LMFDB - Embedded newform 100.9.b.g.51.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(51,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.51"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 94 x^{18} + 5343 x^{16} - 172772 x^{14} + 36131456 x^{12} - 3044563968 x^{10} + \cdots + 11\!\cdots\!76 $ x^20 - 94x^18 + 5343x^16 - 172772x^14 + 36131456x^12 - 3044563968x^10 + 147994443776x^8 - 2898633162752x^6 + 367168164200448x^4 - 26458647810801664*x^2 + 1152921504606846976
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{75}\cdot 3^{4}\cdot 5^{14} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.7
Root			$-3.58697 - 7.15078i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.9.b.g.51.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.17394 - 14.3016i) q^{2} -42.6663i q^{3} +(-153.069 + 205.197i) q^{4} +(-610.194 + 306.085i) q^{6} +869.685i q^{7} +(4032.75 + 717.054i) q^{8} +4740.59 q^{9} -24735.0i q^{11} +(8754.99 + 6530.89i) q^{12} -41128.5 q^{13} +(12437.9 - 6239.07i) q^{14} +(-18675.7 - 62818.7i) q^{16} -40900.7 q^{17} +(-34008.7 - 67797.8i) q^{18} +79502.2i q^{19} +37106.2 q^{21} +(-353749. + 177447. i) q^{22} +428560. i q^{23} +(30594.0 - 172062. i) q^{24} +(295053. + 588201. i) q^{26} -482197. i q^{27} +(-178457. - 133122. i) q^{28} -184740. q^{29} -154752. i q^{31} +(-764426. + 717749. i) q^{32} -1.05535e6 q^{33} +(293419. + 584943. i) q^{34} +(-725638. + 972755. i) q^{36} -1.72203e6 q^{37} +(1.13701e6 - 570344. i) q^{38} +1.75480e6i q^{39} -2.00720e6 q^{41} +(-266198. - 530677. i) q^{42} -1.43073e6i q^{43} +(5.07555e6 + 3.78616e6i) q^{44} +(6.12907e6 - 3.07446e6i) q^{46} +4.98494e6i q^{47} +(-2.68024e6 + 796823. i) q^{48} +5.00845e6 q^{49} +1.74508e6i q^{51} +(6.29550e6 - 8.43945e6i) q^{52} +6.97640e6 q^{53} +(-6.89616e6 + 3.45925e6i) q^{54} +(-623611. + 3.50722e6i) q^{56} +3.39206e6 q^{57} +(1.32531e6 + 2.64206e6i) q^{58} +5.65200e6i q^{59} +6.73713e6 q^{61} +(-2.21319e6 + 1.11018e6i) q^{62} +4.12282e6i q^{63} +(1.57489e7 + 5.78340e6i) q^{64} +(7.57102e6 + 1.50931e7i) q^{66} -4.99529e6i q^{67} +(6.26063e6 - 8.39270e6i) q^{68} +1.82850e7 q^{69} +2.07710e7i q^{71} +(1.91176e7 + 3.39926e6i) q^{72} -3.31772e7 q^{73} +(1.23537e7 + 2.46277e7i) q^{74} +(-1.63136e7 - 1.21693e7i) q^{76} +2.15117e7 q^{77} +(2.50964e7 - 1.25888e7i) q^{78} +7.49445e7i q^{79} +1.05295e7 q^{81} +(1.43996e7 + 2.87061e7i) q^{82} +8.75346e7i q^{83} +(-5.67981e6 + 7.61409e6i) q^{84} +(-2.04616e7 + 1.02639e7i) q^{86} +7.88215e6i q^{87} +(1.77363e7 - 9.97500e7i) q^{88} +1.14653e7 q^{89} -3.57688e7i q^{91} +(-8.79392e7 - 6.55993e7i) q^{92} -6.60268e6 q^{93} +(7.12925e7 - 3.57617e7i) q^{94} +(3.06237e7 + 3.26152e7i) q^{96} -8.74640e7 q^{97} +(-3.59303e7 - 7.16286e7i) q^{98} -1.17258e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9} - 8848 q^{14} - 59200 q^{16} + 410256 q^{21} + 156672 q^{24} - 440448 q^{26} - 660136 q^{29} - 4342528 q^{34} - 7191312 q^{36} + 7068520 q^{41} - 2666880 q^{44}+ \cdots + 28850688 q^{96}+O(q^{100}) $ 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9 - 8848 * q^14 - 59200 * q^16 + 410256 * q^21 + 156672 * q^24 - 440448 * q^26 - 660136 * q^29 - 4342528 * q^34 - 7191312 * q^36 + 7068520 * q^41 - 2666880 * q^44 + 561168 * q^46 - 11719036 * q^49 - 37110816 * q^54 - 35044352 * q^56 - 17660440 * q^61 - 20201728 * q^64 + 31902720 * q^66 - 111747216 * q^69 - 19114368 * q^74 - 54998400 * q^76 - 154212444 * q^81 - 101289216 * q^84 + 94429648 * q^86 - 105006376 * q^89 + 192757872 * q^94 + 28850688 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−7.17394	−	14.3016i	−0.448371	−	0.893847i
$2$	−7.17394	−	14.3016i	−0.448371	−	0.893847i
$3$		−	42.6663i		−	0.526744i	−0.964694	−	0.263372i	$-0.915165\pi$
$3$		−	42.6663i		−	0.526744i	0.964694	−	0.263372i	$-0.0848347\pi$
$4$	−153.069	+	205.197i	−0.597926	+	0.801551i
$5$		0			0
$5$		0			0
$6$	−610.194	+	306.085i	−0.470829	+	0.236177i
$7$			869.685i			0.362218i	0.983463	+	0.181109i	$0.0579687\pi$
$7$			869.685i			0.362218i	−0.983463	+	0.181109i	$0.942031\pi$
$8$	4032.75	+	717.054i	0.984557	+	0.175062i
$9$	4740.59			0.722541
$10$		0			0
$11$		−	24735.0i		−	1.68943i	−0.535214	−	0.844717i	$-0.679769\pi$
$11$		−	24735.0i		−	1.68943i	0.535214	−	0.844717i	$-0.320231\pi$
$12$	8754.99	+	6530.89i	0.422212	+	0.314954i
$13$	−41128.5			−1.44002			−0.720011	−	0.693962i	$-0.755863\pi$
$13$	−41128.5			−1.44002			−0.720011	+	0.693962i	$0.755863\pi$
$14$	12437.9	−	6239.07i	0.323767	−	0.162408i
$15$		0			0
$16$	−18675.7	−	62818.7i	−0.284969	−	0.958537i
$17$	−40900.7			−0.489705			−0.244853	−	0.969560i	$-0.578740\pi$
$17$	−40900.7			−0.489705			−0.244853	+	0.969560i	$0.578740\pi$
$18$	−34008.7	−	67797.8i	−0.323967	−	0.645841i
$19$			79502.2i			0.610049i	0.952345	+	0.305024i	$0.0986646\pi$
$19$			79502.2i			0.610049i	−0.952345	+	0.305024i	$0.901335\pi$
$20$		0			0
$21$	37106.2			0.190796
$22$	−353749.	+	177447.i	−1.51010	+	0.757494i
$23$			428560.i			1.53144i	0.643174	+	0.765720i	$0.277617\pi$
$23$			428560.i			1.53144i	−0.643174	+	0.765720i	$0.722383\pi$
$24$	30594.0	−	172062.i	0.0922129	−	0.518610i
$25$		0			0
$26$	295053.	+	588201.i	0.645665	+	1.28716i
$27$		−	482197.i		−	0.907338i
$28$	−178457.	−	133122.i	−0.290336	−	0.216580i
$29$	−184740.			−0.261197			−0.130598	−	0.991435i	$-0.541690\pi$
$29$	−184740.			−0.261197			−0.130598	+	0.991435i	$0.541690\pi$
$30$		0			0
$31$		−	154752.i		−	0.167567i	−0.996484	−	0.0837835i	$-0.973300\pi$
$31$		−	154752.i		−	0.167567i	0.996484	−	0.0837835i	$-0.0267004\pi$
$32$	−764426.	+	717749.i	−0.729014	+	0.684499i
$33$	−1.05535e6			−0.889899
$34$	293419.	+	584943.i	0.219570	+	0.437722i
$35$		0			0
$36$	−725638.	+	972755.i	−0.432026	+	0.579153i
$37$	−1.72203e6			−0.918825			−0.459413	−	0.888223i	$-0.651940\pi$
$37$	−1.72203e6			−0.918825			−0.459413	+	0.888223i	$0.651940\pi$
$38$	1.13701e6	−	570344.i	0.545291	−	0.273529i
$39$			1.75480e6i			0.758523i
$40$		0			0
$41$	−2.00720e6			−0.710323			−0.355162	−	0.934805i	$-0.615574\pi$
$41$	−2.00720e6			−0.710323			−0.355162	+	0.934805i	$0.615574\pi$
$42$	−266198.	−	530677.i	−0.0855475	−	0.170543i
$43$		−	1.43073e6i		−	0.418488i	−0.977863	−	0.209244i	$-0.932900\pi$
$43$		−	1.43073e6i		−	0.418488i	0.977863	−	0.209244i	$-0.0671002\pi$
$44$	5.07555e6	+	3.78616e6i	1.35417	+	1.01016i
$45$		0			0
$46$	6.12907e6	−	3.07446e6i	1.36887	−	0.686654i
$47$			4.98494e6i			1.02157i	0.859708	+	0.510786i	$0.170646\pi$
$47$			4.98494e6i			1.02157i	−0.859708	+	0.510786i	$0.829354\pi$
$48$	−2.68024e6	+	796823.i	−0.504903	+	0.150106i
$49$	5.00845e6			0.868798
$50$		0			0
$51$			1.74508e6i			0.257949i
$52$	6.29550e6	−	8.43945e6i	0.861027	−	1.15425i
$53$	6.97640e6			0.884154			0.442077	−	0.896977i	$-0.354242\pi$
$53$	6.97640e6			0.884154			0.442077	+	0.896977i	$0.354242\pi$
$54$	−6.89616e6	+	3.45925e6i	−0.811022	+	0.406824i
$55$		0			0
$56$	−623611.	+	3.50722e6i	−0.0634106	+	0.356624i
$57$	3.39206e6			0.321340
$58$	1.32531e6	+	2.64206e6i	0.117113	+	0.233470i
$59$			5.65200e6i			0.466438i	0.972424	+	0.233219i	$0.0749259\pi$
$59$			5.65200e6i			0.466438i	−0.972424	+	0.233219i	$0.925074\pi$
$60$		0			0
$61$	6.73713e6			0.486582			0.243291	−	0.969953i	$-0.421773\pi$
$61$	6.73713e6			0.486582			0.243291	+	0.969953i	$0.421773\pi$
$62$	−2.21319e6	+	1.11018e6i	−0.149779	+	0.0751323i
$63$			4.12282e6i			0.261717i
$64$	1.57489e7	+	5.78340e6i	0.938707	+	0.344717i
$65$		0			0
$66$	7.57102e6	+	1.50931e7i	0.399005	+	0.795434i
$67$		−	4.99529e6i		−	0.247891i	−0.992289	−	0.123946i	$-0.960445\pi$
$67$		−	4.99529e6i		−	0.247891i	0.992289	−	0.123946i	$-0.0395549\pi$
$68$	6.26063e6	−	8.39270e6i	0.292807	−	0.392524i
$69$	1.82850e7			0.806677
$70$		0			0
$71$			2.07710e7i			0.817378i	0.912674	+	0.408689i	$0.134014\pi$
$71$			2.07710e7i			0.817378i	−0.912674	+	0.408689i	$0.865986\pi$
$72$	1.91176e7	+	3.39926e6i	0.711383	+	0.126489i
$73$	−3.31772e7			−1.16828			−0.584141	−	0.811652i	$-0.698569\pi$
$73$	−3.31772e7			−1.16828			−0.584141	+	0.811652i	$0.698569\pi$
$74$	1.23537e7	+	2.46277e7i	0.411975	+	0.821290i
$75$		0			0
$76$	−1.63136e7	−	1.21693e7i	−0.488985	−	0.364764i
$77$	2.15117e7			0.611943
$78$	2.50964e7	−	1.25888e7i	0.678004	−	0.340100i
$79$			7.49445e7i			1.92412i	0.272844	+	0.962058i	$0.412036\pi$
$79$			7.49445e7i			1.92412i	−0.272844	+	0.962058i	$0.587964\pi$
$80$		0			0
$81$	1.05295e7			0.244606
$82$	1.43996e7	+	2.87061e7i	0.318489	+	0.634920i
$83$			8.75346e7i			1.84445i	0.386651	+	0.922226i	$0.373632\pi$
$83$			8.75346e7i			1.84445i	−0.386651	+	0.922226i	$0.626368\pi$
$84$	−5.67981e6	+	7.61409e6i	−0.114082	+	0.152933i
$85$		0			0
$86$	−2.04616e7	+	1.02639e7i	−0.374064	+	0.187638i
$87$			7.88215e6i			0.137584i
$88$	1.77363e7	−	9.97500e7i	0.295756	−	1.66334i
$89$	1.14653e7			0.182737			0.0913685	−	0.995817i	$-0.470876\pi$
$89$	1.14653e7			0.182737			0.0913685	+	0.995817i	$0.470876\pi$
$90$		0			0
$91$		−	3.57688e7i		−	0.521602i
$92$	−8.79392e7	−	6.55993e7i	−1.22753	−	0.915688i
$93$	−6.60268e6			−0.0882649
$94$	7.12925e7	−	3.57617e7i	0.913129	−	0.458044i
$95$		0			0
$96$	3.06237e7	+	3.26152e7i	0.360556	+	0.384004i
$97$	−8.74640e7			−0.987967			−0.493983	−	0.869471i	$-0.664460\pi$
$97$	−8.74640e7			−0.987967			−0.493983	+	0.869471i	$0.664460\pi$
$98$	−3.59303e7	−	7.16286e7i	−0.389544	−	0.776573i
$99$		−	1.17258e8i		−	1.22068i
$100$		0			0
$101$	1.07960e8			1.03747			0.518736	−	0.854934i	$-0.326403\pi$
$101$	1.07960e8			1.03747			0.518736	+	0.854934i	$0.326403\pi$
$102$	2.49573e7	−	1.25191e7i	0.230567	−	0.115657i
$103$			9.62475e7i			0.855147i	0.903981	+	0.427573i	$0.140631\pi$
$103$			9.62475e7i			0.855147i	−0.903981	+	0.427573i	$0.859369\pi$
$104$	−1.65861e8	−	2.94913e7i	−1.41779	−	0.252093i
$105$		0			0
$106$	−5.00483e7	−	9.97734e7i	−0.396430	−	0.790299i
$107$			8.83513e7i			0.674028i	0.941500	+	0.337014i	$0.109417\pi$
$107$			8.83513e7i			0.674028i	−0.941500	+	0.337014i	$0.890583\pi$
$108$	9.89453e7	+	7.38094e7i	0.727278	+	0.542521i
$109$	−4.82155e7			−0.341571			−0.170785	−	0.985308i	$-0.554630\pi$
$109$	−4.82155e7			−0.341571			−0.170785	+	0.985308i	$0.554630\pi$
$110$		0			0
$111$			7.34724e7i			0.483986i
$112$	5.46325e7	−	1.62420e7i	0.347199	−	0.103221i
$113$	−1.83862e8			−1.12766			−0.563830	−	0.825891i	$-0.690672\pi$
$113$	−1.83862e8			−1.12766			−0.563830	+	0.825891i	$0.690672\pi$
$114$	−2.43345e7	−	4.85118e7i	−0.144079	−	0.287229i
$115$		0			0
$116$	2.82779e7	−	3.79080e7i	0.156176	−	0.209363i
$117$	−1.94973e8			−1.04048
$118$	8.08324e7	−	4.05471e7i	0.416924	−	0.209138i
$119$		−	3.55707e7i		−	0.177380i
$120$		0			0
$121$	−3.97461e8			−1.85419
$122$	−4.83318e7	−	9.63515e7i	−0.218169	−	0.434930i
$123$			8.56399e7i			0.374158i
$124$	3.17546e7	+	2.36877e7i	0.134314	+	0.100193i
$125$		0			0
$126$	5.89628e7	−	2.95769e7i	0.233935	−	0.117347i
$127$			3.52941e8i			1.35671i	0.734734	+	0.678355i	$0.237307\pi$
$127$			3.52941e8i			1.35671i	−0.734734	+	0.678355i	$0.762693\pi$
$128$	−3.02700e7	−	2.66723e8i	−0.112765	−	0.993622i
$129$	−6.10437e7			−0.220436
$130$		0			0
$131$		−	1.20638e8i		−	0.409638i	−0.978800	−	0.204819i	$-0.934339\pi$
$131$		−	1.20638e8i		−	0.409638i	0.978800	−	0.204819i	$-0.0656606\pi$
$132$	1.61541e8	−	2.16555e8i	0.532094	−	0.713299i
$133$	−6.91419e7			−0.220971
$134$	−7.14404e7	+	3.58359e7i	−0.221577	+	0.111147i
$135$		0			0
$136$	−1.64942e8	−	2.93280e7i	−0.482143	−	0.0857288i
$137$	2.98009e8			0.845955			0.422978	−	0.906140i	$-0.360985\pi$
$137$	2.98009e8			0.845955			0.422978	+	0.906140i	$0.360985\pi$
$138$	−1.31176e8	−	2.61505e8i	−0.361691	−	0.721046i
$139$		−	4.00098e8i		−	1.07178i	−0.844287	−	0.535891i	$-0.819976\pi$
$139$		−	4.00098e8i		−	1.07178i	0.844287	−	0.535891i	$-0.180024\pi$
$140$		0			0
$141$	2.12689e8			0.538107
$142$	2.97057e8	−	1.49010e8i	0.730611	−	0.366489i
$143$			1.01731e9i			2.43282i
$144$	−8.85339e7	−	2.97798e8i	−0.205902	−	0.692582i
$145$		0			0
$146$	2.38011e8	+	4.74485e8i	0.523825	+	1.04427i
$147$		−	2.13692e8i		−	0.457634i
$148$	2.63589e8	−	3.53355e8i	0.549390	−	0.736486i
$149$	−7.70799e8			−1.56385			−0.781927	−	0.623370i	$-0.785763\pi$
$149$	−7.70799e8			−1.56385			−0.781927	+	0.623370i	$0.785763\pi$
$150$		0			0
$151$		−	5.11492e8i		−	0.983856i	−0.870636	−	0.491928i	$-0.836292\pi$
$151$		−	5.11492e8i		−	0.983856i	0.870636	−	0.491928i	$-0.163708\pi$
$152$	−5.70074e7	+	3.20612e8i	−0.106796	+	0.600628i
$153$	−1.93893e8			−0.353832
$154$	−1.54323e8	−	3.07650e8i	−0.274378	−	0.546984i
$155$		0			0
$156$	−3.60080e8	−	2.68605e8i	−0.607995	−	0.453541i
$157$	8.51365e7			0.140126			0.0700628	−	0.997543i	$-0.477680\pi$
$157$	8.51365e7			0.140126			0.0700628	+	0.997543i	$0.477680\pi$
$158$	1.07182e9	−	5.37647e8i	1.71987	−	0.862719i
$159$		−	2.97657e8i		−	0.465723i
$160$		0			0
$161$	−3.72712e8			−0.554715
$162$	−7.55380e7	−	1.50588e8i	−0.109674	−	0.218640i
$163$			2.79284e8i			0.395636i	0.980239	+	0.197818i	$0.0633855\pi$
$163$			2.79284e8i			0.395636i	−0.980239	+	0.197818i	$0.936614\pi$
$164$	3.07241e8	−	4.11872e8i	0.424721	−	0.569360i
$165$		0			0
$166$	1.25188e9	−	6.27968e8i	1.64866	−	0.827000i
$167$		−	4.30699e8i		−	0.553743i	−0.960907	−	0.276871i	$-0.910702\pi$
$167$		−	4.30699e8i		−	0.553743i	0.960907	−	0.276871i	$-0.0892976\pi$
$168$	1.49640e8	+	2.66072e7i	0.187850	+	0.0334011i
$169$	8.75822e8			1.07367
$170$		0			0
$171$			3.76887e8i			0.440785i
$172$	2.93581e8	+	2.19000e8i	0.335439	+	0.250225i
$173$	−6.81243e8			−0.760533			−0.380266	−	0.924877i	$-0.624168\pi$
$173$	−6.81243e8			−0.760533			−0.380266	+	0.924877i	$0.624168\pi$
$174$	1.12727e8	−	5.65461e7i	0.122979	−	0.0616887i
$175$		0			0
$176$	−1.55382e9	+	4.61944e8i	−1.61938	+	0.481436i
$177$	2.41150e8			0.245693
$178$	−8.22517e7	−	1.63972e8i	−0.0819341	−	0.163339i
$179$			1.86210e9i			1.81381i	0.421336	+	0.906905i	$0.361561\pi$
$179$			1.86210e9i			1.81381i	−0.421336	+	0.906905i	$0.638439\pi$
$180$		0			0
$181$	9.45023e8			0.880498			0.440249	−	0.897876i	$-0.354890\pi$
$181$	9.45023e8			0.880498			0.440249	+	0.897876i	$0.354890\pi$
$182$	−5.11550e8	+	2.56604e8i	−0.466233	+	0.233871i
$183$		−	2.87448e8i		−	0.256304i
$184$	−3.07301e8	+	1.72827e9i	−0.268097	+	1.50779i
$185$		0			0
$186$	4.73672e7	+	9.44285e7i	0.0395755	+	0.0788954i
$187$			1.01168e9i			0.827324i
$188$	−1.02290e9	−	7.63041e8i	−0.818842	−	0.610825i
$189$	4.19359e8			0.328654
$190$		0			0
$191$			6.13867e8i			0.461255i	0.973042	+	0.230627i	$0.0740778\pi$
$191$			6.13867e8i			0.461255i	−0.973042	+	0.230627i	$0.925922\pi$
$192$	2.46756e8	−	6.71946e8i	0.181578	−	0.494458i
$193$	7.45004e8			0.536945			0.268472	−	0.963287i	$-0.413481\pi$
$193$	7.45004e8			0.536945			0.268472	+	0.963287i	$0.413481\pi$
$194$	6.27462e8	+	1.25087e9i	0.442976	+	0.883091i
$195$		0			0
$196$	−7.66639e8	+	1.02772e9i	−0.519477	+	0.696386i
$197$	−2.47398e9			−1.64260			−0.821299	−	0.570498i	$-0.806750\pi$
$197$	−2.47398e9			−1.64260			−0.821299	+	0.570498i	$0.806750\pi$
$198$	−1.67698e9	+	8.41206e8i	−1.09111	+	0.547320i
$199$		−	8.62436e8i		−	0.549939i	−0.961453	−	0.274969i	$-0.911332\pi$
$199$		−	8.62436e8i		−	0.549939i	0.961453	−	0.274969i	$-0.0886677\pi$
$200$		0			0
$201$	−2.13130e8			−0.130575
$202$	−7.74498e8	−	1.54399e9i	−0.465173	−	0.927342i
$203$		−	1.60665e8i		−	0.0946102i
$204$	−3.58085e8	−	2.67118e8i	−0.206759	−	0.154235i
$205$		0			0
$206$	1.37649e9	−	6.90474e8i	0.764371	−	0.383423i
$207$			2.03163e9i			1.10653i
$208$	7.68104e8	+	2.58364e9i	0.410361	+	1.38031i
$209$	1.96649e9			1.03064
$210$		0			0
$211$			2.06407e9i			1.04135i	0.853756	+	0.520673i	$0.174319\pi$
$211$			2.06407e9i			1.04135i	−0.853756	+	0.520673i	$0.825681\pi$
$212$	−1.06787e9	+	1.43154e9i	−0.528659	+	0.708695i
$213$	8.86219e8			0.430549
$214$	1.26356e9	−	6.33827e8i	0.602478	−	0.302215i
$215$		0			0
$216$	3.45761e8	−	1.94458e9i	0.158840	−	0.893326i
$217$	1.34585e8			0.0606958
$218$	3.45895e8	+	6.89557e8i	0.153151	+	0.305312i
$219$			1.41555e9i			0.615386i
$220$		0			0
$221$	1.68218e9			0.705186
$222$	1.05077e9	−	5.27087e8i	0.432609	−	0.217005i
$223$		−	2.49560e9i		−	1.00915i	−0.863368	−	0.504574i	$-0.831649\pi$
$223$		−	2.49560e9i		−	1.00915i	0.863368	−	0.504574i	$-0.168351\pi$
$224$	−6.24216e8	−	6.64810e8i	−0.247938	−	0.264062i
$225$		0			0
$226$	1.31901e9	+	2.62951e9i	0.505610	+	1.00796i
$227$		−	4.05348e9i		−	1.52660i	−0.646045	−	0.763300i	$-0.723578\pi$
$227$		−	4.05348e9i		−	1.52660i	0.646045	−	0.763300i	$-0.276422\pi$
$228$	−5.19220e8	+	6.96041e8i	−0.192137	+	0.257570i
$229$	−2.28775e9			−0.831890			−0.415945	−	0.909390i	$-0.636549\pi$
$229$	−2.28775e9			−0.831890			−0.415945	+	0.909390i	$0.636549\pi$
$230$		0			0
$231$		−	9.17822e8i		−	0.322337i
$232$	−7.45008e8	−	1.32468e8i	−0.257163	−	0.0457257i
$233$	−3.13148e9			−1.06249			−0.531247	−	0.847217i	$-0.678276\pi$
$233$	−3.13148e9			−1.06249			−0.531247	+	0.847217i	$0.678276\pi$
$234$	1.39873e9	+	2.78842e9i	0.466519	+	0.930026i
$235$		0			0
$236$	−1.15977e9	−	8.65146e8i	−0.373874	−	0.278896i
$237$	3.19760e9			1.01352
$238$	−5.08716e8	+	2.55182e8i	−0.158551	+	0.0795321i
$239$			1.66159e9i			0.509251i	0.967040	+	0.254626i	$0.0819523\pi$
$239$			1.66159e9i			0.509251i	−0.967040	+	0.254626i	$0.918048\pi$
$240$		0			0
$241$	−1.60357e9			−0.475358			−0.237679	−	0.971344i	$-0.576387\pi$
$241$	−1.60357e9			−0.475358			−0.237679	+	0.971344i	$0.576387\pi$
$242$	2.85136e9	+	5.68431e9i	0.831364	+	1.65736i
$243$		−	3.61295e9i		−	1.03618i
$244$	−1.03125e9	+	1.38244e9i	−0.290940	+	0.390020i
$245$		0			0
$246$	1.22478e9	−	6.14375e8i	0.334441	−	0.167762i
$247$		−	3.26980e9i		−	0.878484i
$248$	1.10965e8	−	6.24074e8i	0.0293346	−	0.164979i
$249$	3.73477e9			0.971554
$250$		0			0
$251$		−	6.18770e9i		−	1.55896i	−0.626429	−	0.779478i	$-0.715484\pi$
$251$		−	6.18770e9i		−	1.55896i	0.626429	−	0.779478i	$-0.284516\pi$
$252$	−8.45991e8	−	6.31076e8i	−0.209780	−	0.156488i
$253$	1.06004e10			2.58727
$254$	5.04760e9	−	2.53198e9i	1.21269	−	0.608310i
$255$		0			0
$256$	−3.59740e9	+	2.34637e9i	−0.837586	+	0.546306i
$257$	6.20387e9			1.42210			0.711050	−	0.703142i	$-0.248220\pi$
$257$	6.20387e9			1.42210			0.711050	+	0.703142i	$0.248220\pi$
$258$	4.37924e8	+	8.73021e8i	0.0988372	+	0.197036i
$259$		−	1.49762e9i		−	0.332815i
$260$		0			0
$261$	−8.75775e8			−0.188725
$262$	−1.72532e9	+	8.65453e8i	−0.366154	+	0.183670i
$263$			1.96327e9i			0.410353i	0.978725	+	0.205177i	$0.0657769\pi$
$263$			1.96327e9i			0.410353i	−0.978725	+	0.205177i	$0.934223\pi$
$264$	−4.25596e9	−	7.56743e8i	−0.876156	−	0.155787i
$265$		0			0
$266$	4.96020e8	+	9.88836e8i	0.0990769	+	0.197514i
$267$		−	4.89183e8i		−	0.0962557i
$268$	1.02502e9	+	7.64625e8i	0.198698	+	0.148221i
$269$	−6.31601e9			−1.20624			−0.603120	−	0.797651i	$-0.706076\pi$
$269$	−6.31601e9			−1.20624			−0.603120	+	0.797651i	$0.706076\pi$
$270$		0			0
$271$			4.71258e9i			0.873739i	0.899525	+	0.436869i	$0.143913\pi$
$271$			4.71258e9i			0.873739i	−0.899525	+	0.436869i	$0.856087\pi$
$272$	7.63849e8	+	2.56932e9i	0.139551	+	0.469400i
$273$	−1.52612e9			−0.274751
$274$	−2.13790e9	−	4.26200e9i	−0.379302	−	0.756155i
$275$		0			0
$276$	−2.79888e9	+	3.75204e9i	−0.482333	+	0.646593i
$277$	−1.00765e8			−0.0171156			−0.00855780	−	0.999963i	$-0.502724\pi$
$277$	−1.00765e8			−0.0171156			−0.00855780	+	0.999963i	$0.502724\pi$
$278$	−5.72202e9	+	2.87028e9i	−0.958010	+	0.480557i
$279$		−	7.33614e8i		−	0.121074i
$280$		0			0
$281$	−4.26355e9			−0.683827			−0.341914	−	0.939731i	$-0.611075\pi$
$281$	−4.26355e9			−0.683827			−0.341914	+	0.939731i	$0.611075\pi$
$282$	−1.52582e9	−	3.04178e9i	−0.241272	−	0.480985i
$283$		−	1.16260e10i		−	1.81253i	−0.422710	−	0.906265i	$-0.638921\pi$
$283$		−	1.16260e10i		−	1.81253i	0.422710	−	0.906265i	$-0.361079\pi$
$284$	−4.26214e9	−	3.17939e9i	−0.655171	−	0.488732i
$285$		0			0
$286$	1.45492e10	−	7.29814e9i	2.17457	−	1.09081i
$287$		−	1.74563e9i		−	0.257292i
$288$	−3.62383e9	+	3.40256e9i	−0.526742	+	0.494578i
$289$	−5.30289e9			−0.760189
$290$		0			0
$291$			3.73176e9i			0.520405i
$292$	5.07840e9	−	6.80786e9i	0.698547	−	0.936439i
$293$	−3.75705e9			−0.509772			−0.254886	−	0.966971i	$-0.582038\pi$
$293$	−3.75705e9			−0.509772			−0.254886	+	0.966971i	$0.582038\pi$
$294$	−3.05613e9	+	1.53301e9i	−0.409055	+	0.205190i
$295$		0			0
$296$	−6.94450e9	−	1.23479e9i	−0.904636	−	0.160851i
$297$	−1.19271e10			−1.53289
$298$	5.52967e9	+	1.10236e10i	0.701188	+	1.39785i
$299$		−	1.76260e10i		−	2.20531i
$300$		0			0
$301$	1.24428e9			0.151584
$302$	−7.31514e9	+	3.66942e9i	−0.879417	+	0.441133i
$303$		−	4.60624e9i		−	0.546483i
$304$	4.99422e9	−	1.48476e9i	0.584754	−	0.173845i
$305$		0			0
$306$	1.39098e9	+	2.77298e9i	0.158648	+	0.316272i
$307$			5.80347e9i			0.653333i	0.945140	+	0.326666i	$0.105925\pi$
$307$			5.80347e9i			0.653333i	−0.945140	+	0.326666i	$0.894075\pi$
$308$	−3.29277e9	+	4.41413e9i	−0.365897	+	0.490504i
$309$	4.10652e9			0.450443
$310$		0			0
$311$		−	1.22144e10i		−	1.30566i	−0.757503	−	0.652832i	$-0.773581\pi$
$311$		−	1.22144e10i		−	1.30566i	0.757503	−	0.652832i	$-0.226419\pi$
$312$	−1.25829e9	+	7.07666e9i	−0.132789	+	0.746810i
$313$	8.99814e9			0.937509			0.468755	−	0.883328i	$-0.344703\pi$
$313$	8.99814e9			0.937509			0.468755	+	0.883328i	$0.344703\pi$
$314$	−6.10765e8	−	1.21758e9i	−0.0628283	−	0.125251i
$315$		0			0
$316$	−1.53784e10	−	1.14717e10i	−1.54228	−	1.15048i
$317$	−2.25206e9			−0.223019			−0.111510	−	0.993763i	$-0.535569\pi$
$317$	−2.25206e9			−0.223019			−0.111510	+	0.993763i	$0.535569\pi$
$318$	−4.25696e9	+	2.13537e9i	−0.416285	+	0.208817i
$319$			4.56953e9i			0.441275i
$320$		0			0
$321$	3.76962e9			0.355040
$322$	2.67382e9	+	5.33036e9i	0.248718	+	0.495831i
$323$		−	3.25169e9i		−	0.298744i
$324$	−1.61174e9	+	2.16062e9i	−0.146256	+	0.196064i
$325$		0			0
$326$	3.99420e9	−	2.00357e9i	0.353638	−	0.177392i
$327$			2.05718e9i			0.179920i
$328$	−8.09454e9	−	1.43927e9i	−0.699354	−	0.124351i
$329$	−4.33533e9			−0.370032
$330$		0			0
$331$		−	1.68572e9i		−	0.140434i	−0.997532	−	0.0702172i	$-0.977631\pi$
$331$		−	1.68572e9i		−	0.140434i	0.997532	−	0.0702172i	$-0.0223692\pi$
$332$	−1.79619e10	−	1.33988e10i	−1.47842	−	1.10285i
$333$	−8.16342e9			−0.663889
$334$	−6.15966e9	+	3.08981e9i	−0.494961	+	0.248282i
$335$		0			0
$336$	−6.92985e8	−	2.33096e9i	−0.0543709	−	0.182885i
$337$	7.73250e9			0.599515			0.299758	−	0.954015i	$-0.403094\pi$
$337$	7.73250e9			0.599515			0.299758	+	0.954015i	$0.403094\pi$
$338$	−6.28310e9	−	1.25256e10i	−0.481401	−	0.959693i
$339$			7.84470e9i			0.593988i
$340$		0			0
$341$	−3.82778e9			−0.283093
$342$	5.39008e9	−	2.70377e9i	0.393995	−	0.197636i
$343$			9.36933e9i			0.676912i
$344$	1.02591e9	−	5.76976e9i	0.0732613	−	0.412025i
$345$		0			0
$346$	4.88720e9	+	9.74284e9i	0.341001	+	0.679800i
$347$		−	3.07433e9i		−	0.212047i	−0.994364	−	0.106023i	$-0.966188\pi$
$347$		−	3.07433e9i		−	0.212047i	0.994364	−	0.106023i	$-0.0338119\pi$
$348$	−1.61739e9	−	1.20651e9i	−0.110281	−	0.0822650i
$349$	1.30882e10			0.882224			0.441112	−	0.897452i	$-0.354584\pi$
$349$	1.30882e10			0.882224			0.441112	+	0.897452i	$0.354584\pi$
$350$		0			0
$351$			1.98320e10i			1.30659i
$352$	1.77535e10	+	1.89081e10i	1.15642	+	1.23162i
$353$	6.61462e9			0.425996			0.212998	−	0.977053i	$-0.431677\pi$
$353$	6.61462e9			0.425996			0.212998	+	0.977053i	$0.431677\pi$
$354$	−1.72999e9	−	3.44882e9i	−0.110162	−	0.219612i
$355$		0			0
$356$	−1.75499e9	+	2.35265e9i	−0.109263	+	0.146473i
$357$	−1.51767e9			−0.0934338
$358$	2.66310e10	−	1.33586e10i	1.62127	−	0.813260i
$359$			3.34086e9i			0.201132i	0.994930	+	0.100566i	$0.0320653\pi$
$359$			3.34086e9i			0.201132i	−0.994930	+	0.100566i	$0.967935\pi$
$360$		0			0
$361$	1.06630e10			0.627840
$362$	−6.77954e9	−	1.35153e10i	−0.394790	−	0.787030i
$363$			1.69582e10i			0.976681i
$364$	7.33966e9	+	5.47510e9i	0.418091	+	0.311879i
$365$		0			0
$366$	−4.11096e9	+	2.06214e9i	−0.229097	+	0.114919i
$367$		−	9.60705e9i		−	0.529573i	−0.964307	−	0.264787i	$-0.914698\pi$
$367$		−	9.60705e9i		−	0.529573i	0.964307	−	0.264787i	$-0.0853015\pi$
$368$	2.69216e10	−	8.00366e9i	1.46794	−	0.436413i
$369$	−9.51533e9			−0.513237
$370$		0			0
$371$			6.06727e9i			0.320256i
$372$	1.01067e9	−	1.35485e9i	0.0527759	−	0.0707489i
$373$	−1.82578e10			−0.943222			−0.471611	−	0.881807i	$-0.656327\pi$
$373$	−1.82578e10			−0.943222			−0.471611	+	0.881807i	$0.656327\pi$
$374$	1.44686e10	−	7.25772e9i	0.739501	−	0.370948i
$375$		0			0
$376$	−3.57447e9	+	2.01030e10i	−0.178838	+	1.00580i
$377$	7.59806e9			0.376129
$378$	−3.00846e9	−	5.99749e9i	−0.147359	−	0.293767i
$379$			2.08206e10i			1.00910i	0.863382	+	0.504551i	$0.168342\pi$
$379$			2.08206e10i			1.00910i	−0.863382	+	0.504551i	$0.831658\pi$
$380$		0			0
$381$	1.50587e10			0.714639
$382$	8.77925e9	−	4.40385e9i	0.412291	−	0.206813i
$383$			2.29859e10i			1.06824i	0.845410	+	0.534118i	$0.179356\pi$
$383$			2.29859e10i			1.06824i	−0.845410	+	0.534118i	$0.820644\pi$
$384$	−1.13801e10	+	1.29151e9i	−0.523384	+	0.0593981i
$385$		0			0
$386$	−5.34462e9	−	1.06547e10i	−0.240751	−	0.479947i
$387$		−	6.78249e9i		−	0.302374i
$388$	1.33880e10	−	1.79474e10i	0.590731	−	0.791906i
$389$	1.60076e10			0.699083			0.349541	−	0.936921i	$-0.386337\pi$
$389$	1.60076e10			0.699083			0.349541	+	0.936921i	$0.386337\pi$
$390$		0			0
$391$		−	1.75284e10i		−	0.749954i
$392$	2.01978e10	+	3.59133e9i	0.855382	+	0.152094i
$393$	−5.14719e9			−0.215774
$394$	1.77482e10	+	3.53818e10i	0.736494	+	1.46823i
$395$		0			0
$396$	2.40611e10	+	1.79486e10i	0.978441	+	0.729879i
$397$	1.72716e10			0.695299			0.347650	−	0.937625i	$-0.386980\pi$
$397$	1.72716e10			0.695299			0.347650	+	0.937625i	$0.386980\pi$
$398$	−1.23342e10	+	6.18706e9i	−0.491561	+	0.246577i
$399$			2.95002e9i			0.116395i
$400$		0			0
$401$	−1.56829e10			−0.606524			−0.303262	−	0.952907i	$-0.598076\pi$
$401$	−1.56829e10			−0.606524			−0.303262	+	0.952907i	$0.598076\pi$
$402$	1.52899e9	+	3.04810e9i	0.0585462	+	0.116714i
$403$			6.36470e9i			0.241300i
$404$	−1.65253e10	+	2.21530e10i	−0.620332	+	0.831588i
$405$		0			0
$406$	−2.29776e9	+	1.15260e9i	−0.0845671	+	0.0424205i
$407$			4.25943e10i			1.55229i
$408$	−1.25132e9	+	7.03746e9i	−0.0451571	+	0.253966i
$409$	1.05519e8			0.00377082			0.00188541	−	0.999998i	$-0.499400\pi$
$409$	1.05519e8			0.00377082			0.00188541	+	0.999998i	$0.499400\pi$
$410$		0			0
$411$		−	1.27149e10i		−	0.445602i
$412$	−1.97497e10	−	1.47325e10i	−0.685444	−	0.511315i
$413$	−4.91546e9			−0.168952
$414$	2.90554e10	−	1.45748e10i	0.989067	−	0.496136i
$415$		0			0
$416$	3.14397e10	−	2.95199e10i	1.04980	−	0.985694i
$417$	−1.70707e10			−0.564555
$418$	−1.41075e10	−	2.81238e10i	−0.462108	−	0.921232i
$419$			1.28448e10i			0.416746i	0.978049	+	0.208373i	$0.0668168\pi$
$419$			1.28448e10i			0.416746i	−0.978049	+	0.208373i	$0.933183\pi$
$420$		0			0
$421$	−3.08274e10			−0.981315			−0.490658	−	0.871353i	$-0.663243\pi$
$421$	−3.08274e10			−0.981315			−0.490658	+	0.871353i	$0.663243\pi$
$422$	2.95194e10	−	1.48075e10i	0.930804	−	0.466910i
$423$			2.36316e10i			0.738127i
$424$	2.81341e10	+	5.00246e9i	0.870501	+	0.154782i
$425$		0			0
$426$	−6.35768e9	−	1.26743e10i	−0.193046	−	0.384845i
$427$			5.85918e9i			0.176249i
$428$	−1.81294e10	−	1.35239e10i	−0.540268	−	0.403019i
$429$	4.34049e10			1.28147
$430$		0			0
$431$			9.59665e9i			0.278106i	0.990285	+	0.139053i	$0.0444058\pi$
$431$			9.59665e9i			0.278106i	−0.990285	+	0.139053i	$0.955594\pi$
$432$	−3.02909e10	+	9.00536e9i	−0.869717	+	0.258563i
$433$	−6.69168e8			−0.0190363			−0.00951817	−	0.999955i	$-0.503030\pi$
$433$	−6.69168e8			−0.0190363			−0.00951817	+	0.999955i	$0.503030\pi$
$434$	−9.65507e8	−	1.92478e9i	−0.0272143	−	0.0542528i
$435$		0			0
$436$	7.38030e9	−	9.89368e9i	0.204234	−	0.273787i
$437$	−3.40714e10			−0.934254
$438$	2.02445e10	−	1.01550e10i	0.550061	−	0.275921i
$439$		−	3.75455e10i		−	1.01088i	−0.862862	−	0.505440i	$-0.831330\pi$
$439$		−	3.75455e10i		−	1.01088i	0.862862	−	0.505440i	$-0.168670\pi$
$440$		0			0
$441$	2.37430e10			0.627742
$442$	−1.20679e10	−	2.40578e10i	−0.316185	−	0.630329i
$443$		−	1.19986e10i		−	0.311542i	−0.987793	−	0.155771i	$-0.950214\pi$
$443$		−	1.19986e10i		−	0.311542i	0.987793	−	0.155771i	$-0.0497862\pi$
$444$	−1.50763e10	−	1.12464e10i	−0.387939	−	0.289388i
$445$		0			0
$446$	−3.56909e10	+	1.79033e10i	−0.902025	+	0.452473i
$447$			3.28871e10i			0.823751i
$448$	−5.02973e9	+	1.36966e10i	−0.124863	+	0.340016i
$449$	−6.86153e10			−1.68825			−0.844123	−	0.536150i	$-0.819878\pi$
$449$	−6.86153e10			−1.68825			−0.844123	+	0.536150i	$0.819878\pi$
$450$		0			0
$451$			4.96482e10i			1.20004i
$452$	2.81436e10	−	3.77279e10i	0.674257	−	0.903876i
$453$	−2.18235e10			−0.518240
$454$	−5.79711e10	+	2.90795e10i	−1.36455	+	0.684483i
$455$		0			0
$456$	1.36793e10	+	2.43229e9i	0.316377	+	0.0562544i
$457$	−5.08092e10			−1.16487			−0.582435	−	0.812877i	$-0.697900\pi$
$457$	−5.08092e10			−1.16487			−0.582435	+	0.812877i	$0.697900\pi$
$458$	1.64122e10	+	3.27183e10i	0.372996	+	0.743583i
$459$			1.97222e10i			0.444328i
$460$		0			0
$461$	−3.46473e10			−0.767124			−0.383562	−	0.923515i	$-0.625303\pi$
$461$	−3.46473e10			−0.767124			−0.383562	+	0.923515i	$0.625303\pi$
$462$	−1.31263e10	+	6.58440e9i	−0.288120	+	0.144527i
$463$			4.92524e10i			1.07178i	0.844289	+	0.535888i	$0.180023\pi$
$463$			4.92524e10i			1.07178i	−0.844289	+	0.535888i	$0.819977\pi$
$464$	3.45014e9	+	1.16051e10i	0.0744329	+	0.250367i
$465$		0			0
$466$	2.24651e10	+	4.47851e10i	0.476392	+	0.949707i
$467$			7.83687e9i			0.164769i	0.996601	+	0.0823844i	$0.0262535\pi$
$467$			7.83687e9i			0.164769i	−0.996601	+	0.0823844i	$0.973746\pi$
$468$	2.98444e10	−	4.00080e10i	0.622127	−	0.833994i
$469$	4.34433e9			0.0897907
$470$		0			0
$471$		−	3.63246e9i		−	0.0738103i
$472$	−4.05279e9	+	2.27931e10i	−0.0816556	+	0.459235i
$473$	−3.53890e10			−0.707007
$474$	−2.29394e10	−	4.57307e10i	−0.454432	−	0.905929i
$475$		0			0
$476$	7.29900e9	+	5.44477e9i	0.142179	+	0.106060i
$477$	3.30723e10			0.638838
$478$	2.37633e10	−	1.19202e10i	0.455193	−	0.228334i
$479$		−	2.94112e10i		−	0.558689i	−0.960191	−	0.279345i	$-0.909883\pi$
$479$		−	2.94112e10i		−	0.558689i	0.960191	−	0.279345i	$-0.0901172\pi$
$480$		0			0
$481$	7.08244e10			1.32313
$482$	1.15039e10	+	2.29336e10i	0.213137	+	0.424897i
$483$			1.59022e10i			0.292193i
$484$	6.08390e10	−	8.15579e10i	1.10867	−	1.48622i
$485$		0			0
$486$	−5.16707e10	+	2.59191e10i	−0.926189	+	0.464595i
$487$		−	5.85444e10i		−	1.04080i	−0.853921	−	0.520402i	$-0.825782\pi$
$487$		−	5.85444e10i		−	1.04080i	0.853921	−	0.520402i	$-0.174218\pi$
$488$	2.71691e10	+	4.83089e9i	0.479068	+	0.0851820i
$489$	1.19160e10			0.208399
$490$		0			0
$491$		−	8.05466e10i		−	1.38587i	−0.721002	−	0.692933i	$-0.756318\pi$
$491$		−	8.05466e10i		−	1.38587i	0.721002	−	0.692933i	$-0.243682\pi$
$492$	−1.75731e10	−	1.31088e10i	−0.299907	−	0.223719i
$493$	7.55597e9			0.127909
$494$	−4.67633e10	+	2.34574e10i	−0.785231	+	0.393887i
$495$		0			0
$496$	−9.72129e9	+	2.89010e9i	−0.160619	+	0.0477514i
$497$	−1.80642e10			−0.296069
$498$	−2.67931e10	−	5.34131e10i	−0.435617	−	0.868421i
$499$		−	2.25270e10i		−	0.363330i	−0.983360	−	0.181665i	$-0.941851\pi$
$499$		−	2.25270e10i		−	0.363330i	0.983360	−	0.181665i	$-0.0581487\pi$
$500$		0			0
$501$	−1.83763e10			−0.291681
$502$	−8.84937e10	+	4.43902e10i	−1.39347	+	0.698992i
$503$		−	4.17996e10i		−	0.652981i	−0.945200	−	0.326491i	$-0.894134\pi$
$503$		−	4.17996e10i		−	0.652981i	0.945200	−	0.326491i	$-0.105866\pi$
$504$	−2.95629e9	+	1.66263e10i	−0.0458167	+	0.257676i
$505$		0			0
$506$	−7.60468e10	−	1.51603e11i	−1.16006	−	2.31262i
$507$		−	3.73680e10i		−	0.565547i
$508$	−7.24224e10	−	5.40243e10i	−1.08747	−	0.811212i
$509$	−1.06239e10			−0.158276			−0.0791378	−	0.996864i	$-0.525217\pi$
$509$	−1.06239e10			−0.158276			−0.0791378	+	0.996864i	$0.525217\pi$
$510$		0			0
$511$		−	2.88537e10i		−	0.423173i
$512$	5.93643e10	+	3.46158e10i	0.863864	+	0.503726i
$513$	3.83357e10			0.553521
$514$	−4.45062e10	−	8.87250e10i	−0.637629	−	1.27114i
$515$		0			0
$516$	9.34391e9	−	1.25260e10i	0.131804	−	0.176691i
$517$	1.23303e11			1.72588
$518$	−2.14183e10	+	1.07438e10i	−0.297486	+	0.149225i
$519$			2.90661e10i			0.400606i
$520$		0			0
$521$	−6.29819e10			−0.854800			−0.427400	−	0.904063i	$-0.640570\pi$
$521$	−6.29819e10			−0.854800			−0.427400	+	0.904063i	$0.640570\pi$
$522$	6.28276e9	+	1.25249e10i	0.0846191	+	0.168692i
$523$			2.56642e10i			0.343021i	0.985182	+	0.171511i	$0.0548648\pi$
$523$			2.56642e10i			0.343021i	−0.985182	+	0.171511i	$0.945135\pi$
$524$	2.47547e10	+	1.84660e10i	0.328346	+	0.244933i
$525$		0			0
$526$	2.80779e10	−	1.40844e10i	0.366793	−	0.183991i
$527$			6.32945e9i			0.0820584i
$528$	1.97094e10	+	6.62957e10i	0.253593	+	0.853001i
$529$	−1.05353e11			−1.34531
$530$		0			0
$531$			2.67938e10i			0.337021i
$532$	1.05835e10	−	1.41877e10i	0.132124	−	0.177119i
$533$	8.25532e10			1.02288
$534$	−6.99608e9	+	3.50937e9i	−0.0860379	+	0.0431583i
$535$		0			0
$536$	3.58189e9	−	2.01447e10i	0.0433964	−	0.244063i
$537$	7.94490e10			0.955413
$538$	4.53107e10	+	9.03288e10i	0.540843	+	1.07819i
$539$		−	1.23884e11i		−	1.46778i
$540$		0			0
$541$	7.25189e10			0.846569			0.423285	−	0.905997i	$-0.360877\pi$
$541$	7.25189e10			0.846569			0.423285	+	0.905997i	$0.360877\pi$
$542$	6.73972e10	−	3.38078e10i	0.780989	−	0.391760i
$543$		−	4.03206e10i		−	0.463797i
$544$	3.12655e10	−	2.93564e10i	0.357002	−	0.335203i
$545$		0			0
$546$	1.09483e10	+	2.18259e10i	0.123190	+	0.245585i
$547$		−	2.29110e10i		−	0.255914i	−0.991780	−	0.127957i	$-0.959158\pi$
$547$		−	2.29110e10i		−	0.255914i	0.991780	−	0.127957i	$-0.0408420\pi$
$548$	−4.56160e10	+	6.11506e10i	−0.505819	+	0.678077i
$549$	3.19380e10			0.351575
$550$		0			0
$551$		−	1.46872e10i		−	0.159343i
$552$	7.37390e10	+	1.31114e10i	0.794220	+	0.141219i
$553$	−6.51781e10			−0.696949
$554$	7.22884e8	+	1.44110e9i	0.00767414	+	0.0152987i
$555$		0			0
$556$	8.20989e10	+	6.12426e10i	0.859089	+	0.640847i
$557$	−1.28630e11			−1.33636			−0.668178	−	0.744001i	$-0.732926\pi$
$557$	−1.28630e11			−1.33636			−0.668178	+	0.744001i	$0.732926\pi$
$558$	−1.04918e10	+	5.26291e9i	−0.108222	+	0.0542861i
$559$			5.88436e10i			0.602632i
$560$		0			0
$561$	4.31645e10			0.435788
$562$	3.05865e10	+	6.09754e10i	0.306609	+	0.611237i
$563$		−	1.71738e11i		−	1.70936i	−0.519159	−	0.854678i	$-0.673755\pi$
$563$		−	1.71738e11i		−	1.70936i	0.519159	−	0.854678i	$-0.326245\pi$
$564$	−3.25561e10	+	4.36432e10i	−0.321748	+	0.431320i
$565$		0			0
$566$	−1.66270e11	+	8.34044e10i	−1.62012	+	0.812686i
$567$			9.15734e9i			0.0886007i
$568$	−1.48939e10	+	8.37640e10i	−0.143092	+	0.804756i
$569$	8.20809e10			0.783056			0.391528	−	0.920166i	$-0.371947\pi$
$569$	8.20809e10			0.783056			0.391528	+	0.920166i	$0.371947\pi$
$570$		0			0
$571$			1.07462e11i			1.01090i	0.862855	+	0.505452i	$0.168674\pi$
$571$			1.07462e11i			1.01090i	−0.862855	+	0.505452i	$0.831326\pi$
$572$	−2.08750e11	−	1.55719e11i	−1.95003	−	1.45465i
$573$	2.61914e10			0.242963
$574$	−2.49653e10	+	1.25231e10i	−0.229980	+	0.115362i
$575$		0			0
$576$	7.46590e10	+	2.74167e10i	0.678254	+	0.249072i
$577$	−3.37727e10			−0.304693			−0.152346	−	0.988327i	$-0.548683\pi$
$577$	−3.37727e10			−0.304693			−0.152346	+	0.988327i	$0.548683\pi$
$578$	3.80427e10	+	7.58396e10i	0.340847	+	0.679493i
$579$		−	3.17866e10i		−	0.282832i
$580$		0			0
$581$	−7.61276e10			−0.668094
$582$	5.33700e10	−	2.67714e10i	0.465163	−	0.233335i
$583$		−	1.72561e11i		−	1.49372i
$584$	−1.33795e11	−	2.37898e10i	−1.15024	−	0.204522i
$585$		0			0
$586$	2.69528e10	+	5.37316e10i	0.228567	+	0.455659i
$587$			1.01250e11i			0.852793i	0.904536	+	0.426396i	$0.140217\pi$
$587$			1.01250e11i			0.852793i	−0.904536	+	0.426396i	$0.859783\pi$
$588$	4.38489e10	+	3.27096e10i	0.366817	+	0.273631i
$589$	1.23031e10			0.102224
$590$		0			0
$591$			1.05555e11i			0.865229i
$592$	3.21601e10	+	1.08175e11i	0.261836	+	0.880728i
$593$	1.86134e11			1.50525			0.752624	−	0.658451i	$-0.228788\pi$
$593$	1.86134e11			1.50525			0.752624	+	0.658451i	$0.228788\pi$
$594$	8.55645e10	+	1.70577e11i	0.687303	+	1.37017i
$595$		0			0
$596$	1.17986e11	−	1.58166e11i	0.935069	−	1.25351i
$597$	−3.67969e10			−0.289677
$598$	−2.52080e11	+	1.26448e11i	−1.97121	+	0.988798i
$599$			7.77748e10i			0.604131i	0.953287	+	0.302066i	$0.0976762\pi$
$599$			7.77748e10i			0.604131i	−0.953287	+	0.302066i	$0.902324\pi$
$600$		0			0
$601$	−1.76175e11			−1.35035			−0.675176	−	0.737657i	$-0.735932\pi$
$601$	−1.76175e11			−1.35035			−0.675176	+	0.737657i	$0.735932\pi$
$602$	−8.92640e9	−	1.77952e10i	−0.0679658	−	0.135493i
$603$		−	2.36806e10i		−	0.179112i
$604$	1.04957e11	+	7.82937e10i	0.788611	+	0.588273i
$605$		0			0
$606$	−6.58764e10	+	3.30449e10i	−0.488472	+	0.245027i
$607$		−	1.04822e11i		−	0.772143i	−0.922469	−	0.386071i	$-0.873832\pi$
$607$		−	1.04822e11i		−	0.772143i	0.922469	−	0.386071i	$-0.126168\pi$
$608$	−5.70626e10	−	6.07736e10i	−0.417578	−	0.444734i
$609$	−6.85499e9			−0.0498353
$610$		0			0
$611$		−	2.05023e11i		−	1.47109i
$612$	2.96791e10	−	3.97863e10i	0.211565	−	0.283614i
$613$	−1.64383e10			−0.116417			−0.0582085	−	0.998304i	$-0.518539\pi$
$613$	−1.64383e10			−0.116417			−0.0582085	+	0.998304i	$0.518539\pi$
$614$	8.29987e10	−	4.16338e10i	0.583980	−	0.292936i
$615$		0			0
$616$	8.67511e10	+	1.54250e10i	0.602493	+	0.107128i
$617$	2.58887e11			1.78636			0.893181	−	0.449698i	$-0.148468\pi$
$617$	2.58887e11			1.78636			0.893181	+	0.449698i	$0.148468\pi$
$618$	−2.94599e10	−	5.87296e10i	−0.201966	−	0.402628i
$619$			1.40280e11i			0.955508i	0.878494	+	0.477754i	$0.158549\pi$
$619$			1.40280e11i			0.955508i	−0.878494	+	0.477754i	$0.841451\pi$
$620$		0			0
$621$	2.06650e11			1.38953
$622$	−1.74685e11	+	8.76256e10i	−1.16706	+	0.585422i
$623$			9.97123e9i			0.0661906i
$624$	1.10234e11	−	3.27721e10i	0.727072	−	0.216155i
$625$		0			0
$626$	−6.45522e10	−	1.28687e11i	−0.420352	−	0.837990i
$627$		−	8.39026e10i		−	0.542882i
$628$	−1.30318e10	+	1.74698e10i	−0.0837847	+	0.112318i
$629$	7.04320e10			0.449953
$630$		0			0
$631$			3.75788e10i			0.237042i	0.992952	+	0.118521i	$0.0378153\pi$
$631$			3.75788e10i			0.237042i	−0.992952	+	0.118521i	$0.962185\pi$
$632$	−5.37392e10	+	3.02232e11i	−0.336840	+	1.89440i
$633$	8.80662e10			0.548523
$634$	1.61561e10	+	3.22079e10i	0.0999955	+	0.199345i
$635$		0			0
$636$	6.10784e10	+	4.55621e10i	0.373301	+	0.278468i
$637$	−2.05990e11			−1.25109
$638$	6.53514e10	−	3.27816e10i	0.394432	−	0.197855i
$639$			9.84666e10i			0.590589i
$640$		0			0
$641$	−9.09734e10			−0.538868			−0.269434	−	0.963019i	$-0.586837\pi$
$641$	−9.09734e10			−0.538868			−0.269434	+	0.963019i	$0.586837\pi$
$642$	−2.70430e10	−	5.39115e10i	−0.159190	−	0.317352i
$643$		−	3.82679e10i		−	0.223868i	−0.993716	−	0.111934i	$-0.964296\pi$
$643$		−	3.82679e10i		−	0.223868i	0.993716	−	0.111934i	$-0.0357045\pi$
$644$	5.70507e10	−	7.64794e10i	0.331679	−	0.444633i
$645$		0			0
$646$	−4.65043e10	+	2.33274e10i	−0.267032	+	0.133948i
$647$		−	1.00170e11i		−	0.571635i	−0.958284	−	0.285818i	$-0.907735\pi$
$647$		−	1.00170e11i		−	0.571635i	0.958284	−	0.285818i	$-0.0922652\pi$
$648$	4.24628e10	+	7.55021e9i	0.240829	+	0.0428212i
$649$	1.39802e11			0.788016
$650$		0			0
$651$		−	5.74225e9i		−	0.0319711i
$652$	−5.73083e10	−	4.27498e10i	−0.317123	−	0.236561i
$653$	−1.26162e11			−0.693869			−0.346934	−	0.937889i	$-0.612777\pi$
$653$	−1.26162e11			−0.693869			−0.346934	+	0.937889i	$0.612777\pi$
$654$	2.94208e10	−	1.47581e10i	0.160821	−	0.0806712i
$655$		0			0
$656$	3.74859e10	+	1.26090e11i	0.202420	+	0.680871i
$657$	−1.57279e11			−0.844132
$658$	3.11014e10	+	6.20020e10i	0.165912	+	0.330752i
$659$		−	1.89374e9i		−	0.0100410i	−0.999987	−	0.00502051i	$-0.998402\pi$
$659$		−	1.89374e9i		−	0.0100410i	0.999987	−	0.00502051i	$-0.00159809\pi$
$660$		0			0
$661$	2.06198e11			1.08014			0.540068	−	0.841622i	$-0.318399\pi$
$661$	2.06198e11			1.08014			0.540068	+	0.841622i	$0.318399\pi$
$662$	−2.41084e10	+	1.20933e10i	−0.125527	+	0.0629668i
$663$		−	7.17724e10i		−	0.371453i
$664$	−6.27671e10	+	3.53005e11i	−0.322894	+	1.81597i
$665$		0			0
$666$	5.85639e10	+	1.16750e11i	0.297669	+	0.593415i
$667$		−	7.91720e10i		−	0.400008i
$668$	8.83782e10	+	6.59267e10i	0.443853	+	0.331097i
$669$	−1.06478e11			−0.531563
$670$		0			0
$671$		−	1.66643e11i		−	0.822047i
$672$	−2.83650e10	+	2.66330e10i	−0.139093	+	0.130600i
$673$	−2.75305e11			−1.34200			−0.671002	−	0.741455i	$-0.734136\pi$
$673$	−2.75305e11			−1.34200			−0.671002	+	0.741455i	$0.734136\pi$
$674$	−5.54725e10	−	1.10587e11i	−0.268806	−	0.535875i
$675$		0			0
$676$	−1.34061e11	+	1.79716e11i	−0.641973	+	0.860598i
$677$	2.05068e11			0.976208			0.488104	−	0.872785i	$-0.337689\pi$
$677$	2.05068e11			0.976208			0.488104	+	0.872785i	$0.337689\pi$
$678$	1.12191e11	−	5.62774e10i	0.530934	−	0.266327i
$679$		−	7.60661e10i		−	0.357859i
$680$		0			0
$681$	−1.72947e11			−0.804127
$682$	2.74603e10	+	5.47432e10i	0.126931	+	0.253042i
$683$			3.92855e11i			1.80530i	0.430377	+	0.902649i	$0.358380\pi$
$683$			3.92855e11i			1.80530i	−0.430377	+	0.902649i	$0.641620\pi$
$684$	−7.73362e10	−	5.76898e10i	−0.353312	−	0.263557i
$685$		0			0
$686$	1.33996e11	−	6.72151e10i	0.605056	−	0.303508i
$687$			9.76096e10i			0.438193i
$688$	−8.98763e10	+	2.67198e10i	−0.401136	+	0.119256i
$689$	−2.86929e11			−1.27320
$690$		0			0
$691$			1.92324e11i			0.843570i	0.906696	+	0.421785i	$0.138596\pi$
$691$			1.92324e11i			0.843570i	−0.906696	+	0.421785i	$0.861404\pi$
$692$	1.04277e11	−	1.39789e11i	0.454742	−	0.609606i
$693$	1.01978e11			0.442154
$694$	−4.39677e10	+	2.20550e10i	−0.189538	+	0.0950758i
$695$		0			0
$696$	−5.65193e9	+	3.17867e10i	−0.0240857	+	0.135459i
$697$	8.20959e10			0.347849
$698$	−9.38942e10	−	1.87182e11i	−0.395564	−	0.788574i
$699$			1.33609e11i			0.559662i
$700$		0			0
$701$	2.51795e11			1.04274			0.521369	−	0.853331i	$-0.325421\pi$
$701$	2.51795e11			1.04274			0.521369	+	0.853331i	$0.325421\pi$
$702$	2.83629e11	−	1.42274e11i	1.16789	−	0.585836i
$703$		−	1.36905e11i		−	0.560528i
$704$	1.43052e11	−	3.89549e11i	0.582377	−	1.58588i
$705$		0			0
$706$	−4.74529e10	−	9.45993e10i	−0.191005	−	0.380776i
$707$			9.38911e10i			0.375791i
$708$	−3.69126e10	+	4.94832e10i	−0.146907	+	0.196936i
$709$	4.10364e11			1.62400			0.811998	−	0.583661i	$-0.198380\pi$
$709$	4.10364e11			1.62400			0.811998	+	0.583661i	$0.198380\pi$
$710$		0			0
$711$			3.55281e11i			1.39025i
$712$	4.62368e10	+	8.22126e9i	0.179915	+	0.0319903i
$713$	6.63204e10			0.256619
$714$	1.08877e10	+	2.17050e10i	0.0418930	+	0.0835156i
$715$		0			0
$716$	−3.82098e11	−	2.85030e11i	−1.45386	−	1.08452i
$717$	7.08938e10			0.268245
$718$	4.77795e10	−	2.39672e10i	0.179781	−	0.0901817i
$719$		−	2.36375e11i		−	0.884474i	−0.896898	−	0.442237i	$-0.854185\pi$
$719$		−	2.36375e11i		−	0.884474i	0.896898	−	0.442237i	$-0.145815\pi$
$720$		0			0
$721$	−8.37050e10			−0.309749
$722$	−7.64955e10	−	1.52497e11i	−0.281506	−	0.561193i
$723$			6.84185e10i			0.250392i
$724$	−1.44654e11	+	1.93916e11i	−0.526472	+	0.705764i
$725$		0			0
$726$	2.42528e11	−	1.21657e11i	0.873004	−	0.437916i
$727$			1.16942e11i			0.418631i	0.977848	+	0.209316i	$0.0671236\pi$
$727$			1.16942e11i			0.418631i	−0.977848	+	0.209316i	$0.932876\pi$
$728$	2.56482e10	−	1.44247e11i	0.0913127	−	0.513547i
$729$	−8.50669e10			−0.301197
$730$		0			0
$731$			5.85176e10i			0.204936i
$732$	5.89835e10	+	4.39994e10i	0.205441	+	0.153251i
$733$	4.81267e11			1.66713			0.833566	−	0.552420i	$-0.186296\pi$
$733$	4.81267e11			1.66713			0.833566	+	0.552420i	$0.186296\pi$
$734$	−1.37396e11	+	6.89205e10i	−0.473358	+	0.237445i
$735$		0			0
$736$	−3.07599e11	−	3.27602e11i	−1.04827	−	1.11644i
$737$	−1.23558e11			−0.418796
$738$	6.82624e10	+	1.36084e11i	0.230121	+	0.458756i
$739$			9.92996e10i			0.332943i	0.986046	+	0.166471i	$0.0532374\pi$
$739$			9.92996e10i			0.332943i	−0.986046	+	0.166471i	$0.946763\pi$
$740$		0			0
$741$	−1.39510e11			−0.462736
$742$	8.67715e10	−	4.35263e10i	0.286260	−	0.143594i
$743$			6.32997e10i			0.207705i	0.994593	+	0.103852i	$0.0331170\pi$
$743$			6.32997e10i			0.207705i	−0.994593	+	0.103852i	$0.966883\pi$
$744$	−2.66269e10	−	4.73447e9i	−0.0869019	−	0.0154518i
$745$		0			0
$746$	1.30981e11	+	2.61116e11i	0.422914	+	0.843097i
$747$			4.14966e11i			1.33269i
$748$	−2.07593e11	−	1.54857e11i	−0.663143	−	0.494679i
$749$	−7.68378e10			−0.244145
$750$		0			0
$751$		−	4.98905e11i		−	1.56840i	−0.620505	−	0.784202i	$-0.713072\pi$
$751$		−	4.98905e11i		−	1.56840i	0.620505	−	0.784202i	$-0.286928\pi$
$752$	3.13148e11	−	9.30974e10i	0.979214	−	0.291116i
$753$	−2.64006e11			−0.821171
$754$	−5.45081e10	−	1.08664e11i	−0.168646	−	0.336202i
$755$		0			0
$756$	−6.41909e10	+	8.60513e10i	−0.196511	+	0.263433i
$757$	1.79684e11			0.547174			0.273587	−	0.961847i	$-0.411790\pi$
$757$	1.79684e11			0.547174			0.273587	+	0.961847i	$0.411790\pi$
$758$	2.97766e11	−	1.49365e11i	0.901984	−	0.452453i
$759$		−	4.52281e11i		−	1.36283i
$760$		0			0
$761$	−3.04576e11			−0.908148			−0.454074	−	0.890964i	$-0.650030\pi$
$761$	−3.04576e11			−0.908148			−0.454074	+	0.890964i	$0.650030\pi$
$762$	−1.08030e11	−	2.15362e11i	−0.320424	−	0.638778i
$763$		−	4.19323e10i		−	0.123723i
$764$	−1.25964e11	−	9.39640e10i	−0.369719	−	0.275796i
$765$		0			0
$766$	3.28734e11	−	1.64900e11i	0.954839	−	0.478966i
$767$		−	2.32458e11i		−	0.671682i
$768$	1.00111e11	+	1.53488e11i	0.287763	+	0.441193i
$769$	−2.22920e11			−0.637446			−0.318723	−	0.947848i	$-0.603254\pi$
$769$	−2.22920e11			−0.637446			−0.318723	+	0.947848i	$0.603254\pi$
$770$		0			0
$771$		−	2.64696e11i		−	0.749082i
$772$	−1.14037e11	+	1.52873e11i	−0.321053	+	0.430389i
$773$	−5.59182e11			−1.56616			−0.783078	−	0.621924i	$-0.786351\pi$
$773$	−5.59182e11			−1.56616			−0.783078	+	0.621924i	$0.786351\pi$
$774$	−9.70001e10	+	4.86572e10i	−0.270277	+	0.135576i
$775$		0			0
$776$	−3.52720e11	−	6.27164e10i	−0.972710	−	0.172955i
$777$	−6.38979e10			−0.175308
$778$	−1.14838e11	−	2.28934e11i	−0.313449	−	0.624873i
$779$		−	1.59577e11i		−	0.433332i
$780$		0			0
$781$	5.13770e11			1.38091
$782$	−2.50683e11	+	1.25748e11i	−0.670345	+	0.336258i
$783$			8.90808e10i			0.236994i
$784$	−9.35363e10	−	3.14624e11i	−0.247580	−	0.832775i
$785$		0			0
$786$	3.69256e10	+	7.36128e10i	0.0967471	+	0.192869i
$787$		−	1.13289e11i		−	0.295318i	−0.989038	−	0.147659i	$-0.952826\pi$
$787$		−	1.13289e11i		−	0.295318i	0.989038	−	0.147659i	$-0.0471738\pi$
$788$	3.78690e11	−	5.07654e11i	0.982152	−	1.31663i
$789$	8.37655e10			0.216151
$790$		0			0
$791$		−	1.59902e11i		−	0.408458i
$792$	8.40807e10	−	4.72874e11i	0.213696	−	1.20183i
$793$	−2.77088e11			−0.700689
$794$	−1.23906e11	−	2.47011e11i	−0.311752	−	0.621491i
$795$		0			0
$796$	1.76969e11	+	1.32012e11i	0.440804	+	0.328823i
$797$	−7.63543e11			−1.89234			−0.946172	−	0.323663i	$-0.895086\pi$
$797$	−7.63543e11			−1.89234			−0.946172	+	0.323663i	$0.895086\pi$
$798$	4.21899e10	−	2.11633e10i	0.104039	−	0.0521882i
$799$		−	2.03888e11i		−	0.500269i
$800$		0			0
$801$	5.43525e10			0.132035
$802$	1.12508e11	+	2.24289e11i	0.271948	+	0.542140i
$803$			8.20637e11i			1.97374i
$804$	3.26237e10	−	4.37337e10i	0.0780744	−	0.104663i
$805$		0			0
$806$	9.10252e10	−	4.56600e10i	0.215686	−	0.108192i
$807$			2.69480e11i			0.635379i
$808$	4.35375e11	+	7.74130e10i	1.02145	+	0.181622i
$809$	−4.67881e11			−1.09230			−0.546149	−	0.837688i	$-0.683907\pi$
$809$	−4.67881e11			−1.09230			−0.546149	+	0.837688i	$0.683907\pi$
$810$		0			0
$811$			6.66951e11i			1.54174i	0.636994	+	0.770869i	$0.280178\pi$
$811$			6.66951e11i			1.54174i	−0.636994	+	0.770869i	$0.719822\pi$
$812$	3.29681e10	+	2.45929e10i	0.0758349	+	0.0565699i
$813$	2.01068e11			0.460237
$814$	6.09165e11	−	3.05569e11i	1.38751	−	0.696004i
$815$		0			0
$816$	1.09623e11	−	3.25906e10i	0.247254	−	0.0735074i
$817$	1.13746e11			0.255298
$818$	−7.56985e8	−	1.50908e9i	−0.00169073	−	0.00337054i
$819$		−	1.69565e11i		−	0.376879i
$820$		0			0
$821$	−4.34647e11			−0.956674			−0.478337	−	0.878176i	$-0.658760\pi$
$821$	−4.34647e11			−0.956674			−0.478337	+	0.878176i	$0.658760\pi$
$822$	−1.81843e11	+	9.12163e10i	−0.398300	+	0.199795i
$823$			6.53323e11i			1.42406i	0.702149	+	0.712030i	$0.252224\pi$
$823$			6.53323e11i			1.42406i	−0.702149	+	0.712030i	$0.747776\pi$
$824$	−6.90147e10	+	3.88142e11i	−0.149704	+	0.841941i
$825$		0			0
$826$	3.52632e10	+	7.02987e10i	0.0757534	+	0.151017i
$827$			8.42913e10i			0.180203i	0.995933	+	0.0901013i	$0.0287191\pi$
$827$			8.42913e10i			0.180203i	−0.995933	+	0.0901013i	$0.971281\pi$
$828$	−4.16884e11	−	3.10979e11i	−0.886939	−	0.661622i
$829$	−1.67984e11			−0.355672			−0.177836	−	0.984060i	$-0.556910\pi$
$829$	−1.67984e11			−0.355672			−0.177836	+	0.984060i	$0.556910\pi$
$830$		0			0
$831$			4.29928e9i			0.00901553i
$832$	−6.47728e11	−	2.37862e11i	−1.35176	−	0.496401i
$833$	−2.04849e11			−0.425455
$834$	1.22464e11	+	2.44137e11i	0.253130	+	0.504626i
$835$		0			0
$836$	−3.01008e11	+	4.03517e11i	−0.616245	+	0.826108i
$837$	−7.46207e10			−0.152040
$838$	1.83701e11	−	9.21479e10i	0.372507	−	0.186857i
$839$			8.94664e11i			1.80556i	0.430102	+	0.902780i	$0.358477\pi$
$839$			8.94664e11i			1.80556i	−0.430102	+	0.902780i	$0.641523\pi$
$840$		0			0
$841$	−4.66118e11			−0.931776
$842$	2.21154e11	+	4.40880e11i	0.439994	+	0.877146i
$843$			1.81910e11i			0.360202i
$844$	−4.23542e11	−	3.15946e11i	−0.834692	−	0.622648i
$845$		0			0
$846$	3.37968e11	−	1.69532e11i	0.659773	−	0.330955i
$847$		−	3.45666e11i		−	0.671619i
$848$	−1.30289e11	−	4.38248e11i	−0.251956	−	0.847494i
$849$	−4.96039e11			−0.954739
$850$		0			0
$851$		−	7.37991e11i		−	1.40713i
$852$	−1.35653e11	+	1.81850e11i	−0.257437	+	0.345107i
$853$	−1.57864e11			−0.298186			−0.149093	−	0.988823i	$-0.547635\pi$
$853$	−1.57864e11			−0.298186			−0.149093	+	0.988823i	$0.547635\pi$
$854$	8.37954e10	−	4.20334e10i	0.157539	−	0.0790248i
$855$		0			0
$856$	−6.33527e10	+	3.56299e11i	−0.117997	+	0.663619i
$857$	−1.15753e10			−0.0214590			−0.0107295	−	0.999942i	$-0.503415\pi$
$857$	−1.15753e10			−0.0214590			−0.0107295	+	0.999942i	$0.503415\pi$
$858$	−3.11385e11	−	6.20758e11i	−0.574577	−	1.14544i
$859$			5.96689e10i			0.109591i	0.998498	+	0.0547956i	$0.0174507\pi$
$859$			5.96689e10i			0.109591i	−0.998498	+	0.0547956i	$0.982549\pi$
$860$		0			0
$861$	−7.44797e10			−0.135527
$862$	1.37247e11	−	6.88458e10i	0.248584	−	0.124695i
$863$			1.49504e11i			0.269532i	0.990877	+	0.134766i	$0.0430282\pi$
$863$			1.49504e11i			0.269532i	−0.990877	+	0.134766i	$0.956972\pi$
$864$	3.46096e11	+	3.68604e11i	0.621072	+	0.661462i
$865$		0			0
$866$	4.80057e9	+	9.57014e9i	0.00853535	+	0.0170156i
$867$			2.26255e11i			0.400425i
$868$	−2.06008e10	+	2.76165e10i	−0.0362916	+	0.0486508i
$869$	1.85375e12			3.25067
$870$		0			0
$871$			2.05449e11i			0.356969i
$872$	−1.94441e11	−	3.45731e10i	−0.336296	−	0.0597961i
$873$	−4.14631e11			−0.713846
$874$	2.44427e11	+	4.87275e11i	0.418893	+	0.835080i
$875$		0			0
$876$	−2.90466e11	−	2.16676e11i	−0.493263	−	0.367955i
$877$	8.95446e11			1.51370			0.756852	−	0.653587i	$-0.226736\pi$
$877$	8.95446e11			1.51370			0.756852	+	0.653587i	$0.226736\pi$
$878$	−5.36959e11	+	2.69349e11i	−0.903573	+	0.453250i
$879$			1.60299e11i			0.268519i
$880$		0			0
$881$	9.41351e11			1.56260			0.781300	−	0.624155i	$-0.214557\pi$
$881$	9.41351e11			1.56260			0.781300	+	0.624155i	$0.214557\pi$
$882$	−1.70331e11	−	3.39562e11i	−0.281462	−	0.561106i
$883$		−	8.12182e11i		−	1.33601i	−0.744156	−	0.668006i	$-0.767148\pi$
$883$		−	8.12182e11i		−	1.33601i	0.744156	−	0.668006i	$-0.232852\pi$
$884$	−2.57490e11	+	3.45179e11i	−0.421649	+	0.565243i
$885$		0			0
$886$	−1.71599e11	+	8.60775e10i	−0.278471	+	0.139687i
$887$			4.35414e11i			0.703409i	0.936111	+	0.351704i	$0.114398\pi$
$887$			4.35414e11i			0.703409i	−0.936111	+	0.351704i	$0.885602\pi$
$888$	−5.26837e10	+	2.96296e11i	−0.0847275	+	0.476512i
$889$	−3.06947e11			−0.491424
$890$		0			0
$891$		−	2.60447e11i		−	0.413246i
$892$	5.12089e11	+	3.81999e11i	0.808884	+	0.603396i
$893$	−3.96314e11			−0.623209
$894$	4.70337e11	−	2.35930e11i	0.736308	−	0.369346i
$895$		0			0
$896$	2.31965e11	−	2.63254e10i	0.359908	−	0.0408454i
$897$	−7.52036e11			−1.16163
$898$	4.92242e11	+	9.81306e11i	0.756961	+	1.50903i
$899$			2.85888e10i			0.0437680i
$900$		0			0
$901$	−2.85339e11			−0.432975
$902$	7.10046e11	−	3.56173e11i	1.07266	−	0.538065i
$903$		−	5.30888e10i		−	0.0798458i
$904$	−7.41468e11	−	1.31839e11i	−1.11025	−	0.197410i
$905$		0			0
$906$	1.56560e11	+	3.12110e11i	0.232364	+	0.463227i
$907$		−	8.59055e11i		−	1.26938i	−0.772766	−	0.634690i	$-0.781128\pi$
$907$		−	8.59055e11i		−	1.26938i	0.772766	−	0.634690i	$-0.218872\pi$
$908$	8.31763e11	+	6.20463e11i	1.22365	+	0.912793i
$909$	5.11793e11			0.749617
$910$		0			0
$911$			9.78674e11i			1.42090i	0.703746	+	0.710452i	$0.251509\pi$
$911$			9.78674e11i			1.42090i	−0.703746	+	0.710452i	$0.748491\pi$
$912$	−6.33491e10	−	2.13085e11i	−0.0915717	−	0.308016i
$913$	2.16517e12			3.11608
$914$	3.64502e11	+	7.26650e11i	0.522294	+	1.04122i
$915$		0			0
$916$	3.50183e11	−	4.69439e11i	0.497409	−	0.666803i
$917$	1.04917e11			0.148378
$918$	2.82058e11	−	1.41486e11i	0.397161	−	0.199224i
$919$			3.76307e11i			0.527571i	0.964581	+	0.263785i	$0.0849711\pi$
$919$			3.76307e11i			0.527571i	−0.964581	+	0.263785i	$0.915029\pi$
$920$		0			0
$921$	2.47613e11			0.344139
$922$	2.48558e11	+	4.95510e11i	0.343957	+	0.685692i
$923$		−	8.54278e11i		−	1.17704i
$924$	1.88334e11	+	1.40490e11i	0.258370	+	0.192734i
$925$		0			0
$926$	7.04387e11	−	3.53334e11i	0.958004	−	0.480553i
$927$			4.56270e11i			0.617878i
$928$	1.41220e11	−	1.32597e11i	0.190416	−	0.178789i
$929$	−1.22156e12			−1.64003			−0.820013	−	0.572345i	$-0.806034\pi$
$929$	−1.22156e12			−1.64003			−0.820013	+	0.572345i	$0.806034\pi$
$930$		0			0
$931$			3.98183e11i			0.530009i
$932$	4.79333e11	−	6.42571e11i	0.635293	−	0.851643i
$933$	−5.21144e11			−0.687751
$934$	1.12079e11	−	5.62212e10i	0.147278	−	0.0738776i
$935$		0			0
$936$	−7.86278e11	−	1.39806e11i	−1.02441	−	0.182148i
$937$	5.06116e11			0.656586			0.328293	−	0.944576i	$-0.393527\pi$
$937$	5.06116e11			0.656586			0.328293	+	0.944576i	$0.393527\pi$
$938$	−3.11660e10	−	6.21307e10i	−0.0402596	−	0.0802592i
$939$		−	3.83917e11i		−	0.493827i
$940$		0			0
$941$	−6.00360e9			−0.00765690			−0.00382845	−	0.999993i	$-0.501219\pi$
$941$	−6.00360e9			−0.00765690			−0.00382845	+	0.999993i	$0.501219\pi$
$942$	−5.19498e10	+	2.60590e10i	−0.0659751	+	0.0330944i
$943$		−	8.60207e11i		−	1.08782i
$944$	3.55051e11	−	1.05555e11i	0.447098	−	0.132920i
$945$		0			0
$946$	2.53879e11	+	5.06118e11i	0.317002	+	0.631957i
$947$			3.08522e11i			0.383606i	0.981433	+	0.191803i	$0.0614335\pi$
$947$			3.08522e11i			0.383606i	−0.981433	+	0.191803i	$0.938567\pi$
$948$	−4.89454e11	+	6.56138e11i	−0.606008	+	0.812385i
$949$	1.36453e12			1.68235
$950$		0			0
$951$			9.60868e10i			0.117474i
$952$	2.55061e10	−	1.43448e11i	0.0310525	−	0.174641i
$953$	6.14491e11			0.744979			0.372489	−	0.928036i	$-0.378504\pi$
$953$	6.14491e11			0.744979			0.372489	+	0.928036i	$0.378504\pi$
$954$	−2.37259e11	−	4.72985e11i	−0.286436	−	0.571023i
$955$		0			0
$956$	−3.40953e11	−	2.54338e11i	−0.408191	−	0.304495i
$957$	1.94965e11			0.232439
$958$	−4.20625e11	+	2.10994e11i	−0.499383	+	0.250500i
$959$			2.59174e11i			0.306420i
$960$		0			0
$961$	8.28943e11			0.971921
$962$	−5.08090e11	−	1.01290e12i	−0.593253	−	1.18268i
$963$			4.18838e11i			0.487013i
$964$	2.45458e11	−	3.29049e11i	0.284229	−	0.381024i
$965$		0			0
$966$	2.27427e11	−	1.14082e11i	0.261176	−	0.131011i
$967$		−	7.29374e11i		−	0.834150i	−0.908872	−	0.417075i	$-0.863055\pi$
$967$		−	7.29374e11i		−	0.834150i	0.908872	−	0.417075i	$-0.136945\pi$
$968$	−1.60286e12	−	2.85001e11i	−1.82555	−	0.324597i
$969$	−1.38738e11			−0.157362
$970$		0			0
$971$			4.05501e11i			0.456158i	0.973643	+	0.228079i	$0.0732444\pi$
$971$			4.05501e11i			0.456158i	−0.973643	+	0.228079i	$0.926756\pi$
$972$	7.41366e11	+	5.53030e11i	0.830553	+	0.619561i
$973$	3.47959e11			0.388219
$974$	−8.37276e11	+	4.19994e11i	−0.930320	+	0.466667i
$975$		0			0
$976$	−1.25821e11	−	4.23218e11i	−0.138661	−	0.466406i
$977$	5.72274e11			0.628096			0.314048	−	0.949407i	$-0.398315\pi$
$977$	5.72274e11			0.628096			0.314048	+	0.949407i	$0.398315\pi$
$978$	−8.54848e10	−	1.70418e11i	−0.0934401	−	0.186277i
$979$		−	2.83595e11i		−	0.308722i
$980$		0			0
$981$	−2.28570e11			−0.246799
$982$	−1.15194e12	+	5.77837e11i	−1.23875	+	0.621383i
$983$		−	8.31746e11i		−	0.890792i	−0.895334	−	0.445396i	$-0.853063\pi$
$983$		−	8.31746e11i		−	0.890792i	0.895334	−	0.445396i	$-0.146937\pi$
$984$	−6.14084e10	+	3.45364e11i	−0.0655009	+	0.368380i
$985$		0			0
$986$	−5.42061e10	−	1.08062e11i	−0.0573509	−	0.114332i
$987$			1.84972e11i			0.194912i
$988$	6.70954e11	+	5.00506e11i	0.704150	+	0.525269i
$989$	6.13152e11			0.640889
$990$		0			0
$991$		−	1.13988e12i		−	1.18186i	−0.806724	−	0.590928i	$-0.798762\pi$
$991$		−	1.13988e12i		−	1.18186i	0.806724	−	0.590928i	$-0.201238\pi$
$992$	1.11073e11	+	1.18296e11i	0.114699	+	0.122159i
$993$	−7.19234e10			−0.0739729
$994$	1.29591e11	+	2.58346e11i	0.132749	+	0.264641i
$995$		0			0
$996$	−5.71679e11	+	7.66365e11i	−0.580918	+	0.778750i
$997$	−1.49273e11			−0.151078			−0.0755390	−	0.997143i	$-0.524068\pi$
$997$	−1.49273e11			−0.151078			−0.0755390	+	0.997143i	$0.524068\pi$
$998$	−3.22172e11	+	1.61608e11i	−0.324762	+	0.162907i
$999$			8.30355e11i			0.833685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.b.g.51.7		20
4.3	odd	2	inner	100.9.b.g.51.8		20
5.2	odd	4		20.9.d.c.19.17	yes	20
5.3	odd	4		20.9.d.c.19.4	yes	20
5.4	even	2	inner	100.9.b.g.51.14		20
20.3	even	4		20.9.d.c.19.18	yes	20
20.7	even	4		20.9.d.c.19.3	✓	20
20.19	odd	2	inner	100.9.b.g.51.13		20
40.3	even	4		320.9.h.g.319.11		20
40.13	odd	4		320.9.h.g.319.9		20
40.27	even	4		320.9.h.g.319.10		20
40.37	odd	4		320.9.h.g.319.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.d.c.19.3	✓	20	20.7	even	4
20.9.d.c.19.4	yes	20	5.3	odd	4
20.9.d.c.19.17	yes	20	5.2	odd	4
20.9.d.c.19.18	yes	20	20.3	even	4
100.9.b.g.51.7		20	1.1	even	1	trivial
100.9.b.g.51.8		20	4.3	odd	2	inner
100.9.b.g.51.13		20	20.19	odd	2	inner
100.9.b.g.51.14		20	5.4	even	2	inner
320.9.h.g.319.9		20	40.13	odd	4
320.9.h.g.319.10		20	40.27	even	4
320.9.h.g.319.11		20	40.3	even	4
320.9.h.g.319.12		20	40.37	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.17394 - 14.3016i) q^{2} -42.6663i q^{3} +(-153.069 + 205.197i) q^{4} +(-610.194 + 306.085i) q^{6} +869.685i q^{7} +(4032.75 + 717.054i) q^{8} +4740.59 q^{9} -24735.0i q^{11} +(8754.99 + 6530.89i) q^{12} -41128.5 q^{13} +(12437.9 - 6239.07i) q^{14} +(-18675.7 - 62818.7i) q^{16} -40900.7 q^{17} +(-34008.7 - 67797.8i) q^{18} +79502.2i q^{19} +37106.2 q^{21} +(-353749. + 177447. i) q^{22} +428560. i q^{23} +(30594.0 - 172062. i) q^{24} +(295053. + 588201. i) q^{26} -482197. i q^{27} +(-178457. - 133122. i) q^{28} -184740. q^{29} -154752. i q^{31} +(-764426. + 717749. i) q^{32} -1.05535e6 q^{33} +(293419. + 584943. i) q^{34} +(-725638. + 972755. i) q^{36} -1.72203e6 q^{37} +(1.13701e6 - 570344. i) q^{38} +1.75480e6i q^{39} -2.00720e6 q^{41} +(-266198. - 530677. i) q^{42} -1.43073e6i q^{43} +(5.07555e6 + 3.78616e6i) q^{44} +(6.12907e6 - 3.07446e6i) q^{46} +4.98494e6i q^{47} +(-2.68024e6 + 796823. i) q^{48} +5.00845e6 q^{49} +1.74508e6i q^{51} +(6.29550e6 - 8.43945e6i) q^{52} +6.97640e6 q^{53} +(-6.89616e6 + 3.45925e6i) q^{54} +(-623611. + 3.50722e6i) q^{56} +3.39206e6 q^{57} +(1.32531e6 + 2.64206e6i) q^{58} +5.65200e6i q^{59} +6.73713e6 q^{61} +(-2.21319e6 + 1.11018e6i) q^{62} +4.12282e6i q^{63} +(1.57489e7 + 5.78340e6i) q^{64} +(7.57102e6 + 1.50931e7i) q^{66} -4.99529e6i q^{67} +(6.26063e6 - 8.39270e6i) q^{68} +1.82850e7 q^{69} +2.07710e7i q^{71} +(1.91176e7 + 3.39926e6i) q^{72} -3.31772e7 q^{73} +(1.23537e7 + 2.46277e7i) q^{74} +(-1.63136e7 - 1.21693e7i) q^{76} +2.15117e7 q^{77} +(2.50964e7 - 1.25888e7i) q^{78} +7.49445e7i q^{79} +1.05295e7 q^{81} +(1.43996e7 + 2.87061e7i) q^{82} +8.75346e7i q^{83} +(-5.67981e6 + 7.61409e6i) q^{84} +(-2.04616e7 + 1.02639e7i) q^{86} +7.88215e6i q^{87} +(1.77363e7 - 9.97500e7i) q^{88} +1.14653e7 q^{89} -3.57688e7i q^{91} +(-8.79392e7 - 6.55993e7i) q^{92} -6.60268e6 q^{93} +(7.12925e7 - 3.57617e7i) q^{94} +(3.06237e7 + 3.26152e7i) q^{96} -8.74640e7 q^{97} +(-3.59303e7 - 7.16286e7i) q^{98} -1.17258e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 752 q^{4} + 3408 q^{6} - 2556 q^{9} - 8848 q^{14} - 59200 q^{16} + 410256 q^{21} + 156672 q^{24} - 440448 q^{26} - 660136 q^{29} - 4342528 q^{34} - 7191312 q^{36} + 7068520 q^{41} - 2666880 q^{44}+ \cdots + 28850688 q^{96}+O(q^{100}) \) 20 * q + 752 * q^4 + 3408 * q^6 - 2556 * q^9 - 8848 * q^14 - 59200 * q^16 + 410256 * q^21 + 156672 * q^24 - 440448 * q^26 - 660136 * q^29 - 4342528 * q^34 - 7191312 * q^36 + 7068520 * q^41 - 2666880 * q^44 + 561168 * q^46 - 11719036 * q^49 - 37110816 * q^54 - 35044352 * q^56 - 17660440 * q^61 - 20201728 * q^64 + 31902720 * q^66 - 111747216 * q^69 - 19114368 * q^74 - 54998400 * q^76 - 154212444 * q^81 - 101289216 * q^84 + 94429648 * q^86 - 105006376 * q^89 + 192757872 * q^94 + 28850688 * q^96

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