LMFDB - Embedded newform 17.44.d.a.2.14

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)

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);

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")

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			2.14
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.58405e6 - 2.58405e6i) q^{2} +(2.39234e10 - 9.90941e9i) q^{3} +4.55856e12i q^{4} +(5.45301e14 + 1.31647e15i) q^{5} +(-8.74259e16 - 3.62130e16i) q^{6} +(-4.35755e17 + 1.05201e18i) q^{7} +(-1.09500e19 + 1.09500e19i) q^{8} +(2.42022e20 - 2.42022e20i) q^{9} +(1.99275e21 - 4.81092e21i) q^{10} +(-2.06044e21 - 8.53461e20i) q^{11} +(4.51727e22 + 1.09056e23i) q^{12} -1.03481e23i q^{13} +(3.84445e24 - 1.59242e24i) q^{14} +(2.60909e25 + 2.60909e25i) q^{15} +9.66883e25 q^{16} +(2.81351e26 + 4.46589e25i) q^{17} -1.25079e27 q^{18} +(-8.92027e26 - 8.92027e26i) q^{19} +(-6.00122e27 + 2.48579e27i) q^{20} +2.94857e28i q^{21} +(3.11889e27 + 7.52966e27i) q^{22} +(2.14845e29 + 8.89919e28i) q^{23} +(-1.53454e29 + 3.70470e29i) q^{24} +(-6.31860e29 + 6.31860e29i) q^{25} +(-2.67399e29 + 2.67399e29i) q^{26} +(1.38863e29 - 3.35245e29i) q^{27} +(-4.79563e30 - 1.98642e30i) q^{28} +(4.44194e29 + 1.07238e30i) q^{29} -1.34841e32i q^{30} +(9.42263e31 - 3.90298e31i) q^{31} +(-1.53530e32 - 1.53530e32i) q^{32} -5.77500e31 q^{33} +(-6.11625e32 - 8.42427e32i) q^{34} -1.62255e33 q^{35} +(1.10327e33 + 1.10327e33i) q^{36} +(-4.12603e33 + 1.70906e33i) q^{37} +4.61009e33i q^{38} +(-1.02543e33 - 2.47561e33i) q^{39} +(-2.03864e34 - 8.44433e33i) q^{40} +(2.01233e34 - 4.85821e34i) q^{41} +(7.61925e34 - 7.61925e34i) q^{42} +(-1.25809e35 + 1.25809e35i) q^{43} +(3.89055e33 - 9.39263e33i) q^{44} +(4.50589e35 + 1.86640e35i) q^{45} +(-3.25212e35 - 7.85132e35i) q^{46} -2.55497e35i q^{47} +(2.31312e36 - 9.58124e35i) q^{48} +(6.27357e35 + 6.27357e35i) q^{49} +3.26552e36 q^{50} +(7.17343e36 - 1.71963e36i) q^{51} +4.71723e35 q^{52} +(3.49052e36 + 3.49052e36i) q^{53} +(-1.22512e36 + 5.07461e35i) q^{54} -3.17790e36i q^{55} +(-6.74795e36 - 1.62910e37i) q^{56} +(-3.01798e37 - 1.25009e37i) q^{57} +(1.62327e36 - 3.91891e36i) q^{58} +(-3.56605e37 + 3.56605e37i) q^{59} +(-1.18937e38 + 1.18937e38i) q^{60} +(-5.14337e37 + 1.24172e38i) q^{61} +(-3.44341e38 - 1.42631e38i) q^{62} +(1.49146e38 + 3.60070e38i) q^{63} -5.70180e37i q^{64} +(1.36229e38 - 5.64281e37i) q^{65} +(1.49229e38 + 1.49229e38i) q^{66} +1.37915e39 q^{67} +(-2.03580e38 + 1.28256e39i) q^{68} +6.02170e39 q^{69} +(4.19277e39 + 4.19277e39i) q^{70} +(3.39977e39 - 1.40823e39i) q^{71} +5.30027e39i q^{72} +(1.37134e38 + 3.31072e38i) q^{73} +(1.50782e40 + 6.24558e39i) q^{74} +(-8.85491e39 + 2.13776e40i) q^{75} +(4.06636e39 - 4.06636e39i) q^{76} +(1.79569e39 - 1.79569e39i) q^{77} +(-3.74734e39 + 9.04688e39i) q^{78} +(-2.46722e40 - 1.02196e40i) q^{79} +(5.27242e40 + 1.27288e41i) q^{80} +1.02956e41i q^{81} +(-1.77538e41 + 7.35388e40i) q^{82} +(-1.09197e41 - 1.09197e41i) q^{83} -1.34412e41 q^{84} +(9.46288e40 + 3.94744e41i) q^{85} +6.50197e41 q^{86} +(2.12533e40 + 2.12533e40i) q^{87} +(3.19072e40 - 1.32164e40i) q^{88} +1.04667e41i q^{89} +(-6.82059e41 - 1.64663e42i) q^{90} +(1.08862e41 + 4.50922e40i) q^{91} +(-4.05675e41 + 9.79387e41i) q^{92} +(1.86745e42 - 1.86745e42i) q^{93} +(-6.60217e41 + 6.60217e41i) q^{94} +(6.87906e41 - 1.66075e42i) q^{95} +(-5.19437e42 - 2.15158e42i) q^{96} +(1.50743e42 + 3.63925e42i) q^{97} -3.24224e42i q^{98} +(-7.05226e41 + 2.92114e41i) 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 $

$2$	−2.58405e6	−	2.58405e6i	−0.871277	−	0.871277i	0.121334	−	0.992612i	$-0.461283\pi$
$2$	−2.58405e6	−	2.58405e6i	−0.871277	−	0.871277i	−0.992612	+	0.121334i	$0.961283\pi$
$3$	2.39234e10	−	9.90941e9i	1.32043	−	0.546941i	0.392522	−	0.919743i	$-0.371603\pi$
$3$	2.39234e10	−	9.90941e9i	1.32043	−	0.546941i	0.927911	+	0.372801i	$0.121603\pi$
$4$			4.55856e12i			0.518249i
$5$	5.45301e14	+	1.31647e15i	0.511424	+	1.23469i	0.943055	+	0.332637i	$0.107938\pi$
$5$	5.45301e14	+	1.31647e15i	0.511424	+	1.23469i	−0.431631	+	0.902050i	$0.642062\pi$
$6$	−8.74259e16	−	3.62130e16i	−1.62700	−	0.673926i
$7$	−4.35755e17	+	1.05201e18i	−0.294873	+	0.711886i	0.705123	+	0.709085i	$0.250892\pi$
$7$	−4.35755e17	+	1.05201e18i	−0.294873	+	0.711886i	−0.999996	+	0.00280098i	$0.999108\pi$
$8$	−1.09500e19	+	1.09500e19i	−0.419739	+	0.419739i
$9$	2.42022e20	−	2.42022e20i	0.737293	−	0.737293i
$10$	1.99275e21	−	4.81092e21i	0.630162	−	1.52135i
$11$	−2.06044e21	−	8.53461e20i	−0.0839492	−	0.0347729i	0.340314	−	0.940312i	$-0.389467\pi$
$11$	−2.06044e21	−	8.53461e20i	−0.0839492	−	0.0347729i	−0.424263	+	0.905539i	$0.639467\pi$
$12$	4.51727e22	+	1.09056e23i	0.283452	+	0.684313i
$13$		−	1.03481e23i		−	0.116165i	−0.998312	−	0.0580827i	$-0.981501\pi$
$13$		−	1.03481e23i		−	0.116165i	0.998312	−	0.0580827i	$-0.0184987\pi$
$14$	3.84445e24	−	1.59242e24i	0.877166	−	0.363334i
$15$	2.60909e25	+	2.60909e25i	1.35060	+	1.35060i
$16$	9.66883e25			1.24967
$17$	2.81351e26	+	4.46589e25i	0.987636	+	0.156768i
$17$	2.81351e26	+	4.46589e25i	0.987636	+	0.156768i
$18$	−1.25079e27			−1.28477
$19$	−8.92027e26	−	8.92027e26i	−0.286533	−	0.286533i	0.549174	−	0.835708i	$-0.314942\pi$
$19$	−8.92027e26	−	8.92027e26i	−0.286533	−	0.286533i	−0.835708	+	0.549174i	$0.814942\pi$
$20$	−6.00122e27	+	2.48579e27i	−0.639875	+	0.265045i
$21$			2.94857e28i			1.10128i
$22$	3.11889e27	+	7.52966e27i	0.0428462	+	0.103440i
$23$	2.14845e29	+	8.89919e28i	1.13495	+	0.470113i	0.869462	−	0.494001i	$-0.164466\pi$
$23$	2.14845e29	+	8.89919e28i	1.13495	+	0.470113i	0.265491	+	0.964113i	$0.414466\pi$
$24$	−1.53454e29	+	3.70470e29i	−0.324665	+	0.783810i
$25$	−6.31860e29	+	6.31860e29i	−0.555790	+	0.555790i
$26$	−2.67399e29	+	2.67399e29i	−0.101212	+	0.101212i
$27$	1.38863e29	−	3.35245e29i	0.0233488	−	0.0563691i
$28$	−4.79563e30	−	1.98642e30i	−0.368934	−	0.152817i
$29$	4.44194e29	+	1.07238e30i	0.0160700	+	0.0387964i	0.931711	−	0.363201i	$-0.118316\pi$
$29$	4.44194e29	+	1.07238e30i	0.0160700	+	0.0387964i	−0.915641	+	0.401997i	$0.868316\pi$
$30$		−	1.34841e32i		−	2.35350i
$31$	9.42263e31	−	3.90298e31i	0.812635	−	0.336605i	0.0626303	−	0.998037i	$-0.480051\pi$
$31$	9.42263e31	−	3.90298e31i	0.812635	−	0.336605i	0.750005	+	0.661432i	$0.230051\pi$
$32$	−1.53530e32	−	1.53530e32i	−0.669067	−	0.669067i
$33$	−5.77500e31			−0.129868
$34$	−6.11625e32	−	8.42427e32i	−0.723916	−	0.997092i
$35$	−1.62255e33			−1.02976
$36$	1.10327e33	+	1.10327e33i	0.382101	+	0.382101i
$37$	−4.12603e33	+	1.70906e33i	−0.792857	+	0.328412i	−0.742092	−	0.670299i	$-0.766166\pi$
$37$	−4.12603e33	+	1.70906e33i	−0.792857	+	0.328412i	−0.0507653	+	0.998711i	$0.516166\pi$
$38$			4.61009e33i			0.499300i
$39$	−1.02543e33	−	2.47561e33i	−0.0635357	−	0.153389i
$40$	−2.03864e34	−	8.44433e33i	−0.732911	−	0.303582i
$41$	2.01233e34	−	4.85821e34i	0.425449	−	1.02712i	−0.555265	−	0.831674i	$-0.687383\pi$
$41$	2.01233e34	−	4.85821e34i	0.425449	−	1.02712i	0.980714	−	0.195451i	$-0.0626169\pi$
$42$	7.61925e34	−	7.61925e34i	0.959517	−	0.959517i
$43$	−1.25809e35	+	1.25809e35i	−0.955304	+	0.955304i	−0.999043	−	0.0437389i	$-0.986073\pi$
$43$	−1.25809e35	+	1.25809e35i	−0.955304	+	0.955304i	0.0437389	+	0.999043i	$0.486073\pi$
$44$	3.89055e33	−	9.39263e33i	0.0180210	−	0.0435065i
$45$	4.50589e35	+	1.86640e35i	1.28740	+	0.533257i
$46$	−3.25212e35	−	7.85132e35i	−0.579260	−	1.39846i
$47$		−	2.55497e35i		−	0.286604i	−0.989679	−	0.143302i	$-0.954228\pi$
$47$		−	2.55497e35i		−	0.286604i	0.989679	−	0.143302i	$-0.0457720\pi$
$48$	2.31312e36	−	9.58124e35i	1.65010	−	0.683495i
$49$	6.27357e35	+	6.27357e35i	0.287276	+	0.287276i
$50$	3.26552e36			0.968495
$51$	7.17343e36	−	1.71963e36i	1.38985	−	0.333178i
$52$	4.71723e35			0.0602026
$53$	3.49052e36	+	3.49052e36i	0.295773	+	0.295773i	0.839356	−	0.543583i	$-0.182932\pi$
$53$	3.49052e36	+	3.49052e36i	0.295773	+	0.295773i	−0.543583	+	0.839356i	$0.682932\pi$
$54$	−1.22512e36	+	5.07461e35i	−0.0694564	+	0.0287698i
$55$		−	3.17790e36i		−	0.121435i
$56$	−6.74795e36	−	1.62910e37i	−0.175037	−	0.422576i
$57$	−3.01798e37	−	1.25009e37i	−0.535065	−	0.221631i
$58$	1.62327e36	−	3.91891e36i	0.0198010	−	0.0478039i
$59$	−3.56605e37	+	3.56605e37i	−0.301210	+	0.301210i	−0.841487	−	0.540277i	$-0.818319\pi$
$59$	−3.56605e37	+	3.56605e37i	−0.301210	+	0.301210i	0.540277	+	0.841487i	$0.318319\pi$
$60$	−1.18937e38	+	1.18937e38i	−0.699948	+	0.699948i
$61$	−5.14337e37	+	1.24172e38i	−0.212157	+	0.512191i	−0.993754	−	0.111592i	$-0.964405\pi$
$61$	−5.14337e37	+	1.24172e38i	−0.212157	+	0.512191i	0.781598	+	0.623783i	$0.214405\pi$
$62$	−3.44341e38	−	1.42631e38i	−1.00131	−	0.414755i
$63$	1.49146e38	+	3.60070e38i	0.307461	+	0.742276i
$64$		−	5.70180e37i		−	0.0837804i
$65$	1.36229e38	−	5.64281e37i	0.143428	−	0.0594098i
$66$	1.49229e38	+	1.49229e38i	0.113151	+	0.113151i
$67$	1.37915e39			0.756840			0.378420	−	0.925634i	$-0.376467\pi$
$67$	1.37915e39			0.756840			0.378420	+	0.925634i	$0.376467\pi$
$68$	−2.03580e38	+	1.28256e39i	−0.0812445	+	0.511841i
$69$	6.02170e39			1.75575
$70$	4.19277e39	+	4.19277e39i	0.897207	+	0.897207i
$71$	3.39977e39	−	1.40823e39i	0.536284	−	0.222136i	−0.0980692	−	0.995180i	$-0.531267\pi$
$71$	3.39977e39	−	1.40823e39i	0.536284	−	0.222136i	0.634353	+	0.773044i	$0.281267\pi$
$72$			5.30027e39i			0.618942i
$73$	1.37134e38	+	3.31072e38i	0.0119043	+	0.0287396i	0.929720	−	0.368267i	$-0.120049\pi$
$73$	1.37134e38	+	3.31072e38i	0.0119043	+	0.0287396i	−0.917816	+	0.397007i	$0.870049\pi$
$74$	1.50782e40	+	6.24558e39i	0.976936	+	0.404660i
$75$	−8.85491e39	+	2.13776e40i	−0.429899	+	1.03787i
$76$	4.06636e39	−	4.06636e39i	0.148496	−	0.148496i
$77$	1.79569e39	−	1.79569e39i	0.0495087	−	0.0495087i
$78$	−3.74734e39	+	9.04688e39i	−0.0782869	+	0.189001i
$79$	−2.46722e40	−	1.02196e40i	−0.391945	−	0.162349i	0.178002	−	0.984030i	$-0.443037\pi$
$79$	−2.46722e40	−	1.02196e40i	−0.391945	−	0.162349i	−0.569948	+	0.821681i	$0.693037\pi$
$80$	5.27242e40	+	1.27288e41i	0.639110	+	1.54295i
$81$			1.02956e41i			0.955488i
$82$	−1.77538e41	+	7.35388e40i	−1.26559	+	0.524226i
$83$	−1.09197e41	−	1.09197e41i	−0.599835	−	0.599835i	0.340434	−	0.940269i	$-0.389426\pi$
$83$	−1.09197e41	−	1.09197e41i	−0.599835	−	0.599835i	−0.940269	+	0.340434i	$0.889426\pi$
$84$	−1.34412e41			−0.570735
$85$	9.46288e40	+	3.94744e41i	0.311542	+	1.29960i
$86$	6.50197e41			1.66467
$87$	2.12533e40	+	2.12533e40i	0.0424388	+	0.0424388i
$88$	3.19072e40	−	1.32164e40i	0.0498323	−	0.0206412i
$89$			1.04667e41i			0.128211i	0.997943	+	0.0641053i	$0.0204194\pi$
$89$			1.04667e41i			0.128211i	−0.997943	+	0.0641053i	$0.979581\pi$
$90$	−6.82059e41	−	1.64663e42i	−0.657064	−	1.58629i
$91$	1.08862e41	+	4.50922e40i	0.0826965	+	0.0342540i
$92$	−4.05675e41	+	9.79387e41i	−0.243635	+	0.588188i
$93$	1.86745e42	−	1.86745e42i	0.888928	−	0.888928i
$94$	−6.60217e41	+	6.60217e41i	−0.249711	+	0.249711i
$95$	6.87906e41	−	1.66075e42i	0.207239	−	0.500319i
$96$	−5.19437e42	−	2.15158e42i	−1.24940	−	0.517518i
$97$	1.50743e42	+	3.63925e42i	0.290164	+	0.700518i	0.999993	−	0.00385627i	$-0.00122749\pi$
$97$	1.50743e42	+	3.63925e42i	0.290164	+	0.700518i	−0.709828	+	0.704375i	$0.751227\pi$
$98$		−	3.24224e42i		−	0.500593i
$99$	−7.05226e41	+	2.92114e41i	−0.0875330	+	0.0362573i
$100$	−2.88037e42	−	2.88037e42i	−0.288037	−	0.288037i
$101$	−2.25324e43			−1.81927			−0.909635	−	0.415408i	$-0.863639\pi$
$101$	−2.25324e43			−1.81927			−0.909635	+	0.415408i	$0.863639\pi$
$102$	−2.29801e43	−	1.40929e43i	−1.50123	−	0.920654i
$103$	−2.01442e43			−1.06696			−0.533481	−	0.845812i	$-0.679117\pi$
$103$	−2.01442e43			−1.06696			−0.533481	+	0.845812i	$0.679117\pi$
$104$	1.13311e42	+	1.13311e42i	0.0487592	+	0.0487592i
$105$	−3.88171e43	+	1.60786e43i	−1.35973	+	0.563219i
$106$		−	1.80394e43i		−	0.515401i
$107$	3.14164e42	+	7.58458e42i	0.0733508	+	0.177085i	0.956302	−	0.292380i	$-0.0944471\pi$
$107$	3.14164e42	+	7.58458e42i	0.0733508	+	0.177085i	−0.882952	+	0.469464i	$0.844447\pi$
$108$	1.52823e42	+	6.33015e41i	0.0292132	+	0.0121005i
$109$	2.17167e43	−	5.24289e43i	0.340506	−	0.822055i	−0.657159	−	0.753752i	$-0.728242\pi$
$109$	2.17167e43	−	5.24289e43i	0.340506	−	0.822055i	0.997665	−	0.0683022i	$-0.0217582\pi$
$110$	−8.21187e42	+	8.21187e42i	−0.105803	+	0.105803i
$111$	−8.17730e43	+	8.17730e43i	−0.867293	+	0.867293i
$112$	−4.21324e43	+	1.01717e44i	−0.368493	+	0.889620i
$113$	−1.27332e44	−	5.27427e43i	−0.919923	−	0.381045i	−0.128076	−	0.991764i	$-0.540880\pi$
$113$	−1.27332e44	−	5.27427e43i	−0.919923	−	0.381045i	−0.791847	+	0.610720i	$0.790880\pi$
$114$	4.56832e43	+	1.10289e44i	0.273088	+	0.659293i
$115$			3.31366e44i			1.64174i
$116$	−4.88851e42	+	2.02489e42i	−0.0201062	+	0.00832826i
$117$	−2.50445e43	−	2.50445e43i	−0.0856480	−	0.0856480i
$118$	1.84297e44			0.524875
$119$	−1.69582e44	+	2.76523e44i	−0.402827	+	0.656857i
$120$	−5.71392e44			−1.13380
$121$	−4.22445e44	−	4.22445e44i	−0.701268	−	0.701268i
$122$	4.53774e44	−	1.87959e44i	0.631108	−	0.261413i
$123$		−	1.36166e45i		−	1.58894i
$124$	1.77920e44	+	4.29536e44i	0.174445	+	0.421147i
$125$	3.20275e44	+	1.32662e44i	0.264216	+	0.109442i
$126$	5.45039e44	−	1.31584e45i	0.378845	−	0.914612i
$127$	−1.24393e45	+	1.24393e45i	−0.729487	+	0.729487i	−0.970518	−	0.241030i	$-0.922515\pi$
$127$	−1.24393e45	+	1.24393e45i	−0.729487	+	0.729487i	0.241030	+	0.970518i	$0.422515\pi$
$128$	−1.49781e45	+	1.49781e45i	−0.742063	+	0.742063i
$129$	−1.76310e45	+	4.25649e45i	−0.738920	+	1.78391i
$130$	−4.97837e44	−	2.06211e44i	−0.176728	−	0.0732031i
$131$	2.07282e45	+	5.00423e45i	0.624063	+	1.50662i	0.846892	+	0.531765i	$0.178471\pi$
$131$	2.07282e45	+	5.00423e45i	0.624063	+	1.50662i	−0.222829	+	0.974858i	$0.571529\pi$
$132$		−	2.63257e44i		−	0.0673039i
$133$	1.32712e45	−	5.49712e44i	0.288470	−	0.119488i
$134$	−3.56380e45	−	3.56380e45i	−0.659418	−	0.659418i
$135$	5.17062e44			0.0815393
$136$	−3.56981e45	+	2.59178e45i	−0.480351	+	0.348748i
$137$	8.83249e45			1.01529			0.507646	−	0.861566i	$-0.330516\pi$
$137$	8.83249e45			1.01529			0.507646	+	0.861566i	$0.330516\pi$
$138$	−1.55604e46	−	1.55604e46i	−1.52975	−	1.52975i
$139$	1.10932e46	−	4.59496e45i	0.933769	−	0.386780i	0.136662	−	0.990618i	$-0.456363\pi$
$139$	1.10932e46	−	4.59496e45i	0.933769	−	0.386780i	0.797107	+	0.603838i	$0.206363\pi$
$140$		−	7.39652e45i		−	0.533672i
$141$	−2.53182e45	−	6.11236e45i	−0.156755	−	0.378441i
$142$	−1.24241e46	−	5.14624e45i	−0.660794	−	0.273710i
$143$	−8.83167e43	+	2.13215e44i	−0.00403941	+	0.00975200i
$144$	2.34007e46	−	2.34007e46i	0.921371	−	0.921371i
$145$	−1.16954e45	+	1.16954e45i	−0.0396829	+	0.0396829i
$146$	5.01144e44	−	1.20987e45i	0.0146682	−	0.0354121i
$147$	2.12253e46	+	8.79179e45i	0.536451	+	0.222205i
$148$	−7.79084e45	−	1.88087e46i	−0.170199	−	0.410897i
$149$		−	8.79849e45i		−	0.166304i	−0.996537	−	0.0831522i	$-0.973501\pi$
$149$		−	8.79849e45i		−	0.166304i	0.996537	−	0.0831522i	$-0.0264988\pi$
$150$	7.81225e46	−	3.23594e46i	1.27883	−	0.529710i
$151$	7.31851e46	+	7.31851e46i	1.03853	+	1.03853i	0.999227	+	0.0393001i	$0.0125128\pi$
$151$	7.31851e46	+	7.31851e46i	1.03853	+	1.03853i	0.0393001	+	0.999227i	$0.487487\pi$
$152$	1.95354e46			0.240539
$153$	7.89014e46	−	5.72846e46i	0.843760	−	0.612593i
$154$	−9.28032e45			−0.0862715
$155$	1.02763e47	+	1.02763e47i	0.831202	+	0.831202i
$156$	1.12852e46	−	4.67450e45i	0.0794935	−	0.0329273i
$157$			1.51804e47i			0.932054i	0.884771	+	0.466027i	$0.154315\pi$
$157$			1.51804e47i			0.932054i	−0.884771	+	0.466027i	$0.845685\pi$
$158$	3.73464e46	+	9.01621e46i	0.200042	+	0.482944i
$159$	1.18094e47	+	4.89162e46i	0.552320	+	0.228778i
$160$	1.18398e47	−	2.85839e47i	0.483912	−	1.16827i
$161$	−1.87240e47	+	1.87240e47i	−0.669333	+	0.669333i
$162$	2.66045e47	−	2.66045e47i	0.832495	−	0.832495i
$163$	−2.67345e47	+	6.45428e47i	−0.732889	+	1.76935i	−0.100169	+	0.994970i	$0.531938\pi$
$163$	−2.67345e47	+	6.45428e47i	−0.732889	+	1.76935i	−0.632720	+	0.774381i	$0.718062\pi$
$164$	2.21464e47	+	9.17335e46i	0.532306	+	0.220488i
$165$	−3.14911e46	−	7.60263e46i	−0.0664177	−	0.160346i
$166$			5.64342e47i			1.04525i
$167$	−9.58395e47	+	3.96980e47i	−1.56006	+	0.646197i	−0.985099	−	0.171987i	$-0.944981\pi$
$167$	−9.58395e47	+	3.96980e47i	−1.56006	+	0.646197i	−0.574957	+	0.818183i	$0.694981\pi$
$168$	−3.22868e47	−	3.22868e47i	−0.462249	−	0.462249i
$169$	7.82823e47			0.986506
$170$	7.75512e47	−	1.26456e48i	0.860869	−	1.40375i
$171$	−4.31779e47			−0.422518
$172$	−5.73510e47	−	5.73510e47i	−0.495085	−	0.495085i
$173$	−6.67570e47	+	2.76516e47i	−0.508751	+	0.210732i	−0.622268	−	0.782804i	$-0.713788\pi$
$173$	−6.67570e47	+	2.76516e47i	−0.508751	+	0.210732i	0.113517	+	0.993536i	$0.463788\pi$
$174$		−	1.09839e47i		−	0.0739519i
$175$	−3.89384e47	−	9.40057e47i	−0.231772	−	0.559546i
$176$	−1.99220e47	−	8.25197e46i	−0.104909	−	0.0434545i
$177$	−4.99748e47	+	1.20650e48i	−0.232984	+	0.562472i
$178$	2.70465e47	−	2.70465e47i	0.111707	−	0.111707i
$179$	2.29101e48	−	2.29101e48i	0.838853	−	0.838853i	−0.149855	−	0.988708i	$-0.547881\pi$
$179$	2.29101e48	−	2.29101e48i	0.838853	−	0.838853i	0.988708	+	0.149855i	$0.0478806\pi$
$180$	−8.50811e47	+	2.05404e48i	−0.276359	+	0.667191i
$181$	1.17525e48	+	4.86806e47i	0.338877	+	0.140367i	0.545631	−	0.838026i	$-0.316290\pi$
$181$	1.17525e48	+	4.86806e47i	0.338877	+	0.140367i	−0.206754	+	0.978393i	$0.566290\pi$
$182$	−1.64785e47	−	3.97826e47i	−0.0422068	−	0.101896i
$183$			3.48030e48i			0.792352i
$184$	−3.32702e48	+	1.37810e48i	−0.673709	+	0.279059i
$185$	−4.49985e48	−	4.49985e48i	−0.810972	−	0.810972i
$186$	−9.65120e48			−1.54901
$187$	−5.41591e47	−	3.32139e47i	−0.0774600	−	0.0475035i
$188$	1.16470e48			0.148532
$189$	2.92169e47	+	2.92169e47i	0.0332434	+	0.0332434i
$190$	−6.06905e48	+	2.51388e48i	−0.616479	+	0.255354i
$191$			5.02181e48i			0.455662i	0.973701	+	0.227831i	$0.0731634\pi$
$191$			5.02181e48i			0.455662i	−0.973701	+	0.227831i	$0.926837\pi$
$192$	−5.65015e47	−	1.36407e48i	−0.0458230	−	0.110626i
$193$	2.18231e49	+	9.03944e48i	1.58283	+	0.655631i	0.988859	−	0.148854i	$-0.0475584\pi$
$193$	2.18231e49	+	9.03944e48i	1.58283	+	0.655631i	0.593974	+	0.804485i	$0.297558\pi$
$194$	5.50874e48	−	1.32993e49i	0.357532	−	0.863159i
$195$	2.69991e48	−	2.69991e48i	0.156893	−	0.156893i
$196$	−2.85984e48	+	2.85984e48i	−0.148880	+	0.148880i
$197$	−8.41734e48	+	2.03213e49i	−0.392782	+	0.948259i	0.596550	+	0.802576i	$0.296538\pi$
$197$	−8.41734e48	+	2.03213e49i	−0.392782	+	0.948259i	−0.989331	+	0.145683i	$0.953462\pi$
$198$	2.57718e48	+	1.06750e48i	0.107856	+	0.0446753i
$199$	1.77367e49	+	4.28202e49i	0.666089	+	1.60808i	0.788097	+	0.615551i	$0.211067\pi$
$199$	1.77367e49	+	4.28202e49i	0.666089	+	1.60808i	−0.122008	+	0.992529i	$0.538933\pi$
$200$		−	1.38377e49i		−	0.466574i
$201$	3.29941e49	−	1.36666e49i	0.999357	−	0.413947i
$202$	5.82248e49	+	5.82248e49i	1.58509	+	1.58509i
$203$	−1.32171e48			−0.0323572
$204$	7.83904e48	+	3.27005e49i	0.172669	+	0.720288i
$205$	7.49302e49			1.48576
$206$	5.20536e49	+	5.20536e49i	0.929620	+	0.929620i
$207$	7.35352e49	−	3.04593e49i	1.18340	−	0.490182i
$208$		−	1.00054e49i		−	0.145168i
$209$	1.07665e48	+	2.59927e48i	0.0140907	+	0.0340179i
$210$	1.41853e50	+	5.87575e49i	1.67542	+	0.693983i
$211$	5.55087e49	−	1.34010e50i	0.591954	−	1.42910i	−0.289658	−	0.957130i	$-0.593542\pi$
$211$	5.55087e49	−	1.34010e50i	0.591954	−	1.42910i	0.881612	−	0.471974i	$-0.156458\pi$
$212$	−1.59118e49	+	1.59118e49i	−0.153284	+	0.153284i
$213$	6.73794e49	−	6.73794e49i	0.586632	−	0.586632i
$214$	1.14808e49	−	2.77171e49i	0.0903808	−	0.218199i
$215$	−2.34229e50	−	9.70208e49i	−1.66807	−	0.690936i
$216$	2.15038e48	+	5.19148e48i	0.0138599	+	0.0334607i
$217$			1.16134e50i			0.677759i
$218$	−1.91596e50	+	7.93617e49i	−1.01291	+	0.419562i
$219$	6.56145e48	+	6.56145e48i	0.0314378	+	0.0314378i
$220$	1.44867e49			0.0629333
$221$	4.62133e48	−	2.91144e49i	0.0182110	−	0.114729i
$222$	4.22611e50			1.51130
$223$	1.22696e50	+	1.22696e50i	0.398359	+	0.398359i	0.877654	−	0.479295i	$-0.159108\pi$
$223$	1.22696e50	+	1.22696e50i	0.398359	+	0.398359i	−0.479295	+	0.877654i	$0.659108\pi$
$224$	2.28416e50	−	9.46132e49i	0.673589	−	0.279010i
$225$			3.05848e50i			0.819560i
$226$	1.92743e50	+	4.65323e50i	0.469513	+	1.13350i
$227$	9.22255e49	+	3.82010e49i	0.204312	+	0.0846290i	0.482493	−	0.875900i	$-0.339731\pi$
$227$	9.22255e49	+	3.82010e49i	0.204312	+	0.0846290i	−0.278181	+	0.960529i	$0.589731\pi$
$228$	5.69860e49	−	1.37576e50i	0.114860	−	0.277297i
$229$	−5.10557e50	+	5.10557e50i	−0.936659	+	0.936659i	−0.998110	−	0.0614507i	$-0.980427\pi$
$229$	−5.10557e50	+	5.10557e50i	−0.936659	+	0.936659i	0.0614507	+	0.998110i	$0.480427\pi$
$230$	8.56266e50	−	8.56266e50i	1.43041	−	1.43041i
$231$	2.51649e49	−	6.07533e49i	0.0382945	−	0.0924512i
$232$	−1.66065e49	−	6.87864e48i	−0.0230296	−	0.00953917i
$233$	1.75912e50	+	4.24689e50i	0.222404	+	0.536932i	0.995215	−	0.0977044i	$-0.0311500\pi$
$233$	1.75912e50	+	4.24689e50i	0.222404	+	0.536932i	−0.772811	+	0.634636i	$0.781150\pi$
$234$			1.29433e50i			0.149246i
$235$	3.36355e50	−	1.39323e50i	0.353866	−	0.146576i
$236$	−1.62561e50	−	1.62561e50i	−0.156102	−	0.156102i
$237$	−6.91514e50			−0.606333
$238$	1.15276e51	−	2.76341e50i	0.923279	−	0.221330i
$239$	1.27792e51			0.935293			0.467647	−	0.883916i	$-0.345102\pi$
$239$	1.27792e51			0.935293			0.467647	+	0.883916i	$0.345102\pi$
$240$	2.52269e51	+	2.52269e51i	1.68780	+	1.68780i
$241$	−1.73662e51	+	7.19333e50i	−1.06253	+	0.440112i	−0.844347	−	0.535797i	$-0.820011\pi$
$241$	−1.73662e51	+	7.19333e50i	−1.06253	+	0.440112i	−0.218178	+	0.975909i	$0.570011\pi$
$242$			2.18324e51i			1.22200i
$243$	1.06582e51	+	2.57312e51i	0.545945	+	1.31803i
$244$	−5.66046e50	−	2.34464e50i	−0.265442	−	0.109950i
$245$	−4.83800e50	+	1.16800e51i	−0.207776	+	0.501615i
$246$	−3.51860e51	+	3.51860e51i	−1.38441	+	1.38441i
$247$	−9.23075e49	+	9.23075e49i	−0.0332853	+	0.0332853i
$248$	−6.04402e50	+	1.45915e51i	−0.199809	+	0.482381i
$249$	−3.69444e51	−	1.53029e51i	−1.12012	−	0.463967i
$250$	−4.84802e50	−	1.17042e51i	−0.134851	−	0.325559i
$251$		−	4.95848e51i		−	1.26580i	−0.774235	−	0.632898i	$-0.781865\pi$
$251$		−	4.95848e51i		−	1.26580i	0.774235	−	0.632898i	$-0.218135\pi$
$252$	−1.64140e51	+	6.79891e50i	−0.384683	+	0.159341i
$253$	−3.66724e50	−	3.66724e50i	−0.0789312	−	0.0789312i
$254$	6.42879e51			1.27117
$255$	6.17552e51	+	8.50591e51i	1.12217	+	1.54563i
$256$	7.23928e51			1.20931
$257$	−3.00583e51	−	3.00583e51i	−0.461746	−	0.461746i	0.437482	−	0.899227i	$-0.355871\pi$
$257$	−3.00583e51	−	3.00583e51i	−0.461746	−	0.461746i	−0.899227	+	0.437482i	$0.855871\pi$
$258$	1.55549e52	−	6.44307e51i	2.19809	−	0.910477i
$259$		−	5.08533e51i		−	0.661263i
$260$	2.57231e50	+	6.21010e50i	0.0307890	+	0.0743313i
$261$	3.67044e50	+	1.52035e50i	0.0404527	+	0.0167560i
$262$	7.57492e51	−	1.82875e52i	0.768953	−	1.85642i
$263$	−1.23039e51	+	1.23039e51i	−0.115079	+	0.115079i	−0.762301	−	0.647222i	$-0.775930\pi$
$263$	−1.23039e51	+	1.23039e51i	−0.115079	+	0.115079i	0.647222	+	0.762301i	$0.275930\pi$
$264$	6.32363e50	−	6.32363e50i	0.0545107	−	0.0545107i
$265$	−2.69179e51	+	6.49856e51i	−0.213922	+	0.516453i
$266$	−4.84984e51	−	2.00887e51i	−0.355445	−	0.147230i
$267$	1.03719e51	+	2.50399e51i	0.0701237	+	0.169294i
$268$			6.28695e51i			0.392231i
$269$	−8.67845e51	+	3.59473e51i	−0.499768	+	0.207011i	−0.618304	−	0.785939i	$-0.712180\pi$
$269$	−8.67845e51	+	3.59473e51i	−0.499768	+	0.207011i	0.118536	+	0.992950i	$0.462180\pi$
$270$	−1.33612e51	−	1.33612e51i	−0.0710433	−	0.0710433i
$271$	2.96358e51			0.145538			0.0727691	−	0.997349i	$-0.476816\pi$
$271$	2.96358e51			0.145538			0.0727691	+	0.997349i	$0.476816\pi$
$272$	2.72034e52	+	4.31799e51i	1.23422	+	0.195907i
$273$	3.05119e51			0.127930
$274$	−2.28236e52	−	2.28236e52i	−0.884601	−	0.884601i
$275$	1.84118e51	−	7.62640e50i	0.0659846	−	0.0273317i
$276$			2.74503e52i			0.909917i
$277$	1.78557e51	+	4.31074e51i	0.0547597	+	0.132202i	0.948892	−	0.315602i	$-0.102206\pi$
$277$	1.78557e51	+	4.31074e51i	0.0547597	+	0.132202i	−0.894132	+	0.447804i	$0.852206\pi$
$278$	−4.05391e52	−	1.67918e52i	−1.15056	−	0.476579i
$279$	1.33587e52	−	3.22508e52i	0.350974	−	0.847327i
$280$	1.77670e52	−	1.77670e52i	0.432231	−	0.432231i
$281$	−2.85752e52	+	2.85752e52i	−0.643877	+	0.643877i	−0.951506	−	0.307629i	$-0.900464\pi$
$281$	−2.85752e52	+	2.85752e52i	−0.643877	+	0.643877i	0.307629	+	0.951506i	$0.400464\pi$
$282$	−9.25230e51	+	2.23370e52i	−0.193150	+	0.466305i
$283$	−5.87414e52	−	2.43315e52i	−1.13641	−	0.470717i	−0.266456	−	0.963847i	$-0.585853\pi$
$283$	−5.87414e52	−	2.43315e52i	−1.13641	−	0.470717i	−0.869956	+	0.493130i	$0.835853\pi$
$284$	6.41950e51	+	1.54980e52i	0.115122	+	0.277928i
$285$		−	4.65476e52i		−	0.773986i
$286$	7.79174e50	−	3.22745e50i	0.0120161	−	0.00497725i
$287$	4.23397e52	+	4.23397e52i	0.605742	+	0.605742i
$288$	−7.43153e52			−0.986597
$289$	7.71640e52	+	2.51296e52i	0.950848	+	0.309658i
$290$	6.04430e51			0.0691496
$291$	7.21256e52	+	7.21256e52i	0.766285	+	0.766285i
$292$	−1.50921e51	+	6.25136e50i	−0.0148943	+	0.00616940i
$293$			5.26350e52i			0.482637i	0.970446	+	0.241319i	$0.0775799\pi$
$293$			5.26350e52i			0.482637i	−0.970446	+	0.241319i	$0.922420\pi$
$294$	−3.21287e52	−	7.75656e52i	−0.273795	−	0.661000i
$295$	−6.63919e52	−	2.75004e52i	−0.525946	−	0.217854i
$296$	2.64658e52	−	6.38941e52i	0.194946	−	0.470640i
$297$	−5.72236e50	+	5.72236e50i	−0.00392023	+	0.00392023i
$298$	−2.27358e52	+	2.27358e52i	−0.144897	+	0.144897i
$299$	9.20894e51	−	2.22323e52i	0.0546109	−	0.131842i
$300$	−9.74513e52	−	4.03656e52i	−0.537874	−	0.222795i
$301$	−7.75302e52	−	1.87174e53i	−0.398374	−	0.961760i
$302$		−	3.78228e53i		−	1.80969i
$303$	−5.39052e53	+	2.23283e53i	−2.40223	+	0.995035i
$304$	−8.62485e52	−	8.62485e52i	−0.358071	−	0.358071i
$305$	−1.91516e53			−0.740898
$306$	−3.51912e53	−	5.58590e52i	−1.26889	−	0.201411i
$307$	−5.45163e53			−1.83253			−0.916265	−	0.400573i	$-0.868811\pi$
$307$	−5.45163e53			−1.83253			−0.916265	+	0.400573i	$0.868811\pi$
$308$	8.18577e51	+	8.18577e51i	0.0256578	+	0.0256578i
$309$	−4.81918e53	+	1.99617e53i	−1.40885	+	0.583566i
$310$		−	5.31092e53i		−	1.44842i
$311$	8.50440e52	+	2.05314e53i	0.216419	+	0.522481i	0.994385	−	0.105825i	$-0.0337484\pi$
$311$	8.50440e52	+	2.05314e53i	0.216419	+	0.522481i	−0.777966	+	0.628307i	$0.783748\pi$
$312$	3.83364e52	+	1.58795e52i	0.0910517	+	0.0377148i
$313$	−9.83322e52	+	2.37395e53i	−0.218018	+	0.526342i	−0.994613	−	0.103658i	$-0.966945\pi$
$313$	−9.83322e52	+	2.37395e53i	−0.218018	+	0.526342i	0.776595	+	0.630000i	$0.216945\pi$
$314$	3.92270e53	−	3.92270e53i	0.812077	−	0.812077i
$315$	−3.92693e53	+	3.92693e53i	−0.759235	+	0.759235i
$316$	4.65865e52	−	1.12470e53i	0.0841371	−	0.203125i
$317$	−6.19994e51	−	2.56810e51i	−0.0104620	−	0.00433349i	0.377446	−	0.926031i	$-0.376802\pi$
$317$	−6.19994e51	−	2.56810e51i	−0.0104620	−	0.00433349i	−0.387908	+	0.921698i	$0.626802\pi$
$318$	−1.78760e53	−	4.31564e53i	−0.281894	−	0.680553i
$319$		−	2.58867e51i		−	0.00381573i
$320$	7.50626e52	−	3.10920e52i	0.103443	−	0.0428473i
$321$	1.50318e53	+	1.50318e53i	0.193710	+	0.193710i
$322$	9.67676e53			1.16635
$323$	−2.11136e53	−	2.90809e53i	−0.238071	−	0.327910i
$324$	−4.69333e53			−0.495180
$325$	6.53853e52	+	6.53853e52i	0.0645636	+	0.0645636i
$326$	2.35865e54	−	9.76986e53i	2.18015	−	0.903046i
$327$		−	1.46948e54i		−	1.27171i
$328$	3.11623e53	+	7.52324e53i	0.252547	+	0.609702i
$329$	2.68784e53	+	1.11334e53i	0.204029	+	0.0845116i
$330$	−1.15081e53	+	2.77831e53i	−0.0818380	+	0.197574i
$331$	1.16382e54	−	1.16382e54i	0.775501	−	0.775501i	−0.203561	−	0.979062i	$-0.565252\pi$
$331$	1.16382e54	−	1.16382e54i	0.775501	−	0.775501i	0.979062	+	0.203561i	$0.0652516\pi$
$332$	4.97781e53	−	4.97781e53i	0.310864	−	0.310864i
$333$	−5.84959e53	+	1.41222e54i	−0.342432	+	0.826704i
$334$	3.50236e54	+	1.45073e54i	1.92226	+	0.796226i
$335$	7.52053e53	+	1.81562e54i	0.387066	+	0.934461i
$336$			2.85092e54i			1.37623i
$337$	3.07347e54	−	1.27307e54i	1.39183	−	0.576515i	0.444213	−	0.895921i	$-0.353483\pi$
$337$	3.07347e54	−	1.27307e54i	1.39183	−	0.576515i	0.947618	+	0.319406i	$0.103483\pi$
$338$	−2.02286e54	−	2.02286e54i	−0.859520	−	0.859520i
$339$	−3.56887e54			−1.42311
$340$	−1.79946e54	+	4.31371e53i	−0.673513	+	0.161456i
$341$	−2.27458e53			−0.0799248
$342$	1.11574e54	+	1.11574e54i	0.368131	+	0.368131i
$343$	−3.23074e54	+	1.33822e54i	−1.00110	+	0.414670i
$344$		−	2.75523e54i		−	0.801957i
$345$	3.28364e54	+	7.92740e54i	0.897935	+	2.16781i
$346$	2.43957e54	+	1.01050e54i	0.626869	+	0.259658i
$347$	2.29122e54	−	5.53150e54i	0.553329	−	1.33585i	−0.361636	−	0.932319i	$-0.617782\pi$
$347$	2.29122e54	−	5.53150e54i	0.553329	−	1.33585i	0.914964	−	0.403534i	$-0.132218\pi$
$348$	−9.68846e52	+	9.68846e52i	−0.0219938	+	0.0219938i
$349$	1.56862e54	−	1.56862e54i	0.334789	−	0.334789i	−0.519613	−	0.854402i	$-0.673924\pi$
$349$	1.56862e54	−	1.56862e54i	0.334789	−	0.334789i	0.854402	+	0.519613i	$0.173924\pi$
$350$	−1.42297e54	+	3.43535e54i	−0.285583	+	0.689458i
$351$	−3.46913e52	−	1.43696e52i	−0.00654814	−	0.00271233i
$352$	1.85308e53	+	4.47372e53i	0.0329023	+	0.0794331i
$353$		−	2.92215e54i		−	0.488142i	−0.969757	−	0.244071i	$-0.921517\pi$
$353$		−	2.92215e54i		−	0.488142i	0.969757	−	0.244071i	$-0.0784829\pi$
$354$	4.40903e54	−	1.82628e54i	0.693063	−	0.287076i
$355$	3.70779e54	+	3.70779e54i	0.548537	+	0.548537i
$356$	−4.77131e53			−0.0664450
$357$	−1.31680e54	+	8.29582e54i	−0.172644	+	1.08766i
$358$	−1.18402e55			−1.46175
$359$	7.54668e54	+	7.54668e54i	0.877456	+	0.877456i	0.993271	−	0.115815i	$-0.0369480\pi$
$359$	7.54668e54	+	7.54668e54i	0.877456	+	0.877456i	−0.115815	+	0.993271i	$0.536948\pi$
$360$	−6.97767e54	+	2.89024e54i	−0.764199	+	0.316542i
$361$		−	8.10039e54i		−	0.835797i
$362$	−1.77898e54	−	4.29485e54i	−0.172957	−	0.417555i
$363$	−1.42925e55	−	5.92015e54i	−1.30953	−	0.542426i
$364$	−2.05556e53	+	4.96255e53i	−0.0177521	+	0.0428573i
$365$	−3.61067e53	+	3.61067e53i	−0.0293962	+	0.0293962i
$366$	8.99327e54	−	8.99327e54i	0.690358	−	0.690358i
$367$	3.60960e54	−	8.71434e54i	0.261299	−	0.630833i	−0.737720	−	0.675107i	$-0.764098\pi$
$367$	3.60960e54	−	8.71434e54i	0.261299	−	0.630833i	0.999019	+	0.0442742i	$0.0140975\pi$
$368$	2.07730e55	+	8.60448e54i	1.41831	+	0.587484i
$369$	−6.88762e54	−	1.66282e55i	−0.443611	−	1.07097i
$370$			2.32557e55i			1.41316i
$371$	−5.19306e54	+	2.15103e54i	−0.297772	+	0.123341i
$372$	8.51291e54	+	8.51291e54i	0.460686	+	0.460686i
$373$	−6.39305e54			−0.326564			−0.163282	−	0.986579i	$-0.552208\pi$
$373$	−6.39305e54			−0.326564			−0.163282	+	0.986579i	$0.552208\pi$
$374$	5.41236e53	+	2.25777e54i	0.0261004	+	0.108878i
$375$	8.97669e54			0.408737
$376$	2.79769e54	+	2.79769e54i	0.120299	+	0.120299i
$377$	1.10971e53	−	4.59655e52i	0.00450681	−	0.00186678i
$378$		−	1.50996e54i		−	0.0579284i
$379$	4.57376e54	+	1.10420e55i	0.165779	+	0.400227i	0.984836	−	0.173485i	$-0.0555029\pi$
$379$	4.57376e54	+	1.10420e55i	0.165779	+	0.400227i	−0.819057	+	0.573712i	$0.805503\pi$
$380$	7.57064e54	+	3.13586e54i	0.259290	+	0.107401i
$381$	−1.74325e55	+	4.20859e55i	−0.564253	+	1.36223i
$382$	1.29766e55	−	1.29766e55i	0.397008	−	0.397008i
$383$	3.89302e55	−	3.89302e55i	1.12594	−	1.12594i	0.135104	−	0.990831i	$-0.456863\pi$
$383$	3.89302e55	−	3.89302e55i	1.12594	−	1.12594i	0.990831	−	0.135104i	$-0.0431369\pi$
$384$	−2.09903e55	+	5.06750e55i	−0.573980	+	1.38571i
$385$	3.34317e54	+	1.38479e54i	0.0864476	+	0.0358078i
$386$	−3.30337e55	−	7.97505e55i	−0.807850	−	1.95032i
$387$			6.08972e55i			1.40868i
$388$	−1.65897e55	+	6.87170e54i	−0.363043	+	0.150377i
$389$	6.66229e55	+	6.66229e55i	1.37945	+	1.37945i	0.845538	+	0.533915i	$0.179280\pi$
$389$	6.66229e55	+	6.66229e55i	1.37945	+	1.37945i	0.533915	+	0.845538i	$0.320720\pi$
$390$	−1.39534e55			−0.273395
$391$	5.64727e55	+	3.46327e55i	1.04722	+	0.642224i
$392$	−1.37391e55			−0.241162
$393$	9.91779e55	+	9.91779e55i	1.64807	+	1.64807i
$394$	7.42621e55	−	3.07604e55i	1.16842	−	0.483975i
$395$		−	3.80530e55i		−	0.566959i
$396$	−1.33162e54	−	3.21482e54i	−0.0187903	−	0.0453638i
$397$	−8.65205e55	−	3.58380e55i	−1.15644	−	0.479013i	−0.279752	−	0.960072i	$-0.590252\pi$
$397$	−8.65205e55	−	3.58380e55i	−1.15644	−	0.479013i	−0.876688	+	0.481059i	$0.840252\pi$
$398$	6.48171e55	−	1.56482e56i	0.820736	−	1.98143i
$399$	2.63020e55	−	2.63020e55i	0.315552	−	0.315552i
$400$	−6.10935e55	+	6.10935e55i	−0.694553	+	0.694553i
$401$	1.25666e55	−	3.03385e55i	0.135399	−	0.326882i	−0.841608	−	0.540088i	$-0.818391\pi$
$401$	1.25666e55	−	3.03385e55i	0.135399	−	0.326882i	0.977007	+	0.213207i	$0.0683908\pi$
$402$	−1.20574e56	−	4.99432e55i	−1.23138	−	0.510054i
$403$	−4.03883e54	−	9.75060e54i	−0.0391018	−	0.0944001i
$404$		−	1.02715e56i		−	0.942834i
$405$	−1.35539e56	+	5.61422e55i	−1.17973	+	0.488659i
$406$	3.41537e54	+	3.41537e54i	0.0281921	+	0.0281921i
$407$	9.96003e54			0.0779795
$408$	−5.97191e55	+	9.73790e55i	−0.443527	+	0.723222i
$409$	5.51474e55			0.388574			0.194287	−	0.980945i	$-0.437761\pi$
$409$	5.51474e55			0.388574			0.194287	+	0.980945i	$0.437761\pi$
$410$	−1.93624e56	−	1.93624e56i	−1.29451	−	1.29451i
$411$	2.11303e56	−	8.75247e55i	1.34063	−	0.555305i
$412$		−	9.18285e55i		−	0.552952i
$413$	−2.19758e55	−	5.30544e55i	−0.125609	−	0.303246i
$414$	−2.68727e56	−	1.11310e56i	−1.45816	−	0.603988i
$415$	8.42097e55	−	2.03300e56i	0.433838	−	1.04738i
$416$	−1.58874e55	+	1.58874e55i	−0.0777225	+	0.0777225i
$417$	2.19854e56	−	2.19854e56i	1.02143	−	1.02143i
$418$	3.93453e54	−	9.49879e54i	0.0173621	−	0.0419159i
$419$	−1.43055e56	−	5.92552e55i	−0.599654	−	0.248385i	0.0621439	−	0.998067i	$-0.480206\pi$
$419$	−1.43055e56	−	5.92552e55i	−0.599654	−	0.248385i	−0.661798	+	0.749682i	$0.730206\pi$
$420$	−7.32951e55	−	1.76950e56i	−0.291887	−	0.704678i
$421$			3.87275e56i			1.46539i	0.680556	+	0.732696i	$0.261738\pi$
$421$			3.87275e56i			1.46539i	−0.680556	+	0.732696i	$0.738262\pi$
$422$	−4.89726e56	+	2.02851e56i	−1.76090	+	0.729390i
$423$	−6.18358e55	−	6.18358e55i	−0.211311	−	0.211311i
$424$	−7.64424e55			−0.248295
$425$	−2.05993e56	+	1.49556e56i	−0.636048	+	0.461788i
$426$	−3.48224e56			−1.02224
$427$	−1.08217e56	−	1.08217e56i	−0.302062	−	0.302062i
$428$	−3.45748e55	+	1.43214e55i	−0.0917738	+	0.0380139i
$429$			5.97601e54i			0.0150862i
$430$	3.54553e56	+	8.55966e56i	0.851352	+	2.05535i
$431$	−1.65407e56	−	6.85139e55i	−0.377827	−	0.156501i	0.185684	−	0.982609i	$-0.440550\pi$
$431$	−1.65407e56	−	6.85139e55i	−0.377827	−	0.156501i	−0.563511	+	0.826108i	$0.690550\pi$
$432$	1.34264e55	−	3.24142e55i	0.0291783	−	0.0704425i
$433$	−4.98097e56	+	4.98097e56i	−1.02997	+	1.02997i	−0.0304317	+	0.999537i	$0.509688\pi$
$433$	−4.98097e56	+	4.98097e56i	−1.02997	+	1.02997i	−0.999537	+	0.0304317i	$0.990312\pi$
$434$	3.00096e56	−	3.00096e56i	0.590516	−	0.590516i
$435$	−1.63900e55	+	3.95689e55i	−0.0306944	+	0.0741028i
$436$	2.39000e56	+	9.89971e55i	0.426029	+	0.176467i
$437$	−1.12265e56	−	2.71031e56i	−0.190499	−	0.459905i
$438$		−	3.39103e55i		−	0.0547820i
$439$	−9.40416e56	+	3.89533e56i	−1.44655	+	0.599180i	−0.961376	−	0.275239i	$-0.911243\pi$
$439$	−9.40416e56	+	3.89533e56i	−1.44655	+	0.599180i	−0.485172	+	0.874419i	$0.661243\pi$
$440$	3.47980e55	+	3.47980e55i	0.0509709	+	0.0509709i
$441$	3.03668e56			0.423613
$442$	−8.71748e55	+	6.32913e55i	−0.115828	+	0.0840941i
$443$	−2.76052e56			−0.349390			−0.174695	−	0.984623i	$-0.555894\pi$
$443$	−2.76052e56			−0.349390			−0.174695	+	0.984623i	$0.555894\pi$
$444$	−3.72767e56	−	3.72767e56i	−0.449473	−	0.449473i
$445$	−1.37791e56	+	5.70749e55i	−0.158300	+	0.0655700i
$446$		−	6.34104e56i		−	0.694162i
$447$	−8.71879e55	−	2.10490e56i	−0.0909587	−	0.219594i
$448$	5.99833e55	+	2.48459e55i	0.0596421	+	0.0247046i
$449$	−7.45115e55	+	1.79887e56i	−0.0706199	+	0.170492i	−0.955248	−	0.295805i	$-0.904412\pi$
$449$	−7.45115e55	+	1.79887e56i	−0.0706199	+	0.170492i	0.884628	+	0.466297i	$0.154412\pi$
$450$	7.90326e56	−	7.90326e56i	0.714065	−	0.714065i
$451$	−8.29258e55	+	8.29258e55i	−0.0714322	+	0.0714322i
$452$	2.40431e56	−	5.80451e56i	0.197476	−	0.476749i
$453$	2.47606e57	+	1.02562e57i	1.93932	+	0.803293i
$454$	−1.39602e56	−	3.37029e56i	−0.104278	−	0.251748i
$455$			1.67903e56i			0.119623i
$456$	4.67354e56	−	1.93584e56i	0.317615	−	0.131561i
$457$	−1.22349e57	−	1.22349e57i	−0.793234	−	0.793234i	0.188784	−	0.982019i	$-0.439545\pi$
$457$	−1.22349e57	−	1.22349e57i	−0.793234	−	0.793234i	−0.982019	+	0.188784i	$0.939545\pi$
$458$	2.63861e57			1.63218
$459$	5.40408e55	−	8.81199e55i	0.0318970	−	0.0520117i
$460$	−1.51055e57			−0.850828
$461$	1.77018e57	+	1.77018e57i	0.951584	+	0.951584i	0.998881	−	0.0472969i	$-0.0150607\pi$
$461$	1.77018e57	+	1.77018e57i	0.951584	+	0.951584i	−0.0472969	+	0.998881i	$0.515061\pi$
$462$	−2.22017e56	+	9.19625e55i	−0.113916	+	0.0471855i
$463$		−	1.31832e57i		−	0.645700i	−0.946450	−	0.322850i	$-0.895359\pi$
$463$		−	1.31832e57i		−	0.645700i	0.946450	−	0.322850i	$-0.104641\pi$
$464$	4.29484e55	+	1.03687e56i	0.0200822	+	0.0484826i
$465$	3.47678e57	+	1.44013e57i	1.55217	+	0.642928i
$466$	6.42854e56	−	1.55199e57i	0.274041	−	0.661592i
$467$	−8.84415e56	+	8.84415e56i	−0.360034	+	0.360034i	−0.863825	−	0.503791i	$-0.831938\pi$
$467$	−8.84415e56	+	8.84415e56i	−0.360034	+	0.360034i	0.503791	+	0.863825i	$0.331938\pi$
$468$	1.14167e56	−	1.14167e56i	0.0443869	−	0.0443869i
$469$	−6.00973e56	+	1.45088e57i	−0.223171	+	0.538784i
$470$	−1.22918e57	−	5.09141e56i	−0.436024	−	0.180607i
$471$	1.50429e57	+	3.63168e57i	0.509779	+	1.23072i
$472$		−	7.80966e56i		−	0.252859i
$473$	3.66596e56	−	1.51849e56i	0.113416	−	0.0469783i
$474$	1.78691e57	+	1.78691e57i	0.528284	+	0.528284i
$475$	1.12727e57			0.318505
$476$	−1.26055e57	−	7.73048e56i	−0.340415	−	0.208765i
$477$	1.68956e57			0.436143
$478$	−3.30220e57	−	3.30220e57i	−0.814900	−	0.814900i
$479$	3.27112e56	−	1.35494e56i	0.0771762	−	0.0319674i	−0.343761	−	0.939057i	$-0.611701\pi$
$479$	3.27112e56	−	1.35494e56i	0.0771762	−	0.0319674i	0.420938	+	0.907090i	$0.361701\pi$
$480$		−	8.01151e57i		−	1.80729i
$481$	1.76854e56	+	4.26964e56i	0.0381501	+	0.0921026i
$482$	6.34632e57	+	2.62873e57i	1.30921	+	0.542294i
$483$	−2.62399e57	+	6.33486e57i	−0.517724	+	1.24990i
$484$	1.92574e57	−	1.92574e57i	0.363431	−	0.363431i
$485$	−3.96897e57	+	3.96897e57i	−0.716524	+	0.716524i
$486$	3.89493e57	−	9.40320e57i	0.672698	−	1.62404i
$487$	−2.91544e57	−	1.20762e57i	−0.481762	−	0.199552i	0.128567	−	0.991701i	$-0.458962\pi$
$487$	−2.91544e57	−	1.20762e57i	−0.481762	−	0.199552i	−0.610328	+	0.792149i	$0.708962\pi$
$488$	−7.96484e56	−	1.92288e57i	−0.125936	−	0.304037i
$489$			1.80901e58i			2.73716i
$490$	4.26833e57	−	1.76800e57i	0.618076	−	0.256016i
$491$	8.80374e57	+	8.80374e57i	1.22016	+	1.22016i	0.967576	+	0.252579i	$0.0812788\pi$
$491$	8.80374e57	+	8.80374e57i	1.22016	+	1.22016i	0.252579	+	0.967576i	$0.418721\pi$
$492$	6.20721e57			0.823468
$493$	7.70833e55	+	3.21553e56i	0.00978929	+	0.0408360i
$494$	4.77055e56			0.0580014
$495$	−7.69121e56	−	7.69121e56i	−0.0895329	−	0.0895329i
$496$	9.11058e57	−	3.77373e57i	1.01552	−	0.420644i
$497$			4.19022e57i			0.447274i
$498$	5.59229e57	+	1.35010e58i	0.571688	+	1.38018i
$499$	8.02209e57	+	3.32286e57i	0.785463	+	0.325349i	0.739118	−	0.673576i	$-0.235243\pi$
$499$	8.02209e57	+	3.32286e57i	0.785463	+	0.325349i	0.0463450	+	0.998925i	$0.485243\pi$
$500$	−6.04750e56	+	1.46000e57i	−0.0567180	+	0.136929i
$501$	−1.89943e58	+	1.89943e58i	−1.70652	+	1.70652i
$502$	−1.28130e58	+	1.28130e58i	−1.10286	+	1.10286i
$503$	−4.83246e57	+	1.16666e58i	−0.398526	+	0.962126i	0.589490	+	0.807775i	$0.299329\pi$
$503$	−4.83246e57	+	1.16666e58i	−0.398526	+	0.962126i	−0.988016	+	0.154351i	$0.950671\pi$
$504$	−5.57592e57	−	2.30962e57i	−0.440616	−	0.182509i
$505$	−1.22869e58	−	2.96633e58i	−0.930419	−	2.24623i
$506$			1.89527e57i			0.137542i
$507$	1.87278e58	−	7.75732e57i	1.30262	−	0.539561i
$508$	−5.67055e57	−	5.67055e57i	−0.378056	−	0.378056i
$509$	−1.22092e58			−0.780290			−0.390145	−	0.920753i	$-0.627575\pi$
$509$	−1.22092e58			−0.780290			−0.390145	+	0.920753i	$0.627575\pi$
$510$	6.02184e57	−	3.79376e58i	0.368952	−	2.32440i
$511$	−4.08046e56			−0.0239696
$512$	−5.53184e57	−	5.53184e57i	−0.311577	−	0.311577i
$513$	−4.22916e56	+	1.75178e56i	−0.0228418	+	0.00946140i
$514$			1.55345e58i			0.804617i
$515$	−1.09846e58	−	2.65193e58i	−0.545670	−	1.31736i
$516$	−1.94035e58	−	8.03719e57i	−0.924509	−	0.382944i
$517$	−2.18057e56	+	5.26435e56i	−0.00996604	+	0.0240601i
$518$	−1.31408e58	+	1.31408e58i	−0.576144	+	0.576144i
$519$	−1.32304e58	+	1.32304e58i	−0.556514	+	0.556514i
$520$	−8.73825e56	+	2.10960e57i	−0.0352657	+	0.0851389i
$521$	−8.64297e57	−	3.58003e57i	−0.334697	−	0.138636i	0.209005	−	0.977915i	$-0.432978\pi$
$521$	−8.64297e57	−	3.58003e57i	−0.334697	−	0.138636i	−0.543702	+	0.839279i	$0.682978\pi$
$522$	−5.55595e56	−	1.34133e57i	−0.0206463	−	0.0498446i
$523$		−	4.43247e58i		−	1.58074i	−0.612631	−	0.790369i	$-0.709889\pi$
$523$		−	4.43247e58i		−	1.58074i	0.612631	−	0.790369i	$-0.290111\pi$
$524$	−2.28121e58	+	9.44908e57i	−0.780805	+	0.323420i
$525$	−1.86308e58	−	1.86308e58i	−0.612078	−	0.612078i
$526$	6.35880e57			0.200531
$527$	2.82537e58	−	6.77304e57i	0.855356	−	0.205048i
$528$	−5.58375e57			−0.162292
$529$	1.29005e58	+	1.29005e58i	0.360005	+	0.360005i
$530$	2.37483e58	−	9.83689e57i	0.636359	−	0.263588i
$531$			1.72612e58i			0.444160i
$532$	2.50590e57	+	6.04977e57i	0.0619246	+	0.149499i
$533$	−5.02730e57	−	2.08238e57i	−0.119316	−	0.0494225i
$534$	3.79030e57	−	9.15059e57i	0.0864045	−	0.208599i
$535$	−8.27176e57	+	8.27176e57i	−0.181131	+	0.181131i
$536$	−1.51017e58	+	1.51017e58i	−0.317675	+	0.317675i
$537$	3.21062e58	−	7.75112e58i	0.648846	−	1.56645i
$538$	3.17146e58	+	1.31366e58i	0.615800	+	0.255073i
$539$	−7.57204e56	−	1.82805e57i	−0.0141272	−	0.0341060i
$540$			2.35706e57i			0.0422576i
$541$	2.49180e58	−	1.03214e58i	0.429311	−	0.177826i	−0.157555	−	0.987510i	$-0.550361\pi$
$541$	2.49180e58	−	1.03214e58i	0.429311	−	0.177826i	0.586867	+	0.809684i	$0.300361\pi$
$542$	−7.65804e57	−	7.65804e57i	−0.126804	−	0.126804i
$543$	3.29400e58			0.524237
$544$	−3.63394e58	−	5.00524e58i	−0.555907	−	0.765683i
$545$	8.08633e58			1.18912
$546$	−7.88445e57	−	7.88445e57i	−0.111463	−	0.111463i
$547$	1.86224e56	−	7.71364e55i	0.00253109	−	0.00104841i	−0.381418	−	0.924403i	$-0.624564\pi$
$547$	1.86224e56	−	7.71364e55i	0.00253109	−	0.00104841i	0.383949	+	0.923354i	$0.374564\pi$
$548$			4.02634e58i			0.526173i
$549$	1.76042e58	+	4.25004e58i	0.221213	+	0.534056i
$550$	−6.72840e57	−	2.78699e57i	−0.0813044	−	0.0336774i
$551$	5.60358e56	−	1.35282e57i	0.00651188	−	0.0157211i
$552$	−6.59376e58	+	6.59376e58i	−0.736959	+	0.736959i
$553$	2.15021e58	−	2.15021e58i	0.231148	−	0.231148i
$554$	6.52518e57	−	1.57532e58i	0.0674734	−	0.162895i
$555$	−1.52243e59	−	6.30610e58i	−1.51439	−	0.627280i
$556$	2.09464e58	+	5.05691e58i	0.200448	+	0.483924i
$557$			4.24705e56i			0.00391022i	0.999998	+	0.00195511i	$0.000622331\pi$
$557$			4.24705e56i			0.00391022i	−0.999998	+	0.00195511i	$0.999378\pi$
$558$	−1.17858e59	+	4.88182e58i	−1.04405	+	0.432461i
$559$	1.30188e58	+	1.30188e58i	0.110973	+	0.110973i
$560$	−1.56882e59			−1.28686
$561$	−1.62480e58	−	2.57905e57i	−0.128262	−	0.0203591i
$562$	1.47680e59			1.12199
$563$	−2.71645e58	−	2.71645e58i	−0.198642	−	0.198642i	0.600776	−	0.799418i	$-0.294858\pi$
$563$	−2.71645e58	−	2.71645e58i	−0.198642	−	0.198642i	−0.799418	+	0.600776i	$0.794858\pi$
$564$	2.78636e58	−	1.15415e58i	0.196127	−	0.0812383i
$565$		−	1.96390e59i		−	1.33069i
$566$	8.89170e58	+	2.14665e59i	0.580005	+	1.40026i
$567$	−1.08311e59	−	4.48637e58i	−0.680198	−	0.281747i
$568$	−2.18073e58	+	5.26476e58i	−0.131860	+	0.318338i
$569$	−1.78515e58	+	1.78515e58i	−0.103935	+	0.103935i	−0.757162	−	0.653227i	$-0.773415\pi$
$569$	−1.78515e58	+	1.78515e58i	−0.103935	+	0.103935i	0.653227	+	0.757162i	$0.273415\pi$
$570$	−1.20282e59	+	1.20282e59i	−0.674356	+	0.674356i
$571$	1.93187e58	−	4.66394e58i	0.104304	−	0.251812i	−0.863108	−	0.505019i	$-0.831485\pi$
$571$	1.93187e58	−	4.66394e58i	0.104304	−	0.251812i	0.967412	+	0.253207i	$0.0814854\pi$
$572$	−9.71955e56	−	4.02597e56i	−0.00505396	−	0.00209342i
$573$	4.97632e58	+	1.20139e59i	0.249220	+	0.601671i
$574$		−	2.18816e59i		−	1.05554i
$575$	−1.91983e59	+	7.95219e58i	−0.892080	+	0.369511i
$576$	−1.37996e58	−	1.37996e58i	−0.0617707	−	0.0617707i
$577$	−6.93844e58			−0.299214			−0.149607	−	0.988746i	$-0.547801\pi$
$577$	−6.93844e58			−0.299214			−0.149607	+	0.988746i	$0.547801\pi$
$578$	−1.34459e59	−	2.64332e59i	−0.558654	−	1.09825i
$579$	6.11660e59			2.44862
$580$	−5.33142e57	−	5.33142e57i	−0.0205656	−	0.0205656i
$581$	1.62459e59	−	6.72927e58i	0.603889	−	0.250139i
$582$		−	3.72753e59i		−	1.33529i
$583$	−4.21297e57	−	1.01710e58i	−0.0145450	−	0.0351148i
$584$	−5.12686e57	−	2.12361e57i	−0.0170598	−	0.00706642i
$585$	1.93136e58	−	4.66273e58i	0.0619460	−	0.149551i
$586$	1.36012e59	−	1.36012e59i	0.420511	−	0.420511i
$587$	−3.74574e59	+	3.74574e59i	−1.11640	+	1.11640i	−0.124130	+	0.992266i	$0.539614\pi$
$587$	−3.74574e59	+	3.74574e59i	−1.11640	+	1.11640i	−0.992266	+	0.124130i	$0.960386\pi$
$588$	−4.00779e58	+	9.67567e58i	−0.115158	+	0.278015i
$589$	−1.18868e59	−	4.92367e58i	−0.329296	−	0.136399i
$590$	1.00498e59	+	2.42623e59i	0.268434	+	0.648057i
$591$			5.69565e59i			1.46694i
$592$	−3.98938e59	+	1.65246e59i	−0.990807	+	0.410406i
$593$	2.48470e59	+	2.48470e59i	0.595112	+	0.595112i	0.939008	−	0.343896i	$-0.111747\pi$
$593$	2.48470e59	+	2.48470e59i	0.595112	+	0.595112i	−0.343896	+	0.939008i	$0.611747\pi$
$594$	2.95738e57			0.00683122
$595$	−4.56507e59	−	7.24615e58i	−1.01703	−	0.161433i
$596$	4.01085e58			0.0861870
$597$	8.48646e59	+	8.48646e59i	1.75905	+	1.75905i
$598$	−8.12459e58	+	3.36532e58i	−0.162452	+	0.0672900i
$599$		−	7.53768e59i		−	1.45399i	−0.686643	−	0.726995i	$-0.740916\pi$
$599$		−	7.53768e59i		−	1.45399i	0.686643	−	0.726995i	$-0.259084\pi$
$600$	−1.37124e59	−	3.31046e59i	−0.255189	−	0.616080i
$601$	−7.14683e59	−	2.96031e59i	−1.28325	−	0.531541i	−0.366285	−	0.930503i	$-0.619371\pi$
$601$	−7.14683e59	−	2.96031e59i	−1.28325	−	0.531541i	−0.916968	+	0.398962i	$0.869371\pi$
$602$	−2.83326e59	+	6.84011e59i	−0.490866	+	1.18505i
$603$	3.33785e59	−	3.33785e59i	0.558013	−	0.558013i
$604$	−3.33619e59	+	3.33619e59i	−0.538215	+	0.538215i
$605$	3.25777e59	−	7.86496e59i	0.507201	−	1.22449i
$606$	1.96991e60	+	8.15964e59i	2.95996	+	1.22605i
$607$	−3.52665e59	−	8.51410e59i	−0.511453	−	1.23476i	−0.943038	−	0.332685i	$-0.892045\pi$
$607$	−3.52665e59	−	8.51410e59i	−0.511453	−	1.23476i	0.431585	−	0.902072i	$-0.357955\pi$
$608$			2.73906e59i			0.383420i
$609$	−3.16198e58	+	1.30974e58i	−0.0427256	+	0.0176975i
$610$	4.94887e59	+	4.94887e59i	0.645527	+	0.645527i
$611$	−2.64390e58			−0.0332934
$612$	2.61135e59	+	3.59677e59i	0.317476	+	0.437278i
$613$	4.01226e59			0.470966			0.235483	−	0.971879i	$-0.424333\pi$
$613$	4.01226e59			0.470966			0.235483	+	0.971879i	$0.424333\pi$
$614$	1.40873e60	+	1.40873e60i	1.59664	+	1.59664i
$615$	1.79259e60	−	7.42515e59i	1.96185	−	0.812625i
$616$			3.93256e58i			0.0415614i
$617$	−2.44780e59	−	5.90951e59i	−0.249830	−	0.603143i	0.748359	−	0.663294i	$-0.230842\pi$
$617$	−2.44780e59	−	5.90951e59i	−0.249830	−	0.603143i	−0.998189	+	0.0601506i	$0.980842\pi$
$618$	1.76112e60	+	7.29481e59i	1.73595	+	0.719054i
$619$	−1.39947e59	+	3.37861e59i	−0.133234	+	0.321654i	−0.976390	−	0.216013i	$-0.930695\pi$
$619$	−1.39947e59	+	3.37861e59i	−0.133234	+	0.321654i	0.843157	+	0.537668i	$0.180695\pi$
$620$	−4.68453e59	+	4.68453e59i	−0.430769	+	0.430769i
$621$	5.96681e58	−	5.96681e58i	0.0529996	−	0.0529996i
$622$	3.10785e59	−	7.50301e59i	0.266665	−	0.643787i
$623$	−1.10110e59	−	4.56091e58i	−0.0912713	−	0.0378058i
$624$	−9.91473e58	−	2.39363e59i	−0.0793985	−	0.191685i
$625$			1.50986e60i			1.16820i
$626$	8.67536e59	−	3.59345e59i	0.648544	−	0.268636i
$627$	5.15146e58	+	5.15146e58i	0.0372116	+	0.0372116i
$628$	−6.92008e59			−0.483035
$629$	−1.23719e60	+	2.96581e59i	−0.834538	+	0.200057i
$630$	2.02948e60			1.32301
$631$	9.71005e59	+	9.71005e59i	0.611773	+	0.611773i	0.943408	−	0.331635i	$-0.107600\pi$
$631$	9.71005e59	+	9.71005e59i	0.611773	+	0.611773i	−0.331635	+	0.943408i	$0.607600\pi$
$632$	3.82065e59	−	1.58256e59i	0.232659	−	0.0963705i
$633$		−	3.75603e60i		−	2.21080i
$634$	9.38487e57	+	2.26571e58i	0.00533961	+	0.0128910i
$635$	−2.31593e60	−	9.59288e59i	−1.27377	−	0.527611i
$636$	−2.22988e59	+	5.38340e59i	−0.118564	+	0.286239i
$637$	6.49192e58	−	6.49192e58i	0.0333715	−	0.0333715i
$638$	−6.68927e57	+	6.68927e57i	−0.00332456	+	0.00332456i
$639$	4.81995e59	−	1.16364e60i	0.231619	−	0.559178i
$640$	−2.78857e60	−	1.15507e60i	−1.29572	−	0.536707i
$641$	−5.68282e59	−	1.37195e60i	−0.255338	−	0.616441i	0.743281	−	0.668980i	$-0.233269\pi$
$641$	−5.68282e59	−	1.37195e60i	−0.255338	−	0.616441i	−0.998619	+	0.0525385i	$0.983269\pi$
$642$		−	7.76857e59i		−	0.337550i
$643$	−2.58308e60	+	1.06995e60i	−1.08543	+	0.449600i	−0.852412	−	0.522871i	$-0.824861\pi$
$643$	−2.58308e60	+	1.06995e60i	−1.08543	+	0.449600i	−0.233020	+	0.972472i	$0.574861\pi$
$644$	−8.53545e59	−	8.53545e59i	−0.346881	−	0.346881i
$645$	−6.56498e60			−2.58047
$646$	−2.05881e59	+	1.29705e60i	−0.0782741	+	0.493127i
$647$	−3.21938e60			−1.18394			−0.591970	−	0.805960i	$-0.701650\pi$
$647$	−3.21938e60			−1.18394			−0.591970	+	0.805960i	$0.701650\pi$
$648$	−1.12737e60	−	1.12737e60i	−0.401056	−	0.401056i
$649$	1.03911e59	−	4.30414e58i	0.0357603	−	0.0148124i
$650$		−	3.37918e59i		−	0.112506i
$651$	1.15082e60	+	2.77832e60i	0.370694	+	0.894935i
$652$	−2.94222e60	−	1.21871e60i	−0.916964	−	0.379819i
$653$	4.32402e59	−	1.04391e60i	0.130393	−	0.314796i	−0.845177	−	0.534487i	$-0.820505\pi$
$653$	4.32402e59	−	1.04391e60i	0.130393	−	0.314796i	0.975570	+	0.219691i	$0.0705048\pi$
$654$	−3.79721e60	+	3.79721e60i	−1.10801	+	1.10801i
$655$	−5.45762e60	+	5.45762e60i	−1.54105	+	1.54105i
$656$	1.94569e60	−	4.69732e60i	0.531669	−	1.28356i
$657$	1.13316e59	+	4.69370e58i	0.0299665	+	0.0124125i
$658$	−4.06859e59	−	9.82246e59i	−0.104133	−	0.251399i
$659$		−	4.80654e60i		−	1.19068i	−0.803473	−	0.595342i	$-0.797017\pi$
$659$		−	4.80654e60i		−	1.19068i	0.803473	−	0.595342i	$-0.202983\pi$
$660$	3.46571e59	−	1.43554e59i	0.0830993	−	0.0344209i
$661$	6.02071e60	+	6.02071e60i	1.39739	+	1.39739i	0.807449	+	0.589937i	$0.200848\pi$
$661$	6.02071e60	+	6.02071e60i	1.39739	+	1.39739i	0.589937	+	0.807449i	$0.299152\pi$
$662$	−6.01472e60			−1.35135
$663$	−1.77948e59	−	7.42311e59i	−0.0387037	−	0.161453i
$664$	2.39141e60			0.503548
$665$	1.44736e60	+	1.44736e60i	0.295061	+	0.295061i
$666$	5.16080e60	−	2.13767e60i	1.01864	−	0.421935i
$667$			2.69926e59i			0.0515868i
$668$	−1.80966e60	−	4.36890e60i	−0.334890	−	0.808497i
$669$	4.15114e60	+	1.71946e60i	0.743886	+	0.308127i
$670$	2.74831e60	−	6.63500e60i	0.476932	−	1.15142i
$671$	2.11952e59	−	2.11952e59i	0.0356207	−	0.0356207i
$672$	4.52695e60	−	4.52695e60i	0.736828	−	0.736828i
$673$	3.51577e60	−	8.48781e60i	0.554238	−	1.33805i	−0.360031	−	0.932940i	$-0.617234\pi$
$673$	3.51577e60	−	8.48781e60i	0.554238	−	1.33805i	0.914269	−	0.405108i	$-0.132766\pi$
$674$	−1.12317e61	−	4.65232e60i	−1.71498	−	0.710366i
$675$	1.24086e59	+	2.99570e59i	0.0183523	+	0.0443064i
$676$			3.56855e60i			0.511255i
$677$	−4.09891e60	+	1.69782e60i	−0.568868	+	0.235633i	−0.648530	−	0.761189i	$-0.724616\pi$
$677$	−4.09891e60	+	1.69782e60i	−0.568868	+	0.235633i	0.0796618	+	0.996822i	$0.474616\pi$
$678$	9.22215e60	+	9.22215e60i	1.23992	+	1.23992i
$679$	−4.48538e60			−0.584251
$680$	−5.35863e60	−	3.28626e60i	−0.676257	−	0.414725i
$681$	2.58490e60			0.316068
$682$	5.87763e59	+	5.87763e59i	0.0696367	+	0.0696367i
$683$	−9.88503e60	+	4.09452e60i	−1.13484	+	0.470064i	−0.869422	−	0.494070i	$-0.835509\pi$
$683$	−9.88503e60	+	4.09452e60i	−1.13484	+	0.470064i	−0.265414	+	0.964135i	$0.585509\pi$
$684$		−	1.96829e60i		−	0.218969i
$685$	4.81636e60	+	1.16277e61i	0.519245	+	1.25357i
$686$	1.18064e61	+	4.89038e60i	1.23353	+	0.510945i
$687$	−7.15496e60	+	1.72736e61i	−0.724499	+	1.74909i
$688$	−1.21643e61	+	1.21643e61i	−1.19381	+	1.19381i
$689$	3.61201e59	−	3.61201e59i	0.0343586	−	0.0343586i
$690$	1.19997e61	−	2.89699e61i	1.10641	−	2.67111i
$691$	−1.00223e60	−	4.15137e59i	−0.0895754	−	0.0371034i	0.337446	−	0.941345i	$-0.390437\pi$
$691$	−1.00223e60	−	4.15137e59i	−0.0895754	−	0.0371034i	−0.427021	+	0.904242i	$0.640437\pi$
$692$	−1.26052e60	−	3.04316e60i	−0.109211	−	0.263660i
$693$		−	8.69192e59i		−	0.0730048i
$694$	−2.02143e61	+	8.37304e60i	−1.64600	+	0.681796i
$695$	1.20983e61	+	1.20983e61i	0.955103	+	0.955103i
$696$	−4.65448e59			−0.0356264
$697$	7.83135e60	−	1.27699e61i	0.581208	−	0.947728i
$698$	−8.10680e60			−0.583389
$699$	8.41684e60	+	8.41684e60i	0.587341	+	0.587341i
$700$	4.28531e60	−	1.77503e60i	0.289984	−	0.120115i
$701$		−	1.31255e61i		−	0.861351i	−0.902507	−	0.430675i	$-0.858275\pi$
$701$		−	1.31255e61i		−	0.861351i	0.902507	−	0.430675i	$-0.141725\pi$
$702$	5.25123e58	+	1.26776e59i	0.00334205	+	0.00806843i
$703$	5.20505e60	+	2.15600e60i	0.321281	+	0.133079i
$704$	−4.86626e58	+	1.17482e59i	−0.00291329	+	0.00703330i
$705$	6.66615e60	−	6.66615e60i	0.387088	−	0.387088i
$706$	−7.55098e60	+	7.55098e60i	−0.425307	+	0.425307i
$707$	9.81859e60	−	2.37042e61i	0.536453	−	1.29511i
$708$	−5.49989e60	−	2.27813e60i	−0.291501	−	0.120743i
$709$	5.01009e60	+	1.20954e61i	0.257603	+	0.621910i	0.998779	−	0.0494015i	$-0.0157314\pi$
$709$	5.01009e60	+	1.20954e61i	0.257603	+	0.621910i	−0.741176	+	0.671311i	$0.765731\pi$
$710$		−	1.91623e61i		−	0.955855i
$711$	−8.44456e60	+	3.49785e60i	−0.408677	+	0.169280i
$712$	−1.14610e60	−	1.14610e60i	−0.0538150	−	0.0538150i
$713$	2.37174e61			1.08054
$714$	2.48395e61	−	1.80342e61i	1.09807	−	0.797232i
$715$	−3.28851e59			−0.0141065
$716$	1.04437e61	+	1.04437e61i	0.434734	+	0.434734i
$717$	3.05722e61	−	1.26634e61i	1.23499	−	0.511551i
$718$		−	3.90020e61i		−	1.52901i
$719$	1.34482e60	+	3.24668e60i	0.0511674	+	0.123529i	0.947396	−	0.320063i	$-0.103704\pi$
$719$	1.34482e60	+	3.24668e60i	0.0511674	+	0.123529i	−0.896229	+	0.443592i	$0.853704\pi$
$720$	4.35667e61	+	1.80459e61i	1.60882	+	0.666393i
$721$	8.77793e60	−	2.11918e61i	0.314618	−	0.759555i
$722$	−2.09318e61	+	2.09318e61i	−0.728211	+	0.728211i
$723$	−3.44178e61	+	3.44178e61i	−1.16228	+	1.16228i
$724$	−2.21913e60	+	5.35746e60i	−0.0727452	+	0.175622i
$725$	−9.58263e59	−	3.96926e59i	−0.0304942	−	0.0126311i
$726$	2.16346e61	+	5.22306e61i	0.668362	+	1.61357i
$727$		−	3.14995e61i		−	0.944742i	−0.881400	−	0.472371i	$-0.843398\pi$
$727$		−	3.14995e61i		−	0.944742i	0.881400	−	0.472371i	$-0.156602\pi$
$728$	−1.68580e60	+	6.98282e59i	−0.0490887	+	0.0203332i
$729$	2.70986e61	+	2.70986e61i	0.766136	+	0.766136i
$730$	1.86603e60			0.0512246
$731$	−4.10151e61	+	2.97781e61i	−1.09325	+	0.793732i
$732$	−1.58652e61			−0.410635
$733$	−1.45166e61	−	1.45166e61i	−0.364863	−	0.364863i	0.500736	−	0.865600i	$-0.333063\pi$
$733$	−1.45166e61	−	1.45166e61i	−0.364863	−	0.364863i	−0.865600	+	0.500736i	$0.833063\pi$
$734$	−3.18457e61	+	1.31909e61i	−0.777294	+	0.321966i
$735$			3.27366e61i			0.775990i
$736$	−1.93224e61	−	4.66483e61i	−0.444823	−	1.07390i
$737$	−2.84166e60	−	1.17705e60i	−0.0635361	−	0.0263175i
$738$	−2.51701e61	+	6.07661e61i	−0.546605	+	1.31962i
$739$	−1.85860e61	+	1.85860e61i	−0.392040	+	0.392040i	−0.875414	−	0.483374i	$-0.839411\pi$
$739$	−1.85860e61	+	1.85860e61i	−0.392040	+	0.392040i	0.483374	+	0.875414i	$0.339411\pi$
$740$	2.05128e61	−	2.05128e61i	0.420285	−	0.420285i
$741$	−1.29360e60	+	3.12302e60i	−0.0257459	+	0.0621561i
$742$	1.89775e61	+	7.86075e60i	0.366907	+	0.151978i
$743$	3.70441e61	+	8.94324e61i	0.695760	+	1.67971i	0.732839	+	0.680402i	$0.238195\pi$
$743$	3.70441e61	+	8.94324e61i	0.695760	+	1.67971i	−0.0370790	+	0.999312i	$0.511805\pi$
$744$			4.08973e61i			0.746236i
$745$	1.15830e61	−	4.79783e60i	0.205334	−	0.0850520i
$746$	1.65200e61	+	1.65200e61i	0.284528	+	0.284528i
$747$	−5.28561e61			−0.884508
$748$	1.51408e60	−	2.46888e60i	0.0246186	−	0.0401435i
$749$	−9.34801e60			−0.147693
$750$	−2.31963e61	−	2.31963e61i	−0.356124	−	0.356124i
$751$	9.45805e61	−	3.91765e61i	1.41105	−	0.584477i	0.458457	−	0.888717i	$-0.348402\pi$
$751$	9.45805e61	−	3.91765e61i	1.41105	−	0.584477i	0.952595	+	0.304240i	$0.0984025\pi$
$752$		−	2.47036e61i		−	0.358159i
$753$	−4.91356e61	−	1.18624e62i	−0.692316	−	1.67140i
$754$	−4.05531e59	−	1.67976e59i	−0.00555316	−	0.00230019i
$755$	−5.64383e61	+	1.36254e62i	−0.751128	+	1.81338i
$756$	−1.33187e60	+	1.33187e60i	−0.0172283	+	0.0172283i
$757$	−1.16866e61	+	1.16866e61i	−0.146936	+	0.146936i	−0.776748	−	0.629812i	$-0.783132\pi$
$757$	−1.16866e61	+	1.16866e61i	−0.146936	+	0.146936i	0.629812	+	0.776748i	$0.283132\pi$
$758$	1.67144e61	−	4.03520e61i	0.204269	−	0.493148i
$759$	−1.24073e61	−	5.13929e60i	−0.147394	−	0.0610527i
$760$	1.06527e61	+	2.57178e61i	0.123017	+	0.296990i
$761$			7.62521e61i			0.856016i	0.903775	+	0.428008i	$0.140784\pi$
$761$			7.62521e61i			0.856016i	−0.903775	+	0.428008i	$0.859216\pi$
$762$	1.53799e62	−	6.37055e61i	1.67850	−	0.695256i
$763$	4.56923e61	+	4.56923e61i	0.484803	+	0.484803i
$764$	−2.28922e61			−0.236146
$765$	1.18439e62	+	7.26342e61i	1.18788	+	0.728485i
$766$	−2.01196e62			−1.96200
$767$	3.69018e60	+	3.69018e60i	0.0349902	+	0.0349902i
$768$	1.73188e62	−	7.17370e61i	1.59681	−	0.661419i
$769$		−	6.75659e61i		−	0.605774i	−0.953026	−	0.302887i	$-0.902049\pi$
$769$		−	6.75659e61i		−	0.605774i	0.953026	−	0.302887i	$-0.0979506\pi$
$770$	−5.06057e60	−	1.22173e61i	−0.0441213	−	0.106518i
$771$	−1.01696e62	−	4.21238e61i	−0.862252	−	0.357157i
$772$	−4.12068e61	+	9.94821e61i	−0.339780	+	0.820301i
$773$	−1.67006e59	+	1.67006e59i	−0.00133928	+	0.00133928i	−0.707776	−	0.706437i	$-0.750301\pi$
$773$	−1.67006e59	+	1.67006e59i	−0.00133928	+	0.00133928i	0.706437	+	0.707776i	$0.250301\pi$
$774$	1.57362e62	−	1.57362e62i	1.22735	−	1.22735i
$775$	−3.48765e61	+	8.41992e61i	−0.264573	+	0.638736i
$776$	−5.63561e61	−	2.33435e61i	−0.415828	−	0.172242i
$777$	−5.03926e61	−	1.21659e62i	−0.361672	−	0.873154i
$778$		−	3.44314e62i		−	2.40377i
$779$	−6.12870e61	+	2.53859e61i	−0.416211	+	0.172400i
$780$	1.23077e61	+	1.23077e61i	0.0813098	+	0.0813098i
$781$	−8.20687e60			−0.0527449
$782$	−5.64357e61	−	2.35421e62i	−0.352865	−	1.47198i
$783$	4.21192e59			0.00256213
$784$	6.06580e61	+	6.06580e61i	0.358999	+	0.358999i
$785$	−1.99846e62	+	8.27789e61i	−1.15079	+	0.476675i
$786$		−	5.12562e62i		−	2.87185i
$787$	−3.99507e61	−	9.64494e61i	−0.217805	−	0.525827i	0.776778	−	0.629774i	$-0.216853\pi$
$787$	−3.99507e61	−	9.64494e61i	−0.217805	−	0.525827i	−0.994583	+	0.103947i	$0.966853\pi$
$788$	−9.26357e61	−	3.83710e61i	−0.491434	−	0.203558i
$789$	−1.72428e61	+	4.16277e61i	−0.0890125	+	0.214895i
$790$	−9.83310e61	+	9.83310e61i	−0.493978	+	0.493978i
$791$	1.10971e62	−	1.10971e62i	0.542520	−	0.542520i
$792$	4.52358e60	−	1.09209e61i	0.0215224	−	0.0519596i
$793$	1.28494e61	+	5.32239e60i	0.0594989	+	0.0246453i
$794$	1.30966e62	+	3.16181e62i	0.590227	+	1.42493i
$795$			1.82142e62i			0.798944i
$796$	−1.95199e62	+	8.08539e61i	−0.833385	+	0.345199i
$797$	8.98617e61	+	8.98617e61i	0.373440	+	0.373440i	0.868729	−	0.495289i	$-0.164938\pi$
$797$	8.98617e61	+	8.98617e61i	0.373440	+	0.373440i	−0.495289	+	0.868729i	$0.664938\pi$
$798$	−1.35931e62			−0.549867
$799$	1.14102e61	−	7.18843e61i	0.0449301	−	0.283060i
$800$	1.94020e62			0.743722
$801$	2.53316e61	+	2.53316e61i	0.0945288	+	0.0945288i
$802$	−1.10869e62	+	4.59235e61i	−0.402774	+	0.166835i
$803$		−	7.99191e59i		−	0.00282661i
$804$	6.23000e61	+	1.50406e62i	0.214528	+	0.517915i
$805$	−3.48598e62	−	1.44394e62i	−1.16873	−	0.484104i
$806$	−1.47595e61	+	3.56326e61i	−0.0481802	+	0.116317i
$807$	−1.71997e62	+	1.71997e62i	−0.546687	+	0.546687i
$808$	2.46730e62	−	2.46730e62i	0.763619	−	0.763619i
$809$	−2.21497e62	+	5.34741e62i	−0.667535	+	1.61157i	0.118185	+	0.992992i	$0.462292\pi$
$809$	−2.21497e62	+	5.34741e62i	−0.667535	+	1.61157i	−0.785721	+	0.618582i	$0.787708\pi$
$810$	4.95315e62	+	2.05166e62i	1.45363	+	0.602113i
$811$	1.21966e62	+	2.94452e62i	0.348571	+	0.841524i	0.996789	+	0.0800700i	$0.0255144\pi$
$811$	1.21966e62	+	2.94452e62i	0.348571	+	0.841524i	−0.648218	+	0.761454i	$0.724486\pi$
$812$		−	6.02510e60i		−	0.0167691i
$813$	7.08990e61	−	2.93673e61i	0.192173	−	0.0796008i
$814$	−2.57372e61	−	2.57372e61i	−0.0679418	−	0.0679418i
$815$	−9.95471e62			−2.55941
$816$	6.93586e62	−	1.66268e62i	1.73685	−	0.416361i
$817$	2.24451e62			0.547453
$818$	−1.42504e62	−	1.42504e62i	−0.338556	−	0.338556i
$819$	3.72603e61	−	1.54337e61i	0.0862268	−	0.0357163i
$820$			3.41574e62i			0.769994i
$821$	−7.42590e61	−	1.79277e62i	−0.163069	−	0.393683i	0.821132	−	0.570738i	$-0.193343\pi$
$821$	−7.42590e61	−	1.79277e62i	−0.163069	−	0.393683i	−0.984201	+	0.177055i	$0.943343\pi$
$822$	−7.72188e62	−	3.19851e62i	−1.65188	−	0.684232i
$823$	2.74854e62	−	6.63556e62i	0.572803	−	1.38287i	−0.326356	−	0.945247i	$-0.605821\pi$
$823$	2.74854e62	−	6.63556e62i	0.572803	−	1.38287i	0.899159	−	0.437622i	$-0.144179\pi$
$824$	2.20579e62	−	2.20579e62i	0.447846	−	0.447846i
$825$	3.64899e61	−	3.64899e61i	0.0721794	−	0.0721794i
$826$	−8.03085e61	+	1.93882e62i	−0.154771	+	0.373651i
$827$	−1.37252e61	−	5.68518e60i	−0.0257722	−	0.0106752i	0.369760	−	0.929127i	$-0.379440\pi$
$827$	−1.37252e61	−	5.68518e60i	−0.0257722	−	0.0106752i	−0.395532	+	0.918452i	$0.629440\pi$
$828$	1.38851e62	+	3.35215e62i	0.254036	+	0.613297i
$829$			1.01251e62i			0.180500i	0.995919	+	0.0902499i	$0.0287666\pi$
$829$			1.01251e62i			0.180500i	−0.995919	+	0.0902499i	$0.971233\pi$
$830$	−7.42940e62	+	3.07736e62i	−1.29055	+	0.534563i
$831$	8.54338e61	+	8.54338e61i	0.144613	+	0.144613i
$832$	−5.90026e60			−0.00973239
$833$	1.48490e62	+	2.04524e62i	0.238688	+	0.328759i
$834$	−1.13623e63			−1.77990
$835$	−1.04523e63	−	1.04523e63i	−1.59570	−	1.59570i
$836$	−1.18490e61	+	4.90800e60i	−0.0176297	+	0.00730246i
$837$		−	3.70086e61i		−	0.0536668i
$838$	2.16542e62	+	5.22779e62i	0.306053	+	0.738877i
$839$	−5.54271e60	−	2.29587e60i	−0.00763554	−	0.00316275i	0.378862	−	0.925453i	$-0.376315\pi$
$839$	−5.54271e60	−	2.29587e60i	−0.00763554	−	0.00316275i	−0.386498	+	0.922290i	$0.626315\pi$
$840$	2.48987e62	−	6.01107e62i	0.334327	−	0.807137i
$841$	5.39302e62	−	5.39302e62i	0.705860	−	0.705860i
$842$	1.00074e63	−	1.00074e63i	1.27676	−	1.27676i
$843$	−4.00453e62	+	9.66780e62i	−0.498034	+	1.20236i
$844$	6.10892e62	+	2.53040e62i	0.740631	+	0.306779i
$845$	4.26874e62	+	1.03057e63i	0.504523	+	1.21803i
$846$			3.19574e62i			0.368221i
$847$	6.28496e62	−	2.60332e62i	0.706008	−	0.292438i
$848$	3.37492e62	+	3.37492e62i	0.369618	+	0.369618i
$849$	−1.64641e63			−1.75801
$850$	9.18758e62	+	1.45835e62i	0.956520	+	0.151829i
$851$	−1.03855e63			−1.05425
$852$	3.07153e62	+	3.07153e62i	0.304021	+	0.304021i
$853$	9.56705e62	−	3.96280e62i	0.923366	−	0.382471i	0.130208	−	0.991487i	$-0.458436\pi$
$853$	9.56705e62	−	3.96280e62i	0.923366	−	0.382471i	0.793158	+	0.609016i	$0.208436\pi$
$854$			5.59277e62i			0.526360i
$855$	−2.35450e62	−	5.68426e62i	−0.216086	−	0.521678i
$856$	−1.17452e62	−	4.86503e61i	−0.105118	−	0.0435411i
$857$	2.09159e62	−	5.04953e62i	0.182553	−	0.440721i	−0.805939	−	0.591999i	$-0.798339\pi$
$857$	2.09159e62	−	5.04953e62i	0.182553	−	0.440721i	0.988491	+	0.151278i	$0.0483389\pi$
$858$	1.54423e61	−	1.54423e61i	0.0131443	−	0.0131443i
$859$	−9.40868e62	+	9.40868e62i	−0.781044	+	0.781044i	−0.980007	−	0.198963i	$-0.936243\pi$
$859$	−9.40868e62	+	9.40868e62i	−0.781044	+	0.781044i	0.198963	+	0.980007i	$0.436243\pi$
$860$	4.42275e62	−	1.06775e63i	0.358076	−	0.864473i
$861$	1.43247e63	+	5.93350e62i	1.13115	+	0.468536i
$862$	2.50377e62	+	6.04464e62i	0.192836	+	0.465548i
$863$		−	7.06903e62i		−	0.531041i	−0.964105	−	0.265520i	$-0.914456\pi$
$863$		−	7.06903e62i		−	0.531041i	0.964105	−	0.265520i	$-0.0855438\pi$
$864$	−7.27899e61	+	3.01506e61i	−0.0533366	+	0.0220928i
$865$	−7.28053e62	−	7.28053e62i	−0.520375	−	0.520375i
$866$	2.57422e63			1.79478
$867$	2.09505e63	−	1.63462e62i	1.42490	−	0.111175i
$868$	−5.29404e62			−0.351247
$869$	4.21135e61	+	4.21135e61i	0.0272581	+	0.0272581i
$870$	1.44601e62	−	5.98955e61i	0.0913074	−	0.0378208i
$871$		−	1.42716e62i		−	0.0879187i
$872$	3.36298e62	+	8.11894e62i	0.202125	+	0.487972i
$873$	1.24561e63	+	5.15947e62i	0.730423	+	0.302551i
$874$	−4.10260e62	+	9.90456e62i	−0.234727	+	0.566682i
$875$	−2.79123e62	+	2.79123e62i	−0.155820	+	0.155820i
$876$	−2.99108e61	+	2.99108e61i	−0.0162926	+	0.0162926i
$877$	−1.12691e63	+	2.72060e63i	−0.598959	+	1.44601i	0.275685	+	0.961248i	$0.411095\pi$
$877$	−1.12691e63	+	2.72060e63i	−0.598959	+	1.44601i	−0.874644	+	0.484767i	$0.838905\pi$
$878$	3.43666e63	+	1.42351e63i	1.78240	+	0.738293i
$879$	5.21582e62	+	1.25921e63i	0.263974	+	0.637290i
$880$		−	3.07266e62i		−	0.151753i
$881$	1.64135e63	−	6.79871e62i	0.791080	−	0.327676i	0.0497021	−	0.998764i	$-0.484173\pi$
$881$	1.64135e63	−	6.79871e62i	0.791080	−	0.327676i	0.741378	+	0.671088i	$0.234173\pi$
$882$	−7.84693e62	−	7.84693e62i	−0.369084	−	0.369084i
$883$	3.51415e63			1.61311			0.806556	−	0.591158i	$-0.201329\pi$
$883$	3.51415e63			1.61311			0.806556	+	0.591158i	$0.201329\pi$
$884$	1.32720e62	+	2.10666e61i	0.0594582	+	0.00943781i
$885$	−1.86083e63			−0.813631
$886$	7.13332e62	+	7.13332e62i	0.304415	+	0.304415i
$887$	−2.51152e63	+	1.04031e63i	−1.04611	+	0.433314i	−0.838503	−	0.544897i	$-0.816569\pi$
$887$	−2.51152e63	+	1.04031e63i	−1.04611	+	0.433314i	−0.207610	+	0.978212i	$0.566569\pi$
$888$		−	1.79083e63i		−	0.728073i
$889$	−7.66576e62	−	1.85068e63i	−0.304206	−	0.734417i
$890$	5.03544e62	+	2.08575e62i	0.195053	+	0.0807936i
$891$	8.78692e61	−	2.12135e62i	0.0332251	−	0.0802124i
$892$	−5.59316e62	+	5.59316e62i	−0.206449	+	0.206449i
$893$	−2.27910e62	+	2.27910e62i	−0.0821215	+	0.0821215i
$894$	−3.18620e62	+	7.69216e62i	−0.112077	+	0.270577i
$895$	4.26533e63	+	1.76676e63i	1.46473	+	0.606711i
$896$	−9.23023e62	−	2.22838e63i	−0.309450	−	0.747078i
$897$		−	6.23129e62i		−	0.203958i
$898$	6.57378e62	−	2.72295e62i	0.210075	−	0.0870159i
$899$	8.37096e61	+	8.37096e61i	0.0261181	+	0.0261181i
$900$	−1.39423e63			−0.424736
$901$	8.26179e62	+	1.13794e63i	0.245749	+	0.338484i
$902$	4.28569e62			0.124474
$903$	−3.70958e63	−	3.70958e63i	−1.05205	−	1.05205i
$904$	1.97182e63	−	8.16754e62i	0.546067	−	0.226188i
$905$			1.81264e63i			0.490194i
$906$	−3.74802e63	−	9.04851e63i	−0.989795	−	2.38958i
$907$	7.05128e63	+	2.92074e63i	1.81849	+	0.753244i	0.977087	+	0.212839i	$0.0682709\pi$
$907$	7.05128e63	+	2.92074e63i	1.81849	+	0.753244i	0.841405	+	0.540405i	$0.181729\pi$
$908$	−1.74142e62	+	4.20415e62i	−0.0438589	+	0.105885i
$909$	−5.45332e63	+	5.45332e63i	−1.34134	+	1.34134i
$910$	4.33870e62	−	4.33870e62i	0.104224	−	0.104224i
$911$	9.36057e62	−	2.25984e63i	0.219613	−	0.530192i	−0.775223	−	0.631687i	$-0.782363\pi$
$911$	9.36057e62	−	2.25984e63i	0.219613	−	0.530192i	0.994836	+	0.101495i	$0.0323627\pi$
$912$	−2.91803e63	−	1.20869e63i	−0.668654	−	0.276965i
$913$	1.31798e62	+	3.18189e62i	0.0294977	+	0.0712137i
$914$			6.32312e63i			1.38225i
$915$	−4.58172e63	+	1.89781e63i	−0.978306	+	0.405228i
$916$	−2.32741e63	−	2.32741e63i	−0.485422	−	0.485422i
$917$	−6.16772e63			−1.25656
$918$	−3.67351e62	+	8.80621e61i	−0.0731078	+	0.0175255i
$919$	−1.23227e63			−0.239565			−0.119783	−	0.992800i	$-0.538220\pi$
$919$	−1.23227e63			−0.239565			−0.119783	+	0.992800i	$0.538220\pi$
$920$	−3.62845e63	−	3.62845e63i	−0.689102	−	0.689102i
$921$	−1.30422e64	+	5.40224e63i	−2.41973	+	1.00229i
$922$		−	9.14847e63i		−	1.65819i
$923$	−1.45724e62	−	3.51810e62i	−0.0258045	−	0.0622976i
$924$	2.76948e62	+	1.14716e62i	0.0479127	+	0.0198461i
$925$	1.52719e63	−	3.68696e63i	0.258134	−	0.623190i
$926$	−3.40662e63	+	3.40662e63i	−0.562583	+	0.562583i
$927$	−4.87533e63	+	4.87533e63i	−0.786664	+	0.786664i
$928$	9.64456e61	−	2.32840e62i	0.0152055	−	0.0367094i
$929$	−7.52904e63	−	3.11863e63i	−1.15985	−	0.480425i	−0.282025	−	0.959407i	$-0.591006\pi$
$929$	−7.52904e63	−	3.11863e63i	−1.15985	−	0.480425i	−0.877825	+	0.478982i	$0.841006\pi$
$930$	−5.26281e63	−	1.27055e64i	−0.792199	−	1.91254i
$931$		−	1.11924e63i		−	0.164628i
$932$	−1.93597e63	+	8.01906e62i	−0.278264	+	0.115261i
$933$	4.06909e63	+	4.06909e63i	0.571533	+	0.571533i
$934$	4.57075e63			0.627379
$935$	1.41922e62	−	8.94106e62i	0.0190370	−	0.119933i
$936$	5.48476e62			0.0718996
$937$	−7.25537e63	−	7.25537e63i	−0.929519	−	0.929519i	0.0681554	−	0.997675i	$-0.478289\pi$
$937$	−7.25537e63	−	7.25537e63i	−0.929519	−	0.929519i	−0.997675	+	0.0681554i	$0.978289\pi$
$938$	5.30209e63	−	2.19620e63i	0.663874	−	0.274986i
$939$			6.65371e63i			0.814243i
$940$	6.35111e62	+	1.53329e63i	0.0759628	+	0.183390i
$941$	1.36726e63	+	5.66339e62i	0.159836	+	0.0662064i	0.461167	−	0.887313i	$-0.347431\pi$
$941$	1.36726e63	+	5.66339e62i	0.159836	+	0.0662064i	−0.301331	+	0.953520i	$0.597431\pi$
$942$	5.49728e63	−	1.32716e64i	0.628135	−	1.51645i
$943$	8.64682e63	−	8.64682e63i	0.965729	−	0.965729i
$944$	−3.44796e63	+	3.44796e63i	−0.376412	+	0.376412i
$945$	−2.25312e62	+	5.43952e62i	−0.0240437	+	0.0580466i
$946$	−1.33969e63	−	5.54917e62i	−0.139748	−	0.0578854i
$947$	6.42603e63	+	1.55138e64i	0.655267	+	1.58196i	0.805031	+	0.593233i	$0.202149\pi$
$947$	6.42603e63	+	1.55138e64i	0.655267	+	1.58196i	−0.149763	+	0.988722i	$0.547851\pi$
$948$		−	3.15231e63i		−	0.314231i
$949$	3.42595e61	−	1.41908e61i	0.00333855	−	0.00138287i
$950$	−2.91293e63	−	2.91293e63i	−0.277506	−	0.277506i
$951$	−1.73772e62			−0.0161845
$952$	−1.17100e63	−	4.88484e63i	−0.106626	−	0.444791i
$953$	1.79503e64			1.59799			0.798997	−	0.601335i	$-0.205364\pi$
$953$	1.79503e64			1.59799			0.798997	+	0.601335i	$0.205364\pi$
$954$	−4.36592e63	−	4.36592e63i	−0.380002	−	0.380002i
$955$	−6.61107e63	+	2.73840e63i	−0.562600	+	0.233036i
$956$			5.82546e63i			0.484714i
$957$	−2.56522e61	−	6.19300e61i	−0.00208698	−	0.00503842i
$958$	−1.19540e63	−	4.95151e62i	−0.0950944	−	0.0393894i
$959$	−3.84880e63	+	9.29183e63i	−0.299382	+	0.722772i
$960$	1.48765e63	−	1.48765e63i	0.113154	−	0.113154i
$961$	−2.15161e63	+	2.15161e63i	−0.160033	+	0.160033i
$962$	6.46296e62	−	1.56030e63i	0.0470075	−	0.113486i
$963$	2.59598e63	+	1.07529e63i	0.184644	+	0.0764821i
$964$	−3.27912e63	−	7.91651e63i	−0.228088	−	0.550652i
$965$			3.36588e64i			2.28961i
$966$	2.31501e64	−	9.58910e63i	1.54009	−	0.637925i
$967$	1.31298e64	+	1.31298e64i	0.854255	+	0.854255i	0.990654	−	0.136399i	$-0.0435530\pi$
$967$	1.31298e64	+	1.31298e64i	0.854255	+	0.854255i	−0.136399	+	0.990654i	$0.543553\pi$
$968$	9.25154e63			0.588700
$969$	−7.93284e63	−	4.86493e63i	−0.493705	−	0.302772i
$970$	2.05121e64			1.24858
$971$	1.52941e64	+	1.52941e64i	0.910564	+	0.910564i	0.996316	−	0.0857524i	$-0.0273294\pi$
$971$	1.52941e64	+	1.52941e64i	0.910564	+	0.910564i	−0.0857524	+	0.996316i	$0.527329\pi$
$972$	−1.17297e64	+	4.85860e63i	−0.683066	+	0.282935i
$973$			1.36724e64i			0.778787i
$974$	4.41312e63	+	1.06542e64i	0.245883	+	0.593613i
$975$	2.21217e63	+	9.16311e62i	0.120564	+	0.0499394i
$976$	−4.97304e63	+	1.20060e64i	−0.265125	+	0.640068i
$977$	6.59859e63	−	6.59859e63i	0.344126	−	0.344126i	−0.513790	−	0.857916i	$-0.671759\pi$
$977$	6.59859e63	−	6.59859e63i	0.344126	−	0.344126i	0.857916	+	0.513790i	$0.171759\pi$
$978$	4.67457e64	−	4.67457e64i	2.38482	−	2.38482i
$979$	8.93291e61	−	2.15660e62i	0.00445826	−	0.0107632i
$980$	−5.32438e63	−	2.20543e63i	−0.259961	−	0.107679i
$981$	−7.43299e63	−	1.79448e64i	−0.355042	−	0.857148i
$982$		−	4.54987e64i		−	2.12619i
$983$	−3.73659e64	+	1.54775e64i	−1.70834	+	0.707618i	−0.708343	+	0.705868i	$0.750557\pi$
$983$	−3.73659e64	+	1.54775e64i	−1.70834	+	0.707618i	−0.999998	+	0.00175000i	$0.999443\pi$
$984$	1.49102e64	+	1.49102e64i	0.666942	+	0.666942i
$985$	−3.13424e64			−1.37168
$986$	6.31721e62	−	1.03010e63i	0.0270503	−	0.0441087i
$987$	7.53350e63			0.315630
$988$	−4.20789e62	−	4.20789e62i	−0.0172501	−	0.0172501i
$989$	−3.82256e64	+	1.58336e64i	−1.53333	+	0.635124i
$990$			3.97490e63i			0.156016i
$991$	6.42892e63	+	1.55208e64i	0.246919	+	0.596115i	0.997939	−	0.0641641i	$-0.0204381\pi$
$991$	6.42892e63	+	1.55208e64i	0.246919	+	0.596115i	−0.751021	+	0.660279i	$0.770438\pi$
$992$	−2.04589e64	−	8.47434e63i	−0.768919	−	0.318497i
$993$	1.63097e64	−	3.93752e64i	0.599844	−	1.44815i
$994$	1.08277e64	−	1.08277e64i	0.389700	−	0.389700i
$995$	−4.66998e64	+	4.66998e64i	−1.64482	+	1.64482i
$996$	6.97592e63	−	1.68414e64i	0.240450	−	0.580499i
$997$	−2.24119e64	−	9.28332e63i	−0.756020	−	0.313154i	−0.0288248	−	0.999584i	$-0.509176\pi$
$997$	−2.24119e64	−	9.28332e63i	−0.756020	−	0.313154i	−0.727195	+	0.686431i	$0.759176\pi$
$998$	−1.21431e64	−	2.93159e64i	−0.400887	−	0.967826i
$999$			1.62055e63i			0.0523606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.14	✓	252
17.9	even	8	inner	17.44.d.a.9.14	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.14	✓	252	1.1	even	1	trivial
17.44.d.a.9.14	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+(-2.58405e6 - 2.58405e6i) q^{2} +(2.39234e10 - 9.90941e9i) q^{3} +4.55856e12i q^{4} +(5.45301e14 + 1.31647e15i) q^{5} +(-8.74259e16 - 3.62130e16i) q^{6} +(-4.35755e17 + 1.05201e18i) q^{7} +(-1.09500e19 + 1.09500e19i) q^{8} +(2.42022e20 - 2.42022e20i) q^{9} +(1.99275e21 - 4.81092e21i) q^{10} +(-2.06044e21 - 8.53461e20i) q^{11} +(4.51727e22 + 1.09056e23i) q^{12} -1.03481e23i q^{13} +(3.84445e24 - 1.59242e24i) q^{14} +(2.60909e25 + 2.60909e25i) q^{15} +9.66883e25 q^{16} +(2.81351e26 + 4.46589e25i) q^{17} -1.25079e27 q^{18} +(-8.92027e26 - 8.92027e26i) q^{19} +(-6.00122e27 + 2.48579e27i) q^{20} +2.94857e28i q^{21} +(3.11889e27 + 7.52966e27i) q^{22} +(2.14845e29 + 8.89919e28i) q^{23} +(-1.53454e29 + 3.70470e29i) q^{24} +(-6.31860e29 + 6.31860e29i) q^{25} +(-2.67399e29 + 2.67399e29i) q^{26} +(1.38863e29 - 3.35245e29i) q^{27} +(-4.79563e30 - 1.98642e30i) q^{28} +(4.44194e29 + 1.07238e30i) q^{29} -1.34841e32i q^{30} +(9.42263e31 - 3.90298e31i) q^{31} +(-1.53530e32 - 1.53530e32i) q^{32} -5.77500e31 q^{33} +(-6.11625e32 - 8.42427e32i) q^{34} -1.62255e33 q^{35} +(1.10327e33 + 1.10327e33i) q^{36} +(-4.12603e33 + 1.70906e33i) q^{37} +4.61009e33i q^{38} +(-1.02543e33 - 2.47561e33i) q^{39} +(-2.03864e34 - 8.44433e33i) q^{40} +(2.01233e34 - 4.85821e34i) q^{41} +(7.61925e34 - 7.61925e34i) q^{42} +(-1.25809e35 + 1.25809e35i) q^{43} +(3.89055e33 - 9.39263e33i) q^{44} +(4.50589e35 + 1.86640e35i) q^{45} +(-3.25212e35 - 7.85132e35i) q^{46} -2.55497e35i q^{47} +(2.31312e36 - 9.58124e35i) q^{48} +(6.27357e35 + 6.27357e35i) q^{49} +3.26552e36 q^{50} +(7.17343e36 - 1.71963e36i) q^{51} +4.71723e35 q^{52} +(3.49052e36 + 3.49052e36i) q^{53} +(-1.22512e36 + 5.07461e35i) q^{54} -3.17790e36i q^{55} +(-6.74795e36 - 1.62910e37i) q^{56} +(-3.01798e37 - 1.25009e37i) q^{57} +(1.62327e36 - 3.91891e36i) q^{58} +(-3.56605e37 + 3.56605e37i) q^{59} +(-1.18937e38 + 1.18937e38i) q^{60} +(-5.14337e37 + 1.24172e38i) q^{61} +(-3.44341e38 - 1.42631e38i) q^{62} +(1.49146e38 + 3.60070e38i) q^{63} -5.70180e37i q^{64} +(1.36229e38 - 5.64281e37i) q^{65} +(1.49229e38 + 1.49229e38i) q^{66} +1.37915e39 q^{67} +(-2.03580e38 + 1.28256e39i) q^{68} +6.02170e39 q^{69} +(4.19277e39 + 4.19277e39i) q^{70} +(3.39977e39 - 1.40823e39i) q^{71} +5.30027e39i q^{72} +(1.37134e38 + 3.31072e38i) q^{73} +(1.50782e40 + 6.24558e39i) q^{74} +(-8.85491e39 + 2.13776e40i) q^{75} +(4.06636e39 - 4.06636e39i) q^{76} +(1.79569e39 - 1.79569e39i) q^{77} +(-3.74734e39 + 9.04688e39i) q^{78} +(-2.46722e40 - 1.02196e40i) q^{79} +(5.27242e40 + 1.27288e41i) q^{80} +1.02956e41i q^{81} +(-1.77538e41 + 7.35388e40i) q^{82} +(-1.09197e41 - 1.09197e41i) q^{83} -1.34412e41 q^{84} +(9.46288e40 + 3.94744e41i) q^{85} +6.50197e41 q^{86} +(2.12533e40 + 2.12533e40i) q^{87} +(3.19072e40 - 1.32164e40i) q^{88} +1.04667e41i q^{89} +(-6.82059e41 - 1.64663e42i) q^{90} +(1.08862e41 + 4.50922e40i) q^{91} +(-4.05675e41 + 9.79387e41i) q^{92} +(1.86745e42 - 1.86745e42i) q^{93} +(-6.60217e41 + 6.60217e41i) q^{94} +(6.87906e41 - 1.66075e42i) q^{95} +(-5.19437e42 - 2.15158e42i) q^{96} +(1.50743e42 + 3.63925e42i) q^{97} -3.24224e42i q^{98} +(-7.05226e41 + 2.92114e41i) 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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