LMFDB - Embedded newform 20.11.d.d.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,11,Mod(19,20)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("20.19");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	20.d (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:	$12.7071450535$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	20.19
Dual form			20.11.d.d.19.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(17.2353 + 26.9619i) q^{2} +146.443 q^{3} +(-429.889 + 929.393i) q^{4} +(-2538.13 - 1823.05i) q^{5} +(2523.99 + 3948.38i) q^{6} -13979.7 q^{7} +(-32467.5 + 4427.76i) q^{8} -37603.5 q^{9} +O(q^{10})$	\(q+(17.2353 + 26.9619i) q^{2} +146.443 q^{3} +(-429.889 + 929.393i) q^{4} +(-2538.13 - 1823.05i) q^{5} +(2523.99 + 3948.38i) q^{6} -13979.7 q^{7} +(-32467.5 + 4427.76i) q^{8} -37603.5 q^{9} +(5407.52 - 99853.7i) q^{10} +88389.7i q^{11} +(-62954.1 + 136103. i) q^{12} +249490. i q^{13} +(-240944. - 376918. i) q^{14} +(-371691. - 266973. i) q^{15} +(-678968. - 799071. i) q^{16} +410905. i q^{17} +(-648107. - 1.01386e6i) q^{18} -3.01950e6i q^{19} +(2.78545e6 - 1.57521e6i) q^{20} -2.04722e6 q^{21} +(-2.38315e6 + 1.52342e6i) q^{22} -4.53962e6 q^{23} +(-4.75463e6 + 648414. i) q^{24} +(3.11858e6 + 9.25429e6i) q^{25} +(-6.72671e6 + 4.30003e6i) q^{26} -1.41541e7 q^{27} +(6.00970e6 - 1.29926e7i) q^{28} +2.62491e7 q^{29} +(791893. - 1.46229e7i) q^{30} +3.62534e7i q^{31} +(9.84227e6 - 3.20785e7i) q^{32} +1.29440e7i q^{33} +(-1.10788e7 + 7.08207e6i) q^{34} +(3.54822e7 + 2.54857e7i) q^{35} +(1.61653e7 - 3.49484e7i) q^{36} +8.29063e7i q^{37} +(8.14114e7 - 5.20419e7i) q^{38} +3.65360e7i q^{39} +(9.04787e7 + 4.79517e7i) q^{40} +1.07285e8 q^{41} +(-3.52845e7 - 5.51970e7i) q^{42} +1.58335e6 q^{43} +(-8.21488e7 - 3.79977e7i) q^{44} +(9.54425e7 + 6.85531e7i) q^{45} +(-7.82418e7 - 1.22397e8i) q^{46} -4.34667e8 q^{47} +(-9.94300e7 - 1.17018e8i) q^{48} -8.70443e7 q^{49} +(-1.95763e8 + 2.43583e8i) q^{50} +6.01741e7i q^{51} +(-2.31874e8 - 1.07253e8i) q^{52} +3.42615e8i q^{53} +(-2.43950e8 - 3.81621e8i) q^{54} +(1.61139e8 - 2.24345e8i) q^{55} +(4.53884e8 - 6.18986e7i) q^{56} -4.42184e8i q^{57} +(4.52411e8 + 7.07725e8i) q^{58} -8.22725e8i q^{59} +(4.07909e8 - 2.30679e8i) q^{60} -9.43238e8 q^{61} +(-9.77460e8 + 6.24838e8i) q^{62} +5.25684e8 q^{63} +(1.03453e9 - 2.87516e8i) q^{64} +(4.54833e8 - 6.33237e8i) q^{65} +(-3.48996e8 + 2.23094e8i) q^{66} +1.13591e9 q^{67} +(-3.81892e8 - 1.76643e8i) q^{68} -6.64796e8 q^{69} +(-7.55953e7 + 1.39592e9i) q^{70} +2.91342e9i q^{71} +(1.22089e9 - 1.66499e8i) q^{72} -2.08673e9i q^{73} +(-2.23531e9 + 1.42892e9i) q^{74} +(4.56695e8 + 1.35522e9i) q^{75} +(2.80630e9 + 1.29805e9i) q^{76} -1.23566e9i q^{77} +(-9.85080e8 + 6.29709e8i) q^{78} -5.83812e9i q^{79} +(2.66559e8 + 3.26594e9i) q^{80} +1.47685e8 q^{81} +(1.84909e9 + 2.89261e9i) q^{82} -9.99337e8 q^{83} +(8.80078e8 - 1.90267e9i) q^{84} +(7.49101e8 - 1.04293e9i) q^{85} +(2.72896e7 + 4.26902e7i) q^{86} +3.84399e9 q^{87} +(-3.91368e8 - 2.86979e9i) q^{88} -3.97301e9 q^{89} +(-2.03342e8 + 3.75485e9i) q^{90} -3.48778e9i q^{91} +(1.95153e9 - 4.21910e9i) q^{92} +5.30905e9i q^{93} +(-7.49163e9 - 1.17195e10i) q^{94} +(-5.50470e9 + 7.66388e9i) q^{95} +(1.44133e9 - 4.69767e9i) q^{96} +6.44299e9i q^{97} +(-1.50024e9 - 2.34688e9i) q^{98} -3.32376e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	$ 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$-1$

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 $

$2$	17.2353	+	26.9619i	0.538603	+	0.842560i
$2$	17.2353	+	26.9619i	0.538603	+	0.842560i
$3$	146.443			0.602646			0.301323	−	0.953522i	$-0.402572\pi$
$3$	146.443			0.602646			0.301323	+	0.953522i	$0.402572\pi$
$4$	−429.889	+	929.393i	−0.419813	+	0.907611i
$5$	−2538.13	−	1823.05i	−0.812202	−	0.583377i
$5$	−2538.13	−	1823.05i	−0.812202	−	0.583377i
$6$	2523.99	+	3948.38i	0.324587	+	0.507765i
$7$	−13979.7			−0.831776			−0.415888	−	0.909416i	$-0.636529\pi$
$7$	−13979.7			−0.831776			−0.415888	+	0.909416i	$0.636529\pi$
$8$	−32467.5	+	4427.76i	−0.990829	+	0.135124i
$9$	−37603.5			−0.636818
$10$	5407.52	−	99853.7i	0.0540752	−	0.998537i
$11$			88389.7i			0.548830i	0.961611	+	0.274415i	$0.0884843\pi$
$11$			88389.7i			0.548830i	−0.961611	+	0.274415i	$0.911516\pi$
$12$	−62954.1	+	136103.i	−0.252999	+	0.546968i
$13$			249490.i			0.671948i	0.941871	+	0.335974i	$0.109065\pi$
$13$			249490.i			0.671948i	−0.941871	+	0.335974i	$0.890935\pi$
$14$	−240944.	−	376918.i	−0.447997	−	0.700821i
$15$	−371691.	−	266973.i	−0.489470	−	0.351569i
$16$	−678968.	−	799071.i	−0.647514	−	0.762054i
$17$			410905.i			0.289399i	0.989476	+	0.144699i	$0.0462215\pi$
$17$			410905.i			0.289399i	−0.989476	+	0.144699i	$0.953779\pi$
$18$	−648107.	−	1.01386e6i	−0.342992	−	0.536557i
$19$		−	3.01950e6i		−	1.21946i	−0.792610	−	0.609729i	$-0.791278\pi$
$19$		−	3.01950e6i		−	1.21946i	0.792610	−	0.609729i	$-0.208722\pi$
$20$	2.78545e6	−	1.57521e6i	0.870452	−	0.492254i
$21$	−2.04722e6			−0.501266
$22$	−2.38315e6	+	1.52342e6i	−0.462422	+	0.295602i
$23$	−4.53962e6			−0.705311			−0.352655	−	0.935753i	$-0.614721\pi$
$23$	−4.53962e6			−0.705311			−0.352655	+	0.935753i	$0.614721\pi$
$24$	−4.75463e6	+	648414.i	−0.597119	+	0.0814322i
$25$	3.11858e6	+	9.25429e6i	0.319343	+	0.947639i
$26$	−6.72671e6	+	4.30003e6i	−0.566156	+	0.361913i
$27$	−1.41541e7			−0.986421
$28$	6.00970e6	−	1.29926e7i	0.349191	−	0.754929i
$29$	2.62491e7			1.27975			0.639874	−	0.768480i	$-0.278987\pi$
$29$	2.62491e7			1.27975			0.639874	+	0.768480i	$0.278987\pi$
$30$	791893.	−	1.46229e7i	0.0325882	−	0.601764i
$31$			3.62534e7i			1.26631i	0.774025	+	0.633155i	$0.218240\pi$
$31$			3.62534e7i			1.26631i	−0.774025	+	0.633155i	$0.781760\pi$
$32$	9.84227e6	−	3.20785e7i	0.293323	−	0.956014i
$33$			1.29440e7i			0.330750i
$34$	−1.10788e7	+	7.08207e6i	−0.243836	+	0.155871i
$35$	3.54822e7	+	2.54857e7i	0.675570	+	0.485239i
$36$	1.61653e7	−	3.49484e7i	0.267345	−	0.577983i
$37$			8.29063e7i			1.19558i	0.801652	+	0.597791i	$0.203955\pi$
$37$			8.29063e7i			1.19558i	−0.801652	+	0.597791i	$0.796045\pi$
$38$	8.14114e7	−	5.20419e7i	1.02747	−	0.656804i
$39$			3.65360e7i			0.404947i
$40$	9.04787e7	+	4.79517e7i	0.883581	+	0.468278i
$41$	1.07285e8			0.926018			0.463009	−	0.886354i	$-0.346770\pi$
$41$	1.07285e8			0.926018			0.463009	+	0.886354i	$0.346770\pi$
$42$	−3.52845e7	−	5.51970e7i	−0.269984	−	0.422347i
$43$	1.58335e6			0.0107705			0.00538525	−	0.999985i	$-0.498286\pi$
$43$	1.58335e6			0.0107705			0.00538525	+	0.999985i	$0.498286\pi$
$44$	−8.21488e7	−	3.79977e7i	−0.498124	−	0.230406i
$45$	9.54425e7	+	6.85531e7i	0.517225	+	0.371505i
$46$	−7.82418e7	−	1.22397e8i	−0.379883	−	0.594266i
$47$	−4.34667e8			−1.89526			−0.947628	−	0.319376i	$-0.896527\pi$
$47$	−4.34667e8			−1.89526			−0.947628	+	0.319376i	$0.896527\pi$
$48$	−9.94300e7	−	1.17018e8i	−0.390221	−	0.459248i
$49$	−8.70443e7			−0.308148
$50$	−1.95763e8	+	2.43583e8i	−0.626443	+	0.779467i
$51$			6.01741e7i			0.174405i
$52$	−2.31874e8	−	1.07253e8i	−0.609867	−	0.282093i
$53$			3.42615e8i			0.819269i	0.912250	+	0.409635i	$0.134344\pi$
$53$			3.42615e8i			0.819269i	−0.912250	+	0.409635i	$0.865656\pi$
$54$	−2.43950e8	−	3.81621e8i	−0.531290	−	0.831119i
$55$	1.61139e8	−	2.24345e8i	0.320175	−	0.445761i
$56$	4.53884e8	−	6.18986e7i	0.824148	−	0.112393i
$57$		−	4.42184e8i		−	0.734901i
$58$	4.52411e8	+	7.07725e8i	0.689276	+	1.07826i
$59$		−	8.22725e8i		−	1.15079i	−0.817877	−	0.575393i	$-0.804849\pi$
$59$		−	8.22725e8i		−	1.15079i	0.817877	−	0.575393i	$-0.195151\pi$
$60$	4.07909e8	−	2.30679e8i	0.524574	−	0.296654i
$61$	−9.43238e8			−1.11679			−0.558396	−	0.829575i	$-0.688583\pi$
$61$	−9.43238e8			−1.11679			−0.558396	+	0.829575i	$0.688583\pi$
$62$	−9.77460e8	+	6.24838e8i	−1.06694	+	0.682039i
$63$	5.25684e8			0.529690
$64$	1.03453e9	−	2.87516e8i	0.963483	−	0.267770i
$65$	4.54833e8	−	6.33237e8i	0.391999	−	0.545757i
$66$	−3.48996e8	+	2.23094e8i	−0.278677	+	0.178143i
$67$	1.13591e9			0.841333			0.420667	−	0.907215i	$-0.361796\pi$
$67$	1.13591e9			0.841333			0.420667	+	0.907215i	$0.361796\pi$
$68$	−3.81892e8	−	1.76643e8i	−0.262661	−	0.121493i
$69$	−6.64796e8			−0.425053
$70$	−7.55953e7	+	1.39592e9i	−0.0449785	+	0.830559i
$71$			2.91342e9i			1.61477i	0.590023	+	0.807386i	$0.299118\pi$
$71$			2.91342e9i			1.61477i	−0.590023	+	0.807386i	$0.700882\pi$
$72$	1.22089e9	−	1.66499e8i	0.630978	−	0.0860497i
$73$		−	2.08673e9i		−	1.00659i	−0.864114	−	0.503295i	$-0.832121\pi$
$73$		−	2.08673e9i		−	1.00659i	0.864114	−	0.503295i	$-0.167879\pi$
$74$	−2.23531e9	+	1.42892e9i	−1.00735	+	0.643944i
$75$	4.56695e8	+	1.35522e9i	0.192451	+	0.571091i
$76$	2.80630e9	+	1.29805e9i	1.10679	+	0.511944i
$77$		−	1.23566e9i		−	0.456504i
$78$	−9.85080e8	+	6.29709e8i	−0.341192	+	0.218106i
$79$		−	5.83812e9i		−	1.89731i	−0.316318	−	0.948653i	$-0.602447\pi$
$79$		−	5.83812e9i		−	1.89731i	0.316318	−	0.948653i	$-0.397553\pi$
$80$	2.66559e8	+	3.26594e9i	0.0813475	+	0.996686i
$81$	1.47685e8			0.0423556
$82$	1.84909e9	+	2.89261e9i	0.498756	+	0.780225i
$83$	−9.99337e8			−0.253700			−0.126850	−	0.991922i	$-0.540487\pi$
$83$	−9.99337e8			−0.253700			−0.126850	+	0.991922i	$0.540487\pi$
$84$	8.80078e8	−	1.90267e9i	0.210438	−	0.454955i
$85$	7.49101e8	−	1.04293e9i	0.168828	−	0.235050i
$86$	2.72896e7	+	4.26902e7i	0.00580102	+	0.00907478i
$87$	3.84399e9			0.771234
$88$	−3.91368e8	−	2.86979e9i	−0.0741604	−	0.543797i
$89$	−3.97301e9			−0.711492			−0.355746	−	0.934583i	$-0.615773\pi$
$89$	−3.97301e9			−0.711492			−0.355746	+	0.934583i	$0.615773\pi$
$90$	−2.03342e8	+	3.75485e9i	−0.0344361	+	0.635886i
$91$		−	3.48778e9i		−	0.558910i
$92$	1.95153e9	−	4.21910e9i	0.296099	−	0.640148i
$93$			5.30905e9i			0.763136i
$94$	−7.49163e9	−	1.17195e10i	−1.02079	−	1.59687i
$95$	−5.50470e9	+	7.66388e9i	−0.711403	+	0.990445i
$96$	1.44133e9	−	4.69767e9i	0.176770	−	0.576137i
$97$			6.44299e9i			0.750290i	0.926966	+	0.375145i	$0.122407\pi$
$97$			6.44299e9i			0.750290i	−0.926966	+	0.375145i	$0.877593\pi$
$98$	−1.50024e9	−	2.34688e9i	−0.165970	−	0.259633i
$99$		−	3.32376e9i		−	0.349505i
$100$	−9.94152e9	−	1.07992e9i	−0.994152	−	0.107992i
$101$	8.50355e9			0.809083			0.404542	−	0.914520i	$-0.367431\pi$
$101$	8.50355e9			0.809083			0.404542	+	0.914520i	$0.367431\pi$
$102$	−1.62241e9	+	1.03712e9i	−0.146946	+	0.0939350i
$103$	−1.62785e10			−1.40420			−0.702100	−	0.712078i	$-0.747754\pi$
$103$	−1.62785e10			−1.40420			−0.702100	+	0.712078i	$0.747754\pi$
$104$	−1.10468e9	−	8.10030e9i	−0.0907966	−	0.665785i
$105$	5.19612e9	+	3.73219e9i	0.407129	+	0.292427i
$106$	−9.23755e9	+	5.90507e9i	−0.690283	+	0.441261i
$107$	−8.18368e8			−0.0583485			−0.0291743	−	0.999574i	$-0.509288\pi$
$107$	−8.18368e8			−0.0583485			−0.0291743	+	0.999574i	$0.509288\pi$
$108$	6.08467e9	−	1.31547e10i	0.414113	−	0.895286i
$109$	−2.97062e9			−0.193070			−0.0965350	−	0.995330i	$-0.530776\pi$
$109$	−2.97062e9			−0.193070			−0.0965350	+	0.995330i	$0.530776\pi$
$110$	8.82604e9	+	4.77969e8i	0.548027	+	0.0296781i
$111$			1.21410e10i			0.720512i
$112$	9.49174e9	+	1.11707e10i	0.538587	+	0.633858i
$113$			2.00487e10i			1.08816i	0.839033	+	0.544080i	$0.183121\pi$
$113$			2.00487e10i			1.08816i	−0.839033	+	0.544080i	$0.816879\pi$
$114$	1.19221e10	−	7.62117e9i	0.619198	−	0.395820i
$115$	1.15222e10	+	8.27597e9i	0.572855	+	0.411462i
$116$	−1.12842e10	+	2.43957e10i	−0.537255	+	1.16151i
$117$		−	9.38168e9i		−	0.427909i
$118$	2.21822e10	−	1.41799e10i	0.969605	−	0.619817i
$119$		−	5.74431e9i		−	0.240715i
$120$	1.32500e10	+	7.02218e9i	0.532486	+	0.282206i
$121$	1.81247e10			0.698785
$122$	−1.62570e10	−	2.54315e10i	−0.601507	−	0.940963i
$123$	1.57111e10			0.558061
$124$	−3.36936e10	−	1.55849e10i	−1.14932	−	0.531614i
$125$	8.95568e9	−	2.91739e10i	0.293460	−	0.955971i
$126$	9.06032e9	+	1.41734e10i	0.285293	+	0.446296i
$127$	−1.68474e10			−0.509936			−0.254968	−	0.966950i	$-0.582065\pi$
$127$	−1.68474e10			−0.509936			−0.254968	+	0.966950i	$0.582065\pi$
$128$	2.55825e10	+	2.29375e10i	0.744547	+	0.667570i
$129$	2.31871e8			0.00649079
$130$	2.49125e10	+	1.34912e9i	0.670965	+	0.0363357i
$131$		−	6.87972e9i		−	0.178326i	−0.996017	−	0.0891629i	$-0.971581\pi$
$131$		−	6.87972e9i		−	0.178326i	0.996017	−	0.0891629i	$-0.0284192\pi$
$132$	−1.20301e10	−	5.56450e9i	−0.300192	−	0.138853i
$133$			4.22115e10i			1.01432i
$134$	1.95777e10	+	3.06262e10i	0.453145	+	0.708873i
$135$	3.59249e10	+	2.58036e10i	0.801173	+	0.575455i
$136$	−1.81939e9	−	1.33410e10i	−0.0391048	−	0.286745i
$137$		−	3.80906e10i		−	0.789251i	−0.918842	−	0.394626i	$-0.870874\pi$
$137$		−	3.80906e10i		−	0.789251i	0.918842	−	0.394626i	$-0.129126\pi$
$138$	−1.14580e10	−	1.79242e10i	−0.228935	−	0.358132i
$139$		−	1.89688e10i		−	0.365566i	−0.983153	−	0.182783i	$-0.941489\pi$
$139$		−	1.89688e10i		−	0.365566i	0.983153	−	0.182783i	$-0.0585107\pi$
$140$	−3.89396e10	+	2.20209e10i	−0.724021	+	0.409445i
$141$	−6.36540e10			−1.14217
$142$	−7.85513e10	+	5.02137e10i	−1.36054	+	0.869722i
$143$	−2.20523e10			−0.368785
$144$	2.55315e10	+	3.00479e10i	0.412349	+	0.485290i
$145$	−6.66236e10	−	4.78535e10i	−1.03941	−	0.746575i
$146$	5.62623e10	−	3.59655e10i	0.848112	−	0.542153i
$147$	−1.27470e10			−0.185704
$148$	−7.70526e10	−	3.56405e10i	−1.08512	−	0.501921i
$149$	−2.46526e10			−0.335685			−0.167842	−	0.985814i	$-0.553680\pi$
$149$	−2.46526e10			−0.335685			−0.167842	+	0.985814i	$0.553680\pi$
$150$	−2.86682e10	+	3.56711e10i	−0.377523	+	0.469742i
$151$		−	9.59561e10i		−	1.22233i	−0.791504	−	0.611164i	$-0.790701\pi$
$151$		−	9.59561e10i		−	1.22233i	0.791504	−	0.611164i	$-0.209299\pi$
$152$	1.33696e10	+	9.80354e10i	0.164778	+	1.20827i
$153$		−	1.54514e10i		−	0.184294i
$154$	3.33157e10	−	2.12969e10i	0.384632	−	0.245875i
$155$	6.60918e10	−	9.20158e10i	0.738736	−	1.02850i
$156$	−3.39563e10	−	1.57064e10i	−0.367534	−	0.170002i
$157$		−	4.22802e10i		−	0.443240i	−0.975133	−	0.221620i	$-0.928866\pi$
$157$		−	4.22802e10i		−	0.443240i	0.975133	−	0.221620i	$-0.0711344\pi$
$158$	1.57407e11	−	1.00622e11i	1.59859	−	1.02190i
$159$			5.01735e10i			0.493729i
$160$	−8.34617e10	+	6.34764e10i	−0.795953	+	0.605358i
$161$	6.34624e10			0.586661
$162$	2.54539e9	+	3.98186e9i	0.0228129	+	0.0356871i
$163$	−1.44588e11			−1.25659			−0.628297	−	0.777974i	$-0.716248\pi$
$163$	−1.44588e11			−1.25659			−0.628297	+	0.777974i	$0.716248\pi$
$164$	−4.61206e10	+	9.97099e10i	−0.388754	+	0.840464i
$165$	2.35977e10	−	3.28537e10i	0.192952	−	0.268636i
$166$	−1.72239e10	−	2.69440e10i	−0.136644	−	0.213758i
$167$	2.16899e11			1.66984			0.834922	−	0.550368i	$-0.185513\pi$
$167$	2.16899e11			1.66984			0.834922	+	0.550368i	$0.185513\pi$
$168$	6.64681e10	−	9.06460e9i	0.496669	−	0.0677333i
$169$	7.56134e10			0.548486
$170$	4.10304e10	+	2.22198e9i	0.288975	+	0.0156493i
$171$			1.13544e11i			0.776573i
$172$	−6.80666e8	+	1.47156e9i	−0.00452159	+	0.00977541i
$173$			2.64712e11i			1.70821i	0.520097	+	0.854107i	$0.325896\pi$
$173$			2.64712e11i			1.70821i	−0.520097	+	0.854107i	$0.674104\pi$
$174$	6.62524e10	+	1.03641e11i	0.415389	+	0.649811i
$175$	−4.35968e10	−	1.29372e11i	−0.265622	−	0.788224i
$176$	7.06296e10	−	6.00137e10i	0.418238	−	0.355375i
$177$		−	1.20482e11i		−	0.693516i
$178$	−6.84761e10	−	1.07120e11i	−0.383212	−	0.599474i
$179$			3.53056e11i			1.92122i	0.277892	+	0.960612i	$0.410364\pi$
$179$			3.53056e11i			1.92122i	−0.277892	+	0.960612i	$0.589636\pi$
$180$	−1.04742e11	+	5.92334e10i	−0.554320	+	0.313476i
$181$	−1.89345e11			−0.974678			−0.487339	−	0.873213i	$-0.662032\pi$
$181$	−1.89345e11			−0.974678			−0.487339	+	0.873213i	$0.662032\pi$
$182$	9.40372e10	−	6.01129e10i	0.470915	−	0.301031i
$183$	−1.38130e11			−0.673030
$184$	1.47390e11	−	2.01004e10i	0.698842	−	0.0953047i
$185$	1.51143e11	−	2.10427e11i	0.697474	−	0.971053i
$186$	−1.43142e11	+	9.15031e10i	−0.642988	+	0.411028i
$187$	−3.63197e10			−0.158831
$188$	1.86859e11	−	4.03977e11i	0.795653	−	1.72015i
$189$	1.97869e11			0.820482
$190$	−3.01508e11	−	1.63280e10i	−1.21767	−	0.0659424i
$191$			1.77750e11i			0.699266i	0.936887	+	0.349633i	$0.113694\pi$
$191$			1.77750e11i			0.699266i	−0.936887	+	0.349633i	$0.886306\pi$
$192$	1.51500e11	−	4.21047e10i	0.580639	−	0.161371i
$193$			4.76572e11i			1.77968i	0.456271	+	0.889841i	$0.349185\pi$
$193$			4.76572e11i			1.77968i	−0.456271	+	0.889841i	$0.650815\pi$
$194$	−1.73715e11	+	1.11047e11i	−0.632164	+	0.404108i
$195$	6.66070e10	−	9.27331e10i	0.236236	−	0.328898i
$196$	3.74194e10	−	8.08984e10i	0.129365	−	0.279679i
$197$			3.11485e11i			1.04980i	0.851164	+	0.524900i	$0.175897\pi$
$197$			3.11485e11i			1.04980i	−0.851164	+	0.524900i	$0.824103\pi$
$198$	8.96149e10	−	5.72860e10i	0.294479	−	0.188245i
$199$		−	8.32510e10i		−	0.266762i	−0.991065	−	0.133381i	$-0.957417\pi$
$199$		−	8.32510e10i		−	0.266762i	0.991065	−	0.133381i	$-0.0425834\pi$
$200$	−1.42228e11	−	2.86655e11i	−0.444463	−	0.895797i
$201$	1.66345e11			0.507026
$202$	1.46561e11	+	2.29272e11i	0.435775	+	0.681701i
$203$	−3.66953e11			−1.06446
$204$	−5.59254e10	−	2.58682e10i	−0.158292	−	0.0732175i
$205$	−2.72303e11	−	1.95586e11i	−0.752113	−	0.540217i
$206$	−2.80565e11	−	4.38900e11i	−0.756307	−	1.18312i
$207$	1.70706e11			0.449155
$208$	1.99360e11	−	1.69395e11i	0.512060	−	0.435096i
$209$	2.66892e11			0.669275
$210$	−1.10704e10	+	2.04423e11i	−0.0271061	+	0.500533i
$211$		−	4.08040e11i		−	0.975641i	−0.872944	−	0.487820i	$-0.837792\pi$
$211$		−	4.08040e11i		−	0.975641i	0.872944	−	0.487820i	$-0.162208\pi$
$212$	−3.18424e11	−	1.47286e11i	−0.743578	−	0.343940i
$213$			4.26650e11i			0.973136i
$214$	−1.41048e10	−	2.20648e10i	−0.0314267	−	0.0491621i
$215$	−4.01876e9	−	2.88654e9i	−0.00874781	−	0.00628325i
$216$	4.59547e11	−	6.26708e10i	0.977375	−	0.133290i
$217$		−	5.06810e11i		−	1.05329i
$218$	−5.11996e10	−	8.00936e10i	−0.103988	−	0.162673i
$219$		−	3.05587e11i		−	0.606617i
$220$	1.39232e11	+	2.46205e11i	0.270164	+	0.477730i
$221$	−1.02516e11			−0.194461
$222$	−3.27346e11	+	2.09255e11i	−0.607074	+	0.388070i
$223$	−3.09347e11			−0.560947			−0.280473	−	0.959862i	$-0.590491\pi$
$223$	−3.09347e11			−0.560947			−0.280473	+	0.959862i	$0.590491\pi$
$224$	−1.37592e11	+	4.48446e11i	−0.243979	+	0.795189i
$225$	−1.17270e11	−	3.47993e11i	−0.203363	−	0.603474i
$226$	−5.40550e11	+	3.45545e11i	−0.916840	+	0.586087i
$227$	−4.36504e11			−0.724200			−0.362100	−	0.932139i	$-0.617940\pi$
$227$	−4.36504e11			−0.724200			−0.362100	+	0.932139i	$0.617940\pi$
$228$	4.10963e11	+	1.90090e11i	0.667004	+	0.308521i
$229$	−8.85513e11			−1.40610			−0.703052	−	0.711138i	$-0.748180\pi$
$229$	−8.85513e11			−1.40610			−0.703052	+	0.711138i	$0.748180\pi$
$230$	−2.45481e10	+	4.53298e11i	−0.0381398	+	0.704279i
$231$		−	1.80953e11i		−	0.275110i
$232$	−8.52241e11	+	1.16225e11i	−1.26801	+	0.172925i
$233$			3.44547e10i			0.0501729i	0.999685	+	0.0250864i	$0.00798610\pi$
$233$			3.44547e10i			0.0501729i	−0.999685	+	0.0250864i	$0.992014\pi$
$234$	2.52948e11	−	1.61696e11i	0.360539	−	0.230473i
$235$	1.10324e12	+	7.92422e11i	1.53933	+	1.10565i
$236$	7.64635e11	+	3.53680e11i	1.04447	+	0.483115i
$237$		−	8.54951e11i		−	1.14340i
$238$	1.54878e11	−	9.90049e10i	0.202817	−	0.129650i
$239$			3.54744e11i			0.454910i	0.973789	+	0.227455i	$0.0730404\pi$
$239$			3.54744e11i			0.454910i	−0.973789	+	0.227455i	$0.926960\pi$
$240$	3.90357e10	+	4.78274e11i	0.0490237	+	0.600648i
$241$	5.46010e11			0.671608			0.335804	−	0.941932i	$-0.390992\pi$
$241$	5.46010e11			0.671608			0.335804	+	0.941932i	$0.390992\pi$
$242$	3.12385e11	+	4.88676e11i	0.376368	+	0.588768i
$243$	8.57411e11			1.01195
$244$	4.05487e11	−	8.76639e11i	0.468844	−	1.01361i
$245$	2.20930e11	+	1.58686e11i	0.250279	+	0.179767i
$246$	2.70786e11	+	4.23602e11i	0.300573	+	0.470199i
$247$	7.53333e11			0.819412
$248$	−1.60521e11	−	1.17706e12i	−0.171109	−	1.25470i
$249$	−1.46346e11			−0.152892
$250$	9.40939e11	−	2.61359e11i	0.963521	−	0.267632i
$251$			2.78449e11i			0.279497i	0.990187	+	0.139748i	$0.0446293\pi$
$251$			2.78449e11i			0.279497i	−0.990187	+	0.139748i	$0.955371\pi$
$252$	−2.25986e11	+	4.88567e11i	−0.222371	+	0.480752i
$253$		−	4.01256e11i		−	0.387096i
$254$	−2.90371e11	−	4.54239e11i	−0.274653	−	0.429651i
$255$	1.09701e11	−	1.52730e11i	0.101744	−	0.141652i
$256$	−1.77518e11	+	1.08509e12i	−0.161452	+	0.986881i
$257$			1.03896e11i			0.0926688i	0.998926	+	0.0463344i	$0.0147540\pi$
$257$			1.03896e11i			0.0926688i	−0.998926	+	0.0463344i	$0.985246\pi$
$258$	3.99636e9	+	6.25168e9i	0.00349596	+	0.00546888i
$259$		−	1.15900e12i		−	0.994456i
$260$	3.92999e11	+	6.94940e11i	0.330769	+	0.584898i
$261$	−9.87057e11			−0.814966
$262$	1.85490e11	−	1.18574e11i	0.150250	−	0.0960469i
$263$	−3.81998e11			−0.303586			−0.151793	−	0.988412i	$-0.548505\pi$
$263$	−3.81998e11			−0.303586			−0.151793	+	0.988412i	$0.548505\pi$
$264$	−5.73131e10	−	4.20260e11i	−0.0446924	−	0.327717i
$265$	6.24605e11	−	8.69601e11i	0.477943	−	0.665412i
$266$	−1.13810e12	+	7.27529e11i	−0.854621	+	0.546314i
$267$	−5.81820e11			−0.428778
$268$	−4.88313e11	+	1.05570e12i	−0.353203	+	0.763603i
$269$	−9.64366e11			−0.684668			−0.342334	−	0.939578i	$-0.611218\pi$
$269$	−9.64366e11			−0.684668			−0.342334	+	0.939578i	$0.611218\pi$
$270$	−7.65384e10	+	1.41334e12i	−0.0533410	+	0.984978i
$271$			5.71457e10i			0.0390964i	0.999809	+	0.0195482i	$0.00622279\pi$
$271$			5.71457e10i			0.0390964i	−0.999809	+	0.0195482i	$0.993777\pi$
$272$	3.28342e11	−	2.78991e11i	0.220537	−	0.187390i
$273$		−	5.10761e11i		−	0.336825i
$274$	1.02700e12	−	6.56504e11i	0.664991	−	0.425093i
$275$	−8.17984e11	+	2.75651e11i	−0.520093	+	0.175265i
$276$	2.85788e11	−	6.17857e11i	0.178443	−	0.385782i
$277$			1.80699e12i			1.10804i	0.832503	+	0.554021i	$0.186907\pi$
$277$			1.80699e12i			1.10804i	−0.832503	+	0.554021i	$0.813093\pi$
$278$	5.11436e11	−	3.26933e11i	0.308012	−	0.196895i
$279$		−	1.36325e12i		−	0.806409i
$280$	−1.26486e12	−	6.70348e11i	−0.734942	−	0.389503i
$281$	1.67597e12			0.956612			0.478306	−	0.878193i	$-0.341251\pi$
$281$	1.67597e12			0.956612			0.478306	+	0.878193i	$0.341251\pi$
$282$	−1.09710e12	−	1.71623e12i	−0.615175	−	0.962344i
$283$	−1.29146e12			−0.711459			−0.355730	−	0.934589i	$-0.615768\pi$
$283$	−1.29146e12			−0.711459			−0.355730	+	0.934589i	$0.615768\pi$
$284$	−2.70771e12	−	1.25245e12i	−1.46558	−	0.677903i
$285$	−8.06124e11	+	1.12232e12i	−0.428724	+	0.596888i
$286$	−3.80078e11	−	5.94572e11i	−0.198629	−	0.310724i
$287$	−1.49981e12			−0.770240
$288$	−3.70104e11	+	1.20626e12i	−0.186793	+	0.608807i
$289$	1.84715e12			0.916248
$290$	1.41943e11	−	2.62107e12i	0.0692026	−	1.27787i
$291$			9.43530e11i			0.452159i
$292$	1.93940e12	+	8.97063e11i	0.913592	+	0.422580i
$293$			3.77568e12i			1.74847i	0.485507	+	0.874233i	$0.338635\pi$
$293$			3.77568e12i			1.74847i	−0.485507	+	0.874233i	$0.661365\pi$
$294$	−2.19699e11	−	3.43684e11i	−0.100021	−	0.156467i
$295$	−1.49987e12	+	2.08818e12i	−0.671342	+	0.934670i
$296$	−3.67089e11	−	2.69176e12i	−0.161552	−	1.18462i
$297$		−	1.25107e12i		−	0.541378i
$298$	−4.24896e11	−	6.64682e11i	−0.180801	−	0.282835i
$299$		−	1.13259e12i		−	0.473932i
$300$	−1.45586e12	−	1.58147e11i	−0.599121	−	0.0650810i
$301$	−2.21347e10			−0.00895864
$302$	2.58716e12	−	1.65383e12i	1.02988	−	0.658350i
$303$	1.24528e12			0.487591
$304$	−2.41279e12	+	2.05014e12i	−0.929292	+	0.789615i
$305$	2.39406e12	+	1.71957e12i	0.907060	+	0.651510i
$306$	4.16600e11	−	2.66310e11i	0.155279	−	0.0992615i
$307$	3.98468e12			1.46117			0.730587	−	0.682820i	$-0.239246\pi$
$307$	3.98468e12			1.46117			0.730587	+	0.682820i	$0.239246\pi$
$308$	1.14841e12	+	5.31195e11i	0.414328	+	0.191646i
$309$	−2.38388e12			−0.846236
$310$	3.62003e12	+	1.96041e11i	1.26446	+	0.0684760i
$311$			1.39871e12i			0.480758i	0.970679	+	0.240379i	$0.0772717\pi$
$311$			1.39871e12i			0.480758i	−0.970679	+	0.240379i	$0.922728\pi$
$312$	−1.61772e11	−	1.18623e12i	−0.0547182	−	0.401233i
$313$		−	5.82569e12i		−	1.93921i	−0.244667	−	0.969607i	$-0.578679\pi$
$313$		−	5.82569e12i		−	1.93921i	0.244667	−	0.969607i	$-0.421321\pi$
$314$	1.13995e12	−	7.28712e11i	0.373456	−	0.238730i
$315$	−1.33425e12	−	9.58349e11i	−0.430215	−	0.309009i
$316$	5.42591e12	+	2.50974e12i	1.72202	+	0.796514i
$317$			4.41493e12i			1.37920i	0.724190	+	0.689600i	$0.242214\pi$
$317$			4.41493e12i			1.37920i	−0.724190	+	0.689600i	$0.757786\pi$
$318$	−1.35277e12	+	8.64756e11i	−0.415996	+	0.265924i
$319$			2.32015e12i			0.702364i
$320$	−3.14993e12	−	1.15625e12i	−0.938753	−	0.344590i
$321$	−1.19844e11			−0.0351635
$322$	1.09379e12	+	1.71107e12i	0.315977	+	0.494297i
$323$	1.24073e12			0.352909
$324$	−6.34880e10	+	1.37257e11i	−0.0177814	+	0.0384424i
$325$	−2.30885e12	+	7.78054e11i	−0.636764	+	0.214582i
$326$	−2.49202e12	−	3.89838e12i	−0.676806	−	1.05876i
$327$	−4.35027e11			−0.116353
$328$	−3.48327e12	+	4.75032e11i	−0.917525	+	0.125128i
$329$	6.07650e12			1.57643
$330$	1.29251e12	+	6.99952e10i	0.330266	+	0.0178854i
$331$			1.01492e12i			0.255441i	0.991810	+	0.127720i	$0.0407660\pi$
$331$			1.01492e12i			0.255441i	−0.991810	+	0.127720i	$0.959234\pi$
$332$	4.29603e11	−	9.28777e11i	0.106507	−	0.230261i
$333$		−	3.11757e12i		−	0.761368i
$334$	3.73833e12	+	5.84802e12i	0.899383	+	1.40694i
$335$	−2.88308e12	−	2.07081e12i	−0.683332	−	0.490814i
$336$	1.39000e12	+	1.63588e12i	0.324577	+	0.381992i
$337$		−	2.73619e12i		−	0.629503i	−0.949174	−	0.314751i	$-0.898079\pi$
$337$		−	2.73619e12i		−	0.629503i	0.949174	−	0.314751i	$-0.101921\pi$
$338$	1.30322e12	+	2.03868e12i	0.295416	+	0.462132i
$339$			2.93598e12i			0.655775i
$340$	6.47262e11	+	1.14455e12i	0.142458	+	0.251908i
$341$	−3.20442e12			−0.694989
$342$	−3.06135e12	+	1.95696e12i	−0.654309	+	0.418264i
$343$	5.16576e12			1.08809
$344$	−5.14075e10	+	7.01070e9i	−0.0106717	+	0.00145536i
$345$	1.68734e12	+	1.21196e12i	0.345228	+	0.247966i
$346$	−7.13713e12	+	4.56238e12i	−1.43927	+	0.920050i
$347$	−4.92030e12			−0.978013			−0.489006	−	0.872280i	$-0.662641\pi$
$347$	−4.92030e12			−0.978013			−0.489006	+	0.872280i	$0.662641\pi$
$348$	−1.65249e12	+	3.57258e12i	−0.323774	+	0.699980i
$349$	−4.17497e12			−0.806355			−0.403178	−	0.915122i	$-0.632094\pi$
$349$	−4.17497e12			−0.806355			−0.403178	+	0.915122i	$0.632094\pi$
$350$	2.73671e12	−	3.40521e12i	0.521061	−	0.648342i
$351$		−	3.53129e12i		−	0.662824i
$352$	2.83541e12	+	8.69955e11i	0.524689	+	0.160984i
$353$		−	6.96972e12i		−	1.27157i	−0.771864	−	0.635787i	$-0.780676\pi$
$353$		−	6.96972e12i		−	1.27157i	0.771864	−	0.635787i	$-0.219324\pi$
$354$	3.24843e12	−	2.07655e12i	0.584328	−	0.373530i
$355$	5.31132e12	−	7.39464e12i	0.942021	−	1.31152i
$356$	1.70795e12	−	3.69249e12i	0.298694	−	0.645758i
$357$		−	8.41213e11i		−	0.145066i
$358$	−9.51905e12	+	6.08502e12i	−1.61875	+	1.03478i
$359$		−	6.96682e11i		−	0.116832i	−0.998292	−	0.0584161i	$-0.981395\pi$
$359$		−	6.96682e11i		−	0.116832i	0.998292	−	0.0584161i	$-0.0186050\pi$
$360$	−3.40231e12	−	1.80315e12i	−0.562681	−	0.298208i
$361$	−2.98629e12			−0.487076
$362$	−3.26342e12	−	5.10510e12i	−0.524965	−	0.821224i
$363$	2.65423e12			0.421120
$364$	3.24152e12	+	1.49936e12i	0.507273	+	0.234638i
$365$	−3.80423e12	+	5.29640e12i	−0.587222	+	0.817555i
$366$	−2.38072e12	−	3.72426e12i	−0.362496	−	0.567067i
$367$	−3.80852e12			−0.572039			−0.286020	−	0.958224i	$-0.592332\pi$
$367$	−3.80852e12			−0.572039			−0.286020	+	0.958224i	$0.592332\pi$
$368$	3.08226e12	+	3.62748e12i	0.456699	+	0.537485i
$369$	−4.03429e12			−0.589705
$370$	8.27850e12	+	4.48318e11i	1.19383	+	0.0646513i
$371$		−	4.78964e12i		−	0.681449i
$372$	−4.93419e12	−	2.28230e12i	−0.692630	−	0.320375i
$373$		−	9.60132e12i		−	1.32980i	−0.746932	−	0.664901i	$-0.768474\pi$
$373$		−	9.60132e12i		−	1.32980i	0.746932	−	0.664901i	$-0.231526\pi$
$374$	−6.25982e11	−	9.79249e11i	−0.0855468	−	0.133824i
$375$	1.31150e12	−	4.27232e12i	0.176852	−	0.576112i
$376$	1.41126e13	−	1.92460e12i	1.87787	−	0.256095i
$377$			6.54887e12i			0.859924i
$378$	3.41033e12	+	5.33493e12i	0.441914	+	0.691305i
$379$			6.23848e12i			0.797779i	0.916999	+	0.398890i	$0.130604\pi$
$379$			6.23848e12i			0.797779i	−0.916999	+	0.398890i	$0.869396\pi$
$380$	−4.75635e12	−	8.41065e12i	−0.600282	−	1.06148i
$381$	−2.46719e12			−0.307311
$382$	−4.79248e12	+	3.06357e12i	−0.589173	+	0.376627i
$383$	8.64559e12			1.04906			0.524530	−	0.851392i	$-0.324241\pi$
$383$	8.64559e12			1.04906			0.524530	+	0.851392i	$0.324241\pi$
$384$	3.74637e12	+	3.35904e12i	0.448698	+	0.402308i
$385$	−2.25267e12	+	3.13626e12i	−0.266314	+	0.370773i
$386$	−1.28493e13	+	8.21387e12i	−1.49949	+	0.958542i
$387$	−5.95396e10			−0.00685884
$388$	−5.98807e12	−	2.76977e12i	−0.680971	−	0.314981i
$389$	8.65443e12			0.971606			0.485803	−	0.874068i	$-0.338527\pi$
$389$	8.65443e12			0.971606			0.485803	+	0.874068i	$0.338527\pi$
$390$	3.64825e12	+	1.97569e11i	0.404354	+	0.0218976i
$391$		−	1.86535e12i		−	0.204116i
$392$	2.82611e12	−	3.85411e11i	0.305322	−	0.0416384i
$393$		−	1.00749e12i		−	0.107467i
$394$	−8.39823e12	+	5.36854e12i	−0.884518	+	0.565425i
$395$	−1.06432e13	+	1.48179e13i	−1.10684	+	1.54100i
$396$	3.08908e12	+	1.42885e12i	0.317215	+	0.146727i
$397$		−	5.71458e11i		−	0.0579471i	−0.999580	−	0.0289736i	$-0.990776\pi$
$397$		−	5.71458e11i		−	0.0579471i	0.999580	−	0.0289736i	$-0.00922386\pi$
$398$	2.24461e12	−	1.43486e12i	0.224763	−	0.143679i
$399$			6.18158e12i			0.611273i
$400$	5.27742e12	−	8.77533e12i	0.515373	−	0.856966i
$401$	1.44767e13			1.39620			0.698098	−	0.716002i	$-0.254030\pi$
$401$	1.44767e13			1.39620			0.698098	+	0.716002i	$0.254030\pi$
$402$	2.86701e12	+	4.48499e12i	0.273086	+	0.427200i
$403$	−9.04484e12			−0.850894
$404$	−3.65558e12	+	7.90314e12i	−0.339664	+	0.734333i
$405$	−3.74843e11	−	2.69237e11i	−0.0344013	−	0.0247093i
$406$	−6.32455e12	−	9.89376e12i	−0.573323	−	0.896874i
$407$	−7.32807e12			−0.656171
$408$	−2.66436e11	−	1.95370e12i	−0.0235664	−	0.172805i
$409$	7.48900e12			0.654346			0.327173	−	0.944964i	$-0.393904\pi$
$409$	7.48900e12			0.654346			0.327173	+	0.944964i	$0.393904\pi$
$410$	5.80146e11	−	1.07128e13i	0.0500746	−	0.924663i
$411$		−	5.57810e12i		−	0.475639i
$412$	6.99796e12	−	1.51292e13i	0.589502	−	1.27447i
$413$			1.15014e13i			0.957196i
$414$	2.94216e12	+	4.60255e12i	0.241916	+	0.378440i
$415$	2.53645e12	+	1.82184e12i	0.206056	+	0.148003i
$416$	8.00325e12	+	2.45554e12i	0.642391	+	0.197097i
$417$		−	2.77785e12i		−	0.220307i
$418$	4.59997e12	+	7.19593e12i	0.360474	+	0.563904i
$419$			6.35022e12i			0.491721i	0.969305	+	0.245861i	$0.0790705\pi$
$419$			6.35022e12i			0.491721i	−0.969305	+	0.245861i	$0.920929\pi$
$420$	−5.70243e12	+	3.22481e12i	−0.436328	+	0.246750i
$421$	2.25594e12			0.170575			0.0852877	−	0.996356i	$-0.472819\pi$
$421$	2.25594e12			0.170575			0.0852877	+	0.996356i	$0.472819\pi$
$422$	1.10015e13	−	7.03269e12i	0.822035	−	0.525483i
$423$	1.63450e13			1.20693
$424$	−1.51702e12	−	1.11238e13i	−0.110703	−	0.811756i
$425$	−3.80263e12	+	1.28144e12i	−0.274246	+	0.0924175i
$426$	−1.15033e13	+	7.35344e12i	−0.819925	+	0.524134i
$427$	1.31861e13			0.928920
$428$	3.51807e11	−	7.60586e11i	0.0244955	−	0.0529577i
$429$	−3.22940e12			−0.222247
$430$	8.56202e9	−	1.58104e11i	0.000582417	−	0.0107547i
$431$			1.04502e13i			0.702646i	0.936254	+	0.351323i	$0.114268\pi$
$431$			1.04502e13i			0.702646i	−0.936254	+	0.351323i	$0.885732\pi$
$432$	9.61015e12	+	1.13101e13i	0.638722	+	0.751706i
$433$			6.36111e12i			0.417920i	0.977924	+	0.208960i	$0.0670079\pi$
$433$			6.36111e12i			0.417920i	−0.977924	+	0.208960i	$0.932992\pi$
$434$	1.36646e13	−	8.73502e12i	0.887456	−	0.567303i
$435$	−9.75655e12	−	7.00780e12i	−0.626398	−	0.449920i
$436$	1.27704e12	−	2.76088e12i	0.0810533	−	0.175232i
$437$			1.37074e13i			0.860097i
$438$	8.23922e12	−	5.26689e12i	0.511111	−	0.326726i
$439$		−	1.91298e13i		−	1.17324i	−0.809862	−	0.586620i	$-0.800458\pi$
$439$		−	1.91298e13i		−	1.17324i	0.809862	−	0.586620i	$-0.199542\pi$
$440$	−4.23843e12	+	7.99738e12i	−0.257005	+	0.484936i
$441$	3.27317e12			0.196235
$442$	−1.76690e12	−	2.76404e12i	−0.104737	−	0.163845i
$443$	−1.80726e13			−1.05926			−0.529629	−	0.848229i	$-0.677669\pi$
$443$	−1.80726e13			−1.05926			−0.529629	+	0.848229i	$0.677669\pi$
$444$	−1.12838e13	−	5.21930e12i	−0.653944	−	0.302480i
$445$	1.00840e13	+	7.24301e12i	0.577875	+	0.415068i
$446$	−5.33169e12	−	8.34058e12i	−0.302128	−	0.472631i
$447$	−3.61020e12			−0.202299
$448$	−1.44624e13	+	4.01938e12i	−0.801402	+	0.222725i
$449$	−7.71297e12			−0.422659			−0.211329	−	0.977415i	$-0.567779\pi$
$449$	−7.71297e12			−0.422659			−0.211329	+	0.977415i	$0.567779\pi$
$450$	7.36139e12	−	9.15959e12i	0.398930	−	0.496379i
$451$			9.48288e12i			0.508227i
$452$	−1.86331e13	−	8.61869e12i	−0.987626	−	0.456824i
$453$		−	1.40521e13i		−	0.736631i
$454$	−7.52327e12	−	1.17690e13i	−0.390056	−	0.610182i
$455$	−6.35841e12	+	8.85244e12i	−0.326055	+	0.453948i
$456$	1.95788e12	+	1.43566e13i	0.0993030	+	0.728161i
$457$			5.55477e12i			0.278667i	0.990246	+	0.139333i	$0.0444959\pi$
$457$			5.55477e12i			0.278667i	−0.990246	+	0.139333i	$0.955504\pi$
$458$	−1.52621e13	−	2.38751e13i	−0.757332	−	1.18473i
$459$		−	5.81597e12i		−	0.285469i
$460$	−1.26449e13	+	7.15087e12i	−0.613939	+	0.347192i
$461$	−1.48116e13			−0.711372			−0.355686	−	0.934605i	$-0.615753\pi$
$461$	−1.48116e13			−0.711372			−0.355686	+	0.934605i	$0.615753\pi$
$462$	4.87885e12	−	3.11879e12i	0.231797	−	0.148175i
$463$	−2.87422e13			−1.35087			−0.675436	−	0.737418i	$-0.736045\pi$
$463$	−2.87422e13			−1.35087			−0.675436	+	0.737418i	$0.736045\pi$
$464$	−1.78223e13	−	2.09749e13i	−0.828654	−	0.975236i
$465$	9.67868e12	−	1.34751e13i	0.445196	−	0.619821i
$466$	−9.28965e11	+	5.93837e11i	−0.0422736	+	0.0270233i
$467$	1.93804e13			0.872527			0.436264	−	0.899819i	$-0.356302\pi$
$467$	1.93804e13			0.872527			0.436264	+	0.899819i	$0.356302\pi$
$468$	8.71927e12	+	4.03308e12i	0.388374	+	0.179642i
$469$	−1.58796e13			−0.699801
$470$	−2.35047e12	+	4.34032e13i	−0.102486	+	1.89248i
$471$		−	6.19163e12i		−	0.267117i
$472$	3.64282e12	+	2.67118e13i	0.155499	+	1.14023i
$473$			1.39952e11i			0.00591117i
$474$	2.30511e13	−	1.47353e13i	0.963386	−	0.615841i
$475$	2.79433e13	−	9.41656e12i	1.15561	−	0.389425i
$476$	5.33872e12	+	2.46941e12i	0.218475	+	0.101055i
$477$		−	1.28835e13i		−	0.521726i
$478$	−9.56457e12	+	6.11412e12i	−0.383288	+	0.245016i
$479$		−	1.28939e13i		−	0.511335i	−0.966765	−	0.255667i	$-0.917705\pi$
$479$		−	1.28939e13i		−	0.511335i	0.966765	−	0.255667i	$-0.0822952\pi$
$480$	−1.22224e13	+	9.29567e12i	−0.479678	+	0.364817i
$481$	−2.06843e13			−0.803369
$482$	9.41065e12	+	1.47215e13i	0.361730	+	0.565869i
$483$	9.29362e12			0.353549
$484$	−7.79160e12	+	1.68450e13i	−0.293359	+	0.634225i
$485$	1.17459e13	−	1.63532e13i	0.437702	−	0.609386i
$486$	1.47777e13	+	2.31174e13i	0.545038	+	0.852625i
$487$	1.59672e11			0.00582886			0.00291443	−	0.999996i	$-0.499072\pi$
$487$	1.59672e11			0.00582886			0.00291443	+	0.999996i	$0.499072\pi$
$488$	3.06246e13	−	4.17643e12i	1.10655	−	0.150906i
$489$	−2.11739e13			−0.757281
$490$	−4.70694e11	+	8.69169e12i	−0.0166632	+	0.307698i
$491$			4.18477e12i			0.146644i	0.997308	+	0.0733219i	$0.0233601\pi$
$491$			4.18477e12i			0.146644i	−0.997308	+	0.0733219i	$0.976640\pi$
$492$	−6.75403e12	+	1.46018e13i	−0.234281	+	0.506502i
$493$			1.07859e13i			0.370357i
$494$	1.29839e13	+	2.03113e13i	0.441338	+	0.690403i
$495$	−6.05939e12	+	8.43613e12i	−0.203893	+	0.283869i
$496$	2.89690e13	−	2.46149e13i	0.964996	−	0.819953i
$497$		−	4.07286e13i		−	1.34313i
$498$	−2.52231e12	−	3.94576e12i	−0.0823479	−	0.128820i
$499$		−	5.68728e13i		−	1.83824i	−0.393978	−	0.919120i	$-0.628902\pi$
$499$		−	5.68728e13i		−	1.83824i	0.393978	−	0.919120i	$-0.371098\pi$
$500$	2.32641e13	+	2.08649e13i	0.744452	+	0.667676i
$501$	3.17634e13			1.00632
$502$	−7.50751e12	+	4.79915e12i	−0.235493	+	0.150538i
$503$	4.10150e13			1.27380			0.636902	−	0.770945i	$-0.280216\pi$
$503$	4.10150e13			1.27380			0.636902	+	0.770945i	$0.280216\pi$
$504$	−1.70676e13	+	2.32760e12i	−0.524832	+	0.0715741i
$505$	−2.15831e13	−	1.55024e13i	−0.657139	−	0.472000i
$506$	1.08186e13	−	6.91577e12i	0.326151	−	0.208491i
$507$	1.10731e13			0.330543
$508$	7.24252e12	−	1.56579e13i	0.214078	−	0.462823i
$509$	3.18969e13			0.933599			0.466799	−	0.884363i	$-0.345407\pi$
$509$	3.18969e13			0.933599			0.466799	+	0.884363i	$0.345407\pi$
$510$	6.00860e12	+	3.25393e11i	0.174150	+	0.00943098i
$511$			2.91718e13i			0.837258i
$512$	−3.23156e13	+	1.39156e13i	−0.918464	+	0.395505i
$513$			4.27382e13i			1.20290i
$514$	−2.80124e12	+	1.79068e12i	−0.0780790	+	0.0499117i
$515$	4.13170e13	+	2.96766e13i	1.14049	+	0.819178i
$516$	−9.96786e10	+	2.15499e11i	−0.00272492	+	0.00589111i
$517$		−	3.84201e13i		−	1.04017i
$518$	3.12489e13	−	1.99758e13i	0.837888	−	0.535617i
$519$			3.87651e13i			1.02945i
$520$	−1.19634e13	+	2.25735e13i	−0.314659	+	0.593721i
$521$	−1.50084e13			−0.390972			−0.195486	−	0.980707i	$-0.562628\pi$
$521$	−1.50084e13			−0.390972			−0.195486	+	0.980707i	$0.562628\pi$
$522$	−1.70122e13	−	2.66129e13i	−0.438943	−	0.686658i
$523$	−4.78587e13			−1.22307			−0.611537	−	0.791216i	$-0.709448\pi$
$523$	−4.78587e13			−1.22307			−0.611537	+	0.791216i	$0.709448\pi$
$524$	6.39397e12	+	2.95751e12i	0.161850	+	0.0748635i
$525$	−6.38444e12	−	1.89456e13i	−0.160076	−	0.475020i
$526$	−6.58385e12	−	1.02994e13i	−0.163513	−	0.255790i
$527$	−1.48967e13			−0.366468
$528$	1.03432e13	−	8.78858e12i	0.252049	−	0.214165i
$529$	−2.08183e13			−0.502536
$530$	3.42114e13	+	1.85270e12i	0.818071	+	0.0443022i
$531$			3.09373e13i			0.732841i
$532$	−3.92311e13	−	1.81463e13i	−0.920603	−	0.425823i
$533$			2.67665e13i			0.622236i
$534$	−1.00278e13	−	1.56870e13i	−0.230941	−	0.361271i
$535$	2.07713e12	+	1.49193e12i	0.0473908	+	0.0340392i
$536$	−3.68800e13	+	5.02951e12i	−0.833617	+	0.113685i
$537$			5.17025e13i			1.15782i
$538$	−1.66211e13	−	2.60011e13i	−0.368765	−	0.576874i
$539$		−	7.69382e12i		−	0.169121i
$540$	−3.94254e13	+	2.22957e13i	−0.858632	+	0.485569i
$541$	5.80418e12			0.125243			0.0626217	−	0.998037i	$-0.480054\pi$
$541$	5.80418e12			0.125243			0.0626217	+	0.998037i	$0.480054\pi$
$542$	−1.54076e12	+	9.84924e11i	−0.0329411	+	0.0210575i
$543$	−2.77282e13			−0.587385
$544$	1.31812e13	+	4.04424e12i	0.276669	+	0.0848872i
$545$	7.53983e12	+	5.41560e12i	0.156812	+	0.112633i
$546$	1.37711e13	−	8.80311e12i	0.283795	−	0.181415i
$547$	−5.03600e13			−1.02837			−0.514185	−	0.857679i	$-0.671906\pi$
$547$	−5.03600e13			−1.02837			−0.514185	+	0.857679i	$0.671906\pi$
$548$	3.54012e13	+	1.63747e13i	0.716333	+	0.331338i
$549$	3.54690e13			0.711193
$550$	−2.15303e13	−	1.73035e13i	−0.427795	−	0.343811i
$551$		−	7.92590e13i		−	1.56060i
$552$	2.15842e13	−	2.94355e12i	0.421154	−	0.0574350i
$553$			8.16149e13i			1.57813i
$554$	−4.87198e13	+	3.11440e13i	−0.933591	+	0.596795i
$555$	2.21338e13	−	3.08156e13i	0.420330	−	0.585201i
$556$	1.76295e13	+	8.15448e12i	0.331792	+	0.153470i
$557$		−	3.19874e13i		−	0.596627i	−0.954468	−	0.298314i	$-0.903576\pi$
$557$		−	3.19874e13i		−	0.596627i	0.954468	−	0.298314i	$-0.0964242\pi$
$558$	3.67559e13	−	2.34961e13i	0.679448	−	0.434335i
$559$			3.95030e11i			0.00723721i
$560$	−3.72641e12	−	4.56567e13i	−0.0676629	−	0.829019i
$561$	−5.31877e12			−0.0957187
$562$	2.88859e13	+	4.51875e13i	0.515234	+	0.806002i
$563$	−3.34105e13			−0.590665			−0.295332	−	0.955395i	$-0.595430\pi$
$563$	−3.34105e13			−0.590665			−0.295332	+	0.955395i	$0.595430\pi$
$564$	2.73641e13	−	5.91596e13i	0.479497	−	1.03664i
$565$	3.65498e13	−	5.08861e13i	0.634808	−	0.883806i
$566$	−2.22588e13	−	3.48203e13i	−0.383194	−	0.599447i
$567$	−2.06458e12			−0.0352304
$568$	−1.28999e13	−	9.45914e13i	−0.218195	−	1.59996i
$569$	−3.53976e13			−0.593488			−0.296744	−	0.954957i	$-0.595901\pi$
$569$	−3.53976e13			−0.593488			−0.296744	+	0.954957i	$0.595901\pi$
$570$	−4.41537e13	−	2.39112e12i	−0.733825	−	0.0397399i
$571$		−	9.52378e12i		−	0.156902i	−0.996918	−	0.0784511i	$-0.975003\pi$
$571$		−	9.52378e12i		−	0.156902i	0.996918	−	0.0784511i	$-0.0249974\pi$
$572$	9.48003e12	−	2.04953e13i	0.154821	−	0.334714i
$573$			2.60302e13i			0.421410i
$574$	−2.58496e13	−	4.04377e13i	−0.414854	−	0.648973i
$575$	−1.41572e13	−	4.20110e13i	−0.225236	−	0.668380i
$576$	−3.89020e13	+	1.08116e13i	−0.613563	+	0.170521i
$577$			7.27346e13i			1.13727i	0.822592	+	0.568633i	$0.192527\pi$
$577$			7.27346e13i			1.13727i	−0.822592	+	0.568633i	$0.807473\pi$
$578$	3.18362e13	+	4.98027e13i	0.493494	+	0.771994i
$579$			6.97906e13i			1.07252i
$580$	7.31154e13	−	4.13479e13i	1.11396	−	0.629960i
$581$	1.39704e13			0.211022
$582$	−2.54394e13	+	1.62620e13i	−0.380971	+	0.243534i
$583$	−3.02836e13			−0.449640
$584$	9.23955e12	+	6.77510e13i	0.136015	+	0.997359i
$585$	−1.71033e13	+	2.38119e13i	−0.249632	+	0.347548i
$586$	−1.01800e14	+	6.50750e13i	−1.47319	+	0.941729i
$587$	3.06508e13			0.439795			0.219898	−	0.975523i	$-0.429428\pi$
$587$	3.06508e13			0.439795			0.219898	+	0.975523i	$0.429428\pi$
$588$	5.47980e12	−	1.18470e13i	0.0779611	−	0.168547i
$589$	1.09467e14			1.54421
$590$	−8.21521e13	−	4.44890e12i	−1.14910	−	0.0622290i
$591$			4.56148e13i			0.632657i
$592$	6.62481e13	−	5.62907e13i	0.911097	−	0.774156i
$593$			1.36696e13i			0.186416i	0.995647	+	0.0932078i	$0.0297121\pi$
$593$			1.36696e13i			0.186416i	−0.995647	+	0.0932078i	$0.970288\pi$
$594$	3.37313e13	−	2.15626e13i	0.456143	−	0.291588i
$595$	−1.04722e13	+	1.45798e13i	−0.140428	+	0.195509i
$596$	1.05979e13	−	2.29120e13i	0.140925	−	0.304671i
$597$		−	1.21915e13i		−	0.160763i
$598$	3.05367e13	−	1.95205e13i	0.399316	−	0.255261i
$599$			9.08884e13i			1.17862i	0.807906	+	0.589311i	$0.200601\pi$
$599$			9.08884e13i			1.17862i	−0.807906	+	0.589311i	$0.799399\pi$
$600$	−2.08283e13	−	4.19786e13i	−0.267854	−	0.539848i
$601$	2.58195e13			0.329288			0.164644	−	0.986353i	$-0.447352\pi$
$601$	2.58195e13			0.329288			0.164644	+	0.986353i	$0.447352\pi$
$602$	−3.81499e11	−	5.96795e11i	−0.00482515	−	0.00754819i
$603$	−4.27140e13			−0.535776
$604$	8.91810e13	+	4.12505e13i	1.10940	+	0.513150i
$605$	−4.60028e13	−	3.30423e13i	−0.567555	−	0.407655i
$606$	2.14628e13	+	3.35752e13i	0.262618	+	0.410824i
$607$	1.20909e14			1.46729			0.733646	−	0.679532i	$-0.237817\pi$
$607$	1.20909e14			1.46729			0.733646	+	0.679532i	$0.237817\pi$
$608$	−9.68609e13	−	2.97187e13i	−1.16582	−	0.357694i
$609$	−5.37377e13			−0.641494
$610$	−5.10058e12	+	9.41858e13i	−0.0603907	+	1.11516i
$611$		−	1.08445e14i		−	1.27351i
$612$	1.43605e13	+	6.64240e12i	0.167268	+	0.0773692i
$613$		−	4.75439e13i		−	0.549278i	−0.961547	−	0.274639i	$-0.911442\pi$
$613$		−	4.75439e13i		−	0.549278i	0.961547	−	0.274639i	$-0.0885583\pi$
$614$	6.86772e13	+	1.07435e14i	0.786993	+	1.23113i
$615$	−3.98769e13	−	2.86422e13i	−0.453258	−	0.325560i
$616$	5.47119e12	+	4.01187e13i	0.0616848	+	0.452317i
$617$		−	1.10787e14i		−	1.23898i	−0.785006	−	0.619488i	$-0.787340\pi$
$617$		−	1.10787e14i		−	1.23898i	0.785006	−	0.619488i	$-0.212660\pi$
$618$	−4.10868e13	−	6.42738e13i	−0.455785	−	0.713004i
$619$			1.29963e14i			1.43010i	0.699071	+	0.715052i	$0.253597\pi$
$619$			1.29963e14i			1.43010i	−0.699071	+	0.715052i	$0.746403\pi$
$620$	5.71067e13	+	1.00982e14i	0.623346	+	1.10226i
$621$	6.42541e13			0.695734
$622$	−3.77119e13	+	2.41072e13i	−0.405067	+	0.258938i
$623$	5.55414e13			0.591802
$624$	2.91948e13	−	2.48067e13i	0.308591	−	0.262209i
$625$	−7.59163e13	+	5.77206e13i	−0.796040	+	0.605244i
$626$	1.57072e14	−	1.00408e14i	1.63390	−	1.04447i
$627$	3.90845e13			0.403336
$628$	3.92949e13	+	1.81758e13i	0.402289	+	0.186078i
$629$	−3.40666e13			−0.346000
$630$	2.84265e12	−	5.24915e13i	0.0286431	−	0.528915i
$631$			1.72818e13i			0.172760i	0.996262	+	0.0863798i	$0.0275299\pi$
$631$			1.72818e13i			0.172760i	−0.996262	+	0.0863798i	$0.972470\pi$
$632$	2.58498e13	+	1.89549e14i	0.256372	+	1.87991i
$633$		−	5.97545e13i		−	0.587966i
$634$	−1.19035e14	+	7.60926e13i	−1.16206	+	0.742842i
$635$	4.27610e13	+	3.07138e13i	0.414171	+	0.297485i
$636$	−4.66309e13	−	2.15690e13i	−0.448114	−	0.207274i
$637$		−	2.17166e13i		−	0.207060i
$638$	−6.25556e13	+	3.99885e13i	−0.591784	+	0.378296i
$639$		−	1.09555e14i		−	1.02832i
$640$	−2.31153e13	−	1.04857e14i	−0.215278	−	0.976553i
$641$	−2.02056e14			−1.86716			−0.933580	−	0.358369i	$-0.883333\pi$
$641$	−2.02056e14			−1.86716			−0.933580	+	0.358369i	$0.883333\pi$
$642$	−2.06555e12	−	3.23123e12i	−0.0189392	−	0.0296273i
$643$	7.34393e13			0.668150			0.334075	−	0.942547i	$-0.391576\pi$
$643$	7.34393e13			0.668150			0.334075	+	0.942547i	$0.391576\pi$
$644$	−2.72818e13	+	5.89815e13i	−0.246288	+	0.532460i
$645$	−5.88518e11	−	4.22713e11i	−0.00527183	−	0.00378658i
$646$	2.13843e13	+	3.34523e13i	0.190078	+	0.297347i
$647$	2.94516e13			0.259769			0.129885	−	0.991529i	$-0.458539\pi$
$647$	2.94516e13			0.259769			0.129885	+	0.991529i	$0.458539\pi$
$648$	−4.79495e12	+	6.53912e11i	−0.0419671	+	0.00572327i
$649$	7.27204e13			0.631586
$650$	−6.07715e13	−	4.88410e13i	−0.523761	−	0.420937i
$651$		−	7.42187e13i		−	0.634759i
$652$	6.21569e13	−	1.34379e14i	0.527535	−	1.14050i
$653$		−	9.08012e13i		−	0.764761i	−0.924005	−	0.382381i	$-0.875104\pi$
$653$		−	9.08012e13i		−	0.764761i	0.924005	−	0.382381i	$-0.124896\pi$
$654$	−7.49781e12	−	1.17291e13i	−0.0626680	−	0.0980342i
$655$	−1.25421e13	+	1.74616e13i	−0.104031	+	0.144837i
$656$	−7.28430e13	−	8.57283e13i	−0.599609	−	0.705675i
$657$			7.84685e13i			0.641015i
$658$	1.04730e14	+	1.63834e14i	0.849070	+	1.32823i
$659$		−	1.09885e14i		−	0.884119i	−0.896986	−	0.442060i	$-0.854248\pi$
$659$		−	1.09885e14i		−	0.884119i	0.896986	−	0.442060i	$-0.145752\pi$
$660$	2.03896e13	+	3.60549e13i	0.162813	+	0.287902i
$661$	9.98769e13			0.791512			0.395756	−	0.918356i	$-0.370483\pi$
$661$	9.98769e13			0.791512			0.395756	+	0.918356i	$0.370483\pi$
$662$	−2.73640e13	+	1.74924e13i	−0.215224	+	0.137581i
$663$	−1.50128e13			−0.117191
$664$	3.24459e13	−	4.42482e12i	0.251374	−	0.0342811i
$665$	7.69539e13	−	1.07138e14i	0.591728	−	0.823829i
$666$	8.40555e13	−	5.37322e13i	0.641498	−	0.410075i
$667$	−1.19161e14			−0.902620
$668$	−9.32426e13	+	2.01585e14i	−0.701022	+	1.51557i
$669$	−4.53017e13			−0.338052
$670$	6.14243e12	−	1.13424e14i	0.0454953	−	0.840102i
$671$		−	8.33725e13i		−	0.612929i
$672$	−2.01493e13	+	6.56718e13i	−0.147033	+	0.479217i
$673$		−	3.19718e13i		−	0.231575i	−0.993274	−	0.115787i	$-0.963061\pi$
$673$		−	3.19718e13i		−	0.231575i	0.993274	−	0.115787i	$-0.0369392\pi$
$674$	7.37730e13	−	4.71591e13i	0.530393	−	0.339052i
$675$	−4.41407e13	−	1.30986e14i	−0.315007	−	0.934772i
$676$	−3.25054e13	+	7.02746e13i	−0.230262	+	0.497812i
$677$			1.90887e13i			0.134225i	0.997745	+	0.0671123i	$0.0213786\pi$
$677$			1.90887e13i			0.134225i	−0.997745	+	0.0671123i	$0.978621\pi$
$678$	−7.91597e13	+	5.06026e13i	−0.552530	+	0.353203i
$679$		−	9.00708e13i		−	0.624073i
$680$	−1.97036e13	+	3.71781e13i	−0.135519	+	0.255707i
$681$	−6.39229e13			−0.436436
$682$	−5.52292e13	−	8.63974e13i	−0.374323	−	0.585570i
$683$	−9.20549e12			−0.0619360			−0.0309680	−	0.999520i	$-0.509859\pi$
$683$	−9.20549e12			−0.0619360			−0.0309680	+	0.999520i	$0.509859\pi$
$684$	−1.05527e14	−	4.88111e13i	−0.704825	−	0.326015i
$685$	−6.94412e13	+	9.66790e13i	−0.460431	+	0.641031i
$686$	8.90334e13	+	1.39279e14i	0.586047	+	0.916778i
$687$	−1.29677e14			−0.847383
$688$	−1.07505e12	−	1.26521e12i	−0.00697404	−	0.00820769i
$689$	−8.54788e13			−0.550506
$690$	−3.59490e12	+	6.63823e13i	−0.0229848	+	0.424431i
$691$			2.89506e14i			1.83767i	0.394645	+	0.918834i	$0.370868\pi$
$691$			2.89506e14i			1.83767i	−0.394645	+	0.918834i	$0.629132\pi$
$692$	−2.46021e14	−	1.13796e14i	−1.55039	−	0.717131i
$693$			4.64650e13i			0.290710i
$694$	−8.48029e13	−	1.32661e14i	−0.526761	−	0.824034i
$695$	−3.45812e13	+	4.81453e13i	−0.213263	+	0.296914i
$696$	−1.24805e14	+	1.70203e13i	−0.764161	+	0.104213i
$697$			4.40839e13i			0.267988i
$698$	−7.19569e13	−	1.12565e14i	−0.434306	−	0.679402i
$699$			5.04565e12i			0.0302365i
$700$	1.38979e14	+	1.50969e13i	0.826912	+	0.0898253i
$701$	−1.50130e14			−0.886903			−0.443451	−	0.896298i	$-0.646246\pi$
$701$	−1.50130e14			−0.886903			−0.443451	+	0.896298i	$0.646246\pi$
$702$	9.52104e13	−	6.08629e13i	0.558469	−	0.356999i
$703$	2.50335e14			1.45796
$704$	2.54135e13	+	9.14419e13i	0.146960	+	0.528789i
$705$	1.61562e14	+	1.16045e14i	0.927671	+	0.666314i
$706$	1.87917e14	−	1.20125e14i	1.07138	−	0.684874i
$707$	−1.18877e14			−0.672976
$708$	1.11975e14	+	5.17939e13i	0.629442	+	0.291147i
$709$	5.68854e13			0.317519			0.158760	−	0.987317i	$-0.449251\pi$
$709$	5.68854e13			0.317519			0.158760	+	0.987317i	$0.449251\pi$
$710$	2.90916e14	+	1.57544e13i	1.61241	+	0.0873192i
$711$			2.19534e14i			1.20824i
$712$	1.28994e14	−	1.75915e13i	0.704967	−	0.0961400i
$713$		−	1.64577e14i		−	0.893142i
$714$	2.26807e13	−	1.44986e13i	0.122227	−	0.0781329i
$715$	5.59716e13	+	4.02025e13i	0.299528	+	0.215141i
$716$	−3.28128e14	−	1.51775e14i	−1.74372	−	0.806555i
$717$			5.19497e13i			0.274149i
$718$	1.87839e13	−	1.20075e13i	0.0984381	−	0.0629262i
$719$			4.60962e13i			0.239895i	0.992780	+	0.119947i	$0.0382725\pi$
$719$			4.60962e13i			0.239895i	−0.992780	+	0.119947i	$0.961727\pi$
$720$	−1.00236e13	−	1.22811e14i	−0.0518035	−	0.634708i
$721$	2.27568e14			1.16798
$722$	−5.14697e13	−	8.05162e13i	−0.262341	−	0.410390i
$723$	7.99593e13			0.404741
$724$	8.13973e13	−	1.75976e14i	0.409183	−	0.884628i
$725$	8.18600e13	+	2.42917e14i	0.408678	+	1.21274i
$726$	4.57465e13	+	7.15632e13i	0.226817	+	0.354819i
$727$	−1.49821e14			−0.737736			−0.368868	−	0.929482i	$-0.620254\pi$
$727$	−1.49821e14			−0.737736			−0.368868	+	0.929482i	$0.620254\pi$
$728$	1.54430e13	+	1.13239e14i	0.0755224	+	0.553784i
$729$	1.16841e14			0.567490
$730$	−2.08368e14	−	1.12841e13i	−1.00512	−	0.0544316i
$731$			6.50607e11i			0.00311697i
$732$	5.93807e13	−	1.28378e14i	0.282547	−	0.610849i
$733$		−	9.25379e13i		−	0.437320i	−0.975801	−	0.218660i	$-0.929831\pi$
$733$		−	9.25379e13i		−	0.437320i	0.975801	−	0.218660i	$-0.0701686\pi$
$734$	−6.56410e13	−	1.02685e14i	−0.308102	−	0.481977i
$735$	3.23536e13	+	2.32385e13i	0.150829	+	0.108336i
$736$	−4.46802e13	+	1.45624e14i	−0.206884	+	0.674287i
$737$			1.00402e14i			0.461749i
$738$	−6.95321e13	−	1.08772e14i	−0.317617	−	0.496862i
$739$		−	4.85434e13i		−	0.220246i	−0.993918	−	0.110123i	$-0.964876\pi$
$739$		−	4.85434e13i		−	0.220246i	0.993918	−	0.110123i	$-0.0351245\pi$
$740$	1.30595e14	+	2.30931e14i	0.588529	+	1.04070i
$741$	1.10320e14			0.493815
$742$	1.29138e14	−	8.25509e13i	0.574161	−	0.367031i
$743$	4.13114e13			0.182442			0.0912211	−	0.995831i	$-0.470923\pi$
$743$	4.13114e13			0.182442			0.0912211	+	0.995831i	$0.470923\pi$
$744$	−2.35072e13	−	1.72371e14i	−0.103118	−	0.756137i
$745$	6.25716e13	+	4.49430e13i	0.272644	+	0.195831i
$746$	2.58870e14	−	1.65482e14i	1.12044	−	0.716235i
$747$	3.75785e13			0.161561
$748$	1.56134e13	−	3.37553e13i	0.0666792	−	0.144157i
$749$	1.14405e13			0.0485329
$750$	1.37794e14	−	3.82742e13i	0.580662	−	0.161287i
$751$		−	8.29433e13i		−	0.347202i	−0.984816	−	0.173601i	$-0.944460\pi$
$751$		−	8.29433e13i		−	0.347202i	0.984816	−	0.173601i	$-0.0555403\pi$
$752$	2.95125e14	+	3.47330e14i	1.22720	+	1.44429i
$753$			4.07768e13i			0.168437i
$754$	−1.76570e14	+	1.12872e14i	−0.724537	+	0.463158i
$755$	−1.74933e14	+	2.43549e14i	−0.713078	+	0.992777i
$756$	−8.50617e13	+	1.83898e14i	−0.344449	+	0.744678i
$757$			1.93514e14i			0.778455i	0.921142	+	0.389228i	$0.127258\pi$
$757$			1.93514e14i			0.778455i	−0.921142	+	0.389228i	$0.872742\pi$
$758$	−1.68201e14	+	1.07522e14i	−0.672176	+	0.429686i
$759$		−	5.87611e13i		−	0.233282i
$760$	1.44790e14	−	2.73200e14i	0.571045	−	1.07749i
$761$	1.66032e14			0.650531			0.325265	−	0.945623i	$-0.394546\pi$
$761$	1.66032e14			0.650531			0.325265	+	0.945623i	$0.394546\pi$
$762$	−4.25227e13	−	6.65201e13i	−0.165518	−	0.258927i
$763$	4.15283e13			0.160591
$764$	−1.65200e14	−	7.64127e13i	−0.634661	−	0.293561i
$765$	−2.81688e13	+	3.92178e13i	−0.107513	+	0.149684i
$766$	1.49009e14	+	2.33102e14i	0.565028	+	0.883896i
$767$	2.05261e14			0.773268
$768$	−2.59962e13	+	1.58903e14i	−0.0972981	+	0.594739i
$769$	−4.26640e14			−1.58646			−0.793232	−	0.608919i	$-0.791603\pi$
$769$	−4.26640e14			−1.58646			−0.793232	+	0.608919i	$0.791603\pi$
$770$	−1.23385e14	−	6.68185e12i	−0.455836	−	0.0246856i
$771$			1.52148e13i			0.0558464i
$772$	−4.42923e14	−	2.04873e14i	−1.61526	−	0.747134i
$773$		−	4.17310e14i		−	1.51203i	−0.654552	−	0.756017i	$-0.727143\pi$
$773$		−	4.17310e14i		−	1.51203i	0.654552	−	0.756017i	$-0.272857\pi$
$774$	−1.02618e12	−	1.60530e12i	−0.00369420	−	0.00577898i
$775$	−3.35499e14	+	1.13059e14i	−1.20000	+	0.404387i
$776$	−2.85280e13	−	2.09188e14i	−0.101382	−	0.743408i
$777$		−	1.69728e14i		−	0.599305i
$778$	1.49162e14	+	2.33340e14i	0.523310	+	0.818636i
$779$		−	3.23946e14i		−	1.12924i
$780$	5.75519e13	+	1.01769e14i	0.199336	+	0.352486i
$781$	−2.57516e14			−0.886236
$782$	5.02935e13	−	3.21499e13i	0.171980	−	0.109938i
$783$	−3.71531e14			−1.26237
$784$	5.91003e13	+	6.95546e13i	0.199530	+	0.234826i
$785$	−7.70790e13	+	1.07313e14i	−0.258576	+	0.360000i
$786$	2.71637e13	−	1.73643e13i	0.0905476	−	0.0578822i
$787$	1.87778e13			0.0621974			0.0310987	−	0.999516i	$-0.490099\pi$
$787$	1.87778e13			0.0621974			0.0310987	+	0.999516i	$0.490099\pi$
$788$	−2.89492e14	−	1.33904e14i	−0.952809	−	0.440719i
$789$	−5.59409e13			−0.182955
$790$	−5.82958e14	−	3.15698e13i	−1.89453	−	0.102597i
$791$		−	2.80273e14i		−	0.905106i
$792$	1.47168e13	+	1.07914e14i	0.0472267	+	0.346300i
$793$		−	2.35328e14i		−	0.750426i
$794$	1.54076e13	−	9.84926e12i	0.0488239	−	0.0312105i
$795$	9.14689e13	−	1.27347e14i	0.288030	−	0.401008i
$796$	7.73729e13	+	3.57887e13i	0.242116	+	0.111990i
$797$			2.33356e14i			0.725649i	0.931857	+	0.362825i	$0.118188\pi$
$797$			2.33356e14i			0.725649i	−0.931857	+	0.362825i	$0.881812\pi$
$798$	−1.66667e14	+	1.06541e14i	−0.515034	+	0.329234i
$799$		−	1.78607e14i		−	0.548485i
$800$	3.27558e14	−	8.95629e12i	0.999626	−	0.0273324i
$801$	1.49399e14			0.453091
$802$	2.49510e14	+	3.90318e14i	0.751996	+	1.17638i
$803$	1.84446e14			0.552447
$804$	−7.15099e13	+	1.54600e14i	−0.212856	+	0.460182i
$805$	−1.61076e14	−	1.15695e14i	−0.476487	−	0.342244i
$806$	−1.55891e14	−	2.43866e14i	−0.458294	−	0.716929i
$807$	−1.41224e14			−0.412612
$808$	−2.76089e14	+	3.76516e13i	−0.801663	+	0.109327i
$809$	3.46851e14			1.00092			0.500461	−	0.865759i	$-0.333164\pi$
$809$	3.46851e14			1.00092			0.500461	+	0.865759i	$0.333164\pi$
$810$	7.98609e11	−	1.47469e13i	0.00229039	−	0.0422936i
$811$		−	1.48396e14i		−	0.422978i	−0.977380	−	0.211489i	$-0.932169\pi$
$811$		−	1.48396e14i		−	0.422978i	0.977380	−	0.211489i	$-0.0678313\pi$
$812$	1.57749e14	−	3.41044e14i	0.446876	−	0.966118i
$813$			8.36859e12i			0.0235613i
$814$	−1.26301e14	−	1.97579e14i	−0.353416	−	0.552863i
$815$	3.66984e14	+	2.63592e14i	1.02061	+	0.733068i
$816$	4.80834e13	−	4.08562e13i	0.132906	−	0.112930i
$817$		−	4.78093e12i		−	0.0131342i
$818$	1.29075e14	+	2.01918e14i	0.352433	+	0.551325i
$819$			1.31153e14i			0.355924i
$820$	2.98836e14	−	1.68996e14i	0.806054	−	0.455836i
$821$	−4.15425e14			−1.11372			−0.556861	−	0.830605i	$-0.687995\pi$
$821$	−4.15425e14			−1.11372			−0.556861	+	0.830605i	$0.687995\pi$
$822$	1.50396e14	−	9.61403e13i	0.400754	−	0.256181i
$823$	4.98563e14			1.32045			0.660224	−	0.751069i	$-0.270461\pi$
$823$	4.98563e14			1.32045			0.660224	+	0.751069i	$0.270461\pi$
$824$	5.28523e14	−	7.20774e13i	1.39132	−	0.189742i
$825$	−1.19788e14	+	4.03671e13i	−0.313432	+	0.105623i
$826$	−3.10100e14	+	1.98230e14i	−0.806495	+	0.515549i
$827$	6.46871e14			1.67221			0.836104	−	0.548571i	$-0.184828\pi$
$827$	6.46871e14			1.67221			0.836104	+	0.548571i	$0.184828\pi$
$828$	−7.33844e13	+	1.58653e14i	−0.188561	+	0.407658i
$829$	−1.71726e14			−0.438596			−0.219298	−	0.975658i	$-0.570377\pi$
$829$	−1.71726e14			−0.438596			−0.219298	+	0.975658i	$0.570377\pi$
$830$	−5.40393e12	+	9.97874e13i	−0.0137189	+	0.253329i
$831$			2.64620e14i			0.667756i
$832$	7.17323e13	+	2.58105e14i	0.179928	+	0.647410i
$833$		−	3.57669e13i		−	0.0891778i
$834$	7.48961e13	−	4.78771e13i	0.185622	−	0.118658i
$835$	−5.50519e14	−	3.95419e14i	−1.35625	−	0.974148i
$836$	−1.14734e14	+	2.48048e14i	−0.280970	+	0.607441i
$837$		−	5.13133e14i		−	1.24912i
$838$	−1.71214e14	+	1.09448e14i	−0.414304	+	0.264843i
$839$			3.56109e14i			0.856591i	0.903639	+	0.428295i	$0.140886\pi$
$839$			3.56109e14i			0.856591i	−0.903639	+	0.428295i	$0.859114\pi$
$840$	−1.85230e14	−	9.81677e13i	−0.442909	−	0.234732i
$841$	2.68307e14			0.637753
$842$	3.88818e13	+	6.08244e13i	0.0918725	+	0.143720i
$843$	2.45435e14			0.576498
$844$	3.79229e14	+	1.75412e14i	0.885502	+	0.409587i
$845$	−1.91917e14	−	1.37847e14i	−0.445481	−	0.319974i
$846$	2.81711e14	+	4.40693e14i	0.650058	+	1.01691i
$847$	−2.53377e14			−0.581233
$848$	2.73774e14	−	2.32624e14i	0.624327	−	0.530488i
$849$	−1.89126e14			−0.428758
$850$	−1.00090e14	−	8.04402e13i	−0.225577	−	0.181292i
$851$		−	3.76364e14i		−	0.843257i
$852$	−3.96525e14	−	1.83412e14i	−0.883228	−	0.408535i
$853$			3.78193e14i			0.837468i	0.908109	+	0.418734i	$0.137526\pi$
$853$			3.78193e14i			0.837468i	−0.908109	+	0.418734i	$0.862474\pi$
$854$	2.27267e14	+	3.55524e14i	0.500320	+	0.782671i
$855$	2.06996e14	−	2.88188e14i	0.453034	−	0.630734i
$856$	2.65703e13	−	3.62354e12i	0.0578134	−	0.00788431i
$857$		−	3.25573e14i		−	0.704278i	−0.935948	−	0.352139i	$-0.885454\pi$
$857$		−	3.25573e14i		−	0.704278i	0.935948	−	0.352139i	$-0.114546\pi$
$858$	−5.56597e13	−	8.70709e13i	−0.119703	−	0.187256i
$859$			1.71426e14i			0.366531i	0.983063	+	0.183266i	$0.0586668\pi$
$859$			1.71426e14i			0.366531i	−0.983063	+	0.183266i	$0.941333\pi$
$860$	4.41034e12	−	2.49412e12i	0.00937519	−	0.00530181i
$861$	−2.19636e14			−0.464182
$862$	−2.81756e14	+	1.80112e14i	−0.592021	+	0.378447i
$863$	−7.32951e14			−1.53116			−0.765581	−	0.643340i	$-0.777548\pi$
$863$	−7.32951e14			−1.53116			−0.765581	+	0.643340i	$0.777548\pi$
$864$	−1.39308e14	+	4.54041e14i	−0.289340	+	0.943032i
$865$	4.82583e14	−	6.71872e14i	0.996533	−	1.38741i
$866$	−1.71508e14	+	1.09636e14i	−0.352123	+	0.225093i
$867$	2.70502e14			0.552173
$868$	4.71026e14	+	2.17872e14i	0.955974	+	0.442183i
$869$	5.16029e14			1.04130
$870$	2.07865e13	−	3.83837e14i	0.0417047	−	0.770106i
$871$			2.83397e14i			0.565332i
$872$	9.64486e13	−	1.31532e13i	0.191299	−	0.0260885i
$873$		−	2.42279e14i		−	0.477798i
$874$	−3.69577e14	+	2.36251e14i	−0.724683	+	0.463251i
$875$	−1.25197e14	+	4.07842e14i	−0.244093	+	0.795154i
$876$	2.84011e14	+	1.31369e14i	0.550572	+	0.254666i
$877$			6.25010e14i			1.20473i	0.798222	+	0.602364i	$0.205774\pi$
$877$			6.25010e14i			1.20473i	−0.798222	+	0.602364i	$0.794226\pi$
$878$	5.15775e14	−	3.29707e14i	0.988524	−	0.631911i
$879$			5.52922e14i			1.05371i
$880$	−2.88675e14	+	2.35611e13i	−0.547011	+	0.0446460i
$881$	3.05476e14			0.575569			0.287784	−	0.957695i	$-0.407081\pi$
$881$	3.05476e14			0.575569			0.287784	+	0.957695i	$0.407081\pi$
$882$	5.64141e13	+	8.82509e13i	0.105693	+	0.165339i
$883$	−3.59888e13			−0.0670446			−0.0335223	−	0.999438i	$-0.510672\pi$
$883$	−3.59888e13			−0.0670446			−0.0335223	+	0.999438i	$0.510672\pi$
$884$	4.40707e13	−	9.52781e13i	0.0816372	−	0.176495i
$885$	−2.19645e14	+	3.05799e14i	−0.404581	+	0.563275i
$886$	−3.11487e14	−	4.87272e14i	−0.570520	−	0.892488i
$887$	−4.13812e14			−0.753677			−0.376839	−	0.926279i	$-0.622989\pi$
$887$	−4.13812e14			−0.753677			−0.376839	+	0.926279i	$0.622989\pi$
$888$	−5.37576e13	−	3.94189e14i	−0.0973588	−	0.713904i
$889$	2.35522e14			0.424152
$890$	−2.14842e13	+	3.96720e14i	−0.0384741	+	0.710451i
$891$			1.30538e13i			0.0232460i
$892$	1.32985e14	−	2.87505e14i	0.235493	−	0.509121i
$893$			1.31248e15i			2.31118i
$894$	−6.22229e13	−	9.73379e13i	−0.108959	−	0.170449i
$895$	6.43639e14	−	8.96101e14i	1.12080	−	1.56042i
$896$	−3.57634e14	−	3.20659e14i	−0.619297	−	0.555269i
$897$		−	1.65860e14i		−	0.285613i
$898$	−1.32935e14	−	2.07956e14i	−0.227645	−	0.356115i
$899$			9.51618e14i			1.62056i
$900$	3.73836e14	+	4.06088e13i	0.633094	+	0.0687714i
$901$	−1.40782e14			−0.237096
$902$	−2.55676e14	+	1.63440e14i	−0.428211	+	0.273733i
$903$	−3.24148e12			−0.00539888
$904$	−8.87706e13	−	6.50929e14i	−0.147037	−	1.07818i
$905$	4.80582e14	+	3.45186e14i	0.791635	+	0.568604i
$906$	3.78871e14	−	2.42192e14i	0.620656	−	0.396752i
$907$	−8.06692e14			−1.31423			−0.657115	−	0.753791i	$-0.728223\pi$
$907$	−8.06692e14			−1.31423			−0.657115	+	0.753791i	$0.728223\pi$
$908$	1.87648e14	−	4.05684e14i	0.304029	−	0.657292i
$909$	−3.19763e14			−0.515239
$910$	−3.48268e14	−	1.88602e13i	−0.558093	−	0.0302232i
$911$		−	8.50991e14i		−	1.35623i	−0.734956	−	0.678115i	$-0.762797\pi$
$911$		−	8.50991e14i		−	1.35623i	0.734956	−	0.678115i	$-0.237203\pi$
$912$	−3.53336e14	+	3.00228e14i	−0.560034	+	0.475858i
$913$		−	8.83310e13i		−	0.139239i
$914$	−1.49767e14	+	9.57381e13i	−0.234793	+	0.150091i
$915$	3.50593e14	+	2.51819e14i	0.546636	+	0.392630i
$916$	3.80672e14	−	8.22990e14i	0.590301	−	1.27620i
$917$			9.61762e13i			0.148327i
$918$	1.56810e14	−	1.00240e14i	0.240525	−	0.153755i
$919$		−	3.79956e14i		−	0.579637i	−0.957082	−	0.289819i	$-0.906405\pi$
$919$		−	3.79956e14i		−	0.579637i	0.957082	−	0.289819i	$-0.0935950\pi$
$920$	−4.10739e14	−	2.17683e14i	−0.623199	−	0.330282i
$921$	5.83529e14			0.880570
$922$	−2.55282e14	−	3.99349e14i	−0.383147	−	0.599374i
$923$	−7.26868e14			−1.08504
$924$	1.68177e14	+	7.77898e13i	0.249693	+	0.115495i
$925$	−7.67239e14	+	2.58550e14i	−1.13298	+	0.381801i
$926$	−4.95380e14	−	7.74943e14i	−0.727584	−	1.13819i
$927$	6.12130e14			0.894221
$928$	2.58351e14	−	8.42031e14i	0.375379	−	1.22346i
$929$	3.47287e14			0.501891			0.250946	−	0.968001i	$-0.419258\pi$
$929$	3.47287e14			0.501891			0.250946	+	0.968001i	$0.419258\pi$
$930$	5.30128e14	+	2.87088e13i	0.762020	+	0.0412668i
$931$			2.62830e14i			0.375774i
$932$	−3.20220e13	−	1.48117e13i	−0.0455374	−	0.0210632i
$933$			2.04831e14i			0.289726i
$934$	3.34027e14	+	5.22533e14i	0.469946	+	0.735156i
$935$	9.21842e13	+	6.62128e13i	0.129003	+	0.0926582i
$936$	4.15398e13	+	3.04599e14i	0.0578209	+	0.423984i
$937$		−	2.94468e14i		−	0.407700i	−0.979002	−	0.203850i	$-0.934654\pi$
$937$		−	2.94468e14i		−	0.407700i	0.979002	−	0.203850i	$-0.0653455\pi$
$938$	−2.73689e14	−	4.28144e14i	−0.376915	−	0.589624i
$939$		−	8.53131e14i		−	1.16866i
$940$	−1.21074e15	+	6.84693e14i	−1.64973	+	0.932947i
$941$	−6.35492e14			−0.861315			−0.430657	−	0.902515i	$-0.641718\pi$
$941$	−6.35492e14			−0.861315			−0.430657	+	0.902515i	$0.641718\pi$
$942$	1.66938e14	−	1.06715e14i	0.225062	−	0.143870i
$943$	−4.87033e14			−0.653131
$944$	−6.57416e14	+	5.58603e14i	−0.876960	+	0.745150i
$945$	−5.02218e14	−	3.60726e14i	−0.666397	−	0.478650i
$946$	−3.77337e12	+	2.41212e12i	−0.00498051	+	0.00318378i
$947$	−1.19083e15			−1.56351			−0.781753	−	0.623589i	$-0.785674\pi$
$947$	−1.19083e15			−1.56351			−0.781753	+	0.623589i	$0.785674\pi$
$948$	7.94586e14	+	3.67534e14i	1.03777	+	0.480016i
$949$	5.20618e14			0.676376
$950$	7.35499e14	+	5.91107e14i	0.950527	+	0.763921i
$951$			6.46535e14i			0.831169i
$952$	2.54344e13	+	1.86503e14i	0.0325265	+	0.238507i
$953$			8.93473e14i			1.13662i	0.822813	+	0.568312i	$0.192403\pi$
$953$			8.93473e14i			1.13662i	−0.822813	+	0.568312i	$0.807597\pi$
$954$	3.47364e14	−	2.22051e14i	0.439585	−	0.281003i
$955$	3.24047e14	−	4.51152e14i	0.407936	−	0.567945i
$956$	−3.29696e14	−	1.52500e14i	−0.412881	−	0.190977i
$957$			3.39769e14i			0.423277i
$958$	3.47643e14	−	2.22229e14i	0.430830	−	0.275406i
$959$			5.32494e14i			0.656480i
$960$	−4.61285e14	−	1.69325e14i	−0.565736	−	0.207666i
$961$	−4.94679e14			−0.603541
$962$	−3.56500e14	−	5.57687e14i	−0.432697	−	0.676886i
$963$	3.07735e13			0.0371574
$964$	−2.34724e14	+	5.07458e14i	−0.281950	+	0.609558i
$965$	8.68816e14	−	1.20960e15i	1.03822	−	1.44546i
$966$	1.60178e14	+	2.50574e14i	0.190422	+	0.297886i
$967$	8.32138e14			0.984154			0.492077	−	0.870552i	$-0.336238\pi$
$967$	8.32138e14			0.984154			0.492077	+	0.870552i	$0.336238\pi$
$968$	−5.88463e14	+	8.02517e13i	−0.692376	+	0.0944230i
$969$	1.81695e14			0.212679
$970$	6.43356e14	+	3.48406e13i	0.749192	+	0.0405721i
$971$			7.63526e14i			0.884561i	0.896877	+	0.442281i	$0.145830\pi$
$971$			7.63526e14i			0.884561i	−0.896877	+	0.442281i	$0.854170\pi$
$972$	−3.68591e14	+	7.96872e14i	−0.424829	+	0.918454i
$973$			2.65178e14i			0.304069i
$974$	2.75199e12	+	4.30506e12i	0.00313944	+	0.00491116i
$975$	−3.38114e14	+	1.13941e14i	−0.383743	+	0.129317i
$976$	6.40428e14	+	7.53714e14i	0.723138	+	0.851055i
$977$			1.34095e14i			0.150640i	0.997159	+	0.0753201i	$0.0239979\pi$
$977$			1.34095e14i			0.150640i	−0.997159	+	0.0753201i	$0.976002\pi$
$978$	−3.64939e14	−	5.70889e14i	−0.407874	−	0.638054i
$979$		−	3.51173e14i		−	0.390488i
$980$	−2.42457e14	+	1.37113e14i	−0.268228	+	0.151687i
$981$	1.11706e14			0.122951
$982$	−1.12829e14	+	7.21257e13i	−0.123556	+	0.0789829i
$983$	−8.02271e13			−0.0874084			−0.0437042	−	0.999045i	$-0.513916\pi$
$983$	−8.02271e13			−0.0874084			−0.0437042	+	0.999045i	$0.513916\pi$
$984$	−5.10100e14	+	6.95650e13i	−0.552943	+	0.0754076i
$985$	5.67854e14	−	7.90590e14i	0.612428	−	0.852649i
$986$	−2.90808e14	+	1.85898e14i	−0.312048	+	0.199476i
$987$	8.89861e14			0.950028
$988$	−3.23849e14	+	7.00143e14i	−0.344000	+	0.743707i
$989$	−7.18783e12			−0.00759655
$990$	−3.31890e14	−	1.79733e13i	−0.348994	−	0.0188996i
$991$			3.38502e14i			0.354155i	0.984197	+	0.177077i	$0.0566643\pi$
$991$			3.38502e14i			0.354155i	−0.984197	+	0.177077i	$0.943336\pi$
$992$	1.16295e15	+	3.56816e14i	1.21061	+	0.371437i
$993$			1.48627e14i			0.153940i
$994$	1.09812e15	−	7.01970e14i	1.13167	−	0.723414i
$995$	−1.51771e14	+	2.11302e14i	−0.155623	+	0.216665i
$996$	6.29124e13	−	1.36013e14i	0.0641859	−	0.138766i
$997$		−	1.63118e15i		−	1.65587i	−0.560825	−	0.827934i	$-0.689516\pi$
$997$		−	1.63118e15i		−	1.65587i	0.560825	−	0.827934i	$-0.310484\pi$
$998$	1.53340e15	−	9.80220e14i	1.54883	−	0.990082i
$999$		−	1.17346e15i		−	1.17935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.d.d.19.16	yes	24
4.3	odd	2	inner	20.11.d.d.19.10	yes	24
5.2	odd	4		100.11.b.h.51.4		24
5.3	odd	4		100.11.b.h.51.21		24
5.4	even	2	inner	20.11.d.d.19.9	✓	24
20.3	even	4		100.11.b.h.51.22		24
20.7	even	4		100.11.b.h.51.3		24
20.19	odd	2	inner	20.11.d.d.19.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.9	✓	24	5.4	even	2	inner
20.11.d.d.19.10	yes	24	4.3	odd	2	inner
20.11.d.d.19.15	yes	24	20.19	odd	2	inner
20.11.d.d.19.16	yes	24	1.1	even	1	trivial
100.11.b.h.51.3		24	20.7	even	4
100.11.b.h.51.4		24	5.2	odd	4
100.11.b.h.51.21		24	5.3	odd	4
100.11.b.h.51.22		24	20.3	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	20.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(17.2353 + 26.9619i) q^{2} +146.443 q^{3} +(-429.889 + 929.393i) q^{4} +(-2538.13 - 1823.05i) q^{5} +(2523.99 + 3948.38i) q^{6} -13979.7 q^{7} +(-32467.5 + 4427.76i) q^{8} -37603.5 q^{9} +O(q^{10})\)	\(q+(17.2353 + 26.9619i) q^{2} +146.443 q^{3} +(-429.889 + 929.393i) q^{4} +(-2538.13 - 1823.05i) q^{5} +(2523.99 + 3948.38i) q^{6} -13979.7 q^{7} +(-32467.5 + 4427.76i) q^{8} -37603.5 q^{9} +(5407.52 - 99853.7i) q^{10} +88389.7i q^{11} +(-62954.1 + 136103. i) q^{12} +249490. i q^{13} +(-240944. - 376918. i) q^{14} +(-371691. - 266973. i) q^{15} +(-678968. - 799071. i) q^{16} +410905. i q^{17} +(-648107. - 1.01386e6i) q^{18} -3.01950e6i q^{19} +(2.78545e6 - 1.57521e6i) q^{20} -2.04722e6 q^{21} +(-2.38315e6 + 1.52342e6i) q^{22} -4.53962e6 q^{23} +(-4.75463e6 + 648414. i) q^{24} +(3.11858e6 + 9.25429e6i) q^{25} +(-6.72671e6 + 4.30003e6i) q^{26} -1.41541e7 q^{27} +(6.00970e6 - 1.29926e7i) q^{28} +2.62491e7 q^{29} +(791893. - 1.46229e7i) q^{30} +3.62534e7i q^{31} +(9.84227e6 - 3.20785e7i) q^{32} +1.29440e7i q^{33} +(-1.10788e7 + 7.08207e6i) q^{34} +(3.54822e7 + 2.54857e7i) q^{35} +(1.61653e7 - 3.49484e7i) q^{36} +8.29063e7i q^{37} +(8.14114e7 - 5.20419e7i) q^{38} +3.65360e7i q^{39} +(9.04787e7 + 4.79517e7i) q^{40} +1.07285e8 q^{41} +(-3.52845e7 - 5.51970e7i) q^{42} +1.58335e6 q^{43} +(-8.21488e7 - 3.79977e7i) q^{44} +(9.54425e7 + 6.85531e7i) q^{45} +(-7.82418e7 - 1.22397e8i) q^{46} -4.34667e8 q^{47} +(-9.94300e7 - 1.17018e8i) q^{48} -8.70443e7 q^{49} +(-1.95763e8 + 2.43583e8i) q^{50} +6.01741e7i q^{51} +(-2.31874e8 - 1.07253e8i) q^{52} +3.42615e8i q^{53} +(-2.43950e8 - 3.81621e8i) q^{54} +(1.61139e8 - 2.24345e8i) q^{55} +(4.53884e8 - 6.18986e7i) q^{56} -4.42184e8i q^{57} +(4.52411e8 + 7.07725e8i) q^{58} -8.22725e8i q^{59} +(4.07909e8 - 2.30679e8i) q^{60} -9.43238e8 q^{61} +(-9.77460e8 + 6.24838e8i) q^{62} +5.25684e8 q^{63} +(1.03453e9 - 2.87516e8i) q^{64} +(4.54833e8 - 6.33237e8i) q^{65} +(-3.48996e8 + 2.23094e8i) q^{66} +1.13591e9 q^{67} +(-3.81892e8 - 1.76643e8i) q^{68} -6.64796e8 q^{69} +(-7.55953e7 + 1.39592e9i) q^{70} +2.91342e9i q^{71} +(1.22089e9 - 1.66499e8i) q^{72} -2.08673e9i q^{73} +(-2.23531e9 + 1.42892e9i) q^{74} +(4.56695e8 + 1.35522e9i) q^{75} +(2.80630e9 + 1.29805e9i) q^{76} -1.23566e9i q^{77} +(-9.85080e8 + 6.29709e8i) q^{78} -5.83812e9i q^{79} +(2.66559e8 + 3.26594e9i) q^{80} +1.47685e8 q^{81} +(1.84909e9 + 2.89261e9i) q^{82} -9.99337e8 q^{83} +(8.80078e8 - 1.90267e9i) q^{84} +(7.49101e8 - 1.04293e9i) q^{85} +(2.72896e7 + 4.26902e7i) q^{86} +3.84399e9 q^{87} +(-3.91368e8 - 2.86979e9i) q^{88} -3.97301e9 q^{89} +(-2.03342e8 + 3.75485e9i) q^{90} -3.48778e9i q^{91} +(1.95153e9 - 4.21910e9i) q^{92} +5.30905e9i q^{93} +(-7.49163e9 - 1.17195e10i) q^{94} +(-5.50470e9 + 7.66388e9i) q^{95} +(1.44133e9 - 4.69767e9i) q^{96} +6.44299e9i q^{97} +(-1.50024e9 - 2.34688e9i) q^{98} -3.32376e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9}+O(q^{10}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9	\( 24 q + 608 q^{4} + 8280 q^{5} - 19584 q^{6} + 597192 q^{9} + 223600 q^{10} - 1706016 q^{14} - 4733376 q^{16} + 1631520 q^{20} - 13030368 q^{21} + 10190784 q^{24} + 8826200 q^{25} - 9454368 q^{26} + 121656816 q^{29} + 103616160 q^{30} - 335231168 q^{34} - 276632160 q^{36} - 559048000 q^{40} + 892843248 q^{41} + 766329600 q^{44} - 248162040 q^{45} + 433181216 q^{46} - 738102008 q^{49} + 765396000 q^{50} + 139387968 q^{54} - 2629032384 q^{56} + 296160000 q^{60} + 228563248 q^{61} - 1875284992 q^{64} - 2069145600 q^{65} - 1440259200 q^{66} - 943422432 q^{69} + 3242642240 q^{70} + 21045467232 q^{74} + 828422400 q^{76} + 11736799680 q^{80} - 5619065544 q^{81} - 28069573632 q^{84} - 18119744000 q^{85} + 8163556416 q^{86} + 4631088816 q^{89} - 16754463600 q^{90} + 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q + 608 * q^4 + 8280 * q^5 - 19584 * q^6 + 597192 * q^9 + 223600 * q^10 - 1706016 * q^14 - 4733376 * q^16 + 1631520 * q^20 - 13030368 * q^21 + 10190784 * q^24 + 8826200 * q^25 - 9454368 * q^26 + 121656816 * q^29 + 103616160 * q^30 - 335231168 * q^34 - 276632160 * q^36 - 559048000 * q^40 + 892843248 * q^41 + 766329600 * q^44 - 248162040 * q^45 + 433181216 * q^46 - 738102008 * q^49 + 765396000 * q^50 + 139387968 * q^54 - 2629032384 * q^56 + 296160000 * q^60 + 228563248 * q^61 - 1875284992 * q^64 - 2069145600 * q^65 - 1440259200 * q^66 - 943422432 * q^69 + 3242642240 * q^70 + 21045467232 * q^74 + 828422400 * q^76 + 11736799680 * q^80 - 5619065544 * q^81 - 28069573632 * q^84 - 18119744000 * q^85 + 8163556416 * q^86 + 4631088816 * q^89 - 16754463600 * q^90 + 63404384 * q^94 - 5617046784 * q^96

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