LMFDB - Embedded newform 43.9.b.b.42.20

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			42.20
Character	$\chi$	$=$	43.42
Dual form			43.9.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)

$f(q)$	$=$	$q+14.4463i q^{2} +49.3343i q^{3} +47.3041 q^{4} -738.628i q^{5} -712.698 q^{6} +198.404i q^{7} +4381.63i q^{8} +4127.13 q^{9} +O(q^{10})$	\(q+14.4463i q^{2} +49.3343i q^{3} +47.3041 q^{4} -738.628i q^{5} -712.698 q^{6} +198.404i q^{7} +4381.63i q^{8} +4127.13 q^{9} +10670.5 q^{10} +12439.9 q^{11} +2333.71i q^{12} +27835.0 q^{13} -2866.21 q^{14} +36439.7 q^{15} -51188.5 q^{16} -66432.0 q^{17} +59621.8i q^{18} +154260. i q^{19} -34940.1i q^{20} -9788.14 q^{21} +179711. i q^{22} +253326. q^{23} -216164. q^{24} -154946. q^{25} +402113. i q^{26} +527291. i q^{27} +9385.34i q^{28} -332311. i q^{29} +526419. i q^{30} -716916. q^{31} +382211. i q^{32} +613716. i q^{33} -959697. i q^{34} +146547. q^{35} +195230. q^{36} +2.30467e6i q^{37} -2.22849e6 q^{38} +1.37322e6i q^{39} +3.23639e6 q^{40} -126422. q^{41} -141403. i q^{42} +(-149483. - 3.41553e6i) q^{43} +588460. q^{44} -3.04841e6i q^{45} +3.65963e6i q^{46} +3.57846e6 q^{47} -2.52535e6i q^{48} +5.72544e6 q^{49} -2.23840e6i q^{50} -3.27737e6i q^{51} +1.31671e6 q^{52} -4.88694e6 q^{53} -7.61741e6 q^{54} -9.18849e6i q^{55} -869334. q^{56} -7.61030e6 q^{57} +4.80066e6 q^{58} +5.89621e6 q^{59} +1.72374e6 q^{60} -3.89973e6i q^{61} -1.03568e7i q^{62} +818841. i q^{63} -1.86258e7 q^{64} -2.05597e7i q^{65} -8.86593e6 q^{66} +2.99507e7 q^{67} -3.14250e6 q^{68} +1.24977e7i q^{69} +2.11707e6i q^{70} +4.99800e6i q^{71} +1.80835e7i q^{72} -1.46539e7i q^{73} -3.32940e7 q^{74} -7.64416e6i q^{75} +7.29712e6i q^{76} +2.46814e6i q^{77} -1.98379e7 q^{78} -1.87235e7 q^{79} +3.78092e7i q^{80} +1.06456e6 q^{81} -1.82634e6i q^{82} +7.06201e7 q^{83} -463019. q^{84} +4.90685e7i q^{85} +(4.93418e7 - 2.15948e6i) q^{86} +1.63943e7 q^{87} +5.45072e7i q^{88} -1.63314e7i q^{89} +4.40383e7 q^{90} +5.52258e6i q^{91} +1.19834e7 q^{92} -3.53685e7i q^{93} +5.16956e7i q^{94} +1.13941e8 q^{95} -1.88561e7 q^{96} -1.07206e8 q^{97} +8.27114e7i q^{98} +5.13413e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			14.4463i			0.902895i	0.892298	+	0.451447i	$0.149092\pi$
$2$			14.4463i			0.902895i	−0.892298	+	0.451447i	$0.850908\pi$
$3$			49.3343i			0.609065i	0.952502	+	0.304533i	$0.0985003\pi$
$3$			49.3343i			0.609065i	−0.952502	+	0.304533i	$0.901500\pi$
$4$	47.3041			0.184781
$5$		−	738.628i		−	1.18180i	−0.806743	−	0.590902i	$-0.798772\pi$
$5$		−	738.628i		−	1.18180i	0.806743	−	0.590902i	$-0.201228\pi$
$6$	−712.698			−0.549922
$7$			198.404i			0.0826341i	0.999146	+	0.0413171i	$0.0131554\pi$
$7$			198.404i			0.0826341i	−0.999146	+	0.0413171i	$0.986845\pi$
$8$			4381.63i			1.06973i
$9$	4127.13			0.629040
$10$	10670.5			1.06705
$11$	12439.9			0.849665			0.424833	−	0.905272i	$-0.360333\pi$
$11$	12439.9			0.849665			0.424833	+	0.905272i	$0.360333\pi$
$12$			2333.71i			0.112544i
$13$	27835.0			0.974580			0.487290	−	0.873240i	$-0.337986\pi$
$13$	27835.0			0.974580			0.487290	+	0.873240i	$0.337986\pi$
$14$	−2866.21			−0.0746099
$15$	36439.7			0.719796
$16$	−51188.5			−0.781074
$17$	−66432.0			−0.795393			−0.397696	−	0.917517i	$-0.630190\pi$
$17$	−66432.0			−0.795393			−0.397696	+	0.917517i	$0.630190\pi$
$18$			59621.8i			0.567956i
$19$			154260.i			1.18369i	0.806051	+	0.591846i	$0.201601\pi$
$19$			154260.i			1.18369i	−0.806051	+	0.591846i	$0.798399\pi$
$20$		−	34940.1i		−	0.218376i
$21$	−9788.14			−0.0503296
$22$			179711.i			0.767158i
$23$	253326.			0.905250			0.452625	−	0.891701i	$-0.350488\pi$
$23$	253326.			0.905250			0.452625	+	0.891701i	$0.350488\pi$
$24$	−216164.			−0.651537
$25$	−154946.			−0.396662
$26$			402113.i			0.879943i
$27$			527291.i			0.992191i
$28$			9385.34i			0.0152692i
$29$		−	332311.i		−	0.469843i	−0.972014	−	0.234921i	$-0.924517\pi$
$29$		−	332311.i		−	0.469843i	0.972014	−	0.234921i	$-0.0754832\pi$
$30$			526419.i			0.649900i
$31$	−716916.			−0.776285			−0.388143	−	0.921599i	$-0.626883\pi$
$31$	−716916.			−0.776285			−0.388143	+	0.921599i	$0.626883\pi$
$32$			382211.i			0.364505i
$33$			613716.i			0.517501i
$34$		−	959697.i		−	0.718156i
$35$	146547.			0.0976574
$36$	195230.			0.116235
$37$			2.30467e6i			1.22971i	0.788641	+	0.614854i	$0.210785\pi$
$37$			2.30467e6i			1.22971i	−0.788641	+	0.614854i	$0.789215\pi$
$38$	−2.22849e6			−1.06875
$39$			1.37322e6i			0.593583i
$40$	3.23639e6			1.26422
$41$	−126422.			−0.0447392			−0.0223696	−	0.999750i	$-0.507121\pi$
$41$	−126422.			−0.0447392			−0.0223696	+	0.999750i	$0.507121\pi$
$42$		−	141403.i		−	0.0454423i
$43$	−149483.	−	3.41553e6i	−0.0437239	−	0.999044i
$43$	−149483.	−	3.41553e6i	−0.0437239	−	0.999044i
$44$	588460.			0.157002
$45$		−	3.04841e6i		−	0.743402i
$46$			3.65963e6i			0.817346i
$47$	3.57846e6			0.733339			0.366670	−	0.930351i	$-0.380498\pi$
$47$	3.57846e6			0.733339			0.366670	+	0.930351i	$0.380498\pi$
$48$		−	2.52535e6i		−	0.475725i
$49$	5.72544e6			0.993172
$50$		−	2.23840e6i		−	0.358144i
$51$		−	3.27737e6i		−	0.484446i
$52$	1.31671e6			0.180084
$53$	−4.88694e6			−0.619346			−0.309673	−	0.950843i	$-0.600220\pi$
$53$	−4.88694e6			−0.619346			−0.309673	+	0.950843i	$0.600220\pi$
$54$	−7.61741e6			−0.895844
$55$		−	9.18849e6i		−	1.00414i
$56$	−869334.			−0.0883964
$57$	−7.61030e6			−0.720946
$58$	4.80066e6			0.424218
$59$	5.89621e6			0.486592			0.243296	−	0.969952i	$-0.421771\pi$
$59$	5.89621e6			0.486592			0.243296	+	0.969952i	$0.421771\pi$
$60$	1.72374e6			0.133005
$61$		−	3.89973e6i		−	0.281653i	−0.990034	−	0.140827i	$-0.955024\pi$
$61$		−	3.89973e6i		−	0.281653i	0.990034	−	0.140827i	$-0.0449760\pi$
$62$		−	1.03568e7i		−	0.700904i
$63$			818841.i			0.0519801i
$64$	−1.86258e7			−1.11018
$65$		−	2.05597e7i		−	1.15176i
$66$	−8.86593e6			−0.467249
$67$	2.99507e7			1.48630			0.743152	−	0.669122i	$-0.233330\pi$
$67$	2.99507e7			1.48630			0.743152	+	0.669122i	$0.233330\pi$
$68$	−3.14250e6			−0.146974
$69$			1.24977e7i			0.551357i
$70$			2.11707e6i			0.0881743i
$71$			4.99800e6i			0.196681i	0.995153	+	0.0983407i	$0.0313535\pi$
$71$			4.99800e6i			0.196681i	−0.995153	+	0.0983407i	$0.968647\pi$
$72$			1.80835e7i			0.672904i
$73$		−	1.46539e7i		−	0.516014i	−0.966143	−	0.258007i	$-0.916934\pi$
$73$		−	1.46539e7i		−	0.516014i	0.966143	−	0.258007i	$-0.0830657\pi$
$74$	−3.32940e7			−1.11030
$75$		−	7.64416e6i		−	0.241593i
$76$			7.29712e6i			0.218724i
$77$			2.46814e6i			0.0702113i
$78$	−1.98379e7			−0.535942
$79$	−1.87235e7			−0.480705			−0.240352	−	0.970686i	$-0.577263\pi$
$79$	−1.87235e7			−0.480705			−0.240352	+	0.970686i	$0.577263\pi$
$80$			3.78092e7i			0.923077i
$81$	1.06456e6			0.0247304
$82$		−	1.82634e6i		−	0.0403948i
$83$	7.06201e7			1.48804			0.744022	−	0.668155i	$-0.232916\pi$
$83$	7.06201e7			1.48804			0.744022	+	0.668155i	$0.232916\pi$
$84$	−463019.			−0.00929997
$85$			4.90685e7i			0.939999i
$86$	4.93418e7	−	2.15948e6i	0.902031	−	0.0394781i
$87$	1.63943e7			0.286165
$88$			5.45072e7i			0.908914i
$89$		−	1.63314e7i		−	0.260294i	−0.991495	−	0.130147i	$-0.958455\pi$
$89$		−	1.63314e7i		−	0.260294i	0.991495	−	0.130147i	$-0.0415449\pi$
$90$	4.40383e7			0.671214
$91$			5.52258e6i			0.0805335i
$92$	1.19834e7			0.167274
$93$		−	3.53685e7i		−	0.472808i
$94$			5.16956e7i			0.662128i
$95$	1.13941e8			1.39889
$96$	−1.88561e7			−0.222007
$97$	−1.07206e8			−1.21097			−0.605484	−	0.795858i	$-0.707020\pi$
$97$	−1.07206e8			−1.21097			−0.605484	+	0.795858i	$0.707020\pi$
$98$			8.27114e7i			0.896729i
$99$	5.13413e7			0.534473
$100$	−7.32959e6			−0.0732959
$101$	−1.00294e8			−0.963808			−0.481904	−	0.876224i	$-0.660055\pi$
$101$	−1.00294e8			−0.963808			−0.481904	+	0.876224i	$0.660055\pi$
$102$	4.73460e7			0.437404
$103$	−2.18778e8			−1.94382			−0.971908	−	0.235360i	$-0.924373\pi$
$103$	−2.18778e8			−1.94382			−0.971908	+	0.235360i	$0.924373\pi$
$104$			1.21962e8i			1.04254i
$105$			7.22980e6i			0.0594797i
$106$		−	7.05983e7i		−	0.559205i
$107$	−1.66714e6			−0.0127186			−0.00635928	−	0.999980i	$-0.502024\pi$
$107$	−1.66714e6			−0.0127186			−0.00635928	+	0.999980i	$0.502024\pi$
$108$			2.49430e7i			0.183339i
$109$	−2.10448e8			−1.49087			−0.745434	−	0.666579i	$-0.767758\pi$
$109$	−2.10448e8			−1.49087			−0.745434	+	0.666579i	$0.767758\pi$
$110$	1.32740e8			0.906631
$111$	−1.13699e8			−0.748973
$112$		−	1.01560e7i		−	0.0645434i
$113$		−	2.55631e8i		−	1.56783i	−0.620868	−	0.783915i	$-0.713220\pi$
$113$		−	2.55631e8i		−	1.56783i	0.620868	−	0.783915i	$-0.286780\pi$
$114$		−	1.09941e8i		−	0.650938i
$115$		−	1.87114e8i		−	1.06983i
$116$		−	1.57196e7i		−	0.0868182i
$117$	1.14879e8			0.613049
$118$			8.51785e7i			0.439341i
$119$		−	1.31804e7i		−	0.0657266i
$120$			1.59665e8i			0.769989i
$121$	−5.96066e7			−0.278069
$122$	5.63367e7			0.254303
$123$		−	6.23695e6i		−	0.0272491i
$124$	−3.39130e7			−0.143443
$125$		−	1.74079e8i		−	0.713027i
$126$	−1.18292e7			−0.0469326
$127$	2.08712e8			0.802292			0.401146	−	0.916014i	$-0.368612\pi$
$127$	2.08712e8			0.802292			0.401146	+	0.916014i	$0.368612\pi$
$128$		−	1.71228e8i		−	0.637874i
$129$	1.68503e8	−	7.37466e6i	0.608483	−	0.0266307i
$130$	2.97012e8			1.03992
$131$		−	4.36493e8i		−	1.48215i	−0.671423	−	0.741074i	$-0.734317\pi$
$131$		−	4.36493e8i		−	1.48215i	0.671423	−	0.741074i	$-0.265683\pi$
$132$			2.90312e7i			0.0956247i
$133$	−3.06059e7			−0.0978133
$134$			4.32677e8i			1.34198i
$135$	3.89472e8			1.17258
$136$		−	2.91080e8i		−	0.850858i
$137$		−	7.48994e7i		−	0.212616i	−0.994333	−	0.106308i	$-0.966097\pi$
$137$		−	7.48994e7i		−	0.212616i	0.994333	−	0.106308i	$-0.0339029\pi$
$138$	−1.80545e8			−0.497817
$139$	−2.26715e8			−0.607324			−0.303662	−	0.952780i	$-0.598209\pi$
$139$	−2.26715e8			−0.607324			−0.303662	+	0.952780i	$0.598209\pi$
$140$	6.93227e6			0.0180453
$141$			1.76541e8i			0.446651i
$142$	−7.22027e7			−0.177582
$143$	3.46266e8			0.828066
$144$	−2.11261e8			−0.491327
$145$	−2.45454e8			−0.555262
$146$	2.11695e8			0.465906
$147$			2.82460e8i			0.604906i
$148$			1.09020e8i			0.227227i
$149$		−	3.64612e8i		−	0.739751i	−0.929081	−	0.369875i	$-0.879400\pi$
$149$		−	3.64612e8i		−	0.739751i	0.929081	−	0.369875i	$-0.120600\pi$
$150$	1.10430e8			0.218133
$151$		−	6.29194e8i		−	1.21025i	−0.796129	−	0.605127i	$-0.793122\pi$
$151$		−	6.29194e8i		−	1.21025i	0.796129	−	0.605127i	$-0.206878\pi$
$152$	−6.75909e8			−1.26623
$153$	−2.74173e8			−0.500334
$154$	−3.56555e7			−0.0633934
$155$			5.29534e8i			0.917418i
$156$			6.49588e7i			0.109683i
$157$			6.81816e8i			1.12220i	0.827750	+	0.561098i	$0.189621\pi$
$157$			6.81816e8i			1.12220i	−0.827750	+	0.561098i	$0.810379\pi$
$158$		−	2.70485e8i		−	0.434026i
$159$		−	2.41094e8i		−	0.377222i
$160$	2.82312e8			0.430774
$161$			5.02611e7i			0.0748046i
$162$			1.53790e7i			0.0223289i
$163$			8.22150e8i			1.16466i	0.812951	+	0.582332i	$0.197860\pi$
$163$			8.22150e8i			1.16466i	−0.812951	+	0.582332i	$0.802140\pi$
$164$	−5.98029e6			−0.00826698
$165$	4.53308e8			0.611586
$166$			1.02020e9i			1.34355i
$167$	−5.41132e8			−0.695725			−0.347862	−	0.937546i	$-0.613092\pi$
$167$	−5.41132e8			−0.695725			−0.347862	+	0.937546i	$0.613092\pi$
$168$		−	4.28880e7i		−	0.0538392i
$169$	−4.09451e7			−0.0501944
$170$	−7.08859e8			−0.848720
$171$			6.36651e8i			0.744589i
$172$	−7.07117e6	−	1.61568e8i	−0.00807937	−	0.184605i
$173$	3.97704e8			0.443992			0.221996	−	0.975048i	$-0.428743\pi$
$173$	3.97704e8			0.443992			0.221996	+	0.975048i	$0.428743\pi$
$174$			2.36837e8i			0.258377i
$175$		−	3.07420e7i		−	0.0327778i
$176$	−6.36782e8			−0.663652
$177$			2.90885e8i			0.296366i
$178$	2.35929e8			0.235018
$179$		−	9.87563e8i		−	0.961951i	−0.876734	−	0.480975i	$-0.840283\pi$
$179$		−	9.87563e8i		−	0.961951i	0.876734	−	0.480975i	$-0.159717\pi$
$180$		−	1.44202e8i		−	0.137367i
$181$	−1.27942e9			−1.19206			−0.596031	−	0.802962i	$-0.703256\pi$
$181$	−1.27942e9			−1.19206			−0.596031	+	0.802962i	$0.703256\pi$
$182$	−7.97810e7			−0.0727133
$183$	1.92390e8			0.171545
$184$			1.10998e9i			0.968376i
$185$	1.70230e9			1.45328
$186$	5.10945e8			0.426896
$187$	−8.26410e8			−0.675817
$188$	1.69276e8			0.135508
$189$	−1.04617e8			−0.0819888
$190$			1.64602e9i			1.26305i
$191$			3.56434e8i			0.267822i	0.990993	+	0.133911i	$0.0427536\pi$
$191$			3.56434e8i			0.267822i	−0.990993	+	0.133911i	$0.957246\pi$
$192$		−	9.18890e8i		−	0.676174i
$193$	1.31721e9			0.949347			0.474674	−	0.880162i	$-0.342566\pi$
$193$	1.31721e9			0.949347			0.474674	+	0.880162i	$0.342566\pi$
$194$		−	1.54873e9i		−	1.09338i
$195$	1.01430e9			0.701499
$196$	2.70836e8			0.183520
$197$	1.33673e9			0.887519			0.443759	−	0.896146i	$-0.353644\pi$
$197$	1.33673e9			0.887519			0.443759	+	0.896146i	$0.353644\pi$
$198$			7.41692e8i			0.482573i
$199$		−	1.52102e9i		−	0.969890i	−0.874545	−	0.484945i	$-0.838840\pi$
$199$		−	1.52102e9i		−	0.969890i	0.874545	−	0.484945i	$-0.161160\pi$
$200$		−	6.78916e8i		−	0.424323i
$201$			1.47760e9i			0.905256i
$202$		−	1.44888e9i		−	0.870217i
$203$	6.59319e7			0.0388250
$204$		−	1.55033e8i		−	0.0895166i
$205$			9.33791e7i			0.0528730i
$206$		−	3.16054e9i		−	1.75506i
$207$	1.04551e9			0.569438
$208$	−1.42483e9			−0.761219
$209$			1.91899e9i			1.00574i
$210$	−1.04444e8			−0.0537039
$211$			9.39023e8i			0.473747i	0.971541	+	0.236873i	$0.0761227\pi$
$211$			9.39023e8i			0.473747i	−0.971541	+	0.236873i	$0.923877\pi$
$212$	−2.31172e8			−0.114444
$213$	−2.46573e8			−0.119792
$214$		−	2.40841e7i		−	0.0114835i
$215$	−2.52281e9	+	1.10413e8i	−1.18067	+	0.0516731i
$216$	−2.31039e9			−1.06138
$217$		−	1.42239e8i		−	0.0641477i
$218$		−	3.04020e9i		−	1.34610i
$219$	7.22939e8			0.314286
$220$		−	4.34653e8i		−	0.185546i
$221$	−1.84913e9			−0.775174
$222$		−	1.64254e9i		−	0.676243i
$223$		−	1.73592e9i		−	0.701958i	−0.936383	−	0.350979i	$-0.885849\pi$
$223$		−	1.73592e9i		−	0.701958i	0.936383	−	0.350979i	$-0.114151\pi$
$224$	−7.58324e7			−0.0301205
$225$	−6.39483e8			−0.249516
$226$	3.69292e9			1.41559
$227$		−	6.10500e8i		−	0.229923i	−0.993370	−	0.114961i	$-0.963326\pi$
$227$		−	6.10500e8i		−	0.229923i	0.993370	−	0.114961i	$-0.0366745\pi$
$228$	−3.59998e8			−0.133217
$229$	−4.14557e9			−1.50745			−0.753724	−	0.657192i	$-0.771744\pi$
$229$	−4.14557e9			−1.50745			−0.753724	+	0.657192i	$0.771744\pi$
$230$	2.70310e9			0.965943
$231$	−1.21764e8			−0.0427633
$232$	1.45606e9			0.502606
$233$		−	6.91935e8i		−	0.234769i	−0.993087	−	0.117385i	$-0.962549\pi$
$233$		−	6.91935e8i		−	0.234769i	0.993087	−	0.117385i	$-0.0374511\pi$
$234$			1.65957e9i			0.553519i
$235$		−	2.64315e9i		−	0.866664i
$236$	2.78915e8			0.0899132
$237$		−	9.23710e8i		−	0.292781i
$238$	1.90408e8			0.0593442
$239$	2.94993e9			0.904106			0.452053	−	0.891991i	$-0.350692\pi$
$239$	2.94993e9			0.904106			0.452053	+	0.891991i	$0.350692\pi$
$240$	−1.86529e9			−0.562214
$241$			6.00192e9i			1.77919i	0.456752	+	0.889594i	$0.349013\pi$
$241$			6.00192e9i			1.77919i	−0.456752	+	0.889594i	$0.650987\pi$
$242$		−	8.61096e8i		−	0.251067i
$243$			3.51208e9i			1.00725i
$244$		−	1.84473e8i		−	0.0520443i
$245$		−	4.22897e9i		−	1.17373i
$246$	9.01010e7			0.0246031
$247$			4.29382e9i			1.15360i
$248$		−	3.14126e9i		−	0.830418i
$249$			3.48399e9i			0.906316i
$250$	2.51480e9			0.643788
$251$	−5.22577e9			−1.31661			−0.658303	−	0.752753i	$-0.728725\pi$
$251$	−5.22577e9			−1.31661			−0.658303	+	0.752753i	$0.728725\pi$
$252$			3.87345e7i			0.00960496i
$253$	3.15136e9			0.769160
$254$			3.01512e9i			0.724385i
$255$	−2.42076e9			−0.572521
$256$	−2.29459e9			−0.534251
$257$		−	7.78874e9i		−	1.78540i	−0.450656	−	0.892698i	$-0.648810\pi$
$257$		−	7.78874e9i		−	1.78540i	0.450656	−	0.892698i	$-0.351190\pi$
$258$	1.06537e8	+	2.43424e9i	0.0240447	+	0.549396i
$259$	−4.57257e8			−0.101616
$260$		−	9.72557e8i		−	0.212824i
$261$		−	1.37149e9i		−	0.295550i
$262$	6.30571e9			1.33822
$263$			4.65449e9i			0.972858i	0.873720	+	0.486429i	$0.161701\pi$
$263$			4.65449e9i			0.972858i	−0.873720	+	0.486429i	$0.838299\pi$
$264$	−2.68907e9			−0.553588
$265$			3.60963e9i			0.731947i
$266$		−	4.42142e8i		−	0.0883151i
$267$	8.05699e8			0.158536
$268$	1.41679e9			0.274642
$269$	−5.29425e9			−1.01110			−0.505551	−	0.862797i	$-0.668711\pi$
$269$	−5.29425e9			−1.01110			−0.505551	+	0.862797i	$0.668711\pi$
$270$			5.62643e9i			1.05871i
$271$	1.58476e9			0.293823			0.146912	−	0.989150i	$-0.453067\pi$
$271$	1.58476e9			0.293823			0.146912	+	0.989150i	$0.453067\pi$
$272$	3.40055e9			0.621261
$273$	−2.72453e8			−0.0490502
$274$	1.08202e9			0.191970
$275$	−1.92752e9			−0.337030
$276$			5.91190e8i			0.101880i
$277$			9.51951e9i			1.61695i	0.588533	+	0.808473i	$0.299706\pi$
$277$			9.51951e9i			1.61695i	−0.588533	+	0.808473i	$0.700294\pi$
$278$		−	3.27519e9i		−	0.548349i
$279$	−2.95880e9			−0.488314
$280$			6.42114e8i			0.104467i
$281$	6.79176e9			1.08932			0.544662	−	0.838656i	$-0.316658\pi$
$281$	6.79176e9			1.08932			0.544662	+	0.838656i	$0.316658\pi$
$282$	−2.55036e9			−0.403279
$283$	6.59772e9			1.02860			0.514302	−	0.857609i	$-0.328051\pi$
$283$	6.59772e9			1.02860			0.514302	+	0.857609i	$0.328051\pi$
$284$			2.36426e8i			0.0363431i
$285$			5.62118e9i			0.852017i
$286$			5.00226e9i			0.747657i
$287$		−	2.50828e7i		−	0.00369698i
$288$			1.57743e9i			0.229288i
$289$	−2.56255e9			−0.367350
$290$		−	3.54591e9i		−	0.501343i
$291$		−	5.28893e9i		−	0.737558i
$292$		−	6.93188e8i		−	0.0953498i
$293$	2.95135e9			0.400452			0.200226	−	0.979750i	$-0.435832\pi$
$293$	2.95135e9			0.400452			0.200226	+	0.979750i	$0.435832\pi$
$294$	−4.08051e9			−0.546167
$295$		−	4.35511e9i		−	0.575057i
$296$	−1.00982e10			−1.31546
$297$			6.55947e9i			0.843030i
$298$	5.26729e9			0.667917
$299$	7.05133e9			0.882239
$300$		−	3.61600e8i		−	0.0446420i
$301$	6.77657e8	−	2.96582e7i	0.0825551	−	0.00361309i
$302$	9.08953e9			1.09273
$303$		−	4.94794e9i		−	0.587022i
$304$		−	7.89633e9i		−	0.924551i
$305$	−2.88045e9			−0.332859
$306$		−	3.96079e9i		−	0.451748i
$307$	−2.01113e9			−0.226405			−0.113202	−	0.993572i	$-0.536111\pi$
$307$	−2.01113e9			−0.226405			−0.113202	+	0.993572i	$0.536111\pi$
$308$			1.16753e8i			0.0129737i
$309$		−	1.07933e10i		−	1.18391i
$310$	−7.64982e9			−0.828332
$311$	−1.19451e9			−0.127687			−0.0638435	−	0.997960i	$-0.520336\pi$
$311$	−1.19451e9			−0.127687			−0.0638435	+	0.997960i	$0.520336\pi$
$312$	−6.01693e9			−0.634975
$313$			6.10803e9i			0.636390i	0.948025	+	0.318195i	$0.103077\pi$
$313$			6.10803e9i			0.636390i	−0.948025	+	0.318195i	$0.896923\pi$
$314$	−9.84972e9			−1.01322
$315$	6.04819e8			0.0614304
$316$	−8.85697e8			−0.0888254
$317$	−4.65744e9			−0.461223			−0.230611	−	0.973046i	$-0.574073\pi$
$317$	−4.65744e9			−0.461223			−0.230611	+	0.973046i	$0.574073\pi$
$318$	3.48292e9			0.340592
$319$		−	4.13393e9i		−	0.399209i
$320$			1.37575e10i			1.31202i
$321$		−	8.22474e7i		−	0.00774643i
$322$	−7.26087e8			−0.0675406
$323$		−	1.02478e10i		−	0.941500i
$324$	5.03581e7			0.00456972
$325$	−4.31292e9			−0.386579
$326$	−1.18770e10			−1.05157
$327$		−	1.03823e10i		−	0.908036i
$328$		−	5.53935e8i		−	0.0478590i
$329$			7.09983e8i			0.0605988i
$330$			6.54862e9i			0.552197i
$331$		−	1.46486e10i		−	1.22035i	−0.792266	−	0.610176i	$-0.791099\pi$
$331$		−	1.46486e10i		−	1.22035i	0.792266	−	0.610176i	$-0.208901\pi$
$332$	3.34062e9			0.274963
$333$			9.51168e9i			0.773535i
$334$		−	7.81736e9i		−	0.628166i
$335$		−	2.21224e10i		−	1.75652i
$336$	5.01040e8			0.0393111
$337$	1.59260e10			1.23477			0.617387	−	0.786660i	$-0.288191\pi$
$337$	1.59260e10			1.23477			0.617387	+	0.786660i	$0.288191\pi$
$338$		−	5.91505e8i		−	0.0453202i
$339$	1.26114e10			0.954911
$340$			2.32114e9i			0.173694i
$341$	−8.91840e9			−0.659583
$342$	−9.19725e9			−0.672285
$343$			2.27971e9i			0.164704i
$344$	1.49656e10	−	6.54980e8i	1.06871	−	0.0467729i
$345$	9.23113e9			0.651596
$346$			5.74535e9i			0.400878i
$347$		−	1.08692e10i		−	0.749688i	−0.927088	−	0.374844i	$-0.877696\pi$
$347$		−	1.08692e10i		−	0.749688i	0.927088	−	0.374844i	$-0.122304\pi$
$348$	7.75517e8			0.0528779
$349$			3.33672e9i			0.224915i	0.993657	+	0.112458i	$0.0358722\pi$
$349$			3.33672e9i			0.224915i	−0.993657	+	0.112458i	$0.964128\pi$
$350$	4.44109e8			0.0295949
$351$			1.46771e10i			0.966970i
$352$			4.75469e9i			0.309707i
$353$	2.37900e10			1.53213			0.766065	−	0.642764i	$-0.222212\pi$
$353$	2.37900e10			1.53213			0.766065	+	0.642764i	$0.222212\pi$
$354$	−4.20222e9			−0.267588
$355$	3.69166e9			0.232439
$356$		−	7.72542e8i		−	0.0480975i
$357$	6.50246e8			0.0400318
$358$	1.42666e10			0.868540
$359$	8.83406e9			0.531842			0.265921	−	0.963995i	$-0.414324\pi$
$359$	8.83406e9			0.531842			0.265921	+	0.963995i	$0.414324\pi$
$360$	1.33570e10			0.795241
$361$	−6.81256e9			−0.401127
$362$		−	1.84829e10i		−	1.07631i
$363$		−	2.94065e9i		−	0.169362i
$364$			2.61241e8i			0.0148811i
$365$	−1.08238e10			−0.609827
$366$			2.77933e9i			0.154887i
$367$	−3.31879e10			−1.82943			−0.914714	−	0.404101i	$-0.867584\pi$
$367$	−3.31879e10			−1.82943			−0.914714	+	0.404101i	$0.867584\pi$
$368$	−1.29674e10			−0.707068
$369$	−5.21761e8			−0.0281427
$370$			2.45919e10i			1.31215i
$371$		−	9.69591e8i		−	0.0511791i
$372$		−	1.67307e9i		−	0.0873662i
$373$		−	6.01756e8i		−	0.0310874i	−0.999879	−	0.0155437i	$-0.995052\pi$
$373$		−	6.01756e8i		−	0.0310874i	0.999879	−	0.0155437i	$-0.00494792\pi$
$374$		−	1.19386e10i		−	0.610192i
$375$	8.58806e9			0.434280
$376$			1.56795e10i			0.784477i
$377$		−	9.24986e9i		−	0.457899i
$378$		−	1.51133e9i		−	0.0740273i
$379$	−2.14209e10			−1.03820			−0.519099	−	0.854714i	$-0.673732\pi$
$379$	−2.14209e10			−1.03820			−0.519099	+	0.854714i	$0.673732\pi$
$380$	5.38986e9			0.258489
$381$			1.02967e10i			0.488648i
$382$	−5.14916e9			−0.241815
$383$			1.03097e10i			0.479128i	0.970881	+	0.239564i	$0.0770045\pi$
$383$			1.03097e10i			0.479128i	−0.970881	+	0.239564i	$0.922996\pi$
$384$	8.44741e9			0.388507
$385$	1.82304e9			0.0829761
$386$			1.90288e10i			0.857160i
$387$	−6.16937e8	−	1.40963e10i	−0.0275041	−	0.628438i
$388$	−5.07128e9			−0.223764
$389$			8.19319e9i			0.357812i	0.983866	+	0.178906i	$0.0572558\pi$
$389$			8.19319e9i			0.357812i	−0.983866	+	0.178906i	$0.942744\pi$
$390$			1.46529e10i			0.633379i
$391$	−1.68290e10			−0.720030
$392$			2.50867e10i			1.06243i
$393$	2.15340e10			0.902725
$394$			1.93108e10i			0.801336i
$395$			1.38297e10i			0.568099i
$396$	2.42865e9			0.0987607
$397$	−1.88316e10			−0.758098			−0.379049	−	0.925377i	$-0.623749\pi$
$397$	−1.88316e10			−0.758098			−0.379049	+	0.925377i	$0.623749\pi$
$398$	2.19731e10			0.875709
$399$		−	1.50992e9i		−	0.0595747i
$400$	7.93146e9			0.309823
$401$	−6.25242e9			−0.241808			−0.120904	−	0.992664i	$-0.538579\pi$
$401$	−6.25242e9			−0.241808			−0.120904	+	0.992664i	$0.538579\pi$
$402$	−2.13458e10			−0.817351
$403$	−1.99553e10			−0.756552
$404$	−4.74432e9			−0.178094
$405$		−	7.86315e8i		−	0.0292265i
$406$			9.52473e8i			0.0350549i
$407$			2.86700e10i			1.04484i
$408$	1.43602e10			0.518228
$409$		−	3.02005e10i		−	1.07925i	−0.841906	−	0.539624i	$-0.818567\pi$
$409$		−	3.02005e10i		−	1.07925i	0.841906	−	0.539624i	$-0.181433\pi$
$410$	−1.34898e9			−0.0477388
$411$	3.69511e9			0.129497
$412$	−1.03491e10			−0.359181
$413$			1.16984e9i			0.0402091i
$414$			1.51038e10i			0.514143i
$415$		−	5.21620e10i		−	1.75858i
$416$			1.06388e10i			0.355239i
$417$		−	1.11848e10i		−	0.369900i
$418$	−2.77223e10			−0.908079
$419$		−	5.63631e9i		−	0.182868i	−0.995811	−	0.0914342i	$-0.970855\pi$
$419$		−	5.63631e9i		−	0.182868i	0.995811	−	0.0914342i	$-0.0291451\pi$
$420$			3.41999e8i			0.0109907i
$421$			2.23614e10i			0.711821i	0.934520	+	0.355911i	$0.115829\pi$
$421$			2.23614e10i			0.711821i	−0.934520	+	0.355911i	$0.884171\pi$
$422$	−1.35654e10			−0.427743
$423$	1.47688e10			0.461299
$424$		−	2.14127e10i		−	0.662535i
$425$	1.02934e10			0.315502
$426$		−	3.56207e9i		−	0.108159i
$427$	7.73724e8			0.0232742
$428$	−7.88627e7			−0.00235015
$429$			1.70828e10i			0.504346i
$430$	−1.59506e9	−	3.64453e10i	−0.0466554	−	1.06602i
$431$	−3.86516e10			−1.12010			−0.560052	−	0.828457i	$-0.689219\pi$
$431$	−3.86516e10			−1.12010			−0.560052	+	0.828457i	$0.689219\pi$
$432$		−	2.69912e10i		−	0.774975i
$433$			4.84787e10i			1.37911i	0.724232	+	0.689556i	$0.242194\pi$
$433$			4.84787e10i			1.37911i	−0.724232	+	0.689556i	$0.757806\pi$
$434$	2.05483e9			0.0579186
$435$		−	1.21093e10i		−	0.338191i
$436$	−9.95506e9			−0.275485
$437$			3.90781e10i			1.07154i
$438$			1.04438e10i			0.283767i
$439$	4.03504e10			1.08640			0.543200	−	0.839603i	$-0.317213\pi$
$439$	4.03504e10			1.08640			0.543200	+	0.839603i	$0.317213\pi$
$440$	4.02605e10			1.07416
$441$	2.36296e10			0.624744
$442$		−	2.67132e10i		−	0.699900i
$443$	5.75175e10			1.49343			0.746715	−	0.665144i	$-0.231630\pi$
$443$	5.75175e10			1.49343			0.746715	+	0.665144i	$0.231630\pi$
$444$	−5.37844e9			−0.138396
$445$	−1.20628e10			−0.307616
$446$	2.50777e10			0.633794
$447$	1.79878e10			0.450556
$448$		−	3.69544e9i		−	0.0917390i
$449$			5.96814e10i			1.46843i	0.678916	+	0.734216i	$0.262450\pi$
$449$			5.96814e10i			1.46843i	−0.678916	+	0.734216i	$0.737550\pi$
$450$		−	9.23817e9i		−	0.225287i
$451$	−1.57269e9			−0.0380133
$452$		−	1.20924e10i		−	0.289706i
$453$	3.10408e10			0.737124
$454$	8.81948e9			0.207596
$455$	4.07913e9			0.0951749
$456$		−	3.33455e10i		−	0.771219i
$457$		−	5.34965e10i		−	1.22648i	−0.789897	−	0.613240i	$-0.789866\pi$
$457$		−	5.34965e10i		−	1.22648i	0.789897	−	0.613240i	$-0.210134\pi$
$458$		−	5.98882e10i		−	1.36107i
$459$		−	3.50290e10i		−	0.789182i
$460$		−	8.85124e9i		−	0.197685i
$461$	−3.98268e10			−0.881804			−0.440902	−	0.897555i	$-0.645341\pi$
$461$	−3.98268e10			−0.881804			−0.440902	+	0.897555i	$0.645341\pi$
$462$		−	1.75904e9i		−	0.0386107i
$463$		−	5.57576e10i		−	1.21333i	−0.794957	−	0.606666i	$-0.792506\pi$
$463$		−	5.57576e10i		−	1.21333i	0.794957	−	0.606666i	$-0.207494\pi$
$464$			1.70105e10i			0.366982i
$465$	−2.61242e10			−0.558767
$466$	9.99591e9			0.211972
$467$		−	3.57499e10i		−	0.751635i	−0.926694	−	0.375818i	$-0.877362\pi$
$467$		−	3.57499e10i		−	0.751635i	0.926694	−	0.375818i	$-0.122638\pi$
$468$	5.43422e9			0.113280
$469$			5.94235e9i			0.122819i
$470$	3.81838e10			0.782506
$471$	−3.36369e10			−0.683490
$472$			2.58350e10i			0.520524i
$473$	−1.85957e9	−	4.24890e10i	−0.0371507	−	0.848852i
$474$	1.33442e10			0.264350
$475$		−	2.39020e10i		−	0.469526i
$476$		−	6.23487e8i		−	0.0121451i
$477$	−2.01690e10			−0.389593
$478$			4.26156e10i			0.816313i
$479$	1.36640e10			0.259559			0.129779	−	0.991543i	$-0.458573\pi$
$479$	1.36640e10			0.259559			0.129779	+	0.991543i	$0.458573\pi$
$480$			1.39277e10i			0.262369i
$481$			6.41505e10i			1.19845i
$482$	−8.67056e10			−1.60642
$483$	−2.47959e9			−0.0455609
$484$	−2.81964e9			−0.0513821
$485$			7.91854e10i			1.43113i
$486$	−5.07366e10			−0.909444
$487$	−4.93586e10			−0.877499			−0.438750	−	0.898609i	$-0.644579\pi$
$487$	−4.93586e10			−0.877499			−0.438750	+	0.898609i	$0.644579\pi$
$488$	1.70871e10			0.301294
$489$	−4.05602e10			−0.709356
$490$	6.10930e10			1.05976
$491$		−	3.03520e10i		−	0.522229i	−0.965308	−	0.261114i	$-0.915910\pi$
$491$		−	3.03520e10i		−	0.522229i	0.965308	−	0.261114i	$-0.0840900\pi$
$492$		−	2.95033e8i		−	0.00503513i
$493$			2.20761e10i			0.373709i
$494$	−6.20299e10			−1.04158
$495$		−	3.79221e10i		−	0.631643i
$496$	3.66978e10			0.606337
$497$	−9.91626e8			−0.0162526
$498$	−5.03308e10			−0.818308
$499$		−	9.99001e10i		−	1.61125i	−0.592423	−	0.805627i	$-0.701829\pi$
$499$		−	9.99001e10i		−	1.61125i	0.592423	−	0.805627i	$-0.298171\pi$
$500$		−	8.23464e9i		−	0.131754i
$501$		−	2.66964e10i		−	0.423742i
$502$		−	7.54932e10i		−	1.18876i
$503$			4.91660e8i			0.00768057i	0.999993	+	0.00384028i	$0.00122240\pi$
$503$			4.91660e8i			0.00768057i	−0.999993	+	0.00384028i	$0.998778\pi$
$504$	−3.58785e9			−0.0556048
$505$			7.40801e10i			1.13903i
$506$			4.55256e10i			0.694470i
$507$		−	2.02000e9i		−	0.0305716i
$508$	9.87292e9			0.148249
$509$	−5.80539e10			−0.864888			−0.432444	−	0.901661i	$-0.642349\pi$
$509$	−5.80539e10			−0.864888			−0.432444	+	0.901661i	$0.642349\pi$
$510$		−	3.49711e10i		−	0.516926i
$511$	2.90740e9			0.0426403
$512$		−	7.69827e10i		−	1.12025i
$513$	−8.13399e10			−1.17445
$514$	1.12519e11			1.61202
$515$			1.61596e11i			2.29721i
$516$	7.97086e9	−	3.48851e8i	0.112436	−	0.00492086i
$517$	4.45159e10			0.623093
$518$		−	6.60568e9i		−	0.0917484i
$519$			1.96204e10i			0.270420i
$520$	9.00848e10			1.23208
$521$			1.29089e11i			1.75202i	0.482292	+	0.876011i	$0.339804\pi$
$521$			1.29089e11i			1.75202i	−0.482292	+	0.876011i	$0.660196\pi$
$522$	1.98130e10			0.266850
$523$			1.17907e11i			1.57592i	0.615729	+	0.787958i	$0.288862\pi$
$523$			1.17907e11i			1.57592i	−0.615729	+	0.787958i	$0.711138\pi$
$524$		−	2.06479e10i		−	0.273874i
$525$	1.51664e9			0.0199638
$526$	−6.72403e10			−0.878388
$527$	4.76262e10			0.617452
$528$		−	3.14152e10i		−	0.404207i
$529$	−1.41368e10			−0.180522
$530$	−5.21459e10			−0.660871
$531$	2.43344e10			0.306086
$532$	−1.44778e9			−0.0180741
$533$	−3.51896e9			−0.0436019
$534$			1.16394e10i			0.143141i
$535$			1.23140e9i			0.0150309i
$536$			1.31233e11i			1.58995i
$537$	4.87207e10			0.585891
$538$		−	7.64823e10i		−	0.912919i
$539$	7.12241e10			0.843863
$540$	1.84236e10			0.216670
$541$	1.00163e11			1.16928			0.584638	−	0.811294i	$-0.301237\pi$
$541$	1.00163e11			1.16928			0.584638	+	0.811294i	$0.301237\pi$
$542$			2.28939e10i			0.265292i
$543$		−	6.31192e10i		−	0.726043i
$544$		−	2.53910e10i		−	0.289925i
$545$			1.55443e11i			1.76192i
$546$		−	3.93594e9i		−	0.0442871i
$547$	1.44716e11			1.61647			0.808235	−	0.588859i	$-0.200423\pi$
$547$	1.44716e11			1.61647			0.808235	+	0.588859i	$0.200423\pi$
$548$		−	3.54304e9i		−	0.0392875i
$549$		−	1.60947e10i		−	0.177171i
$550$		−	2.78456e10i		−	0.304303i
$551$	5.12622e10			0.556149
$552$	−5.47601e10			−0.589804
$553$		−	3.71483e9i		−	0.0397226i
$554$	−1.37522e11			−1.45993
$555$			8.39815e10i			0.885140i
$556$	−1.07245e10			−0.112222
$557$	−5.90654e10			−0.613639			−0.306819	−	0.951768i	$-0.599265\pi$
$557$	−5.90654e10			−0.613639			−0.306819	+	0.951768i	$0.599265\pi$
$558$		−	4.27438e10i		−	0.440896i
$559$	−4.16087e9	−	9.50712e10i	−0.0426125	−	0.973648i
$560$	−7.50152e9			−0.0762777
$561$		−	4.07704e10i		−	0.411617i
$562$			9.81159e10i			0.983545i
$563$	−6.86390e9			−0.0683183			−0.0341592	−	0.999416i	$-0.510875\pi$
$563$	−6.86390e9			−0.0683183			−0.0341592	+	0.999416i	$0.510875\pi$
$564$			8.35110e9i			0.0825329i
$565$	−1.88816e11			−1.85287
$566$			9.53128e10i			0.928721i
$567$			2.11214e8i			0.00204357i
$568$	−2.18994e10			−0.210396
$569$	1.96344e11			1.87313			0.936567	−	0.350488i	$-0.113984\pi$
$569$	1.96344e11			1.87313			0.936567	+	0.350488i	$0.113984\pi$
$570$	−8.12054e10			−0.769281
$571$			8.07361e10i			0.759493i	0.925091	+	0.379746i	$0.123989\pi$
$571$			8.07361e10i			0.759493i	−0.925091	+	0.379746i	$0.876011\pi$
$572$	1.63798e10			0.153011
$573$	−1.75844e10			−0.163121
$574$	3.62353e8			0.00333799
$575$	−3.92519e10			−0.359079
$576$	−7.68711e10			−0.698350
$577$		−	3.65362e10i		−	0.329625i	−0.986325	−	0.164812i	$-0.947298\pi$
$577$		−	3.65362e10i		−	0.329625i	0.986325	−	0.164812i	$-0.0527019\pi$
$578$		−	3.70194e10i		−	0.331679i
$579$			6.49835e10i			0.578214i
$580$	−1.16110e10			−0.102602
$581$			1.40113e10i			0.122963i
$582$	7.64056e10			0.665937
$583$	−6.07933e10			−0.526237
$584$	6.42078e10			0.551997
$585$		−	8.48525e10i		−	0.724504i
$586$			4.26362e10i			0.361566i
$587$		−	2.20512e11i		−	1.85729i	−0.370968	−	0.928646i	$-0.620974\pi$
$587$		−	2.20512e11i		−	1.85729i	0.370968	−	0.928646i	$-0.379026\pi$
$588$			1.33615e10i			0.111775i
$589$		−	1.10591e11i		−	0.918883i
$590$	6.29153e10			0.519216
$591$			6.59464e10i			0.540557i
$592$		−	1.17973e11i		−	0.960494i
$593$		−	4.75066e10i		−	0.384181i	−0.981377	−	0.192090i	$-0.938473\pi$
$593$		−	4.75066e10i		−	0.384181i	0.981377	−	0.192090i	$-0.0615266\pi$
$594$	−9.47602e10			−0.761167
$595$	−9.73542e9			−0.0776760
$596$		−	1.72476e10i		−	0.136692i
$597$	7.50384e10			0.590726
$598$			1.01866e11i			0.796569i
$599$	−1.31062e11			−1.01805			−0.509026	−	0.860751i	$-0.669994\pi$
$599$	−1.31062e11			−1.01805			−0.509026	+	0.860751i	$0.669994\pi$
$600$	3.34939e10			0.258440
$601$		−	9.34024e10i		−	0.715913i	−0.933738	−	0.357956i	$-0.883474\pi$
$601$		−	9.34024e10i		−	0.715913i	0.933738	−	0.357956i	$-0.116526\pi$
$602$	4.28451e8	+	9.78964e9i	0.00326224	+	0.0745385i
$603$	1.23610e11			0.934944
$604$		−	2.97634e10i		−	0.223633i
$605$			4.40271e10i			0.328624i
$606$	7.14795e10			0.530019
$607$		−	1.69612e11i		−	1.24940i	−0.780866	−	0.624699i	$-0.785222\pi$
$607$		−	1.69612e11i		−	1.24940i	0.780866	−	0.624699i	$-0.214778\pi$
$608$	−5.89599e10			−0.431462
$609$			3.25270e9i			0.0236470i
$610$		−	4.16119e10i		−	0.300537i
$611$	9.96064e10			0.714698
$612$	−1.29695e10			−0.0924524
$613$	3.40764e10			0.241330			0.120665	−	0.992693i	$-0.461497\pi$
$613$	3.40764e10			0.241330			0.120665	+	0.992693i	$0.461497\pi$
$614$		−	2.90534e10i		−	0.204420i
$615$	−4.60679e9			−0.0322031
$616$	−1.08145e10			−0.0751073
$617$	−1.79585e11			−1.23916			−0.619582	−	0.784932i	$-0.712698\pi$
$617$	−1.79585e11			−1.23916			−0.619582	+	0.784932i	$0.712698\pi$
$618$	1.55923e11			1.06895
$619$	−3.84231e10			−0.261716			−0.130858	−	0.991401i	$-0.541773\pi$
$619$	−3.84231e10			−0.261716			−0.130858	+	0.991401i	$0.541773\pi$
$620$			2.50491e10i			0.169522i
$621$			1.33577e11i			0.898182i
$622$		−	1.72562e10i		−	0.115288i
$623$	3.24023e9			0.0215091
$624$		−	7.02930e10i		−	0.463632i
$625$	−1.89105e11			−1.23932
$626$	−8.82384e10			−0.574593
$627$	−9.46717e10			−0.612562
$628$			3.22527e10i			0.207361i
$629$		−	1.53104e11i		−	0.978101i
$630$			8.73740e9i			0.0554651i
$631$			1.33200e11i			0.840208i	0.907476	+	0.420104i	$0.138006\pi$
$631$			1.33200e11i			0.840208i	−0.907476	+	0.420104i	$0.861994\pi$
$632$		−	8.20393e10i		−	0.514226i
$633$	−4.63260e10			−0.288543
$634$		−	6.72829e10i		−	0.416435i
$635$		−	1.54160e11i		−	0.948152i
$636$		−	1.14047e10i		−	0.0697037i
$637$	1.59367e11			0.967925
$638$	5.97200e10			0.360443
$639$			2.06274e10i			0.123720i
$640$	−1.26474e11			−0.753843
$641$			3.22936e11i			1.91286i	0.291956	+	0.956432i	$0.405694\pi$
$641$			3.22936e11i			1.91286i	−0.291956	+	0.956432i	$0.594306\pi$
$642$	1.18817e9			0.00699421
$643$	−8.28778e10			−0.484836			−0.242418	−	0.970172i	$-0.577940\pi$
$643$	−8.28778e10			−0.484836			−0.242418	+	0.970172i	$0.577940\pi$
$644$			2.37755e9i			0.0138225i
$645$	−5.44713e9	−	1.24461e11i	−0.0314723	−	0.719108i
$646$	1.48043e11			0.850075
$647$		−	1.35729e11i		−	0.774560i	−0.921962	−	0.387280i	$-0.873415\pi$
$647$		−	1.35729e11i		−	0.774560i	0.921962	−	0.387280i	$-0.126585\pi$
$648$			4.66451e9i			0.0264549i
$649$	7.33486e10			0.413440
$650$		−	6.23059e10i		−	0.349040i
$651$	7.01727e9			0.0390701
$652$			3.88910e10i			0.215208i
$653$		−	2.27648e11i		−	1.25202i	−0.779816	−	0.626009i	$-0.784687\pi$
$653$		−	2.27648e11i		−	1.25202i	0.779816	−	0.626009i	$-0.215313\pi$
$654$	1.49986e11			0.819861
$655$	−3.22406e11			−1.75161
$656$	6.47137e9			0.0349446
$657$		−	6.04784e10i		−	0.324593i
$658$	−1.02566e10			−0.0547144
$659$	1.34412e11			0.712685			0.356343	−	0.934355i	$-0.384024\pi$
$659$	1.34412e11			0.712685			0.356343	+	0.934355i	$0.384024\pi$
$660$	2.14433e10			0.113010
$661$	3.17172e11			1.66146			0.830729	−	0.556678i	$-0.187924\pi$
$661$	3.17172e11			1.66146			0.830729	+	0.556678i	$0.187924\pi$
$662$	2.11619e11			1.10185
$663$		−	9.12256e10i		−	0.472131i
$664$			3.09431e11i			1.59181i
$665$			2.26063e10i			0.115596i
$666$	−1.37409e11			−0.698421
$667$		−	8.41830e10i		−	0.425325i
$668$	−2.55977e10			−0.128557
$669$	8.56405e10			0.427538
$670$	3.19587e11			1.58595
$671$		−	4.85124e10i		−	0.239311i
$672$		−	3.74114e9i		−	0.0183454i
$673$			1.83900e11i			0.896439i	0.893924	+	0.448219i	$0.147942\pi$
$673$			1.83900e11i			0.896439i	−0.893924	+	0.448219i	$0.852058\pi$
$674$			2.30072e11i			1.11487i
$675$		−	8.17018e10i		−	0.393565i
$676$	−1.93687e9			−0.00927499
$677$			2.28590e11i			1.08818i	0.839025	+	0.544092i	$0.183126\pi$
$677$			2.28590e11i			1.08818i	−0.839025	+	0.544092i	$0.816874\pi$
$678$			1.82188e11i			0.862184i
$679$		−	2.12702e10i		−	0.100067i
$680$	−2.15000e11			−1.00555
$681$	3.01186e10			0.140038
$682$		−	1.28838e11i		−	0.595534i
$683$	−2.31405e11			−1.06338			−0.531692	−	0.846938i	$-0.678443\pi$
$683$	−2.31405e11			−1.06338			−0.531692	+	0.846938i	$0.678443\pi$
$684$			3.01162e10i			0.137586i
$685$	−5.53228e10			−0.251271
$686$	−3.29335e10			−0.148710
$687$		−	2.04519e11i		−	0.918134i
$688$	7.65183e9	+	1.74836e11i	0.0341516	+	0.780327i
$689$	−1.36028e11			−0.603603
$690$			1.33356e11i			0.588322i
$691$			5.16820e10i			0.226687i	0.993556	+	0.113344i	$0.0361561\pi$
$691$			5.16820e10i			0.226687i	−0.993556	+	0.113344i	$0.963844\pi$
$692$	1.88130e10			0.0820415
$693$			1.01863e10i			0.0441657i
$694$	1.57020e11			0.676889
$695$			1.67458e11i			0.717738i
$696$			7.18337e10i			0.306120i
$697$	8.39849e9			0.0355852
$698$	−4.82034e10			−0.203075
$699$	3.41361e10			0.142990
$700$		−	1.45422e9i		−	0.00605674i
$701$	4.23537e11			1.75396			0.876979	−	0.480530i	$-0.159556\pi$
$701$	4.23537e11			1.75396			0.876979	+	0.480530i	$0.159556\pi$
$702$	−2.12030e11			−0.873072
$703$	−3.55519e11			−1.45560
$704$	−2.31704e11			−0.943284
$705$	1.30398e11			0.527855
$706$			3.43678e11i			1.38335i
$707$		−	1.98988e10i		−	0.0796434i
$708$			1.37601e10i			0.0547630i
$709$	9.66397e10			0.382446			0.191223	−	0.981547i	$-0.438755\pi$
$709$	9.66397e10			0.382446			0.191223	+	0.981547i	$0.438755\pi$
$710$			5.33309e10i			0.209868i
$711$	−7.72743e10			−0.302382
$712$	7.15581e10			0.278445
$713$	−1.81614e11			−0.702733
$714$			9.39365e9i			0.0361445i
$715$		−	2.55761e11i		−	0.978613i
$716$		−	4.67157e10i		−	0.177751i
$717$			1.45532e11i			0.550660i
$718$			1.27620e11i			0.480197i
$719$	1.22535e11			0.458506			0.229253	−	0.973367i	$-0.426372\pi$
$719$	1.22535e11			0.458506			0.229253	+	0.973367i	$0.426372\pi$
$720$			1.56044e11i			0.580652i
$721$		−	4.34066e10i		−	0.160626i
$722$		−	9.84164e10i		−	0.362175i
$723$	−2.96100e11			−1.08364
$724$	−6.05217e10			−0.220271
$725$			5.14903e10i			0.186369i
$726$	4.24816e10			0.152916
$727$			2.91321e11i			1.04288i	0.853289	+	0.521439i	$0.174605\pi$
$727$			2.91321e11i			1.04288i	−0.853289	+	0.521439i	$0.825395\pi$
$728$	−2.41979e10			−0.0861493
$729$	−1.66281e11			−0.588753
$730$		−	1.56363e11i		−	0.550610i
$731$	9.93048e9	+	2.26901e11i	0.0347777	+	0.794632i
$732$	9.10084e9			0.0316984
$733$		−	3.02333e11i		−	1.04730i	−0.851934	−	0.523649i	$-0.824570\pi$
$733$		−	3.02333e11i		−	1.04730i	0.851934	−	0.523649i	$-0.175430\pi$
$734$		−	4.79443e11i		−	1.65178i
$735$	2.08633e11			0.714881
$736$			9.68241e10i			0.329968i
$737$	3.72585e11			1.26286
$738$		−	7.53752e9i		−	0.0254099i
$739$		−	4.15049e11i		−	1.39162i	−0.718224	−	0.695812i	$-0.755045\pi$
$739$		−	4.15049e11i		−	1.39162i	0.718224	−	0.695812i	$-0.244955\pi$
$740$	8.05255e10			0.268538
$741$	−2.11833e11			−0.702619
$742$	1.40070e10			0.0462094
$743$			5.51999e11i			1.81127i	0.424059	+	0.905634i	$0.360605\pi$
$743$			5.51999e11i			1.81127i	−0.424059	+	0.905634i	$0.639395\pi$
$744$	1.54972e11			0.505779
$745$	−2.69312e11			−0.874241
$746$	8.69315e9			0.0280687
$747$	2.91458e11			0.936039
$748$	−3.90926e10			−0.124879
$749$		−	3.30769e8i		−	0.00105099i
$750$			1.24066e11i			0.392109i
$751$			3.96084e11i			1.24517i	0.782554	+	0.622583i	$0.213917\pi$
$751$			3.96084e11i			1.24517i	−0.782554	+	0.622583i	$0.786083\pi$
$752$	−1.83176e11			−0.572793
$753$		−	2.57810e11i		−	0.801899i
$754$	1.33626e11			0.413435
$755$	−4.64740e11			−1.43028
$756$	−4.94880e9			−0.0151500
$757$		−	3.94309e11i		−	1.20075i	−0.799718	−	0.600376i	$-0.795018\pi$
$757$		−	3.94309e11i		−	1.20075i	0.799718	−	0.600376i	$-0.204982\pi$
$758$		−	3.09452e11i		−	0.937383i
$759$			1.55470e11i			0.468468i
$760$			4.99245e11i			1.49644i
$761$		−	2.99271e11i		−	0.892330i	−0.894951	−	0.446165i	$-0.852790\pi$
$761$		−	2.99271e11i		−	0.892330i	0.894951	−	0.446165i	$-0.147210\pi$
$762$	−1.48749e11			−0.441198
$763$		−	4.17539e10i		−	0.123197i
$764$			1.68608e10i			0.0494885i
$765$			2.02512e11i			0.591297i
$766$	−1.48937e11			−0.432602
$767$	1.64121e11			0.474223
$768$		−	1.13202e11i		−	0.325394i
$769$	−2.06441e11			−0.590324			−0.295162	−	0.955447i	$-0.595374\pi$
$769$	−2.06441e11			−0.590324			−0.295162	+	0.955447i	$0.595374\pi$
$770$			2.63362e10i			0.0749186i
$771$	3.84252e11			1.08742
$772$	6.23093e10			0.175422
$773$		−	5.73479e11i		−	1.60620i	−0.595844	−	0.803100i	$-0.703182\pi$
$773$		−	5.73479e11i		−	1.60620i	0.595844	−	0.803100i	$-0.296818\pi$
$774$	2.03640e11	−	8.91247e9i	0.567413	−	0.0248333i
$775$	1.11083e11			0.307923
$776$		−	4.69737e11i		−	1.29541i
$777$		−	2.25585e10i		−	0.0618907i
$778$	−1.18361e11			−0.323066
$779$		−	1.95019e10i		−	0.0529574i
$780$	4.79804e10			0.129624
$781$			6.21749e10i			0.167113i
$782$		−	2.43116e11i		−	0.650111i
$783$	1.75225e11			0.466174
$784$	−2.93076e11			−0.775741
$785$	5.03608e11			1.32622
$786$			3.11088e11i			0.815065i
$787$	9.98492e10			0.260283			0.130141	−	0.991495i	$-0.458457\pi$
$787$	9.98492e10			0.260283			0.130141	+	0.991495i	$0.458457\pi$
$788$	6.32326e10			0.163997
$789$	−2.29626e11			−0.592534
$790$	−1.99788e11			−0.512934
$791$	5.07183e10			0.129556
$792$			2.24958e11i			0.571743i
$793$		−	1.08549e11i		−	0.274494i
$794$		−	2.72047e11i		−	0.684482i
$795$	−1.78079e11			−0.445803
$796$		−	7.19504e10i		−	0.179218i
$797$	4.70952e11			1.16719			0.583597	−	0.812044i	$-0.301645\pi$
$797$	4.70952e11			1.16719			0.583597	+	0.812044i	$0.301645\pi$
$798$	2.18127e10			0.0537897
$799$	−2.37724e11			−0.583293
$800$		−	5.92222e10i		−	0.144585i
$801$		−	6.74018e10i		−	0.163735i
$802$		−	9.03244e10i		−	0.218327i
$803$		−	1.82293e11i		−	0.438439i
$804$			6.98963e10i			0.167275i
$805$	3.71242e10			0.0884044
$806$		−	2.88281e11i		−	0.683087i
$807$		−	2.61188e11i		−	0.615827i
$808$		−	4.39452e11i		−	1.03102i
$809$	−3.04836e11			−0.711660			−0.355830	−	0.934551i	$-0.615802\pi$
$809$	−3.04836e11			−0.711660			−0.355830	+	0.934551i	$0.615802\pi$
$810$	1.13594e10			0.0263884
$811$			6.57511e11i			1.51992i	0.649972	+	0.759958i	$0.274781\pi$
$811$			6.57511e11i			1.51992i	−0.649972	+	0.759958i	$0.725219\pi$
$812$	3.11885e9			0.00717414
$813$			7.81830e10i			0.178958i
$814$	−4.14176e11			−0.943381
$815$	6.07263e11			1.37641
$816$			1.67764e11i			0.378388i
$817$	5.26880e11	−	2.30593e10i	1.18256	−	0.0517557i
$818$	4.36286e11			0.974447
$819$			2.27924e10i			0.0506588i
$820$			4.41721e9i			0.00976995i
$821$	1.36289e11			0.299976			0.149988	−	0.988688i	$-0.452076\pi$
$821$	1.36289e11			0.299976			0.149988	+	0.988688i	$0.452076\pi$
$822$			5.33807e10i			0.116922i
$823$	−5.09389e11			−1.11033			−0.555163	−	0.831742i	$-0.687344\pi$
$823$	−5.09389e11			−1.11033			−0.555163	+	0.831742i	$0.687344\pi$
$824$		−	9.58604e11i		−	2.07936i
$825$		−	9.50930e10i		−	0.205273i
$826$	−1.68998e10			−0.0363046
$827$	5.20804e11			1.11340			0.556702	−	0.830712i	$-0.312067\pi$
$827$	5.20804e11			1.11340			0.556702	+	0.830712i	$0.312067\pi$
$828$	4.94569e10			0.105222
$829$			2.19315e11i			0.464356i	0.972673	+	0.232178i	$0.0745852\pi$
$829$			2.19315e11i			0.464356i	−0.972673	+	0.232178i	$0.925415\pi$
$830$	7.53548e11			1.58781
$831$	−4.69638e11			−0.984826
$832$	−5.18448e11			−1.08196
$833$	−3.80352e11			−0.789962
$834$	1.61579e11			0.333980
$835$			3.99695e11i			0.822211i
$836$			9.07758e10i			0.185842i
$837$		−	3.78023e11i		−	0.770224i
$838$	8.14239e10			0.165111
$839$		−	2.52134e11i		−	0.508843i	−0.967093	−	0.254422i	$-0.918115\pi$
$839$		−	2.52134e11i		−	0.508843i	0.967093	−	0.254422i	$-0.0818851\pi$
$840$	−3.16783e10			−0.0636274
$841$	3.89816e11			0.779248
$842$	−3.23040e11			−0.642700
$843$			3.35067e11i			0.663469i
$844$			4.44196e10i			0.0875396i
$845$			3.02432e10i			0.0593199i
$846$			2.13354e11i			0.416505i
$847$		−	1.18262e10i		−	0.0229780i
$848$	2.50155e11			0.483756
$849$			3.25494e11i			0.626487i
$850$			1.48702e11i			0.284865i
$851$			5.83834e11i			1.11319i
$852$	−1.16639e10			−0.0221353
$853$	−5.17472e11			−0.977441			−0.488721	−	0.872440i	$-0.662536\pi$
$853$	−5.17472e11			−0.977441			−0.488721	+	0.872440i	$0.662536\pi$
$854$			1.11775e10i			0.0210141i
$855$	4.70248e11			0.879959
$856$		−	7.30480e9i		−	0.0136055i
$857$	−1.01140e12			−1.87499			−0.937493	−	0.348004i	$-0.886859\pi$
$857$	−1.01140e12			−1.87499			−0.937493	+	0.348004i	$0.886859\pi$
$858$	−2.46783e11			−0.455372
$859$			2.69878e11i			0.495673i	0.968802	+	0.247836i	$0.0797195\pi$
$859$			2.69878e11i			0.495673i	−0.968802	+	0.247836i	$0.920280\pi$
$860$	−1.19339e11	+	5.22296e9i	−0.218167	+	0.00954824i
$861$	1.23744e9			0.00225170
$862$		−	5.58373e11i		−	1.01134i
$863$			8.78350e11i			1.58352i	0.610830	+	0.791762i	$0.290836\pi$
$863$			8.78350e11i			1.58352i	−0.610830	+	0.791762i	$0.709164\pi$
$864$	−2.01537e11			−0.361659
$865$		−	2.93755e11i		−	0.524712i
$866$	−7.00339e11			−1.24519
$867$		−	1.26421e11i		−	0.223740i
$868$		−	6.72850e9i		−	0.0118533i
$869$	−2.32919e11			−0.408438
$870$	1.74935e11			0.305351
$871$	8.33677e11			1.44852
$872$		−	9.22106e11i		−	1.59483i
$873$	−4.42453e11			−0.761746
$874$	−5.64534e11			−0.967486
$875$	3.45380e10			0.0589204
$876$	3.41979e10			0.0580742
$877$	3.14794e11			0.532143			0.266071	−	0.963953i	$-0.414274\pi$
$877$	3.14794e11			0.532143			0.266071	+	0.963953i	$0.414274\pi$
$878$			5.82914e11i			0.980904i
$879$			1.45603e11i			0.243902i
$880$			4.70345e11i			0.784307i
$881$	−1.01754e12			−1.68907			−0.844536	−	0.535499i	$-0.820123\pi$
$881$	−1.01754e12			−1.68907			−0.844536	+	0.535499i	$0.820123\pi$
$882$			3.41361e11i			0.564078i
$883$	−1.07546e11			−0.176910			−0.0884551	−	0.996080i	$-0.528193\pi$
$883$	−1.07546e11			−0.176910			−0.0884551	+	0.996080i	$0.528193\pi$
$884$	−8.74715e10			−0.143238
$885$	2.14856e11			0.350247
$886$			8.30915e11i			1.34841i
$887$		−	6.99926e11i		−	1.13073i	−0.824842	−	0.565363i	$-0.808736\pi$
$887$		−	6.99926e11i		−	1.13073i	0.824842	−	0.565363i	$-0.191264\pi$
$888$		−	4.98188e11i		−	0.801201i
$889$			4.14094e10i			0.0662967i
$890$		−	1.74264e11i		−	0.277745i
$891$	1.32431e10			0.0210125
$892$		−	8.21162e10i		−	0.129709i
$893$			5.52013e11i			0.868048i
$894$			2.59858e11i			0.406805i
$895$	−7.29442e11			−1.13684
$896$	3.39724e10			0.0527101
$897$			3.47872e11i			0.537341i
$898$	−8.62176e11			−1.32584
$899$			2.38239e11i			0.364732i
$900$	−3.02501e10			−0.0461060
$901$	3.24649e11			0.492624
$902$		−	2.27195e10i		−	0.0343220i
$903$	1.46316e9	+	3.34317e10i	0.00220061	+	0.0502814i
$904$	1.12008e12			1.67716
$905$			9.45015e11i			1.40878i
$906$			4.48426e11i			0.665545i
$907$	1.10133e12			1.62737			0.813686	−	0.581304i	$-0.197457\pi$
$907$	1.10133e12			1.62737			0.813686	+	0.581304i	$0.197457\pi$
$908$		−	2.88791e10i		−	0.0424855i
$909$	−4.13927e11			−0.606273
$910$			5.89284e10i			0.0859329i
$911$			3.52973e11i			0.512470i	0.966615	+	0.256235i	$0.0824820\pi$
$911$			3.52973e11i			0.512470i	−0.966615	+	0.256235i	$0.917518\pi$
$912$	3.89560e11			0.563112
$913$	8.78510e11			1.26434
$914$	7.72827e11			1.10738
$915$		−	1.42105e11i		−	0.202733i
$916$	−1.96102e11			−0.278548
$917$	8.66021e10			0.122476
$918$	5.06040e11			0.712548
$919$	5.69223e11			0.798032			0.399016	−	0.916944i	$-0.369352\pi$
$919$	5.69223e11			0.798032			0.399016	+	0.916944i	$0.369352\pi$
$920$	8.19863e11			1.14443
$921$		−	9.92175e10i		−	0.137895i
$922$		−	5.75351e11i		−	0.796176i
$923$			1.39119e11i			0.191682i
$924$	−5.75993e9			−0.00790186
$925$		−	3.57100e11i		−	0.487779i
$926$	8.05491e11			1.09551
$927$	−9.02926e11			−1.22274
$928$	1.27013e11			0.171260
$929$		−	1.29888e12i		−	1.74383i	−0.489654	−	0.871917i	$-0.662877\pi$
$929$		−	1.29888e12i		−	1.74383i	0.489654	−	0.871917i	$-0.337123\pi$
$930$		−	3.77398e11i		−	0.504508i
$931$			8.83205e11i			1.17561i
$932$		−	3.27313e10i		−	0.0433810i
$933$		−	5.89300e10i		−	0.0777697i
$934$	5.16454e11			0.678647
$935$			6.10410e11i			0.798684i
$936$			5.03355e11i			0.655799i
$937$			4.96703e11i			0.644375i	0.946676	+	0.322187i	$0.104418\pi$
$937$			4.96703e11i			0.644375i	−0.946676	+	0.322187i	$0.895582\pi$
$938$	−8.58451e10			−0.110893
$939$	−3.01335e11			−0.387603
$940$		−	1.25032e11i		−	0.160143i
$941$	−1.29560e12			−1.65239			−0.826196	−	0.563383i	$-0.809500\pi$
$941$	−1.29560e12			−1.65239			−0.826196	+	0.563383i	$0.809500\pi$
$942$		−	4.85929e11i		−	0.617119i
$943$	−3.20261e10			−0.0405002
$944$	−3.01818e11			−0.380065
$945$			7.72730e10i			0.0968948i
$946$	6.13810e11	−	2.68639e10i	0.766424	−	0.0335432i
$947$	5.77458e10			0.0717993			0.0358996	−	0.999355i	$-0.488570\pi$
$947$	5.77458e10			0.0717993			0.0358996	+	0.999355i	$0.488570\pi$
$948$		−	4.36952e10i		−	0.0541004i
$949$		−	4.07890e11i		−	0.502896i
$950$	3.45296e11			0.423933
$951$		−	2.29772e11i		−	0.280915i
$952$	5.77516e10			0.0703099
$953$		−	3.06639e11i		−	0.371755i	−0.982573	−	0.185877i	$-0.940487\pi$
$953$		−	3.06639e11i		−	0.371755i	0.982573	−	0.185877i	$-0.0595127\pi$
$954$		−	2.91368e11i		−	0.351762i
$955$	2.63272e11			0.316513
$956$	1.39543e11			0.167062
$957$	2.03944e11			0.243144
$958$			1.97394e11i			0.234354i
$959$	1.48604e10			0.0175693
$960$	−6.78718e11			−0.799106
$961$	−3.38923e11			−0.397381
$962$	−9.26738e11			−1.08207
$963$	−6.88052e9			−0.00800048
$964$			2.83915e11i			0.328761i
$965$		−	9.72926e11i		−	1.12194i
$966$		−	3.58210e10i		−	0.0411366i
$967$	3.21502e10			0.0367687			0.0183843	−	0.999831i	$-0.494148\pi$
$967$	3.21502e10			0.0367687			0.0183843	+	0.999831i	$0.494148\pi$
$968$		−	2.61174e11i		−	0.297460i
$969$	5.05568e11			0.573435
$970$	−1.14394e12			−1.29216
$971$	4.78192e11			0.537930			0.268965	−	0.963150i	$-0.413318\pi$
$971$	4.78192e11			0.537930			0.268965	+	0.963150i	$0.413318\pi$
$972$			1.66135e11i			0.186122i
$973$		−	4.49812e10i		−	0.0501857i
$974$		−	7.13050e11i		−	0.792289i
$975$		−	2.12775e11i		−	0.235452i
$976$			1.99621e11i			0.219992i
$977$	−1.55625e12			−1.70806			−0.854028	−	0.520228i	$-0.825847\pi$
$977$	−1.55625e12			−1.70806			−0.854028	+	0.520228i	$0.825847\pi$
$978$		−	5.85945e11i		−	0.640474i
$979$		−	2.03162e11i		−	0.221162i
$980$		−	2.00047e11i		−	0.216884i
$981$	−8.68547e11			−0.937815
$982$	4.38474e11			0.471517
$983$			4.74192e11i			0.507856i	0.967223	+	0.253928i	$0.0817226\pi$
$983$			4.74192e11i			0.507856i	−0.967223	+	0.253928i	$0.918277\pi$
$984$	2.73280e10			0.0291492
$985$		−	9.87343e11i		−	1.04887i
$986$	−3.18918e11			−0.337420
$987$	−3.50265e10			−0.0369086
$988$			2.03115e11i			0.213164i
$989$	−3.78681e10	−	8.65244e11i	−0.0395811	−	0.904385i
$990$	5.47834e11			0.570307
$991$		−	2.36242e11i		−	0.244942i	−0.992472	−	0.122471i	$-0.960918\pi$
$991$		−	2.36242e11i		−	0.244942i	0.992472	−	0.122471i	$-0.0390818\pi$
$992$		−	2.74013e11i		−	0.282960i
$993$	7.22680e11			0.743274
$994$		−	1.43253e10i		−	0.0146744i
$995$	−1.12347e12			−1.14622
$996$			1.64807e11i			0.167470i
$997$			1.06171e12i			1.07454i	0.843410	+	0.537271i	$0.180545\pi$
$997$			1.06171e12i			1.07454i	−0.843410	+	0.537271i	$0.819455\pi$
$998$	1.44319e12			1.45479
$999$	−1.21523e12			−1.22011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.20	yes	28
43.42	odd	2	inner	43.9.b.b.42.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.9	✓	28	43.42	odd	2	inner
43.9.b.b.42.20	yes	28	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	43.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+14.4463i q^{2} +49.3343i q^{3} +47.3041 q^{4} -738.628i q^{5} -712.698 q^{6} +198.404i q^{7} +4381.63i q^{8} +4127.13 q^{9} +O(q^{10})\)	\(q+14.4463i q^{2} +49.3343i q^{3} +47.3041 q^{4} -738.628i q^{5} -712.698 q^{6} +198.404i q^{7} +4381.63i q^{8} +4127.13 q^{9} +10670.5 q^{10} +12439.9 q^{11} +2333.71i q^{12} +27835.0 q^{13} -2866.21 q^{14} +36439.7 q^{15} -51188.5 q^{16} -66432.0 q^{17} +59621.8i q^{18} +154260. i q^{19} -34940.1i q^{20} -9788.14 q^{21} +179711. i q^{22} +253326. q^{23} -216164. q^{24} -154946. q^{25} +402113. i q^{26} +527291. i q^{27} +9385.34i q^{28} -332311. i q^{29} +526419. i q^{30} -716916. q^{31} +382211. i q^{32} +613716. i q^{33} -959697. i q^{34} +146547. q^{35} +195230. q^{36} +2.30467e6i q^{37} -2.22849e6 q^{38} +1.37322e6i q^{39} +3.23639e6 q^{40} -126422. q^{41} -141403. i q^{42} +(-149483. - 3.41553e6i) q^{43} +588460. q^{44} -3.04841e6i q^{45} +3.65963e6i q^{46} +3.57846e6 q^{47} -2.52535e6i q^{48} +5.72544e6 q^{49} -2.23840e6i q^{50} -3.27737e6i q^{51} +1.31671e6 q^{52} -4.88694e6 q^{53} -7.61741e6 q^{54} -9.18849e6i q^{55} -869334. q^{56} -7.61030e6 q^{57} +4.80066e6 q^{58} +5.89621e6 q^{59} +1.72374e6 q^{60} -3.89973e6i q^{61} -1.03568e7i q^{62} +818841. i q^{63} -1.86258e7 q^{64} -2.05597e7i q^{65} -8.86593e6 q^{66} +2.99507e7 q^{67} -3.14250e6 q^{68} +1.24977e7i q^{69} +2.11707e6i q^{70} +4.99800e6i q^{71} +1.80835e7i q^{72} -1.46539e7i q^{73} -3.32940e7 q^{74} -7.64416e6i q^{75} +7.29712e6i q^{76} +2.46814e6i q^{77} -1.98379e7 q^{78} -1.87235e7 q^{79} +3.78092e7i q^{80} +1.06456e6 q^{81} -1.82634e6i q^{82} +7.06201e7 q^{83} -463019. q^{84} +4.90685e7i q^{85} +(4.93418e7 - 2.15948e6i) q^{86} +1.63943e7 q^{87} +5.45072e7i q^{88} -1.63314e7i q^{89} +4.40383e7 q^{90} +5.52258e6i q^{91} +1.19834e7 q^{92} -3.53685e7i q^{93} +5.16956e7i q^{94} +1.13941e8 q^{95} -1.88561e7 q^{96} -1.07206e8 q^{97} +8.27114e7i q^{98} +5.13413e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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

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