LMFDB - Embedded newform 38.10.c.b.7.1

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			7.1
Root			$113.220 + 196.103i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.b.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 - 13.8564i) q^{2} +(-108.720 - 188.309i) q^{3} +(-128.000 + 221.703i) q^{4} +(-480.308 - 831.918i) q^{5} +(-1739.52 + 3012.94i) q^{6} -4308.78 q^{7} +4096.00 q^{8} +(-13798.6 + 23899.8i) q^{9} +O(q^{10})$	\(q+(-8.00000 - 13.8564i) q^{2} +(-108.720 - 188.309i) q^{3} +(-128.000 + 221.703i) q^{4} +(-480.308 - 831.918i) q^{5} +(-1739.52 + 3012.94i) q^{6} -4308.78 q^{7} +4096.00 q^{8} +(-13798.6 + 23899.8i) q^{9} +(-7684.93 + 13310.7i) q^{10} -46980.2 q^{11} +55664.6 q^{12} +(-35122.2 + 60833.5i) q^{13} +(34470.2 + 59704.2i) q^{14} +(-104438. + 180892. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-176513. - 305730. i) q^{17} +441554. q^{18} +(514015. - 241819. i) q^{19} +245918. q^{20} +(468450. + 811380. i) q^{21} +(375841. + 650976. i) q^{22} +(473632. - 820355. i) q^{23} +(-445317. - 771312. i) q^{24} +(515171. - 892303. i) q^{25} +1.12391e6 q^{26} +1.72085e6 q^{27} +(551524. - 955267. i) q^{28} +(-1.53799e6 + 2.66387e6i) q^{29} +3.34202e6 q^{30} +2.95243e6 q^{31} +(-524288. + 908093. i) q^{32} +(5.10768e6 + 8.84677e6i) q^{33} +(-2.82421e6 + 4.89168e6i) q^{34} +(2.06954e6 + 3.58455e6i) q^{35} +(-3.53244e6 - 6.11836e6i) q^{36} +1.34465e7 q^{37} +(-7.46286e6 - 5.18785e6i) q^{38} +1.52740e7 q^{39} +(-1.96734e6 - 3.40753e6i) q^{40} +(-8.44173e6 - 1.46215e7i) q^{41} +(7.49521e6 - 1.29821e7i) q^{42} +(37037.9 + 64151.5i) q^{43} +(6.01346e6 - 1.04156e7i) q^{44} +2.65103e7 q^{45} -1.51562e7 q^{46} +(-1.15086e7 + 1.99335e7i) q^{47} +(-7.12507e6 + 1.23410e7i) q^{48} -2.17880e7 q^{49} -1.64855e7 q^{50} +(-3.83811e7 + 6.64780e7i) q^{51} +(-8.99129e6 - 1.55734e7i) q^{52} +(-3.19791e7 + 5.53895e7i) q^{53} +(-1.37668e7 - 2.38448e7i) q^{54} +(2.25649e7 + 3.90836e7i) q^{55} -1.76488e7 q^{56} +(-1.01420e8 - 7.05029e7i) q^{57} +4.92155e7 q^{58} +(-4.48577e7 - 7.76958e7i) q^{59} +(-2.67362e7 - 4.63084e7i) q^{60} +(-8.22227e7 + 1.42414e8i) q^{61} +(-2.36194e7 - 4.09100e7i) q^{62} +(5.94550e7 - 1.02979e8i) q^{63} +1.67772e7 q^{64} +6.74779e7 q^{65} +(8.17230e7 - 1.41548e8i) q^{66} +(9.56832e7 - 1.65728e8i) q^{67} +9.03749e7 q^{68} -2.05973e8 q^{69} +(3.31126e7 - 5.73528e7i) q^{70} +(-1.80473e7 - 3.12589e7i) q^{71} +(-5.65190e7 + 9.78937e7i) q^{72} +(1.80983e8 + 3.13472e8i) q^{73} +(-1.07572e8 - 1.86320e8i) q^{74} -2.24038e8 q^{75} +(-1.21822e7 + 1.44911e8i) q^{76} +2.02427e8 q^{77} +(-1.22192e8 - 2.11642e8i) q^{78} +(1.48824e8 + 2.57771e8i) q^{79} +(-3.14775e7 + 5.45206e7i) q^{80} +(8.45062e7 + 1.46369e8i) q^{81} +(-1.35068e8 + 2.33944e8i) q^{82} +6.78948e8 q^{83} -2.39847e8 q^{84} +(-1.69562e8 + 2.93689e8i) q^{85} +(592606. - 1.02642e6i) q^{86} +6.68839e8 q^{87} -1.92431e8 q^{88} +(-3.90880e8 + 6.77025e8i) q^{89} +(-2.12082e8 - 3.67337e8i) q^{90} +(1.51334e8 - 2.62118e8i) q^{91} +(1.21250e8 + 2.10011e8i) q^{92} +(-3.20988e8 - 5.55967e8i) q^{93} +3.68276e8 q^{94} +(-4.48059e8 - 3.11471e8i) q^{95} +2.28002e8 q^{96} +(4.56647e8 + 7.90935e8i) q^{97} +(1.74304e8 + 3.01904e8i) q^{98} +(6.48260e8 - 1.12282e9i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$3$	−108.720	−	188.309i	−0.774932	−	1.34222i	−0.934832	−	0.355089i	$-0.884451\pi$
$3$	−108.720	−	188.309i	−0.774932	−	1.34222i	0.159900	−	0.987133i	$-0.448883\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−480.308	−	831.918i	−0.343680	−	0.595272i	0.641433	−	0.767179i	$-0.278340\pi$
$5$	−480.308	−	831.918i	−0.343680	−	0.595272i	−0.985113	+	0.171907i	$0.945007\pi$
$6$	−1739.52	+	3012.94i	−0.547960	+	0.949094i
$7$	−4308.78			−0.678286			−0.339143	−	0.940735i	$-0.610137\pi$
$7$	−4308.78			−0.678286			−0.339143	+	0.940735i	$0.610137\pi$
$8$	4096.00			0.353553
$9$	−13798.6	+	23899.8i	−0.701040	+	1.21424i
$10$	−7684.93	+	13310.7i	−0.243019	+	0.420921i
$11$	−46980.2			−0.967492			−0.483746	−	0.875208i	$-0.660724\pi$
$11$	−46980.2			−0.967492			−0.483746	+	0.875208i	$0.660724\pi$
$12$	55664.6			0.774932
$13$	−35122.2	+	60833.5i	−0.341065	+	0.590742i	−0.984631	−	0.174649i	$-0.944121\pi$
$13$	−35122.2	+	60833.5i	−0.341065	+	0.590742i	0.643566	+	0.765391i	$0.277454\pi$
$14$	34470.2	+	59704.2i	0.239810	+	0.415364i
$15$	−104438.	+	180892.i	−0.532658	+	0.922591i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−176513.	−	305730.i	−0.512575	−	0.887806i	−0.999894	−	0.0145820i	$-0.995358\pi$
$17$	−176513.	−	305730.i	−0.512575	−	0.887806i	0.487318	−	0.873224i	$-0.337975\pi$
$18$	441554.			0.991421
$19$	514015.	−	241819.i	0.904867	−	0.425695i
$19$	514015.	−	241819.i	0.904867	−	0.425695i
$20$	245918.			0.343680
$21$	468450.	+	811380.i	0.525626	+	0.910411i
$22$	375841.	+	650976.i	0.342060	+	0.592466i
$23$	473632.	−	820355.i	0.352912	−	0.611261i	−0.633847	−	0.773459i	$-0.718525\pi$
$23$	473632.	−	820355.i	0.352912	−	0.611261i	0.986758	+	0.162198i	$0.0518583\pi$
$24$	−445317.	−	771312.i	−0.273980	−	0.474547i
$25$	515171.	−	892303.i	0.263768	−	0.456859i
$26$	1.12391e6			0.482339
$27$	1.72085e6			0.623171
$28$	551524.	−	955267.i	0.169572	−	0.293707i
$29$	−1.53799e6	+	2.66387e6i	−0.403795	+	0.699394i	−0.994180	−	0.107728i	$-0.965643\pi$
$29$	−1.53799e6	+	2.66387e6i	−0.403795	+	0.699394i	0.590385	+	0.807122i	$0.298976\pi$
$30$	3.34202e6			0.753292
$31$	2.95243e6			0.574185			0.287092	−	0.957903i	$-0.407311\pi$
$31$	2.95243e6			0.574185			0.287092	+	0.957903i	$0.407311\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$	5.10768e6	+	8.84677e6i	0.749741	+	1.29859i
$34$	−2.82421e6	+	4.89168e6i	−0.362445	+	0.627774i
$35$	2.06954e6	+	3.58455e6i	0.233114	+	0.403765i
$36$	−3.53244e6	−	6.11836e6i	−0.350520	−	0.607119i
$37$	1.34465e7			1.17951			0.589755	−	0.807582i	$-0.299224\pi$
$37$	1.34465e7			1.17951			0.589755	+	0.807582i	$0.299224\pi$
$38$	−7.46286e6	−	5.18785e6i	−0.580602	−	0.403610i
$39$	1.52740e7			1.05721
$40$	−1.96734e6	−	3.40753e6i	−0.121509	−	0.210460i
$41$	−8.44173e6	−	1.46215e7i	−0.466556	−	0.808099i	0.532714	−	0.846295i	$-0.321172\pi$
$41$	−8.44173e6	−	1.46215e7i	−0.466556	−	0.808099i	−0.999270	+	0.0381963i	$0.987839\pi$
$42$	7.49521e6	−	1.29821e7i	0.371674	−	0.643758i
$43$	37037.9	+	64151.5i	0.00165211	+	0.00286153i	0.866850	−	0.498569i	$-0.166141\pi$
$43$	37037.9	+	64151.5i	0.00165211	+	0.00286153i	−0.865198	+	0.501430i	$0.832807\pi$
$44$	6.01346e6	−	1.04156e7i	0.241873	−	0.418936i
$45$	2.65103e7			0.963735
$46$	−1.51562e7			−0.499093
$47$	−1.15086e7	+	1.99335e7i	−0.344020	+	0.595860i	−0.985175	−	0.171551i	$-0.945122\pi$
$47$	−1.15086e7	+	1.99335e7i	−0.344020	+	0.595860i	0.641155	+	0.767411i	$0.278455\pi$
$48$	−7.12507e6	+	1.23410e7i	−0.193733	+	0.335556i
$49$	−2.17880e7			−0.539928
$50$	−1.64855e7			−0.373024
$51$	−3.83811e7	+	6.64780e7i	−0.794422	+	1.37598i
$52$	−8.99129e6	−	1.55734e7i	−0.170532	−	0.295371i
$53$	−3.19791e7	+	5.53895e7i	−0.556705	+	0.964242i	0.441063	+	0.897476i	$0.354601\pi$
$53$	−3.19791e7	+	5.53895e7i	−0.556705	+	0.964242i	−0.997769	+	0.0667659i	$0.978732\pi$
$54$	−1.37668e7	−	2.38448e7i	−0.220324	−	0.381613i
$55$	2.25649e7	+	3.90836e7i	0.332508	+	0.575921i
$56$	−1.76488e7			−0.239810
$57$	−1.01420e8	−	7.05029e7i	−1.27259	−	0.884648i
$58$	4.92155e7			0.571053
$59$	−4.48577e7	−	7.76958e7i	−0.481951	−	0.834764i	0.517834	−	0.855481i	$-0.326738\pi$
$59$	−4.48577e7	−	7.76958e7i	−0.481951	−	0.834764i	−0.999785	+	0.0207170i	$0.993405\pi$
$60$	−2.67362e7	−	4.63084e7i	−0.266329	−	0.461295i
$61$	−8.22227e7	+	1.42414e8i	−0.760339	+	1.31695i	0.182336	+	0.983236i	$0.441634\pi$
$61$	−8.22227e7	+	1.42414e8i	−0.760339	+	1.31695i	−0.942676	+	0.333710i	$0.891699\pi$
$62$	−2.36194e7	−	4.09100e7i	−0.203005	−	0.351615i
$63$	5.94550e7	−	1.02979e8i	0.475506	−	0.823601i
$64$	1.67772e7			0.125000
$65$	6.74779e7			0.468869
$66$	8.17230e7	−	1.41548e8i	0.530147	−	0.918242i
$67$	9.56832e7	−	1.65728e8i	0.580095	−	1.00475i	−0.415373	−	0.909651i	$-0.636349\pi$
$67$	9.56832e7	−	1.65728e8i	0.580095	−	1.00475i	0.995467	−	0.0951025i	$-0.0303179\pi$
$68$	9.03749e7			0.512575
$69$	−2.05973e8			−1.09393
$70$	3.31126e7	−	5.73528e7i	0.164836	−	0.285505i
$71$	−1.80473e7	−	3.12589e7i	−0.0842851	−	0.145986i	0.820801	−	0.571214i	$-0.193527\pi$
$71$	−1.80473e7	−	3.12589e7i	−0.0842851	−	0.145986i	−0.905086	+	0.425228i	$0.860194\pi$
$72$	−5.65190e7	+	9.78937e7i	−0.247855	+	0.429298i
$73$	1.80983e8	+	3.13472e8i	0.745909	+	1.29195i	0.949769	+	0.312952i	$0.101318\pi$
$73$	1.80983e8	+	3.13472e8i	0.745909	+	1.29195i	−0.203860	+	0.979000i	$0.565349\pi$
$74$	−1.07572e8	−	1.86320e8i	−0.417020	−	0.722300i
$75$	−2.24038e8			−0.817608
$76$	−1.21822e7	+	1.44911e8i	−0.0418855	+	0.498243i
$77$	2.02427e8			0.656237
$78$	−1.22192e8	−	2.11642e8i	−0.373780	−	0.647406i
$79$	1.48824e8	+	2.57771e8i	0.429885	+	0.744582i	0.996863	−	0.0791508i	$-0.0252209\pi$
$79$	1.48824e8	+	2.57771e8i	0.429885	+	0.744582i	−0.566978	+	0.823733i	$0.691888\pi$
$80$	−3.14775e7	+	5.45206e7i	−0.0859201	+	0.148818i
$81$	8.45062e7	+	1.46369e8i	0.218125	+	0.377804i
$82$	−1.35068e8	+	2.33944e8i	−0.329905	+	0.571412i
$83$	6.78948e8			1.57031			0.785155	−	0.619299i	$-0.212583\pi$
$83$	6.78948e8			1.57031			0.785155	+	0.619299i	$0.212583\pi$
$84$	−2.39847e8			−0.525626
$85$	−1.69562e8	+	2.93689e8i	−0.352324	+	0.610243i
$86$	592606.	−	1.02642e6i	0.00116822	−	0.00202341i
$87$	6.68839e8			1.25166
$88$	−1.92431e8			−0.342060
$89$	−3.90880e8	+	6.77025e8i	−0.660372	+	1.14380i	0.320146	+	0.947368i	$0.396268\pi$
$89$	−3.90880e8	+	6.77025e8i	−0.660372	+	1.14380i	−0.980518	+	0.196430i	$0.937065\pi$
$90$	−2.12082e8	−	3.67337e8i	−0.340732	−	0.590165i
$91$	1.51334e8	−	2.62118e8i	0.231340	−	0.400692i
$92$	1.21250e8	+	2.10011e8i	0.176456	+	0.305631i
$93$	−3.20988e8	−	5.55967e8i	−0.444954	−	0.770683i
$94$	3.68276e8			0.486518
$95$	−4.48059e8	−	3.11471e8i	−0.564389	−	0.392339i
$96$	2.28002e8			0.273980
$97$	4.56647e8	+	7.90935e8i	0.523730	+	0.907127i	0.999618	+	0.0276214i	$0.00879327\pi$
$97$	4.56647e8	+	7.90935e8i	0.523730	+	0.907127i	−0.475888	+	0.879506i	$0.657873\pi$
$98$	1.74304e8	+	3.01904e8i	0.190893	+	0.330637i
$99$	6.48260e8	−	1.12282e9i	0.678251	−	1.17477i
$100$	1.31884e8	+	2.28430e8i	0.131884	+	0.228430i
$101$	−4.08242e8	+	7.07096e8i	−0.390366	+	0.676133i	−0.992498	−	0.122263i	$-0.960985\pi$
$101$	−4.08242e8	+	7.07096e8i	−0.390366	+	0.676133i	0.602132	+	0.798397i	$0.294318\pi$
$102$	1.22819e9			1.12348
$103$	8.37127e8			0.732865			0.366433	−	0.930445i	$-0.380579\pi$
$103$	8.37127e8			0.732865			0.366433	+	0.930445i	$0.380579\pi$
$104$	−1.43861e8	+	2.49174e8i	−0.120585	+	0.208859i
$105$	4.50001e8	−	7.79424e8i	0.361295	−	0.625781i
$106$	1.02333e9			0.787300
$107$	1.21307e9			0.894662			0.447331	−	0.894368i	$-0.352375\pi$
$107$	1.21307e9			0.894662			0.447331	+	0.894368i	$0.352375\pi$
$108$	−2.20269e8	+	3.81518e8i	−0.155793	+	0.269841i
$109$	−1.25894e9	−	2.18055e9i	−0.854252	−	1.47961i	−0.877337	−	0.479874i	$-0.840682\pi$
$109$	−1.25894e9	−	2.18055e9i	−0.854252	−	1.47961i	0.0230853	−	0.999733i	$-0.492651\pi$
$110$	3.61039e8	−	6.25338e8i	0.235119	−	0.407238i
$111$	−1.46190e9	−	2.53209e9i	−0.914041	−	1.58317i
$112$	1.41190e8	+	2.44548e8i	0.0847858	+	0.146853i
$113$	−1.35482e9			−0.781679			−0.390840	−	0.920459i	$-0.627815\pi$
$113$	−1.35482e9			−0.781679			−0.390840	+	0.920459i	$0.627815\pi$
$114$	−1.65556e8	+	1.96934e9i	−0.0918062	+	1.09207i
$115$	−9.09957e8			−0.485155
$116$	−3.93724e8	−	6.81950e8i	−0.201898	−	0.349697i
$117$	−9.69274e8	−	1.67883e9i	−0.478200	−	0.828268i
$118$	−7.17723e8	+	1.24313e9i	−0.340791	+	0.590267i
$119$	7.60557e8	+	1.31732e9i	0.347673	+	0.602187i
$120$	−4.27779e8	+	7.40934e8i	−0.188323	+	0.326185i
$121$	−1.50811e8			−0.0639586
$122$	2.63113e9			1.07528
$123$	−1.83557e9	+	3.17930e9i	−0.723099	+	1.25244i
$124$	−3.77911e8	+	6.54560e8i	−0.143546	+	0.248629i
$125$	−2.86597e9			−1.04997
$126$	−1.90256e9			−0.672467
$127$	−1.89285e9	+	3.27852e9i	−0.645655	+	1.11831i	0.338495	+	0.940968i	$0.390082\pi$
$127$	−1.89285e9	+	3.27852e9i	−0.645655	+	1.11831i	−0.984150	+	0.177339i	$0.943251\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$	8.05352e6	−	1.39491e7i	0.00256054	−	0.00443499i
$130$	−5.39823e8	−	9.35002e8i	−0.165770	−	0.287123i
$131$	−8.21718e8	−	1.42326e9i	−0.243782	−	0.422243i	0.718006	−	0.696037i	$-0.245055\pi$
$131$	−8.21718e8	−	1.42326e9i	−0.243782	−	0.422243i	−0.961789	+	0.273793i	$0.911722\pi$
$132$	−2.61513e9			−0.749741
$133$	−2.21478e9	+	1.04194e9i	−0.613759	+	0.288743i
$134$	−3.06186e9			−0.820378
$135$	−8.26540e8	−	1.43161e9i	−0.214171	−	0.370956i
$136$	−7.22999e8	−	1.25227e9i	−0.181223	−	0.313887i
$137$	2.70615e9	−	4.68720e9i	0.656312	−	1.13676i	−0.325252	−	0.945627i	$-0.605449\pi$
$137$	2.70615e9	−	4.68720e9i	0.656312	−	1.13676i	0.981563	−	0.191137i	$-0.0612176\pi$
$138$	1.64779e9	+	2.85405e9i	0.386763	+	0.669893i
$139$	1.38354e8	−	2.39637e8i	0.0314359	−	0.0544486i	−0.849879	−	0.526977i	$-0.823325\pi$
$139$	1.38354e8	−	2.39637e8i	0.0314359	−	0.0544486i	0.881315	+	0.472529i	$0.156659\pi$
$140$	−1.05960e9			−0.233114
$141$	5.00488e9			1.06637
$142$	−2.88758e8	+	5.00143e8i	−0.0595986	+	0.103228i
$143$	1.65005e9	−	2.85797e9i	0.329978	−	0.571538i
$144$	1.80861e9			0.350520
$145$	2.95483e9			0.555106
$146$	2.89573e9	−	5.01556e9i	0.527437	−	0.913548i
$147$	2.36880e9	+	4.10287e9i	0.418408	+	0.724703i
$148$	−1.72115e9	+	2.98113e9i	−0.294878	+	0.510743i
$149$	−4.01335e9	−	6.95132e9i	−0.667066	−	1.15539i	−0.978721	−	0.205196i	$-0.934217\pi$
$149$	−4.01335e9	−	6.95132e9i	−0.667066	−	1.15539i	0.311655	−	0.950195i	$-0.399117\pi$
$150$	1.79230e9	+	3.10436e9i	0.289068	+	0.500681i
$151$	−2.16979e9			−0.339643			−0.169821	−	0.985475i	$-0.554319\pi$
$151$	−2.16979e9			−0.339643			−0.169821	+	0.985475i	$0.554319\pi$
$152$	2.10541e9	−	9.90489e8i	0.319919	−	0.150506i
$153$	9.74254e9			1.43734
$154$	−1.61942e9	−	2.80491e9i	−0.232015	−	0.401861i
$155$	−1.41807e9	−	2.45618e9i	−0.197336	−	0.341796i
$156$	−1.95507e9	+	3.38627e9i	−0.264302	+	0.457785i
$157$	5.85446e9	+	1.01402e10i	0.769021	+	1.33198i	0.938094	+	0.346380i	$0.112589\pi$
$157$	5.85446e9	+	1.01402e10i	0.769021	+	1.33198i	−0.169073	+	0.985604i	$0.554077\pi$
$158$	2.38119e9	−	4.12434e9i	0.303974	−	0.526499i
$159$	1.39071e10			1.72564
$160$	1.00728e9			0.121509
$161$	−2.04078e9	+	3.53473e9i	−0.239375	+	0.414610i
$162$	1.35210e9	−	2.34190e9i	0.154238	−	0.267148i
$163$	−1.28230e10			−1.42280			−0.711402	−	0.702786i	$-0.751939\pi$
$163$	−1.28230e10			−1.42280			−0.711402	+	0.702786i	$0.751939\pi$
$164$	4.32216e9			0.466556
$165$	4.90652e9	−	8.49835e9i	0.515343	−	0.892599i
$166$	−5.43159e9	−	9.40779e9i	−0.555188	−	0.961615i
$167$	−6.38176e9	+	1.10535e10i	−0.634916	+	1.09971i	0.351617	+	0.936144i	$0.385632\pi$
$167$	−6.38176e9	+	1.10535e10i	−0.634916	+	1.09971i	−0.986533	+	0.163563i	$0.947701\pi$
$168$	1.91877e9	+	3.32341e9i	0.185837	+	0.321879i
$169$	2.83511e9	+	4.91055e9i	0.267350	+	0.463063i
$170$	5.42597e9			0.498261
$171$	−1.31325e9	+	1.56216e10i	−0.117454	+	1.39715i
$172$	−1.89634e7			−0.00165211
$173$	−8.25819e9	−	1.43036e10i	−0.700934	−	1.21405i	−0.968139	−	0.250414i	$-0.919433\pi$
$173$	−8.25819e9	−	1.43036e10i	−0.700934	−	1.21405i	0.267205	−	0.963640i	$-0.413900\pi$
$174$	−5.35071e9	−	9.26771e9i	−0.442527	−	0.766480i
$175$	−2.21976e9	+	3.84473e9i	−0.178910	+	0.309881i
$176$	1.53945e9	+	2.66640e9i	0.120937	+	0.209468i
$177$	−9.75386e9	+	1.68942e10i	−0.746959	+	1.29377i
$178$	1.25082e10			0.933907
$179$	3.43746e9			0.250264			0.125132	−	0.992140i	$-0.460064\pi$
$179$	3.43746e9			0.250264			0.125132	+	0.992140i	$0.460064\pi$
$180$	−3.39331e9	+	5.87739e9i	−0.240934	+	0.417310i
$181$	−6.94508e8	+	1.20292e9i	−0.0480977	+	0.0833076i	−0.889072	−	0.457768i	$-0.848649\pi$
$181$	−6.94508e8	+	1.20292e9i	−0.0480977	+	0.0833076i	0.840974	+	0.541075i	$0.181983\pi$
$182$	−4.84268e9			−0.327164
$183$	3.57570e10			2.35685
$184$	1.94000e9	−	3.36018e9i	0.124773	−	0.216113i
$185$	−6.45847e9	−	1.11864e10i	−0.405375	−	0.702129i
$186$	−5.13581e9	+	8.89548e9i	−0.314630	+	0.544955i
$187$	8.29263e9	+	1.43633e10i	0.495913	+	0.858946i
$188$	−2.94621e9	−	5.10299e9i	−0.172010	−	0.297930i
$189$	−7.41478e9			−0.422688
$190$	−7.31399e8	+	8.70025e9i	−0.0407158	+	0.484329i
$191$	2.25719e10			1.22721			0.613605	−	0.789613i	$-0.289719\pi$
$191$	2.25719e10			1.22721			0.613605	+	0.789613i	$0.289719\pi$
$192$	−1.82402e9	−	3.15929e9i	−0.0968665	−	0.167778i
$193$	−1.34652e10	−	2.33224e10i	−0.698562	−	1.20995i	−0.968965	−	0.247198i	$-0.920490\pi$
$193$	−1.34652e10	−	2.33224e10i	−0.698562	−	1.20995i	0.270403	−	0.962747i	$-0.412843\pi$
$194$	7.30635e9	−	1.26550e10i	0.370333	−	0.641436i
$195$	−7.33620e9	−	1.27067e10i	−0.363342	−	0.629327i
$196$	2.78887e9	−	4.83046e9i	0.134982	−	0.233796i
$197$	8.66105e9			0.409706			0.204853	−	0.978793i	$-0.434328\pi$
$197$	8.66105e9			0.409706			0.204853	+	0.978793i	$0.434328\pi$
$198$	−2.07443e10			−0.959192
$199$	−1.03519e10	+	1.79299e10i	−0.467928	+	0.810475i	−0.999328	−	0.0366455i	$-0.988333\pi$
$199$	−1.03519e10	+	1.79299e10i	−0.467928	+	0.810475i	0.531400	+	0.847121i	$0.321666\pi$
$200$	2.11014e9	−	3.65487e9i	0.0932560	−	0.161524i
$201$	−4.16107e10			−1.79814
$202$	1.30638e10			0.552061
$203$	6.62684e9	−	1.14780e10i	0.273889	−	0.474389i
$204$	−9.82556e9	−	1.70184e10i	−0.397211	−	0.687990i
$205$	−8.10926e9	+	1.40456e10i	−0.320692	+	0.555455i
$206$	−6.69702e9	−	1.15996e10i	−0.259107	−	0.448786i
$207$	1.30709e10	+	2.26395e10i	0.494811	+	0.857037i
$208$	4.60354e9			0.170532
$209$	−2.41485e10	+	1.13607e10i	−0.875452	+	0.411856i
$210$	−1.44000e10			−0.510948
$211$	−2.98524e9	−	5.17059e9i	−0.103683	−	0.179585i	0.809516	−	0.587097i	$-0.199729\pi$
$211$	−2.98524e9	−	5.17059e9i	−0.103683	−	0.179585i	−0.913199	+	0.407513i	$0.866396\pi$
$212$	−8.18666e9	−	1.41797e10i	−0.278353	−	0.482121i
$213$	−3.92422e9	+	6.79694e9i	−0.130631	+	0.226259i
$214$	−9.70456e9	−	1.68088e10i	−0.316311	−	0.547866i
$215$	3.55792e7	−	6.16249e7i	0.00113559	−	0.00196691i
$216$	7.04862e9			0.220324
$217$	−1.27214e10			−0.389462
$218$	−2.01430e10	+	3.48888e10i	−0.604047	+	1.04624i
$219$	3.93530e10	−	6.81614e10i	1.15606	−	2.00235i
$220$	−1.15533e10			−0.332508
$221$	2.47982e10			0.699286
$222$	−2.33905e10	+	4.05135e10i	−0.646325	+	1.11947i
$223$	−1.90123e9	−	3.29302e9i	−0.0514828	−	0.0891708i	0.839136	−	0.543922i	$-0.183061\pi$
$223$	−1.90123e9	−	3.29302e9i	−0.0514828	−	0.0891708i	−0.890618	+	0.454752i	$0.849728\pi$
$224$	2.25904e9	−	3.91277e9i	0.0599526	−	0.103841i
$225$	1.42173e10	+	2.46250e10i	0.369824	+	0.640553i
$226$	1.08386e10	+	1.87729e10i	0.276365	+	0.478679i
$227$	−3.08784e9			−0.0771861			−0.0385931	−	0.999255i	$-0.512288\pi$
$227$	−3.08784e9			−0.0771861			−0.0385931	+	0.999255i	$0.512288\pi$
$228$	2.86125e10	−	1.34607e10i	0.701211	−	0.329885i
$229$	−7.82684e10			−1.88073			−0.940365	−	0.340166i	$-0.889517\pi$
$229$	−7.82684e10			−1.88073			−0.940365	+	0.340166i	$0.889517\pi$
$230$	7.27966e9	+	1.26087e10i	0.171528	+	0.297096i
$231$	−2.20079e10	−	3.81188e10i	−0.508539	−	0.880815i
$232$	−6.29959e9	+	1.09112e10i	−0.142763	+	0.247273i
$233$	2.77648e10	+	4.80900e10i	0.617152	+	1.06894i	0.990003	+	0.141047i	$0.0450470\pi$
$233$	2.77648e10	+	4.80900e10i	0.617152	+	1.06894i	−0.372851	+	0.927891i	$0.621620\pi$
$234$	−1.55084e10	+	2.68613e10i	−0.338139	+	0.585674i
$235$	2.21108e10			0.472931
$236$	2.29671e10			0.481951
$237$	3.23604e10	−	5.60498e10i	0.666263	−	1.15400i
$238$	1.21689e10	−	2.10772e10i	0.245842	−	0.425810i
$239$	−1.98975e10			−0.394465			−0.197233	−	0.980357i	$-0.563195\pi$
$239$	−1.98975e10			−0.394465			−0.197233	+	0.980357i	$0.563195\pi$
$240$	1.36889e10			0.266329
$241$	−2.86714e10	+	4.96603e10i	−0.547485	+	0.948271i	0.450961	+	0.892544i	$0.351081\pi$
$241$	−2.86714e10	+	4.96603e10i	−0.547485	+	0.948271i	−0.998446	+	0.0557279i	$0.982252\pi$
$242$	1.20649e9	+	2.08970e9i	0.0226128	+	0.0391665i
$243$	3.53108e10	−	6.11601e10i	0.649650	−	1.12523i
$244$	−2.10490e10	−	3.64580e10i	−0.380170	−	0.658473i
$245$	1.04650e10	+	1.81259e10i	0.185563	+	0.321404i
$246$	5.87382e10			1.02262
$247$	−3.34269e9	+	3.97625e10i	−0.0571426	+	0.679732i
$248$	1.20931e10			0.203005
$249$	−7.38153e10	−	1.27852e11i	−1.21688	−	2.10771i
$250$	2.29277e10	+	3.97120e10i	0.371220	+	0.642971i
$251$	3.54478e10	−	6.13975e10i	0.563713	−	0.976379i	−0.433455	−	0.901175i	$-0.642706\pi$
$251$	3.54478e10	−	6.13975e10i	0.563713	−	0.976379i	0.997168	−	0.0752043i	$-0.0239609\pi$
$252$	1.52205e10	+	2.63626e10i	0.237753	+	0.411800i
$253$	−2.22513e10	+	3.85404e10i	−0.341439	+	0.591390i
$254$	6.05713e10			0.913094
$255$	7.37389e10			1.09211
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−4.62545e10	+	8.01151e10i	−0.661386	+	1.14555i	0.318866	+	0.947800i	$0.396698\pi$
$257$	−4.62545e10	+	8.01151e10i	−0.661386	+	1.14555i	−0.980252	+	0.197754i	$0.936635\pi$
$258$	−2.57713e8			−0.00362115
$259$	−5.79380e10			−0.800046
$260$	−8.63718e9	+	1.49600e10i	−0.117217	+	0.203026i
$261$	−4.24440e10	−	7.35152e10i	−0.566154	−	0.980607i
$262$	−1.31475e10	+	2.27721e10i	−0.172380	+	0.298571i
$263$	3.22796e10	+	5.59100e10i	0.416033	+	0.720590i	0.995536	−	0.0943798i	$-0.0300868\pi$
$263$	3.22796e10	+	5.59100e10i	0.416033	+	0.720590i	−0.579503	+	0.814970i	$0.696753\pi$
$264$	2.09211e10	+	3.62364e10i	0.265074	+	0.459121i
$265$	6.14393e10			0.765315
$266$	3.21558e10	+	2.23533e10i	0.393815	+	0.273763i
$267$	1.69986e11			2.04698
$268$	2.44949e10	+	4.24264e10i	0.290047	+	0.502377i
$269$	−4.32699e10	−	7.49458e10i	−0.503850	−	0.872694i	−0.999990	−	0.00445114i	$-0.998583\pi$
$269$	−4.32699e10	−	7.49458e10i	−0.503850	−	0.872694i	0.496140	−	0.868242i	$-0.334750\pi$
$270$	−1.32246e10	+	2.29057e10i	−0.151442	+	0.262305i
$271$	8.05468e10	+	1.39511e11i	0.907165	+	1.57126i	0.817984	+	0.575241i	$0.195092\pi$
$271$	8.05468e10	+	1.39511e11i	0.907165	+	1.57126i	0.0891811	+	0.996015i	$0.471575\pi$
$272$	−1.15680e10	+	2.00363e10i	−0.128144	+	0.221952i
$273$	−6.58121e10			−0.717090
$274$	−8.65969e10			−0.928165
$275$	−2.42028e10	+	4.19205e10i	−0.255193	+	0.442008i
$276$	2.63646e10	−	4.56648e10i	0.273483	−	0.473686i
$277$	−5.19873e10			−0.530565			−0.265282	−	0.964171i	$-0.585465\pi$
$277$	−5.19873e10			−0.530565			−0.265282	+	0.964171i	$0.585465\pi$
$278$	−4.42733e9			−0.0444571
$279$	−4.07393e10	+	7.05625e10i	−0.402527	+	0.697197i
$280$	8.47684e9	+	1.46823e10i	0.0824181	+	0.142752i
$281$	9.30212e10	−	1.61117e11i	0.890027	−	1.54157i	0.0501868	−	0.998740i	$-0.484018\pi$
$281$	9.30212e10	−	1.61117e11i	0.890027	−	1.54157i	0.839841	−	0.542833i	$-0.182648\pi$
$282$	−4.00390e10	−	6.93496e10i	−0.377018	−	0.653015i
$283$	−6.66910e10	−	1.15512e11i	−0.618057	−	1.07051i	−0.989840	−	0.142186i	$-0.954587\pi$
$283$	−6.66910e10	−	1.15512e11i	−0.618057	−	1.07051i	0.371783	−	0.928320i	$-0.378747\pi$
$284$	9.24024e9			0.0842851
$285$	−9.93971e9	+	1.18236e11i	−0.0892425	+	1.06157i
$286$	−5.28015e10			−0.466659
$287$	3.63735e10	+	6.30008e10i	0.316459	+	0.548122i
$288$	−1.44689e10	−	2.50608e10i	−0.123928	−	0.214649i
$289$	−3.02003e9	+	5.23085e9i	−0.0254666	+	0.0441095i
$290$	−2.36386e10	−	4.09433e10i	−0.196260	−	0.339932i
$291$	9.92932e10	−	1.71981e11i	0.811711	−	1.40592i
$292$	−9.26635e10			−0.745909
$293$	3.80251e10			0.301416			0.150708	−	0.988578i	$-0.451845\pi$
$293$	3.80251e10			0.301416			0.150708	+	0.988578i	$0.451845\pi$
$294$	3.79007e10	−	6.56460e10i	0.295859	−	0.512442i
$295$	−4.30910e10	+	7.46358e10i	−0.331274	+	0.573784i
$296$	5.50769e10			0.417020
$297$	−8.08460e10			−0.602913
$298$	−6.42136e10	+	1.11221e11i	−0.471687	+	0.816985i
$299$	3.32700e10	+	5.76254e10i	0.240732	+	0.416959i
$300$	2.86768e10	−	4.96697e10i	0.204402	−	0.354035i
$301$	−1.59588e8	−	2.76415e8i	−0.00112060	−	0.00194094i
$302$	1.73583e10	+	3.00655e10i	0.120082	+	0.207988i
$303$	1.77536e11			1.21003
$304$	−3.05679e10	−	2.12494e10i	−0.205274	−	0.142698i
$305$	1.57969e11			1.04525
$306$	−7.79403e10	−	1.34997e11i	−0.508178	−	0.880190i
$307$	−4.20325e9	−	7.28024e9i	−0.0270061	−	0.0467760i	0.852206	−	0.523206i	$-0.175264\pi$
$307$	−4.20325e9	−	7.28024e9i	−0.0270061	−	0.0467760i	−0.879213	+	0.476430i	$0.841931\pi$
$308$	−2.59107e10	+	4.48786e10i	−0.164059	+	0.284159i
$309$	−9.10125e10	−	1.57638e11i	−0.567921	−	0.983668i
$310$	−2.26892e10	+	3.92988e10i	−0.139538	+	0.241686i
$311$	−4.30357e10			−0.260860			−0.130430	−	0.991458i	$-0.541636\pi$
$311$	−4.30357e10			−0.260860			−0.130430	+	0.991458i	$0.541636\pi$
$312$	6.25621e10			0.373780
$313$	−7.98991e10	+	1.38389e11i	−0.470535	+	0.814991i	−0.999432	−	0.0336951i	$-0.989272\pi$
$313$	−7.98991e10	+	1.38389e11i	−0.470535	+	0.814991i	0.528897	+	0.848686i	$0.322606\pi$
$314$	9.36714e10	−	1.62244e11i	0.543780	−	0.941855i
$315$	−1.14227e11			−0.653688
$316$	−7.61981e10			−0.429885
$317$	−2.24872e9	+	3.89490e9i	−0.0125075	+	0.0216636i	−0.872211	−	0.489129i	$-0.837315\pi$
$317$	−2.24872e9	+	3.89490e9i	−0.0125075	+	0.0216636i	0.859704	+	0.510793i	$0.170648\pi$
$318$	−1.11257e11	−	1.92702e11i	−0.610104	−	1.05673i
$319$	7.22548e10	−	1.25149e11i	0.390669	−	0.676658i
$320$	−8.05823e9	−	1.39573e10i	−0.0429600	−	0.0744090i
$321$	−1.31885e11	−	2.28432e11i	−0.693303	−	1.20084i
$322$	6.53049e10			0.338528
$323$	−1.64662e11	−	1.14466e11i	−0.841747	−	0.585146i
$324$	−4.32672e10			−0.218125
$325$	3.61879e10	+	6.26793e10i	0.179924	+	0.311637i
$326$	1.02584e11	+	1.77680e11i	0.503037	+	0.871285i
$327$	−2.73744e11	+	4.74139e11i	−1.32398	+	2.29319i
$328$	−3.45773e10	−	5.98897e10i	−0.164953	−	0.285706i
$329$	4.95882e10	−	8.58892e10i	0.233344	−	0.404164i
$330$	−1.57009e11			−0.728804
$331$	−2.81586e11			−1.28939			−0.644696	−	0.764439i	$-0.723016\pi$
$331$	−2.81586e11			−1.28939			−0.644696	+	0.764439i	$0.723016\pi$
$332$	−8.69054e10	+	1.50525e11i	−0.392578	+	0.679964i
$333$	−1.85543e11	+	3.21369e11i	−0.826885	+	1.43221i
$334$	2.04216e11			0.897907
$335$	−1.83830e11			−0.797469
$336$	3.07004e10	−	5.31746e10i	0.131406	−	0.227603i
$337$	1.77308e11	+	3.07106e11i	0.748847	+	1.29704i	0.948376	+	0.317148i	$0.102725\pi$
$337$	1.77308e11	+	3.07106e11i	0.748847	+	1.29704i	−0.199529	+	0.979892i	$0.563941\pi$
$338$	4.53617e10	−	7.85688e10i	0.189045	−	0.327435i
$339$	1.47296e11	+	2.55124e11i	0.605749	+	1.04919i
$340$	−4.34078e10	−	7.51844e10i	−0.176162	−	0.305122i
$341$	−1.38706e11			−0.555519
$342$	2.26966e11	−	1.06776e11i	0.897104	−	0.422043i
$343$	2.67755e11			1.04451
$344$	1.51707e8	+	2.62765e8i	0.000584108	+	0.00101170i
$345$	9.89306e10	+	1.71353e11i	0.375962	+	0.651186i
$346$	−1.32131e11	+	2.28858e11i	−0.495635	+	0.858466i
$347$	−1.79688e11	−	3.11229e11i	−0.665330	−	1.15239i	−0.979196	−	0.202918i	$-0.934958\pi$
$347$	−1.79688e11	−	3.11229e11i	−0.665330	−	1.15239i	0.313866	−	0.949467i	$-0.398376\pi$
$348$	−8.56114e10	+	1.48283e11i	−0.312914	+	0.541983i
$349$	−1.91646e11			−0.691490			−0.345745	−	0.938329i	$-0.612374\pi$
$349$	−1.91646e11			−0.691490			−0.345745	+	0.938329i	$0.612374\pi$
$350$	7.10323e10			0.253017
$351$	−6.04402e10	+	1.04686e11i	−0.212542	+	0.368133i
$352$	2.46311e10	−	4.26624e10i	0.0855150	−	0.148116i
$353$	4.28920e9			0.0147025			0.00735123	−	0.999973i	$-0.497660\pi$
$353$	4.28920e9			0.0147025			0.00735123	+	0.999973i	$0.497660\pi$
$354$	3.12124e11			1.05636
$355$	−1.73366e10	+	3.00278e10i	−0.0579343	+	0.100345i
$356$	−1.00065e11	−	1.73318e11i	−0.330186	−	0.571899i
$357$	1.65376e11	−	2.86439e11i	0.538846	−	0.933308i
$358$	−2.74997e10	−	4.76309e10i	−0.0884818	−	0.153255i
$359$	1.77890e11	+	3.08115e11i	0.565233	+	0.979012i	0.997028	+	0.0770402i	$0.0245470\pi$
$359$	1.77890e11	+	3.08115e11i	0.565233	+	0.979012i	−0.431795	+	0.901972i	$0.642120\pi$
$360$	1.08586e11			0.340732
$361$	2.05735e11	−	2.48597e11i	0.637568	−	0.770394i
$362$	2.22243e10			0.0680204
$363$	1.63962e10	+	2.83990e10i	0.0495636	+	0.0858466i
$364$	3.87415e10	+	6.71022e10i	0.115670	+	0.200346i
$365$	1.73855e11	−	3.01126e11i	0.512708	−	0.888037i
$366$	−2.86056e11	−	4.95464e11i	−0.833271	−	1.44327i
$367$	3.26433e11	−	5.65399e11i	0.939284	−	1.62689i	0.172473	−	0.985014i	$-0.444824\pi$
$367$	3.26433e11	−	5.65399e11i	0.939284	−	1.62689i	0.766811	−	0.641873i	$-0.221842\pi$
$368$	−6.20799e10			−0.176456
$369$	4.65935e11			1.30830
$370$	−1.03335e11	+	1.78982e11i	−0.286643	+	0.496481i
$371$	1.37791e11	−	2.38661e11i	0.377606	−	0.654032i
$372$	1.64346e11			0.444954
$373$	1.86874e11			0.499873			0.249937	−	0.968262i	$-0.419590\pi$
$373$	1.86874e11			0.499873			0.249937	+	0.968262i	$0.419590\pi$
$374$	1.32682e11	−	2.29812e11i	0.350663	−	0.607366i
$375$	3.11588e11	+	5.39686e11i	0.813654	+	1.40929i
$376$	−4.71394e10	+	8.16478e10i	−0.121629	+	0.210668i
$377$	−1.08035e11	−	1.87122e11i	−0.275441	−	0.477077i
$378$	5.93182e10	+	1.02742e11i	0.149443	+	0.258843i
$379$	3.56475e10			0.0887467			0.0443734	−	0.999015i	$-0.485871\pi$
$379$	3.56475e10			0.0887467			0.0443734	+	0.999015i	$0.485871\pi$
$380$	1.26405e11	−	5.94674e10i	0.310985	−	0.146303i
$381$	8.23165e11			2.00136
$382$	−1.80576e11	−	3.12766e11i	−0.433884	−	0.751510i
$383$	1.62743e11	+	2.81879e11i	0.386463	+	0.669374i	0.991971	−	0.126466i	$-0.0403633\pi$
$383$	1.62743e11	+	2.81879e11i	0.386463	+	0.669374i	−0.605508	+	0.795839i	$0.707030\pi$
$384$	−2.91843e10	+	5.05487e10i	−0.0684950	+	0.118637i
$385$	−9.72274e10	−	1.68403e11i	−0.225536	−	0.390639i
$386$	−2.15443e11	+	3.73159e11i	−0.493958	+	0.855561i
$387$	−2.04428e9			−0.00463277
$388$	−2.33803e11			−0.523730
$389$	−1.32780e11	+	2.29981e11i	−0.294007	+	0.509236i	−0.974754	−	0.223284i	$-0.928322\pi$
$389$	−1.32780e11	+	2.29981e11i	−0.294007	+	0.509236i	0.680746	+	0.732519i	$0.261656\pi$
$390$	−1.17379e11	+	2.03307e11i	−0.256922	+	0.445001i
$391$	−3.34410e11			−0.723575
$392$	−8.92438e10			−0.190893
$393$	−1.78674e11	+	3.09473e11i	−0.377829	+	0.654420i
$394$	−6.92884e10	−	1.20011e11i	−0.144853	−	0.250893i
$395$	1.42963e11	−	2.47619e11i	0.295486	−	0.511797i
$396$	1.65954e11	+	2.87442e11i	0.339126	+	0.587383i
$397$	1.76146e11	+	3.05093e11i	0.355889	+	0.616417i	0.987270	−	0.159055i	$-0.0508449\pi$
$397$	1.76146e11	+	3.05093e11i	0.355889	+	0.616417i	−0.631381	+	0.775473i	$0.717512\pi$
$398$	3.31259e11			0.661750
$399$	4.36997e11	+	3.03782e11i	0.863179	+	0.600044i
$400$	−6.75245e10			−0.131884
$401$	−4.88615e11	−	8.46307e11i	−0.943664	−	1.63447i	−0.758404	−	0.651785i	$-0.774021\pi$
$401$	−4.88615e11	−	8.46307e11i	−0.943664	−	1.63447i	−0.185260	−	0.982690i	$-0.559313\pi$
$402$	3.32886e11	+	5.76575e11i	0.635738	+	1.10113i
$403$	−1.03696e11	+	1.79606e11i	−0.195834	+	0.339195i
$404$	−1.04510e11	−	1.81017e11i	−0.195183	−	0.338067i
$405$	8.11780e10	−	1.40604e11i	0.149931	−	0.259688i
$406$	−2.12059e11			−0.387337
$407$	−6.31720e11			−1.14117
$408$	−1.57209e11	+	2.72294e11i	−0.280871	+	0.486482i
$409$	−5.42927e11	+	9.40376e11i	−0.959370	+	1.66168i	−0.235336	+	0.971914i	$0.575619\pi$
$409$	−5.42927e11	+	9.40376e11i	−0.959370	+	1.66168i	−0.724034	+	0.689764i	$0.757714\pi$
$410$	2.59496e11			0.453527
$411$	−1.17685e12			−2.03439
$412$	−1.07152e11	+	1.85593e11i	−0.183216	+	0.317340i
$413$	1.93282e11	+	3.34774e11i	0.326901	+	0.566209i
$414$	2.09134e11	−	3.62232e11i	0.349884	−	0.606017i
$415$	−3.26104e11	−	5.64829e11i	−0.539685	−	0.934761i
$416$	−3.68283e10	−	6.37885e10i	−0.0602923	−	0.104429i
$417$	−6.01675e10			−0.0974428
$418$	3.50606e11	+	2.43726e11i	0.561728	+	0.390489i
$419$	−3.67200e11			−0.582023			−0.291011	−	0.956720i	$-0.593992\pi$
$419$	−3.67200e11			−0.582023			−0.291011	+	0.956720i	$0.593992\pi$
$420$	1.15200e11	+	1.99533e11i	0.180647	+	0.312890i
$421$	1.31323e11	+	2.27458e11i	0.203738	+	0.352885i	0.949730	−	0.313070i	$-0.101358\pi$
$421$	1.31323e11	+	2.27458e11i	0.203738	+	0.352885i	−0.745992	+	0.665955i	$0.768024\pi$
$422$	−4.77639e10	+	8.27294e10i	−0.0733151	+	0.126985i
$423$	−3.17606e11	−	5.50109e11i	−0.482344	−	0.835444i
$424$	−1.30987e11	+	2.26875e11i	−0.196825	+	0.340911i
$425$	−3.63739e11			−0.540803
$426$	1.25575e11			0.184739
$427$	3.54279e11	−	6.13630e11i	0.515728	−	0.893267i
$428$	−1.55273e11	+	2.68941e11i	−0.223666	+	0.387400i
$429$	−7.17573e11			−1.02284
$430$	−1.13853e9			−0.00160597
$431$	4.15707e11	−	7.20026e11i	0.580283	−	1.00508i	−0.415163	−	0.909747i	$-0.636275\pi$
$431$	4.15707e11	−	7.20026e11i	0.580283	−	1.00508i	0.995446	−	0.0953319i	$-0.0303912\pi$
$432$	−5.63889e10	−	9.76685e10i	−0.0778963	−	0.134920i
$433$	2.65895e11	−	4.60544e11i	0.363509	−	0.629615i	−0.625027	−	0.780603i	$-0.714912\pi$
$433$	2.65895e11	−	4.60544e11i	0.363509	−	0.629615i	0.988536	+	0.150988i	$0.0482454\pi$
$434$	1.01771e11	+	1.76272e11i	0.137695	+	0.238495i
$435$	−3.21249e11	−	5.56419e11i	−0.430170	−	0.745076i
$436$	6.44578e11			0.854252
$437$	4.50771e10	−	5.36208e11i	0.0591275	−	0.703342i
$438$	−1.25930e12			−1.63491
$439$	−3.11690e11	−	5.39863e11i	−0.400528	−	0.693734i	0.593262	−	0.805009i	$-0.297840\pi$
$439$	−3.11690e11	−	5.39863e11i	−0.400528	−	0.693734i	−0.993790	+	0.111275i	$0.964506\pi$
$440$	9.24260e10	+	1.60087e11i	0.117559	+	0.203619i
$441$	3.00644e11	−	5.20730e11i	0.378511	−	0.655601i
$442$	−1.98385e11	−	3.43614e11i	−0.247235	−	0.428223i
$443$	3.05883e11	−	5.29805e11i	0.377345	−	0.653581i	−0.613330	−	0.789827i	$-0.710170\pi$
$443$	3.05883e11	−	5.29805e11i	0.377345	−	0.653581i	0.990675	+	0.136246i	$0.0435037\pi$
$444$	7.48495e11			0.914041
$445$	7.50972e11			0.907828
$446$	−3.04196e10	+	5.26883e10i	−0.0364038	+	0.0630533i
$447$	−8.72662e11	+	1.51150e12i	−1.03386	+	1.79070i
$448$	−7.22893e10			−0.0847858
$449$	−7.92806e11			−0.920574			−0.460287	−	0.887770i	$-0.652253\pi$
$449$	−7.92806e11			−0.920574			−0.460287	+	0.887770i	$0.652253\pi$
$450$	2.27476e11	−	3.94000e11i	0.261505	−	0.452940i
$451$	3.96594e11	+	6.86921e11i	0.451390	+	0.781830i
$452$	1.73417e11	−	3.00367e11i	0.195420	−	0.338477i
$453$	2.35900e11	+	4.08591e11i	0.263200	+	0.455876i
$454$	2.47028e10	+	4.27864e10i	0.0272894	+	0.0472666i
$455$	−2.90747e11			−0.318027
$456$	−4.15417e11	−	2.88780e11i	−0.449928	−	0.312770i
$457$	−1.33507e10			−0.0143180			−0.00715898	−	0.999974i	$-0.502279\pi$
$457$	−1.33507e10			−0.0143180			−0.00715898	+	0.999974i	$0.502279\pi$
$458$	6.26147e11	+	1.08452e12i	0.664939	+	1.15171i
$459$	−3.03754e11	−	5.26117e11i	−0.319422	−	0.553255i
$460$	1.16475e11	−	2.01740e11i	0.121289	−	0.210078i
$461$	5.63429e11	+	9.75887e11i	0.581012	+	1.00634i	0.995360	+	0.0962231i	$0.0306762\pi$
$461$	5.63429e11	+	9.75887e11i	0.581012	+	1.00634i	−0.414348	+	0.910118i	$0.635990\pi$
$462$	−3.52126e11	+	6.09900e11i	−0.359591	+	0.622831i
$463$	1.61777e12			1.63607			0.818036	−	0.575167i	$-0.195063\pi$
$463$	1.61777e12			1.63607			0.818036	+	0.575167i	$0.195063\pi$
$464$	2.01587e11			0.201898
$465$	−3.08346e11	+	5.34071e11i	−0.305844	+	0.529737i
$466$	4.44236e11	−	7.69440e11i	0.436392	−	0.755854i
$467$	−1.97176e12			−1.91835			−0.959177	−	0.282805i	$-0.908735\pi$
$467$	−1.97176e12			−1.91835			−0.959177	+	0.282805i	$0.908735\pi$
$468$	4.96268e11			0.478200
$469$	−4.12278e11	+	7.14086e11i	−0.393470	+	0.681511i
$470$	−1.76886e11	−	3.06376e11i	−0.167207	−	0.289610i
$471$	1.27299e12	−	2.20489e12i	1.19188	−	2.06440i
$472$	−1.83737e11	−	3.18242e11i	−0.170395	−	0.295134i
$473$	−1.74005e9	−	3.01385e9i	−0.00159840	−	0.00276851i
$474$	−1.03553e12			−0.942238
$475$	4.90305e10	−	5.83235e11i	0.0441921	−	0.525681i
$476$	−3.89405e11			−0.347673
$477$	−8.82533e11	−	1.52859e12i	−0.780546	−	1.35194i
$478$	1.59180e11	+	2.75708e11i	0.139464	+	0.241560i
$479$	−1.09985e11	+	1.90499e11i	−0.0954603	+	0.165342i	−0.909801	−	0.415046i	$-0.863766\pi$
$479$	−1.09985e11	+	1.90499e11i	−0.0954603	+	0.165342i	0.814340	+	0.580388i	$0.197099\pi$
$480$	−1.09511e11	−	1.89679e11i	−0.0941615	−	0.163093i
$481$	−4.72272e11	+	8.17998e11i	−0.402290	+	0.696786i
$482$	9.17484e11			0.774260
$483$	8.87493e11			0.741998
$484$	1.93038e10	−	3.34352e10i	0.0159896	−	0.0276949i
$485$	4.38662e11	−	7.59785e11i	0.359991	−	0.623523i
$486$	−1.12995e12			−0.918744
$487$	−2.86848e11			−0.231085			−0.115543	−	0.993303i	$-0.536861\pi$
$487$	−2.86848e11			−0.231085			−0.115543	+	0.993303i	$0.536861\pi$
$488$	−3.36784e11	+	5.83327e11i	−0.268821	+	0.465611i
$489$	1.39411e12	+	2.41468e12i	1.10258	+	1.90972i
$490$	1.67439e11	−	2.90014e11i	0.131213	−	0.227267i
$491$	9.25427e11	+	1.60289e12i	0.718580	+	1.24462i	0.961562	+	0.274587i	$0.0885411\pi$
$491$	9.25427e11	+	1.60289e12i	0.718580	+	1.24462i	−0.242982	+	0.970031i	$0.578126\pi$
$492$	−4.69906e11	−	8.13901e11i	−0.361549	−	0.626222i
$493$	1.08590e12			0.827902
$494$	5.77707e11	−	2.71783e11i	0.436452	−	0.205329i
$495$	−1.24546e12			−0.932406
$496$	−9.67451e10	−	1.67567e11i	−0.0717731	−	0.124315i
$497$	7.77620e10	+	1.34688e11i	0.0571694	+	0.0990203i
$498$	−1.18104e12	+	2.04563e12i	−0.860467	+	1.49037i
$499$	8.17468e11	+	1.41590e12i	0.590226	+	1.02230i	0.994202	+	0.107532i	$0.0342947\pi$
$499$	8.17468e11	+	1.41590e12i	0.590226	+	1.02230i	−0.403976	+	0.914770i	$0.632372\pi$
$500$	3.66844e11	−	6.35392e11i	0.262492	−	0.454649i
$501$	2.77530e12			1.96807
$502$	−1.13433e12			−0.797210
$503$	−1.27391e12	+	2.20647e12i	−0.887322	+	1.53689i	−0.0442927	+	0.999019i	$0.514103\pi$
$503$	−1.27391e12	+	2.20647e12i	−0.887322	+	1.53689i	−0.843029	+	0.537868i	$0.819230\pi$
$504$	2.43528e11	−	4.21802e11i	0.168117	−	0.291187i
$505$	7.84328e11			0.536644
$506$	7.12043e11			0.482868
$507$	6.16466e11	−	1.06775e12i	0.414356	−	0.717685i
$508$	−4.84571e11	−	8.39301e11i	−0.322828	−	0.559154i
$509$	−1.13744e12	+	1.97010e12i	−0.751099	+	1.30094i	0.196191	+	0.980566i	$0.437143\pi$
$509$	−1.13744e12	+	1.97010e12i	−0.751099	+	1.30094i	−0.947290	+	0.320377i	$0.896191\pi$
$510$	−5.89911e11	−	1.02176e12i	−0.386119	−	0.668778i
$511$	−7.79817e11	−	1.35068e12i	−0.505940	−	0.876313i
$512$	6.87195e10			0.0441942
$513$	8.84545e11	−	4.16134e11i	0.563886	−	0.265280i
$514$	1.48014e12			0.935341
$515$	−4.02079e11	−	6.96421e11i	−0.251871	−	0.436254i
$516$	2.06170e9	+	3.57097e9i	0.00128027	+	0.00221749i
$517$	5.40678e11	−	9.36481e11i	0.332837	−	0.576490i
$518$	4.63504e11	+	8.02813e11i	0.282859	+	0.489926i
$519$	−1.79566e12	+	3.11017e12i	−1.08635	+	1.88162i
$520$	2.76390e11			0.165770
$521$	1.10554e12			0.657362			0.328681	−	0.944441i	$-0.393396\pi$
$521$	1.10554e12			0.657362			0.328681	+	0.944441i	$0.393396\pi$
$522$	−6.79104e11	+	1.17624e12i	−0.400331	+	0.693394i
$523$	2.86541e11	−	4.96303e11i	0.167467	−	0.290061i	−0.770062	−	0.637969i	$-0.779775\pi$
$523$	2.86541e11	−	4.96303e11i	0.167467	−	0.290061i	0.937529	+	0.347908i	$0.113108\pi$
$524$	4.20720e11			0.243782
$525$	9.65329e11			0.554573
$526$	5.16474e11	−	8.94559e11i	0.294180	−	0.509534i
$527$	−5.21143e11	−	9.02646e11i	−0.294313	−	0.509765i
$528$	3.34737e11	−	5.79782e11i	0.187435	−	0.324647i
$529$	4.51921e11	+	7.82750e11i	0.250907	+	0.434583i
$530$	−4.91515e11	−	8.51328e11i	−0.270580	−	0.468658i
$531$	2.47589e12			1.35147
$532$	5.24902e10	−	6.24390e11i	0.0284103	−	0.337951i
$533$	1.18597e12			0.636504
$534$	−1.35989e12	−	2.35540e12i	−0.723715	−	1.25351i
$535$	−5.82647e11	−	1.00917e12i	−0.307478	−	0.532567i
$536$	3.91918e11	−	6.78823e11i	0.205095	−	0.355234i
$537$	−3.73721e11	−	6.47303e11i	−0.193938	−	0.335910i
$538$	−6.92319e11	+	1.19913e12i	−0.356276	+	0.617088i
$539$	1.02361e12			0.522376
$540$	4.23188e11			0.214171
$541$	8.04688e11	−	1.39376e12i	0.403869	−	0.699521i	−0.590321	−	0.807169i	$-0.700999\pi$
$541$	8.04688e11	−	1.39376e12i	0.403869	−	0.699521i	0.994189	+	0.107648i	$0.0343320\pi$
$542$	1.28875e12	−	2.23218e12i	0.641463	−	1.11105i
$543$	3.02028e11			0.149090
$544$	3.70175e11			0.181223
$545$	−1.20936e12	+	2.09467e12i	−0.587179	+	1.01702i
$546$	5.26497e11	+	9.11919e11i	0.253530	+	0.439126i
$547$	−5.16254e11	+	8.94179e11i	−0.246559	+	0.427053i	−0.962569	−	0.271038i	$-0.912633\pi$
$547$	−5.16254e11	+	8.94179e11i	−0.246559	+	0.427053i	0.716010	+	0.698090i	$0.245967\pi$
$548$	6.92776e11	+	1.19992e12i	0.328156	+	0.568382i
$549$	−2.26911e12	−	3.93022e12i	−1.06606	−	1.84646i
$550$	7.74491e11			0.360898
$551$	−1.46375e11	+	1.74118e12i	−0.0676526	+	0.804752i
$552$	−8.43666e11			−0.386763
$553$	−6.41251e11	−	1.11068e12i	−0.291585	−	0.505040i
$554$	4.15898e11	+	7.20357e11i	0.187583	+	0.324903i
$555$	−1.40433e12	+	2.43237e12i	−0.628276	+	1.08821i
$556$	3.54187e10	+	6.13469e10i	0.0157179	+	0.0272243i
$557$	−1.81828e12	+	3.14936e12i	−0.800412	+	1.38635i	0.118934	+	0.992902i	$0.462052\pi$
$557$	−1.81828e12	+	3.14936e12i	−0.800412	+	1.38635i	−0.919345	+	0.393452i	$0.871281\pi$
$558$	1.30366e12			0.569259
$559$	−5.20341e9			−0.00225390
$560$	1.35629e11	−	2.34917e11i	0.0582784	−	0.100941i
$561$	1.80315e12	−	3.12315e12i	0.768597	−	1.33125i
$562$	−2.97668e12			−1.25869
$563$	−3.81672e12			−1.60104			−0.800521	−	0.599305i	$-0.795444\pi$
$563$	−3.81672e12			−1.60104			−0.800521	+	0.599305i	$0.795444\pi$
$564$	−6.40624e11	+	1.10959e12i	−0.266592	+	0.461751i
$565$	6.50731e11	+	1.12710e12i	0.268648	+	0.465312i
$566$	−1.06706e12	+	1.84820e12i	−0.437032	+	0.756962i
$567$	−3.64118e11	−	6.30672e11i	−0.147951	−	0.256259i
$568$	−7.39219e10	−	1.28037e11i	−0.0297993	−	0.0516139i
$569$	−1.58469e12			−0.633782			−0.316891	−	0.948462i	$-0.602639\pi$
$569$	−1.58469e12			−0.633782			−0.316891	+	0.948462i	$0.602639\pi$
$570$	1.71785e12	−	8.08162e11i	0.681629	−	0.320673i
$571$	−2.47191e12			−0.973130			−0.486565	−	0.873644i	$-0.661750\pi$
$571$	−2.47191e12			−0.973130			−0.486565	+	0.873644i	$0.661750\pi$
$572$	4.22412e11	+	7.31640e11i	0.164989	+	0.285769i
$573$	−2.45402e12	−	4.25049e12i	−0.951005	−	1.64719i
$574$	5.81976e11	−	1.00801e12i	0.223770	−	0.387581i
$575$	−4.88003e11	−	8.45247e11i	−0.186173	−	0.322462i
$576$	−2.31502e11	+	4.00973e11i	−0.0876300	+	0.151780i
$577$	4.65508e12			1.74838			0.874191	−	0.485582i	$-0.161392\pi$
$577$	4.65508e12			1.74838			0.874191	+	0.485582i	$0.161392\pi$
$578$	9.66411e10			0.0360153
$579$	−2.92788e12	+	5.07123e12i	−1.08268	+	1.87525i
$580$	−3.78218e11	+	6.55092e11i	−0.138776	+	0.240368i
$581$	−2.92544e12			−1.06512
$582$	−3.17738e12			−1.14793
$583$	1.50239e12	−	2.60221e12i	0.538608	−	0.932897i
$584$	7.41308e11	+	1.28398e12i	0.263719	+	0.456774i
$585$	−9.31099e11	+	1.61271e12i	−0.328696	+	0.569318i
$586$	−3.04200e11	−	5.26891e11i	−0.106566	−	0.184579i
$587$	−1.43013e12	−	2.47706e12i	−0.497169	−	0.861122i	0.502826	−	0.864388i	$-0.332294\pi$
$587$	−1.43013e12	−	2.47706e12i	−0.497169	−	0.861122i	−0.999995	+	0.00326570i	$0.998960\pi$
$588$	−1.21282e12			−0.418408
$589$	1.51759e12	−	7.13952e11i	0.519561	−	0.244427i
$590$	1.37891e12			0.468493
$591$	−9.41629e11	−	1.63095e12i	−0.317494	−	0.549916i
$592$	−4.40615e11	−	7.63168e11i	−0.147439	−	0.255372i
$593$	−9.54072e11	+	1.65250e12i	−0.316836	+	0.548776i	−0.979826	−	0.199852i	$-0.935954\pi$
$593$	−9.54072e11	+	1.65250e12i	−0.316836	+	0.548776i	0.662990	+	0.748628i	$0.269287\pi$
$594$	6.46768e11	+	1.12024e12i	0.213162	+	0.369207i
$595$	7.30603e11	−	1.26544e12i	0.238977	−	0.413919i
$596$	2.05483e12			0.667066
$597$	4.50181e12			1.45045
$598$	5.32321e11	−	9.22007e11i	0.170223	−	0.294835i
$599$	7.38064e11	−	1.27837e12i	0.234247	−	0.405727i	−0.724807	−	0.688952i	$-0.758071\pi$
$599$	7.38064e11	−	1.27837e12i	0.234247	−	0.405727i	0.959054	+	0.283225i	$0.0914043\pi$
$600$	−9.17658e11			−0.289068
$601$	3.26923e12			1.02214			0.511071	−	0.859539i	$-0.329249\pi$
$601$	3.26923e12			1.02214			0.511071	+	0.859539i	$0.329249\pi$
$602$	−2.55341e9	+	4.42263e9i	−0.000792385	+	0.00137245i
$603$	2.64058e12	+	4.57363e12i	0.813340	+	1.40875i
$604$	2.77734e11	−	4.81049e11i	0.0849106	−	0.147070i
$605$	7.24357e10	+	1.25462e11i	0.0219813	+	0.0380727i
$606$	−1.42029e12	−	2.46002e12i	−0.427810	−	0.740988i
$607$	−3.61205e12			−1.07995			−0.539977	−	0.841680i	$-0.681567\pi$
$607$	−3.61205e12			−1.07995			−0.539977	+	0.841680i	$0.681567\pi$
$608$	−4.98981e10	+	5.93556e11i	−0.0148087	+	0.176155i
$609$	−2.88188e12			−0.848981
$610$	−1.26375e12	−	2.18888e12i	−0.369553	−	0.640085i
$611$	−8.08418e11	−	1.40022e12i	−0.234666	−	0.406454i
$612$	−1.24704e12	+	2.15994e12i	−0.359336	+	0.622388i
$613$	−1.71676e12	−	2.97352e12i	−0.491064	−	0.850547i	0.508884	−	0.860835i	$-0.330058\pi$
$613$	−1.71676e12	−	2.97352e12i	−0.491064	−	0.850547i	−0.999947	+	0.0102884i	$0.996725\pi$
$614$	−6.72519e10	+	1.16484e11i	−0.0190962	+	0.0330756i
$615$	3.52655e12			0.994060
$616$	8.29142e11			0.232015
$617$	−1.99129e12	+	3.44902e12i	−0.553161	+	0.958103i	0.444883	+	0.895589i	$0.353245\pi$
$617$	−1.99129e12	+	3.44902e12i	−0.553161	+	0.958103i	−0.998044	+	0.0625145i	$0.980088\pi$
$618$	−1.45620e12	+	2.52221e12i	−0.401581	+	0.695558i
$619$	3.59249e11			0.0983531			0.0491765	−	0.998790i	$-0.484340\pi$
$619$	3.59249e11			0.0983531			0.0491765	+	0.998790i	$0.484340\pi$
$620$	7.26054e11			0.197336
$621$	8.15052e11	−	1.41171e12i	0.219924	−	0.380920i
$622$	3.44285e11	+	5.96320e11i	0.0922278	+	0.159743i
$623$	1.68422e12	−	2.91715e12i	0.447921	−	0.775823i
$624$	−5.00497e11	−	8.66886e11i	−0.132151	−	0.228892i
$625$	3.70352e11	+	6.41469e11i	0.0970856	+	0.168157i
$626$	2.55677e12			0.665437
$627$	4.76474e12	+	3.31224e12i	1.23122	+	0.855890i
$628$	−2.99748e12			−0.769021
$629$	−2.37349e12	−	4.11101e12i	−0.604588	−	1.04718i
$630$	9.13815e11	+	1.58277e12i	0.231114	+	0.400301i
$631$	2.41989e12	−	4.19136e12i	0.607663	−	1.05250i	−0.383962	−	0.923349i	$-0.625441\pi$
$631$	2.41989e12	−	4.19136e12i	0.607663	−	1.05250i	0.991625	−	0.129154i	$-0.0412261\pi$
$632$	6.09584e11	+	1.05583e12i	0.151987	+	0.263250i
$633$	−6.49111e11	+	1.12429e12i	−0.160695	+	0.278332i
$634$	7.19591e10			0.0176882
$635$	3.63661e12			0.887596
$636$	−1.78011e12	+	3.08324e12i	−0.431409	+	0.747222i
$637$	7.65244e11	−	1.32544e12i	0.184150	−	0.318958i
$638$	−2.31215e12			−0.552489
$639$	9.96111e11			0.236349
$640$	−1.28932e11	+	2.23316e11i	−0.0303773	+	0.0526151i
$641$	−2.78075e11	−	4.81640e11i	−0.0650580	−	0.112684i	0.831662	−	0.555283i	$-0.187390\pi$
$641$	−2.78075e11	−	4.81640e11i	−0.0650580	−	0.112684i	−0.896720	+	0.442599i	$0.854057\pi$
$642$	−2.11016e12	+	3.65490e12i	−0.490239	+	0.849119i
$643$	1.20375e12	+	2.08496e12i	0.277708	+	0.481004i	0.970815	−	0.239831i	$-0.0770920\pi$
$643$	1.20375e12	+	2.08496e12i	0.277708	+	0.481004i	−0.693107	+	0.720835i	$0.743759\pi$
$644$	−5.22439e11	−	9.04891e11i	−0.119688	−	0.207305i
$645$	−1.54727e10			−0.00352003
$646$	−2.68789e11	+	3.19735e12i	−0.0607248	+	0.722343i
$647$	−4.04655e12			−0.907854			−0.453927	−	0.891039i	$-0.649977\pi$
$647$	−4.04655e12			−0.907854			−0.453927	+	0.891039i	$0.649977\pi$
$648$	3.46137e11	+	5.99527e11i	0.0771189	+	0.133574i
$649$	2.10742e12	+	3.65016e12i	0.466284	+	0.807628i
$650$	5.79007e11	−	1.00287e12i	0.127225	−	0.220361i
$651$	1.38307e12	+	2.39554e12i	0.301806	+	0.522744i
$652$	1.64134e12	−	2.84289e12i	0.355701	−	0.616092i
$653$	1.27645e12			0.274723			0.137361	−	0.990521i	$-0.456138\pi$
$653$	1.27645e12			0.274723			0.137361	+	0.990521i	$0.456138\pi$
$654$	8.75981e12			1.87238
$655$	−7.89355e11	+	1.36720e12i	−0.167566	+	0.290233i
$656$	−5.53237e11	+	9.58235e11i	−0.116639	+	0.202025i
$657$	−9.98925e12			−2.09165
$658$	−1.58682e12			−0.329998
$659$	−1.60847e12	+	2.78595e12i	−0.332221	+	0.575424i	−0.982947	−	0.183889i	$-0.941131\pi$
$659$	−1.60847e12	+	2.78595e12i	−0.332221	+	0.575424i	0.650726	+	0.759313i	$0.274465\pi$
$660$	1.25607e12	+	2.17558e12i	0.257671	+	0.446300i
$661$	3.61128e12	−	6.25493e12i	0.735792	−	1.27443i	−0.218583	−	0.975818i	$-0.570143\pi$
$661$	3.61128e12	−	6.25493e12i	0.735792	−	1.27443i	0.954375	−	0.298611i	$-0.0965233\pi$
$662$	2.25269e12	+	3.90177e12i	0.455869	+	0.789588i
$663$	−2.69606e12	−	4.66971e12i	−0.541899	−	0.938597i
$664$	2.78097e12			0.555188
$665$	1.93059e12	+	1.34206e12i	0.382817	+	0.266118i
$666$	5.93737e12			1.16939
$667$	1.45688e12	+	2.52339e12i	0.285008	+	0.493649i
$668$	−1.63373e12	−	2.82970e12i	−0.317458	−	0.549853i
$669$	−4.13403e11	+	7.16034e11i	−0.0797913	+	0.138203i
$670$	1.47064e12	+	2.54722e12i	0.281948	+	0.488348i
$671$	3.86284e12	−	6.69063e12i	0.735622	−	1.27414i
$672$	−9.82412e11			−0.185837
$673$	−3.88039e12			−0.729135			−0.364568	−	0.931177i	$-0.618783\pi$
$673$	−3.88039e12			−0.729135			−0.364568	+	0.931177i	$0.618783\pi$
$674$	2.83692e12	−	4.91369e12i	0.529515	−	0.917146i
$675$	8.86534e11	−	1.53552e12i	0.164372	−	0.284701i
$676$	−1.45158e12			−0.267350
$677$	4.52099e12			0.827151			0.413575	−	0.910470i	$-0.364280\pi$
$677$	4.52099e12			0.827151			0.413575	+	0.910470i	$0.364280\pi$
$678$	2.35674e12	−	4.08199e12i	0.428329	−	0.741887i
$679$	−1.96759e12	−	3.40796e12i	−0.355239	−	0.615292i
$680$	−6.94524e11	+	1.20295e12i	−0.124565	+	0.215754i
$681$	3.35711e11	+	5.81468e11i	0.0598140	+	0.103601i
$682$	1.10964e12	+	1.92196e12i	0.196406	+	0.340185i
$683$	8.33610e11			0.146578			0.0732891	−	0.997311i	$-0.476650\pi$
$683$	8.33610e11			0.146578			0.0732891	+	0.997311i	$0.476650\pi$
$684$	−3.29526e12	−	2.29072e12i	−0.575621	−	0.400147i
$685$	−5.19915e12			−0.902245
$686$	−2.14204e12	−	3.71012e12i	−0.369291	−	0.639630i
$687$	8.50934e12	+	1.47386e13i	1.45744	+	2.52436i
$688$	2.42731e9	−	4.20423e9i	0.000413027	−	0.000715383i
$689$	−2.24636e12	−	3.89080e12i	−0.379745	−	0.657738i
$690$	1.58289e12	−	2.74164e12i	0.265846	−	0.460458i
$691$	3.33044e12			0.555712			0.277856	−	0.960623i	$-0.410376\pi$
$691$	3.33044e12			0.555712			0.277856	+	0.960623i	$0.410376\pi$
$692$	4.22819e12			0.700934
$693$	−2.79321e12	+	4.83798e12i	−0.460048	+	0.796827i
$694$	−2.87501e12	+	4.97967e12i	−0.470459	+	0.814859i
$695$	−2.65810e11			−0.0432156
$696$	2.73957e12			0.442527
$697$	−2.98016e12	+	5.16178e12i	−0.478290	+	0.828423i
$698$	1.53317e12	+	2.65553e12i	0.244479	+	0.423449i
$699$	6.03717e12	−	1.04567e13i	0.956502	−	1.65671i
$700$	−5.68258e11	−	9.84252e11i	−0.0894550	−	0.154941i
$701$	−5.59221e11	−	9.68600e11i	−0.0874687	−	0.151500i	0.818972	−	0.573834i	$-0.194544\pi$
$701$	−5.59221e11	−	9.68600e11i	−0.0874687	−	0.151500i	−0.906441	+	0.422334i	$0.861211\pi$
$702$	1.93409e12			0.300579
$703$	6.91171e12	−	3.25162e12i	1.06730	−	0.502112i
$704$	−7.88197e11			−0.120937
$705$	−2.40388e12	−	4.16364e12i	−0.366490	−	0.634779i
$706$	−3.43136e10	−	5.94329e10i	−0.00519810	−	0.00900338i
$707$	1.75903e12	−	3.04672e12i	0.264780	−	0.458612i
$708$	−2.49699e12	−	4.32491e12i	−0.373480	−	0.646886i
$709$	−6.30973e12	+	1.09288e13i	−0.937784	+	1.62429i	−0.168190	+	0.985755i	$0.553792\pi$
$709$	−6.30973e12	+	1.09288e13i	−0.937784	+	1.62429i	−0.769593	+	0.638534i	$0.779541\pi$
$710$	5.54770e11			0.0819314
$711$	−8.21426e12			−1.20547
$712$	−1.60105e12	+	2.77309e12i	−0.233477	+	0.404394i
$713$	1.39836e12	−	2.42204e12i	0.202636	−	0.350977i
$714$	−5.29202e12			−0.762043
$715$	−3.17012e12			−0.453627
$716$	−4.39995e11	+	7.62094e11i	−0.0625661	+	0.108368i
$717$	2.16326e12	+	3.74687e12i	0.305684	+	0.529460i
$718$	2.84625e12	−	4.92984e12i	0.399680	−	0.692266i
$719$	−2.23717e12	−	3.87489e12i	−0.312190	−	0.540729i	0.666646	−	0.745374i	$-0.267729\pi$
$719$	−2.23717e12	−	3.87489e12i	−0.312190	−	0.540729i	−0.978836	+	0.204645i	$0.934396\pi$
$720$	−8.68688e11	−	1.50461e12i	−0.120467	−	0.208655i
$721$	−3.60700e12			−0.497092
$722$	−5.09054e12	−	8.61979e11i	−0.697182	−	0.118054i
$723$	1.24686e13			1.69705
$724$	−1.77794e11	−	3.07948e11i	−0.0240488	−	0.0416538i
$725$	1.58465e12	+	2.74470e12i	0.213016	+	0.368955i
$726$	2.62339e11	−	4.54384e11i	0.0350467	−	0.0607027i
$727$	−4.06953e12	−	7.04863e12i	−0.540305	−	0.935836i	−0.998886	−	0.0471834i	$-0.984975\pi$
$727$	−4.06953e12	−	7.04863e12i	−0.540305	−	0.935836i	0.458581	−	0.888653i	$-0.348358\pi$
$728$	6.19864e11	−	1.07364e12i	0.0817909	−	0.141666i
$729$	−1.20293e13			−1.57749
$730$	−5.56337e12			−0.725079
$731$	1.30754e10	−	2.26472e10i	0.00169366	−	0.00293350i
$732$	−4.57690e12	+	7.92742e12i	−0.589212	+	1.02054i
$733$	4.64395e11			0.0594183			0.0297091	−	0.999559i	$-0.490542\pi$
$733$	4.64395e11			0.0594183			0.0297091	+	0.999559i	$0.490542\pi$
$734$	−1.04459e13			−1.32835
$735$	2.27550e12	−	3.94128e12i	0.287597	−	0.498132i
$736$	4.96639e11	+	8.60205e11i	0.0623866	+	0.108057i
$737$	−4.49521e12	+	7.78594e12i	−0.561237	+	0.972092i
$738$	−3.72748e12	−	6.45619e12i	−0.462553	−	0.801166i
$739$	2.77906e12	+	4.81348e12i	0.342767	+	0.593689i	0.984945	−	0.172866i	$-0.0553026\pi$
$739$	2.77906e12	+	4.81348e12i	0.342767	+	0.593689i	−0.642179	+	0.766555i	$0.721969\pi$
$740$	3.30673e12			0.405375
$741$	7.85104e12	−	3.69352e12i	0.956633	−	0.450048i
$742$	−4.40931e12			−0.534015
$743$	−1.20360e11	−	2.08469e11i	−0.0144888	−	0.0250953i	0.858690	−	0.512495i	$-0.171279\pi$
$743$	−1.20360e11	−	2.08469e11i	−0.0144888	−	0.0250953i	−0.873179	+	0.487400i	$0.837945\pi$
$744$	−1.31477e12	−	2.27724e12i	−0.157315	−	0.272478i
$745$	−3.85528e12	+	6.67755e12i	−0.458515	+	0.794171i
$746$	−1.49500e12	−	2.58941e12i	−0.176732	−	0.306109i
$747$	−9.36852e12	+	1.62268e13i	−1.10085	+	1.90673i
$748$	−4.24583e12			−0.495913
$749$	−5.22685e12			−0.606837
$750$	4.98540e12	−	8.63497e12i	0.575340	−	0.996518i
$751$	−2.49826e12	+	4.32712e12i	−0.286588	+	0.496386i	−0.972993	−	0.230834i	$-0.925855\pi$
$751$	−2.49826e12	+	4.32712e12i	−0.286588	+	0.496386i	0.686405	+	0.727220i	$0.259188\pi$
$752$	1.50846e12			0.172010
$753$	−1.54156e13			−1.74736
$754$	−1.72856e12	+	2.99395e12i	−0.194766	+	0.337345i
$755$	1.04217e12	+	1.80509e12i	0.116728	+	0.202180i
$756$	9.49091e11	−	1.64387e12i	0.105672	−	0.183029i
$757$	5.30213e12	+	9.18355e12i	0.586839	+	1.01643i	0.994643	+	0.103365i	$0.0329610\pi$
$757$	5.30213e12	+	9.18355e12i	0.586839	+	1.01643i	−0.407805	+	0.913069i	$0.633706\pi$
$758$	−2.85180e11	−	4.93946e11i	−0.0313767	−	0.0543461i
$759$	9.67666e12			1.05837
$760$	−1.83525e12	−	1.27578e12i	−0.199542	−	0.138713i
$761$	−3.97220e12			−0.429339			−0.214669	−	0.976687i	$-0.568867\pi$
$761$	−3.97220e12			−0.429339			−0.214669	+	0.976687i	$0.568867\pi$
$762$	−6.58532e12	−	1.14061e13i	−0.707586	−	1.22558i
$763$	5.42450e12	+	9.39550e12i	0.579427	+	1.00360i
$764$	−2.88921e12	+	5.00426e12i	−0.306802	+	0.531398i
$765$	−4.67942e12	−	8.10499e12i	−0.493987	−	0.855610i
$766$	2.60389e12	−	4.51007e12i	0.273271	−	0.473319i
$767$	6.30201e12			0.657507
$768$	9.33898e11			0.0968665
$769$	−3.14108e12	+	5.44051e12i	−0.323900	+	0.561011i	−0.981289	−	0.192540i	$-0.938327\pi$
$769$	−3.14108e12	+	5.44051e12i	−0.323900	+	0.561011i	0.657389	+	0.753551i	$0.271661\pi$
$770$	−1.55564e12	+	2.69444e12i	−0.159478	+	0.276224i
$771$	2.01152e13			2.05012
$772$	6.89419e12			0.698562
$773$	4.18432e12	−	7.24745e12i	0.421519	−	0.730092i	−0.574570	−	0.818456i	$-0.694831\pi$
$773$	4.18432e12	−	7.24745e12i	0.421519	−	0.730092i	0.996088	+	0.0883639i	$0.0281638\pi$
$774$	1.63542e10	+	2.83264e10i	0.00163793	+	0.00283698i
$775$	1.52101e12	−	2.63446e12i	0.151451	−	0.262321i
$776$	1.87042e12	+	3.23967e12i	0.185167	+	0.320718i
$777$	6.29902e12	+	1.09102e13i	0.619981	+	1.07384i
$778$	4.24895e12			0.415789
$779$	−7.87492e12	−	5.47431e12i	−0.766175	−	0.532611i
$780$	3.75613e12			0.363342
$781$	8.47868e11	+	1.46855e12i	0.0815452	+	0.141240i
$782$	2.67528e12	+	4.63372e12i	0.255822	+	0.443097i
$783$	−2.64665e12	+	4.58413e12i	−0.251633	+	0.435842i
$784$	7.13950e11	+	1.23660e12i	0.0674910	+	0.116898i
$785$	5.62389e12	−	9.74086e12i	0.528595	−	0.915553i
$786$	5.71758e12			0.534332
$787$	−1.42938e13			−1.32819			−0.664096	−	0.747647i	$-0.731183\pi$
$787$	−1.42938e13			−1.32819			−0.664096	+	0.747647i	$0.731183\pi$
$788$	−1.10861e12	+	1.92018e12i	−0.102426	+	0.177408i
$789$	7.01888e12	−	1.21571e13i	0.644795	−	1.11682i
$790$	−4.57482e12			−0.417880
$791$	5.83762e12			0.530202
$792$	2.65527e12	−	4.59906e12i	0.239798	−	0.415342i
$793$	−5.77569e12	−	1.00038e13i	−0.518650	−	0.898328i
$794$	2.81833e12	−	4.88149e12i	0.251651	−	0.435873i
$795$	−6.67968e12	−	1.15696e13i	−0.593067	−	1.02722i
$796$	−2.65007e12	−	4.59006e12i	−0.233964	−	0.405238i
$797$	4.32984e12			0.380110			0.190055	−	0.981773i	$-0.439133\pi$
$797$	4.32984e12			0.380110			0.190055	+	0.981773i	$0.439133\pi$
$798$	7.13342e11	−	8.48546e12i	0.0622709	−	0.740734i
$799$	8.12572e12			0.705344
$800$	5.40196e11	+	9.35647e11i	0.0466280	+	0.0807620i
$801$	−1.07872e13	−	1.86840e13i	−0.925895	−	1.60370i
$802$	−7.81785e12	+	1.35409e13i	−0.667271	+	1.15575i
$803$	−8.50263e12	−	1.47270e13i	−0.721661	−	1.24995i
$804$	5.32617e12	−	9.22520e12i	0.449534	−	0.778616i
$805$	3.92080e12			0.329074
$806$	3.31827e12			0.276951
$807$	−9.40862e12	+	1.62962e13i	−0.780899	+	1.35256i
$808$	−1.67216e12	+	2.89627e12i	−0.138015	+	0.239049i
$809$	2.27169e13			1.86458			0.932289	−	0.361715i	$-0.117809\pi$
$809$	2.27169e13			1.86458			0.932289	+	0.361715i	$0.117809\pi$
$810$	−2.59769e12			−0.212034
$811$	−5.11572e12	+	8.86069e12i	−0.415253	+	0.719240i	−0.995455	−	0.0952331i	$-0.969640\pi$
$811$	−5.11572e12	+	8.86069e12i	−0.415253	+	0.719240i	0.580202	+	0.814473i	$0.302974\pi$
$812$	1.69647e12	+	2.93837e12i	0.136944	+	0.237195i
$813$	1.75141e13	−	3.03353e13i	1.40598	−	2.43523i
$814$	5.05376e12	+	8.75336e12i	0.403464	+	0.698820i
$815$	6.15898e12	+	1.06677e13i	0.488989	+	0.846955i
$816$	5.03068e12			0.397211
$817$	3.45511e10	+	2.40184e10i	0.00271308	+	0.00188601i
$818$	1.73737e13			1.35675
$819$	4.17639e12	+	7.23371e12i	0.324357	+	0.561802i
$820$	−2.07597e12	−	3.59568e12i	−0.160346	−	0.277728i
$821$	−3.94865e12	+	6.83926e12i	−0.303322	+	0.525370i	−0.976886	−	0.213759i	$-0.931429\pi$
$821$	−3.94865e12	+	6.83926e12i	−0.303322	+	0.525370i	0.673564	+	0.739129i	$0.264763\pi$
$822$	9.41482e12	+	1.63069e13i	0.719265	+	1.24580i
$823$	−4.38756e12	+	7.59947e12i	−0.333368	+	0.577410i	−0.983170	−	0.182693i	$-0.941518\pi$
$823$	−4.38756e12	+	7.59947e12i	−0.333368	+	0.577410i	0.649802	+	0.760103i	$0.274852\pi$
$824$	3.42887e12			0.259107
$825$	1.05253e13			0.791030
$826$	3.09251e12	−	5.35639e12i	0.231154	−	0.400370i
$827$	−7.66148e12	+	1.32701e13i	−0.569558	+	0.986503i	0.427052	+	0.904227i	$0.359552\pi$
$827$	−7.66148e12	+	1.32701e13i	−0.569558	+	0.986503i	−0.996610	+	0.0822759i	$0.973781\pi$
$828$	−6.69230e12			−0.494811
$829$	−9.08452e12			−0.668047			−0.334023	−	0.942565i	$-0.608406\pi$
$829$	−9.08452e12			−0.668047			−0.334023	+	0.942565i	$0.608406\pi$
$830$	−5.21767e12	+	9.03727e12i	−0.381615	+	0.660976i
$831$	5.65206e12	+	9.78965e12i	0.411152	+	0.712136i
$832$	−5.89253e11	+	1.02062e12i	−0.0426331	+	0.0738427i
$833$	3.84588e12	+	6.66126e12i	0.276754	+	0.479351i
$834$	4.81340e11	+	8.33705e11i	0.0344512	+	0.0596713i
$835$	1.22608e13			0.872832
$836$	5.72320e11	−	6.80795e12i	0.0405239	−	0.482046i
$837$	5.08070e12			0.357815
$838$	2.93760e12	+	5.08808e12i	0.205776	+	0.356415i
$839$	−1.49623e12	−	2.59154e12i	−0.104248	−	0.180563i	0.809183	−	0.587557i	$-0.199910\pi$
$839$	−1.49623e12	−	2.59154e12i	−0.104248	−	0.180563i	−0.913431	+	0.406994i	$0.866577\pi$
$840$	1.84320e12	−	3.19252e12i	0.127737	−	0.221247i
$841$	2.52277e12	+	4.36957e12i	0.173899	+	0.301201i
$842$	2.10117e12	−	3.63934e12i	0.144065	−	0.249527i
$843$	−4.04531e13			−2.75884
$844$	1.52844e12			0.103683
$845$	2.72345e12	−	4.71715e12i	0.183766	−	0.318291i
$846$	−5.08169e12	+	8.80175e12i	−0.341068	+	0.590748i
$847$	6.49811e11			0.0433822
$848$	4.19157e12			0.278353
$849$	−1.45013e13	+	2.51170e13i	−0.957905	+	1.65914i
$850$	2.90991e12	+	5.04011e12i	0.191203	+	0.331173i
$851$	6.36870e12	−	1.10309e13i	0.416263	−	0.720989i
$852$	−1.00460e12	−	1.74002e12i	−0.0653153	−	0.113129i
$853$	5.40185e12	+	9.35629e12i	0.349359	+	0.605108i	0.986136	−	0.165940i	$-0.0530659\pi$
$853$	5.40185e12	+	9.35629e12i	0.349359	+	0.605108i	−0.636777	+	0.771048i	$0.719733\pi$
$854$	−1.13369e13			−0.729349
$855$	1.36267e13	−	6.41067e12i	0.872052	−	0.410257i
$856$	4.96874e12			0.316311
$857$	−8.06764e11	−	1.39736e12i	−0.0510896	−	0.0884898i	0.839350	−	0.543592i	$-0.182936\pi$
$857$	−8.06764e11	−	1.39736e12i	−0.0510896	−	0.0884898i	−0.890439	+	0.455102i	$0.849603\pi$
$858$	5.74058e12	+	9.94298e12i	0.361629	+	0.626360i
$859$	2.69734e12	−	4.67194e12i	0.169031	−	0.292771i	−0.769048	−	0.639191i	$-0.779269\pi$
$859$	2.69734e12	−	4.67194e12i	0.169031	−	0.292771i	0.938080	+	0.346420i	$0.112603\pi$
$860$	9.10827e9	+	1.57760e10i	0.000567797	+	0.000983453i
$861$	7.90906e12	−	1.36989e13i	0.490468	−	0.849516i
$862$	−1.33026e13			−0.820644
$863$	−2.95296e13			−1.81221			−0.906107	−	0.423049i	$-0.860960\pi$
$863$	−2.95296e13			−1.81221			−0.906107	+	0.423049i	$0.860960\pi$
$864$	−9.02223e11	+	1.56270e12i	−0.0550810	+	0.0954031i
$865$	−7.93294e12	+	1.37403e13i	−0.481795	+	0.834493i
$866$	−8.50864e12			−0.514079
$867$	1.31335e12			0.0789397
$868$	1.62833e12	−	2.82036e12i	0.0973654	−	0.168642i
$869$	−6.99179e12	−	1.21101e13i	−0.415910	−	0.720378i
$870$	−5.13998e12	+	8.90270e12i	−0.304176	+	0.526848i
$871$	6.72121e12	+	1.16415e13i	0.395700	+	0.685373i
$872$	−5.15662e12	−	8.93153e12i	−0.302024	−	0.523120i
$873$	−2.52043e13			−1.46862
$874$	−7.79053e12	+	3.66506e12i	−0.451612	+	0.212461i
$875$	1.23488e13			0.712179
$876$	1.00744e13	+	1.74493e13i	0.578029	+	1.00118i
$877$	−5.04700e12	−	8.74167e12i	−0.288095	−	0.498995i	0.685260	−	0.728298i	$-0.259689\pi$
$877$	−5.04700e12	−	8.74167e12i	−0.288095	−	0.498995i	−0.973355	+	0.229303i	$0.926355\pi$
$878$	−4.98704e12	+	8.63780e12i	−0.283216	+	0.490544i
$879$	−4.13408e12	−	7.16044e12i	−0.233577	−	0.404567i
$880$	1.47882e12	−	2.56138e12i	0.0831270	−	0.143980i
$881$	1.91406e13			1.07045			0.535223	−	0.844711i	$-0.320227\pi$
$881$	1.91406e13			1.07045			0.535223	+	0.844711i	$0.320227\pi$
$882$	−9.62060e12			−0.535296
$883$	1.10949e13	−	1.92170e13i	0.614188	−	1.06380i	−0.376338	−	0.926482i	$-0.622817\pi$
$883$	1.10949e13	−	1.92170e13i	0.614188	−	1.06380i	0.990526	−	0.137323i	$-0.0438497\pi$
$884$	−3.17417e12	+	5.49782e12i	−0.174821	+	0.302800i
$885$	1.87394e13			1.02686
$886$	−9.78826e12			−0.533647
$887$	7.12903e12	−	1.23478e13i	0.386700	−	0.669784i	−0.605303	−	0.795995i	$-0.706948\pi$
$887$	7.12903e12	−	1.23478e13i	0.386700	−	0.669784i	0.992003	+	0.126211i	$0.0402815\pi$
$888$	−5.98796e12	−	1.03715e13i	−0.323162	−	0.559734i
$889$	8.15589e12	−	1.41264e13i	0.437939	−	0.758532i
$890$	−6.00777e12	−	1.04058e13i	−0.320966	−	0.555929i
$891$	−3.97012e12	−	6.87644e12i	−0.211034	−	0.365522i
$892$	9.73428e11			0.0514828
$893$	−1.09531e12	+	1.30291e13i	−0.0576377	+	0.685621i
$894$	2.79252e13			1.46210
$895$	−1.65104e12	−	2.85968e12i	−0.0860110	−	0.148975i
$896$	5.78314e11	+	1.00167e12i	0.0299763	+	0.0519205i
$897$	7.23424e12	−	1.25301e13i	0.373101	−	0.646231i
$898$	6.34245e12	+	1.09854e13i	0.325472	+	0.563734i
$899$	−4.54079e12	+	7.86488e12i	−0.231853	+	0.401581i
$900$	−7.27924e12			−0.369824
$901$	2.25790e13			1.14141
$902$	6.34550e12	−	1.09907e13i	0.319181	−	0.552837i
$903$	−3.47008e10	+	6.01036e10i	−0.00173678	+	0.00300819i
$904$	−5.54934e12			−0.276365
$905$	1.33431e12			0.0661209
$906$	3.77440e12	−	6.53745e12i	0.186110	−	0.322353i
$907$	−3.55937e12	−	6.16501e12i	−0.174639	−	0.302483i	0.765398	−	0.643558i	$-0.222542\pi$
$907$	−3.55937e12	−	6.16501e12i	−0.174639	−	0.302483i	−0.940036	+	0.341075i	$0.889209\pi$
$908$	3.95244e11	−	6.84583e11i	0.0192965	−	0.0334226i
$909$	−1.12663e13	−	1.95138e13i	−0.547324	−	0.947994i
$910$	2.32598e12	+	4.02871e12i	0.112440	+	0.194751i
$911$	1.45744e13			0.701065			0.350532	−	0.936551i	$-0.386001\pi$
$911$	1.45744e13			0.701065			0.350532	+	0.936551i	$0.386001\pi$
$912$	−6.78116e11	+	8.06643e12i	−0.0324584	+	0.386104i
$913$	−3.18971e13			−1.51926
$914$	1.06806e11	+	1.84993e11i	0.00506217	+	0.00876793i
$915$	−1.71744e13	−	2.97469e13i	−0.810002	−	1.40296i
$916$	1.00184e13	−	1.73523e13i	0.470183	−	0.814380i
$917$	3.54060e12	+	6.13250e12i	0.165354	+	0.286402i
$918$	−4.86006e12	+	8.41787e12i	−0.225865	+	0.391210i
$919$	−3.23498e13			−1.49607			−0.748036	−	0.663658i	$-0.769003\pi$
$919$	−3.23498e13			−1.49607			−0.748036	+	0.663658i	$0.769003\pi$
$920$	−3.72719e12			−0.171528
$921$	−9.13954e11	+	1.58301e12i	−0.0418558	+	0.0724964i
$922$	9.01486e12	−	1.56142e13i	0.410837	−	0.711591i
$923$	2.53545e12			0.114987
$924$	1.12680e13			0.508539
$925$	6.92726e12	−	1.19984e13i	0.311117	−	0.538870i
$926$	−1.29422e13	−	2.24165e13i	−0.578439	−	1.00189i
$927$	−1.15512e13	+	2.00072e13i	−0.513768	+	0.889872i
$928$	−1.61269e12	−	2.79327e12i	−0.0713816	−	0.123637i
$929$	1.34302e12	+	2.32618e12i	0.0591577	+	0.102464i	0.894088	−	0.447892i	$-0.147825\pi$
$929$	1.34302e12	+	2.32618e12i	0.0591577	+	0.102464i	−0.834930	+	0.550356i	$0.814492\pi$
$930$	9.86707e12			0.432529
$931$	−1.11994e13	+	5.26875e12i	−0.488563	+	0.229844i
$932$	−1.42156e13			−0.617152
$933$	4.67884e12	+	8.10399e12i	0.202149	+	0.350132i
$934$	1.57741e13	+	2.73216e13i	0.678241	+	1.17475i
$935$	7.96603e12	−	1.37976e13i	0.340871	−	0.590406i
$936$	−3.97014e12	−	6.87649e12i	−0.169069	−	0.292837i
$937$	−6.55490e12	+	1.13534e13i	−0.277804	+	0.481170i	−0.970839	−	0.239734i	$-0.922940\pi$
$937$	−6.55490e12	+	1.13534e13i	−0.277804	+	0.481170i	0.693035	+	0.720904i	$0.256273\pi$
$938$	1.31929e13			0.556451
$939$	3.47465e13			1.45853
$940$	−2.83018e12	+	4.90201e12i	−0.118233	+	0.204785i
$941$	3.58877e12	−	6.21593e12i	0.149208	−	0.258436i	−0.781727	−	0.623621i	$-0.785661\pi$
$941$	3.58877e12	−	6.21593e12i	0.149208	−	0.258436i	0.930935	+	0.365185i	$0.118994\pi$
$942$	−4.07358e13			−1.68557
$943$	−1.59931e13			−0.658613
$944$	−2.93980e12	+	5.09187e12i	−0.120488	+	0.208691i
$945$	3.56138e12	+	6.16848e12i	0.145270	+	0.251614i
$946$	−2.78407e10	+	4.82216e10i	−0.00113024	+	0.00195763i
$947$	−4.38699e12	−	7.59849e12i	−0.177252	−	0.307010i	0.763686	−	0.645588i	$-0.223388\pi$
$947$	−4.38699e12	−	7.59849e12i	−0.177252	−	0.307010i	−0.940938	+	0.338578i	$0.890054\pi$
$948$	8.28425e12	+	1.43487e13i	0.333132	+	0.577001i
$949$	−2.54262e13			−1.01761
$950$	−8.47379e12	+	3.98649e12i	−0.337537	+	0.158794i
$951$	9.77925e11			0.0387698
$952$	3.11524e12	+	5.39576e12i	0.122921	+	0.212905i
$953$	1.38810e13	+	2.40425e13i	0.545132	+	0.944196i	0.998599	+	0.0529226i	$0.0168536\pi$
$953$	1.38810e13	+	2.40425e13i	0.545132	+	0.944196i	−0.453467	+	0.891273i	$0.649813\pi$
$954$	−1.41205e13	+	2.44575e13i	−0.551929	+	0.955969i
$955$	−1.08415e13	−	1.87780e13i	−0.421768	−	0.730523i
$956$	2.54688e12	−	4.41133e12i	0.0986163	−	0.170808i
$957$	−3.14222e13			−1.21097
$958$	3.51951e12			0.135001
$959$	−1.16602e13	+	2.01961e13i	−0.445167	+	0.771052i
$960$	−1.75218e12	+	3.03487e12i	−0.0665823	+	0.115324i
$961$	−1.77228e13			−0.670312
$962$	1.51127e13			0.568924
$963$	−1.67386e13	+	2.89922e13i	−0.627194	+	1.08633i
$964$	−7.33988e12	−	1.27130e13i	−0.273742	−	0.474136i
$965$	−1.29349e13	+	2.24039e13i	−0.480164	+	0.831669i
$966$	−7.09994e12	−	1.22975e13i	−0.262336	−	0.454379i
$967$	4.80427e12	+	8.32124e12i	0.176688	+	0.306033i	0.940744	−	0.339117i	$-0.110128\pi$
$967$	4.80427e12	+	8.32124e12i	0.176688	+	0.306033i	−0.764056	+	0.645150i	$0.776795\pi$
$968$	−6.17722e11			−0.0226128
$969$	−3.65285e12	+	4.34519e13i	−0.133099	+	1.58326i
$970$	−1.40372e13			−0.509105
$971$	−1.39802e13	−	2.42144e13i	−0.504693	−	0.874153i	−0.999985	−	0.00542696i	$-0.998273\pi$
$971$	−1.39802e13	−	2.42144e13i	−0.504693	−	0.874153i	0.495293	−	0.868726i	$-0.335061\pi$
$972$	9.03957e12	+	1.56570e13i	0.324825	+	0.562613i
$973$	−5.96138e11	+	1.03254e12i	−0.0213225	+	0.0369317i
$974$	2.29479e12	+	3.97469e12i	0.0817009	+	0.141510i
$975$	7.86870e12	−	1.36290e13i	0.278858	−	0.482995i
$976$	1.07771e13			0.380170
$977$	−2.22585e13			−0.781575			−0.390787	−	0.920481i	$-0.627797\pi$
$977$	−2.22585e13			−0.781575			−0.390787	+	0.920481i	$0.627797\pi$
$978$	2.23058e13	−	3.86348e13i	0.779639	−	1.35037i
$979$	1.83636e13	−	3.18067e13i	0.638905	−	1.10662i
$980$	−5.35806e12			−0.185563
$981$	6.94864e13			2.39546
$982$	1.48068e13	−	2.56462e13i	0.508113	−	0.880078i
$983$	1.55963e13	+	2.70137e13i	0.532760	+	0.922768i	0.999268	+	0.0382508i	$0.0121786\pi$
$983$	1.55963e13	+	2.70137e13i	0.532760	+	0.922768i	−0.466508	+	0.884517i	$0.654488\pi$
$984$	−7.51849e12	+	1.30224e13i	−0.255654	+	0.442806i
$985$	−4.15997e12	−	7.20528e12i	−0.140808	−	0.243886i
$986$	−8.68720e12	−	1.50467e13i	−0.292707	−	0.506984i
$987$	−2.15649e13			−0.723303
$988$	−8.38759e12	−	5.83069e12i	−0.280047	−	0.194677i
$989$	7.01694e10			0.00233219
$990$	9.96365e12	+	1.72576e13i	0.329655	+	0.570980i
$991$	−7.11470e12	−	1.23230e13i	−0.234328	−	0.405869i	0.724749	−	0.689013i	$-0.241956\pi$
$991$	−7.11470e12	−	1.23230e13i	−0.234328	−	0.405869i	−0.959077	+	0.283144i	$0.908622\pi$
$992$	−1.54792e12	+	2.68108e12i	−0.0507512	+	0.0879037i
$993$	3.06140e13	+	5.30250e13i	0.999191	+	1.73065i
$994$	1.24419e12	−	2.15500e12i	0.0404249	−	0.0700180i
$995$	1.98883e13			0.643271
$996$	3.77934e13			1.21688
$997$	3.07617e12	−	5.32808e12i	0.0986012	−	0.170782i	−0.812505	−	0.582955i	$-0.801897\pi$
$997$	3.07617e12	−	5.32808e12i	0.0986012	−	0.170782i	0.911106	+	0.412172i	$0.135230\pi$
$998$	1.30795e13	−	2.26543e13i	0.417353	−	0.722876i
$999$	2.31395e13			0.735037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.b.7.1	✓	16
19.11	even	3	inner	38.10.c.b.11.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.b.7.1	✓	16	1.1	even	1	trivial
38.10.c.b.11.1	yes	16	19.11	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-108.720 - 188.309i) q^{3} +(-128.000 + 221.703i) q^{4} +(-480.308 - 831.918i) q^{5} +(-1739.52 + 3012.94i) q^{6} -4308.78 q^{7} +4096.00 q^{8} +(-13798.6 + 23899.8i) q^{9} +O(q^{10})\)	\(q+(-8.00000 - 13.8564i) q^{2} +(-108.720 - 188.309i) q^{3} +(-128.000 + 221.703i) q^{4} +(-480.308 - 831.918i) q^{5} +(-1739.52 + 3012.94i) q^{6} -4308.78 q^{7} +4096.00 q^{8} +(-13798.6 + 23899.8i) q^{9} +(-7684.93 + 13310.7i) q^{10} -46980.2 q^{11} +55664.6 q^{12} +(-35122.2 + 60833.5i) q^{13} +(34470.2 + 59704.2i) q^{14} +(-104438. + 180892. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-176513. - 305730. i) q^{17} +441554. q^{18} +(514015. - 241819. i) q^{19} +245918. q^{20} +(468450. + 811380. i) q^{21} +(375841. + 650976. i) q^{22} +(473632. - 820355. i) q^{23} +(-445317. - 771312. i) q^{24} +(515171. - 892303. i) q^{25} +1.12391e6 q^{26} +1.72085e6 q^{27} +(551524. - 955267. i) q^{28} +(-1.53799e6 + 2.66387e6i) q^{29} +3.34202e6 q^{30} +2.95243e6 q^{31} +(-524288. + 908093. i) q^{32} +(5.10768e6 + 8.84677e6i) q^{33} +(-2.82421e6 + 4.89168e6i) q^{34} +(2.06954e6 + 3.58455e6i) q^{35} +(-3.53244e6 - 6.11836e6i) q^{36} +1.34465e7 q^{37} +(-7.46286e6 - 5.18785e6i) q^{38} +1.52740e7 q^{39} +(-1.96734e6 - 3.40753e6i) q^{40} +(-8.44173e6 - 1.46215e7i) q^{41} +(7.49521e6 - 1.29821e7i) q^{42} +(37037.9 + 64151.5i) q^{43} +(6.01346e6 - 1.04156e7i) q^{44} +2.65103e7 q^{45} -1.51562e7 q^{46} +(-1.15086e7 + 1.99335e7i) q^{47} +(-7.12507e6 + 1.23410e7i) q^{48} -2.17880e7 q^{49} -1.64855e7 q^{50} +(-3.83811e7 + 6.64780e7i) q^{51} +(-8.99129e6 - 1.55734e7i) q^{52} +(-3.19791e7 + 5.53895e7i) q^{53} +(-1.37668e7 - 2.38448e7i) q^{54} +(2.25649e7 + 3.90836e7i) q^{55} -1.76488e7 q^{56} +(-1.01420e8 - 7.05029e7i) q^{57} +4.92155e7 q^{58} +(-4.48577e7 - 7.76958e7i) q^{59} +(-2.67362e7 - 4.63084e7i) q^{60} +(-8.22227e7 + 1.42414e8i) q^{61} +(-2.36194e7 - 4.09100e7i) q^{62} +(5.94550e7 - 1.02979e8i) q^{63} +1.67772e7 q^{64} +6.74779e7 q^{65} +(8.17230e7 - 1.41548e8i) q^{66} +(9.56832e7 - 1.65728e8i) q^{67} +9.03749e7 q^{68} -2.05973e8 q^{69} +(3.31126e7 - 5.73528e7i) q^{70} +(-1.80473e7 - 3.12589e7i) q^{71} +(-5.65190e7 + 9.78937e7i) q^{72} +(1.80983e8 + 3.13472e8i) q^{73} +(-1.07572e8 - 1.86320e8i) q^{74} -2.24038e8 q^{75} +(-1.21822e7 + 1.44911e8i) q^{76} +2.02427e8 q^{77} +(-1.22192e8 - 2.11642e8i) q^{78} +(1.48824e8 + 2.57771e8i) q^{79} +(-3.14775e7 + 5.45206e7i) q^{80} +(8.45062e7 + 1.46369e8i) q^{81} +(-1.35068e8 + 2.33944e8i) q^{82} +6.78948e8 q^{83} -2.39847e8 q^{84} +(-1.69562e8 + 2.93689e8i) q^{85} +(592606. - 1.02642e6i) q^{86} +6.68839e8 q^{87} -1.92431e8 q^{88} +(-3.90880e8 + 6.77025e8i) q^{89} +(-2.12082e8 - 3.67337e8i) q^{90} +(1.51334e8 - 2.62118e8i) q^{91} +(1.21250e8 + 2.10011e8i) q^{92} +(-3.20988e8 - 5.55967e8i) q^{93} +3.68276e8 q^{94} +(-4.48059e8 - 3.11471e8i) q^{95} +2.28002e8 q^{96} +(4.56647e8 + 7.90935e8i) q^{97} +(1.74304e8 + 3.01904e8i) q^{98} +(6.48260e8 - 1.12282e9i) 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

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