LMFDB - Embedded newform 17.44.d.a.2.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [17,44,Mod(2,17)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("17.2"); S:= CuspForms(chi, 44); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(17, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 44, names="a")

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	17.d (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$199.087672088$
Analytic rank:	$0$
Dimension:	$252$
Relative dimension:	$63$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			2.9
Character	$\chi$	$=$	17.2
Dual form			17.44.d.a.9.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.30953e6 - 3.30953e6i) q^{2} +(-1.25934e10 + 5.21635e9i) q^{3} +1.31099e13i q^{4} +(4.61615e14 + 1.11444e15i) q^{5} +(5.89418e16 + 2.44145e16i) q^{6} +(-7.15817e17 + 1.72813e18i) q^{7} +(1.42765e19 - 1.42765e19i) q^{8} +(-1.00730e20 + 1.00730e20i) q^{9} +(2.16054e21 - 5.21599e21i) q^{10} +(-3.84052e22 - 1.59079e22i) q^{11} +(-6.83856e22 - 1.65097e23i) q^{12} +1.28497e24i q^{13} +(8.08832e24 - 3.35029e24i) q^{14} +(-1.16266e25 - 1.16266e25i) q^{15} +2.08183e25 q^{16} +(-4.20936e24 + 2.84842e26i) q^{17} +6.66737e26 q^{18} +(2.77300e27 + 2.77300e27i) q^{19} +(-1.46101e28 + 6.05171e27i) q^{20} -2.54970e28i q^{21} +(7.44552e28 + 1.79751e29i) q^{22} +(1.40394e29 + 5.81530e28i) q^{23} +(-1.05318e29 + 2.54261e29i) q^{24} +(-2.24996e29 + 2.24996e29i) q^{25} +(4.25264e30 - 4.25264e30i) q^{26} +(2.45539e30 - 5.92783e30i) q^{27} +(-2.26556e31 - 9.38426e30i) q^{28} +(-8.63436e30 - 2.08452e31i) q^{29} +7.69570e31i q^{30} +(-1.20378e32 + 4.98621e31i) q^{31} +(-1.94477e32 - 1.94477e32i) q^{32} +5.66632e32 q^{33} +(9.56624e32 - 9.28762e32i) q^{34} -2.25633e33 q^{35} +(-1.32056e33 - 1.32056e33i) q^{36} +(-3.38990e32 + 1.40414e32i) q^{37} -1.83546e34i q^{38} +(-6.70284e33 - 1.61821e34i) q^{39} +(2.25006e34 + 9.32005e33i) q^{40} +(4.09911e33 - 9.89614e33i) q^{41} +(-8.43830e34 + 8.43830e34i) q^{42} +(2.18524e34 - 2.18524e34i) q^{43} +(2.08551e35 - 5.03487e35i) q^{44} +(-1.58756e35 - 6.57588e34i) q^{45} +(-2.72178e35 - 6.57096e35i) q^{46} +1.08185e36i q^{47} +(-2.62173e35 + 1.08595e35i) q^{48} +(-9.29864e35 - 9.29864e35i) q^{49} +1.48926e36 q^{50} +(-1.43283e36 - 3.60908e36i) q^{51} -1.68458e37 q^{52} +(-7.27071e36 - 7.27071e36i) q^{53} +(-2.77445e37 + 1.14922e37i) q^{54} -5.01436e37i q^{55} +(1.44524e37 + 3.48912e37i) q^{56} +(-4.93863e37 - 2.04565e37i) q^{57} +(-4.04121e37 + 9.75634e37i) q^{58} +(4.43123e37 - 4.43123e37i) q^{59} +(1.52423e38 - 1.52423e38i) q^{60} +(1.49188e38 - 3.60172e38i) q^{61} +(5.63414e38 + 2.33374e38i) q^{62} +(-1.01971e38 - 2.46179e38i) q^{63} +1.10413e39i q^{64} +(-1.43202e39 + 5.93162e38i) q^{65} +(-1.87528e39 - 1.87528e39i) q^{66} -3.62029e39 q^{67} +(-3.73424e39 - 5.51841e37i) q^{68} -2.07138e39 q^{69} +(7.46739e39 + 7.46739e39i) q^{70} +(1.12987e40 - 4.68009e39i) q^{71} +2.87615e39i q^{72} +(2.21682e39 + 5.35187e39i) q^{73} +(1.58660e39 + 6.57192e38i) q^{74} +(1.65980e39 - 4.00712e39i) q^{75} +(-3.63536e40 + 3.63536e40i) q^{76} +(5.49821e40 - 5.49821e40i) q^{77} +(-3.13719e40 + 7.57384e40i) q^{78} +(-2.72236e40 - 1.12764e40i) q^{79} +(9.61005e39 + 2.32007e40i) q^{80} +4.06982e40i q^{81} +(-4.63177e40 + 1.91854e40i) q^{82} +(-3.98646e40 - 3.98646e40i) q^{83} +3.34262e41 q^{84} +(-3.19382e41 + 1.26796e41i) q^{85} -1.44643e41 q^{86} +(2.17471e41 + 2.17471e41i) q^{87} +(-7.75404e41 + 3.21183e41i) q^{88} -4.19228e41i q^{89} +(3.07776e41 + 7.43038e41i) q^{90} +(-2.22060e42 - 9.19802e41i) q^{91} +(-7.62378e41 + 1.84054e42i) q^{92} +(1.25586e42 - 1.25586e42i) q^{93} +(3.58041e42 - 3.58041e42i) q^{94} +(-1.81028e42 + 4.37039e42i) q^{95} +(3.46357e42 + 1.43466e42i) q^{96} +(-2.36685e42 - 5.71408e42i) q^{97} +6.15483e42i q^{98} +(5.47096e42 - 2.26615e42i) 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 $

$2$	−3.30953e6	−	3.30953e6i	−1.11589	−	1.11589i	−0.992338	−	0.123551i	$-0.960572\pi$
$2$	−3.30953e6	−	3.30953e6i	−1.11589	−	1.11589i	−0.123551	−	0.992338i	$-0.539428\pi$
$3$	−1.25934e10	+	5.21635e9i	−0.695080	+	0.287912i	−0.702115	−	0.712064i	$-0.747761\pi$
$3$	−1.25934e10	+	5.21635e9i	−0.695080	+	0.287912i	0.00703464	+	0.999975i	$0.497761\pi$
$4$			1.31099e13i			1.49042i
$5$	4.61615e14	+	1.11444e15i	0.432937	+	1.04520i	0.978335	+	0.207026i	$0.0663786\pi$
$5$	4.61615e14	+	1.11444e15i	0.432937	+	1.04520i	−0.545398	+	0.838177i	$0.683621\pi$
$6$	5.89418e16	+	2.44145e16i	1.09691	+	0.454355i
$7$	−7.15817e17	+	1.72813e18i	−0.484389	+	1.16942i	0.473116	+	0.881000i	$0.343129\pi$
$7$	−7.15817e17	+	1.72813e18i	−0.484389	+	1.16942i	−0.957505	+	0.288417i	$0.906871\pi$
$8$	1.42765e19	−	1.42765e19i	0.547253	−	0.547253i
$9$	−1.00730e20	+	1.00730e20i	−0.306863	+	0.306863i
$10$	2.16054e21	−	5.21599e21i	0.683221	−	1.64944i
$11$	−3.84052e22	−	1.59079e22i	−1.56476	−	0.648144i	−0.578850	−	0.815434i	$-0.696498\pi$
$11$	−3.84052e22	−	1.59079e22i	−1.56476	−	0.648144i	−0.985908	+	0.167290i	$0.946498\pi$
$12$	−6.83856e22	−	1.65097e23i	−0.429109	−	1.03596i
$13$			1.28497e24i			1.44248i	0.692684	+	0.721241i	$0.256428\pi$
$13$			1.28497e24i			1.44248i	−0.692684	+	0.721241i	$0.743572\pi$
$14$	8.08832e24	−	3.35029e24i	1.84546	−	0.764417i
$15$	−1.16266e25	−	1.16266e25i	−0.601853	−	0.601853i
$16$	2.08183e25			0.269070
$17$	−4.20936e24	+	2.84842e26i	−0.0147763	+	0.999891i
$17$	−4.20936e24	+	2.84842e26i	−0.0147763	+	0.999891i
$18$	6.66737e26			0.684851
$19$	2.77300e27	+	2.77300e27i	0.890732	+	0.890732i	0.994592	−	0.103860i	$-0.0331193\pi$
$19$	2.77300e27	+	2.77300e27i	0.890732	+	0.890732i	−0.103860	+	0.994592i	$0.533119\pi$
$20$	−1.46101e28	+	6.05171e27i	−1.55779	+	0.645258i
$21$		−	2.54970e28i		−	0.952300i
$22$	7.44552e28	+	1.79751e29i	1.02284	+	2.46935i
$23$	1.40394e29	+	5.81530e28i	0.741650	+	0.307202i	0.721330	−	0.692592i	$-0.243531\pi$
$23$	1.40394e29	+	5.81530e28i	0.741650	+	0.307202i	0.0203208	+	0.999794i	$0.493531\pi$
$24$	−1.05318e29	+	2.54261e29i	−0.222824	+	0.537946i
$25$	−2.24996e29	+	2.24996e29i	−0.197909	+	0.197909i
$26$	4.25264e30	−	4.25264e30i	1.60965	−	1.60965i
$27$	2.45539e30	−	5.92783e30i	0.412857	−	0.996724i
$28$	−2.26556e31	−	9.38426e30i	−1.74292	−	0.721942i
$29$	−8.63436e30	−	2.08452e31i	−0.312373	−	0.754135i	−0.999616	−	0.0277072i	$-0.991179\pi$
$29$	−8.63436e30	−	2.08452e31i	−0.312373	−	0.754135i	0.687243	−	0.726427i	$-0.258821\pi$
$30$			7.69570e31i			1.34320i
$31$	−1.20378e32	+	4.98621e31i	−1.03817	+	0.430025i	−0.835656	−	0.549253i	$-0.814912\pi$
$31$	−1.20378e32	+	4.98621e31i	−1.03817	+	0.430025i	−0.202517	+	0.979279i	$0.564912\pi$
$32$	−1.94477e32	−	1.94477e32i	−0.847506	−	0.847506i
$33$	5.66632e32			1.27424
$34$	9.56624e32	−	9.28762e32i	1.13226	−	1.09928i
$35$	−2.25633e33			−1.43199
$36$	−1.32056e33	−	1.32056e33i	−0.457355	−	0.457355i
$37$	−3.38990e32	+	1.40414e32i	−0.0651403	+	0.0269820i	−0.415016	−	0.909814i	$-0.636224\pi$
$37$	−3.38990e32	+	1.40414e32i	−0.0651403	+	0.0269820i	0.349875	+	0.936796i	$0.386224\pi$
$38$		−	1.83546e34i		−	1.98792i
$39$	−6.70284e33	−	1.61821e34i	−0.415308	−	1.00264i
$40$	2.25006e34	+	9.32005e33i	0.808918	+	0.335065i
$41$	4.09911e33	−	9.89614e33i	0.0866637	−	0.209225i	−0.874606	−	0.484835i	$-0.838880\pi$
$41$	4.09911e33	−	9.89614e33i	0.0866637	−	0.209225i	0.961270	+	0.275610i	$0.0888798\pi$
$42$	−8.43830e34	+	8.43830e34i	−1.06266	+	1.06266i
$43$	2.18524e34	−	2.18524e34i	0.165931	−	0.165931i	−0.619257	−	0.785188i	$-0.712566\pi$
$43$	2.18524e34	−	2.18524e34i	0.165931	−	0.165931i	0.785188	+	0.619257i	$0.212566\pi$
$44$	2.08551e35	−	5.03487e35i	0.966006	−	2.33214i
$45$	−1.58756e35	−	6.57588e34i	−0.453587	−	0.187882i
$46$	−2.72178e35	−	6.57096e35i	−0.484797	−	1.17040i
$47$			1.08185e36i			1.21356i	0.794868	+	0.606782i	$0.207540\pi$
$47$			1.08185e36i			1.21356i	−0.794868	+	0.606782i	$0.792460\pi$
$48$	−2.62173e35	+	1.08595e35i	−0.187025	+	0.0774685i
$49$	−9.29864e35	−	9.29864e35i	−0.425798	−	0.425798i
$50$	1.48926e36			0.441689
$51$	−1.43283e36	−	3.60908e36i	−0.277610	−	0.699259i
$52$	−1.68458e37			−2.14990
$53$	−7.27071e36	−	7.27071e36i	−0.616092	−	0.616092i	0.328435	−	0.944527i	$-0.393479\pi$
$53$	−7.27071e36	−	7.27071e36i	−0.616092	−	0.616092i	−0.944527	+	0.328435i	$0.893479\pi$
$54$	−2.77445e37	+	1.14922e37i	−1.57294	+	0.651532i
$55$		−	5.01436e37i		−	1.91610i
$56$	1.44524e37	+	3.48912e37i	0.374884	+	0.905051i
$57$	−4.93863e37	−	2.04565e37i	−0.875583	−	0.362678i
$58$	−4.04121e37	+	9.75634e37i	−0.492957	+	1.19010i
$59$	4.43123e37	−	4.43123e37i	0.374288	−	0.374288i	−0.494748	−	0.869036i	$-0.664740\pi$
$59$	4.43123e37	−	4.43123e37i	0.374288	−	0.374288i	0.869036	+	0.494748i	$0.164740\pi$
$60$	1.52423e38	−	1.52423e38i	0.897013	−	0.897013i
$61$	1.49188e38	−	3.60172e38i	0.615380	−	1.48566i	−0.241635	−	0.970367i	$-0.577684\pi$
$61$	1.49188e38	−	3.60172e38i	0.615380	−	1.48566i	0.857015	−	0.515291i	$-0.172316\pi$
$62$	5.63414e38	+	2.33374e38i	1.63835	+	0.678626i
$63$	−1.01971e38	−	2.46179e38i	−0.210210	−	0.507492i
$64$			1.10413e39i			1.62238i
$65$	−1.43202e39	+	5.93162e38i	−1.50769	+	0.624505i
$66$	−1.87528e39	−	1.87528e39i	−1.42191	−	1.42191i
$67$	−3.62029e39			−1.98672			−0.993358	−	0.115068i	$-0.963291\pi$
$67$	−3.62029e39			−1.98672			−0.993358	+	0.115068i	$0.963291\pi$
$68$	−3.73424e39	−	5.51841e37i	−1.49026	−	0.0220228i
$69$	−2.07138e39			−0.603954
$70$	7.46739e39	+	7.46739e39i	1.59794	+	1.59794i
$71$	1.12987e40	−	4.68009e39i	1.78228	−	0.738243i	0.790164	−	0.612896i	$-0.209996\pi$
$71$	1.12987e40	−	4.68009e39i	1.78228	−	0.738243i	0.992113	−	0.125347i	$-0.0400045\pi$
$72$			2.87615e39i			0.335864i
$73$	2.21682e39	+	5.35187e39i	0.192437	+	0.464584i	0.990419	−	0.138098i	$-0.0440988\pi$
$73$	2.21682e39	+	5.35187e39i	0.192437	+	0.464584i	−0.797982	+	0.602682i	$0.794099\pi$
$74$	1.58660e39	+	6.57192e38i	0.102798	+	0.0425805i
$75$	1.65980e39	−	4.00712e39i	0.0805822	−	0.194543i
$76$	−3.63536e40	+	3.63536e40i	−1.32756	+	1.32756i
$77$	5.49821e40	−	5.49821e40i	1.51590	−	1.51590i
$78$	−3.13719e40	+	7.57384e40i	−0.655400	+	1.58227i
$79$	−2.72236e40	−	1.12764e40i	−0.432477	−	0.179138i	0.155815	−	0.987786i	$-0.450200\pi$
$79$	−2.72236e40	−	1.12764e40i	−0.432477	−	0.179138i	−0.588292	+	0.808648i	$0.700200\pi$
$80$	9.61005e39	+	2.32007e40i	0.116491	+	0.281233i
$81$			4.06982e40i			0.377700i
$82$	−4.63177e40	+	1.91854e40i	−0.330179	+	0.136764i
$83$	−3.98646e40	−	3.98646e40i	−0.218982	−	0.218982i	0.589088	−	0.808069i	$-0.299487\pi$
$83$	−3.98646e40	−	3.98646e40i	−0.218982	−	0.218982i	−0.808069	+	0.589088i	$0.799487\pi$
$84$	3.34262e41			1.41933
$85$	−3.19382e41	+	1.26796e41i	−1.05149	+	0.417446i
$86$	−1.44643e41			−0.370322
$87$	2.17471e41	+	2.17471e41i	0.434248	+	0.434248i
$88$	−7.75404e41	+	3.21183e41i	−1.21102	+	0.501620i
$89$		−	4.19228e41i		−	0.513530i	−0.966474	−	0.256765i	$-0.917343\pi$
$89$		−	4.19228e41i		−	0.513530i	0.966474	−	0.256765i	$-0.0826566\pi$
$90$	3.07776e41	+	7.43038e41i	0.296498	+	0.715808i
$91$	−2.22060e42	−	9.19802e41i	−1.68686	−	0.698722i
$92$	−7.62378e41	+	1.84054e42i	−0.457859	+	1.10537i
$93$	1.25586e42	−	1.25586e42i	0.597804	−	0.597804i
$94$	3.58041e42	−	3.58041e42i	1.35420	−	1.35420i
$95$	−1.81028e42	+	4.37039e42i	−0.545365	+	1.31663i
$96$	3.46357e42	+	1.43466e42i	0.833092	+	0.345078i
$97$	−2.36685e42	−	5.71408e42i	−0.455594	−	1.09990i	−0.970163	−	0.242452i	$-0.922048\pi$
$97$	−2.36685e42	−	5.71408e42i	−0.455594	−	1.09990i	0.514569	−	0.857449i	$-0.327952\pi$
$98$			6.15483e42i			0.950288i
$99$	5.47096e42	−	2.26615e42i	0.679058	−	0.281275i
$100$	−2.94967e42	−	2.94967e42i	−0.294967	−	0.294967i
$101$	1.01857e43			0.822397			0.411199	−	0.911546i	$-0.365110\pi$
$101$	1.01857e43			0.822397			0.411199	+	0.911546i	$0.365110\pi$
$102$	−7.20238e42	+	1.66863e43i	−0.470514	+	1.09008i
$103$	−6.51126e42			−0.344877			−0.172439	−	0.985020i	$-0.555165\pi$
$103$	−6.51126e42			−0.344877			−0.172439	+	0.985020i	$0.555165\pi$
$104$	1.83449e43	+	1.83449e43i	0.789404	+	0.789404i
$105$	2.84148e43	−	1.17698e43i	0.995348	−	0.412287i
$106$			4.81252e43i			1.37498i
$107$	3.18332e43	+	7.68522e43i	0.743241	+	1.79434i	0.592161	+	0.805820i	$0.298275\pi$
$107$	3.18332e43	+	7.68522e43i	0.743241	+	1.79434i	0.151080	+	0.988522i	$0.451725\pi$
$108$	7.77131e43	+	3.21898e43i	1.48554	+	0.615330i
$109$	8.48301e41	−	2.04798e42i	0.0133009	−	0.0321111i	−0.917090	−	0.398681i	$-0.869468\pi$
$109$	8.48301e41	−	2.04798e42i	0.0133009	−	0.0321111i	0.930390	+	0.366570i	$0.119468\pi$
$110$	−1.65952e44	+	1.65952e44i	−2.13815	+	2.13815i
$111$	3.53658e42	−	3.53658e42i	0.0375093	−	0.0375093i
$112$	−1.49021e43	+	3.59768e43i	−0.130335	+	0.314655i
$113$	1.68195e43	+	6.96685e42i	0.121514	+	0.0503326i	0.442612	−	0.896713i	$-0.354052\pi$
$113$	1.68195e43	+	6.96685e42i	0.121514	+	0.0503326i	−0.321098	+	0.947046i	$0.604052\pi$
$114$	9.57441e43	+	2.31147e44i	0.572345	+	1.38176i
$115$			1.83304e44i			0.908175i
$116$	2.73278e44	−	1.13195e44i	1.12398	−	0.465566i
$117$	−1.29435e44	−	1.29435e44i	−0.442645	−	0.442645i
$118$	−2.93306e44			−0.835329
$119$	−4.89232e44	−	2.11169e44i	−1.16213	−	0.501615i
$120$	−3.31975e44			−0.658732
$121$	7.95934e44	+	7.95934e44i	1.32127	+	1.32127i
$122$	−1.68574e45	+	6.98258e44i	−2.34453	+	0.971135i
$123$			1.46008e44i			0.170379i
$124$	−6.53685e44	−	1.57814e45i	−0.640918	−	1.54731i
$125$	9.12363e44	+	3.77913e44i	0.752667	+	0.311765i
$126$	−4.77262e44	+	1.15221e45i	−0.331734	+	0.800877i
$127$	−1.70609e45	+	1.70609e45i	−1.00051	+	1.00051i	−0.000509171		1.00000i	$0.500162\pi$
$127$	−1.70609e45	+	1.70609e45i	−1.00051	+	1.00051i	−1.00000		0.000509171i	$0.999838\pi$
$128$	1.94352e45	−	1.94352e45i	0.962886	−	0.962886i
$129$	−1.61206e44	+	3.89186e44i	−0.0675620	+	0.163109i
$130$	6.70239e45	+	2.77622e45i	2.37929	+	0.985535i
$131$	−2.32618e45	−	5.61591e45i	−0.700344	−	1.69078i	−0.722824	−	0.691033i	$-0.757156\pi$
$131$	−2.32618e45	−	5.61591e45i	−0.700344	−	1.69078i	0.0224796	−	0.999747i	$-0.492844\pi$
$132$			7.42847e45i			1.89915i
$133$	−6.77707e45	+	2.80716e45i	−1.47310	+	0.610177i
$134$	1.19815e46	+	1.19815e46i	2.21695	+	2.21695i
$135$	7.73965e45			1.22052
$136$	4.00647e45	+	4.12666e45i	0.539107	+	0.555280i
$137$	−1.13554e46			−1.30530			−0.652649	−	0.757660i	$-0.726342\pi$
$137$	−1.13554e46			−1.30530			−0.652649	+	0.757660i	$0.726342\pi$
$138$	6.85528e45	+	6.85528e45i	0.673946	+	0.673946i
$139$	9.50240e45	−	3.93602e45i	0.799862	−	0.331314i	0.0549607	−	0.998489i	$-0.482497\pi$
$139$	9.50240e45	−	3.93602e45i	0.799862	−	0.331314i	0.744901	+	0.667175i	$0.232497\pi$
$140$		−	2.95802e46i		−	2.13426i
$141$	−5.64330e45	−	1.36241e46i	−0.349399	−	0.843524i
$142$	−5.28823e46	−	2.19046e46i	−2.81262	−	1.16503i
$143$	2.04412e46	−	4.93495e46i	0.934936	−	2.25714i
$144$	−2.09703e45	+	2.09703e45i	−0.0825678	+	0.0825678i
$145$	1.92449e46	−	1.92449e46i	0.652986	−	0.652986i
$146$	1.03756e46	−	2.50488e46i	0.303686	−	0.733163i
$147$	1.65606e46	+	6.85963e45i	0.418556	+	0.173372i
$148$	−1.84081e45	−	4.44411e45i	−0.0402145	−	0.0970864i
$149$		−	3.54951e46i		−	0.670909i	−0.942056	−	0.335455i	$-0.891110\pi$
$149$		−	3.54951e46i		−	0.670909i	0.942056	−	0.335455i	$-0.108890\pi$
$150$	−1.87548e46	+	7.76851e45i	−0.307009	+	0.127167i
$151$	−1.70967e46	−	1.70967e46i	−0.242609	−	0.242609i	0.575320	−	0.817929i	$-0.304878\pi$
$151$	−1.70967e46	−	1.70967e46i	−0.242609	−	0.242609i	−0.817929	+	0.575320i	$0.804878\pi$
$152$	7.91777e46			0.974913
$153$	−2.82681e46	−	2.91162e46i	−0.302295	−	0.311364i
$154$	−3.63930e47			−3.38316
$155$	−1.11136e47	−	1.11136e47i	−0.898928	−	0.898928i
$156$	2.12145e47	−	8.78734e46i	1.49436	−	0.618983i
$157$			6.44469e46i			0.395694i	0.980233	+	0.197847i	$0.0633949\pi$
$157$			6.44469e46i			0.395694i	−0.980233	+	0.197847i	$0.936605\pi$
$158$	5.27777e46	+	1.27417e47i	0.282698	+	0.682494i
$159$	1.29489e47	+	5.36362e46i	0.605614	+	0.250853i
$160$	1.26959e47	−	3.06506e47i	0.518899	−	1.25273i
$161$	−2.00992e47	+	2.00992e47i	−0.718494	+	0.718494i
$162$	1.34692e47	−	1.34692e47i	0.421471	−	0.421471i
$163$	1.09445e47	−	2.64225e47i	0.300030	−	0.724336i	−0.699919	−	0.714222i	$-0.746781\pi$
$163$	1.09445e47	−	2.64225e47i	0.300030	−	0.724336i	0.999949	−	0.0101137i	$-0.00321936\pi$
$164$	1.29737e47	+	5.37388e46i	0.311832	+	0.129165i
$165$	2.61566e47	+	6.31476e47i	0.551667	+	1.33184i
$166$			2.63866e47i			0.488719i
$167$	−3.38798e47	+	1.40335e47i	−0.551488	+	0.228434i	−0.640985	−	0.767553i	$-0.721474\pi$
$167$	−3.38798e47	+	1.40335e47i	−0.551488	+	0.228434i	0.0894969	+	0.995987i	$0.471474\pi$
$168$	−3.64009e47	−	3.64009e47i	−0.521150	−	0.521150i
$169$	−8.57614e47			−1.08076
$170$	1.47664e48	+	6.37368e47i	1.63917	+	0.707519i
$171$	−5.58648e47			−0.546666
$172$	2.86483e47	+	2.86483e47i	0.247307	+	0.247307i
$173$	2.25606e48	−	9.34492e47i	1.71933	−	0.712171i	0.719489	−	0.694504i	$-0.244376\pi$
$173$	2.25606e48	−	9.34492e47i	1.71933	−	0.712171i	0.999844	−	0.0176665i	$-0.00562370\pi$
$174$		−	1.43946e48i		−	0.969146i
$175$	−2.27768e47	−	5.49880e47i	−0.135573	−	0.327303i
$176$	−7.99531e47	−	3.31176e47i	−0.421030	−	0.174396i
$177$	−3.26893e47	+	7.89190e47i	−0.152398	+	0.367922i
$178$	−1.38745e48	+	1.38745e48i	−0.573042	+	0.573042i
$179$	−1.15823e48	+	1.15823e48i	−0.424086	+	0.424086i	−0.886608	−	0.462522i	$-0.846945\pi$
$179$	−1.15823e48	+	1.15823e48i	−0.424086	+	0.424086i	0.462522	+	0.886608i	$0.346945\pi$
$180$	8.62089e47	−	2.08127e48i	0.280023	−	0.676035i
$181$	1.72758e48	+	7.15588e47i	0.498138	+	0.206335i	0.617583	−	0.786505i	$-0.288112\pi$
$181$	1.72758e48	+	7.15588e47i	0.498138	+	0.206335i	−0.119446	+	0.992841i	$0.538112\pi$
$182$	4.30502e48	+	1.03932e49i	1.10266	+	2.66205i
$183$			5.31400e48i			1.20983i
$184$	2.83456e48	−	1.17411e48i	0.573988	−	0.237754i
$185$	−3.12966e47	−	3.12966e47i	−0.0564034	−	0.0564034i
$186$	−8.31263e48			−1.33417
$187$	4.69292e48	−	1.08725e49i	0.671194	−	1.55501i
$188$	−1.41829e49			−1.80872
$189$	8.48648e48	+	8.48648e48i	0.965604	+	0.965604i
$190$	2.04551e49	−	8.47278e48i	2.07778	−	0.860644i
$191$		−	3.53374e47i		−	0.0320640i	−0.999871	−	0.0160320i	$-0.994897\pi$
$191$		−	3.53374e47i		−	0.0320640i	0.999871	−	0.0160320i	$-0.00510336\pi$
$192$	−5.75953e48	−	1.39047e49i	−0.467101	−	1.12768i
$193$	1.10618e48	+	4.58194e47i	0.0802311	+	0.0332328i	0.422438	−	0.906392i	$-0.361174\pi$
$193$	1.10618e48	+	4.58194e47i	0.0802311	+	0.0332328i	−0.342207	+	0.939625i	$0.611174\pi$
$194$	−1.10777e49	+	2.67440e49i	−0.718976	+	1.73576i
$195$	1.49398e49	−	1.49398e49i	0.868162	−	0.868162i
$196$	1.21904e49	−	1.21904e49i	0.634618	−	0.634618i
$197$	−2.34854e48	+	5.66987e48i	−0.109591	+	0.264575i	−0.969155	−	0.246453i	$-0.920735\pi$
$197$	−2.34854e48	+	5.66987e48i	−0.109591	+	0.264575i	0.859564	+	0.511028i	$0.170735\pi$
$198$	−2.56062e49	−	1.06064e49i	−1.07163	−	0.443882i
$199$	2.97422e48	+	7.18039e48i	0.111694	+	0.269654i	0.969836	−	0.243759i	$-0.0783807\pi$
$199$	2.97422e48	+	7.18039e48i	0.111694	+	0.269654i	−0.858141	+	0.513414i	$0.828381\pi$
$200$			6.42434e48i			0.216612i
$201$	4.55917e49	−	1.88847e49i	1.38093	−	0.571999i
$202$	−3.37099e49	−	3.37099e49i	−0.917705	−	0.917705i
$203$	4.22039e49			1.03321
$204$	4.73146e49	−	1.87841e49i	1.04219	−	0.413755i
$205$	1.29208e49			0.256202
$206$	2.15492e49	+	2.15492e49i	0.384845	+	0.384845i
$207$	−1.99996e49	+	8.28411e48i	−0.321854	+	0.133316i
$208$			2.67509e49i			0.388129i
$209$	−6.23848e49	−	1.50610e50i	−0.816458	−	1.97110i
$210$	−1.32992e50	−	5.50871e49i	−1.57076	−	0.650632i
$211$	4.52293e49	−	1.09193e50i	0.482333	−	1.16446i	−0.476164	−	0.879356i	$-0.657973\pi$
$211$	4.52293e49	−	1.09193e50i	0.482333	−	1.16446i	0.958498	−	0.285100i	$-0.0920267\pi$
$212$	9.53180e49	−	9.53180e49i	0.918235	−	0.918235i
$213$	−1.17876e50	+	1.17876e50i	−1.02628	+	1.02628i
$214$	1.48992e50	−	3.59698e50i	1.17291	−	2.83166i
$215$	3.44406e49	+	1.42658e49i	0.245270	+	0.101594i
$216$	−4.95745e49	−	1.19683e50i	−0.319524	−	0.771398i
$217$		−	2.43721e50i		−	1.42236i
$218$	−9.58532e48	+	3.97037e48i	−0.0506748	+	0.0209902i
$219$	−5.58344e49	−	5.58344e49i	−0.267518	−	0.267518i
$220$	6.57375e50			2.85579
$221$	−3.66014e50	−	5.40890e48i	−1.44233	−	0.0213145i
$222$	−2.34088e49			−0.0837125
$223$	4.10487e50	+	4.10487e50i	1.33274	+	1.33274i	0.902912	+	0.429824i	$0.141425\pi$
$223$	4.10487e50	+	4.10487e50i	1.33274	+	1.33274i	0.429824	+	0.902912i	$0.358575\pi$
$224$	4.75291e50	−	1.96872e50i	1.40161	−	0.580566i
$225$		−	4.53277e49i		−	0.121462i
$226$	−3.26075e49	−	7.87214e49i	−0.0794303	−	0.191762i
$227$	1.90416e50	+	7.88729e49i	0.421840	+	0.174732i	0.583497	−	0.812115i	$-0.301684\pi$
$227$	1.90416e50	+	7.88729e49i	0.421840	+	0.174732i	−0.161657	+	0.986847i	$0.551684\pi$
$228$	2.68182e50	−	6.47448e50i	0.540543	−	1.30499i
$229$	4.51473e50	−	4.51473e50i	0.828265	−	0.828265i	−0.159012	−	0.987277i	$-0.550831\pi$
$229$	4.51473e50	−	4.51473e50i	0.828265	−	0.828265i	0.987277	+	0.159012i	$0.0508309\pi$
$230$	6.06651e50	−	6.06651e50i	1.01342	−	1.01342i
$231$	−4.05605e50	+	9.79216e50i	−0.617228	+	1.49012i
$232$	−4.20866e50	−	1.74328e50i	−0.583650	−	0.241756i
$233$	−2.90596e50	−	7.01562e50i	−0.367399	−	0.886979i	−0.994175	−	0.107780i	$-0.965626\pi$
$233$	−2.90596e50	−	7.01562e50i	−0.367399	−	0.886979i	0.626776	−	0.779200i	$-0.284374\pi$
$234$			8.56737e50i			0.987886i
$235$	−1.20565e51	+	4.99398e50i	−1.26842	+	0.525397i
$236$	5.80928e50	+	5.80928e50i	0.557846	+	0.557846i
$237$	4.01658e50			0.352182
$238$	9.20259e50	+	2.31800e51i	0.737064	+	1.85656i
$239$	2.23336e51			1.63457			0.817286	−	0.576232i	$-0.195478\pi$
$239$	2.23336e51			1.63457			0.817286	+	0.576232i	$0.195478\pi$
$240$	−2.42046e50	−	2.42046e50i	−0.161941	−	0.161941i
$241$	−2.67550e51	+	1.10823e51i	−1.63696	+	0.678052i	−0.995986	−	0.0895101i	$-0.971470\pi$
$241$	−2.67550e51	+	1.10823e51i	−1.63696	+	0.678052i	−0.640975	+	0.767562i	$0.721470\pi$
$242$		−	5.26833e51i		−	2.94878i
$243$	5.93703e50	+	1.43333e51i	0.304113	+	0.734193i
$244$	4.72181e51	+	1.95584e51i	2.21425	+	0.917174i
$245$	6.07037e50	−	1.46552e51i	0.260702	−	0.629390i
$246$	4.83218e50	−	4.83218e50i	0.190125	−	0.190125i
$247$	−3.56322e51	+	3.56322e51i	−1.28487	+	1.28487i
$248$	−1.00672e51	+	2.43044e51i	−0.332811	+	0.803477i
$249$	7.09976e50	+	2.94082e50i	0.215257	+	0.0891625i
$250$	−1.76878e51	−	4.27021e51i	−0.491998	−	1.18779i
$251$		−	2.01304e51i		−	0.513887i	−0.966426	−	0.256944i	$-0.917285\pi$
$251$		−	2.01304e51i		−	0.513887i	0.966426	−	0.256944i	$-0.0827155\pi$
$252$	3.22737e51	−	1.33682e51i	0.756376	−	0.313301i
$253$	−4.46675e51	−	4.46675e51i	−0.961392	−	0.961392i
$254$	1.12927e52			2.23292
$255$	3.36068e51	−	3.26280e51i	0.610680	−	0.592894i
$256$	−3.15223e51			−0.526574
$257$	−4.82473e51	−	4.82473e51i	−0.741158	−	0.741158i	0.231643	−	0.972801i	$-0.425590\pi$
$257$	−4.82473e51	−	4.82473e51i	−0.741158	−	0.741158i	−0.972801	+	0.231643i	$0.925590\pi$
$258$	1.82154e51	−	7.54506e50i	0.257404	−	0.106620i
$259$		−	6.86331e50i		−	0.0892460i
$260$	−7.77627e51	−	1.87736e52i	−0.930774	−	2.24709i
$261$	2.96947e51	+	1.23000e51i	0.327272	+	0.135560i
$262$	−1.08874e52	+	2.62846e52i	−1.10522	+	2.66823i
$263$	−4.76012e51	+	4.76012e51i	−0.445214	+	0.445214i	−0.893760	−	0.448546i	$-0.851942\pi$
$263$	−4.76012e51	+	4.76012e51i	−0.445214	+	0.445214i	0.448546	+	0.893760i	$0.351942\pi$
$264$	8.08955e51	−	8.08955e51i	0.697333	−	0.697333i
$265$	4.74648e51	−	1.14590e52i	0.377212	−	0.910671i
$266$	3.17193e52	+	1.31386e52i	2.32471	+	0.962925i
$267$	2.18684e51	+	5.27950e51i	0.147851	+	0.356944i
$268$		−	4.74616e52i		−	2.96104i
$269$	−1.29643e52	+	5.36997e51i	−0.746576	+	0.309242i	−0.723344	−	0.690488i	$-0.757396\pi$
$269$	−1.29643e52	+	5.36997e51i	−0.746576	+	0.309242i	−0.0232321	+	0.999730i	$0.507396\pi$
$270$	−2.56146e52	−	2.56146e52i	−1.36197	−	1.36197i
$271$	−2.30545e51			−0.113218			−0.0566090	−	0.998396i	$-0.518029\pi$
$271$	−2.30545e51			−0.113218			−0.0566090	+	0.998396i	$0.518029\pi$
$272$	−8.76318e49	+	5.92993e51i	−0.00397585	+	0.269041i
$273$	3.27628e52			1.37368
$274$	3.75810e52	+	3.75810e52i	1.45657	+	1.45657i
$275$	1.22202e52	−	5.06179e51i	0.437953	−	0.181406i
$276$		−	2.71555e52i		−	0.900144i
$277$	−5.81218e51	−	1.40319e52i	−0.178248	−	0.430328i	0.809351	−	0.587325i	$-0.199819\pi$
$277$	−5.81218e51	−	1.40319e52i	−0.178248	−	0.430328i	−0.987599	+	0.156996i	$0.949819\pi$
$278$	−4.44748e52	−	1.84221e52i	−1.26227	−	0.522848i
$279$	7.10304e51	−	1.71483e52i	0.186618	−	0.450536i
$280$	−3.22126e52	+	3.22126e52i	−0.783661	+	0.783661i
$281$	4.23199e52	−	4.23199e52i	0.953583	−	0.953583i	−0.0453864	−	0.998970i	$-0.514452\pi$
$281$	4.23199e52	−	4.23199e52i	0.953583	−	0.953583i	0.998970	+	0.0453864i	$0.0144519\pi$
$282$	−2.64128e52	+	6.37661e52i	−0.551389	+	1.33117i
$283$	−6.01369e51	−	2.49095e51i	−0.116341	−	0.0481900i	0.323754	−	0.946141i	$-0.395055\pi$
$283$	−6.01369e51	−	2.49095e51i	−0.116341	−	0.0481900i	−0.440095	+	0.897951i	$0.645055\pi$
$284$	6.13553e52	+	1.48125e53i	1.10029	+	2.65634i
$285$		−	6.44810e52i		−	1.07218i
$286$	−2.30974e53	+	9.56727e52i	−3.56200	+	1.47543i
$287$	1.41676e52	+	1.41676e52i	0.202692	+	0.202692i
$288$	3.91792e52			0.520137
$289$	−8.11174e52	−	2.39801e51i	−0.999563	−	0.0295493i
$290$	−1.27383e53			−1.45732
$291$	5.96132e52	+	5.96132e52i	0.633349	+	0.633349i
$292$	−7.01623e52	+	2.90622e52i	−0.692425	+	0.286812i
$293$		−	1.56653e53i		−	1.43643i	−0.695823	−	0.718214i	$-0.744960\pi$
$293$		−	1.56653e53i		−	1.43643i	0.695823	−	0.718214i	$-0.255040\pi$
$294$	−3.21057e52	−	7.75100e52i	−0.273599	−	0.660526i
$295$	6.98386e52	+	2.89281e52i	0.553251	+	0.229164i
$296$	−2.83498e51	+	6.84424e51i	−0.0208823	+	0.0504142i
$297$	−1.88599e53	+	1.88599e53i	−1.29204	+	1.29204i
$298$	−1.17472e53	+	1.17472e53i	−0.748661	+	0.748661i
$299$	−7.47248e52	+	1.80402e53i	−0.443133	+	1.06982i
$300$	5.25328e52	+	2.17598e52i	0.289950	+	0.120101i
$301$	2.21216e52	+	5.34063e52i	0.113668	+	0.274418i
$302$			1.13164e53i			0.541450i
$303$	−1.28272e53	+	5.31322e52i	−0.571632	+	0.236778i
$304$	5.77291e52	+	5.77291e52i	0.239670	+	0.239670i
$305$	4.70257e53			1.81924
$306$	−2.80654e51	+	1.89915e53i	−0.0101195	+	0.684776i
$307$	−1.94364e52			−0.0653341			−0.0326670	−	0.999466i	$-0.510400\pi$
$307$	−1.94364e52			−0.0653341			−0.0326670	+	0.999466i	$0.510400\pi$
$308$	7.20808e53	+	7.20808e53i	2.25933	+	2.25933i
$309$	8.19987e52	−	3.39650e52i	0.239717	−	0.0992942i
$310$			7.35618e53i			2.00621i
$311$	−1.28179e53	−	3.09452e53i	−0.326189	−	0.787490i	−0.998869	−	0.0475563i	$-0.984857\pi$
$311$	−1.28179e53	−	3.09452e53i	−0.326189	−	0.787490i	0.672679	−	0.739934i	$-0.265143\pi$
$312$	−3.26718e53	−	1.35331e53i	−0.775978	−	0.321420i
$313$	−6.60348e52	+	1.59422e53i	−0.146410	+	0.353464i	−0.980023	−	0.198884i	$-0.936268\pi$
$313$	−6.60348e52	+	1.59422e53i	−0.146410	+	0.353464i	0.833613	+	0.552348i	$0.186268\pi$
$314$	2.13289e53	−	2.13289e53i	0.441551	−	0.441551i
$315$	2.27280e53	−	2.27280e53i	0.439425	−	0.439425i
$316$	1.47832e53	−	3.56898e53i	0.266990	−	0.644572i
$317$	−4.31612e53	−	1.78780e53i	−0.728316	−	0.301678i	−0.0124559	−	0.999922i	$-0.503965\pi$
$317$	−4.31612e53	−	1.78780e53i	−0.728316	−	0.301678i	−0.715860	+	0.698244i	$0.753965\pi$
$318$	−2.51038e53	−	6.06059e53i	−0.395873	−	0.955722i
$319$			9.37918e53i			1.38250i
$320$	−1.23049e54	+	5.09684e53i	−1.69571	+	0.702387i
$321$	−8.01775e53	−	8.01775e53i	−1.03322	−	1.03322i
$322$	1.33038e54			1.60352
$323$	−8.01540e53	+	7.78195e53i	−0.903797	+	0.877473i
$324$	−5.33547e53			−0.562931
$325$	−2.89113e53	−	2.89113e53i	−0.285480	−	0.285480i
$326$	−1.23667e54	+	5.12246e53i	−1.14308	+	0.473479i
$327$			3.02160e52i			0.0261493i
$328$	−8.27615e52	−	1.99804e53i	−0.0670719	−	0.161926i
$329$	−1.86958e54	−	7.74405e53i	−1.41916	−	0.587836i
$330$	1.22423e54	−	2.95555e54i	0.870588	−	2.10179i
$331$	1.19931e54	−	1.19931e54i	0.799152	−	0.799152i	−0.183810	−	0.982962i	$-0.558843\pi$
$331$	1.19931e54	−	1.19931e54i	0.799152	−	0.799152i	0.982962	+	0.183810i	$0.0588432\pi$
$332$	5.22619e53	−	5.22619e53i	0.326375	−	0.326375i
$333$	2.00025e52	−	4.82904e52i	0.0117094	−	0.0282689i
$334$	1.58570e54	+	6.56819e53i	0.870307	+	0.360493i
$335$	−1.67118e54	−	4.03459e54i	−0.860123	−	2.07652i
$336$		−	5.30804e53i		−	0.256236i
$337$	4.42837e53	−	1.83429e53i	0.200540	−	0.0830664i	−0.280153	−	0.959955i	$-0.590385\pi$
$337$	4.42837e53	−	1.83429e53i	0.200540	−	0.0830664i	0.480693	+	0.876889i	$0.340385\pi$
$338$	2.83830e54	+	2.83830e54i	1.20601	+	1.20601i
$339$	−2.48155e53			−0.0989532
$340$	−1.66228e54	−	4.18706e54i	−0.622169	−	1.56716i
$341$	5.41633e54			1.90321
$342$	1.84886e54	+	1.84886e54i	0.610019	+	0.610019i
$343$	−1.50138e54	+	6.21893e53i	−0.465230	+	0.192704i
$344$		−	6.23955e53i		−	0.181613i
$345$	−9.56179e53	−	2.30842e54i	−0.261474	−	0.631255i
$346$	−1.05592e55	−	4.37378e54i	−2.71329	−	1.12388i
$347$	−2.42024e54	+	5.84297e54i	−0.584486	+	1.41107i	0.304222	+	0.952601i	$0.401604\pi$
$347$	−2.42024e54	+	5.84297e54i	−0.584486	+	1.41107i	−0.888708	+	0.458474i	$0.848396\pi$
$348$	−2.85102e54	+	2.85102e54i	−0.647212	+	0.647212i
$349$	3.70187e54	−	3.70187e54i	0.790085	−	0.790085i	−0.191423	−	0.981508i	$-0.561310\pi$
$349$	3.70187e54	−	3.70187e54i	0.790085	−	0.790085i	0.981508	+	0.191423i	$0.0613101\pi$
$350$	−1.06604e54	+	2.57365e54i	−0.213949	+	0.516518i
$351$	7.61708e54	+	3.15510e54i	1.43776	+	0.595539i
$352$	4.37519e54	+	1.05626e55i	0.776836	+	1.87545i
$353$		−	6.26743e54i		−	1.04697i	−0.852036	−	0.523484i	$-0.824632\pi$
$353$		−	6.26743e54i		−	1.04697i	0.852036	−	0.523484i	$-0.175368\pi$
$354$	3.69371e54	−	1.52998e54i	0.580621	−	0.240501i
$355$	1.04313e55	+	1.04313e55i	1.54323	+	1.54323i
$356$	5.49603e54			0.765374
$357$	7.26262e54	+	1.07326e53i	0.952196	+	0.0140714i
$358$	7.66637e54			0.946466
$359$	−9.26013e53	−	9.26013e53i	−0.107668	−	0.107668i	0.651221	−	0.758889i	$-0.274257\pi$
$359$	−9.26013e53	−	9.26013e53i	−0.107668	−	0.107668i	−0.758889	+	0.651221i	$0.774257\pi$
$360$	−3.20529e54	+	1.32768e54i	−0.351046	+	0.145408i
$361$			5.68723e54i			0.586808i
$362$	−3.34922e54	−	8.08574e54i	−0.325619	−	0.786114i
$363$	−1.41754e55	−	5.87162e54i	−1.29880	−	0.537980i
$364$	1.20585e55	−	2.91118e55i	1.04139	−	2.51414i
$365$	−4.94101e54	+	4.94101e54i	−0.402272	+	0.402272i
$366$	1.75868e55	−	1.75868e55i	1.35003	−	1.35003i
$367$	−3.83791e54	+	9.26554e54i	−0.277827	+	0.670734i	−0.999775	−	0.0212136i	$-0.993247\pi$
$367$	−3.83791e54	+	9.26554e54i	−0.277827	+	0.670734i	0.721948	+	0.691947i	$0.243247\pi$
$368$	2.92276e54	+	1.21065e54i	0.199556	+	0.0826588i
$369$	5.83934e53	+	1.40974e54i	0.0376094	+	0.0907972i
$370$			2.07154e54i			0.125880i
$371$	1.77693e55	−	7.36027e54i	1.01890	−	0.422041i
$372$	1.64642e55	+	1.64642e55i	0.890979	+	0.890979i
$373$	−3.52883e55			−1.80257			−0.901283	−	0.433231i	$-0.857373\pi$
$373$	−3.52883e55			−1.80257			−0.901283	+	0.433231i	$0.857373\pi$
$374$	−5.15140e55	+	2.04514e55i	−2.48420	+	0.986240i
$375$	−1.34611e55			−0.612924
$376$	1.54451e55	+	1.54451e55i	0.664127	+	0.664127i
$377$	2.67854e55	−	1.10949e55i	1.08783	−	0.450592i
$378$		−	5.61725e55i		−	2.15501i
$379$	2.71212e54	+	6.54763e54i	0.0983027	+	0.237324i	0.965379	−	0.260852i	$-0.0840035\pi$
$379$	2.71212e54	+	6.54763e54i	0.0983027	+	0.237324i	−0.867076	+	0.498176i	$0.834003\pi$
$380$	−5.72953e55	−	2.37325e55i	−1.96233	−	0.812823i
$381$	1.25858e55	−	3.03849e55i	0.407376	−	0.983493i
$382$	−1.16950e54	+	1.16950e54i	−0.0357799	+	0.0357799i
$383$	−1.41414e54	+	1.41414e54i	−0.0408996	+	0.0408996i	−0.727261	−	0.686361i	$-0.759207\pi$
$383$	−1.41414e54	+	1.41414e54i	−0.0408996	+	0.0408996i	0.686361	+	0.727261i	$0.259207\pi$
$384$	−1.43374e55	+	3.46136e55i	−0.392057	+	0.946510i
$385$	8.66548e55	+	3.58936e55i	2.24072	+	0.928135i
$386$	−2.14452e54	−	5.17733e54i	−0.0524449	−	0.126613i
$387$			4.40239e54i			0.101836i
$388$	7.49107e55	−	3.10290e55i	1.63931	−	0.679026i
$389$	4.17356e55	+	4.17356e55i	0.864152	+	0.864152i	0.991817	−	0.127666i	$-0.0407484\pi$
$389$	4.17356e55	+	4.17356e55i	0.864152	+	0.864152i	−0.127666	+	0.991817i	$0.540748\pi$
$390$	−9.88874e55			−1.93755
$391$	−1.71554e55	+	3.97453e55i	−0.318127	+	0.737030i
$392$	−2.65505e55			−0.466039
$393$	5.85890e55	+	5.85890e55i	0.973591	+	0.973591i
$394$	2.65371e55	−	1.09920e55i	0.417528	−	0.172946i
$395$		−	3.55444e55i		−	0.529582i
$396$	2.97089e55	+	7.17235e55i	0.419218	+	1.01208i
$397$	−2.30249e55	−	9.53724e54i	−0.307753	−	0.127476i	0.223462	−	0.974713i	$-0.428264\pi$
$397$	−2.30249e55	−	9.53724e54i	−0.307753	−	0.127476i	−0.531215	+	0.847237i	$0.678264\pi$
$398$	1.39205e55	−	3.36070e55i	0.176266	−	0.425543i
$399$	7.07031e55	−	7.07031e55i	0.848245	−	0.848245i
$400$	−4.68404e54	+	4.68404e54i	−0.0532514	+	0.0532514i
$401$	4.69742e55	−	1.13406e56i	0.506122	−	1.22189i	−0.439977	−	0.898009i	$-0.645013\pi$
$401$	4.69742e55	−	1.13406e56i	0.506122	−	1.22189i	0.946099	−	0.323878i	$-0.104987\pi$
$402$	−2.13387e56	−	8.83876e55i	−2.17925	−	0.902674i
$403$	−6.40712e55	−	1.54682e56i	−0.620304	−	1.49755i
$404$			1.33533e56i			1.22572i
$405$	−4.53556e55	+	1.87869e55i	−0.394773	+	0.163520i
$406$	−1.39675e56	−	1.39675e56i	−1.15295	−	1.15295i
$407$	1.52527e55			0.119417
$408$	−7.19810e55	−	3.10694e55i	−0.534595	−	0.230749i
$409$	−1.73433e56			−1.22203			−0.611014	−	0.791620i	$-0.709238\pi$
$409$	−1.73433e56			−1.22203			−0.611014	+	0.791620i	$0.709238\pi$
$410$	−4.27619e55	−	4.27619e55i	−0.285893	−	0.285893i
$411$	1.43003e56	−	5.92336e55i	0.907287	−	0.375811i
$412$		−	8.53617e55i		−	0.514012i
$413$	4.48581e55	+	1.08297e56i	0.256398	+	0.619000i
$414$	9.36058e55	+	3.87728e55i	0.507920	+	0.210387i
$415$	2.60245e55	−	6.28287e55i	0.134075	−	0.323686i
$416$	2.49896e56	−	2.49896e56i	1.22251	−	1.22251i
$417$	−9.91356e55	+	9.91356e55i	−0.460579	+	0.460579i
$418$	−2.91985e56	+	7.04913e56i	−1.28846	+	3.11061i
$419$	2.15102e56	+	8.90983e55i	0.901662	+	0.373481i	0.784859	−	0.619674i	$-0.212735\pi$
$419$	2.15102e56	+	8.90983e55i	0.901662	+	0.373481i	0.116803	+	0.993155i	$0.462735\pi$
$420$	1.54300e56	+	3.72514e56i	0.614480	+	1.48349i
$421$		−	6.65998e55i		−	0.252004i	−0.992030	−	0.126002i	$-0.959785\pi$
$421$		−	6.65998e55i		−	0.252004i	0.992030	−	0.126002i	$-0.0402146\pi$
$422$	−5.11066e56	+	2.11690e56i	−1.83764	+	0.761173i
$423$	−1.08975e56	−	1.08975e56i	−0.372398	−	0.372398i
$424$	−2.07601e56			−0.674317
$425$	−6.31413e55	−	6.50355e55i	−0.194963	−	0.200811i
$426$	7.80229e56			2.29042
$427$	5.15635e56	+	5.15635e56i	1.43927	+	1.43927i
$428$	−1.00752e57	+	4.17329e56i	−2.67432	+	1.10774i
$429$			7.28105e56i			1.83807i
$430$	−6.67692e55	−	1.61195e56i	−0.160326	−	0.387062i
$431$	−1.29161e56	−	5.35003e55i	−0.295033	−	0.122207i	0.230257	−	0.973130i	$-0.426043\pi$
$431$	−1.29161e56	−	5.35003e55i	−0.295033	−	0.122207i	−0.525290	+	0.850923i	$0.676043\pi$
$432$	5.11170e55	−	1.23407e56i	0.111087	−	0.268189i
$433$	9.26679e55	−	9.26679e55i	0.191619	−	0.191619i	−0.604776	−	0.796396i	$-0.706737\pi$
$433$	9.26679e55	−	9.26679e55i	0.191619	−	0.191619i	0.796396	+	0.604776i	$0.206737\pi$
$434$	−8.06602e56	+	8.06602e56i	−1.58719	+	1.58719i
$435$	−1.41970e56	+	3.42747e56i	−0.265876	+	0.641880i
$436$	2.68487e55	+	1.11211e55i	0.0478591	+	0.0198239i
$437$	2.28053e56	+	5.50570e56i	0.386978	+	0.934247i
$438$			3.69571e56i			0.597042i
$439$	4.50014e56	−	1.86402e56i	0.692212	−	0.286724i	−0.00870949	−	0.999962i	$-0.502772\pi$
$439$	4.50014e56	−	1.86402e56i	0.692212	−	0.286724i	0.700921	+	0.713238i	$0.252772\pi$
$440$	−7.15877e56	−	7.15877e56i	−1.04859	−	1.04859i
$441$	1.87330e56			0.261324
$442$	1.19343e57	+	1.22923e57i	1.58569	+	1.63326i
$443$	6.28216e56			0.795113			0.397556	−	0.917578i	$-0.369858\pi$
$443$	6.28216e56			0.795113			0.397556	+	0.917578i	$0.369858\pi$
$444$	4.63641e55	+	4.63641e55i	0.0559046	+	0.0559046i
$445$	4.67204e56	−	1.93522e56i	0.536743	−	0.222326i
$446$		−	2.71703e57i		−	2.97437i
$447$	1.85155e56	+	4.47003e56i	0.193163	+	0.466336i
$448$	−1.90809e57	−	7.90356e56i	−1.89724	−	0.785861i
$449$	−4.60154e55	+	1.11091e56i	−0.0436121	+	0.105289i	−0.944184	−	0.329417i	$-0.893148\pi$
$449$	−4.60154e55	+	1.11091e56i	−0.0436121	+	0.105289i	0.900572	+	0.434706i	$0.143148\pi$
$450$	−1.50013e56	+	1.50013e56i	−0.135538	+	0.135538i
$451$	−3.14854e56	+	3.14854e56i	−0.271215	+	0.271215i
$452$	−9.13344e55	+	2.20501e56i	−0.0750167	+	0.181106i
$453$	3.04487e56	+	1.26123e56i	0.238483	+	0.0987829i
$454$	−3.69155e56	−	8.91219e56i	−0.275745	−	0.665708i
$455$		−	2.89932e57i		−	2.06562i
$456$	−9.97114e56	+	4.13018e56i	−0.677643	+	0.280689i
$457$	−5.03293e56	−	5.03293e56i	−0.326304	−	0.326304i	0.524875	−	0.851179i	$-0.324112\pi$
$457$	−5.03293e56	−	5.03293e56i	−0.326304	−	0.326304i	−0.851179	+	0.524875i	$0.824112\pi$
$458$	−2.98833e57			−1.84850
$459$	1.67816e57	+	7.24351e56i	0.990515	+	0.427540i
$460$	−2.40310e57			−1.35356
$461$	4.24911e56	+	4.24911e56i	0.228417	+	0.228417i	0.812031	−	0.583614i	$-0.198362\pi$
$461$	4.24911e56	+	4.24911e56i	0.228417	+	0.228417i	−0.583614	+	0.812031i	$0.698362\pi$
$462$	4.58310e57	−	1.89838e57i	2.35157	−	0.974051i
$463$			1.97895e56i			0.0969269i	0.998825	+	0.0484634i	$0.0154324\pi$
$463$			1.97895e56i			0.0969269i	−0.998825	+	0.0484634i	$0.984568\pi$
$464$	−1.79753e56	−	4.33961e56i	−0.0840502	−	0.202915i
$465$	1.97931e57	+	8.19856e56i	0.883639	+	0.366015i
$466$	−1.36010e57	+	3.28357e57i	−0.579794	+	1.39975i
$467$	3.23676e57	−	3.23676e57i	1.31764	−	1.31764i	0.402008	−	0.915636i	$-0.368312\pi$
$467$	3.23676e57	−	3.23676e57i	1.31764	−	1.31764i	0.915636	−	0.402008i	$-0.131688\pi$
$468$	1.69687e57	−	1.69687e57i	0.659726	−	0.659726i
$469$	2.59147e57	−	6.25635e57i	0.962342	−	2.32330i
$470$	5.64291e57	+	2.33737e57i	2.00170	+	0.829132i
$471$	−3.36177e56	−	8.11604e56i	−0.113925	−	0.275039i
$472$		−	1.26525e57i		−	0.409661i
$473$	−1.18687e57	+	4.91620e56i	−0.367190	+	0.152095i
$474$	−1.32930e57	−	1.32930e57i	−0.392996	−	0.392996i
$475$	−1.24783e57			−0.352567
$476$	2.76840e57	−	6.41377e57i	0.747617	−	1.73206i
$477$	1.46476e57			0.378112
$478$	−7.39137e57	−	7.39137e57i	−1.82400	−	1.82400i
$479$	−6.31826e57	+	2.61711e57i	−1.49068	+	0.617460i	−0.971465	−	0.237184i	$-0.923775\pi$
$479$	−6.31826e57	+	2.61711e57i	−1.49068	+	0.617460i	−0.519215	+	0.854644i	$0.673775\pi$
$480$			4.52220e57i			1.02015i
$481$	−1.80428e56	−	4.35592e56i	−0.0389211	−	0.0939638i
$482$	1.25224e58	+	5.18693e57i	2.58330	+	1.07004i
$483$	1.48273e57	−	3.57962e57i	0.292548	−	0.706274i
$484$	−1.04346e58	+	1.04346e58i	−1.96925	+	1.96925i
$485$	5.27541e57	−	5.27541e57i	0.952377	−	0.952377i
$486$	2.77876e57	−	6.70851e57i	0.479922	−	1.15863i
$487$	3.94055e57	+	1.63223e57i	0.651154	+	0.269717i	0.683711	−	0.729753i	$-0.260365\pi$
$487$	3.94055e57	+	1.63223e57i	0.651154	+	0.269717i	−0.0325566	+	0.999470i	$0.510365\pi$
$488$	−3.01212e57	−	7.27191e57i	−0.476263	−	1.14980i
$489$			3.89839e57i			0.589854i
$490$	−6.85917e57	+	2.84116e57i	−0.993244	+	0.411415i
$491$	−4.06441e57	−	4.06441e57i	−0.563308	−	0.563308i	0.366938	−	0.930245i	$-0.380406\pi$
$491$	−4.06441e57	−	4.06441e57i	−0.563308	−	0.563308i	−0.930245	+	0.366938i	$0.880406\pi$
$492$	−1.91415e57			−0.253937
$493$	5.97393e57	−	2.37169e57i	0.758668	−	0.301195i
$494$	2.35851e58			2.86754
$495$	5.05096e57	+	5.05096e57i	0.587979	+	0.587979i
$496$	−2.50606e57	+	1.03804e57i	−0.279341	+	0.115707i
$497$			2.28758e58i			2.44182i
$498$	−1.37641e57	−	3.32296e57i	−0.140708	−	0.339699i
$499$	−8.45425e57	−	3.50186e57i	−0.827777	−	0.342876i	−0.0717547	−	0.997422i	$-0.522860\pi$
$499$	−8.45425e57	−	3.50186e57i	−0.827777	−	0.342876i	−0.756022	+	0.654546i	$0.772860\pi$
$500$	−4.95439e57	+	1.19610e58i	−0.464660	+	1.12179i
$501$	3.53457e57	−	3.53457e57i	0.317560	−	0.317560i
$502$	−6.66222e57	+	6.66222e57i	−0.573441	+	0.573441i
$503$	1.91477e57	−	4.62265e57i	0.157908	−	0.381223i	−0.825049	−	0.565062i	$-0.808852\pi$
$503$	1.91477e57	−	4.62265e57i	0.157908	−	0.381223i	0.982956	+	0.183838i	$0.0588523\pi$
$504$	−4.97038e57	−	2.05880e57i	−0.392765	−	0.162689i
$505$	4.70188e57	+	1.13513e58i	0.356047	+	0.859573i
$506$			2.95657e58i			2.14562i
$507$	1.08003e58	−	4.47361e57i	0.751213	−	0.311163i
$508$	−2.23666e58	−	2.23666e58i	−1.49118	−	1.49118i
$509$	3.42704e56			0.0219022			0.0109511	−	0.999940i	$-0.496514\pi$
$509$	3.42704e56			0.0219022			0.0109511	+	0.999940i	$0.496514\pi$
$510$	−2.19206e58	−	3.23940e56i	−1.34306	−	0.0198475i
$511$	−1.08356e58			−0.636507
$512$	−6.66299e57	−	6.66299e57i	−0.375288	−	0.375288i
$513$	2.32467e58	−	9.62908e57i	1.25556	−	0.520070i
$514$			3.19351e58i			1.65410i
$515$	−3.00570e57	−	7.25640e57i	−0.149310	−	0.360467i
$516$	−5.10217e57	−	2.11339e57i	−0.243101	−	0.100696i
$517$	1.72100e58	−	4.15486e58i	0.786564	−	1.89893i
$518$	−2.27143e57	+	2.27143e57i	−0.0995887	+	0.0995887i
$519$	−2.35368e58	+	2.35368e58i	−0.990032	+	0.990032i
$520$	−1.19760e58	+	2.89126e58i	−0.483325	+	1.16685i
$521$	2.91602e58	+	1.20785e58i	1.12922	+	0.467739i	0.867516	−	0.497409i	$-0.165715\pi$
$521$	2.91602e58	+	1.20785e58i	1.12922	+	0.467739i	0.261705	+	0.965148i	$0.415715\pi$
$522$	−5.75685e57	−	1.38983e58i	−0.213929	−	0.516470i
$523$			4.14748e57i			0.147910i	0.997262	+	0.0739550i	$0.0235621\pi$
$523$			4.14748e57i			0.147910i	−0.997262	+	0.0739550i	$0.976438\pi$
$524$	7.36238e58	−	3.04960e58i	2.51997	−	1.04381i
$525$	5.73672e57	+	5.73672e57i	0.188469	+	0.188469i
$526$	3.15075e58			0.993619
$527$	−1.36961e58	−	3.44986e58i	−0.414638	−	1.04441i
$528$	1.17963e58			0.342860
$529$	−9.00993e57	−	9.00993e57i	−0.251434	−	0.251434i
$530$	−5.36326e58	+	2.22153e58i	−1.43714	+	0.595281i
$531$			8.92716e57i			0.229711i
$532$	−3.68014e58	−	8.88465e58i	−0.909420	−	2.19553i
$533$	1.27162e58	+	5.26724e57i	0.301803	+	0.125011i
$534$	1.02352e58	−	2.47101e58i	0.233325	−	0.563296i
$535$	−7.09523e58	+	7.09523e58i	−1.55368	+	1.55368i
$536$	−5.16853e58	+	5.16853e58i	−1.08724	+	1.08724i
$537$	8.54427e57	−	2.06277e58i	0.172674	−	0.416873i
$538$	6.06777e58	+	2.51335e58i	1.17818	+	0.488016i
$539$	2.09194e58	+	5.05038e58i	0.390293	+	0.942250i
$540$			1.01466e59i			1.81909i
$541$	−2.55439e58	+	1.05806e58i	−0.440095	+	0.182293i	−0.591718	−	0.806145i	$-0.701550\pi$
$541$	−2.55439e58	+	1.05806e58i	−0.440095	+	0.182293i	0.151623	+	0.988438i	$0.451550\pi$
$542$	7.62994e57	+	7.62994e57i	0.126339	+	0.126339i
$543$	−2.54888e58			−0.405652
$544$	5.62138e58	−	5.45765e58i	0.859937	−	0.834891i
$545$	2.67393e57			0.0393211
$546$	−1.08430e59	−	1.08430e59i	−1.53287	−	1.53287i
$547$	−9.69973e58	+	4.01776e58i	−1.31835	+	0.546080i	−0.927311	−	0.374292i	$-0.877886\pi$
$547$	−9.69973e58	+	4.01776e58i	−1.31835	+	0.546080i	−0.391044	+	0.920372i	$0.627886\pi$
$548$		−	1.48868e59i		−	1.94544i
$549$	2.12524e58	+	5.13079e58i	0.267056	+	0.644731i
$550$	−5.71954e58	−	2.36911e58i	−0.691136	−	0.286278i
$551$	3.38606e58	−	8.17467e58i	0.393491	−	0.949972i
$552$	−2.95721e58	+	2.95721e58i	−0.330516	+	0.330516i
$553$	3.89742e58	−	3.89742e58i	0.418974	−	0.418974i
$554$	−2.72032e58	+	6.56744e58i	−0.281294	+	0.679104i
$555$	5.57384e57	+	2.30876e57i	0.0554441	+	0.0229657i
$556$	5.16007e58	+	1.24575e59i	0.493796	+	1.19213i
$557$		−	6.48778e58i		−	0.597324i	−0.954359	−	0.298662i	$-0.903460\pi$
$557$		−	6.48778e58i		−	0.597324i	0.954359	−	0.298662i	$-0.0965403\pi$
$558$	−8.02603e58	+	3.32449e58i	−0.710994	+	0.294503i
$559$	2.80797e58	+	2.80797e58i	0.239353	+	0.239353i
$560$	−4.69730e58			−0.385306
$561$	−2.38516e57	+	1.61401e59i	−0.0188285	+	1.27410i
$562$	−2.80118e59			−2.12819
$563$	−5.49642e58	−	5.49642e58i	−0.401929	−	0.401929i	0.476983	−	0.878912i	$-0.341730\pi$
$563$	−5.49642e58	−	5.49642e58i	−0.401929	−	0.401929i	−0.878912	+	0.476983i	$0.841730\pi$
$564$	1.78610e59	−	7.39828e58i	1.25720	−	0.520751i
$565$			2.19602e58i			0.148797i
$566$	1.16586e58	+	2.81464e58i	0.0760490	+	0.183598i
$567$	−7.03319e58	−	2.91324e58i	−0.441689	−	0.182954i
$568$	9.44914e58	−	2.28122e59i	0.571351	−	1.37936i
$569$	6.47617e57	−	6.47617e57i	0.0377055	−	0.0377055i	−0.688003	−	0.725708i	$-0.741512\pi$
$569$	6.47617e57	−	6.47617e57i	0.0377055	−	0.0377055i	0.725708	+	0.688003i	$0.241512\pi$
$570$	−2.13402e59	+	2.13402e59i	−1.19643	+	1.19643i
$571$	−2.36252e58	+	5.70364e58i	−0.127556	+	0.307947i	−0.974736	−	0.223358i	$-0.928298\pi$
$571$	−2.36252e58	+	5.70364e58i	−0.127556	+	0.307947i	0.847181	+	0.531305i	$0.178298\pi$
$572$	6.46965e59	+	2.67982e59i	3.36408	+	1.39345i
$573$	1.84332e57	+	4.45018e57i	0.00923160	+	0.0222871i
$574$		−	9.37764e58i		−	0.452364i
$575$	−4.46723e58	+	1.85039e58i	−0.207577	+	0.0859812i
$576$	−1.11219e59	−	1.11219e59i	−0.497848	−	0.497848i
$577$	3.06351e58			0.132111			0.0660555	−	0.997816i	$-0.478959\pi$
$577$	3.06351e58			0.132111			0.0660555	+	0.997816i	$0.478959\pi$
$578$	2.60524e59	+	2.76397e59i	1.08243	+	1.14838i
$579$	−1.63206e58			−0.0653352
$580$	2.52298e59	+	2.52298e59i	0.973223	+	0.973223i
$581$	9.74270e58	−	4.03556e58i	0.362153	−	0.150009i
$582$		−	3.94583e59i		−	1.41349i
$583$	1.63571e59	+	3.94895e59i	0.564718	+	1.36335i
$584$	1.08055e59	+	4.47578e58i	0.359557	+	0.148933i
$585$	8.44981e58	−	2.03996e59i	0.271016	−	0.654292i
$586$	−5.18446e59	+	5.18446e59i	−1.60289	+	1.60289i
$587$	1.01389e59	−	1.01389e59i	0.302183	−	0.302183i	−0.539684	−	0.841867i	$-0.681456\pi$
$587$	1.01389e59	−	1.01389e59i	0.302183	−	0.302183i	0.841867	+	0.539684i	$0.181456\pi$
$588$	−8.99289e58	+	2.17107e59i	−0.258396	+	0.623824i
$589$	−4.72075e59	−	1.95540e59i	−1.30777	−	0.541697i
$590$	−1.35394e59	−	3.26871e59i	−0.361645	−	0.873089i
$591$		−	8.36535e58i		−	0.215453i
$592$	−7.05720e57	+	2.92319e57i	−0.0175273	+	0.00726005i
$593$	−7.55641e58	−	7.55641e58i	−0.180984	−	0.180984i	0.610801	−	0.791784i	$-0.290848\pi$
$593$	−7.55641e58	−	7.55641e58i	−0.180984	−	0.180984i	−0.791784	+	0.610801i	$0.790848\pi$
$594$	1.24835e60			2.88355
$595$	9.49771e57	−	6.42698e59i	0.0211594	−	1.43183i
$596$	4.65336e59			0.999936
$597$	−7.49108e58	−	7.49108e58i	−0.155273	−	0.155273i
$598$	8.44348e59	−	3.49740e59i	1.68829	−	0.699311i
$599$			5.56922e59i			1.07428i	0.843493	+	0.537141i	$0.180496\pi$
$599$			5.56922e59i			1.07428i	−0.843493	+	0.537141i	$0.819504\pi$
$600$	−3.35116e58	−	8.09041e58i	−0.0623653	−	0.150563i
$601$	−6.32819e59	−	2.62122e59i	−1.13626	−	0.470655i	−0.266357	−	0.963875i	$-0.585820\pi$
$601$	−6.32819e59	−	2.62122e59i	−1.13626	−	0.470655i	−0.869905	+	0.493220i	$0.835820\pi$
$602$	1.03538e59	−	2.49962e59i	0.179380	−	0.433061i
$603$	3.64672e59	−	3.64672e59i	0.609650	−	0.609650i
$604$	2.24135e59	−	2.24135e59i	0.361589	−	0.361589i
$605$	−5.19604e59	+	1.25443e60i	−0.808968	+	1.95302i
$606$	6.00364e59	+	2.48679e59i	0.902097	+	0.373661i
$607$	−7.21370e57	−	1.74154e58i	−0.0104617	−	0.0252567i	0.918562	−	0.395276i	$-0.129351\pi$
$607$	−7.21370e57	−	1.74154e58i	−0.0104617	−	0.0252567i	−0.929024	+	0.370019i	$0.879351\pi$
$608$		−	1.07857e60i		−	1.50980i
$609$	−5.31489e59	+	2.20150e59i	−0.718163	+	0.297473i
$610$	−1.55633e60	−	1.55633e60i	−2.03007	−	2.03007i
$611$	−1.39014e60			−1.75054
$612$	3.81709e59	−	3.70592e59i	0.464063	−	0.450547i
$613$	−1.91686e59			−0.225004			−0.112502	−	0.993651i	$-0.535886\pi$
$613$	−1.91686e59			−0.225004			−0.112502	+	0.993651i	$0.535886\pi$
$614$	6.43252e58	+	6.43252e58i	0.0729056	+	0.0729056i
$615$	−1.62717e59	+	6.73996e58i	−0.178081	+	0.0737636i
$616$		−	1.56991e60i		−	1.65916i
$617$	−2.19702e59	−	5.30407e59i	−0.224235	−	0.541351i	0.771222	−	0.636566i	$-0.219646\pi$
$617$	−2.19702e59	−	5.30407e59i	−0.224235	−	0.541351i	−0.995457	+	0.0952158i	$0.969646\pi$
$618$	−3.83785e59	−	1.58969e59i	−0.378300	−	0.156697i
$619$	6.79587e59	−	1.64067e60i	0.646988	−	1.56197i	−0.170082	−	0.985430i	$-0.554403\pi$
$619$	6.79587e59	−	1.64067e60i	0.646988	−	1.56197i	0.817071	−	0.576538i	$-0.195597\pi$
$620$	1.45698e60	−	1.45698e60i	1.33978	−	1.33978i
$621$	6.89443e59	−	6.89443e59i	0.612391	−	0.612391i
$622$	−5.99928e59	+	1.44835e60i	−0.514761	+	1.24274i
$623$	7.24483e59	+	3.00091e59i	0.600531	+	0.248748i
$624$	−1.39542e59	−	3.36884e59i	−0.111747	−	0.269781i
$625$			1.55297e60i			1.20155i
$626$	7.46156e59	−	3.09068e59i	0.557804	−	0.231050i
$627$	1.57127e60	+	1.57127e60i	1.13501	+	1.13501i
$628$	−8.44890e59			−0.589750
$629$	−3.85690e58	−	9.71497e58i	−0.0260165	−	0.0655319i
$630$	−1.50438e60			−0.980699
$631$	−2.54054e59	−	2.54054e59i	−0.160064	−	0.160064i	0.622531	−	0.782595i	$-0.286104\pi$
$631$	−2.54054e59	−	2.54054e59i	−0.160064	−	0.160064i	−0.782595	+	0.622531i	$0.786104\pi$
$632$	−5.49647e59	+	2.27671e59i	−0.334708	+	0.138641i
$633$			1.61104e60i			0.948260i
$634$	8.36757e59	+	2.02011e60i	0.476080	+	1.14936i
$635$	−2.68888e60	−	1.11377e60i	−1.47889	−	0.612578i
$636$	−7.03163e59	+	1.69759e60i	−0.373877	+	0.902618i
$637$	1.19485e60	−	1.19485e60i	0.614207	−	0.614207i
$638$	3.10407e60	−	3.10407e60i	1.54272	−	1.54272i
$639$	−6.66696e59	+	1.60955e60i	−0.320375	+	0.773455i
$640$	3.06309e60	+	1.26878e60i	1.42328	+	0.589543i
$641$	−1.39364e60	−	3.36455e60i	−0.626187	−	1.51175i	−0.844325	−	0.535831i	$-0.819998\pi$
$641$	−1.39364e60	−	3.36455e60i	−0.626187	−	1.51175i	0.218138	−	0.975918i	$-0.430002\pi$
$642$			5.30700e60i			2.30593i
$643$	3.86778e59	−	1.60209e59i	0.162527	−	0.0673209i	−0.299937	−	0.953959i	$-0.596966\pi$
$643$	3.86778e59	−	1.60209e59i	0.162527	−	0.0673209i	0.462464	+	0.886638i	$0.346966\pi$
$644$	−2.63498e60	−	2.63498e60i	−1.07086	−	1.07086i
$645$	−5.08139e59			−0.199732
$646$	5.22818e60	+	7.72613e58i	1.98770	+	0.0293740i
$647$	−4.23283e60			−1.55664			−0.778321	−	0.627867i	$-0.783928\pi$
$647$	−4.23283e60			−1.55664			−0.778321	+	0.627867i	$0.783928\pi$
$648$	5.81029e59	+	5.81029e59i	0.206698	+	0.206698i
$649$	−2.40674e60	+	9.96905e59i	−0.828263	+	0.343078i
$650$			1.91366e60i			0.637128i
$651$	1.27133e60	+	3.06927e60i	0.409513	+	0.988653i
$652$	3.46395e60	+	1.43482e60i	1.07956	+	0.447170i
$653$	−1.18350e60	+	2.85722e60i	−0.356891	+	0.861610i	0.638843	+	0.769337i	$0.279413\pi$
$653$	−1.18350e60	+	2.85722e60i	−0.356891	+	0.861610i	−0.995734	+	0.0922732i	$0.970587\pi$
$654$	1.00001e59	−	1.00001e59i	0.0291797	−	0.0291797i
$655$	5.18478e60	−	5.18478e60i	1.46400	−	1.46400i
$656$	8.53366e58	−	2.06021e59i	0.0233186	−	0.0562961i
$657$	−7.62394e59	−	3.15794e59i	−0.201616	−	0.0835119i
$658$	3.62451e60	+	8.75034e60i	0.927668	+	2.23959i
$659$			6.13973e60i			1.52094i	0.649372	+	0.760471i	$0.275032\pi$
$659$			6.13973e60i			1.52094i	−0.649372	+	0.760471i	$0.724968\pi$
$660$	−8.27857e60	+	3.42910e60i	−1.98500	+	0.822214i
$661$	2.70214e60	+	2.70214e60i	0.627158	+	0.627158i	0.947352	−	0.320194i	$-0.103748\pi$
$661$	2.70214e60	+	2.70214e60i	0.627158	+	0.627158i	−0.320194	+	0.947352i	$0.603748\pi$
$662$	−7.93829e60			−1.78353
$663$	4.63756e60	−	1.84114e60i	1.00867	−	0.400447i
$664$	−1.13826e60			−0.239677
$665$	−6.25680e60	−	6.25680e60i	−1.27552	−	1.27552i
$666$	−2.26017e59	+	9.36194e58i	−0.0446114	+	0.0184786i
$667$		−	3.42865e60i		−	0.655266i
$668$	−1.83977e60	−	4.44159e60i	−0.340462	−	0.821949i
$669$	−7.31065e60	−	3.02817e60i	−1.31007	−	0.542649i
$670$	−7.82177e60	+	1.88834e61i	−1.35737	+	3.27697i
$671$	−1.14592e61	+	1.14592e61i	−1.92584	+	1.92584i
$672$	−4.95857e60	+	4.95857e60i	−0.807080	+	0.807080i
$673$	3.22028e60	−	7.77445e60i	0.507657	−	1.22559i	−0.437572	−	0.899183i	$-0.644162\pi$
$673$	3.22028e60	−	7.77445e60i	0.507657	−	1.22559i	0.945229	−	0.326408i	$-0.105838\pi$
$674$	−2.07265e60	−	8.58518e59i	−0.316474	−	0.131088i
$675$	7.81287e59	+	1.88619e60i	0.115553	+	0.278968i
$676$		−	1.12432e61i		−	1.61078i
$677$	1.01760e61	−	4.21502e60i	1.41228	−	0.584983i	0.459368	−	0.888246i	$-0.348076\pi$
$677$	1.01760e61	−	4.21502e60i	1.41228	−	0.584983i	0.952907	+	0.303263i	$0.0980759\pi$
$678$	8.21276e59	+	8.21276e59i	0.110421	+	0.110421i
$679$	1.15689e61			1.50693
$680$	−2.74946e60	+	6.36989e60i	−0.346981	+	0.803878i
$681$	−2.80941e60			−0.343520
$682$	−1.79255e61	−	1.79255e61i	−2.12377	−	2.12377i
$683$	7.04495e60	−	2.91811e60i	0.808785	−	0.335010i	0.0603157	−	0.998179i	$-0.480789\pi$
$683$	7.04495e60	−	2.91811e60i	0.808785	−	0.335010i	0.748469	+	0.663170i	$0.230789\pi$
$684$		−	7.32380e60i		−	0.814761i
$685$	−5.24182e60	−	1.26549e61i	−0.565112	−	1.36430i
$686$	7.02704e60	+	2.91069e60i	0.734182	+	0.304108i
$687$	−3.33053e60	+	8.04061e60i	−0.337243	+	0.814178i
$688$	4.54931e59	−	4.54931e59i	0.0446472	−	0.0446472i
$689$	9.34264e60	−	9.34264e60i	0.888702	−	0.888702i
$690$	−4.47528e60	+	1.08043e61i	−0.412634	+	0.996187i
$691$	7.35052e60	+	3.04469e60i	0.656962	+	0.272123i	0.686160	−	0.727451i	$-0.259295\pi$
$691$	7.35052e60	+	3.04469e60i	0.656962	+	0.272123i	−0.0291975	+	0.999574i	$0.509295\pi$
$692$	1.22511e61	+	2.95767e61i	1.06143	+	2.56253i
$693$			1.10767e61i			0.930349i
$694$	2.73473e61	−	1.13276e61i	2.22683	−	0.922382i
$695$	8.77291e60	+	8.77291e60i	0.692580	+	0.692580i
$696$	6.20948e60			0.475288
$697$	2.80158e60	+	1.20926e60i	0.207921	+	0.0897458i
$698$	−2.45029e61			−1.76330
$699$	7.31918e60	+	7.31918e60i	0.510744	+	0.510744i
$700$	7.20885e60	−	2.98600e60i	0.487818	−	0.202061i
$701$			1.19109e61i			0.781641i	0.920467	+	0.390820i	$0.127809\pi$
$701$			1.19109e61i			0.781641i	−0.920467	+	0.390820i	$0.872191\pi$
$702$	−1.47671e61	−	3.56509e61i	−0.939824	−	2.26893i
$703$	−1.32939e60	−	5.50650e59i	−0.0820563	−	0.0339888i
$704$	1.75645e61	−	4.24044e61i	1.05153	−	2.53863i
$705$	1.25782e61	−	1.25782e61i	0.730386	−	0.730386i
$706$	−2.07422e61	+	2.07422e61i	−1.16830	+	1.16830i
$707$	−7.29110e60	+	1.76023e61i	−0.398360	+	0.961726i
$708$	−1.03462e61	−	4.28552e60i	−0.548359	−	0.227138i
$709$	−2.87681e60	−	6.94524e60i	−0.147917	−	0.357103i	0.832503	−	0.554020i	$-0.186907\pi$
$709$	−2.87681e60	−	6.94524e60i	−0.147917	−	0.357103i	−0.980420	+	0.196917i	$0.936907\pi$
$710$		−	6.90456e61i		−	3.44415i
$711$	3.87810e60	−	1.60636e60i	0.187682	−	0.0777404i
$712$	−5.98513e60	−	5.98513e60i	−0.281031	−	0.281031i
$713$	−1.97999e61			−0.902066
$714$	−2.36806e61	−	2.43910e61i	−1.04684	−	1.07825i
$715$	6.44329e61			2.76394
$716$	−1.51842e61	−	1.51842e61i	−0.632065	−	0.632065i
$717$	−2.81255e61	+	1.16500e61i	−1.13616	+	0.470612i
$718$			6.12933e60i			0.240291i
$719$	1.05484e61	+	2.54660e61i	0.401341	+	0.968923i	0.987341	+	0.158612i	$0.0507019\pi$
$719$	1.05484e61	+	2.54660e61i	0.401341	+	0.968923i	−0.586000	+	0.810311i	$0.699298\pi$
$720$	−3.30503e60	−	1.36899e60i	−0.122047	−	0.0505534i
$721$	4.66087e60	−	1.12523e61i	0.167055	−	0.403306i
$722$	1.88221e61	−	1.88221e61i	0.654813	−	0.654813i
$723$	2.79127e61	−	2.79127e61i	0.942601	−	0.942601i
$724$	−9.38126e60	+	2.26484e61i	−0.307526	+	0.742434i
$725$	6.63278e60	+	2.74739e60i	0.211071	+	0.0874285i
$726$	2.74814e61	+	6.63460e61i	0.848989	+	2.04964i
$727$		−	8.86931e60i		−	0.266011i	−0.991115	−	0.133006i	$-0.957537\pi$
$727$		−	8.86931e60i		−	0.266011i	0.991115	−	0.133006i	$-0.0424629\pi$
$728$	−4.48341e61	+	1.85709e61i	−1.30552	+	0.540764i
$729$	−2.44000e61	−	2.44000e61i	−0.689840	−	0.689840i
$730$	3.27049e61			0.897782
$731$	6.13251e60	+	6.31648e60i	0.163461	+	0.168365i
$732$	−6.96659e61			−1.80315
$733$	7.51982e60	+	7.51982e60i	0.189004	+	0.189004i	0.795266	−	0.606261i	$-0.207331\pi$
$733$	7.51982e60	+	7.51982e60i	0.189004	+	0.189004i	−0.606261	+	0.795266i	$0.707331\pi$
$734$	4.33662e61	−	1.79629e61i	1.05849	−	0.438441i
$735$			2.16223e61i			0.512536i
$736$	−1.59939e61	−	3.86127e61i	−0.368198	−	0.888909i
$737$	1.39038e62	+	5.75914e61i	3.10873	+	1.28768i
$738$	2.73303e60	−	6.59812e60i	0.0593517	−	0.143288i
$739$	−2.48814e61	+	2.48814e61i	−0.524831	+	0.524831i	−0.919027	−	0.394195i	$-0.871023\pi$
$739$	−2.48814e61	+	2.48814e61i	−0.524831	+	0.524831i	0.394195	+	0.919027i	$0.371023\pi$
$740$	4.10294e60	−	4.10294e60i	0.0840646	−	0.0840646i
$741$	2.62860e61	−	6.34599e61i	0.523157	−	1.26301i
$742$	−8.31669e61	−	3.44488e61i	−1.60793	−	0.666025i
$743$	1.24238e61	+	2.99938e61i	0.233343	+	0.563341i	0.996567	−	0.0827939i	$-0.0263843\pi$
$743$	1.24238e61	+	2.99938e61i	0.233343	+	0.563341i	−0.763223	+	0.646135i	$0.776384\pi$
$744$		−	3.58588e61i		−	0.654301i
$745$	3.95571e61	−	1.63851e61i	0.701237	−	0.290462i
$746$	1.16788e62	+	1.16788e62i	2.01146	+	2.01146i
$747$	8.03111e60			0.134395
$748$	1.42536e62	+	6.15235e61i	2.31762	+	1.00036i
$749$	−1.55598e62			−2.45835
$750$	4.45498e61	+	4.45498e61i	0.683956	+	0.683956i
$751$	−8.84006e61	+	3.66167e61i	−1.31885	+	0.546287i	−0.927455	−	0.373934i	$-0.878009\pi$
$751$	−8.84006e61	+	3.66167e61i	−1.31885	+	0.546287i	−0.391398	+	0.920221i	$0.628009\pi$
$752$			2.25223e61i			0.326534i
$753$	1.05007e61	+	2.53510e61i	0.147954	+	0.357193i
$754$	−1.25366e62	−	5.19283e61i	−1.71671	−	0.711083i
$755$	1.11611e61	−	2.69453e61i	0.148541	−	0.358611i
$756$	−1.11257e62	+	1.11257e62i	−1.43915	+	1.43915i
$757$	2.51313e61	−	2.51313e61i	0.315976	−	0.315976i	−0.531243	−	0.847219i	$-0.678275\pi$
$757$	2.51313e61	−	2.51313e61i	0.315976	−	0.315976i	0.847219	+	0.531243i	$0.178275\pi$
$758$	1.26937e61	−	3.06454e61i	0.155132	−	0.374522i
$759$	7.95516e61	+	3.29514e61i	0.945041	+	0.391449i
$760$	3.65496e61	+	8.82386e61i	0.422076	+	1.01898i
$761$			4.10979e61i			0.461371i	0.973028	+	0.230685i	$0.0740968\pi$
$761$			4.10979e61i			0.461371i	−0.973028	+	0.230685i	$0.925903\pi$
$762$	−1.42213e62	+	5.89065e61i	−1.55206	+	0.642882i
$763$	2.93196e60	+	2.93196e60i	0.0311085	+	0.0311085i
$764$	4.63269e60			0.0477888
$765$	1.93991e61	−	4.49436e61i	0.194564	−	0.450761i
$766$	9.36027e60			0.0912788
$767$	5.69400e61	+	5.69400e61i	0.539904	+	0.539904i
$768$	3.96973e61	−	1.64431e61i	0.366011	−	0.151607i
$769$		−	1.21224e62i		−	1.08686i	−0.839455	−	0.543429i	$-0.817126\pi$
$769$		−	1.21224e62i		−	1.08686i	0.839455	−	0.543429i	$-0.182874\pi$
$770$	−1.67996e62	−	4.05577e62i	−1.46470	−	3.53609i
$771$	8.59270e61	+	3.55921e61i	0.728552	+	0.301776i
$772$	−6.00686e60	+	1.45018e61i	−0.0495308	+	0.119578i
$773$	9.44017e61	−	9.44017e61i	0.757043	−	0.757043i	−0.218740	−	0.975783i	$-0.570195\pi$
$773$	9.44017e61	−	9.44017e61i	0.757043	−	0.757043i	0.975783	+	0.218740i	$0.0701947\pi$
$774$	1.45698e61	−	1.45698e61i	0.113638	−	0.113638i
$775$	1.58657e61	−	3.83033e61i	0.120358	−	0.290569i
$776$	−1.15368e62	−	4.77869e61i	−0.851250	−	0.352599i
$777$	3.58014e60	+	8.64322e60i	0.0256950	+	0.0620331i
$778$		−	2.76250e62i		−	1.92860i
$779$	3.88088e61	−	1.60751e61i	0.263557	−	0.109169i
$780$	1.95859e62	+	1.95859e62i	1.29393	+	1.29393i
$781$	−5.08380e62			−3.26732
$782$	1.88314e62	−	7.47619e61i	1.17744	−	0.467450i
$783$	−1.44768e62			−0.880630
$784$	−1.93582e61	−	1.93582e61i	−0.114570	−	0.114570i
$785$	−7.18221e61	+	2.97497e61i	−0.413581	+	0.171311i
$786$		−	3.87804e62i		−	2.17284i
$787$	4.15767e61	+	1.00375e62i	0.226670	+	0.547229i	0.995768	−	0.0919013i	$-0.0292944\pi$
$787$	4.15767e61	+	1.00375e62i	0.226670	+	0.547229i	−0.769098	+	0.639130i	$0.779294\pi$
$788$	−7.43312e61	−	3.07890e61i	−0.394328	−	0.163336i
$789$	3.51155e61	−	8.47763e61i	0.181277	−	0.437642i
$790$	−1.17635e62	+	1.17635e62i	−0.590955	+	0.590955i
$791$	−2.40793e61	+	2.40793e61i	−0.117720	+	0.117720i
$792$	4.57537e61	−	1.10459e62i	0.217688	−	0.525546i
$793$	4.62810e62	+	1.91702e62i	2.14304	+	0.887675i
$794$	4.46379e61	+	1.07765e62i	0.201170	+	0.485667i
$795$			1.69067e62i			0.741593i
$796$	−9.41340e61	+	3.89916e61i	−0.401898	+	0.166471i
$797$	3.11943e62	+	3.11943e62i	1.29635	+	1.29635i	0.930789	+	0.365558i	$0.119122\pi$
$797$	3.11943e62	+	3.11943e62i	1.29635	+	1.29635i	0.365558	+	0.930789i	$0.380878\pi$
$798$	−4.67988e62			−1.89309
$799$	−3.08156e62	−	4.55389e60i	−1.21343	−	0.0179319i
$800$	8.75130e61			0.335458
$801$	4.22289e61	+	4.22289e61i	0.157583	+	0.157583i
$802$	−5.30782e62	+	2.19857e62i	−1.92827	+	0.798714i
$803$		−	2.40805e62i		−	0.851689i
$804$	2.47576e62	+	5.97701e62i	0.852518	+	2.05816i
$805$	−3.16775e62	−	1.31212e62i	−1.06204	−	0.439910i
$806$	−2.99878e62	+	7.23969e62i	−0.978906	+	2.36329i
$807$	1.35252e62	−	1.35252e62i	0.429896	−	0.429896i
$808$	1.45417e62	−	1.45417e62i	0.450060	−	0.450060i
$809$	1.19131e60	−	2.87608e60i	0.00359032	−	0.00866779i	−0.922074	−	0.387013i	$-0.873507\pi$
$809$	1.19131e60	−	2.87608e60i	0.00359032	−	0.00866779i	0.925665	+	0.378345i	$0.123507\pi$
$810$	2.12281e62	+	8.79298e61i	0.622994	+	0.258053i
$811$	−1.28252e62	−	3.09627e62i	−0.366534	−	0.884892i	−0.994313	−	0.106500i	$-0.966036\pi$
$811$	−1.28252e62	−	3.09627e62i	−0.366534	−	0.884892i	0.627778	−	0.778392i	$-0.283964\pi$
$812$			5.53287e62i			1.53991i
$813$	2.90333e61	−	1.20260e61i	0.0786956	−	0.0325968i
$814$	−5.04792e61	−	5.04792e61i	−0.133256	−	0.133256i
$815$	3.44984e62			0.886972
$816$	−2.98290e61	−	7.51350e61i	−0.0746965	−	0.188150i
$817$	1.21194e62			0.295601
$818$	5.73982e62	+	5.73982e62i	1.36365	+	1.36365i
$819$	3.16333e62	−	1.31029e62i	0.732049	−	0.303225i
$820$			1.69391e62i			0.381849i
$821$	2.58316e61	+	6.23629e61i	0.0567248	+	0.136946i	0.949701	−	0.313158i	$-0.101387\pi$
$821$	2.58316e61	+	6.23629e61i	0.0567248	+	0.136946i	−0.892976	+	0.450104i	$0.851387\pi$
$822$	−6.69306e62	−	2.77236e62i	−1.43180	−	0.593069i
$823$	−2.03384e62	+	4.91013e62i	−0.423858	+	1.02328i	0.557340	+	0.830284i	$0.311822\pi$
$823$	−2.03384e62	+	4.91013e62i	−0.423858	+	1.02328i	−0.981199	+	0.193000i	$0.938178\pi$
$824$	−9.29583e61	+	9.29583e61i	−0.188735	+	0.188735i
$825$	−1.27490e62	+	1.27490e62i	−0.252183	+	0.252183i
$826$	2.09953e62	−	5.06872e62i	0.404624	−	0.976848i
$827$	−6.08936e62	−	2.52230e62i	−1.14341	−	0.473618i	−0.271094	−	0.962553i	$-0.587385\pi$
$827$	−6.08936e62	−	2.52230e62i	−1.14341	−	0.473618i	−0.872320	+	0.488935i	$0.837385\pi$
$828$	−1.08604e62	−	2.62192e62i	−0.198697	−	0.479697i
$829$			3.14145e62i			0.560025i	0.959996	+	0.280013i	$0.0903387\pi$
$829$			3.14145e62i			0.560025i	−0.959996	+	0.280013i	$0.909661\pi$
$830$	−2.94062e62	+	1.21804e62i	−0.510811	+	0.211585i
$831$	1.46390e62	+	1.46390e62i	0.247793	+	0.247793i
$832$	−1.41878e63			−2.34025
$833$	2.68779e62	−	2.60951e62i	0.432043	−	0.419460i
$834$	6.56184e62			1.02791
$835$	−3.12789e62	−	3.12789e62i	−0.477520	−	0.477520i
$836$	1.97448e63	−	8.17856e62i	2.93777	−	1.21686i
$837$			8.36010e62i			1.21231i
$838$	−4.17014e62	−	1.00676e63i	−0.589392	−	1.42292i
$839$	1.25514e63	+	5.19895e62i	1.72906	+	0.716199i	0.999478	+	0.0323037i	$0.0102844\pi$
$839$	1.25514e63	+	5.19895e62i	1.72906	+	0.716199i	0.729580	+	0.683896i	$0.239716\pi$
$840$	2.37633e62	−	5.73697e62i	0.319082	−	0.770333i
$841$	1.80286e62	−	1.80286e62i	0.235965	−	0.235965i
$842$	−2.20414e62	+	2.20414e62i	−0.281209	+	0.281209i
$843$	−3.12195e62	+	7.53705e62i	−0.388269	+	0.937365i
$844$	1.43151e63	+	5.92950e62i	1.73553	+	0.718879i
$845$	−3.95888e62	−	9.55758e62i	−0.467900	−	1.12961i
$846$			7.21309e62i			0.831110i
$847$	−1.94522e63	+	8.05738e62i	−2.18512	+	0.905108i
$848$	−1.51364e62	−	1.51364e62i	−0.165772	−	0.165772i
$849$	8.87263e61			0.0947408
$850$	−6.26884e60	+	4.24205e62i	−0.00652650	+	0.441640i
$851$	−5.57576e61			−0.0566003
$852$	−1.54534e63	−	1.54534e63i	−1.52958	−	1.52958i
$853$	−1.12473e62	+	4.65877e61i	−0.108553	+	0.0449642i	−0.436299	−	0.899802i	$-0.643711\pi$
$853$	−1.12473e62	+	4.65877e61i	−0.108553	+	0.0449642i	0.327746	+	0.944766i	$0.393711\pi$
$854$		−	3.41302e63i		−	3.21214i
$855$	−2.57881e62	−	6.22579e62i	−0.236672	−	0.571377i
$856$	1.55165e63	+	6.42716e62i	1.38870	+	0.575219i
$857$	−5.27450e61	+	1.27338e62i	−0.0460356	+	0.111140i	−0.945225	−	0.326421i	$-0.894157\pi$
$857$	−5.27450e61	+	1.27338e62i	−0.0460356	+	0.111140i	0.899189	+	0.437560i	$0.144157\pi$
$858$	2.40968e63	−	2.40968e63i	2.05108	−	2.05108i
$859$	−2.79712e62	+	2.79712e62i	−0.232198	+	0.232198i	−0.813610	−	0.581412i	$-0.802501\pi$
$859$	−2.79712e62	+	2.79712e62i	−0.232198	+	0.232198i	0.581412	+	0.813610i	$0.302501\pi$
$860$	−1.87022e62	+	4.51512e62i	−0.151418	+	0.365555i
$861$	−2.52322e62	−	1.04515e62i	−0.199245	−	0.0825298i
$862$	2.50402e62	+	6.04523e62i	0.192855	+	0.465593i
$863$			2.10072e63i			1.57810i	0.614326	+	0.789052i	$0.289428\pi$
$863$			2.10072e63i			1.57810i	−0.614326	+	0.789052i	$0.710572\pi$
$864$	−1.63034e63	+	6.75309e62i	−1.19463	+	0.494831i
$865$	2.08287e63	+	2.08287e63i	1.48873	+	1.48873i
$866$	−6.13374e62			−0.427652
$867$	1.03405e63	−	3.92937e62i	0.703284	−	0.267247i
$868$	3.19515e63			2.11991
$869$	8.66143e62	+	8.66143e62i	0.560615	+	0.560615i
$870$	1.60418e63	−	6.64475e62i	1.01296	−	0.419580i
$871$		−	4.65197e63i		−	2.86580i
$872$	−1.71273e61	−	4.13489e61i	−0.0102940	−	0.0248519i
$873$	8.13991e62	+	3.37166e62i	0.477324	+	0.197714i
$874$	1.06738e63	−	2.57688e63i	0.610692	−	1.47434i
$875$	−1.30617e63	+	1.30617e63i	−0.729166	+	0.729166i
$876$	7.31982e62	−	7.31982e62i	0.398715	−	0.398715i
$877$	2.92294e62	−	7.05660e62i	0.155356	−	0.375063i	−0.826968	−	0.562248i	$-0.809937\pi$
$877$	2.92294e62	−	7.05660e62i	0.155356	−	0.375063i	0.982325	+	0.187185i	$0.0599365\pi$
$878$	−2.10624e63	−	8.72432e62i	−1.09238	−	0.452480i
$879$	8.17154e62	+	1.97278e63i	0.413564	+	0.998432i
$880$		−	1.04390e63i		−	0.515564i
$881$	−2.76988e62	+	1.14732e62i	−0.133499	+	0.0552973i	−0.448433	−	0.893816i	$-0.648018\pi$
$881$	−2.76988e62	+	1.14732e62i	−0.133499	+	0.0552973i	0.314934	+	0.949114i	$0.398018\pi$
$882$	−6.19975e62	−	6.19975e62i	−0.291608	−	0.291608i
$883$	1.39143e63			0.638712			0.319356	−	0.947635i	$-0.396533\pi$
$883$	1.39143e63			0.638712			0.319356	+	0.947635i	$0.396533\pi$
$884$	7.09099e61	−	4.79839e63i	0.0317675	−	2.14967i
$885$	−1.03040e63			−0.450533
$886$	−2.07910e63	−	2.07910e63i	−0.887258	−	0.887258i
$887$	−2.36857e63	+	9.81096e62i	−0.986573	+	0.408652i	−0.816856	−	0.576841i	$-0.804285\pi$
$887$	−2.36857e63	+	9.81096e62i	−0.986573	+	0.408652i	−0.169717	+	0.985493i	$0.554285\pi$
$888$		−	1.00980e62i		−	0.0410542i
$889$	−1.72710e63	−	4.16959e63i	−0.685378	−	1.65465i
$890$	−2.18669e63	−	9.05758e62i	−0.847037	−	0.350854i
$891$	6.47424e62	−	1.56302e63i	0.244804	−	0.591009i
$892$	−5.38142e63	+	5.38142e63i	−1.98634	+	1.98634i
$893$	−2.99996e63	+	2.99996e63i	−1.08096	+	1.08096i
$894$	8.66595e62	−	2.09215e63i	0.304831	−	0.735928i
$895$	−1.82543e63	−	7.56117e62i	−0.626858	−	0.259653i
$896$	1.96746e63	+	4.74987e63i	0.659605	+	1.59243i
$897$		−	2.66166e63i		−	0.871193i
$898$	5.19948e62	−	2.15369e62i	0.166157	−	0.0688245i
$899$	2.07877e63	+	2.07877e63i	0.648594	+	0.648594i
$900$	5.94240e62			0.181029
$901$	2.10161e63	−	2.04040e63i	0.625128	−	0.606921i
$902$	2.08404e63			0.605293
$903$	−5.57171e62	−	5.57171e62i	−0.158016	−	0.158016i
$904$	3.39586e62	−	1.40661e62i	0.0940435	−	0.0389541i
$905$			2.25561e63i			0.609985i
$906$	−5.90302e62	−	1.42511e63i	−0.155890	−	0.376351i
$907$	6.33331e63	+	2.62334e63i	1.63333	+	0.676548i	0.995599	−	0.0937114i	$-0.0298731\pi$
$907$	6.33331e63	+	2.62334e63i	1.63333	+	0.676548i	0.637731	+	0.770259i	$0.279873\pi$
$908$	−1.03401e63	+	2.49633e63i	−0.260423	+	0.628718i
$909$	−1.02601e63	+	1.02601e63i	−0.252364	+	0.252364i
$910$	−9.59537e63	+	9.59537e63i	−2.30500	+	2.30500i
$911$	−2.12895e63	+	5.13973e63i	−0.499481	+	1.20585i	0.450282	+	0.892886i	$0.351323\pi$
$911$	−2.12895e63	+	5.13973e63i	−0.499481	+	1.20585i	−0.949764	+	0.312969i	$0.898677\pi$
$912$	−1.02814e63	−	4.25869e62i	−0.235593	−	0.0975859i
$913$	8.96842e62	+	2.16517e63i	0.200722	+	0.484585i
$914$			3.33132e63i			0.728238i
$915$	−5.92213e63	+	2.45303e63i	−1.26452	+	0.523780i
$916$	5.91875e63	+	5.91875e63i	1.23446	+	1.23446i
$917$	1.13702e64			2.31647
$918$	−3.15666e63	−	7.95119e63i	−0.628219	−	1.58239i
$919$	9.43318e63			1.83390			0.916948	−	0.399007i	$-0.130645\pi$
$919$	9.43318e63			1.83390			0.916948	+	0.399007i	$0.130645\pi$
$920$	2.61695e63	+	2.61695e63i	0.497002	+	0.497002i
$921$	2.44769e62	−	1.01387e62i	0.0454124	−	0.0188104i
$922$		−	2.81251e63i		−	0.509776i
$923$	6.01377e63	+	1.45185e64i	1.06490	+	2.57090i
$924$	−1.28374e64	−	5.31742e63i	−2.22090	−	0.919928i
$925$	4.46788e61	−	1.07864e62i	0.00755186	−	0.0182318i
$926$	6.54940e62	−	6.54940e62i	0.108160	−	0.108160i
$927$	6.55879e62	−	6.55879e62i	0.105830	−	0.105830i
$928$	−2.37472e63	+	5.73308e63i	−0.374396	+	0.903871i
$929$	3.01156e63	+	1.24743e63i	0.463932	+	0.192167i	0.602391	−	0.798201i	$-0.294215\pi$
$929$	3.01156e63	+	1.24743e63i	0.463932	+	0.192167i	−0.138459	+	0.990368i	$0.544215\pi$
$930$	−3.83724e63	−	9.26391e63i	−0.577611	−	1.39448i
$931$		−	5.15703e63i		−	0.758545i
$932$	9.19738e63	−	3.80968e63i	1.32197	−	0.547578i
$933$	3.22842e63	+	3.22842e63i	0.453455	+	0.453455i
$934$	−2.14243e64			−2.94069
$935$	1.42830e64	+	2.11072e62i	1.91589	+	0.0283127i
$936$	−3.69577e63			−0.484478
$937$	6.32777e63	+	6.32777e63i	0.810680	+	0.810680i	0.984736	−	0.174056i	$-0.0556874\pi$
$937$	6.32777e63	+	6.32777e63i	0.810680	+	0.810680i	−0.174056	+	0.984736i	$0.555687\pi$
$938$	−2.92821e64	+	1.21290e64i	−3.66641	+	1.51868i
$939$		−	2.35212e63i		−	0.287839i
$940$	−6.54704e63	−	1.58059e64i	−0.783062	−	1.89048i
$941$	7.24046e63	+	2.99910e63i	0.846427	+	0.350601i	0.763384	−	0.645945i	$-0.223536\pi$
$941$	7.24046e63	+	2.99910e63i	0.846427	+	0.350601i	0.0830424	+	0.996546i	$0.473536\pi$
$942$	−1.57344e63	+	3.79862e63i	−0.179786	+	0.434041i
$943$	1.15098e63	−	1.15098e63i	0.128548	−	0.128548i
$944$	9.22507e62	−	9.22507e62i	0.100710	−	0.100710i
$945$	−5.54017e63	+	1.33752e64i	−0.591207	+	1.42730i
$946$	5.55502e63	+	2.30097e63i	0.579464	+	0.240022i
$947$	−6.82697e63	−	1.64818e64i	−0.696151	−	1.68066i	−0.732004	−	0.681300i	$-0.761415\pi$
$947$	−6.82697e63	−	1.64818e64i	−0.696151	−	1.68066i	0.0358527	−	0.999357i	$-0.488585\pi$
$948$			5.26569e63i			0.524899i
$949$	−6.87699e63	+	2.84854e63i	−0.670155	+	0.277587i
$950$	4.12972e63	+	4.12972e63i	0.393426	+	0.393426i
$951$	6.36803e63			0.593095
$952$	−9.99932e63	+	3.96978e63i	−0.910492	+	0.361470i
$953$	1.39598e63			0.124275			0.0621373	−	0.998068i	$-0.480208\pi$
$953$	1.39598e63			0.124275			0.0621373	+	0.998068i	$0.480208\pi$
$954$	−4.84765e63	−	4.84765e63i	−0.421931	−	0.421931i
$955$	3.93814e62	−	1.63123e62i	0.0335134	−	0.0138817i
$956$			2.92791e64i			2.43620i
$957$	−4.89250e63	−	1.18116e64i	−0.398038	−	0.960949i
$958$	2.95719e64	+	1.22491e64i	2.35245	+	0.974417i
$959$	8.12837e63	−	1.96236e64i	0.632271	−	1.52644i
$960$	1.28373e64	−	1.28373e64i	0.976431	−	0.976431i
$961$	2.49769e63	−	2.49769e63i	0.185775	−	0.185775i
$962$	−8.44472e62	+	2.03873e63i	−0.0614216	+	0.148285i
$963$	−1.09479e64	−	4.53476e63i	−0.778690	−	0.322544i
$964$	−1.45287e64	−	3.50754e64i	−1.01058	−	2.43976i
$965$			1.44428e63i			0.0982456i
$966$	−1.67540e64	+	6.93972e63i	−1.11458	+	0.461672i
$967$	−5.15444e63	−	5.15444e63i	−0.335361	−	0.335361i	0.519257	−	0.854618i	$-0.326209\pi$
$967$	−5.15444e63	−	5.15444e63i	−0.335361	−	0.335361i	−0.854618	+	0.519257i	$0.826209\pi$
$968$	2.27264e64			1.44614
$969$	6.03476e63	−	1.39812e64i	0.375577	−	0.870128i
$970$	−3.49182e64			−2.12549
$971$	−4.57728e63	−	4.57728e63i	−0.272517	−	0.272517i	0.557596	−	0.830113i	$-0.311724\pi$
$971$	−4.57728e63	−	4.57728e63i	−0.272517	−	0.272517i	−0.830113	+	0.557596i	$0.811724\pi$
$972$	−1.87907e64	+	7.78337e63i	−1.09425	+	0.453255i
$973$			1.92389e64i			1.09586i
$974$	−7.63945e63	−	1.84433e64i	−0.425642	−	1.02759i
$975$	5.14902e63	+	2.13280e63i	0.280625	+	0.116238i
$976$	3.10585e63	−	7.49818e63i	0.165580	−	0.399747i
$977$	1.11183e64	−	1.11183e64i	0.579836	−	0.579836i	−0.355022	−	0.934858i	$-0.615527\pi$
$977$	1.11183e64	−	1.11183e64i	0.579836	−	0.579836i	0.934858	+	0.355022i	$0.115527\pi$
$978$	1.29018e64	−	1.29018e64i	0.658212	−	0.658212i
$979$	−6.66906e63	+	1.61005e64i	−0.332841	+	0.803549i
$980$	1.92127e64	+	7.95817e63i	0.938055	+	0.388555i
$981$	1.20844e62	+	2.91742e62i	0.00577218	+	0.0139353i
$982$			2.69026e64i			1.25718i
$983$	1.22774e64	−	5.08548e63i	0.561316	−	0.232505i	−0.0839405	−	0.996471i	$-0.526751\pi$
$983$	1.22774e64	−	5.08548e63i	0.561316	−	0.232505i	0.645256	+	0.763966i	$0.276751\pi$
$984$	2.08449e63	+	2.08449e63i	0.0932407	+	0.0932407i
$985$	−7.40284e63			−0.323981
$986$	−2.76201e64	−	1.19217e64i	−1.18269	−	0.510489i
$987$	2.75839e64			1.15568
$988$	−4.67133e64	−	4.67133e64i	−1.91499	−	1.91499i
$989$	4.33873e63	−	1.79716e63i	0.174037	−	0.0720886i
$990$		−	3.34326e64i		−	1.31224i
$991$	−1.03902e64	−	2.50842e64i	−0.399062	−	0.963421i	−0.987889	−	0.155162i	$-0.950410\pi$
$991$	−1.03902e64	−	2.50842e64i	−0.399062	−	0.963421i	0.588827	−	0.808259i	$-0.299590\pi$
$992$	3.31077e64	+	1.37136e64i	1.24431	+	0.515409i
$993$	−8.84733e63	+	2.13594e64i	−0.325389	+	0.785560i
$994$	7.57081e64	−	7.57081e64i	2.72480	−	2.72480i
$995$	−6.62916e63	+	6.62916e63i	−0.233487	+	0.233487i
$996$	−3.85537e63	+	9.30769e63i	−0.132889	+	0.320824i
$997$	−4.34405e63	−	1.79936e63i	−0.146538	−	0.0606978i	0.308209	−	0.951319i	$-0.400270\pi$
$997$	−4.34405e63	−	1.79936e63i	−0.146538	−	0.0606978i	−0.454747	+	0.890621i	$0.650270\pi$
$998$	1.63901e64	+	3.95691e64i	0.541095	+	1.30632i
$999$			2.35425e63i			0.0760666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.44.d.a.2.9	✓	252
17.9	even	8	inner	17.44.d.a.9.9	yes	252

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.44.d.a.2.9	✓	252	1.1	even	1	trivial
17.44.d.a.9.9	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+(-3.30953e6 - 3.30953e6i) q^{2} +(-1.25934e10 + 5.21635e9i) q^{3} +1.31099e13i q^{4} +(4.61615e14 + 1.11444e15i) q^{5} +(5.89418e16 + 2.44145e16i) q^{6} +(-7.15817e17 + 1.72813e18i) q^{7} +(1.42765e19 - 1.42765e19i) q^{8} +(-1.00730e20 + 1.00730e20i) q^{9} +(2.16054e21 - 5.21599e21i) q^{10} +(-3.84052e22 - 1.59079e22i) q^{11} +(-6.83856e22 - 1.65097e23i) q^{12} +1.28497e24i q^{13} +(8.08832e24 - 3.35029e24i) q^{14} +(-1.16266e25 - 1.16266e25i) q^{15} +2.08183e25 q^{16} +(-4.20936e24 + 2.84842e26i) q^{17} +6.66737e26 q^{18} +(2.77300e27 + 2.77300e27i) q^{19} +(-1.46101e28 + 6.05171e27i) q^{20} -2.54970e28i q^{21} +(7.44552e28 + 1.79751e29i) q^{22} +(1.40394e29 + 5.81530e28i) q^{23} +(-1.05318e29 + 2.54261e29i) q^{24} +(-2.24996e29 + 2.24996e29i) q^{25} +(4.25264e30 - 4.25264e30i) q^{26} +(2.45539e30 - 5.92783e30i) q^{27} +(-2.26556e31 - 9.38426e30i) q^{28} +(-8.63436e30 - 2.08452e31i) q^{29} +7.69570e31i q^{30} +(-1.20378e32 + 4.98621e31i) q^{31} +(-1.94477e32 - 1.94477e32i) q^{32} +5.66632e32 q^{33} +(9.56624e32 - 9.28762e32i) q^{34} -2.25633e33 q^{35} +(-1.32056e33 - 1.32056e33i) q^{36} +(-3.38990e32 + 1.40414e32i) q^{37} -1.83546e34i q^{38} +(-6.70284e33 - 1.61821e34i) q^{39} +(2.25006e34 + 9.32005e33i) q^{40} +(4.09911e33 - 9.89614e33i) q^{41} +(-8.43830e34 + 8.43830e34i) q^{42} +(2.18524e34 - 2.18524e34i) q^{43} +(2.08551e35 - 5.03487e35i) q^{44} +(-1.58756e35 - 6.57588e34i) q^{45} +(-2.72178e35 - 6.57096e35i) q^{46} +1.08185e36i q^{47} +(-2.62173e35 + 1.08595e35i) q^{48} +(-9.29864e35 - 9.29864e35i) q^{49} +1.48926e36 q^{50} +(-1.43283e36 - 3.60908e36i) q^{51} -1.68458e37 q^{52} +(-7.27071e36 - 7.27071e36i) q^{53} +(-2.77445e37 + 1.14922e37i) q^{54} -5.01436e37i q^{55} +(1.44524e37 + 3.48912e37i) q^{56} +(-4.93863e37 - 2.04565e37i) q^{57} +(-4.04121e37 + 9.75634e37i) q^{58} +(4.43123e37 - 4.43123e37i) q^{59} +(1.52423e38 - 1.52423e38i) q^{60} +(1.49188e38 - 3.60172e38i) q^{61} +(5.63414e38 + 2.33374e38i) q^{62} +(-1.01971e38 - 2.46179e38i) q^{63} +1.10413e39i q^{64} +(-1.43202e39 + 5.93162e38i) q^{65} +(-1.87528e39 - 1.87528e39i) q^{66} -3.62029e39 q^{67} +(-3.73424e39 - 5.51841e37i) q^{68} -2.07138e39 q^{69} +(7.46739e39 + 7.46739e39i) q^{70} +(1.12987e40 - 4.68009e39i) q^{71} +2.87615e39i q^{72} +(2.21682e39 + 5.35187e39i) q^{73} +(1.58660e39 + 6.57192e38i) q^{74} +(1.65980e39 - 4.00712e39i) q^{75} +(-3.63536e40 + 3.63536e40i) q^{76} +(5.49821e40 - 5.49821e40i) q^{77} +(-3.13719e40 + 7.57384e40i) q^{78} +(-2.72236e40 - 1.12764e40i) q^{79} +(9.61005e39 + 2.32007e40i) q^{80} +4.06982e40i q^{81} +(-4.63177e40 + 1.91854e40i) q^{82} +(-3.98646e40 - 3.98646e40i) q^{83} +3.34262e41 q^{84} +(-3.19382e41 + 1.26796e41i) q^{85} -1.44643e41 q^{86} +(2.17471e41 + 2.17471e41i) q^{87} +(-7.75404e41 + 3.21183e41i) q^{88} -4.19228e41i q^{89} +(3.07776e41 + 7.43038e41i) q^{90} +(-2.22060e42 - 9.19802e41i) q^{91} +(-7.62378e41 + 1.84054e42i) q^{92} +(1.25586e42 - 1.25586e42i) q^{93} +(3.58041e42 - 3.58041e42i) q^{94} +(-1.81028e42 + 4.37039e42i) q^{95} +(3.46357e42 + 1.43466e42i) q^{96} +(-2.36685e42 - 5.71408e42i) q^{97} +6.15483e42i q^{98} +(5.47096e42 - 2.26615e42i) 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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