LMFDB - Embedded newform 14.16.c.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,16,Mod(9,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	14.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:	$19.9770907140$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7979102 x^{8} - 3342530557 x^{7} + 48610066963550 x^{6} + \cdots + 51\!\cdots\!56 $ x^10 - x^9 + 7979102x^8 - 3342530557x^7 + 48610066963550x^6 - 20531463882664153x^5 + 122945882607722292337x^4 - 89586690298994071428648x^3 + 238785864099387585455090736x^2 - 108333121326673799746890760320x + 51761574501460447109413728819456
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{3}\cdot 5^{4}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$1086.67 + 1882.17i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.16.c.b.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(64.0000 + 110.851i) q^{2} +(-1325.39 + 2295.64i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(56213.5 + 97364.6i) q^{5} -339300. q^{6} +(875396. + 1.99531e6i) q^{7} -2.09715e6 q^{8} +(3.66114e6 + 6.34128e6i) q^{9} +O(q^{10})$	\(q+(64.0000 + 110.851i) q^{2} +(-1325.39 + 2295.64i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(56213.5 + 97364.6i) q^{5} -339300. q^{6} +(875396. + 1.99531e6i) q^{7} -2.09715e6 q^{8} +(3.66114e6 + 6.34128e6i) q^{9} +(-7.19532e6 + 1.24627e7i) q^{10} +(-8.67876e6 + 1.50321e7i) q^{11} +(-2.17152e7 - 3.76118e7i) q^{12} -1.47156e8 q^{13} +(-1.65157e8 + 2.24738e8i) q^{14} -2.98019e8 q^{15} +(-1.34218e8 - 2.32472e8i) q^{16} +(4.40441e8 - 7.62866e8i) q^{17} +(-4.68626e8 + 8.11684e8i) q^{18} +(-5.31595e8 - 9.20749e8i) q^{19} -1.84200e9 q^{20} +(-5.74075e9 - 6.34961e8i) q^{21} -2.22176e9 q^{22} +(-3.90880e9 - 6.77025e9i) q^{23} +(2.77954e9 - 4.81431e9i) q^{24} +(8.93888e9 - 1.54826e10i) q^{25} +(-9.41799e9 - 1.63124e10i) q^{26} -5.74455e10 q^{27} +(-3.54826e10 - 3.92458e9i) q^{28} -1.50600e11 q^{29} +(-1.90732e10 - 3.30358e10i) q^{30} +(-3.78211e10 + 6.55081e10i) q^{31} +(1.71799e10 - 2.97564e10i) q^{32} +(-2.30055e10 - 3.98466e10i) q^{33} +1.12753e11 q^{34} +(-1.45063e11 + 1.97396e11i) q^{35} -1.19968e11 q^{36} +(1.65066e11 + 2.85902e11i) q^{37} +(6.80441e10 - 1.17856e11i) q^{38} +(1.95039e11 - 3.37818e11i) q^{39} +(-1.17888e11 - 2.04188e11i) q^{40} +1.73261e12 q^{41} +(-2.97022e11 - 6.77006e11i) q^{42} +2.25167e12 q^{43} +(-1.42193e11 - 2.46285e11i) q^{44} +(-4.11611e11 + 7.12931e11i) q^{45} +(5.00327e11 - 8.66592e11i) q^{46} +(2.29306e12 + 3.97171e12i) q^{47} +7.11563e11 q^{48} +(-3.21492e12 + 3.49336e12i) q^{49} +2.28835e12 q^{50} +(1.16751e12 + 2.02219e12i) q^{51} +(1.20550e12 - 2.08799e12i) q^{52} +(-4.14674e12 + 7.18236e12i) q^{53} +(-3.67651e12 - 6.36791e12i) q^{54} -1.95145e12 q^{55} +(-1.83584e12 - 4.18446e12i) q^{56} +2.81828e12 q^{57} +(-9.63837e12 - 1.66941e13i) q^{58} +(2.16425e12 - 3.74859e12i) q^{59} +(2.44137e12 - 4.22858e12i) q^{60} +(-7.31929e12 - 1.26774e13i) q^{61} -9.68221e12 q^{62} +(-9.44784e12 + 1.28562e13i) q^{63} +4.39805e12 q^{64} +(-8.27215e12 - 1.43278e13i) q^{65} +(2.94470e12 - 5.10037e12i) q^{66} +(-3.20477e13 + 5.55082e13i) q^{67} +(7.21619e12 + 1.24988e13i) q^{68} +2.07227e13 q^{69} +(-3.11656e13 - 3.44710e12i) q^{70} -3.29232e13 q^{71} +(-7.67797e12 - 1.32986e13i) q^{72} +(6.70692e13 - 1.16167e14i) q^{73} +(-2.11284e13 + 3.65955e13i) q^{74} +(2.36950e13 + 4.10409e13i) q^{75} +1.74193e13 q^{76} +(-3.75909e13 - 4.15777e12i) q^{77} +4.99300e13 q^{78} +(9.06672e13 + 1.57040e14i) q^{79} +(1.50897e13 - 2.61361e13i) q^{80} +(2.36043e13 - 4.08839e13i) q^{81} +(1.10887e14 + 1.92062e14i) q^{82} +5.42515e13 q^{83} +(5.60376e13 - 7.62536e13i) q^{84} +9.90349e13 q^{85} +(1.44107e14 + 2.49600e14i) q^{86} +(1.99603e14 - 3.45723e14i) q^{87} +(1.82007e13 - 3.15245e13i) q^{88} +(1.39254e13 + 2.41195e13i) q^{89} -1.05372e14 q^{90} +(-1.28820e14 - 2.93621e14i) q^{91} +1.28084e14 q^{92} +(-1.00255e14 - 1.73647e14i) q^{93} +(-2.93512e14 + 5.08378e14i) q^{94} +(5.97655e13 - 1.03517e14i) q^{95} +(4.55400e13 + 7.88776e13i) q^{96} -1.18440e15 q^{97} +(-5.92999e14 - 1.32803e14i) q^{98} -1.27097e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9}+O(q^{10}) $ 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9	\( 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9} - 1404032 q^{10} - 3405409 q^{11} + 39239680 q^{12} + 369408276 q^{13} + 411547520 q^{14} + 453669790 q^{15} - 1342177280 q^{16} - 3201713287 q^{17} + 5824692992 q^{18} - 1063446451 q^{19} - 359432192 q^{20} + 21058786691 q^{21} - 871784704 q^{22} - 31680429991 q^{23} - 5022679040 q^{24} + 39012502244 q^{25} + 23642129664 q^{26} + 66427564750 q^{27} + 13761560576 q^{28} + 294935242276 q^{29} + 29034866560 q^{30} + 30201804075 q^{31} + 171798691840 q^{32} - 482562276049 q^{33} - 819638601472 q^{34} - 1540311474205 q^{35} + 1491121405952 q^{36} + 1369689837461 q^{37} + 136121145728 q^{38} - 1048775641458 q^{39} - 23003660288 q^{40} + 3634838274156 q^{41} - 871978643968 q^{42} + 415602663752 q^{43} - 55794221056 q^{44} - 7616412162898 q^{45} + 4055095038848 q^{46} - 12606978599835 q^{47} - 1285805834240 q^{48} - 8067928630838 q^{49} + 9987200574464 q^{50} + 6857137867217 q^{51} - 3026192596992 q^{52} + 10616682242361 q^{53} + 4251364144000 q^{54} - 40851384759514 q^{55} - 4981314813952 q^{56} + 44665526899814 q^{57} + 18875855505664 q^{58} + 39993786962755 q^{59} - 3716462919680 q^{60} + 5148862074165 q^{61} + 7731661843200 q^{62} - 97668254816810 q^{63} + 43980465111040 q^{64} + 91302240851010 q^{65} + 61767971334272 q^{66} - 29267240444285 q^{67} - 52456870494208 q^{68} - 279695242712578 q^{69} + 18327124839296 q^{70} - 37767657205600 q^{71} + 95431769980928 q^{72} + 243869659370917 q^{73} - 175320299195008 q^{74} + 295809815641460 q^{75} + 34847013306368 q^{76} + 35960055270559 q^{77} - 268486564213248 q^{78} + 137356615917609 q^{79} + 2944468516864 q^{80} - 352056899083285 q^{81} + 232629649545984 q^{82} - 914604166510648 q^{83} - 456640427573248 q^{84} + 264981492485402 q^{85} + 26598570480128 q^{86} + 13\!\cdots\!90 q^{87}+ \cdots + 39\!\cdots\!96 q^{99}+O(q^{100}) \) 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9 - 1404032 * q^10 - 3405409 * q^11 + 39239680 * q^12 + 369408276 * q^13 + 411547520 * q^14 + 453669790 * q^15 - 1342177280 * q^16 - 3201713287 * q^17 + 5824692992 * q^18 - 1063446451 * q^19 - 359432192 * q^20 + 21058786691 * q^21 - 871784704 * q^22 - 31680429991 * q^23 - 5022679040 * q^24 + 39012502244 * q^25 + 23642129664 * q^26 + 66427564750 * q^27 + 13761560576 * q^28 + 294935242276 * q^29 + 29034866560 * q^30 + 30201804075 * q^31 + 171798691840 * q^32 - 482562276049 * q^33 - 819638601472 * q^34 - 1540311474205 * q^35 + 1491121405952 * q^36 + 1369689837461 * q^37 + 136121145728 * q^38 - 1048775641458 * q^39 - 23003660288 * q^40 + 3634838274156 * q^41 - 871978643968 * q^42 + 415602663752 * q^43 - 55794221056 * q^44 - 7616412162898 * q^45 + 4055095038848 * q^46 - 12606978599835 * q^47 - 1285805834240 * q^48 - 8067928630838 * q^49 + 9987200574464 * q^50 + 6857137867217 * q^51 - 3026192596992 * q^52 + 10616682242361 * q^53 + 4251364144000 * q^54 - 40851384759514 * q^55 - 4981314813952 * q^56 + 44665526899814 * q^57 + 18875855505664 * q^58 + 39993786962755 * q^59 - 3716462919680 * q^60 + 5148862074165 * q^61 + 7731661843200 * q^62 - 97668254816810 * q^63 + 43980465111040 * q^64 + 91302240851010 * q^65 + 61767971334272 * q^66 - 29267240444285 * q^67 - 52456870494208 * q^68 - 279695242712578 * q^69 + 18327124839296 * q^70 - 37767657205600 * q^71 + 95431769980928 * q^72 + 243869659370917 * q^73 - 175320299195008 * q^74 + 295809815641460 * q^75 + 34847013306368 * q^76 + 35960055270559 * q^77 - 268486564213248 * q^78 + 137356615917609 * q^79 + 2944468516864 * q^80 - 352056899083285 * q^81 + 232629649545984 * q^82 - 914604166510648 * q^83 - 456640427573248 * q^84 + 264981492485402 * q^85 + 26598570480128 * q^86 + 1332529214868790 * q^87 + 7141660295168 * q^88 + 315332760149685 * q^89 - 1949801513701888 * q^90 - 2638730194011720 * q^91 + 1038104329945088 * q^92 + 2962720310885787 * q^93 + 1613693260778880 * q^94 - 1346257729549705 * q^95 - 82291573391360 * q^96 + 58320039716044 * q^97 - 1279096378461056 * q^98 + 3930453838067596 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	64.0000	+	110.851i	0.353553	+	0.612372i
$2$	64.0000	+	110.851i	0.353553	+	0.612372i
$3$	−1325.39	+	2295.64i	−0.349892	+	0.606031i	−0.986230	−	0.165380i	$-0.947115\pi$
$3$	−1325.39	+	2295.64i	−0.349892	+	0.606031i	0.636338	+	0.771410i	$0.280448\pi$
$4$	−8192.00	+	14189.0i	−0.250000	+	0.433013i
$5$	56213.5	+	97364.6i	0.321785	+	0.557347i	0.980856	−	0.194733i	$-0.0623840\pi$
$5$	56213.5	+	97364.6i	0.321785	+	0.557347i	−0.659072	+	0.752080i	$0.729051\pi$
$6$	−339300.			−0.494822
$7$	875396.	+	1.99531e6i	0.401762	+	0.915744i
$7$	875396.	+	1.99531e6i	0.401762	+	0.915744i
$8$	−2.09715e6			−0.353553
$9$	3.66114e6	+	6.34128e6i	0.255151	+	0.441935i
$10$	−7.19532e6	+	1.24627e7i	−0.227536	+	0.394104i
$11$	−8.67876e6	+	1.50321e7i	−0.134280	+	0.232580i	−0.925322	−	0.379181i	$-0.876206\pi$
$11$	−8.67876e6	+	1.50321e7i	−0.134280	+	0.232580i	0.791042	+	0.611762i	$0.209539\pi$
$12$	−2.17152e7	−	3.76118e7i	−0.174946	−	0.303015i
$13$	−1.47156e8			−0.650434			−0.325217	−	0.945639i	$-0.605437\pi$
$13$	−1.47156e8			−0.650434			−0.325217	+	0.945639i	$0.605437\pi$
$14$	−1.65157e8	+	2.24738e8i	−0.418732	+	0.569793i
$15$	−2.98019e8			−0.450359
$16$	−1.34218e8	−	2.32472e8i	−0.125000	−	0.216506i
$17$	4.40441e8	−	7.62866e8i	0.260328	−	0.450901i	−0.706001	−	0.708211i	$-0.749503\pi$
$17$	4.40441e8	−	7.62866e8i	0.260328	−	0.450901i	0.966329	+	0.257309i	$0.0828360\pi$
$18$	−4.68626e8	+	8.11684e8i	−0.180419	+	0.312495i
$19$	−5.31595e8	−	9.20749e8i	−0.136436	−	0.236314i	0.789709	−	0.613481i	$-0.210231\pi$
$19$	−5.31595e8	−	9.20749e8i	−0.136436	−	0.236314i	−0.926145	+	0.377168i	$0.876898\pi$
$20$	−1.84200e9			−0.321785
$21$	−5.74075e9	−	6.34961e8i	−0.695542	−	0.0769311i
$22$	−2.22176e9			−0.189901
$23$	−3.90880e9	−	6.77025e9i	−0.239379	−	0.414616i	0.721158	−	0.692771i	$-0.243610\pi$
$23$	−3.90880e9	−	6.77025e9i	−0.239379	−	0.414616i	−0.960536	+	0.278155i	$0.910277\pi$
$24$	2.77954e9	−	4.81431e9i	0.123706	−	0.214264i
$25$	8.93888e9	−	1.54826e10i	0.292909	−	0.507334i
$26$	−9.41799e9	−	1.63124e10i	−0.229963	−	0.398308i
$27$	−5.74455e10			−1.05689
$28$	−3.54826e10	−	3.92458e9i	−0.496969	−	0.0549678i
$29$	−1.50600e11			−1.62121			−0.810604	−	0.585595i	$-0.800861\pi$
$29$	−1.50600e11			−1.62121			−0.810604	+	0.585595i	$0.800861\pi$
$30$	−1.90732e10	−	3.30358e10i	−0.159226	−	0.275788i
$31$	−3.78211e10	+	6.55081e10i	−0.246900	+	0.427644i	−0.962664	−	0.270698i	$-0.912745\pi$
$31$	−3.78211e10	+	6.55081e10i	−0.246900	+	0.427644i	0.715764	+	0.698342i	$0.246079\pi$
$32$	1.71799e10	−	2.97564e10i	0.0883883	−	0.153093i
$33$	−2.30055e10	−	3.98466e10i	−0.0939672	−	0.162756i
$34$	1.12753e11			0.368159
$35$	−1.45063e11	+	1.97396e11i	−0.381106	+	0.518594i
$36$	−1.19968e11			−0.255151
$37$	1.65066e11	+	2.85902e11i	0.285854	+	0.495113i	0.972816	−	0.231580i	$-0.0743895\pi$
$37$	1.65066e11	+	2.85902e11i	0.285854	+	0.495113i	−0.686962	+	0.726693i	$0.741056\pi$
$38$	6.80441e10	−	1.17856e11i	0.0964747	−	0.167099i
$39$	1.95039e11	−	3.37818e11i	0.227582	−	0.394183i
$40$	−1.17888e11	−	2.04188e11i	−0.113768	−	0.197052i
$41$	1.73261e12			1.38938			0.694692	−	0.719307i	$-0.255541\pi$
$41$	1.73261e12			1.38938			0.694692	+	0.719307i	$0.255541\pi$
$42$	−2.97022e11	−	6.77006e11i	−0.198801	−	0.453130i
$43$	2.25167e12			1.26325			0.631627	−	0.775273i	$-0.282388\pi$
$43$	2.25167e12			1.26325			0.631627	+	0.775273i	$0.282388\pi$
$44$	−1.42193e11	−	2.46285e11i	−0.0671402	−	0.116290i
$45$	−4.11611e11	+	7.12931e11i	−0.164207	+	0.284416i
$46$	5.00327e11	−	8.66592e11i	0.169266	−	0.293178i
$47$	2.29306e12	+	3.97171e12i	0.660210	+	1.14352i	0.980560	+	0.196219i	$0.0628663\pi$
$47$	2.29306e12	+	3.97171e12i	0.660210	+	1.14352i	−0.320350	+	0.947299i	$0.603800\pi$
$48$	7.11563e11			0.174946
$49$	−3.21492e12	+	3.49336e12i	−0.677174	+	0.735823i
$50$	2.28835e12			0.414236
$51$	1.16751e12	+	2.02219e12i	0.182173	+	0.315534i
$52$	1.20550e12	−	2.08799e12i	0.162608	−	0.281646i
$53$	−4.14674e12	+	7.18236e12i	−0.484884	+	0.839844i	−0.999849	−	0.0173675i	$-0.994471\pi$
$53$	−4.14674e12	+	7.18236e12i	−0.484884	+	0.839844i	0.514965	+	0.857211i	$0.327805\pi$
$54$	−3.67651e12	−	6.36791e12i	−0.373665	−	0.647208i
$55$	−1.95145e12			−0.172837
$56$	−1.83584e12	−	4.18446e12i	−0.142044	−	0.323764i
$57$	2.81828e12			0.190951
$58$	−9.63837e12	−	1.66941e13i	−0.573183	−	0.992783i
$59$	2.16425e12	−	3.74859e12i	0.113218	−	0.196100i	−0.803848	−	0.594835i	$-0.797217\pi$
$59$	2.16425e12	−	3.74859e12i	0.113218	−	0.196100i	0.917066	+	0.398735i	$0.130551\pi$
$60$	2.44137e12	−	4.22858e12i	0.112590	−	0.195011i
$61$	−7.31929e12	−	1.26774e13i	−0.298192	−	0.516483i	0.677531	−	0.735495i	$-0.263050\pi$
$61$	−7.31929e12	−	1.26774e13i	−0.298192	−	0.516483i	−0.975722	+	0.219011i	$0.929717\pi$
$62$	−9.68221e12			−0.349170
$63$	−9.44784e12	+	1.28562e13i	−0.302189	+	0.411206i
$64$	4.39805e12			0.125000
$65$	−8.27215e12	−	1.43278e13i	−0.209300	−	0.362518i
$66$	2.94470e12	−	5.10037e12i	0.0664449	−	0.115086i
$67$	−3.20477e13	+	5.55082e13i	−0.646004	+	1.11891i	0.338064	+	0.941123i	$0.390228\pi$
$67$	−3.20477e13	+	5.55082e13i	−0.646004	+	1.11891i	−0.984069	+	0.177789i	$0.943105\pi$
$68$	7.21619e12	+	1.24988e13i	0.130164	+	0.225451i
$69$	2.07227e13			0.335027
$70$	−3.11656e13	−	3.44710e12i	−0.452314	−	0.0500286i
$71$	−3.29232e13			−0.429600			−0.214800	−	0.976658i	$-0.568910\pi$
$71$	−3.29232e13			−0.429600			−0.214800	+	0.976658i	$0.568910\pi$
$72$	−7.67797e12	−	1.32986e13i	−0.0902096	−	0.156248i
$73$	6.70692e13	−	1.16167e14i	0.710562	−	1.23073i	−0.254085	−	0.967182i	$-0.581774\pi$
$73$	6.70692e13	−	1.16167e14i	0.710562	−	1.23073i	0.964646	−	0.263547i	$-0.0848925\pi$
$74$	−2.11284e13	+	3.65955e13i	−0.202129	+	0.350098i
$75$	2.36950e13	+	4.10409e13i	0.204973	+	0.355024i
$76$	1.74193e13			0.136436
$77$	−3.75909e13	−	4.15777e12i	−0.266933	−	0.0295244i
$78$	4.99300e13			0.321849
$79$	9.06672e13	+	1.57040e14i	0.531187	+	0.920042i	0.999338	+	0.0363938i	$0.0115871\pi$
$79$	9.06672e13	+	1.57040e14i	0.531187	+	0.920042i	−0.468151	+	0.883649i	$0.655080\pi$
$80$	1.50897e13	−	2.61361e13i	0.0804462	−	0.139337i
$81$	2.36043e13	−	4.08839e13i	0.114645	−	0.198570i
$82$	1.10887e14	+	1.92062e14i	0.491221	+	0.850820i
$83$	5.42515e13			0.219445			0.109723	−	0.993962i	$-0.465004\pi$
$83$	5.42515e13			0.219445			0.109723	+	0.993962i	$0.465004\pi$
$84$	5.60376e13	−	7.62536e13i	0.207198	−	0.281946i
$85$	9.90349e13			0.335078
$86$	1.44107e14	+	2.49600e14i	0.446628	+	0.773582i
$87$	1.99603e14	−	3.45723e14i	0.567248	−	0.982502i
$88$	1.82007e13	−	3.15245e13i	0.0474753	−	0.0822296i
$89$	1.39254e13	+	2.41195e13i	0.0333720	+	0.0578020i	0.882229	−	0.470820i	$-0.156042\pi$
$89$	1.39254e13	+	2.41195e13i	0.0333720	+	0.0578020i	−0.848857	+	0.528623i	$0.822709\pi$
$90$	−1.05372e14			−0.232224
$91$	−1.28820e14	−	2.93621e14i	−0.261320	−	0.595631i
$92$	1.28084e14			0.239379
$93$	−1.00255e14	−	1.73647e14i	−0.172777	−	0.299258i
$94$	−2.93512e14	+	5.08378e14i	−0.466839	+	0.808589i
$95$	5.97655e13	−	1.03517e14i	0.0878059	−	0.152084i
$96$	4.55400e13	+	7.88776e13i	0.0618528	+	0.107132i
$97$	−1.18440e15			−1.48836			−0.744182	−	0.667977i	$-0.767161\pi$
$97$	−1.18440e15			−1.48836			−0.744182	+	0.667977i	$0.767161\pi$
$98$	−5.92999e14	−	1.32803e14i	−0.690015	−	0.154530i
$99$	−1.27097e14			−0.137047
$100$	1.46455e14	+	2.53667e14i	0.146455	+	0.253667i
$101$	3.31820e13	−	5.74729e13i	0.0307958	−	0.0533399i	−0.850217	−	0.526433i	$-0.823529\pi$
$101$	3.31820e13	−	5.74729e13i	0.0307958	−	0.0533399i	0.881013	+	0.473093i	$0.156863\pi$
$102$	−1.49441e14	+	2.58840e14i	−0.128816	+	0.223116i
$103$	−8.80878e14	−	1.52573e15i	−0.705727	−	1.22235i	−0.966429	−	0.256935i	$-0.917287\pi$
$103$	−8.80878e14	−	1.52573e15i	−0.705727	−	1.22235i	0.260702	−	0.965419i	$-0.416046\pi$
$104$	3.08609e14			0.229963
$105$	−2.60885e14	−	5.94639e14i	−0.180938	−	0.412414i
$106$	−1.06157e15			−0.685729
$107$	1.09468e15	+	1.89604e15i	0.659036	+	1.14148i	0.980866	+	0.194686i	$0.0623687\pi$
$107$	1.09468e15	+	1.89604e15i	0.659036	+	1.14148i	−0.321830	+	0.946797i	$0.604298\pi$
$108$	4.70594e14	−	8.15092e14i	0.264221	−	0.457645i
$109$	−8.69567e14	+	1.50613e15i	−0.455622	+	0.789160i	−0.998724	−	0.0505068i	$-0.983916\pi$
$109$	−8.69567e14	+	1.50613e15i	−0.455622	+	0.789160i	0.543102	+	0.839667i	$0.317250\pi$
$110$	−1.24893e14	−	2.16321e14i	−0.0611073	−	0.105841i
$111$	−8.75105e14			−0.400072
$112$	3.46359e14	−	4.71310e14i	0.148044	−	0.201452i
$113$	2.44997e15			0.979652			0.489826	−	0.871820i	$-0.337060\pi$
$113$	2.44997e15			0.979652			0.489826	+	0.871820i	$0.337060\pi$
$114$	1.80370e14	+	3.12410e14i	0.0675115	+	0.116933i
$115$	4.39455e14	−	7.61158e14i	0.154057	−	0.266834i
$116$	1.23371e15	−	2.13685e15i	0.405302	−	0.702003i
$117$	−5.38759e14	−	9.33158e14i	−0.165959	−	0.287449i
$118$	5.54048e14			0.160115
$119$	1.90771e15	+	2.11004e14i	0.517500	+	0.0572386i
$120$	6.24991e14			0.159226
$121$	1.93798e15	+	3.35668e15i	0.463938	+	0.803563i
$122$	9.36870e14	−	1.62271e15i	0.210853	−	0.365209i
$123$	−2.29638e15	+	3.97745e15i	−0.486134	+	0.842009i
$124$	−6.19661e14	−	1.07328e15i	−0.123450	−	0.213822i
$125$	5.44094e15			1.02058
$126$	−2.02979e15	−	2.24507e14i	−0.358651	−	0.0396689i
$127$	2.37860e15			0.396089			0.198044	−	0.980193i	$-0.436541\pi$
$127$	2.37860e15			0.396089			0.198044	+	0.980193i	$0.436541\pi$
$128$	2.81475e14	+	4.87529e14i	0.0441942	+	0.0765466i
$129$	−2.98433e15	+	5.16902e15i	−0.442002	+	0.765571i
$130$	1.05884e15	−	1.83396e15i	0.147997	−	0.256339i
$131$	2.37224e15	+	4.10883e15i	0.313057	+	0.542230i	0.979023	−	0.203752i	$-0.0653136\pi$
$131$	2.37224e15	+	4.10883e15i	0.313057	+	0.542230i	−0.665966	+	0.745982i	$0.731980\pi$
$132$	7.53843e14			0.0939672
$133$	1.37182e15	−	1.86671e15i	0.161588	−	0.219882i
$134$	−8.20420e15			−0.913588
$135$	−3.22921e15	−	5.59316e15i	−0.340089	−	0.589052i
$136$	−9.23672e14	+	1.59985e15i	−0.0920398	+	0.159418i
$137$	−4.37677e15	+	7.58079e15i	−0.412810	+	0.715007i	−0.995196	−	0.0979051i	$-0.968786\pi$
$137$	−4.37677e15	+	7.58079e15i	−0.412810	+	0.715007i	0.582386	+	0.812912i	$0.302119\pi$
$138$	1.32626e15	+	2.29714e15i	0.118450	+	0.205161i
$139$	1.33549e16			1.12987			0.564935	−	0.825136i	$-0.308901\pi$
$139$	1.33549e16			1.12987			0.564935	+	0.825136i	$0.308901\pi$
$140$	−1.61248e15	−	3.67536e15i	−0.129281	−	0.294672i
$141$	−1.21568e16			−0.924010
$142$	−2.10708e15	−	3.64957e15i	−0.151886	−	0.263075i
$143$	1.27713e15	−	2.21206e15i	0.0873405	−	0.151278i
$144$	9.82780e14	−	1.70222e15i	0.0637878	−	0.110484i
$145$	−8.46572e15	−	1.46631e16i	−0.521680	−	0.903576i
$146$	1.71697e16			1.00489
$147$	−3.75849e15	−	1.20104e16i	−0.208994	−	0.667847i
$148$	−5.40887e15			−0.285854
$149$	−1.47064e16	−	2.54722e16i	−0.738939	−	1.27988i	−0.952974	−	0.303053i	$-0.901994\pi$
$149$	−1.47064e16	−	2.54722e16i	−0.738939	−	1.27988i	0.214035	−	0.976826i	$-0.431339\pi$
$150$	−3.03296e15	+	5.25324e15i	−0.144938	+	0.251040i
$151$	−1.03931e16	+	1.80013e16i	−0.472515	+	0.818421i	−0.999505	−	0.0314509i	$-0.989987\pi$
$151$	−1.03931e16	+	1.80013e16i	−0.472515	+	0.818421i	0.526990	+	0.849872i	$0.323321\pi$
$152$	1.11483e15	+	1.93095e15i	0.0482374	+	0.0835495i
$153$	6.45007e15			0.265692
$154$	−1.94492e15	−	4.43309e15i	−0.0762951	−	0.173901i
$155$	−8.50422e15			−0.317795
$156$	3.19552e15	+	5.53480e15i	0.113791	+	0.197091i
$157$	−9.85935e15	+	1.70769e16i	−0.334658	+	0.579645i	−0.983419	−	0.181348i	$-0.941954\pi$
$157$	−9.85935e15	+	1.70769e16i	−0.334658	+	0.579645i	0.648761	+	0.760992i	$0.275287\pi$
$158$	−1.16054e16	+	2.01012e16i	−0.375606	+	0.650568i
$159$	−1.09921e16	−	1.90389e16i	−0.339314	−	0.587709i
$160$	3.86296e15			0.113768
$161$	1.00870e16	−	1.37259e16i	0.283509	−	0.385786i
$162$	6.04270e15			0.162132
$163$	2.29458e16	+	3.97433e16i	0.587891	+	1.01826i	0.994508	+	0.104658i	$0.0333748\pi$
$163$	2.29458e16	+	3.97433e16i	0.587891	+	1.01826i	−0.406618	+	0.913598i	$0.633292\pi$
$164$	−1.41936e16	+	2.45840e16i	−0.347346	+	0.601621i
$165$	2.58643e15	−	4.47984e15i	0.0604744	−	0.104745i
$166$	3.47209e15	+	6.01384e15i	0.0775855	+	0.134382i
$167$	8.81501e16			1.88299			0.941497	−	0.337020i	$-0.109419\pi$
$167$	8.81501e16			1.88299			0.941497	+	0.337020i	$0.109419\pi$
$168$	1.20392e16	+	1.33161e15i	0.245911	+	0.0271993i
$169$	−2.95310e16			−0.576936
$170$	6.33823e15	+	1.09781e16i	0.118468	+	0.205193i
$171$	3.89248e15	−	6.74198e15i	0.0696235	−	0.120591i
$172$	−1.84456e16	+	3.19488e16i	−0.315813	+	0.547005i
$173$	−5.55245e16	−	9.61713e16i	−0.910205	−	1.57652i	−0.813774	−	0.581181i	$-0.802591\pi$
$173$	−5.55245e16	−	9.61713e16i	−0.910205	−	1.57652i	−0.0964300	−	0.995340i	$-0.530742\pi$
$174$	5.10984e16			0.802209
$175$	3.87176e16	+	4.28239e15i	0.582268	+	0.0644023i
$176$	4.65937e15			0.0671402
$177$	5.73694e15	+	9.93668e15i	0.0792284	+	0.137228i
$178$	−1.78245e15	+	3.08729e15i	−0.0235976	+	0.0408722i
$179$	−5.31678e15	+	9.20893e15i	−0.0674918	+	0.116899i	−0.897797	−	0.440410i	$-0.854833\pi$
$179$	−5.31678e15	+	9.20893e15i	−0.0674918	+	0.116899i	0.830305	+	0.557310i	$0.188166\pi$
$180$	−6.74383e15	−	1.16807e16i	−0.0821037	−	0.142208i
$181$	9.27805e16			1.08360			0.541798	−	0.840509i	$-0.317744\pi$
$181$	9.27805e16			1.08360			0.541798	+	0.840509i	$0.317744\pi$
$182$	2.43038e16	−	3.30716e16i	0.272357	−	0.370612i
$183$	3.88037e16			0.417339
$184$	8.19736e15	+	1.41982e16i	0.0846331	+	0.146589i
$185$	−1.85578e16	+	3.21431e16i	−0.183967	+	0.318640i
$186$	1.28327e16	−	2.22269e16i	0.122172	−	0.211608i
$187$	7.64496e15	+	1.32415e16i	0.0699139	+	0.121094i
$188$	−7.51392e16			−0.660210
$189$	−5.02876e16	−	1.14621e17i	−0.424617	−	0.967836i
$190$	1.53000e16			0.124176
$191$	7.98565e16	+	1.38316e17i	0.623103	+	1.07925i	0.988904	+	0.148554i	$0.0474618\pi$
$191$	7.98565e16	+	1.38316e17i	0.623103	+	1.07925i	−0.365801	+	0.930693i	$0.619205\pi$
$192$	−5.82912e15	+	1.00963e16i	−0.0437365	+	0.0757538i
$193$	−1.13388e17	+	1.96394e17i	−0.818255	+	1.41726i	0.0887118	+	0.996057i	$0.471725\pi$
$193$	−1.13388e17	+	1.96394e17i	−0.818255	+	1.41726i	−0.906967	+	0.421202i	$0.861608\pi$
$194$	−7.58014e16	−	1.31292e17i	−0.526216	−	0.911433i
$195$	4.38553e16			0.292929
$196$	−2.32306e16	−	7.42341e16i	−0.149327	−	0.477181i
$197$	−2.94220e17			−1.82044			−0.910218	−	0.414129i	$-0.864086\pi$
$197$	−2.94220e17			−1.82044			−0.910218	+	0.414129i	$0.864086\pi$
$198$	−8.13418e15	−	1.40888e16i	−0.0484535	−	0.0839239i
$199$	−1.02031e17	+	1.76722e17i	−0.585237	+	1.01366i	0.409609	+	0.912261i	$0.365665\pi$
$199$	−1.02031e17	+	1.76722e17i	−0.585237	+	1.01366i	−0.994846	+	0.101399i	$0.967668\pi$
$200$	−1.87462e16	+	3.24694e16i	−0.103559	+	0.179370i
$201$	−8.49513e16	−	1.47140e17i	−0.452064	−	0.782997i
$202$	8.49458e15			0.0435519
$203$	−1.31834e17	−	3.00492e17i	−0.651340	−	1.48461i
$204$	−3.82570e16			−0.182173
$205$	9.73961e16	+	1.68695e17i	0.447082	+	0.774369i
$206$	1.12752e17	−	1.95293e17i	0.499024	−	0.864335i
$207$	2.86214e16	−	4.95737e16i	0.122155	−	0.211579i
$208$	1.97510e16	+	3.42097e16i	0.0813042	+	0.140823i
$209$	1.84543e16			0.0732826
$210$	4.92198e16	−	6.69763e16i	0.188580	−	0.256612i
$211$	1.61133e17			0.595753			0.297876	−	0.954604i	$-0.403722\pi$
$211$	1.61133e17			0.595753			0.297876	+	0.954604i	$0.403722\pi$
$212$	−6.79402e16	−	1.17676e17i	−0.242442	−	0.419922i
$213$	4.36360e16	−	7.55798e16i	0.150313	−	0.260351i
$214$	−1.40119e17	+	2.42693e17i	−0.466008	+	0.807150i
$215$	1.26574e17	+	2.19232e17i	0.406496	+	0.704071i
$216$	1.20472e17			0.373665
$217$	−1.63817e17	−	1.81191e16i	−0.490808	−	0.0542862i
$218$	−2.22609e17			−0.644346
$219$	1.77786e17	+	3.07934e17i	0.497240	+	0.861245i
$220$	1.59863e16	−	2.76891e16i	0.0432094	−	0.0748408i
$221$	−6.48136e16	+	1.12260e17i	−0.169326	+	0.293281i
$222$	−5.60067e16	−	9.70065e16i	−0.141447	−	0.244993i
$223$	7.44998e17			1.81915			0.909576	−	0.415538i	$-0.136407\pi$
$223$	7.44998e17			1.81915			0.909576	+	0.415538i	$0.136407\pi$
$224$	7.44123e16	+	8.23044e15i	0.175705	+	0.0194340i
$225$	1.30906e17			0.298945
$226$	1.56798e17	+	2.71582e17i	0.346359	+	0.599912i
$227$	2.32750e17	−	4.03135e17i	0.497389	−	0.861503i	−0.502607	−	0.864515i	$-0.667626\pi$
$227$	2.32750e17	−	4.03135e17i	0.497389	−	0.861503i	0.999995	+	0.00301253i	$0.000958921\pi$
$228$	−2.30873e16	+	3.99884e16i	−0.0477378	+	0.0826843i
$229$	4.30869e16	+	7.46287e16i	0.0862142	+	0.149327i	0.905908	−	0.423475i	$-0.139190\pi$
$229$	4.30869e16	+	7.46287e16i	0.0862142	+	0.149327i	−0.819694	+	0.572802i	$0.805856\pi$
$230$	1.12500e17			0.217869
$231$	5.93673e16	−	8.07845e16i	0.111290	−	0.151439i
$232$	3.15830e17			0.573183
$233$	−2.77738e17	−	4.81056e17i	−0.488052	−	0.845331i	0.511854	−	0.859073i	$-0.328959\pi$
$233$	−2.77738e17	−	4.81056e17i	−0.488052	−	0.845331i	−0.999906	+	0.0137420i	$0.995626\pi$
$234$	6.89612e16	−	1.19444e17i	0.117351	−	0.203257i
$235$	−2.57802e17	+	4.46527e17i	−0.424891	+	0.735933i
$236$	3.54590e16	+	6.14169e16i	0.0566092	+	0.0980500i
$237$	−4.80677e17			−0.743432
$238$	9.87035e16	+	2.24976e17i	0.147913	+	0.337140i
$239$	2.51662e17			0.365454			0.182727	−	0.983164i	$-0.441508\pi$
$239$	2.51662e17			0.365454			0.182727	+	0.983164i	$0.441508\pi$
$240$	3.99994e16	+	6.92810e16i	0.0562949	+	0.0975057i
$241$	−1.15200e17	+	1.99532e17i	−0.157153	+	0.272198i	−0.933841	−	0.357688i	$-0.883565\pi$
$241$	−1.15200e17	+	1.99532e17i	−0.157153	+	0.272198i	0.776688	+	0.629886i	$0.216898\pi$
$242$	−2.48062e17	+	4.29656e17i	−0.328053	+	0.568205i
$243$	−3.49570e17	−	6.05474e17i	−0.448216	−	0.776333i
$244$	2.39839e17			0.298192
$245$	−5.20852e17	−	1.16646e17i	−0.628013	−	0.140645i
$246$	−5.87874e17			−0.687498
$247$	7.82274e16	+	1.35494e17i	0.0887425	+	0.153706i
$248$	7.93166e16	−	1.37380e17i	0.0872924	−	0.151195i
$249$	−7.19043e16	+	1.24542e17i	−0.0767821	+	0.132990i
$250$	3.48220e17	+	6.03135e17i	0.360831	+	0.624978i
$251$	6.39141e17			0.642752			0.321376	−	0.946952i	$-0.395855\pi$
$251$	6.39141e17			0.642752			0.321376	+	0.946952i	$0.395855\pi$
$252$	−1.05020e17	−	2.39373e17i	−0.102510	−	0.233653i
$253$	1.35694e17			0.128575
$254$	1.52230e17	+	2.63670e17i	0.140039	+	0.242554i
$255$	−1.31260e17	+	2.27349e17i	−0.117241	+	0.203068i
$256$	−3.60288e16	+	6.24037e16i	−0.0312500	+	0.0541266i
$257$	−9.87071e17	−	1.70966e18i	−0.831476	−	1.44016i	−0.896868	−	0.442299i	$-0.854163\pi$
$257$	−9.87071e17	−	1.70966e18i	−0.831476	−	1.44016i	0.0653915	−	0.997860i	$-0.479170\pi$
$258$	−7.63989e17			−0.625086
$259$	−4.25964e17	+	5.79634e17i	−0.338552	+	0.460687i
$260$	2.71062e17			0.209300
$261$	−5.51366e17	−	9.54994e17i	−0.413653	−	0.716468i
$262$	−3.03646e17	+	5.25931e17i	−0.221365	+	0.383415i
$263$	1.02624e18	−	1.77750e18i	0.727080	−	1.25934i	−0.231033	−	0.972946i	$-0.574210\pi$
$263$	1.02624e18	−	1.77750e18i	0.727080	−	1.25934i	0.958112	−	0.286393i	$-0.0924563\pi$
$264$	4.82460e16	+	8.35645e16i	0.0332224	+	0.0575430i
$265$	−9.32410e17			−0.624113
$266$	2.94724e17	+	3.25982e16i	0.191780	+	0.0212120i
$267$	−7.38262e16			−0.0467064
$268$	−5.25069e17	−	9.09446e17i	−0.323002	−	0.559456i
$269$	−6.97628e16	+	1.20833e17i	−0.0417332	+	0.0722841i	−0.886138	−	0.463422i	$-0.846621\pi$
$269$	−6.97628e16	+	1.20833e17i	−0.0417332	+	0.0722841i	0.844404	+	0.535706i	$0.179955\pi$
$270$	4.13339e17	−	7.15924e17i	0.240480	−	0.416523i
$271$	6.05387e17	+	1.04856e18i	0.342581	+	0.593368i	0.984911	−	0.173060i	$-0.0553655\pi$
$271$	6.05387e17	+	1.04856e18i	0.342581	+	0.593368i	−0.642330	+	0.766428i	$0.722032\pi$
$272$	−2.36460e17			−0.130164
$273$	8.44786e17	+	9.34383e16i	0.452404	+	0.0500386i
$274$	−1.12045e18			−0.583801
$275$	1.55157e17	+	2.68739e17i	0.0786639	+	0.136250i
$276$	−1.69761e17	+	2.94034e17i	−0.0837566	+	0.145071i
$277$	−9.26557e15	+	1.60484e16i	−0.00444912	+	0.00770609i	−0.868241	−	0.496142i	$-0.834750\pi$
$277$	−9.26557e15	+	1.60484e16i	−0.00444912	+	0.00770609i	0.863792	+	0.503848i	$0.168083\pi$
$278$	8.54711e17	+	1.48040e18i	0.399469	+	0.691901i
$279$	−5.53874e17			−0.251988
$280$	3.04219e17	−	4.13969e17i	0.134741	−	0.183351i
$281$	1.13047e18			0.487484			0.243742	−	0.969840i	$-0.421625\pi$
$281$	1.13047e18			0.487484			0.243742	+	0.969840i	$0.421625\pi$
$282$	−7.78036e17	−	1.34760e18i	−0.326687	−	0.565838i
$283$	−2.08935e18	+	3.61886e18i	−0.854305	+	1.47970i	0.0229836	+	0.999736i	$0.492683\pi$
$283$	−2.08935e18	+	3.61886e18i	−0.854305	+	1.47970i	−0.877288	+	0.479964i	$0.840650\pi$
$284$	2.69707e17	−	4.67145e17i	0.107400	−	0.186022i
$285$	1.58425e17	+	2.74400e17i	0.0614452	+	0.106426i
$286$	3.26946e17			0.123518
$287$	1.51672e18	+	3.45709e18i	0.558202	+	1.27232i
$288$	2.51592e17			0.0902096
$289$	1.04323e18	+	1.80694e18i	0.364459	+	0.631261i
$290$	1.08361e18	−	1.87687e18i	0.368883	−	0.638925i
$291$	1.56979e18	−	2.71895e18i	0.520767	−	0.901994i
$292$	1.09886e18	+	1.90329e18i	0.355281	+	0.615365i
$293$	−4.18073e17			−0.131748			−0.0658741	−	0.997828i	$-0.520984\pi$
$293$	−4.18073e17			−0.131748			−0.0658741	+	0.997828i	$0.520984\pi$
$294$	1.09082e18	−	1.18530e18i	0.335081	−	0.364101i
$295$	4.86640e17			0.145728
$296$	−3.46168e17	−	5.99580e17i	−0.101065	−	0.175049i
$297$	4.98556e17	−	8.63524e17i	0.141919	−	0.245811i
$298$	1.88242e18	−	3.26044e18i	0.522509	−	0.905011i
$299$	5.75204e17	+	9.96283e17i	0.155700	+	0.269680i
$300$	−7.76438e17			−0.204973
$301$	1.97110e18	+	4.49276e18i	0.507528	+	1.15682i
$302$	−2.66062e18			−0.668238
$303$	8.79580e16	+	1.52348e17i	0.0215504	+	0.0373264i
$304$	−1.42699e17	+	2.47162e17i	−0.0341090	+	0.0590785i
$305$	8.22886e17	−	1.42528e18i	0.191907	−	0.332393i
$306$	4.12804e17	+	7.14998e17i	0.0939363	+	0.162702i
$307$	−4.73172e18			−1.05071			−0.525353	−	0.850884i	$-0.676067\pi$
$307$	−4.73172e18			−1.05071			−0.525353	+	0.850884i	$0.676067\pi$
$308$	3.66939e17	−	4.99315e17i	0.0795176	−	0.108204i
$309$	4.67002e18			0.987712
$310$	−5.44270e17	−	9.42704e17i	−0.112357	−	0.194609i
$311$	1.99278e18	−	3.45160e18i	0.401566	−	0.695533i	−0.592349	−	0.805682i	$-0.701799\pi$
$311$	1.99278e18	−	3.45160e18i	0.401566	−	0.695533i	0.993915	+	0.110148i	$0.0351326\pi$
$312$	−4.09027e17	+	7.08455e17i	−0.0804622	+	0.139365i
$313$	−2.46052e17	−	4.26175e17i	−0.0472546	−	0.0818474i	0.841431	−	0.540365i	$-0.181714\pi$
$313$	−2.46052e17	−	4.26175e17i	−0.0472546	−	0.0818474i	−0.888685	+	0.458518i	$0.848381\pi$
$314$	−2.52399e18			−0.473278
$315$	−1.78284e18	−	1.97192e17i	−0.326424	−	0.0361045i
$316$	−2.97098e18			−0.531187
$317$	−1.37877e18	−	2.38810e18i	−0.240740	−	0.416973i	0.720186	−	0.693781i	$-0.244057\pi$
$317$	−1.37877e18	−	2.38810e18i	−0.240740	−	0.416973i	−0.960925	+	0.276808i	$0.910723\pi$
$318$	1.40699e18	−	2.43697e18i	0.239931	−	0.415573i
$319$	1.30702e18	−	2.26382e18i	0.217696	−	0.377061i
$320$	2.47229e17	+	4.28214e17i	0.0402231	+	0.0696684i
$321$	−5.80351e18			−0.922365
$322$	2.16710e18	+	2.39694e17i	0.336480	+	0.0372167i
$323$	−9.36544e17			−0.142072
$324$	3.86733e17	+	6.69841e17i	0.0573223	+	0.0992851i
$325$	−1.31541e18	+	2.27836e18i	−0.190518	+	0.329987i
$326$	−2.93706e18	+	5.08715e18i	−0.415701	+	0.720016i
$327$	−2.30503e18	−	3.99243e18i	−0.318837	−	0.552242i
$328$	−3.63355e18			−0.491221
$329$	−5.91742e18	+	8.05218e18i	−0.781922	+	1.06401i
$330$	6.62127e17			0.0855238
$331$	−6.50459e18	−	1.12663e19i	−0.821315	−	1.42256i	−0.904703	−	0.426042i	$-0.859908\pi$
$331$	−6.50459e18	−	1.12663e19i	−0.821315	−	1.42256i	0.0833883	−	0.996517i	$-0.473426\pi$
$332$	−4.44428e17	+	7.69772e17i	−0.0548613	+	0.0950225i
$333$	−1.20866e18	+	2.09346e18i	−0.145872	+	0.252657i
$334$	5.64160e18	+	9.77155e18i	0.665739	+	1.15309i
$335$	−7.20604e18			−0.831497
$336$	6.22899e17	+	1.41979e18i	0.0702867	+	0.160206i
$337$	1.43383e19			1.58225			0.791123	−	0.611657i	$-0.209497\pi$
$337$	1.43383e19			1.58225			0.791123	+	0.611657i	$0.209497\pi$
$338$	−1.88998e18	−	3.27355e18i	−0.203978	−	0.353300i
$339$	−3.24716e18	+	5.62425e18i	−0.342772	+	0.593699i
$340$	−8.11294e17	+	1.40520e18i	−0.0837695	+	0.145093i
$341$	−6.56481e17	−	1.13706e18i	−0.0663077	−	0.114848i
$342$	9.96476e17			0.0984625
$343$	−9.78466e18	−	3.35668e18i	−0.945888	−	0.324492i
$344$	−4.72209e18			−0.446628
$345$	1.16490e18	+	2.01766e18i	0.107806	+	0.186726i
$346$	7.10714e18	−	1.23099e19i	0.643612	−	1.11477i
$347$	8.32210e18	−	1.44143e19i	0.737500	−	1.27739i	−0.216118	−	0.976367i	$-0.569340\pi$
$347$	8.32210e18	−	1.44143e19i	0.737500	−	1.27739i	0.953618	−	0.301020i	$-0.0973270\pi$
$348$	3.27030e18	+	5.66432e18i	0.283624	+	0.491251i
$349$	1.05199e19			0.892940			0.446470	−	0.894799i	$-0.352681\pi$
$349$	1.05199e19			0.892940			0.446470	+	0.894799i	$0.352681\pi$
$350$	2.00322e18	+	4.56596e18i	0.166425	+	0.379334i
$351$	8.45346e18			0.687434
$352$	2.98200e17	+	5.16497e17i	0.0237376	+	0.0411148i
$353$	5.15733e18	−	8.93276e18i	0.401897	−	0.696106i	−0.592058	−	0.805895i	$-0.701684\pi$
$353$	5.15733e18	−	8.93276e18i	0.401897	−	0.696106i	0.993955	+	0.109790i	$0.0350177\pi$
$354$	−7.34329e17	+	1.27189e18i	−0.0560230	+	0.0970346i
$355$	−1.85072e18	−	3.20555e18i	−0.138239	−	0.239436i
$356$	−4.56307e17			−0.0333720
$357$	−3.01285e18	+	4.09976e18i	−0.215758	+	0.293594i
$358$	−1.36110e18			−0.0954478
$359$	1.01955e19	+	1.76592e19i	0.700166	+	1.21272i	0.968408	+	0.249372i	$0.0802241\pi$
$359$	1.01955e19	+	1.76592e19i	0.700166	+	1.21272i	−0.268242	+	0.963352i	$0.586443\pi$
$360$	8.63210e17	−	1.49512e18i	0.0580561	−	0.100556i
$361$	7.02538e18	−	1.21683e19i	0.462771	−	0.801542i
$362$	5.93795e18	+	1.02848e19i	0.383109	+	0.663564i
$363$	−1.02743e19			−0.649312
$364$	5.22147e18	+	5.77526e17i	0.323246	+	0.0357529i
$365$	1.50808e19			0.914592
$366$	2.48343e18	+	4.30143e18i	0.147552	+	0.255567i
$367$	−1.05143e18	+	1.82114e18i	−0.0612049	+	0.106010i	−0.895004	−	0.446058i	$-0.852828\pi$
$367$	−1.05143e18	+	1.82114e18i	−0.0612049	+	0.106010i	0.833799	+	0.552068i	$0.186161\pi$
$368$	−1.04926e18	+	1.81737e18i	−0.0598446	+	0.103654i
$369$	6.34333e18	+	1.09870e19i	0.354503	+	0.614017i
$370$	−4.75080e18			−0.260168
$371$	−1.79610e19	−	1.98660e18i	−0.963890	−	0.106612i
$372$	3.28517e18			0.172777
$373$	1.29241e18	+	2.23852e18i	0.0666168	+	0.115384i	0.897410	−	0.441197i	$-0.145446\pi$
$373$	1.29241e18	+	2.23852e18i	0.0666168	+	0.115384i	−0.830793	+	0.556581i	$0.812113\pi$
$374$	−9.78555e17	+	1.69491e18i	−0.0494366	+	0.0856267i
$375$	−7.21136e18	+	1.24904e19i	−0.357094	+	0.618505i
$376$	−4.80891e18	−	8.32927e18i	−0.233420	−	0.404295i
$377$	2.21616e19			1.05449
$378$	9.48751e18	−	1.29102e19i	0.442552	−	0.602205i
$379$	−1.25116e19			−0.572160			−0.286080	−	0.958206i	$-0.592352\pi$
$379$	−1.25116e19			−0.572160			−0.286080	+	0.958206i	$0.592352\pi$
$380$	9.79199e17	+	1.69602e18i	0.0439030	+	0.0760422i
$381$	−3.15257e18	+	5.46040e18i	−0.138588	+	0.240042i
$382$	−1.02216e19	+	1.77044e19i	−0.440601	+	0.763143i
$383$	−9.21208e18	−	1.59558e19i	−0.389374	−	0.674415i	0.602992	−	0.797748i	$-0.293975\pi$
$383$	−9.21208e18	−	1.59558e19i	−0.389374	−	0.674415i	−0.992365	+	0.123332i	$0.960642\pi$
$384$	−1.49226e18			−0.0618528
$385$	−1.70829e18	−	3.89374e18i	−0.0694396	−	0.158275i
$386$	−2.90274e19			−1.15719
$387$	8.24367e18	+	1.42784e19i	0.322321	+	0.558276i
$388$	9.70258e18	−	1.68054e19i	0.372091	−	0.644481i
$389$	−4.29488e17	+	7.43895e17i	−0.0161558	+	0.0279827i	−0.873990	−	0.485943i	$-0.838476\pi$
$389$	−4.29488e17	+	7.43895e17i	−0.0161558	+	0.0279827i	0.857834	+	0.513926i	$0.171809\pi$
$390$	2.80674e18	+	4.86141e18i	0.103566	+	0.179382i
$391$	−6.88639e18			−0.249268
$392$	6.74219e18	−	7.32612e18i	0.239417	−	0.260153i
$393$	−1.25765e19			−0.438144
$394$	−1.88301e19	−	3.26147e19i	−0.643622	−	1.11479i
$395$	−1.01934e19	+	1.76556e19i	−0.341855	+	0.592111i
$396$	1.04118e18	−	1.80337e18i	0.0342618	−	0.0593432i
$397$	−1.78349e19	−	3.08909e19i	−0.575892	−	0.997474i	−0.995944	−	0.0899744i	$-0.971321\pi$
$397$	−1.78349e19	−	3.08909e19i	−0.575892	−	0.997474i	0.420052	−	0.907500i	$-0.362012\pi$
$398$	−2.61198e19			−0.827651
$399$	2.46711e18	+	5.62333e18i	0.0767170	+	0.174862i
$400$	−4.79903e18			−0.146455
$401$	7.55626e18	+	1.30878e19i	0.226321	+	0.391999i	0.956715	−	0.291027i	$-0.0939969\pi$
$401$	7.55626e18	+	1.30878e19i	0.226321	+	0.391999i	−0.730394	+	0.683026i	$0.760664\pi$
$402$	1.08738e19	−	1.88339e19i	0.319657	−	0.553663i
$403$	5.56561e18	−	9.63992e18i	0.160592	−	0.278154i
$404$	5.43653e17	+	9.41635e17i	0.0153979	+	0.0266700i
$405$	5.30752e18			0.147563
$406$	2.48725e19	−	3.38455e19i	0.678851	−	0.923752i
$407$	−5.73026e18			−0.153538
$408$	−2.44845e18	−	4.24084e18i	−0.0644080	−	0.111558i
$409$	−2.06423e19	+	3.57535e19i	−0.533129	+	0.923407i	0.466122	+	0.884721i	$0.345651\pi$
$409$	−2.06423e19	+	3.57535e19i	−0.533129	+	0.923407i	−0.999251	+	0.0386868i	$0.987683\pi$
$410$	−1.24667e19	+	2.15930e19i	−0.316135	+	0.547562i
$411$	−1.16019e19	−	2.00950e19i	−0.288878	−	0.500351i
$412$	2.88646e19			0.705727
$413$	9.37415e18	+	1.03684e18i	0.225064	+	0.0248934i
$414$	7.32707e18			0.172754
$415$	3.04966e18	+	5.28217e18i	0.0706140	+	0.122307i
$416$	−2.52812e18	+	4.37884e18i	−0.0574908	+	0.0995769i
$417$	−1.77004e19	+	3.06580e19i	−0.395332	+	0.684736i
$418$	1.18108e18	+	2.04568e18i	0.0259093	+	0.0448763i
$419$	4.33332e19			0.933718			0.466859	−	0.884332i	$-0.345386\pi$
$419$	4.33332e19			0.933718			0.466859	+	0.884332i	$0.345386\pi$
$420$	1.05745e19	+	1.16960e18i	0.223815	+	0.0247553i
$421$	−5.29267e18			−0.110042			−0.0550211	−	0.998485i	$-0.517523\pi$
$421$	−5.29267e18			−0.110042			−0.0550211	+	0.998485i	$0.517523\pi$
$422$	1.03125e19	+	1.78618e19i	0.210630	+	0.364822i
$423$	−1.67905e19	+	2.90819e19i	−0.336907	+	0.583540i
$424$	8.69634e18	−	1.50625e19i	0.171432	−	0.296930i
$425$	−7.87410e18	−	1.36383e19i	−0.152505	−	0.264146i
$426$	1.11708e19			0.212575
$427$	1.88880e19	−	2.57020e19i	0.353164	−	0.480571i
$428$	−3.58705e19			−0.659036
$429$	3.38539e18	+	5.86368e18i	0.0611195	+	0.105862i
$430$	−1.62015e19	+	2.80618e19i	−0.287436	+	0.497853i
$431$	4.58602e18	−	7.94321e18i	0.0799569	−	0.138489i	−0.823274	−	0.567644i	$-0.807855\pi$
$431$	4.58602e18	−	7.94321e18i	0.0799569	−	0.138489i	0.903231	+	0.429154i	$0.141188\pi$
$432$	7.71021e18	+	1.33545e19i	0.132111	+	0.228822i
$433$	6.69173e19			1.12688			0.563442	−	0.826156i	$-0.309477\pi$
$433$	6.69173e19			1.12688			0.563442	+	0.826156i	$0.309477\pi$
$434$	−8.47577e18	−	1.93190e19i	−0.140283	−	0.319750i
$435$	4.48815e19			0.730126
$436$	−1.42470e19	−	2.46765e19i	−0.227811	−	0.394580i
$437$	−4.15580e18	+	7.19805e18i	−0.0653196	+	0.113137i
$438$	−2.27566e19	+	3.94155e19i	−0.351602	+	0.608992i
$439$	−4.66123e19	−	8.07349e19i	−0.707973	−	1.22625i	−0.965608	−	0.260003i	$-0.916276\pi$
$439$	−4.66123e19	−	8.07349e19i	−0.707973	−	1.22625i	0.257634	−	0.966242i	$-0.417057\pi$
$440$	4.09249e18			0.0611073
$441$	−3.39227e19	−	7.59704e18i	−0.497967	−	0.111521i
$442$	−1.65923e19			−0.239463
$443$	3.72588e19	+	6.45342e19i	0.528690	+	0.915718i	0.999440	+	0.0334515i	$0.0106499\pi$
$443$	3.72588e19	+	6.45342e19i	0.528690	+	0.915718i	−0.470750	+	0.882266i	$0.656017\pi$
$444$	7.16886e18	−	1.24168e19i	0.100018	−	0.173236i
$445$	−1.56559e18	+	2.71168e18i	−0.0214772	+	0.0371996i
$446$	4.76799e19	+	8.25840e19i	0.643167	+	1.11400i
$447$	7.79667e19			1.03420
$448$	3.85003e18	+	8.77545e18i	0.0502203	+	0.114468i
$449$	4.31071e19			0.552969			0.276485	−	0.961018i	$-0.410831\pi$
$449$	4.31071e19			0.552969			0.276485	+	0.961018i	$0.410831\pi$
$450$	8.37798e18	+	1.45111e19i	0.105693	+	0.183065i
$451$	−1.50369e19	+	2.60447e19i	−0.186567	+	0.323143i
$452$	−2.00701e19	+	3.47625e19i	−0.244913	+	0.424202i
$453$	−2.75497e19	−	4.77174e19i	−0.330659	−	0.572718i
$454$	5.95840e19			0.703414
$455$	2.13469e19	−	2.90480e19i	0.247885	−	0.337311i
$456$	−5.91036e18			−0.0675115
$457$	−4.21778e19	−	7.30542e19i	−0.473928	−	0.820868i	0.525626	−	0.850716i	$-0.323831\pi$
$457$	−4.21778e19	−	7.30542e19i	−0.473928	−	0.820868i	−0.999554	+	0.0298476i	$0.990498\pi$
$458$	−5.51512e18	+	9.55247e18i	−0.0609627	+	0.105590i
$459$	−2.53014e19	+	4.38232e19i	−0.275137	+	0.476551i
$460$	7.20003e18	+	1.24708e19i	0.0770283	+	0.133417i
$461$	1.18686e20			1.24923			0.624615	−	0.780932i	$-0.285256\pi$
$461$	1.18686e20			1.24923			0.624615	+	0.780932i	$0.285256\pi$
$462$	1.27546e19	+	1.41073e18i	0.132084	+	0.0146093i
$463$	−1.01731e20			−1.03657			−0.518283	−	0.855209i	$-0.673429\pi$
$463$	−1.01731e20			−1.03657			−0.518283	+	0.855209i	$0.673429\pi$
$464$	2.02131e19	+	3.50102e19i	0.202651	+	0.351002i
$465$	1.12714e19	−	1.95226e19i	0.111194	−	0.192593i
$466$	3.55505e19	−	6.15752e19i	0.345105	−	0.597739i
$467$	−3.25904e19	−	5.64482e19i	−0.311324	−	0.539229i	0.667325	−	0.744767i	$-0.267439\pi$
$467$	−3.25904e19	−	5.64482e19i	−0.311324	−	0.539229i	−0.978649	+	0.205537i	$0.934106\pi$
$468$	1.76541e19			0.165959
$469$	−1.38810e20	−	1.53532e19i	−1.28418	−	0.142038i
$470$	−6.59974e19			−0.600887
$471$	−2.61350e19	−	4.52671e19i	−0.234188	−	0.405626i
$472$	−4.53876e18	+	7.86136e18i	−0.0400287	+	0.0693318i
$473$	−1.95417e19	+	3.38472e19i	−0.169630	+	0.293808i
$474$	−3.07634e19	−	5.32837e19i	−0.262843	−	0.455257i
$475$	−1.90074e19			−0.159853
$476$	−1.86219e19	+	2.53399e19i	−0.154160	+	0.209774i
$477$	−6.07272e19			−0.494875
$478$	1.61064e19	+	2.78970e19i	0.129208	+	0.223794i
$479$	2.87363e19	−	4.97727e19i	0.226942	−	0.393075i	−0.729958	−	0.683492i	$-0.760461\pi$
$479$	2.87363e19	−	4.97727e19i	0.226942	−	0.393075i	0.956900	+	0.290417i	$0.0937939\pi$
$480$	−5.11993e18	+	8.86797e18i	−0.0398065	+	0.0689469i
$481$	−2.42904e19	−	4.20722e19i	−0.185929	−	0.322038i
$482$	−2.94912e19			−0.222249
$483$	1.81406e19	+	4.13482e19i	0.134601	+	0.306799i
$484$	−6.35038e19			−0.463938
$485$	−6.65790e19	−	1.15318e20i	−0.478933	−	0.829536i
$486$	4.47450e19	−	7.75006e19i	0.316937	−	0.548951i
$487$	−1.40869e19	+	2.43992e19i	−0.0982536	+	0.170180i	−0.910962	−	0.412491i	$-0.864659\pi$
$487$	−1.40869e19	+	2.43992e19i	−0.0982536	+	0.170180i	0.812708	+	0.582671i	$0.197992\pi$
$488$	1.53497e19	+	2.65864e19i	0.105427	+	0.182604i
$489$	−1.21649e20			−0.822793
$490$	−2.04042e19	−	6.52024e19i	−0.135909	−	0.434303i
$491$	2.39931e20			1.57389			0.786946	−	0.617021i	$-0.211661\pi$
$491$	2.39931e20			1.57389			0.786946	+	0.617021i	$0.211661\pi$
$492$	−3.76240e19	−	6.51666e19i	−0.243067	−	0.421005i
$493$	−6.63302e19	+	1.14887e20i	−0.422046	+	0.731005i
$494$	−1.00131e19	+	1.73432e19i	−0.0627504	+	0.108687i
$495$	−7.14454e18	−	1.23747e19i	−0.0440997	−	0.0763829i
$496$	2.03051e19			0.123450
$497$	−2.88208e19	−	6.56918e19i	−0.172597	−	0.393403i
$498$	−1.84075e19			−0.108586
$499$	1.36711e20	+	2.36791e20i	0.794420	+	1.37598i	0.923207	+	0.384303i	$0.125558\pi$
$499$	1.36711e20	+	2.36791e20i	0.794420	+	1.37598i	−0.128787	+	0.991672i	$0.541108\pi$
$500$	−4.45722e19	+	7.72013e19i	−0.255146	+	0.441926i
$501$	−1.16833e20	+	2.02361e20i	−0.658845	+	1.14115i
$502$	4.09050e19	+	7.08496e19i	0.227247	+	0.393604i
$503$	−2.07497e20			−1.13567			−0.567835	−	0.823143i	$-0.692219\pi$
$503$	−2.07497e20			−1.13567			−0.567835	+	0.823143i	$0.692219\pi$
$504$	1.98136e19	−	2.69615e19i	0.106840	−	0.145383i
$505$	7.46109e18			0.0396385
$506$	8.68443e18	+	1.50419e19i	0.0454582	+	0.0787360i
$507$	3.91400e19	−	6.77925e19i	0.201865	−	0.349641i
$508$	−1.94855e19	+	3.37498e19i	−0.0990222	+	0.171512i
$509$	8.81830e19	+	1.52737e20i	0.441572	+	0.764825i	0.997806	−	0.0662006i	$-0.0210877\pi$
$509$	8.81830e19	+	1.52737e20i	0.441572	+	0.764825i	−0.556235	+	0.831025i	$0.687754\pi$
$510$	−3.36025e19			−0.165804
$511$	2.90501e20	+	3.21312e19i	1.41251	+	0.156232i
$512$	−9.22337e18			−0.0441942
$513$	3.05377e19	+	5.28929e19i	0.144197	+	0.249757i
$514$	1.26345e20	−	2.18836e20i	0.587942	−	1.01835i
$515$	9.90344e19	−	1.71533e20i	0.454184	−	0.786670i
$516$	−4.88953e19	−	8.46892e19i	−0.221001	−	0.382785i
$517$	−7.96038e19			−0.354613
$518$	−9.15149e19	−	1.01221e19i	−0.401808	−	0.0444423i
$519$	2.94366e20			1.27389
$520$	1.73480e19	+	3.00476e19i	0.0739986	+	0.128169i
$521$	1.98017e20	−	3.42975e20i	0.832566	−	1.44205i	−0.0634310	−	0.997986i	$-0.520204\pi$
$521$	1.98017e20	−	3.42975e20i	0.832566	−	1.44205i	0.895997	−	0.444060i	$-0.146462\pi$
$522$	7.05748e19	−	1.22239e20i	0.292497	−	0.506619i
$523$	1.92780e20	+	3.33905e20i	0.787589	+	1.36414i	0.927440	+	0.373972i	$0.122004\pi$
$523$	1.92780e20	+	3.33905e20i	0.787589	+	1.36414i	−0.139850	+	0.990173i	$0.544662\pi$
$524$	−7.77334e19			−0.313057
$525$	−6.11467e19	+	8.32058e19i	−0.242761	+	0.330338i
$526$	2.62718e20			1.02825
$527$	3.33159e19	+	5.77049e19i	0.128550	+	0.222655i
$528$	−6.17548e18	+	1.06963e19i	−0.0234918	+	0.0406890i
$529$	1.02760e20	−	1.77986e20i	0.385396	−	0.667525i
$530$	−5.96743e19	−	1.03359e20i	−0.220657	−	0.382189i
$531$	3.16945e19			0.115551
$532$	1.52488e19	+	3.47568e19i	0.0548148	+	0.124940i
$533$	−2.54964e20			−0.903702
$534$	−4.72488e18	−	8.18373e18i	−0.0165132	−	0.0286017i
$535$	−1.23071e20	+	2.13166e20i	−0.424135	+	0.734623i
$536$	6.72088e19	−	1.16409e20i	0.228397	−	0.395595i
$537$	−1.40936e19	−	2.44108e19i	−0.0472297	−	0.0818042i
$538$	−1.78593e19			−0.0590197
$539$	−2.46109e19	−	7.86450e19i	−0.0802068	−	0.256304i
$540$	1.05815e20			0.340089
$541$	9.82497e19	+	1.70174e20i	0.311424	+	0.539402i	0.978671	−	0.205435i	$-0.0658608\pi$
$541$	9.82497e19	+	1.70174e20i	0.311424	+	0.539402i	−0.667247	+	0.744837i	$0.732527\pi$
$542$	−7.74895e19	+	1.34216e20i	−0.242241	+	0.419574i
$543$	−1.22970e20	+	2.12991e20i	−0.379142	+	0.656692i
$544$	−1.51334e19	−	2.62119e19i	−0.0460199	−	0.0797088i
$545$	−1.95526e20			−0.586448
$546$	4.37085e19	+	9.96256e19i	0.129307	+	0.294731i
$547$	−3.49320e20			−1.01934			−0.509670	−	0.860370i	$-0.670232\pi$
$547$	−3.49320e20			−1.01934			−0.509670	+	0.860370i	$0.670232\pi$
$548$	−7.17090e19	−	1.24204e20i	−0.206405	−	0.357504i
$549$	5.35939e19	−	9.28274e19i	0.152168	−	0.263563i
$550$	−1.98601e19	+	3.43987e19i	−0.0556238	+	0.0963432i
$551$	8.00579e19	+	1.38664e20i	0.221191	+	0.383114i
$552$	−4.34588e19			−0.118450
$553$	−2.33974e20	+	3.18381e20i	−0.629112	+	0.856069i
$554$	−2.37199e18			−0.00629200
$555$	−4.91927e19	−	8.52042e19i	−0.128737	−	0.222979i
$556$	−1.09403e20	+	1.89492e20i	−0.282467	+	0.489248i
$557$	3.52391e20	−	6.10359e20i	0.897658	−	1.55479i	0.0671768	−	0.997741i	$-0.478601\pi$
$557$	3.52391e20	−	6.10359e20i	0.897658	−	1.55479i	0.830481	−	0.557047i	$-0.188066\pi$
$558$	−3.54479e19	−	6.13976e19i	−0.0890911	−	0.154310i
$559$	−3.31346e20			−0.821663
$560$	6.53590e19	+	7.22909e18i	0.159917	+	0.0176878i
$561$	−4.05302e19			−0.0978492
$562$	7.23498e19	+	1.25314e20i	0.172351	+	0.298522i
$563$	−4.05091e19	+	7.01639e19i	−0.0952226	+	0.164930i	−0.909701	−	0.415263i	$-0.863690\pi$
$563$	−4.05091e19	+	7.01639e19i	−0.0952226	+	0.164930i	0.814479	+	0.580193i	$0.197023\pi$
$564$	9.95886e19	−	1.72493e20i	0.231002	−	0.400108i
$565$	1.37721e20	+	2.38540e20i	0.315237	+	0.546006i
$566$	−5.34874e20			−1.20817
$567$	1.02239e20	+	1.13082e19i	0.227899	+	0.0252070i
$568$	6.90449e19			0.151886
$569$	−4.02778e20	−	6.97633e20i	−0.874428	−	1.51455i	−0.857371	−	0.514699i	$-0.827904\pi$
$569$	−4.02778e20	−	6.97633e20i	−0.874428	−	1.51455i	−0.0170574	−	0.999855i	$-0.505430\pi$
$570$	−2.02784e19	+	3.51233e19i	−0.0434483	+	0.0752547i
$571$	2.18892e20	−	3.79131e20i	0.462869	−	0.801713i	−0.536233	−	0.844070i	$-0.680153\pi$
$571$	2.18892e20	−	3.79131e20i	0.462869	−	0.801713i	0.999103	+	0.0423568i	$0.0134866\pi$
$572$	2.09245e19	+	3.62424e19i	0.0436702	+	0.0756391i
$573$	−4.23364e20			−0.872076
$574$	−2.86152e20	+	3.89384e20i	−0.581779	+	0.791661i
$575$	−1.39761e20			−0.280465
$576$	1.61019e19	+	2.78892e19i	0.0318939	+	0.0552418i
$577$	8.52466e19	−	1.47651e20i	0.166670	−	0.288681i	−0.770577	−	0.637347i	$-0.780032\pi$
$577$	8.52466e19	−	1.47651e20i	0.166670	−	0.288681i	0.937247	+	0.348666i	$0.113365\pi$
$578$	−1.33534e20	+	2.31288e20i	−0.257711	+	0.446369i
$579$	−3.00567e20	−	5.20598e20i	−0.572602	−	0.991775i
$580$	2.77405e20			0.521680
$581$	4.74915e19	+	1.08248e20i	0.0881648	+	0.200955i
$582$	4.01865e20			0.736475
$583$	−7.19771e19	−	1.24668e20i	−0.130221	−	0.225549i
$584$	−1.40654e20	+	2.43621e20i	−0.251222	+	0.435129i
$585$	6.05710e19	−	1.04912e20i	0.106806	−	0.184994i
$586$	−2.67567e19	−	4.63439e19i	−0.0465800	−	0.0806790i
$587$	−3.75867e19			−0.0646023			−0.0323012	−	0.999478i	$-0.510284\pi$
$587$	−3.75867e19			−0.0646023			−0.0323012	+	0.999478i	$0.510284\pi$
$588$	2.01204e20	+	4.50600e19i	0.341435	+	0.0764648i
$589$	8.04220e19			0.134744
$590$	3.11449e19	+	5.39446e19i	0.0515225	+	0.0892397i
$591$	3.89956e20	−	6.75424e20i	0.636956	−	1.10324i
$592$	4.43095e19	−	7.67463e19i	0.0714634	−	0.123778i
$593$	4.88963e20	+	8.46909e20i	0.778693	+	1.34874i	0.932696	+	0.360665i	$0.117450\pi$
$593$	4.88963e20	+	8.46909e20i	0.778693	+	1.34874i	−0.154003	+	0.988070i	$0.549217\pi$
$594$	1.27630e20			0.200704
$595$	8.66947e19	+	1.97605e20i	0.134622	+	0.306846i
$596$	4.81898e20			0.738939
$597$	−2.70460e20	−	4.68451e20i	−0.409540	−	0.709344i
$598$	−7.36262e19	+	1.27524e20i	−0.110096	+	0.190693i
$599$	2.59424e20	−	4.49336e20i	0.383097	−	0.663544i	−0.608406	−	0.793626i	$-0.708191\pi$
$599$	2.59424e20	−	4.49336e20i	0.383097	−	0.663544i	0.991503	+	0.130082i	$0.0415240\pi$
$600$	−4.96920e19	−	8.60691e19i	−0.0724690	−	0.125520i
$601$	8.84945e20			1.27455			0.637276	−	0.770636i	$-0.280061\pi$
$601$	8.84945e20			1.27455			0.637276	+	0.770636i	$0.280061\pi$
$602$	−3.71878e20	+	5.06036e20i	−0.528965	+	0.719793i
$603$	−4.69324e20			−0.659315
$604$	−1.70280e20	−	2.94933e20i	−0.236258	−	0.409210i
$605$	−2.17881e20	+	3.77382e20i	−0.298576	+	0.517149i
$606$	−1.12586e19	+	1.95005e19i	−0.0152385	+	0.0263938i
$607$	5.02265e20	+	8.69948e20i	0.671456	+	1.16300i	0.977491	+	0.210975i	$0.0676640\pi$
$607$	5.02265e20	+	8.69948e20i	0.671456	+	1.16300i	−0.306036	+	0.952020i	$0.599003\pi$
$608$	−3.65309e19			−0.0482374
$609$	8.64554e20	+	9.56248e19i	1.12762	+	0.124721i
$610$	2.10659e20			0.271397
$611$	−3.37438e20	−	5.84461e20i	−0.429423	−	0.743783i
$612$	−5.28389e19	+	9.15197e19i	−0.0664230	+	0.115048i
$613$	−7.37934e20	+	1.27814e21i	−0.916356	+	1.58718i	−0.111452	+	0.993770i	$0.535550\pi$
$613$	−7.37934e20	+	1.27814e21i	−0.916356	+	1.58718i	−0.804904	+	0.593405i	$0.797783\pi$
$614$	−3.02830e20	−	5.24517e20i	−0.371481	−	0.643424i
$615$	−5.16351e20			−0.625722
$616$	7.88338e19	+	8.71949e18i	0.0943750	+	0.0104384i
$617$	7.44699e20			0.880729			0.440364	−	0.897819i	$-0.354849\pi$
$617$	7.44699e20			0.880729			0.440364	+	0.897819i	$0.354849\pi$
$618$	2.98882e20	+	5.17678e20i	0.349209	+	0.604848i
$619$	−7.42649e19	+	1.28631e20i	−0.0857243	+	0.148479i	−0.905700	−	0.423920i	$-0.860654\pi$
$619$	−7.42649e19	+	1.28631e20i	−0.0857243	+	0.148479i	0.819975	+	0.572399i	$0.193987\pi$
$620$	6.96666e19	−	1.20666e20i	0.0794487	−	0.137609i
$621$	2.24543e20	+	3.88920e20i	0.252996	+	0.438201i
$622$	5.10153e20			0.567900
$623$	−3.59355e19	+	4.88995e19i	−0.0395242	+	0.0537829i
$624$	−1.04711e20			−0.113791
$625$	3.30610e19	+	5.72633e19i	0.0354990	+	0.0614860i
$626$	3.14947e19	−	5.45504e19i	0.0334141	−	0.0578749i
$627$	−2.44592e19	+	4.23645e19i	−0.0256410	+	0.0444115i
$628$	−1.61536e20	−	2.79788e20i	−0.167329	−	0.289822i
$629$	2.90807e20			0.297663
$630$	−9.22425e19	−	2.10250e20i	−0.0932990	−	0.212658i
$631$	−4.46725e20			−0.446499			−0.223250	−	0.974761i	$-0.571666\pi$
$631$	−4.46725e20			−0.446499			−0.223250	+	0.974761i	$0.571666\pi$
$632$	−1.90143e20	−	3.29337e20i	−0.187803	−	0.325284i
$633$	−2.13564e20	+	3.69903e20i	−0.208449	+	0.361044i
$634$	1.76483e20	−	3.05677e20i	0.170229	−	0.294844i
$635$	1.33709e20	+	2.31591e20i	0.127455	+	0.220759i
$636$	3.60189e20			0.339314
$637$	4.73096e20	−	5.14070e20i	0.440457	−	0.478604i
$638$	3.34596e20			0.307869
$639$	−1.20536e20	−	2.08775e20i	−0.109613	−	0.189855i
$640$	−3.16454e19	+	5.48114e19i	−0.0284420	+	0.0492630i
$641$	2.43408e20	−	4.21595e20i	0.216222	−	0.374507i	−0.737428	−	0.675426i	$-0.763960\pi$
$641$	2.43408e20	−	4.21595e20i	0.216222	−	0.374507i	0.953650	+	0.300919i	$0.0972933\pi$
$642$	−3.71425e20	−	6.43326e20i	−0.326105	−	0.564831i
$643$	−1.16641e21			−1.01220			−0.506102	−	0.862474i	$-0.668914\pi$
$643$	−1.16641e21			−1.01220			−0.506102	+	0.862474i	$0.668914\pi$
$644$	1.12124e20	+	2.55566e20i	0.0961733	+	0.219209i
$645$	−6.71039e20			−0.568918
$646$	−5.99388e19	−	1.03817e20i	−0.0502301	−	0.0870011i
$647$	1.03353e20	−	1.79012e20i	0.0856129	−	0.148286i	−0.820039	−	0.572307i	$-0.806049\pi$
$647$	1.03353e20	−	1.79012e20i	0.0856129	−	0.148286i	0.905652	+	0.424021i	$0.139382\pi$
$648$	−4.95018e19	+	8.57397e19i	−0.0405330	+	0.0702052i
$649$	3.75660e19	+	6.50662e19i	0.0304060	+	0.0526648i
$650$	−3.36745e20			−0.269433
$651$	2.58717e20	−	3.52050e20i	0.204629	−	0.278450i
$652$	−7.51889e20			−0.587891
$653$	1.11162e20	+	1.92539e20i	0.0859228	+	0.148823i	0.905784	−	0.423740i	$-0.139283\pi$
$653$	1.11162e20	+	1.92539e20i	0.0859228	+	0.148823i	−0.819861	+	0.572562i	$0.805950\pi$
$654$	2.95044e20	−	5.11031e20i	0.225452	−	0.390494i
$655$	−2.66703e20	+	4.61944e20i	−0.201474	+	0.348963i
$656$	−2.32547e20	−	4.02783e20i	−0.173673	−	0.300810i
$657$	9.82200e20			0.725203
$658$	−1.27131e21	−	1.40614e20i	−0.928019	−	0.102644i
$659$	−1.06996e21			−0.772198			−0.386099	−	0.922457i	$-0.626178\pi$
$659$	−1.06996e21			−0.772198			−0.386099	+	0.922457i	$0.626178\pi$
$660$	4.23761e19	+	7.33976e19i	0.0302372	+	0.0523724i
$661$	7.41445e20	−	1.28422e21i	0.523080	−	0.906001i	−0.476559	−	0.879142i	$-0.658116\pi$
$661$	7.41445e20	−	1.28422e21i	0.523080	−	0.906001i	0.999639	−	0.0268585i	$-0.00855036\pi$
$662$	8.32587e20	−	1.44208e21i	0.580757	−	1.00590i
$663$	−1.71806e20	−	2.97578e20i	−0.118492	−	0.205234i
$664$	−1.13774e20			−0.0775855
$665$	2.58866e20	+	2.86322e19i	0.174547	+	0.0193060i
$666$	−3.09416e20			−0.206294
$667$	5.88664e20	+	1.01960e21i	0.388082	+	0.672178i
$668$	−7.22125e20	+	1.25076e21i	−0.470749	+	0.815361i
$669$	−9.87413e20	+	1.71025e21i	−0.636507	+	1.10246i
$670$	−4.61187e20	−	7.98799e20i	−0.293979	−	0.509186i
$671$	2.54090e20			0.160165
$672$	−1.17519e20	+	1.59915e20i	−0.0732555	+	0.0996829i
$673$	−5.22502e20			−0.322089			−0.161044	−	0.986947i	$-0.551486\pi$
$673$	−5.22502e20			−0.322089			−0.161044	+	0.986947i	$0.551486\pi$
$674$	9.17652e20	+	1.58942e21i	0.559408	+	0.968924i
$675$	−5.13499e20	+	8.89406e20i	−0.309572	+	0.536194i
$676$	2.41918e20	−	4.19014e20i	0.144234	−	0.249821i
$677$	3.10568e20	+	5.37919e20i	0.183122	+	0.317177i	0.942942	−	0.332956i	$-0.108046\pi$
$677$	3.10568e20	+	5.37919e20i	0.183122	+	0.317177i	−0.759820	+	0.650134i	$0.774713\pi$
$678$	−8.31273e20			−0.484753
$679$	−1.03682e21	−	2.36323e21i	−0.597969	−	1.36296i
$680$	−2.07691e20			−0.118468
$681$	6.16969e20	+	1.06862e21i	0.348065	+	0.602866i
$682$	8.40295e19	−	1.45543e20i	0.0468866	−	0.0812101i
$683$	−9.52109e20	+	1.64910e21i	−0.525450	+	0.910106i	0.474111	+	0.880465i	$0.342770\pi$
$683$	−9.52109e20	+	1.64910e21i	−0.525450	+	0.910106i	−0.999561	+	0.0296407i	$0.990564\pi$
$684$	6.37745e19	+	1.10461e20i	0.0348118	+	0.0602957i
$685$	−9.84134e20			−0.531343
$686$	−2.54126e20	−	1.29947e21i	−0.135712	−	0.693961i
$687$	−2.28428e20			−0.120663
$688$	−3.02213e20	−	5.23449e20i	−0.157907	−	0.273502i
$689$	6.10218e20	−	1.05693e21i	0.315385	−	0.546263i
$690$	−1.49107e20	+	2.58261e20i	−0.0762306	+	0.132035i
$691$	−1.29297e21	−	2.23949e21i	−0.653888	−	1.13257i	−0.982171	−	0.187987i	$-0.939804\pi$
$691$	−1.29297e21	−	2.23949e21i	−0.653888	−	1.13257i	0.328284	−	0.944579i	$-0.393530\pi$
$692$	1.81943e21			0.910205
$693$	−1.11260e20	−	2.53597e20i	−0.0550604	−	0.125500i
$694$	2.13046e21			1.04298
$695$	7.50723e20	+	1.30029e21i	0.363575	+	0.629730i
$696$	−4.18598e20	+	7.25033e20i	−0.200552	+	0.347367i
$697$	7.63113e20	−	1.32175e21i	0.361695	−	0.626475i
$698$	6.73276e20	+	1.16615e21i	0.315702	+	0.546812i
$699$	1.47244e21			0.683062
$700$	−3.77937e20	+	5.14281e20i	−0.173454	+	0.236029i
$701$	1.19851e21			0.544198			0.272099	−	0.962269i	$-0.412282\pi$
$701$	1.19851e21			0.544198			0.272099	+	0.962269i	$0.412282\pi$
$702$	5.41021e20	+	9.37076e20i	0.243045	+	0.420966i
$703$	1.75496e20	−	3.03968e20i	0.0780014	−	0.135102i
$704$	−3.81696e19	+	6.61117e19i	−0.0167850	+	0.0290726i
$705$	−6.83377e20	−	1.18364e21i	−0.297332	−	0.514994i
$706$	1.32028e21			0.568368
$707$	1.43723e20	+	1.58966e19i	0.0612183	+	0.00677111i
$708$	−1.87988e20			−0.0792284
$709$	7.52905e20	+	1.30407e21i	0.313974	+	0.543818i	0.979219	−	0.202807i	$-0.0650063\pi$
$709$	7.52905e20	+	1.30407e21i	0.313974	+	0.543818i	−0.665245	+	0.746625i	$0.731673\pi$
$710$	2.36893e20	−	4.10310e20i	0.0977494	−	0.169307i
$711$	−6.63891e20	+	1.14989e21i	−0.271066	+	0.469500i
$712$	−2.92037e19	−	5.05822e19i	−0.0117988	−	0.0204361i
$713$	5.91341e20			0.236411
$714$	−6.47286e20	−	7.15937e19i	−0.256070	−	0.0283229i
$715$	2.87168e20			0.112419
$716$	−8.71101e19	−	1.50879e20i	−0.0337459	−	0.0584496i
$717$	−3.33550e20	+	5.77725e20i	−0.127869	+	0.221476i
$718$	−1.30503e21	+	2.26037e21i	−0.495092	+	0.857525i
$719$	9.70934e20	+	1.68171e21i	0.364521	+	0.631369i	0.988699	−	0.149913i	$-0.0478993\pi$
$719$	9.70934e20	+	1.68171e21i	0.364521	+	0.631369i	−0.624178	+	0.781282i	$0.714566\pi$
$720$	2.20982e20			0.0821037
$721$	2.27317e21	−	3.09323e21i	0.835829	−	1.13736i
$722$	1.79850e21			0.654456
$723$	−3.05369e20	−	5.28915e20i	−0.109973	−	0.190480i
$724$	−7.60058e20	+	1.31646e21i	−0.270899	+	0.469211i
$725$	−1.34619e21	+	2.33167e21i	−0.474867	+	0.822493i
$726$	−6.57557e20	−	1.13892e21i	−0.229567	−	0.397621i
$727$	4.32715e21			1.49518			0.747591	−	0.664159i	$-0.231210\pi$
$727$	4.32715e21			1.49518			0.747591	+	0.664159i	$0.231210\pi$
$728$	2.70155e20	+	6.15769e20i	0.0923905	+	0.210587i
$729$	2.53066e21			0.856598
$730$	9.65170e20	+	1.67172e21i	0.323357	+	0.560071i
$731$	9.91726e20	−	1.71772e21i	0.328860	−	0.569603i
$732$	−3.17880e20	+	5.50584e20i	−0.104335	+	0.180713i
$733$	−2.23515e21	−	3.87140e21i	−0.726152	−	1.25773i	−0.958498	−	0.285099i	$-0.907973\pi$
$733$	−2.23515e21	−	3.87140e21i	−0.726152	−	1.25773i	0.232346	−	0.972633i	$-0.425360\pi$
$734$	−2.69167e20			−0.0865569
$735$	9.58108e20	−	1.04109e21i	0.304972	−	0.331385i
$736$	−2.68611e20			−0.0846331
$737$	−5.56268e20	−	9.63485e20i	−0.173491	−	0.300496i
$738$	−8.11947e20	+	1.40633e21i	−0.250671	+	0.434176i
$739$	1.21450e20	−	2.10357e20i	0.0371161	−	0.0642870i	−0.846871	−	0.531799i	$-0.821516\pi$
$739$	1.21450e20	−	2.10357e20i	0.0371161	−	0.0642870i	0.883987	+	0.467512i	$0.154850\pi$
$740$	−3.04051e20	−	5.26633e20i	−0.0919833	−	0.159320i
$741$	−4.14727e20			−0.124201
$742$	−9.29290e20	−	2.11815e21i	−0.275500	−	0.627953i
$743$	−5.29587e21			−1.55425			−0.777125	−	0.629346i	$-0.783323\pi$
$743$	−5.29587e21			−1.55425			−0.777125	+	0.629346i	$0.783323\pi$
$744$	2.10251e20	+	3.64165e20i	0.0610859	+	0.105804i
$745$	1.65339e21	−	2.86376e21i	0.475558	−	0.823691i
$746$	−1.65428e20	+	2.86530e20i	−0.0471052	+	0.0815886i
$747$	1.98622e20	+	3.44024e20i	0.0559917	+	0.0969804i
$748$	−2.50510e20			−0.0699139
$749$	−2.82490e21	+	3.84401e21i	−0.780530	+	1.06211i
$750$	−1.84611e21			−0.505007
$751$	−1.56870e21	−	2.71707e21i	−0.424855	−	0.735871i	0.571552	−	0.820566i	$-0.306342\pi$
$751$	−1.56870e21	−	2.71707e21i	−0.424855	−	0.735871i	−0.996407	+	0.0846951i	$0.973008\pi$
$752$	6.15540e20	−	1.06615e21i	0.165053	−	0.285880i
$753$	−8.47110e20	+	1.46724e21i	−0.224894	+	0.389528i
$754$	1.41834e21	+	2.45665e21i	0.372818	+	0.645740i
$755$	−2.33692e21			−0.608193
$756$	2.03831e21	+	2.25450e20i	0.525240	+	0.0580946i
$757$	−5.00864e21			−1.27791			−0.638955	−	0.769244i	$-0.720633\pi$
$757$	−5.00864e21			−1.27791			−0.638955	+	0.769244i	$0.720633\pi$
$758$	−8.00740e20	−	1.38692e21i	−0.202289	−	0.350375i
$759$	−1.79848e20	+	3.11505e20i	−0.0449875	+	0.0779206i
$760$	−1.25337e20	+	2.17091e20i	−0.0310441	+	0.0537699i
$761$	−5.87976e20	−	1.01840e21i	−0.144203	−	0.249767i	0.784872	−	0.619658i	$-0.212729\pi$
$761$	−5.87976e20	−	1.01840e21i	−0.144203	−	0.249767i	−0.929075	+	0.369891i	$0.879395\pi$
$762$	−8.07057e20			−0.195994
$763$	−3.76641e21	−	4.16588e20i	−0.905720	−	0.100178i
$764$	−2.61674e21			−0.623103
$765$	3.62581e20	+	6.28008e20i	0.0854956	+	0.148083i
$766$	1.17915e21	−	2.04234e21i	0.275329	−	0.476884i
$767$	−3.18482e20	+	5.51628e20i	−0.0736411	+	0.127550i
$768$	−9.55044e19	−	1.65418e20i	−0.0218683	−	0.0378769i
$769$	3.42137e20			0.0775804			0.0387902	−	0.999247i	$-0.487650\pi$
$769$	3.42137e20			0.0775804			0.0387902	+	0.999247i	$0.487650\pi$
$770$	3.22296e20	−	4.38566e20i	0.0723725	−	0.0984815i
$771$	5.23301e21			1.16371
$772$	−1.85776e21	−	3.21773e21i	−0.409128	−	0.708630i
$773$	−3.35867e21	+	5.81739e21i	−0.732523	+	1.26877i	0.223278	+	0.974755i	$0.428324\pi$
$773$	−3.35867e21	+	5.81739e21i	−0.732523	+	1.26877i	−0.955801	+	0.294013i	$0.905009\pi$
$774$	−1.05519e21	+	1.82764e21i	−0.227915	+	0.394761i
$775$	6.76157e20	+	1.17114e21i	0.144639	+	0.250522i
$776$	2.48386e21			0.526216
$777$	−7.66064e20	−	1.74610e21i	−0.160734	−	0.366363i
$778$	−1.09949e20			−0.0228478
$779$	−9.21047e20	−	1.59530e21i	−0.189562	−	0.328331i
$780$	−3.59263e20	+	6.22261e20i	−0.0732323	+	0.126842i
$781$	2.85732e20	−	4.94903e20i	0.0576868	−	0.0999165i
$782$	−4.40729e20	−	7.63365e20i	−0.0881294	−	0.152645i
$783$	8.65127e21			1.71343
$784$	1.24361e21	+	2.78508e20i	0.243957	+	0.0546346i
$785$	−2.21691e21			−0.430751
$786$	−8.04899e20	−	1.39413e21i	−0.154907	−	0.268308i
$787$	−1.06923e21	+	1.85196e21i	−0.203826	+	0.353037i	−0.949758	−	0.312985i	$-0.898671\pi$
$787$	−1.06923e21	+	1.85196e21i	−0.203826	+	0.353037i	0.745932	+	0.666022i	$0.232004\pi$
$788$	2.41025e21	−	4.17468e21i	0.455109	−	0.788272i
$789$	2.72034e21	+	4.71177e21i	0.508799	+	0.881265i
$790$	−2.60952e21			−0.483457
$791$	2.14469e21	+	4.88843e21i	0.393587	+	0.897110i
$792$	2.66541e20			0.0484535
$793$	1.07708e21	+	1.86556e21i	0.193954	+	0.335938i
$794$	2.28286e21	−	3.95404e21i	0.407217	−	0.705321i
$795$	1.23581e21	−	2.14048e21i	0.218372	−	0.378232i
$796$	−1.67167e21	−	2.89541e21i	−0.292619	−	0.506830i
$797$	−6.32059e21			−1.09602			−0.548012	−	0.836471i	$-0.684615\pi$
$797$	−6.32059e21			−1.09602			−0.548012	+	0.836471i	$0.684615\pi$
$798$	−4.65458e20	+	6.33375e20i	−0.0799574	+	0.108803i
$799$	4.03984e21			0.687485
$800$	−3.07138e20	−	5.31978e20i	−0.0517795	−	0.0896848i
$801$	−1.01966e20	+	1.76610e20i	−0.0170298	+	0.0294965i
$802$	−9.67202e20	+	1.67524e21i	−0.160033	+	0.277185i
$803$	1.16416e21	+	2.01638e21i	0.190829	+	0.330526i
$804$	2.78368e21			0.452064
$805$	1.90344e21	+	2.10532e20i	0.306246	+	0.0338726i
$806$	1.42480e21			0.227112
$807$	−1.84926e20	−	3.20301e20i	−0.0292043	−	0.0505832i
$808$	−6.95876e19	+	1.20529e20i	−0.0108880	+	0.0188585i
$809$	5.16714e21	−	8.94975e21i	0.801007	−	1.38739i	−0.117946	−	0.993020i	$-0.537631\pi$
$809$	5.16714e21	−	8.94975e21i	0.801007	−	1.38739i	0.918954	−	0.394365i	$-0.129036\pi$
$810$	3.39681e20	+	5.88345e20i	0.0521716	+	0.0903638i
$811$	8.11039e21			1.23420			0.617099	−	0.786885i	$-0.288308\pi$
$811$	8.11039e21			1.23420			0.617099	+	0.786885i	$0.288308\pi$
$812$	5.34366e21	+	5.91040e20i	0.805690	+	0.0891141i
$813$	−3.20949e21			−0.479465
$814$	−3.66737e20	−	6.35207e20i	−0.0542839	−	0.0940225i
$815$	−2.57973e21	+	4.46822e21i	−0.378348	+	0.655319i
$816$	3.13402e20	−	5.42827e20i	0.0455433	−	0.0788834i
$817$	−1.19697e21	−	2.07322e21i	−0.172353	−	0.298524i
$818$	−5.28442e21			−0.753959
$819$	1.39031e21	−	1.89187e21i	0.196554	−	0.267462i
$820$	−3.19147e21			−0.447082
$821$	5.56594e20	+	9.64049e20i	0.0772618	+	0.133821i	0.902068	−	0.431595i	$-0.142049\pi$
$821$	5.56594e20	+	9.64049e20i	0.0772618	+	0.133821i	−0.824806	+	0.565416i	$0.808716\pi$
$822$	1.48504e21	−	2.57216e21i	0.204267	−	0.353801i
$823$	1.28692e21	−	2.22900e21i	0.175409	−	0.303817i	−0.764894	−	0.644156i	$-0.777209\pi$
$823$	1.28692e21	−	2.22900e21i	0.175409	−	0.303817i	0.940303	+	0.340339i	$0.110542\pi$
$824$	1.84733e21	+	3.19968e21i	0.249512	+	0.432168i
$825$	−8.22573e20			−0.110096
$826$	4.85011e20	+	1.10549e21i	0.0643282	+	0.146624i
$827$	6.60185e21			0.867709			0.433854	−	0.900983i	$-0.357153\pi$
$827$	6.60185e21			0.867709			0.433854	+	0.900983i	$0.357153\pi$
$828$	4.68932e20	+	8.12215e20i	0.0610777	+	0.105790i
$829$	−6.35583e21	+	1.10086e22i	−0.820376	+	1.42093i	0.0850259	+	0.996379i	$0.472903\pi$
$829$	−6.35583e21	+	1.10086e22i	−0.820376	+	1.42093i	−0.905402	+	0.424555i	$0.860431\pi$
$830$	−3.90357e20	+	6.76118e20i	−0.0499317	+	0.0864842i
$831$	−2.45610e19	−	4.25408e19i	−0.00311342	−	0.00539260i
$832$	−6.47199e20			−0.0813042
$833$	1.24899e21	+	3.99118e21i	0.155496	+	0.496894i
$834$	−4.53130e21			−0.559084
$835$	4.95522e21	+	8.58269e21i	0.605919	+	1.04948i
$836$	−1.51178e20	+	2.61848e20i	−0.0183207	+	0.0317323i
$837$	2.17265e21	−	3.76315e21i	0.260945	−	0.451971i
$838$	2.77332e21	+	4.80354e21i	0.330119	+	0.571783i
$839$	−1.09034e22			−1.28631			−0.643155	−	0.765736i	$-0.722375\pi$
$839$	−1.09034e22			−1.28631			−0.643155	+	0.765736i	$0.722375\pi$
$840$	5.47115e20	+	1.24705e21i	0.0639711	+	0.145810i
$841$	1.40510e22			1.62831
$842$	−3.38731e20	−	5.86699e20i	−0.0389058	−	0.0673868i
$843$	−1.49831e21	+	2.59514e21i	−0.170567	+	0.295430i
$844$	−1.32000e21	+	2.28631e21i	−0.148938	+	0.257968i
$845$	−1.66004e21	−	2.87527e21i	−0.185649	−	0.321554i
$846$	−4.29836e21			−0.476458
$847$	−5.00111e21	+	6.80529e21i	−0.549466	+	0.747690i
$848$	2.22626e21			0.242442
$849$	−5.53840e21	−	9.59280e21i	−0.597829	−	1.03547i
$850$	1.00788e21	−	1.74571e21i	0.107837	−	0.186780i
$851$	1.29042e21	−	2.23507e21i	0.136854	−	0.237039i
$852$	7.14932e20	+	1.23830e21i	0.0751567	+	0.130175i
$853$	−1.68210e22			−1.75281			−0.876406	−	0.481573i	$-0.840066\pi$
$853$	−1.68210e22			−1.75281			−0.876406	+	0.481573i	$0.840066\pi$
$854$	4.05793e21	+	4.48831e20i	0.419151	+	0.0463605i
$855$	8.75240e20			0.0896151
$856$	−2.29571e21	−	3.97629e21i	−0.233004	−	0.403575i
$857$	6.05907e21	−	1.04946e22i	0.609606	−	1.05587i	−0.381699	−	0.924287i	$-0.624661\pi$
$857$	6.05907e21	−	1.04946e22i	0.609606	−	1.05587i	0.991305	−	0.131583i	$-0.0420058\pi$
$858$	−4.33331e20	+	7.50550e20i	−0.0432180	+	0.0748558i
$859$	−2.79566e21	−	4.84223e21i	−0.276399	−	0.478736i	0.694088	−	0.719890i	$-0.255808\pi$
$859$	−2.79566e21	−	4.84223e21i	−0.276399	−	0.478736i	−0.970487	+	0.241153i	$0.922474\pi$
$860$	−4.14757e21			−0.406496
$861$	−9.94648e21	−	1.10014e21i	−0.966375	−	0.106887i
$862$	1.17402e21			0.113076
$863$	−3.41028e21	−	5.90679e21i	−0.325619	−	0.563989i	0.656018	−	0.754745i	$-0.272239\pi$
$863$	−3.41028e21	−	5.90679e21i	−0.325619	−	0.563989i	−0.981637	+	0.190756i	$0.938906\pi$
$864$	−9.86906e20	+	1.70937e21i	−0.0934164	+	0.161802i
$865$	6.24245e21	−	1.08122e22i	0.585780	−	1.01460i
$866$	4.28271e21	+	7.41786e21i	0.398414	+	0.690073i
$867$	−5.53077e21			−0.510085
$868$	1.59908e21	−	2.17596e21i	0.146209	−	0.198954i
$869$	−3.14752e21			−0.285312
$870$	2.87242e21	+	4.97517e21i	0.258139	+	0.447109i
$871$	4.71601e21	−	8.16837e21i	0.420183	−	0.727779i
$872$	1.82361e21	−	3.15859e21i	0.161087	−	0.279010i
$873$	−4.33624e21	−	7.51059e21i	−0.379758	−	0.657760i
$874$	−1.06388e21			−0.0923759
$875$	4.76298e21	+	1.08563e22i	0.410032	+	0.934594i
$876$	−5.82568e21			−0.497240
$877$	−8.30398e20	−	1.43829e21i	−0.0702731	−	0.121717i	0.828748	−	0.559622i	$-0.189054\pi$
$877$	−8.30398e20	−	1.43829e21i	−0.0702731	−	0.121717i	−0.899021	+	0.437906i	$0.855720\pi$
$878$	5.96638e21	−	1.03341e22i	0.500613	−	0.867087i
$879$	5.54109e20	−	9.59745e20i	0.0460976	−	0.0798435i
$880$	2.61920e20	+	4.53658e20i	0.0216047	+	0.0374204i
$881$	−7.78379e21			−0.636607			−0.318304	−	0.947989i	$-0.603113\pi$
$881$	−7.78379e21			−0.636607			−0.318304	+	0.947989i	$0.603113\pi$
$882$	−1.32891e21	−	4.24658e21i	−0.107766	−	0.344370i
$883$	4.32083e21			0.347426			0.173713	−	0.984796i	$-0.444424\pi$
$883$	4.32083e21			0.347426			0.173713	+	0.984796i	$0.444424\pi$
$884$	−1.06191e21	−	1.83927e21i	−0.0846631	−	0.146641i
$885$	−6.44987e20	+	1.11715e21i	−0.0509890	+	0.0883155i
$886$	−4.76913e21	+	8.26037e21i	−0.373840	+	0.647510i
$887$	−1.77038e21	−	3.06638e21i	−0.137606	−	0.238341i	0.788984	−	0.614414i	$-0.210608\pi$
$887$	−1.77038e21	−	3.06638e21i	−0.137606	−	0.238341i	−0.926590	+	0.376073i	$0.877274\pi$
$888$	1.83523e21			0.141447
$889$	2.08221e21	+	4.74602e21i	0.159134	+	0.362716i
$890$	−4.00791e20			−0.0303733
$891$	4.09712e20	+	7.09642e20i	0.0307890	+	0.0533282i
$892$	−6.10303e21	+	1.05708e22i	−0.454788	+	0.787716i
$893$	2.43796e21	−	4.22267e21i	0.180153	−	0.312034i
$894$	4.98987e21	+	8.64270e21i	0.365643	+	0.633313i
$895$	−1.19550e21			−0.0868713
$896$	−7.26367e20	+	9.88409e20i	−0.0523415	+	0.0712241i
$897$	−3.04948e21			−0.217913
$898$	2.75885e21	+	4.77847e21i	0.195504	+	0.338623i
$899$	5.69584e21	−	9.86549e21i	0.400277	−	0.693300i
$900$	−1.07238e21	+	1.85742e21i	−0.0747361	+	0.129447i
$901$	3.65279e21	+	6.32682e21i	0.252458	+	0.437270i
$902$	−3.84945e21			−0.263846
$903$	−1.29262e22	−	1.42972e21i	−0.878647	−	0.0971835i
$904$	−5.13795e21			−0.346359
$905$	5.21551e21	+	9.03353e21i	0.348685	+	0.603939i
$906$	3.52636e21	−	6.10783e21i	0.233811	−	0.404973i
$907$	−6.12553e21	+	1.06097e22i	−0.402800	+	0.697670i	−0.994063	−	0.108809i	$-0.965296\pi$
$907$	−6.12553e21	+	1.06097e22i	−0.402800	+	0.697670i	0.591263	+	0.806479i	$0.298630\pi$
$908$	3.81338e21	+	6.60496e21i	0.248694	+	0.430751i
$909$	4.85935e20			0.0314304
$910$	4.58620e21	+	5.07261e20i	0.294200	+	0.0325403i
$911$	1.14854e22			0.730734			0.365367	−	0.930864i	$-0.380944\pi$
$911$	1.14854e22			0.730734			0.365367	+	0.930864i	$0.380944\pi$
$912$	−3.78263e20	−	6.55171e20i	−0.0238689	−	0.0413422i
$913$	−4.70835e20	+	8.15511e20i	−0.0294672	+	0.0510386i
$914$	5.39876e21	−	9.35093e21i	0.335118	−	0.580441i
$915$	2.18129e21	+	3.77810e21i	0.134293	+	0.232603i
$916$	−1.41187e21			−0.0862142
$917$	−6.12173e21	+	8.33019e21i	−0.370770	+	0.504528i
$918$	−6.47715e21			−0.389102
$919$	−2.86805e20	−	4.96760e20i	−0.0170891	−	0.0295992i	0.857354	−	0.514727i	$-0.172107\pi$
$919$	−2.86805e20	−	4.96760e20i	−0.0170891	−	0.0295992i	−0.874444	+	0.485127i	$0.838773\pi$
$920$	−9.21604e20	+	1.59626e21i	−0.0544673	+	0.0943401i
$921$	6.27137e21	−	1.08623e22i	0.367634	−	0.636760i
$922$	7.59591e21	+	1.31565e22i	0.441670	+	0.764995i
$923$	4.84484e21			0.279426
$924$	6.59911e20	+	1.50415e21i	0.0377525	+	0.0860499i
$925$	5.90201e21			0.334917
$926$	−6.51080e21	−	1.12770e22i	−0.366481	−	0.634764i
$927$	6.45004e21	−	1.11718e22i	0.360134	−	0.623770i
$928$	−2.58728e21	+	4.48130e21i	−0.143296	+	0.248196i
$929$	9.97428e21	+	1.72760e22i	0.547979	+	0.949127i	0.998413	+	0.0563172i	$0.0179358\pi$
$929$	9.97428e21	+	1.72760e22i	0.547979	+	0.949127i	−0.450434	+	0.892810i	$0.648731\pi$
$930$	2.88548e21			0.157252
$931$	4.92555e21	+	1.10308e21i	0.266276	+	0.0596329i
$932$	9.10092e21			0.488052
$933$	5.28243e21	+	9.14943e21i	0.281010	+	0.486723i
$934$	4.17157e21	−	7.22537e21i	0.220140	−	0.381293i
$935$	−8.59500e20	+	1.48870e21i	−0.0449944	+	0.0779326i
$936$	1.12986e21	+	1.95697e21i	0.0586753	+	0.101629i
$937$	2.11441e22			1.08929			0.544644	−	0.838667i	$-0.316665\pi$
$937$	2.11441e22			1.08929			0.544644	+	0.838667i	$0.316665\pi$
$938$	−7.18193e21	−	1.63699e22i	−0.367045	−	0.836613i
$939$	1.30446e21			0.0661361
$940$	−4.22383e21	−	7.31589e21i	−0.212446	−	0.367967i
$941$	−4.75586e21	+	8.23738e21i	−0.237305	+	0.411024i	−0.959940	−	0.280206i	$-0.909597\pi$
$941$	−4.75586e21	+	8.23738e21i	−0.237305	+	0.411024i	0.722635	+	0.691230i	$0.242931\pi$
$942$	3.34528e21	−	5.79419e21i	0.165596	−	0.286821i
$943$	−6.77244e21	−	1.17302e22i	−0.332589	−	0.576060i
$944$	−1.16192e21			−0.0566092
$945$	8.33322e21	−	1.13395e22i	0.402786	−	0.548094i
$946$	−5.00267e21			−0.239893
$947$	−3.62886e21	−	6.28537e21i	−0.172642	−	0.299024i	0.766701	−	0.642004i	$-0.221897\pi$
$947$	−3.62886e21	−	6.28537e21i	−0.172642	−	0.299024i	−0.939343	+	0.342980i	$0.888564\pi$
$948$	3.93771e21	−	6.82031e21i	0.185858	−	0.321915i
$949$	−9.86965e21	+	1.70947e22i	−0.462174	+	0.800508i
$950$	−1.21648e21	−	2.10700e21i	−0.0565167	−	0.0978898i
$951$	7.30963e21			0.336931
$952$	−4.00076e21	−	4.42508e20i	−0.182964	−	0.0202369i
$953$	2.72531e22			1.23657			0.618286	−	0.785953i	$-0.287827\pi$
$953$	2.72531e22			1.23657			0.618286	+	0.785953i	$0.287827\pi$
$954$	−3.88654e21	−	6.73168e21i	−0.174965	−	0.303048i
$955$	−8.97802e21	+	1.55504e22i	−0.401010	+	0.694570i
$956$	−2.06161e21	+	3.57082e21i	−0.0913635	+	0.158246i
$957$	3.46461e21	+	6.00088e21i	0.152340	+	0.263861i
$958$	7.35649e21			0.320944
$959$	−1.89574e22	−	2.09680e21i	−0.820615	−	0.0907649i
$960$	−1.31070e21			−0.0562949
$961$	8.87176e21	+	1.53663e22i	0.378080	+	0.654855i
$962$	3.10917e21	−	5.38525e21i	0.131472	−	0.227716i
$963$	−8.01555e21	+	1.38833e22i	−0.336307	+	0.582501i
$964$	−1.88743e21	−	3.26913e21i	−0.0785767	−	0.136099i
$965$	−2.54958e22			−1.05321
$966$	−3.42250e21	+	4.65720e21i	−0.140286	+	0.190896i
$967$	−1.13331e22			−0.460948			−0.230474	−	0.973078i	$-0.574028\pi$
$967$	−1.13331e22			−0.460948			−0.230474	+	0.973078i	$0.574028\pi$
$968$	−4.06424e21	−	7.03948e21i	−0.164027	−	0.284103i
$969$	1.24129e21	−	2.14997e21i	0.0497100	−	0.0861002i
$970$	8.52212e21	−	1.47607e22i	0.338657	−	0.586570i
$971$	−1.47245e22	−	2.55036e22i	−0.580626	−	1.00567i	−0.995405	−	0.0957521i	$-0.969474\pi$
$971$	−1.47245e22	−	2.55036e22i	−0.580626	−	1.00567i	0.414779	−	0.909922i	$-0.363859\pi$
$972$	1.14547e22			0.448216
$973$	1.16908e22	+	2.66470e22i	0.453939	+	1.03467i
$974$	−3.60625e21			−0.138952
$975$	−3.48686e21	−	6.03942e21i	−0.133322	−	0.230920i
$976$	−1.96476e21	+	3.40306e21i	−0.0745479	+	0.129121i
$977$	2.34167e21	−	4.05590e21i	0.0881692	−	0.152714i	−0.818568	−	0.574410i	$-0.805232\pi$
$977$	2.34167e21	−	4.05590e21i	0.0881692	−	0.152714i	0.906737	+	0.421696i	$0.138565\pi$
$978$	−7.78551e21	−	1.34849e22i	−0.290901	−	0.503856i
$979$	−4.83420e20			−0.0179248
$980$	5.92190e21	−	6.43479e21i	0.217904	−	0.236777i
$981$	−1.27344e22			−0.465010
$982$	1.53556e22	+	2.65966e22i	0.556455	+	0.963808i
$983$	−6.14253e21	+	1.06392e22i	−0.220900	+	0.382610i	−0.955082	−	0.296343i	$-0.904233\pi$
$983$	−6.14253e21	+	1.06392e22i	−0.220900	+	0.382610i	0.734181	+	0.678953i	$0.237566\pi$
$984$	4.81587e21	−	8.34133e21i	0.171874	−	0.297695i
$985$	−1.65391e22	−	2.86466e22i	−0.585789	−	1.01462i
$986$	−1.69805e22			−0.596863
$987$	−1.06420e22	−	2.42566e22i	−0.371232	−	0.846156i
$988$	−2.56335e21			−0.0887425
$989$	−8.80132e21	−	1.52443e22i	−0.302396	−	0.523765i
$990$	9.14501e20	−	1.58396e21i	0.0311832	−	0.0540108i
$991$	−2.38724e22	+	4.13482e22i	−0.807873	+	1.39928i	0.106461	+	0.994317i	$0.466048\pi$
$991$	−2.38724e22	+	4.13482e22i	−0.807873	+	1.39928i	−0.914334	+	0.404961i	$0.867285\pi$
$992$	1.29952e21	+	2.25084e21i	0.0436462	+	0.0755975i
$993$	3.44844e22			1.14949
$994$	5.43748e21	−	7.39909e21i	0.179887	−	0.244783i
$995$	−2.29420e22			−0.753281
$996$	−1.17808e21	−	2.04049e21i	−0.0383910	−	0.0664952i
$997$	−1.07692e22	+	1.86529e22i	−0.348314	+	0.603298i	−0.985950	−	0.167040i	$-0.946579\pi$
$997$	−1.07692e22	+	1.86529e22i	−0.348314	+	0.603298i	0.637636	+	0.770338i	$0.279912\pi$
$998$	−1.74990e22	+	3.03092e22i	−0.561740	+	0.972962i
$999$	−9.48228e21	−	1.64238e22i	−0.302115	−	0.523278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.16.c.b.11.2	yes	10
3.2	odd	2		126.16.g.c.109.2		10
7.2	even	3	inner	14.16.c.b.9.2	✓	10
7.3	odd	6		98.16.a.i.1.2		5
7.4	even	3		98.16.a.h.1.4		5
7.5	odd	6		98.16.c.n.79.4		10
7.6	odd	2		98.16.c.n.67.4		10
21.2	odd	6		126.16.g.c.37.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.16.c.b.9.2	✓	10	7.2	even	3	inner
14.16.c.b.11.2	yes	10	1.1	even	1	trivial
98.16.a.h.1.4		5	7.4	even	3
98.16.a.i.1.2		5	7.3	odd	6
98.16.c.n.67.4		10	7.6	odd	2
98.16.c.n.79.4		10	7.5	odd	6
126.16.g.c.37.2		10	21.2	odd	6
126.16.g.c.109.2		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(64.0000 + 110.851i) q^{2} +(-1325.39 + 2295.64i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(56213.5 + 97364.6i) q^{5} -339300. q^{6} +(875396. + 1.99531e6i) q^{7} -2.09715e6 q^{8} +(3.66114e6 + 6.34128e6i) q^{9} +O(q^{10})\)	\(q+(64.0000 + 110.851i) q^{2} +(-1325.39 + 2295.64i) q^{3} +(-8192.00 + 14189.0i) q^{4} +(56213.5 + 97364.6i) q^{5} -339300. q^{6} +(875396. + 1.99531e6i) q^{7} -2.09715e6 q^{8} +(3.66114e6 + 6.34128e6i) q^{9} +(-7.19532e6 + 1.24627e7i) q^{10} +(-8.67876e6 + 1.50321e7i) q^{11} +(-2.17152e7 - 3.76118e7i) q^{12} -1.47156e8 q^{13} +(-1.65157e8 + 2.24738e8i) q^{14} -2.98019e8 q^{15} +(-1.34218e8 - 2.32472e8i) q^{16} +(4.40441e8 - 7.62866e8i) q^{17} +(-4.68626e8 + 8.11684e8i) q^{18} +(-5.31595e8 - 9.20749e8i) q^{19} -1.84200e9 q^{20} +(-5.74075e9 - 6.34961e8i) q^{21} -2.22176e9 q^{22} +(-3.90880e9 - 6.77025e9i) q^{23} +(2.77954e9 - 4.81431e9i) q^{24} +(8.93888e9 - 1.54826e10i) q^{25} +(-9.41799e9 - 1.63124e10i) q^{26} -5.74455e10 q^{27} +(-3.54826e10 - 3.92458e9i) q^{28} -1.50600e11 q^{29} +(-1.90732e10 - 3.30358e10i) q^{30} +(-3.78211e10 + 6.55081e10i) q^{31} +(1.71799e10 - 2.97564e10i) q^{32} +(-2.30055e10 - 3.98466e10i) q^{33} +1.12753e11 q^{34} +(-1.45063e11 + 1.97396e11i) q^{35} -1.19968e11 q^{36} +(1.65066e11 + 2.85902e11i) q^{37} +(6.80441e10 - 1.17856e11i) q^{38} +(1.95039e11 - 3.37818e11i) q^{39} +(-1.17888e11 - 2.04188e11i) q^{40} +1.73261e12 q^{41} +(-2.97022e11 - 6.77006e11i) q^{42} +2.25167e12 q^{43} +(-1.42193e11 - 2.46285e11i) q^{44} +(-4.11611e11 + 7.12931e11i) q^{45} +(5.00327e11 - 8.66592e11i) q^{46} +(2.29306e12 + 3.97171e12i) q^{47} +7.11563e11 q^{48} +(-3.21492e12 + 3.49336e12i) q^{49} +2.28835e12 q^{50} +(1.16751e12 + 2.02219e12i) q^{51} +(1.20550e12 - 2.08799e12i) q^{52} +(-4.14674e12 + 7.18236e12i) q^{53} +(-3.67651e12 - 6.36791e12i) q^{54} -1.95145e12 q^{55} +(-1.83584e12 - 4.18446e12i) q^{56} +2.81828e12 q^{57} +(-9.63837e12 - 1.66941e13i) q^{58} +(2.16425e12 - 3.74859e12i) q^{59} +(2.44137e12 - 4.22858e12i) q^{60} +(-7.31929e12 - 1.26774e13i) q^{61} -9.68221e12 q^{62} +(-9.44784e12 + 1.28562e13i) q^{63} +4.39805e12 q^{64} +(-8.27215e12 - 1.43278e13i) q^{65} +(2.94470e12 - 5.10037e12i) q^{66} +(-3.20477e13 + 5.55082e13i) q^{67} +(7.21619e12 + 1.24988e13i) q^{68} +2.07227e13 q^{69} +(-3.11656e13 - 3.44710e12i) q^{70} -3.29232e13 q^{71} +(-7.67797e12 - 1.32986e13i) q^{72} +(6.70692e13 - 1.16167e14i) q^{73} +(-2.11284e13 + 3.65955e13i) q^{74} +(2.36950e13 + 4.10409e13i) q^{75} +1.74193e13 q^{76} +(-3.75909e13 - 4.15777e12i) q^{77} +4.99300e13 q^{78} +(9.06672e13 + 1.57040e14i) q^{79} +(1.50897e13 - 2.61361e13i) q^{80} +(2.36043e13 - 4.08839e13i) q^{81} +(1.10887e14 + 1.92062e14i) q^{82} +5.42515e13 q^{83} +(5.60376e13 - 7.62536e13i) q^{84} +9.90349e13 q^{85} +(1.44107e14 + 2.49600e14i) q^{86} +(1.99603e14 - 3.45723e14i) q^{87} +(1.82007e13 - 3.15245e13i) q^{88} +(1.39254e13 + 2.41195e13i) q^{89} -1.05372e14 q^{90} +(-1.28820e14 - 2.93621e14i) q^{91} +1.28084e14 q^{92} +(-1.00255e14 - 1.73647e14i) q^{93} +(-2.93512e14 + 5.08378e14i) q^{94} +(5.97655e13 - 1.03517e14i) q^{95} +(4.55400e13 + 7.88776e13i) q^{96} -1.18440e15 q^{97} +(-5.92999e14 - 1.32803e14i) q^{98} -1.27097e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9}+O(q^{10}) \) 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9	\( 10 q + 640 q^{2} + 2395 q^{3} - 81920 q^{4} + 10969 q^{5} + 613120 q^{6} + 2375276 q^{7} - 20971520 q^{8} - 45505414 q^{9} - 1404032 q^{10} - 3405409 q^{11} + 39239680 q^{12} + 369408276 q^{13} + 411547520 q^{14} + 453669790 q^{15} - 1342177280 q^{16} - 3201713287 q^{17} + 5824692992 q^{18} - 1063446451 q^{19} - 359432192 q^{20} + 21058786691 q^{21} - 871784704 q^{22} - 31680429991 q^{23} - 5022679040 q^{24} + 39012502244 q^{25} + 23642129664 q^{26} + 66427564750 q^{27} + 13761560576 q^{28} + 294935242276 q^{29} + 29034866560 q^{30} + 30201804075 q^{31} + 171798691840 q^{32} - 482562276049 q^{33} - 819638601472 q^{34} - 1540311474205 q^{35} + 1491121405952 q^{36} + 1369689837461 q^{37} + 136121145728 q^{38} - 1048775641458 q^{39} - 23003660288 q^{40} + 3634838274156 q^{41} - 871978643968 q^{42} + 415602663752 q^{43} - 55794221056 q^{44} - 7616412162898 q^{45} + 4055095038848 q^{46} - 12606978599835 q^{47} - 1285805834240 q^{48} - 8067928630838 q^{49} + 9987200574464 q^{50} + 6857137867217 q^{51} - 3026192596992 q^{52} + 10616682242361 q^{53} + 4251364144000 q^{54} - 40851384759514 q^{55} - 4981314813952 q^{56} + 44665526899814 q^{57} + 18875855505664 q^{58} + 39993786962755 q^{59} - 3716462919680 q^{60} + 5148862074165 q^{61} + 7731661843200 q^{62} - 97668254816810 q^{63} + 43980465111040 q^{64} + 91302240851010 q^{65} + 61767971334272 q^{66} - 29267240444285 q^{67} - 52456870494208 q^{68} - 279695242712578 q^{69} + 18327124839296 q^{70} - 37767657205600 q^{71} + 95431769980928 q^{72} + 243869659370917 q^{73} - 175320299195008 q^{74} + 295809815641460 q^{75} + 34847013306368 q^{76} + 35960055270559 q^{77} - 268486564213248 q^{78} + 137356615917609 q^{79} + 2944468516864 q^{80} - 352056899083285 q^{81} + 232629649545984 q^{82} - 914604166510648 q^{83} - 456640427573248 q^{84} + 264981492485402 q^{85} + 26598570480128 q^{86} + 13\!\cdots\!90 q^{87}+ \cdots + 39\!\cdots\!96 q^{99}+O(q^{100}) \) 10 * q + 640 * q^2 + 2395 * q^3 - 81920 * q^4 + 10969 * q^5 + 613120 * q^6 + 2375276 * q^7 - 20971520 * q^8 - 45505414 * q^9 - 1404032 * q^10 - 3405409 * q^11 + 39239680 * q^12 + 369408276 * q^13 + 411547520 * q^14 + 453669790 * q^15 - 1342177280 * q^16 - 3201713287 * q^17 + 5824692992 * q^18 - 1063446451 * q^19 - 359432192 * q^20 + 21058786691 * q^21 - 871784704 * q^22 - 31680429991 * q^23 - 5022679040 * q^24 + 39012502244 * q^25 + 23642129664 * q^26 + 66427564750 * q^27 + 13761560576 * q^28 + 294935242276 * q^29 + 29034866560 * q^30 + 30201804075 * q^31 + 171798691840 * q^32 - 482562276049 * q^33 - 819638601472 * q^34 - 1540311474205 * q^35 + 1491121405952 * q^36 + 1369689837461 * q^37 + 136121145728 * q^38 - 1048775641458 * q^39 - 23003660288 * q^40 + 3634838274156 * q^41 - 871978643968 * q^42 + 415602663752 * q^43 - 55794221056 * q^44 - 7616412162898 * q^45 + 4055095038848 * q^46 - 12606978599835 * q^47 - 1285805834240 * q^48 - 8067928630838 * q^49 + 9987200574464 * q^50 + 6857137867217 * q^51 - 3026192596992 * q^52 + 10616682242361 * q^53 + 4251364144000 * q^54 - 40851384759514 * q^55 - 4981314813952 * q^56 + 44665526899814 * q^57 + 18875855505664 * q^58 + 39993786962755 * q^59 - 3716462919680 * q^60 + 5148862074165 * q^61 + 7731661843200 * q^62 - 97668254816810 * q^63 + 43980465111040 * q^64 + 91302240851010 * q^65 + 61767971334272 * q^66 - 29267240444285 * q^67 - 52456870494208 * q^68 - 279695242712578 * q^69 + 18327124839296 * q^70 - 37767657205600 * q^71 + 95431769980928 * q^72 + 243869659370917 * q^73 - 175320299195008 * q^74 + 295809815641460 * q^75 + 34847013306368 * q^76 + 35960055270559 * q^77 - 268486564213248 * q^78 + 137356615917609 * q^79 + 2944468516864 * q^80 - 352056899083285 * q^81 + 232629649545984 * q^82 - 914604166510648 * q^83 - 456640427573248 * q^84 + 264981492485402 * q^85 + 26598570480128 * q^86 + 1332529214868790 * q^87 + 7141660295168 * q^88 + 315332760149685 * q^89 - 1949801513701888 * q^90 - 2638730194011720 * q^91 + 1038104329945088 * q^92 + 2962720310885787 * q^93 + 1613693260778880 * q^94 - 1346257729549705 * q^95 - 82291573391360 * q^96 + 58320039716044 * q^97 - 1279096378461056 * q^98 + 3930453838067596 * q^99

Introduction

L-functions

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