LMFDB - Embedded newform 43.9.b.b.42.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,9,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, 9, names="a")

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

chi := DirichletCharacter("43.42");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 9 $
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:	$17.5172802326$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			42.11
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.2230i q^{2} -141.129i q^{3} +151.490 q^{4} +508.524i q^{5} -1442.77 q^{6} +610.830i q^{7} -4165.77i q^{8} -13356.5 q^{9} +O(q^{10})$	\(q-10.2230i q^{2} -141.129i q^{3} +151.490 q^{4} +508.524i q^{5} -1442.77 q^{6} +610.830i q^{7} -4165.77i q^{8} -13356.5 q^{9} +5198.64 q^{10} -23389.3 q^{11} -21379.7i q^{12} -38247.2 q^{13} +6244.51 q^{14} +71767.6 q^{15} -3805.23 q^{16} +8276.38 q^{17} +136543. i q^{18} +43946.0i q^{19} +77036.4i q^{20} +86206.0 q^{21} +239109. i q^{22} -109327. q^{23} -587913. q^{24} +132028. q^{25} +391001. i q^{26} +959041. i q^{27} +92534.7i q^{28} -1.33800e6i q^{29} -733681. i q^{30} -624882. q^{31} -1.02754e6i q^{32} +3.30091e6i q^{33} -84609.5i q^{34} -310621. q^{35} -2.02338e6 q^{36} -12892.0i q^{37} +449260. q^{38} +5.39780e6i q^{39} +2.11840e6 q^{40} +4.22110e6 q^{41} -881284. i q^{42} +(-1.81225e6 - 2.89896e6i) q^{43} -3.54325e6 q^{44} -6.79209e6i q^{45} +1.11765e6i q^{46} +1.43455e6 q^{47} +537029. i q^{48} +5.39169e6 q^{49} -1.34973e6i q^{50} -1.16804e6i q^{51} -5.79407e6 q^{52} -1.03918e7 q^{53} +9.80428e6 q^{54} -1.18940e7i q^{55} +2.54458e6 q^{56} +6.20207e6 q^{57} -1.36784e7 q^{58} +8.60085e6 q^{59} +1.08721e7 q^{60} -1.46732e7i q^{61} +6.38818e6i q^{62} -8.15853e6i q^{63} -1.14787e7 q^{64} -1.94496e7i q^{65} +3.37453e7 q^{66} -9.05284e6 q^{67} +1.25379e6 q^{68} +1.54293e7i q^{69} +3.17548e6i q^{70} -1.39287e7i q^{71} +5.56401e7i q^{72} +4.77368e7i q^{73} -131795. q^{74} -1.86331e7i q^{75} +6.65739e6i q^{76} -1.42869e7i q^{77} +5.51817e7 q^{78} -2.98664e7 q^{79} -1.93505e6i q^{80} +4.77169e7 q^{81} -4.31523e7i q^{82} -3.68875e7 q^{83} +1.30594e7 q^{84} +4.20874e6i q^{85} +(-2.96361e7 + 1.85266e7i) q^{86} -1.88831e8 q^{87} +9.74345e7i q^{88} -9.08768e7i q^{89} -6.94355e7 q^{90} -2.33625e7i q^{91} -1.65620e7 q^{92} +8.81892e7i q^{93} -1.46654e7i q^{94} -2.23476e7 q^{95} -1.45016e8 q^{96} -4.00745e7 q^{97} -5.51192e7i q^{98} +3.12399e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	$ 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) $ 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * 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 $

$2$		−	10.2230i		−	0.638938i	−0.947597	−	0.319469i	$-0.896496\pi$
$2$		−	10.2230i		−	0.638938i	0.947597	−	0.319469i	$-0.103504\pi$
$3$		−	141.129i		−	1.74234i	−0.490984	−	0.871168i	$-0.663363\pi$
$3$		−	141.129i		−	1.74234i	0.490984	−	0.871168i	$-0.336637\pi$
$4$	151.490			0.591759
$5$			508.524i			0.813638i	0.913509	+	0.406819i	$0.133362\pi$
$5$			508.524i			0.813638i	−0.913509	+	0.406819i	$0.866638\pi$
$6$	−1442.77			−1.11324
$7$			610.830i			0.254406i	0.991877	+	0.127203i	$0.0406000\pi$
$7$			610.830i			0.254406i	−0.991877	+	0.127203i	$0.959400\pi$
$8$		−	4165.77i		−	1.01703i
$9$	−13356.5			−2.03574
$10$	5198.64			0.519864
$11$	−23389.3			−1.59752			−0.798760	−	0.601650i	$-0.794510\pi$
$11$	−23389.3			−1.59752			−0.798760	+	0.601650i	$0.794510\pi$
$12$		−	21379.7i		−	1.03104i
$13$	−38247.2			−1.33914			−0.669570	−	0.742749i	$-0.733522\pi$
$13$	−38247.2			−1.33914			−0.669570	+	0.742749i	$0.733522\pi$
$14$	6244.51			0.162550
$15$	71767.6			1.41763
$16$	−3805.23			−0.0580631
$17$	8276.38			0.0990934			0.0495467	−	0.998772i	$-0.484222\pi$
$17$	8276.38			0.0990934			0.0495467	+	0.998772i	$0.484222\pi$
$18$			136543.i			1.30071i
$19$			43946.0i			0.337214i	0.985683	+	0.168607i	$0.0539268\pi$
$19$			43946.0i			0.337214i	−0.985683	+	0.168607i	$0.946073\pi$
$20$			77036.4i			0.481477i
$21$	86206.0			0.443262
$22$			239109.i			1.02072i
$23$	−109327.			−0.390676			−0.195338	−	0.980736i	$-0.562580\pi$
$23$	−109327.			−0.390676			−0.195338	+	0.980736i	$0.562580\pi$
$24$	−587913.			−1.77202
$25$	132028.			0.337993
$26$			391001.i			0.855627i
$27$			959041.i			1.80460i
$28$			92534.7i			0.150547i
$29$		−	1.33800e6i		−	1.89175i	−0.324534	−	0.945874i	$-0.605208\pi$
$29$		−	1.33800e6i		−	1.89175i	0.324534	−	0.945874i	$-0.394792\pi$
$30$		−	733681.i		−	0.905778i
$31$	−624882.			−0.676630			−0.338315	−	0.941033i	$-0.609857\pi$
$31$	−624882.			−0.676630			−0.338315	+	0.941033i	$0.609857\pi$
$32$		−	1.02754e6i		−	0.979936i
$33$			3.30091e6i			2.78342i
$34$		−	84609.5i		−	0.0633145i
$35$	−310621.			−0.206995
$36$	−2.02338e6			−1.20467
$37$		−	12892.0i		−	0.00687879i	−0.999994	−	0.00343939i	$-0.998905\pi$
$37$		−	12892.0i		−	0.00687879i	0.999994	−	0.00343939i	$-0.00109480\pi$
$38$	449260.			0.215459
$39$			5.39780e6i			2.33323i
$40$	2.11840e6			0.827498
$41$	4.22110e6			1.49379			0.746895	−	0.664941i	$-0.231544\pi$
$41$	4.22110e6			1.49379			0.746895	+	0.664941i	$0.231544\pi$
$42$		−	881284.i		−	0.283217i
$43$	−1.81225e6	−	2.89896e6i	−0.530082	−	0.847946i
$43$	−1.81225e6	−	2.89896e6i	−0.530082	−	0.847946i
$44$	−3.54325e6			−0.945346
$45$		−	6.79209e6i		−	1.65635i
$46$			1.11765e6i			0.249618i
$47$	1.43455e6			0.293985			0.146992	−	0.989138i	$-0.453041\pi$
$47$	1.43455e6			0.293985			0.146992	+	0.989138i	$0.453041\pi$
$48$			537029.i			0.101166i
$49$	5.39169e6			0.935277
$50$		−	1.34973e6i		−	0.215956i
$51$		−	1.16804e6i		−	0.172654i
$52$	−5.79407e6			−0.792448
$53$	−1.03918e7			−1.31700			−0.658500	−	0.752581i	$-0.728809\pi$
$53$	−1.03918e7			−1.31700			−0.658500	+	0.752581i	$0.728809\pi$
$54$	9.80428e6			1.15303
$55$		−	1.18940e7i		−	1.29980i
$56$	2.54458e6			0.258740
$57$	6.20207e6			0.587540
$58$	−1.36784e7			−1.20871
$59$	8.60085e6			0.709796			0.354898	−	0.934905i	$-0.384516\pi$
$59$	8.60085e6			0.709796			0.354898	+	0.934905i	$0.384516\pi$
$60$	1.08721e7			0.838896
$61$		−	1.46732e7i		−	1.05975i	−0.848075	−	0.529877i	$-0.822238\pi$
$61$		−	1.46732e7i		−	1.05975i	0.848075	−	0.529877i	$-0.177762\pi$
$62$			6.38818e6i			0.432325i
$63$		−	8.15853e6i		−	0.517905i
$64$	−1.14787e7			−0.684181
$65$		−	1.94496e7i		−	1.08958i
$66$	3.37453e7			1.77843
$67$	−9.05284e6			−0.449247			−0.224624	−	0.974446i	$-0.572115\pi$
$67$	−9.05284e6			−0.449247			−0.224624	+	0.974446i	$0.572115\pi$
$68$	1.25379e6			0.0586394
$69$			1.54293e7i			0.680690i
$70$			3.17548e6i			0.132257i
$71$		−	1.39287e7i		−	0.548123i	−0.961712	−	0.274061i	$-0.911633\pi$
$71$		−	1.39287e7i		−	0.548123i	0.961712	−	0.274061i	$-0.0883672\pi$
$72$			5.56401e7i			2.07042i
$73$			4.77368e7i			1.68098i	0.541828	+	0.840489i	$0.317732\pi$
$73$			4.77368e7i			1.68098i	−0.541828	+	0.840489i	$0.682268\pi$
$74$	−131795.			−0.00439512
$75$		−	1.86331e7i		−	0.588897i
$76$			6.65739e6i			0.199549i
$77$		−	1.42869e7i		−	0.406419i
$78$	5.51817e7			1.49079
$79$	−2.98664e7			−0.766788			−0.383394	−	0.923585i	$-0.625245\pi$
$79$	−2.98664e7			−0.766788			−0.383394	+	0.923585i	$0.625245\pi$
$80$		−	1.93505e6i		−	0.0472424i
$81$	4.77169e7			1.10849
$82$		−	4.31523e7i		−	0.954439i
$83$	−3.68875e7			−0.777261			−0.388631	−	0.921394i	$-0.627052\pi$
$83$	−3.68875e7			−0.777261			−0.388631	+	0.921394i	$0.627052\pi$
$84$	1.30594e7			0.262304
$85$			4.20874e6i			0.0806262i
$86$	−2.96361e7	+	1.85266e7i	−0.541785	+	0.338689i
$87$	−1.88831e8			−3.29606
$88$			9.74345e7i			1.62473i
$89$		−	9.08768e7i		−	1.44841i	−0.689582	−	0.724207i	$-0.742206\pi$
$89$		−	9.08768e7i		−	1.44841i	0.689582	−	0.724207i	$-0.257794\pi$
$90$	−6.94355e7			−1.05831
$91$		−	2.33625e7i		−	0.340686i
$92$	−1.65620e7			−0.231186
$93$			8.81892e7i			1.17892i
$94$		−	1.46654e7i		−	0.187838i
$95$	−2.23476e7			−0.274370
$96$	−1.45016e8			−1.70738
$97$	−4.00745e7			−0.452670			−0.226335	−	0.974050i	$-0.572674\pi$
$97$	−4.00745e7			−0.452670			−0.226335	+	0.974050i	$0.572674\pi$
$98$		−	5.51192e7i		−	0.597584i
$99$	3.12399e8			3.25213
$100$	2.00010e7			0.200010
$101$	2.84924e7			0.273807			0.136903	−	0.990584i	$-0.456285\pi$
$101$	2.84924e7			0.273807			0.136903	+	0.990584i	$0.456285\pi$
$102$	−1.19409e7			−0.110315
$103$	1.33245e8			1.18386			0.591932	−	0.805988i	$-0.298365\pi$
$103$	1.33245e8			1.18386			0.591932	+	0.805988i	$0.298365\pi$
$104$			1.59329e8i			1.36195i
$105$			4.38378e7i			0.360655i
$106$			1.06235e8i			0.841481i
$107$	−1.39954e8			−1.06770			−0.533852	−	0.845578i	$-0.679256\pi$
$107$	−1.39954e8			−1.06770			−0.533852	+	0.845578i	$0.679256\pi$
$108$			1.45285e8i			1.06789i
$109$	2.11298e8			1.49689			0.748446	−	0.663196i	$-0.230800\pi$
$109$	2.11298e8			1.49689			0.748446	+	0.663196i	$0.230800\pi$
$110$	−1.21593e8			−0.830494
$111$	−1.81943e6			−0.0119852
$112$		−	2.32434e6i		−	0.0147716i
$113$			5.53627e7i			0.339550i	0.985483	+	0.169775i	$0.0543041\pi$
$113$			5.53627e7i			0.339550i	−0.985483	+	0.169775i	$0.945696\pi$
$114$		−	6.34038e7i		−	0.375401i
$115$		−	5.55955e7i		−	0.317869i
$116$		−	2.02693e8i		−	1.11946i
$117$	5.10848e8			2.72614
$118$		−	8.79265e7i		−	0.453515i
$119$			5.05546e6i			0.0252100i
$120$		−	2.98968e8i		−	1.44178i
$121$	3.32700e8			1.55207
$122$	−1.50004e8			−0.677117
$123$		−	5.95720e8i		−	2.60269i
$124$	−9.46636e7			−0.400402
$125$			2.65782e8i			1.08864i
$126$	−8.34047e7			−0.330909
$127$	−8.40413e7			−0.323056			−0.161528	−	0.986868i	$-0.551642\pi$
$127$	−8.40413e7			−0.323056			−0.161528	+	0.986868i	$0.551642\pi$
$128$		−	1.45703e8i		−	0.542787i
$129$	−4.09128e8	+	2.55761e8i	−1.47741	+	0.923582i
$130$	−1.98833e8			−0.696171
$131$		−	5.12788e8i		−	1.74122i	−0.491978	−	0.870608i	$-0.663726\pi$
$131$		−	5.12788e8i		−	1.74122i	0.491978	−	0.870608i	$-0.336274\pi$
$132$			5.00056e8i			1.64711i
$133$	−2.68435e7			−0.0857893
$134$			9.25472e7i			0.287041i
$135$	−4.87695e8			−1.46830
$136$		−	3.44775e7i		−	0.100781i
$137$		−	2.04952e8i		−	0.581794i	−0.956754	−	0.290897i	$-0.906046\pi$
$137$		−	2.04952e8i		−	0.581794i	0.956754	−	0.290897i	$-0.0939538\pi$
$138$	1.57734e8			0.434918
$139$	−4.64854e8			−1.24525			−0.622626	−	0.782520i	$-0.713934\pi$
$139$	−4.64854e8			−1.24525			−0.622626	+	0.782520i	$0.713934\pi$
$140$	−4.70561e7			−0.122491
$141$		−	2.02457e8i		−	0.512221i
$142$	−1.42393e8			−0.350216
$143$	8.94575e8			2.13930
$144$	5.08244e7			0.118201
$145$	6.80404e8			1.53920
$146$	4.88014e8			1.07404
$147$		−	7.60925e8i		−	1.62957i
$148$		−	1.95301e6i		−	0.00407058i
$149$			7.12509e6i			0.0144559i	0.999974	+	0.00722795i	$0.00230075\pi$
$149$			7.12509e6i			0.0144559i	−0.999974	+	0.00722795i	$0.997699\pi$
$150$	−1.90486e8			−0.376269
$151$			4.53627e8i			0.872552i	0.899813	+	0.436276i	$0.143703\pi$
$151$			4.53627e8i			0.872552i	−0.899813	+	0.436276i	$0.856297\pi$
$152$	1.83069e8			0.342958
$153$	−1.10543e8			−0.201728
$154$	−1.46055e8			−0.259677
$155$		−	3.17768e8i		−	0.550532i
$156$			8.17714e8i			1.38071i
$157$			4.62842e8i			0.761789i	0.924619	+	0.380894i	$0.124384\pi$
$157$			4.62842e8i			0.761789i	−0.924619	+	0.380894i	$0.875616\pi$
$158$			3.05325e8i			0.489930i
$159$			1.46658e9i			2.29466i
$160$	5.22527e8			0.797313
$161$		−	6.67803e7i		−	0.0993905i
$162$		−	4.87810e8i		−	0.708257i
$163$			3.93979e8i			0.558113i	0.960275	+	0.279057i	$0.0900217\pi$
$163$			3.93979e8i			0.558113i	−0.960275	+	0.279057i	$0.909978\pi$
$164$	6.39455e8			0.883964
$165$	−1.67859e9			−2.26470
$166$			3.77101e8i			0.496622i
$167$	−1.50142e9			−1.93035			−0.965173	−	0.261614i	$-0.915745\pi$
$167$	−1.50142e9			−1.93035			−0.965173	+	0.261614i	$0.915745\pi$
$168$		−	3.59114e8i		−	0.450812i
$169$	6.47117e8			0.793297
$170$	4.30260e7			0.0515151
$171$		−	5.86964e8i		−	0.686479i
$172$	−2.74537e8	−	4.39164e8i	−0.313681	−	0.501780i
$173$	1.15836e9			1.29318			0.646591	−	0.762837i	$-0.276194\pi$
$173$	1.15836e9			1.29318			0.646591	+	0.762837i	$0.276194\pi$
$174$			1.93042e9i			2.10598i
$175$			8.06469e7i			0.0859875i
$176$	8.90015e7			0.0927570
$177$		−	1.21383e9i		−	1.23670i
$178$	−9.29034e8			−0.925447
$179$			1.24575e9i			1.21344i	0.794916	+	0.606719i	$0.207515\pi$
$179$			1.24575e9i			1.21344i	−0.794916	+	0.606719i	$0.792485\pi$
$180$		−	1.02893e9i		−	0.980162i
$181$	−2.15685e8			−0.200958			−0.100479	−	0.994939i	$-0.532037\pi$
$181$	−2.15685e8			−0.200958			−0.100479	+	0.994939i	$0.532037\pi$
$182$	−2.38835e8			−0.217677
$183$	−2.07082e9			−1.84645
$184$			4.55433e8i			0.397331i
$185$	6.55587e6			0.00559685
$186$	9.01559e8			0.753255
$187$	−1.93579e8			−0.158304
$188$	2.17321e8			0.173968
$189$	−5.85811e8			−0.459103
$190$			2.28460e8i			0.175305i
$191$		−	1.65296e9i		−	1.24202i	−0.783803	−	0.621009i	$-0.786723\pi$
$191$		−	1.65296e9i		−	1.24202i	0.783803	−	0.621009i	$-0.213277\pi$
$192$			1.61997e9i			1.19207i
$193$	1.26825e9			0.914065			0.457033	−	0.889450i	$-0.348912\pi$
$193$	1.26825e9			0.914065			0.457033	+	0.889450i	$0.348912\pi$
$194$			4.09682e8i			0.289228i
$195$	−2.74491e9			−1.89841
$196$	8.16788e8			0.553458
$197$	1.60703e9			1.06699			0.533494	−	0.845804i	$-0.320879\pi$
$197$	1.60703e9			1.06699			0.533494	+	0.845804i	$0.320879\pi$
$198$		−	3.19365e9i		−	2.07791i
$199$		−	1.63024e9i		−	1.03953i	−0.854309	−	0.519766i	$-0.826019\pi$
$199$		−	1.63024e9i		−	1.03953i	0.854309	−	0.519766i	$-0.173981\pi$
$200$		−	5.50001e8i		−	0.343750i
$201$			1.27762e9i			0.782740i
$202$		−	2.91278e8i		−	0.174945i
$203$	8.17288e8			0.481273
$204$		−	1.76947e8i		−	0.102170i
$205$			2.14653e9i			1.21541i
$206$		−	1.36216e9i		−	0.756415i
$207$	1.46023e9			0.795314
$208$	1.45539e8			0.0777547
$209$		−	1.02787e9i		−	0.538706i
$210$	4.48154e8			0.230436
$211$			2.53499e9i			1.27893i	0.768821	+	0.639464i	$0.220844\pi$
$211$			2.53499e9i			1.27893i	−0.768821	+	0.639464i	$0.779156\pi$
$212$	−1.57425e9			−0.779346
$213$	−1.96575e9			−0.955015
$214$			1.43075e9i			0.682197i
$215$	1.47419e9	−	9.21570e8i	0.689922	−	0.431295i
$216$	3.99515e9			1.83535
$217$		−	3.81697e8i		−	0.172139i
$218$		−	2.16010e9i		−	0.956420i
$219$	6.73707e9			2.92883
$220$		−	1.80183e9i		−	0.769170i
$221$	−3.16548e8			−0.132700
$222$			1.86001e7i			0.00765778i
$223$			3.90361e9i			1.57851i	0.614067	+	0.789254i	$0.289532\pi$
$223$			3.90361e9i			1.57851i	−0.614067	+	0.789254i	$0.710468\pi$
$224$	6.27650e8			0.249302
$225$	−1.76343e9			−0.688065
$226$	5.65974e8			0.216951
$227$		−	4.89808e9i		−	1.84469i	−0.386373	−	0.922343i	$-0.626272\pi$
$227$		−	4.89808e9i		−	1.84469i	0.386373	−	0.922343i	$-0.373728\pi$
$228$	9.39553e8			0.347682
$229$	−4.85451e9			−1.76524			−0.882619	−	0.470089i	$-0.844222\pi$
$229$	−4.85451e9			−1.76524			−0.882619	+	0.470089i	$0.844222\pi$
$230$	−5.68353e8			−0.203099
$231$	−2.01630e9			−0.708119
$232$	−5.57379e9			−1.92397
$233$		−	2.29736e8i		−	0.0779480i	−0.999240	−	0.0389740i	$-0.987591\pi$
$233$		−	2.29736e8i		−	0.0779480i	0.999240	−	0.0389740i	$-0.0124089\pi$
$234$		−	5.22240e9i		−	1.74183i
$235$			7.29504e8i			0.239197i
$236$	1.30294e9			0.420028
$237$			4.21503e9i			1.33600i
$238$	5.16820e7			0.0161076
$239$	5.01758e9			1.53781			0.768905	−	0.639363i	$-0.220802\pi$
$239$	5.01758e9			1.53781			0.768905	+	0.639363i	$0.220802\pi$
$240$	−2.73092e8			−0.0823122
$241$		−	8.41073e8i		−	0.249325i	−0.992199	−	0.124662i	$-0.960215\pi$
$241$		−	8.41073e8i		−	0.249325i	0.992199	−	0.124662i	$-0.0397848\pi$
$242$		−	3.40120e9i		−	0.991677i
$243$		−	4.41986e8i		−	0.126760i
$244$		−	2.22284e9i		−	0.627118i
$245$			2.74180e9i			0.760977i
$246$	−6.09005e9			−1.66295
$247$		−	1.68081e9i		−	0.451577i
$248$			2.60312e9i			0.688157i
$249$			5.20591e9i			1.35425i
$250$	2.71709e9			0.695574
$251$	6.10592e8			0.153835			0.0769177	−	0.997037i	$-0.475492\pi$
$251$	6.10592e8			0.153835			0.0769177	+	0.997037i	$0.475492\pi$
$252$		−	1.23594e9i		−	0.306475i
$253$	2.55709e9			0.624113
$254$			8.59154e8i			0.206413i
$255$	5.93976e8			0.140478
$256$	−4.42806e9			−1.03099
$257$		−	2.83448e9i		−	0.649743i	−0.945758	−	0.324871i	$-0.894679\pi$
$257$		−	2.83448e9i		−	0.649743i	0.945758	−	0.324871i	$-0.105321\pi$
$258$	2.61464e9	+	4.18252e9i	0.590111	+	0.943972i
$259$	7.87479e6			0.00175001
$260$		−	2.94643e9i		−	0.644766i
$261$			1.78709e10i			3.85110i
$262$	−5.24223e9			−1.11253
$263$		−	3.92497e9i		−	0.820378i	−0.912001	−	0.410189i	$-0.865463\pi$
$263$		−	3.92497e9i		−	0.820378i	0.912001	−	0.410189i	$-0.134537\pi$
$264$	1.37509e10			2.83083
$265$		−	5.28446e9i		−	1.07156i
$266$			2.74422e8i			0.0548140i
$267$	−1.28254e10			−2.52363
$268$	−1.37142e9			−0.265846
$269$	5.01380e9			0.957543			0.478771	−	0.877940i	$-0.341082\pi$
$269$	5.01380e9			0.957543			0.478771	+	0.877940i	$0.341082\pi$
$270$			4.98571e9i			0.938149i
$271$	5.99686e9			1.11185			0.555926	−	0.831232i	$-0.312364\pi$
$271$	5.99686e9			1.11185			0.555926	+	0.831232i	$0.312364\pi$
$272$	−3.14935e7			−0.00575368
$273$	−3.29714e9			−0.593589
$274$	−2.09522e9			−0.371730
$275$	−3.08805e9			−0.539950
$276$			2.33738e9i			0.402804i
$277$		−	3.81516e9i		−	0.648027i	−0.946052	−	0.324014i	$-0.894968\pi$
$277$		−	3.81516e9i		−	0.648027i	0.946052	−	0.324014i	$-0.105032\pi$
$278$			4.75220e9i			0.795638i
$279$	8.34623e9			1.37744
$280$			1.29398e9i			0.210521i
$281$	−9.65432e9			−1.54845			−0.774224	−	0.632912i	$-0.781859\pi$
$281$	−9.65432e9			−1.54845			−0.774224	+	0.632912i	$0.781859\pi$
$282$	−2.06972e9			−0.327277
$283$	−2.68907e9			−0.419234			−0.209617	−	0.977784i	$-0.567222\pi$
$283$	−2.68907e9			−0.419234			−0.209617	+	0.977784i	$0.567222\pi$
$284$		−	2.11006e9i		−	0.324356i
$285$			3.15390e9i			0.478045i
$286$		−	9.14524e9i		−	1.36688i
$287$			2.57837e9i			0.380030i
$288$			1.37243e10i			1.99489i
$289$	−6.90726e9			−0.990180
$290$		−	6.95577e9i		−	0.983452i
$291$			5.65569e9i			0.788703i
$292$			7.23166e9i			0.994734i
$293$	−8.49101e9			−1.15210			−0.576049	−	0.817415i	$-0.695406\pi$
$293$	−8.49101e9			−1.15210			−0.576049	+	0.817415i	$0.695406\pi$
$294$	−7.77894e9			−1.04119
$295$			4.37374e9i			0.577517i
$296$	−5.37050e7			−0.00699597
$297$		−	2.24313e10i		−	2.88289i
$298$	7.28398e7			0.00923642
$299$	4.18146e9			0.523170
$300$		−	2.82273e9i		−	0.348485i
$301$	1.77077e9	−	1.10697e9i	0.215723	−	0.134856i
$302$	4.63743e9			0.557507
$303$		−	4.02112e9i		−	0.477064i
$304$		−	1.67225e8i		−	0.0195797i
$305$	7.46166e9			0.862256
$306$			1.13008e9i			0.128892i
$307$	−8.44085e9			−0.950239			−0.475120	−	0.879921i	$-0.657595\pi$
$307$	−8.44085e9			−0.950239			−0.475120	+	0.879921i	$0.657595\pi$
$308$		−	2.16432e9i		−	0.240502i
$309$		−	1.88048e10i		−	2.06269i
$310$	−3.24854e9			−0.351756
$311$	6.75741e9			0.722335			0.361168	−	0.932501i	$-0.382378\pi$
$311$	6.75741e9			0.722335			0.361168	+	0.932501i	$0.382378\pi$
$312$	2.24860e10			2.37298
$313$		−	8.86708e9i		−	0.923854i	−0.886918	−	0.461927i	$-0.847158\pi$
$313$		−	8.86708e9i		−	0.923854i	0.886918	−	0.461927i	$-0.152842\pi$
$314$	4.73164e9			0.486735
$315$	4.14881e9			0.421387
$316$	−4.52447e9			−0.453753
$317$	−3.54232e9			−0.350793			−0.175397	−	0.984498i	$-0.556121\pi$
$317$	−3.54232e9			−0.350793			−0.175397	+	0.984498i	$0.556121\pi$
$318$	1.49929e10			1.46614
$319$			3.12948e10i			3.02211i
$320$		−	5.83717e9i		−	0.556676i
$321$			1.97516e10i			1.86030i
$322$	−6.82695e8			−0.0635044
$323$			3.63714e8i			0.0334157i
$324$	7.22864e9			0.655959
$325$	−5.04972e9			−0.452620
$326$	4.02765e9			0.356600
$327$		−	2.98204e10i		−	2.60809i
$328$		−	1.75841e10i		−	1.51924i
$329$			8.76267e8i			0.0747916i
$330$			1.71603e10i			1.44700i
$331$			8.57562e9i			0.714420i	0.934024	+	0.357210i	$0.116272\pi$
$331$			8.57562e9i			0.714420i	−0.934024	+	0.357210i	$0.883728\pi$
$332$	−5.58810e9			−0.459951
$333$			1.72191e8i			0.0140034i
$334$			1.53490e10i			1.23337i
$335$		−	4.60359e9i		−	0.365525i
$336$	−3.28033e8			−0.0257372
$337$	1.16877e10			0.906166			0.453083	−	0.891468i	$-0.350324\pi$
$337$	1.16877e10			0.906166			0.453083	+	0.891468i	$0.350324\pi$
$338$		−	6.61548e9i		−	0.506867i
$339$	7.81331e9			0.591611
$340$			6.37583e8i			0.0477113i
$341$	1.46156e10			1.08093
$342$	−6.00054e9			−0.438617
$343$			6.81471e9i			0.492347i
$344$	−1.20764e10	+	7.54940e9i	−0.862391	+	0.539112i
$345$	−7.84616e9			−0.553835
$346$		−	1.18419e10i		−	0.826262i
$347$		−	1.00908e10i		−	0.695995i	−0.937495	−	0.347998i	$-0.886862\pi$
$347$		−	1.00908e10i		−	0.695995i	0.937495	−	0.347998i	$-0.113138\pi$
$348$	−2.86060e10			−1.95047
$349$		−	1.53839e10i		−	1.03697i	−0.855088	−	0.518483i	$-0.826497\pi$
$349$		−	1.53839e10i		−	1.03697i	0.855088	−	0.518483i	$-0.173503\pi$
$350$	8.24453e8			0.0549407
$351$		−	3.66806e10i		−	2.41662i
$352$			2.40334e10i			1.56547i
$353$	8.54458e9			0.550290			0.275145	−	0.961403i	$-0.411274\pi$
$353$	8.54458e9			0.550290			0.275145	+	0.961403i	$0.411274\pi$
$354$	−1.24090e10			−0.790177
$355$	7.08309e9			0.445974
$356$		−	1.37669e10i		−	0.857112i
$357$	7.13474e8			0.0439243
$358$	1.27353e10			0.775312
$359$	2.58791e10			1.55801			0.779006	−	0.627016i	$-0.215724\pi$
$359$	2.58791e10			1.55801			0.779006	+	0.627016i	$0.215724\pi$
$360$	−2.82943e10			−1.68457
$361$	1.50523e10			0.886287
$362$			2.20494e9i			0.128400i
$363$		−	4.69538e10i		−	2.70423i
$364$		−	3.53919e9i		−	0.201604i
$365$	−2.42753e10			−1.36771
$366$			2.11700e10i			1.17977i
$367$	2.44465e9			0.134757			0.0673786	−	0.997727i	$-0.478536\pi$
$367$	2.44465e9			0.134757			0.0673786	+	0.997727i	$0.478536\pi$
$368$	4.16015e8			0.0226839
$369$	−5.63790e10			−3.04097
$370$		−	6.70207e7i		−	0.00357604i
$371$		−	6.34760e9i		−	0.335053i
$372$			1.33598e10i			0.697635i
$373$			7.22158e9i			0.373076i	0.982448	+	0.186538i	$0.0597267\pi$
$373$			7.22158e9i			0.373076i	−0.982448	+	0.186538i	$0.940273\pi$
$374$			1.97896e9i			0.101146i
$375$	3.75096e10			1.89678
$376$		−	5.97602e9i		−	0.298993i
$377$			5.11746e10i			2.53332i
$378$			5.98874e9i			0.293338i
$379$	4.92413e9			0.238656			0.119328	−	0.992855i	$-0.461926\pi$
$379$	4.92413e9			0.238656			0.119328	+	0.992855i	$0.461926\pi$
$380$	−3.38544e9			−0.162361
$381$			1.18607e10i			0.562872i
$382$	−1.68982e10			−0.793572
$383$			2.26540e10i			1.05281i	0.850234	+	0.526404i	$0.176460\pi$
$383$			2.26540e10i			1.05281i	−0.850234	+	0.526404i	$0.823540\pi$
$384$	−2.05630e10			−0.945717
$385$	7.26522e9			0.330678
$386$		−	1.29654e10i		−	0.584031i
$387$	2.42052e10	+	3.87199e10i	1.07911	+	1.72620i
$388$	−6.07090e9			−0.267871
$389$			4.06348e9i			0.177460i	0.996056	+	0.0887299i	$0.0282808\pi$
$389$			4.06348e9i			0.177460i	−0.996056	+	0.0887299i	$0.971719\pi$
$390$			2.80612e10i			1.21296i
$391$	−9.04834e8			−0.0387135
$392$		−	2.24606e10i		−	0.951209i
$393$	−7.23694e10			−3.03378
$394$		−	1.64287e10i		−	0.681739i
$395$		−	1.51878e10i		−	0.623888i
$396$	4.73253e10			1.92448
$397$	3.30903e10			1.33211			0.666053	−	0.745905i	$-0.267983\pi$
$397$	3.30903e10			1.33211			0.666053	+	0.745905i	$0.267983\pi$
$398$	−1.66659e10			−0.664196
$399$			3.78841e9i			0.149474i
$400$	−5.02398e8			−0.0196249
$401$	8.53281e9			0.330001			0.165000	−	0.986294i	$-0.447237\pi$
$401$	8.53281e9			0.330001			0.165000	+	0.986294i	$0.447237\pi$
$402$	1.30611e10			0.500122
$403$	2.39000e10			0.906103
$404$	4.31633e9			0.162028
$405$			2.42652e10i			0.901911i
$406$		−	8.35514e9i		−	0.307503i
$407$			3.01534e8i			0.0109890i
$408$	−4.86579e9			−0.175595
$409$			2.02511e10i			0.723694i	0.932237	+	0.361847i	$0.117854\pi$
$409$			2.02511e10i			0.723694i	−0.932237	+	0.361847i	$0.882146\pi$
$410$	2.19440e10			0.776568
$411$	−2.89247e10			−1.01368
$412$	2.01853e10			0.700562
$413$			5.25366e9i			0.180577i
$414$		−	1.49279e10i		−	0.508156i
$415$		−	1.87582e10i		−	0.632410i
$416$			3.93004e10i			1.31227i
$417$			6.56045e10i			2.16965i
$418$	−1.05079e10			−0.344199
$419$		−	4.85618e10i		−	1.57557i	−0.615948	−	0.787787i	$-0.711227\pi$
$419$		−	4.85618e10i		−	1.57557i	0.615948	−	0.787787i	$-0.288773\pi$
$420$			6.64100e9i			0.213420i
$421$			5.23909e10i			1.66774i	0.551964	+	0.833868i	$0.313879\pi$
$421$			5.23909e10i			1.66774i	−0.551964	+	0.833868i	$0.686121\pi$
$422$	2.59152e10			0.817155
$423$	−1.91606e10			−0.598476
$424$			4.32897e10i			1.33943i
$425$	1.09272e9			0.0334929
$426$			2.00959e10i			0.610195i
$427$	8.96282e9			0.269608
$428$	−2.12017e10			−0.631823
$429$		−	1.26251e11i		−	3.72739i
$430$	−9.42121e9	−	1.50707e10i	−0.275571	−	0.440817i
$431$	−8.47294e9			−0.245542			−0.122771	−	0.992435i	$-0.539178\pi$
$431$	−8.47294e9			−0.245542			−0.122771	+	0.992435i	$0.539178\pi$
$432$		−	3.64937e9i		−	0.104781i
$433$			1.82972e10i			0.520516i	0.965539	+	0.260258i	$0.0838076\pi$
$433$			1.82972e10i			0.520516i	−0.965539	+	0.260258i	$0.916192\pi$
$434$	−3.90209e9			−0.109986
$435$		−	9.60249e10i		−	2.68180i
$436$	3.20096e10			0.885798
$437$		−	4.80450e9i		−	0.131741i
$438$		−	6.88731e10i		−	1.87134i
$439$	4.05234e10			1.09106			0.545529	−	0.838092i	$-0.316329\pi$
$439$	4.05234e10			1.09106			0.545529	+	0.838092i	$0.316329\pi$
$440$	−4.95478e10			−1.32195
$441$	−7.20140e10			−1.90398
$442$			3.23608e9i			0.0847871i
$443$	−5.19815e10			−1.34969			−0.674845	−	0.737960i	$-0.735789\pi$
$443$	−5.19815e10			−1.34969			−0.674845	+	0.737960i	$0.735789\pi$
$444$	−2.75626e8			−0.00709233
$445$	4.62130e10			1.17849
$446$	3.99066e10			1.00857
$447$	1.00556e9			0.0251870
$448$		−	7.01150e9i		−	0.174060i
$449$		−	1.28565e10i		−	0.316328i	−0.987413	−	0.158164i	$-0.949443\pi$
$449$		−	1.28565e10i		−	0.316328i	0.987413	−	0.158164i	$-0.0505575\pi$
$450$			1.80276e10i			0.439631i
$451$	−9.87285e10			−2.38636
$452$			8.38691e9i			0.200932i
$453$	6.40201e10			1.52028
$454$	−5.00731e10			−1.17864
$455$	1.18804e10			0.277195
$456$		−	2.58364e10i		−	0.597549i
$457$		−	5.62798e10i		−	1.29029i	−0.764060	−	0.645146i	$-0.776797\pi$
$457$		−	5.62798e10i		−	1.29029i	0.764060	−	0.645146i	$-0.223203\pi$
$458$			4.96277e10i			1.12788i
$459$			7.93739e9i			0.178824i
$460$		−	8.42218e9i		−	0.188102i
$461$	−4.05469e10			−0.897746			−0.448873	−	0.893596i	$-0.648174\pi$
$461$	−4.05469e10			−0.897746			−0.448873	+	0.893596i	$0.648174\pi$
$462$			2.06126e10i			0.452444i
$463$		−	1.79105e9i		−	0.0389748i	−0.999810	−	0.0194874i	$-0.993797\pi$
$463$		−	1.79105e9i		−	0.0389748i	0.999810	−	0.0194874i	$-0.00620342\pi$
$464$			5.09138e9i			0.109841i
$465$	−4.48463e10			−0.959213
$466$	−2.34859e9			−0.0498039
$467$		−	6.60966e9i		−	0.138967i	−0.997583	−	0.0694835i	$-0.977865\pi$
$467$		−	6.60966e9i		−	0.138967i	0.997583	−	0.0694835i	$-0.0221351\pi$
$468$	7.73884e10			1.61322
$469$		−	5.52974e9i		−	0.114291i
$470$	7.45773e9			0.152832
$471$	6.53206e10			1.32729
$472$		−	3.58292e10i		−	0.721887i
$473$	4.23871e10	+	6.78046e10i	0.846817	+	1.35461i
$474$	4.30903e10			0.853623
$475$			5.80213e9i			0.113976i
$476$			7.65853e8i			0.0149182i
$477$	1.38797e11			2.68107
$478$		−	5.12947e10i		−	0.982564i
$479$	−5.75458e10			−1.09313			−0.546565	−	0.837417i	$-0.684065\pi$
$479$	−5.75458e10			−1.09313			−0.546565	+	0.837417i	$0.684065\pi$
$480$		−	7.37439e10i		−	1.38919i
$481$			4.93081e8i			0.00921166i
$482$	−8.59829e9			−0.159303
$483$	−9.42466e9			−0.173172
$484$	5.04008e10			0.918452
$485$		−	2.03789e10i		−	0.368309i
$486$	−4.51842e9			−0.0809919
$487$	1.42045e10			0.252528			0.126264	−	0.991997i	$-0.459701\pi$
$487$	1.42045e10			0.252528			0.126264	+	0.991997i	$0.459701\pi$
$488$	−6.11252e10			−1.07781
$489$	5.56019e10			0.972421
$490$	2.80295e10			0.486217
$491$			6.76583e10i			1.16411i	0.813149	+	0.582056i	$0.197752\pi$
$491$			6.76583e10i			1.16411i	−0.813149	+	0.582056i	$0.802248\pi$
$492$		−	9.02458e10i		−	1.54016i
$493$		−	1.10738e10i		−	0.187460i
$494$	−1.71829e10			−0.288529
$495$			1.58862e11i			2.64606i
$496$	2.37782e9			0.0392873
$497$	8.50808e9			0.139446
$498$	5.32200e10			0.865282
$499$		−	6.92061e10i		−	1.11620i	−0.829773	−	0.558100i	$-0.811530\pi$
$499$		−	6.92061e10i		−	1.11620i	0.829773	−	0.558100i	$-0.188470\pi$
$500$			4.02633e10i			0.644213i
$501$			2.11894e11i			3.36331i
$502$		−	6.24209e9i		−	0.0982913i
$503$			6.26497e10i			0.978695i	0.872089	+	0.489348i	$0.162765\pi$
$503$			6.26497e10i			0.978695i	−0.872089	+	0.489348i	$0.837235\pi$
$504$	−3.39866e10			−0.526727
$505$			1.44891e10i			0.222780i
$506$		−	2.61411e10i		−	0.398770i
$507$		−	9.13271e10i		−	1.38219i
$508$	−1.27314e10			−0.191171
$509$	3.06030e10			0.455924			0.227962	−	0.973670i	$-0.426794\pi$
$509$	3.06030e10			0.455924			0.227962	+	0.973670i	$0.426794\pi$
$510$		−	6.07222e9i		−	0.0897567i
$511$	−2.91591e10			−0.427652
$512$			7.96805e9i			0.115950i
$513$	−4.21460e10			−0.608537
$514$	−2.89769e10			−0.415145
$515$			6.77582e10i			0.963237i
$516$	−6.19789e10	+	3.87453e10i	−0.874269	+	0.546537i
$517$	−3.35532e10			−0.469647
$518$		−	8.05040e7i		−	0.00111815i
$519$		−	1.63479e11i		−	2.25316i
$520$	−8.10227e10			−1.10814
$521$			6.05568e10i			0.821886i	0.911661	+	0.410943i	$0.134801\pi$
$521$			6.05568e10i			0.821886i	−0.911661	+	0.410943i	$0.865199\pi$
$522$	1.82695e11			2.46061
$523$		−	1.12688e11i		−	1.50616i	−0.657931	−	0.753078i	$-0.728568\pi$
$523$		−	1.12688e11i		−	1.50616i	0.657931	−	0.753078i	$-0.271432\pi$
$524$		−	7.76823e10i		−	1.03038i
$525$	1.13816e10			0.149819
$526$	−4.01250e10			−0.524170
$527$	−5.17177e9			−0.0670496
$528$		−	1.25607e10i		−	0.161614i
$529$	−6.63585e10			−0.847372
$530$	−5.40231e10			−0.684661
$531$	−1.14877e11			−1.44496
$532$	−4.06653e9			−0.0507666
$533$	−1.61445e11			−2.00040
$534$			1.31114e11i			1.61244i
$535$		−	7.11701e10i		−	0.868725i
$536$			3.77121e10i			0.456900i
$537$	1.75811e11			2.11422
$538$		−	5.12561e10i		−	0.611810i
$539$	−1.26108e11			−1.49412
$540$	−7.38810e10			−0.868876
$541$	−1.14693e9			−0.0133890			−0.00669451	−	0.999978i	$-0.502131\pi$
$541$	−1.14693e9			−0.0133890			−0.00669451	+	0.999978i	$0.502131\pi$
$542$		−	6.13059e10i		−	0.710404i
$543$			3.04394e10i			0.350136i
$544$		−	8.50429e9i		−	0.0971052i
$545$			1.07450e11i			1.21793i
$546$			3.37066e10i			0.379267i
$547$	−2.05760e10			−0.229833			−0.114916	−	0.993375i	$-0.536660\pi$
$547$	−2.05760e10			−0.229833			−0.114916	+	0.993375i	$0.536660\pi$
$548$		−	3.10482e10i		−	0.344282i
$549$			1.95982e11i			2.15738i
$550$			3.15692e10i			0.344995i
$551$	5.87997e10			0.637923
$552$	6.42749e10			0.692285
$553$		−	1.82433e10i		−	0.195076i
$554$	−3.90024e10			−0.414049
$555$		−	9.25225e8i		−	0.00975159i
$556$	−7.04208e10			−0.736888
$557$	−5.52422e10			−0.573919			−0.286959	−	0.957943i	$-0.592644\pi$
$557$	−5.52422e10			−0.573919			−0.286959	+	0.957943i	$0.592644\pi$
$558$		−	8.53235e10i		−	0.880100i
$559$	6.93133e10	+	1.10877e11i	0.709854	+	1.13552i
$560$	1.18198e9			0.0120188
$561$			2.73196e10i			0.275819i
$562$			9.86962e10i			0.989361i
$563$	6.10219e10			0.607368			0.303684	−	0.952773i	$-0.401783\pi$
$563$	6.10219e10			0.607368			0.303684	+	0.952773i	$0.401783\pi$
$564$		−	3.06703e10i		−	0.303111i
$565$	−2.81533e10			−0.276271
$566$			2.74904e10i			0.267865i
$567$			2.91469e10i			0.282007i
$568$	−5.80239e10			−0.557460
$569$	1.19187e11			1.13705			0.568525	−	0.822666i	$-0.307514\pi$
$569$	1.19187e11			1.13705			0.568525	+	0.822666i	$0.307514\pi$
$570$	3.22424e10			0.305441
$571$			5.18835e10i			0.488073i	0.969766	+	0.244036i	$0.0784716\pi$
$571$			5.18835e10i			0.488073i	−0.969766	+	0.244036i	$0.921528\pi$
$572$	1.35519e11			1.26595
$573$	−2.33281e11			−2.16401
$574$	2.63587e10			0.242815
$575$	−1.44343e10			−0.132046
$576$	1.53314e11			1.39281
$577$		−	1.07678e11i		−	0.971460i	−0.874109	−	0.485730i	$-0.838554\pi$
$577$		−	1.07678e11i		−	0.971460i	0.874109	−	0.485730i	$-0.161446\pi$
$578$			7.06129e10i			0.632664i
$579$		−	1.78988e11i		−	1.59261i
$580$	1.03074e11			0.910834
$581$		−	2.25320e10i		−	0.197740i
$582$	5.78181e10			0.503932
$583$	2.43056e11			2.10393
$584$	1.98861e11			1.70961
$585$			2.59778e11i			2.21809i
$586$			8.68037e10i			0.736118i
$587$		−	1.96919e11i		−	1.65858i	−0.558819	−	0.829289i	$-0.688746\pi$
$587$		−	1.96919e11i		−	1.65858i	0.558819	−	0.829289i	$-0.311254\pi$
$588$		−	1.15273e11i		−	0.964311i
$589$		−	2.74611e10i		−	0.228169i
$590$	4.47127e10			0.368997
$591$		−	2.26799e11i		−	1.85905i
$592$			4.90568e7i			0.000399404i
$593$		−	4.01305e10i		−	0.324530i	−0.986747	−	0.162265i	$-0.948120\pi$
$593$		−	4.01305e10i		−	0.324530i	0.986747	−	0.162265i	$-0.0518800\pi$
$594$	−2.29315e11			−1.84199
$595$	−2.57082e9			−0.0205118
$596$			1.07938e9i			0.00855440i
$597$	−2.30074e11			−1.81122
$598$		−	4.27471e10i		−	0.334273i
$599$	−1.50298e11			−1.16747			−0.583734	−	0.811945i	$-0.698409\pi$
$599$	−1.50298e11			−1.16747			−0.583734	+	0.811945i	$0.698409\pi$
$600$	−7.76212e10			−0.598929
$601$		−	9.06889e10i		−	0.695114i	−0.937659	−	0.347557i	$-0.887011\pi$
$601$		−	9.06889e10i		−	0.695114i	0.937659	−	0.347557i	$-0.112989\pi$
$602$	−1.13166e10	−	1.81026e10i	−0.0861647	−	0.137834i
$603$	1.20914e11			0.914550
$604$			6.87201e10i			0.516340i
$605$			1.69186e11i			1.26282i
$606$	−4.11079e10			−0.304814
$607$		−	5.62467e9i		−	0.0414326i	−0.999785	−	0.0207163i	$-0.993405\pi$
$607$		−	5.62467e9i		−	0.0414326i	0.999785	−	0.0207163i	$-0.00659468\pi$
$608$	4.51562e10			0.330448
$609$		−	1.15343e11i		−	0.838539i
$610$		−	7.62806e10i		−	0.550928i
$611$	−5.48676e10			−0.393687
$612$	−1.67462e10			−0.119374
$613$	2.46512e11			1.74581			0.872905	−	0.487891i	$-0.162234\pi$
$613$	2.46512e11			1.74581			0.872905	+	0.487891i	$0.162234\pi$
$614$			8.62909e10i			0.607144i
$615$	3.02938e11			2.11765
$616$	−5.95159e10			−0.413343
$617$	−1.65485e11			−1.14187			−0.570936	−	0.820994i	$-0.693420\pi$
$617$	−1.65485e11			−1.14187			−0.570936	+	0.820994i	$0.693420\pi$
$618$	−1.92241e11			−1.31793
$619$	−1.66265e10			−0.113250			−0.0566250	−	0.998396i	$-0.518034\pi$
$619$	−1.66265e10			−0.113250			−0.0566250	+	0.998396i	$0.518034\pi$
$620$		−	4.81387e10i		−	0.325782i
$621$		−	1.04849e11i		−	0.705016i
$622$		−	6.90811e10i		−	0.461527i
$623$	5.55102e10			0.368486
$624$		−	2.05398e10i		−	0.135475i
$625$	−8.35828e10			−0.547768
$626$	−9.06482e10			−0.590285
$627$	−1.45062e11			−0.938607
$628$			7.01161e10i			0.450795i
$629$		−	1.06699e8i		−	0.000681643i
$630$		−	4.24133e10i		−	0.269240i
$631$		−	7.50263e10i		−	0.473256i	−0.971600	−	0.236628i	$-0.923958\pi$
$631$		−	7.50263e10i		−	0.473256i	0.971600	−	0.236628i	$-0.0760423\pi$
$632$			1.24417e11i			0.779850i
$633$	3.57761e11			2.22832
$634$			3.62132e10i			0.224135i
$635$		−	4.27370e10i		−	0.262851i
$636$			2.22173e11i			1.35788i
$637$	−2.06217e11			−1.25247
$638$	3.19927e11			1.93094
$639$			1.86039e11i			1.11583i
$640$	7.40936e10			0.441632
$641$		−	2.82104e11i		−	1.67100i	−0.549489	−	0.835501i	$-0.685178\pi$
$641$		−	2.82104e11i		−	1.67100i	0.549489	−	0.835501i	$-0.314822\pi$
$642$	2.01921e11			1.18862
$643$	1.95960e11			1.14637			0.573183	−	0.819427i	$-0.305708\pi$
$643$	1.95960e11			1.14637			0.573183	+	0.819427i	$0.305708\pi$
$644$		−	1.01166e10i		−	0.0588152i
$645$	−1.30061e11	−	2.08051e11i	−0.751461	−	1.20208i
$646$	3.71825e9			0.0213505
$647$			2.37614e9i			0.0135598i	0.999977	+	0.00677992i	$0.00215813\pi$
$647$			2.37614e9i			0.0135598i	−0.999977	+	0.00677992i	$0.997842\pi$
$648$		−	1.98778e11i		−	1.12737i
$649$	−2.01168e11			−1.13391
$650$			5.16233e10i			0.289196i
$651$	−5.38686e10			−0.299924
$652$			5.96839e10i			0.330268i
$653$			1.28525e11i			0.706862i	0.935461	+	0.353431i	$0.114985\pi$
$653$			1.28525e11i			0.706862i	−0.935461	+	0.353431i	$0.885015\pi$
$654$	−3.04854e11			−1.66641
$655$	2.60765e11			1.41672
$656$	−1.60622e10			−0.0867342
$657$		−	6.37596e11i		−	3.42203i
$658$	8.95809e9			0.0477872
$659$	1.48704e11			0.788464			0.394232	−	0.919011i	$-0.371011\pi$
$659$	1.48704e11			0.788464			0.394232	+	0.919011i	$0.371011\pi$
$660$	−2.54291e11			−1.34015
$661$	−5.70041e10			−0.298607			−0.149304	−	0.988791i	$-0.547703\pi$
$661$	−5.70041e10			−0.298607			−0.149304	+	0.988791i	$0.547703\pi$
$662$	8.76686e10			0.456470
$663$			4.46743e10i			0.231208i
$664$			1.53665e11i			0.790502i
$665$		−	1.36506e10i		−	0.0698015i
$666$	1.76031e9			0.00894731
$667$			1.46280e11i			0.739061i
$668$	−2.27450e11			−1.14230
$669$	5.50913e11			2.75029
$670$	−4.70625e10			−0.233548
$671$			3.43195e11i			1.69298i
$672$		−	8.85798e10i		−	0.434368i
$673$			2.33498e11i			1.13821i	0.822264	+	0.569106i	$0.192711\pi$
$673$			2.33498e11i			1.13821i	−0.822264	+	0.569106i	$0.807289\pi$
$674$		−	1.19483e11i		−	0.578983i
$675$			1.26621e11i			0.609943i
$676$	9.80318e10			0.469440
$677$			7.17939e10i			0.341769i	0.985291	+	0.170885i	$0.0546625\pi$
$677$			7.17939e10i			0.341769i	−0.985291	+	0.170885i	$0.945337\pi$
$678$		−	7.98754e10i		−	0.378002i
$679$		−	2.44787e10i		−	0.115162i
$680$	1.75327e10			0.0819996
$681$	−6.91262e11			−3.21406
$682$		−	1.49415e11i		−	0.690648i
$683$	−3.60964e11			−1.65875			−0.829374	−	0.558694i	$-0.811303\pi$
$683$	−3.60964e11			−1.65875			−0.829374	+	0.558694i	$0.811303\pi$
$684$		−	8.89193e10i		−	0.406230i
$685$	1.04223e11			0.473370
$686$	6.96668e10			0.314579
$687$			6.85113e11i			3.07564i
$688$	6.89600e9	+	1.10312e10i	0.0307782	+	0.0492344i
$689$	3.97456e11			1.76365
$690$			8.02113e10i			0.353866i
$691$		−	2.51135e11i		−	1.10153i	−0.834662	−	0.550763i	$-0.814337\pi$
$691$		−	2.51135e11i		−	1.10153i	0.834662	−	0.550763i	$-0.185663\pi$
$692$	1.75480e11			0.765251
$693$			1.90822e11i			0.827363i
$694$	−1.03158e11			−0.444697
$695$		−	2.36389e11i		−	1.01318i
$696$			7.86626e11i			3.35221i
$697$	3.49354e10			0.148025
$698$	−1.57270e11			−0.662557
$699$	−3.24224e10			−0.135812
$700$			1.22172e10i			0.0508839i
$701$	−9.21164e10			−0.381474			−0.190737	−	0.981641i	$-0.561088\pi$
$701$	−9.21164e10			−0.381474			−0.190737	+	0.981641i	$0.561088\pi$
$702$	−3.74986e11			−1.54407
$703$	5.66550e8			0.00231962
$704$	2.68478e11			1.09299
$705$	1.02954e11			0.416763
$706$		−	8.73513e10i		−	0.351601i
$707$			1.74040e10i			0.0696582i
$708$		−	1.83884e11i		−	0.731830i
$709$	−4.42941e11			−1.75291			−0.876457	−	0.481480i	$-0.840100\pi$
$709$	−4.42941e11			−1.75291			−0.876457	+	0.481480i	$0.840100\pi$
$710$		−	7.24104e10i		−	0.284949i
$711$	3.98911e11			1.56098
$712$	−3.78572e11			−1.47309
$713$	6.83167e10			0.264343
$714$		−	7.29384e9i		−	0.0280649i
$715$			4.54913e11i			1.74062i
$716$			1.88718e11i			0.718063i
$717$		−	7.08127e11i		−	2.67938i
$718$		−	2.64562e11i		−	0.995473i
$719$	−5.11725e10			−0.191479			−0.0957395	−	0.995406i	$-0.530522\pi$
$719$	−5.11725e10			−0.191479			−0.0957395	+	0.995406i	$0.530522\pi$
$720$			2.58454e10i			0.0961731i
$721$			8.13900e10i			0.301183i
$722$		−	1.53880e11i		−	0.566282i
$723$	−1.18700e11			−0.434408
$724$	−3.26741e10			−0.118919
$725$		−	1.76654e11i		−	0.639397i
$726$	−4.80008e11			−1.72784
$727$		−	1.66037e11i		−	0.594385i	−0.954818	−	0.297192i	$-0.903950\pi$
$727$		−	1.66037e11i		−	0.594385i	0.954818	−	0.297192i	$-0.0960502\pi$
$728$	−9.73230e10			−0.346489
$729$	2.50693e11			0.887632
$730$			2.48167e11i			0.873881i
$731$	−1.49988e10	−	2.39929e10i	−0.0525277	−	0.0840259i
$732$	−3.13708e11			−1.09265
$733$			2.79590e11i			0.968513i	0.874926	+	0.484257i	$0.160910\pi$
$733$			2.79590e11i			0.968513i	−0.874926	+	0.484257i	$0.839090\pi$
$734$		−	2.49916e10i		−	0.0861014i
$735$	3.86949e11			1.32588
$736$			1.12338e11i			0.382838i
$737$	2.11740e11			0.717682
$738$			5.76362e11i			1.94299i
$739$		−	1.64286e11i		−	0.550837i	−0.961324	−	0.275418i	$-0.911184\pi$
$739$		−	1.64286e11i		−	0.550837i	0.961324	−	0.275418i	$-0.0888163\pi$
$740$	9.93150e8			0.00331198
$741$	−2.37212e11			−0.786799
$742$	−6.48915e10			−0.214078
$743$			4.46894e11i			1.46639i	0.680019	+	0.733195i	$0.261972\pi$
$743$			4.46894e11i			1.46639i	−0.680019	+	0.733195i	$0.738028\pi$
$744$	3.67376e11			1.19900
$745$	−3.62328e9			−0.0117619
$746$	7.38263e10			0.238372
$747$	4.92687e11			1.58230
$748$	−2.93253e10			−0.0936776
$749$		−	8.54882e10i		−	0.271631i
$750$		−	3.83461e11i		−	1.21193i
$751$			1.65073e11i			0.518939i	0.965751	+	0.259469i	$0.0835477\pi$
$751$			1.65073e11i			0.518939i	−0.965751	+	0.259469i	$0.916452\pi$
$752$	−5.45880e9			−0.0170697
$753$		−	8.61725e10i		−	0.268033i
$754$	5.23158e11			1.61863
$755$	−2.30680e11			−0.709942
$756$	−8.87446e10			−0.271678
$757$		−	4.16379e11i		−	1.26796i	−0.773350	−	0.633979i	$-0.781420\pi$
$757$		−	4.16379e11i		−	1.26796i	0.773350	−	0.633979i	$-0.218580\pi$
$758$		−	5.03394e10i		−	0.152487i
$759$		−	3.60880e11i		−	1.08742i
$760$			9.30951e10i			0.279044i
$761$		−	5.59476e11i		−	1.66818i	−0.551628	−	0.834090i	$-0.685993\pi$
$761$		−	5.59476e11i		−	1.66818i	0.551628	−	0.834090i	$-0.314007\pi$
$762$	1.21252e11			0.359640
$763$			1.29067e11i			0.380819i
$764$		−	2.50407e11i		−	0.734975i
$765$		−	5.62139e10i		−	0.164134i
$766$	2.31592e11			0.672679
$767$	−3.28958e11			−0.950516
$768$			6.24929e11i			1.79633i
$769$	3.83384e11			1.09630			0.548150	−	0.836380i	$-0.315332\pi$
$769$	3.83384e11			1.09630			0.548150	+	0.836380i	$0.315332\pi$
$770$		−	7.42723e10i		−	0.211283i
$771$	−4.00029e11			−1.13207
$772$	1.92128e11			0.540906
$773$			1.08957e11i			0.305168i	0.988291	+	0.152584i	$0.0487594\pi$
$773$			1.08957e11i			0.305168i	−0.988291	+	0.152584i	$0.951241\pi$
$774$	3.95834e11	−	2.47450e11i	1.10293	−	0.689483i
$775$	−8.25023e10			−0.228696
$776$			1.66941e11i			0.460381i
$777$		−	1.11136e9i		−	0.00304910i
$778$	4.15410e10			0.113386
$779$			1.85500e11i			0.503727i
$780$	−4.15827e11			−1.12340
$781$			3.25783e11i			0.875637i
$782$			9.25012e9i			0.0247355i
$783$	1.28319e12			3.41386
$784$	−2.05166e10			−0.0543051
$785$	−2.35366e11			−0.619820
$786$			7.39832e11i			1.93840i
$787$	3.10785e9			0.00810141			0.00405071	−	0.999992i	$-0.498711\pi$
$787$	3.10785e9			0.00810141			0.00405071	+	0.999992i	$0.498711\pi$
$788$	2.43450e11			0.631400
$789$	−5.53929e11			−1.42937
$790$	−1.55265e11			−0.398626
$791$	−3.38172e10			−0.0863837
$792$		−	1.30138e12i		−	3.30753i
$793$			5.61208e11i			1.41916i
$794$		−	3.38282e11i		−	0.851132i
$795$	−7.45792e11			−1.86702
$796$		−	2.46965e11i		−	0.615152i
$797$	−1.39632e11			−0.346060			−0.173030	−	0.984917i	$-0.555356\pi$
$797$	−1.39632e11			−0.346060			−0.173030	+	0.984917i	$0.555356\pi$
$798$	3.87289e10			0.0955045
$799$	1.18729e10			0.0291320
$800$		−	1.35664e11i		−	0.331211i
$801$			1.21379e12i			2.94859i
$802$		−	8.72310e10i		−	0.210850i
$803$		−	1.11653e12i		−	2.68540i
$804$			1.93547e11i			0.463193i
$805$	3.39594e10			0.0808679
$806$		−	2.44330e11i		−	0.578943i
$807$		−	7.07594e11i		−	1.66836i
$808$		−	1.18693e11i		−	0.278471i
$809$	2.09300e11			0.488623			0.244312	−	0.969697i	$-0.421438\pi$
$809$	2.09300e11			0.488623			0.244312	+	0.969697i	$0.421438\pi$
$810$	2.48063e11			0.576265
$811$		−	5.69929e11i		−	1.31746i	−0.752379	−	0.658730i	$-0.771094\pi$
$811$		−	5.69929e11i		−	1.31746i	0.752379	−	0.658730i	$-0.228906\pi$
$812$	1.23811e11			0.284797
$813$		−	8.46332e11i		−	1.93722i
$814$	3.08258e9			0.00702129
$815$	−2.00348e11			−0.454102
$816$			4.44466e9i			0.0100248i
$817$	1.27398e11	−	7.96410e10i	0.285939	−	0.178751i
$818$	2.07027e11			0.462396
$819$			3.12041e11i			0.693547i
$820$			3.25178e11i			0.719227i
$821$	4.64555e11			1.02250			0.511252	−	0.859431i	$-0.329182\pi$
$821$	4.64555e11			1.02250			0.511252	+	0.859431i	$0.329182\pi$
$822$			2.95697e11i			0.647680i
$823$	−7.12381e11			−1.55279			−0.776395	−	0.630246i	$-0.782954\pi$
$823$	−7.12381e11			−1.55279			−0.776395	+	0.630246i	$0.782954\pi$
$824$		−	5.55068e11i		−	1.20403i
$825$			4.35815e11i			0.940776i
$826$	5.37081e10			0.115377
$827$	−6.92473e11			−1.48041			−0.740203	−	0.672383i	$-0.765271\pi$
$827$	−6.92473e11			−1.48041			−0.740203	+	0.672383i	$0.765271\pi$
$828$	2.21210e11			0.470634
$829$		−	3.05973e11i		−	0.647836i	−0.946085	−	0.323918i	$-0.895000\pi$
$829$		−	3.05973e11i		−	0.647836i	0.946085	−	0.323918i	$-0.105000\pi$
$830$	−1.91765e11			−0.404070
$831$	−5.38430e11			−1.12908
$832$	4.39026e11			0.916215
$833$	4.46237e10			0.0926799
$834$	6.70675e11			1.38627
$835$		−	7.63506e11i		−	1.57060i
$836$		−	1.55712e11i		−	0.318784i
$837$		−	5.99288e11i		−	1.22105i
$838$	−4.96448e11			−1.00669
$839$			2.00550e11i			0.404739i	0.979309	+	0.202370i	$0.0648642\pi$
$839$			2.00550e11i			0.404739i	−0.979309	+	0.202370i	$0.935136\pi$
$840$	1.82618e11			0.366798
$841$	−1.28999e12			−2.57871
$842$	5.35592e11			1.06558
$843$			1.36251e12i			2.69792i
$844$			3.84026e11i			0.756816i
$845$			3.29074e11i			0.645457i
$846$			1.95879e11i			0.382389i
$847$			2.03223e11i			0.394857i
$848$	3.95430e10			0.0764692
$849$			3.79507e11i			0.730448i
$850$		−	1.11709e10i		−	0.0213999i
$851$			1.40944e9i			0.00268738i
$852$	−2.97792e11			−0.565138
$853$	9.68289e11			1.82898			0.914490	−	0.404609i	$-0.132592\pi$
$853$	9.68289e11			1.82898			0.914490	+	0.404609i	$0.132592\pi$
$854$		−	9.16269e10i		−	0.172263i
$855$	2.98485e11			0.558545
$856$			5.83018e11i			1.08589i
$857$	−9.03629e11			−1.67520			−0.837600	−	0.546284i	$-0.816042\pi$
$857$	−9.03629e11			−1.67520			−0.837600	+	0.546284i	$0.816042\pi$
$858$	−1.29066e12			−2.38157
$859$		−	1.38859e11i		−	0.255036i	−0.991836	−	0.127518i	$-0.959299\pi$
$859$		−	1.38859e11i		−	0.255036i	0.991836	−	0.127518i	$-0.0407011\pi$
$860$	2.23325e11	−	1.39609e11i	0.408267	−	0.255223i
$861$	3.63884e11			0.662140
$862$			8.66189e10i			0.156886i
$863$		−	2.95981e11i		−	0.533605i	−0.963751	−	0.266803i	$-0.914033\pi$
$863$		−	2.95981e11i		−	0.533605i	0.963751	−	0.266803i	$-0.0859672\pi$
$864$	9.85450e11			1.76840
$865$			5.89054e11i			1.05218i
$866$	1.87053e11			0.332577
$867$			9.74817e11i			1.72523i
$868$		−	5.78233e10i		−	0.101865i
$869$	6.98555e11			1.22496
$870$	−9.81663e11			−1.71350
$871$	3.46246e11			0.601605
$872$		−	8.80222e11i		−	1.52239i
$873$	5.35255e11			0.921517
$874$	−4.91164e10			−0.0841746
$875$	−1.62347e11			−0.276957
$876$	1.02060e12			1.73316
$877$	2.10271e11			0.355452			0.177726	−	0.984080i	$-0.443126\pi$
$877$	2.10271e11			0.355452			0.177726	+	0.984080i	$0.443126\pi$
$878$		−	4.14271e11i		−	0.697119i
$879$			1.19833e12i			2.00734i
$880$			4.52594e10i			0.0754707i
$881$	6.57140e11			1.09082			0.545412	−	0.838168i	$-0.316373\pi$
$881$	6.57140e11			1.09082			0.545412	+	0.838168i	$0.316373\pi$
$882$			7.36199e11i			1.21652i
$883$	4.57073e11			0.751869			0.375935	−	0.926646i	$-0.377322\pi$
$883$	4.57073e11			0.751869			0.375935	+	0.926646i	$0.377322\pi$
$884$	−4.79540e10			−0.0785264
$885$	6.17263e11			1.00623
$886$			5.31407e11i			0.862367i
$887$		−	2.15040e11i		−	0.347395i	−0.984799	−	0.173698i	$-0.944428\pi$
$887$		−	2.15040e11i		−	0.347395i	0.984799	−	0.173698i	$-0.0555716\pi$
$888$			7.57935e9i			0.0121893i
$889$		−	5.13349e10i		−	0.0821875i
$890$		−	4.72436e11i		−	0.752979i
$891$	−1.11606e12			−1.77084
$892$			5.91358e11i			0.934095i
$893$			6.30429e10i			0.0991358i
$894$		−	1.02798e10i		−	0.0160930i
$895$	−6.33492e11			−0.987300
$896$	8.89998e10			0.138088
$897$		−	5.90126e11i		−	0.911539i
$898$	−1.31432e11			−0.202114
$899$			8.36091e11i			1.28001i
$900$	−2.67143e11			−0.407168
$901$	−8.60062e10			−0.130506
$902$			1.00930e12i			1.52474i
$903$	−1.56226e11	−	2.49908e11i	−0.234965	−	0.375862i
$904$	2.30629e11			0.345334
$905$		−	1.09681e11i		−	0.163507i
$906$		−	6.54478e11i		−	0.971364i
$907$	−1.16366e12			−1.71948			−0.859738	−	0.510735i	$-0.829373\pi$
$907$	−1.16366e12			−1.71948			−0.859738	+	0.510735i	$0.829373\pi$
$908$		−	7.42011e11i		−	1.09161i
$909$	−3.80559e11			−0.557399
$910$		−	1.21453e11i		−	0.177110i
$911$			1.03563e12i			1.50359i	0.659395	+	0.751797i	$0.270813\pi$
$911$			1.03563e12i			1.50359i	−0.659395	+	0.751797i	$0.729187\pi$
$912$	−2.36003e10			−0.0341144
$913$	8.62773e11			1.24169
$914$	−5.75349e11			−0.824416
$915$		−	1.05306e12i		−	1.50234i
$916$	−7.35411e11			−1.04460
$917$	3.13226e11			0.442976
$918$	8.11440e10			0.114258
$919$	−4.00458e11			−0.561428			−0.280714	−	0.959791i	$-0.590571\pi$
$919$	−4.00458e11			−0.561428			−0.280714	+	0.959791i	$0.590571\pi$
$920$	−2.31598e11			−0.323284
$921$			1.19125e12i			1.65564i
$922$			4.14511e11i			0.573604i
$923$			5.32734e11i			0.734013i
$924$	−3.05449e11			−0.419036
$925$		−	1.70211e9i		−	0.00232498i
$926$	−1.83099e10			−0.0249025
$927$	−1.77968e12			−2.41004
$928$	−1.37484e12			−1.85379
$929$		−	1.01464e11i		−	0.136223i	−0.997678	−	0.0681113i	$-0.978303\pi$
$929$		−	1.01464e11i		−	0.136223i	0.997678	−	0.0681113i	$-0.0216973\pi$
$930$			4.58464e11i			0.612877i
$931$			2.36943e11i			0.315388i
$932$		−	3.48027e10i		−	0.0461264i
$933$		−	9.53669e11i		−	1.25855i
$934$	−6.75706e10			−0.0887913
$935$		−	9.84394e10i		−	0.128802i
$936$		−	2.12808e12i		−	2.77258i
$937$		−	1.08546e12i		−	1.40817i	−0.710115	−	0.704085i	$-0.751357\pi$
$937$		−	1.08546e12i		−	1.40817i	0.710115	−	0.704085i	$-0.248643\pi$
$938$	−5.65306e10			−0.0730251
$939$	−1.25141e12			−1.60967
$940$			1.10513e11i			0.141547i
$941$	8.11626e9			0.0103514			0.00517568	−	0.999987i	$-0.498353\pi$
$941$	8.11626e9			0.0103514			0.00517568	+	0.999987i	$0.498353\pi$
$942$		−	6.67773e11i		−	0.848057i
$943$	−4.61481e11			−0.583589
$944$	−3.27282e10			−0.0412130
$945$		−	2.97899e11i		−	0.373544i
$946$	6.93167e11	−	4.33324e11i	0.865512	−	0.541063i
$947$	1.10138e12			1.36943			0.684713	−	0.728813i	$-0.259928\pi$
$947$	1.10138e12			1.36943			0.684713	+	0.728813i	$0.259928\pi$
$948$			6.38536e11i			0.790591i
$949$		−	1.82580e12i		−	2.25107i
$950$	5.93152e10			0.0728235
$951$			4.99926e11i			0.611200i
$952$	2.10599e10			0.0256394
$953$			1.42579e12i			1.72855i	0.503017	+	0.864277i	$0.332223\pi$
$953$			1.42579e12i			1.72855i	−0.503017	+	0.864277i	$0.667777\pi$
$954$		−	1.41893e12i		−	1.71304i
$955$	8.40568e11			1.01055
$956$	7.60114e11			0.910012
$957$	4.41661e12			5.26553
$958$			5.88291e11i			0.698442i
$959$	1.25191e11			0.148012
$960$	−8.23796e11			−0.969917
$961$	−4.62413e11			−0.542171
$962$	5.04077e9			0.00588568
$963$	1.86930e12			2.17357
$964$		−	1.27414e11i		−	0.147540i
$965$			6.44938e11i			0.743719i
$966$			9.63483e10i			0.110646i
$967$	2.21670e10			0.0253513			0.0126756	−	0.999920i	$-0.495965\pi$
$967$	2.21670e10			0.0253513			0.0126756	+	0.999920i	$0.495965\pi$
$968$		−	1.38595e12i		−	1.57851i
$969$	5.13307e10			0.0582214
$970$	−2.08333e11			−0.235327
$971$	−1.94301e11			−0.218574			−0.109287	−	0.994010i	$-0.534857\pi$
$971$	−1.94301e11			−0.218574			−0.109287	+	0.994010i	$0.534857\pi$
$972$		−	6.69565e10i		−	0.0750115i
$973$		−	2.83946e11i		−	0.316800i
$974$		−	1.45212e11i		−	0.161350i
$975$			7.12663e11i			0.788616i
$976$			5.58348e10i			0.0615326i
$977$	5.07790e10			0.0557321			0.0278661	−	0.999612i	$-0.491129\pi$
$977$	5.07790e10			0.0557321			0.0278661	+	0.999612i	$0.491129\pi$
$978$		−	5.68419e11i		−	0.621317i
$979$			2.12554e12i			2.31387i
$980$			4.15356e11i			0.450315i
$981$	−2.82220e12			−3.04728
$982$	6.91671e11			0.743795
$983$		−	3.96924e11i		−	0.425103i	−0.977150	−	0.212551i	$-0.931823\pi$
$983$		−	3.96924e11i		−	0.425103i	0.977150	−	0.212551i	$-0.0681773\pi$
$984$	−2.48164e12			−2.64702
$985$			8.17214e11i			0.868143i
$986$	−1.13207e11			−0.119775
$987$	1.23667e11			0.130312
$988$		−	2.54627e11i		−	0.267224i
$989$	1.98128e11	+	3.16935e11i	0.207091	+	0.331273i
$990$	1.62405e12			1.69067
$991$			4.78133e10i			0.0495740i	0.999693	+	0.0247870i	$0.00789076\pi$
$991$			4.78133e10i			0.0495740i	−0.999693	+	0.0247870i	$0.992109\pi$
$992$			6.42090e11i			0.663054i
$993$	1.21027e12			1.24476
$994$		−	8.69781e10i		−	0.0890973i
$995$	8.29014e11			0.845803
$996$			7.88644e11i			0.801390i
$997$			3.74693e11i			0.379223i	0.981859	+	0.189612i	$0.0607229\pi$
$997$			3.74693e11i			0.379223i	−0.981859	+	0.189612i	$0.939277\pi$
$998$	−7.07494e11			−0.713183
$999$	1.23639e10			0.0124135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.11	✓	28
43.42	odd	2	inner	43.9.b.b.42.18	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.11	✓	28	1.1	even	1	trivial
43.9.b.b.42.18	yes	28	43.42	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.2230i q^{2} -141.129i q^{3} +151.490 q^{4} +508.524i q^{5} -1442.77 q^{6} +610.830i q^{7} -4165.77i q^{8} -13356.5 q^{9} +O(q^{10})\)	\(q-10.2230i q^{2} -141.129i q^{3} +151.490 q^{4} +508.524i q^{5} -1442.77 q^{6} +610.830i q^{7} -4165.77i q^{8} -13356.5 q^{9} +5198.64 q^{10} -23389.3 q^{11} -21379.7i q^{12} -38247.2 q^{13} +6244.51 q^{14} +71767.6 q^{15} -3805.23 q^{16} +8276.38 q^{17} +136543. i q^{18} +43946.0i q^{19} +77036.4i q^{20} +86206.0 q^{21} +239109. i q^{22} -109327. q^{23} -587913. q^{24} +132028. q^{25} +391001. i q^{26} +959041. i q^{27} +92534.7i q^{28} -1.33800e6i q^{29} -733681. i q^{30} -624882. q^{31} -1.02754e6i q^{32} +3.30091e6i q^{33} -84609.5i q^{34} -310621. q^{35} -2.02338e6 q^{36} -12892.0i q^{37} +449260. q^{38} +5.39780e6i q^{39} +2.11840e6 q^{40} +4.22110e6 q^{41} -881284. i q^{42} +(-1.81225e6 - 2.89896e6i) q^{43} -3.54325e6 q^{44} -6.79209e6i q^{45} +1.11765e6i q^{46} +1.43455e6 q^{47} +537029. i q^{48} +5.39169e6 q^{49} -1.34973e6i q^{50} -1.16804e6i q^{51} -5.79407e6 q^{52} -1.03918e7 q^{53} +9.80428e6 q^{54} -1.18940e7i q^{55} +2.54458e6 q^{56} +6.20207e6 q^{57} -1.36784e7 q^{58} +8.60085e6 q^{59} +1.08721e7 q^{60} -1.46732e7i q^{61} +6.38818e6i q^{62} -8.15853e6i q^{63} -1.14787e7 q^{64} -1.94496e7i q^{65} +3.37453e7 q^{66} -9.05284e6 q^{67} +1.25379e6 q^{68} +1.54293e7i q^{69} +3.17548e6i q^{70} -1.39287e7i q^{71} +5.56401e7i q^{72} +4.77368e7i q^{73} -131795. q^{74} -1.86331e7i q^{75} +6.65739e6i q^{76} -1.42869e7i q^{77} +5.51817e7 q^{78} -2.98664e7 q^{79} -1.93505e6i q^{80} +4.77169e7 q^{81} -4.31523e7i q^{82} -3.68875e7 q^{83} +1.30594e7 q^{84} +4.20874e6i q^{85} +(-2.96361e7 + 1.85266e7i) q^{86} -1.88831e8 q^{87} +9.74345e7i q^{88} -9.08768e7i q^{89} -6.94355e7 q^{90} -2.33625e7i q^{91} -1.65620e7 q^{92} +8.81892e7i q^{93} -1.46654e7i q^{94} -2.23476e7 q^{95} -1.45016e8 q^{96} -4.00745e7 q^{97} -5.51192e7i q^{98} +3.12399e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9} + 24982 q^{10} + 4538 q^{11} + 22086 q^{13} + 24732 q^{14} + 15388 q^{15} + 525812 q^{16} - 135136 q^{17} - 261352 q^{21} - 184432 q^{23} + 1770326 q^{24} - 2640434 q^{25} - 110272 q^{31} + 10947816 q^{35} + 11602066 q^{36} - 7189158 q^{38} - 21389338 q^{40} + 1301336 q^{41} + 2473420 q^{43} - 8818480 q^{44} + 1983566 q^{47} - 15560936 q^{49} + 12927876 q^{52} + 23942594 q^{53} - 13757972 q^{54} + 34967256 q^{56} + 35225148 q^{57} + 22565734 q^{58} - 5554336 q^{59} - 44902072 q^{60} - 170444572 q^{64} - 48457584 q^{66} - 130953802 q^{67} + 150021122 q^{68} + 205870278 q^{74} + 267860612 q^{78} + 7380250 q^{79} - 57601004 q^{81} - 42603970 q^{83} + 251931292 q^{84} - 45482652 q^{86} - 106687410 q^{87} - 255044692 q^{90} - 409532014 q^{92} + 123322986 q^{95} - 692987086 q^{96} - 318744840 q^{97} - 609707206 q^{99}+O(q^{100}) \) 28 * q - 4284 * q^4 - 1794 * q^6 - 80754 * q^9 + 24982 * q^10 + 4538 * q^11 + 22086 * q^13 + 24732 * q^14 + 15388 * q^15 + 525812 * q^16 - 135136 * q^17 - 261352 * q^21 - 184432 * q^23 + 1770326 * q^24 - 2640434 * q^25 - 110272 * q^31 + 10947816 * q^35 + 11602066 * q^36 - 7189158 * q^38 - 21389338 * q^40 + 1301336 * q^41 + 2473420 * q^43 - 8818480 * q^44 + 1983566 * q^47 - 15560936 * q^49 + 12927876 * q^52 + 23942594 * q^53 - 13757972 * q^54 + 34967256 * q^56 + 35225148 * q^57 + 22565734 * q^58 - 5554336 * q^59 - 44902072 * q^60 - 170444572 * q^64 - 48457584 * q^66 - 130953802 * q^67 + 150021122 * q^68 + 205870278 * q^74 + 267860612 * q^78 + 7380250 * q^79 - 57601004 * q^81 - 42603970 * q^83 + 251931292 * q^84 - 45482652 * q^86 - 106687410 * q^87 - 255044692 * q^90 - 409532014 * q^92 + 123322986 * q^95 - 692987086 * q^96 - 318744840 * q^97 - 609707206 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more