LMFDB - Embedded newform 14.15.d.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,15,Mod(3,14)]

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([1]))

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, 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:	$17.4060555413$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 5366534 x^{18} + 786490608 x^{17} + 19826027932115 x^{16} + \cdots + 13\!\cdots\!24 $ x^20 - 4x^19 + 5366534x^18 + 786490608x^17 + 19826027932115x^16 + 3116508483645696x^15 + 38794655189396647126x^14 + 6995731541198679243060x^13 + 54561557157067963809187457x^12 + 6630233353755658208901796272x^11 + 34794459335155646904361009621528x^10 - 507937593458729410665953593711872x^9 + 15479722701777718863087638126396034896x^8 - 883719083612311978219332637069278729984x^7 + 3763299771642320209476548571825975912308608x^6 - 633899212255257611286599422411160802422874624x^5 + 597491591633081375797803556549613553954788912384x^4 - 42265294259314426139494021682209240856866274451456x^3 + 11534106439702605092537039760142524539554443571202048x^2 + 525642005044107600688521330249536141111741609738240000*x + 136102482846251121074713416730051821278073355281841537024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{76}\cdot 3^{12}\cdot 7^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.3
Root			$87.1998 - 151.035i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.15.d.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.2548 + 78.3837i) q^{2} +(-746.556 + 431.025i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(45757.7 + 26418.2i) q^{5} -78023.8i q^{6} +(-602075. + 561898. i) q^{7} +741455. q^{8} +(-2.01992e6 + 3.49860e6i) q^{9} +O(q^{10})$	\(q+(-45.2548 + 78.3837i) q^{2} +(-746.556 + 431.025i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(45757.7 + 26418.2i) q^{5} -78023.8i q^{6} +(-602075. + 561898. i) q^{7} +741455. q^{8} +(-2.01992e6 + 3.49860e6i) q^{9} +(-4.14152e6 + 2.39111e6i) q^{10} +(-1.49968e7 - 2.59753e7i) q^{11} +(6.11579e6 + 3.53095e6i) q^{12} +6.10988e7i q^{13} +(-1.67968e7 - 7.26214e7i) q^{14} -4.55476e7 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(6.07711e8 - 3.50862e8i) q^{17} +(-1.82822e8 - 3.16658e8i) q^{18} +(-8.10189e8 - 4.67763e8i) q^{19} -4.32836e8i q^{20} +(2.07291e8 - 6.78997e8i) q^{21} +2.71472e9 q^{22} +(2.67149e9 - 4.62716e9i) q^{23} +(-5.53538e8 + 3.19585e8i) q^{24} +(-1.65591e9 - 2.86812e9i) q^{25} +(-4.78915e9 - 2.76502e9i) q^{26} -7.60570e9i q^{27} +(6.45247e9 + 1.96987e9i) q^{28} -2.60644e10 q^{29} +(2.06125e9 - 3.57019e9i) q^{30} +(1.46354e10 - 8.44977e9i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} +(2.23920e10 + 1.29280e10i) q^{33} +6.35129e10i q^{34} +(-4.23939e10 + 9.80541e9i) q^{35} +3.30944e10 q^{36} +(-1.69601e8 + 2.93758e8i) q^{37} +(7.33299e10 - 4.23371e10i) q^{38} +(-2.63351e10 - 4.56137e10i) q^{39} +(3.39273e10 + 1.95879e10i) q^{40} +2.65621e11i q^{41} +(4.38414e10 + 4.69761e10i) q^{42} -1.33135e11 q^{43} +(-1.22854e11 + 2.12790e11i) q^{44} +(-1.84854e11 + 1.06725e11i) q^{45} +(2.41796e11 + 4.18803e11i) q^{46} +(-3.25071e11 - 1.87680e11i) q^{47} -5.78511e10i q^{48} +(4.67649e10 - 6.76609e11i) q^{49} +2.99752e11 q^{50} +(-3.02461e11 + 5.23877e11i) q^{51} +(4.33464e11 - 2.50261e11i) q^{52} +(-7.07618e11 - 1.22563e12i) q^{53} +(5.96162e11 + 3.44194e11i) q^{54} -1.58476e12i q^{55} +(-4.46411e11 + 4.16622e11i) q^{56} +8.06469e11 q^{57} +(1.17954e12 - 2.04302e12i) q^{58} +(1.85845e12 - 1.07298e12i) q^{59} +(1.86563e11 + 3.23137e11i) q^{60} +(-1.76997e12 - 1.02189e12i) q^{61} +1.52957e12i q^{62} +(-7.49715e11 - 3.24141e12i) q^{63} +5.49756e11 q^{64} +(-1.61412e12 + 2.79574e12i) q^{65} +(-2.02669e12 + 1.17011e12i) q^{66} +(3.51155e12 + 6.08219e12i) q^{67} +(-4.97837e12 - 2.87426e12i) q^{68} +4.60591e12i q^{69} +(1.14995e12 - 3.76673e12i) q^{70} +1.32667e12 q^{71} +(-1.49768e12 + 2.59406e12i) q^{72} +(-1.14065e13 + 6.58554e12i) q^{73} +(-1.53506e10 - 2.65880e10i) q^{74} +(2.47246e12 + 1.42748e12i) q^{75} +7.66382e12i q^{76} +(2.36247e13 + 7.21237e12i) q^{77} +4.76716e12 q^{78} +(-2.22090e12 + 3.84672e12i) q^{79} +(-3.07075e12 + 1.77290e12i) q^{80} +(-6.38297e12 - 1.10556e13i) q^{81} +(-2.08203e13 - 1.20206e13i) q^{82} +2.90141e13i q^{83} +(-5.66620e12 + 1.31055e12i) q^{84} +3.70766e13 q^{85} +(6.02501e12 - 1.04356e13i) q^{86} +(1.94586e13 - 1.12344e13i) q^{87} +(-1.11195e13 - 1.92595e13i) q^{88} +(-9.69029e11 - 5.59469e11i) q^{89} -1.93194e13i q^{90} +(-3.43313e13 - 3.67861e13i) q^{91} -4.37697e13 q^{92} +(-7.28412e12 + 1.26165e13i) q^{93} +(2.94221e13 - 1.69868e13i) q^{94} +(-2.47149e13 - 4.28075e13i) q^{95} +(4.53458e12 + 2.61804e12i) q^{96} -3.91392e13i q^{97} +(5.09188e13 + 3.42854e13i) q^{98} +1.21170e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) $ 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9 - 3933696 * q^10 + 8400426 * q^11 + 35831808 * q^12 - 114693888 * q^14 + 562720524 * q^15 - 671088640 * q^16 + 2180481042 * q^17 - 251755008 * q^18 - 3919727442 * q^19 + 7585509006 * q^21 + 5394565632 * q^22 - 6905098386 * q^23 - 2371878912 * q^24 + 14165082644 * q^25 + 12652202496 * q^26 - 17334943744 * q^28 + 27884908704 * q^29 + 54103511808 * q^30 + 45638710782 * q^31 - 37041090498 * q^33 - 18274367202 * q^35 - 287497125888 * q^36 - 27026027926 * q^37 - 354043974912 * q^38 - 126125404380 * q^39 + 32224837632 * q^40 - 298475364864 * q^42 + 726682953656 * q^43 + 68816289792 * q^44 + 498861631944 * q^45 - 286664984832 * q^46 - 2044625353338 * q^47 + 2939974016204 * q^49 + 1161106642944 * q^50 - 2419609945602 * q^51 + 1314350333952 * q^52 + 1546271487546 * q^53 - 5213176950528 * q^54 + 1720927125504 * q^56 + 14789884876092 * q^57 - 2365863040512 * q^58 - 6798944731566 * q^59 - 2304903266304 * q^60 - 2214453865554 * q^61 - 4417730390688 * q^63 + 10995116277760 * q^64 + 7516703932836 * q^65 - 8476063570944 * q^66 - 4655820763226 * q^67 - 17862500696064 * q^68 + 20497461621504 * q^70 + 96606137494152 * q^71 - 2062377025536 * q^72 - 65348368908666 * q^73 - 566532483072 * q^74 - 186663280957308 * q^75 + 77525241691422 * q^77 + 88663911671808 * q^78 - 60517474082978 * q^79 - 225083129856 * q^80 - 107180264511342 * q^81 - 43979002397184 * q^82 + 18842436550656 * q^84 + 416326699526124 * q^85 + 2363335174656 * q^86 - 126768392660088 * q^87 - 22096140828672 * q^88 - 237147002561826 * q^89 + 203506111374408 * q^91 + 113133131956224 * q^92 - 94175068190130 * q^93 - 221058962902272 * q^94 + 25202514515490 * q^95 + 19430432047104 * q^96 + 165606984015360 * q^98 + 1056686373672768 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−45.2548	+	78.3837i	−0.353553	+	0.612372i
$2$	−45.2548	+	78.3837i	−0.353553	+	0.612372i
$3$	−746.556	+	431.025i	−0.341361	+	0.197085i	−0.660874	−	0.750497i	$-0.729814\pi$
$3$	−746.556	+	431.025i	−0.341361	+	0.197085i	0.319513	+	0.947582i	$0.396481\pi$
$4$	−4096.00	−	7094.48i	−0.250000	−	0.433013i
$5$	45757.7	+	26418.2i	0.585699	+	0.338153i	0.763395	−	0.645932i	$-0.223531\pi$
$5$	45757.7	+	26418.2i	0.585699	+	0.338153i	−0.177696	+	0.984085i	$0.556864\pi$
$6$		−	78023.8i		−	0.278720i
$7$	−602075.	+	561898.i	−0.731079	+	0.682293i
$7$	−602075.	+	561898.i	−0.731079	+	0.682293i
$8$	741455.			0.353553
$9$	−2.01992e6	+	3.49860e6i	−0.422315	+	0.731471i
$10$	−4.14152e6	+	2.39111e6i	−0.414152	+	0.239111i
$11$	−1.49968e7	−	2.59753e7i	−0.769575	−	1.33294i	−0.937794	−	0.347193i	$-0.887135\pi$
$11$	−1.49968e7	−	2.59753e7i	−0.769575	−	1.33294i	0.168218	−	0.985750i	$-0.446199\pi$
$12$	6.11579e6	+	3.53095e6i	0.170680	+	0.0985424i
$13$			6.10988e7i			0.973709i	0.873483	+	0.486855i	$0.161856\pi$
$13$			6.10988e7i			0.973709i	−0.873483	+	0.486855i	$0.838144\pi$
$14$	−1.67968e7	−	7.26214e7i	−0.159342	−	0.688919i
$15$	−4.55476e7			−0.266580
$16$	−3.35544e7	+	5.81180e7i	−0.125000	+	0.216506i
$17$	6.07711e8	−	3.50862e8i	1.48100	−	0.855055i	0.481231	−	0.876594i	$-0.340190\pi$
$17$	6.07711e8	−	3.50862e8i	1.48100	−	0.855055i	0.999768	+	0.0215382i	$0.00685636\pi$
$18$	−1.82822e8	−	3.16658e8i	−0.298622	−	0.517228i
$19$	−8.10189e8	−	4.67763e8i	−0.906382	−	0.523300i	−0.0271164	−	0.999632i	$-0.508632\pi$
$19$	−8.10189e8	−	4.67763e8i	−0.906382	−	0.523300i	−0.879265	+	0.476333i	$0.841966\pi$
$20$		−	4.32836e8i		−	0.338153i
$21$	2.07291e8	−	6.78997e8i	0.115092	−	0.376993i
$22$	2.71472e9			1.08834
$23$	2.67149e9	−	4.62716e9i	0.784619	−	1.35900i	−0.144607	−	0.989489i	$-0.546192\pi$
$23$	2.67149e9	−	4.62716e9i	0.784619	−	1.35900i	0.929226	−	0.369511i	$-0.120475\pi$
$24$	−5.53538e8	+	3.19585e8i	−0.120689	+	0.0696800i
$25$	−1.65591e9	−	2.86812e9i	−0.271305	−	0.469913i
$26$	−4.78915e9	−	2.76502e9i	−0.596273	−	0.344258i
$27$		−	7.60570e9i		−	0.727097i
$28$	6.45247e9	+	1.96987e9i	0.478211	+	0.145993i
$29$	−2.60644e10			−1.51099			−0.755496	−	0.655154i	$-0.772604\pi$
$29$	−2.60644e10			−1.51099			−0.755496	+	0.655154i	$0.772604\pi$
$30$	2.06125e9	−	3.57019e9i	0.0942501	−	0.163246i
$31$	1.46354e10	−	8.44977e9i	0.531953	−	0.307123i	−0.209858	−	0.977732i	$-0.567300\pi$
$31$	1.46354e10	−	8.44977e9i	0.531953	−	0.307123i	0.741812	+	0.670608i	$0.233967\pi$
$32$	−3.03700e9	−	5.26024e9i	−0.0883883	−	0.153093i
$33$	2.23920e10	+	1.29280e10i	0.525406	+	0.303343i
$34$			6.35129e10i			1.20923i
$35$	−4.23939e10	+	9.80541e9i	−0.658912	+	0.152402i
$36$	3.30944e10			0.422315
$37$	−1.69601e8	+	2.93758e8i	−0.00178656	+	0.00309441i	−0.866917	−	0.498452i	$-0.833902\pi$
$37$	−1.69601e8	+	2.93758e8i	−0.00178656	+	0.00309441i	0.865131	+	0.501546i	$0.167235\pi$
$38$	7.33299e10	−	4.23371e10i	0.640909	−	0.370029i
$39$	−2.63351e10	−	4.56137e10i	−0.191903	−	0.332386i
$40$	3.39273e10	+	1.95879e10i	0.207076	+	0.119555i
$41$			2.65621e11i			1.36388i	0.731410	+	0.681938i	$0.238863\pi$
$41$			2.65621e11i			1.36388i	−0.731410	+	0.681938i	$0.761137\pi$
$42$	4.38414e10	+	4.69761e10i	0.190169	+	0.203766i
$43$	−1.33135e11			−0.489794			−0.244897	−	0.969549i	$-0.578754\pi$
$43$	−1.33135e11			−0.489794			−0.244897	+	0.969549i	$0.578754\pi$
$44$	−1.22854e11	+	2.12790e11i	−0.384788	+	0.666472i
$45$	−1.84854e11	+	1.06725e11i	−0.494699	+	0.285615i
$46$	2.41796e11	+	4.18803e11i	0.554809	+	0.960958i
$47$	−3.25071e11	−	1.87680e11i	−0.641642	−	0.370452i	0.143604	−	0.989635i	$-0.454131\pi$
$47$	−3.25071e11	−	1.87680e11i	−0.641642	−	0.370452i	−0.785247	+	0.619183i	$0.787464\pi$
$48$		−	5.78511e10i		−	0.0985424i
$49$	4.67649e10	−	6.76609e11i	0.0689521	−	0.997620i
$50$	2.99752e11			0.383683
$51$	−3.02461e11	+	5.23877e11i	−0.337037	+	0.583765i
$52$	4.33464e11	−	2.50261e11i	0.421628	−	0.243427i
$53$	−7.07618e11	−	1.22563e12i	−0.602376	−	1.04335i	−0.992460	−	0.122567i	$-0.960888\pi$
$53$	−7.07618e11	−	1.22563e12i	−0.602376	−	1.04335i	0.390084	−	0.920779i	$-0.372446\pi$
$54$	5.96162e11	+	3.44194e11i	0.445254	+	0.257068i
$55$		−	1.58476e12i		−	1.04094i
$56$	−4.46411e11	+	4.16622e11i	−0.258475	+	0.241227i
$57$	8.06469e11			0.412538
$58$	1.17954e12	−	2.04302e12i	0.534216	−	0.925289i
$59$	1.85845e12	−	1.07298e12i	0.746770	−	0.431148i	−0.0777555	−	0.996972i	$-0.524775\pi$
$59$	1.85845e12	−	1.07298e12i	0.746770	−	0.431148i	0.824526	+	0.565824i	$0.191442\pi$
$60$	1.86563e11	+	3.23137e11i	0.0666449	+	0.115432i
$61$	−1.76997e12	−	1.02189e12i	−0.563193	−	0.325160i	0.191233	−	0.981545i	$-0.438751\pi$
$61$	−1.76997e12	−	1.02189e12i	−0.563193	−	0.325160i	−0.754426	+	0.656385i	$0.772085\pi$
$62$			1.52957e12i			0.434338i
$63$	−7.49715e11	−	3.24141e12i	−0.190332	−	0.822906i
$64$	5.49756e11			0.125000
$65$	−1.61412e12	+	2.79574e12i	−0.329263	+	0.570300i
$66$	−2.02669e12	+	1.17011e12i	−0.371518	+	0.214496i
$67$	3.51155e12	+	6.08219e12i	0.579396	+	1.00354i	0.995549	+	0.0942485i	$0.0300448\pi$
$67$	3.51155e12	+	6.08219e12i	0.579396	+	1.00354i	−0.416153	+	0.909295i	$0.636622\pi$
$68$	−4.97837e12	−	2.87426e12i	−0.740500	−	0.427528i
$69$			4.60591e12i			0.618546i
$70$	1.14995e12	−	3.76673e12i	0.139634	−	0.457381i
$71$	1.32667e12			0.145866			0.0729330	−	0.997337i	$-0.476764\pi$
$71$	1.32667e12			0.145866			0.0729330	+	0.997337i	$0.476764\pi$
$72$	−1.49768e12	+	2.59406e12i	−0.149311	+	0.258614i
$73$	−1.14065e13	+	6.58554e12i	−1.03250	+	0.596116i	−0.917701	−	0.397272i	$-0.869957\pi$
$73$	−1.14065e13	+	6.58554e12i	−1.03250	+	0.596116i	−0.114803	+	0.993388i	$0.536624\pi$
$74$	−1.53506e10	−	2.65880e10i	−0.00126329	−	0.00218808i
$75$	2.47246e12	+	1.42748e12i	0.185226	+	0.106940i
$76$			7.66382e12i			0.523300i
$77$	2.36247e13	+	7.21237e12i	1.47208	+	0.449411i
$78$	4.76716e12			0.271392
$79$	−2.22090e12	+	3.84672e12i	−0.115648	+	0.200309i	−0.918039	−	0.396491i	$-0.870228\pi$
$79$	−2.22090e12	+	3.84672e12i	−0.115648	+	0.200309i	0.802390	+	0.596800i	$0.203561\pi$
$80$	−3.07075e12	+	1.77290e12i	−0.146425	+	0.0845383i
$81$	−6.38297e12	−	1.10556e13i	−0.279015	−	0.483269i
$82$	−2.08203e13	−	1.20206e13i	−0.835200	−	0.482203i
$83$			2.90141e13i			1.06921i	0.845103	+	0.534604i	$0.179539\pi$
$83$			2.90141e13i			1.06921i	−0.845103	+	0.534604i	$0.820461\pi$
$84$	−5.66620e12	+	1.31055e12i	−0.192016	+	0.0444119i
$85$	3.70766e13			1.15656
$86$	6.02501e12	−	1.04356e13i	0.173168	−	0.299937i
$87$	1.94586e13	−	1.12344e13i	0.515793	−	0.297793i
$88$	−1.11195e13	−	1.92595e13i	−0.272086	−	0.471267i
$89$	−9.69029e11	−	5.59469e11i	−0.0219082	−	0.0126487i	0.489006	−	0.872280i	$-0.337360\pi$
$89$	−9.69029e11	−	5.59469e11i	−0.0219082	−	0.0126487i	−0.510914	+	0.859632i	$0.670693\pi$
$90$		−	1.93194e13i		−	0.403920i
$91$	−3.43313e13	−	3.67861e13i	−0.664355	−	0.711858i
$92$	−4.37697e13			−0.784619
$93$	−7.28412e12	+	1.26165e13i	−0.121059	+	0.209680i
$94$	2.94221e13	−	1.69868e13i	0.453710	−	0.261949i
$95$	−2.47149e13	−	4.28075e13i	−0.353911	−	0.612992i
$96$	4.53458e12	+	2.61804e12i	0.0603447	+	0.0348400i
$97$		−	3.91392e13i		−	0.484406i	−0.970226	−	0.242203i	$-0.922130\pi$
$97$		−	3.91392e13i		−	0.484406i	0.970226	−	0.242203i	$-0.0778701\pi$
$98$	5.09188e13	+	3.42854e13i	0.586537	+	0.394936i
$99$	1.21170e14			1.30001
$100$	−1.35652e13	+	2.34957e13i	−0.135652	+	0.234957i
$101$	−6.83990e13	+	3.94902e13i	−0.637970	+	0.368332i	−0.783832	−	0.620973i	$-0.786738\pi$
$101$	−6.83990e13	+	3.94902e13i	−0.637970	+	0.368332i	0.145862	+	0.989305i	$0.453404\pi$
$102$	−2.73756e13	−	4.74159e13i	−0.238321	−	0.412784i
$103$	−1.39636e14	−	8.06187e13i	−1.13537	−	0.655504i	−0.190087	−	0.981767i	$-0.560877\pi$
$103$	−1.39636e14	−	8.06187e13i	−1.13537	−	0.655504i	−0.945279	+	0.326263i	$0.894210\pi$
$104$			4.53020e13i			0.344258i
$105$	2.74231e13	−	2.55931e13i	0.194891	−	0.181885i
$106$	1.28092e14			0.851888
$107$	−3.07806e13	+	5.33135e13i	−0.191686	+	0.332010i	−0.945809	−	0.324723i	$-0.894729\pi$
$107$	−3.07806e13	+	5.33135e13i	−0.191686	+	0.332010i	0.754123	+	0.656733i	$0.228062\pi$
$108$	−5.39585e13	+	3.11529e13i	−0.314842	+	0.181774i
$109$	4.56239e13	+	7.90229e13i	0.249578	+	0.432283i	0.963409	−	0.268036i	$-0.0863746\pi$
$109$	4.56239e13	+	7.90229e13i	0.249578	+	0.432283i	−0.713830	+	0.700319i	$0.753041\pi$
$110$	1.24219e14	+	7.17181e13i	0.637442	+	0.368027i
$111$		−	2.92409e11i		−	0.00140841i
$112$	−1.24541e13	−	5.38455e13i	−0.0563360	−	0.243570i
$113$	−3.38777e13			−0.144001			−0.0720004	−	0.997405i	$-0.522938\pi$
$113$	−3.38777e13			−0.144001			−0.0720004	+	0.997405i	$0.522938\pi$
$114$	−3.64966e13	+	6.32140e13i	−0.145854	+	0.252627i
$115$	2.44483e14	−	1.41152e14i	0.919101	−	0.530643i
$116$	1.06760e14	+	1.84913e14i	0.377748	+	0.654278i
$117$	−2.13761e14	−	1.23415e14i	−0.712240	−	0.411212i
$118$			1.94230e14i			0.609735i
$119$	−1.68739e14	+	5.52717e14i	−0.499329	+	1.63559i
$120$	−3.37715e13			−0.0942501
$121$	−2.59936e14	+	4.50222e14i	−0.684492	+	1.18557i
$122$	1.60199e14	−	9.24912e13i	0.398238	−	0.229923i
$123$	−1.14489e14	−	1.98301e14i	−0.268799	−	0.465574i
$124$	−1.19893e14	−	6.92205e13i	−0.265977	−	0.153562i
$125$		−	4.97473e14i		−	1.04328i
$126$	2.88002e14	+	8.79240e13i	0.571217	+	0.174387i
$127$	−4.40638e14			−0.826906			−0.413453	−	0.910526i	$-0.635677\pi$
$127$	−4.40638e14			−0.826906			−0.413453	+	0.910526i	$0.635677\pi$
$128$	−2.48791e13	+	4.30919e13i	−0.0441942	+	0.0765466i
$129$	9.93929e13	−	5.73845e13i	0.167197	−	0.0965310i
$130$	−1.46094e14	−	2.53042e14i	−0.232824	−	0.403263i
$131$	8.40492e12	+	4.85258e12i	0.0126950	+	0.00732949i	0.506334	−	0.862337i	$-0.331000\pi$
$131$	8.40492e12	+	4.85258e12i	0.0126950	+	0.00732949i	−0.493639	+	0.869667i	$0.664334\pi$
$132$		−	2.11813e14i		−	0.303343i
$133$	7.50629e14	−	1.73615e14i	1.01968	−	0.235845i
$134$	−6.35659e14			−0.819390
$135$	2.00929e14	−	3.48019e14i	0.245870	−	0.425860i
$136$	4.50591e14	−	2.60149e14i	0.523612	−	0.302308i
$137$	5.62249e14	+	9.73844e14i	0.620704	+	1.07509i	0.989355	+	0.145523i	$0.0464865\pi$
$137$	5.62249e14	+	9.73844e14i	0.620704	+	1.07509i	−0.368651	+	0.929568i	$0.620180\pi$
$138$	−3.61028e14	−	2.08440e14i	−0.378781	−	0.218689i
$139$		−	1.61426e15i		−	1.61016i	−0.593165	−	0.805081i	$-0.702122\pi$
$139$		−	1.61426e15i		−	1.61016i	0.593165	−	0.805081i	$-0.297878\pi$
$140$	2.43210e14	+	2.60600e14i	0.230720	+	0.247217i
$141$	3.23578e14			0.292042
$142$	−6.00382e13	+	1.03989e14i	−0.0515714	+	0.0893243i
$143$	1.58706e15	−	9.16289e14i	1.29790	−	0.749342i
$144$	−1.35555e14	−	2.34787e14i	−0.105579	−	0.182868i
$145$	−1.19265e15	−	6.88576e14i	−0.884986	−	0.510947i
$146$		−	1.19211e15i		−	0.843036i
$147$	2.56722e14	+	5.25284e14i	0.173078	+	0.354138i
$148$	2.77875e12			0.00178656
$149$	−1.10305e15	+	1.91053e15i	−0.676534	+	1.17179i	0.299484	+	0.954101i	$0.403185\pi$
$149$	−1.10305e15	+	1.91053e15i	−0.676534	+	1.17179i	−0.976018	+	0.217690i	$0.930148\pi$
$150$	−2.23782e14	+	1.29201e14i	−0.130974	+	0.0756180i
$151$	−7.55996e14	−	1.30942e15i	−0.422358	−	0.731546i	0.573812	−	0.818987i	$-0.305464\pi$
$151$	−7.55996e14	−	1.30942e15i	−0.422358	−	0.731546i	−0.996170	+	0.0874416i	$0.972131\pi$
$152$	−6.00719e14	−	3.46825e14i	−0.320454	−	0.185014i
$153$			2.83486e15i			1.44441i
$154$	−1.63446e15	+	1.52539e15i	−0.795665	+	0.742569i
$155$	8.92912e14			0.415419
$156$	−2.15737e14	+	3.73668e14i	−0.0959517	+	0.166193i
$157$	3.54745e14	−	2.04812e14i	0.150876	−	0.0871081i	−0.422662	−	0.906288i	$-0.638904\pi$
$157$	3.54745e14	−	2.04812e14i	0.150876	−	0.0871081i	0.573537	+	0.819179i	$0.305571\pi$
$158$	−2.01013e14	−	3.48165e14i	−0.0817758	−	0.141640i
$159$	1.05655e15	+	6.10001e14i	0.411255	+	0.237438i
$160$		−	3.20929e14i		−	0.119555i
$161$	9.91553e14	+	4.28700e15i	0.353618	+	1.52888i
$162$	1.15544e15			0.394587
$163$	−2.63887e15	+	4.57065e15i	−0.863186	+	1.49508i	0.00565104	+	0.999984i	$0.498201\pi$
$163$	−2.63887e15	+	4.57065e15i	−0.863186	+	1.49508i	−0.868837	+	0.495098i	$0.835132\pi$
$164$	1.88444e15	−	1.08798e15i	0.590576	−	0.340969i
$165$	6.83071e14	+	1.18311e15i	0.205153	+	0.355336i
$166$	−2.27423e15	−	1.31303e15i	−0.654753	−	0.378022i
$167$		−	7.01298e15i		−	1.93592i	−0.251106	−	0.967960i	$-0.580794\pi$
$167$		−	7.01298e15i		−	1.93592i	0.251106	−	0.967960i	$-0.419206\pi$
$168$	1.53697e14	−	5.03446e14i	0.0406912	−	0.133287i
$169$	2.04311e14			0.0518902
$170$	−1.67790e15	+	2.90620e15i	−0.408906	+	0.708245i
$171$	3.27303e15	−	1.88969e15i	0.765557	−	0.441995i
$172$	5.45322e14	+	9.44525e14i	0.122449	+	0.212087i
$173$	−2.83973e15	−	1.63952e15i	−0.612286	−	0.353504i	0.161573	−	0.986861i	$-0.448343\pi$
$173$	−2.83973e15	−	1.63952e15i	−0.612286	−	0.353504i	−0.773860	+	0.633357i	$0.781676\pi$
$174$			2.03364e15i			0.421144i
$175$	2.60858e15	+	7.96372e14i	0.518964	+	0.158434i
$176$	2.01284e15			0.384788
$177$	−9.24959e14	+	1.60208e15i	−0.169945	+	0.294354i
$178$	8.77065e13	−	5.06374e13i	0.0154914	−	0.00894398i
$179$	−2.19406e15	−	3.80022e15i	−0.372629	−	0.645413i	0.617340	−	0.786697i	$-0.288210\pi$
$179$	−2.19406e15	−	3.80022e15i	−0.372629	−	0.645413i	−0.989969	+	0.141284i	$0.954877\pi$
$180$	1.51432e15	+	8.74295e14i	0.247349	+	0.142807i
$181$			2.32948e14i			0.0366023i	0.999833	+	0.0183012i	$0.00582576\pi$
$181$			2.32948e14i			0.0366023i	−0.999833	+	0.0183012i	$0.994174\pi$
$182$	4.43708e15	−	1.02627e15i	0.670807	−	0.155153i
$183$	1.76184e15			0.256336
$184$	1.98079e15	−	3.43083e15i	0.277405	−	0.480479i
$185$	−1.55211e13	+	8.96114e12i	−0.00209277	+	0.00120826i
$186$	−6.59283e14	−	1.14191e15i	−0.0856015	−	0.148266i
$187$	−1.82275e16	−	1.05237e16i	−2.27948	−	1.31606i
$188$			3.07495e15i			0.370452i
$189$	4.27362e15	+	4.57920e15i	0.496094	+	0.531565i
$190$	4.47388e15			0.500506
$191$	1.38855e15	−	2.40504e15i	0.149737	−	0.259352i	−0.781393	−	0.624039i	$-0.785491\pi$
$191$	1.38855e15	−	2.40504e15i	0.149737	−	0.259352i	0.931130	+	0.364687i	$0.118824\pi$
$192$	−4.10424e14	+	2.36958e14i	−0.0426701	+	0.0246356i
$193$	−7.24969e15	−	1.25568e16i	−0.726806	−	1.25886i	−0.958227	−	0.286010i	$-0.907671\pi$
$193$	−7.24969e15	−	1.25568e16i	−0.726806	−	1.25886i	0.231421	−	0.972854i	$-0.425663\pi$
$194$	3.06788e15	+	1.77124e15i	0.296637	+	0.171264i
$195$		−	2.78291e15i		−	0.259571i
$196$	−4.99174e15	+	2.43962e15i	−0.449220	+	0.219548i
$197$	4.36142e15			0.378760			0.189380	−	0.981904i	$-0.439352\pi$
$197$	4.36142e15			0.378760			0.189380	+	0.981904i	$0.439352\pi$
$198$	−5.48351e15	+	9.49773e15i	−0.459624	+	0.796092i
$199$	1.19405e15	−	6.89387e14i	0.0966167	−	0.0557817i	−0.450913	−	0.892568i	$-0.648902\pi$
$199$	1.19405e15	−	6.89387e14i	0.0966167	−	0.0557817i	0.547530	+	0.836786i	$0.315568\pi$
$200$	−1.22778e15	−	2.12659e15i	−0.0959207	−	0.166139i
$201$	−5.24314e15	−	3.02713e15i	−0.395566	−	0.228380i
$202$		−	7.14848e15i		−	0.520900i
$203$	1.56927e16	−	1.46455e16i	1.10465	−	1.03094i
$204$	4.95551e15			0.337037
$205$	−7.01723e15	+	1.21542e16i	−0.461199	+	0.798821i
$206$	1.26384e16	−	7.29677e15i	0.802825	−	0.463511i
$207$	1.07924e16	+	1.86930e16i	0.662713	+	1.14785i
$208$	−3.55094e15	−	2.05014e15i	−0.210814	−	0.121714i
$209$			2.80599e16i			1.61087i
$210$	7.65055e14	+	3.30773e15i	0.0424774	+	0.183652i
$211$	−3.85254e15			−0.206905			−0.103452	−	0.994634i	$-0.532989\pi$
$211$	−3.85254e15			−0.206905			−0.103452	+	0.994634i	$0.532989\pi$
$212$	−5.79680e15	+	1.00404e16i	−0.301188	+	0.521673i
$213$	−9.90433e14	+	5.71827e14i	−0.0497929	+	0.0287480i
$214$	−2.78594e15	−	4.82539e15i	−0.135542	−	0.234766i
$215$	−6.09196e15	−	3.51720e15i	−0.286872	−	0.165626i
$216$		−	5.63928e15i		−	0.257068i
$217$	−4.06371e15	+	1.33110e16i	−0.179352	+	0.587479i
$218$	−8.25881e15			−0.352957
$219$	5.67706e15	−	9.83295e15i	0.234971	−	0.406982i
$220$	−1.12430e16	+	6.49118e15i	−0.450739	+	0.260234i
$221$	2.14373e16	+	3.71304e16i	0.832575	+	1.44206i
$222$	2.29201e13	+	1.32329e13i	0.000862474	+	0.000497950i
$223$		−	3.21148e16i		−	1.17104i	−0.810658	−	0.585519i	$-0.800891\pi$
$223$		−	3.21148e16i		−	1.17104i	0.810658	−	0.585519i	$-0.199109\pi$
$224$	4.78422e15	+	1.46057e15i	0.169073	+	0.0516163i
$225$	1.33792e16			0.458304
$226$	1.53313e15	−	2.65546e15i	0.0509120	−	0.0881822i
$227$	−1.88855e16	+	1.09036e16i	−0.608062	+	0.351065i	−0.772207	−	0.635371i	$-0.780847\pi$
$227$	−1.88855e16	+	1.09036e16i	−0.608062	+	0.351065i	0.164144	+	0.986436i	$0.447514\pi$
$228$	−3.30330e15	−	5.72148e15i	−0.103134	−	0.178634i
$229$	5.68686e15	+	3.28331e15i	0.172197	+	0.0994177i	0.583621	−	0.812026i	$-0.301635\pi$
$229$	5.68686e15	+	3.28331e15i	0.172197	+	0.0994177i	−0.411425	+	0.911444i	$0.634969\pi$
$230$			2.55513e16i			0.750443i
$231$	−2.07459e16	+	4.79837e15i	−0.591082	+	0.136713i
$232$	−1.93256e16			−0.534216
$233$	−1.00381e16	+	1.73865e16i	−0.269252	+	0.466358i	−0.968669	−	0.248356i	$-0.920110\pi$
$233$	−1.00381e16	+	1.73865e16i	−0.269252	+	0.466358i	0.699417	+	0.714714i	$0.253443\pi$
$234$	1.93474e16	−	1.11702e16i	0.503630	−	0.290771i
$235$	−9.91634e15	−	1.71756e16i	−0.250539	−	0.433947i
$236$	−1.52244e16	−	8.78983e15i	−0.373385	−	0.215574i
$237$		−	3.82905e15i		−	0.0911702i
$238$	−3.56877e16	−	3.82395e16i	−0.825050	−	0.884043i
$239$	4.21922e16			0.947212			0.473606	−	0.880737i	$-0.342952\pi$
$239$	4.21922e16			0.947212			0.473606	+	0.880737i	$0.342952\pi$
$240$	1.52832e15	−	2.64714e15i	0.0333225	−	0.0577162i
$241$	2.56080e16	−	1.47848e16i	0.542320	−	0.313109i	−0.203699	−	0.979034i	$-0.565296\pi$
$241$	2.56080e16	−	1.47848e16i	0.542320	−	0.313109i	0.746019	+	0.665925i	$0.231963\pi$
$242$	−2.35267e16	−	4.07494e16i	−0.484009	−	0.838328i
$243$	4.10346e16	+	2.36913e16i	0.820175	+	0.473528i
$244$			1.67427e16i			0.325160i
$245$	2.00147e16	−	2.97246e16i	0.377734	−	0.560988i
$246$	2.07247e16			0.380140
$247$	2.85797e16	−	4.95016e16i	0.509542	−	0.882552i
$248$	1.08515e16	−	6.26512e15i	0.188074	−	0.108585i
$249$	−1.25058e16	−	2.16606e16i	−0.210725	−	0.364986i
$250$	3.89938e16	+	2.25131e16i	0.638874	+	0.368854i
$251$		−	2.96823e16i		−	0.472914i	−0.971642	−	0.236457i	$-0.924014\pi$
$251$		−	2.96823e16i		−	0.472914i	0.971642	−	0.236457i	$-0.0759862\pi$
$252$	−1.99253e16	+	1.85957e16i	−0.308746	+	0.288143i
$253$	−1.60256e17			−2.41529
$254$	1.99410e16	−	3.45388e16i	0.292355	−	0.506374i
$255$	−2.76798e16	+	1.59809e16i	−0.394804	+	0.227940i
$256$	−2.25180e15	−	3.90023e15i	−0.0312500	−	0.0541266i
$257$	8.36892e16	+	4.83180e16i	1.13015	+	0.652494i	0.943973	−	0.330021i	$-0.107056\pi$
$257$	8.36892e16	+	4.83180e16i	1.13015	+	0.652494i	0.186180	+	0.982516i	$0.440389\pi$
$258$			1.03877e16i			0.136516i
$259$	−6.29494e13	−	2.72163e14i	−0.000805180	−	0.00348121i
$260$	2.64458e16			0.329263
$261$	5.26480e16	−	9.11891e16i	0.638114	−	1.10525i
$262$	−7.60726e14	+	4.39205e14i	−0.00897675	+	0.00518273i
$263$	2.98508e16	+	5.17031e16i	0.342978	+	0.594055i	0.984984	−	0.172644i	$-0.0552311\pi$
$263$	2.98508e16	+	5.17031e16i	0.342978	+	0.594055i	−0.642007	+	0.766699i	$0.721898\pi$
$264$	1.66026e16	+	9.58554e15i	0.185759	+	0.107248i
$265$		−	7.47760e16i		−	0.814782i
$266$	−2.03610e16	+	6.66940e16i	−0.216086	+	0.707808i
$267$	9.64580e14			0.00997147
$268$	2.87666e16	−	4.98253e16i	0.289698	−	0.501772i
$269$	−1.66624e17	+	9.62005e16i	−1.63483	+	0.943868i	−0.652253	+	0.758001i	$0.726176\pi$
$269$	−1.66624e17	+	9.62005e16i	−1.63483	+	0.943868i	−0.982575	+	0.185867i	$0.940491\pi$
$270$	1.81860e16	+	3.14991e16i	0.173857	+	0.301129i
$271$	−5.58434e16	−	3.22412e16i	−0.520220	−	0.300349i	0.216805	−	0.976215i	$-0.430437\pi$
$271$	−5.58434e16	−	3.22412e16i	−0.520220	−	0.300349i	−0.737025	+	0.675866i	$0.763770\pi$
$272$			4.70919e16i			0.427528i
$273$	4.14859e16	+	1.26652e16i	0.367081	+	0.112066i
$274$	−1.01778e17			−0.877808
$275$	−4.96669e16	+	8.60256e16i	−0.417579	+	0.723267i
$276$	3.26766e16	−	1.88658e16i	0.267838	−	0.154637i
$277$	7.38339e16	+	1.27884e17i	0.590062	+	1.02202i	0.994224	+	0.107330i	$0.0342300\pi$
$277$	7.38339e16	+	1.27884e17i	0.590062	+	1.02202i	−0.404162	+	0.914688i	$0.632437\pi$
$278$	1.26532e17	+	7.30530e16i	0.986019	+	0.569278i
$279$			6.82714e16i			0.518811i
$280$	−3.14332e16	+	7.27027e15i	−0.232960	+	0.0538821i
$281$	−8.84673e16			−0.639497			−0.319749	−	0.947502i	$-0.603598\pi$
$281$	−8.84673e16			−0.639497			−0.319749	+	0.947502i	$0.603598\pi$
$282$	−1.46435e16	+	2.53633e16i	−0.103253	+	0.178839i
$283$	−1.31200e17	+	7.57484e16i	−0.902463	+	0.521037i	−0.877998	−	0.478664i	$-0.841121\pi$
$283$	−1.31200e17	+	7.57484e16i	−0.902463	+	0.521037i	−0.0244643	+	0.999701i	$0.507788\pi$
$284$	−5.43403e15	−	9.41202e15i	−0.0364665	−	0.0631618i
$285$	3.69022e16	+	2.13055e16i	0.241623	+	0.139501i
$286$			1.65866e17i			1.05973i
$287$	−1.49252e17	−	1.59924e17i	−0.930564	−	0.997101i
$288$	2.45380e16			0.149311
$289$	1.62020e17	−	2.80627e17i	0.962239	−	1.66665i
$290$	1.07946e17	−	6.23228e16i	0.625779	−	0.361294i
$291$	1.68700e16	+	2.92196e16i	0.0954692	+	0.165357i
$292$	9.34419e16	+	5.39487e16i	0.516252	+	0.298058i
$293$		−	1.20045e17i		−	0.647549i	−0.946134	−	0.323774i	$-0.895048\pi$
$293$		−	1.20045e17i		−	0.647549i	0.946134	−	0.323774i	$-0.104952\pi$
$294$	−5.27916e16	−	3.64877e15i	−0.278057	−	0.0192183i
$295$	1.13385e17			0.583177
$296$	−1.25752e14	+	2.17809e14i	−0.000631644	+	0.00109404i
$297$	−1.97560e17	+	1.14061e17i	−0.969180	+	0.559556i
$298$	−9.98363e16	−	1.72921e17i	−0.478382	−	0.828581i
$299$	2.82714e17	+	1.63225e17i	1.32327	+	0.763991i
$300$		−	2.33878e16i		−	0.106940i
$301$	8.01573e16	−	7.48084e16i	0.358078	−	0.334183i
$302$	1.36850e17			0.597305
$303$	3.40425e16	−	5.89633e16i	0.145185	−	0.251468i
$304$	5.43709e16	−	3.13910e16i	0.226595	−	0.130825i
$305$	−5.39932e16	−	9.35190e16i	−0.219908	−	0.380891i
$306$	−2.22206e17	−	1.28291e17i	−0.884518	−	0.510677i
$307$		−	1.45767e16i		−	0.0567142i	−0.999598	−	0.0283571i	$-0.990972\pi$
$307$		−	1.45767e16i		−	0.0567142i	0.999598	−	0.0283571i	$-0.00902756\pi$
$308$	−4.55986e16	−	1.97147e17i	−0.173419	−	0.749781i
$309$	1.38995e17			0.516760
$310$	−4.04086e16	+	6.99897e16i	−0.146873	+	0.254391i
$311$	−1.26836e17	+	7.32286e16i	−0.450732	+	0.260230i	−0.708139	−	0.706073i	$-0.750465\pi$
$311$	−1.26836e17	+	7.32286e16i	−0.450732	+	0.260230i	0.257407	+	0.966303i	$0.417132\pi$
$312$	−1.95263e16	−	3.38205e16i	−0.0678481	−	0.117516i
$313$	−2.07815e17	−	1.19982e17i	−0.706102	−	0.407668i	0.103514	−	0.994628i	$-0.466991\pi$
$313$	−2.07815e17	−	1.19982e17i	−0.706102	−	0.407668i	−0.809616	+	0.586960i	$0.800325\pi$
$314$			3.70750e16i			0.123189i
$315$	5.13271e16	−	1.68126e17i	0.166791	−	0.546336i
$316$	3.63873e16			0.115648
$317$	1.97544e17	−	3.42157e17i	0.614115	−	1.06368i	−0.376424	−	0.926447i	$-0.622847\pi$
$317$	1.97544e17	−	3.42157e17i	0.614115	−	1.06368i	0.990539	−	0.137230i	$-0.0438201\pi$
$318$	−9.56283e16	+	5.52110e16i	−0.290801	+	0.167894i
$319$	3.90884e17	+	6.77031e17i	1.16282	+	2.01407i
$320$	2.51556e16	+	1.45236e16i	0.0732123	+	0.0422692i
$321$		−	5.30687e16i		−	0.151114i
$322$	−3.80903e17	−	1.16286e17i	−1.06126	−	0.323993i
$323$	−6.56481e17			−1.78980
$324$	−5.22893e16	+	9.05678e16i	−0.139508	+	0.241634i
$325$	1.75239e17	−	1.01174e17i	0.457559	−	0.264172i
$326$	−2.38843e17	−	4.13688e17i	−0.610365	−	1.05718i
$327$	−6.81217e16	−	3.93301e16i	−0.170393	−	0.0983763i
$328$			1.96946e17i			0.482203i
$329$	3.01174e17	−	6.96594e16i	0.721848	−	0.166958i
$330$	−1.23649e17			−0.290130
$331$	−1.77772e17	+	3.07911e17i	−0.408384	+	0.707342i	−0.994709	−	0.102734i	$-0.967241\pi$
$331$	−1.77772e17	+	3.07911e17i	−0.408384	+	0.707342i	0.586325	+	0.810076i	$0.300574\pi$
$332$	2.05840e17	−	1.18842e17i	0.462980	−	0.267302i
$333$	−6.85162e14	−	1.18674e15i	−0.00150898	−	0.00261363i
$334$	5.49703e17	+	3.17371e17i	1.18550	+	0.684451i
$335$			3.71076e17i			0.783699i
$336$	3.25064e16	+	3.48307e16i	0.0672348	+	0.0720423i
$337$	7.21778e17			1.46216			0.731079	−	0.682293i	$-0.239017\pi$
$337$	7.21778e17			1.46216			0.731079	+	0.682293i	$0.239017\pi$
$338$	−9.24608e15	+	1.60147e16i	−0.0183460	+	0.0317761i
$339$	2.52916e16	−	1.46021e16i	0.0491563	−	0.0283804i
$340$	−1.51866e17	−	2.63040e17i	−0.289140	−	0.500805i
$341$	−4.38970e17	−	2.53440e17i	−0.818756	−	0.472709i
$342$			3.42070e17i			0.625075i
$343$	3.52029e17	+	4.33646e17i	0.630260	+	0.776384i
$344$	−9.87138e16			−0.173168
$345$	−1.21680e17	+	2.10756e17i	−0.209163	+	0.362282i
$346$	2.57023e17	−	1.48392e17i	0.432952	−	0.249965i
$347$	−5.78628e16	−	1.00221e17i	−0.0955198	−	0.165445i	0.814306	−	0.580436i	$-0.197118\pi$
$347$	−5.78628e16	−	1.00221e17i	−0.0955198	−	0.165445i	−0.909825	+	0.414991i	$0.863785\pi$
$348$	−1.59404e17	−	9.20322e16i	−0.257897	−	0.148897i
$349$			4.52169e17i			0.717006i	0.933529	+	0.358503i	$0.116713\pi$
$349$			4.52169e17i			0.717006i	−0.933529	+	0.358503i	$0.883287\pi$
$350$	−1.80473e17	+	1.68430e17i	−0.280502	+	0.261784i
$351$	4.64699e17			0.707981
$352$	−9.10908e16	+	1.57774e17i	−0.136043	+	0.235633i
$353$	−5.52373e17	+	3.18913e17i	−0.808741	+	0.466927i	−0.846518	−	0.532359i	$-0.821306\pi$
$353$	−5.52373e17	+	3.18913e17i	−0.808741	+	0.466927i	0.0377775	+	0.999286i	$0.487972\pi$
$354$	−8.37177e16	−	1.45003e17i	−0.120170	−	0.208140i
$355$	6.07053e16	+	3.50482e16i	0.0854335	+	0.0493251i
$356$			9.16634e15i			0.0126487i
$357$	−1.12261e17	−	4.85365e17i	−0.151898	−	0.656736i
$358$	3.97167e17			0.526978
$359$	−2.84387e16	+	4.92573e16i	−0.0370040	+	0.0640929i	−0.883934	−	0.467611i	$-0.845115\pi$
$359$	−2.84387e16	+	4.92573e16i	−0.0370040	+	0.0640929i	0.846930	+	0.531704i	$0.178448\pi$
$360$	−1.37061e17	+	7.91321e16i	−0.174902	+	0.100980i
$361$	3.81006e16	+	6.59922e16i	0.0476850	+	0.0825929i
$362$	−1.82593e16	−	1.05420e16i	−0.0224142	−	0.0129409i
$363$		−	4.48155e17i		−	0.539612i
$364$	−1.20357e17	+	3.94238e17i	−0.142155	+	0.465639i
$365$	−6.95913e17			−0.806315
$366$	−7.97320e16	+	1.38100e17i	−0.0906285	+	0.156973i
$367$	−5.18527e17	+	2.99372e17i	−0.578241	+	0.333848i	−0.760434	−	0.649415i	$-0.775014\pi$
$367$	−5.18527e17	+	2.99372e17i	−0.578241	+	0.333848i	0.182193	+	0.983263i	$0.441680\pi$
$368$	1.79281e17	+	3.10523e17i	0.196155	+	0.339750i
$369$	−9.29302e17	−	5.36533e17i	−0.997636	−	0.575986i
$370$		−	1.62214e15i		−	0.00170874i
$371$	1.11472e18	+	3.40312e17i	1.15225	+	0.351771i
$372$	1.19343e17			0.121059
$373$	1.42476e17	−	2.46776e17i	0.141834	−	0.245664i	−0.786353	−	0.617777i	$-0.788033\pi$
$373$	1.42476e17	−	2.46776e17i	0.141834	−	0.245664i	0.928187	+	0.372113i	$0.121367\pi$
$374$	1.64977e18	−	9.52492e17i	1.61184	−	0.930594i
$375$	2.14423e17	+	3.71392e17i	0.205614	+	0.356134i
$376$	−2.41026e17	−	1.39156e17i	−0.226855	−	0.130975i
$377$		−	1.59250e18i		−	1.47127i
$378$	−5.52336e17	+	1.27751e17i	−0.500912	+	0.115857i
$379$	−7.15600e17			−0.637082			−0.318541	−	0.947909i	$-0.603193\pi$
$379$	−7.15600e17			−0.637082			−0.318541	+	0.947909i	$0.603193\pi$
$380$	−2.02465e17	+	3.50679e17i	−0.176956	+	0.306496i
$381$	3.28961e17	−	1.89926e17i	0.282273	−	0.162971i
$382$	1.25677e17	+	2.17680e17i	0.105880	+	0.183389i
$383$	−1.54412e18	−	8.91499e17i	−1.27729	−	0.737445i	−0.300942	−	0.953642i	$-0.597301\pi$
$383$	−1.54412e18	−	8.91499e17i	−1.27729	−	0.737445i	−0.976350	+	0.216197i	$0.930635\pi$
$384$		−	4.28940e16i		−	0.0348400i
$385$	8.90473e17	+	9.54144e17i	0.710225	+	0.761007i
$386$	1.31233e18			1.02786
$387$	2.68922e17	−	4.65787e17i	0.206848	−	0.358270i
$388$	−2.77672e17	+	1.60314e17i	−0.209754	+	0.121102i
$389$	−5.52484e17	−	9.56930e17i	−0.409895	−	0.709959i	0.584983	−	0.811046i	$-0.301101\pi$
$389$	−5.52484e17	−	9.56930e17i	−0.409895	−	0.709959i	−0.994878	+	0.101087i	$0.967768\pi$
$390$	2.18134e17	+	1.25940e17i	0.158954	+	0.0917722i
$391$		−	3.74930e18i		−	2.68357i
$392$	3.46741e16	−	5.01675e17i	0.0243782	−	0.352712i
$393$	−8.36633e15			−0.00577813
$394$	−1.97375e17	+	3.41864e17i	−0.133912	+	0.231942i
$395$	−2.03247e17	+	1.17345e17i	−0.135470	+	0.0782138i
$396$	−4.96311e17	−	8.59636e17i	−0.325003	−	0.562922i
$397$	2.24764e18	+	1.29768e18i	1.44608	+	0.834897i	0.998245	−	0.0592169i	$-0.0188604\pi$
$397$	2.24764e18	+	1.29768e18i	1.44608	+	0.834897i	0.447839	+	0.894114i	$0.352194\pi$
$398$			1.24792e17i			0.0788872i
$399$	−4.85555e17	+	4.53153e17i	−0.301598	+	0.281472i
$400$	2.22253e17			0.135652
$401$	−1.54583e18	+	2.67745e18i	−0.927150	+	1.60587i	−0.139084	+	0.990281i	$0.544416\pi$
$401$	−1.54583e18	+	2.67745e18i	−0.927150	+	1.60587i	−0.788066	+	0.615591i	$0.788918\pi$
$402$	4.74555e17	−	2.73985e17i	0.279708	−	0.161489i
$403$	5.16271e17	+	8.94207e17i	0.299049	+	0.517968i
$404$	5.60324e17	+	3.23503e17i	0.318985	+	0.184166i
$405$		−	6.74507e17i		−	0.377400i
$406$	4.37799e17	+	1.89283e18i	0.240765	+	1.04095i
$407$	1.01739e16			0.00549956
$408$	−2.24261e17	+	3.88431e17i	−0.119161	+	0.206392i
$409$	2.29789e18	−	1.32669e18i	1.20024	−	0.692957i	0.239628	−	0.970865i	$-0.422974\pi$
$409$	2.29789e18	−	1.32669e18i	1.20024	−	0.692957i	0.960608	+	0.277908i	$0.0896411\pi$
$410$	−6.35127e17	−	1.10007e18i	−0.326117	−	0.564852i
$411$	−8.39501e17	−	4.84686e17i	−0.423768	−	0.244663i
$412$			1.32086e18i			0.655504i
$413$	−5.16023e17	+	1.69027e18i	−0.251778	+	0.824719i
$414$	−1.95363e18			−0.937218
$415$	−7.66500e17	+	1.32762e18i	−0.361556	+	0.626233i
$416$	3.21394e17	−	1.85557e17i	0.149068	−	0.0860646i
$417$	6.95785e17	+	1.20514e18i	0.317339	+	0.549646i
$418$	−2.19943e18	−	1.26984e18i	−0.986455	−	0.569530i
$419$			3.49977e18i			1.54362i	0.635852	+	0.771811i	$0.280649\pi$
$419$			3.49977e18i			1.54362i	−0.635852	+	0.771811i	$0.719351\pi$
$420$	−2.93895e17	−	8.97231e16i	−0.127481	−	0.0389188i
$421$	−7.81184e16			−0.0333257			−0.0166628	−	0.999861i	$-0.505304\pi$
$421$	−7.81184e16			−0.0333257			−0.0166628	+	0.999861i	$0.505304\pi$
$422$	1.74346e17	−	3.01977e17i	0.0731519	−	0.126703i
$423$	1.31323e18	−	7.58196e17i	0.541951	−	0.312895i
$424$	−5.24667e17	−	9.08750e17i	−0.212972	−	0.368878i
$425$	−2.01263e18	−	1.16199e18i	−0.803604	−	0.463961i
$426$		−	1.03512e17i		−	0.0406558i
$427$	1.63985e18	−	3.79287e17i	0.633593	−	0.146545i
$428$	5.04309e17			0.191686
$429$	−7.89886e17	+	1.36812e18i	−0.295368	+	0.511593i
$430$	5.51382e17	−	3.18340e17i	0.202849	−	0.117115i
$431$	8.81897e17	+	1.52749e18i	0.319210	+	0.552888i	0.980323	−	0.197398i	$-0.0632490\pi$
$431$	8.81897e17	+	1.52749e18i	0.319210	+	0.552888i	−0.661113	+	0.750286i	$0.729916\pi$
$432$	4.42028e17	+	2.55205e17i	0.157421	+	0.0908872i
$433$			5.49478e17i			0.192546i	0.995355	+	0.0962731i	$0.0306922\pi$
$433$			5.49478e17i			0.192546i	−0.995355	+	0.0962731i	$0.969308\pi$
$434$	−8.59463e17	−	9.20916e17i	−0.296346	−	0.317535i
$435$	1.18717e18			0.402799
$436$	3.73751e17	−	6.47356e17i	0.124789	−	0.216141i
$437$	−4.32882e18	+	2.49925e18i	−1.42233	+	0.821182i
$438$	5.13828e17	+	8.89977e17i	0.166150	+	0.287780i
$439$	−7.26767e17	−	4.19599e17i	−0.231283	−	0.133531i	0.379881	−	0.925035i	$-0.375965\pi$
$439$	−7.26767e17	−	4.19599e17i	−0.231283	−	0.133531i	−0.611164	+	0.791504i	$0.709298\pi$
$440$		−	1.17503e18i		−	0.368027i
$441$	2.27273e18	+	1.53031e18i	0.700611	+	0.471746i
$442$	−3.88056e18			−1.17744
$443$	1.03363e18	−	1.79031e18i	0.308703	−	0.534689i	−0.669376	−	0.742924i	$-0.733439\pi$
$443$	1.03363e18	−	1.79031e18i	0.308703	−	0.534689i	0.978079	+	0.208235i	$0.0667718\pi$
$444$	−2.07449e15	+	1.19771e15i	−0.000609861	+	0.000352104i
$445$	−2.95604e16	−	5.12000e16i	−0.00855440	−	0.0148167i
$446$	2.51728e18	+	1.45335e18i	0.717112	+	0.414025i
$447$		−	1.90176e18i		−	0.533338i
$448$	−3.30994e17	+	3.08907e17i	−0.0913848	+	0.0852866i
$449$	3.35365e18			0.911576			0.455788	−	0.890088i	$-0.349357\pi$
$449$	3.35365e18			0.911576			0.455788	+	0.890088i	$0.349357\pi$
$450$	−6.05475e17	+	1.04871e18i	−0.162035	+	0.280653i
$451$	6.89958e18	−	3.98347e18i	1.81797	−	1.04961i
$452$	1.38763e17	+	2.40345e17i	0.0360002	+	0.0623542i
$453$	1.12879e18	+	6.51706e17i	0.288353	+	0.166481i
$454$		−	1.97376e18i		−	0.496481i
$455$	−5.99099e17	−	2.59022e18i	−0.148395	−	0.641588i
$456$	5.97961e17			0.145854
$457$	1.18023e18	−	2.04422e18i	0.283500	−	0.491037i	−0.688744	−	0.725004i	$-0.741838\pi$
$457$	1.18023e18	−	2.04422e18i	0.283500	−	0.491037i	0.972244	+	0.233968i	$0.0751710\pi$
$458$	−5.14716e17	+	2.97172e17i	−0.121761	+	0.0702990i
$459$	−2.66855e18	−	4.62207e18i	−0.621709	−	1.07683i
$460$	−2.00280e18	−	1.15632e18i	−0.459550	−	0.265322i
$461$			2.47332e17i			0.0558952i	0.999609	+	0.0279476i	$0.00889715\pi$
$461$			2.47332e17i			0.0558952i	−0.999609	+	0.0279476i	$0.991103\pi$
$462$	5.62737e17	−	1.84329e18i	0.125260	−	0.410298i
$463$	−4.53486e18			−0.994253			−0.497126	−	0.867678i	$-0.665612\pi$
$463$	−4.53486e18			−0.994253			−0.497126	+	0.867678i	$0.665612\pi$
$464$	8.74577e17	−	1.51481e18i	0.188874	−	0.327139i
$465$	−6.66609e17	+	3.84867e17i	−0.141808	+	0.0818728i
$466$	−9.08543e17	−	1.57364e18i	−0.190390	−	0.329765i
$467$	−2.43120e18	−	1.40366e18i	−0.501884	−	0.289763i	0.227607	−	0.973753i	$-0.426910\pi$
$467$	−2.43120e18	−	1.40366e18i	−0.501884	−	0.289763i	−0.729491	+	0.683990i	$0.760243\pi$
$468$			2.02203e18i			0.411212i
$469$	−5.53178e18	−	1.68880e18i	−1.10829	−	0.338351i
$470$	1.79505e18			0.354316
$471$	−1.76558e17	+	3.05808e17i	−0.0343354	+	0.0594706i
$472$	1.37796e18	−	7.95564e17i	0.264023	−	0.152434i
$473$	1.99661e18	+	3.45823e18i	0.376933	+	0.652868i
$474$	3.00135e17	+	1.73283e17i	0.0558301	+	0.0322335i
$475$			3.09830e18i			0.567894i
$476$	4.61239e18	−	1.06681e18i	0.833063	−	0.192682i
$477$	5.71732e18			1.01757
$478$	−1.90940e18	+	3.30718e18i	−0.334890	+	0.580046i
$479$	−2.56464e18	+	1.48070e18i	−0.443280	+	0.255928i	−0.704988	−	0.709219i	$-0.749048\pi$
$479$	−2.56464e18	+	1.48070e18i	−0.443280	+	0.255928i	0.261708	+	0.965147i	$0.415714\pi$
$480$	1.38328e17	+	2.39591e17i	0.0235625	+	0.0408115i
$481$	−1.79483e16	−	1.03624e16i	−0.00301306	−	0.00173959i
$482$			2.67633e18i			0.442802i
$483$	−2.58805e18	−	2.77310e18i	−0.422030	−	0.452206i
$484$	4.25879e18			0.684492
$485$	1.03399e18	−	1.79092e18i	0.163804	−	0.283716i
$486$	−3.71403e18	+	2.14430e18i	−0.579951	+	0.334835i
$487$	−1.89194e18	−	3.27693e18i	−0.291208	−	0.504388i	0.682887	−	0.730524i	$-0.260724\pi$
$487$	−1.89194e18	−	3.27693e18i	−0.291208	−	0.504388i	−0.974096	+	0.226136i	$0.927391\pi$
$488$	−1.31235e18	−	7.57688e17i	−0.199119	−	0.114961i
$489$		−	4.54967e18i		−	0.680484i
$490$	1.42417e18	+	2.91401e18i	0.209985	+	0.429653i
$491$	−2.65019e17			−0.0385218			−0.0192609	−	0.999814i	$-0.506131\pi$
$491$	−2.65019e17			−0.0385218			−0.0192609	+	0.999814i	$0.506131\pi$
$492$	−9.37895e17	+	1.62448e18i	−0.134400	+	0.232787i
$493$	−1.58396e19	+	9.14502e18i	−2.23778	+	1.29198i
$494$	2.58674e18	+	4.48037e18i	0.360300	+	0.624059i
$495$	5.54445e18	+	3.20109e18i	0.761416	+	0.439604i
$496$			1.13411e18i			0.153562i
$497$	−7.98754e17	+	7.45452e17i	−0.106639	+	0.0995234i
$498$	2.26379e18			0.298009
$499$	1.92065e18	−	3.32666e18i	0.249312	−	0.431822i	−0.714023	−	0.700122i	$-0.753129\pi$
$499$	1.92065e18	−	3.32666e18i	0.249312	−	0.431822i	0.963335	+	0.268301i	$0.0864621\pi$
$500$	−3.52931e18	+	2.03765e18i	−0.451752	+	0.260819i
$501$	3.02277e18	+	5.23558e18i	0.381540	+	0.660847i
$502$	2.32661e18	+	1.34327e18i	0.289599	+	0.167200i
$503$			8.78543e18i			1.07842i	0.842172	+	0.539209i	$0.181277\pi$
$503$			8.78543e18i			1.07842i	−0.842172	+	0.539209i	$0.818723\pi$
$504$	−5.55880e17	−	2.40336e18i	−0.0672926	−	0.290941i
$505$	−4.17304e18			−0.498211
$506$	7.25235e18	−	1.25614e19i	0.853935	−	1.47906i
$507$	−1.52530e17	+	8.80632e16i	−0.0177133	+	0.0102268i
$508$	1.80485e18	+	3.12610e18i	0.206726	+	0.358061i
$509$	7.49323e18	+	4.32622e18i	0.846535	+	0.488747i	0.859480	−	0.511169i	$-0.170787\pi$
$509$	7.49323e18	+	4.32622e18i	0.846535	+	0.488747i	−0.0129454	+	0.999916i	$0.504121\pi$
$510$		−	2.89286e18i		−	0.322356i
$511$	3.16716e18	−	1.03743e19i	0.348115	−	1.14028i
$512$	4.07619e17			0.0441942
$513$	−3.55766e18	+	6.16205e18i	−0.380490	+	0.659028i
$514$	−7.57468e18	+	4.37324e18i	−0.799139	+	0.461383i
$515$	−4.25961e18	−	7.37786e18i	−0.443322	−	0.767856i
$516$	−8.14227e17	−	4.70094e17i	−0.0835983	−	0.0482655i
$517$			1.12584e19i			1.14036i
$518$	2.41819e16	+	7.38249e15i	0.00241647	+	0.000737725i
$519$	2.82669e18			0.278681
$520$	−1.19680e18	+	2.07292e18i	−0.116412	+	0.201632i
$521$	1.45792e19	−	8.41731e18i	1.39917	−	0.807810i	0.404862	−	0.914378i	$-0.367319\pi$
$521$	1.45792e19	−	8.41731e18i	1.39917	−	0.807810i	0.994305	+	0.106568i	$0.0339861\pi$
$522$	4.76516e18	+	8.25349e18i	0.451215	+	0.781527i
$523$	2.13207e18	+	1.23095e18i	0.199200	+	0.115008i	0.596282	−	0.802775i	$-0.296644\pi$
$523$	2.13207e18	+	1.23095e18i	0.199200	+	0.115008i	−0.397082	+	0.917783i	$0.629977\pi$
$524$		−	7.95047e16i		−	0.00732949i
$525$	−2.29070e18	+	5.29824e17i	−0.208379	+	0.0481966i
$526$	−5.40357e18			−0.485044
$527$	5.92941e18	−	1.02700e19i	0.525215	−	0.909699i
$528$	−1.50270e18	+	8.67584e17i	−0.131351	+	0.0758358i
$529$	−8.47731e18	−	1.46831e19i	−0.731254	−	1.26657i
$530$	5.86122e18	+	3.38398e18i	0.498950	+	0.288069i
$531$			8.66931e18i			0.728321i
$532$	−4.30629e18	−	4.61420e18i	−0.357044	−	0.382573i
$533$	−1.62291e19			−1.32802
$534$	−4.36519e16	+	7.56073e16i	−0.00352545	+	0.00610625i
$535$	−2.81690e18	+	1.62634e18i	−0.224540	+	0.129638i
$536$	2.60366e18	+	4.50967e18i	0.204847	+	0.354806i
$537$	3.27598e18	+	1.89139e18i	0.254402	+	0.146879i
$538$		−	1.74142e19i		−	1.33483i
$539$	−1.82764e19	+	8.93227e18i	−1.38283	+	0.675834i
$540$	−3.29202e18			−0.245870
$541$	9.42386e18	−	1.63226e19i	0.694781	−	1.20340i	−0.275473	−	0.961309i	$-0.588834\pi$
$541$	9.42386e18	−	1.63226e19i	0.694781	−	1.20340i	0.970254	−	0.242088i	$-0.0778322\pi$
$542$	5.05437e18	−	2.91814e18i	0.367851	−	0.212379i
$543$	−1.00406e17	−	1.73909e17i	−0.00721376	−	0.0124946i
$544$	−3.69124e18	−	2.13114e18i	−0.261806	−	0.151154i
$545$			4.82121e18i			0.337583i
$546$	−2.87019e18	+	2.67866e18i	−0.198409	+	0.185169i
$547$	4.25712e18			0.290539			0.145270	−	0.989392i	$-0.453595\pi$
$547$	4.25712e18			0.290539			0.145270	+	0.989392i	$0.453595\pi$
$548$	4.60594e18	−	7.97773e18i	0.310352	−	0.537546i
$549$	7.15040e18	−	4.12828e18i	0.475690	−	0.274640i
$550$	−4.49533e18	−	7.78615e18i	−0.295273	−	0.511427i
$551$	2.11171e19	+	1.21920e19i	1.36953	+	0.790701i
$552$			3.41508e18i			0.218689i
$553$	−8.24312e17	−	3.56393e18i	−0.0521213	−	0.225348i
$554$	−1.33654e19			−0.834473
$555$	7.72494e15	−	1.33800e16i	0.000476260	−	0.000824907i
$556$	−1.14523e19	+	6.61200e18i	−0.697221	+	0.402540i
$557$	−3.65174e18	−	6.32500e18i	−0.219540	−	0.380254i	0.735128	−	0.677929i	$-0.237122\pi$
$557$	−3.65174e18	−	6.32500e18i	−0.219540	−	0.380254i	−0.954667	+	0.297675i	$0.903789\pi$
$558$	−5.35136e18	−	3.08961e18i	−0.317706	−	0.183428i
$559$		−	8.13440e18i		−	0.476917i
$560$	8.52633e17	−	2.79286e18i	0.0493680	−	0.161709i
$561$	1.81438e19			1.03750
$562$	4.00357e18	−	6.93439e18i	0.226096	−	0.391611i
$563$	−5.96440e18	+	3.44355e18i	−0.332666	+	0.192065i	−0.657024	−	0.753870i	$-0.728185\pi$
$563$	−5.96440e18	+	3.44355e18i	−0.332666	+	0.192065i	0.324358	+	0.945934i	$0.394852\pi$
$564$	−1.32538e18	−	2.29562e18i	−0.0730106	−	0.126458i
$565$	−1.55017e18	−	8.94990e17i	−0.0843411	−	0.0486944i
$566$		−	1.37119e19i		−	0.736858i
$567$	1.00552e19	+	3.06974e18i	0.533713	+	0.162937i
$568$	9.83665e17			0.0515714
$569$	1.00207e18	−	1.73564e18i	0.0518936	−	0.0898823i	−0.838912	−	0.544267i	$-0.816808\pi$
$569$	1.00207e18	−	1.73564e18i	0.0518936	−	0.0898823i	0.890805	+	0.454385i	$0.150141\pi$
$570$	−3.34000e18	+	1.92835e18i	−0.170853	+	0.0986421i
$571$	1.41738e19	+	2.45497e19i	0.716196	+	1.24049i	0.962496	+	0.271295i	$0.0874518\pi$
$571$	1.41738e19	+	2.45497e19i	0.716196	+	1.24049i	−0.246300	+	0.969194i	$0.579215\pi$
$572$	−1.30012e19	−	7.50624e18i	−0.648950	−	0.374671i
$573$			2.39400e18i			0.118043i
$574$	1.92898e19	−	4.46158e18i	0.939601	−	0.217323i
$575$	−1.76950e19			−0.851483
$576$	−1.11046e18	+	1.92338e18i	−0.0527894	+	0.0914339i
$577$	3.20756e19	−	1.85188e19i	1.50641	−	0.869727i	0.506439	−	0.862276i	$-0.330962\pi$
$577$	3.20756e19	−	1.85188e19i	1.50641	−	0.869727i	0.999972	−	0.00745083i	$-0.00237169\pi$
$578$	1.46644e19	+	2.53994e19i	0.680406	+	1.17850i
$579$	1.08246e19	+	6.24959e18i	0.496206	+	0.286485i
$580$			1.12816e19i			0.510947i
$581$	−1.63029e19	−	1.74686e19i	−0.729513	−	0.781675i
$582$	−3.05379e18			−0.135014
$583$	−2.12241e19	+	3.67612e19i	−0.927147	+	1.60587i
$584$	−8.45740e18	+	4.88288e18i	−0.365045	+	0.210759i
$585$	−6.52080e18	−	1.12944e19i	−0.278106	−	0.481693i
$586$	9.40961e18	+	5.43264e18i	0.396541	+	0.228943i
$587$		−	9.55103e17i		−	0.0397726i	−0.999802	−	0.0198863i	$-0.993670\pi$
$587$		−	9.55103e17i		−	0.0397726i	0.999802	−	0.0198863i	$-0.00633042\pi$
$588$	2.67508e18	−	3.97287e18i	0.110077	−	0.163480i
$589$	−1.58099e19			−0.642870
$590$	−5.13120e18	+	8.88750e18i	−0.206184	+	0.357121i
$591$	−3.25605e18	+	1.87988e18i	−0.129294	+	0.0746480i
$592$	−1.13818e16	−	1.97138e16i	−0.000446640	−	0.000773603i
$593$	2.10659e19	+	1.21624e19i	0.816953	+	0.471668i	0.849365	−	0.527806i	$-0.176985\pi$
$593$	2.10659e19	+	1.21624e19i	0.816953	+	0.471668i	−0.0324113	+	0.999475i	$0.510319\pi$
$594$		−	2.06473e19i		−	0.791332i
$595$	−2.23229e19	+	2.08333e19i	−0.845536	+	0.789113i
$596$	1.80723e19			0.676534
$597$	−5.94286e17	+	1.02933e18i	−0.0219874	+	0.0380834i
$598$	−2.55883e19	+	1.47734e19i	−0.935694	+	0.540223i
$599$	1.40869e19	+	2.43993e19i	0.509131	+	0.881840i	0.999944	+	0.0105754i	$0.00336631\pi$
$599$	1.40869e19	+	2.43993e19i	0.509131	+	0.881840i	−0.490814	+	0.871265i	$0.663300\pi$
$600$	1.83322e18	+	1.05841e18i	0.0654871	+	0.0378090i
$601$			7.76795e18i			0.274274i	0.990552	+	0.137137i	$0.0437901\pi$
$601$			7.76795e18i			0.274274i	−0.990552	+	0.137137i	$0.956210\pi$
$602$	2.23625e18	+	9.66847e18i	0.0780449	+	0.337429i
$603$	−2.83722e19			−0.978751
$604$	−6.19312e18	+	1.07268e19i	−0.211179	+	0.365773i
$605$	−2.37881e19	+	1.37341e19i	−0.801812	+	0.462926i
$606$	3.08117e18	+	5.33675e18i	0.102662	+	0.177815i
$607$	−2.87710e19	−	1.66109e19i	−0.947619	−	0.547108i	−0.0552784	−	0.998471i	$-0.517605\pi$
$607$	−2.87710e19	−	1.66109e19i	−0.947619	−	0.547108i	−0.892340	+	0.451363i	$0.850938\pi$
$608$			5.68238e18i			0.185014i
$609$	−5.40292e18	+	1.76977e19i	−0.173903	+	0.569633i
$610$	9.77382e18			0.310996
$611$	1.14670e19	−	1.98614e19i	0.360713	−	0.624773i
$612$	2.01118e19	−	1.16116e19i	0.625448	−	0.361103i
$613$	−2.00344e19	−	3.47006e19i	−0.615960	−	1.06687i	−0.990215	−	0.139548i	$-0.955435\pi$
$613$	−2.00344e19	−	3.47006e19i	−0.615960	−	1.06687i	0.374255	−	0.927326i	$-0.377898\pi$
$614$	1.14258e18	+	6.59668e17i	0.0347302	+	0.0200515i
$615$		−	1.20984e19i		−	0.363582i
$616$	1.75166e19	+	5.34765e18i	0.520458	+	0.158891i
$617$	4.16417e19			1.22330			0.611650	−	0.791129i	$-0.290506\pi$
$617$	4.16417e19			1.22330			0.611650	+	0.791129i	$0.290506\pi$
$618$	−6.29018e18	+	1.08949e19i	−0.182702	+	0.316449i
$619$	4.32091e19	−	2.49468e19i	1.24091	−	0.716440i	0.271631	−	0.962401i	$-0.412437\pi$
$619$	4.32091e19	−	2.49468e19i	1.24091	−	0.716440i	0.969280	+	0.245961i	$0.0791035\pi$
$620$	−3.65737e18	−	6.33474e18i	−0.103855	−	0.179882i
$621$	−3.51928e19	−	2.03185e19i	−0.988125	−	0.570494i
$622$		−	1.32558e19i		−	0.368021i
$623$	8.97792e17	−	2.07653e17i	0.0246467	−	0.00570062i
$624$	3.53464e18			0.0959517
$625$	3.03548e18	−	5.25760e18i	0.0814830	−	0.141133i
$626$	1.88093e19	−	1.08596e19i	0.499290	−	0.288265i
$627$	−1.20945e19	−	2.09483e19i	−0.317479	−	0.549889i
$628$	−2.90607e18	−	1.67782e18i	−0.0754378	−	0.0435541i
$629$			2.38027e17i			0.00611043i
$630$	1.08555e19	+	1.16317e19i	0.275592	+	0.295297i
$631$	3.91315e19			0.982475			0.491237	−	0.871026i	$-0.336545\pi$
$631$	3.91315e19			0.982475			0.491237	+	0.871026i	$0.336545\pi$
$632$	−1.64670e18	+	2.85217e18i	−0.0408879	+	0.0708199i
$633$	2.87614e18	−	1.66054e18i	0.0706292	−	0.0407778i
$634$	1.78797e19	+	3.09685e19i	0.434245	+	0.752134i
$635$	−2.01626e19	−	1.16409e19i	−0.484318	−	0.279621i
$636$		−	9.99426e18i		−	0.237438i
$637$	4.13400e19	+	2.85728e18i	0.971392	+	0.0671393i
$638$	−7.07575e19			−1.64448
$639$	−2.67976e18	+	4.64149e18i	−0.0616014	+	0.106697i
$640$	−2.27682e18	+	1.31452e18i	−0.0517689	+	0.0298888i
$641$	−2.94294e19	−	5.09732e19i	−0.661873	−	1.14640i	−0.980123	−	0.198391i	$-0.936428\pi$
$641$	−2.94294e19	−	5.09732e19i	−0.661873	−	1.14640i	0.318250	−	0.948007i	$-0.396905\pi$
$642$	4.15972e18	+	2.40162e18i	0.0925378	+	0.0534267i
$643$			9.22815e18i			0.203066i	0.994832	+	0.101533i	$0.0323748\pi$
$643$			9.22815e18i			0.203066i	−0.994832	+	0.101533i	$0.967625\pi$
$644$	2.63526e19	−	2.45941e19i	0.573618	−	0.535340i
$645$	6.06399e18			0.130569
$646$	2.97090e19	−	5.14574e19i	0.632790	−	1.09602i
$647$	−7.26734e18	+	4.19580e18i	−0.153125	+	0.0884066i	−0.574605	−	0.818431i	$-0.694844\pi$
$647$	−7.26734e18	+	4.19580e18i	−0.153125	+	0.0884066i	0.421480	+	0.906838i	$0.361511\pi$
$648$	−4.73269e18	−	8.19726e18i	−0.0986468	−	0.170861i
$649$	−5.57418e19	−	3.21825e19i	−1.14939	−	0.663602i
$650$			1.83145e19i			0.373595i
$651$	−2.70358e18	−	1.16890e19i	−0.0545597	−	0.235890i
$652$	4.32352e19			0.863186
$653$	−3.35947e19	+	5.81877e19i	−0.663557	+	1.14931i	0.316118	+	0.948720i	$0.397621\pi$
$653$	−3.35947e19	+	5.81877e19i	−0.663557	+	1.14931i	−0.979674	+	0.200594i	$0.935713\pi$
$654$	6.16567e18	−	3.55975e18i	0.120486	−	0.0695625i
$655$	2.56393e17	+	4.44086e17i	0.00495698	+	0.00858575i
$656$	−1.54373e19	−	8.91275e18i	−0.295288	−	0.170485i
$657$		−	5.32090e19i		−	1.00700i
$658$	−8.16941e18	+	2.67595e19i	−0.152971	+	0.501069i
$659$	7.80431e19			1.44589			0.722947	−	0.690903i	$-0.242787\pi$
$659$	7.80431e19			1.44589			0.722947	+	0.690903i	$0.242787\pi$
$660$	5.59571e18	−	9.69206e18i	0.102577	−	0.177668i
$661$	4.15373e19	−	2.39816e19i	0.753404	−	0.434978i	−0.0735183	−	0.997294i	$-0.523423\pi$
$661$	4.15373e19	−	2.39816e19i	0.753404	−	0.434978i	0.826923	+	0.562316i	$0.190089\pi$
$662$	−1.60901e19	−	2.78689e19i	−0.288771	−	0.500166i
$663$	−3.20083e19	−	1.84800e19i	−0.568418	−	0.328176i
$664$			2.15126e19i			0.378022i
$665$	3.89337e19	+	1.18861e19i	0.676977	+	0.206674i
$666$	1.24028e17			0.00213402
$667$	−6.96308e19	+	1.20604e20i	−1.18555	+	2.05344i
$668$	−4.97534e19	+	2.87252e19i	−0.838278	+	0.483980i
$669$	1.38423e19	+	2.39755e19i	0.230794	+	0.399747i
$670$	−2.90863e19	−	1.67930e19i	−0.479916	−	0.277079i
$671$			6.13007e19i			1.00094i
$672$	−4.20123e18	+	9.71715e17i	−0.0678878	+	0.0157020i
$673$	6.21850e18			0.0994443			0.0497222	−	0.998763i	$-0.484166\pi$
$673$	6.21850e18			0.0994443			0.0497222	+	0.998763i	$0.484166\pi$
$674$	−3.26640e19	+	5.65756e19i	−0.516951	+	0.895386i
$675$	−2.18141e19	+	1.25944e19i	−0.341673	+	0.197265i
$676$	−8.36859e17	−	1.44948e18i	−0.0129726	−	0.0224691i
$677$	3.06290e18	+	1.76837e18i	0.0469907	+	0.0271301i	0.523311	−	0.852142i	$-0.324696\pi$
$677$	3.06290e18	+	1.76837e18i	0.0469907	+	0.0271301i	−0.476321	+	0.879272i	$0.658030\pi$
$678$			2.64327e18i			0.0401359i
$679$	2.19922e19	+	2.35647e19i	0.330507	+	0.354139i
$680$	2.74907e19			0.408906
$681$	9.39941e18	−	1.62802e19i	0.138379	−	0.239680i
$682$	3.97311e19	−	2.29387e19i	0.578948	−	0.334256i
$683$	−4.62063e19	−	8.00316e19i	−0.666432	−	1.15429i	−0.978895	−	0.204364i	$-0.934487\pi$
$683$	−4.62063e19	−	8.00316e19i	−0.666432	−	1.15429i	0.312463	−	0.949930i	$-0.398846\pi$
$684$	−2.68127e19	−	1.54803e19i	−0.382779	−	0.220997i
$685$			5.94145e19i			0.839573i
$686$	−4.99218e19	+	7.96875e18i	−0.698267	+	0.111461i
$687$	−5.66075e18			−0.0783749
$688$	4.46728e18	−	7.73755e18i	0.0612243	−	0.106044i
$689$	7.48845e19	−	4.32346e19i	1.01592	−	0.586539i
$690$	−1.10132e19	−	1.90755e19i	−0.147901	−	0.256172i
$691$	9.81500e19	+	5.66669e19i	1.30480	+	0.753327i	0.981223	−	0.192875i	$-0.0617812\pi$
$691$	9.81500e19	+	5.66669e19i	1.30480	+	0.753327i	0.323577	+	0.946202i	$0.395114\pi$
$692$			2.68619e19i			0.353504i
$693$	−7.29532e19	+	6.80850e19i	−0.950412	+	0.886990i
$694$	1.04743e19			0.135085
$695$	4.26459e19	−	7.38648e19i	0.544482	−	0.943070i
$696$	1.44276e19	−	8.32981e18i	0.182361	−	0.105286i
$697$	9.31963e19	+	1.61421e20i	1.16619	+	2.01990i
$698$	−3.54427e19	−	2.04628e19i	−0.439075	−	0.253500i
$699$		−	1.73066e19i		−	0.212262i
$700$	−5.03488e18	−	2.17684e19i	−0.0611368	−	0.264326i
$701$	−1.22869e20			−1.47713			−0.738564	−	0.674184i	$-0.764496\pi$
$701$	−1.22869e20			−1.47713			−0.738564	+	0.674184i	$0.764496\pi$
$702$	−2.10299e19	+	3.64248e19i	−0.250309	+	0.433548i
$703$	2.74818e17	−	1.58666e17i	0.00323861	−	0.00186981i
$704$	−8.24460e18	−	1.42801e19i	−0.0961969	−	0.166618i
$705$	1.48062e19	+	8.54837e18i	0.171049	+	0.0987551i
$706$		−	5.77294e19i		−	0.660334i
$707$	1.89919e19	−	6.22093e19i	0.215096	−	0.704562i
$708$	1.51545e19			0.169945
$709$	−6.38871e19	+	1.10656e20i	−0.709397	+	1.22871i	0.255683	+	0.966761i	$0.417700\pi$
$709$	−6.38871e19	+	1.10656e20i	−0.709397	+	1.22871i	−0.965081	+	0.261952i	$0.915634\pi$
$710$	−5.49442e18	+	3.17220e18i	−0.0604106	+	0.0348781i
$711$	−8.97209e18	−	1.55401e19i	−0.0976802	−	0.169187i
$712$	−7.18491e17	−	4.14821e17i	−0.00774572	−	0.00447199i
$713$		−	9.02939e19i		−	0.963900i
$714$	4.31251e19	+	1.31656e19i	0.455871	+	0.139173i
$715$	9.68270e19			1.01357
$716$	−1.79737e19	+	3.11314e19i	−0.186315	+	0.322707i
$717$	−3.14989e19	+	1.81859e19i	−0.323341	+	0.186681i
$718$	−2.57398e18	−	4.45827e18i	−0.0261658	−	0.0453205i
$719$	1.01909e19	+	5.88373e18i	0.102591	+	0.0592312i	0.550418	−	0.834889i	$-0.314468\pi$
$719$	1.01909e19	+	5.88373e18i	0.102591	+	0.0592312i	−0.447826	+	0.894121i	$0.647802\pi$
$720$		−	1.43244e19i		−	0.142807i
$721$	1.29371e20	−	2.99225e19i	1.27729	−	0.295428i
$722$	−6.89695e18			−0.0674368
$723$	−1.27452e19	+	2.20753e19i	−0.123418	+	0.213766i
$724$	1.65264e18	−	9.54154e17i	0.0158493	−	0.00915058i
$725$	4.31604e19	+	7.47560e19i	0.409939	+	0.710035i
$726$	3.51280e19	+	2.02812e19i	0.330443	+	0.190782i
$727$		−	1.64026e20i		−	1.52817i	−0.645115	−	0.764086i	$-0.723190\pi$
$727$		−	1.64026e20i		−	1.52817i	0.645115	−	0.764086i	$-0.276810\pi$
$728$	−2.54551e19	−	2.72752e19i	−0.234885	−	0.251680i
$729$	2.02129e19			0.184730
$730$	3.14934e19	−	5.45482e19i	0.285075	−	0.493765i
$731$	−8.09078e19	+	4.67121e19i	−0.725385	+	0.418801i
$732$	−7.21651e18	−	1.24994e19i	−0.0640840	−	0.110997i
$733$	−1.53100e20	−	8.83921e19i	−1.34662	−	0.777473i	−0.358854	−	0.933394i	$-0.616832\pi$
$733$	−1.53100e20	−	8.83921e19i	−1.34662	−	0.777473i	−0.987770	+	0.155920i	$0.950166\pi$
$734$		−	5.41921e19i		−	0.472132i
$735$	−2.13003e18	+	3.08179e19i	−0.0183812	+	0.265945i
$736$	−3.24533e19			−0.277405
$737$	1.05324e20	−	1.82427e20i	0.891777	−	1.54460i
$738$	8.41108e19	−	4.85614e19i	0.705435	−	0.407283i
$739$	−4.35947e19	−	7.55082e19i	−0.362178	−	0.627311i	0.626141	−	0.779710i	$-0.284633\pi$
$739$	−4.35947e19	−	7.55082e19i	−0.362178	−	0.627311i	−0.988319	+	0.152399i	$0.951300\pi$
$740$	1.27149e17	+	7.34096e16i	0.00104639	+	0.000604131i
$741$			4.92743e19i			0.401692i
$742$	−7.71212e19	+	7.19749e19i	−0.622797	+	0.581237i
$743$	−1.10986e20			−0.887866			−0.443933	−	0.896060i	$-0.646417\pi$
$743$	−1.10986e20			−0.887866			−0.443933	+	0.896060i	$0.646417\pi$
$744$	−5.40084e18	+	9.35454e18i	−0.0428007	+	0.0741330i
$745$	−1.00946e20	+	5.82810e19i	−0.792490	+	0.457544i
$746$	1.28955e19	+	2.23356e19i	0.100292	+	0.173710i
$747$	−1.01509e20	−	5.86061e19i	−0.782094	−	0.451542i
$748$			1.72420e20i			1.31606i
$749$	−1.14245e19	−	4.93942e19i	−0.0863905	−	0.373511i
$750$	−3.88147e19			−0.290782
$751$	8.98664e19	−	1.55653e20i	0.666987	−	1.15526i	−0.311755	−	0.950163i	$-0.600917\pi$
$751$	8.98664e19	−	1.55653e20i	0.666987	−	1.15526i	0.978742	−	0.205094i	$-0.0657499\pi$
$752$	2.18151e19	−	1.25950e19i	0.160411	−	0.0926131i
$753$	1.27938e19	+	2.21595e19i	0.0932042	+	0.161434i
$754$	1.24826e20	+	7.20685e19i	0.900963	+	0.520171i
$755$		−	7.98883e19i		−	0.571287i
$756$	1.49823e19	−	4.90755e19i	0.106151	−	0.347706i
$757$	−1.29956e20			−0.912275			−0.456138	−	0.889909i	$-0.650768\pi$
$757$	−1.29956e20			−0.912275			−0.456138	+	0.889909i	$0.650768\pi$
$758$	3.23843e19	−	5.60913e19i	0.225243	−	0.390132i
$759$	1.19640e20	−	6.90742e19i	0.824487	−	0.476018i
$760$	−1.83250e19	−	3.17399e19i	−0.125126	−	0.216725i
$761$	2.33157e20	+	1.34613e20i	1.57745	+	0.910743i	0.995213	+	0.0977267i	$0.0311571\pi$
$761$	2.33157e20	+	1.34613e20i	1.57745	+	0.910743i	0.582240	+	0.813017i	$0.302176\pi$
$762$			3.43802e19i			0.230475i
$763$	−7.18718e19	−	2.19417e19i	−0.477405	−	0.145747i
$764$	−2.27500e19			−0.149737
$765$	−7.48919e19	+	1.29717e20i	−0.488433	+	0.845990i
$766$	1.39758e20	−	8.06893e19i	0.903182	−	0.521452i
$767$	6.55576e19	+	1.13549e20i	0.419813	+	0.727137i
$768$	3.36219e18	+	1.94116e18i	0.0213351	+	0.0123178i
$769$			7.79508e19i			0.490158i	0.969503	+	0.245079i	$0.0788140\pi$
$769$			7.79508e19i			0.490158i	−0.969503	+	0.245079i	$0.921186\pi$
$770$	−1.15088e20	+	2.66189e19i	−0.717122	+	0.165865i
$771$	−8.33049e19			−0.514387
$772$	−5.93895e19	+	1.02866e20i	−0.363403	+	0.629432i
$773$	−6.96434e19	+	4.02086e19i	−0.422302	+	0.243816i	−0.696062	−	0.717982i	$-0.745066\pi$
$773$	−6.96434e19	+	4.02086e19i	−0.422302	+	0.243816i	0.273760	+	0.961798i	$0.411733\pi$
$774$	2.43401e19	+	4.21583e19i	0.146263	+	0.253335i
$775$	−4.84700e19	−	2.79841e19i	−0.288643	−	0.166648i
$776$		−	2.90200e19i		−	0.171264i
$777$	1.64304e17	+	1.76052e17i	0.000960952	+	0.00102966i
$778$	1.00010e20			0.579679
$779$	1.24247e20	−	2.15203e20i	0.713716	−	1.23619i
$780$	−1.97433e19	+	1.13988e19i	−0.112398	+	0.0648928i
$781$	−1.98958e19	−	3.44606e19i	−0.112255	−	0.194431i
$782$	2.93884e20	+	1.69674e20i	1.64335	+	0.948786i
$783$			1.98238e20i			1.09864i
$784$	3.77540e19	+	2.54211e19i	0.207372	+	0.139631i
$785$	2.16431e19			0.117824
$786$	3.78617e17	−	6.55783e17i	0.00204288	−	0.00353836i
$787$	−2.15601e20	+	1.24477e20i	−1.15300	+	0.665683i	−0.949616	−	0.313416i	$-0.898526\pi$
$787$	−2.15601e20	+	1.24477e20i	−1.15300	+	0.665683i	−0.203381	+	0.979100i	$0.565193\pi$
$788$	−1.78644e19	−	3.09420e19i	−0.0946901	−	0.164008i
$789$	−4.45706e19	−	2.57329e19i	−0.234158	−	0.135191i
$790$		−	2.12416e19i		−	0.110611i
$791$	2.03969e19	−	1.90358e19i	0.105276	−	0.0982508i
$792$	8.98419e19			0.459624
$793$	6.24365e19	−	1.08143e20i	0.316611	−	0.548386i
$794$	−2.03433e20	+	1.17452e20i	−1.02254	+	0.590361i
$795$	3.22303e19	+	5.58245e19i	0.160581	+	0.278135i
$796$	−9.78169e18	−	5.64746e18i	−0.0483084	−	0.0278908i
$797$		−	7.40235e19i		−	0.362378i	−0.983448	−	0.181189i	$-0.942005\pi$
$797$		−	7.40235e19i		−	0.362378i	0.983448	−	0.181189i	$-0.0579945\pi$
$798$	−1.35461e19	−	5.85669e19i	−0.0657347	−	0.284205i
$799$	−2.63399e20			−1.26703
$800$	−1.00580e19	+	1.74210e19i	−0.0479603	+	0.0830697i
$801$	3.91472e18	−	2.26017e18i	0.0185043	−	0.0106835i
$802$	−1.39912e20	−	2.42335e20i	−0.655594	−	1.13552i
$803$	3.42122e20	+	1.97524e20i	1.58918	+	0.917513i
$804$			4.95965e19i			0.228380i
$805$	−6.78838e19	+	2.22358e20i	−0.309881	+	1.01504i
$806$	−9.34550e19			−0.422919
$807$	8.29296e19	−	1.43638e20i	0.372044	−	0.644400i
$808$	−5.07148e19	+	2.92802e19i	−0.225556	+	0.130225i
$809$	7.43623e19	+	1.28799e20i	0.327879	+	0.567903i	0.982091	−	0.188409i	$-0.0603329\pi$
$809$	7.43623e19	+	1.28799e20i	0.327879	+	0.567903i	−0.654212	+	0.756311i	$0.727000\pi$
$810$	5.28704e19	+	3.05247e19i	0.231109	+	0.133431i
$811$		−	1.63702e20i		−	0.709428i	−0.934975	−	0.354714i	$-0.884578\pi$
$811$		−	1.63702e20i		−	0.709428i	0.934975	−	0.354714i	$-0.115422\pi$
$812$	−1.68180e20	−	5.13436e19i	−0.722573	−	0.220594i
$813$	5.55870e19			0.236777
$814$	−4.60420e17	+	7.97471e17i	−0.00194439	+	0.00336778i
$815$	−2.41497e20	+	1.39428e20i	−1.01113	+	0.583779i
$816$	−2.02978e19	−	3.51568e19i	−0.0842592	−	0.145941i
$817$	1.07865e20	+	6.22757e19i	0.443940	+	0.256309i
$818$			2.40156e20i			0.979989i
$819$	1.98046e20	−	4.58067e19i	0.801271	−	0.185328i
$820$	1.14970e20			0.461199
$821$	−1.81784e20	+	3.14859e20i	−0.723025	+	1.25232i	0.236757	+	0.971569i	$0.423915\pi$
$821$	−1.81784e20	+	3.14859e20i	−0.723025	+	1.25232i	−0.959782	+	0.280746i	$0.909418\pi$
$822$	7.59830e19	−	4.38688e19i	0.299649	−	0.173003i
$823$	1.28867e20	+	2.23204e20i	0.503898	+	0.872776i	0.999990	+	0.00450654i	$0.00143448\pi$
$823$	1.28867e20	+	2.23204e20i	0.503898	+	0.872776i	−0.496092	+	0.868270i	$0.665232\pi$
$824$	−1.03534e20	−	5.97752e19i	−0.401413	−	0.231756i
$825$		−	8.56306e19i		−	0.329194i
$826$	−1.09137e20	−	1.16941e20i	−0.416018	−	0.445765i
$827$	1.67041e20			0.631372			0.315686	−	0.948864i	$-0.397765\pi$
$827$	1.67041e20			0.631372			0.315686	+	0.948864i	$0.397765\pi$
$828$	8.84113e19	−	1.53133e20i	0.331357	−	0.573926i
$829$	−1.98821e20	+	1.14789e20i	−0.738890	+	0.426598i	−0.821666	−	0.569970i	$-0.806955\pi$
$829$	−1.98821e20	+	1.14789e20i	−0.738890	+	0.426598i	0.0827754	+	0.996568i	$0.473622\pi$
$830$	−6.93757e19	−	1.20162e20i	−0.255659	−	0.442814i
$831$	−1.10242e20	−	6.36485e19i	−0.402848	−	0.232585i
$832$			3.35894e19i			0.121714i
$833$	−2.08977e20	−	4.27591e20i	−0.750902	−	1.53643i
$834$	−1.25951e20			−0.448784
$835$	1.85270e20	−	3.20898e20i	0.654638	−	1.13387i
$836$	1.99070e20	−	1.14933e20i	0.697529	−	0.402718i
$837$	−6.42664e19	−	1.11313e20i	−0.223309	−	0.386782i
$838$	−2.74325e20	−	1.58381e20i	−0.945272	−	0.545753i
$839$			1.34567e20i			0.459837i	0.973210	+	0.229918i	$0.0738459\pi$
$839$			1.34567e20i			0.459837i	−0.973210	+	0.229918i	$0.926154\pi$
$840$	2.03330e19	−	1.89761e19i	0.0689043	−	0.0643062i
$841$	3.81795e20			1.28309
$842$	3.53524e18	−	6.12321e18i	0.0117824	−	0.0204077i
$843$	6.60459e19	−	3.81316e19i	0.218299	−	0.126035i
$844$	1.57800e19	+	2.73318e19i	0.0517262	+	0.0895924i
$845$	9.34882e18	+	5.39754e18i	0.0303920	+	0.0175469i
$846$			1.37248e20i			0.442501i
$847$	−9.64779e19	−	4.17124e20i	−0.308492	−	1.33377i
$848$	9.49748e19			0.301188
$849$	6.52989e19	−	1.13101e20i	0.205377	−	0.355723i
$850$	1.82163e20	−	1.05172e20i	0.568234	−	0.328070i
$851$	9.06177e17	+	1.56954e18i	0.00280354	+	0.00485587i
$852$	8.11363e18	+	4.68440e18i	0.0248965	+	0.0143740i
$853$		−	2.00068e20i		−	0.608883i	−0.952531	−	0.304442i	$-0.901530\pi$
$853$		−	2.00068e20i		−	0.608883i	0.952531	−	0.304442i	$-0.0984699\pi$
$854$	−4.44814e19	+	1.45702e20i	−0.134268	+	0.439806i
$855$	1.99689e20			0.597848
$856$	−2.28224e19	+	3.95296e19i	−0.0677712	+	0.117383i
$857$	1.10496e20	−	6.37951e19i	0.325449	−	0.187898i	−0.328370	−	0.944549i	$-0.606499\pi$
$857$	1.10496e20	−	6.37951e19i	0.325449	−	0.187898i	0.653819	+	0.756651i	$0.273166\pi$
$858$	−7.14924e19	−	1.23828e20i	−0.208857	−	0.361751i
$859$	−9.96688e18	−	5.75438e18i	−0.0288807	−	0.0166743i	0.485490	−	0.874242i	$-0.338641\pi$
$859$	−9.96688e18	−	5.75438e18i	−0.0288807	−	0.0166743i	−0.514371	+	0.857568i	$0.671974\pi$
$860$			5.76257e19i			0.165626i
$861$	1.80356e20	+	5.50608e19i	0.514172	+	0.156971i
$862$	−1.59640e20			−0.451432
$863$	7.00947e19	−	1.21408e20i	0.196612	−	0.340542i	−0.750816	−	0.660512i	$-0.770339\pi$
$863$	7.00947e19	−	1.21408e20i	0.196612	−	0.340542i	0.947428	+	0.319970i	$0.103673\pi$
$864$	−4.00078e19	+	2.30985e19i	−0.111314	+	0.0642669i
$865$	−8.66264e19	−	1.50041e20i	−0.239077	−	0.414093i
$866$	−4.30701e19	−	2.48665e19i	−0.117910	−	0.0680753i
$867$			2.79338e20i			0.758571i
$868$	1.11080e20	−	2.56919e19i	0.299224	−	0.0692084i
$869$	1.33226e20			0.356001
$870$	−5.37253e19	+	9.30549e19i	−0.142411	+	0.246663i
$871$	−3.71614e20	+	2.14552e20i	−0.977159	+	0.564163i
$872$	3.38281e19	+	5.85920e19i	0.0882393	+	0.152835i
$873$	1.36933e20	+	7.90581e19i	0.354329	+	0.204572i
$874$		−	4.52412e20i		−	1.16133i
$875$	2.79529e20	+	2.99516e20i	0.711821	+	0.762718i
$876$	−9.30129e19			−0.234971
$877$	−4.21114e19	+	7.29390e19i	−0.105536	+	0.182794i	−0.913957	−	0.405811i	$-0.866989\pi$
$877$	−4.21114e19	+	7.29390e19i	−0.105536	+	0.182794i	0.808421	+	0.588605i	$0.200323\pi$
$878$	6.57794e19	−	3.79778e19i	0.163542	−	0.0944209i
$879$	5.17426e19	+	8.96207e19i	0.127622	+	0.221048i
$880$	9.21031e19	+	5.31757e19i	0.225370	+	0.130117i
$881$			5.08110e20i			1.23346i	0.787173	+	0.616732i	$0.211544\pi$
$881$			5.08110e20i			1.23346i	−0.787173	+	0.616732i	$0.788456\pi$
$882$	−2.22803e20	+	1.08891e20i	−0.536588	+	0.262247i
$883$	−5.79499e20			−1.38461			−0.692306	−	0.721604i	$-0.743405\pi$
$883$	−5.79499e20			−1.38461			−0.692306	+	0.721604i	$0.743405\pi$
$884$	1.75614e20	−	3.04173e20i	0.416288	−	0.721031i
$885$	−8.46480e19	+	4.88716e19i	−0.199074	+	0.114935i
$886$	9.35538e19	+	1.62040e20i	0.218286	+	0.378082i
$887$	1.73630e19	+	1.00245e19i	0.0401938	+	0.0232059i	0.519962	−	0.854189i	$-0.325946\pi$
$887$	1.73630e19	+	1.00245e19i	0.0401938	+	0.0232059i	−0.479768	+	0.877395i	$0.659279\pi$
$888$		−	2.16809e17i		−	0.000497950i
$889$	2.65297e20	−	2.47594e20i	0.604533	−	0.564192i
$890$	5.35100e18			0.0120978
$891$	−1.91449e20	+	3.31599e20i	−0.429446	+	0.743823i
$892$	−2.27838e20	+	1.31542e20i	−0.507075	+	0.292760i
$893$	1.75579e20	+	3.04112e20i	0.387715	+	0.671543i
$894$	1.49067e20	+	8.60638e19i	0.326602	+	0.188564i
$895$		−	2.31853e20i		−	0.504024i
$896$	−9.23415e18	−	3.99240e19i	−0.0199178	−	0.0861149i
$897$	−2.81416e20			−0.602284
$898$	−1.51769e20	+	2.62871e20i	−0.322291	+	0.558224i
$899$	−3.81464e20	+	2.20238e20i	−0.803777	+	0.464061i
$900$	−5.48014e19	−	9.49187e19i	−0.114576	−	0.198452i
$901$	−8.60055e20	−	4.96553e20i	−1.78424	−	1.03013i
$902$			7.21086e20i			1.48437i
$903$	−2.75977e19	+	9.03985e19i	−0.0563714	+	0.184649i
$904$	−2.51188e19			−0.0509120
$905$	−6.15407e18	+	1.06592e19i	−0.0123772	+	0.0214379i
$906$	−1.02166e20	+	5.89857e19i	−0.203896	+	0.117720i
$907$	2.01250e20	+	3.48575e20i	0.398552	+	0.690312i	0.993547	−	0.113417i	$-0.0361797\pi$
$907$	2.01250e20	+	3.48575e20i	0.398552	+	0.690312i	−0.594996	+	0.803729i	$0.702846\pi$
$908$	1.54710e20	+	8.93220e19i	0.304031	+	0.175532i
$909$		−	3.19068e20i		−	0.622209i
$910$	2.30143e20	+	7.02603e19i	0.445357	+	0.135963i
$911$	9.50184e19			0.182465			0.0912324	−	0.995830i	$-0.470919\pi$
$911$	9.50184e19			0.182465			0.0912324	+	0.995830i	$0.470919\pi$
$912$	−2.70606e19	+	4.68703e19i	−0.0515672	+	0.0893170i
$913$	7.53649e20	−	4.35119e20i	1.42519	−	0.822835i
$914$	1.06822e20	+	1.85022e20i	0.200465	+	0.347215i
$915$	8.06180e19	+	4.65448e19i	0.150136	+	0.0866809i
$916$		−	5.37938e19i		−	0.0994177i
$917$	−7.78704e18	+	1.80109e18i	−0.0142819	+	0.00330331i
$918$	4.83059e20			0.879229
$919$	−5.13486e20	+	8.89383e20i	−0.927512	+	1.60650i	−0.140043	+	0.990145i	$0.544724\pi$
$919$	−5.13486e20	+	8.89383e20i	−0.927512	+	1.60650i	−0.787470	+	0.616353i	$0.788609\pi$
$920$	1.81273e20	−	1.04658e20i	0.324951	−	0.187611i
$921$	6.28294e18	+	1.08824e19i	0.0111775	+	0.0193600i
$922$	−1.93868e19	−	1.11930e19i	−0.0342287	−	0.0197619i
$923$			8.10579e19i			0.142031i
$924$	1.19017e20	+	1.27527e20i	0.206969	+	0.221768i
$925$	1.12338e18			0.00193881
$926$	2.05224e20	−	3.55459e20i	0.351522	−	0.608853i
$927$	5.64106e20	−	3.25687e20i	0.958965	−	0.553659i
$928$	7.91576e19	+	1.37105e20i	0.133554	+	0.231322i
$929$	−7.49067e20	−	4.32474e20i	−1.25433	−	0.724186i	−0.282362	−	0.959308i	$-0.591118\pi$
$929$	−7.49067e20	−	4.32474e20i	−1.25433	−	0.724186i	−0.971966	+	0.235122i	$0.924451\pi$
$930$		−	6.96683e19i		−	0.115786i
$931$	−3.54381e20	+	5.26306e20i	−0.584551	+	0.868142i
$932$	1.64464e20			0.269252
$933$	6.31267e19	−	1.09339e20i	0.102575	−	0.177665i
$934$	2.20048e20	−	1.27044e20i	0.354886	−	0.204893i
$935$	−5.56033e20	−	9.63077e20i	−0.890059	−	1.54163i
$936$	−1.58494e20	−	9.15065e19i	−0.251815	−	0.145385i
$937$		−	1.04686e21i		−	1.65087i	−0.564496	−	0.825436i	$-0.690929\pi$
$937$		−	1.04686e21i		−	1.65087i	0.564496	−	0.825436i	$-0.309071\pi$
$938$	3.82714e20	−	3.57175e20i	0.599038	−	0.559064i
$939$	2.06861e20			0.321381
$940$	−8.12346e19	+	1.40702e20i	−0.125270	+	0.216974i
$941$	3.15413e20	−	1.82104e20i	0.482783	−	0.278735i	−0.238793	−	0.971071i	$-0.576752\pi$
$941$	3.15413e20	−	1.82104e20i	0.482783	−	0.278735i	0.721575	+	0.692336i	$0.243418\pi$
$942$	−1.59802e19	−	2.76786e19i	−0.0242788	−	0.0420521i
$943$	1.22907e21	+	7.09603e20i	1.85351	+	1.07012i
$944$			1.44013e20i			0.215574i
$945$	7.45770e19	+	3.22435e20i	0.110811	+	0.479093i
$946$	−3.61425e20			−0.533064
$947$	1.46735e20	−	2.54153e20i	0.214825	−	0.372087i	−0.738394	−	0.674370i	$-0.764415\pi$
$947$	1.46735e20	−	2.54153e20i	0.214825	−	0.372087i	0.953218	+	0.302283i	$0.0977486\pi$
$948$	−2.71651e19	+	1.56838e19i	−0.0394779	+	0.0227926i
$949$	−4.02368e20	−	6.96923e20i	−0.580444	−	1.00536i
$950$	−2.42856e20	−	1.40213e20i	−0.347763	−	0.200781i
$951$			3.40586e20i			0.484131i
$952$	−1.25112e20	+	4.09815e20i	−0.176539	+	0.578268i
$953$	4.52445e20			0.633747			0.316873	−	0.948468i	$-0.397367\pi$
$953$	4.52445e20			0.633747			0.316873	+	0.948468i	$0.397367\pi$
$954$	−2.58737e20	+	4.48145e20i	−0.359765	+	0.623132i
$955$	1.27074e20	−	7.33662e19i	0.175401	−	0.101268i
$956$	−1.72819e20	−	2.99332e20i	−0.236803	−	0.410155i
$957$	−5.83634e20	−	3.36961e20i	−0.793884	−	0.458349i
$958$		−	2.68035e20i		−	0.361937i
$959$	−8.85716e20	−	2.70400e20i	−1.18731	−	0.362474i
$960$	−2.50401e19			−0.0333225
$961$	−2.35675e20	+	4.08201e20i	−0.311350	+	0.539275i
$962$	1.62449e18	−	9.37901e17i	0.00213055	−	0.00123008i
$963$	−1.24349e20	−	2.15378e20i	−0.161904	−	0.280425i
$964$	−2.09780e20	−	1.21117e20i	−0.271160	−	0.156554i
$965$		−	7.66096e20i		−	0.983087i
$966$	3.34488e20	−	7.73647e19i	0.426129	−	0.0985605i
$967$	−1.30568e20			−0.165140			−0.0825699	−	0.996585i	$-0.526313\pi$
$967$	−1.30568e20			−0.165140			−0.0825699	+	0.996585i	$0.526313\pi$
$968$	−1.92731e20	+	3.33819e20i	−0.242004	+	0.419164i
$969$	4.90100e20	−	2.82960e20i	0.610968	−	0.352743i
$970$	9.35860e19	+	1.62096e20i	0.115827	+	0.200618i
$971$	−6.44849e20	−	3.72304e20i	−0.792361	−	0.457470i	0.0484319	−	0.998826i	$-0.484578\pi$
$971$	−6.44849e20	−	3.72304e20i	−0.792361	−	0.457470i	−0.840793	+	0.541357i	$0.817911\pi$
$972$		−	3.88159e20i		−	0.473528i
$973$	9.07048e20	+	9.71904e20i	1.09860	+	1.17715i
$974$	3.42477e20			0.411831
$975$	−8.72172e19	+	1.51065e20i	−0.104129	+	0.180356i
$976$	1.18781e20	−	6.85781e19i	0.140798	−	0.0812899i
$977$	1.07569e20	+	1.86315e20i	0.126597	+	0.219273i	0.922356	−	0.386340i	$-0.126261\pi$
$977$	1.07569e20	+	1.86315e20i	0.126597	+	0.219273i	−0.795759	+	0.605614i	$0.792928\pi$
$978$	3.56620e20	+	2.05894e20i	0.416709	+	0.240587i
$979$			3.35611e19i			0.0389365i
$980$	−2.92861e20	−	2.02415e19i	−0.337349	−	0.0233164i
$981$	−3.68627e20			−0.421603
$982$	1.19934e19	−	2.07731e19i	0.0136195	−	0.0235897i
$983$	6.78524e20	−	3.91746e20i	0.765052	−	0.441703i	−0.0660548	−	0.997816i	$-0.521041\pi$
$983$	6.78524e20	−	3.91746e20i	0.765052	−	0.441703i	0.831107	+	0.556113i	$0.187708\pi$
$984$	−8.48885e19	−	1.47031e20i	−0.0950349	−	0.164605i
$985$	1.99569e20	+	1.15221e20i	0.221840	+	0.128079i
$986$		−	1.65543e21i		−	1.82714i
$987$	−1.94818e20	+	1.81818e20i	−0.213506	+	0.199258i
$988$	−4.68251e20			−0.509542
$989$	−3.55669e20	+	6.16038e20i	−0.384302	+	0.665630i
$990$	−5.01826e20	+	2.89729e20i	−0.538402	+	0.310847i
$991$	6.64565e20	+	1.15106e21i	0.707981	+	1.22626i	0.965605	+	0.260014i	$0.0837272\pi$
$991$	6.64565e20	+	1.15106e21i	0.707981	+	1.22626i	−0.257624	+	0.966245i	$0.582939\pi$
$992$	−8.88956e19	−	5.13239e19i	−0.0940370	−	0.0542923i
$993$		−	3.06497e20i		−	0.321945i
$994$	−2.22838e19	−	9.63445e19i	−0.0232426	−	0.100490i
$995$	7.28495e19			0.0754510
$996$	−1.02447e20	+	1.77444e20i	−0.105362	+	0.182493i
$997$	−2.64322e20	+	1.52607e20i	−0.269940	+	0.155850i	−0.628861	−	0.777518i	$-0.716478\pi$
$997$	−2.64322e20	+	1.52607e20i	−0.269940	+	0.155850i	0.358920	+	0.933368i	$0.383145\pi$
$998$	1.73837e20	+	3.01095e20i	0.176290	+	0.305344i
$999$	2.23424e18	+	1.28994e18i	0.00224994	+	0.00129900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.15.d.a.5.3	yes	20
3.2	odd	2		126.15.n.b.19.7		20
7.2	even	3		98.15.b.c.97.15		20
7.3	odd	6	inner	14.15.d.a.3.3	✓	20
7.4	even	3		98.15.d.b.31.3		20
7.5	odd	6		98.15.b.c.97.16		20
7.6	odd	2		98.15.d.b.19.3		20
21.17	even	6		126.15.n.b.73.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.3	✓	20	7.3	odd	6	inner
14.15.d.a.5.3	yes	20	1.1	even	1	trivial
98.15.b.c.97.15		20	7.2	even	3
98.15.b.c.97.16		20	7.5	odd	6
98.15.d.b.19.3		20	7.6	odd	2
98.15.d.b.31.3		20	7.4	even	3
126.15.n.b.19.7		20	3.2	odd	2
126.15.n.b.73.7		20	21.17	even	6

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:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-45.2548 + 78.3837i) q^{2} +(-746.556 + 431.025i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(45757.7 + 26418.2i) q^{5} -78023.8i q^{6} +(-602075. + 561898. i) q^{7} +741455. q^{8} +(-2.01992e6 + 3.49860e6i) q^{9} +O(q^{10})\)	\(q+(-45.2548 + 78.3837i) q^{2} +(-746.556 + 431.025i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(45757.7 + 26418.2i) q^{5} -78023.8i q^{6} +(-602075. + 561898. i) q^{7} +741455. q^{8} +(-2.01992e6 + 3.49860e6i) q^{9} +(-4.14152e6 + 2.39111e6i) q^{10} +(-1.49968e7 - 2.59753e7i) q^{11} +(6.11579e6 + 3.53095e6i) q^{12} +6.10988e7i q^{13} +(-1.67968e7 - 7.26214e7i) q^{14} -4.55476e7 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(6.07711e8 - 3.50862e8i) q^{17} +(-1.82822e8 - 3.16658e8i) q^{18} +(-8.10189e8 - 4.67763e8i) q^{19} -4.32836e8i q^{20} +(2.07291e8 - 6.78997e8i) q^{21} +2.71472e9 q^{22} +(2.67149e9 - 4.62716e9i) q^{23} +(-5.53538e8 + 3.19585e8i) q^{24} +(-1.65591e9 - 2.86812e9i) q^{25} +(-4.78915e9 - 2.76502e9i) q^{26} -7.60570e9i q^{27} +(6.45247e9 + 1.96987e9i) q^{28} -2.60644e10 q^{29} +(2.06125e9 - 3.57019e9i) q^{30} +(1.46354e10 - 8.44977e9i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} +(2.23920e10 + 1.29280e10i) q^{33} +6.35129e10i q^{34} +(-4.23939e10 + 9.80541e9i) q^{35} +3.30944e10 q^{36} +(-1.69601e8 + 2.93758e8i) q^{37} +(7.33299e10 - 4.23371e10i) q^{38} +(-2.63351e10 - 4.56137e10i) q^{39} +(3.39273e10 + 1.95879e10i) q^{40} +2.65621e11i q^{41} +(4.38414e10 + 4.69761e10i) q^{42} -1.33135e11 q^{43} +(-1.22854e11 + 2.12790e11i) q^{44} +(-1.84854e11 + 1.06725e11i) q^{45} +(2.41796e11 + 4.18803e11i) q^{46} +(-3.25071e11 - 1.87680e11i) q^{47} -5.78511e10i q^{48} +(4.67649e10 - 6.76609e11i) q^{49} +2.99752e11 q^{50} +(-3.02461e11 + 5.23877e11i) q^{51} +(4.33464e11 - 2.50261e11i) q^{52} +(-7.07618e11 - 1.22563e12i) q^{53} +(5.96162e11 + 3.44194e11i) q^{54} -1.58476e12i q^{55} +(-4.46411e11 + 4.16622e11i) q^{56} +8.06469e11 q^{57} +(1.17954e12 - 2.04302e12i) q^{58} +(1.85845e12 - 1.07298e12i) q^{59} +(1.86563e11 + 3.23137e11i) q^{60} +(-1.76997e12 - 1.02189e12i) q^{61} +1.52957e12i q^{62} +(-7.49715e11 - 3.24141e12i) q^{63} +5.49756e11 q^{64} +(-1.61412e12 + 2.79574e12i) q^{65} +(-2.02669e12 + 1.17011e12i) q^{66} +(3.51155e12 + 6.08219e12i) q^{67} +(-4.97837e12 - 2.87426e12i) q^{68} +4.60591e12i q^{69} +(1.14995e12 - 3.76673e12i) q^{70} +1.32667e12 q^{71} +(-1.49768e12 + 2.59406e12i) q^{72} +(-1.14065e13 + 6.58554e12i) q^{73} +(-1.53506e10 - 2.65880e10i) q^{74} +(2.47246e12 + 1.42748e12i) q^{75} +7.66382e12i q^{76} +(2.36247e13 + 7.21237e12i) q^{77} +4.76716e12 q^{78} +(-2.22090e12 + 3.84672e12i) q^{79} +(-3.07075e12 + 1.77290e12i) q^{80} +(-6.38297e12 - 1.10556e13i) q^{81} +(-2.08203e13 - 1.20206e13i) q^{82} +2.90141e13i q^{83} +(-5.66620e12 + 1.31055e12i) q^{84} +3.70766e13 q^{85} +(6.02501e12 - 1.04356e13i) q^{86} +(1.94586e13 - 1.12344e13i) q^{87} +(-1.11195e13 - 1.92595e13i) q^{88} +(-9.69029e11 - 5.59469e11i) q^{89} -1.93194e13i q^{90} +(-3.43313e13 - 3.67861e13i) q^{91} -4.37697e13 q^{92} +(-7.28412e12 + 1.26165e13i) q^{93} +(2.94221e13 - 1.69868e13i) q^{94} +(-2.47149e13 - 4.28075e13i) q^{95} +(4.53458e12 + 2.61804e12i) q^{96} -3.91392e13i q^{97} +(5.09188e13 + 3.42854e13i) q^{98} +1.21170e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9 - 3933696 * q^10 + 8400426 * q^11 + 35831808 * q^12 - 114693888 * q^14 + 562720524 * q^15 - 671088640 * q^16 + 2180481042 * q^17 - 251755008 * q^18 - 3919727442 * q^19 + 7585509006 * q^21 + 5394565632 * q^22 - 6905098386 * q^23 - 2371878912 * q^24 + 14165082644 * q^25 + 12652202496 * q^26 - 17334943744 * q^28 + 27884908704 * q^29 + 54103511808 * q^30 + 45638710782 * q^31 - 37041090498 * q^33 - 18274367202 * q^35 - 287497125888 * q^36 - 27026027926 * q^37 - 354043974912 * q^38 - 126125404380 * q^39 + 32224837632 * q^40 - 298475364864 * q^42 + 726682953656 * q^43 + 68816289792 * q^44 + 498861631944 * q^45 - 286664984832 * q^46 - 2044625353338 * q^47 + 2939974016204 * q^49 + 1161106642944 * q^50 - 2419609945602 * q^51 + 1314350333952 * q^52 + 1546271487546 * q^53 - 5213176950528 * q^54 + 1720927125504 * q^56 + 14789884876092 * q^57 - 2365863040512 * q^58 - 6798944731566 * q^59 - 2304903266304 * q^60 - 2214453865554 * q^61 - 4417730390688 * q^63 + 10995116277760 * q^64 + 7516703932836 * q^65 - 8476063570944 * q^66 - 4655820763226 * q^67 - 17862500696064 * q^68 + 20497461621504 * q^70 + 96606137494152 * q^71 - 2062377025536 * q^72 - 65348368908666 * q^73 - 566532483072 * q^74 - 186663280957308 * q^75 + 77525241691422 * q^77 + 88663911671808 * q^78 - 60517474082978 * q^79 - 225083129856 * q^80 - 107180264511342 * q^81 - 43979002397184 * q^82 + 18842436550656 * q^84 + 416326699526124 * q^85 + 2363335174656 * q^86 - 126768392660088 * q^87 - 22096140828672 * q^88 - 237147002561826 * q^89 + 203506111374408 * q^91 + 113133131956224 * q^92 - 94175068190130 * q^93 - 221058962902272 * q^94 + 25202514515490 * q^95 + 19430432047104 * q^96 + 165606984015360 * q^98 + 1056686373672768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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