LMFDB - Embedded newform 38.10.c.b.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, 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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} - 2 x^{15} + 104960 x^{14} - 3899480 x^{13} + 8040649724 x^{12} - 270026959304 x^{11} + \cdots + 13\!\cdots\!00 $ x^16 - 2x^15 + 104960x^14 - 3899480x^13 + 8040649724x^12 - 270026959304x^11 + 275078771318560x^10 - 7559006944968384x^9 + 6786319237849450512x^8 - 132172428275143142112x^7 + 58413131602192832245632x^6 + 306187936352529387788160x^5 + 338231098965100183334201088x^4 + 833605976716998105836915712x^3 + 801869139824974932731497058304x^2 + 7085244797393532409215050711040*x + 1344731733940407880332419688038400
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.5
Root			$-24.6030 + 42.6137i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.10.c.b.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 + 13.8564i) q^{2} +(29.1030 - 50.4079i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1358.85 + 2353.60i) q^{5} +(465.648 + 806.526i) q^{6} +3587.38 q^{7} +4096.00 q^{8} +(8147.53 + 14111.9i) q^{9} +O(q^{10})$	\(q+(-8.00000 + 13.8564i) q^{2} +(29.1030 - 50.4079i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1358.85 + 2353.60i) q^{5} +(465.648 + 806.526i) q^{6} +3587.38 q^{7} +4096.00 q^{8} +(8147.53 + 14111.9i) q^{9} +(-21741.6 - 37657.5i) q^{10} +20369.8 q^{11} -14900.7 q^{12} +(-61465.3 - 106461. i) q^{13} +(-28699.0 + 49708.2i) q^{14} +(79093.2 + 136993. i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(-202409. + 350582. i) q^{17} -260721. q^{18} +(-489149. + 288827. i) q^{19} +695731. q^{20} +(104404. - 180832. i) q^{21} +(-162959. + 282253. i) q^{22} +(-847122. - 1.46726e6i) q^{23} +(119206. - 206471. i) q^{24} +(-2.71638e6 - 4.70491e6i) q^{25} +1.96689e6 q^{26} +2.09414e6 q^{27} +(-459185. - 795331. i) q^{28} +(-1.13343e6 - 1.96316e6i) q^{29} -2.53098e6 q^{30} -7.59798e6 q^{31} +(-524288. - 908093. i) q^{32} +(592823. - 1.02680e6i) q^{33} +(-3.23854e6 - 5.60932e6i) q^{34} +(-4.87471e6 + 8.44325e6i) q^{35} +(2.08577e6 - 3.61266e6i) q^{36} +1.05364e7 q^{37} +(-88916.9 - 9.08846e6i) q^{38} -7.15531e6 q^{39} +(-5.56585e6 + 9.64033e6i) q^{40} +(1.35987e7 - 2.35537e7i) q^{41} +(1.67046e6 + 2.89332e6i) q^{42} +(-1.11895e7 + 1.93808e7i) q^{43} +(-2.60734e6 - 4.51604e6i) q^{44} -4.42851e7 q^{45} +2.71079e7 q^{46} +(2.05030e7 + 3.55122e7i) q^{47} +(1.90729e6 + 3.30353e6i) q^{48} -2.74843e7 q^{49} +8.69242e7 q^{50} +(1.17814e7 + 2.04060e7i) q^{51} +(-1.57351e7 + 2.72540e7i) q^{52} +(-1.12164e7 - 1.94274e7i) q^{53} +(-1.67531e7 + 2.90172e7i) q^{54} +(-2.76795e7 + 4.79424e7i) q^{55} +1.46939e7 q^{56} +(323469. + 3.30627e7i) q^{57} +3.62697e7 q^{58} +(2.23466e7 - 3.87055e7i) q^{59} +(2.02479e7 - 3.50703e7i) q^{60} +(-3.80863e7 - 6.59675e7i) q^{61} +(6.07838e7 - 1.05281e8i) q^{62} +(2.92283e7 + 5.06249e7i) q^{63} +1.67772e7 q^{64} +3.34089e8 q^{65} +(9.48517e6 + 1.64288e7i) q^{66} +(-3.18209e7 - 5.51153e7i) q^{67} +1.03633e8 q^{68} -9.86151e7 q^{69} +(-7.79954e7 - 1.35092e8i) q^{70} +(-1.76962e8 + 3.06508e8i) q^{71} +(3.33723e7 + 5.78025e7i) q^{72} +(-1.16149e8 + 2.01176e8i) q^{73} +(-8.42915e7 + 1.45997e8i) q^{74} -3.16220e8 q^{75} +(1.26645e8 + 7.14756e7i) q^{76} +7.30743e7 q^{77} +(5.72424e7 - 9.91468e7i) q^{78} +(1.24372e8 - 2.15419e8i) q^{79} +(-8.90536e7 - 1.54245e8i) q^{80} +(-9.94221e7 + 1.72204e8i) q^{81} +(2.17579e8 + 3.76858e8i) q^{82} -1.03989e7 q^{83} -5.34546e7 q^{84} +(-5.50086e8 - 9.52777e8i) q^{85} +(-1.79033e8 - 3.10093e8i) q^{86} -1.31945e8 q^{87} +8.34348e7 q^{88} +(2.35426e8 + 4.07770e8i) q^{89} +(3.54281e8 - 6.13632e8i) q^{90} +(-2.20500e8 - 3.81916e8i) q^{91} +(-2.16863e8 + 3.75618e8i) q^{92} +(-2.21124e8 + 3.82998e8i) q^{93} -6.56094e8 q^{94} +(-1.51031e7 - 1.54373e9i) q^{95} -6.10334e7 q^{96} +(7.33534e7 - 1.27052e8i) q^{97} +(2.19875e8 - 3.80834e8i) q^{98} +(1.65964e8 + 2.87458e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) $ 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9 - 5456 * q^10 + 106682 * q^11 - 35840 * q^12 - 683 * q^13 - 29632 * q^14 + 2299 * q^15 - 524288 * q^16 - 611267 * q^17 + 1698048 * q^18 - 1609677 * q^19 + 174592 * q^20 - 941048 * q^21 - 853456 * q^22 - 416119 * q^23 + 286720 * q^24 - 3309027 * q^25 + 21856 * q^26 - 16903604 * q^27 - 474112 * q^28 - 5079157 * q^29 - 73568 * q^30 + 8618324 * q^31 - 8388608 * q^32 - 7592195 * q^33 - 9780272 * q^34 - 2035632 * q^35 - 13584384 * q^36 - 33091520 * q^37 + 18612624 * q^38 + 37931126 * q^39 - 1396736 * q^40 - 7394646 * q^41 - 15056768 * q^42 - 98675599 * q^43 - 13655296 * q^44 + 89231852 * q^45 + 13315808 * q^46 + 34129475 * q^47 + 4587520 * q^48 + 65004400 * q^49 + 105888864 * q^50 + 16027749 * q^51 - 174848 * q^52 - 110053995 * q^53 + 135228832 * q^54 + 135992300 * q^55 + 15171584 * q^56 + 14986101 * q^57 + 162533024 * q^58 - 2017760 * q^59 + 588544 * q^60 - 221861413 * q^61 - 68946592 * q^62 + 56812456 * q^63 + 268435456 * q^64 + 262635974 * q^65 - 121475120 * q^66 + 237580440 * q^67 + 312968704 * q^68 - 135348410 * q^69 - 32570112 * q^70 - 431190909 * q^71 - 217350144 * q^72 + 199873544 * q^73 + 264732160 * q^74 - 1822944486 * q^75 + 114275328 * q^76 + 2014342624 * q^77 - 303449008 * q^78 - 296762835 * q^79 - 22347776 * q^80 - 1069077456 * q^81 - 118314336 * q^82 + 1592138306 * q^83 + 481816576 * q^84 - 293558115 * q^85 - 1578809584 * q^86 - 1647860854 * q^87 + 436969472 * q^88 - 444394631 * q^89 - 713854816 * q^90 - 284099544 * q^91 - 106526464 * q^92 + 1322110374 * q^93 - 1092143200 * q^94 + 8705459 * q^95 - 146800640 * q^96 - 611719542 * q^97 - 520035200 * q^98 + 1201848626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$	29.1030	−	50.4079i	0.207440	−	0.359296i	−0.743467	−	0.668772i	$-0.766820\pi$
$3$	29.1030	−	50.4079i	0.207440	−	0.359296i	0.950907	+	0.309476i	$0.100154\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−1358.85	+	2353.60i	−0.972314	+	1.68410i	−0.283785	+	0.958888i	$0.591590\pi$
$5$	−1358.85	+	2353.60i	−0.972314	+	1.68410i	−0.688529	+	0.725209i	$0.741743\pi$
$6$	465.648	+	806.526i	0.146682	+	0.254061i
$7$	3587.38			0.564724			0.282362	−	0.959308i	$-0.408882\pi$
$7$	3587.38			0.564724			0.282362	+	0.959308i	$0.408882\pi$
$8$	4096.00			0.353553
$9$	8147.53	+	14111.9i	0.413937	+	0.716961i
$10$	−21741.6	−	37657.5i	−0.687530	−	1.19084i
$11$	20369.8			0.419489			0.209744	−	0.977756i	$-0.432737\pi$
$11$	20369.8			0.419489			0.209744	+	0.977756i	$0.432737\pi$
$12$	−14900.7			−0.207440
$13$	−61465.3	−	106461.i	−0.596878	−	1.03382i	−0.993279	−	0.115745i	$-0.963074\pi$
$13$	−61465.3	−	106461.i	−0.596878	−	1.03382i	0.396401	−	0.918077i	$-0.370259\pi$
$14$	−28699.0	+	49708.2i	−0.199660	+	0.345821i
$15$	79093.2	+	136993.i	0.403393	+	0.698698i
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−202409.	+	350582.i	−0.587772	+	1.01805i	0.406751	+	0.913539i	$0.366662\pi$
$17$	−202409.	+	350582.i	−0.587772	+	1.01805i	−0.994524	+	0.104513i	$0.966672\pi$
$18$	−260721.			−0.585396
$19$	−489149.	+	288827.i	−0.861092	+	0.508448i
$19$	−489149.	+	288827.i	−0.861092	+	0.508448i
$20$	695731.			0.972314
$21$	104404.	−	180832.i	0.117146	−	0.202903i
$22$	−162959.	+	282253.i	−0.148312	+	0.256883i
$23$	−847122.	−	1.46726e6i	−0.631205	−	1.09328i	−0.987306	−	0.158832i	$-0.949227\pi$
$23$	−847122.	−	1.46726e6i	−0.631205	−	1.09328i	0.356101	−	0.934448i	$-0.384106\pi$
$24$	119206.	−	206471.i	0.0733411	−	0.127030i
$25$	−2.71638e6	−	4.70491e6i	−1.39079	−	2.40892i
$26$	1.96689e6			0.844112
$27$	2.09414e6			0.758348
$28$	−459185.	−	795331.i	−0.141181	−	0.244533i
$29$	−1.13343e6	−	1.96316e6i	−0.297580	−	0.515423i	0.678002	−	0.735060i	$-0.262846\pi$
$29$	−1.13343e6	−	1.96316e6i	−0.297580	−	0.515423i	−0.975582	+	0.219637i	$0.929513\pi$
$30$	−2.53098e6			−0.570484
$31$	−7.59798e6			−1.47765			−0.738823	−	0.673900i	$-0.764618\pi$
$31$	−7.59798e6			−1.47765			−0.738823	+	0.673900i	$0.764618\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$	592823.	−	1.02680e6i	0.0870187	−	0.150721i
$34$	−3.23854e6	−	5.60932e6i	−0.415618	−	0.719871i
$35$	−4.87471e6	+	8.44325e6i	−0.549089	+	0.951050i
$36$	2.08577e6	−	3.61266e6i	0.206969	−	0.358480i
$37$	1.05364e7			0.924242			0.462121	−	0.886817i	$-0.347089\pi$
$37$	1.05364e7			0.924242			0.462121	+	0.886817i	$0.347089\pi$
$38$	−88916.9	−	9.08846e6i	−0.00691764	−	0.707073i
$39$	−7.15531e6			−0.495265
$40$	−5.56585e6	+	9.64033e6i	−0.343765	+	0.595418i
$41$	1.35987e7	−	2.35537e7i	0.751572	−	1.30176i	−0.195489	−	0.980706i	$-0.562629\pi$
$41$	1.35987e7	−	2.35537e7i	0.751572	−	1.30176i	0.947061	−	0.321054i	$-0.104037\pi$
$42$	1.67046e6	+	2.89332e6i	0.0828349	+	0.143474i
$43$	−1.11895e7	+	1.93808e7i	−0.499119	+	0.864499i	−0.999999	−	0.00101725i	$-0.999676\pi$
$43$	−1.11895e7	+	1.93808e7i	−0.499119	+	0.864499i	0.500881	+	0.865516i	$0.333010\pi$
$44$	−2.60734e6	−	4.51604e6i	−0.104872	−	0.181644i
$45$	−4.42851e7			−1.60991
$46$	2.71079e7			0.892659
$47$	2.05030e7	+	3.55122e7i	0.612881	+	1.06154i	0.990752	+	0.135683i	$0.0433228\pi$
$47$	2.05030e7	+	3.55122e7i	0.612881	+	1.06154i	−0.377872	+	0.925858i	$0.623344\pi$
$48$	1.90729e6	+	3.30353e6i	0.0518600	+	0.0898241i
$49$	−2.74843e7			−0.681087
$50$	8.69242e7			1.96687
$51$	1.17814e7	+	2.04060e7i	0.243855	+	0.422369i
$52$	−1.57351e7	+	2.72540e7i	−0.298439	+	0.516911i
$53$	−1.12164e7	−	1.94274e7i	−0.195260	−	0.338200i	0.751726	−	0.659476i	$-0.229222\pi$
$53$	−1.12164e7	−	1.94274e7i	−0.195260	−	0.338200i	−0.946986	+	0.321276i	$0.895888\pi$
$54$	−1.67531e7	+	2.90172e7i	−0.268117	+	0.464392i
$55$	−2.76795e7	+	4.79424e7i	−0.407875	+	0.706460i
$56$	1.46939e7			0.199660
$57$	323469.	+	3.30627e7i	0.00405878	+	0.414860i
$58$	3.62697e7			0.420841
$59$	2.23466e7	−	3.87055e7i	0.240092	−	0.415852i	−0.720648	−	0.693301i	$-0.756156\pi$
$59$	2.23466e7	−	3.87055e7i	0.240092	−	0.415852i	0.960740	+	0.277449i	$0.0894890\pi$
$60$	2.02479e7	−	3.50703e7i	0.201697	−	0.349349i
$61$	−3.80863e7	−	6.59675e7i	−0.352196	−	0.610022i	0.634438	−	0.772974i	$-0.281232\pi$
$61$	−3.80863e7	−	6.59675e7i	−0.352196	−	0.610022i	−0.986634	+	0.162952i	$0.947898\pi$
$62$	6.07838e7	−	1.05281e8i	0.522427	−	0.904870i
$63$	2.92283e7	+	5.06249e7i	0.233760	+	0.404885i
$64$	1.67772e7			0.125000
$65$	3.34089e8			2.32141
$66$	9.48517e6	+	1.64288e7i	0.0615315	+	0.106576i
$67$	−3.18209e7	−	5.51153e7i	−0.192919	−	0.334146i	0.753297	−	0.657680i	$-0.228462\pi$
$67$	−3.18209e7	−	5.51153e7i	−0.192919	−	0.334146i	−0.946216	+	0.323534i	$0.895129\pi$
$68$	1.03633e8			0.587772
$69$	−9.86151e7			−0.523748
$70$	−7.79954e7	−	1.35092e8i	−0.388264	−	0.672494i
$71$	−1.76962e8	+	3.06508e8i	−0.826453	+	1.43146i	0.0743500	+	0.997232i	$0.476312\pi$
$71$	−1.76962e8	+	3.06508e8i	−0.826453	+	1.43146i	−0.900803	+	0.434227i	$0.857022\pi$
$72$	3.33723e7	+	5.78025e7i	0.146349	+	0.253484i
$73$	−1.16149e8	+	2.01176e8i	−0.478700	+	0.829132i	−0.999702	−	0.0244235i	$-0.992225\pi$
$73$	−1.16149e8	+	2.01176e8i	−0.478700	+	0.829132i	0.521002	+	0.853555i	$0.325558\pi$
$74$	−8.42915e7	+	1.45997e8i	−0.326769	+	0.565981i
$75$	−3.16220e8			−1.15402
$76$	1.26645e8	+	7.14756e7i	0.435438	+	0.245752i
$77$	7.30743e7			0.236895
$78$	5.72424e7	−	9.91468e7i	0.175103	−	0.303287i
$79$	1.24372e8	−	2.15419e8i	0.359253	−	0.622245i	−0.628583	−	0.777743i	$-0.716365\pi$
$79$	1.24372e8	−	2.15419e8i	0.359253	−	0.622245i	0.987836	+	0.155498i	$0.0496981\pi$
$80$	−8.90536e7	−	1.54245e8i	−0.243078	−	0.421024i
$81$	−9.94221e7	+	1.72204e8i	−0.256626	+	0.444489i
$82$	2.17579e8	+	3.76858e8i	0.531441	+	0.920483i
$83$	−1.03989e7			−0.0240512			−0.0120256	−	0.999928i	$-0.503828\pi$
$83$	−1.03989e7			−0.0240512			−0.0120256	+	0.999928i	$0.503828\pi$
$84$	−5.34546e7			−0.117146
$85$	−5.50086e8	−	9.52777e8i	−1.14300	−	1.97973i
$86$	−1.79033e8	−	3.10093e8i	−0.352930	−	0.611293i
$87$	−1.31945e8			−0.246920
$88$	8.34348e7			0.148312
$89$	2.35426e8	+	4.07770e8i	0.397741	+	0.688907i	0.993447	−	0.114295i	$-0.0364610\pi$
$89$	2.35426e8	+	4.07770e8i	0.397741	+	0.688907i	−0.595706	+	0.803202i	$0.703128\pi$
$90$	3.54281e8	−	6.13632e8i	0.569188	−	0.985863i
$91$	−2.20500e8	−	3.81916e8i	−0.337071	−	0.583824i
$92$	−2.16863e8	+	3.75618e8i	−0.315603	+	0.546640i
$93$	−2.21124e8	+	3.82998e8i	−0.306523	+	0.530913i
$94$	−6.56094e8			−0.866744
$95$	−1.51031e7	−	1.54373e9i	−0.0190243	−	1.94453i
$96$	−6.10334e7			−0.0733411
$97$	7.33534e7	−	1.27052e8i	0.0841293	−	0.145716i	−0.820891	−	0.571086i	$-0.806522\pi$
$97$	7.33534e7	−	1.27052e8i	0.0841293	−	0.145716i	0.905020	+	0.425369i	$0.139856\pi$
$98$	2.19875e8	−	3.80834e8i	0.240801	−	0.417079i
$99$	1.65964e8	+	2.87458e8i	0.173642	+	0.300757i
$100$	−6.95394e8	+	1.20446e9i	−0.695394	+	1.20446i
$101$	5.27585e8	+	9.13804e8i	0.504483	+	0.873790i	0.999987	+	0.00518394i	$0.00165011\pi$
$101$	5.27585e8	+	9.13804e8i	0.504483	+	0.873790i	−0.495504	+	0.868606i	$0.665017\pi$
$102$	−3.77005e8			−0.344863
$103$	1.36105e9			1.19153			0.595767	−	0.803157i	$-0.296848\pi$
$103$	1.36105e9			1.19153			0.595767	+	0.803157i	$0.296848\pi$
$104$	−2.51762e8	−	4.36065e8i	−0.211028	−	0.365511i
$105$	2.83737e8	+	4.91448e8i	0.227806	+	0.394571i
$106$	3.58926e8			0.276139
$107$	−1.35847e9			−1.00189			−0.500947	−	0.865478i	$-0.667015\pi$
$107$	−1.35847e9			−1.00189			−0.500947	+	0.865478i	$0.667015\pi$
$108$	−2.68050e8	−	4.64276e8i	−0.189587	−	0.328374i
$109$	2.56346e7	−	4.44004e7i	0.0173943	−	0.0301278i	−0.857197	−	0.514988i	$-0.827796\pi$
$109$	2.56346e7	−	4.44004e7i	0.0173943	−	0.0301278i	0.874592	+	0.484860i	$0.161130\pi$
$110$	−4.42873e8	−	7.67078e8i	−0.288411	−	0.499542i
$111$	3.06642e8	−	5.31119e8i	0.191725	−	0.332077i
$112$	−1.17551e8	+	2.03605e8i	−0.0705905	+	0.122266i
$113$	−2.26258e9			−1.30542			−0.652710	−	0.757608i	$-0.726368\pi$
$113$	−2.26258e9			−1.30542			−0.652710	+	0.757608i	$0.726368\pi$
$114$	−4.60718e8	−	2.60019e8i	−0.255484	−	0.144190i
$115$	4.60444e9			2.45492
$116$	−2.90158e8	+	5.02568e8i	−0.148790	+	0.257712i
$117$	1.00158e9	−	1.73479e9i	0.494140	−	0.855875i
$118$	3.57546e8	+	6.19288e8i	0.169771	+	0.294052i
$119$	−7.26117e8	+	1.25767e9i	−0.331929	+	0.574918i
$120$	3.23966e8	+	5.61125e8i	0.142621	+	0.247027i
$121$	−1.94302e9			−0.824029
$122$	1.21876e9			0.498081
$123$	−7.91527e8	−	1.37096e9i	−0.311812	−	0.540074i
$124$	9.72541e8	+	1.68449e9i	0.369411	+	0.639839i
$125$	9.45662e9			3.46450
$126$	−9.35305e8			−0.330587
$127$	−3.64498e7	−	6.31329e7i	−0.0124331	−	0.0215347i	0.859742	−	0.510729i	$-0.170624\pi$
$127$	−3.64498e7	−	6.31329e7i	−0.0124331	−	0.0215347i	−0.872175	+	0.489194i	$0.837291\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$	6.51298e8	+	1.12808e9i	0.207074	+	0.358663i
$130$	−2.67271e9	+	4.62927e9i	−0.820742	+	1.42157i
$131$	−1.35239e9	+	2.34241e9i	−0.401219	+	0.694932i	−0.993873	−	0.110525i	$-0.964747\pi$
$131$	−1.35239e9	+	2.34241e9i	−0.401219	+	0.694932i	0.592654	+	0.805457i	$0.298080\pi$
$132$	−3.03526e8			−0.0870187
$133$	−1.75476e9	+	1.03613e9i	−0.486279	+	0.287133i
$134$	1.01827e9			0.272829
$135$	−2.84562e9	+	4.92876e9i	−0.737352	+	1.27713i
$136$	−8.29066e8	+	1.43598e9i	−0.207809	+	0.359936i
$137$	4.07777e7	+	7.06291e7i	0.00988964	+	0.0171294i	0.870928	−	0.491411i	$-0.163519\pi$
$137$	4.07777e7	+	7.06291e7i	0.00988964	+	0.0171294i	−0.861038	+	0.508540i	$0.830185\pi$
$138$	7.88921e8	−	1.36645e9i	0.185173	−	0.320729i
$139$	1.07411e9	+	1.86041e9i	0.244051	+	0.422709i	0.961864	−	0.273527i	$-0.0881901\pi$
$139$	1.07411e9	+	1.86041e9i	0.244051	+	0.422709i	−0.717813	+	0.696236i	$0.754857\pi$
$140$	2.49585e9			0.549089
$141$	2.38679e9			0.508544
$142$	−2.83140e9	−	4.90413e9i	−0.584391	−	1.01219i
$143$	−1.25204e9	−	2.16859e9i	−0.250383	−	0.433677i
$144$	−1.06791e9			−0.206969
$145$	6.16064e9			1.15736
$146$	−1.85839e9	−	3.21882e9i	−0.338492	−	0.586285i
$147$	−7.99876e8	+	1.38543e9i	−0.141285	+	0.244712i
$148$	−1.34866e9	−	2.33595e9i	−0.231061	−	0.400209i
$149$	1.61033e9	−	2.78918e9i	0.267656	−	0.463594i	−0.700600	−	0.713554i	$-0.747084\pi$
$149$	1.61033e9	−	2.78918e9i	0.267656	−	0.463594i	0.968256	+	0.249960i	$0.0804176\pi$
$150$	2.52976e9	−	4.38167e9i	0.408007	−	0.706690i
$151$	−4.91230e9			−0.768933			−0.384467	−	0.923139i	$-0.625615\pi$
$151$	−4.91230e9			−0.768933			−0.384467	+	0.923139i	$0.625615\pi$
$152$	−2.00355e9	+	1.18304e9i	−0.304442	+	0.179764i
$153$	−6.59653e9			−0.973204
$154$	−5.84595e8	+	1.01255e9i	−0.0837551	+	0.145068i
$155$	1.03245e10	−	1.78826e10i	1.43674	−	2.48850i
$156$	9.15879e8	+	1.58635e9i	0.123816	+	0.214456i
$157$	−3.91542e9	+	6.78171e9i	−0.514316	+	0.890822i	0.485546	+	0.874211i	$0.338621\pi$
$157$	−3.91542e9	+	6.78171e9i	−0.514316	+	0.890822i	−0.999862	+	0.0166107i	$0.994712\pi$
$158$	1.98995e9	+	3.44670e9i	0.254030	+	0.439994i
$159$	−1.30573e9			−0.162019
$160$	2.84971e9			0.343765
$161$	−3.03895e9	−	5.26361e9i	−0.356457	−	0.617401i
$162$	−1.59075e9	−	2.75527e9i	−0.181462	−	0.314301i
$163$	−1.61986e10			−1.79735			−0.898674	−	0.438617i	$-0.855468\pi$
$163$	−1.61986e10			−1.79735			−0.898674	+	0.438617i	$0.855468\pi$
$164$	−6.96254e9			−0.751572
$165$	1.61112e9	+	2.79053e9i	0.169219	+	0.293096i
$166$	8.31912e7	−	1.44091e8i	0.00850337	−	0.0147283i
$167$	5.30092e9	+	9.18146e9i	0.527384	+	0.913456i	0.999491	+	0.0319142i	$0.0101603\pi$
$167$	5.30092e9	+	9.18146e9i	0.527384	+	0.913456i	−0.472107	+	0.881541i	$0.656506\pi$
$168$	4.27637e8	−	7.40689e8i	0.0414175	−	0.0717371i
$169$	−2.25373e9	+	3.90357e9i	−0.212526	+	0.368105i
$170$	1.76028e10			1.61644
$171$	−8.06127e9	−	4.54961e9i	−0.720976	−	0.406904i
$172$	5.72904e9			0.499119
$173$	6.54979e9	−	1.13446e10i	0.555930	−	0.962899i	−0.441901	−	0.897064i	$-0.645696\pi$
$173$	6.54979e9	−	1.13446e10i	0.555930	−	0.962899i	0.997831	−	0.0658347i	$-0.0209710\pi$
$174$	1.05556e9	−	1.82828e9i	0.0872993	−	0.151207i
$175$	−9.74470e9	−	1.68783e10i	−0.785411	−	1.36037i
$176$	−6.67479e8	+	1.15611e9i	−0.0524361	+	0.0908220i
$177$	−1.30071e9	−	2.25289e9i	−0.0996094	−	0.172529i
$178$	−7.53364e9			−0.562490
$179$	−1.54722e10			−1.12645			−0.563226	−	0.826303i	$-0.690440\pi$
$179$	−1.54722e10			−1.12645			−0.563226	+	0.826303i	$0.690440\pi$
$180$	5.66849e9	+	9.81811e9i	0.402477	+	0.697111i
$181$	−5.91844e9	−	1.02510e10i	−0.409877	−	0.709928i	0.584998	−	0.811035i	$-0.301095\pi$
$181$	−5.91844e9	−	1.02510e10i	−0.409877	−	0.709928i	−0.994876	+	0.101106i	$0.967762\pi$
$182$	7.05599e9			0.476690
$183$	−4.43371e9			−0.292238
$184$	−3.46981e9	−	6.00989e9i	−0.223165	−	0.386533i
$185$	−1.43174e10	+	2.47985e10i	−0.898654	+	1.55651i
$186$	−3.53798e9	−	6.12797e9i	−0.216744	−	0.375412i
$187$	−4.12303e9	+	7.14130e9i	−0.246564	+	0.427061i
$188$	5.24876e9	−	9.09111e9i	0.306440	−	0.530770i
$189$	7.51247e9			0.428257
$190$	2.15114e10	+	1.21406e10i	1.19751	+	0.675847i
$191$	1.09529e10			0.595498			0.297749	−	0.954644i	$-0.403764\pi$
$191$	1.09529e10			0.595498			0.297749	+	0.954644i	$0.403764\pi$
$192$	4.88267e8	−	8.45704e8i	0.0259300	−	0.0449120i
$193$	−1.85150e10	+	3.20689e10i	−0.960541	+	1.66371i	−0.239397	+	0.970922i	$0.576950\pi$
$193$	−1.85150e10	+	3.20689e10i	−0.960541	+	1.66371i	−0.721144	+	0.692785i	$0.756384\pi$
$194$	1.17365e9	+	2.03283e9i	0.0594884	+	0.103037i
$195$	9.72298e9	−	1.68407e10i	0.481553	−	0.834074i
$196$	3.51799e9	+	6.09334e9i	0.170272	+	0.294919i
$197$	2.14009e10			1.01236			0.506179	−	0.862428i	$-0.331057\pi$
$197$	2.14009e10			1.01236			0.506179	+	0.862428i	$0.331057\pi$
$198$	−5.31084e9			−0.245567
$199$	1.72652e10	+	2.99041e10i	0.780426	+	1.35174i	0.931694	+	0.363245i	$0.118331\pi$
$199$	1.72652e10	+	2.99041e10i	0.780426	+	1.35174i	−0.151267	+	0.988493i	$0.548335\pi$
$200$	−1.11263e10	−	1.92713e10i	−0.491718	−	0.851680i
$201$	−3.70433e9			−0.160076
$202$	−1.68827e10			−0.713446
$203$	−4.06604e9	−	7.04259e9i	−0.168050	−	0.291072i
$204$	3.01604e9	−	5.22393e9i	0.121927	−	0.211184i
$205$	3.69572e10	+	6.40118e10i	1.46153	+	2.53144i
$206$	−1.08884e10	+	1.88592e10i	−0.421271	+	0.729662i
$207$	1.38039e10	−	2.39091e10i	0.522559	−	0.905098i
$208$	8.05639e9			0.298439
$209$	−9.96388e9	+	5.88336e9i	−0.361219	+	0.213288i
$210$	−9.07960e9			−0.322166
$211$	4.70941e9	−	8.15693e9i	0.163567	−	0.283306i	−0.772579	−	0.634919i	$-0.781033\pi$
$211$	4.70941e9	−	8.15693e9i	0.163567	−	0.283306i	0.936145	+	0.351613i	$0.114367\pi$
$212$	−2.87140e9	+	4.97342e9i	−0.0976299	+	0.169100i
$213$	1.03003e10	+	1.78406e10i	0.342879	+	0.593883i
$214$	1.08677e10	−	1.88235e10i	0.354223	−	0.613532i
$215$	−3.04098e10	−	5.26713e10i	−0.970600	−	1.68113i
$216$	8.57759e9			0.268117
$217$	−2.72568e10			−0.834462
$218$	4.10153e8	+	7.10406e8i	0.0122996	+	0.0213036i
$219$	6.76058e9	+	1.17097e10i	0.198603	+	0.343990i
$220$	1.41719e10			0.407875
$221$	4.97645e10			1.40331
$222$	4.90627e9	+	8.49791e9i	0.135570	+	0.234814i
$223$	1.03048e10	−	1.78485e10i	0.279041	−	0.483313i	−0.692106	−	0.721796i	$-0.743317\pi$
$223$	1.03048e10	−	1.78485e10i	0.279041	−	0.483313i	0.971147	+	0.238483i	$0.0766501\pi$
$224$	−1.88082e9	−	3.25768e9i	−0.0499150	−	0.0864553i
$225$	4.42636e10	−	7.66668e10i	1.15140	−	1.99428i
$226$	1.81006e10	−	3.13512e10i	0.461535	−	0.799403i
$227$	8.31349e9			0.207810			0.103905	−	0.994587i	$-0.466866\pi$
$227$	8.31349e9			0.207810			0.103905	+	0.994587i	$0.466866\pi$
$228$	7.28868e9	−	4.30374e9i	0.178625	−	0.105472i
$229$	4.47524e10			1.07537			0.537683	−	0.843147i	$-0.319300\pi$
$229$	4.47524e10			1.07537			0.537683	+	0.843147i	$0.319300\pi$
$230$	−3.68356e10	+	6.38010e10i	−0.867944	+	1.50332i
$231$	2.12668e9	−	3.68352e9i	0.0491415	−	0.0851156i
$232$	−4.64253e9	−	8.04109e9i	−0.105210	−	0.182230i
$233$	−3.18755e10	+	5.52100e10i	−0.708525	+	1.22720i	0.256879	+	0.966444i	$0.417306\pi$
$233$	−3.18755e10	+	5.52100e10i	−0.708525	+	1.22720i	−0.965404	+	0.260758i	$0.916028\pi$
$234$	1.60253e10	+	2.77566e10i	0.349410	+	0.605195i
$235$	−1.11442e11			−2.38365
$236$	−1.14415e10			−0.240092
$237$	−7.23920e9	−	1.25387e10i	−0.149047	−	0.258157i
$238$	−1.16179e10	−	2.01227e10i	−0.234709	−	0.406528i
$239$	−8.54845e10			−1.69471			−0.847357	−	0.531023i	$-0.821808\pi$
$239$	−8.54845e10			−1.69471			−0.847357	+	0.531023i	$0.821808\pi$
$240$	−1.03669e10			−0.201697
$241$	1.68752e10	+	2.92287e10i	0.322235	+	0.558127i	0.980949	−	0.194267i	$-0.0622327\pi$
$241$	1.68752e10	+	2.92287e10i	0.322235	+	0.558127i	−0.658714	+	0.752393i	$0.728899\pi$
$242$	1.55441e10	−	2.69232e10i	0.291338	−	0.504613i
$243$	2.63964e10	+	4.57200e10i	0.485643	+	0.841158i
$244$	−9.75010e9	+	1.68877e10i	−0.176098	+	0.305011i
$245$	3.73471e10	−	6.46870e10i	0.662230	−	1.14702i
$246$	2.53289e10			0.440968
$247$	6.08146e10	+	3.43225e10i	1.03961	+	0.586735i
$248$	−3.11213e10			−0.522427
$249$	−3.02639e8	+	5.24186e8i	−0.00498917	+	0.00864149i
$250$	−7.56529e10	+	1.31035e11i	−1.22489	+	2.12157i
$251$	−8.51637e9	−	1.47508e10i	−0.135433	−	0.234576i	0.790330	−	0.612681i	$-0.209909\pi$
$251$	−8.51637e9	−	1.47508e10i	−0.135433	−	0.234576i	−0.925763	+	0.378105i	$0.876576\pi$
$252$	7.48244e9	−	1.29600e10i	0.116880	−	0.202442i
$253$	−1.72557e10	−	2.98878e10i	−0.264783	−	0.458618i
$254$	1.16639e9			0.0175830
$255$	−6.40366e10			−0.948414
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	1.19282e10	+	2.06602e10i	0.170559	+	0.295418i	0.938616	−	0.344965i	$-0.112109\pi$
$257$	1.19282e10	+	2.06602e10i	0.170559	+	0.295418i	−0.768056	+	0.640382i	$0.778776\pi$
$258$	−2.08415e10			−0.292847
$259$	3.77982e10			0.521942
$260$	−4.27634e10	−	7.40683e10i	−0.580352	−	1.00520i
$261$	1.84693e10	−	3.19898e10i	0.246359	−	0.426706i
$262$	−2.16383e10	−	3.74786e10i	−0.283705	−	0.491391i
$263$	3.43090e10	−	5.94250e10i	0.442189	−	0.765893i	−0.555663	−	0.831408i	$-0.687536\pi$
$263$	3.43090e10	−	5.94250e10i	0.442189	−	0.765893i	0.997852	+	0.0655145i	$0.0208689\pi$
$264$	2.42820e9	−	4.20577e9i	0.0307657	−	0.0532878i
$265$	6.09657e10			0.759415
$266$	−3.18979e8	−	3.26038e10i	−0.00390656	−	0.399301i
$267$	2.74065e10			0.330029
$268$	−8.14614e9	+	1.41095e10i	−0.0964596	+	0.167073i
$269$	4.98168e9	−	8.62852e9i	0.0580083	−	0.100473i	−0.835563	−	0.549395i	$-0.814858\pi$
$269$	4.98168e9	−	8.62852e9i	0.0580083	−	0.100473i	0.893571	+	0.448921i	$0.148192\pi$
$270$	−4.55299e10	−	7.88602e10i	−0.521387	−	0.903068i
$271$	−1.25865e10	+	2.18004e10i	−0.141756	+	0.245529i	−0.928158	−	0.372186i	$-0.878608\pi$
$271$	−1.25865e10	+	2.18004e10i	−0.141756	+	0.245529i	0.786402	+	0.617715i	$0.211942\pi$
$272$	−1.32651e10	−	2.29758e10i	−0.146943	−	0.254513i
$273$	−2.56688e10			−0.279688
$274$	−1.30489e9			−0.0139861
$275$	−5.53323e10	−	9.58383e10i	−0.583420	−	1.01051i
$276$	1.26227e10	+	2.18632e10i	0.130937	+	0.226790i
$277$	2.15191e10			0.219617			0.109808	−	0.993953i	$-0.464976\pi$
$277$	2.15191e10			0.219617			0.109808	+	0.993953i	$0.464976\pi$
$278$	−3.43714e10			−0.345141
$279$	−6.19047e10	−	1.07222e11i	−0.611653	−	1.05941i
$280$	−1.99668e10	+	3.45835e10i	−0.194132	+	0.336247i
$281$	3.62815e10	+	6.28414e10i	0.347142	+	0.601267i	0.985740	−	0.168273i	$-0.0538189\pi$
$281$	3.62815e10	+	6.28414e10i	0.347142	+	0.601267i	−0.638599	+	0.769540i	$0.720486\pi$
$282$	−1.90943e10	+	3.30723e10i	−0.179797	+	0.311418i
$283$	−7.69052e10	+	1.33204e11i	−0.712717	+	1.23446i	0.251117	+	0.967957i	$0.419202\pi$
$283$	−7.69052e10	+	1.33204e11i	−0.712717	+	1.23446i	−0.963834	+	0.266505i	$0.914131\pi$
$284$	9.06047e10			0.826453
$285$	−7.82558e10	−	4.41659e10i	−0.702611	−	0.396539i
$286$	4.00652e10			0.354096
$287$	4.87837e10	−	8.44959e10i	0.424430	−	0.735135i
$288$	8.54330e9	−	1.47974e10i	0.0731745	−	0.126742i
$289$	−2.26447e10	−	3.92217e10i	−0.190953	−	0.330740i
$290$	−4.92851e10	+	8.53644e10i	−0.409190	+	0.708738i
$291$	−4.26961e9	−	7.39518e9i	−0.0349035	−	0.0604547i
$292$	5.94683e10			0.478700
$293$	2.62610e10			0.208165			0.104082	−	0.994569i	$-0.466809\pi$
$293$	2.62610e10			0.208165			0.104082	+	0.994569i	$0.466809\pi$
$294$	−1.27980e10	−	2.21668e10i	−0.0999033	−	0.173038i
$295$	6.07314e10	+	1.05190e11i	0.466890	+	0.808677i
$296$	4.31572e10			0.326769
$297$	4.26573e10			0.318119
$298$	2.57653e10	+	4.46268e10i	0.189261	+	0.327810i
$299$	−1.04137e11	+	1.80371e11i	−0.753504	+	1.30511i
$300$	4.04761e10	+	7.01067e10i	0.288505	+	0.499705i
$301$	−4.01411e10	+	6.95264e10i	−0.281864	+	0.488203i
$302$	3.92984e10	−	6.80668e10i	0.271859	−	0.470873i
$303$	6.14172e10			0.418599
$304$	−3.64204e8	−	3.72263e10i	−0.00244576	−	0.249988i
$305$	2.07014e11			1.36978
$306$	5.27722e10	−	9.14041e10i	0.344080	−	0.595963i
$307$	7.33574e10	−	1.27059e11i	0.471326	−	0.816360i	−0.528136	−	0.849160i	$-0.677109\pi$
$307$	7.33574e10	−	1.27059e11i	0.471326	−	0.816360i	0.999462	+	0.0327994i	$0.0104422\pi$
$308$	−9.35351e9	−	1.62008e10i	−0.0592238	−	0.102579i
$309$	3.96106e10	−	6.86076e10i	0.247172	−	0.428114i
$310$	1.65192e11	+	2.86121e11i	1.01593	+	1.75963i
$311$	2.06404e10			0.125111			0.0625556	−	0.998041i	$-0.480075\pi$
$311$	2.06404e10			0.125111			0.0625556	+	0.998041i	$0.480075\pi$
$312$	−2.93081e10			−0.175103
$313$	−4.02986e10	−	6.97992e10i	−0.237323	−	0.411056i	0.722622	−	0.691243i	$-0.242937\pi$
$313$	−4.02986e10	−	6.97992e10i	−0.237323	−	0.411056i	−0.959945	+	0.280187i	$0.909603\pi$
$314$	−6.26468e10	−	1.08507e11i	−0.363677	−	0.629906i
$315$	−1.58867e11			−0.909154
$316$	−6.36785e10			−0.359253
$317$	8.20370e10	+	1.42092e11i	0.456292	+	0.790321i	0.998761	−	0.0497543i	$-0.0158438\pi$
$317$	8.20370e10	+	1.42092e11i	0.456292	+	0.790321i	−0.542469	+	0.840076i	$0.682510\pi$
$318$	1.04458e10	−	1.80927e10i	0.0572823	−	0.0992158i
$319$	−2.30878e10	−	3.99892e10i	−0.124831	−	0.216214i
$320$	−2.27977e10	+	3.94868e10i	−0.121539	+	0.210512i
$321$	−3.95354e10	+	6.84774e10i	−0.207833	+	0.359977i
$322$	9.72463e10			0.504106
$323$	−2.24969e9	−	2.29948e11i	−0.0115004	−	1.17549i
$324$	5.09041e10			0.256626
$325$	−3.33927e11	+	5.78378e11i	−1.66026	+	2.87566i
$326$	1.29588e11	−	2.24454e11i	0.635459	−	1.10065i
$327$	−1.49209e9	−	2.58437e9i	−0.00721654	−	0.0124994i
$328$	5.57003e10	−	9.64758e10i	0.265721	−	0.460242i
$329$	7.35519e10	+	1.27396e11i	0.346108	+	0.599477i
$330$	−5.15557e10			−0.239312
$331$	2.94932e11			1.35051			0.675253	−	0.737587i	$-0.264035\pi$
$331$	2.94932e11			1.35051			0.675253	+	0.737587i	$0.264035\pi$
$332$	1.33106e9	+	2.30546e9i	0.00601279	+	0.0104145i
$333$	8.58459e10	+	1.48689e11i	0.382578	+	0.662645i
$334$	−1.69629e11			−0.745833
$335$	1.72959e11			0.750312
$336$	6.84219e9	+	1.18510e10i	0.0292866	+	0.0507258i
$337$	−1.26394e11	+	2.18920e11i	−0.533816	+	0.924596i	0.465404	+	0.885098i	$0.345909\pi$
$337$	−1.26394e11	+	2.18920e11i	−0.533816	+	0.924596i	−0.999220	+	0.0394973i	$0.987424\pi$
$338$	−3.60597e10	−	6.24572e10i	−0.150278	−	0.260290i
$339$	−6.58477e10	+	1.14052e11i	−0.270796	+	0.469032i
$340$	−1.40822e11	+	2.43911e11i	−0.571499	+	0.989866i
$341$	−1.54769e11			−0.619856
$342$	1.27531e11	−	7.53033e10i	0.504080	−	0.297644i
$343$	−2.43360e11			−0.949350
$344$	−4.58323e10	+	7.93839e10i	−0.176465	+	0.305647i
$345$	1.34003e11	−	2.32100e11i	0.509248	−	0.882043i
$346$	1.04797e11	+	1.81513e11i	0.393102	+	0.680872i
$347$	−1.13767e11	+	1.97049e11i	−0.421242	+	0.729613i	−0.996061	−	0.0886677i	$-0.971739\pi$
$347$	−1.13767e11	+	1.97049e11i	−0.421242	+	0.729613i	0.574819	+	0.818281i	$0.305072\pi$
$348$	1.68889e10	+	2.92525e10i	0.0617299	+	0.106919i
$349$	1.48379e11			0.535375			0.267687	−	0.963506i	$-0.413741\pi$
$349$	1.48379e11			0.535375			0.267687	+	0.963506i	$0.413741\pi$
$350$	3.11830e11			1.11074
$351$	−1.28717e11	−	2.22944e11i	−0.452641	−	0.783997i
$352$	−1.06797e10	−	1.84977e10i	−0.0370779	−	0.0642208i
$353$	−6.84759e10			−0.234721			−0.117360	−	0.993089i	$-0.537443\pi$
$353$	−6.84759e10			−0.234721			−0.117360	+	0.993089i	$0.537443\pi$
$354$	4.16227e10			0.140869
$355$	−4.80931e11	−	8.32996e11i	−1.60714	−	2.78366i
$356$	6.02691e10	−	1.04389e11i	0.198870	−	0.344454i
$357$	4.22644e10	+	7.32041e10i	0.137711	+	0.238522i
$358$	1.23777e11	−	2.14389e11i	0.398261	−	0.689809i
$359$	−4.96110e10	+	8.59289e10i	−0.157635	+	0.273032i	−0.934015	−	0.357233i	$-0.883720\pi$
$359$	−4.96110e10	+	8.59289e10i	−0.157635	+	0.273032i	0.776380	+	0.630265i	$0.217054\pi$
$360$	−1.81392e11			−0.569188
$361$	1.55845e11	−	2.82559e11i	0.482960	−	0.875642i
$362$	1.89390e11			0.579654
$363$	−5.65477e10	+	9.79434e10i	−0.170936	+	0.296071i
$364$	−5.64479e10	+	9.77706e10i	−0.168536	+	0.291912i
$365$	−3.15658e11	−	5.46736e11i	−0.930892	−	1.61235i
$366$	3.54697e10	−	6.14353e10i	0.103322	−	0.178959i
$367$	3.82989e10	+	6.63356e10i	0.110202	+	0.190875i	0.915852	−	0.401517i	$-0.131517\pi$
$367$	3.82989e10	+	6.63356e10i	0.110202	+	0.190875i	−0.805650	+	0.592392i	$0.798184\pi$
$368$	1.11034e11			0.315603
$369$	4.43184e11			1.24441
$370$	−2.29079e11	−	3.96776e11i	−0.635444	−	1.10062i
$371$	−4.02376e10	−	6.96935e10i	−0.110268	−	0.190990i
$372$	1.13215e11			0.306523
$373$	−6.14476e11			−1.64367			−0.821836	−	0.569723i	$-0.807050\pi$
$373$	−6.14476e11			−1.64367			−0.821836	+	0.569723i	$0.807050\pi$
$374$	−6.59685e10	−	1.14261e11i	−0.174347	−	0.301978i
$375$	2.75216e11	−	4.76688e11i	0.718676	−	1.24478i
$376$	8.39801e10	+	1.45458e11i	0.216686	+	0.375311i
$377$	−1.39333e11	+	2.41332e11i	−0.355237	+	0.615289i
$378$	−6.00998e10	+	1.04096e11i	−0.151412	+	0.262253i
$379$	3.53566e11			0.880225			0.440112	−	0.897943i	$-0.354939\pi$
$379$	3.53566e11			0.880225			0.440112	+	0.897943i	$0.354939\pi$
$380$	−3.40316e11	+	2.00946e11i	−0.837252	+	0.494371i
$381$	−4.24319e9			−0.0103165
$382$	−8.76234e10	+	1.51768e11i	−0.210540	+	0.364666i
$383$	−2.68946e11	+	4.65828e11i	−0.638661	+	1.10619i	0.347066	+	0.937841i	$0.387178\pi$
$383$	−2.68946e11	+	4.65828e11i	−0.638661	+	1.10619i	−0.985727	+	0.168353i	$0.946155\pi$
$384$	7.81228e9	+	1.35313e10i	0.0183353	+	0.0317576i
$385$	−9.92970e10	+	1.71987e11i	−0.230337	+	0.398955i
$386$	−2.96240e11	−	5.13103e11i	−0.679205	−	1.17642i
$387$	−3.64668e11			−0.826416
$388$	−3.75569e10			−0.0841293
$389$	−3.15547e11	−	5.46543e11i	−0.698700	−	1.21018i	−0.968917	−	0.247384i	$-0.920429\pi$
$389$	−3.15547e11	−	5.46543e11i	−0.698700	−	1.21018i	0.270218	−	0.962799i	$-0.412904\pi$
$390$	1.55568e11	+	2.69451e11i	0.340509	+	0.589779i
$391$	6.85859e11			1.48402
$392$	−1.12576e11			−0.240801
$393$	7.87173e10	+	1.36342e11i	0.166458	+	0.288313i
$394$	−1.71207e11	+	2.96540e11i	−0.357923	+	0.619941i
$395$	3.38006e11	+	5.85443e11i	0.698614	+	1.21003i
$396$	4.24867e10	−	7.35892e10i	0.0868210	−	0.150378i
$397$	8.66840e10	−	1.50141e11i	0.175139	−	0.303349i	−0.765071	−	0.643946i	$-0.777296\pi$
$397$	8.66840e10	−	1.50141e11i	0.175139	−	0.303349i	0.940209	+	0.340597i	$0.110629\pi$
$398$	−5.52485e11			−1.10369
$399$	1.16040e9	+	1.18608e11i	0.00229209	+	0.234281i
$400$	3.56042e11			0.695394
$401$	7.54460e9	−	1.30676e10i	0.0145709	−	0.0252376i	−0.858648	−	0.512566i	$-0.828695\pi$
$401$	7.54460e9	−	1.30676e10i	0.0145709	−	0.0252376i	0.873219	+	0.487328i	$0.162028\pi$
$402$	2.96346e10	−	5.13287e10i	0.0565956	−	0.0980264i
$403$	4.67012e11	+	8.08889e11i	0.881974	+	1.52762i
$404$	1.35062e11	−	2.33934e11i	0.252241	−	0.436895i
$405$	−2.70199e11	−	4.67999e11i	−0.499042	−	0.864365i
$406$	1.30113e11			0.237659
$407$	2.14625e11			0.387709
$408$	4.82566e10	+	8.35830e10i	0.0862157	+	0.149330i
$409$	−2.26545e11	−	3.92387e11i	−0.400313	−	0.693362i	0.593451	−	0.804870i	$-0.297765\pi$
$409$	−2.26545e11	−	3.92387e11i	−0.400313	−	0.693362i	−0.993764	+	0.111508i	$0.964432\pi$
$410$	−1.18263e12			−2.06691
$411$	4.74702e9			0.00820602
$412$	−1.74214e11	−	3.01748e11i	−0.297883	−	0.515949i
$413$	8.01659e10	−	1.38851e11i	0.135586	−	0.234842i
$414$	2.20862e11	+	3.82545e11i	0.369505	+	0.640001i
$415$	1.41305e10	−	2.44748e10i	0.0233853	−	0.0405045i
$416$	−6.44511e10	+	1.11633e11i	−0.105514	+	0.182756i
$417$	1.25039e11			0.202504
$418$	−1.81122e9	−	1.85130e11i	−0.00290187	−	0.296609i
$419$	3.28666e11			0.520945			0.260472	−	0.965481i	$-0.416122\pi$
$419$	3.28666e11			0.520945			0.260472	+	0.965481i	$0.416122\pi$
$420$	7.26368e10	−	1.25811e11i	0.113903	−	0.197286i
$421$	−9.69807e9	+	1.67976e10i	−0.0150458	+	0.0260601i	−0.873450	−	0.486913i	$-0.838123\pi$
$421$	−9.69807e9	+	1.67976e10i	−0.0150458	+	0.0260601i	0.858404	+	0.512973i	$0.171456\pi$
$422$	7.53505e10	+	1.30511e11i	0.115659	+	0.200328i
$423$	−3.34097e11	+	5.78673e11i	−0.507389	+	0.878823i
$424$	−4.59425e10	−	7.95747e10i	−0.0690348	−	0.119572i
$425$	2.19928e12			3.26987
$426$	−3.29609e11			−0.484904
$427$	−1.36630e11	−	2.36650e11i	−0.198894	−	0.344494i
$428$	1.73884e11	+	3.01175e11i	0.250473	+	0.433833i
$429$	−1.45752e11			−0.207758
$430$	9.73113e11			1.37264
$431$	5.17486e11	+	8.96311e11i	0.722355	+	1.25116i	0.960054	+	0.279816i	$0.0902735\pi$
$431$	5.17486e11	+	8.96311e11i	0.722355	+	1.25116i	−0.237699	+	0.971339i	$0.576393\pi$
$432$	−6.86208e10	+	1.18855e11i	−0.0947935	+	0.164187i
$433$	−3.82743e11	−	6.62931e11i	−0.523254	−	0.906302i	−0.999634	−	0.0270624i	$-0.991385\pi$
$433$	−3.82743e11	−	6.62931e11i	−0.523254	−	0.906302i	0.476380	−	0.879239i	$-0.341949\pi$
$434$	2.18055e11	−	3.77682e11i	0.295027	−	0.511001i
$435$	1.79293e11	−	3.10545e11i	0.240083	−	0.415837i
$436$	−1.31249e10			−0.0173943
$437$	8.38152e11	+	4.73036e11i	1.09940	+	0.620479i
$438$	−2.16338e11			−0.280867
$439$	−5.66375e11	+	9.80989e11i	−0.727802	+	1.26059i	0.230008	+	0.973189i	$0.426125\pi$
$439$	−5.66375e11	+	9.80989e11i	−0.727802	+	1.26059i	−0.957810	+	0.287402i	$0.907209\pi$
$440$	−1.13375e11	+	1.96372e11i	−0.144205	+	0.249771i
$441$	−2.23929e11	−	3.87857e11i	−0.281927	−	0.488313i
$442$	−3.98116e11	+	6.89557e11i	−0.496146	+	0.859350i
$443$	−2.16512e9	−	3.75009e9i	−0.00267094	−	0.00462621i	0.864687	−	0.502311i	$-0.167517\pi$
$443$	−2.16512e9	−	3.75009e9i	−0.00267094	−	0.00462621i	−0.867358	+	0.497685i	$0.834184\pi$
$444$	−1.57001e11			−0.191725
$445$	−1.27964e12			−1.54691
$446$	1.64877e11	+	2.85575e11i	0.197312	+	0.341754i
$447$	−9.37309e10	−	1.62347e11i	−0.111045	−	0.192336i
$448$	6.01862e10			0.0705905
$449$	1.11164e11			0.129079			0.0645395	−	0.997915i	$-0.479442\pi$
$449$	1.11164e11			0.129079			0.0645395	+	0.997915i	$0.479442\pi$
$450$	7.08218e11	+	1.22667e12i	0.814162	+	1.41017i
$451$	2.77003e11	−	4.79784e11i	0.315276	−	0.546074i
$452$	2.89610e11	+	5.01619e11i	0.326355	+	0.565263i
$453$	−1.42963e11	+	2.47619e11i	−0.159507	+	0.276275i
$454$	−6.65079e10	+	1.15195e11i	−0.0734721	+	0.127257i
$455$	1.19850e12			1.31096
$456$	1.32493e9	+	1.35425e11i	0.00143499	+	0.146675i
$457$	−6.27200e11			−0.672641			−0.336320	−	0.941748i	$-0.609182\pi$
$457$	−6.27200e11			−0.672641			−0.336320	+	0.941748i	$0.609182\pi$
$458$	−3.58019e11	+	6.20107e11i	−0.380200	+	0.658525i
$459$	−4.23872e11	+	7.34168e11i	−0.445736	+	0.772038i
$460$	−5.89369e11	−	1.02082e12i	−0.613729	−	1.06301i
$461$	4.96034e11	−	8.59157e11i	0.511514	−	0.885969i	−0.488397	−	0.872622i	$-0.662418\pi$
$461$	4.96034e11	−	8.59157e11i	0.511514	−	0.885969i	0.999911	−	0.0133469i	$-0.00424857\pi$
$462$	3.40269e10	+	5.89363e10i	0.0347483	+	0.0601858i
$463$	1.15022e12			1.16323			0.581615	−	0.813464i	$-0.302421\pi$
$463$	1.15022e12			1.16323			0.581615	+	0.813464i	$0.302421\pi$
$464$	1.48561e11			0.148790
$465$	−6.00948e11	−	1.04087e12i	−0.596072	−	1.03243i
$466$	−5.10008e11	−	8.83360e11i	−0.501003	−	0.867763i
$467$	−1.12091e12			−1.09055			−0.545273	−	0.838259i	$-0.683574\pi$
$467$	−1.12091e12			−1.09055			−0.545273	+	0.838259i	$0.683574\pi$
$468$	−5.12810e11			−0.494140
$469$	−1.14154e11	−	1.97720e11i	−0.108946	−	0.188700i
$470$	8.91534e11	−	1.54418e12i	0.842747	−	1.45968i
$471$	2.27901e11	+	3.94736e11i	0.213379	+	0.369584i
$472$	9.15318e10	−	1.58538e11i	0.0848854	−	0.147026i
$473$	−2.27929e11	+	3.94784e11i	−0.209375	+	0.362648i
$474$	2.31654e11			0.210784
$475$	2.68762e12	+	1.51684e12i	2.42241	+	1.36715i
$476$	3.71772e11			0.331929
$477$	1.82772e11	−	3.16571e11i	0.161651	−	0.279987i
$478$	6.83876e11	−	1.18451e12i	0.599172	−	1.03780i
$479$	−1.12369e12	−	1.94629e12i	−0.975300	−	1.68927i	−0.678943	−	0.734191i	$-0.737562\pi$
$479$	−1.12369e12	−	1.94629e12i	−0.975300	−	1.68927i	−0.296357	−	0.955077i	$-0.595772\pi$
$480$	8.29353e10	−	1.43648e11i	0.0713105	−	0.123513i
$481$	−6.47626e11	−	1.12172e12i	−0.551660	−	0.955502i
$482$	−5.40006e11			−0.455708
$483$	−3.53770e11			−0.295773
$484$	2.48706e11	+	4.30772e11i	0.206007	+	0.356815i
$485$	1.99352e11	+	3.45288e11i	0.163600	+	0.283364i
$486$	−8.44686e11			−0.686803
$487$	−1.49532e12			−1.20463			−0.602316	−	0.798258i	$-0.705755\pi$
$487$	−1.49532e12			−1.20463			−0.602316	+	0.798258i	$0.705755\pi$
$488$	−1.56002e11	−	2.70203e11i	−0.124520	−	0.215675i
$489$	−4.71427e11	+	8.16535e11i	−0.372842	+	0.645781i
$490$	5.97553e11	+	1.03499e12i	0.468267	+	0.811063i
$491$	6.39418e11	−	1.10750e12i	0.496499	−	0.859961i	−0.503493	−	0.863999i	$-0.667952\pi$
$491$	6.39418e11	−	1.10750e12i	0.496499	−	0.859961i	0.999992	+	0.00403802i	$0.00128535\pi$
$492$	−2.02631e11	+	3.50967e11i	−0.155906	+	0.270037i
$493$	9.17664e11			0.699637
$494$	−9.62102e11	+	5.68092e11i	−0.726859	+	0.429188i
$495$	−9.02079e11			−0.675338
$496$	2.48971e11	−	4.31230e11i	0.184706	−	0.319920i
$497$	−6.34831e11	+	1.09956e12i	−0.466718	+	0.808379i
$498$	−4.84223e9	−	8.38698e9i	−0.00352787	−	0.00611046i
$499$	7.53614e11	−	1.30530e12i	0.544122	−	0.942447i	−0.454539	−	0.890727i	$-0.650196\pi$
$499$	7.53614e11	−	1.30530e12i	0.544122	−	0.942447i	0.998662	−	0.0517206i	$-0.0164705\pi$
$500$	−1.21045e12	−	2.09656e12i	−0.866125	−	1.50017i
$501$	6.17090e11			0.437602
$502$	2.72524e11			0.191531
$503$	5.36793e11	+	9.29752e11i	0.373896	+	0.647607i	0.990161	−	0.139932i	$-0.0446884\pi$
$503$	5.36793e11	+	9.29752e11i	0.373896	+	0.647607i	−0.616265	+	0.787539i	$0.711355\pi$
$504$	1.19719e11	+	2.07359e11i	0.0826468	+	0.143148i
$505$	−2.86764e12			−1.96206
$506$	5.52183e11			0.374460
$507$	1.31181e11	+	2.27211e11i	0.0881726	+	0.152719i
$508$	−9.33115e9	+	1.61620e10i	−0.00621654	+	0.0107674i
$509$	6.71640e11	+	1.16331e12i	0.443513	+	0.768187i	0.997947	−	0.0640406i	$-0.0203987\pi$
$509$	6.71640e11	+	1.16331e12i	0.443513	+	0.768187i	−0.554434	+	0.832227i	$0.687065\pi$
$510$	5.12293e11	−	8.87318e11i	0.335315	−	0.580782i
$511$	−4.16671e11	+	7.21695e11i	−0.270333	+	0.468231i
$512$	6.87195e10			0.0441942
$513$	−1.02435e12	+	6.04844e11i	−0.653008	+	0.385581i
$514$	−3.81702e11			−0.241207
$515$	−1.84946e12	+	3.20336e12i	−1.15854	+	2.00666i
$516$	1.66732e11	−	2.88789e11i	0.103537	−	0.179332i
$517$	4.17642e11	+	7.23377e11i	0.257097	+	0.445304i
$518$	−3.02385e11	+	5.23747e11i	−0.184534	+	0.319623i
$519$	−3.81237e11	−	6.60322e11i	−0.230644	−	0.399487i
$520$	1.36843e12			0.820742
$521$	−5.12717e11			−0.304865			−0.152433	−	0.988314i	$-0.548711\pi$
$521$	−5.12717e11			−0.304865			−0.152433	+	0.988314i	$0.548711\pi$
$522$	2.95509e11	+	5.11836e11i	0.174202	+	0.301727i
$523$	−1.24281e12	−	2.15260e12i	−0.726350	−	1.25807i	−0.958416	−	0.285375i	$-0.907882\pi$
$523$	−1.24281e12	−	2.15260e12i	−0.726350	−	1.25807i	0.232066	−	0.972700i	$-0.425451\pi$
$524$	6.92424e11			0.401219
$525$	−1.13440e12			−0.651702
$526$	5.48944e11	+	9.50800e11i	0.312675	+	0.541568i
$527$	1.53790e12	−	2.66372e12i	0.868519	−	1.50432i
$528$	3.88513e10	+	6.72924e10i	0.0217547	+	0.0376802i
$529$	−5.34654e11	+	9.26048e11i	−0.296840	+	0.514142i
$530$	−4.87726e11	+	8.44766e11i	−0.268494	+	0.465045i
$531$	7.28279e11			0.397533
$532$	4.54323e11	+	2.56410e11i	0.245902	+	0.138782i
$533$	−3.34340e12			−1.79438
$534$	−2.19252e11	+	3.79755e11i	−0.116683	+	0.202101i
$535$	1.84595e12	−	3.19728e12i	0.974155	−	1.68729i
$536$	−1.30338e11	−	2.25752e11i	−0.0682072	−	0.118138i
$537$	−4.50287e11	+	7.79920e11i	−0.233671	+	0.404730i
$538$	7.97069e10	+	1.38056e11i	0.0410181	+	0.0710454i
$539$	−5.59851e11			−0.285708
$540$	1.45696e12			0.737352
$541$	−1.72033e12	−	2.97969e12i	−0.863422	−	1.49549i	−0.868606	−	0.495504i	$-0.834983\pi$
$541$	−1.72033e12	−	2.97969e12i	−0.863422	−	1.49549i	0.00518398	−	0.999987i	$-0.498350\pi$
$542$	−2.01383e11	−	3.48806e11i	−0.100237	−	0.173615i
$543$	−6.88978e11			−0.340100
$544$	4.24482e11			0.207809
$545$	6.96671e10	+	1.20667e11i	0.0338254	+	0.0585874i
$546$	2.05350e11	−	3.55677e11i	0.0988846	−	0.171273i
$547$	7.60693e10	+	1.31756e11i	0.0363301	+	0.0629255i	0.883619	−	0.468207i	$-0.155100\pi$
$547$	7.60693e10	+	1.31756e11i	0.0363301	+	0.0629255i	−0.847289	+	0.531133i	$0.821767\pi$
$548$	1.04391e10	−	1.80810e10i	0.00494482	−	0.00856468i
$549$	6.20619e11	−	1.07494e12i	0.291575	−	0.505022i
$550$	1.77063e12			0.825080
$551$	1.12143e12	+	6.32911e11i	0.518310	+	0.292523i
$552$	−4.03928e11			−0.185173
$553$	4.46170e11	−	7.72788e11i	0.202879	−	0.351397i
$554$	−1.72153e11	+	2.98178e11i	−0.0776463	+	0.134487i
$555$	8.33360e11	+	1.44342e12i	0.372833	+	0.645766i
$556$	2.74971e11	−	4.76265e11i	0.122026	−	0.211355i
$557$	1.69263e12	+	2.93172e12i	0.745098	+	1.29055i	0.950149	+	0.311797i	$0.100931\pi$
$557$	1.69263e12	+	2.93172e12i	0.745098	+	1.29055i	−0.205051	+	0.978751i	$0.565736\pi$
$558$	1.98095e12			0.865008
$559$	2.75107e12			1.19165
$560$	−3.19469e11	−	5.53337e11i	−0.137272	−	0.237762i
$561$	2.39985e11	+	4.15667e11i	0.102294	+	0.177179i
$562$	−1.16101e12			−0.490933
$563$	−1.41764e12			−0.594674			−0.297337	−	0.954773i	$-0.596098\pi$
$563$	−1.41764e12			−0.594674			−0.297337	+	0.954773i	$0.596098\pi$
$564$	−3.05509e11	−	5.29157e11i	−0.127136	−	0.220206i
$565$	3.07450e12	−	5.32519e12i	1.26928	−	2.19845i
$566$	−1.23048e12	−	2.13126e12i	−0.503967	−	0.872896i
$567$	−3.56665e11	+	6.17762e11i	−0.144923	+	0.251014i
$568$	−7.24838e11	+	1.25546e12i	−0.292195	+	0.506097i
$569$	−2.96842e11			−0.118719			−0.0593596	−	0.998237i	$-0.518906\pi$
$569$	−2.96842e11			−0.118719			−0.0593596	+	0.998237i	$0.518906\pi$
$570$	1.23803e12	−	7.31017e11i	0.491240	−	0.290062i
$571$	1.99986e12			0.787296			0.393648	−	0.919261i	$-0.371213\pi$
$571$	1.99986e12			0.787296			0.393648	+	0.919261i	$0.371213\pi$
$572$	−3.20522e11	+	5.55160e11i	−0.125192	+	0.216838i
$573$	3.18763e11	−	5.52114e11i	0.123530	−	0.213960i
$574$	7.80540e11	+	1.35193e12i	0.300118	+	0.519819i
$575$	−4.60221e12	+	7.97127e12i	−1.75574	+	3.04104i
$576$	1.36693e11	+	2.36759e11i	0.0517422	+	0.0896201i
$577$	3.40971e11			0.128064			0.0640319	−	0.997948i	$-0.479604\pi$
$577$	3.40971e11			0.128064			0.0640319	+	0.997948i	$0.479604\pi$
$578$	7.24630e11			0.270048
$579$	1.07768e12	+	1.86661e12i	0.398509	+	0.690238i
$580$	−7.88562e11	−	1.36583e12i	−0.289341	−	0.501153i
$581$	−3.73048e10			−0.0135823
$582$	1.36627e11			0.0493611
$583$	−2.28477e11	−	3.95733e11i	−0.0819093	−	0.141871i
$584$	−4.75747e11	+	8.24017e11i	−0.169246	+	0.293142i
$585$	2.72200e12	+	4.71464e12i	0.960918	+	1.66436i
$586$	−2.10088e11	+	3.63883e11i	−0.0735973	+	0.127474i
$587$	−2.16345e12	+	3.74721e12i	−0.752101	+	1.30268i	0.194701	+	0.980863i	$0.437626\pi$
$587$	−2.16345e12	+	3.74721e12i	−0.752101	+	1.30268i	−0.946803	+	0.321815i	$0.895707\pi$
$588$	4.09537e11			0.141285
$589$	3.71654e12	−	2.19450e12i	1.27239	−	0.751307i
$590$	−1.94341e12			−0.660282
$591$	6.22831e11	−	1.07878e12i	0.210004	−	0.363737i
$592$	−3.45258e11	+	5.98004e11i	−0.115530	+	0.200104i
$593$	8.71822e11	+	1.51004e12i	0.289522	+	0.501467i	0.973696	−	0.227852i	$-0.0731703\pi$
$593$	8.71822e11	+	1.51004e12i	0.289522	+	0.501467i	−0.684174	+	0.729319i	$0.739837\pi$
$594$	−3.41258e11	+	5.91076e11i	−0.112472	+	0.194807i
$595$	−1.97337e12	−	3.41797e12i	−0.645478	−	1.11800i
$596$	−8.24489e11			−0.267656
$597$	2.00987e12			0.647566
$598$	−1.66620e12	−	2.88594e12i	−0.532808	−	0.922851i
$599$	2.70345e12	+	4.68252e12i	0.858022	+	1.48614i	0.873813	+	0.486262i	$0.161640\pi$
$599$	2.70345e12	+	4.68252e12i	0.858022	+	1.48614i	−0.0157913	+	0.999875i	$0.505027\pi$
$600$	−1.29524e12			−0.408007
$601$	−7.87779e11			−0.246303			−0.123151	−	0.992388i	$-0.539300\pi$
$601$	−7.87779e11			−0.246303			−0.123151	+	0.992388i	$0.539300\pi$
$602$	−6.42258e11	−	1.11242e12i	−0.199308	−	0.345212i
$603$	5.18523e11	−	8.98108e11i	0.159713	−	0.276631i
$604$	6.28774e11	+	1.08907e12i	0.192233	+	0.332958i
$605$	2.64027e12	−	4.57308e12i	0.801215	−	1.38774i
$606$	−4.91338e11	+	8.51022e11i	−0.147997	+	0.256339i
$607$	−5.38625e12			−1.61041			−0.805207	−	0.592994i	$-0.797946\pi$
$607$	−5.38625e12			−1.61041			−0.805207	+	0.592994i	$0.797946\pi$
$608$	5.18737e11	+	2.92764e11i	0.153950	+	0.0868864i
$609$	−4.73336e11			−0.139441
$610$	−1.65612e12	+	2.86848e12i	−0.484291	+	0.838817i
$611$	2.52044e12	−	4.36553e12i	0.731630	−	1.26722i
$612$	8.44355e11	+	1.46247e12i	0.243301	+	0.421410i
$613$	1.65424e12	−	2.86523e12i	0.473181	−	0.819574i	−0.526348	−	0.850269i	$-0.676439\pi$
$613$	1.65424e12	−	2.86523e12i	0.473181	−	0.819574i	0.999529	+	0.0306957i	$0.00977229\pi$
$614$	1.17372e12	+	2.03294e12i	0.333278	+	0.577254i
$615$	4.30226e12			1.21272
$616$	2.99312e11			0.0837551
$617$	−2.27680e12	−	3.94353e12i	−0.632471	−	1.09547i	−0.987045	−	0.160444i	$-0.948707\pi$
$617$	−2.27680e12	−	3.94353e12i	−0.632471	−	1.09547i	0.354574	−	0.935028i	$-0.384626\pi$
$618$	6.33770e11	+	1.09772e12i	0.174777	+	0.302722i
$619$	5.77140e12			1.58006			0.790030	−	0.613069i	$-0.210065\pi$
$619$	5.77140e12			1.58006			0.790030	+	0.613069i	$0.210065\pi$
$620$	−5.28615e12			−1.43674
$621$	−1.77399e12	−	3.07264e12i	−0.478673	−	0.829086i
$622$	−1.65123e11	+	2.86002e11i	−0.0442335	+	0.0766147i
$623$	8.44564e11	+	1.46283e12i	0.224614	+	0.389042i
$624$	2.34465e11	−	4.06105e11i	0.0619081	−	0.107228i
$625$	−7.54469e12	+	1.30678e13i	−1.97779	+	3.42564i
$626$	1.28955e12			0.335626
$627$	6.58900e9	+	6.73481e11i	0.00170261	+	0.174029i
$628$	2.00470e12			0.514316
$629$	−2.13267e12	+	3.69389e12i	−0.543244	+	0.940926i
$630$	1.27094e12	−	2.20133e12i	0.321434	−	0.556741i
$631$	−3.21931e12	−	5.57601e12i	−0.808409	−	1.40021i	−0.913965	−	0.405792i	$-0.866996\pi$
$631$	−3.21931e12	−	5.57601e12i	−0.808409	−	1.40021i	0.105557	−	0.994413i	$-0.466338\pi$
$632$	5.09428e11	−	8.82355e11i	0.127015	−	0.219997i
$633$	−2.74116e11	−	4.74783e11i	−0.0678606	−	0.117538i
$634$	−2.62518e12			−0.645295
$635$	1.98119e11			0.0483554
$636$	1.67133e11	+	2.89483e11i	0.0405047	+	0.0701562i
$637$	1.68933e12	+	2.92601e12i	0.406526	+	0.704123i
$638$	7.38809e11			0.176538
$639$	−5.76723e12			−1.36840
$640$	−3.64763e11	−	6.31789e11i	−0.0859412	−	0.148855i
$641$	2.19718e12	−	3.80563e12i	0.514049	−	0.890359i	−0.485818	−	0.874060i	$-0.661478\pi$
$641$	2.19718e12	−	3.80563e12i	0.514049	−	0.890359i	0.999867	−	0.0162992i	$-0.00518843\pi$
$642$	−6.32567e11	−	1.09564e12i	−0.146960	−	0.254542i
$643$	1.30793e12	−	2.26539e12i	0.301741	−	0.522630i	−0.674790	−	0.738010i	$-0.735766\pi$
$643$	1.30793e12	−	2.26539e12i	0.301741	−	0.522630i	0.976530	+	0.215380i	$0.0690990\pi$
$644$	−7.77970e11	+	1.34748e12i	−0.178228	+	0.308700i
$645$	−3.54006e12			−0.805365
$646$	3.20425e12	+	1.80841e12i	0.723903	+	0.408555i
$647$	3.58082e12			0.803366			0.401683	−	0.915779i	$-0.368425\pi$
$647$	3.58082e12			0.803366			0.401683	+	0.915779i	$0.368425\pi$
$648$	−4.07233e11	+	7.05348e11i	−0.0907309	+	0.157151i
$649$	4.55197e11	−	7.88425e11i	0.100716	−	0.174445i
$650$	−5.34283e12	−	9.25405e12i	−1.17398	−	2.03340i
$651$	−7.93256e11	+	1.37396e12i	−0.173101	+	0.299819i
$652$	2.07342e12	+	3.59126e12i	0.449337	+	0.778275i
$653$	7.93013e12			1.70676			0.853378	−	0.521293i	$-0.174550\pi$
$653$	7.93013e12			1.70676			0.853378	+	0.521293i	$0.174550\pi$
$654$	4.77468e10			0.0102057
$655$	−3.67539e12	−	6.36597e12i	−0.780221	−	1.35138i
$656$	8.91205e11	+	1.54361e12i	0.187893	+	0.325440i
$657$	−3.78531e12			−0.792607
$658$	−2.35366e12			−0.489471
$659$	−5.12434e11	−	8.87562e11i	−0.105841	−	0.183322i	0.808241	−	0.588853i	$-0.200420\pi$
$659$	−5.12434e11	−	8.87562e11i	−0.105841	−	0.183322i	−0.914081	+	0.405531i	$0.867087\pi$
$660$	4.12446e11	−	7.14377e11i	0.0846095	−	0.146548i
$661$	−4.58332e11	−	7.93854e11i	−0.0933842	−	0.161746i	0.815549	−	0.578688i	$-0.196435\pi$
$661$	−4.58332e11	−	7.93854e11i	−0.0933842	−	0.161746i	−0.908933	+	0.416942i	$0.863102\pi$
$662$	−2.35946e12	+	4.08670e12i	−0.477476	+	0.827012i
$663$	1.44830e12	−	2.50852e12i	0.291103	−	0.504205i
$664$	−4.25939e10			−0.00850337
$665$	−5.41805e10	−	5.53795e12i	−0.0107435	−	1.09813i
$666$	−2.74707e12			−0.541048
$667$	−1.92031e12	+	3.32607e12i	−0.375668	+	0.650676i
$668$	1.35703e12	−	2.35045e12i	0.263692	−	0.456728i
$669$	−5.99802e11	−	1.03889e12i	−0.115768	−	0.200517i
$670$	−1.38367e12	+	2.39659e12i	−0.265275	+	0.459470i
$671$	−7.75812e11	−	1.34375e12i	−0.147742	−	0.255897i
$672$	−2.18950e11			−0.0414175
$673$	6.95745e12			1.30732			0.653661	−	0.756788i	$-0.273232\pi$
$673$	6.95745e12			1.30732			0.653661	+	0.756788i	$0.273232\pi$
$674$	−2.02230e12	−	3.50273e12i	−0.377465	−	0.653788i
$675$	−5.68848e12	−	9.85274e12i	−1.05470	−	1.82680i
$676$	1.15391e12			0.212526
$677$	5.79124e12			1.05955			0.529776	−	0.848138i	$-0.322276\pi$
$677$	5.79124e12			1.05955			0.529776	+	0.848138i	$0.322276\pi$
$678$	−1.05356e12	−	1.82483e12i	−0.191482	−	0.331656i
$679$	2.63146e11	−	4.55783e11i	0.0475098	−	0.0822894i
$680$	−2.25315e12	−	3.90258e12i	−0.404111	−	0.699941i
$681$	2.41948e11	−	4.19066e11i	0.0431082	−	0.0746655i
$682$	1.23816e12	−	2.14455e12i	0.219152	−	0.379583i
$683$	3.24453e12			0.570504			0.285252	−	0.958453i	$-0.407923\pi$
$683$	3.24453e12			0.570504			0.285252	+	0.958453i	$0.407923\pi$
$684$	2.31825e10	+	2.36955e12i	0.00404956	+	0.413918i
$685$	−2.21643e11			−0.0384633
$686$	1.94688e12	−	3.37210e12i	0.335646	−	0.581356i
$687$	1.30243e12	−	2.25587e12i	0.223074	−	0.386375i
$688$	−7.33317e11	−	1.27014e12i	−0.124780	−	0.216125i
$689$	−1.37884e12	+	2.38823e12i	−0.233092	+	0.403728i
$690$	2.14405e12	+	3.71360e12i	0.360093	+	0.623699i
$691$	−1.02913e13			−1.71719			−0.858595	−	0.512654i	$-0.828662\pi$
$691$	−1.02913e13			−1.71719			−0.858595	+	0.512654i	$0.828662\pi$
$692$	−3.35349e12			−0.555930
$693$	5.95375e11	+	1.03122e12i	0.0980598	+	0.169845i
$694$	−1.82026e12	−	3.15279e12i	−0.297863	−	0.515914i
$695$	−5.83820e12			−0.949178
$696$	−5.40446e11			−0.0872993
$697$	5.50500e12	+	9.53493e12i	0.883506	+	1.53028i
$698$	−1.18703e12	+	2.05600e12i	−0.189284	+	0.327849i
$699$	1.85535e12	+	3.21355e12i	0.293953	+	0.509141i
$700$	−2.49464e12	+	4.32085e12i	−0.392706	+	0.680186i
$701$	−1.31287e10	+	2.27396e10i	−0.00205348	+	0.00355673i	−0.867050	−	0.498221i	$-0.833987\pi$
$701$	−1.31287e10	+	2.27396e10i	−0.00205348	+	0.00355673i	0.864997	+	0.501777i	$0.167320\pi$
$702$	4.11894e12			0.640131
$703$	−5.15388e12	+	3.04321e12i	−0.795858	+	0.469930i
$704$	3.41749e11			0.0524361
$705$	−3.24329e12	+	5.61754e12i	−0.494464	+	0.856437i
$706$	5.47807e11	−	9.48830e11i	0.0829864	−	0.143737i
$707$	1.89265e12	+	3.27816e12i	0.284893	+	0.493450i
$708$	−3.32981e11	+	5.76741e11i	−0.0498047	+	0.0862643i
$709$	−3.86838e12	−	6.70022e12i	−0.574937	−	0.995821i	−0.996048	−	0.0888118i	$-0.971693\pi$
$709$	−3.86838e12	−	6.70022e12i	−0.574937	−	0.995821i	0.421111	−	0.907009i	$-0.361640\pi$
$710$	1.53898e13			2.27284
$711$	4.05330e12			0.594833
$712$	9.64306e11	+	1.67023e12i	0.140623	+	0.243565i
$713$	6.43641e12	+	1.11482e13i	0.932698	+	1.61548i
$714$	−1.35246e12			−0.194752
$715$	6.80533e12			0.973805
$716$	1.98044e12	+	3.43022e12i	0.281613	+	0.487768i
$717$	−2.48785e12	+	4.30909e12i	−0.351551	+	0.608905i
$718$	−7.93777e11	−	1.37486e12i	−0.111465	−	0.193063i
$719$	2.99448e12	−	5.18659e12i	0.417870	−	0.723772i	−0.577855	−	0.816140i	$-0.696110\pi$
$719$	2.99448e12	−	5.18659e12i	0.417870	−	0.723772i	0.995725	+	0.0923672i	$0.0294434\pi$
$720$	1.45113e12	−	2.51344e12i	0.201239	−	0.348555i
$721$	4.88260e12			0.672887
$722$	2.66849e12	+	4.41993e12i	0.365467	+	0.605338i
$723$	1.96448e12			0.267377
$724$	−1.51512e12	+	2.62427e12i	−0.204939	+	0.354964i
$725$	−6.15766e12	+	1.06654e13i	−0.827741	+	1.43369i
$726$	−9.04762e11	−	1.56709e12i	−0.120870	−	0.209354i
$727$	−4.46136e12	+	7.72731e12i	−0.592329	+	1.02594i	0.401589	+	0.915820i	$0.368458\pi$
$727$	−4.46136e12	+	7.72731e12i	−0.592329	+	1.02594i	−0.993918	+	0.110123i	$0.964875\pi$
$728$	−9.03166e11	−	1.56433e12i	−0.119173	−	0.206413i
$729$	−8.40988e11			−0.110285
$730$	1.01011e13			1.31648
$731$	−4.52972e12	−	7.84570e12i	−0.586736	−	1.01626i
$732$	5.67515e11	+	9.82964e11i	0.0730596	+	0.126543i
$733$	−7.82643e12			−1.00137			−0.500686	−	0.865629i	$-0.666919\pi$
$733$	−7.82643e12			−1.00137			−0.500686	+	0.865629i	$0.666919\pi$
$734$	−1.22556e12			−0.155849
$735$	−2.17382e12	−	3.76517e12i	−0.274746	−	0.475874i
$736$	−8.88271e11	+	1.53853e12i	−0.111582	+	0.193266i
$737$	−6.48185e11	−	1.12269e12i	−0.0809274	−	0.140170i
$738$	−3.54547e12	+	6.14093e12i	−0.439967	+	0.762045i
$739$	−3.81889e12	+	6.61452e12i	−0.471018	+	0.815827i	−0.999450	−	0.0331483i	$-0.989447\pi$
$739$	−3.81889e12	+	6.61452e12i	−0.471018	+	0.815827i	0.528432	+	0.848975i	$0.322780\pi$
$740$	7.33052e12			0.898654
$741$	3.50001e12	−	2.06665e12i	0.426469	−	0.251817i
$742$	1.28760e12			0.155942
$743$	7.56589e11	−	1.31045e12i	0.0910773	−	0.157750i	−0.816887	−	0.576797i	$-0.804302\pi$
$743$	7.56589e11	−	1.31045e12i	0.0910773	−	0.157750i	0.907965	+	0.419047i	$0.137636\pi$
$744$	−9.05724e11	+	1.56876e12i	−0.108372	+	0.187706i
$745$	4.37640e12	+	7.58014e12i	0.520491	+	0.901517i
$746$	4.91581e12	−	8.51443e12i	0.581126	−	1.00654i
$747$	−8.47253e10	−	1.46749e11i	−0.00995567	−	0.0172437i
$748$	2.11099e12			0.246564
$749$	−4.87333e12			−0.565793
$750$	4.40346e12	+	7.62701e12i	0.508180	+	0.880194i
$751$	−5.19924e12	−	9.00534e12i	−0.596431	−	1.03305i	−0.993343	−	0.115192i	$-0.963252\pi$
$751$	−5.19924e12	−	9.00534e12i	−0.596431	−	1.03305i	0.396913	−	0.917856i	$-0.370082\pi$
$752$	−2.68736e12			−0.306440
$753$	−9.91408e11			−0.112376
$754$	−2.22933e12	−	3.86132e12i	−0.251191	−	0.435075i
$755$	6.67508e12	−	1.15616e13i	0.747644	−	1.29496i
$756$	−9.61597e11	−	1.66553e12i	−0.107064	−	0.185441i
$757$	1.76552e11	−	3.05797e11i	0.0195408	−	0.0338456i	−0.856090	−	0.516827i	$-0.827113\pi$
$757$	1.76552e11	−	3.05797e11i	0.0195408	−	0.0338456i	0.875630	+	0.482982i	$0.160446\pi$
$758$	−2.82853e12	+	4.89915e12i	−0.311207	+	0.539026i
$759$	−2.00877e12			−0.219707
$760$	−6.18622e10	−	6.32313e12i	−0.00672612	−	0.687497i
$761$	1.30124e13			1.40646			0.703230	−	0.710963i	$-0.251741\pi$
$761$	1.30124e13			1.40646			0.703230	+	0.710963i	$0.251741\pi$
$762$	3.39456e10	−	5.87954e10i	0.00364742	−	0.00631751i
$763$	9.19609e10	−	1.59281e11i	0.00982297	−	0.0170139i
$764$	−1.40197e12	−	2.42829e12i	−0.148874	−	0.257858i
$765$	8.96369e12	−	1.55256e13i	0.946260	−	1.63897i
$766$	−4.30313e12	−	7.45325e12i	−0.451602	−	0.782197i
$767$	−5.49417e12			−0.573223
$768$	−2.49993e11			−0.0259300
$769$	1.55511e12	+	2.69353e12i	0.160359	+	0.277749i	0.934997	−	0.354655i	$-0.115402\pi$
$769$	1.55511e12	+	2.69353e12i	0.160359	+	0.277749i	−0.774639	+	0.632404i	$0.782068\pi$
$770$	−1.58875e12	−	2.75180e12i	−0.162873	−	0.282104i
$771$	1.38859e12			0.141523
$772$	9.47969e12			0.960541
$773$	1.07376e12	+	1.85981e12i	0.108168	+	0.187353i	0.915028	−	0.403390i	$-0.132168\pi$
$773$	1.07376e12	+	1.85981e12i	0.108168	+	0.187353i	−0.806860	+	0.590743i	$0.798835\pi$
$774$	2.91735e12	−	5.05299e12i	0.292182	−	0.506074i
$775$	2.06390e13	+	3.57478e13i	2.05509	+	3.55952i
$776$	3.00455e11	−	5.20404e11i	0.0297442	−	0.0515185i
$777$	1.10004e12	−	1.90533e12i	0.108272	−	0.187532i
$778$	1.00975e13			0.988111
$779$	1.51144e11	+	1.54489e13i	0.0147053	+	1.50307i
$780$	−4.97817e12			−0.481553
$781$	−3.60469e12	+	6.24351e12i	−0.346688	+	0.600481i
$782$	−5.48688e12	+	9.50355e12i	−0.524680	+	0.908773i
$783$	−2.37356e12	−	4.11113e12i	−0.225669	−	0.390870i
$784$	9.00606e11	−	1.55990e12i	0.0851359	−	0.147460i
$785$	−1.06409e13	−	1.84307e13i	−1.00015	−	1.73232i
$786$	−2.51895e12			−0.235407
$787$	−1.24799e13			−1.15964			−0.579820	−	0.814744i	$-0.696877\pi$
$787$	−1.24799e13			−1.15964			−0.579820	+	0.814744i	$0.696877\pi$
$788$	−2.73932e12	−	4.74464e12i	−0.253090	−	0.438364i
$789$	−1.99699e12	−	3.45889e12i	−0.183455	−	0.317753i
$790$	−1.08162e13			−0.987989
$791$	−8.11672e12			−0.737201
$792$	6.79788e11	+	1.17743e12i	0.0613917	+	0.106334i
$793$	−4.68198e12	+	8.10943e12i	−0.420436	+	0.728217i
$794$	1.38694e12	+	2.40226e12i	0.123842	+	0.214500i
$795$	1.77429e12	−	3.07315e12i	0.157533	−	0.272855i
$796$	4.41988e12	−	7.65546e12i	0.390213	−	0.675869i
$797$	3.85165e12			0.338130			0.169065	−	0.985605i	$-0.445925\pi$
$797$	3.85165e12			0.338130			0.169065	+	0.985605i	$0.445925\pi$
$798$	−1.65277e12	−	9.32789e11i	−0.144278	−	0.0814273i
$799$	−1.65999e13			−1.44094
$800$	−2.84833e12	+	4.93346e12i	−0.245859	+	0.425840i
$801$	−3.83629e12	+	6.64464e12i	−0.329280	+	0.570329i
$802$	1.20714e11	+	2.09082e11i	0.0103032	+	0.0178456i
$803$	−2.36594e12	+	4.09792e12i	−0.200809	+	0.347811i
$804$	4.74154e11	+	8.21259e11i	0.0400191	+	0.0693151i
$805$	1.65179e13			1.38635
$806$	−1.49444e13			−1.24730
$807$	−2.89964e11	−	5.02232e11i	−0.0240665	−	0.0416844i
$808$	2.16099e12	+	3.74294e12i	0.178362	+	0.308931i
$809$	−4.77405e12			−0.391849			−0.195925	−	0.980619i	$-0.562771\pi$
$809$	−4.77405e12			−0.391849			−0.195925	+	0.980619i	$0.562771\pi$
$810$	8.64638e12			0.705751
$811$	−6.86646e12	−	1.18930e13i	−0.557364	−	0.965382i	−0.997715	−	0.0675570i	$-0.978480\pi$
$811$	−6.86646e12	−	1.18930e13i	−0.557364	−	0.965382i	0.440352	−	0.897825i	$-0.354854\pi$
$812$	−1.04091e12	+	1.80290e12i	−0.0840252	+	0.145536i
$813$	7.32607e11	+	1.26891e12i	0.0588117	+	0.101865i
$814$	−1.71700e12	+	2.97394e12i	−0.137076	+	0.237422i
$815$	2.20114e13	−	3.81249e13i	1.74759	−	3.02691i
$816$	−1.54421e12			−0.121927
$817$	−1.24367e11	−	1.27120e13i	−0.00976578	−	0.998190i
$818$	7.24944e12			0.566128
$819$	3.59305e12	−	6.22335e12i	0.279053	−	0.483333i
$820$	9.46104e12	−	1.63870e13i	0.730763	−	1.26572i
$821$	1.98417e12	+	3.43668e12i	0.152417	+	0.263995i	0.932116	−	0.362161i	$-0.117961\pi$
$821$	1.98417e12	+	3.43668e12i	0.152417	+	0.263995i	−0.779698	+	0.626156i	$0.784628\pi$
$822$	−3.79761e10	+	6.57766e10i	−0.00290127	+	0.00502514i
$823$	8.97433e12	+	1.55440e13i	0.681872	+	1.18104i	0.974409	+	0.224782i	$0.0721671\pi$
$823$	8.97433e12	+	1.55440e13i	0.681872	+	1.18104i	−0.292537	+	0.956254i	$0.594500\pi$
$824$	5.57486e12			0.421271
$825$	−6.44134e12			−0.484098
$826$	1.28265e12	+	2.22162e12i	0.0958736	+	0.166058i
$827$	−5.45707e12	−	9.45191e12i	−0.405681	−	0.702660i	0.588720	−	0.808337i	$-0.299632\pi$
$827$	−5.45707e12	−	9.45191e12i	−0.405681	−	0.702660i	−0.994400	+	0.105678i	$0.966299\pi$
$828$	−7.06760e12			−0.522559
$829$	−1.09623e12			−0.0806130			−0.0403065	−	0.999187i	$-0.512833\pi$
$829$	−1.09623e12			−0.0806130			−0.0403065	+	0.999187i	$0.512833\pi$
$830$	2.26089e11	+	3.91597e11i	0.0165359	+	0.0286410i
$831$	6.26271e11	−	1.08473e12i	0.0455573	−	0.0789075i
$832$	−1.03122e12	−	1.78612e12i	−0.0746097	−	0.129228i
$833$	5.56307e12	−	9.63551e12i	0.400324	−	0.693382i
$834$	−1.00031e12	+	1.73259e12i	−0.0715959	+	0.124008i
$835$	−2.88126e13			−2.05113
$836$	2.57973e12	+	1.45595e12i	0.182661	+	0.103090i
$837$	−1.59112e13			−1.12057
$838$	−2.62933e12	+	4.55413e12i	−0.184182	+	0.319012i
$839$	−1.10120e13	+	1.90734e13i	−0.767254	+	1.32892i	0.171793	+	0.985133i	$0.445044\pi$
$839$	−1.10120e13	+	1.90734e13i	−0.767254	+	1.32892i	−0.939047	+	0.343790i	$0.888289\pi$
$840$	1.16219e12	+	2.01297e12i	0.0805415	+	0.139502i
$841$	4.68425e12	−	8.11336e12i	0.322892	−	0.559266i
$842$	−1.55169e11	−	2.68761e11i	−0.0106390	−	0.0184273i
$843$	4.22360e12			0.288044
$844$	−2.41122e12			−0.163567
$845$	−6.12496e12	−	1.06087e13i	−0.413283	−	0.715828i
$846$	−5.34555e12	−	9.25876e12i	−0.358778	−	0.621422i
$847$	−6.97034e12			−0.465349
$848$	1.47016e12			0.0976299
$849$	4.47635e12	+	7.75326e12i	0.295692	+	0.512153i
$850$	−1.75942e13	+	3.04741e13i	−1.15607	+	2.00238i
$851$	−8.92564e12	−	1.54597e13i	−0.583387	−	1.01046i
$852$	2.63687e12	−	4.56719e12i	0.171439	−	0.296942i
$853$	1.48478e13	−	2.57172e13i	0.960266	−	1.66323i	0.238438	−	0.971158i	$-0.423365\pi$
$853$	1.48478e13	−	2.57172e13i	0.960266	−	1.66323i	0.721828	−	0.692072i	$-0.243302\pi$
$854$	4.37216e12			0.281278
$855$	2.16620e13	−	1.27907e13i	1.38628	−	0.818555i
$856$	−5.56428e12			−0.354223
$857$	−1.39546e13	+	2.41701e13i	−0.883699	+	1.53061i	−0.0365018	+	0.999334i	$0.511621\pi$
$857$	−1.39546e13	+	2.41701e13i	−0.883699	+	1.53061i	−0.847197	+	0.531278i	$0.821712\pi$
$858$	1.16602e12	−	2.01960e12i	0.0734535	−	0.127225i
$859$	9.33265e12	+	1.61646e13i	0.584838	+	1.01297i	0.994896	+	0.100910i	$0.0321754\pi$
$859$	9.33265e12	+	1.61646e13i	0.584838	+	1.01297i	−0.410057	+	0.912060i	$0.634491\pi$
$860$	−7.78491e12	+	1.34839e13i	−0.485300	+	0.840564i
$861$	−2.83951e12	−	4.91817e12i	−0.176088	−	0.304993i
$862$	−1.65595e13			−1.02156
$863$	−1.90601e13			−1.16971			−0.584854	−	0.811139i	$-0.698848\pi$
$863$	−1.90601e13			−1.16971			−0.584854	+	0.811139i	$0.698848\pi$
$864$	−1.09793e12	−	1.90167e12i	−0.0670291	−	0.116098i
$865$	1.78004e13	+	3.08311e13i	1.08108	+	1.87248i
$866$	1.22478e13			0.739992
$867$	−2.63611e12			−0.158445
$868$	3.48887e12	+	6.04291e12i	0.208615	+	0.361333i
$869$	2.53344e12	−	4.38804e12i	0.150703	−	0.261025i
$870$	2.86869e12	+	4.96872e12i	0.169765	+	0.294041i
$871$	−3.91176e12	+	6.77537e12i	−0.230298	+	0.398888i
$872$	1.04999e11	−	1.81864e11i	0.00614981	−	0.0106518i
$873$	2.39060e12			0.139297
$874$	−1.32598e13	+	7.82950e12i	−0.768662	+	0.453871i
$875$	3.39245e13			1.95649
$876$	1.73071e12	−	2.99767e12i	0.0993014	−	0.171995i
$877$	−6.58592e12	+	1.14072e13i	−0.375940	+	0.651147i	−0.990467	−	0.137748i	$-0.956013\pi$
$877$	−6.58592e12	+	1.14072e13i	−0.375940	+	0.651147i	0.614527	+	0.788896i	$0.289347\pi$
$878$	−9.06199e12	−	1.56958e13i	−0.514634	−	0.891372i
$879$	7.64274e11	−	1.32376e12i	0.0431816	−	0.0747928i
$880$	−1.81401e12	−	3.14195e12i	−0.101969	−	0.176615i
$881$	8.05514e12			0.450486			0.225243	−	0.974303i	$-0.427682\pi$
$881$	8.05514e12			0.450486			0.225243	+	0.974303i	$0.427682\pi$
$882$	7.16574e12			0.398705
$883$	6.41461e12	+	1.11104e13i	0.355097	+	0.615046i	0.987135	−	0.159892i	$-0.0511145\pi$
$883$	6.41461e12	+	1.11104e13i	0.355097	+	0.615046i	−0.632038	+	0.774938i	$0.717781\pi$
$884$	−6.36986e12	−	1.10329e13i	−0.350828	−	0.607652i
$885$	7.06987e12			0.387406
$886$	6.92837e10			0.00377728
$887$	7.11112e12	+	1.23168e13i	0.385729	+	0.668102i	0.991870	−	0.127255i	$-0.0406167\pi$
$887$	7.11112e12	+	1.23168e13i	0.385729	+	0.668102i	−0.606141	+	0.795357i	$0.707283\pi$
$888$	1.25601e12	−	2.17546e12i	0.0677849	−	0.117407i
$889$	−1.30759e11	−	2.26482e11i	−0.00702125	−	0.0121612i
$890$	1.02371e13	−	1.77312e13i	0.546917	−	0.947288i
$891$	−2.02521e12	+	3.50777e12i	−0.107652	+	0.186458i
$892$	−5.27606e12			−0.279041
$893$	−2.02859e13	−	1.14489e13i	−1.06749	−	0.602466i
$894$	2.99939e12			0.157041
$895$	2.10244e13	−	3.64153e13i	1.09527	−	1.89706i
$896$	−4.81490e11	+	8.33965e11i	−0.0249575	+	0.0432277i
$897$	6.06141e12	+	1.04987e13i	0.312614	+	0.541463i
$898$	−8.89311e11	+	1.54033e12i	−0.0456363	+	0.0790444i
$899$	8.61177e12	+	1.49160e13i	0.439718	+	0.761613i
$900$	−2.26630e13			−1.15140
$901$	9.08121e12			0.459073
$902$	4.43205e12	+	7.67654e12i	0.222934	+	0.386132i
$903$	2.33645e12	+	4.04686e12i	0.116940	+	0.202546i
$904$	−9.26751e12			−0.461535
$905$	3.21691e13			1.59412
$906$	−2.28740e12	−	3.96190e12i	−0.112789	−	0.195356i
$907$	1.03515e12	−	1.79293e12i	0.0507889	−	0.0879690i	−0.839513	−	0.543339i	$-0.817160\pi$
$907$	1.03515e12	−	1.79293e12i	0.0507889	−	0.0879690i	0.890302	+	0.455370i	$0.150493\pi$
$908$	−1.06413e12	−	1.84312e12i	−0.0519526	−	0.0899845i
$909$	−8.59703e12	+	1.48905e13i	−0.417649	+	0.723388i
$910$	−9.58802e12	+	1.66069e13i	−0.463493	+	0.802793i
$911$	1.64970e13			0.793546			0.396773	−	0.917917i	$-0.370130\pi$
$911$	1.64970e13			0.793546			0.396773	+	0.917917i	$0.370130\pi$
$912$	−1.88710e12	−	1.06504e12i	−0.0903271	−	0.0509787i
$913$	−2.11824e11			−0.0100892
$914$	5.01760e12	−	8.69074e12i	0.237814	−	0.411907i
$915$	6.02474e12	−	1.04352e13i	0.284147	−	0.492158i
$916$	−5.72831e12	−	9.92172e12i	−0.268842	−	0.465648i
$917$	−4.85154e12	+	8.40311e12i	−0.226578	+	0.392444i
$918$	−6.78195e12	−	1.17467e13i	−0.315183	−	0.545913i
$919$	−3.40146e12			−0.157306			−0.0786532	−	0.996902i	$-0.525062\pi$
$919$	−3.40146e12			−0.157306			−0.0786532	+	0.996902i	$0.525062\pi$
$920$	1.88598e13			0.867944
$921$	−4.26984e12	−	7.39558e12i	−0.195544	−	0.338691i
$922$	7.93655e12	+	1.37465e13i	0.361695	+	0.626474i
$923$	4.35082e13			1.97317
$924$	−1.08886e12			−0.0491415
$925$	−2.86210e13	−	4.95730e13i	−1.28543	−	2.22642i
$926$	−9.20174e12	+	1.59379e13i	−0.411264	+	0.712330i
$927$	1.10892e13	+	1.92070e13i	0.493220	+	0.854283i
$928$	−1.18849e12	+	2.05852e12i	−0.0526052	+	0.0911149i
$929$	−1.21859e13	+	2.11065e13i	−0.536767	+	0.929707i	0.462309	+	0.886719i	$0.347021\pi$
$929$	−1.21859e13	+	2.11065e13i	−0.536767	+	0.929707i	−0.999076	+	0.0429884i	$0.986312\pi$
$930$	1.92304e13			0.842974
$931$	1.34439e13	−	7.93822e12i	0.586479	−	0.346298i
$932$	1.63203e13			0.708525
$933$	6.00698e11	−	1.04044e12i	0.0259531	−	0.0449520i
$934$	8.96726e12	−	1.55318e13i	0.385566	−	0.667820i
$935$	−1.12052e13	−	1.94079e13i	−0.479475	−	0.830475i
$936$	4.10248e12	−	7.10570e12i	0.174705	−	0.302598i
$937$	1.23218e13	+	2.13420e13i	0.522211	+	0.904497i	0.999666	+	0.0258402i	$0.00822611\pi$
$937$	1.23218e13	+	2.13420e13i	0.522211	+	0.904497i	−0.477455	+	0.878656i	$0.658441\pi$
$938$	3.65291e12			0.154073
$939$	−4.69124e12			−0.196921
$940$	1.42645e13	+	2.47069e13i	0.595912	+	1.03215i
$941$	−6.23889e12	−	1.08061e13i	−0.259390	−	0.449277i	0.706688	−	0.707525i	$-0.250188\pi$
$941$	−6.23889e12	−	1.08061e13i	−0.259390	−	0.449277i	−0.966079	+	0.258248i	$0.916855\pi$
$942$	−7.29284e12			−0.301764
$943$	−4.60790e13			−1.89758
$944$	1.46451e12	+	2.53660e12i	0.0600231	+	0.103963i
$945$	−1.02083e13	+	1.76813e13i	−0.416400	+	0.721227i
$946$	−3.64686e12	−	6.31655e12i	−0.148050	−	0.256431i
$947$	−9.40337e11	+	1.62871e12i	−0.0379935	+	0.0658066i	−0.884397	−	0.466736i	$-0.845430\pi$
$947$	−9.40337e11	+	1.62871e12i	−0.0379935	+	0.0658066i	0.846403	+	0.532542i	$0.178763\pi$
$948$	−1.85323e12	+	3.20990e12i	−0.0745234	+	0.129078i
$949$	2.85566e13			1.14290
$950$	−4.25189e13	+	2.51061e13i	−1.69366	+	1.00005i
$951$	9.55009e12			0.378613
$952$	−2.97418e12	+	5.15142e12i	−0.117355	+	0.203264i
$953$	−2.33207e13	+	4.03927e13i	−0.915850	+	1.58630i	−0.110198	+	0.993910i	$0.535148\pi$
$953$	−2.33207e13	+	4.03927e13i	−0.915850	+	1.58630i	−0.805652	+	0.592389i	$0.798185\pi$
$954$	2.92436e12	+	5.06513e12i	0.114304	+	0.197981i
$955$	−1.48834e13	+	2.57788e13i	−0.579011	+	1.00288i
$956$	1.09420e13	+	1.89521e13i	0.423679	+	0.733833i
$957$	−2.68769e12			−0.103580
$958$	3.59582e13			1.37928
$959$	1.46285e11	+	2.53373e11i	0.00558492	+	0.00967336i
$960$	1.32696e12	+	2.29837e12i	0.0504242	+	0.0873372i
$961$	3.12896e13			1.18344
$962$	2.07240e13			0.780164
$963$	−1.10681e13	−	1.91706e13i	−0.414721	−	0.718318i
$964$	4.32005e12	−	7.48255e12i	0.161117	−	0.279063i
$965$	−5.03182e13	−	8.71537e13i	−1.86790	−	3.23529i
$966$	2.83016e12	−	4.90198e12i	0.104572	−	0.181123i
$967$	−4.39025e12	+	7.60414e12i	−0.161462	+	0.279660i	−0.935393	−	0.353609i	$-0.884954\pi$
$967$	−4.39025e12	+	7.60414e12i	−0.161462	+	0.279660i	0.773931	+	0.633270i	$0.218288\pi$
$968$	−7.95860e12			−0.291338
$969$	−1.16567e13	−	6.57878e12i	−0.424734	−	0.239711i
$970$	−6.37928e12			−0.231366
$971$	−1.53021e13	+	2.65040e13i	−0.552413	+	0.956807i	0.445687	+	0.895189i	$0.352959\pi$
$971$	−1.53021e13	+	2.65040e13i	−0.552413	+	0.956807i	−0.998100	+	0.0616181i	$0.980374\pi$
$972$	6.75749e12	−	1.17043e13i	0.242821	−	0.420579i
$973$	3.85323e12	+	6.67399e12i	0.137822	+	0.238714i
$974$	1.19626e13	−	2.07198e13i	0.425902	−	0.737684i
$975$	1.94365e13	+	3.36651e13i	0.688808	+	1.19305i
$976$	4.99205e12			0.176098
$977$	−1.30523e13			−0.458313			−0.229156	−	0.973390i	$-0.573597\pi$
$977$	−1.30523e13			−0.458313			−0.229156	+	0.973390i	$0.573597\pi$
$978$	−7.54283e12	−	1.30646e13i	−0.263639	−	0.456636i
$979$	4.79559e12	+	8.30621e12i	0.166848	+	0.288989i
$980$	−1.91217e13			−0.662230
$981$	8.35434e11			0.0288006
$982$	1.02307e13	+	1.77201e13i	0.351078	+	0.608084i
$983$	5.17924e12	−	8.97070e12i	0.176919	−	0.306433i	−0.763905	−	0.645329i	$-0.776720\pi$
$983$	5.17924e12	−	8.97070e12i	0.176919	−	0.306433i	0.940824	+	0.338896i	$0.110054\pi$
$984$	−3.24209e12	−	5.61547e12i	−0.110242	−	0.190945i
$985$	−2.90806e13	+	5.03691e13i	−0.984330	+	1.70491i
$986$	−7.34131e12	+	1.27155e13i	−0.247359	+	0.428438i
$987$	8.56232e12			0.287187
$988$	−1.74890e11	−	1.78760e13i	−0.00583927	−	0.596849i
$989$	3.79156e13			1.26019
$990$	7.21664e12	−	1.24996e13i	0.238768	−	0.413559i
$991$	2.72906e13	−	4.72687e13i	0.898838	−	1.55683i	0.0698569	−	0.997557i	$-0.477746\pi$
$991$	2.72906e13	−	4.72687e13i	0.898838	−	1.55683i	0.828981	−	0.559276i	$-0.188921\pi$
$992$	3.98353e12	+	6.89967e12i	0.130607	+	0.226217i
$993$	8.58341e12	−	1.48669e13i	0.280149	−	0.485232i
$994$	−1.01573e13	−	1.75930e13i	−0.330019	−	0.571610i
$995$	−9.38431e13			−3.03528
$996$	1.54951e11			0.00498917
$997$	−2.29766e13	−	3.97966e13i	−0.736473	−	1.27561i	−0.954074	−	0.299571i	$-0.903156\pi$
$997$	−2.29766e13	−	3.97966e13i	−0.736473	−	1.27561i	0.217601	−	0.976038i	$-0.430177\pi$
$998$	1.20578e13	+	2.08848e13i	0.384752	+	0.666411i
$999$	2.20648e13			0.700897

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.b.11.5	yes	16
19.7	even	3	inner	38.10.c.b.7.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.b.7.5	✓	16	19.7	even	3	inner
38.10.c.b.11.5	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(29.1030 - 50.4079i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1358.85 + 2353.60i) q^{5} +(465.648 + 806.526i) q^{6} +3587.38 q^{7} +4096.00 q^{8} +(8147.53 + 14111.9i) q^{9} +O(q^{10})\)	\(q+(-8.00000 + 13.8564i) q^{2} +(29.1030 - 50.4079i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1358.85 + 2353.60i) q^{5} +(465.648 + 806.526i) q^{6} +3587.38 q^{7} +4096.00 q^{8} +(8147.53 + 14111.9i) q^{9} +(-21741.6 - 37657.5i) q^{10} +20369.8 q^{11} -14900.7 q^{12} +(-61465.3 - 106461. i) q^{13} +(-28699.0 + 49708.2i) q^{14} +(79093.2 + 136993. i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(-202409. + 350582. i) q^{17} -260721. q^{18} +(-489149. + 288827. i) q^{19} +695731. q^{20} +(104404. - 180832. i) q^{21} +(-162959. + 282253. i) q^{22} +(-847122. - 1.46726e6i) q^{23} +(119206. - 206471. i) q^{24} +(-2.71638e6 - 4.70491e6i) q^{25} +1.96689e6 q^{26} +2.09414e6 q^{27} +(-459185. - 795331. i) q^{28} +(-1.13343e6 - 1.96316e6i) q^{29} -2.53098e6 q^{30} -7.59798e6 q^{31} +(-524288. - 908093. i) q^{32} +(592823. - 1.02680e6i) q^{33} +(-3.23854e6 - 5.60932e6i) q^{34} +(-4.87471e6 + 8.44325e6i) q^{35} +(2.08577e6 - 3.61266e6i) q^{36} +1.05364e7 q^{37} +(-88916.9 - 9.08846e6i) q^{38} -7.15531e6 q^{39} +(-5.56585e6 + 9.64033e6i) q^{40} +(1.35987e7 - 2.35537e7i) q^{41} +(1.67046e6 + 2.89332e6i) q^{42} +(-1.11895e7 + 1.93808e7i) q^{43} +(-2.60734e6 - 4.51604e6i) q^{44} -4.42851e7 q^{45} +2.71079e7 q^{46} +(2.05030e7 + 3.55122e7i) q^{47} +(1.90729e6 + 3.30353e6i) q^{48} -2.74843e7 q^{49} +8.69242e7 q^{50} +(1.17814e7 + 2.04060e7i) q^{51} +(-1.57351e7 + 2.72540e7i) q^{52} +(-1.12164e7 - 1.94274e7i) q^{53} +(-1.67531e7 + 2.90172e7i) q^{54} +(-2.76795e7 + 4.79424e7i) q^{55} +1.46939e7 q^{56} +(323469. + 3.30627e7i) q^{57} +3.62697e7 q^{58} +(2.23466e7 - 3.87055e7i) q^{59} +(2.02479e7 - 3.50703e7i) q^{60} +(-3.80863e7 - 6.59675e7i) q^{61} +(6.07838e7 - 1.05281e8i) q^{62} +(2.92283e7 + 5.06249e7i) q^{63} +1.67772e7 q^{64} +3.34089e8 q^{65} +(9.48517e6 + 1.64288e7i) q^{66} +(-3.18209e7 - 5.51153e7i) q^{67} +1.03633e8 q^{68} -9.86151e7 q^{69} +(-7.79954e7 - 1.35092e8i) q^{70} +(-1.76962e8 + 3.06508e8i) q^{71} +(3.33723e7 + 5.78025e7i) q^{72} +(-1.16149e8 + 2.01176e8i) q^{73} +(-8.42915e7 + 1.45997e8i) q^{74} -3.16220e8 q^{75} +(1.26645e8 + 7.14756e7i) q^{76} +7.30743e7 q^{77} +(5.72424e7 - 9.91468e7i) q^{78} +(1.24372e8 - 2.15419e8i) q^{79} +(-8.90536e7 - 1.54245e8i) q^{80} +(-9.94221e7 + 1.72204e8i) q^{81} +(2.17579e8 + 3.76858e8i) q^{82} -1.03989e7 q^{83} -5.34546e7 q^{84} +(-5.50086e8 - 9.52777e8i) q^{85} +(-1.79033e8 - 3.10093e8i) q^{86} -1.31945e8 q^{87} +8.34348e7 q^{88} +(2.35426e8 + 4.07770e8i) q^{89} +(3.54281e8 - 6.13632e8i) q^{90} +(-2.20500e8 - 3.81916e8i) q^{91} +(-2.16863e8 + 3.75618e8i) q^{92} +(-2.21124e8 + 3.82998e8i) q^{93} -6.56094e8 q^{94} +(-1.51031e7 - 1.54373e9i) q^{95} -6.10334e7 q^{96} +(7.33534e7 - 1.27052e8i) q^{97} +(2.19875e8 - 3.80834e8i) q^{98} +(1.65964e8 + 2.87458e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9 - 5456 * q^10 + 106682 * q^11 - 35840 * q^12 - 683 * q^13 - 29632 * q^14 + 2299 * q^15 - 524288 * q^16 - 611267 * q^17 + 1698048 * q^18 - 1609677 * q^19 + 174592 * q^20 - 941048 * q^21 - 853456 * q^22 - 416119 * q^23 + 286720 * q^24 - 3309027 * q^25 + 21856 * q^26 - 16903604 * q^27 - 474112 * q^28 - 5079157 * q^29 - 73568 * q^30 + 8618324 * q^31 - 8388608 * q^32 - 7592195 * q^33 - 9780272 * q^34 - 2035632 * q^35 - 13584384 * q^36 - 33091520 * q^37 + 18612624 * q^38 + 37931126 * q^39 - 1396736 * q^40 - 7394646 * q^41 - 15056768 * q^42 - 98675599 * q^43 - 13655296 * q^44 + 89231852 * q^45 + 13315808 * q^46 + 34129475 * q^47 + 4587520 * q^48 + 65004400 * q^49 + 105888864 * q^50 + 16027749 * q^51 - 174848 * q^52 - 110053995 * q^53 + 135228832 * q^54 + 135992300 * q^55 + 15171584 * q^56 + 14986101 * q^57 + 162533024 * q^58 - 2017760 * q^59 + 588544 * q^60 - 221861413 * q^61 - 68946592 * q^62 + 56812456 * q^63 + 268435456 * q^64 + 262635974 * q^65 - 121475120 * q^66 + 237580440 * q^67 + 312968704 * q^68 - 135348410 * q^69 - 32570112 * q^70 - 431190909 * q^71 - 217350144 * q^72 + 199873544 * q^73 + 264732160 * q^74 - 1822944486 * q^75 + 114275328 * q^76 + 2014342624 * q^77 - 303449008 * q^78 - 296762835 * q^79 - 22347776 * q^80 - 1069077456 * q^81 - 118314336 * q^82 + 1592138306 * q^83 + 481816576 * q^84 - 293558115 * q^85 - 1578809584 * q^86 - 1647860854 * q^87 + 436969472 * q^88 - 444394631 * q^89 - 713854816 * q^90 - 284099544 * q^91 - 106526464 * q^92 + 1322110374 * q^93 - 1092143200 * q^94 + 8705459 * q^95 - 146800640 * q^96 - 611719542 * q^97 - 520035200 * q^98 + 1201848626 * q^99

Introduction

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