LMFDB - Embedded newform 43.9.b.b.42.5

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			42.5
Character	$\chi$	$=$	43.42
Dual form			43.9.b.b.42.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-23.8212i q^{2} +128.615i q^{3} -311.450 q^{4} +1187.44i q^{5} +3063.75 q^{6} -1045.51i q^{7} +1320.89i q^{8} -9980.70 q^{9} +O(q^{10})$	\(q-23.8212i q^{2} +128.615i q^{3} -311.450 q^{4} +1187.44i q^{5} +3063.75 q^{6} -1045.51i q^{7} +1320.89i q^{8} -9980.70 q^{9} +28286.2 q^{10} -7720.54 q^{11} -40057.0i q^{12} -32771.9 q^{13} -24905.4 q^{14} -152722. q^{15} -48266.1 q^{16} +74818.8 q^{17} +237752. i q^{18} -221516. i q^{19} -369827. i q^{20} +134468. q^{21} +183913. i q^{22} +272622. q^{23} -169885. q^{24} -1.01938e6 q^{25} +780665. i q^{26} -439823. i q^{27} +325625. i q^{28} +11057.0i q^{29} +3.63801e6i q^{30} -669910. q^{31} +1.48790e6i q^{32} -992974. i q^{33} -1.78227e6i q^{34} +1.24148e6 q^{35} +3.10849e6 q^{36} +3.02251e6i q^{37} -5.27678e6 q^{38} -4.21494e6i q^{39} -1.56847e6 q^{40} -874510. q^{41} -3.20319e6i q^{42} +(-3.02666e6 - 1.58983e6i) q^{43} +2.40456e6 q^{44} -1.18514e7i q^{45} -6.49420e6i q^{46} -2.23823e6 q^{47} -6.20772e6i q^{48} +4.67171e6 q^{49} +2.42828e7i q^{50} +9.62278e6i q^{51} +1.02068e7 q^{52} -1.95235e6 q^{53} -1.04771e7 q^{54} -9.16765e6i q^{55} +1.38100e6 q^{56} +2.84902e7 q^{57} +263392. q^{58} -2.07104e7 q^{59} +4.75651e7 q^{60} +1.01183e7i q^{61} +1.59581e7i q^{62} +1.04349e7i q^{63} +2.30875e7 q^{64} -3.89145e7i q^{65} -2.36538e7 q^{66} -2.69928e7 q^{67} -2.33023e7 q^{68} +3.50632e7i q^{69} -2.95735e7i q^{70} +1.28888e7i q^{71} -1.31834e7i q^{72} +1.98955e7i q^{73} +7.19998e7 q^{74} -1.31107e8i q^{75} +6.89912e7i q^{76} +8.07192e6i q^{77} -1.00405e8 q^{78} +4.68555e7 q^{79} -5.73129e7i q^{80} -8.91576e6 q^{81} +2.08319e7i q^{82} +2.60253e7 q^{83} -4.18801e7 q^{84} +8.88425e7i q^{85} +(-3.78716e7 + 7.20986e7i) q^{86} -1.42210e6 q^{87} -1.01979e7i q^{88} -2.43427e7i q^{89} -2.82316e8 q^{90} +3.42634e7i q^{91} -8.49083e7 q^{92} -8.61602e7i q^{93} +5.33175e7i q^{94} +2.63036e8 q^{95} -1.91366e8 q^{96} +3.57432e6 q^{97} -1.11286e8i q^{98} +7.70564e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	23.8212i		−	1.48883i	−0.667720	−	0.744413i	$-0.732730\pi$
$2$		−	23.8212i		−	1.48883i	0.667720	−	0.744413i	$-0.267270\pi$
$3$			128.615i			1.58783i	0.608026	+	0.793917i	$0.291961\pi$
$3$			128.615i			1.58783i	−0.608026	+	0.793917i	$0.708039\pi$
$4$	−311.450			−1.21660
$5$			1187.44i			1.89990i	0.312406	+	0.949949i	$0.398865\pi$
$5$			1187.44i			1.89990i	−0.312406	+	0.949949i	$0.601135\pi$
$6$	3063.75			2.36401
$7$		−	1045.51i		−	0.435448i	−0.976010	−	0.217724i	$-0.930137\pi$
$7$		−	1045.51i		−	0.435448i	0.976010	−	0.217724i	$-0.0698633\pi$
$8$			1320.89i			0.322482i
$9$	−9980.70			−1.52122
$10$	28286.2			2.82862
$11$	−7720.54			−0.527323			−0.263662	−	0.964615i	$-0.584930\pi$
$11$	−7720.54			−0.527323			−0.263662	+	0.964615i	$0.584930\pi$
$12$		−	40057.0i		−	1.93176i
$13$	−32771.9			−1.14743			−0.573717	−	0.819054i	$-0.694499\pi$
$13$	−32771.9			−1.14743			−0.573717	+	0.819054i	$0.694499\pi$
$14$	−24905.4			−0.648307
$15$	−152722.			−3.01672
$16$	−48266.1			−0.736482
$17$	74818.8			0.895808			0.447904	−	0.894082i	$-0.352171\pi$
$17$	74818.8			0.895808			0.447904	+	0.894082i	$0.352171\pi$
$18$			237752.i			2.26482i
$19$		−	221516.i		−	1.69977i	−0.526966	−	0.849886i	$-0.676671\pi$
$19$		−	221516.i		−	1.69977i	0.526966	−	0.849886i	$-0.323329\pi$
$20$		−	369827.i		−	2.31142i
$21$	134468.			0.691420
$22$			183913.i			0.785092i
$23$	272622.			0.974205			0.487102	−	0.873345i	$-0.338054\pi$
$23$	272622.			0.974205			0.487102	+	0.873345i	$0.338054\pi$
$24$	−169885.			−0.512047
$25$	−1.01938e6			−2.60961
$26$			780665.i			1.70833i
$27$		−	439823.i		−	0.827604i
$28$			325625.i			0.529767i
$29$			11057.0i			0.0156332i	0.999969	+	0.00781658i	$0.00248812\pi$
$29$			11057.0i			0.0156332i	−0.999969	+	0.00781658i	$0.997512\pi$
$30$			3.63801e6i			4.49137i
$31$	−669910.			−0.725387			−0.362694	−	0.931908i	$-0.618143\pi$
$31$	−669910.			−0.725387			−0.362694	+	0.931908i	$0.618143\pi$
$32$			1.48790e6i			1.41898i
$33$		−	992974.i		−	0.837302i
$34$		−	1.78227e6i		−	1.33370i
$35$	1.24148e6			0.827307
$36$	3.10849e6			1.85071
$37$			3.02251e6i			1.61273i	0.591421	+	0.806363i	$0.298567\pi$
$37$			3.02251e6i			1.61273i	−0.591421	+	0.806363i	$0.701433\pi$
$38$	−5.27678e6			−2.53066
$39$		−	4.21494e6i		−	1.82193i
$40$	−1.56847e6			−0.612682
$41$	−874510.			−0.309478			−0.154739	−	0.987955i	$-0.549454\pi$
$41$	−874510.			−0.309478			−0.154739	+	0.987955i	$0.549454\pi$
$42$		−	3.20319e6i		−	1.02940i
$43$	−3.02666e6	−	1.58983e6i	−0.885298	−	0.465025i
$43$	−3.02666e6	−	1.58983e6i	−0.885298	−	0.465025i
$44$	2.40456e6			0.641542
$45$		−	1.18514e7i		−	2.89015i
$46$		−	6.49420e6i		−	1.45042i
$47$	−2.23823e6			−0.458685			−0.229342	−	0.973346i	$-0.573658\pi$
$47$	−2.23823e6			−0.458685			−0.229342	+	0.973346i	$0.573658\pi$
$48$		−	6.20772e6i		−	1.16941i
$49$	4.67171e6			0.810385
$50$			2.42828e7i			3.88525i
$51$			9.62278e6i			1.42239i
$52$	1.02068e7			1.39597
$53$	−1.95235e6			−0.247431			−0.123715	−	0.992318i	$-0.539481\pi$
$53$	−1.95235e6			−0.247431			−0.123715	+	0.992318i	$0.539481\pi$
$54$	−1.04771e7			−1.23216
$55$		−	9.16765e6i		−	1.00186i
$56$	1.38100e6			0.140424
$57$	2.84902e7			2.69896
$58$	263392.			0.0232750
$59$	−2.07104e7			−1.70915			−0.854574	−	0.519330i	$-0.826182\pi$
$59$	−2.07104e7			−1.70915			−0.854574	+	0.519330i	$0.826182\pi$
$60$	4.75651e7			3.67015
$61$			1.01183e7i			0.730783i	0.930854	+	0.365392i	$0.119065\pi$
$61$			1.01183e7i			0.730783i	−0.930854	+	0.365392i	$0.880935\pi$
$62$			1.59581e7i			1.07997i
$63$			1.04349e7i			0.662411i
$64$	2.30875e7			1.37612
$65$		−	3.89145e7i		−	2.18001i
$66$	−2.36538e7			−1.24660
$67$	−2.69928e7			−1.33952			−0.669760	−	0.742577i	$-0.733603\pi$
$67$	−2.69928e7			−1.33952			−0.669760	+	0.742577i	$0.733603\pi$
$68$	−2.33023e7			−1.08984
$69$			3.50632e7i			1.54688i
$70$		−	2.95735e7i		−	1.23172i
$71$			1.28888e7i			0.507200i	0.967309	+	0.253600i	$0.0816148\pi$
$71$			1.28888e7i			0.507200i	−0.967309	+	0.253600i	$0.918385\pi$
$72$		−	1.31834e7i		−	0.490564i
$73$			1.98955e7i			0.700589i	0.936640	+	0.350294i	$0.113918\pi$
$73$			1.98955e7i			0.700589i	−0.936640	+	0.350294i	$0.886082\pi$
$74$	7.19998e7			2.40107
$75$		−	1.31107e8i		−	4.14363i
$76$			6.89912e7i			2.06795i
$77$			8.07192e6i			0.229622i
$78$	−1.00405e8			−2.71254
$79$	4.68555e7			1.20296			0.601482	−	0.798886i	$-0.294577\pi$
$79$	4.68555e7			1.20296			0.601482	+	0.798886i	$0.294577\pi$
$80$		−	5.73129e7i		−	1.39924i
$81$	−8.91576e6			−0.207118
$82$			2.08319e7i			0.460759i
$83$	2.60253e7			0.548382			0.274191	−	0.961675i	$-0.411590\pi$
$83$	2.60253e7			0.548382			0.274191	+	0.961675i	$0.411590\pi$
$84$	−4.18801e7			−0.841182
$85$			8.88425e7i			1.70194i
$86$	−3.78716e7	+	7.20986e7i	−0.692340	+	1.31805i
$87$	−1.42210e6			−0.0248229
$88$		−	1.01979e7i		−	0.170052i
$89$		−	2.43427e7i		−	0.387980i	−0.981004	−	0.193990i	$-0.937857\pi$
$89$		−	2.43427e7i		−	0.387980i	0.981004	−	0.193990i	$-0.0621429\pi$
$90$	−2.82316e8			−4.30294
$91$			3.42634e7i			0.499648i
$92$	−8.49083e7			−1.18522
$93$		−	8.61602e7i		−	1.15179i
$94$			5.33175e7i			0.682901i
$95$	2.63036e8			3.22939
$96$	−1.91366e8			−2.25310
$97$	3.57432e6			0.0403744			0.0201872	−	0.999796i	$-0.493574\pi$
$97$	3.57432e6			0.0403744			0.0201872	+	0.999796i	$0.493574\pi$
$98$		−	1.11286e8i		−	1.20652i
$99$	7.70564e7			0.802173
$100$	3.17486e8			3.17486
$101$	−4.79756e7			−0.461036			−0.230518	−	0.973068i	$-0.574042\pi$
$101$	−4.79756e7			−0.461036			−0.230518	+	0.973068i	$0.574042\pi$
$102$	2.29226e8			2.11770
$103$	2.85028e7			0.253243			0.126622	−	0.991951i	$-0.459587\pi$
$103$	2.85028e7			0.253243			0.126622	+	0.991951i	$0.459587\pi$
$104$		−	4.32879e7i		−	0.370027i
$105$			1.59672e8i			1.31363i
$106$			4.65073e7i			0.368381i
$107$	−1.05259e8			−0.803016			−0.401508	−	0.915855i	$-0.631514\pi$
$107$	−1.05259e8			−0.803016			−0.401508	+	0.915855i	$0.631514\pi$
$108$			1.36983e8i			1.00686i
$109$	4.41249e7			0.312592			0.156296	−	0.987710i	$-0.450045\pi$
$109$	4.41249e7			0.312592			0.156296	+	0.987710i	$0.450045\pi$
$110$	−2.18384e8			−1.49160
$111$	−3.88739e8			−2.56074
$112$			5.04628e7i			0.320700i
$113$			2.43450e8i			1.49313i	0.665314	+	0.746563i	$0.268298\pi$
$113$			2.43450e8i			1.49313i	−0.665314	+	0.746563i	$0.731702\pi$
$114$		−	6.78671e8i		−	4.01827i
$115$			3.23722e8i			1.85089i
$116$		−	3.44371e6i		−	0.0190193i
$117$	3.27086e8			1.74549
$118$			4.93346e8i			2.54462i
$119$		−	7.82239e7i		−	0.390078i
$120$		−	2.01728e8i		−	0.972838i
$121$	−1.54752e8			−0.721930
$122$	2.41030e8			1.08801
$123$		−	1.12475e8i		−	0.491399i
$124$	2.08644e8			0.882507
$125$		−	7.46605e8i		−	3.05809i
$126$	2.48573e8			0.986215
$127$	4.14402e8			1.59297			0.796483	−	0.604661i	$-0.206691\pi$
$127$	4.14402e8			1.59297			0.796483	+	0.604661i	$0.206691\pi$
$128$		−	1.69070e8i		−	0.629834i
$129$	2.04475e8	−	3.89272e8i	0.738382	−	1.40571i
$130$	−9.26990e8			−3.24565
$131$			7.37862e7i			0.250548i	0.992122	+	0.125274i	$0.0399809\pi$
$131$			7.37862e7i			0.250548i	−0.992122	+	0.125274i	$0.960019\pi$
$132$			3.09262e8i			1.01866i
$133$	−2.31598e8			−0.740163
$134$			6.43002e8i			1.99431i
$135$	5.22261e8			1.57236
$136$			9.88270e7i			0.288882i
$137$		−	3.82975e8i		−	1.08715i	−0.839362	−	0.543573i	$-0.817071\pi$
$137$		−	3.82975e8i		−	1.08715i	0.839362	−	0.543573i	$-0.182929\pi$
$138$	8.35248e8			2.30303
$139$	−1.29166e8			−0.346011			−0.173005	−	0.984921i	$-0.555348\pi$
$139$	−1.29166e8			−0.346011			−0.173005	+	0.984921i	$0.555348\pi$
$140$	−3.86658e8			−1.00650
$141$		−	2.87869e8i		−	0.728315i
$142$	3.07027e8			0.755133
$143$	2.53017e8			0.605069
$144$	4.81729e8			1.12035
$145$	−1.31295e7			−0.0297014
$146$	4.73935e8			1.04305
$147$			6.00849e8i			1.28676i
$148$		−	9.41360e8i		−	1.96205i
$149$			1.46858e8i			0.297957i	0.988840	+	0.148979i	$0.0475985\pi$
$149$			1.46858e8i			0.297957i	−0.988840	+	0.148979i	$0.952401\pi$
$150$	−3.12313e9			−6.16914
$151$			4.27850e7i			0.0822970i	0.999153	+	0.0411485i	$0.0131017\pi$
$151$			4.27850e7i			0.0822970i	−0.999153	+	0.0411485i	$0.986898\pi$
$152$	2.92597e8			0.548146
$153$	−7.46744e8			−1.36272
$154$	1.92283e8			0.341867
$155$		−	7.95475e8i		−	1.37816i
$156$			1.31274e9i			2.21657i
$157$			7.84735e8i			1.29159i	0.763511	+	0.645795i	$0.223474\pi$
$157$			7.84735e8i			1.29159i	−0.763511	+	0.645795i	$0.776526\pi$
$158$		−	1.11616e9i		−	1.79100i
$159$		−	2.51100e8i		−	0.392879i
$160$	−1.76679e9			−2.69591
$161$		−	2.85030e8i		−	0.424216i
$162$			2.12384e8i			0.308363i
$163$			8.52878e8i			1.20819i	0.796911	+	0.604097i	$0.206466\pi$
$163$			8.52878e8i			1.20819i	−0.796911	+	0.604097i	$0.793534\pi$
$164$	2.72366e8			0.376511
$165$	1.17909e9			1.59079
$166$		−	6.19954e8i		−	0.816446i
$167$	6.08443e8			0.782266			0.391133	−	0.920334i	$-0.372083\pi$
$167$	6.08443e8			0.782266			0.391133	+	0.920334i	$0.372083\pi$
$168$			1.77617e8i			0.222970i
$169$	2.58264e8			0.316605
$170$	2.11634e9			2.53390
$171$			2.21088e9i			2.58572i
$172$	9.42652e8	+	4.95151e8i	1.07705	+	0.565750i
$173$	−1.45079e9			−1.61965			−0.809824	−	0.586673i	$-0.800437\pi$
$173$	−1.45079e9			−1.61965			−0.809824	+	0.586673i	$0.800437\pi$
$174$			3.38760e7i			0.0369569i
$175$			1.06577e9i			1.13635i
$176$	3.72640e8			0.388364
$177$		−	2.66365e9i		−	2.71384i
$178$	−5.79873e8			−0.577634
$179$			4.36516e8i			0.425194i	0.977140	+	0.212597i	$0.0681922\pi$
$179$			4.36516e8i			0.425194i	−0.977140	+	0.212597i	$0.931808\pi$
$180$			3.69113e9i			3.51617i
$181$	1.12797e9			1.05095			0.525474	−	0.850810i	$-0.323888\pi$
$181$	1.12797e9			1.05095			0.525474	+	0.850810i	$0.323888\pi$
$182$	8.16195e8			0.743889
$183$	−1.30136e9			−1.16036
$184$			3.60103e8i			0.314163i
$185$	−3.58904e9			−3.06401
$186$	−2.05244e9			−1.71482
$187$	−5.77642e8			−0.472381
$188$	6.97098e8			0.558036
$189$	−4.59840e8			−0.360379
$190$		−	6.26584e9i		−	4.80800i
$191$			1.96549e9i			1.47685i	0.674335	+	0.738425i	$0.264430\pi$
$191$			1.96549e9i			1.47685i	−0.674335	+	0.738425i	$0.735570\pi$
$192$			2.96939e9i			2.18506i
$193$	4.37331e8			0.315197			0.157598	−	0.987503i	$-0.449625\pi$
$193$	4.37331e8			0.315197			0.157598	+	0.987503i	$0.449625\pi$
$194$		−	8.51445e7i		−	0.0601104i
$195$	5.00497e9			3.46149
$196$	−1.45500e9			−0.985915
$197$	−1.98231e9			−1.31615			−0.658077	−	0.752950i	$-0.728630\pi$
$197$	−1.98231e9			−1.31615			−0.658077	+	0.752950i	$0.728630\pi$
$198$		−	1.83558e9i		−	1.19430i
$199$		−	3.04777e9i		−	1.94344i	−0.236143	−	0.971718i	$-0.575883\pi$
$199$		−	3.04777e9i		−	1.94344i	0.236143	−	0.971718i	$-0.424117\pi$
$200$		−	1.34648e9i		−	0.841552i
$201$		−	3.47167e9i		−	2.12694i
$202$			1.14284e9i			0.686402i
$203$	1.15603e7			0.00680744
$204$		−	2.99702e9i		−	1.73049i
$205$		−	1.03843e9i		−	0.587976i
$206$		−	6.78970e8i		−	0.377035i
$207$	−2.72096e9			−1.48198
$208$	1.58177e9			0.845065
$209$			1.71022e9i			0.896330i
$210$	3.80358e9			1.95576
$211$			2.99574e8i			0.151138i	0.997141	+	0.0755690i	$0.0240773\pi$
$211$			2.99574e8i			0.151138i	−0.997141	+	0.0755690i	$0.975923\pi$
$212$	6.08059e8			0.301025
$213$	−1.65769e9			−0.805350
$214$			2.50740e9i			1.19555i
$215$	1.88782e9	−	3.59396e9i	0.883499	−	1.68197i
$216$	5.80955e8			0.266887
$217$			7.00399e8i			0.315869i
$218$		−	1.05111e9i		−	0.465395i
$219$	−2.55885e9			−1.11242
$220$			2.85526e9i			1.21886i
$221$	−2.45195e9			−1.02788
$222$			9.26022e9i			3.81250i
$223$			2.78431e9i			1.12589i	0.826493	+	0.562947i	$0.190333\pi$
$223$			2.78431e9i			1.12589i	−0.826493	+	0.562947i	$0.809667\pi$
$224$	1.55562e9			0.617891
$225$	1.01741e10			3.96978
$226$	5.79928e9			2.22301
$227$		−	9.25556e8i		−	0.348578i	−0.984695	−	0.174289i	$-0.944237\pi$
$227$		−	9.25556e8i		−	0.348578i	0.984695	−	0.174289i	$-0.0557626\pi$
$228$	−8.87327e9			−3.28355
$229$	−4.49307e9			−1.63381			−0.816905	−	0.576772i	$-0.804312\pi$
$229$	−4.49307e9			−1.63381			−0.816905	+	0.576772i	$0.804312\pi$
$230$	7.71144e9			2.75565
$231$	−1.03817e9			−0.364602
$232$	−1.46051e7			−0.00504141
$233$		−	1.03025e9i		−	0.349559i	−0.984608	−	0.174779i	$-0.944079\pi$
$233$		−	1.03025e9i		−	0.349559i	0.984608	−	0.174779i	$-0.0559212\pi$
$234$		−	7.79158e9i		−	2.59874i
$235$		−	2.65776e9i		−	0.871454i
$236$	6.45024e9			2.07935
$237$			6.02630e9i			1.91011i
$238$	−1.86339e9			−0.580758
$239$	−4.62921e8			−0.141878			−0.0709390	−	0.997481i	$-0.522600\pi$
$239$	−4.62921e8			−0.141878			−0.0709390	+	0.997481i	$0.522600\pi$
$240$	7.37127e9			2.22176
$241$			2.39828e9i			0.710938i	0.934688	+	0.355469i	$0.115679\pi$
$241$			2.39828e9i			0.710938i	−0.934688	+	0.355469i	$0.884321\pi$
$242$			3.68638e9i			1.07483i
$243$		−	4.03237e9i		−	1.15647i
$244$		−	3.15135e9i		−	0.889072i
$245$			5.54735e9i			1.53965i
$246$	−2.67928e9			−0.731608
$247$			7.25949e9i			1.95038i
$248$		−	8.84875e8i		−	0.233924i
$249$			3.34723e9i			0.870740i
$250$	−1.77850e10			−4.55297
$251$	6.66643e9			1.67957			0.839786	−	0.542918i	$-0.182681\pi$
$251$	6.66643e9			1.67957			0.839786	+	0.542918i	$0.182681\pi$
$252$		−	3.24996e9i		−	0.805890i
$253$	−2.10479e9			−0.513721
$254$		−	9.87155e9i		−	2.37165i
$255$	−1.14264e10			−2.70240
$256$	1.88296e9			0.438412
$257$		−	5.34258e9i		−	1.22467i	−0.790599	−	0.612334i	$-0.790231\pi$
$257$		−	5.34258e9i		−	1.22467i	0.790599	−	0.612334i	$-0.209769\pi$
$258$	−9.27293e9	−	4.87084e9i	−2.09285	−	1.09932i
$259$	3.16007e9			0.702259
$260$			1.21199e10i			2.65220i
$261$		−	1.10357e8i		−	0.0237814i
$262$	1.75768e9			0.373022
$263$		−	1.45518e9i		−	0.304155i	−0.988369	−	0.152078i	$-0.951404\pi$
$263$		−	1.45518e9i		−	0.304155i	0.988369	−	0.152078i	$-0.0485964\pi$
$264$	1.31160e9			0.270015
$265$		−	2.31829e9i		−	0.470093i
$266$			5.51694e9i			1.10197i
$267$	3.13083e9			0.616047
$268$	8.40692e9			1.62966
$269$	−3.65582e9			−0.698194			−0.349097	−	0.937087i	$-0.613512\pi$
$269$	−3.65582e9			−0.698194			−0.349097	+	0.937087i	$0.613512\pi$
$270$		−	1.24409e10i		−	2.34097i
$271$	−7.70139e9			−1.42788			−0.713940	−	0.700207i	$-0.753091\pi$
$271$	−7.70139e9			−1.42788			−0.713940	+	0.700207i	$0.753091\pi$
$272$	−3.61121e9			−0.659747
$273$	−4.40677e9			−0.793359
$274$	−9.12293e9			−1.61857
$275$	7.87016e9			1.37611
$276$		−	1.09204e10i		−	1.88193i
$277$			2.17850e9i			0.370032i	0.982736	+	0.185016i	$0.0592336\pi$
$277$			2.17850e9i			0.370032i	−0.982736	+	0.185016i	$0.940766\pi$
$278$			3.07690e9i			0.515150i
$279$	6.68617e9			1.10347
$280$			1.63985e9i			0.266792i
$281$	2.46057e9			0.394649			0.197324	−	0.980338i	$-0.436775\pi$
$281$	2.46057e9			0.394649			0.197324	+	0.980338i	$0.436775\pi$
$282$	−6.85740e9			−1.08433
$283$	−2.55764e9			−0.398744			−0.199372	−	0.979924i	$-0.563890\pi$
$283$	−2.55764e9			−0.398744			−0.199372	+	0.979924i	$0.563890\pi$
$284$		−	4.01422e9i		−	0.617061i
$285$			3.38303e10i			5.12774i
$286$		−	6.02716e9i		−	0.900842i
$287$			9.14311e8i			0.134762i
$288$		−	1.48503e10i		−	2.15857i
$289$	−1.37791e9			−0.197528
$290$			3.12761e8i			0.0442202i
$291$			4.59709e8i			0.0641078i
$292$		−	6.19645e9i		−	0.852338i
$293$	8.21345e9			1.11444			0.557218	−	0.830366i	$-0.311869\pi$
$293$	8.21345e9			1.11444			0.557218	+	0.830366i	$0.311869\pi$
$294$	1.43130e10			1.91576
$295$		−	2.45922e10i		−	3.24721i
$296$	−3.99239e9			−0.520075
$297$			3.39567e9i			0.436415i
$298$	3.49834e9			0.443606
$299$	−8.93435e9			−1.11784
$300$			4.08333e10i			5.04114i
$301$	−1.66218e9	+	3.16441e9i	−0.202494	+	0.385502i
$302$	1.01919e9			0.122526
$303$		−	6.17036e9i		−	0.732048i
$304$			1.06917e10i			1.25185i
$305$	−1.20148e10			−1.38841
$306$			1.77883e10i			2.02885i
$307$	1.23393e10			1.38911			0.694554	−	0.719441i	$-0.255602\pi$
$307$	1.23393e10			1.38911			0.694554	+	0.719441i	$0.255602\pi$
$308$		−	2.51400e9i		−	0.279359i
$309$			3.66587e9i			0.402108i
$310$	−1.89492e10			−2.05184
$311$	1.48263e10			1.58486			0.792430	−	0.609963i	$-0.208816\pi$
$311$	1.48263e10			1.58486			0.792430	+	0.609963i	$0.208816\pi$
$312$	5.56745e9			0.587541
$313$		−	4.43851e8i		−	0.0462445i	−0.999733	−	0.0231223i	$-0.992639\pi$
$313$		−	4.43851e8i		−	0.0462445i	0.999733	−	0.0231223i	$-0.00736070\pi$
$314$	1.86933e10			1.92295
$315$	−1.23908e10			−1.25851
$316$	−1.45932e10			−1.46353
$317$	1.69495e10			1.67850			0.839249	−	0.543748i	$-0.182995\pi$
$317$	1.69495e10			1.67850			0.839249	+	0.543748i	$0.182995\pi$
$318$	−5.98151e9			−0.584928
$319$		−	8.53663e7i		−	0.00824373i
$320$			2.74150e10i			2.61450i
$321$		−	1.35378e10i		−	1.27506i
$322$	−6.78976e9			−0.631584
$323$		−	1.65736e10i		−	1.52267i
$324$	2.77681e9			0.251980
$325$	3.34069e10			2.99436
$326$	2.03166e10			1.79879
$327$			5.67510e9i			0.496344i
$328$		−	1.15513e9i		−	0.0998010i
$329$			2.34010e9i			0.199734i
$330$		−	2.80874e10i		−	2.36841i
$331$			1.21801e10i			1.01470i	0.861740	+	0.507351i	$0.169375\pi$
$331$			1.21801e10i			1.01470i	−0.861740	+	0.507351i	$0.830625\pi$
$332$	−8.10558e9			−0.667163
$333$		−	3.01667e10i		−	2.45330i
$334$		−	1.44939e10i		−	1.16466i
$335$		−	3.20523e10i		−	2.54495i
$336$	−6.49025e9			−0.509218
$337$	1.06848e10			0.828411			0.414205	−	0.910183i	$-0.364059\pi$
$337$	1.06848e10			0.828411			0.414205	+	0.910183i	$0.364059\pi$
$338$		−	6.15217e9i		−	0.471369i
$339$	−3.13113e10			−2.37084
$340$		−	2.76700e10i		−	2.07059i
$341$	5.17207e9			0.382514
$342$	5.26659e10			3.84969
$343$		−	1.09115e10i		−	0.788329i
$344$	2.09998e9	−	3.99787e9i	0.149962	−	0.285492i
$345$	−4.16353e10			−2.93890
$346$			3.45596e10i			2.41137i
$347$			4.88319e9i			0.336810i	0.985718	+	0.168405i	$0.0538617\pi$
$347$			4.88319e9i			0.336810i	−0.985718	+	0.168405i	$0.946138\pi$
$348$	4.42912e8			0.0301995
$349$			1.60675e10i			1.08304i	0.840687	+	0.541521i	$0.182152\pi$
$349$			1.60675e10i			1.08304i	−0.840687	+	0.541521i	$0.817848\pi$
$350$	2.53880e10			1.69183
$351$			1.44138e10i			0.949621i
$352$		−	1.14874e10i		−	0.748259i
$353$	1.51491e10			0.975634			0.487817	−	0.872946i	$-0.337793\pi$
$353$	1.51491e10			0.975634			0.487817	+	0.872946i	$0.337793\pi$
$354$	−6.34514e10			−4.04044
$355$	−1.53046e10			−0.963629
$356$			7.58154e9i			0.472017i
$357$	1.00607e10			0.619379
$358$	1.03983e10			0.633040
$359$	−1.52025e10			−0.915242			−0.457621	−	0.889147i	$-0.651298\pi$
$359$	−1.52025e10			−0.915242			−0.457621	+	0.889147i	$0.651298\pi$
$360$	1.56544e10			0.932022
$361$	−3.20858e10			−1.88923
$362$		−	2.68695e10i		−	1.56468i
$363$		−	1.99034e10i		−	1.14630i
$364$		−	1.06713e10i		−	0.607873i
$365$	−2.36246e10			−1.33105
$366$			3.10000e10i			1.72758i
$367$	−9.87809e9			−0.544514			−0.272257	−	0.962225i	$-0.587770\pi$
$367$	−9.87809e9			−0.544514			−0.272257	+	0.962225i	$0.587770\pi$
$368$	−1.31584e10			−0.717485
$369$	8.72822e9			0.470783
$370$			8.54952e10i			4.56178i
$371$			2.04120e9i			0.107743i
$372$			2.68346e10i			1.40127i
$373$		−	2.67857e10i		−	1.38378i	−0.722002	−	0.691891i	$-0.756778\pi$
$373$		−	2.67857e10i		−	1.38378i	0.722002	−	0.691891i	$-0.243222\pi$
$374$			1.37601e10i			0.703292i
$375$	9.60243e10			4.85575
$376$		−	2.95645e9i		−	0.147917i
$377$		−	3.62360e8i		−	0.0179380i
$378$			1.09539e10i			0.536541i
$379$	1.56805e10			0.759983			0.379991	−	0.924990i	$-0.375927\pi$
$379$	1.56805e10			0.759983			0.379991	+	0.924990i	$0.375927\pi$
$380$	−8.19226e10			−3.92888
$381$			5.32981e10i			2.52937i
$382$	4.68203e10			2.19877
$383$		−	2.95831e10i		−	1.37483i	−0.726266	−	0.687414i	$-0.758746\pi$
$383$		−	2.95831e10i		−	1.37483i	0.726266	−	0.687414i	$-0.241254\pi$
$384$	2.17448e10			1.00007
$385$	−9.58488e9			−0.436259
$386$		−	1.04178e10i		−	0.469273i
$387$	3.02081e10	+	1.58676e10i	1.34673	+	0.707403i
$388$	−1.11322e9			−0.0491195
$389$		−	1.92230e10i		−	0.839502i	−0.907639	−	0.419751i	$-0.862117\pi$
$389$		−	1.92230e10i		−	0.839502i	0.907639	−	0.419751i	$-0.137883\pi$
$390$		−	1.19224e11i		−	5.15355i
$391$	2.03973e10			0.872701
$392$			6.17079e9i			0.261334i
$393$	−9.48998e9			−0.397828
$394$			4.72210e10i			1.95952i
$395$			5.56380e10i			2.28551i
$396$	−2.39992e10			−0.975924
$397$	−2.76966e10			−1.11497			−0.557486	−	0.830186i	$-0.688234\pi$
$397$	−2.76966e10			−1.11497			−0.557486	+	0.830186i	$0.688234\pi$
$398$	−7.26016e10			−2.89344
$399$		−	2.97868e10i		−	1.17526i
$400$	4.92015e10			1.92193
$401$	−3.55121e10			−1.37340			−0.686702	−	0.726939i	$-0.740942\pi$
$401$	−3.55121e10			−1.37340			−0.686702	+	0.726939i	$0.740942\pi$
$402$	−8.26994e10			−3.16664
$403$	2.19542e10			0.832334
$404$	1.49420e10			0.560897
$405$		−	1.05869e10i		−	0.393503i
$406$		−	2.75379e8i		−	0.0101351i
$407$		−	2.33354e10i		−	0.850428i
$408$	−1.27106e10			−0.458696
$409$		−	5.61655e9i		−	0.200713i	−0.994952	−	0.100357i	$-0.968002\pi$
$409$		−	5.61655e9i		−	0.200713i	0.994952	−	0.100357i	$-0.0319984\pi$
$410$	−2.47365e10			−0.875394
$411$	4.92561e10			1.72621
$412$	−8.87718e9			−0.308096
$413$			2.16529e10i			0.744246i
$414$			6.48166e10i			2.20640i
$415$			3.09034e10i			1.04187i
$416$		−	4.87614e10i		−	1.62818i
$417$		−	1.66127e10i		−	0.549408i
$418$	4.07396e10			1.33448
$419$			3.04720e10i			0.988655i	0.869276	+	0.494328i	$0.164586\pi$
$419$			3.04720e10i			0.988655i	−0.869276	+	0.494328i	$0.835414\pi$
$420$		−	4.97299e10i		−	1.59816i
$421$			2.98892e10i			0.951449i	0.879594	+	0.475724i	$0.157814\pi$
$421$			2.98892e10i			0.951449i	−0.879594	+	0.475724i	$0.842186\pi$
$422$	7.13620e9			0.225018
$423$	2.23391e10			0.697758
$424$		−	2.57883e9i		−	0.0797919i
$425$	−7.62687e10			−2.33771
$426$			3.94882e10i			1.19903i
$427$	1.05788e10			0.318219
$428$	3.27829e10			0.976951
$429$			3.25416e10i			0.960749i
$430$	−8.56125e10	−	4.49701e10i	−2.50417	−	1.31538i
$431$	1.21255e10			0.351390			0.175695	−	0.984445i	$-0.443783\pi$
$431$	1.21255e10			0.351390			0.175695	+	0.984445i	$0.443783\pi$
$432$			2.12285e10i			0.609516i
$433$		−	6.14766e9i		−	0.174887i	−0.996169	−	0.0874436i	$-0.972130\pi$
$433$		−	6.14766e9i		−	0.174887i	0.996169	−	0.0874436i	$-0.0278698\pi$
$434$	1.66844e10			0.470273
$435$		−	1.68865e9i		−	0.0471609i
$436$	−1.37427e10			−0.380300
$437$		−	6.03903e10i		−	1.65593i
$438$			6.09549e10i			1.65620i
$439$	2.09828e10			0.564945			0.282472	−	0.959275i	$-0.408845\pi$
$439$	2.09828e10			0.564945			0.282472	+	0.959275i	$0.408845\pi$
$440$	1.21094e10			0.323082
$441$	−4.66269e10			−1.23277
$442$			5.84084e10i			1.53033i
$443$	4.56919e10			1.18638			0.593191	−	0.805062i	$-0.297868\pi$
$443$	4.56919e10			1.18638			0.593191	+	0.805062i	$0.297868\pi$
$444$	1.21073e11			3.11540
$445$	2.89054e10			0.737122
$446$	6.63256e10			1.67626
$447$	−1.88881e10			−0.473106
$448$		−	2.41383e10i		−	0.599231i
$449$			4.66900e10i			1.14878i	0.818580	+	0.574392i	$0.194762\pi$
$449$			4.66900e10i			1.14878i	−0.818580	+	0.574392i	$0.805238\pi$
$450$		−	2.42360e11i		−	5.91031i
$451$	6.75169e9			0.163195
$452$		−	7.58226e10i		−	1.81654i
$453$	−5.50278e9			−0.130674
$454$	−2.20479e10			−0.518971
$455$	−4.06856e10			−0.949281
$456$			3.76323e10i			0.870364i
$457$		−	5.13987e10i		−	1.17839i	−0.807992	−	0.589193i	$-0.799446\pi$
$457$		−	5.13987e10i		−	1.17839i	0.807992	−	0.589193i	$-0.200554\pi$
$458$			1.07030e11i			2.43246i
$459$		−	3.29070e10i		−	0.741374i
$460$		−	1.00823e11i		−	2.25179i
$461$	−5.31807e9			−0.117747			−0.0588736	−	0.998265i	$-0.518751\pi$
$461$	−5.31807e9			−0.117747			−0.0588736	+	0.998265i	$0.518751\pi$
$462$			2.47304e10i			0.542828i
$463$			1.73963e10i			0.378558i	0.981923	+	0.189279i	$0.0606151\pi$
$463$			1.73963e10i			0.378558i	−0.981923	+	0.189279i	$0.939385\pi$
$464$		−	5.33680e8i		−	0.0115135i
$465$	1.02310e11			2.18829
$466$	−2.45419e10			−0.520432
$467$		−	1.29922e10i		−	0.273158i	−0.990629	−	0.136579i	$-0.956389\pi$
$467$		−	1.29922e10i		−	0.273158i	0.990629	−	0.136579i	$-0.0436108\pi$
$468$	−1.01871e11			−2.12357
$469$			2.82213e10i			0.583292i
$470$	−6.33111e10			−1.29744
$471$	−1.00928e11			−2.05083
$472$		−	2.73560e10i		−	0.551169i
$473$	2.33674e10	+	1.22743e10i	0.466838	+	0.245218i
$474$	1.43554e11			2.84382
$475$			2.25809e11i			4.43574i
$476$			2.43628e10i			0.474570i
$477$	1.94858e10			0.376396
$478$			1.10273e10i			0.211231i
$479$	−4.10168e10			−0.779148			−0.389574	−	0.920995i	$-0.627378\pi$
$479$	−4.10168e10			−0.779148			−0.389574	+	0.920995i	$0.627378\pi$
$480$		−	2.27235e11i		−	4.28065i
$481$		−	9.90532e10i		−	1.85050i
$482$	5.71299e10			1.05846
$483$	3.66590e10			0.673584
$484$	4.81975e10			0.878301
$485$			4.24427e9i			0.0767072i
$486$	−9.60560e10			−1.72179
$487$	−1.49123e10			−0.265112			−0.132556	−	0.991176i	$-0.542318\pi$
$487$	−1.49123e10			−0.265112			−0.132556	+	0.991176i	$0.542318\pi$
$488$	−1.33651e10			−0.235664
$489$	−1.09692e11			−1.91841
$490$	1.32145e11			2.29227
$491$		−	2.57099e10i		−	0.442359i	−0.975233	−	0.221180i	$-0.929009\pi$
$491$		−	2.57099e10i		−	0.442359i	0.975233	−	0.221180i	$-0.0709907\pi$
$492$			3.50303e10i			0.597837i
$493$			8.27274e8i			0.0140043i
$494$	1.72930e11			2.90377
$495$			9.14995e10i			1.52405i
$496$	3.23340e10			0.534235
$497$	1.34754e10			0.220860
$498$	7.97351e10			1.29638
$499$			4.88036e10i			0.787136i	0.919296	+	0.393568i	$0.128759\pi$
$499$			4.88036e10i			0.787136i	−0.919296	+	0.393568i	$0.871241\pi$
$500$			2.32530e11i			3.72048i
$501$			7.82546e10i			1.24211i
$502$		−	1.58802e11i		−	2.50059i
$503$		−	6.69023e10i		−	1.04513i	−0.852601	−	0.522563i	$-0.824976\pi$
$503$		−	6.69023e10i		−	1.04513i	0.852601	−	0.522563i	$-0.175024\pi$
$504$	−1.37834e10			−0.213616
$505$		−	5.69679e10i		−	0.875921i
$506$			5.01387e10i			0.764841i
$507$			3.32165e10i			0.502716i
$508$	−1.29065e11			−1.93800
$509$	−3.93507e9			−0.0586248			−0.0293124	−	0.999570i	$-0.509332\pi$
$509$	−3.93507e9			−0.0586248			−0.0293124	+	0.999570i	$0.509332\pi$
$510$			2.72192e11i			4.02341i
$511$	2.08010e10			0.305070
$512$		−	8.81363e10i		−	1.28255i
$513$	−9.74278e10			−1.40674
$514$	−1.27267e11			−1.82332
$515$			3.38452e10i			0.481136i
$516$	−6.36837e10	+	1.21239e11i	−0.898316	+	1.71018i
$517$	1.72804e10			0.241875
$518$		−	7.52767e10i		−	1.04554i
$519$		−	1.86593e11i		−	2.57173i
$520$	5.14016e10			0.703012
$521$			2.38175e10i			0.323256i	0.986852	+	0.161628i	$0.0516744\pi$
$521$			2.38175e10i			0.323256i	−0.986852	+	0.161628i	$0.948326\pi$
$522$	−2.62884e9			−0.0354064
$523$		−	8.63612e10i		−	1.15428i	−0.816645	−	0.577141i	$-0.804168\pi$
$523$		−	8.63612e10i		−	1.15428i	0.816645	−	0.577141i	$-0.195832\pi$
$524$		−	2.29807e10i		−	0.304817i
$525$	−1.37074e11			−1.80434
$526$	−3.46643e10			−0.452834
$527$	−5.01219e10			−0.649808
$528$			4.79270e10i			0.616658i
$529$	−3.98798e9			−0.0509250
$530$	−5.52244e10			−0.699887
$531$	2.06704e11			2.59998
$532$	7.21311e10			0.900484
$533$	2.86593e10			0.355105
$534$		−	7.45801e10i		−	0.917187i
$535$		−	1.24988e11i		−	1.52565i
$536$		−	3.56544e10i		−	0.431971i
$537$	−5.61422e10			−0.675138
$538$			8.70861e10i			1.03949i
$539$	−3.60681e10			−0.427335
$540$	−1.62658e11			−1.91294
$541$	1.11202e11			1.29815			0.649074	−	0.760725i	$-0.275157\pi$
$541$	1.11202e11			1.29815			0.649074	+	0.760725i	$0.275157\pi$
$542$			1.83456e11i			2.12586i
$543$			1.45073e11i			1.66873i
$544$			1.11323e11i			1.27113i
$545$			5.23955e10i			0.593892i
$546$			1.04975e11i			1.18117i
$547$	−4.80348e10			−0.536546			−0.268273	−	0.963343i	$-0.586453\pi$
$547$	−4.80348e10			−0.536546			−0.268273	+	0.963343i	$0.586453\pi$
$548$			1.19278e11i			1.32262i
$549$		−	1.00988e11i		−	1.11168i
$550$		−	1.87477e11i		−	2.04879i
$551$	2.44931e9			0.0265728
$552$	−4.63145e10			−0.498839
$553$		−	4.89880e10i		−	0.523829i
$554$	5.18945e10			0.550912
$555$		−	4.61602e11i		−	4.86515i
$556$	4.02288e10			0.420957
$557$	−4.60143e10			−0.478049			−0.239024	−	0.971014i	$-0.576828\pi$
$557$	−4.60143e10			−0.478049			−0.239024	+	0.971014i	$0.576828\pi$
$558$		−	1.59273e11i		−	1.64287i
$559$	9.91892e10	+	5.21016e10i	1.01582	+	0.533585i
$560$	−5.99213e10			−0.609297
$561$		−	7.42931e10i		−	0.750062i
$562$		−	5.86138e10i		−	0.587563i
$563$	3.36946e10			0.335372			0.167686	−	0.985840i	$-0.446371\pi$
$563$	3.36946e10			0.335372			0.167686	+	0.985840i	$0.446371\pi$
$564$			8.96569e10i			0.886069i
$565$	−2.89082e11			−2.83679
$566$			6.09261e10i			0.593660i
$567$			9.32153e9i			0.0901893i
$568$	−1.70246e10			−0.163563
$569$	−4.56726e10			−0.435719			−0.217860	−	0.975980i	$-0.569907\pi$
$569$	−4.56726e10			−0.435719			−0.217860	+	0.975980i	$0.569907\pi$
$570$	8.05878e11			7.63431
$571$		−	1.77572e10i		−	0.167043i	−0.996506	−	0.0835217i	$-0.973383\pi$
$571$		−	1.77572e10i		−	0.167043i	0.996506	−	0.0835217i	$-0.0266168\pi$
$572$	−7.88020e10			−0.736128
$573$	−2.52790e11			−2.34499
$574$	2.17800e10			0.200637
$575$	−2.77906e11			−2.54229
$576$	−2.30430e11			−2.09338
$577$			1.55926e11i			1.40675i	0.710821	+	0.703373i	$0.248323\pi$
$577$			1.55926e11i			1.40675i	−0.710821	+	0.703373i	$0.751677\pi$
$578$			3.28234e10i			0.294085i
$579$			5.62472e10i			0.500480i
$580$	4.08919e9			0.0361348
$581$		−	2.72098e10i		−	0.238792i
$582$	1.09508e10			0.0954454
$583$	1.50732e10			0.130476
$584$	−2.62797e10			−0.225927
$585$			3.88394e11i			3.31626i
$586$		−	1.95654e11i		−	1.65920i
$587$		−	2.42355e10i		−	0.204127i	−0.994778	−	0.102063i	$-0.967456\pi$
$587$		−	2.42355e10i		−	0.204127i	0.994778	−	0.102063i	$-0.0325445\pi$
$588$		−	1.87134e11i		−	1.56547i
$589$			1.48396e11i			1.23299i
$590$	−5.85817e11			−4.83452
$591$		−	2.54954e11i		−	2.08983i
$592$		−	1.45885e11i		−	1.18774i
$593$			6.73194e10i			0.544404i	0.962240	+	0.272202i	$0.0877519\pi$
$593$			6.73194e10i			0.544404i	−0.962240	+	0.272202i	$0.912248\pi$
$594$	8.08889e10			0.649746
$595$	9.28859e10			0.741109
$596$		−	4.57390e10i		−	0.362495i
$597$	3.91988e11			3.08585
$598$			2.12827e11i			1.66426i
$599$	6.22767e10			0.483747			0.241874	−	0.970308i	$-0.422238\pi$
$599$	6.22767e10			0.483747			0.241874	+	0.970308i	$0.422238\pi$
$600$	1.73177e11			1.33624
$601$			1.57836e11i			1.20979i	0.796307	+	0.604893i	$0.206784\pi$
$601$			1.57836e11i			1.20979i	−0.796307	+	0.604893i	$0.793216\pi$
$602$	7.53800e10	+	3.95952e10i	0.573945	+	0.301479i
$603$	2.69407e11			2.03770
$604$		−	1.33254e10i		−	0.100123i
$605$		−	1.83758e11i		−	1.37159i
$606$	−1.46985e11			−1.08989
$607$			1.00707e11i			0.741833i	0.928666	+	0.370917i	$0.120956\pi$
$607$			1.00707e11i			0.741833i	−0.928666	+	0.370917i	$0.879044\pi$
$608$	3.29595e11			2.41194
$609$			1.48682e9i			0.0108091i
$610$			2.86208e11i			2.06711i
$611$	7.33511e10			0.526310
$612$	2.32573e11			1.65788
$613$	−1.80424e11			−1.27777			−0.638884	−	0.769303i	$-0.720604\pi$
$613$	−1.80424e11			−1.27777			−0.638884	+	0.769303i	$0.720604\pi$
$614$		−	2.93936e11i		−	2.06814i
$615$	1.33557e11			0.933608
$616$	−1.06621e10			−0.0740490
$617$	3.85259e10			0.265835			0.132918	−	0.991127i	$-0.457565\pi$
$617$	3.85259e10			0.265835			0.132918	+	0.991127i	$0.457565\pi$
$618$	8.73254e10			0.598669
$619$	−5.48744e9			−0.0373773			−0.0186886	−	0.999825i	$-0.505949\pi$
$619$	−5.48744e9			−0.0373773			−0.0186886	+	0.999825i	$0.505949\pi$
$620$			2.47751e11i			1.67667i
$621$		−	1.19906e11i		−	0.806256i
$622$		−	3.53180e11i		−	2.35958i
$623$	−2.54506e10			−0.168945
$624$			2.03439e11i			1.34182i
$625$	4.88351e11			3.20046
$626$	−1.05731e10			−0.0688500
$627$	−2.19960e11			−1.42322
$628$		−	2.44406e11i		−	1.57135i
$629$			2.26140e11i			1.44469i
$630$			2.95164e11i			1.87371i
$631$			1.07158e11i			0.675936i	0.941158	+	0.337968i	$0.109740\pi$
$631$			1.07158e11i			0.675936i	−0.941158	+	0.337968i	$0.890260\pi$
$632$			6.18908e10i			0.387934i
$633$	−3.85295e10			−0.239982
$634$		−	4.03758e11i		−	2.49899i
$635$			4.92075e11i			3.02647i
$636$			7.82052e10i			0.477977i
$637$	−1.53101e11			−0.929863
$638$	−2.03353e9			−0.0122735
$639$		−	1.28639e11i		−	0.771561i
$640$	2.00759e11			1.19662
$641$			3.02938e10i			0.179441i	0.995967	+	0.0897203i	$0.0285973\pi$
$641$			3.02938e10i			0.179441i	−0.995967	+	0.0897203i	$0.971403\pi$
$642$	−3.22488e11			−1.89834
$643$	5.55577e10			0.325013			0.162506	−	0.986707i	$-0.448042\pi$
$643$	5.55577e10			0.325013			0.162506	+	0.986707i	$0.448042\pi$
$644$			8.87726e10i			0.516102i
$645$	4.62236e11	+	2.42801e11i	2.67070	+	1.40285i
$646$	−3.94802e11			−2.26699
$647$		−	2.27072e10i		−	0.129583i	−0.997899	−	0.0647913i	$-0.979362\pi$
$647$		−	2.27072e10i		−	0.129583i	0.997899	−	0.0647913i	$-0.0206382\pi$
$648$		−	1.17767e10i		−	0.0667919i
$649$	1.59895e11			0.901274
$650$		−	7.95794e11i		−	4.45807i
$651$	−9.00815e10			−0.501547
$652$		−	2.65629e11i		−	1.46989i
$653$			6.93373e10i			0.381341i	0.981654	+	0.190671i	$0.0610663\pi$
$653$			6.93373e10i			0.381341i	−0.981654	+	0.190671i	$0.938934\pi$
$654$	1.35188e11			0.738969
$655$	−8.76164e10			−0.476015
$656$	4.22092e10			0.227925
$657$		−	1.98571e11i		−	1.06575i
$658$	5.57440e10			0.297368
$659$	7.72055e10			0.409361			0.204680	−	0.978829i	$-0.434384\pi$
$659$	7.72055e10			0.409361			0.204680	+	0.978829i	$0.434384\pi$
$660$	−3.67228e11			−1.93535
$661$	−1.37353e11			−0.719501			−0.359750	−	0.933049i	$-0.617138\pi$
$661$	−1.37353e11			−0.719501			−0.359750	+	0.933049i	$0.617138\pi$
$662$	2.90144e11			1.51071
$663$		−	3.15357e11i		−	1.63210i
$664$			3.43764e10i			0.176843i
$665$		−	2.75007e11i		−	1.40623i
$666$	−7.18608e11			−3.65254
$667$			3.01440e9i			0.0152299i
$668$	−1.89500e11			−0.951705
$669$	−3.58102e11			−1.78773
$670$	−7.63524e11			−3.78899
$671$		−	7.81188e10i		−	0.385359i
$672$			2.00075e11i			0.981108i
$673$		−	1.37895e11i		−	0.672184i	−0.941829	−	0.336092i	$-0.890895\pi$
$673$		−	1.37895e11i		−	0.672184i	0.941829	−	0.336092i	$-0.109105\pi$
$674$		−	2.54524e11i		−	1.23336i
$675$			4.48346e11i			2.15972i
$676$	−8.04364e10			−0.385182
$677$		−	2.93763e11i		−	1.39844i	−0.714908	−	0.699218i	$-0.753532\pi$
$677$		−	2.93763e11i		−	1.39844i	0.714908	−	0.699218i	$-0.246468\pi$
$678$			7.45872e11i			3.52976i
$679$		−	3.73699e9i		−	0.0175810i
$680$	−1.17351e11			−0.548846
$681$	1.19040e11			0.553483
$682$		−	1.23205e11i		−	0.569496i
$683$	−1.66608e11			−0.765619			−0.382810	−	0.923827i	$-0.625044\pi$
$683$	−1.66608e11			−0.765619			−0.382810	+	0.923827i	$0.625044\pi$
$684$		−	6.88580e11i		−	3.14579i
$685$	4.54758e11			2.06547
$686$	−2.59925e11			−1.17368
$687$		−	5.77875e11i		−	2.59422i
$688$	1.46085e11	+	7.67347e10i	0.652006	+	0.342482i
$689$	6.39821e10			0.283911
$690$			9.91803e11i			4.37552i
$691$			3.05698e11i			1.34085i	0.741977	+	0.670425i	$0.233888\pi$
$691$			3.05698e11i			1.34085i	−0.741977	+	0.670425i	$0.766112\pi$
$692$	4.51849e11			1.97047
$693$		−	8.05634e10i		−	0.349305i
$694$	1.16323e11			0.501452
$695$		−	1.53377e11i		−	0.657385i
$696$		−	1.87843e9i		−	0.00800492i
$697$	−6.54298e10			−0.277233
$698$	3.82746e11			1.61246
$699$	1.32505e11			0.555041
$700$		−	3.31935e11i		−	1.38249i
$701$	2.10620e11			0.872221			0.436111	−	0.899893i	$-0.356356\pi$
$701$	2.10620e11			0.872221			0.436111	+	0.899893i	$0.356356\pi$
$702$	3.43354e11			1.41382
$703$	6.69534e11			2.74127
$704$	−1.78248e11			−0.725663
$705$	3.41827e11			1.38372
$706$		−	3.60869e11i		−	1.45255i
$707$			5.01590e10i			0.200757i
$708$			8.29595e11i			3.30166i
$709$	−3.74546e11			−1.48225			−0.741123	−	0.671369i	$-0.765707\pi$
$709$	−3.74546e11			−1.48225			−0.741123	+	0.671369i	$0.765707\pi$
$710$			3.64575e11i			1.43468i
$711$	−4.67651e11			−1.82997
$712$	3.21539e10			0.125116
$713$	−1.82633e11			−0.706676
$714$		−	2.39659e11i		−	0.922148i
$715$			3.00441e11i			1.14957i
$716$		−	1.35953e11i		−	0.517292i
$717$		−	5.95383e10i		−	0.225279i
$718$			3.62141e11i			1.36264i
$719$	−7.82761e10			−0.292896			−0.146448	−	0.989218i	$-0.546784\pi$
$719$	−7.82761e10			−0.292896			−0.146448	+	0.989218i	$0.546784\pi$
$720$			5.72023e11i			2.12855i
$721$		−	2.98000e10i		−	0.110274i
$722$			7.64323e11i			2.81273i
$723$	−3.08454e11			−1.12885
$724$	−3.51305e11			−1.27859
$725$		−	1.12713e10i		−	0.0407965i
$726$	−4.74122e11			−1.70665
$727$			3.82480e11i			1.36921i	0.728913	+	0.684606i	$0.240026\pi$
$727$			3.82480e11i			1.36921i	−0.728913	+	0.684606i	$0.759974\pi$
$728$	−4.52580e10			−0.161127
$729$	4.60125e11			1.62917
$730$			5.62767e11i			1.98170i
$731$	−2.26451e11	−	1.18949e11i	−0.793057	−	0.416573i
$732$	4.05309e11			1.41170
$733$		−	1.33780e11i		−	0.463421i	−0.972785	−	0.231711i	$-0.925568\pi$
$733$		−	1.33780e11i		−	0.463421i	0.972785	−	0.231711i	$-0.0744322\pi$
$734$			2.35308e11i			0.810686i
$735$	−7.13470e11			−2.44470
$736$			4.05636e11i			1.38237i
$737$	2.08399e11			0.706360
$738$		−	2.07917e11i		−	0.700913i
$739$		−	1.57627e11i		−	0.528509i	−0.964453	−	0.264254i	$-0.914874\pi$
$739$		−	1.57627e11i		−	0.528509i	0.964453	−	0.264254i	$-0.0851259\pi$
$740$	1.11780e12			3.72768
$741$	−9.33676e11			−3.09687
$742$	4.86239e10			0.160411
$743$		−	1.29006e11i		−	0.423307i	−0.977345	−	0.211654i	$-0.932115\pi$
$743$		−	1.29006e11i		−	0.423307i	0.977345	−	0.211654i	$-0.0678848\pi$
$744$	1.13808e11			0.371433
$745$	−1.74385e11			−0.566088
$746$	−6.38068e11			−2.06021
$747$	−2.59751e11			−0.834208
$748$	1.79906e11			0.574699
$749$			1.10050e11i			0.349672i
$750$		−	2.28741e12i		−	7.22936i
$751$		−	2.48684e11i		−	0.781788i	−0.920436	−	0.390894i	$-0.872166\pi$
$751$		−	2.48684e11i		−	0.781788i	0.920436	−	0.390894i	$-0.127834\pi$
$752$	1.08031e11			0.337813
$753$			8.57400e11i			2.66688i
$754$	−8.63185e9			−0.0267066
$755$	−5.08045e10			−0.156356
$756$	1.43217e11			0.438438
$757$		−	1.23839e11i		−	0.377117i	−0.982062	−	0.188558i	$-0.939619\pi$
$757$		−	1.23839e11i		−	0.377117i	0.982062	−	0.188558i	$-0.0603814\pi$
$758$		−	3.73529e11i		−	1.13148i
$759$		−	2.70707e11i		−	0.815703i
$760$			3.47441e11i			1.04142i
$761$		−	2.24574e9i		−	0.00669608i	−0.999994	−	0.00334804i	$-0.998934\pi$
$761$		−	2.24574e9i		−	0.00669608i	0.999994	−	0.00334804i	$-0.00106572\pi$
$762$	1.26962e12			3.76578
$763$		−	4.61331e10i		−	0.136118i
$764$		−	6.12151e11i		−	1.79674i
$765$		−	8.86710e11i		−	2.58902i
$766$	−7.04705e11			−2.04688
$767$	6.78717e11			1.96113
$768$			2.42177e11i			0.696125i
$769$	−2.16341e10			−0.0618635			−0.0309317	−	0.999521i	$-0.509847\pi$
$769$	−2.16341e10			−0.0618635			−0.0309317	+	0.999521i	$0.509847\pi$
$770$			2.28324e11i			0.649513i
$771$	6.87133e11			1.94457
$772$	−1.36207e11			−0.383469
$773$		−	1.23331e11i		−	0.345425i	−0.984972	−	0.172712i	$-0.944747\pi$
$773$		−	1.23331e11i		−	0.345425i	0.984972	−	0.172712i	$-0.0552531\pi$
$774$	3.77985e11	−	7.19595e11i	1.05320	−	2.00504i
$775$	6.82892e11			1.89298
$776$			4.72126e9i			0.0130200i
$777$			4.06431e11i			1.11507i
$778$	−4.57914e11			−1.24987
$779$			1.93718e11i			0.526042i
$780$	−1.55880e12			−4.21125
$781$		−	9.95086e10i		−	0.267459i
$782$		−	4.85888e11i		−	1.29930i
$783$	4.86314e9			0.0129381
$784$	−2.25485e11			−0.596834
$785$	−9.31823e11			−2.45389
$786$			2.26063e11i			0.592296i
$787$	−2.14761e11			−0.559831			−0.279915	−	0.960025i	$-0.590306\pi$
$787$	−2.14761e11			−0.559831			−0.279915	+	0.960025i	$0.590306\pi$
$788$	6.17391e11			1.60124
$789$	1.87158e11			0.482948
$790$	1.32536e12			3.40272
$791$	2.54530e11			0.650180
$792$			1.01783e11i			0.258686i
$793$		−	3.31596e11i		−	0.838526i
$794$			6.59766e11i			1.66000i
$795$	2.98166e11			0.746430
$796$			9.49229e11i			2.36439i
$797$	4.86223e11			1.20504			0.602521	−	0.798103i	$-0.294163\pi$
$797$	4.86223e11			1.20504			0.602521	+	0.798103i	$0.294163\pi$
$798$	−7.09558e11			−1.74975
$799$	−1.67462e11			−0.410893
$800$		−	1.51674e12i		−	3.70297i
$801$			2.42957e11i			0.590201i
$802$			8.45940e11i			2.04476i
$803$		−	1.53604e11i		−	0.369437i
$804$			1.08125e12i			2.58763i
$805$	3.38455e11			0.805967
$806$		−	5.22976e11i		−	1.23920i
$807$		−	4.70192e11i		−	1.10862i
$808$		−	6.33702e10i		−	0.148676i
$809$	4.55725e11			1.06392			0.531959	−	0.846770i	$-0.321456\pi$
$809$	4.55725e11			1.06392			0.531959	+	0.846770i	$0.321456\pi$
$810$	−2.52193e11			−0.585858
$811$			3.83583e10i			0.0886698i	0.999017	+	0.0443349i	$0.0141169\pi$
$811$			3.83583e10i			0.0886698i	−0.999017	+	0.0443349i	$0.985883\pi$
$812$	−3.60044e9			−0.00828194
$813$		−	9.90510e11i		−	2.26724i
$814$	−5.55877e11			−1.26614
$815$	−1.01274e12			−2.29544
$816$		−	4.64454e11i		−	1.04757i
$817$	−3.52172e11	+	6.70453e11i	−0.790436	+	1.50480i
$818$	−1.33793e11			−0.298827
$819$		−	3.41972e11i		−	0.760073i
$820$			3.23417e11i			0.715333i
$821$	7.24878e11			1.59548			0.797741	−	0.603000i	$-0.206028\pi$
$821$	7.24878e11			1.59548			0.797741	+	0.603000i	$0.206028\pi$
$822$		−	1.17334e12i		−	2.57002i
$823$	4.18426e11			0.912052			0.456026	−	0.889967i	$-0.349272\pi$
$823$	4.18426e11			0.912052			0.456026	+	0.889967i	$0.349272\pi$
$824$			3.76489e10i			0.0816663i
$825$			1.01222e12i			2.18503i
$826$	5.15799e11			1.10805
$827$	−1.75466e11			−0.375122			−0.187561	−	0.982253i	$-0.560058\pi$
$827$	−1.75466e11			−0.375122			−0.187561	+	0.982253i	$0.560058\pi$
$828$	8.47444e11			1.80297
$829$		−	3.36853e10i		−	0.0713217i	−0.999364	−	0.0356608i	$-0.988646\pi$
$829$		−	3.36853e10i		−	0.0713217i	0.999364	−	0.0356608i	$-0.0113536\pi$
$830$	7.36156e11			1.55116
$831$	−2.80187e11			−0.587549
$832$	−7.56622e11			−1.57901
$833$	3.49531e11			0.725949
$834$	−3.95733e11			−0.817972
$835$			7.22487e11i			1.48622i
$836$		−	5.32649e11i		−	1.09048i
$837$			2.94642e11i			0.600333i
$838$	7.25880e11			1.47194
$839$		−	4.53076e11i		−	0.914372i	−0.889371	−	0.457186i	$-0.848857\pi$
$839$		−	4.53076e11i		−	0.914372i	0.889371	−	0.457186i	$-0.151143\pi$
$840$	−2.10909e11			−0.423621
$841$	5.00124e11			0.999756
$842$	7.11996e11			1.41654
$843$			3.16465e11i			0.626637i
$844$		−	9.33022e10i		−	0.183875i
$845$			3.06672e11i			0.601517i
$846$		−	5.32145e11i		−	1.03884i
$847$			1.61795e11i			0.314363i
$848$	9.42323e10			0.182228
$849$		−	3.28950e11i		−	0.633139i
$850$			1.81681e12i			3.48044i
$851$			8.24004e11i			1.57113i
$852$	5.16287e11			0.979790
$853$	−9.50642e11			−1.79565			−0.897824	−	0.440355i	$-0.854853\pi$
$853$	−9.50642e11			−1.79565			−0.897824	+	0.440355i	$0.854853\pi$
$854$		−	2.52000e11i		−	0.473772i
$855$	−2.62528e12			−4.91260
$856$		−	1.39035e11i		−	0.258958i
$857$	−6.23613e11			−1.15609			−0.578045	−	0.816005i	$-0.696184\pi$
$857$	−6.23613e11			−1.15609			−0.578045	+	0.816005i	$0.696184\pi$
$858$	7.75180e11			1.43039
$859$			7.70810e11i			1.41571i	0.706357	+	0.707855i	$0.250337\pi$
$859$			7.70810e11i			1.41571i	−0.706357	+	0.707855i	$0.749663\pi$
$860$	−5.87960e11	+	1.11934e12i	−1.07487	+	2.04629i
$861$	−1.17594e11			−0.213979
$862$		−	2.88843e11i		−	0.523159i
$863$			9.80353e11i			1.76742i	0.468037	+	0.883709i	$0.344961\pi$
$863$			9.80353e11i			1.76742i	−0.468037	+	0.883709i	$0.655039\pi$
$864$	6.54414e11			1.17435
$865$		−	1.72272e12i		−	3.07716i
$866$	−1.46445e11			−0.260377
$867$		−	1.77219e11i		−	0.313641i
$868$		−	2.18139e11i		−	0.384286i
$869$	−3.61750e11			−0.634351
$870$	−4.02256e10			−0.0702143
$871$	8.84606e11			1.53701
$872$			5.82839e10i			0.100805i
$873$	−3.56742e10			−0.0614182
$874$	−1.43857e12			−2.46539
$875$	−7.80584e11			−1.33164
$876$	7.96954e11			1.35337
$877$	1.96302e11			0.331839			0.165919	−	0.986139i	$-0.446941\pi$
$877$	1.96302e11			0.331839			0.165919	+	0.986139i	$0.446941\pi$
$878$		−	4.99836e11i		−	0.841104i
$879$			1.05637e12i			1.76954i
$880$			4.42487e11i			0.737852i
$881$	−1.18673e12			−1.96992			−0.984962	−	0.172771i	$-0.944728\pi$
$881$	−1.18673e12			−1.96992			−0.984962	+	0.172771i	$0.944728\pi$
$882$			1.11071e12i			1.83538i
$883$	2.15504e11			0.354497			0.177249	−	0.984166i	$-0.443280\pi$
$883$	2.15504e11			0.354497			0.177249	+	0.984166i	$0.443280\pi$
$884$	7.63660e11			1.25052
$885$	3.16292e12			5.15602
$886$		−	1.08844e12i		−	1.76632i
$887$		−	2.28915e11i		−	0.369812i	−0.982756	−	0.184906i	$-0.940802\pi$
$887$		−	2.28915e11i		−	0.369812i	0.982756	−	0.184906i	$-0.0591980\pi$
$888$		−	5.13479e11i		−	0.825792i
$889$		−	4.33262e11i		−	0.693655i
$890$		−	6.88562e11i		−	1.09745i
$891$	6.88345e10			0.109218
$892$		−	8.67172e11i		−	1.36976i
$893$			4.95805e11i			0.779660i
$894$			4.49938e11i			0.704373i
$895$	−5.18334e11			−0.807826
$896$	−1.76764e11			−0.274260
$897$		−	1.14909e12i		−	1.77494i
$898$	1.11221e12			1.71034
$899$		−	7.40722e9i		−	0.0113401i
$900$	−3.16873e12			−4.82964
$901$	−1.46072e11			−0.221651
$902$		−	1.60834e11i		−	0.242969i
$903$	−4.06989e11	−	2.13781e11i	−0.612112	−	0.321527i
$904$	−3.21570e11			−0.481506
$905$			1.33939e12i			1.99669i
$906$			1.31083e11i			0.194551i
$907$	−1.53390e11			−0.226657			−0.113328	−	0.993558i	$-0.536151\pi$
$907$	−1.53390e11			−0.226657			−0.113328	+	0.993558i	$0.536151\pi$
$908$			2.88264e11i			0.424080i
$909$	4.78830e11			0.701335
$910$			9.69179e11i			1.41331i
$911$			1.45999e11i			0.211971i	0.994368	+	0.105985i	$0.0337997\pi$
$911$			1.45999e11i			0.211971i	−0.994368	+	0.105985i	$0.966200\pi$
$912$	−1.37511e12			−1.98773
$913$	−2.00929e11			−0.289175
$914$	−1.22438e12			−1.75441
$915$		−	1.54528e12i		−	2.20457i
$916$	1.39937e12			1.98770
$917$	7.71444e10			0.109101
$918$	−7.83885e11			−1.10378
$919$	−1.10838e11			−0.155391			−0.0776957	−	0.996977i	$-0.524756\pi$
$919$	−1.10838e11			−0.155391			−0.0776957	+	0.996977i	$0.524756\pi$
$920$	−4.27599e11			−0.596878
$921$			1.58701e12i			2.20567i
$922$			1.26683e11i			0.175305i
$923$		−	4.22391e11i		−	0.581979i
$924$	3.23337e11			0.443575
$925$		−	3.08108e12i		−	4.20859i
$926$	4.14401e11			0.563607
$927$	−2.84477e11			−0.385238
$928$	−1.64518e10			−0.0221831
$929$			1.01988e12i			1.36927i	0.728888	+	0.684633i	$0.240037\pi$
$929$			1.01988e12i			1.36927i	−0.728888	+	0.684633i	$0.759963\pi$
$930$		−	2.43714e12i		−	3.25798i
$931$		−	1.03486e12i		−	1.37747i
$932$			3.20872e11i			0.425273i
$933$			1.90688e12i			2.51649i
$934$	−3.09489e11			−0.406685
$935$		−	6.85912e11i		−	0.897475i
$936$			4.32043e11i			0.562890i
$937$			7.67098e11i			0.995158i	0.867419	+	0.497579i	$0.165778\pi$
$937$			7.67098e11i			0.995158i	−0.867419	+	0.497579i	$0.834222\pi$
$938$	6.72266e11			0.868420
$939$	5.70857e10			0.0734286
$940$			8.27759e11i			1.06021i
$941$	−4.08673e11			−0.521215			−0.260608	−	0.965445i	$-0.583923\pi$
$941$	−4.08673e11			−0.521215			−0.260608	+	0.965445i	$0.583923\pi$
$942$			2.40424e12i			3.05333i
$943$	−2.38411e11			−0.301495
$944$	9.99609e11			1.25876
$945$		−	5.46030e11i		−	0.684683i
$946$	2.92389e11	−	5.56640e11i	0.365087	−	0.695041i
$947$	6.69336e11			0.832231			0.416116	−	0.909312i	$-0.363391\pi$
$947$	6.69336e11			0.832231			0.416116	+	0.909312i	$0.363391\pi$
$948$		−	1.87689e12i		−	2.32384i
$949$		−	6.52012e11i		−	0.803880i
$950$	5.37904e12			6.60405
$951$			2.17996e12i			2.66517i
$952$	1.03325e11			0.125793
$953$		−	6.17905e11i		−	0.749118i	−0.927203	−	0.374559i	$-0.877794\pi$
$953$		−	6.17905e11i		−	0.749118i	0.927203	−	0.374559i	$-0.122206\pi$
$954$		−	4.64175e11i		−	0.560388i
$955$	−2.33389e12			−2.80586
$956$	1.44177e11			0.172609
$957$	1.09793e10			0.0130897
$958$			9.77070e11i			1.16002i
$959$	−4.00405e11			−0.473396
$960$	−3.52596e12			−4.15138
$961$	−4.04111e11			−0.473814
$962$	−2.35957e12			−2.75507
$963$	1.05056e12			1.22156
$964$		−	7.46945e11i		−	0.864928i
$965$			5.19303e11i			0.598841i
$966$		−	8.73262e11i		−	1.00285i
$967$	1.66198e12			1.90072			0.950362	−	0.311145i	$-0.100713\pi$
$967$	1.66198e12			1.90072			0.950362	+	0.311145i	$0.100713\pi$
$968$		−	2.04410e11i		−	0.232809i
$969$	2.13160e12			2.41775
$970$	1.01104e11			0.114204
$971$	1.24122e11			0.139628			0.0698138	−	0.997560i	$-0.477759\pi$
$971$	1.24122e11			0.139628			0.0698138	+	0.997560i	$0.477759\pi$
$972$			1.25588e12i			1.40697i
$973$			1.35045e11i			0.150670i
$974$			3.55230e11i			0.394706i
$975$			4.29662e12i			4.75454i
$976$		−	4.88372e11i		−	0.538209i
$977$	−7.69622e11			−0.844694			−0.422347	−	0.906434i	$-0.638794\pi$
$977$	−7.69622e11			−0.844694			−0.422347	+	0.906434i	$0.638794\pi$
$978$			2.61301e12i			2.85618i
$979$			1.87939e11i			0.204591i
$980$		−	1.72772e12i		−	1.87314i
$981$	−4.40397e11			−0.475520
$982$	−6.12442e11			−0.658596
$983$		−	5.29094e11i		−	0.566655i	−0.959023	−	0.283327i	$-0.908562\pi$
$983$		−	5.29094e11i		−	0.566655i	0.959023	−	0.283327i	$-0.0914383\pi$
$984$	1.48566e11			0.158467
$985$		−	2.35387e12i		−	2.50056i
$986$	1.97067e10			0.0208500
$987$	−3.00971e11			−0.317144
$988$		−	2.26097e12i		−	2.37283i
$989$	−8.25135e11	−	4.33422e11i	−0.862461	−	0.453029i
$990$	2.17963e12			2.26904
$991$		−	9.90323e11i		−	1.02679i	−0.858152	−	0.513396i	$-0.828387\pi$
$991$		−	9.90323e11i		−	1.02679i	0.858152	−	0.513396i	$-0.171613\pi$
$992$		−	9.96762e11i		−	1.02931i
$993$	−1.56654e12			−1.61118
$994$		−	3.21001e11i		−	0.328822i
$995$	3.61904e12			3.69233
$996$		−	1.04250e12i		−	1.05934i
$997$		−	1.72782e12i		−	1.74871i	−0.485285	−	0.874356i	$-0.661284\pi$
$997$		−	1.72782e12i		−	1.74871i	0.485285	−	0.874356i	$-0.338716\pi$
$998$	1.16256e12			1.17191
$999$	1.32937e12			1.33470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.9.b.b.42.5	✓	28
43.42	odd	2	inner	43.9.b.b.42.24	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.9.b.b.42.5	✓	28	1.1	even	1	trivial
43.9.b.b.42.24	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)

\(f(q)\)	\(=\)	\(q-23.8212i q^{2} +128.615i q^{3} -311.450 q^{4} +1187.44i q^{5} +3063.75 q^{6} -1045.51i q^{7} +1320.89i q^{8} -9980.70 q^{9} +O(q^{10})\)	\(q-23.8212i q^{2} +128.615i q^{3} -311.450 q^{4} +1187.44i q^{5} +3063.75 q^{6} -1045.51i q^{7} +1320.89i q^{8} -9980.70 q^{9} +28286.2 q^{10} -7720.54 q^{11} -40057.0i q^{12} -32771.9 q^{13} -24905.4 q^{14} -152722. q^{15} -48266.1 q^{16} +74818.8 q^{17} +237752. i q^{18} -221516. i q^{19} -369827. i q^{20} +134468. q^{21} +183913. i q^{22} +272622. q^{23} -169885. q^{24} -1.01938e6 q^{25} +780665. i q^{26} -439823. i q^{27} +325625. i q^{28} +11057.0i q^{29} +3.63801e6i q^{30} -669910. q^{31} +1.48790e6i q^{32} -992974. i q^{33} -1.78227e6i q^{34} +1.24148e6 q^{35} +3.10849e6 q^{36} +3.02251e6i q^{37} -5.27678e6 q^{38} -4.21494e6i q^{39} -1.56847e6 q^{40} -874510. q^{41} -3.20319e6i q^{42} +(-3.02666e6 - 1.58983e6i) q^{43} +2.40456e6 q^{44} -1.18514e7i q^{45} -6.49420e6i q^{46} -2.23823e6 q^{47} -6.20772e6i q^{48} +4.67171e6 q^{49} +2.42828e7i q^{50} +9.62278e6i q^{51} +1.02068e7 q^{52} -1.95235e6 q^{53} -1.04771e7 q^{54} -9.16765e6i q^{55} +1.38100e6 q^{56} +2.84902e7 q^{57} +263392. q^{58} -2.07104e7 q^{59} +4.75651e7 q^{60} +1.01183e7i q^{61} +1.59581e7i q^{62} +1.04349e7i q^{63} +2.30875e7 q^{64} -3.89145e7i q^{65} -2.36538e7 q^{66} -2.69928e7 q^{67} -2.33023e7 q^{68} +3.50632e7i q^{69} -2.95735e7i q^{70} +1.28888e7i q^{71} -1.31834e7i q^{72} +1.98955e7i q^{73} +7.19998e7 q^{74} -1.31107e8i q^{75} +6.89912e7i q^{76} +8.07192e6i q^{77} -1.00405e8 q^{78} +4.68555e7 q^{79} -5.73129e7i q^{80} -8.91576e6 q^{81} +2.08319e7i q^{82} +2.60253e7 q^{83} -4.18801e7 q^{84} +8.88425e7i q^{85} +(-3.78716e7 + 7.20986e7i) q^{86} -1.42210e6 q^{87} -1.01979e7i q^{88} -2.43427e7i q^{89} -2.82316e8 q^{90} +3.42634e7i q^{91} -8.49083e7 q^{92} -8.61602e7i q^{93} +5.33175e7i q^{94} +2.63036e8 q^{95} -1.91366e8 q^{96} +3.57432e6 q^{97} -1.11286e8i q^{98} +7.70564e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4284 q^{4} - 1794 q^{6} - 80754 q^{9}+O(q^{10}) \) 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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