LMFDB - Embedded newform 20.9.b.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(11,20)]

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, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.14757220122$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{58}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.5
Root			$3.05707 + 7.10588i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.35022 - 14.2118i) q^{2} +110.171i q^{3} +(-147.949 + 208.919i) q^{4} -279.508 q^{5} +(1565.72 - 809.778i) q^{6} -3540.70i q^{7} +(4056.56 + 567.011i) q^{8} -5576.56 q^{9} +O(q^{10})$	\(q+(-7.35022 - 14.2118i) q^{2} +110.171i q^{3} +(-147.949 + 208.919i) q^{4} -279.508 q^{5} +(1565.72 - 809.778i) q^{6} -3540.70i q^{7} +(4056.56 + 567.011i) q^{8} -5576.56 q^{9} +(2054.45 + 3972.31i) q^{10} -15969.8i q^{11} +(-23016.7 - 16299.6i) q^{12} -24176.2 q^{13} +(-50319.6 + 26024.9i) q^{14} -30793.6i q^{15} +(-21758.4 - 61818.6i) q^{16} +43810.0 q^{17} +(40988.9 + 79252.8i) q^{18} -50919.1i q^{19} +(41352.9 - 58394.7i) q^{20} +390081. q^{21} +(-226960. + 117382. i) q^{22} -270875. i q^{23} +(-62467.9 + 446914. i) q^{24} +78125.0 q^{25} +(177701. + 343587. i) q^{26} +108456. i q^{27} +(739720. + 523841. i) q^{28} -1.32588e6 q^{29} +(-437632. + 226340. i) q^{30} -1.18623e6i q^{31} +(-718623. + 763605. i) q^{32} +1.75941e6 q^{33} +(-322013. - 622618. i) q^{34} +989655. i q^{35} +(825045. - 1.16505e6i) q^{36} +2.97108e6 q^{37} +(-723650. + 374266. i) q^{38} -2.66351e6i q^{39} +(-1.13384e6 - 158484. i) q^{40} -4.92072e6 q^{41} +(-2.86718e6 - 5.54374e6i) q^{42} +2.86229e6i q^{43} +(3.33641e6 + 2.36272e6i) q^{44} +1.55870e6 q^{45} +(-3.84961e6 + 1.99099e6i) q^{46} +12696.5i q^{47} +(6.81059e6 - 2.39714e6i) q^{48} -6.77174e6 q^{49} +(-574236. - 1.11029e6i) q^{50} +4.82658e6i q^{51} +(3.57684e6 - 5.05088e6i) q^{52} -5.50364e6 q^{53} +(1.54135e6 - 797176. i) q^{54} +4.46371e6i q^{55} +(2.00761e6 - 1.43631e7i) q^{56} +5.60979e6 q^{57} +(9.74547e6 + 1.88430e7i) q^{58} +6.68863e6i q^{59} +(6.43338e6 + 4.55587e6i) q^{60} -2.50550e6 q^{61} +(-1.68584e7 + 8.71902e6i) q^{62} +1.97449e7i q^{63} +(1.61342e7 + 4.60023e6i) q^{64} +6.75746e6 q^{65} +(-1.29320e7 - 2.50043e7i) q^{66} -3.86718e6i q^{67} +(-6.48163e6 + 9.15275e6i) q^{68} +2.98424e7 q^{69} +(1.40647e7 - 7.27418e6i) q^{70} -3.21701e7i q^{71} +(-2.26217e7 - 3.16197e6i) q^{72} +1.91362e7 q^{73} +(-2.18381e7 - 4.22243e7i) q^{74} +8.60708e6i q^{75} +(1.06380e7 + 7.53341e6i) q^{76} -5.65444e7 q^{77} +(-3.78532e7 + 1.95774e7i) q^{78} -5.33471e7i q^{79} +(6.08166e6 + 1.72788e7i) q^{80} -4.85365e7 q^{81} +(3.61683e7 + 6.99321e7i) q^{82} -6.22776e6i q^{83} +(-5.77119e7 + 8.14954e7i) q^{84} -1.22453e7 q^{85} +(4.06782e7 - 2.10385e7i) q^{86} -1.46072e8i q^{87} +(9.05507e6 - 6.47827e7i) q^{88} +3.83322e7 q^{89} +(-1.14568e7 - 2.21518e7i) q^{90} +8.56008e7i q^{91} +(5.65909e7 + 4.00755e7i) q^{92} +1.30687e8 q^{93} +(180440. - 93322.2i) q^{94} +1.42323e7i q^{95} +(-8.41269e7 - 7.91711e7i) q^{96} +7.87237e7 q^{97} +(4.97738e7 + 9.62384e7i) q^{98} +8.90568e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

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 $

$2$	−7.35022	−	14.2118i	−0.459389	−	0.888235i
$2$	−7.35022	−	14.2118i	−0.459389	−	0.888235i
$3$			110.171i			1.36013i	0.733151	+	0.680065i	$0.238049\pi$
$3$			110.171i			1.36013i	−0.733151	+	0.680065i	$0.761951\pi$
$4$	−147.949	+	208.919i	−0.577924	+	0.816090i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$	1565.72	−	809.778i	1.20812	−	0.624829i
$7$		−	3540.70i		−	1.47468i	−0.675524	−	0.737338i	$-0.736082\pi$
$7$		−	3540.70i		−	1.47468i	0.675524	−	0.737338i	$-0.263918\pi$
$8$	4056.56	+	567.011i	0.990372	+	0.138430i
$9$	−5576.56			−0.849956
$10$	2054.45	+	3972.31i	0.205445	+	0.397231i
$11$		−	15969.8i		−	1.09076i	−0.838188	−	0.545381i	$-0.816385\pi$
$11$		−	15969.8i		−	1.09076i	0.838188	−	0.545381i	$-0.183615\pi$
$12$	−23016.7	−	16299.6i	−1.10999	−	0.786053i
$13$	−24176.2			−0.846477			−0.423239	−	0.906018i	$-0.639107\pi$
$13$	−24176.2			−0.846477			−0.423239	+	0.906018i	$0.639107\pi$
$14$	−50319.6	+	26024.9i	−1.30986	+	0.677449i
$15$		−	30793.6i		−	0.608269i
$16$	−21758.4	−	61818.6i	−0.332007	−	0.943277i
$17$	43810.0			0.524539			0.262269	−	0.964995i	$-0.415529\pi$
$17$	43810.0			0.524539			0.262269	+	0.964995i	$0.415529\pi$
$18$	40988.9	+	79252.8i	0.390460	+	0.754961i
$19$		−	50919.1i		−	0.390721i	−0.980732	−	0.195360i	$-0.937412\pi$
$19$		−	50919.1i		−	0.390721i	0.980732	−	0.195360i	$-0.0625876\pi$
$20$	41352.9	−	58394.7i	0.258456	−	0.364967i
$21$	390081.			2.00575
$22$	−226960.	+	117382.i	−0.968853	+	0.501083i
$23$		−	270875.i		−	0.967959i	−0.875079	−	0.483980i	$-0.839191\pi$
$23$		−	270875.i		−	0.967959i	0.875079	−	0.483980i	$-0.160809\pi$
$24$	−62467.9	+	446914.i	−0.188283	+	1.34704i
$25$	78125.0			0.200000
$26$	177701.	+	343587.i	0.388862	+	0.751871i
$27$			108456.i			0.204079i
$28$	739720.	+	523841.i	1.20347	+	0.852251i
$29$	−1.32588e6			−1.87461			−0.937305	−	0.348511i	$-0.886687\pi$
$29$	−1.32588e6			−1.87461			−0.937305	+	0.348511i	$0.886687\pi$
$30$	−437632.	+	226340.i	−0.540286	+	0.279432i
$31$		−	1.18623e6i		−	1.28446i	−0.766512	−	0.642230i	$-0.778009\pi$
$31$		−	1.18623e6i		−	1.28446i	0.766512	−	0.642230i	$-0.221991\pi$
$32$	−718623.	+	763605.i	−0.685332	+	0.728231i
$33$	1.75941e6			1.48358
$34$	−322013.	−	622618.i	−0.240967	−	0.465914i
$35$			989655.i			0.659495i
$36$	825045.	−	1.16505e6i	0.491210	−	0.693641i
$37$	2.97108e6			1.58529			0.792643	−	0.609686i	$-0.208705\pi$
$37$	2.97108e6			1.58529			0.792643	+	0.609686i	$0.208705\pi$
$38$	−723650.	+	374266.i	−0.347052	+	0.179493i
$39$		−	2.66351e6i		−	1.15132i
$40$	−1.13384e6	−	158484.i	−0.442908	−	0.0619079i
$41$	−4.92072e6			−1.74138			−0.870689	−	0.491834i	$-0.836327\pi$
$41$	−4.92072e6			−1.74138			−0.870689	+	0.491834i	$0.836327\pi$
$42$	−2.86718e6	−	5.54374e6i	−0.921420	−	1.78158i
$43$			2.86229e6i			0.837221i	0.908166	+	0.418611i	$0.137483\pi$
$43$			2.86229e6i			0.837221i	−0.908166	+	0.418611i	$0.862517\pi$
$44$	3.33641e6	+	2.36272e6i	0.890160	+	0.630378i
$45$	1.55870e6			0.380112
$46$	−3.84961e6	+	1.99099e6i	−0.859776	+	0.444669i
$47$			12696.5i			0.00260192i	0.999999	+	0.00130096i	$0.000414108\pi$
$47$			12696.5i			0.00260192i	−0.999999	+	0.00130096i	$0.999586\pi$
$48$	6.81059e6	−	2.39714e6i	1.28298	−	0.451573i
$49$	−6.77174e6			−1.17467
$50$	−574236.	−	1.11029e6i	−0.0918777	−	0.177647i
$51$			4.82658e6i			0.713442i
$52$	3.57684e6	−	5.05088e6i	0.489200	−	0.690802i
$53$	−5.50364e6			−0.697504			−0.348752	−	0.937215i	$-0.613394\pi$
$53$	−5.50364e6			−0.697504			−0.348752	+	0.937215i	$0.613394\pi$
$54$	1.54135e6	−	797176.i	0.181270	−	0.0937517i
$55$			4.46371e6i			0.487803i
$56$	2.00761e6	−	1.43631e7i	0.204140	−	1.46048i
$57$	5.60979e6			0.531431
$58$	9.74547e6	+	1.88430e7i	0.861174	+	1.66509i
$59$			6.68863e6i			0.551987i	0.961159	+	0.275994i	$0.0890068\pi$
$59$			6.68863e6i			0.551987i	−0.961159	+	0.275994i	$0.910993\pi$
$60$	6.43338e6	+	4.55587e6i	0.496402	+	0.351534i
$61$	−2.50550e6			−0.180957			−0.0904784	−	0.995898i	$-0.528840\pi$
$61$	−2.50550e6			−0.180957			−0.0904784	+	0.995898i	$0.528840\pi$
$62$	−1.68584e7	+	8.71902e6i	−1.14090	+	0.590066i
$63$			1.97449e7i			1.25341i
$64$	1.61342e7	+	4.60023e6i	0.961674	+	0.274195i
$65$	6.75746e6			0.378556
$66$	−1.29320e7	−	2.50043e7i	−0.681539	−	1.31777i
$67$		−	3.86718e6i		−	0.191909i	−0.995386	−	0.0959546i	$-0.969410\pi$
$67$		−	3.86718e6i		−	0.191909i	0.995386	−	0.0959546i	$-0.0305904\pi$
$68$	−6.48163e6	+	9.15275e6i	−0.303144	+	0.428071i
$69$	2.98424e7			1.31655
$70$	1.40647e7	−	7.27418e6i	0.585787	−	0.302965i
$71$		−	3.21701e7i		−	1.26596i	−0.774170	−	0.632978i	$-0.781832\pi$
$71$		−	3.21701e7i		−	1.26596i	0.774170	−	0.632978i	$-0.218168\pi$
$72$	−2.26217e7	−	3.16197e6i	−0.841773	−	0.117660i
$73$	1.91362e7			0.673853			0.336927	−	0.941531i	$-0.390613\pi$
$73$	1.91362e7			0.673853			0.336927	+	0.941531i	$0.390613\pi$
$74$	−2.18381e7	−	4.22243e7i	−0.728262	−	1.40811i
$75$			8.60708e6i			0.272026i
$76$	1.06380e7	+	7.53341e6i	0.318863	+	0.225807i
$77$	−5.65444e7			−1.60852
$78$	−3.78532e7	+	1.95774e7i	−1.02264	+	0.528903i
$79$		−	5.33471e7i		−	1.36963i	−0.728718	−	0.684814i	$-0.759884\pi$
$79$		−	5.33471e7i		−	1.36963i	0.728718	−	0.684814i	$-0.240116\pi$
$80$	6.08166e6	+	1.72788e7i	0.148478	+	0.421846i
$81$	−4.85365e7			−1.12753
$82$	3.61683e7	+	6.99321e7i	0.799969	+	1.54675i
$83$		−	6.22776e6i		−	0.131226i	−0.997845	−	0.0656129i	$-0.979100\pi$
$83$		−	6.22776e6i		−	0.131226i	0.997845	−	0.0656129i	$-0.0209003\pi$
$84$	−5.77119e7	+	8.14954e7i	−1.15917	+	1.63688i
$85$	−1.22453e7			−0.234581
$86$	4.06782e7	−	2.10385e7i	0.743650	−	0.384610i
$87$		−	1.46072e8i		−	2.54971i
$88$	9.05507e6	−	6.47827e7i	0.150995	−	1.08026i
$89$	3.83322e7			0.610947			0.305473	−	0.952201i	$-0.401185\pi$
$89$	3.83322e7			0.610947			0.305473	+	0.952201i	$0.401185\pi$
$90$	−1.14568e7	−	2.21518e7i	−0.174619	−	0.337629i
$91$			8.56008e7i			1.24828i
$92$	5.65909e7	+	4.00755e7i	0.789942	+	0.559407i
$93$	1.30687e8			1.74703
$94$	180440.	−	93322.2i	0.00231111	−	0.00119529i
$95$			1.42323e7i			0.174736i
$96$	−8.41269e7	−	7.91711e7i	−0.990489	−	0.932141i
$97$	7.87237e7			0.889239			0.444620	−	0.895720i	$-0.353339\pi$
$97$	7.87237e7			0.889239			0.444620	+	0.895720i	$0.353339\pi$
$98$	4.97738e7	+	9.62384e7i	0.539630	+	1.04338i
$99$			8.90568e7i			0.927100i
$100$	−1.15585e7	+	1.63218e7i	−0.115585	+	0.163218i
$101$	−1.16450e7			−0.111906			−0.0559530	−	0.998433i	$-0.517820\pi$
$101$	−1.16450e7			−0.111906			−0.0559530	+	0.998433i	$0.517820\pi$
$102$	6.85942e7	−	3.54764e7i	0.633704	−	0.327747i
$103$			6.88569e7i			0.611785i	0.952066	+	0.305892i	$0.0989547\pi$
$103$			6.88569e7i			0.611785i	−0.952066	+	0.305892i	$0.901045\pi$
$104$	−9.80725e7	−	1.37082e7i	−0.838328	−	0.117178i
$105$	−1.09031e8			−0.897000
$106$	4.04529e7	+	7.82164e7i	0.320425	+	0.619547i
$107$		−	7.69690e7i		−	0.587193i	−0.955929	−	0.293596i	$-0.905148\pi$
$107$		−	7.69690e7i		−	0.587193i	0.955929	−	0.293596i	$-0.0948521\pi$
$108$	−2.26585e7	−	1.60459e7i	−0.166547	−	0.117942i
$109$	−4.29484e6			−0.0304257			−0.0152129	−	0.999884i	$-0.504843\pi$
$109$	−4.29484e6			−0.0304257			−0.0152129	+	0.999884i	$0.504843\pi$
$110$	6.34372e7	−	3.28092e7i	0.433284	−	0.224091i
$111$			3.27326e8i			2.15620i
$112$	−2.18881e8	+	7.70399e7i	−1.39103	+	0.489603i
$113$	−2.34309e8			−1.43706			−0.718530	−	0.695496i	$-0.755185\pi$
$113$	−2.34309e8			−1.43706			−0.718530	+	0.695496i	$0.755185\pi$
$114$	−4.12331e7	−	7.97250e7i	−0.244133	−	0.472036i
$115$			7.57118e7i			0.432884i
$116$	1.96161e8	−	2.77001e8i	1.08338	−	1.52985i
$117$	1.34820e8			0.719469
$118$	9.50572e7	−	4.91629e7i	0.490294	−	0.253577i
$119$		−	1.55118e8i		−	0.773525i
$120$	1.74603e7	−	1.24916e8i	0.0842029	−	0.602413i
$121$	−4.06770e7			−0.189761
$122$	1.84160e7	+	3.56076e7i	0.0831295	+	0.160732i
$123$		−	5.42118e8i		−	2.36850i
$124$	2.47825e8	+	1.75500e8i	1.04824	+	0.742321i
$125$	−2.18366e7			−0.0894427
$126$	2.80610e8	−	1.45129e8i	1.11332	−	0.575802i
$127$			2.94344e8i			1.13146i	0.824589	+	0.565732i	$0.191406\pi$
$127$			2.94344e8i			1.13146i	−0.824589	+	0.565732i	$0.808594\pi$
$128$	−5.32125e7	−	2.63108e8i	−0.198232	−	0.980155i
$129$	−3.15341e8			−1.13873
$130$	−4.96688e7	−	9.60355e7i	−0.173904	−	0.336247i
$131$			3.43317e8i			1.16576i	0.812558	+	0.582881i	$0.198075\pi$
$131$			3.43317e8i			1.16576i	−0.812558	+	0.582881i	$0.801925\pi$
$132$	−2.60302e8	+	3.67574e8i	−0.857396	+	1.21073i
$133$	−1.80289e8			−0.576186
$134$	−5.49595e7	+	2.84246e7i	−0.170461	+	0.0881609i
$135$		−	3.03144e7i		−	0.0912670i
$136$	1.77718e8	+	2.48407e7i	0.519489	+	0.0726121i
$137$	2.03539e8			0.577784			0.288892	−	0.957362i	$-0.406713\pi$
$137$	2.03539e8			0.577784			0.288892	+	0.957362i	$0.406713\pi$
$138$	−2.19348e8	−	4.24114e8i	−0.604808	−	1.16941i
$139$		−	2.51305e8i		−	0.673197i	−0.941648	−	0.336599i	$-0.890723\pi$
$139$		−	2.51305e8i		−	0.673197i	0.941648	−	0.336599i	$-0.109277\pi$
$140$	−2.06758e8	−	1.46418e8i	−0.538208	−	0.381138i
$141$	−1.39878e6			−0.00353895
$142$	−4.57193e8	+	2.36457e8i	−1.12447	+	0.581566i
$143$			3.86091e8i			0.923305i
$144$	1.21337e8	+	3.44735e8i	0.282191	+	0.801744i
$145$	3.70593e8			0.838351
$146$	−1.40656e8	−	2.71960e8i	−0.309560	−	0.598540i
$147$		−	7.46047e8i		−	1.59771i
$148$	−4.39567e8	+	6.20716e8i	−0.916175	+	1.29374i
$149$	7.65026e8			1.55214			0.776070	−	0.630647i	$-0.217210\pi$
$149$	7.65026e8			1.55214			0.776070	+	0.630647i	$0.217210\pi$
$150$	1.22322e8	−	6.32639e7i	0.241623	−	0.124966i
$151$			5.12585e8i			0.985958i	0.870041	+	0.492979i	$0.164092\pi$
$151$			5.12585e8i			0.985958i	−0.870041	+	0.492979i	$0.835908\pi$
$152$	2.88717e7	−	2.06557e8i	0.0540876	−	0.386959i
$153$	−2.44309e8			−0.445835
$154$	4.15613e8	+	8.03596e8i	0.738936	+	1.42874i
$155$			3.31560e8i			0.574428i
$156$	5.56458e8	+	3.94063e8i	0.939581	+	0.665376i
$157$	1.16971e9			1.92522			0.962610	−	0.270890i	$-0.0873179\pi$
$157$	1.16971e9			1.92522			0.962610	+	0.270890i	$0.0873179\pi$
$158$	−7.58157e8	+	3.92113e8i	−1.21655	+	0.629191i
$159$		−	6.06339e8i		−	0.948696i
$160$	2.00861e8	−	2.13434e8i	0.306490	−	0.325675i
$161$	−9.59085e8			−1.42743
$162$	3.56754e8	+	6.89789e8i	0.517975	+	1.00151i
$163$		−	8.79268e8i		−	1.24558i	−0.782390	−	0.622789i	$-0.786000\pi$
$163$		−	8.79268e8i		−	1.24558i	0.782390	−	0.622789i	$-0.214000\pi$
$164$	7.28014e8	−	1.02803e9i	1.00638	−	1.42112i
$165$	−4.91769e8			−0.663477
$166$	−8.85075e7	+	4.57754e7i	−0.116559	+	0.0602837i
$167$		−	4.63319e8i		−	0.595682i	−0.954616	−	0.297841i	$-0.903734\pi$
$167$		−	4.63319e8i		−	0.595682i	0.954616	−	0.297841i	$-0.0962665\pi$
$168$	1.58239e9	+	2.21180e8i	1.98644	+	0.277657i
$169$	−2.31240e8			−0.283476
$170$	9.00054e7	+	1.74027e8i	0.107764	+	0.208363i
$171$			2.83954e8i			0.332095i
$172$	−5.97988e8	−	4.23472e8i	−0.683248	−	0.483851i
$173$	4.71680e8			0.526579			0.263289	−	0.964717i	$-0.415193\pi$
$173$	4.71680e8			0.526579			0.263289	+	0.964717i	$0.415193\pi$
$174$	−2.07595e9	+	1.07366e9i	−2.26475	+	1.17131i
$175$		−	2.76617e8i		−	0.294935i
$176$	−9.87233e8	+	3.47478e8i	−1.02889	+	0.362140i
$177$	−7.36890e8			−0.750775
$178$	−2.81750e8	−	5.44768e8i	−0.280662	−	0.542664i
$179$			8.30768e8i			0.809222i	0.914489	+	0.404611i	$0.132593\pi$
$179$			8.30768e8i			0.809222i	−0.914489	+	0.404611i	$0.867407\pi$
$180$	−2.30607e8	+	3.25642e8i	−0.219676	+	0.310206i
$181$	6.19754e8			0.577437			0.288719	−	0.957414i	$-0.406771\pi$
$181$	6.19754e8			0.577437			0.288719	+	0.957414i	$0.406771\pi$
$182$	1.21654e9	−	6.29184e8i	1.10877	−	0.573446i
$183$		−	2.76032e8i		−	0.246125i
$184$	1.53589e8	−	1.09882e9i	0.133995	−	0.958640i
$185$	−8.30442e8			−0.708961
$186$	−9.60579e8	−	1.85730e9i	−0.802567	−	1.55178i
$187$		−	6.99639e8i		−	0.572147i
$188$	−2.65255e6	−	1.87843e6i	−0.00212340	−	0.00150371i
$189$	3.84010e8			0.300951
$190$	2.02266e8	−	1.04611e8i	0.155206	−	0.0802715i
$191$			4.24020e7i			0.0318605i	0.999873	+	0.0159303i	$0.00507097\pi$
$191$			4.24020e7i			0.0318605i	−0.999873	+	0.0159303i	$0.994929\pi$
$192$	−5.06810e8	+	1.77752e9i	−0.372941	+	1.30800i
$193$	4.21151e8			0.303535			0.151767	−	0.988416i	$-0.451504\pi$
$193$	4.21151e8			0.303535			0.151767	+	0.988416i	$0.451504\pi$
$194$	−5.78636e8	−	1.11880e9i	−0.408506	−	0.789854i
$195$			7.44474e8i			0.514886i
$196$	1.00187e9	−	1.41475e9i	0.678871	−	0.958637i
$197$	−1.93944e9			−1.28769			−0.643846	−	0.765155i	$-0.722662\pi$
$197$	−1.93944e9			−1.28769			−0.643846	+	0.765155i	$0.722662\pi$
$198$	1.26565e9	−	6.54587e8i	0.823483	−	0.425899i
$199$		−	2.11255e8i		−	0.134708i	−0.997729	−	0.0673542i	$-0.978544\pi$
$199$		−	2.11255e8i		−	0.134708i	0.997729	−	0.0673542i	$-0.0214557\pi$
$200$	3.16919e8	+	4.42977e7i	0.198074	+	0.0276861i
$201$	4.26050e8			0.261022
$202$	8.55931e7	+	1.65496e8i	0.0514083	+	0.0993989i
$203$			4.69452e9i			2.76444i
$204$	−1.00836e9	−	7.14085e8i	−0.582233	−	0.412315i
$205$	1.37538e9			0.778768
$206$	9.78578e8	−	5.06113e8i	0.543409	−	0.281047i
$207$			1.51055e9i			0.822723i
$208$	5.26036e8	+	1.49454e9i	0.281036	+	0.798463i
$209$	−8.13170e8			−0.426183
$210$	8.01401e8	+	1.54952e9i	0.412072	+	0.796747i
$211$		−	2.01406e9i		−	1.01611i	−0.861324	−	0.508056i	$-0.830364\pi$
$211$		−	2.01406e9i		−	1.01611i	0.861324	−	0.508056i	$-0.169636\pi$
$212$	8.14256e8	−	1.14982e9i	0.403104	−	0.569226i
$213$	3.54420e9			1.72187
$214$	−1.09387e9	+	5.65739e8i	−0.521565	+	0.269750i
$215$		−	8.00035e8i		−	0.374417i
$216$	−6.14958e7	+	4.39959e8i	−0.0282508	+	0.202114i
$217$	−4.20007e9			−1.89416
$218$	3.15680e7	+	6.10373e7i	0.0139772	+	0.0270252i
$219$			2.10825e9i			0.916528i
$220$	−9.32554e8	−	6.60399e8i	−0.398092	−	0.281913i
$221$	−1.05916e9			−0.444010
$222$	4.65188e9	−	2.40592e9i	1.91521	−	0.990532i
$223$			9.06863e8i			0.366710i	0.983047	+	0.183355i	$0.0586957\pi$
$223$			9.06863e8i			0.366710i	−0.983047	+	0.183355i	$0.941304\pi$
$224$	2.70370e9	+	2.54443e9i	1.07390	+	1.01064i
$225$	−4.35669e8			−0.169991
$226$	1.72222e9	+	3.32994e9i	0.660169	+	1.27645i
$227$		−	9.31268e7i		−	0.0350729i	−0.999846	−	0.0175364i	$-0.994418\pi$
$227$		−	9.31268e7i		−	0.0350729i	0.999846	−	0.0175364i	$-0.00558230\pi$
$228$	−8.29960e8	+	1.17199e9i	−0.307127	+	0.433696i
$229$	−5.17840e8			−0.188301			−0.0941507	−	0.995558i	$-0.530014\pi$
$229$	−5.17840e8			−0.188301			−0.0941507	+	0.995558i	$0.530014\pi$
$230$	1.07600e9	−	5.56498e8i	0.384503	−	0.198862i
$231$		−	6.22953e9i		−	2.18780i
$232$	−5.37850e9	−	7.51786e8i	−1.85656	−	0.259503i
$233$	−1.20417e9			−0.408569			−0.204284	−	0.978912i	$-0.565487\pi$
$233$	−1.20417e9			−0.408569			−0.204284	+	0.978912i	$0.565487\pi$
$234$	−9.90959e8	−	1.91604e9i	−0.330516	−	0.639058i
$235$		−	3.54879e6i		−	0.00116361i
$236$	−1.39738e9	−	9.89573e8i	−0.450471	−	0.319007i
$237$	5.87728e9			1.86287
$238$	−2.20450e9	+	1.14015e9i	−0.687072	+	0.355349i
$239$			2.12088e9i			0.650018i	0.945711	+	0.325009i	$0.105367\pi$
$239$			2.12088e9i			0.650018i	−0.945711	+	0.325009i	$0.894633\pi$
$240$	−1.90362e9	+	6.70020e8i	−0.573766	+	0.201949i
$241$	−6.85448e8			−0.203192			−0.101596	−	0.994826i	$-0.532395\pi$
$241$	−6.85448e8			−0.203192			−0.101596	+	0.994826i	$0.532395\pi$
$242$	2.98984e8	+	5.78092e8i	0.0871740	+	0.168552i
$243$		−	4.63572e9i		−	1.32951i
$244$	3.70685e8	−	5.23447e8i	0.104579	−	0.147677i
$245$	1.89276e9			0.525329
$246$	−7.70446e9	+	3.98469e9i	−2.10379	+	1.08806i
$247$			1.23103e9i			0.330736i
$248$	6.72603e8	−	4.81200e9i	0.177808	−	1.27209i
$249$	6.86116e8			0.178484
$250$	1.60504e8	+	3.10337e8i	0.0410890	+	0.0794462i
$251$			4.44219e9i			1.11919i	0.828768	+	0.559593i	$0.189042\pi$
$251$			4.44219e9i			1.11919i	−0.828768	+	0.559593i	$0.810958\pi$
$252$	−4.12509e9	−	2.92123e9i	−1.02290	−	0.724376i
$253$	−4.32582e9			−1.05581
$254$	4.18315e9	−	2.16350e9i	1.00501	−	0.519782i
$255$		−	1.34907e9i		−	0.319061i
$256$	−3.34811e9	+	2.69015e9i	−0.779543	+	0.626349i
$257$	1.71181e9			0.392395			0.196198	−	0.980564i	$-0.437141\pi$
$257$	1.71181e9			0.392395			0.196198	+	0.980564i	$0.437141\pi$
$258$	2.31782e9	+	4.48155e9i	0.523120	+	1.01146i
$259$		−	1.05197e10i		−	2.33778i
$260$	−9.99758e8	+	1.41176e9i	−0.218777	+	0.308936i
$261$	7.39383e9			1.59334
$262$	4.87914e9	−	2.52345e9i	1.03547	−	0.535538i
$263$		−	2.50597e9i		−	0.523785i	−0.965097	−	0.261892i	$-0.915653\pi$
$263$		−	2.50597e9i		−	0.523785i	0.965097	−	0.261892i	$-0.0843465\pi$
$264$	7.13715e9	+	9.97603e8i	1.46930	+	0.205372i
$265$	1.53831e9			0.311933
$266$	1.32516e9	+	2.56223e9i	0.264693	+	0.511789i
$267$			4.22308e9i			0.830967i
$268$	8.07929e8	+	5.72145e8i	0.156615	+	0.110909i
$269$	3.62847e8			0.0692970			0.0346485	−	0.999400i	$-0.488969\pi$
$269$	3.62847e8			0.0692970			0.0346485	+	0.999400i	$0.488969\pi$
$270$	−4.30821e8	+	2.22817e8i	−0.0810666	+	0.0419270i
$271$		−	1.05662e10i		−	1.95903i	−0.201368	−	0.979516i	$-0.564539\pi$
$271$		−	1.05662e10i		−	1.95903i	0.201368	−	0.979516i	$-0.435461\pi$
$272$	−9.53236e8	−	2.70827e9i	−0.174151	−	0.494785i
$273$	−9.43069e9			−1.69782
$274$	−1.49606e9	−	2.89265e9i	−0.265428	−	0.513209i
$275$		−	1.24764e9i		−	0.218152i
$276$	−4.41515e9	+	6.23465e9i	−0.760867	+	1.07442i
$277$	−1.36227e9			−0.231390			−0.115695	−	0.993285i	$-0.536909\pi$
$277$	−1.36227e9			−0.231390			−0.115695	+	0.993285i	$0.536909\pi$
$278$	−3.57149e9	+	1.84715e9i	−0.597958	+	0.309259i
$279$			6.61506e9i			1.09173i
$280$	−5.61145e8	+	4.01460e9i	−0.0912942	+	0.653146i
$281$	−3.01499e9			−0.483572			−0.241786	−	0.970330i	$-0.577733\pi$
$281$	−3.01499e9			−0.483572			−0.241786	+	0.970330i	$0.577733\pi$
$282$	1.02814e7	+	1.98792e7i	0.00162575	+	0.00314342i
$283$			1.38220e9i			0.215490i	0.994179	+	0.107745i	$0.0343629\pi$
$283$			1.38220e9i			0.215490i	−0.994179	+	0.107745i	$0.965637\pi$
$284$	6.72094e9	+	4.75952e9i	1.03313	+	0.731627i
$285$	−1.56798e9			−0.237663
$286$	5.48703e9	−	2.83785e9i	0.820112	−	0.424156i
$287$			1.74228e10i			2.56797i
$288$	4.00744e9	−	4.25829e9i	0.582502	−	0.618964i
$289$	−5.05644e9			−0.724859
$290$	−2.72394e9	−	5.26679e9i	−0.385129	−	0.744653i
$291$			8.67304e9i			1.20948i
$292$	−2.83118e9	+	3.99793e9i	−0.389436	+	0.549925i
$293$	5.86750e9			0.796127			0.398064	−	0.917358i	$-0.369682\pi$
$293$	5.86750e9			0.796127			0.398064	+	0.917358i	$0.369682\pi$
$294$	−1.06026e10	+	5.48361e9i	−1.41914	+	0.733968i
$295$		−	1.86953e9i		−	0.246856i
$296$	1.20524e10	+	1.68463e9i	1.57002	+	0.219452i
$297$	1.73203e9			0.222602
$298$	−5.62310e9	−	1.08724e10i	−0.713035	−	1.37867i
$299$			6.54873e9i			0.819355i
$300$	−1.79818e9	−	1.27341e9i	−0.221998	−	0.157211i
$301$	1.01345e10			1.23463
$302$	7.28474e9	−	3.76761e9i	0.875762	−	0.452938i
$303$		−	1.28293e9i		−	0.152207i
$304$	−3.14775e9	+	1.10792e9i	−0.368558	+	0.129722i
$305$	7.00308e8			0.0809263
$306$	1.79573e9	+	3.47207e9i	0.204812	+	0.396007i
$307$		−	5.79386e9i		−	0.652250i	−0.945327	−	0.326125i	$-0.894257\pi$
$307$		−	5.79386e9i		−	0.652250i	0.945327	−	0.326125i	$-0.105743\pi$
$308$	8.36567e9	−	1.18132e10i	0.929603	−	1.31270i
$309$	−7.58601e9			−0.832107
$310$	4.71206e9	−	2.43704e9i	0.510227	−	0.263886i
$311$		−	8.37260e9i		−	0.894991i	−0.894286	−	0.447496i	$-0.852316\pi$
$311$		−	8.37260e9i		−	0.894991i	0.894286	−	0.447496i	$-0.147684\pi$
$312$	1.51024e9	−	1.08047e10i	0.159378	−	1.14024i
$313$	1.22771e10			1.27914			0.639572	−	0.768731i	$-0.279111\pi$
$313$	1.22771e10			1.27914			0.639572	+	0.768731i	$0.279111\pi$
$314$	−8.59764e9	−	1.66237e10i	−0.884424	−	1.71005i
$315$		−	5.51887e9i		−	0.560542i
$316$	1.11452e10	+	7.89263e9i	1.11774	+	0.791541i
$317$	−1.38443e10			−1.37099			−0.685495	−	0.728077i	$-0.740414\pi$
$317$	−1.38443e10			−1.37099			−0.685495	+	0.728077i	$0.740414\pi$
$318$	−8.61715e9	+	4.45672e9i	−0.842665	+	0.435820i
$319$			2.11740e10i			2.04475i
$320$	−4.50965e9	−	1.28580e9i	−0.430074	−	0.122624i
$321$	8.47972e9			0.798659
$322$	7.04948e9	+	1.36303e10i	0.655743	+	1.26789i
$323$		−	2.23077e9i		−	0.204948i
$324$	7.18091e9	−	1.01402e10i	0.651627	−	0.920167i
$325$	−1.88877e9			−0.169295
$326$	−1.24959e10	+	6.46281e9i	−1.10637	+	0.572204i
$327$		−	4.73165e8i		−	0.0413830i
$328$	−1.99612e10	−	2.79010e9i	−1.72461	−	0.241060i
$329$	4.49546e7			0.00383699
$330$	3.61461e9	+	6.98891e9i	0.304794	+	0.589323i
$331$			7.71740e9i			0.642923i	0.946923	+	0.321462i	$0.104174\pi$
$331$			7.71740e9i			0.642923i	−0.946923	+	0.321462i	$0.895826\pi$
$332$	1.30110e9	+	9.21389e8i	0.107092	+	0.0758386i
$333$	−1.65684e10			−1.34742
$334$	−6.58458e9	+	3.40549e9i	−0.529105	+	0.273649i
$335$			1.08091e9i			0.0858244i
$336$	−8.48754e9	−	2.41143e10i	−0.665924	−	1.89198i
$337$	−1.47787e10			−1.14582			−0.572910	−	0.819618i	$-0.694186\pi$
$337$	−1.47787e10			−1.14582			−0.572910	+	0.819618i	$0.694186\pi$
$338$	1.69966e9	+	3.28633e9i	0.130226	+	0.251793i
$339$		−	2.58139e10i		−	1.95459i
$340$	1.81167e9	−	2.55827e9i	0.135570	−	0.191439i
$341$	−1.89438e10			−1.40104
$342$	4.03548e9	−	2.08712e9i	0.294979	−	0.152561i
$343$			3.56527e9i			0.257582i
$344$	−1.62295e9	+	1.16111e10i	−0.115897	+	0.829161i
$345$	−8.34121e9			−0.588780
$346$	−3.46695e9	−	6.70341e9i	−0.241904	−	0.467726i
$347$		−	2.69899e10i		−	1.86158i	−0.365549	−	0.930792i	$-0.619119\pi$
$347$		−	2.69899e10i		−	1.86158i	0.365549	−	0.930792i	$-0.380881\pi$
$348$	3.05173e10	+	2.16112e10i	2.08080	+	1.47354i
$349$	2.02677e10			1.36617			0.683083	−	0.730340i	$-0.260639\pi$
$349$	2.02677e10			1.36617			0.683083	+	0.730340i	$0.260639\pi$
$350$	−3.93122e9	+	2.03320e9i	−0.261972	+	0.135490i
$351$		−	2.62206e9i		−	0.172748i
$352$	1.21947e10	+	1.14763e10i	0.794326	+	0.747534i
$353$	9.41747e9			0.606506			0.303253	−	0.952910i	$-0.401927\pi$
$353$	9.41747e9			0.606506			0.303253	+	0.952910i	$0.401927\pi$
$354$	5.41630e9	+	1.04725e10i	0.344897	+	0.666865i
$355$			8.99181e9i			0.566153i
$356$	−5.67119e9	+	8.00832e9i	−0.353081	+	0.498588i
$357$	1.70894e10			1.05210
$358$	1.18067e10	−	6.10633e9i	0.718780	−	0.371747i
$359$		−	3.30369e9i		−	0.198894i	−0.995043	−	0.0994469i	$-0.968293\pi$
$359$		−	3.30369e9i		−	0.198894i	0.995043	−	0.0994469i	$-0.0317073\pi$
$360$	6.32295e9	+	8.83798e8i	0.376452	+	0.0526190i
$361$	1.43908e10			0.847337
$362$	−4.55533e9	−	8.80780e9i	−0.265268	−	0.512900i
$363$		−	4.48141e9i		−	0.258100i
$364$	−1.78836e10	−	1.26645e10i	−1.01871	−	0.721412i
$365$	−5.34874e9			−0.301356
$366$	−3.92291e9	+	2.02890e9i	−0.218617	+	0.113067i
$367$			1.14531e10i			0.631335i	0.948870	+	0.315667i	$0.102228\pi$
$367$			1.14531e10i			0.631335i	−0.948870	+	0.315667i	$0.897772\pi$
$368$	−1.67451e10	+	5.89380e9i	−0.913053	+	0.321369i
$369$	2.74407e10			1.48009
$370$	6.10393e9	+	1.18021e10i	0.325689	+	0.629725i
$371$			1.94867e10i			1.02859i
$372$	−1.93350e10	+	2.73031e10i	−1.00965	+	1.42574i
$373$	2.26449e10			1.16986			0.584932	−	0.811083i	$-0.301121\pi$
$373$	2.26449e10			1.16986			0.584932	+	0.811083i	$0.301121\pi$
$374$	−9.94311e9	+	5.14250e9i	−0.508201	+	0.262838i
$375$		−	2.40575e9i		−	0.121654i
$376$	−7.19907e6	+	5.15043e7i	−0.000360184	+	0.00257687i
$377$	3.20547e10			1.58681
$378$	−2.82256e9	−	5.45746e9i	−0.138253	−	0.267315i
$379$		−	5.61760e9i		−	0.272266i	−0.990691	−	0.136133i	$-0.956533\pi$
$379$		−	5.61760e9i		−	0.272266i	0.990691	−	0.136133i	$-0.0434675\pi$
$380$	−2.97340e9	−	2.10565e9i	−0.142600	−	0.100984i
$381$	−3.24281e10			−1.53894
$382$	6.02607e8	−	3.11664e8i	0.0282996	−	0.0146364i
$383$			4.10535e9i			0.190790i	0.995440	+	0.0953950i	$0.0304114\pi$
$383$			4.10535e9i			0.190790i	−0.995440	+	0.0953950i	$0.969589\pi$
$384$	2.89868e10	−	5.86246e9i	1.33314	−	0.269622i
$385$	1.58046e10			0.719352
$386$	−3.09555e9	−	5.98530e9i	−0.139440	−	0.269610i
$387$		−	1.59618e10i		−	0.711602i
$388$	−1.16471e10	+	1.64469e10i	−0.513913	+	0.725699i
$389$	−1.37663e9			−0.0601199			−0.0300599	−	0.999548i	$-0.509570\pi$
$389$	−1.37663e9			−0.0601199			−0.0300599	+	0.999548i	$0.509570\pi$
$390$	1.05803e10	−	5.47205e9i	0.457340	−	0.236533i
$391$		−	1.18670e10i		−	0.507732i
$392$	−2.74700e10	−	3.83965e9i	−1.16336	−	0.162610i
$393$	−3.78234e10			−1.58559
$394$	1.42553e10	+	2.75629e10i	0.591551	+	1.14377i
$395$			1.49110e10i			0.612516i
$396$	−1.86057e10	−	1.31758e10i	−0.756597	−	0.535793i
$397$	−3.04208e10			−1.22464			−0.612321	−	0.790610i	$-0.709764\pi$
$397$	−3.04208e10			−1.22464			−0.612321	+	0.790610i	$0.709764\pi$
$398$	−3.00231e9	+	1.55277e9i	−0.119653	+	0.0618835i
$399$		−	1.98626e10i		−	0.783689i
$400$	−1.69988e9	−	4.82958e9i	−0.0664014	−	0.188655i
$401$	−1.95473e10			−0.755977			−0.377989	−	0.925810i	$-0.623384\pi$
$401$	−1.95473e10			−0.755977			−0.377989	+	0.925810i	$0.623384\pi$
$402$	−3.13156e9	−	6.05492e9i	−0.119910	−	0.231849i
$403$			2.86785e10i			1.08727i
$404$	1.72286e9	−	2.43286e9i	0.0646732	−	0.0913254i
$405$	1.35664e10			0.504247
$406$	6.67175e10	−	3.45058e10i	2.45548	−	1.26995i
$407$		−	4.74477e10i		−	1.72917i
$408$	−2.73672e9	+	1.95793e10i	−0.0987620	+	0.706573i
$409$	−4.37475e10			−1.56336			−0.781681	−	0.623678i	$-0.785638\pi$
$409$	−4.37475e10			−1.56336			−0.781681	+	0.623678i	$0.785638\pi$
$410$	−1.01094e10	−	1.95466e10i	−0.357757	−	0.691729i
$411$			2.24240e10i			0.785862i
$412$	−1.43855e10	−	1.01873e10i	−0.499271	−	0.353565i
$413$	2.36824e10			0.814002
$414$	2.14676e10	−	1.11029e10i	0.730772	−	0.377949i
$415$			1.74071e9i			0.0586860i
$416$	1.73736e10	−	1.84611e10i	0.580118	−	0.616431i
$417$	2.76865e10			0.915637
$418$	5.97697e9	+	1.15566e10i	0.195784	+	0.378551i
$419$			1.93115e10i			0.626555i	0.949662	+	0.313277i	$0.101427\pi$
$419$			1.93115e10i			0.626555i	−0.949662	+	0.313277i	$0.898573\pi$
$420$	1.61310e10	−	2.27786e10i	0.518398	−	0.732033i
$421$	−3.65545e10			−1.16362			−0.581812	−	0.813323i	$-0.697656\pi$
$421$	−3.65545e10			−1.16362			−0.581812	+	0.813323i	$0.697656\pi$
$422$	−2.86233e10	+	1.48038e10i	−0.902547	+	0.466791i
$423$		−	7.08030e7i		−	0.00221152i
$424$	−2.23259e10	−	3.12062e9i	−0.690788	−	0.0965557i
$425$	3.42266e9			0.104908
$426$	−2.60506e10	−	5.03693e10i	−0.791005	−	1.52942i
$427$			8.87121e9i			0.266853i
$428$	1.60803e10	+	1.13875e10i	0.479202	+	0.339353i
$429$	−4.25359e10			−1.25582
$430$	−1.13699e10	+	5.88043e9i	−0.332570	+	0.172003i
$431$		−	3.98669e10i		−	1.15532i	−0.816276	−	0.577662i	$-0.803965\pi$
$431$		−	3.98669e10i		−	1.15532i	0.816276	−	0.577662i	$-0.196035\pi$
$432$	6.70460e9	−	2.35983e9i	0.192503	−	0.0677557i
$433$	3.21564e10			0.914779			0.457389	−	0.889266i	$-0.348785\pi$
$433$	3.21564e10			0.914779			0.457389	+	0.889266i	$0.348785\pi$
$434$	3.08714e10	+	5.96904e10i	0.870157	+	1.68246i
$435$			4.08285e10i			1.14027i
$436$	6.35416e8	−	8.97275e8i	0.0175838	−	0.0248302i
$437$	−1.37927e10			−0.378201
$438$	2.99620e10	−	1.54961e10i	0.814093	−	0.421043i
$439$		−	2.72016e10i		−	0.732379i	−0.930540	−	0.366189i	$-0.880662\pi$
$439$		−	2.72016e10i		−	0.732379i	0.930540	−	0.366189i	$-0.119338\pi$
$440$	−2.53097e9	+	1.81073e10i	−0.0675268	+	0.483107i
$441$	3.77630e10			0.998418
$442$	7.78507e9	+	1.50526e10i	0.203973	+	0.394386i
$443$			1.32228e10i			0.343327i	0.985156	+	0.171663i	$0.0549142\pi$
$443$			1.32228e10i			0.343327i	−0.985156	+	0.171663i	$0.945086\pi$
$444$	−6.83846e10	−	4.84274e10i	−1.75965	−	1.24612i
$445$	−1.07142e10			−0.273224
$446$	1.28881e10	−	6.66564e9i	0.325724	−	0.168462i
$447$			8.42834e10i			2.11111i
$448$	1.62880e10	−	5.71264e10i	0.404349	−	1.41816i
$449$	2.82958e10			0.696203			0.348102	−	0.937457i	$-0.386826\pi$
$449$	2.82958e10			0.696203			0.348102	+	0.937457i	$0.386826\pi$
$450$	3.20226e9	+	6.19163e9i	0.0780920	+	0.150992i
$451$			7.85831e10i			1.89943i
$452$	3.46657e10	−	4.89516e10i	0.830512	−	1.17277i
$453$	−5.64718e10			−1.34103
$454$	−1.32350e9	+	6.84502e8i	−0.0311530	+	0.0161121i
$455$		−	2.39261e10i		−	0.558248i
$456$	2.27565e10	+	3.18081e9i	0.526315	+	0.0735662i
$457$	7.89688e10			1.81047			0.905234	−	0.424914i	$-0.139696\pi$
$457$	7.89688e10			1.81047			0.905234	+	0.424914i	$0.139696\pi$
$458$	3.80623e9	+	7.35942e9i	0.0865035	+	0.167256i
$459$			4.75146e9i			0.107047i
$460$	−1.58176e10	−	1.12015e10i	−0.353273	−	0.250174i
$461$	2.63713e10			0.583885			0.291943	−	0.956436i	$-0.405698\pi$
$461$	2.63713e10			0.583885			0.291943	+	0.956436i	$0.405698\pi$
$462$	−8.85326e10	+	4.57884e10i	−1.94328	+	1.00505i
$463$		−	2.74281e10i		−	0.596858i	−0.954432	−	0.298429i	$-0.903537\pi$
$463$		−	2.74281e10i		−	0.596858i	0.954432	−	0.298429i	$-0.0964627\pi$
$464$	2.88489e10	+	8.19638e10i	0.622383	+	1.76828i
$465$	−3.65282e10			−0.781297
$466$	8.85093e9	+	1.71134e10i	0.187692	+	0.362905i
$467$		−	8.24023e10i		−	1.73249i	−0.499616	−	0.866247i	$-0.666525\pi$
$467$		−	8.24023e10i		−	1.73249i	0.499616	−	0.866247i	$-0.333475\pi$
$468$	−1.99465e10	+	2.81665e10i	−0.415799	+	0.587151i
$469$	−1.36925e10			−0.283004
$470$	−5.04345e7	+	2.60843e7i	−0.00103356	+	0.000534550i
$471$			1.28868e11i			2.61855i
$472$	−3.79252e9	+	2.71328e10i	−0.0764118	+	0.546673i
$473$	4.57104e10			0.913209
$474$	−4.31993e10	−	8.35266e10i	−0.855782	−	1.65467i
$475$		−	3.97805e9i		−	0.0781441i
$476$	3.24071e10	+	2.29495e10i	0.631266	+	0.447039i
$477$	3.06914e10			0.592847
$478$	3.01415e10	−	1.55890e10i	0.577369	−	0.298611i
$479$		−	1.28142e10i		−	0.243415i	−0.992566	−	0.121708i	$-0.961163\pi$
$479$		−	1.28142e10i		−	0.243415i	0.992566	−	0.121708i	$-0.0388370\pi$
$480$	2.35142e10	+	2.21290e10i	0.442960	+	0.416866i
$481$	−7.18296e10			−1.34191
$482$	5.03819e9	+	9.74143e9i	0.0933441	+	0.180482i
$483$		−	1.05663e11i		−	1.94149i
$484$	6.01810e9	−	8.49820e9i	0.109668	−	0.154862i
$485$	−2.20039e10			−0.397680
$486$	−6.58817e10	+	3.40735e10i	−1.18092	+	0.610762i
$487$		−	2.27188e10i		−	0.403895i	−0.979396	−	0.201948i	$-0.935273\pi$
$487$		−	2.27188e10i		−	0.403895i	0.979396	−	0.201948i	$-0.0647271\pi$
$488$	−1.01637e10	−	1.42064e9i	−0.179215	−	0.0250499i
$489$	9.68695e10			1.69415
$490$	−1.39122e10	−	2.68995e10i	−0.241330	−	0.466615i
$491$		−	8.70411e10i		−	1.49761i	−0.662791	−	0.748805i	$-0.730628\pi$
$491$		−	8.70411e10i		−	1.49761i	0.662791	−	0.748805i	$-0.269372\pi$
$492$	1.13259e11	+	8.02057e10i	1.93291	+	1.36882i
$493$	−5.80866e10			−0.983305
$494$	1.74951e10	−	9.04835e9i	0.293772	−	0.151936i
$495$		−	2.48921e10i		−	0.414612i
$496$	−7.33308e10	+	2.58104e10i	−1.21160	+	0.426449i
$497$	−1.13904e11			−1.86688
$498$	−5.04310e9	−	9.75092e9i	−0.0819937	−	0.158536i
$499$		−	1.34972e10i		−	0.217691i	−0.994059	−	0.108846i	$-0.965285\pi$
$499$		−	1.34972e10i		−	0.217691i	0.994059	−	0.108846i	$-0.0347154\pi$
$500$	3.23070e9	−	4.56208e9i	0.0516911	−	0.0729933i
$501$	5.10441e10			0.810205
$502$	6.31313e10	−	3.26510e10i	0.994100	−	0.514141i
$503$			4.13249e10i			0.645565i	0.946473	+	0.322782i	$0.104618\pi$
$503$			4.13249e10i			0.645565i	−0.946473	+	0.322782i	$0.895382\pi$
$504$	−1.11956e10	+	8.00966e10i	−0.173510	+	1.24134i
$505$	3.25487e9			0.0500459
$506$	3.17957e10	+	6.14776e10i	0.485028	+	0.937810i
$507$		−	2.54759e10i		−	0.385564i
$508$	−6.14942e10	−	4.35479e10i	−0.923377	−	0.653901i
$509$	−3.37390e9			−0.0502645			−0.0251322	−	0.999684i	$-0.508001\pi$
$509$	−3.37390e9			−0.0502645			−0.0251322	+	0.999684i	$0.508001\pi$
$510$	−1.91727e10	+	9.91595e9i	−0.283401	+	0.146573i
$511$		−	6.77557e10i		−	0.993715i
$512$	6.28411e10	+	2.78094e10i	0.914458	+	0.404680i
$513$	5.52248e9			0.0797379
$514$	−1.25822e10	−	2.43279e10i	−0.180262	−	0.348539i
$515$		−	1.92461e10i		−	0.273598i
$516$	4.66542e10	−	6.58807e10i	0.658100	−	0.929307i
$517$	2.02761e8			0.00283807
$518$	−1.49504e11	+	7.73221e10i	−2.07650	+	1.07395i
$519$			5.19653e10i			0.716216i
$520$	2.74121e10	+	3.83156e9i	0.374912	+	0.0524037i
$521$	1.24497e11			1.68969			0.844847	−	0.535007i	$-0.179691\pi$
$521$	1.24497e11			1.68969			0.844847	+	0.535007i	$0.179691\pi$
$522$	−5.43462e10	−	1.05079e11i	−0.731960	−	1.41526i
$523$		−	4.47960e10i		−	0.598733i	−0.954138	−	0.299366i	$-0.903225\pi$
$523$		−	4.47960e10i		−	0.598733i	0.954138	−	0.299366i	$-0.0967753\pi$
$524$	−7.17254e10	−	5.07932e10i	−0.951367	−	0.673722i
$525$	3.04751e10			0.401151
$526$	−3.56142e10	+	1.84194e10i	−0.465244	+	0.240621i
$527$		−	5.19686e10i		−	0.673749i
$528$	−3.82819e10	−	1.08764e11i	−0.492558	−	1.39943i
$529$	4.93792e9			0.0630553
$530$	−1.13069e10	−	2.18622e10i	−0.143298	−	0.277070i
$531$		−	3.72995e10i		−	0.469165i
$532$	2.66735e10	−	3.76658e10i	0.332992	−	0.470220i
$533$	1.18964e11			1.47404
$534$	6.00174e10	−	3.10405e10i	0.738095	−	0.381737i
$535$			2.15135e10i			0.262601i
$536$	2.19274e9	−	1.56875e10i	0.0265661	−	0.190061i
$537$	−9.15263e10			−1.10065
$538$	−2.66700e9	−	5.15670e9i	−0.0318342	−	0.0615520i
$539$			1.08144e11i			1.28129i
$540$	6.33326e9	+	4.48497e9i	0.0744821	+	0.0527454i
$541$	−8.68526e10			−1.01390			−0.506948	−	0.861977i	$-0.669226\pi$
$541$	−8.68526e10			−1.01390			−0.506948	+	0.861977i	$0.669226\pi$
$542$	−1.50164e11	+	7.76638e10i	−1.74008	+	0.899957i
$543$			6.82787e10i			0.785391i
$544$	−3.14829e10	+	3.34536e10i	−0.359483	+	0.381985i
$545$	1.20044e9			0.0136068
$546$	6.93176e10	+	1.34027e11i	0.779961	+	1.50807i
$547$			1.65768e11i			1.85162i	0.377993	+	0.925808i	$0.376614\pi$
$547$			1.65768e11i			1.85162i	−0.377993	+	0.925808i	$0.623386\pi$
$548$	−3.01133e10	+	4.25232e10i	−0.333916	+	0.471524i
$549$	1.39721e10			0.153805
$550$	−1.77312e10	+	9.17045e9i	−0.193771	+	0.100217i
$551$			6.75124e10i			0.732448i
$552$	1.21058e11	+	1.69210e10i	1.30388	+	0.182251i
$553$	−1.88886e11			−2.01976
$554$	1.00130e10	+	1.93603e10i	0.106298	+	0.205529i
$555$		−	9.14903e10i		−	0.964280i
$556$	5.25025e10	+	3.71803e10i	0.549390	+	0.389057i
$557$	−9.73769e10			−1.01166			−0.505831	−	0.862633i	$-0.668814\pi$
$557$	−9.73769e10			−1.01166			−0.505831	+	0.862633i	$0.668814\pi$
$558$	9.40117e10	−	4.86221e10i	0.969717	−	0.501530i
$559$		−	6.91995e10i		−	0.708689i
$560$	6.11791e10	−	2.15333e10i	0.622087	−	0.218957i
$561$	7.70796e10			0.778195
$562$	2.21608e10	+	4.28484e10i	0.222147	+	0.429525i
$563$			1.96004e9i			0.0195088i	0.999952	+	0.00975440i	$0.00310497\pi$
$563$			1.96004e9i			0.0195088i	−0.999952	+	0.00975440i	$0.996895\pi$
$564$	2.06948e8	−	2.92233e8i	0.00204524	−	0.00288810i
$565$	6.54913e10			0.642673
$566$	1.96435e10	−	1.01595e10i	0.191405	−	0.0989934i
$567$			1.71853e11i			1.66274i
$568$	1.82408e10	−	1.30500e11i	0.175247	−	1.25377i
$569$	7.88598e10			0.752327			0.376164	−	0.926553i	$-0.377243\pi$
$569$	7.88598e10			0.752327			0.376164	+	0.926553i	$0.377243\pi$
$570$	1.15250e10	+	2.22838e10i	0.109180	+	0.211101i
$571$		−	5.71331e10i		−	0.537457i	−0.963216	−	0.268728i	$-0.913397\pi$
$571$		−	5.71331e10i		−	0.537457i	0.963216	−	0.268728i	$-0.0866034\pi$
$572$	−8.06617e10	−	5.71216e10i	−0.753500	−	0.533601i
$573$	−4.67145e9			−0.0433345
$574$	2.47608e11	−	1.28061e11i	2.28096	−	1.17970i
$575$		−	2.11621e10i		−	0.193592i
$576$	−8.99735e10	−	2.56535e10i	−0.817381	−	0.233054i
$577$	1.51459e11			1.36644			0.683221	−	0.730212i	$-0.260579\pi$
$577$	1.51459e11			1.36644			0.683221	+	0.730212i	$0.260579\pi$
$578$	3.71659e10	+	7.18610e10i	0.332992	+	0.643845i
$579$			4.63984e10i			0.412847i
$580$	−5.48288e10	+	7.74241e10i	−0.484503	+	0.684170i
$581$	−2.20506e10			−0.193516
$582$	1.23259e11	−	6.37487e10i	1.07430	−	0.555622i
$583$			8.78922e10i			0.760810i
$584$	7.76274e10	+	1.08505e10i	0.667365	+	0.0932817i
$585$	−3.76834e10			−0.321756
$586$	−4.31274e10	−	8.33875e10i	−0.365732	−	0.707148i
$587$			1.33645e11i			1.12564i	0.826580	+	0.562819i	$0.190283\pi$
$587$			1.33645e11i			1.12564i	−0.826580	+	0.562819i	$0.809717\pi$
$588$	1.55863e11	+	1.10377e11i	1.30387	+	0.923353i
$589$	−6.04015e10			−0.501865
$590$	−2.65693e10	+	1.37414e10i	−0.219266	+	0.113403i
$591$		−	2.13670e11i		−	1.75143i
$592$	−6.46460e10	−	1.83668e11i	−0.526326	−	1.49536i
$593$	−1.58419e11			−1.28112			−0.640558	−	0.767910i	$-0.721297\pi$
$593$	−1.58419e11			−1.28112			−0.640558	+	0.767910i	$0.721297\pi$
$594$	−1.27308e10	−	2.46152e10i	−0.102261	−	0.197723i
$595$			4.33568e10i			0.345931i
$596$	−1.13185e11	+	1.59829e11i	−0.897020	+	1.26669i
$597$	2.32741e10			0.183221
$598$	9.30690e10	−	4.81346e10i	0.727781	−	0.376403i
$599$			4.31245e10i			0.334978i	0.985874	+	0.167489i	$0.0535659\pi$
$599$			4.31245e10i			0.334978i	−0.985874	+	0.167489i	$0.946434\pi$
$600$	−4.88031e9	+	3.49152e10i	−0.0376567	+	0.269407i
$601$	4.15092e10			0.318160			0.159080	−	0.987266i	$-0.449147\pi$
$601$	4.15092e10			0.318160			0.159080	+	0.987266i	$0.449147\pi$
$602$	−7.44909e10	−	1.44029e11i	−0.567175	−	1.09664i
$603$			2.15656e10i			0.163114i
$604$	−1.07089e11	−	7.58363e10i	−0.804630	−	0.569809i
$605$	1.13696e10			0.0848637
$606$	−1.82328e10	+	9.42985e9i	−0.135195	+	0.0699221i
$607$		−	2.83174e10i		−	0.208592i	−0.994546	−	0.104296i	$-0.966741\pi$
$607$		−	2.83174e10i		−	0.208592i	0.994546	−	0.104296i	$-0.0332590\pi$
$608$	3.88821e10	+	3.65916e10i	0.284535	+	0.267773i
$609$	−5.17199e11			−3.76000
$610$	−5.14742e9	−	9.95262e9i	−0.0371766	−	0.0718816i
$611$		−	3.06954e8i		−	0.00220246i
$612$	3.61452e10	−	5.10409e10i	0.257659	−	0.363842i
$613$	2.40024e11			1.69986			0.849928	−	0.526899i	$-0.176645\pi$
$613$	2.40024e11			1.69986			0.849928	+	0.526899i	$0.176645\pi$
$614$	−8.23410e10	+	4.25861e10i	−0.579352	+	0.299636i
$615$			1.51527e11i			1.05923i
$616$	−2.29376e11	−	3.20613e10i	−1.59303	−	0.222668i
$617$	−1.16795e10			−0.0805904			−0.0402952	−	0.999188i	$-0.512830\pi$
$617$	−1.16795e10			−0.0805904			−0.0402952	+	0.999188i	$0.512830\pi$
$618$	5.57588e10	+	1.07811e11i	0.382260	+	0.739107i
$619$		−	2.19401e11i		−	1.49443i	−0.664583	−	0.747215i	$-0.731391\pi$
$619$		−	2.19401e11i		−	1.49443i	0.664583	−	0.747215i	$-0.268609\pi$
$620$	−6.92693e10	−	4.90539e10i	−0.468785	−	0.331976i
$621$	2.93780e10			0.197540
$622$	−1.18989e11	+	6.15404e10i	−0.794963	+	0.411149i
$623$		−	1.35723e11i		−	0.900948i
$624$	−1.64655e11	+	5.79537e10i	−1.08601	+	0.382246i
$625$	6.10352e9			0.0400000
$626$	−9.02396e10	−	1.74480e11i	−0.587624	−	1.13618i
$627$		−	8.95874e10i		−	0.579665i
$628$	−1.73057e11	+	2.44375e11i	−1.11263	+	1.57115i
$629$	1.30163e11			0.831544
$630$	−7.84330e10	+	4.05649e10i	−0.497893	+	0.257507i
$631$		−	2.35335e10i		−	0.148446i	−0.997242	−	0.0742230i	$-0.976352\pi$
$631$		−	2.35335e10i		−	0.148446i	0.997242	−	0.0742230i	$-0.0236477\pi$
$632$	3.02484e10	−	2.16406e11i	0.189598	−	1.35644i
$633$	2.21890e11			1.38205
$634$	1.01759e11	+	1.96752e11i	0.629817	+	1.21776i
$635$		−	8.22718e10i		−	0.506006i
$636$	1.26676e11	+	8.97071e10i	0.774222	+	0.548275i
$637$	1.63715e11			0.994332
$638$	3.00920e11	−	1.55634e11i	1.81622	−	0.939336i
$639$			1.79398e11i			1.07601i
$640$	1.48734e10	+	7.35410e10i	0.0886521	+	0.438339i
$641$	−8.47231e10			−0.501845			−0.250923	−	0.968007i	$-0.580734\pi$
$641$	−8.47231e10			−0.501845			−0.250923	+	0.968007i	$0.580734\pi$
$642$	−6.23278e10	−	1.20512e11i	−0.366895	−	0.709397i
$643$			2.37102e11i			1.38705i	0.720435	+	0.693523i	$0.243942\pi$
$643$			2.37102e11i			1.38705i	−0.720435	+	0.693523i	$0.756058\pi$
$644$	1.41895e11	−	2.00371e11i	0.824944	−	1.16491i
$645$	8.81404e10			0.509256
$646$	−3.17031e10	+	1.63966e10i	−0.182042	+	0.0941508i
$647$		−	2.88712e11i		−	1.64758i	−0.566892	−	0.823792i	$-0.691854\pi$
$647$		−	2.88712e11i		−	1.64758i	0.566892	−	0.823792i	$-0.308146\pi$
$648$	−1.96891e11	−	2.75207e10i	−1.11667	−	0.156084i
$649$	1.06816e11			0.602086
$650$	1.38829e10	+	2.68427e10i	0.0777724	+	0.150374i
$651$		−	4.62724e11i		−	2.57631i
$652$	1.83696e11	+	1.30086e11i	1.01650	+	0.719850i
$653$	7.01205e10			0.385649			0.192824	−	0.981233i	$-0.438235\pi$
$653$	7.01205e10			0.385649			0.192824	+	0.981233i	$0.438235\pi$
$654$	−6.72451e9	+	3.47787e9i	−0.0367578	+	0.0190109i
$655$		−	9.59600e10i		−	0.521345i
$656$	1.07067e11	+	3.04192e11i	0.578149	+	1.64260i
$657$	−1.06714e11			−0.572746
$658$	−3.30426e8	−	6.38884e8i	−0.00176267	−	0.00340815i
$659$			1.30280e11i			0.690774i	0.938460	+	0.345387i	$0.112252\pi$
$659$			1.30280e11i			0.690774i	−0.938460	+	0.345387i	$0.887748\pi$
$660$	7.27566e10	−	1.02740e11i	0.383439	−	0.541457i
$661$	−9.13098e10			−0.478312			−0.239156	−	0.970981i	$-0.576871\pi$
$661$	−9.13098e10			−0.478312			−0.239156	+	0.970981i	$0.576871\pi$
$662$	1.09678e11	−	5.67246e10i	0.571067	−	0.295352i
$663$		−	1.16688e11i		−	0.603912i
$664$	3.53121e9	−	2.52633e10i	0.0181656	−	0.129962i
$665$	5.03923e10			0.257678
$666$	1.21781e11	+	2.35466e11i	0.618991	+	1.19683i
$667$			3.59146e11i			1.81454i
$668$	9.67962e10	+	6.85474e10i	0.486130	+	0.344259i
$669$	−9.99097e10			−0.498773
$670$	1.53617e10	−	7.94493e9i	0.0762323	−	0.0394267i
$671$			4.00124e10i			0.197381i
$672$	−2.80321e11	+	2.97868e11i	−1.37461	+	1.46065i
$673$	−2.19105e11			−1.06805			−0.534026	−	0.845468i	$-0.679321\pi$
$673$	−2.19105e11			−1.06805			−0.534026	+	0.845468i	$0.679321\pi$
$674$	1.08627e11	+	2.10031e11i	0.526377	+	1.01776i
$675$			8.47313e9i			0.0408158i
$676$	3.42117e10	−	4.83105e10i	0.163828	−	0.231342i
$677$	−8.12354e10			−0.386715			−0.193357	−	0.981128i	$-0.561938\pi$
$677$	−8.12354e10			−0.386715			−0.193357	+	0.981128i	$0.561938\pi$
$678$	−3.66862e11	+	1.89738e11i	−1.73614	+	0.897916i
$679$		−	2.78737e11i		−	1.31134i
$680$	−4.96737e10	−	6.94320e9i	−0.232322	−	0.0324731i
$681$	1.02598e10			0.0477037
$682$	1.39241e11	+	2.69225e11i	0.643622	+	1.24445i
$683$			2.91761e11i			1.34074i	0.742028	+	0.670369i	$0.233864\pi$
$683$			2.91761e11i			1.34074i	−0.742028	+	0.670369i	$0.766136\pi$
$684$	−5.93233e10	−	4.20105e10i	−0.271020	−	0.191926i
$685$	−5.68909e10			−0.258393
$686$	5.06688e10	−	2.62055e10i	0.228794	−	0.118330i
$687$		−	5.70507e10i		−	0.256115i
$688$	1.76943e11	−	6.22789e10i	0.789732	−	0.277963i
$689$	1.33057e11			0.590421
$690$	6.13097e10	+	1.18543e11i	0.270479	+	0.522975i
$691$			1.35594e11i			0.594743i	0.954762	+	0.297371i	$0.0961100\pi$
$691$			1.35594e11i			0.594743i	−0.954762	+	0.297371i	$0.903890\pi$
$692$	−6.97845e10	+	9.85430e10i	−0.304323	+	0.429736i
$693$	3.15323e11			1.36717
$694$	−3.83574e11	+	1.98381e11i	−1.65353	+	0.855191i
$695$			7.02420e10i			0.301063i
$696$	8.28247e10	−	5.92552e11i	0.352958	−	2.52517i
$697$	−2.15577e11			−0.913420
$698$	−1.48972e11	−	2.88040e11i	−0.627601	−	1.21348i
$699$		−	1.32664e11i		−	0.555707i
$700$	5.77906e10	+	4.09251e10i	0.240694	+	0.170450i
$701$	1.48441e11			0.614725			0.307363	−	0.951592i	$-0.400554\pi$
$701$	1.48441e11			0.614725			0.307363	+	0.951592i	$0.400554\pi$
$702$	−3.72641e10	+	1.92727e10i	−0.153441	+	0.0793587i
$703$		−	1.51285e11i		−	0.619404i
$704$	7.34650e10	−	2.57661e11i	0.299082	−	1.04896i
$705$	3.90972e8			0.00158267
$706$	−6.92204e10	−	1.33839e11i	−0.278622	−	0.538720i
$707$			4.12314e10i			0.165025i
$708$	1.09022e11	−	1.53950e11i	0.433891	−	0.612700i
$709$	4.79726e11			1.89849			0.949245	−	0.314536i	$-0.101849\pi$
$709$	4.79726e11			1.89849			0.949245	+	0.314536i	$0.101849\pi$
$710$	1.27789e11	−	6.60917e10i	0.502877	−	0.260084i
$711$			2.97493e11i			1.16412i
$712$	1.55497e11	+	2.17347e10i	0.605064	+	0.0845735i
$713$	−3.21318e11			−1.24330
$714$	−1.25611e11	−	2.42871e11i	−0.483321	−	0.934508i
$715$		−	1.07916e11i		−	0.412915i
$716$	−1.73563e11	−	1.22911e11i	−0.660399	−	0.467669i
$717$	−2.33659e11			−0.884110
$718$	−4.69512e10	+	2.42828e10i	−0.176664	+	0.0913695i
$719$			4.02314e11i			1.50539i	0.658368	+	0.752696i	$0.271247\pi$
$719$			4.02314e11i			1.50539i	−0.658368	+	0.752696i	$0.728753\pi$
$720$	−3.39147e10	−	9.63564e10i	−0.126200	−	0.358551i
$721$	2.43801e11			0.902184
$722$	−1.05776e11	−	2.04519e11i	−0.389257	−	0.752635i
$723$		−	7.55163e10i		−	0.276368i
$724$	−9.16917e10	+	1.29478e11i	−0.333715	+	0.471241i
$725$	−1.03584e11			−0.374922
$726$	−6.36887e10	+	3.29393e10i	−0.229253	+	0.118568i
$727$		−	3.49293e11i		−	1.25041i	−0.780461	−	0.625204i	$-0.785016\pi$
$727$		−	3.49293e11i		−	1.25041i	0.780461	−	0.625204i	$-0.214984\pi$
$728$	−4.85366e10	+	3.47245e11i	−0.172800	+	1.23626i
$729$	1.92272e11			0.680777
$730$	3.93144e10	+	7.60151e10i	0.138440	+	0.267675i
$731$			1.25397e11i			0.439155i
$732$	5.76684e10	+	4.08386e10i	0.200860	+	0.142242i
$733$	−1.75651e11			−0.608464			−0.304232	−	0.952598i	$-0.598400\pi$
$733$	−1.75651e11			−0.608464			−0.304232	+	0.952598i	$0.598400\pi$
$734$	1.62769e11	−	8.41829e10i	0.560774	−	0.290028i
$735$			2.08526e11i			0.714516i
$736$	2.06841e11	+	1.94657e11i	0.704898	+	0.663373i
$737$	−6.17583e10			−0.209327
$738$	−2.01695e11	−	3.89981e11i	−0.679939	−	1.31467i
$739$			1.85701e11i			0.622640i	0.950305	+	0.311320i	$0.100771\pi$
$739$			1.85701e11i			0.622640i	−0.950305	+	0.311320i	$0.899229\pi$
$740$	1.22863e11	−	1.73495e11i	0.409726	−	0.578576i
$741$	−1.35624e11			−0.449844
$742$	2.76941e11	−	1.43232e11i	0.913632	−	0.472523i
$743$		−	2.85901e11i		−	0.938126i	−0.883165	−	0.469063i	$-0.844592\pi$
$743$		−	2.85901e11i		−	0.938126i	0.883165	−	0.469063i	$-0.155408\pi$
$744$	5.30141e11	+	7.41010e10i	1.73021	+	0.241842i
$745$	−2.13831e11			−0.694138
$746$	−1.66445e11	−	3.21824e11i	−0.537422	−	1.03911i
$747$			3.47295e10i			0.111536i
$748$	1.46168e11	+	1.03511e11i	0.466924	+	0.330658i
$749$	−2.72524e11			−0.865919
$750$	−3.41900e10	+	1.76828e10i	−0.108057	+	0.0558864i
$751$			6.18679e11i			1.94494i	0.233031	+	0.972469i	$0.425136\pi$
$751$			6.18679e11i			1.94494i	−0.233031	+	0.972469i	$0.574864\pi$
$752$	7.84881e8	−	2.76256e8i	0.00245433	−	0.000863854i
$753$	−4.89399e11			−1.52224
$754$	−2.35609e11	−	4.55554e11i	−0.728964	−	1.40946i
$755$		−	1.43272e11i		−	0.440934i
$756$	−5.68138e10	+	8.02271e10i	−0.173927	+	0.245603i
$757$	9.34034e10			0.284433			0.142216	−	0.989836i	$-0.454577\pi$
$757$	9.34034e10			0.284433			0.142216	+	0.989836i	$0.454577\pi$
$758$	−7.98360e10	+	4.12905e10i	−0.241836	+	0.125076i
$759$		−	4.76579e11i		−	1.43604i
$760$	−8.06988e9	+	5.77343e10i	−0.0241887	+	0.173053i
$761$	−3.21388e11			−0.958276			−0.479138	−	0.877740i	$-0.659051\pi$
$761$	−3.21388e11			−0.958276			−0.479138	+	0.877740i	$0.659051\pi$
$762$	2.38354e11	+	4.60861e11i	0.706971	+	1.36694i
$763$			1.52067e10i			0.0448681i
$764$	−8.85859e9	−	6.27332e9i	−0.0260011	−	0.0184130i
$765$	6.82865e10			0.199384
$766$	5.83443e10	−	3.01752e10i	0.169466	−	0.0876467i
$767$		−	1.61706e11i		−	0.467245i
$768$	−2.96375e11	−	3.68863e11i	−0.851916	−	1.06028i
$769$	2.44957e10			0.0700461			0.0350231	−	0.999387i	$-0.488850\pi$
$769$	2.44957e10			0.0700461			0.0350231	+	0.999387i	$0.488850\pi$
$770$	−1.16168e11	−	2.24612e11i	−0.330462	−	0.638954i
$771$			1.88591e11i			0.533709i
$772$	−6.23087e10	+	8.79865e10i	−0.175420	+	0.247712i
$773$	1.61194e11			0.451472			0.225736	−	0.974189i	$-0.427521\pi$
$773$	1.61194e11			0.451472			0.225736	+	0.974189i	$0.427521\pi$
$774$	−2.26845e11	+	1.17322e11i	−0.632070	+	0.326902i
$775$		−	9.26739e10i		−	0.256892i
$776$	3.19348e11	+	4.46372e10i	0.880678	+	0.123098i
$777$	1.15896e12			3.17969
$778$	1.01185e10	+	1.95643e10i	0.0276184	+	0.0534006i
$779$			2.50558e11i			0.680392i
$780$	−1.55535e11	−	1.10144e11i	−0.420193	−	0.297565i
$781$	−5.13751e11			−1.38086
$782$	−1.68651e11	+	8.72252e10i	−0.450986	+	0.233246i
$783$		−	1.43799e11i		−	0.382569i
$784$	1.47342e11	+	4.18620e11i	0.389999	+	1.10804i
$785$	−3.26945e11			−0.860985
$786$	2.78010e11	+	5.37538e11i	0.728401	+	1.40838i
$787$		−	4.76190e11i		−	1.24131i	−0.784083	−	0.620657i	$-0.786866\pi$
$787$		−	4.76190e11i		−	1.24131i	0.784083	−	0.620657i	$-0.213134\pi$
$788$	2.86938e11	−	4.05187e11i	0.744189	−	1.05087i
$789$	2.76084e11			0.712416
$790$	2.11911e11	−	1.09599e11i	0.544059	−	0.281383i
$791$			8.29617e11i			2.11920i
$792$	−5.04962e10	+	3.61265e11i	−0.128339	+	0.918174i
$793$	6.05735e10			0.153176
$794$	2.23600e11	+	4.32334e11i	0.562586	+	1.08777i
$795$			1.69477e11i			0.424270i
$796$	4.41352e10	+	3.12549e10i	0.109934	+	0.0778512i
$797$	−1.59422e11			−0.395107			−0.197553	−	0.980292i	$-0.563300\pi$
$797$	−1.59422e11			−0.395107			−0.197553	+	0.980292i	$0.563300\pi$
$798$	−2.82282e11	+	1.45994e11i	−0.696100	+	0.360018i
$799$			5.56235e8i			0.00136481i
$800$	−5.61424e10	+	5.96567e10i	−0.137066	+	0.145646i
$801$	−2.13762e11			−0.519278
$802$	1.43677e11	+	2.77801e11i	0.347287	+	0.671486i
$803$		−	3.05603e11i		−	0.735013i
$804$	−6.30335e10	+	8.90100e10i	−0.150851	+	0.213017i
$805$	2.68072e11			0.638364
$806$	4.07572e11	−	2.10793e11i	0.965748	−	0.499478i
$807$			3.99751e10i			0.0942530i
$808$	−4.72386e10	−	6.60283e9i	−0.110829	−	0.0154912i
$809$	−4.86253e11			−1.13519			−0.567594	−	0.823308i	$-0.692126\pi$
$809$	−4.86253e11			−1.13519			−0.567594	+	0.823308i	$0.692126\pi$
$810$	−9.97157e10	−	1.92802e11i	−0.231645	−	0.447890i
$811$		−	3.39760e11i		−	0.785396i	−0.919667	−	0.392698i	$-0.871542\pi$
$811$		−	3.39760e11i		−	0.785396i	0.919667	−	0.392698i	$-0.128458\pi$
$812$	−9.80776e11	−	6.94548e11i	−2.25603	−	1.59764i
$813$	1.16408e12			2.66454
$814$	−6.74315e11	+	3.48751e11i	−1.53591	+	0.794360i
$815$			2.45763e11i			0.557039i
$816$	2.98372e11	−	1.05019e11i	0.672973	−	0.236867i
$817$	1.45745e11			0.327120
$818$	3.21553e11	+	6.21729e11i	0.718191	+	1.38863i
$819$		−	4.77358e11i		−	1.06098i
$820$	−2.03486e11	+	2.87344e11i	−0.450069	+	0.635545i
$821$	6.74268e11			1.48409			0.742044	−	0.670351i	$-0.233856\pi$
$821$	6.74268e11			1.48409			0.742044	+	0.670351i	$0.233856\pi$
$822$	3.18685e11	−	1.64822e11i	0.698031	−	0.361016i
$823$			3.11660e11i			0.679332i	0.940546	+	0.339666i	$0.110314\pi$
$823$			3.11660e11i			0.679332i	−0.940546	+	0.339666i	$0.889686\pi$
$824$	−3.90426e10	+	2.79322e11i	−0.0846896	+	0.605894i
$825$	1.37454e11			0.296716
$826$	−1.74071e11	−	3.36569e11i	−0.373943	−	0.723026i
$827$			3.10210e11i			0.663183i	0.943423	+	0.331592i	$0.107586\pi$
$827$			3.10210e11i			0.663183i	−0.943423	+	0.331592i	$0.892414\pi$
$828$	−3.15583e11	−	2.23484e11i	−0.671416	−	0.475472i
$829$	−3.09076e11			−0.654406			−0.327203	−	0.944954i	$-0.606106\pi$
$829$	−3.09076e11			−0.654406			−0.327203	+	0.944954i	$0.606106\pi$
$830$	2.47386e10	−	1.27946e10i	0.0521270	−	0.0269597i
$831$		−	1.50082e11i		−	0.314720i
$832$	−3.90065e11	−	1.11216e11i	−0.814035	−	0.232100i
$833$	−2.96670e11			−0.616160
$834$	−2.03501e11	−	3.93473e11i	−0.420633	−	0.813301i
$835$			1.29502e11i			0.266397i
$836$	1.20307e11	−	1.69887e11i	0.246302	−	0.347804i
$837$	1.28653e11			0.262132
$838$	2.74450e11	−	1.41943e11i	0.556528	−	0.287832i
$839$		−	5.22492e11i		−	1.05446i	−0.849722	−	0.527232i	$-0.823230\pi$
$839$		−	5.22492e11i		−	1.05446i	0.849722	−	0.527232i	$-0.176770\pi$
$840$	−4.42291e11	−	6.18217e10i	−0.888364	−	0.124172i
$841$	1.25770e12			2.51416
$842$	2.68684e11	+	5.19504e11i	0.534556	+	1.03357i
$843$		−	3.32163e11i		−	0.657721i
$844$	4.20775e11	+	2.97977e11i	0.829240	+	0.587236i
$845$	6.46336e10			0.126774
$846$	−1.00624e9	+	5.20417e8i	−0.00196435	+	0.00101594i
$847$			1.44025e11i			0.279836i
$848$	1.19750e11	+	3.40227e11i	0.231576	+	0.657939i
$849$	−1.52278e11			−0.293094
$850$	−2.51573e10	−	4.86420e10i	−0.0481934	−	0.0931828i
$851$		−	8.04790e11i		−	1.53449i
$852$	−5.24359e11	+	7.40450e11i	−0.995108	+	1.40520i
$853$	−5.25270e11			−0.992171			−0.496086	−	0.868274i	$-0.665230\pi$
$853$	−5.25270e11			−0.992171			−0.496086	+	0.868274i	$0.665230\pi$
$854$	1.26076e11	−	6.52053e10i	0.237028	−	0.122589i
$855$		−	7.93674e10i		−	0.148518i
$856$	4.36422e10	−	3.12230e11i	0.0812853	−	0.581539i
$857$	3.18270e11			0.590028			0.295014	−	0.955493i	$-0.404676\pi$
$857$	3.18270e11			0.590028			0.295014	+	0.955493i	$0.404676\pi$
$858$	3.12648e11	+	6.04510e11i	0.576907	+	1.11546i
$859$		−	8.61467e11i		−	1.58222i	−0.611676	−	0.791108i	$-0.709504\pi$
$859$		−	8.61467e11i		−	1.58222i	0.611676	−	0.791108i	$-0.290496\pi$
$860$	1.67143e11	+	1.18364e11i	0.305558	+	0.216385i
$861$	−1.91948e12			−3.49277
$862$	−5.66579e11	+	2.93031e11i	−1.02620	+	0.530742i
$863$			1.40931e11i			0.254075i	0.991898	+	0.127038i	$0.0405469\pi$
$863$			1.40931e11i			0.254075i	−0.991898	+	0.127038i	$0.959453\pi$
$864$	−8.28176e10	−	7.79390e10i	−0.148617	−	0.139862i
$865$	−1.31839e11			−0.235493
$866$	−2.36357e11	−	4.57000e11i	−0.420239	−	0.812539i
$867$		−	5.57071e11i		−	0.985903i
$868$	6.21394e11	−	8.77474e11i	1.09468	−	1.54581i
$869$	−8.51945e11			−1.49394
$870$	5.80245e11	−	3.00098e11i	1.01283	−	0.523825i
$871$			9.34940e10i			0.162447i
$872$	−1.74223e10	−	2.43522e9i	−0.0301328	−	0.00421185i
$873$	−4.39008e11			−0.755814
$874$	1.01379e11	+	1.96018e11i	0.173741	+	0.335932i
$875$			7.73168e10i			0.131899i
$876$	−4.40454e11	−	3.11913e11i	−0.747970	−	0.529684i
$877$	−4.00362e11			−0.676790			−0.338395	−	0.941004i	$-0.609884\pi$
$877$	−4.00362e11			−0.676790			−0.338395	+	0.941004i	$0.609884\pi$
$878$	−3.86582e11	+	1.99937e11i	−0.650525	+	0.336447i
$879$			6.46426e11i			1.08284i
$880$	2.75940e11	−	9.71231e10i	0.460134	−	0.161954i
$881$	4.94890e11			0.821496			0.410748	−	0.911749i	$-0.365268\pi$
$881$	4.94890e11			0.821496			0.410748	+	0.911749i	$0.365268\pi$
$882$	−2.77567e11	−	5.36680e11i	−0.458662	−	0.886831i
$883$		−	7.88039e11i		−	1.29630i	−0.761513	−	0.648149i	$-0.775543\pi$
$883$		−	7.88039e11i		−	1.29630i	0.761513	−	0.648149i	$-0.224457\pi$
$884$	1.56701e11	−	2.21279e11i	0.256604	−	0.362353i
$885$	2.05967e11			0.335757
$886$	1.87919e11	−	9.71903e10i	0.304955	−	0.157720i
$887$			2.78785e10i			0.0450375i	0.999746	+	0.0225188i	$0.00716855\pi$
$887$			2.78785e10i			0.0450375i	−0.999746	+	0.0225188i	$0.992831\pi$
$888$	−1.85597e11	+	1.32782e12i	−0.298483	+	2.13544i
$889$	1.04218e12			1.66854
$890$	7.87514e10	+	1.52267e11i	0.125516	+	0.242687i
$891$			7.75120e11i			1.22987i
$892$	−1.89461e11	−	1.34169e11i	−0.299268	−	0.211930i
$893$	6.46496e8			0.00101662
$894$	1.19782e12	−	6.19501e11i	1.87517	−	0.969822i
$895$		−	2.32207e11i		−	0.361895i
$896$	−9.31587e11	+	1.88410e11i	−1.44541	+	0.292328i
$897$	−7.21478e11			−1.11443
$898$	−2.07980e11	−	4.02133e11i	−0.319828	−	0.618392i
$899$			1.57279e12i			2.40786i
$900$	6.44566e10	−	9.10196e10i	0.0982421	−	0.138728i
$901$	−2.41114e11			−0.365868
$902$	1.11680e12	−	5.77603e11i	1.68714	−	0.872576i
$903$			1.11653e12i			1.67926i
$904$	−9.50489e11	−	1.32856e11i	−1.42322	−	0.198933i
$905$	−1.73226e11			−0.258238
$906$	4.15080e11	+	8.02564e11i	0.616054	+	1.19115i
$907$			5.94476e11i			0.878426i	0.898383	+	0.439213i	$0.144743\pi$
$907$			5.94476e11i			0.878426i	−0.898383	+	0.439213i	$0.855257\pi$
$908$	1.94560e10	+	1.37780e10i	0.0286226	+	0.0202695i
$909$	6.49390e10			0.0951152
$910$	−3.40033e11	+	1.75862e11i	−0.495856	+	0.256453i
$911$		−	5.11180e11i		−	0.742165i	−0.928600	−	0.371082i	$-0.878987\pi$
$911$		−	5.11180e11i		−	0.742165i	0.928600	−	0.371082i	$-0.121013\pi$
$912$	−1.22060e11	−	3.46789e11i	−0.176439	−	0.501287i
$913$	−9.94564e10			−0.143136
$914$	−5.80438e11	−	1.12229e12i	−0.831708	−	1.60812i
$915$			7.71534e10i			0.110070i
$916$	7.66137e10	−	1.08187e11i	0.108824	−	0.153671i
$917$	1.21558e12			1.71912
$918$	6.75267e10	−	3.49243e10i	0.0950834	−	0.0491764i
$919$		−	7.89745e11i		−	1.10720i	−0.832784	−	0.553598i	$-0.813254\pi$
$919$		−	7.89745e11i		−	1.10720i	0.832784	−	0.553598i	$-0.186746\pi$
$920$	−4.29294e10	+	3.07130e11i	−0.0599244	+	0.428717i
$921$	6.38313e11			0.887146
$922$	−1.93835e11	−	3.74783e11i	−0.268230	−	0.518628i
$923$			7.77751e11i			1.07160i
$924$	1.30147e12	+	9.21650e11i	1.78544	+	1.26438i
$925$	2.32116e11			0.317057
$926$	−3.89801e11	+	2.01602e11i	−0.530151	+	0.274190i
$927$		−	3.83985e11i		−	0.519990i
$928$	9.52804e11	−	1.01245e12i	1.28473	−	1.36515i
$929$	1.28241e12			1.72172			0.860862	−	0.508839i	$-0.169925\pi$
$929$	1.28241e12			1.72172			0.860862	+	0.508839i	$0.169925\pi$
$930$	2.68490e11	+	5.19130e11i	0.358919	+	0.693976i
$931$			3.44811e11i			0.458968i
$932$	1.78156e11	−	2.51575e11i	0.236122	−	0.333429i
$933$	9.22414e11			1.21730
$934$	−1.17108e12	+	6.05675e11i	−1.53886	+	0.795888i
$935$			1.95555e11i			0.255872i
$936$	5.46907e11	+	7.64446e10i	0.712542	+	0.0995963i
$937$	−4.16365e11			−0.540152			−0.270076	−	0.962839i	$-0.587049\pi$
$937$	−4.16365e11			−0.540152			−0.270076	+	0.962839i	$0.587049\pi$
$938$	1.00643e11	+	1.94595e11i	0.130009	+	0.251374i
$939$			1.35258e12i			1.73980i
$940$	7.41409e8	+	5.25038e8i	0.000949613	+	0.000672480i
$941$	−1.33006e12			−1.69634			−0.848171	−	0.529723i	$-0.822296\pi$
$941$	−1.33006e12			−1.69634			−0.848171	+	0.529723i	$0.822296\pi$
$942$	1.83144e12	−	9.47207e11i	2.32589	−	1.20293i
$943$			1.33290e12i			1.68558i
$944$	4.13482e11	−	1.45534e11i	0.520677	−	0.183264i
$945$	−1.07334e11			−0.134589
$946$	−3.35981e11	−	6.49625e11i	−0.419518	−	0.811145i
$947$		−	1.36285e11i		−	0.169453i	−0.996404	−	0.0847265i	$-0.972998\pi$
$947$		−	1.36285e11i		−	0.169453i	0.996404	−	0.0847265i	$-0.0270017\pi$
$948$	−8.69536e11	+	1.22788e12i	−1.07660	+	1.52027i
$949$	−4.62642e11			−0.570401
$950$	−5.65352e10	+	2.92396e10i	−0.0694104	+	0.0358985i
$951$		−	1.52524e12i		−	1.86473i
$952$	8.79536e10	−	6.29246e11i	0.107079	−	0.766078i
$953$	1.22326e12			1.48302			0.741509	−	0.670943i	$-0.234111\pi$
$953$	1.22326e12			1.48302			0.741509	+	0.670943i	$0.234111\pi$
$954$	−2.25588e11	−	4.36179e11i	−0.272347	−	0.526588i
$955$		−	1.18517e10i		−	0.0142485i
$956$	−4.43093e11	−	3.13782e11i	−0.530473	−	0.375661i
$957$	−2.33275e12			−2.78113
$958$	−1.82112e11	+	9.41868e10i	−0.216210	+	0.111822i
$959$		−	7.20671e11i		−	0.852045i
$960$	1.41658e11	−	4.96831e11i	0.166784	−	0.584957i
$961$	−5.54240e11			−0.649837
$962$	5.27963e11	+	1.02083e12i	0.616457	+	1.19193i
$963$			4.29222e11i			0.499088i
$964$	1.01411e11	−	1.43203e11i	0.117430	−	0.165823i
$965$	−1.17715e11			−0.135745
$966$	−1.50166e12	+	7.76646e11i	−1.72450	+	0.891897i
$967$			7.99217e10i			0.0914027i	0.998955	+	0.0457014i	$0.0145523\pi$
$967$			7.99217e10i			0.0914027i	−0.998955	+	0.0457014i	$0.985448\pi$
$968$	−1.65009e11	−	2.30643e10i	−0.187934	−	0.0262687i
$969$	2.45765e11			0.278756
$970$	1.61734e11	+	3.12715e11i	0.182690	+	0.353233i
$971$			3.43166e11i			0.386036i	0.981195	+	0.193018i	$0.0618276\pi$
$971$			3.43166e11i			0.386036i	−0.981195	+	0.193018i	$0.938172\pi$
$972$	9.68490e11	+	6.85848e11i	1.08500	+	0.768356i
$973$	−8.89796e11			−0.992748
$974$	−3.22874e11	+	1.66988e11i	−0.358754	+	0.185545i
$975$		−	2.08087e11i		−	0.230264i
$976$	5.45156e10	+	1.54886e11i	0.0600789	+	0.170692i
$977$	−2.96831e11			−0.325785			−0.162893	−	0.986644i	$-0.552082\pi$
$977$	−2.96831e11			−0.325785			−0.162893	+	0.986644i	$0.552082\pi$
$978$	−7.12011e11	−	1.37669e12i	−0.778272	−	1.50480i
$979$		−	6.12158e11i		−	0.666397i
$980$	−2.80031e11	+	3.95434e11i	−0.303600	+	0.428716i
$981$	2.39505e10			0.0258605
$982$	−1.23701e12	+	6.39771e11i	−1.33023	+	0.687984i
$983$		−	9.12247e11i		−	0.977009i	−0.872561	−	0.488504i	$-0.837543\pi$
$983$		−	9.12247e11i		−	0.977009i	0.872561	−	0.488504i	$-0.162457\pi$
$984$	3.07387e11	−	2.19914e12i	0.327873	−	2.34570i
$985$	5.42091e11			0.575873
$986$	4.26949e11	+	8.25513e11i	0.451719	+	0.873407i
$987$			4.95267e9i			0.00521880i
$988$	−2.57186e11	−	1.82130e11i	−0.269911	−	0.191140i
$989$	7.75323e11			0.810396
$990$	−3.53761e11	+	1.82963e11i	−0.368273	+	0.190468i
$991$		−	9.63646e11i		−	0.999132i	−0.866276	−	0.499566i	$-0.833493\pi$
$991$		−	9.63646e11i		−	0.999132i	0.866276	−	0.499566i	$-0.166507\pi$
$992$	9.05808e11	+	8.52449e11i	0.935383	+	0.880281i
$993$	−8.50231e11			−0.874460
$994$	8.37223e11	+	1.61878e12i	0.857621	+	1.65822i
$995$			5.90475e10i			0.0602434i
$996$	−1.01510e11	+	1.43343e11i	−0.103150	+	0.145659i
$997$	−1.13678e12			−1.15052			−0.575261	−	0.817970i	$-0.695100\pi$
$997$	−1.13678e12			−1.15052			−0.575261	+	0.817970i	$0.695100\pi$
$998$	−1.91819e11	+	9.92073e10i	−0.193361	+	0.100005i
$999$			3.22232e11i			0.323524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.5	✓	16
3.2	odd	2		180.9.c.a.91.12		16
4.3	odd	2	inner	20.9.b.a.11.6	yes	16
5.2	odd	4		100.9.d.c.99.27		32
5.3	odd	4		100.9.d.c.99.6		32
5.4	even	2		100.9.b.d.51.12		16
8.3	odd	2		320.9.b.d.191.14		16
8.5	even	2		320.9.b.d.191.3		16
12.11	even	2		180.9.c.a.91.11		16
20.3	even	4		100.9.d.c.99.28		32
20.7	even	4		100.9.d.c.99.5		32
20.19	odd	2		100.9.b.d.51.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.5	✓	16	1.1	even	1	trivial
20.9.b.a.11.6	yes	16	4.3	odd	2	inner
100.9.b.d.51.11		16	20.19	odd	2
100.9.b.d.51.12		16	5.4	even	2
100.9.d.c.99.5		32	20.7	even	4
100.9.d.c.99.6		32	5.3	odd	4
100.9.d.c.99.27		32	5.2	odd	4
100.9.d.c.99.28		32	20.3	even	4
180.9.c.a.91.11		16	12.11	even	2
180.9.c.a.91.12		16	3.2	odd	2
320.9.b.d.191.3		16	8.5	even	2
320.9.b.d.191.14		16	8.3	odd	2

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.35022 - 14.2118i) q^{2} +110.171i q^{3} +(-147.949 + 208.919i) q^{4} -279.508 q^{5} +(1565.72 - 809.778i) q^{6} -3540.70i q^{7} +(4056.56 + 567.011i) q^{8} -5576.56 q^{9} +O(q^{10})\)	\(q+(-7.35022 - 14.2118i) q^{2} +110.171i q^{3} +(-147.949 + 208.919i) q^{4} -279.508 q^{5} +(1565.72 - 809.778i) q^{6} -3540.70i q^{7} +(4056.56 + 567.011i) q^{8} -5576.56 q^{9} +(2054.45 + 3972.31i) q^{10} -15969.8i q^{11} +(-23016.7 - 16299.6i) q^{12} -24176.2 q^{13} +(-50319.6 + 26024.9i) q^{14} -30793.6i q^{15} +(-21758.4 - 61818.6i) q^{16} +43810.0 q^{17} +(40988.9 + 79252.8i) q^{18} -50919.1i q^{19} +(41352.9 - 58394.7i) q^{20} +390081. q^{21} +(-226960. + 117382. i) q^{22} -270875. i q^{23} +(-62467.9 + 446914. i) q^{24} +78125.0 q^{25} +(177701. + 343587. i) q^{26} +108456. i q^{27} +(739720. + 523841. i) q^{28} -1.32588e6 q^{29} +(-437632. + 226340. i) q^{30} -1.18623e6i q^{31} +(-718623. + 763605. i) q^{32} +1.75941e6 q^{33} +(-322013. - 622618. i) q^{34} +989655. i q^{35} +(825045. - 1.16505e6i) q^{36} +2.97108e6 q^{37} +(-723650. + 374266. i) q^{38} -2.66351e6i q^{39} +(-1.13384e6 - 158484. i) q^{40} -4.92072e6 q^{41} +(-2.86718e6 - 5.54374e6i) q^{42} +2.86229e6i q^{43} +(3.33641e6 + 2.36272e6i) q^{44} +1.55870e6 q^{45} +(-3.84961e6 + 1.99099e6i) q^{46} +12696.5i q^{47} +(6.81059e6 - 2.39714e6i) q^{48} -6.77174e6 q^{49} +(-574236. - 1.11029e6i) q^{50} +4.82658e6i q^{51} +(3.57684e6 - 5.05088e6i) q^{52} -5.50364e6 q^{53} +(1.54135e6 - 797176. i) q^{54} +4.46371e6i q^{55} +(2.00761e6 - 1.43631e7i) q^{56} +5.60979e6 q^{57} +(9.74547e6 + 1.88430e7i) q^{58} +6.68863e6i q^{59} +(6.43338e6 + 4.55587e6i) q^{60} -2.50550e6 q^{61} +(-1.68584e7 + 8.71902e6i) q^{62} +1.97449e7i q^{63} +(1.61342e7 + 4.60023e6i) q^{64} +6.75746e6 q^{65} +(-1.29320e7 - 2.50043e7i) q^{66} -3.86718e6i q^{67} +(-6.48163e6 + 9.15275e6i) q^{68} +2.98424e7 q^{69} +(1.40647e7 - 7.27418e6i) q^{70} -3.21701e7i q^{71} +(-2.26217e7 - 3.16197e6i) q^{72} +1.91362e7 q^{73} +(-2.18381e7 - 4.22243e7i) q^{74} +8.60708e6i q^{75} +(1.06380e7 + 7.53341e6i) q^{76} -5.65444e7 q^{77} +(-3.78532e7 + 1.95774e7i) q^{78} -5.33471e7i q^{79} +(6.08166e6 + 1.72788e7i) q^{80} -4.85365e7 q^{81} +(3.61683e7 + 6.99321e7i) q^{82} -6.22776e6i q^{83} +(-5.77119e7 + 8.14954e7i) q^{84} -1.22453e7 q^{85} +(4.06782e7 - 2.10385e7i) q^{86} -1.46072e8i q^{87} +(9.05507e6 - 6.47827e7i) q^{88} +3.83322e7 q^{89} +(-1.14568e7 - 2.21518e7i) q^{90} +8.56008e7i q^{91} +(5.65909e7 + 4.00755e7i) q^{92} +1.30687e8 q^{93} +(180440. - 93322.2i) q^{94} +1.42323e7i q^{95} +(-8.41269e7 - 7.91711e7i) q^{96} +7.87237e7 q^{97} +(4.97738e7 + 9.62384e7i) q^{98} +8.90568e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

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