LMFDB - Embedded newform 43.11.b.b.42.26

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			42.26
Character	$\chi$	$=$	43.42
Dual form			43.11.b.b.42.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+41.1797i q^{2} +18.8325i q^{3} -671.767 q^{4} -4211.22i q^{5} -775.516 q^{6} +20378.0i q^{7} +14504.9i q^{8} +58694.3 q^{9} +O(q^{10})$	\(q+41.1797i q^{2} +18.8325i q^{3} -671.767 q^{4} -4211.22i q^{5} -775.516 q^{6} +20378.0i q^{7} +14504.9i q^{8} +58694.3 q^{9} +173417. q^{10} -306949. q^{11} -12651.0i q^{12} +198968. q^{13} -839160. q^{14} +79307.8 q^{15} -1.28519e6 q^{16} -2.08922e6 q^{17} +2.41701e6i q^{18} -2.97711e6i q^{19} +2.82896e6i q^{20} -383769. q^{21} -1.26401e7i q^{22} +1.17271e6 q^{23} -273163. q^{24} -7.96877e6 q^{25} +8.19343e6i q^{26} +2.21740e6i q^{27} -1.36893e7i q^{28} +2.43453e7i q^{29} +3.26587e6i q^{30} -3.70189e7 q^{31} -3.80709e7i q^{32} -5.78061e6i q^{33} -8.60332e7i q^{34} +8.58163e7 q^{35} -3.94289e7 q^{36} -7.72003e7i q^{37} +1.22597e8 q^{38} +3.74706e6i q^{39} +6.10832e7 q^{40} -6.69942e7 q^{41} -1.58035e7i q^{42} +(2.69450e7 - 1.44518e8i) q^{43} +2.06198e8 q^{44} -2.47175e8i q^{45} +4.82916e7i q^{46} -4.29292e8 q^{47} -2.42034e7i q^{48} -1.32788e8 q^{49} -3.28152e8i q^{50} -3.93451e7i q^{51} -1.33660e8 q^{52} +2.00012e8 q^{53} -9.13119e7 q^{54} +1.29263e9i q^{55} -2.95580e8 q^{56} +5.60664e7 q^{57} -1.00253e9 q^{58} +3.24891e8 q^{59} -5.32764e7 q^{60} -8.68845e8i q^{61} -1.52443e9i q^{62} +1.19607e9i q^{63} +2.51710e8 q^{64} -8.37897e8i q^{65} +2.38044e8 q^{66} -1.36258e9 q^{67} +1.40347e9 q^{68} +2.20850e7i q^{69} +3.53389e9i q^{70} +2.65191e9i q^{71} +8.51353e8i q^{72} -1.07991e7i q^{73} +3.17909e9 q^{74} -1.50072e8i q^{75} +1.99992e9i q^{76} -6.25501e9i q^{77} -1.54303e8 q^{78} +8.01396e8 q^{79} +5.41224e9i q^{80} +3.42408e9 q^{81} -2.75880e9i q^{82} -5.22410e9 q^{83} +2.57803e8 q^{84} +8.79815e9i q^{85} +(5.95121e9 + 1.10959e9i) q^{86} -4.58482e8 q^{87} -4.45225e9i q^{88} +6.11548e9i q^{89} +1.01786e10 q^{90} +4.05456e9i q^{91} -7.87784e8 q^{92} -6.97159e8i q^{93} -1.76781e10i q^{94} -1.25373e10 q^{95} +7.16971e8 q^{96} +3.80330e8 q^{97} -5.46816e9i q^{98} -1.80162e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			41.1797i			1.28687i	0.765503	+	0.643433i	$0.222490\pi$
$2$			41.1797i			1.28687i	−0.765503	+	0.643433i	$0.777510\pi$
$3$			18.8325i			0.0775000i	0.999249	+	0.0387500i	$0.0123376\pi$
$3$			18.8325i			0.0775000i	−0.999249	+	0.0387500i	$0.987662\pi$
$4$	−671.767			−0.656022
$5$		−	4211.22i		−	1.34759i	−0.738918	−	0.673796i	$-0.764663\pi$
$5$		−	4211.22i		−	1.34759i	0.738918	−	0.673796i	$-0.235337\pi$
$6$	−775.516			−0.0997320
$7$			20378.0i			1.21247i	0.795285	+	0.606236i	$0.207321\pi$
$7$			20378.0i			1.21247i	−0.795285	+	0.606236i	$0.792679\pi$
$8$			14504.9i			0.442653i
$9$	58694.3			0.993994
$10$	173417.			1.73417
$11$	−306949.			−1.90591			−0.952956	−	0.303110i	$-0.901975\pi$
$11$	−306949.			−1.90591			−0.952956	+	0.303110i	$0.901975\pi$
$12$		−	12651.0i		−	0.0508417i
$13$	198968.			0.535878			0.267939	−	0.963436i	$-0.413657\pi$
$13$	198968.			0.535878			0.267939	+	0.963436i	$0.413657\pi$
$14$	−839160.			−1.56029
$15$	79307.8			0.104438
$16$	−1.28519e6			−1.22566
$17$	−2.08922e6			−1.47143			−0.735713	−	0.677293i	$-0.763153\pi$
$17$	−2.08922e6			−1.47143			−0.735713	+	0.677293i	$0.763153\pi$
$18$			2.41701e6i			1.27914i
$19$		−	2.97711e6i		−	1.20234i	−0.799121	−	0.601170i	$-0.794702\pi$
$19$		−	2.97711e6i		−	1.20234i	0.799121	−	0.601170i	$-0.205298\pi$
$20$			2.82896e6i			0.884050i
$21$	−383769.			−0.0939665
$22$		−	1.26401e7i		−	2.45265i
$23$	1.17271e6			0.182201			0.0911003	−	0.995842i	$-0.470962\pi$
$23$	1.17271e6			0.182201			0.0911003	+	0.995842i	$0.470962\pi$
$24$	−273163.			−0.0343056
$25$	−7.96877e6			−0.816002
$26$			8.19343e6i			0.689603i
$27$			2.21740e6i			0.154534i
$28$		−	1.36893e7i		−	0.795408i
$29$			2.43453e7i			1.18693i	0.804860	+	0.593464i	$0.202240\pi$
$29$			2.43453e7i			1.18693i	−0.804860	+	0.593464i	$0.797760\pi$
$30$			3.26587e6i			0.134398i
$31$	−3.70189e7			−1.29305			−0.646525	−	0.762893i	$-0.723778\pi$
$31$	−3.70189e7			−1.29305			−0.646525	+	0.762893i	$0.723778\pi$
$32$		−	3.80709e7i		−	1.13460i
$33$		−	5.78061e6i		−	0.147708i
$34$		−	8.60332e7i		−	1.89353i
$35$	8.58163e7			1.63392
$36$	−3.94289e7			−0.652082
$37$		−	7.72003e7i		−	1.11330i	−0.830749	−	0.556648i	$-0.812087\pi$
$37$		−	7.72003e7i		−	1.11330i	0.830749	−	0.556648i	$-0.187913\pi$
$38$	1.22597e8			1.54725
$39$			3.74706e6i			0.0415305i
$40$	6.10832e7			0.596516
$41$	−6.69942e7			−0.578253			−0.289127	−	0.957291i	$-0.593365\pi$
$41$	−6.69942e7			−0.578253			−0.289127	+	0.957291i	$0.593365\pi$
$42$		−	1.58035e7i		−	0.120922i
$43$	2.69450e7	−	1.44518e8i	0.183289	−	0.983059i
$43$	2.69450e7	−	1.44518e8i	0.183289	−	0.983059i
$44$	2.06198e8			1.25032
$45$		−	2.47175e8i		−	1.33950i
$46$			4.82916e7i			0.234468i
$47$	−4.29292e8			−1.87182			−0.935909	−	0.352242i	$-0.885420\pi$
$47$	−4.29292e8			−1.87182			−0.935909	+	0.352242i	$0.885420\pi$
$48$		−	2.42034e7i		−	0.0949884i
$49$	−1.32788e8			−0.470086
$50$		−	3.28152e8i		−	1.05009i
$51$		−	3.93451e7i		−	0.114036i
$52$	−1.33660e8			−0.351548
$53$	2.00012e8			0.478275			0.239137	−	0.970986i	$-0.423135\pi$
$53$	2.00012e8			0.478275			0.239137	+	0.970986i	$0.423135\pi$
$54$	−9.13119e7			−0.198865
$55$			1.29263e9i			2.56839i
$56$	−2.95580e8			−0.536704
$57$	5.60664e7			0.0931813
$58$	−1.00253e9			−1.52742
$59$	3.24891e8			0.454441			0.227221	−	0.973843i	$-0.427036\pi$
$59$	3.24891e8			0.454441			0.227221	+	0.973843i	$0.427036\pi$
$60$	−5.32764e7			−0.0685138
$61$		−	8.68845e8i		−	1.02871i	−0.857577	−	0.514355i	$-0.828031\pi$
$61$		−	8.68845e8i		−	1.02871i	0.857577	−	0.514355i	$-0.171969\pi$
$62$		−	1.52443e9i		−	1.66398i
$63$			1.19607e9i			1.20519i
$64$	2.51710e8			0.234423
$65$		−	8.37897e8i		−	0.722144i
$66$	2.38044e8			0.190080
$67$	−1.36258e9			−1.00923			−0.504614	−	0.863345i	$-0.668365\pi$
$67$	−1.36258e9			−1.00923			−0.504614	+	0.863345i	$0.668365\pi$
$68$	1.40347e9			0.965288
$69$			2.20850e7i			0.0141205i
$70$			3.53389e9i			2.10263i
$71$			2.65191e9i			1.46983i	0.678159	+	0.734916i	$0.262778\pi$
$71$			2.65191e9i			1.46983i	−0.678159	+	0.734916i	$0.737222\pi$
$72$			8.51353e8i			0.439995i
$73$		−	1.07991e7i		−	0.00520922i	−0.999997	−	0.00260461i	$-0.999171\pi$
$73$		−	1.07991e7i		−	0.00520922i	0.999997	−	0.00260461i	$-0.000829074\pi$
$74$	3.17909e9			1.43266
$75$		−	1.50072e8i		−	0.0632402i
$76$			1.99992e9i			0.788761i
$77$		−	6.25501e9i		−	2.31086i
$78$	−1.54303e8			−0.0534442
$79$	8.01396e8			0.260442			0.130221	−	0.991485i	$-0.458431\pi$
$79$	8.01396e8			0.260442			0.130221	+	0.991485i	$0.458431\pi$
$80$			5.41224e9i			1.65168i
$81$	3.42408e9			0.982017
$82$		−	2.75880e9i		−	0.744134i
$83$	−5.22410e9			−1.32624			−0.663118	−	0.748515i	$-0.730767\pi$
$83$	−5.22410e9			−1.32624			−0.663118	+	0.748515i	$0.730767\pi$
$84$	2.57803e8			0.0616441
$85$			8.79815e9i			1.98288i
$86$	5.95121e9	+	1.10959e9i	1.26506	+	0.235868i
$87$	−4.58482e8			−0.0919869
$88$		−	4.45225e9i		−	0.843658i
$89$			6.11548e9i			1.09517i	0.836751	+	0.547584i	$0.184452\pi$
$89$			6.11548e9i			1.09517i	−0.836751	+	0.547584i	$0.815548\pi$
$90$	1.01786e10			1.72375
$91$			4.05456e9i			0.649737i
$92$	−7.87784e8			−0.119528
$93$		−	6.97159e8i		−	0.100211i
$94$		−	1.76781e10i		−	2.40878i
$95$	−1.25373e10			−1.62026
$96$	7.16971e8			0.0879316
$97$	3.80330e8			0.0442897			0.0221448	−	0.999755i	$-0.492951\pi$
$97$	3.80330e8			0.0442897			0.0221448	+	0.999755i	$0.492951\pi$
$98$		−	5.46816e9i		−	0.604938i
$99$	−1.80162e10			−1.89446
$100$	5.35316e9			0.535316
$101$	−1.00808e9			−0.0959149			−0.0479575	−	0.998849i	$-0.515271\pi$
$101$	−1.00808e9			−0.0959149			−0.0479575	+	0.998849i	$0.515271\pi$
$102$	1.62022e9			0.146748
$103$	−7.72985e9			−0.666784			−0.333392	−	0.942788i	$-0.608193\pi$
$103$	−7.72985e9			−0.666784			−0.333392	+	0.942788i	$0.608193\pi$
$104$			2.88600e9i			0.237208i
$105$			1.61614e9i			0.126628i
$106$			8.23644e9i			0.615475i
$107$	1.71519e10			1.22291			0.611453	−	0.791281i	$-0.290585\pi$
$107$	1.71519e10			1.22291			0.611453	+	0.791281i	$0.290585\pi$
$108$		−	1.48958e9i		−	0.101378i
$109$	−1.06240e10			−0.690490			−0.345245	−	0.938513i	$-0.612204\pi$
$109$	−1.06240e10			−0.690490			−0.345245	+	0.938513i	$0.612204\pi$
$110$	−5.32301e10			−3.30517
$111$	1.45387e9			0.0862804
$112$		−	2.61897e10i		−	1.48607i
$113$			1.02518e10i			0.556426i	0.960519	+	0.278213i	$0.0897420\pi$
$113$			1.02518e10i			0.556426i	−0.960519	+	0.278213i	$0.910258\pi$
$114$			2.30880e9i			0.119912i
$115$		−	4.93852e9i		−	0.245532i
$116$		−	1.63543e10i		−	0.778651i
$117$	1.16783e10			0.532659
$118$			1.33789e10i			0.584804i
$119$		−	4.25740e10i		−	1.78406i
$120$			1.15035e9i			0.0462299i
$121$	6.82802e10			2.63250
$122$	3.57788e10			1.32381
$123$		−	1.26167e9i		−	0.0448146i
$124$	2.48681e10			0.848269
$125$		−	7.56694e9i		−	0.247953i
$126$	−4.92539e10			−1.55092
$127$	−4.52404e10			−1.36933			−0.684664	−	0.728858i	$-0.740051\pi$
$127$	−4.52404e10			−1.36933			−0.684664	+	0.728858i	$0.740051\pi$
$128$		−	2.86193e10i		−	0.832931i
$129$	2.72163e9	+	5.07441e8i	0.0761871	+	0.0142049i
$130$	3.45044e10			0.929303
$131$			2.50465e10i			0.649218i	0.945848	+	0.324609i	$0.105233\pi$
$131$			2.50465e10i			0.649218i	−0.945848	+	0.324609i	$0.894767\pi$
$132$			3.88322e9i			0.0968998i
$133$	6.06676e10			1.45780
$134$		−	5.61108e10i		−	1.29874i
$135$	9.33797e9			0.208249
$136$		−	3.03038e10i		−	0.651332i
$137$			9.00858e10i			1.86661i	0.359086	+	0.933304i	$0.383088\pi$
$137$			9.00858e10i			1.86661i	−0.359086	+	0.933304i	$0.616912\pi$
$138$	−9.09452e8			−0.0181712
$139$	5.76790e10			1.11159			0.555794	−	0.831320i	$-0.312414\pi$
$139$	5.76790e10			1.11159			0.555794	+	0.831320i	$0.312414\pi$
$140$	−5.76485e10			−1.07188
$141$		−	8.08464e9i		−	0.145066i
$142$	−1.09205e11			−1.89147
$143$	−6.10729e10			−1.02134
$144$	−7.54336e10			−1.21830
$145$	1.02523e11			1.59949
$146$	4.44703e8			0.00670356
$147$		−	2.50072e9i		−	0.0364317i
$148$			5.18606e10i			0.730347i
$149$			2.29987e10i			0.313164i	0.987665	+	0.156582i	$0.0500476\pi$
$149$			2.29987e10i			0.313164i	−0.987665	+	0.156582i	$0.949952\pi$
$150$	6.17991e9			0.0813816
$151$			9.49837e10i			1.20994i	0.796248	+	0.604971i	$0.206815\pi$
$151$			9.49837e10i			1.20994i	−0.796248	+	0.604971i	$0.793185\pi$
$152$	4.31826e10			0.532219
$153$	−1.22625e11			−1.46259
$154$	2.57579e11			2.97377
$155$			1.55895e11i			1.74250i
$156$		−	2.51715e9i		−	0.0272449i
$157$		−	1.21491e11i		−	1.27364i	−0.771012	−	0.636820i	$-0.780249\pi$
$157$		−	1.21491e11i		−	1.27364i	0.771012	−	0.636820i	$-0.219751\pi$
$158$			3.30012e10i			0.335154i
$159$			3.76673e9i			0.0370663i
$160$	−1.60325e11			−1.52898
$161$			2.38974e10i			0.220913i
$162$			1.41003e11i			1.26372i
$163$			1.84974e11i			1.60758i	0.594912	+	0.803791i	$0.297187\pi$
$163$			1.84974e11i			1.60758i	−0.594912	+	0.803791i	$0.702813\pi$
$164$	4.50045e10			0.379347
$165$	−2.43435e10			−0.199050
$166$		−	2.15127e11i		−	1.70669i
$167$	8.11760e10			0.624950			0.312475	−	0.949926i	$-0.398842\pi$
$167$	8.11760e10			0.624950			0.312475	+	0.949926i	$0.398842\pi$
$168$		−	5.56651e9i		−	0.0415946i
$169$	−9.82703e10			−0.712835
$170$	−3.62305e11			−2.55170
$171$		−	1.74740e11i		−	1.19512i
$172$	−1.81007e10	+	9.70824e10i	−0.120241	+	0.644908i
$173$	1.35005e10			0.0871203			0.0435602	−	0.999051i	$-0.486130\pi$
$173$	1.35005e10			0.0871203			0.0435602	+	0.999051i	$0.486130\pi$
$174$		−	1.88802e10i		−	0.118375i
$175$		−	1.62388e11i		−	0.989380i
$176$	3.94489e11			2.33599
$177$			6.11851e9i			0.0352192i
$178$	−2.51834e11			−1.40933
$179$			2.77340e11i			1.50920i	0.656185	+	0.754600i	$0.272169\pi$
$179$			2.77340e11i			1.50920i	−0.656185	+	0.754600i	$0.727831\pi$
$180$			1.66044e11i			0.878740i
$181$	1.47844e11			0.761044			0.380522	−	0.924772i	$-0.375744\pi$
$181$	1.47844e11			0.761044			0.380522	+	0.924772i	$0.375744\pi$
$182$	−1.66966e11			−0.836123
$183$	1.63625e10			0.0797251
$184$			1.70099e10i			0.0806517i
$185$	−3.25108e11			−1.50027
$186$	2.87088e10			0.128958
$187$	6.41283e11			2.80441
$188$	2.88384e11			1.22795
$189$	−4.51862e10			−0.187369
$190$		−	5.16281e11i		−	2.08506i
$191$			2.41346e10i			0.0949452i	0.998873	+	0.0474726i	$0.0151167\pi$
$191$			2.41346e10i			0.0949452i	−0.998873	+	0.0474726i	$0.984883\pi$
$192$			4.74032e9i			0.0181678i
$193$	3.27870e11			1.22438			0.612188	−	0.790712i	$-0.290290\pi$
$193$	3.27870e11			1.22438			0.612188	+	0.790712i	$0.290290\pi$
$194$			1.56619e10i			0.0569948i
$195$	1.57797e10			0.0559662
$196$	8.92024e10			0.308387
$197$	2.22343e11			0.749362			0.374681	−	0.927154i	$-0.377752\pi$
$197$	2.22343e11			0.749362			0.374681	+	0.927154i	$0.377752\pi$
$198$		−	7.41900e11i		−	2.43792i
$199$		−	8.68831e10i		−	0.278401i	−0.990264	−	0.139200i	$-0.955547\pi$
$199$		−	8.68831e10i		−	0.278401i	0.990264	−	0.139200i	$-0.0444532\pi$
$200$		−	1.15586e11i		−	0.361206i
$201$		−	2.56609e10i		−	0.0782152i
$202$		−	4.15122e10i		−	0.123430i
$203$	−4.96108e11			−1.43912
$204$			2.64308e10i			0.0748098i
$205$			2.82128e11i			0.779249i
$206$		−	3.18313e11i		−	0.858060i
$207$	6.88312e10			0.181106
$208$	−2.55712e11			−0.656803
$209$			9.13821e11i			2.29155i
$210$	−6.65519e10			−0.162954
$211$		−	6.37697e10i		−	0.152476i	−0.997090	−	0.0762381i	$-0.975709\pi$
$211$		−	6.37697e10i		−	0.152476i	0.997090	−	0.0762381i	$-0.0242909\pi$
$212$	−1.34362e11			−0.313759
$213$	−4.99421e10			−0.113912
$214$			7.06309e11i			1.57372i
$215$	−6.08598e11	−	1.13471e11i	−1.32476	−	0.246998i
$216$	−3.21631e10			−0.0684052
$217$		−	7.54372e11i		−	1.56779i
$218$		−	4.37495e11i		−	0.888568i
$219$	2.03374e8			0.000403714
$220$		−	8.68346e11i		−	1.68492i
$221$	−4.15686e11			−0.788505
$222$			5.98701e10i			0.111031i
$223$		−	2.01118e11i		−	0.364692i	−0.983234	−	0.182346i	$-0.941631\pi$
$223$		−	2.01118e11i		−	0.364692i	0.983234	−	0.182346i	$-0.0583691\pi$
$224$	7.75810e11			1.37567
$225$	−4.67722e11			−0.811101
$226$	−4.22165e11			−0.716045
$227$		−	7.86063e11i		−	1.30415i	−0.758154	−	0.652076i	$-0.773898\pi$
$227$		−	7.86063e11i		−	1.30415i	0.758154	−	0.652076i	$-0.226102\pi$
$228$	−3.76636e10			−0.0611290
$229$	−6.66086e11			−1.05768			−0.528839	−	0.848722i	$-0.677372\pi$
$229$	−6.66086e11			−1.05768			−0.528839	+	0.848722i	$0.677372\pi$
$230$	2.03367e11			0.315966
$231$	1.17797e11			0.179092
$232$	−3.53125e11			−0.525398
$233$		−	6.74973e11i		−	0.982895i	−0.870907	−	0.491447i	$-0.836468\pi$
$233$		−	6.74973e11i		−	0.982895i	0.870907	−	0.491447i	$-0.163532\pi$
$234$			4.80908e11i			0.685461i
$235$			1.80784e12i			2.52245i
$236$	−2.18251e11			−0.298123
$237$			1.50923e10i			0.0201843i
$238$	1.75319e12			2.29585
$239$	2.80487e11			0.359686			0.179843	−	0.983695i	$-0.442441\pi$
$239$	2.80487e11			0.359686			0.179843	+	0.983695i	$0.442441\pi$
$240$	−1.01926e11			−0.128006
$241$		−	8.56037e9i		−	0.0105295i	−0.999986	−	0.00526474i	$-0.998324\pi$
$241$		−	8.56037e9i		−	0.0105295i	0.999986	−	0.00526474i	$-0.00167583\pi$
$242$			2.81176e12i			3.38767i
$243$			1.95419e11i			0.230641i
$244$			5.83661e11i			0.674857i
$245$			5.59199e11i			0.633484i
$246$	5.19551e10			0.0576704
$247$		−	5.92349e11i		−	0.644307i
$248$		−	5.36954e11i		−	0.572373i
$249$		−	9.83828e10i		−	0.102783i
$250$	3.11604e11			0.319083
$251$	−1.08237e12			−1.08645			−0.543224	−	0.839588i	$-0.682797\pi$
$251$	−1.08237e12			−1.08645			−0.543224	+	0.839588i	$0.682797\pi$
$252$		−	8.03482e11i		−	0.790630i
$253$	−3.59961e11			−0.347258
$254$		−	1.86299e12i		−	1.76214i
$255$	−1.65691e11			−0.153673
$256$	1.43628e12			1.30629
$257$		−	1.25145e11i		−	0.111621i	−0.998441	−	0.0558106i	$-0.982226\pi$
$257$		−	1.25145e11i		−	0.111621i	0.998441	−	0.0558106i	$-0.0177743\pi$
$258$	−2.08963e10	+	1.12076e11i	−0.0182797	+	0.0980425i
$259$	1.57319e12			1.34984
$260$			5.62872e11i			0.473743i
$261$			1.42893e12i			1.17980i
$262$	−1.03141e12			−0.835456
$263$			8.17179e10i			0.0649439i	0.999473	+	0.0324720i	$0.0103380\pi$
$263$			8.17179e10i			0.0649439i	−0.999473	+	0.0324720i	$0.989662\pi$
$264$	8.38470e10			0.0653835
$265$		−	8.42296e11i		−	0.644519i
$266$			2.49827e12i			1.87599i
$267$	−1.15170e11			−0.0848755
$268$	9.15339e11			0.662076
$269$	1.08953e12			0.773534			0.386767	−	0.922177i	$-0.373592\pi$
$269$	1.08953e12			0.773534			0.386767	+	0.922177i	$0.373592\pi$
$270$			3.84535e11i			0.267989i
$271$	1.20425e12			0.823892			0.411946	−	0.911208i	$-0.364849\pi$
$271$	1.20425e12			0.823892			0.411946	+	0.911208i	$0.364849\pi$
$272$	2.68505e12			1.80346
$273$	−7.63576e10			−0.0503546
$274$	−3.70970e12			−2.40207
$275$	2.44601e12			1.55523
$276$		−	1.48359e10i		−	0.00926339i
$277$		−	9.20016e11i		−	0.564153i	−0.959392	−	0.282076i	$-0.908977\pi$
$277$		−	9.20016e11i		−	0.564153i	0.959392	−	0.282076i	$-0.0910231\pi$
$278$			2.37520e12i			1.43046i
$279$	−2.17280e12			−1.28528
$280$			1.24475e12i			0.723258i
$281$	−1.19875e12			−0.684224			−0.342112	−	0.939659i	$-0.611142\pi$
$281$	−1.19875e12			−0.684224			−0.342112	+	0.939659i	$0.611142\pi$
$282$	3.32923e11			0.186680
$283$	−2.28969e12			−1.26137			−0.630687	−	0.776037i	$-0.717227\pi$
$283$	−2.28969e12			−1.26137			−0.630687	+	0.776037i	$0.717227\pi$
$284$		−	1.78147e12i		−	0.964242i
$285$		−	2.36108e11i		−	0.125570i
$286$		−	2.51496e12i		−	1.31432i
$287$		−	1.36521e12i		−	0.701116i
$288$		−	2.23455e12i		−	1.12779i
$289$	2.34883e12			1.16510
$290$			4.22188e12i			2.05833i
$291$			7.16257e9i			0.00343245i
$292$			7.25446e9i			0.00341736i
$293$	−2.04015e11			−0.0944767			−0.0472384	−	0.998884i	$-0.515042\pi$
$293$	−2.04015e11			−0.0944767			−0.0472384	+	0.998884i	$0.515042\pi$
$294$	1.02979e11			0.0468827
$295$		−	1.36819e12i		−	0.612401i
$296$	1.11978e12			0.492804
$297$		−	6.80629e11i		−	0.294529i
$298$	−9.47080e11			−0.403000
$299$	2.33331e11			0.0976373
$300$			1.00813e11i			0.0414869i
$301$	2.94499e12	+	5.49085e11i	1.19193	+	0.222232i
$302$	−3.91140e12			−1.55703
$303$		−	1.89846e10i		−	0.00743340i
$304$			3.82617e12i			1.47366i
$305$	−3.65890e12			−1.38628
$306$		−	5.04966e12i		−	1.88215i
$307$	−1.58303e12			−0.580492			−0.290246	−	0.956952i	$-0.593737\pi$
$307$	−1.58303e12			−0.580492			−0.290246	+	0.956952i	$0.593737\pi$
$308$			4.20190e12i			1.51598i
$309$		−	1.45572e11i		−	0.0516757i
$310$	−6.41970e12			−2.24237
$311$	−1.19646e12			−0.411242			−0.205621	−	0.978632i	$-0.565921\pi$
$311$	−1.19646e12			−0.411242			−0.205621	+	0.978632i	$0.565921\pi$
$312$	−5.43506e10			−0.0183836
$313$		−	3.25449e12i		−	1.08333i	−0.840594	−	0.541665i	$-0.817794\pi$
$313$		−	3.25449e12i		−	1.08333i	0.840594	−	0.541665i	$-0.182206\pi$
$314$	5.00297e12			1.63900
$315$	5.03693e12			1.62410
$316$	−5.38351e11			−0.170856
$317$	−5.13842e11			−0.160521			−0.0802607	−	0.996774i	$-0.525575\pi$
$317$	−5.13842e11			−0.160521			−0.0802607	+	0.996774i	$0.525575\pi$
$318$	−1.55113e11			−0.0476993
$319$		−	7.47275e12i		−	2.26218i
$320$		−	1.06001e12i		−	0.315907i
$321$			3.23013e11i			0.0947752i
$322$	−9.84087e11			−0.284285
$323$			6.21983e12i			1.76915i
$324$	−2.30018e12			−0.644225
$325$	−1.58553e12			−0.437278
$326$	−7.61718e12			−2.06874
$327$		−	2.00077e11i		−	0.0535130i
$328$		−	9.71742e11i		−	0.255966i
$329$		−	8.74812e12i		−	2.26953i
$330$		−	1.00246e12i		−	0.256151i
$331$		−	2.16998e12i		−	0.546154i	−0.961992	−	0.273077i	$-0.911959\pi$
$331$		−	2.16998e12i		−	0.546154i	0.961992	−	0.273077i	$-0.0880413\pi$
$332$	3.50937e12			0.870040
$333$		−	4.53122e12i		−	1.10661i
$334$			3.34280e12i			0.804226i
$335$			5.73815e12i			1.36003i
$336$	4.93217e11			0.115171
$337$	4.97435e11			0.114442			0.0572211	−	0.998362i	$-0.481776\pi$
$337$	4.97435e11			0.114442			0.0572211	+	0.998362i	$0.481776\pi$
$338$		−	4.04674e12i		−	0.917322i
$339$	−1.93067e11			−0.0431230
$340$		−	5.91031e12i		−	1.30081i
$341$	1.13629e13			2.46444
$342$	7.19572e12			1.53796
$343$			3.05033e12i			0.642505i
$344$	2.09621e12	+	3.90833e11i	0.435154	+	0.0811333i
$345$	9.30047e10			0.0190287
$346$			5.55947e11i			0.112112i
$347$		−	5.03418e12i		−	1.00065i	−0.865838	−	0.500324i	$-0.833214\pi$
$347$		−	5.03418e12i		−	1.00065i	0.865838	−	0.500324i	$-0.166786\pi$
$348$	3.07993e11			0.0603455
$349$			7.27438e12i			1.40498i	0.711695	+	0.702488i	$0.247928\pi$
$349$			7.27438e12i			1.40498i	−0.711695	+	0.702488i	$0.752072\pi$
$350$	6.68708e12			1.27320
$351$			4.41191e11i			0.0828116i
$352$			1.16858e13i			2.16245i
$353$	7.54518e11			0.137656			0.0688282	−	0.997629i	$-0.478074\pi$
$353$	7.54518e11			0.137656			0.0688282	+	0.997629i	$0.478074\pi$
$354$	−2.51958e11			−0.0453223
$355$	1.11678e13			1.98073
$356$		−	4.10818e12i		−	0.718454i
$357$	8.01775e11			0.138265
$358$	−1.14208e13			−1.94214
$359$	−6.02737e12			−1.01078			−0.505389	−	0.862892i	$-0.668651\pi$
$359$	−6.02737e12			−1.01078			−0.505389	+	0.862892i	$0.668651\pi$
$360$	3.58524e12			0.592933
$361$	−2.73212e12			−0.445620
$362$			6.08815e12i			0.979361i
$363$			1.28589e12i			0.204019i
$364$		−	2.72372e12i		−	0.426242i
$365$	−4.54774e10			−0.00701990
$366$			6.73804e11i			0.102595i
$367$	−9.28837e12			−1.39511			−0.697556	−	0.716530i	$-0.745729\pi$
$367$	−9.28837e12			−1.39511			−0.697556	+	0.716530i	$0.745729\pi$
$368$	−1.50715e12			−0.223315
$369$	−3.93218e12			−0.574780
$370$		−	1.33878e13i		−	1.93064i
$371$			4.07585e12i			0.579894i
$372$			4.68328e11i			0.0657408i
$373$		−	3.36263e12i		−	0.465731i	−0.972509	−	0.232866i	$-0.925190\pi$
$373$		−	3.36263e12i		−	0.465731i	0.972509	−	0.232866i	$-0.0748102\pi$
$374$			2.64078e13i			3.60890i
$375$	1.42504e11			0.0192164
$376$		−	6.22682e12i		−	0.828566i
$377$			4.84392e12i			0.636049i
$378$		−	1.86075e12i		−	0.241118i
$379$	5.76499e11			0.0737229			0.0368615	−	0.999320i	$-0.488264\pi$
$379$	5.76499e11			0.0737229			0.0368615	+	0.999320i	$0.488264\pi$
$380$	8.42213e12			1.06293
$381$		−	8.51989e11i		−	0.106123i
$382$	−9.93854e11			−0.122182
$383$			4.64396e12i			0.563501i	0.959488	+	0.281751i	$0.0909151\pi$
$383$			4.64396e12i			0.563501i	−0.959488	+	0.281751i	$0.909085\pi$
$384$	5.38973e11			0.0645522
$385$	−2.63412e13			−3.11410
$386$			1.35016e13i			1.57561i
$387$	1.58152e12	−	8.48239e12i	0.182188	−	0.977155i
$388$	−2.55493e11			−0.0290550
$389$			6.56720e12i			0.737279i	0.929572	+	0.368640i	$0.120176\pi$
$389$			6.56720e12i			0.737279i	−0.929572	+	0.368640i	$0.879824\pi$
$390$			6.49803e11i			0.0720209i
$391$	−2.45003e12			−0.268095
$392$		−	1.92607e12i		−	0.208085i
$393$	−4.71688e11			−0.0503143
$394$			9.15600e12i			0.964328i
$395$		−	3.37486e12i		−	0.350970i
$396$	1.21027e13			1.24281
$397$	3.69878e11			0.0375064			0.0187532	−	0.999824i	$-0.494030\pi$
$397$	3.69878e11			0.0375064			0.0187532	+	0.999824i	$0.494030\pi$
$398$	3.57782e12			0.358264
$399$			1.14252e12i			0.112980i
$400$	1.02414e13			1.00014
$401$	1.28581e13			1.24009			0.620047	−	0.784564i	$-0.287113\pi$
$401$	1.28581e13			1.24009			0.620047	+	0.784564i	$0.287113\pi$
$402$	1.05671e12			0.100652
$403$	−7.36557e12			−0.692917
$404$	6.77191e11			0.0629223
$405$		−	1.44196e13i		−	1.32336i
$406$		−	2.04296e13i		−	1.85195i
$407$			2.36966e13i			2.12184i
$408$	5.70696e11			0.0504782
$409$		−	1.08776e13i		−	0.950424i	−0.879871	−	0.475212i	$-0.842371\pi$
$409$		−	1.08776e13i		−	0.950424i	0.879871	−	0.475212i	$-0.157629\pi$
$410$	−1.16179e13			−1.00279
$411$	−1.69654e12			−0.144662
$412$	5.19265e12			0.437425
$413$			6.62063e12i			0.550997i
$414$			2.83445e12i			0.233059i
$415$			2.19998e13i			1.78722i
$416$		−	7.57489e12i		−	0.608008i
$417$			1.08624e12i			0.0861481i
$418$	−3.76309e13			−2.94892
$419$		−	1.20480e13i		−	0.932919i	−0.884543	−	0.466459i	$-0.845529\pi$
$419$		−	1.20480e13i		−	0.932919i	0.884543	−	0.466459i	$-0.154471\pi$
$420$		−	1.08567e12i		−	0.0830710i
$421$			2.17260e12i			0.164274i	0.996621	+	0.0821372i	$0.0261746\pi$
$421$			2.17260e12i			0.164274i	−0.996621	+	0.0821372i	$0.973825\pi$
$422$	2.62602e12			0.196216
$423$	−2.51970e13			−1.86058
$424$			2.90115e12i			0.211710i
$425$	1.66485e13			1.20069
$426$		−	2.05660e12i		−	0.146589i
$427$	1.77053e13			1.24728
$428$	−1.15221e13			−0.802253
$429$		−	1.15016e12i		−	0.0791535i
$430$	4.67271e12	−	2.50619e13i	0.317853	−	1.70479i
$431$	2.01490e13			1.35477			0.677386	−	0.735628i	$-0.263113\pi$
$431$	2.01490e13			1.35477			0.677386	+	0.735628i	$0.263113\pi$
$432$		−	2.84979e12i		−	0.189406i
$433$			2.69988e13i			1.77380i	0.461961	+	0.886900i	$0.347146\pi$
$433$			2.69988e13i			1.77380i	−0.461961	+	0.886900i	$0.652854\pi$
$434$	3.10648e13			2.01753
$435$			1.93077e12i			0.123961i
$436$	7.13688e12			0.452977
$437$		−	3.49127e12i		−	0.219067i
$438$			8.37486e9i			0.000519526i
$439$	−2.46701e12			−0.151303			−0.0756516	−	0.997134i	$-0.524104\pi$
$439$	−2.46701e12			−0.151303			−0.0756516	+	0.997134i	$0.524104\pi$
$440$	−1.87494e13			−1.13691
$441$	−7.79389e12			−0.467263
$442$		−	1.71178e13i		−	1.01470i
$443$	−2.40592e13			−1.41014			−0.705070	−	0.709138i	$-0.749084\pi$
$443$	−2.40592e13			−1.41014			−0.705070	+	0.709138i	$0.749084\pi$
$444$	−9.76665e11			−0.0566018
$445$	2.57537e13			1.47584
$446$	8.28197e12			0.469309
$447$	−4.33123e11			−0.0242702
$448$			5.12934e12i			0.284231i
$449$		−	2.08597e13i		−	1.14308i	−0.820575	−	0.571539i	$-0.806346\pi$
$449$		−	2.08597e13i		−	1.14308i	0.820575	−	0.571539i	$-0.193654\pi$
$450$		−	1.92606e13i		−	1.04378i
$451$	2.05638e13			1.10210
$452$		−	6.88680e12i		−	0.365027i
$453$	−1.78878e12			−0.0937704
$454$	3.23698e13			1.67827
$455$	1.70747e13			0.875579
$456$			8.13236e11i			0.0412470i
$457$		−	5.28568e12i		−	0.265167i	−0.991172	−	0.132583i	$-0.957673\pi$
$457$		−	5.28568e12i		−	0.265167i	0.991172	−	0.132583i	$-0.0423273\pi$
$458$		−	2.74292e13i		−	1.36109i
$459$		−	4.63263e12i		−	0.227386i
$460$			3.31754e12i			0.161074i
$461$	−2.05871e13			−0.988760			−0.494380	−	0.869246i	$-0.664605\pi$
$461$	−2.05871e13			−0.988760			−0.494380	+	0.869246i	$0.664605\pi$
$462$			4.85086e12i			0.230467i
$463$			5.27910e12i			0.248116i	0.992275	+	0.124058i	$0.0395909\pi$
$463$			5.27910e12i			0.248116i	−0.992275	+	0.124058i	$0.960409\pi$
$464$		−	3.12884e13i		−	1.45477i
$465$	−2.93589e12			−0.135044
$466$	2.77952e13			1.26485
$467$		−	2.92808e13i		−	1.31825i	−0.752032	−	0.659127i	$-0.770926\pi$
$467$		−	2.92808e13i		−	1.31825i	0.752032	−	0.659127i	$-0.229074\pi$
$468$	−7.84508e12			−0.349436
$469$		−	2.77668e13i		−	1.22366i
$470$	−7.44465e13			−3.24605
$471$	2.28798e12			0.0987071
$472$			4.71250e12i			0.201160i
$473$	−8.27073e12	+	4.43596e13i	−0.349332	+	1.87362i
$474$	−6.21495e11			−0.0259744
$475$			2.37239e13i			0.981112i
$476$			2.85998e13i			1.17038i
$477$	1.17396e13			0.475402
$478$			1.15504e13i			0.462868i
$479$	−2.31846e13			−0.919435			−0.459718	−	0.888065i	$-0.652049\pi$
$479$	−2.31846e13			−0.919435			−0.459718	+	0.888065i	$0.652049\pi$
$480$		−	3.01932e12i		−	0.118496i
$481$		−	1.53604e13i		−	0.596591i
$482$	3.52513e11			0.0135500
$483$	−4.50047e11			−0.0171207
$484$	−4.58684e13			−1.72698
$485$		−	1.60166e12i		−	0.0596844i
$486$	−8.04731e12			−0.296804
$487$	−6.90238e12			−0.251973			−0.125986	−	0.992032i	$-0.540210\pi$
$487$	−6.90238e12			−0.251973			−0.125986	+	0.992032i	$0.540210\pi$
$488$	1.26025e13			0.455362
$489$	−3.48352e12			−0.124588
$490$	−2.30276e13			−0.815209
$491$			4.35665e13i			1.52667i	0.646002	+	0.763336i	$0.276440\pi$
$491$			4.35665e13i			1.52667i	−0.646002	+	0.763336i	$0.723560\pi$
$492$			8.47547e11i			0.0293994i
$493$		−	5.08625e13i		−	1.74648i
$494$	2.43927e13			0.829136
$495$			7.58701e13i			2.55296i
$496$	4.75765e13			1.58484
$497$	−5.40407e13			−1.78213
$498$	4.05137e12			0.132268
$499$			1.71296e13i			0.553660i	0.960919	+	0.276830i	$0.0892839\pi$
$499$			1.71296e13i			0.553660i	−0.960919	+	0.276830i	$0.910716\pi$
$500$			5.08322e12i			0.162663i
$501$			1.52875e12i			0.0484336i
$502$		−	4.45718e13i		−	1.39811i
$503$		−	8.11768e11i		−	0.0252111i	−0.999921	−	0.0126056i	$-0.995987\pi$
$503$		−	8.11768e11i		−	0.0252111i	0.999921	−	0.0126056i	$-0.00401258\pi$
$504$	−1.73489e13			−0.533481
$505$			4.24523e12i			0.129254i
$506$		−	1.48231e13i		−	0.446874i
$507$		−	1.85068e12i		−	0.0552447i
$508$	3.03910e13			0.898310
$509$	−5.59364e13			−1.63721			−0.818607	−	0.574355i	$-0.805253\pi$
$509$	−5.59364e13			−1.63721			−0.818607	+	0.574355i	$0.805253\pi$
$510$		−	6.82311e12i		−	0.197757i
$511$	2.20064e11			0.00631603
$512$			2.98396e13i			0.848092i
$513$	6.60145e12			0.185803
$514$	5.15342e12			0.143641
$515$			3.25521e13i			0.898552i
$516$	−1.82830e12	−	3.40882e11i	−0.0499804	−	0.00931870i
$517$	1.31771e14			3.56752
$518$			6.47834e13i			1.73706i
$519$			2.54248e11i			0.00675182i
$520$	1.21536e13			0.319660
$521$		−	1.30236e12i		−	0.0339267i	−0.999856	−	0.0169633i	$-0.994600\pi$
$521$		−	1.30236e12i		−	0.0339267i	0.999856	−	0.0169633i	$-0.00539985\pi$
$522$	−5.88429e13			−1.51824
$523$		−	1.21766e13i		−	0.311185i	−0.987821	−	0.155592i	$-0.950271\pi$
$523$		−	1.21766e13i		−	0.311185i	0.987821	−	0.155592i	$-0.0497287\pi$
$524$		−	1.68254e13i		−	0.425901i
$525$	3.05817e12			0.0766769
$526$	−3.36512e12			−0.0835741
$527$	7.73405e13			1.90263
$528$			7.42921e12i			0.181039i
$529$	−4.00513e13			−0.966803
$530$	3.46855e13			0.829409
$531$	1.90693e13			0.451712
$532$	−4.07545e13			−0.956350
$533$	−1.33297e13			−0.309873
$534$		−	4.74266e12i		−	0.109223i
$535$		−	7.22304e13i		−	1.64798i
$536$		−	1.97641e13i		−	0.446738i
$537$	−5.22299e12			−0.116963
$538$			4.48667e13i			0.995434i
$539$	4.07591e13			0.895943
$540$	−6.27294e12			−0.136616
$541$	−1.10489e13			−0.238414			−0.119207	−	0.992869i	$-0.538035\pi$
$541$	−1.10489e13			−0.238414			−0.119207	+	0.992869i	$0.538035\pi$
$542$			4.95906e13i			1.06024i
$543$			2.78426e12i			0.0589809i
$544$			7.95384e13i			1.66948i
$545$			4.47402e13i			0.930499i
$546$		−	3.14438e12i		−	0.0647995i
$547$	8.07039e13			1.64800			0.824002	−	0.566588i	$-0.191737\pi$
$547$	8.07039e13			1.64800			0.824002	+	0.566588i	$0.191737\pi$
$548$		−	6.05166e13i		−	1.22454i
$549$		−	5.09963e13i		−	1.02253i
$550$			1.00726e14i			2.00137i
$551$	7.24786e13			1.42709
$552$	−3.20339e11			−0.00625050
$553$			1.63308e13i			0.315779i
$554$	3.78860e13			0.725988
$555$		−	6.12259e12i		−	0.116271i
$556$	−3.87468e13			−0.729226
$557$	3.13382e12			0.0584518			0.0292259	−	0.999573i	$-0.490696\pi$
$557$	3.13382e12			0.0584518			0.0292259	+	0.999573i	$0.490696\pi$
$558$		−	8.94753e13i		−	1.65399i
$559$	5.36118e12	−	2.87544e13i	0.0982203	−	0.526800i
$560$	−1.10291e14			−2.00262
$561$			1.20769e13i			0.217342i
$562$		−	4.93643e13i		−	0.880504i
$563$	−5.11185e13			−0.903725			−0.451863	−	0.892088i	$-0.649240\pi$
$563$	−5.11185e13			−0.903725			−0.451863	+	0.892088i	$0.649240\pi$
$564$			5.43099e12i			0.0951664i
$565$	4.31725e13			0.749834
$566$		−	9.42885e13i		−	1.62322i
$567$			6.97760e13i			1.19067i
$568$	−3.84656e13			−0.650625
$569$	−2.55807e13			−0.428895			−0.214447	−	0.976736i	$-0.568795\pi$
$569$	−2.55807e13			−0.428895			−0.214447	+	0.976736i	$0.568795\pi$
$570$	9.72286e12			0.161592
$571$			2.03558e13i			0.335357i	0.985842	+	0.167678i	$0.0536270\pi$
$571$			2.03558e13i			0.335357i	−0.985842	+	0.167678i	$0.946373\pi$
$572$	4.10268e13			0.670019
$573$	−4.54514e11			−0.00735825
$574$	5.62189e13			0.902241
$575$	−9.34502e12			−0.148676
$576$	1.47739e13			0.233015
$577$			3.08235e13i			0.481951i	0.970531	+	0.240976i	$0.0774674\pi$
$577$			3.08235e13i			0.481951i	−0.970531	+	0.240976i	$0.922533\pi$
$578$			9.67240e13i			1.49932i
$579$			6.17460e12i			0.0948891i
$580$	−6.88718e13			−1.04930
$581$		−	1.06457e14i		−	1.60802i
$582$	−2.94952e11			−0.00441710
$583$	−6.13935e13			−0.911549
$584$	1.56639e11			0.00230588
$585$		−	4.91798e13i		−	0.717807i
$586$		−	8.40129e12i		−	0.121579i
$587$			1.42551e13i			0.204541i	0.994757	+	0.102270i	$0.0326107\pi$
$587$			1.42551e13i			0.204541i	−0.994757	+	0.102270i	$0.967389\pi$
$588$			1.67990e12i			0.0239000i
$589$			1.10209e14i			1.55468i
$590$	5.63416e13			0.788077
$591$			4.18727e12i			0.0580755i
$592$			9.92175e13i			1.36452i
$593$		−	8.86135e13i		−	1.20844i	−0.796816	−	0.604222i	$-0.793484\pi$
$593$		−	8.86135e13i		−	1.20844i	0.796816	−	0.604222i	$-0.206516\pi$
$594$	2.80281e13			0.379019
$595$	−1.79289e14			−2.40419
$596$		−	1.54498e13i		−	0.205443i
$597$	1.63623e12			0.0215760
$598$			9.60848e12i			0.125646i
$599$	1.17392e14			1.52232			0.761159	−	0.648566i	$-0.224631\pi$
$599$	1.17392e14			1.52232			0.761159	+	0.648566i	$0.224631\pi$
$600$	2.17677e12			0.0279935
$601$		−	8.60541e13i		−	1.09749i	−0.835991	−	0.548743i	$-0.815106\pi$
$601$		−	8.60541e13i		−	1.09749i	0.835991	−	0.548743i	$-0.184894\pi$
$602$	−2.26111e13	+	1.21274e14i	−0.285983	+	1.53385i
$603$	−7.99760e13			−1.00317
$604$		−	6.38069e13i		−	0.793748i
$605$		−	2.87543e14i		−	3.54753i
$606$	7.81779e11			0.00956579
$607$		−	2.31920e12i		−	0.0281446i	−0.999901	−	0.0140723i	$-0.995521\pi$
$607$		−	2.31920e12i		−	0.0281446i	0.999901	−	0.0140723i	$-0.00447950\pi$
$608$	−1.13341e14			−1.36418
$609$		−	9.34295e12i		−	0.111532i
$610$		−	1.50672e14i		−	1.78396i
$611$	−8.54153e13			−1.00307
$612$	8.23755e13			0.959491
$613$	−4.60706e13			−0.532257			−0.266129	−	0.963938i	$-0.585745\pi$
$613$	−4.60706e13			−0.532257			−0.266129	+	0.963938i	$0.585745\pi$
$614$		−	6.51885e13i		−	0.747014i
$615$	−5.31317e12			−0.0603918
$616$	9.07280e13			1.02291
$617$	−1.11511e14			−1.24707			−0.623535	−	0.781796i	$-0.714304\pi$
$617$	−1.11511e14			−1.24707			−0.623535	+	0.781796i	$0.714304\pi$
$618$	5.99462e12			0.0664997
$619$	1.41742e14			1.55972			0.779859	−	0.625955i	$-0.215291\pi$
$619$	1.41742e14			1.55972			0.779859	+	0.625955i	$0.215291\pi$
$620$		−	1.04725e14i		−	1.14312i
$621$			2.60036e12i			0.0281563i
$622$		−	4.92700e13i		−	0.529213i
$623$	−1.24621e14			−1.32786
$624$		−	4.81570e12i		−	0.0509022i
$625$	−1.09686e14			−1.15014
$626$	1.34019e14			1.39410
$627$	−1.72095e13			−0.177595
$628$			8.16138e13i			0.835536i
$629$			1.61288e14i			1.63813i
$630$			2.07419e14i			2.09000i
$631$		−	1.17813e14i		−	1.17774i	−0.808230	−	0.588868i	$-0.799574\pi$
$631$		−	1.17813e14i		−	1.17774i	0.808230	−	0.588868i	$-0.200426\pi$
$632$			1.16241e13i			0.115286i
$633$	1.20094e12			0.0118169
$634$		−	2.11598e13i		−	0.206569i
$635$			1.90517e14i			1.84530i
$636$		−	2.53036e12i		−	0.0243163i
$637$	−2.64205e13			−0.251909
$638$	3.07726e14			2.91112
$639$			1.55652e14i			1.46100i
$640$	−1.20522e14			−1.12245
$641$		−	1.89395e14i		−	1.75017i	−0.483973	−	0.875083i	$-0.660807\pi$
$641$		−	1.89395e14i		−	1.75017i	0.483973	−	0.875083i	$-0.339193\pi$
$642$	−1.33016e13			−0.121963
$643$	4.33309e13			0.394224			0.197112	−	0.980381i	$-0.436844\pi$
$643$	4.33309e13			0.394224			0.197112	+	0.980381i	$0.436844\pi$
$644$		−	1.60535e13i		−	0.144924i
$645$	2.13695e12	−	1.14614e13i	0.0191424	−	0.102669i
$646$	−2.56131e14			−2.27666
$647$		−	5.57765e13i		−	0.491960i	−0.969275	−	0.245980i	$-0.920890\pi$
$647$		−	5.57765e13i		−	0.491960i	0.969275	−	0.245980i	$-0.0791098\pi$
$648$			4.96658e13i			0.434693i
$649$	−9.97249e13			−0.866124
$650$		−	6.52916e13i		−	0.562717i
$651$	1.42067e13			0.121503
$652$		−	1.24259e14i		−	1.05461i
$653$			8.97054e13i			0.755531i	0.925901	+	0.377766i	$0.123308\pi$
$653$			8.97054e13i			0.755531i	−0.925901	+	0.377766i	$0.876692\pi$
$654$	8.23912e12			0.0688640
$655$	1.05476e14			0.874880
$656$	8.61006e13			0.708740
$657$		−	6.33845e11i		−	0.00517793i
$658$	3.60245e14			2.92057
$659$	−1.01949e14			−0.820264			−0.410132	−	0.912026i	$-0.634517\pi$
$659$	−1.01949e14			−0.820264			−0.410132	+	0.912026i	$0.634517\pi$
$660$	1.63531e13			0.130581
$661$	1.91888e14			1.52069			0.760346	−	0.649518i	$-0.225029\pi$
$661$	1.91888e14			1.52069			0.760346	+	0.649518i	$0.225029\pi$
$662$	8.93589e13			0.702826
$663$		−	7.82841e12i		−	0.0611091i
$664$		−	7.57748e13i		−	0.587063i
$665$		−	2.55485e14i		−	1.96452i
$666$	1.86594e14			1.42406
$667$			2.85498e13i			0.216259i
$668$	−5.45313e13			−0.409981
$669$	3.78755e12			0.0282636
$670$	−2.36295e14			−1.75017
$671$			2.66691e14i			1.96063i
$672$			1.46104e13i			0.106615i
$673$			2.47373e14i			1.79174i	0.444311	+	0.895872i	$0.353448\pi$
$673$			2.47373e14i			1.79174i	−0.444311	+	0.895872i	$0.646552\pi$
$674$			2.04842e13i			0.147272i
$675$		−	1.76700e13i		−	0.126101i
$676$	6.60147e13			0.467635
$677$		−	1.53590e14i		−	1.07999i	−0.841667	−	0.539996i	$-0.818426\pi$
$677$		−	1.53590e14i		−	1.07999i	0.841667	−	0.539996i	$-0.181574\pi$
$678$		−	7.95042e12i		−	0.0554935i
$679$			7.75037e12i			0.0536999i
$680$	−1.27616e14			−0.877729
$681$	1.48035e13			0.101072
$682$			4.67921e14i			3.17140i
$683$	5.59491e13			0.376434			0.188217	−	0.982127i	$-0.439729\pi$
$683$	5.59491e13			0.376434			0.188217	+	0.982127i	$0.439729\pi$
$684$			1.17384e14i			0.784024i
$685$	3.79371e14			2.51543
$686$	−1.25612e14			−0.826817
$687$		−	1.25441e13i		−	0.0819699i
$688$	−3.46295e13	+	1.85734e14i	−0.224649	+	1.20489i
$689$	3.97960e13			0.256297
$690$			3.82990e12i			0.0244874i
$691$			5.03376e13i			0.319523i	0.987156	+	0.159762i	$0.0510726\pi$
$691$			5.03376e13i			0.319523i	−0.987156	+	0.159762i	$0.948927\pi$
$692$	−9.06919e12			−0.0571529
$693$		−	3.67133e14i		−	2.29698i
$694$	2.07306e14			1.28770
$695$		−	2.42899e14i		−	1.49797i
$696$		−	6.65022e12i		−	0.0407183i
$697$	1.39965e14			0.850858
$698$	−2.99557e14			−1.80802
$699$	1.27114e13			0.0761743
$700$			1.09087e14i			0.649055i
$701$	−1.59980e14			−0.945095			−0.472548	−	0.881305i	$-0.656666\pi$
$701$	−1.59980e14			−0.945095			−0.472548	+	0.881305i	$0.656666\pi$
$702$	−1.81681e13			−0.106567
$703$	−2.29834e14			−1.33856
$704$	−7.72621e13			−0.446790
$705$	−3.40462e13			−0.195489
$706$			3.10708e13i			0.177145i
$707$		−	2.05426e13i		−	0.116294i
$708$		−	4.11021e12i		−	0.0231046i
$709$	−3.37818e14			−1.88561			−0.942803	−	0.333350i	$-0.891821\pi$
$709$	−3.37818e14			−1.88561			−0.942803	+	0.333350i	$0.891821\pi$
$710$			4.59886e14i			2.54893i
$711$	4.70374e13			0.258878
$712$	−8.87042e13			−0.484780
$713$	−4.34123e13			−0.235594
$714$			3.30169e13i			0.177928i
$715$			2.57192e14i			1.37634i
$716$		−	1.86307e14i		−	0.990068i
$717$			5.28228e12i			0.0278757i
$718$		−	2.48205e14i		−	1.30074i
$719$	−1.71498e14			−0.892512			−0.446256	−	0.894905i	$-0.647243\pi$
$719$	−1.71498e14			−0.892512			−0.446256	+	0.894905i	$0.647243\pi$
$720$			3.17668e14i			1.64176i
$721$		−	1.57519e14i		−	0.808456i
$722$		−	1.12508e14i		−	0.573453i
$723$	1.61213e11			0.000816035
$724$	−9.93164e13			−0.499262
$725$		−	1.94002e14i		−	0.968537i
$726$	−5.29524e13			−0.262544
$727$		−	3.28609e13i		−	0.161811i	−0.996722	−	0.0809053i	$-0.974219\pi$
$727$		−	3.28609e13i		−	0.161811i	0.996722	−	0.0809053i	$-0.0257811\pi$
$728$	−5.88109e13			−0.287608
$729$	1.98508e14			0.964143
$730$		−	1.87274e12i		−	0.00903366i
$731$	−5.62939e13	+	3.01929e14i	−0.269696	+	1.44650i
$732$	−1.09918e13			−0.0523014
$733$			3.08912e14i			1.45987i	0.683515	+	0.729937i	$0.260451\pi$
$733$			3.08912e14i			1.45987i	−0.683515	+	0.729937i	$0.739549\pi$
$734$		−	3.82492e14i		−	1.79532i
$735$	−1.05311e13			−0.0490950
$736$		−	4.46460e13i		−	0.206725i
$737$	4.18244e14			1.92350
$738$		−	1.61926e14i		−	0.739665i
$739$			2.73153e14i			1.23932i	0.784869	+	0.619661i	$0.212730\pi$
$739$			2.73153e14i			1.23932i	−0.784869	+	0.619661i	$0.787270\pi$
$740$	2.18397e14			0.984209
$741$	1.11554e13			0.0499338
$742$	−1.67842e14			−0.746246
$743$		−	2.07176e14i		−	0.914946i	−0.889224	−	0.457473i	$-0.848755\pi$
$743$		−	2.07176e14i		−	0.914946i	0.889224	−	0.457473i	$-0.151245\pi$
$744$	1.01122e13			0.0443589
$745$	9.68527e13			0.422017
$746$	1.38472e14			0.599333
$747$	−3.06625e14			−1.31827
$748$	−4.30792e14			−1.83975
$749$			3.49521e14i			1.48274i
$750$			5.86828e12i			0.0247289i
$751$		−	2.30080e13i		−	0.0963115i	−0.998840	−	0.0481558i	$-0.984666\pi$
$751$		−	2.30080e13i		−	0.0963115i	0.998840	−	0.0481558i	$-0.0153344\pi$
$752$	5.51724e14			2.29421
$753$		−	2.03838e13i		−	0.0841997i
$754$	−1.99471e14			−0.818509
$755$	3.99998e14			1.63051
$756$	3.03546e13			0.122918
$757$			1.51453e14i			0.609256i	0.952471	+	0.304628i	$0.0985321\pi$
$757$			1.51453e14i			0.609256i	−0.952471	+	0.304628i	$0.901468\pi$
$758$			2.37401e13i			0.0948715i
$759$		−	6.77896e12i		−	0.0269125i
$760$		−	1.81851e14i		−	0.717214i
$761$		−	1.71220e14i		−	0.670858i	−0.942065	−	0.335429i	$-0.891119\pi$
$761$		−	1.71220e14i		−	0.670858i	0.942065	−	0.335429i	$-0.108881\pi$
$762$	3.50847e13			0.136566
$763$		−	2.16497e14i		−	0.837200i
$764$		−	1.62128e13i		−	0.0622861i
$765$			5.16402e14i			1.97097i
$766$	−1.91237e14			−0.725150
$767$	6.46428e13			0.243525
$768$			2.70488e13i			0.101238i
$769$	1.83718e14			0.683155			0.341577	−	0.939854i	$-0.389039\pi$
$769$	1.83718e14			0.683155			0.341577	+	0.939854i	$0.389039\pi$
$770$		−	1.08472e15i		−	4.00743i
$771$	2.35679e12			0.00865064
$772$	−2.20252e14			−0.803218
$773$		−	3.49327e14i		−	1.26571i	−0.774270	−	0.632855i	$-0.781883\pi$
$773$		−	3.49327e14i		−	1.26571i	0.774270	−	0.632855i	$-0.218117\pi$
$774$	3.49302e14	+	6.51264e13i	1.25747	+	0.234451i
$775$	2.94995e14			1.05513
$776$			5.51664e12i			0.0196050i
$777$			2.96271e13i			0.104612i
$778$	−2.70435e14			−0.948779
$779$			1.99449e14i			0.695257i
$780$	−1.06003e13			−0.0367150
$781$		−	8.14002e14i		−	2.80137i
$782$		−	1.00892e14i		−	0.345002i
$783$	−5.39832e13			−0.183421
$784$	1.70658e14			0.576165
$785$	−5.11627e14			−1.71635
$786$		−	1.94240e13i		−	0.0647478i
$787$	−3.93245e14			−1.30253			−0.651267	−	0.758848i	$-0.725762\pi$
$787$	−3.93245e14			−1.30253			−0.651267	+	0.758848i	$0.725762\pi$
$788$	−1.49362e14			−0.491598
$789$	−1.53895e12			−0.00503315
$790$	1.38976e14			0.451651
$791$	−2.08911e14			−0.674650
$792$		−	2.61322e14i		−	0.838591i
$793$		−	1.72872e14i		−	0.551263i
$794$			1.52315e13i			0.0482657i
$795$	1.58625e13			0.0499502
$796$			5.83652e13i			0.182637i
$797$	−2.18666e13			−0.0679969			−0.0339984	−	0.999422i	$-0.510824\pi$
$797$	−2.18666e13			−0.0679969			−0.0339984	+	0.999422i	$0.510824\pi$
$798$	−4.70487e13			−0.145390
$799$	8.96884e14			2.75424
$800$			3.03379e14i			0.925838i
$801$			3.58944e14i			1.08859i
$802$			5.29493e14i			1.59584i
$803$			3.31477e12i			0.00992831i
$804$			1.72381e13i			0.0513109i
$805$	1.00637e14			0.297700
$806$		−	3.03312e14i		−	0.891691i
$807$			2.05186e13i			0.0599489i
$808$		−	1.46220e13i		−	0.0424570i
$809$	−5.48438e14			−1.58265			−0.791326	−	0.611395i	$-0.790609\pi$
$809$	−5.48438e14			−1.58265			−0.791326	+	0.611395i	$0.790609\pi$
$810$	5.93794e14			1.70298
$811$		−	2.07834e14i		−	0.592395i	−0.955127	−	0.296198i	$-0.904281\pi$
$811$		−	2.07834e14i		−	0.592395i	0.955127	−	0.296198i	$-0.0957187\pi$
$812$	3.33269e14			0.944092
$813$			2.26790e13i			0.0638516i
$814$	−9.75817e14			−2.73053
$815$	7.78967e14			2.16636
$816$			5.05662e13i			0.139768i
$817$	−4.30246e14	−	8.02182e13i	−1.18197	−	0.220375i
$818$	4.47937e14			1.22307
$819$			2.37980e14i			0.645834i
$820$		−	1.89524e14i		−	0.511205i
$821$	2.05536e14			0.551027			0.275513	−	0.961297i	$-0.411152\pi$
$821$	2.05536e14			0.551027			0.275513	+	0.961297i	$0.411152\pi$
$822$		−	6.98630e13i		−	0.186161i
$823$	3.65767e14			0.968734			0.484367	−	0.874865i	$-0.339050\pi$
$823$	3.65767e14			0.968734			0.484367	+	0.874865i	$0.339050\pi$
$824$		−	1.12120e14i		−	0.295154i
$825$			4.60644e13i			0.120530i
$826$	−2.72635e14			−0.709058
$827$	1.09701e14			0.283584			0.141792	−	0.989896i	$-0.454714\pi$
$827$	1.09701e14			0.283584			0.141792	+	0.989896i	$0.454714\pi$
$828$	−4.62385e13			−0.118810
$829$		−	3.06525e14i		−	0.782876i	−0.920205	−	0.391438i	$-0.871978\pi$
$829$		−	3.06525e14i		−	0.782876i	0.920205	−	0.391438i	$-0.128022\pi$
$830$	−9.05947e14			−2.29992
$831$	1.73262e13			0.0437218
$832$	5.00821e13			0.125622
$833$	2.77422e14			0.691698
$834$	−4.47310e13			−0.110861
$835$		−	3.41850e14i		−	0.842177i
$836$		−	6.13875e14i		−	1.50331i
$837$		−	8.20858e13i		−	0.199821i
$838$	4.96132e14			1.20054
$839$			6.66576e14i			1.60339i	0.597731	+	0.801697i	$0.296069\pi$
$839$			6.66576e14i			1.60339i	−0.597731	+	0.801697i	$0.703931\pi$
$840$	−2.34418e13			−0.0560525
$841$	−1.71985e14			−0.408800
$842$	−8.94672e13			−0.211399
$843$		−	2.25755e13i		−	0.0530273i
$844$			4.28384e13i			0.100028i
$845$			4.13838e14i			0.960610i
$846$		−	1.03761e15i		−	2.39431i
$847$			1.39141e15i			3.19183i
$848$	−2.57055e14			−0.586201
$849$		−	4.31205e13i		−	0.0977564i
$850$			6.85580e14i			1.54512i
$851$		−	9.05332e13i		−	0.202843i
$852$	3.35494e13			0.0747287
$853$	−3.35384e14			−0.742673			−0.371337	−	0.928498i	$-0.621100\pi$
$853$	−3.35384e14			−0.742673			−0.371337	+	0.928498i	$0.621100\pi$
$854$			7.29100e14i			1.60508i
$855$	−7.35867e14			−1.61053
$856$			2.48786e14i			0.541323i
$857$	−1.16896e14			−0.252868			−0.126434	−	0.991975i	$-0.540353\pi$
$857$	−1.16896e14			−0.252868			−0.126434	+	0.991975i	$0.540353\pi$
$858$	4.73630e13			0.101860
$859$			2.09378e14i			0.447678i	0.974626	+	0.223839i	$0.0718589\pi$
$859$			2.09378e14i			0.447678i	−0.974626	+	0.223839i	$0.928141\pi$
$860$	4.08835e14	+	7.62262e13i	0.869073	+	0.162036i
$861$	2.57103e13			0.0543364
$862$			8.29728e14i			1.74341i
$863$		−	2.08207e12i		−	0.00434952i	−0.999998	−	0.00217476i	$-0.999308\pi$
$863$		−	2.08207e12i		−	0.00434952i	0.999998	−	0.00217476i	$-0.000692249\pi$
$864$	8.44185e13			0.175335
$865$		−	5.68536e13i		−	0.117403i
$866$	−1.11180e15			−2.28264
$867$			4.42343e13i			0.0902950i
$868$			5.06762e14i			1.02850i
$869$	−2.45988e14			−0.496380
$870$	−7.95085e13			−0.159521
$871$	−2.71110e14			−0.540823
$872$		−	1.54100e14i		−	0.305648i
$873$	2.23232e13			0.0440236
$874$	1.43770e14			0.281910
$875$	1.54199e14			0.300636
$876$	−1.36620e11			−0.000264846
$877$	−5.29764e14			−1.02114			−0.510569	−	0.859837i	$-0.670565\pi$
$877$	−5.29764e14			−1.02114			−0.510569	+	0.859837i	$0.670565\pi$
$878$		−	1.01591e14i		−	0.194707i
$879$		−	3.84212e12i		−	0.00732194i
$880$		−	1.66128e15i		−	3.14797i
$881$	−2.91535e14			−0.549301			−0.274651	−	0.961544i	$-0.588562\pi$
$881$	−2.91535e14			−0.549301			−0.274651	+	0.961544i	$0.588562\pi$
$882$		−	3.20950e14i		−	0.601304i
$883$	7.92798e14			1.47693			0.738464	−	0.674293i	$-0.235552\pi$
$883$	7.92798e14			1.47693			0.738464	+	0.674293i	$0.235552\pi$
$884$	2.79244e14			0.517277
$885$	2.57664e13			0.0474610
$886$		−	9.90749e14i		−	1.81466i
$887$			8.53074e14i			1.55370i	0.629683	+	0.776852i	$0.283185\pi$
$887$			8.53074e14i			1.55370i	−0.629683	+	0.776852i	$0.716815\pi$
$888$			2.10883e13i			0.0381923i
$889$		−	9.21909e14i		−	1.66027i
$890$			1.06053e15i			1.89921i
$891$	−1.05102e15			−1.87164
$892$			1.35104e14i			0.239246i
$893$			1.27805e15i			2.25056i
$894$		−	1.78359e13i		−	0.0312325i
$895$	1.16794e15			2.03378
$896$	5.83204e14			1.00991
$897$			4.39420e12i			0.00756688i
$898$	8.58996e14			1.47099
$899$		−	9.01236e14i		−	1.53476i
$900$	3.14200e14			0.532100
$901$	−4.17869e14			−0.703746
$902$			8.46811e14i			1.41825i
$903$	−1.03406e13	+	5.54615e13i	−0.0172230	+	0.0923746i
$904$	−1.48701e14			−0.246304
$905$		−	6.22602e14i		−	1.02558i
$906$		−	7.36614e13i		−	0.120670i
$907$	7.23935e14			1.17940			0.589702	−	0.807621i	$-0.299245\pi$
$907$	7.23935e14			1.17940			0.589702	+	0.807621i	$0.299245\pi$
$908$			5.28051e14i			0.855552i
$909$	−5.91683e13			−0.0953388
$910$			7.03130e14i			1.12675i
$911$			5.12940e13i			0.0817476i	0.999164	+	0.0408738i	$0.0130142\pi$
$911$			5.12940e13i			0.0817476i	−0.999164	+	0.0408738i	$0.986986\pi$
$912$	−7.20563e13			−0.114208
$913$	1.60353e15			2.52769
$914$	2.17662e14			0.341234
$915$		−	6.89062e13i		−	0.107437i
$916$	4.47455e14			0.693859
$917$	−5.10397e14			−0.787158
$918$	1.90770e14			0.292615
$919$	−3.73452e14			−0.569715			−0.284858	−	0.958570i	$-0.591946\pi$
$919$	−3.73452e14			−0.569715			−0.284858	+	0.958570i	$0.591946\pi$
$920$	7.16326e13			0.108685
$921$		−	2.98123e13i		−	0.0449881i
$922$		−	8.47771e14i		−	1.27240i
$923$			5.27645e14i			0.787650i
$924$	−7.91323e13			−0.117488
$925$			6.15192e14i			0.908452i
$926$	−2.17392e14			−0.319292
$927$	−4.53698e14			−0.662779
$928$	9.26847e14			1.34669
$929$			1.34751e15i			1.94739i	0.227863	+	0.973693i	$0.426826\pi$
$929$			1.34751e15i			1.94739i	−0.227863	+	0.973693i	$0.573174\pi$
$930$		−	1.20899e14i		−	0.173783i
$931$			3.95324e14i			0.565203i
$932$			4.53424e14i			0.644801i
$933$		−	2.25324e13i		−	0.0318713i
$934$	1.20578e15			1.69641
$935$		−	2.70058e15i		−	3.77920i
$936$			1.69392e14i			0.235783i
$937$		−	5.65207e13i		−	0.0782545i	−0.999234	−	0.0391272i	$-0.987542\pi$
$937$		−	5.65207e13i		−	0.0782545i	0.999234	−	0.0391272i	$-0.0124578\pi$
$938$	1.14343e15			1.57469
$939$	6.12901e13			0.0839580
$940$		−	1.21445e15i		−	1.65478i
$941$	−7.49414e14			−1.01572			−0.507860	−	0.861440i	$-0.669563\pi$
$941$	−7.49414e14			−1.01572			−0.507860	+	0.861440i	$0.669563\pi$
$942$			9.42184e13i			0.127023i
$943$	−7.85645e13			−0.105358
$944$	−4.17548e14			−0.556989
$945$			1.90289e14i			0.252496i
$946$	−1.82672e15	−	3.40586e14i	−2.41110	−	0.449543i
$947$	−9.26325e14			−1.21622			−0.608112	−	0.793851i	$-0.708073\pi$
$947$	−9.26325e14			−1.21622			−0.608112	+	0.793851i	$0.708073\pi$
$948$		−	1.01385e13i		−	0.0132413i
$949$		−	2.14867e12i		−	0.00279151i
$950$	−9.76944e14			−1.26256
$951$		−	9.67692e12i		−	0.0124404i
$952$	6.17531e14			0.789721
$953$		−	3.90713e14i		−	0.497043i	−0.968626	−	0.248521i	$-0.920055\pi$
$953$		−	3.90713e14i		−	0.497043i	0.968626	−	0.248521i	$-0.0799446\pi$
$954$			4.83433e14i			0.611778i
$955$	1.01636e14			0.127947
$956$	−1.88422e14			−0.235962
$957$	1.40731e14			0.175319
$958$		−	9.54733e14i		−	1.18319i
$959$	−1.83577e15			−2.26321
$960$	1.99626e13			0.0244827
$961$	5.50772e14			0.671978
$962$	6.32535e14			0.767732
$963$	1.00672e15			1.21556
$964$			5.75057e12i			0.00690758i
$965$		−	1.38073e15i		−	1.64996i
$966$		−	1.85328e13i		−	0.0220321i
$967$	−1.60988e14			−0.190397			−0.0951985	−	0.995458i	$-0.530349\pi$
$967$	−1.60988e14			−0.190397			−0.0951985	+	0.995458i	$0.530349\pi$
$968$			9.90395e14i			1.16528i
$969$	−1.17135e14			−0.137109
$970$	6.59557e13			0.0768057
$971$	−5.69117e14			−0.659334			−0.329667	−	0.944097i	$-0.606936\pi$
$971$	−5.69117e14			−0.659334			−0.329667	+	0.944097i	$0.606936\pi$
$972$		−	1.31276e14i		−	0.151305i
$973$			1.17538e15i			1.34777i
$974$		−	2.84238e14i		−	0.324255i
$975$		−	2.98595e13i		−	0.0338890i
$976$			1.11664e15i			1.26085i
$977$	1.19917e15			1.34713			0.673565	−	0.739128i	$-0.264762\pi$
$977$	1.19917e15			1.34713			0.673565	+	0.739128i	$0.264762\pi$
$978$		−	1.43450e14i		−	0.160327i
$979$		−	1.87714e15i		−	2.08729i
$980$		−	3.75651e14i		−	0.415580i
$981$	−6.23572e14			−0.686343
$982$	−1.79406e15			−1.96462
$983$		−	5.25418e14i		−	0.572450i	−0.958162	−	0.286225i	$-0.907599\pi$
$983$		−	5.25418e14i		−	0.572450i	0.958162	−	0.286225i	$-0.0924005\pi$
$984$	1.83003e13			0.0198373
$985$		−	9.36334e14i		−	1.00983i
$986$	2.09450e15			2.24748
$987$	1.64749e14			0.175888
$988$			3.97920e14i			0.422680i
$989$	3.15985e13	−	1.69477e14i	0.0333953	−	0.179114i
$990$	−3.12431e15			−3.28532
$991$			1.60507e15i			1.67929i	0.543134	+	0.839646i	$0.317237\pi$
$991$			1.60507e15i			1.67929i	−0.543134	+	0.839646i	$0.682763\pi$
$992$			1.40935e15i			1.46710i
$993$	4.08660e13			0.0423269
$994$		−	2.22538e15i		−	2.29336i
$995$	−3.65884e14			−0.375170
$996$			6.60903e13i			0.0674281i
$997$			7.58882e13i			0.0770368i	0.999258	+	0.0385184i	$0.0122638\pi$
$997$			7.58882e13i			0.0770368i	−0.999258	+	0.0385184i	$0.987736\pi$
$998$	−7.05390e14			−0.712486
$999$	1.71184e14			0.172043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.11.b.b.42.26	yes	34
43.42	odd	2	inner	43.11.b.b.42.9	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.11.b.b.42.9	✓	34	43.42	odd	2	inner
43.11.b.b.42.26	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)

\(f(q)\)	\(=\)	\(q+41.1797i q^{2} +18.8325i q^{3} -671.767 q^{4} -4211.22i q^{5} -775.516 q^{6} +20378.0i q^{7} +14504.9i q^{8} +58694.3 q^{9} +O(q^{10})\)	\(q+41.1797i q^{2} +18.8325i q^{3} -671.767 q^{4} -4211.22i q^{5} -775.516 q^{6} +20378.0i q^{7} +14504.9i q^{8} +58694.3 q^{9} +173417. q^{10} -306949. q^{11} -12651.0i q^{12} +198968. q^{13} -839160. q^{14} +79307.8 q^{15} -1.28519e6 q^{16} -2.08922e6 q^{17} +2.41701e6i q^{18} -2.97711e6i q^{19} +2.82896e6i q^{20} -383769. q^{21} -1.26401e7i q^{22} +1.17271e6 q^{23} -273163. q^{24} -7.96877e6 q^{25} +8.19343e6i q^{26} +2.21740e6i q^{27} -1.36893e7i q^{28} +2.43453e7i q^{29} +3.26587e6i q^{30} -3.70189e7 q^{31} -3.80709e7i q^{32} -5.78061e6i q^{33} -8.60332e7i q^{34} +8.58163e7 q^{35} -3.94289e7 q^{36} -7.72003e7i q^{37} +1.22597e8 q^{38} +3.74706e6i q^{39} +6.10832e7 q^{40} -6.69942e7 q^{41} -1.58035e7i q^{42} +(2.69450e7 - 1.44518e8i) q^{43} +2.06198e8 q^{44} -2.47175e8i q^{45} +4.82916e7i q^{46} -4.29292e8 q^{47} -2.42034e7i q^{48} -1.32788e8 q^{49} -3.28152e8i q^{50} -3.93451e7i q^{51} -1.33660e8 q^{52} +2.00012e8 q^{53} -9.13119e7 q^{54} +1.29263e9i q^{55} -2.95580e8 q^{56} +5.60664e7 q^{57} -1.00253e9 q^{58} +3.24891e8 q^{59} -5.32764e7 q^{60} -8.68845e8i q^{61} -1.52443e9i q^{62} +1.19607e9i q^{63} +2.51710e8 q^{64} -8.37897e8i q^{65} +2.38044e8 q^{66} -1.36258e9 q^{67} +1.40347e9 q^{68} +2.20850e7i q^{69} +3.53389e9i q^{70} +2.65191e9i q^{71} +8.51353e8i q^{72} -1.07991e7i q^{73} +3.17909e9 q^{74} -1.50072e8i q^{75} +1.99992e9i q^{76} -6.25501e9i q^{77} -1.54303e8 q^{78} +8.01396e8 q^{79} +5.41224e9i q^{80} +3.42408e9 q^{81} -2.75880e9i q^{82} -5.22410e9 q^{83} +2.57803e8 q^{84} +8.79815e9i q^{85} +(5.95121e9 + 1.10959e9i) q^{86} -4.58482e8 q^{87} -4.45225e9i q^{88} +6.11548e9i q^{89} +1.01786e10 q^{90} +4.05456e9i q^{91} -7.87784e8 q^{92} -6.97159e8i q^{93} -1.76781e10i q^{94} -1.25373e10 q^{95} +7.16971e8 q^{96} +3.80330e8 q^{97} -5.46816e9i q^{98} -1.80162e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16156 q^{4} + 12798 q^{6} - 790716 q^{9}+O(q^{10}) \) 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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