Properties

Label 3.41.b.a.2.11
Level $3$
Weight $41$
Character 3.2
Analytic conductor $30.403$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3,41,Mod(2,3)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 41, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3.2");
 
S:= CuspForms(chi, 41);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3 \)
Weight: \( k \) \(=\) \( 41 \)
Character orbit: \([\chi]\) \(=\) 3.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(30.4026855589\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.11
Root \(245022. i\) of defining polynomial
Character \(\chi\) \(=\) 3.2
Dual form 3.41.b.a.2.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.47013e6i q^{2} +(1.53875e9 + 3.12889e9i) q^{3} -1.06178e12 q^{4} +3.18557e13i q^{5} +(-4.59988e15 + 2.26216e15i) q^{6} +7.85404e14 q^{7} +5.54756e16i q^{8} +(-7.42219e18 + 9.62912e18i) q^{9} +O(q^{10})\) \(q+1.47013e6i q^{2} +(1.53875e9 + 3.12889e9i) q^{3} -1.06178e12 q^{4} +3.18557e13i q^{5} +(-4.59988e15 + 2.26216e15i) q^{6} +7.85404e14 q^{7} +5.54756e16i q^{8} +(-7.42219e18 + 9.62912e18i) q^{9} -4.68322e19 q^{10} -8.83914e20i q^{11} +(-1.63380e21 - 3.32218e21i) q^{12} -1.50265e22 q^{13} +1.15465e21i q^{14} +(-9.96730e22 + 4.90179e22i) q^{15} -1.24899e24 q^{16} -2.97100e24i q^{17} +(-1.41561e25 - 1.09116e25i) q^{18} -6.09769e25 q^{19} -3.38237e25i q^{20} +(1.20854e24 + 2.45744e24i) q^{21} +1.29947e27 q^{22} +1.99164e27i q^{23} +(-1.73577e26 + 8.53628e25i) q^{24} +8.08016e27 q^{25} -2.20910e28i q^{26} +(-4.15493e28 - 8.40642e27i) q^{27} -8.33924e26 q^{28} -8.61658e28i q^{29} +(-7.20628e28 - 1.46532e29i) q^{30} +3.82717e29 q^{31} -1.77519e30i q^{32} +(2.76567e30 - 1.36012e30i) q^{33} +4.36777e30 q^{34} +2.50196e28i q^{35} +(7.88071e30 - 1.02240e31i) q^{36} -1.30186e31 q^{37} -8.96441e31i q^{38} +(-2.31220e31 - 4.70163e31i) q^{39} -1.76722e30 q^{40} +1.97826e32i q^{41} +(-3.61276e30 + 1.77671e30i) q^{42} +8.12325e32 q^{43} +9.38519e32i q^{44} +(-3.06743e32 - 2.36439e32i) q^{45} -2.92797e33 q^{46} +4.06950e33i q^{47} +(-1.92188e33 - 3.90795e33i) q^{48} -6.36619e33 q^{49} +1.18789e34i q^{50} +(9.29593e33 - 4.57162e33i) q^{51} +1.59548e34 q^{52} +2.48872e34i q^{53} +(1.23586e34 - 6.10829e34i) q^{54} +2.81577e34 q^{55} +4.35708e31i q^{56} +(-9.38279e34 - 1.90790e35i) q^{57} +1.26675e35 q^{58} -1.16497e35i q^{59} +(1.05830e35 - 5.20460e34i) q^{60} -5.58865e35 q^{61} +5.62644e35i q^{62} +(-5.82942e33 + 7.56275e33i) q^{63} +1.23648e36 q^{64} -4.78682e35i q^{65} +(1.99955e36 + 4.06589e36i) q^{66} -4.40203e36 q^{67} +3.15454e36i q^{68} +(-6.23160e36 + 3.06462e36i) q^{69} -3.67822e34 q^{70} -1.87733e37i q^{71} +(-5.34181e35 - 4.11750e35i) q^{72} +8.39273e35 q^{73} -1.91391e37i q^{74} +(1.24333e37 + 2.52819e37i) q^{75} +6.47438e37 q^{76} -6.94230e35i q^{77} +(6.91202e37 - 3.39924e37i) q^{78} -8.62105e37 q^{79} -3.97876e37i q^{80} +(-3.76310e37 - 1.42938e38i) q^{81} -2.90830e38 q^{82} +1.72703e38i q^{83} +(-1.28320e36 - 2.60925e36i) q^{84} +9.46435e37 q^{85} +1.19423e39i q^{86} +(2.69603e38 - 1.32587e38i) q^{87} +4.90356e37 q^{88} +3.16586e38i q^{89} +(3.47597e38 - 4.50952e38i) q^{90} -1.18019e37 q^{91} -2.11467e39i q^{92} +(5.88904e38 + 1.19748e39i) q^{93} -5.98270e39 q^{94} -1.94246e39i q^{95} +(5.55436e39 - 2.73156e39i) q^{96} +2.49823e39 q^{97} -9.35914e39i q^{98} +(8.51131e39 + 6.56057e39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots - 23\!\cdots\!20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 372082572 q^{3} - 4781373657072 q^{4} + 84\!\cdots\!52 q^{6}+ \cdots + 54\!\cdots\!80 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.47013e6i 1.40203i 0.713148 + 0.701014i \(0.247269\pi\)
−0.713148 + 0.701014i \(0.752731\pi\)
\(3\) 1.53875e9 + 3.12889e9i 0.441308 + 0.897356i
\(4\) −1.06178e12 −0.965680
\(5\) 3.18557e13i 0.334032i 0.985954 + 0.167016i \(0.0534131\pi\)
−0.985954 + 0.167016i \(0.946587\pi\)
\(6\) −4.59988e15 + 2.26216e15i −1.25812 + 0.618726i
\(7\) 7.85404e14 0.00984311 0.00492156 0.999988i \(-0.498433\pi\)
0.00492156 + 0.999988i \(0.498433\pi\)
\(8\) 5.54756e16i 0.0481174i
\(9\) −7.42219e18 + 9.62912e18i −0.610495 + 0.792020i
\(10\) −4.68322e19 −0.468322
\(11\) 8.83914e20i 1.31388i −0.753942 0.656941i \(-0.771850\pi\)
0.753942 0.656941i \(-0.228150\pi\)
\(12\) −1.63380e21 3.32218e21i −0.426162 0.866559i
\(13\) −1.50265e22 −0.790664 −0.395332 0.918538i \(-0.629370\pi\)
−0.395332 + 0.918538i \(0.629370\pi\)
\(14\) 1.15465e21i 0.0138003i
\(15\) −9.96730e22 + 4.90179e22i −0.299745 + 0.147411i
\(16\) −1.24899e24 −1.03314
\(17\) 2.97100e24i 0.731012i −0.930809 0.365506i \(-0.880896\pi\)
0.930809 0.365506i \(-0.119104\pi\)
\(18\) −1.41561e25 1.09116e25i −1.11043 0.855930i
\(19\) −6.09769e25 −1.62216 −0.811079 0.584936i \(-0.801119\pi\)
−0.811079 + 0.584936i \(0.801119\pi\)
\(20\) 3.38237e25i 0.322568i
\(21\) 1.20854e24 + 2.45744e24i 0.00434384 + 0.00883277i
\(22\) 1.29947e27 1.84210
\(23\) 1.99164e27i 1.16052i 0.814431 + 0.580261i \(0.197049\pi\)
−0.814431 + 0.580261i \(0.802951\pi\)
\(24\) −1.73577e26 + 8.53628e25i −0.0431784 + 0.0212346i
\(25\) 8.08016e27 0.888423
\(26\) 2.20910e28i 1.10853i
\(27\) −4.15493e28 8.40642e27i −0.980140 0.198306i
\(28\) −8.33924e26 −0.00950530
\(29\) 8.61658e28i 0.486827i −0.969923 0.243414i \(-0.921733\pi\)
0.969923 0.243414i \(-0.0782673\pi\)
\(30\) −7.20628e28 1.46532e29i −0.206674 0.420251i
\(31\) 3.82717e29 0.569696 0.284848 0.958573i \(-0.408057\pi\)
0.284848 + 0.958573i \(0.408057\pi\)
\(32\) 1.77519e30i 1.40038i
\(33\) 2.76567e30 1.36012e30i 1.17902 0.579826i
\(34\) 4.36777e30 1.02490
\(35\) 2.50196e28i 0.00328791i
\(36\) 7.88071e30 1.02240e31i 0.589543 0.764838i
\(37\) −1.30186e31 −0.563030 −0.281515 0.959557i \(-0.590837\pi\)
−0.281515 + 0.959557i \(0.590837\pi\)
\(38\) 8.96441e31i 2.27431i
\(39\) −2.31220e31 4.70163e31i −0.348926 0.709507i
\(40\) −1.76722e30 −0.0160727
\(41\) 1.97826e32i 1.09801i 0.835820 + 0.549004i \(0.184993\pi\)
−0.835820 + 0.549004i \(0.815007\pi\)
\(42\) −3.61276e30 + 1.77671e30i −0.0123838 + 0.00609019i
\(43\) 8.12325e32 1.73925 0.869623 0.493717i \(-0.164362\pi\)
0.869623 + 0.493717i \(0.164362\pi\)
\(44\) 9.38519e32i 1.26879i
\(45\) −3.06743e32 2.36439e32i −0.264560 0.203925i
\(46\) −2.92797e33 −1.62708
\(47\) 4.06950e33i 1.47090i 0.677577 + 0.735452i \(0.263030\pi\)
−0.677577 + 0.735452i \(0.736970\pi\)
\(48\) −1.92188e33 3.90795e33i −0.455934 0.927096i
\(49\) −6.36619e33 −0.999903
\(50\) 1.18789e34i 1.24559i
\(51\) 9.29593e33 4.57162e33i 0.655978 0.322601i
\(52\) 1.59548e34 0.763528
\(53\) 2.48872e34i 0.813690i 0.913497 + 0.406845i \(0.133371\pi\)
−0.913497 + 0.406845i \(0.866629\pi\)
\(54\) 1.23586e34 6.10829e34i 0.278030 1.37418i
\(55\) 2.81577e34 0.438878
\(56\) 4.35708e31i 0.000473625i
\(57\) −9.38279e34 1.90790e35i −0.715871 1.45565i
\(58\) 1.26675e35 0.682545
\(59\) 1.16497e35i 0.445938i −0.974826 0.222969i \(-0.928425\pi\)
0.974826 0.222969i \(-0.0715748\pi\)
\(60\) 1.05830e35 5.20460e34i 0.289458 0.142352i
\(61\) −5.58865e35 −1.09827 −0.549136 0.835733i \(-0.685043\pi\)
−0.549136 + 0.835733i \(0.685043\pi\)
\(62\) 5.62644e35i 0.798730i
\(63\) −5.82942e33 + 7.56275e33i −0.00600917 + 0.00779595i
\(64\) 1.23648e36 0.930223
\(65\) 4.78682e35i 0.264107i
\(66\) 1.99955e36 + 4.06589e36i 0.812932 + 1.65302i
\(67\) −4.40203e36 −1.32482 −0.662410 0.749141i \(-0.730466\pi\)
−0.662410 + 0.749141i \(0.730466\pi\)
\(68\) 3.15454e36i 0.705924i
\(69\) −6.23160e36 + 3.06462e36i −1.04140 + 0.512148i
\(70\) −3.67822e34 −0.00460974
\(71\) 1.87733e37i 1.77163i −0.464039 0.885815i \(-0.653600\pi\)
0.464039 0.885815i \(-0.346400\pi\)
\(72\) −5.34181e35 4.11750e35i −0.0381100 0.0293754i
\(73\) 8.39273e35 0.0454408 0.0227204 0.999742i \(-0.492767\pi\)
0.0227204 + 0.999742i \(0.492767\pi\)
\(74\) 1.91391e37i 0.789383i
\(75\) 1.24333e37 + 2.52819e37i 0.392068 + 0.797231i
\(76\) 6.47438e37 1.56649
\(77\) 6.94230e35i 0.0129327i
\(78\) 6.91202e37 3.39924e37i 0.994748 0.489204i
\(79\) −8.62105e37 −0.961653 −0.480827 0.876816i \(-0.659663\pi\)
−0.480827 + 0.876816i \(0.659663\pi\)
\(80\) 3.97876e37i 0.345102i
\(81\) −3.76310e37 1.42938e38i −0.254593 0.967048i
\(82\) −2.90830e38 −1.53944
\(83\) 1.72703e38i 0.717363i 0.933460 + 0.358682i \(0.116774\pi\)
−0.933460 + 0.358682i \(0.883226\pi\)
\(84\) −1.28320e36 2.60925e36i −0.00419476 0.00852963i
\(85\) 9.46435e37 0.244181
\(86\) 1.19423e39i 2.43847i
\(87\) 2.69603e38 1.32587e38i 0.436857 0.214841i
\(88\) 4.90356e37 0.0632206
\(89\) 3.16586e38i 0.325605i 0.986659 + 0.162803i \(0.0520534\pi\)
−0.986659 + 0.162803i \(0.947947\pi\)
\(90\) 3.47597e38 4.50952e38i 0.285908 0.370920i
\(91\) −1.18019e37 −0.00778259
\(92\) 2.11467e39i 1.12069i
\(93\) 5.88904e38 + 1.19748e39i 0.251412 + 0.511220i
\(94\) −5.98270e39 −2.06225
\(95\) 1.94246e39i 0.541852i
\(96\) 5.55436e39 2.73156e39i 1.25664 0.617997i
\(97\) 2.49823e39 0.459408 0.229704 0.973261i \(-0.426224\pi\)
0.229704 + 0.973261i \(0.426224\pi\)
\(98\) 9.35914e39i 1.40189i
\(99\) 8.51131e39 + 6.56057e39i 1.04062 + 0.802118i
\(100\) −8.57932e39 −0.857932
\(101\) 1.38822e39i 0.113771i 0.998381 + 0.0568855i \(0.0181170\pi\)
−0.998381 + 0.0568855i \(0.981883\pi\)
\(102\) 6.72088e39 + 1.36662e40i 0.452296 + 0.919699i
\(103\) −5.22898e38 −0.0289516 −0.0144758 0.999895i \(-0.504608\pi\)
−0.0144758 + 0.999895i \(0.504608\pi\)
\(104\) 8.33606e38i 0.0380447i
\(105\) −7.82836e37 + 3.84989e37i −0.00295043 + 0.00145098i
\(106\) −3.65875e40 −1.14081
\(107\) 2.81098e40i 0.726411i 0.931709 + 0.363206i \(0.118318\pi\)
−0.931709 + 0.363206i \(0.881682\pi\)
\(108\) 4.41160e40 + 8.92574e39i 0.946502 + 0.191500i
\(109\) −9.91057e40 −1.76835 −0.884176 0.467154i \(-0.845279\pi\)
−0.884176 + 0.467154i \(0.845279\pi\)
\(110\) 4.13956e40i 0.615319i
\(111\) −2.00324e40 4.07339e40i −0.248470 0.505238i
\(112\) −9.80964e38 −0.0101693
\(113\) 4.74724e39i 0.0411977i 0.999788 + 0.0205988i \(0.00655728\pi\)
−0.999788 + 0.0205988i \(0.993443\pi\)
\(114\) 2.80486e41 1.37939e41i 2.04087 1.00367i
\(115\) −6.34451e40 −0.387651
\(116\) 9.14888e40i 0.470120i
\(117\) 1.11530e41 1.44692e41i 0.482696 0.626222i
\(118\) 1.71266e41 0.625217
\(119\) 2.33344e39i 0.00719543i
\(120\) −2.71930e39 5.52942e39i −0.00709303 0.0144230i
\(121\) −3.28711e41 −0.726284
\(122\) 8.21605e41i 1.53981i
\(123\) −6.18974e41 + 3.04403e41i −0.985304 + 0.484560i
\(124\) −4.06360e41 −0.550145
\(125\) 5.47126e41i 0.630793i
\(126\) −1.11182e40 8.57002e39i −0.0109301 0.00842502i
\(127\) 8.29339e41 0.696078 0.348039 0.937480i \(-0.386848\pi\)
0.348039 + 0.937480i \(0.386848\pi\)
\(128\) 1.34053e41i 0.0961781i
\(129\) 1.24996e42 + 2.54167e42i 0.767543 + 1.56072i
\(130\) 7.03725e41 0.370285
\(131\) 3.01248e42i 1.35987i 0.733272 + 0.679935i \(0.237992\pi\)
−0.733272 + 0.679935i \(0.762008\pi\)
\(132\) −2.93652e42 + 1.44414e42i −1.13856 + 0.559927i
\(133\) −4.78915e40 −0.0159671
\(134\) 6.47156e42i 1.85743i
\(135\) 2.67793e41 1.32358e42i 0.0662405 0.327398i
\(136\) 1.64818e41 0.0351744
\(137\) 1.97127e42i 0.363359i −0.983358 0.181679i \(-0.941847\pi\)
0.983358 0.181679i \(-0.0581533\pi\)
\(138\) −4.50540e42 9.16128e42i −0.718045 1.46007i
\(139\) 2.34490e42 0.323466 0.161733 0.986835i \(-0.448292\pi\)
0.161733 + 0.986835i \(0.448292\pi\)
\(140\) 2.65653e40i 0.00317507i
\(141\) −1.27330e43 + 6.26193e42i −1.31992 + 0.649121i
\(142\) 2.75992e43 2.48387
\(143\) 1.32822e43i 1.03884i
\(144\) 9.27026e42 1.20267e43i 0.630728 0.818270i
\(145\) 2.74488e42 0.162616
\(146\) 1.23384e42i 0.0637093i
\(147\) −9.79594e42 1.99191e43i −0.441265 0.897269i
\(148\) 1.38229e43 0.543707
\(149\) 2.99713e43i 1.03034i 0.857088 + 0.515170i \(0.172271\pi\)
−0.857088 + 0.515170i \(0.827729\pi\)
\(150\) −3.71677e43 + 1.82786e43i −1.11774 + 0.549690i
\(151\) −7.32154e43 −1.92781 −0.963904 0.266252i \(-0.914215\pi\)
−0.963904 + 0.266252i \(0.914215\pi\)
\(152\) 3.38273e42i 0.0780541i
\(153\) 2.86081e43 + 2.20513e43i 0.578976 + 0.446279i
\(154\) 1.02061e42 0.0181320
\(155\) 1.21917e43i 0.190297i
\(156\) 2.45504e43 + 4.99208e43i 0.336951 + 0.685156i
\(157\) 2.98232e43 0.360214 0.180107 0.983647i \(-0.442356\pi\)
0.180107 + 0.983647i \(0.442356\pi\)
\(158\) 1.26741e44i 1.34826i
\(159\) −7.78692e43 + 3.82951e43i −0.730169 + 0.359088i
\(160\) 5.65499e43 0.467770
\(161\) 1.56424e42i 0.0114231i
\(162\) 2.10138e44 5.53226e43i 1.35583 0.356946i
\(163\) 6.16652e43 0.351794 0.175897 0.984409i \(-0.443717\pi\)
0.175897 + 0.984409i \(0.443717\pi\)
\(164\) 2.10047e44i 1.06032i
\(165\) 4.33276e43 + 8.81023e43i 0.193680 + 0.393830i
\(166\) −2.53897e44 −1.00576
\(167\) 1.03723e44i 0.364373i −0.983264 0.182186i \(-0.941683\pi\)
0.983264 0.182186i \(-0.0583174\pi\)
\(168\) −1.36328e41 + 6.70443e40i −0.000425010 + 0.000209014i
\(169\) −1.35392e44 −0.374851
\(170\) 1.39138e44i 0.342349i
\(171\) 4.52582e44 5.87154e44i 0.990319 1.28478i
\(172\) −8.62508e44 −1.67955
\(173\) 4.64474e44i 0.805451i 0.915321 + 0.402726i \(0.131937\pi\)
−0.915321 + 0.402726i \(0.868063\pi\)
\(174\) 1.94921e44 + 3.96352e44i 0.301213 + 0.612486i
\(175\) 6.34619e42 0.00874485
\(176\) 1.10400e45i 1.35743i
\(177\) 3.64506e44 1.79259e44i 0.400165 0.196796i
\(178\) −4.65423e44 −0.456507
\(179\) 7.06105e44i 0.619168i 0.950872 + 0.309584i \(0.100190\pi\)
−0.950872 + 0.309584i \(0.899810\pi\)
\(180\) 3.25692e44 + 2.51046e44i 0.255480 + 0.196926i
\(181\) 1.48674e45 1.04391 0.521955 0.852973i \(-0.325203\pi\)
0.521955 + 0.852973i \(0.325203\pi\)
\(182\) 1.73504e43i 0.0109114i
\(183\) −8.59951e44 1.74862e45i −0.484676 0.985541i
\(184\) −1.10487e44 −0.0558413
\(185\) 4.14719e44i 0.188070i
\(186\) −1.76045e45 + 8.65766e44i −0.716745 + 0.352486i
\(187\) −2.62611e45 −0.960463
\(188\) 4.32090e45i 1.42042i
\(189\) −3.26330e43 6.60244e42i −0.00964763 0.00195195i
\(190\) 2.85568e45 0.759692
\(191\) 7.76747e45i 1.86043i −0.367020 0.930213i \(-0.619622\pi\)
0.367020 0.930213i \(-0.380378\pi\)
\(192\) 1.90263e45 + 3.86880e45i 0.410515 + 0.834741i
\(193\) 5.76691e45 1.12149 0.560747 0.827987i \(-0.310514\pi\)
0.560747 + 0.827987i \(0.310514\pi\)
\(194\) 3.67273e45i 0.644102i
\(195\) 1.49774e45 7.36569e44i 0.236998 0.116552i
\(196\) 6.75947e45 0.965587
\(197\) 6.43416e45i 0.830170i 0.909783 + 0.415085i \(0.136248\pi\)
−0.909783 + 0.415085i \(0.863752\pi\)
\(198\) −9.64491e45 + 1.25127e46i −1.12459 + 1.45898i
\(199\) −4.76778e45 −0.502638 −0.251319 0.967904i \(-0.580864\pi\)
−0.251319 + 0.967904i \(0.580864\pi\)
\(200\) 4.48252e44i 0.0427486i
\(201\) −6.77360e45 1.37734e46i −0.584654 1.18883i
\(202\) −2.04087e45 −0.159510
\(203\) 6.76750e43i 0.00479190i
\(204\) −9.87020e45 + 4.85403e45i −0.633465 + 0.311530i
\(205\) −6.30188e45 −0.366769
\(206\) 7.68729e44i 0.0405909i
\(207\) −1.91777e46 1.47823e46i −0.919157 0.708493i
\(208\) 1.87680e46 0.816868
\(209\) 5.38983e46i 2.13132i
\(210\) −5.65984e43 1.15087e44i −0.00203432 0.00413658i
\(211\) 4.75899e46 1.55548 0.777742 0.628583i \(-0.216365\pi\)
0.777742 + 0.628583i \(0.216365\pi\)
\(212\) 2.64247e46i 0.785764i
\(213\) 5.87394e46 2.88873e46i 1.58978 0.781834i
\(214\) −4.13252e46 −1.01845
\(215\) 2.58772e46i 0.580963i
\(216\) 4.66351e44 2.30497e45i 0.00954197 0.0471618i
\(217\) 3.00587e44 0.00560759
\(218\) 1.45698e47i 2.47928i
\(219\) 1.29143e45 + 2.62599e45i 0.0200534 + 0.0407766i
\(220\) −2.98972e46 −0.423816
\(221\) 4.46439e46i 0.577985i
\(222\) 5.98842e46 2.94503e46i 0.708358 0.348361i
\(223\) −1.24456e47 −1.34561 −0.672804 0.739821i \(-0.734910\pi\)
−0.672804 + 0.739821i \(0.734910\pi\)
\(224\) 1.39424e45i 0.0137841i
\(225\) −5.99725e46 + 7.78048e46i −0.542377 + 0.703649i
\(226\) −6.97908e45 −0.0577603
\(227\) 9.40746e46i 0.712780i 0.934337 + 0.356390i \(0.115992\pi\)
−0.934337 + 0.356390i \(0.884008\pi\)
\(228\) 9.96243e46 + 2.02576e47i 0.691303 + 1.40570i
\(229\) 4.05603e45 0.0257864 0.0128932 0.999917i \(-0.495896\pi\)
0.0128932 + 0.999917i \(0.495896\pi\)
\(230\) 9.32726e46i 0.543498i
\(231\) 2.17217e45 1.06824e45i 0.0116052 0.00570729i
\(232\) 4.78010e45 0.0234249
\(233\) 8.72200e46i 0.392191i −0.980585 0.196095i \(-0.937174\pi\)
0.980585 0.196095i \(-0.0628263\pi\)
\(234\) 2.12717e47 + 1.63964e47i 0.877980 + 0.676753i
\(235\) −1.29637e47 −0.491328
\(236\) 1.23694e47i 0.430633i
\(237\) −1.32656e47 2.69743e47i −0.424385 0.862945i
\(238\) 3.43046e45 0.0100882
\(239\) 3.37265e47i 0.912039i 0.889970 + 0.456020i \(0.150725\pi\)
−0.889970 + 0.456020i \(0.849275\pi\)
\(240\) 1.24491e47 6.12230e46i 0.309679 0.152296i
\(241\) −7.05542e47 −1.61503 −0.807517 0.589844i \(-0.799189\pi\)
−0.807517 + 0.589844i \(0.799189\pi\)
\(242\) 4.83248e47i 1.01827i
\(243\) 3.89333e47 3.37689e47i 0.755433 0.655226i
\(244\) 5.93389e47 1.06058
\(245\) 2.02800e47i 0.333999i
\(246\) −4.47513e47 9.09973e47i −0.679366 1.38142i
\(247\) 9.16271e47 1.28258
\(248\) 2.12314e46i 0.0274123i
\(249\) −5.40370e47 + 2.65747e47i −0.643730 + 0.316578i
\(250\) −8.04347e47 −0.884389
\(251\) 1.12398e48i 1.14100i 0.821298 + 0.570499i \(0.193250\pi\)
−0.821298 + 0.570499i \(0.806750\pi\)
\(252\) 6.18954e45 8.02995e45i 0.00580293 0.00752839i
\(253\) 1.76043e48 1.52479
\(254\) 1.21924e48i 0.975920i
\(255\) 1.45632e47 + 2.96129e47i 0.107759 + 0.219117i
\(256\) 1.55660e48 1.06507
\(257\) 1.62765e48i 1.03015i −0.857146 0.515073i \(-0.827765\pi\)
0.857146 0.515073i \(-0.172235\pi\)
\(258\) −3.73659e48 + 1.83761e48i −2.18817 + 1.07612i
\(259\) −1.02249e46 −0.00554197
\(260\) 5.08253e47i 0.255043i
\(261\) 8.29701e47 + 6.39539e47i 0.385577 + 0.297206i
\(262\) −4.42874e48 −1.90658
\(263\) 1.72240e48i 0.687098i −0.939135 0.343549i \(-0.888371\pi\)
0.939135 0.343549i \(-0.111629\pi\)
\(264\) 7.54534e46 + 1.53427e47i 0.0278997 + 0.0567313i
\(265\) −7.92801e47 −0.271798
\(266\) 7.04068e46i 0.0223863i
\(267\) −9.90561e47 + 4.87145e47i −0.292184 + 0.143692i
\(268\) 4.67397e48 1.27935
\(269\) 3.60605e48i 0.916192i −0.888903 0.458096i \(-0.848532\pi\)
0.888903 0.458096i \(-0.151468\pi\)
\(270\) 1.94584e48 + 3.93691e47i 0.459021 + 0.0928710i
\(271\) 4.48842e48 0.983349 0.491674 0.870779i \(-0.336385\pi\)
0.491674 + 0.870779i \(0.336385\pi\)
\(272\) 3.71076e48i 0.755239i
\(273\) −1.81601e46 3.69268e46i −0.00343452 0.00698375i
\(274\) 2.89803e48 0.509439
\(275\) 7.14216e48i 1.16728i
\(276\) 6.61657e48 3.25394e48i 1.00566 0.494571i
\(277\) −4.95445e48 −0.700488 −0.350244 0.936659i \(-0.613901\pi\)
−0.350244 + 0.936659i \(0.613901\pi\)
\(278\) 3.44731e48i 0.453508i
\(279\) −2.84060e48 + 3.68522e48i −0.347797 + 0.451211i
\(280\) −1.38798e45 −0.000158206
\(281\) 3.18401e48i 0.337947i −0.985621 0.168973i \(-0.945955\pi\)
0.985621 0.168973i \(-0.0540452\pi\)
\(282\) −9.20586e48 1.87192e49i −0.910085 1.85057i
\(283\) −1.24165e49 −1.14359 −0.571794 0.820397i \(-0.693752\pi\)
−0.571794 + 0.820397i \(0.693752\pi\)
\(284\) 1.99330e49i 1.71083i
\(285\) 6.07775e48 2.98896e48i 0.486234 0.239124i
\(286\) −1.95265e49 −1.45648
\(287\) 1.55373e47i 0.0108078i
\(288\) 1.70935e49 + 1.31758e49i 1.10913 + 0.854922i
\(289\) 7.69112e48 0.465621
\(290\) 4.03533e48i 0.227992i
\(291\) 3.84415e48 + 7.81669e48i 0.202740 + 0.412252i
\(292\) −8.91120e47 −0.0438813
\(293\) 3.17462e49i 1.45996i 0.683471 + 0.729978i \(0.260470\pi\)
−0.683471 + 0.729978i \(0.739530\pi\)
\(294\) 2.92837e49 1.44013e49i 1.25800 0.618666i
\(295\) 3.71110e48 0.148957
\(296\) 7.22217e47i 0.0270915i
\(297\) −7.43055e48 + 3.67260e49i −0.260551 + 1.28779i
\(298\) −4.40618e49 −1.44457
\(299\) 2.99274e49i 0.917583i
\(300\) −1.32014e49 2.68437e49i −0.378612 0.769870i
\(301\) 6.38004e47 0.0171196
\(302\) 1.07636e50i 2.70284i
\(303\) −4.34359e48 + 2.13612e48i −0.102093 + 0.0502080i
\(304\) 7.61596e49 1.67592
\(305\) 1.78031e49i 0.366858i
\(306\) −3.24184e49 + 4.20577e49i −0.625695 + 0.811741i
\(307\) −1.26028e49 −0.227877 −0.113939 0.993488i \(-0.536347\pi\)
−0.113939 + 0.993488i \(0.536347\pi\)
\(308\) 7.37117e47i 0.0124888i
\(309\) −8.04607e47 1.63609e48i −0.0127766 0.0259799i
\(310\) −1.79234e49 −0.266801
\(311\) 4.17051e49i 0.582079i 0.956711 + 0.291039i \(0.0940011\pi\)
−0.956711 + 0.291039i \(0.905999\pi\)
\(312\) 2.60826e48 1.28271e48i 0.0341396 0.0167894i
\(313\) 8.98638e49 1.10331 0.551656 0.834072i \(-0.313996\pi\)
0.551656 + 0.834072i \(0.313996\pi\)
\(314\) 4.38440e49i 0.505030i
\(315\) −2.40917e47 1.85701e47i −0.00260409 0.00200725i
\(316\) 9.15363e49 0.928649
\(317\) 3.17725e49i 0.302598i 0.988488 + 0.151299i \(0.0483456\pi\)
−0.988488 + 0.151299i \(0.951654\pi\)
\(318\) −5.62988e49 1.14478e50i −0.503451 1.02372i
\(319\) −7.61631e49 −0.639633
\(320\) 3.93889e49i 0.310724i
\(321\) −8.79524e49 + 4.32539e49i −0.651849 + 0.320571i
\(322\) −2.29964e48 −0.0160156
\(323\) 1.81162e50i 1.18582i
\(324\) 3.99557e49 + 1.51769e50i 0.245855 + 0.933859i
\(325\) −1.21417e50 −0.702444
\(326\) 9.06560e49i 0.493224i
\(327\) −1.52498e50 3.10090e50i −0.780388 1.58684i
\(328\) −1.09745e49 −0.0528333
\(329\) 3.19620e48i 0.0144783i
\(330\) −1.29522e50 + 6.36973e49i −0.552160 + 0.271545i
\(331\) 2.81121e50 1.12806 0.564031 0.825754i \(-0.309250\pi\)
0.564031 + 0.825754i \(0.309250\pi\)
\(332\) 1.83373e50i 0.692744i
\(333\) 9.66269e49 1.25358e50i 0.343727 0.445931i
\(334\) 1.52487e50 0.510861
\(335\) 1.40230e50i 0.442532i
\(336\) −1.50945e48 3.06932e48i −0.00448781 0.00912551i
\(337\) 2.00107e50 0.560613 0.280307 0.959910i \(-0.409564\pi\)
0.280307 + 0.959910i \(0.409564\pi\)
\(338\) 1.99044e50i 0.525551i
\(339\) −1.48536e49 + 7.30480e48i −0.0369690 + 0.0181809i
\(340\) −1.00490e50 −0.235801
\(341\) 3.38288e50i 0.748513i
\(342\) 8.63193e50 + 6.65355e50i 1.80130 + 1.38845i
\(343\) −1.00005e49 −0.0196853
\(344\) 4.50642e49i 0.0836880i
\(345\) −9.76258e49 1.98512e50i −0.171074 0.347861i
\(346\) −6.82838e50 −1.12926
\(347\) 2.08623e49i 0.0325666i −0.999867 0.0162833i \(-0.994817\pi\)
0.999867 0.0162833i \(-0.00518337\pi\)
\(348\) −2.86258e50 + 1.40778e50i −0.421864 + 0.207467i
\(349\) −5.22713e50 −0.727369 −0.363684 0.931522i \(-0.618481\pi\)
−0.363684 + 0.931522i \(0.618481\pi\)
\(350\) 9.32974e48i 0.0122605i
\(351\) 6.24342e50 + 1.26319e50i 0.774961 + 0.156793i
\(352\) −1.56911e51 −1.83993
\(353\) 4.45127e50i 0.493162i −0.969122 0.246581i \(-0.920693\pi\)
0.969122 0.246581i \(-0.0793071\pi\)
\(354\) 2.63535e50 + 5.35871e50i 0.275913 + 0.561042i
\(355\) 5.98037e50 0.591781
\(356\) 3.36143e50i 0.314430i
\(357\) 7.30106e48 3.59057e48i 0.00645686 0.00317540i
\(358\) −1.03807e51 −0.868091
\(359\) 2.36020e51i 1.86663i 0.359054 + 0.933317i \(0.383100\pi\)
−0.359054 + 0.933317i \(0.616900\pi\)
\(360\) 1.31166e49 1.70167e49i 0.00981232 0.0127299i
\(361\) 2.30517e51 1.63140
\(362\) 2.18570e51i 1.46359i
\(363\) −5.05802e50 1.02850e51i −0.320515 0.651735i
\(364\) 1.25310e49 0.00751549
\(365\) 2.67357e49i 0.0151787i
\(366\) 2.57071e51 1.26424e51i 1.38176 0.679529i
\(367\) 7.49900e50 0.381665 0.190832 0.981623i \(-0.438881\pi\)
0.190832 + 0.981623i \(0.438881\pi\)
\(368\) 2.48754e51i 1.19898i
\(369\) −1.90489e51 1.46830e51i −0.869645 0.670328i
\(370\) 6.09691e50 0.263679
\(371\) 1.95465e49i 0.00800924i
\(372\) −6.25284e50 1.27145e51i −0.242783 0.493675i
\(373\) −3.43410e51 −1.26368 −0.631838 0.775100i \(-0.717699\pi\)
−0.631838 + 0.775100i \(0.717699\pi\)
\(374\) 3.86073e51i 1.34660i
\(375\) −1.71189e51 + 8.41887e50i −0.566046 + 0.278374i
\(376\) −2.25758e50 −0.0707760
\(377\) 1.29477e51i 0.384917i
\(378\) 9.70646e48 4.79748e49i 0.00273668 0.0135262i
\(379\) −6.62305e50 −0.177123 −0.0885613 0.996071i \(-0.528227\pi\)
−0.0885613 + 0.996071i \(0.528227\pi\)
\(380\) 2.06246e51i 0.523256i
\(381\) 1.27614e51 + 2.59491e51i 0.307185 + 0.624629i
\(382\) 1.14192e52 2.60837
\(383\) 5.12395e51i 1.11078i −0.831589 0.555391i \(-0.812568\pi\)
0.831589 0.555391i \(-0.187432\pi\)
\(384\) 4.19436e50 2.06273e50i 0.0863060 0.0424442i
\(385\) 2.21152e49 0.00431993
\(386\) 8.47813e51i 1.57237i
\(387\) −6.02923e51 + 7.82198e51i −1.06180 + 1.37752i
\(388\) −2.65257e51 −0.443641
\(389\) 2.31289e51i 0.367420i −0.982980 0.183710i \(-0.941189\pi\)
0.982980 0.183710i \(-0.0588107\pi\)
\(390\) 1.08285e51 + 2.20188e51i 0.163410 + 0.332277i
\(391\) 5.91716e51 0.848356
\(392\) 3.53168e50i 0.0481127i
\(393\) −9.42569e51 + 4.63543e51i −1.22029 + 0.600122i
\(394\) −9.45906e51 −1.16392
\(395\) 2.74630e51i 0.321223i
\(396\) −9.03711e51 6.96586e51i −1.00491 0.774589i
\(397\) 1.17777e52 1.24523 0.622616 0.782528i \(-0.286070\pi\)
0.622616 + 0.782528i \(0.286070\pi\)
\(398\) 7.00927e51i 0.704712i
\(399\) −7.36928e49 1.49847e50i −0.00704640 0.0143282i
\(400\) −1.00921e52 −0.917867
\(401\) 4.24297e51i 0.367098i 0.983011 + 0.183549i \(0.0587587\pi\)
−0.983011 + 0.183549i \(0.941241\pi\)
\(402\) 2.02488e52 9.95809e51i 1.66678 0.819700i
\(403\) −5.75091e51 −0.450438
\(404\) 1.47398e51i 0.109866i
\(405\) 4.55341e51 1.19876e51i 0.323025 0.0850420i
\(406\) 9.94912e49 0.00671837
\(407\) 1.15074e52i 0.739754i
\(408\) 2.53613e50 + 5.15697e50i 0.0155227 + 0.0315640i
\(409\) 2.21554e52 1.29126 0.645630 0.763651i \(-0.276595\pi\)
0.645630 + 0.763651i \(0.276595\pi\)
\(410\) 9.26460e51i 0.514221i
\(411\) 6.16789e51 3.03329e51i 0.326062 0.160353i
\(412\) 5.55201e50 0.0279580
\(413\) 9.14972e49i 0.00438942i
\(414\) 2.17319e52 2.81938e52i 0.993326 1.28868i
\(415\) −5.50160e51 −0.239622
\(416\) 2.66749e52i 1.10723i
\(417\) 3.60820e51 + 7.33692e51i 0.142748 + 0.290264i
\(418\) −7.92376e52 −2.98817
\(419\) 3.58632e52i 1.28934i −0.764460 0.644672i \(-0.776994\pi\)
0.764460 0.644672i \(-0.223006\pi\)
\(420\) 8.31197e49 4.08772e49i 0.00284917 0.00140118i
\(421\) 2.87166e52 0.938621 0.469311 0.883033i \(-0.344502\pi\)
0.469311 + 0.883033i \(0.344502\pi\)
\(422\) 6.99634e52i 2.18083i
\(423\) −3.91857e52 3.02046e52i −1.16499 0.897978i
\(424\) −1.38063e51 −0.0391526
\(425\) 2.40062e52i 0.649448i
\(426\) 4.24681e52 + 8.63547e52i 1.09615 + 2.22892i
\(427\) −4.38935e50 −0.0108104
\(428\) 2.98464e52i 0.701481i
\(429\) −4.15584e52 + 2.04379e52i −0.932208 + 0.458448i
\(430\) −3.80429e52 −0.814526
\(431\) 2.54987e52i 0.521162i 0.965452 + 0.260581i \(0.0839141\pi\)
−0.965452 + 0.260581i \(0.916086\pi\)
\(432\) 5.18947e52 + 1.04996e52i 1.01262 + 0.204878i
\(433\) −5.65399e52 −1.05341 −0.526705 0.850048i \(-0.676573\pi\)
−0.526705 + 0.850048i \(0.676573\pi\)
\(434\) 4.41903e50i 0.00786199i
\(435\) 4.22367e51 + 8.58840e51i 0.0717636 + 0.145924i
\(436\) 1.05228e53 1.70766
\(437\) 1.21444e53i 1.88255i
\(438\) −3.86055e51 + 1.89857e51i −0.0571699 + 0.0281154i
\(439\) 7.68897e52 1.08787 0.543936 0.839127i \(-0.316933\pi\)
0.543936 + 0.839127i \(0.316933\pi\)
\(440\) 1.56207e51i 0.0211177i
\(441\) 4.72511e52 6.13008e52i 0.610436 0.791944i
\(442\) −6.56324e52 −0.810350
\(443\) 7.92880e52i 0.935692i 0.883810 + 0.467846i \(0.154970\pi\)
−0.883810 + 0.467846i \(0.845030\pi\)
\(444\) 2.12699e52 + 4.32503e52i 0.239942 + 0.487898i
\(445\) −1.00851e52 −0.108762
\(446\) 1.82967e53i 1.88658i
\(447\) −9.37769e52 + 4.61183e52i −0.924582 + 0.454697i
\(448\) 9.71135e50 0.00915629
\(449\) 1.28592e53i 1.15955i 0.814777 + 0.579774i \(0.196859\pi\)
−0.814777 + 0.579774i \(0.803141\pi\)
\(450\) −1.14383e53 8.81674e52i −0.986535 0.760428i
\(451\) 1.74861e53 1.44265
\(452\) 5.04051e51i 0.0397838i
\(453\) −1.12660e53 2.29083e53i −0.850756 1.72993i
\(454\) −1.38302e53 −0.999336
\(455\) 3.75959e50i 0.00259963i
\(456\) 1.05842e52 5.20516e51i 0.0700423 0.0344459i
\(457\) 2.32780e53 1.47442 0.737209 0.675665i \(-0.236143\pi\)
0.737209 + 0.675665i \(0.236143\pi\)
\(458\) 5.96290e51i 0.0361533i
\(459\) −2.49755e52 + 1.23443e53i −0.144964 + 0.716494i
\(460\) 6.73645e52 0.374347
\(461\) 3.68046e53i 1.95832i 0.203089 + 0.979160i \(0.434902\pi\)
−0.203089 + 0.979160i \(0.565098\pi\)
\(462\) 1.57046e51 + 3.19337e51i 0.00800178 + 0.0162708i
\(463\) −9.46582e52 −0.461890 −0.230945 0.972967i \(-0.574182\pi\)
−0.230945 + 0.972967i \(0.574182\pi\)
\(464\) 1.07620e53i 0.502962i
\(465\) −3.81465e52 + 1.87600e52i −0.170764 + 0.0839794i
\(466\) 1.28225e53 0.549862
\(467\) 3.32159e53i 1.36461i 0.731068 + 0.682304i \(0.239022\pi\)
−0.731068 + 0.682304i \(0.760978\pi\)
\(468\) −1.18420e53 + 1.53631e53i −0.466130 + 0.604730i
\(469\) −3.45737e51 −0.0130404
\(470\) 1.90584e53i 0.688856i
\(471\) 4.58903e52 + 9.33134e52i 0.158965 + 0.323240i
\(472\) 6.46274e51 0.0214574
\(473\) 7.18025e53i 2.28516i
\(474\) 3.96558e53 1.95022e53i 1.20987 0.595000i
\(475\) −4.92703e53 −1.44116
\(476\) 2.47759e51i 0.00694849i
\(477\) −2.39642e53 1.84718e53i −0.644459 0.496753i
\(478\) −4.95824e53 −1.27870
\(479\) 2.50146e53i 0.618705i 0.950947 + 0.309353i \(0.100112\pi\)
−0.950947 + 0.309353i \(0.899888\pi\)
\(480\) 8.70159e52 + 1.76938e53i 0.206431 + 0.419756i
\(481\) 1.95625e53 0.445167
\(482\) 1.03724e54i 2.26432i
\(483\) −4.89433e51 + 2.40697e51i −0.0102506 + 0.00504113i
\(484\) 3.49017e53 0.701358
\(485\) 7.95831e52i 0.153457i
\(486\) 4.96447e53 + 5.72371e53i 0.918645 + 1.05914i
\(487\) 3.98927e53 0.708457 0.354229 0.935159i \(-0.384743\pi\)
0.354229 + 0.935159i \(0.384743\pi\)
\(488\) 3.10034e52i 0.0528460i
\(489\) 9.48871e52 + 1.92943e53i 0.155249 + 0.315684i
\(490\) 2.98142e53 0.468276
\(491\) 4.07385e53i 0.614292i −0.951662 0.307146i \(-0.900626\pi\)
0.951662 0.307146i \(-0.0993740\pi\)
\(492\) 6.57212e53 3.23208e53i 0.951488 0.467930i
\(493\) −2.55999e53 −0.355877
\(494\) 1.34704e54i 1.79821i
\(495\) −2.08992e53 + 2.71134e53i −0.267933 + 0.347600i
\(496\) −4.78010e53 −0.588577
\(497\) 1.47446e52i 0.0174384i
\(498\) −3.90683e53 7.94415e53i −0.443851 0.902527i
\(499\) −7.38488e53 −0.805995 −0.402998 0.915201i \(-0.632032\pi\)
−0.402998 + 0.915201i \(0.632032\pi\)
\(500\) 5.80925e53i 0.609144i
\(501\) 3.24538e53 1.59603e53i 0.326972 0.160801i
\(502\) −1.65240e54 −1.59971
\(503\) 8.34228e53i 0.776114i 0.921635 + 0.388057i \(0.126854\pi\)
−0.921635 + 0.388057i \(0.873146\pi\)
\(504\) −4.19548e50 3.23391e50i −0.000375121 0.000289146i
\(505\) −4.42228e52 −0.0380031
\(506\) 2.58807e54i 2.13779i
\(507\) −2.08334e53 4.23626e53i −0.165425 0.336375i
\(508\) −8.80573e53 −0.672188
\(509\) 2.04133e54i 1.49816i −0.662480 0.749080i \(-0.730496\pi\)
0.662480 0.749080i \(-0.269504\pi\)
\(510\) −4.35348e53 + 2.14099e53i −0.307209 + 0.151081i
\(511\) 6.59169e50 0.000447279
\(512\) 2.14101e54i 1.39707i
\(513\) 2.53355e54 + 5.12597e53i 1.58994 + 0.321684i
\(514\) 2.39286e54 1.44429
\(515\) 1.66573e52i 0.00967075i
\(516\) −1.32718e54 2.69869e54i −0.741201 1.50716i
\(517\) 3.59709e54 1.93259
\(518\) 1.50320e52i 0.00776999i
\(519\) −1.45329e54 + 7.14707e53i −0.722776 + 0.355452i
\(520\) 2.65551e52 0.0127081
\(521\) 2.09664e54i 0.965539i −0.875747 0.482770i \(-0.839631\pi\)
0.875747 0.482770i \(-0.160369\pi\)
\(522\) −9.40207e53 + 1.21977e54i −0.416690 + 0.540590i
\(523\) −7.49003e53 −0.319484 −0.159742 0.987159i \(-0.551066\pi\)
−0.159742 + 0.987159i \(0.551066\pi\)
\(524\) 3.19858e54i 1.31320i
\(525\) 9.76517e51 + 1.98565e52i 0.00385917 + 0.00784724i
\(526\) 2.53215e54 0.963330
\(527\) 1.13705e54i 0.416455i
\(528\) −3.45429e54 + 1.69878e54i −1.21809 + 0.599043i
\(529\) −1.02143e54 −0.346812
\(530\) 1.16552e54i 0.381068i
\(531\) 1.12176e54 + 8.64662e53i 0.353192 + 0.272243i
\(532\) 5.08501e52 0.0154191
\(533\) 2.97263e54i 0.868155i
\(534\) −7.16168e53 1.45626e54i −0.201460 0.409649i
\(535\) −8.95460e53 −0.242644
\(536\) 2.44205e53i 0.0637469i
\(537\) −2.20932e54 + 1.08652e54i −0.555614 + 0.273244i
\(538\) 5.30137e54 1.28453
\(539\) 5.62716e54i 1.31375i
\(540\) −2.84336e53 + 1.40535e54i −0.0639671 + 0.316162i
\(541\) −2.63120e54 −0.570438 −0.285219 0.958462i \(-0.592066\pi\)
−0.285219 + 0.958462i \(0.592066\pi\)
\(542\) 6.59857e54i 1.37868i
\(543\) 2.28771e54 + 4.65183e54i 0.460686 + 0.936758i
\(544\) −5.27408e54 −1.02369
\(545\) 3.15709e54i 0.590686i
\(546\) 5.42873e52 2.66978e52i 0.00979141 0.00481529i
\(547\) −4.02299e54 −0.699523 −0.349762 0.936839i \(-0.613737\pi\)
−0.349762 + 0.936839i \(0.613737\pi\)
\(548\) 2.09305e54i 0.350888i
\(549\) 4.14800e54 5.38137e54i 0.670489 0.869854i
\(550\) 1.04999e55 1.63656
\(551\) 5.25412e54i 0.789711i
\(552\) −1.70012e53 3.45702e53i −0.0246432 0.0501095i
\(553\) −6.77101e52 −0.00946566
\(554\) 7.28370e54i 0.982103i
\(555\) 1.29761e54 6.38147e53i 0.168766 0.0829967i
\(556\) −2.48976e54 −0.312364
\(557\) 3.05699e54i 0.369991i 0.982739 + 0.184995i \(0.0592270\pi\)
−0.982739 + 0.184995i \(0.940773\pi\)
\(558\) −5.41777e54 4.17605e54i −0.632610 0.487620i
\(559\) −1.22064e55 −1.37516
\(560\) 3.12493e52i 0.00339688i
\(561\) −4.04091e54 8.21680e54i −0.423860 0.861877i
\(562\) 4.68092e54 0.473811
\(563\) 1.63777e55i 1.59988i 0.600083 + 0.799938i \(0.295134\pi\)
−0.600083 + 0.799938i \(0.704866\pi\)
\(564\) 1.35196e55 6.64877e54i 1.27462 0.626843i
\(565\) −1.51227e53 −0.0137613
\(566\) 1.82539e55i 1.60334i
\(567\) −2.95556e52 1.12264e53i −0.00250598 0.00951877i
\(568\) 1.04146e54 0.0852462
\(569\) 1.09842e55i 0.868010i −0.900910 0.434005i \(-0.857100\pi\)
0.900910 0.434005i \(-0.142900\pi\)
\(570\) 4.39416e54 + 8.93509e54i 0.335258 + 0.681714i
\(571\) −1.49352e55 −1.10024 −0.550120 0.835085i \(-0.685418\pi\)
−0.550120 + 0.835085i \(0.685418\pi\)
\(572\) 1.41027e55i 1.00319i
\(573\) 2.43035e55 1.19522e55i 1.66946 0.821021i
\(574\) −2.28419e53 −0.0151528
\(575\) 1.60927e55i 1.03103i
\(576\) −9.17738e54 + 1.19062e55i −0.567896 + 0.736755i
\(577\) 7.87830e54 0.470887 0.235443 0.971888i \(-0.424346\pi\)
0.235443 + 0.971888i \(0.424346\pi\)
\(578\) 1.13070e55i 0.652814i
\(579\) 8.87381e54 + 1.80440e55i 0.494925 + 1.00638i
\(580\) −2.91445e54 −0.157035
\(581\) 1.35642e53i 0.00706109i
\(582\) −1.14916e55 + 5.65140e54i −0.577989 + 0.284247i
\(583\) 2.19981e55 1.06909
\(584\) 4.65592e52i 0.00218649i
\(585\) 4.60928e54 + 3.55287e54i 0.209178 + 0.161236i
\(586\) −4.66711e55 −2.04690
\(587\) 2.21712e54i 0.0939782i 0.998895 + 0.0469891i \(0.0149626\pi\)
−0.998895 + 0.0469891i \(0.985037\pi\)
\(588\) 1.04011e55 + 2.11496e55i 0.426121 + 0.866475i
\(589\) −2.33369e55 −0.924138
\(590\) 5.45580e54i 0.208842i
\(591\) −2.01317e55 + 9.90053e54i −0.744958 + 0.366361i
\(592\) 1.62602e55 0.581690
\(593\) 4.82567e55i 1.66903i −0.550987 0.834514i \(-0.685749\pi\)
0.550987 0.834514i \(-0.314251\pi\)
\(594\) −5.39920e55 1.09239e55i −1.80551 0.365299i
\(595\) 7.43334e52 0.00240350
\(596\) 3.18229e55i 0.994979i
\(597\) −7.33641e54 1.49179e55i −0.221818 0.451045i
\(598\) 4.39972e55 1.28648
\(599\) 6.29039e55i 1.77886i 0.457075 + 0.889428i \(0.348897\pi\)
−0.457075 + 0.889428i \(0.651103\pi\)
\(600\) −1.40253e54 + 6.89745e53i −0.0383607 + 0.0188653i
\(601\) 1.93988e55 0.513198 0.256599 0.966518i \(-0.417398\pi\)
0.256599 + 0.966518i \(0.417398\pi\)
\(602\) 9.37950e53i 0.0240021i
\(603\) 3.26727e55 4.23877e55i 0.808796 1.04928i
\(604\) 7.77384e55 1.86164
\(605\) 1.04713e55i 0.242602i
\(606\) −3.14038e54 6.38564e54i −0.0703930 0.143137i
\(607\) −1.78014e55 −0.386082 −0.193041 0.981191i \(-0.561835\pi\)
−0.193041 + 0.981191i \(0.561835\pi\)
\(608\) 1.08245e56i 2.27163i
\(609\) 2.11747e53 1.04135e53i 0.00430004 0.00211470i
\(610\) 2.61728e55 0.514345
\(611\) 6.11505e55i 1.16299i
\(612\) −3.03754e55 2.34136e55i −0.559106 0.430963i
\(613\) 2.54745e55 0.453833 0.226916 0.973914i \(-0.427136\pi\)
0.226916 + 0.973914i \(0.427136\pi\)
\(614\) 1.85278e55i 0.319490i
\(615\) −9.69700e54 1.97179e55i −0.161858 0.329123i
\(616\) 3.85128e52 0.000622287
\(617\) 5.04493e55i 0.789137i −0.918867 0.394568i \(-0.870894\pi\)
0.918867 0.394568i \(-0.129106\pi\)
\(618\) 2.40526e54 1.18288e54i 0.0364245 0.0179131i
\(619\) −1.10845e56 −1.62519 −0.812595 0.582829i \(-0.801946\pi\)
−0.812595 + 0.582829i \(0.801946\pi\)
\(620\) 1.29449e55i 0.183766i
\(621\) 1.67425e55 8.27511e55i 0.230139 1.13747i
\(622\) −6.13121e55 −0.816090
\(623\) 2.48648e53i 0.00320497i
\(624\) 2.88792e55 + 5.87230e55i 0.360490 + 0.733021i
\(625\) 5.60595e55 0.677718
\(626\) 1.32112e56i 1.54687i
\(627\) −1.68642e56 + 8.29358e55i −1.91256 + 0.940570i
\(628\) −3.16656e55 −0.347852
\(629\) 3.86784e55i 0.411582i
\(630\) 2.73004e53 3.54180e53i 0.00281422 0.00365101i
\(631\) 6.65827e55 0.664927 0.332464 0.943116i \(-0.392120\pi\)
0.332464 + 0.943116i \(0.392120\pi\)
\(632\) 4.78258e54i 0.0462723i
\(633\) 7.32288e55 + 1.48903e56i 0.686448 + 1.39582i
\(634\) −4.67098e55 −0.424251
\(635\) 2.64192e55i 0.232512i
\(636\) 8.26797e55 4.06608e55i 0.705110 0.346764i
\(637\) 9.56618e55 0.790587
\(638\) 1.11970e56i 0.896783i
\(639\) 1.80770e56 + 1.39339e56i 1.40317 + 1.08157i
\(640\) 4.27035e54 0.0321266
\(641\) 9.15350e55i 0.667462i −0.942668 0.333731i \(-0.891692\pi\)
0.942668 0.333731i \(-0.108308\pi\)
\(642\) −6.35889e55 1.29302e56i −0.449449 0.913911i
\(643\) 5.36382e54 0.0367498 0.0183749 0.999831i \(-0.494151\pi\)
0.0183749 + 0.999831i \(0.494151\pi\)
\(644\) 1.66087e54i 0.0110311i
\(645\) −8.09669e55 + 3.98185e55i −0.521331 + 0.256384i
\(646\) −2.66333e56 −1.66255
\(647\) 7.57259e55i 0.458309i −0.973390 0.229155i \(-0.926404\pi\)
0.973390 0.229155i \(-0.0735962\pi\)
\(648\) 7.92959e54 2.08760e54i 0.0465319 0.0122503i
\(649\) −1.02973e56 −0.585909
\(650\) 1.78499e56i 0.984845i
\(651\) 4.62527e53 + 9.40503e53i 0.00247467 + 0.00503200i
\(652\) −6.54747e55 −0.339720
\(653\) 1.47287e56i 0.741140i 0.928804 + 0.370570i \(0.120838\pi\)
−0.928804 + 0.370570i \(0.879162\pi\)
\(654\) 4.55874e56 2.24193e56i 2.22479 1.09412i
\(655\) −9.59647e55 −0.454240
\(656\) 2.47083e56i 1.13440i
\(657\) −6.22924e54 + 8.08146e54i −0.0277414 + 0.0359900i
\(658\) −4.69884e54 −0.0202989
\(659\) 3.56702e55i 0.149485i −0.997203 0.0747425i \(-0.976187\pi\)
0.997203 0.0747425i \(-0.0238135\pi\)
\(660\) −4.60042e55 9.35450e55i −0.187033 0.380314i
\(661\) 1.95144e56 0.769707 0.384854 0.922978i \(-0.374252\pi\)
0.384854 + 0.922978i \(0.374252\pi\)
\(662\) 4.13285e56i 1.58157i
\(663\) −1.39686e56 + 6.86956e55i −0.518658 + 0.255069i
\(664\) −9.58083e54 −0.0345177
\(665\) 1.52562e54i 0.00533351i
\(666\) 1.84293e56 + 1.42054e56i 0.625208 + 0.481914i
\(667\) 1.71611e56 0.564974
\(668\) 1.10131e56i 0.351868i
\(669\) −1.91506e56 3.89408e56i −0.593827 1.20749i
\(670\) 2.06157e56 0.620442
\(671\) 4.93988e56i 1.44300i
\(672\) 4.36242e54 2.14538e54i 0.0123692 0.00608301i
\(673\) −3.95837e56 −1.08947 −0.544735 0.838609i \(-0.683370\pi\)
−0.544735 + 0.838609i \(0.683370\pi\)
\(674\) 2.94183e56i 0.785995i
\(675\) −3.35725e56 6.79252e55i −0.870779 0.176180i
\(676\) 1.43756e56 0.361986
\(677\) 1.03199e56i 0.252292i 0.992012 + 0.126146i \(0.0402607\pi\)
−0.992012 + 0.126146i \(0.959739\pi\)
\(678\) −1.07390e55 2.18367e55i −0.0254901 0.0518315i
\(679\) 1.96212e54 0.00452200
\(680\) 5.25040e54i 0.0117494i
\(681\) −2.94349e56 + 1.44757e56i −0.639617 + 0.314555i
\(682\) 4.97329e56 1.04944
\(683\) 6.20211e56i 1.27094i −0.772125 0.635471i \(-0.780806\pi\)
0.772125 0.635471i \(-0.219194\pi\)
\(684\) −4.80541e56 + 6.23426e56i −0.956331 + 1.24069i
\(685\) 6.27964e55 0.121373
\(686\) 1.47021e55i 0.0275993i
\(687\) 6.24120e54 + 1.26909e55i 0.0113798 + 0.0231396i
\(688\) −1.01459e57 −1.79689
\(689\) 3.73969e56i 0.643355i
\(690\) 2.91839e56 1.43523e56i 0.487711 0.239850i
\(691\) 7.95190e56 1.29095 0.645476 0.763780i \(-0.276659\pi\)
0.645476 + 0.763780i \(0.276659\pi\)
\(692\) 4.93167e56i 0.777808i
\(693\) 6.68482e54 + 5.15270e54i 0.0102429 + 0.00789533i
\(694\) 3.06703e55 0.0456593
\(695\) 7.46985e55i 0.108048i
\(696\) 7.35536e54 + 1.49564e55i 0.0103376 + 0.0210204i
\(697\) 5.87740e56 0.802657
\(698\) 7.68457e56i 1.01979i
\(699\) 2.72901e56 1.34209e56i 0.351935 0.173077i
\(700\) −6.73824e54 −0.00844472
\(701\) 3.53553e56i 0.430620i 0.976546 + 0.215310i \(0.0690762\pi\)
−0.976546 + 0.215310i \(0.930924\pi\)
\(702\) −1.85706e56 + 9.17865e56i −0.219829 + 1.08652i
\(703\) 7.93837e56 0.913324
\(704\) 1.09294e57i 1.22220i
\(705\) −1.99478e56 4.05619e56i −0.216827 0.440896i
\(706\) 6.54395e56 0.691426
\(707\) 1.09031e54i 0.00111986i
\(708\) −3.87023e56 + 1.90333e56i −0.386431 + 0.190042i
\(709\) 5.27547e55 0.0512079 0.0256039 0.999672i \(-0.491849\pi\)
0.0256039 + 0.999672i \(0.491849\pi\)
\(710\) 8.79193e56i 0.829693i
\(711\) 6.39871e56 8.30131e56i 0.587084 0.761649i
\(712\) −1.75628e55 −0.0156673
\(713\) 7.62233e56i 0.661145i
\(714\) 5.27861e54 + 1.07335e55i 0.00445200 + 0.00905270i
\(715\) −4.23113e56 −0.347005
\(716\) 7.49726e56i 0.597919i
\(717\) −1.05526e57 + 5.18965e56i −0.818424 + 0.402490i
\(718\) −3.46980e57 −2.61707
\(719\) 1.10786e57i 0.812660i 0.913726 + 0.406330i \(0.133192\pi\)
−0.913726 + 0.406330i \(0.866808\pi\)
\(720\) 3.83119e56 + 2.95311e56i 0.273328 + 0.210683i
\(721\) −4.10686e53 −0.000284974
\(722\) 3.38891e57i 2.28726i
\(723\) −1.08565e57 2.20756e57i −0.712728 1.44926i
\(724\) −1.57858e57 −1.00808
\(725\) 6.96233e56i 0.432509i
\(726\) 1.51203e57 7.43596e56i 0.913750 0.449371i
\(727\) 2.26670e57 1.33262 0.666308 0.745677i \(-0.267874\pi\)
0.666308 + 0.745677i \(0.267874\pi\)
\(728\) 6.54718e53i 0.000374478i
\(729\) 1.65567e57 + 6.98562e56i 0.921349 + 0.388735i
\(730\) −3.93050e55 −0.0212809
\(731\) 2.41342e57i 1.27141i
\(732\) 9.13075e56 + 1.85665e57i 0.468042 + 0.951717i
\(733\) −2.19626e57 −1.09548 −0.547740 0.836648i \(-0.684512\pi\)
−0.547740 + 0.836648i \(0.684512\pi\)
\(734\) 1.10245e57i 0.535104i
\(735\) 6.34537e56 3.12057e56i 0.299716 0.147397i
\(736\) 3.53553e57 1.62517
\(737\) 3.89101e57i 1.74066i
\(738\) 2.15859e57 2.80043e57i 0.939818 1.21927i
\(739\) −3.97320e57 −1.68365 −0.841824 0.539752i \(-0.818518\pi\)
−0.841824 + 0.539752i \(0.818518\pi\)
\(740\) 4.40339e56i 0.181615i
\(741\) 1.40991e57 + 2.86691e57i 0.566013 + 1.15093i
\(742\) −2.87360e55 −0.0112292
\(743\) 2.93565e57i 1.11668i −0.829613 0.558339i \(-0.811439\pi\)
0.829613 0.558339i \(-0.188561\pi\)
\(744\) −6.64307e55 + 3.26698e55i −0.0245986 + 0.0120973i
\(745\) −9.54759e56 −0.344166
\(746\) 5.04857e57i 1.77171i
\(747\) −1.66298e57 1.28184e57i −0.568166 0.437947i
\(748\) 2.78834e57 0.927500
\(749\) 2.20776e55i 0.00715015i
\(750\) −1.23769e57 2.51671e57i −0.390288 0.793612i
\(751\) −3.66179e56 −0.112433 −0.0562166 0.998419i \(-0.517904\pi\)
−0.0562166 + 0.998419i \(0.517904\pi\)
\(752\) 5.08277e57i 1.51965i
\(753\) −3.51681e57 + 1.72952e57i −1.02388 + 0.503531i
\(754\) −1.90349e57 −0.539664
\(755\) 2.33233e57i 0.643949i
\(756\) 3.46489e55 + 7.01032e54i 0.00931652 + 0.00188496i
\(757\) 1.69184e57 0.443039 0.221520 0.975156i \(-0.428898\pi\)
0.221520 + 0.975156i \(0.428898\pi\)
\(758\) 9.73676e56i 0.248331i
\(759\) 2.70886e57 + 5.50820e57i 0.672901 + 1.36828i
\(760\) 1.07759e56 0.0260725
\(761\) 1.28568e57i 0.302999i 0.988457 + 0.151499i \(0.0484102\pi\)
−0.988457 + 0.151499i \(0.951590\pi\)
\(762\) −3.81486e57 + 1.87610e57i −0.875747 + 0.430681i
\(763\) −7.78380e55 −0.0174061
\(764\) 8.24732e57i 1.79658i
\(765\) −7.02462e56 + 9.11333e56i −0.149071 + 0.193396i
\(766\) 7.53288e57 1.55735
\(767\) 1.75055e57i 0.352587i
\(768\) 2.39521e57 + 4.87042e57i 0.470023 + 0.955744i
\(769\) 3.55428e57 0.679555 0.339777 0.940506i \(-0.389648\pi\)
0.339777 + 0.940506i \(0.389648\pi\)
\(770\) 3.25123e55i 0.00605665i
\(771\) 5.09273e57 2.50454e57i 0.924407 0.454611i
\(772\) −6.12317e57 −1.08301
\(773\) 9.17318e57i 1.58099i 0.612466 + 0.790497i \(0.290178\pi\)
−0.612466 + 0.790497i \(0.709822\pi\)
\(774\) −1.14993e58 8.86377e57i −1.93132 1.48867i
\(775\) 3.09241e57 0.506131
\(776\) 1.38591e56i 0.0221055i
\(777\) −1.57335e55 3.19926e55i −0.00244571 0.00497312i
\(778\) 3.40025e57 0.515133
\(779\) 1.20628e58i 1.78114i
\(780\) −1.59027e57 + 7.82072e56i −0.228864 + 0.112552i
\(781\) −1.65940e58 −2.32771
\(782\) 8.69900e57i 1.18942i
\(783\) −7.24346e56 + 3.58013e57i −0.0965408 + 0.477159i
\(784\) 7.95132e57 1.03304
\(785\) 9.50040e56i 0.120323i
\(786\) −6.81470e57 1.38570e58i −0.841387 1.71088i
\(787\) −1.58399e57 −0.190659 −0.0953297 0.995446i \(-0.530391\pi\)
−0.0953297 + 0.995446i \(0.530391\pi\)
\(788\) 6.83164e57i 0.801679i
\(789\) 5.38919e57 2.65033e57i 0.616572 0.303222i
\(790\) 4.03743e57 0.450363
\(791\) 3.72851e54i 0.000405513i
\(792\) −3.63952e56 + 4.72170e56i −0.0385958 + 0.0500720i
\(793\) 8.39780e57 0.868364
\(794\) 1.73148e58i 1.74585i
\(795\) −1.21992e57 2.48058e57i −0.119947 0.243900i
\(796\) 5.06232e57 0.485387
\(797\) 5.79622e57i 0.541974i −0.962583 0.270987i \(-0.912650\pi\)
0.962583 0.270987i \(-0.0873500\pi\)
\(798\) 2.20295e56 1.08338e56i 0.0200885 0.00987925i
\(799\) 1.20905e58 1.07525
\(800\) 1.43438e58i 1.24413i
\(801\) −3.04844e57 2.34976e57i −0.257886 0.198780i
\(802\) −6.23773e57 −0.514682
\(803\) 7.41845e56i 0.0597038i
\(804\) 7.19205e57 + 1.46243e58i 0.564588 + 1.14803i
\(805\) −4.98300e55 −0.00381569
\(806\) 8.45459e57i 0.631527i
\(807\) 1.12829e58 5.54880e57i 0.822150 0.404323i
\(808\) −7.70124e55 −0.00547436
\(809\) 7.60503e57i 0.527389i −0.964606 0.263694i \(-0.915059\pi\)
0.964606 0.263694i \(-0.0849410\pi\)
\(810\) 1.76234e57 + 6.69411e57i 0.119231 + 0.452890i
\(811\) −1.24011e57 −0.0818548 −0.0409274 0.999162i \(-0.513031\pi\)
−0.0409274 + 0.999162i \(0.513031\pi\)
\(812\) 7.18557e55i 0.00462744i
\(813\) 6.90654e57 + 1.40438e58i 0.433960 + 0.882414i
\(814\) −1.69173e58 −1.03716
\(815\) 1.96439e57i 0.117510i
\(816\) −1.16105e58 + 5.70991e57i −0.677718 + 0.333293i
\(817\) −4.95331e58 −2.82133
\(818\) 3.25714e58i 1.81038i
\(819\) 8.75960e55 1.13642e56i 0.00475123 0.00616397i
\(820\) 6.69119e57 0.354182
\(821\) 2.11936e58i 1.09482i −0.836865 0.547409i \(-0.815614\pi\)
0.836865 0.547409i \(-0.184386\pi\)
\(822\) 4.45933e57 + 9.06761e57i 0.224819 + 0.457148i
\(823\) −1.61545e58 −0.794874 −0.397437 0.917630i \(-0.630100\pi\)
−0.397437 + 0.917630i \(0.630100\pi\)
\(824\) 2.90081e55i 0.00139308i
\(825\) 2.23470e58 1.09900e58i 1.04747 0.515131i
\(826\) 1.34513e56 0.00615408
\(827\) 9.15034e57i 0.408627i 0.978906 + 0.204313i \(0.0654962\pi\)
−0.978906 + 0.204313i \(0.934504\pi\)
\(828\) 2.03624e58 + 1.56955e58i 0.887612 + 0.684177i
\(829\) 1.73502e58 0.738269 0.369135 0.929376i \(-0.379654\pi\)
0.369135 + 0.929376i \(0.379654\pi\)
\(830\) 8.08808e57i 0.335957i
\(831\) −7.62364e57 1.55019e58i −0.309131 0.628587i
\(832\) −1.85800e58 −0.735493
\(833\) 1.89140e58i 0.730941i
\(834\) −1.07862e58 + 5.30454e57i −0.406958 + 0.200137i
\(835\) 3.30418e57 0.121712
\(836\) 5.72280e58i 2.05818i
\(837\) −1.59016e58 3.21728e57i −0.558382 0.112974i
\(838\) 5.27236e58 1.80769
\(839\) 3.59646e58i 1.20403i 0.798486 + 0.602014i \(0.205635\pi\)
−0.798486 + 0.602014i \(0.794365\pi\)
\(840\) −2.13575e54 4.34283e54i −6.98175e−5 0.000141967i
\(841\) 2.39025e58 0.762999
\(842\) 4.22171e58i 1.31597i
\(843\) 9.96241e57 4.89939e57i 0.303259 0.149139i
\(844\) −5.05298e58 −1.50210
\(845\) 4.31301e57i 0.125212i
\(846\) 4.44048e58 5.76082e58i 1.25899 1.63334i
\(847\) −2.58171e56 −0.00714890
\(848\) 3.10839e58i 0.840657i
\(849\) −1.91058e58 3.88497e58i −0.504674 1.02621i
\(850\) 3.52922e58 0.910543
\(851\) 2.59284e58i 0.653409i
\(852\) −6.23681e58 + 3.06718e58i −1.53522 + 0.755002i
\(853\) 6.51802e58 1.56724 0.783619 0.621242i \(-0.213371\pi\)
0.783619 + 0.621242i \(0.213371\pi\)
\(854\) 6.45292e56i 0.0151565i
\(855\) 1.87042e58 + 1.44173e58i 0.429158 + 0.330798i
\(856\) −1.55941e57 −0.0349530
\(857\) 6.66361e58i 1.45913i 0.683913 + 0.729564i \(0.260277\pi\)
−0.683913 + 0.729564i \(0.739723\pi\)
\(858\) −3.00464e58 6.10963e58i −0.642756 1.30698i
\(859\) −8.25379e58 −1.72500 −0.862502 0.506053i \(-0.831104\pi\)
−0.862502 + 0.506053i \(0.831104\pi\)
\(860\) 2.74758e58i 0.561025i
\(861\) −4.86145e56 + 2.39080e56i −0.00969845 + 0.00476957i
\(862\) −3.74865e58 −0.730683
\(863\) 3.26696e58i 0.622197i 0.950378 + 0.311098i \(0.100697\pi\)
−0.950378 + 0.311098i \(0.899303\pi\)
\(864\) −1.49230e58 + 7.37577e58i −0.277703 + 1.37256i
\(865\) −1.47962e58 −0.269046
\(866\) 8.31212e58i 1.47691i
\(867\) 1.18347e58 + 2.40647e58i 0.205482 + 0.417828i
\(868\) −3.19157e56 −0.00541513
\(869\) 7.62027e58i 1.26350i
\(870\) −1.26261e58 + 6.20935e57i −0.204590 + 0.100615i
\(871\) 6.61473e58 1.04749
\(872\) 5.49795e57i 0.0850885i
\(873\) −1.85424e58 + 2.40558e58i −0.280466 + 0.363860i
\(874\) 1.78538e59 2.63939
\(875\) 4.29715e56i 0.00620897i
\(876\) −1.37121e57 2.78821e57i −0.0193652 0.0393771i
\(877\) −1.90902e58 −0.263524 −0.131762 0.991281i \(-0.542063\pi\)
−0.131762 + 0.991281i \(0.542063\pi\)
\(878\) 1.13038e59i 1.52523i
\(879\) −9.93303e58 + 4.88494e58i −1.31010 + 0.644290i
\(880\) −3.51688e58 −0.453423
\(881\) 1.22884e59i 1.54874i −0.632733 0.774370i \(-0.718067\pi\)
0.632733 0.774370i \(-0.281933\pi\)
\(882\) 9.01203e58 + 6.94653e58i 1.11033 + 0.855847i
\(883\) 2.29805e58 0.276787 0.138393 0.990377i \(-0.455806\pi\)
0.138393 + 0.990377i \(0.455806\pi\)
\(884\) 4.74018e58i 0.558148i
\(885\) 5.71043e57 + 1.16116e58i 0.0657361 + 0.133668i
\(886\) −1.16564e59 −1.31187
\(887\) 1.96194e58i 0.215881i 0.994157 + 0.107940i \(0.0344255\pi\)
−0.994157 + 0.107940i \(0.965574\pi\)
\(888\) 2.25974e57 1.11131e57i 0.0243108 0.0119557i
\(889\) 6.51366e56 0.00685157
\(890\) 1.48264e58i 0.152488i
\(891\) −1.26345e59 + 3.32626e58i −1.27059 + 0.334504i
\(892\) 1.32144e59 1.29943
\(893\) 2.48146e59i 2.38604i
\(894\) −6.77999e58 1.37864e59i −0.637498 1.29629i
\(895\) −2.24935e58 −0.206822
\(896\) 1.05286e56i 0.000946692i
\(897\) 9.36394e58 4.60507e58i 0.823398 0.404937i
\(898\) −1.89048e59 −1.62572
\(899\) 3.29771e58i 0.277344i
\(900\) 6.36774e58 8.26113e58i 0.523763 0.679500i
\(901\) 7.39399e58 0.594817
\(902\) 2.57068e59i 2.02264i
\(903\) 9.81725e56 + 1.99624e57i 0.00755501 + 0.0153624i
\(904\) −2.63356e56 −0.00198233
\(905\) 4.73612e58i 0.348699i
\(906\) 3.36782e59 1.65625e59i 2.42541 1.19278i
\(907\) −1.32909e59 −0.936284 −0.468142 0.883653i \(-0.655076\pi\)
−0.468142 + 0.883653i \(0.655076\pi\)
\(908\) 9.98862e58i 0.688317i
\(909\) −1.33673e58 1.03036e58i −0.0901089 0.0694565i
\(910\) 5.52709e56 0.00364476
\(911\) 9.58216e56i 0.00618153i 0.999995 + 0.00309077i \(0.000983823\pi\)
−0.999995 + 0.00309077i \(0.999016\pi\)
\(912\) 1.17190e59 + 2.38295e59i 0.739597 + 1.50390i
\(913\) 1.52655e59 0.942530
\(914\) 3.42217e59i 2.06717i
\(915\) 5.57037e58 2.73944e58i 0.329202 0.161897i
\(916\) −4.30660e57 −0.0249015
\(917\) 2.36601e57i 0.0133854i
\(918\) −1.81477e59 3.67173e58i −1.00454 0.203244i
\(919\) 8.88524e58 0.481237 0.240619 0.970620i \(-0.422650\pi\)
0.240619 + 0.970620i \(0.422650\pi\)
\(920\) 3.51965e57i 0.0186528i
\(921\) −1.93926e58 3.94329e58i −0.100564 0.204487i
\(922\) −5.41076e59 −2.74562
\(923\) 2.82097e59i 1.40076i
\(924\) −2.30635e57 + 1.13423e57i −0.0112069 + 0.00551142i
\(925\) −1.05193e59 −0.500209
\(926\) 1.39160e59i 0.647582i
\(927\) 3.88105e57 5.03505e57i 0.0176748 0.0229302i
\(928\) −1.52960e59 −0.681741
\(929\) 3.17122e59i 1.38329i −0.722239 0.691643i \(-0.756887\pi\)
0.722239 0.691643i \(-0.243113\pi\)
\(930\) −2.75796e58 5.60804e58i −0.117741 0.239416i
\(931\) 3.88190e59 1.62200
\(932\) 9.26081e58i 0.378731i
\(933\) −1.30491e59 + 6.41736e58i −0.522332 + 0.256876i
\(934\) −4.88317e59 −1.91322
\(935\) 8.36567e58i 0.320825i
\(936\) 8.02689e57 + 6.18718e57i 0.0301322 + 0.0232261i
\(937\) 3.88543e59 1.42773 0.713866 0.700282i \(-0.246942\pi\)
0.713866 + 0.700282i \(0.246942\pi\)
\(938\) 5.08279e57i 0.0182829i
\(939\) 1.38278e59 + 2.81174e59i 0.486900 + 0.990063i
\(940\) 1.37646e59 0.474466
\(941\) 1.95897e59i 0.661051i −0.943797 0.330525i \(-0.892774\pi\)
0.943797 0.330525i \(-0.107226\pi\)
\(942\) −1.37183e59 + 6.74648e58i −0.453192 + 0.222874i
\(943\) −3.93997e59 −1.27426
\(944\) 1.45504e59i 0.460717i
\(945\) 2.10326e56 1.03955e57i 0.000652013 0.00322261i
\(946\) 1.05559e60 3.20386
\(947\) 4.05743e59i 1.20573i 0.797842 + 0.602866i \(0.205975\pi\)
−0.797842 + 0.602866i \(0.794025\pi\)
\(948\) 1.40851e59 + 2.86407e59i 0.409820 + 0.833329i
\(949\) −1.26114e58 −0.0359284
\(950\) 7.24338e59i 2.02055i
\(951\) −9.94125e58 + 4.88898e58i −0.271538 + 0.133539i
\(952\) 1.29449e56 0.000346226
\(953\) 4.59879e59i 1.20444i −0.798330 0.602220i \(-0.794283\pi\)
0.798330 0.602220i \(-0.205717\pi\)
\(954\) 2.71559e59 3.52305e59i 0.696461 0.903549i
\(955\) 2.47439e59 0.621441
\(956\) 3.58100e59i 0.880738i
\(957\) −1.17196e59 2.38306e59i −0.282275 0.573979i
\(958\) −3.67748e59 −0.867442
\(959\) 1.54825e57i 0.00357658i
\(960\) −1.23244e59 + 6.06096e58i −0.278830 + 0.137125i
\(961\) −3.04830e59 −0.675446
\(962\) 2.87595e59i 0.624137i
\(963\) −2.70673e59 2.08636e59i −0.575333 0.443470i
\(964\) 7.49128e59 1.55961
\(965\) 1.83709e59i 0.374615i
\(966\) −3.53856e57 7.19531e57i −0.00706780 0.0143717i
\(967\) −6.05101e59 −1.18386 −0.591928 0.805991i \(-0.701633\pi\)
−0.591928 + 0.805991i \(0.701633\pi\)
\(968\) 1.82354e58i 0.0349469i
\(969\) −5.66837e59 + 2.78763e59i −1.06410 + 0.523310i
\(970\) −1.16998e59 −0.215151
\(971\) 4.08611e59i 0.736081i 0.929810 + 0.368040i \(0.119971\pi\)
−0.929810 + 0.368040i \(0.880029\pi\)
\(972\) −4.13385e59 + 3.58550e59i −0.729506 + 0.632739i
\(973\) 1.84169e57 0.00318391
\(974\) 5.86475e59i 0.993277i
\(975\) −1.86830e59 3.79899e59i −0.309994 0.630342i
\(976\) 6.98018e59 1.13467
\(977\) 5.00416e59i 0.796966i 0.917176 + 0.398483i \(0.130463\pi\)
−0.917176 + 0.398483i \(0.869537\pi\)
\(978\) −2.83652e59 + 1.39497e59i −0.442598 + 0.217664i
\(979\) 2.79835e59 0.427807
\(980\) 2.15328e59i 0.322537i
\(981\) 7.35581e59 9.54301e59i 1.07957 1.40057i
\(982\) 5.98909e59 0.861254
\(983\) 3.00318e59i 0.423167i 0.977360 + 0.211583i \(0.0678620\pi\)
−0.977360 + 0.211583i \(0.932138\pi\)
\(984\) −1.68870e58 3.43379e58i −0.0233158 0.0474103i
\(985\) −2.04965e59 −0.277303
\(986\) 3.76352e59i 0.498949i
\(987\) −1.00006e58 + 4.91814e57i −0.0129922 + 0.00638937i
\(988\) −9.72875e59 −1.23856
\(989\) 1.61786e60i 2.01843i
\(990\) −3.98603e59 3.07246e59i −0.487345 0.375649i
\(991\) 8.35257e58 0.100080 0.0500400 0.998747i \(-0.484065\pi\)
0.0500400 + 0.998747i \(0.484065\pi\)
\(992\) 6.79394e59i 0.797789i
\(993\) 4.32573e59 + 8.79595e59i 0.497823 + 1.01227i
\(994\) 2.16765e58 0.0244490
\(995\) 1.51881e59i 0.167897i
\(996\) 5.73752e59 2.82164e59i 0.621637 0.305713i
\(997\) 6.98796e58 0.0742074 0.0371037 0.999311i \(-0.488187\pi\)
0.0371037 + 0.999311i \(0.488187\pi\)
\(998\) 1.08567e60i 1.13003i
\(999\) 5.40915e59 + 1.09440e59i 0.551848 + 0.111652i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3.41.b.a.2.11 yes 12
3.2 odd 2 inner 3.41.b.a.2.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3.41.b.a.2.2 12 3.2 odd 2 inner
3.41.b.a.2.11 yes 12 1.1 even 1 trivial