LMFDB - Embedded newform 17.44.d.a.2.12

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			2.12
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.13678e6 - 3.13678e6i) q^{2} +(-1.51005e10 + 6.25485e9i) q^{3} +1.08827e13i q^{4} +(5.61563e14 + 1.35573e15i) q^{5} +(6.69872e16 + 2.77470e16i) q^{6} +(-1.25921e17 + 3.04000e17i) q^{7} +(6.54523e18 - 6.54523e18i) q^{8} +(-4.32097e19 + 4.32097e19i) q^{9} +(2.49114e21 - 6.01414e21i) q^{10} +(4.19427e22 + 1.73732e22i) q^{11} +(-6.80696e22 - 1.64335e23i) q^{12} +3.97241e23i q^{13} +(1.34857e24 - 5.58596e23i) q^{14} +(-1.69598e25 - 1.69598e25i) q^{15} +5.46633e25 q^{16} +(-2.14069e26 - 1.87956e26i) q^{17} +2.71079e26 q^{18} +(-5.39829e26 - 5.39829e26i) q^{19} +(-1.47540e28 + 6.11132e27i) q^{20} -5.37819e27i q^{21} +(-7.70690e28 - 1.86061e29i) q^{22} +(-2.46607e27 - 1.02148e27i) q^{23} +(-5.78971e28 + 1.39776e29i) q^{24} +(-7.18773e29 + 7.18773e29i) q^{25} +(1.24606e30 - 1.24606e30i) q^{26} +(2.43542e30 - 5.87961e30i) q^{27} +(-3.30835e30 - 1.37036e30i) q^{28} +(9.82440e30 + 2.37182e31i) q^{29} +1.06398e32i q^{30} +(9.92999e31 - 4.11314e31i) q^{31} +(-2.29039e32 - 2.29039e32i) q^{32} -7.42023e32 q^{33} +(8.19115e31 + 1.26106e33i) q^{34} -4.82856e32 q^{35} +(-4.70238e32 - 4.70238e32i) q^{36} +(-5.45202e33 + 2.25830e33i) q^{37} +3.38665e33i q^{38} +(-2.48468e33 - 5.99855e33i) q^{39} +(1.25492e34 + 5.19803e33i) q^{40} +(-2.17605e34 + 5.25344e34i) q^{41} +(-1.68702e34 + 1.68702e34i) q^{42} +(-1.06052e35 + 1.06052e35i) q^{43} +(-1.89068e35 + 4.56449e35i) q^{44} +(-8.28458e34 - 3.43158e34i) q^{45} +(4.53136e33 + 1.09397e34i) q^{46} -4.94615e35i q^{47} +(-8.25445e35 + 3.41911e35i) q^{48} +(1.46763e36 + 1.46763e36i) q^{49} +4.50927e36 q^{50} +(4.40819e36 + 1.49926e36i) q^{51} -4.32306e36 q^{52} +(8.37462e36 + 8.37462e36i) q^{53} +(-2.60824e37 + 1.08037e37i) q^{54} +6.66192e37i q^{55} +(1.16557e36 + 2.81394e36i) q^{56} +(1.15283e37 + 4.77516e36i) q^{57} +(4.35818e37 - 1.05216e38i) q^{58} +(-4.22937e37 + 4.22937e37i) q^{59} +(1.84569e38 - 1.84569e38i) q^{60} +(-1.89850e37 + 4.58339e37i) q^{61} +(-4.40502e38 - 1.82462e38i) q^{62} +(-7.69475e36 - 1.85768e37i) q^{63} +9.56069e38i q^{64} +(-5.38553e38 + 2.23076e38i) q^{65} +(2.32756e39 + 2.32756e39i) q^{66} +6.26094e38 q^{67} +(2.04547e39 - 2.32965e39i) q^{68} +4.36282e37 q^{69} +(1.51461e39 + 1.51461e39i) q^{70} +(7.89039e37 - 3.26831e37i) q^{71} +5.65635e38i q^{72} +(-6.57878e39 - 1.58826e40i) q^{73} +(2.41856e40 + 1.00180e40i) q^{74} +(6.35804e39 - 1.53497e40i) q^{75} +(5.87480e39 - 5.87480e39i) q^{76} +(-1.05629e40 + 1.05629e40i) q^{77} +(-1.10222e40 + 2.66101e40i) q^{78} +(-4.22987e40 - 1.75207e40i) q^{79} +(3.06969e40 + 7.41089e40i) q^{80} +8.39595e40i q^{81} +(2.33047e41 - 9.65312e40i) q^{82} +(-1.40496e41 - 1.40496e41i) q^{83} +5.85292e40 q^{84} +(1.34605e41 - 3.95769e41i) q^{85} +6.65321e41 q^{86} +(-2.96707e41 - 2.96707e41i) q^{87} +(3.88236e41 - 1.60813e41i) q^{88} +1.23098e42i q^{89} +(1.52228e41 + 3.67510e41i) q^{90} +(-1.20761e41 - 5.00210e40i) q^{91} +(1.11165e40 - 2.68375e40i) q^{92} +(-1.24221e42 + 1.24221e42i) q^{93} +(-1.55150e42 + 1.55150e42i) q^{94} +(4.28716e41 - 1.03501e42i) q^{95} +(4.89122e42 + 2.02601e42i) q^{96} +(-4.76552e41 - 1.15050e42i) q^{97} -9.20727e42i q^{98} +(-2.56302e42 + 1.06164e42i) 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 $

$2$	−3.13678e6	−	3.13678e6i	−1.05764	−	1.05764i	−0.998234	−	0.0594099i	$-0.981078\pi$
$2$	−3.13678e6	−	3.13678e6i	−1.05764	−	1.05764i	−0.0594099	−	0.998234i	$-0.518922\pi$
$3$	−1.51005e10	+	6.25485e9i	−0.833461	+	0.345231i	−0.758272	−	0.651938i	$-0.773956\pi$
$3$	−1.51005e10	+	6.25485e9i	−0.833461	+	0.345231i	−0.0751892	+	0.997169i	$0.523956\pi$
$4$			1.08827e13i			1.23722i
$5$	5.61563e14	+	1.35573e15i	0.526676	+	1.27151i	0.933689	+	0.358086i	$0.116570\pi$
$5$	5.61563e14	+	1.35573e15i	0.526676	+	1.27151i	−0.407013	+	0.913423i	$0.633430\pi$
$6$	6.69872e16	+	2.77470e16i	1.24664	+	0.516374i
$7$	−1.25921e17	+	3.04000e17i	−0.0852100	+	0.205715i	−0.960741	−	0.277447i	$-0.910512\pi$
$7$	−1.25921e17	+	3.04000e17i	−0.0852100	+	0.205715i	0.875531	+	0.483162i	$0.160512\pi$
$8$	6.54523e18	−	6.54523e18i	0.250894	−	0.250894i
$9$	−4.32097e19	+	4.32097e19i	−0.131634	+	0.131634i
$10$	2.49114e21	−	6.01414e21i	0.787767	−	1.90184i
$11$	4.19427e22	+	1.73732e22i	1.70889	+	0.707844i	0.999997	+	0.00252445i	$0.000803558\pi$
$11$	4.19427e22	+	1.73732e22i	1.70889	+	0.707844i	0.708890	+	0.705319i	$0.249196\pi$
$12$	−6.80696e22	−	1.64335e23i	−0.427127	−	1.03117i
$13$			3.97241e23i			0.445936i	0.974826	+	0.222968i	$0.0715745\pi$
$13$			3.97241e23i			0.445936i	−0.974826	+	0.222968i	$0.928426\pi$
$14$	1.34857e24	−	5.58596e23i	0.307695	−	0.127452i
$15$	−1.69598e25	−	1.69598e25i	−0.877928	−	0.877928i
$16$	5.46633e25			0.706507
$17$	−2.14069e26	−	1.87956e26i	−0.751453	−	0.659787i
$17$	−2.14069e26	−	1.87956e26i	−0.751453	−	0.659787i
$18$	2.71079e26			0.278443
$19$	−5.39829e26	−	5.39829e26i	−0.173402	−	0.173402i	0.615070	−	0.788472i	$-0.289128\pi$
$19$	−5.39829e26	−	5.39829e26i	−0.173402	−	0.173402i	−0.788472	+	0.615070i	$0.789128\pi$
$20$	−1.47540e28	+	6.11132e27i	−1.57314	+	0.651614i
$21$		−	5.37819e27i		−	0.200873i
$22$	−7.70690e28	−	1.86061e29i	−1.05875	−	2.55604i
$23$	−2.46607e27	−	1.02148e27i	−0.0130274	−	0.00539611i	0.376160	−	0.926555i	$-0.377244\pi$
$23$	−2.46607e27	−	1.02148e27i	−0.0130274	−	0.00539611i	−0.389188	+	0.921159i	$0.627244\pi$
$24$	−5.78971e28	+	1.39776e29i	−0.122494	+	0.295727i
$25$	−7.18773e29	+	7.18773e29i	−0.632239	+	0.632239i
$26$	1.24606e30	−	1.24606e30i	0.471641	−	0.471641i
$27$	2.43542e30	−	5.87961e30i	0.409498	−	0.988617i
$28$	−3.30835e30	−	1.37036e30i	−0.254515	−	0.105424i
$29$	9.82440e30	+	2.37182e31i	0.355426	+	0.858074i	0.995931	+	0.0901202i	$0.0287251\pi$
$29$	9.82440e30	+	2.37182e31i	0.355426	+	0.858074i	−0.640505	+	0.767954i	$0.721275\pi$
$30$			1.06398e32i			1.85707i
$31$	9.92999e31	−	4.11314e31i	0.856392	−	0.354729i	0.0890964	−	0.996023i	$-0.471602\pi$
$31$	9.92999e31	−	4.11314e31i	0.856392	−	0.354729i	0.767295	+	0.641294i	$0.221602\pi$
$32$	−2.29039e32	−	2.29039e32i	−0.998127	−	0.998127i
$33$	−7.42023e32			−1.66866
$34$	8.19115e31	+	1.26106e33i	0.0969501	+	1.49259i
$35$	−4.82856e32			−0.306447
$36$	−4.70238e32	−	4.70238e32i	−0.162860	−	0.162860i
$37$	−5.45202e33	+	2.25830e33i	−1.04766	+	0.433955i	−0.839056	−	0.544045i	$-0.816892\pi$
$37$	−5.45202e33	+	2.25830e33i	−1.04766	+	0.433955i	−0.208604	+	0.978000i	$0.566892\pi$
$38$			3.38665e33i			0.366795i
$39$	−2.48468e33	−	5.99855e33i	−0.153951	−	0.371670i
$40$	1.25492e34	+	5.19803e33i	0.451154	+	0.186874i
$41$	−2.17605e34	+	5.25344e34i	−0.460061	+	1.11069i	0.508311	+	0.861174i	$0.330270\pi$
$41$	−2.17605e34	+	5.25344e34i	−0.460061	+	1.11069i	−0.968372	+	0.249512i	$0.919730\pi$
$42$	−1.68702e34	+	1.68702e34i	−0.212452	+	0.212452i
$43$	−1.06052e35	+	1.06052e35i	−0.805277	+	0.805277i	−0.983915	−	0.178638i	$-0.942831\pi$
$43$	−1.06052e35	+	1.06052e35i	−0.805277	+	0.805277i	0.178638	+	0.983915i	$0.442831\pi$
$44$	−1.89068e35	+	4.56449e35i	−0.875759	+	2.11427i
$45$	−8.28458e34	−	3.43158e34i	−0.236702	−	0.0980450i
$46$	4.53136e33	+	1.09397e34i	0.00807115	+	0.0194855i
$47$		−	4.94615e35i		−	0.554834i	−0.960750	−	0.277417i	$-0.910522\pi$
$47$		−	4.94615e35i		−	0.554834i	0.960750	−	0.277417i	$-0.0894783\pi$
$48$	−8.25445e35	+	3.41911e35i	−0.588846	+	0.243908i
$49$	1.46763e36	+	1.46763e36i	0.672049	+	0.672049i
$50$	4.50927e36			1.33737
$51$	4.40819e36	+	1.49926e36i	0.854086	+	0.290482i
$52$	−4.32306e36			−0.551720
$53$	8.37462e36	+	8.37462e36i	0.709633	+	0.709633i	0.966458	−	0.256825i	$-0.0826764\pi$
$53$	8.37462e36	+	8.37462e36i	0.709633	+	0.709633i	−0.256825	+	0.966458i	$0.582676\pi$
$54$	−2.60824e37	+	1.08037e37i	−1.47871	+	0.612501i
$55$			6.66192e37i			2.54567i
$56$	1.16557e36	+	2.81394e36i	0.0302340	+	0.0729914i
$57$	1.15283e37	+	4.77516e36i	0.204388	+	0.0846601i
$58$	4.35818e37	−	1.05216e38i	0.531623	−	1.28345i
$59$	−4.22937e37	+	4.22937e37i	−0.357238	+	0.357238i	−0.862794	−	0.505556i	$-0.831287\pi$
$59$	−4.22937e37	+	4.22937e37i	−0.357238	+	0.357238i	0.505556	+	0.862794i	$0.331287\pi$
$60$	1.84569e38	−	1.84569e38i	1.08619	−	1.08619i
$61$	−1.89850e37	+	4.58339e37i	−0.0783105	+	0.189058i	−0.958186	−	0.286146i	$-0.907626\pi$
$61$	−1.89850e37	+	4.58339e37i	−0.0783105	+	0.189058i	0.879876	+	0.475204i	$0.157626\pi$
$62$	−4.40502e38	−	1.82462e38i	−1.28093	−	0.530580i
$63$	−7.69475e36	−	1.85768e37i	−0.0158625	−	0.0382956i
$64$			9.56069e38i			1.40482i
$65$	−5.38553e38	+	2.23076e38i	−0.567011	+	0.234864i
$66$	2.32756e39	+	2.32756e39i	1.76485	+	1.76485i
$67$	6.26094e38			0.343583			0.171791	−	0.985133i	$-0.445045\pi$
$67$	6.26094e38			0.343583			0.171791	+	0.985133i	$0.445045\pi$
$68$	2.04547e39	−	2.32965e39i	0.816301	−	0.929712i
$69$	4.36282e37			0.0127207
$70$	1.51461e39	+	1.51461e39i	0.324111	+	0.324111i
$71$	7.89039e37	−	3.26831e37i	0.0124464	−	0.00515547i	−0.376452	−	0.926436i	$-0.622856\pi$
$71$	7.89039e37	−	3.26831e37i	0.0124464	−	0.00515547i	0.388898	+	0.921281i	$0.372856\pi$
$72$			5.65635e38i			0.0660522i
$73$	−6.57878e39	−	1.58826e40i	−0.571089	−	1.37873i	−0.900629	−	0.434589i	$-0.856894\pi$
$73$	−6.57878e39	−	1.58826e40i	−0.571089	−	1.37873i	0.329540	−	0.944142i	$-0.393106\pi$
$74$	2.41856e40	+	1.00180e40i	1.56702	+	0.649081i
$75$	6.35804e39	−	1.53497e40i	0.308678	−	0.745215i
$76$	5.87480e39	−	5.87480e39i	0.214536	−	0.214536i
$77$	−1.05629e40	+	1.05629e40i	−0.291229	+	0.291229i
$78$	−1.10222e40	+	2.66101e40i	−0.230269	+	0.555919i
$79$	−4.22987e40	−	1.75207e40i	−0.671962	−	0.278336i	0.0205003	−	0.999790i	$-0.493474\pi$
$79$	−4.22987e40	−	1.75207e40i	−0.671962	−	0.278336i	−0.692462	+	0.721454i	$0.743474\pi$
$80$	3.06969e40	+	7.41089e40i	0.372100	+	0.898329i
$81$			8.39595e40i			0.779187i
$82$	2.33047e41	−	9.65312e40i	1.66129	−	0.688129i
$83$	−1.40496e41	−	1.40496e41i	−0.771765	−	0.771765i	0.206650	−	0.978415i	$-0.433744\pi$
$83$	−1.40496e41	−	1.40496e41i	−0.771765	−	0.771765i	−0.978415	+	0.206650i	$0.933744\pi$
$84$	5.85292e40			0.248524
$85$	1.34605e41	−	3.95769e41i	0.443152	−	1.30297i
$86$	6.65321e41			1.70339
$87$	−2.96707e41	−	2.96707e41i	−0.592468	−	0.592468i
$88$	3.88236e41	−	1.60813e41i	0.606343	−	0.251156i
$89$			1.23098e42i			1.50788i	0.656944	+	0.753939i	$0.271849\pi$
$89$			1.23098e42i			1.50788i	−0.656944	+	0.753939i	$0.728151\pi$
$90$	1.52228e41	+	3.67510e41i	0.146649	+	0.354043i
$91$	−1.20761e41	−	5.00210e40i	−0.0917357	−	0.0379982i
$92$	1.11165e40	−	2.68375e40i	0.00667618	−	0.0161177i
$93$	−1.24221e42	+	1.24221e42i	−0.591306	+	0.591306i
$94$	−1.55150e42	+	1.55150e42i	−0.586816	+	0.586816i
$95$	4.28716e41	−	1.03501e42i	0.129155	−	0.311809i
$96$	4.89122e42	+	2.02601e42i	1.17648	+	0.487316i
$97$	−4.76552e41	−	1.15050e42i	−0.0917314	−	0.221459i	0.871354	−	0.490655i	$-0.163242\pi$
$97$	−4.76552e41	−	1.15050e42i	−0.0917314	−	0.221459i	−0.963086	+	0.269195i	$0.913242\pi$
$98$		−	9.20727e42i		−	1.42158i
$99$	−2.56302e42	+	1.06164e42i	−0.318123	+	0.131771i
$100$	−7.82219e42	−	7.82219e42i	−0.782219	−	0.782219i
$101$	1.79649e43			1.45049			0.725244	−	0.688492i	$-0.241727\pi$
$101$	1.79649e43			1.45049			0.725244	+	0.688492i	$0.241727\pi$
$102$	−9.12466e42	−	1.85304e43i	−0.596092	−	1.21054i
$103$	−2.39412e43			−1.26808			−0.634038	−	0.773302i	$-0.718604\pi$
$103$	−2.39412e43			−1.26808			−0.634038	+	0.773302i	$0.718604\pi$
$104$	2.60004e42	+	2.60004e42i	0.111883	+	0.111883i
$105$	7.29139e42	−	3.02019e42i	0.255411	−	0.105795i
$106$		−	5.25387e43i		−	1.50108i
$107$	−1.19949e43	−	2.89583e43i	−0.280057	−	0.676118i	0.719779	−	0.694203i	$-0.244243\pi$
$107$	−1.19949e43	−	2.89583e43i	−0.280057	−	0.676118i	−0.999836	+	0.0180852i	$0.994243\pi$
$108$	6.39861e43	+	2.65039e43i	1.22314	+	0.506640i
$109$	1.98982e43	−	4.80385e43i	0.311992	−	0.753216i	−0.687639	−	0.726053i	$-0.741353\pi$
$109$	1.98982e43	−	4.80385e43i	0.311992	−	0.753216i	0.999631	−	0.0271628i	$-0.00864726\pi$
$110$	2.08970e44	−	2.08970e44i	2.69241	−	2.69241i
$111$	6.82031e43	−	6.82031e43i	0.723369	−	0.723369i
$112$	−6.88327e42	+	1.66177e43i	−0.0602015	+	0.145339i
$113$	1.86444e44	+	7.72276e43i	1.34698	+	0.557938i	0.935450	−	0.353458i	$-0.114994\pi$
$113$	1.86444e44	+	7.72276e43i	1.34698	+	0.557938i	0.411531	+	0.911396i	$0.364994\pi$
$114$	−2.11830e43	−	5.11403e43i	−0.126629	−	0.305709i
$115$		−	3.91696e42i		−	0.0194064i
$116$	−2.58118e44	+	1.06916e44i	−1.06163	+	0.439740i
$117$	−1.71647e43	−	1.71647e43i	−0.0587001	−	0.0587001i
$118$	2.65332e44			0.755661
$119$	8.40944e43	−	4.14095e43i	0.199760	−	0.0983648i
$120$	−2.22012e44			−0.440534
$121$	1.03140e45	+	1.03140e45i	1.71214	+	1.71214i
$122$	2.03323e44	−	8.42191e43i	0.282781	−	0.117132i
$123$		−	9.29407e44i		−	1.08454i
$124$	4.47620e44	+	1.08065e45i	0.438878	+	1.05954i
$125$	1.63190e44	+	6.75955e43i	0.134626	+	0.0557638i
$126$	−3.41345e43	+	8.24080e43i	−0.0237261	+	0.0572800i
$127$	2.55440e44	−	2.55440e44i	0.149799	−	0.149799i	−0.628229	−	0.778028i	$-0.716220\pi$
$127$	2.55440e44	−	2.55440e44i	0.149799	−	0.149799i	0.778028	+	0.628229i	$0.216220\pi$
$128$	9.84328e44	−	9.84328e44i	0.487670	−	0.487670i
$129$	9.38099e44	−	2.26477e45i	0.393161	−	0.949174i
$130$	2.38906e45	+	9.89583e44i	0.848097	+	0.351293i
$131$	−1.46330e45	−	3.53273e45i	−0.440556	−	1.06360i	−0.975754	−	0.218870i	$-0.929763\pi$
$131$	−1.46330e45	−	3.53273e45i	−0.440556	−	1.06360i	0.535198	−	0.844727i	$-0.320237\pi$
$132$		−	8.07522e45i		−	2.06450i
$133$	2.32084e44	−	9.61325e43i	0.0504470	−	0.0208958i
$134$	−1.96392e45	−	1.96392e45i	−0.363388	−	0.363388i
$135$	9.33883e45			1.47271
$136$	−2.63134e45	+	1.70917e44i	−0.354072	+	0.0229985i
$137$	−1.16580e46			−1.34008			−0.670040	−	0.742325i	$-0.733723\pi$
$137$	−1.16580e46			−1.34008			−0.670040	+	0.742325i	$0.733723\pi$
$138$	−1.36852e44	−	1.36852e44i	−0.0134540	−	0.0134540i
$139$	−1.46997e46	+	6.08880e45i	−1.23734	+	0.512523i	−0.902882	−	0.429887i	$-0.858553\pi$
$139$	−1.46997e46	+	6.08880e45i	−1.23734	+	0.512523i	−0.334458	+	0.942411i	$0.608553\pi$
$140$		−	5.25478e45i		−	0.379142i
$141$	3.09374e45	+	7.46894e45i	0.191546	+	0.462432i
$142$	−3.50024e44	−	1.44985e44i	−0.0186165	−	0.00771121i
$143$	−6.90136e45	+	1.66613e46i	−0.315653	+	0.762053i
$144$	−2.36198e45	+	2.36198e45i	−0.0930001	+	0.0930001i
$145$	−2.66385e46	+	2.66385e46i	−0.903854	+	0.903854i
$146$	−2.91840e46	+	7.04564e46i	−0.854197	+	2.06221i
$147$	−3.13418e46	−	1.29822e46i	−0.792139	−	0.328115i
$148$	−2.45764e46	−	5.93327e46i	−0.536898	−	1.29619i
$149$			9.71113e46i			1.83554i	0.397107	+	0.917772i	$0.370014\pi$
$149$			9.71113e46i			1.83554i	−0.397107	+	0.917772i	$0.629986\pi$
$150$	−6.80923e46	+	2.82048e46i	−1.11464	+	0.461701i
$151$	−2.50019e46	−	2.50019e46i	−0.354787	−	0.354787i	0.507100	−	0.861887i	$-0.330718\pi$
$151$	−2.50019e46	−	2.50019e46i	−0.354787	−	0.354787i	−0.861887	+	0.507100i	$0.830718\pi$
$152$	−7.06662e45			−0.0870111
$153$	1.73713e46	−	1.12834e45i	0.185767	−	0.0120663i
$154$	6.62672e46			0.616032
$155$	1.11526e47	+	1.11526e47i	0.902082	+	0.902082i
$156$	6.52805e46	−	2.70401e46i	0.459837	−	0.190471i
$157$			2.41690e47i			1.48394i	0.670434	+	0.741969i	$0.266108\pi$
$157$			2.41690e47i			1.48394i	−0.670434	+	0.741969i	$0.733892\pi$
$158$	7.77232e46	+	1.87640e47i	0.416316	+	1.00508i
$159$	−1.78843e47	−	7.40793e46i	−0.836439	−	0.346464i
$160$	1.81896e47	−	4.39136e47i	0.743437	−	1.79482i
$161$	6.21060e44	−	6.21060e44i	0.00222013	−	0.00222013i
$162$	2.63362e47	−	2.63362e47i	0.824102	−	0.824102i
$163$	−1.64680e47	+	3.97573e47i	−0.451448	+	1.08989i	0.520324	+	0.853969i	$0.325811\pi$
$163$	−1.64680e47	+	3.97573e47i	−0.451448	+	1.08989i	−0.971772	+	0.235923i	$0.924189\pi$
$164$	−5.71717e47	−	2.36813e47i	−1.37416	−	0.569197i
$165$	−4.16693e47	−	1.00599e48i	−0.878843	−	2.12172i
$166$			8.81411e47i			1.63250i
$167$	5.43762e47	−	2.25234e47i	0.885126	−	0.366631i	0.106643	−	0.994297i	$-0.465990\pi$
$167$	5.43762e47	−	2.25234e47i	0.885126	−	0.366631i	0.778482	+	0.627666i	$0.215990\pi$
$168$	−3.52015e46	−	3.52015e46i	−0.0503978	−	0.0503978i
$169$	6.35731e47			0.801141
$170$	−1.66367e48	+	8.19217e47i	−1.84678	+	0.909383i
$171$	4.66517e46			0.0456511
$172$	−1.15413e48	−	1.15413e48i	−0.996305	−	0.996305i
$173$	1.19950e48	−	4.96850e47i	0.914134	−	0.378647i	0.124496	−	0.992220i	$-0.460268\pi$
$173$	1.19950e48	−	4.96850e47i	0.914134	−	0.378647i	0.789638	+	0.613573i	$0.210268\pi$
$174$			1.86141e48i			1.25324i
$175$	−1.27999e47	−	3.09016e47i	−0.0761881	−	0.183934i
$176$	2.29272e48	+	9.49678e47i	1.20734	+	0.500097i
$177$	3.74117e47	−	9.03199e47i	0.174414	−	0.421074i
$178$	3.86132e48	−	3.86132e48i	1.59480	−	1.59480i
$179$	−2.09946e48	+	2.09946e48i	−0.768720	+	0.768720i	−0.977881	−	0.209161i	$-0.932927\pi$
$179$	−2.09946e48	+	2.09946e48i	−0.768720	+	0.768720i	0.209161	+	0.977881i	$0.432927\pi$
$180$	3.73449e47	−	9.01586e47i	0.121303	−	0.292852i
$181$	−3.53865e48	−	1.46576e48i	−1.02035	−	0.422642i	−0.191128	−	0.981565i	$-0.561215\pi$
$181$	−3.53865e48	−	1.46576e48i	−1.02035	−	0.422642i	−0.829219	+	0.558923i	$0.811215\pi$
$182$	2.21897e47	+	5.35707e47i	0.0568352	+	0.137212i
$183$		−	8.10865e47i		−	0.184608i
$184$	−2.28268e46	+	9.45518e45i	−0.00462234	+	0.00191464i
$185$	−6.12331e48	−	6.12331e48i	−1.10355	−	1.10355i
$186$	7.79309e48			1.25078
$187$	−5.71322e48	−	1.16024e49i	−0.817122	−	1.65941i
$188$	5.38274e48			0.686451
$189$	1.48074e48	+	1.48074e48i	0.168480	+	0.168480i
$190$	−4.59140e48	+	1.90182e48i	−0.466383	+	0.193182i
$191$			1.61251e49i			1.46314i	0.681769	+	0.731568i	$0.261211\pi$
$191$			1.61251e49i			1.46314i	−0.681769	+	0.731568i	$0.738789\pi$
$192$	−5.98007e48	−	1.44372e49i	−0.484986	−	1.17086i
$193$	7.11520e48	+	2.94721e48i	0.516066	+	0.213761i	0.625488	−	0.780234i	$-0.284900\pi$
$193$	7.11520e48	+	2.94721e48i	0.516066	+	0.213761i	−0.109422	+	0.993995i	$0.534900\pi$
$194$	−2.11402e48	+	5.10370e48i	−0.137206	+	0.331244i
$195$	6.73713e48	−	6.73713e48i	0.391499	−	0.391499i
$196$	−1.59718e49	+	1.59718e49i	−0.831472	+	0.831472i
$197$	−6.91094e48	+	1.66845e49i	−0.322488	+	0.778555i	0.676620	+	0.736332i	$0.263444\pi$
$197$	−6.91094e48	+	1.66845e49i	−0.322488	+	0.778555i	−0.999108	+	0.0422227i	$0.986556\pi$
$198$	1.13698e49	+	4.70951e48i	0.475828	+	0.197094i
$199$	−1.18671e49	−	2.86496e49i	−0.445659	−	1.07591i	−0.973932	−	0.226841i	$-0.927160\pi$
$199$	−1.18671e49	−	2.86496e49i	−0.445659	−	1.07591i	0.528273	−	0.849074i	$-0.322840\pi$
$200$			9.40907e48i			0.317250i
$201$	−9.45435e48	+	3.91612e48i	−0.286363	+	0.118615i
$202$	−5.63518e49	−	5.63518e49i	−1.53410	−	1.53410i
$203$	−8.44745e48			−0.206805
$204$	−1.63160e49	+	4.79730e49i	−0.359390	+	1.05669i
$205$	−8.34426e49			−1.65455
$206$	7.50983e49	+	7.50983e49i	1.34117	+	1.34117i
$207$	1.50696e47	−	6.24203e46i	0.00242515	−	0.00100453i
$208$			2.17145e49i			0.315057i
$209$	−1.32633e49	−	3.20205e49i	−0.173583	−	0.419066i
$210$	−3.23452e49	−	1.33978e49i	−0.382028	−	0.158241i
$211$	−1.78823e49	+	4.31718e49i	−0.190700	+	0.460391i	−0.990092	−	0.140419i	$-0.955155\pi$
$211$	−1.78823e49	+	4.31718e49i	−0.190700	+	0.460391i	0.799392	+	0.600810i	$0.205155\pi$
$212$	−9.11385e49	+	9.11385e49i	−0.877972	+	0.877972i
$213$	−9.87064e47	+	9.87064e47i	−0.00859377	+	0.00859377i
$214$	−5.32105e49	+	1.28461e50i	−0.418891	+	1.01129i
$215$	−2.03332e50	−	8.42230e49i	−1.44804	−	0.599797i
$216$	−2.25431e49	−	5.44238e49i	−0.145297	−	0.350779i
$217$			3.53665e49i			0.206399i
$218$	−2.13102e50	+	8.82699e49i	−1.12661	+	0.466657i
$219$	1.98686e50	+	1.98686e50i	0.951961	+	0.951961i
$220$	−7.24997e50			−3.14955
$221$	7.46637e49	−	8.50370e49i	0.294222	−	0.335100i
$222$	−4.27876e50			−1.53013
$223$	−6.32434e49	−	6.32434e49i	−0.205334	−	0.205334i	0.596947	−	0.802281i	$-0.296380\pi$
$223$	−6.32434e49	−	6.32434e49i	−0.205334	−	0.205334i	−0.802281	+	0.596947i	$0.796380\pi$
$224$	9.84690e49	−	4.07872e49i	0.290380	−	0.120279i
$225$		−	6.21159e49i		−	0.166448i
$226$	−3.42588e50	−	8.27080e50i	−0.834527	−	2.01473i
$227$	−1.91296e50	−	7.92373e49i	−0.423789	−	0.175539i	0.160588	−	0.987022i	$-0.448661\pi$
$227$	−1.91296e50	−	7.92373e49i	−0.423789	−	0.175539i	−0.584377	+	0.811482i	$0.698661\pi$
$228$	−5.19667e49	+	1.25459e50i	−0.104743	+	0.252872i
$229$	−1.67119e50	+	1.67119e50i	−0.306594	+	0.306594i	−0.843587	−	0.536993i	$-0.819560\pi$
$229$	−1.67119e50	+	1.67119e50i	−0.306594	+	0.306594i	0.536993	+	0.843587i	$0.319560\pi$
$230$	−1.22866e49	+	1.22866e49i	−0.0205251	+	0.0205251i
$231$	9.34364e49	−	2.25575e50i	0.142187	−	0.343269i
$232$	2.19544e50	+	9.09382e49i	0.304460	+	0.126111i
$233$	3.20850e50	+	7.74600e50i	0.405648	+	0.979322i	0.986269	+	0.165147i	$0.0528100\pi$
$233$	3.20850e50	+	7.74600e50i	0.405648	+	0.979322i	−0.580621	+	0.814174i	$0.697190\pi$
$234$			1.07684e50i			0.124168i
$235$	6.70566e50	−	2.77757e50i	0.705476	−	0.292218i
$236$	−4.60270e50	−	4.60270e50i	−0.441982	−	0.441982i
$237$	7.48323e50			0.656144
$238$	−3.93678e50	−	1.33893e50i	−0.315309	−	0.107239i
$239$	−7.02886e50			−0.514434			−0.257217	−	0.966354i	$-0.582806\pi$
$239$	−7.02886e50			−0.514434			−0.257217	+	0.966354i	$0.582806\pi$
$240$	−9.27080e50	−	9.27080e50i	−0.620262	−	0.620262i
$241$	7.81428e50	−	3.23678e50i	0.478104	−	0.198037i	−0.130599	−	0.991435i	$-0.541690\pi$
$241$	7.81428e50	−	3.23678e50i	0.478104	−	0.198037i	0.608703	+	0.793398i	$0.291690\pi$
$242$		−	6.47053e51i		−	3.62167i
$243$	2.74289e50	+	6.62192e50i	0.140499	+	0.339195i
$244$	−4.98797e50	−	2.06608e50i	−0.233907	−	0.0968873i
$245$	−1.16555e51	+	2.81388e51i	−0.500564	+	1.20847i
$246$	−2.91535e51	+	2.91535e51i	−1.14706	+	1.14706i
$247$	2.14442e50	−	2.14442e50i	0.0773261	−	0.0773261i
$248$	3.80727e50	−	9.19155e50i	0.125864	−	0.303863i
$249$	3.00035e51	+	1.24278e51i	0.909673	+	0.376799i
$250$	−2.99859e50	−	7.23923e50i	−0.0834078	−	0.201364i
$251$			1.04775e51i			0.267470i	0.991017	+	0.133735i	$0.0426970\pi$
$251$			1.04775e51i			0.267470i	−0.991017	+	0.133735i	$0.957303\pi$
$252$	2.02165e50	−	8.37397e49i	0.0473800	−	0.0196255i
$253$	−8.56871e49	−	8.56871e49i	−0.0184427	−	0.0184427i
$254$	−1.60252e51			−0.316867
$255$	4.42875e50	+	6.81826e51i	0.0804762	+	1.23897i
$256$	2.23443e51			0.373256
$257$	−5.41985e51	−	5.41985e51i	−0.832579	−	0.832579i	0.155290	−	0.987869i	$-0.450369\pi$
$257$	−5.41985e51	−	5.41985e51i	−0.832579	−	0.832579i	−0.987869	+	0.155290i	$0.950369\pi$
$258$	−1.00467e52	+	4.16148e51i	−1.41971	+	0.588064i
$259$		−	1.94178e51i		−	0.252497i
$260$	−2.42767e51	−	5.86091e51i	−0.290578	−	0.701517i
$261$	−1.44937e51	−	6.00347e50i	−0.159738	−	0.0661654i
$262$	−6.49133e51	+	1.56715e52i	−0.658955	+	1.59086i
$263$	5.75854e51	−	5.75854e51i	0.538597	−	0.538597i	−0.384520	−	0.923117i	$-0.625633\pi$
$263$	5.75854e51	−	5.75854e51i	0.538597	−	0.538597i	0.923117	+	0.384520i	$0.125633\pi$
$264$	−4.85672e51	+	4.85672e51i	−0.418657	+	0.418657i
$265$	−6.65087e51	+	1.60566e52i	−0.528558	+	1.27605i
$266$	−1.02954e51	−	4.26451e50i	−0.0754553	−	0.0312546i
$267$	−7.69960e51	−	1.85885e52i	−0.520566	−	1.25676i
$268$			6.81359e51i			0.425087i
$269$	−1.35450e52	+	5.61054e51i	−0.780021	+	0.323095i	−0.736924	−	0.675976i	$-0.763722\pi$
$269$	−1.35450e52	+	5.61054e51i	−0.780021	+	0.323095i	−0.0430969	+	0.999071i	$0.513722\pi$
$270$	−2.92939e52	−	2.92939e52i	−1.55760	−	1.55760i
$271$	2.78420e52			1.36729			0.683645	−	0.729815i	$-0.260394\pi$
$271$	2.78420e52			1.36729			0.683645	+	0.729815i	$0.260394\pi$
$272$	−1.17017e52	−	1.02743e52i	−0.530907	−	0.466144i
$273$	2.13644e51			0.0895763
$274$	3.65685e52	+	3.65685e52i	1.41733	+	1.41733i
$275$	−4.26346e52	+	1.76598e52i	−1.52795	+	0.632898i
$276$			4.74792e50i			0.0157383i
$277$	−1.28467e52	−	3.10146e52i	−0.393981	−	0.951155i	−0.989064	−	0.147490i	$-0.952881\pi$
$277$	−1.28467e52	−	3.10146e52i	−0.393981	−	0.951155i	0.595082	−	0.803665i	$-0.297119\pi$
$278$	6.52089e52	+	2.70104e52i	1.85073	+	0.766598i
$279$	−2.51344e51	+	6.06799e51i	−0.0660357	+	0.159424i
$280$	−3.16041e51	+	3.16041e51i	−0.0768857	+	0.0768857i
$281$	−9.40850e51	+	9.40850e51i	−0.211999	+	0.211999i	−0.805116	−	0.593117i	$-0.797897\pi$
$281$	−9.40850e51	+	9.40850e51i	−0.211999	+	0.211999i	0.593117	+	0.805116i	$0.297897\pi$
$282$	1.37241e52	−	3.31328e52i	0.286502	−	0.691676i
$283$	−1.36581e52	−	5.65736e51i	−0.264230	−	0.109447i	0.246636	−	0.969108i	$-0.420675\pi$
$283$	−1.36581e52	−	5.65736e51i	−0.264230	−	0.109447i	−0.510865	+	0.859661i	$0.670675\pi$
$284$	3.55680e50	+	8.58688e50i	0.00637845	+	0.0153989i
$285$			1.83108e52i			0.304469i
$286$	7.39110e52	−	3.06150e52i	1.13983	−	0.472133i
$287$	−1.32304e52	−	1.32304e52i	−0.189283	−	0.189283i
$288$	1.97934e52			0.262774
$289$	1.04982e52	+	8.04709e52i	0.129363	+	0.991597i
$290$	1.67119e53			1.91191
$291$	1.43924e52	+	1.43924e52i	0.152909	+	0.152909i
$292$	1.72845e53	−	7.15949e52i	1.70579	−	0.706563i
$293$			1.40169e53i			1.28528i	0.766168	+	0.642640i	$0.222161\pi$
$293$			1.40169e53i			1.28528i	−0.766168	+	0.642640i	$0.777839\pi$
$294$	5.75900e52	+	1.39035e53i	0.490772	+	1.18483i
$295$	−8.10896e52	−	3.35884e52i	−0.642380	−	0.266082i
$296$	−2.09036e52	+	5.04658e52i	−0.153975	+	0.371728i
$297$	2.04296e53	−	2.04296e53i	1.39957	−	1.39957i
$298$	3.04617e53	−	3.04617e53i	1.94135	−	1.94135i
$299$	4.05774e50	−	9.79624e50i	0.00240632	−	0.00580937i
$300$	1.67046e53	+	6.91927e52i	0.921995	+	0.381903i
$301$	−1.88856e52	−	4.55939e52i	−0.0970401	−	0.234275i
$302$			1.56851e53i			0.750477i
$303$	−2.71279e53	+	1.12367e53i	−1.20893	+	0.500753i
$304$	−2.95089e52	−	2.95089e52i	−0.122510	−	0.122510i
$305$	−7.27999e52			−0.281633
$306$	−5.80295e52	−	5.09508e52i	−0.209237	−	0.183713i
$307$	5.54981e51			0.0186553			0.00932767	−	0.999956i	$-0.497031\pi$
$307$	5.54981e51			0.0186553			0.00932767	+	0.999956i	$0.497031\pi$
$308$	−1.14953e53	−	1.14953e53i	−0.360314	−	0.360314i
$309$	3.61525e53	−	1.49749e53i	1.05689	−	0.437779i
$310$		−	6.99668e53i		−	1.90816i
$311$	−1.65818e53	−	4.00319e53i	−0.421971	−	1.01873i	−0.981765	−	0.190096i	$-0.939120\pi$
$311$	−1.65818e53	−	4.00319e53i	−0.421971	−	1.01873i	0.559795	−	0.828631i	$-0.310880\pi$
$312$	−5.55248e52	−	2.29991e52i	−0.131875	−	0.0546245i
$313$	9.55430e52	−	2.30661e53i	0.211834	−	0.511412i	−0.781871	−	0.623440i	$-0.785735\pi$
$313$	9.55430e52	−	2.30661e53i	0.211834	−	0.511412i	0.993705	+	0.112028i	$0.0357346\pi$
$314$	7.58128e53	−	7.58128e53i	1.56948	−	1.56948i
$315$	2.08641e52	−	2.08641e52i	0.0403387	−	0.0403387i
$316$	1.90673e53	−	4.60324e53i	0.344363	−	0.831365i
$317$	8.75250e53	+	3.62541e53i	1.47692	+	0.611762i	0.968426	−	0.249301i	$-0.0802009\pi$
$317$	8.75250e53	+	3.62541e53i	1.47692	+	0.611762i	0.508498	+	0.861063i	$0.330201\pi$
$318$	3.28621e53	+	7.93362e53i	0.518218	+	1.25109i
$319$			1.16549e54i			1.71794i
$320$	−1.29617e54	+	5.36893e53i	−1.78624	+	0.739884i
$321$	3.62260e53	+	3.62260e53i	0.466833	+	0.466833i
$322$	−3.89626e51			−0.00469620
$323$	1.40967e52	+	2.17025e53i	0.0158951	+	0.244712i
$324$	−9.13706e53			−0.964026
$325$	−2.85526e53	−	2.85526e53i	−0.281938	−	0.281938i
$326$	1.76367e54	−	7.30534e53i	1.63019	−	0.675246i
$327$			8.49867e53i			0.735485i
$328$	2.01423e53	+	4.86278e53i	0.163238	+	0.394091i
$329$	1.50363e53	+	6.22824e52i	0.114138	+	0.0472774i
$330$	−1.84848e54	+	4.46263e54i	−1.31452	+	3.17352i
$331$	−1.68375e54	+	1.68375e54i	−1.12195	+	1.12195i	−0.130505	+	0.991448i	$0.541660\pi$
$331$	−1.68375e54	+	1.68375e54i	−1.12195	+	1.12195i	−0.991448	+	0.130505i	$0.958340\pi$
$332$	1.52898e54	−	1.52898e54i	0.954843	−	0.954843i
$333$	1.38000e53	−	3.33160e53i	0.0807842	−	0.195030i
$334$	−2.41217e54	−	9.99154e53i	−1.32391	−	0.548382i
$335$	3.51591e53	+	8.48817e53i	0.180957	+	0.436868i
$336$		−	2.93990e53i		−	0.141918i
$337$	−3.53585e54	+	1.46460e54i	−1.60122	+	0.663247i	−0.991588	−	0.129436i	$-0.958683\pi$
$337$	−3.53585e54	+	1.46460e54i	−1.60122	+	0.663247i	−0.609633	+	0.792684i	$0.708683\pi$
$338$	−1.99415e54	−	1.99415e54i	−0.847322	−	0.847322i
$339$	−3.29845e54			−1.31527
$340$	4.30704e54	+	1.46486e54i	1.61206	+	0.548277i
$341$	4.87949e54			1.71457
$342$	−1.46336e53	−	1.46336e53i	−0.0482826	−	0.0482826i
$343$	−1.29485e54	+	5.36343e53i	−0.401231	+	0.166195i
$344$			1.38826e54i			0.404079i
$345$	2.45000e52	+	5.91482e52i	0.00669969	+	0.0161745i
$346$	−5.32109e54	−	2.20407e54i	−1.36730	−	0.566355i
$347$	−4.08337e53	+	9.85812e53i	−0.0986131	+	0.238073i	−0.965485	−	0.260457i	$-0.916127\pi$
$347$	−4.08337e53	+	9.85812e53i	−0.0986131	+	0.238073i	0.866872	+	0.498530i	$0.166127\pi$
$348$	3.22898e54	−	3.22898e54i	0.733013	−	0.733013i
$349$	4.80442e54	−	4.80442e54i	1.02540	−	1.02540i	0.0257342	−	0.999669i	$-0.491808\pi$
$349$	4.80442e54	−	4.80442e54i	1.02540	−	1.02540i	0.999669	−	0.0257342i	$-0.00819237\pi$
$350$	−5.67812e53	+	1.37082e54i	−0.113957	+	0.275117i
$351$	2.33562e54	+	9.67447e53i	0.440859	+	0.182610i
$352$	−5.62737e54	−	1.35857e55i	−0.999167	−	2.41220i
$353$			3.58577e53i			0.0598999i	0.999551	+	0.0299500i	$0.00953479\pi$
$353$			3.58577e53i			0.0598999i	−0.999551	+	0.0299500i	$0.990465\pi$
$354$	−4.00666e54	+	1.65961e54i	−0.629814	+	0.260878i
$355$	8.86191e52	+	8.86191e52i	0.0131104	+	0.0131104i
$356$	−1.33964e55			−1.86558
$357$	−1.01086e54	+	1.15130e54i	−0.132533	+	0.150946i
$358$	1.31711e55			1.62606
$359$	−7.25051e54	−	7.25051e54i	−0.843020	−	0.843020i	0.146230	−	0.989251i	$-0.453286\pi$
$359$	−7.25051e54	−	7.25051e54i	−0.843020	−	0.843020i	−0.989251	+	0.146230i	$0.953286\pi$
$360$	−7.66850e53	+	3.17640e53i	−0.0839860	+	0.0347881i
$361$		−	9.10898e54i		−	0.939863i
$362$	6.50221e54	+	1.56977e55i	0.632160	+	1.52617i
$363$	−2.20259e55	−	9.12341e54i	−2.01809	−	0.835920i
$364$	5.44364e53	−	1.31421e54i	0.0470121	−	0.113497i
$365$	1.78381e55	−	1.78381e55i	1.45229	−	1.45229i
$366$	−2.54351e54	+	2.54351e54i	−0.195249	+	0.195249i
$367$	−3.29878e52	+	7.96396e52i	−0.00238799	+	0.00576512i	−0.925069	−	0.379799i	$-0.875993\pi$
$367$	−3.29878e52	+	7.96396e52i	−0.00238799	+	0.00576512i	0.922681	+	0.385564i	$0.125993\pi$
$368$	−1.34804e53	−	5.58374e52i	−0.00920393	−	0.00381239i
$369$	−1.32973e54	−	3.21026e54i	−0.0856441	−	0.206763i
$370$			3.84149e55i			2.33434i
$371$	−3.60043e54	+	1.49135e54i	−0.206450	+	0.0855145i
$372$	−1.35186e55	−	1.35186e55i	−0.731575	−	0.731575i
$373$	−1.47538e55			−0.753638			−0.376819	−	0.926287i	$-0.622982\pi$
$373$	−1.47538e55			−0.753638			−0.376819	+	0.926287i	$0.622982\pi$
$374$	−1.84731e55	+	5.43154e55i	−0.890843	+	2.61929i
$375$	−2.88705e54			−0.131457
$376$	−3.23737e54	−	3.23737e54i	−0.139205	−	0.139205i
$377$	−9.42185e54	+	3.90266e54i	−0.382646	+	0.158497i
$378$		−	9.28949e54i		−	0.356384i
$379$	7.96671e54	+	1.92333e55i	0.288759	+	0.697127i	0.999983	−	0.00583918i	$-0.00185868\pi$
$379$	7.96671e54	+	1.92333e55i	0.288759	+	0.697127i	−0.711224	+	0.702966i	$0.751859\pi$
$380$	1.12637e55	+	4.66559e54i	0.385776	+	0.159794i
$381$	−2.25954e54	+	5.45501e54i	−0.0731363	+	0.176567i
$382$	5.05808e55	−	5.05808e55i	1.54748	−	1.54748i
$383$	3.90212e55	−	3.90212e55i	1.12857	−	1.12857i	0.138157	−	0.990410i	$-0.455882\pi$
$383$	3.90212e55	−	3.90212e55i	1.12857	−	1.12857i	0.990410	−	0.138157i	$-0.0441177\pi$
$384$	−8.70706e54	+	2.10207e55i	−0.238095	+	0.574812i
$385$	−2.02523e55	−	8.38877e54i	−0.523683	−	0.216916i
$386$	−1.30741e55	−	3.15636e55i	−0.319730	−	0.771897i
$387$		−	9.16491e54i		−	0.212003i
$388$	1.25205e55	−	5.18617e54i	0.273994	−	0.113492i
$389$	−2.16286e55	−	2.16286e55i	−0.447829	−	0.447829i	0.446804	−	0.894632i	$-0.352562\pi$
$389$	−2.16286e55	−	2.16286e55i	−0.447829	−	0.447829i	−0.894632	+	0.446804i	$0.852562\pi$
$390$	−4.22658e55			−0.828133
$391$	3.35916e53	+	6.82179e53i	0.00622917	+	0.0126502i
$392$	1.92120e55			0.337226
$393$	4.41933e55	+	4.41933e55i	0.734373	+	0.734373i
$394$	7.40137e55	−	3.06575e55i	1.16451	−	0.482356i
$395$		−	6.71848e55i		−	1.00100i
$396$	−1.15535e55	−	2.78926e55i	−0.163030	−	0.393588i
$397$	−3.58956e55	−	1.48684e55i	−0.479783	−	0.198733i	0.129666	−	0.991558i	$-0.458609\pi$
$397$	−3.58956e55	−	1.48684e55i	−0.479783	−	0.198733i	−0.609449	+	0.792825i	$0.708609\pi$
$398$	−5.26432e55	+	1.27092e56i	−0.666587	+	1.60928i
$399$	−2.90330e54	+	2.90330e54i	−0.0348317	+	0.0348317i
$400$	−3.92905e55	+	3.92905e55i	−0.446681	+	0.446681i
$401$	−5.14465e55	+	1.24203e56i	−0.554309	+	1.33822i	0.359906	+	0.932989i	$0.382809\pi$
$401$	−5.14465e55	+	1.24203e56i	−0.554309	+	1.33822i	−0.914214	+	0.405231i	$0.867191\pi$
$402$	4.19403e55	+	1.73722e55i	0.428323	+	0.177417i
$403$	1.63391e55	+	3.94460e55i	0.158186	+	0.381895i
$404$			1.95506e56i			1.79457i
$405$	−1.13827e56	+	4.71485e55i	−0.990743	+	0.410379i
$406$	2.64978e55	+	2.64978e55i	0.218726	+	0.218726i
$407$	−2.67906e56			−2.09750
$408$	3.86656e55	−	1.90396e55i	0.287165	−	0.141405i
$409$	−2.30924e56			−1.62712			−0.813558	−	0.581484i	$-0.802472\pi$
$409$	−2.30924e56			−1.62712			−0.813558	+	0.581484i	$0.802472\pi$
$410$	2.61741e56	+	2.61741e56i	1.74992	+	1.74992i
$411$	1.76042e56	−	7.29188e55i	1.11690	−	0.462637i
$412$		−	2.60545e56i		−	1.56889i
$413$	−7.53164e54	−	1.81830e55i	−0.0430490	−	0.103930i
$414$	−6.68499e53	−	2.76901e53i	−0.00362738	−	0.00150251i
$415$	1.11578e56	−	2.69373e56i	0.574835	−	1.38778i
$416$	9.09838e55	−	9.09838e55i	0.445100	−	0.445100i
$417$	1.83888e56	−	1.83888e56i	0.854336	−	0.854336i
$418$	−5.88371e55	+	1.42045e56i	−0.259634	+	0.626811i
$419$	2.76206e56	+	1.14408e56i	1.15780	+	0.479575i	0.877141	−	0.480234i	$-0.159448\pi$
$419$	2.76206e56	+	1.14408e56i	1.15780	+	0.479575i	0.280656	+	0.959809i	$0.409448\pi$
$420$	3.28678e55	+	7.93500e55i	0.130892	+	0.316000i
$421$		−	2.10356e56i		−	0.795957i	−0.917395	−	0.397979i	$-0.869712\pi$
$421$		−	2.10356e56i		−	0.795957i	0.917395	−	0.397979i	$-0.130288\pi$
$422$	1.91513e56	−	7.93275e55i	0.688623	−	0.285237i
$423$	2.13721e55	+	2.13721e55i	0.0730348	+	0.0730348i
$424$	1.09628e56			0.356085
$425$	2.88964e56	−	1.87695e55i	0.892241	−	0.0579549i
$426$	6.19241e54			0.0181783
$427$	−1.15429e55	−	1.15429e55i	−0.0322193	−	0.0322193i
$428$	3.15145e56	−	1.30537e56i	0.836506	−	0.346492i
$429$		−	2.94762e56i		−	0.744115i
$430$	3.73620e56	+	9.01998e56i	0.897136	+	2.16588i
$431$	−3.01492e56	−	1.24882e56i	−0.688675	−	0.285259i	0.0107728	−	0.999942i	$-0.496571\pi$
$431$	−3.01492e56	−	1.24882e56i	−0.688675	−	0.285259i	−0.699448	+	0.714683i	$0.746571\pi$
$432$	1.33128e56	−	3.21399e56i	0.289313	−	0.698464i
$433$	4.09288e56	−	4.09288e56i	0.846330	−	0.846330i	−0.143343	−	0.989673i	$-0.545785\pi$
$433$	4.09288e56	−	4.09288e56i	0.846330	−	0.846330i	0.989673	+	0.143343i	$0.0457853\pi$
$434$	1.10937e56	−	1.10937e56i	0.218297	−	0.218297i
$435$	2.35636e56	−	5.68876e56i	0.441289	−	1.06537i
$436$	5.22788e56	+	2.16546e56i	0.931893	+	0.386003i
$437$	7.79832e53	+	1.88268e54i	0.00132328	+	0.00319467i
$438$		−	1.24647e57i		−	2.01367i
$439$	6.61269e56	−	2.73907e56i	1.01716	−	0.421323i	0.189101	−	0.981958i	$-0.439443\pi$
$439$	6.61269e56	−	2.73907e56i	1.01716	−	0.421323i	0.828064	+	0.560634i	$0.189443\pi$
$440$	4.36038e56	+	4.36038e56i	0.638693	+	0.638693i
$441$	−1.26832e56			−0.176929
$442$	−5.00946e56	+	3.25386e55i	−0.665598	+	0.0432335i
$443$	4.98090e56			0.630416			0.315208	−	0.949023i	$-0.397926\pi$
$443$	4.98090e56			0.630416			0.315208	+	0.949023i	$0.397926\pi$
$444$	7.42234e56	+	7.42234e56i	0.894967	+	0.894967i
$445$	−1.66888e57	+	6.91274e56i	−1.91728	+	0.794164i
$446$			3.96761e56i			0.434340i
$447$	−6.07416e56	−	1.46643e57i	−0.633687	−	1.52985i
$448$	−2.90645e56	−	1.20389e56i	−0.288992	−	0.119705i
$449$	1.61351e56	−	3.89537e56i	0.152924	−	0.369192i	−0.828788	−	0.559563i	$-0.810969\pi$
$449$	1.61351e56	−	3.89537e56i	0.152924	−	0.369192i	0.981712	+	0.190371i	$0.0609691\pi$
$450$	−1.94844e56	+	1.94844e56i	−0.176043	+	0.176043i
$451$	−1.82538e57	+	1.82538e57i	−1.57238	+	1.57238i
$452$	−8.40445e56	+	2.02901e57i	−0.690292	+	1.66651i
$453$	5.33925e56	+	2.21159e56i	0.418185	+	0.173218i
$454$	3.51503e56	+	8.48603e56i	0.262560	+	0.633875i
$455$		−	1.91810e56i		−	0.136655i
$456$	1.06710e56	−	4.42006e55i	0.0725203	−	0.0300389i
$457$	5.57426e56	+	5.57426e56i	0.361401	+	0.361401i	0.864328	−	0.502928i	$-0.167744\pi$
$457$	5.57426e56	+	5.57426e56i	0.361401	+	0.361401i	−0.502928	+	0.864328i	$0.667744\pi$
$458$	1.04843e57			0.648533
$459$	−1.62645e57	+	8.00892e56i	−0.959995	+	0.472717i
$460$	4.26271e55			0.0240100
$461$	−1.33314e57	−	1.33314e57i	−0.716647	−	0.716647i	0.251270	−	0.967917i	$-0.419152\pi$
$461$	−1.33314e57	−	1.33314e57i	−0.716647	−	0.716647i	−0.967917	+	0.251270i	$0.919152\pi$
$462$	−1.00067e57	+	4.14491e56i	−0.513439	+	0.212673i
$463$			8.00907e56i			0.392275i	0.980576	+	0.196138i	$0.0628399\pi$
$463$			8.00907e56i			0.392275i	−0.980576	+	0.196138i	$0.937160\pi$
$464$	5.37034e56	+	1.29652e57i	0.251111	+	0.606235i
$465$	−2.38169e57	−	9.86527e56i	−1.06328	−	0.440424i
$466$	1.42332e57	−	3.43619e57i	0.606742	−	1.46480i
$467$	2.90079e56	−	2.90079e56i	0.118087	−	0.118087i	−0.645594	−	0.763681i	$-0.723390\pi$
$467$	2.90079e56	−	2.90079e56i	0.118087	−	0.118087i	0.763681	+	0.645594i	$0.223390\pi$
$468$	1.86798e56	−	1.86798e56i	0.0726250	−	0.0726250i
$469$	−7.88385e55	+	1.90333e56i	−0.0292767	+	0.0706802i
$470$	−2.97468e57	−	1.23215e57i	−1.05520	−	0.437080i
$471$	−1.51173e57	−	3.64965e57i	−0.512302	−	1.23681i
$472$			5.53645e56i			0.179258i
$473$	−6.29054e57	+	2.60563e57i	−1.94614	+	0.806117i
$474$	−2.34732e57	−	2.34732e57i	−0.693967	−	0.693967i
$475$	7.76029e56			0.219263
$476$	4.50647e56	+	9.15174e56i	0.121699	+	0.247146i
$477$	−7.23729e56			−0.186823
$478$	2.20480e57	+	2.20480e57i	0.544088	+	0.544088i
$479$	−6.11370e57	+	2.53238e57i	−1.44242	+	0.597469i	−0.960383	−	0.278684i	$-0.910102\pi$
$479$	−6.11370e57	+	2.53238e57i	−1.44242	+	0.597469i	−0.482034	+	0.876153i	$0.660102\pi$
$480$			7.76893e57i			1.75257i
$481$	−8.97090e56	−	2.16577e57i	−0.193516	−	0.467189i
$482$	−3.46648e57	−	1.43586e57i	−0.715117	−	0.296211i
$483$	−5.49371e54	+	1.32630e55i	−0.00108393	+	0.00261684i
$484$	−1.12244e58	+	1.12244e58i	−2.11830	+	2.11830i
$485$	1.29216e57	−	1.29216e57i	0.233274	−	0.233274i
$486$	1.21677e57	−	2.93754e57i	0.210149	−	0.507345i
$487$	1.45491e57	+	6.02643e56i	0.240416	+	0.0995835i	0.499638	−	0.866234i	$-0.333466\pi$
$487$	1.45491e57	+	6.02643e56i	0.240416	+	0.0995835i	−0.259222	+	0.965818i	$0.583466\pi$
$488$	1.75732e56	+	4.24255e56i	0.0277860	+	0.0670812i
$489$		−	7.03362e57i		−	1.06424i
$490$	1.24826e58	−	5.17046e57i	1.80755	−	0.748710i
$491$	−5.00617e56	−	5.00617e56i	−0.0693831	−	0.0693831i	0.671564	−	0.740947i	$-0.265623\pi$
$491$	−5.00617e56	−	5.00617e56i	−0.0693831	−	0.0693831i	−0.740947	+	0.671564i	$0.765623\pi$
$492$	1.01145e58			1.34182
$493$	2.35487e57	−	6.92388e57i	0.299060	−	0.879308i
$494$	−1.34532e57			−0.163567
$495$	−2.87859e57	−	2.87859e57i	−0.335096	−	0.335096i
$496$	5.42806e57	−	2.24838e57i	0.605047	−	0.250619i
$497$			2.81023e55i			0.00299971i
$498$	−5.51309e57	−	1.33098e58i	−0.563591	−	1.36063i
$499$	1.25036e58	+	5.17915e57i	1.22426	+	0.507104i	0.898760	−	0.438440i	$-0.144469\pi$
$499$	1.25036e58	+	5.17915e57i	1.22426	+	0.507104i	0.325496	+	0.945544i	$0.394469\pi$
$500$	−7.35621e56	+	1.77595e57i	−0.0689921	+	0.166562i
$501$	−6.80230e57	+	6.80230e57i	−0.611145	+	0.611145i
$502$	3.28658e57	−	3.28658e57i	0.282887	−	0.282887i
$503$	5.22831e57	−	1.26223e58i	0.431171	−	1.04094i	−0.547739	−	0.836649i	$-0.684511\pi$
$503$	5.22831e57	−	1.26223e58i	0.431171	−	1.04094i	0.978910	−	0.204290i	$-0.0654885\pi$
$504$	−1.71953e56	−	7.12254e55i	−0.0135879	−	0.00562831i
$505$	1.00884e58	+	2.43556e58i	0.763937	+	1.84431i
$506$			5.37563e56i			0.0390116i
$507$	−9.59988e57	+	3.97640e57i	−0.667720	+	0.276579i
$508$	2.77987e57	+	2.77987e57i	0.185334	+	0.185334i
$509$	−3.36011e57			−0.214744			−0.107372	−	0.994219i	$-0.534244\pi$
$509$	−3.36011e57			−0.214744			−0.107372	+	0.994219i	$0.534244\pi$
$510$	1.99982e58	−	2.27766e58i	1.22527	−	1.39550i
$511$	5.65672e57			0.332288
$512$	−1.56672e58	−	1.56672e58i	−0.882442	−	0.882442i
$513$	−4.48870e57	+	1.85928e57i	−0.242436	+	0.100420i
$514$			3.40018e58i			1.76114i
$515$	−1.34445e58	−	3.24579e58i	−0.667866	−	1.61237i
$516$	2.46468e58	+	1.02091e58i	1.17434	+	0.486426i
$517$	8.59305e57	−	2.07454e58i	0.392736	−	0.948148i
$518$	−6.09095e57	+	6.09095e57i	−0.267052	+	0.267052i
$519$	−1.50054e58	+	1.50054e58i	−0.631175	+	0.631175i
$520$	−2.06487e57	+	4.98504e57i	−0.0833338	+	0.201186i
$521$	2.37837e57	+	9.85155e56i	0.0921020	+	0.0381499i	0.428259	−	0.903656i	$-0.359127\pi$
$521$	2.37837e57	+	9.85155e56i	0.0921020	+	0.0381499i	−0.336157	+	0.941806i	$0.609127\pi$
$522$	2.66319e57	+	6.42950e57i	0.0989659	+	0.238925i
$523$			2.22828e58i			0.794664i	0.917675	+	0.397332i	$0.130064\pi$
$523$			2.22828e58i			0.794664i	−0.917675	+	0.397332i	$0.869936\pi$
$524$	3.84456e58	−	1.59247e58i	1.31590	−	0.545065i
$525$	3.86569e57	+	3.86569e57i	0.127000	+	0.127000i
$526$	−3.61266e58			−1.13929
$527$	−2.89879e58	−	9.85903e57i	−0.877584	−	0.298474i
$528$	−4.05615e58			−1.17892
$529$	−2.53335e58	−	2.53335e58i	−0.706966	−	0.706966i
$530$	7.12285e58	−	2.95038e58i	1.90863	−	0.790582i
$531$		−	3.65500e57i		−	0.0940491i
$532$	1.04618e57	+	2.52570e57i	0.0258527	+	0.0624141i
$533$	−2.08688e58	−	8.64416e57i	−0.495294	−	0.205158i
$534$	−3.41560e58	+	8.24600e58i	−0.778629	+	1.87978i
$535$	3.25239e58	−	3.25239e58i	0.712190	−	0.712190i
$536$	4.09793e57	−	4.09793e57i	0.0862029	−	0.0862029i
$537$	1.85712e58	−	4.48349e58i	0.375312	−	0.906084i
$538$	6.00869e58	+	2.48888e58i	1.16670	+	0.483264i
$539$	3.60588e58	+	8.70537e58i	0.672749	+	1.62416i
$540$			1.01632e59i			1.82206i
$541$	1.24341e57	−	5.15037e56i	0.0214226	−	0.00887355i	−0.371946	−	0.928254i	$-0.621309\pi$
$541$	1.24341e57	−	5.15037e56i	0.0214226	−	0.00887355i	0.393369	+	0.919381i	$0.371309\pi$
$542$	−8.73342e58	−	8.73342e58i	−1.44610	−	1.44610i
$543$	6.26036e58			0.996329
$544$	5.98096e57	+	9.20794e58i	0.0914944	+	1.40860i
$545$	7.63014e58			1.12204
$546$	−6.70154e57	−	6.70154e57i	−0.0947398	−	0.0947398i
$547$	−9.50674e58	+	3.93782e58i	−1.29212	+	0.535215i	−0.919618	−	0.392814i	$-0.871502\pi$
$547$	−9.50674e58	+	3.93782e58i	−1.29212	+	0.535215i	−0.372506	+	0.928030i	$0.621502\pi$
$548$		−	1.26870e59i		−	1.65797i
$549$	−1.16013e57	−	2.80081e57i	−0.0145781	−	0.0351947i
$550$	1.89131e59	+	7.83405e58i	2.28541	+	0.946647i
$551$	7.50028e57	−	1.81073e58i	0.0871602	−	0.210423i
$552$	2.85556e56	−	2.85556e56i	0.00319155	−	0.00319155i
$553$	1.06526e58	−	1.06526e58i	0.114516	−	0.114516i
$554$	−5.69888e58	+	1.37583e59i	−0.589291	+	1.42267i
$555$	1.30766e59	+	5.41649e58i	1.30075	+	0.538789i
$556$	−6.62626e58	−	1.59972e59i	−0.634104	−	1.53086i
$557$		−	1.26629e59i		−	1.16586i	−0.812523	−	0.582928i	$-0.801907\pi$
$557$		−	1.26629e59i		−	1.16586i	0.812523	−	0.582928i	$-0.198093\pi$
$558$	2.69181e58	−	1.11498e58i	0.238456	−	0.0987718i
$559$	−4.21281e58	−	4.21281e58i	−0.359102	−	0.359102i
$560$	−2.63945e58			−0.216507
$561$	1.58844e59	+	1.39467e59i	1.25392	+	1.10096i
$562$	5.90248e58			0.448439
$563$	−1.14762e59	−	1.14762e59i	−0.839205	−	0.839205i	0.149549	−	0.988754i	$-0.452218\pi$
$563$	−1.14762e59	−	1.14762e59i	−0.839205	−	0.839205i	−0.988754	+	0.149549i	$0.952218\pi$
$564$	−8.12823e58	+	3.36682e58i	−0.572131	+	0.236984i
$565$			2.96136e59i			2.00655i
$566$	2.50965e58	+	6.05883e58i	0.163704	+	0.395217i
$567$	−2.55237e58	−	1.05723e58i	−0.160291	−	0.0663946i
$568$	3.02526e56	−	7.30363e56i	0.00182925	−	0.00441621i
$569$	2.27172e58	−	2.27172e58i	0.132264	−	0.132264i	−0.637876	−	0.770139i	$-0.720187\pi$
$569$	2.27172e58	−	2.27172e58i	0.132264	−	0.132264i	0.770139	+	0.637876i	$0.220187\pi$
$570$	5.74370e58	−	5.74370e58i	0.322020	−	0.322020i
$571$	−2.25534e57	+	5.44487e57i	−0.0121769	+	0.0293975i	−0.929851	−	0.367936i	$-0.880064\pi$
$571$	−2.25534e57	+	5.44487e57i	−0.0121769	+	0.0293975i	0.917674	+	0.397334i	$0.130064\pi$
$572$	−1.81320e59	−	7.51054e58i	−0.942827	−	0.390532i
$573$	−1.00860e59	−	2.43497e59i	−0.505120	−	1.21947i
$574$			8.30017e58i			0.400388i
$575$	2.50675e57	−	1.03833e57i	0.0116480	−	0.00482478i
$576$	−4.13114e58	−	4.13114e58i	−0.184921	−	0.184921i
$577$	3.15892e59			1.36226			0.681128	−	0.732164i	$-0.261490\pi$
$577$	3.15892e59			1.36226			0.681128	+	0.732164i	$0.261490\pi$
$578$	2.19489e59	−	2.85350e59i	0.911937	−	1.18558i
$579$	−1.25878e59			−0.503918
$580$	−2.89899e59	−	2.89899e59i	−1.11827	−	1.11827i
$581$	6.04023e58	−	2.50194e58i	0.224526	−	0.0930017i
$582$		−	9.02915e58i		−	0.323447i
$583$	2.05760e59	+	4.96748e59i	0.710373	+	1.71499i
$584$	−1.47015e59	−	6.08955e58i	−0.489198	−	0.202633i
$585$	1.36317e58	−	3.29097e58i	0.0437218	−	0.105554i
$586$	4.39679e59	−	4.39679e59i	1.35937	−	1.35937i
$587$	9.80309e58	−	9.80309e58i	0.292176	−	0.292176i	−0.545764	−	0.837939i	$-0.683760\pi$
$587$	9.80309e58	−	9.80309e58i	0.292176	−	0.292176i	0.837939	+	0.545764i	$0.183760\pi$
$588$	1.41281e59	−	3.41083e59i	0.405950	−	0.980050i
$589$	−7.58089e58	−	3.14011e58i	−0.210011	−	0.0869893i
$590$	1.49001e59	+	3.59720e59i	0.397989	+	0.960829i
$591$		−	2.95172e59i		−	0.760228i
$592$	−2.98025e59	+	1.23446e59i	−0.740179	+	0.306592i
$593$	−2.39351e59	−	2.39351e59i	−0.573271	−	0.573271i	0.359770	−	0.933041i	$-0.382855\pi$
$593$	−2.39351e59	−	2.39351e59i	−0.573271	−	0.573271i	−0.933041	+	0.359770i	$0.882855\pi$
$594$	−1.28166e60			−2.96050
$595$	1.03365e59	+	9.07556e58i	0.230280	+	0.202189i
$596$	−1.05683e60			−2.27097
$597$	3.58398e59	+	3.58398e59i	0.742878	+	0.742878i
$598$	−4.34569e57	+	1.80004e57i	−0.00868927	+	0.00359921i
$599$		−	6.39874e59i		−	1.23429i	−0.786849	−	0.617145i	$-0.788289\pi$
$599$		−	6.39874e59i		−	1.23429i	0.786849	−	0.617145i	$-0.211711\pi$
$600$	−5.88523e58	−	1.42082e59i	−0.109525	−	0.264416i
$601$	−9.70514e59	−	4.02000e59i	−1.74261	−	0.721813i	−0.998557	−	0.0536939i	$-0.982900\pi$
$601$	−9.70514e59	−	4.02000e59i	−1.74261	−	0.721813i	−0.744054	−	0.668119i	$-0.767100\pi$
$602$	−8.37780e58	+	2.02258e59i	−0.145146	+	0.350414i
$603$	−2.70533e58	+	2.70533e58i	−0.0452271	+	0.0452271i
$604$	2.72088e59	−	2.72088e59i	0.438950	−	0.438950i
$605$	−8.19104e59	+	1.97749e60i	−1.27526	+	3.07875i
$606$	1.20341e60	+	4.98471e59i	1.80823	+	0.748994i
$607$	4.44379e59	+	1.07283e60i	0.644461	+	1.55587i	0.820600	+	0.571502i	$0.193639\pi$
$607$	4.44379e59	+	1.07283e60i	0.644461	+	1.55587i	−0.176139	+	0.984365i	$0.556361\pi$
$608$			2.47284e59i			0.346154i
$609$	1.27561e59	−	5.28375e58i	0.172364	−	0.0713954i
$610$	2.28357e59	+	2.28357e59i	0.297868	+	0.297868i
$611$	1.96481e59			0.247420
$612$	1.22794e58	+	1.89047e59i	0.0149287	+	0.229834i
$613$	−1.30407e60			−1.53074			−0.765371	−	0.643589i	$-0.777444\pi$
$613$	−1.30407e60			−1.53074			−0.765371	+	0.643589i	$0.777444\pi$
$614$	−1.74085e58	−	1.74085e58i	−0.0197307	−	0.0197307i
$615$	1.26003e60	−	5.21921e59i	1.37900	−	0.571202i
$616$			1.38274e59i			0.146135i
$617$	2.70405e59	+	6.52816e59i	0.275984	+	0.666285i	0.999717	−	0.0237957i	$-0.00757512\pi$
$617$	2.70405e59	+	6.52816e59i	0.275984	+	0.666285i	−0.723733	+	0.690080i	$0.757575\pi$
$618$	−1.60375e60	−	6.64296e59i	−1.58083	−	0.654801i
$619$	7.85841e59	−	1.89719e60i	0.748145	−	1.80618i	0.179187	−	0.983815i	$-0.442653\pi$
$619$	7.85841e59	−	1.89719e60i	0.748145	−	1.80618i	0.568958	−	0.822367i	$-0.307347\pi$
$620$	−1.21371e60	+	1.21371e60i	−1.11607	+	1.11607i
$621$	−1.20118e58	+	1.20118e58i	−0.0106694	+	0.0106694i
$622$	−7.35580e59	+	1.77585e60i	−0.631156	+	1.52375i
$623$	−3.74219e59	−	1.55007e59i	−0.310194	−	0.128486i
$624$	−1.35821e59	−	3.27901e59i	−0.108767	−	0.262587i
$625$			1.41483e60i			1.09467i
$626$	−1.02323e60	+	4.23836e59i	−0.764937	+	0.316847i
$627$	4.00566e59	+	4.00566e59i	0.289349	+	0.289349i
$628$	−2.63024e60			−1.83596
$629$	1.59157e60	+	5.41306e59i	1.07358	+	0.365135i
$630$	−1.30892e59			−0.0853280
$631$	8.07123e59	+	8.07123e59i	0.508521	+	0.508521i	0.914072	−	0.405551i	$-0.132921\pi$
$631$	8.07123e59	+	8.07123e59i	0.508521	+	0.508521i	−0.405551	+	0.914072i	$0.632921\pi$
$632$	−3.91532e59	+	1.62178e59i	−0.238424	+	0.0987585i
$633$		−	7.63768e59i		−	0.449554i
$634$	−1.60826e60	−	3.88268e60i	−0.915033	−	2.20909i
$635$	4.89753e59	+	2.02863e59i	0.269366	+	0.111575i
$636$	8.06182e59	−	1.94630e60i	0.428652	−	1.03486i
$637$	−5.83003e59	+	5.83003e59i	−0.299690	+	0.299690i
$638$	3.65587e60	−	3.65587e60i	1.81697	−	1.81697i
$639$	−1.99719e57	+	4.82164e57i	−0.000959733	+	0.00231700i
$640$	1.88725e60	+	7.81724e59i	0.876920	+	0.363232i
$641$	4.67919e59	+	1.12966e60i	0.210244	+	0.507573i	0.993461	−	0.114176i	$-0.0364226\pi$
$641$	4.67919e59	+	1.12966e60i	0.210244	+	0.507573i	−0.783217	+	0.621748i	$0.786423\pi$
$642$		−	2.27266e60i		−	0.987487i
$643$	−8.43263e59	+	3.49291e59i	−0.354346	+	0.146775i	−0.552754	−	0.833345i	$-0.686423\pi$
$643$	−8.43263e59	+	3.49291e59i	−0.354346	+	0.146775i	0.198408	+	0.980120i	$0.436423\pi$
$644$	6.75881e57	+	6.75881e57i	0.00274678	+	0.00274678i
$645$	3.59723e60			1.41395
$646$	6.36541e59	−	7.24977e59i	0.242007	−	0.275629i
$647$	−5.76578e59			−0.212039			−0.106020	−	0.994364i	$-0.533811\pi$
$647$	−5.76578e59			−0.212039			−0.106020	+	0.994364i	$0.533811\pi$
$648$	5.49534e59	+	5.49534e59i	0.195493	+	0.195493i
$649$	−2.50869e60	+	1.03913e60i	−0.863348	+	0.357610i
$650$			1.79127e60i			0.596380i
$651$	−2.21212e59	−	5.34054e59i	−0.0712554	−	0.172026i
$652$	−4.32667e60	−	1.79217e60i	−1.34844	−	0.558541i
$653$	−1.05821e60	+	2.55474e60i	−0.319108	+	0.770396i	0.680193	+	0.733033i	$0.261896\pi$
$653$	−1.05821e60	+	2.55474e60i	−0.319108	+	0.770396i	−0.999302	+	0.0373632i	$0.988104\pi$
$654$	2.66585e60	−	2.66585e60i	0.777881	−	0.777881i
$655$	3.96770e60	−	3.96770e60i	1.12034	−	1.12034i
$656$	−1.18950e60	+	2.87171e60i	−0.325036	+	0.784707i
$657$	9.70548e59	+	4.02014e59i	0.256662	+	0.106313i
$658$	−2.76290e59	−	6.67022e59i	−0.0707144	−	0.170720i
$659$		−	4.49374e60i		−	1.11320i	−0.830782	−	0.556598i	$-0.812106\pi$
$659$		−	4.49374e60i		−	1.11320i	0.830782	−	0.556598i	$-0.187894\pi$
$660$	1.09478e61	−	4.53475e60i	2.62503	−	1.08732i
$661$	−8.54033e59	−	8.54033e59i	−0.198218	−	0.198218i	0.601018	−	0.799236i	$-0.294762\pi$
$661$	−8.54033e59	−	8.54033e59i	−0.198218	−	0.198218i	−0.799236	+	0.601018i	$0.794762\pi$
$662$	1.05631e61			2.37325
$663$	−5.95569e59	+	1.75111e60i	−0.129536	+	0.380867i
$664$	−1.83916e60			−0.387262
$665$	2.60660e59	+	2.60660e59i	0.0531385	+	0.0531385i
$666$	−1.47793e60	+	6.12177e59i	−0.291714	+	0.120832i
$667$		−	6.85262e58i		−	0.0130964i
$668$	2.45115e60	+	5.91760e60i	0.453603	+	1.09510i
$669$	1.35059e60	+	5.59431e59i	0.242025	+	0.100250i
$670$	1.55969e60	−	3.76542e60i	0.270663	−	0.653439i
$671$	−1.59257e60	+	1.59257e60i	−0.267647	+	0.267647i
$672$	−1.23182e60	+	1.23182e60i	−0.200496	+	0.200496i
$673$	−1.86900e60	+	4.51217e60i	−0.294636	+	0.711314i	0.705361	+	0.708848i	$0.250785\pi$
$673$	−1.86900e60	+	4.51217e60i	−0.294636	+	0.711314i	−0.999997	+	0.00246593i	$0.999215\pi$
$674$	1.56853e61	+	6.49707e60i	2.39500	+	0.992042i
$675$	2.47560e60	+	5.97662e60i	0.366141	+	0.883943i
$676$			6.91847e60i			0.991188i
$677$	−2.01489e60	+	8.34596e59i	−0.279638	+	0.115830i	−0.518095	−	0.855323i	$-0.673358\pi$
$677$	−2.01489e60	+	8.34596e59i	−0.279638	+	0.115830i	0.238457	+	0.971153i	$0.423358\pi$
$678$	1.03465e61	+	1.03465e61i	1.39109	+	1.39109i
$679$	4.09760e59			0.0533740
$680$	−1.70938e60	−	3.47142e60i	−0.215724	−	0.438092i
$681$	3.38429e60			0.413813
$682$	−1.53059e61	−	1.53059e61i	−1.81340	−	1.81340i
$683$	−1.29177e60	+	5.35070e59i	−0.148300	+	0.0614279i	−0.455599	−	0.890185i	$-0.650575\pi$
$683$	−1.29177e60	+	5.35070e59i	−0.148300	+	0.0614279i	0.307299	+	0.951613i	$0.400575\pi$
$684$			5.07697e59i			0.0564804i
$685$	−6.54669e60	−	1.58051e61i	−0.705788	−	1.70392i
$686$	5.74404e60	+	2.37926e60i	0.600135	+	0.248584i
$687$	1.47828e60	−	3.56889e60i	0.149688	−	0.361379i
$688$	−5.79713e60	+	5.79713e60i	−0.568934	+	0.568934i
$689$	−3.32674e60	+	3.32674e60i	−0.316451	+	0.316451i
$690$	1.08684e59	−	2.62386e59i	0.0100210	−	0.0241927i
$691$	−7.46406e60	−	3.09171e60i	−0.667109	−	0.276326i	0.0233175	−	0.999728i	$-0.492577\pi$
$691$	−7.46406e60	−	3.09171e60i	−0.667109	−	0.276326i	−0.690427	+	0.723402i	$0.742577\pi$
$692$	5.40707e60	+	1.30538e61i	0.468469	+	1.13098i
$693$		−	9.12842e59i		−	0.0766710i
$694$	4.37314e60	−	1.81141e60i	0.356094	−	0.147499i
$695$	−1.65096e61	−	1.65096e61i	−1.30336	−	1.30336i
$696$	−3.88404e60			−0.297293
$697$	1.45324e61	−	7.15598e60i	1.07853	−	0.531086i
$698$	−3.01409e61			−2.16902
$699$	−9.69001e60	−	9.69001e60i	−0.676184	−	0.676184i
$700$	3.36293e60	−	1.39297e60i	0.227567	−	0.0942614i
$701$		−	1.76851e61i		−	1.16057i	−0.814414	−	0.580285i	$-0.802941\pi$
$701$		−	1.76851e61i		−	1.16057i	0.814414	−	0.580285i	$-0.197059\pi$
$702$	−4.29167e60	−	1.03610e61i	−0.273136	−	0.659408i
$703$	4.16226e60	+	1.72406e60i	0.256915	+	0.106418i
$704$	−1.66100e61	+	4.01001e61i	−0.994391	+	2.40067i
$705$	−8.38857e60	+	8.38857e60i	−0.487104	+	0.487104i
$706$	1.12478e60	−	1.12478e60i	0.0633528	−	0.0633528i
$707$	−2.26215e60	+	5.46132e60i	−0.123596	+	0.298387i
$708$	9.82924e60	+	4.07141e60i	0.520961	+	0.215789i
$709$	1.37853e61	+	3.32806e61i	0.708796	+	1.71119i	0.702988	+	0.711202i	$0.251849\pi$
$709$	1.37853e61	+	3.32806e61i	0.708796	+	1.71119i	0.00580851	+	0.999983i	$0.498151\pi$
$710$		−	5.55957e59i		−	0.0277324i
$711$	2.58478e60	−	1.07065e60i	0.125091	−	0.0518145i
$712$	8.05706e60	+	8.05706e60i	0.378318	+	0.378318i
$713$	−2.86895e59			−0.0130707
$714$	6.78223e60	−	4.40535e59i	0.299820	−	0.0194746i
$715$	−2.64639e61			−1.13520
$716$	−2.28478e61	−	2.28478e61i	−0.951076	−	0.951076i
$717$	1.06140e61	−	4.39644e60i	0.428761	−	0.177599i
$718$			4.54865e61i			1.78323i
$719$	−1.45791e61	−	3.51971e61i	−0.554703	−	1.33917i	−0.913911	−	0.405914i	$-0.866953\pi$
$719$	−1.45791e61	−	3.51971e61i	−0.554703	−	1.33917i	0.359208	−	0.933257i	$-0.383047\pi$
$720$	−4.52862e60	−	1.87582e60i	−0.167231	−	0.0692695i
$721$	3.01470e60	−	7.27814e60i	0.108053	−	0.260863i
$722$	−2.85729e61	+	2.85729e61i	−0.994041	+	0.994041i
$723$	−9.77543e60	+	9.77543e60i	−0.330113	+	0.330113i
$724$	1.59514e61	−	3.85101e61i	0.522901	−	1.26239i
$725$	−2.41095e61	−	9.98649e60i	−0.767222	−	0.317794i
$726$	4.04722e61	+	9.77084e61i	1.25031	+	3.01852i
$727$		−	2.60191e61i		−	0.780374i	−0.920736	−	0.390187i	$-0.872410\pi$
$727$		−	2.60191e61i		−	0.780374i	0.920736	−	0.390187i	$-0.127590\pi$
$728$	−1.11781e60	+	4.63013e59i	−0.0325495	+	0.0134824i
$729$	−2.77719e61	−	2.77719e61i	−0.785169	−	0.785169i
$730$	−1.11909e62			−3.07201
$731$	4.26353e61	−	2.76935e60i	1.13644	−	0.0738166i
$732$	8.82440e60			0.228401
$733$	−5.11429e60	−	5.11429e60i	−0.128543	−	0.128543i	0.639908	−	0.768451i	$-0.278972\pi$
$733$	−5.11429e60	−	5.11429e60i	−0.128543	−	0.128543i	−0.768451	+	0.639908i	$0.778972\pi$
$734$	3.53288e59	−	1.46336e59i	0.00862309	−	0.00357180i
$735$		−	4.97814e61i		−	1.18002i
$736$	3.30868e59	+	7.98786e59i	0.00761696	+	0.0183890i
$737$	2.62600e61	+	1.08773e61i	0.587144	+	0.243203i
$738$	−5.89880e60	+	1.42410e61i	−0.128101	+	0.309263i
$739$	3.74738e61	−	3.74738e61i	0.790446	−	0.790446i	−0.191120	−	0.981567i	$-0.561212\pi$
$739$	3.74738e61	−	3.74738e61i	0.790446	−	0.790446i	0.981567	+	0.191120i	$0.0612120\pi$
$740$	6.66381e61	−	6.66381e61i	1.36534	−	1.36534i
$741$	−1.89689e60	+	4.57950e60i	−0.0377529	+	0.0911437i
$742$	1.59718e61	+	6.61573e60i	0.308794	+	0.127907i
$743$	−3.35782e61	−	8.10649e61i	−0.630664	−	1.52256i	−0.838790	−	0.544455i	$-0.816736\pi$
$743$	−3.35782e61	−	8.10649e61i	−0.630664	−	1.52256i	0.208126	−	0.978102i	$-0.433264\pi$
$744$			1.62611e61i			0.296710i
$745$	−1.31657e62	+	5.45341e61i	−2.33391	+	0.966737i
$746$	4.62793e61	+	4.62793e61i	0.797080	+	0.797080i
$747$	1.21416e61			0.203180
$748$	1.26266e62	−	6.21753e61i	2.05306	−	1.01096i
$749$	1.03138e61			0.162951
$750$	9.05606e60	+	9.05606e60i	0.139034	+	0.139034i
$751$	9.87000e61	−	4.08829e61i	1.47251	−	0.609934i	0.505080	−	0.863072i	$-0.331463\pi$
$751$	9.87000e61	−	4.08829e61i	1.47251	−	0.609934i	0.967430	+	0.253138i	$0.0814628\pi$
$752$		−	2.70373e61i		−	0.391994i
$753$	−6.55354e60	−	1.58216e61i	−0.0923388	−	0.222925i
$754$	4.17961e61	+	1.73125e61i	0.572336	+	0.237069i
$755$	1.98558e61	−	4.79360e61i	0.264257	−	0.637973i
$756$	−1.61144e61	+	1.61144e61i	−0.208447	+	0.208447i
$757$	−2.88787e61	+	2.88787e61i	−0.363091	+	0.363091i	−0.864950	−	0.501858i	$-0.832650\pi$
$757$	−2.88787e61	+	2.88787e61i	−0.363091	+	0.363091i	0.501858	+	0.864950i	$0.332650\pi$
$758$	3.53410e61	−	8.53206e61i	0.431907	−	1.04272i
$759$	1.82988e60	+	7.57961e59i	0.0217383	+	0.00900428i
$760$	−3.96835e60	−	9.58045e60i	−0.0458266	−	0.110635i
$761$		−	5.35660e61i		−	0.601339i	−0.953728	−	0.300670i	$-0.902790\pi$
$761$		−	5.35660e61i		−	0.601339i	0.953728	−	0.300670i	$-0.0972101\pi$
$762$	2.41989e61	−	1.00235e61i	0.264097	−	0.109392i
$763$	1.20981e61	+	1.20981e61i	0.128363	+	0.128363i
$764$	−1.75484e62			−1.81022
$765$	1.12848e61	+	2.29173e61i	0.113181	+	0.229849i
$766$	−2.44802e62			−2.38724
$767$	−1.68008e61	−	1.68008e61i	−0.159305	−	0.159305i
$768$	−3.37411e61	+	1.39760e61i	−0.311095	+	0.128860i
$769$			1.76219e62i			1.57993i	0.613153	+	0.789964i	$0.289901\pi$
$769$			1.76219e62i			1.57993i	−0.613153	+	0.789964i	$0.710099\pi$
$770$	3.72132e61	+	8.98407e61i	0.324449	+	0.783290i
$771$	1.15743e62	+	4.79423e61i	0.981354	+	0.406490i
$772$	−3.20736e61	+	7.74326e61i	−0.264470	+	0.638487i
$773$	4.03118e61	−	4.03118e61i	0.323276	−	0.323276i	−0.526747	−	0.850022i	$-0.676588\pi$
$773$	4.03118e61	−	4.03118e61i	0.323276	−	0.323276i	0.850022	+	0.526747i	$0.176588\pi$
$774$	−2.87483e61	+	2.87483e61i	−0.224224	+	0.224224i
$775$	−4.18100e61	+	1.00938e62i	−0.317171	+	0.765718i
$776$	−1.06494e61	−	4.41114e60i	−0.0785777	−	0.0325479i
$777$	1.21456e61	+	2.93220e61i	0.0871697	+	0.210446i
$778$			1.35688e62i			0.947286i
$779$	4.01066e61	−	1.66127e61i	0.272371	−	0.112820i
$780$	7.33182e61	+	7.33182e61i	0.484371	+	0.484371i
$781$	3.87725e60			0.0249188
$782$	1.08615e60	−	3.19354e60i	0.00679117	−	0.0199677i
$783$	1.63380e62			0.993853
$784$	8.02255e61	+	8.02255e61i	0.474807	+	0.474807i
$785$	−3.27667e62	+	1.35724e62i	−1.88684	+	0.781555i
$786$		−	2.77250e62i		−	1.55341i
$787$	1.73309e61	+	4.18406e61i	0.0944855	+	0.228108i	0.964055	−	0.265702i	$-0.0856037\pi$
$787$	1.73309e61	+	4.18406e61i	0.0944855	+	0.228108i	−0.869570	+	0.493810i	$0.835604\pi$
$788$	−1.81572e62	−	7.52097e61i	−0.963244	−	0.398989i
$789$	−5.09383e61	+	1.22976e62i	−0.262959	+	0.634840i
$790$	−2.10744e62	+	2.10744e62i	−1.05870	+	1.05870i
$791$	−4.69544e61	+	4.69544e61i	−0.229553	+	0.229553i
$792$	−9.82690e60	+	2.37242e61i	−0.0467547	+	0.112876i
$793$	−1.82071e61	−	7.54164e60i	−0.0843078	−	0.0349214i
$794$	6.59575e61	+	1.59236e62i	0.297251	+	0.717628i
$795$		−	2.84064e62i		−	1.24601i
$796$	3.11785e62	−	1.29146e62i	1.33114	−	0.551378i
$797$	1.11174e62	+	1.11174e62i	0.462008	+	0.462008i	0.899313	−	0.437305i	$-0.144067\pi$
$797$	1.11174e62	+	1.11174e62i	0.462008	+	0.462008i	−0.437305	+	0.899313i	$0.644067\pi$
$798$	1.82141e61			0.0736791
$799$	−9.29656e61	+	1.05882e62i	−0.366072	+	0.416932i
$800$	3.29255e62			1.26211
$801$	−5.31903e61	−	5.31903e61i	−0.198488	−	0.198488i
$802$	5.50973e62	−	2.28221e62i	2.00162	−	0.829098i
$803$		−	7.80452e62i		−	2.76034i
$804$	−4.26180e61	−	1.02889e62i	−0.146753	−	0.354294i
$805$	1.19076e60	+	4.93228e59i	0.00399220	+	0.00165362i
$806$	7.24814e61	−	1.74986e62i	0.236605	−	0.571214i
$807$	1.69444e62	−	1.69444e62i	0.538575	−	0.538575i
$808$	1.17584e62	−	1.17584e62i	0.363919	−	0.363919i
$809$	8.85812e61	−	2.13854e62i	0.266961	−	0.644501i	−0.732376	−	0.680900i	$-0.761589\pi$
$809$	8.85812e61	−	2.13854e62i	0.266961	−	0.644501i	0.999337	+	0.0363989i	$0.0115887\pi$
$810$	5.04944e62	+	2.09155e62i	1.48189	+	0.613818i
$811$	4.79768e61	+	1.15826e62i	0.137114	+	0.331023i	0.977490	−	0.210981i	$-0.0676658\pi$
$811$	4.79768e61	+	1.15826e62i	0.137114	+	0.331023i	−0.840376	+	0.542004i	$0.817666\pi$
$812$		−	9.19310e61i		−	0.255863i
$813$	−4.20429e62	+	1.74147e62i	−1.13958	+	0.472031i
$814$	8.40363e62	+	8.40363e62i	2.21841	+	2.21841i
$815$	−6.31482e62			−1.62357
$816$	2.40966e62	+	8.19547e61i	0.603417	+	0.205227i
$817$	1.14500e62			0.279273
$818$	7.24359e62	+	7.24359e62i	1.72091	+	1.72091i
$819$	7.37946e60	−	3.05667e60i	0.0170774	−	0.00707367i
$820$		−	9.08081e62i		−	2.04704i
$821$	−1.92840e62	−	4.65556e62i	−0.423466	−	1.02234i	−0.981317	−	0.192397i	$-0.938374\pi$
$821$	−1.92840e62	−	4.65556e62i	−0.423466	−	1.02234i	0.557851	−	0.829941i	$-0.311626\pi$
$822$	−7.80934e62	−	3.23473e62i	−1.67059	−	0.691982i
$823$	4.14498e60	−	1.00069e61i	0.00863825	−	0.0208546i	−0.919502	−	0.393086i	$-0.871407\pi$
$823$	4.14498e60	−	1.00069e61i	0.00863825	−	0.0208546i	0.928140	+	0.372232i	$0.121407\pi$
$824$	−1.56701e62	+	1.56701e62i	−0.318153	+	0.318153i
$825$	5.33346e62	−	5.33346e62i	1.05499	−	1.05499i
$826$	−3.34110e61	+	8.06612e61i	−0.0643899	+	0.155451i
$827$	7.90907e62	+	3.27604e62i	1.48510	+	0.615150i	0.970245	−	0.242125i	$-0.0778444\pi$
$827$	7.90907e62	+	3.27604e62i	1.48510	+	0.615150i	0.514859	+	0.857275i	$0.327844\pi$
$828$	6.79301e59	+	1.63998e60i	0.00124283	+	0.00300045i
$829$			8.91018e62i			1.58842i	0.607647	+	0.794208i	$0.292114\pi$
$829$			8.91018e62i			1.58842i	−0.607647	+	0.794208i	$0.707886\pi$
$830$	−1.19496e63	+	4.94968e62i	−2.07574	+	0.859801i
$831$	3.87983e62	+	3.87983e62i	0.656736	+	0.656736i
$832$	−3.79790e62			−0.626458
$833$	−3.83245e61	−	5.90023e62i	−0.0616041	−	0.948422i
$834$	−1.15363e63			−1.80717
$835$	6.10714e62	+	6.10714e62i	0.932349	+	0.932349i
$836$	3.48469e62	−	1.44341e62i	0.518477	−	0.214760i
$837$		−	6.84017e62i		−	0.991904i
$838$	−5.07525e62	−	1.22527e63i	−0.717317	−	1.73176i
$839$	−3.03232e62	−	1.25603e62i	−0.417727	−	0.173028i	0.163912	−	0.986475i	$-0.447589\pi$
$839$	−3.03232e62	−	1.25603e62i	−0.417727	−	0.173028i	−0.581640	+	0.813447i	$0.697589\pi$
$840$	2.79560e61	−	6.74917e61i	0.0375379	−	0.0906245i
$841$	7.42207e61	−	7.42207e61i	0.0971429	−	0.0971429i
$842$	−6.59840e62	+	6.59840e62i	−0.841839	+	0.841839i
$843$	8.32247e61	−	2.00922e62i	0.103504	−	0.249882i
$844$	−4.69826e62	−	1.94608e62i	−0.569605	−	0.235938i
$845$	3.57003e62	+	8.61882e62i	0.421942	+	1.01866i
$846$		−	1.34079e62i		−	0.154490i
$847$	−4.43419e62	+	1.83670e62i	−0.498106	+	0.206322i
$848$	4.57784e62	+	4.57784e62i	0.501361	+	0.501361i
$849$	2.41630e62			0.258010
$850$	−9.65294e62	−	8.47542e62i	−1.00497	−	0.882377i
$851$	1.57519e61			0.0159899
$852$	−1.07419e61	−	1.07419e61i	−0.0106324	−	0.0106324i
$853$	1.18104e63	−	4.89202e62i	1.13988	−	0.472154i	0.268752	−	0.963209i	$-0.413389\pi$
$853$	1.18104e63	−	4.89202e62i	1.13988	−	0.472154i	0.871129	+	0.491055i	$0.163389\pi$
$854$			7.24152e61i			0.0681531i
$855$	2.61979e61	+	6.32473e61i	0.0240433	+	0.0580457i
$856$	−2.68049e62	−	1.11029e62i	−0.239899	−	0.0993693i
$857$	1.62625e62	−	3.92612e62i	0.141938	−	0.342670i	−0.836884	−	0.547380i	$-0.815625\pi$
$857$	1.62625e62	−	3.92612e62i	0.141938	−	0.342670i	0.978823	+	0.204710i	$0.0656252\pi$
$858$	−9.24604e62	+	9.24604e62i	−0.787008	+	0.787008i
$859$	−4.02626e62	+	4.02626e62i	−0.334233	+	0.334233i	−0.854191	−	0.519959i	$-0.825947\pi$
$859$	−4.02626e62	+	4.02626e62i	−0.334233	+	0.334233i	0.519959	+	0.854191i	$0.325947\pi$
$860$	9.16574e62	−	2.21281e63i	0.742080	−	1.79154i
$861$	2.82540e62	+	1.17032e62i	0.223107	+	0.0924137i
$862$	5.53987e62	+	1.33744e63i	0.426671	+	1.03008i
$863$		−	1.17002e63i		−	0.878942i	−0.898257	−	0.439471i	$-0.855166\pi$
$863$		−	1.17002e63i		−	0.878942i	0.898257	−	0.439471i	$-0.144834\pi$
$864$	−1.90447e63	+	7.88857e62i	−1.39550	+	0.578033i
$865$	1.34719e63	+	1.34719e63i	0.962905	+	0.962905i
$866$	−2.56770e63			−1.79023
$867$	−6.61861e62	−	1.14949e63i	−0.450149	−	0.781798i
$868$	−3.84883e62			−0.255361
$869$	−1.46973e63	−	1.46973e63i	−0.951289	−	0.951289i
$870$	−2.52358e63	+	1.04530e63i	−1.59350	+	0.660051i
$871$			2.48710e62i			0.153216i
$872$	−1.84185e62	−	4.44661e62i	−0.110700	−	0.267254i
$873$	7.03043e61	+	2.91210e61i	0.0412264	+	0.0170765i
$874$	3.45940e60	−	8.35172e60i	0.00197927	−	0.00477837i
$875$	−4.10981e61	+	4.10981e61i	−0.0229429	+	0.0229429i
$876$	−2.16224e63	+	2.16224e63i	−1.17779	+	1.17779i
$877$	−5.35979e62	+	1.29397e63i	−0.284876	+	0.687752i	−0.999936	−	0.0113112i	$-0.996399\pi$
$877$	−5.35979e62	+	1.29397e63i	−0.284876	+	0.687752i	0.715060	+	0.699063i	$0.246399\pi$
$878$	−2.93344e63	−	1.21507e63i	−1.52141	−	0.630188i
$879$	−8.76734e62	−	2.11662e63i	−0.443718	−	1.07123i
$880$			3.64163e63i			1.79853i
$881$	1.37444e63	−	5.69312e62i	0.662436	−	0.274390i	−0.0260273	−	0.999661i	$-0.508286\pi$
$881$	1.37444e63	−	5.69312e62i	0.662436	−	0.274390i	0.688463	+	0.725271i	$0.258286\pi$
$882$	3.97843e62	+	3.97843e62i	0.187127	+	0.187127i
$883$	2.01091e63			0.923075			0.461538	−	0.887121i	$-0.347298\pi$
$883$	2.01091e63			0.923075			0.461538	+	0.887121i	$0.347298\pi$
$884$	9.25432e62	+	8.12543e62i	0.414592	+	0.364018i
$885$	1.43459e63			0.627259
$886$	−1.56240e63	−	1.56240e63i	−0.666756	−	0.666756i
$887$	−9.10709e62	+	3.77228e62i	−0.379334	+	0.157125i	−0.564199	−	0.825639i	$-0.690815\pi$
$887$	−9.10709e62	+	3.77228e62i	−0.379334	+	0.157125i	0.184865	+	0.982764i	$0.440815\pi$
$888$		−	8.92810e62i		−	0.362978i
$889$	4.54885e61	+	1.09819e62i	0.0180515	+	0.0435802i
$890$	7.40330e63	+	3.06655e63i	2.86774	+	1.18786i
$891$	−1.45865e63	+	3.52148e63i	−0.551543	+	1.33154i
$892$	6.88259e62	−	6.88259e62i	0.254043	−	0.254043i
$893$	−2.67007e62	+	2.67007e62i	−0.0962093	+	0.0962093i
$894$	−2.69455e63	+	6.50521e63i	−0.947827	+	2.28826i
$895$	−4.02530e63	−	1.66733e63i	−1.38230	−	0.572568i
$896$	1.75289e62	+	4.23184e62i	0.0587667	+	0.141875i
$897$			1.73309e61i			0.00567262i
$898$	−1.72801e63	+	7.15767e62i	−0.552213	+	0.228734i
$899$	1.95112e63	+	1.95112e63i	0.608768	+	0.608768i
$900$	6.75988e62			0.205933
$901$	−2.18688e62	−	3.36680e63i	−0.0650493	−	1.00146i
$902$	1.14517e64			3.32604
$903$	5.70365e62	+	5.70365e62i	0.161758	+	0.161758i
$904$	1.72579e63	−	7.14846e62i	0.477933	−	0.197966i
$905$		−	5.62058e63i		−	1.51998i
$906$	−9.81078e62	−	2.36853e63i	−0.259088	−	0.625494i
$907$	−3.31723e62	−	1.37404e62i	−0.0855498	−	0.0354359i	0.339498	−	0.940607i	$-0.389743\pi$
$907$	−3.31723e62	−	1.37404e62i	−0.0855498	−	0.0354359i	−0.425048	+	0.905171i	$0.639743\pi$
$908$	8.62316e62	−	2.08181e63i	0.217180	−	0.524320i
$909$	−7.76255e62	+	7.76255e62i	−0.190933	+	0.190933i
$910$	−6.01667e62	+	6.01667e62i	−0.144533	+	0.144533i
$911$	2.21398e63	−	5.34502e63i	0.519432	−	1.25402i	−0.418821	−	0.908069i	$-0.637557\pi$
$911$	2.21398e63	−	5.34502e63i	0.519432	−	1.25402i	0.938253	−	0.345950i	$-0.112443\pi$
$912$	6.30173e62	+	2.61026e62i	0.144401	+	0.0598129i
$913$	−3.45191e63	−	8.33364e63i	−0.772569	−	1.86515i
$914$		−	3.49705e63i		−	0.764466i
$915$	1.09932e63	−	4.55352e62i	0.234730	−	0.0972286i
$916$	−1.81871e63	−	1.81871e63i	−0.379324	−	0.379324i
$917$	1.25821e63			0.256338
$918$	7.61405e63	+	2.58961e63i	1.51530	+	0.515366i
$919$	2.30426e63			0.447969			0.223985	−	0.974593i	$-0.428093\pi$
$919$	2.30426e63			0.447969			0.223985	+	0.974593i	$0.428093\pi$
$920$	−2.56374e61	−	2.56374e61i	−0.00486895	−	0.00486895i
$921$	−8.38051e61	+	3.47132e61i	−0.0155485	+	0.00644040i
$922$			8.36352e63i			1.51591i
$923$	1.29831e61	+	3.13439e61i	0.00229901	+	0.00555030i
$924$	2.45487e63	+	1.01684e63i	0.424699	+	0.175916i
$925$	2.29556e63	−	5.54197e63i	0.388008	−	0.936735i
$926$	2.51227e63	−	2.51227e63i	0.414887	−	0.414887i
$927$	1.03449e63	−	1.03449e63i	0.166922	−	0.166922i
$928$	3.18223e63	−	7.68258e63i	0.501707	−	1.21123i
$929$	−9.56658e63	−	3.96261e63i	−1.47373	−	0.610440i	−0.506026	−	0.862518i	$-0.668886\pi$
$929$	−9.56658e63	−	3.96261e63i	−1.47373	−	0.610440i	−0.967707	+	0.252078i	$0.918886\pi$
$930$	4.37631e63	+	1.05654e64i	0.658757	+	1.59038i
$931$		−	1.58454e63i		−	0.233069i
$932$	−8.42974e63	+	3.49171e63i	−1.21164	+	0.501876i
$933$	5.00787e63	+	5.00787e63i	0.703392	+	0.703392i
$934$	−1.81983e63			−0.249789
$935$	1.25215e64	−	1.42611e64i	1.67960	−	1.91295i
$936$	−2.24693e62			−0.0294550
$937$	−8.28809e63	−	8.28809e63i	−1.06183	−	1.06183i	−0.997958	−	0.0638672i	$-0.979657\pi$
$937$	−8.28809e63	−	8.28809e63i	−1.06183	−	1.06183i	−0.0638672	−	0.997958i	$-0.520343\pi$
$938$	8.44332e62	−	3.49734e62i	0.105719	−	0.0437901i
$939$			4.08071e63i			0.499374i
$940$	3.02275e63	+	7.29756e63i	0.361538	+	0.872829i
$941$	7.03237e63	+	2.91290e63i	0.822101	+	0.340525i	0.753771	−	0.657138i	$-0.228233\pi$
$941$	7.03237e63	+	2.91290e63i	0.822101	+	0.340525i	0.0683300	+	0.997663i	$0.478233\pi$
$942$	−6.70617e63	+	1.61901e64i	−0.766267	+	1.84993i
$943$	1.07326e62	−	1.07326e62i	0.0119868	−	0.0119868i
$944$	−2.31192e63	+	2.31192e63i	−0.252391	+	0.252391i
$945$	−1.17596e63	+	2.83901e63i	−0.125489	+	0.302958i
$946$	2.79053e64	+	1.15588e64i	2.91090	+	1.20574i
$947$	−6.12123e63	−	1.47780e64i	−0.624186	−	1.50692i	−0.846745	−	0.531999i	$-0.821441\pi$
$947$	−6.12123e63	−	1.47780e64i	−0.624186	−	1.50692i	0.222559	−	0.974919i	$-0.428559\pi$
$948$			8.14377e63i			0.811795i
$949$	6.30921e63	−	2.61336e63i	0.614825	−	0.254669i
$950$	−2.43423e63	−	2.43423e63i	−0.231902	−	0.231902i
$951$	−1.54844e64			−1.44216
$952$	2.79383e62	−	8.21452e62i	0.0254393	−	0.0747976i
$953$	−1.16249e64			−1.03488			−0.517442	−	0.855718i	$-0.673116\pi$
$953$	−1.16249e64			−1.03488			−0.517442	+	0.855718i	$0.673116\pi$
$954$	2.27018e63	+	2.27018e63i	0.197592	+	0.197592i
$955$	−2.18613e64	+	9.05525e63i	−1.86039	+	0.770598i
$956$		−	7.64930e63i		−	0.636468i
$957$	−7.28994e63	−	1.75995e64i	−0.593085	−	1.43183i
$958$	2.71209e64	+	1.12338e64i	2.15747	+	0.893654i
$959$	1.46798e63	−	3.54403e63i	0.114188	−	0.275675i
$960$	1.62148e64	−	1.62148e64i	1.23333	−	1.23333i
$961$	−1.33819e63	+	1.33819e63i	−0.0995328	+	0.0995328i
$962$	−3.97956e63	+	9.60751e63i	−0.289448	+	0.698790i
$963$	1.76958e63	+	7.32983e62i	0.125865	+	0.0521349i
$964$	3.52249e63	+	8.50405e63i	0.245016	+	0.591520i
$965$			1.13014e64i			0.768765i
$966$	5.88356e61	−	2.43705e61i	0.00391410	−	0.00162127i
$967$	1.45909e64	+	1.45909e64i	0.949324	+	0.949324i	0.998776	−	0.0494528i	$-0.0157477\pi$
$967$	1.45909e64	+	1.45909e64i	0.949324	+	0.949324i	−0.0494528	+	0.998776i	$0.515748\pi$
$968$	1.35015e64			0.859133
$969$	−1.57032e63	−	3.18902e63i	−0.0977300	−	0.198470i
$970$	−8.10642e63			−0.493443
$971$	2.47824e63	+	2.47824e63i	0.147547	+	0.147547i	0.777021	−	0.629475i	$-0.216730\pi$
$971$	2.47824e63	+	2.47824e63i	0.147547	+	0.147547i	−0.629475	+	0.777021i	$0.716730\pi$
$972$	−7.20644e63	+	2.98500e63i	−0.419658	+	0.173828i
$973$		−	5.23541e63i		−	0.298212i
$974$	−2.67337e63	−	6.45409e63i	−0.148950	−	0.359598i
$975$	6.09752e63	+	2.52567e63i	0.332318	+	0.137651i
$976$	−1.03779e63	+	2.50543e63i	−0.0553269	+	0.133571i
$977$	2.28577e64	−	2.28577e64i	1.19206	−	1.19206i	0.215576	−	0.976487i	$-0.430837\pi$
$977$	2.28577e64	−	2.28577e64i	1.19206	−	1.19206i	0.976487	−	0.215576i	$-0.0691630\pi$
$978$	−2.20629e64	+	2.20629e64i	−1.12558	+	1.12558i
$979$	−2.13861e64	+	5.16306e64i	−1.06734	+	2.57679i
$980$	−3.06226e64	−	1.26843e64i	−1.49514	−	0.619307i
$981$	1.21593e63	+	2.93552e63i	0.0580799	+	0.140217i
$982$			3.14065e63i			0.146765i
$983$	−1.30134e64	+	5.39033e63i	−0.594964	+	0.246442i	−0.659784	−	0.751455i	$-0.729352\pi$
$983$	−1.30134e64	+	5.39033e63i	−0.594964	+	0.246442i	0.0648209	+	0.997897i	$0.479352\pi$
$984$	−6.08318e63	−	6.08318e63i	−0.272105	−	0.272105i
$985$	−2.65007e64			−1.15979
$986$	−2.91054e64	+	1.43320e64i	−1.24629	+	0.613695i
$987$	−2.66013e63			−0.111451
$988$	2.33371e63	+	2.33371e63i	0.0956694	+	0.0956694i
$989$	3.69860e62	−	1.53201e62i	0.0148360	−	0.00614528i
$990$			1.80590e64i			0.708823i
$991$	−1.21962e64	−	2.94443e64i	−0.468428	−	1.13088i	−0.964850	−	0.262803i	$-0.915353\pi$
$991$	−1.21962e64	−	2.94443e64i	−0.468428	−	1.13088i	0.496422	−	0.868081i	$-0.334647\pi$
$992$	−3.21643e64	−	1.33229e64i	−1.20885	−	0.500723i
$993$	1.48939e64	−	3.59570e64i	0.547771	−	1.32244i
$994$	8.81508e61	−	8.81508e61i	0.00317263	−	0.00317263i
$995$	3.21772e64	−	3.21772e64i	1.13332	−	1.13332i
$996$	−1.35248e64	+	3.26519e64i	−0.466183	+	1.12547i
$997$	−2.29331e64	−	9.49918e63i	−0.773599	−	0.320435i	−0.0392699	−	0.999229i	$-0.512503\pi$
$997$	−2.29331e64	−	9.49918e63i	−0.773599	−	0.320435i	−0.734329	+	0.678793i	$0.762503\pi$
$998$	−2.29751e64	−	5.54668e64i	−0.758492	−	1.83116i
$999$			3.75557e64i			1.21344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.12	✓	252
17.9	even	8	inner	17.44.d.a.9.12	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.12	✓	252	1.1	even	1	trivial
17.44.d.a.9.12	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+(-3.13678e6 - 3.13678e6i) q^{2} +(-1.51005e10 + 6.25485e9i) q^{3} +1.08827e13i q^{4} +(5.61563e14 + 1.35573e15i) q^{5} +(6.69872e16 + 2.77470e16i) q^{6} +(-1.25921e17 + 3.04000e17i) q^{7} +(6.54523e18 - 6.54523e18i) q^{8} +(-4.32097e19 + 4.32097e19i) q^{9} +(2.49114e21 - 6.01414e21i) q^{10} +(4.19427e22 + 1.73732e22i) q^{11} +(-6.80696e22 - 1.64335e23i) q^{12} +3.97241e23i q^{13} +(1.34857e24 - 5.58596e23i) q^{14} +(-1.69598e25 - 1.69598e25i) q^{15} +5.46633e25 q^{16} +(-2.14069e26 - 1.87956e26i) q^{17} +2.71079e26 q^{18} +(-5.39829e26 - 5.39829e26i) q^{19} +(-1.47540e28 + 6.11132e27i) q^{20} -5.37819e27i q^{21} +(-7.70690e28 - 1.86061e29i) q^{22} +(-2.46607e27 - 1.02148e27i) q^{23} +(-5.78971e28 + 1.39776e29i) q^{24} +(-7.18773e29 + 7.18773e29i) q^{25} +(1.24606e30 - 1.24606e30i) q^{26} +(2.43542e30 - 5.87961e30i) q^{27} +(-3.30835e30 - 1.37036e30i) q^{28} +(9.82440e30 + 2.37182e31i) q^{29} +1.06398e32i q^{30} +(9.92999e31 - 4.11314e31i) q^{31} +(-2.29039e32 - 2.29039e32i) q^{32} -7.42023e32 q^{33} +(8.19115e31 + 1.26106e33i) q^{34} -4.82856e32 q^{35} +(-4.70238e32 - 4.70238e32i) q^{36} +(-5.45202e33 + 2.25830e33i) q^{37} +3.38665e33i q^{38} +(-2.48468e33 - 5.99855e33i) q^{39} +(1.25492e34 + 5.19803e33i) q^{40} +(-2.17605e34 + 5.25344e34i) q^{41} +(-1.68702e34 + 1.68702e34i) q^{42} +(-1.06052e35 + 1.06052e35i) q^{43} +(-1.89068e35 + 4.56449e35i) q^{44} +(-8.28458e34 - 3.43158e34i) q^{45} +(4.53136e33 + 1.09397e34i) q^{46} -4.94615e35i q^{47} +(-8.25445e35 + 3.41911e35i) q^{48} +(1.46763e36 + 1.46763e36i) q^{49} +4.50927e36 q^{50} +(4.40819e36 + 1.49926e36i) q^{51} -4.32306e36 q^{52} +(8.37462e36 + 8.37462e36i) q^{53} +(-2.60824e37 + 1.08037e37i) q^{54} +6.66192e37i q^{55} +(1.16557e36 + 2.81394e36i) q^{56} +(1.15283e37 + 4.77516e36i) q^{57} +(4.35818e37 - 1.05216e38i) q^{58} +(-4.22937e37 + 4.22937e37i) q^{59} +(1.84569e38 - 1.84569e38i) q^{60} +(-1.89850e37 + 4.58339e37i) q^{61} +(-4.40502e38 - 1.82462e38i) q^{62} +(-7.69475e36 - 1.85768e37i) q^{63} +9.56069e38i q^{64} +(-5.38553e38 + 2.23076e38i) q^{65} +(2.32756e39 + 2.32756e39i) q^{66} +6.26094e38 q^{67} +(2.04547e39 - 2.32965e39i) q^{68} +4.36282e37 q^{69} +(1.51461e39 + 1.51461e39i) q^{70} +(7.89039e37 - 3.26831e37i) q^{71} +5.65635e38i q^{72} +(-6.57878e39 - 1.58826e40i) q^{73} +(2.41856e40 + 1.00180e40i) q^{74} +(6.35804e39 - 1.53497e40i) q^{75} +(5.87480e39 - 5.87480e39i) q^{76} +(-1.05629e40 + 1.05629e40i) q^{77} +(-1.10222e40 + 2.66101e40i) q^{78} +(-4.22987e40 - 1.75207e40i) q^{79} +(3.06969e40 + 7.41089e40i) q^{80} +8.39595e40i q^{81} +(2.33047e41 - 9.65312e40i) q^{82} +(-1.40496e41 - 1.40496e41i) q^{83} +5.85292e40 q^{84} +(1.34605e41 - 3.95769e41i) q^{85} +6.65321e41 q^{86} +(-2.96707e41 - 2.96707e41i) q^{87} +(3.88236e41 - 1.60813e41i) q^{88} +1.23098e42i q^{89} +(1.52228e41 + 3.67510e41i) q^{90} +(-1.20761e41 - 5.00210e40i) q^{91} +(1.11165e40 - 2.68375e40i) q^{92} +(-1.24221e42 + 1.24221e42i) q^{93} +(-1.55150e42 + 1.55150e42i) q^{94} +(4.28716e41 - 1.03501e42i) q^{95} +(4.89122e42 + 2.02601e42i) q^{96} +(-4.76552e41 - 1.15050e42i) q^{97} -9.20727e42i q^{98} +(-2.56302e42 + 1.06164e42i) 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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