LMFDB - Embedded newform 43.9.b.b.42.6

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			42.6
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23.5327i q^{2} +46.0777i q^{3} -297.789 q^{4} -373.886i q^{5} +1084.33 q^{6} -2487.41i q^{7} +983.414i q^{8} +4437.84 q^{9} +O(q^{10})$	\(q-23.5327i q^{2} +46.0777i q^{3} -297.789 q^{4} -373.886i q^{5} +1084.33 q^{6} -2487.41i q^{7} +983.414i q^{8} +4437.84 q^{9} -8798.55 q^{10} +7400.35 q^{11} -13721.4i q^{12} -36285.4 q^{13} -58535.4 q^{14} +17227.8 q^{15} -53091.6 q^{16} -88832.2 q^{17} -104435. i q^{18} +41818.3i q^{19} +111339. i q^{20} +114614. q^{21} -174150. i q^{22} -294498. q^{23} -45313.5 q^{24} +250835. q^{25} +853895. i q^{26} +506802. i q^{27} +740723. i q^{28} +43140.9i q^{29} -405417. i q^{30} -557310. q^{31} +1.50114e6i q^{32} +340991. i q^{33} +2.09046e6i q^{34} -930005. q^{35} -1.32154e6 q^{36} -3.70010e6i q^{37} +984099. q^{38} -1.67195e6i q^{39} +367684. q^{40} +1.14292e6 q^{41} -2.69718e6i q^{42} +(-2.60367e6 - 2.21565e6i) q^{43} -2.20374e6 q^{44} -1.65925e6i q^{45} +6.93034e6i q^{46} -721451. q^{47} -2.44634e6i q^{48} -422388. q^{49} -5.90282e6i q^{50} -4.09318e6i q^{51} +1.08054e7 q^{52} -8.22613e6 q^{53} +1.19264e7 q^{54} -2.76688e6i q^{55} +2.44615e6 q^{56} -1.92689e6 q^{57} +1.01522e6 q^{58} +5.76533e6 q^{59} -5.13025e6 q^{60} +1.24108e7i q^{61} +1.31150e7i q^{62} -1.10387e7i q^{63} +2.17346e7 q^{64} +1.35666e7i q^{65} +8.02445e6 q^{66} +2.60940e7 q^{67} +2.64533e7 q^{68} -1.35698e7i q^{69} +2.18856e7i q^{70} -3.21676e7i q^{71} +4.36424e6i q^{72} -1.56616e7i q^{73} -8.70735e7 q^{74} +1.15579e7i q^{75} -1.24530e7i q^{76} -1.84077e7i q^{77} -3.93455e7 q^{78} +2.11723e7 q^{79} +1.98502e7i q^{80} +5.76445e6 q^{81} -2.68960e7i q^{82} -5.69127e7 q^{83} -3.41308e7 q^{84} +3.32131e7i q^{85} +(-5.21402e7 + 6.12715e7i) q^{86} -1.98783e6 q^{87} +7.27761e6i q^{88} -6.26121e7i q^{89} -3.90466e7 q^{90} +9.02566e7i q^{91} +8.76983e7 q^{92} -2.56796e7i q^{93} +1.69777e7i q^{94} +1.56353e7 q^{95} -6.91693e7 q^{96} +1.82440e7 q^{97} +9.93994e6i q^{98} +3.28416e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	23.5327i		−	1.47080i	−0.677636	−	0.735398i	$-0.736995\pi$
$2$		−	23.5327i		−	1.47080i	0.677636	−	0.735398i	$-0.263005\pi$
$3$			46.0777i			0.568861i	0.958697	+	0.284430i	$0.0918044\pi$
$3$			46.0777i			0.568861i	−0.958697	+	0.284430i	$0.908196\pi$
$4$	−297.789			−1.16324
$5$		−	373.886i		−	0.598217i	−0.954219	−	0.299108i	$-0.903311\pi$
$5$		−	373.886i		−	0.598217i	0.954219	−	0.299108i	$-0.0966892\pi$
$6$	1084.33			0.836678
$7$		−	2487.41i		−	1.03599i	−0.855384	−	0.517994i	$-0.826679\pi$
$7$		−	2487.41i		−	1.03599i	0.855384	−	0.517994i	$-0.173321\pi$
$8$			983.414i			0.240091i
$9$	4437.84			0.676398
$10$	−8798.55			−0.879855
$11$	7400.35			0.505454			0.252727	−	0.967538i	$-0.418673\pi$
$11$	7400.35			0.505454			0.252727	+	0.967538i	$0.418673\pi$
$12$		−	13721.4i		−	0.661721i
$13$	−36285.4			−1.27045			−0.635227	−	0.772325i	$-0.719094\pi$
$13$	−36285.4			−1.27045			−0.635227	+	0.772325i	$0.719094\pi$
$14$	−58535.4			−1.52373
$15$	17227.8			0.340302
$16$	−53091.6			−0.810114
$17$	−88832.2			−1.06359			−0.531795	−	0.846873i	$-0.678482\pi$
$17$	−88832.2			−1.06359			−0.531795	+	0.846873i	$0.678482\pi$
$18$		−	104435.i		−	0.994843i
$19$			41818.3i			0.320887i	0.987045	+	0.160443i	$0.0512924\pi$
$19$			41818.3i			0.320887i	−0.987045	+	0.160443i	$0.948708\pi$
$20$			111339.i			0.695869i
$21$	114614.			0.589332
$22$		−	174150.i		−	0.743419i
$23$	−294498.			−1.05238			−0.526188	−	0.850368i	$-0.676379\pi$
$23$	−294498.			−1.05238			−0.526188	+	0.850368i	$0.676379\pi$
$24$	−45313.5			−0.136579
$25$	250835.			0.642137
$26$			853895.i			1.86858i
$27$			506802.i			0.953637i
$28$			740723.i			1.20510i
$29$			43140.9i			0.0609954i	0.999535	+	0.0304977i	$0.00970923\pi$
$29$			43140.9i			0.0609954i	−0.999535	+	0.0304977i	$0.990291\pi$
$30$		−	405417.i		−	0.500515i
$31$	−557310.			−0.603463			−0.301731	−	0.953393i	$-0.597565\pi$
$31$	−557310.			−0.603463			−0.301731	+	0.953393i	$0.597565\pi$
$32$			1.50114e6i			1.43160i
$33$			340991.i			0.287533i
$34$			2.09046e6i			1.56432i
$35$	−930005.			−0.619745
$36$	−1.32154e6			−0.786812
$37$		−	3.70010e6i		−	1.97427i	−0.159887	−	0.987135i	$-0.551113\pi$
$37$		−	3.70010e6i		−	1.97427i	0.159887	−	0.987135i	$-0.448887\pi$
$38$	984099.			0.471959
$39$		−	1.67195e6i		−	0.722711i
$40$	367684.			0.143627
$41$	1.14292e6			0.404463			0.202232	−	0.979338i	$-0.435181\pi$
$41$	1.14292e6			0.404463			0.202232	+	0.979338i	$0.435181\pi$
$42$		−	2.69718e6i		−	0.866787i
$43$	−2.60367e6	−	2.21565e6i	−0.761574	−	0.648078i
$43$	−2.60367e6	−	2.21565e6i	−0.761574	−	0.648078i
$44$	−2.20374e6			−0.587963
$45$		−	1.65925e6i		−	0.404632i
$46$			6.93034e6i			1.54783i
$47$	−721451.			−0.147848			−0.0739240	−	0.997264i	$-0.523552\pi$
$47$	−721451.			−0.147848			−0.0739240	+	0.997264i	$0.523552\pi$
$48$		−	2.44634e6i		−	0.460842i
$49$	−422388.			−0.0732702
$50$		−	5.90282e6i		−	0.944452i
$51$		−	4.09318e6i		−	0.605035i
$52$	1.08054e7			1.47784
$53$	−8.22613e6			−1.04254			−0.521269	−	0.853392i	$-0.674541\pi$
$53$	−8.22613e6			−1.04254			−0.521269	+	0.853392i	$0.674541\pi$
$54$	1.19264e7			1.40260
$55$		−	2.76688e6i		−	0.302371i
$56$	2.44615e6			0.248732
$57$	−1.92689e6			−0.182540
$58$	1.01522e6			0.0897118
$59$	5.76533e6			0.475791			0.237895	−	0.971291i	$-0.423542\pi$
$59$	5.76533e6			0.475791			0.237895	+	0.971291i	$0.423542\pi$
$60$	−5.13025e6			−0.395853
$61$			1.24108e7i			0.896355i	0.893945	+	0.448178i	$0.147927\pi$
$61$			1.24108e7i			0.896355i	−0.893945	+	0.448178i	$0.852073\pi$
$62$			1.31150e7i			0.887570i
$63$		−	1.10387e7i		−	0.700740i
$64$	2.17346e7			1.29548
$65$			1.35666e7i			0.760007i
$66$	8.02445e6			0.422902
$67$	2.60940e7			1.29492			0.647458	−	0.762101i	$-0.275832\pi$
$67$	2.60940e7			1.29492			0.647458	+	0.762101i	$0.275832\pi$
$68$	2.64533e7			1.23721
$69$		−	1.35698e7i		−	0.598655i
$70$			2.18856e7i			0.911518i
$71$		−	3.21676e7i		−	1.26586i	−0.774209	−	0.632930i	$-0.781852\pi$
$71$		−	3.21676e7i		−	1.26586i	0.774209	−	0.632930i	$-0.218148\pi$
$72$			4.36424e6i			0.162397i
$73$		−	1.56616e7i		−	0.551498i	−0.961230	−	0.275749i	$-0.911074\pi$
$73$		−	1.56616e7i		−	0.551498i	0.961230	−	0.275749i	$-0.0889258\pi$
$74$	−8.70735e7			−2.90375
$75$			1.15579e7i			0.365286i
$76$		−	1.24530e7i		−	0.373268i
$77$		−	1.84077e7i		−	0.523644i
$78$	−3.93455e7			−1.06296
$79$	2.11723e7			0.543576			0.271788	−	0.962357i	$-0.412385\pi$
$79$	2.11723e7			0.543576			0.271788	+	0.962357i	$0.412385\pi$
$80$			1.98502e7i			0.484624i
$81$	5.76445e6			0.133911
$82$		−	2.68960e7i		−	0.594883i
$83$	−5.69127e7			−1.19921			−0.599607	−	0.800294i	$-0.704676\pi$
$83$	−5.69127e7			−1.19921			−0.599607	+	0.800294i	$0.704676\pi$
$84$	−3.41308e7			−0.685535
$85$			3.32131e7i			0.636258i
$86$	−5.21402e7	+	6.12715e7i	−0.953189	+	1.12012i
$87$	−1.98783e6			−0.0346979
$88$			7.27761e6i			0.121355i
$89$		−	6.26121e7i		−	0.997926i	−0.866623	−	0.498963i	$-0.833714\pi$
$89$		−	6.26121e7i		−	0.997926i	0.866623	−	0.498963i	$-0.166286\pi$
$90$	−3.90466e7			−0.595132
$91$			9.02566e7i			1.31617i
$92$	8.76983e7			1.22417
$93$		−	2.56796e7i		−	0.343286i
$94$			1.69777e7i			0.217454i
$95$	1.56353e7			0.191960
$96$	−6.91693e7			−0.814383
$97$	1.82440e7			0.206079			0.103039	−	0.994677i	$-0.467143\pi$
$97$	1.82440e7			0.206079			0.103039	+	0.994677i	$0.467143\pi$
$98$			9.93994e6i			0.107765i
$99$	3.28416e7			0.341888
$100$	−7.46958e7			−0.746958
$101$	1.12667e8			1.08271			0.541354	−	0.840795i	$-0.317912\pi$
$101$	1.12667e8			1.08271			0.541354	+	0.840795i	$0.317912\pi$
$102$	−9.63237e7			−0.889882
$103$	5.41519e6			0.0481132			0.0240566	−	0.999711i	$-0.492342\pi$
$103$	5.41519e6			0.0481132			0.0240566	+	0.999711i	$0.492342\pi$
$104$		−	3.56836e7i		−	0.305025i
$105$		−	4.28525e7i		−	0.352549i
$106$			1.93583e8i			1.53336i
$107$	1.01525e8			0.774527			0.387264	−	0.921969i	$-0.373420\pi$
$107$	1.01525e8			0.774527			0.387264	+	0.921969i	$0.373420\pi$
$108$		−	1.50920e8i		−	1.10931i
$109$	1.10356e8			0.781791			0.390896	−	0.920435i	$-0.372165\pi$
$109$	1.10356e8			0.781791			0.390896	+	0.920435i	$0.372165\pi$
$110$	−6.51123e7			−0.444726
$111$	1.70492e8			1.12308
$112$			1.32060e8i			0.839268i
$113$		−	5.64521e7i		−	0.346231i	−0.984901	−	0.173116i	$-0.944617\pi$
$113$		−	5.64521e7i		−	0.346231i	0.984901	−	0.173116i	$-0.0553835\pi$
$114$			4.53450e7i			0.268479i
$115$			1.10109e8i			0.629549i
$116$		−	1.28469e7i		−	0.0709523i
$117$	−1.61029e8			−0.859332
$118$		−	1.35674e8i		−	0.699791i
$119$			2.20962e8i			1.10187i
$120$			1.69421e7i			0.0817036i
$121$	−1.59594e8			−0.744517
$122$	2.92060e8			1.31836
$123$			5.26630e7i			0.230083i
$124$	1.65961e8			0.701971
$125$		−	2.39832e8i		−	0.982354i
$126$	−2.59771e8			−1.03064
$127$	−3.89323e6			−0.0149656			−0.00748281	−	0.999972i	$-0.502382\pi$
$127$	−3.89323e6			−0.0149656			−0.00748281	+	0.999972i	$0.502382\pi$
$128$		−	1.27181e8i		−	0.473785i
$129$	1.02092e8	−	1.19971e8i	0.368666	−	0.433230i
$130$	3.19259e8			1.11782
$131$		−	5.05331e8i		−	1.71590i	−0.513736	−	0.857948i	$-0.671739\pi$
$131$		−	5.05331e8i		−	1.71590i	0.513736	−	0.857948i	$-0.328261\pi$
$132$		−	1.01543e8i		−	0.334469i
$133$	1.04019e8			0.332435
$134$		−	6.14063e8i		−	1.90456i
$135$	1.89486e8			0.570481
$136$		−	8.73588e7i		−	0.255359i
$137$			2.61606e8i			0.742618i	0.928509	+	0.371309i	$0.121091\pi$
$137$			2.61606e8i			0.742618i	−0.928509	+	0.371309i	$0.878909\pi$
$138$	−3.19334e8			−0.880500
$139$	6.91310e8			1.85188			0.925942	−	0.377666i	$-0.123273\pi$
$139$	6.91310e8			1.85188			0.925942	+	0.377666i	$0.123273\pi$
$140$	2.76946e8			0.720912
$141$		−	3.32428e7i		−	0.0841048i
$142$	−7.56992e8			−1.86182
$143$	−2.68525e8			−0.642156
$144$	−2.35612e8			−0.547959
$145$	1.61298e7			0.0364885
$146$	−3.68559e8			−0.811141
$147$		−	1.94627e7i		−	0.0416805i
$148$			1.10185e9i			2.29655i
$149$		−	5.93902e8i		−	1.20495i	−0.798137	−	0.602476i	$-0.794181\pi$
$149$		−	5.93902e8i		−	1.20495i	0.798137	−	0.602476i	$-0.205819\pi$
$150$	2.71989e8			0.537261
$151$			1.81225e8i			0.348587i	0.984694	+	0.174293i	$0.0557641\pi$
$151$			1.81225e8i			0.348587i	−0.984694	+	0.174293i	$0.944236\pi$
$152$	−4.11247e7			−0.0770422
$153$	−3.94223e8			−0.719410
$154$	−4.33183e8			−0.770173
$155$			2.08370e8i			0.361002i
$156$			4.97889e8i			0.840686i
$157$		−	2.30311e8i		−	0.379067i	−0.981874	−	0.189533i	$-0.939302\pi$
$157$		−	2.30311e8i		−	0.379067i	0.981874	−	0.189533i	$-0.0606975\pi$
$158$		−	4.98243e8i		−	0.799489i
$159$		−	3.79041e8i		−	0.593059i
$160$	5.61256e8			0.856409
$161$			7.32536e8i			1.09025i
$162$		−	1.35653e8i		−	0.196956i
$163$			8.19691e8i			1.16118i	0.814196	+	0.580590i	$0.197178\pi$
$163$			8.19691e8i			1.16118i	−0.814196	+	0.580590i	$0.802822\pi$
$164$	−3.40348e8			−0.470488
$165$	1.27492e8			0.172007
$166$			1.33931e9i			1.76380i
$167$	2.35824e8			0.303195			0.151597	−	0.988442i	$-0.451558\pi$
$167$	2.35824e8			0.303195			0.151597	+	0.988442i	$0.451558\pi$
$168$			1.12713e8i			0.141494i
$169$	5.00903e8			0.614054
$170$	7.81594e8			0.935805
$171$			1.85583e8i			0.217047i
$172$	7.75345e8	+	6.59796e8i	0.885893	+	0.753869i
$173$	−1.31006e9			−1.46254			−0.731270	−	0.682088i	$-0.761072\pi$
$173$	−1.31006e9			−1.46254			−0.731270	+	0.682088i	$0.761072\pi$
$174$			4.67792e7i			0.0510335i
$175$		−	6.23927e8i		−	0.665245i
$176$	−3.92896e8			−0.409475
$177$			2.65653e8i			0.270659i
$178$	−1.47343e9			−1.46774
$179$		−	5.68976e8i		−	0.554219i	−0.960838	−	0.277110i	$-0.910623\pi$
$179$		−	5.68976e8i		−	0.554219i	0.960838	−	0.277110i	$-0.0893765\pi$
$180$			4.94106e8i			0.470684i
$181$	3.63916e8			0.339068			0.169534	−	0.985524i	$-0.445774\pi$
$181$	3.63916e8			0.339068			0.169534	+	0.985524i	$0.445774\pi$
$182$	2.12398e9			1.93582
$183$	−5.71861e8			−0.509901
$184$		−	2.89614e8i		−	0.252667i
$185$	−1.38341e9			−1.18104
$186$	−6.04311e8			−0.504904
$187$	−6.57389e8			−0.537596
$188$	2.14840e8			0.171982
$189$	1.26062e9			0.987956
$190$		−	3.67940e8i		−	0.282334i
$191$		−	1.85510e9i		−	1.39390i	−0.717118	−	0.696952i	$-0.754539\pi$
$191$		−	1.85510e9i		−	1.39390i	0.717118	−	0.696952i	$-0.245461\pi$
$192$			1.00148e9i			0.736948i
$193$	−2.33960e9			−1.68621			−0.843105	−	0.537749i	$-0.819275\pi$
$193$	−2.33960e9			−1.68621			−0.843105	+	0.537749i	$0.819275\pi$
$194$		−	4.29331e8i		−	0.303099i
$195$	−6.25118e8			−0.432338
$196$	1.25783e8			0.0852307
$197$	2.19809e8			0.145942			0.0729710	−	0.997334i	$-0.476752\pi$
$197$	2.19809e8			0.145942			0.0729710	+	0.997334i	$0.476752\pi$
$198$		−	7.72852e8i		−	0.502847i
$199$		−	4.33133e8i		−	0.276190i	−0.990419	−	0.138095i	$-0.955902\pi$
$199$		−	4.33133e8i		−	0.276190i	0.990419	−	0.138095i	$-0.0440980\pi$
$200$			2.46674e8i			0.154171i
$201$			1.20235e9i			0.736627i
$202$		−	2.65136e9i		−	1.59244i
$203$	1.07309e8			0.0631905
$204$			1.21891e9i			0.703800i
$205$		−	4.27320e8i		−	0.241957i
$206$		−	1.27434e8i		−	0.0707647i
$207$	−1.30694e9			−0.711825
$208$	1.92645e9			1.02921
$209$			3.09470e8i			0.162193i
$210$	−1.00844e9			−0.518527
$211$		−	1.78019e9i		−	0.898127i	−0.893500	−	0.449063i	$-0.851758\pi$
$211$		−	1.78019e9i		−	0.898127i	0.893500	−	0.449063i	$-0.148242\pi$
$212$	2.44965e9			1.21272
$213$	1.48221e9			0.720097
$214$		−	2.38915e9i		−	1.13917i
$215$	−8.28399e8	+	9.73475e8i	−0.387691	+	0.455587i
$216$	−4.98396e8			−0.228960
$217$			1.38626e9i			0.625180i
$218$		−	2.59698e9i		−	1.14986i
$219$	7.21649e8			0.313725
$220$			8.23948e8i			0.351730i
$221$	3.22331e9			1.35124
$222$		−	4.01215e9i		−	1.65183i
$223$			1.99684e8i			0.0807465i	0.999185	+	0.0403732i	$0.0128547\pi$
$223$			1.99684e8i			0.0807465i	−0.999185	+	0.0403732i	$0.987145\pi$
$224$	3.73396e9			1.48312
$225$	1.11317e9			0.434340
$226$	−1.32847e9			−0.509236
$227$			5.20422e9i			1.95998i	0.199036	+	0.979992i	$0.436219\pi$
$227$			5.20422e9i			1.95998i	−0.199036	+	0.979992i	$0.563781\pi$
$228$	5.73808e8			0.212338
$229$	−3.23276e9			−1.17552			−0.587762	−	0.809034i	$-0.699991\pi$
$229$	−3.23276e9			−1.17552			−0.587762	+	0.809034i	$0.699991\pi$
$230$	2.59115e9			0.925938
$231$	8.48183e8			0.297880
$232$	−4.24254e7			−0.0146445
$233$		−	2.31185e9i		−	0.784397i	−0.919881	−	0.392199i	$-0.871715\pi$
$233$		−	2.31185e9i		−	0.784397i	0.919881	−	0.392199i	$-0.128285\pi$
$234$			3.78946e9i			1.26390i
$235$			2.69740e8i			0.0884451i
$236$	−1.71685e9			−0.553458
$237$			9.75573e8i			0.309219i
$238$	5.19983e9			1.62062
$239$	1.60464e9			0.491798			0.245899	−	0.969295i	$-0.420917\pi$
$239$	1.60464e9			0.491798			0.245899	+	0.969295i	$0.420917\pi$
$240$	−9.14651e8			−0.275683
$241$			2.76525e9i			0.819723i	0.912148	+	0.409861i	$0.134423\pi$
$241$			2.76525e9i			0.819723i	−0.912148	+	0.409861i	$0.865577\pi$
$242$			3.75568e9i			1.09503i
$243$			3.59074e9i			1.02981i
$244$		−	3.69580e9i		−	1.04268i
$245$			1.57925e8i			0.0438314i
$246$	1.23930e9			0.338406
$247$		−	1.51740e9i		−	0.407672i
$248$		−	5.48067e8i		−	0.144886i
$249$		−	2.62241e9i		−	0.682186i
$250$	−5.64391e9			−1.44484
$251$	4.50337e9			1.13460			0.567299	−	0.823512i	$-0.307988\pi$
$251$	4.50337e9			1.13460			0.567299	+	0.823512i	$0.307988\pi$
$252$			3.28721e9i			0.815128i
$253$	−2.17939e9			−0.531927
$254$			9.16182e7i			0.0220114i
$255$	−1.53038e9			−0.361942
$256$	2.57114e9			0.598640
$257$			4.59914e9i			1.05425i	0.849787	+	0.527126i	$0.176730\pi$
$257$			4.59914e9i			1.05425i	−0.849787	+	0.527126i	$0.823270\pi$
$258$	−2.82325e9	−	2.40250e9i	−0.637192	−	0.542232i
$259$	−9.20365e9			−2.04532
$260$		−	4.03999e9i		−	0.884070i
$261$			1.91453e8i			0.0412572i
$262$	−1.18918e10			−2.52373
$263$		−	4.72634e9i		−	0.987875i	−0.869498	−	0.493937i	$-0.835557\pi$
$263$		−	4.72634e9i		−	0.987875i	0.869498	−	0.493937i	$-0.164443\pi$
$264$	−3.35335e8			−0.0690341
$265$			3.07563e9i			0.623664i
$266$		−	2.44785e9i		−	0.488944i
$267$	2.88502e9			0.567681
$268$	−7.77052e9			−1.50630
$269$	−6.99220e9			−1.33538			−0.667690	−	0.744440i	$-0.732717\pi$
$269$	−6.99220e9			−1.33538			−0.667690	+	0.744440i	$0.732717\pi$
$270$		−	4.45912e9i		−	0.839062i
$271$	4.98868e8			0.0924929			0.0462464	−	0.998930i	$-0.485274\pi$
$271$	4.98868e8			0.0924929			0.0462464	+	0.998930i	$0.485274\pi$
$272$	4.71624e9			0.861630
$273$	−4.15882e9			−0.748720
$274$	6.15631e9			1.09224
$275$	1.85626e9			0.324570
$276$			4.04094e9i			0.696379i
$277$			2.44613e9i			0.415489i	0.978183	+	0.207745i	$0.0666123\pi$
$277$			2.44613e9i			0.415489i	−0.978183	+	0.207745i	$0.933388\pi$
$278$		−	1.62684e10i		−	2.72374i
$279$	−2.47326e9			−0.408181
$280$		−	9.14581e8i		−	0.148796i
$281$	5.33032e9			0.854925			0.427462	−	0.904033i	$-0.359408\pi$
$281$	5.33032e9			0.854925			0.427462	+	0.904033i	$0.359408\pi$
$282$	−7.82293e8			−0.123701
$283$	6.55249e9			1.02155			0.510776	−	0.859714i	$-0.329358\pi$
$283$	6.55249e9			1.02155			0.510776	+	0.859714i	$0.329358\pi$
$284$			9.57917e9i			1.47250i
$285$			7.20437e8i			0.109198i
$286$			6.31912e9i			0.944480i
$287$		−	2.84290e9i		−	0.419019i
$288$			6.66185e9i			0.968333i
$289$	9.15395e8			0.131225
$290$		−	3.79577e8i		−	0.0536671i
$291$			8.40641e8i			0.117230i
$292$			4.66385e9i			0.641524i
$293$	−6.99212e9			−0.948720			−0.474360	−	0.880331i	$-0.657321\pi$
$293$	−6.99212e9			−0.948720			−0.474360	+	0.880331i	$0.657321\pi$
$294$	−4.58010e8			−0.0613035
$295$		−	2.15557e9i		−	0.284626i
$296$	3.63873e9			0.474005
$297$			3.75051e9i			0.482019i
$298$	−1.39761e10			−1.77224
$299$	1.06860e10			1.33700
$300$		−	3.44181e9i		−	0.424915i
$301$	−5.51122e9	+	6.47639e9i	−0.671400	+	0.788982i
$302$	4.26472e9			0.512700
$303$			5.19144e9i			0.615910i
$304$		−	2.22020e9i		−	0.259955i
$305$	4.64022e9			0.536215
$306$			9.27715e9i			1.05811i
$307$	1.24677e10			1.40357			0.701783	−	0.712391i	$-0.252387\pi$
$307$	1.24677e10			1.40357			0.701783	+	0.712391i	$0.252387\pi$
$308$			5.48161e9i			0.609123i
$309$			2.49519e8i			0.0273697i
$310$	4.90352e9			0.530959
$311$	7.46273e9			0.797731			0.398865	−	0.917010i	$-0.369404\pi$
$311$	7.46273e9			0.797731			0.398865	+	0.917010i	$0.369404\pi$
$312$	1.64422e9			0.173517
$313$		−	1.52569e10i		−	1.58960i	−0.606869	−	0.794802i	$-0.707575\pi$
$313$		−	1.52569e10i		−	1.58960i	0.606869	−	0.794802i	$-0.292425\pi$
$314$	−5.41984e9			−0.557530
$315$	−4.12722e9			−0.419194
$316$	−6.30489e9			−0.632309
$317$	2.80977e9			0.278250			0.139125	−	0.990275i	$-0.455571\pi$
$317$	2.80977e9			0.278250			0.139125	+	0.990275i	$0.455571\pi$
$318$	−8.91988e9			−0.872269
$319$			3.19258e8i			0.0308304i
$320$		−	8.12624e9i		−	0.774979i
$321$			4.67803e9i			0.440598i
$322$	1.72386e10			1.60353
$323$		−	3.71481e9i		−	0.341292i
$324$	−1.71659e9			−0.155771
$325$	−9.10164e9			−0.815805
$326$	1.92896e10			1.70786
$327$			5.08496e9i			0.444730i
$328$			1.12396e9i			0.0971082i
$329$			1.79454e9i			0.153169i
$330$		−	3.00023e9i		−	0.252987i
$331$		−	6.18867e9i		−	0.515567i	−0.966203	−	0.257784i	$-0.917008\pi$
$331$		−	6.18867e9i		−	0.515567i	0.966203	−	0.257784i	$-0.0829922\pi$
$332$	1.69480e10			1.39497
$333$		−	1.64205e10i		−	1.33539i
$334$		−	5.54957e9i		−	0.445937i
$335$		−	9.75617e9i		−	0.774641i
$336$	−6.08504e9			−0.477426
$337$	1.61697e10			1.25367			0.626835	−	0.779152i	$-0.284350\pi$
$337$	1.61697e10			1.25367			0.626835	+	0.779152i	$0.284350\pi$
$338$		−	1.17876e10i		−	0.903148i
$339$	2.60118e9			0.196957
$340$		−	9.89049e9i		−	0.740120i
$341$	−4.12429e9			−0.305022
$342$	4.36728e9			0.319232
$343$		−	1.32888e10i		−	0.960081i
$344$	2.17890e9	−	2.56049e9i	0.155598	−	0.182847i
$345$	−5.07355e9			−0.358126
$346$			3.08294e10i			2.15110i
$347$		−	2.32144e10i		−	1.60118i	−0.599214	−	0.800589i	$-0.704520\pi$
$347$		−	2.32144e10i		−	1.60118i	0.599214	−	0.800589i	$-0.295480\pi$
$348$	5.91956e8			0.0403620
$349$			1.73500e10i			1.16949i	0.811216	+	0.584747i	$0.198806\pi$
$349$			1.73500e10i			1.16949i	−0.811216	+	0.584747i	$0.801194\pi$
$350$	−1.46827e10			−0.978440
$351$		−	1.83895e10i		−	1.21155i
$352$			1.11090e10i			0.723609i
$353$	−1.64013e10			−1.05628			−0.528139	−	0.849158i	$-0.677110\pi$
$353$	−1.64013e10			−1.05628			−0.528139	+	0.849158i	$0.677110\pi$
$354$	6.25154e9			0.398083
$355$	−1.20270e10			−0.757258
$356$			1.86452e10i			1.16083i
$357$	−1.01814e10			−0.626809
$358$	−1.33896e10			−0.815143
$359$	−3.19339e10			−1.92254			−0.961269	−	0.275613i	$-0.911119\pi$
$359$	−3.19339e10			−1.92254			−0.961269	+	0.275613i	$0.911119\pi$
$360$	1.63173e9			0.0971488
$361$	1.52348e10			0.897032
$362$		−	8.56394e9i		−	0.498700i
$363$		−	7.35371e9i		−	0.423526i
$364$		−	2.68775e10i		−	1.53103i
$365$	−5.85563e9			−0.329915
$366$			1.34574e10i			0.749960i
$367$	−4.75693e9			−0.262218			−0.131109	−	0.991368i	$-0.541854\pi$
$367$	−4.75693e9			−0.262218			−0.131109	+	0.991368i	$0.541854\pi$
$368$	1.56354e10			0.852545
$369$	5.07209e9			0.273578
$370$			3.25555e10i			1.73707i
$371$			2.04617e10i			1.08006i
$372$			7.64711e9i			0.399324i
$373$		−	1.66167e10i		−	0.858439i	−0.903200	−	0.429220i	$-0.858789\pi$
$373$		−	1.66167e10i		−	0.858439i	0.903200	−	0.429220i	$-0.141211\pi$
$374$			1.54702e10i			0.790693i
$375$	1.10509e10			0.558822
$376$		−	7.09485e8i		−	0.0354970i
$377$		−	1.56539e9i		−	0.0774919i
$378$		−	2.96659e10i		−	1.45308i
$379$	3.60255e10			1.74603			0.873017	−	0.487689i	$-0.162160\pi$
$379$	3.60255e10			1.74603			0.873017	+	0.487689i	$0.162160\pi$
$380$	−4.65601e9			−0.223295
$381$		−	1.79391e8i		−	0.00851335i
$382$	−4.36555e10			−2.05015
$383$		−	5.37123e9i		−	0.249619i	−0.992181	−	0.124810i	$-0.960168\pi$
$383$		−	5.37123e9i		−	0.249619i	0.992181	−	0.124810i	$-0.0398320\pi$
$384$	5.86020e9			0.269518
$385$	−6.88236e9			−0.313252
$386$			5.50571e10i			2.48007i
$387$	−1.15547e10	−	9.83270e9i	−0.515127	−	0.438358i
$388$	−5.43286e9			−0.239719
$389$			3.33530e10i			1.45659i	0.685266	+	0.728293i	$0.259686\pi$
$389$			3.33530e10i			1.45659i	−0.685266	+	0.728293i	$0.740314\pi$
$390$			1.47107e10i			0.635881i
$391$	2.61609e10			1.11930
$392$		−	4.15382e8i		−	0.0175915i
$393$	2.32845e10			0.976106
$394$		−	5.17270e9i		−	0.214651i
$395$		−	7.91603e9i		−	0.325176i
$396$	−9.77987e9			−0.397697
$397$	3.58311e10			1.44244			0.721220	−	0.692706i	$-0.243582\pi$
$397$	3.58311e10			1.44244			0.721220	+	0.692706i	$0.243582\pi$
$398$	−1.01928e10			−0.406220
$399$			4.79296e9i			0.189109i
$400$	−1.33172e10			−0.520204
$401$	−3.38981e10			−1.31098			−0.655492	−	0.755202i	$-0.727539\pi$
$401$	−3.38981e10			−1.31098			−0.655492	+	0.755202i	$0.727539\pi$
$402$	2.82946e10			1.08343
$403$	2.02223e10			0.766672
$404$	−3.35511e10			−1.25945
$405$		−	2.15524e9i		−	0.0801081i
$406$		−	2.52527e9i		−	0.0929403i
$407$		−	2.73820e10i		−	0.997902i
$408$	4.02529e9			0.145264
$409$			3.60185e10i			1.28716i	0.765380	+	0.643579i	$0.222551\pi$
$409$			3.60185e10i			1.28716i	−0.765380	+	0.643579i	$0.777449\pi$
$410$	−1.00560e10			−0.355869
$411$	−1.20542e10			−0.422446
$412$	−1.61258e9			−0.0559672
$413$		−	1.43407e10i		−	0.492913i
$414$			3.07558e10i			1.04695i
$415$			2.12788e10i			0.717390i
$416$		−	5.44697e10i		−	1.81879i
$417$			3.18540e10i			1.05346i
$418$	7.28267e9			0.238553
$419$		−	5.29067e9i		−	0.171654i	−0.996310	−	0.0858271i	$-0.972647\pi$
$419$		−	5.29067e9i		−	0.171654i	0.996310	−	0.0858271i	$-0.0273533\pi$
$420$			1.27610e10i			0.410098i
$421$			4.80310e10i			1.52895i	0.644654	+	0.764474i	$0.277001\pi$
$421$			4.80310e10i			1.52895i	−0.644654	+	0.764474i	$0.722999\pi$
$422$	−4.18928e10			−1.32096
$423$	−3.20169e9			−0.100004
$424$		−	8.08970e9i		−	0.250305i
$425$	−2.22822e10			−0.682970
$426$		−	3.48804e10i		−	1.05912i
$427$	3.08707e10			0.928613
$428$	−3.02330e10			−0.900960
$429$		−	1.23730e10i		−	0.365297i
$430$	2.29085e10	+	1.94945e10i	0.670075	+	0.570214i
$431$	2.78280e10			0.806442			0.403221	−	0.915103i	$-0.367891\pi$
$431$	2.78280e10			0.806442			0.403221	+	0.915103i	$0.367891\pi$
$432$		−	2.69069e10i		−	0.772554i
$433$			2.80139e10i			0.796932i	0.917183	+	0.398466i	$0.130457\pi$
$433$			2.80139e10i			0.796932i	−0.917183	+	0.398466i	$0.869543\pi$
$434$	3.26224e10			0.919512
$435$			7.43223e8i			0.0207569i
$436$	−3.28629e10			−0.909410
$437$		−	1.23154e10i		−	0.337694i
$438$		−	1.69824e10i		−	0.461426i
$439$	−4.49882e10			−1.21127			−0.605634	−	0.795743i	$-0.707081\pi$
$439$	−4.49882e10			−1.21127			−0.605634	+	0.795743i	$0.707081\pi$
$440$	2.72099e9			0.0725967
$441$	−1.87449e9			−0.0495598
$442$		−	7.58534e10i		−	1.98740i
$443$	2.77199e10			0.719742			0.359871	−	0.933002i	$-0.382821\pi$
$443$	2.77199e10			0.719742			0.359871	+	0.933002i	$0.382821\pi$
$444$	−5.07707e10			−1.30642
$445$	−2.34098e10			−0.596976
$446$	4.69911e9			0.118762
$447$	2.73657e10			0.685450
$448$		−	5.40627e10i		−	1.34210i
$449$		−	5.79249e10i		−	1.42521i	−0.701564	−	0.712607i	$-0.747514\pi$
$449$		−	5.79249e10i		−	1.42521i	0.701564	−	0.712607i	$-0.252486\pi$
$450$		−	2.61958e10i		−	0.638825i
$451$	8.45798e9			0.204438
$452$			1.68108e10i			0.402750i
$453$	−8.35045e9			−0.198297
$454$	1.22470e11			2.88274
$455$	3.37456e10			0.787358
$456$		−	1.89493e9i		−	0.0438263i
$457$			6.50756e10i			1.49195i	0.665975	+	0.745974i	$0.268016\pi$
$457$			6.50756e10i			1.49195i	−0.665975	+	0.745974i	$0.731984\pi$
$458$			7.60756e10i			1.72895i
$459$		−	4.50203e10i		−	1.01428i
$460$		−	3.27891e10i		−	0.732316i
$461$	−1.47188e10			−0.325888			−0.162944	−	0.986635i	$-0.552099\pi$
$461$	−1.47188e10			−0.325888			−0.162944	+	0.986635i	$0.552099\pi$
$462$		−	1.99601e10i		−	0.438121i
$463$		−	2.13619e10i		−	0.464854i	−0.972614	−	0.232427i	$-0.925333\pi$
$463$		−	2.13619e10i		−	0.464854i	0.972614	−	0.232427i	$-0.0746667\pi$
$464$		−	2.29042e9i		−	0.0494132i
$465$	−9.60123e9			−0.205360
$466$	−5.44042e10			−1.15369
$467$			4.57818e10i			0.962554i	0.876569	+	0.481277i	$0.159827\pi$
$467$			4.57818e10i			0.962554i	−0.876569	+	0.481277i	$0.840173\pi$
$468$	4.79528e10			0.999609
$469$		−	6.49064e10i		−	1.34152i
$470$	6.34772e9			0.130085
$471$	1.06122e10			0.215636
$472$			5.66971e9i			0.114233i
$473$	−1.92681e10	−	1.63966e10i	−0.384941	−	0.327573i
$474$	2.29579e10			0.454798
$475$			1.04895e10i			0.206053i
$476$		−	6.58000e10i		−	1.28173i
$477$	−3.65063e10			−0.705171
$478$		−	3.77616e10i		−	0.723334i
$479$	1.62487e10			0.308658			0.154329	−	0.988020i	$-0.450678\pi$
$479$	1.62487e10			0.308658			0.154329	+	0.988020i	$0.450678\pi$
$480$			2.58614e10i			0.487177i
$481$			1.34260e11i			2.50822i
$482$	6.50740e10			1.20564
$483$	−3.37536e10			−0.620200
$484$	4.75253e10			0.866051
$485$		−	6.82116e9i		−	0.123280i
$486$	8.44998e10			1.51464
$487$	7.51248e10			1.33557			0.667786	−	0.744353i	$-0.267242\pi$
$487$	7.51248e10			1.33557			0.667786	+	0.744353i	$0.267242\pi$
$488$	−1.22050e10			−0.215207
$489$	−3.77695e10			−0.660549
$490$	3.71640e9			0.0644671
$491$		−	1.57898e10i		−	0.271676i	−0.990731	−	0.135838i	$-0.956627\pi$
$491$		−	1.57898e10i		−	0.271676i	0.990731	−	0.135838i	$-0.0433726\pi$
$492$		−	1.56825e10i		−	0.267642i
$493$		−	3.83230e9i		−	0.0648742i
$494$	−3.57085e10			−0.599602
$495$		−	1.22790e10i		−	0.204523i
$496$	2.95885e10			0.488873
$497$	−8.00139e10			−1.31141
$498$	−6.17124e10			−1.00336
$499$			1.13287e11i			1.82716i	0.406657	+	0.913581i	$0.366694\pi$
$499$			1.13287e11i			1.82716i	−0.406657	+	0.913581i	$0.633306\pi$
$500$			7.14195e10i			1.14271i
$501$			1.08662e10i			0.172475i
$502$		−	1.05976e11i		−	1.66876i
$503$			6.13184e10i			0.957897i	0.877843	+	0.478949i	$0.158982\pi$
$503$			6.13184e10i			0.957897i	−0.877843	+	0.478949i	$0.841018\pi$
$504$	1.08556e10			0.168242
$505$		−	4.21246e10i		−	0.647695i
$506$			5.12869e10i			0.782356i
$507$			2.30804e10i			0.349311i
$508$	1.15936e9			0.0174086
$509$	−3.60434e10			−0.536976			−0.268488	−	0.963283i	$-0.586524\pi$
$509$	−3.60434e10			−0.536976			−0.268488	+	0.963283i	$0.586524\pi$
$510$			3.60141e10i			0.532343i
$511$	−3.89567e10			−0.571345
$512$		−	9.30642e10i		−	1.35426i
$513$	−2.11936e10			−0.306010
$514$	1.08230e11			1.55059
$515$		−	2.02466e9i		−	0.0287822i
$516$	−3.04019e10	+	3.57261e10i	−0.428846	+	0.503950i
$517$	−5.33898e9			−0.0747303
$518$			2.16587e11i			3.00825i
$519$		−	6.03647e10i		−	0.831982i
$520$	−1.33416e10			−0.182471
$521$		−	3.97439e10i		−	0.539411i	−0.962943	−	0.269705i	$-0.913074\pi$
$521$		−	3.97439e10i		−	0.539411i	0.962943	−	0.269705i	$-0.0869263\pi$
$522$	4.50540e9			0.0606809
$523$		−	1.18662e11i		−	1.58601i	−0.609218	−	0.793003i	$-0.708517\pi$
$523$		−	1.18662e11i		−	1.58601i	0.609218	−	0.793003i	$-0.291483\pi$
$524$			1.50482e11i			1.99600i
$525$	2.87491e10			0.378432
$526$	−1.11224e11			−1.45296
$527$	4.95071e10			0.641837
$528$		−	1.81038e10i		−	0.232934i
$529$	8.41811e9			0.107496
$530$	7.23780e10			0.917283
$531$	2.55856e10			0.321824
$532$	−3.09758e10			−0.386701
$533$	−4.14713e10			−0.513852
$534$		−	6.78924e10i		−	0.834942i
$535$		−	3.79586e10i		−	0.463335i
$536$			2.56612e10i			0.310898i
$537$	2.62171e10			0.315274
$538$			1.64546e11i			1.96407i
$539$	−3.12582e9			−0.0370347
$540$	−5.64268e10			−0.663606
$541$	−1.01448e11			−1.18428			−0.592141	−	0.805834i	$-0.701717\pi$
$541$	−1.01448e11			−1.18428			−0.592141	+	0.805834i	$0.701717\pi$
$542$		−	1.17397e10i		−	0.136038i
$543$			1.67684e10i			0.192883i
$544$		−	1.33350e11i		−	1.52264i
$545$		−	4.12606e10i		−	0.467681i
$546$			9.78683e10i			1.10121i
$547$	−8.17603e10			−0.913257			−0.456629	−	0.889657i	$-0.650943\pi$
$547$	−8.17603e10			−0.913257			−0.456629	+	0.889657i	$0.650943\pi$
$548$		−	7.79035e10i		−	0.863843i
$549$			5.50772e10i			0.606293i
$550$		−	4.36829e10i		−	0.477376i
$551$	−1.80408e9			−0.0195726
$552$	1.33447e10			0.143732
$553$		−	5.26642e10i		−	0.563138i
$554$	5.75640e10			0.611100
$555$		−	6.37446e10i		−	0.671848i
$556$	−2.05865e11			−2.15418
$557$	−1.33090e11			−1.38269			−0.691343	−	0.722526i	$-0.742981\pi$
$557$	−1.33090e11			−1.38269			−0.691343	+	0.722526i	$0.742981\pi$
$558$			5.82025e10i			0.600350i
$559$	9.44754e10	+	8.03958e10i	0.967545	+	0.823353i
$560$	4.93755e10			0.502064
$561$		−	3.02910e10i		−	0.305817i
$562$		−	1.25437e11i		−	1.25742i
$563$	−7.48660e10			−0.745162			−0.372581	−	0.928000i	$-0.621527\pi$
$563$	−7.48660e10			−0.745162			−0.372581	+	0.928000i	$0.621527\pi$
$564$			9.89934e9i			0.0978340i
$565$	−2.11066e10			−0.207122
$566$		−	1.54198e11i		−	1.50250i
$567$		−	1.43385e10i		−	0.138731i
$568$	3.16341e10			0.303922
$569$	−1.64918e11			−1.57333			−0.786663	−	0.617383i	$-0.788193\pi$
$569$	−1.64918e11			−1.57333			−0.786663	+	0.617383i	$0.788193\pi$
$570$	1.69538e10			0.160609
$571$		−	2.56402e10i		−	0.241200i	−0.992701	−	0.120600i	$-0.961518\pi$
$571$		−	2.56402e10i		−	0.241200i	0.992701	−	0.120600i	$-0.0384818\pi$
$572$	7.99638e10			0.746981
$573$	8.54785e10			0.792937
$574$	−6.69012e10			−0.616291
$575$	−7.38703e10			−0.675769
$576$	9.64547e10			0.876261
$577$		−	7.01456e10i		−	0.632844i	−0.948618	−	0.316422i	$-0.897518\pi$
$577$		−	7.01456e10i		−	0.632844i	0.948618	−	0.316422i	$-0.102482\pi$
$578$		−	2.15417e10i		−	0.193005i
$579$		−	1.07803e11i		−	0.959218i
$580$	−4.80327e9			−0.0424449
$581$			1.41565e11i			1.24237i
$582$	1.97826e10			0.172421
$583$	−6.08762e10			−0.526955
$584$	1.54018e10			0.132410
$585$			6.02065e10i			0.514067i
$586$			1.64544e11i			1.39537i
$587$			1.89363e11i			1.59493i	0.603363	+	0.797467i	$0.293827\pi$
$587$			1.89363e11i			1.59493i	−0.603363	+	0.797467i	$0.706173\pi$
$588$			5.79577e9i			0.0484844i
$589$		−	2.33058e10i		−	0.193643i
$590$	−5.07265e10			−0.418627
$591$			1.01283e10i			0.0830207i
$592$			1.96444e11i			1.59938i
$593$			6.58027e10i			0.532139i	0.963954	+	0.266069i	$0.0857250\pi$
$593$			6.58027e10i			0.532139i	−0.963954	+	0.266069i	$0.914275\pi$
$594$	8.82597e10			0.708951
$595$	8.26144e10			0.659155
$596$			1.76858e11i			1.40165i
$597$	1.99578e10			0.157114
$598$		−	2.51471e11i		−	1.96645i
$599$	9.67186e10			0.751282			0.375641	−	0.926765i	$-0.377423\pi$
$599$	9.67186e10			0.751282			0.375641	+	0.926765i	$0.377423\pi$
$600$	−1.13662e10			−0.0877021
$601$			8.07367e10i			0.618833i	0.950927	+	0.309416i	$0.100134\pi$
$601$			8.07367e10i			0.618833i	−0.950927	+	0.309416i	$0.899866\pi$
$602$	1.52407e11	+	1.29694e11i	1.16043	+	0.987492i
$603$	1.15801e11			0.875878
$604$		−	5.39669e10i		−	0.405490i
$605$			5.96698e10i			0.445382i
$606$	1.22169e11			0.905878
$607$		−	2.18215e11i		−	1.60742i	−0.595019	−	0.803712i	$-0.702855\pi$
$607$		−	2.18215e11i		−	1.60742i	0.595019	−	0.803712i	$-0.297145\pi$
$608$	−6.27753e10			−0.459383
$609$			4.94455e9i			0.0359466i
$610$		−	1.09197e11i		−	0.788662i
$611$	2.61782e10			0.187834
$612$	1.17395e11			0.836846
$613$	2.66467e11			1.88713			0.943564	−	0.331189i	$-0.107450\pi$
$613$	2.66467e11			1.88713			0.943564	+	0.331189i	$0.107450\pi$
$614$		−	2.93399e11i		−	2.06436i
$615$	1.96899e10			0.137640
$616$	1.81024e10			0.125722
$617$	1.98336e11			1.36855			0.684277	−	0.729222i	$-0.260118\pi$
$617$	1.98336e11			1.36855			0.684277	+	0.729222i	$0.260118\pi$
$618$	5.87187e9			0.0402553
$619$	2.63949e11			1.79786			0.898932	−	0.438088i	$-0.144344\pi$
$619$	2.63949e11			1.79786			0.898932	+	0.438088i	$0.144344\pi$
$620$		−	6.20504e10i		−	0.419931i
$621$		−	1.49252e11i		−	1.00358i
$622$		−	1.75618e11i		−	1.17330i
$623$	−1.55742e11			−1.03384
$624$			8.87665e10i			0.585478i
$625$	8.31237e9			0.0544759
$626$	−3.59036e11			−2.33798
$627$	−1.42597e10			−0.0922655
$628$			6.85841e10i			0.440945i
$629$			3.28688e11i			2.09982i
$630$			9.71247e10i			0.616549i
$631$		−	7.50901e10i		−	0.473658i	−0.971551	−	0.236829i	$-0.923892\pi$
$631$		−	7.50901e10i		−	0.473658i	0.971551	−	0.236829i	$-0.0761082\pi$
$632$			2.08212e10i			0.130508i
$633$	8.20273e10			0.510909
$634$		−	6.61217e10i		−	0.409248i
$635$			1.45562e9i			0.00895269i
$636$			1.12874e11i			0.689870i
$637$	1.53265e10			0.0930864
$638$	7.51300e9			0.0453452
$639$		−	1.42755e11i		−	0.856224i
$640$	−4.75510e10			−0.283426
$641$		−	1.48724e11i		−	0.880948i	−0.897765	−	0.440474i	$-0.854810\pi$
$641$		−	1.48724e11i		−	0.880948i	0.897765	−	0.440474i	$-0.145190\pi$
$642$	1.10087e11			0.648029
$643$	−1.86069e11			−1.08851			−0.544253	−	0.838921i	$-0.683187\pi$
$643$	−1.86069e11			−1.08851			−0.544253	+	0.838921i	$0.683187\pi$
$644$		−	2.18141e11i		−	1.26822i
$645$	−4.48555e10	−	3.81707e10i	−0.259165	−	0.220542i
$646$	−8.74196e10			−0.501971
$647$			8.09539e10i			0.461977i	0.972956	+	0.230989i	$0.0741960\pi$
$647$			8.09539e10i			0.461977i	−0.972956	+	0.230989i	$0.925804\pi$
$648$			5.66884e9i			0.0321510i
$649$	4.26654e10			0.240490
$650$			2.14187e11i			1.19988i
$651$	−6.38756e10			−0.355640
$652$		−	2.44095e11i		−	1.35073i
$653$			4.75870e10i			0.261719i	0.991401	+	0.130860i	$0.0417737\pi$
$653$			4.75870e10i			0.261719i	−0.991401	+	0.130860i	$0.958226\pi$
$654$	1.19663e11			0.654107
$655$	−1.88936e11			−1.02648
$656$	−6.06793e10			−0.327661
$657$		−	6.95036e10i		−	0.373032i
$658$	4.22304e10			0.225280
$659$	1.65374e10			0.0876850			0.0438425	−	0.999038i	$-0.486040\pi$
$659$	1.65374e10			0.0876850			0.0438425	+	0.999038i	$0.486040\pi$
$660$	−3.79656e10			−0.200085
$661$	1.78227e11			0.933615			0.466808	−	0.884359i	$-0.345404\pi$
$661$	1.78227e11			0.933615			0.466808	+	0.884359i	$0.345404\pi$
$662$	−1.45636e11			−0.758294
$663$			1.48523e11i			0.768669i
$664$		−	5.59688e10i		−	0.287921i
$665$		−	3.88912e10i		−	0.198868i
$666$	−3.86419e11			−1.96409
$667$		−	1.27049e10i		−	0.0641902i
$668$	−7.02258e10			−0.352688
$669$	−9.20098e9			−0.0459335
$670$	−2.29589e11			−1.13934
$671$			9.18442e10i			0.453066i
$672$			1.72052e11i			0.843690i
$673$			4.02539e11i			1.96222i	0.193456	+	0.981109i	$0.438030\pi$
$673$			4.02539e11i			1.96222i	−0.193456	+	0.981109i	$0.561970\pi$
$674$		−	3.80518e11i		−	1.84389i
$675$			1.27123e11i			0.612365i
$676$	−1.49163e11			−0.714292
$677$		−	3.11966e11i		−	1.48509i	−0.669796	−	0.742545i	$-0.733618\pi$
$677$		−	3.11966e11i		−	1.48509i	0.669796	−	0.742545i	$-0.266382\pi$
$678$		−	6.12130e10i		−	0.289684i
$679$		−	4.53802e10i		−	0.213495i
$680$	−3.26622e10			−0.152760
$681$	−2.39799e11			−1.11496
$682$			9.70558e10i			0.448626i
$683$	2.47854e11			1.13897			0.569487	−	0.822000i	$-0.307142\pi$
$683$	2.47854e11			1.13897			0.569487	+	0.822000i	$0.307142\pi$
$684$		−	5.52647e10i		−	0.252478i
$685$	9.78108e10			0.444247
$686$	−3.12721e11			−1.41208
$687$		−	1.48958e11i		−	0.668709i
$688$	1.38233e11	+	1.17632e11i	0.616962	+	0.525017i
$689$	2.98489e11			1.32450
$690$			1.19394e11i			0.526730i
$691$		−	1.76475e11i		−	0.774052i	−0.922069	−	0.387026i	$-0.873502\pi$
$691$		−	1.76475e11i		−	0.774052i	0.922069	−	0.387026i	$-0.126498\pi$
$692$	3.90123e11			1.70128
$693$		−	8.16904e10i		−	0.354191i
$694$	−5.46298e11			−2.35501
$695$		−	2.58471e11i		−	1.10783i
$696$		−	1.95487e9i		−	0.00833067i
$697$	−1.01528e11			−0.430184
$698$	4.08293e11			1.72009
$699$	1.06525e11			0.446213
$700$			1.85799e11i			0.773840i
$701$	−2.51419e11			−1.04118			−0.520589	−	0.853807i	$-0.674288\pi$
$701$	−2.51419e11			−1.04118			−0.520589	+	0.853807i	$0.674288\pi$
$702$	−4.32756e11			−1.78194
$703$	1.54732e11			0.633518
$704$	1.60843e11			0.654806
$705$	−1.24290e10			−0.0503129
$706$			3.85966e11i			1.55357i
$707$		−	2.80249e11i		−	1.12167i
$708$		−	7.91086e10i		−	0.314841i
$709$	2.53180e11			1.00195			0.500973	−	0.865463i	$-0.332976\pi$
$709$	2.53180e11			1.00195			0.500973	+	0.865463i	$0.332976\pi$
$710$			2.83028e11i			1.11377i
$711$	9.39595e10			0.367674
$712$	6.15736e10			0.239593
$713$	1.64127e11			0.635070
$714$			2.39596e11i			0.921907i
$715$			1.00398e11i			0.384148i
$716$			1.69435e11i			0.644690i
$717$			7.39382e10i			0.279764i
$718$			7.51493e11i			2.82766i
$719$	−2.91790e11			−1.09183			−0.545914	−	0.837841i	$-0.683818\pi$
$719$	−2.91790e11			−1.09183			−0.545914	+	0.837841i	$0.683818\pi$
$720$			8.80921e10i			0.327798i
$721$		−	1.34698e10i		−	0.0498447i
$722$		−	3.58516e11i		−	1.31935i
$723$	−1.27417e11			−0.466308
$724$	−1.08370e11			−0.394418
$725$			1.08212e10i			0.0391674i
$726$	−1.73053e11			−0.622920
$727$			7.09422e10i			0.253961i	0.991905	+	0.126980i	$0.0405285\pi$
$727$			7.09422e10i			0.253961i	−0.991905	+	0.126980i	$0.959471\pi$
$728$	−8.87597e10			−0.316002
$729$	−1.27632e11			−0.451909
$730$			1.37799e11i			0.485238i
$731$	2.31290e11	+	1.96821e11i	0.810003	+	0.689289i
$732$	1.70294e11			0.593137
$733$			5.49791e11i			1.90450i	0.305316	+	0.952251i	$0.401238\pi$
$733$			5.49791e11i			1.90450i	−0.305316	+	0.952251i	$0.598762\pi$
$734$			1.11944e11i			0.385669i
$735$	−7.27681e9			−0.0249340
$736$		−	4.42084e11i		−	1.50659i
$737$	1.93105e11			0.654520
$738$		−	1.19360e11i		−	0.402377i
$739$			2.61314e11i			0.876162i	0.898936	+	0.438081i	$0.144342\pi$
$739$			2.61314e11i			0.876162i	−0.898936	+	0.438081i	$0.855658\pi$
$740$	4.11966e11			1.37383
$741$	6.99181e10			0.231909
$742$	4.81520e11			1.58854
$743$			1.87745e11i			0.616045i	0.951379	+	0.308023i	$0.0996673\pi$
$743$			1.87745e11i			0.616045i	−0.951379	+	0.308023i	$0.900333\pi$
$744$	2.52537e10			0.0824201
$745$	−2.22052e11			−0.720823
$746$	−3.91036e11			−1.26259
$747$	−2.52570e11			−0.811146
$748$	1.95763e11			0.625352
$749$		−	2.52533e11i		−	0.802400i
$750$		−	2.60059e11i		−	0.821913i
$751$		−	1.34471e10i		−	0.0422736i	−0.999777	−	0.0211368i	$-0.993271\pi$
$751$		−	1.34471e10i		−	0.0422736i	0.999777	−	0.0211368i	$-0.00672855\pi$
$752$	3.83030e10			0.119774
$753$			2.07505e11i			0.645429i
$754$	−3.68378e10			−0.113975
$755$	6.77575e10			0.208531
$756$	−3.75399e11			−1.14923
$757$		−	2.39956e11i		−	0.730716i	−0.930867	−	0.365358i	$-0.880947\pi$
$757$		−	2.39956e11i		−	0.730716i	0.930867	−	0.365358i	$-0.119053\pi$
$758$		−	8.47778e11i		−	2.56806i
$759$		−	1.00421e11i		−	0.302593i
$760$			1.53759e10i			0.0460879i
$761$		−	1.35338e11i		−	0.403535i	−0.979433	−	0.201768i	$-0.935331\pi$
$761$		−	1.35338e11i		−	0.403535i	0.979433	−	0.201768i	$-0.0646686\pi$
$762$	−4.22156e9			−0.0125214
$763$		−	2.74501e11i		−	0.809926i
$764$			5.52427e11i			1.62144i
$765$			1.47394e11i			0.430363i
$766$	−1.26400e11			−0.367139
$767$	−2.09197e11			−0.604470
$768$			1.18472e11i			0.340543i
$769$	−5.25701e11			−1.50326			−0.751629	−	0.659586i	$-0.770732\pi$
$769$	−5.25701e11			−1.50326			−0.751629	+	0.659586i	$0.770732\pi$
$770$			1.61961e11i			0.460730i
$771$	−2.11918e11			−0.599722
$772$	6.96707e11			1.96147
$773$		−	3.97129e11i		−	1.11228i	−0.831089	−	0.556140i	$-0.812282\pi$
$773$		−	3.97129e11i		−	1.11228i	0.831089	−	0.556140i	$-0.187718\pi$
$774$	−2.31390e11	+	2.71913e11i	−0.644735	+	0.757647i
$775$	−1.39793e11			−0.387505
$776$			1.79414e10i			0.0494777i
$777$		−	4.24083e11i		−	1.16350i
$778$	7.84886e11			2.14234
$779$			4.77949e10i			0.129787i
$780$	1.86153e11			0.502913
$781$		−	2.38051e11i		−	0.639833i
$782$		−	6.15637e11i		−	1.64626i
$783$	−2.18639e10			−0.0581675
$784$	2.24253e10			0.0593572
$785$	−8.61099e10			−0.226764
$786$		−	5.47948e11i		−	1.43565i
$787$	4.89399e11			1.27575			0.637873	−	0.770141i	$-0.279814\pi$
$787$	4.89399e11			1.27575			0.637873	+	0.770141i	$0.279814\pi$
$788$	−6.54567e10			−0.169766
$789$	2.17779e11			0.561963
$790$	−1.86286e11			−0.478268
$791$	−1.40419e11			−0.358691
$792$			3.22969e10i			0.0820843i
$793$		−	4.50331e11i		−	1.13878i
$794$		−	8.43202e11i		−	2.12153i
$795$	−1.41718e11			−0.354778
$796$			1.28982e11i			0.321275i
$797$	5.70493e11			1.41389			0.706947	−	0.707266i	$-0.250072\pi$
$797$	5.70493e11			1.41389			0.706947	+	0.707266i	$0.250072\pi$
$798$	1.12791e11			0.278141
$799$	6.40880e10			0.157250
$800$			3.76539e11i			0.919285i
$801$		−	2.77863e11i		−	0.674995i
$802$			7.97714e11i			1.92819i
$803$		−	1.15901e11i		−	0.278757i
$804$		−	3.58048e11i		−	0.856873i
$805$	2.73885e11			0.652205
$806$		−	4.75885e11i		−	1.12762i
$807$		−	3.22185e11i		−	0.759645i
$808$			1.10798e11i			0.259949i
$809$	−4.95126e11			−1.15590			−0.577952	−	0.816071i	$-0.696148\pi$
$809$	−4.95126e11			−1.15590			−0.577952	+	0.816071i	$0.696148\pi$
$810$	−5.07188e10			−0.117823
$811$			3.93370e11i			0.909323i	0.890664	+	0.454661i	$0.150240\pi$
$811$			3.93370e11i			0.909323i	−0.890664	+	0.454661i	$0.849760\pi$
$812$	−3.19555e10			−0.0735057
$813$			2.29867e10i			0.0526155i
$814$	−6.44374e11			−1.46771
$815$	3.06470e11			0.694637
$816$			2.17314e11i			0.490147i
$817$	9.26546e10	−	1.08881e11i	0.207960	−	0.244379i
$818$	8.47613e11			1.89315
$819$			4.00545e11i			0.890257i
$820$			1.27251e11i			0.281454i
$821$	−5.77560e11			−1.27123			−0.635615	−	0.772006i	$-0.719253\pi$
$821$	−5.77560e11			−1.27123			−0.635615	+	0.772006i	$0.719253\pi$
$822$			2.83669e11i			0.621332i
$823$	−4.32530e11			−0.942794			−0.471397	−	0.881921i	$-0.656250\pi$
$823$	−4.32530e11			−0.942794			−0.471397	+	0.881921i	$0.656250\pi$
$824$			5.32537e9i			0.0115516i
$825$			8.55323e10i			0.184635i
$826$	−3.37476e11			−0.724975
$827$	−7.27704e11			−1.55572			−0.777862	−	0.628435i	$-0.783696\pi$
$827$	−7.27704e11			−1.55572			−0.777862	+	0.628435i	$0.783696\pi$
$828$	3.89192e11			0.828023
$829$			4.79249e10i			0.101471i	0.998712	+	0.0507356i	$0.0161566\pi$
$829$			4.79249e10i			0.101471i	−0.998712	+	0.0507356i	$0.983843\pi$
$830$	5.00749e11			1.05513
$831$	−1.12712e11			−0.236356
$832$	−7.88649e11			−1.64585
$833$	3.75216e10			0.0779295
$834$	7.49611e11			1.54943
$835$		−	8.81711e10i		−	0.181376i
$836$		−	9.21568e10i		−	0.188670i
$837$		−	2.82446e11i		−	0.575484i
$838$	−1.24504e11			−0.252468
$839$			2.04478e11i			0.412667i	0.978482	+	0.206333i	$0.0661531\pi$
$839$			2.04478e11i			0.412667i	−0.978482	+	0.206333i	$0.933847\pi$
$840$	4.21418e10			0.0846439
$841$	4.98385e11			0.996280
$842$	1.13030e12			2.24877
$843$			2.45609e11i			0.486333i
$844$			5.30123e11i			1.04474i
$845$		−	1.87280e11i		−	0.367337i
$846$			7.53444e10i			0.147085i
$847$			3.96974e11i			0.771310i
$848$	4.36739e11			0.844575
$849$			3.01924e11i			0.581121i
$850$			5.24360e11i			1.00451i
$851$			1.08967e12i			2.07768i
$852$	−4.41386e11			−0.837646
$853$	7.68747e11			1.45207			0.726034	−	0.687658i	$-0.241361\pi$
$853$	7.68747e11			1.45207			0.726034	+	0.687658i	$0.241361\pi$
$854$		−	7.26471e11i		−	1.36580i
$855$	6.93869e10			0.129841
$856$			9.98409e10i			0.185957i
$857$	−3.77473e11			−0.699782			−0.349891	−	0.936790i	$-0.613781\pi$
$857$	−3.77473e11			−0.699782			−0.349891	+	0.936790i	$0.613781\pi$
$858$	−2.91171e11			−0.537277
$859$		−	2.09913e11i		−	0.385538i	−0.981244	−	0.192769i	$-0.938253\pi$
$859$		−	2.09913e11i		−	0.385538i	0.981244	−	0.192769i	$-0.0617468\pi$
$860$	2.46688e11	−	2.89890e11i	0.450977	−	0.529956i
$861$	1.30994e11			0.238363
$862$		−	6.54869e11i		−	1.18611i
$863$			3.75693e11i			0.677314i	0.940910	+	0.338657i	$0.109973\pi$
$863$			3.75693e11i			0.677314i	−0.940910	+	0.338657i	$0.890027\pi$
$864$	−7.60782e11			−1.36523
$865$			4.89814e11i			0.874917i
$866$	6.59243e11			1.17212
$867$			4.21793e10i			0.0746488i
$868$		−	4.12813e11i		−	0.727234i
$869$	1.56683e11			0.274753
$870$	1.74901e10			0.0305291
$871$	−9.46833e11			−1.64513
$872$			1.08526e11i			0.187701i
$873$	8.09640e10			0.139391
$874$	−2.89815e11			−0.496679
$875$	−5.96561e11			−1.01771
$876$	−2.14899e11			−0.364938
$877$	−2.74793e11			−0.464523			−0.232262	−	0.972653i	$-0.574613\pi$
$877$	−2.74793e11			−0.464523			−0.232262	+	0.972653i	$0.574613\pi$
$878$			1.05869e12i			1.78153i
$879$		−	3.22181e11i		−	0.539690i
$880$			1.46898e11i			0.244955i
$881$	3.90265e11			0.647823			0.323911	−	0.946087i	$-0.395002\pi$
$881$	3.90265e11			0.647823			0.323911	+	0.946087i	$0.395002\pi$
$882$			4.41119e10i			0.0728923i
$883$	3.41392e11			0.561579			0.280789	−	0.959769i	$-0.409404\pi$
$883$	3.41392e11			0.561579			0.280789	+	0.959769i	$0.409404\pi$
$884$	−9.59868e11			−1.57182
$885$	9.93239e10			0.161913
$886$		−	6.52325e11i		−	1.05859i
$887$			6.14485e11i			0.992698i	0.868123	+	0.496349i	$0.165326\pi$
$887$			6.14485e11i			0.992698i	−0.868123	+	0.496349i	$0.834674\pi$
$888$			1.67664e11i			0.269643i
$889$			9.68404e9i			0.0155042i
$890$			5.50895e11i			0.878030i
$891$	4.26589e10			0.0676860
$892$		−	5.94637e10i		−	0.0939275i
$893$		−	3.01698e10i		−	0.0474425i
$894$		−	6.43989e11i		−	1.00816i
$895$	−2.12732e11			−0.331543
$896$	−3.16350e11			−0.490835
$897$			4.92386e11i			0.760564i
$898$	−1.36313e12			−2.09620
$899$		−	2.40429e10i		−	0.0368085i
$900$	−3.31489e11			−0.505241
$901$	7.30745e11			1.10883
$902$		−	1.99039e11i		−	0.300686i
$903$	−2.98417e11	−	2.53944e11i	−0.448821	−	0.381933i
$904$	5.55158e10			0.0831272
$905$		−	1.36063e11i		−	0.202836i
$906$			1.96509e11i			0.291655i
$907$	5.42630e11			0.801815			0.400908	−	0.916118i	$-0.368695\pi$
$907$	5.42630e11			0.801815			0.400908	+	0.916118i	$0.368695\pi$
$908$		−	1.54976e12i		−	2.27993i
$909$	4.99999e11			0.732342
$910$		−	7.94127e11i		−	1.15804i
$911$		−	1.37471e11i		−	0.199590i	−0.995008	−	0.0997949i	$-0.968181\pi$
$911$		−	1.37471e11i		−	0.199590i	0.995008	−	0.0997949i	$-0.0318187\pi$
$912$	1.02302e11			0.147878
$913$	−4.21174e11			−0.606147
$914$	1.53141e12			2.19435
$915$			2.13811e11i			0.305031i
$916$	9.62681e11			1.36742
$917$	−1.25696e12			−1.77765
$918$	−1.05945e12			−1.49180
$919$	2.61231e11			0.366237			0.183119	−	0.983091i	$-0.441381\pi$
$919$	2.61231e11			0.366237			0.183119	+	0.983091i	$0.441381\pi$
$920$	−1.08282e11			−0.151149
$921$			5.74483e11i			0.798434i
$922$			3.46373e11i			0.479314i
$923$			1.16722e12i			1.60822i
$924$	−2.52580e11			−0.346506
$925$		−	9.28113e11i		−	1.26775i
$926$	−5.02705e11			−0.683706
$927$	2.40318e10			0.0325437
$928$	−6.47608e10			−0.0873213
$929$			8.83331e10i			0.118593i	0.998240	+	0.0592967i	$0.0188858\pi$
$929$			8.83331e10i			0.118593i	−0.998240	+	0.0592967i	$0.981114\pi$
$930$			2.25943e11i			0.302042i
$931$		−	1.76635e10i		−	0.0235114i
$932$			6.88444e11i			0.912442i
$933$			3.43866e11i			0.453797i
$934$	1.07737e12			1.41572
$935$			2.45788e11i			0.321599i
$936$		−	1.58358e11i		−	0.206318i
$937$		−	7.68952e11i		−	0.997564i	−0.866728	−	0.498782i	$-0.833781\pi$
$937$		−	7.68952e11i		−	0.997564i	0.866728	−	0.498782i	$-0.166219\pi$
$938$	−1.52742e12			−1.97310
$939$	7.03003e11			0.904263
$940$		−	8.03257e10i		−	0.102883i
$941$	−9.97007e11			−1.27157			−0.635784	−	0.771867i	$-0.719323\pi$
$941$	−9.97007e11			−1.27157			−0.635784	+	0.771867i	$0.719323\pi$
$942$		−	2.49734e11i		−	0.317157i
$943$	−3.36587e11			−0.425648
$944$	−3.06091e11			−0.385445
$945$		−	4.71328e11i		−	0.591012i
$946$	−3.85856e11	+	4.53430e11i	−0.481793	+	0.566169i
$947$	−2.90821e11			−0.361598			−0.180799	−	0.983520i	$-0.557868\pi$
$947$	−2.90821e11			−0.361598			−0.180799	+	0.983520i	$0.557868\pi$
$948$		−	2.90515e11i		−	0.359696i
$949$			5.68287e11i			0.700653i
$950$	2.46846e11			0.303062
$951$			1.29468e11i			0.158285i
$952$	−2.17297e11			−0.264549
$953$		−	4.33449e11i		−	0.525493i	−0.964865	−	0.262746i	$-0.915372\pi$
$953$		−	4.33449e11i		−	0.525493i	0.964865	−	0.262746i	$-0.0846283\pi$
$954$			8.59093e11i			1.03716i
$955$	−6.93593e11			−0.833857
$956$	−4.77845e11			−0.572079
$957$	−1.47107e10			−0.0175382
$958$		−	3.82377e11i		−	0.453972i
$959$	6.50721e11			0.769343
$960$	3.74439e11			0.440855
$961$	−5.42296e11			−0.635833
$962$	3.15950e12			3.68908
$963$	4.50551e11			0.523888
$964$		−	8.23463e11i		−	0.953533i
$965$			8.74741e11i			1.00872i
$966$			7.94314e11i			0.912187i
$967$	−1.00411e12			−1.14835			−0.574175	−	0.818733i	$-0.694677\pi$
$967$	−1.00411e12			−1.14835			−0.574175	+	0.818733i	$0.694677\pi$
$968$		−	1.56947e11i		−	0.178752i
$969$	1.71170e11			0.194148
$970$	−1.60521e11			−0.181319
$971$	4.65426e11			0.523569			0.261785	−	0.965126i	$-0.415689\pi$
$971$	4.65426e11			0.523569			0.261785	+	0.965126i	$0.415689\pi$
$972$		−	1.06928e12i		−	1.19792i
$973$		−	1.71957e12i		−	1.91853i
$974$		−	1.76789e12i		−	1.96435i
$975$		−	4.19383e11i		−	0.464079i
$976$		−	6.58909e11i		−	0.726150i
$977$	1.62647e12			1.78512			0.892560	−	0.450930i	$-0.148907\pi$
$977$	1.62647e12			1.78512			0.892560	+	0.450930i	$0.148907\pi$
$978$			8.88818e11i			0.971533i
$979$		−	4.63351e11i		−	0.504405i
$980$		−	4.70283e10i		−	0.0509865i
$981$	4.89744e11			0.528802
$982$	−3.71577e11			−0.399580
$983$		−	2.12076e11i		−	0.227131i	−0.993530	−	0.113566i	$-0.963773\pi$
$983$		−	2.12076e11i		−	0.227131i	0.993530	−	0.113566i	$-0.0362272\pi$
$984$	−5.17896e10			−0.0552410
$985$		−	8.21834e10i		−	0.0873050i
$986$	−9.01845e10			−0.0954166
$987$	−8.26883e10			−0.0871316
$988$			4.51864e11i			0.474220i
$989$	7.66776e11	+	6.52504e11i	0.801463	+	0.682021i
$990$	−2.88958e11			−0.300811
$991$		−	6.41703e11i		−	0.665334i	−0.943044	−	0.332667i	$-0.892052\pi$
$991$		−	6.41703e11i		−	0.665334i	0.943044	−	0.332667i	$-0.107948\pi$
$992$		−	8.36604e11i		−	0.863919i
$993$	2.85160e11			0.293286
$994$			1.88295e12i			1.92882i
$995$	−1.61942e11			−0.165222
$996$			7.80924e11i			0.793545i
$997$			1.47250e10i			0.0149030i	0.999972	+	0.00745151i	$0.00237191\pi$
$997$			1.47250e10i			0.0149030i	−0.999972	+	0.00745151i	$0.997628\pi$
$998$	2.66595e12			2.68738
$999$	1.87522e12			1.88274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.6	✓	28
43.42	odd	2	inner	43.9.b.b.42.23	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.6	✓	28	1.1	even	1	trivial
43.9.b.b.42.23	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)

\(f(q)\)	\(=\)	\(q-23.5327i q^{2} +46.0777i q^{3} -297.789 q^{4} -373.886i q^{5} +1084.33 q^{6} -2487.41i q^{7} +983.414i q^{8} +4437.84 q^{9} +O(q^{10})\)	\(q-23.5327i q^{2} +46.0777i q^{3} -297.789 q^{4} -373.886i q^{5} +1084.33 q^{6} -2487.41i q^{7} +983.414i q^{8} +4437.84 q^{9} -8798.55 q^{10} +7400.35 q^{11} -13721.4i q^{12} -36285.4 q^{13} -58535.4 q^{14} +17227.8 q^{15} -53091.6 q^{16} -88832.2 q^{17} -104435. i q^{18} +41818.3i q^{19} +111339. i q^{20} +114614. q^{21} -174150. i q^{22} -294498. q^{23} -45313.5 q^{24} +250835. q^{25} +853895. i q^{26} +506802. i q^{27} +740723. i q^{28} +43140.9i q^{29} -405417. i q^{30} -557310. q^{31} +1.50114e6i q^{32} +340991. i q^{33} +2.09046e6i q^{34} -930005. q^{35} -1.32154e6 q^{36} -3.70010e6i q^{37} +984099. q^{38} -1.67195e6i q^{39} +367684. q^{40} +1.14292e6 q^{41} -2.69718e6i q^{42} +(-2.60367e6 - 2.21565e6i) q^{43} -2.20374e6 q^{44} -1.65925e6i q^{45} +6.93034e6i q^{46} -721451. q^{47} -2.44634e6i q^{48} -422388. q^{49} -5.90282e6i q^{50} -4.09318e6i q^{51} +1.08054e7 q^{52} -8.22613e6 q^{53} +1.19264e7 q^{54} -2.76688e6i q^{55} +2.44615e6 q^{56} -1.92689e6 q^{57} +1.01522e6 q^{58} +5.76533e6 q^{59} -5.13025e6 q^{60} +1.24108e7i q^{61} +1.31150e7i q^{62} -1.10387e7i q^{63} +2.17346e7 q^{64} +1.35666e7i q^{65} +8.02445e6 q^{66} +2.60940e7 q^{67} +2.64533e7 q^{68} -1.35698e7i q^{69} +2.18856e7i q^{70} -3.21676e7i q^{71} +4.36424e6i q^{72} -1.56616e7i q^{73} -8.70735e7 q^{74} +1.15579e7i q^{75} -1.24530e7i q^{76} -1.84077e7i q^{77} -3.93455e7 q^{78} +2.11723e7 q^{79} +1.98502e7i q^{80} +5.76445e6 q^{81} -2.68960e7i q^{82} -5.69127e7 q^{83} -3.41308e7 q^{84} +3.32131e7i q^{85} +(-5.21402e7 + 6.12715e7i) q^{86} -1.98783e6 q^{87} +7.27761e6i q^{88} -6.26121e7i q^{89} -3.90466e7 q^{90} +9.02566e7i q^{91} +8.76983e7 q^{92} -2.56796e7i q^{93} +1.69777e7i q^{94} +1.56353e7 q^{95} -6.91693e7 q^{96} +1.82440e7 q^{97} +9.93994e6i q^{98} +3.28416e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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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