LMFDB - Embedded newform 20.11.d.d.19.2

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			19.2
Character	$\chi$	$=$	20.19
Dual form			20.11.d.d.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-31.7400 + 4.07116i) q^{2} +190.073 q^{3} +(990.851 - 258.437i) q^{4} +(101.732 - 3123.34i) q^{5} +(-6032.92 + 773.819i) q^{6} +14056.7 q^{7} +(-30397.4 + 12236.7i) q^{8} -22921.2 q^{9} +O(q^{10})$	\(q+(-31.7400 + 4.07116i) q^{2} +190.073 q^{3} +(990.851 - 258.437i) q^{4} +(101.732 - 3123.34i) q^{5} +(-6032.92 + 773.819i) q^{6} +14056.7 q^{7} +(-30397.4 + 12236.7i) q^{8} -22921.2 q^{9} +(9486.66 + 99549.0i) q^{10} +173205. i q^{11} +(188334. - 49122.0i) q^{12} -664258. i q^{13} +(-446160. + 57227.2i) q^{14} +(19336.6 - 593664. i) q^{15} +(914997. - 512145. i) q^{16} -1.08730e6i q^{17} +(727518. - 93315.9i) q^{18} -2.14038e6i q^{19} +(-706386. - 3.12106e6i) q^{20} +2.67181e6 q^{21} +(-705145. - 5.49751e6i) q^{22} +6.85374e6 q^{23} +(-5.77774e6 + 2.32587e6i) q^{24} +(-9.74493e6 - 635490. i) q^{25} +(2.70430e6 + 2.10835e7i) q^{26} -1.55803e7 q^{27} +(1.39281e7 - 3.63278e6i) q^{28} +1.60930e7 q^{29} +(1.80316e6 + 1.89216e7i) q^{30} -3.87488e7i q^{31} +(-2.69569e7 + 1.99806e7i) q^{32} +3.29216e7i q^{33} +(4.42658e6 + 3.45109e7i) q^{34} +(1.43002e6 - 4.39040e7i) q^{35} +(-2.27115e7 + 5.92369e6i) q^{36} -1.29585e7i q^{37} +(8.71384e6 + 6.79357e7i) q^{38} -1.26258e8i q^{39} +(3.51270e7 + 9.61866e7i) q^{40} +4.48926e7 q^{41} +(-8.48031e7 + 1.08774e7i) q^{42} +8.66330e7 q^{43} +(4.47625e7 + 1.71620e8i) q^{44} +(-2.33183e6 + 7.15908e7i) q^{45} +(-2.17538e8 + 2.79027e7i) q^{46} -2.64135e8 q^{47} +(1.73916e8 - 9.73451e7i) q^{48} -8.48835e7 q^{49} +(3.11891e8 - 1.95027e7i) q^{50} -2.06667e8i q^{51} +(-1.71669e8 - 6.58180e8i) q^{52} -2.29181e8i q^{53} +(4.94519e8 - 6.34301e7i) q^{54} +(5.40978e8 + 1.76205e7i) q^{55} +(-4.27289e8 + 1.72008e8i) q^{56} -4.06829e8i q^{57} +(-5.10790e8 + 6.55170e7i) q^{58} +5.54778e8i q^{59} +(-1.34265e8 - 5.93230e8i) q^{60} +8.72720e8 q^{61} +(1.57753e8 + 1.22989e9i) q^{62} -3.22197e8 q^{63} +(7.74268e8 - 7.43929e8i) q^{64} +(-2.07470e9 - 6.75765e7i) q^{65} +(-1.34029e8 - 1.04493e9i) q^{66} +1.53061e8 q^{67} +(-2.80999e8 - 1.07735e9i) q^{68} +1.30271e9 q^{69} +(1.33351e8 + 1.39933e9i) q^{70} +3.28433e9i q^{71} +(6.96746e8 - 2.80480e8i) q^{72} +1.61594e9i q^{73} +(5.27562e7 + 4.11303e8i) q^{74} +(-1.85225e9 - 1.20790e8i) q^{75} +(-5.53154e8 - 2.12080e9i) q^{76} +2.43469e9i q^{77} +(5.14015e8 + 4.00741e9i) q^{78} +3.08746e9i q^{79} +(-1.50652e9 - 2.90995e9i) q^{80} -1.60793e9 q^{81} +(-1.42489e9 + 1.82765e8i) q^{82} +1.89093e9 q^{83} +(2.64736e9 - 6.90494e8i) q^{84} +(-3.39602e9 - 1.10614e8i) q^{85} +(-2.74973e9 + 3.52697e8i) q^{86} +3.05884e9 q^{87} +(-2.11946e9 - 5.26498e9i) q^{88} +8.69033e9 q^{89} +(-2.17446e8 - 2.28178e9i) q^{90} -9.33729e9i q^{91} +(6.79104e9 - 1.77126e9i) q^{92} -7.36511e9i q^{93} +(8.38362e9 - 1.07533e9i) q^{94} +(-6.68515e9 - 2.17746e8i) q^{95} +(-5.12379e9 + 3.79777e9i) q^{96} -5.78965e9i q^{97} +(2.69420e9 - 3.45574e8i) q^{98} -3.97006e9i 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 $

$2$	−31.7400	+	4.07116i	−0.991874	+	0.127224i
$2$	−31.7400	+	4.07116i	−0.991874	+	0.127224i
$3$	190.073			0.782194			0.391097	−	0.920349i	$-0.372096\pi$
$3$	190.073			0.782194			0.391097	+	0.920349i	$0.372096\pi$
$4$	990.851	−	258.437i	0.967628	−	0.252380i
$5$	101.732	−	3123.34i	0.0325543	−	0.999470i
$5$	101.732	−	3123.34i	0.0325543	−	0.999470i
$6$	−6032.92	+	773.819i	−0.775838	+	0.0995137i
$7$	14056.7			0.836362			0.418181	−	0.908364i	$-0.362668\pi$
$7$	14056.7			0.836362			0.418181	+	0.908364i	$0.362668\pi$
$8$	−30397.4	+	12236.7i	−0.927657	+	0.373434i
$9$	−22921.2			−0.388173
$10$	9486.66	+	99549.0i	0.0948666	+	0.995490i
$11$			173205.i			1.07547i	0.843115	+	0.537733i	$0.180719\pi$
$11$			173205.i			1.07547i	−0.843115	+	0.537733i	$0.819281\pi$
$12$	188334.	−	49122.0i	0.756873	−	0.197410i
$13$		−	664258.i		−	1.78904i	−0.447029	−	0.894519i	$-0.647518\pi$
$13$		−	664258.i		−	1.78904i	0.447029	−	0.894519i	$-0.352482\pi$
$14$	−446160.	+	57227.2i	−0.829566	+	0.106405i
$15$	19336.6	−	593664.i	0.0254638	−	0.781779i
$16$	914997.	−	512145.i	0.872609	−	0.488420i
$17$		−	1.08730e6i		−	0.765782i	−0.923793	−	0.382891i	$-0.874928\pi$
$17$		−	1.08730e6i		−	0.765782i	0.923793	−	0.382891i	$-0.125072\pi$
$18$	727518.	−	93315.9i	0.385018	−	0.0493848i
$19$		−	2.14038e6i		−	0.864417i	−0.901774	−	0.432209i	$-0.857734\pi$
$19$		−	2.14038e6i		−	0.864417i	0.901774	−	0.432209i	$-0.142266\pi$
$20$	−706386.	−	3.12106e6i	−0.220746	−	0.975331i
$21$	2.67181e6			0.654197
$22$	−705145.	−	5.49751e6i	−0.136825	−	1.06673i
$23$	6.85374e6			1.06485			0.532425	−	0.846477i	$-0.321281\pi$
$23$	6.85374e6			1.06485			0.532425	+	0.846477i	$0.321281\pi$
$24$	−5.77774e6	+	2.32587e6i	−0.725607	+	0.292098i
$25$	−9.74493e6	−	635490.i	−0.997880	−	0.0650742i
$26$	2.70430e6	+	2.10835e7i	0.227608	+	1.77450i
$27$	−1.55803e7			−1.08582
$28$	1.39281e7	−	3.63278e6i	0.809287	−	0.211081i
$29$	1.60930e7			0.784595			0.392298	−	0.919838i	$-0.371680\pi$
$29$	1.60930e7			0.784595			0.392298	+	0.919838i	$0.371680\pi$
$30$	1.80316e6	+	1.89216e7i	0.0742041	+	0.778666i
$31$		−	3.87488e7i		−	1.35347i	−0.736225	−	0.676737i	$-0.763393\pi$
$31$		−	3.87488e7i		−	1.35347i	0.736225	−	0.676737i	$-0.236607\pi$
$32$	−2.69569e7	+	1.99806e7i	−0.803379	+	0.595468i
$33$			3.29216e7i			0.841223i
$34$	4.42658e6	+	3.45109e7i	0.0974258	+	0.759560i
$35$	1.43002e6	−	4.39040e7i	0.0272272	−	0.835919i
$36$	−2.27115e7	+	5.92369e6i	−0.375607	+	0.0979670i
$37$		−	1.29585e7i		−	0.186873i	−0.995625	−	0.0934365i	$-0.970215\pi$
$37$		−	1.29585e7i		−	0.186873i	0.995625	−	0.0934365i	$-0.0297852\pi$
$38$	8.71384e6	+	6.79357e7i	0.109974	+	0.857393i
$39$		−	1.26258e8i		−	1.39938i
$40$	3.51270e7	+	9.61866e7i	0.343037	+	0.939322i
$41$	4.48926e7			0.387485			0.193743	−	0.981052i	$-0.437937\pi$
$41$	4.48926e7			0.387485			0.193743	+	0.981052i	$0.437937\pi$
$42$	−8.48031e7	+	1.08774e7i	−0.648881	+	0.0832295i
$43$	8.66330e7			0.589307			0.294653	−	0.955604i	$-0.404796\pi$
$43$	8.66330e7			0.589307			0.294653	+	0.955604i	$0.404796\pi$
$44$	4.47625e7	+	1.71620e8i	0.271426	+	1.04065i
$45$	−2.33183e6	+	7.15908e7i	−0.0126367	+	0.387967i
$46$	−2.17538e8	+	2.79027e7i	−1.05620	+	0.135474i
$47$	−2.64135e8			−1.15169			−0.575845	−	0.817559i	$-0.695327\pi$
$47$	−2.64135e8			−1.15169			−0.575845	+	0.817559i	$0.695327\pi$
$48$	1.73916e8	−	9.73451e7i	0.682549	−	0.382039i
$49$	−8.48835e7			−0.300499
$50$	3.11891e8	−	1.95027e7i	0.998051	−	0.0624088i
$51$		−	2.06667e8i		−	0.598990i
$52$	−1.71669e8	−	6.58180e8i	−0.451518	−	1.73112i
$53$		−	2.29181e8i		−	0.548025i	−0.961726	−	0.274012i	$-0.911649\pi$
$53$		−	2.29181e8i		−	0.548025i	0.961726	−	0.274012i	$-0.0883509\pi$
$54$	4.94519e8	−	6.34301e7i	1.07700	−	0.138142i
$55$	5.40978e8	+	1.76205e7i	1.07490	+	0.0350111i
$56$	−4.27289e8	+	1.72008e8i	−0.775857	+	0.312326i
$57$		−	4.06829e8i		−	0.676142i
$58$	−5.10790e8	+	6.55170e7i	−0.778220	+	0.0998192i
$59$			5.54778e8i			0.775996i	0.921660	+	0.387998i	$0.126833\pi$
$59$			5.54778e8i			0.775996i	−0.921660	+	0.387998i	$0.873167\pi$
$60$	−1.34265e8	−	5.93230e8i	−0.172666	−	0.762898i
$61$	8.72720e8			1.03330			0.516649	−	0.856197i	$-0.327179\pi$
$61$	8.72720e8			1.03330			0.516649	+	0.856197i	$0.327179\pi$
$62$	1.57753e8	+	1.22989e9i	0.172194	+	1.34248i
$63$	−3.22197e8			−0.324653
$64$	7.74268e8	−	7.43929e8i	0.721093	−	0.692838i
$65$	−2.07470e9	−	6.75765e7i	−1.78809	−	0.0582410i
$66$	−1.34029e8	−	1.04493e9i	−0.107024	−	0.834387i
$67$	1.53061e8			0.113368			0.0566841	−	0.998392i	$-0.481947\pi$
$67$	1.53061e8			0.113368			0.0566841	+	0.998392i	$0.481947\pi$
$68$	−2.80999e8	−	1.07735e9i	−0.193268	−	0.740993i
$69$	1.30271e9			0.832920
$70$	1.33351e8	+	1.39933e9i	0.0793428	+	0.832590i
$71$			3.28433e9i			1.82035i	0.414221	+	0.910176i	$0.364054\pi$
$71$			3.28433e9i			1.82035i	−0.414221	+	0.910176i	$0.635946\pi$
$72$	6.96746e8	−	2.80480e8i	0.360091	−	0.144957i
$73$			1.61594e9i			0.779493i	0.920922	+	0.389747i	$0.127437\pi$
$73$			1.61594e9i			0.779493i	−0.920922	+	0.389747i	$0.872563\pi$
$74$	5.27562e7	+	4.11303e8i	0.0237747	+	0.185355i
$75$	−1.85225e9	−	1.20790e8i	−0.780536	−	0.0509006i
$76$	−5.53154e8	−	2.12080e9i	−0.218162	−	0.836434i
$77$			2.43469e9i			0.899478i
$78$	5.14015e8	+	4.00741e9i	0.178034	+	1.38800i
$79$			3.08746e9i			1.00338i	0.865047	+	0.501690i	$0.167288\pi$
$79$			3.08746e9i			1.00338i	−0.865047	+	0.501690i	$0.832712\pi$
$80$	−1.50652e9	−	2.90995e9i	−0.459754	−	0.888046i
$81$	−1.60793e9			−0.461150
$82$	−1.42489e9	+	1.82765e8i	−0.384337	+	0.0492974i
$83$	1.89093e9			0.480049			0.240024	−	0.970767i	$-0.422845\pi$
$83$	1.89093e9			0.480049			0.240024	+	0.970767i	$0.422845\pi$
$84$	2.64736e9	−	6.90494e8i	0.633020	−	0.165106i
$85$	−3.39602e9	−	1.10614e8i	−0.765377	−	0.0249295i
$86$	−2.74973e9	+	3.52697e8i	−0.584518	+	0.0749738i
$87$	3.05884e9			0.613706
$88$	−2.11946e9	−	5.26498e9i	−0.401616	−	0.997663i
$89$	8.69033e9			1.55627			0.778137	−	0.628095i	$-0.216165\pi$
$89$	8.69033e9			1.55627			0.778137	+	0.628095i	$0.216165\pi$
$90$	−2.17446e8	−	2.28178e9i	−0.0368246	−	0.386422i
$91$		−	9.33729e9i		−	1.49628i
$92$	6.79104e9	−	1.77126e9i	1.03038	−	0.268747i
$93$		−	7.36511e9i		−	1.05868i
$94$	8.38362e9	−	1.07533e9i	1.14233	−	0.146523i
$95$	−6.68515e9	−	2.17746e8i	−0.863959	−	0.0281405i
$96$	−5.12379e9	+	3.79777e9i	−0.628398	+	0.465771i
$97$		−	5.78965e9i		−	0.674207i	−0.941468	−	0.337104i	$-0.890553\pi$
$97$		−	5.78965e9i		−	0.674207i	0.941468	−	0.337104i	$-0.109447\pi$
$98$	2.69420e9	−	3.45574e8i	0.298057	−	0.0382306i
$99$		−	3.97006e9i		−	0.417466i
$100$	−9.82001e9	+	1.88877e9i	−0.982001	+	0.188877i
$101$	−1.07828e10			−1.02594			−0.512971	−	0.858406i	$-0.671455\pi$
$101$	−1.07828e10			−1.02594			−0.512971	+	0.858406i	$0.671455\pi$
$102$	8.41374e8	+	6.55960e9i	0.0762058	+	0.594123i
$103$	7.05867e9			0.608887			0.304444	−	0.952530i	$-0.401529\pi$
$103$	7.05867e9			0.608887			0.304444	+	0.952530i	$0.401529\pi$
$104$	8.12832e9	+	2.01917e10i	0.668089	+	1.65961i
$105$	2.71809e8	−	8.34497e9i	0.0212970	−	0.653851i
$106$	9.33035e8	+	7.27421e9i	0.0697218	+	0.543571i
$107$	−1.81193e9			−0.129188			−0.0645942	−	0.997912i	$-0.520575\pi$
$107$	−1.81193e9			−0.129188			−0.0645942	+	0.997912i	$0.520575\pi$
$108$	−1.54378e10	+	4.02654e9i	−1.05067	+	0.274039i
$109$	1.33028e10			0.864588			0.432294	−	0.901733i	$-0.357704\pi$
$109$	1.33028e10			0.864588			0.432294	+	0.901733i	$0.357704\pi$
$110$	−1.72424e10	+	1.64313e9i	−1.07062	+	0.102026i
$111$		−	2.46307e9i		−	0.146171i
$112$	1.28619e10	−	7.19909e9i	0.729817	−	0.408496i
$113$			2.35102e10i			1.27604i	0.770019	+	0.638020i	$0.220246\pi$
$113$			2.35102e10i			1.27604i	−0.770019	+	0.638020i	$0.779754\pi$
$114$	1.65627e9	+	1.29127e10i	0.0860214	+	0.670648i
$115$	6.97247e8	−	2.14066e10i	0.0346655	−	1.06429i
$116$	1.59457e10	−	4.15902e9i	0.759197	−	0.198016i
$117$			1.52256e10i			0.694456i
$118$	−2.25859e9	−	1.76086e10i	−0.0987251	−	0.769690i
$119$		−	1.52839e10i		−	0.640471i
$120$	6.67670e9	+	1.82825e10i	0.268322	+	0.734732i
$121$	−4.06247e9			−0.156626
$122$	−2.77001e10	+	3.55298e9i	−1.02490	+	0.131460i
$123$	8.53287e9			0.303089
$124$	−1.00141e10	−	3.83943e10i	−0.341590	−	1.30966i
$125$	−2.97623e9	+	3.03721e10i	−0.0975250	+	0.995233i
$126$	1.02265e10	−	1.31172e9i	0.322015	−	0.0413036i
$127$	−4.14600e10			−1.25490			−0.627452	−	0.778655i	$-0.715902\pi$
$127$	−4.14600e10			−1.25490			−0.627452	+	0.778655i	$0.715902\pi$
$128$	−2.15466e10	+	2.67645e10i	−0.627088	+	0.778948i
$129$	1.64666e10			0.460952
$130$	6.61262e10	−	6.30158e9i	1.78097	−	0.169720i
$131$		−	1.38898e9i		−	0.0360030i	−0.999838	−	0.0180015i	$-0.994270\pi$
$131$		−	1.38898e9i		−	0.0360030i	0.999838	−	0.0180015i	$-0.00573037\pi$
$132$	8.50816e9	+	3.26204e10i	0.212308	+	0.813991i
$133$		−	3.00868e10i		−	0.722966i
$134$	−4.85816e9	+	6.23137e8i	−0.112447	+	0.0144231i
$135$	−1.58502e9	+	4.86627e10i	−0.0353482	+	1.08524i
$136$	1.33050e10	+	3.30512e10i	0.285970	+	0.710383i
$137$		−	4.15616e10i		−	0.861170i	−0.902550	−	0.430585i	$-0.858307\pi$
$137$		−	4.15616e10i		−	0.861170i	0.902550	−	0.430585i	$-0.141693\pi$
$138$	−4.13481e10	+	5.30355e9i	−0.826152	+	0.105967i
$139$			7.90047e10i			1.52258i	0.648414	+	0.761288i	$0.275433\pi$
$139$			7.90047e10i			1.52258i	−0.648414	+	0.761288i	$0.724567\pi$
$140$	−9.92948e9	−	4.38719e10i	−0.184623	−	0.815730i
$141$	−5.02049e10			−0.900846
$142$	−1.33711e10	−	1.04245e11i	−0.231592	−	1.80556i
$143$	1.15053e11			1.92405
$144$	−2.09728e10	+	1.17390e10i	−0.338723	+	0.189591i
$145$	1.63717e9	−	5.02638e10i	0.0255420	−	0.784179i
$146$	−6.57877e9	−	5.12900e10i	−0.0991701	−	0.773159i
$147$	−1.61341e10			−0.235048
$148$	−3.34896e9	−	1.28400e10i	−0.0471630	−	0.180824i
$149$	−3.37967e9			−0.0460197			−0.0230098	−	0.999735i	$-0.507325\pi$
$149$	−3.37967e9			−0.0460197			−0.0230098	+	0.999735i	$0.507325\pi$
$150$	5.92821e10	−	3.70695e9i	0.780669	−	0.0488158i
$151$			6.40458e10i			0.815841i	0.913017	+	0.407921i	$0.133746\pi$
$151$			6.40458e10i			0.815841i	−0.913017	+	0.407921i	$0.866254\pi$
$152$	2.61912e10	+	6.50622e10i	0.322803	+	0.801882i
$153$			2.49223e10i			0.297256i
$154$	−9.91203e9	−	7.72771e10i	−0.114435	−	0.892169i
$155$	−1.21026e11	−	3.94201e9i	−1.35276	−	0.0440614i
$156$	−3.26296e10	−	1.25102e11i	−0.353174	−	1.35408i
$157$		−	1.27096e10i		−	0.133239i	−0.997778	−	0.0666197i	$-0.978779\pi$
$157$		−	1.27096e10i		−	0.133239i	0.997778	−	0.0666197i	$-0.0212214\pi$
$158$	−1.25695e10	−	9.79958e10i	−0.127654	−	0.995227i
$159$		−	4.35612e10i		−	0.428662i
$160$	5.96638e10	+	8.62284e10i	0.568999	+	0.822339i
$161$	9.63413e10			0.890601
$162$	5.10356e10	−	6.54614e9i	0.457402	−	0.0586692i
$163$	1.71627e11			1.49158			0.745790	−	0.666181i	$-0.232072\pi$
$163$	1.71627e11			1.49158			0.745790	+	0.666181i	$0.232072\pi$
$164$	4.44819e10	−	1.16019e10i	0.374942	−	0.0977935i
$165$	1.02825e11	+	3.34919e9i	0.840777	+	0.0273855i
$166$	−6.00181e10	+	7.69829e9i	−0.476148	+	0.0610737i
$167$	−1.27551e11			−0.981976			−0.490988	−	0.871166i	$-0.663364\pi$
$167$	−1.27551e11			−0.981976			−0.490988	+	0.871166i	$0.663364\pi$
$168$	−8.12161e10	+	3.26941e10i	−0.606870	+	0.244300i
$169$	−3.03380e11			−2.20066
$170$	1.08240e11	−	1.03149e10i	0.762329	−	0.0726471i
$171$			4.90601e10i			0.335543i
$172$	8.58405e10	−	2.23892e10i	0.570230	−	0.148729i
$173$			1.87423e11i			1.20946i	0.796429	+	0.604732i	$0.206720\pi$
$173$			1.87423e11i			1.20946i	−0.796429	+	0.604732i	$0.793280\pi$
$174$	−9.70874e10	+	1.24530e10i	−0.608719	+	0.0780780i
$175$	−1.36982e11	−	8.93291e9i	−0.834589	−	0.0544256i
$176$	8.87060e10	+	1.58482e11i	0.525279	+	0.938461i
$177$			1.05448e11i			0.606979i
$178$	−2.75831e11	+	3.53797e10i	−1.54363	+	0.197995i
$179$		−	1.33805e11i		−	0.728126i	−0.931374	−	0.364063i	$-0.881389\pi$
$179$		−	1.33805e11i		−	0.728126i	0.931374	−	0.364063i	$-0.118611\pi$
$180$	1.61912e10	+	7.15384e10i	0.0856874	+	0.378597i
$181$	3.51003e11			1.80683			0.903417	−	0.428764i	$-0.141051\pi$
$181$	3.51003e11			1.80683			0.903417	+	0.428764i	$0.141051\pi$
$182$	3.80136e10	+	2.96365e11i	0.190363	+	1.48413i
$183$	1.65881e11			0.808239
$184$	−2.08336e11	+	8.38672e10i	−0.987816	+	0.397652i
$185$	−4.04739e10	−	1.31830e9i	−0.186774	−	0.00608353i
$186$	2.99845e10	+	2.33768e11i	0.134689	+	1.05008i
$187$	1.88326e11			0.823573
$188$	−2.61718e11	+	6.82622e10i	−1.11441	+	0.290664i
$189$	−2.19009e11			−0.908139
$190$	2.13073e11	−	2.03051e10i	0.860519	−	0.0820043i
$191$		−	3.35424e11i		−	1.31956i	−0.751460	−	0.659778i	$-0.770650\pi$
$191$		−	3.35424e11i		−	1.31956i	0.751460	−	0.659778i	$-0.229350\pi$
$192$	1.47168e11	−	1.41401e11i	0.564035	−	0.541934i
$193$		−	4.42274e11i		−	1.65160i	−0.563964	−	0.825800i	$-0.690724\pi$
$193$		−	4.42274e11i		−	1.65160i	0.563964	−	0.825800i	$-0.309276\pi$
$194$	2.35706e10	+	1.83763e11i	0.0857752	+	0.668729i
$195$	−3.94346e11	−	1.28445e10i	−1.39863	−	0.0455557i
$196$	−8.41069e10	+	2.19370e10i	−0.290771	+	0.0758399i
$197$			6.39016e10i			0.215368i	0.994185	+	0.107684i	$0.0343434\pi$
$197$			6.39016e10i			0.215368i	−0.994185	+	0.107684i	$0.965657\pi$
$198$	1.61628e10	+	1.26010e11i	0.0531116	+	0.414074i
$199$		−	2.95320e11i		−	0.946298i	−0.880982	−	0.473149i	$-0.843117\pi$
$199$		−	2.95320e11i		−	0.946298i	0.880982	−	0.473149i	$-0.156883\pi$
$200$	3.03997e11	−	9.99285e10i	0.949991	−	0.312276i
$201$	2.90928e10			0.0886759
$202$	3.42244e11	−	4.38983e10i	1.01761	−	0.130524i
$203$	2.26214e11			0.656206
$204$	−5.34104e10	−	2.04776e11i	−0.151173	−	0.579600i
$205$	4.56703e9	−	1.40215e11i	0.0126143	−	0.387280i
$206$	−2.24042e11	+	2.87370e10i	−0.603939	+	0.0774649i
$207$	−1.57096e11			−0.413346
$208$	−3.40196e11	−	6.07793e11i	−0.873802	−	1.56113i
$209$	3.70725e11			0.929651
$210$	2.53465e10	+	2.65976e11i	0.0620614	+	0.651247i
$211$			1.50649e11i			0.360208i	0.983648	+	0.180104i	$0.0576435\pi$
$211$			1.50649e11i			0.360208i	−0.983648	+	0.180104i	$0.942356\pi$
$212$	−5.92290e10	−	2.27085e11i	−0.138310	−	0.530284i
$213$			6.24264e11i			1.42387i
$214$	5.75107e10	−	7.37668e9i	0.128139	−	0.0164358i
$215$	8.81338e9	−	2.70585e11i	0.0191845	−	0.588994i
$216$	4.73602e11	−	1.90652e11i	1.00727	−	0.405483i
$217$		−	5.44682e11i		−	1.13199i
$218$	−4.22229e11	+	5.41577e10i	−0.857563	+	0.109996i
$219$			3.07148e11i			0.609715i
$220$	5.40583e11	−	1.22349e11i	1.04894	−	0.237404i
$221$	−7.22248e11			−1.37001
$222$	1.00275e10	+	7.81776e10i	0.0185964	+	0.144983i
$223$	8.28926e11			1.50311			0.751556	−	0.659669i	$-0.229304\pi$
$223$	8.28926e11			1.50311			0.751556	+	0.659669i	$0.229304\pi$
$224$	−3.78926e11	+	2.80862e11i	−0.671916	+	0.498027i
$225$	2.23365e11	+	1.45662e10i	0.387350	+	0.0252600i
$226$	−9.57139e10	−	7.46214e11i	−0.162343	−	1.26567i
$227$	−5.67893e11			−0.942187			−0.471093	−	0.882083i	$-0.656140\pi$
$227$	−5.67893e11			−0.942187			−0.471093	+	0.882083i	$0.656140\pi$
$228$	−1.05140e11	−	4.03107e11i	−0.170645	−	0.654254i
$229$	6.29580e10			0.0999708			0.0499854	−	0.998750i	$-0.484083\pi$
$229$	6.29580e10			0.0999708			0.0499854	+	0.998750i	$0.484083\pi$
$230$	6.50191e10	+	6.82283e11i	0.101019	+	1.06005i
$231$			4.62770e11i			0.703567i
$232$	−4.89185e11	+	1.96925e11i	−0.727835	+	0.292995i
$233$		−	3.90579e11i		−	0.568760i	−0.958712	−	0.284380i	$-0.908212\pi$
$233$		−	3.90579e11i		−	0.568760i	0.958712	−	0.284380i	$-0.0917877\pi$
$234$	−6.19858e10	−	4.83259e11i	−0.0883513	−	0.688813i
$235$	−2.68710e10	+	8.24983e11i	−0.0374925	+	1.15108i
$236$	1.43375e11	+	5.49703e11i	0.195846	+	0.750875i
$237$			5.86843e11i			0.784838i
$238$	6.22233e10	+	4.85111e11i	0.0814832	+	0.635267i
$239$			8.56345e11i			1.09814i	0.835775	+	0.549072i	$0.185019\pi$
$239$			8.56345e11i			1.09814i	−0.835775	+	0.549072i	$0.814981\pi$
$240$	−2.86349e11	−	5.53103e11i	−0.359617	−	0.694625i
$241$	−2.19603e11			−0.270117			−0.135059	−	0.990838i	$-0.543122\pi$
$241$	−2.19603e11			−0.270117			−0.135059	+	0.990838i	$0.543122\pi$
$242$	1.28943e11	−	1.65390e10i	0.155353	−	0.0199265i
$243$	6.14379e11			0.725112
$244$	8.64735e11	−	2.25543e11i	0.999848	−	0.260784i
$245$	−8.63539e9	+	2.65120e11i	−0.00978254	+	0.300339i
$246$	−2.70833e11	+	3.47387e10i	−0.300626	+	0.0385601i
$247$	−1.42177e12			−1.54648
$248$	4.74158e11	+	1.17786e12i	0.505434	+	1.25556i
$249$	3.59415e11			0.375491
$250$	−2.91844e10	−	9.76126e11i	−0.0298848	−	0.999553i
$251$		−	3.77174e11i		−	0.378593i	−0.981920	−	0.189297i	$-0.939379\pi$
$251$		−	3.77174e11i		−	0.378593i	0.981920	−	0.189297i	$-0.0606208\pi$
$252$	−3.19250e11	+	8.32677e10i	−0.314143	+	0.0819358i
$253$			1.18710e12i			1.14521i
$254$	1.31594e12	−	1.68790e11i	1.24471	−	0.159654i
$255$	−6.45492e11	−	2.10247e10i	−0.598673	−	0.0194997i
$256$	5.74926e11	−	9.37223e11i	0.522892	−	0.852399i
$257$		−	8.23925e11i		−	0.734889i	−0.930045	−	0.367445i	$-0.880233\pi$
$257$		−	8.23925e11i		−	0.734889i	0.930045	−	0.367445i	$-0.119767\pi$
$258$	−5.22650e11	+	6.70383e10i	−0.457206	+	0.0586441i
$259$		−	1.82154e11i		−	0.156293i
$260$	−2.07319e12	+	4.69222e11i	−1.74491	+	0.394923i
$261$	−3.68870e11			−0.304558
$262$	5.65476e9	+	4.40861e10i	0.00458044	+	0.0357105i
$263$	1.08787e12			0.864568			0.432284	−	0.901737i	$-0.357708\pi$
$263$	1.08787e12			0.864568			0.432284	+	0.901737i	$0.357708\pi$
$264$	−4.02852e11	−	1.00073e12i	−0.314142	−	0.780366i
$265$	−7.15812e11	−	2.33152e10i	−0.547734	−	0.0178406i
$266$	1.22488e11	+	9.54954e11i	0.0919784	+	0.717091i
$267$	1.65180e12			1.21731
$268$	1.51661e11	−	3.95567e10i	0.109698	−	0.0286119i
$269$	1.57558e12			1.11861			0.559305	−	0.828962i	$-0.311068\pi$
$269$	1.57558e12			1.11861			0.559305	+	0.828962i	$0.311068\pi$
$270$	−1.47805e11	−	1.55101e12i	−0.103008	−	1.08092i
$271$			7.48035e11i			0.511771i	0.966707	+	0.255885i	$0.0823670\pi$
$271$			7.48035e11i			0.511771i	−0.966707	+	0.255885i	$0.917633\pi$
$272$	−5.56857e11	−	9.94877e11i	−0.374023	−	0.668228i
$273$		−	1.77477e12i		−	1.17038i
$274$	1.69204e11	+	1.31916e12i	0.109561	+	0.854172i
$275$	1.10070e11	−	1.68787e12i	0.0699850	−	1.07319i
$276$	1.29079e12	−	3.36669e11i	0.805957	−	0.210212i
$277$			1.35578e12i			0.831360i	0.909511	+	0.415680i	$0.136456\pi$
$277$			1.35578e12i			0.831360i	−0.909511	+	0.415680i	$0.863544\pi$
$278$	−3.21641e11	−	2.50761e12i	−0.193708	−	1.51020i
$279$			8.88169e11i			0.525381i
$280$	4.93771e11	+	1.35207e12i	0.286903	+	0.785613i
$281$	−6.65579e11			−0.379899			−0.189949	−	0.981794i	$-0.560832\pi$
$281$	−6.65579e11			−0.379899			−0.189949	+	0.981794i	$0.560832\pi$
$282$	1.59350e12	−	2.04392e11i	0.893526	−	0.114609i
$283$	−3.17294e12			−1.74795			−0.873977	−	0.485968i	$-0.838467\pi$
$283$	−3.17294e12			−1.74795			−0.873977	+	0.485968i	$0.838467\pi$
$284$	8.48794e11	+	3.25429e12i	0.459421	+	1.76142i
$285$	−1.27067e12	−	4.13877e10i	−0.675784	−	0.0220114i
$286$	−3.65177e12	+	4.68398e11i	−1.90841	+	0.244785i
$287$	6.31043e11			0.324078
$288$	6.17885e11	−	4.57979e11i	0.311850	−	0.231144i
$289$	8.33769e11			0.413577
$290$	1.52668e11	+	1.60204e12i	0.0744319	+	0.781057i
$291$		−	1.10046e12i		−	0.527361i
$292$	4.17620e11	+	1.60116e12i	0.196728	+	0.754259i
$293$			3.22248e11i			0.149229i	0.997212	+	0.0746144i	$0.0237726\pi$
$293$			3.22248e11i			0.149229i	−0.997212	+	0.0746144i	$0.976227\pi$
$294$	5.12095e11	−	6.56844e10i	0.233138	−	0.0299037i
$295$	1.73276e12	+	5.64389e10i	0.775584	+	0.0252620i
$296$	1.58569e11	+	3.93906e11i	0.0697848	+	0.173354i
$297$		−	2.69859e12i		−	1.16776i
$298$	1.07271e11	−	1.37592e10i	0.0456457	−	0.00585480i
$299$		−	4.55265e12i		−	1.90506i
$300$	−1.86652e12	+	3.59005e11i	−0.768115	+	0.147739i
$301$	1.21778e12			0.492874
$302$	−2.60741e11	−	2.03281e12i	−0.103794	−	0.809212i
$303$	−2.04951e12			−0.802486
$304$	−1.09619e12	−	1.95844e12i	−0.422199	−	0.754298i
$305$	8.87838e10	−	2.72580e12i	0.0336383	−	1.03275i
$306$	−1.01463e11	−	7.91032e11i	−0.0378180	−	0.294840i
$307$	1.97279e12			0.723418			0.361709	−	0.932291i	$-0.382193\pi$
$307$	1.97279e12			0.723418			0.361709	+	0.932291i	$0.382193\pi$
$308$	6.29215e11	+	2.41242e12i	0.227010	+	0.870361i
$309$	1.34166e12			0.476268
$310$	3.85740e12	−	3.67597e11i	1.34737	−	0.128399i
$311$		−	5.13332e12i		−	1.76440i	−0.470879	−	0.882198i	$-0.656063\pi$
$311$		−	5.13332e12i		−	1.76440i	0.470879	−	0.882198i	$-0.343937\pi$
$312$	1.54498e12	+	3.83791e12i	0.522575	+	1.29814i
$313$			2.38086e10i			0.00792523i	0.999992	+	0.00396261i	$0.00126134\pi$
$313$			2.38086e10i			0.00792523i	−0.999992	+	0.00396261i	$0.998739\pi$
$314$	5.17427e10	+	4.03401e11i	0.0169512	+	0.132157i
$315$	−3.27779e10	+	1.00633e12i	−0.0105689	+	0.324481i
$316$	7.97913e11	+	3.05921e12i	0.253233	+	0.970899i
$317$			5.06007e12i			1.58074i	0.612630	+	0.790370i	$0.290111\pi$
$317$			5.06007e12i			1.58074i	−0.612630	+	0.790370i	$0.709889\pi$
$318$	1.77345e11	+	1.38263e12i	0.0545360	+	0.425178i
$319$			2.78738e12i			0.843805i
$320$	−2.24478e12	−	2.49399e12i	−0.668996	−	0.743266i
$321$	−3.44400e11			−0.101050
$322$	−3.05787e12	+	3.92221e11i	−0.883364	+	0.113306i
$323$	−2.32724e12			−0.661956
$324$	−1.59322e12	+	4.15549e11i	−0.446221	+	0.116385i
$325$	−4.22129e11	+	6.47314e12i	−0.116420	+	1.78525i
$326$	−5.44742e12	+	6.98720e11i	−1.47946	+	0.189764i
$327$	2.52850e12			0.676276
$328$	−1.36462e12	+	5.49337e11i	−0.359453	+	0.144700i
$329$	−3.71287e12			−0.963230
$330$	−3.27731e12	+	3.12316e11i	−0.837429	+	0.0798039i
$331$			4.65034e12i			1.17043i	0.810879	+	0.585214i	$0.198990\pi$
$331$			4.65034e12i			1.17043i	−0.810879	+	0.585214i	$0.801010\pi$
$332$	1.87363e12	−	4.88687e11i	0.464509	−	0.121155i
$333$			2.97025e11i			0.0725390i
$334$	4.04846e12	−	5.19280e11i	0.973996	−	0.124931i
$335$	1.55713e10	−	4.78063e11i	0.00369063	−	0.113308i
$336$	2.44469e12	−	1.36835e12i	0.570858	−	0.319523i
$337$		−	2.23573e11i		−	0.0514362i	−0.999669	−	0.0257181i	$-0.991813\pi$
$337$		−	2.23573e11i		−	0.0514362i	0.999669	−	0.0257181i	$-0.00818723\pi$
$338$	9.62926e12	−	1.23511e12i	2.18278	−	0.279976i
$339$			4.46866e12i			0.998111i
$340$	−3.39353e12	+	7.68055e11i	−0.746892	+	0.169043i
$341$	6.71148e12			1.45561
$342$	−1.99732e11	−	1.55717e12i	−0.0426891	−	0.332816i
$343$	−5.16386e12			−1.08769
$344$	−2.63342e12	+	1.06010e12i	−0.546674	+	0.220067i
$345$	1.32528e11	−	4.06882e12i	0.0271152	−	0.832478i
$346$	−7.63031e11	−	5.94881e12i	−0.153873	−	1.19964i
$347$	−3.16769e12			−0.629644			−0.314822	−	0.949151i	$-0.601945\pi$
$347$	−3.16769e12			−0.629644			−0.314822	+	0.949151i	$0.601945\pi$
$348$	3.03085e12	−	7.90517e11i	0.593839	−	0.154887i
$349$	−8.37634e12			−1.61781			−0.808904	−	0.587941i	$-0.799939\pi$
$349$	−8.37634e12			−1.61781			−0.808904	+	0.587941i	$0.799939\pi$
$350$	4.38417e12	−	2.74145e11i	0.834732	−	0.0521963i
$351$			1.03494e13i			1.94257i
$352$	−3.46073e12	−	4.66907e12i	−0.640405	−	0.864007i
$353$		−	2.56251e12i		−	0.467512i	−0.972295	−	0.233756i	$-0.924898\pi$
$353$		−	2.56251e12i		−	0.467512i	0.972295	−	0.233756i	$-0.0751017\pi$
$354$	−4.29298e11	−	3.34693e12i	−0.0772222	−	0.602047i
$355$	1.02581e13	+	3.34123e11i	1.81939	+	0.0592604i
$356$	8.61082e12	−	2.24590e12i	1.50589	−	0.392772i
$357$		−	2.90506e12i		−	0.500973i
$358$	5.44741e11	+	4.24696e12i	0.0926349	+	0.722209i
$359$		−	9.99628e12i		−	1.67636i	−0.545397	−	0.838178i	$-0.683621\pi$
$359$		−	9.99628e12i		−	1.67636i	0.545397	−	0.838178i	$-0.316379\pi$
$360$	−8.05153e11	−	2.20471e12i	−0.133158	−	0.364619i
$361$	1.54983e12			0.252783
$362$	−1.11408e13	+	1.42899e12i	−1.79215	+	0.229872i
$363$	−7.72167e11			−0.122512
$364$	−2.41310e12	−	9.25187e12i	−0.377632	−	1.44785i
$365$	5.04715e12	+	1.64394e11i	0.779080	+	0.0253759i
$366$	−5.26504e12	+	6.75327e11i	−0.801672	+	0.102827i
$367$	2.30492e12			0.346199			0.173099	−	0.984904i	$-0.444622\pi$
$367$	2.30492e12			0.346199			0.173099	+	0.984904i	$0.444622\pi$
$368$	6.27115e12	−	3.51011e12i	0.929198	−	0.520094i
$369$	−1.02899e12			−0.150411
$370$	1.29001e12	−	1.22933e11i	0.186030	−	0.0177280i
$371$		−	3.22154e12i		−	0.458347i
$372$	−1.90342e12	−	7.29773e12i	−0.267189	−	1.02441i
$373$			5.12634e11i			0.0710008i	0.999370	+	0.0355004i	$0.0113025\pi$
$373$			5.12634e11i			0.0710008i	−0.999370	+	0.0355004i	$0.988697\pi$
$374$	−5.97746e12	+	7.66705e11i	−0.816880	+	0.104778i
$375$	−5.65701e11	+	5.77292e12i	−0.0762835	+	0.778465i
$376$	8.02902e12	−	3.23214e12i	1.06837	−	0.430081i
$377$		−	1.06899e13i		−	1.40367i
$378$	6.95133e12	−	8.91620e11i	0.900759	−	0.115537i
$379$			1.30188e13i			1.66485i	0.554141	+	0.832423i	$0.313047\pi$
$379$			1.30188e13i			1.66485i	−0.554141	+	0.832423i	$0.686953\pi$
$380$	−6.68026e12	+	1.51194e12i	−0.843093	+	0.190816i
$381$	−7.88043e12			−0.981578
$382$	1.36557e12	+	1.06464e13i	0.167879	+	1.30883i
$383$	−7.62061e10			−0.00924689			−0.00462345	−	0.999989i	$-0.501472\pi$
$383$	−7.62061e10			−0.00924689			−0.00462345	+	0.999989i	$0.501472\pi$
$384$	−4.09543e12	+	5.08720e12i	−0.490505	+	0.609289i
$385$	7.60439e12	+	2.47687e11i	0.899002	+	0.0292819i
$386$	1.80057e12	+	1.40378e13i	0.210123	+	1.63818i
$387$	−1.98573e12			−0.228753
$388$	−1.49626e12	−	5.73668e12i	−0.170156	−	0.652382i
$389$	−5.68167e12			−0.637863			−0.318932	−	0.947778i	$-0.603324\pi$
$389$	−5.68167e12			−0.637863			−0.318932	+	0.947778i	$0.603324\pi$
$390$	1.25688e13	−	1.19776e12i	1.39306	−	0.132754i
$391$		−	7.45209e12i		−	0.815444i
$392$	2.58024e12	−	1.03869e12i	0.278760	−	0.112217i
$393$		−	2.64008e11i		−	0.0281614i
$394$	−2.60154e11	−	2.02823e12i	−0.0273999	−	0.213618i
$395$	9.64319e12	+	3.14094e11i	1.00285	+	0.0326644i
$396$	−1.02601e12	−	3.93374e12i	−0.105360	−	0.403952i
$397$			1.23091e13i			1.24818i	0.781354	+	0.624088i	$0.214529\pi$
$397$			1.23091e13i			1.24818i	−0.781354	+	0.624088i	$0.785471\pi$
$398$	1.20230e12	+	9.37346e12i	0.120392	+	0.938609i
$399$		−	5.71869e12i		−	0.565499i
$400$	−9.24204e12	+	4.40935e12i	−0.902543	+	0.430600i
$401$	3.21421e11			0.0309993			0.0154997	−	0.999880i	$-0.495066\pi$
$401$	3.21421e11			0.0309993			0.0154997	+	0.999880i	$0.495066\pi$
$402$	−9.23405e11	+	1.18442e11i	−0.0879553	+	0.0112817i
$403$	−2.57392e13			−2.42142
$404$	−1.06841e13	+	2.78666e12i	−0.992731	+	0.258927i
$405$	−1.63578e11	+	5.02212e12i	−0.0150124	+	0.460905i
$406$	−7.18004e12	+	9.20955e11i	−0.650873	+	0.0834850i
$407$	2.24448e12			0.200976
$408$	2.52892e12	+	6.28214e12i	0.223684	+	0.555657i
$409$	1.03801e13			0.906952			0.453476	−	0.891268i	$-0.350184\pi$
$409$	1.03801e13			0.906952			0.453476	+	0.891268i	$0.350184\pi$
$410$	4.25880e11	+	4.46901e12i	0.0367594	+	0.385738i
$411$		−	7.89974e12i		−	0.673602i
$412$	6.99409e12	−	1.82422e12i	0.589176	−	0.153671i
$413$			7.79837e12i			0.649013i
$414$	4.98622e12	−	6.39563e11i	0.409987	−	0.0525874i
$415$	1.92369e11	−	5.90603e12i	0.0156277	−	0.479795i
$416$	1.32723e13	+	1.79063e13i	1.06531	+	1.43728i
$417$			1.50167e13i			1.19095i
$418$	−1.17668e13	+	1.50928e12i	−0.922097	+	0.118274i
$419$		−	1.57632e13i		−	1.22061i	−0.792168	−	0.610303i	$-0.791048\pi$
$419$		−	1.57632e13i		−	1.22061i	0.792168	−	0.610303i	$-0.208952\pi$
$420$	−1.88733e12	−	8.33887e12i	−0.144411	−	0.638059i
$421$	−1.50088e13			−1.13484			−0.567421	−	0.823428i	$-0.692059\pi$
$421$	−1.50088e13			−1.13484			−0.567421	+	0.823428i	$0.692059\pi$
$422$	−6.13316e11	−	4.78159e12i	−0.0458271	−	0.357281i
$423$	6.05428e12			0.447055
$424$	2.80443e12	+	6.96653e12i	0.204651	+	0.508379i
$425$	−6.90969e11	+	1.05957e13i	−0.0498327	+	0.764159i
$426$	−2.54148e12	−	1.98141e13i	−0.181150	−	1.41230i
$427$	1.22676e13			0.864211
$428$	−1.79536e12	+	4.68271e11i	−0.125006	+	0.0326046i
$429$	2.18684e13			1.50498
$430$	8.21858e11	+	8.62423e12i	0.0559055	+	0.586649i
$431$		−	5.91866e11i		−	0.0397958i	−0.999802	−	0.0198979i	$-0.993666\pi$
$431$		−	5.91866e11i		−	0.0397958i	0.999802	−	0.0198979i	$-0.00633411\pi$
$432$	−1.42560e13	+	7.97940e12i	−0.947496	+	0.530336i
$433$		−	2.30044e13i		−	1.51137i	−0.654933	−	0.755687i	$-0.727303\pi$
$433$		−	2.30044e13i		−	1.51137i	0.654933	−	0.755687i	$-0.272697\pi$
$434$	2.21749e12	+	1.72882e13i	0.144017	+	1.12280i
$435$	3.11183e11	−	9.55380e12i	0.0199788	−	0.613380i
$436$	1.31811e13	−	3.43793e12i	0.836600	−	0.218205i
$437$		−	1.46696e13i		−	0.920475i
$438$	−1.25045e12	−	9.74886e12i	−0.0775702	−	0.604760i
$439$		−	4.54425e12i		−	0.278701i	−0.990243	−	0.139351i	$-0.955498\pi$
$439$		−	4.54425e12i		−	0.278701i	0.990243	−	0.139351i	$-0.0445015\pi$
$440$	−1.66600e13	+	6.08417e12i	−1.01021	+	0.368925i
$441$	1.94563e12			0.116645
$442$	2.29241e13	−	2.94039e12i	1.35888	−	0.174298i
$443$	2.40350e12			0.140872			0.0704362	−	0.997516i	$-0.477561\pi$
$443$	2.40350e12			0.140872			0.0704362	+	0.997516i	$0.477561\pi$
$444$	−6.36548e11	−	2.44053e12i	−0.0368906	−	0.141439i
$445$	8.84087e11	−	2.71429e13i	0.0506635	−	1.55545i
$446$	−2.63101e13	+	3.37469e12i	−1.49090	+	0.191232i
$447$	−6.42385e11			−0.0359963
$448$	1.08837e13	−	1.04572e13i	0.603095	−	0.579463i
$449$	−2.55386e13			−1.39947			−0.699737	−	0.714401i	$-0.746699\pi$
$449$	−2.55386e13			−1.39947			−0.699737	+	0.714401i	$0.746699\pi$
$450$	−7.14891e12	+	4.47026e11i	−0.387416	+	0.0242254i
$451$			7.77561e12i			0.416727i
$452$	6.07591e12	+	2.32951e13i	0.322047	+	1.23473i
$453$			1.21734e13i			0.638146i
$454$	1.80249e13	−	2.31198e12i	0.934530	−	0.119869i
$455$	−2.91636e13	−	9.49904e11i	−1.49549	−	0.0487105i
$456$	4.97825e12	+	1.23666e13i	0.252495	+	0.627228i
$457$		−	1.43833e13i		−	0.721569i	−0.932649	−	0.360785i	$-0.882509\pi$
$457$		−	1.43833e13i		−	0.721569i	0.932649	−	0.360785i	$-0.117491\pi$
$458$	−1.99828e12	+	2.56312e11i	−0.0991585	+	0.0127187i
$459$			1.69405e13i			0.831502i
$460$	−4.84139e12	−	2.13910e13i	−0.235061	−	1.03858i
$461$	3.07398e13			1.47638			0.738188	−	0.674595i	$-0.235682\pi$
$461$	3.07398e13			1.47638			0.738188	+	0.674595i	$0.235682\pi$
$462$	−1.88401e12	−	1.46883e13i	−0.0895104	−	0.697849i
$463$	1.66750e13			0.783718			0.391859	−	0.920025i	$-0.371832\pi$
$463$	1.66750e13			0.783718			0.391859	+	0.920025i	$0.371832\pi$
$464$	1.47250e13	−	8.24193e12i	0.684645	−	0.383212i
$465$	−2.30038e13	−	7.49269e11i	−1.05812	−	0.0344646i
$466$	1.59011e12	+	1.23970e13i	0.0723598	+	0.564138i
$467$	6.59007e12			0.296692			0.148346	−	0.988936i	$-0.452605\pi$
$467$	6.59007e12			0.296692			0.148346	+	0.988936i	$0.452605\pi$
$468$	3.93485e12	+	1.50863e13i	0.175267	+	0.671975i
$469$	2.15154e12			0.0948168
$470$	−2.50575e12	−	2.62943e13i	−0.109257	−	1.14650i
$471$		−	2.41575e12i		−	0.104219i
$472$	−6.78865e12	−	1.68638e13i	−0.289784	−	0.719857i
$473$			1.50053e13i			0.633779i
$474$	−2.38913e12	−	1.86264e13i	−0.0998500	−	0.778460i
$475$	−1.36019e12	+	2.08579e13i	−0.0562512	+	0.862585i
$476$	−3.94993e12	−	1.51441e13i	−0.161642	−	0.619738i
$477$			5.25311e12i			0.212728i
$478$	−3.48632e12	−	2.71804e13i	−0.139710	−	1.08922i
$479$			3.32507e13i			1.31863i	0.751867	+	0.659315i	$0.229154\pi$
$479$			3.32507e13i			1.31863i	−0.751867	+	0.659315i	$0.770846\pi$
$480$	1.13405e13	+	1.63897e13i	0.445067	+	0.643228i
$481$	−8.60779e12			−0.334323
$482$	6.97018e12	−	8.94037e11i	0.267922	−	0.0343653i
$483$	1.83119e13			0.696622
$484$	−4.02531e12	+	1.04989e12i	−0.151556	+	0.0395293i
$485$	−1.80831e13	−	5.88994e11i	−0.673850	−	0.0219484i
$486$	−1.95004e13	+	2.50124e12i	−0.719220	+	0.0922515i
$487$	−3.49858e12			−0.127717			−0.0638583	−	0.997959i	$-0.520341\pi$
$487$	−3.49858e12			−0.127717			−0.0638583	+	0.997959i	$0.520341\pi$
$488$	−2.65285e13	+	1.06792e13i	−0.958546	+	0.385869i
$489$	3.26216e13			1.16670
$490$	−8.05260e11	−	8.45006e12i	−0.0285073	−	0.299143i
$491$			1.49892e13i			0.525254i	0.964897	+	0.262627i	$0.0845889\pi$
$491$			1.49892e13i			0.525254i	−0.964897	+	0.262627i	$0.915411\pi$
$492$	8.45481e12	−	2.20521e12i	0.293277	−	0.0764935i
$493$		−	1.74979e13i		−	0.600829i
$494$	4.51268e13	−	5.78824e12i	1.53391	−	0.196749i
$495$	−1.23999e13	−	4.03884e11i	−0.417245	−	0.0135903i
$496$	−1.98450e13	−	3.54550e13i	−0.661064	−	1.18105i
$497$			4.61670e13i			1.52247i
$498$	−1.14078e13	+	1.46324e12i	−0.372440	+	0.0477714i
$499$		−	2.01950e13i		−	0.652741i	−0.945242	−	0.326370i	$-0.894174\pi$
$499$		−	2.01950e13i		−	0.652741i	0.945242	−	0.326370i	$-0.105826\pi$
$500$	4.90028e12	+	3.08634e13i	0.156809	+	0.987629i
$501$	−2.42440e13			−0.768096
$502$	1.53553e12	+	1.19715e13i	0.0481661	+	0.375517i
$503$	3.87916e13			1.20475			0.602376	−	0.798213i	$-0.294221\pi$
$503$	3.87916e13			1.20475			0.602376	+	0.798213i	$0.294221\pi$
$504$	9.79397e12	−	3.94263e12i	0.301166	−	0.121237i
$505$	−1.09695e12	+	3.36783e13i	−0.0333989	+	1.02540i
$506$	−4.83288e12	−	3.76786e13i	−0.145698	−	1.13590i
$507$	−5.76643e13			−1.72134
$508$	−4.10807e13	+	1.07148e13i	−1.21428	+	0.316713i
$509$	2.53824e13			0.742923			0.371462	−	0.928448i	$-0.378857\pi$
$509$	2.53824e13			0.742923			0.371462	+	0.928448i	$0.378857\pi$
$510$	2.05735e13	−	1.96058e12i	0.596289	−	0.0568242i
$511$			2.27149e13i			0.651938i
$512$	−1.44325e13	+	3.20880e13i	−0.410197	+	0.911997i
$513$			3.33479e13i			0.938602i
$514$	3.35433e12	+	2.61513e13i	0.0934954	+	0.728917i
$515$	7.18095e11	−	2.20467e13i	0.0198219	−	0.608564i
$516$	1.63160e13	−	4.25558e12i	0.446030	−	0.116335i
$517$		−	4.57494e13i		−	1.23860i
$518$	7.41580e11	+	5.78158e12i	0.0198843	+	0.155023i
$519$			3.56242e13i			0.946036i
$520$	6.38926e13	−	2.33334e13i	1.68048	−	0.613707i
$521$	9.37998e12			0.244351			0.122175	−	0.992509i	$-0.461013\pi$
$521$	9.37998e12			0.244351			0.122175	+	0.992509i	$0.461013\pi$
$522$	1.17079e13	−	1.50173e12i	0.302084	−	0.0387471i
$523$	1.03783e13			0.265227			0.132614	−	0.991168i	$-0.457663\pi$
$523$	1.03783e13			0.265227			0.132614	+	0.991168i	$0.457663\pi$
$524$	−3.58964e11	−	1.37627e12i	−0.00908645	−	0.0348376i
$525$	−2.60366e13	−	1.69791e12i	−0.652811	−	0.0425713i
$526$	−3.45290e13	+	4.42890e12i	−0.857543	+	0.109994i
$527$	−4.21316e13			−1.03647
$528$	1.68606e13	+	3.01231e13i	0.410870	+	0.734058i
$529$	5.54730e12			0.133907
$530$	2.28148e13	−	2.17417e12i	0.545553	−	0.0519892i
$531$		−	1.27162e13i		−	0.301220i
$532$	−7.77554e12	−	2.98115e13i	−0.182462	−	0.699562i
$533$		−	2.98202e13i		−	0.693226i
$534$	−5.24280e13	+	6.72473e12i	−1.20742	+	0.154871i
$535$	−1.84332e11	+	5.65929e12i	−0.00420564	+	0.129120i
$536$	−4.65267e12	+	1.87296e12i	−0.105167	+	0.0423356i
$537$		−	2.54327e13i		−	0.569536i
$538$	−5.00089e13	+	6.41444e12i	−1.10952	+	0.142314i
$539$		−	1.47022e13i		−	0.323176i
$540$	1.10057e13	+	4.86272e13i	0.239690	+	1.05903i
$541$	−1.08616e13			−0.234373			−0.117187	−	0.993110i	$-0.537388\pi$
$541$	−1.08616e13			−0.234373			−0.117187	+	0.993110i	$0.537388\pi$
$542$	−3.04537e12	−	2.37426e13i	−0.0651094	−	0.507612i
$543$	6.67163e13			1.41329
$544$	2.17249e13	+	2.93103e13i	0.455999	+	0.615214i
$545$	1.35332e12	−	4.15491e13i	0.0281461	−	0.864130i
$546$	7.22537e12	+	5.63311e13i	0.148901	+	1.16087i
$547$	3.51242e13			0.717248			0.358624	−	0.933482i	$-0.383246\pi$
$547$	3.51242e13			0.717248			0.358624	+	0.933482i	$0.383246\pi$
$548$	−1.07410e13	−	4.11813e13i	−0.217342	−	0.833293i
$549$	−2.00038e13			−0.401098
$550$	3.37797e12	+	5.40210e13i	0.0671185	+	1.07337i
$551$		−	3.44451e13i		−	0.678218i
$552$	−3.95991e13	+	1.59409e13i	−0.772664	+	0.311041i
$553$			4.33996e13i			0.839189i
$554$	−5.51959e12	−	4.30323e13i	−0.105769	−	0.824605i
$555$	−7.69300e12	−	2.50573e11i	−0.146094	−	0.00475850i
$556$	2.04178e13	+	7.82819e13i	0.384268	+	1.47329i
$557$		−	1.87712e13i		−	0.350120i	−0.984558	−	0.175060i	$-0.943988\pi$
$557$		−	1.87712e13i		−	0.350120i	0.984558	−	0.175060i	$-0.0560119\pi$
$558$	−3.61588e12	−	2.81905e13i	−0.0668410	−	0.521112i
$559$		−	5.75467e13i		−	1.05429i
$560$	−2.11768e13	−	4.09044e13i	−0.384521	−	0.742728i
$561$	3.57957e13			0.644194
$562$	2.11255e13	−	2.70968e12i	0.376812	−	0.0483322i
$563$	−7.50975e12			−0.132765			−0.0663825	−	0.997794i	$-0.521146\pi$
$563$	−7.50975e12			−0.132765			−0.0663825	+	0.997794i	$0.521146\pi$
$564$	−4.97456e13	+	1.29748e13i	−0.871684	+	0.227355i
$565$	7.34305e13	+	2.39175e12i	1.27536	+	0.0415407i
$566$	1.00709e14	−	1.29176e13i	1.73375	−	0.222381i
$567$	−2.26022e13			−0.385688
$568$	−4.01894e13	−	9.98354e13i	−0.679783	−	1.68866i
$569$	−5.40193e13			−0.905707			−0.452853	−	0.891585i	$-0.649594\pi$
$569$	−5.40193e13			−0.905707			−0.452853	+	0.891585i	$0.649594\pi$
$570$	4.04994e13	−	3.85945e12i	0.673093	−	0.0641433i
$571$		−	7.48542e13i		−	1.23321i	−0.787274	−	0.616603i	$-0.788508\pi$
$571$		−	7.48542e13i		−	1.23321i	0.787274	−	0.616603i	$-0.211492\pi$
$572$	1.14000e14	−	2.97339e13i	1.86176	−	0.485592i
$573$		−	6.37552e13i		−	1.03215i
$574$	−2.00293e13	+	2.56908e12i	−0.321445	+	0.0412304i
$575$	−6.67892e13	−	4.35549e12i	−1.06259	−	0.0692943i
$576$	−1.77472e13	+	1.70517e13i	−0.279909	+	0.268941i
$577$			7.48813e13i			1.17083i	0.810733	+	0.585416i	$0.199069\pi$
$577$			7.48813e13i			1.17083i	−0.810733	+	0.585416i	$0.800931\pi$
$578$	−2.64638e13	+	3.39441e12i	−0.410217	+	0.0526169i
$579$		−	8.40644e13i		−	1.29187i
$580$	−1.13678e13	−	5.02271e13i	−0.173196	−	0.765240i
$581$	2.65803e13			0.401495
$582$	4.48014e12	+	3.49285e13i	0.0670929	+	0.523076i
$583$	3.96953e13			0.589382
$584$	−1.97738e13	−	4.91206e13i	−0.291090	−	0.723102i
$585$	4.75547e13	+	1.54893e12i	0.694088	+	0.0226075i
$586$	−1.31193e12	−	1.02282e13i	−0.0189855	−	0.148016i
$587$	4.76751e13			0.684071			0.342035	−	0.939687i	$-0.388884\pi$
$587$	4.76751e13			0.684071			0.342035	+	0.939687i	$0.388884\pi$
$588$	−1.59865e13	+	4.16964e12i	−0.227439	+	0.0593215i
$589$	−8.29373e13			−1.16997
$590$	−5.52276e13	+	5.26299e12i	−0.772496	+	0.0736160i
$591$			1.21460e13i			0.168459i
$592$	−6.63665e12	−	1.18570e13i	−0.0912725	−	0.163067i
$593$			8.03970e13i			1.09639i	0.836349	+	0.548197i	$0.184686\pi$
$593$			8.03970e13i			1.09639i	−0.836349	+	0.548197i	$0.815314\pi$
$594$	1.09864e13	+	8.56531e13i	0.148567	+	1.15827i
$595$	−4.77369e13	−	1.55487e12i	−0.640132	−	0.0208501i
$596$	−3.34875e12	+	8.73433e11i	−0.0445299	+	0.0116144i
$597$		−	5.61325e13i		−	0.740189i
$598$	1.85346e13	+	1.44501e14i	0.242369	+	1.88958i
$599$			5.37083e13i			0.696477i	0.937406	+	0.348239i	$0.113220\pi$
$599$			5.37083e13i			0.696477i	−0.937406	+	0.348239i	$0.886780\pi$
$600$	5.77817e13	−	1.89937e13i	0.743077	−	0.244261i
$601$	−3.12372e13			−0.398382			−0.199191	−	0.979961i	$-0.563831\pi$
$601$	−3.12372e13			−0.398382			−0.199191	+	0.979961i	$0.563831\pi$
$602$	−3.86522e13	+	4.95777e12i	−0.488869	+	0.0627053i
$603$	−3.50835e12			−0.0440064
$604$	1.65518e13	+	6.34598e13i	0.205902	+	0.789431i
$605$	−4.13285e11	+	1.26885e13i	−0.00509885	+	0.156543i
$606$	6.50515e13	−	8.34390e12i	0.795965	−	0.102095i
$607$	−7.33861e13			−0.890574			−0.445287	−	0.895388i	$-0.646898\pi$
$607$	−7.33861e13			−0.890574			−0.445287	+	0.895388i	$0.646898\pi$
$608$	4.27661e13	+	5.76982e13i	0.514733	+	0.694455i
$609$	4.29973e13			0.513280
$610$	8.27919e12	+	8.68784e13i	0.0980254	+	1.02864i
$611$			1.75453e14i			2.06042i
$612$	6.44084e12	+	2.46942e13i	0.0750214	+	0.287633i
$613$		−	4.41534e13i		−	0.510108i	−0.966927	−	0.255054i	$-0.917907\pi$
$613$		−	4.41534e13i		−	0.510108i	0.966927	−	0.255054i	$-0.0820933\pi$
$614$	−6.26164e13	+	8.03156e12i	−0.717540	+	0.0920360i
$615$	8.68069e11	−	2.66511e13i	0.00986685	−	0.302928i
$616$	−2.97926e13	−	7.40085e13i	−0.335896	−	0.834407i
$617$			5.60294e13i			0.626600i	0.949654	+	0.313300i	$0.101434\pi$
$617$			5.60294e13i			0.626600i	−0.949654	+	0.313300i	$0.898566\pi$
$618$	−4.25844e13	+	5.46213e12i	−0.472398	+	0.0605926i
$619$			7.65763e13i			0.842638i	0.906913	+	0.421319i	$0.138433\pi$
$619$			7.65763e13i			0.842638i	−0.906913	+	0.421319i	$0.861567\pi$
$620$	−1.20937e14	+	2.73716e13i	−1.32009	+	0.298774i
$621$	−1.06784e14			−1.15624
$622$	2.08986e13	+	1.62931e14i	0.224473	+	1.75006i
$623$	1.22158e14			1.30161
$624$	−6.46622e13	−	1.15525e14i	−0.683483	−	1.22111i
$625$	9.45597e13	+	1.23856e13i	0.991531	+	0.129872i
$626$	−9.69285e10	−	7.55683e11i	−0.00100828	−	0.00786083i
$627$	7.04648e13			0.727167
$628$	−3.28462e12	−	1.25933e13i	−0.0336269	−	0.128926i
$629$	−1.40898e13			−0.143104
$630$	−3.05657e12	−	3.20744e13i	−0.0307987	−	0.323189i
$631$		−	4.84894e13i		−	0.484731i	−0.970185	−	0.242365i	$-0.922077\pi$
$631$		−	4.84894e13i		−	0.484731i	0.970185	−	0.242365i	$-0.0779232\pi$
$632$	−3.77803e13	−	9.38508e13i	−0.374697	−	0.930792i
$633$			2.86343e13i			0.281753i
$634$	−2.06004e13	−	1.60606e14i	−0.201108	−	1.56789i
$635$	−4.21782e12	+	1.29494e14i	−0.0408526	+	1.25424i
$636$	−1.12578e13	−	4.31627e13i	−0.108186	−	0.414785i
$637$			5.63845e13i			0.537604i
$638$	−1.13479e13	−	8.84712e13i	−0.107352	−	0.836948i
$639$		−	7.52809e13i		−	0.706611i
$640$	8.14026e13	+	7.00202e13i	0.758121	+	0.652114i
$641$	1.29283e13			0.119468			0.0597338	−	0.998214i	$-0.480975\pi$
$641$	1.29283e13			0.119468			0.0597338	+	0.998214i	$0.480975\pi$
$642$	1.09312e13	−	1.40211e12i	0.100229	−	0.0128560i
$643$	−1.48437e14			−1.35048			−0.675238	−	0.737600i	$-0.735959\pi$
$643$	−1.48437e14			−1.35048			−0.675238	+	0.737600i	$0.735959\pi$
$644$	9.54599e13	−	2.48982e13i	0.861770	−	0.224770i
$645$	1.67519e12	−	5.14309e13i	0.0150060	−	0.460708i
$646$	7.38666e13	−	9.47458e12i	0.656576	−	0.0842165i
$647$	8.95550e12			0.0789894			0.0394947	−	0.999220i	$-0.487425\pi$
$647$	8.95550e12			0.0789894			0.0394947	+	0.999220i	$0.487425\pi$
$648$	4.88769e13	−	1.96757e13i	0.427788	−	0.172209i
$649$	−9.60902e13			−0.834557
$650$	−1.29548e13	−	2.07176e14i	−0.111652	−	1.78555i
$651$		−	1.03529e14i		−	0.885439i
$652$	1.70056e14	−	4.43547e13i	1.44329	−	0.376445i
$653$		−	7.28446e13i		−	0.613524i	−0.951786	−	0.306762i	$-0.900754\pi$
$653$		−	7.28446e13i		−	0.613524i	0.951786	−	0.306762i	$-0.0992456\pi$
$654$	−8.02545e13	+	1.02939e13i	−0.670781	+	0.0860384i
$655$	−4.33826e12	−	1.41304e11i	−0.0359840	−	0.00117206i
$656$	4.10766e13	−	2.29915e13i	0.338123	−	0.189256i
$657$		−	3.70394e13i		−	0.302578i
$658$	1.17846e14	−	1.51157e13i	0.955403	−	0.122546i
$659$			2.12839e14i			1.71247i	0.516584	+	0.856237i	$0.327203\pi$
$659$			2.12839e14i			1.71247i	−0.516584	+	0.856237i	$0.672797\pi$
$660$	1.02750e14	−	2.32554e13i	0.820471	−	0.185696i
$661$	1.49053e14			1.18123			0.590613	−	0.806955i	$-0.298886\pi$
$661$	1.49053e14			1.18123			0.590613	+	0.806955i	$0.298886\pi$
$662$	−1.89323e13	−	1.47602e14i	−0.148906	−	1.16092i
$663$	−1.37280e14			−1.07162
$664$	−5.74795e13	+	2.31388e13i	−0.445321	+	0.179267i
$665$	−9.39714e13	−	3.06080e12i	−0.722582	−	0.0235357i
$666$	−1.20924e12	−	9.42756e12i	−0.00922869	−	0.0719495i
$667$	1.10297e14			0.835477
$668$	−1.26384e14	+	3.29639e13i	−0.950187	+	0.247831i
$669$	1.57557e14			1.17573
$670$	1.45204e12	+	1.52371e13i	0.0107548	+	0.112857i
$671$			1.51159e14i			1.11128i
$672$	−7.20237e13	+	5.33843e13i	−0.525569	+	0.389553i
$673$			9.10177e13i			0.659251i	0.944112	+	0.329625i	$0.106922\pi$
$673$			9.10177e13i			0.659251i	−0.944112	+	0.329625i	$0.893078\pi$
$674$	9.10200e11	+	7.09618e12i	0.00654391	+	0.0510182i
$675$	1.51829e14	+	9.90115e12i	1.08352	+	0.0706589i
$676$	−3.00604e14	+	7.84045e13i	−2.12942	+	0.555402i
$677$		−	1.25381e14i		−	0.881636i	−0.897596	−	0.440818i	$-0.854688\pi$
$677$		−	1.25381e14i		−	0.881636i	0.897596	−	0.440818i	$-0.145312\pi$
$678$	−1.81926e13	−	1.41835e14i	−0.126984	−	0.990001i
$679$		−	8.13835e13i		−	0.563881i
$680$	1.04584e14	−	3.81937e13i	0.719316	−	0.262692i
$681$	−1.07941e14			−0.736973
$682$	−2.13022e14	+	2.73235e13i	−1.44379	+	0.185189i
$683$	−1.14583e14			−0.770931			−0.385465	−	0.922722i	$-0.625959\pi$
$683$	−1.14583e14			−0.770931			−0.385465	+	0.922722i	$0.625959\pi$
$684$	1.26790e13	+	4.86113e13i	0.0846843	+	0.324681i
$685$	−1.29811e14	−	4.22815e12i	−0.860714	−	0.0280348i
$686$	1.63901e14	−	2.10229e13i	1.07885	−	0.138380i
$687$	1.19666e13			0.0781966
$688$	7.92689e13	−	4.43687e13i	0.514234	−	0.287829i
$689$	−1.52236e14			−0.980437
$690$	1.23584e13	+	1.29684e14i	0.0790162	+	0.829163i
$691$			3.74076e13i			0.237449i	0.992927	+	0.118724i	$0.0378805\pi$
$691$			3.74076e13i			0.237449i	−0.992927	+	0.118724i	$0.962119\pi$
$692$	4.84372e13	+	1.85709e14i	0.305245	+	1.17031i
$693$		−	5.58061e13i		−	0.349153i
$694$	1.00542e14	−	1.28962e13i	0.624528	−	0.0801057i
$695$	2.46759e14	+	8.03734e12i	1.52177	+	0.0495665i
$696$	−9.29809e13	+	3.74301e13i	−0.569308	+	0.229179i
$697$		−	4.88118e13i		−	0.296729i
$698$	2.65865e14	−	3.41014e13i	1.60466	−	0.205824i
$699$		−	7.42385e13i		−	0.444881i
$700$	−1.38037e14	+	2.65500e13i	−0.821308	+	0.157970i
$701$	2.22503e14			1.31446			0.657229	−	0.753691i	$-0.271729\pi$
$701$	2.22503e14			1.31446			0.657229	+	0.753691i	$0.271729\pi$
$702$	−4.21339e13	−	3.28488e14i	−0.247142	−	1.92679i
$703$	−2.77362e13			−0.161536
$704$	1.28852e14	+	1.34107e14i	0.745123	+	0.775511i
$705$	−5.10746e12	+	1.56807e14i	−0.0293264	+	0.900368i
$706$	1.04324e13	+	8.13341e13i	0.0594786	+	0.463713i
$707$	−1.51570e14			−0.858059
$708$	2.72518e13	+	1.04484e14i	0.153189	+	0.587330i
$709$	9.78657e13			0.546260			0.273130	−	0.961977i	$-0.411941\pi$
$709$	9.78657e13			0.546260			0.273130	+	0.961977i	$0.411941\pi$
$710$	−3.26952e14	+	3.11573e13i	−1.81214	+	0.172691i
$711$		−	7.07682e13i		−	0.389485i
$712$	−2.64164e14	+	1.06341e14i	−1.44369	+	0.581166i
$713$		−	2.65574e14i		−	1.44125i
$714$	1.18270e13	+	9.22065e13i	0.0637357	+	0.496902i
$715$	1.17046e13	−	3.59349e14i	0.0626362	−	1.92303i
$716$	−3.45801e13	−	1.32581e14i	−0.183764	−	0.704555i
$717$			1.62768e14i			0.858961i
$718$	4.06965e13	+	3.17282e14i	0.213272	+	1.66273i
$719$		−	1.39680e14i		−	0.726926i	−0.931609	−	0.363463i	$-0.881594\pi$
$719$		−	1.39680e14i		−	0.726926i	0.931609	−	0.363463i	$-0.118406\pi$
$720$	3.45313e13	+	6.66996e13i	0.178464	+	0.344715i
$721$	9.92219e13			0.509250
$722$	−4.91915e13	+	6.30960e12i	−0.250729	+	0.0321600i
$723$	−4.17405e13			−0.211284
$724$	3.47792e14	−	9.07122e13i	1.74834	−	0.456009i
$725$	−1.56825e14	−	1.02269e13i	−0.782932	−	0.0510569i
$726$	2.45086e13	−	3.14362e12i	0.121516	−	0.0155864i
$727$	−3.31152e13			−0.163063			−0.0815315	−	0.996671i	$-0.525981\pi$
$727$	−3.31152e13			−0.163063			−0.0815315	+	0.996671i	$0.525981\pi$
$728$	1.14258e14	+	2.83830e14i	0.558764	+	1.38804i
$729$	2.11724e14			1.02833
$730$	−1.60866e14	+	1.53299e13i	−0.775978	+	0.0739478i
$731$		−	9.41962e13i		−	0.451281i
$732$	1.64363e14	−	4.28697e13i	0.782075	−	0.203983i
$733$			3.51027e14i			1.65890i	0.558580	+	0.829451i	$0.311347\pi$
$733$			3.51027e14i			1.65890i	−0.558580	+	0.829451i	$0.688653\pi$
$734$	−7.31581e13	+	9.38370e12i	−0.343386	+	0.0440447i
$735$	−1.64136e12	+	5.03922e13i	−0.00765184	+	0.234924i
$736$	−1.84756e14	+	1.36942e14i	−0.855479	+	0.634084i
$737$			2.65109e13i			0.121924i
$738$	3.26602e13	−	4.18919e12i	0.149189	−	0.0191359i
$739$		−	6.54869e13i		−	0.297120i	−0.988903	−	0.148560i	$-0.952536\pi$
$739$		−	6.54869e13i		−	0.297120i	0.988903	−	0.148560i	$-0.0474639\pi$
$740$	−4.04443e13	+	9.15372e12i	−0.182263	+	0.0412514i
$741$	−2.70239e14			−1.20964
$742$	1.31154e13	+	1.02252e14i	0.0583126	+	0.454622i
$743$	−3.94592e14			−1.74262			−0.871312	−	0.490729i	$-0.836731\pi$
$743$	−3.94592e14			−1.74262			−0.871312	+	0.490729i	$0.836731\pi$
$744$	9.01246e13	+	2.23880e14i	0.395347	+	0.982091i
$745$	−3.43822e11	+	1.05559e13i	−0.00149814	+	0.0459953i
$746$	−2.08702e12	−	1.62710e13i	−0.00903300	−	0.0704239i
$747$	−4.33424e13			−0.186342
$748$	1.86603e14	−	4.86704e13i	0.796912	−	0.207853i
$749$	−2.54699e13			−0.108048
$750$	−5.54717e12	−	1.85535e14i	−0.0233757	−	0.781845i
$751$		−	2.64643e14i		−	1.10780i	−0.832584	−	0.553899i	$-0.813140\pi$
$751$		−	2.64643e14i		−	1.10780i	0.832584	−	0.553899i	$-0.186860\pi$
$752$	−2.41682e14	+	1.35275e14i	−1.00498	+	0.562509i
$753$		−	7.16906e13i		−	0.296133i
$754$	4.35202e13	+	3.39296e14i	0.178580	+	1.39227i
$755$	2.00037e14	+	6.51552e12i	0.815409	+	0.0265592i
$756$	−2.17005e14	+	5.66000e13i	−0.878741	+	0.229196i
$757$			2.99343e13i			0.120418i	0.998186	+	0.0602089i	$0.0191767\pi$
$757$			2.99343e13i			0.120418i	−0.998186	+	0.0602089i	$0.980823\pi$
$758$	−5.30015e13	−	4.13215e14i	−0.211808	−	1.65132i
$759$			2.25636e14i			0.895777i
$760$	2.05876e14	−	7.51853e13i	0.811966	−	0.296527i
$761$	1.89021e14			0.740605			0.370302	−	0.928911i	$-0.379254\pi$
$761$	1.89021e14			0.740605			0.370302	+	0.928911i	$0.379254\pi$
$762$	2.50125e14	−	3.20825e13i	0.973602	−	0.124880i
$763$	1.86993e14			0.723109
$764$	−8.66861e13	−	3.32356e14i	−0.333030	−	1.27684i
$765$	7.78408e13	+	2.53540e12i	0.297098	+	0.00967696i
$766$	2.41878e12	−	3.10247e11i	0.00917176	−	0.00117643i
$767$	3.68516e14			1.38829
$768$	1.09278e14	−	1.78141e14i	0.409003	−	0.666741i
$769$	1.99563e14			0.742076			0.371038	−	0.928618i	$-0.379002\pi$
$769$	1.99563e14			0.742076			0.371038	+	0.928618i	$0.379002\pi$
$770$	−2.42371e14	+	2.30971e13i	−0.895422	+	0.0853304i
$771$		−	1.56606e14i		−	0.574826i
$772$	−1.14300e14	−	4.38228e14i	−0.416831	−	1.59813i
$773$			1.95460e14i			0.708208i	0.935206	+	0.354104i	$0.115214\pi$
$773$			1.95460e14i			0.708208i	−0.935206	+	0.354104i	$0.884786\pi$
$774$	6.30271e13	−	8.08424e12i	0.226894	−	0.0291028i
$775$	−2.46245e13	+	3.77604e14i	−0.0880762	+	1.35060i
$776$	7.08462e13	+	1.75990e14i	0.251772	+	0.625433i
$777$		−	3.46227e13i		−	0.122252i
$778$	1.80336e14	−	2.31310e13i	0.632680	−	0.0811514i
$779$		−	9.60873e13i		−	0.334949i
$780$	−3.94057e14	+	8.91866e13i	−1.36485	+	0.308906i
$781$	−5.68862e14			−1.95773
$782$	3.03387e13	+	2.36529e14i	0.103744	+	0.808818i
$783$	−2.50734e14			−0.851929
$784$	−7.76681e13	+	4.34727e13i	−0.262218	+	0.146770i
$785$	−3.96964e13	−	1.29297e12i	−0.133169	−	0.00433752i
$786$	1.07482e12	+	8.37959e12i	0.00358280	+	0.0279325i
$787$	1.04188e14			0.345100			0.172550	−	0.985001i	$-0.444799\pi$
$787$	1.04188e14			0.345100			0.172550	+	0.985001i	$0.444799\pi$
$788$	1.65145e13	+	6.33169e13i	0.0543545	+	0.208396i
$789$	2.06775e14			0.676260
$790$	−3.07353e14	+	2.92896e13i	−0.998855	+	0.0951872i
$791$			3.30477e14i			1.06723i
$792$	4.85805e13	+	1.20680e14i	0.155896	+	0.387265i
$793$		−	5.79711e14i		−	1.84861i
$794$	−5.01125e13	−	3.90692e14i	−0.158798	−	1.23803i
$795$	−1.36057e14	−	4.43159e12i	−0.428434	−	0.0139548i
$796$	−7.63217e13	−	2.92619e14i	−0.238827	−	0.915665i
$797$		−	1.43104e14i		−	0.445000i	−0.974933	−	0.222500i	$-0.928578\pi$
$797$		−	1.43104e14i		−	0.445000i	0.974933	−	0.222500i	$-0.0714217\pi$
$798$	2.32817e13	+	1.81511e14i	0.0719450	+	0.560904i
$799$			2.87194e14i			0.881945i
$800$	2.75391e14	−	1.77578e14i	0.840426	−	0.541926i
$801$	−1.99193e14			−0.604103
$802$	−1.02019e13	+	1.30856e12i	−0.0307474	+	0.00394385i
$803$	−2.79889e14			−0.838318
$804$	2.88267e13	−	7.51867e12i	0.0858053	−	0.0223800i
$805$	9.80102e12	−	3.00907e14i	0.0289929	−	0.890129i
$806$	8.16961e14	−	1.04788e14i	2.40174	−	0.308062i
$807$	2.99475e14			0.874971
$808$	3.27768e14	−	1.31945e14i	0.951722	−	0.383122i
$809$	−4.37170e13			−0.126156			−0.0630780	−	0.998009i	$-0.520092\pi$
$809$	−4.37170e13			−0.126156			−0.0630780	+	0.998009i	$0.520092\pi$
$810$	−1.52539e13	−	1.60068e14i	−0.0437477	−	0.459070i
$811$			3.48250e14i			0.992629i	0.868143	+	0.496314i	$0.165314\pi$
$811$			3.48250e14i			0.992629i	−0.868143	+	0.496314i	$0.834686\pi$
$812$	2.24145e14	−	5.84622e13i	0.634963	−	0.165613i
$813$			1.42181e14i			0.400304i
$814$	−7.12396e13	+	9.13763e12i	−0.199342	+	0.0255689i
$815$	1.74600e13	−	5.36049e14i	0.0485574	−	1.49079i
$816$	−1.05843e14	−	1.89099e14i	−0.292559	−	0.522684i
$817$		−	1.85428e14i		−	0.509407i
$818$	−3.29464e14	+	4.22590e13i	−0.899583	+	0.115386i
$819$			2.14022e14i			0.580816i
$820$	−3.17115e13	−	1.40112e14i	−0.0855357	−	0.377927i
$821$	3.27880e14			0.879021			0.439511	−	0.898237i	$-0.355152\pi$
$821$	3.27880e14			0.879021			0.439511	+	0.898237i	$0.355152\pi$
$822$	3.21611e13	+	2.50737e14i	0.0856982	+	0.668129i
$823$	1.64425e14			0.435481			0.217740	−	0.976007i	$-0.430131\pi$
$823$	1.64425e14			0.435481			0.217740	+	0.976007i	$0.430131\pi$
$824$	−2.14566e14	+	8.63749e13i	−0.564838	+	0.227379i
$825$	2.09213e13	−	3.20818e14i	0.0547419	−	0.839440i
$826$	−3.17484e13	−	2.47520e14i	−0.0825699	−	0.643739i
$827$	−8.72181e13			−0.225465			−0.112732	−	0.993625i	$-0.535960\pi$
$827$	−8.72181e13			−0.225465			−0.112732	+	0.993625i	$0.535960\pi$
$828$	−1.55659e14	+	4.05994e13i	−0.399965	+	0.104320i
$829$	2.12343e14			0.542333			0.271166	−	0.962532i	$-0.412591\pi$
$829$	2.12343e14			0.542333			0.271166	+	0.962532i	$0.412591\pi$
$830$	1.79386e13	+	1.88240e14i	0.0455406	+	0.477884i
$831$			2.57697e14i			0.650285i
$832$	−4.94160e14	−	5.14313e14i	−1.23951	−	1.29006i
$833$			9.22939e13i			0.230117i
$834$	−6.11353e13	−	4.76629e14i	−0.151517	−	1.18127i
$835$	−1.29760e13	+	3.98385e14i	−0.0319676	+	0.981455i
$836$	3.67333e14	−	9.58090e13i	0.899556	−	0.234625i
$837$			6.03719e14i			1.46963i
$838$	6.41747e13	+	5.00325e14i	0.155290	+	1.21069i
$839$		−	7.14552e12i		−	0.0171879i	−0.999963	−	0.00859397i	$-0.997264\pi$
$839$		−	7.14552e12i		−	0.0171879i	0.999963	−	0.00859397i	$-0.00273558\pi$
$840$	9.38526e13	+	2.56992e14i	0.224414	+	0.614502i
$841$	−1.61724e14			−0.384410
$842$	4.76379e14	−	6.11033e13i	1.12562	−	0.144379i
$843$	−1.26509e14			−0.297155
$844$	3.89333e13	+	1.49271e14i	0.0909094	+	0.348548i
$845$	−3.08635e13	+	9.47559e14i	−0.0716410	+	2.19949i
$846$	−1.92163e14	+	2.46480e13i	−0.443422	+	0.0568760i
$847$	−5.71051e13			−0.130996
$848$	−1.17374e14	−	2.09700e14i	−0.267666	−	0.478211i
$849$	−6.03091e14			−1.36724
$850$	−2.12054e13	−	3.39119e14i	−0.0477915	−	0.764290i
$851$		−	8.88144e13i		−	0.198992i
$852$	1.61333e14	+	6.18552e14i	0.359356	+	1.37778i
$853$		−	1.73226e14i		−	0.383591i	−0.981435	−	0.191795i	$-0.938569\pi$
$853$		−	1.73226e14i		−	0.383591i	0.981435	−	0.191795i	$-0.0614310\pi$
$854$	−3.89373e14	+	4.99433e13i	−0.857189	+	0.109948i
$855$	1.53232e14	+	4.99100e12i	0.335365	+	0.0109234i
$856$	5.50782e13	−	2.21721e13i	0.119842	−	0.0482434i
$857$			1.24930e14i			0.270248i	0.990829	+	0.135124i	$0.0431432\pi$
$857$			1.24930e14i			0.270248i	−0.990829	+	0.135124i	$0.956857\pi$
$858$	−6.94103e14	+	8.90298e13i	−1.49275	+	0.191469i
$859$		−	3.15975e14i		−	0.675596i	−0.941219	−	0.337798i	$-0.890318\pi$
$859$		−	3.15975e14i		−	0.675596i	0.941219	−	0.337798i	$-0.109682\pi$
$860$	−6.11964e13	−	2.70387e14i	−0.130087	−	0.574769i
$861$	1.19944e14			0.253492
$862$	2.40958e12	+	1.87858e13i	0.00506297	+	0.0394724i
$863$	−1.53961e14			−0.321631			−0.160816	−	0.986984i	$-0.551412\pi$
$863$	−1.53961e14			−0.321631			−0.160816	+	0.986984i	$0.551412\pi$
$864$	4.19998e14	−	3.11304e14i	0.872325	−	0.646571i
$865$	5.85388e14	+	1.90670e13i	1.20882	+	0.0393733i
$866$	9.36547e13	+	7.30160e14i	0.192283	+	1.49909i
$867$	1.58477e14			0.323498
$868$	−1.40766e14	−	5.39699e14i	−0.285693	−	1.09535i
$869$	−5.34762e14			−1.07910
$870$	2.90181e13	+	3.04504e14i	0.0582202	+	0.610938i
$871$		−	1.01672e14i		−	0.202820i
$872$	−4.04370e14	+	1.62782e14i	−0.802041	+	0.322867i
$873$			1.32706e14i			0.261709i
$874$	5.97225e13	+	4.65614e14i	0.117106	+	0.912996i
$875$	−4.18360e13	+	4.26933e14i	−0.0815662	+	0.832375i
$876$	7.93784e13	+	3.04338e14i	0.153880	+	0.589977i
$877$			1.51963e14i			0.292913i	0.989217	+	0.146457i	$0.0467869\pi$
$877$			1.51963e14i			0.292913i	−0.989217	+	0.146457i	$0.953213\pi$
$878$	1.85004e13	+	1.44234e14i	0.0354575	+	0.276437i
$879$			6.12508e13i			0.116726i
$880$	5.04017e14	−	2.60937e14i	0.955063	−	0.494449i
$881$	5.87645e14			1.10722			0.553612	−	0.832774i	$-0.313249\pi$
$881$	5.87645e14			1.10722			0.553612	+	0.832774i	$0.313249\pi$
$882$	−6.17543e13	+	7.92098e12i	−0.115697	+	0.0148401i
$883$	4.47094e14			0.832904			0.416452	−	0.909158i	$-0.363273\pi$
$883$	4.47094e14			0.832904			0.416452	+	0.909158i	$0.363273\pi$
$884$	−7.15641e14	+	1.86656e14i	−1.32566	+	0.345764i
$885$	3.29352e14	+	1.07275e13i	0.606657	+	0.0197598i
$886$	−7.62871e13	+	9.78504e12i	−0.139728	+	0.0179223i
$887$	−4.52899e14			−0.824866			−0.412433	−	0.910988i	$-0.635321\pi$
$887$	−4.52899e14			−0.824866			−0.412433	+	0.910988i	$0.635321\pi$
$888$	3.01398e13	+	7.48709e13i	0.0545853	+	0.135596i
$889$	−5.82792e14			−1.04955
$890$	8.24421e13	+	8.65113e14i	0.147638	+	1.54926i
$891$		−	2.78501e14i		−	0.495950i
$892$	8.21342e14	−	2.14225e14i	1.45445	−	0.379355i
$893$			5.65349e14i			0.995542i
$894$	2.03893e13	−	2.61525e12i	0.0357038	−	0.00457959i
$895$	−4.17918e14	−	1.36123e13i	−0.727740	−	0.0237037i
$896$	−3.02875e14	+	3.76221e14i	−0.524473	+	0.651483i
$897$		−	8.65337e14i		−	1.49013i
$898$	8.10593e14	−	1.03972e14i	1.38810	−	0.178046i
$899$		−	6.23583e14i		−	1.06193i
$900$	2.25086e14	−	4.32930e13i	0.381186	−	0.0733170i
$901$	−2.49189e14			−0.419668
$902$	−3.16558e13	−	2.46798e14i	−0.0530176	−	0.413341i
$903$	2.31467e14			0.385523
$904$	−2.87688e14	−	7.14651e14i	−0.476518	−	1.18373i
$905$	3.57084e13	−	1.09630e15i	0.0588203	−	1.80588i
$906$	−4.95598e13	−	3.86383e14i	−0.0811874	−	0.632961i
$907$	−9.97795e14			−1.62557			−0.812783	−	0.582566i	$-0.802049\pi$
$907$	−9.97795e14			−1.62557			−0.812783	+	0.582566i	$0.802049\pi$
$908$	−5.62697e14	+	1.46765e14i	−0.911686	+	0.237789i
$909$	2.47154e14			0.398243
$910$	9.29518e14	−	8.85797e13i	1.48954	−	0.141947i
$911$		−	1.01348e15i		−	1.61518i	−0.589741	−	0.807592i	$-0.700770\pi$
$911$		−	1.01348e15i		−	1.61518i	0.589741	−	0.807592i	$-0.299230\pi$
$912$	−2.08356e14	−	3.72247e14i	−0.330241	−	0.590007i
$913$			3.27519e14i			0.516276i
$914$	5.85568e13	+	4.56526e14i	0.0918008	+	0.715706i
$915$	1.68754e13	−	5.18102e14i	0.0263117	−	0.807811i
$916$	6.23820e13	−	1.62707e13i	0.0967346	−	0.0252306i
$917$		−	1.95245e13i		−	0.0301116i
$918$	−6.89676e13	−	5.37692e14i	−0.105787	−	0.824745i
$919$		−	3.29429e14i		−	0.502556i	−0.967915	−	0.251278i	$-0.919149\pi$
$919$		−	3.29429e14i		−	0.502556i	0.967915	−	0.251278i	$-0.0808508\pi$
$920$	2.40752e14	+	6.59238e14i	0.365284	+	1.00024i
$921$	3.74975e14			0.565853
$922$	−9.75681e14	+	1.25147e14i	−1.46438	+	0.187830i
$923$	2.18164e15			3.25668
$924$	1.19597e14	+	4.58536e14i	0.177566	+	0.680791i
$925$	−8.23501e12	+	1.26280e14i	−0.0121606	+	0.186477i
$926$	−5.29262e14	+	6.78864e13i	−0.777349	+	0.0997075i
$927$	−1.61793e14			−0.236353
$928$	−4.33817e14	+	3.21547e14i	−0.630328	+	0.467201i
$929$	−6.89030e14			−0.995771			−0.497886	−	0.867243i	$-0.665890\pi$
$929$	−6.89030e14			−0.995771			−0.497886	+	0.867243i	$0.665890\pi$
$930$	7.33189e14	−	6.98702e13i	1.05390	−	0.100433i
$931$			1.81683e14i			0.259756i
$932$	−1.00940e14	−	3.87005e14i	−0.143544	−	0.550348i
$933$		−	9.75705e14i		−	1.38010i
$934$	−2.09169e14	+	2.68292e13i	−0.294281	+	0.0377463i
$935$	1.91588e13	−	5.88206e14i	0.0268109	−	0.823136i
$936$	−1.86311e14	−	4.62819e14i	−0.259334	−	0.644216i
$937$		−	1.02170e15i		−	1.41458i	−0.706924	−	0.707289i	$-0.749918\pi$
$937$		−	1.02170e15i		−	1.41458i	0.706924	−	0.707289i	$-0.250082\pi$
$938$	−6.82898e13	+	8.75927e12i	−0.0940463	+	0.0120630i
$939$			4.52537e12i			0.00619906i
$940$	1.86581e14	+	8.24380e14i	0.254231	+	1.12328i
$941$	7.35996e14			0.997532			0.498766	−	0.866737i	$-0.333787\pi$
$941$	7.35996e14			0.997532			0.498766	+	0.866737i	$0.333787\pi$
$942$	9.83490e12	+	7.66758e13i	0.0132591	+	0.103372i
$943$	3.07682e14			0.412614
$944$	2.84127e14	+	5.07620e14i	0.379012	+	0.677141i
$945$	−2.22803e13	+	6.84039e14i	−0.0295639	+	0.907657i
$946$	−6.10888e13	−	4.76266e14i	−0.0806318	−	0.628629i
$947$	−7.17168e14			−0.941609			−0.470805	−	0.882237i	$-0.656036\pi$
$947$	−7.17168e14			−0.941609			−0.470805	+	0.882237i	$0.656036\pi$
$948$	1.51662e14	+	5.81474e14i	0.198077	+	0.759431i
$949$	1.07340e15			1.39454
$950$	−4.17433e13	−	6.67566e14i	−0.0539472	−	0.862732i
$951$			9.61783e14i			1.23644i
$952$	1.87025e14	+	4.64592e14i	0.239174	+	0.594137i
$953$		−	4.43899e14i		−	0.564702i	−0.959311	−	0.282351i	$-0.908886\pi$
$953$		−	4.43899e14i		−	0.564702i	0.959311	−	0.282351i	$-0.0911143\pi$
$954$	−2.13863e13	−	1.66734e14i	−0.0270641	−	0.211000i
$955$	−1.04765e15	−	3.41235e13i	−1.31886	−	0.0429573i
$956$	2.21311e14	+	8.48510e14i	0.277149	+	1.06259i
$957$			5.29805e14i			0.660019i
$958$	−1.35369e14	−	1.05538e15i	−0.167761	−	1.30791i
$959$		−	5.84220e14i		−	0.720250i
$960$	−4.26672e14	−	4.74040e14i	−0.523285	−	0.581378i
$961$	−6.81841e14			−0.831891
$962$	2.73211e14	−	3.50437e13i	0.331606	−	0.0425339i
$963$	4.15317e13			0.0501474
$964$	−2.17593e14	+	5.67534e13i	−0.261373	+	0.0681722i
$965$	−1.38137e15	−	4.49935e13i	−1.65072	−	0.0537667i
$966$	−5.81219e14	+	7.45507e13i	−0.690962	+	0.0886270i
$967$	1.42458e15			1.68482			0.842410	−	0.538837i	$-0.181136\pi$
$967$	1.42458e15			1.68482			0.842410	+	0.538837i	$0.181136\pi$
$968$	1.23489e14	−	4.97113e13i	0.145295	−	0.0584895i
$969$	−4.42346e14			−0.517778
$970$	5.76354e14	−	5.49244e13i	0.671167	−	0.0639597i
$971$			4.62402e14i			0.535702i	0.963460	+	0.267851i	$0.0863136\pi$
$971$			4.62402e14i			0.535702i	−0.963460	+	0.267851i	$0.913686\pi$
$972$	6.08758e14	−	1.58778e14i	0.701639	−	0.183004i
$973$			1.11055e15i			1.27343i
$974$	1.11045e14	−	1.42433e13i	0.126679	−	0.0162486i
$975$	−8.02354e13	+	1.23037e15i	−0.0910632	+	1.39641i
$976$	7.98535e14	−	4.46959e14i	0.901665	−	0.504683i
$977$			1.24483e15i			1.39842i	0.714918	+	0.699209i	$0.246464\pi$
$977$			1.24483e15i			1.39842i	−0.714918	+	0.699209i	$0.753536\pi$
$978$	−1.03541e15	+	1.32808e14i	−1.15722	+	0.148433i
$979$			1.50521e15i			1.67372i
$980$	5.99605e13	+	2.64926e14i	0.0663338	+	0.293086i
$981$	−3.04915e14			−0.335609
$982$	−6.10233e13	−	4.75755e14i	−0.0668249	−	0.520986i
$983$	−7.82351e14			−0.852382			−0.426191	−	0.904633i	$-0.640145\pi$
$983$	−7.82351e14			−0.852382			−0.426191	+	0.904633i	$0.640145\pi$
$984$	−2.59378e14	+	1.04414e14i	−0.281162	+	0.113184i
$985$	1.99587e14	+	6.50085e12i	0.215253	+	0.00701115i
$986$	7.12367e13	+	5.55383e14i	0.0764398	+	0.595947i
$987$	−7.05717e14			−0.753433
$988$	−1.40876e15	+	3.67437e14i	−1.49641	+	0.390300i
$989$	5.93761e14			0.627524
$990$	3.95216e14	−	3.76626e13i	0.415583	−	0.0396036i
$991$		−	5.07172e14i		−	0.530624i	−0.964163	−	0.265312i	$-0.914525\pi$
$991$		−	5.07172e14i		−	0.530624i	0.964163	−	0.265312i	$-0.0854750\pi$
$992$	7.74224e14	+	1.04455e15i	0.805950	+	1.08735i
$993$			8.83905e14i			0.915502i
$994$	−1.87953e14	−	1.46534e15i	−0.193695	−	1.51010i
$995$	−9.22387e14	−	3.00436e13i	−0.945797	−	0.0308061i
$996$	3.56127e14	−	9.28863e13i	0.363336	−	0.0947665i
$997$			5.76576e14i			0.585303i	0.956219	+	0.292652i	$0.0945376\pi$
$997$			5.76576e14i			0.585303i	−0.956219	+	0.292652i	$0.905462\pi$
$998$	8.22170e13	+	6.40988e14i	0.0830442	+	0.647437i
$999$			2.01898e14i			0.202911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.11.d.d.19.2	yes	24
4.3	odd	2	inner	20.11.d.d.19.24	yes	24
5.2	odd	4		100.11.b.h.51.11		24
5.3	odd	4		100.11.b.h.51.14		24
5.4	even	2	inner	20.11.d.d.19.23	yes	24
20.3	even	4		100.11.b.h.51.13		24
20.7	even	4		100.11.b.h.51.12		24
20.19	odd	2	inner	20.11.d.d.19.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.1	✓	24	20.19	odd	2	inner
20.11.d.d.19.2	yes	24	1.1	even	1	trivial
20.11.d.d.19.23	yes	24	5.4	even	2	inner
20.11.d.d.19.24	yes	24	4.3	odd	2	inner
100.11.b.h.51.11		24	5.2	odd	4
100.11.b.h.51.12		24	20.7	even	4
100.11.b.h.51.13		24	20.3	even	4
100.11.b.h.51.14		24	5.3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-31.7400 + 4.07116i) q^{2} +190.073 q^{3} +(990.851 - 258.437i) q^{4} +(101.732 - 3123.34i) q^{5} +(-6032.92 + 773.819i) q^{6} +14056.7 q^{7} +(-30397.4 + 12236.7i) q^{8} -22921.2 q^{9} +O(q^{10})\)	\(q+(-31.7400 + 4.07116i) q^{2} +190.073 q^{3} +(990.851 - 258.437i) q^{4} +(101.732 - 3123.34i) q^{5} +(-6032.92 + 773.819i) q^{6} +14056.7 q^{7} +(-30397.4 + 12236.7i) q^{8} -22921.2 q^{9} +(9486.66 + 99549.0i) q^{10} +173205. i q^{11} +(188334. - 49122.0i) q^{12} -664258. i q^{13} +(-446160. + 57227.2i) q^{14} +(19336.6 - 593664. i) q^{15} +(914997. - 512145. i) q^{16} -1.08730e6i q^{17} +(727518. - 93315.9i) q^{18} -2.14038e6i q^{19} +(-706386. - 3.12106e6i) q^{20} +2.67181e6 q^{21} +(-705145. - 5.49751e6i) q^{22} +6.85374e6 q^{23} +(-5.77774e6 + 2.32587e6i) q^{24} +(-9.74493e6 - 635490. i) q^{25} +(2.70430e6 + 2.10835e7i) q^{26} -1.55803e7 q^{27} +(1.39281e7 - 3.63278e6i) q^{28} +1.60930e7 q^{29} +(1.80316e6 + 1.89216e7i) q^{30} -3.87488e7i q^{31} +(-2.69569e7 + 1.99806e7i) q^{32} +3.29216e7i q^{33} +(4.42658e6 + 3.45109e7i) q^{34} +(1.43002e6 - 4.39040e7i) q^{35} +(-2.27115e7 + 5.92369e6i) q^{36} -1.29585e7i q^{37} +(8.71384e6 + 6.79357e7i) q^{38} -1.26258e8i q^{39} +(3.51270e7 + 9.61866e7i) q^{40} +4.48926e7 q^{41} +(-8.48031e7 + 1.08774e7i) q^{42} +8.66330e7 q^{43} +(4.47625e7 + 1.71620e8i) q^{44} +(-2.33183e6 + 7.15908e7i) q^{45} +(-2.17538e8 + 2.79027e7i) q^{46} -2.64135e8 q^{47} +(1.73916e8 - 9.73451e7i) q^{48} -8.48835e7 q^{49} +(3.11891e8 - 1.95027e7i) q^{50} -2.06667e8i q^{51} +(-1.71669e8 - 6.58180e8i) q^{52} -2.29181e8i q^{53} +(4.94519e8 - 6.34301e7i) q^{54} +(5.40978e8 + 1.76205e7i) q^{55} +(-4.27289e8 + 1.72008e8i) q^{56} -4.06829e8i q^{57} +(-5.10790e8 + 6.55170e7i) q^{58} +5.54778e8i q^{59} +(-1.34265e8 - 5.93230e8i) q^{60} +8.72720e8 q^{61} +(1.57753e8 + 1.22989e9i) q^{62} -3.22197e8 q^{63} +(7.74268e8 - 7.43929e8i) q^{64} +(-2.07470e9 - 6.75765e7i) q^{65} +(-1.34029e8 - 1.04493e9i) q^{66} +1.53061e8 q^{67} +(-2.80999e8 - 1.07735e9i) q^{68} +1.30271e9 q^{69} +(1.33351e8 + 1.39933e9i) q^{70} +3.28433e9i q^{71} +(6.96746e8 - 2.80480e8i) q^{72} +1.61594e9i q^{73} +(5.27562e7 + 4.11303e8i) q^{74} +(-1.85225e9 - 1.20790e8i) q^{75} +(-5.53154e8 - 2.12080e9i) q^{76} +2.43469e9i q^{77} +(5.14015e8 + 4.00741e9i) q^{78} +3.08746e9i q^{79} +(-1.50652e9 - 2.90995e9i) q^{80} -1.60793e9 q^{81} +(-1.42489e9 + 1.82765e8i) q^{82} +1.89093e9 q^{83} +(2.64736e9 - 6.90494e8i) q^{84} +(-3.39602e9 - 1.10614e8i) q^{85} +(-2.74973e9 + 3.52697e8i) q^{86} +3.05884e9 q^{87} +(-2.11946e9 - 5.26498e9i) q^{88} +8.69033e9 q^{89} +(-2.17446e8 - 2.28178e9i) q^{90} -9.33729e9i q^{91} +(6.79104e9 - 1.77126e9i) q^{92} -7.36511e9i q^{93} +(8.38362e9 - 1.07533e9i) q^{94} +(-6.68515e9 - 2.17746e8i) q^{95} +(-5.12379e9 + 3.79777e9i) q^{96} -5.78965e9i q^{97} +(2.69420e9 - 3.45574e8i) q^{98} -3.97006e9i 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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