LMFDB - Embedded newform 17.44.d.a.2.10

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			2.10
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.18305e6 - 3.18305e6i) q^{2} +(-2.05920e10 + 8.52950e9i) q^{3} +1.14675e13i q^{4} +(-7.09250e14 - 1.71228e15i) q^{5} +(9.26951e16 + 3.83956e16i) q^{6} +(6.03290e17 - 1.45647e18i) q^{7} +(8.50312e18 - 8.50312e18i) q^{8} +(1.19166e20 - 1.19166e20i) q^{9} +(-3.19269e21 + 7.70785e21i) q^{10} +(-7.71531e21 - 3.19579e21i) q^{11} +(-9.78117e22 - 2.36138e23i) q^{12} +3.57985e23i q^{13} +(-6.55631e24 + 2.71571e24i) q^{14} +(2.92098e25 + 2.92098e25i) q^{15} +4.67373e25 q^{16} +(-2.84099e26 - 2.09853e25i) q^{17} -7.58624e26 q^{18} +(2.85685e27 + 2.85685e27i) q^{19} +(1.96355e28 - 8.13331e27i) q^{20} +3.51374e28i q^{21} +(1.43859e28 + 3.47305e28i) q^{22} +(-3.41330e29 - 1.41384e29i) q^{23} +(-1.02569e29 + 2.47624e29i) q^{24} +(-1.62498e30 + 1.62498e30i) q^{25} +(1.13948e30 - 1.13948e30i) q^{26} +(1.36242e30 - 3.28917e30i) q^{27} +(1.67020e31 + 6.91821e30i) q^{28} +(-1.56978e31 - 3.78978e31i) q^{29} -1.85952e32i q^{30} +(-6.34896e30 + 2.62983e30i) q^{31} +(-2.23561e32 - 2.23561e32i) q^{32} +1.86132e32 q^{33} +(8.37504e32 + 9.71098e32i) q^{34} -2.92177e33 q^{35} +(1.36654e33 + 1.36654e33i) q^{36} +(-6.55931e33 + 2.71695e33i) q^{37} -1.81870e34i q^{38} +(-3.05343e33 - 7.37163e33i) q^{39} +(-2.05906e34 - 8.52889e33i) q^{40} +(-3.03074e34 + 7.31685e34i) q^{41} +(1.11844e35 - 1.11844e35i) q^{42} +(1.35915e35 - 1.35915e35i) q^{43} +(3.66476e34 - 8.84751e34i) q^{44} +(-2.88565e35 - 1.19528e35i) q^{45} +(6.36440e35 + 1.53650e36i) q^{46} -5.80326e35i q^{47} +(-9.62415e35 + 3.98646e35i) q^{48} +(-2.13156e35 - 2.13156e35i) q^{49} +1.03448e37 q^{50} +(6.02917e36 - 1.99109e36i) q^{51} -4.10518e36 q^{52} +(2.94231e36 + 2.94231e36i) q^{53} +(-1.48062e37 + 6.13294e36i) q^{54} +1.54774e37i q^{55} +(-7.25470e36 - 1.75144e37i) q^{56} +(-8.31957e37 - 3.44608e37i) q^{57} +(-7.06636e37 + 1.70597e38i) q^{58} +(-5.50470e37 + 5.50470e37i) q^{59} +(-3.34962e38 + 3.34962e38i) q^{60} +(-8.63184e37 + 2.08391e38i) q^{61} +(2.85799e37 + 1.18382e37i) q^{62} +(-1.01670e38 - 2.45454e38i) q^{63} +1.01211e39i q^{64} +(6.12970e38 - 2.53901e38i) q^{65} +(-5.92468e38 - 5.92468e38i) q^{66} -2.18147e39 q^{67} +(2.40648e38 - 3.25790e39i) q^{68} +8.23461e39 q^{69} +(9.30013e39 + 9.30013e39i) q^{70} +(5.44266e39 - 2.25442e39i) q^{71} -2.02657e39i q^{72} +(3.83003e39 + 9.24651e39i) q^{73} +(2.95268e40 + 1.22304e40i) q^{74} +(1.96014e40 - 4.73220e40i) q^{75} +(-3.27608e40 + 3.27608e40i) q^{76} +(-9.30913e39 + 9.30913e39i) q^{77} +(-1.37450e40 + 3.31834e40i) q^{78} +(-2.53586e40 - 1.05039e40i) q^{79} +(-3.31484e40 - 8.00274e40i) q^{80} +1.34671e41i q^{81} +(3.29368e41 - 1.36429e41i) q^{82} +(5.46405e40 + 5.46405e40i) q^{83} -4.02937e41 q^{84} +(1.65565e41 + 5.01342e41i) q^{85} -8.65249e41 q^{86} +(6.46498e41 + 6.46498e41i) q^{87} +(-9.27784e40 + 3.84301e40i) q^{88} +7.49178e40i q^{89} +(5.38054e41 + 1.29898e42i) q^{90} +(5.21394e41 + 2.15968e41i) q^{91} +(1.62131e42 - 3.91420e42i) q^{92} +(1.08307e41 - 1.08307e41i) q^{93} +(-1.84720e42 + 1.84720e42i) q^{94} +(2.86551e42 - 6.91794e42i) q^{95} +(6.51044e42 + 2.69671e42i) q^{96} +(8.92999e41 + 2.15589e42i) q^{97} +1.35697e42i q^{98} +(-1.30024e42 + 5.38575e41i) 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 $

$2$	−3.18305e6	−	3.18305e6i	−1.07324	−	1.07324i	−0.997097	−	0.0761462i	$-0.975738\pi$
$2$	−3.18305e6	−	3.18305e6i	−1.07324	−	1.07324i	−0.0761462	−	0.997097i	$-0.524262\pi$
$3$	−2.05920e10	+	8.52950e9i	−1.13656	+	0.470778i	−0.870006	−	0.493042i	$-0.835885\pi$
$3$	−2.05920e10	+	8.52950e9i	−1.13656	+	0.470778i	−0.266554	+	0.963820i	$0.585885\pi$
$4$			1.14675e13i			1.30370i
$5$	−7.09250e14	−	1.71228e15i	−0.665188	−	1.60591i	−0.789563	−	0.613670i	$-0.789692\pi$
$5$	−7.09250e14	−	1.71228e15i	−0.665188	−	1.60591i	0.124375	−	0.992235i	$-0.460308\pi$
$6$	9.26951e16	+	3.83956e16i	1.72506	+	0.714545i
$7$	6.03290e17	−	1.45647e18i	0.408242	−	0.985584i	−0.577358	−	0.816491i	$-0.695916\pi$
$7$	6.03290e17	−	1.45647e18i	0.408242	−	0.985584i	0.985600	−	0.169093i	$-0.0540838\pi$
$8$	8.50312e18	−	8.50312e18i	0.325945	−	0.325945i
$9$	1.19166e20	−	1.19166e20i	0.363028	−	0.363028i
$10$	−3.19269e21	+	7.70785e21i	−1.00962	+	2.43743i
$11$	−7.71531e21	−	3.19579e21i	−0.314348	−	0.130207i	0.219931	−	0.975515i	$-0.429417\pi$
$11$	−7.71531e21	−	3.19579e21i	−0.314348	−	0.130207i	−0.534279	+	0.845308i	$0.679417\pi$
$12$	−9.78117e22	−	2.36138e23i	−0.613754	−	1.48173i
$13$			3.57985e23i			0.401867i	0.979605	+	0.200933i	$0.0643975\pi$
$13$			3.57985e23i			0.401867i	−0.979605	+	0.200933i	$0.935603\pi$
$14$	−6.55631e24	+	2.71571e24i	−1.49591	+	0.619628i
$15$	2.92098e25	+	2.92098e25i	1.51205	+	1.51205i
$16$	4.67373e25			0.604065
$17$	−2.84099e26	−	2.09853e25i	−0.997283	−	0.0736654i
$17$	−2.84099e26	−	2.09853e25i	−0.997283	−	0.0736654i
$18$	−7.58624e26			−0.779234
$19$	2.85685e27	+	2.85685e27i	0.917666	+	0.917666i	0.996859	−	0.0791934i	$-0.0252345\pi$
$19$	2.85685e27	+	2.85685e27i	0.917666	+	0.917666i	−0.0791934	+	0.996859i	$0.525234\pi$
$20$	1.96355e28	−	8.13331e27i	2.09362	−	0.867206i
$21$			3.51374e28i			1.31237i
$22$	1.43859e28	+	3.47305e28i	0.197628	+	0.477116i
$23$	−3.41330e29	−	1.41384e29i	−1.80313	−	0.746880i	−0.985165	−	0.171608i	$-0.945104\pi$
$23$	−3.41330e29	−	1.41384e29i	−1.80313	−	0.746880i	−0.817962	−	0.575272i	$-0.804896\pi$
$24$	−1.02569e29	+	2.47624e29i	−0.217008	+	0.523903i
$25$	−1.62498e30	+	1.62498e30i	−1.42935	+	1.42935i
$26$	1.13948e30	−	1.13948e30i	0.431301	−	0.431301i
$27$	1.36242e30	−	3.28917e30i	0.229081	−	0.553051i
$28$	1.67020e31	+	6.91821e30i	1.28491	+	0.532226i
$29$	−1.56978e31	−	3.78978e31i	−0.567912	−	1.37106i	−0.903312	−	0.428985i	$-0.858871\pi$
$29$	−1.56978e31	−	3.78978e31i	−0.567912	−	1.37106i	0.335400	−	0.942076i	$-0.391129\pi$
$30$		−	1.85952e32i		−	3.24560i
$31$	−6.34896e30	+	2.62983e30i	−0.0547553	+	0.0226804i	−0.409893	−	0.912134i	$-0.634434\pi$
$31$	−6.34896e30	+	2.62983e30i	−0.0547553	+	0.0226804i	0.355138	+	0.934814i	$0.384434\pi$
$32$	−2.23561e32	−	2.23561e32i	−0.974253	−	0.974253i
$33$	1.86132e32			0.418574
$34$	8.37504e32	+	9.71098e32i	0.991266	+	1.14939i
$35$	−2.92177e33			−1.85431
$36$	1.36654e33	+	1.36654e33i	0.473280	+	0.473280i
$37$	−6.55931e33	+	2.71695e33i	−1.26044	+	0.522090i	−0.910043	−	0.414513i	$-0.863952\pi$
$37$	−6.55931e33	+	2.71695e33i	−1.26044	+	0.522090i	−0.350393	+	0.936603i	$0.613952\pi$
$38$		−	1.81870e34i		−	1.96976i
$39$	−3.05343e33	−	7.37163e33i	−0.189190	−	0.456745i
$40$	−2.05906e34	−	8.52889e33i	−0.740250	−	0.306622i
$41$	−3.03074e34	+	7.31685e34i	−0.640760	+	1.54693i	0.184897	+	0.982758i	$0.440805\pi$
$41$	−3.03074e34	+	7.31685e34i	−0.640760	+	1.54693i	−0.825657	+	0.564173i	$0.809195\pi$
$42$	1.11844e35	−	1.11844e35i	1.40849	−	1.40849i
$43$	1.35915e35	−	1.35915e35i	1.03204	−	1.03204i	0.0325708	−	0.999469i	$-0.489631\pi$
$43$	1.35915e35	−	1.35915e35i	1.03204	−	1.03204i	0.999469	−	0.0325708i	$-0.0103694\pi$
$44$	3.66476e34	−	8.84751e34i	0.169751	−	0.409816i
$45$	−2.88565e35	−	1.19528e35i	−0.824470	−	0.341507i
$46$	6.36440e35	+	1.53650e36i	1.13361	+	2.73678i
$47$		−	5.80326e35i		−	0.650981i	−0.945545	−	0.325490i	$-0.894471\pi$
$47$		−	5.80326e35i		−	0.650981i	0.945545	−	0.325490i	$-0.105529\pi$
$48$	−9.62415e35	+	3.98646e35i	−0.686556	+	0.284381i
$49$	−2.13156e35	−	2.13156e35i	−0.0976073	−	0.0976073i
$50$	1.03448e37			3.06808
$51$	6.02917e36	−	1.99109e36i	1.16815	−	0.385774i
$52$	−4.10518e36			−0.523914
$53$	2.94231e36	+	2.94231e36i	0.249320	+	0.249320i	0.820692	−	0.571372i	$-0.193588\pi$
$53$	2.94231e36	+	2.94231e36i	0.249320	+	0.249320i	−0.571372	+	0.820692i	$0.693588\pi$
$54$	−1.48062e37	+	6.13294e36i	−0.839418	+	0.347698i
$55$			1.54774e37i			0.591425i
$56$	−7.25470e36	−	1.75144e37i	−0.188181	−	0.454310i
$57$	−8.31957e37	−	3.44608e37i	−1.47500	−	0.610964i
$58$	−7.06636e37	+	1.70597e38i	−0.861974	+	2.08099i
$59$	−5.50470e37	+	5.50470e37i	−0.464959	+	0.464959i	−0.900277	−	0.435318i	$-0.856636\pi$
$59$	−5.50470e37	+	5.50470e37i	−0.464959	+	0.464959i	0.435318	+	0.900277i	$0.356636\pi$
$60$	−3.34962e38	+	3.34962e38i	−1.97126	+	1.97126i
$61$	−8.63184e37	+	2.08391e38i	−0.356051	+	0.859583i	0.639796	+	0.768544i	$0.279019\pi$
$61$	−8.63184e37	+	2.08391e38i	−0.356051	+	0.859583i	−0.995847	+	0.0910386i	$0.970981\pi$
$62$	2.85799e37	+	1.18382e37i	0.0831073	+	0.0344242i
$63$	−1.01670e38	−	2.45454e38i	−0.209591	−	0.505998i
$64$			1.01211e39i			1.48716i
$65$	6.12970e38	−	2.53901e38i	0.645360	−	0.267317i
$66$	−5.92468e38	−	5.92468e38i	−0.449231	−	0.449231i
$67$	−2.18147e39			−1.19713			−0.598563	−	0.801075i	$-0.704262\pi$
$67$	−2.18147e39			−1.19713			−0.598563	+	0.801075i	$0.704262\pi$
$68$	2.40648e38	−	3.25790e39i	0.0960376	−	1.30016i
$69$	8.23461e39			2.40098
$70$	9.30013e39	+	9.30013e39i	1.99013	+	1.99013i
$71$	5.44266e39	−	2.25442e39i	0.858533	−	0.355616i	0.0903992	−	0.995906i	$-0.471186\pi$
$71$	5.44266e39	−	2.25442e39i	0.858533	−	0.355616i	0.768134	+	0.640290i	$0.221186\pi$
$72$		−	2.02657e39i		−	0.236654i
$73$	3.83003e39	+	9.24651e39i	0.332476	+	0.802669i	0.998394	+	0.0566439i	$0.0180400\pi$
$73$	3.83003e39	+	9.24651e39i	0.332476	+	0.802669i	−0.665918	+	0.746025i	$0.731960\pi$
$74$	2.95268e40	+	1.22304e40i	1.91308	+	0.792425i
$75$	1.96014e40	−	4.73220e40i	0.951634	−	2.29745i
$76$	−3.27608e40	+	3.27608e40i	−1.19636	+	1.19636i
$77$	−9.30913e39	+	9.30913e39i	−0.256660	+	0.256660i
$78$	−1.37450e40	+	3.31834e40i	−0.287152	+	0.693246i
$79$	−2.53586e40	−	1.05039e40i	−0.402849	−	0.166866i	0.172053	−	0.985088i	$-0.444960\pi$
$79$	−2.53586e40	−	1.05039e40i	−0.402849	−	0.166866i	−0.574902	+	0.818222i	$0.694960\pi$
$80$	−3.31484e40	−	8.00274e40i	−0.401817	−	0.970072i
$81$			1.34671e41i			1.24982i
$82$	3.29368e41	−	1.36429e41i	2.34792	−	0.972542i
$83$	5.46405e40	+	5.46405e40i	0.300148	+	0.300148i	0.841072	−	0.540923i	$-0.181925\pi$
$83$	5.46405e40	+	5.46405e40i	0.300148	+	0.300148i	−0.540923	+	0.841072i	$0.681925\pi$
$84$	−4.02937e41			−1.71093
$85$	1.65565e41	+	5.01342e41i	0.545081	+	1.65054i
$86$	−8.65249e41			−2.21526
$87$	6.46498e41	+	6.46498e41i	1.29093	+	1.29093i
$88$	−9.27784e40	+	3.84301e40i	−0.144900	+	0.0600197i
$89$			7.49178e40i			0.0917698i	0.998947	+	0.0458849i	$0.0146107\pi$
$89$			7.49178e40i			0.0917698i	−0.998947	+	0.0458849i	$0.985389\pi$
$90$	5.38054e41	+	1.29898e42i	0.518337	+	1.25138i
$91$	5.21394e41	+	2.15968e41i	0.396074	+	0.164059i
$92$	1.62131e42	−	3.91420e42i	0.973708	−	2.35074i
$93$	1.08307e41	−	1.08307e41i	0.0515552	−	0.0515552i
$94$	−1.84720e42	+	1.84720e42i	−0.698661	+	0.698661i
$95$	2.86551e42	−	6.91794e42i	0.863264	−	2.08410i
$96$	6.51044e42	+	2.69671e42i	1.56595	+	0.648639i
$97$	8.92999e41	+	2.15589e42i	0.171893	+	0.414987i	0.986224	−	0.165414i	$-0.0528960\pi$
$97$	8.92999e41	+	2.15589e42i	0.171893	+	0.414987i	−0.814331	+	0.580401i	$0.802896\pi$
$98$			1.35697e42i			0.209513i
$99$	−1.30024e42	+	5.38575e41i	−0.161386	+	0.0668482i
$100$	−1.86345e43	−	1.86345e43i	−1.86345	−	1.86345i
$101$	6.90397e42			0.557429			0.278714	−	0.960374i	$-0.410092\pi$
$101$	6.90397e42			0.557429			0.278714	+	0.960374i	$0.410092\pi$
$102$	−2.55289e43	−	1.28534e43i	−1.66774	−	0.839681i
$103$	3.37794e43			1.78917			0.894586	−	0.446896i	$-0.147471\pi$
$103$	3.37794e43			1.78917			0.894586	+	0.446896i	$0.147471\pi$
$104$	3.04399e42	+	3.04399e42i	0.130986	+	0.130986i
$105$	6.01651e43	−	2.49212e43i	2.10754	−	0.872970i
$106$		−	1.87310e43i		−	0.535162i
$107$	4.13906e42	+	9.99258e42i	0.0966386	+	0.233306i	0.964805	−	0.262968i	$-0.0847012\pi$
$107$	4.13906e42	+	9.99258e42i	0.0966386	+	0.233306i	−0.868166	+	0.496274i	$0.834701\pi$
$108$	3.77184e43	+	1.56235e43i	0.721013	+	0.298653i
$109$	5.84630e42	−	1.41142e43i	0.0916666	−	0.221303i	−0.871396	−	0.490580i	$-0.836785\pi$
$109$	5.84630e42	−	1.41142e43i	0.0916666	−	0.221303i	0.963063	+	0.269277i	$0.0867849\pi$
$110$	4.92653e43	−	4.92653e43i	0.634743	−	0.634743i
$111$	1.11895e44	−	1.11895e44i	1.18677	−	1.18677i
$112$	2.81961e43	−	6.80715e43i	0.246605	−	0.595357i
$113$	−1.21745e44	−	5.04283e43i	−0.879556	−	0.364324i	−0.103232	−	0.994657i	$-0.532918\pi$
$113$	−1.21745e44	−	5.04283e43i	−0.879556	−	0.364324i	−0.776325	+	0.630333i	$0.782918\pi$
$114$	1.55126e44	+	3.74506e44i	0.927319	+	2.23875i
$115$			6.84730e44i			3.39247i
$116$	4.34592e44	−	1.80014e44i	1.78745	−	0.740387i
$117$	4.26597e43	+	4.26597e43i	0.145889	+	0.145889i
$118$	3.50434e44			0.998029
$119$	−2.01959e44	+	4.01122e44i	−0.479736	+	0.952833i
$120$	4.96749e44			0.985689
$121$	−3.76649e44	−	3.76649e44i	−0.625246	−	0.625246i
$122$	9.38074e44	−	3.88563e44i	1.30467	−	0.540412i
$123$		−	1.76519e45i		−	2.05983i
$124$	−3.01575e43	−	7.28065e43i	−0.0295684	−	0.0713845i
$125$	1.98831e45	+	8.23585e44i	1.64028	+	0.679428i
$126$	−4.57670e44	+	1.10491e45i	−0.318116	+	0.768001i
$127$	7.71782e44	−	7.71782e44i	0.452600	−	0.452600i	−0.443617	−	0.896217i	$-0.646305\pi$
$127$	7.71782e44	−	7.71782e44i	0.452600	−	0.452600i	0.896217	+	0.443617i	$0.146305\pi$
$128$	1.25511e45	−	1.25511e45i	0.621826	−	0.621826i
$129$	−1.63948e45	+	3.95806e45i	−0.687113	+	1.65884i
$130$	−2.75929e45	−	1.14294e45i	−0.979524	−	0.405732i
$131$	6.50487e44	+	1.57041e45i	0.195842	+	0.472804i	0.991043	−	0.133541i	$-0.0426348\pi$
$131$	6.50487e44	+	1.57041e45i	0.195842	+	0.472804i	−0.795201	+	0.606346i	$0.792635\pi$
$132$			2.13447e45i			0.545695i
$133$	5.88442e45	−	2.43741e45i	1.27907	−	0.529807i
$134$	6.94371e45	+	6.94371e45i	1.28481	+	1.28481i
$135$	−6.59828e45			−1.04053
$136$	−2.59417e45	+	2.23729e45i	−0.349070	+	0.301048i
$137$	5.14478e45			0.591391			0.295695	−	0.955282i	$-0.404449\pi$
$137$	5.14478e45			0.591391			0.295695	+	0.955282i	$0.404449\pi$
$138$	−2.62112e46	−	2.62112e46i	−2.57683	−	2.57683i
$139$	9.69880e45	−	4.01737e45i	0.816394	−	0.338161i	0.0648919	−	0.997892i	$-0.479330\pi$
$139$	9.69880e45	−	4.01737e45i	0.816394	−	0.338161i	0.751502	+	0.659731i	$0.229330\pi$
$140$		−	3.35053e46i		−	2.41747i
$141$	4.94989e45	+	1.19501e46i	0.306468	+	0.739878i
$142$	−2.45002e46	−	1.01483e46i	−1.30308	−	0.539752i
$143$	1.14404e45	−	2.76196e45i	0.0523260	−	0.126326i
$144$	5.56951e45	−	5.56951e45i	0.219293	−	0.219293i
$145$	−5.37580e46	+	5.37580e46i	−1.82403	+	1.82403i
$146$	1.72409e46	−	4.16232e46i	0.504631	−	1.21829i
$147$	6.20744e45	+	2.57120e45i	0.156888	+	0.0649851i
$148$	−3.11566e46	−	7.52187e46i	−0.680649	−	1.64323i
$149$			1.04020e47i			1.96613i	0.183258	+	0.983065i	$0.441336\pi$
$149$			1.04020e47i			1.96613i	−0.183258	+	0.983065i	$0.558664\pi$
$150$	−2.13020e47	+	8.82359e46i	−3.48706	+	1.44439i
$151$	2.18711e46	+	2.18711e46i	0.310361	+	0.310361i	0.845049	−	0.534688i	$-0.179571\pi$
$151$	2.18711e46	+	2.18711e46i	0.310361	+	0.310361i	−0.534688	+	0.845049i	$0.679571\pi$
$152$	4.85842e46			0.598216
$153$	−3.63558e46	+	3.13544e46i	−0.388784	+	0.335299i
$154$	5.92628e46			0.550918
$155$	9.00600e45	+	9.00600e45i	0.0728451	+	0.0728451i
$156$	8.45339e46	−	3.50151e46i	0.595459	−	0.246647i
$157$		−	2.64449e46i		−	0.162368i	−0.996699	−	0.0811838i	$-0.974130\pi$
$157$		−	2.64449e46i		−	0.162368i	0.996699	−	0.0811838i	$-0.0258701\pi$
$158$	4.72832e46	+	1.14152e47i	0.253268	+	0.611442i
$159$	−8.56845e46	−	3.54917e46i	−0.400741	−	0.165993i
$160$	−2.24239e47	+	5.41360e47i	−0.916497	+	2.21262i
$161$	−4.11842e47	+	4.11842e47i	−1.47223	+	1.47223i
$162$	4.28665e47	−	4.28665e47i	1.34136	−	1.34136i
$163$	1.12376e46	−	2.71301e46i	0.0308065	−	0.0743734i	−0.907728	−	0.419560i	$-0.862184\pi$
$163$	1.12376e46	−	2.71301e46i	0.0308065	−	0.0743734i	0.938534	+	0.345187i	$0.112184\pi$
$164$	−8.39057e47	−	3.47549e47i	−2.01673	−	0.835359i
$165$	−1.32014e47	−	3.18711e47i	−0.278430	−	0.672190i
$166$		−	3.47847e47i		−	0.644264i
$167$	3.43414e47	−	1.42247e47i	0.559002	−	0.231546i	−0.0852496	−	0.996360i	$-0.527169\pi$
$167$	3.43414e47	−	1.42247e47i	0.559002	−	0.231546i	0.644252	+	0.764813i	$0.277169\pi$
$168$	2.98778e47	+	2.98778e47i	0.427759	+	0.427759i
$169$	6.65379e47			0.838503
$170$	1.06879e48	−	2.12279e48i	1.18643	−	2.35644i
$171$	6.80880e47			0.666276
$172$	1.55861e48	+	1.55861e48i	1.34547	+	1.34547i
$173$	−2.16795e48	+	8.97995e47i	−1.65218	+	0.684357i	−0.997441	−	0.0714948i	$-0.977223\pi$
$173$	−2.16795e48	+	8.97995e47i	−1.65218	+	0.684357i	−0.654743	+	0.755852i	$0.727223\pi$
$174$		−	4.11566e48i		−	2.77096i
$175$	1.38640e48	+	3.34708e48i	0.825224	+	1.99227i
$176$	−3.60593e47	−	1.49362e47i	−0.189887	−	0.0786537i
$177$	6.64006e47	−	1.60305e48i	0.309561	−	0.747347i
$178$	2.38467e47	−	2.38467e47i	0.0984913	−	0.0984913i
$179$	−2.70826e48	+	2.70826e48i	−0.991631	+	0.991631i	−0.999965	−	0.00833391i	$-0.997347\pi$
$179$	−2.70826e48	+	2.70826e48i	−0.991631	+	0.991631i	0.00833391	+	0.999965i	$0.497347\pi$
$180$	1.37068e48	−	3.30911e48i	0.445222	−	1.07486i
$181$	1.82833e48	+	7.57321e47i	0.527189	+	0.218369i	0.630371	−	0.776294i	$-0.282903\pi$
$181$	1.82833e48	+	7.57321e47i	0.527189	+	0.218369i	−0.103183	+	0.994662i	$0.532903\pi$
$182$	−9.72183e47	−	2.34706e48i	−0.249008	−	0.601158i
$183$		−	5.02745e48i		−	1.14459i
$184$	−4.10458e48	+	1.70017e48i	−0.831161	+	0.344278i
$185$	9.30438e48	+	9.30438e48i	1.67685	+	1.67685i
$186$	−6.89492e47			−0.110663
$187$	2.12485e48	+	1.06983e48i	0.303902	+	0.153010i
$188$	6.65487e48			0.848684
$189$	−3.96864e48	−	3.96864e48i	−0.451558	−	0.451558i
$190$	−3.11412e49	+	1.28991e49i	−3.16324	+	1.31026i
$191$		−	2.11470e49i		−	1.91881i	−0.282038	−	0.959403i	$-0.591011\pi$
$191$		−	2.11470e49i		−	1.91881i	0.282038	−	0.959403i	$-0.408989\pi$
$192$	−8.63275e48	−	2.08413e49i	−0.700120	−	1.69024i
$193$	8.61926e48	+	3.57022e48i	0.625155	+	0.258948i	0.672693	−	0.739922i	$-0.265137\pi$
$193$	8.61926e48	+	3.57022e48i	0.625155	+	0.258948i	−0.0475377	+	0.998869i	$0.515137\pi$
$194$	4.01984e48	−	9.70475e48i	0.260899	−	0.629865i
$195$	−1.04567e49	+	1.04567e49i	−0.607643	+	0.607643i
$196$	2.44436e48	−	2.44436e48i	0.127251	−	0.127251i
$197$	6.79871e48	−	1.64135e49i	0.317251	−	0.765911i	−0.682147	−	0.731215i	$-0.738954\pi$
$197$	6.79871e48	−	1.64135e49i	0.317251	−	0.765911i	0.999398	−	0.0346962i	$-0.0110464\pi$
$198$	5.85302e48	+	2.42440e48i	0.244951	+	0.101462i
$199$	1.18379e49	+	2.85793e49i	0.444564	+	1.07327i	0.974329	+	0.225129i	$0.0722803\pi$
$199$	1.18379e49	+	2.85793e49i	0.444564	+	1.07327i	−0.529765	+	0.848145i	$0.677720\pi$
$200$			2.76349e49i			0.931778i
$201$	4.49208e49	−	1.86068e49i	1.36061	−	0.563581i
$202$	−2.19756e49	−	2.19756e49i	−0.598256	−	0.598256i
$203$	−6.46673e49			−1.58314
$204$	2.28328e49	+	6.91394e49i	0.502934	+	1.52292i
$205$	1.46780e50			2.91045
$206$	−1.07522e50	−	1.07522e50i	−1.92022	−	1.92022i
$207$	−5.75233e49	+	2.38269e49i	−0.925723	+	0.383447i
$208$			1.67312e49i			0.242754i
$209$	−1.29116e49	−	3.11713e49i	−0.168980	−	0.407953i
$210$	−2.70834e50	−	1.12183e50i	−3.19881	−	1.32499i
$211$	−1.34227e49	+	3.24052e49i	−0.143142	+	0.345575i	−0.979149	−	0.203144i	$-0.934884\pi$
$211$	−1.34227e49	+	3.24052e49i	−0.143142	+	0.345575i	0.836007	+	0.548719i	$0.184884\pi$
$212$	−3.37408e49	+	3.37408e49i	−0.325039	+	0.325039i
$213$	−9.28463e49	+	9.28463e49i	−0.808357	+	0.808357i
$214$	1.86320e49	−	4.49817e49i	0.146678	−	0.354111i
$215$	−3.29123e50	−	1.36327e50i	−2.34386	−	0.970858i
$216$	−1.63834e49	−	3.95530e49i	−0.105596	−	0.254932i
$217$			1.08336e49i			0.0632251i
$218$	−6.35352e49	+	2.63171e49i	−0.335892	+	0.139131i
$219$	−1.57736e50	−	1.57736e50i	−0.755758	−	0.755758i
$220$	−1.77487e50			−0.771042
$221$	7.51241e48	−	1.01703e50i	0.0296037	−	0.400775i
$222$	−7.12335e50			−2.54739
$223$	−1.84606e50	−	1.84606e50i	−0.599364	−	0.599364i	0.340779	−	0.940143i	$-0.389309\pi$
$223$	−1.84606e50	−	1.84606e50i	−0.599364	−	0.599364i	−0.940143	+	0.340779i	$0.889309\pi$
$224$	−4.60482e50	+	1.90738e50i	−1.35794	+	0.562477i
$225$			3.87287e50i			1.03779i
$226$	2.27003e50	+	5.48035e50i	0.552969	+	1.33499i
$227$	7.65778e48	+	3.17196e48i	0.0169647	+	0.00702702i	0.391150	−	0.920327i	$-0.372077\pi$
$227$	7.65778e48	+	3.17196e48i	0.0169647	+	0.00702702i	−0.374185	+	0.927354i	$0.622077\pi$
$228$	3.95178e50	−	9.54045e50i	0.796515	−	1.92296i
$229$	3.66484e50	−	3.66484e50i	0.672344	−	0.672344i	−0.285912	−	0.958256i	$-0.592296\pi$
$229$	3.66484e50	−	3.66484e50i	0.672344	−	0.672344i	0.958256	+	0.285912i	$0.0922965\pi$
$230$	2.17953e51	−	2.17953e51i	3.64094	−	3.64094i
$231$	1.12292e50	−	2.71096e50i	0.170880	−	0.412540i
$232$	−4.55729e50	−	1.88769e50i	−0.631997	−	0.261782i
$233$	−5.29045e49	−	1.27723e50i	−0.0668868	−	0.161479i	0.886901	−	0.461959i	$-0.152853\pi$
$233$	−5.29045e49	−	1.27723e50i	−0.0668868	−	0.161479i	−0.953788	+	0.300480i	$0.902853\pi$
$234$		−	2.71576e50i		−	0.313148i
$235$	−9.93682e50	+	4.11596e50i	−1.04541	+	0.433025i
$236$	−6.31250e50	−	6.31250e50i	−0.606168	−	0.606168i
$237$	6.11777e50			0.536418
$238$	1.91963e51	−	6.33946e50i	1.53749	−	0.507747i
$239$	1.12193e51			0.821130			0.410565	−	0.911831i	$-0.365331\pi$
$239$	1.12193e51			0.821130			0.410565	+	0.911831i	$0.365331\pi$
$240$	1.36519e51	+	1.36519e51i	0.913377	+	0.913377i
$241$	−7.46650e49	+	3.09273e49i	−0.0456826	+	0.0189224i	−0.405408	−	0.914136i	$-0.632870\pi$
$241$	−7.46650e49	+	3.09273e49i	−0.0456826	+	0.0189224i	0.359725	+	0.933058i	$0.382870\pi$
$242$			2.39778e51i			1.34208i
$243$	−7.01456e50	−	1.69347e51i	−0.359307	−	0.867444i
$244$	−2.38972e51	−	9.89854e50i	−1.12064	−	0.464184i
$245$	−2.13802e50	+	5.16165e50i	−0.0918210	+	0.221675i
$246$	−5.61869e51	+	5.61869e51i	−2.21070	+	2.21070i
$247$	−1.02271e51	+	1.02271e51i	−0.368780	+	0.368780i
$248$	−3.16243e49	+	7.63477e49i	−0.0104546	+	0.0252397i
$249$	−1.59122e51	−	6.59103e50i	−0.482440	−	0.199833i
$250$	−3.70737e51	−	8.95039e51i	−1.03123	−	2.48961i
$251$			5.26811e51i			1.34484i	0.740171	+	0.672418i	$0.234744\pi$
$251$			5.26811e51i			1.34484i	−0.740171	+	0.672418i	$0.765256\pi$
$252$	2.81474e51	−	1.16590e51i	0.659669	−	0.273244i
$253$	2.18164e51	+	2.18164e51i	0.469560	+	0.469560i
$254$	−4.91324e51			−0.971500
$255$	−7.68551e51	−	8.91146e51i	−1.39656	−	1.61933i
$256$	9.12405e50			0.152415
$257$	−2.53345e51	−	2.53345e51i	−0.389180	−	0.389180i	0.485215	−	0.874395i	$-0.338741\pi$
$257$	−2.53345e51	−	2.53345e51i	−0.389180	−	0.389180i	−0.874395	+	0.485215i	$0.838741\pi$
$258$	1.78172e52	−	7.38014e51i	2.51777	−	1.04290i
$259$			1.11925e52i			1.45540i
$260$	2.91160e51	+	7.02922e51i	0.348501	+	0.841357i
$261$	−6.38679e51	−	2.64549e51i	−0.703901	−	0.291565i
$262$	2.92817e51	−	7.06923e51i	0.297248	−	0.717620i
$263$	1.80236e51	−	1.80236e51i	0.168575	−	0.168575i	−0.617778	−	0.786353i	$-0.711967\pi$
$263$	1.80236e51	−	1.80236e51i	0.168575	−	0.168575i	0.786353	+	0.617778i	$0.211967\pi$
$264$	1.58271e51	−	1.58271e51i	0.136432	−	0.136432i
$265$	2.95123e51	−	7.12489e51i	0.234540	−	0.566229i
$266$	−2.64887e52	−	1.09720e52i	−1.94136	−	0.804138i
$267$	−6.39011e50	−	1.54271e51i	−0.0432032	−	0.104302i
$268$		−	2.50159e52i		−	1.56069i
$269$	−9.37060e51	+	3.88143e51i	−0.539627	+	0.223521i	−0.635814	−	0.771843i	$-0.719335\pi$
$269$	−9.37060e51	+	3.88143e51i	−0.539627	+	0.223521i	0.0961869	+	0.995363i	$0.469335\pi$
$270$	2.10026e52	+	2.10026e52i	1.11674	+	1.11674i
$271$	−2.57029e52			−1.26224			−0.631121	−	0.775684i	$-0.717405\pi$
$271$	−2.57029e52			−1.26224			−0.631121	+	0.775684i	$0.717405\pi$
$272$	−1.32780e52	−	9.80796e50i	−0.602424	−	0.0444987i
$273$	−1.25787e52			−0.527396
$274$	−1.63761e52	−	1.63761e52i	−0.634706	−	0.634706i
$275$	1.77304e52	−	7.34415e51i	0.635425	−	0.263202i
$276$			9.44302e52i			3.13015i
$277$	−1.93557e52	−	4.67287e52i	−0.593599	−	1.43307i	−0.880004	−	0.474966i	$-0.842461\pi$
$277$	−1.93557e52	−	4.67287e52i	−0.593599	−	1.43307i	0.286406	−	0.958108i	$-0.407539\pi$
$278$	−4.36592e52	−	1.80842e52i	−1.23912	−	0.513260i
$279$	−4.43196e50	+	1.06997e51i	−0.0116441	+	0.0281113i
$280$	−2.48442e52	+	2.48442e52i	−0.604403	+	0.604403i
$281$	1.22920e52	−	1.22920e52i	0.276973	−	0.276973i	−0.554926	−	0.831900i	$-0.687254\pi$
$281$	1.22920e52	−	1.22920e52i	0.276973	−	0.276973i	0.831900	+	0.554926i	$0.187254\pi$
$282$	2.22820e52	−	5.37934e52i	0.465155	−	1.12298i
$283$	1.71698e52	+	7.11195e51i	0.332167	+	0.137588i	0.542533	−	0.840035i	$-0.317466\pi$
$283$	1.71698e52	+	7.11195e51i	0.332167	+	0.137588i	−0.210366	+	0.977623i	$0.567466\pi$
$284$	2.58525e52	+	6.24136e52i	0.463617	+	1.11927i
$285$			1.66896e53i			2.77511i
$286$	−1.24330e52	+	5.14991e51i	−0.191737	+	0.0794201i
$287$	8.82835e52	+	8.82835e52i	1.26305	+	1.26305i
$288$	−5.32820e52			−0.707362
$289$	8.02721e52	+	1.19238e52i	0.989147	+	0.146930i
$290$	3.42228e53			3.91524
$291$	−3.67773e52	−	3.67773e52i	−0.390734	−	0.390734i
$292$	−1.06034e53	+	4.39208e52i	−1.04644	+	0.433449i
$293$			1.14452e53i			1.04947i	0.851267	+	0.524733i	$0.175835\pi$
$293$			1.14452e53i			1.04947i	−0.851267	+	0.524733i	$0.824165\pi$
$294$	−1.15743e52	−	2.79428e52i	−0.0986341	−	0.238124i
$295$	1.33298e53	+	5.52138e52i	1.05597	+	0.437396i
$296$	−3.26720e52	+	7.88772e52i	−0.240660	+	0.581005i
$297$	−2.10230e52	+	2.10230e52i	−0.144022	+	0.144022i
$298$	3.31101e53	−	3.31101e53i	2.11013	−	2.11013i
$299$	5.06132e52	−	1.22191e53i	0.300146	−	0.724617i
$300$	5.42664e53	+	2.24779e53i	2.99519	+	1.24065i
$301$	−1.15960e53	−	2.79953e53i	−0.595840	−	1.43848i
$302$		−	1.39234e53i		−	0.666186i
$303$	−1.42167e53	+	5.88874e52i	−0.633551	+	0.262425i
$304$	1.33521e53	+	1.33521e53i	0.554330	+	0.554330i
$305$	4.18046e53			1.61725
$306$	2.15525e53	+	1.59200e52i	0.777117	+	0.0574026i
$307$	−9.11906e52			−0.306531			−0.153266	−	0.988185i	$-0.548979\pi$
$307$	−9.11906e52			−0.306531			−0.153266	+	0.988185i	$0.548979\pi$
$308$	−1.06752e53	−	1.06752e53i	−0.334608	−	0.334608i
$309$	−6.95587e53	+	2.88122e53i	−2.03350	+	0.842303i
$310$		−	5.73331e52i		−	0.156361i
$311$	−9.99921e52	−	2.41402e53i	−0.254459	−	0.614318i	0.744095	−	0.668073i	$-0.232881\pi$
$311$	−9.99921e52	−	2.41402e53i	−0.254459	−	0.614318i	−0.998554	+	0.0537557i	$0.982881\pi$
$312$	−8.86455e52	−	3.67182e52i	−0.210539	−	0.0872082i
$313$	−2.39115e53	+	5.77275e53i	−0.530156	+	1.27991i	0.401263	+	0.915963i	$0.368571\pi$
$313$	−2.39115e53	+	5.77275e53i	−0.530156	+	1.27991i	−0.931419	+	0.363948i	$0.881429\pi$
$314$	−8.41753e52	+	8.41753e52i	−0.174260	+	0.174260i
$315$	−3.48177e53	+	3.48177e53i	−0.673167	+	0.673167i
$316$	1.20453e53	−	2.90799e53i	0.217543	−	0.525194i
$317$	6.21967e52	+	2.57627e52i	0.104953	+	0.0434728i	0.434542	−	0.900652i	$-0.356910\pi$
$317$	6.21967e52	+	2.57627e52i	0.104953	+	0.0434728i	−0.329589	+	0.944124i	$0.606910\pi$
$318$	1.59766e53	+	3.85709e53i	0.251943	+	0.608243i
$319$			3.42560e53i			0.504936i
$320$	1.73301e54	−	7.17836e53i	2.38823	−	0.989238i
$321$	−1.70463e53	−	1.70463e53i	−0.219671	−	0.219671i
$322$	2.62182e54			3.16011
$323$	−7.51677e53	−	8.71580e53i	−0.847572	−	0.982773i
$324$	−1.54434e54			−1.62939
$325$	−5.81719e53	−	5.81719e53i	−0.574409	−	0.574409i
$326$	−1.22126e53	+	5.05863e52i	−0.112884	+	0.0467579i
$327$			3.40506e53i			0.294678i
$328$	3.64453e53	+	8.79867e53i	0.295362	+	0.713066i
$329$	−8.45228e53	−	3.50105e53i	−0.641596	−	0.265758i
$330$	−5.94264e53	+	1.43468e54i	−0.422600	+	1.02025i
$331$	−8.27867e53	+	8.27867e53i	−0.551644	+	0.551644i	−0.926915	−	0.375271i	$-0.877550\pi$
$331$	−8.27867e53	+	8.27867e53i	−0.551644	+	0.551644i	0.375271	+	0.926915i	$0.377550\pi$
$332$	−6.26589e53	+	6.26589e53i	−0.391304	+	0.391304i
$333$	−4.57879e53	+	1.10542e54i	−0.268040	+	0.647106i
$334$	−1.54588e54	−	6.40324e53i	−0.848451	−	0.351440i
$335$	1.54720e54	+	3.73528e54i	0.796314	+	1.92247i
$336$			1.64223e54i			0.792755i
$337$	−1.24891e54	+	5.17315e53i	−0.565572	+	0.234268i	−0.647102	−	0.762403i	$-0.724019\pi$
$337$	−1.24891e54	+	5.17315e53i	−0.565572	+	0.234268i	0.0815300	+	0.996671i	$0.474019\pi$
$338$	−2.11793e54	−	2.11793e54i	−0.899917	−	0.899917i
$339$	2.93710e54			1.17118
$340$	−5.74912e54	+	1.89861e54i	−2.15181	+	0.710622i
$341$	5.73886e52			0.0201654
$342$	−2.16727e54	−	2.16727e54i	−0.715076	−	0.715076i
$343$	2.74161e54	−	1.13561e54i	0.849536	−	0.351889i
$344$		−	2.31141e54i		−	0.672776i
$345$	−5.84040e54	−	1.41000e55i	−1.59710	−	3.85574i
$346$	9.75905e54	+	4.04233e54i	2.50768	+	1.03871i
$347$	1.67896e54	−	4.05337e54i	0.405468	−	0.978887i	−0.580847	−	0.814013i	$-0.697278\pi$
$347$	1.67896e54	−	4.05337e54i	0.405468	−	0.978887i	0.986315	−	0.164874i	$-0.0527216\pi$
$348$	−7.41369e54	+	7.41369e54i	−1.68299	+	1.68299i
$349$	−1.00120e54	+	1.00120e54i	−0.213686	+	0.213686i	−0.805831	−	0.592145i	$-0.798281\pi$
$349$	−1.00120e54	+	1.00120e54i	−0.213686	+	0.213686i	0.592145	+	0.805831i	$0.298281\pi$
$350$	6.24091e54	−	1.50669e55i	1.25252	−	3.02385i
$351$	1.17747e54	+	4.87725e53i	0.222253	+	0.0920602i
$352$	1.01039e54	+	2.43930e54i	0.179400	+	0.433109i
$353$			1.13707e55i			1.89946i	0.313065	+	0.949732i	$0.398644\pi$
$353$			1.13707e55i			1.89946i	−0.313065	+	0.949732i	$0.601356\pi$
$354$	−7.21615e54	+	2.98903e54i	−1.13432	+	0.469850i
$355$	−7.72042e54	−	7.72042e54i	−1.14217	−	1.14217i
$356$	−8.59117e53			−0.119640
$357$	7.37369e53	−	9.98252e54i	0.0966759	−	1.30880i
$358$	1.72410e55			2.12852
$359$	−2.80191e54	−	2.80191e54i	−0.325780	−	0.325780i	0.525199	−	0.850979i	$-0.323991\pi$
$359$	−2.80191e54	−	2.80191e54i	−0.325780	−	0.325780i	−0.850979	+	0.525199i	$0.823991\pi$
$360$	−3.47006e54	+	1.43735e54i	−0.380044	+	0.157419i
$361$			6.63134e54i			0.684221i
$362$	−3.40909e54	−	8.23026e54i	−0.331439	−	0.800165i
$363$	1.09686e55	+	4.54333e54i	1.00498	+	0.416277i
$364$	−2.47661e54	+	5.97907e54i	−0.213884	+	0.516361i
$365$	1.31162e55	−	1.31162e55i	1.06785	−	1.06785i
$366$	−1.60026e55	+	1.60026e55i	−1.22842	+	1.22842i
$367$	1.41836e54	−	3.42423e54i	0.102676	−	0.247881i	−0.864191	−	0.503165i	$-0.832169\pi$
$367$	1.41836e54	−	3.42423e54i	0.102676	−	0.247881i	0.966866	+	0.255284i	$0.0821690\pi$
$368$	−1.59529e55	−	6.60789e54i	−1.08921	−	0.451164i
$369$	5.10760e54	+	1.23308e55i	0.328965	+	0.794193i
$370$		−	5.92325e55i		−	3.59934i
$371$	6.06045e54	−	2.51032e54i	0.347509	−	0.143943i
$372$	1.24201e54	+	1.24201e54i	0.0672126	+	0.0672126i
$373$	1.27707e55			0.652341			0.326170	−	0.945311i	$-0.394242\pi$
$373$	1.27707e55			0.652341			0.326170	+	0.945311i	$0.394242\pi$
$374$	−3.35818e54	−	1.01688e55i	−0.161944	−	0.490378i
$375$	−4.79681e55			−2.18414
$376$	−4.93458e54	−	4.93458e54i	−0.212184	−	0.212184i
$377$	1.35668e55	−	5.61956e54i	0.550984	−	0.228225i
$378$			2.52647e55i			0.969262i
$379$	−1.55190e55	−	3.74661e55i	−0.562496	−	1.35799i	−0.907764	−	0.419481i	$-0.862212\pi$
$379$	−1.55190e55	−	3.74661e55i	−0.562496	−	1.35799i	0.345268	−	0.938504i	$-0.387788\pi$
$380$	7.93313e55	+	3.28601e55i	2.71705	+	1.12544i
$381$	−9.30964e54	+	2.24755e55i	−0.301333	+	0.727481i
$382$	−6.73118e55	+	6.73118e55i	−2.05935	+	2.05935i
$383$	−3.73945e54	+	3.73945e54i	−0.108152	+	0.108152i	−0.759112	−	0.650960i	$-0.774367\pi$
$383$	−3.73945e54	+	3.73945e54i	−0.108152	+	0.108152i	0.650960	+	0.759112i	$0.274367\pi$
$384$	−1.51398e55	+	3.65508e55i	−0.414000	+	0.999484i
$385$	2.25424e55	+	9.33735e54i	0.582899	+	0.241445i
$386$	−1.60714e55	−	3.87997e55i	−0.393030	−	0.948858i
$387$		−	3.23931e55i		−	0.749319i
$388$	−2.47226e55	+	1.02404e55i	−0.541019	+	0.224097i
$389$	−2.26504e55	−	2.26504e55i	−0.468987	−	0.468987i	0.432600	−	0.901586i	$-0.357596\pi$
$389$	−2.26504e55	−	2.26504e55i	−0.468987	−	0.468987i	−0.901586	+	0.432600i	$0.857596\pi$
$390$	6.65680e55			1.30430
$391$	9.40047e55	+	4.73299e55i	1.74321	+	0.877679i
$392$	−3.62499e54			−0.0636292
$393$	−2.67897e55	−	2.67897e55i	−0.445172	−	0.445172i
$394$	−7.38857e55	+	3.06044e55i	−1.16250	+	0.481522i
$395$			5.08709e55i			0.757934i
$396$	−6.17610e54	−	1.49104e55i	−0.0871501	−	0.210399i
$397$	−5.66327e54	−	2.34580e54i	−0.0756957	−	0.0313542i	0.344514	−	0.938781i	$-0.388044\pi$
$397$	−5.66327e54	−	2.34580e54i	−0.0756957	−	0.0313542i	−0.420210	+	0.907427i	$0.638044\pi$
$398$	5.32885e55	−	1.28650e56i	0.674758	−	1.62901i
$399$	−1.00382e56	+	1.00382e56i	−1.20431	+	1.20431i
$400$	−7.59473e55	+	7.59473e55i	−0.863421	+	0.863421i
$401$	5.98461e55	−	1.44481e56i	0.644810	−	1.55671i	−0.175308	−	0.984514i	$-0.556092\pi$
$401$	5.98461e55	−	1.44481e56i	0.644810	−	1.55671i	0.820118	−	0.572195i	$-0.193908\pi$
$402$	−2.02211e56	−	8.37587e55i	−2.06512	−	0.855401i
$403$	−9.41437e53	−	2.27283e54i	−0.00911450	−	0.0220043i
$404$			7.91711e55i			0.726720i
$405$	2.30595e56	−	9.55157e55i	2.00709	−	0.831365i
$406$	2.05839e56	+	2.05839e56i	1.69909	+	1.69909i
$407$	5.92899e55			0.464195
$408$	3.43363e55	−	6.81973e55i	0.255012	−	0.506493i
$409$	−7.53229e55			−0.530733			−0.265367	−	0.964148i	$-0.585493\pi$
$409$	−7.53229e55			−0.530733			−0.265367	+	0.964148i	$0.585493\pi$
$410$	−4.67209e56	−	4.67209e56i	−3.12362	−	3.12362i
$411$	−1.05941e56	+	4.38824e55i	−0.672151	+	0.278414i
$412$			3.87365e56i			2.33254i
$413$	4.69650e55	+	1.13384e56i	0.268441	+	0.648073i
$414$	2.58941e56	+	1.07257e56i	1.40506	+	0.581994i
$415$	5.48062e55	−	1.32314e56i	0.282355	−	0.681665i
$416$	8.00315e55	−	8.00315e55i	0.391520	−	0.391520i
$417$	−1.65452e56	+	1.65452e56i	−0.768681	+	0.768681i
$418$	−5.81216e55	+	1.40318e56i	−0.256477	+	0.619189i
$419$	−5.84247e55	−	2.42003e55i	−0.244903	−	0.101442i	0.256856	−	0.966450i	$-0.417314\pi$
$419$	−5.84247e55	−	2.42003e55i	−0.244903	−	0.101442i	−0.501759	+	0.865008i	$0.667314\pi$
$420$	2.85783e56	+	6.89942e56i	1.13809	+	2.74760i
$421$		−	4.73730e56i		−	1.79253i	−0.443523	−	0.896263i	$-0.646271\pi$
$421$		−	4.73730e56i		−	1.79253i	0.443523	−	0.896263i	$-0.353729\pi$
$422$	1.45872e56	−	6.04223e55i	0.524512	−	0.217260i
$423$	−6.91554e55	−	6.91554e55i	−0.236324	−	0.236324i
$424$	5.00376e55			0.162529
$425$	4.95758e56	−	4.27556e56i	1.53076	−	1.32017i
$426$	5.91068e56			1.73513
$427$	2.51440e56	+	2.51440e56i	0.701836	+	0.701836i
$428$	−1.14590e56	+	4.74646e55i	−0.304162	+	0.125988i
$429$			6.66325e55i			0.168211i
$430$	6.13678e56	+	1.48155e57i	1.47356	+	3.55750i
$431$	1.83082e56	+	7.58352e55i	0.418201	+	0.173224i	0.581854	−	0.813294i	$-0.302328\pi$
$431$	1.83082e56	+	7.58352e55i	0.418201	+	0.173224i	−0.163653	+	0.986518i	$0.552328\pi$
$432$	6.36757e55	−	1.53727e56i	0.138380	−	0.334079i
$433$	−6.22729e56	+	6.22729e56i	−1.28768	+	1.28768i	−0.351493	+	0.936191i	$0.614326\pi$
$433$	−6.22729e56	+	6.22729e56i	−1.28768	+	1.28768i	−0.936191	+	0.351493i	$0.885674\pi$
$434$	3.44839e55	−	3.44839e55i	0.0678559	−	0.0678559i
$435$	6.48457e56	−	1.56551e57i	1.21440	−	2.93182i
$436$	1.61854e56	+	6.70422e55i	0.288513	+	0.119506i
$437$	−5.71217e56	−	1.37904e57i	−0.969282	−	2.34005i
$438$			1.00416e57i			1.62222i
$439$	8.56910e56	−	3.54944e56i	1.31810	−	0.545975i	0.390862	−	0.920449i	$-0.372177\pi$
$439$	8.56910e56	−	3.54944e56i	1.31810	−	0.545975i	0.927237	+	0.374474i	$0.122177\pi$
$440$	1.31606e56	+	1.31606e56i	0.192772	+	0.192772i
$441$	−5.08021e55			−0.0708684
$442$	−3.47638e56	+	2.99814e56i	−0.461901	+	0.398357i
$443$	−3.97255e56			−0.502793			−0.251396	−	0.967884i	$-0.580890\pi$
$443$	−3.97255e56			−0.502793			−0.251396	+	0.967884i	$0.580890\pi$
$444$	1.28315e57	+	1.28315e57i	1.54720	+	1.54720i
$445$	1.28280e56	−	5.31354e55i	0.147374	−	0.0610441i
$446$			1.17522e57i			1.28653i
$447$	−8.87238e56	−	2.14198e57i	−0.925611	−	2.23462i
$448$	1.47410e57	+	6.10593e56i	1.46572	+	0.607120i
$449$	−5.98640e56	+	1.44524e57i	−0.567374	+	1.36976i	0.336388	+	0.941724i	$0.390795\pi$
$449$	−5.98640e56	+	1.44524e57i	−0.567374	+	1.36976i	−0.903761	+	0.428037i	$0.859205\pi$
$450$	1.23275e57	−	1.23275e57i	1.11380	−	1.11380i
$451$	4.67661e56	−	4.67661e56i	0.402843	−	0.402843i
$452$	5.78285e56	−	1.39610e57i	0.474970	−	1.14668i
$453$	−6.36921e56	−	2.63821e56i	−0.498855	−	0.206632i
$454$	−1.42786e55	−	3.44716e55i	−0.0106656	−	0.0257490i
$455$		−	1.04595e57i		−	0.745187i
$456$	−1.00045e57	+	4.14399e56i	−0.679908	+	0.281627i
$457$	−7.52949e56	−	7.52949e56i	−0.488166	−	0.488166i	0.419561	−	0.907727i	$-0.362184\pi$
$457$	−7.52949e56	−	7.52949e56i	−0.488166	−	0.488166i	−0.907727	+	0.419561i	$0.862184\pi$
$458$	−2.33307e57			−1.44318
$459$	−4.56086e56	+	9.05860e56i	−0.269200	+	0.534673i
$460$	−7.85212e57			−4.42276
$461$	4.96076e56	+	4.96076e56i	0.266673	+	0.266673i	0.827758	−	0.561085i	$-0.189616\pi$
$461$	4.96076e56	+	4.96076e56i	0.266673	+	0.266673i	−0.561085	+	0.827758i	$0.689616\pi$
$462$	−1.22034e57	+	5.05482e56i	−0.626150	+	0.259360i
$463$			2.01531e57i			0.987075i	0.869724	+	0.493538i	$0.164296\pi$
$463$			2.01531e57i			0.987075i	−0.869724	+	0.493538i	$0.835704\pi$
$464$	−7.33671e56	−	1.77124e57i	−0.343056	−	0.828210i
$465$	−2.62269e56	−	1.08635e56i	−0.117087	−	0.0484989i
$466$	−2.38150e56	+	5.74945e56i	−0.101520	+	0.245092i
$467$	1.96642e57	−	1.96642e57i	0.800503	−	0.800503i	−0.182671	−	0.983174i	$-0.558474\pi$
$467$	1.96642e57	−	1.96642e57i	0.800503	−	0.800503i	0.983174	+	0.182671i	$0.0584744\pi$
$468$	−4.89199e56	+	4.89199e56i	−0.190195	+	0.190195i
$469$	−1.31606e57	+	3.17724e57i	−0.488718	+	1.17987i
$470$	4.47306e57	+	1.85280e57i	1.58672	+	0.657242i
$471$	2.25562e56	+	5.44554e56i	0.0764391	+	0.184540i
$472$			9.36142e56i			0.303102i
$473$	−1.48299e57	+	6.14273e56i	−0.458799	+	0.190041i
$474$	−1.94731e57	−	1.94731e57i	−0.575707	−	0.575707i
$475$	−9.28466e57			−2.62333
$476$	−4.59985e57	−	2.31595e57i	−1.24221	−	0.625433i
$477$	7.01249e56			0.181020
$478$	−3.57116e57	−	3.57116e57i	−0.881272	−	0.881272i
$479$	−2.94806e57	+	1.22113e57i	−0.695540	+	0.288102i	−0.702306	−	0.711875i	$-0.747846\pi$
$479$	−2.94806e57	+	1.22113e57i	−0.695540	+	0.288102i	0.00676589	+	0.999977i	$0.497846\pi$
$480$		−	1.30604e58i		−	2.94624i
$481$	−9.72627e56	−	2.34813e57i	−0.209811	−	0.506528i
$482$	3.36105e56	+	1.39219e56i	0.0693368	+	0.0287202i
$483$	4.96786e57	−	1.19935e58i	0.980180	−	2.36636i
$484$	4.31921e57	−	4.31921e57i	0.815134	−	0.815134i
$485$	3.05813e57	−	3.05813e57i	0.552088	−	0.552088i
$486$	−3.15761e57	+	7.62314e57i	−0.545354	+	1.31660i
$487$	−1.77603e57	−	7.35655e56i	−0.293479	−	0.121563i	0.231086	−	0.972933i	$-0.425772\pi$
$487$	−1.77603e57	−	7.35655e56i	−0.293479	−	0.121563i	−0.524565	+	0.851370i	$0.675772\pi$
$488$	1.03800e57	+	2.50595e57i	0.164124	+	0.396229i
$489$			6.54515e56i			0.0990327i
$490$	2.32352e57	−	9.62433e56i	0.336458	−	0.139365i
$491$	5.91308e57	+	5.91308e57i	0.819524	+	0.819524i	0.986039	−	0.166515i	$-0.0532514\pi$
$491$	5.91308e57	+	5.91308e57i	0.819524	+	0.819524i	−0.166515	+	0.986039i	$0.553251\pi$
$492$	2.02423e58			2.68541
$493$	3.66443e57	+	1.10962e58i	0.465369	+	1.40917i
$494$	6.51065e57			0.791580
$495$	1.84439e57	+	1.84439e57i	0.214704	+	0.214704i
$496$	−2.96733e56	+	1.22911e56i	−0.0330758	+	0.0137004i
$497$		−	9.28714e57i		−	0.991334i
$498$	2.96696e57	+	7.16287e57i	0.303306	+	0.732244i
$499$	−4.86628e57	−	2.01568e57i	−0.476470	−	0.197360i	0.131506	−	0.991315i	$-0.458019\pi$
$499$	−4.86628e57	−	2.01568e57i	−0.476470	−	0.197360i	−0.607977	+	0.793955i	$0.708019\pi$
$500$	−9.44444e57	+	2.28009e58i	−0.885770	+	2.13844i
$501$	−5.85829e57	+	5.85829e57i	−0.526332	+	0.526332i
$502$	1.67686e58	−	1.67686e58i	1.44334	−	1.44334i
$503$	−8.24953e57	+	1.99161e58i	−0.680326	+	1.64245i	0.0830864	+	0.996542i	$0.473522\pi$
$503$	−8.24953e57	+	1.99161e58i	−0.680326	+	1.64245i	−0.763413	+	0.645911i	$0.776478\pi$
$504$	−2.95164e57	−	1.22261e57i	−0.233242	−	0.0966121i
$505$	−4.89664e57	−	1.18215e58i	−0.370795	−	0.895178i
$506$		−	1.38885e58i		−	1.00790i
$507$	−1.37015e58	+	5.67534e57i	−0.953008	+	0.394749i
$508$	8.85039e57	+	8.85039e57i	0.590055	+	0.590055i
$509$	4.34320e57			0.277573			0.138787	−	0.990322i	$-0.455680\pi$
$509$	4.34320e57			0.277573			0.138787	+	0.990322i	$0.455680\pi$
$510$	−3.90226e57	+	5.28289e58i	−0.239088	+	3.23678i
$511$	1.57779e58			0.926828
$512$	−1.39443e58	−	1.39443e58i	−0.785404	−	0.785404i
$513$	1.32889e58	−	5.50443e57i	0.717736	−	0.297296i
$514$			1.61282e58i			0.835370i
$515$	−2.39581e58	−	5.78399e58i	−1.19014	−	2.87324i
$516$	−4.53889e58	−	1.88007e58i	−2.16263	−	0.895789i
$517$	−1.85460e57	+	4.47740e57i	−0.0847624	+	0.204635i
$518$	3.56264e58	−	3.56264e58i	1.56200	−	1.56200i
$519$	3.69831e58	−	3.69831e58i	1.55562	−	1.55562i
$520$	3.05321e57	−	7.37111e57i	0.123221	−	0.297482i
$521$	1.60709e58	+	6.65680e57i	0.622344	+	0.257783i	0.671496	−	0.741008i	$-0.265652\pi$
$521$	1.60709e58	+	6.65680e57i	0.622344	+	0.257783i	−0.0491525	+	0.998791i	$0.515652\pi$
$522$	1.19087e58	+	2.87502e58i	0.442536	+	1.06838i
$523$			2.33835e58i			0.833918i	0.908925	+	0.416959i	$0.136904\pi$
$523$			2.33835e58i			0.833918i	−0.908925	+	0.416959i	$0.863096\pi$
$524$	−1.80087e58	+	7.45944e57i	−0.616395	+	0.255319i
$525$	−5.70977e58	−	5.70977e58i	−1.87583	−	1.87583i
$526$	−1.14740e58			−0.361844
$527$	1.85892e57	−	6.13897e56i	0.0562773	−	0.0185852i
$528$	8.69932e57			0.252846
$529$	7.11785e58	+	7.11785e58i	1.98633	+	1.98633i
$530$	−3.20728e58	+	1.32850e58i	−0.859419	+	0.355983i
$531$			1.31195e58i			0.337586i
$532$	2.79509e58	+	6.74794e58i	0.690709	+	1.66752i
$533$	−2.61932e58	−	1.08496e58i	−0.621660	−	0.257500i
$534$	−2.87651e57	+	6.94451e57i	−0.0655736	+	0.158309i
$535$	1.41745e58	−	1.41745e58i	0.310385	−	0.310385i
$536$	−1.85493e58	+	1.85493e58i	−0.390197	+	0.390197i
$537$	3.26685e58	−	7.88687e58i	0.660209	−	1.59389i
$538$	4.21818e58	+	1.74723e58i	0.819043	+	0.339259i
$539$	9.63365e56	+	2.32577e57i	0.0179735	+	0.0433919i
$540$		−	7.56656e58i		−	1.35654i
$541$	−2.59566e58	+	1.07516e58i	−0.447206	+	0.185239i	−0.594909	−	0.803793i	$-0.702812\pi$
$541$	−2.59566e58	+	1.07516e58i	−0.447206	+	0.185239i	0.147703	+	0.989032i	$0.452812\pi$
$542$	8.18136e58	+	8.18136e58i	1.35469	+	1.35469i
$543$	−4.41087e58			−0.701985
$544$	5.88221e58	+	6.82051e58i	0.899838	+	1.04338i
$545$	−2.83140e58			−0.416367
$546$	4.00384e58	+	4.00384e58i	0.566025	+	0.566025i
$547$	8.58183e57	−	3.55471e57i	0.116641	−	0.0483144i	−0.323600	−	0.946194i	$-0.604893\pi$
$547$	8.58183e57	−	3.55471e57i	0.116641	−	0.0483144i	0.440241	+	0.897880i	$0.354893\pi$
$548$			5.89976e58i			0.770996i
$549$	1.45470e58	+	3.51195e58i	0.182796	+	0.441309i
$550$	−7.98133e58	−	3.30598e58i	−0.964445	−	0.399486i
$551$	6.34220e58	−	1.53114e59i	0.737022	−	1.77933i
$552$	7.00199e58	−	7.00199e58i	0.782585	−	0.782585i
$553$	−3.05971e58	+	3.05971e58i	−0.328920	+	0.328920i
$554$	−8.71296e58	+	2.10350e59i	−0.900961	+	2.17511i
$555$	−2.70958e59	−	1.12234e59i	−2.69527	−	1.11642i
$556$	4.60691e58	+	1.11221e59i	0.440861	+	1.06433i
$557$			1.78876e59i			1.64690i	0.567392	+	0.823448i	$0.307952\pi$
$557$			1.78876e59i			1.64690i	−0.567392	+	0.823448i	$0.692048\pi$
$558$	4.81648e57	−	1.99505e57i	0.0426672	−	0.0176733i
$559$	4.86556e58	+	4.86556e58i	0.414743	+	0.414743i
$560$	−1.36556e59			−1.12013
$561$	−5.28801e58	−	3.90604e57i	−0.417437	−	0.0308344i
$562$	−7.82523e58			−0.594519
$563$	5.74249e57	+	5.74249e57i	0.0419923	+	0.0419923i	0.727791	−	0.685799i	$-0.240547\pi$
$563$	5.74249e57	+	5.74249e57i	0.0419923	+	0.0419923i	−0.685799	+	0.727791i	$0.740547\pi$
$564$	−1.37037e59	+	5.67627e58i	−0.964580	+	0.399542i
$565$			2.44227e59i			1.65483i
$566$	−3.20145e58	−	7.72898e58i	−0.208830	−	0.504161i
$567$	1.96145e59	+	8.12459e58i	1.23180	+	0.510230i
$568$	2.71100e58	−	6.54493e58i	0.163923	−	0.395745i
$569$	−1.35343e58	+	1.35343e58i	−0.0787992	+	0.0787992i	−0.745408	−	0.666609i	$-0.767745\pi$
$569$	−1.35343e58	+	1.35343e58i	−0.0787992	+	0.0787992i	0.666609	+	0.745408i	$0.267745\pi$
$570$	5.31237e59	−	5.31237e59i	2.97837	−	2.97837i
$571$	−8.16244e58	+	1.97059e59i	−0.440701	+	1.06395i	0.535003	+	0.844850i	$0.320311\pi$
$571$	−8.16244e58	+	1.97059e59i	−0.440701	+	1.06395i	−0.975703	+	0.219095i	$0.929689\pi$
$572$	3.16727e58	+	1.31193e58i	0.164691	+	0.0682174i
$573$	1.80373e59	+	4.35459e59i	0.903332	+	2.18084i
$574$		−	5.62021e59i		−	2.71111i
$575$	7.84402e59	−	3.24910e59i	3.64485	−	1.50975i
$576$	1.20609e59	+	1.20609e59i	0.539879	+	0.539879i
$577$	3.87205e59			1.66979			0.834894	−	0.550411i	$-0.185529\pi$
$577$	3.87205e59			1.66979			0.834894	+	0.550411i	$0.185529\pi$
$578$	−2.17556e59	−	2.93464e59i	−0.903903	−	1.21929i
$579$	−2.07940e59			−0.832433
$580$	−6.16468e59	−	6.16468e59i	−2.37798	−	2.37798i
$581$	1.12546e59	−	4.66182e58i	0.418355	−	0.173288i
$582$			2.34128e59i			0.838704i
$583$	−1.32978e58	−	3.21038e58i	−0.0459100	−	0.110837i
$584$	1.11191e59	+	4.60570e58i	0.369994	+	0.153257i
$585$	4.27890e58	−	1.03302e59i	0.137240	−	0.331327i
$586$	3.64305e59	−	3.64305e59i	1.12633	−	1.12633i
$587$	−1.13728e59	+	1.13728e59i	−0.338961	+	0.338961i	−0.855976	−	0.517015i	$-0.827043\pi$
$587$	−1.13728e59	+	1.13728e59i	−0.338961	+	0.338961i	0.517015	+	0.855976i	$0.327043\pi$
$588$	−2.94852e58	+	7.11836e58i	−0.0847211	+	0.204535i
$589$	−2.56510e58	−	1.06250e58i	−0.0710601	−	0.0294341i
$590$	−2.48545e59	−	6.00042e59i	−0.663877	−	1.60274i
$591$			3.95978e59i			1.01986i
$592$	−3.06564e59	+	1.26983e59i	−0.761386	+	0.315376i
$593$	−3.26249e59	−	3.26249e59i	−0.781399	−	0.781399i	0.198668	−	0.980067i	$-0.436339\pi$
$593$	−3.26249e59	−	3.26249e59i	−0.781399	−	0.781399i	−0.980067	+	0.198668i	$0.936339\pi$
$594$	1.33834e59			0.309142
$595$	8.30073e59	+	6.13142e58i	1.84927	+	0.136599i
$596$	−1.19285e60			−2.56324
$597$	−4.87534e59	−	4.87534e59i	−1.01055	−	1.01055i
$598$	−5.50044e59	+	2.27836e59i	−1.09982	+	0.455560i
$599$			7.80631e59i			1.50581i	0.658131	+	0.752903i	$0.271347\pi$
$599$			7.80631e59i			1.50581i	−0.658131	+	0.752903i	$0.728653\pi$
$600$	−2.35711e59	−	5.69058e59i	−0.438661	−	1.05902i
$601$	−8.29116e57	−	3.43431e57i	−0.0148872	−	0.00616650i	0.375227	−	0.926933i	$-0.377565\pi$
$601$	−8.29116e57	−	3.43431e57i	−0.0148872	−	0.00616650i	−0.390115	+	0.920766i	$0.627565\pi$
$602$	−5.21996e59	+	1.26021e60i	−0.904363	+	2.18332i
$603$	−2.59957e59	+	2.59957e59i	−0.434590	+	0.434590i
$604$	−2.50807e59	+	2.50807e59i	−0.404618	+	0.404618i
$605$	−3.77790e59	+	9.12066e59i	−0.588180	+	1.41999i
$606$	6.39964e59	+	2.65082e59i	0.961600	+	0.398308i
$607$	−1.20895e59	−	2.91867e59i	−0.175328	−	0.423280i	0.811648	−	0.584147i	$-0.198571\pi$
$607$	−1.20895e59	−	2.91867e59i	−0.175328	−	0.423280i	−0.986976	+	0.160867i	$0.948571\pi$
$608$		−	1.27736e60i		−	1.78808i
$609$	1.33163e60	−	5.51579e59i	1.79933	−	0.745308i
$610$	−1.33066e60	−	1.33066e60i	−1.73570	−	1.73570i
$611$	2.07748e59			0.261608
$612$	−3.59555e59	−	4.16910e59i	−0.437129	−	0.506858i
$613$	−1.09613e60			−1.28665			−0.643326	−	0.765592i	$-0.722446\pi$
$613$	−1.09613e60			−1.28665			−0.643326	+	0.765592i	$0.722446\pi$
$614$	2.90264e59	+	2.90264e59i	0.328983	+	0.328983i
$615$	−3.02251e60	+	1.25196e60i	−3.30790	+	1.37018i
$616$			1.58313e59i			0.167314i
$617$	−1.07394e59	−	2.59272e59i	−0.109610	−	0.264621i	0.859551	−	0.511049i	$-0.170743\pi$
$617$	−1.07394e59	−	2.59272e59i	−0.109610	−	0.264621i	−0.969161	+	0.246428i	$0.920743\pi$
$618$	3.13119e60	+	1.29698e60i	3.08644	+	1.27844i
$619$	−3.24220e59	+	7.82735e59i	−0.308667	+	0.745188i	0.691082	+	0.722777i	$0.257134\pi$
$619$	−3.24220e59	+	7.82735e59i	−0.308667	+	0.745188i	−0.999749	+	0.0224115i	$0.992866\pi$
$620$	−1.03276e59	+	1.03276e59i	−0.0949683	+	0.0949683i
$621$	−9.30069e59	+	9.30069e59i	−0.826125	+	0.826125i
$622$	−4.50115e59	+	1.08667e60i	−0.386216	+	0.932408i
$623$	1.09115e59	+	4.51971e58i	0.0904468	+	0.0374643i
$624$	−1.42709e59	−	3.44530e59i	−0.114283	−	0.275904i
$625$		−	1.37607e60i		−	1.06468i
$626$	2.59861e60	−	1.07638e60i	1.94264	−	0.804668i
$627$	5.31752e59	+	5.31752e59i	0.384111	+	0.384111i
$628$	3.03256e59			0.211679
$629$	1.92051e60	−	6.34236e59i	1.29547	−	0.427821i
$630$	2.21652e60			1.44494
$631$	−2.05663e60	−	2.05663e60i	−1.29576	−	1.29576i	−0.931165	−	0.364598i	$-0.881206\pi$
$631$	−2.05663e60	−	2.05663e60i	−1.29576	−	1.29576i	−0.364598	−	0.931165i	$-0.618794\pi$
$632$	−3.04943e59	+	1.26311e59i	−0.185695	+	0.0769175i
$633$		−	7.81778e59i		−	0.460154i
$634$	−1.15971e59	−	2.79979e59i	−0.0659828	−	0.159297i
$635$	−1.86889e60	−	7.74121e59i	−1.02790	−	0.425769i
$636$	4.07000e59	−	9.82585e59i	0.216405	−	0.522447i
$637$	7.63067e58	−	7.63067e58i	0.0392252	−	0.0392252i
$638$	1.09038e60	−	1.09038e60i	0.541919	−	0.541919i
$639$	3.79931e59	−	9.17234e59i	0.182573	−	0.440770i
$640$	−3.03930e60	−	1.25892e60i	−1.41222	−	0.584963i
$641$	5.65136e59	+	1.36436e60i	0.253925	+	0.613029i	0.998514	−	0.0544937i	$-0.0173545\pi$
$641$	5.65136e59	+	1.36436e60i	0.253925	+	0.613029i	−0.744589	+	0.667523i	$0.767354\pi$
$642$			1.08519e60i			0.471521i
$643$	−2.68328e60	+	1.11145e60i	−1.12754	+	0.467040i	−0.866942	−	0.498408i	$-0.833918\pi$
$643$	−2.68328e60	+	1.11145e60i	−1.12754	+	0.467040i	−0.260593	+	0.965449i	$0.583918\pi$
$644$	−4.72279e60	−	4.72279e60i	−1.91934	−	1.91934i
$645$	7.94012e60			3.12099
$646$	−3.81659e59	+	5.16690e60i	−0.145103	+	1.96440i
$647$	−3.21541e60			−1.18248			−0.591240	−	0.806496i	$-0.701361\pi$
$647$	−3.21541e60			−1.18248			−0.591240	+	0.806496i	$0.701361\pi$
$648$	1.14513e60	+	1.14513e60i	0.407372	+	0.407372i
$649$	6.00623e59	−	2.48786e59i	0.206700	−	0.0856180i
$650$			3.70328e60i			1.23296i
$651$	−9.24053e58	−	2.23086e59i	−0.0297650	−	0.0718590i
$652$	3.11113e59	+	1.28867e59i	0.0969606	+	0.0401624i
$653$	9.24453e59	−	2.23183e60i	0.278774	−	0.673019i	−0.721029	−	0.692905i	$-0.756330\pi$
$653$	9.24453e59	−	2.23183e60i	0.278774	−	0.673019i	0.999802	+	0.0198863i	$0.00633044\pi$
$654$	1.08385e60	−	1.08385e60i	0.316261	−	0.316261i
$655$	2.22763e60	−	2.22763e60i	0.629008	−	0.629008i
$656$	−1.41648e60	+	3.41970e60i	−0.387061	+	0.934447i
$657$	1.55828e60	+	6.45462e59i	0.412089	+	0.170693i
$658$	1.57600e60	+	3.80480e60i	0.403366	+	0.973811i
$659$			4.34050e60i			1.07523i	0.843189	+	0.537617i	$0.180675\pi$
$659$			4.34050e60i			1.07523i	−0.843189	+	0.537617i	$0.819325\pi$
$660$	3.65481e60	−	1.51387e60i	0.876334	−	0.362990i
$661$	5.13567e60	+	5.13567e60i	1.19197	+	1.19197i	0.976513	+	0.215458i	$0.0691246\pi$
$661$	5.13567e60	+	5.13567e60i	1.19197	+	1.19197i	0.215458	+	0.976513i	$0.430875\pi$
$662$	5.27028e60			1.18410
$663$	7.12781e59	+	2.15835e60i	0.155030	+	0.469441i
$664$	9.29230e59			0.195663
$665$	−8.34705e60	−	8.34705e60i	−1.70164	−	1.70164i
$666$	4.97605e60	−	2.06115e60i	0.982175	−	0.406830i
$667$			1.51551e61i			2.89636i
$668$	1.63121e60	+	3.93809e60i	0.301867	+	0.728772i
$669$	5.37600e60	+	2.22681e60i	0.963380	+	0.399045i
$670$	6.96475e60	−	1.68144e61i	1.20864	−	2.91792i
$671$	1.33195e60	−	1.33195e60i	0.223848	−	0.223848i
$672$	7.85536e60	−	7.85536e60i	1.27858	−	1.27858i
$673$	1.84267e59	−	4.44861e59i	0.0290486	−	0.0701294i	−0.908690	−	0.417472i	$-0.862916\pi$
$673$	1.84267e59	−	4.44861e59i	0.0290486	−	0.0701294i	0.937738	+	0.347343i	$0.112916\pi$
$674$	5.62197e60	+	2.32870e60i	0.858423	+	0.355570i
$675$	3.13094e60	+	7.55875e60i	0.463066	+	1.11794i
$676$			7.63021e60i			1.09316i
$677$	−6.55687e60	+	2.71594e60i	−0.909997	+	0.376933i	−0.788056	−	0.615604i	$-0.788912\pi$
$677$	−6.55687e60	+	2.71594e60i	−0.909997	+	0.376933i	−0.121941	+	0.992537i	$0.538912\pi$
$678$	−9.34892e60	−	9.34892e60i	−1.25696	−	1.25696i
$679$	3.67873e60			0.479178
$680$	5.67079e60	+	2.85515e60i	0.715652	+	0.360319i
$681$	−1.84744e59			−0.0225896
$682$	−1.82670e59	−	1.82670e59i	−0.0216423	−	0.0216423i
$683$	9.06686e60	−	3.75562e60i	1.04091	−	0.431158i	0.204269	−	0.978915i	$-0.434518\pi$
$683$	9.06686e60	−	3.75562e60i	1.04091	−	0.431158i	0.836637	+	0.547757i	$0.184518\pi$
$684$			7.80798e60i			0.868625i
$685$	−3.64893e60	−	8.80931e60i	−0.393386	−	0.949718i
$686$	−1.23414e61	−	5.11196e60i	−1.28942	−	0.534096i
$687$	−4.42072e60	+	1.06726e61i	−0.447634	+	1.08068i
$688$	6.35231e60	−	6.35231e60i	0.623420	−	0.623420i
$689$	−1.05330e60	+	1.05330e60i	−0.100193	+	0.100193i
$690$	−2.62906e61	+	6.34711e61i	−2.42407	+	5.85222i
$691$	−5.15806e60	−	2.13654e60i	−0.461008	−	0.190956i	0.140078	−	0.990141i	$-0.455265\pi$
$691$	−5.15806e60	−	2.13654e60i	−0.461008	−	0.190956i	−0.601085	+	0.799185i	$0.705265\pi$
$692$	−1.02977e61	−	2.48609e61i	−0.892197	−	2.15395i
$693$			2.21867e60i			0.186350i
$694$	−1.82463e61	+	7.55785e60i	−1.48575	+	0.615417i
$695$	−1.37577e61	−	1.37577e61i	−1.08611	−	1.08611i
$696$	1.09945e61			0.841544
$697$	1.01458e61	−	2.01511e61i	0.752974	−	1.49553i
$698$	6.37376e60			0.458674
$699$	2.17882e60	+	2.17882e60i	0.152042	+	0.152042i
$700$	−3.83825e61	+	1.58986e61i	−2.59732	+	1.07584i
$701$		−	1.29275e61i		−	0.848353i	−0.905580	−	0.424177i	$-0.860564\pi$
$701$		−	1.29275e61i		−	0.848353i	0.905580	−	0.424177i	$-0.139436\pi$
$702$	−2.19550e60	−	5.30040e60i	−0.139728	−	0.337334i
$703$	−2.65009e61	−	1.09770e61i	−1.63576	−	0.677555i
$704$	3.23447e60	−	7.80871e60i	0.193638	−	0.467484i
$705$	1.69512e61	−	1.69512e61i	0.984316	−	0.984316i
$706$	3.61935e61	−	3.61935e61i	2.03859	−	2.03859i
$707$	4.16509e60	−	1.00554e61i	0.227566	−	0.549393i
$708$	1.83829e61	+	7.61446e60i	0.974316	+	0.403575i
$709$	−1.23568e61	−	2.98319e61i	−0.635347	−	1.53386i	−0.832814	−	0.553554i	$-0.813271\pi$
$709$	−1.23568e61	−	2.98319e61i	−0.635347	−	1.53386i	0.197467	−	0.980310i	$-0.436729\pi$
$710$			4.91489e61i			2.45165i
$711$	−4.27360e60	+	1.77018e60i	−0.206822	+	0.0856686i
$712$	6.37035e59	+	6.37035e59i	0.0299119	+	0.0299119i
$713$	2.53891e60			0.115670
$714$	−3.41219e61	+	2.94277e61i	−1.50842	+	1.30090i
$715$	−5.54067e60			−0.237674
$716$	−3.10569e61	−	3.10569e61i	−1.29279	−	1.29279i
$717$	−2.31029e61	+	9.56952e60i	−0.933263	+	0.386570i
$718$			1.78372e61i			0.699281i
$719$	1.51228e61	+	3.65098e61i	0.575390	+	1.38911i	0.896911	+	0.442211i	$0.145806\pi$
$719$	1.51228e61	+	3.65098e61i	0.575390	+	1.38911i	−0.321521	+	0.946902i	$0.604194\pi$
$720$	−1.34868e61	−	5.58640e60i	−0.498034	−	0.206292i
$721$	2.03788e61	−	4.91987e61i	0.730416	−	1.76338i
$722$	2.11079e61	−	2.11079e61i	0.734336	−	0.734336i
$723$	1.27371e60	−	1.27371e60i	0.0430127	−	0.0430127i
$724$	−8.68456e60	+	2.09664e61i	−0.284688	+	0.687297i
$725$	8.70919e61	+	3.60746e61i	2.77147	+	1.14798i
$726$	−2.04519e61	−	4.93751e61i	−0.631823	−	1.52536i
$727$		−	4.80864e61i		−	1.44222i	−0.692819	−	0.721111i	$-0.743632\pi$
$727$		−	4.80864e61i		−	1.44222i	0.692819	−	0.721111i	$-0.256368\pi$
$728$	6.26988e60	−	2.59707e60i	0.182572	−	0.0756239i
$729$	−2.37015e60	−	2.37015e60i	−0.0670092	−	0.0670092i
$730$	−8.34988e61			−2.29213
$731$	−4.14657e61	+	3.57612e61i	−1.10526	+	0.953211i
$732$	5.76521e61			1.49220
$733$	−3.04017e61	−	3.04017e61i	−0.764122	−	0.764122i	0.212943	−	0.977065i	$-0.431695\pi$
$733$	−3.04017e61	−	3.04017e61i	−0.764122	−	0.764122i	−0.977065	+	0.212943i	$0.931695\pi$
$734$	−1.54142e61	+	6.38477e60i	−0.376232	+	0.155840i
$735$		−	1.24525e61i		−	0.295175i
$736$	4.47003e61	+	1.07916e62i	1.02905	+	2.48435i
$737$	1.68307e61	+	6.97150e60i	0.376314	+	0.155875i
$738$	2.29919e61	−	5.55074e61i	0.499302	−	1.20542i
$739$	2.74400e61	−	2.74400e61i	0.578801	−	0.578801i	−0.355772	−	0.934573i	$-0.615782\pi$
$739$	2.74400e61	−	2.74400e61i	0.578801	−	0.578801i	0.934573	+	0.355772i	$0.115782\pi$
$740$	−1.06698e62	+	1.06698e62i	−2.18612	+	2.18612i
$741$	1.23364e61	−	2.97828e61i	0.245526	−	0.592753i
$742$	−2.72812e61	−	1.13002e61i	−0.527447	−	0.218476i
$743$	−1.76394e61	−	4.25854e61i	−0.331303	−	0.799836i	−0.998489	−	0.0549451i	$-0.982502\pi$
$743$	−1.76394e61	−	4.25854e61i	−0.331303	−	0.799836i	0.667187	−	0.744891i	$-0.267498\pi$
$744$		−	1.84189e60i		−	0.0336083i
$745$	1.78112e62	−	7.37762e61i	3.15742	−	1.30785i
$746$	−4.06497e61	−	4.06497e61i	−0.700120	−	0.700120i
$747$	1.30226e61			0.217924
$748$	−1.22682e61	+	2.43667e61i	−0.199479	+	0.396197i
$749$	1.70509e61			0.269395
$750$	1.52685e62	+	1.52685e62i	2.34411	+	2.34411i
$751$	−4.04810e61	+	1.67678e61i	−0.603939	+	0.250160i	−0.663634	−	0.748057i	$-0.730987\pi$
$751$	−4.04810e61	+	1.67678e61i	−0.603939	+	0.250160i	0.0596957	+	0.998217i	$0.480987\pi$
$752$		−	2.71229e61i		−	0.393235i
$753$	−4.49343e61	−	1.08481e62i	−0.633120	−	1.52849i
$754$	−6.10711e61	−	2.52965e61i	−0.836280	−	0.346399i
$755$	2.19374e61	−	5.29617e61i	0.291962	−	0.704859i
$756$	4.55103e61	−	4.55103e61i	0.588696	−	0.588696i
$757$	−2.19882e61	+	2.19882e61i	−0.276458	+	0.276458i	−0.831693	−	0.555235i	$-0.812628\pi$
$757$	−2.19882e61	+	2.19882e61i	−0.276458	+	0.276458i	0.555235	+	0.831693i	$0.312628\pi$
$758$	−6.98587e61	+	1.68654e62i	−0.853753	+	2.06114i
$759$	−6.35326e61	−	2.63161e61i	−0.754742	−	0.312624i
$760$	−3.44584e61	−	8.31899e61i	−0.397926	−	0.960679i
$761$			8.60551e61i			0.966065i	0.875602	+	0.483033i	$0.160465\pi$
$761$			8.60551e61i			0.966065i	−0.875602	+	0.483033i	$0.839535\pi$
$762$	1.01173e62	−	4.19074e61i	1.10417	−	0.457361i
$763$	−1.70299e61	−	1.70299e61i	−0.180690	−	0.180690i
$764$	2.42502e62			2.50155
$765$	7.94728e61	+	4.00133e61i	0.797073	+	0.401314i
$766$	2.38057e61			0.232146
$767$	−1.97060e61	−	1.97060e61i	−0.186852	−	0.186852i
$768$	−1.87883e61	+	7.78236e60i	−0.173229	+	0.0717538i
$769$			1.07044e62i			0.959726i	0.877344	+	0.479863i	$0.159314\pi$
$769$			1.07044e62i			0.959726i	−0.877344	+	0.479863i	$0.840686\pi$
$770$	−4.20321e61	−	1.01475e62i	−0.366464	−	0.884722i
$771$	7.37780e61	+	3.05599e61i	0.625544	+	0.259109i
$772$	−4.09413e61	+	9.88412e61i	−0.337590	+	0.815016i
$773$	−3.74658e61	+	3.74658e61i	−0.300453	+	0.300453i	−0.841191	−	0.540738i	$-0.818145\pi$
$773$	−3.74658e61	+	3.74658e61i	−0.300453	+	0.300453i	0.540738	+	0.841191i	$0.318145\pi$
$774$	−1.03109e62	+	1.03109e62i	−0.804201	+	0.804201i
$775$	6.04354e60	−	1.45904e61i	0.0458463	−	0.110683i
$776$	2.59251e61	+	1.07385e61i	0.191290	+	0.0792350i
$777$	−9.54667e61	−	2.30477e62i	−0.685173	−	1.65415i
$778$			1.44195e62i			1.00667i
$779$	−2.95615e62	+	1.22448e62i	−2.00757	+	0.831562i
$780$	−1.19911e62	−	1.19911e62i	−0.792185	−	0.792185i
$781$	−4.91965e61			−0.316182
$782$	−1.48568e62	−	4.49875e62i	−0.928925	−	2.81285i
$783$	−1.46039e62			−0.888364
$784$	−9.96235e60	−	9.96235e60i	−0.0589612	−	0.0589612i
$785$	−4.52811e61	+	1.87560e61i	−0.260747	+	0.108005i
$786$			1.70546e62i			0.955555i
$787$	9.89790e60	+	2.38956e61i	0.0539618	+	0.130275i	0.948561	−	0.316593i	$-0.102539\pi$
$787$	9.89790e60	+	2.38956e61i	0.0539618	+	0.130275i	−0.894600	+	0.446869i	$0.852539\pi$
$788$	1.88222e62	+	7.79640e61i	0.998519	+	0.413600i
$789$	−2.17411e61	+	5.24876e61i	−0.112234	+	0.270957i
$790$	1.61924e62	−	1.61924e62i	0.813448	−	0.813448i
$791$	−1.46895e62	+	1.46895e62i	−0.718144	+	0.718144i
$792$	−6.47649e60	+	1.56356e61i	−0.0308140	+	0.0743917i
$793$	−7.46008e61	−	3.09007e61i	−0.345438	−	0.143085i
$794$	1.05596e61	+	2.54932e61i	0.0475892	+	0.114891i
$795$			1.71888e62i			0.753969i
$796$	−3.27732e62	+	1.35751e62i	−1.39923	+	0.579579i
$797$	−4.02216e61	−	4.02216e61i	−0.167150	−	0.167150i	0.618576	−	0.785725i	$-0.287710\pi$
$797$	−4.02216e61	−	4.02216e61i	−0.167150	−	0.167150i	−0.785725	+	0.618576i	$0.787710\pi$
$798$	6.39043e62			2.58504
$799$	−1.21783e61	+	1.64870e62i	−0.0479547	+	0.649212i
$800$	7.26567e62			2.78510
$801$	8.92768e60	+	8.92768e60i	0.0333150	+	0.0333150i
$802$	−6.50383e62	+	2.69397e62i	−2.36276	+	0.978689i
$803$		−	8.35796e61i		−	0.295608i
$804$	2.13373e62	+	5.15128e62i	0.734741	+	1.77382i
$805$	9.97288e62	+	4.13090e62i	3.34356	+	1.38495i
$806$	−4.23789e60	+	1.02312e61i	−0.0138339	+	0.0333981i
$807$	1.59853e62	−	1.59853e62i	0.508089	−	0.508089i
$808$	5.87053e61	−	5.87053e61i	0.181691	−	0.181691i
$809$	−7.80569e61	+	1.88446e62i	−0.235244	+	0.567928i	−0.996779	−	0.0801947i	$-0.974446\pi$
$809$	−7.80569e61	+	1.88446e62i	−0.235244	+	0.567928i	0.761536	+	0.648123i	$0.224446\pi$
$810$	−1.03803e63	−	4.29965e62i	−3.04636	−	1.26184i
$811$	9.20024e61	+	2.22113e62i	0.262936	+	0.634785i	0.999118	−	0.0419998i	$-0.0133729\pi$
$811$	9.20024e61	+	2.22113e62i	0.262936	+	0.634785i	−0.736181	+	0.676785i	$0.763373\pi$
$812$		−	7.41570e62i		−	2.06394i
$813$	5.29275e62	−	2.19233e62i	1.43461	−	0.594236i
$814$	−1.88722e62	−	1.88722e62i	−0.498194	−	0.498194i
$815$	−5.44246e61			−0.139929
$816$	2.81787e62	−	9.30584e61i	0.705640	−	0.233033i
$817$	7.76579e62			1.89414
$818$	2.39756e62	+	2.39756e62i	0.569605	+	0.569605i
$819$	8.78688e61	−	3.63964e61i	0.203344	−	0.0842277i
$820$			1.68320e63i			3.79436i
$821$	−2.75551e62	−	6.65239e62i	−0.605096	−	1.46083i	−0.868275	−	0.496084i	$-0.834771\pi$
$821$	−2.75551e62	−	6.65239e62i	−0.605096	−	1.46083i	0.263178	−	0.964747i	$-0.415229\pi$
$822$	4.76896e62	+	1.97537e62i	1.02019	+	0.422575i
$823$	2.74147e62	−	6.61850e62i	0.571331	−	1.37931i	−0.329092	−	0.944298i	$-0.606743\pi$
$823$	2.74147e62	−	6.61850e62i	0.571331	−	1.37931i	0.900422	−	0.435016i	$-0.143257\pi$
$824$	2.87231e62	−	2.87231e62i	0.583171	−	0.583171i
$825$	−3.02462e62	+	3.02462e62i	−0.598289	+	0.598289i
$826$	2.11413e62	−	5.10397e62i	0.407438	−	0.983641i
$827$	7.65306e61	+	3.17000e61i	0.143703	+	0.0595238i	0.453376	−	0.891319i	$-0.350220\pi$
$827$	7.65306e61	+	3.17000e61i	0.143703	+	0.0595238i	−0.309673	+	0.950843i	$0.600220\pi$
$828$	−2.73235e62	−	6.59647e62i	−0.499900	−	1.20687i
$829$		−	2.69527e62i		−	0.480486i	−0.970713	−	0.240243i	$-0.922773\pi$
$829$		−	2.69527e62i		−	0.480486i	0.970713	−	0.240243i	$-0.0772271\pi$
$830$	−5.95611e62	+	2.46710e62i	−1.03463	+	0.428557i
$831$	7.97144e62	+	7.97144e62i	1.34932	+	1.34932i
$832$	−3.62318e62			−0.597639
$833$	5.60844e61	+	6.50307e61i	0.0901519	+	0.104532i
$834$	1.05328e63			1.64996
$835$	−4.87133e62	−	4.87133e62i	−0.743683	−	0.743683i
$836$	3.57456e62	−	1.48063e62i	0.531849	−	0.220299i
$837$			2.44657e61i			0.0354781i
$838$	1.08938e62	+	2.62999e62i	0.153969	+	0.371713i
$839$	−4.50139e62	−	1.86454e62i	−0.620105	−	0.256856i	0.0504375	−	0.998727i	$-0.483938\pi$
$839$	−4.50139e62	−	1.86454e62i	−0.620105	−	0.256856i	−0.670542	+	0.741871i	$0.733938\pi$
$840$	2.99683e62	−	7.23500e62i	0.402400	−	0.971480i
$841$	−6.49565e62	+	6.49565e62i	−0.850176	+	0.850176i
$842$	−1.50790e63	+	1.50790e63i	−1.92382	+	1.92382i
$843$	−1.48273e62	+	3.57963e62i	−0.184404	+	0.445190i
$844$	−3.71606e62	−	1.53924e62i	−0.450526	−	0.186614i
$845$	−4.71920e62	−	1.13932e63i	−0.557762	−	1.34656i
$846$			4.40250e62i			0.507266i
$847$	−7.75806e62	+	3.21349e62i	−0.871484	+	0.360981i
$848$	1.37516e62	+	1.37516e62i	0.150606	+	0.150606i
$849$	−4.14222e62			−0.442300
$850$	−2.93895e63	−	2.17089e62i	−3.05975	−	0.226011i
$851$	2.62302e63			2.66267
$852$	−1.06471e63	−	1.06471e63i	−1.05386	−	1.05386i
$853$	7.72774e62	−	3.20094e62i	0.745845	−	0.308939i	0.0227998	−	0.999740i	$-0.492742\pi$
$853$	7.72774e62	−	3.20094e62i	0.745845	−	0.308939i	0.723045	+	0.690801i	$0.242742\pi$
$854$		−	1.60069e63i		−	1.50648i
$855$	−4.82914e62	−	1.16586e63i	−0.443199	−	1.06998i
$856$	1.20163e62	+	4.97732e61i	0.107544	+	0.0445461i
$857$	−2.38360e62	+	5.75452e62i	−0.208039	+	0.502251i	−0.993114	−	0.117149i	$-0.962624\pi$
$857$	−2.38360e62	+	5.75452e62i	−0.208039	+	0.502251i	0.785075	+	0.619401i	$0.212624\pi$
$858$	2.12094e62	−	2.12094e62i	0.180531	−	0.180531i
$859$	−1.42680e60	+	1.42680e60i	−0.00118443	+	0.00118443i	−0.707699	−	0.706514i	$-0.750267\pi$
$859$	−1.42680e60	+	1.42680e60i	−0.00118443	+	0.00118443i	0.706514	+	0.707699i	$0.250267\pi$
$860$	1.56333e63	−	3.77421e63i	1.26571	−	3.05569i
$861$	−2.57095e63	−	1.06492e63i	−2.03014	−	0.840911i
$862$	−3.41372e62	−	8.24146e62i	−0.262919	−	0.634743i
$863$			1.05432e63i			0.792030i	0.918244	+	0.396015i	$0.129607\pi$
$863$			1.05432e63i			0.792030i	−0.918244	+	0.396015i	$0.870393\pi$
$864$	−1.03991e63	+	4.30747e62i	−0.761995	+	0.315629i
$865$	3.07524e63	+	3.07524e63i	2.19803	+	2.19803i
$866$	3.96435e63			2.76399
$867$	−1.75467e63	+	4.39145e62i	−1.19340	+	0.298674i
$868$	−1.24234e62			−0.0824266
$869$	1.62081e62	+	1.62081e62i	0.104908	+	0.104908i
$870$	−7.04717e63	+	2.91903e63i	−4.44991	+	1.84321i
$871$		−	7.80931e62i		−	0.481086i
$872$	−7.03031e61	−	1.69727e62i	−0.0422542	−	0.102011i
$873$	3.63325e62	+	1.50494e62i	0.213054	+	0.0882497i
$874$	−2.57134e63	+	6.20776e63i	−1.47117	+	3.55172i
$875$	2.39905e63	−	2.39905e63i	1.33927	−	1.33927i
$876$	1.80883e63	−	1.80883e63i	0.985282	−	0.985282i
$877$	6.62511e62	−	1.59944e63i	0.352129	−	0.850114i	−0.644228	−	0.764833i	$-0.722821\pi$
$877$	6.62511e62	−	1.59944e63i	0.352129	−	0.850114i	0.996357	−	0.0852809i	$-0.0271788\pi$
$878$	−3.85739e63	−	1.59778e63i	−2.00060	−	0.828678i
$879$	−9.76215e62	−	2.35679e63i	−0.494066	−	1.19278i
$880$			7.23371e62i			0.357260i
$881$	−1.35003e63	+	5.59203e62i	−0.650673	+	0.269518i	−0.683508	−	0.729943i	$-0.739547\pi$
$881$	−1.35003e63	+	5.59203e62i	−0.650673	+	0.269518i	0.0328347	+	0.999461i	$0.489547\pi$
$882$	1.61706e62	+	1.61706e62i	0.0760590	+	0.0760590i
$883$	−2.22367e63			−1.02074			−0.510370	−	0.859955i	$-0.670492\pi$
$883$	−2.22367e63			−1.02074			−0.510370	+	0.859955i	$0.670492\pi$
$884$	1.16628e63	+	8.61484e61i	0.522491	+	0.0385943i
$885$	−3.21582e63			−1.40608
$886$	1.26448e63	+	1.26448e63i	0.539619	+	0.539619i
$887$	3.67651e63	−	1.52286e63i	1.53136	−	0.634311i	0.551534	−	0.834153i	$-0.314043\pi$
$887$	3.67651e63	−	1.52286e63i	1.53136	−	0.634311i	0.979828	+	0.199842i	$0.0640428\pi$
$888$		−	1.90292e63i		−	0.773643i
$889$	−6.58469e62	−	1.58969e63i	−0.261305	−	0.630846i
$890$	−5.77455e62	−	2.39190e62i	−0.223683	−	0.0926525i
$891$	4.30381e62	−	1.03903e63i	0.162736	−	0.392879i
$892$	2.11696e63	−	2.11696e63i	0.781391	−	0.781391i
$893$	1.65790e63	−	1.65790e63i	0.597383	−	0.597383i
$894$	−3.99391e63	+	9.64215e63i	−1.40489	+	3.39170i
$895$	6.55814e63	+	2.71647e63i	2.25209	+	0.932845i
$896$	−1.07084e63	−	2.58523e63i	−0.359006	−	0.866717i
$897$			2.94786e63i			0.964873i
$898$	6.50577e63	−	2.69478e63i	2.07902	−	0.861157i
$899$	1.99329e62	+	1.99329e62i	0.0621924	+	0.0621924i
$900$	−4.44120e63			−1.35296
$901$	−7.74163e62	−	8.97653e62i	−0.230276	−	0.267009i
$902$	−2.97718e63			−0.864697
$903$	4.77571e63	+	4.77571e63i	1.35441	+	1.35441i
$904$	−1.46401e63	+	6.06412e62i	−0.405436	+	0.167937i
$905$		−	3.66775e63i		−	0.991872i
$906$	1.18759e63	+	2.86710e63i	0.313626	+	0.757159i
$907$	3.20128e63	+	1.32601e63i	0.825594	+	0.341972i	0.755157	−	0.655544i	$-0.227561\pi$
$907$	3.20128e63	+	1.32601e63i	0.825594	+	0.341972i	0.0704370	+	0.997516i	$0.477561\pi$
$908$	−3.63743e61	+	8.78154e61i	−0.00916113	+	0.0221169i
$909$	8.22721e62	−	8.22721e62i	0.202362	−	0.202362i
$910$	−3.32930e63	+	3.32930e63i	−0.799766	+	0.799766i
$911$	1.27443e63	−	3.07674e63i	0.298999	−	0.721848i	−0.700963	−	0.713197i	$-0.747246\pi$
$911$	1.27443e63	−	3.07674e63i	0.298999	−	0.721848i	0.999963	−	0.00865064i	$-0.00275362\pi$
$912$	−3.88834e63	−	1.61060e63i	−0.890996	−	0.369062i
$913$	−2.46949e62	−	5.96188e62i	−0.0552696	−	0.133433i
$914$			4.79334e63i			1.04784i
$915$	−8.60841e63	+	3.56572e63i	−1.83810	+	0.761366i
$916$	4.20264e63	+	4.20264e63i	0.876535	+	0.876535i
$917$	2.67969e63			0.545939
$918$	4.33514e63	−	1.43165e63i	0.862751	−	0.284918i
$919$	1.38179e62			0.0268633			0.0134316	−	0.999910i	$-0.495724\pi$
$919$	1.38179e62			0.0268633			0.0134316	+	0.999910i	$0.495724\pi$
$920$	5.82234e63	+	5.82234e63i	1.10576	+	1.10576i
$921$	1.87780e63	−	7.77810e62i	0.348391	−	0.144308i
$922$		−	3.15807e63i		−	0.572409i
$923$	8.07049e62	+	1.94839e63i	0.142910	+	0.345016i
$924$	3.10879e63	+	1.28770e63i	0.537828	+	0.222776i
$925$	6.24376e63	−	1.50738e64i	1.05536	−	2.54785i
$926$	6.41482e63	−	6.41482e63i	1.05937	−	1.05937i
$927$	4.02537e63	−	4.02537e63i	0.649519	−	0.649519i
$928$	−4.96306e63	+	1.19819e64i	−0.782470	+	1.88905i
$929$	−8.90999e62	−	3.69064e62i	−0.137259	−	0.0568544i	0.312997	−	0.949754i	$-0.398667\pi$
$929$	−8.90999e62	−	3.69064e62i	−0.137259	−	0.0568544i	−0.450255	+	0.892900i	$0.648667\pi$
$930$	4.89022e62	+	1.18060e63i	0.0736114	+	0.177714i
$931$		−	1.21791e63i		−	0.179142i
$932$	1.46466e63	−	6.06681e62i	0.210520	−	0.0872004i
$933$	4.11808e63	+	4.11808e63i	0.578415	+	0.578415i
$934$	−1.25184e64			−1.71827
$935$	3.24798e62	−	4.39712e63i	0.0435676	−	0.589819i
$936$	7.25482e62			0.0951033
$937$	−1.24665e63	−	1.24665e63i	−0.159714	−	0.159714i	0.622726	−	0.782440i	$-0.286025\pi$
$937$	−1.24665e63	−	1.24665e63i	−0.159714	−	0.159714i	−0.782440	+	0.622726i	$0.786025\pi$
$938$	1.43024e64	−	5.92423e63i	1.79080	−	0.741773i
$939$		−	1.39268e64i		−	1.70428i
$940$	−4.71997e63	−	1.13950e64i	−0.564534	−	1.36291i
$941$	−8.28276e63	−	3.43083e63i	−0.968274	−	0.401072i	−0.158204	−	0.987406i	$-0.550571\pi$
$941$	−8.28276e63	−	3.43083e63i	−0.968274	−	0.401072i	−0.810069	+	0.586334i	$0.800571\pi$
$942$	1.01537e63	−	2.45131e63i	0.116019	−	0.280094i
$943$	2.06896e64	−	2.06896e64i	2.31074	−	2.31074i
$944$	−2.57275e63	+	2.57275e63i	−0.280866	+	0.280866i
$945$	−3.98067e63	+	9.61019e63i	−0.424788	+	1.02553i
$946$	6.67567e63	+	2.76515e63i	0.696362	+	0.288443i
$947$	4.29239e63	+	1.03627e64i	0.437698	+	1.05670i	0.976742	+	0.214418i	$0.0687856\pi$
$947$	4.29239e63	+	1.03627e64i	0.437698	+	1.05670i	−0.539044	+	0.842278i	$0.681214\pi$
$948$			7.01553e63i			0.699329i
$949$	−3.31011e63	+	1.37109e63i	−0.322566	+	0.133611i
$950$	2.95535e64	+	2.95535e64i	2.81547	+	2.81547i
$951$	−1.50050e63			−0.139751
$952$	1.69351e63	+	5.12807e63i	0.154203	+	0.466938i
$953$	1.53270e64			1.36445			0.682226	−	0.731141i	$-0.261012\pi$
$953$	1.53270e64			1.36445			0.682226	+	0.731141i	$0.261012\pi$
$954$	−2.23211e63	−	2.23211e63i	−0.194279	−	0.194279i
$955$	−3.62096e64	+	1.49985e64i	−3.08142	+	1.27637i
$956$			1.28657e64i			1.07051i
$957$	−2.92186e63	−	7.05400e63i	−0.237713	−	0.573890i
$958$	1.32707e64	+	5.49690e63i	1.05569	+	0.437280i
$959$	3.10379e63	−	7.49322e63i	0.241431	−	0.582865i
$960$	−2.95634e64	+	2.95634e64i	−2.24865	+	2.24865i
$961$	−9.47348e63	+	9.47348e63i	−0.704623	+	0.704623i
$962$	−4.37829e63	+	1.05701e64i	−0.318449	+	0.768805i
$963$	1.68402e63	+	6.97543e62i	0.119779	+	0.0496142i
$964$	−3.54658e62	−	8.56219e62i	−0.0246691	−	0.0595564i
$965$		−	1.72908e64i		−	1.17619i
$966$	−5.39887e64	+	2.23628e64i	−3.59165	+	1.48771i
$967$	−1.17954e64	−	1.17954e64i	−0.767440	−	0.767440i	0.210215	−	0.977655i	$-0.432584\pi$
$967$	−1.17954e64	−	1.17954e64i	−0.767440	−	0.767440i	−0.977655	+	0.210215i	$0.932584\pi$
$968$	−6.40538e63			−0.407591
$969$	2.29127e64	+	1.15362e64i	1.42598	+	0.717961i
$970$	−1.94683e64			−1.18505
$971$	−4.28431e63	−	4.28431e63i	−0.255075	−	0.255075i	0.567973	−	0.823047i	$-0.307728\pi$
$971$	−4.28431e63	−	4.28431e63i	−0.255075	−	0.255075i	−0.823047	+	0.567973i	$0.807728\pi$
$972$	1.94198e64	−	8.04393e63i	1.13089	−	0.468429i
$973$		−	1.65496e64i		−	0.942676i
$974$	3.31155e63	+	7.99480e63i	0.184508	+	0.445441i
$975$	1.69405e64	+	7.01700e63i	0.923269	+	0.382430i
$976$	−4.03429e63	+	9.73964e63i	−0.215078	+	0.519244i
$977$	−5.07761e63	+	5.07761e63i	−0.264805	+	0.264805i	−0.827003	−	0.562198i	$-0.809956\pi$
$977$	−5.07761e63	+	5.07761e63i	−0.264805	+	0.264805i	0.562198	+	0.827003i	$0.309956\pi$
$978$	2.08335e63	−	2.08335e63i	0.106286	−	0.106286i
$979$	2.39421e62	−	5.78014e62i	0.0119491	−	0.0288476i
$980$	−5.91910e63	−	2.45177e63i	−0.288998	−	0.119707i
$981$	−9.85257e62	−	2.37862e63i	−0.0470615	−	0.113617i
$982$		−	3.76432e64i		−	1.75910i
$983$	1.57935e63	−	6.54189e62i	0.0722068	−	0.0299090i	−0.346288	−	0.938128i	$-0.612558\pi$
$983$	1.57935e63	−	6.54189e62i	0.0722068	−	0.0299090i	0.418495	+	0.908219i	$0.362558\pi$
$984$	−1.50097e64	−	1.50097e64i	−0.671392	−	0.671392i
$985$	−3.29266e64			−1.44101
$986$	2.36555e64	−	4.69836e64i	1.01293	−	2.01184i
$987$	2.03912e64			0.854325
$988$	−1.17279e64	−	1.17279e64i	−0.480778	−	0.480778i
$989$	−6.56082e64	+	2.71758e64i	−2.63171	+	1.09009i
$990$		−	1.17415e64i		−	0.460859i
$991$	−1.38501e64	−	3.34370e64i	−0.531946	−	1.28423i	−0.930232	−	0.366971i	$-0.880395\pi$
$991$	−1.38501e64	−	3.34370e64i	−0.531946	−	1.28423i	0.398286	−	0.917261i	$-0.369605\pi$
$992$	2.00731e63	+	8.31455e62i	0.0754420	+	0.0312491i
$993$	9.98617e63	−	2.41088e64i	0.367274	−	0.886678i
$994$	−2.95614e64	+	2.95614e64i	−1.06394	+	1.06394i
$995$	4.05397e64	−	4.05397e64i	1.42786	−	1.42786i
$996$	7.55824e63	−	1.82472e64i	0.260522	−	0.628957i
$997$	3.20536e64	+	1.32770e64i	1.08126	+	0.447873i	0.850951	−	0.525244i	$-0.176026\pi$
$997$	3.20536e64	+	1.32770e64i	1.08126	+	0.447873i	0.230310	+	0.973117i	$0.426026\pi$
$998$	9.07360e63	+	2.19056e64i	0.299553	+	0.723184i
$999$			2.52763e64i			0.816686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.10	✓	252
17.9	even	8	inner	17.44.d.a.9.10	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.10	✓	252	1.1	even	1	trivial
17.44.d.a.9.10	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+(-3.18305e6 - 3.18305e6i) q^{2} +(-2.05920e10 + 8.52950e9i) q^{3} +1.14675e13i q^{4} +(-7.09250e14 - 1.71228e15i) q^{5} +(9.26951e16 + 3.83956e16i) q^{6} +(6.03290e17 - 1.45647e18i) q^{7} +(8.50312e18 - 8.50312e18i) q^{8} +(1.19166e20 - 1.19166e20i) q^{9} +(-3.19269e21 + 7.70785e21i) q^{10} +(-7.71531e21 - 3.19579e21i) q^{11} +(-9.78117e22 - 2.36138e23i) q^{12} +3.57985e23i q^{13} +(-6.55631e24 + 2.71571e24i) q^{14} +(2.92098e25 + 2.92098e25i) q^{15} +4.67373e25 q^{16} +(-2.84099e26 - 2.09853e25i) q^{17} -7.58624e26 q^{18} +(2.85685e27 + 2.85685e27i) q^{19} +(1.96355e28 - 8.13331e27i) q^{20} +3.51374e28i q^{21} +(1.43859e28 + 3.47305e28i) q^{22} +(-3.41330e29 - 1.41384e29i) q^{23} +(-1.02569e29 + 2.47624e29i) q^{24} +(-1.62498e30 + 1.62498e30i) q^{25} +(1.13948e30 - 1.13948e30i) q^{26} +(1.36242e30 - 3.28917e30i) q^{27} +(1.67020e31 + 6.91821e30i) q^{28} +(-1.56978e31 - 3.78978e31i) q^{29} -1.85952e32i q^{30} +(-6.34896e30 + 2.62983e30i) q^{31} +(-2.23561e32 - 2.23561e32i) q^{32} +1.86132e32 q^{33} +(8.37504e32 + 9.71098e32i) q^{34} -2.92177e33 q^{35} +(1.36654e33 + 1.36654e33i) q^{36} +(-6.55931e33 + 2.71695e33i) q^{37} -1.81870e34i q^{38} +(-3.05343e33 - 7.37163e33i) q^{39} +(-2.05906e34 - 8.52889e33i) q^{40} +(-3.03074e34 + 7.31685e34i) q^{41} +(1.11844e35 - 1.11844e35i) q^{42} +(1.35915e35 - 1.35915e35i) q^{43} +(3.66476e34 - 8.84751e34i) q^{44} +(-2.88565e35 - 1.19528e35i) q^{45} +(6.36440e35 + 1.53650e36i) q^{46} -5.80326e35i q^{47} +(-9.62415e35 + 3.98646e35i) q^{48} +(-2.13156e35 - 2.13156e35i) q^{49} +1.03448e37 q^{50} +(6.02917e36 - 1.99109e36i) q^{51} -4.10518e36 q^{52} +(2.94231e36 + 2.94231e36i) q^{53} +(-1.48062e37 + 6.13294e36i) q^{54} +1.54774e37i q^{55} +(-7.25470e36 - 1.75144e37i) q^{56} +(-8.31957e37 - 3.44608e37i) q^{57} +(-7.06636e37 + 1.70597e38i) q^{58} +(-5.50470e37 + 5.50470e37i) q^{59} +(-3.34962e38 + 3.34962e38i) q^{60} +(-8.63184e37 + 2.08391e38i) q^{61} +(2.85799e37 + 1.18382e37i) q^{62} +(-1.01670e38 - 2.45454e38i) q^{63} +1.01211e39i q^{64} +(6.12970e38 - 2.53901e38i) q^{65} +(-5.92468e38 - 5.92468e38i) q^{66} -2.18147e39 q^{67} +(2.40648e38 - 3.25790e39i) q^{68} +8.23461e39 q^{69} +(9.30013e39 + 9.30013e39i) q^{70} +(5.44266e39 - 2.25442e39i) q^{71} -2.02657e39i q^{72} +(3.83003e39 + 9.24651e39i) q^{73} +(2.95268e40 + 1.22304e40i) q^{74} +(1.96014e40 - 4.73220e40i) q^{75} +(-3.27608e40 + 3.27608e40i) q^{76} +(-9.30913e39 + 9.30913e39i) q^{77} +(-1.37450e40 + 3.31834e40i) q^{78} +(-2.53586e40 - 1.05039e40i) q^{79} +(-3.31484e40 - 8.00274e40i) q^{80} +1.34671e41i q^{81} +(3.29368e41 - 1.36429e41i) q^{82} +(5.46405e40 + 5.46405e40i) q^{83} -4.02937e41 q^{84} +(1.65565e41 + 5.01342e41i) q^{85} -8.65249e41 q^{86} +(6.46498e41 + 6.46498e41i) q^{87} +(-9.27784e40 + 3.84301e40i) q^{88} +7.49178e40i q^{89} +(5.38054e41 + 1.29898e42i) q^{90} +(5.21394e41 + 2.15968e41i) q^{91} +(1.62131e42 - 3.91420e42i) q^{92} +(1.08307e41 - 1.08307e41i) q^{93} +(-1.84720e42 + 1.84720e42i) q^{94} +(2.86551e42 - 6.91794e42i) q^{95} +(6.51044e42 + 2.69671e42i) q^{96} +(8.92999e41 + 2.15589e42i) q^{97} +1.35697e42i q^{98} +(-1.30024e42 + 5.38575e41i) 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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