LMFDB - Embedded newform 17.44.d.a.2.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [17,44,Mod(2,17)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 44, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17.2"); S:= CuspForms(chi, 44); N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$199.087672088$
Analytic rank:	$0$
Dimension:	$252$
Relative dimension:	$63$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			2.11
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.17742e6 - 3.17742e6i) q^{2} +(2.68747e10 - 1.11319e10i) q^{3} +1.13958e13i q^{4} +(-5.29509e14 - 1.27835e15i) q^{5} +(-1.20763e17 - 5.00216e16i) q^{6} +(8.49333e17 - 2.05047e18i) q^{7} +(8.26049e18 - 8.26049e18i) q^{8} +(3.66220e20 - 3.66220e20i) q^{9} +(-2.37937e21 + 5.74432e21i) q^{10} +(-3.79921e22 - 1.57368e22i) q^{11} +(1.26857e23 + 3.06260e23i) q^{12} -1.45301e24i q^{13} +(-9.21389e24 + 3.81652e24i) q^{14} +(-2.84609e25 - 2.84609e25i) q^{15} +4.77449e25 q^{16} +(2.75185e26 + 7.36611e25i) q^{17} -2.32727e27 q^{18} +(-1.57699e27 - 1.57699e27i) q^{19} +(1.45679e28 - 6.03421e27i) q^{20} -6.45606e28i q^{21} +(7.07142e28 + 1.70719e29i) q^{22} +(-1.34123e29 - 5.55555e28i) q^{23} +(1.30044e29 - 3.13953e29i) q^{24} +(-5.49908e29 + 5.49908e29i) q^{25} +(-4.61680e30 + 4.61680e30i) q^{26} +(2.11123e30 - 5.09697e30i) q^{27} +(2.33669e31 + 9.67887e30i) q^{28} +(1.27301e31 + 3.07331e31i) q^{29} +1.80864e32i q^{30} +(1.74819e31 - 7.24125e30i) q^{31} +(-2.24365e32 - 2.24365e32i) q^{32} -1.19621e33 q^{33} +(-6.40326e32 - 1.10843e33i) q^{34} -3.07095e33 q^{35} +(4.17339e33 + 4.17339e33i) q^{36} +(-5.77908e33 + 2.39377e33i) q^{37} +1.00215e34i q^{38} +(-1.61747e34 - 3.90491e34i) q^{39} +(-1.49338e34 - 6.18578e33i) q^{40} +(-7.69016e33 + 1.85657e34i) q^{41} +(-2.05136e35 + 2.05136e35i) q^{42} +(4.91051e34 - 4.91051e34i) q^{43} +(1.79335e35 - 4.32952e35i) q^{44} +(-6.62074e35 - 2.74240e35i) q^{45} +(2.49641e35 + 6.02687e35i) q^{46} +1.08093e36i q^{47} +(1.28313e36 - 5.31490e35i) q^{48} +(-1.93888e36 - 1.93888e36i) q^{49} +3.49457e36 q^{50} +(8.21552e36 - 1.08371e36i) q^{51} +1.65582e37 q^{52} +(-1.76984e36 - 1.76984e36i) q^{53} +(-2.29035e37 + 9.48693e36i) q^{54} +5.68999e37i q^{55} +(-9.92200e36 - 2.39538e37i) q^{56} +(-5.99360e37 - 2.48263e37i) q^{57} +(5.72032e37 - 1.38101e38i) q^{58} +(8.14503e37 - 8.14503e37i) q^{59} +(3.24336e38 - 3.24336e38i) q^{60} +(1.25476e38 - 3.02926e38i) q^{61} +(-7.85558e37 - 3.25389e37i) q^{62} +(-4.39881e38 - 1.06197e39i) q^{63} +1.00584e39i q^{64} +(-1.85745e39 + 7.69380e38i) q^{65} +(3.80085e39 + 3.80085e39i) q^{66} +1.42347e39 q^{67} +(-8.39430e38 + 3.13597e39i) q^{68} -4.22295e39 q^{69} +(9.75768e39 + 9.75768e39i) q^{70} +(5.02622e39 - 2.08193e39i) q^{71} -6.05032e39i q^{72} +(-4.12225e39 - 9.95200e39i) q^{73} +(2.59686e40 + 1.07565e40i) q^{74} +(-8.65713e39 + 2.09002e40i) q^{75} +(1.79711e40 - 1.79711e40i) q^{76} +(-6.45359e40 + 6.45359e40i) q^{77} +(-7.26816e40 + 1.75469e41i) q^{78} +(1.49326e40 + 6.18527e39i) q^{79} +(-2.52814e40 - 6.10346e40i) q^{80} +9.52694e39i q^{81} +(8.34257e40 - 3.45561e40i) q^{82} +(-2.41181e40 - 2.41181e40i) q^{83} +7.35723e41 q^{84} +(-5.15486e40 - 3.90787e41i) q^{85} -3.12055e41 q^{86} +(6.84235e41 + 6.84235e41i) q^{87} +(-4.43827e41 + 1.83839e41i) q^{88} -1.54199e42i q^{89} +(1.23231e42 + 2.97506e42i) q^{90} +(-2.97935e42 - 1.23409e42i) q^{91} +(6.33102e41 - 1.52844e42i) q^{92} +(3.89214e41 - 3.89214e41i) q^{93} +(3.43456e42 - 3.43456e42i) q^{94} +(-1.18091e42 + 2.85097e42i) q^{95} +(-8.52737e42 - 3.53215e42i) q^{96} +(-2.87026e42 - 6.92942e42i) q^{97} +1.23212e43i q^{98} +(-1.96766e43 + 8.15032e42i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 252 q - 4 q^{2} - 4 q^{3} + 18\!\cdots\!80 q^{5} + 22\!\cdots\!40 q^{6} - 4 q^{7} + 35184372088828 q^{8} + 63\!\cdots\!24 q^{9} - 91\!\cdots\!16 q^{10} + 31\!\cdots\!84 q^{11} + 16\!\cdots\!88 q^{12} - 10\!\cdots\!24 q^{14}+ \cdots + 44\!\cdots\!04 q^{99}+O(q^{100}) $ 252 * q - 4 * q^2 - 4 * q^3 + 1884797015207680 * q^5 + 221515217735603540 * q^6 - 4 * q^7 + 35184372088828 * q^8 + 637940004494872277024 * q^9 - 9172644062832164339716 * q^10 + 31271856798939564695884 * q^11 + 160659040662715870080488 * q^12 - 10620825937570937944957524 * q^14 + 28748551219070162352205864 * q^15 - 4410161389954167229328130056 * q^16 + 754786259037235794349028848 * q^17 - 5367540473535552290321072136 * q^18 - 1520391448988386966886847848 * q^19 + 40480648156465003912941797372 * q^20 + 44147261648104882038875094724 * q^22 - 408953067900897227251175991228 * q^23 + 2569128406481727809325689264168 * q^24 + 42966318811420029473026445436 * q^25 + 3889861661153663431806873373452 * q^26 + 16724820032498576287206262041608 * q^27 - 78718748571558344076653664853948 * q^28 - 109059849142312592102640344707492 * q^29 + 155238807707320954847178663148116 * q^31 - 1248943358044888932820031011401380 * q^32 + 932475890510175608977160850636416 * q^33 - 2007434777522200770802818693652196 * q^34 - 6260674670597673932268376573918712 * q^35 + 4479760017879839550046604218909532 * q^36 - 17669696250349968942205391131252928 * q^37 - 33477298925576849377795174615937792 * q^39 + 257430816220235129125050811116411896 * q^40 - 311812241725106436964393322934514756 * q^41 - 726966897646418372795388468485943264 * q^42 + 145483863855225967728840460948874008 * q^43 - 576839823783400550140919165196100820 * q^44 - 1562721042700452296454407377932847652 * q^45 + 3255942875929625188695035486970932036 * q^46 + 18708730728755605295119242540553548420 * q^48 - 2949590196379917026003323686456465704 * q^49 + 10905341656561025307088825016657498256 * q^50 - 46185381700203116194868436729164991716 * q^51 + 7454763265891936095016769109884927992 * q^52 - 14713371751943584240669151627479277652 * q^53 - 6755810910541176993304440587421505708 * q^54 + 149884478723227700332950860917188035940 * q^56 + 126920003429662656894363296666266565000 * q^57 - 271066615350358579055879450872780742344 * q^58 + 116874962636142679544094000646084191712 * q^59 - 872542987975341146926551197816579820832 * q^60 - 1358609311184572224052031653816889387984 * q^61 + 2607817901743511605570070357854955329636 * q^62 - 1091602845873954611663873790764312528604 * q^63 + 3372175859531725606529403976394593343084 * q^65 - 15969791388639223448787929109583645824044 * q^66 + 9601127564424465892797427904090648719472 * q^67 - 2858492589626501237506636670893985611548 * q^68 - 6004549631066595629803136354269922710016 * q^69 - 7491013725132007196906975517093826622728 * q^70 + 13161829513880573377255430143542971678068 * q^71 - 5385412878117054164021091482584340053276 * q^73 + 32055566966732570990968100291615084999196 * q^74 - 92628007303509329473535996431096556198300 * q^75 + 71952475208360471612122707267334932460688 * q^76 - 30844870660765075778153922644400106294552 * q^77 - 677870507408395262113905402805586249209560 * q^78 + 457431588401674274986102860554036176833980 * q^79 - 1042654222461388078925088086647718502523144 * q^80 + 381292868041103076294441011271187965819712 * q^82 - 1858164188395191584401285897298593856353872 * q^83 + 3414349628994907313966613712851584874618464 * q^84 + 1539811331574045767550650365721669563617076 * q^85 - 7527689568349034083014688245960811056896160 * q^86 + 4598921143806943863791357477672994697217920 * q^87 - 2748890833517697603875507243022514861012312 * q^88 + 7440815478668874256881493485280295170489540 * q^90 - 2237820543008860122477949024778651580244448 * q^91 + 8095910074397868366682337486060370784743852 * q^92 - 4703810315457730631257609089619508247525608 * q^93 - 19029062207054913342048301316319385806697928 * q^94 + 7308723736731156227266260213147210681429192 * q^95 - 51985923233339651510401162209778533343281372 * q^96 + 30389671344271765040956456332036809733752352 * q^97 + 44417034354379298005913817665478379237257004 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−3.17742e6	−	3.17742e6i	−1.07134	−	1.07134i	−0.997251	−	0.0740931i	$-0.976394\pi$
$2$	−3.17742e6	−	3.17742e6i	−1.07134	−	1.07134i	−0.0740931	−	0.997251i	$-0.523606\pi$
$3$	2.68747e10	−	1.11319e10i	1.48333	−	0.614415i	0.513475	−	0.858104i	$-0.328358\pi$
$3$	2.68747e10	−	1.11319e10i	1.48333	−	0.614415i	0.969853	+	0.243690i	$0.0783579\pi$
$4$			1.13958e13i			1.29556i
$5$	−5.29509e14	−	1.27835e15i	−0.496614	−	1.19893i	−0.951296	−	0.308278i	$-0.900247\pi$
$5$	−5.29509e14	−	1.27835e15i	−0.496614	−	1.19893i	0.454683	−	0.890653i	$-0.349753\pi$
$6$	−1.20763e17	−	5.00216e16i	−2.24741	−	0.930906i
$7$	8.49333e17	−	2.05047e18i	0.574739	−	1.38754i	−0.322742	−	0.946487i	$-0.604605\pi$
$7$	8.49333e17	−	2.05047e18i	0.574739	−	1.38754i	0.897480	−	0.441055i	$-0.145395\pi$
$8$	8.26049e18	−	8.26049e18i	0.316644	−	0.316644i
$9$	3.66220e20	−	3.66220e20i	1.11565	−	1.11565i
$10$	−2.37937e21	+	5.74432e21i	−0.752424	+	1.81651i
$11$	−3.79921e22	−	1.57368e22i	−1.54793	−	0.641172i	−0.564987	−	0.825100i	$-0.691119\pi$
$11$	−3.79921e22	−	1.57368e22i	−1.54793	−	0.641172i	−0.982940	+	0.183928i	$0.941119\pi$
$12$	1.26857e23	+	3.06260e23i	0.796010	+	1.92174i
$13$		−	1.45301e24i		−	1.63112i	−0.578675	−	0.815558i	$-0.696430\pi$
$13$		−	1.45301e24i		−	1.63112i	0.578675	−	0.815558i	$-0.303570\pi$
$14$	−9.21389e24	+	3.81652e24i	−2.10228	+	0.870792i
$15$	−2.84609e25	−	2.84609e25i	−1.47328	−	1.47328i
$16$	4.77449e25			0.617088
$17$	2.75185e26	+	7.36611e25i	0.965991	+	0.258575i
$17$	2.75185e26	+	7.36611e25i	0.965991	+	0.258575i
$18$	−2.32727e27			−2.39049
$19$	−1.57699e27	−	1.57699e27i	−0.506554	−	0.506554i	0.406913	−	0.913467i	$-0.366605\pi$
$19$	−1.57699e27	−	1.57699e27i	−0.506554	−	0.506554i	−0.913467	+	0.406913i	$0.866605\pi$
$20$	1.45679e28	−	6.03421e27i	1.55328	−	0.643392i
$21$		−	6.45606e28i		−	2.41131i
$22$	7.07142e28	+	1.70719e29i	0.971446	+	2.34528i
$23$	−1.34123e29	−	5.55555e28i	−0.708523	−	0.293480i	−0.000829953	−	1.00000i	$-0.500264\pi$
$23$	−1.34123e29	−	5.55555e28i	−0.708523	−	0.293480i	−0.707693	+	0.706520i	$0.750264\pi$
$24$	1.30044e29	−	3.13953e29i	0.275136	−	0.664238i
$25$	−5.49908e29	+	5.49908e29i	−0.483704	+	0.483704i
$26$	−4.61680e30	+	4.61680e30i	−1.74749	+	1.74749i
$27$	2.11123e30	−	5.09697e30i	0.354990	−	0.857021i
$28$	2.33669e31	+	9.67887e30i	1.79764	+	0.744607i
$29$	1.27301e31	+	3.07331e31i	0.460547	+	1.11186i	0.968173	+	0.250282i	$0.0805233\pi$
$29$	1.27301e31	+	3.07331e31i	0.460547	+	1.11186i	−0.507626	+	0.861578i	$0.669477\pi$
$30$			1.80864e32i			3.15678i
$31$	1.74819e31	−	7.24125e30i	0.150769	−	0.0624507i	−0.306023	−	0.952024i	$-0.598998\pi$
$31$	1.74819e31	−	7.24125e30i	0.150769	−	0.0624507i	0.456792	+	0.889574i	$0.348998\pi$
$32$	−2.24365e32	−	2.24365e32i	−0.977758	−	0.977758i
$33$	−1.19621e33			−2.69003
$34$	−6.40326e32	−	1.10843e33i	−0.757887	−	1.31193i
$35$	−3.07095e33			−1.94899
$36$	4.17339e33	+	4.17339e33i	1.44539	+	1.44539i
$37$	−5.77908e33	+	2.39377e33i	−1.11051	+	0.459988i	−0.861113	−	0.508414i	$-0.830232\pi$
$37$	−5.77908e33	+	2.39377e33i	−1.11051	+	0.459988i	−0.249396	+	0.968402i	$0.580232\pi$
$38$			1.00215e34i			1.08539i
$39$	−1.61747e34	−	3.90491e34i	−1.00218	−	2.41948i
$40$	−1.49338e34	−	6.18578e33i	−0.536884	−	0.222385i
$41$	−7.69016e33	+	1.85657e34i	−0.162586	+	0.392517i	−0.984086	−	0.177691i	$-0.943137\pi$
$41$	−7.69016e33	+	1.85657e34i	−0.162586	+	0.392517i	0.821501	+	0.570208i	$0.193137\pi$
$42$	−2.05136e35	+	2.05136e35i	−2.58334	+	2.58334i
$43$	4.91051e34	−	4.91051e34i	0.372868	−	0.372868i	−0.495653	−	0.868521i	$-0.665071\pi$
$43$	4.91051e34	−	4.91051e34i	0.372868	−	0.372868i	0.868521	+	0.495653i	$0.165071\pi$
$44$	1.79335e35	−	4.32952e35i	0.830675	−	2.00543i
$45$	−6.62074e35	−	2.74240e35i	−1.89164	−	0.783541i
$46$	2.49641e35	+	6.02687e35i	0.444654	+	1.07349i
$47$			1.08093e36i			1.21253i	0.795262	+	0.606266i	$0.207333\pi$
$47$			1.08093e36i			1.21253i	−0.795262	+	0.606266i	$0.792667\pi$
$48$	1.28313e36	−	5.31490e35i	0.915344	−	0.379148i
$49$	−1.93888e36	−	1.93888e36i	−0.887841	−	0.887841i
$50$	3.49457e36			1.03643
$51$	8.21552e36	−	1.08371e36i	1.59175	−	0.209968i
$52$	1.65582e37			2.11321
$53$	−1.76984e36	−	1.76984e36i	−0.149970	−	0.149970i	0.628135	−	0.778105i	$-0.283819\pi$
$53$	−1.76984e36	−	1.76984e36i	−0.149970	−	0.149970i	−0.778105	+	0.628135i	$0.783819\pi$
$54$	−2.29035e37	+	9.48693e36i	−1.29848	+	0.537848i
$55$			5.68999e37i			2.17427i
$56$	−9.92200e36	−	2.39538e37i	−0.257369	−	0.621344i
$57$	−5.99360e37	−	2.48263e37i	−1.06262	−	0.440152i
$58$	5.72032e37	−	1.38101e38i	0.697780	−	1.68459i
$59$	8.14503e37	−	8.14503e37i	0.687978	−	0.687978i	−0.273807	−	0.961785i	$-0.588283\pi$
$59$	8.14503e37	−	8.14503e37i	0.687978	−	0.687978i	0.961785	+	0.273807i	$0.0882830\pi$
$60$	3.24336e38	−	3.24336e38i	1.90872	−	1.90872i
$61$	1.25476e38	−	3.02926e38i	0.517570	−	1.24952i	−0.421822	−	0.906679i	$-0.638609\pi$
$61$	1.25476e38	−	3.02926e38i	0.517570	−	1.24952i	0.939392	−	0.342845i	$-0.111391\pi$
$62$	−7.85558e37	−	3.25389e37i	−0.228432	−	0.0946197i
$63$	−4.39881e38	−	1.06197e39i	−0.906804	−	2.18922i
$64$			1.00584e39i			1.47794i
$65$	−1.85745e39	+	7.69380e38i	−1.95560	+	0.810035i
$66$	3.80085e39	+	3.80085e39i	2.88195	+	2.88195i
$67$	1.42347e39			0.781163			0.390581	−	0.920568i	$-0.372274\pi$
$67$	1.42347e39			0.781163			0.390581	+	0.920568i	$0.372274\pi$
$68$	−8.39430e38	+	3.13597e39i	−0.334999	+	1.25150i
$69$	−4.22295e39			−1.23129
$70$	9.75768e39	+	9.75768e39i	2.08804	+	2.08804i
$71$	5.02622e39	−	2.08193e39i	0.792843	−	0.328406i	0.0507572	−	0.998711i	$-0.483837\pi$
$71$	5.02622e39	−	2.08193e39i	0.792843	−	0.328406i	0.742086	+	0.670305i	$0.233837\pi$
$72$		−	6.05032e39i		−	0.706528i
$73$	−4.12225e39	−	9.95200e39i	−0.357843	−	0.863911i	−0.995603	−	0.0936749i	$-0.970139\pi$
$73$	−4.12225e39	−	9.95200e39i	−0.357843	−	0.863911i	0.637759	−	0.770236i	$-0.279861\pi$
$74$	2.59686e40	+	1.07565e40i	1.68254	+	0.696932i
$75$	−8.65713e39	+	2.09002e40i	−0.420297	+	1.01469i
$76$	1.79711e40	−	1.79711e40i	0.656270	−	0.656270i
$77$	−6.45359e40	+	6.45359e40i	−1.77931	+	1.77931i
$78$	−7.26816e40	+	1.75469e41i	−1.51842	+	3.66578i
$79$	1.49326e40	+	6.18527e39i	0.237220	+	0.0982599i	0.498127	−	0.867104i	$-0.334021\pi$
$79$	1.49326e40	+	6.18527e39i	0.237220	+	0.0982599i	−0.260906	+	0.965364i	$0.584021\pi$
$80$	−2.52814e40	−	6.10346e40i	−0.306454	−	0.739846i
$81$			9.52694e39i			0.0884149i
$82$	8.34257e40	−	3.45561e40i	0.594706	−	0.246335i
$83$	−2.41181e40	−	2.41181e40i	−0.132484	−	0.132484i	0.637755	−	0.770239i	$-0.279863\pi$
$83$	−2.41181e40	−	2.41181e40i	−0.132484	−	0.132484i	−0.770239	+	0.637755i	$0.779863\pi$
$84$	7.35723e41			3.12399
$85$	−5.15486e40	−	3.90787e41i	−0.169711	−	1.28657i
$86$	−3.12055e41			−0.798940
$87$	6.84235e41	+	6.84235e41i	1.36629	+	1.36629i
$88$	−4.43827e41	+	1.83839e41i	−0.693165	+	0.287118i
$89$		−	1.54199e42i		−	1.88885i	−0.328725	−	0.944426i	$-0.606619\pi$
$89$		−	1.54199e42i		−	1.88885i	0.328725	−	0.944426i	$-0.393381\pi$
$90$	1.23231e42	+	2.97506e42i	1.18715	+	2.86604i
$91$	−2.97935e42	−	1.23409e42i	−2.26324	−	0.937466i
$92$	6.33102e41	−	1.52844e42i	0.380220	−	0.917933i
$93$	3.89214e41	−	3.89214e41i	0.185270	−	0.185270i
$94$	3.43456e42	−	3.43456e42i	1.29904	−	1.29904i
$95$	−1.18091e42	+	2.85097e42i	−0.355762	+	0.858886i
$96$	−8.52737e42	−	3.53215e42i	−2.05108	−	0.849587i
$97$	−2.87026e42	−	6.92942e42i	−0.552496	−	1.33384i	−0.915599	−	0.402093i	$-0.868283\pi$
$97$	−2.87026e42	−	6.92942e42i	−0.552496	−	1.33384i	0.363103	−	0.931749i	$-0.381717\pi$
$98$			1.23212e43i			1.90237i
$99$	−1.96766e43	+	8.15032e42i	−2.44227	+	1.01162i
$100$	−6.26667e42	−	6.26667e42i	−0.626667	−	0.626667i
$101$	1.20836e43			0.975631			0.487815	−	0.872947i	$-0.337794\pi$
$101$	1.20836e43			0.975631			0.487815	+	0.872947i	$0.337794\pi$
$102$	−2.95475e43	−	2.26607e43i	−1.93027	−	1.48037i
$103$	−1.95014e43			−1.03292			−0.516458	−	0.856313i	$-0.672750\pi$
$103$	−1.95014e43			−1.03292			−0.516458	+	0.856313i	$0.672750\pi$
$104$	−1.20025e43	−	1.20025e43i	−0.516483	−	0.516483i
$105$	−8.25310e43	+	3.41854e43i	−2.89099	+	1.19749i
$106$			1.12471e43i			0.321338i
$107$	1.16334e43	+	2.80854e43i	0.271615	+	0.655738i	0.999553	−	0.0299061i	$-0.00952084\pi$
$107$	1.16334e43	+	2.80854e43i	0.271615	+	0.655738i	−0.727937	+	0.685644i	$0.759521\pi$
$108$	5.80843e43	+	2.40593e43i	1.11032	+	0.459909i
$109$	−2.74075e43	+	6.61677e43i	−0.429735	+	1.03747i	0.549637	+	0.835404i	$0.314766\pi$
$109$	−2.74075e43	+	6.61677e43i	−0.429735	+	1.03747i	−0.979372	+	0.202068i	$0.935234\pi$
$110$	1.80795e44	−	1.80795e44i	2.32939	−	2.32939i
$111$	−1.28664e44	+	1.28664e44i	−1.36463	+	1.36463i
$112$	4.05513e43	−	9.78995e43i	0.354664	−	0.856235i
$113$	−3.61697e43	−	1.49820e43i	−0.261311	−	0.108239i	0.248182	−	0.968714i	$-0.420167\pi$
$113$	−3.61697e43	−	1.49820e43i	−0.261311	−	0.108239i	−0.509493	+	0.860475i	$0.670167\pi$
$114$	1.11558e44	+	2.69325e44i	0.666879	+	1.60999i
$115$			2.00873e44i			0.995217i
$116$	−3.50230e44	+	1.45070e44i	−1.44048	+	0.596666i
$117$	−5.32120e44	−	5.32120e44i	−1.81976	−	1.81976i
$118$	−5.17603e44			−1.47412
$119$	3.84764e44	−	5.01697e44i	0.913976	−	1.19174i
$120$	−4.70201e44			−0.933012
$121$	7.69788e44	+	7.69788e44i	1.27787	+	1.27787i
$122$	−1.36121e45	+	5.63832e44i	−1.89317	+	0.784175i
$123$			5.84554e44i			0.682126i
$124$	8.25202e43	+	1.99221e44i	0.0809085	+	0.195330i
$125$	−4.59158e44	−	1.90190e44i	−0.378789	−	0.156900i
$126$	−1.97663e45	+	4.77200e45i	−1.37391	+	3.31691i
$127$	−1.14082e44	+	1.14082e44i	−0.0669015	+	0.0669015i	−0.739766	−	0.672864i	$-0.765064\pi$
$127$	−1.14082e44	+	1.14082e44i	−0.0669015	+	0.0669015i	0.672864	+	0.739766i	$0.265064\pi$
$128$	1.22242e45	−	1.22242e45i	0.605628	−	0.605628i
$129$	7.73055e44	−	1.86632e45i	0.323990	−	0.782181i
$130$	8.34652e45	+	3.45724e45i	2.96294	+	1.22729i
$131$	4.20084e44	+	1.01417e45i	0.126475	+	0.305337i	0.974416	−	0.224754i	$-0.0721579\pi$
$131$	4.20084e44	+	1.01417e45i	0.126475	+	0.305337i	−0.847941	+	0.530091i	$0.822158\pi$
$132$		−	1.36318e46i		−	3.48509i
$133$	−4.57296e45	+	1.89418e45i	−0.994002	+	0.411729i
$134$	−4.52297e45	−	4.52297e45i	−0.836894	−	0.836894i
$135$	−7.63363e45			−1.20380
$136$	2.88164e45	−	1.66469e45i	0.387752	−	0.223999i
$137$	−1.23112e46			−1.41517			−0.707585	−	0.706628i	$-0.750215\pi$
$137$	−1.23112e46			−1.41517			−0.707585	+	0.706628i	$0.750215\pi$
$138$	1.34181e46	+	1.34181e46i	1.31914	+	1.31914i
$139$	1.03504e46	−	4.28727e45i	0.871242	−	0.360880i	0.0981479	−	0.995172i	$-0.468708\pi$
$139$	1.03504e46	−	4.28727e45i	0.871242	−	0.360880i	0.773094	+	0.634292i	$0.218708\pi$
$140$		−	3.49961e46i		−	2.52503i
$141$	1.20328e46	+	2.90497e46i	0.744998	+	1.79858i
$142$	−2.25856e46	−	9.35525e45i	−1.20124	−	0.497572i
$143$	−2.28657e46	+	5.52027e46i	−1.04583	+	2.52485i
$144$	1.74851e46	−	1.74851e46i	0.688455	−	0.688455i
$145$	3.25470e46	−	3.25470e46i	1.10433	−	1.10433i
$146$	−1.85235e46	+	4.47197e46i	−0.542172	+	1.30892i
$147$	−7.36903e46	−	3.05235e46i	−1.86246	−	0.771457i
$148$	−2.72791e46	−	6.58575e46i	−0.595941	−	1.43873i
$149$		−	4.59820e46i		−	0.869127i	−0.900641	−	0.434564i	$-0.856903\pi$
$149$		−	4.59820e46i		−	0.869127i	0.900641	−	0.434564i	$-0.143097\pi$
$150$	9.39157e46	−	3.89012e46i	1.53736	−	0.636797i
$151$	5.22779e46	+	5.22779e46i	0.741846	+	0.741846i	0.972933	−	0.231087i	$-0.0742281\pi$
$151$	5.22779e46	+	5.22779e46i	0.741846	+	0.741846i	−0.231087	+	0.972933i	$0.574228\pi$
$152$	−2.60534e46			−0.320795
$153$	1.27755e47	−	7.38022e46i	1.36619	−	0.789230i
$154$	4.10115e47			3.81250
$155$	−1.85137e46	−	1.85137e46i	−0.149748	−	0.149748i
$156$	4.44998e47	−	1.84324e47i	3.13458	−	1.29838i
$157$			2.00809e47i			1.23294i	0.787380	+	0.616468i	$0.211437\pi$
$157$			2.00809e47i			1.23294i	−0.787380	+	0.616468i	$0.788563\pi$
$158$	−2.77938e46	−	6.71002e46i	−0.148875	−	0.359415i
$159$	−6.72658e46	−	2.78624e46i	−0.314598	−	0.130311i
$160$	−1.68014e47	+	4.05621e47i	−0.686697	+	1.65783i
$161$	−2.27830e47	+	2.27830e47i	−0.814431	+	0.814431i
$162$	3.02710e46	−	3.02710e46i	0.0947228	−	0.0947228i
$163$	1.28644e47	−	3.10574e47i	0.352660	−	0.851395i	−0.643631	−	0.765336i	$-0.722573\pi$
$163$	1.28644e47	−	3.10574e47i	0.352660	−	0.851395i	0.996290	−	0.0860590i	$-0.0274274\pi$
$164$	−2.11572e47	−	8.76359e46i	−0.508528	−	0.210639i
$165$	6.33403e47	+	1.52917e48i	1.33590	+	3.22516i
$166$			1.53266e47i			0.283872i
$167$	9.46867e47	−	3.92205e47i	1.54129	−	0.638424i	0.559576	−	0.828779i	$-0.310964\pi$
$167$	9.46867e47	−	3.92205e47i	1.54129	−	0.638424i	0.981715	+	0.190355i	$0.0609641\pi$
$168$	−5.33302e47	−	5.33302e47i	−0.763526	−	0.763526i
$169$	−1.31769e48			−1.66054
$170$	−1.07790e48	+	1.40548e48i	−1.19654	+	1.56018i
$171$	−1.15505e48			−1.13028
$172$	5.59594e47	+	5.59594e47i	0.483072	+	0.483072i
$173$	−1.84025e48	+	7.62257e47i	−1.40244	+	0.580912i	−0.950385	−	0.311076i	$-0.899311\pi$
$173$	−1.84025e48	+	7.62257e47i	−1.40244	+	0.580912i	−0.452060	+	0.891988i	$0.649311\pi$
$174$		−	4.34820e48i		−	2.92752i
$175$	6.60516e47	+	1.59463e48i	0.393156	+	0.949163i
$176$	−1.81393e48	−	7.51353e47i	−0.955207	−	0.395660i
$177$	1.28226e48	−	3.09565e48i	0.597793	−	1.44320i
$178$	−4.89956e48	+	4.89956e48i	−2.02361	+	2.02361i
$179$	2.17764e48	−	2.17764e48i	0.797345	−	0.797345i	−0.185331	−	0.982676i	$-0.559336\pi$
$179$	2.17764e48	−	2.17764e48i	0.797345	−	0.797345i	0.982676	+	0.185331i	$0.0593359\pi$
$180$	3.12520e48	−	7.54489e48i	1.01512	−	2.45072i
$181$	4.14558e47	+	1.71716e47i	0.119535	+	0.0495132i	0.441649	−	0.897188i	$-0.354393\pi$
$181$	4.14558e47	+	1.71716e47i	0.119535	+	0.0495132i	−0.322114	+	0.946701i	$0.604393\pi$
$182$	5.54542e48	+	1.33878e49i	1.42036	+	3.42906i
$183$		−	9.53783e48i		−	2.17146i
$184$	−1.56684e48	+	6.49005e47i	−0.317278	+	0.131421i
$185$	6.12016e48	+	6.12016e48i	1.10299	+	1.10299i
$186$	−2.47339e48			−0.396975
$187$	−9.29566e48	−	7.12908e48i	−1.32949	−	1.01962i
$188$	−1.23181e49			−1.57091
$189$	−8.65806e48	−	8.65806e48i	−0.985126	−	0.985126i
$190$	1.28110e49	−	5.30648e48i	1.30131	−	0.539019i
$191$		−	5.89374e48i		−	0.534778i	−0.963589	−	0.267389i	$-0.913839\pi$
$191$		−	5.89374e48i		−	0.534778i	0.963589	−	0.267389i	$-0.0861609\pi$
$192$	1.11968e49	+	2.70316e49i	0.908070	+	2.19227i
$193$	−8.62426e47	−	3.57229e47i	−0.0625518	−	0.0259098i	0.351188	−	0.936305i	$-0.385778\pi$
$193$	−8.62426e47	−	3.57229e47i	−0.0625518	−	0.0259098i	−0.413740	+	0.910395i	$0.635778\pi$
$194$	−1.28976e49	+	3.11377e49i	−0.837092	+	2.02092i
$195$	−4.13538e49	+	4.13538e49i	−2.40310	+	2.40310i
$196$	2.20952e49	−	2.20952e49i	1.15025	−	1.15025i
$197$	3.54209e48	−	8.55136e48i	0.165286	−	0.399035i	−0.819436	−	0.573171i	$-0.805713\pi$
$197$	3.54209e48	−	8.55136e48i	0.165286	−	0.399035i	0.984722	+	0.174136i	$0.0557131\pi$
$198$	8.84177e49	+	3.66238e49i	3.70031	+	1.53272i
$199$	−1.65458e49	−	3.99450e49i	−0.621363	−	1.50010i	−0.850103	−	0.526616i	$-0.823460\pi$
$199$	−1.65458e49	−	3.99450e49i	−0.621363	−	1.50010i	0.228740	−	0.973488i	$-0.426540\pi$
$200$			9.08502e48i			0.306324i
$201$	3.82555e49	−	1.58460e49i	1.15872	−	0.479958i
$202$	−3.83945e49	−	3.83945e49i	−1.04524	−	1.04524i
$203$	7.38295e49			1.80745
$204$	1.23497e49	+	9.36228e49i	0.272025	+	2.06221i
$205$	2.78054e49			0.551343
$206$	6.19640e49	+	6.19640e49i	1.10661	+	1.10661i
$207$	−6.94640e49	+	2.87729e49i	−1.11789	+	0.463043i
$208$		−	6.93735e49i		−	1.00654i
$209$	3.50963e49	+	8.47299e49i	0.459320	+	1.10890i
$210$	3.70856e50	+	1.53614e50i	4.38017	+	1.81433i
$211$	2.46500e49	−	5.95103e49i	0.262871	−	0.634628i	−0.736242	−	0.676718i	$-0.763402\pi$
$211$	2.46500e49	−	5.95103e49i	0.262871	−	0.634628i	0.999114	+	0.0420902i	$0.0134017\pi$
$212$	2.01689e49	−	2.01689e49i	0.194294	−	0.194294i
$213$	1.11903e50	−	1.11903e50i	0.974269	−	0.974269i
$214$	5.22751e49	−	1.26203e50i	0.411527	−	0.993514i
$215$	−8.87751e49	−	3.67718e49i	−0.632214	−	0.261872i
$216$	−2.46637e49	−	5.95433e49i	−0.158965	−	0.383776i
$217$		−	4.19965e49i		−	0.245092i
$218$	2.97327e50	−	1.23157e50i	1.57188	−	0.651095i
$219$	−2.21569e50	−	2.21569e50i	−1.06160	−	1.06160i
$220$	−6.48423e50			−2.81689
$221$	1.07030e50	−	3.99845e50i	0.421766	−	1.57564i
$222$	8.17639e50			2.92397
$223$	2.56765e50	+	2.56765e50i	0.833645	+	0.833645i	0.988013	−	0.154369i	$-0.0493343\pi$
$223$	2.56765e50	+	2.56765e50i	0.833645	+	0.833645i	−0.154369	+	0.988013i	$0.549334\pi$
$224$	−6.50616e50	+	2.69494e50i	−1.91863	+	0.794725i
$225$			4.02775e50i			1.07929i
$226$	6.73222e49	+	1.62530e50i	0.163994	+	0.395916i
$227$	−2.51120e50	−	1.04017e50i	−0.556322	−	0.230436i	0.0867658	−	0.996229i	$-0.472347\pi$
$227$	−2.51120e50	−	1.04017e50i	−0.556322	−	0.230436i	−0.643087	+	0.765793i	$0.722347\pi$
$228$	2.82917e50	−	6.83021e50i	0.570242	−	1.37669i
$229$	4.75175e50	−	4.75175e50i	0.871748	−	0.871748i	−0.120915	−	0.992663i	$-0.538583\pi$
$229$	4.75175e50	−	4.75175e50i	0.871748	−	0.871748i	0.992663	+	0.120915i	$0.0385828\pi$
$230$	6.38257e50	−	6.38257e50i	1.06622	−	1.06622i
$231$	−1.01598e51	+	2.45279e51i	−1.54606	+	3.73253i
$232$	3.59028e50	+	1.48714e50i	0.497893	+	0.206234i
$233$	4.94088e50	+	1.19283e51i	0.624672	+	1.50809i	0.846160	+	0.532929i	$0.178909\pi$
$233$	4.94088e50	+	1.19283e51i	0.624672	+	1.50809i	−0.221488	+	0.975163i	$0.571091\pi$
$234$			3.38153e51i			3.89917i
$235$	1.38181e51	−	5.72362e50i	1.45374	−	0.602160i
$236$	9.28195e50	+	9.28195e50i	0.891315	+	0.891315i
$237$	4.70163e50			0.412248
$238$	−2.81665e51	+	3.71544e50i	−2.25595	+	0.297581i
$239$	−7.66895e50			−0.561282			−0.280641	−	0.959813i	$-0.590547\pi$
$239$	−7.66895e50			−0.561282			−0.280641	+	0.959813i	$0.590547\pi$
$240$	−1.35886e51	−	1.35886e51i	−0.909145	−	0.909145i
$241$	6.94477e50	−	2.87662e50i	0.424905	−	0.176001i	−0.159976	−	0.987121i	$-0.551142\pi$
$241$	6.94477e50	−	2.87662e50i	0.424905	−	0.176001i	0.584880	+	0.811120i	$0.301142\pi$
$242$		−	4.89188e51i		−	2.73807i
$243$	7.99080e50	+	1.92915e51i	0.409313	+	0.988169i
$244$	3.45209e51	+	1.42990e51i	1.61883	+	0.670541i
$245$	−1.45191e51	+	3.50522e51i	−0.623546	+	1.50537i
$246$	1.85737e51	−	1.85737e51i	0.730792	−	0.730792i
$247$	−2.29137e51	+	2.29137e51i	−0.826249	+	0.826249i
$248$	8.45931e49	−	2.04226e50i	0.0279656	−	0.0675148i
$249$	−9.16647e50	−	3.79687e50i	−0.277918	−	0.115117i
$250$	8.54626e50	+	2.06325e51i	0.237720	+	0.573907i
$251$			1.25600e51i			0.320631i	0.987066	+	0.160316i	$0.0512512\pi$
$251$			1.25600e51i			0.320631i	−0.987066	+	0.160316i	$0.948749\pi$
$252$	1.21020e52	−	5.01282e51i	2.83626	−	1.17482i
$253$	4.22134e51	+	4.22134e51i	0.908571	+	0.908571i
$254$	7.24970e50			0.143349
$255$	−5.73555e51	−	9.92846e51i	−1.04222	−	1.80413i
$256$	1.07916e51			0.180271
$257$	2.32980e51	+	2.32980e51i	0.357895	+	0.357895i	0.863037	−	0.505141i	$-0.168560\pi$
$257$	2.32980e51	+	2.32980e51i	0.357895	+	0.357895i	−0.505141	+	0.863037i	$0.668560\pi$
$258$	−8.38639e51	+	3.47376e51i	−1.18509	+	0.490880i
$259$			1.38830e52i			1.80525i
$260$	−8.76773e51	−	2.11672e52i	−1.04945	−	2.53359i
$261$	1.59171e52	+	6.59308e51i	1.75426	+	0.726637i
$262$	1.88767e51	−	4.55723e51i	0.191623	−	0.462619i
$263$	5.80398e51	−	5.80398e51i	0.542847	−	0.542847i	−0.381515	−	0.924362i	$-0.624598\pi$
$263$	5.80398e51	−	5.80398e51i	0.542847	−	0.542847i	0.924362	+	0.381515i	$0.124598\pi$
$264$	−9.88127e51	+	9.88127e51i	−0.851781	+	0.851781i
$265$	−1.32533e51	+	3.19963e51i	−0.105326	+	0.254280i
$266$	2.05488e52	+	8.51159e51i	1.50602	+	0.623815i
$267$	−1.71653e52	−	4.14407e52i	−1.16054	−	2.80179i
$268$			1.62217e52i			1.01204i
$269$	2.68632e52	−	1.11271e52i	1.54697	−	0.640778i	0.564208	−	0.825633i	$-0.309182\pi$
$269$	2.68632e52	−	1.11271e52i	1.54697	−	0.640778i	0.982766	+	0.184855i	$0.0591815\pi$
$270$	2.42552e52	+	2.42552e52i	1.28969	+	1.28969i
$271$	−2.00613e52			−0.985189			−0.492594	−	0.870259i	$-0.663951\pi$
$271$	−2.00613e52			−0.985189			−0.492594	+	0.870259i	$0.663951\pi$
$272$	1.31387e52	+	3.51694e51i	0.596102	+	0.159563i
$273$	−9.38069e52			−3.93312
$274$	3.91178e52	+	3.91178e52i	1.51613	+	1.51613i
$275$	2.95460e52	−	1.22383e52i	1.05888	−	0.438601i
$276$		−	4.81241e52i		−	1.59521i
$277$	−7.41897e51	−	1.79110e52i	−0.227525	−	0.549293i	0.768350	−	0.640029i	$-0.221078\pi$
$277$	−7.41897e51	−	1.79110e52i	−0.227525	−	0.549293i	−0.995875	+	0.0907366i	$0.971078\pi$
$278$	−4.65100e52	−	1.92651e52i	−1.32003	−	0.546773i
$279$	3.75034e51	−	9.05413e51i	0.0985327	−	0.237879i
$280$	−2.53676e52	+	2.53676e52i	−0.617136	+	0.617136i
$281$	−2.76530e52	+	2.76530e52i	−0.623098	+	0.623098i	−0.946322	−	0.323225i	$-0.895233\pi$
$281$	−2.76530e52	+	2.76530e52i	−0.623098	+	0.623098i	0.323225	+	0.946322i	$0.395233\pi$
$282$	5.40698e52	−	1.30536e53i	1.12875	−	2.72505i
$283$	1.37724e52	+	5.70472e51i	0.266442	+	0.110364i	0.511905	−	0.859042i	$-0.328940\pi$
$283$	1.37724e52	+	5.70472e51i	0.266442	+	0.110364i	−0.245463	+	0.969406i	$0.578940\pi$
$284$	2.37254e52	+	5.72781e52i	0.425470	+	1.02717i
$285$			8.97649e52i			1.49259i
$286$	2.48056e53	−	1.02748e53i	3.82542	−	1.58454i
$287$	3.15369e52	+	3.15369e52i	0.451189	+	0.451189i
$288$	−1.64334e53			−2.18167
$289$	7.03009e52	+	4.05409e52i	0.866278	+	0.499562i
$290$	−2.06830e53			−2.36623
$291$	−1.54275e53	−	1.54275e53i	−1.63906	−	1.63906i
$292$	1.13411e53	−	4.69766e52i	1.11925	−	0.463607i
$293$		−	2.41069e52i		−	0.221049i	−0.993873	−	0.110524i	$-0.964747\pi$
$293$		−	2.41069e52i		−	0.221049i	0.993873	−	0.110524i	$-0.0352530\pi$
$294$	1.37159e53	+	3.31130e53i	1.16884	+	2.82183i
$295$	−1.47251e53	−	6.09932e52i	−1.16650	−	0.483179i
$296$	−2.79643e52	+	6.75118e52i	−0.205984	+	0.497288i
$297$	−1.60420e53	+	1.60420e53i	−1.09900	+	1.09900i
$298$	−1.46104e53	+	1.46104e53i	−0.931135	+	0.931135i
$299$	−8.07224e52	+	1.94881e53i	−0.478700	+	1.15568i
$300$	−2.38175e53	−	9.86553e52i	−1.31459	−	0.544519i
$301$	−5.89821e52	−	1.42395e53i	−0.303068	−	0.731671i
$302$		−	3.32217e53i		−	1.58955i
$303$	3.24743e53	−	1.34513e53i	1.44718	−	0.599442i
$304$	−7.52931e52	−	7.52931e52i	−0.312589	−	0.312589i
$305$	−4.53685e53			−1.75513
$306$	−6.40429e53	−	1.71429e53i	−2.30919	−	0.618121i
$307$	1.82172e53			0.612361			0.306181	−	0.951973i	$-0.400949\pi$
$307$	1.82172e53			0.612361			0.306181	+	0.951973i	$0.400949\pi$
$308$	−7.35441e53	−	7.35441e53i	−2.30519	−	2.30519i
$309$	−5.24094e53	+	2.17087e53i	−1.53215	+	0.634639i
$310$			1.17651e53i			0.320864i
$311$	1.01317e53	+	2.44600e53i	0.257830	+	0.622456i	0.998794	−	0.0490880i	$-0.0156315\pi$
$311$	1.01317e53	+	2.44600e53i	0.257830	+	0.622456i	−0.740965	+	0.671544i	$0.765631\pi$
$312$	−4.56176e53	−	1.88954e53i	−1.08345	−	0.448779i
$313$	1.93078e53	−	4.66131e53i	0.428084	−	1.03349i	−0.551810	−	0.833970i	$-0.686063\pi$
$313$	1.93078e53	−	4.66131e53i	0.428084	−	1.03349i	0.979894	−	0.199517i	$-0.0639373\pi$
$314$	6.38054e53	−	6.38054e53i	1.32090	−	1.32090i
$315$	−1.12464e54	+	1.12464e54i	−2.17439	+	2.17439i
$316$	−7.04864e52	+	1.70169e53i	−0.127301	+	0.307333i
$317$	6.26113e53	+	2.59344e53i	1.05652	+	0.437626i	0.842216	−	0.539141i	$-0.181251\pi$
$317$	6.26113e53	+	2.59344e53i	1.05652	+	0.437626i	0.214306	+	0.976767i	$0.431251\pi$
$318$	1.25201e53	+	3.02262e53i	0.197435	+	0.476651i
$319$		−	1.36795e54i		−	2.01637i
$320$	1.28581e54	−	5.32599e53i	1.77195	−	0.733966i
$321$	6.25288e53	+	6.25288e53i	0.805790	+	0.805790i
$322$	1.44782e54			1.74507
$323$	−3.17801e53	−	5.50126e53i	−0.358345	−	0.620309i
$324$	−1.08567e53			−0.114547
$325$	7.99019e53	+	7.99019e53i	0.788978	+	0.788978i
$326$	−1.39558e54	+	5.78067e53i	−1.28996	+	0.534318i
$327$			2.08334e54i			1.80295i
$328$	8.98372e52	+	2.16886e53i	0.0728062	+	0.175770i
$329$	2.21642e54	+	9.18070e53i	1.68244	+	0.696889i
$330$	2.84623e54	−	6.87140e54i	2.02404	−	4.88647i
$331$	−1.15212e54	+	1.15212e54i	−0.767706	+	0.767706i	−0.977702	−	0.209996i	$-0.932655\pi$
$331$	−1.15212e54	+	1.15212e54i	−0.767706	+	0.767706i	0.209996	+	0.977702i	$0.432655\pi$
$332$	2.74846e53	−	2.74846e53i	0.171641	−	0.171641i
$333$	−1.23977e54	+	2.99307e54i	−0.725754	+	1.75213i
$334$	−4.25479e54	−	1.76239e54i	−2.33523	−	0.967282i
$335$	−7.53743e53	−	1.81970e54i	−0.387936	−	0.936560i
$336$		−	3.08244e54i		−	1.48799i
$337$	−2.12898e52	+	8.81853e51i	−0.00964115	+	0.00399349i	−0.387499	−	0.921870i	$-0.626661\pi$
$337$	−2.12898e52	+	8.81853e51i	−0.00964115	+	0.00399349i	0.377858	+	0.925864i	$0.376661\pi$
$338$	4.18686e54	+	4.18686e54i	1.77901	+	1.77901i
$339$	−1.13883e54			−0.454114
$340$	4.45335e54	−	5.87440e53i	1.66682	−	0.219870i
$341$	−7.78129e53			−0.273421
$342$	3.67007e54	+	3.67007e54i	1.21091	+	1.21091i
$343$	−1.14452e54	+	4.74077e53i	−0.354651	+	0.146901i
$344$		−	8.11265e53i		−	0.236133i
$345$	2.23609e54	+	5.39841e54i	0.611476	+	1.47623i
$346$	8.26925e54	+	3.42523e54i	2.12486	+	0.880145i
$347$	1.54521e53	−	3.73048e53i	0.0373168	−	0.0900908i	−0.904122	−	0.427274i	$-0.859474\pi$
$347$	1.54521e53	−	3.73048e53i	0.0373168	−	0.0900908i	0.941439	+	0.337183i	$0.109474\pi$
$348$	−7.79744e54	+	7.79744e54i	−1.77010	+	1.77010i
$349$	3.97772e54	−	3.97772e54i	0.848960	−	0.848960i	−0.141043	−	0.990003i	$-0.545046\pi$
$349$	3.97772e54	−	3.97772e54i	0.848960	−	0.848960i	0.990003	+	0.141043i	$0.0450456\pi$
$350$	2.96806e54	−	7.16553e54i	0.595675	−	1.43809i
$351$	−7.40592e54	−	3.06763e54i	−1.39790	−	0.579029i
$352$	4.99331e54	+	1.20549e55i	0.886586	+	2.14041i
$353$			2.45030e54i			0.409320i	0.978833	+	0.204660i	$0.0656089\pi$
$353$			2.45030e54i			0.409320i	−0.978833	+	0.204660i	$0.934391\pi$
$354$	−1.39104e55	+	5.76189e54i	−2.18661	+	0.905722i
$355$	−5.32287e54	−	5.32287e54i	−0.787474	−	0.787474i
$356$	1.75723e55			2.44712
$357$	4.75560e54	−	1.77661e55i	0.623504	−	2.32930i
$358$	−1.38385e55			−1.70846
$359$	−1.06487e54	−	1.06487e54i	−0.123813	−	0.123813i	0.642485	−	0.766298i	$-0.277903\pi$
$359$	−1.06487e54	−	1.06487e54i	−0.123813	−	0.123813i	−0.766298	+	0.642485i	$0.777903\pi$
$360$	−7.73442e54	+	3.20370e54i	−0.847079	+	0.350872i
$361$		−	4.71803e54i		−	0.486805i
$362$	−7.71612e53	−	1.86284e54i	−0.0750179	−	0.181109i
$363$	2.92571e55	+	1.21187e55i	2.68064	+	1.11036i
$364$	1.40635e55	−	3.39522e55i	1.21454	−	2.93216i
$365$	−1.05394e55	+	1.05394e55i	−0.858059	+	0.858059i
$366$	−3.03057e55	+	3.03057e55i	−2.32638	+	2.32638i
$367$	1.40510e54	−	3.39221e54i	0.101715	−	0.245563i	−0.864827	−	0.502070i	$-0.832572\pi$
$367$	1.40510e54	−	3.39221e54i	0.101715	−	0.245563i	0.966542	+	0.256508i	$0.0825719\pi$
$368$	−6.40368e54	−	2.65249e54i	−0.437221	−	0.181103i
$369$	3.98284e54	+	9.61542e54i	0.256523	+	0.619300i
$370$		−	3.88926e55i		−	2.36336i
$371$	−5.13220e54	+	2.12583e54i	−0.294283	+	0.121896i
$372$	4.43542e54	+	4.43542e54i	0.240028	+	0.240028i
$373$	−3.23360e55			−1.65176			−0.825880	−	0.563846i	$-0.809321\pi$
$373$	−3.23360e55			−1.65176			−0.825880	+	0.563846i	$0.809321\pi$
$374$	6.88413e54	+	5.21882e55i	0.331978	+	2.51671i
$375$	−1.44569e55			−0.658270
$376$	8.92901e54	+	8.92901e54i	0.383941	+	0.383941i
$377$	4.46554e55	−	1.84969e55i	1.81357	−	0.751206i
$378$			5.50205e55i			2.11082i
$379$	−3.96051e54	−	9.56152e54i	−0.143552	−	0.346564i	0.835708	−	0.549174i	$-0.185058\pi$
$379$	−3.96051e54	−	9.56152e54i	−0.143552	−	0.346564i	−0.979260	+	0.202610i	$0.935058\pi$
$380$	−3.24892e55	−	1.34575e55i	−1.11274	−	0.460910i
$381$	−1.79597e54	+	4.33586e54i	−0.0581316	+	0.140342i
$382$	−1.87269e55	+	1.87269e55i	−0.572931	+	0.572931i
$383$	−1.39864e55	+	1.39864e55i	−0.404512	+	0.404512i	−0.879820	−	0.475308i	$-0.842337\pi$
$383$	−1.39864e55	+	1.39864e55i	−0.404512	+	0.404512i	0.475308	+	0.879820i	$0.342337\pi$
$384$	1.92444e55	−	4.64600e55i	0.526238	−	1.27045i
$385$	1.16672e56	+	4.83270e55i	3.01689	+	1.24964i
$386$	1.60522e54	+	3.87535e54i	0.0392562	+	0.0947728i
$387$		−	3.59666e55i		−	0.831981i
$388$	7.89666e55	−	3.27090e55i	1.72807	−	0.715790i
$389$	3.65301e55	+	3.65301e55i	0.756369	+	0.756369i	0.975660	−	0.219290i	$-0.0703742\pi$
$389$	3.65301e55	+	3.65301e55i	0.756369	+	0.756369i	−0.219290	+	0.975660i	$0.570374\pi$
$390$	2.62796e56			5.14908
$391$	−3.28163e55	−	2.51677e55i	−0.608541	−	0.466705i
$392$	−3.20322e55			−0.562259
$393$	2.25793e55	+	2.25793e55i	0.375207	+	0.375207i
$394$	−3.84259e55	+	1.59165e55i	−0.604582	+	0.250426i
$395$		−	2.23642e55i		−	0.333208i
$396$	−9.28798e55	−	2.24232e56i	−1.31061	−	3.16410i
$397$	3.36846e55	+	1.39526e55i	0.450231	+	0.186492i	0.596265	−	0.802788i	$-0.296651\pi$
$397$	3.36846e55	+	1.39526e55i	0.450231	+	0.186492i	−0.146034	+	0.989280i	$0.546651\pi$
$398$	−7.43491e55	+	1.79495e56i	−0.941434	+	2.27282i
$399$	−1.01811e56	+	1.01811e56i	−1.22146	+	1.22146i
$400$	−2.62553e55	+	2.62553e55i	−0.298488	+	0.298488i
$401$	1.00542e55	−	2.42729e55i	0.108329	−	0.261528i	−0.860414	−	0.509595i	$-0.829795\pi$
$401$	1.00542e55	−	2.42729e55i	0.108329	−	0.261528i	0.968743	+	0.248067i	$0.0797952\pi$
$402$	−1.71903e56	−	7.12045e55i	−1.75559	−	0.727189i
$403$	−1.05216e55	−	2.54013e55i	−0.101864	−	0.245922i
$404$			1.37702e56i			1.26399i
$405$	1.21787e55	−	5.04460e54i	0.106003	−	0.0439080i
$406$	−2.34587e56	−	2.34587e56i	−1.93640	−	1.93640i
$407$	2.57230e56			2.01392
$408$	5.89123e55	−	7.68162e55i	0.437534	−	0.570505i
$409$	−9.72865e55			−0.685491			−0.342745	−	0.939428i	$-0.611357\pi$
$409$	−9.72865e55			−0.685491			−0.342745	+	0.939428i	$0.611357\pi$
$410$	−8.83494e55	−	8.83494e55i	−0.590678	−	0.590678i
$411$	−3.30861e56	+	1.37047e56i	−2.09916	+	0.869502i
$412$		−	2.22235e56i		−	1.33820i
$413$	−9.78331e55	−	2.36190e56i	−0.559190	−	1.35000i
$414$	3.12140e56	+	1.29292e56i	1.69372	+	0.701562i
$415$	−1.80606e55	+	4.36021e55i	−0.0930459	+	0.224633i
$416$	−3.26004e56	+	3.26004e56i	−1.59484	+	1.59484i
$417$	2.30439e56	−	2.30439e56i	1.07061	−	1.07061i
$418$	1.57707e56	−	3.80737e56i	0.695921	−	1.68010i
$419$	3.62442e56	+	1.50128e56i	1.51928	+	0.629306i	0.977447	−	0.211182i	$-0.0677312\pi$
$419$	3.62442e56	+	1.50128e56i	1.51928	+	0.629306i	0.541831	+	0.840487i	$0.317731\pi$
$420$	−3.89572e56	−	9.40510e56i	−1.55141	−	3.74545i
$421$		−	1.83373e56i		−	0.693858i	−0.937891	−	0.346929i	$-0.887225\pi$
$421$		−	1.83373e56i		−	0.693858i	0.937891	−	0.346929i	$-0.112775\pi$
$422$	−2.67412e56	+	1.10766e56i	−0.961531	+	0.398279i
$423$	3.95858e56	+	3.95858e56i	1.35276	+	1.35276i
$424$	−2.92396e55			−0.0949740
$425$	−1.91833e56	+	1.10820e56i	−0.592328	+	0.342180i
$426$	−7.11123e56			−2.08756
$427$	−5.14570e56	−	5.14570e56i	−1.43630	−	1.43630i
$428$	−3.20057e56	+	1.32572e56i	−0.849546	+	0.351893i
$429$			1.73810e57i			4.38775i
$430$	1.65236e56	+	3.98915e56i	0.396764	+	0.957874i
$431$	6.59046e56	+	2.72986e56i	1.50541	+	0.623561i	0.974604	−	0.223933i	$-0.0718898\pi$
$431$	6.59046e56	+	2.72986e56i	1.50541	+	0.623561i	0.530805	+	0.847494i	$0.321890\pi$
$432$	1.00801e56	−	2.43354e56i	0.219060	−	0.528857i
$433$	2.63214e56	−	2.63214e56i	0.544277	−	0.544277i	−0.380503	−	0.924780i	$-0.624249\pi$
$433$	2.63214e56	−	2.63214e56i	0.544277	−	0.544277i	0.924780	+	0.380503i	$0.124249\pi$
$434$	−1.33440e56	+	1.33440e56i	−0.262577	+	0.262577i
$435$	5.12382e56	−	1.23700e57i	0.959567	−	2.31660i
$436$	−7.54036e56	−	3.12332e56i	−1.34410	−	0.556746i
$437$	1.23900e56	+	2.99120e56i	0.210242	+	0.507569i
$438$			1.40803e57i			2.27468i
$439$	−4.01655e56	+	1.66371e56i	−0.617826	+	0.255912i	−0.669571	−	0.742748i	$-0.733522\pi$
$439$	−4.01655e56	+	1.66371e56i	−0.617826	+	0.255912i	0.0517444	+	0.998660i	$0.483522\pi$
$440$	4.70021e56	+	4.70021e56i	0.688470	+	0.688470i
$441$	−1.42011e57			−1.98104
$442$	−1.61055e57	+	9.30397e56i	−2.13991	+	1.23620i
$443$	1.34872e57			1.70703			0.853513	−	0.521071i	$-0.174467\pi$
$443$	1.34872e57			1.70703			0.853513	+	0.521071i	$0.174467\pi$
$444$	−1.46624e57	−	1.46624e57i	−1.76795	−	1.76795i
$445$	−1.97121e57	+	8.16501e56i	−2.26460	+	0.938029i
$446$		−	1.63170e57i		−	1.78624i
$447$	−5.11867e56	−	1.23576e57i	−0.534005	−	1.28920i
$448$	2.06244e57	+	8.54290e56i	2.05071	+	0.849431i
$449$	−3.22085e56	+	7.77582e56i	−0.305263	+	0.736970i	0.694583	+	0.719413i	$0.255589\pi$
$449$	−3.22085e56	+	7.77582e56i	−0.305263	+	0.736970i	−0.999846	+	0.0175571i	$0.994411\pi$
$450$	1.27978e57	−	1.27978e57i	1.15629	−	1.15629i
$451$	5.84330e56	−	5.84330e56i	0.503341	−	0.503341i
$452$	1.70732e56	−	4.12184e56i	0.140230	−	0.338544i
$453$	1.98691e57	+	8.23004e56i	1.55620	+	0.644600i
$454$	4.67407e56	+	1.12842e57i	0.349136	+	0.842888i
$455$			4.46210e57i			3.17903i
$456$	−7.00178e56	+	2.90023e56i	−0.475844	+	0.197101i
$457$	1.35292e57	+	1.35292e57i	0.877148	+	0.877148i	0.993239	−	0.116091i	$-0.0370364\pi$
$457$	1.35292e57	+	1.35292e57i	0.877148	+	0.877148i	−0.116091	+	0.993239i	$0.537036\pi$
$458$	−3.01966e57			−1.86788
$459$	9.56429e56	−	1.24709e57i	0.564521	−	0.736083i
$460$	−2.28912e57			−1.28936
$461$	−4.32595e56	−	4.32595e56i	−0.232548	−	0.232548i	0.581208	−	0.813755i	$-0.302580\pi$
$461$	−4.32595e56	−	4.32595e56i	−0.232548	−	0.232548i	−0.813755	+	0.581208i	$0.802580\pi$
$462$	1.10217e58	−	4.56535e57i	5.65519	−	2.34246i
$463$		−	2.91575e57i		−	1.42810i	−0.700094	−	0.714051i	$-0.746859\pi$
$463$		−	2.91575e57i		−	1.42810i	0.700094	−	0.714051i	$-0.253141\pi$
$464$	6.07796e56	+	1.46735e57i	0.284198	+	0.686115i
$465$	−7.03643e56	−	2.91458e56i	−0.314133	−	0.130118i
$466$	2.22021e57	−	5.36005e57i	0.946447	−	2.28493i
$467$	1.29963e57	−	1.29963e57i	0.529062	−	0.529062i	−0.391231	−	0.920293i	$-0.627951\pi$
$467$	1.29963e57	−	1.29963e57i	0.529062	−	0.529062i	0.920293	+	0.391231i	$0.127951\pi$
$468$	6.06395e57	−	6.06395e57i	2.35760	−	2.35760i
$469$	1.20900e57	−	2.91880e57i	0.448964	−	1.08390i
$470$	−6.20920e57	−	2.57194e57i	−2.20258	−	0.912339i
$471$	2.23538e57	+	5.39669e57i	0.757534	+	1.82885i
$472$		−	1.34564e57i		−	0.435688i
$473$	−2.63836e57	+	1.09285e57i	−0.816244	+	0.338100i
$474$	−1.49390e57	−	1.49390e57i	−0.441660	−	0.441660i
$475$	1.73440e57			0.490045
$476$	5.71726e57	+	4.38471e57i	1.54397	+	1.18411i
$477$	−1.29630e57			−0.334628
$478$	2.43674e57	+	2.43674e57i	0.601326	+	0.601326i
$479$	−7.31955e57	+	3.03186e57i	−1.72691	+	0.715311i	−0.727336	+	0.686282i	$0.759242\pi$
$479$	−7.31955e57	+	3.03186e57i	−1.72691	+	0.715311i	−0.999579	+	0.0290294i	$0.990758\pi$
$480$			1.27713e58i			2.88103i
$481$	3.47817e57	+	8.39704e57i	0.750294	+	1.81137i
$482$	−3.12066e57	−	1.29262e57i	−0.643777	−	0.266661i
$483$	−3.58670e57	+	8.65905e57i	−0.707671	+	1.70847i
$484$	−8.77239e57	+	8.77239e57i	−1.65555	+	1.65555i
$485$	−7.33839e57	+	7.33839e57i	−1.32481	+	1.32481i
$486$	3.59070e57	−	8.66872e57i	0.620154	−	1.49718i
$487$	−3.56970e57	−	1.47862e57i	−0.589874	−	0.244334i	0.0677227	−	0.997704i	$-0.478427\pi$
$487$	−3.56970e57	−	1.47862e57i	−0.589874	−	0.244334i	−0.657596	+	0.753371i	$0.728427\pi$
$488$	−1.46582e57	−	3.53881e57i	−0.231769	−	0.559540i
$489$		−	9.77864e57i		−	1.47958i
$490$	1.57509e58	−	6.52422e57i	2.28081	−	0.944741i
$491$	3.15294e57	+	3.15294e57i	0.436983	+	0.436983i	0.890995	−	0.454013i	$-0.150008\pi$
$491$	3.15294e57	+	3.15294e57i	0.436983	+	0.436983i	−0.454013	+	0.890995i	$0.650008\pi$
$492$	−6.66149e57			−0.883734
$493$	1.23929e57	+	9.39501e57i	0.157386	+	1.19313i
$494$	1.45613e58			1.77039
$495$	2.08379e58	+	2.08379e58i	2.42573	+	2.42573i
$496$	8.34673e56	−	3.45733e56i	0.0930379	−	0.0385376i
$497$		−	1.20744e58i		−	1.28885i
$498$	1.70614e57	+	4.11899e57i	0.174415	+	0.421076i
$499$	−3.46201e57	−	1.43401e57i	−0.338974	−	0.140408i	0.206702	−	0.978404i	$-0.433727\pi$
$499$	−3.46201e57	−	1.43401e57i	−0.338974	−	0.140408i	−0.545676	+	0.837996i	$0.683727\pi$
$500$	2.16737e57	−	5.23250e57i	0.203272	−	0.490743i
$501$	2.10808e58	−	2.10808e58i	1.89398	−	1.89398i
$502$	3.99085e57	−	3.99085e57i	0.343507	−	0.343507i
$503$	−8.49341e57	+	2.05049e58i	−0.700439	+	1.69101i	0.0221719	+	0.999754i	$0.492942\pi$
$503$	−8.49341e57	+	2.05049e58i	−0.700439	+	1.69101i	−0.722611	+	0.691255i	$0.757058\pi$
$504$	−1.24060e58	−	5.13874e57i	−0.980337	−	0.406069i
$505$	−6.39836e57	−	1.54470e58i	−0.484511	−	1.16971i
$506$		−	2.68259e58i		−	1.94678i
$507$	−3.54126e58	+	1.46684e58i	−2.46313	+	1.02026i
$508$	−1.30006e57	−	1.30006e57i	−0.0866748	−	0.0866748i
$509$	3.96108e57			0.253152			0.126576	−	0.991957i	$-0.459601\pi$
$509$	3.96108e57			0.253152			0.126576	+	0.991957i	$0.459601\pi$
$510$	−1.33226e58	+	4.97711e58i	−0.816265	+	3.04943i
$511$	−2.39075e58			−1.40438
$512$	−1.41814e58	−	1.41814e58i	−0.798760	−	0.798760i
$513$	−1.13673e58	+	4.70847e57i	−0.613949	+	0.254306i
$514$		−	1.48055e58i		−	0.766858i
$515$	1.03262e58	+	2.49296e58i	0.512960	+	1.23840i
$516$	2.12683e58	+	8.80961e57i	1.01336	+	0.419748i
$517$	1.70104e58	−	4.10668e58i	0.777442	−	1.87691i
$518$	4.41119e58	−	4.41119e58i	1.93404	−	1.93404i
$519$	−4.09709e58	+	4.09709e58i	−1.72337	+	1.72337i
$520$	−8.98797e57	+	2.16989e58i	−0.362735	+	0.875721i
$521$	−4.40489e57	−	1.82457e57i	−0.170579	−	0.0706560i	0.295760	−	0.955262i	$-0.404427\pi$
$521$	−4.40489e57	−	1.82457e57i	−0.170579	−	0.0706560i	−0.466339	+	0.884606i	$0.654427\pi$
$522$	−2.96263e58	−	7.15242e58i	−1.10093	−	2.65789i
$523$		−	1.45277e58i		−	0.518096i	−0.965864	−	0.259048i	$-0.916591\pi$
$523$		−	1.45277e58i		−	0.518096i	0.965864	−	0.259048i	$-0.0834087\pi$
$524$	−1.15574e58	+	4.78721e57i	−0.395581	+	0.163855i
$525$	3.55024e58	+	3.55024e58i	1.16636	+	1.16636i
$526$	−3.68833e58			−1.16315
$527$	5.34417e57	−	7.04947e56i	0.161790	−	0.0213417i
$528$	−5.71128e58			−1.65998
$529$	−1.04360e58	−	1.04360e58i	−0.291232	−	0.291232i
$530$	1.43777e58	−	5.95542e57i	0.385263	−	0.159581i
$531$		−	5.96575e58i		−	1.53509i
$532$	−2.15858e58	−	5.21127e58i	−0.533419	−	1.28779i
$533$	2.69760e58	+	1.11738e58i	0.640240	+	0.265196i
$534$	−7.71331e58	+	1.86216e59i	−1.75834	+	4.24501i
$535$	2.97430e58	−	2.97430e58i	0.651296	−	0.651296i
$536$	1.17586e58	−	1.17586e58i	0.247350	−	0.247350i
$537$	3.42823e58	−	8.27648e58i	0.692824	−	1.67262i
$538$	−1.20711e59	−	5.00000e58i	−2.34384	−	0.970848i
$539$	4.31502e58	+	1.04174e59i	0.805053	+	1.94357i
$540$		−	8.69916e58i		−	1.55959i
$541$	6.74994e58	−	2.79592e58i	1.16294	−	0.481707i	0.284090	−	0.958798i	$-0.408309\pi$
$541$	6.74994e58	−	2.79592e58i	1.16294	−	0.481707i	0.878854	+	0.477090i	$0.158309\pi$
$542$	6.37431e58	+	6.37431e58i	1.05548	+	1.05548i
$543$	1.30527e58			0.207732
$544$	−4.52150e58	−	7.82690e58i	−0.691682	−	1.19733i
$545$	9.90979e58			1.45727
$546$	2.98063e59	+	2.98063e59i	4.21373	+	4.21373i
$547$	−4.96262e58	+	2.05559e58i	−0.674503	+	0.279388i	−0.693527	−	0.720431i	$-0.743944\pi$
$547$	−4.96262e58	+	2.05559e58i	−0.674503	+	0.279388i	0.0190239	+	0.999819i	$0.493944\pi$
$548$		−	1.40297e59i		−	1.83343i
$549$	−6.49857e58	−	1.56889e59i	−0.816605	−	1.97146i
$550$	−1.32766e59	−	5.49935e58i	−1.60431	−	0.664529i
$551$	2.83906e58	−	6.85410e58i	0.329925	−	0.796509i
$552$	−3.48837e58	+	3.48837e58i	−0.389881	+	0.389881i
$553$	2.53655e58	−	2.53655e58i	0.272679	−	0.272679i
$554$	−3.33374e58	+	8.04837e58i	−0.344725	+	0.832239i
$555$	2.32607e59	+	9.63488e58i	2.31378	+	0.958401i
$556$	4.88571e58	+	1.17951e59i	0.467541	+	1.12874i
$557$		−	3.44060e58i		−	0.316772i	−0.987377	−	0.158386i	$-0.949371\pi$
$557$		−	3.44060e58i		−	0.316772i	0.987377	−	0.158386i	$-0.0506291\pi$
$558$	−4.06851e58	+	1.68523e58i	−0.360413	+	0.149288i
$559$	−7.13500e58	−	7.13500e58i	−0.608191	−	0.608191i
$560$	−1.46622e59			−1.20270
$561$	−3.29179e59	−	8.81140e58i	−2.59854	−	0.695574i
$562$	1.75730e59			1.33510
$563$	7.44626e58	+	7.44626e58i	0.544513	+	0.544513i	0.924848	−	0.380336i	$-0.124192\pi$
$563$	7.44626e58	+	7.44626e58i	0.544513	+	0.544513i	−0.380336	+	0.924848i	$0.624192\pi$
$564$	−3.31046e59	+	1.37124e59i	−2.33017	+	0.965188i
$565$			5.41706e58i			0.367047i
$566$	−2.56344e58	−	6.18870e58i	−0.167213	−	0.403688i
$567$	1.95347e58	+	8.09154e57i	0.122679	+	0.0508154i
$568$	2.43213e58	−	5.87169e58i	0.147061	−	0.355037i
$569$	−1.11621e59	+	1.11621e59i	−0.649877	+	0.649877i	−0.952963	−	0.303086i	$-0.901983\pi$
$569$	−1.11621e59	+	1.11621e59i	−0.649877	+	0.649877i	0.303086	+	0.952963i	$0.401983\pi$
$570$	2.85220e59	−	2.85220e59i	1.59908	−	1.59908i
$571$	5.12660e58	−	1.23767e59i	0.276792	−	0.668234i	−0.722952	−	0.690899i	$-0.757215\pi$
$571$	5.12660e58	−	1.23767e59i	0.276792	−	0.668234i	0.999743	+	0.0226649i	$0.00721507\pi$
$572$	−6.29081e59	−	2.60574e59i	−3.27109	−	1.35493i
$573$	−6.56084e58	−	1.58393e59i	−0.328575	−	0.793251i
$574$		−	2.00412e59i		−	0.966757i
$575$	1.04306e59	−	4.32048e58i	0.484673	−	0.200758i
$576$	3.68357e59	+	3.68357e59i	1.64887	+	1.64887i
$577$	−2.34861e59			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$577$	−2.34861e59			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$578$	−9.45600e58	−	3.52190e59i	−0.392879	−	1.46329i
$579$	−2.71541e58			−0.108704
$580$	3.70900e59	+	3.70900e59i	1.43072	+	1.43072i
$581$	−6.99377e58	+	2.89692e58i	−0.259971	+	0.107683i
$582$			9.80391e59i			3.51201i
$583$	3.93883e58	+	9.50918e58i	0.135986	+	0.328299i
$584$	−1.16260e59	−	4.81566e58i	−0.386861	−	0.160243i
$585$	−3.98472e59	+	9.61997e59i	−1.27805	+	3.08548i
$586$	−7.65977e58	+	7.65977e58i	−0.236819	+	0.236819i
$587$	−1.12752e59	+	1.12752e59i	−0.336050	+	0.336050i	−0.854878	−	0.518829i	$-0.826368\pi$
$587$	−1.12752e59	+	1.12752e59i	−0.336050	+	0.336050i	0.518829	+	0.854878i	$0.326368\pi$
$588$	3.47841e59	−	8.39763e59i	0.999467	−	2.41293i
$589$	−3.89882e58	−	1.61494e58i	−0.108008	−	0.0447382i
$590$	2.74076e59	+	6.61677e59i	0.732069	+	1.76737i
$591$		−	2.69246e59i		−	0.693454i
$592$	−2.75922e59	+	1.14290e59i	−0.685282	+	0.283853i
$593$	1.15670e58	+	1.15670e58i	0.0277042	+	0.0277042i	0.720823	−	0.693119i	$-0.243764\pi$
$593$	1.15670e58	+	1.15670e58i	0.0277042	+	0.0277042i	−0.693119	+	0.720823i	$0.743764\pi$
$594$	1.01944e60			2.35481
$595$	−8.45080e59	−	2.26209e59i	−1.88271	−	0.503960i
$596$	5.24004e59			1.12600
$597$	−8.89326e59	−	8.89326e59i	−1.84337	−	1.84337i
$598$	8.75707e59	−	3.62730e59i	1.75099	−	0.725283i
$599$		−	3.08715e59i		−	0.595498i	−0.954644	−	0.297749i	$-0.903764\pi$
$599$		−	3.08715e59i		−	0.595498i	0.954644	−	0.297749i	$-0.0962359\pi$
$600$	1.01133e59	+	2.44158e59i	0.188210	+	0.454379i
$601$	−4.96906e58	−	2.05825e58i	−0.0892222	−	0.0369571i	0.337626	−	0.941280i	$-0.390376\pi$
$601$	−4.96906e58	−	2.05825e58i	−0.0892222	−	0.0369571i	−0.426848	+	0.904323i	$0.640376\pi$
$602$	−2.65038e59	+	6.39860e59i	−0.459181	+	1.10856i
$603$	5.21305e59	−	5.21305e59i	0.871505	−	0.871505i
$604$	−5.95751e59	+	5.95751e59i	−0.961105	+	0.961105i
$605$	5.76448e59	−	1.39167e60i	0.897469	−	2.16668i
$606$	−1.45925e60	−	6.04439e59i	−2.19264	−	0.908220i
$607$	−1.52154e59	−	3.67331e59i	−0.220661	−	0.532722i	0.774319	−	0.632795i	$-0.218092\pi$
$607$	−1.52154e59	−	3.67331e59i	−0.220661	−	0.532722i	−0.994980	+	0.100073i	$0.968092\pi$
$608$			7.07643e59i			0.990575i
$609$	1.98415e60	−	8.21862e59i	2.68104	−	1.11052i
$610$	1.44155e60	+	1.44155e60i	1.88034	+	1.88034i
$611$	1.57060e60			1.97778
$612$	8.41038e59	+	1.45587e60i	1.02249	+	1.76998i
$613$	1.21339e60			1.42430			0.712148	−	0.702029i	$-0.247722\pi$
$613$	1.21339e60			1.42430			0.712148	+	0.702029i	$0.247722\pi$
$614$	−5.78838e59	−	5.78838e59i	−0.656050	−	0.656050i
$615$	7.47264e59	−	3.09527e59i	0.817822	−	0.338753i
$616$			1.06620e60i			1.12681i
$617$	4.36124e59	+	1.05290e60i	0.445122	+	1.07462i	0.974127	+	0.226000i	$0.0725650\pi$
$617$	4.36124e59	+	1.05290e60i	0.445122	+	1.07462i	−0.529006	+	0.848618i	$0.677435\pi$
$618$	2.35504e60	+	9.75490e59i	2.32138	+	0.961547i
$619$	1.18906e59	−	2.87063e59i	0.113202	−	0.273293i	−0.857117	−	0.515121i	$-0.827747\pi$
$619$	1.18906e59	−	2.87063e59i	0.113202	−	0.273293i	0.970319	+	0.241828i	$0.0777470\pi$
$620$	2.10979e59	−	2.10979e59i	0.194007	−	0.194007i
$621$	−5.66329e59	+	5.66329e59i	−0.503037	+	0.503037i
$622$	4.55271e59	−	1.09912e60i	0.390640	−	0.943089i
$623$	−3.16182e60	−	1.30967e60i	−2.62086	−	1.08560i
$624$	−7.72258e59	−	1.86440e60i	−0.618435	−	1.49303i
$625$			1.57180e60i			1.21612i
$626$	−2.09458e60	+	8.67604e59i	−1.56585	+	0.648595i
$627$	1.88641e60	+	1.88641e60i	1.36265	+	1.36265i
$628$	−2.28839e60			−1.59734
$629$	−1.76665e60	+	2.33038e59i	−1.19168	+	0.157195i
$630$	7.14692e60			4.65905
$631$	1.41634e60	+	1.41634e60i	0.892353	+	0.892353i	0.994744	−	0.102392i	$-0.0326495\pi$
$631$	1.41634e60	+	1.41634e60i	0.892353	+	0.892353i	−0.102392	+	0.994744i	$0.532649\pi$
$632$	1.74444e59	−	7.22570e58i	0.106228	−	0.0440010i
$633$		−	1.87372e60i		−	1.10287i
$634$	−1.16538e60	−	2.81346e60i	−0.663051	−	1.60075i
$635$	2.06244e59	+	8.54289e58i	0.113435	+	0.0469861i
$636$	3.17516e59	−	7.66550e59i	0.168825	−	0.407580i
$637$	−2.81720e60	+	2.81720e60i	−1.44817	+	1.44817i
$638$	−4.34654e60	+	4.34654e60i	−2.16022	+	2.16022i
$639$	1.07826e60	−	2.60315e60i	0.518149	−	1.25092i
$640$	−2.20996e60	−	9.15396e59i	−1.02687	−	0.425343i
$641$	−2.81924e59	−	6.80626e59i	−0.126673	−	0.305816i	0.847801	−	0.530314i	$-0.177926\pi$
$641$	−2.81924e59	−	6.80626e59i	−0.126673	−	0.305816i	−0.974475	+	0.224498i	$0.927926\pi$
$642$		−	3.97360e60i		−	1.72656i
$643$	−7.62604e59	+	3.15881e59i	−0.320452	+	0.132736i	−0.537110	−	0.843512i	$-0.680484\pi$
$643$	−7.62604e59	+	3.15881e59i	−0.320452	+	0.132736i	0.216659	+	0.976247i	$0.430484\pi$
$644$	−2.59632e60	−	2.59632e60i	−1.05514	−	1.05514i
$645$	−2.79515e60			−1.09868
$646$	−7.38194e59	+	2.75777e60i	−0.280654	+	1.04848i
$647$	−2.47025e60			−0.908445			−0.454222	−	0.890888i	$-0.650083\pi$
$647$	−2.47025e60			−0.908445			−0.454222	+	0.890888i	$0.650083\pi$
$648$	7.86972e58	+	7.86972e58i	0.0279960	+	0.0279960i
$649$	−4.37623e60	+	1.81270e60i	−1.50605	+	0.623827i
$650$		−	5.07763e60i		−	1.69053i
$651$	−4.67500e59	−	1.12864e60i	−0.150588	−	0.363551i
$652$	3.53925e60	+	1.46601e60i	1.10303	+	0.456891i
$653$	−2.19127e60	+	5.29019e60i	−0.660788	+	1.59528i	0.135783	+	0.990739i	$0.456645\pi$
$653$	−2.19127e60	+	5.29019e60i	−0.660788	+	1.59528i	−0.796571	+	0.604545i	$0.793355\pi$
$654$	6.61963e60	−	6.61963e60i	1.93158	−	1.93158i
$655$	1.07403e60	−	1.07403e60i	0.303269	−	0.303269i
$656$	−3.67166e59	+	8.86416e59i	−0.100330	+	0.242217i
$657$	−5.15427e60	−	2.13497e60i	−1.36305	−	0.564594i
$658$	−4.12539e60	−	9.95956e60i	−1.05586	−	2.54908i
$659$			1.69771e60i			0.420558i	0.977641	+	0.210279i	$0.0674373\pi$
$659$			1.69771e60i			0.420558i	−0.977641	+	0.210279i	$0.932563\pi$
$660$	−1.74262e61	+	7.21817e60i	−4.17838	+	1.73074i
$661$	7.84805e59	+	7.84805e59i	0.182150	+	0.182150i	0.792292	−	0.610142i	$-0.208888\pi$
$661$	7.84805e59	+	7.84805e59i	0.182150	+	0.182150i	−0.610142	+	0.792292i	$0.708888\pi$
$662$	7.32151e60			1.64495
$663$	−1.57463e60	−	1.19372e61i	−0.342482	−	2.59634i
$664$	−3.98454e59			−0.0839006
$665$	4.84285e60	+	4.84285e60i	0.987269	+	0.987269i
$666$	1.34495e61	−	5.57095e60i	2.65466	−	1.09960i
$667$		−	4.82924e60i		−	0.922940i
$668$	4.46951e60	+	1.07903e61i	0.827115	+	1.99683i
$669$	9.75877e60	+	4.04221e60i	1.74877	+	0.724365i
$670$	−3.38698e60	+	8.17689e60i	−0.587766	+	1.41899i
$671$	−9.53418e60	+	9.53418e60i	−1.60232	+	1.60232i
$672$	−1.44852e61	+	1.44852e61i	−2.35768	+	2.35768i
$673$	−2.38554e59	+	5.75920e59i	−0.0376065	+	0.0907900i	−0.941567	−	0.336826i	$-0.890647\pi$
$673$	−2.38554e59	+	5.75920e59i	−0.0376065	+	0.0907900i	0.903960	+	0.427616i	$0.140647\pi$
$674$	9.56667e58	+	3.96264e58i	0.0146074	+	0.00605058i
$675$	1.64188e60	+	3.96385e60i	0.242835	+	0.586254i
$676$		−	1.50162e61i		−	2.15133i
$677$	8.95449e60	−	3.70907e60i	1.24275	−	0.514765i	0.338179	−	0.941082i	$-0.390189\pi$
$677$	8.95449e60	−	3.70907e60i	1.24275	−	0.514765i	0.904574	+	0.426317i	$0.140189\pi$
$678$	3.61853e60	+	3.61853e60i	0.486513	+	0.486513i
$679$	−1.66464e61			−2.16830
$680$	−3.65391e60	−	2.80228e60i	−0.461122	−	0.353646i
$681$	−7.90670e60			−0.966791
$682$	2.47244e60	+	2.47244e60i	0.292929	+	0.292929i
$683$	4.10635e60	−	1.70090e60i	0.471423	−	0.195270i	−0.134308	−	0.990940i	$-0.542881\pi$
$683$	4.10635e60	−	1.70090e60i	0.471423	−	0.195270i	0.605730	+	0.795670i	$0.292881\pi$
$684$		−	1.31628e61i		−	1.46434i
$685$	6.51890e60	+	1.57380e61i	0.702793	+	1.69669i
$686$	5.14296e60	+	2.13028e60i	0.537335	+	0.222571i
$687$	7.48062e60	−	1.80598e61i	0.757474	−	1.82870i
$688$	2.34452e60	−	2.34452e60i	0.230092	−	0.230092i
$689$	−2.57159e60	+	2.57159e60i	−0.244618	+	0.244618i
$690$	1.00480e61	−	2.42580e61i	0.926453	−	2.23666i
$691$	−5.04626e60	−	2.09023e60i	−0.451016	−	0.186817i	0.145600	−	0.989343i	$-0.453489\pi$
$691$	−5.04626e60	−	2.09023e60i	−0.451016	−	0.186817i	−0.596616	+	0.802527i	$0.703489\pi$
$692$	−8.68656e60	−	2.09712e61i	−0.752604	−	1.81695i
$693$			4.72687e61i			3.97017i
$694$	−1.67631e60	+	6.94349e59i	−0.136497	+	0.0565391i
$695$	−1.09613e61	−	1.09613e61i	−0.865341	−	0.865341i
$696$	1.13042e61			0.865252
$697$	−3.48379e60	+	4.54254e60i	−0.258551	+	0.337127i
$698$	−2.52777e61			−1.81906
$699$	2.65570e61	+	2.65570e61i	1.85319	+	1.85319i
$700$	−1.81721e61	+	7.52714e60i	−1.22970	+	0.509357i
$701$		−	2.75441e61i		−	1.80755i	−0.428007	−	0.903775i	$-0.640784\pi$
$701$		−	2.75441e61i		−	1.80755i	0.428007	−	0.903775i	$-0.359216\pi$
$702$	1.37846e61	+	3.32788e61i	0.877293	+	2.11797i
$703$	1.28885e61	+	5.33859e60i	0.795542	+	0.329524i
$704$	1.58287e61	−	3.82138e61i	0.947616	−	2.28775i
$705$	3.07642e61	−	3.07642e61i	1.78640	−	1.78640i
$706$	7.78562e60	−	7.78562e60i	0.438523	−	0.438523i
$707$	1.02630e61	−	2.47770e61i	0.560733	−	1.35373i
$708$	3.52775e61	+	1.46124e61i	1.86975	+	0.774475i
$709$	−9.53527e60	−	2.30202e61i	−0.490274	−	1.18363i	−0.954581	−	0.297952i	$-0.903696\pi$
$709$	−9.53527e60	−	2.30202e61i	−0.490274	−	1.18363i	0.464307	−	0.885674i	$-0.346304\pi$
$710$			3.38259e61i			1.68731i
$711$	7.73378e60	−	3.20344e60i	0.374279	−	0.155031i
$712$	−1.27376e61	−	1.27376e61i	−0.598093	−	0.598093i
$713$	−2.74702e60			−0.125152
$714$	−7.15609e61	+	4.13398e61i	−3.16347	+	1.82750i
$715$	8.26759e61			3.54649
$716$	2.48161e61	+	2.48161e61i	1.03301	+	1.03301i
$717$	−2.06101e61	+	8.53699e60i	−0.832565	+	0.344860i
$718$			6.76705e60i			0.265292i
$719$	−5.86471e60	−	1.41587e61i	−0.223139	−	0.538705i	0.772174	−	0.635411i	$-0.219169\pi$
$719$	−5.86471e60	−	1.41587e61i	−0.223139	−	0.538705i	−0.995313	+	0.0967059i	$0.969169\pi$
$720$	−3.16106e61	−	1.30936e61i	−1.16731	−	0.483514i
$721$	−1.65632e61	+	3.99870e61i	−0.593657	+	1.43321i
$722$	−1.49911e61	+	1.49911e61i	−0.521536	+	0.521536i
$723$	1.54617e61	−	1.54617e61i	0.522135	−	0.522135i
$724$	−1.95685e60	+	4.72424e60i	−0.0641471	+	0.154865i
$725$	−2.39008e61	−	9.90003e60i	−0.760580	−	0.315043i
$726$	−5.44558e61	−	1.31468e62i	−1.68231	−	4.06146i
$727$		−	2.48984e61i		−	0.746760i	−0.927678	−	0.373380i	$-0.878199\pi$
$727$		−	2.48984e61i		−	0.746760i	0.927678	−	0.373380i	$-0.121801\pi$
$728$	−3.48050e61	+	1.44167e61i	−1.01349	+	0.419799i
$729$	4.07388e61	+	4.07388e61i	1.15177	+	1.15177i
$730$	6.69758e61			1.83855
$731$	1.71301e61	−	9.89586e60i	0.456601	−	0.263773i
$732$	1.08692e62			2.81325
$733$	−1.15813e61	−	1.15813e61i	−0.291086	−	0.291086i	0.546423	−	0.837509i	$-0.315989\pi$
$733$	−1.15813e61	−	1.15813e61i	−0.291086	−	0.291086i	−0.837509	+	0.546423i	$0.815989\pi$
$734$	−1.52430e61	+	6.31388e60i	−0.372054	+	0.154110i
$735$			1.10364e62i			2.61608i
$736$	1.76278e61	+	4.25572e61i	0.405812	+	0.979717i
$737$	−5.40808e61	−	2.24010e61i	−1.20918	−	0.500860i
$738$	1.78971e61	−	4.32073e61i	0.388660	−	0.938308i
$739$	−6.38991e61	+	6.38991e61i	−1.34784	+	1.34784i	−0.459842	+	0.888001i	$0.652094\pi$
$739$	−6.38991e61	+	6.38991e61i	−1.34784	+	1.34784i	−0.888001	+	0.459842i	$0.847906\pi$
$740$	−6.97444e61	+	6.97444e61i	−1.42898	+	1.42898i
$741$	−3.60727e61	+	8.70873e61i	−0.717939	+	1.73326i
$742$	2.30618e61	+	9.55250e60i	0.445871	+	0.184686i
$743$	−2.96812e61	−	7.16568e61i	−0.557471	−	1.34585i	−0.911762	−	0.410719i	$-0.865278\pi$
$743$	−2.96812e61	−	7.16568e61i	−0.557471	−	1.34585i	0.354291	−	0.935135i	$-0.384722\pi$
$744$		−	6.43019e60i		−	0.117329i
$745$	−5.87811e61	+	2.43479e61i	−1.04202	+	0.431620i
$746$	1.02745e62	+	1.02745e62i	1.76960	+	1.76960i
$747$	−1.76651e61			−0.295612
$748$	8.12419e61	−	1.05932e62i	1.32098	−	1.72243i
$749$	6.74690e61			1.06597
$750$	4.59357e61	+	4.59357e61i	0.705234	+	0.705234i
$751$	−5.09667e61	+	2.11111e61i	−0.760376	+	0.314958i	−0.728967	−	0.684549i	$-0.759999\pi$
$751$	−5.09667e61	+	2.11111e61i	−0.760376	+	0.314958i	−0.0314086	+	0.999507i	$0.509999\pi$
$752$			5.16088e61i			0.748239i
$753$	1.39817e61	+	3.37548e61i	0.197001	+	0.475602i
$754$	−2.00661e62	−	8.31165e61i	−2.74776	−	1.13816i
$755$	3.91478e61	−	9.45111e61i	0.521012	−	1.25783i
$756$	9.86659e61	−	9.86659e61i	1.27629	−	1.27629i
$757$	−2.86052e61	+	2.86052e61i	−0.359652	+	0.359652i	−0.863685	−	0.504032i	$-0.831849\pi$
$757$	−2.86052e61	+	2.86052e61i	−0.359652	+	0.359652i	0.504032	+	0.863685i	$0.331849\pi$
$758$	−1.77967e61	+	4.29651e61i	−0.217497	+	0.525083i
$759$	1.60439e62	+	6.64559e61i	1.90595	+	0.789470i
$760$	1.37955e61	+	3.33053e61i	0.159311	+	0.384611i
$761$			1.61576e62i			1.81388i	0.421263	+	0.906939i	$0.361587\pi$
$761$			1.61576e62i			1.81388i	−0.421263	+	0.906939i	$0.638413\pi$
$762$	1.94834e61	−	8.07028e60i	0.212634	−	0.0880758i
$763$	1.12397e62	+	1.12397e62i	1.19255	+	1.19255i
$764$	6.71641e61			0.692836
$765$	−1.61992e62	−	1.24236e62i	−1.62470	−	1.24602i
$766$	8.88811e61			0.866744
$767$	−1.18348e62	−	1.18348e62i	−1.12217	−	1.12217i
$768$	2.90021e61	−	1.20131e61i	0.267401	−	0.110761i
$769$			2.71929e61i			0.243803i	0.992542	+	0.121902i	$0.0388992\pi$
$769$			2.71929e61i			0.243803i	−0.992542	+	0.121902i	$0.961101\pi$
$770$	−2.17160e62	−	5.24270e62i	−1.89334	−	4.57092i
$771$	8.85477e61	+	3.66777e61i	0.750772	+	0.310980i
$772$	4.07092e60	−	9.82807e60i	0.0335676	−	0.0810394i
$773$	1.33721e61	−	1.33721e61i	0.107236	−	0.107236i	−0.651453	−	0.758689i	$-0.725840\pi$
$773$	1.33721e61	−	1.33721e61i	0.107236	−	0.107236i	0.758689	+	0.651453i	$0.225840\pi$
$774$	−1.14281e62	+	1.14281e62i	−0.891338	+	0.891338i
$775$	−5.63143e60	+	1.35955e61i	−0.0427201	+	0.103135i
$776$	−8.09502e61	−	3.35307e61i	−0.597298	−	0.247409i
$777$	1.54544e62	+	3.73101e62i	1.10917	+	2.67778i
$778$		−	2.32142e62i		−	1.62066i
$779$	4.14052e61	−	1.71506e61i	0.281189	−	0.116473i
$780$	−4.71261e62	−	4.71261e62i	−3.11335	−	3.11335i
$781$	−2.23720e62			−1.43783
$782$	2.43029e61	+	1.84239e62i	0.151955	+	1.15196i
$783$	1.83522e62			1.11638
$784$	−9.25715e61	−	9.25715e61i	−0.547876	−	0.547876i
$785$	2.56704e62	−	1.06330e62i	1.47821	−	0.612293i
$786$		−	1.43488e62i		−	0.803951i
$787$	1.11004e61	+	2.67988e61i	0.0605177	+	0.146103i	0.951246	−	0.308434i	$-0.0998049\pi$
$787$	1.11004e61	+	2.67988e61i	0.0605177	+	0.146103i	−0.890728	+	0.454537i	$0.849805\pi$
$788$	9.74499e61	+	4.03651e61i	0.516973	+	0.214137i
$789$	9.13713e61	−	2.20590e62i	0.471687	−	1.13875i
$790$	−7.10603e61	+	7.10603e61i	−0.356981	+	0.356981i
$791$	−6.14403e61	+	6.14403e61i	−0.300372	+	0.300372i
$792$	−9.52129e61	+	2.29864e62i	−0.453006	+	1.09365i
$793$	−4.40153e62	−	1.82317e62i	−2.03812	−	0.844217i
$794$	−6.26967e61	−	1.51363e62i	−0.282556	−	0.682150i
$795$			1.00743e62i			0.441895i
$796$	4.55207e62	−	1.88553e62i	1.94347	−	0.805012i
$797$	−1.40686e62	−	1.40686e62i	−0.584651	−	0.584651i	0.351527	−	0.936178i	$-0.385663\pi$
$797$	−1.40686e62	−	1.40686e62i	−0.584651	−	0.584651i	−0.936178	+	0.351527i	$0.885663\pi$
$798$	6.46994e62			2.61721
$799$	−7.96224e61	+	2.97456e62i	−0.313530	+	1.17130i
$800$	2.46761e62			0.945891
$801$	−5.64710e62	−	5.64710e62i	−2.10730	−	2.10730i
$802$	−1.09072e62	+	4.51789e61i	−0.396244	+	0.164130i
$803$			4.42968e62i			1.56671i
$804$	1.80578e62	+	4.35954e62i	0.621813	+	1.50119i
$805$	4.11884e62	+	1.70608e62i	1.38090	+	0.571990i
$806$	−4.72792e61	+	1.14142e62i	−0.154336	+	0.372599i
$807$	5.98075e62	−	5.98075e62i	1.90097	−	1.90097i
$808$	9.98162e61	−	9.98162e61i	0.308928	−	0.308928i
$809$	−1.51850e62	+	3.66599e62i	−0.457638	+	1.10484i	0.511713	+	0.859156i	$0.329011\pi$
$809$	−1.51850e62	+	3.66599e62i	−0.457638	+	1.10484i	−0.969351	+	0.245679i	$0.920989\pi$
$810$	−5.47257e61	−	2.26681e61i	−0.160607	−	0.0665255i
$811$	6.78533e61	+	1.63812e62i	0.193920	+	0.468164i	0.990693	−	0.136114i	$-0.0434615\pi$
$811$	6.78533e61	+	1.63812e62i	0.193920	+	0.468164i	−0.796773	+	0.604278i	$0.793461\pi$
$812$			8.41350e62i			2.34165i
$813$	−5.39142e62	+	2.23320e62i	−1.46136	+	0.605315i
$814$	−8.17326e62	−	8.17326e62i	−2.15760	−	2.15760i
$815$	−4.65140e62			−1.19590
$816$	3.92249e62	−	5.17414e61i	0.982253	−	0.129569i
$817$	−1.54876e62			−0.377756
$818$	3.09120e62	+	3.09120e62i	0.734397	+	0.734397i
$819$	−1.54304e63	+	6.39150e62i	−3.57087	+	1.47910i
$820$			3.16866e62i			0.714296i
$821$	6.87874e61	+	1.66068e62i	0.151054	+	0.364676i	0.981234	−	0.192819i	$-0.0617629\pi$
$821$	6.87874e61	+	1.66068e62i	0.151054	+	0.364676i	−0.830181	+	0.557494i	$0.811763\pi$
$822$	1.48674e63	+	6.15827e62i	3.18046	+	1.31739i
$823$	3.37121e61	−	8.13883e61i	0.0702570	−	0.169615i	−0.884850	−	0.465875i	$-0.845739\pi$
$823$	3.37121e61	−	8.13883e61i	0.0702570	−	0.169615i	0.955107	+	0.296260i	$0.0957395\pi$
$824$	−1.61091e62	+	1.61091e62i	−0.327067	+	0.327067i
$825$	6.57804e62	−	6.57804e62i	1.30118	−	1.30118i
$826$	−4.39617e62	+	1.06133e63i	−0.847235	+	2.04541i
$827$	−3.04450e62	−	1.26107e62i	−0.571673	−	0.236795i	0.0780708	−	0.996948i	$-0.475124\pi$
$827$	−3.04450e62	−	1.26107e62i	−0.571673	−	0.236795i	−0.649744	+	0.760153i	$0.725124\pi$
$828$	−3.27892e62	−	7.91601e62i	−0.599900	−	1.44829i
$829$		−	8.35207e62i		−	1.48892i	−0.667667	−	0.744460i	$-0.732707\pi$
$829$		−	8.35207e62i		−	1.48892i	0.667667	−	0.744460i	$-0.267293\pi$
$830$	1.95928e62	−	8.11560e61i	0.340343	−	0.140975i
$831$	−3.98766e62	−	3.98766e62i	−0.674987	−	0.674987i
$832$	1.46148e63			2.41070
$833$	−3.90731e62	−	6.76371e62i	−0.628073	−	1.08722i
$834$	−1.46440e63			−2.29398
$835$	−1.00275e63	−	1.00275e63i	−1.53085	−	1.53085i
$836$	−9.65568e62	+	3.99952e62i	−1.43664	+	0.595076i
$837$		−	1.04393e62i		−	0.151382i
$838$	−6.74609e62	−	1.62865e63i	−0.953467	−	2.30187i
$839$	−3.99882e62	−	1.65636e62i	−0.550870	−	0.228178i	0.0898461	−	0.995956i	$-0.471362\pi$
$839$	−3.99882e62	−	1.65636e62i	−0.550870	−	0.228178i	−0.640716	+	0.767778i	$0.721362\pi$
$840$	−3.99358e62	+	9.64135e62i	−0.536238	+	1.29459i
$841$	−2.42215e62	+	2.42215e62i	−0.317021	+	0.317021i
$842$	−5.82652e62	+	5.82652e62i	−0.743361	+	0.743361i
$843$	−4.35337e62	+	1.05100e63i	−0.541418	+	1.30710i
$844$	6.78170e62	+	2.80907e62i	0.822197	+	0.340565i
$845$	6.97730e62	+	1.68447e63i	0.824648	+	1.99088i
$846$		−	2.51561e63i		−	2.89855i
$847$	2.23224e63	−	9.24623e62i	2.50753	−	1.03865i
$848$	−8.45010e61	−	8.45010e61i	−0.0925445	−	0.0925445i
$849$	4.33635e62			0.463029
$850$	9.61655e62	+	2.57414e62i	1.00118	+	0.267994i
$851$	9.08094e62			0.921818
$852$	1.27523e63	+	1.27523e63i	1.26222	+	1.26222i
$853$	3.38165e61	−	1.40073e61i	0.0326381	−	0.0135191i	−0.366305	−	0.930495i	$-0.619377\pi$
$853$	3.38165e61	−	1.40073e61i	0.0326381	−	0.0135191i	0.398943	+	0.916976i	$0.369377\pi$
$854$			3.27000e63i			3.07754i
$855$	6.11610e62	+	1.47656e63i	0.561310	+	1.35512i
$856$	3.28097e62	+	1.35902e62i	0.293641	+	0.121630i
$857$	−4.01945e61	+	9.70381e61i	−0.0350816	+	0.0846944i	−0.940449	−	0.339934i	$-0.889595\pi$
$857$	−4.01945e61	+	9.70381e61i	−0.0350816	+	0.0846944i	0.905368	+	0.424628i	$0.139595\pi$
$858$	5.52265e63	−	5.52265e63i	4.70079	−	4.70079i
$859$	−6.91665e62	+	6.91665e62i	−0.574173	+	0.574173i	−0.933292	−	0.359119i	$-0.883077\pi$
$859$	−6.91665e62	+	6.91665e62i	−0.574173	+	0.574173i	0.359119	+	0.933292i	$0.383077\pi$
$860$	4.19046e62	−	1.01167e63i	0.339270	−	0.819070i
$861$	1.19861e63	+	4.96481e62i	0.946478	+	0.392044i
$862$	−1.22667e63	−	2.96145e63i	−0.944763	−	2.28086i
$863$			5.30870e62i			0.398801i	0.979918	+	0.199400i	$0.0638994\pi$
$863$			5.30870e62i			0.398801i	−0.979918	+	0.199400i	$0.936101\pi$
$864$	−1.61727e63	+	6.69896e62i	−1.18505	+	0.490865i
$865$	1.94886e63	+	1.94886e63i	1.39295	+	1.39295i
$866$	−1.67268e63			−1.16622
$867$	2.34061e63	+	3.06944e62i	1.59191	+	0.208761i
$868$	4.78585e62			0.317530
$869$	−4.69983e62	−	4.69983e62i	−0.304198	−	0.304198i
$870$	−5.55852e63	+	2.30241e63i	−3.50990	+	1.45385i
$871$		−	2.06832e63i		−	1.27417i
$872$	3.20178e62	+	7.72977e62i	0.192436	+	0.464582i
$873$	−3.58884e63	−	1.48655e63i	−2.10449	−	0.871710i
$874$	5.56749e62	−	1.34411e63i	0.318540	−	0.769023i
$875$	−7.79957e62	+	7.79957e62i	−0.435409	+	0.435409i
$876$	2.52497e63	−	2.52497e63i	1.37536	−	1.37536i
$877$	−1.19678e63	+	2.88927e63i	−0.636094	+	1.53567i	0.195747	+	0.980654i	$0.437287\pi$
$877$	−1.19678e63	+	2.88927e63i	−0.636094	+	1.53567i	−0.831841	+	0.555013i	$0.812713\pi$
$878$	1.80486e63	+	7.47596e62i	0.936075	+	0.387735i
$879$	−2.68356e62	−	6.47868e62i	−0.135816	−	0.327888i
$880$			2.71668e63i			1.34172i
$881$	1.53803e63	−	6.37072e62i	0.741280	−	0.307048i	0.0201016	−	0.999798i	$-0.493601\pi$
$881$	1.53803e63	−	6.37072e62i	0.741280	−	0.307048i	0.721178	+	0.692750i	$0.243601\pi$
$882$	4.51229e63	+	4.51229e63i	2.12238	+	2.12238i
$883$	3.25206e63			1.49280			0.746402	−	0.665495i	$-0.231780\pi$
$883$	3.25206e63			1.49280			0.746402	+	0.665495i	$0.231780\pi$
$884$	4.55658e63	+	1.21970e63i	2.04134	+	0.546422i
$885$	−4.63629e63			−2.02717
$886$	−4.28543e63	−	4.28543e63i	−1.82881	−	1.82881i
$887$	2.03832e63	−	8.44298e62i	0.849012	−	0.351672i	0.0846116	−	0.996414i	$-0.473035\pi$
$887$	2.03832e63	−	8.44298e62i	0.849012	−	0.351672i	0.764401	+	0.644742i	$0.223035\pi$
$888$			2.12566e63i			0.864201i
$889$	1.37028e62	+	3.30815e62i	0.0543778	+	0.131280i
$890$	8.85771e63	+	3.66898e63i	3.43112	+	1.42122i
$891$	1.49924e62	−	3.61948e62i	0.0566892	−	0.136860i
$892$	−2.92605e63	+	2.92605e63i	−1.08003	+	1.08003i
$893$	1.70461e63	−	1.70461e63i	0.614214	−	0.614214i
$894$	−2.30010e63	+	5.55292e63i	−0.809076	+	1.95328i
$895$	−3.93687e63	−	1.63070e63i	−1.35193	−	0.559989i
$896$	−1.46830e63	−	3.54478e63i	−0.492256	−	1.18841i
$897$			6.13597e63i			2.00838i
$898$	3.49410e63	−	1.44730e63i	1.11659	−	0.462507i
$899$	4.45093e62	+	4.45093e62i	0.138873	+	0.138873i
$900$	−4.58996e63			−1.39828
$901$	−3.56666e62	−	6.17403e62i	−0.106091	−	0.183648i
$902$	−3.71332e63			−1.07850
$903$	−3.17026e63	−	3.17026e63i	−0.899099	−	0.899099i
$904$	−4.22538e62	+	1.75021e62i	−0.117016	+	0.0484696i
$905$		−	6.20875e62i		−	0.167904i
$906$	−3.69820e63	−	8.92826e63i	−0.976640	−	2.35782i
$907$	3.77306e63	+	1.56285e63i	0.973054	+	0.403052i	0.811848	−	0.583869i	$-0.198462\pi$
$907$	3.77306e63	+	1.56285e63i	0.973054	+	0.403052i	0.161206	+	0.986921i	$0.448462\pi$
$908$	1.18537e63	−	2.86173e63i	0.298543	−	0.720747i
$909$	4.42524e63	−	4.42524e63i	1.08846	−	1.08846i
$910$	1.41780e64	−	1.41780e64i	3.40584	−	3.40584i
$911$	−2.87714e63	+	6.94602e63i	−0.675018	+	1.62964i	0.0979499	+	0.995191i	$0.468772\pi$
$911$	−2.87714e63	+	6.94602e63i	−0.675018	+	1.62964i	−0.772968	+	0.634446i	$0.781228\pi$
$912$	−2.86164e63	−	1.18533e63i	−0.655731	−	0.271613i
$913$	5.36754e62	+	1.29584e63i	0.120131	+	0.290021i
$914$		−	8.59756e63i		−	1.87945i
$915$	−1.21927e64	+	5.05037e63i	−2.60343	+	1.07838i
$916$	5.41502e63	+	5.41502e63i	1.12940	+	1.12940i
$917$	2.43632e63			0.496357
$918$	−7.00151e63	+	9.23567e62i	−1.39339	+	0.183802i
$919$	−1.98404e63			−0.385715			−0.192857	−	0.981227i	$-0.561775\pi$
$919$	−1.98404e63			−0.385715			−0.192857	+	0.981227i	$0.561775\pi$
$920$	1.65931e63	+	1.65931e63i	0.315129	+	0.315129i
$921$	4.89584e63	−	2.02792e63i	0.908333	−	0.376244i
$922$			2.74907e63i			0.498277i
$923$	−3.02506e63	−	7.30313e63i	−0.535669	−	1.29322i
$924$	−2.79516e64	−	1.15779e64i	−4.83570	−	2.00301i
$925$	1.86161e63	−	4.49432e63i	0.314660	−	0.759656i
$926$	−9.26455e63	+	9.26455e63i	−1.52999	+	1.52999i
$927$	−7.14180e63	+	7.14180e63i	−1.15237	+	1.15237i
$928$	4.03926e63	−	9.75164e63i	0.636826	−	1.53743i
$929$	−2.03646e63	−	8.43528e62i	−0.313717	−	0.129946i	0.220269	−	0.975439i	$-0.429306\pi$
$929$	−2.03646e63	−	8.43528e62i	−0.313717	−	0.129946i	−0.533986	+	0.845493i	$0.679306\pi$
$930$	1.30968e63	+	3.16185e63i	0.197143	+	0.475946i
$931$			6.11518e63i			0.899479i
$932$	−1.35934e64	+	5.63055e63i	−1.95382	+	0.809299i
$933$	5.44572e63	+	5.44572e63i	0.764892	+	0.764892i
$934$	−8.25892e63			−1.13361
$935$	−4.19131e63	+	1.56580e64i	−0.562212	+	2.10033i
$936$	−8.79114e63			−1.15243
$937$	3.97804e63	+	3.97804e63i	0.509646	+	0.509646i	0.914418	−	0.404772i	$-0.132649\pi$
$937$	3.97804e63	+	3.97804e63i	0.509646	+	0.509646i	−0.404772	+	0.914418i	$0.632649\pi$
$938$	−1.31157e64	+	5.43272e63i	−1.64222	+	0.680230i
$939$		−	1.46765e64i		−	1.79602i
$940$	6.52255e63	+	1.57468e64i	0.780133	+	1.88341i
$941$	−6.49102e63	−	2.68867e63i	−0.758815	−	0.314311i	−0.0304824	−	0.999535i	$-0.509704\pi$
$941$	−6.49102e63	−	2.68867e63i	−0.758815	−	0.314311i	−0.728333	+	0.685224i	$0.759704\pi$
$942$	1.00448e64	−	2.42503e64i	1.14775	−	2.77091i
$943$	2.06285e63	−	2.06285e63i	0.230392	−	0.230392i
$944$	3.88883e63	−	3.88883e63i	0.424543	−	0.424543i
$945$	−6.48349e63	+	1.56525e64i	−0.691871	+	1.67032i
$946$	1.18556e64	+	4.91075e63i	1.23670	+	0.512258i
$947$	6.77451e62	+	1.63551e63i	0.0690802	+	0.166774i	0.954649	−	0.297734i	$-0.0962310\pi$
$947$	6.77451e62	+	1.63551e63i	0.0690802	+	0.166774i	−0.885569	+	0.464509i	$0.846231\pi$
$948$			5.35790e63i			0.534091i
$949$	−1.44603e64	+	5.98965e63i	−1.40914	+	0.583684i
$950$	−5.51090e63	−	5.51090e63i	−0.525007	−	0.525007i
$951$	1.97136e64			1.83605
$952$	−9.65922e62	−	7.32260e63i	−0.0879524	−	0.666762i
$953$	1.90242e64			1.69359			0.846797	−	0.531917i	$-0.178528\pi$
$953$	1.90242e64			1.69359			0.846797	+	0.531917i	$0.178528\pi$
$954$	4.11890e63	+	4.11890e63i	0.358502	+	0.358502i
$955$	−7.53425e63	+	3.12079e63i	−0.641162	+	0.265578i
$956$		−	8.73942e63i		−	0.727173i
$957$	−1.52278e64	−	3.67632e64i	−1.23889	−	2.99093i
$958$	3.28907e64	+	1.36238e64i	2.61646	+	1.08378i
$959$	−1.04563e64	+	2.52438e64i	−0.813353	+	1.96361i
$960$	2.86269e64	−	2.86269e64i	2.17743	−	2.17743i
$961$	−9.25369e63	+	9.25369e63i	−0.688275	+	0.688275i
$962$	1.56293e64	−	3.77325e64i	1.13678	−	2.74442i
$963$	1.45458e64	+	6.02508e63i	1.03460	+	0.428546i
$964$	3.27815e63	+	7.91415e63i	0.228020	+	0.550488i
$965$			1.29164e63i			0.0878625i
$966$	3.89098e64	−	1.61170e64i	2.58852	−	1.07220i
$967$	1.94361e63	+	1.94361e63i	0.126456	+	0.126456i	0.767502	−	0.641046i	$-0.221499\pi$
$967$	1.94361e63	+	1.94361e63i	0.126456	+	0.126456i	−0.641046	+	0.767502i	$0.721499\pi$
$968$	1.27177e64			0.809258
$969$	−1.46648e64	−	1.12468e64i	−0.912670	−	0.699950i
$970$	4.66342e64			2.83865
$971$	−3.20351e62	−	3.20351e62i	−0.0190727	−	0.0190727i	0.697506	−	0.716579i	$-0.254293\pi$
$971$	−3.20351e62	−	3.20351e62i	−0.0190727	−	0.0190727i	−0.716579	+	0.697506i	$0.754293\pi$
$972$	−2.19843e64	+	9.10619e63i	−1.28023	+	0.530288i
$973$		−	2.48645e64i		−	1.41630i
$974$	6.64423e63	+	1.60406e64i	0.370192	+	0.893723i
$975$	3.03680e64	+	1.25788e64i	1.65507	+	0.685554i
$976$	5.99083e63	−	1.44631e64i	0.319386	−	0.771066i
$977$	−1.41264e64	+	1.41264e64i	−0.736713	+	0.736713i	−0.971940	−	0.235228i	$-0.924416\pi$
$977$	−1.41264e64	+	1.41264e64i	−0.736713	+	0.736713i	0.235228	+	0.971940i	$0.424416\pi$
$978$	−3.10708e64	+	3.10708e64i	−1.58514	+	1.58514i
$979$	−2.42661e64	+	5.85836e64i	−1.21108	+	2.92380i
$980$	−3.99449e64	−	1.65457e64i	−1.95030	−	0.807840i
$981$	1.41947e64	+	3.42691e64i	0.678022	+	1.63689i
$982$		−	2.00364e64i		−	0.936318i
$983$	−2.64215e64	+	1.09441e64i	−1.20797	+	0.500358i	−0.893567	−	0.448931i	$-0.851805\pi$
$983$	−2.64215e64	+	1.09441e64i	−1.20797	+	0.500358i	−0.314405	+	0.949289i	$0.601805\pi$
$984$	4.82870e63	+	4.82870e63i	0.215991	+	0.215991i
$985$	−1.28072e64			−0.560499
$986$	2.59141e64	−	3.37896e64i	1.10964	−	1.44687i
$987$	6.97855e64			2.92379
$988$	−2.61121e64	−	2.61121e64i	−1.07045	−	1.07045i
$989$	−9.31417e63	+	3.85806e63i	−0.373615	+	0.154756i
$990$		−	1.32421e65i		−	5.19758i
$991$	1.34872e63	+	3.25609e63i	0.0518009	+	0.125058i	0.947662	−	0.319277i	$-0.103440\pi$
$991$	1.34872e63	+	3.25609e63i	0.0518009	+	0.125058i	−0.895861	+	0.444335i	$0.853440\pi$
$992$	−5.54703e63	−	2.29765e63i	−0.208478	−	0.0863542i
$993$	−1.81376e64	+	4.37881e64i	−0.667070	+	1.61045i
$994$	−3.83653e64	+	3.83653e64i	−1.38080	+	1.38080i
$995$	−4.23025e64	+	4.23025e64i	−1.48994	+	1.48994i
$996$	4.32686e63	−	1.04460e64i	0.149141	−	0.360058i
$997$	−2.28687e64	−	9.47252e63i	−0.771428	−	0.319536i	−0.0379770	−	0.999279i	$-0.512091\pi$
$997$	−2.28687e64	−	9.47252e63i	−0.771428	−	0.319536i	−0.733451	+	0.679743i	$0.762091\pi$
$998$	6.44380e63	+	1.55567e64i	0.212733	+	0.513583i
$999$			3.45096e64i			1.11502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.11	✓	252
17.9	even	8	inner	17.44.d.a.9.11	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.11	✓	252	1.1	even	1	trivial
17.44.d.a.9.11	yes	252	17.9	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.17742e6 - 3.17742e6i) q^{2} +(2.68747e10 - 1.11319e10i) q^{3} +1.13958e13i q^{4} +(-5.29509e14 - 1.27835e15i) q^{5} +(-1.20763e17 - 5.00216e16i) q^{6} +(8.49333e17 - 2.05047e18i) q^{7} +(8.26049e18 - 8.26049e18i) q^{8} +(3.66220e20 - 3.66220e20i) q^{9} +(-2.37937e21 + 5.74432e21i) q^{10} +(-3.79921e22 - 1.57368e22i) q^{11} +(1.26857e23 + 3.06260e23i) q^{12} -1.45301e24i q^{13} +(-9.21389e24 + 3.81652e24i) q^{14} +(-2.84609e25 - 2.84609e25i) q^{15} +4.77449e25 q^{16} +(2.75185e26 + 7.36611e25i) q^{17} -2.32727e27 q^{18} +(-1.57699e27 - 1.57699e27i) q^{19} +(1.45679e28 - 6.03421e27i) q^{20} -6.45606e28i q^{21} +(7.07142e28 + 1.70719e29i) q^{22} +(-1.34123e29 - 5.55555e28i) q^{23} +(1.30044e29 - 3.13953e29i) q^{24} +(-5.49908e29 + 5.49908e29i) q^{25} +(-4.61680e30 + 4.61680e30i) q^{26} +(2.11123e30 - 5.09697e30i) q^{27} +(2.33669e31 + 9.67887e30i) q^{28} +(1.27301e31 + 3.07331e31i) q^{29} +1.80864e32i q^{30} +(1.74819e31 - 7.24125e30i) q^{31} +(-2.24365e32 - 2.24365e32i) q^{32} -1.19621e33 q^{33} +(-6.40326e32 - 1.10843e33i) q^{34} -3.07095e33 q^{35} +(4.17339e33 + 4.17339e33i) q^{36} +(-5.77908e33 + 2.39377e33i) q^{37} +1.00215e34i q^{38} +(-1.61747e34 - 3.90491e34i) q^{39} +(-1.49338e34 - 6.18578e33i) q^{40} +(-7.69016e33 + 1.85657e34i) q^{41} +(-2.05136e35 + 2.05136e35i) q^{42} +(4.91051e34 - 4.91051e34i) q^{43} +(1.79335e35 - 4.32952e35i) q^{44} +(-6.62074e35 - 2.74240e35i) q^{45} +(2.49641e35 + 6.02687e35i) q^{46} +1.08093e36i q^{47} +(1.28313e36 - 5.31490e35i) q^{48} +(-1.93888e36 - 1.93888e36i) q^{49} +3.49457e36 q^{50} +(8.21552e36 - 1.08371e36i) q^{51} +1.65582e37 q^{52} +(-1.76984e36 - 1.76984e36i) q^{53} +(-2.29035e37 + 9.48693e36i) q^{54} +5.68999e37i q^{55} +(-9.92200e36 - 2.39538e37i) q^{56} +(-5.99360e37 - 2.48263e37i) q^{57} +(5.72032e37 - 1.38101e38i) q^{58} +(8.14503e37 - 8.14503e37i) q^{59} +(3.24336e38 - 3.24336e38i) q^{60} +(1.25476e38 - 3.02926e38i) q^{61} +(-7.85558e37 - 3.25389e37i) q^{62} +(-4.39881e38 - 1.06197e39i) q^{63} +1.00584e39i q^{64} +(-1.85745e39 + 7.69380e38i) q^{65} +(3.80085e39 + 3.80085e39i) q^{66} +1.42347e39 q^{67} +(-8.39430e38 + 3.13597e39i) q^{68} -4.22295e39 q^{69} +(9.75768e39 + 9.75768e39i) q^{70} +(5.02622e39 - 2.08193e39i) q^{71} -6.05032e39i q^{72} +(-4.12225e39 - 9.95200e39i) q^{73} +(2.59686e40 + 1.07565e40i) q^{74} +(-8.65713e39 + 2.09002e40i) q^{75} +(1.79711e40 - 1.79711e40i) q^{76} +(-6.45359e40 + 6.45359e40i) q^{77} +(-7.26816e40 + 1.75469e41i) q^{78} +(1.49326e40 + 6.18527e39i) q^{79} +(-2.52814e40 - 6.10346e40i) q^{80} +9.52694e39i q^{81} +(8.34257e40 - 3.45561e40i) q^{82} +(-2.41181e40 - 2.41181e40i) q^{83} +7.35723e41 q^{84} +(-5.15486e40 - 3.90787e41i) q^{85} -3.12055e41 q^{86} +(6.84235e41 + 6.84235e41i) q^{87} +(-4.43827e41 + 1.83839e41i) q^{88} -1.54199e42i q^{89} +(1.23231e42 + 2.97506e42i) q^{90} +(-2.97935e42 - 1.23409e42i) q^{91} +(6.33102e41 - 1.52844e42i) q^{92} +(3.89214e41 - 3.89214e41i) q^{93} +(3.43456e42 - 3.43456e42i) q^{94} +(-1.18091e42 + 2.85097e42i) q^{95} +(-8.52737e42 - 3.53215e42i) q^{96} +(-2.87026e42 - 6.92942e42i) q^{97} +1.23212e43i q^{98} +(-1.96766e43 + 8.15032e42i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 252 q - 4 q^{2} - 4 q^{3} + 18\!\cdots\!80 q^{5} + 22\!\cdots\!40 q^{6} - 4 q^{7} + 35184372088828 q^{8} + 63\!\cdots\!24 q^{9} - 91\!\cdots\!16 q^{10} + 31\!\cdots\!84 q^{11} + 16\!\cdots\!88 q^{12} - 10\!\cdots\!24 q^{14}+ \cdots + 44\!\cdots\!04 q^{99}+O(q^{100}) \) 252 * q - 4 * q^2 - 4 * q^3 + 1884797015207680 * q^5 + 221515217735603540 * q^6 - 4 * q^7 + 35184372088828 * q^8 + 637940004494872277024 * q^9 - 9172644062832164339716 * q^10 + 31271856798939564695884 * q^11 + 160659040662715870080488 * q^12 - 10620825937570937944957524 * q^14 + 28748551219070162352205864 * q^15 - 4410161389954167229328130056 * q^16 + 754786259037235794349028848 * q^17 - 5367540473535552290321072136 * q^18 - 1520391448988386966886847848 * q^19 + 40480648156465003912941797372 * q^20 + 44147261648104882038875094724 * q^22 - 408953067900897227251175991228 * q^23 + 2569128406481727809325689264168 * q^24 + 42966318811420029473026445436 * q^25 + 3889861661153663431806873373452 * q^26 + 16724820032498576287206262041608 * q^27 - 78718748571558344076653664853948 * q^28 - 109059849142312592102640344707492 * q^29 + 155238807707320954847178663148116 * q^31 - 1248943358044888932820031011401380 * q^32 + 932475890510175608977160850636416 * q^33 - 2007434777522200770802818693652196 * q^34 - 6260674670597673932268376573918712 * q^35 + 4479760017879839550046604218909532 * q^36 - 17669696250349968942205391131252928 * q^37 - 33477298925576849377795174615937792 * q^39 + 257430816220235129125050811116411896 * q^40 - 311812241725106436964393322934514756 * q^41 - 726966897646418372795388468485943264 * q^42 + 145483863855225967728840460948874008 * q^43 - 576839823783400550140919165196100820 * q^44 - 1562721042700452296454407377932847652 * q^45 + 3255942875929625188695035486970932036 * q^46 + 18708730728755605295119242540553548420 * q^48 - 2949590196379917026003323686456465704 * q^49 + 10905341656561025307088825016657498256 * q^50 - 46185381700203116194868436729164991716 * q^51 + 7454763265891936095016769109884927992 * q^52 - 14713371751943584240669151627479277652 * q^53 - 6755810910541176993304440587421505708 * q^54 + 149884478723227700332950860917188035940 * q^56 + 126920003429662656894363296666266565000 * q^57 - 271066615350358579055879450872780742344 * q^58 + 116874962636142679544094000646084191712 * q^59 - 872542987975341146926551197816579820832 * q^60 - 1358609311184572224052031653816889387984 * q^61 + 2607817901743511605570070357854955329636 * q^62 - 1091602845873954611663873790764312528604 * q^63 + 3372175859531725606529403976394593343084 * q^65 - 15969791388639223448787929109583645824044 * q^66 + 9601127564424465892797427904090648719472 * q^67 - 2858492589626501237506636670893985611548 * q^68 - 6004549631066595629803136354269922710016 * q^69 - 7491013725132007196906975517093826622728 * q^70 + 13161829513880573377255430143542971678068 * q^71 - 5385412878117054164021091482584340053276 * q^73 + 32055566966732570990968100291615084999196 * q^74 - 92628007303509329473535996431096556198300 * q^75 + 71952475208360471612122707267334932460688 * q^76 - 30844870660765075778153922644400106294552 * q^77 - 677870507408395262113905402805586249209560 * q^78 + 457431588401674274986102860554036176833980 * q^79 - 1042654222461388078925088086647718502523144 * q^80 + 381292868041103076294441011271187965819712 * q^82 - 1858164188395191584401285897298593856353872 * q^83 + 3414349628994907313966613712851584874618464 * q^84 + 1539811331574045767550650365721669563617076 * q^85 - 7527689568349034083014688245960811056896160 * q^86 + 4598921143806943863791357477672994697217920 * q^87 - 2748890833517697603875507243022514861012312 * q^88 + 7440815478668874256881493485280295170489540 * q^90 - 2237820543008860122477949024778651580244448 * q^91 + 8095910074397868366682337486060370784743852 * q^92 - 4703810315457730631257609089619508247525608 * q^93 - 19029062207054913342048301316319385806697928 * q^94 + 7308723736731156227266260213147210681429192 * q^95 - 51985923233339651510401162209778533343281372 * q^96 + 30389671344271765040956456332036809733752352 * q^97 + 44417034354379298005913817665478379237257004 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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