LMFDB - Embedded newform 38.10.c.a.7.4

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			7.4
Root			$2.70706 + 4.68876i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(9.29294 + 16.0959i) q^{3} +(-128.000 + 221.703i) q^{4} +(830.940 + 1439.23i) q^{5} +(-148.687 + 257.534i) q^{6} +10512.6 q^{7} -4096.00 q^{8} +(9668.78 - 16746.8i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(9.29294 + 16.0959i) q^{3} +(-128.000 + 221.703i) q^{4} +(830.940 + 1439.23i) q^{5} +(-148.687 + 257.534i) q^{6} +10512.6 q^{7} -4096.00 q^{8} +(9668.78 - 16746.8i) q^{9} +(-13295.0 + 23027.7i) q^{10} -1255.59 q^{11} -4757.99 q^{12} +(-25967.0 + 44976.1i) q^{13} +(84100.4 + 145666. i) q^{14} +(-15443.8 + 26749.4i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(63648.2 + 110242. i) q^{17} +309401. q^{18} +(234883. + 517221. i) q^{19} -425441. q^{20} +(97692.6 + 169208. i) q^{21} +(-10044.7 - 17398.0i) q^{22} +(-563811. + 976550. i) q^{23} +(-38063.9 - 65928.6i) q^{24} +(-404360. + 700372. i) q^{25} -830943. q^{26} +725232. q^{27} +(-1.34561e6 + 2.33066e6i) q^{28} +(-254917. + 441529. i) q^{29} -494200. q^{30} -5.84821e6 q^{31} +(524288. - 908093. i) q^{32} +(-11668.1 - 20209.8i) q^{33} +(-1.01837e6 + 1.76387e6i) q^{34} +(8.73530e6 + 1.51300e7i) q^{35} +(2.47521e6 + 4.28719e6i) q^{36} -424795. q^{37} +(-5.28776e6 + 7.39240e6i) q^{38} -965239. q^{39} +(-3.40353e6 - 5.89509e6i) q^{40} +(-246553. - 427042. i) q^{41} +(-1.56308e6 + 2.70734e6i) q^{42} +(-9.44266e6 - 1.63552e7i) q^{43} +(160715. - 278367. i) q^{44} +3.21367e7 q^{45} -1.80420e7 q^{46} +(2.97214e6 - 5.14790e6i) q^{47} +(609022. - 1.05486e6i) q^{48} +7.01602e7 q^{49} -1.29395e7 q^{50} +(-1.18296e6 + 2.04894e6i) q^{51} +(-6.64755e6 - 1.15139e7i) q^{52} +(-7.52938e6 + 1.30413e7i) q^{53} +(5.80185e6 + 1.00491e7i) q^{54} +(-1.04332e6 - 1.80708e6i) q^{55} -4.30594e7 q^{56} +(-6.14236e6 + 8.58715e6i) q^{57} -8.15733e6 q^{58} +(-5.37568e7 - 9.31095e7i) q^{59} +(-3.95360e6 - 6.84784e6i) q^{60} +(8.28710e7 - 1.43537e8i) q^{61} +(-4.67857e7 - 8.10352e7i) q^{62} +(1.01644e8 - 1.76052e8i) q^{63} +1.67772e7 q^{64} -8.63080e7 q^{65} +(186690. - 323357. i) q^{66} +(9.61665e7 - 1.66565e8i) q^{67} -3.25879e7 q^{68} -2.09579e7 q^{69} +(-1.39765e8 + 2.42080e8i) q^{70} +(-4.00571e6 - 6.93809e6i) q^{71} +(-3.96033e7 + 6.85950e7i) q^{72} +(1.81159e8 + 3.13777e8i) q^{73} +(-3.39836e6 - 5.88613e6i) q^{74} -1.50308e7 q^{75} +(-1.44734e8 - 1.41302e7i) q^{76} -1.31995e7 q^{77} +(-7.72191e6 - 1.33747e7i) q^{78} +(2.90075e8 + 5.02424e8i) q^{79} +(5.44565e7 - 9.43214e7i) q^{80} +(-1.83571e8 - 3.17954e8i) q^{81} +(3.94485e6 - 6.83268e6i) q^{82} +3.99967e8 q^{83} -5.00186e7 q^{84} +(-1.05776e8 + 1.83209e8i) q^{85} +(1.51083e8 - 2.61683e8i) q^{86} -9.47570e6 q^{87} +5.14290e6 q^{88} +(-5.32095e8 + 9.21616e8i) q^{89} +(2.57094e8 + 4.45299e8i) q^{90} +(-2.72979e8 + 4.72814e8i) q^{91} +(-1.44336e8 - 2.49997e8i) q^{92} +(-5.43471e7 - 9.41319e7i) q^{93} +9.51086e7 q^{94} +(-5.49227e8 + 7.67830e8i) q^{95} +1.94887e7 q^{96} +(-1.86510e8 - 3.23044e8i) q^{97} +(5.61281e8 + 9.72168e8i) q^{98} +(-1.21400e7 + 2.10271e7i) 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
$3$	9.29294	+	16.0959i	0.0662381	+	0.114728i	0.897243	−	0.441538i	$-0.145567\pi$
$3$	9.29294	+	16.0959i	0.0662381	+	0.114728i	−0.831004	+	0.556266i	$0.812234\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	830.940	+	1439.23i	0.594572	+	1.02983i	0.993607	+	0.112894i	$0.0360119\pi$
$5$	830.940	+	1439.23i	0.594572	+	1.02983i	−0.399035	+	0.916936i	$0.630655\pi$
$6$	−148.687	+	257.534i	−0.0468374	+	0.0811247i
$7$	10512.6			1.65488			0.827441	−	0.561553i	$-0.189796\pi$
$7$	10512.6			1.65488			0.827441	+	0.561553i	$0.189796\pi$
$8$	−4096.00			−0.353553
$9$	9668.78	−	16746.8i	0.491225	−	0.850827i
$10$	−13295.0	+	23027.7i	−0.420426	+	0.728199i
$11$	−1255.59			−0.0258572			−0.0129286	−	0.999916i	$-0.504115\pi$
$11$	−1255.59			−0.0258572			−0.0129286	+	0.999916i	$0.504115\pi$
$12$	−4757.99			−0.0662381
$13$	−25967.0	+	44976.1i	−0.252160	+	0.436754i	−0.964120	−	0.265466i	$-0.914474\pi$
$13$	−25967.0	+	44976.1i	−0.252160	+	0.436754i	0.711960	+	0.702220i	$0.247808\pi$
$14$	84100.4	+	145666.i	0.585089	+	1.01340i
$15$	−15443.8	+	26749.4i	−0.0787666	+	0.136428i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	63648.2	+	110242.i	0.184827	+	0.320130i	0.943518	−	0.331320i	$-0.107494\pi$
$17$	63648.2	+	110242.i	0.184827	+	0.320130i	−0.758691	+	0.651451i	$0.774161\pi$
$18$	309401.			0.694697
$19$	234883.	+	517221.i	0.413485	+	0.910511i
$19$	234883.	+	517221.i	0.413485	+	0.910511i
$20$	−425441.			−0.594572
$21$	97692.6	+	169208.i	0.109616	+	0.189861i
$22$	−10044.7	−	17398.0i	−0.00914188	−	0.0158342i
$23$	−563811.	+	976550.i	−0.420106	+	0.727645i	−0.995949	−	0.0899153i	$-0.971340\pi$
$23$	−563811.	+	976550.i	−0.420106	+	0.727645i	0.575844	+	0.817560i	$0.304674\pi$
$24$	−38063.9	−	65928.6i	−0.0234187	−	0.0405624i
$25$	−404360.	+	700372.i	−0.207032	+	0.358591i
$26$	−830943.			−0.356608
$27$	725232.			0.262627
$28$	−1.34561e6	+	2.33066e6i	−0.413720	+	0.716585i
$29$	−254917.	+	441529.i	−0.0669279	+	0.115923i	−0.897548	−	0.440918i	$-0.854653\pi$
$29$	−254917.	+	441529.i	−0.0669279	+	0.115923i	0.830620	+	0.556840i	$0.187986\pi$
$30$	−494200.			−0.111393
$31$	−5.84821e6			−1.13735			−0.568676	−	0.822561i	$-0.692544\pi$
$31$	−5.84821e6			−1.13735			−0.568676	+	0.822561i	$0.692544\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	−11668.1	−	20209.8i	−0.00171273	−	0.00296653i
$34$	−1.01837e6	+	1.76387e6i	−0.130693	+	0.226366i
$35$	8.73530e6	+	1.51300e7i	0.983947	+	1.70425i
$36$	2.47521e6	+	4.28719e6i	0.245613	+	0.425413i
$37$	−424795.			−0.0372624			−0.0186312	−	0.999826i	$-0.505931\pi$
$37$	−424795.			−0.0372624			−0.0186312	+	0.999826i	$0.505931\pi$
$38$	−5.28776e6	+	7.39240e6i	−0.411382	+	0.575121i
$39$	−965239.			−0.0668104
$40$	−3.40353e6	−	5.89509e6i	−0.210213	−	0.364100i
$41$	−246553.	−	427042.i	−0.0136265	−	0.0236017i	0.859132	−	0.511754i	$-0.171004\pi$
$41$	−246553.	−	427042.i	−0.0136265	−	0.0236017i	−0.872758	+	0.488153i	$0.837671\pi$
$42$	−1.56308e6	+	2.70734e6i	−0.0775104	+	0.134252i
$43$	−9.44266e6	−	1.63552e7i	−0.421198	−	0.729536i	0.574859	−	0.818252i	$-0.305057\pi$
$43$	−9.44266e6	−	1.63552e7i	−0.421198	−	0.729536i	−0.996057	+	0.0887163i	$0.971724\pi$
$44$	160715.	−	278367.i	0.00646429	−	0.0111965i
$45$	3.21367e7			1.16828
$46$	−1.80420e7			−0.594119
$47$	2.97214e6	−	5.14790e6i	0.0888443	−	0.153883i	−0.818179	−	0.574964i	$-0.805016\pi$
$47$	2.97214e6	−	5.14790e6i	0.0888443	−	0.153883i	0.907023	+	0.421081i	$0.138349\pi$
$48$	609022.	−	1.05486e6i	0.0165595	−	0.0286819i
$49$	7.01602e7			1.73863
$50$	−1.29395e7			−0.292788
$51$	−1.18296e6	+	2.04894e6i	−0.0244852	+	0.0424096i
$52$	−6.64755e6	−	1.15139e7i	−0.126080	−	0.218377i
$53$	−7.52938e6	+	1.30413e7i	−0.131074	+	0.227027i	−0.924091	−	0.382173i	$-0.875176\pi$
$53$	−7.52938e6	+	1.30413e7i	−0.131074	+	0.227027i	0.793017	+	0.609200i	$0.208509\pi$
$54$	5.80185e6	+	1.00491e7i	0.0928528	+	0.160826i
$55$	−1.04332e6	−	1.80708e6i	−0.0153739	−	0.0266285i
$56$	−4.30594e7			−0.585089
$57$	−6.14236e6	+	8.58715e6i	−0.0770723	+	0.107749i
$58$	−8.15733e6			−0.0946503
$59$	−5.37568e7	−	9.31095e7i	−0.577563	−	1.00037i	−0.995758	−	0.0920114i	$-0.970670\pi$
$59$	−5.37568e7	−	9.31095e7i	−0.577563	−	1.00037i	0.418195	−	0.908357i	$-0.362663\pi$
$60$	−3.95360e6	−	6.84784e6i	−0.0393833	−	0.0682139i
$61$	8.28710e7	−	1.43537e8i	0.766334	−	1.32733i	−0.173204	−	0.984886i	$-0.555412\pi$
$61$	8.28710e7	−	1.43537e8i	0.766334	−	1.32733i	0.939538	−	0.342444i	$-0.111255\pi$
$62$	−4.67857e7	−	8.10352e7i	−0.402115	−	0.696484i
$63$	1.01644e8	−	1.76052e8i	0.812919	−	1.40802i
$64$	1.67772e7			0.125000
$65$	−8.63080e7			−0.599710
$66$	186690.	−	323357.i	0.00121108	−	0.00209765i
$67$	9.61665e7	−	1.66565e8i	0.583025	−	1.00983i	−0.412094	−	0.911141i	$-0.635202\pi$
$67$	9.61665e7	−	1.66565e8i	0.583025	−	1.00983i	0.995119	−	0.0986872i	$-0.0314643\pi$
$68$	−3.25879e7			−0.184827
$69$	−2.09579e7			−0.111308
$70$	−1.39765e8	+	2.42080e8i	−0.695756	+	1.20508i
$71$	−4.00571e6	−	6.93809e6i	−0.0187075	−	0.0324024i	0.856520	−	0.516114i	$-0.172622\pi$
$71$	−4.00571e6	−	6.93809e6i	−0.0187075	−	0.0324024i	−0.875228	+	0.483711i	$0.839288\pi$
$72$	−3.96033e7	+	6.85950e7i	−0.173674	+	0.300813i
$73$	1.81159e8	+	3.13777e8i	0.746634	+	1.29321i	0.949428	+	0.313986i	$0.101664\pi$
$73$	1.81159e8	+	3.13777e8i	0.746634	+	1.29321i	−0.202794	+	0.979221i	$0.565002\pi$
$74$	−3.39836e6	−	5.88613e6i	−0.0131743	−	0.0228185i
$75$	−1.50308e7			−0.0548537
$76$	−1.44734e8	−	1.41302e7i	−0.497634	−	0.0485832i
$77$	−1.31995e7			−0.0427905
$78$	−7.72191e6	−	1.33747e7i	−0.0236210	−	0.0409128i
$79$	2.90075e8	+	5.02424e8i	0.837892	+	1.45127i	0.891654	+	0.452717i	$0.149545\pi$
$79$	2.90075e8	+	5.02424e8i	0.837892	+	1.45127i	−0.0537623	+	0.998554i	$0.517121\pi$
$80$	5.44565e7	−	9.43214e7i	0.148643	−	0.257457i
$81$	−1.83571e8	−	3.17954e8i	−0.473829	−	0.820696i
$82$	3.94485e6	−	6.83268e6i	0.00963536	−	0.0166889i
$83$	3.99967e8			0.925067			0.462534	−	0.886602i	$-0.346940\pi$
$83$	3.99967e8			0.925067			0.462534	+	0.886602i	$0.346940\pi$
$84$	−5.00186e7			−0.109616
$85$	−1.05776e8	+	1.83209e8i	−0.219786	+	0.380681i
$86$	1.51083e8	−	2.61683e8i	0.297832	−	0.515860i
$87$	−9.47570e6			−0.0177327
$88$	5.14290e6			0.00914188
$89$	−5.32095e8	+	9.21616e8i	−0.898947	+	1.55702i	−0.0701055	+	0.997540i	$0.522334\pi$
$89$	−5.32095e8	+	9.21616e8i	−0.898947	+	1.55702i	−0.828842	+	0.559483i	$0.811000\pi$
$90$	2.57094e8	+	4.45299e8i	0.413048	+	0.715420i
$91$	−2.72979e8	+	4.72814e8i	−0.417295	+	0.722777i
$92$	−1.44336e8	−	2.49997e8i	−0.210053	−	0.363822i
$93$	−5.43471e7	−	9.41319e7i	−0.0753361	−	0.130486i
$94$	9.51086e7			0.125645
$95$	−5.49227e8	+	7.67830e8i	−0.691824	+	0.967184i
$96$	1.94887e7			0.0234187
$97$	−1.86510e8	−	3.23044e8i	−0.213909	−	0.370501i	0.739026	−	0.673677i	$-0.235286\pi$
$97$	−1.86510e8	−	3.23044e8i	−0.213909	−	0.370501i	−0.952934	+	0.303177i	$0.901953\pi$
$98$	5.61281e8	+	9.72168e8i	0.614700	+	1.06469i
$99$	−1.21400e7	+	2.10271e7i	−0.0127017	+	0.0220000i
$100$	−1.03516e8	−	1.79295e8i	−0.103516	−	0.179295i
$101$	6.62492e8	−	1.14747e9i	0.633482	−	1.09722i	−0.353353	−	0.935490i	$-0.614958\pi$
$101$	6.62492e8	−	1.14747e9i	0.633482	−	1.09722i	0.986835	−	0.161733i	$-0.0517082\pi$
$102$	−3.78547e7			−0.0346273
$103$	1.35861e9			1.18940			0.594698	−	0.803949i	$-0.297272\pi$
$103$	1.35861e9			1.18940			0.594698	+	0.803949i	$0.297272\pi$
$104$	1.06361e8	−	1.84222e8i	0.0891521	−	0.154416i
$105$	−1.62353e8	+	2.81204e8i	−0.130349	+	0.225772i
$106$	−2.40940e8			−0.185367
$107$	−1.72949e9			−1.27553			−0.637766	−	0.770230i	$-0.720141\pi$
$107$	−1.72949e9			−1.27553			−0.637766	+	0.770230i	$0.720141\pi$
$108$	−9.28297e7	+	1.60786e8i	−0.0656568	+	0.113721i
$109$	−1.25439e9	−	2.17266e9i	−0.851161	−	1.47425i	−0.880161	−	0.474676i	$-0.842565\pi$
$109$	−1.25439e9	−	2.17266e9i	−0.851161	−	1.47425i	0.0289994	−	0.999579i	$-0.490768\pi$
$110$	1.66931e7	−	2.89133e7i	0.0108710	−	0.0188292i
$111$	−3.94759e6	−	6.83743e6i	−0.00246819	−	0.00427503i
$112$	−3.44475e8	−	5.96649e8i	−0.206860	−	0.358292i
$113$	4.80191e8			0.277052			0.138526	−	0.990359i	$-0.455764\pi$
$113$	4.80191e8			0.277052			0.138526	+	0.990359i	$0.455764\pi$
$114$	−1.68126e8	−	1.64139e7i	−0.0932315	−	0.00910204i
$115$	−1.87397e9			−0.999133
$116$	−6.52587e7	−	1.13031e8i	−0.0334640	−	0.0579613i
$117$	5.02138e8	+	8.69729e8i	0.247735	+	0.429089i
$118$	8.60109e8	−	1.48975e9i	0.408399	−	0.707368i
$119$	6.69105e8	+	1.15892e9i	0.305867	+	0.529778i
$120$	6.32576e7	−	1.09565e8i	0.0278482	−	0.0482345i
$121$	−2.35637e9			−0.999331
$122$	2.65187e9			1.08376
$123$	4.58241e6	−	7.93696e6i	0.00180518	−	0.00312666i
$124$	7.48571e8	−	1.29656e9i	0.284338	−	0.492488i
$125$	1.90186e9			0.696762
$126$	3.25259e9			1.14964
$127$	1.65214e9	−	2.86159e9i	0.563548	−	0.976093i	−0.433635	−	0.901088i	$-0.642769\pi$
$127$	1.65214e9	−	2.86159e9i	0.563548	−	0.976093i	0.997183	−	0.0750049i	$-0.0238972\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	1.75500e8	−	3.03975e8i	0.0557987	−	0.0966461i
$130$	−6.90464e8	−	1.19592e9i	−0.212029	−	0.367246i
$131$	−3.23453e9	−	5.60238e9i	−0.959601	−	1.66208i	−0.723469	−	0.690357i	$-0.757453\pi$
$131$	−3.23453e9	−	5.60238e9i	−0.959601	−	1.66208i	−0.236133	−	0.971721i	$-0.575880\pi$
$132$	5.97408e6			0.00171273
$133$	2.46922e9	+	5.43731e9i	0.684270	+	1.50679i
$134$	3.07733e9			0.824522
$135$	6.02624e8	+	1.04378e9i	0.156151	+	0.270461i
$136$	−2.60703e8	−	4.51551e8i	−0.0653463	−	0.113183i
$137$	−3.02912e9	+	5.24659e9i	−0.734639	+	1.27243i	0.220242	+	0.975445i	$0.429315\pi$
$137$	−3.02912e9	+	5.24659e9i	−0.734639	+	1.27243i	−0.954881	+	0.296988i	$0.904018\pi$
$138$	−1.67663e8	−	2.90401e8i	−0.0393533	−	0.0681619i
$139$	3.01617e9	−	5.22415e9i	0.685312	−	1.18700i	−0.288026	−	0.957623i	$-0.592999\pi$
$139$	3.01617e9	−	5.22415e9i	0.685312	−	1.18700i	0.973338	−	0.229373i	$-0.0736677\pi$
$140$	−4.47247e9			−0.983947
$141$	1.10480e8			0.0235395
$142$	6.40913e7	−	1.11009e8i	0.0132282	−	0.0229120i
$143$	3.26039e7	−	5.64716e7i	0.00652014	−	0.0112932i
$144$	−1.26731e9			−0.245613
$145$	−8.47282e8			−0.159174
$146$	−2.89855e9	+	5.02043e9i	−0.527950	+	0.914436i
$147$	6.51994e8	+	1.12929e9i	0.115164	+	0.199470i
$148$	5.43737e7	−	9.41780e7i	0.00931561	−	0.0161351i
$149$	−1.51754e9	−	2.62845e9i	−0.252232	−	0.436879i	0.711908	−	0.702273i	$-0.247831\pi$
$149$	−1.51754e9	−	2.62845e9i	−0.252232	−	0.436879i	−0.964140	+	0.265394i	$0.914498\pi$
$150$	−1.20246e8	−	2.08273e8i	−0.0193937	−	0.0335909i
$151$	−5.96720e8			−0.0934059			−0.0467029	−	0.998909i	$-0.514871\pi$
$151$	−5.96720e8			−0.0934059			−0.0467029	+	0.998909i	$0.514871\pi$
$152$	−9.62080e8	−	2.11854e9i	−0.146189	−	0.321914i
$153$	2.46160e9			0.363167
$154$	−1.05596e8	−	1.82897e8i	−0.0151287	−	0.0262037i
$155$	−4.85951e9	−	8.41692e9i	−0.676238	−	1.17128i
$156$	1.23551e8	−	2.13996e8i	0.0167026	−	0.0289298i
$157$	1.33453e9	+	2.31148e9i	0.175299	+	0.303627i	0.940265	−	0.340444i	$-0.110577\pi$
$157$	1.33453e9	+	2.31148e9i	0.175299	+	0.303627i	−0.764966	+	0.644071i	$0.777244\pi$
$158$	−4.64119e9	+	8.03879e9i	−0.592479	+	1.02620i
$159$	−2.79880e8			−0.0347284
$160$	1.74261e9			0.210213
$161$	−5.92710e9	+	1.02660e10i	−0.695225	+	1.20417i
$162$	2.93714e9	−	5.08727e9i	0.335048	−	0.580320i
$163$	1.64590e9			0.182625			0.0913123	−	0.995822i	$-0.470894\pi$
$163$	1.64590e9			0.182625			0.0913123	+	0.995822i	$0.470894\pi$
$164$	1.26235e8			0.0136265
$165$	1.93910e7	−	3.35862e7i	0.00203668	−	0.00352764i
$166$	3.19974e9	+	5.54211e9i	0.327061	+	0.566486i
$167$	−9.80067e8	+	1.69753e9i	−0.0975060	+	0.168885i	−0.910652	−	0.413175i	$-0.864420\pi$
$167$	−9.80067e8	+	1.69753e9i	−0.0975060	+	0.168885i	0.813146	+	0.582060i	$0.197753\pi$
$168$	−4.00149e8	−	6.93078e8i	−0.0387552	−	0.0671259i
$169$	3.95368e9	+	6.84798e9i	0.372831	+	0.645761i
$170$	−3.38482e9			−0.310825
$171$	1.09328e10	+	1.06736e9i	0.977801	+	0.0954612i
$172$	4.83464e9			0.421198
$173$	7.11204e9	+	1.23184e10i	0.603652	+	1.04556i	0.992263	+	0.124155i	$0.0396219\pi$
$173$	7.11204e9	+	1.23184e10i	0.603652	+	1.04556i	−0.388610	+	0.921402i	$0.627045\pi$
$174$	−7.58056e7	−	1.31299e8i	−0.00626946	−	0.0108590i
$175$	−4.25086e9	+	7.36270e9i	−0.342614	+	0.593425i
$176$	4.11432e7	+	7.12621e7i	0.00323214	+	0.00559824i
$177$	9.99118e8	−	1.73052e9i	0.0765133	−	0.132525i
$178$	−1.70270e10			−1.27130
$179$	−6.79304e9			−0.494567			−0.247284	−	0.968943i	$-0.579538\pi$
$179$	−6.79304e9			−0.494567			−0.247284	+	0.968943i	$0.579538\pi$
$180$	−4.11350e9	+	7.12479e9i	−0.292069	+	0.505878i
$181$	2.66484e9	−	4.61563e9i	0.184551	−	0.319652i	−0.758874	−	0.651237i	$-0.774250\pi$
$181$	2.66484e9	−	4.61563e9i	0.184551	−	0.319652i	0.943425	+	0.331585i	$0.107584\pi$
$182$	−8.73534e9			−0.590145
$183$	3.08046e9			0.203042
$184$	2.30937e9	−	3.99995e9i	0.148530	−	0.257261i
$185$	−3.52979e8	−	6.11377e8i	−0.0221552	−	0.0383739i
$186$	8.69553e8	−	1.50611e9i	0.0532706	−	0.0922674i
$187$	−7.99160e7	−	1.38419e8i	−0.00477911	−	0.00827766i
$188$	7.60869e8	+	1.31786e9i	0.0444221	+	0.0769414i
$189$	7.62404e9			0.434617
$190$	−1.50332e10	−	1.46767e9i	−0.836873	−	0.0817026i
$191$	2.38518e10			1.29680			0.648398	−	0.761302i	$-0.275439\pi$
$191$	2.38518e10			1.29680			0.648398	+	0.761302i	$0.275439\pi$
$192$	1.55910e8	+	2.70044e8i	0.00827976	+	0.0143410i
$193$	−1.54218e10	−	2.67113e10i	−0.800067	−	1.38576i	−0.919571	−	0.392923i	$-0.871464\pi$
$193$	−1.54218e10	−	2.67113e10i	−0.800067	−	1.38576i	0.119505	−	0.992834i	$-0.461869\pi$
$194$	2.98415e9	−	5.16870e9i	0.151256	−	0.261983i
$195$	−8.02056e8	−	1.38920e9i	−0.0397236	−	0.0688033i
$196$	−8.98050e9	+	1.55547e10i	−0.434659	+	0.752851i
$197$	1.52752e10			0.722586			0.361293	−	0.932452i	$-0.382335\pi$
$197$	1.52752e10			0.722586			0.361293	+	0.932452i	$0.382335\pi$
$198$	−3.88481e8			−0.0179629
$199$	1.32688e10	−	2.29822e10i	0.599780	−	1.03885i	−0.393073	−	0.919507i	$-0.628588\pi$
$199$	1.32688e10	−	2.29822e10i	0.599780	−	1.03885i	0.992853	−	0.119343i	$-0.0380787\pi$
$200$	1.65626e9	−	2.86873e9i	0.0731970	−	0.126781i
$201$	3.57468e9			0.154474
$202$	2.11997e10			0.895879
$203$	−2.67982e9	+	4.64159e9i	−0.110758	+	0.191838i
$204$	−3.02837e8	−	5.24530e8i	−0.0122426	−	0.0212048i
$205$	4.09742e8	−	7.09693e8i	0.0162038	−	0.0280659i
$206$	1.08689e10	+	1.88254e10i	0.420515	+	0.728353i
$207$	1.09027e10	+	1.88841e10i	0.412733	+	0.714874i
$208$	3.40354e9			0.126080
$209$	−2.94917e8	−	6.49418e8i	−0.0106916	−	0.0235432i
$210$	−5.19531e9			−0.184342
$211$	−1.81994e10	−	3.15223e10i	−0.632100	−	1.09483i	−0.987122	−	0.159972i	$-0.948860\pi$
$211$	−1.81994e10	−	3.15223e10i	−0.632100	−	1.09483i	0.355021	−	0.934858i	$-0.384474\pi$
$212$	−1.92752e9	−	3.33856e9i	−0.0655372	−	0.113514i
$213$	7.44497e7	−	1.28951e8i	0.00247830	−	0.00429255i
$214$	−1.38359e10	−	2.39645e10i	−0.450969	−	0.781101i
$215$	1.56926e10	−	2.71803e10i	0.500865	−	0.867524i
$216$	−2.97055e9			−0.0928528
$217$	−6.14796e10			−1.88218
$218$	2.00702e10	−	3.47626e10i	0.601862	−	1.04246i
$219$	−3.36700e9	+	5.83182e9i	−0.0989111	+	0.171319i
$220$	5.34180e8			0.0153739
$221$	−6.61101e9			−0.186424
$222$	6.31615e7	−	1.09399e8i	0.00174528	−	0.00302291i
$223$	−3.61019e10	−	6.25303e10i	−0.977593	−	1.69324i	−0.671100	−	0.741367i	$-0.734178\pi$
$223$	−3.61019e10	−	6.25303e10i	−0.977593	−	1.69324i	−0.306493	−	0.951873i	$-0.599155\pi$
$224$	5.51161e9	−	9.54638e9i	0.146272	−	0.253351i
$225$	7.81934e9	+	1.35435e10i	0.203399	+	0.352297i
$226$	3.84153e9	+	6.65372e9i	0.0979526	+	0.169659i
$227$	6.73012e10			1.68231			0.841156	−	0.540793i	$-0.181876\pi$
$227$	6.73012e10			1.68231			0.841156	+	0.540793i	$0.181876\pi$
$228$	−1.11757e9	−	2.46093e9i	−0.0273885	−	0.0603105i
$229$	−4.21847e10			−1.01367			−0.506834	−	0.862044i	$-0.669184\pi$
$229$	−4.21847e10			−1.01367			−0.506834	+	0.862044i	$0.669184\pi$
$230$	−1.49918e10	−	2.59665e10i	−0.353247	−	0.611842i
$231$	−1.22662e8	−	2.12456e8i	−0.00283436	−	0.00490926i
$232$	1.04414e9	−	1.80850e9i	0.0236626	−	0.0409848i
$233$	2.54803e10	+	4.41331e10i	0.566373	+	0.980986i	0.996921	+	0.0784187i	$0.0249871\pi$
$233$	2.54803e10	+	4.41331e10i	0.566373	+	0.980986i	−0.430548	+	0.902568i	$0.641680\pi$
$234$	−8.03421e9	+	1.39157e10i	−0.175175	+	0.303412i
$235$	9.87869e9			0.211297
$236$	2.75235e10			0.577563
$237$	−5.39130e9	+	9.33800e9i	−0.111001	+	0.192259i
$238$	−1.07057e10	+	1.85428e10i	−0.216281	+	0.374609i
$239$	−4.23730e10			−0.840037			−0.420018	−	0.907516i	$-0.637976\pi$
$239$	−4.23730e10			−0.840037			−0.420018	+	0.907516i	$0.637976\pi$
$240$	2.02424e9			0.0393833
$241$	−3.25608e10	+	5.63969e10i	−0.621753	+	1.07691i	0.367406	+	0.930061i	$0.380246\pi$
$241$	−3.25608e10	+	5.63969e10i	−0.621753	+	1.07691i	−0.989159	+	0.146848i	$0.953087\pi$
$242$	−1.88510e10	−	3.26508e10i	−0.353317	−	0.611963i
$243$	1.05492e10	−	1.82718e10i	0.194085	−	0.336165i
$244$	2.12150e10	+	3.67454e10i	0.383167	+	0.663665i
$245$	5.82989e10	+	1.00977e11i	1.03374	+	1.79050i
$246$	1.46637e8			0.00255291
$247$	−2.93618e10	−	2.86655e9i	−0.501934	−	0.0490030i
$248$	2.39543e10			0.402115
$249$	3.71688e9	+	6.43782e9i	0.0612747	+	0.106131i
$250$	1.52149e10	+	2.63530e10i	0.246342	+	0.426678i
$251$	1.17173e10	−	2.02950e10i	0.186336	−	0.322743i	−0.757690	−	0.652615i	$-0.773672\pi$
$251$	1.17173e10	−	2.02950e10i	0.186336	−	0.322743i	0.944026	+	0.329871i	$0.107005\pi$
$252$	2.60208e10	+	4.50693e10i	0.406460	+	0.704009i
$253$	7.07916e8	−	1.22615e9i	0.0108627	−	0.0188148i
$254$	5.28686e10			0.796977
$255$	−3.93187e9			−0.0582329
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−4.88865e10	+	8.46739e10i	−0.699021	+	1.21074i	0.269786	+	0.962920i	$0.413047\pi$
$257$	−4.88865e10	+	8.46739e10i	−0.699021	+	1.21074i	−0.968806	+	0.247819i	$0.920286\pi$
$258$	5.61601e9			0.0789112
$259$	−4.46568e9			−0.0616649
$260$	1.10474e10	−	1.91347e10i	0.149927	−	0.259682i
$261$	4.92947e9	+	8.53809e9i	0.0657533	+	0.113888i
$262$	5.17525e10	−	8.96380e10i	0.678541	−	1.17527i
$263$	−5.12340e10	−	8.87398e10i	−0.660324	−	1.14371i	−0.980531	−	0.196367i	$-0.937086\pi$
$263$	−5.12340e10	−	8.87398e10i	−0.660324	−	1.14371i	0.320207	−	0.947348i	$-0.396248\pi$
$264$	4.77926e7	+	8.27793e7i	0.000605541	+	0.00104883i
$265$	−2.50258e10			−0.311733
$266$	−5.55879e10	+	7.77130e10i	−0.680789	+	0.951758i
$267$	−1.97789e10			−0.238178
$268$	2.46186e10	+	4.26407e10i	0.291512	+	0.504914i
$269$	4.06111e10	+	7.03405e10i	0.472889	+	0.819068i	0.999519	−	0.0310267i	$-0.00987769\pi$
$269$	4.06111e10	+	7.03405e10i	0.472889	+	0.819068i	−0.526629	+	0.850095i	$0.676544\pi$
$270$	−9.64199e9	+	1.67004e10i	−0.110415	+	0.191245i
$271$	−2.46808e10	−	4.27484e10i	−0.277970	−	0.481458i	0.692910	−	0.721024i	$-0.256328\pi$
$271$	−2.46808e10	−	4.27484e10i	−0.277970	−	0.481458i	−0.970880	+	0.239566i	$0.922995\pi$
$272$	4.17125e9	−	7.22482e9i	0.0462068	−	0.0800326i
$273$	−1.01471e10			−0.110563
$274$	−9.69319e10			−1.03894
$275$	5.07711e8	−	8.79380e8i	0.00535327	−	0.00927213i
$276$	2.68261e9	−	4.64641e9i	0.0278270	−	0.0481978i
$277$	−5.33841e10			−0.544820			−0.272410	−	0.962181i	$-0.587821\pi$
$277$	−5.33841e10			−0.544820			−0.272410	+	0.962181i	$0.587821\pi$
$278$	9.65173e10			0.969178
$279$	−5.65451e10	+	9.79389e10i	−0.558696	+	0.967690i
$280$	−3.57798e10	−	6.19724e10i	−0.347878	−	0.602542i
$281$	−2.05333e10	+	3.55647e10i	−0.196463	+	0.340284i	−0.947379	−	0.320114i	$-0.896279\pi$
$281$	−2.05333e10	+	3.55647e10i	−0.196463	+	0.340284i	0.750916	+	0.660397i	$0.229612\pi$
$282$	8.83839e8	+	1.53085e9i	0.00832247	+	0.0144149i
$283$	7.52748e10	+	1.30380e11i	0.697606	+	1.20829i	0.969294	+	0.245904i	$0.0790849\pi$
$283$	7.52748e10	+	1.30380e11i	0.697606	+	1.20829i	−0.271688	+	0.962385i	$0.587582\pi$
$284$	2.05092e9			0.0187075
$285$	−1.74628e10	−	1.70487e9i	−0.156788	−	0.0153069i
$286$	1.04332e9			0.00922087
$287$	−2.59190e9	−	4.48931e9i	−0.0225502	−	0.0390581i
$288$	−1.01385e10	−	1.75603e10i	−0.0868371	−	0.150406i
$289$	5.11917e10	−	8.86667e10i	0.431678	−	0.747688i
$290$	−6.77825e9	−	1.17403e10i	−0.0562765	−	0.0974737i
$291$	3.46645e9	−	6.00406e9i	0.0283378	−	0.0490825i
$292$	−9.27535e10			−0.746634
$293$	4.54996e10			0.360664			0.180332	−	0.983606i	$-0.442283\pi$
$293$	4.54996e10			0.360664			0.180332	+	0.983606i	$0.442283\pi$
$294$	−1.04319e10	+	1.80686e10i	−0.0814331	+	0.141046i
$295$	8.93374e10	−	1.54737e11i	0.686806	−	1.18958i
$296$	1.73996e9			0.0131743
$297$	−9.10594e8			−0.00679080
$298$	2.42806e10	−	4.20552e10i	0.178355	−	0.308920i
$299$	−2.92810e10	−	5.07161e10i	−0.211868	−	0.366966i
$300$	1.92394e9	−	3.33236e9i	0.0137134	−	0.0237524i
$301$	−9.92664e10	−	1.71935e11i	−0.697033	−	1.20730i
$302$	−4.77376e9	−	8.26839e9i	−0.0330240	−	0.0571992i
$303$	2.46260e10			0.167842
$304$	2.16587e10	−	3.02793e10i	0.145446	−	0.203336i
$305$	2.75443e11			1.82256
$306$	1.96928e10	+	3.41090e10i	0.128399	+	0.222394i
$307$	−1.14747e11	−	1.98747e11i	−0.737256	−	1.27696i	−0.953727	−	0.300675i	$-0.902788\pi$
$307$	−1.14747e11	−	1.98747e11i	−0.737256	−	1.27696i	0.216471	−	0.976289i	$-0.430545\pi$
$308$	1.68953e9	−	2.92635e9i	0.0106976	−	0.0185288i
$309$	1.26255e10	+	2.18679e10i	0.0787833	+	0.136457i
$310$	7.77522e10	−	1.34671e11i	0.478173	−	0.828220i
$311$	−2.62032e11			−1.58830			−0.794151	−	0.607720i	$-0.792084\pi$
$311$	−2.62032e11			−1.58830			−0.794151	+	0.607720i	$0.792084\pi$
$312$	3.95362e9			0.0236210
$313$	−6.50834e10	+	1.12728e11i	−0.383284	+	0.663867i	−0.991530	−	0.129882i	$-0.958540\pi$
$313$	−6.50834e10	+	1.12728e11i	−0.383284	+	0.663867i	0.608245	+	0.793749i	$0.291874\pi$
$314$	−2.13525e10	+	3.69836e10i	−0.123955	+	0.214697i
$315$	3.37839e11			1.93336
$316$	−1.48518e11			−0.837892
$317$	3.20863e10	−	5.55751e10i	0.178465	−	0.309110i	−0.762890	−	0.646528i	$-0.776220\pi$
$317$	3.20863e10	−	5.55751e10i	0.178465	−	0.309110i	0.941355	+	0.337418i	$0.109554\pi$
$318$	−2.23904e9	−	3.87814e9i	−0.0122784	−	0.0212667i
$319$	3.20071e8	−	5.54379e8i	0.00173056	−	0.00299743i
$320$	1.39409e10	+	2.41463e10i	0.0743215	+	0.128729i
$321$	−1.60721e10	−	2.78376e10i	−0.0844888	−	0.146339i
$322$	−1.89667e11			−0.983197
$323$	−4.20696e10	+	5.88141e10i	−0.215059	+	0.300656i
$324$	9.39884e10			0.473829
$325$	−2.10000e10	−	3.63731e10i	−0.104411	−	0.180845i
$326$	1.31672e10	+	2.28063e10i	0.0645676	+	0.111834i
$327$	2.33139e10	−	4.03808e10i	0.112759	−	0.195304i
$328$	1.00988e9	+	1.74917e9i	0.00481768	+	0.00834447i
$329$	3.12448e10	−	5.41176e10i	0.147027	−	0.254658i
$330$	6.20513e8			0.00288030
$331$	2.33010e11			1.06696			0.533481	−	0.845812i	$-0.320884\pi$
$331$	2.33010e11			1.06696			0.533481	+	0.845812i	$0.320884\pi$
$332$	−5.11958e10	+	8.86738e10i	−0.231267	+	0.400566i
$333$	−4.10725e9	+	7.11396e9i	−0.0183042	+	0.0317039i
$334$	−3.13621e10			−0.137894
$335$	3.19634e11			1.38660
$336$	6.40238e9	−	1.10892e10i	0.0274040	−	0.0474652i
$337$	−3.75648e10	−	6.50642e10i	−0.158652	−	0.274794i	0.775731	−	0.631064i	$-0.217382\pi$
$337$	−3.75648e10	−	6.50642e10i	−0.158652	−	0.274794i	−0.934383	+	0.356270i	$0.884048\pi$
$338$	−6.32589e10	+	1.09568e11i	−0.263631	+	0.456622i
$339$	4.46239e9	+	7.72908e9i	0.0183514	+	0.0317855i
$340$	−2.70786e10	−	4.69015e10i	−0.109893	−	0.190341i
$341$	7.34295e9			0.0294087
$342$	7.26730e10	+	1.60029e11i	0.287247	+	0.632529i
$343$	3.13343e11			1.22235
$344$	3.86771e10	+	6.69907e10i	0.148916	+	0.257930i
$345$	−1.74147e10	−	3.01632e10i	−0.0661806	−	0.114628i
$346$	−1.13793e11	+	1.97095e11i	−0.426847	+	0.739320i
$347$	−6.92543e10	−	1.19952e11i	−0.256427	−	0.444145i	0.708855	−	0.705354i	$-0.249212\pi$
$347$	−6.92543e10	−	1.19952e11i	−0.256427	−	0.444145i	−0.965282	+	0.261209i	$0.915879\pi$
$348$	1.21289e9	−	2.10079e9i	0.00443318	−	0.00767848i
$349$	−4.11685e11			−1.48543			−0.742713	−	0.669610i	$-0.766461\pi$
$349$	−4.11685e11			−1.48543			−0.742713	+	0.669610i	$0.766461\pi$
$350$	−1.36027e11			−0.484530
$351$	−1.88321e10	+	3.26181e10i	−0.0662241	+	0.114704i
$352$	−6.58291e8	+	1.14019e9i	−0.00228547	+	0.00395855i
$353$	4.34707e11			1.49008			0.745041	−	0.667019i	$-0.232430\pi$
$353$	4.34707e11			1.49008			0.745041	+	0.667019i	$0.232430\pi$
$354$	3.19718e10			0.108206
$355$	6.65701e9	−	1.15303e10i	0.0222460	−	0.0385312i
$356$	−1.36216e11	−	2.35934e11i	−0.449474	−	0.778511i
$357$	−1.24359e10	+	2.15396e10i	−0.0405201	+	0.0701829i
$358$	−5.43443e10	−	9.41271e10i	−0.174856	−	0.302859i
$359$	−3.38791e10	−	5.86804e10i	−0.107648	−	0.186452i	0.807169	−	0.590321i	$-0.200999\pi$
$359$	−3.38791e10	−	5.86804e10i	−0.107648	−	0.186452i	−0.914817	+	0.403868i	$0.867665\pi$
$360$	−1.31632e11			−0.413048
$361$	−2.12348e11	+	2.42973e11i	−0.658060	+	0.752966i
$362$	8.52747e10			0.260995
$363$	−2.18976e10	−	3.79278e10i	−0.0661938	−	0.114651i
$364$	−6.98827e10	−	1.21040e11i	−0.208648	−	0.361388i
$365$	−3.01065e11	+	5.21460e11i	−0.887855	+	1.53781i
$366$	2.46437e10	+	4.26841e10i	0.0717862	+	0.124337i
$367$	−8.87909e10	+	1.53790e11i	−0.255488	+	0.442519i	−0.965028	−	0.262147i	$-0.915570\pi$
$367$	−8.87909e10	+	1.53790e11i	−0.255488	+	0.442519i	0.709540	+	0.704665i	$0.248903\pi$
$368$	7.38999e10			0.210053
$369$	−9.53547e9			−0.0267746
$370$	5.64766e9	−	9.78204e9i	0.0156661	−	0.0271345i
$371$	−7.91530e10	+	1.37097e11i	−0.216913	+	0.375704i
$372$	2.78257e10			0.0753361
$373$	1.40892e11			0.376874			0.188437	−	0.982085i	$-0.439658\pi$
$373$	1.40892e11			0.376874			0.188437	+	0.982085i	$0.439658\pi$
$374$	1.27866e9	−	2.21470e9i	0.00337934	−	0.00585319i
$375$	1.76739e10	+	3.06121e10i	0.0461521	+	0.0799379i
$376$	−1.21739e10	+	2.10858e10i	−0.0314112	+	0.0544058i
$377$	−1.32388e10	−	2.29303e10i	−0.0337531	−	0.0584621i
$378$	6.09923e10	+	1.05642e11i	0.153660	+	0.266148i
$379$	−3.12280e11			−0.777442			−0.388721	−	0.921355i	$-0.627083\pi$
$379$	−3.12280e11			−0.777442			−0.388721	+	0.921355i	$0.627083\pi$
$380$	−9.99289e10	−	2.20047e11i	−0.245847	−	0.541364i
$381$	6.14131e10			0.149313
$382$	1.90815e11	+	3.30501e11i	0.458486	+	0.794122i
$383$	−5.75763e8	−	9.97251e8i	−0.00136725	−	0.00236815i	0.865341	−	0.501184i	$-0.167102\pi$
$383$	−5.75763e8	−	9.97251e8i	−0.00136725	−	0.00236815i	−0.866708	+	0.498815i	$0.833769\pi$
$384$	−2.49456e9	+	4.32070e9i	−0.00585467	+	0.0101406i
$385$	−1.09680e10	−	1.89971e10i	−0.0254421	−	0.0440670i
$386$	2.46748e11	−	4.27381e11i	0.565733	−	0.979878i
$387$	−3.65196e11			−0.827612
$388$	9.54929e10			0.213909
$389$	1.38214e11	−	2.39394e11i	0.306041	−	0.530078i	−0.671452	−	0.741048i	$-0.734329\pi$
$389$	1.38214e11	−	2.39394e11i	0.306041	−	0.530078i	0.977493	+	0.210970i	$0.0676623\pi$
$390$	1.28329e10	−	2.22272e10i	0.0280888	−	0.0486513i
$391$	−1.43542e11			−0.310588
$392$	−2.87376e11			−0.614700
$393$	6.01167e10	−	1.04125e11i	0.127124	−	0.220186i
$394$	1.22202e11	+	2.11660e11i	0.255473	+	0.442491i
$395$	−4.82069e11	+	8.34969e11i	−0.996374	+	1.72577i
$396$	−3.10785e9	−	5.38295e9i	−0.00635084	−	0.0110000i
$397$	1.58190e11	+	2.73992e11i	0.319610	+	0.553581i	0.980407	−	0.196984i	$-0.0631147\pi$
$397$	1.58190e11	+	2.73992e11i	0.319610	+	0.553581i	−0.660797	+	0.750565i	$0.729781\pi$
$398$	4.24601e11			0.848217
$399$	−6.45719e10	+	9.02728e10i	−0.127546	+	0.178311i
$400$	5.30003e10			0.103516
$401$	3.43039e11	+	5.94161e11i	0.662512	+	1.14750i	0.979953	+	0.199227i	$0.0638430\pi$
$401$	3.43039e11	+	5.94161e11i	0.662512	+	1.14750i	−0.317441	+	0.948278i	$0.602824\pi$
$402$	2.85974e10	+	4.95322e10i	0.0546147	+	0.0945955i
$403$	1.51860e11	−	2.63030e11i	0.286795	−	0.496744i
$404$	1.69598e11	+	2.93752e11i	0.316741	+	0.548611i
$405$	3.05073e11	−	5.28402e11i	0.563451	−	0.975926i
$406$	−8.57544e10			−0.156635
$407$	5.33368e8			0.000963500
$408$	4.84540e9	−	8.39248e9i	0.00865683	−	0.0149941i
$409$	1.70805e11	−	2.95843e11i	0.301818	−	0.522765i	−0.674730	−	0.738065i	$-0.735740\pi$
$409$	1.70805e11	−	2.95843e11i	0.301818	−	0.522765i	0.976548	+	0.215300i	$0.0690731\pi$
$410$	1.31117e10			0.0229157
$411$	−1.12598e11			−0.194644
$412$	−1.73902e11	+	3.01207e11i	−0.297349	+	0.515023i
$413$	−5.65121e11	−	9.78819e11i	−0.955799	−	1.65549i
$414$	−1.74444e11	+	3.02146e11i	−0.291846	+	0.505493i
$415$	3.32349e11	+	5.75645e11i	0.550019	+	0.952661i
$416$	2.72284e10	+	4.71609e10i	0.0445760	+	0.0772079i
$417$	1.12116e11			0.181575
$418$	6.63926e9	−	9.28183e9i	0.0106372	−	0.0148710i
$419$	−6.33405e11			−1.00396			−0.501982	−	0.864878i	$-0.667396\pi$
$419$	−6.33405e11			−1.00396			−0.501982	+	0.864878i	$0.667396\pi$
$420$	−4.15625e10	−	7.19883e10i	−0.0651747	−	0.112886i
$421$	1.63849e11	+	2.83795e11i	0.254199	+	0.440286i	0.964678	−	0.263433i	$-0.0848547\pi$
$421$	1.63849e11	+	2.83795e11i	0.254199	+	0.440286i	−0.710478	+	0.703719i	$0.751521\pi$
$422$	2.91190e11	−	5.04357e11i	0.446962	−	0.774162i
$423$	−5.74740e10	−	9.95479e10i	−0.0872850	−	0.151182i
$424$	3.08403e10	−	5.34170e10i	0.0463418	−	0.0802663i
$425$	−1.02947e11			−0.153061
$426$	2.38239e9			0.00350485
$427$	8.71186e11	−	1.50894e12i	1.26819	−	2.19657i
$428$	2.21375e11	−	3.83433e11i	0.318883	−	0.552322i
$429$	1.21194e9			0.00172753
$430$	5.02162e11			0.708330
$431$	−5.37022e11	+	9.30149e11i	−0.749625	+	1.29839i	0.198377	+	0.980126i	$0.436433\pi$
$431$	−5.37022e11	+	9.30149e11i	−0.749625	+	1.29839i	−0.948002	+	0.318263i	$0.896900\pi$
$432$	−2.37644e10	−	4.11611e10i	−0.0328284	−	0.0568605i
$433$	5.70440e11	−	9.88031e11i	0.779856	−	1.35075i	−0.152169	−	0.988354i	$-0.548626\pi$
$433$	5.70440e11	−	9.88031e11i	0.779856	−	1.35075i	0.932025	−	0.362395i	$-0.118041\pi$
$434$	−4.91837e11	−	8.51886e11i	−0.665453	−	1.15260i
$435$	−7.87374e9	−	1.36377e10i	−0.0105434	−	0.0182617i
$436$	6.42246e11			0.851161
$437$	−6.37522e11	−	6.22403e10i	−0.836236	−	0.0816404i
$438$	−1.07744e11			−0.139881
$439$	5.95323e11	+	1.03113e12i	0.765002	+	1.32502i	0.940246	+	0.340497i	$0.110595\pi$
$439$	5.95323e11	+	1.03113e12i	0.765002	+	1.32502i	−0.175244	+	0.984525i	$0.556071\pi$
$440$	4.27344e9	+	7.40181e9i	0.00543551	+	0.00941458i
$441$	6.78363e11	−	1.17496e12i	0.854061	−	1.47928i
$442$	−5.28881e10	−	9.16048e10i	−0.0659109	−	0.114161i
$443$	−2.09324e11	+	3.62559e11i	−0.258227	+	0.447262i	−0.965767	−	0.259411i	$-0.916472\pi$
$443$	−2.09324e11	+	3.62559e11i	−0.258227	+	0.447262i	0.707540	+	0.706673i	$0.249805\pi$
$444$	2.02117e9			0.00246819
$445$	−1.76856e12			−2.13796
$446$	5.77630e11	−	1.00048e12i	0.691262	−	1.19730i
$447$	2.82048e10	−	4.88521e10i	0.0334148	−	0.0578761i
$448$	1.76371e11			0.206860
$449$	1.47036e11			0.170732			0.0853660	−	0.996350i	$-0.472794\pi$
$449$	1.47036e11			0.170732			0.0853660	+	0.996350i	$0.472794\pi$
$450$	−1.25109e11	+	2.16696e11i	−0.143825	+	0.249112i
$451$	3.09569e8	+	5.36190e8i	0.000352341	+	0.000610273i
$452$	−6.14644e10	+	1.06460e11i	−0.0692629	+	0.119967i
$453$	−5.54528e9	−	9.60471e9i	−0.00618703	−	0.0107162i
$454$	5.38410e11	+	9.32553e11i	0.594787	+	1.03020i
$455$	−9.07318e11			−0.992449
$456$	2.51591e10	−	3.51730e10i	0.0272492	−	0.0380949i
$457$	−1.38521e12			−1.48557			−0.742783	−	0.669532i	$-0.766495\pi$
$457$	−1.38521e12			−1.48557			−0.742783	+	0.669532i	$0.766495\pi$
$458$	−3.37478e11	−	5.84529e11i	−0.358386	−	0.620742i
$459$	4.61597e10	+	7.99510e10i	0.0485407	+	0.0840749i
$460$	2.39869e11	−	4.15465e11i	0.249783	−	0.432637i
$461$	7.20032e11	+	1.24713e12i	0.742502	+	1.28605i	0.951353	+	0.308104i	$0.0996946\pi$
$461$	7.20032e11	+	1.24713e12i	0.742502	+	1.28605i	−0.208850	+	0.977948i	$0.566972\pi$
$462$	1.96259e9	−	3.39930e9i	0.00200420	−	0.00347137i
$463$	−7.56258e10			−0.0764813			−0.0382407	−	0.999269i	$-0.512175\pi$
$463$	−7.56258e10			−0.0764813			−0.0382407	+	0.999269i	$0.512175\pi$
$464$	3.34124e10			0.0334640
$465$	9.03183e10	−	1.56436e11i	0.0895855	−	0.155167i
$466$	−4.07684e11	+	7.06130e11i	−0.400486	+	0.693662i
$467$	1.52022e10			0.0147904			0.00739522	−	0.999973i	$-0.497646\pi$
$467$	1.52022e10			0.0147904			0.00739522	+	0.999973i	$0.497646\pi$
$468$	−2.57095e11			−0.247735
$469$	1.01096e12	−	1.75103e12i	0.964837	−	1.67115i
$470$	7.90295e10	+	1.36883e11i	0.0747049	+	0.129393i
$471$	−2.48034e10	+	4.29608e10i	−0.0232230	+	0.0402234i
$472$	2.20188e11	+	3.81377e11i	0.204199	+	0.353684i
$473$	1.18561e10	+	2.05354e10i	0.0108910	+	0.0188637i
$474$	−1.72521e11			−0.156979
$475$	−4.57225e11	−	4.46381e10i	−0.412106	−	0.0402332i
$476$	−3.42582e11			−0.305867
$477$	1.45600e11	+	2.52186e11i	0.128774	+	0.223043i
$478$	−3.38984e11	−	5.87137e11i	−0.296998	−	0.514415i
$479$	4.24831e11	−	7.35830e11i	0.368729	−	0.638657i	−0.620638	−	0.784097i	$-0.713127\pi$
$479$	4.24831e11	−	7.35830e11i	0.368729	−	0.638657i	0.989367	+	0.145440i	$0.0464599\pi$
$480$	1.61940e10	+	2.80488e10i	0.0139241	+	0.0241173i
$481$	1.10306e10	−	1.91056e10i	0.00939610	−	0.0162745i
$482$	−1.04195e12			−0.879292
$483$	−2.20321e11			−0.184202
$484$	3.01616e11	−	5.22413e11i	0.249833	−	0.432723i
$485$	3.09956e11	−	5.36860e11i	0.254368	−	0.440579i
$486$	3.37574e11			0.274477
$487$	2.63077e11			0.211935			0.105967	−	0.994370i	$-0.466206\pi$
$487$	2.63077e11			0.211935			0.105967	+	0.994370i	$0.466206\pi$
$488$	−3.39440e11	+	5.87927e11i	−0.270940	+	0.469282i
$489$	1.52953e10	+	2.64922e10i	0.0120967	+	0.0209521i
$490$	−9.32782e11	+	1.61563e12i	−0.730967	+	1.26607i
$491$	8.11495e11	+	1.40555e12i	0.630114	+	1.09139i	0.987528	+	0.157443i	$0.0503251\pi$
$491$	8.11495e11	+	1.40555e12i	0.630114	+	1.09139i	−0.357414	+	0.933946i	$0.616342\pi$
$492$	1.17310e9	+	2.03186e9i	0.000902590	+	0.00156333i
$493$	−6.49000e10			−0.0494804
$494$	−1.95174e11	−	4.29781e11i	−0.147452	−	0.324696i
$495$	−4.03505e10			−0.0302083
$496$	1.91634e11	+	3.31920e11i	0.142169	+	0.246244i
$497$	−4.21102e10	−	7.29371e10i	−0.0309588	−	0.0536222i
$498$	−5.94700e10	+	1.03005e11i	−0.0433277	+	0.0750458i
$499$	3.92335e11	+	6.79545e11i	0.283273	+	0.490643i	0.972189	−	0.234198i	$-0.0752464\pi$
$499$	3.92335e11	+	6.79545e11i	0.283273	+	0.490643i	−0.688916	+	0.724841i	$0.741913\pi$
$500$	−2.43438e11	+	4.21648e11i	−0.174190	+	0.301707i
$501$	−3.64308e10			−0.0258344
$502$	3.74954e11			0.263519
$503$	2.99507e11	−	5.18762e11i	0.208618	−	0.361336i	−0.742662	−	0.669667i	$-0.766437\pi$
$503$	2.99507e11	−	5.18762e11i	0.208618	−	0.361336i	0.951279	+	0.308330i	$0.0997702\pi$
$504$	−4.16332e11	+	7.21108e11i	−0.287410	+	0.497809i
$505$	2.20196e12			1.50660
$506$	2.26533e10			0.0153622
$507$	−7.34827e10	+	1.27276e11i	−0.0493912	+	0.0855480i
$508$	4.22948e11	+	7.32568e11i	0.281774	+	0.488047i
$509$	−8.67747e11	+	1.50298e12i	−0.573011	+	0.992484i	0.423244	+	0.906016i	$0.360891\pi$
$509$	−8.67747e11	+	1.50298e12i	−0.573011	+	0.992484i	−0.996255	+	0.0864681i	$0.972442\pi$
$510$	−3.14550e10	−	5.44816e10i	−0.0205884	−	0.0356602i
$511$	1.90445e12	+	3.29860e12i	1.23559	+	2.14011i
$512$	−6.87195e10			−0.0441942
$513$	1.70345e11	+	3.75105e11i	0.108593	+	0.239125i
$514$	−1.56437e12			−0.988565
$515$	1.12892e12	+	1.95535e12i	0.707182	+	1.22487i
$516$	4.49280e10	+	7.78177e10i	0.0278993	+	0.0483231i
$517$	−3.73179e9	+	6.46365e9i	−0.00229726	+	0.00397897i
$518$	−3.57254e10	−	6.18782e10i	−0.0218018	−	0.0377619i
$519$	−1.32184e11	+	2.28949e11i	−0.0799696	+	0.138511i
$520$	3.53518e11			0.212029
$521$	−2.75171e12			−1.63619			−0.818093	−	0.575086i	$-0.804969\pi$
$521$	−2.75171e12			−1.63619			−0.818093	+	0.575086i	$0.804969\pi$
$522$	−7.88715e10	+	1.36609e11i	−0.0464946	+	0.0805310i
$523$	1.71703e11	−	2.97398e11i	0.100351	−	0.173812i	−0.811479	−	0.584382i	$-0.801337\pi$
$523$	1.71703e11	−	2.97398e11i	0.100351	−	0.173812i	0.911829	+	0.410570i	$0.134670\pi$
$524$	1.65608e12			0.959601
$525$	−1.58012e11			−0.0907764
$526$	8.19743e11	−	1.41984e12i	0.466919	−	0.808728i
$527$	−3.72228e11	−	6.44718e11i	−0.210214	−	0.364101i
$528$	−7.64682e8	+	1.32447e9i	−0.000428182	+	0.000741633i
$529$	2.64810e11	+	4.58664e11i	0.147022	+	0.254650i
$530$	−2.00207e11	−	3.46768e11i	−0.110214	−	0.190896i
$531$	−2.07905e12			−1.13485
$532$	−1.52153e12	−	1.48544e11i	−0.823526	−	0.0803995i
$533$	2.56090e10			0.0137442
$534$	−1.58231e11	−	2.74065e11i	−0.0842087	−	0.145854i
$535$	−1.43710e12	−	2.48914e12i	−0.758396	−	1.31358i
$536$	−3.93898e11	+	6.82251e11i	−0.206130	+	0.357028i
$537$	−6.31273e10	−	1.09340e11i	−0.0327592	−	0.0567406i
$538$	−6.49778e11	+	1.12545e12i	−0.334383	+	0.579169i
$539$	−8.80924e10			−0.0449561
$540$	−3.08544e11			−0.156151
$541$	1.35006e12	−	2.33837e12i	0.677587	−	1.17361i	−0.298119	−	0.954529i	$-0.596359\pi$
$541$	1.35006e12	−	2.33837e12i	0.677587	−	1.17361i	0.975706	−	0.219086i	$-0.0703075\pi$
$542$	3.94893e11	−	6.83975e11i	0.196554	−	0.340442i
$543$	9.90567e10			0.0488973
$544$	1.33480e11			0.0653463
$545$	2.08464e12	−	3.61070e12i	1.01215	−	1.75310i
$546$	−8.11770e10	−	1.40603e11i	−0.0390900	−	0.0677059i
$547$	−1.26553e12	+	2.19196e12i	−0.604406	+	1.04686i	0.387739	+	0.921769i	$0.373256\pi$
$547$	−1.26553e12	+	2.19196e12i	−0.604406	+	1.04686i	−0.992145	+	0.125092i	$0.960077\pi$
$548$	−7.75455e11	−	1.34313e12i	−0.367320	−	0.636216i
$549$	−1.60252e12	−	2.77565e12i	−0.752885	−	1.30404i
$550$	1.62467e10			0.00757067
$551$	−2.88243e11	−	2.81408e10i	−0.133222	−	0.0130063i
$552$	8.58435e10			0.0393533
$553$	3.04943e12	+	5.28176e12i	1.38661	+	2.40168i
$554$	−4.27073e11	−	7.39712e11i	−0.192623	−	0.333633i
$555$	6.56042e9	−	1.13630e10i	0.00293504	−	0.00508363i
$556$	7.72138e11	+	1.33738e12i	0.342656	+	0.593498i
$557$	1.81494e12	−	3.14357e12i	0.798940	−	1.38381i	−0.121366	−	0.992608i	$-0.538728\pi$
$557$	1.81494e12	−	3.14357e12i	0.798940	−	1.38381i	0.920307	−	0.391197i	$-0.127939\pi$
$558$	−1.80944e12			−0.790116
$559$	9.80789e11			0.424837
$560$	5.72477e11	−	9.91559e11i	0.245987	−	0.426062i
$561$	1.48531e9	−	2.57263e9i	0.000633118	−	0.00109659i
$562$	−6.57066e11			−0.277840
$563$	3.16179e12			1.32631			0.663156	−	0.748481i	$-0.269217\pi$
$563$	3.16179e12			1.32631			0.663156	+	0.748481i	$0.269217\pi$
$564$	−1.41414e10	+	2.44937e10i	−0.00588487	+	0.0101929i
$565$	3.99010e11	+	6.91105e11i	0.164727	+	0.285316i
$566$	−1.20440e12	+	2.08608e12i	−0.493282	+	0.854390i
$567$	−1.92980e12	−	3.34251e12i	−0.784131	−	1.35816i
$568$	1.64074e10	+	2.84184e10i	0.00661412	+	0.0114560i
$569$	−4.07971e12			−1.63164			−0.815820	−	0.578305i	$-0.803714\pi$
$569$	−4.07971e12			−1.63164			−0.815820	+	0.578305i	$0.803714\pi$
$570$	−1.16079e11	−	2.55611e11i	−0.0460593	−	0.101424i
$571$	2.45374e12			0.965977			0.482989	−	0.875627i	$-0.339551\pi$
$571$	2.45374e12			0.965977			0.482989	+	0.875627i	$0.339551\pi$
$572$	8.34659e9	+	1.44567e10i	0.00326007	+	0.00564661i
$573$	2.21654e11	+	3.83916e11i	0.0858972	+	0.148778i
$574$	4.14704e10	−	7.18289e10i	0.0159454	−	0.0276182i
$575$	−4.55966e11	−	7.89756e11i	−0.173951	−	0.301292i
$576$	1.62215e11	−	2.80965e11i	0.0614031	−	0.106353i
$577$	−2.16617e12			−0.813581			−0.406791	−	0.913521i	$-0.633352\pi$
$577$	−2.16617e12			−0.813581			−0.406791	+	0.913521i	$0.633352\pi$
$578$	1.63814e12			0.610485
$579$	2.86627e11	−	4.96453e11i	0.105990	−	0.183580i
$580$	1.08452e11	−	1.87845e11i	0.0397935	−	0.0689243i
$581$	4.20468e12			1.53088
$582$	1.10926e11			0.0400757
$583$	9.45381e9	−	1.63745e10i	0.00338921	−	0.00587028i
$584$	−7.42028e11	−	1.28523e12i	−0.263975	−	0.457218i
$585$	−8.34493e11	+	1.44539e12i	−0.294592	+	0.510249i
$586$	3.63997e11	+	6.30460e11i	0.127514	+	0.220861i
$587$	−7.65779e11	−	1.32637e12i	−0.266215	−	0.461097i	0.701666	−	0.712506i	$-0.252440\pi$
$587$	−7.65779e11	−	1.32637e12i	−0.266215	−	0.461097i	−0.967881	+	0.251408i	$0.919106\pi$
$588$	−3.33821e11			−0.115164
$589$	−1.37364e12	−	3.02482e12i	−0.470279	−	1.03557i
$590$	2.85880e12			0.971290
$591$	1.41952e11	+	2.45868e11i	0.0478627	+	0.0829006i
$592$	1.39197e10	+	2.41096e10i	0.00465780	+	0.00806755i
$593$	9.61000e11	−	1.66450e12i	0.319137	−	0.552762i	−0.661171	−	0.750235i	$-0.729940\pi$
$593$	9.61000e11	−	1.66450e12i	0.319137	−	0.552762i	0.980308	+	0.197473i	$0.0632736\pi$
$594$	−7.28475e9	−	1.26176e10i	−0.00240091	−	0.00415850i
$595$	−1.11197e12	+	1.92599e12i	−0.363720	+	0.629982i
$596$	7.76979e11			0.252232
$597$	4.93224e11			0.158913
$598$	4.68495e11	−	8.11458e11i	0.149813	−	0.259484i
$599$	5.39302e11	−	9.34098e11i	0.171163	−	0.296464i	−0.767663	−	0.640853i	$-0.778581\pi$
$599$	5.39302e11	−	9.34098e11i	0.171163	−	0.296464i	0.938827	+	0.344389i	$0.111914\pi$
$600$	6.15661e10			0.0193937
$601$	−1.88580e12			−0.589605			−0.294802	−	0.955558i	$-0.595254\pi$
$601$	−1.88580e12			−0.589605			−0.294802	+	0.955558i	$0.595254\pi$
$602$	1.58826e12	−	2.75095e12i	0.492877	−	0.853687i
$603$	−1.85963e12	−	3.22097e12i	−0.572793	−	0.992106i
$604$	7.63801e10	−	1.32294e11i	0.0233515	−	0.0404459i
$605$	−1.95800e12	−	3.39136e12i	−0.594175	−	1.02914i
$606$	1.97008e11	+	3.41228e11i	0.0593413	+	0.102782i
$607$	−3.54409e12			−1.05963			−0.529817	−	0.848112i	$-0.677739\pi$
$607$	−3.54409e12			−1.05963			−0.529817	+	0.848112i	$0.677739\pi$
$608$	5.92831e11	+	5.78772e10i	0.175940	+	0.0171768i
$609$	−9.96139e10			−0.0293455
$610$	2.20355e12	+	3.81665e12i	0.644374	+	1.11609i
$611$	1.54355e11	+	2.67351e11i	0.0448060	+	0.0776062i
$612$	−3.15085e11	+	5.45743e11i	−0.0907918	+	0.157256i
$613$	2.40000e12	+	4.15692e12i	0.686497	+	1.18905i	0.972964	+	0.230958i	$0.0741860\pi$
$613$	2.40000e12	+	4.15692e12i	0.686497	+	1.18905i	−0.286466	+	0.958090i	$0.592481\pi$
$614$	1.83595e12	−	3.17996e12i	0.521318	−	0.902950i
$615$	1.52308e10			0.00429324
$616$	5.40650e10			0.0151287
$617$	−2.04341e12	+	3.53930e12i	−0.567640	+	0.983182i	0.429158	+	0.903229i	$0.358810\pi$
$617$	−2.04341e12	+	3.53930e12i	−0.567640	+	0.983182i	−0.996799	+	0.0799527i	$0.974523\pi$
$618$	−2.02007e11	+	3.49887e11i	−0.0557082	+	0.0964894i
$619$	1.59317e12			0.436169			0.218084	−	0.975930i	$-0.430019\pi$
$619$	1.59317e12			0.436169			0.218084	+	0.975930i	$0.430019\pi$
$620$	2.48807e12			0.676238
$621$	−4.08894e11	+	7.08225e11i	−0.110331	+	0.191099i
$622$	−2.09626e12	−	3.63083e12i	−0.561550	−	0.972633i
$623$	−5.59368e12	+	9.68854e12i	−1.48765	+	2.57669i
$624$	3.16289e10	+	5.47829e10i	0.00835130	+	0.0144649i
$625$	2.37010e12	+	4.10513e12i	0.621308	+	1.07614i
$626$	−2.08267e12			−0.542045
$627$	7.71229e9	−	1.07819e10i	0.00199287	−	0.00278607i
$628$	−6.83280e11			−0.175299
$629$	−2.70374e10	−	4.68302e10i	−0.00688711	−	0.0119288i
$630$	2.70271e12	+	4.68123e12i	0.683545	+	1.18393i
$631$	1.46281e12	−	2.53366e12i	0.367329	−	0.636233i	−0.621818	−	0.783162i	$-0.713606\pi$
$631$	1.46281e12	−	2.53366e12i	0.367329	−	0.636233i	0.989147	+	0.146929i	$0.0469389\pi$
$632$	−1.18815e12	−	2.05793e12i	−0.296239	−	0.513102i
$633$	3.38252e11	−	5.85870e11i	0.0837382	−	0.145039i
$634$	1.02676e12			0.252388
$635$	5.49132e12			1.34028
$636$	3.58247e10	−	6.20502e10i	0.00868211	−	0.0150379i
$637$	−1.82185e12	+	3.15553e12i	−0.438414	+	0.759356i
$638$	1.02423e10			0.00244739
$639$	−1.54921e11			−0.0367585
$640$	−2.23054e11	+	3.86340e11i	−0.0525533	+	0.0910249i
$641$	3.37588e12	+	5.84720e12i	0.789817	+	1.36800i	0.926079	+	0.377330i	$0.123158\pi$
$641$	3.37588e12	+	5.84720e12i	0.789817	+	1.36800i	−0.136262	+	0.990673i	$0.543509\pi$
$642$	2.57153e11	−	4.45402e11i	0.0597426	−	0.103477i
$643$	−1.76559e12	−	3.05810e12i	−0.407325	−	0.705508i	0.587264	−	0.809396i	$-0.300205\pi$
$643$	−1.76559e12	−	3.05810e12i	−0.407325	−	0.705508i	−0.994589	+	0.103887i	$0.966872\pi$
$644$	−1.51734e12	−	2.62810e12i	−0.347613	−	0.602083i
$645$	5.83320e11			0.132705
$646$	−1.15151e12	−	1.12420e11i	−0.260148	−	0.0253979i
$647$	−3.12958e12			−0.702130			−0.351065	−	0.936351i	$-0.614180\pi$
$647$	−3.12958e12			−0.702130			−0.351065	+	0.936351i	$0.614180\pi$
$648$	7.51907e11	+	1.30234e12i	0.167524	+	0.290160i
$649$	6.74965e10	+	1.16907e11i	0.0149341	+	0.0258667i
$650$	3.36000e11	−	5.81970e11i	0.0738295	−	0.127876i
$651$	−5.71326e11	−	9.89566e11i	−0.124672	−	0.215939i
$652$	−2.10675e11	+	3.64900e11i	−0.0456562	+	0.0790788i
$653$	−7.15983e12			−1.54097			−0.770484	−	0.637460i	$-0.779985\pi$
$653$	−7.15983e12			−1.54097			−0.770484	+	0.637460i	$0.779985\pi$
$654$	7.46044e11			0.159465
$655$	5.37541e12	−	9.31048e12i	1.14110	−	1.97645i
$656$	−1.61581e10	+	2.79866e10i	−0.00340661	+	0.00590043i
$657$	7.00635e12			1.46706
$658$	9.99834e11			0.207927
$659$	−3.26754e12	+	5.65955e12i	−0.674896	+	1.16895i	0.301603	+	0.953434i	$0.402478\pi$
$659$	−3.26754e12	+	5.65955e12i	−0.674896	+	1.16895i	−0.976499	+	0.215521i	$0.930855\pi$
$660$	4.96410e9	+	8.59808e9i	0.00101834	+	0.00176382i
$661$	1.24094e12	−	2.14937e12i	0.252839	−	0.437929i	−0.711468	−	0.702719i	$-0.751969\pi$
$661$	1.24094e12	−	2.14937e12i	0.252839	−	0.437929i	0.964306	+	0.264790i	$0.0853025\pi$
$662$	1.86408e12	+	3.22868e12i	0.377228	+	0.653378i
$663$	−6.14357e10	−	1.06410e11i	−0.0123484	−	0.0213880i
$664$	−1.63827e12			−0.327061
$665$	−5.77378e12	+	8.07186e12i	−1.14489	+	1.60058i
$666$	−1.31432e11			−0.0258861
$667$	−2.87450e11	−	4.97878e11i	−0.0562336	−	0.0973994i
$668$	−2.50897e11	−	4.34566e11i	−0.0487530	−	0.0844427i
$669$	6.70985e11	−	1.16218e12i	0.129508	−	0.224314i
$670$	2.55707e12	+	4.42898e12i	0.490238	+	0.849117i
$671$	−1.04052e11	+	1.80223e11i	−0.0198152	+	0.0343210i
$672$	2.04876e11			0.0387552
$673$	−4.50414e12			−0.846339			−0.423169	−	0.906051i	$-0.639082\pi$
$673$	−4.50414e12			−0.846339			−0.423169	+	0.906051i	$0.639082\pi$
$674$	6.01037e11	−	1.04103e12i	0.112184	−	0.194309i
$675$	−2.93255e11	+	5.07932e11i	−0.0543724	+	0.0941757i
$676$	−2.02428e12			−0.372831
$677$	−4.27382e12			−0.781928			−0.390964	−	0.920406i	$-0.627858\pi$
$677$	−4.27382e12			−0.781928			−0.390964	+	0.920406i	$0.627858\pi$
$678$	−7.13982e10	+	1.23665e11i	−0.0129764	+	0.0224757i
$679$	−1.96069e12	−	3.39602e12i	−0.353993	−	0.613135i
$680$	4.33257e11	−	7.50424e11i	0.0777062	−	0.134591i
$681$	6.25426e11	+	1.08327e12i	0.111433	+	0.193008i
$682$	5.87436e10	+	1.01747e11i	0.0103975	+	0.0180091i
$683$	−8.41250e12			−1.47922			−0.739609	−	0.673037i	$-0.764989\pi$
$683$	−8.41250e12			−1.47922			−0.739609	+	0.673037i	$0.764989\pi$
$684$	−1.63604e12	+	2.28722e12i	−0.285786	+	0.399535i
$685$	−1.00681e13			−1.74719
$686$	2.50674e12	+	4.34181e12i	0.432167	+	0.748535i
$687$	−3.92020e11	−	6.78999e11i	−0.0671434	−	0.116296i
$688$	−6.18834e11	+	1.07185e12i	−0.105299	+	0.182384i
$689$	−3.91030e11	−	6.77285e11i	−0.0661034	−	0.114495i
$690$	2.78636e11	−	4.82611e11i	0.0467968	−	0.0810544i
$691$	2.59752e12			0.433420			0.216710	−	0.976236i	$-0.430467\pi$
$691$	2.59752e12			0.433420			0.216710	+	0.976236i	$0.430467\pi$
$692$	−3.64137e12			−0.603652
$693$	−1.27623e11	+	2.21049e11i	−0.0210198	+	0.0364073i
$694$	1.10807e12	−	1.91923e12i	0.181321	−	0.314058i
$695$	1.00250e13			1.62987
$696$	3.88125e10			0.00626946
$697$	3.13853e10	−	5.43610e10i	0.00503708	−	0.00872448i
$698$	−3.29348e12	−	5.70448e12i	−0.525177	−	0.909634i
$699$	−4.73573e11	+	8.20253e11i	−0.0750309	+	0.129957i
$700$	−1.08822e12	−	1.88485e12i	−0.171307	−	0.296713i
$701$	4.11174e12	+	7.12175e12i	0.643125	+	1.11392i	0.984731	+	0.174081i	$0.0556956\pi$
$701$	4.11174e12	+	7.12175e12i	0.643125	+	1.11392i	−0.341607	+	0.939843i	$0.610971\pi$
$702$	−6.02627e11			−0.0936551
$703$	−9.97770e10	−	2.19713e11i	−0.0154075	−	0.0339278i
$704$	−2.10653e10			−0.00323214
$705$	9.18021e10	+	1.59006e11i	0.0139959	+	0.0242417i
$706$	3.47765e12	+	6.02347e12i	0.526823	+	0.912485i
$707$	6.96448e12	−	1.20628e13i	1.04834	−	1.81577i
$708$	2.55774e11	+	4.43014e11i	0.0382567	+	0.0662625i
$709$	2.20586e12	−	3.82066e12i	0.327846	−	0.567846i	−0.654238	−	0.756289i	$-0.727011\pi$
$709$	2.20586e12	−	3.82066e12i	0.327846	−	0.567846i	0.982084	+	0.188442i	$0.0603439\pi$
$710$	2.13024e11			0.0314606
$711$	1.12187e13			1.64637
$712$	2.17946e12	−	3.77494e12i	0.317826	−	0.550491i
$713$	3.29729e12	−	5.71107e12i	0.477808	−	0.827589i
$714$	−3.97949e11			−0.0573041
$715$	1.08367e11			0.0155068
$716$	8.69509e11	−	1.50603e12i	0.123642	−	0.214154i
$717$	−3.93770e11	−	6.82029e11i	−0.0556424	−	0.0963755i
$718$	5.42066e11	−	9.38886e11i	0.0761188	−	0.131842i
$719$	4.79696e12	+	8.30858e12i	0.669401	+	1.15944i	0.978072	+	0.208267i	$0.0667823\pi$
$719$	4.79696e12	+	8.30858e12i	0.669401	+	1.15944i	−0.308671	+	0.951169i	$0.599884\pi$
$720$	−1.05306e12	−	1.82395e12i	−0.146034	−	0.252939i
$721$	1.42824e13			1.96831
$722$	−5.06551e12	−	9.98594e11i	−0.693755	−	0.136764i
$723$	−1.21034e12			−0.164735
$724$	6.82198e11	+	1.18160e12i	0.0922756	+	0.159826i
$725$	−2.06156e11	−	3.57073e11i	−0.0277125	−	0.0479994i
$726$	3.50362e11	−	6.06845e11i	0.0468061	−	0.0810705i
$727$	−1.93102e12	−	3.34462e12i	−0.256378	−	0.444060i	0.708891	−	0.705318i	$-0.249196\pi$
$727$	−1.93102e12	−	3.34462e12i	−0.256378	−	0.444060i	−0.965269	+	0.261258i	$0.915863\pi$
$728$	1.11812e12	−	1.93665e12i	0.147536	−	0.255540i
$729$	−6.83433e12			−0.896235
$730$	−9.63408e12			−1.25562
$731$	1.20202e12	−	2.08195e12i	0.155698	−	0.269676i
$732$	−3.94299e11	+	6.82946e11i	−0.0507605	+	0.0879198i
$733$	9.44834e11			0.120889			0.0604446	−	0.998172i	$-0.480748\pi$
$733$	9.44834e11			0.120889			0.0604446	+	0.998172i	$0.480748\pi$
$734$	−2.84131e12			−0.361315
$735$	−1.08354e12	+	1.87674e12i	−0.136946	+	0.237198i
$736$	5.91199e11	+	1.02399e12i	0.0742649	+	0.128631i
$737$	−1.20746e11	+	2.09138e11i	−0.0150754	+	0.0261113i
$738$	−7.62838e10	−	1.32127e11i	−0.00946626	−	0.0163960i
$739$	6.38360e12	+	1.10567e13i	0.787346	+	1.36372i	0.927588	+	0.373605i	$0.121879\pi$
$739$	6.38360e12	+	1.10567e13i	0.787346	+	1.36372i	−0.140242	+	0.990117i	$0.544788\pi$
$740$	1.80725e11			0.0221552
$741$	−2.26718e11	−	4.99242e11i	−0.0276251	−	0.0608316i
$742$	−2.53290e12			−0.306761
$743$	−1.26723e12	−	2.19490e12i	−0.152548	−	0.264220i	0.779616	−	0.626258i	$-0.215414\pi$
$743$	−1.26723e12	−	2.19490e12i	−0.152548	−	0.264220i	−0.932163	+	0.362038i	$0.882081\pi$
$744$	2.22606e11	+	3.85564e11i	0.0266353	+	0.0461337i
$745$	2.52196e12	−	4.36817e12i	0.299941	−	0.519513i
$746$	1.12713e12	+	1.95225e12i	0.133245	+	0.230787i
$747$	3.86720e12	−	6.69818e12i	0.454416	−	0.787072i
$748$	4.09170e10			0.00477911
$749$	−1.81814e13			−2.11086
$750$	−2.82783e11	+	4.89794e11i	−0.0326345	+	0.0565246i
$751$	−2.18584e11	+	3.78599e11i	−0.0250749	+	0.0434310i	−0.878291	−	0.478127i	$-0.841316\pi$
$751$	−2.18584e11	+	3.78599e11i	−0.0250749	+	0.0434310i	0.853216	+	0.521558i	$0.174649\pi$
$752$	−3.89565e11			−0.0444221
$753$	4.35554e11			0.0493702
$754$	2.11821e11	−	3.66885e11i	0.0238670	−	0.0413389i
$755$	−4.95838e11	−	8.58817e11i	−0.0555366	−	0.0961921i
$756$	−9.75877e11	+	1.69027e12i	−0.108654	+	0.188195i
$757$	−2.14686e12	−	3.71847e12i	−0.237614	−	0.411560i	0.722415	−	0.691460i	$-0.243032\pi$
$757$	−2.14686e12	−	3.71847e12i	−0.237614	−	0.411560i	−0.960029	+	0.279900i	$0.909699\pi$
$758$	−2.49824e12	−	4.32708e12i	−0.274867	−	0.476084i
$759$	2.63145e10			0.00287811
$760$	2.24963e12	−	3.14503e12i	0.244597	−	0.341951i
$761$	1.76046e13			1.90281			0.951407	−	0.307937i	$-0.0996386\pi$
$761$	1.76046e13			1.90281			0.951407	+	0.307937i	$0.0996386\pi$
$762$	4.91305e11	+	8.50964e11i	0.0527902	+	0.0914353i
$763$	−1.31868e13	−	2.28402e13i	−1.40857	−	2.43972i
$764$	−3.05303e12	+	5.28801e12i	−0.324199	+	0.561529i
$765$	2.04544e12	+	3.54281e12i	0.215929	+	0.374000i
$766$	9.21221e9	−	1.59560e10i	0.000966795	−	0.00167454i
$767$	5.58361e12			0.582554
$768$	−7.98258e10			−0.00827976
$769$	1.65405e12	−	2.86491e12i	0.170562	−	0.295421i	−0.768055	−	0.640384i	$-0.778775\pi$
$769$	1.65405e12	−	2.86491e12i	0.170562	−	0.295421i	0.938616	+	0.344963i	$0.112108\pi$
$770$	1.75487e11	−	3.03953e11i	0.0179903	−	0.0311600i
$771$	−1.81720e12			−0.185207
$772$	7.89595e12			0.800067
$773$	−1.27657e11	+	2.21108e11i	−0.0128599	+	0.0222739i	−0.872384	−	0.488822i	$-0.837427\pi$
$773$	−1.27657e11	+	2.21108e11i	−0.0128599	+	0.0222739i	0.859524	+	0.511096i	$0.170760\pi$
$774$	−2.92157e12	−	5.06030e12i	−0.292605	−	0.506807i
$775$	2.36478e12	−	4.09592e12i	0.235469	−	0.407844i
$776$	7.63943e11	+	1.32319e12i	0.0756281	+	0.130992i
$777$	−4.14993e10	−	7.18788e10i	−0.00408457	−	0.00707468i
$778$	4.42285e12			0.432807
$779$	1.62964e11	−	2.27827e11i	0.0158553	−	0.0221660i
$780$	4.10652e11			0.0397236
$781$	5.02953e9	+	8.71140e9i	0.000483724	+	0.000837834i
$782$	−1.14834e12	−	1.98898e12i	−0.109809	−	0.190196i
$783$	−1.84874e11	+	3.20211e11i	−0.0175771	+	0.0304444i
$784$	−2.29901e12	−	3.98200e12i	−0.217329	−	0.376425i
$785$	−2.21783e12	+	3.84139e12i	−0.208456	+	0.361057i
$786$	1.92373e12			0.179781
$787$	−1.69765e13			−1.57747			−0.788736	−	0.614732i	$-0.789264\pi$
$787$	−1.69765e13			−1.57747			−0.788736	+	0.614732i	$0.789264\pi$
$788$	−1.95523e12	+	3.38655e12i	−0.180646	+	0.312889i
$789$	9.52228e11	−	1.64931e12i	0.0874772	−	0.151515i
$790$	−1.54262e13			−1.40909
$791$	5.04803e12			0.458488
$792$	4.97255e10	−	8.61272e10i	0.00449072	−	0.00777816i
$793$	4.30382e12	+	7.45443e12i	0.386478	+	0.669399i
$794$	−2.53103e12	+	4.38388e12i	−0.225999	+	0.391441i
$795$	−2.32564e11	−	4.02812e11i	−0.0206486	−	0.0357644i
$796$	3.39681e12	+	5.88344e12i	0.299890	+	0.519425i
$797$	4.04928e12			0.355480			0.177740	−	0.984078i	$-0.443121\pi$
$797$	4.04928e12			0.355480			0.177740	+	0.984078i	$0.443121\pi$
$798$	−1.76743e12	−	1.72552e11i	−0.154287	−	0.0150628i
$799$	7.56686e11			0.0656834
$800$	4.24002e11	+	7.34394e11i	0.0365985	+	0.0633905i
$801$	1.02894e13	+	1.78218e13i	0.883171	+	1.52970i
$802$	−5.48862e12	+	9.50658e12i	−0.468467	+	0.811408i
$803$	−2.27462e11	−	3.93975e11i	−0.0193058	−	0.0334387i
$804$	−4.57559e11	+	7.92515e11i	−0.0386184	+	0.0668891i
$805$	−1.97003e13			−1.65345
$806$	4.85953e12			0.405589
$807$	−7.54793e11	+	1.30734e12i	−0.0626466	+	0.108507i
$808$	−2.71357e12	+	4.70003e12i	−0.223970	+	0.387927i
$809$	6.38849e12			0.524360			0.262180	−	0.965019i	$-0.415559\pi$
$809$	6.38849e12			0.524360			0.262180	+	0.965019i	$0.415559\pi$
$810$	9.76234e12			0.796840
$811$	4.43441e11	−	7.68062e11i	0.0359950	−	0.0623451i	−0.847467	−	0.530849i	$-0.821873\pi$
$811$	4.43441e11	−	7.68062e11i	0.0359950	−	0.0623451i	0.883462	+	0.468503i	$0.155207\pi$
$812$	−6.86035e11	−	1.18825e12i	−0.0553789	−	0.0959191i
$813$	4.58715e11	−	7.94518e11i	0.0368244	−	0.0637817i
$814$	4.26694e9	+	7.39056e9i	0.000340649	+	0.000590021i
$815$	1.36764e12	+	2.36883e12i	0.108584	+	0.188072i
$816$	1.55053e11			0.0122426
$817$	6.24132e12	−	8.72549e12i	0.490091	−	0.685158i
$818$	5.46576e12			0.426836
$819$	5.27875e12	+	9.14307e12i	0.409972	+	0.710092i
$820$	1.04894e11	+	1.81681e11i	0.00810191	+	0.0140329i
$821$	−7.76691e12	+	1.34527e13i	−0.596629	+	1.03339i	0.396686	+	0.917954i	$0.370160\pi$
$821$	−7.76691e12	+	1.34527e13i	−0.596629	+	1.03339i	−0.993315	+	0.115437i	$0.963173\pi$
$822$	−9.00783e11	−	1.56020e12i	−0.0688172	−	0.119195i
$823$	−5.03205e12	+	8.71577e12i	−0.382337	+	0.662227i	−0.991396	−	0.130898i	$-0.958214\pi$
$823$	−5.03205e12	+	8.71577e12i	−0.382337	+	0.662227i	0.609059	+	0.793125i	$0.291547\pi$
$824$	−5.56485e12			−0.420515
$825$	1.88725e10			0.00141836
$826$	9.04194e12	−	1.56611e13i	0.675852	−	1.17061i
$827$	5.66253e12	−	9.80779e12i	0.420955	−	0.729116i	−0.575078	−	0.818099i	$-0.695028\pi$
$827$	5.66253e12	−	9.80779e12i	0.420955	−	0.729116i	0.996033	+	0.0889829i	$0.0283616\pi$
$828$	−5.58220e12			−0.412733
$829$	−2.72980e12			−0.200741			−0.100370	−	0.994950i	$-0.532003\pi$
$829$	−2.72980e12			−0.200741			−0.100370	+	0.994950i	$0.532003\pi$
$830$	−5.31758e12	+	9.21032e12i	−0.388922	+	0.673633i
$831$	−4.96096e11	−	8.59263e11i	−0.0360878	−	0.0625060i
$832$	−4.35654e11	+	7.54574e11i	−0.0315200	+	0.0545943i
$833$	4.46557e12	+	7.73459e12i	0.321347	+	0.556589i
$834$	8.96930e11	+	1.55353e12i	0.0641965	+	0.111192i
$835$	−3.25751e12			−0.231898
$836$	1.81727e11	+	1.77417e10i	0.0128674	+	0.00125622i
$837$	−4.24131e12			−0.298700
$838$	−5.06724e12	−	8.77671e12i	−0.354955	−	0.614800i
$839$	−1.15030e13	−	1.99238e13i	−0.801461	−	1.38817i	−0.918654	−	0.395062i	$-0.870723\pi$
$839$	−1.15030e13	−	1.99238e13i	−0.801461	−	1.38817i	0.117193	−	0.993109i	$-0.462610\pi$
$840$	6.64999e11	−	1.15181e12i	0.0460855	−	0.0798224i
$841$	7.12361e12	+	1.23385e13i	0.491041	+	0.850509i
$842$	−2.62159e12	+	4.54072e12i	−0.179746	+	0.311329i
$843$	−7.63259e11			−0.0520533
$844$	9.31809e12			0.632100
$845$	−6.57054e12	+	1.13805e13i	−0.443349	+	0.767904i
$846$	9.19584e11	−	1.59277e12i	0.0617198	−	0.106902i
$847$	−2.47715e13			−1.65378
$848$	9.86891e11			0.0655372
$849$	−1.39905e12	+	2.42322e12i	−0.0924162	+	0.160070i
$850$	−8.23578e11	−	1.42648e12i	−0.0541152	−	0.0937303i
$851$	2.39504e11	−	4.14833e11i	0.0156542	−	0.0271138i
$852$	1.90591e10	+	3.30114e10i	0.00123915	+	0.00214627i
$853$	1.14076e12	+	1.97586e12i	0.0737776	+	0.127787i	0.900554	−	0.434744i	$-0.143161\pi$
$853$	1.14076e12	+	1.97586e12i	0.0737776	+	0.127787i	−0.826776	+	0.562531i	$0.809828\pi$
$854$	2.78779e13			1.79350
$855$	7.54837e12	+	1.66218e13i	0.483065	+	1.06373i
$856$	7.08400e12			0.450969
$857$	7.49592e12	+	1.29833e13i	0.474691	+	0.822189i	0.999580	−	0.0289815i	$-0.00922640\pi$
$857$	7.49592e12	+	1.29833e13i	0.474691	+	0.822189i	−0.524889	+	0.851171i	$0.675893\pi$
$858$	9.69555e9	+	1.67932e10i	0.000610773	+	0.00105789i
$859$	−4.45980e12	+	7.72459e12i	−0.279477	+	0.484068i	−0.971255	−	0.238042i	$-0.923494\pi$
$859$	−4.45980e12	+	7.72459e12i	−0.279477	+	0.484068i	0.691778	+	0.722110i	$0.256828\pi$
$860$	4.01730e12	+	6.95816e12i	0.250433	+	0.433762i
$861$	4.81728e10	−	8.34377e10i	0.00298736	−	0.00517426i
$862$	−1.71847e13			−1.06013
$863$	8.20587e11			0.0503589			0.0251794	−	0.999683i	$-0.491984\pi$
$863$	8.20587e11			0.0503589			0.0251794	+	0.999683i	$0.491984\pi$
$864$	3.80230e11	−	6.58578e11i	0.0232132	−	0.0402064i
$865$	−1.18194e13	+	2.04717e13i	−0.717830	+	1.24332i
$866$	1.82541e13			1.10288
$867$	1.90289e12			0.114374
$868$	7.86939e12	−	1.36302e13i	0.470546	−	0.815010i
$869$	−3.64215e11	−	6.30839e11i	−0.0216655	−	0.0375257i
$870$	1.25980e11	−	2.18204e11i	0.00745529	−	0.0129129i
$871$	4.99431e12	+	8.65039e12i	0.294031	+	0.509277i
$872$	5.13797e12	+	8.89922e12i	0.300931	+	0.521228i
$873$	−7.21328e12			−0.420309
$874$	−4.23775e12	−	9.33169e12i	−0.245660	−	0.540952i
$875$	1.99934e13			1.15306
$876$	−8.61953e11	−	1.49295e12i	−0.0494556	−	0.0856596i
$877$	−1.53974e13	−	2.66691e13i	−0.878919	−	1.52233i	−0.852528	−	0.522681i	$-0.824932\pi$
$877$	−1.53974e13	−	2.66691e13i	−0.878919	−	1.52233i	−0.0263913	−	0.999652i	$-0.508402\pi$
$878$	−9.52517e12	+	1.64981e13i	−0.540938	+	0.936932i
$879$	4.22825e11	+	7.32354e11i	0.0238897	+	0.0413782i
$880$	−6.83750e10	+	1.18429e11i	−0.00384349	+	0.00665711i
$881$	−7.56580e12			−0.423120			−0.211560	−	0.977365i	$-0.567854\pi$
$881$	−7.56580e12			−0.423120			−0.211560	+	0.977365i	$0.567854\pi$
$882$	2.17076e13			1.20782
$883$	−4.27648e12	+	7.40709e12i	−0.236736	+	0.410038i	−0.959776	−	0.280768i	$-0.909411\pi$
$883$	−4.27648e12	+	7.40709e12i	−0.236736	+	0.410038i	0.723040	+	0.690806i	$0.242744\pi$
$884$	8.46209e11	−	1.46568e12i	0.0466061	−	0.0807241i
$885$	3.32083e12			0.181971
$886$	−6.69836e12			−0.365188
$887$	3.32905e12	−	5.76609e12i	0.180578	−	0.312770i	−0.761500	−	0.648165i	$-0.775537\pi$
$887$	3.32905e12	−	5.76609e12i	0.180578	−	0.312770i	0.942077	+	0.335395i	$0.108870\pi$
$888$	1.61693e10	+	2.80061e10i	0.000872638	+	0.00151145i
$889$	1.73682e13	−	3.00827e13i	0.932605	−	1.61532i
$890$	−1.41485e13	−	2.45058e13i	−0.755882	−	1.30923i
$891$	2.30490e11	+	3.99220e11i	0.0122519	+	0.0212209i
$892$	1.84842e13			0.977593
$893$	3.36071e12	+	3.28101e11i	0.176848	+	0.0172654i
$894$	9.02553e11			0.0472556
$895$	−5.64461e12	−	9.77675e12i	−0.294056	−	0.509320i
$896$	1.41097e12	+	2.44387e12i	0.0731361	+	0.126676i
$897$	5.44213e11	−	9.42604e11i	0.0280674	−	0.0486142i
$898$	1.17629e12	+	2.03739e12i	0.0603629	+	0.104552i
$899$	1.49081e12	−	2.58215e12i	0.0761206	−	0.131845i
$900$	−4.00350e12			−0.203399
$901$	−1.91693e12			−0.0969044
$902$	−4.95311e9	+	8.57904e9i	−0.000249143	+	0.000431528i
$903$	1.84495e12	−	3.19556e12i	0.0923402	−	0.159938i
$904$	−1.96686e12			−0.0979526
$905$	8.85727e12			0.438916
$906$	8.87245e10	−	1.53675e11i	0.00437489	−	0.00757753i
$907$	−1.03120e13	−	1.78610e13i	−0.505955	−	0.876339i	−0.999976	−	0.00688951i	$-0.997807\pi$
$907$	−1.03120e13	−	1.78610e13i	−0.505955	−	0.876339i	0.494022	−	0.869450i	$-0.335526\pi$
$908$	−8.61456e12	+	1.49208e13i	−0.420578	+	0.728462i
$909$	−1.28110e13	−	2.21893e13i	−0.622364	−	1.07797i
$910$	−7.25854e12	−	1.25722e13i	−0.350884	−	0.607748i
$911$	−3.00499e13			−1.44548			−0.722738	−	0.691122i	$-0.757117\pi$
$911$	−3.00499e13			−1.44548			−0.722738	+	0.691122i	$0.757117\pi$
$912$	6.88644e11	+	6.72312e10i	0.0329623	+	0.00321806i
$913$	−5.02195e11			−0.0239196
$914$	−1.10817e13	−	1.91940e13i	−0.525227	−	0.909720i
$915$	2.55968e12	+	4.43349e12i	0.120723	+	0.209099i
$916$	5.39964e12	−	9.35246e12i	0.253417	−	0.438931i
$917$	−3.40032e13	−	5.88953e13i	−1.58803	−	2.75054i
$918$	−7.38555e11	+	1.27922e12i	−0.0343235	+	0.0594500i
$919$	1.92915e13			0.892166			0.446083	−	0.894992i	$-0.352819\pi$
$919$	1.92915e13			0.892166			0.446083	+	0.894992i	$0.352819\pi$
$920$	7.67580e12			0.353247
$921$	2.13267e12	−	3.69390e12i	0.0976688	−	0.169167i
$922$	−1.15205e13	+	1.99541e13i	−0.525029	+	0.909376i
$923$	4.16065e11			0.0188692
$924$	6.28028e10			0.00283436
$925$	1.71770e11	−	2.97514e11i	0.00771453	−	0.0133620i
$926$	−6.05006e11	−	1.04790e12i	−0.0270402	−	0.0468351i
$927$	1.31361e13	−	2.27524e13i	0.584261	−	1.01197i
$928$	2.67299e11	+	4.62976e11i	0.0118313	+	0.0204924i
$929$	−4.97438e12	−	8.61588e12i	−0.219113	−	0.379515i	0.735424	−	0.677607i	$-0.236983\pi$
$929$	−4.97438e12	−	8.61588e12i	−0.219113	−	0.379515i	−0.954537	+	0.298092i	$0.903650\pi$
$930$	2.89019e12			0.126693
$931$	1.64794e13	+	3.62883e13i	0.718900	+	1.58305i
$932$	−1.30459e13			−0.566373
$933$	−2.43505e12	−	4.21764e12i	−0.105206	−	0.182222i
$934$	1.21618e11	+	2.10648e11i	0.00522921	+	0.00905726i
$935$	1.32811e11	−	2.30035e11i	0.00568305	−	0.00984333i
$936$	−2.05676e12	−	3.56241e12i	−0.0875874	−	0.151706i
$937$	9.30455e11	−	1.61159e12i	0.0394337	−	0.0683011i	−0.845635	−	0.533762i	$-0.820778\pi$
$937$	9.30455e11	−	1.61159e12i	0.0394337	−	0.0683011i	0.885069	+	0.465461i	$0.154111\pi$
$938$	3.23506e13			1.36449
$939$	−2.41927e12			−0.101552
$940$	−1.26447e12	+	2.19013e12i	−0.0528243	+	0.0914944i
$941$	1.01717e13	−	1.76178e13i	0.422901	−	0.732486i	−0.573321	−	0.819331i	$-0.694345\pi$
$941$	1.01717e13	−	1.76178e13i	0.422901	−	0.732486i	0.996222	+	0.0868449i	$0.0276785\pi$
$942$	−7.93710e11			−0.0328422
$943$	5.56038e11			0.0228982
$944$	−3.52301e12	+	6.10203e12i	−0.144391	+	0.250092i
$945$	6.33512e12	+	1.09727e13i	0.258411	+	0.447582i
$946$	−1.89698e11	+	3.28566e11i	−0.00770108	+	0.0133387i
$947$	1.13488e13	+	1.96567e13i	0.458537	+	0.794210i	0.998884	−	0.0472327i	$-0.0150402\pi$
$947$	1.13488e13	+	1.96567e13i	0.458537	+	0.794210i	−0.540347	+	0.841442i	$0.681707\pi$
$948$	−1.38017e12	−	2.39053e12i	−0.0555003	−	0.0961294i
$949$	−1.88166e13			−0.753085
$950$	−3.03927e12	−	6.69260e12i	−0.121064	−	0.266587i
$951$	1.19271e12			0.0472847
$952$	−2.74065e12	−	4.74695e12i	−0.108140	−	0.187305i
$953$	2.05255e13	+	3.55512e13i	0.806075	+	1.39616i	0.915563	+	0.402175i	$0.131746\pi$
$953$	2.05255e13	+	3.55512e13i	0.806075	+	1.39616i	−0.109488	+	0.993988i	$0.534921\pi$
$954$	−2.32960e12	+	4.03498e12i	−0.0910570	+	0.157715i
$955$	1.98194e13	+	3.43283e13i	0.771039	+	1.33548i
$956$	5.42374e12	−	9.39419e12i	0.210009	−	0.363747i
$957$	1.18976e10			0.000458517
$958$	1.35946e13			0.521461
$959$	−3.18438e13	+	5.51551e13i	−1.21574	+	2.10573i
$960$	−2.59103e11	+	4.48780e11i	−0.00984583	+	0.0170535i
$961$	7.76192e12			0.293571
$962$	3.52980e11			0.0132881
$963$	−1.67221e13	+	2.89635e13i	−0.626574	+	1.08526i
$964$	−8.33556e12	−	1.44376e13i	−0.310877	−	0.538454i
$965$	2.56291e13	−	4.43910e13i	0.951395	−	1.64786i
$966$	−1.76257e12	−	3.05285e12i	−0.0651251	−	0.112800i
$967$	−4.84153e12	−	8.38577e12i	−0.178059	−	0.308407i	0.763157	−	0.646213i	$-0.223648\pi$
$967$	−4.84153e12	−	8.38577e12i	−0.178059	−	0.308407i	−0.941216	+	0.337807i	$0.890315\pi$
$968$	9.65170e12			0.353317
$969$	−1.33761e12	−	1.30589e11i	−0.0487387	−	0.00475828i
$970$	9.91861e12			0.359731
$971$	−9.67082e12	−	1.67503e13i	−0.349121	−	0.604696i	0.636972	−	0.770887i	$-0.280187\pi$
$971$	−9.67082e12	−	1.67503e13i	−0.349121	−	0.604696i	−0.986094	+	0.166191i	$0.946853\pi$
$972$	2.70060e12	+	4.67757e12i	0.0970424	+	0.168082i
$973$	3.17076e13	−	5.49192e13i	1.13411	−	1.96434i
$974$	2.10462e12	+	3.64530e12i	0.0749303	+	0.129783i
$975$	3.90304e11	−	6.76027e11i	0.0138319	−	0.0239576i
$976$	−1.08621e13			−0.383167
$977$	6.80674e12			0.239009			0.119504	−	0.992834i	$-0.461869\pi$
$977$	6.80674e12			0.239009			0.119504	+	0.992834i	$0.461869\pi$
$978$	−2.44724e11	+	4.23875e11i	−0.00855366	+	0.0148154i
$979$	6.68093e11	−	1.15717e12i	0.0232442	−	0.0402602i
$980$	−2.98490e13			−1.03374
$981$	−4.85135e13			−1.67245
$982$	−1.29839e13	+	2.24888e13i	−0.445558	+	0.771729i
$983$	3.03637e12	+	5.25916e12i	0.103720	+	0.179649i	0.913215	−	0.407479i	$-0.133592\pi$
$983$	3.03637e12	+	5.25916e12i	0.103720	+	0.179649i	−0.809494	+	0.587128i	$0.800259\pi$
$984$	−1.87695e10	+	3.25098e10i	−0.000638228	+	0.00110544i
$985$	1.26928e13	+	2.19846e13i	0.429629	+	0.744140i
$986$	−5.19200e11	−	8.99280e11i	−0.0174940	−	0.0303004i
$987$	1.16143e12			0.0389551
$988$	4.39383e12	−	6.14267e12i	0.146702	−	0.205093i
$989$	2.12955e13			0.707791
$990$	−3.22804e11	−	5.59113e11i	−0.0106802	−	0.0184987i
$991$	1.19642e13	+	2.07225e13i	0.394049	+	0.682514i	0.992979	−	0.118288i	$-0.0377405\pi$
$991$	1.19642e13	+	2.07225e13i	0.394049	+	0.682514i	−0.598930	+	0.800801i	$0.704407\pi$
$992$	−3.06615e12	+	5.31072e12i	−0.100529	+	0.174121i
$993$	2.16535e12	+	3.75049e12i	0.0706734	+	0.122410i
$994$	6.73764e11	−	1.16699e12i	0.0218912	−	0.0379166i
$995$	4.41022e13			1.42645
$996$	−1.90304e12			−0.0612747
$997$	−1.64194e13	+	2.84393e13i	−0.526295	+	0.911570i	0.473236	+	0.880936i	$0.343086\pi$
$997$	−1.64194e13	+	2.84393e13i	−0.526295	+	0.911570i	−0.999531	+	0.0306340i	$0.990247\pi$
$998$	−6.27737e12	+	1.08727e13i	−0.200304	+	0.346937i
$999$	−3.08075e11			−0.00978613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.7.4	✓	14
19.11	even	3	inner	38.10.c.a.11.4	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.4	✓	14	1.1	even	1	trivial
38.10.c.a.11.4	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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(9.29294 + 16.0959i) q^{3} +(-128.000 + 221.703i) q^{4} +(830.940 + 1439.23i) q^{5} +(-148.687 + 257.534i) q^{6} +10512.6 q^{7} -4096.00 q^{8} +(9668.78 - 16746.8i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(9.29294 + 16.0959i) q^{3} +(-128.000 + 221.703i) q^{4} +(830.940 + 1439.23i) q^{5} +(-148.687 + 257.534i) q^{6} +10512.6 q^{7} -4096.00 q^{8} +(9668.78 - 16746.8i) q^{9} +(-13295.0 + 23027.7i) q^{10} -1255.59 q^{11} -4757.99 q^{12} +(-25967.0 + 44976.1i) q^{13} +(84100.4 + 145666. i) q^{14} +(-15443.8 + 26749.4i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(63648.2 + 110242. i) q^{17} +309401. q^{18} +(234883. + 517221. i) q^{19} -425441. q^{20} +(97692.6 + 169208. i) q^{21} +(-10044.7 - 17398.0i) q^{22} +(-563811. + 976550. i) q^{23} +(-38063.9 - 65928.6i) q^{24} +(-404360. + 700372. i) q^{25} -830943. q^{26} +725232. q^{27} +(-1.34561e6 + 2.33066e6i) q^{28} +(-254917. + 441529. i) q^{29} -494200. q^{30} -5.84821e6 q^{31} +(524288. - 908093. i) q^{32} +(-11668.1 - 20209.8i) q^{33} +(-1.01837e6 + 1.76387e6i) q^{34} +(8.73530e6 + 1.51300e7i) q^{35} +(2.47521e6 + 4.28719e6i) q^{36} -424795. q^{37} +(-5.28776e6 + 7.39240e6i) q^{38} -965239. q^{39} +(-3.40353e6 - 5.89509e6i) q^{40} +(-246553. - 427042. i) q^{41} +(-1.56308e6 + 2.70734e6i) q^{42} +(-9.44266e6 - 1.63552e7i) q^{43} +(160715. - 278367. i) q^{44} +3.21367e7 q^{45} -1.80420e7 q^{46} +(2.97214e6 - 5.14790e6i) q^{47} +(609022. - 1.05486e6i) q^{48} +7.01602e7 q^{49} -1.29395e7 q^{50} +(-1.18296e6 + 2.04894e6i) q^{51} +(-6.64755e6 - 1.15139e7i) q^{52} +(-7.52938e6 + 1.30413e7i) q^{53} +(5.80185e6 + 1.00491e7i) q^{54} +(-1.04332e6 - 1.80708e6i) q^{55} -4.30594e7 q^{56} +(-6.14236e6 + 8.58715e6i) q^{57} -8.15733e6 q^{58} +(-5.37568e7 - 9.31095e7i) q^{59} +(-3.95360e6 - 6.84784e6i) q^{60} +(8.28710e7 - 1.43537e8i) q^{61} +(-4.67857e7 - 8.10352e7i) q^{62} +(1.01644e8 - 1.76052e8i) q^{63} +1.67772e7 q^{64} -8.63080e7 q^{65} +(186690. - 323357. i) q^{66} +(9.61665e7 - 1.66565e8i) q^{67} -3.25879e7 q^{68} -2.09579e7 q^{69} +(-1.39765e8 + 2.42080e8i) q^{70} +(-4.00571e6 - 6.93809e6i) q^{71} +(-3.96033e7 + 6.85950e7i) q^{72} +(1.81159e8 + 3.13777e8i) q^{73} +(-3.39836e6 - 5.88613e6i) q^{74} -1.50308e7 q^{75} +(-1.44734e8 - 1.41302e7i) q^{76} -1.31995e7 q^{77} +(-7.72191e6 - 1.33747e7i) q^{78} +(2.90075e8 + 5.02424e8i) q^{79} +(5.44565e7 - 9.43214e7i) q^{80} +(-1.83571e8 - 3.17954e8i) q^{81} +(3.94485e6 - 6.83268e6i) q^{82} +3.99967e8 q^{83} -5.00186e7 q^{84} +(-1.05776e8 + 1.83209e8i) q^{85} +(1.51083e8 - 2.61683e8i) q^{86} -9.47570e6 q^{87} +5.14290e6 q^{88} +(-5.32095e8 + 9.21616e8i) q^{89} +(2.57094e8 + 4.45299e8i) q^{90} +(-2.72979e8 + 4.72814e8i) q^{91} +(-1.44336e8 - 2.49997e8i) q^{92} +(-5.43471e7 - 9.41319e7i) q^{93} +9.51086e7 q^{94} +(-5.49227e8 + 7.67830e8i) q^{95} +1.94887e7 q^{96} +(-1.86510e8 - 3.23044e8i) q^{97} +(5.61281e8 + 9.72168e8i) q^{98} +(-1.21400e7 + 2.10271e7i) 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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