LMFDB - Embedded newform 38.10.c.a.7.6

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:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 93094 x^{12} + 3763497 x^{11} + 6525212431 x^{10} + 244392759522 x^{9} + \cdots + 37\!\cdots\!25 $ x^14 - 3x^13 + 93094x^12 + 3763497x^11 + 6525212431x^10 + 244392759522x^9 + 198778066371639x^8 + 9216645483921129x^7 + 4530154246073222607x^6 + 142122715974381300066x^5 + 8185019559882294055671x^4 - 135327799885026117969495x^3 + 2044710563339570147369550x^2 - 9649457865335314261798875*x + 37683939484136051622500625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.6
Root			$-98.6185 - 170.812i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.a.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(110.618 + 191.597i) q^{3} +(-128.000 + 221.703i) q^{4} +(1160.30 + 2009.69i) q^{5} +(-1769.90 + 3065.55i) q^{6} -7717.55 q^{7} -4096.00 q^{8} +(-14631.4 + 25342.3i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(110.618 + 191.597i) q^{3} +(-128.000 + 221.703i) q^{4} +(1160.30 + 2009.69i) q^{5} +(-1769.90 + 3065.55i) q^{6} -7717.55 q^{7} -4096.00 q^{8} +(-14631.4 + 25342.3i) q^{9} +(-18564.7 + 32155.1i) q^{10} +53039.7 q^{11} -56636.7 q^{12} +(67363.5 - 116677. i) q^{13} +(-61740.4 - 106938. i) q^{14} +(-256700. + 444618. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(148923. + 257941. i) q^{17} -468205. q^{18} +(544157. - 163037. i) q^{19} -594072. q^{20} +(-853704. - 1.47866e6i) q^{21} +(424318. + 734940. i) q^{22} +(1.03916e6 - 1.79987e6i) q^{23} +(-453093. - 784781. i) q^{24} +(-1.71601e6 + 2.97222e6i) q^{25} +2.15563e6 q^{26} -2.11941e6 q^{27} +(987846. - 1.71100e6i) q^{28} +(-680593. + 1.17882e6i) q^{29} -8.21442e6 q^{30} -7.94452e6 q^{31} +(524288. - 908093. i) q^{32} +(5.86717e6 + 1.01622e7i) q^{33} +(-2.38276e6 + 4.12706e6i) q^{34} +(-8.95464e6 - 1.55099e7i) q^{35} +(-3.74564e6 - 6.48764e6i) q^{36} -1.61818e7 q^{37} +(6.61236e6 + 6.23577e6i) q^{38} +2.98066e7 q^{39} +(-4.75257e6 - 8.23170e6i) q^{40} +(-158872. - 275175. i) q^{41} +(1.36593e7 - 2.36585e7i) q^{42} +(1.90010e7 + 3.29106e7i) q^{43} +(-6.78908e6 + 1.17590e7i) q^{44} -6.79071e7 q^{45} +3.32530e7 q^{46} +(1.64263e7 - 2.84511e7i) q^{47} +(7.24949e6 - 1.25565e7i) q^{48} +1.92070e7 q^{49} -5.49124e7 q^{50} +(-3.29472e7 + 5.70662e7i) q^{51} +(1.72451e7 + 2.98693e7i) q^{52} +(1.95002e7 - 3.37754e7i) q^{53} +(-1.69553e7 - 2.93674e7i) q^{54} +(6.15418e7 + 1.06593e8i) q^{55} +3.16111e7 q^{56} +(9.14311e7 + 8.62239e7i) q^{57} -2.17790e7 q^{58} +(1.98937e7 + 3.44568e7i) q^{59} +(-6.57153e7 - 1.13822e8i) q^{60} +(1.73879e7 - 3.01167e7i) q^{61} +(-6.35561e7 - 1.10082e8i) q^{62} +(1.12919e8 - 1.95581e8i) q^{63} +1.67772e7 q^{64} +3.12647e8 q^{65} +(-9.38748e7 + 1.62596e8i) q^{66} +(-6.40663e7 + 1.10966e8i) q^{67} -7.62483e7 q^{68} +4.59800e8 q^{69} +(1.43274e8 - 2.48158e8i) q^{70} +(1.00126e8 + 1.73423e8i) q^{71} +(5.99302e7 - 1.03802e8i) q^{72} +(-8.97147e7 - 1.55390e8i) q^{73} +(-1.29454e8 - 2.24222e8i) q^{74} -7.59291e8 q^{75} +(-3.35065e7 + 1.41510e8i) q^{76} -4.09337e8 q^{77} +(2.38453e8 + 4.13012e8i) q^{78} +(2.19417e6 + 3.80041e6i) q^{79} +(7.60412e7 - 1.31707e8i) q^{80} +(5.35442e7 + 9.27413e7i) q^{81} +(2.54195e6 - 4.40279e6i) q^{82} -3.25511e8 q^{83} +4.37096e8 q^{84} +(-3.45588e8 + 5.98577e8i) q^{85} +(-3.04015e8 + 5.26570e8i) q^{86} -3.01145e8 q^{87} -2.17251e8 q^{88} +(1.85092e8 - 3.20589e8i) q^{89} +(-5.43256e8 - 9.40948e8i) q^{90} +(-5.19881e8 + 9.00461e8i) q^{91} +(2.66024e8 + 4.60767e8i) q^{92} +(-8.78810e8 - 1.52214e9i) q^{93} +5.25641e8 q^{94} +(9.59037e8 + 9.04417e8i) q^{95} +2.31984e8 q^{96} +(-3.76321e8 - 6.51807e8i) q^{97} +(1.53656e8 + 2.66140e8i) q^{98} +(-7.76045e8 + 1.34415e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) $ 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * 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
$3$	110.618	+	191.597i	0.788464	+	1.36566i	0.926907	+	0.375290i	$0.122457\pi$
$3$	110.618	+	191.597i	0.788464	+	1.36566i	−0.138443	+	0.990370i	$0.544210\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	1160.30	+	2009.69i	0.830240	+	1.43802i	0.897847	+	0.440307i	$0.145130\pi$
$5$	1160.30	+	2009.69i	0.830240	+	1.43802i	−0.0676070	+	0.997712i	$0.521536\pi$
$6$	−1769.90	+	3065.55i	−0.557529	+	0.965668i
$7$	−7717.55			−1.21489			−0.607447	−	0.794360i	$-0.707806\pi$
$7$	−7717.55			−1.21489			−0.607447	+	0.794360i	$0.707806\pi$
$8$	−4096.00			−0.353553
$9$	−14631.4	+	25342.3i	−0.743352	+	1.28752i
$10$	−18564.7	+	32155.1i	−0.587069	+	1.01683i
$11$	53039.7			1.09228			0.546140	−	0.837694i	$-0.316097\pi$
$11$	53039.7			1.09228			0.546140	+	0.837694i	$0.316097\pi$
$12$	−56636.7			−0.788464
$13$	67363.5	−	116677.i	0.654154	−	1.13303i	−0.327952	−	0.944694i	$-0.606358\pi$
$13$	67363.5	−	116677.i	0.654154	−	1.13303i	0.982105	−	0.188333i	$-0.0603083\pi$
$14$	−61740.4	−	106938.i	−0.429530	−	0.743967i
$15$	−256700.	+	444618.i	−1.30923	+	2.26765i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	148923.	+	257941.i	0.432454	+	0.749033i	0.997084	−	0.0763115i	$-0.0243144\pi$
$17$	148923.	+	257941.i	0.432454	+	0.749033i	−0.564630	+	0.825344i	$0.690981\pi$
$18$	−468205.			−1.05126
$19$	544157.	−	163037.i	0.957928	−	0.287008i
$19$	544157.	−	163037.i	0.957928	−	0.287008i
$20$	−594072.			−0.830240
$21$	−853704.	−	1.47866e6i	−0.957900	−	1.65913i
$22$	424318.	+	734940.i	0.386179	+	0.668882i
$23$	1.03916e6	−	1.79987e6i	0.774294	−	1.34112i	−0.160897	−	0.986971i	$-0.551439\pi$
$23$	1.03916e6	−	1.79987e6i	0.774294	−	1.34112i	0.935190	−	0.354145i	$-0.115228\pi$
$24$	−453093.	−	784781.i	−0.278764	−	0.482834i
$25$	−1.71601e6	+	2.97222e6i	−0.878598	+	1.52178i
$26$	2.15563e6			0.925113
$27$	−2.11941e6			−0.767499
$28$	987846.	−	1.71100e6i	0.303723	−	0.526064i
$29$	−680593.	+	1.17882e6i	−0.178688	+	0.309498i	−0.941432	−	0.337204i	$-0.890519\pi$
$29$	−680593.	+	1.17882e6i	−0.178688	+	0.309498i	0.762743	+	0.646702i	$0.223852\pi$
$30$	−8.21442e6			−1.85153
$31$	−7.94452e6			−1.54504			−0.772520	−	0.634990i	$-0.781004\pi$
$31$	−7.94452e6			−1.54504			−0.772520	+	0.634990i	$0.781004\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	5.86717e6	+	1.01622e7i	0.861224	+	1.49168i
$34$	−2.38276e6	+	4.12706e6i	−0.305791	+	0.529646i
$35$	−8.95464e6	−	1.55099e7i	−1.00865	−	1.74704i
$36$	−3.74564e6	−	6.48764e6i	−0.371676	−	0.643762i
$37$	−1.61818e7			−1.41945			−0.709724	−	0.704480i	$-0.751180\pi$
$37$	−1.61818e7			−1.41945			−0.709724	+	0.704480i	$0.751180\pi$
$38$	6.61236e6	+	6.23577e6i	0.514435	+	0.485136i
$39$	2.98066e7			2.06311
$40$	−4.75257e6	−	8.23170e6i	−0.293534	−	0.508416i
$41$	−158872.	−	275175.i	−0.00878052	−	0.0152083i	0.861602	−	0.507585i	$-0.169462\pi$
$41$	−158872.	−	275175.i	−0.00878052	−	0.0152083i	−0.870382	+	0.492377i	$0.836128\pi$
$42$	1.36593e7	−	2.36585e7i	0.677338	−	1.17318i
$43$	1.90010e7	+	3.29106e7i	0.847554	+	1.46801i	0.883384	+	0.468649i	$0.155259\pi$
$43$	1.90010e7	+	3.29106e7i	0.847554	+	1.46801i	−0.0358300	+	0.999358i	$0.511407\pi$
$44$	−6.78908e6	+	1.17590e7i	−0.273070	+	0.472971i
$45$	−6.79071e7			−2.46864
$46$	3.32530e7			1.09502
$47$	1.64263e7	−	2.84511e7i	0.491019	−	0.850471i	−0.508927	−	0.860810i	$-0.669958\pi$
$47$	1.64263e7	−	2.84511e7i	0.491019	−	0.850471i	0.999947	+	0.0103390i	$0.00329108\pi$
$48$	7.24949e6	−	1.25565e7i	0.197116	−	0.341415i
$49$	1.92070e7			0.475966
$50$	−5.49124e7			−1.24253
$51$	−3.29472e7	+	5.70662e7i	−0.681950	+	1.18117i
$52$	1.72451e7	+	2.98693e7i	0.327077	+	0.566514i
$53$	1.95002e7	−	3.37754e7i	0.339467	−	0.587974i	−0.644865	−	0.764296i	$-0.723087\pi$
$53$	1.95002e7	−	3.37754e7i	0.339467	−	0.587974i	0.984333	+	0.176322i	$0.0564199\pi$
$54$	−1.69553e7	−	2.93674e7i	−0.271352	−	0.469995i
$55$	6.15418e7	+	1.06593e8i	0.906855	+	1.57072i
$56$	3.16111e7			0.429530
$57$	9.14311e7	+	8.62239e7i	1.14725	+	1.08191i
$58$	−2.17790e7			−0.252704
$59$	1.98937e7	+	3.44568e7i	0.213737	+	0.370204i	0.952881	−	0.303344i	$-0.0981030\pi$
$59$	1.98937e7	+	3.44568e7i	0.213737	+	0.370204i	−0.739144	+	0.673548i	$0.764770\pi$
$60$	−6.57153e7	−	1.13822e8i	−0.654615	−	1.13383i
$61$	1.73879e7	−	3.01167e7i	0.160791	−	0.278499i	−0.774361	−	0.632744i	$-0.781929\pi$
$61$	1.73879e7	−	3.01167e7i	0.160791	−	0.278499i	0.935153	+	0.354245i	$0.115262\pi$
$62$	−6.35561e7	−	1.10082e8i	−0.546254	−	0.946140i
$63$	1.12919e8	−	1.95581e8i	0.903094	−	1.56420i
$64$	1.67772e7			0.125000
$65$	3.12647e8			2.17242
$66$	−9.38748e7	+	1.62596e8i	−0.608977	+	1.05478i
$67$	−6.40663e7	+	1.10966e8i	−0.388413	+	0.672750i	−0.992236	−	0.124368i	$-0.960310\pi$
$67$	−6.40663e7	+	1.10966e8i	−0.388413	+	0.672750i	0.603824	+	0.797118i	$0.293643\pi$
$68$	−7.62483e7			−0.432454
$69$	4.59800e8			2.44201
$70$	1.43274e8	−	2.48158e8i	0.713226	−	1.23534i
$71$	1.00126e8	+	1.73423e8i	0.467610	+	0.809924i	0.999315	−	0.0370054i	$-0.0117819\pi$
$71$	1.00126e8	+	1.73423e8i	0.467610	+	0.809924i	−0.531705	+	0.846930i	$0.678449\pi$
$72$	5.99302e7	−	1.03802e8i	0.262815	−	0.455208i
$73$	−8.97147e7	−	1.55390e8i	−0.369752	−	0.640429i	0.619775	−	0.784780i	$-0.287224\pi$
$73$	−8.97147e7	−	1.55390e8i	−0.369752	−	0.640429i	−0.989527	+	0.144351i	$0.953891\pi$
$74$	−1.29454e8	−	2.24222e8i	−0.501850	−	0.869231i
$75$	−7.59291e8			−2.77097
$76$	−3.35065e7	+	1.41510e8i	−0.115204	+	0.486547i
$77$	−4.09337e8			−1.32700
$78$	2.38453e8	+	4.13012e8i	0.729419	+	1.26339i
$79$	2.19417e6	+	3.80041e6i	0.00633793	+	0.0109776i	0.869177	−	0.494501i	$-0.164649\pi$
$79$	2.19417e6	+	3.80041e6i	0.00633793	+	0.0109776i	−0.862839	+	0.505479i	$0.831316\pi$
$80$	7.60412e7	−	1.31707e8i	0.207560	−	0.359505i
$81$	5.35442e7	+	9.27413e7i	0.138207	+	0.239382i
$82$	2.54195e6	−	4.40279e6i	0.00620877	−	0.0107539i
$83$	−3.25511e8			−0.752861			−0.376430	−	0.926445i	$-0.622849\pi$
$83$	−3.25511e8			−0.752861			−0.376430	+	0.926445i	$0.622849\pi$
$84$	4.37096e8			0.957900
$85$	−3.45588e8	+	5.98577e8i	−0.718082	+	1.24375i
$86$	−3.04015e8	+	5.26570e8i	−0.599311	+	1.03804i
$87$	−3.01145e8			−0.563558
$88$	−2.17251e8			−0.386179
$89$	1.85092e8	−	3.20589e8i	0.312704	−	0.541619i	−0.666243	−	0.745735i	$-0.732099\pi$
$89$	1.85092e8	−	3.20589e8i	0.312704	−	0.541619i	0.978947	+	0.204116i	$0.0654320\pi$
$90$	−5.43256e8	−	9.40948e8i	−0.872798	−	1.51173i
$91$	−5.19881e8	+	9.00461e8i	−0.794727	+	1.37651i
$92$	2.66024e8	+	4.60767e8i	0.387147	+	0.670558i
$93$	−8.78810e8	−	1.52214e9i	−1.21821	−	2.11000i
$94$	5.25641e8			0.694406
$95$	9.59037e8	+	9.04417e8i	1.20803	+	1.13923i
$96$	2.31984e8			0.278764
$97$	−3.76321e8	−	6.51807e8i	−0.431604	−	0.747560i	0.565407	−	0.824812i	$-0.308719\pi$
$97$	−3.76321e8	−	6.51807e8i	−0.431604	−	0.747560i	−0.997012	+	0.0772514i	$0.975386\pi$
$98$	1.53656e8	+	2.66140e8i	0.168280	+	0.291469i
$99$	−7.76045e8	+	1.34415e9i	−0.811949	+	1.40634i
$100$	−4.39299e8	−	7.60889e8i	−0.439299	−	0.760889i
$101$	1.31129e8	−	2.27122e8i	0.125387	−	0.217177i	−0.796497	−	0.604642i	$-0.793316\pi$
$101$	1.31129e8	−	2.27122e8i	0.125387	−	0.217177i	0.921884	+	0.387466i	$0.126649\pi$
$102$	−1.05431e9			−0.964422
$103$	3.96930e8			0.347494			0.173747	−	0.984790i	$-0.444413\pi$
$103$	3.96930e8			0.347494			0.173747	+	0.984790i	$0.444413\pi$
$104$	−2.75921e8	+	4.77909e8i	−0.231278	+	0.400586i
$105$	1.98110e9	−	3.43136e9i	1.59058	−	2.75496i
$106$	6.24007e8			0.480079
$107$	9.02169e8			0.665367			0.332683	−	0.943039i	$-0.392046\pi$
$107$	9.02169e8			0.665367			0.332683	+	0.943039i	$0.392046\pi$
$108$	2.71284e8	−	4.69878e8i	0.191875	−	0.332337i
$109$	−8.53000e7	−	1.47744e8i	−0.0578802	−	0.100251i	0.835633	−	0.549287i	$-0.185101\pi$
$109$	−8.53000e7	−	1.47744e8i	−0.0578802	−	0.100251i	−0.893514	+	0.449036i	$0.851767\pi$
$110$	−9.84668e8	+	1.70550e9i	−0.641243	+	1.11067i
$111$	−1.79001e9	−	3.10038e9i	−1.11918	−	1.93848i
$112$	2.52889e8	+	4.38016e8i	0.151862	+	0.263032i
$113$	−4.16406e6			−0.00240250			−0.00120125	−	0.999999i	$-0.500382\pi$
$113$	−4.16406e6			−0.00240250			−0.00120125	+	0.999999i	$0.500382\pi$
$114$	−4.63304e8	+	1.95670e9i	−0.256918	+	1.08506i
$115$	4.82292e9			2.57140
$116$	−1.74232e8	−	3.01778e8i	−0.0893442	−	0.154749i
$117$	1.97125e9	+	3.41430e9i	0.972533	+	1.68448i
$118$	−3.18298e8	+	5.51309e8i	−0.151135	+	0.261774i
$119$	−1.14932e9	−	1.99068e9i	−0.525386	−	0.909995i
$120$	1.05145e9	−	1.82116e9i	0.462883	−	0.801736i
$121$	4.55263e8			0.193076
$122$	5.56413e8			0.227393
$123$	3.51484e7	−	6.08788e7i	0.0138463	−	0.0239824i
$124$	1.01690e9	−	1.76132e9i	0.386260	−	0.669022i
$125$	−3.43193e9			−1.25731
$126$	3.61339e9			1.27717
$127$	−1.56847e9	+	2.71666e9i	−0.535006	+	0.926657i	0.464157	+	0.885753i	$0.346357\pi$
$127$	−1.56847e9	+	2.71666e9i	−0.535006	+	0.926657i	−0.999163	+	0.0409044i	$0.986976\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	−4.20372e9	+	7.28105e9i	−1.33653	+	2.31494i
$130$	2.50117e9	+	4.33216e9i	0.768066	+	1.33033i
$131$	1.50571e9	+	2.60796e9i	0.446704	+	0.773714i	0.998169	−	0.0604836i	$-0.0192643\pi$
$131$	1.50571e9	+	2.60796e9i	0.446704	+	0.773714i	−0.551465	+	0.834198i	$0.685931\pi$
$132$	−3.00399e9			−0.861224
$133$	−4.19956e9	+	1.25824e9i	−1.16378	+	0.348684i
$134$	−2.05012e9			−0.549298
$135$	−2.45914e9	−	4.25936e9i	−0.637208	−	1.10368i
$136$	−6.09987e8	−	1.05653e9i	−0.152896	−	0.264823i
$137$	3.50230e9	−	6.06616e9i	0.849397	−	1.47120i	−0.0323510	−	0.999477i	$-0.510299\pi$
$137$	3.50230e9	−	6.06616e9i	0.849397	−	1.47120i	0.881748	−	0.471721i	$-0.156367\pi$
$138$	3.67840e9	+	6.37117e9i	0.863382	+	1.49542i
$139$	1.98416e9	−	3.43666e9i	0.450826	−	0.780854i	−0.547611	−	0.836733i	$-0.684463\pi$
$139$	1.98416e9	−	3.43666e9i	0.450826	−	0.780854i	0.998438	+	0.0558790i	$0.0177961\pi$
$140$	4.58478e9			1.00865
$141$	7.26820e9			1.54861
$142$	−1.60201e9	+	2.77477e9i	−0.330650	+	0.572703i
$143$	3.57294e9	−	6.18852e9i	0.714519	−	1.23758i
$144$	1.91777e9			0.371676
$145$	−3.15876e9			−0.593418
$146$	1.43543e9	−	2.48625e9i	0.261454	−	0.452852i
$147$	2.12465e9	+	3.67999e9i	0.375283	+	0.650009i
$148$	2.07127e9	−	3.58755e9i	0.354862	−	0.614639i
$149$	−2.26117e9	−	3.91645e9i	−0.375832	−	0.650961i	0.614619	−	0.788824i	$-0.289310\pi$
$149$	−2.26117e9	−	3.91645e9i	−0.375832	−	0.650961i	−0.990451	+	0.137863i	$0.955976\pi$
$150$	−6.07433e9	−	1.05210e10i	−0.979687	−	1.69687i
$151$	8.38256e9			1.31214			0.656070	−	0.754700i	$-0.272217\pi$
$151$	8.38256e9			1.31214			0.656070	+	0.754700i	$0.272217\pi$
$152$	−2.22887e9	+	6.67798e8i	−0.338679	+	0.101473i
$153$	−8.71578e9			−1.28586
$154$	−3.27469e9	−	5.67193e9i	−0.469167	−	0.812621i
$155$	−9.21799e9	−	1.59660e10i	−1.28275	−	2.22180i
$156$	−3.81525e9	+	6.60820e9i	−0.515777	+	0.893352i
$157$	2.10121e9	+	3.63941e9i	0.276008	+	0.478060i	0.970389	−	0.241548i	$-0.0776551\pi$
$157$	2.10121e9	+	3.63941e9i	0.276008	+	0.478060i	−0.694381	+	0.719608i	$0.744322\pi$
$158$	−3.51066e7	+	6.08065e7i	−0.00448159	+	0.00776235i
$159$	8.62834e9			1.07063
$160$	2.43332e9			0.293534
$161$	−8.01974e9	+	1.38906e10i	−0.940685	+	1.62931i
$162$	−8.56707e8	+	1.48386e9i	−0.0977271	+	0.169268i
$163$	5.84387e9			0.648420			0.324210	−	0.945985i	$-0.394902\pi$
$163$	5.84387e9			0.648420			0.324210	+	0.945985i	$0.394902\pi$
$164$	8.13425e7			0.00878052
$165$	−1.36153e10	+	2.35824e10i	−1.43005	+	2.47691i
$166$	−2.60409e9	−	4.51042e9i	−0.266177	−	0.461031i
$167$	−3.65321e9	+	6.32754e9i	−0.363455	+	0.629522i	−0.988527	−	0.151045i	$-0.951736\pi$
$167$	−3.65321e9	+	6.32754e9i	−0.363455	+	0.629522i	0.625072	+	0.780567i	$0.285070\pi$
$168$	3.49677e9	+	6.05658e9i	0.338669	+	0.586592i
$169$	−3.77344e9	−	6.53579e9i	−0.355834	−	0.616322i
$170$	−1.10588e10			−1.01552
$171$	−3.83005e9	+	1.61757e10i	−0.342549	+	1.44670i
$172$	−9.72849e9			−0.847554
$173$	6.19284e9	+	1.07263e10i	0.525633	+	0.910423i	0.999554	+	0.0298556i	$0.00950474\pi$
$173$	6.19284e9	+	1.07263e10i	0.525633	+	0.910423i	−0.473921	+	0.880567i	$0.657162\pi$
$174$	−2.40916e9	−	4.17278e9i	−0.199248	−	0.345107i
$175$	1.32434e10	−	2.29383e10i	1.06740	−	1.84880i
$176$	−1.73801e9	−	3.01031e9i	−0.136535	−	0.236486i
$177$	−4.40121e9	+	7.62312e9i	−0.337049	+	0.583785i
$178$	5.92295e9			0.442230
$179$	−1.11124e10			−0.809037			−0.404519	−	0.914530i	$-0.632561\pi$
$179$	−1.11124e10			−0.809037			−0.404519	+	0.914530i	$0.632561\pi$
$180$	8.69210e9	−	1.50552e10i	0.617161	−	1.06895i
$181$	4.07093e9	−	7.05106e9i	0.281929	−	0.488316i	−0.689930	−	0.723876i	$-0.742359\pi$
$181$	4.07093e9	−	7.05106e9i	0.281929	−	0.488316i	0.971860	+	0.235560i	$0.0756923\pi$
$182$	−1.66362e10			−1.12391
$183$	7.69369e9			0.507113
$184$	−4.25639e9	+	7.37228e9i	−0.273754	+	0.474156i
$185$	−1.87757e10	−	3.25205e10i	−1.17848	−	2.04119i
$186$	1.40610e10	−	2.43543e10i	0.861404	−	1.49200i
$187$	7.89881e9	+	1.36811e10i	0.472361	+	0.818154i
$188$	4.20513e9	+	7.28349e9i	0.245510	+	0.425235i
$189$	1.63566e10			0.932429
$190$	−4.85968e9	+	2.05241e10i	−0.270531	+	1.14255i
$191$	−1.12793e9			−0.0613243			−0.0306622	−	0.999530i	$-0.509762\pi$
$191$	−1.12793e9			−0.0613243			−0.0306622	+	0.999530i	$0.509762\pi$
$192$	1.85587e9	+	3.21446e9i	0.0985581	+	0.170708i
$193$	−1.52532e10	−	2.64193e10i	−0.791321	−	1.37061i	−0.925149	−	0.379603i	$-0.876060\pi$
$193$	−1.52532e10	−	2.64193e10i	−0.791321	−	1.37061i	0.133828	−	0.991005i	$-0.457273\pi$
$194$	6.02114e9	−	1.04289e10i	0.305190	−	0.528605i
$195$	3.45845e10	+	5.99021e10i	1.71288	+	2.96679i
$196$	−2.45849e9	+	4.25823e9i	−0.118992	+	0.206100i
$197$	1.32146e10			0.625107			0.312554	−	0.949900i	$-0.398816\pi$
$197$	1.32146e10			0.625107			0.312554	+	0.949900i	$0.398816\pi$
$198$	−2.48335e10			−1.14827
$199$	1.02596e10	−	1.77702e10i	0.463760	−	0.803255i	−0.535385	−	0.844608i	$-0.679833\pi$
$199$	1.02596e10	−	1.77702e10i	0.463760	−	0.803255i	0.999145	+	0.0413529i	$0.0131668\pi$
$200$	7.02879e9	−	1.21742e10i	0.310631	−	0.538029i
$201$	−2.83477e10			−1.22500
$202$	4.19613e9			0.177324
$203$	5.25251e9	−	9.09762e9i	0.217087	−	0.376007i
$204$	−8.43448e9	−	1.46089e10i	−0.340975	−	0.590586i
$205$	3.68677e8	−	6.38568e8i	0.0145799	−	0.0252531i
$206$	3.17544e9	+	5.50003e9i	0.122858	+	0.212795i
$207$	3.04086e10	+	5.26693e10i	1.15115	+	1.99384i
$208$	−8.82947e9			−0.327077
$209$	2.88619e10	−	8.64741e9i	1.04633	−	0.313493i
$210$	6.33952e10			2.24941
$211$	−2.49606e10	−	4.32331e10i	−0.866931	−	1.50157i	−0.865117	−	0.501571i	$-0.832756\pi$
$211$	−2.49606e10	−	4.32331e10i	−0.866931	−	1.50157i	−0.00181466	−	0.999998i	$-0.500578\pi$
$212$	4.99205e9	+	8.64649e9i	0.169734	+	0.293987i
$213$	−2.21515e10	+	3.83676e10i	−0.737388	+	1.27719i
$214$	7.21735e9	+	1.25008e10i	0.235243	+	0.407452i
$215$	−4.40935e10	+	7.63722e10i	−1.40735	+	2.43760i
$216$	8.68109e9			0.271352
$217$	6.13122e10			1.87706
$218$	1.36480e9	−	2.36390e9i	0.0409274	−	0.0708884i
$219$	1.98482e10	−	3.43781e10i	0.583073	−	1.00991i
$220$	−3.15094e10			−0.906855
$221$	4.01278e10			1.13157
$222$	2.86401e10	−	4.96061e10i	0.791382	−	1.37071i
$223$	−1.28118e10	−	2.21907e10i	−0.346927	−	0.600896i	0.638775	−	0.769394i	$-0.279442\pi$
$223$	−1.28118e10	−	2.21907e10i	−0.346927	−	0.600896i	−0.985702	+	0.168498i	$0.946108\pi$
$224$	−4.04622e9	+	7.00826e9i	−0.107382	+	0.185992i
$225$	−5.02153e10	−	8.69755e10i	−1.30622	−	2.26243i
$226$	−3.33125e7	−	5.76989e7i	−0.000849414	−	0.00147123i
$227$	1.91170e10			0.477863			0.238931	−	0.971036i	$-0.423203\pi$
$227$	1.91170e10			0.477863			0.238931	+	0.971036i	$0.423203\pi$
$228$	−3.08192e10	+	9.23385e9i	−0.755292	+	0.226296i
$229$	−7.32315e10			−1.75970			−0.879849	−	0.475254i	$-0.842356\pi$
$229$	−7.32315e10			−1.75970			−0.879849	+	0.475254i	$0.842356\pi$
$230$	3.85834e10	+	6.68283e10i	0.909127	+	1.57465i
$231$	−4.52802e10	−	7.84276e10i	−1.04630	−	1.81224i
$232$	2.78771e9	−	4.82845e9i	0.0631759	−	0.109424i
$233$	1.88961e9	+	3.27291e9i	0.0420022	+	0.0727499i	0.886262	−	0.463184i	$-0.153293\pi$
$233$	1.88961e9	+	3.27291e9i	0.0420022	+	0.0727499i	−0.844260	+	0.535934i	$0.819960\pi$
$234$	−3.15399e10	+	5.46288e10i	−0.687685	+	1.19110i
$235$	7.62374e10			1.63066
$236$	−1.01856e10			−0.213737
$237$	−4.85431e8	+	8.40790e8i	−0.00999447	+	0.0173109i
$238$	1.83891e10	−	3.18508e10i	0.371504	−	0.643464i
$239$	4.67645e10			0.927098			0.463549	−	0.886071i	$-0.346576\pi$
$239$	4.67645e10			0.927098			0.463549	+	0.886071i	$0.346576\pi$
$240$	3.36462e10			0.654615
$241$	−3.30201e10	+	5.71925e10i	−0.630524	+	1.09210i	0.356921	+	0.934135i	$0.383827\pi$
$241$	−3.30201e10	+	5.71925e10i	−0.630524	+	1.09210i	−0.987445	+	0.157965i	$0.949507\pi$
$242$	3.64210e9	+	6.30830e9i	0.0682626	+	0.118234i
$243$	−3.27041e10	+	5.66452e10i	−0.601692	+	1.04216i
$244$	4.45130e9	+	7.70988e9i	0.0803957	+	0.139249i
$245$	2.22858e10	+	3.86001e10i	0.395167	+	0.684449i
$246$	1.12475e9			0.0195816
$247$	1.76337e10	−	7.44733e10i	0.301444	−	1.27311i
$248$	3.25407e10			0.546254
$249$	−3.60076e10	−	6.23670e10i	−0.593604	−	1.02815i
$250$	−2.74554e10	−	4.75542e10i	−0.444527	−	0.769943i
$251$	−4.91390e10	+	8.51112e10i	−0.781438	+	1.35349i	0.149666	+	0.988737i	$0.452180\pi$
$251$	−4.91390e10	+	8.51112e10i	−0.781438	+	1.35349i	−0.931104	+	0.364754i	$0.881153\pi$
$252$	2.89072e10	+	5.00687e10i	0.451547	+	0.782102i
$253$	5.51166e10	−	9.54647e10i	0.845746	−	1.46487i
$254$	−5.01909e10			−0.756612
$255$	−1.52914e11			−2.26473
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−3.66918e10	+	6.35521e10i	−0.524650	+	0.908721i	0.474938	+	0.880020i	$0.342471\pi$
$257$	−3.66918e10	+	6.35521e10i	−0.524650	+	0.908721i	−0.999588	+	0.0287018i	$0.990863\pi$
$258$	−1.34519e11			−1.89014
$259$	1.24884e11			1.72448
$260$	−4.00188e10	+	6.93145e10i	−0.543105	+	0.940685i
$261$	−1.99161e10	−	3.44956e10i	−0.265657	−	0.460131i
$262$	−2.40913e10	+	4.17274e10i	−0.315868	+	0.547099i
$263$	3.97549e10	+	6.88574e10i	0.512377	+	0.887462i	0.999897	+	0.0143507i	$0.00456812\pi$
$263$	3.97549e10	+	6.88574e10i	0.512377	+	0.887462i	−0.487520	+	0.873112i	$0.662099\pi$
$264$	−2.40319e10	−	4.16245e10i	−0.304489	−	0.527390i
$265$	9.05041e10			1.12736
$266$	−5.10312e10	−	4.81248e10i	−0.624983	−	0.589389i
$267$	8.18985e10			0.986223
$268$	−1.64010e10	−	2.84073e10i	−0.194206	−	0.336375i
$269$	−6.65846e10	−	1.15328e11i	−0.775333	−	1.34292i	−0.934607	−	0.355682i	$-0.884249\pi$
$269$	−6.65846e10	−	1.15328e11i	−0.775333	−	1.34292i	0.159274	−	0.987234i	$-0.449085\pi$
$270$	3.93463e10	−	6.81497e10i	0.450574	−	0.780418i
$271$	−8.52380e10	−	1.47636e11i	−0.960000	−	1.66277i	−0.722487	−	0.691384i	$-0.757001\pi$
$271$	−8.52380e10	−	1.47636e11i	−0.960000	−	1.66277i	−0.237513	−	0.971384i	$-0.576332\pi$
$272$	9.75979e9	−	1.69044e10i	0.108114	−	0.187258i
$273$	−2.30034e11			−2.50646
$274$	1.12074e11			1.20123
$275$	−9.10168e10	+	1.57646e11i	−0.959676	+	1.66221i
$276$	−5.88544e10	+	1.01939e11i	−0.610503	+	1.05742i
$277$	−2.37651e10			−0.242538			−0.121269	−	0.992620i	$-0.538696\pi$
$277$	−2.37651e10			−0.242538			−0.121269	+	0.992620i	$0.538696\pi$
$278$	6.34930e10			0.637564
$279$	1.16239e11	−	2.01333e11i	1.14851	−	1.98928i
$280$	3.66782e10	+	6.35285e10i	0.356613	+	0.617672i
$281$	−1.18712e9	+	2.05614e9i	−0.0113583	+	0.0196732i	−0.871649	−	0.490131i	$-0.836949\pi$
$281$	−1.18712e9	+	2.05614e9i	−0.0113583	+	0.0196732i	0.860290	+	0.509804i	$0.170282\pi$
$282$	5.81456e10	+	1.00711e11i	0.547515	+	0.948323i
$283$	9.50404e10	+	1.64615e11i	0.880784	+	1.52556i	0.850471	+	0.526022i	$0.176317\pi$
$283$	9.50404e10	+	1.64615e11i	0.880784	+	1.52556i	0.0303132	+	0.999540i	$0.490350\pi$
$284$	−5.12644e10			−0.467610
$285$	−6.71963e10	+	2.83794e11i	−0.603314	+	2.54801i
$286$	1.14334e11			1.01048
$287$	1.22610e9	+	2.12367e9i	0.0106674	+	0.0184765i
$288$	1.53421e10	+	2.65734e10i	0.131407	+	0.227604i
$289$	1.49381e10	−	2.58736e10i	0.125967	−	0.218181i
$290$	−2.52701e10	−	4.37690e10i	−0.209805	−	0.363393i
$291$	8.32561e10	−	1.44204e11i	0.680609	−	1.17885i
$292$	4.59339e10			0.369752
$293$	−3.59871e10			−0.285261			−0.142630	−	0.989776i	$-0.545556\pi$
$293$	−3.59871e10			−0.285261			−0.142630	+	0.989776i	$0.545556\pi$
$294$	−3.39943e10	+	5.88799e10i	−0.265365	+	0.459625i
$295$	−4.61651e10	+	7.99602e10i	−0.354907	+	0.614717i
$296$	6.62807e10			0.501850
$297$	−1.12413e11			−0.838323
$298$	3.61787e10	−	6.26633e10i	0.265754	−	0.460299i
$299$	−1.40003e11	−	2.42491e11i	−1.01301	−	1.75459i
$300$	9.71892e10	−	1.68337e11i	0.692744	−	1.19987i
$301$	−1.46641e11	−	2.53989e11i	−1.02969	−	1.78347i
$302$	6.70605e10	+	1.16152e11i	0.463912	+	0.803519i
$303$	5.80212e10			0.395453
$304$	−2.70842e10	−	2.55417e10i	−0.181880	−	0.171522i
$305$	8.07005e10			0.533982
$306$	−6.97263e10	−	1.20769e11i	−0.454621	−	0.787427i
$307$	1.05381e11	+	1.82525e11i	0.677080	+	1.17274i	0.975856	+	0.218414i	$0.0700884\pi$
$307$	1.05381e11	+	1.82525e11i	0.677080	+	1.17274i	−0.298776	+	0.954323i	$0.596578\pi$
$308$	5.23951e10	−	9.07509e10i	0.331751	−	0.574610i
$309$	4.39078e10	+	7.60506e10i	0.273986	+	0.474558i
$310$	1.47488e11	−	2.55456e11i	0.907045	−	1.57105i
$311$	2.24839e11			1.36285			0.681426	−	0.731887i	$-0.261360\pi$
$311$	2.24839e11			1.36285			0.681426	+	0.731887i	$0.261360\pi$
$312$	−1.22088e11			−0.729419
$313$	1.15546e11	−	2.00132e11i	0.680465	−	1.17860i	−0.294373	−	0.955690i	$-0.595111\pi$
$313$	1.15546e11	−	2.00132e11i	0.680465	−	1.17860i	0.974839	−	0.222910i	$-0.0715557\pi$
$314$	−3.36194e10	+	5.82305e10i	−0.195167	+	0.338039i
$315$	5.24076e11			2.99914
$316$	−1.12341e9			−0.00633793
$317$	−6.75045e10	+	1.16921e11i	−0.375462	+	0.650319i	−0.990396	−	0.138259i	$-0.955849\pi$
$317$	−6.75045e10	+	1.16921e11i	−0.375462	+	0.650319i	0.614934	+	0.788579i	$0.289183\pi$
$318$	6.90267e10	+	1.19558e11i	0.378525	+	0.655625i
$319$	−3.60985e10	+	6.25244e10i	−0.195178	+	0.338058i
$320$	1.94665e10	+	3.37170e10i	0.103780	+	0.179752i
$321$	9.97966e10	+	1.72853e11i	0.524618	+	0.908665i
$322$	−2.56632e11			−1.33033
$323$	1.23091e11	+	1.16081e11i	0.629239	+	0.593402i
$324$	−2.74146e10			−0.138207
$325$	2.31193e11	+	4.00439e11i	1.14948	+	1.99095i
$326$	4.67510e10	+	8.09751e10i	0.229251	+	0.397075i
$327$	1.88715e10	−	3.26864e10i	0.0912729	−	0.158089i
$328$	6.50740e8	+	1.12711e9i	0.00310438	+	0.00537695i
$329$	−1.26771e11	+	2.19573e11i	−0.596536	+	1.03323i
$330$	−4.35690e11			−2.02239
$331$	−1.29506e11			−0.593014			−0.296507	−	0.955031i	$-0.595822\pi$
$331$	−1.29506e11			−0.593014			−0.296507	+	0.955031i	$0.595822\pi$
$332$	4.16655e10	−	7.21667e10i	0.188215	−	0.325998i
$333$	2.36763e11	−	4.10085e11i	1.05515	−	1.82757i
$334$	−1.16903e11			−0.514003
$335$	−2.97344e11			−1.28990
$336$	−5.59483e10	+	9.69053e10i	−0.239475	+	0.414783i
$337$	−5.03028e10	−	8.71269e10i	−0.212450	−	0.367975i	0.740031	−	0.672573i	$-0.234811\pi$
$337$	−5.03028e10	−	8.71269e10i	−0.212450	−	0.367975i	−0.952481	+	0.304599i	$0.901478\pi$
$338$	6.03750e10	−	1.04573e11i	0.251612	−	0.435805i
$339$	−4.60622e8	−	7.97821e8i	−0.00189429	−	0.00328101i
$340$	−8.84707e10	−	1.53236e11i	−0.359041	−	0.621877i
$341$	−4.21375e11			−1.68762
$342$	−2.54777e11	+	7.63345e10i	−1.00703	+	0.301720i
$343$	1.63200e11			0.636645
$344$	−7.78279e10	−	1.34802e11i	−0.299656	−	0.519019i
$345$	5.33504e11	+	9.24056e11i	2.02746	+	3.51166i
$346$	−9.90855e10	+	1.71621e11i	−0.371679	+	0.643766i
$347$	−1.41770e11	−	2.45553e11i	−0.524930	−	0.909205i	−0.999579	−	0.0290297i	$-0.990758\pi$
$347$	−1.41770e11	−	2.45553e11i	−0.524930	−	0.909205i	0.474649	−	0.880175i	$-0.342575\pi$
$348$	3.85465e10	−	6.67645e10i	0.140890	−	0.244028i
$349$	−4.25087e11			−1.53378			−0.766891	−	0.641777i	$-0.778198\pi$
$349$	−4.25087e11			−1.53378			−0.766891	+	0.641777i	$0.778198\pi$
$350$	4.23789e11			1.50954
$351$	−1.42771e11	+	2.47286e11i	−0.502062	+	0.869597i
$352$	2.78081e10	−	4.81650e10i	0.0965448	−	0.167221i
$353$	−4.36686e10			−0.149687			−0.0748434	−	0.997195i	$-0.523846\pi$
$353$	−4.36686e10			−0.149687			−0.0748434	+	0.997195i	$0.523846\pi$
$354$	−1.40839e11			−0.476659
$355$	−2.32351e11	+	4.02444e11i	−0.776457	+	1.34486i
$356$	4.73836e10	+	8.20708e10i	0.156352	+	0.270809i
$357$	2.54271e11	−	4.40411e11i	0.828496	−	1.43500i
$358$	−8.88991e10	−	1.53978e11i	−0.286038	−	0.495432i
$359$	−1.91694e11	−	3.32024e11i	−0.609094	−	1.05498i	−0.991390	−	0.130941i	$-0.958200\pi$
$359$	−1.91694e11	−	3.32024e11i	−0.609094	−	1.05498i	0.382296	−	0.924040i	$-0.375133\pi$
$360$	2.78147e11			0.872798
$361$	2.69526e11	−	1.77435e11i	0.835253	−	0.549866i
$362$	1.30270e11			0.398708
$363$	5.03605e10	+	8.72269e10i	0.152233	+	0.263676i
$364$	−1.33090e11	−	2.30518e11i	−0.397363	−	0.688254i
$365$	2.08191e11	−	3.60598e11i	0.613966	−	1.06342i
$366$	6.15496e10	+	1.06607e11i	0.179292	+	0.310542i
$367$	2.72483e11	−	4.71955e11i	0.784047	−	1.35801i	−0.145519	−	0.989355i	$-0.546485\pi$
$367$	2.72483e11	−	4.71955e11i	0.784047	−	1.35801i	0.929566	−	0.368655i	$-0.120181\pi$
$368$	−1.36204e11			−0.387147
$369$	9.29809e9			0.0261081
$370$	3.00411e11	−	5.20327e11i	0.833313	−	1.44334i
$371$	−1.50494e11	+	2.60663e11i	−0.412417	+	0.714326i
$372$	4.49951e11			1.21821
$373$	−1.40020e11			−0.374542			−0.187271	−	0.982308i	$-0.559964\pi$
$373$	−1.40020e11			−0.374542			−0.187271	+	0.982308i	$0.559964\pi$
$374$	−1.26381e11	+	2.18898e11i	−0.334010	+	0.578522i
$375$	−3.79634e11	−	6.57546e11i	−0.991345	−	1.71706i
$376$	−6.72820e10	+	1.16536e11i	−0.173602	+	0.300687i
$377$	9.16943e10	+	1.58819e11i	0.233779	+	0.404918i
$378$	1.30853e11	+	2.26644e11i	0.329663	+	0.570994i
$379$	2.99995e11			0.746857			0.373428	−	0.927659i	$-0.378182\pi$
$379$	2.99995e11			0.746857			0.373428	+	0.927659i	$0.378182\pi$
$380$	−3.23268e11	+	9.68554e10i	−0.795311	+	0.238286i
$381$	−6.94006e11			−1.68733
$382$	−9.02345e9	−	1.56291e10i	−0.0216814	−	0.0375533i
$383$	2.33490e11	+	4.04417e11i	0.554465	+	0.960361i	0.997945	+	0.0640768i	$0.0204103\pi$
$383$	2.33490e11	+	4.04417e11i	0.554465	+	0.960361i	−0.443480	+	0.896284i	$0.646256\pi$
$384$	−2.96939e10	+	5.14314e10i	−0.0696911	+	0.120708i
$385$	−4.74952e11	−	8.22640e11i	−1.10173	−	1.90826i
$386$	2.44051e11	−	4.22709e11i	0.559548	−	0.969166i
$387$	−1.11204e12			−2.52013
$388$	1.92676e11			0.431604
$389$	1.14176e11	−	1.97759e11i	0.252815	−	0.437888i	−0.711485	−	0.702701i	$-0.751977\pi$
$389$	1.14176e11	−	1.97759e11i	0.252815	−	0.437888i	0.964300	+	0.264813i	$0.0853103\pi$
$390$	−5.53352e11	+	9.58434e11i	−1.21119	+	2.09783i
$391$	6.19015e11			1.33939
$392$	−7.86717e10			−0.168280
$393$	−3.33118e11	+	5.76978e11i	−0.704421	+	1.22009i
$394$	1.05716e11	+	1.83106e11i	0.221009	+	0.382798i
$395$	−5.09176e9	+	8.81920e9i	−0.0105240	+	0.0182281i
$396$	−1.98668e11	−	3.44102e11i	−0.405974	−	0.703168i
$397$	2.55061e11	+	4.41779e11i	0.515332	+	0.892582i	0.999842	+	0.0177958i	$0.00566488\pi$
$397$	2.55061e11	+	4.41779e11i	0.515332	+	0.892582i	−0.484509	+	0.874786i	$0.661002\pi$
$398$	3.28308e11			0.655855
$399$	−7.05624e11	−	6.65437e11i	−1.39378	−	1.31440i
$400$	2.24921e11			0.439299
$401$	4.01514e11	+	6.95442e11i	0.775444	+	1.34311i	0.934544	+	0.355846i	$0.115807\pi$
$401$	4.01514e11	+	6.95442e11i	0.775444	+	1.34311i	−0.159100	+	0.987262i	$0.550859\pi$
$402$	−2.26782e11	−	3.92797e11i	−0.433102	−	0.750155i
$403$	−5.35170e11	+	9.26942e11i	−1.01069	+	1.75057i
$404$	3.35690e10	+	5.81433e10i	0.0626935	+	0.108588i
$405$	−1.24254e11	+	2.15215e11i	−0.229490	+	0.397488i
$406$	1.68080e11			0.307008
$407$	−8.58278e11			−1.55043
$408$	1.34952e11	−	2.33743e11i	0.241106	−	0.417607i
$409$	7.92650e10	−	1.37291e11i	0.140064	−	0.242598i	−0.787457	−	0.616370i	$-0.788603\pi$
$409$	7.92650e10	−	1.37291e11i	0.140064	−	0.242598i	0.927521	+	0.373772i	$0.121936\pi$
$410$	1.17977e10			0.0206191
$411$	1.54968e12			2.67888
$412$	−5.08071e10	+	8.80005e10i	−0.0868734	+	0.150469i
$413$	−1.53530e11	−	2.65922e11i	−0.259668	−	0.449759i
$414$	−4.86538e11	+	8.42709e11i	−0.813983	+	1.40986i
$415$	−3.77690e11	−	6.54178e11i	−0.625056	−	1.08263i
$416$	−7.06358e10	−	1.22345e11i	−0.115639	−	0.200293i
$417$	8.77937e11			1.42184
$418$	3.50717e11	+	3.30743e11i	0.561907	+	0.529905i
$419$	8.75198e11			1.38721			0.693606	−	0.720354i	$-0.256021\pi$
$419$	8.75198e11			1.38721			0.693606	+	0.720354i	$0.256021\pi$
$420$	5.07161e11	+	8.78429e11i	0.795288	+	1.37748i
$421$	−5.35192e11	−	9.26979e11i	−0.830309	−	1.43814i	−0.897793	−	0.440417i	$-0.854830\pi$
$421$	−5.35192e11	−	9.26979e11i	−0.830309	−	1.43814i	0.0674839	−	0.997720i	$-0.478503\pi$
$422$	3.99370e11	−	6.91730e11i	0.613013	−	1.06177i
$423$	4.80679e11	+	8.32560e11i	0.730001	+	1.26440i
$424$	−7.98729e10	+	1.38344e11i	−0.120020	+	0.207880i
$425$	−1.02221e12			−1.51981
$426$	−7.08849e11			−1.04282
$427$	−1.34192e11	+	2.32427e11i	−0.195344	+	0.338347i
$428$	−1.15478e11	+	2.00013e11i	−0.166342	+	0.288112i
$429$	1.58093e12			2.25349
$430$	−1.41099e12			−1.99029
$431$	4.50927e11	−	7.81028e11i	0.629446	−	1.09023i	−0.358217	−	0.933638i	$-0.616615\pi$
$431$	4.50927e11	−	7.81028e11i	0.629446	−	1.09023i	0.987663	−	0.156594i	$-0.0500513\pi$
$432$	6.94488e10	+	1.20289e11i	0.0959373	+	0.166168i
$433$	5.39128e10	−	9.33797e10i	0.0737049	−	0.127661i	−0.826817	−	0.562470i	$-0.809851\pi$
$433$	5.39128e10	−	9.33797e10i	0.0737049	−	0.127661i	0.900522	+	0.434810i	$0.143184\pi$
$434$	4.90498e11	+	8.49567e11i	0.663641	+	1.14946i
$435$	−3.49417e11	−	6.05208e11i	−0.467889	−	0.810407i
$436$	4.36736e10			0.0578802
$437$	2.72019e11	−	1.14883e12i	0.356807	−	1.50692i
$438$	6.35143e11			0.824589
$439$	5.46559e11	+	9.46668e11i	0.702339	+	1.21649i	0.967643	+	0.252322i	$0.0811943\pi$
$439$	5.46559e11	+	9.46668e11i	0.702339	+	1.21649i	−0.265304	+	0.964165i	$0.585472\pi$
$440$	−2.52075e11	−	4.36607e11i	−0.320622	−	0.555333i
$441$	−2.81025e11	+	4.86749e11i	−0.353811	+	0.612818i
$442$	3.21022e11	+	5.56027e11i	0.400069	+	0.692940i
$443$	−5.43557e10	+	9.41469e10i	−0.0670546	+	0.116142i	−0.897604	−	0.440804i	$-0.854693\pi$
$443$	−5.43557e10	+	9.41469e10i	−0.0670546	+	0.116142i	0.830549	+	0.556946i	$0.188027\pi$
$444$	9.16484e11			1.11918
$445$	8.59047e11			1.03848
$446$	2.04989e11	−	3.55051e11i	0.245315	−	0.424898i
$447$	5.00254e11	−	8.66464e11i	0.592661	−	1.02652i
$448$	−1.29479e11			−0.151862
$449$	−2.46596e11			−0.286336			−0.143168	−	0.989698i	$-0.545729\pi$
$449$	−2.46596e11			−0.286336			−0.143168	+	0.989698i	$0.545729\pi$
$450$	8.03446e11	−	1.39161e12i	0.923635	−	1.59978i
$451$	−8.42653e9	−	1.45952e10i	−0.00959079	−	0.0166117i
$452$	5.33000e8	−	9.23183e8i	0.000600626	−	0.00104032i
$453$	9.27266e11	+	1.60607e12i	1.03458	+	1.79194i
$454$	1.52936e11	+	2.64893e11i	0.168950	+	0.292630i
$455$	−2.41287e12			−2.63926
$456$	−3.74502e11	−	3.53173e11i	−0.405613	−	0.382513i
$457$	8.26746e10			0.0886644			0.0443322	−	0.999017i	$-0.485884\pi$
$457$	8.26746e10			0.0886644			0.0443322	+	0.999017i	$0.485884\pi$
$458$	−5.85852e11	−	1.01472e12i	−0.622147	−	1.07759i
$459$	−3.15628e11	−	5.46683e11i	−0.331908	−	0.574882i
$460$	−6.17334e11	+	1.06925e12i	−0.642850	+	1.11345i
$461$	−1.83090e11	−	3.17121e11i	−0.188804	−	0.327018i	0.756048	−	0.654516i	$-0.227128\pi$
$461$	−1.83090e11	−	3.17121e11i	−0.188804	−	0.327018i	−0.944852	+	0.327499i	$0.893794\pi$
$462$	7.24483e11	−	1.25484e12i	0.739843	−	1.28145i
$463$	4.49349e11			0.454432			0.227216	−	0.973844i	$-0.427038\pi$
$463$	4.49349e11			0.454432			0.227216	+	0.973844i	$0.427038\pi$
$464$	8.92067e10			0.0893442
$465$	2.03936e12	−	3.53228e12i	2.02281	−	3.50362i
$466$	−3.02338e10	+	5.23665e10i	−0.0297000	+	0.0514419i
$467$	−8.95871e11			−0.871605			−0.435802	−	0.900042i	$-0.643535\pi$
$467$	−8.95871e11			−0.871605			−0.435802	+	0.900042i	$0.643535\pi$
$468$	−1.00928e12			−0.972533
$469$	4.94435e11	−	8.56387e11i	0.471880	−	0.817320i
$470$	6.09899e11	+	1.05638e12i	0.576524	+	0.998569i
$471$	−4.64866e11	+	8.05171e11i	−0.435245	+	0.753866i
$472$	−8.14844e10	−	1.41135e11i	−0.0755676	−	0.130887i
$473$	1.00781e12	+	1.74557e12i	0.925767	+	1.60347i
$474$	−1.55338e10			−0.0141343
$475$	−4.49199e11	+	1.89713e12i	−0.404872	+	1.70992i
$476$	5.88450e11			0.525386
$477$	5.70631e11	+	9.88362e11i	0.504688	+	0.874144i
$478$	3.74116e11	+	6.47988e11i	0.327779	+	0.567729i
$479$	6.74452e11	−	1.16819e12i	0.585385	−	1.01392i	−0.409443	−	0.912336i	$-0.634277\pi$
$479$	6.74452e11	−	1.16819e12i	0.585385	−	1.01392i	0.994827	−	0.101580i	$-0.0323899\pi$
$480$	2.69170e11	+	4.66216e11i	0.231441	+	0.400868i
$481$	−1.09006e12	+	1.88805e12i	−0.928537	+	1.60827i
$482$	−1.05664e12			−0.891695
$483$	−3.54853e12			−2.96679
$484$	−5.82736e10	+	1.00933e11i	−0.0482689	+	0.0836043i
$485$	8.73288e11	−	1.51258e12i	0.716671	−	1.24131i
$486$	−1.04653e12			−0.850921
$487$	3.62757e11			0.292238			0.146119	−	0.989267i	$-0.453322\pi$
$487$	3.62757e11			0.292238			0.146119	+	0.989267i	$0.453322\pi$
$488$	−7.12208e10	+	1.23358e11i	−0.0568484	+	0.0984642i
$489$	6.46440e11	+	1.11967e12i	0.511256	+	0.885522i
$490$	−3.56572e11	+	6.17601e11i	−0.279425	+	0.483978i
$491$	2.36413e11	+	4.09480e11i	0.183571	+	0.317955i	0.943094	−	0.332526i	$-0.107901\pi$
$491$	2.36413e11	+	4.09480e11i	0.183571	+	0.317955i	−0.759523	+	0.650481i	$0.774567\pi$
$492$	8.99799e9	+	1.55850e10i	0.00692313	+	0.0119912i
$493$	−4.05423e11			−0.309098
$494$	1.17300e12	−	3.51447e11i	0.886192	−	0.265515i
$495$	−3.60177e12			−2.69645
$496$	2.60326e11	+	4.50898e11i	0.193130	+	0.334511i
$497$	−7.72726e11	−	1.33840e12i	−0.568096	−	0.983972i
$498$	5.76121e11	−	9.97871e11i	0.419741	−	0.727014i
$499$	5.47227e11	+	9.47825e11i	0.395107	+	0.684346i	0.993115	−	0.117145i	$-0.0373741\pi$
$499$	5.47227e11	+	9.47825e11i	0.395107	+	0.684346i	−0.598008	+	0.801490i	$0.704041\pi$
$500$	4.39286e11	−	7.60866e11i	0.314328	−	0.544432i
$501$	−1.61645e12			−1.14628
$502$	−1.57245e12			−1.10512
$503$	−4.32282e10	+	7.48734e10i	−0.0301100	+	0.0521521i	−0.880688	−	0.473697i	$-0.842919\pi$
$503$	−4.32282e10	+	7.48734e10i	−0.0301100	+	0.0521521i	0.850578	+	0.525849i	$0.176252\pi$
$504$	−4.62515e11	+	8.01099e11i	−0.319292	+	0.553030i
$505$	6.08594e11			0.416406
$506$	1.76373e12			1.19607
$507$	8.34824e11	−	1.44596e12i	0.561124	−	0.971896i
$508$	−4.01527e11	−	6.95466e11i	−0.267503	−	0.463329i
$509$	−1.09337e12	+	1.89377e12i	−0.721998	+	1.25054i	0.238200	+	0.971216i	$0.423443\pi$
$509$	−1.09337e12	+	1.89377e12i	−0.721998	+	1.25054i	−0.960198	+	0.279321i	$0.909891\pi$
$510$	−1.22331e12	−	2.11884e12i	−0.800703	−	1.38686i
$511$	6.92377e11	+	1.19923e12i	0.449209	+	0.778054i
$512$	−6.87195e10			−0.0441942
$513$	−1.15329e12	+	3.45541e11i	−0.735209	+	0.220278i
$514$	−1.17414e12			−0.741968
$515$	4.60557e11	+	7.97708e11i	0.288503	+	0.499702i
$516$	−1.07615e12	−	1.86395e12i	−0.668266	−	1.15747i
$517$	8.71245e11	−	1.50904e12i	0.536331	−	0.928952i
$518$	9.99071e11	+	1.73044e12i	0.609695	+	1.05602i
$519$	−1.37009e12	+	2.37306e12i	−0.828886	+	1.43567i
$520$	−1.28060e12			−0.768066
$521$	−3.20922e11			−0.190823			−0.0954113	−	0.995438i	$-0.530417\pi$
$521$	−3.20922e11			−0.190823			−0.0954113	+	0.995438i	$0.530417\pi$
$522$	3.18657e11	−	5.51930e11i	0.187848	−	0.325362i
$523$	−1.92290e11	+	3.33056e11i	−0.112383	+	0.194653i	−0.916730	−	0.399506i	$-0.869182\pi$
$523$	−1.92290e11	+	3.33056e11i	−0.112383	+	0.194653i	0.804348	+	0.594159i	$0.202515\pi$
$524$	−7.70923e11			−0.446704
$525$	5.85987e12			3.36644
$526$	−6.36078e11	+	1.10172e12i	−0.362305	+	0.627531i
$527$	−1.18312e12	−	2.04922e12i	−0.668159	−	1.15729i
$528$	3.84511e11	−	6.65993e11i	0.215306	−	0.372921i
$529$	−1.25912e12	−	2.18086e12i	−0.699062	−	1.21081i
$530$	7.24033e11	+	1.25406e12i	0.398581	+	0.690363i
$531$	−1.16429e12			−0.635529
$532$	2.58588e11	−	1.09211e12i	0.139961	−	0.591103i
$533$	−4.28087e10			−0.0229752
$534$	6.55188e11	+	1.13482e12i	0.348682	+	0.603936i
$535$	1.04678e12	+	1.81308e12i	0.552414	+	0.956809i
$536$	2.62416e11	−	4.54517e11i	0.137325	−	0.237853i
$537$	−1.22924e12	−	2.12910e12i	−0.637897	−	1.10487i
$538$	1.06535e12	−	1.84525e12i	0.548243	−	0.949585i
$539$	1.01873e12			0.519889
$540$	1.25908e12			0.637208
$541$	−1.30885e12	+	2.26700e12i	−0.656907	+	1.13780i	0.324505	+	0.945884i	$0.394802\pi$
$541$	−1.30885e12	+	2.26700e12i	−0.656907	+	1.13780i	−0.981412	+	0.191912i	$0.938531\pi$
$542$	1.36381e12	−	2.36218e12i	0.678822	−	1.17575i
$543$	1.80128e12			0.889165
$544$	3.12313e11			0.152896
$545$	1.97946e11	−	3.42853e11i	0.0961089	−	0.166465i
$546$	−1.84027e12	−	3.18744e12i	−0.886166	−	1.53488i
$547$	−6.82342e11	+	1.18185e12i	−0.325881	+	0.564443i	−0.981690	−	0.190484i	$-0.938994\pi$
$547$	−6.82342e11	+	1.18185e12i	−0.325881	+	0.564443i	0.655809	+	0.754927i	$0.272328\pi$
$548$	8.96588e11	+	1.55294e12i	0.424698	+	0.735599i
$549$	5.08819e11	+	8.81300e11i	0.239049	+	0.414046i
$550$	−2.91254e12			−1.35719
$551$	−1.78158e11	+	7.52426e11i	−0.0823425	+	0.347761i
$552$	−1.88334e12			−0.863382
$553$	−1.69336e10	−	2.93298e10i	−0.00769991	−	0.0133366i
$554$	−1.90121e11	−	3.29299e11i	−0.0857502	−	0.148524i
$555$	4.15388e12	−	7.19473e12i	1.85838	−	3.21881i
$556$	5.07944e11	+	8.79784e11i	0.225413	+	0.390427i
$557$	−9.45755e11	+	1.63810e12i	−0.416323	+	0.721092i	−0.995566	−	0.0940623i	$-0.970015\pi$
$557$	−9.45755e11	+	1.63810e12i	−0.416323	+	0.721092i	0.579243	+	0.815155i	$0.303348\pi$
$558$	3.71966e12			1.62424
$559$	5.11989e12			2.21772
$560$	−5.86852e11	+	1.01646e12i	−0.252163	+	0.436760i
$561$	−1.74751e12	+	3.02677e12i	−0.744880	+	1.29017i
$562$	−3.79877e10			−0.0160631
$563$	−1.19599e12			−0.501694			−0.250847	−	0.968027i	$-0.580709\pi$
$563$	−1.19599e12			−0.501694			−0.250847	+	0.968027i	$0.580709\pi$
$564$	−9.30329e11	+	1.61138e12i	−0.387151	+	0.670566i
$565$	−4.83155e9	−	8.36848e9i	−0.00199466	−	0.00345485i
$566$	−1.52065e12	+	2.63384e12i	−0.622808	+	1.07874i
$567$	−4.13230e11	−	7.15736e11i	−0.167907	−	0.290823i
$568$	−4.10116e11	−	7.10341e11i	−0.165325	−	0.286351i
$569$	2.90977e12			1.16373			0.581866	−	0.813285i	$-0.302323\pi$
$569$	2.90977e12			1.16373			0.581866	+	0.813285i	$0.302323\pi$
$570$	−4.46993e12	+	1.33925e12i	−1.77363	+	0.531404i
$571$	−4.52992e12			−1.78332			−0.891658	−	0.452710i	$-0.850457\pi$
$571$	−4.52992e12			−1.78332			−0.891658	+	0.452710i	$0.850457\pi$
$572$	9.14673e11	+	1.58426e12i	0.357259	+	0.618791i
$573$	−1.24770e11	−	2.16108e11i	−0.0483520	−	0.0837482i
$574$	−1.96177e10	+	3.39788e10i	−0.00754299	+	0.0130648i
$575$	3.56641e12	+	6.17721e12i	1.36059	+	2.35661i
$576$	−2.45474e11	+	4.25174e11i	−0.0929190	+	0.160940i
$577$	3.23398e12			1.21464			0.607318	−	0.794459i	$-0.292245\pi$
$577$	3.23398e12			1.21464			0.607318	+	0.794459i	$0.292245\pi$
$578$	4.78020e11			0.178144
$579$	3.37457e12	−	5.84492e12i	1.24786	−	2.16135i
$580$	4.04321e11	−	7.00305e11i	0.148354	−	0.256957i
$581$	2.51215e12			0.914646
$582$	2.66420e12			0.962527
$583$	1.03429e12	−	1.79143e12i	0.370793	−	0.642233i
$584$	3.67471e11	+	6.36479e11i	0.130727	+	0.226426i
$585$	−4.57446e12	+	7.92319e12i	−1.61487	+	2.79704i
$586$	−2.87897e11	−	4.98651e11i	−0.100855	−	0.174686i
$587$	−1.40821e12	−	2.43909e12i	−0.489549	−	0.847923i	0.510379	−	0.859950i	$-0.329505\pi$
$587$	−1.40821e12	−	2.43909e12i	−0.489549	−	0.847923i	−0.999928	+	0.0120265i	$0.996172\pi$
$588$	−1.08782e12			−0.375283
$589$	−4.32306e12	+	1.29525e12i	−1.48004	+	0.443439i
$590$	−1.47728e12			−0.501914
$591$	1.46177e12	+	2.53187e12i	0.492875	+	0.853684i
$592$	5.30246e11	+	9.18412e11i	0.177431	+	0.307319i
$593$	−9.86287e11	+	1.70830e12i	−0.327535	+	0.567307i	−0.982022	−	0.188766i	$-0.939551\pi$
$593$	−9.86287e11	+	1.70830e12i	−0.327535	+	0.567307i	0.654487	+	0.756073i	$0.272885\pi$
$594$	−8.99302e11	−	1.55764e12i	−0.296392	−	0.513366i
$595$	2.66710e12	−	4.61955e12i	0.872393	−	1.51103i
$596$	1.15772e12			0.375832
$597$	4.53962e12			1.46263
$598$	2.24004e12	−	3.87986e12i	0.716309	−	1.24068i
$599$	2.39810e12	−	4.15363e12i	0.761108	−	1.31828i	−0.181172	−	0.983451i	$-0.557989\pi$
$599$	2.39810e12	−	4.15363e12i	0.761108	−	1.31828i	0.942280	−	0.334826i	$-0.108678\pi$
$600$	3.11006e12			0.979687
$601$	−5.16477e12			−1.61479			−0.807395	−	0.590011i	$-0.799123\pi$
$601$	−5.16477e12			−1.61479			−0.807395	+	0.590011i	$0.799123\pi$
$602$	2.34625e12	−	4.06383e12i	0.728100	−	1.26111i
$603$	−1.87476e12	−	3.24718e12i	−0.577455	−	1.00018i
$604$	−1.07297e12	+	1.85843e12i	−0.328035	+	0.568174i
$605$	5.28240e11	+	9.14938e11i	0.160299	+	0.277647i
$606$	4.64169e11	+	8.03965e11i	0.139814	+	0.242164i
$607$	−4.18781e12			−1.25210			−0.626048	−	0.779785i	$-0.715329\pi$
$607$	−4.18781e12			−1.25210			−0.626048	+	0.779785i	$0.715329\pi$
$608$	1.37242e11	−	5.79623e11i	0.0407307	−	0.172020i
$609$	2.32410e12			0.684663
$610$	6.45604e11	+	1.11822e12i	0.188791	+	0.326996i
$611$	−2.21306e12	−	3.83314e12i	−0.642404	−	1.11268i
$612$	1.11562e12	−	1.93231e12i	0.321466	−	0.556795i
$613$	−7.34521e11	−	1.27223e12i	−0.210103	−	0.363909i	0.741644	−	0.670794i	$-0.234047\pi$
$613$	−7.34521e11	−	1.27223e12i	−0.210103	−	0.363909i	−0.951747	+	0.306885i	$0.900713\pi$
$614$	−1.68610e12	+	2.92041e12i	−0.478768	+	0.829251i
$615$	1.63130e11			0.0459829
$616$	1.67664e12			0.469167
$617$	4.28368e11	−	7.41956e11i	0.118996	−	0.206108i	−0.800374	−	0.599501i	$-0.795366\pi$
$617$	4.28368e11	−	7.41956e11i	0.118996	−	0.206108i	0.919370	+	0.393393i	$0.128699\pi$
$618$	−7.02525e11	+	1.21681e12i	−0.193738	+	0.335563i
$619$	−6.35140e11			−0.173885			−0.0869423	−	0.996213i	$-0.527710\pi$
$619$	−6.35140e11			−0.173885			−0.0869423	+	0.996213i	$0.527710\pi$
$620$	4.71961e12			1.28275
$621$	−2.20240e12	+	3.81466e12i	−0.594269	+	1.02930i
$622$	1.79871e12	+	3.11545e12i	0.481841	+	0.834573i
$623$	−1.42846e12	+	2.47416e12i	−0.379902	+	0.658009i
$624$	−9.76703e11	−	1.69170e12i	−0.257888	−	0.446676i
$625$	−6.30463e11	−	1.09199e12i	−0.165272	−	0.286260i
$626$	3.69748e12			0.962324
$627$	4.84948e12	+	4.57329e12i	1.25312	+	1.18175i
$628$	−1.07582e12			−0.276008
$629$	−2.40984e12	−	4.17396e12i	−0.613846	−	1.06321i
$630$	4.19261e12	+	7.26181e12i	1.06036	+	1.83659i
$631$	−1.53436e12	+	2.65759e12i	−0.385297	+	0.667354i	−0.991810	−	0.127719i	$-0.959234\pi$
$631$	−1.53436e12	+	2.65759e12i	−0.385297	+	0.667354i	0.606513	+	0.795073i	$0.292568\pi$
$632$	−8.98730e9	−	1.55665e10i	−0.00224080	−	0.00388117i
$633$	5.52222e12	−	9.56476e12i	1.36709	−	2.36787i
$634$	−2.16014e12			−0.530983
$635$	−7.27954e12			−1.77673
$636$	−1.10443e12	+	1.91292e12i	−0.267658	+	0.463597i
$637$	1.29385e12	−	2.24101e12i	0.311355	−	0.539283i
$638$	−1.15515e12			−0.276023
$639$	−5.85993e12			−1.39040
$640$	−3.11465e11	+	5.39473e11i	−0.0733836	+	0.127104i
$641$	−2.48590e12	−	4.30571e12i	−0.581598	−	1.00736i	−0.995290	−	0.0969410i	$-0.969094\pi$
$641$	−2.48590e12	−	4.30571e12i	−0.581598	−	1.00736i	0.413692	−	0.910417i	$-0.364239\pi$
$642$	−1.59675e12	+	2.76564e12i	−0.370961	+	0.642523i
$643$	−2.00455e12	−	3.47199e12i	−0.462454	−	0.800994i	0.536629	−	0.843819i	$-0.319698\pi$
$643$	−2.00455e12	−	3.47199e12i	−0.462454	−	0.800994i	−0.999083	+	0.0428247i	$0.986364\pi$
$644$	−2.05305e12	−	3.55599e12i	−0.470342	−	0.814657i
$645$	−1.95102e13			−4.43857
$646$	−6.23733e11	+	2.63425e12i	−0.140913	+	0.595128i
$647$	3.65459e12			0.819917			0.409959	−	0.912104i	$-0.365543\pi$
$647$	3.65459e12			0.819917			0.409959	+	0.912104i	$0.365543\pi$
$648$	−2.19317e11	−	3.79868e11i	−0.0488635	−	0.0846341i
$649$	1.05515e12	+	1.82758e12i	0.233461	+	0.404367i
$650$	−3.69909e12	+	6.40702e12i	−0.812803	+	1.40782i
$651$	6.78226e12	+	1.17472e13i	1.47999	+	2.56343i
$652$	−7.48016e11	+	1.29560e12i	−0.162105	+	0.280774i
$653$	8.92252e11			0.192034			0.0960170	−	0.995380i	$-0.469390\pi$
$653$	8.92252e11			0.192034			0.0960170	+	0.995380i	$0.469390\pi$
$654$	6.03888e11			0.129079
$655$	−3.49414e12	+	6.05202e12i	−0.741744	+	1.28474i
$656$	−1.04118e10	+	1.80338e10i	−0.00219513	+	0.00380208i
$657$	5.25061e12			1.09942
$658$	−4.05666e12			−0.843630
$659$	6.60689e11	−	1.14435e12i	0.136462	−	0.236360i	−0.789693	−	0.613502i	$-0.789760\pi$
$659$	6.60689e11	−	1.14435e12i	0.136462	−	0.236360i	0.926155	+	0.377143i	$0.123093\pi$
$660$	−3.48552e12	−	6.03710e12i	−0.715023	−	1.23846i
$661$	−7.58645e11	+	1.31401e12i	−0.154572	+	0.267727i	−0.932903	−	0.360127i	$-0.882733\pi$
$661$	−7.58645e11	+	1.31401e12i	−0.154572	+	0.267727i	0.778331	+	0.627854i	$0.216067\pi$
$662$	−1.03605e12	−	1.79449e12i	−0.209662	−	0.363145i
$663$	4.43887e12	+	7.68836e12i	0.892200	+	1.54533i
$664$	1.33329e12			0.266177
$665$	−7.40141e12	−	6.97988e12i	−1.46763	−	1.38405i
$666$	7.57640e12			1.49221
$667$	1.41449e12	+	2.44996e12i	0.276715	+	0.479284i
$668$	−9.35221e11	−	1.61985e12i	−0.181727	−	0.314761i
$669$	2.83445e12	−	4.90941e12i	0.547080	−	0.947570i
$670$	−2.37875e12	−	4.12012e12i	−0.456050	−	0.789901i
$671$	9.22249e11	−	1.59738e12i	0.175629	−	0.304199i
$672$	−1.79035e12			−0.338669
$673$	−2.38251e12			−0.447679			−0.223840	−	0.974626i	$-0.571859\pi$
$673$	−2.38251e12			−0.447679			−0.223840	+	0.974626i	$0.571859\pi$
$674$	8.04844e11	−	1.39403e12i	0.150225	−	0.260197i
$675$	3.63693e12	−	6.29935e12i	0.674323	−	1.16796i
$676$	1.93200e12			0.355834
$677$	−1.00027e12			−0.183008			−0.0915040	−	0.995805i	$-0.529167\pi$
$677$	−1.00027e12			−0.183008			−0.0915040	+	0.995805i	$0.529167\pi$
$678$	7.36996e9	−	1.27651e10i	0.00133946	−	0.00232002i
$679$	2.90428e12	+	5.03035e12i	0.524353	+	0.908206i
$680$	1.41553e12	−	2.45177e12i	0.253880	−	0.439734i
$681$	2.11469e12	+	3.66276e12i	0.376778	+	0.652598i
$682$	−3.37100e12	−	5.83874e12i	−0.596663	−	1.03345i
$683$	1.12289e12			0.197445			0.0987223	−	0.995115i	$-0.468524\pi$
$683$	1.12289e12			0.197445			0.0987223	+	0.995115i	$0.468524\pi$
$684$	−3.09594e12	−	2.91962e12i	−0.540804	−	0.510004i
$685$	1.62548e13			2.82081
$686$	1.30560e12	+	2.26137e12i	0.225088	+	0.389864i
$687$	−8.10075e12	−	1.40309e13i	−1.38746	−	2.40315i
$688$	1.24525e12	−	2.15683e12i	0.211889	−	0.367002i
$689$	−2.62721e12	−	4.55045e12i	−0.444127	−	0.769251i
$690$	−8.53607e12	+	1.47849e13i	−1.43363	+	2.48312i
$691$	−3.89397e12			−0.649743			−0.324872	−	0.945758i	$-0.605321\pi$
$691$	−3.89397e12			−0.649743			−0.324872	+	0.945758i	$0.605321\pi$
$692$	−3.17073e12			−0.525633
$693$	5.98917e12	−	1.03735e13i	0.986432	−	1.70855i
$694$	2.26832e12	−	3.92884e12i	0.371181	−	0.642905i
$695$	9.20883e12			1.49718
$696$	1.23349e12			0.199248
$697$	4.73193e10	−	8.19594e10i	0.00759435	−	0.0131538i
$698$	−3.40070e12	−	5.89019e12i	−0.542274	−	0.939246i
$699$	−4.18053e11	+	7.24088e11i	−0.0662344	+	0.114721i
$700$	3.39031e12	+	5.87220e12i	0.533702	+	0.924399i
$701$	−2.10803e12	−	3.65121e12i	−0.329720	−	0.571091i	0.652736	−	0.757585i	$-0.273621\pi$
$701$	−2.10803e12	−	3.65121e12i	−0.329720	−	0.571091i	−0.982456	+	0.186494i	$0.940288\pi$
$702$	−4.56866e12			−0.710023
$703$	−8.80544e12	+	2.63823e12i	−1.35973	+	0.407393i
$704$	8.89859e11			0.136535
$705$	8.43326e12	+	1.46068e13i	1.28571	+	2.22692i
$706$	−3.49349e11	−	6.05090e11i	−0.0529223	−	0.0916641i
$707$	−1.01199e12	+	1.75283e12i	−0.152332	+	0.263847i
$708$	−1.12671e12	−	1.95152e12i	−0.168524	−	0.291893i
$709$	3.22785e12	−	5.59081e12i	0.479740	−	0.830934i	−0.519990	−	0.854172i	$-0.674064\pi$
$709$	3.22785e12	−	5.59081e12i	0.479740	−	0.830934i	0.999730	+	0.0232386i	$0.00739774\pi$
$710$	−7.43524e12			−1.09808
$711$	−1.28415e11			−0.0188453
$712$	−7.58137e11	+	1.31313e12i	−0.110557	+	0.191491i
$713$	−8.25560e12	+	1.42991e13i	−1.19632	+	2.07208i
$714$	8.13669e12			1.17167
$715$	1.65827e13			2.37289
$716$	1.42238e12	−	2.46364e12i	0.202259	−	0.350323i
$717$	5.17302e12	+	8.95993e12i	0.730984	+	1.26610i
$718$	3.06711e12	−	5.31239e12i	0.430694	−	0.745984i
$719$	−3.35296e12	−	5.80750e12i	−0.467895	−	0.810418i	0.531432	−	0.847101i	$-0.321654\pi$
$719$	−3.35296e12	−	5.80750e12i	−0.467895	−	0.810418i	−0.999327	+	0.0366829i	$0.988321\pi$
$720$	2.22518e12	+	3.85412e12i	0.308581	+	0.534477i
$721$	−3.06333e12			−0.422168
$722$	4.61482e12	+	2.31518e12i	0.632029	+	0.317079i
$723$	−1.46105e13			−1.98858
$724$	1.04216e12	+	1.80507e12i	0.140965	+	0.244158i
$725$	−2.33581e12	−	4.04575e12i	−0.313991	−	0.543848i
$726$	−8.05767e11	+	1.39563e12i	−0.107645	+	0.186447i
$727$	4.50406e12	+	7.80126e12i	0.597997	+	1.03576i	0.993116	+	0.117132i	$0.0373701\pi$
$727$	4.50406e12	+	7.80126e12i	0.597997	+	1.03576i	−0.395119	+	0.918630i	$0.629297\pi$
$728$	2.12943e12	−	3.68829e12i	0.280978	−	0.486669i
$729$	−1.23629e13			−1.62124
$730$	6.66212e12			0.868279
$731$	−5.65934e12	+	9.80227e12i	−0.733057	+	1.26969i
$732$	−9.84793e11	+	1.70571e12i	−0.126778	+	0.219587i
$733$	9.74891e12			1.24735			0.623675	−	0.781684i	$-0.285639\pi$
$733$	9.74891e12			1.24735			0.623675	+	0.781684i	$0.285639\pi$
$734$	8.71946e12			1.10881
$735$	−4.93044e12	+	8.53977e12i	−0.623150	+	1.07933i
$736$	−1.08963e12	−	1.88730e12i	−0.136877	−	0.237078i
$737$	−3.39806e12	+	5.88561e12i	−0.424255	+	0.734832i
$738$	7.43847e10	+	1.28838e11i	0.00923060	+	0.0159879i
$739$	−2.11695e12	−	3.66666e12i	−0.261102	−	0.452241i	0.705433	−	0.708776i	$-0.250752\pi$
$739$	−2.11695e12	−	3.66666e12i	−0.261102	−	0.452241i	−0.966535	+	0.256535i	$0.917419\pi$
$740$	9.61316e12			1.17848
$741$	1.62195e13	−	4.85957e12i	1.97631	−	0.592128i
$742$	−4.81580e12			−0.583245
$743$	6.17673e12	+	1.06984e13i	0.743547	+	1.28786i	0.950870	+	0.309589i	$0.100192\pi$
$743$	6.17673e12	+	1.06984e13i	0.743547	+	1.28786i	−0.207323	+	0.978273i	$0.566475\pi$
$744$	3.59961e12	+	6.23470e12i	0.430702	+	0.745998i
$745$	5.24724e12	−	9.08849e12i	0.624062	−	1.08091i
$746$	−1.12016e12	−	1.94018e12i	−0.132421	−	0.229359i
$747$	4.76269e12	−	8.24922e12i	0.559641	−	0.969327i
$748$	−4.04419e12			−0.472361
$749$	−6.96253e12			−0.808350
$750$	6.07415e12	−	1.05207e13i	0.700987	−	1.21414i
$751$	−1.84240e12	+	3.19113e12i	−0.211351	+	0.366070i	−0.952138	−	0.305670i	$-0.901120\pi$
$751$	−1.84240e12	+	3.19113e12i	−0.211351	+	0.366070i	0.740787	+	0.671740i	$0.234453\pi$
$752$	−2.15302e12			−0.245510
$753$	−2.17427e13			−2.46454
$754$	−1.46711e12	+	2.54111e12i	−0.165307	+	0.286320i
$755$	9.72625e12	+	1.68464e13i	1.08939	+	1.88688i
$756$	−2.09365e12	+	3.62631e12i	−0.233107	+	0.403754i
$757$	−5.06902e12	−	8.77980e12i	−0.561038	−	0.971746i	−0.997406	−	0.0719782i	$-0.977069\pi$
$757$	−5.06902e12	−	8.77980e12i	−0.561038	−	0.971746i	0.436368	−	0.899768i	$-0.356265\pi$
$758$	2.39996e12	+	4.15685e12i	0.264054	+	0.457354i
$759$	2.43877e13			2.66736
$760$	−3.92821e12	−	3.70449e12i	−0.427104	−	0.402780i
$761$	−7.00785e12			−0.757450			−0.378725	−	0.925509i	$-0.623637\pi$
$761$	−7.00785e12			−0.757450			−0.378725	+	0.925509i	$0.623637\pi$
$762$	−5.55204e12	−	9.61642e12i	−0.596562	−	1.03328i
$763$	6.58307e11	+	1.14022e12i	0.0703182	+	0.121795i
$764$	1.44375e11	−	2.50065e11i	0.0153311	−	0.0265542i
$765$	−1.01129e13	−	1.75160e13i	−1.06758	−	1.84910i
$766$	−3.73584e12	+	6.47067e12i	−0.392066	+	0.679078i
$767$	5.36043e12			0.559268
$768$	−9.50206e11			−0.0985581
$769$	1.60742e12	−	2.78414e12i	0.165753	−	0.287093i	−0.771169	−	0.636630i	$-0.780328\pi$
$769$	1.60742e12	−	2.78414e12i	0.165753	−	0.287093i	0.936923	+	0.349537i	$0.113661\pi$
$770$	7.59923e12	−	1.31622e13i	0.779043	−	1.34934i
$771$	−1.62352e13			−1.65467
$772$	7.80963e12			0.791321
$773$	2.44731e12	−	4.23887e12i	0.246537	−	0.427014i	−0.716026	−	0.698074i	$-0.754041\pi$
$773$	2.44731e12	−	4.23887e12i	0.246537	−	0.427014i	0.962563	+	0.271060i	$0.0873740\pi$
$774$	−8.89634e12	−	1.54089e13i	−0.890999	−	1.54326i
$775$	1.36329e13	−	2.36129e13i	1.35747	−	2.35121i
$776$	1.54141e12	+	2.66980e12i	0.152595	+	0.264302i
$777$	1.38145e13	+	2.39274e13i	1.35969	+	2.35505i
$778$	3.65364e12			0.357534
$779$	−1.31315e11	−	1.23836e11i	−0.0127760	−	0.0120484i
$780$	−1.77073e13			−1.71288
$781$	5.31065e12	+	9.19831e12i	0.510761	+	0.884664i
$782$	4.95212e12	+	8.57733e12i	0.473545	+	0.820204i
$783$	1.44245e12	−	2.49840e12i	0.137143	−	0.237539i
$784$	−6.29374e11	−	1.09011e12i	−0.0594958	−	0.103050i
$785$	−4.87606e12	+	8.44558e12i	−0.458306	+	0.793809i
$786$	−1.06598e13			−0.996202
$787$	6.08793e12			0.565696			0.282848	−	0.959165i	$-0.408721\pi$
$787$	6.08793e12			0.565696			0.282848	+	0.959165i	$0.408721\pi$
$788$	−1.69146e12	+	2.92970e12i	−0.156277	+	0.270679i
$789$	−8.79524e12	+	1.52338e13i	−0.807981	+	1.39946i
$790$	−1.62936e11			−0.0148832
$791$	3.21364e10			0.00291879
$792$	3.17868e12	−	5.50564e12i	0.287067	−	0.497215i
$793$	−2.34262e12	−	4.05754e12i	−0.210365	−	0.364362i
$794$	−4.08098e12	+	7.06847e12i	−0.364395	+	0.631151i
$795$	1.00114e13	+	1.73403e13i	0.888881	+	1.53959i
$796$	2.62647e12	+	4.54917e12i	0.231880	+	0.401628i
$797$	1.01153e13			0.888011			0.444005	−	0.896024i	$-0.353557\pi$
$797$	1.01153e13			0.888011			0.444005	+	0.896024i	$0.353557\pi$
$798$	3.57557e12	−	1.51009e13i	0.312128	−	1.31823i
$799$	9.78497e12			0.849374
$800$	1.79937e12	+	3.11660e12i	0.155316	+	0.269015i
$801$	5.41632e12	+	9.38133e12i	0.464898	+	0.805227i
$802$	−6.42422e12	+	1.11271e13i	−0.548322	+	0.949721i
$803$	−4.75844e12	−	8.24186e12i	−0.403873	−	0.699528i
$804$	3.62850e12	−	6.28475e12i	0.306250	−	0.530440i
$805$	−3.72211e13			−3.12398
$806$	−1.71255e13			−1.42934
$807$	1.47310e13	−	2.55148e13i	1.22265	−	2.11768i
$808$	−5.37105e11	+	9.30292e11i	−0.0443310	+	0.0767836i
$809$	−2.39765e12			−0.196796			−0.0983982	−	0.995147i	$-0.531372\pi$
$809$	−2.39765e12			−0.196796			−0.0983982	+	0.995147i	$0.531372\pi$
$810$	−3.97614e12			−0.324548
$811$	9.96513e12	−	1.72601e13i	0.808889	−	1.40104i	−0.104744	−	0.994499i	$-0.533402\pi$
$811$	9.96513e12	−	1.72601e13i	0.808889	−	1.40104i	0.913634	−	0.406538i	$-0.133264\pi$
$812$	1.34464e12	+	2.32899e12i	0.108544	+	0.188003i
$813$	1.88578e13	−	3.26626e13i	1.51385	−	2.62207i
$814$	−6.86623e12	−	1.18927e13i	−0.548161	−	0.949443i
$815$	6.78062e12	+	1.17444e13i	0.538345	+	0.932440i
$816$	4.31845e12			0.340975
$817$	1.57051e13	+	1.48107e13i	1.23323	+	1.16299i
$818$	2.53648e12			0.198080
$819$	−1.52132e13	−	2.63500e13i	−1.18152	−	2.04646i
$820$	9.43814e10	+	1.63473e11i	0.00728994	+	0.0126266i
$821$	−6.79506e12	+	1.17694e13i	−0.521974	+	0.904086i	0.477699	+	0.878523i	$0.341471\pi$
$821$	−6.79506e12	+	1.17694e13i	−0.521974	+	0.904086i	−0.999673	+	0.0255622i	$0.991862\pi$
$822$	1.23974e13	+	2.14729e13i	0.947126	+	1.64047i
$823$	4.18359e12	−	7.24619e12i	0.317870	−	0.550567i	−0.662173	−	0.749351i	$-0.730366\pi$
$823$	4.18359e12	−	7.24619e12i	0.317870	−	0.550567i	0.980043	+	0.198784i	$0.0636991\pi$
$824$	−1.62583e12			−0.122858
$825$	−4.02726e13			−3.02668
$826$	2.45648e12	−	4.25476e12i	0.183613	−	0.318027i
$827$	−4.25904e12	+	7.37688e12i	−0.316619	+	0.548400i	−0.979780	−	0.200076i	$-0.935881\pi$
$827$	−4.25904e12	+	7.37688e12i	−0.316619	+	0.548400i	0.663161	+	0.748477i	$0.269214\pi$
$828$	−1.55692e13			−1.15115
$829$	−1.71607e13			−1.26194			−0.630971	−	0.775806i	$-0.717343\pi$
$829$	−1.71607e13			−1.26194			−0.630971	+	0.775806i	$0.717343\pi$
$830$	6.04304e12	−	1.04668e13i	0.441981	−	0.765534i
$831$	−2.62886e12	−	4.55331e12i	−0.191233	−	0.331225i
$832$	1.13017e12	−	1.95752e12i	0.0817692	−	0.141628i
$833$	2.86035e12	+	4.95427e12i	0.205834	+	0.356515i
$834$	7.02350e12	+	1.21651e13i	0.502697	+	0.870697i
$835$	−1.69552e13			−1.20702
$836$	−1.77717e12	+	7.50563e12i	−0.125835	+	0.531446i
$837$	1.68377e13			1.18582
$838$	7.00158e12	+	1.21271e13i	0.490454	+	0.849491i
$839$	−1.03046e13	−	1.78481e13i	−0.717965	−	1.24355i	−0.961805	−	0.273736i	$-0.911741\pi$
$839$	−1.03046e13	−	1.78481e13i	−0.717965	−	1.24355i	0.243840	−	0.969815i	$-0.421593\pi$
$840$	−8.11458e12	+	1.40549e13i	−0.562353	+	0.974025i
$841$	6.32716e12	+	1.09590e13i	0.436141	+	0.755418i
$842$	8.56307e12	−	1.48317e13i	0.587117	−	1.01692i
$843$	−5.25268e11			−0.0358226
$844$	1.27798e13			0.866931
$845$	8.75661e12	−	1.51669e13i	0.590855	−	1.02339i
$846$	−7.69086e12	+	1.33210e13i	−0.516189	+	0.894065i
$847$	−3.51351e12			−0.234567
$848$	−2.55593e12			−0.169734
$849$	−2.10265e13	+	3.64189e13i	−1.38893	+	2.40570i
$850$	−8.17769e12	−	1.41642e13i	−0.537336	−	0.930693i
$851$	−1.68154e13	+	2.91252e13i	−1.09907	+	1.90364i
$852$	−5.67080e12	−	9.82211e12i	−0.368694	−	0.638596i
$853$	−3.44314e12	−	5.96370e12i	−0.222682	−	0.385696i	0.732940	−	0.680294i	$-0.238148\pi$
$853$	−3.44314e12	−	5.96370e12i	−0.222682	−	0.385696i	−0.955621	+	0.294598i	$0.904814\pi$
$854$	−4.29414e12			−0.276259
$855$	−3.69521e13	+	1.10713e13i	−2.36478	+	0.708521i
$856$	−3.69528e12			−0.235243
$857$	−1.21783e13	−	2.10934e13i	−0.771209	−	1.33577i	−0.936901	−	0.349595i	$-0.886319\pi$
$857$	−1.21783e13	−	2.10934e13i	−0.771209	−	1.33577i	0.165692	−	0.986178i	$-0.447014\pi$
$858$	1.26475e13	+	2.19061e13i	0.796729	+	1.37998i
$859$	4.64593e12	−	8.04699e12i	0.291141	−	0.504271i	−0.682939	−	0.730476i	$-0.739298\pi$
$859$	4.64593e12	−	8.04699e12i	0.291141	−	0.504271i	0.974080	+	0.226204i	$0.0726317\pi$
$860$	−1.12879e13	−	1.95513e13i	−0.703674	−	1.21880i
$861$	−2.71259e11	+	4.69835e11i	−0.0168217	+	0.0291361i
$862$	1.44297e13			0.890171
$863$	−5.45477e12			−0.334756			−0.167378	−	0.985893i	$-0.553530\pi$
$863$	−5.45477e12			−0.334756			−0.167378	+	0.985893i	$0.553530\pi$
$864$	−1.11118e12	+	1.92462e12i	−0.0678379	+	0.117499i
$865$	−1.43711e13	+	2.48914e13i	−0.872803	+	1.51174i
$866$	1.72521e12			0.104235
$867$	6.60972e12			0.397281
$868$	−7.84796e12	+	1.35931e13i	−0.469265	+	0.812791i
$869$	1.16378e11	+	2.01572e11i	0.00692280	+	0.0119906i
$870$	5.59067e12	−	9.68333e12i	0.330847	−	0.573044i
$871$	8.63147e12	+	1.49501e13i	0.508163	+	0.880164i
$872$	3.49389e11	+	6.05159e11i	0.0204637	+	0.0354442i
$873$	2.20244e13			1.28334
$874$	1.80949e13	−	5.42146e12i	1.04895	−	0.314279i
$875$	2.64861e13			1.52750
$876$	5.08114e12	+	8.80079e12i	0.291536	+	0.504956i
$877$	6.34894e12	+	1.09967e13i	0.362413	+	0.627717i	0.988357	−	0.152150i	$-0.0486198\pi$
$877$	6.34894e12	+	1.09967e13i	0.362413	+	0.627717i	−0.625945	+	0.779867i	$0.715286\pi$
$878$	−8.74495e12	+	1.51467e13i	−0.496629	+	0.860186i
$879$	−3.98084e12	−	6.89501e12i	−0.224918	−	0.389569i
$880$	4.03320e12	−	6.98571e12i	0.226714	−	0.392680i
$881$	2.03963e13			1.14067			0.570334	−	0.821413i	$-0.306814\pi$
$881$	2.03963e13			1.14067			0.570334	+	0.821413i	$0.306814\pi$
$882$	−8.99280e12			−0.500364
$883$	−5.05226e12	+	8.75077e12i	−0.279681	+	0.484421i	−0.971305	−	0.237836i	$-0.923562\pi$
$883$	−5.05226e12	+	8.75077e12i	−0.279681	+	0.484421i	0.691625	+	0.722257i	$0.256895\pi$
$884$	−5.13636e12	+	8.89643e12i	−0.282891	+	0.489982i
$885$	−2.04268e13			−1.11933
$886$	−1.73938e12			−0.0948295
$887$	−8.84244e11	+	1.53156e12i	−0.0479640	+	0.0830762i	−0.889011	−	0.457886i	$-0.848607\pi$
$887$	−8.84244e11	+	1.53156e12i	−0.0479640	+	0.0830762i	0.841047	+	0.540963i	$0.181940\pi$
$888$	7.33187e12	+	1.26992e13i	0.395691	+	0.685357i
$889$	1.21047e13	−	2.09660e13i	0.649975	−	1.12579i
$890$	6.87238e12	+	1.19033e13i	0.367157	+	0.635935i
$891$	2.83997e12	+	4.91897e12i	0.150961	+	0.261472i
$892$	6.55965e12			0.346927
$893$	4.29989e12	−	1.81600e13i	0.226270	−	0.955616i
$894$	1.60081e13			0.838149
$895$	−1.28937e13	−	2.23325e13i	−0.671696	−	1.16341i
$896$	−1.03583e12	−	1.79411e12i	−0.0536912	−	0.0929959i
$897$	3.09737e13	−	5.36481e13i	1.59745	−	2.76687i
$898$	−1.97276e12	−	3.41693e12i	−0.101235	−	0.175345i
$899$	5.40698e12	−	9.36517e12i	0.276081	−	0.478186i
$900$	2.57103e13			1.30622
$901$	1.16161e13			0.587216
$902$	1.34824e11	−	2.33523e11i	0.00678171	−	0.0117463i
$903$	3.24424e13	−	5.61919e13i	1.62375	−	2.81241i
$904$	1.70560e10			0.000849414
$905$	1.88940e13			0.936277
$906$	−1.48363e13	+	2.56972e13i	−0.731556	+	1.26709i
$907$	1.84448e11	+	3.19474e11i	0.00904986	+	0.0156748i	0.870515	−	0.492142i	$-0.163786\pi$
$907$	1.84448e11	+	3.19474e11i	0.00904986	+	0.0156748i	−0.861465	+	0.507817i	$0.830453\pi$
$908$	−2.44697e12	+	4.23828e12i	−0.119466	+	0.206921i
$909$	3.83720e12	+	6.64623e12i	0.186414	+	0.322878i
$910$	−1.93029e13	−	3.34336e13i	−0.933119	−	1.61621i
$911$	−3.41025e13			−1.64042			−0.820208	−	0.572066i	$-0.806142\pi$
$911$	−3.41025e13			−1.64042			−0.820208	+	0.572066i	$0.806142\pi$
$912$	1.89769e12	−	8.01463e12i	0.0908342	−	0.383625i
$913$	−1.72650e13			−0.822335
$914$	6.61397e11	+	1.14557e12i	0.0313476	+	0.0542956i
$915$	8.92696e12	+	1.54620e13i	0.421026	+	0.729238i
$916$	9.37363e12	−	1.62356e13i	0.439924	−	0.761971i
$917$	−1.16204e13	−	2.01271e13i	−0.542698	−	0.939981i
$918$	5.05004e12	−	8.74693e12i	0.234694	−	0.406503i
$919$	−2.85486e13			−1.32027			−0.660137	−	0.751145i	$-0.729502\pi$
$919$	−2.85486e13			−1.32027			−0.660137	+	0.751145i	$0.729502\pi$
$920$	−1.97547e13			−0.909127
$921$	−2.33142e13	+	4.03814e13i	−1.06771	+	1.84932i
$922$	2.92944e12	−	5.07394e12i	0.133504	−	0.231236i
$923$	2.69793e13			1.22355
$924$	2.31835e13			1.04630
$925$	2.77682e13	−	4.80959e13i	1.24712	−	2.16008i
$926$	3.59479e12	+	6.22636e12i	0.160666	+	0.278282i
$927$	−5.80765e12	+	1.00591e13i	−0.258310	+	0.447406i
$928$	7.13654e11	+	1.23608e12i	0.0315880	+	0.0547119i
$929$	4.20253e12	+	7.27900e12i	0.185114	+	0.320628i	0.943615	−	0.331045i	$-0.107401\pi$
$929$	4.20253e12	+	7.27900e12i	0.185114	+	0.320628i	−0.758501	+	0.651672i	$0.774068\pi$
$930$	6.52595e13			2.86069
$931$	1.04516e13	−	3.13144e12i	0.455942	−	0.136606i
$932$	−9.67483e11			−0.0420022
$933$	2.48713e13	+	4.30784e13i	1.07456	+	1.86119i
$934$	−7.16697e12	−	1.24136e13i	−0.308159	−	0.533747i
$935$	−1.83299e13	+	3.17483e13i	−0.784347	+	1.35853i
$936$	−8.07422e12	−	1.39850e13i	−0.343842	−	0.595552i
$937$	7.89248e11	−	1.36702e12i	0.0334492	−	0.0579357i	−0.848816	−	0.528688i	$-0.822684\pi$
$937$	7.89248e11	−	1.36702e12i	0.0334492	−	0.0579357i	0.882265	+	0.470752i	$0.156017\pi$
$938$	1.58219e13			0.667339
$939$	5.11262e13			2.14609
$940$	−9.75838e12	+	1.69020e13i	−0.407664	+	0.706095i
$941$	6.33037e12	−	1.09645e13i	0.263194	−	0.455865i	−0.703895	−	0.710304i	$-0.748557\pi$
$941$	6.33037e12	−	1.09645e13i	0.263194	−	0.455865i	0.967089	+	0.254439i	$0.0818908\pi$
$942$	−1.48757e13			−0.615529
$943$	−6.60372e11			−0.0271948
$944$	1.30375e12	−	2.25816e12i	0.0534344	−	0.0925510i
$945$	1.89785e13	+	3.28718e13i	0.774140	+	1.34085i
$946$	−1.61249e13	+	2.79291e13i	−0.654616	+	1.13383i
$947$	1.50951e13	+	2.61455e13i	0.609905	+	1.05639i	0.991256	+	0.131956i	$0.0421256\pi$
$947$	1.50951e13	+	2.61455e13i	0.609905	+	1.05639i	−0.381351	+	0.924430i	$0.624541\pi$
$948$	−1.24270e11	−	2.15242e11i	−0.00499723	−	0.00865546i
$949$	−2.41740e13			−0.967498
$950$	−2.98810e13	+	8.95273e12i	−1.19025	+	0.356615i
$951$	−2.98690e13			−1.18415
$952$	4.70760e12	+	8.15381e12i	0.185752	+	0.321732i
$953$	−2.09399e13	−	3.62689e13i	−0.822348	−	1.42435i	−0.903929	−	0.427683i	$-0.859330\pi$
$953$	−2.09399e13	−	3.62689e13i	−0.822348	−	1.42435i	0.0815806	−	0.996667i	$-0.474003\pi$
$954$	−9.13009e12	+	1.58138e13i	−0.356868	+	0.618113i
$955$	−1.30873e12	−	2.26680e12i	−0.0509139	−	0.0881855i
$956$	−5.98586e12	+	1.03678e13i	−0.231775	+	0.401445i
$957$	−1.59726e13			−0.615563
$958$	2.15825e13			0.827859
$959$	−2.70292e13	+	4.68159e13i	−1.03193	+	1.78735i
$960$	−4.30672e12	+	7.45946e12i	−0.163654	+	0.283457i
$961$	3.66757e13			1.38715
$962$	−3.48820e13			−1.31315
$963$	−1.32000e13	+	2.28631e13i	−0.494602	+	0.856675i
$964$	−8.45314e12	−	1.46413e13i	−0.315262	−	0.546050i
$965$	3.53964e13	−	6.13084e13i	1.31397	−	2.27587i
$966$	−2.83882e13	−	4.91699e13i	−1.04892	−	1.81678i
$967$	−1.00207e13	−	1.73564e13i	−0.368536	−	0.638323i	0.620801	−	0.783968i	$-0.286807\pi$
$967$	−1.00207e13	−	1.73564e13i	−0.368536	−	0.638323i	−0.989337	+	0.145645i	$0.953474\pi$
$968$	−1.86476e12			−0.0682626
$969$	−8.62455e12	+	3.64245e13i	−0.314253	+	1.32720i
$970$	2.79452e13			1.01353
$971$	−2.32880e13	−	4.03359e13i	−0.840708	−	1.45615i	−0.889297	−	0.457329i	$-0.848806\pi$
$971$	−2.32880e13	−	4.03359e13i	−0.840708	−	1.45615i	0.0485899	−	0.998819i	$-0.484527\pi$
$972$	−8.37225e12	−	1.45012e13i	−0.300846	−	0.521080i
$973$	−1.53128e13	+	2.65226e13i	−0.547706	+	0.948654i
$974$	2.90206e12	+	5.02651e12i	0.103322	+	0.178958i
$975$	−5.11485e13	+	8.85918e13i	−1.81264	+	3.13959i
$976$	−2.27907e12			−0.0803957
$977$	2.31432e13			0.812639			0.406319	−	0.913731i	$-0.366812\pi$
$977$	2.31432e13			0.812639			0.406319	+	0.913731i	$0.366812\pi$
$978$	−1.03430e13	+	1.79147e13i	−0.361513	+	0.626158i
$979$	9.81723e12	−	1.70039e13i	0.341560	−	0.591599i
$980$	−1.14103e13			−0.395167
$981$	4.99223e12			0.172101
$982$	−3.78261e12	+	6.55168e12i	−0.129805	+	0.224828i
$983$	5.89727e12	+	1.02144e13i	0.201447	+	0.348916i	0.948995	−	0.315292i	$-0.102102\pi$
$983$	5.89727e12	+	1.02144e13i	0.201447	+	0.348916i	−0.747548	+	0.664208i	$0.768769\pi$
$984$	−1.43968e11	+	2.49359e11i	−0.00489539	+	0.00847906i
$985$	1.53328e13	+	2.65572e13i	0.518989	+	0.898916i
$986$	−3.24338e12	−	5.61770e12i	−0.109283	−	0.189283i
$987$	−5.60927e13			−1.88139
$988$	1.42538e13	+	1.34420e13i	0.475910	+	0.448806i
$989$	7.89799e13			2.62502
$990$	−2.88142e13	−	4.99076e13i	−0.953340	−	1.65123i
$991$	−1.01794e13	−	1.76313e13i	−0.335268	−	0.580701i	0.648268	−	0.761412i	$-0.275494\pi$
$991$	−1.01794e13	−	1.76313e13i	−0.335268	−	0.580701i	−0.983536	+	0.180711i	$0.942160\pi$
$992$	−4.16521e12	+	7.21436e12i	−0.136564	+	0.236535i
$993$	−1.43258e13	−	2.48130e13i	−0.467570	−	0.809855i
$994$	1.23636e13	−	2.14144e13i	0.401705	−	0.695773i
$995$	4.76169e13			1.54013
$996$	1.84359e13			0.593604
$997$	−1.45017e12	+	2.51176e12i	−0.0464826	+	0.0805101i	−0.888331	−	0.459204i	$-0.848135\pi$
$997$	−1.45017e12	+	2.51176e12i	−0.0464826	+	0.0805101i	0.841848	+	0.539715i	$0.181468\pi$
$998$	−8.75563e12	+	1.51652e13i	−0.279383	+	0.483906i
$999$	3.42959e13			1.08942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.7.6	✓	14
19.11	even	3	inner	38.10.c.a.11.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.6	✓	14	1.1	even	1	trivial
38.10.c.a.11.6	yes	14	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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(110.618 + 191.597i) q^{3} +(-128.000 + 221.703i) q^{4} +(1160.30 + 2009.69i) q^{5} +(-1769.90 + 3065.55i) q^{6} -7717.55 q^{7} -4096.00 q^{8} +(-14631.4 + 25342.3i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(110.618 + 191.597i) q^{3} +(-128.000 + 221.703i) q^{4} +(1160.30 + 2009.69i) q^{5} +(-1769.90 + 3065.55i) q^{6} -7717.55 q^{7} -4096.00 q^{8} +(-14631.4 + 25342.3i) q^{9} +(-18564.7 + 32155.1i) q^{10} +53039.7 q^{11} -56636.7 q^{12} +(67363.5 - 116677. i) q^{13} +(-61740.4 - 106938. i) q^{14} +(-256700. + 444618. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(148923. + 257941. i) q^{17} -468205. q^{18} +(544157. - 163037. i) q^{19} -594072. q^{20} +(-853704. - 1.47866e6i) q^{21} +(424318. + 734940. i) q^{22} +(1.03916e6 - 1.79987e6i) q^{23} +(-453093. - 784781. i) q^{24} +(-1.71601e6 + 2.97222e6i) q^{25} +2.15563e6 q^{26} -2.11941e6 q^{27} +(987846. - 1.71100e6i) q^{28} +(-680593. + 1.17882e6i) q^{29} -8.21442e6 q^{30} -7.94452e6 q^{31} +(524288. - 908093. i) q^{32} +(5.86717e6 + 1.01622e7i) q^{33} +(-2.38276e6 + 4.12706e6i) q^{34} +(-8.95464e6 - 1.55099e7i) q^{35} +(-3.74564e6 - 6.48764e6i) q^{36} -1.61818e7 q^{37} +(6.61236e6 + 6.23577e6i) q^{38} +2.98066e7 q^{39} +(-4.75257e6 - 8.23170e6i) q^{40} +(-158872. - 275175. i) q^{41} +(1.36593e7 - 2.36585e7i) q^{42} +(1.90010e7 + 3.29106e7i) q^{43} +(-6.78908e6 + 1.17590e7i) q^{44} -6.79071e7 q^{45} +3.32530e7 q^{46} +(1.64263e7 - 2.84511e7i) q^{47} +(7.24949e6 - 1.25565e7i) q^{48} +1.92070e7 q^{49} -5.49124e7 q^{50} +(-3.29472e7 + 5.70662e7i) q^{51} +(1.72451e7 + 2.98693e7i) q^{52} +(1.95002e7 - 3.37754e7i) q^{53} +(-1.69553e7 - 2.93674e7i) q^{54} +(6.15418e7 + 1.06593e8i) q^{55} +3.16111e7 q^{56} +(9.14311e7 + 8.62239e7i) q^{57} -2.17790e7 q^{58} +(1.98937e7 + 3.44568e7i) q^{59} +(-6.57153e7 - 1.13822e8i) q^{60} +(1.73879e7 - 3.01167e7i) q^{61} +(-6.35561e7 - 1.10082e8i) q^{62} +(1.12919e8 - 1.95581e8i) q^{63} +1.67772e7 q^{64} +3.12647e8 q^{65} +(-9.38748e7 + 1.62596e8i) q^{66} +(-6.40663e7 + 1.10966e8i) q^{67} -7.62483e7 q^{68} +4.59800e8 q^{69} +(1.43274e8 - 2.48158e8i) q^{70} +(1.00126e8 + 1.73423e8i) q^{71} +(5.99302e7 - 1.03802e8i) q^{72} +(-8.97147e7 - 1.55390e8i) q^{73} +(-1.29454e8 - 2.24222e8i) q^{74} -7.59291e8 q^{75} +(-3.35065e7 + 1.41510e8i) q^{76} -4.09337e8 q^{77} +(2.38453e8 + 4.13012e8i) q^{78} +(2.19417e6 + 3.80041e6i) q^{79} +(7.60412e7 - 1.31707e8i) q^{80} +(5.35442e7 + 9.27413e7i) q^{81} +(2.54195e6 - 4.40279e6i) q^{82} -3.25511e8 q^{83} +4.37096e8 q^{84} +(-3.45588e8 + 5.98577e8i) q^{85} +(-3.04015e8 + 5.26570e8i) q^{86} -3.01145e8 q^{87} -2.17251e8 q^{88} +(1.85092e8 - 3.20589e8i) q^{89} +(-5.43256e8 - 9.40948e8i) q^{90} +(-5.19881e8 + 9.00461e8i) q^{91} +(2.66024e8 + 4.60767e8i) q^{92} +(-8.78810e8 - 1.52214e9i) q^{93} +5.25641e8 q^{94} +(9.59037e8 + 9.04417e8i) q^{95} +2.31984e8 q^{96} +(-3.76321e8 - 6.51807e8i) q^{97} +(1.53656e8 + 2.66140e8i) q^{98} +(-7.76045e8 + 1.34415e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9}+O(q^{10}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9	\( 14 q + 112 q^{2} + 165 q^{3} - 1792 q^{4} + 909 q^{5} - 2640 q^{6} + 3692 q^{7} - 57344 q^{8} - 52286 q^{9} - 14544 q^{10} + 15656 q^{11} - 84480 q^{12} + 6423 q^{13} + 29536 q^{14} - 227715 q^{15} - 458752 q^{16} + 313667 q^{17} - 1673152 q^{18} + 1134224 q^{19} - 465408 q^{20} - 1227046 q^{21} + 125248 q^{22} + 3449345 q^{23} - 675840 q^{24} - 2398648 q^{25} + 205536 q^{26} - 1873854 q^{27} - 472576 q^{28} - 7002615 q^{29} - 7286880 q^{30} - 18666588 q^{31} + 7340032 q^{32} - 13827668 q^{33} - 5018672 q^{34} + 2584932 q^{35} - 13385216 q^{36} - 6866080 q^{37} + 22760176 q^{38} + 4568410 q^{39} - 3723264 q^{40} + 3564107 q^{41} + 19632736 q^{42} + 19837521 q^{43} - 2003968 q^{44} - 77788260 q^{45} + 110379040 q^{46} + 60353825 q^{47} + 10813440 q^{48} - 79579650 q^{49} - 76756736 q^{50} - 161350373 q^{51} + 1644288 q^{52} + 54744235 q^{53} - 14990832 q^{54} + 143199990 q^{55} - 15122432 q^{56} + 330686241 q^{57} - 224083680 q^{58} + 164456585 q^{59} - 58295040 q^{60} + 49328881 q^{61} - 149332704 q^{62} + 138012360 q^{63} + 234881024 q^{64} + 788015550 q^{65} + 221242688 q^{66} - 171522309 q^{67} - 160597504 q^{68} + 630323350 q^{69} - 41358912 q^{70} - 74596055 q^{71} + 214163456 q^{72} + 58695287 q^{73} - 54928640 q^{74} - 1115757144 q^{75} + 73801472 q^{76} - 965186644 q^{77} + 36547280 q^{78} + 121854617 q^{79} + 59572224 q^{80} - 368486747 q^{81} - 57025712 q^{82} - 732607256 q^{83} + 628247552 q^{84} + 634697565 q^{85} - 317400336 q^{86} - 2979036210 q^{87} - 64126976 q^{88} - 1652463181 q^{89} - 622306080 q^{90} - 1141270092 q^{91} + 883032320 q^{92} - 1839612746 q^{93} + 1931322400 q^{94} + 2397253503 q^{95} + 346030080 q^{96} + 248805607 q^{97} - 636637200 q^{98} + 520684712 q^{99}+O(q^{100}) \) 14 * q + 112 * q^2 + 165 * q^3 - 1792 * q^4 + 909 * q^5 - 2640 * q^6 + 3692 * q^7 - 57344 * q^8 - 52286 * q^9 - 14544 * q^10 + 15656 * q^11 - 84480 * q^12 + 6423 * q^13 + 29536 * q^14 - 227715 * q^15 - 458752 * q^16 + 313667 * q^17 - 1673152 * q^18 + 1134224 * q^19 - 465408 * q^20 - 1227046 * q^21 + 125248 * q^22 + 3449345 * q^23 - 675840 * q^24 - 2398648 * q^25 + 205536 * q^26 - 1873854 * q^27 - 472576 * q^28 - 7002615 * q^29 - 7286880 * q^30 - 18666588 * q^31 + 7340032 * q^32 - 13827668 * q^33 - 5018672 * q^34 + 2584932 * q^35 - 13385216 * q^36 - 6866080 * q^37 + 22760176 * q^38 + 4568410 * q^39 - 3723264 * q^40 + 3564107 * q^41 + 19632736 * q^42 + 19837521 * q^43 - 2003968 * q^44 - 77788260 * q^45 + 110379040 * q^46 + 60353825 * q^47 + 10813440 * q^48 - 79579650 * q^49 - 76756736 * q^50 - 161350373 * q^51 + 1644288 * q^52 + 54744235 * q^53 - 14990832 * q^54 + 143199990 * q^55 - 15122432 * q^56 + 330686241 * q^57 - 224083680 * q^58 + 164456585 * q^59 - 58295040 * q^60 + 49328881 * q^61 - 149332704 * q^62 + 138012360 * q^63 + 234881024 * q^64 + 788015550 * q^65 + 221242688 * q^66 - 171522309 * q^67 - 160597504 * q^68 + 630323350 * q^69 - 41358912 * q^70 - 74596055 * q^71 + 214163456 * q^72 + 58695287 * q^73 - 54928640 * q^74 - 1115757144 * q^75 + 73801472 * q^76 - 965186644 * q^77 + 36547280 * q^78 + 121854617 * q^79 + 59572224 * q^80 - 368486747 * q^81 - 57025712 * q^82 - 732607256 * q^83 + 628247552 * q^84 + 634697565 * q^85 - 317400336 * q^86 - 2979036210 * q^87 - 64126976 * q^88 - 1652463181 * q^89 - 622306080 * q^90 - 1141270092 * q^91 + 883032320 * q^92 - 1839612746 * q^93 + 1931322400 * q^94 + 2397253503 * q^95 + 346030080 * q^96 + 248805607 * q^97 - 636637200 * q^98 + 520684712 * q^99

Introduction

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