2.65418e7 q^{36} +2.30677e7i q^{37} -9.22138e6 q^{38} +7.03054e7i q^{39} +3.56564e7 q^{40} -7.74946e7 q^{41} -2.66712e7i q^{42} +(2.90004e7 + 1.44120e8i) q^{43} +3.13708e7 q^{44} +8.55925e7i q^{45} -3.35702e7i q^{46} -2.22341e8 q^{47} +2.79979e8i q^{48} +9.83663e6 q^{49} -2.76142e6i q^{50} +3.00818e8i q^{51} +2.38529e8 q^{52} -1.87870e8 q^{53} -5.22312e7 q^{54} -1.01165e8i q^{55} -1.83749e8 q^{56} -4.89603e8 q^{57} -6.79736e7 q^{58} -5.73654e8 q^{59} +9.32302e8 q^{60} +4.87066e7i q^{61} -2.80245e7i q^{62} -4.41086e8i q^{63} +8.87048e8 q^{64} -7.69213e8i q^{65} -5.10003e7 q^{66} +6.11603e8 q^{67} +1.02060e9 q^{68} -1.78239e9i q^{69} +2.91810e8i q^{70} -2.16541e9i q^{71} -2.97276e8i q^{72} +5.90470e8i q^{73} -1.27234e8 q^{74} -1.46616e8i q^{75} +1.66110e9i q^{76} +5.21336e8i q^{77} -3.87783e8 q^{78} +3.70326e9 q^{79} -3.06326e9i q^{80} -4.35058e9 q^{81} -4.27437e8i q^{82} +4.86372e9 q^{83} -4.80445e9 q^{84} -3.29126e9i q^{85} +(-7.94920e8 + 1.59958e8i) q^{86} -3.60901e9 q^{87} +3.51362e8i q^{88} -6.61537e9i q^{89} -4.72102e8 q^{90} +3.96400e9i q^{91} -6.04721e9 q^{92} -1.48794e9i q^{93} -1.22637e9i q^{94} +5.35675e9 q^{95} -4.88146e9 q^{96} +3.91240e9 q^{97} +5.42559e7i q^{98} -8.43438e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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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