LMFDB - Embedded newform 17.44.d.a.2.6

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			2.6
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.48662e6 - 3.48662e6i) q^{2} +(2.29447e10 - 9.50399e9i) q^{3} +1.55169e13i q^{4} +(2.88501e14 + 6.96503e14i) q^{5} +(-1.13136e17 - 4.68624e16i) q^{6} +(9.32651e17 - 2.25162e18i) q^{7} +(2.34328e19 - 2.34328e19i) q^{8} +(2.04019e20 - 2.04019e20i) q^{9} +(1.42255e21 - 3.43433e21i) q^{10} +(2.95107e22 + 1.22238e22i) q^{11} +(1.47472e23 + 3.56030e23i) q^{12} +4.80661e23i q^{13} +(-1.11023e25 + 4.59874e24i) q^{14} +(1.32391e25 + 1.32391e25i) q^{15} -2.69144e25 q^{16} +(-2.69145e26 + 9.33484e25i) q^{17} -1.42267e27 q^{18} +(1.16285e26 + 1.16285e26i) q^{19} +(-1.08075e28 + 4.47663e27i) q^{20} -6.05266e28i q^{21} +(-6.02731e28 - 1.45512e29i) q^{22} +(3.27648e29 + 1.35716e29i) q^{23} +(3.14953e29 - 7.60363e29i) q^{24} +(4.02004e29 - 4.02004e29i) q^{25} +(1.67588e30 - 1.67588e30i) q^{26} +(-3.77602e29 + 9.11611e29i) q^{27} +(3.49381e31 + 1.44718e31i) q^{28} +(-1.86945e31 - 4.51325e31i) q^{29} -9.23193e31i q^{30} +(-1.46613e32 + 6.07290e31i) q^{31} +(-1.12277e32 - 1.12277e32i) q^{32} +7.93288e32 q^{33} +(1.26387e33 + 6.12934e32i) q^{34} +1.83733e33 q^{35} +(3.16573e33 + 3.16573e33i) q^{36} +(-2.48768e33 + 1.03043e33i) q^{37} -8.10881e32i q^{38} +(4.56819e33 + 1.10286e34i) q^{39} +(2.30814e34 + 9.56063e33i) q^{40} +(2.04685e33 - 4.94153e33i) q^{41} +(-2.11033e35 + 2.11033e35i) q^{42} +(1.66250e35 - 1.66250e35i) q^{43} +(-1.89675e35 + 4.57915e35i) q^{44} +(2.00959e35 + 8.32400e34i) q^{45} +(-6.69192e35 - 1.61557e36i) q^{46} +6.83109e35i q^{47} +(-6.17542e35 + 2.55794e35i) q^{48} +(-2.65576e36 - 2.65576e36i) q^{49} -2.80327e36 q^{50} +(-5.28825e36 + 4.69980e36i) q^{51} -7.45835e36 q^{52} +(-2.17077e36 - 2.17077e36i) q^{53} +(4.49499e36 - 1.86189e36i) q^{54} +2.40809e37i q^{55} +(-3.09071e37 - 7.46164e37i) q^{56} +(3.77329e36 + 1.56295e36i) q^{57} +(-9.21792e37 + 2.22540e38i) q^{58} +(9.82038e37 - 9.82038e37i) q^{59} +(-2.05430e38 + 2.05430e38i) q^{60} +(-2.37035e37 + 5.72252e37i) q^{61} +(7.22921e38 + 2.99444e38i) q^{62} +(-2.69094e38 - 6.49651e38i) q^{63} +1.01967e39i q^{64} +(-3.34781e38 + 1.38671e38i) q^{65} +(-2.76589e39 - 2.76589e39i) q^{66} +1.25248e39 q^{67} +(-1.44848e39 - 4.17629e39i) q^{68} +8.80761e39 q^{69} +(-6.40606e39 - 6.40606e39i) q^{70} +(-5.99916e39 + 2.48493e39i) q^{71} -9.56146e39i q^{72} +(-2.94618e39 - 7.11271e39i) q^{73} +(1.22663e40 + 5.08086e39i) q^{74} +(5.40321e39 - 1.30445e40i) q^{75} +(-1.80438e39 + 1.80438e39i) q^{76} +(5.50465e40 - 5.50465e40i) q^{77} +(2.25249e40 - 5.43800e40i) q^{78} +(-2.82670e40 - 1.17086e40i) q^{79} +(-7.76483e39 - 1.87460e40i) q^{80} +1.19216e41i q^{81} +(-2.43658e40 + 1.00926e40i) q^{82} +(1.40419e41 + 1.40419e41i) q^{83} +9.39183e41 q^{84} +(-1.42666e41 - 1.60529e41i) q^{85} -1.15930e42 q^{86} +(-8.57878e41 - 8.57878e41i) q^{87} +(9.77956e41 - 4.05083e41i) q^{88} -3.45203e41i q^{89} +(-4.10441e41 - 9.90893e41i) q^{90} +(1.08226e42 + 4.48289e41i) q^{91} +(-2.10589e42 + 5.08407e42i) q^{92} +(-2.78681e42 + 2.78681e42i) q^{93} +(2.38174e42 - 2.38174e42i) q^{94} +(-4.74444e40 + 1.14541e41i) q^{95} +(-3.64323e42 - 1.50908e42i) q^{96} +(1.26737e42 + 3.05971e42i) q^{97} +1.85192e43i q^{98} +(8.51462e42 - 3.52687e42i) 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 $

$2$	−3.48662e6	−	3.48662e6i	−1.17560	−	1.17560i	−0.980854	−	0.194745i	$-0.937612\pi$
$2$	−3.48662e6	−	3.48662e6i	−1.17560	−	1.17560i	−0.194745	−	0.980854i	$-0.562388\pi$
$3$	2.29447e10	−	9.50399e9i	1.26641	−	0.524565i	0.354540	−	0.935041i	$-0.384638\pi$
$3$	2.29447e10	−	9.50399e9i	1.26641	−	0.524565i	0.911871	+	0.410476i	$0.134638\pi$
$4$			1.55169e13i			1.76407i
$5$	2.88501e14	+	6.96503e14i	0.270578	+	0.653232i	0.999508	−	0.0313553i	$-0.00998233\pi$
$5$	2.88501e14	+	6.96503e14i	0.270578	+	0.653232i	−0.728931	+	0.684588i	$0.759982\pi$
$6$	−1.13136e17	−	4.68624e16i	−2.10547	−	0.872114i
$7$	9.32651e17	−	2.25162e18i	0.631119	−	1.52366i	−0.207098	−	0.978320i	$-0.566402\pi$
$7$	9.32651e17	−	2.25162e18i	0.631119	−	1.52366i	0.838217	−	0.545337i	$-0.183598\pi$
$8$	2.34328e19	−	2.34328e19i	0.898234	−	0.898234i
$9$	2.04019e20	−	2.04019e20i	0.621522	−	0.621522i
$10$	1.42255e21	−	3.43433e21i	0.449848	−	1.08603i
$11$	2.95107e22	+	1.22238e22i	1.20237	+	0.498037i	0.891763	−	0.452502i	$-0.149468\pi$
$11$	2.95107e22	+	1.22238e22i	1.20237	+	0.498037i	0.310605	+	0.950539i	$0.399468\pi$
$12$	1.47472e23	+	3.56030e23i	0.925366	+	2.23403i
$13$			4.80661e23i			0.539581i	0.962919	+	0.269790i	$0.0869544\pi$
$13$			4.80661e23i			0.539581i	−0.962919	+	0.269790i	$0.913046\pi$
$14$	−1.11023e25	+	4.59874e24i	−2.53315	+	1.04927i
$15$	1.32391e25	+	1.32391e25i	0.685325	+	0.685325i
$16$	−2.69144e25			−0.347861
$17$	−2.69145e26	+	9.33484e25i	−0.944787	+	0.327684i
$17$	−2.69145e26	+	9.33484e25i	−0.944787	+	0.327684i
$18$	−1.42267e27			−1.46132
$19$	1.16285e26	+	1.16285e26i	0.0373526	+	0.0373526i	0.725536	−	0.688184i	$-0.241592\pi$
$19$	1.16285e26	+	1.16285e26i	0.0373526	+	0.0373526i	−0.688184	+	0.725536i	$0.741592\pi$
$20$	−1.08075e28	+	4.47663e27i	−1.15234	+	0.477317i
$21$		−	6.05266e28i		−	2.26064i
$22$	−6.02731e28	−	1.45512e29i	−0.828011	−	1.99899i
$23$	3.27648e29	+	1.35716e29i	1.73085	+	0.716941i	0.999385	+	0.0350587i	$0.0111618\pi$
$23$	3.27648e29	+	1.35716e29i	1.73085	+	0.716941i	0.731462	+	0.681882i	$0.238838\pi$
$24$	3.14953e29	−	7.60363e29i	0.666352	−	1.60871i
$25$	4.02004e29	−	4.02004e29i	0.353607	−	0.353607i
$26$	1.67588e30	−	1.67588e30i	0.634331	−	0.634331i
$27$	−3.77602e29	+	9.11611e29i	−0.0634911	+	0.153281i
$28$	3.49381e31	+	1.44718e31i	2.68783	+	1.11334i
$29$	−1.86945e31	−	4.51325e31i	−0.676327	−	1.63280i	−0.770652	−	0.637257i	$-0.780069\pi$
$29$	−1.86945e31	−	4.51325e31i	−0.676327	−	1.63280i	0.0943246	−	0.995541i	$-0.469931\pi$
$30$		−	9.23193e31i		−	1.61133i
$31$	−1.46613e32	+	6.07290e31i	−1.26443	+	0.523745i	−0.911267	−	0.411816i	$-0.864895\pi$
$31$	−1.46613e32	+	6.07290e31i	−1.26443	+	0.523745i	−0.353165	+	0.935561i	$0.614895\pi$
$32$	−1.12277e32	−	1.12277e32i	−0.489289	−	0.489289i
$33$	7.93288e32			1.78394
$34$	1.26387e33	+	6.12934e32i	1.49592	+	0.725466i
$35$	1.83733e33			1.16607
$36$	3.16573e33	+	3.16573e33i	1.09640	+	1.09640i
$37$	−2.48768e33	+	1.03043e33i	−0.478032	+	0.198007i	−0.608671	−	0.793423i	$-0.708297\pi$
$37$	−2.48768e33	+	1.03043e33i	−0.478032	+	0.198007i	0.130639	+	0.991430i	$0.458297\pi$
$38$		−	8.10881e32i		−	0.0878233i
$39$	4.56819e33	+	1.10286e34i	0.283045	+	0.683331i
$40$	2.30814e34	+	9.56063e33i	0.829798	+	0.343713i
$41$	2.04685e33	−	4.94153e33i	0.0432746	−	0.104474i	−0.900764	−	0.434308i	$-0.856993\pi$
$41$	2.04685e33	−	4.94153e33i	0.0432746	−	0.104474i	0.944039	+	0.329834i	$0.106993\pi$
$42$	−2.11033e35	+	2.11033e35i	−2.65760	+	2.65760i
$43$	1.66250e35	−	1.66250e35i	1.26238	−	1.26238i	0.312438	−	0.949938i	$-0.398854\pi$
$43$	1.66250e35	−	1.66250e35i	1.26238	−	1.26238i	0.949938	−	0.312438i	$-0.101146\pi$
$44$	−1.89675e35	+	4.57915e35i	−0.878570	+	2.12106i
$45$	2.00959e35	+	8.32400e34i	0.574168	+	0.237828i
$46$	−6.69192e35	−	1.61557e36i	−1.19195	−	2.87762i
$47$			6.83109e35i			0.766277i	0.923691	+	0.383139i	$0.125157\pi$
$47$			6.83109e35i			0.766277i	−0.923691	+	0.383139i	$0.874843\pi$
$48$	−6.17542e35	+	2.55794e35i	−0.440534	+	0.182475i
$49$	−2.65576e36	−	2.65576e36i	−1.21611	−	1.21611i
$50$	−2.80327e36			−0.831399
$51$	−5.28825e36	+	4.69980e36i	−1.02460	+	0.910584i
$52$	−7.45835e36			−0.951856
$53$	−2.17077e36	−	2.17077e36i	−0.183943	−	0.183943i	0.609129	−	0.793071i	$-0.291519\pi$
$53$	−2.17077e36	−	2.17077e36i	−0.183943	−	0.183943i	−0.793071	+	0.609129i	$0.791519\pi$
$54$	4.49499e36	−	1.86189e36i	0.254837	−	0.105557i
$55$			2.40809e37i			0.920184i
$56$	−3.09071e37	−	7.46164e37i	−0.801708	−	1.93549i
$57$	3.77329e36	+	1.56295e36i	0.0668976	+	0.0277099i
$58$	−9.21792e37	+	2.22540e38i	−1.12443	+	2.71460i
$59$	9.82038e37	−	9.82038e37i	0.829488	−	0.829488i	−0.157958	−	0.987446i	$-0.550491\pi$
$59$	9.82038e37	−	9.82038e37i	0.829488	−	0.829488i	0.987446	+	0.157958i	$0.0504910\pi$
$60$	−2.05430e38	+	2.05430e38i	−1.20896	+	1.20896i
$61$	−2.37035e37	+	5.72252e37i	−0.0977734	+	0.236046i	−0.965197	−	0.261525i	$-0.915775\pi$
$61$	−2.37035e37	+	5.72252e37i	−0.0977734	+	0.236046i	0.867423	+	0.497571i	$0.165775\pi$
$62$	7.22921e38	+	2.99444e38i	2.10218	+	0.870751i
$63$	−2.69094e38	−	6.49651e38i	−0.554731	−	1.33924i
$64$			1.01967e39i			1.49828i
$65$	−3.34781e38	+	1.38671e38i	−0.352472	+	0.145999i
$66$	−2.76589e39	−	2.76589e39i	−2.09720	−	2.09720i
$67$	1.25248e39			0.687326			0.343663	−	0.939093i	$-0.388332\pi$
$67$	1.25248e39			0.687326			0.343663	+	0.939093i	$0.388332\pi$
$68$	−1.44848e39	−	4.17629e39i	−0.578056	−	1.66667i
$69$	8.80761e39			2.56805
$70$	−6.40606e39	−	6.40606e39i	−1.37083	−	1.37083i
$71$	−5.99916e39	+	2.48493e39i	−0.946316	+	0.391977i	−0.801845	−	0.597532i	$-0.796148\pi$
$71$	−5.99916e39	+	2.48493e39i	−0.946316	+	0.391977i	−0.144471	+	0.989509i	$0.546148\pi$
$72$		−	9.56146e39i		−	1.11654i
$73$	−2.94618e39	−	7.11271e39i	−0.255751	−	0.617438i	0.742897	−	0.669405i	$-0.233451\pi$
$73$	−2.94618e39	−	7.11271e39i	−0.255751	−	0.617438i	−0.998649	+	0.0519669i	$0.983451\pi$
$74$	1.22663e40	+	5.08086e39i	0.794750	+	0.329196i
$75$	5.40321e39	−	1.30445e40i	0.262322	−	0.633301i
$76$	−1.80438e39	+	1.80438e39i	−0.0658924	+	0.0658924i
$77$	5.50465e40	−	5.50465e40i	1.51768	−	1.51768i
$78$	2.25249e40	−	5.43800e40i	0.470576	−	1.13607i
$79$	−2.82670e40	−	1.17086e40i	−0.449052	−	0.186003i	0.146685	−	0.989183i	$-0.453140\pi$
$79$	−2.82670e40	−	1.17086e40i	−0.449052	−	0.186003i	−0.595737	+	0.803180i	$0.703140\pi$
$80$	−7.76483e39	−	1.87460e40i	−0.0941233	−	0.227234i
$81$			1.19216e41i			1.10639i
$82$	−2.43658e40	+	1.00926e40i	−0.173693	+	0.0719460i
$83$	1.40419e41	+	1.40419e41i	0.771343	+	0.771343i	0.978341	−	0.206998i	$-0.0663694\pi$
$83$	1.40419e41	+	1.40419e41i	0.771343	+	0.771343i	−0.206998	+	0.978341i	$0.566369\pi$
$84$	9.39183e41			3.98791
$85$	−1.42666e41	−	1.60529e41i	−0.469692	−	0.528502i
$86$	−1.15930e42			−2.96810
$87$	−8.57878e41	−	8.57878e41i	−1.71302	−	1.71302i
$88$	9.77956e41	−	4.05083e41i	1.52736	−	0.632654i
$89$		−	3.45203e41i		−	0.422853i	−0.977394	−	0.211426i	$-0.932189\pi$
$89$		−	3.45203e41i		−	0.422853i	0.977394	−	0.211426i	$-0.0678109\pi$
$90$	−4.10441e41	−	9.90893e41i	−0.395401	−	0.954581i
$91$	1.08226e42	+	4.48289e41i	0.822136	+	0.340540i
$92$	−2.10589e42	+	5.08407e42i	−1.26473	+	3.05333i
$93$	−2.78681e42	+	2.78681e42i	−1.32655	+	1.32655i
$94$	2.38174e42	−	2.38174e42i	0.900834	−	0.900834i
$95$	−4.74444e40	+	1.14541e41i	−0.0142931	+	0.0345067i
$96$	−3.64323e42	−	1.50908e42i	−0.876305	−	0.362978i
$97$	1.26737e42	+	3.05971e42i	0.243956	+	0.588963i	0.997669	−	0.0682417i	$-0.0217389\pi$
$97$	1.26737e42	+	3.05971e42i	0.243956	+	0.588963i	−0.753713	+	0.657204i	$0.771739\pi$
$98$			1.85192e43i			2.85932i
$99$	8.51462e42	−	3.52687e42i	1.05684	−	0.437757i
$100$	6.23785e42	+	6.23785e42i	0.623785	+	0.623785i
$101$	2.02873e43			1.63801			0.819003	−	0.573790i	$-0.194527\pi$
$101$	2.02873e43			1.63801			0.819003	+	0.573790i	$0.194527\pi$
$102$	3.48245e43	+	2.05172e42i	2.27500	+	0.134034i
$103$	1.16423e43			0.616651			0.308325	−	0.951281i	$-0.400231\pi$
$103$	1.16423e43			0.616651			0.308325	+	0.951281i	$0.400231\pi$
$104$	1.12632e43	+	1.12632e43i	0.484670	+	0.484670i
$105$	4.21569e43	−	1.74620e43i	1.47672	−	0.611678i
$106$			1.51373e43i			0.432485i
$107$	1.78474e43	+	4.30874e43i	0.416699	+	1.00600i	0.983297	+	0.182007i	$0.0582593\pi$
$107$	1.78474e43	+	4.30874e43i	0.416699	+	1.00600i	−0.566598	+	0.823994i	$0.691741\pi$
$108$	−1.41454e43	−	5.85920e42i	−0.270398	−	0.112002i
$109$	3.99225e43	−	9.63813e43i	0.625961	−	1.51120i	−0.218638	−	0.975806i	$-0.570161\pi$
$109$	3.99225e43	−	9.63813e43i	0.625961	−	1.51120i	0.844600	−	0.535398i	$-0.179839\pi$
$110$	8.39608e43	−	8.39608e43i	1.08177	−	1.08177i
$111$	−4.72857e43	+	4.72857e43i	−0.501517	+	0.501517i
$112$	−2.51018e43	+	6.06010e43i	−0.219542	+	0.530020i
$113$	3.03603e43	+	1.25757e43i	0.219341	+	0.0908541i	0.489648	−	0.871920i	$-0.337125\pi$
$113$	3.03603e43	+	1.25757e43i	0.219341	+	0.0908541i	−0.270307	+	0.962774i	$0.587125\pi$
$114$	−7.70661e42	−	1.86054e43i	−0.0460690	−	0.111220i
$115$			2.67362e44i			1.32463i
$116$	7.00316e44	−	2.90080e44i	2.88036	−	1.19309i
$117$	9.80638e43	+	9.80638e43i	0.335361	+	0.335361i
$118$	−6.84798e44			−1.95029
$119$	−4.08330e43	+	6.93073e44i	−0.0969956	+	1.64634i
$120$	6.20459e44			1.23116
$121$	2.95503e44	+	2.95503e44i	0.490542	+	0.490542i
$122$	2.82167e44	−	1.16878e44i	0.392437	−	0.162553i
$123$		−	1.32835e44i		−	0.155007i
$124$	−9.42325e44	−	2.27497e45i	−0.923920	−	2.23054i
$125$	1.18781e45	+	4.92006e44i	0.979898	+	0.405887i
$126$	−1.32686e45	+	3.20331e45i	−0.922267	+	2.22655i
$127$	1.63368e45	−	1.63368e45i	0.958050	−	0.958050i	−0.0411049	−	0.999155i	$-0.513088\pi$
$127$	1.63368e45	−	1.63368e45i	0.958050	−	0.958050i	0.999155	+	0.0411049i	$0.0130878\pi$
$128$	2.56761e45	−	2.56761e45i	1.27208	−	1.27208i
$129$	2.23451e45	−	5.39458e45i	0.936489	−	2.26088i
$130$	1.65075e45	+	6.83761e44i	0.586001	+	0.242730i
$131$	2.68825e44	+	6.49000e44i	0.0809349	+	0.195394i	0.959167	−	0.282841i	$-0.0912768\pi$
$131$	2.68825e44	+	6.49000e44i	0.0809349	+	0.195394i	−0.878232	+	0.478235i	$0.841277\pi$
$132$			1.23094e46i			3.14699i
$133$	3.70283e44	−	1.53376e44i	0.0804865	−	0.0333386i
$134$	−4.36692e45	−	4.36692e45i	−0.808019	−	0.808019i
$135$	−7.43878e44			−0.117307
$136$	−4.11940e45	+	8.49423e45i	−0.554303	+	1.14298i
$137$	1.19254e46			1.37082			0.685412	−	0.728155i	$-0.259622\pi$
$137$	1.19254e46			1.37082			0.685412	+	0.728155i	$0.259622\pi$
$138$	−3.07088e46	−	3.07088e46i	−3.01899	−	3.01899i
$139$	1.03957e46	−	4.30604e45i	0.875056	−	0.362460i	0.100479	−	0.994939i	$-0.467963\pi$
$139$	1.03957e46	−	4.30604e45i	0.875056	−	0.362460i	0.774577	+	0.632479i	$0.217963\pi$
$140$			2.85096e46i			2.05702i
$141$	6.49226e45	+	1.56737e46i	0.401962	+	0.970421i
$142$	2.95808e46	+	1.22528e46i	1.57330	+	0.651680i
$143$	−5.87548e45	+	1.41847e46i	−0.268731	+	0.648775i
$144$	−5.49105e45	+	5.49105e45i	−0.216203	+	0.216203i
$145$	2.60415e46	−	2.60415e46i	0.883597	−	0.883597i
$146$	−1.45271e46	+	3.50715e46i	−0.425199	+	1.02652i
$147$	−8.61759e46	−	3.56952e46i	−2.17803	−	0.902168i
$148$	−1.59890e46	−	3.86010e46i	−0.349298	−	0.843279i
$149$		−	2.67655e46i		−	0.505906i	−0.967479	−	0.252953i	$-0.918598\pi$
$149$		−	2.67655e46i		−	0.505906i	0.967479	−	0.252953i	$-0.0814018\pi$
$150$	−6.43200e46	+	2.66422e46i	−1.05289	+	0.436122i
$151$	−6.84185e46	−	6.84185e46i	−0.970888	−	0.970888i	0.0286998	−	0.999588i	$-0.490863\pi$
$151$	−6.84185e46	−	6.84185e46i	−0.970888	−	0.970888i	−0.999588	+	0.0286998i	$0.990863\pi$
$152$	5.44976e45			0.0671027
$153$	−3.58657e46	+	7.39554e46i	−0.383543	+	0.790868i
$154$	−3.83852e47			−3.56836
$155$	−8.45958e46	−	8.45958e46i	−0.684254	−	0.684254i
$156$	−1.71129e47	+	7.08841e46i	−1.20544	+	0.499310i
$157$			4.19421e46i			0.257518i	0.991676	+	0.128759i	$0.0410993\pi$
$157$			4.19421e46i			0.257518i	−0.991676	+	0.128759i	$0.958901\pi$
$158$	5.77328e46	+	1.39379e47i	0.309240	+	0.746570i
$159$	−7.04385e46	−	2.91766e46i	−0.329437	−	0.136457i
$160$	4.58092e46	−	1.10593e47i	0.187229	−	0.452011i
$161$	6.11162e47	−	6.11162e47i	2.18474	−	2.18474i
$162$	4.15660e47	−	4.15660e47i	1.30067	−	1.30067i
$163$	1.24597e47	−	3.00805e47i	0.341566	−	0.824614i	−0.655991	−	0.754768i	$-0.727749\pi$
$163$	1.24597e47	−	3.00805e47i	0.341566	−	0.824614i	0.997558	−	0.0698459i	$-0.0222508\pi$
$164$	7.66771e46	+	3.17607e46i	0.184299	+	0.0763391i
$165$	2.28864e47	+	5.52527e47i	0.482696	+	1.16533i
$166$		−	9.79176e47i		−	1.81358i
$167$	4.76569e47	−	1.97401e47i	0.775750	−	0.321326i	0.0405510	−	0.999177i	$-0.487089\pi$
$167$	4.76569e47	−	1.97401e47i	0.775750	−	0.321326i	0.735199	+	0.677851i	$0.237089\pi$
$168$	−1.41831e48	−	1.41831e48i	−2.03058	−	2.03058i
$169$	5.62497e47			0.708853
$170$	−6.22814e46	+	1.05712e48i	−0.0691364	+	1.17348i
$171$	4.74486e46			0.0464309
$172$	2.57968e48	+	2.57968e48i	2.22691	+	2.22691i
$173$	−5.67733e47	+	2.35163e47i	−0.432666	+	0.179216i	−0.588377	−	0.808586i	$-0.700233\pi$
$173$	−5.67733e47	+	2.35163e47i	−0.432666	+	0.179216i	0.155711	+	0.987803i	$0.450233\pi$
$174$			5.98218e48i			4.02764i
$175$	−5.30231e47	−	1.28009e48i	−0.315607	−	0.761943i
$176$	−7.94265e47	−	3.28995e47i	−0.418257	−	0.173248i
$177$	1.31992e48	−	3.18658e48i	0.615352	−	1.48559i
$178$	−1.20359e48	+	1.20359e48i	−0.497105	+	0.497105i
$179$	−1.20166e48	+	1.20166e48i	−0.439989	+	0.439989i	−0.892008	−	0.452019i	$-0.850704\pi$
$179$	−1.20166e48	+	1.20166e48i	−0.439989	+	0.439989i	0.452019	+	0.892008i	$0.350704\pi$
$180$	−1.29163e48	+	3.11826e48i	−0.419544	+	1.01287i
$181$	−1.65323e48	−	6.84789e47i	−0.476698	−	0.197455i	0.131380	−	0.991332i	$-0.458059\pi$
$181$	−1.65323e48	−	6.84789e47i	−0.476698	−	0.197455i	−0.608078	+	0.793877i	$0.708059\pi$
$182$	−2.21043e48	−	5.33645e48i	−0.566164	−	1.36684i
$183$			1.53829e48i			0.350219i
$184$	1.08579e49	−	4.49750e48i	2.19869	−	0.910726i
$185$	−1.43539e48	−	1.43539e48i	−0.258689	−	0.258689i
$186$	1.94331e49			3.11899
$187$	−9.08373e48	−	5.35176e47i	−1.29918	−	0.0765425i
$188$	−1.05997e49			−1.35176
$189$	1.70043e48	+	1.70043e48i	0.193477	+	0.193477i
$190$	5.64781e47	−	2.33940e47i	0.0573690	−	0.0237630i
$191$			2.38775e47i			0.0216657i	0.999941	+	0.0108328i	$0.00344826\pi$
$191$			2.38775e47i			0.0216657i	−0.999941	+	0.0108328i	$0.996552\pi$
$192$	9.69097e48	+	2.33961e49i	0.785943	+	1.89743i
$193$	9.20495e48	+	3.81282e48i	0.667636	+	0.276544i	0.690648	−	0.723191i	$-0.257326\pi$
$193$	9.20495e48	+	3.81282e48i	0.667636	+	0.276544i	−0.0230120	+	0.999735i	$0.507326\pi$
$194$	6.24918e48	−	1.50869e49i	0.405589	−	0.979178i
$195$	−6.36352e48	+	6.36352e48i	−0.369788	+	0.369788i
$196$	4.12092e49	−	4.12092e49i	2.14530	−	2.14530i
$197$	−3.43392e48	+	8.29023e48i	−0.160238	+	0.386850i	−0.983524	−	0.180778i	$-0.942139\pi$
$197$	−3.43392e48	+	8.29023e48i	−0.160238	+	0.386850i	0.823286	+	0.567627i	$0.192139\pi$
$198$	−4.19841e49	−	1.73904e49i	−1.75704	−	0.727792i
$199$	4.19892e48	+	1.01371e49i	0.157687	+	0.380691i	0.982902	−	0.184128i	$-0.0589461\pi$
$199$	4.19892e48	+	1.01371e49i	0.157687	+	0.380691i	−0.825215	+	0.564819i	$0.808946\pi$
$200$		−	1.88402e49i		−	0.635243i
$201$	2.87377e49	−	1.19036e49i	0.870437	−	0.360547i
$202$	−7.07341e49	−	7.07341e49i	−1.92564	−	1.92564i
$203$	−1.19057e50			−2.91467
$204$	−7.29262e49	−	8.20572e49i	−1.60633	−	1.80746i
$205$	4.03230e48			0.0799549
$206$	−4.05923e49	−	4.05923e49i	−0.724934	−	0.724934i
$207$	9.45350e49	−	3.91577e49i	1.52135	−	0.630165i
$208$		−	1.29367e49i		−	0.187699i
$209$	2.01022e48	+	4.85309e48i	0.0263086	+	0.0635146i
$210$	−2.07868e50	−	8.61018e49i	−2.45512	−	1.01694i
$211$	1.14604e49	−	2.76678e49i	0.122215	−	0.295054i	−0.850917	−	0.525300i	$-0.823953\pi$
$211$	1.14604e49	−	2.76678e49i	0.122215	−	0.295054i	0.973132	+	0.230246i	$0.0739531\pi$
$212$	3.36836e49	−	3.36836e49i	0.324487	−	0.324487i
$213$	−1.14032e50	+	1.14032e50i	−0.992808	+	0.992808i
$214$	8.80021e49	−	2.12456e50i	0.692783	−	1.67253i
$215$	1.63756e50	+	6.78301e49i	1.16620	+	0.483054i
$216$	1.25133e49	+	3.02099e49i	0.0806524	+	0.194712i
$217$			3.86755e50i			2.25711i
$218$	−4.75239e50	+	1.96850e50i	−2.51245	+	1.04069i
$219$	−1.35198e50	−	1.35198e50i	−0.647773	−	0.647773i
$220$	−3.73660e50			−1.62326
$221$	−4.48689e49	−	1.29367e50i	−0.176812	−	0.509789i
$222$	3.29734e50			1.17917
$223$	−1.19286e50	−	1.19286e50i	−0.387290	−	0.387290i	0.486430	−	0.873720i	$-0.338299\pi$
$223$	−1.19286e50	−	1.19286e50i	−0.387290	−	0.387290i	−0.873720	+	0.486430i	$0.838299\pi$
$224$	−3.57520e50	+	1.48090e50i	−1.05431	+	0.436709i
$225$		−	1.64033e50i		−	0.439548i
$226$	−6.20083e49	−	1.49701e50i	−0.151049	−	0.364665i
$227$	7.39988e50	+	3.06513e50i	1.63934	+	0.679037i	0.996231	−	0.0867381i	$-0.0276443\pi$
$227$	7.39988e50	+	3.06513e50i	1.63934	+	0.679037i	0.643109	+	0.765775i	$0.277644\pi$
$228$	−2.42521e49	+	5.85496e49i	−0.0488820	+	0.118012i
$229$	−1.27091e50	+	1.27091e50i	−0.233159	+	0.233159i	−0.814010	−	0.580851i	$-0.802720\pi$
$229$	−1.27091e50	+	1.27091e50i	−0.233159	+	0.233159i	0.580851	+	0.814010i	$0.302720\pi$
$230$	9.32188e50	−	9.32188e50i	1.55724	−	1.55724i
$231$	7.39862e50	−	1.78618e51i	1.12588	−	2.71812i
$232$	−1.49565e51	−	6.19517e50i	−2.07413	−	0.859135i
$233$	−1.65059e50	−	3.98489e50i	−0.208683	−	0.503806i	0.784533	−	0.620087i	$-0.212903\pi$
$233$	−1.65059e50	−	3.98489e50i	−0.208683	−	0.503806i	−0.993216	+	0.116281i	$0.962903\pi$
$234$		−	6.83821e50i		−	0.788500i
$235$	−4.75787e50	+	1.97077e50i	−0.500557	+	0.207337i
$236$	1.52382e51	+	1.52382e51i	1.46327	+	1.46327i
$237$	−7.59854e50			−0.666255
$238$	2.55885e51	−	2.27411e51i	2.04946	−	1.82141i
$239$	−1.24241e51			−0.909309			−0.454655	−	0.890668i	$-0.650237\pi$
$239$	−1.24241e51			−0.909309			−0.454655	+	0.890668i	$0.650237\pi$
$240$	−3.56323e50	−	3.56323e50i	−0.238398	−	0.238398i
$241$	3.02818e50	−	1.25431e50i	0.185275	−	0.0767433i	−0.288118	−	0.957595i	$-0.593029\pi$
$241$	3.02818e50	−	1.25431e50i	0.185275	−	0.0767433i	0.473392	+	0.880852i	$0.343029\pi$
$242$		−	2.06061e51i		−	1.15336i
$243$	1.00908e51	+	2.43613e51i	0.516880	+	1.24786i
$244$	−8.87957e50	−	3.67804e50i	−0.416400	−	0.172479i
$245$	1.08356e51	−	2.61594e51i	0.465351	−	1.12346i
$246$	−4.63144e50	+	4.63144e50i	−0.182226	+	0.182226i
$247$	−5.58936e49	+	5.58936e49i	−0.0201547	+	0.0201547i
$248$	−2.01250e51	+	4.85860e51i	−0.665310	+	1.60620i
$249$	4.55641e51	+	1.88733e51i	1.38146	+	0.572218i
$250$	−2.42599e51	−	5.85686e51i	−0.674806	−	1.62913i
$251$		−	6.46879e51i		−	1.65135i	−0.564148	−	0.825673i	$-0.690795\pi$
$251$		−	6.46879e51i		−	1.65135i	0.564148	−	0.825673i	$-0.309205\pi$
$252$	1.00806e52	−	4.17550e51i	2.36251	−	0.978582i
$253$	8.01017e51	+	8.01017e51i	1.72405	+	1.72405i
$254$	−1.13921e52			−2.25256
$255$	−4.79909e51	−	2.32739e51i	−0.872056	−	0.422916i
$256$	−8.93542e51			−1.49264
$257$	8.86577e50	+	8.86577e50i	0.136193	+	0.136193i	0.771917	−	0.635724i	$-0.219298\pi$
$257$	8.86577e50	+	8.86577e50i	0.136193	+	0.136193i	−0.635724	+	0.771917i	$0.719298\pi$
$258$	−2.65997e52	+	1.10179e52i	−3.75883	+	1.55696i
$259$			6.56233e51i			0.853322i
$260$	−2.15174e51	−	5.19476e51i	−0.257551	−	0.621783i
$261$	−1.30219e52	−	5.39385e51i	−1.43517	−	0.594467i
$262$	1.32552e51	−	3.20010e51i	0.134558	−	0.324852i
$263$	4.20926e51	−	4.20926e51i	0.393693	−	0.393693i	−0.482309	−	0.876001i	$-0.660202\pi$
$263$	4.20926e51	−	4.20926e51i	0.393693	−	0.393693i	0.876001	+	0.482309i	$0.160202\pi$
$264$	1.85890e52	−	1.85890e52i	1.60240	−	1.60240i
$265$	8.85677e50	−	2.13821e51i	0.0703865	−	0.169928i
$266$	−1.82580e51	−	7.56270e50i	−0.133813	−	0.0554270i
$267$	−3.28080e51	−	7.92056e51i	−0.221814	−	0.535506i
$268$			1.94346e52i			1.21249i
$269$	1.86664e52	−	7.73190e51i	1.07495	−	0.445258i	0.226214	−	0.974078i	$-0.427365\pi$
$269$	1.86664e52	−	7.73190e51i	1.07495	−	0.445258i	0.848734	+	0.528819i	$0.177365\pi$
$270$	2.59362e51	+	2.59362e51i	0.137906	+	0.137906i
$271$	−1.87102e52			−0.918838			−0.459419	−	0.888220i	$-0.651942\pi$
$271$	−1.87102e52			−0.918838			−0.459419	+	0.888220i	$0.651942\pi$
$272$	7.24387e51	−	2.51242e51i	0.328654	−	0.113988i
$273$	2.90927e52			1.21980
$274$	−4.15794e52	−	4.15794e52i	−1.61154	−	1.61154i
$275$	1.67774e52	−	6.94945e51i	0.601275	−	0.249056i
$276$			1.36667e53i			4.53020i
$277$	2.00195e52	+	4.83313e52i	0.613957	+	1.48222i	0.858619	+	0.512614i	$0.171323\pi$
$277$	2.00195e52	+	4.83313e52i	0.613957	+	1.48222i	−0.244663	+	0.969608i	$0.578677\pi$
$278$	−5.12593e52	−	2.12323e52i	−1.45482	−	0.602607i
$279$	−1.75219e52	+	4.23016e52i	−0.460353	+	1.11139i
$280$	4.30538e52	−	4.30538e52i	1.04740	−	1.04740i
$281$	−3.46683e52	+	3.46683e52i	−0.781172	+	0.781172i	−0.980029	−	0.198857i	$-0.936277\pi$
$281$	−3.46683e52	+	3.46683e52i	−0.781172	+	0.781172i	0.198857	+	0.980029i	$0.436277\pi$
$282$	3.20121e52	−	7.72841e52i	0.668281	−	1.61337i
$283$	−1.78423e52	−	7.39051e51i	−0.345177	−	0.142977i	0.203358	−	0.979104i	$-0.434814\pi$
$283$	−1.78423e52	−	7.39051e51i	−0.345177	−	0.142977i	−0.548535	+	0.836127i	$0.684814\pi$
$284$	−3.85584e52	−	9.30883e52i	−0.691473	−	1.66936i
$285$			3.07902e51i			0.0511973i
$286$	6.99420e52	−	2.89709e52i	1.07862	−	0.446779i
$287$	−9.21745e51	−	9.21745e51i	−0.131871	−	0.131871i
$288$	−4.58132e52			−0.608208
$289$	6.37250e52	−	5.02485e52i	0.785246	−	0.619183i
$290$	−1.81594e53			−2.07751
$291$	5.81589e52	+	5.81589e52i	0.617898	+	0.617898i
$292$	1.10367e53	−	4.57155e52i	1.08920	−	0.451162i
$293$		−	6.92094e52i		−	0.634616i	−0.948322	−	0.317308i	$-0.897221\pi$
$293$		−	6.92094e52i		−	0.634616i	0.948322	−	0.317308i	$-0.102779\pi$
$294$	1.76007e53	+	4.24918e53i	1.49990	+	3.62107i
$295$	9.67311e52	+	4.00673e52i	0.766289	+	0.317407i
$296$	−3.41474e52	+	8.24390e52i	−0.251527	+	0.607241i
$297$	−2.22866e52	+	2.22866e52i	−0.152679	+	0.152679i
$298$	−9.33209e52	+	9.33209e52i	−0.594743	+	0.594743i
$299$	−6.52334e52	+	1.57487e53i	−0.386847	+	0.933932i
$300$	2.02410e53	+	8.38409e52i	1.11718	+	0.462753i
$301$	−2.19278e53	−	5.29384e53i	−1.12672	−	2.72014i
$302$			4.77098e53i			2.28275i
$303$	4.65486e53	−	1.92811e53i	2.07439	−	0.859239i
$304$	−3.12974e51	−	3.12974e51i	−0.0129935	−	0.0129935i
$305$	−4.66960e52			−0.180648
$306$	3.82904e53	−	1.32804e53i	1.38064	−	0.478851i
$307$	1.07822e52			0.0362436			0.0181218	−	0.999836i	$-0.494231\pi$
$307$	1.07822e52			0.0362436			0.0181218	+	0.999836i	$0.494231\pi$
$308$	8.54150e53	+	8.54150e53i	2.67728	+	2.67728i
$309$	2.67129e53	−	1.10649e53i	0.780933	−	0.323473i
$310$			5.89906e53i			1.60882i
$311$	1.54377e53	+	3.72698e53i	0.392856	+	0.948437i	0.989315	+	0.145794i	$0.0465736\pi$
$311$	1.54377e53	+	3.72698e53i	0.392856	+	0.948437i	−0.596459	+	0.802643i	$0.703426\pi$
$312$	3.65476e53	+	1.51385e53i	0.868032	+	0.359550i
$313$	−2.32606e53	+	5.61560e53i	−0.515724	+	1.24507i	0.424783	+	0.905295i	$0.360350\pi$
$313$	−2.32606e53	+	5.61560e53i	−0.515724	+	1.24507i	−0.940507	+	0.339773i	$0.889650\pi$
$314$	1.46236e53	−	1.46236e53i	0.302738	−	0.302738i
$315$	3.74850e53	−	3.74850e53i	0.724737	−	0.724737i
$316$	1.81680e53	−	4.38615e53i	0.328122	−	0.792157i
$317$	3.57076e53	+	1.47906e53i	0.602541	+	0.249581i	0.663036	−	0.748588i	$-0.269268\pi$
$317$	3.57076e53	+	1.47906e53i	0.602541	+	0.249581i	−0.0604944	+	0.998169i	$0.519268\pi$
$318$	1.43864e53	+	3.47319e53i	0.226866	+	0.547704i
$319$		−	1.56041e54i		−	2.30006i
$320$	−7.10206e53	+	2.94177e53i	−0.978723	+	0.405400i
$321$	8.19003e53	+	8.19003e53i	1.05543	+	1.05543i
$322$	−4.26178e54			−5.13676
$323$	−4.21525e52	−	2.04425e52i	−0.0475301	−	0.0230504i
$324$	−1.84986e54			−1.95174
$325$	1.93228e53	+	1.93228e53i	0.190799	+	0.190799i
$326$	−1.48321e54	+	6.14367e53i	−1.37096	+	0.567871i
$327$		−	2.59086e54i		−	2.24216i
$328$	−6.78305e52	−	1.63757e53i	−0.0549714	−	0.132713i
$329$	1.53810e54	+	6.37102e53i	1.16754	+	0.483612i
$330$	1.12849e54	−	2.72441e54i	0.802505	−	1.93742i
$331$	−8.16132e53	+	8.16132e53i	−0.543824	+	0.543824i	−0.924648	−	0.380824i	$-0.875640\pi$
$331$	−8.16132e53	+	8.16132e53i	−0.543824	+	0.543824i	0.380824	+	0.924648i	$0.375640\pi$
$332$	−2.17887e54	+	2.17887e54i	−1.36070	+	1.36070i
$333$	−2.97306e53	+	7.17759e53i	−0.174041	+	0.420173i
$334$	−2.34988e54	−	9.73351e53i	−1.28972	−	0.534220i
$335$	3.61342e53	+	8.72356e53i	0.185975	+	0.448983i
$336$			1.62904e54i			0.786387i
$337$	3.23516e54	−	1.34005e54i	1.46505	−	0.606845i	0.499328	−	0.866413i	$-0.333580\pi$
$337$	3.23516e54	−	1.34005e54i	1.46505	−	0.606845i	0.965725	+	0.259568i	$0.0835803\pi$
$338$	−1.96121e54	−	1.96121e54i	−0.833326	−	0.833326i
$339$	8.16126e53			0.325435
$340$	2.49091e54	−	2.21373e54i	0.932311	−	0.828568i
$341$	−5.06899e54			−1.78116
$342$	−1.65435e53	−	1.65435e53i	−0.0545841	−	0.0545841i
$343$	−3.53955e54	+	1.46613e54i	−1.09679	+	0.454306i
$344$		−	7.79139e54i		−	2.26782i
$345$	2.54100e54	+	6.13452e54i	0.694856	+	1.67753i
$346$	2.79939e54	+	1.15954e54i	0.719328	+	0.297955i
$347$	−4.48243e53	+	1.08215e54i	−0.108250	+	0.261340i	−0.968717	−	0.248167i	$-0.920172\pi$
$347$	−4.48243e53	+	1.08215e54i	−0.108250	+	0.261340i	0.860467	+	0.509506i	$0.170172\pi$
$348$	1.33116e55	−	1.33116e55i	3.02187	−	3.02187i
$349$	2.57093e54	−	2.57093e54i	0.548710	−	0.548710i	−0.377358	−	0.926068i	$-0.623167\pi$
$349$	2.57093e54	−	2.57093e54i	0.548710	−	0.548710i	0.926068	+	0.377358i	$0.123167\pi$
$350$	−2.61447e54	+	6.31189e54i	−0.524712	+	1.26677i
$351$	−4.38175e53	−	1.81498e53i	−0.0827075	−	0.0342586i
$352$	−1.94093e54	−	4.68582e54i	−0.344622	−	0.831991i
$353$		−	1.16938e55i		−	1.95344i	−0.214527	−	0.976718i	$-0.568821\pi$
$353$		−	1.16938e55i		−	1.95344i	0.214527	−	0.976718i	$-0.431179\pi$
$354$	−1.57125e55	+	6.50831e54i	−2.46987	+	1.02305i
$355$	−3.46153e54	−	3.46153e54i	−0.512104	−	0.512104i
$356$	5.35647e54			0.745940
$357$	5.65006e54	+	1.62904e55i	0.740775	+	2.13582i
$358$	8.37946e54			1.03450
$359$	−6.29174e54	−	6.29174e54i	−0.731543	−	0.731543i	0.239382	−	0.970925i	$-0.423055\pi$
$359$	−6.29174e54	−	6.29174e54i	−0.731543	−	0.731543i	−0.970925	+	0.239382i	$0.923055\pi$
$360$	6.65958e54	−	2.75849e54i	0.729362	−	0.302112i
$361$		−	9.66476e54i		−	0.997210i
$362$	3.37657e54	+	8.15176e54i	0.328278	+	0.792533i
$363$	9.58866e54	+	3.97175e54i	0.878548	+	0.363906i
$364$	−6.95604e54	+	1.67934e55i	−0.600735	+	1.45030i
$365$	4.10405e54	−	4.10405e54i	0.334130	−	0.334130i
$366$	5.36343e54	−	5.36343e54i	0.411717	−	0.411717i
$367$	−8.81760e54	+	2.12876e55i	−0.638308	+	1.54101i	0.190625	+	0.981663i	$0.438949\pi$
$367$	−8.81760e54	+	2.12876e55i	−0.638308	+	1.54101i	−0.828933	+	0.559349i	$0.811051\pi$
$368$	−8.81845e54	−	3.65272e54i	−0.602094	−	0.249395i
$369$	−5.90569e53	−	1.42576e54i	−0.0380368	−	0.0918289i
$370$			1.00093e55i			0.608230i
$371$	−6.91231e54	+	2.86317e54i	−0.396355	+	0.164176i
$372$	−4.32426e55	−	4.32426e55i	−2.34012	−	2.34012i
$373$	−3.59532e55			−1.83653			−0.918264	−	0.395968i	$-0.870409\pi$
$373$	−3.59532e55			−1.83653			−0.918264	+	0.395968i	$0.870409\pi$
$374$	2.98055e55	+	3.35374e55i	1.43733	+	1.61730i
$375$	3.19298e55			1.45387
$376$	1.60071e55	+	1.60071e55i	0.688296	+	0.688296i
$377$	2.16934e55	−	8.98571e54i	0.881026	−	0.364933i
$378$		−	1.18575e55i		−	0.454903i
$379$	−5.66262e54	−	1.36708e55i	−0.205246	−	0.495508i	0.787417	−	0.616420i	$-0.211418\pi$
$379$	−5.66262e54	−	1.36708e55i	−0.205246	−	0.495508i	−0.992663	+	0.120913i	$0.961418\pi$
$380$	−1.77732e54	−	7.36190e53i	−0.0608721	−	0.0252140i
$381$	2.19578e55	−	5.30108e55i	0.710726	−	1.71584i
$382$	8.32518e53	−	8.32518e53i	0.0254701	−	0.0254701i
$383$	−3.64675e55	+	3.64675e55i	−1.05471	+	1.05471i	−0.0562954	+	0.998414i	$0.517929\pi$
$383$	−3.64675e55	+	3.64675e55i	−1.05471	+	1.05471i	−0.998414	+	0.0562954i	$0.982071\pi$
$384$	3.45105e55	−	8.33156e55i	0.943690	−	2.27827i
$385$	5.42210e55	+	2.24591e55i	1.40204	+	0.580746i
$386$	−1.88003e55	−	4.53880e55i	−0.459767	−	1.10998i
$387$		−	6.78361e55i		−	1.56919i
$388$	−4.74771e55	+	1.96657e55i	−1.03897	+	0.430355i
$389$	−5.45665e55	−	5.45665e55i	−1.12982	−	1.12982i	−0.990206	−	0.139616i	$-0.955413\pi$
$389$	−5.45665e55	−	5.45665e55i	−1.12982	−	1.12982i	−0.139616	−	0.990206i	$-0.544587\pi$
$390$	4.43743e55			0.869445
$391$	−1.00854e56	−	5.94188e54i	−1.87021	−	0.110185i
$392$	−1.24464e56			−2.18471
$393$	1.23362e55	+	1.23362e55i	0.204994	+	0.204994i
$394$	4.08776e55	−	1.69321e55i	0.643156	−	0.266404i
$395$		−	2.30659e55i		−	0.343664i
$396$	5.47260e55	+	1.32120e56i	0.772232	+	1.86433i
$397$	−1.45380e55	−	6.02183e54i	−0.194316	−	0.0804883i	0.283404	−	0.959001i	$-0.408536\pi$
$397$	−1.45380e55	−	6.02183e54i	−0.194316	−	0.0804883i	−0.477719	+	0.878512i	$0.658536\pi$
$398$	2.07041e55	−	4.99842e55i	0.262163	−	0.632916i
$399$	7.03832e54	−	7.03832e54i	0.0844407	−	0.0844407i
$400$	−1.08197e55	+	1.08197e55i	−0.123006	+	0.123006i
$401$	1.75122e55	−	4.22782e55i	0.188685	−	0.455526i	−0.801022	−	0.598635i	$-0.795710\pi$
$401$	1.75122e55	−	4.22782e55i	0.188685	−	0.455526i	0.989707	+	0.143109i	$0.0457100\pi$
$402$	−1.41701e56	−	5.86943e55i	−1.44714	−	0.599426i
$403$	−2.91900e55	−	7.04710e55i	−0.282603	−	0.682263i
$404$			3.14796e56i			2.88955i
$405$	−8.30343e55	+	3.43939e55i	−0.722727	+	0.299363i
$406$	4.15105e56	+	4.15105e56i	3.42648	+	3.42648i
$407$	−8.60089e55			−0.673385
$408$	−1.37892e55	+	2.34048e56i	−0.102410	+	1.73825i
$409$	−8.26654e55			−0.582469			−0.291234	−	0.956652i	$-0.594066\pi$
$409$	−8.26654e55			−0.582469			−0.291234	+	0.956652i	$0.594066\pi$
$410$	−1.40591e55	−	1.40591e55i	−0.0939949	−	0.0939949i
$411$	2.73625e56	−	1.13339e56i	1.73603	−	0.719086i
$412$			1.80653e56i			1.08781i
$413$	−1.29528e56	−	3.12708e56i	−0.740349	−	1.78736i
$414$	−4.66135e56	−	1.93079e56i	−2.52932	−	1.04768i
$415$	−5.72913e55	+	1.38313e56i	−0.295158	+	0.712575i
$416$	5.39671e55	−	5.39671e55i	0.264011	−	0.264011i
$417$	1.97601e56	−	1.97601e56i	0.918046	−	0.918046i
$418$	9.91201e54	−	2.39297e55i	0.0437393	−	0.105596i
$419$	2.10205e56	+	8.70698e55i	0.881133	+	0.364977i	0.776936	−	0.629579i	$-0.216773\pi$
$419$	2.10205e56	+	8.70698e55i	0.881133	+	0.364977i	0.104197	+	0.994557i	$0.466773\pi$
$420$	2.70955e56	+	6.54144e56i	1.07904	+	2.60503i
$421$			1.56672e56i			0.592825i	0.955060	+	0.296413i	$0.0957903\pi$
$421$			1.56672e56i			0.592825i	−0.955060	+	0.296413i	$0.904210\pi$
$422$	−1.36425e56	+	5.65090e55i	−0.490542	+	0.203189i
$423$	1.39367e56	+	1.39367e56i	0.476258	+	0.476258i
$424$	−1.01734e56			−0.330447
$425$	−7.06709e55	+	1.45724e56i	−0.218212	+	0.449954i
$426$	7.95171e56			2.33429
$427$	1.06742e56	+	1.06742e56i	0.297946	+	0.297946i
$428$	−6.68581e56	+	2.76935e56i	−1.77465	+	0.735085i
$429$			3.81303e56i			0.962582i
$430$	−3.34458e56	−	8.07453e56i	−0.803101	−	1.93886i
$431$	1.55707e56	+	6.44959e55i	0.355669	+	0.147323i	0.553362	−	0.832941i	$-0.313345\pi$
$431$	1.55707e56	+	6.44959e55i	0.355669	+	0.147323i	−0.197692	+	0.980264i	$0.563345\pi$
$432$	1.01629e55	−	2.45355e55i	0.0220861	−	0.0533205i
$433$	1.05046e56	−	1.05046e56i	0.217215	−	0.217215i	−0.590109	−	0.807324i	$-0.700915\pi$
$433$	1.05046e56	−	1.05046e56i	0.217215	−	0.217215i	0.807324	+	0.590109i	$0.200915\pi$
$434$	1.34847e57	−	1.34847e57i	2.65345	−	2.65345i
$435$	3.50016e56	−	8.45012e56i	0.655493	−	1.58250i
$436$	1.49554e57	+	6.19472e56i	2.66586	+	1.10424i
$437$	2.23187e55	+	5.38822e55i	0.0378721	+	0.0914312i
$438$			9.42768e56i			1.52304i
$439$	−6.27941e54	+	2.60102e54i	−0.00965900	+	0.00400089i	−0.387508	−	0.921866i	$-0.626664\pi$
$439$	−6.27941e54	+	2.60102e54i	−0.00965900	+	0.00400089i	0.377849	+	0.925867i	$0.376664\pi$
$440$	5.64282e56	+	5.64282e56i	0.826540	+	0.826540i
$441$	−1.08365e57			−1.51168
$442$	−2.94613e56	+	6.07495e56i	−0.391448	+	0.807167i
$443$	5.80070e56			0.734176			0.367088	−	0.930186i	$-0.380355\pi$
$443$	5.80070e56			0.734176			0.367088	+	0.930186i	$0.380355\pi$
$444$	−7.33726e56	−	7.33726e56i	−0.884708	−	0.884708i
$445$	2.40435e56	−	9.95913e55i	0.276221	−	0.114415i
$446$			8.31811e56i			0.910594i
$447$	−2.54379e56	−	6.14124e56i	−0.265380	−	0.640685i
$448$	2.29592e57	+	9.51001e56i	2.28286	+	0.945592i
$449$	4.05195e56	−	9.78227e56i	0.384032	−	0.927135i	−0.607145	−	0.794591i	$-0.707685\pi$
$449$	4.05195e56	−	9.78227e56i	0.384032	−	0.927135i	0.991177	−	0.132544i	$-0.0423147\pi$
$450$	−5.71919e56	+	5.71919e56i	−0.516732	+	0.516732i
$451$	1.20808e56	−	1.20808e56i	0.104064	−	0.104064i
$452$	−1.95135e56	+	4.71098e56i	−0.160272	+	0.386932i
$453$	−2.22009e57	−	9.19591e56i	−1.73884	−	0.720250i
$454$	−1.51136e57	−	3.64875e57i	−1.12893	−	2.72548i
$455$			8.83132e56i			0.629188i
$456$	1.25043e56	−	5.17945e55i	0.0849796	−	0.0351997i
$457$	−7.81117e56	−	7.81117e56i	−0.506428	−	0.506428i	0.407000	−	0.913428i	$-0.366575\pi$
$457$	−7.81117e56	−	7.81117e56i	−0.506428	−	0.506428i	−0.913428	+	0.407000i	$0.866575\pi$
$458$	8.86236e56			0.548204
$459$	1.65320e55	−	2.80604e56i	0.00975784	−	0.165623i
$460$	−4.14862e57			−2.33674
$461$	1.08692e57	+	1.08692e57i	0.584287	+	0.584287i	0.936078	−	0.351792i	$-0.114427\pi$
$461$	1.08692e57	+	1.08692e57i	0.584287	+	0.584287i	−0.351792	+	0.936078i	$0.614427\pi$
$462$	−8.80735e57	+	3.64812e57i	−4.51900	+	1.87183i
$463$		−	8.70901e56i		−	0.426557i	−0.976991	−	0.213279i	$-0.931586\pi$
$463$		−	8.70901e56i		−	0.426557i	0.976991	−	0.213279i	$-0.0684142\pi$
$464$	5.03151e56	+	1.21471e57i	0.235268	+	0.567986i
$465$	−2.74502e57	−	1.13702e57i	−1.22548	−	0.507611i
$466$	−8.13878e56	+	1.96488e57i	−0.346946	+	0.837602i
$467$	1.55495e56	−	1.55495e56i	0.0632999	−	0.0632999i	−0.674748	−	0.738048i	$-0.735748\pi$
$467$	1.55495e56	−	1.55495e56i	0.0632999	−	0.0632999i	0.738048	+	0.674748i	$0.235748\pi$
$468$	−1.52164e57	+	1.52164e57i	−0.591599	+	0.591599i
$469$	1.16813e57	−	2.82011e57i	0.433785	−	1.04725i
$470$	2.34602e57	+	9.71753e56i	0.832200	+	0.344708i
$471$	3.98617e56	+	9.62347e56i	0.135085	+	0.326123i
$472$		−	4.60238e57i		−	1.49015i
$473$	6.93835e57	−	2.87396e57i	2.14655	−	0.889131i
$474$	2.64932e57	+	2.64932e57i	0.783249	+	0.783249i
$475$	9.34940e55			0.0264163
$476$	−1.07543e58	−	6.33601e56i	−2.90425	−	0.171107i
$477$	−8.85755e56			−0.228649
$478$	4.33182e57	+	4.33182e57i	1.06898	+	1.06898i
$479$	4.99612e57	−	2.06946e57i	1.17874	−	0.488251i	0.294670	−	0.955599i	$-0.404790\pi$
$479$	4.99612e57	−	2.06946e57i	1.17874	−	0.488251i	0.884074	+	0.467348i	$0.154790\pi$
$480$		−	2.97289e57i		−	0.670645i
$481$	−4.95287e56	−	1.19573e57i	−0.106841	−	0.257937i
$482$	−1.49314e57	−	6.18480e56i	−0.308028	−	0.127589i
$483$	8.21443e57	−	1.98314e58i	1.62074	−	3.91282i
$484$	−4.58528e57	+	4.58528e57i	−0.865347	+	0.865347i
$485$	−1.76546e57	+	1.76546e57i	−0.318720	+	0.318720i
$486$	4.97558e57	−	1.20121e58i	0.859337	−	2.07462i
$487$	1.15696e57	+	4.79229e56i	0.191182	+	0.0791900i	0.476220	−	0.879326i	$-0.342006\pi$
$487$	1.15696e57	+	4.79229e56i	0.191182	+	0.0791900i	−0.285039	+	0.958516i	$0.592006\pi$
$488$	7.85509e56	+	1.89639e57i	0.124201	+	0.299848i
$489$		−	8.08603e57i		−	1.22347i
$490$	−1.28987e58	+	5.34282e57i	−1.86780	+	0.773668i
$491$	−7.42773e57	−	7.42773e57i	−1.02945	−	1.02945i	−0.999553	−	0.0298934i	$-0.990483\pi$
$491$	−7.42773e57	−	7.42773e57i	−1.02945	−	1.02945i	−0.0298934	−	0.999553i	$-0.509517\pi$
$492$	2.06118e57			0.273443
$493$	9.24457e57	+	1.04021e58i	1.17403	+	1.32103i
$494$	3.89759e56			0.0473878
$495$	4.91295e57	+	4.91295e57i	0.571914	+	0.571914i
$496$	3.94600e57	−	1.63449e57i	0.439846	−	0.182190i
$497$			1.58254e58i			1.68925i
$498$	−9.30608e57	−	2.24669e58i	−0.951340	−	2.29674i
$499$	1.04095e58	+	4.31176e57i	1.01922	+	0.422175i	0.828810	−	0.559530i	$-0.189018\pi$
$499$	1.04095e58	+	4.31176e57i	1.01922	+	0.422175i	0.190410	+	0.981705i	$0.439018\pi$
$500$	−7.63440e57	+	1.84311e58i	−0.716011	+	1.72860i
$501$	9.05862e57	−	9.05862e57i	0.813862	−	0.813862i
$502$	−2.25542e58	+	2.25542e58i	−1.94132	+	1.94132i
$503$	7.94743e57	−	1.91868e58i	0.655413	−	1.58231i	−0.149400	−	0.988777i	$-0.547734\pi$
$503$	7.94743e57	−	1.91868e58i	0.655413	−	1.58231i	0.804812	−	0.593529i	$-0.202266\pi$
$504$	−2.15288e58	−	8.91751e57i	−1.70123	−	0.704672i
$505$	5.85291e57	+	1.41302e58i	0.443208	+	1.07000i
$506$		−	5.58568e58i		−	4.05359i
$507$	1.29063e58	−	5.34596e57i	0.897699	−	0.371839i
$508$	2.53497e58	+	2.53497e58i	1.69006	+	1.69006i
$509$	−1.99441e58			−1.27463			−0.637314	−	0.770605i	$-0.719954\pi$
$509$	−1.99441e58			−1.27463			−0.637314	+	0.770605i	$0.719954\pi$
$510$	8.61787e57	+	2.48473e58i	0.528009	+	1.52237i
$511$	−1.87629e58			−1.10217
$512$	8.56939e57	+	8.56939e57i	0.482665	+	0.482665i
$513$	−1.49916e56	+	6.20972e55i	−0.00809700	+	0.00335389i
$514$		−	6.18230e57i		−	0.320216i
$515$	3.35882e57	+	8.10891e57i	0.166852	+	0.402816i
$516$	8.37070e58	+	3.46726e58i	3.98835	+	1.65203i
$517$	−8.35015e57	+	2.01590e58i	−0.381634	+	0.921347i
$518$	2.28803e58	−	2.28803e58i	1.00316	−	1.00316i
$519$	−1.07915e58	+	1.07915e58i	−0.453922	+	0.453922i
$520$	−4.59542e57	+	1.10943e58i	−0.185461	+	0.447743i
$521$	−3.08071e58	−	1.27607e58i	−1.19300	−	0.494156i	−0.304268	−	0.952586i	$-0.598412\pi$
$521$	−3.08071e58	−	1.27607e58i	−1.19300	−	0.494156i	−0.888731	+	0.458430i	$0.848412\pi$
$522$	2.65961e58	+	6.42087e58i	0.988330	+	2.38604i
$523$		−	9.55367e57i		−	0.340709i	−0.985383	−	0.170355i	$-0.945509\pi$
$523$		−	9.55367e57i		−	0.340709i	0.985383	−	0.170355i	$-0.0544913\pi$
$524$	−1.00705e58	+	4.17132e57i	−0.344688	+	0.142774i
$525$	−2.43319e58	−	2.43319e58i	−0.799377	−	0.799377i
$526$	−2.93522e58			−0.925649
$527$	3.37911e58	−	3.00310e58i	1.02300	−	0.909162i
$528$	−2.13509e58			−0.620564
$529$	6.35957e58	+	6.35957e58i	1.77472	+	1.77472i
$530$	−1.05431e58	+	4.36711e57i	−0.282513	+	0.117021i
$531$		−	4.00708e58i		−	1.03109i
$532$	2.37992e57	+	5.74563e57i	0.0588115	+	0.141983i
$533$	2.37520e57	+	9.83839e56i	0.0563722	+	0.0233501i
$534$	−1.61771e58	+	3.90549e58i	−0.368776	+	0.890304i
$535$	−2.48615e58	+	2.48615e58i	−0.544403	+	0.544403i
$536$	2.93491e58	−	2.93491e58i	0.617379	−	0.617379i
$537$	−1.61511e58	+	3.89923e58i	−0.326404	+	0.788010i
$538$	−9.20409e58	−	3.81246e58i	−1.78715	−	0.740263i
$539$	−4.59102e58	−	1.10837e59i	−0.856545	−	2.06788i
$540$		−	1.15427e58i		−	0.206938i
$541$	−8.27568e58	+	3.42790e58i	−1.42581	+	0.590591i	−0.956314	−	0.292342i	$-0.905565\pi$
$541$	−8.27568e58	+	3.42790e58i	−1.42581	+	0.590591i	−0.469499	+	0.882933i	$0.655565\pi$
$542$	6.52353e58	+	6.52353e58i	1.08018	+	1.08018i
$543$	−4.44410e58			−0.707273
$544$	4.06996e58	+	1.97379e58i	0.622607	+	0.301942i
$545$	7.86475e58			1.15654
$546$	−1.01435e59	−	1.01435e59i	−1.43399	−	1.43399i
$547$	−7.05402e58	+	2.92187e58i	−0.958759	+	0.397131i	−0.806516	−	0.591212i	$-0.798650\pi$
$547$	−7.05402e58	+	2.92187e58i	−0.958759	+	0.397131i	−0.152243	+	0.988343i	$0.548650\pi$
$548$			1.85045e59i			2.41822i
$549$	6.83907e57	+	1.65110e58i	0.0859393	+	0.207476i
$550$	−8.27265e58	−	3.42665e58i	−0.999648	−	0.414068i
$551$	3.07434e57	−	7.42211e57i	0.0357267	−	0.0862518i
$552$	2.06387e59	−	2.06387e59i	2.30671	−	2.30671i
$553$	−5.27264e58	+	5.27264e58i	−0.566811	+	0.566811i
$554$	9.87124e58	−	2.38313e59i	1.02073	−	2.46427i
$555$	−4.65765e58	−	1.92926e58i	−0.463306	−	0.191908i
$556$	6.68163e58	+	1.61309e59i	0.639403	+	1.54366i
$557$		−	3.06292e58i		−	0.282000i	−0.990010	−	0.141000i	$-0.954968\pi$
$557$		−	3.06292e58i		−	0.282000i	0.990010	−	0.141000i	$-0.0450318\pi$
$558$	2.08582e59	−	8.63973e58i	1.84774	−	0.765359i
$559$	7.99096e58	+	7.99096e58i	0.681154	+	0.681154i
$560$	−4.94507e58			−0.405629
$561$	−2.13509e59	+	7.40522e58i	−1.68545	+	0.584570i
$562$	2.41750e59			1.83669
$563$	−1.13033e58	−	1.13033e58i	−0.0826557	−	0.0826557i	0.664570	−	0.747226i	$-0.268615\pi$
$563$	−1.13033e58	−	1.13033e58i	−0.0826557	−	0.0826557i	−0.747226	+	0.664570i	$0.768615\pi$
$564$	−2.43207e59	+	1.00740e59i	−1.71189	+	0.709087i
$565$			2.47741e58i			0.167864i
$566$	3.64413e58	+	8.79770e58i	0.237706	+	0.573873i
$567$	2.68429e59	+	1.11187e59i	1.68575	+	0.698262i
$568$	−8.23482e58	+	1.98806e59i	−0.497926	+	1.20210i
$569$	−1.23684e59	+	1.23684e59i	−0.720114	+	0.720114i	−0.968628	−	0.248514i	$-0.920058\pi$
$569$	−1.23684e59	+	1.23684e59i	−0.720114	+	0.720114i	0.248514	+	0.968628i	$0.420058\pi$
$570$	1.07353e58	−	1.07353e58i	0.0601875	−	0.0601875i
$571$	−6.04106e57	+	1.45844e58i	−0.0326165	+	0.0787432i	−0.939348	−	0.342964i	$-0.888569\pi$
$571$	−6.04106e57	+	1.45844e58i	−0.0326165	+	0.0787432i	0.906732	+	0.421707i	$0.138569\pi$
$572$	−2.20102e59	−	9.11691e58i	−1.14448	−	0.474060i
$573$	2.26932e57	+	5.47862e57i	0.0113650	+	0.0274376i
$574$			6.42754e58i			0.310055i
$575$	1.86274e59	−	7.71573e58i	0.865554	−	0.358524i
$576$	2.08033e59	+	2.08033e59i	0.931211	+	0.931211i
$577$	−3.39692e59			−1.46489			−0.732446	−	0.680826i	$-0.761621\pi$
$577$	−3.39692e59			−1.46489			−0.732446	+	0.680826i	$0.761621\pi$
$578$	−3.97382e59	−	4.69873e58i	−1.65105	−	0.195223i
$579$	2.47441e59			0.990566
$580$	4.04083e59	+	4.04083e59i	1.55872	+	1.55872i
$581$	4.47133e59	−	1.85209e59i	1.66207	−	0.688453i
$582$		−	4.05555e59i		−	1.45280i
$583$	−3.75261e58	−	9.05959e58i	−0.129556	−	0.312777i
$584$	−2.35708e59	−	9.76335e58i	−0.784329	−	0.324880i
$585$	−4.00102e58	+	9.65932e58i	−0.128327	+	0.309810i
$586$	−2.41307e59	+	2.41307e59i	−0.746054	+	0.746054i
$587$	3.94291e59	−	3.94291e59i	1.17516	−	1.17516i	0.194198	−	0.980962i	$-0.437789\pi$
$587$	3.94291e59	−	3.94291e59i	1.17516	−	1.17516i	0.980962	−	0.194198i	$-0.0622105\pi$
$588$	5.53879e59	−	1.33718e60i	1.59148	−	3.84218i
$589$	−2.41107e58	−	9.98699e57i	−0.0667931	−	0.0276666i
$590$	−1.97565e59	−	4.76963e59i	−0.527705	−	1.27399i
$591$			2.22852e59i			0.573966i
$592$	6.69543e58	−	2.77334e58i	0.166288	−	0.0688789i
$593$	4.46106e59	+	4.46106e59i	1.06847	+	1.06847i	0.997477	+	0.0709927i	$0.0226167\pi$
$593$	4.46106e59	+	4.46106e59i	1.06847	+	1.06847i	0.0709927	+	0.997477i	$0.477383\pi$
$594$	1.55410e59			0.358979
$595$	−4.94508e59	+	1.71512e59i	−1.10169	+	0.382102i
$596$	4.15317e59			0.892452
$597$	1.92686e59	+	1.92686e59i	0.399394	+	0.399394i
$598$	7.76542e59	−	3.21654e59i	1.55271	−	0.643152i
$599$			6.42094e58i			0.123857i	0.998081	+	0.0619287i	$0.0197252\pi$
$599$			6.42094e58i			0.123857i	−0.998081	+	0.0619287i	$0.980275\pi$
$600$	−1.79057e59	−	4.32281e59i	−0.333226	−	0.804479i
$601$	−6.15422e59	−	2.54916e59i	−1.10502	−	0.457716i	−0.245803	−	0.969320i	$-0.579052\pi$
$601$	−6.15422e59	−	2.54916e59i	−1.10502	−	0.457716i	−0.859222	+	0.511603i	$0.829052\pi$
$602$	−1.08122e60	+	2.61030e60i	−1.87322	+	4.52236i
$603$	2.55529e59	−	2.55529e59i	0.427188	−	0.427188i
$604$	1.06164e60	−	1.06164e60i	1.71271	−	1.71271i
$605$	−1.20566e59	+	2.91071e59i	−0.187708	+	0.453167i
$606$	−2.29523e60	−	9.50714e59i	−3.44877	−	1.42853i
$607$	3.59576e58	+	8.68092e58i	0.0521475	+	0.125895i	0.947806	−	0.318847i	$-0.103295\pi$
$607$	3.59576e58	+	8.68092e58i	0.0521475	+	0.125895i	−0.895659	+	0.444742i	$0.853295\pi$
$608$		−	2.61122e58i		−	0.0365525i
$609$	−2.73171e60	+	1.13151e60i	−3.69117	+	1.52893i
$610$	1.62811e59	+	1.62811e59i	0.212370	+	0.212370i
$611$	−3.28343e59			−0.413468
$612$	−1.14756e60	−	5.56524e59i	−1.39514	−	0.676595i
$613$	8.51075e57			0.00999005			0.00499502	−	0.999988i	$-0.498410\pi$
$613$	8.51075e57			0.00999005			0.00499502	+	0.999988i	$0.498410\pi$
$614$	−3.75933e58	−	3.75933e58i	−0.0426079	−	0.0426079i
$615$	9.25198e58	−	3.83230e58i	0.101256	−	0.0419415i
$616$		−	2.57979e60i		−	2.72646i
$617$	−4.07986e59	−	9.84965e59i	−0.416403	−	1.00529i	−0.983381	−	0.181554i	$-0.941887\pi$
$617$	−4.07986e59	−	9.84965e59i	−0.416403	−	1.00529i	0.566978	−	0.823733i	$-0.308113\pi$
$618$	−1.31717e60	−	5.45588e59i	−1.29834	−	0.537790i
$619$	−4.99698e59	+	1.20638e60i	−0.475728	+	1.14851i	0.485867	+	0.874033i	$0.338504\pi$
$619$	−4.99698e59	+	1.20638e60i	−0.475728	+	1.14851i	−0.961594	+	0.274475i	$0.911496\pi$
$620$	1.31266e60	−	1.31266e60i	1.20707	−	1.20707i
$621$	−2.47441e59	+	2.47441e59i	−0.219787	+	0.219787i
$622$	7.61203e59	−	1.83771e60i	0.653141	−	1.57682i
$623$	−7.77266e59	−	3.21954e59i	−0.644283	−	0.266871i
$624$	−1.22950e59	−	2.96828e59i	−0.0984602	−	0.237704i
$625$			3.22923e59i			0.249849i
$626$	2.76895e60	−	1.14694e60i	2.06999	−	0.857416i
$627$	9.22474e58	+	9.22474e58i	0.0666350	+	0.0666350i
$628$	−6.50810e59			−0.454278
$629$	5.73356e59	−	5.09555e59i	0.386754	−	0.343718i
$630$	−2.61391e60			−1.70400
$631$	2.12412e60	+	2.12412e60i	1.33828	+	1.33828i	0.897724	+	0.440559i	$0.145220\pi$
$631$	2.12412e60	+	2.12412e60i	1.33828	+	1.33828i	0.440559	+	0.897724i	$0.354780\pi$
$632$	−9.36738e59	+	3.88010e59i	−0.570428	+	0.236279i
$633$		−	7.43747e59i		−	0.437770i
$634$	−7.29297e59	−	1.76068e60i	−0.414940	−	1.00175i
$635$	1.60918e60	+	6.66546e59i	0.885056	+	0.366602i
$636$	4.52729e59	−	1.09299e60i	0.240719	−	0.581148i
$637$	1.27652e60	−	1.27652e60i	0.656191	−	0.656191i
$638$	−5.44055e60	+	5.44055e60i	−2.70395	+	2.70395i
$639$	−7.16969e59	+	1.73092e60i	−0.344534	+	0.831778i
$640$	2.52911e60	+	1.04759e60i	1.17516	+	0.486768i
$641$	7.88500e59	+	1.90361e60i	0.354286	+	0.855322i	0.996081	+	0.0884456i	$0.0281900\pi$
$641$	7.88500e59	+	1.90361e60i	0.354286	+	0.855322i	−0.641795	+	0.766876i	$0.721810\pi$
$642$		−	5.71110e60i		−	2.48151i
$643$	−3.79239e60	+	1.57086e60i	−1.59359	+	0.660087i	−0.990491	−	0.137580i	$-0.956068\pi$
$643$	−3.79239e60	+	1.57086e60i	−1.59359	+	0.660087i	−0.603099	+	0.797666i	$0.706068\pi$
$644$	9.48333e60	+	9.48333e60i	3.85403	+	3.85403i
$645$	4.40199e60			1.73028
$646$	7.56945e58	+	2.18244e59i	0.0287783	+	0.0829744i
$647$	1.51290e60			0.556377			0.278189	−	0.960526i	$-0.410266\pi$
$647$	1.51290e60			0.556377			0.278189	+	0.960526i	$0.410266\pi$
$648$	2.79357e60	+	2.79357e60i	0.993794	+	0.993794i
$649$	4.09849e60	−	1.69765e60i	1.41047	−	0.584234i
$650$		−	1.34742e60i		−	0.448607i
$651$	3.67572e60	+	8.87397e60i	1.18400	+	2.85842i
$652$	4.66755e60	+	1.93336e60i	1.45467	+	0.602545i
$653$	2.43473e60	−	5.87796e60i	0.734205	−	1.77253i	0.106162	−	0.994349i	$-0.466144\pi$
$653$	2.43473e60	−	5.87796e60i	0.734205	−	1.77253i	0.628043	−	0.778178i	$-0.283856\pi$
$654$	−9.03333e60	+	9.03333e60i	−2.63588	+	2.63588i
$655$	−3.74474e59	+	3.74474e59i	−0.105739	+	0.105739i
$656$	−5.50897e58	+	1.32998e59i	−0.0150535	+	0.0363424i
$657$	−2.05220e60	−	8.50050e59i	−0.542706	−	0.224796i
$658$	−3.14144e60	−	7.58410e60i	−0.804028	−	1.94110i
$659$			1.82029e60i			0.450924i	0.974252	+	0.225462i	$0.0723892\pi$
$659$			1.82029e60i			0.450924i	−0.974252	+	0.225462i	$0.927611\pi$
$660$	−8.57350e60	+	3.55126e60i	−2.05572	+	0.851507i
$661$	−8.33693e59	−	8.33693e59i	−0.193497	−	0.193497i	0.603708	−	0.797205i	$-0.293689\pi$
$661$	−8.33693e59	−	8.33693e59i	−0.193497	−	0.193497i	−0.797205	+	0.603708i	$0.793689\pi$
$662$	5.69107e60			1.27864
$663$	−2.25901e60	−	2.54185e60i	−0.491334	−	0.552853i
$664$	6.58083e60			1.38569
$665$	2.13654e59	+	2.13654e59i	0.0435557	+	0.0435557i
$666$	3.53914e60	−	1.46596e60i	0.698557	−	0.289352i
$667$		−	1.73247e61i		−	3.31101i
$668$	3.06305e60	+	7.39487e60i	0.566840	+	1.36847i
$669$	−3.87068e60	−	1.60329e60i	−0.693626	−	0.287309i
$670$	1.78171e60	−	4.30143e60i	0.309192	−	0.746456i
$671$	−1.39901e60	+	1.39901e60i	−0.235119	+	0.235119i
$672$	−6.79573e60	+	6.79573e60i	−1.10611	+	1.10611i
$673$	−1.23840e60	+	2.98976e60i	−0.195226	+	0.471317i	−0.990932	−	0.134366i	$-0.957100\pi$
$673$	−1.23840e60	+	2.98976e60i	−0.195226	+	0.471317i	0.795706	+	0.605683i	$0.207100\pi$
$674$	−1.59520e61	−	6.60753e60i	−2.43572	−	1.00891i
$675$	2.14674e59	+	5.18269e59i	0.0317503	+	0.0766521i
$676$			8.72820e60i			1.25046i
$677$	−3.02294e60	+	1.25214e60i	−0.419539	+	0.173779i	−0.582458	−	0.812861i	$-0.697909\pi$
$677$	−3.02294e60	+	1.25214e60i	−0.419539	+	0.173779i	0.162919	+	0.986639i	$0.447909\pi$
$678$	−2.84552e60	−	2.84552e60i	−0.382581	−	0.382581i
$679$	8.07132e60			1.05134
$680$	−7.10470e60	−	4.18580e59i	−0.896612	−	0.0528247i
$681$	1.98919e61			2.43228
$682$	1.76736e61	+	1.76736e61i	2.09393	+	2.09393i
$683$	−3.26129e60	+	1.35087e60i	−0.374408	+	0.155085i	−0.561949	−	0.827172i	$-0.689948\pi$
$683$	−3.26129e60	+	1.35087e60i	−0.374408	+	0.155085i	0.187541	+	0.982257i	$0.439948\pi$
$684$			7.36254e59i			0.0819071i
$685$	3.44050e60	+	8.30609e60i	0.370914	+	0.895467i
$686$	1.74529e61	+	7.22922e60i	1.82347	+	0.755306i
$687$	−1.70819e60	+	4.12394e60i	−0.172968	+	0.417582i
$688$	−4.47451e60	+	4.47451e60i	−0.439131	+	0.439131i
$689$	1.04340e60	−	1.04340e60i	0.0992519	−	0.0992519i
$690$	1.25292e61	−	3.02482e61i	1.15523	−	2.78897i
$691$	−1.63027e61	−	6.75279e60i	−1.45707	−	0.603539i	−0.493202	−	0.869915i	$-0.664174\pi$
$691$	−1.63027e61	−	6.75279e60i	−1.45707	−	0.603539i	−0.963869	+	0.266376i	$0.914174\pi$
$692$	−3.64899e60	−	8.80944e60i	−0.316149	−	0.763251i
$693$		−	2.24610e61i		−	1.88654i
$694$	5.33590e60	−	2.21020e60i	0.434489	−	0.179971i
$695$	5.99834e60	+	5.99834e60i	0.473541	+	0.473541i
$696$	−4.02050e61			−3.07738
$697$	−8.96144e58	+	1.52106e60i	−0.00665079	+	0.112886i
$698$	−1.79277e61			−1.29013
$699$	−7.57446e60	−	7.57446e60i	−0.528558	−	0.528558i
$700$	1.98630e61	−	8.22753e60i	1.34412	−	0.556752i
$701$		−	2.27353e61i		−	1.49198i	−0.665956	−	0.745991i	$-0.731976\pi$
$701$		−	2.27353e61i		−	1.49198i	0.665956	−	0.745991i	$-0.268024\pi$
$702$	8.94935e59	+	2.16056e60i	0.0569565	+	0.137505i
$703$	−4.09102e59	−	1.69456e59i	−0.0252518	−	0.0104596i
$704$	−1.24642e61	+	3.00914e61i	−0.746198	+	1.80148i
$705$	−9.04375e60	+	9.04375e60i	−0.525149	+	0.525149i
$706$	−4.07718e61	+	4.07718e61i	−2.29646	+	2.29646i
$707$	1.89210e61	−	4.56793e61i	1.03378	−	2.49576i
$708$	4.94458e61	+	2.04811e61i	2.62068	+	1.08552i
$709$	4.96674e60	+	1.19908e61i	0.255374	+	0.616528i	0.998622	−	0.0524889i	$-0.0167154\pi$
$709$	4.96674e60	+	1.19908e61i	0.255374	+	0.616528i	−0.743247	+	0.669017i	$0.766715\pi$
$710$			2.41380e61i			1.20406i
$711$	−8.15576e60	+	3.37822e60i	−0.394701	+	0.163490i
$712$	−8.08907e60	−	8.08907e60i	−0.379821	−	0.379821i
$713$	−5.62793e61			−2.56403
$714$	3.70988e61	−	7.64980e61i	1.64002	−	3.38172i
$715$	−1.15747e61			−0.496513
$716$	−1.86460e61	−	1.86460e61i	−0.776170	−	0.776170i
$717$	−2.85068e61	+	1.18079e61i	−1.15156	+	0.476991i
$718$			4.38738e61i			1.72000i
$719$	8.96572e60	+	2.16452e61i	0.341125	+	0.823549i	0.997603	+	0.0692036i	$0.0220458\pi$
$719$	8.96572e60	+	2.16452e61i	0.341125	+	0.823549i	−0.656477	+	0.754346i	$0.727954\pi$
$720$	−5.40870e60	−	2.24036e60i	−0.199730	−	0.0827310i
$721$	1.08582e61	−	2.62141e61i	0.389180	−	0.939565i
$722$	−3.36973e61	+	3.36973e61i	−1.17232	+	1.17232i
$723$	5.75597e60	−	5.75597e60i	0.194377	−	0.194377i
$724$	1.06258e61	−	2.56529e61i	0.348323	−	0.840926i
$725$	−2.56587e61	−	1.06282e61i	−0.816522	−	0.338214i
$726$	−1.95840e61	−	4.72799e61i	−0.605012	−	1.46063i
$727$			2.94836e61i			0.884282i	0.896946	+	0.442141i	$0.145781\pi$
$727$			2.94836e61i			0.884282i	−0.896946	+	0.442141i	$0.854219\pi$
$728$	3.58652e61	−	1.48558e61i	1.04436	−	0.432586i
$729$	1.86343e61	+	1.86343e61i	0.526831	+	0.526831i
$730$	−2.86185e61			−0.785606
$731$	−2.92261e61	+	6.02644e61i	−0.779017	+	1.60634i
$732$	−2.38695e61			−0.617810
$733$	6.60865e60	+	6.60865e60i	0.166103	+	0.166103i	0.785264	−	0.619161i	$-0.212527\pi$
$733$	6.60865e60	+	6.60865e60i	0.166103	+	0.166103i	−0.619161	+	0.785264i	$0.712527\pi$
$734$	1.04965e62	−	4.34780e61i	2.56201	−	1.06122i
$735$		−	7.03198e61i		−	1.66686i
$736$	−2.15495e61	−	5.20251e61i	−0.496094	−	1.19768i
$737$	3.69616e61	+	1.53100e61i	0.826419	+	0.342314i
$738$	−2.91199e60	+	7.03016e60i	−0.0632380	+	0.152670i
$739$	3.84826e61	−	3.84826e61i	0.811726	−	0.811726i	−0.173167	−	0.984893i	$-0.555400\pi$
$739$	3.84826e61	−	3.84826e61i	0.811726	−	0.811726i	0.984893	+	0.173167i	$0.0553999\pi$
$740$	2.22728e61	−	2.22728e61i	0.456345	−	0.456345i
$741$	−7.51247e59	+	1.81367e60i	−0.0149517	+	0.0360966i
$742$	3.40834e61	+	1.41178e61i	0.658959	+	0.272950i
$743$	4.30897e60	+	1.04028e61i	0.0809308	+	0.195384i	0.959165	−	0.282846i	$-0.0912785\pi$
$743$	4.30897e60	+	1.04028e61i	0.0809308	+	0.195384i	−0.878235	+	0.478230i	$0.841279\pi$
$744$			1.30606e62i			2.38311i
$745$	1.86422e61	−	7.72186e60i	0.330474	−	0.136887i
$746$	1.25355e62	+	1.25355e62i	2.15902	+	2.15902i
$747$	5.72963e61			0.958813
$748$	8.30427e60	−	1.40951e62i	0.135026	−	2.29184i
$749$	1.13662e62			1.79579
$750$	−1.11327e62	−	1.11327e62i	−1.70916	−	1.70916i
$751$	2.17313e61	−	9.00138e60i	0.324210	−	0.134292i	−0.214642	−	0.976693i	$-0.568858\pi$
$751$	2.17313e61	−	9.00138e60i	0.324210	−	0.134292i	0.538852	+	0.842401i	$0.318858\pi$
$752$		−	1.83855e61i		−	0.266558i
$753$	−6.14793e61	−	1.48424e62i	−0.866238	−	2.09128i
$754$	−1.06966e62	−	4.43069e61i	−1.46475	−	0.606719i
$755$	2.79149e61	−	6.73925e61i	0.371515	−	0.896916i
$756$	−2.63854e61	+	2.63854e61i	−0.341307	+	0.341307i
$757$	1.01362e61	−	1.01362e61i	0.127442	−	0.127442i	−0.640509	−	0.767951i	$-0.721277\pi$
$757$	1.01362e61	−	1.01362e61i	0.127442	−	0.127442i	0.767951	+	0.640509i	$0.221277\pi$
$758$	−2.79214e61	+	6.74081e61i	−0.341231	+	0.823805i
$759$	2.59919e62	+	1.07662e62i	3.08774	+	1.27898i
$760$	1.57226e60	+	3.79577e60i	0.0181565	+	0.0438337i
$761$		−	7.18585e61i		−	0.806693i	−0.915047	−	0.403346i	$-0.867847\pi$
$761$		−	7.18585e61i		−	0.806693i	0.915047	−	0.403346i	$-0.132153\pi$
$762$	−2.61387e62	+	1.08270e62i	−2.85267	+	1.18162i
$763$	−1.79780e62	−	1.79780e62i	−1.90750	−	1.90750i
$764$	−3.70505e60			−0.0382196
$765$	−6.18574e61	−	3.64439e60i	−0.620399	−	0.0365514i
$766$	2.54297e62			2.47983
$767$	4.72027e61	+	4.72027e61i	0.447576	+	0.447576i
$768$	−2.05020e62	+	8.49221e61i	−1.89030	+	0.782987i
$769$			9.49404e61i			0.851206i	0.904910	+	0.425603i	$0.139938\pi$
$769$			9.49404e61i			0.851206i	−0.904910	+	0.425603i	$0.860062\pi$
$770$	−1.10742e62	−	2.67354e62i	−0.965517	−	2.33097i
$771$	2.87682e61	+	1.19162e61i	0.243918	+	0.101034i
$772$	−5.91630e61	+	1.42832e62i	−0.487841	+	1.17775i
$773$	1.17690e61	−	1.17690e61i	0.0943798	−	0.0943798i	−0.658340	−	0.752720i	$-0.728741\pi$
$773$	1.17690e61	−	1.17690e61i	0.0943798	−	0.0943798i	0.752720	+	0.658340i	$0.228741\pi$
$774$	−2.36518e62	+	2.36518e62i	−1.84474	+	1.84474i
$775$	−3.45256e61	+	8.33523e61i	−0.261912	+	0.632311i
$776$	1.01396e62	+	4.19994e61i	0.748156	+	0.309896i
$777$	6.23683e61	+	1.50570e62i	0.447623	+	1.08066i
$778$			3.80505e62i			2.65643i
$779$	8.12642e59	−	3.36607e59i	0.00551879	−	0.00228596i
$780$	−9.87419e61	−	9.87419e61i	−0.652330	−	0.652330i
$781$	−2.07415e62			−1.33304
$782$	3.30921e62	+	3.72355e62i	2.06909	+	2.32815i
$783$	4.82024e61			0.293218
$784$	7.14783e61	+	7.14783e61i	0.423037	+	0.423037i
$785$	−2.92128e61	+	1.21003e61i	−0.168219	+	0.0696786i
$786$		−	8.60230e61i		−	0.481981i
$787$	6.42449e60	+	1.55101e61i	0.0350253	+	0.0845585i	0.940424	−	0.340003i	$-0.110428\pi$
$787$	6.42449e60	+	1.55101e61i	0.0350253	+	0.0845585i	−0.905399	+	0.424562i	$0.860428\pi$
$788$	−1.28638e62	−	5.32838e61i	−0.682428	−	0.282671i
$789$	5.65753e61	−	1.36585e62i	0.292059	−	0.705094i
$790$	−8.04221e61	+	8.04221e61i	−0.404011	+	0.404011i
$791$	5.66312e61	−	5.66312e61i	0.276861	−	0.276861i
$792$	1.16877e62	−	2.82166e62i	0.556080	−	1.34250i
$793$	−2.75059e61	−	1.13933e61i	−0.127366	−	0.0527566i
$794$	2.96926e61	+	7.16842e61i	0.133816	+	0.323059i
$795$		−	5.74781e61i		−	0.252121i
$796$	−1.57296e62	+	6.51542e61i	−0.671563	+	0.278171i
$797$	−1.35001e62	−	1.35001e62i	−0.561027	−	0.561027i	0.368572	−	0.929599i	$-0.379847\pi$
$797$	−1.35001e62	−	1.35001e62i	−0.561027	−	0.561027i	−0.929599	+	0.368572i	$0.879847\pi$
$798$	−4.90798e61			−0.198537
$799$	−6.37671e61	−	1.83855e62i	−0.251097	−	0.723969i
$800$	−9.02716e61			−0.346032
$801$	−7.04279e61	−	7.04279e61i	−0.262812	−	0.262812i
$802$	−2.08466e62	+	8.63496e61i	−0.757333	+	0.313698i
$803$		−	2.45915e62i		−	0.869762i
$804$	1.84706e62	+	4.45920e62i	0.636028	+	1.53551i
$805$	6.01997e62	+	2.49355e62i	2.01829	+	0.836002i
$806$	−1.43931e62	+	3.47480e62i	−0.469840	+	1.13430i
$807$	3.54811e62	−	3.54811e62i	1.12776	−	1.12776i
$808$	4.75389e62	−	4.75389e62i	1.47131	−	1.47131i
$809$	−1.51431e62	+	3.65586e62i	−0.456374	+	1.10178i	0.513481	+	0.858101i	$0.328356\pi$
$809$	−1.51431e62	+	3.65586e62i	−0.456374	+	1.10178i	−0.969855	+	0.243683i	$0.921644\pi$
$810$	4.09427e62	+	1.69590e62i	1.20157	+	0.497706i
$811$	1.47059e62	+	3.55031e62i	0.420284	+	1.01465i	0.982264	+	0.187504i	$0.0600397\pi$
$811$	1.47059e62	+	3.55031e62i	0.420284	+	1.01465i	−0.561980	+	0.827151i	$0.689960\pi$
$812$		−	1.84739e63i		−	5.14166i
$813$	−4.29299e62	+	1.77822e62i	−1.16363	+	0.481990i
$814$	2.99880e62	+	2.99880e62i	0.791631	+	0.791631i
$815$	2.45458e62			0.631085
$816$	1.42330e62	−	1.26492e62i	0.356417	−	0.316757i
$817$	3.86646e61			0.0943061
$818$	2.88223e62	+	2.88223e62i	0.684750	+	0.684750i
$819$	3.12262e62	−	1.29343e62i	0.722628	−	0.299322i
$820$			6.25688e61i			0.141046i
$821$	−4.26707e61	−	1.03016e62i	−0.0937026	−	0.226218i	0.870078	−	0.492914i	$-0.164068\pi$
$821$	−4.26707e61	−	1.03016e62i	−0.0937026	−	0.226218i	−0.963781	+	0.266696i	$0.914068\pi$
$822$	−1.34919e63	−	5.58855e62i	−2.88623	−	1.19551i
$823$	1.91582e62	−	4.62519e62i	0.399262	−	0.963903i	−0.588580	−	0.808439i	$-0.700313\pi$
$823$	1.91582e62	−	4.62519e62i	0.399262	−	0.963903i	0.987842	−	0.155464i	$-0.0496873\pi$
$824$	2.72812e62	−	2.72812e62i	0.553897	−	0.553897i
$825$	3.18905e62	−	3.18905e62i	0.630815	−	0.630815i
$826$	−6.38678e62	+	1.54190e63i	−1.23087	+	2.97157i
$827$	−7.18135e62	−	2.97461e62i	−1.34846	−	0.558550i	−0.412596	−	0.910914i	$-0.635378\pi$
$827$	−7.18135e62	−	2.97461e62i	−1.34846	−	0.558550i	−0.935863	+	0.352364i	$0.885378\pi$
$828$	6.07605e62	+	1.46689e63i	1.11165	+	2.68377i
$829$			8.57072e62i			1.52790i	0.645275	+	0.763950i	$0.276743\pi$
$829$			8.57072e62i			1.52790i	−0.645275	+	0.763950i	$0.723257\pi$
$830$	6.81999e62	−	2.82493e62i	1.18469	−	0.490714i
$831$	9.18680e62	+	9.18680e62i	1.55504	+	1.55504i
$832$	−4.90117e62			−0.808441
$833$	9.62696e62	+	4.66873e62i	1.54747	+	0.750467i
$834$	−1.37792e63			−2.15851
$835$	2.74981e62	+	2.74981e62i	0.419801	+	0.419801i
$836$	−7.53048e61	+	3.11923e61i	−0.112044	+	0.0464101i
$837$		−	1.56585e62i		−	0.227067i
$838$	−4.29325e62	−	1.03648e63i	−0.606792	−	1.46493i
$839$	1.53914e62	+	6.37531e61i	0.212029	+	0.0878252i	0.486170	−	0.873864i	$-0.338394\pi$
$839$	1.53914e62	+	6.37531e61i	0.212029	+	0.0878252i	−0.274141	+	0.961689i	$0.588394\pi$
$840$	5.78672e62	−	1.39704e63i	0.777012	−	1.87587i
$841$	−1.14720e63	+	1.14720e63i	−1.50150	+	1.50150i
$842$	5.46255e62	−	5.46255e62i	0.696924	−	0.696924i
$843$	−4.65965e62	+	1.12494e63i	−0.579509	+	1.39906i
$844$	4.29318e62	+	1.77829e62i	0.520495	+	0.215596i
$845$	1.62281e62	+	3.91780e62i	0.191800	+	0.463045i
$846$		−	9.71838e62i		−	1.11978i
$847$	9.40960e62	−	3.89759e62i	1.05701	−	0.437827i
$848$	5.84250e61	+	5.84250e61i	0.0639864	+	0.0639864i
$849$	−4.79624e62			−0.512136
$850$	7.54485e62	−	2.61681e62i	0.785495	−	0.272436i
$851$	−9.54927e62			−0.969359
$852$	−1.76942e63	−	1.76942e63i	−1.75138	−	1.75138i
$853$	−9.78583e62	+	4.05343e62i	−0.944482	+	0.391217i	−0.801154	−	0.598458i	$-0.795780\pi$
$853$	−9.78583e62	+	4.05343e62i	−0.944482	+	0.391217i	−0.143328	+	0.989675i	$0.545780\pi$
$854$		−	7.44339e62i		−	0.700530i
$855$	1.36890e61	+	3.30481e61i	0.0125632	+	0.0303302i
$856$	1.42787e63	+	5.91444e62i	1.27792	+	0.529331i
$857$	7.44710e62	−	1.79789e63i	0.649979	−	1.56919i	−0.162827	−	0.986655i	$-0.552061\pi$
$857$	7.44710e62	−	1.79789e63i	0.649979	−	1.56919i	0.812806	−	0.582534i	$-0.197939\pi$
$858$	1.32946e63	−	1.32946e63i	1.13161	−	1.13161i
$859$	−3.75805e62	+	3.75805e62i	−0.311968	+	0.311968i	−0.845672	−	0.533704i	$-0.820800\pi$
$859$	−3.75805e62	+	3.75805e62i	−0.311968	+	0.311968i	0.533704	+	0.845672i	$0.320800\pi$
$860$	−1.05251e63	+	2.54099e63i	−0.852139	+	2.05725i
$861$	−2.99094e62	−	1.23889e62i	−0.236178	−	0.0978281i
$862$	−3.18018e62	−	7.67762e62i	−0.244932	−	0.591317i
$863$			9.82356e62i			0.737967i	0.929436	+	0.368984i	$0.120294\pi$
$863$			9.82356e62i			0.737967i	−0.929436	+	0.368984i	$0.879706\pi$
$864$	1.44749e62	−	5.99569e61i	0.106064	−	0.0439333i
$865$	−3.27583e62	−	3.27583e62i	−0.234139	−	0.234139i
$866$	−7.32510e62			−0.510715
$867$	9.84586e62	−	1.75858e63i	0.669643	−	1.19605i
$868$	−6.00124e63			−3.98168
$869$	−6.91057e62	−	6.91057e62i	−0.447289	−	0.447289i
$870$	−4.16660e63	+	1.72586e63i	−2.63098	+	1.08979i
$871$			6.02018e62i			0.370868i
$872$	−1.32299e63	−	3.19398e63i	−0.795155	−	1.91968i
$873$	8.82806e62	+	3.65670e62i	0.517677	+	0.214429i
$874$	1.10050e62	−	2.65683e62i	0.0629641	−	0.152009i
$875$	2.21562e63	−	2.21562e63i	1.23686	−	1.23686i
$876$	2.09785e63	−	2.09785e63i	1.14271	−	1.14271i
$877$	−2.74557e62	+	6.62840e62i	−0.145929	+	0.352304i	−0.979896	−	0.199511i	$-0.936065\pi$
$877$	−2.74557e62	+	6.62840e62i	−0.145929	+	0.352304i	0.833967	+	0.551815i	$0.186065\pi$
$878$	3.09627e61	+	1.28252e61i	0.0160585	+	0.00665167i
$879$	−6.57765e62	−	1.58799e63i	−0.332897	−	0.803685i
$880$		−	6.48123e62i		−	0.320096i
$881$	2.56583e63	−	1.06280e63i	1.23665	−	0.512237i	0.333983	−	0.942579i	$-0.391607\pi$
$881$	2.56583e63	−	1.06280e63i	1.23665	−	0.512237i	0.902666	+	0.430342i	$0.141607\pi$
$882$	3.77827e63	+	3.77827e63i	1.77713	+	1.77713i
$883$	9.88067e62			0.453556			0.226778	−	0.973946i	$-0.427181\pi$
$883$	9.88067e62			0.453556			0.226778	+	0.973946i	$0.427181\pi$
$884$	2.00738e63	−	6.96226e62i	0.899301	−	0.311908i
$885$	2.60026e63			1.13694
$886$	−2.02248e63	−	2.02248e63i	−0.863096	−	0.863096i
$887$	−2.63150e63	+	1.09000e63i	−1.09609	+	0.454014i	−0.856125	−	0.516768i	$-0.827135\pi$
$887$	−2.63150e63	+	1.09000e63i	−1.09609	+	0.454014i	−0.239962	+	0.970782i	$0.577135\pi$
$888$			2.21607e63i			0.900959i
$889$	−2.15478e63	−	5.20209e63i	−0.855096	−	2.06438i
$890$	−1.18554e63	−	4.91067e62i	−0.459231	−	0.190220i
$891$	−1.45727e63	+	3.51815e63i	−0.551022	+	1.33028i
$892$	1.85095e63	−	1.85095e63i	0.683204	−	0.683204i
$893$	−7.94352e61	+	7.94352e61i	−0.0286224	+	0.0286224i
$894$	−1.25430e63	+	3.02814e63i	−0.441208	+	1.06517i
$895$	−1.18364e63	−	4.90280e62i	−0.406466	−	0.168364i
$896$	−3.38660e63	−	8.17598e63i	−1.13538	−	2.74105i
$897$			4.23347e63i			1.38567i
$898$	−4.82346e63	+	1.99794e63i	−1.54141	+	0.638472i
$899$	5.48170e63	+	5.48170e63i	1.71034	+	1.71034i
$900$	2.54528e63			0.775392
$901$	7.86889e62	+	3.81613e62i	0.234062	+	0.113512i
$902$	−8.42422e62			−0.244675
$903$	−1.00625e64	−	1.00625e64i	−2.85378	−	2.85378i
$904$	1.00611e63	−	4.16745e62i	0.278628	−	0.115411i
$905$		−	1.34904e63i		−	0.364821i
$906$	4.53433e63	+	1.09469e64i	1.19745	+	2.89090i
$907$	−2.33175e63	−	9.65840e62i	−0.601346	−	0.249086i	0.0611774	−	0.998127i	$-0.480514\pi$
$907$	−2.33175e63	−	9.65840e62i	−0.601346	−	0.249086i	−0.662523	+	0.749041i	$0.730514\pi$
$908$	−4.75613e63	+	1.14823e64i	−1.19787	+	2.89190i
$909$	4.13900e63	−	4.13900e63i	1.01806	−	1.01806i
$910$	3.07914e63	−	3.07914e63i	0.739673	−	0.739673i
$911$	2.03572e63	−	4.91467e63i	0.477611	−	1.15305i	−0.483116	−	0.875556i	$-0.660495\pi$
$911$	2.03572e63	−	4.91467e63i	0.477611	−	1.15305i	0.960726	−	0.277497i	$-0.0895050\pi$
$912$	−1.01556e62	−	4.20658e61i	−0.0232710	−	0.00963918i
$913$	2.42743e63	+	5.86033e63i	0.543281	+	1.31160i
$914$			5.44691e63i			1.19071i
$915$	−1.07142e63	+	4.43798e62i	−0.228775	+	0.0947615i
$916$	−1.97206e63	−	1.97206e63i	−0.411308	−	0.411308i
$917$	1.71202e63			0.348793
$918$	−1.03600e63	+	9.20717e62i	−0.206178	+	0.183235i
$919$	5.15781e63			1.00273			0.501363	−	0.865237i	$-0.332832\pi$
$919$	5.15781e63			1.00273			0.501363	+	0.865237i	$0.332832\pi$
$920$	6.26504e63	+	6.26504e63i	1.18983	+	1.18983i
$921$	2.47393e62	−	1.02474e62i	0.0458993	−	0.0190121i
$922$		−	7.57931e63i		−	1.37377i
$923$	−1.19441e63	−	2.88356e63i	−0.211503	−	0.510614i
$924$	2.77160e64	+	1.14803e64i	4.79494	+	1.98613i
$925$	−5.85819e62	+	1.41429e63i	−0.0990185	+	0.239052i
$926$	−3.03650e63	+	3.03650e63i	−0.501460	+	0.501460i
$927$	2.37525e63	−	2.37525e63i	0.383262	−	0.383262i
$928$	−2.96838e63	+	7.16630e63i	−0.467991	+	1.12983i
$929$	8.77359e63	+	3.63414e63i	1.35157	+	0.559840i	0.936730	−	0.350053i	$-0.113836\pi$
$929$	8.77359e63	+	3.63414e63i	1.35157	+	0.559840i	0.414843	+	0.909893i	$0.363836\pi$
$930$	5.60646e63	+	1.35352e64i	0.843928	+	2.03742i
$931$		−	6.17650e62i		−	0.0908499i
$932$	6.18330e63	−	2.56121e63i	0.888747	−	0.368131i
$933$	7.08423e63	+	7.08423e63i	0.995033	+	0.995033i
$934$	−1.08430e63			−0.148830
$935$	−2.24791e63	−	6.48124e63i	−0.301529	−	0.869378i
$936$	4.59582e63			0.602465
$937$	−5.13572e63	−	5.13572e63i	−0.657962	−	0.657962i	0.296936	−	0.954897i	$-0.404035\pi$
$937$	−5.13572e63	−	5.13572e63i	−0.657962	−	0.657962i	−0.954897	+	0.296936i	$0.904035\pi$
$938$	−1.39054e64	+	5.75982e63i	−1.74110	+	0.721187i
$939$			1.50955e64i			1.84730i
$940$	−3.05803e63	−	7.38273e63i	−0.365757	−	0.883015i
$941$	5.96882e63	+	2.47237e63i	0.697769	+	0.289025i	0.703233	−	0.710960i	$-0.251739\pi$
$941$	5.96882e63	+	2.47237e63i	0.697769	+	0.289025i	−0.00546396	+	0.999985i	$0.501739\pi$
$942$	1.96551e63	−	4.74516e63i	0.224585	−	0.542196i
$943$	1.34129e63	−	1.34129e63i	0.149803	−	0.149803i
$944$	−2.64310e63	+	2.64310e63i	−0.288546	+	0.288546i
$945$	−6.93779e62	+	1.67493e63i	−0.0740350	+	0.178736i
$946$	−3.42117e64	−	1.41710e64i	−3.56875	−	1.47822i
$947$	2.75794e62	+	6.65827e62i	0.0281230	+	0.0678948i	0.937317	−	0.348478i	$-0.113301\pi$
$947$	2.75794e62	+	6.65827e62i	0.0281230	+	0.0678948i	−0.909194	+	0.416372i	$0.863301\pi$
$948$		−	1.17906e64i		−	1.17532i
$949$	3.41880e63	−	1.41611e63i	0.333158	−	0.137999i
$950$	−3.25978e62	−	3.25978e62i	−0.0310549	−	0.0310549i
$951$	9.59869e63			0.893986
$952$	1.52838e64	+	1.71975e64i	1.39167	+	1.56592i
$953$	1.06621e64			0.949173			0.474587	−	0.880209i	$-0.342598\pi$
$953$	1.06621e64			0.949173			0.474587	+	0.880209i	$0.342598\pi$
$954$	3.08829e63	+	3.08829e63i	0.268799	+	0.268799i
$955$	−1.66308e62	+	6.88869e61i	−0.0141527	+	0.00586224i
$956$		−	1.92784e64i		−	1.60408i
$957$	−1.48301e64	−	3.58031e64i	−1.20653	−	2.91282i
$958$	−2.46350e64	−	1.02041e64i	−1.95972	−	0.811741i
$959$	1.11223e64	−	2.68515e64i	0.865154	−	2.08867i
$960$	−1.34996e64	+	1.34996e64i	−1.02681	+	1.02681i
$961$	8.30043e63	−	8.30043e63i	0.617373	−	0.617373i
$962$	−2.44217e63	+	5.89592e63i	−0.177628	+	0.428832i
$963$	1.24318e64	+	5.14943e63i	0.884239	+	0.366264i
$964$	1.94631e63	+	4.69880e63i	0.135380	+	0.326836i
$965$			7.51127e63i			0.510948i
$966$	−9.77850e64	+	4.05039e64i	−6.50525	+	2.69456i
$967$	7.09625e63	+	7.09625e63i	0.461700	+	0.461700i	0.899212	−	0.437512i	$-0.144140\pi$
$967$	7.09625e63	+	7.09625e63i	0.461700	+	0.461700i	−0.437512	+	0.899212i	$0.644140\pi$
$968$	1.38489e64			0.881242
$969$	−1.16146e63	−	6.84284e61i	−0.0722841	−	0.00425868i
$970$	1.23109e64			0.749374
$971$	−1.12705e64	−	1.12705e64i	−0.671010	−	0.671010i	0.286939	−	0.957949i	$-0.407362\pi$
$971$	−1.12705e64	−	1.12705e64i	−0.671010	−	0.671010i	−0.957949	+	0.286939i	$0.907362\pi$
$972$	−3.78011e64	+	1.56577e64i	−2.20130	+	0.911810i
$973$		−	2.74232e64i		−	1.56204i
$974$	−2.36299e63	−	5.70477e63i	−0.131657	−	0.317849i
$975$	6.26997e63	+	2.59711e63i	0.341717	+	0.141544i
$976$	6.37965e62	−	1.54018e63i	0.0340115	−	0.0821110i
$977$	−2.46340e63	+	2.46340e63i	−0.128470	+	0.128470i	−0.768418	−	0.639948i	$-0.778956\pi$
$977$	−2.46340e63	+	2.46340e63i	−0.128470	+	0.128470i	0.639948	+	0.768418i	$0.278956\pi$
$978$	−2.81929e64	+	2.81929e64i	−1.43831	+	1.43831i
$979$	4.21968e63	−	1.01872e64i	0.210597	−	0.508425i
$980$	4.05912e64	+	1.68134e64i	1.98185	+	0.820909i
$981$	−1.15187e64	−	2.78085e64i	−0.550198	−	1.32829i
$982$			5.17952e64i			2.42043i
$983$	−2.61937e64	+	1.08498e64i	−1.19756	+	0.496045i	−0.890209	−	0.455552i	$-0.849442\pi$
$983$	−2.61937e64	+	1.08498e64i	−1.19756	+	0.496045i	−0.307349	+	0.951597i	$0.599442\pi$
$984$	−3.11269e63	−	3.11269e63i	−0.139233	−	0.139233i
$985$	−6.76485e63			−0.296060
$986$	4.03576e63	−	6.85003e64i	0.172811	−	2.93318i
$987$	4.13462e64			1.73228
$988$	−8.67294e62	−	8.67294e62i	−0.0355543	−	0.0355543i
$989$	7.70341e64	−	3.19086e64i	3.09003	−	1.27993i
$990$		−	3.42591e64i		−	1.34468i
$991$	−1.24874e63	−	3.01473e63i	−0.0479610	−	0.115788i	0.898083	−	0.439825i	$-0.144960\pi$
$991$	−1.24874e63	−	3.01473e63i	−0.0479610	−	0.115788i	−0.946044	+	0.324037i	$0.894960\pi$
$992$	2.32797e64	+	9.64277e63i	0.874936	+	0.362410i
$993$	−1.09694e64	+	2.64824e64i	−0.403434	+	0.973975i
$994$	5.51771e64	−	5.51771e64i	1.98587	−	1.98587i
$995$	−5.84912e63	+	5.84912e63i	−0.206013	+	0.206013i
$996$	−2.92855e64	+	7.07013e64i	−1.00943	+	2.43698i
$997$	4.70511e62	+	1.94892e62i	0.0158717	+	0.00657428i	0.390605	−	0.920558i	$-0.372266\pi$
$997$	4.70511e62	+	1.94892e62i	0.0158717	+	0.00657428i	−0.374733	+	0.927133i	$0.622266\pi$
$998$	−2.12605e64	−	5.13274e64i	−0.701886	−	1.69450i
$999$		−	2.65688e63i		−	0.0858449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.6	✓	252
17.9	even	8	inner	17.44.d.a.9.6	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.6	✓	252	1.1	even	1	trivial
17.44.d.a.9.6	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+(-3.48662e6 - 3.48662e6i) q^{2} +(2.29447e10 - 9.50399e9i) q^{3} +1.55169e13i q^{4} +(2.88501e14 + 6.96503e14i) q^{5} +(-1.13136e17 - 4.68624e16i) q^{6} +(9.32651e17 - 2.25162e18i) q^{7} +(2.34328e19 - 2.34328e19i) q^{8} +(2.04019e20 - 2.04019e20i) q^{9} +(1.42255e21 - 3.43433e21i) q^{10} +(2.95107e22 + 1.22238e22i) q^{11} +(1.47472e23 + 3.56030e23i) q^{12} +4.80661e23i q^{13} +(-1.11023e25 + 4.59874e24i) q^{14} +(1.32391e25 + 1.32391e25i) q^{15} -2.69144e25 q^{16} +(-2.69145e26 + 9.33484e25i) q^{17} -1.42267e27 q^{18} +(1.16285e26 + 1.16285e26i) q^{19} +(-1.08075e28 + 4.47663e27i) q^{20} -6.05266e28i q^{21} +(-6.02731e28 - 1.45512e29i) q^{22} +(3.27648e29 + 1.35716e29i) q^{23} +(3.14953e29 - 7.60363e29i) q^{24} +(4.02004e29 - 4.02004e29i) q^{25} +(1.67588e30 - 1.67588e30i) q^{26} +(-3.77602e29 + 9.11611e29i) q^{27} +(3.49381e31 + 1.44718e31i) q^{28} +(-1.86945e31 - 4.51325e31i) q^{29} -9.23193e31i q^{30} +(-1.46613e32 + 6.07290e31i) q^{31} +(-1.12277e32 - 1.12277e32i) q^{32} +7.93288e32 q^{33} +(1.26387e33 + 6.12934e32i) q^{34} +1.83733e33 q^{35} +(3.16573e33 + 3.16573e33i) q^{36} +(-2.48768e33 + 1.03043e33i) q^{37} -8.10881e32i q^{38} +(4.56819e33 + 1.10286e34i) q^{39} +(2.30814e34 + 9.56063e33i) q^{40} +(2.04685e33 - 4.94153e33i) q^{41} +(-2.11033e35 + 2.11033e35i) q^{42} +(1.66250e35 - 1.66250e35i) q^{43} +(-1.89675e35 + 4.57915e35i) q^{44} +(2.00959e35 + 8.32400e34i) q^{45} +(-6.69192e35 - 1.61557e36i) q^{46} +6.83109e35i q^{47} +(-6.17542e35 + 2.55794e35i) q^{48} +(-2.65576e36 - 2.65576e36i) q^{49} -2.80327e36 q^{50} +(-5.28825e36 + 4.69980e36i) q^{51} -7.45835e36 q^{52} +(-2.17077e36 - 2.17077e36i) q^{53} +(4.49499e36 - 1.86189e36i) q^{54} +2.40809e37i q^{55} +(-3.09071e37 - 7.46164e37i) q^{56} +(3.77329e36 + 1.56295e36i) q^{57} +(-9.21792e37 + 2.22540e38i) q^{58} +(9.82038e37 - 9.82038e37i) q^{59} +(-2.05430e38 + 2.05430e38i) q^{60} +(-2.37035e37 + 5.72252e37i) q^{61} +(7.22921e38 + 2.99444e38i) q^{62} +(-2.69094e38 - 6.49651e38i) q^{63} +1.01967e39i q^{64} +(-3.34781e38 + 1.38671e38i) q^{65} +(-2.76589e39 - 2.76589e39i) q^{66} +1.25248e39 q^{67} +(-1.44848e39 - 4.17629e39i) q^{68} +8.80761e39 q^{69} +(-6.40606e39 - 6.40606e39i) q^{70} +(-5.99916e39 + 2.48493e39i) q^{71} -9.56146e39i q^{72} +(-2.94618e39 - 7.11271e39i) q^{73} +(1.22663e40 + 5.08086e39i) q^{74} +(5.40321e39 - 1.30445e40i) q^{75} +(-1.80438e39 + 1.80438e39i) q^{76} +(5.50465e40 - 5.50465e40i) q^{77} +(2.25249e40 - 5.43800e40i) q^{78} +(-2.82670e40 - 1.17086e40i) q^{79} +(-7.76483e39 - 1.87460e40i) q^{80} +1.19216e41i q^{81} +(-2.43658e40 + 1.00926e40i) q^{82} +(1.40419e41 + 1.40419e41i) q^{83} +9.39183e41 q^{84} +(-1.42666e41 - 1.60529e41i) q^{85} -1.15930e42 q^{86} +(-8.57878e41 - 8.57878e41i) q^{87} +(9.77956e41 - 4.05083e41i) q^{88} -3.45203e41i q^{89} +(-4.10441e41 - 9.90893e41i) q^{90} +(1.08226e42 + 4.48289e41i) q^{91} +(-2.10589e42 + 5.08407e42i) q^{92} +(-2.78681e42 + 2.78681e42i) q^{93} +(2.38174e42 - 2.38174e42i) q^{94} +(-4.74444e40 + 1.14541e41i) q^{95} +(-3.64323e42 - 1.50908e42i) q^{96} +(1.26737e42 + 3.05971e42i) q^{97} +1.85192e43i q^{98} +(8.51462e42 - 3.52687e42i) 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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