LMFDB - Embedded newform 17.44.d.a.2.4

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			2.4
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.80683e6 - 3.80683e6i) q^{2} +(2.44978e10 - 1.01473e10i) q^{3} +2.01878e13i q^{4} +(-5.36168e13 - 1.29442e14i) q^{5} +(-1.31888e17 - 5.46298e16i) q^{6} +(-6.31645e17 + 1.52492e18i) q^{7} +(4.33664e19 - 4.33664e19i) q^{8} +(2.65060e20 - 2.65060e20i) q^{9} +(-2.88655e20 + 6.96875e20i) q^{10} +(-1.70618e22 - 7.06722e21i) q^{11} +(2.04852e23 + 4.94557e23i) q^{12} +8.26295e23i q^{13} +(8.20970e24 - 3.40057e24i) q^{14} +(-2.62698e24 - 2.62698e24i) q^{15} -1.52603e26 q^{16} +(-2.82528e26 + 3.64818e25i) q^{17} -2.01808e27 q^{18} +(-2.21022e27 - 2.21022e27i) q^{19} +(2.61316e27 - 1.08241e27i) q^{20} +4.37668e28i q^{21} +(3.80476e28 + 9.18551e28i) q^{22} +(-1.61458e29 - 6.68780e28i) q^{23} +(6.22328e29 - 1.50243e30i) q^{24} +(7.90007e29 - 7.90007e29i) q^{25} +(3.14557e30 - 3.14557e30i) q^{26} +(4.72814e29 - 1.14147e30i) q^{27} +(-3.07849e31 - 1.27515e31i) q^{28} +(4.13362e30 + 9.97945e30i) q^{29} +2.00010e31i q^{30} +(9.72964e31 - 4.03015e31i) q^{31} +(1.99480e32 + 1.99480e32i) q^{32} -4.89689e32 q^{33} +(1.21442e33 + 9.36655e32i) q^{34} +2.31257e32 q^{35} +(5.35099e33 + 5.35099e33i) q^{36} +(2.03855e33 - 8.44394e32i) q^{37} +1.68278e34i q^{38} +(8.38468e33 + 2.02424e34i) q^{39} +(-7.93862e33 - 3.28828e33i) q^{40} +(-1.50367e34 + 3.63019e34i) q^{41} +(1.66613e35 - 1.66613e35i) q^{42} +(-2.81014e34 + 2.81014e34i) q^{43} +(1.42672e35 - 3.44441e35i) q^{44} +(-4.85217e34 - 2.00984e34i) q^{45} +(3.60049e35 + 8.69235e35i) q^{46} -9.57862e35i q^{47} +(-3.73844e36 + 1.54851e36i) q^{48} +(-3.82231e35 - 3.82231e35i) q^{49} -6.01484e36 q^{50} +(-6.55111e36 + 3.76062e36i) q^{51} -1.66811e37 q^{52} +(8.07927e36 + 8.07927e36i) q^{53} +(-6.14533e36 + 2.54548e36i) q^{54} +2.58744e36i q^{55} +(3.87384e37 + 9.35227e37i) q^{56} +(-7.65731e37 - 3.17176e37i) q^{57} +(2.22541e37 - 5.37261e37i) q^{58} +(-1.58916e38 + 1.58916e38i) q^{59} +(5.30331e37 - 5.30331e37i) q^{60} +(4.77385e37 - 1.15251e38i) q^{61} +(-5.23812e38 - 2.16970e38i) q^{62} +(2.36773e38 + 5.71621e38i) q^{63} -1.76458e38i q^{64} +(1.06958e38 - 4.43033e37i) q^{65} +(1.86416e39 + 1.86416e39i) q^{66} -2.45211e39 q^{67} +(-7.36489e38 - 5.70362e39i) q^{68} -4.63399e39 q^{69} +(-8.80355e38 - 8.80355e38i) q^{70} +(-2.17587e39 + 9.01275e38i) q^{71} -2.29894e40i q^{72} +(1.04078e39 + 2.51267e39i) q^{73} +(-1.09749e40 - 4.54594e39i) q^{74} +(1.13370e40 - 2.73699e40i) q^{75} +(4.46195e40 - 4.46195e40i) q^{76} +(2.15540e40 - 2.15540e40i) q^{77} +(4.51403e40 - 1.08978e41i) q^{78} +(9.32407e40 + 3.86215e40i) q^{79} +(8.18209e39 + 1.97533e40i) q^{80} +9.02864e40i q^{81} +(1.95437e41 - 8.09529e40i) q^{82} +(-2.87478e40 - 2.87478e40i) q^{83} -8.83556e41 q^{84} +(1.98705e40 + 3.46150e40i) q^{85} +2.13954e41 q^{86} +(2.02529e41 + 2.02529e41i) q^{87} +(-1.04639e42 + 4.33429e41i) q^{88} +7.78073e41i q^{89} +(1.08203e41 + 2.61225e41i) q^{90} +(-1.26004e42 - 5.21925e41i) q^{91} +(1.35012e42 - 3.25948e42i) q^{92} +(1.97459e42 - 1.97459e42i) q^{93} +(-3.64642e42 + 3.64642e42i) q^{94} +(-1.67591e41 + 4.04600e41i) q^{95} +(6.91099e42 + 2.86263e42i) q^{96} +(1.86859e42 + 4.51117e42i) q^{97} +2.91018e42i q^{98} +(-6.39565e42 + 2.64916e42i) 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 $

$2$	−3.80683e6	−	3.80683e6i	−1.28357	−	1.28357i	−0.938623	−	0.344944i	$-0.887898\pi$
$2$	−3.80683e6	−	3.80683e6i	−1.28357	−	1.28357i	−0.344944	−	0.938623i	$-0.612102\pi$
$3$	2.44978e10	−	1.01473e10i	1.35213	−	0.560072i	0.415248	−	0.909708i	$-0.363695\pi$
$3$	2.44978e10	−	1.01473e10i	1.35213	−	0.560072i	0.936886	+	0.349636i	$0.113695\pi$
$4$			2.01878e13i			2.29509i
$5$	−5.36168e13	−	1.29442e14i	−0.0502858	−	0.121401i	0.896740	−	0.442557i	$-0.145929\pi$
$5$	−5.36168e13	−	1.29442e14i	−0.0502858	−	0.121401i	−0.947026	+	0.321156i	$0.895929\pi$
$6$	−1.31888e17	−	5.46298e16i	−2.45445	−	1.01666i
$7$	−6.31645e17	+	1.52492e18i	−0.427430	+	1.03191i	0.552670	+	0.833400i	$0.313609\pi$
$7$	−6.31645e17	+	1.52492e18i	−0.427430	+	1.03191i	−0.980100	+	0.198507i	$0.936391\pi$
$8$	4.33664e19	−	4.33664e19i	1.66234	−	1.66234i
$9$	2.65060e20	−	2.65060e20i	0.807478	−	0.807478i
$10$	−2.88655e20	+	6.96875e20i	−0.0912808	+	0.220371i
$11$	−1.70618e22	−	7.06722e21i	−0.695155	−	0.287943i	0.00699090	−	0.999976i	$-0.497775\pi$
$11$	−1.70618e22	−	7.06722e21i	−0.695155	−	0.287943i	−0.702146	+	0.712033i	$0.747775\pi$
$12$	2.04852e23	+	4.94557e23i	1.28542	+	3.10327i
$13$			8.26295e23i			0.927584i	0.885944	+	0.463792i	$0.153512\pi$
$13$			8.26295e23i			0.927584i	−0.885944	+	0.463792i	$0.846488\pi$
$14$	8.20970e24	−	3.40057e24i	1.87316	−	0.775887i
$15$	−2.62698e24	−	2.62698e24i	−0.135986	−	0.135986i
$16$	−1.52603e26			−1.97235
$17$	−2.82528e26	+	3.64818e25i	−0.991766	+	0.128063i
$17$	−2.82528e26	+	3.64818e25i	−0.991766	+	0.128063i
$18$	−2.01808e27			−2.07291
$19$	−2.21022e27	−	2.21022e27i	−0.709958	−	0.709958i	0.256569	−	0.966526i	$-0.417408\pi$
$19$	−2.21022e27	−	2.21022e27i	−0.709958	−	0.709958i	−0.966526	+	0.256569i	$0.917408\pi$
$20$	2.61316e27	−	1.08241e27i	0.278626	−	0.115411i
$21$			4.37668e28i			1.63467i
$22$	3.80476e28	+	9.18551e28i	0.522685	+	1.26187i
$23$	−1.61458e29	−	6.68780e28i	−0.852924	−	0.353293i	−0.0869878	−	0.996209i	$-0.527724\pi$
$23$	−1.61458e29	−	6.68780e28i	−0.852924	−	0.353293i	−0.765936	+	0.642917i	$0.777724\pi$
$24$	6.22328e29	−	1.50243e30i	1.31667	−	3.17873i
$25$	7.90007e29	−	7.90007e29i	0.694897	−	0.694897i
$26$	3.14557e30	−	3.14557e30i	1.19062	−	1.19062i
$27$	4.72814e29	−	1.14147e30i	0.0795005	−	0.191931i
$28$	−3.07849e31	−	1.27515e31i	−2.36832	−	0.980990i
$29$	4.13362e30	+	9.97945e30i	0.149546	+	0.361035i	0.980845	−	0.194790i	$-0.0624024\pi$
$29$	4.13362e30	+	9.97945e30i	0.149546	+	0.361035i	−0.831299	+	0.555825i	$0.812402\pi$
$30$			2.00010e31i			0.349095i
$31$	9.72964e31	−	4.03015e31i	0.839113	−	0.347572i	0.0786090	−	0.996906i	$-0.474952\pi$
$31$	9.72964e31	−	4.03015e31i	0.839113	−	0.347572i	0.760504	+	0.649334i	$0.224952\pi$
$32$	1.99480e32	+	1.99480e32i	0.869309	+	0.869309i
$33$	−4.89689e32			−1.10121
$34$	1.21442e33	+	9.36655e32i	1.43738	+	1.10862i
$35$	2.31257e32			0.146768
$36$	5.35099e33	+	5.35099e33i	1.85324	+	1.85324i
$37$	2.03855e33	−	8.44394e32i	0.391727	−	0.162259i	−0.178121	−	0.984009i	$-0.557002\pi$
$37$	2.03855e33	−	8.44394e32i	0.391727	−	0.162259i	0.569848	+	0.821750i	$0.307002\pi$
$38$			1.68278e34i			1.82256i
$39$	8.38468e33	+	2.02424e34i	0.519514	+	1.25422i
$40$	−7.93862e33	−	3.28828e33i	−0.285401	−	0.118217i
$41$	−1.50367e34	+	3.63019e34i	−0.317907	+	0.767496i	0.681457	+	0.731858i	$0.261346\pi$
$41$	−1.50367e34	+	3.63019e34i	−0.317907	+	0.767496i	−0.999365	+	0.0356385i	$0.988654\pi$
$42$	1.66613e35	−	1.66613e35i	2.09821	−	2.09821i
$43$	−2.81014e34	+	2.81014e34i	−0.213381	+	0.213381i	−0.805702	−	0.592321i	$-0.798212\pi$
$43$	−2.81014e34	+	2.81014e34i	−0.213381	+	0.213381i	0.592321	+	0.805702i	$0.298212\pi$
$44$	1.42672e35	−	3.44441e35i	0.660855	−	1.59544i
$45$	−4.85217e34	−	2.00984e34i	−0.138633	−	0.0574237i
$46$	3.60049e35	+	8.69235e35i	0.641310	+	1.54826i
$47$		−	9.57862e35i		−	1.07448i	−0.843429	−	0.537241i	$-0.819467\pi$
$47$		−	9.57862e35i		−	1.07448i	0.843429	−	0.537241i	$-0.180533\pi$
$48$	−3.73844e36	+	1.54851e36i	−2.66688	+	1.10466i
$49$	−3.82231e35	−	3.82231e35i	−0.175029	−	0.175029i
$50$	−6.01484e36			−1.78390
$51$	−6.55111e36	+	3.76062e36i	−1.26928	+	0.728619i
$52$	−1.66811e37			−2.12889
$53$	8.07927e36	+	8.07927e36i	0.684607	+	0.684607i	0.961035	−	0.276428i	$-0.0891507\pi$
$53$	8.07927e36	+	8.07927e36i	0.684607	+	0.684607i	−0.276428	+	0.961035i	$0.589151\pi$
$54$	−6.14533e36	+	2.54548e36i	−0.348401	+	0.144312i
$55$			2.58744e36i			0.0988718i
$56$	3.87384e37	+	9.35227e37i	1.00484	+	2.42591i
$57$	−7.65731e37	−	3.17176e37i	−1.35759	−	0.562330i
$58$	2.22541e37	−	5.37261e37i	0.271461	−	0.655365i
$59$	−1.58916e38	+	1.58916e38i	−1.34230	+	1.34230i	−0.448539	+	0.893763i	$0.648056\pi$
$59$	−1.58916e38	+	1.58916e38i	−1.34230	+	1.34230i	−0.893763	+	0.448539i	$0.851944\pi$
$60$	5.30331e37	−	5.30331e37i	0.312101	−	0.312101i
$61$	4.77385e37	−	1.15251e38i	0.196914	−	0.475394i	−0.794321	−	0.607498i	$-0.792173\pi$
$61$	4.77385e37	−	1.15251e38i	0.196914	−	0.475394i	0.991236	+	0.132104i	$0.0421733\pi$
$62$	−5.23812e38	−	2.16970e38i	−1.52319	−	0.630926i
$63$	2.36773e38	+	5.71621e38i	0.488102	+	1.17838i
$64$		−	1.76458e38i		−	0.259282i
$65$	1.06958e38	−	4.43033e37i	0.112609	−	0.0466443i
$66$	1.86416e39	+	1.86416e39i	1.41348	+	1.41348i
$67$	−2.45211e39			−1.34565			−0.672824	−	0.739802i	$-0.734919\pi$
$67$	−2.45211e39			−1.34565			−0.672824	+	0.739802i	$0.734919\pi$
$68$	−7.36489e38	−	5.70362e39i	−0.293917	−	2.27619i
$69$	−4.63399e39			−1.35114
$70$	−8.80355e38	−	8.80355e38i	−0.188387	−	0.188387i
$71$	−2.17587e39	+	9.01275e38i	−0.343225	+	0.142168i	−0.547636	−	0.836717i	$-0.684472\pi$
$71$	−2.17587e39	+	9.01275e38i	−0.343225	+	0.142168i	0.204411	+	0.978885i	$0.434472\pi$
$72$		−	2.29894e40i		−	2.68460i
$73$	1.04078e39	+	2.51267e39i	0.0903478	+	0.218119i	0.962594	−	0.270948i	$-0.0873373\pi$
$73$	1.04078e39	+	2.51267e39i	0.0903478	+	0.218119i	−0.872246	+	0.489067i	$0.837337\pi$
$74$	−1.09749e40	−	4.54594e39i	−0.711078	−	0.294538i
$75$	1.13370e40	−	2.73699e40i	0.550402	−	1.32879i
$76$	4.46195e40	−	4.46195e40i	1.62942	−	1.62942i
$77$	2.15540e40	−	2.15540e40i	0.594260	−	0.594260i
$78$	4.51403e40	−	1.08978e41i	0.943042	−	2.27670i
$79$	9.32407e40	+	3.86215e40i	1.48123	+	0.613546i	0.969388	−	0.245533i	$-0.0789629\pi$
$79$	9.32407e40	+	3.86215e40i	1.48123	+	0.613546i	0.511843	+	0.859079i	$0.328963\pi$
$80$	8.18209e39	+	1.97533e40i	0.0991813	+	0.239445i
$81$			9.02864e40i			0.837904i
$82$	1.95437e41	−	8.09529e40i	1.39319	−	0.577078i
$83$	−2.87478e40	−	2.87478e40i	−0.157916	−	0.157916i	0.623727	−	0.781642i	$-0.285618\pi$
$83$	−2.87478e40	−	2.87478e40i	−0.157916	−	0.157916i	−0.781642	+	0.623727i	$0.785618\pi$
$84$	−8.83556e41			−3.75171
$85$	1.98705e40	+	3.46150e40i	0.0654188	+	0.113961i
$86$	2.13954e41			0.547778
$87$	2.02529e41	+	2.02529e41i	0.404412	+	0.404412i
$88$	−1.04639e42	+	4.33429e41i	−1.63424	+	0.676924i
$89$			7.78073e41i			0.953093i	0.879149	+	0.476547i	$0.158112\pi$
$89$			7.78073e41i			0.953093i	−0.879149	+	0.476547i	$0.841888\pi$
$90$	1.08203e41	+	2.61225e41i	0.104238	+	0.251652i
$91$	−1.26004e42	−	5.21925e41i	−0.957181	−	0.396477i
$92$	1.35012e42	−	3.25948e42i	0.810839	−	1.95754i
$93$	1.97459e42	−	1.97459e42i	0.939927	−	0.939927i
$94$	−3.64642e42	+	3.64642e42i	−1.37917	+	1.37917i
$95$	−1.67591e41	+	4.04600e41i	−0.0504886	+	0.121890i
$96$	6.91099e42	+	2.86263e42i	1.66230	+	0.688546i
$97$	1.86859e42	+	4.51117e42i	0.359684	+	0.868354i	0.995344	+	0.0963851i	$0.0307280\pi$
$97$	1.86859e42	+	4.51117e42i	0.359684	+	0.868354i	−0.635660	+	0.771969i	$0.719272\pi$
$98$			2.91018e42i			0.449323i
$99$	−6.39565e42	+	2.64916e42i	−0.793830	+	0.328815i
$100$	1.59485e43	+	1.59485e43i	1.59485	+	1.59485i
$101$	1.60195e43			1.29342			0.646709	−	0.762736i	$-0.276145\pi$
$101$	1.60195e43			1.29342			0.646709	+	0.762736i	$0.276145\pi$
$102$	3.92550e43	+	1.06229e43i	2.56443	+	0.693969i
$103$	2.85853e43			1.51406			0.757029	−	0.653382i	$-0.226650\pi$
$103$	2.85853e43			1.51406			0.757029	+	0.653382i	$0.226650\pi$
$104$	3.58335e43	+	3.58335e43i	1.54196	+	1.54196i
$105$	5.66527e42	−	2.34663e42i	0.198450	−	0.0822006i
$106$		−	6.15129e43i		−	1.75748i
$107$	−2.08121e43	−	5.02450e43i	−0.485921	−	1.17312i	−0.956755	−	0.290895i	$-0.906047\pi$
$107$	−2.08121e43	−	5.02450e43i	−0.485921	−	1.17312i	0.470834	−	0.882222i	$-0.343953\pi$
$108$	2.30439e43	+	9.54510e42i	0.440499	+	0.182461i
$109$	9.99836e42	−	2.41382e43i	0.156769	−	0.378473i	−0.825907	−	0.563806i	$-0.809336\pi$
$109$	9.99836e42	−	2.41382e43i	0.156769	−	0.378473i	0.982676	+	0.185333i	$0.0593365\pi$
$110$	9.84995e42	−	9.84995e42i	0.126909	−	0.126909i
$111$	4.13715e43	−	4.13715e43i	0.438791	−	0.438791i
$112$	9.63910e43	−	2.32708e44i	0.843042	−	2.03528i
$113$	−8.47455e43	−	3.51027e43i	−0.612252	−	0.253603i	0.0549392	−	0.998490i	$-0.482504\pi$
$113$	−8.47455e43	−	3.51027e43i	−0.612252	−	0.253603i	−0.667191	+	0.744887i	$0.732504\pi$
$114$	1.70757e44	+	4.12245e44i	1.02076	+	2.46434i
$115$			2.44852e43i			0.121311i
$116$	−2.01464e44	+	8.34489e43i	−0.828609	+	0.343221i
$117$	2.19018e44	+	2.19018e44i	0.749004	+	0.749004i
$118$	1.20994e45			3.44587
$119$	1.22825e44	−	4.53877e44i	0.291761	−	1.07815i
$120$	−2.27846e44			−0.452110
$121$	−1.84803e44	−	1.84803e44i	−0.306777	−	0.306777i
$122$	−6.20474e44	+	2.57009e44i	−0.862953	+	0.357447i
$123$			1.04190e45i			1.21581i
$124$	8.13599e44	+	1.96420e45i	0.797709	+	1.92584i
$125$	−2.91777e44	−	1.20858e44i	−0.240705	−	0.0997034i
$126$	1.27471e45	−	3.07742e45i	0.886022	−	2.13905i
$127$	1.14022e45	−	1.14022e45i	0.668663	−	0.668663i	−0.288743	−	0.957407i	$-0.593237\pi$
$127$	1.14022e45	−	1.14022e45i	0.668663	−	0.668663i	0.957407	+	0.288743i	$0.0932374\pi$
$128$	1.08289e45	−	1.08289e45i	0.536502	−	0.536502i
$129$	−4.03268e44	+	9.73575e44i	−0.169011	+	0.408028i
$130$	−5.75825e44	−	2.38514e44i	−0.204413	−	0.0846706i
$131$	−1.58242e45	−	3.82030e45i	−0.476419	−	1.15018i	−0.961277	−	0.275584i	$-0.911129\pi$
$131$	−1.58242e45	−	3.82030e45i	−0.476419	−	1.15018i	0.484858	−	0.874593i	$-0.338871\pi$
$132$		−	9.88576e45i		−	2.52738i
$133$	4.76649e45	−	1.97434e45i	1.03607	−	0.429153i
$134$	9.33477e45	+	9.33477e45i	1.72723	+	1.72723i
$135$	−1.73106e44			−0.0272983
$136$	−1.06701e46	+	1.38343e46i	−1.43576	+	1.86153i
$137$	−1.55200e46			−1.78402			−0.892009	−	0.452019i	$-0.850704\pi$
$137$	−1.55200e46			−1.78402			−0.892009	+	0.452019i	$0.850704\pi$
$138$	1.76408e46	+	1.76408e46i	1.73427	+	1.73427i
$139$	4.28804e45	−	1.77616e45i	0.360945	−	0.149508i	−0.194839	−	0.980835i	$-0.562418\pi$
$139$	4.28804e45	−	1.77616e45i	0.360945	−	0.149508i	0.555783	+	0.831327i	$0.312418\pi$
$140$			4.66857e45i			0.336846i
$141$	−9.71972e45	−	2.34655e46i	−0.601787	−	1.45284i
$142$	1.17142e46	+	4.85217e45i	0.623035	+	0.258069i
$143$	5.83961e45	−	1.40981e46i	0.267091	−	0.644815i
$144$	−4.04491e46	+	4.04491e46i	−1.59263	+	1.59263i
$145$	1.07013e45	−	1.07013e45i	0.0363099	−	0.0363099i
$146$	5.60322e45	−	1.35274e46i	0.164003	−	0.395938i
$147$	−1.32424e46	−	5.48520e45i	−0.334692	−	0.138634i
$148$	1.70465e46	+	4.11538e46i	0.372398	+	0.899049i
$149$		−	9.15387e46i		−	1.73021i	−0.501587	−	0.865107i	$-0.667250\pi$
$149$		−	9.15387e46i		−	1.73021i	0.501587	−	0.865107i	$-0.332750\pi$
$150$	−1.47350e47	+	6.10345e46i	−2.41206	+	0.999110i
$151$	5.98449e46	+	5.98449e46i	0.849224	+	0.849224i	0.990036	−	0.140812i	$-0.0449713\pi$
$151$	5.98449e46	+	5.98449e46i	0.849224	+	0.849224i	−0.140812	+	0.990036i	$0.544971\pi$
$152$	−1.91698e47			−2.36038
$153$	−6.52170e46	+	8.45568e46i	−0.697421	+	0.904238i
$154$	−1.64105e47			−1.52555
$155$	−1.04334e46	−	1.04334e46i	−0.0843909	−	0.0843909i
$156$	−4.08650e47	+	1.69268e47i	−2.87854	+	1.19233i
$157$		−	2.15137e47i		−	1.32091i	−0.750866	−	0.660455i	$-0.770364\pi$
$157$		−	2.15137e47i		−	1.32091i	0.750866	−	0.660455i	$-0.229636\pi$
$158$	−2.07926e47	−	5.01977e47i	−1.11373	−	2.68879i
$159$	2.79907e47	+	1.15941e47i	1.30911	+	0.542251i
$160$	1.51257e46	−	3.65166e46i	0.0618208	−	0.149249i
$161$	2.03968e47	−	2.03968e47i	0.729130	−	0.729130i
$162$	3.43705e47	−	3.43705e47i	1.07551	−	1.07551i
$163$	2.47867e47	−	5.98405e47i	0.679494	−	1.64044i	−0.0854461	−	0.996343i	$-0.527232\pi$
$163$	2.47867e47	−	5.98405e47i	0.679494	−	1.64044i	0.764940	−	0.644101i	$-0.222768\pi$
$164$	−7.32856e47	−	3.03559e47i	−1.76147	−	0.729626i
$165$	2.62556e46	+	6.33865e46i	0.0553753	+	0.133688i
$166$			2.18876e47i			0.405391i
$167$	9.56648e47	−	3.96257e47i	1.55721	−	0.645019i	0.572611	−	0.819827i	$-0.305931\pi$
$167$	9.56648e47	−	3.96257e47i	1.55721	−	0.645019i	0.984602	+	0.174808i	$0.0559306\pi$
$168$	1.89801e48	+	1.89801e48i	2.71737	+	2.71737i
$169$	1.10767e47			0.139588
$170$	5.61298e46	−	2.07417e47i	0.0623077	−	0.230246i
$171$	−1.17168e48			−1.14655
$172$	−5.67306e47	−	5.67306e47i	−0.489729	−	0.489729i
$173$	−7.42480e46	+	3.07545e46i	−0.0565840	+	0.0234379i	−0.410796	−	0.911727i	$-0.634749\pi$
$173$	−7.42480e46	+	3.07545e46i	−0.0565840	+	0.0234379i	0.354212	+	0.935165i	$0.384749\pi$
$174$		−	1.54199e48i		−	1.03818i
$175$	7.05698e47	+	1.70370e48i	0.420050	+	1.01409i
$176$	2.60368e48	+	1.07848e48i	1.37109	+	0.567924i
$177$	−2.28052e48	+	5.50567e48i	−1.06319	+	2.56676i
$178$	2.96199e48	−	2.96199e48i	1.22336	−	1.22336i
$179$	2.29478e48	−	2.29478e48i	0.840235	−	0.840235i	−0.148654	−	0.988889i	$-0.547494\pi$
$179$	2.29478e48	−	2.29478e48i	0.840235	−	0.840235i	0.988889	+	0.148654i	$0.0474941\pi$
$180$	4.05742e47	−	9.79548e47i	0.131793	−	0.318176i
$181$	−2.57594e48	−	1.06699e48i	−0.742757	−	0.307660i	−0.0209746	−	0.999780i	$-0.506677\pi$
$181$	−2.57594e48	−	1.06699e48i	−0.742757	−	0.307660i	−0.721783	+	0.692120i	$0.756677\pi$
$182$	2.80987e48	+	6.78363e48i	0.719701	+	1.73751i
$183$		−	3.30781e48i		−	0.753082i
$184$	−9.90210e48	+	4.10158e48i	−2.00514	+	0.830555i
$185$	−2.18601e47	−	2.18601e47i	−0.0393967	−	0.0393967i
$186$	−1.50339e49			−2.41292
$187$	5.07825e48	+	1.37424e48i	0.726306	+	0.196548i
$188$	1.93371e49			2.46603
$189$	1.44201e48	+	1.44201e48i	0.164074	+	0.164074i
$190$	2.17824e48	−	9.02255e47i	0.221260	−	0.0916488i
$191$		−	2.53051e48i		−	0.229610i	−0.993388	−	0.114805i	$-0.963376\pi$
$191$		−	2.53051e48i		−	0.229610i	0.993388	−	0.114805i	$-0.0366243\pi$
$192$	−1.79058e48	−	4.32284e48i	−0.145217	−	0.350584i
$193$	1.21602e49	+	5.03693e48i	0.881981	+	0.365329i	0.777265	−	0.629174i	$-0.216607\pi$
$193$	1.21602e49	+	5.03693e48i	0.881981	+	0.365329i	0.104716	+	0.994502i	$0.466607\pi$
$194$	1.00599e49	−	2.42867e49i	0.652912	−	1.57627i
$195$	2.17066e48	−	2.17066e48i	0.126139	−	0.126139i
$196$	7.71642e48	−	7.71642e48i	0.401708	−	0.401708i
$197$	−4.55555e48	+	1.09981e49i	−0.212577	+	0.513207i	−0.993818	−	0.111023i	$-0.964587\pi$
$197$	−4.55555e48	+	1.09981e49i	−0.212577	+	0.513207i	0.781241	+	0.624230i	$0.214587\pi$
$198$	3.44321e49	+	1.42622e49i	1.44099	+	0.596878i
$199$	1.34080e48	+	3.23698e48i	0.0503527	+	0.121562i	0.947054	−	0.321073i	$-0.104044\pi$
$199$	1.34080e48	+	3.23698e48i	0.0503527	+	0.121562i	−0.896702	+	0.442635i	$0.854044\pi$
$200$		−	6.85195e49i		−	2.31031i
$201$	−6.00712e49	+	2.48823e49i	−1.81950	+	0.753660i
$202$	−6.09835e49	−	6.09835e49i	−1.66019	−	1.66019i
$203$	−1.78289e49			−0.436475
$204$	−7.59188e49	−	1.32253e50i	−1.67225	−	2.91310i
$205$	5.50522e48			0.109161
$206$	−1.08819e50	−	1.08819e50i	−1.94339	−	1.94339i
$207$	−6.05227e49	+	2.50693e49i	−0.973994	+	0.403441i
$208$		−	1.26095e50i		−	1.82952i
$209$	2.20901e49	+	5.33303e49i	0.289104	+	0.697958i
$210$	−3.05000e49	−	1.26335e49i	−0.360234	−	0.149214i
$211$	1.75742e48	−	4.24280e48i	0.0187415	−	0.0452459i	−0.914232	−	0.405192i	$-0.867205\pi$
$211$	1.75742e48	−	4.24280e48i	0.0187415	−	0.0452459i	0.932973	+	0.359946i	$0.117205\pi$
$212$	−1.63103e50	+	1.63103e50i	−1.57123	+	1.57123i
$213$	−4.41585e49	+	4.41585e49i	−0.384461	+	0.384461i
$214$	−1.12046e50	+	2.70502e50i	−0.882062	+	2.12949i
$215$	5.14421e48	+	2.13080e48i	0.0366347	+	0.0151746i
$216$	−2.89974e49	−	7.00059e49i	−0.186898	−	0.451211i
$217$			1.73826e50i			1.01445i
$218$	−1.29952e50	+	5.38279e49i	−0.687019	+	0.284572i
$219$	5.09936e49	+	5.09936e49i	0.244325	+	0.244325i
$220$	−5.22348e49			−0.226920
$221$	−3.01448e49	−	2.33451e50i	−0.118790	−	0.919946i
$222$	−3.14989e50			−1.12644
$223$	6.22416e49	+	6.22416e49i	0.202081	+	0.202081i	0.800891	−	0.598810i	$-0.204359\pi$
$223$	6.22416e49	+	6.22416e49i	0.202081	+	0.202081i	−0.598810	+	0.800891i	$0.704359\pi$
$224$	−4.30192e50	+	1.78191e50i	−1.26861	+	0.525477i
$225$		−	4.18799e50i		−	1.12223i
$226$	1.88982e50	+	4.56242e50i	0.460350	+	1.11138i
$227$	−1.33864e50	−	5.54484e49i	−0.296557	−	0.122838i	0.229444	−	0.973322i	$-0.426309\pi$
$227$	−1.33864e50	−	5.54484e49i	−0.296557	−	0.122838i	−0.526001	+	0.850484i	$0.676309\pi$
$228$	6.40310e50	−	1.54585e51i	1.29060	−	3.11578i
$229$	5.04608e50	−	5.04608e50i	0.925745	−	0.925745i	−0.0716828	−	0.997427i	$-0.522837\pi$
$229$	5.04608e50	−	5.04608e50i	0.925745	−	0.925745i	0.997427	+	0.0716828i	$0.0228369\pi$
$230$	9.32112e49	−	9.32112e49i	0.155711	−	0.155711i
$231$	3.09310e50	−	7.46739e50i	0.470691	−	1.13635i
$232$	6.12034e50	+	2.53513e50i	0.848758	+	0.351567i
$233$	2.46557e50	+	5.95240e50i	0.311720	+	0.752558i	0.999642	+	0.0267731i	$0.00852318\pi$
$233$	2.46557e50	+	5.95240e50i	0.311720	+	0.752558i	−0.687922	+	0.725785i	$0.741477\pi$
$234$		−	1.66753e51i		−	1.92279i
$235$	−1.23988e50	+	5.13575e49i	−0.130443	+	0.0540312i
$236$	−3.20818e51	−	3.20818e51i	−3.08071	−	3.08071i
$237$	2.67609e51			2.34645
$238$	−2.19541e51	+	1.26026e51i	−1.75837	+	1.00938i
$239$	−6.88309e50			−0.503766			−0.251883	−	0.967758i	$-0.581050\pi$
$239$	−6.88309e50			−0.503766			−0.251883	+	0.967758i	$0.581050\pi$
$240$	4.00886e50	+	4.00886e50i	0.268213	+	0.268213i
$241$	−7.81246e50	+	3.23603e50i	−0.477993	+	0.197991i	−0.608654	−	0.793436i	$-0.708290\pi$
$241$	−7.81246e50	+	3.23603e50i	−0.477993	+	0.197991i	0.130661	+	0.991427i	$0.458290\pi$
$242$			1.40702e51i			0.787538i
$243$	1.07137e51	+	2.58651e51i	0.548787	+	1.32489i
$244$	2.32667e51	+	9.63738e50i	1.09107	+	0.451937i
$245$	−2.89829e49	+	6.99709e49i	−0.0124472	+	0.0300502i
$246$	3.96633e51	−	3.96633e51i	1.56057	−	1.56057i
$247$	1.82629e51	−	1.82629e51i	0.658545	−	0.658545i
$248$	2.47166e51	−	5.96713e51i	0.817106	−	1.97267i
$249$	−9.95969e50	−	4.12544e50i	−0.301967	−	0.125079i
$250$	6.50660e50	+	1.57083e51i	0.180985	+	0.436937i
$251$		−	7.64678e51i		−	1.95206i	−0.217632	−	0.976031i	$-0.569833\pi$
$251$		−	7.64678e51i		−	1.95206i	0.217632	−	0.976031i	$-0.430167\pi$
$252$	−1.15398e52	+	4.77994e51i	−2.70450	+	1.12024i
$253$	2.28212e51	+	2.28212e51i	0.491186	+	0.491186i
$254$	−8.68123e51			−1.71655
$255$	8.38033e50	+	6.46358e50i	0.152282	+	0.117452i
$256$	−9.79694e51			−1.63656
$257$	−6.14335e51	−	6.14335e51i	−0.943720	−	0.943720i	0.0547782	−	0.998499i	$-0.482555\pi$
$257$	−6.14335e51	−	6.14335e51i	−0.943720	−	0.943720i	−0.998499	+	0.0547782i	$0.982555\pi$
$258$	5.24141e51	−	2.17106e51i	0.740669	−	0.306795i
$259$			3.64199e51i			0.473580i
$260$	8.94388e50	+	2.15924e51i	0.107053	+	0.258449i
$261$	3.74082e51	+	1.54950e51i	0.412283	+	0.170773i
$262$	−8.51923e51	+	2.05673e52i	−0.864814	+	2.08785i
$263$	6.93575e51	−	6.93575e51i	0.648702	−	0.648702i	−0.303978	−	0.952679i	$-0.598315\pi$
$263$	6.93575e51	−	6.93575e51i	0.648702	−	0.648702i	0.952679	+	0.303978i	$0.0983148\pi$
$264$	−2.12361e52	+	2.12361e52i	−1.83058	+	1.83058i
$265$	6.12616e50	−	1.47898e51i	0.0486857	−	0.117538i
$266$	−2.56612e52	−	1.06292e52i	−1.88071	−	0.779015i
$267$	7.89535e51	+	1.90611e52i	0.533801	+	1.28871i
$268$		−	4.95028e52i		−	3.08838i
$269$	1.60463e51	−	6.64660e50i	0.0924062	−	0.0382759i	−0.336002	−	0.941861i	$-0.609075\pi$
$269$	1.60463e51	−	6.64660e50i	0.0924062	−	0.0382759i	0.428408	+	0.903586i	$0.359075\pi$
$270$	6.58985e50	+	6.58985e50i	0.0350392	+	0.0350392i
$271$	3.06866e52			1.50699			0.753493	−	0.657456i	$-0.228367\pi$
$271$	3.06866e52			1.50699			0.753493	+	0.657456i	$0.228367\pi$
$272$	4.31146e52	−	5.56725e51i	1.95611	−	0.252586i
$273$	−3.61643e52			−1.51629
$274$	5.90819e52	+	5.90819e52i	2.28991	+	2.28991i
$275$	−1.90621e52	+	7.89577e51i	−0.683152	+	0.282971i
$276$		−	9.35501e52i		−	3.10098i
$277$	−6.36960e50	−	1.53776e51i	−0.0195343	−	0.0471599i	0.913811	−	0.406139i	$-0.133125\pi$
$277$	−6.36960e50	−	1.53776e51i	−0.0195343	−	0.0471599i	−0.933346	+	0.358979i	$0.883125\pi$
$278$	−2.30854e52	−	9.56228e51i	−0.655200	−	0.271393i
$279$	1.51071e52	−	3.64717e52i	0.396909	−	0.958222i
$280$	1.00288e52	−	1.00288e52i	0.243978	−	0.243978i
$281$	−5.71519e52	+	5.71519e52i	−1.28779	+	1.28779i	−0.351662	+	0.936127i	$0.614383\pi$
$281$	−5.71519e52	+	5.71519e52i	−1.28779	+	1.28779i	−0.936127	+	0.351662i	$0.885617\pi$
$282$	−5.23278e52	+	1.26330e53i	−1.09239	+	2.63726i
$283$	4.54760e51	+	1.88368e51i	0.0879780	+	0.0364417i	0.426238	−	0.904611i	$-0.359838\pi$
$283$	4.54760e51	+	1.88368e51i	0.0879780	+	0.0364417i	−0.338260	+	0.941053i	$0.609838\pi$
$284$	−1.81948e52	−	4.39261e52i	−0.326289	−	0.787732i
$285$			1.16124e52i			0.193089i
$286$	−7.58994e52	+	3.14386e52i	−1.17049	+	0.484834i
$287$	−4.58598e52	−	4.58598e52i	−0.656102	−	0.656102i
$288$	1.05748e53			1.40390
$289$	7.84910e52	−	2.06143e52i	0.967200	−	0.254018i
$290$	−8.14762e51			−0.0932125
$291$	9.15525e52	+	9.15525e52i	0.972682	+	0.972682i
$292$	−5.07253e52	+	2.10111e52i	−0.500603	+	0.207356i
$293$			4.59175e52i			0.421041i	0.977589	+	0.210520i	$0.0675158\pi$
$293$			4.59175e52i			0.421041i	−0.977589	+	0.210520i	$0.932484\pi$
$294$	2.95305e52	+	7.12929e52i	0.251654	+	0.607546i
$295$	2.90911e52	+	1.20499e52i	0.230455	+	0.0954577i
$296$	5.17862e52	−	1.25023e53i	0.381454	−	0.920911i
$297$	−1.61341e52	+	1.61341e52i	−0.110530	+	0.110530i
$298$	−3.48472e53	+	3.48472e53i	−2.22085	+	2.22085i
$299$	5.52610e52	−	1.33412e53i	0.327709	−	0.791158i
$300$	5.52538e53	+	2.28869e53i	3.04969	+	1.26322i
$301$	−2.51024e52	−	6.06026e52i	−0.128984	−	0.311395i
$302$		−	4.55639e53i		−	2.18007i
$303$	3.92442e53	−	1.62555e53i	1.74888	−	0.724408i
$304$	3.37286e53	+	3.37286e53i	1.40029	+	1.40029i
$305$	−1.74780e52			−0.0676151
$306$	5.70164e53	−	7.36233e52i	2.05584	−	0.265463i
$307$	−1.35524e53			−0.455555			−0.227778	−	0.973713i	$-0.573146\pi$
$307$	−1.35524e53			−0.455555			−0.227778	+	0.973713i	$0.573146\pi$
$308$	4.35128e53	+	4.35128e53i	1.36388	+	1.36388i
$309$	7.00276e53	−	2.90064e53i	2.04721	−	0.847981i
$310$			7.94367e52i			0.216643i
$311$	2.74994e53	+	6.63893e53i	0.699801	+	1.68947i	0.724036	+	0.689762i	$0.242285\pi$
$311$	2.74994e53	+	6.63893e53i	0.699801	+	1.68947i	−0.0242356	+	0.999706i	$0.507715\pi$
$312$	1.24145e54	+	5.14227e53i	2.94854	+	1.22132i
$313$	2.92103e53	−	7.05198e53i	0.647638	−	1.56354i	−0.168514	−	0.985699i	$-0.553897\pi$
$313$	2.92103e53	−	7.05198e53i	0.647638	−	1.56354i	0.816152	−	0.577837i	$-0.196103\pi$
$314$	−8.18991e53	+	8.18991e53i	−1.69548	+	1.69548i
$315$	6.12970e52	−	6.12970e52i	0.118512	−	0.118512i
$316$	−7.79685e53	+	1.88233e54i	−1.40814	+	3.39956i
$317$	−7.02057e53	−	2.90801e53i	−1.18467	−	0.490707i	−0.298656	−	0.954361i	$-0.596538\pi$
$317$	−7.02057e53	−	2.90801e53i	−1.18467	−	0.490707i	−0.886016	+	0.463654i	$0.846538\pi$
$318$	−6.24190e53	−	1.50693e54i	−0.984314	−	2.37635i
$319$		−	1.99481e53i		−	0.294036i
$320$	−2.28412e52	+	9.46113e51i	−0.0314771	+	0.0130382i
$321$	−1.01970e54	−	1.01970e54i	−1.31406	−	1.31406i
$322$	−1.55294e54			−1.87178
$323$	7.05080e53	+	5.43815e53i	0.795031	+	0.613192i
$324$	−1.82269e54			−1.92307
$325$	6.52779e53	+	6.52779e53i	0.644576	+	0.644576i
$326$	−3.22161e54	+	1.33444e54i	−2.97780	+	1.23344i
$327$		−	6.92788e53i		−	0.599548i
$328$	9.22194e53	+	2.22637e54i	0.747368	+	1.80431i
$329$	1.46067e54	+	6.05028e53i	1.10876	+	0.459265i
$330$	1.41351e53	−	3.41252e53i	0.100519	−	0.242675i
$331$	1.75124e54	−	1.75124e54i	1.16693	−	1.16693i	0.184001	−	0.982926i	$-0.441095\pi$
$331$	1.75124e54	−	1.75124e54i	1.16693	−	1.16693i	0.982926	−	0.184001i	$-0.0589051\pi$
$332$	5.80355e53	−	5.80355e53i	0.362431	−	0.362431i
$333$	3.16523e53	−	7.64154e53i	0.185291	−	0.447332i
$334$	−5.15028e54	−	2.13332e54i	−2.82671	−	1.17086i
$335$	1.31474e53	+	3.17407e53i	0.0676670	+	0.163363i
$336$		−	6.67895e54i		−	3.22414i
$337$	4.96422e53	−	2.05625e53i	0.224806	−	0.0931178i	−0.267437	−	0.963575i	$-0.586177\pi$
$337$	4.96422e53	−	2.05625e53i	0.224806	−	0.0931178i	0.492244	+	0.870457i	$0.336177\pi$
$338$	−4.21673e53	−	4.21673e53i	−0.179170	−	0.179170i
$339$	−2.43227e54			−0.969882
$340$	−6.98802e53	+	4.01143e53i	−0.261552	+	0.150142i
$341$	−1.94487e54			−0.683394
$342$	4.46039e54	+	4.46039e54i	1.47168	+	1.47168i
$343$	−2.50584e54	+	1.03795e54i	−0.776481	+	0.321629i
$344$			2.43731e54i			0.709422i
$345$	2.48459e53	+	5.99834e53i	0.0679430	+	0.164029i
$346$	3.99727e53	+	1.65572e53i	0.102713	+	0.0425453i
$347$	6.08231e53	−	1.46840e54i	0.146887	−	0.354618i	−0.833262	−	0.552879i	$-0.813529\pi$
$347$	6.08231e53	−	1.46840e54i	0.146887	−	0.354618i	0.980149	+	0.198261i	$0.0635293\pi$
$348$	−4.08863e54	+	4.08863e54i	−0.928162	+	0.928162i
$349$	−4.60723e53	+	4.60723e53i	−0.0983317	+	0.0983317i	−0.754561	−	0.656230i	$-0.772150\pi$
$349$	−4.60723e53	+	4.60723e53i	−0.0983317	+	0.0983317i	0.656230	+	0.754561i	$0.272150\pi$
$350$	3.79924e54	−	9.17219e54i	0.762490	−	1.84081i
$351$	9.43195e53	+	3.90684e53i	0.178032	+	0.0737434i
$352$	−1.99371e54	−	4.81325e54i	−0.353993	−	0.854616i
$353$			1.76107e54i			0.294185i	0.989123	+	0.147093i	$0.0469915\pi$
$353$			1.76107e54i			0.294185i	−0.989123	+	0.147093i	$0.953008\pi$
$354$	2.96407e55	−	1.22776e55i	4.65928	−	1.92994i
$355$	2.33326e53	+	2.33326e53i	0.0345187	+	0.0345187i
$356$	−1.57076e55			−2.18744
$357$	−1.59669e54	−	1.23653e55i	−0.209341	−	1.62121i
$358$	−1.74717e55			−2.15700
$359$	8.56309e54	+	8.56309e54i	0.995635	+	0.995635i	0.999991	−	0.00435562i	$-0.00138644\pi$
$359$	8.56309e54	+	8.56309e54i	0.995635	+	0.995635i	−0.00435562	+	0.999991i	$0.501386\pi$
$360$	−2.97581e54	+	1.23262e54i	−0.325913	+	0.134997i
$361$			7.83032e52i			0.00807932i
$362$	5.74433e54	+	1.38680e55i	0.558476	+	1.34828i
$363$	−6.40250e54	−	2.65200e54i	−0.586621	−	0.242986i
$364$	1.05365e55	−	2.54374e55i	0.909951	−	2.19682i
$365$	2.69442e53	−	2.69442e53i	0.0219366	−	0.0219366i
$366$	−1.25923e55	+	1.25923e55i	−0.966632	+	0.966632i
$367$	−3.48107e54	+	8.40405e54i	−0.251995	+	0.608370i	−0.998365	−	0.0571612i	$-0.981795\pi$
$367$	−3.48107e54	+	8.40405e54i	−0.251995	+	0.608370i	0.746370	+	0.665532i	$0.231795\pi$
$368$	2.46390e55	+	1.02058e55i	1.68226	+	0.696817i
$369$	5.63655e54	+	1.36078e55i	0.363033	+	0.876440i
$370$			1.66435e54i			0.101137i
$371$	−1.74235e55	+	7.21706e54i	−0.999072	+	0.413829i
$372$	3.98628e55	+	3.98628e55i	2.15722	+	2.15722i
$373$	1.73435e55			0.885923			0.442962	−	0.896541i	$-0.353928\pi$
$373$	1.73435e55			0.885923			0.442962	+	0.896541i	$0.353928\pi$
$374$	−1.41005e55	−	2.45636e55i	−0.679981	−	1.18455i
$375$	−8.37427e54			−0.381307
$376$	−4.15390e55	−	4.15390e55i	−1.78615	−	1.78615i
$377$	−8.24598e54	+	3.41559e54i	−0.334891	+	0.138716i
$378$		−	1.09790e55i		−	0.421201i
$379$	4.65433e54	+	1.12365e55i	0.168700	+	0.407277i	0.985507	−	0.169633i	$-0.0542583\pi$
$379$	4.65433e54	+	1.12365e55i	0.168700	+	0.407277i	−0.816808	+	0.576910i	$0.804258\pi$
$380$	−8.16800e54	−	3.38330e54i	−0.279749	−	0.115876i
$381$	1.63626e55	−	3.95029e55i	0.529623	−	1.27862i
$382$	−9.63321e54	+	9.63321e54i	−0.294720	+	0.294720i
$383$	−3.07010e53	+	3.07010e53i	−0.00887929	+	0.00887929i	−0.711532	−	0.702653i	$-0.751999\pi$
$383$	−3.07010e53	+	3.07010e53i	−0.00887929	+	0.00887929i	0.702653	+	0.711532i	$0.251999\pi$
$384$	1.55400e55	−	3.75170e55i	0.424943	−	1.02590i
$385$	−3.94565e54	−	1.63434e54i	−0.102027	−	0.0422608i
$386$	−2.71172e55	−	6.54666e55i	−0.663159	−	1.60101i
$387$			1.48971e55i			0.344601i
$388$	−9.10707e55	+	3.77227e55i	−1.99295	+	0.825508i
$389$	−2.35659e55	−	2.35659e55i	−0.487941	−	0.487941i	0.419715	−	0.907656i	$-0.362130\pi$
$389$	−2.35659e55	−	2.35659e55i	−0.487941	−	0.487941i	−0.907656	+	0.419715i	$0.862130\pi$
$390$	−1.65267e55			−0.323815
$391$	4.80561e55	+	1.30046e55i	0.891145	+	0.241155i
$392$	−3.31520e55			−0.581915
$393$	−7.75316e55	−	7.75316e55i	−1.28836	−	1.28836i
$394$	5.92100e55	−	2.45256e55i	0.931593	−	0.385878i
$395$		−	1.41401e55i		−	0.210675i
$396$	−5.34809e55	−	1.29114e56i	−0.754661	−	1.82191i
$397$	−8.04212e55	−	3.33115e55i	−1.07492	−	0.445245i	−0.226193	−	0.974083i	$-0.572628\pi$
$397$	−8.04212e55	−	3.33115e55i	−1.07492	−	0.445245i	−0.848723	+	0.528838i	$0.822628\pi$
$398$	7.21843e54	−	1.74268e55i	0.0914022	−	0.220664i
$399$	9.67340e55	−	9.67340e55i	1.16054	−	1.16054i
$400$	−1.20558e56	+	1.20558e56i	−1.37058	+	1.37058i
$401$	5.48104e55	−	1.32324e56i	0.590553	−	1.42572i	−0.292417	−	0.956291i	$-0.594459\pi$
$401$	5.48104e55	−	1.32324e56i	0.590553	−	1.42572i	0.882970	−	0.469430i	$-0.155541\pi$
$402$	3.23404e56	+	1.33958e56i	3.30282	+	1.36807i
$403$	3.33009e55	+	8.03955e55i	0.322402	+	0.778347i
$404$			3.23399e56i			2.96851i
$405$	1.16869e55	−	4.84087e54i	0.101722	−	0.0421347i
$406$	6.78716e55	+	6.78716e55i	0.560245	+	0.560245i
$407$	−4.07488e55			−0.319032
$408$	−1.21013e56	+	4.47183e56i	−0.898753	+	3.32117i
$409$	1.66849e56			1.17564			0.587818	−	0.808993i	$-0.299987\pi$
$409$	1.66849e56			1.17564			0.587818	+	0.808993i	$0.299987\pi$
$410$	−2.09575e55	−	2.09575e55i	−0.140115	−	0.140115i
$411$	−3.80205e56	+	1.57486e56i	−2.41223	+	0.999178i
$412$			5.77075e56i			3.47490i
$413$	−1.41957e56	−	3.42714e56i	−0.811391	−	1.95887i
$414$	3.25835e56	+	1.34965e56i	1.76803	+	0.732342i
$415$	−2.17982e54	+	5.26254e54i	−0.0112302	+	0.0271120i
$416$	−1.64829e56	+	1.64829e56i	−0.806357	+	0.806357i
$417$	8.70241e55	−	8.70241e55i	0.404310	−	0.404310i
$418$	1.18926e56	−	2.87113e56i	0.524792	−	1.26696i
$419$	−3.72412e56	−	1.54258e56i	−1.56107	−	0.646616i	−0.575794	−	0.817595i	$-0.695307\pi$
$419$	−3.72412e56	−	1.54258e56i	−1.56107	−	0.646616i	−0.985275	+	0.170979i	$0.945307\pi$
$420$	4.73734e55	+	1.14370e56i	0.188658	+	0.455461i
$421$		−	8.26047e55i		−	0.312564i	−0.987712	−	0.156282i	$-0.950049\pi$
$421$		−	8.26047e55i		−	0.312564i	0.987712	−	0.156282i	$-0.0499509\pi$
$422$	−2.28418e55	+	9.46139e54i	−0.0821321	+	0.0340202i
$423$	−2.53891e56	−	2.53891e56i	−0.867620	−	0.867620i
$424$	7.00738e56			2.27609
$425$	−1.94378e56	+	2.52020e56i	−0.600185	+	0.778166i
$426$	3.36208e56			0.986964
$427$	1.45595e56	+	1.45595e56i	0.406395	+	0.406395i
$428$	1.01434e57	−	4.20152e56i	2.69241	−	1.11523i
$429$		−	4.04628e56i		−	1.02147i
$430$	−1.14715e55	−	2.76948e55i	−0.0275455	−	0.0665006i
$431$	5.68616e56	+	2.35529e56i	1.29885	+	0.538000i	0.921610	−	0.388117i	$-0.126874\pi$
$431$	5.68616e56	+	2.35529e56i	1.29885	+	0.538000i	0.377237	+	0.926117i	$0.376874\pi$
$432$	−7.21530e55	+	1.74193e56i	−0.156803	+	0.378555i
$433$	−9.55734e55	+	9.55734e55i	−0.197627	+	0.197627i	−0.798982	−	0.601355i	$-0.794628\pi$
$433$	−9.55734e55	+	9.55734e55i	−0.197627	+	0.197627i	0.601355	+	0.798982i	$0.294628\pi$
$434$	6.61726e56	−	6.61726e56i	1.30211	−	1.30211i
$435$	1.53569e55	−	3.70748e55i	0.0287597	−	0.0694321i
$436$	4.87298e56	+	2.01845e56i	0.868630	+	0.359798i
$437$	2.09042e56	+	5.04671e56i	0.354717	+	0.856362i
$438$		−	3.88248e56i		−	0.627214i
$439$	−5.46208e56	+	2.26247e56i	−0.840177	+	0.348013i	−0.760923	−	0.648842i	$-0.775254\pi$
$439$	−5.46208e56	+	2.26247e56i	−0.840177	+	0.348013i	−0.0792537	+	0.996854i	$0.525254\pi$
$440$	1.12208e56	+	1.12208e56i	0.164358	+	0.164358i
$441$	−2.02629e56			−0.282665
$442$	−7.73954e56	+	1.00347e57i	−1.02834	+	1.33329i
$443$	1.49895e57			1.89717			0.948584	−	0.316525i	$-0.102516\pi$
$443$	1.49895e57			1.89717			0.948584	+	0.316525i	$0.102516\pi$
$444$	8.35202e56	+	8.35202e56i	1.00707	+	1.00707i
$445$	1.00716e56	−	4.17178e55i	0.115706	−	0.0479271i
$446$		−	4.73887e56i		−	0.518770i
$447$	−9.28872e56	−	2.24250e57i	−0.969045	−	2.33948i
$448$	2.69086e56	+	1.11459e56i	0.267555	+	0.110825i
$449$	6.33344e56	−	1.52903e57i	0.600265	−	1.44917i	−0.273044	−	0.962002i	$-0.588030\pi$
$449$	6.33344e56	−	1.52903e57i	0.600265	−	1.44917i	0.873309	−	0.487166i	$-0.161970\pi$
$450$	−1.59430e57	+	1.59430e57i	−1.44046	+	1.44046i
$451$	5.13107e56	−	5.13107e56i	0.441990	−	0.441990i
$452$	7.08648e56	−	1.71083e57i	0.582042	−	1.40517i
$453$	2.07333e57	+	8.58802e56i	1.62389	+	0.672638i
$454$	2.98516e56	+	7.20681e56i	0.222980	+	0.538322i
$455$			1.91086e56i			0.136140i
$456$	−4.69618e57	+	1.94522e57i	−3.19154	+	1.32198i
$457$	−4.58963e56	−	4.58963e56i	−0.297563	−	0.297563i	0.542496	−	0.840059i	$-0.317480\pi$
$457$	−4.58963e56	−	4.58963e56i	−0.297563	−	0.297563i	−0.840059	+	0.542496i	$0.817480\pi$
$458$	−3.84191e57			−2.37651
$459$	−9.19401e55	+	3.39747e56i	−0.0542665	+	0.200532i
$460$	−4.94304e56			−0.278420
$461$	−1.14785e57	−	1.14785e57i	−0.617044	−	0.617044i	0.327728	−	0.944772i	$-0.393717\pi$
$461$	−1.14785e57	−	1.14785e57i	−0.617044	−	0.617044i	−0.944772	+	0.327728i	$0.893717\pi$
$462$	−4.02020e57	+	1.66522e57i	−2.06274	+	0.854416i
$463$			1.40030e57i			0.685853i	0.939362	+	0.342926i	$0.111418\pi$
$463$			1.40030e57i			0.685853i	−0.939362	+	0.342926i	$0.888582\pi$
$464$	−6.30805e56	−	1.52290e57i	−0.294957	−	0.712088i
$465$	−3.61467e56	−	1.49725e56i	−0.161373	−	0.0668428i
$466$	1.32738e57	−	3.20458e57i	0.565846	−	1.36607i
$467$	−1.72902e57	+	1.72902e57i	−0.703863	+	0.703863i	−0.965238	−	0.261374i	$-0.915824\pi$
$467$	−1.72902e57	+	1.72902e57i	−0.703863	+	0.703863i	0.261374	+	0.965238i	$0.415824\pi$
$468$	−4.42150e57	+	4.42150e57i	−1.71903	+	1.71903i
$469$	1.54886e57	−	3.73928e57i	0.575170	−	1.38858i
$470$	6.67510e56	+	2.76492e56i	0.236785	+	0.0980795i
$471$	−2.18306e57	−	5.27038e57i	−0.739804	−	1.78605i
$472$			1.37833e58i			4.46272i
$473$	6.78058e56	−	2.80861e56i	0.209774	−	0.0868914i
$474$	−1.01874e58	−	1.01874e58i	−3.01183	−	3.01183i
$475$	−3.49217e57			−0.986695
$476$	9.16279e57	+	2.47957e57i	2.47445	+	0.669618i
$477$	4.28299e57			1.10561
$478$	2.62028e57	+	2.62028e57i	0.646618	+	0.646618i
$479$	2.49764e57	−	1.03455e57i	0.589272	−	0.244084i	−0.0680656	−	0.997681i	$-0.521683\pi$
$479$	2.49764e57	−	1.03455e57i	0.589272	−	0.244084i	0.657337	+	0.753597i	$0.271683\pi$
$480$		−	1.04806e57i		−	0.236428i
$481$	6.97719e56	+	1.68444e57i	0.150509	+	0.363360i
$482$	4.20597e57	+	1.74217e57i	0.867671	+	0.359401i
$483$	2.92703e57	−	7.06648e57i	0.577516	−	1.39425i
$484$	3.73076e57	−	3.73076e57i	0.704081	−	0.704081i
$485$	4.83749e56	−	4.83749e56i	0.0873318	−	0.0873318i
$486$	5.76790e57	−	1.39249e58i	0.996180	−	2.40499i
$487$	5.16224e57	+	2.13827e57i	0.853033	+	0.353338i	0.765979	−	0.642866i	$-0.222255\pi$
$487$	5.16224e57	+	2.13827e57i	0.853033	+	0.353338i	0.0870542	+	0.996204i	$0.472255\pi$
$488$	−2.92778e57	−	7.06827e57i	−0.462926	−	1.11760i
$489$		−	1.71748e58i		−	2.59867i
$490$	3.76700e56	−	1.56034e56i	0.0545482	−	0.0225946i
$491$	3.48463e57	+	3.48463e57i	0.482952	+	0.482952i	0.906073	−	0.423121i	$-0.139066\pi$
$491$	3.48463e57	+	3.48463e57i	0.482952	+	0.482952i	−0.423121	+	0.906073i	$0.639066\pi$
$492$	−2.10337e58			−2.79039
$493$	−1.53193e57	−	2.66867e57i	−0.194550	−	0.338911i
$494$	−1.39048e58			−1.69057
$495$	6.85828e56	+	6.85828e56i	0.0798368	+	0.0798368i
$496$	−1.48477e58	+	6.15014e57i	−1.65502	+	0.685533i
$497$		−	3.88732e57i		−	0.414943i
$498$	2.22100e57	+	5.36197e57i	0.227048	+	0.548142i
$499$	7.93509e57	+	3.28682e57i	0.776944	+	0.321821i	0.735682	−	0.677327i	$-0.236862\pi$
$499$	7.93509e57	+	3.28682e57i	0.776944	+	0.321821i	0.0412627	+	0.999148i	$0.486862\pi$
$500$	2.43986e57	−	5.89034e57i	0.228828	−	0.552440i
$501$	1.94148e58	−	1.94148e58i	1.74430	−	1.74430i
$502$	−2.91100e58	+	2.91100e58i	−2.50560	+	2.50560i
$503$	1.25308e57	−	3.02520e57i	0.103340	−	0.249484i	−0.863750	−	0.503921i	$-0.831890\pi$
$503$	1.25308e57	−	3.02520e57i	0.103340	−	0.249484i	0.967089	+	0.254437i	$0.0818902\pi$
$504$	3.50572e58	+	1.45212e58i	2.77026	+	1.14748i
$505$	−8.58914e56	−	2.07360e57i	−0.0650406	−	0.157022i
$506$		−	1.73753e58i		−	1.26094i
$507$	2.71355e57	−	1.12399e57i	0.188742	−	0.0781793i
$508$	2.30185e58	+	2.30185e58i	1.53464	+	1.53464i
$509$	−2.32121e58			−1.48348			−0.741741	−	0.670686i	$-0.766000\pi$
$509$	−2.32121e58			−1.48348			−0.741741	+	0.670686i	$0.766000\pi$
$510$	−7.29672e56	−	5.65083e57i	−0.0447063	−	0.346221i
$511$	−4.48903e57			−0.263696
$512$	2.77700e58	+	2.77700e58i	1.56413	+	1.56413i
$513$	−3.56793e57	+	1.47788e57i	−0.192705	+	0.0798210i
$514$			4.67734e58i			2.42266i
$515$	−1.53265e57	−	3.70015e57i	−0.0761356	−	0.183808i
$516$	−1.96544e58	−	8.14110e57i	−0.936462	−	0.387895i
$517$	−6.76942e57	+	1.63428e58i	−0.309389	+	0.746931i
$518$	1.38644e58	−	1.38644e58i	0.607872	−	0.607872i
$519$	−1.50684e57	+	1.50684e57i	−0.0633822	+	0.0633822i
$520$	2.71709e57	−	6.55965e57i	0.109656	−	0.264733i
$521$	2.80051e57	+	1.16001e57i	0.108449	+	0.0449212i	0.436248	−	0.899826i	$-0.356307\pi$
$521$	2.80051e57	+	1.16001e57i	0.108449	+	0.0449212i	−0.327799	+	0.944747i	$0.606307\pi$
$522$	−8.34199e57	−	2.01393e58i	−0.309994	−	0.748392i
$523$		−	2.31265e58i		−	0.824752i	−0.911014	−	0.412376i	$-0.864699\pi$
$523$		−	2.31265e58i		−	0.824752i	0.911014	−	0.412376i	$-0.135301\pi$
$524$	7.71236e58	−	3.19456e58i	2.63976	−	1.09342i
$525$	3.45760e58	+	3.45760e58i	1.13593	+	1.13593i
$526$	−5.28065e58			−1.66530
$527$	−2.60186e58	+	1.49358e58i	−0.787692	+	0.452169i
$528$	7.47282e58			2.17198
$529$	−3.74264e57	−	3.74264e57i	−0.104443	−	0.104443i
$530$	−7.96237e57	+	3.29812e57i	−0.213359	+	0.0883762i
$531$			8.42449e58i			2.16776i
$532$	3.98577e58	+	9.62250e58i	0.984945	+	2.37787i
$533$	−2.99961e58	−	1.24248e58i	−0.711917	−	0.294886i
$534$	4.25060e58	−	1.02619e59i	0.968976	−	2.33932i
$535$	−5.38795e57	+	5.38795e57i	−0.117982	+	0.117982i
$536$	−1.06339e59	+	1.06339e59i	−2.23692	+	2.23692i
$537$	3.29312e58	−	7.95029e58i	0.665518	−	1.60670i
$538$	−8.63880e57	−	3.57831e57i	−0.167739	−	0.0694799i
$539$	3.82023e57	+	9.22286e57i	0.0712741	+	0.172071i
$540$		−	3.49463e57i		−	0.0626521i
$541$	−6.00203e57	+	2.48612e57i	−0.103409	+	0.0428333i	−0.433788	−	0.901015i	$-0.642823\pi$
$541$	−6.00203e57	+	2.48612e57i	−0.103409	+	0.0428333i	0.330379	+	0.943848i	$0.392823\pi$
$542$	−1.16819e59	−	1.16819e59i	−1.93432	−	1.93432i
$543$	−7.39320e58			−1.17662
$544$	−6.36359e58	−	4.90811e58i	−0.973478	−	0.750824i
$545$	−3.66058e57			−0.0538301
$546$	1.37671e59	+	1.37671e59i	1.94626	+	1.94626i
$547$	−1.48954e58	+	6.16989e57i	−0.202454	+	0.0838591i	−0.481606	−	0.876388i	$-0.659946\pi$
$547$	−1.48954e58	+	6.16989e57i	−0.202454	+	0.0838591i	0.279153	+	0.960247i	$0.409946\pi$
$548$		−	3.13315e59i		−	4.09448i
$549$	−1.78949e58	−	4.32021e58i	−0.224866	−	0.542874i
$550$	1.02624e59	+	4.25083e58i	1.24008	+	0.513660i
$551$	1.29205e58	−	3.11930e58i	0.150149	−	0.362491i
$552$	−2.00959e59	+	2.00959e59i	−2.24604	+	2.24604i
$553$	−1.17790e59	+	1.17790e59i	−1.26625	+	1.26625i
$554$	−3.42918e57	+	8.27878e57i	−0.0354593	+	0.0856064i
$555$	−7.57344e57	−	3.13702e57i	−0.0753345	−	0.0312046i
$556$	3.58569e58	+	8.65662e58i	0.343135	+	0.828400i
$557$			1.16165e59i			1.06952i	0.845004	+	0.534759i	$0.179598\pi$
$557$			1.16165e59i			1.06952i	−0.845004	+	0.534759i	$0.820402\pi$
$558$	−1.96352e59	+	8.13316e58i	−1.73940	+	0.720484i
$559$	−2.32200e58	−	2.32200e58i	−0.197929	−	0.197929i
$560$	−3.52905e58			−0.289478
$561$	1.38351e59	−	1.78648e58i	1.09214	−	0.141025i
$562$	4.35135e59			3.30593
$563$	5.95185e57	+	5.95185e57i	0.0435233	+	0.0435233i	0.728533	−	0.685010i	$-0.240202\pi$
$563$	5.95185e57	+	5.95185e57i	0.0435233	+	0.0435233i	−0.685010	+	0.728533i	$0.740202\pi$
$564$	4.73717e59	−	1.96220e59i	3.33441	−	1.38116i
$565$			1.28518e58i			0.0870805i
$566$	−1.01411e58	−	2.44828e58i	−0.0661504	−	0.159701i
$567$	−1.37680e59	−	5.70289e58i	−0.864639	−	0.358145i
$568$	−5.52746e58	+	1.33445e59i	−0.334223	+	0.806886i
$569$	−1.26791e59	+	1.26791e59i	−0.738203	+	0.738203i	−0.972230	−	0.234027i	$-0.924810\pi$
$569$	−1.26791e59	+	1.26791e59i	−0.738203	+	0.738203i	0.234027	+	0.972230i	$0.424810\pi$
$570$	4.42065e58	−	4.42065e58i	0.247843	−	0.247843i
$571$	−6.57556e57	+	1.58748e58i	−0.0355023	+	0.0857102i	−0.940636	−	0.339416i	$-0.889770\pi$
$571$	−6.57556e57	+	1.58748e58i	−0.0355023	+	0.0857102i	0.905134	+	0.425127i	$0.139770\pi$
$572$	2.84610e59	+	1.17889e59i	1.47991	+	0.612998i
$573$	−2.56778e58	−	6.19918e58i	−0.128598	−	0.310463i
$574$			3.49161e59i			1.68430i
$575$	−1.80387e59	+	7.47186e58i	−0.838197	+	0.347192i
$576$	−4.67721e58	−	4.67721e58i	−0.209365	−	0.209365i
$577$	1.90116e59			0.819858			0.409929	−	0.912117i	$-0.365553\pi$
$577$	1.90116e59			0.819858			0.409929	+	0.912117i	$0.365553\pi$
$578$	−3.77277e59	−	2.20327e59i	−1.56751	−	0.915417i
$579$	3.49010e59			1.39717
$580$	2.16036e58	+	2.16036e58i	0.0833346	+	0.0833346i
$581$	6.19966e58	−	2.56798e58i	0.230452	−	0.0954564i
$582$		−	6.97050e59i		−	2.49701i
$583$	−8.07488e58	−	1.94945e59i	−0.278780	−	0.673036i
$584$	1.54100e59	+	6.38304e58i	0.512775	+	0.212399i
$585$	1.66072e58	−	4.00933e58i	0.0532653	−	0.128594i
$586$	1.74800e59	−	1.74800e59i	0.540434	−	0.540434i
$587$	1.96157e59	−	1.96157e59i	0.584636	−	0.584636i	−0.351538	−	0.936174i	$-0.614341\pi$
$587$	1.96157e59	−	1.96157e59i	0.584636	−	0.584636i	0.936174	+	0.351538i	$0.114341\pi$
$588$	1.10734e59	−	2.67336e59i	0.318177	−	0.768148i
$589$	−3.04121e59	−	1.25971e59i	−0.842495	−	0.348973i
$590$	−6.48728e58	−	1.56617e59i	−0.173279	−	0.418331i
$591$			3.15655e59i			0.812983i
$592$	−3.11089e59	+	1.28857e59i	−0.772623	+	0.320031i
$593$	3.36549e59	+	3.36549e59i	0.806070	+	0.806070i	0.984037	−	0.177966i	$-0.0569518\pi$
$593$	3.36549e59	+	3.36549e59i	0.806070	+	0.806070i	−0.177966	+	0.984037i	$0.556952\pi$
$594$	1.22840e59			0.283746
$595$	−6.53364e58	+	8.43667e57i	−0.145559	+	0.0187956i
$596$	1.84797e60			3.97100
$597$	6.56932e58	+	6.56932e58i	0.136167	+	0.136167i
$598$	−7.18245e59	+	2.97507e59i	−1.43614	+	0.594869i
$599$			5.64642e59i			1.08917i	0.838705	+	0.544586i	$0.183313\pi$
$599$			5.64642e59i			1.08917i	−0.838705	+	0.544586i	$0.816687\pi$
$600$	−6.95289e59	−	1.67858e60i	−1.29394	−	3.12384i
$601$	2.32868e59	+	9.64570e58i	0.418127	+	0.173194i	0.581820	−	0.813317i	$-0.302341\pi$
$601$	2.32868e59	+	9.64570e58i	0.418127	+	0.173194i	−0.163693	+	0.986511i	$0.552341\pi$
$602$	−1.35143e59	+	3.26264e59i	−0.234137	+	0.565256i
$603$	−6.49957e59	+	6.49957e59i	−1.08658	+	1.08658i
$604$	−1.20814e60	+	1.20814e60i	−1.94905	+	1.94905i
$605$	−1.40128e58	+	3.38298e58i	−0.0218164	+	0.0526695i
$606$	−2.11278e60	−	8.75142e59i	−3.17463	−	1.31497i
$607$	2.03778e59	+	4.91962e59i	0.295529	+	0.713469i	0.999993	+	0.00372975i	$0.00118722\pi$
$607$	2.03778e59	+	4.91962e59i	0.295529	+	0.713469i	−0.704465	+	0.709739i	$0.748813\pi$
$608$		−	8.81786e59i		−	1.23434i
$609$	−4.36768e59	+	1.80915e59i	−0.590173	+	0.244458i
$610$	6.65356e58	+	6.65356e58i	0.0867886	+	0.0867886i
$611$	7.91477e59			0.996672
$612$	−1.70702e60	−	1.31659e60i	−2.07531	−	1.60064i
$613$	−3.36693e59			−0.395215			−0.197608	−	0.980281i	$-0.563317\pi$
$613$	−3.36693e59			−0.395215			−0.197608	+	0.980281i	$0.563317\pi$
$614$	5.15917e59	+	5.15917e59i	0.584736	+	0.584736i
$615$	1.34866e59	−	5.58632e58i	0.147600	−	0.0611380i
$616$		−	1.86944e60i		−	1.97572i
$617$	7.19900e59	+	1.73799e60i	0.734752	+	1.77385i	0.626061	+	0.779774i	$0.284666\pi$
$617$	7.19900e59	+	1.73799e60i	0.734752	+	1.77385i	0.108691	+	0.994076i	$0.465334\pi$
$618$	−3.77006e60	−	1.56161e60i	−3.71617	−	1.53929i
$619$	−6.71807e59	+	1.62188e60i	−0.639581	+	1.54408i	0.187658	+	0.982234i	$0.439910\pi$
$619$	−6.71807e59	+	1.62188e60i	−0.639581	+	1.54408i	−0.827239	+	0.561850i	$0.810090\pi$
$620$	2.10628e59	−	2.10628e59i	0.193685	−	0.193685i
$621$	−1.52679e59	+	1.52679e59i	−0.135616	+	0.135616i
$622$	1.48048e60	−	3.57418e60i	1.27031	−	3.06679i
$623$	−1.18650e60	−	4.91466e59i	−0.983504	−	0.407381i
$624$	−1.27953e60	−	3.08906e60i	−1.02466	−	2.47376i
$625$		−	1.22590e60i		−	0.948498i
$626$	−3.79656e60	+	1.57258e60i	−2.83819	+	1.17562i
$627$	1.08232e60	+	1.08232e60i	0.781814	+	0.781814i
$628$	4.34315e60			3.03161
$629$	−5.45141e59	+	3.12935e59i	−0.367722	+	0.211089i
$630$	−4.66694e59			−0.304236
$631$	−1.01874e60	−	1.01874e60i	−0.641847	−	0.641847i	0.309162	−	0.951009i	$-0.399951\pi$
$631$	−1.01874e60	−	1.01874e60i	−0.641847	−	0.641847i	−0.951009	+	0.309162i	$0.899951\pi$
$632$	5.71839e60	−	2.36864e60i	3.48222	−	1.44238i
$633$		−	1.21772e59i		−	0.0716751i
$634$	1.56558e60	+	3.77964e60i	0.890751	+	2.15046i
$635$	−2.08727e59	−	8.64576e58i	−0.114801	−	0.0475519i
$636$	−2.34060e60	+	5.65072e60i	−1.24451	+	3.00452i
$637$	3.15836e59	−	3.15836e59i	0.162354	−	0.162354i
$638$	−7.59389e59	+	7.59389e59i	−0.377415	+	0.377415i
$639$	−3.37845e59	+	8.15629e59i	−0.162349	+	0.391944i
$640$	−1.98234e59	−	8.21111e58i	−0.0921103	−	0.0381533i
$641$	−1.17607e60	−	2.83929e60i	−0.528428	−	1.27574i	−0.932553	−	0.361034i	$-0.882424\pi$
$641$	−1.17607e60	−	2.83929e60i	−0.528428	−	1.27574i	0.404125	−	0.914704i	$-0.367576\pi$
$642$			7.76367e60i			3.37337i
$643$	2.86002e60	−	1.18466e60i	1.20180	−	0.497804i	0.310223	−	0.950664i	$-0.399596\pi$
$643$	2.86002e60	−	1.18466e60i	1.20180	−	0.497804i	0.891581	+	0.452860i	$0.149596\pi$
$644$	4.11767e60	+	4.11767e60i	1.67342	+	1.67342i
$645$	1.47644e59			0.0580338
$646$	−6.13910e59	−	4.75433e60i	−0.233403	−	1.80755i
$647$	3.42352e60			1.25902			0.629508	−	0.776994i	$-0.283257\pi$
$647$	3.42352e60			1.25902			0.629508	+	0.776994i	$0.283257\pi$
$648$	3.91540e60	+	3.91540e60i	1.39288	+	1.39288i
$649$	3.83450e60	−	1.58830e60i	1.31961	−	0.546602i
$650$		−	4.97004e60i		−	1.65471i
$651$	1.76387e60	+	4.25835e60i	0.568165	+	1.37167i
$652$	1.20805e61	+	5.00390e60i	3.76497	+	1.55950i
$653$	−1.05484e60	+	2.54662e60i	−0.318093	+	0.767945i	0.681262	+	0.732040i	$0.261431\pi$
$653$	−1.05484e60	+	2.54662e60i	−0.318093	+	0.767945i	−0.999355	+	0.0359053i	$0.988569\pi$
$654$	−2.63733e60	+	2.63733e60i	−0.769560	+	0.769560i
$655$	−4.09665e59	+	4.09665e59i	−0.115675	+	0.115675i
$656$	2.29465e60	−	5.53979e60i	0.627025	−	1.51377i
$657$	9.41878e59	+	3.90139e59i	0.249080	+	0.103172i
$658$	−3.25727e60	−	7.86375e60i	−0.833676	−	2.01267i
$659$		−	2.35514e60i		−	0.583419i	−0.956507	−	0.291710i	$-0.905776\pi$
$659$		−	2.35514e60i		−	0.583419i	0.956507	−	0.291710i	$-0.0942241\pi$
$660$	−1.27964e60	+	5.30043e59i	−0.306826	+	0.127091i
$661$	3.01292e60	+	3.01292e60i	0.699287	+	0.699287i	0.964257	−	0.264970i	$-0.0853619\pi$
$661$	3.01292e60	+	3.01292e60i	0.699287	+	0.699287i	−0.264970	+	0.964257i	$0.585362\pi$
$662$	−1.33334e61			−2.99566
$663$	−3.10738e60	−	5.41315e60i	−0.675856	−	1.17736i
$664$	−2.49338e60			−0.525018
$665$	−5.11127e59	−	5.11127e59i	−0.104199	−	0.104199i
$666$	−4.11395e60	+	1.70405e60i	−0.812014	+	0.336347i
$667$		−	1.88771e60i		−	0.360769i
$668$	7.99956e60	+	1.93127e61i	1.48038	+	3.57395i
$669$	2.15637e60	+	8.93196e59i	0.386421	+	0.160061i
$670$	7.07814e59	−	1.70881e60i	0.122832	−	0.296542i
$671$	−1.62901e60	+	1.62901e60i	−0.273772	+	0.273772i
$672$	−8.73058e60	+	8.73058e60i	−1.42103	+	1.42103i
$673$	3.52074e60	−	8.49982e60i	0.555022	−	1.33994i	−0.358643	−	0.933475i	$-0.616760\pi$
$673$	3.52074e60	−	8.49982e60i	0.555022	−	1.33994i	0.913665	−	0.406467i	$-0.133240\pi$
$674$	−2.67257e60	−	1.10702e60i	−0.408077	−	0.169031i
$675$	−5.28246e59	−	1.27530e60i	−0.0781278	−	0.188617i
$676$			2.23615e60i			0.320367i
$677$	−5.85914e59	+	2.42694e59i	−0.0813163	+	0.0336823i	−0.422971	−	0.906143i	$-0.639013\pi$
$677$	−5.85914e59	+	2.42694e59i	−0.0813163	+	0.0336823i	0.341655	+	0.939826i	$0.389013\pi$
$678$	9.25926e60	+	9.25926e60i	1.24491	+	1.24491i
$679$	−8.05948e60			−1.04980
$680$	2.36284e60	+	6.39416e59i	0.298190	+	0.0806941i
$681$	−3.84203e60			−0.469783
$682$	7.40379e60	+	7.40379e60i	0.877183	+	0.877183i
$683$	1.06536e61	−	4.41288e60i	1.22307	−	0.506614i	0.324688	−	0.945821i	$-0.394741\pi$
$683$	1.06536e61	−	4.41288e60i	1.22307	−	0.506614i	0.898386	+	0.439207i	$0.144741\pi$
$684$		−	2.36537e61i		−	2.63144i
$685$	8.32131e59	+	2.00894e60i	0.0897108	+	0.216581i
$686$	1.34906e61	+	5.58801e60i	1.40950	+	0.583833i
$687$	7.24136e60	−	1.74822e61i	0.733247	−	1.77021i
$688$	4.28836e60	−	4.28836e60i	0.420862	−	0.420862i
$689$	−6.67587e60	+	6.67587e60i	−0.635030	+	0.635030i
$690$	1.33762e60	−	3.22931e60i	0.123333	−	0.297752i
$691$	−1.57957e61	−	6.54281e60i	−1.41176	−	0.584772i	−0.458987	−	0.888443i	$-0.651788\pi$
$691$	−1.57957e61	−	6.54281e60i	−1.41176	−	0.584772i	−0.952777	+	0.303671i	$0.901788\pi$
$692$	−6.20867e59	−	1.49891e60i	−0.0537920	−	0.129865i
$693$		−	1.14262e61i		−	0.959705i
$694$	−7.90538e60	+	3.27452e60i	−0.643716	+	0.266636i
$695$	−4.59822e59	−	4.59822e59i	−0.0363008	−	0.0363008i
$696$	1.75659e61			1.34454
$697$	2.92393e60	−	1.08049e61i	0.217002	−	0.801889i
$698$	3.50779e60			0.252431
$699$	1.20802e61	+	1.20802e61i	0.842974	+	0.842974i
$700$	−3.43941e61	+	1.42465e61i	−2.32743	+	0.964052i
$701$			1.34617e61i			0.883410i	0.897160	+	0.441705i	$0.145626\pi$
$701$			1.34617e61i			0.883410i	−0.897160	+	0.441705i	$0.854374\pi$
$702$	−2.10332e60	−	5.07785e60i	−0.133862	−	0.323171i
$703$	−6.37192e60	−	2.63934e60i	−0.393306	−	0.162913i
$704$	−1.24707e60	+	3.01070e60i	−0.0746585	+	0.180241i
$705$	−2.51629e60	+	2.51629e60i	−0.146115	+	0.146115i
$706$	6.70410e60	−	6.70410e60i	0.377606	−	0.377606i
$707$	−1.01186e61	+	2.44285e61i	−0.552846	+	1.33469i
$708$	−1.11148e62	−	4.60388e61i	−5.89094	−	2.44011i
$709$	−7.35479e60	−	1.77560e61i	−0.378160	−	0.912960i	−0.992311	−	0.123771i	$-0.960501\pi$
$709$	−7.35479e60	−	1.77560e61i	−0.378160	−	0.912960i	0.614150	−	0.789189i	$-0.289499\pi$
$710$		−	1.77647e60i		−	0.0886141i
$711$	3.49514e61	−	1.44774e61i	1.69149	−	0.700637i
$712$	3.37423e61	+	3.37423e61i	1.58436	+	1.58436i
$713$	−1.84045e61			−0.838494
$714$	−4.09944e61	+	5.31510e61i	−1.81223	+	2.34963i
$715$	−2.13799e60			−0.0917119
$716$	4.63266e61	+	4.63266e61i	1.92842	+	1.92842i
$717$	−1.68620e61	+	6.98449e60i	−0.681159	+	0.282145i
$718$		−	6.51965e61i		−	2.55593i
$719$	−1.53858e61	−	3.71447e61i	−0.585396	−	1.41327i	−0.887861	−	0.460111i	$-0.847810\pi$
$719$	−1.53858e61	−	3.71447e61i	−0.585396	−	1.41327i	0.302465	−	0.953160i	$-0.402190\pi$
$720$	7.40457e60	+	3.06707e60i	0.273433	+	0.113260i
$721$	−1.80557e61	+	4.35904e61i	−0.647153	+	1.56237i
$722$	2.98087e59	−	2.98087e59i	0.0103703	−	0.0103703i
$723$	−1.58551e61	+	1.58551e61i	−0.535421	+	0.535421i
$724$	2.15402e61	−	5.20027e61i	0.706108	−	1.70470i
$725$	1.11494e61	+	4.61824e60i	0.354801	+	0.146964i
$726$	1.42775e61	+	3.44690e61i	0.441078	+	1.06486i
$727$			1.26739e61i			0.380120i	0.981773	+	0.190060i	$0.0608682\pi$
$727$			1.26739e61i			0.380120i	−0.981773	+	0.190060i	$0.939132\pi$
$728$	−7.72774e61	+	3.20093e61i	−2.25023	+	0.932078i
$729$	3.15357e61	+	3.15357e61i	0.891580	+	0.891580i
$730$	−2.05144e60			−0.0563142
$731$	6.91423e60	−	8.96461e60i	0.184298	−	0.238950i
$732$	6.67775e61			1.72839
$733$	−4.76414e61	−	4.76414e61i	−1.19743	−	1.19743i	−0.974935	−	0.222491i	$-0.928581\pi$
$733$	−4.76414e61	−	4.76414e61i	−1.19743	−	1.19743i	−0.222491	−	0.974935i	$-0.571419\pi$
$734$	4.52446e61	−	1.87409e61i	1.10434	−	0.457431i
$735$			2.00823e60i			0.0476032i
$736$	−1.88667e61	−	4.55483e61i	−0.434334	−	1.04857i
$737$	4.18374e61	+	1.73296e61i	0.935435	+	0.387470i
$738$	3.03453e61	−	7.32601e61i	0.658992	−	1.59095i
$739$	5.50064e61	−	5.50064e61i	1.16027	−	1.16027i	0.175849	−	0.984417i	$-0.443733\pi$
$739$	5.50064e61	−	5.50064e61i	1.16027	−	1.16027i	0.984417	−	0.175849i	$-0.0562671\pi$
$740$	4.41307e60	−	4.41307e60i	0.0904189	−	0.0904189i
$741$	2.62081e61	−	6.32720e61i	0.521608	−	1.25927i
$742$	9.38025e61	+	3.88543e61i	1.81355	+	0.751199i
$743$	−2.10441e61	−	5.08051e61i	−0.395250	−	0.954218i	−0.988776	−	0.149403i	$-0.952265\pi$
$743$	−2.10441e61	−	5.08051e61i	−0.395250	−	0.954218i	0.593527	−	0.804814i	$-0.297735\pi$
$744$		−	1.71262e62i		−	3.12495i
$745$	−1.18490e61	+	4.90801e60i	−0.210049	+	0.0870053i
$746$	−6.60237e61	−	6.60237e61i	−1.13714	−	1.13714i
$747$	−1.52398e61			−0.255027
$748$	−2.77430e61	+	1.02519e62i	−0.451095	+	1.66694i
$749$	8.97657e61			1.41824
$750$	3.18794e61	+	3.18794e61i	0.489433	+	0.489433i
$751$	6.93838e61	−	2.87397e61i	1.03514	−	0.428770i	0.200576	−	0.979678i	$-0.435719\pi$
$751$	6.93838e61	−	2.87397e61i	1.03514	−	0.428770i	0.834566	+	0.550909i	$0.185719\pi$
$752$			1.46173e62i			2.11925i
$753$	−7.75942e61	−	1.87329e62i	−1.09330	−	2.63945i
$754$	4.43936e61	+	1.83884e61i	0.607906	+	0.251803i
$755$	4.53777e60	−	1.09551e61i	0.0603925	−	0.145800i
$756$	−2.91111e61	+	2.91111e61i	−0.376565	+	0.376565i
$757$	−9.62714e61	+	9.62714e61i	−1.21042	+	1.21042i	−0.239530	+	0.970889i	$0.576993\pi$
$757$	−9.62714e61	+	9.62714e61i	−1.21042	+	1.21042i	−0.970889	+	0.239530i	$0.923007\pi$
$758$	2.50574e61	−	6.04939e61i	0.306230	−	0.739305i
$759$	7.90641e61	+	3.27494e61i	0.939250	+	0.389050i
$760$	1.02782e61	+	2.48139e61i	0.118693	+	0.286551i
$761$			1.50709e62i			1.69188i	0.533276	+	0.845941i	$0.320961\pi$
$761$			1.50709e62i			1.69188i	−0.533276	+	0.845941i	$0.679039\pi$
$762$	−2.12671e62	+	8.80911e61i	−2.32100	+	0.961391i
$763$	3.04935e61	+	3.04935e61i	0.323541	+	0.323541i
$764$	5.10855e61			0.526975
$765$	1.44420e61	+	3.90818e60i	0.144846	+	0.0391971i
$766$	2.33747e60			0.0227943
$767$	−1.31312e62	−	1.31312e62i	−1.24510	−	1.24510i
$768$	−2.40003e62	+	9.94126e61i	−2.21284	+	0.916590i
$769$		−	5.33677e61i		−	0.478479i	−0.970961	−	0.239239i	$-0.923102\pi$
$769$		−	5.33677e61i		−	0.478479i	0.970961	−	0.239239i	$-0.0768980\pi$
$770$	8.79876e60	+	2.12421e61i	0.0767134	+	0.185202i
$771$	−2.12837e62	−	8.81600e61i	−1.80459	−	0.747485i
$772$	−1.01685e62	+	2.45489e62i	−0.838462	+	2.02423i
$773$	1.23329e62	−	1.23329e62i	0.989023	−	0.989023i	−0.0109176	−	0.999940i	$-0.503475\pi$
$773$	1.23329e62	−	1.23329e62i	0.989023	−	0.989023i	0.999940	+	0.0109176i	$0.00347523\pi$
$774$	5.67108e61	−	5.67108e61i	0.442319	−	0.442319i
$775$	4.50264e61	−	1.08703e62i	0.341570	−	0.824624i
$776$	2.76667e62	+	1.14599e62i	2.04141	+	0.845581i
$777$	3.69564e61	+	8.92206e61i	0.265239	+	0.640344i
$778$			1.79423e62i			1.25261i
$779$	1.13469e62	−	4.70006e61i	0.770591	−	0.319189i
$780$	4.38210e61	+	4.38210e61i	0.289500	+	0.289500i
$781$	4.34938e61			0.279531
$782$	−1.33435e62	−	2.32448e62i	−0.834305	−	1.45338i
$783$	1.33457e61			0.0811829
$784$	5.83297e61	+	5.83297e61i	0.345219	+	0.345219i
$785$	−2.78479e61	+	1.15350e61i	−0.160359	+	0.0664230i
$786$			5.90299e62i			3.30741i
$787$	2.01425e61	+	4.86282e61i	0.109814	+	0.265113i	0.969227	−	0.246167i	$-0.0791713\pi$
$787$	2.01425e61	+	4.86282e61i	0.109814	+	0.265113i	−0.859414	+	0.511281i	$0.829171\pi$
$788$	−2.22027e62	−	9.19666e61i	−1.17786	−	0.487884i
$789$	9.95313e61	−	2.40290e62i	0.513812	−	1.24045i
$790$	−5.38288e61	+	5.38288e61i	−0.270416	+	0.270416i
$791$	1.07058e62	−	1.07058e62i	0.523389	−	0.523389i
$792$	−1.62472e62	+	3.92241e62i	−0.773011	+	1.86621i
$793$	9.52314e61	+	3.94461e61i	0.440968	+	0.182655i
$794$	1.79338e62	+	4.32961e62i	0.808225	+	1.95123i
$795$		−	4.24482e61i		−	0.186194i
$796$	−6.53475e61	+	2.70678e61i	−0.278996	+	0.115564i
$797$	9.23383e61	+	9.23383e61i	0.383732	+	0.383732i	0.872445	−	0.488713i	$-0.162533\pi$
$797$	9.23383e61	+	9.23383e61i	0.383732	+	0.383732i	−0.488713	+	0.872445i	$0.662533\pi$
$798$	−7.36500e62			−2.97928
$799$	3.49445e61	+	2.70622e62i	0.137602	+	1.06563i
$800$	3.15181e62			1.20816
$801$	2.06236e62	+	2.06236e62i	0.769602	+	0.769602i
$802$	−7.12389e62	+	2.95081e62i	−2.58802	+	1.07199i
$803$		−	5.02260e61i		−	0.177641i
$804$	−5.02320e62	−	1.21271e63i	−1.72972	−	4.17591i
$805$	−3.73382e61	−	1.54660e61i	−0.125182	−	0.0518520i
$806$	1.79281e62	−	4.32823e62i	0.585237	−	1.41289i
$807$	3.25654e61	−	3.25654e61i	0.103508	−	0.103508i
$808$	6.94708e62	−	6.94708e62i	2.15010	−	2.15010i
$809$	1.08067e61	−	2.60897e61i	0.0325687	−	0.0786277i	−0.906758	−	0.421651i	$-0.861451\pi$
$809$	1.08067e61	−	2.60897e61i	0.0325687	−	0.0786277i	0.939327	+	0.343023i	$0.111451\pi$
$810$	−6.29183e61	−	2.60616e61i	−0.184650	−	0.0764846i
$811$	2.23066e62	+	5.38529e62i	0.637507	+	1.53908i	0.829991	+	0.557778i	$0.188346\pi$
$811$	2.23066e62	+	5.38529e62i	0.637507	+	1.53908i	−0.192484	+	0.981300i	$0.561654\pi$
$812$		−	3.59927e62i		−	1.00175i
$813$	7.51754e62	−	3.11387e62i	2.03765	−	0.844021i
$814$	1.55124e62	+	1.55124e62i	0.409500	+	0.409500i
$815$	−9.07487e61			−0.233320
$816$	9.99720e62	−	5.73883e62i	2.50346	−	1.43709i
$817$	1.24220e62			0.302983
$818$	−6.35166e62	−	6.35166e62i	−1.50901	−	1.50901i
$819$	−4.72328e62	+	1.95645e62i	−1.09305	+	0.452756i
$820$			1.11139e62i			0.250534i
$821$	−3.71946e61	−	8.97957e61i	−0.0816774	−	0.197187i	0.877765	−	0.479091i	$-0.159034\pi$
$821$	−3.71946e61	−	8.97957e61i	−0.0816774	−	0.197187i	−0.959442	+	0.281905i	$0.909034\pi$
$822$	2.04690e63	+	8.47853e62i	4.37877	+	1.81375i
$823$	−2.00467e62	+	4.83971e62i	−0.417780	+	1.00861i	0.565210	+	0.824947i	$0.308795\pi$
$823$	−2.00467e62	+	4.83971e62i	−0.417780	+	1.00861i	−0.982989	+	0.183662i	$0.941205\pi$
$824$	1.23964e63	−	1.23964e63i	2.51687	−	2.51687i
$825$	−3.86858e62	+	3.86858e62i	−0.765229	+	0.765229i
$826$	−7.64249e62	+	1.84506e63i	−1.47287	+	3.55582i
$827$	1.90243e62	+	7.88013e61i	0.357224	+	0.147967i	0.554076	−	0.832466i	$-0.313072\pi$
$827$	1.90243e62	+	7.88013e61i	0.357224	+	0.147967i	−0.196852	+	0.980433i	$0.563072\pi$
$828$	−5.06096e62	−	1.22182e63i	−0.925935	−	2.23540i
$829$		−	1.98563e62i		−	0.353978i	−0.984213	−	0.176989i	$-0.943364\pi$
$829$		−	1.98563e62i		−	0.353978i	0.984213	−	0.176989i	$-0.0566358\pi$
$830$	2.83318e61	−	1.17354e61i	0.0492147	−	0.0203854i
$831$	−3.12082e61	−	3.12082e61i	−0.0528259	−	0.0528259i
$832$	1.45807e62			0.240506
$833$	1.21935e62	+	9.40464e61i	0.196003	+	0.151173i
$834$	−6.62572e62			−1.03792
$835$	−1.02585e62	−	1.02585e62i	−0.156612	−	0.156612i
$836$	−1.07662e63	+	4.45952e62i	−1.60188	+	0.663519i
$837$		−	1.30116e62i		−	0.188684i
$838$	8.30475e62	+	2.00494e63i	1.17376	+	2.83371i
$839$	4.01015e62	+	1.66106e62i	0.552431	+	0.228825i	0.641396	−	0.767210i	$-0.278356\pi$
$839$	4.01015e62	+	1.66106e62i	0.552431	+	0.228825i	−0.0889644	+	0.996035i	$0.528356\pi$
$840$	1.43918e62	−	3.47448e62i	0.193245	−	0.466536i
$841$	4.57753e62	−	4.57753e62i	0.599124	−	0.599124i
$842$	−3.14462e62	+	3.14462e62i	−0.401198	+	0.401198i
$843$	−8.20156e62	+	1.98003e63i	−1.02001	+	2.46252i
$844$	8.56529e61	+	3.54786e61i	0.103843	+	0.0430134i
$845$	−5.93899e60	−	1.43380e61i	−0.00701929	−	0.0169461i
$846$			1.93304e63i			2.22730i
$847$	3.98540e62	−	1.65081e62i	0.447691	−	0.185440i
$848$	−1.23292e63	−	1.23292e63i	−1.35028	−	1.35028i
$849$	1.30520e62			0.139368
$850$	1.69936e63	−	2.19433e62i	1.76921	−	0.228452i
$851$	−3.85610e62			−0.391438
$852$	−8.91464e62	−	8.91464e62i	−0.882373	−	0.882373i
$853$	5.16798e62	−	2.14065e62i	0.498789	−	0.206605i	−0.119083	−	0.992884i	$-0.537995\pi$
$853$	5.16798e62	−	2.14065e62i	0.498789	−	0.206605i	0.617871	+	0.786279i	$0.287995\pi$
$854$		−	1.10851e63i		−	1.04327i
$855$	6.28218e61	+	1.51665e62i	0.0576553	+	0.139192i
$856$	−3.08149e63	−	1.27640e63i	−2.75788	−	1.14235i
$857$	5.47359e62	−	1.32144e63i	0.477732	−	1.15335i	−0.482937	−	0.875655i	$-0.660430\pi$
$857$	5.47359e62	−	1.32144e63i	0.477732	−	1.15335i	0.960670	−	0.277693i	$-0.0895699\pi$
$858$	−1.54035e63	+	1.54035e63i	−1.31112	+	1.31112i
$859$	2.86003e62	−	2.86003e62i	0.237420	−	0.237420i	−0.578361	−	0.815781i	$-0.696307\pi$
$859$	2.86003e62	−	2.86003e62i	0.237420	−	0.237420i	0.815781	+	0.578361i	$0.196307\pi$
$860$	−4.30163e61	+	1.03851e62i	−0.0348270	+	0.0840799i
$861$	−1.58882e63	−	6.58109e62i	−1.25460	−	0.519673i
$862$	−1.26801e63	−	3.06124e63i	−0.976598	−	2.35772i
$863$			9.93473e62i			0.746318i	0.927767	+	0.373159i	$0.121725\pi$
$863$			9.93473e62i			0.746318i	−0.927767	+	0.373159i	$0.878275\pi$
$864$	3.22018e62	−	1.33384e62i	0.235958	−	0.0977370i
$865$	7.96188e60	+	7.96188e60i	0.00569075	+	0.00569075i
$866$	7.27664e62			0.507336
$867$	1.71368e63	−	1.30148e63i	1.16552	−	0.885168i
$868$	−3.50917e63			−2.32825
$869$	−1.31791e63	−	1.31791e63i	−0.853020	−	0.853020i
$870$	−1.99599e62	+	8.26765e61i	−0.126036	+	0.0522057i
$871$		−	2.02617e63i		−	1.24820i
$872$	−6.13193e62	−	1.48038e63i	−0.368547	−	0.889752i
$873$	1.69102e63	+	7.00444e62i	0.991614	+	0.410740i
$874$	1.12541e63	−	2.71698e63i	0.643896	−	1.55450i
$875$	3.68599e62	−	3.68599e62i	0.205769	−	0.205769i
$876$	−1.02945e63	+	1.02945e63i	−0.560747	+	0.560747i
$877$	−1.05988e63	+	2.55878e63i	−0.563335	+	1.36001i	0.343749	+	0.939061i	$0.388303\pi$
$877$	−1.05988e63	+	2.55878e63i	−0.563335	+	1.36001i	−0.907084	+	0.420949i	$0.861697\pi$
$878$	2.94060e63	+	1.21804e63i	1.52512	+	0.631726i
$879$	4.65939e62	+	1.12488e63i	0.235813	+	0.569303i
$880$		−	3.94852e62i		−	0.195010i
$881$	−1.13588e63	+	4.70496e62i	−0.547457	+	0.226764i	−0.639230	−	0.769016i	$-0.720747\pi$
$881$	−1.13588e63	+	4.70496e62i	−0.547457	+	0.226764i	0.0917727	+	0.995780i	$0.470747\pi$
$882$	7.71373e62	+	7.71373e62i	0.362819	+	0.362819i
$883$	−1.52535e63			−0.700189			−0.350095	−	0.936714i	$-0.613851\pi$
$883$	−1.52535e63			−0.700189			−0.350095	+	0.936714i	$0.613851\pi$
$884$	4.71288e63	−	6.08558e62i	2.11136	−	0.272633i
$885$	8.34941e62			0.365070
$886$	−5.70623e63	−	5.70623e63i	−2.43514	−	2.43514i
$887$	3.55686e63	−	1.47330e63i	1.48152	−	0.613668i	0.512071	−	0.858943i	$-0.328878\pi$
$887$	3.55686e63	−	1.47330e63i	1.48152	−	0.613668i	0.969453	+	0.245275i	$0.0788784\pi$
$888$		−	3.58827e63i		−	1.45884i
$889$	1.01853e63	+	2.45896e63i	0.404192	+	0.975805i
$890$	−5.42220e62	−	2.24595e62i	−0.210034	−	0.0869991i
$891$	6.38074e62	−	1.54045e63i	0.241268	−	0.582474i
$892$	−1.25652e63	+	1.25652e63i	−0.463795	+	0.463795i
$893$	−2.11708e63	+	2.11708e63i	−0.762836	+	0.762836i
$894$	−5.00074e63	+	1.20729e64i	−1.75905	+	4.24672i
$895$	−4.20080e62	−	1.74003e62i	−0.144257	−	0.0597532i
$896$	9.67328e62	+	2.33534e63i	0.324304	+	0.782938i
$897$		−	3.82904e63i		−	1.25329i
$898$	−8.23178e63	+	3.40971e63i	−2.63059	+	1.08962i
$899$	8.04373e62	+	8.04373e62i	0.250971	+	0.250971i
$900$	8.45464e63			2.57562
$901$	−2.57737e63	−	1.98787e63i	−0.766643	−	0.591297i
$902$	−3.90662e63			−1.13465
$903$	−1.22991e63	−	1.22991e63i	−0.348807	−	0.348807i
$904$	−5.19739e63	+	2.15283e63i	−1.43934	+	0.596195i
$905$			3.90645e62i			0.105642i
$906$	−4.62351e63	−	1.11621e64i	−1.22100	−	2.94775i
$907$	−8.98117e62	−	3.72012e62i	−0.231620	−	0.0959402i	0.263855	−	0.964562i	$-0.415006\pi$
$907$	−8.98117e62	−	3.72012e62i	−0.231620	−	0.0959402i	−0.495475	+	0.868622i	$0.665006\pi$
$908$	1.11938e63	−	2.70243e63i	0.281924	−	0.680626i
$909$	4.24613e63	−	4.24613e63i	1.04441	−	1.04441i
$910$	7.27433e62	−	7.27433e62i	0.174744	−	0.174744i
$911$	−1.97789e63	+	4.77505e63i	−0.464042	+	1.12030i	0.502681	+	0.864472i	$0.332347\pi$
$911$	−1.97789e63	+	4.77505e63i	−0.464042	+	1.12030i	−0.966723	+	0.255825i	$0.917653\pi$
$912$	1.16853e64	+	4.84021e63i	2.67763	+	1.10911i
$913$	2.87321e62	+	6.93655e62i	0.0643052	+	0.155247i
$914$			3.49439e63i			0.763885i
$915$	−4.28171e62	+	1.77354e62i	−0.0914247	+	0.0378694i
$916$	1.01869e64	+	1.01869e64i	2.12467	+	2.12467i
$917$	6.82520e63			1.39051
$918$	1.64336e63	−	9.43361e62i	0.327051	−	0.187741i
$919$	6.39412e63			1.24308			0.621538	−	0.783384i	$-0.286508\pi$
$919$	6.39412e63			1.24308			0.621538	+	0.783384i	$0.286508\pi$
$920$	1.06184e63	+	1.06184e63i	0.201660	+	0.201660i
$921$	−3.32004e63	+	1.37520e63i	−0.615972	+	0.255144i
$922$			8.73935e63i			1.58403i
$923$	−7.44719e62	−	1.79791e63i	−0.131873	−	0.318370i
$924$	1.50750e64	+	6.24429e63i	2.60802	+	1.08028i
$925$	9.43389e62	−	2.27754e63i	0.159457	−	0.384963i
$926$	5.33072e63	−	5.33072e63i	0.880338	−	0.880338i
$927$	7.57683e63	−	7.57683e63i	1.22257	−	1.22257i
$928$	−1.16612e63	+	2.81527e63i	−0.183850	+	0.443853i
$929$	−3.39189e63	−	1.40497e63i	−0.522521	−	0.216435i	0.105803	−	0.994387i	$-0.466259\pi$
$929$	−3.39189e63	−	1.40497e63i	−0.522521	−	0.216435i	−0.628324	+	0.777952i	$0.716259\pi$
$930$	8.06068e62	+	1.94602e63i	0.121336	+	0.292930i
$931$			1.68963e63i			0.248527i
$932$	−1.20166e64	+	4.97744e63i	−1.72719	+	0.715425i
$933$	1.34735e64	+	1.34735e64i	1.89245	+	1.89245i
$934$	1.31642e64			1.80691
$935$	−9.43946e61	−	7.31023e62i	−0.0126619	−	0.0980577i
$936$	1.89961e64			2.49019
$937$	−5.04784e63	−	5.04784e63i	−0.646702	−	0.646702i	0.305492	−	0.952195i	$-0.401179\pi$
$937$	−5.04784e63	−	5.04784e63i	−0.646702	−	0.646702i	−0.952195	+	0.305492i	$0.901179\pi$
$938$	−2.01311e64	+	8.33856e63i	−2.52061	+	1.04407i
$939$		−	2.02398e64i		−	2.47683i
$940$	−1.03680e63	−	2.50305e63i	−0.124006	−	0.299378i
$941$	−3.99831e62	−	1.65615e62i	−0.0467412	−	0.0193608i	0.359190	−	0.933264i	$-0.383053\pi$
$941$	−3.99831e62	−	1.65615e62i	−0.0467412	−	0.0193608i	−0.405932	+	0.913903i	$0.633053\pi$
$942$	−1.17529e64	+	2.83740e64i	−1.34292	+	3.24210i
$943$	4.85559e63	−	4.85559e63i	0.542302	−	0.542302i
$944$	2.42512e64	−	2.42512e64i	2.64749	−	2.64749i
$945$	1.09341e62	−	2.63974e62i	0.0116681	−	0.0281693i
$946$	−3.65044e63	−	1.51206e63i	−0.380791	−	0.157729i
$947$	−1.86078e63	−	4.49231e63i	−0.189745	−	0.458084i	0.800166	−	0.599779i	$-0.204745\pi$
$947$	−1.86078e63	−	4.49231e63i	−0.189745	−	0.458084i	−0.989910	+	0.141695i	$0.954745\pi$
$948$			5.40245e64i			5.38532i
$949$	−2.07620e63	+	8.59992e62i	−0.202324	+	0.0838052i
$950$	1.32941e64	+	1.32941e64i	1.26649	+	1.26649i
$951$	−2.01497e64			−1.87667
$952$	−1.43565e64	−	2.50095e64i	−1.30724	−	2.27725i
$953$	3.07361e63			0.273622			0.136811	−	0.990597i	$-0.456315\pi$
$953$	3.07361e63			0.273622			0.136811	+	0.990597i	$0.456315\pi$
$954$	−1.63046e64	−	1.63046e64i	−1.41913	−	1.41913i
$955$	−3.27555e62	+	1.35678e62i	−0.0278748	+	0.0115461i
$956$		−	1.38955e64i		−	1.15619i
$957$	−2.02419e63	−	4.88683e63i	−0.164682	−	0.397576i
$958$	−1.34465e64	−	5.56970e63i	−1.06967	−	0.443071i
$959$	9.80311e63	−	2.36668e64i	0.762542	−	1.84094i
$960$	−4.63553e62	+	4.63553e62i	−0.0352589	+	0.0352589i
$961$	−1.66450e63	+	1.66450e63i	−0.123803	+	0.123803i
$962$	3.75629e63	−	9.06848e63i	0.273209	−	0.659585i
$963$	−1.88344e64	−	7.80147e63i	−1.33964	−	0.554896i
$964$	−6.53284e63	−	1.57717e64i	−0.454408	−	1.09704i
$965$		−	1.84411e63i		−	0.125444i
$966$	−3.80436e64	+	1.57582e64i	−2.53089	+	1.04833i
$967$	−9.28537e63	−	9.28537e63i	−0.604129	−	0.604129i	0.337276	−	0.941406i	$-0.390494\pi$
$967$	−9.28537e63	−	9.28537e63i	−0.604129	−	0.604129i	−0.941406	+	0.337276i	$0.890494\pi$
$968$	−1.60285e64			−1.01993
$969$	2.27911e64	+	6.16758e63i	1.41842	+	0.383843i
$970$	−3.68310e63			−0.224193
$971$	6.37903e63	+	6.37903e63i	0.379788	+	0.379788i	0.871026	−	0.491238i	$-0.163455\pi$
$971$	6.37903e63	+	6.37903e63i	0.379788	+	0.379788i	−0.491238	+	0.871026i	$0.663455\pi$
$972$	−5.22161e64	+	2.16286e64i	−3.04074	+	1.25952i
$973$			7.66084e63i			0.436365i
$974$	−1.15118e64	−	2.77918e64i	−0.641393	−	1.54846i
$975$	2.26156e64	+	9.36768e63i	1.23256	+	0.510544i
$976$	−7.28506e63	+	1.75877e64i	−0.388384	+	0.937643i
$977$	2.63589e63	−	2.63589e63i	0.137466	−	0.137466i	−0.635025	−	0.772491i	$-0.719010\pi$
$977$	2.63589e63	−	2.63589e63i	0.137466	−	0.137466i	0.772491	+	0.635025i	$0.219010\pi$
$978$	−6.53814e64	+	6.53814e64i	−3.33556	+	3.33556i
$979$	5.49882e63	−	1.32753e64i	0.274436	−	0.662548i
$980$	−1.41256e63	−	5.85102e62i	−0.0689678	−	0.0285674i
$981$	−3.74791e63	−	9.04825e63i	−0.179021	−	0.432196i
$982$		−	2.65308e64i		−	1.23980i
$983$	3.46902e64	−	1.43692e64i	1.58601	−	0.656948i	0.596661	−	0.802493i	$-0.296494\pi$
$983$	3.46902e64	−	1.43692e64i	1.58601	−	0.656948i	0.989352	+	0.145546i	$0.0464937\pi$
$984$	4.51834e64	+	4.51834e64i	2.02108	+	2.02108i
$985$	1.66787e63			0.0729933
$986$	−4.32737e63	+	1.59910e64i	−0.185298	+	0.684733i
$987$	4.19225e64			1.75642
$988$	3.68689e64	+	3.68689e64i	1.51142	+	1.51142i
$989$	6.41655e63	−	2.65782e63i	0.257384	−	0.106612i
$990$		−	5.22166e63i		−	0.204952i
$991$	−1.35876e64	−	3.28034e64i	−0.521867	−	1.25990i	−0.936742	−	0.350020i	$-0.886175\pi$
$991$	−1.35876e64	−	3.28034e64i	−0.521867	−	1.25990i	0.414876	−	0.909878i	$-0.363825\pi$
$992$	2.74480e64	+	1.13693e64i	1.03160	+	0.427301i
$993$	2.51311e64	−	6.06719e64i	0.924279	−	2.23141i
$994$	−1.47984e64	+	1.47984e64i	−0.532607	+	0.532607i
$995$	3.47113e62	−	3.47113e62i	0.0122257	−	0.0122257i
$996$	8.32836e63	−	2.01065e64i	0.287067	−	0.693042i
$997$	2.93714e64	+	1.21660e64i	0.990782	+	0.410395i	0.818409	−	0.574636i	$-0.194857\pi$
$997$	2.93714e64	+	1.21660e64i	0.990782	+	0.410395i	0.172373	+	0.985032i	$0.444857\pi$
$998$	−1.76952e64	−	4.27199e64i	−0.584182	−	1.41034i
$999$		−	2.72619e63i		−	0.0880843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.4	✓	252
17.9	even	8	inner	17.44.d.a.9.4	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.4	✓	252	1.1	even	1	trivial
17.44.d.a.9.4	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+(-3.80683e6 - 3.80683e6i) q^{2} +(2.44978e10 - 1.01473e10i) q^{3} +2.01878e13i q^{4} +(-5.36168e13 - 1.29442e14i) q^{5} +(-1.31888e17 - 5.46298e16i) q^{6} +(-6.31645e17 + 1.52492e18i) q^{7} +(4.33664e19 - 4.33664e19i) q^{8} +(2.65060e20 - 2.65060e20i) q^{9} +(-2.88655e20 + 6.96875e20i) q^{10} +(-1.70618e22 - 7.06722e21i) q^{11} +(2.04852e23 + 4.94557e23i) q^{12} +8.26295e23i q^{13} +(8.20970e24 - 3.40057e24i) q^{14} +(-2.62698e24 - 2.62698e24i) q^{15} -1.52603e26 q^{16} +(-2.82528e26 + 3.64818e25i) q^{17} -2.01808e27 q^{18} +(-2.21022e27 - 2.21022e27i) q^{19} +(2.61316e27 - 1.08241e27i) q^{20} +4.37668e28i q^{21} +(3.80476e28 + 9.18551e28i) q^{22} +(-1.61458e29 - 6.68780e28i) q^{23} +(6.22328e29 - 1.50243e30i) q^{24} +(7.90007e29 - 7.90007e29i) q^{25} +(3.14557e30 - 3.14557e30i) q^{26} +(4.72814e29 - 1.14147e30i) q^{27} +(-3.07849e31 - 1.27515e31i) q^{28} +(4.13362e30 + 9.97945e30i) q^{29} +2.00010e31i q^{30} +(9.72964e31 - 4.03015e31i) q^{31} +(1.99480e32 + 1.99480e32i) q^{32} -4.89689e32 q^{33} +(1.21442e33 + 9.36655e32i) q^{34} +2.31257e32 q^{35} +(5.35099e33 + 5.35099e33i) q^{36} +(2.03855e33 - 8.44394e32i) q^{37} +1.68278e34i q^{38} +(8.38468e33 + 2.02424e34i) q^{39} +(-7.93862e33 - 3.28828e33i) q^{40} +(-1.50367e34 + 3.63019e34i) q^{41} +(1.66613e35 - 1.66613e35i) q^{42} +(-2.81014e34 + 2.81014e34i) q^{43} +(1.42672e35 - 3.44441e35i) q^{44} +(-4.85217e34 - 2.00984e34i) q^{45} +(3.60049e35 + 8.69235e35i) q^{46} -9.57862e35i q^{47} +(-3.73844e36 + 1.54851e36i) q^{48} +(-3.82231e35 - 3.82231e35i) q^{49} -6.01484e36 q^{50} +(-6.55111e36 + 3.76062e36i) q^{51} -1.66811e37 q^{52} +(8.07927e36 + 8.07927e36i) q^{53} +(-6.14533e36 + 2.54548e36i) q^{54} +2.58744e36i q^{55} +(3.87384e37 + 9.35227e37i) q^{56} +(-7.65731e37 - 3.17176e37i) q^{57} +(2.22541e37 - 5.37261e37i) q^{58} +(-1.58916e38 + 1.58916e38i) q^{59} +(5.30331e37 - 5.30331e37i) q^{60} +(4.77385e37 - 1.15251e38i) q^{61} +(-5.23812e38 - 2.16970e38i) q^{62} +(2.36773e38 + 5.71621e38i) q^{63} -1.76458e38i q^{64} +(1.06958e38 - 4.43033e37i) q^{65} +(1.86416e39 + 1.86416e39i) q^{66} -2.45211e39 q^{67} +(-7.36489e38 - 5.70362e39i) q^{68} -4.63399e39 q^{69} +(-8.80355e38 - 8.80355e38i) q^{70} +(-2.17587e39 + 9.01275e38i) q^{71} -2.29894e40i q^{72} +(1.04078e39 + 2.51267e39i) q^{73} +(-1.09749e40 - 4.54594e39i) q^{74} +(1.13370e40 - 2.73699e40i) q^{75} +(4.46195e40 - 4.46195e40i) q^{76} +(2.15540e40 - 2.15540e40i) q^{77} +(4.51403e40 - 1.08978e41i) q^{78} +(9.32407e40 + 3.86215e40i) q^{79} +(8.18209e39 + 1.97533e40i) q^{80} +9.02864e40i q^{81} +(1.95437e41 - 8.09529e40i) q^{82} +(-2.87478e40 - 2.87478e40i) q^{83} -8.83556e41 q^{84} +(1.98705e40 + 3.46150e40i) q^{85} +2.13954e41 q^{86} +(2.02529e41 + 2.02529e41i) q^{87} +(-1.04639e42 + 4.33429e41i) q^{88} +7.78073e41i q^{89} +(1.08203e41 + 2.61225e41i) q^{90} +(-1.26004e42 - 5.21925e41i) q^{91} +(1.35012e42 - 3.25948e42i) q^{92} +(1.97459e42 - 1.97459e42i) q^{93} +(-3.64642e42 + 3.64642e42i) q^{94} +(-1.67591e41 + 4.04600e41i) q^{95} +(6.91099e42 + 2.86263e42i) q^{96} +(1.86859e42 + 4.51117e42i) q^{97} +2.91018e42i q^{98} +(-6.39565e42 + 2.64916e42i) 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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