LMFDB - Embedded newform 38.10.c.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$14$
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			7.1
Root			$125.259 + 216.954i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(-113.259 - 196.170i) q^{3} +(-128.000 + 221.703i) q^{4} +(563.006 + 975.155i) q^{5} +(1812.14 - 3138.71i) q^{6} +3883.37 q^{7} -4096.00 q^{8} +(-15813.5 + 27389.8i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(-113.259 - 196.170i) q^{3} +(-128.000 + 221.703i) q^{4} +(563.006 + 975.155i) q^{5} +(1812.14 - 3138.71i) q^{6} +3883.37 q^{7} -4096.00 q^{8} +(-15813.5 + 27389.8i) q^{9} +(-9008.10 + 15602.5i) q^{10} +15531.5 q^{11} +57988.4 q^{12} +(31704.0 - 54912.9i) q^{13} +(31067.0 + 53809.6i) q^{14} +(127531. - 220889. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-194058. - 336118. i) q^{17} -506032. q^{18} +(-299995. - 482380. i) q^{19} -288259. q^{20} +(-439825. - 761800. i) q^{21} +(124252. + 215210. i) q^{22} +(1.03946e6 - 1.80039e6i) q^{23} +(463907. + 803510. i) q^{24} +(342611. - 593419. i) q^{25} +1.01453e6 q^{26} +2.70551e6 q^{27} +(-497072. + 860954. i) q^{28} +(-877176. + 1.51931e6i) q^{29} +4.08098e6 q^{30} +5.35854e6 q^{31} +(524288. - 908093. i) q^{32} +(-1.75907e6 - 3.04680e6i) q^{33} +(3.10492e6 - 5.37788e6i) q^{34} +(2.18636e6 + 3.78689e6i) q^{35} +(-4.04825e6 - 7.01178e6i) q^{36} -3.73447e6 q^{37} +(4.28410e6 - 8.01590e6i) q^{38} -1.43630e7 q^{39} +(-2.30607e6 - 3.99424e6i) q^{40} +(-5.25338e6 - 9.09913e6i) q^{41} +(7.03720e6 - 1.21888e7i) q^{42} +(-1.21044e6 - 2.09654e6i) q^{43} +(-1.98803e6 + 3.44337e6i) q^{44} -3.56124e7 q^{45} +3.32627e7 q^{46} +(7.75370e6 - 1.34298e7i) q^{47} +(-7.42251e6 + 1.28562e7i) q^{48} -2.52730e7 q^{49} +1.09635e7 q^{50} +(-4.39574e7 + 7.61364e7i) q^{51} +(8.11622e6 + 1.40577e7i) q^{52} +(4.64556e7 - 8.04634e7i) q^{53} +(2.16441e7 + 3.74887e7i) q^{54} +(8.74431e6 + 1.51456e7i) q^{55} -1.59063e7 q^{56} +(-6.06513e7 + 1.13484e8i) q^{57} -2.80696e7 q^{58} +(7.63235e7 + 1.32196e8i) q^{59} +(3.26478e7 + 5.65477e7i) q^{60} +(4.07725e7 - 7.06201e7i) q^{61} +(4.28683e7 + 7.42500e7i) q^{62} +(-6.14097e7 + 1.06365e8i) q^{63} +1.67772e7 q^{64} +7.13982e7 q^{65} +(2.81451e7 - 4.87488e7i) q^{66} +(-1.20835e7 + 2.09292e7i) q^{67} +9.93575e7 q^{68} -4.70910e8 q^{69} +(-3.49818e7 + 6.05903e7i) q^{70} +(-4.31819e7 - 7.47932e7i) q^{71} +(6.47720e7 - 1.12188e8i) q^{72} +(-2.08408e8 - 3.60973e8i) q^{73} +(-2.98757e7 - 5.17463e7i) q^{74} -1.55214e8 q^{75} +(1.45344e8 - 4.76499e6i) q^{76} +6.03145e7 q^{77} +(-1.14904e8 - 1.99019e8i) q^{78} +(1.95659e8 + 3.38892e8i) q^{79} +(3.68972e7 - 6.39078e7i) q^{80} +(4.83443e6 + 8.37347e6i) q^{81} +(8.40541e7 - 1.45586e8i) q^{82} +5.21784e8 q^{83} +2.25191e8 q^{84} +(2.18511e8 - 3.78473e8i) q^{85} +(1.93670e7 - 3.35447e7i) q^{86} +3.97390e8 q^{87} -6.36169e7 q^{88} +(-5.36976e8 + 9.30070e8i) q^{89} +(-2.84899e8 - 4.93459e8i) q^{90} +(1.23118e8 - 2.13247e8i) q^{91} +(2.66101e8 + 4.60901e8i) q^{92} +(-6.06900e8 - 1.05118e9i) q^{93} +2.48118e8 q^{94} +(3.01497e8 - 5.64125e8i) q^{95} -2.37520e8 q^{96} +(2.40853e8 + 4.17170e8i) q^{97} +(-2.02184e8 - 3.50193e8i) q^{98} +(-2.45607e8 + 4.25403e8i) 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
$3$	−113.259	−	196.170i	−0.807282	−	1.39825i	−0.914740	−	0.404044i	$-0.867604\pi$
$3$	−113.259	−	196.170i	−0.807282	−	1.39825i	0.107458	−	0.994210i	$-0.465729\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	563.006	+	975.155i	0.402854	+	0.697764i	0.994069	−	0.108750i	$-0.0346847\pi$
$5$	563.006	+	975.155i	0.402854	+	0.697764i	−0.591215	+	0.806514i	$0.701351\pi$
$6$	1812.14	−	3138.71i	0.570835	−	0.988714i
$7$	3883.37			0.611319			0.305660	−	0.952141i	$-0.401123\pi$
$7$	3883.37			0.611319			0.305660	+	0.952141i	$0.401123\pi$
$8$	−4096.00			−0.353553
$9$	−15813.5	+	27389.8i	−0.803408	+	1.39154i
$10$	−9008.10	+	15602.5i	−0.284861	+	0.493394i
$11$	15531.5			0.319849			0.159925	−	0.987129i	$-0.448875\pi$
$11$	15531.5			0.319849			0.159925	+	0.987129i	$0.448875\pi$
$12$	57988.4			0.807282
$13$	31704.0	−	54912.9i	0.307871	−	0.533248i	−0.670025	−	0.742338i	$-0.733717\pi$
$13$	31704.0	−	54912.9i	0.307871	−	0.533248i	0.977896	+	0.209090i	$0.0670501\pi$
$14$	31067.0	+	53809.6i	0.216134	+	0.374355i
$15$	127531.	−	220889.i	0.650434	−	1.12659i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	−194058.	−	336118.i	−0.563522	−	0.976048i	−0.997186	−	0.0749733i	$-0.976113\pi$
$17$	−194058.	−	336118.i	−0.563522	−	0.976048i	0.433664	−	0.901075i	$-0.357220\pi$
$18$	−506032.			−1.13619
$19$	−299995.	−	482380.i	−0.528108	−	0.849177i
$19$	−299995.	−	482380.i	−0.528108	−	0.849177i
$20$	−288259.			−0.402854
$21$	−439825.	−	761800.i	−0.493507	−	0.854779i
$22$	124252.	+	215210.i	0.113084	+	0.195867i
$23$	1.03946e6	−	1.80039e6i	0.774519	−	1.34151i	−0.160546	−	0.987028i	$-0.551326\pi$
$23$	1.03946e6	−	1.80039e6i	0.774519	−	1.34151i	0.935065	−	0.354477i	$-0.115341\pi$
$24$	463907.	+	803510.i	0.285417	+	0.494357i
$25$	342611.	−	593419.i	0.175417	−	0.303830i
$26$	1.01453e6			0.435395
$27$	2.70551e6			0.979744
$28$	−497072.	+	860954.i	−0.152830	+	0.264709i
$29$	−877176.	+	1.51931e6i	−0.230301	+	0.398893i	−0.957897	−	0.287113i	$-0.907304\pi$
$29$	−877176.	+	1.51931e6i	−0.230301	+	0.398893i	0.727596	+	0.686006i	$0.240638\pi$
$30$	4.08098e6			0.919853
$31$	5.35854e6			1.04212			0.521061	−	0.853520i	$-0.325536\pi$
$31$	5.35854e6			1.04212			0.521061	+	0.853520i	$0.325536\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	−1.75907e6	−	3.04680e6i	−0.258209	−	0.447230i
$34$	3.10492e6	−	5.37788e6i	0.398470	−	0.690170i
$35$	2.18636e6	+	3.78689e6i	0.246273	+	0.426557i
$36$	−4.04825e6	−	7.01178e6i	−0.401704	−	0.695772i
$37$	−3.73447e6			−0.327583			−0.163791	−	0.986495i	$-0.552372\pi$
$37$	−3.73447e6			−0.327583			−0.163791	+	0.986495i	$0.552372\pi$
$38$	4.28410e6	−	8.01590e6i	0.333298	−	0.623628i
$39$	−1.43630e7			−0.994155
$40$	−2.30607e6	−	3.99424e6i	−0.142431	−	0.246697i
$41$	−5.25338e6	−	9.09913e6i	−0.290343	−	0.502889i	0.683548	−	0.729906i	$-0.260436\pi$
$41$	−5.25338e6	−	9.09913e6i	−0.290343	−	0.502889i	−0.973891	+	0.227017i	$0.927103\pi$
$42$	7.03720e6	−	1.21888e7i	0.348962	−	0.604420i
$43$	−1.21044e6	−	2.09654e6i	−0.0539927	−	0.0935182i	0.837766	−	0.546030i	$-0.183861\pi$
$43$	−1.21044e6	−	2.09654e6i	−0.0539927	−	0.0935182i	−0.891759	+	0.452512i	$0.850528\pi$
$44$	−1.98803e6	+	3.44337e6i	−0.0799623	+	0.138499i
$45$	−3.56124e7			−1.29463
$46$	3.32627e7			1.09533
$47$	7.75370e6	−	1.34298e7i	0.231776	−	0.401448i	−0.726555	−	0.687108i	$-0.758880\pi$
$47$	7.75370e6	−	1.34298e7i	0.231776	−	0.401448i	0.958331	+	0.285661i	$0.0922130\pi$
$48$	−7.42251e6	+	1.28562e7i	−0.201820	+	0.349563i
$49$	−2.52730e7			−0.626289
$50$	1.09635e7			0.248077
$51$	−4.39574e7	+	7.61364e7i	−0.909842	+	1.57589i
$52$	8.11622e6	+	1.40577e7i	0.153936	+	0.266624i
$53$	4.64556e7	−	8.04634e7i	0.808717	−	1.40074i	−0.105036	−	0.994468i	$-0.533496\pi$
$53$	4.64556e7	−	8.04634e7i	0.808717	−	1.40074i	0.913753	−	0.406271i	$-0.133171\pi$
$54$	2.16441e7	+	3.74887e7i	0.346392	+	0.599968i
$55$	8.74431e6	+	1.51456e7i	0.128853	+	0.223179i
$56$	−1.59063e7			−0.216134
$57$	−6.06513e7	+	1.13484e8i	−0.761032	+	1.42395i
$58$	−2.80696e7			−0.325695
$59$	7.63235e7	+	1.32196e8i	0.820019	+	1.42031i	0.905667	+	0.423989i	$0.139371\pi$
$59$	7.63235e7	+	1.32196e8i	0.820019	+	1.42031i	−0.0856479	+	0.996325i	$0.527296\pi$
$60$	3.26478e7	+	5.65477e7i	0.325217	+	0.563293i
$61$	4.07725e7	−	7.06201e7i	0.377036	−	0.653046i	−0.613593	−	0.789622i	$-0.710277\pi$
$61$	4.07725e7	−	7.06201e7i	0.377036	−	0.653046i	0.990630	+	0.136576i	$0.0436098\pi$
$62$	4.28683e7	+	7.42500e7i	0.368446	+	0.638167i
$63$	−6.14097e7	+	1.06365e8i	−0.491139	+	0.850678i
$64$	1.67772e7			0.125000
$65$	7.13982e7			0.496109
$66$	2.81451e7	−	4.87488e7i	0.182581	−	0.316240i
$67$	−1.20835e7	+	2.09292e7i	−0.0732579	+	0.126886i	−0.900327	−	0.435213i	$-0.856673\pi$
$67$	−1.20835e7	+	2.09292e7i	−0.0732579	+	0.126886i	0.827069	+	0.562100i	$0.190006\pi$
$68$	9.93575e7			0.563522
$69$	−4.70910e8			−2.50102
$70$	−3.49818e7	+	6.05903e7i	−0.174141	+	0.301621i
$71$	−4.31819e7	−	7.47932e7i	−0.201669	−	0.349301i	0.747397	−	0.664377i	$-0.231303\pi$
$71$	−4.31819e7	−	7.47932e7i	−0.201669	−	0.349301i	−0.949066	+	0.315077i	$0.897970\pi$
$72$	6.47720e7	−	1.12188e8i	0.284048	−	0.491985i
$73$	−2.08408e8	−	3.60973e8i	−0.858937	−	1.48772i	−0.872943	−	0.487821i	$-0.837792\pi$
$73$	−2.08408e8	−	3.60973e8i	−0.858937	−	1.48772i	0.0140061	−	0.999902i	$-0.495542\pi$
$74$	−2.98757e7	−	5.17463e7i	−0.115818	−	0.200603i
$75$	−1.55214e8			−0.566443
$76$	1.45344e8	−	4.76499e6i	0.499732	−	0.0163833i
$77$	6.03145e7			0.195530
$78$	−1.14904e8	−	1.99019e8i	−0.351487	−	0.608793i
$79$	1.95659e8	+	3.38892e8i	0.565169	+	0.978902i	0.997034	+	0.0769634i	$0.0245225\pi$
$79$	1.95659e8	+	3.38892e8i	0.565169	+	0.978902i	−0.431865	+	0.901938i	$0.642144\pi$
$80$	3.68972e7	−	6.39078e7i	0.100714	−	0.174441i
$81$	4.83443e6	+	8.37347e6i	0.0124785	+	0.0216134i
$82$	8.40541e7	−	1.45586e8i	0.205304	−	0.355596i
$83$	5.21784e8			1.20681			0.603406	−	0.797434i	$-0.293810\pi$
$83$	5.21784e8			1.20681			0.603406	+	0.797434i	$0.293810\pi$
$84$	2.25191e8			0.493507
$85$	2.18511e8	−	3.78473e8i	0.454034	−	0.786411i
$86$	1.93670e7	−	3.35447e7i	0.0381786	−	0.0661273i
$87$	3.97390e8			0.743671
$88$	−6.36169e7			−0.113084
$89$	−5.36976e8	+	9.30070e8i	−0.907193	+	1.57131i	−0.0892478	+	0.996009i	$0.528446\pi$
$89$	−5.36976e8	+	9.30070e8i	−0.907193	+	1.57131i	−0.817946	+	0.575296i	$0.804887\pi$
$90$	−2.84899e8	−	4.93459e8i	−0.457720	−	0.792794i
$91$	1.23118e8	−	2.13247e8i	0.188208	−	0.325985i
$92$	2.66101e8	+	4.60901e8i	0.387259	+	0.670753i
$93$	−6.06900e8	−	1.05118e9i	−0.841286	−	1.45715i
$94$	2.48118e8			0.327781
$95$	3.01497e8	−	5.64125e8i	0.379775	−	0.710590i
$96$	−2.37520e8			−0.285417
$97$	2.40853e8	+	4.17170e8i	0.276236	+	0.478454i	0.970446	−	0.241318i	$-0.0775797\pi$
$97$	2.40853e8	+	4.17170e8i	0.276236	+	0.478454i	−0.694211	+	0.719772i	$0.744246\pi$
$98$	−2.02184e8	−	3.50193e8i	−0.221427	−	0.383522i
$99$	−2.45607e8	+	4.25403e8i	−0.256970	+	0.445084i
$100$	8.77083e7	+	1.51915e8i	0.0877083	+	0.151915i
$101$	9.00400e8	−	1.55954e9i	0.860973	−	1.49125i	−0.0100188	−	0.999950i	$-0.503189\pi$
$101$	9.00400e8	−	1.55954e9i	0.860973	−	1.49125i	0.870991	−	0.491298i	$-0.163478\pi$
$102$	−1.40664e9			−1.28671
$103$	−6.78117e8			−0.593659			−0.296829	−	0.954930i	$-0.595929\pi$
$103$	−6.78117e8			−0.593659			−0.296829	+	0.954930i	$0.595929\pi$
$104$	−1.29860e8	+	2.24923e8i	−0.108849	+	0.188532i
$105$	4.95249e8	−	8.57796e8i	0.397623	−	0.688703i
$106$	1.48658e9			1.14370
$107$	−7.26008e8			−0.535445			−0.267722	−	0.963496i	$-0.586271\pi$
$107$	−7.26008e8			−0.535445			−0.267722	+	0.963496i	$0.586271\pi$
$108$	−3.46306e8	+	5.99819e8i	−0.244936	+	0.424242i
$109$	3.49459e8	+	6.05281e8i	0.237125	+	0.410712i	0.959888	−	0.280383i	$-0.0904616\pi$
$109$	3.49459e8	+	6.05281e8i	0.237125	+	0.410712i	−0.722763	+	0.691096i	$0.757128\pi$
$110$	−1.39909e8	+	2.42330e8i	−0.0911126	+	0.157812i
$111$	4.22960e8	+	7.32588e8i	0.264451	+	0.458043i
$112$	−1.27250e8	−	2.20404e8i	−0.0764149	−	0.132355i
$113$	1.94073e9			1.11973			0.559863	−	0.828585i	$-0.310854\pi$
$113$	1.94073e9			1.11973			0.559863	+	0.828585i	$0.310854\pi$
$114$	−2.05768e9	+	6.74595e7i	−1.14106	+	0.0374086i
$115$	2.34089e9			1.24807
$116$	−2.24557e8	−	3.88944e8i	−0.115150	−	0.199446i
$117$	1.00270e9	+	1.73673e9i	0.494692	+	0.856832i
$118$	−1.22118e9	+	2.11514e9i	−0.579841	+	1.00431i
$119$	−7.53598e8	−	1.30527e9i	−0.344492	−	0.596677i
$120$	−5.22365e8	+	9.04763e8i	−0.229963	+	0.398308i
$121$	−2.11672e9			−0.897696
$122$	1.30472e9			0.533210
$123$	−1.18998e9	+	2.06111e9i	−0.468778	+	0.811947i
$124$	−6.85892e8	+	1.18800e9i	−0.260530	+	0.451252i
$125$	2.97081e9			1.08838
$126$	−1.96511e9			−0.694575
$127$	−1.42318e9	+	2.46502e9i	−0.485448	+	0.840820i	−0.999860	−	0.0167229i	$-0.994677\pi$
$127$	−1.42318e9	+	2.46502e9i	−0.485448	+	0.840820i	0.514413	+	0.857543i	$0.328010\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	−2.74185e8	+	4.74903e8i	−0.0871747	+	0.150991i
$130$	5.71185e8	+	9.89322e8i	0.175401	+	0.303803i
$131$	−7.71494e8	−	1.33627e9i	−0.228882	−	0.396436i	0.728595	−	0.684945i	$-0.240174\pi$
$131$	−7.71494e8	−	1.33627e9i	−0.228882	−	0.396436i	−0.957477	+	0.288509i	$0.906840\pi$
$132$	9.00644e8			0.258209
$133$	−1.16499e9	−	1.87326e9i	−0.322843	−	0.519118i
$134$	−3.86671e8			−0.103602
$135$	1.52322e9	+	2.63830e9i	0.394694	+	0.683631i
$136$	7.94860e8	+	1.37674e9i	0.199235	+	0.345085i
$137$	−2.21139e9	+	3.83025e9i	−0.536319	+	0.928932i	0.462779	+	0.886474i	$0.346852\pi$
$137$	−2.21139e9	+	3.83025e9i	−0.536319	+	0.928932i	−0.999098	+	0.0424585i	$0.986481\pi$
$138$	−3.76728e9	−	6.52512e9i	−0.884244	−	1.53156i
$139$	2.31412e9	−	4.00818e9i	0.525799	−	0.910711i	−0.473749	−	0.880660i	$-0.657100\pi$
$139$	2.31412e9	−	4.00818e9i	0.525799	−	0.910711i	0.999548	−	0.0300512i	$-0.00956705\pi$
$140$	−1.11942e9			−0.246273
$141$	−3.51269e9			−0.748434
$142$	6.90910e8	−	1.19669e9i	0.142601	−	0.246993i
$143$	4.92410e8	−	8.52878e8i	0.0984724	−	0.170559i
$144$	2.07271e9			0.401704
$145$	−1.97542e9			−0.371111
$146$	3.33453e9	−	5.77557e9i	0.607360	−	1.05198i
$147$	2.86238e9	+	4.95779e9i	0.505592	+	0.875710i
$148$	4.78012e8	−	8.27940e8i	0.0818956	−	0.141847i
$149$	−9.16638e8	−	1.58766e9i	−0.152356	−	0.263888i	0.779737	−	0.626107i	$-0.215353\pi$
$149$	−9.16638e8	−	1.58766e9i	−0.152356	−	0.263888i	−0.932093	+	0.362219i	$0.882019\pi$
$150$	−1.24171e9	−	2.15071e9i	−0.200268	−	0.346874i
$151$	−3.59113e9			−0.562128			−0.281064	−	0.959689i	$-0.590687\pi$
$151$	−3.59113e9			−0.562128			−0.281064	+	0.959689i	$0.590687\pi$
$152$	1.22878e9	+	1.97583e9i	0.186714	+	0.300229i
$153$	1.22749e10			1.81095
$154$	4.82516e8	+	8.35742e8i	0.0691303	+	0.119737i
$155$	3.01689e9	+	5.22540e9i	0.419823	+	0.727155i
$156$	1.83846e9	−	3.18431e9i	0.248539	−	0.430482i
$157$	−1.80240e9	−	3.12185e9i	−0.236757	−	0.410075i	0.723025	−	0.690822i	$-0.242751\pi$
$157$	−1.80240e9	−	3.12185e9i	−0.236757	−	0.410075i	−0.959782	+	0.280747i	$0.909418\pi$
$158$	−3.13055e9	+	5.42227e9i	−0.399635	+	0.692188i
$159$	−2.10460e10			−2.61145
$160$	1.18071e9			0.142431
$161$	4.03661e9	−	6.99161e9i	0.473478	−	0.820088i
$162$	−7.73508e7	+	1.33976e8i	−0.00882363	+	0.0152830i
$163$	−5.35714e9			−0.594413			−0.297207	−	0.954813i	$-0.596055\pi$
$163$	−5.35714e9			−0.594413			−0.297207	+	0.954813i	$0.596055\pi$
$164$	2.68973e9			0.290343
$165$	1.98074e9	−	3.43074e9i	0.208041	−	0.360338i
$166$	4.17428e9	+	7.23006e9i	0.426673	+	0.739019i
$167$	8.62635e9	−	1.49413e10i	0.858229	−	1.48650i	−0.0153886	−	0.999882i	$-0.504899\pi$
$167$	8.62635e9	−	1.49413e10i	0.858229	−	1.48650i	0.873617	−	0.486614i	$-0.161768\pi$
$168$	1.80152e9	+	3.12033e9i	0.174481	+	0.302210i
$169$	3.29196e9	+	5.70185e9i	0.310431	+	0.537682i
$170$	6.99236e9			0.642102
$171$	1.79562e10	−	5.88681e8i	1.60595	−	0.0526499i
$172$	6.19746e8			0.0539927
$173$	1.95418e9	+	3.38475e9i	0.165866	+	0.287289i	0.936963	−	0.349430i	$-0.113625\pi$
$173$	1.95418e9	+	3.38475e9i	0.165866	+	0.287289i	−0.771096	+	0.636719i	$0.780291\pi$
$174$	3.17912e9	+	5.50640e9i	0.262927	+	0.455404i
$175$	1.33048e9	−	2.30447e9i	0.107236	−	0.185737i
$176$	−5.08935e8	−	8.81502e8i	−0.0399812	−	0.0692494i
$177$	1.72886e10	−	2.99447e10i	1.32397	−	2.29319i
$178$	−1.71832e10			−1.28297
$179$	−1.63553e10			−1.19075			−0.595376	−	0.803447i	$-0.702997\pi$
$179$	−1.63553e10			−1.19075			−0.595376	+	0.803447i	$0.702997\pi$
$180$	4.55838e9	−	7.89535e9i	0.323657	−	0.560590i
$181$	−1.30718e10	+	2.26411e10i	−0.905279	+	1.56799i	−0.0847370	+	0.996403i	$0.527005\pi$
$181$	−1.30718e10	+	2.26411e10i	−0.905279	+	1.56799i	−0.820542	+	0.571586i	$0.806328\pi$
$182$	3.93979e9			0.266166
$183$	−1.84713e10			−1.21750
$184$	−4.25762e9	+	7.37442e9i	−0.273834	+	0.474294i
$185$	−2.10253e9	−	3.64168e9i	−0.131968	−	0.228575i
$186$	9.71040e9	−	1.68189e10i	0.594879	−	1.03036i
$187$	−3.01400e9	−	5.22040e9i	−0.180242	−	0.312188i
$188$	1.98495e9	+	3.43803e9i	0.115888	+	0.200724i
$189$	1.05065e10			0.598936
$190$	1.02287e10	−	3.35340e8i	0.569416	−	0.0186679i
$191$	−3.01937e10			−1.64160			−0.820799	−	0.571217i	$-0.806471\pi$
$191$	−3.01937e10			−1.64160			−0.820799	+	0.571217i	$0.806471\pi$
$192$	−1.90016e9	−	3.29118e9i	−0.100910	−	0.174782i
$193$	3.77833e9	+	6.54425e9i	0.196016	+	0.339510i	0.947233	−	0.320546i	$-0.103866\pi$
$193$	3.77833e9	+	6.54425e9i	0.196016	+	0.339510i	−0.751217	+	0.660055i	$0.770533\pi$
$194$	−3.85365e9	+	6.67472e9i	−0.195328	+	0.338318i
$195$	−8.08645e9	−	1.40061e10i	−0.400500	−	0.693686i
$196$	3.23495e9	−	5.60309e9i	0.156572	−	0.271191i
$197$	−3.64564e10			−1.72455			−0.862274	−	0.506442i	$-0.830961\pi$
$197$	−3.64564e10			−1.72455			−0.862274	+	0.506442i	$0.830961\pi$
$198$	−7.85941e9			−0.363410
$199$	−4.26861e9	+	7.39345e9i	−0.192951	+	0.334202i	−0.946227	−	0.323503i	$-0.895139\pi$
$199$	−4.26861e9	+	7.39345e9i	−0.192951	+	0.334202i	0.753276	+	0.657705i	$0.228473\pi$
$200$	−1.40333e9	+	2.43064e9i	−0.0620191	+	0.107420i
$201$	5.47422e9			0.236559
$202$	2.88128e10			1.21760
$203$	−3.40640e9	+	5.90006e9i	−0.140787	+	0.243851i
$204$	−1.12531e10	−	1.94909e10i	−0.454921	−	0.787946i
$205$	5.91538e9	−	1.02457e10i	0.233932	−	0.405182i
$206$	−5.42493e9	−	9.39626e9i	−0.209890	−	0.363540i
$207$	3.28749e10	+	5.69410e10i	1.24451	+	2.15555i
$208$	−4.15551e9			−0.153936
$209$	−4.65936e9	−	7.49207e9i	−0.168915	−	0.271609i
$210$	1.58480e10			0.562324
$211$	1.81426e10	+	3.14240e10i	0.630129	+	1.09141i	0.987525	+	0.157462i	$0.0503312\pi$
$211$	1.81426e10	+	3.14240e10i	0.630129	+	1.09141i	−0.357396	+	0.933953i	$0.616335\pi$
$212$	1.18926e10	+	2.05986e10i	0.404359	+	0.700369i
$213$	−9.78143e9	+	1.69419e10i	−0.325607	+	0.563968i
$214$	−5.80807e9	−	1.00599e10i	−0.189308	−	0.327891i
$215$	1.36297e9	−	2.36073e9i	0.0435024	−	0.0753484i
$216$	−1.10818e10			−0.346392
$217$	2.08092e10			0.637069
$218$	−5.59135e9	+	9.68450e9i	−0.167673	+	0.290418i
$219$	−4.72080e10	+	8.17666e10i	−1.38681	+	2.40202i
$220$	−4.47709e9			−0.128853
$221$	−2.46096e10			−0.693968
$222$	−6.76736e9	+	1.17214e10i	−0.186995	+	0.323886i
$223$	1.74409e10	+	3.02085e10i	0.472277	+	0.818007i	0.999497	−	0.0317216i	$-0.0100990\pi$
$223$	1.74409e10	+	3.02085e10i	0.472277	+	0.818007i	−0.527220	+	0.849729i	$0.676766\pi$
$224$	2.03601e9	−	3.52647e9i	0.0540335	−	0.0935888i
$225$	1.08357e10	+	1.87680e10i	0.281862	+	0.488200i
$226$	1.55258e10	+	2.68915e10i	0.395883	+	0.685689i
$227$	6.51855e10			1.62943			0.814714	−	0.579864i	$-0.196894\pi$
$227$	6.51855e10			1.62943			0.814714	+	0.579864i	$0.196894\pi$
$228$	−1.73962e10	−	2.79724e10i	−0.426332	−	0.685525i
$229$	3.11766e10			0.749151			0.374576	−	0.927196i	$-0.377788\pi$
$229$	3.11766e10			0.749151			0.374576	+	0.927196i	$0.377788\pi$
$230$	1.87271e10	+	3.24363e10i	0.441260	+	0.764286i
$231$	−6.83113e9	−	1.18319e10i	−0.157848	−	0.273401i
$232$	3.59291e9	−	6.22310e9i	0.0814236	−	0.141030i
$233$	−3.91702e10	−	6.78447e10i	−0.870671	−	1.50805i	−0.861304	−	0.508090i	$-0.830352\pi$
$233$	−3.91702e10	−	6.78447e10i	−0.870671	−	1.50805i	−0.00936638	−	0.999956i	$-0.502981\pi$
$234$	−1.60432e10	+	2.77877e10i	−0.349800	+	0.605872i
$235$	1.74615e10			0.373488
$236$	−3.90776e10			−0.820019
$237$	4.43202e10	−	7.67648e10i	0.912502	−	1.58050i
$238$	1.20576e10	−	2.08843e10i	0.243592	−	0.421914i
$239$	1.00229e10			0.198703			0.0993514	−	0.995052i	$-0.468323\pi$
$239$	1.00229e10			0.198703			0.0993514	+	0.995052i	$0.468323\pi$
$240$	−1.67157e10			−0.325217
$241$	1.77720e10	−	3.07821e10i	0.339360	−	0.587789i	−0.644952	−	0.764223i	$-0.723123\pi$
$241$	1.77720e10	−	3.07821e10i	0.339360	−	0.587789i	0.984312	+	0.176434i	$0.0564562\pi$
$242$	−1.69338e10	−	2.93301e10i	−0.317384	−	0.549725i
$243$	2.77214e10	−	4.80149e10i	0.510019	−	0.883380i
$244$	1.04378e10	+	1.80787e10i	0.188518	+	0.326523i
$245$	−1.42289e10	−	2.46451e10i	−0.252303	−	0.437002i
$246$	−3.80794e10			−0.662952
$247$	−3.60000e10	+	1.18023e9i	−0.615412	+	0.0201758i
$248$	−2.19486e10			−0.368446
$249$	−5.90965e10	−	1.02358e11i	−0.974238	−	1.68743i
$250$	2.37665e10	+	4.11648e10i	0.384800	+	0.666493i
$251$	−5.34971e8	+	9.26597e8i	−0.00850743	+	0.0147353i	−0.870248	−	0.492614i	$-0.836041\pi$
$251$	−5.34971e8	+	9.26597e8i	−0.00850743	+	0.0147353i	0.861740	+	0.507350i	$0.169375\pi$
$252$	−1.57209e10	−	2.72294e10i	−0.245569	−	0.425339i
$253$	1.61443e10	−	2.79628e10i	0.247729	−	0.429080i
$254$	−4.55417e10			−0.686527
$255$	−9.89931e10			−1.46613
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	1.95260e10	−	3.38200e10i	0.279199	−	0.483587i	−0.691987	−	0.721910i	$-0.743264\pi$
$257$	1.95260e10	−	3.38200e10i	0.279199	−	0.483587i	0.971186	+	0.238323i	$0.0765976\pi$
$258$	−8.77393e9			−0.123284
$259$	−1.45023e10			−0.200258
$260$	−9.13897e9	+	1.58292e10i	−0.124027	+	0.214821i
$261$	−2.77424e10	−	4.80513e10i	−0.370051	−	0.640947i
$262$	1.23439e10	−	2.13803e10i	0.161844	−	0.280322i
$263$	1.14182e10	+	1.97769e10i	0.147162	+	0.254892i	0.930178	−	0.367110i	$-0.119653\pi$
$263$	1.14182e10	+	1.97769e10i	0.147162	+	0.254892i	−0.783015	+	0.622002i	$0.786319\pi$
$264$	7.20516e9	+	1.24797e10i	0.0912905	+	0.158120i
$265$	1.04619e11			1.30318
$266$	1.66367e10	−	3.11287e10i	0.203752	−	0.381236i
$267$	2.43268e11			2.92944
$268$	−3.09337e9	−	5.35787e9i	−0.0366290	−	0.0634432i
$269$	−3.49038e10	−	6.04552e10i	−0.406432	−	0.703961i	0.588055	−	0.808821i	$-0.299894\pi$
$269$	−3.49038e10	−	6.04552e10i	−0.406432	−	0.703961i	−0.994487	+	0.104860i	$0.966561\pi$
$270$	−2.43715e10	+	4.22127e10i	−0.279091	+	0.483400i
$271$	8.20367e10	+	1.42092e11i	0.923946	+	1.60032i	0.793248	+	0.608899i	$0.208389\pi$
$271$	8.20367e10	+	1.42092e11i	0.923946	+	1.60032i	0.130698	+	0.991422i	$0.458278\pi$
$272$	−1.27178e10	+	2.20278e10i	−0.140880	+	0.244012i
$273$	−5.57769e10			−0.607746
$274$	−7.07646e10			−0.758470
$275$	5.32124e9	−	9.21667e9i	0.0561069	−	0.0971800i
$276$	6.02765e10	−	1.04402e11i	0.625255	−	1.08297i
$277$	1.83621e11			1.87397			0.936984	−	0.349372i	$-0.113605\pi$
$277$	1.83621e11			1.87397			0.936984	+	0.349372i	$0.113605\pi$
$278$	7.40520e10			0.743593
$279$	−8.47371e10	+	1.46769e11i	−0.837249	+	1.45016i
$280$	−8.95535e9	−	1.55111e10i	−0.0870705	−	0.150811i
$281$	−8.83750e9	+	1.53070e10i	−0.0845573	+	0.146457i	−0.905202	−	0.424981i	$-0.860281\pi$
$281$	−8.83750e9	+	1.53070e10i	−0.0845573	+	0.146457i	0.820645	+	0.571438i	$0.193614\pi$
$282$	−2.81015e10	−	4.86732e10i	−0.264611	−	0.458320i
$283$	5.72266e10	+	9.91194e10i	0.530346	+	0.918585i	0.999373	+	0.0354019i	$0.0112711\pi$
$283$	5.72266e10	+	9.91194e10i	0.530346	+	0.918585i	−0.469028	+	0.883184i	$0.655396\pi$
$284$	2.21091e10			0.201669
$285$	−1.44811e11	+	4.74752e9i	−1.30017	+	0.0426250i
$286$	1.57571e10			0.139261
$287$	−2.04009e10	−	3.53353e10i	−0.177492	−	0.307426i
$288$	1.65816e10	+	2.87202e10i	0.142024	+	0.245993i
$289$	−1.60228e10	+	2.77523e10i	−0.135113	+	0.234023i
$290$	−1.58034e10	−	2.73722e10i	−0.131208	−	0.227258i
$291$	5.45574e10	−	9.44961e10i	0.446000	−	0.772495i
$292$	1.06705e11			0.858937
$293$	1.97318e10			0.156409			0.0782047	−	0.996937i	$-0.475081\pi$
$293$	1.97318e10			0.156409			0.0782047	+	0.996937i	$0.475081\pi$
$294$	−4.57981e10	+	7.93247e10i	−0.357507	+	0.619221i
$295$	−8.59412e10	+	1.48854e11i	−0.660697	+	1.14436i
$296$	1.52964e10			0.115818
$297$	4.20206e10			0.313371
$298$	1.46662e10	−	2.54026e10i	0.107732	−	0.186597i
$299$	−6.59100e10	−	1.14159e11i	−0.476904	−	0.826022i
$300$	1.98674e10	−	3.44114e10i	0.141611	−	0.245277i
$301$	−4.70059e9	−	8.14167e9i	−0.0330068	−	0.0571695i
$302$	−2.87291e10	−	4.97602e10i	−0.198742	−	0.344232i
$303$	−4.07912e11			−2.78019
$304$	−1.75477e10	+	3.28331e10i	−0.117839	+	0.220486i
$305$	9.18207e10			0.607563
$306$	9.81993e10	+	1.70086e11i	0.640268	+	1.10898i
$307$	−7.61996e10	−	1.31981e11i	−0.489587	−	0.847989i	0.510341	−	0.859972i	$-0.329519\pi$
$307$	−7.61996e10	−	1.31981e11i	−0.489587	−	0.847989i	−0.999928	+	0.0119826i	$0.996186\pi$
$308$	−7.72026e9	+	1.33719e10i	−0.0488825	+	0.0846670i
$309$	7.68025e10	+	1.33026e11i	0.479250	+	0.830086i
$310$	−4.82702e10	+	8.36065e10i	−0.296860	+	0.514177i
$311$	−1.37792e10			−0.0835224			−0.0417612	−	0.999128i	$-0.513297\pi$
$311$	−1.37792e10			−0.0835224			−0.0417612	+	0.999128i	$0.513297\pi$
$312$	5.88308e10			0.351487
$313$	−1.07275e11	+	1.85806e11i	−0.631757	+	1.09424i	0.355435	+	0.934701i	$0.384333\pi$
$313$	−1.07275e11	+	1.85806e11i	−0.631757	+	1.09424i	−0.987192	+	0.159534i	$0.949001\pi$
$314$	2.88384e10	−	4.99496e10i	0.167413	−	0.289967i
$315$	−1.38296e11			−0.791430
$316$	−1.00178e11			−0.565169
$317$	−3.08189e10	+	5.33798e10i	−0.171415	+	0.296900i	−0.938915	−	0.344149i	$-0.888167\pi$
$317$	−3.08189e10	+	5.33798e10i	−0.171415	+	0.296900i	0.767500	+	0.641050i	$0.221501\pi$
$318$	−1.68368e11	−	2.91621e11i	−0.923287	−	1.59918i
$319$	−1.36238e10	+	2.35972e10i	−0.0736616	+	0.127586i
$320$	9.44568e9	+	1.63604e10i	0.0503568	+	0.0872205i
$321$	8.22266e10	+	1.42421e11i	0.432255	+	0.748687i
$322$	1.29171e11			0.669599
$323$	−1.03920e11	+	1.94443e11i	−0.531237	+	0.993989i
$324$	−2.47523e9			−0.0124785
$325$	−2.17242e10	−	3.76275e10i	−0.108011	−	0.187081i
$326$	−4.28571e10	−	7.42307e10i	−0.210157	−	0.364002i
$327$	7.91585e10	−	1.37106e11i	0.382853	−	0.663122i
$328$	2.15179e10	+	3.72700e10i	0.102652	+	0.177798i
$329$	3.01105e10	−	5.21529e10i	0.141689	−	0.245413i
$330$	6.33836e10			0.294214
$331$	3.26065e11			1.49306			0.746531	−	0.665351i	$-0.231718\pi$
$331$	3.26065e11			1.49306			0.746531	+	0.665351i	$0.231718\pi$
$332$	−6.67884e10	+	1.15681e11i	−0.301703	+	0.522565i
$333$	5.90549e10	−	1.02286e11i	0.263183	−	0.455846i
$334$	2.76043e11			1.21372
$335$	−2.72122e10			−0.118049
$336$	−2.88244e10	+	4.99253e10i	−0.123377	+	0.213695i
$337$	1.62502e11	+	2.81461e11i	0.686316	+	1.18873i	0.973021	+	0.230715i	$0.0741064\pi$
$337$	1.62502e11	+	2.81461e11i	0.686316	+	1.18873i	−0.286706	+	0.958019i	$0.592560\pi$
$338$	−5.26714e10	+	9.12296e10i	−0.219508	+	0.380199i
$339$	−2.19804e11	−	3.80711e11i	−0.903934	−	1.56566i
$340$	5.59389e10	+	9.68890e10i	0.227017	+	0.393205i
$341$	8.32259e10			0.333322
$342$	1.51807e11	+	2.44100e11i	0.600032	+	0.964827i
$343$	−2.54853e11			−0.994182
$344$	4.95796e9	+	8.58745e9i	0.0190893	+	0.0330637i
$345$	−2.65125e11	−	4.59211e11i	−1.00755	−	1.74512i
$346$	−3.12670e10	+	5.41559e10i	−0.117285	+	0.203144i
$347$	2.37197e11	+	4.10838e11i	0.878268	+	1.52120i	0.853241	+	0.521518i	$0.174634\pi$
$347$	2.37197e11	+	4.10838e11i	0.878268	+	1.52120i	0.0250272	+	0.999687i	$0.492033\pi$
$348$	−5.08660e10	+	8.81024e10i	−0.185918	+	0.322019i
$349$	−1.24435e11			−0.448981			−0.224490	−	0.974476i	$-0.572072\pi$
$349$	−1.24435e11			−0.448981			−0.224490	+	0.974476i	$0.572072\pi$
$350$	4.25755e10			0.151654
$351$	8.57756e10	−	1.48568e11i	0.301635	−	0.522447i
$352$	8.14296e9	−	1.41040e10i	0.0282710	−	0.0489667i
$353$	−4.02069e11			−1.37821			−0.689104	−	0.724663i	$-0.741996\pi$
$353$	−4.02069e11			−1.37821			−0.689104	+	0.724663i	$0.741996\pi$
$354$	5.53234e11			1.87238
$355$	4.86233e10	−	8.42180e10i	0.162486	−	0.281435i
$356$	−1.37466e11	−	2.38098e11i	−0.453597	−	0.785653i
$357$	−1.70703e11	+	2.95666e11i	−0.556204	+	0.963373i
$358$	−1.30843e11	−	2.26626e11i	−0.420994	−	0.729183i
$359$	−1.70106e11	−	2.94632e11i	−0.540499	−	0.936172i	−0.998875	−	0.0474135i	$-0.984902\pi$
$359$	−1.70106e11	−	2.94632e11i	−0.540499	−	0.936172i	0.458376	−	0.888758i	$-0.348431\pi$
$360$	1.45868e11			0.457720
$361$	−1.42694e11	+	2.89423e11i	−0.442203	+	0.896915i
$362$	−4.18298e11			−1.28026
$363$	2.39737e11	+	4.15236e11i	0.724694	+	1.25521i
$364$	3.15183e10	+	5.45913e10i	0.0941038	+	0.162992i
$365$	2.34670e11	−	4.06460e11i	0.692054	−	1.19867i
$366$	−1.47771e11	−	2.55946e11i	−0.430451	−	0.745563i
$367$	1.44455e11	−	2.50203e11i	0.415657	−	0.719939i	−0.579840	−	0.814730i	$-0.696885\pi$
$367$	1.44455e11	−	2.50203e11i	0.415657	−	0.719939i	0.995497	+	0.0947912i	$0.0302184\pi$
$368$	−1.36244e11			−0.387259
$369$	3.32297e11			0.933057
$370$	3.36404e10	−	5.82670e10i	0.0933155	−	0.161627i
$371$	1.80404e11	−	3.12470e11i	0.494384	−	0.856299i
$372$	3.10733e11			0.841286
$373$	2.84395e11			0.760734			0.380367	−	0.924836i	$-0.375798\pi$
$373$	2.84395e11			0.760734			0.380367	+	0.924836i	$0.375798\pi$
$374$	4.82240e10	−	8.35264e10i	0.127450	−	0.220750i
$375$	−3.36470e11	−	5.82782e11i	−0.878628	−	1.52183i
$376$	−3.17591e10	+	5.50084e10i	−0.0819452	+	0.141933i
$377$	5.56199e10	+	9.63366e10i	0.141806	+	0.245615i
$378$	8.40522e10	+	1.45583e11i	0.211756	+	0.366772i
$379$	−1.65261e11			−0.411428			−0.205714	−	0.978612i	$-0.565952\pi$
$379$	−1.65261e11			−0.411428			−0.205714	+	0.978612i	$0.565952\pi$
$380$	8.64763e10	+	1.39051e11i	0.212751	+	0.342095i
$381$	6.44748e11			1.56757
$382$	−2.41550e11	−	4.18377e11i	−0.580393	−	1.00527i
$383$	4.58399e10	+	7.93970e10i	0.108855	+	0.188543i	0.915307	−	0.402757i	$-0.131948\pi$
$383$	4.58399e10	+	7.93970e10i	0.108855	+	0.188543i	−0.806452	+	0.591300i	$0.798615\pi$
$384$	3.04026e10	−	5.26589e10i	0.0713543	−	0.123589i
$385$	3.39574e10	+	5.88160e10i	0.0787702	+	0.136434i
$386$	−6.04532e10	+	1.04708e11i	−0.138604	+	0.240070i
$387$	7.65651e10			0.173513
$388$	−1.23317e11			−0.276236
$389$	1.57370e11	−	2.72573e11i	0.348457	−	0.603546i	−0.637518	−	0.770435i	$-0.720039\pi$
$389$	1.57370e11	−	2.72573e11i	0.348457	−	0.603546i	0.985976	+	0.166889i	$0.0533722\pi$
$390$	1.29383e11	−	2.24098e11i	0.283196	−	0.490510i
$391$	−8.06859e11			−1.74583
$392$	1.03518e11			0.221427
$393$	−1.74757e11	+	3.02687e11i	−0.369545	+	0.640071i
$394$	−2.91651e11	−	5.05154e11i	−0.609720	−	1.05607i
$395$	−2.20315e11	+	3.81596e11i	−0.455362	+	0.788710i
$396$	−6.28753e10	−	1.08903e11i	−0.128485	−	0.222542i
$397$	2.48079e11	+	4.29685e11i	0.501225	+	0.868147i	0.999999	+	0.00141482i	$0.000450352\pi$
$397$	2.48079e11	+	4.29685e11i	0.501225	+	0.868147i	−0.498774	+	0.866732i	$0.666216\pi$
$398$	−1.36596e11			−0.272874
$399$	−2.35532e11	+	4.40699e11i	−0.465234	+	0.870491i
$400$	−4.49066e10			−0.0877083
$401$	−2.31570e11	−	4.01091e11i	−0.447232	−	0.774628i	0.550973	−	0.834523i	$-0.314257\pi$
$401$	−2.31570e11	−	4.01091e11i	−0.447232	−	0.774628i	−0.998205	+	0.0598951i	$0.980923\pi$
$402$	4.37937e10	+	7.58530e10i	0.0836363	+	0.144862i
$403$	1.69887e11	−	2.94253e11i	0.320839	−	0.555710i
$404$	2.30502e11	+	3.99242e11i	0.430486	+	0.745624i
$405$	−5.44362e9	+	9.42863e9i	−0.0100540	+	0.0174141i
$406$	−1.09005e11			−0.199103
$407$	−5.80017e10			−0.104777
$408$	1.80049e11	−	3.11855e11i	0.321678	−	0.557162i
$409$	2.20922e11	−	3.82648e11i	0.390377	−	0.676153i	−0.602122	−	0.798404i	$-0.705678\pi$
$409$	2.20922e11	−	3.82648e11i	0.390377	−	0.676153i	0.992499	+	0.122251i	$0.0390113\pi$
$410$	1.89292e11			0.330830
$411$	1.00184e12			1.73184
$412$	8.67990e10	−	1.50340e11i	0.148415	−	0.257062i
$413$	2.96393e11	+	5.13367e11i	0.501294	+	0.868266i
$414$	−5.25999e11	+	9.11057e11i	−0.880001	+	1.52421i
$415$	2.93768e11	+	5.08821e11i	0.486170	+	0.842071i
$416$	−3.32440e10	−	5.75804e10i	−0.0544244	−	0.0942659i
$417$	−1.04838e12			−1.69787
$418$	6.65383e10	−	1.24499e11i	0.106605	−	0.199467i
$419$	9.61230e11			1.52358			0.761788	−	0.647826i	$-0.224322\pi$
$419$	9.61230e11			1.52358			0.761788	+	0.647826i	$0.224322\pi$
$420$	1.26784e11	+	2.19596e11i	0.198811	+	0.344352i
$421$	−2.49718e11	−	4.32525e11i	−0.387419	−	0.671030i	0.604682	−	0.796467i	$-0.293300\pi$
$421$	−2.49718e11	−	4.32525e11i	−0.387419	−	0.671030i	−0.992102	+	0.125437i	$0.959967\pi$
$422$	−2.90282e11	+	5.02783e11i	−0.445568	+	0.771747i
$423$	2.45226e11	+	4.24744e11i	0.372421	+	0.645053i
$424$	−1.90282e11	+	3.29578e11i	−0.285925	+	0.495236i
$425$	−2.65945e11			−0.395404
$426$	−3.13006e11			−0.460478
$427$	1.58335e11	−	2.74244e11i	0.230490	−	0.399220i
$428$	9.29290e10	−	1.60958e11i	0.133861	−	0.231854i
$429$	−2.23078e11			−0.317980
$430$	4.36151e10			0.0615217
$431$	4.42771e11	−	7.66902e11i	0.618061	−	1.07051i	−0.371778	−	0.928322i	$-0.621252\pi$
$431$	4.42771e11	−	7.66902e11i	0.618061	−	1.07051i	0.989839	−	0.142192i	$-0.0454151\pi$
$432$	−8.86543e10	−	1.53554e11i	−0.122468	−	0.212121i
$433$	−3.66800e11	+	6.35317e11i	−0.501458	+	0.868550i	0.498541	+	0.866866i	$0.333869\pi$
$433$	−3.66800e11	+	6.35317e11i	−0.501458	+	0.868550i	−0.999999	+	0.00168384i	$0.999464\pi$
$434$	1.66474e11	+	2.88341e11i	0.225238	+	0.390124i
$435$	2.23733e11	+	3.87517e11i	0.299591	+	0.518907i
$436$	−1.78923e11			−0.237125
$437$	−1.18031e12	+	3.86954e10i	−1.54821	+	0.0507567i
$438$	−1.51065e12			−1.96124
$439$	3.70198e11	+	6.41201e11i	0.475711	+	0.823956i	0.999613	−	0.0278230i	$-0.00885748\pi$
$439$	3.70198e11	+	6.41201e11i	0.475711	+	0.823956i	−0.523902	+	0.851779i	$0.675524\pi$
$440$	−3.58167e10	−	6.20364e10i	−0.0455563	−	0.0789059i
$441$	3.99654e11	−	6.92222e11i	0.503166	−	0.871508i
$442$	−1.96877e11	−	3.41001e11i	−0.245355	−	0.424967i
$443$	6.59016e11	−	1.14145e12i	0.812979	−	1.40812i	−0.0977908	−	0.995207i	$-0.531178\pi$
$443$	6.59016e11	−	1.14145e12i	0.812979	−	1.40812i	0.910770	−	0.412914i	$-0.135489\pi$
$444$	−2.16556e11			−0.264451
$445$	−1.20928e12			−1.46187
$446$	−2.79054e11	+	4.83336e11i	−0.333950	+	0.578418i
$447$	−2.07634e11	+	3.59633e11i	−0.245989	+	0.426065i
$448$	6.51522e10			0.0764149
$449$	2.70023e11			0.313540			0.156770	−	0.987635i	$-0.449892\pi$
$449$	2.70023e11			0.313540			0.156770	+	0.987635i	$0.449892\pi$
$450$	−1.73372e11	+	3.00289e11i	−0.199307	+	0.345209i
$451$	−8.15928e10	−	1.41323e11i	−0.0928661	−	0.160849i
$452$	−2.48413e11	+	4.30264e11i	−0.279931	+	0.484855i
$453$	4.06727e11	+	7.04471e11i	0.453796	+	0.785998i
$454$	5.21484e11	+	9.03237e11i	0.576089	+	0.997816i
$455$	2.77266e11			0.303281
$456$	2.48428e11	−	4.64829e11i	0.269066	−	0.503444i
$457$	−1.09307e12			−1.17226			−0.586131	−	0.810216i	$-0.699350\pi$
$457$	−1.09307e12			−1.17226			−0.586131	+	0.810216i	$0.699350\pi$
$458$	2.49413e11	+	4.31996e11i	0.264865	+	0.458760i
$459$	−5.25025e11	−	9.09371e11i	−0.552107	−	0.956277i
$460$	−2.99633e11	+	5.18980e11i	−0.312018	+	0.540431i
$461$	2.65163e11	+	4.59276e11i	0.273438	+	0.473609i	0.969740	−	0.244140i	$-0.0785058\pi$
$461$	2.65163e11	+	4.59276e11i	0.273438	+	0.473609i	−0.696302	+	0.717749i	$0.745172\pi$
$462$	1.09298e11	−	1.89310e11i	0.111615	−	0.193323i
$463$	1.15718e12			1.17027			0.585133	−	0.810937i	$-0.301042\pi$
$463$	1.15718e12			1.17027			0.585133	+	0.810937i	$0.301042\pi$
$464$	1.14973e11			0.115150
$465$	6.83377e11	−	1.18364e12i	0.677832	−	1.17404i
$466$	6.26723e11	−	1.08552e12i	0.615657	−	1.06635i
$467$	1.14045e12			1.10956			0.554782	−	0.831996i	$-0.312802\pi$
$467$	1.14045e12			1.10956			0.554782	+	0.831996i	$0.312802\pi$
$468$	−5.13383e11			−0.494692
$469$	−4.69246e10	+	8.12758e10i	−0.0447840	+	0.0775681i
$470$	1.39692e11	+	2.41954e11i	0.132048	+	0.228714i
$471$	−4.08275e11	+	7.07152e11i	−0.382259	+	0.662093i
$472$	−3.12621e11	−	5.41475e11i	−0.289921	−	0.502157i
$473$	−1.87999e10	−	3.25624e10i	−0.0172695	−	0.0299117i
$474$	1.41825e12			1.29047
$475$	−3.89035e11	+	1.27542e10i	−0.350645	+	0.0114956i
$476$	3.85842e11			0.344492
$477$	1.46925e12	+	2.54482e12i	1.29946	+	2.25073i
$478$	8.01834e10	+	1.38882e11i	0.0702521	+	0.121680i
$479$	2.31632e11	−	4.01199e11i	0.201043	−	0.348217i	−0.747822	−	0.663900i	$-0.768900\pi$
$479$	2.31632e11	−	4.01199e11i	0.201043	−	0.348217i	0.948865	+	0.315683i	$0.102233\pi$
$480$	−1.33725e11	−	2.31619e11i	−0.114982	−	0.199154i
$481$	−1.18397e11	+	2.05070e11i	−0.100853	+	0.174683i
$482$	5.68705e11			0.479928
$483$	−1.82872e12			−1.52892
$484$	2.70940e11	−	4.69282e11i	0.224424	−	0.388714i
$485$	−2.71204e11	+	4.69739e11i	−0.222565	+	0.385495i
$486$	8.87084e11			0.721276
$487$	−1.66700e12			−1.34294			−0.671469	−	0.741033i	$-0.734336\pi$
$487$	−1.66700e12			−1.34294			−0.671469	+	0.741033i	$0.734336\pi$
$488$	−1.67004e11	+	2.89260e11i	−0.133302	+	0.230887i
$489$	6.06741e11	+	1.05091e12i	0.479859	+	0.831140i
$490$	2.27662e11	−	3.94322e11i	0.178405	−	0.309007i
$491$	7.75299e11	+	1.34286e12i	0.602008	+	1.04271i	0.992517	+	0.122109i	$0.0389659\pi$
$491$	7.75299e11	+	1.34286e12i	0.602008	+	1.04271i	−0.390509	+	0.920599i	$0.627701\pi$
$492$	−3.04635e11	−	5.27644e11i	−0.234389	−	0.405973i
$493$	6.80890e11			0.519118
$494$	−3.04353e11	−	4.89388e11i	−0.229936	−	0.369728i
$495$	−5.53112e11			−0.414085
$496$	−1.75588e11	−	3.04128e11i	−0.130265	−	0.225626i
$497$	−1.67691e11	−	2.90450e11i	−0.123284	−	0.213534i
$498$	9.45545e11	−	1.63773e12i	0.688890	−	1.19319i
$499$	−2.59754e11	−	4.49906e11i	−0.187547	−	0.324840i	0.756885	−	0.653548i	$-0.226720\pi$
$499$	−2.59754e11	−	4.49906e11i	−0.187547	−	0.324840i	−0.944432	+	0.328708i	$0.893387\pi$
$500$	−3.80264e11	+	6.58636e11i	−0.272095	+	0.471282i
$501$	−3.90803e12			−2.77133
$502$	−1.71191e10			−0.0120313
$503$	1.04432e12	−	1.80881e12i	0.727406	−	1.25990i	−0.230571	−	0.973056i	$-0.574059\pi$
$503$	1.04432e12	−	1.80881e12i	0.727406	−	1.25990i	0.957976	−	0.286848i	$-0.0926074\pi$
$504$	2.51534e11	−	4.35670e11i	0.173644	−	0.300760i
$505$	2.02772e12			1.38739
$506$	5.16618e11			0.350342
$507$	7.45686e11	−	1.29157e12i	0.501210	−	0.868122i
$508$	−3.64333e11	−	6.31044e11i	−0.242724	−	0.420410i
$509$	3.77526e11	−	6.53894e11i	0.249297	−	0.431795i	−0.714034	−	0.700111i	$-0.753134\pi$
$509$	3.77526e11	−	6.53894e11i	0.249297	−	0.431795i	0.963331	+	0.268316i	$0.0864672\pi$
$510$	−7.91944e11	−	1.37169e12i	−0.518357	−	0.897821i
$511$	−8.09326e11	−	1.40179e12i	−0.525085	−	0.909474i
$512$	−6.87195e10			−0.0441942
$513$	−8.11641e11	−	1.30509e12i	−0.517411	−	0.831976i
$514$	6.24832e11			0.394847
$515$	−3.81784e11	−	6.61269e11i	−0.239158	−	0.414234i
$516$	−7.01915e10	−	1.21575e11i	−0.0435874	−	0.0754955i
$517$	1.20426e11	−	2.08584e11i	0.0741334	−	0.128403i
$518$	−1.16019e11	−	2.00950e11i	−0.0708017	−	0.122632i
$519$	4.42656e11	−	7.66703e11i	0.267802	−	0.463846i
$520$	−2.92447e11			−0.175401
$521$	1.00399e12			0.596978			0.298489	−	0.954413i	$-0.403517\pi$
$521$	1.00399e12			0.596978			0.298489	+	0.954413i	$0.403517\pi$
$522$	4.43878e11	−	7.68820e11i	0.261666	−	0.453218i
$523$	−1.13662e12	+	1.96868e12i	−0.664288	+	1.15058i	0.315190	+	0.949028i	$0.397932\pi$
$523$	−1.13662e12	+	1.96868e12i	−0.664288	+	1.15058i	−0.979478	+	0.201551i	$0.935402\pi$
$524$	3.95005e11			0.228882
$525$	−6.02755e11			−0.346277
$526$	−1.82691e11	+	3.16430e11i	−0.104059	+	0.180236i
$527$	−1.03986e12	−	1.80110e12i	−0.587258	−	1.01716i
$528$	−1.15282e11	+	1.99675e11i	−0.0645521	+	0.111808i
$529$	−1.26037e12	−	2.18303e12i	−0.699758	−	1.21202i
$530$	8.36953e11	+	1.44965e12i	0.460744	+	0.798032i
$531$	−4.82776e12			−2.63524
$532$	5.64426e11	−	1.85043e10i	0.305495	−	0.0100154i
$533$	−6.66213e11			−0.357553
$534$	1.94615e12	+	3.37083e12i	1.03571	+	1.79391i
$535$	−4.08747e11	−	7.07971e11i	−0.215706	−	0.373614i
$536$	4.94938e10	−	8.57259e10i	0.0259006	−	0.0448611i
$537$	1.85238e12	+	3.20842e12i	0.961272	+	1.66497i
$538$	5.58461e11	−	9.67284e11i	0.287391	−	0.497776i
$539$	−3.92527e11			−0.200318
$540$	−7.79889e11			−0.394694
$541$	1.89637e12	−	3.28462e12i	0.951779	−	1.64853i	0.210208	−	0.977657i	$-0.432586\pi$
$541$	1.89637e12	−	3.28462e12i	0.951779	−	1.64853i	0.741572	−	0.670874i	$-0.234081\pi$
$542$	−1.31259e12	+	2.27347e12i	−0.653328	+	1.13160i
$543$	5.92198e12			2.92326
$544$	−4.06968e11			−0.199235
$545$	−3.93495e11	+	6.81554e11i	−0.191054	+	0.330915i
$546$	−4.46215e11	−	7.72867e11i	−0.214871	−	0.372167i
$547$	7.57142e11	−	1.31141e12i	0.361605	−	0.626318i	−0.626620	−	0.779325i	$-0.715562\pi$
$547$	7.57142e11	−	1.31141e12i	0.361605	−	0.626318i	0.988225	+	0.153007i	$0.0488956\pi$
$548$	−5.66117e11	−	9.80543e11i	−0.268160	−	0.464466i
$549$	1.28951e12	+	2.23350e12i	0.605828	+	1.04933i
$550$	1.70280e11			0.0793471
$551$	9.96035e11	−	3.26542e10i	0.460354	−	0.0150923i
$552$	1.92885e12			0.884244
$553$	7.59818e11	+	1.31604e12i	0.345499	+	0.598422i
$554$	1.46896e12	+	2.54432e12i	0.662548	+	1.14757i
$555$	−4.76258e11	+	8.24904e11i	−0.213071	+	0.369050i
$556$	5.92416e11	+	1.02609e12i	0.262900	+	0.455356i
$557$	−1.39689e12	+	2.41949e12i	−0.614914	+	1.06506i	0.375485	+	0.926828i	$0.377476\pi$
$557$	−1.39689e12	+	2.41949e12i	−0.614914	+	1.06506i	−0.990400	+	0.138234i	$0.955857\pi$
$558$	−2.71159e12			−1.18405
$559$	−1.53503e11			−0.0664912
$560$	1.43286e11	−	2.48178e11i	0.0615682	−	0.106639i
$561$	−6.82722e11	+	1.18251e12i	−0.291012	+	0.504048i
$562$	−2.82800e11			−0.119582
$563$	−1.96907e12			−0.825986			−0.412993	−	0.910734i	$-0.635517\pi$
$563$	−1.96907e12			−0.825986			−0.412993	+	0.910734i	$0.635517\pi$
$564$	4.49624e11	−	7.78772e11i	0.187109	−	0.324081i
$565$	1.09264e12	+	1.89251e12i	0.451086	+	0.781304i
$566$	−9.15625e11	+	1.58591e12i	−0.375011	+	0.649538i
$567$	1.87739e10	+	3.25173e10i	0.00762835	+	0.0132127i
$568$	1.76873e11	+	3.06353e11i	0.0713007	+	0.123496i
$569$	−1.80423e12			−0.721582			−0.360791	−	0.932647i	$-0.617493\pi$
$569$	−1.80423e12			−0.721582			−0.360791	+	0.932647i	$0.617493\pi$
$570$	−1.22427e12	−	1.96858e12i	−0.485782	−	0.781118i
$571$	−2.41198e12			−0.949536			−0.474768	−	0.880111i	$-0.657468\pi$
$571$	−2.41198e12			−0.949536			−0.474768	+	0.880111i	$0.657468\pi$
$572$	1.26057e11	+	2.18337e11i	0.0492362	+	0.0852796i
$573$	3.41970e12	+	5.92309e12i	1.32523	+	2.29537i
$574$	3.26414e11	−	5.65365e11i	0.125506	−	0.217383i
$575$	−7.12259e11	−	1.23367e12i	−0.271727	−	0.470645i
$576$	−2.65306e11	+	4.59524e11i	−0.100426	+	0.173943i
$577$	−4.84113e12			−1.81826			−0.909129	−	0.416515i	$-0.863251\pi$
$577$	−4.84113e12			−1.81826			−0.909129	+	0.416515i	$0.863251\pi$
$578$	−5.12729e11			−0.191079
$579$	8.55855e11	−	1.48238e12i	0.316480	−	0.548160i
$580$	2.52854e11	−	4.37956e11i	0.0927777	−	0.160696i
$581$	2.02628e12			0.737748
$582$	1.74584e12			0.630739
$583$	7.21524e11	−	1.24972e12i	0.258668	−	0.448025i
$584$	8.53639e11	+	1.47855e12i	0.303680	+	0.525990i
$585$	−1.12905e12	+	1.95558e12i	−0.398578	+	0.690357i
$586$	1.57855e11	+	2.73412e11i	0.0552991	+	0.0957808i
$587$	6.93533e11	+	1.20123e12i	0.241099	+	0.417596i	0.961028	−	0.276452i	$-0.0891588\pi$
$587$	6.93533e11	+	1.20123e12i	0.241099	+	0.417596i	−0.719928	+	0.694048i	$0.755825\pi$
$588$	−1.46554e12			−0.505592
$589$	−1.60753e12	−	2.58485e12i	−0.550353	−	0.884946i
$590$	−2.75012e12			−0.934366
$591$	4.12899e12	+	7.15163e12i	1.39220	+	2.41136i
$592$	1.22371e11	+	2.11953e11i	0.0409478	+	0.0709237i
$593$	4.49264e11	−	7.78148e11i	0.149195	−	0.258414i	−0.781735	−	0.623611i	$-0.785665\pi$
$593$	4.49264e11	−	7.78148e11i	0.149195	−	0.258414i	0.930930	+	0.365197i	$0.118998\pi$
$594$	3.36165e11	+	5.82254e11i	0.110793	+	0.191899i
$595$	8.48561e11	−	1.46975e12i	0.277560	−	0.480748i
$596$	4.69319e11			0.152356
$597$	1.93383e12			0.623065
$598$	1.05456e12	−	1.82655e12i	0.337222	−	0.584085i
$599$	7.86254e11	−	1.36183e12i	0.249541	−	0.432218i	−0.713857	−	0.700291i	$-0.753054\pi$
$599$	7.86254e11	−	1.36183e12i	0.249541	−	0.432218i	0.963399	+	0.268073i	$0.0863869\pi$
$600$	6.35758e11			0.200268
$601$	−1.80603e12			−0.564663			−0.282332	−	0.959317i	$-0.591108\pi$
$601$	−1.80603e12			−0.564663			−0.282332	+	0.959317i	$0.591108\pi$
$602$	7.52095e10	−	1.30267e11i	0.0233393	−	0.0404249i
$603$	−3.82163e11	−	6.61926e11i	−0.117712	−	0.203883i
$604$	4.59665e11	−	7.96164e11i	0.140532	−	0.243409i
$605$	−1.19173e12	−	2.06413e12i	−0.361641	−	0.626381i
$606$	−3.26330e12	−	5.65219e12i	−0.982946	−	1.70251i
$607$	−1.60553e11			−0.0480030			−0.0240015	−	0.999712i	$-0.507641\pi$
$607$	−1.60553e11			−0.0480030			−0.0240015	+	0.999712i	$0.507641\pi$
$608$	−5.95330e11	+	1.95174e10i	−0.176682	+	0.00579237i
$609$	1.54322e12			0.454620
$610$	7.34566e11	+	1.27231e12i	0.214806	+	0.372055i
$611$	−4.91646e11	−	8.51556e11i	−0.142714	−	0.247188i
$612$	−1.57119e12	+	2.72138e12i	−0.452738	+	0.784165i
$613$	−2.68395e12	−	4.64873e12i	−0.767718	−	1.32973i	−0.938797	−	0.344470i	$-0.888059\pi$
$613$	−2.68395e12	−	4.64873e12i	−0.767718	−	1.32973i	0.171079	−	0.985257i	$-0.445275\pi$
$614$	1.21919e12	−	2.11170e12i	0.346190	−	0.599619i
$615$	−2.67987e12			−0.755397
$616$	−2.47048e11			−0.0691303
$617$	−1.00241e12	+	1.73623e12i	−0.278461	+	0.482308i	−0.971002	−	0.239070i	$-0.923158\pi$
$617$	−1.00241e12	+	1.73623e12i	−0.278461	+	0.482308i	0.692542	+	0.721378i	$0.256491\pi$
$618$	−1.22884e12	+	2.12841e12i	−0.338881	+	0.586959i
$619$	−8.66768e11			−0.237298			−0.118649	−	0.992936i	$-0.537856\pi$
$619$	−8.66768e11			−0.237298			−0.118649	+	0.992936i	$0.537856\pi$
$620$	−1.54465e12			−0.419823
$621$	2.81227e12	−	4.87099e12i	0.758830	−	1.31433i
$622$	−1.10234e11	−	1.90931e11i	−0.0295296	−	0.0511468i
$623$	−2.08528e12	+	3.61181e12i	−0.554585	+	0.960569i
$624$	4.70646e11	+	8.15184e11i	0.124269	+	0.215241i
$625$	1.00342e12	+	1.73798e12i	0.263041	+	0.455601i
$626$	−3.43281e12			−0.893439
$627$	−9.42004e11	+	1.76257e12i	−0.243416	+	0.455451i
$628$	9.22829e11			0.236757
$629$	7.24702e11	+	1.25522e12i	0.184600	+	0.319736i
$630$	−1.10637e12	−	1.91629e12i	−0.279813	−	0.484650i
$631$	8.15946e11	−	1.41326e12i	0.204894	−	0.354887i	−0.745205	−	0.666836i	$-0.767648\pi$
$631$	8.15946e11	−	1.41326e12i	0.204894	−	0.354887i	0.950099	+	0.311949i	$0.100982\pi$
$632$	−8.01420e11	−	1.38810e12i	−0.199818	−	0.346094i
$633$	4.10962e12	−	7.11806e12i	1.01738	−	1.76216i
$634$	−9.86203e11			−0.242418
$635$	−3.20503e12			−0.782259
$636$	2.69388e12	−	4.66594e12i	0.652863	−	1.13079i
$637$	−8.01255e11	+	1.38782e12i	−0.192816	+	0.333967i
$638$	−4.35962e11			−0.104173
$639$	2.73142e12			0.648090
$640$	−1.51131e11	+	2.61766e11i	−0.0356076	+	0.0616742i
$641$	−2.24054e12	−	3.88073e12i	−0.524194	−	0.907930i	−0.999603	−	0.0281656i	$-0.991033\pi$
$641$	−2.24054e12	−	3.88073e12i	−0.524194	−	0.907930i	0.475409	−	0.879765i	$-0.342300\pi$
$642$	−1.31563e12	+	2.27873e12i	−0.305650	+	0.529402i
$643$	2.47738e12	+	4.29095e12i	0.571536	+	0.989930i	0.996408	+	0.0846766i	$0.0269857\pi$
$643$	2.47738e12	+	4.29095e12i	0.571536	+	0.989930i	−0.424872	+	0.905253i	$0.639681\pi$
$644$	1.03337e12	+	1.78985e12i	0.236739	+	0.410044i
$645$	−6.17472e11			−0.140475
$646$	−3.52565e12	+	1.15585e11i	−0.796512	+	0.0261130i
$647$	5.46260e12			1.22555			0.612774	−	0.790258i	$-0.290054\pi$
$647$	5.46260e12			1.22555			0.612774	+	0.790258i	$0.290054\pi$
$648$	−1.98018e10	−	3.42977e10i	−0.00441182	−	0.00764149i
$649$	1.18542e12	+	2.05320e12i	0.262283	+	0.454287i
$650$	3.47588e11	−	6.02040e11i	0.0763756	−	0.132286i
$651$	−2.35682e12	−	4.08213e12i	−0.514294	−	0.890784i
$652$	6.85713e11	−	1.18769e12i	0.148603	−	0.257388i
$653$	1.56051e12			0.335858			0.167929	−	0.985799i	$-0.446292\pi$
$653$	1.56051e12			0.335858			0.167929	+	0.985799i	$0.446292\pi$
$654$	2.53307e12			0.541436
$655$	8.68712e11	−	1.50465e12i	0.184412	−	0.319412i
$656$	−3.44286e11	+	5.96320e11i	−0.0725858	+	0.125722i
$657$	1.31826e13			2.76031
$658$	9.63536e11			0.200379
$659$	−9.49012e11	+	1.64374e12i	−0.196014	+	0.339506i	−0.947233	−	0.320547i	$-0.896133\pi$
$659$	−9.49012e11	+	1.64374e12i	−0.196014	+	0.339506i	0.751218	+	0.660054i	$0.229467\pi$
$660$	5.07068e11	+	8.78268e11i	0.104020	+	0.180169i
$661$	−1.61799e12	+	2.80244e12i	−0.329663	+	0.570992i	−0.982445	−	0.186553i	$-0.940268\pi$
$661$	−1.61799e12	+	2.80244e12i	−0.329663	+	0.570992i	0.652782	+	0.757546i	$0.273602\pi$
$662$	2.60852e12	+	4.51808e12i	0.527877	+	0.914310i
$663$	2.78725e12	+	4.82765e12i	0.560228	+	0.970343i
$664$	−2.13723e12			−0.426673
$665$	1.17082e12	−	2.19071e12i	0.232164	−	0.434397i
$666$	1.88976e12			0.372196
$667$	1.82357e12	+	3.15852e12i	0.356745	+	0.617900i
$668$	2.20835e12	+	3.82497e12i	0.429114	+	0.743248i
$669$	3.95066e12	−	6.84274e12i	0.762521	−	1.32072i
$670$	−2.17698e11	−	3.77064e11i	−0.0417367	−	0.0722900i
$671$	6.33257e11	−	1.09683e12i	0.120595	−	0.208876i
$672$	−9.22380e11			−0.174481
$673$	−3.27621e12			−0.615608			−0.307804	−	0.951450i	$-0.599594\pi$
$673$	−3.27621e12			−0.615608			−0.307804	+	0.951450i	$0.599594\pi$
$674$	−2.60003e12	+	4.50338e12i	−0.485298	+	0.840561i
$675$	9.26937e11	−	1.60550e12i	0.171863	−	0.297676i
$676$	−1.68549e12			−0.310431
$677$	6.44833e12			1.17977			0.589887	−	0.807486i	$-0.299172\pi$
$677$	6.44833e12			1.17977			0.589887	+	0.807486i	$0.299172\pi$
$678$	3.51686e12	−	6.09138e12i	0.639178	−	1.10709i
$679$	9.35323e11	+	1.62003e12i	0.168868	+	0.292488i
$680$	−8.95022e11	+	1.55022e12i	−0.160525	+	0.278038i
$681$	−7.38282e12	−	1.27874e13i	−1.31541	−	2.27835i
$682$	6.65807e11	+	1.15321e12i	0.117847	+	0.204117i
$683$	−2.80409e11			−0.0493058			−0.0246529	−	0.999696i	$-0.507848\pi$
$683$	−2.80409e11			−0.0493058			−0.0246529	+	0.999696i	$0.507848\pi$
$684$	−2.16789e12	+	4.05630e12i	−0.378690	+	0.708561i
$685$	−4.98011e12			−0.864234
$686$	−2.03882e12	−	3.53134e12i	−0.351496	−	0.608809i
$687$	−3.53102e12	−	6.11591e12i	−0.604776	−	1.04750i
$688$	−7.93274e10	+	1.37399e11i	−0.0134982	+	0.0233795i
$689$	−2.94566e12	−	5.10202e12i	−0.497961	−	0.862494i
$690$	4.24200e12	−	7.34737e12i	0.712443	−	1.23399i
$691$	1.67745e12			0.279897			0.139949	−	0.990159i	$-0.455306\pi$
$691$	1.67745e12			0.279897			0.139949	+	0.990159i	$0.455306\pi$
$692$	−1.00054e12			−0.165866
$693$	−9.53783e11	+	1.65200e12i	−0.157090	+	0.272089i
$694$	−3.79516e12	+	6.57340e12i	−0.621029	+	1.07565i
$695$	5.21146e12			0.847282
$696$	−1.62771e12			−0.262927
$697$	−2.03892e12	+	3.53151e12i	−0.327229	+	0.566778i
$698$	−9.95479e11	−	1.72422e12i	−0.158739	−	0.274943i
$699$	−8.87271e12	+	1.53680e13i	−1.40575	+	2.43484i
$700$	3.40604e11	+	5.89944e11i	0.0536178	+	0.0928687i
$701$	5.46339e11	+	9.46287e11i	0.0854537	+	0.148010i	0.905584	−	0.424166i	$-0.139433\pi$
$701$	5.46339e11	+	9.46287e11i	0.0854537	+	0.148010i	−0.820131	+	0.572176i	$0.806099\pi$
$702$	2.74482e12			0.426576
$703$	1.12032e12	+	1.80143e12i	0.172999	+	0.278176i
$704$	2.60575e11			0.0399812
$705$	−1.97767e12	−	3.42542e12i	−0.301510	−	0.522231i
$706$	−3.21655e12	−	5.57123e12i	−0.487270	−	0.843976i
$707$	3.49659e12	−	6.05627e12i	0.526329	−	0.911629i
$708$	4.42587e12	+	7.66584e12i	0.661987	+	1.14659i
$709$	−2.63561e12	+	4.56501e12i	−0.391717	+	0.678474i	−0.992676	−	0.120806i	$-0.961452\pi$
$709$	−2.63561e12	+	4.56501e12i	−0.391717	+	0.678474i	0.600959	+	0.799280i	$0.294786\pi$
$710$	1.55595e12			0.229790
$711$	−1.23762e13			−1.81625
$712$	2.19945e12	−	3.80957e12i	0.320741	−	0.555540i
$713$	5.56997e12	−	9.64748e12i	0.807143	−	1.39801i
$714$	−5.46249e12			−0.786591
$715$	1.10892e12			0.158680
$716$	2.09348e12	−	3.62602e12i	0.297688	−	0.515611i
$717$	−1.13518e12	−	1.96619e12i	−0.160409	−	0.277837i
$718$	2.72170e12	−	4.71412e12i	0.382190	−	0.661973i
$719$	−6.82480e10	−	1.18209e11i	−0.00952379	−	0.0164957i	0.861224	−	0.508225i	$-0.169698\pi$
$719$	−6.82480e10	−	1.18209e11i	−0.00952379	−	0.0164957i	−0.870748	+	0.491729i	$0.836365\pi$
$720$	1.16695e12	+	2.02121e12i	0.161828	+	0.280295i
$721$	−2.63338e12			−0.362915
$722$	−5.15192e12	+	3.38166e11i	−0.705588	+	0.0463141i
$723$	−8.05134e12			−1.09584
$724$	−3.34639e12	−	5.79611e12i	−0.452640	−	0.783995i
$725$	6.01059e11	+	1.04106e12i	0.0807972	+	0.139945i
$726$	−3.83579e12	+	6.64378e12i	−0.512436	+	0.887565i
$727$	7.06155e12	+	1.22310e13i	0.937552	+	1.62389i	0.770020	+	0.638020i	$0.220246\pi$
$727$	7.06155e12	+	1.22310e13i	0.937552	+	1.62389i	0.167532	+	0.985867i	$0.446420\pi$
$728$	−5.04293e11	+	8.73462e11i	−0.0665414	+	0.115253i
$729$	−1.23684e13			−1.62196
$730$	7.50944e12			0.978711
$731$	−4.69790e11	+	8.13701e11i	−0.0608521	+	0.105399i
$732$	2.36433e12	−	4.09514e12i	0.304375	−	0.527192i
$733$	−3.60766e12			−0.461591			−0.230796	−	0.973002i	$-0.574133\pi$
$733$	−3.60766e12			−0.461591			−0.230796	+	0.973002i	$0.574133\pi$
$734$	4.62256e12			0.587828
$735$	−3.22308e12	+	5.58254e12i	−0.407360	+	0.705568i
$736$	−1.08995e12	−	1.88785e12i	−0.136917	−	0.237147i
$737$	−1.87674e11	+	3.25061e11i	−0.0234315	+	0.0405845i
$738$	2.65838e12	+	4.60445e12i	0.329885	+	0.571378i
$739$	4.40631e12	+	7.63196e12i	0.543470	+	0.941317i	0.998702	+	0.0509440i	$0.0162230\pi$
$739$	4.40631e12	+	7.63196e12i	0.543470	+	0.941317i	−0.455232	+	0.890373i	$0.650444\pi$
$740$	1.07649e12			0.131968
$741$	4.30883e12	+	6.92842e12i	0.525021	+	0.844214i
$742$	5.77294e12			0.699165
$743$	2.57572e12	+	4.46127e12i	0.310062	+	0.537043i	0.978375	−	0.206837i	$-0.0663169\pi$
$743$	2.57572e12	+	4.46127e12i	0.310062	+	0.537043i	−0.668314	+	0.743880i	$0.732984\pi$
$744$	2.48586e12	+	4.30564e12i	0.297440	+	0.515180i
$745$	1.03215e12	−	1.78773e12i	0.122755	−	0.212617i
$746$	2.27516e12	+	3.94070e12i	0.268960	+	0.465852i
$747$	−8.25123e12	+	1.42916e13i	−0.969563	+	1.67933i
$748$	1.54317e12			0.180242
$749$	−2.81936e12			−0.327328
$750$	5.38351e12	−	9.32452e12i	0.621284	−	1.07610i
$751$	7.60637e12	−	1.31746e13i	0.872565	−	1.51133i	0.0132309	−	0.999912i	$-0.495788\pi$
$751$	7.60637e12	−	1.31746e13i	0.872565	−	1.51133i	0.859334	−	0.511415i	$-0.170878\pi$
$752$	−1.01629e12			−0.115888
$753$	2.42360e11			0.0274716
$754$	−8.89919e11	+	1.54138e12i	−0.100272	+	0.173676i
$755$	−2.02183e12	−	3.50191e12i	−0.226456	−	0.392233i
$756$	−1.34483e12	+	2.32932e12i	−0.149734	+	0.259347i
$757$	6.01755e12	+	1.04227e13i	0.666021	+	1.15358i	0.979007	+	0.203825i	$0.0653373\pi$
$757$	6.01755e12	+	1.04227e13i	0.666021	+	1.15358i	−0.312986	+	0.949758i	$0.601329\pi$
$758$	−1.32209e12	−	2.28992e12i	−0.145462	−	0.251947i
$759$	−7.31393e12			−0.799949
$760$	−1.23493e12	+	2.31066e12i	−0.134271	+	0.251231i
$761$	−1.38508e13			−1.49707			−0.748537	−	0.663093i	$-0.769243\pi$
$761$	−1.38508e13			−1.49707			−0.748537	+	0.663093i	$0.769243\pi$
$762$	5.15798e12	+	8.93389e12i	0.554221	+	0.959938i
$763$	1.35708e12	+	2.35053e12i	0.144959	+	0.251076i
$764$	3.86480e12	−	6.69403e12i	0.410400	−	0.710833i
$765$	6.91085e12	+	1.19699e13i	0.729550	+	1.26362i
$766$	−7.33438e11	+	1.27035e12i	−0.0769722	+	0.133320i
$767$	9.67903e12			1.00984
$768$	9.72883e11			0.100910
$769$	2.21637e12	−	3.83886e12i	0.228546	−	0.395853i	−0.728832	−	0.684693i	$-0.759936\pi$
$769$	2.21637e12	−	3.83886e12i	0.228546	−	0.395853i	0.957377	+	0.288840i	$0.0932696\pi$
$770$	−5.43319e11	+	9.41056e11i	−0.0556989	+	0.0964733i
$771$	−8.84595e12			−0.901570
$772$	−1.93450e12			−0.196016
$773$	−5.93536e12	+	1.02803e13i	−0.597915	+	1.03562i	0.395213	+	0.918589i	$0.370671\pi$
$773$	−5.93536e12	+	1.02803e13i	−0.597915	+	1.03562i	−0.993128	+	0.117030i	$0.962663\pi$
$774$	6.12521e11	+	1.06092e12i	0.0613461	+	0.106254i
$775$	1.83589e12	−	3.17986e12i	0.182805	−	0.316628i
$776$	−9.86535e11	−	1.70873e12i	−0.0976640	−	0.169159i
$777$	1.64251e12	+	2.84492e12i	0.161664	+	0.280011i
$778$	5.03585e12			0.492793
$779$	−2.81325e12	+	5.26382e12i	−0.273709	+	0.512133i
$780$	4.14026e12			0.400500
$781$	−6.70678e11	−	1.16165e12i	−0.0645036	−	0.111724i
$782$	−6.45487e12	−	1.11802e13i	−0.617245	−	1.06910i
$783$	−2.37321e12	+	4.11052e12i	−0.225636	+	0.390813i
$784$	8.28146e11	+	1.43439e12i	0.0782861	+	0.135595i
$785$	2.02953e12	−	3.51524e12i	0.190757	−	0.330401i
$786$	−5.59221e12			−0.522615
$787$	1.47348e13			1.36917			0.684586	−	0.728932i	$-0.259983\pi$
$787$	1.47348e13			1.36917			0.684586	+	0.728932i	$0.259983\pi$
$788$	4.66642e12	−	8.08247e12i	0.431137	−	0.746751i
$789$	2.58641e12	−	4.47980e12i	0.237603	−	0.411540i
$790$	−7.05007e12			−0.643979
$791$	7.53657e12			0.684510
$792$	1.00600e12	−	1.74245e12i	0.0908525	−	0.157361i
$793$	−2.58530e12	−	4.47788e12i	−0.232157	−	0.402108i
$794$	−3.96926e12	+	6.87496e12i	−0.354419	+	0.613872i
$795$	−1.18490e13	−	2.05231e13i	−1.05203	−	1.82218i
$796$	−1.09276e12	−	1.89272e12i	−0.0964757	−	0.167101i
$797$	5.12915e12			0.450280			0.225140	−	0.974326i	$-0.427716\pi$
$797$	5.12915e12			0.450280			0.225140	+	0.974326i	$0.427716\pi$
$798$	−7.99076e12	+	2.61971e11i	−0.697550	+	0.0228686i
$799$	−6.01865e12			−0.522443
$800$	−3.59253e11	−	6.22245e11i	−0.0310096	−	0.0537101i
$801$	−1.69829e13	−	2.94153e13i	−1.45769	−	2.52480i
$802$	3.70512e12	−	6.41745e12i	0.316241	−	0.547745i
$803$	−3.23688e12	−	5.60644e12i	−0.274731	−	0.475847i
$804$	−7.00700e11	+	1.21365e12i	−0.0591398	+	0.102433i
$805$	9.09054e12			0.762971
$806$	5.43638e12			0.453735
$807$	−7.90631e12	+	1.36941e13i	−0.656210	+	1.13659i
$808$	−3.68804e12	+	6.38787e12i	−0.304400	+	0.527236i
$809$	7.93116e12			0.650981			0.325491	−	0.945545i	$-0.394471\pi$
$809$	7.93116e12			0.650981			0.325491	+	0.945545i	$0.394471\pi$
$810$	−1.74196e11			−0.0142186
$811$	−3.47404e12	+	6.01721e12i	−0.281995	+	0.488429i	−0.971876	−	0.235493i	$-0.924329\pi$
$811$	−3.47404e12	+	6.01721e12i	−0.281995	+	0.488429i	0.689881	+	0.723923i	$0.257663\pi$
$812$	−8.72039e11	−	1.51042e12i	−0.0703937	−	0.121925i
$813$	1.85827e13	−	3.21862e13i	1.49177	−	2.58382i
$814$	−4.64014e11	−	8.03696e11i	−0.0370443	−	0.0641626i
$815$	−3.01610e12	−	5.22404e12i	−0.239462	−	0.414760i
$816$	5.76158e12			0.454921
$817$	−6.48205e11	+	1.21285e12i	−0.0508995	+	0.0952371i
$818$	7.06951e12			0.552077
$819$	3.89386e12	+	6.74437e12i	0.302415	+	0.523798i
$820$	1.51434e12	+	2.62291e12i	0.116966	+	0.202591i
$821$	−3.92273e12	+	6.79437e12i	−0.301331	+	0.521921i	−0.976438	−	0.215799i	$-0.930764\pi$
$821$	−3.92273e12	+	6.79437e12i	−0.301331	+	0.521921i	0.675106	+	0.737720i	$0.264098\pi$
$822$	8.01469e12	+	1.38819e13i	0.612299	+	1.06053i
$823$	−6.93947e12	+	1.20195e13i	−0.527262	+	0.913245i	0.472233	+	0.881474i	$0.343448\pi$
$823$	−6.93947e12	+	1.20195e13i	−0.527262	+	0.913245i	−0.999495	+	0.0317713i	$0.989885\pi$
$824$	2.77757e12			0.209890
$825$	−2.41070e12			−0.181176
$826$	−4.74228e12	+	8.21387e12i	−0.354468	+	0.613957i
$827$	6.90979e12	−	1.19681e13i	0.513677	−	0.889715i	−0.486197	−	0.873849i	$-0.661616\pi$
$827$	6.90979e12	−	1.19681e13i	0.513677	−	0.889715i	0.999874	−	0.0158657i	$-0.00505042\pi$
$828$	−1.68320e13			−1.24451
$829$	1.72478e13			1.26835			0.634174	−	0.773190i	$-0.281340\pi$
$829$	1.72478e13			1.26835			0.634174	+	0.773190i	$0.281340\pi$
$830$	−4.70029e12	+	8.14113e12i	−0.343774	+	0.595434i
$831$	−2.07966e13	−	3.60208e13i	−1.51282	−	2.62028i
$832$	5.31905e11	−	9.21286e11i	0.0384839	−	0.0666560i
$833$	4.90442e12	+	8.49470e12i	0.352927	+	0.611288i
$834$	−8.38702e12	−	1.45267e13i	−0.600289	−	1.03973i
$835$	1.94268e13			1.38296
$836$	2.25741e12	−	7.40074e10i	0.159839	−	0.00524018i
$837$	1.44976e13			1.02101
$838$	7.68984e12	+	1.33192e13i	0.538666	+	0.932996i
$839$	−8.86859e12	−	1.53609e13i	−0.617911	−	1.07025i	−0.989866	−	0.142003i	$-0.954646\pi$
$839$	−8.86859e12	−	1.53609e13i	−0.617911	−	1.07025i	0.371955	−	0.928251i	$-0.378687\pi$
$840$	−2.02854e12	+	3.51353e12i	−0.140581	+	0.243493i
$841$	5.71470e12	+	9.89815e12i	0.393923	+	0.682295i
$842$	3.99550e12	−	6.92040e12i	0.273947	−	0.474490i
$843$	4.00369e12			0.273046
$844$	−9.28903e12			−0.630129
$845$	−3.70679e12	+	6.42035e12i	−0.250117	+	0.433215i
$846$	−3.92361e12	+	6.79590e12i	−0.263342	+	0.456121i
$847$	−8.22002e12			−0.548779
$848$	−6.08903e12			−0.404359
$849$	1.29628e13	−	2.24522e13i	0.856277	−	1.48311i
$850$	−2.12756e12	−	3.68504e12i	−0.139796	−	0.242135i
$851$	−3.88182e12	+	6.72351e12i	−0.253719	+	0.439454i
$852$	−2.50404e12	−	4.33713e12i	−0.162804	−	0.281984i
$853$	7.88752e12	+	1.36616e13i	0.510117	+	0.883549i	0.999931	+	0.0117221i	$0.00373134\pi$
$853$	7.88752e12	+	1.36616e13i	0.510117	+	0.883549i	−0.489814	+	0.871827i	$0.662935\pi$
$854$	5.06672e12			0.325961
$855$	1.06835e13	+	1.71787e13i	0.683703	+	1.09937i
$856$	2.97373e12			0.189308
$857$	−4.71772e12	−	8.17133e12i	−0.298757	−	0.517463i	0.677095	−	0.735896i	$-0.263239\pi$
$857$	−4.71772e12	−	8.17133e12i	−0.298757	−	0.517463i	−0.975852	+	0.218433i	$0.929905\pi$
$858$	−1.78463e12	−	3.09106e12i	−0.112423	−	0.194722i
$859$	8.70378e12	−	1.50754e13i	0.545429	−	0.944711i	−0.453151	−	0.891434i	$-0.649700\pi$
$859$	8.70378e12	−	1.50754e13i	0.545429	−	0.944711i	0.998580	−	0.0532771i	$-0.0169667\pi$
$860$	3.48921e11	+	6.04348e11i	0.0217512	+	0.0376742i
$861$	−4.62114e12	+	8.00405e12i	−0.286573	+	0.496359i
$862$	1.41687e13			0.874071
$863$	1.59391e12			0.0978173			0.0489086	−	0.998803i	$-0.484426\pi$
$863$	1.59391e12			0.0978173			0.0489086	+	0.998803i	$0.484426\pi$
$864$	1.41847e12	−	2.45686e12i	0.0865980	−	0.149992i
$865$	−2.20044e12	+	3.81127e12i	−0.133640	+	0.231471i
$866$	−1.17376e13			−0.709168
$867$	7.25886e12			0.436297
$868$	−2.66358e12	+	4.61345e12i	−0.159267	+	0.275859i
$869$	3.03888e12	+	5.26349e12i	0.180769	+	0.313101i
$870$	−3.57973e12	+	6.20028e12i	−0.211843	+	0.366923i
$871$	7.66188e11	+	1.32708e12i	0.0451080	+	0.0781293i
$872$	−1.43138e12	−	2.47923e12i	−0.0838363	−	0.145209i
$873$	−1.52349e13			−0.887720
$874$	−9.97864e12	−	1.60453e13i	−0.578455	−	0.930133i
$875$	1.15368e13			0.665347
$876$	−1.20852e13	−	2.09322e13i	−0.693405	−	1.20101i
$877$	8.21583e11	+	1.42302e12i	0.0468979	+	0.0812295i	0.888521	−	0.458835i	$-0.151733\pi$
$877$	8.21583e11	+	1.42302e12i	0.0468979	+	0.0812295i	−0.841624	+	0.540065i	$0.818400\pi$
$878$	−5.92316e12	+	1.02592e13i	−0.336378	+	0.582625i
$879$	−2.23480e12	−	3.87078e12i	−0.126266	−	0.218700i
$880$	5.73067e11	−	9.92582e11i	0.0322132	−	0.0557949i
$881$	−4.44251e12			−0.248449			−0.124224	−	0.992254i	$-0.539644\pi$
$881$	−4.44251e12			−0.248449			−0.124224	+	0.992254i	$0.539644\pi$
$882$	1.27889e13			0.711584
$883$	6.39881e12	−	1.10831e13i	0.354222	−	0.613531i	−0.632762	−	0.774346i	$-0.718079\pi$
$883$	6.39881e12	−	1.10831e13i	0.354222	−	0.613531i	0.986985	+	0.160815i	$0.0514122\pi$
$884$	3.15003e12	−	5.45601e12i	0.173492	−	0.300497i
$885$	3.89343e13			2.13347
$886$	2.10885e13			1.14973
$887$	−1.17270e13	+	2.03118e13i	−0.636109	+	1.10177i	0.350171	+	0.936686i	$0.386124\pi$
$887$	−1.17270e13	+	2.03118e13i	−0.636109	+	1.10177i	−0.986279	+	0.165086i	$0.947210\pi$
$888$	−1.73244e12	−	3.00068e12i	−0.0934977	−	0.161943i
$889$	−5.52673e12	+	9.57258e12i	−0.296763	+	0.514009i
$890$	−9.67427e12	−	1.67563e13i	−0.516848	−	0.895207i
$891$	7.50857e10	+	1.30052e11i	0.00399124	+	0.00691303i
$892$	−8.92973e12			−0.472277
$893$	−8.80434e12	+	2.88643e11i	−0.463303	+	0.0151890i
$894$	−6.64429e12			−0.347880
$895$	−9.20816e12	−	1.59490e13i	−0.479700	−	0.830864i
$896$	5.21218e11	+	9.02776e11i	0.0270167	+	0.0467944i
$897$	−1.49297e13	+	2.58591e13i	−0.769992	+	1.33366i
$898$	2.16019e12	+	3.74155e12i	0.110853	+	0.192003i
$899$	−4.70038e12	+	8.14129e12i	−0.240002	+	0.415695i
$900$	−5.54790e12			−0.281862
$901$	−3.60602e13			−1.82292
$902$	1.30548e12	−	2.26117e12i	0.0656663	−	0.113737i
$903$	−1.06476e12	+	1.84423e12i	−0.0532916	+	0.0923037i
$904$	−7.94922e12			−0.395883
$905$	−2.94381e13			−1.45878
$906$	−6.50763e12	+	1.12715e13i	−0.320882	+	0.555784i
$907$	1.12087e13	+	1.94140e13i	0.549947	+	0.952535i	0.998278	+	0.0586678i	$0.0186853\pi$
$907$	1.12087e13	+	1.94140e13i	0.549947	+	0.952535i	−0.448331	+	0.893868i	$0.647981\pi$
$908$	−8.34375e12	+	1.44518e13i	−0.407357	+	0.705563i
$909$	2.84769e13	+	4.93235e13i	1.38342	+	2.39616i
$910$	2.21813e12	+	3.84191e12i	0.107226	+	0.185721i
$911$	4.11128e12			0.197763			0.0988813	−	0.995099i	$-0.468474\pi$
$911$	4.11128e12			0.197763			0.0988813	+	0.995099i	$0.468474\pi$
$912$	8.42828e12	−	2.76314e11i	0.403424	−	0.0132259i
$913$	8.10408e12			0.385998
$914$	−8.74456e12	−	1.51460e13i	−0.414457	−	0.717861i
$915$	−1.03995e13	−	1.80124e13i	−0.490475	−	0.849527i
$916$	−3.99061e12	+	6.91194e12i	−0.187288	+	0.324392i
$917$	−2.99600e12	−	5.18923e12i	−0.139920	−	0.242349i
$918$	8.40041e12	−	1.45499e13i	0.390399	−	0.676190i
$919$	−1.05548e12			−0.0488125			−0.0244062	−	0.999702i	$-0.507770\pi$
$919$	−1.05548e12			−0.0488125			−0.0244062	+	0.999702i	$0.507770\pi$
$920$	−9.58827e12			−0.441260
$921$	−1.72605e13	+	2.98961e13i	−0.790469	+	1.36913i
$922$	−4.24261e12	+	7.34842e12i	−0.193350	+	0.334892i
$923$	−5.47615e12			−0.248352
$924$	3.49754e12			0.157848
$925$	−1.27947e12	+	2.21610e12i	−0.0574634	+	0.0995295i
$926$	9.25740e12	+	1.60343e13i	0.413752	+	0.716639i
$927$	1.07234e13	−	1.85735e13i	0.476951	−	0.826103i
$928$	9.19785e11	+	1.59311e12i	0.0407118	+	0.0705149i
$929$	−2.59110e12	−	4.48792e12i	−0.114134	−	0.197685i	0.803300	−	0.595575i	$-0.203076\pi$
$929$	−2.59110e12	−	4.48792e12i	−0.114134	−	0.197685i	−0.917433	+	0.397890i	$0.869743\pi$
$930$	2.18681e13			0.958599
$931$	7.58178e12	+	1.21912e13i	0.330748	+	0.531830i
$932$	2.00551e13			0.870671
$933$	1.56062e12	+	2.70306e12i	0.0674262	+	0.116786i
$934$	9.12364e12	+	1.58026e13i	0.392290	+	0.679466i
$935$	3.39380e12	−	5.87824e12i	0.145223	−	0.251533i
$936$	−4.10706e12	−	7.11364e12i	−0.174900	−	0.302936i
$937$	1.08639e13	−	1.88168e13i	0.460422	−	0.797475i	−0.538560	−	0.842587i	$-0.681031\pi$
$937$	1.08639e13	−	1.88168e13i	0.460422	−	0.797475i	0.998982	+	0.0451126i	$0.0143647\pi$
$938$	−1.50159e12			−0.0633341
$939$	4.85994e13			2.04002
$940$	−2.23507e12	+	3.87126e12i	−0.0933720	+	0.161725i
$941$	1.01200e13	−	1.75284e13i	0.420754	−	0.728768i	−0.575259	−	0.817971i	$-0.695099\pi$
$941$	1.01200e13	−	1.75284e13i	0.420754	−	0.728768i	0.996013	+	0.0892034i	$0.0284321\pi$
$942$	−1.30648e13			−0.540597
$943$	−2.18427e13			−0.899505
$944$	5.00193e12	−	8.66361e12i	0.205005	−	0.355079i
$945$	5.91524e12	+	1.02455e13i	0.241284	+	0.417917i
$946$	3.00799e11	−	5.20999e11i	0.0122114	−	0.0211508i
$947$	6.07799e12	+	1.05274e13i	0.245576	+	0.425349i	0.962293	−	0.272014i	$-0.0876897\pi$
$947$	6.07799e12	+	1.05274e13i	0.245576	+	0.425349i	−0.716718	+	0.697363i	$0.754356\pi$
$948$	1.13460e13	+	1.96518e13i	0.456251	+	0.790250i
$949$	−2.64295e13			−1.05777
$950$	−3.28901e12	−	5.28859e12i	−0.131011	−	0.210661i
$951$	1.39620e13			0.553522
$952$	3.08674e12	+	5.34639e12i	0.121796	+	0.210957i
$953$	1.35407e13	+	2.34532e13i	0.531770	+	0.921053i	0.999312	+	0.0370824i	$0.0118064\pi$
$953$	1.35407e13	+	2.34532e13i	0.531770	+	0.921053i	−0.467542	+	0.883971i	$0.654860\pi$
$954$	−2.35080e13	+	4.07170e13i	−0.918857	+	1.59151i
$955$	−1.69993e13	−	2.94436e13i	−0.661325	−	1.14545i
$956$	−1.28293e12	+	2.22211e12i	−0.0496757	+	0.0860409i
$957$	6.17206e12			0.237863
$958$	7.41224e12			0.284318
$959$	−8.58767e12	+	1.48743e13i	−0.327862	+	0.567874i
$960$	2.13961e12	−	3.70591e12i	0.0813043	−	0.140823i
$961$	2.27428e12			0.0860177
$962$	−3.78872e12			−0.142628
$963$	1.14807e13	−	1.98852e13i	0.430181	−	0.745095i
$964$	4.54964e12	+	7.88021e12i	0.169680	+	0.293894i
$965$	−4.25444e12	+	7.36891e12i	−0.157932	+	0.273546i
$966$	−1.46298e13	−	2.53395e13i	−0.540555	−	0.936269i
$967$	−2.73322e12	−	4.73408e12i	−0.100521	−	0.174107i	0.811379	−	0.584521i	$-0.198718\pi$
$967$	−2.73322e12	−	4.73408e12i	−0.100521	−	0.174107i	−0.911899	+	0.410414i	$0.865384\pi$
$968$	8.67009e12			0.317384
$969$	4.99137e13	−	1.63638e12i	1.81871	−	0.0596248i
$970$	−8.67852e12			−0.314755
$971$	−1.99901e13	−	3.46238e13i	−0.721652	−	1.24994i	−0.960337	−	0.278841i	$-0.910050\pi$
$971$	−1.99901e13	−	3.46238e13i	−0.721652	−	1.24994i	0.238685	−	0.971097i	$-0.423284\pi$
$972$	7.09668e12	+	1.22918e13i	0.255010	+	0.441690i
$973$	8.98661e12	−	1.55653e13i	0.321431	−	0.556735i
$974$	−1.33360e13	−	2.30987e13i	−0.474800	−	0.822378i
$975$	−4.92091e12	+	8.52327e12i	−0.174391	+	0.302055i
$976$	−5.34413e12			−0.188518
$977$	−3.51363e13			−1.23376			−0.616880	−	0.787057i	$-0.711604\pi$
$977$	−3.51363e13			−1.23376			−0.616880	+	0.787057i	$0.711604\pi$
$978$	−9.70786e12	+	1.68145e13i	−0.339312	+	0.587705i
$979$	−8.34003e12	+	1.44453e13i	−0.290165	+	0.502581i
$980$	7.28518e12			0.252303
$981$	−2.21047e13			−0.762033
$982$	−1.24048e13	+	2.14857e13i	−0.425684	+	0.737306i
$983$	2.13777e13	+	3.70273e13i	0.730248	+	1.26483i	0.956777	+	0.290823i	$0.0939290\pi$
$983$	2.13777e13	+	3.70273e13i	0.730248	+	1.26483i	−0.226529	+	0.974005i	$0.572738\pi$
$984$	4.87416e12	−	8.44230e12i	0.165738	−	0.287067i
$985$	−2.05252e13	−	3.55506e13i	−0.694742	−	1.20333i
$986$	5.44712e12	+	9.43469e12i	0.183536	+	0.317894i
$987$	−1.36411e13			−0.457532
$988$	4.34633e12	−	8.13235e12i	0.145117	−	0.271525i
$989$	−5.03281e12			−0.167274
$990$	−4.42490e12	−	7.66415e12i	−0.146401	−	0.253574i
$991$	1.79846e13	+	3.11502e13i	0.592338	+	1.02596i	0.993917	+	0.110134i	$0.0351281\pi$
$991$	1.79846e13	+	3.11502e13i	0.592338	+	1.02596i	−0.401579	+	0.915824i	$0.631539\pi$
$992$	2.80942e12	−	4.86605e12i	0.0921114	−	0.159542i
$993$	−3.69296e13	−	6.39639e13i	−1.20532	−	2.08768i
$994$	2.68306e12	−	4.64720e12i	0.0871750	−	0.150991i
$995$	−9.61302e12			−0.310925
$996$	3.02574e13			0.974238
$997$	−9.69001e12	+	1.67836e13i	−0.310596	+	0.537968i	−0.978492	−	0.206287i	$-0.933862\pi$
$997$	−9.69001e12	+	1.67836e13i	−0.310596	+	0.537968i	0.667895	+	0.744255i	$0.267195\pi$
$998$	4.15606e12	−	7.19850e12i	0.132615	−	0.229697i
$999$	−1.01036e13			−0.320947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.a.7.1	✓	14
19.11	even	3	inner	38.10.c.a.11.1	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.a.7.1	✓	14	1.1	even	1	trivial
38.10.c.a.11.1	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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(-113.259 - 196.170i) q^{3} +(-128.000 + 221.703i) q^{4} +(563.006 + 975.155i) q^{5} +(1812.14 - 3138.71i) q^{6} +3883.37 q^{7} -4096.00 q^{8} +(-15813.5 + 27389.8i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(-113.259 - 196.170i) q^{3} +(-128.000 + 221.703i) q^{4} +(563.006 + 975.155i) q^{5} +(1812.14 - 3138.71i) q^{6} +3883.37 q^{7} -4096.00 q^{8} +(-15813.5 + 27389.8i) q^{9} +(-9008.10 + 15602.5i) q^{10} +15531.5 q^{11} +57988.4 q^{12} +(31704.0 - 54912.9i) q^{13} +(31067.0 + 53809.6i) q^{14} +(127531. - 220889. i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(-194058. - 336118. i) q^{17} -506032. q^{18} +(-299995. - 482380. i) q^{19} -288259. q^{20} +(-439825. - 761800. i) q^{21} +(124252. + 215210. i) q^{22} +(1.03946e6 - 1.80039e6i) q^{23} +(463907. + 803510. i) q^{24} +(342611. - 593419. i) q^{25} +1.01453e6 q^{26} +2.70551e6 q^{27} +(-497072. + 860954. i) q^{28} +(-877176. + 1.51931e6i) q^{29} +4.08098e6 q^{30} +5.35854e6 q^{31} +(524288. - 908093. i) q^{32} +(-1.75907e6 - 3.04680e6i) q^{33} +(3.10492e6 - 5.37788e6i) q^{34} +(2.18636e6 + 3.78689e6i) q^{35} +(-4.04825e6 - 7.01178e6i) q^{36} -3.73447e6 q^{37} +(4.28410e6 - 8.01590e6i) q^{38} -1.43630e7 q^{39} +(-2.30607e6 - 3.99424e6i) q^{40} +(-5.25338e6 - 9.09913e6i) q^{41} +(7.03720e6 - 1.21888e7i) q^{42} +(-1.21044e6 - 2.09654e6i) q^{43} +(-1.98803e6 + 3.44337e6i) q^{44} -3.56124e7 q^{45} +3.32627e7 q^{46} +(7.75370e6 - 1.34298e7i) q^{47} +(-7.42251e6 + 1.28562e7i) q^{48} -2.52730e7 q^{49} +1.09635e7 q^{50} +(-4.39574e7 + 7.61364e7i) q^{51} +(8.11622e6 + 1.40577e7i) q^{52} +(4.64556e7 - 8.04634e7i) q^{53} +(2.16441e7 + 3.74887e7i) q^{54} +(8.74431e6 + 1.51456e7i) q^{55} -1.59063e7 q^{56} +(-6.06513e7 + 1.13484e8i) q^{57} -2.80696e7 q^{58} +(7.63235e7 + 1.32196e8i) q^{59} +(3.26478e7 + 5.65477e7i) q^{60} +(4.07725e7 - 7.06201e7i) q^{61} +(4.28683e7 + 7.42500e7i) q^{62} +(-6.14097e7 + 1.06365e8i) q^{63} +1.67772e7 q^{64} +7.13982e7 q^{65} +(2.81451e7 - 4.87488e7i) q^{66} +(-1.20835e7 + 2.09292e7i) q^{67} +9.93575e7 q^{68} -4.70910e8 q^{69} +(-3.49818e7 + 6.05903e7i) q^{70} +(-4.31819e7 - 7.47932e7i) q^{71} +(6.47720e7 - 1.12188e8i) q^{72} +(-2.08408e8 - 3.60973e8i) q^{73} +(-2.98757e7 - 5.17463e7i) q^{74} -1.55214e8 q^{75} +(1.45344e8 - 4.76499e6i) q^{76} +6.03145e7 q^{77} +(-1.14904e8 - 1.99019e8i) q^{78} +(1.95659e8 + 3.38892e8i) q^{79} +(3.68972e7 - 6.39078e7i) q^{80} +(4.83443e6 + 8.37347e6i) q^{81} +(8.40541e7 - 1.45586e8i) q^{82} +5.21784e8 q^{83} +2.25191e8 q^{84} +(2.18511e8 - 3.78473e8i) q^{85} +(1.93670e7 - 3.35447e7i) q^{86} +3.97390e8 q^{87} -6.36169e7 q^{88} +(-5.36976e8 + 9.30070e8i) q^{89} +(-2.84899e8 - 4.93459e8i) q^{90} +(1.23118e8 - 2.13247e8i) q^{91} +(2.66101e8 + 4.60901e8i) q^{92} +(-6.06900e8 - 1.05118e9i) q^{93} +2.48118e8 q^{94} +(3.01497e8 - 5.64125e8i) q^{95} -2.37520e8 q^{96} +(2.40853e8 + 4.17170e8i) q^{97} +(-2.02184e8 - 3.50193e8i) q^{98} +(-2.45607e8 + 4.25403e8i) 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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