LMFDB - Embedded newform 45.10.e.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,10,Mod(16,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("45.16");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	45.e (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:	$23.1766126274$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	45.31
Dual form			45.10.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-20.9424 - 36.2733i) q^{2} +(-70.5260 - 121.281i) q^{3} +(-621.169 + 1075.90i) q^{4} +(312.500 - 541.266i) q^{5} +(-2922.28 + 5098.13i) q^{6} +(1139.06 + 1972.90i) q^{7} +30590.0 q^{8} +(-9735.16 + 17106.9i) q^{9} -26178.0 q^{10} +(15392.4 + 26660.3i) q^{11} +(174294. - 542.666i) q^{12} +(80844.7 - 140027. i) q^{13} +(47709.2 - 82634.7i) q^{14} +(-87684.6 + 273.006i) q^{15} +(-322590. - 558743. i) q^{16} +479287. q^{17} +(824403. - 5133.61i) q^{18} +148729. q^{19} +(388230. + 672435. i) q^{20} +(158943. - 277287. i) q^{21} +(644706. - 1.11666e6i) q^{22} +(-798956. + 1.38383e6i) q^{23} +(-2.15739e6 - 3.70999e6i) q^{24} +(-195312. - 338291. i) q^{25} -6.77233e6 q^{26} +(2.76133e6 - 25792.9i) q^{27} -2.83019e6 q^{28} +(3.16108e6 + 5.47514e6i) q^{29} +(1.84623e6 + 3.17489e6i) q^{30} +(-2.35019e6 + 4.07064e6i) q^{31} +(-5.68059e6 + 9.83907e6i) q^{32} +(2.14783e6 - 3.74705e6i) q^{33} +(-1.00374e7 - 1.73853e7i) q^{34} +1.42382e6 q^{35} +(-1.23581e7 - 2.11003e7i) q^{36} -1.02614e6 q^{37} +(-3.11474e6 - 5.39489e6i) q^{38} +(-2.26843e7 + 70627.6i) q^{39} +(9.55938e6 - 1.65573e7i) q^{40} +(1.12560e7 - 1.94960e7i) q^{41} +(-1.33868e7 + 41679.7i) q^{42} +(-907878. - 1.57249e6i) q^{43} -3.82450e7 q^{44} +(6.21716e6 + 1.06152e7i) q^{45} +6.69282e7 q^{46} +(1.79902e7 + 3.11599e7i) q^{47} +(-4.50139e7 + 7.85300e7i) q^{48} +(1.75819e7 - 3.04527e7i) q^{49} +(-8.18063e6 + 1.41693e7i) q^{50} +(-3.38022e7 - 5.81284e7i) q^{51} +(1.00436e8 + 1.73961e8i) q^{52} -8.27475e7 q^{53} +(-5.87644e7 - 9.96223e7i) q^{54} +1.92404e7 q^{55} +(3.48438e7 + 6.03512e7i) q^{56} +(-1.04893e7 - 1.80380e7i) q^{57} +(1.32401e8 - 2.29325e8i) q^{58} +(5.64844e7 - 9.78338e7i) q^{59} +(5.41732e7 - 9.45091e7i) q^{60} +(8.20377e7 + 1.42093e8i) q^{61} +1.96874e8 q^{62} +(-4.48393e7 + 279217. i) q^{63} +1.45528e8 q^{64} +(-5.05280e7 - 8.75170e7i) q^{65} +(-1.80899e8 + 563228. i) q^{66} +(1.20673e8 - 2.09012e8i) q^{67} +(-2.97718e8 + 5.15662e8i) q^{68} +(2.24180e8 - 697984. i) q^{69} +(-2.98182e7 - 5.16467e7i) q^{70} +7.06238e7 q^{71} +(-2.97799e8 + 5.23301e8i) q^{72} -9.04161e7 q^{73} +(2.14898e7 + 3.72214e7i) q^{74} +(-2.72537e7 + 4.75460e7i) q^{75} +(-9.23857e7 + 1.60017e8i) q^{76} +(-3.50655e7 + 6.07353e7i) q^{77} +(4.77626e8 + 8.21355e8i) q^{78} +(-1.41210e8 - 2.44582e8i) q^{79} -4.03238e8 q^{80} +(-1.97874e8 - 3.33078e8i) q^{81} -9.42914e8 q^{82} +(1.17513e8 + 2.03538e8i) q^{83} +(1.99602e8 + 3.43248e8i) q^{84} +(1.49777e8 - 2.59422e8i) q^{85} +(-3.80263e7 + 6.58635e7i) q^{86} +(4.41093e8 - 7.69519e8i) q^{87} +(4.70852e8 + 8.15540e8i) q^{88} +3.12559e7 q^{89} +(2.54847e8 - 4.47825e8i) q^{90} +3.68347e8 q^{91} +(-9.92572e8 - 1.71919e9i) q^{92} +(6.59441e8 - 2.05317e6i) q^{93} +(7.53515e8 - 1.30513e9i) q^{94} +(4.64778e7 - 8.05018e7i) q^{95} +(1.59392e9 - 4.96268e6i) q^{96} +(-4.09009e8 - 7.08425e8i) q^{97} -1.47283e9 q^{98} +(-6.05924e8 + 3.77313e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 16 q^{2} - 285 q^{3} - 3840 q^{4} + 10625 q^{5} + 1635 q^{6} + 9946 q^{7} + 38772 q^{8} + 7959 q^{9} - 20000 q^{10} - 32881 q^{11} + 595719 q^{12} + 100272 q^{13} - 333129 q^{14} - 157500 q^{15}+ \cdots - 3426367056 q^{99}+O(q^{100}) $ 34 * q - 16 * q^2 - 285 * q^3 - 3840 * q^4 + 10625 * q^5 + 1635 * q^6 + 9946 * q^7 + 38772 * q^8 + 7959 * q^9 - 20000 * q^10 - 32881 * q^11 + 595719 * q^12 + 100272 * q^13 - 333129 * q^14 - 157500 * q^15 - 292740 * q^16 - 103174 * q^17 - 401577 * q^18 - 1954002 * q^19 + 2400000 * q^20 + 846540 * q^21 - 603517 * q^22 - 2528832 * q^23 + 2610864 * q^24 - 6640625 * q^25 - 11356132 * q^26 + 13389570 * q^27 + 1233322 * q^28 + 4997116 * q^29 - 2246250 * q^30 + 7154764 * q^31 - 3848138 * q^32 + 37701447 * q^33 - 1842211 * q^34 + 12432500 * q^35 + 31228485 * q^36 - 29485864 * q^37 - 27825985 * q^38 - 48378006 * q^39 + 12116250 * q^40 - 1432577 * q^41 + 645597 * q^42 + 30233475 * q^43 + 172245706 * q^44 - 4490625 * q^45 - 38739414 * q^46 - 51256132 * q^47 - 273587937 * q^48 - 97033283 * q^49 - 6250000 * q^50 + 191039205 * q^51 + 170396546 * q^52 + 198356324 * q^53 + 65145240 * q^54 - 41101250 * q^55 - 446494149 * q^56 - 442487301 * q^57 + 199102621 * q^58 - 163581061 * q^59 + 110338125 * q^60 + 263506344 * q^61 + 682090404 * q^62 - 131178564 * q^63 - 504872168 * q^64 - 62670000 * q^65 - 888863958 * q^66 + 624947419 * q^67 - 77685671 * q^68 + 1347472386 * q^69 + 208205625 * q^70 + 520490800 * q^71 - 150538482 * q^72 - 1740248610 * q^73 - 479177876 * q^74 + 12890625 * q^75 + 1071379103 * q^76 - 777961272 * q^77 + 2208863298 * q^78 + 847184266 * q^79 - 365925000 * q^80 - 455780961 * q^81 - 2343238688 * q^82 - 663595350 * q^83 - 1445250609 * q^84 - 32241875 * q^85 - 1041586195 * q^86 + 945629148 * q^87 + 1122086037 * q^88 + 729648408 * q^89 - 437745000 * q^90 - 2090033068 * q^91 + 157159431 * q^92 - 150985728 * q^93 + 3068174993 * q^94 - 610625625 * q^95 + 1273538655 * q^96 + 186406391 * q^97 - 1334731394 * q^98 - 3426367056 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−20.9424	−	36.2733i	−0.925532	−	1.60307i	−0.790703	−	0.612200i	$-0.790285\pi$
$2$	−20.9424	−	36.2733i	−0.925532	−	1.60307i	−0.134829	−	0.990869i	$-0.543049\pi$
$3$	−70.5260	−	121.281i	−0.502694	−	0.864464i
$3$	−70.5260	−	121.281i	−0.502694	−	0.864464i
$4$	−621.169	+	1075.90i	−1.21322	+	2.10136i
$5$	312.500	−	541.266i	0.223607	−	0.387298i
$5$	312.500	−	541.266i	0.223607	−	0.387298i
$6$	−2922.28	+	5098.13i	−0.920537	+	1.60594i
$7$	1139.06	+	1972.90i	0.179310	+	0.310574i	0.941644	−	0.336609i	$-0.109280\pi$
$7$	1139.06	+	1972.90i	0.179310	+	0.310574i	−0.762334	+	0.647183i	$0.775947\pi$
$8$	30590.0			2.64043
$9$	−9735.16	+	17106.9i	−0.494598	+	0.869122i
$10$	−26178.0			−0.827821
$11$	15392.4	+	26660.3i	0.316984	+	0.549033i	0.979857	−	0.199699i	$-0.0639964\pi$
$11$	15392.4	+	26660.3i	0.316984	+	0.549033i	−0.662873	+	0.748732i	$0.730663\pi$
$12$	174294.	−	542.666i	2.42643	−	0.00755469i
$13$	80844.7	−	140027.i	0.785067	−	1.35978i	−0.143892	−	0.989593i	$-0.545962\pi$
$13$	80844.7	−	140027.i	0.785067	−	1.35978i	0.928959	−	0.370182i	$-0.120705\pi$
$14$	47709.2	−	82634.7i	0.331914	−	0.574892i
$15$	−87684.6	+	273.006i	−0.447211	+	0.00139239i
$16$	−322590.	−	558743.i	−1.23058	−	2.13143i
$17$	479287.			1.39179			0.695897	−	0.718141i	$-0.255007\pi$
$17$	479287.			1.39179			0.695897	+	0.718141i	$0.255007\pi$
$18$	824403.	−	5133.61i	1.85103	−	0.0115265i
$19$	148729.			0.261821			0.130910	−	0.991394i	$-0.458210\pi$
$19$	148729.			0.261821			0.130910	+	0.991394i	$0.458210\pi$
$20$	388230.	+	672435.i	0.542568	+	0.939756i
$21$	158943.	−	277287.i	0.178342	−	0.311131i
$22$	644706.	−	1.11666e6i	0.586759	−	1.01630i
$23$	−798956.	+	1.38383e6i	−0.595316	+	1.03112i	0.398186	+	0.917305i	$0.369640\pi$
$23$	−798956.	+	1.38383e6i	−0.595316	+	1.03112i	−0.993502	+	0.113813i	$0.963694\pi$
$24$	−2.15739e6	−	3.70999e6i	−1.32733	−	2.28256i
$25$	−195312.	−	338291.i	−0.100000	−	0.173205i
$26$	−6.77233e6			−2.90642
$27$	2.76133e6	−	25792.9i	0.999956	−	0.00934034i
$28$	−2.83019e6			−0.870169
$29$	3.16108e6	+	5.47514e6i	0.829935	+	1.43749i	0.898089	+	0.439814i	$0.144956\pi$
$29$	3.16108e6	+	5.47514e6i	0.829935	+	1.43749i	−0.0681538	+	0.997675i	$0.521711\pi$
$30$	1.84623e6	+	3.17489e6i	0.416141	+	0.715622i
$31$	−2.35019e6	+	4.07064e6i	−0.457062	+	0.791654i	−0.998804	−	0.0488906i	$-0.984431\pi$
$31$	−2.35019e6	+	4.07064e6i	−0.457062	+	0.791654i	0.541743	+	0.840544i	$0.317765\pi$
$32$	−5.68059e6	+	9.83907e6i	−0.957676	+	1.65874i
$33$	2.14783e6	−	3.74705e6i	0.315274	−	0.550017i
$34$	−1.00374e7	−	1.73853e7i	−1.28815	−	2.23114i
$35$	1.42382e6			0.160380
$36$	−1.23581e7	−	2.11003e7i	−1.22628	−	2.09376i
$37$	−1.02614e6			−0.0900114			−0.0450057	−	0.998987i	$-0.514331\pi$
$37$	−1.02614e6			−0.0900114			−0.0450057	+	0.998987i	$0.514331\pi$
$38$	−3.11474e6	−	5.39489e6i	−0.242323	−	0.419717i
$39$	−2.26843e7	+	70627.6i	−1.57013	+	0.00488859i
$40$	9.55938e6	−	1.65573e7i	0.590418	−	1.02263i
$41$	1.12560e7	−	1.94960e7i	0.622097	−	1.07750i	−0.366998	−	0.930222i	$-0.619614\pi$
$41$	1.12560e7	−	1.94960e7i	0.622097	−	1.07750i	0.989095	−	0.147282i	$-0.0470524\pi$
$42$	−1.33868e7	+	41679.7i	−0.663825	+	0.00206682i
$43$	−907878.	−	1.57249e6i	−0.0404967	−	0.0701423i	0.845067	−	0.534661i	$-0.179561\pi$
$43$	−907878.	−	1.57249e6i	−0.0404967	−	0.0701423i	−0.885563	+	0.464519i	$0.846227\pi$
$44$	−3.82450e7			−1.53829
$45$	6.21716e6	+	1.06152e7i	0.226014	+	0.385898i
$46$	6.69282e7			2.20394
$47$	1.79902e7	+	3.11599e7i	0.537768	+	0.931442i	0.999024	+	0.0441746i	$0.0140658\pi$
$47$	1.79902e7	+	3.11599e7i	0.537768	+	0.931442i	−0.461256	+	0.887267i	$0.652601\pi$
$48$	−4.50139e7	+	7.85300e7i	−1.22394	+	2.13526i
$49$	1.75819e7	−	3.04527e7i	0.435696	−	0.754647i
$50$	−8.18063e6	+	1.41693e7i	−0.185106	+	0.320614i
$51$	−3.38022e7	−	5.81284e7i	−0.699647	−	1.20316i
$52$	1.00436e8	+	1.73961e8i	1.90492	+	3.29941i
$53$	−8.27475e7			−1.44050			−0.720251	−	0.693714i	$-0.755973\pi$
$53$	−8.27475e7			−1.44050			−0.720251	+	0.693714i	$0.755973\pi$
$54$	−5.87644e7	−	9.96223e7i	−0.940465	−	1.59435i
$55$	1.92404e7			0.283520
$56$	3.48438e7	+	6.03512e7i	0.473456	+	0.820049i
$57$	−1.04893e7	−	1.80380e7i	−0.131616	−	0.226335i
$58$	1.32401e8	−	2.29325e8i	1.53626	−	2.66089i
$59$	5.64844e7	−	9.78338e7i	0.606868	−	1.05113i	−0.384885	−	0.922964i	$-0.625759\pi$
$59$	5.64844e7	−	9.78338e7i	0.606868	−	1.05113i	0.991753	−	0.128162i	$-0.0409076\pi$
$60$	5.41732e7	−	9.45091e7i	0.539640	−	0.941441i
$61$	8.20377e7	+	1.42093e8i	0.758628	+	1.31398i	0.943550	+	0.331229i	$0.107463\pi$
$61$	8.20377e7	+	1.42093e8i	0.758628	+	1.31398i	−0.184922	+	0.982753i	$0.559203\pi$
$62$	1.96874e8			1.69210
$63$	−4.48393e7	+	279217.i	−0.358613	+	0.00223311i
$64$	1.45528e8			1.08427
$65$	−5.05280e7	−	8.75170e7i	−0.351093	−	0.608110i
$66$	−1.80899e8	+	563228.i	−1.17351	+	0.00365373i
$67$	1.20673e8	−	2.09012e8i	0.731601	−	1.26717i	−0.224598	−	0.974451i	$-0.572107\pi$
$67$	1.20673e8	−	2.09012e8i	0.731601	−	1.26717i	0.956199	−	0.292718i	$-0.0945597\pi$
$68$	−2.97718e8	+	5.15662e8i	−1.68855	+	2.92466i
$69$	2.24180e8	−	697984.i	1.19063	−	0.00370702i
$70$	−2.98182e7	−	5.16467e7i	−0.148437	−	0.257100i
$71$	7.06238e7			0.329829			0.164914	−	0.986308i	$-0.447265\pi$
$71$	7.06238e7			0.329829			0.164914	+	0.986308i	$0.447265\pi$
$72$	−2.97799e8	+	5.23301e8i	−1.30595	+	2.29486i
$73$	−9.04161e7			−0.372643			−0.186321	−	0.982489i	$-0.559657\pi$
$73$	−9.04161e7			−0.372643			−0.186321	+	0.982489i	$0.559657\pi$
$74$	2.14898e7	+	3.72214e7i	0.0833085	+	0.144294i
$75$	−2.72537e7	+	4.75460e7i	−0.0994602	+	0.173516i
$76$	−9.23857e7	+	1.60017e8i	−0.317646	+	0.550179i
$77$	−3.50655e7	+	6.07353e7i	−0.113677	+	0.196894i
$78$	4.77626e8	+	8.21355e8i	1.46104	+	2.51250i
$79$	−1.41210e8	−	2.44582e8i	−0.407889	−	0.706485i	0.586764	−	0.809758i	$-0.300402\pi$
$79$	−1.41210e8	−	2.44582e8i	−0.407889	−	0.706485i	−0.994653	+	0.103273i	$0.967068\pi$
$80$	−4.03238e8			−1.10067
$81$	−1.97874e8	−	3.33078e8i	−0.510746	−	0.859731i
$82$	−9.42914e8			−2.30308
$83$	1.17513e8	+	2.03538e8i	0.271790	+	0.470754i	0.969320	−	0.245801i	$-0.0790510\pi$
$83$	1.17513e8	+	2.03538e8i	0.271790	+	0.470754i	−0.697530	+	0.716555i	$0.745718\pi$
$84$	1.99602e8	+	3.43248e8i	0.437429	+	0.752231i
$85$	1.49777e8	−	2.59422e8i	0.311215	−	0.539040i
$86$	−3.80263e7	+	6.58635e7i	−0.0749620	+	0.129838i
$87$	4.41093e8	−	7.69519e8i	0.825455	−	1.44007i
$88$	4.70852e8	+	8.15540e8i	0.836976	+	1.44968i
$89$	3.12559e7			0.0528052			0.0264026	−	0.999651i	$-0.491595\pi$
$89$	3.12559e7			0.0528052			0.0264026	+	0.999651i	$0.491595\pi$
$90$	2.54847e8	−	4.47825e8i	0.409438	−	0.719478i
$91$	3.68347e8			0.563081
$92$	−9.92572e8	−	1.71919e9i	−1.44450	−	2.50194i
$93$	6.59441e8	−	2.05317e6i	0.914119	−	0.00284611i
$94$	7.53515e8	−	1.30513e9i	0.995444	−	1.72416i
$95$	4.64778e7	−	8.05018e7i	0.0585449	−	0.101403i
$96$	1.59392e9	−	4.96268e6i	1.91534	−	0.00596342i
$97$	−4.09009e8	−	7.08425e8i	−0.469095	−	0.812496i	0.530281	−	0.847822i	$-0.322086\pi$
$97$	−4.09009e8	−	7.08425e8i	−0.469095	−	0.812496i	−0.999376	+	0.0353261i	$0.988753\pi$
$98$	−1.47283e9			−1.61300
$99$	−6.05924e8	+	3.77313e6i	−0.633957	+	0.00394769i
$100$	4.85288e8			0.485288
$101$	−2.87253e8	−	4.97536e8i	−0.274674	−	0.475750i	0.695379	−	0.718644i	$-0.255237\pi$
$101$	−2.87253e8	−	4.97536e8i	−0.274674	−	0.475750i	−0.970053	+	0.242894i	$0.921903\pi$
$102$	−1.40061e9	+	2.44346e9i	−1.28120	+	2.23514i
$103$	−4.16993e8	+	7.22252e8i	−0.365057	+	0.632297i	−0.988785	−	0.149344i	$-0.952284\pi$
$103$	−4.16993e8	+	7.22252e8i	−0.365057	+	0.632297i	0.623728	+	0.781641i	$0.285617\pi$
$104$	2.47304e9	−	4.28344e9i	2.07292	−	3.59039i
$105$	−1.00416e8	−	1.72683e8i	−0.0806219	−	0.138643i
$106$	1.73293e9	+	3.00153e9i	1.33323	+	2.30922i
$107$	1.69782e9			1.25217			0.626087	−	0.779753i	$-0.284655\pi$
$107$	1.69782e9			1.25217			0.626087	+	0.779753i	$0.284655\pi$
$108$	−1.68750e9	+	2.98692e9i	−1.19354	+	2.11260i
$109$	−6.46440e8			−0.438641			−0.219320	−	0.975653i	$-0.570384\pi$
$109$	−6.46440e8			−0.438641			−0.219320	+	0.975653i	$0.570384\pi$
$110$	−4.02941e8	−	6.97914e8i	−0.262406	−	0.454501i
$111$	7.23693e7	+	1.24451e8i	0.0452482	+	0.0778117i
$112$	7.34898e8	−	1.27288e9i	0.441312	−	0.764375i
$113$	1.42397e9	−	2.46639e9i	0.821577	−	1.42301i	−0.0829296	−	0.996555i	$-0.526428\pi$
$113$	1.42397e9	−	2.46639e9i	0.821577	−	1.42301i	0.904507	−	0.426459i	$-0.140239\pi$
$114$	−4.34627e8	+	7.58239e8i	−0.241016	+	0.420469i
$115$	4.99347e8	+	8.64895e8i	0.266233	+	0.461130i
$116$	−7.85424e9			−4.02757
$117$	1.60840e9	+	2.74619e9i	0.793519	+	1.35486i
$118$	−4.73167e9			−2.24670
$119$	5.45935e8	+	9.45587e8i	0.249563	+	0.432255i
$120$	−2.68228e9	+	8.35127e6i	−1.18083	+	0.00367652i
$121$	7.05125e8	−	1.22131e9i	0.299042	−	0.517955i
$122$	3.43613e9	−	5.95155e9i	1.40427	−	2.43227i
$123$	−3.15834e9	+	9.83350e6i	−1.24419	+	0.00387378i
$124$	−2.91972e9	−	5.05711e9i	−1.10903	−	1.92090i
$125$	−2.44141e8			−0.0894427
$126$	9.49170e8	+	1.62062e9i	0.335488	+	0.572814i
$127$	2.13259e9			0.727429			0.363714	−	0.931511i	$-0.381508\pi$
$127$	2.13259e9			0.727429			0.363714	+	0.931511i	$0.381508\pi$
$128$	−1.39248e8	−	2.41184e8i	−0.0458505	−	0.0794153i
$129$	−1.26684e8	+	2.21010e8i	−0.0402781	+	0.0702681i
$130$	−2.11635e9	+	3.66563e9i	−0.649895	+	1.12565i
$131$	−2.96824e9	+	5.14114e9i	−0.880599	+	1.52524i	−0.0299227	+	0.999552i	$0.509526\pi$
$131$	−2.96824e9	+	5.14114e9i	−0.880599	+	1.52524i	−0.850676	+	0.525690i	$0.823807\pi$
$132$	2.69727e9	+	4.63839e9i	0.773288	+	1.32979i
$133$	1.69411e8	+	2.93428e8i	0.0469471	+	0.0813147i
$134$	−1.01087e10			−2.70848
$135$	8.48954e8	−	1.50267e9i	0.219980	−	0.389370i
$136$	1.46614e10			3.67494
$137$	3.88593e9	+	6.73063e9i	0.942438	+	1.63235i	0.760802	+	0.648984i	$0.224806\pi$
$137$	3.88593e9	+	6.73063e9i	0.942438	+	1.63235i	0.181636	+	0.983366i	$0.441861\pi$
$138$	−4.72018e9	−	8.11712e9i	−1.10791	−	1.90522i
$139$	−1.51806e9	+	2.62935e9i	−0.344922	+	0.597423i	−0.985340	−	0.170604i	$-0.945428\pi$
$139$	−1.51806e9	+	2.62935e9i	−0.344922	+	0.597423i	0.640417	+	0.768027i	$0.278761\pi$
$140$	−8.84433e8	+	1.53188e9i	−0.194576	+	0.337015i
$141$	2.51033e9	−	4.37945e9i	0.534866	−	0.933112i
$142$	−1.47903e9	−	2.56176e9i	−0.305267	−	0.528739i
$143$	4.97756e9			0.995416
$144$	1.26988e10	−	7.90766e7i	2.46112	−	0.0153256i
$145$	3.95135e9			0.742316
$146$	1.89353e9	+	3.27969e9i	0.344893	+	0.597372i
$147$	−4.93332e9	+	1.53599e7i	−0.871388	+	0.00271307i
$148$	6.37404e8	−	1.10402e9i	0.109204	−	0.189146i
$149$	−1.60981e9	+	2.78827e9i	−0.267569	+	0.463443i	−0.968233	−	0.250048i	$-0.919554\pi$
$149$	−1.60981e9	+	2.78827e9i	−0.267569	+	0.463443i	0.700665	+	0.713491i	$0.252887\pi$
$150$	2.29541e9	−	7.14676e6i	0.370211	−	0.00115265i
$151$	−5.55728e8	−	9.62549e8i	−0.0869893	−	0.150670i	0.819248	−	0.573440i	$-0.194391\pi$
$151$	−5.55728e8	−	9.62549e8i	−0.0869893	−	0.150670i	−0.906237	+	0.422770i	$0.861058\pi$
$152$	4.54962e9			0.691320
$153$	−4.66594e9	+	8.19912e9i	−0.688378	+	1.20964i
$154$	2.93743e9			0.420847
$155$	1.46887e9	+	2.54415e9i	0.204404	+	0.354038i
$156$	1.40148e10	−	2.44498e10i	1.89464	−	3.30533i
$157$	4.27220e9	−	7.39966e9i	0.561181	−	0.971994i	−0.436213	−	0.899843i	$-0.643681\pi$
$157$	4.27220e9	−	7.39966e9i	0.561181	−	0.971994i	0.997394	−	0.0721502i	$-0.0229861\pi$
$158$	−5.91454e9	+	1.02443e10i	−0.755029	+	1.30775i
$159$	5.83585e9	+	1.00357e10i	0.724131	+	1.24526i
$160$	3.55037e9	+	6.14942e9i	0.428286	+	0.741812i
$161$	−3.64023e9			−0.426984
$162$	−7.93788e9	+	1.41530e10i	−0.905496	+	1.61447i
$163$	5.40066e8			0.0599243			0.0299621	−	0.999551i	$-0.490461\pi$
$163$	5.40066e8			0.0599243			0.0299621	+	0.999551i	$0.490461\pi$
$164$	1.39838e10	+	2.42206e10i	1.50948	+	2.61450i
$165$	−1.35695e9	−	2.33350e9i	−0.142524	−	0.245093i
$166$	4.92200e9	−	8.52516e9i	0.503101	−	0.871397i
$167$	7.00039e9	−	1.21250e10i	0.696463	−	1.20631i	−0.273222	−	0.961951i	$-0.588089\pi$
$167$	7.00039e9	−	1.21250e10i	0.696463	−	1.20631i	0.969685	−	0.244358i	$-0.0785773\pi$
$168$	4.86206e9	−	8.48222e9i	0.470900	−	0.821519i
$169$	−7.76949e9	−	1.34572e10i	−0.732660	−	1.26900i
$170$	−1.25468e10			−1.15216
$171$	−1.44790e9	+	2.54429e9i	−0.129496	+	0.227554i
$172$	2.25578e9			0.196526
$173$	−6.13664e8	−	1.06290e9i	−0.0520863	−	0.0902161i	0.838807	−	0.544429i	$-0.183254\pi$
$173$	−6.13664e8	−	1.06290e9i	−0.0520863	−	0.0902161i	−0.890893	+	0.454213i	$0.849920\pi$
$174$	−3.71505e10	+	1.15668e8i	−3.07251	+	0.00956627i
$175$	4.44944e8	−	7.70666e8i	0.0358620	−	0.0621148i
$176$	9.93085e9	−	1.72007e10i	0.780152	−	1.35126i
$177$	−1.58490e10	+	4.93459e7i	−1.21373	+	0.00377895i
$178$	−6.54573e8	−	1.13375e9i	−0.0488729	−	0.0846503i
$179$	2.64812e10			1.92796			0.963982	−	0.265968i	$-0.0856914\pi$
$179$	2.64812e10			1.92796			0.963982	+	0.265968i	$0.0856914\pi$
$180$	−1.52828e10	+	9.51669e7i	−1.08512	+	0.00675709i
$181$	−7.31339e9			−0.506483			−0.253242	−	0.967403i	$-0.581497\pi$
$181$	−7.31339e9			−0.506483			−0.253242	+	0.967403i	$0.581497\pi$
$182$	−7.71407e9	−	1.33612e10i	−0.521150	−	0.902658i
$183$	1.14474e10	−	1.99709e10i	0.754534	−	1.31634i
$184$	−2.44401e10	+	4.23314e10i	−1.57189	+	2.72259i
$185$	−3.20668e8	+	5.55413e8i	−0.0201272	+	0.0348613i
$186$	−1.38848e10	−	2.38771e10i	−0.850609	−	1.46276i
$187$	7.37735e9	+	1.27779e10i	0.441177	+	0.764142i
$188$	−4.46997e10			−2.60972
$189$	3.19620e9	+	5.41846e9i	0.182203	+	0.308886i
$190$	−3.89342e9			−0.216741
$191$	3.53981e9	+	6.13113e9i	0.192455	+	0.333342i	0.946063	−	0.323982i	$-0.105022\pi$
$191$	3.53981e9	+	6.13113e9i	0.192455	+	0.333342i	−0.753608	+	0.657324i	$0.771688\pi$
$192$	−1.02635e10	−	1.76498e10i	−0.545056	−	0.937312i
$193$	1.41070e10	−	2.44341e10i	0.731860	−	1.26762i	−0.224227	−	0.974537i	$-0.571986\pi$
$193$	1.41070e10	−	2.44341e10i	0.731860	−	1.26762i	0.956087	−	0.293082i	$-0.0946809\pi$
$194$	−1.71313e10	+	2.96722e10i	−0.868324	+	1.50398i
$195$	−7.05061e9	+	1.23003e10i	−0.349198	+	0.609200i
$196$	2.18426e10	+	3.78326e10i	1.05719	+	1.83111i
$197$	2.38139e9			0.112650			0.0563251	−	0.998412i	$-0.482062\pi$
$197$	2.38139e9			0.112650			0.0563251	+	0.998412i	$0.482062\pi$
$198$	1.28264e10	+	2.18998e10i	0.593076	+	1.01262i
$199$	2.65971e10			1.20225			0.601125	−	0.799155i	$-0.294719\pi$
$199$	2.65971e10			1.20225			0.601125	+	0.799155i	$0.294719\pi$
$200$	−5.97461e9	−	1.03483e10i	−0.264043	−	0.457336i
$201$	−3.38598e10	+	1.05423e8i	−1.46319	+	0.00455566i
$202$	−1.20315e10	+	2.08392e10i	−0.508440	+	0.880644i
$203$	−7.20129e9	+	1.24730e10i	−0.297631	+	0.515512i
$204$	8.35369e10	−	2.60092e8i	3.37709	−	0.0105146i
$205$	−7.03502e9	−	1.21850e10i	−0.278210	−	0.481874i
$206$	3.49313e10			1.35149
$207$	−1.58951e10	−	2.71395e10i	−0.601725	−	1.02739i
$208$	−1.04319e11			−3.86436
$209$	2.28929e9	+	3.96516e9i	0.0829931	+	0.143748i
$210$	−4.16080e9	+	7.25882e9i	−0.147635	+	0.257561i
$211$	1.38138e10	−	2.39262e10i	0.479779	−	0.831002i	−0.519952	−	0.854196i	$-0.674050\pi$
$211$	1.38138e10	−	2.39262e10i	0.479779	−	0.831002i	0.999731	+	0.0231934i	$0.00738335\pi$
$212$	5.14002e10	−	8.90277e10i	1.74764	−	3.02701i
$213$	−4.98082e9	−	8.56533e9i	−0.165803	−	0.285125i
$214$	−3.55564e10	−	6.15856e10i	−1.15893	−	2.00732i
$215$	−1.13485e9			−0.0362213
$216$	8.44691e10	−	7.89005e8i	2.64032	−	0.0246625i
$217$	−1.07080e10			−0.327823
$218$	1.35380e10	+	2.34485e10i	0.405976	+	0.703171i
$219$	6.37669e9	+	1.09658e10i	0.187325	+	0.322137i
$220$	−1.19516e10	+	2.07007e10i	−0.343971	+	0.595776i
$221$	3.87478e10	−	6.71132e10i	1.09265	−	1.89253i
$222$	2.99866e9	−	5.23138e9i	0.0828588	−	0.144553i
$223$	−2.19962e10	−	3.80986e10i	−0.595630	−	1.03166i	−0.993458	−	0.114201i	$-0.963569\pi$
$223$	−2.19962e10	−	3.80986e10i	−0.595630	−	1.03166i	0.397828	−	0.917460i	$-0.369764\pi$
$224$	−2.58821e10			−0.686883
$225$	7.68852e9	−	4.78769e7i	0.199996	−	0.00124539i
$226$	−1.19286e11			−3.04159
$227$	1.81450e10	+	3.14281e10i	0.453567	+	0.785601i	0.998605	−	0.0528105i	$-0.0168179\pi$
$227$	1.81450e10	+	3.14281e10i	0.453567	+	0.785601i	−0.545038	+	0.838412i	$0.683485\pi$
$228$	2.59226e10	−	8.07100e7i	0.635289	−	0.00197797i
$229$	−5.08813e9	+	8.81290e9i	−0.122264	+	0.211767i	−0.920660	−	0.390365i	$-0.872349\pi$
$229$	−5.08813e9	+	8.81290e9i	−0.122264	+	0.211767i	0.798396	+	0.602132i	$0.205682\pi$
$230$	2.09151e10	−	3.62260e10i	0.492815	−	0.853581i
$231$	9.83907e9	−	3.06340e7i	0.227353	−	0.000707863i
$232$	9.66974e10	+	1.67485e11i	2.19139	+	3.79559i
$233$	4.63961e10			1.03129			0.515644	−	0.856803i	$-0.327553\pi$
$233$	4.63961e10			1.03129			0.515644	+	0.856803i	$0.327553\pi$
$234$	6.59298e10	−	1.15854e11i	1.43751	−	2.52603i
$235$	2.24877e10			0.480995
$236$	7.01726e10	+	1.21543e11i	1.47253	+	2.55049i
$237$	−1.97042e10	+	3.43755e10i	−0.405688	+	0.707752i
$238$	2.28664e10	−	3.96057e10i	0.461957	−	0.800132i
$239$	−2.42471e10	+	4.19972e10i	−0.480694	+	0.832587i	−0.999755	−	0.0221505i	$-0.992949\pi$
$239$	−2.42471e10	+	4.19972e10i	−0.480694	+	0.832587i	0.519060	+	0.854738i	$0.326282\pi$
$240$	2.84388e10	+	4.89051e10i	0.553299	+	0.951489i
$241$	−1.34444e10	−	2.32863e10i	−0.256722	−	0.444656i	0.708640	−	0.705571i	$-0.249309\pi$
$241$	−1.34444e10	−	2.32863e10i	−0.256722	−	0.444656i	−0.965362	+	0.260914i	$0.915976\pi$
$242$	−5.90680e10			−1.10709
$243$	−2.64407e10	+	4.74889e10i	−0.486458	+	0.873704i
$244$	−2.03837e11			−3.68153
$245$	−1.09887e10	−	1.90330e10i	−0.194849	−	0.337489i
$246$	6.64999e10	+	1.14358e11i	1.15775	+	1.99093i
$247$	1.20239e10	−	2.08261e10i	0.205547	−	0.356017i
$248$	−7.18923e10	+	1.24521e11i	−1.20684	+	2.09031i
$249$	1.63976e10	−	2.86068e10i	0.270323	−	0.471598i
$250$	5.11289e9	+	8.85579e9i	0.0827821	+	0.143383i
$251$	−4.26509e10			−0.678260			−0.339130	−	0.940740i	$-0.610133\pi$
$251$	−4.26509e10			−0.678260			−0.339130	+	0.940740i	$0.610133\pi$
$252$	2.75523e10	−	4.84158e10i	0.430384	−	0.756283i
$253$	−4.91912e10			−0.754823
$254$	−4.46615e10	−	7.73561e10i	−0.673259	−	1.16612i
$255$	−4.20261e10	+	1.30848e8i	−0.622427	+	0.00193793i
$256$	3.14228e10	−	5.44259e10i	0.457262	−	0.792002i
$257$	−3.28316e10	+	5.68660e10i	−0.469454	+	0.813118i	−0.999390	−	0.0349196i	$-0.988882\pi$
$257$	−3.28316e10	+	5.68660e10i	−0.469454	+	0.813118i	0.529936	+	0.848037i	$0.322216\pi$
$258$	1.06698e10	−	3.32206e7i	0.149923	−	0.000466787i
$259$	−1.16883e9	−	2.02447e9i	−0.0161399	−	0.0279552i
$260$	1.25546e11			1.70381
$261$	−1.24437e11	+	7.74874e8i	−1.65984	+	0.0103359i
$262$	2.48648e11			3.26009
$263$	4.53847e9	+	7.86085e9i	0.0584936	+	0.101314i	0.893789	−	0.448487i	$-0.148037\pi$
$263$	4.53847e9	+	7.86085e9i	0.0584936	+	0.101314i	−0.835296	+	0.549801i	$0.814704\pi$
$264$	6.57022e10	−	1.14622e11i	0.832458	−	1.45228i
$265$	−2.58586e10	+	4.47884e10i	−0.322106	+	0.557904i
$266$	7.09573e9	−	1.22902e10i	0.0869020	−	0.150519i
$267$	−2.20435e9	−	3.79074e9i	−0.0265448	−	0.0456482i
$268$	1.49917e11	+	2.59663e11i	1.77518	+	3.07471i
$269$	5.36532e10			0.624755			0.312378	−	0.949958i	$-0.398875\pi$
$269$	5.36532e10			0.624755			0.312378	+	0.949958i	$0.398875\pi$
$270$	−7.22861e10	+	6.75206e8i	−0.827785	+	0.00773213i
$271$	−6.90335e10			−0.777496			−0.388748	−	0.921344i	$-0.627092\pi$
$271$	−6.90335e10			−0.777496			−0.388748	+	0.921344i	$0.627092\pi$
$272$	−1.54613e11	−	2.67798e11i	−1.71272	−	2.96652i
$273$	−2.59781e10	−	4.46735e10i	−0.283058	−	0.486764i
$274$	1.62762e11	−	2.81911e11i	1.74451	−	3.02159i
$275$	6.01264e9	−	1.04142e10i	0.0633969	−	0.109807i
$276$	−1.38502e11	+	2.41627e11i	−1.43670	+	2.50643i
$277$	7.48658e10	+	1.29671e11i	0.764055	+	1.32338i	0.940745	+	0.339116i	$0.110128\pi$
$277$	7.48658e10	+	1.29671e11i	0.764055	+	1.32338i	−0.176690	+	0.984267i	$0.556539\pi$
$278$	1.27167e11			1.27695
$279$	−4.67567e10	−	7.98328e10i	−0.461982	−	0.788792i
$280$	4.35547e10			0.423472
$281$	6.93041e8	+	1.20038e9i	0.00663102	+	0.0114853i	0.869322	−	0.494246i	$-0.164556\pi$
$281$	6.93041e8	+	1.20038e9i	0.00663102	+	0.0114853i	−0.862691	+	0.505732i	$0.831223\pi$
$282$	−2.11429e11	+	6.58286e8i	−1.99088	+	0.00619860i
$283$	−6.61565e10	+	1.14586e11i	−0.613103	+	1.06193i	0.377611	+	0.925964i	$0.376746\pi$
$283$	−6.61565e10	+	1.14586e11i	−0.613103	+	1.06193i	−0.990714	+	0.135962i	$0.956588\pi$
$284$	−4.38693e10	+	7.59839e10i	−0.400155	+	0.693089i
$285$	−1.30412e10	+	4.06039e7i	−0.117089	+	0.000364558i
$286$	−1.04242e11	−	1.80553e11i	−0.921290	−	1.59572i
$287$	5.12851e10			0.446193
$288$	−1.13015e11	−	1.92962e11i	−0.967986	−	1.65275i
$289$	1.11128e11			0.937093
$290$	−8.27507e10	−	1.43328e11i	−0.687038	−	1.18998i
$291$	−5.70727e10	+	9.95674e10i	−0.466563	+	0.813952i
$292$	5.61636e10	−	9.72783e10i	0.452098	−	0.783056i
$293$	−5.30297e10	+	9.18502e10i	−0.420354	+	0.728074i	−0.995974	−	0.0896431i	$-0.971427\pi$
$293$	−5.30297e10	+	9.18502e10i	−0.420354	+	0.728074i	0.575620	+	0.817717i	$0.304761\pi$
$294$	1.03873e11	+	1.78626e11i	0.810846	+	1.39438i
$295$	−3.53027e10	−	6.11461e10i	−0.271400	−	0.470078i
$296$	−3.13896e10			−0.237669
$297$	4.31910e10	+	7.32209e10i	0.322099	+	0.546048i
$298$	1.34853e11			0.990574
$299$	1.29183e11	+	2.23751e11i	0.934726	+	1.61899i
$300$	−3.42254e10	−	5.88562e10i	−0.243951	−	0.419514i
$301$	2.06825e9	−	3.58232e9i	0.0145229	−	0.0251544i
$302$	−2.32765e10	+	4.03162e10i	−0.161023	+	0.278900i
$303$	−4.00829e10	+	6.99275e10i	−0.273192	+	0.476603i
$304$	−4.79785e10	−	8.31012e10i	−0.322192	−	0.558054i
$305$	1.02547e11			0.678538
$306$	3.95125e11	−	2.46047e9i	2.57625	−	0.0160425i
$307$	6.74466e10			0.433348			0.216674	−	0.976244i	$-0.430479\pi$
$307$	6.74466e10			0.433348			0.216674	+	0.976244i	$0.430479\pi$
$308$	−4.35632e10	−	7.54537e10i	−0.275830	−	0.477752i
$309$	1.17004e11	−	3.64293e8i	0.730111	−	0.00227320i
$310$	6.15232e10	−	1.06561e11i	0.378365	−	0.655348i
$311$	−5.92372e10	+	1.02602e11i	−0.359065	+	0.621919i	−0.987805	−	0.155697i	$-0.950238\pi$
$311$	−5.92372e10	+	1.02602e11i	−0.359065	+	0.621919i	0.628740	+	0.777616i	$0.283571\pi$
$312$	−6.93913e11	+	2.16050e9i	−4.14581	+	0.0129080i
$313$	−2.74073e10	−	4.74708e10i	−0.161405	−	0.279561i	0.773968	−	0.633225i	$-0.218269\pi$
$313$	−2.74073e10	−	4.74708e10i	−0.161405	−	0.279561i	−0.935373	+	0.353663i	$0.884936\pi$
$314$	−3.57880e11			−2.07756
$315$	−1.38611e10	+	2.43572e10i	−0.0793234	+	0.139390i
$316$	3.50860e11			1.97944
$317$	−8.94538e10	−	1.54939e11i	−0.497545	−	0.861773i	0.502451	−	0.864606i	$-0.332432\pi$
$317$	−8.94538e10	−	1.54939e11i	−0.497545	−	0.861773i	−0.999996	+	0.00283253i	$0.999098\pi$
$318$	2.41811e11	−	4.21857e11i	1.32603	−	2.31336i
$319$	−9.73128e10	+	1.68551e11i	−0.526153	+	0.911324i
$320$	4.54775e10	−	7.87694e10i	0.242450	−	0.419936i
$321$	−1.19740e11	−	2.05913e11i	−0.629460	−	1.08246i
$322$	7.62351e10	+	1.32043e11i	0.395188	+	0.684485i
$323$	7.12838e10			0.364401
$324$	4.81269e11	−	5.99403e9i	2.42625	−	0.0302180i
$325$	−6.31600e10			−0.314027
$326$	−1.13103e10	−	1.95900e10i	−0.0554618	−	0.0960627i
$327$	4.55908e10	+	7.84009e10i	0.220502	+	0.379189i
$328$	3.44322e11	−	5.96384e11i	1.64260	−	2.84507i
$329$	−4.09837e10	+	7.09858e10i	−0.192854	+	0.334034i
$330$	−5.62259e10	+	9.80902e10i	−0.260990	+	0.455316i
$331$	−1.08982e11	−	1.88762e11i	−0.499032	−	0.864349i	0.500967	−	0.865466i	$-0.332978\pi$
$331$	−1.08982e11	−	1.88762e11i	−0.499032	−	0.864349i	−0.999999	+	0.00111752i	$0.999644\pi$
$332$	−2.91981e11			−1.31896
$333$	9.98961e9	−	1.75541e10i	0.0445194	−	0.0782309i
$334$	−5.86420e11			−2.57840
$335$	−7.54207e10	−	1.30633e11i	−0.327182	−	0.566695i
$336$	−2.06206e11	+	6.42022e8i	−0.882620	+	0.00274804i
$337$	−8.38988e10	+	1.45317e11i	−0.354341	+	0.613736i	−0.987005	−	0.160690i	$-0.948628\pi$
$337$	−8.38988e10	+	1.45317e11i	−0.354341	+	0.613736i	0.632664	+	0.774426i	$0.281961\pi$
$338$	−3.25424e11	+	5.63650e11i	−1.35620	+	2.34901i
$339$	−3.99554e11	+	1.24401e9i	−1.64315	+	0.00511594i
$340$	1.86074e11	+	3.22289e11i	0.755144	+	1.30795i
$341$	−1.44700e11			−0.579526
$342$	1.22612e11	−	7.63516e8i	0.484638	−	0.00301787i
$343$	1.72037e11			0.671118
$344$	−2.77720e10	−	4.81026e10i	−0.106929	−	0.185206i
$345$	6.96784e10	−	1.21559e11i	0.264796	−	0.461956i
$346$	−2.57032e10	+	4.45192e10i	−0.0964150	+	0.166996i
$347$	1.73983e11	−	3.01348e11i	0.644206	−	1.11580i	−0.340278	−	0.940325i	$-0.610521\pi$
$347$	1.73983e11	−	3.01348e11i	0.644206	−	1.11580i	0.984484	−	0.175473i	$-0.0561455\pi$
$348$	5.53928e11	+	9.52571e11i	2.02464	+	3.48169i
$349$	1.29653e11	+	2.24566e11i	0.467810	+	0.810271i	0.999323	−	0.0367793i	$-0.0117098\pi$
$349$	1.29653e11	+	2.24566e11i	0.467810	+	0.810271i	−0.531513	+	0.847050i	$0.678377\pi$
$350$	−3.72728e10			−0.132766
$351$	2.19627e11	−	3.88746e11i	0.772332	−	1.36705i
$352$	−3.49750e11			−1.21427
$353$	−1.67487e11	−	2.90097e11i	−0.574111	−	0.994390i	−0.996138	−	0.0878063i	$-0.972014\pi$
$353$	−1.67487e11	−	2.90097e11i	−0.574111	−	0.994390i	0.422026	−	0.906584i	$-0.361319\pi$
$354$	3.33706e11	+	5.73862e11i	1.12940	+	1.94219i
$355$	2.20700e10	−	3.82263e10i	0.0737520	−	0.127742i
$356$	−1.94151e10	+	3.36280e10i	−0.0640643	+	0.110963i
$357$	7.61791e10	−	1.32900e11i	0.248216	−	0.433030i
$358$	−5.54580e11	−	9.60560e11i	−1.78439	−	3.09066i
$359$	1.56077e11			0.495921			0.247961	−	0.968770i	$-0.420240\pi$
$359$	1.56077e11			0.495921			0.247961	+	0.968770i	$0.420240\pi$
$360$	1.90183e11	+	3.24720e11i	0.596775	+	1.01894i
$361$	−3.00567e11			−0.931450
$362$	1.53160e11	+	2.65281e11i	0.468767	+	0.811927i
$363$	−1.97852e11	+	6.16011e8i	−0.598081	+	0.00186213i
$364$	−2.28806e11	+	3.96303e11i	−0.683141	+	1.18324i
$365$	−2.82550e10	+	4.89392e10i	−0.0833255	+	0.144324i
$366$	−9.64147e11	+	3.00188e9i	−2.80853	+	0.00874435i
$367$	1.59980e11	+	2.77093e11i	0.460328	+	0.797311i	0.998977	−	0.0452189i	$-0.0143985\pi$
$367$	1.59980e11	+	2.77093e11i	0.460328	+	0.797311i	−0.538649	+	0.842530i	$0.681065\pi$
$368$	1.03094e12			2.93035
$369$	2.23938e11	+	3.82353e11i	0.628794	+	1.07361i
$370$	2.68622e10			0.0745134
$371$	−9.42542e10	−	1.63253e11i	−0.258296	−	0.447382i
$372$	−4.07415e11	+	7.10765e11i	−1.10305	+	1.92434i
$373$	1.21689e10	−	2.10772e10i	0.0325509	−	0.0563799i	−0.849291	−	0.527925i	$-0.822970\pi$
$373$	1.21689e10	−	2.10772e10i	0.0325509	−	0.0563799i	0.881842	+	0.471545i	$0.156304\pi$
$374$	3.08999e11	−	5.35202e11i	0.816648	−	1.41448i
$375$	1.72183e10	+	2.96096e10i	0.0449623	+	0.0773201i
$376$	5.50320e11	+	9.53182e11i	1.41994	+	2.45941i
$377$	1.02223e12			2.60622
$378$	1.29609e11	−	2.29412e11i	0.326530	−	0.577967i
$379$	−4.52566e11			−1.12669			−0.563347	−	0.826221i	$-0.690486\pi$
$379$	−4.52566e11			−1.12669			−0.563347	+	0.826221i	$0.690486\pi$
$380$	5.77410e10	+	1.00010e11i	0.142056	+	0.246048i
$381$	−1.50403e11	−	2.58643e11i	−0.365674	−	0.628836i
$382$	1.48264e11	−	2.56801e11i	0.356247	−	0.617038i
$383$	1.05793e11	−	1.83238e11i	0.251224	−	0.435132i	−0.712639	−	0.701531i	$-0.752500\pi$
$383$	1.05793e11	−	1.83238e11i	0.251224	−	0.435132i	0.963863	+	0.266398i	$0.0858337\pi$
$384$	−1.94305e10	+	3.38979e10i	−0.0456030	+	0.0795577i
$385$	2.19160e10	+	3.79596e10i	0.0508379	+	0.0880538i
$386$	−1.18174e12			−2.70944
$387$	3.57388e10	−	2.22548e8i	0.0809918	−	0.000504341i
$388$	1.01625e12			2.27646
$389$	−2.77379e11	−	4.80434e11i	−0.614186	−	1.06380i	−0.990527	−	0.137320i	$-0.956151\pi$
$389$	−2.77379e11	−	4.80434e11i	−0.614186	−	1.06380i	0.376341	−	0.926481i	$-0.377182\pi$
$390$	5.93830e11	−	1.84889e9i	1.29978	−	0.00404688i
$391$	−3.82929e11	+	6.63252e11i	−0.828558	+	1.43510i
$392$	5.37831e11	−	9.31550e11i	1.15043	−	1.99259i
$393$	8.32861e11	−	2.59312e9i	1.76119	−	0.00548347i
$394$	−4.98720e10	−	8.63808e10i	−0.104261	−	0.180586i
$395$	−1.76512e11			−0.364827
$396$	3.72321e11	−	6.54254e11i	0.760833	−	1.33696i
$397$	3.07655e11			0.621594			0.310797	−	0.950476i	$-0.399404\pi$
$397$	3.07655e11			0.621594			0.310797	+	0.950476i	$0.399404\pi$
$398$	−5.57007e11	−	9.64764e11i	−1.11272	−	1.92729i
$399$	2.36394e10	−	4.12406e10i	0.0466937	−	0.0814605i
$400$	−1.26012e11	+	2.18259e11i	−0.246117	+	0.426287i
$401$	3.81720e11	−	6.61158e11i	0.737217	−	1.27690i	−0.216527	−	0.976277i	$-0.569473\pi$
$401$	3.81720e11	−	6.61158e11i	0.737217	−	1.27690i	0.953744	−	0.300620i	$-0.0971936\pi$
$402$	7.12929e11	+	1.22600e12i	1.36154	+	2.34138i
$403$	3.80000e11	+	6.58180e11i	0.717648	+	1.24300i
$404$	7.13729e11			1.33296
$405$	−2.42119e11	+	3.01550e9i	−0.447179	+	0.00556944i
$406$	6.03250e11			1.10187
$407$	−1.57947e10	−	2.73572e10i	−0.0285322	−	0.0494193i
$408$	−1.03401e12	−	1.77815e12i	−1.84737	−	3.17685i
$409$	2.86822e11	−	4.96790e11i	0.506824	−	0.877845i	−0.493145	−	0.869947i	$-0.664153\pi$
$409$	2.86822e11	−	4.96790e11i	0.506824	−	0.877845i	0.999969	−	0.00789753i	$-0.00251389\pi$
$410$	−2.94661e11	+	5.10367e11i	−0.514985	+	0.891980i
$411$	5.42239e11	−	9.45974e11i	0.937351	−	1.63528i
$412$	−5.18045e11	−	8.97281e11i	−0.885789	−	1.53423i
$413$	2.57356e11			0.435270
$414$	−6.51557e11	+	1.14494e12i	−1.09006	+	1.91549i
$415$	1.46891e11			0.243097
$416$	9.18491e11	+	1.59087e12i	1.50368	+	2.60445i
$417$	4.25953e11	−	1.32621e9i	0.689841	−	0.00214782i
$418$	9.58863e10	−	1.66080e11i	0.153626	−	0.266087i
$419$	−1.87228e11	+	3.24289e11i	−0.296762	+	0.514006i	−0.975393	−	0.220473i	$-0.929240\pi$
$419$	−1.87228e11	+	3.24289e11i	−0.296762	+	0.514006i	0.678631	+	0.734479i	$0.262573\pi$
$420$	2.48164e11	−	7.72659e8i	0.389150	−	0.00121162i
$421$	1.93880e11	+	3.35810e11i	0.300790	+	0.520983i	0.976315	−	0.216354i	$-0.0694164\pi$
$421$	1.93880e11	+	3.35810e11i	0.300790	+	0.520983i	−0.675525	+	0.737337i	$0.736083\pi$
$422$	−1.15718e12			−1.77621
$423$	−7.08188e11	+	4.40993e9i	−1.07552	+	0.00669731i
$424$	−2.53125e12			−3.80354
$425$	−9.36107e10	−	1.62138e11i	−0.139179	−	0.241066i
$426$	−2.06383e11	+	3.60049e11i	−0.303620	+	0.529686i
$427$	−1.86891e11	+	3.23705e11i	−0.272059	+	0.471220i
$428$	−1.05463e12	+	1.82668e12i	−1.51916	+	2.63127i
$429$	−3.51048e11	−	6.03684e11i	−0.500390	−	0.860502i
$430$	2.37664e10	+	4.11647e10i	0.0335240	+	0.0580653i
$431$	−6.61269e11			−0.923061			−0.461530	−	0.887124i	$-0.652699\pi$
$431$	−6.61269e11			−0.923061			−0.461530	+	0.887124i	$0.652699\pi$
$432$	−9.05189e11	−	1.53455e12i	−1.25044	−	2.11985i
$433$	−9.41264e11			−1.28681			−0.643407	−	0.765524i	$-0.722480\pi$
$433$	−9.41264e11			−1.28681			−0.643407	+	0.765524i	$0.722480\pi$
$434$	2.24251e11	+	3.88414e11i	0.303410	+	0.525522i
$435$	−2.78673e11	−	4.79223e11i	−0.373158	−	0.641706i
$436$	4.01548e11	−	6.95502e11i	0.532168	−	0.921742i
$437$	−1.18828e11	+	2.05816e11i	−0.155866	+	0.269968i
$438$	2.64221e11	−	4.60953e11i	0.343032	−	0.598443i
$439$	5.30107e11	+	9.18173e11i	0.681198	+	1.17987i	0.974615	+	0.223886i	$0.0718742\pi$
$439$	5.30107e11	+	9.18173e11i	0.681198	+	1.17987i	−0.293417	+	0.955985i	$0.594792\pi$
$440$	5.88566e11			0.748614
$441$	3.49790e11	+	5.97235e11i	0.440387	+	0.751920i
$442$	−3.24589e12			−4.04514
$443$	4.20201e10	+	7.27810e10i	0.0518371	+	0.0897845i	0.890780	−	0.454436i	$-0.150159\pi$
$443$	4.20201e10	+	7.27810e10i	0.0518371	+	0.0897845i	−0.838943	+	0.544220i	$0.816826\pi$
$444$	−1.78850e11	+	5.56849e8i	−0.218406	+	0.000680008i
$445$	9.76745e9	−	1.69177e10i	0.0118076	−	0.0204513i
$446$	−9.21308e11	+	1.59575e12i	−1.10255	+	1.90967i
$447$	4.51697e11	−	1.40636e9i	0.535135	−	0.00166614i
$448$	1.65765e11	+	2.87113e11i	0.194420	+	0.336746i
$449$	7.21216e10			0.0837447			0.0418723	−	0.999123i	$-0.486668\pi$
$449$	7.21216e10			0.0837447			0.0418723	+	0.999123i	$0.486668\pi$
$450$	−1.62753e11	−	2.77885e11i	−0.187099	−	0.319455i
$451$	6.93028e11			0.788780
$452$	1.76905e12	+	3.06409e12i	1.99351	+	3.45286i
$453$	−7.75456e10	+	1.35284e11i	−0.0865198	+	0.150940i
$454$	7.60001e11	−	1.31636e12i	0.839582	−	1.45420i
$455$	1.15108e11	−	1.99374e11i	0.125909	−	0.218080i
$456$	−3.20866e11	−	5.51782e11i	−0.347522	−	0.597621i
$457$	−5.33855e11	−	9.24664e11i	−0.572533	−	0.991656i	−0.996305	−	0.0858873i	$-0.972628\pi$
$457$	−5.33855e11	−	9.24664e11i	−0.572533	−	0.991656i	0.423772	−	0.905769i	$-0.360706\pi$
$458$	4.26231e11			0.452637
$459$	1.32347e12	−	1.23622e10i	1.39173	−	0.0129998i
$460$	−1.24072e12			−1.29200
$461$	1.98811e11	+	3.44351e11i	0.205015	+	0.355097i	0.950138	−	0.311831i	$-0.100942\pi$
$461$	1.98811e11	+	3.44351e11i	0.205015	+	0.355097i	−0.745122	+	0.666928i	$0.767609\pi$
$462$	−2.07165e11	−	3.56254e11i	−0.211557	−	0.363807i
$463$	−1.98895e10	+	3.44496e10i	−0.0201145	+	0.0348394i	−0.875907	−	0.482479i	$-0.839736\pi$
$463$	−1.98895e10	+	3.44496e10i	−0.0201145	+	0.0348394i	0.855793	+	0.517319i	$0.173070\pi$
$464$	2.03947e12	−	3.53246e12i	2.04261	−	3.53790i
$465$	2.04964e11	−	3.57574e11i	0.203301	−	0.354673i
$466$	−9.71646e11	−	1.68294e12i	−0.954490	−	1.65323i
$467$	−8.19805e11			−0.797599			−0.398799	−	0.917038i	$-0.630573\pi$
$467$	−8.19805e11			−0.797599			−0.398799	+	0.917038i	$0.630573\pi$
$468$	−3.95370e12	+	2.46200e10i	−3.80976	+	0.0237236i
$469$	5.49814e11			0.524733
$470$	−4.70947e11	−	8.15704e11i	−0.445176	−	0.771067i
$471$	−1.19874e12	+	3.73228e9i	−1.12236	+	0.00349446i
$472$	1.72786e12	−	2.99274e12i	1.60239	−	2.77543i
$473$	2.79488e10	−	4.84087e10i	0.0256736	−	0.0444681i
$474$	1.65957e12	−	5.16706e9i	1.51005	−	0.00470155i
$475$	−2.90486e10	−	5.03137e10i	−0.0261821	−	0.0453487i
$476$	−1.35647e12			−1.21110
$477$	8.05561e11	−	1.41556e12i	0.712468	−	1.25197i
$478$	2.03117e12			1.77959
$479$	−7.01967e10	−	1.21584e11i	−0.0609266	−	0.105528i	0.833953	−	0.551835i	$-0.186072\pi$
$479$	−7.01967e10	−	1.21584e11i	−0.0609266	−	0.105528i	−0.894880	+	0.446307i	$0.852739\pi$
$480$	4.95414e11	−	8.64286e11i	0.425974	−	0.743142i
$481$	−8.29578e10	+	1.43687e11i	−0.0706650	+	0.122395i
$482$	−5.63115e11	+	9.75343e11i	−0.475210	+	0.823087i
$483$	2.56731e11	+	4.41490e11i	0.214642	+	0.369113i
$484$	8.76003e11	+	1.51728e12i	0.725607	+	1.25679i
$485$	−5.11262e11			−0.419571
$486$	2.27631e12	−	3.54393e10i	1.85084	−	0.0288152i
$487$	4.90579e11			0.395210			0.197605	−	0.980282i	$-0.436684\pi$
$487$	4.90579e11			0.395210			0.197605	+	0.980282i	$0.436684\pi$
$488$	2.50953e12	+	4.34664e12i	2.00311	+	3.46948i
$489$	−3.80887e10	−	6.54998e10i	−0.0301236	−	0.0518024i
$490$	−4.60259e11	+	7.97192e11i	−0.360678	+	0.624713i
$491$	4.54493e11	−	7.87205e11i	0.352907	−	0.611253i	−0.633850	−	0.773456i	$-0.718527\pi$
$491$	4.54493e11	−	7.87205e11i	0.352907	−	0.611253i	0.986757	+	0.162203i	$0.0518599\pi$
$492$	1.95128e12	−	3.40415e12i	1.50133	−	2.61918i
$493$	1.51506e12	+	2.62416e12i	1.15510	+	2.00069i
$494$	−1.00724e12			−0.760961
$495$	−1.87309e11	+	3.29145e11i	−0.140228	+	0.246413i
$496$	3.03259e12			2.24981
$497$	8.04446e10	+	1.39334e11i	0.0591416	+	0.102436i
$498$	−1.38107e12	+	4.29996e9i	−1.00620	+	0.00313280i
$499$	−1.10076e12	+	1.90657e12i	−0.794766	+	1.37658i	0.128221	+	0.991746i	$0.459073\pi$
$499$	−1.10076e12	+	1.90657e12i	−0.794766	+	1.37658i	−0.922988	+	0.384830i	$0.874260\pi$
$500$	1.51652e11	−	2.62670e11i	0.108514	−	0.187951i
$501$	−1.96425e12	+	6.11568e9i	−1.39292	+	0.00433686i
$502$	8.93212e11	+	1.54709e12i	0.627751	+	1.08730i
$503$	2.31081e12			1.60957			0.804783	−	0.593569i	$-0.202281\pi$
$503$	2.31081e12			1.60957			0.804783	+	0.593569i	$0.202281\pi$
$504$	−1.37163e12	+	8.54126e9i	−0.946893	+	0.00589636i
$505$	−3.59066e11			−0.245676
$506$	1.03018e12	+	1.78433e12i	0.698613	+	1.21003i
$507$	−1.08415e12	+	1.89137e12i	−0.728706	+	1.27128i
$508$	−1.32470e12	+	2.29444e12i	−0.882531	+	1.52859i
$509$	8.10971e11	−	1.40464e12i	0.535519	−	0.927547i	−0.463619	−	0.886035i	$-0.653449\pi$
$509$	8.10971e11	−	1.40464e12i	0.535519	−	0.927547i	0.999138	−	0.0415117i	$-0.0132174\pi$
$510$	8.84874e11	+	1.52168e12i	0.579183	+	0.995999i
$511$	−1.02989e11	−	1.78382e11i	−0.0668186	−	0.115733i
$512$	−2.77487e12			−1.78455
$513$	4.10689e11	−	3.83614e9i	0.261809	−	0.00244550i
$514$	2.75029e12			1.73798
$515$	2.60620e11	+	4.51408e11i	0.163258	+	0.282772i
$516$	−1.59091e11	−	2.73583e11i	−0.0987922	−	0.169889i
$517$	−5.53822e11	+	9.59249e11i	−0.340928	+	0.590505i
$518$	−4.89562e10	+	8.47946e10i	−0.0298761	+	0.0517469i
$519$	−8.56300e10	+	1.49388e11i	−0.0518051	+	0.0903778i
$520$	−1.54565e12	−	2.67715e12i	−0.927036	−	1.60567i
$521$	7.25182e11			0.431199			0.215599	−	0.976482i	$-0.430829\pi$
$521$	7.25182e11			0.431199			0.215599	+	0.976482i	$0.430829\pi$
$522$	2.63411e12	+	4.49750e12i	1.55280	+	2.65127i
$523$	−1.39032e10			−0.00812565			−0.00406282	−	0.999992i	$-0.501293\pi$
$523$	−1.39032e10			−0.00812565			−0.00406282	+	0.999992i	$0.501293\pi$
$524$	−3.68755e12	−	6.38703e12i	−2.13672	−	3.70091i
$525$	−1.24847e11	+	3.88712e8i	−0.0717236	+	0.000223312i
$526$	1.90093e11	−	3.29250e11i	0.108275	−	0.187538i
$527$	−1.12641e12	+	1.95100e12i	−0.636136	+	1.10182i
$528$	−2.78651e12	+	8.67579e9i	−1.56030	+	0.00485799i
$529$	−3.76084e11	−	6.51397e11i	−0.208802	−	0.361655i
$530$	2.16617e12			1.19248
$531$	1.12375e12	+	1.91870e12i	0.613401	+	1.04733i
$532$	−4.20930e11			−0.227828
$533$	−1.81998e12	−	3.15230e12i	−0.976775	−	1.69182i
$534$	−9.13383e10	+	1.59346e11i	−0.0486091	+	0.0848020i
$535$	5.30569e11	−	9.18972e11i	0.279995	−	0.484965i
$536$	3.69139e12	−	6.39368e12i	1.93174	−	3.34587i
$537$	−1.86761e12	−	3.21167e12i	−0.969176	−	1.66666i
$538$	−1.12363e12	−	1.94618e12i	−0.578231	−	1.00153i
$539$	1.08251e12			0.552435
$540$	1.08938e12	+	1.84680e12i	0.551322	+	0.934647i
$541$	−1.26309e12			−0.633938			−0.316969	−	0.948436i	$-0.602665\pi$
$541$	−1.26309e12			−0.633938			−0.316969	+	0.948436i	$0.602665\pi$
$542$	1.44573e12	+	2.50407e12i	0.719598	+	1.24638i
$543$	5.15784e11	+	8.86975e11i	0.254606	+	0.437837i
$544$	−2.72263e12	+	4.71573e12i	−1.33289	+	2.30863i
$545$	−2.02013e11	+	3.49896e11i	−0.0980831	+	0.169885i
$546$	−1.07641e12	+	1.87788e12i	−0.518337	+	0.904276i
$547$	3.89639e11	+	6.74875e11i	0.186089	+	0.322315i	0.943943	−	0.330109i	$-0.107086\pi$
$547$	3.89639e11	+	6.74875e11i	0.186089	+	0.322315i	−0.757854	+	0.652424i	$0.773752\pi$
$548$	−9.65528e12			−4.57354
$549$	−3.22943e12	+	2.01099e10i	−1.51723	+	0.00944787i
$550$	−5.03676e11			−0.234703
$551$	4.70143e11	+	8.14312e11i	0.217294	+	0.376364i
$552$	6.85766e12	−	2.13513e10i	3.14377	−	0.00978812i
$553$	3.21692e11	−	5.57186e11i	0.146277	−	0.253360i
$554$	3.13574e12	−	5.43126e12i	1.41432	−	2.44967i
$555$	8.99765e10	−	2.80142e8i	0.0402541	−	0.000125331i
$556$	−1.88594e12	−	3.26654e12i	−0.836933	−	1.44961i
$557$	2.38171e12			1.04843			0.524215	−	0.851586i	$-0.324359\pi$
$557$	2.38171e12			1.04843			0.524215	+	0.851586i	$0.324359\pi$
$558$	−1.91660e12	+	3.36791e12i	−0.836909	+	1.47064i
$559$	−2.93589e11			−0.127170
$560$	−4.59311e11	−	7.95550e11i	−0.197361	−	0.341839i
$561$	1.02943e12	−	1.79591e12i	0.438796	−	0.765512i
$562$	2.90279e10	−	5.02778e10i	0.0122744	−	0.0212600i
$563$	−1.73079e12	+	2.99782e12i	−0.726035	+	1.25753i	0.232511	+	0.972594i	$0.425306\pi$
$563$	−1.73079e12	+	2.99782e12i	−0.726035	+	1.25753i	−0.958547	+	0.284936i	$0.908028\pi$
$564$	3.15249e12	+	5.42123e12i	1.31189	+	2.25601i
$565$	−8.89983e11	−	1.54150e12i	−0.367421	−	0.636391i
$566$	5.54190e12			2.26979
$567$	4.31741e11	−	7.69780e11i	0.175428	−	0.312783i
$568$	2.16039e12			0.870891
$569$	7.13542e11	+	1.23589e12i	0.285374	+	0.494282i	0.972700	−	0.232067i	$-0.0745489\pi$
$569$	7.13542e11	+	1.23589e12i	0.285374	+	0.494282i	−0.687326	+	0.726349i	$0.741216\pi$
$570$	2.74588e11	+	4.72198e11i	0.108954	+	0.187365i
$571$	−2.05967e12	+	3.56745e12i	−0.810840	+	1.40442i	0.101437	+	0.994842i	$0.467656\pi$
$571$	−2.05967e12	+	3.56745e12i	−0.810840	+	1.40442i	−0.912277	+	0.409574i	$0.865677\pi$
$572$	−3.09191e12	+	5.35534e12i	−1.20766	+	2.09173i
$573$	4.93941e11	−	8.61716e11i	0.191416	−	0.333940i
$574$	−1.07403e12	−	1.86028e12i	−0.412966	−	0.715278i
$575$	6.24184e11			0.238126
$576$	−1.41674e12	+	2.48954e12i	−0.536277	+	0.942362i
$577$	−4.19907e11			−0.157711			−0.0788555	−	0.996886i	$-0.525127\pi$
$577$	−4.19907e11			−0.157711			−0.0788555	+	0.996886i	$0.525127\pi$
$578$	−2.32729e12	−	4.03098e12i	−0.867310	−	1.50222i
$579$	−3.95831e12	+	1.23242e10i	−1.46371	+	0.00455728i
$580$	−2.45445e12	+	4.25123e12i	−0.900593	+	1.55987i
$581$	−2.67708e11	+	4.63683e11i	−0.0974694	+	0.168822i
$582$	4.80688e12	−	1.49662e10i	1.73664	−	0.00540703i
$583$	−1.27368e12	−	2.20608e12i	−0.456616	−	0.790883i
$584$	−2.76583e12			−0.983938
$585$	1.98905e12	−	1.23859e10i	0.702172	−	0.00437247i
$586$	4.44228e12			1.55620
$587$	−1.11356e12	−	1.92875e12i	−0.387118	−	0.670508i	0.604943	−	0.796269i	$-0.293196\pi$
$587$	−1.11356e12	−	1.92875e12i	−0.387118	−	0.670508i	−0.992061	+	0.125761i	$0.959863\pi$
$588$	3.04790e12	−	5.31728e12i	1.05148	−	1.83439i
$589$	−3.49541e11	+	6.05422e11i	−0.119668	+	0.207271i
$590$	−1.47865e12	+	2.56109e12i	−0.502378	+	0.870144i
$591$	−1.67950e11	−	2.88817e11i	−0.0566286	−	0.0973821i
$592$	3.31022e11	+	5.73347e11i	0.110767	+	0.191853i
$593$	−6.27364e11			−0.208340			−0.104170	−	0.994559i	$-0.533219\pi$
$593$	−6.27364e11			−0.208340			−0.104170	+	0.994559i	$0.533219\pi$
$594$	1.75144e12	−	3.10010e12i	0.577241	−	1.02173i
$595$	6.82419e11			0.223216
$596$	−1.99992e12	−	3.46397e12i	−0.649239	−	1.12452i
$597$	−1.87579e12	−	3.22572e12i	−0.604364	−	1.03930i
$598$	5.41079e12	−	9.37177e12i	1.73024	−	2.99686i
$599$	−2.04830e12	+	3.54775e12i	−0.650088	+	1.12599i	0.333013	+	0.942922i	$0.391935\pi$
$599$	−2.04830e12	+	3.54775e12i	−0.650088	+	1.12599i	−0.983101	+	0.183063i	$0.941399\pi$
$600$	−8.33691e11	+	1.45443e12i	−0.262618	+	0.458156i
$601$	−2.00268e12	−	3.46874e12i	−0.626146	−	1.08452i	−0.988318	−	0.152406i	$-0.951298\pi$
$601$	−2.00268e12	−	3.46874e12i	−0.626146	−	1.08452i	0.362171	−	0.932111i	$-0.382035\pi$
$602$	−1.73257e11			−0.0537657
$603$	2.40078e12	+	4.09911e12i	0.739477	+	1.26259i
$604$	1.38080e12			0.422149
$605$	−4.40703e11	−	7.63320e11i	−0.133736	−	0.231637i
$606$	3.37594e12	−	1.05110e10i	1.01687	−	0.00316604i
$607$	1.58572e12	−	2.74655e12i	0.474109	−	0.821181i	−0.525451	−	0.850824i	$-0.676104\pi$
$607$	1.58572e12	−	2.74655e12i	0.474109	−	0.821181i	0.999561	+	0.0296425i	$0.00943687\pi$
$608$	−8.44867e11	+	1.46335e12i	−0.250739	+	0.434293i
$609$	2.02062e12	−	6.29120e9i	0.595259	−	0.00185334i
$610$	−2.14758e12	−	3.71972e12i	−0.628009	−	1.08774i
$611$	5.81765e12			1.68874
$612$	−5.92307e12	−	1.01131e13i	−1.70673	−	2.91409i
$613$	3.60074e11			0.102996			0.0514980	−	0.998673i	$-0.483600\pi$
$613$	3.60074e11			0.102996			0.0514980	+	0.998673i	$0.483600\pi$
$614$	−1.41249e12	−	2.44651e12i	−0.401078	−	0.694687i
$615$	−9.81659e11	+	1.71257e12i	−0.276709	+	0.482738i
$616$	−1.07266e12	+	1.85789e12i	−0.300156	+	0.519886i
$617$	2.15172e12	−	3.72689e12i	0.597727	−	1.03529i	−0.395429	−	0.918497i	$-0.629404\pi$
$617$	2.15172e12	−	3.72689e12i	0.597727	−	1.03529i	0.993156	−	0.116797i	$-0.0372628\pi$
$618$	−2.46357e12	−	4.23650e12i	−0.679385	−	1.16831i
$619$	7.97363e11	+	1.38107e12i	0.218297	+	0.378102i	0.954287	−	0.298890i	$-0.0966165\pi$
$619$	7.97363e11	+	1.38107e12i	0.218297	+	0.378102i	−0.735990	+	0.676992i	$0.763283\pi$
$620$	−3.64965e12			−0.991949
$621$	−2.17049e12	+	3.84182e12i	−0.585659	+	1.03663i
$622$	4.96228e12			1.32930
$623$	3.56022e10	+	6.16648e10i	0.00946849	+	0.0163999i
$624$	7.35720e12	+	1.26519e13i	1.94259	+	3.34061i
$625$	−7.62939e10	+	1.32145e11i	−0.0200000	+	0.0346410i
$626$	−1.14795e12	+	1.98831e12i	−0.298771	+	0.517486i
$627$	3.19444e11	−	5.57294e11i	0.0825451	−	0.144006i
$628$	5.30751e12	+	9.19287e12i	1.36167	+	2.35848i
$629$	−4.91814e11			−0.125277
$630$	1.17380e12	−	7.30934e9i	0.296867	−	0.00184861i
$631$	−7.40943e11			−0.186060			−0.0930299	−	0.995663i	$-0.529655\pi$
$631$	−7.40943e11			−0.186060			−0.0930299	+	0.995663i	$0.529655\pi$
$632$	−4.31961e12	−	7.48178e12i	−1.07700	−	1.86543i
$633$	−3.87602e12	+	1.20680e10i	−0.959554	+	0.00298757i
$634$	−3.74676e12	+	6.48957e12i	−0.920988	+	1.59520i
$635$	6.66434e11	−	1.15430e12i	0.162658	−	0.281732i
$636$	−1.44224e13	+	4.49042e10i	−3.49527	+	0.0108825i
$637$	−2.84281e12	−	4.92389e12i	−0.684101	−	1.18490i
$638$	8.15186e12			1.94789
$639$	−6.87535e11	+	1.20816e12i	−0.163133	+	0.286662i
$640$	−1.74060e11			−0.0410099
$641$	1.72109e12	+	2.98101e12i	0.402663	+	0.697434i	0.994046	−	0.108957i	$-0.0347512\pi$
$641$	1.72109e12	+	2.98101e12i	0.402663	+	0.697434i	−0.591383	+	0.806391i	$0.701418\pi$
$642$	−4.96151e12	+	8.65570e12i	−1.15267	+	2.01092i
$643$	2.72513e12	−	4.72006e12i	0.628692	−	1.08893i	−0.359123	−	0.933290i	$-0.616924\pi$
$643$	2.72513e12	−	4.72006e12i	0.628692	−	1.08893i	0.987815	−	0.155636i	$-0.0497426\pi$
$644$	2.26119e12	−	3.91650e12i	0.518026	−	0.897247i
$645$	8.00363e10	+	1.37636e11i	0.0182083	+	0.0313121i
$646$	−1.49285e12	−	2.58570e12i	−0.337265	−	0.584159i
$647$	8.92285e11			0.200186			0.100093	−	0.994978i	$-0.468086\pi$
$647$	8.92285e11			0.200186			0.100093	+	0.994978i	$0.468086\pi$
$648$	−6.05296e12	−	1.01889e13i	−1.34859	−	2.27006i
$649$	3.47771e12			0.769471
$650$	1.32272e12	+	2.29102e12i	0.290642	+	0.503407i
$651$	7.55192e11	+	1.29868e12i	0.164794	+	0.283391i
$652$	−3.35472e11	+	5.81055e11i	−0.0727013	+	0.125922i
$653$	1.93873e11	−	3.35798e11i	0.0417261	−	0.0722718i	−0.844408	−	0.535700i	$-0.820048\pi$
$653$	1.93873e11	−	3.35798e11i	0.0417261	−	0.0722718i	0.886134	+	0.463429i	$0.153381\pi$
$654$	1.88908e12	−	3.29563e12i	0.403785	−	0.704432i
$655$	1.85515e12	+	3.21321e12i	0.393816	+	0.682109i
$656$	−1.45244e13			−3.06217
$657$	8.80216e11	−	1.54674e12i	0.184308	−	0.323872i
$658$	3.43319e12			0.713972
$659$	−5.15142e11	−	8.92253e11i	−0.106400	−	0.184291i	0.807909	−	0.589307i	$-0.200599\pi$
$659$	−5.15142e11	−	8.92253e11i	−0.106400	−	0.184291i	−0.914309	+	0.405016i	$0.867266\pi$
$660$	3.35350e12	−	1.04411e10i	0.687940	−	0.00214190i
$661$	4.63323e12	−	8.02500e12i	0.944012	−	1.63508i	0.186295	−	0.982494i	$-0.440352\pi$
$661$	4.63323e12	−	8.02500e12i	0.944012	−	1.63508i	0.757717	−	0.652583i	$-0.226315\pi$
$662$	−4.56468e12	+	7.90627e12i	−0.923740	+	1.59996i
$663$	−1.08723e13	+	3.38509e10i	−2.18529	+	0.00680392i
$664$	3.59472e12	+	6.22624e12i	0.717643	+	1.24299i
$665$	2.11763e11			0.0419907
$666$	−8.45950e11	+	5.26779e9i	−0.166614	+	0.00103751i
$667$	−1.01022e13			−1.97629
$668$	8.69684e12	+	1.50634e13i	1.68993	+	2.92704i
$669$	−3.06933e12	+	5.35467e12i	−0.592415	+	1.03351i
$670$	−3.15898e12	+	5.47152e12i	−0.605634	+	1.04899i
$671$	−2.52551e12	+	4.37430e12i	−0.480947	+	0.833024i
$672$	1.82536e12	+	3.13900e12i	0.345292	+	0.593786i
$673$	6.38666e11	+	1.10620e12i	0.120007	+	0.207858i	0.919770	−	0.392458i	$-0.128375\pi$
$673$	6.38666e11	+	1.10620e12i	0.120007	+	0.207858i	−0.799763	+	0.600316i	$0.795042\pi$
$674$	7.02817e12			1.31181
$675$	−5.48047e11	−	9.29095e11i	−0.101613	−	0.172263i
$676$	1.93047e13			3.55551
$677$	−5.34992e11	−	9.26633e11i	−0.0978810	−	0.169535i	0.812926	−	0.582366i	$-0.197873\pi$
$677$	−5.34992e11	−	9.26633e11i	−0.0978810	−	0.169535i	−0.910807	+	0.412832i	$0.864540\pi$
$678$	8.41274e12	+	1.44671e13i	1.52899	+	2.62934i
$679$	9.31770e11	−	1.61387e12i	0.168227	−	0.291377i
$680$	4.58169e12	−	7.93571e12i	0.821741	−	1.42330i
$681$	2.53194e12	−	4.41715e12i	0.451119	−	0.787009i
$682$	3.03036e12	+	5.24873e12i	0.536370	+	0.929019i
$683$	−1.31990e12			−0.232086			−0.116043	−	0.993244i	$-0.537021\pi$
$683$	−1.31990e12			−0.232086			−0.116043	+	0.993244i	$0.537021\pi$
$684$	−1.83800e12	−	3.13822e12i	−0.321066	−	0.548190i
$685$	4.85742e12			0.842942
$686$	−3.60287e12	−	6.24036e12i	−0.621142	−	1.07585i
$687$	1.42768e12	−	4.44509e9i	0.244527	−	0.000761335i
$688$	−5.85746e11	+	1.01454e12i	−0.0996692	+	0.172632i
$689$	−6.68970e12	+	1.15869e13i	−1.13089	+	1.95876i
$690$	−5.86858e12	+	1.82718e10i	−0.985625	+	0.00306875i
$691$	4.51855e12	+	7.82635e12i	0.753959	+	1.30590i	0.945890	+	0.324487i	$0.105192\pi$
$691$	4.51855e12	+	7.82635e12i	0.753959	+	1.30590i	−0.191931	+	0.981408i	$0.561475\pi$
$692$	1.52476e12			0.252768
$693$	−6.97626e11	−	1.19113e12i	−0.114901	−	0.196183i
$694$	−1.45745e13			−2.38493
$695$	9.48785e11	+	1.64334e12i	0.154254	+	0.267176i
$696$	1.34930e13	−	2.35396e13i	2.17956	−	3.80240i
$697$	5.39487e12	−	9.34419e12i	0.865831	−	1.49966i
$698$	5.43051e12	−	9.40591e12i	0.865946	−	1.49986i
$699$	−3.27213e12	−	5.62697e12i	−0.518422	−	0.891512i
$700$	5.52771e11	+	9.57427e11i	0.0870169	+	0.150718i
$701$	5.06904e12			0.792857			0.396428	−	0.918066i	$-0.370249\pi$
$701$	5.06904e12			0.792857			0.396428	+	0.918066i	$0.370249\pi$
$702$	−1.87006e13	+	1.74678e11i	−2.90629	+	0.0271469i
$703$	−1.52616e11			−0.0235669
$704$	2.24002e12	+	3.87983e12i	0.343696	+	0.595300i
$705$	−1.58597e12	−	2.72733e12i	−0.241793	−	0.415803i
$706$	−7.01518e12	+	1.21506e13i	−1.06272	+	1.84068i
$707$	6.54395e11	−	1.13344e12i	0.0985037	−	0.170613i
$708$	9.79180e12	−	1.70825e13i	1.46458	−	2.55507i
$709$	−1.27819e12	−	2.21388e12i	−0.189970	−	0.329038i	0.755270	−	0.655414i	$-0.227506\pi$
$709$	−1.27819e12	−	2.21388e12i	−0.189970	−	0.329038i	−0.945240	+	0.326376i	$0.894173\pi$
$710$	−1.84879e12			−0.273039
$711$	5.55875e12	−	3.46147e10i	0.815763	−	0.00507981i
$712$	9.56117e11			0.139428
$713$	−3.75539e12	−	6.50453e12i	−0.544192	−	0.942568i
$714$	−6.41610e12	+	1.99765e10i	−0.923909	+	0.00287659i
$715$	1.55549e12	−	2.69419e12i	0.222582	−	0.385523i
$716$	−1.64493e13	+	2.84910e13i	−2.33904	+	4.05134i
$717$	6.80351e12	−	2.11828e10i	0.961384	−	0.00299327i
$718$	−3.26862e12	−	5.66141e12i	−0.458991	−	0.794996i
$719$	8.51796e12			1.18865			0.594327	−	0.804224i	$-0.297419\pi$
$719$	8.51796e12			1.18865			0.594327	+	0.804224i	$0.297419\pi$
$720$	3.92559e12	−	6.89816e12i	0.544388	−	0.956615i
$721$	−1.89991e12			−0.261833
$722$	6.29460e12	+	1.09026e13i	0.862087	+	1.49318i
$723$	−1.87601e12	+	3.27284e12i	−0.255337	+	0.445453i
$724$	4.54285e12	−	7.86844e12i	0.614475	−	1.06430i
$725$	1.23480e12	−	2.13873e12i	0.165987	−	0.287498i
$726$	4.16583e12	+	7.16383e12i	0.556528	+	0.957041i
$727$	7.91646e10	+	1.37117e11i	0.0105106	+	0.0182048i	0.871233	−	0.490870i	$-0.163321\pi$
$727$	7.91646e10	+	1.37117e11i	0.0105106	+	0.0182048i	−0.860722	+	0.509075i	$0.829988\pi$
$728$	1.12677e13			1.48678
$729$	7.62427e12	−	1.42445e11i	0.999826	−	0.0186799i
$730$	2.36691e12			0.308482
$731$	−4.35134e11	−	7.53674e11i	−0.0563631	−	0.0976238i
$732$	1.43758e13	+	2.47215e13i	1.85068	+	3.18255i
$733$	−2.62267e12	+	4.54260e12i	−0.335564	+	0.581214i	−0.983593	−	0.180401i	$-0.942260\pi$
$733$	−2.62267e12	+	4.54260e12i	−0.335564	+	0.581214i	0.648029	+	0.761616i	$0.275594\pi$
$734$	6.70071e12	−	1.16060e13i	0.852096	−	1.47587i
$735$	−1.53335e12	+	2.67504e12i	−0.193797	+	0.338094i
$736$	−9.07708e12	−	1.57220e13i	−1.14024	−	1.97495i
$737$	7.42978e12			0.927624
$738$	9.17942e12	−	1.61304e13i	1.13910	−	2.00166i
$739$	−1.39374e13			−1.71902			−0.859509	−	0.511120i	$-0.829231\pi$
$739$	−1.39374e13			−1.71902			−0.859509	+	0.511120i	$0.829231\pi$
$740$	−3.98377e11	−	6.90010e11i	−0.0488373	−	0.0845888i
$741$	−3.37381e12	+	1.05044e10i	−0.411092	+	0.00127993i
$742$	−3.94782e12	+	6.83782e12i	−0.478123	+	0.828133i
$743$	−3.70534e12	+	6.41784e12i	−0.446045	+	0.772572i	−0.998124	−	0.0612191i	$-0.980501\pi$
$743$	−3.70534e12	+	6.41784e12i	−0.446045	+	0.772572i	0.552080	+	0.833791i	$0.313834\pi$
$744$	2.01723e13	−	6.28066e10i	2.41367	−	0.00751496i
$745$	1.00613e12	+	1.74267e12i	0.119660	+	0.207258i
$746$	−1.01939e12			−0.120508
$747$	−4.62592e12	+	2.88059e10i	−0.543570	+	0.00338485i
$748$	−1.83303e13			−2.14098
$749$	1.93391e12	+	3.34964e12i	0.224527	+	0.388893i
$750$	7.13447e11	−	1.24466e12i	0.0823353	−	0.143640i
$751$	−4.91443e12	+	8.51204e12i	−0.563759	+	0.976459i	0.433405	+	0.901199i	$0.357312\pi$
$751$	−4.91443e12	+	8.51204e12i	−0.563759	+	0.976459i	−0.997164	+	0.0752595i	$0.976021\pi$
$752$	1.16069e13	−	2.01038e13i	1.32354	−	2.29244i
$753$	3.00800e12	+	5.17274e12i	0.340957	+	0.586332i
$754$	−2.14079e13	−	3.70795e13i	−2.41214	−	4.17795i
$755$	−6.94660e11			−0.0778056
$756$	−7.81507e12	+	7.29986e10i	−0.870131	+	0.00812768i
$757$	−6.43963e12			−0.712738			−0.356369	−	0.934345i	$-0.615985\pi$
$757$	−6.43963e12			−0.712738			−0.356369	+	0.934345i	$0.615985\pi$
$758$	9.47783e12	+	1.64161e13i	1.04279	+	1.80617i
$759$	3.46926e12	+	5.96596e12i	0.379445	+	0.652518i
$760$	1.42176e12	−	2.46255e12i	0.154584	−	0.267747i
$761$	−7.82636e12	+	1.35557e13i	−0.845919	+	1.46518i	0.0389008	+	0.999243i	$0.487614\pi$
$761$	−7.82636e12	+	1.35557e13i	−0.845919	+	1.46518i	−0.884820	+	0.465932i	$0.845719\pi$
$762$	−6.23202e12	+	1.08722e13i	−0.669625	+	1.16821i
$763$	−7.36332e11	−	1.27536e12i	−0.0786527	−	0.136230i
$764$	−8.79527e12			−0.933962
$765$	2.97980e12	+	5.08774e12i	0.314565	+	0.537092i
$766$	−8.86220e12			−0.930062
$767$	−9.13293e12	−	1.58187e13i	−0.952864	−	1.65041i
$768$	−8.81696e12	+	2.74516e10i	−0.914520	+	0.00284736i
$769$	5.61285e12	−	9.72174e12i	0.578782	−	1.00248i	−0.416838	−	0.908981i	$-0.636862\pi$
$769$	5.61285e12	−	9.72174e12i	0.578782	−	1.00248i	0.995619	−	0.0934984i	$-0.0298050\pi$
$770$	9.17946e11	−	1.58993e12i	0.0941042	−	0.162993i
$771$	9.21225e12	−	2.86824e10i	0.938903	−	0.00292328i
$772$	1.75257e13	+	3.03554e13i	1.77581	+	3.07580i
$773$	−1.27658e13			−1.28600			−0.643001	−	0.765865i	$-0.722311\pi$
$773$	−1.27658e13			−1.28600			−0.643001	+	0.765865i	$0.722311\pi$
$774$	−7.56530e11	−	1.29171e12i	−0.0757690	−	0.129369i
$775$	1.83608e12			0.182825
$776$	−1.25116e13	−	2.16707e13i	−1.23861	−	2.14534i
$777$	−1.63097e11	+	2.84535e11i	−0.0160528	+	0.0280053i
$778$	−1.16179e13	+	2.01229e13i	−1.13690	+	1.96916i
$779$	1.67410e12	−	2.89962e12i	0.162878	−	0.282113i
$780$	−8.85422e12	−	1.52263e13i	−0.856495	−	1.47288i
$781$	1.08707e12	+	1.88286e12i	0.104551	+	0.181087i
$782$	3.20778e13			3.06743
$783$	8.86999e12	+	1.50371e13i	0.843325	+	1.42967i
$784$	−2.26870e13			−2.14464
$785$	−2.67012e12	−	4.62479e12i	−0.250968	−	0.434689i
$786$	−1.75362e13	−	3.01563e13i	−1.63883	−	2.81823i
$787$	7.38443e11	−	1.27902e12i	0.0686169	−	0.118848i	−0.829676	−	0.558245i	$-0.811475\pi$
$787$	7.38443e11	−	1.27902e12i	0.0686169	−	0.118848i	0.898293	+	0.439398i	$0.144808\pi$
$788$	−1.47924e12	+	2.56212e12i	−0.136670	+	0.236719i
$789$	6.33292e11	−	1.10482e12i	0.0581779	−	0.101495i
$790$	3.69659e12	+	6.40267e12i	0.337659	+	0.584843i
$791$	6.48794e12			0.589268
$792$	−1.85352e13	+	1.15420e11i	−1.67392	+	0.0104236i
$793$	2.65293e13			2.38230
$794$	−6.44303e12	−	1.11597e13i	−0.575305	−	0.996457i
$795$	7.25569e12	−	2.25906e10i	0.644209	−	0.00200575i
$796$	−1.65213e13	+	2.86157e13i	−1.45859	+	2.52636i
$797$	−2.09135e12	+	3.62232e12i	−0.183596	+	0.317998i	−0.943103	−	0.332502i	$-0.892107\pi$
$797$	−2.09135e12	+	3.62232e12i	−0.183596	+	0.317998i	0.759506	+	0.650500i	$0.225441\pi$
$798$	−1.99100e12	+	6.19898e9i	−0.173803	+	0.000541137i
$799$	8.62245e12	+	1.49345e13i	0.748463	+	1.29638i
$800$	4.43796e12			0.383070
$801$	−3.04281e11	+	5.34692e11i	−0.0261173	+	0.0458941i
$802$	−3.19765e13			−2.72927
$803$	−1.39172e12	−	2.41052e12i	−0.118122	−	0.204593i
$804$	2.09192e13	−	3.64951e13i	1.76560	−	3.08022i
$805$	−1.13757e12	+	1.97033e12i	−0.0954766	+	0.165370i
$806$	1.59162e13	−	2.75677e13i	1.32841	−	2.30088i
$807$	−3.78394e12	−	6.50711e12i	−0.314061	−	0.540079i
$808$	−8.78707e12	−	1.52196e13i	−0.725259	−	1.25618i
$809$	−6.09463e12			−0.500240			−0.250120	−	0.968215i	$-0.580470\pi$
$809$	−6.09463e12			−0.500240			−0.250120	+	0.968215i	$0.580470\pi$
$810$	5.17994e12	+	8.71931e12i	0.422807	+	0.711704i
$811$	1.92538e13			1.56287			0.781435	−	0.623987i	$-0.214488\pi$
$811$	1.92538e13			1.56287			0.781435	+	0.623987i	$0.214488\pi$
$812$	−8.94643e12	−	1.54957e13i	−0.722184	−	1.25086i
$813$	4.86866e12	+	8.37246e12i	0.390843	+	0.672118i
$814$	−6.61556e11	+	1.14585e12i	−0.0528150	+	0.0914782i
$815$	1.68771e11	−	2.92319e11i	0.0133995	−	0.0232086i
$816$	−2.15746e13	+	3.76384e13i	−1.70348	+	2.97184i
$817$	−1.35028e11	−	2.33875e11i	−0.0106029	−	0.0183647i
$818$	−2.40269e13			−1.87633
$819$	−3.58592e12	+	6.30129e12i	−0.278499	+	0.489386i
$820$	1.74797e13			1.35012
$821$	5.92335e12	+	1.02596e13i	0.455013	+	0.788105i	0.998689	−	0.0511899i	$-0.0163014\pi$
$821$	5.92335e12	+	1.02596e13i	0.455013	+	0.788105i	−0.543676	+	0.839295i	$0.682968\pi$
$822$	−4.56694e13	+	1.42192e11i	−3.48901	+	0.0108630i
$823$	6.36258e12	−	1.10203e13i	0.483430	−	0.837326i	−0.516389	−	0.856354i	$-0.672724\pi$
$823$	6.36258e12	−	1.10203e13i	0.483430	−	0.837326i	0.999819	+	0.0190285i	$0.00605732\pi$
$824$	−1.27558e13	+	2.20937e13i	−0.963908	+	1.66954i
$825$	−1.68709e12	+	5.25276e9i	−0.126793	+	0.000394771i
$826$	−5.38965e12	−	9.33514e12i	−0.402856	−	0.697767i
$827$	−3.05426e12			−0.227055			−0.113527	−	0.993535i	$-0.536215\pi$
$827$	−3.05426e12			−0.227055			−0.113527	+	0.993535i	$0.536215\pi$
$828$	3.90728e13	−	2.43309e11i	2.88894	−	0.0179896i
$829$	−7.69460e12			−0.565836			−0.282918	−	0.959144i	$-0.591302\pi$
$829$	−7.69460e12			−0.565836			−0.282918	+	0.959144i	$0.591302\pi$
$830$	−3.07625e12	−	5.32822e12i	−0.224994	−	0.389700i
$831$	1.04467e13	−	1.82250e13i	0.759931	−	1.32575i
$832$	1.17652e13	−	2.03779e13i	0.851224	−	1.47436i
$833$	8.42677e12	−	1.45956e13i	0.606399	−	1.05031i
$834$	−8.96858e12	−	1.54229e13i	−0.641913	−	1.10388i
$835$	−4.37524e12	−	7.57814e12i	−0.311468	−	0.539478i
$836$	−5.68813e12			−0.402755
$837$	−6.38464e12	+	1.13010e13i	−0.449647	+	0.795888i
$838$	1.56840e13			1.09865
$839$	1.14408e12	+	1.98160e12i	0.0797127	+	0.138066i	0.903126	−	0.429376i	$-0.141266\pi$
$839$	1.14408e12	+	1.98160e12i	0.0797127	+	0.138066i	−0.823413	+	0.567442i	$0.807933\pi$
$840$	−3.07174e12	−	5.28236e12i	−0.212877	−	0.366076i
$841$	−1.27312e13	+	2.20511e13i	−0.877584	+	1.52002i
$842$	8.12062e12	−	1.40653e13i	0.556781	−	0.964373i
$843$	9.67061e10	−	1.68711e11i	0.00659523	−	0.0115059i
$844$	1.71614e13	+	2.97244e13i	1.16416	+	2.01638i
$845$	−9.71187e12			−0.655311
$846$	1.49911e13	+	2.55960e13i	1.00616	+	1.71793i
$847$	3.21271e12			0.214485
$848$	2.66936e13	+	4.62346e13i	1.77266	+	3.07033i
$849$	1.85629e13	−	5.77957e10i	1.22620	−	0.00381778i
$850$	−3.92087e12	+	6.79114e12i	−0.257630	+	0.446229i
$851$	8.19838e11	−	1.42000e12i	0.0535852	−	0.0928123i
$852$	1.23093e13	−	3.83251e10i	0.800306	−	0.00249176i
$853$	−1.02023e13	−	1.76710e13i	−0.659826	−	1.14285i	−0.980660	−	0.195717i	$-0.937297\pi$
$853$	−1.02023e13	−	1.76710e13i	−0.659826	−	1.14285i	0.320835	−	0.947135i	$-0.396037\pi$
$854$	1.56558e13			1.00720
$855$	9.24671e11	+	1.57879e12i	0.0591752	+	0.101036i
$856$	5.19364e13			3.30628
$857$	−8.61148e12	−	1.49155e13i	−0.545336	−	0.944550i	−0.998586	−	0.0531663i	$-0.983069\pi$
$857$	−8.61148e12	−	1.49155e13i	−0.545336	−	0.944550i	0.453250	−	0.891384i	$-0.350265\pi$
$858$	−1.45458e13	+	2.53763e13i	−0.916317	+	1.59858i
$859$	6.57540e11	−	1.13889e12i	0.0412053	−	0.0713696i	−0.844687	−	0.535260i	$-0.820214\pi$
$859$	6.57540e11	−	1.13889e12i	0.0412053	−	0.0713696i	0.885893	+	0.463891i	$0.153547\pi$
$860$	7.04932e11	−	1.22098e12i	0.0439445	−	0.0761140i
$861$	−3.61693e12	−	6.21991e12i	−0.224298	−	0.385718i
$862$	1.38486e13	+	2.39864e13i	0.854322	+	1.47973i
$863$	−2.34273e13			−1.43771			−0.718857	−	0.695157i	$-0.755335\pi$
$863$	−2.34273e13			−1.43771			−0.718857	+	0.695157i	$0.755335\pi$
$864$	−1.54322e13	+	2.73154e13i	−0.942141	+	1.66762i
$865$	−7.67080e11			−0.0465874
$866$	1.97123e13	+	3.41428e13i	1.19099	+	2.06285i
$867$	−7.83741e12	−	1.34777e13i	−0.471071	−	0.810084i
$868$	6.65146e12	−	1.15207e13i	0.397721	−	0.688873i
$869$	4.34710e12	−	7.52939e12i	0.258589	−	0.447890i
$870$	−1.15469e13	+	2.01445e13i	−0.683329	+	1.19212i
$871$	−1.95116e13	−	3.37950e13i	−1.14871	−	1.98963i
$872$	−1.97746e13			−1.15820
$873$	1.61007e13	−	1.00260e11i	0.938171	−	0.00584205i
$874$	9.95416e12			0.577036
$875$	−2.78090e11	−	4.81666e11i	−0.0160380	−	0.0277786i
$876$	−1.57590e13	+	4.90657e10i	−0.904191	+	0.00281520i
$877$	4.02006e12	−	6.96294e12i	0.229474	−	0.397461i	−0.728178	−	0.685388i	$-0.759633\pi$
$877$	4.02006e12	−	6.96294e12i	0.229474	−	0.397461i	0.957652	+	0.287927i	$0.0929660\pi$
$878$	2.22034e13	−	3.84575e13i	1.26094	−	2.18402i
$879$	1.48797e13	−	4.63278e10i	0.840704	−	0.00261753i
$880$	−6.20678e12	−	1.07505e13i	−0.348895	−	0.604303i
$881$	2.51233e13			1.40503			0.702515	−	0.711669i	$-0.252060\pi$
$881$	2.51233e13			1.40503			0.702515	+	0.711669i	$0.252060\pi$
$882$	1.43382e13	−	2.51956e13i	0.797787	−	1.40190i
$883$	−5.69628e12			−0.315332			−0.157666	−	0.987492i	$-0.550397\pi$
$883$	−5.69628e12			−0.315332			−0.157666	+	0.987492i	$0.550397\pi$
$884$	4.81378e13	+	8.33772e13i	2.65125	+	4.59211i
$885$	−4.92610e12	+	8.59394e12i	−0.269935	+	0.470921i
$886$	1.76001e12	−	3.04842e12i	0.0959538	−	0.166197i
$887$	−4.01769e12	+	6.95884e12i	−0.217932	+	0.377468i	−0.954175	−	0.299248i	$-0.903264\pi$
$887$	−4.01769e12	+	6.95884e12i	−0.217932	+	0.377468i	0.736244	+	0.676716i	$0.236598\pi$
$888$	2.21378e12	+	3.80696e12i	0.119475	+	0.205456i
$889$	2.42914e12	+	4.20740e12i	0.130435	+	0.225920i
$890$	−8.18216e11			−0.0437132
$891$	5.83422e12	−	1.04022e13i	0.310122	−	0.552938i
$892$	5.46535e13			2.89052
$893$	2.67566e12	+	4.63438e12i	0.140799	+	0.243871i
$894$	−9.51063e12	−	1.63551e13i	−0.497955	−	0.856316i
$895$	8.27537e12	−	1.43334e13i	0.431106	−	0.746697i
$896$	3.17223e11	−	5.49446e11i	0.0164429	−	0.0284799i
$897$	1.80260e13	−	3.14477e13i	0.929680	−	1.62189i
$898$	−1.51040e12	−	2.61609e12i	−0.0775084	−	0.134248i
$899$	−2.97165e13			−1.51733
$900$	−4.72436e12	+	8.30179e12i	−0.240022	+	0.421774i
$901$	−3.96598e13			−2.00488
$902$	−1.45137e13	−	2.51384e13i	−0.730042	−	1.26447i
$903$	−5.80332e11	+	1.80687e9i	−0.0290457	+	9.04339e-5i
$904$	4.35593e13	−	7.54470e13i	2.16932	−	3.75737i
$905$	−2.28543e12	+	3.95849e12i	−0.113253	+	0.196160i
$906$	6.53119e12	−	2.03349e10i	0.322044	−	0.00100269i
$907$	1.03150e13	+	1.78661e13i	0.506100	+	0.876591i	0.999975	+	0.00705824i	$0.00224673\pi$
$907$	1.03150e13	+	1.78661e13i	0.506100	+	0.876591i	−0.493875	+	0.869533i	$0.664420\pi$
$908$	−4.50845e13			−2.20111
$909$	1.13078e13	−	7.04142e10i	0.549338	−	0.00342076i
$910$	−9.64259e12			−0.466131
$911$	−1.00910e13	−	1.74782e13i	−0.485403	−	0.840742i	0.514457	−	0.857516i	$-0.327994\pi$
$911$	−1.00910e13	−	1.74782e13i	−0.485403	−	0.840742i	−0.999859	+	0.0167742i	$0.994660\pi$
$912$	−6.69486e12	+	1.16797e13i	−0.320453	+	0.559054i
$913$	−3.61760e12	+	6.26586e12i	−0.172307	+	0.298444i
$914$	−2.23604e13	+	3.87294e13i	−1.05980	+	1.83562i
$915$	−7.23224e12	−	1.24370e13i	−0.341097	−	0.586572i
$916$	−6.32117e12	−	1.09486e13i	−0.296666	−	0.513841i
$917$	−1.35240e13			−0.631601
$918$	−2.81650e13	−	4.77477e13i	−1.30893	−	2.21901i
$919$	1.42209e12			0.0657667			0.0328833	−	0.999459i	$-0.489531\pi$
$919$	1.42209e12			0.0657667			0.0328833	+	0.999459i	$0.489531\pi$
$920$	1.52750e13	+	2.64572e13i	0.702971	+	1.21758i
$921$	−4.75674e12	−	8.17999e12i	−0.217842	−	0.374614i
$922$	8.32716e12	−	1.44231e13i	0.379497	−	0.657307i
$923$	5.70957e12	−	9.88926e12i	0.258938	−	0.448493i
$924$	−6.07876e12	+	1.06048e13i	−0.274341	+	0.478608i
$925$	2.00417e11	+	3.47133e11i	0.00900114	+	0.0155904i
$926$	1.66614e12			0.0744665
$927$	−8.29603e12	−	1.41647e13i	−0.368987	−	0.630012i
$928$	−7.18271e13			−3.17923
$929$	−5.05215e12	−	8.75058e12i	−0.222539	−	0.385448i	0.733040	−	0.680186i	$-0.238101\pi$
$929$	−5.05215e12	−	8.75058e12i	−0.222539	−	0.385448i	−0.955578	+	0.294738i	$0.904768\pi$
$930$	−1.72628e13	+	5.37479e10i	−0.756727	+	0.00235607i
$931$	2.61494e12	−	4.52920e12i	0.114074	−	0.197582i
$932$	−2.88198e13	+	4.99174e13i	−1.25118	+	2.16711i
$933$	1.66214e13	−	5.17509e10i	0.718126	−	0.00223589i
$934$	1.71687e13	+	2.97370e13i	0.738203	+	1.27861i
$935$	9.22169e12			0.394601
$936$	4.92010e13	+	8.40061e13i	2.09523	+	3.57742i
$937$	1.78563e13			0.756768			0.378384	−	0.925649i	$-0.376480\pi$
$937$	1.78563e13			0.756768			0.378384	+	0.925649i	$0.376480\pi$
$938$	−1.15144e13	−	1.99436e13i	−0.485657	−	0.841183i
$939$	−3.82438e12	+	6.67191e12i	−0.160534	+	0.280063i
$940$	−1.39687e13	+	2.41944e13i	−0.583552	+	1.01074i
$941$	−9.72541e12	+	1.68449e13i	−0.404347	+	0.700350i	−0.994245	−	0.107128i	$-0.965835\pi$
$941$	−9.72541e12	+	1.68449e13i	−0.404347	+	0.700350i	0.589898	+	0.807478i	$0.299168\pi$
$942$	2.52399e13	+	4.34041e13i	1.04438	+	1.79598i
$943$	1.79861e13	+	3.11529e13i	0.740688	+	1.28291i
$944$	−7.28852e13			−2.98721
$945$	3.93164e12	−	3.67245e10i	0.160373	−	0.00149800i
$946$	−2.34126e12			−0.0950472
$947$	1.80874e13	+	3.13283e13i	0.730806	+	1.26579i	0.956539	+	0.291603i	$0.0941887\pi$
$947$	1.80874e13	+	3.13283e13i	0.730806	+	1.26579i	−0.225734	+	0.974189i	$0.572478\pi$
$948$	−2.47447e13	−	4.25526e13i	−0.995051	−	1.71115i
$949$	−7.30967e12	+	1.26607e13i	−0.292550	+	0.506711i
$950$	−1.21670e12	+	2.10738e12i	−0.0484647	+	0.0839433i
$951$	−1.24823e13	+	2.17763e13i	−0.494859	+	0.863318i
$952$	1.67002e13	+	2.89255e13i	0.658953	+	1.14134i
$953$	−9.99271e12			−0.392433			−0.196216	−	0.980561i	$-0.562865\pi$
$953$	−9.99271e12			−0.392433			−0.196216	+	0.980561i	$0.562865\pi$
$954$	−6.82173e13	+	4.24794e11i	−2.66641	+	0.0166039i
$955$	4.42476e12			0.172137
$956$	−3.01231e13	−	5.21747e13i	−1.16638	−	2.02022i
$957$	2.73051e13	−	8.50145e10i	1.05230	−	0.00327634i
$958$	−2.94018e12	+	5.09253e12i	−0.112779	+	0.195339i
$959$	−8.85260e12	+	1.53332e13i	−0.337977	+	0.585393i
$960$	−1.27606e13	+	3.97301e10i	−0.484898	+	0.00150973i
$961$	2.17306e12	+	3.76385e12i	0.0821895	+	0.142356i
$962$	6.94934e12			0.261611
$963$	−1.65286e13	+	2.90445e13i	−0.619322	+	1.08829i
$964$	3.34049e13			1.24584
$965$	−8.81690e12	−	1.52713e13i	−0.327298	−	0.566896i
$966$	1.06378e13	−	1.85583e13i	0.393055	−	0.685712i
$967$	−1.02959e13	+	1.78330e13i	−0.378656	+	0.655852i	−0.990867	−	0.134843i	$-0.956947\pi$
$967$	−1.02959e13	+	1.78330e13i	−0.378656	+	0.655852i	0.612211	+	0.790695i	$0.290280\pi$
$968$	2.15698e13	−	3.73600e13i	0.789599	−	1.36763i
$969$	−5.02736e12	−	8.64537e12i	−0.183182	−	0.315011i
$970$	1.07070e13	+	1.85452e13i	0.388326	+	0.672601i
$971$	7.51171e12			0.271177			0.135588	−	0.990765i	$-0.456708\pi$
$971$	7.51171e12			0.271177			0.135588	+	0.990765i	$0.456708\pi$
$972$	−3.46690e13	−	5.79461e13i	−1.24578	−	2.08222i
$973$	−6.91661e12			−0.247392
$974$	−1.02739e13	−	1.77949e13i	−0.365780	−	0.633549i
$975$	4.45442e12	+	7.66010e12i	0.157859	+	0.271465i
$976$	5.29291e13	−	9.16759e13i	1.86711	−	3.23393i
$977$	8.96515e12	−	1.55281e13i	0.314798	−	0.545246i	−0.664597	−	0.747202i	$-0.731397\pi$
$977$	8.96515e12	−	1.55281e13i	0.314798	−	0.545246i	0.979395	+	0.201956i	$0.0647299\pi$
$978$	−1.57822e12	+	2.75333e12i	−0.0551625	+	0.0962349i
$979$	4.81101e11	+	8.33292e11i	0.0167384	+	0.0289918i
$980$	2.73033e13			0.945579
$981$	6.29320e12	−	1.10586e13i	0.216951	−	0.381232i
$982$	−3.80727e13			−1.30651
$983$	−2.45403e13	−	4.25051e13i	−0.838281	−	1.45194i	−0.891331	−	0.453353i	$-0.850228\pi$
$983$	−2.45403e13	−	4.25051e13i	−0.838281	−	1.45194i	0.0530507	−	0.998592i	$-0.483105\pi$
$984$	−9.66137e13	+	3.00807e11i	−3.28519	+	0.0102285i
$985$	7.44184e11	−	1.28896e12i	0.0251894	−	0.0436293i
$986$	6.34581e13	−	1.09913e14i	2.13816	−	3.70341i
$987$	1.14996e13	−	3.58042e10i	0.385707	−	0.00120090i
$988$	1.49378e13	+	2.58730e13i	0.498747	+	0.863855i
$989$	2.90142e12			0.0964333
$990$	1.58619e13	−	9.87729e10i	0.524803	−	0.00326798i
$991$	−8.94424e12			−0.294586			−0.147293	−	0.989093i	$-0.547056\pi$
$991$	−8.94424e12			−0.294586			−0.147293	+	0.989093i	$0.547056\pi$
$992$	−2.67009e13	−	4.62473e13i	−0.875433	−	1.51629i
$993$	−1.52072e13	+	2.65301e13i	−0.496338	+	0.865898i
$994$	3.36941e12	−	5.83598e12i	0.109475	−	0.189616i
$995$	8.31158e12	−	1.43961e13i	0.268831	−	0.465630i
$996$	2.05923e13	+	3.54117e13i	0.663036	+	1.14020i
$997$	8.70718e12	+	1.50813e13i	0.279093	+	0.483404i	0.971160	−	0.238430i	$-0.0766328\pi$
$997$	8.70718e12	+	1.50813e13i	0.279093	+	0.483404i	−0.692066	+	0.721834i	$0.743299\pi$
$998$	9.22101e13			2.94233
$999$	−2.83350e12	+	2.64670e10i	−0.0900075	+	0.000840737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.10.e.a.31.1	yes	34
3.2	odd	2		135.10.e.a.91.17		34
9.2	odd	6		135.10.e.a.46.17		34
9.7	even	3	inner	45.10.e.a.16.1	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.10.e.a.16.1	✓	34	9.7	even	3	inner
45.10.e.a.31.1	yes	34	1.1	even	1	trivial
135.10.e.a.46.17		34	9.2	odd	6
135.10.e.a.91.17		34	3.2	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	45.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-20.9424 - 36.2733i) q^{2} +(-70.5260 - 121.281i) q^{3} +(-621.169 + 1075.90i) q^{4} +(312.500 - 541.266i) q^{5} +(-2922.28 + 5098.13i) q^{6} +(1139.06 + 1972.90i) q^{7} +30590.0 q^{8} +(-9735.16 + 17106.9i) q^{9} -26178.0 q^{10} +(15392.4 + 26660.3i) q^{11} +(174294. - 542.666i) q^{12} +(80844.7 - 140027. i) q^{13} +(47709.2 - 82634.7i) q^{14} +(-87684.6 + 273.006i) q^{15} +(-322590. - 558743. i) q^{16} +479287. q^{17} +(824403. - 5133.61i) q^{18} +148729. q^{19} +(388230. + 672435. i) q^{20} +(158943. - 277287. i) q^{21} +(644706. - 1.11666e6i) q^{22} +(-798956. + 1.38383e6i) q^{23} +(-2.15739e6 - 3.70999e6i) q^{24} +(-195312. - 338291. i) q^{25} -6.77233e6 q^{26} +(2.76133e6 - 25792.9i) q^{27} -2.83019e6 q^{28} +(3.16108e6 + 5.47514e6i) q^{29} +(1.84623e6 + 3.17489e6i) q^{30} +(-2.35019e6 + 4.07064e6i) q^{31} +(-5.68059e6 + 9.83907e6i) q^{32} +(2.14783e6 - 3.74705e6i) q^{33} +(-1.00374e7 - 1.73853e7i) q^{34} +1.42382e6 q^{35} +(-1.23581e7 - 2.11003e7i) q^{36} -1.02614e6 q^{37} +(-3.11474e6 - 5.39489e6i) q^{38} +(-2.26843e7 + 70627.6i) q^{39} +(9.55938e6 - 1.65573e7i) q^{40} +(1.12560e7 - 1.94960e7i) q^{41} +(-1.33868e7 + 41679.7i) q^{42} +(-907878. - 1.57249e6i) q^{43} -3.82450e7 q^{44} +(6.21716e6 + 1.06152e7i) q^{45} +6.69282e7 q^{46} +(1.79902e7 + 3.11599e7i) q^{47} +(-4.50139e7 + 7.85300e7i) q^{48} +(1.75819e7 - 3.04527e7i) q^{49} +(-8.18063e6 + 1.41693e7i) q^{50} +(-3.38022e7 - 5.81284e7i) q^{51} +(1.00436e8 + 1.73961e8i) q^{52} -8.27475e7 q^{53} +(-5.87644e7 - 9.96223e7i) q^{54} +1.92404e7 q^{55} +(3.48438e7 + 6.03512e7i) q^{56} +(-1.04893e7 - 1.80380e7i) q^{57} +(1.32401e8 - 2.29325e8i) q^{58} +(5.64844e7 - 9.78338e7i) q^{59} +(5.41732e7 - 9.45091e7i) q^{60} +(8.20377e7 + 1.42093e8i) q^{61} +1.96874e8 q^{62} +(-4.48393e7 + 279217. i) q^{63} +1.45528e8 q^{64} +(-5.05280e7 - 8.75170e7i) q^{65} +(-1.80899e8 + 563228. i) q^{66} +(1.20673e8 - 2.09012e8i) q^{67} +(-2.97718e8 + 5.15662e8i) q^{68} +(2.24180e8 - 697984. i) q^{69} +(-2.98182e7 - 5.16467e7i) q^{70} +7.06238e7 q^{71} +(-2.97799e8 + 5.23301e8i) q^{72} -9.04161e7 q^{73} +(2.14898e7 + 3.72214e7i) q^{74} +(-2.72537e7 + 4.75460e7i) q^{75} +(-9.23857e7 + 1.60017e8i) q^{76} +(-3.50655e7 + 6.07353e7i) q^{77} +(4.77626e8 + 8.21355e8i) q^{78} +(-1.41210e8 - 2.44582e8i) q^{79} -4.03238e8 q^{80} +(-1.97874e8 - 3.33078e8i) q^{81} -9.42914e8 q^{82} +(1.17513e8 + 2.03538e8i) q^{83} +(1.99602e8 + 3.43248e8i) q^{84} +(1.49777e8 - 2.59422e8i) q^{85} +(-3.80263e7 + 6.58635e7i) q^{86} +(4.41093e8 - 7.69519e8i) q^{87} +(4.70852e8 + 8.15540e8i) q^{88} +3.12559e7 q^{89} +(2.54847e8 - 4.47825e8i) q^{90} +3.68347e8 q^{91} +(-9.92572e8 - 1.71919e9i) q^{92} +(6.59441e8 - 2.05317e6i) q^{93} +(7.53515e8 - 1.30513e9i) q^{94} +(4.64778e7 - 8.05018e7i) q^{95} +(1.59392e9 - 4.96268e6i) q^{96} +(-4.09009e8 - 7.08425e8i) q^{97} -1.47283e9 q^{98} +(-6.05924e8 + 3.77313e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 16 q^{2} - 285 q^{3} - 3840 q^{4} + 10625 q^{5} + 1635 q^{6} + 9946 q^{7} + 38772 q^{8} + 7959 q^{9} - 20000 q^{10} - 32881 q^{11} + 595719 q^{12} + 100272 q^{13} - 333129 q^{14} - 157500 q^{15}+ \cdots - 3426367056 q^{99}+O(q^{100}) \) 34 * q - 16 * q^2 - 285 * q^3 - 3840 * q^4 + 10625 * q^5 + 1635 * q^6 + 9946 * q^7 + 38772 * q^8 + 7959 * q^9 - 20000 * q^10 - 32881 * q^11 + 595719 * q^12 + 100272 * q^13 - 333129 * q^14 - 157500 * q^15 - 292740 * q^16 - 103174 * q^17 - 401577 * q^18 - 1954002 * q^19 + 2400000 * q^20 + 846540 * q^21 - 603517 * q^22 - 2528832 * q^23 + 2610864 * q^24 - 6640625 * q^25 - 11356132 * q^26 + 13389570 * q^27 + 1233322 * q^28 + 4997116 * q^29 - 2246250 * q^30 + 7154764 * q^31 - 3848138 * q^32 + 37701447 * q^33 - 1842211 * q^34 + 12432500 * q^35 + 31228485 * q^36 - 29485864 * q^37 - 27825985 * q^38 - 48378006 * q^39 + 12116250 * q^40 - 1432577 * q^41 + 645597 * q^42 + 30233475 * q^43 + 172245706 * q^44 - 4490625 * q^45 - 38739414 * q^46 - 51256132 * q^47 - 273587937 * q^48 - 97033283 * q^49 - 6250000 * q^50 + 191039205 * q^51 + 170396546 * q^52 + 198356324 * q^53 + 65145240 * q^54 - 41101250 * q^55 - 446494149 * q^56 - 442487301 * q^57 + 199102621 * q^58 - 163581061 * q^59 + 110338125 * q^60 + 263506344 * q^61 + 682090404 * q^62 - 131178564 * q^63 - 504872168 * q^64 - 62670000 * q^65 - 888863958 * q^66 + 624947419 * q^67 - 77685671 * q^68 + 1347472386 * q^69 + 208205625 * q^70 + 520490800 * q^71 - 150538482 * q^72 - 1740248610 * q^73 - 479177876 * q^74 + 12890625 * q^75 + 1071379103 * q^76 - 777961272 * q^77 + 2208863298 * q^78 + 847184266 * q^79 - 365925000 * q^80 - 455780961 * q^81 - 2343238688 * q^82 - 663595350 * q^83 - 1445250609 * q^84 - 32241875 * q^85 - 1041586195 * q^86 + 945629148 * q^87 + 1122086037 * q^88 + 729648408 * q^89 - 437745000 * q^90 - 2090033068 * q^91 + 157159431 * q^92 - 150985728 * q^93 + 3068174993 * q^94 - 610625625 * q^95 + 1273538655 * q^96 + 186406391 * q^97 - 1334731394 * q^98 - 3426367056 * q^99

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